ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWW342+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n020.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 09:07:00 AM UTC 2026

% Result   : Theorem 218.63s 218.90s
% Output   : Proof 218.83s
% 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_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_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_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_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_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_com_Osimps_I64_J,axiom,
    ! [V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSKIP) = V_f1_2,
    file('theBenchmark.p',fact_com_Osimps_I64_J) ).

fof(fact_com_Orecs_I1_J,axiom,
    ! [V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSKIP) = V_f1_2,
    file('theBenchmark.p',fact_com_Orecs_I1_J) ).

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_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_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_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__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_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_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_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_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_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_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_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_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_Osimps_I67_J,axiom,
    ! [V_com2_2,V_com1_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSemi(V_com1_2,V_com2_2)) = hAPP(hAPP(V_f4_2,V_com1_2),V_com2_2),
    file('theBenchmark.p',fact_com_Osimps_I67_J) ).

fof(fact_com_Orecs_I4_J,axiom,
    ! [V_com2_2,V_com1_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSemi(V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(hAPP(V_f4_2,V_com1_2),V_com2_2),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com1_2)),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com2_2)),
    file('theBenchmark.p',fact_com_Orecs_I4_J) ).

fof(fact_com_Osimps_I68_J,axiom,
    ! [V_com2_2,V_com1_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(V_f5_2,V_fun_2),V_com1_2),V_com2_2),
    file('theBenchmark.p',fact_com_Osimps_I68_J) ).

fof(fact_com_Orecs_I5_J,axiom,
    ! [V_com2_2,V_com1_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(hAPP(hAPP(V_f5_2,V_fun_2),V_com1_2),V_com2_2),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com1_2)),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com2_2)),
    file('theBenchmark.p',fact_com_Orecs_I5_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_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_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_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_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_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_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_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_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_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_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_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_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_I71_J,axiom,
    ! [V_fun_2,V_pname_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = hAPP(hAPP(hAPP(V_f8_2,V_vname_2),V_pname_2),V_fun_2),
    file('theBenchmark.p',fact_com_Osimps_I71_J) ).

fof(fact_com_Osimps_I66_J,axiom,
    ! [V_com_2,V_fun_2,V_loc_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(V_f3_2,V_loc_2),V_fun_2),V_com_2),
    file('theBenchmark.p',fact_com_Osimps_I66_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_com_Orecs_I2_J,axiom,
    ! [V_fun_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = hAPP(hAPP(V_f2_2,V_vname_2),V_fun_2),
    file('theBenchmark.p',fact_com_Orecs_I2_J) ).

fof(fact_com_Orecs_I3_J,axiom,
    ! [V_com_2,V_fun_2,V_loc_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(hAPP(V_f3_2,V_loc_2),V_fun_2),V_com_2),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com_2)),
    file('theBenchmark.p',fact_com_Orecs_I3_J) ).

fof(fact_com_Orecs_I8_J,axiom,
    ! [V_fun_2,V_pname_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = hAPP(hAPP(hAPP(V_f8_2,V_vname_2),V_pname_2),V_fun_2),
    file('theBenchmark.p',fact_com_Orecs_I8_J) ).

fof(fact_com_Osimps_I65_J,axiom,
    ! [V_fun_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = hAPP(hAPP(V_f2_2,V_vname_2),V_fun_2),
    file('theBenchmark.p',fact_com_Osimps_I65_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_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_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_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_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_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_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_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_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_I69_J,axiom,
    ! [V_com_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(V_f6_2,V_fun_2),V_com_2),
    file('theBenchmark.p',fact_com_Osimps_I69_J) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_Orecs_I7_J,axiom,
    ! [V_pname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,hAPP(c_Com_Ocom_OBODY,V_pname_2)) = hAPP(V_f7_2,V_pname_2),
    file('theBenchmark.p',fact_com_Orecs_I7_J) ).

fof(fact_com_Orecs_I6_J,axiom,
    ! [V_com_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(V_f6_2,V_fun_2),V_com_2),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com_2)),
    file('theBenchmark.p',fact_com_Orecs_I6_J) ).

fof(fact_com_Osimps_I70_J,axiom,
    ! [V_pname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,hAPP(c_Com_Ocom_OBODY,V_pname_2)) = hAPP(V_f7_2,V_pname_2),
    file('theBenchmark.p',fact_com_Osimps_I70_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_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_def__nat__rec__Suc,axiom,
    ! [V_n_2,V_h_2,V_c_2,T_b,V_f_2] :
      ( ! [B_n] : hAPP(V_f_2,B_n) = hAPP(c_Nat_Onat_Onat__rec(T_b,V_c_2,V_h_2),B_n)
     => hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_h_2,V_n_2),hAPP(V_f_2,V_n_2)) ),
    file('theBenchmark.p',fact_def__nat__rec__Suc) ).

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_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_evaln__WHILE__case,axiom,
    ! [V_t_2,V_n_2,V_s_2,V_c_2,V_b_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s_2,V_n_2,V_t_2)
     => ( ( V_t_2 = V_s_2
         => hBOOL(hAPP(V_b_2,V_s_2)) )
       => ~ ( hBOOL(hAPP(V_b_2,V_s_2))
           => ! [B_s1] :
                ( c_Natural_Oevaln(V_c_2,V_s_2,V_n_2,B_s1)
               => ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),B_s1,V_n_2,V_t_2) ) ) ) ),
    file('theBenchmark.p',fact_evaln__WHILE__case) ).

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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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,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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_def__nat__rec__0,axiom,
    ! [V_h_2,V_c_2,T_b,V_f_2] :
      ( ! [B_n] : hAPP(V_f_2,B_n) = hAPP(c_Nat_Onat_Onat__rec(T_b,V_c_2,V_h_2),B_n)
     => hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_c_2 ),
    file('theBenchmark.p',fact_def__nat__rec__0) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_evalc__WHILE__case,axiom,
    ! [V_t_2,V_s_2,V_c_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_t_2))
     => ( ( V_t_2 = V_s_2
         => hBOOL(hAPP(V_b_2,V_s_2)) )
       => ~ ( hBOOL(hAPP(V_b_2,V_s_2))
           => ! [B_s1] :
                ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),B_s1))
               => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),B_s1),V_t_2)) ) ) ) ),
    file('theBenchmark.p',fact_evalc__WHILE__case) ).

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_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_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_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_sum_Osize_I1_J,axiom,
    ! [V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Sum__Type_Osum_Osum__size(T_b,T_c,V_fa_2,V_fb_2,hAPP(c_Sum__Type_OInl(T_b,T_c),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_sum_Osize_I1_J) ).

fof(fact_sum_Osize_I2_J,axiom,
    ! [V_b_2,V_fb_2,V_fa_2,T_c,T_b] : c_Sum__Type_Osum_Osum__size(T_b,T_c,V_fa_2,V_fb_2,hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fb_2,V_b_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_sum_Osize_I2_J) ).

fof(fact_option_Oexhaust,axiom,
    ! [T_a,V_y] :
      ( V_y != c_Option_Ooption_ONone(T_a)
     => ~ ! [B_a] : V_y != hAPP(c_Option_Ooption_OSome(T_a),B_a) ),
    file('theBenchmark.p',fact_option_Oexhaust) ).

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_not0__implies__Suc,axiom,
    ! [V_n] :
      ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ),
    file('theBenchmark.p',fact_not0__implies__Suc) ).

fof(fact_nat__induct,axiom,
    ! [V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( ! [B_n] :
            ( hBOOL(hAPP(V_P_2,B_n))
           => hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_n))) )
       => hBOOL(hAPP(V_P_2,V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__induct) ).

fof(fact_zero__induct,axiom,
    ! [V_k_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_k_2))
     => ( ! [B_n] :
            ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_n)))
           => hBOOL(hAPP(V_P_2,B_n)) )
       => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    file('theBenchmark.p',fact_zero__induct) ).

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_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_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_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_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_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__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_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__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__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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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__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_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_Inl__not__Inr,axiom,
    ! [V_b,V_a,T_b,T_a] : hAPP(c_Sum__Type_OInl(T_a,T_b),V_a) != hAPP(c_Sum__Type_OInr(T_b,T_a),V_b),
    file('theBenchmark.p',fact_Inl__not__Inr) ).

fof(fact_sum_Osimps_I3_J,axiom,
    ! [V_b_H,V_a,T_b,T_a] : hAPP(c_Sum__Type_OInl(T_a,T_b),V_a) != hAPP(c_Sum__Type_OInr(T_b,T_a),V_b_H),
    file('theBenchmark.p',fact_sum_Osimps_I3_J) ).

fof(fact_Inr__not__Inl,axiom,
    ! [V_a,V_b,T_a,T_b] : hAPP(c_Sum__Type_OInr(T_b,T_a),V_b) != hAPP(c_Sum__Type_OInl(T_a,T_b),V_a),
    file('theBenchmark.p',fact_Inr__not__Inl) ).

fof(fact_sum_Osimps_I4_J,axiom,
    ! [V_a_1,V_b_H_1,T_a_1,T_b_1] : hAPP(c_Sum__Type_OInr(T_b_1,T_a_1),V_b_H_1) != hAPP(c_Sum__Type_OInl(T_a_1,T_b_1),V_a_1),
    file('theBenchmark.p',fact_sum_Osimps_I4_J) ).

fof(fact_sum_Osize_I3_J,axiom,
    ! [V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_sum(T_a,T_b)),hAPP(c_Sum__Type_OInl(T_a,T_b),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_sum_Osize_I3_J) ).

fof(fact_sum_Osize_I4_J,axiom,
    ! [V_b,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_sum(T_a,T_b)),hAPP(c_Sum__Type_OInr(T_b,T_a),V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_sum_Osize_I4_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_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_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_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_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_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_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_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_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_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_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__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_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__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_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_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_Inr__inject,axiom,
    ! [V_y,V_x,T_a,T_b] :
      ( hAPP(c_Sum__Type_OInr(T_b,T_a),V_x) = hAPP(c_Sum__Type_OInr(T_b,T_a),V_y)
     => V_x = V_y ),
    file('theBenchmark.p',fact_Inr__inject) ).

fof(fact_sum_Osimps_I2_J,axiom,
    ! [V_b_H_2,V_b_2,T_b,T_c] :
      ( hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_2) = hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_H_2)
    <=> V_b_2 = V_b_H_2 ),
    file('theBenchmark.p',fact_sum_Osimps_I2_J) ).

fof(fact_Inl__inject,axiom,
    ! [V_y,V_x,T_b,T_a] :
      ( hAPP(c_Sum__Type_OInl(T_a,T_b),V_x) = hAPP(c_Sum__Type_OInl(T_a,T_b),V_y)
     => V_x = V_y ),
    file('theBenchmark.p',fact_Inl__inject) ).

fof(fact_sum_Osimps_I1_J,axiom,
    ! [V_a_H_2,V_a_2,T_c,T_b] :
      ( hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_2) = hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_H_2)
    <=> V_a_2 = V_a_H_2 ),
    file('theBenchmark.p',fact_sum_Osimps_I1_J) ).

fof(fact_Projl_Osimps,axiom,
    ! [V_x,T_b,T_a] : c_Sum__Type_OProjl(T_a,T_b,hAPP(c_Sum__Type_OInl(T_a,T_b),V_x)) = V_x,
    file('theBenchmark.p',fact_Projl_Osimps) ).

fof(fact_Projr_Osimps,axiom,
    ! [V_x,T_b,T_a] : c_Sum__Type_OProjr(T_a,T_b,hAPP(c_Sum__Type_OInr(T_b,T_a),V_x)) = V_x,
    file('theBenchmark.p',fact_Projr_Osimps) ).

fof(fact_sum_Orecs_I1_J,axiom,
    ! [V_a_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : c_Sum__Type_Osum_Osum__rec(T_c,T_b,T_d,V_f1_2,V_f2_2,hAPP(c_Sum__Type_OInl(T_c,T_d),V_a_2)) = hAPP(V_f1_2,V_a_2),
    file('theBenchmark.p',fact_sum_Orecs_I1_J) ).

fof(fact_sum_Orecs_I2_J,axiom,
    ! [V_b_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : c_Sum__Type_Osum_Osum__rec(T_c,T_b,T_d,V_f1_2,V_f2_2,hAPP(c_Sum__Type_OInr(T_d,T_c),V_b_2)) = hAPP(V_f2_2,V_b_2),
    file('theBenchmark.p',fact_sum_Orecs_I2_J) ).

fof(fact_Suml_Osimps,axiom,
    ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_OSuml(T_c,T_b,T_d,V_f_2),hAPP(c_Sum__Type_OInl(T_c,T_d),V_x_2)) = hAPP(V_f_2,V_x_2),
    file('theBenchmark.p',fact_Suml_Osimps) ).

fof(fact_Sumr_Osimps,axiom,
    ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_OSumr(T_c,T_b,T_d,V_f_2),hAPP(c_Sum__Type_OInr(T_c,T_d),V_x_2)) = hAPP(V_f_2,V_x_2),
    file('theBenchmark.p',fact_Sumr_Osimps) ).

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_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_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_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_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_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_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__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__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_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_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_Suml__inject,axiom,
    ! [V_g_2,V_f_2,T_c,T_d,T_b] :
      ( c_Sum__Type_OSuml(T_b,T_d,T_c,V_f_2) = c_Sum__Type_OSuml(T_b,T_d,T_c,V_g_2)
     => V_f_2 = V_g_2 ),
    file('theBenchmark.p',fact_Suml__inject) ).

fof(fact_Sumr__inject,axiom,
    ! [V_g_2,V_f_2,T_b,T_d,T_c] :
      ( c_Sum__Type_OSumr(T_c,T_d,T_b,V_f_2) = c_Sum__Type_OSumr(T_c,T_d,T_b,V_g_2)
     => V_f_2 = V_g_2 ),
    file('theBenchmark.p',fact_Sumr__inject) ).

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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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__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_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_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_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__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_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_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__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_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,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_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_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_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_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_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__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_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_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_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_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_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_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__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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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__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_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__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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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__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_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_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__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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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__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__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__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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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__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_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_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_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_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_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_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__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__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__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__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__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__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_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__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_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__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__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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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__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__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_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__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_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_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_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_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_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_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__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__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_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_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_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_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_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_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_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_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_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_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_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__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,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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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__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_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_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_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_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_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_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__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_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__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_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_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_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_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_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__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__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__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_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_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_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_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_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_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__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_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__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_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_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__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_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_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_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_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_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_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_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_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_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__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__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__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_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_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_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__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_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_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_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__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_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_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_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_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_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_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_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_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_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__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_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_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__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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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__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_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_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_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_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_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_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_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__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_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__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__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_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_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_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_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_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_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_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__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_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__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__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_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_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__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_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_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_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__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_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__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_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_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__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_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_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_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_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__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_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_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__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_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_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_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_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_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,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_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_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_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_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__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_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_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__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_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__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_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__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_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_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__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_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__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_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_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__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_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_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,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_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_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__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_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_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__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_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_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_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_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_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_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_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_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__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_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__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_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__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__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__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__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_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_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_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_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_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_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__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__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_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_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__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__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__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_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__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_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_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_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_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_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_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__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__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__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__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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_pred__Pls,axiom,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    file('theBenchmark.p',fact_pred__Pls) ).

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,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_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_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_I37_J,axiom,
    c_Int_OPls != c_Int_OMin,
    file('theBenchmark.p',fact_rel__simps_I37_J) ).

fof(fact_rel__simps_I40_J,axiom,
    c_Int_OMin != c_Int_OPls,
    file('theBenchmark.p',fact_rel__simps_I40_J) ).

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__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_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_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,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_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_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_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_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_succ__Min,axiom,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    file('theBenchmark.p',fact_succ__Min) ).

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__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_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_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__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_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_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_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__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_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_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_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_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_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_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_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_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_I46_J,axiom,
    ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
    file('theBenchmark.p',fact_rel__simps_I46_J) ).

fof(fact_Bit1__Min,axiom,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    file('theBenchmark.p',fact_Bit1__Min) ).

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_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_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__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_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_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_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_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_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_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_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_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_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_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__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_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_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__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_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_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__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_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_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_Bit0__Pls,axiom,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    file('theBenchmark.p',fact_Bit0__Pls) ).

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_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_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_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_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_I45_J,axiom,
    ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
    file('theBenchmark.p',fact_rel__simps_I45_J) ).

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_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__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_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_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_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_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_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__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__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__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__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_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_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_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_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_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__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_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_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_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_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_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__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_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_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_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_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_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_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_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__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,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_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_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__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_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_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__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_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__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_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_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__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_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__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__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_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__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_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_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_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_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_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_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_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_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_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_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_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__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__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__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_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__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_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__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_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_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__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_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_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_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_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__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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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__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_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_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_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_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_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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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__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_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__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_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_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_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__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_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_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__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__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__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__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_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__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__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__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__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,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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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__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__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_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_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_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__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_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_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_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__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_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__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__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_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__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_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__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__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__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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_surjective__sum,axiom,
    ! [V_f_2,T_c,T_d,T_b] : c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,hAPP(hAPP(c_COMBB(tc_sum(T_b,T_c),T_d,T_b),V_f_2),c_Sum__Type_OInl(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_sum(T_b,T_c),T_d,T_c),V_f_2),c_Sum__Type_OInr(T_c,T_b))) = V_f_2,
    file('theBenchmark.p',fact_surjective__sum) ).

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_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_sum__case__KK,axiom,
    ! [V_x_2,V_a_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_a_2),hAPP(c_COMBK(T_b,T_d),V_a_2)),V_x_2) = V_a_2,
    file('theBenchmark.p',fact_sum__case__KK) ).

fof(fact_sum__case__inject,axiom,
    ! [V_g2_2,V_g1_2,V_f2_2,V_f1_2,T_c,T_d,T_b] :
      ( c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f1_2,V_f2_2) = c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_g1_2,V_g2_2)
     => ~ ( V_f1_2 = V_g1_2
         => V_f2_2 != V_g2_2 ) ),
    file('theBenchmark.p',fact_sum__case__inject) ).

fof(fact_sum__case__weak__cong,axiom,
    ! [V_g_2,V_f_2,T_c,T_d,T_b,V_t_2,V_s_2] :
      ( V_s_2 = V_t_2
     => hAPP(c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f_2,V_g_2),V_s_2) = hAPP(c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f_2,V_g_2),V_t_2) ),
    file('theBenchmark.p',fact_sum__case__weak__cong) ).

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_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_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_sum_Osimps_I6_J,axiom,
    ! [V_b_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,V_f1_2,V_f2_2),hAPP(c_Sum__Type_OInr(T_d,T_c),V_b_2)) = hAPP(V_f2_2,V_b_2),
    file('theBenchmark.p',fact_sum_Osimps_I6_J) ).

fof(fact_sum_Osimps_I5_J,axiom,
    ! [V_a_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,V_f1_2,V_f2_2),hAPP(c_Sum__Type_OInl(T_c,T_d),V_a_2)) = hAPP(V_f1_2,V_a_2),
    file('theBenchmark.p',fact_sum_Osimps_I5_J) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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__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__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__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__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_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__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_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__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,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__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__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_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_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_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__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_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__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_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__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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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__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__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_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_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_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_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__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_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_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__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_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_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_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_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_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_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_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__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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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__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__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__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_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_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_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__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_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_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_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_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__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_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_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_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__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__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_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_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__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_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_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_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__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__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_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__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_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_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__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_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_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_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__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_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_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_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__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_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_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_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_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_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_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_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_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__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_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_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__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_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_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_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_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_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_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_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_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__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_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__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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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__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_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_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_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_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_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__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_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_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_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__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__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_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_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__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_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_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_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__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__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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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__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__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__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__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_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__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_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__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__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_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_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_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_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__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_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_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_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_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_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_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_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__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__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__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__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_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__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__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__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__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_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__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_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_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_InrI,axiom,
    ! [V_A_2,T_c,V_B_2,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_member(tc_sum(T_c,T_b)),hAPP(c_Sum__Type_OInr(T_b,T_c),V_b_2)),c_Sum__Type_OPlus(T_c,T_b,V_A_2,V_B_2))) ),
    file('theBenchmark.p',fact_InrI) ).

fof(fact_InlI,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_member(tc_sum(T_b,T_c)),hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_2)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ),
    file('theBenchmark.p',fact_InlI) ).

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__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_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_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_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_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__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_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__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_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__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_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__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__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_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_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_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,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__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__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__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_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_Plus__def,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) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_sum(T_b,T_c),c_Sum__Type_OInl(T_b,T_c)),V_A_2)),hAPP(c_Set_Oimage(T_c,tc_sum(T_b,T_c),c_Sum__Type_OInr(T_c,T_b)),V_B_2)),
    file('theBenchmark.p',fact_Plus__def) ).

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__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_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_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_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_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_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_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__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_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_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__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_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_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_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__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_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__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_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_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_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__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_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_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__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_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_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__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_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_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__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_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__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__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__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__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__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__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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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__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_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__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__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_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_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_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_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_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_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_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_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__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_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_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__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__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,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_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_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_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_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_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_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_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_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_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_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__Inl,axiom,
    ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(T_b,tc_sum(T_b,T_c),c_Sum__Type_OInl(T_b,T_c),V_A_2),
    file('theBenchmark.p',fact_inj__Inl) ).

fof(fact_inj__Inr,axiom,
    ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(T_b,tc_sum(T_c,T_b),c_Sum__Type_OInr(T_b,T_c),V_A_2),
    file('theBenchmark.p',fact_inj__Inr) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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__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_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__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__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__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__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_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__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__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__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__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__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__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_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__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_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_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__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_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__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_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_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__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_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_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_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_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_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__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_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__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__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_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_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_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__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_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__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_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_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__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_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_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__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_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_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__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__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_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__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__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_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_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__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_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_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__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_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_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_setsum__Plus,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))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(T_b,T_c),T_d),V_f_2),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(tc_sum(T_b,T_c),T_d,T_b,V_f_2),c_Sum__Type_OInl(T_b,T_c))),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(c_Fun_Ocomp(tc_sum(T_b,T_c),T_d,T_c,V_f_2),c_Sum__Type_OInr(T_c,T_b))),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__Plus) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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__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__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__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_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_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_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__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_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_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_identity__equivp,axiom,
    ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal),
    file('theBenchmark.p',fact_identity__equivp) ).

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_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__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__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_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_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_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_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_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__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_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__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__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_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_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__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_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_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_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__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_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_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_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_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_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__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_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__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_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_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_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_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__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_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__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_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__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_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__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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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,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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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__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__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_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__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__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__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__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__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__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_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_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__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__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_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__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_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__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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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__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_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__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_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__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_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__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__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__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_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__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_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_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_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_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_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_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__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__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__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_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_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__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_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__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_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_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_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_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_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_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_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_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__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_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__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_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__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_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__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_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_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__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_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_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__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_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_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__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_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_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_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_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_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_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_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_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_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_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__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_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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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__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__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_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_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_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_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,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_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_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_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_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_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_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_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_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_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_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_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__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__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_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_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__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_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_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_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_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_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_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_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_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__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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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__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_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_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_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_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_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__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__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__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__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_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_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_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_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_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__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_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__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__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__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__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_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_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__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__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__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_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_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_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_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_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_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__map__o__sum__case,axiom,
    ! [V_h_2,V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),tc_sum(T_b,T_c),hAPP(c_Option_Omap(T_e,T_d),V_f_2)),c_Sum__Type_Osum_Osum__case(T_b,tc_Option_Ooption(T_e),T_c,V_g_2,V_h_2)) = c_Sum__Type_Osum_Osum__case(T_b,tc_Option_Ooption(T_d),T_c,hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),T_b,hAPP(c_Option_Omap(T_e,T_d),V_f_2)),V_g_2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),T_c,hAPP(c_Option_Omap(T_e,T_d),V_f_2)),V_h_2)),
    file('theBenchmark.p',fact_option__map__o__sum__case) ).

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__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__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_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__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_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__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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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__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__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__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__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_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_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_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__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_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_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_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_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_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_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__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_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_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__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_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_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__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_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_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_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__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_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,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_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_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_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_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__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_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__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_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__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_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_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_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_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_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_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_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_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_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_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__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__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__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__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_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_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_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_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_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__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__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_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_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_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__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__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__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__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_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_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_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_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_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_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_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_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__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__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_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_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),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),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),c_List_Otl(T_a,V_xs)) = 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] : 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),c_List_Otl(T_a,V_xs)),
    file('theBenchmark.p',fact_tl__drop) ).

fof(fact_tl_Osimps_I1_J,axiom,
    ! [T_a] : 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),c_List_Otl(T_a,V_xs)) = 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),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),c_List_Otl(T_c,V_xs_2)) = 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] : 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)
     => c_List_Otl(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),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] : 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,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)),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] : 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))),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),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)),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_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_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_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__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_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_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__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_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_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_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_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__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_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__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_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_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_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_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_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_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_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__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__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__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__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_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_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_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_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_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_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_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_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_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,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_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_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_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_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_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_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_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__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_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__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_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_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(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,v_n,B_x) ),
    file('theBenchmark.p',conj_0) ).

fof(conj_1,conjecture,
    ! [B_Z,B_s] :
      ( v_P(B_Z,B_s)
     => ! [B_s_H] :
          ( c_Natural_Oevaln(c_Com_Ocom_OSKIP,B_s,v_n,B_s_H)
         => v_P(B_Z,B_s_H) ) ),
    file('theBenchmark.p',conj_1) ).

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_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_2_2,plain,
    ! [U_4,U_3] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_3,U_4,U_3),
    inference(variable_rename,[status(thm)],[f_2_1]) ).

fof(f_2_3,plain,
    ! [U_3,U_4] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_3,U_4,U_3),
    inference(definitional_conversion,[status(esa)],[f_2_2]) ).

cnf(f_2_4,plain,
    c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_3,U_4,U_3),
    inference(clausify,[status(thm)],[f_2_3]) ).

fof(f_3_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_3_2,plain,
    ! [U_7,U_6,U_5] :
      ( U_7 = U_5
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_5,U_6,U_7) ),
    inference(variable_rename,[status(thm)],[f_3_1]) ).

fof(f_3_3,plain,
    ! [U_7,U_5,U_6] :
      ( U_7 = U_5
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_5,U_6,U_7) ),
    inference(definitional_conversion,[status(esa)],[f_3_2]) ).

cnf(f_3_4,plain,
    ( U_7 = U_5
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_5,U_6,U_7) ),
    inference(clausify,[status(thm)],[f_3_3]) ).

fof(f_4_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_4_2,plain,
    ! [U_9,U_8] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_8,U_9,U_8),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

fof(f_4_3,plain,
    ! [U_9,U_8] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_8,U_9,U_8),
    inference(definitional_conversion,[status(esa)],[f_4_2]) ).

cnf(f_4_4,plain,
    c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_8,U_9,U_8),
    inference(clausify,[status(thm)],[f_4_3]) ).

fof(f_5_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_5_2,plain,
    ! [U_20,U_19,U_18,U_17,U_16] :
      ( ( c_Hoare__Mirabelle_Otriple__valid(U_16,U_17,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_16),U_18),U_19),U_20))
        | ? [U_15,U_14] :
            ( ? [U_13] :
                ( ~ hBOOL(hAPP(hAPP(U_20,U_15),U_13))
                & c_Natural_Oevaln(U_19,U_14,U_17,U_13) )
            & hBOOL(hAPP(hAPP(U_18,U_15),U_14)) ) )
      & ( ! [U_12,U_11] :
            ( ! [U_10] :
                ( hBOOL(hAPP(hAPP(U_20,U_12),U_10))
                | ~ c_Natural_Oevaln(U_19,U_11,U_17,U_10) )
            | ~ hBOOL(hAPP(hAPP(U_18,U_12),U_11)) )
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_16,U_17,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_16),U_18),U_19),U_20)) ) ),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

fof(f_5_3,plain,
    ( ! [U_30,U_28,U_26,U_24] :
        ( ! [U_22] : c_Hoare__Mirabelle_Otriple__valid(U_22,U_24,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_22),U_26),U_28),U_30))
        | ? [U_15,U_14] :
            ( ? [U_13] :
                ( ~ hBOOL(hAPP(hAPP(U_30,U_15),U_13))
                & c_Natural_Oevaln(U_28,U_14,U_24,U_13) )
            & hBOOL(hAPP(hAPP(U_26,U_15),U_14)) ) )
    & ! [U_29,U_27,U_25,U_23] :
        ( ! [U_21] : ~ c_Hoare__Mirabelle_Otriple__valid(U_21,U_23,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_21),U_25),U_27),U_29))
        | ! [U_12,U_11] :
            ( ! [U_10] :
                ( hBOOL(hAPP(hAPP(U_29,U_12),U_10))
                | ~ c_Natural_Oevaln(U_27,U_11,U_23,U_10) )
            | ~ hBOOL(hAPP(hAPP(U_25,U_12),U_11)) ) ) ),
    inference(miniscope,[status(thm)],[f_5_2]) ).

fof(f_5_4,plain,
    ( ! [U_30,U_28,U_26,U_24] :
        ( ! [U_22] : c_Hoare__Mirabelle_Otriple__valid(U_22,U_24,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_22),U_26),U_28),U_30))
        | ? [U_14] :
            ( ? [U_13] :
                ( ~ hBOOL(hAPP(hAPP(U_30,sK2(U_30,U_28,U_26,U_24)),U_13))
                & c_Natural_Oevaln(U_28,U_14,U_24,U_13) )
            & hBOOL(hAPP(hAPP(U_26,sK2(U_30,U_28,U_26,U_24)),U_14)) ) )
    & ! [U_29,U_27,U_25,U_23] :
        ( ! [U_21] : ~ c_Hoare__Mirabelle_Otriple__valid(U_21,U_23,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_21),U_25),U_27),U_29))
        | ! [U_12,U_11] :
            ( ! [U_10] :
                ( hBOOL(hAPP(hAPP(U_29,U_12),U_10))
                | ~ c_Natural_Oevaln(U_27,U_11,U_23,U_10) )
            | ~ hBOOL(hAPP(hAPP(U_25,U_12),U_11)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_15,sK2(U_30,U_28,U_26,U_24))],[f_5_3]) ).

fof(f_5_5,plain,
    ( ! [U_30,U_28,U_26,U_24] :
        ( ! [U_22] : c_Hoare__Mirabelle_Otriple__valid(U_22,U_24,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_22),U_26),U_28),U_30))
        | ( ? [U_13] :
              ( ~ hBOOL(hAPP(hAPP(U_30,sK2(U_30,U_28,U_26,U_24)),U_13))
              & c_Natural_Oevaln(U_28,sK3(U_30,U_28,U_26,U_24),U_24,U_13) )
          & hBOOL(hAPP(hAPP(U_26,sK2(U_30,U_28,U_26,U_24)),sK3(U_30,U_28,U_26,U_24))) ) )
    & ! [U_29,U_27,U_25,U_23] :
        ( ! [U_21] : ~ c_Hoare__Mirabelle_Otriple__valid(U_21,U_23,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_21),U_25),U_27),U_29))
        | ! [U_12,U_11] :
            ( ! [U_10] :
                ( hBOOL(hAPP(hAPP(U_29,U_12),U_10))
                | ~ c_Natural_Oevaln(U_27,U_11,U_23,U_10) )
            | ~ hBOOL(hAPP(hAPP(U_25,U_12),U_11)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_14,sK3(U_30,U_28,U_26,U_24))],[f_5_4]) ).

fof(f_5_6,plain,
    ( ! [U_30,U_28,U_26,U_24] :
        ( ! [U_22] : c_Hoare__Mirabelle_Otriple__valid(U_22,U_24,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_22),U_26),U_28),U_30))
        | ( ~ hBOOL(hAPP(hAPP(U_30,sK2(U_30,U_28,U_26,U_24)),sK4(U_30,U_28,U_26,U_24)))
          & c_Natural_Oevaln(U_28,sK3(U_30,U_28,U_26,U_24),U_24,sK4(U_30,U_28,U_26,U_24))
          & hBOOL(hAPP(hAPP(U_26,sK2(U_30,U_28,U_26,U_24)),sK3(U_30,U_28,U_26,U_24))) ) )
    & ! [U_29,U_27,U_25,U_23] :
        ( ! [U_21] : ~ c_Hoare__Mirabelle_Otriple__valid(U_21,U_23,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_21),U_25),U_27),U_29))
        | ! [U_12,U_11] :
            ( ! [U_10] :
                ( hBOOL(hAPP(hAPP(U_29,U_12),U_10))
                | ~ c_Natural_Oevaln(U_27,U_11,U_23,U_10) )
            | ~ hBOOL(hAPP(hAPP(U_25,U_12),U_11)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_13,sK4(U_30,U_28,U_26,U_24))],[f_5_5]) ).

fof(f_5_7,plain,
    ( ! [U_26,U_24,U_30,U_28] :
        ( ~ hBOOL(hAPP(hAPP(U_30,sK2(U_30,U_28,U_26,U_24)),sK4(U_30,U_28,U_26,U_24)))
        | ~ sP0(U_26,U_24,U_30,U_28) )
    & ! [U_26,U_24,U_30,U_28] :
        ( c_Natural_Oevaln(U_28,sK3(U_30,U_28,U_26,U_24),U_24,sK4(U_30,U_28,U_26,U_24))
        | ~ sP0(U_26,U_24,U_30,U_28) )
    & ! [U_26,U_24,U_30,U_28] :
        ( hBOOL(hAPP(hAPP(U_26,sK2(U_30,U_28,U_26,U_24)),sK3(U_30,U_28,U_26,U_24)))
        | ~ sP0(U_26,U_24,U_30,U_28) )
    & ! [U_22,U_26,U_24,U_30,U_28] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_22,U_24,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_22),U_26),U_28),U_30))
        | sP0(U_26,U_24,U_30,U_28) )
    & ! [U_27,U_11,U_29,U_12,U_10,U_23,U_21,U_25] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(U_21,U_23,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_21),U_25),U_27),U_29))
        | hBOOL(hAPP(hAPP(U_29,U_12),U_10))
        | ~ c_Natural_Oevaln(U_27,U_11,U_23,U_10)
        | ~ hBOOL(hAPP(hAPP(U_25,U_12),U_11)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_5_6]) ).

cnf(f_5_8,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_21,U_23,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_21),U_25),U_27),U_29))
    | hBOOL(hAPP(hAPP(U_29,U_12),U_10))
    | ~ c_Natural_Oevaln(U_27,U_11,U_23,U_10)
    | ~ hBOOL(hAPP(hAPP(U_25,U_12),U_11)) ),
    inference(clausify,[status(thm)],[f_5_7]) ).

cnf(f_5_9,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_22,U_24,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_22),U_26),U_28),U_30))
    | sP0(U_26,U_24,U_30,U_28) ),
    inference(clausify,[status(thm)],[f_5_7]) ).

cnf(f_5_10,plain,
    ( hBOOL(hAPP(hAPP(U_26,sK2(U_30,U_28,U_26,U_24)),sK3(U_30,U_28,U_26,U_24)))
    | ~ sP0(U_26,U_24,U_30,U_28) ),
    inference(clausify,[status(thm)],[f_5_7]) ).

cnf(f_5_11,plain,
    ( c_Natural_Oevaln(U_28,sK3(U_30,U_28,U_26,U_24),U_24,sK4(U_30,U_28,U_26,U_24))
    | ~ sP0(U_26,U_24,U_30,U_28) ),
    inference(clausify,[status(thm)],[f_5_7]) ).

cnf(f_5_12,plain,
    ( ~ hBOOL(hAPP(hAPP(U_30,sK2(U_30,U_28,U_26,U_24)),sK4(U_30,U_28,U_26,U_24)))
    | ~ sP0(U_26,U_24,U_30,U_28) ),
    inference(clausify,[status(thm)],[f_5_7]) ).

fof(f_6_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_6_2,plain,
    ! [U_33,U_32,U_31] :
      ( c_Hoare__Mirabelle_Otriple__valid(U_31,U_32,U_33)
      | ~ c_Hoare__Mirabelle_Otriple__valid(U_31,hAPP(c_Nat_OSuc,U_32),U_33) ),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

fof(f_6_3,plain,
    ! [U_31,U_32,U_33] :
      ( c_Hoare__Mirabelle_Otriple__valid(U_31,U_32,U_33)
      | ~ c_Hoare__Mirabelle_Otriple__valid(U_31,hAPP(c_Nat_OSuc,U_32),U_33) ),
    inference(definitional_conversion,[status(esa)],[f_6_2]) ).

cnf(f_6_4,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_31,U_32,U_33)
    | ~ c_Hoare__Mirabelle_Otriple__valid(U_31,hAPP(c_Nat_OSuc,U_32),U_33) ),
    inference(clausify,[status(thm)],[f_6_3]) ).

fof(f_7_1,plain,
    ! [V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSKIP) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I64_J]) ).

fof(f_7_2,plain,
    ! [U_42,U_41,U_40,U_39,U_38,U_37,U_36,U_35,U_34] : c_Com_Ocom_Ocom__case(U_34,U_35,U_36,U_37,U_38,U_39,U_40,U_41,U_42,c_Com_Ocom_OSKIP) = U_35,
    inference(variable_rename,[status(thm)],[f_7_1]) ).

fof(f_7_3,plain,
    ! [U_40,U_41,U_37,U_34,U_38,U_39,U_36,U_42,U_35] : c_Com_Ocom_Ocom__case(U_34,U_35,U_36,U_37,U_38,U_39,U_40,U_41,U_42,c_Com_Ocom_OSKIP) = U_35,
    inference(definitional_conversion,[status(esa)],[f_7_2]) ).

cnf(f_7_4,plain,
    c_Com_Ocom_Ocom__case(U_34,U_35,U_36,U_37,U_38,U_39,U_40,U_41,U_42,c_Com_Ocom_OSKIP) = U_35,
    inference(clausify,[status(thm)],[f_7_3]) ).

fof(f_8_1,plain,
    ! [V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSKIP) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_com_Orecs_I1_J]) ).

fof(f_8_2,plain,
    ! [U_51,U_50,U_49,U_48,U_47,U_46,U_45,U_44,U_43] : c_Com_Ocom_Ocom__rec(U_43,U_44,U_45,U_46,U_47,U_48,U_49,U_50,U_51,c_Com_Ocom_OSKIP) = U_44,
    inference(variable_rename,[status(thm)],[f_8_1]) ).

fof(f_8_3,plain,
    ! [U_43,U_44,U_45,U_48,U_49,U_47,U_46,U_50,U_51] : c_Com_Ocom_Ocom__rec(U_43,U_44,U_45,U_46,U_47,U_48,U_49,U_50,U_51,c_Com_Ocom_OSKIP) = U_44,
    inference(definitional_conversion,[status(esa)],[f_8_2]) ).

cnf(f_8_4,plain,
    c_Com_Ocom_Ocom__rec(U_43,U_44,U_45,U_46,U_47,U_48,U_49,U_50,U_51,c_Com_Ocom_OSKIP) = U_44,
    inference(clausify,[status(thm)],[f_8_3]) ).

fof(f_9_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_9_2,plain,
    ! [U_60,U_59,U_58] :
      ( ( c_Hoare__Mirabelle_Ohoare__valids(U_58,U_59,U_60)
        | ? [U_57] :
            ( ? [U_56] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_58,U_57,U_56)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_58)),U_56),U_60)) )
            & ! [U_55] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_58,U_57,U_55)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_58)),U_55),U_59)) ) ) )
      & ( ! [U_54] :
            ( ! [U_53] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_58,U_54,U_53)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_58)),U_53),U_60)) )
            | ? [U_52] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_58,U_54,U_52)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_58)),U_52),U_59)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_58,U_59,U_60) ) ),
    inference(variable_rename,[status(thm)],[f_9_1]) ).

fof(f_9_3,plain,
    ( ! [U_66,U_64,U_62] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_62,U_64,U_66)
        | ? [U_57] :
            ( ? [U_56] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_62,U_57,U_56)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_62)),U_56),U_66)) )
            & ! [U_55] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_62,U_57,U_55)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_62)),U_55),U_64)) ) ) )
    & ! [U_65,U_63,U_61] :
        ( ! [U_54] :
            ( ! [U_53] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_61,U_54,U_53)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_61)),U_53),U_65)) )
            | ? [U_52] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_61,U_54,U_52)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_61)),U_52),U_63)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_61,U_63,U_65) ) ),
    inference(miniscope,[status(thm)],[f_9_2]) ).

fof(f_9_4,plain,
    ( ! [U_66,U_64,U_62] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_62,U_64,U_66)
        | ? [U_57] :
            ( ? [U_56] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_62,U_57,U_56)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_62)),U_56),U_66)) )
            & ! [U_55] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_62,U_57,U_55)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_62)),U_55),U_64)) ) ) )
    & ! [U_65,U_63,U_61] :
        ( ! [U_54] :
            ( ! [U_53] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_61,U_54,U_53)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_61)),U_53),U_65)) )
            | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_61,U_54,sK5(U_65,U_63,U_61,U_54))
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_61)),sK5(U_65,U_63,U_61,U_54)),U_63)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_61,U_63,U_65) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_52,sK5(U_65,U_63,U_61,U_54))],[f_9_3]) ).

fof(f_9_5,plain,
    ( ! [U_66,U_64,U_62] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_62,U_64,U_66)
        | ( ? [U_56] :
              ( ~ c_Hoare__Mirabelle_Otriple__valid(U_62,sK6(U_66,U_64,U_62),U_56)
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_62)),U_56),U_66)) )
          & ! [U_55] :
              ( c_Hoare__Mirabelle_Otriple__valid(U_62,sK6(U_66,U_64,U_62),U_55)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_62)),U_55),U_64)) ) ) )
    & ! [U_65,U_63,U_61] :
        ( ! [U_54] :
            ( ! [U_53] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_61,U_54,U_53)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_61)),U_53),U_65)) )
            | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_61,U_54,sK5(U_65,U_63,U_61,U_54))
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_61)),sK5(U_65,U_63,U_61,U_54)),U_63)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_61,U_63,U_65) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_57,sK6(U_66,U_64,U_62))],[f_9_4]) ).

fof(f_9_6,plain,
    ( ! [U_66,U_64,U_62] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_62,U_64,U_66)
        | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_62,sK6(U_66,U_64,U_62),sK7(U_66,U_64,U_62))
          & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_62)),sK7(U_66,U_64,U_62)),U_66))
          & ! [U_55] :
              ( c_Hoare__Mirabelle_Otriple__valid(U_62,sK6(U_66,U_64,U_62),U_55)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_62)),U_55),U_64)) ) ) )
    & ! [U_65,U_63,U_61] :
        ( ! [U_54] :
            ( ! [U_53] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_61,U_54,U_53)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_61)),U_53),U_65)) )
            | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_61,U_54,sK5(U_65,U_63,U_61,U_54))
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_61)),sK5(U_65,U_63,U_61,U_54)),U_63)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_61,U_63,U_65) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_56,sK7(U_66,U_64,U_62))],[f_9_5]) ).

fof(f_9_7,plain,
    ( ! [U_55,U_62,U_66,U_64] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(U_62,sK6(U_66,U_64,U_62),sK7(U_66,U_64,U_62))
        | ~ sP2(U_55,U_62,U_66,U_64) )
    & ! [U_55,U_62,U_66,U_64] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_62)),sK7(U_66,U_64,U_62)),U_66))
        | ~ sP2(U_55,U_62,U_66,U_64) )
    & ! [U_55,U_62,U_66,U_64] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_62,sK6(U_66,U_64,U_62),U_55)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_62)),U_55),U_64))
        | ~ sP2(U_55,U_62,U_66,U_64) )
    & ! [U_54,U_61,U_65,U_63] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(U_61,U_54,sK5(U_65,U_63,U_61,U_54))
        | ~ sP1(U_54,U_61,U_65,U_63) )
    & ! [U_54,U_61,U_65,U_63] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_61)),sK5(U_65,U_63,U_61,U_54)),U_63))
        | ~ sP1(U_54,U_61,U_65,U_63) )
    & ! [U_55,U_62,U_66,U_64] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_62,U_64,U_66)
        | sP2(U_55,U_62,U_66,U_64) )
    & ! [U_54,U_53,U_61,U_65,U_63] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_61,U_54,U_53)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_61)),U_53),U_65))
        | sP1(U_54,U_61,U_65,U_63)
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_61,U_63,U_65) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1,sP2])],[f_9_6]) ).

cnf(f_9_8,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_61,U_54,U_53)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_61)),U_53),U_65))
    | sP1(U_54,U_61,U_65,U_63)
    | ~ c_Hoare__Mirabelle_Ohoare__valids(U_61,U_63,U_65) ),
    inference(clausify,[status(thm)],[f_9_7]) ).

cnf(f_9_9,plain,
    ( c_Hoare__Mirabelle_Ohoare__valids(U_62,U_64,U_66)
    | sP2(U_55,U_62,U_66,U_64) ),
    inference(clausify,[status(thm)],[f_9_7]) ).

cnf(f_9_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_61)),sK5(U_65,U_63,U_61,U_54)),U_63))
    | ~ sP1(U_54,U_61,U_65,U_63) ),
    inference(clausify,[status(thm)],[f_9_7]) ).

cnf(f_9_11,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_61,U_54,sK5(U_65,U_63,U_61,U_54))
    | ~ sP1(U_54,U_61,U_65,U_63) ),
    inference(clausify,[status(thm)],[f_9_7]) ).

cnf(f_9_12,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_62,sK6(U_66,U_64,U_62),U_55)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_62)),U_55),U_64))
    | ~ sP2(U_55,U_62,U_66,U_64) ),
    inference(clausify,[status(thm)],[f_9_7]) ).

cnf(f_9_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_62)),sK7(U_66,U_64,U_62)),U_66))
    | ~ sP2(U_55,U_62,U_66,U_64) ),
    inference(clausify,[status(thm)],[f_9_7]) ).

cnf(f_9_14,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_62,sK6(U_66,U_64,U_62),sK7(U_66,U_64,U_62))
    | ~ sP2(U_55,U_62,U_66,U_64) ),
    inference(clausify,[status(thm)],[f_9_7]) ).

fof(f_10_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_10_2,plain,
    ! [U_72,U_71,U_70,U_69,U_68,U_67] :
      ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_67,U_71),U_68,U_69,U_72)
      | ~ c_Natural_Oevaln(U_71,U_70,U_69,U_72)
      | ~ c_Natural_Oevaln(U_67,U_68,U_69,U_70) ),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

fof(f_10_3,plain,
    ! [U_68,U_69,U_70,U_71,U_72,U_67] :
      ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_67,U_71),U_68,U_69,U_72)
      | ~ c_Natural_Oevaln(U_71,U_70,U_69,U_72)
      | ~ c_Natural_Oevaln(U_67,U_68,U_69,U_70) ),
    inference(definitional_conversion,[status(esa)],[f_10_2]) ).

cnf(f_10_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_67,U_71),U_68,U_69,U_72)
    | ~ c_Natural_Oevaln(U_71,U_70,U_69,U_72)
    | ~ c_Natural_Oevaln(U_67,U_68,U_69,U_70) ),
    inference(clausify,[status(thm)],[f_10_3]) ).

fof(f_11_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_11_2,plain,
    ! [U_78,U_77,U_76,U_75,U_74,U_73] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_73,U_78,U_75),U_74,U_76,U_77)
      | ~ c_Natural_Oevaln(U_75,U_74,U_76,U_77)
      | hBOOL(hAPP(U_73,U_74)) ),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

fof(f_11_3,plain,
    ! [U_73,U_75,U_77,U_74,U_78,U_76] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_73,U_78,U_75),U_74,U_76,U_77)
      | ~ c_Natural_Oevaln(U_75,U_74,U_76,U_77)
      | hBOOL(hAPP(U_73,U_74)) ),
    inference(definitional_conversion,[status(esa)],[f_11_2]) ).

cnf(f_11_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_73,U_78,U_75),U_74,U_76,U_77)
    | ~ c_Natural_Oevaln(U_75,U_74,U_76,U_77)
    | hBOOL(hAPP(U_73,U_74)) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

fof(f_12_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_12_2,plain,
    ! [U_84,U_83,U_82,U_81,U_80,U_79] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_79,U_81,U_84),U_80,U_82,U_83)
      | ~ c_Natural_Oevaln(U_81,U_80,U_82,U_83)
      | ~ hBOOL(hAPP(U_79,U_80)) ),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

fof(f_12_3,plain,
    ! [U_79,U_82,U_80,U_81,U_83,U_84] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_79,U_81,U_84),U_80,U_82,U_83)
      | ~ c_Natural_Oevaln(U_81,U_80,U_82,U_83)
      | ~ hBOOL(hAPP(U_79,U_80)) ),
    inference(definitional_conversion,[status(esa)],[f_12_2]) ).

cnf(f_12_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_79,U_81,U_84),U_80,U_82,U_83)
    | ~ c_Natural_Oevaln(U_81,U_80,U_82,U_83)
    | ~ hBOOL(hAPP(U_79,U_80)) ),
    inference(clausify,[status(thm)],[f_12_3]) ).

fof(f_13_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_13_2,plain,
    ! [U_90,U_89,U_88,U_87,U_86,U_85] :
      ( ( c_Natural_Oevaln(U_87,U_88,U_89,U_90)
        & ~ hBOOL(hAPP(U_85,U_88)) )
      | ( c_Natural_Oevaln(U_86,U_88,U_89,U_90)
        & hBOOL(hAPP(U_85,U_88)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_85,U_86,U_87),U_88,U_89,U_90) ),
    inference(variable_rename,[status(thm)],[f_13_1]) ).

fof(f_13_3,plain,
    ( ! [U_89,U_90,U_87,U_85,U_88] :
        ( c_Natural_Oevaln(U_87,U_88,U_89,U_90)
        | ~ sP4(U_89,U_90,U_87,U_85,U_88) )
    & ! [U_89,U_90,U_87,U_85,U_88] :
        ( ~ hBOOL(hAPP(U_85,U_88))
        | ~ sP4(U_89,U_90,U_87,U_85,U_88) )
    & ! [U_89,U_90,U_86,U_85,U_88] :
        ( c_Natural_Oevaln(U_86,U_88,U_89,U_90)
        | ~ sP3(U_89,U_90,U_86,U_85,U_88) )
    & ! [U_89,U_90,U_86,U_85,U_88] :
        ( hBOOL(hAPP(U_85,U_88))
        | ~ sP3(U_89,U_90,U_86,U_85,U_88) )
    & ! [U_89,U_90,U_86,U_87,U_85,U_88] :
        ( sP4(U_89,U_90,U_87,U_85,U_88)
        | sP3(U_89,U_90,U_86,U_85,U_88)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_85,U_86,U_87),U_88,U_89,U_90) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3,sP4])],[f_13_2]) ).

cnf(f_13_4,plain,
    ( sP4(U_89,U_90,U_87,U_85,U_88)
    | sP3(U_89,U_90,U_86,U_85,U_88)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_85,U_86,U_87),U_88,U_89,U_90) ),
    inference(clausify,[status(thm)],[f_13_3]) ).

cnf(f_13_5,plain,
    ( hBOOL(hAPP(U_85,U_88))
    | ~ sP3(U_89,U_90,U_86,U_85,U_88) ),
    inference(clausify,[status(thm)],[f_13_3]) ).

cnf(f_13_6,plain,
    ( c_Natural_Oevaln(U_86,U_88,U_89,U_90)
    | ~ sP3(U_89,U_90,U_86,U_85,U_88) ),
    inference(clausify,[status(thm)],[f_13_3]) ).

cnf(f_13_7,plain,
    ( ~ hBOOL(hAPP(U_85,U_88))
    | ~ sP4(U_89,U_90,U_87,U_85,U_88) ),
    inference(clausify,[status(thm)],[f_13_3]) ).

cnf(f_13_8,plain,
    ( c_Natural_Oevaln(U_87,U_88,U_89,U_90)
    | ~ sP4(U_89,U_90,U_87,U_85,U_88) ),
    inference(clausify,[status(thm)],[f_13_3]) ).

fof(f_14_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_14_2,plain,
    ! [U_93,U_92,U_91] :
      ( ( hBOOL(hAPP(c_Com_OWT,U_93))
        & hBOOL(hAPP(c_Com_OWT,U_92)) )
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_91,U_92,U_93))) ),
    inference(variable_rename,[status(thm)],[f_14_1]) ).

fof(f_14_3,plain,
    ! [U_93,U_92] :
      ( ! [U_91] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_91,U_92,U_93)))
      | ( hBOOL(hAPP(c_Com_OWT,U_93))
        & hBOOL(hAPP(c_Com_OWT,U_92)) ) ),
    inference(miniscope,[status(thm)],[f_14_2]) ).

fof(f_14_4,plain,
    ( ! [U_93,U_92] :
        ( hBOOL(hAPP(c_Com_OWT,U_93))
        | ~ sP5(U_93,U_92) )
    & ! [U_93,U_92] :
        ( hBOOL(hAPP(c_Com_OWT,U_92))
        | ~ sP5(U_93,U_92) )
    & ! [U_91,U_93,U_92] :
        ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_91,U_92,U_93)))
        | sP5(U_93,U_92) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_14_3]) ).

cnf(f_14_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_91,U_92,U_93)))
    | sP5(U_93,U_92) ),
    inference(clausify,[status(thm)],[f_14_4]) ).

cnf(f_14_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_92))
    | ~ sP5(U_93,U_92) ),
    inference(clausify,[status(thm)],[f_14_4]) ).

cnf(f_14_7,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_93))
    | ~ sP5(U_93,U_92) ),
    inference(clausify,[status(thm)],[f_14_4]) ).

fof(f_15_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_15_2,plain,
    ! [U_95,U_94] :
      ( ( hBOOL(hAPP(c_Com_OWT,U_95))
        & hBOOL(hAPP(c_Com_OWT,U_94)) )
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_94,U_95))) ),
    inference(variable_rename,[status(thm)],[f_15_1]) ).

fof(f_15_3,plain,
    ( ! [U_94,U_95] :
        ( hBOOL(hAPP(c_Com_OWT,U_95))
        | ~ sP6(U_94,U_95) )
    & ! [U_94,U_95] :
        ( hBOOL(hAPP(c_Com_OWT,U_94))
        | ~ sP6(U_94,U_95) )
    & ! [U_94,U_95] :
        ( sP6(U_94,U_95)
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_94,U_95))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_15_2]) ).

cnf(f_15_4,plain,
    ( sP6(U_94,U_95)
    | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_94,U_95))) ),
    inference(clausify,[status(thm)],[f_15_3]) ).

cnf(f_15_5,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_94))
    | ~ sP6(U_94,U_95) ),
    inference(clausify,[status(thm)],[f_15_3]) ).

cnf(f_15_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_95))
    | ~ sP6(U_94,U_95) ),
    inference(clausify,[status(thm)],[f_15_3]) ).

fof(f_16_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_16_2,plain,
    ! [U_100,U_99,U_98,U_97,U_96] : c_Com_Ocom_OSemi(U_96,U_97) != c_Com_Ocom_OCond(U_98,U_99,U_100),
    inference(variable_rename,[status(thm)],[f_16_1]) ).

fof(f_16_3,plain,
    ! [U_97,U_98,U_96,U_99,U_100] : c_Com_Ocom_OSemi(U_96,U_97) != c_Com_Ocom_OCond(U_98,U_99,U_100),
    inference(definitional_conversion,[status(esa)],[f_16_2]) ).

cnf(f_16_4,plain,
    c_Com_Ocom_OSemi(U_96,U_97) != c_Com_Ocom_OCond(U_98,U_99,U_100),
    inference(clausify,[status(thm)],[f_16_3]) ).

fof(f_17_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_17_2,plain,
    ! [U_105,U_104,U_103,U_102,U_101] : c_Com_Ocom_OCond(U_101,U_102,U_103) != c_Com_Ocom_OSemi(U_104,U_105),
    inference(variable_rename,[status(thm)],[f_17_1]) ).

fof(f_17_3,plain,
    ! [U_102,U_101,U_103,U_104,U_105] : c_Com_Ocom_OCond(U_101,U_102,U_103) != c_Com_Ocom_OSemi(U_104,U_105),
    inference(definitional_conversion,[status(esa)],[f_17_2]) ).

cnf(f_17_4,plain,
    c_Com_Ocom_OCond(U_101,U_102,U_103) != c_Com_Ocom_OSemi(U_104,U_105),
    inference(clausify,[status(thm)],[f_17_3]) ).

fof(f_18_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_18_2,plain,
    ! [U_107,U_106] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_106,U_107)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_107))
        | ~ hBOOL(hAPP(c_Com_OWT,U_106)) )
      & ( ( hBOOL(hAPP(c_Com_OWT,U_107))
          & hBOOL(hAPP(c_Com_OWT,U_106)) )
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_106,U_107))) ) ),
    inference(variable_rename,[status(thm)],[f_18_1]) ).

fof(f_18_3,plain,
    ( ! [U_111,U_109] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_109,U_111)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_111))
        | ~ hBOOL(hAPP(c_Com_OWT,U_109)) )
    & ! [U_110,U_108] :
        ( ( hBOOL(hAPP(c_Com_OWT,U_110))
          & hBOOL(hAPP(c_Com_OWT,U_108)) )
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_108,U_110))) ) ),
    inference(miniscope,[status(thm)],[f_18_2]) ).

fof(f_18_4,plain,
    ( ! [U_110,U_108] :
        ( hBOOL(hAPP(c_Com_OWT,U_110))
        | ~ sP7(U_110,U_108) )
    & ! [U_110,U_108] :
        ( hBOOL(hAPP(c_Com_OWT,U_108))
        | ~ sP7(U_110,U_108) )
    & ! [U_111,U_109] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_109,U_111)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_111))
        | ~ hBOOL(hAPP(c_Com_OWT,U_109)) )
    & ! [U_110,U_108] :
        ( sP7(U_110,U_108)
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_108,U_110))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_18_3]) ).

cnf(f_18_5,plain,
    ( sP7(U_110,U_108)
    | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_108,U_110))) ),
    inference(clausify,[status(thm)],[f_18_4]) ).

cnf(f_18_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_109,U_111)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_111))
    | ~ hBOOL(hAPP(c_Com_OWT,U_109)) ),
    inference(clausify,[status(thm)],[f_18_4]) ).

cnf(f_18_7,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_108))
    | ~ sP7(U_110,U_108) ),
    inference(clausify,[status(thm)],[f_18_4]) ).

cnf(f_18_8,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_110))
    | ~ sP7(U_110,U_108) ),
    inference(clausify,[status(thm)],[f_18_4]) ).

fof(f_19_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_19_2,plain,
    ! [U_114,U_113,U_112] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_112,U_113,U_114)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_114))
        | ~ hBOOL(hAPP(c_Com_OWT,U_113)) )
      & ( ( hBOOL(hAPP(c_Com_OWT,U_114))
          & hBOOL(hAPP(c_Com_OWT,U_113)) )
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_112,U_113,U_114))) ) ),
    inference(variable_rename,[status(thm)],[f_19_1]) ).

fof(f_19_3,plain,
    ( ! [U_120,U_118] :
        ( ! [U_116] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_116,U_118,U_120)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_120))
        | ~ hBOOL(hAPP(c_Com_OWT,U_118)) )
    & ! [U_119,U_117] :
        ( ! [U_115] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_115,U_117,U_119)))
        | ( hBOOL(hAPP(c_Com_OWT,U_119))
          & hBOOL(hAPP(c_Com_OWT,U_117)) ) ) ),
    inference(miniscope,[status(thm)],[f_19_2]) ).

fof(f_19_4,plain,
    ( ! [U_119,U_117] :
        ( hBOOL(hAPP(c_Com_OWT,U_119))
        | ~ sP8(U_119,U_117) )
    & ! [U_119,U_117] :
        ( hBOOL(hAPP(c_Com_OWT,U_117))
        | ~ sP8(U_119,U_117) )
    & ! [U_118,U_116,U_120] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_116,U_118,U_120)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_120))
        | ~ hBOOL(hAPP(c_Com_OWT,U_118)) )
    & ! [U_119,U_115,U_117] :
        ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_115,U_117,U_119)))
        | sP8(U_119,U_117) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_19_3]) ).

cnf(f_19_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_115,U_117,U_119)))
    | sP8(U_119,U_117) ),
    inference(clausify,[status(thm)],[f_19_4]) ).

cnf(f_19_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_116,U_118,U_120)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_120))
    | ~ hBOOL(hAPP(c_Com_OWT,U_118)) ),
    inference(clausify,[status(thm)],[f_19_4]) ).

cnf(f_19_7,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_117))
    | ~ sP8(U_119,U_117) ),
    inference(clausify,[status(thm)],[f_19_4]) ).

cnf(f_19_8,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_119))
    | ~ sP8(U_119,U_117) ),
    inference(clausify,[status(thm)],[f_19_4]) ).

fof(f_20_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_20_2,plain,
    ! [U_124,U_123,U_122,U_121] :
      ( ( c_Com_Ocom_OSemi(U_121,U_122) = c_Com_Ocom_OSemi(U_123,U_124)
        | U_122 != U_124
        | U_121 != U_123 )
      & ( ( U_122 = U_124
          & U_121 = U_123 )
        | c_Com_Ocom_OSemi(U_121,U_122) != c_Com_Ocom_OSemi(U_123,U_124) ) ),
    inference(variable_rename,[status(thm)],[f_20_1]) ).

fof(f_20_3,plain,
    ( ! [U_132,U_130,U_128,U_126] :
        ( c_Com_Ocom_OSemi(U_126,U_128) = c_Com_Ocom_OSemi(U_130,U_132)
        | U_128 != U_132
        | U_126 != U_130 )
    & ! [U_131,U_129,U_127,U_125] :
        ( ( U_127 = U_131
          & U_125 = U_129 )
        | c_Com_Ocom_OSemi(U_125,U_127) != c_Com_Ocom_OSemi(U_129,U_131) ) ),
    inference(miniscope,[status(thm)],[f_20_2]) ).

fof(f_20_4,plain,
    ( ! [U_125,U_131,U_127,U_129] :
        ( U_127 = U_131
        | ~ sP9(U_125,U_131,U_127,U_129) )
    & ! [U_125,U_131,U_127,U_129] :
        ( U_125 = U_129
        | ~ sP9(U_125,U_131,U_127,U_129) )
    & ! [U_128,U_130,U_126,U_132] :
        ( c_Com_Ocom_OSemi(U_126,U_128) = c_Com_Ocom_OSemi(U_130,U_132)
        | U_128 != U_132
        | U_126 != U_130 )
    & ! [U_125,U_131,U_127,U_129] :
        ( sP9(U_125,U_131,U_127,U_129)
        | c_Com_Ocom_OSemi(U_125,U_127) != c_Com_Ocom_OSemi(U_129,U_131) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_20_3]) ).

cnf(f_20_5,plain,
    ( sP9(U_125,U_131,U_127,U_129)
    | c_Com_Ocom_OSemi(U_125,U_127) != c_Com_Ocom_OSemi(U_129,U_131) ),
    inference(clausify,[status(thm)],[f_20_4]) ).

cnf(f_20_6,plain,
    ( c_Com_Ocom_OSemi(U_126,U_128) = c_Com_Ocom_OSemi(U_130,U_132)
    | U_128 != U_132
    | U_126 != U_130 ),
    inference(clausify,[status(thm)],[f_20_4]) ).

cnf(f_20_7,plain,
    ( U_125 = U_129
    | ~ sP9(U_125,U_131,U_127,U_129) ),
    inference(clausify,[status(thm)],[f_20_4]) ).

cnf(f_20_8,plain,
    ( U_127 = U_131
    | ~ sP9(U_125,U_131,U_127,U_129) ),
    inference(clausify,[status(thm)],[f_20_4]) ).

fof(f_21_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_21_2,plain,
    ! [U_138,U_137,U_136,U_135,U_134,U_133] :
      ( ( c_Com_Ocom_OCond(U_133,U_134,U_135) = c_Com_Ocom_OCond(U_136,U_137,U_138)
        | U_135 != U_138
        | U_134 != U_137
        | U_133 != U_136 )
      & ( ( U_135 = U_138
          & U_134 = U_137
          & U_133 = U_136 )
        | c_Com_Ocom_OCond(U_133,U_134,U_135) != c_Com_Ocom_OCond(U_136,U_137,U_138) ) ),
    inference(variable_rename,[status(thm)],[f_21_1]) ).

fof(f_21_3,plain,
    ( ! [U_150,U_148,U_146,U_144,U_142,U_140] :
        ( c_Com_Ocom_OCond(U_140,U_142,U_144) = c_Com_Ocom_OCond(U_146,U_148,U_150)
        | U_144 != U_150
        | U_142 != U_148
        | U_140 != U_146 )
    & ! [U_149,U_147,U_145,U_143,U_141,U_139] :
        ( ( U_143 = U_149
          & U_141 = U_147
          & U_139 = U_145 )
        | c_Com_Ocom_OCond(U_139,U_141,U_143) != c_Com_Ocom_OCond(U_145,U_147,U_149) ) ),
    inference(miniscope,[status(thm)],[f_21_2]) ).

fof(f_21_4,plain,
    ( ! [U_145,U_139,U_141,U_143,U_149,U_147] :
        ( U_143 = U_149
        | ~ sP10(U_145,U_139,U_141,U_143,U_149,U_147) )
    & ! [U_145,U_139,U_141,U_143,U_149,U_147] :
        ( U_141 = U_147
        | ~ sP10(U_145,U_139,U_141,U_143,U_149,U_147) )
    & ! [U_145,U_139,U_141,U_143,U_149,U_147] :
        ( U_139 = U_145
        | ~ sP10(U_145,U_139,U_141,U_143,U_149,U_147) )
    & ! [U_146,U_140,U_148,U_144,U_142,U_150] :
        ( c_Com_Ocom_OCond(U_140,U_142,U_144) = c_Com_Ocom_OCond(U_146,U_148,U_150)
        | U_144 != U_150
        | U_142 != U_148
        | U_140 != U_146 )
    & ! [U_145,U_139,U_141,U_143,U_149,U_147] :
        ( sP10(U_145,U_139,U_141,U_143,U_149,U_147)
        | c_Com_Ocom_OCond(U_139,U_141,U_143) != c_Com_Ocom_OCond(U_145,U_147,U_149) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_21_3]) ).

cnf(f_21_5,plain,
    ( sP10(U_145,U_139,U_141,U_143,U_149,U_147)
    | c_Com_Ocom_OCond(U_139,U_141,U_143) != c_Com_Ocom_OCond(U_145,U_147,U_149) ),
    inference(clausify,[status(thm)],[f_21_4]) ).

cnf(f_21_6,plain,
    ( c_Com_Ocom_OCond(U_140,U_142,U_144) = c_Com_Ocom_OCond(U_146,U_148,U_150)
    | U_144 != U_150
    | U_142 != U_148
    | U_140 != U_146 ),
    inference(clausify,[status(thm)],[f_21_4]) ).

cnf(f_21_7,plain,
    ( U_139 = U_145
    | ~ sP10(U_145,U_139,U_141,U_143,U_149,U_147) ),
    inference(clausify,[status(thm)],[f_21_4]) ).

cnf(f_21_8,plain,
    ( U_141 = U_147
    | ~ sP10(U_145,U_139,U_141,U_143,U_149,U_147) ),
    inference(clausify,[status(thm)],[f_21_4]) ).

cnf(f_21_9,plain,
    ( U_143 = U_149
    | ~ sP10(U_145,U_139,U_141,U_143,U_149,U_147) ),
    inference(clausify,[status(thm)],[f_21_4]) ).

fof(f_22_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_22_2,plain,
    ! [U_157,U_156,U_155,U_154,U_153,U_152,U_151] :
      ( ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_151),U_152),U_153),U_154) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_151),U_155),U_156),U_157)
        | U_154 != U_157
        | U_153 != U_156
        | U_152 != U_155 )
      & ( ( U_154 = U_157
          & U_153 = U_156
          & U_152 = U_155 )
        | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_151),U_152),U_153),U_154) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_151),U_155),U_156),U_157) ) ),
    inference(variable_rename,[status(thm)],[f_22_1]) ).

fof(f_22_3,plain,
    ( ! [U_171,U_169,U_167,U_165,U_163,U_161] :
        ( ! [U_159] : hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_159),U_161),U_163),U_165) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_159),U_167),U_169),U_171)
        | U_165 != U_171
        | U_163 != U_169
        | U_161 != U_167 )
    & ! [U_170,U_168,U_166,U_164,U_162,U_160] :
        ( ! [U_158] : hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_158),U_160),U_162),U_164) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_158),U_166),U_168),U_170)
        | ( U_164 = U_170
          & U_162 = U_168
          & U_160 = U_166 ) ) ),
    inference(miniscope,[status(thm)],[f_22_2]) ).

fof(f_22_4,plain,
    ( ! [U_160,U_164,U_162,U_166,U_168,U_170] :
        ( U_164 = U_170
        | ~ sP11(U_160,U_164,U_162,U_166,U_168,U_170) )
    & ! [U_160,U_164,U_162,U_166,U_168,U_170] :
        ( U_162 = U_168
        | ~ sP11(U_160,U_164,U_162,U_166,U_168,U_170) )
    & ! [U_160,U_164,U_162,U_166,U_168,U_170] :
        ( U_160 = U_166
        | ~ sP11(U_160,U_164,U_162,U_166,U_168,U_170) )
    & ! [U_159,U_165,U_161,U_171,U_163,U_167,U_169] :
        ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_159),U_161),U_163),U_165) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_159),U_167),U_169),U_171)
        | U_165 != U_171
        | U_163 != U_169
        | U_161 != U_167 )
    & ! [U_160,U_158,U_164,U_162,U_166,U_168,U_170] :
        ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_158),U_160),U_162),U_164) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_158),U_166),U_168),U_170)
        | sP11(U_160,U_164,U_162,U_166,U_168,U_170) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_22_3]) ).

cnf(f_22_5,plain,
    ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_158),U_160),U_162),U_164) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_158),U_166),U_168),U_170)
    | sP11(U_160,U_164,U_162,U_166,U_168,U_170) ),
    inference(clausify,[status(thm)],[f_22_4]) ).

cnf(f_22_6,plain,
    ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_159),U_161),U_163),U_165) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_159),U_167),U_169),U_171)
    | U_165 != U_171
    | U_163 != U_169
    | U_161 != U_167 ),
    inference(clausify,[status(thm)],[f_22_4]) ).

cnf(f_22_7,plain,
    ( U_160 = U_166
    | ~ sP11(U_160,U_164,U_162,U_166,U_168,U_170) ),
    inference(clausify,[status(thm)],[f_22_4]) ).

cnf(f_22_8,plain,
    ( U_162 = U_168
    | ~ sP11(U_160,U_164,U_162,U_166,U_168,U_170) ),
    inference(clausify,[status(thm)],[f_22_4]) ).

cnf(f_22_9,plain,
    ( U_164 = U_170
    | ~ sP11(U_160,U_164,U_162,U_166,U_168,U_170) ),
    inference(clausify,[status(thm)],[f_22_4]) ).

fof(f_23_1,plain,
    ! [V_com2_2,V_com1_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSemi(V_com1_2,V_com2_2)) = hAPP(hAPP(V_f4_2,V_com1_2),V_com2_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I67_J]) ).

fof(f_23_2,plain,
    ! [U_182,U_181,U_180,U_179,U_178,U_177,U_176,U_175,U_174,U_173,U_172] : c_Com_Ocom_Ocom__case(U_172,U_173,U_174,U_175,U_176,U_177,U_178,U_179,U_180,c_Com_Ocom_OSemi(U_181,U_182)) = hAPP(hAPP(U_176,U_181),U_182),
    inference(variable_rename,[status(thm)],[f_23_1]) ).

fof(f_23_3,plain,
    ! [U_173,U_176,U_174,U_178,U_172,U_179,U_177,U_182,U_175,U_180,U_181] : c_Com_Ocom_Ocom__case(U_172,U_173,U_174,U_175,U_176,U_177,U_178,U_179,U_180,c_Com_Ocom_OSemi(U_181,U_182)) = hAPP(hAPP(U_176,U_181),U_182),
    inference(definitional_conversion,[status(esa)],[f_23_2]) ).

cnf(f_23_4,plain,
    c_Com_Ocom_Ocom__case(U_172,U_173,U_174,U_175,U_176,U_177,U_178,U_179,U_180,c_Com_Ocom_OSemi(U_181,U_182)) = hAPP(hAPP(U_176,U_181),U_182),
    inference(clausify,[status(thm)],[f_23_3]) ).

fof(f_24_1,plain,
    ! [V_com2_2,V_com1_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OSemi(V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(hAPP(V_f4_2,V_com1_2),V_com2_2),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com1_2)),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com2_2)),
    inference(fof_nnf,[status(thm)],[fact_com_Orecs_I4_J]) ).

fof(f_24_2,plain,
    ! [U_193,U_192,U_191,U_190,U_189,U_188,U_187,U_186,U_185,U_184,U_183] : c_Com_Ocom_Ocom__rec(U_183,U_184,U_185,U_186,U_187,U_188,U_189,U_190,U_191,c_Com_Ocom_OSemi(U_192,U_193)) = hAPP(hAPP(hAPP(hAPP(U_187,U_192),U_193),c_Com_Ocom_Ocom__rec(U_183,U_184,U_185,U_186,U_187,U_188,U_189,U_190,U_191,U_192)),c_Com_Ocom_Ocom__rec(U_183,U_184,U_185,U_186,U_187,U_188,U_189,U_190,U_191,U_193)),
    inference(variable_rename,[status(thm)],[f_24_1]) ).

fof(f_24_3,plain,
    ! [U_183,U_185,U_184,U_186,U_187,U_188,U_189,U_190,U_191,U_192,U_193] : c_Com_Ocom_Ocom__rec(U_183,U_184,U_185,U_186,U_187,U_188,U_189,U_190,U_191,c_Com_Ocom_OSemi(U_192,U_193)) = hAPP(hAPP(hAPP(hAPP(U_187,U_192),U_193),c_Com_Ocom_Ocom__rec(U_183,U_184,U_185,U_186,U_187,U_188,U_189,U_190,U_191,U_192)),c_Com_Ocom_Ocom__rec(U_183,U_184,U_185,U_186,U_187,U_188,U_189,U_190,U_191,U_193)),
    inference(definitional_conversion,[status(esa)],[f_24_2]) ).

cnf(f_24_4,plain,
    c_Com_Ocom_Ocom__rec(U_183,U_184,U_185,U_186,U_187,U_188,U_189,U_190,U_191,c_Com_Ocom_OSemi(U_192,U_193)) = hAPP(hAPP(hAPP(hAPP(U_187,U_192),U_193),c_Com_Ocom_Ocom__rec(U_183,U_184,U_185,U_186,U_187,U_188,U_189,U_190,U_191,U_192)),c_Com_Ocom_Ocom__rec(U_183,U_184,U_185,U_186,U_187,U_188,U_189,U_190,U_191,U_193)),
    inference(clausify,[status(thm)],[f_24_3]) ).

fof(f_25_1,plain,
    ! [V_com2_2,V_com1_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(V_f5_2,V_fun_2),V_com1_2),V_com2_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I68_J]) ).

fof(f_25_2,plain,
    ! [U_205,U_204,U_203,U_202,U_201,U_200,U_199,U_198,U_197,U_196,U_195,U_194] : c_Com_Ocom_Ocom__case(U_194,U_195,U_196,U_197,U_198,U_199,U_200,U_201,U_202,c_Com_Ocom_OCond(U_203,U_204,U_205)) = hAPP(hAPP(hAPP(U_199,U_203),U_204),U_205),
    inference(variable_rename,[status(thm)],[f_25_1]) ).

fof(f_25_3,plain,
    ! [U_194,U_203,U_195,U_198,U_202,U_197,U_196,U_200,U_199,U_201,U_204,U_205] : c_Com_Ocom_Ocom__case(U_194,U_195,U_196,U_197,U_198,U_199,U_200,U_201,U_202,c_Com_Ocom_OCond(U_203,U_204,U_205)) = hAPP(hAPP(hAPP(U_199,U_203),U_204),U_205),
    inference(definitional_conversion,[status(esa)],[f_25_2]) ).

cnf(f_25_4,plain,
    c_Com_Ocom_Ocom__case(U_194,U_195,U_196,U_197,U_198,U_199,U_200,U_201,U_202,c_Com_Ocom_OCond(U_203,U_204,U_205)) = hAPP(hAPP(hAPP(U_199,U_203),U_204),U_205),
    inference(clausify,[status(thm)],[f_25_3]) ).

fof(f_26_1,plain,
    ! [V_com2_2,V_com1_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2)) = hAPP(hAPP(hAPP(hAPP(hAPP(V_f5_2,V_fun_2),V_com1_2),V_com2_2),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com1_2)),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com2_2)),
    inference(fof_nnf,[status(thm)],[fact_com_Orecs_I5_J]) ).

fof(f_26_2,plain,
    ! [U_217,U_216,U_215,U_214,U_213,U_212,U_211,U_210,U_209,U_208,U_207,U_206] : c_Com_Ocom_Ocom__rec(U_206,U_207,U_208,U_209,U_210,U_211,U_212,U_213,U_214,c_Com_Ocom_OCond(U_215,U_216,U_217)) = hAPP(hAPP(hAPP(hAPP(hAPP(U_211,U_215),U_216),U_217),c_Com_Ocom_Ocom__rec(U_206,U_207,U_208,U_209,U_210,U_211,U_212,U_213,U_214,U_216)),c_Com_Ocom_Ocom__rec(U_206,U_207,U_208,U_209,U_210,U_211,U_212,U_213,U_214,U_217)),
    inference(variable_rename,[status(thm)],[f_26_1]) ).

fof(f_26_3,plain,
    ! [U_209,U_210,U_208,U_206,U_207,U_211,U_212,U_213,U_214,U_215,U_216,U_217] : c_Com_Ocom_Ocom__rec(U_206,U_207,U_208,U_209,U_210,U_211,U_212,U_213,U_214,c_Com_Ocom_OCond(U_215,U_216,U_217)) = hAPP(hAPP(hAPP(hAPP(hAPP(U_211,U_215),U_216),U_217),c_Com_Ocom_Ocom__rec(U_206,U_207,U_208,U_209,U_210,U_211,U_212,U_213,U_214,U_216)),c_Com_Ocom_Ocom__rec(U_206,U_207,U_208,U_209,U_210,U_211,U_212,U_213,U_214,U_217)),
    inference(definitional_conversion,[status(esa)],[f_26_2]) ).

cnf(f_26_4,plain,
    c_Com_Ocom_Ocom__rec(U_206,U_207,U_208,U_209,U_210,U_211,U_212,U_213,U_214,c_Com_Ocom_OCond(U_215,U_216,U_217)) = hAPP(hAPP(hAPP(hAPP(hAPP(U_211,U_215),U_216),U_217),c_Com_Ocom_Ocom__rec(U_206,U_207,U_208,U_209,U_210,U_211,U_212,U_213,U_214,U_216)),c_Com_Ocom_Ocom__rec(U_206,U_207,U_208,U_209,U_210,U_211,U_212,U_213,U_214,U_217)),
    inference(clausify,[status(thm)],[f_26_3]) ).

fof(f_27_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_27_2,plain,
    ! [U_219,U_218] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_218,U_219)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_219))
      | ~ hBOOL(hAPP(c_Com_OWT,U_218)) ),
    inference(variable_rename,[status(thm)],[f_27_1]) ).

fof(f_27_3,plain,
    ! [U_218,U_219] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_218,U_219)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_219))
      | ~ hBOOL(hAPP(c_Com_OWT,U_218)) ),
    inference(definitional_conversion,[status(esa)],[f_27_2]) ).

cnf(f_27_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_218,U_219)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_219))
    | ~ hBOOL(hAPP(c_Com_OWT,U_218)) ),
    inference(clausify,[status(thm)],[f_27_3]) ).

fof(f_28_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_28_2,plain,
    ! [U_222,U_221,U_220] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_222,U_220,U_221)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_221))
      | ~ hBOOL(hAPP(c_Com_OWT,U_220)) ),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

fof(f_28_3,plain,
    ! [U_221,U_220,U_222] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_222,U_220,U_221)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_221))
      | ~ hBOOL(hAPP(c_Com_OWT,U_220)) ),
    inference(definitional_conversion,[status(esa)],[f_28_2]) ).

cnf(f_28_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_222,U_220,U_221)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_221))
    | ~ hBOOL(hAPP(c_Com_OWT,U_220)) ),
    inference(clausify,[status(thm)],[f_28_3]) ).

fof(f_29_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_29_2,plain,
    ! [U_227,U_226,U_225] :
      ( ! [U_224] :
          ( c_Hoare__Mirabelle_Otriple__valid(U_225,U_227,U_224)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_225)),U_224),U_226)) )
      | ? [U_223] :
          ( ~ c_Hoare__Mirabelle_Otriple__valid(U_225,hAPP(c_Nat_OSuc,U_227),U_223)
          & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_225)),U_223),U_226)) ) ),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

fof(f_29_3,plain,
    ! [U_227,U_226,U_225] :
      ( ! [U_224] :
          ( c_Hoare__Mirabelle_Otriple__valid(U_225,U_227,U_224)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_225)),U_224),U_226)) )
      | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_225,hAPP(c_Nat_OSuc,U_227),sK8(U_227,U_226,U_225))
        & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_225)),sK8(U_227,U_226,U_225)),U_226)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_223,sK8(U_227,U_226,U_225))],[f_29_2]) ).

fof(f_29_4,plain,
    ( ! [U_225,U_226,U_227] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(U_225,hAPP(c_Nat_OSuc,U_227),sK8(U_227,U_226,U_225))
        | ~ sP12(U_225,U_226,U_227) )
    & ! [U_225,U_226,U_227] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_225)),sK8(U_227,U_226,U_225)),U_226))
        | ~ sP12(U_225,U_226,U_227) )
    & ! [U_224,U_225,U_226,U_227] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_225,U_227,U_224)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_225)),U_224),U_226))
        | sP12(U_225,U_226,U_227) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_29_3]) ).

cnf(f_29_5,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_225,U_227,U_224)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_225)),U_224),U_226))
    | sP12(U_225,U_226,U_227) ),
    inference(clausify,[status(thm)],[f_29_4]) ).

cnf(f_29_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_225)),sK8(U_227,U_226,U_225)),U_226))
    | ~ sP12(U_225,U_226,U_227) ),
    inference(clausify,[status(thm)],[f_29_4]) ).

cnf(f_29_7,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_225,hAPP(c_Nat_OSuc,U_227),sK8(U_227,U_226,U_225))
    | ~ sP12(U_225,U_226,U_227) ),
    inference(clausify,[status(thm)],[f_29_4]) ).

fof(f_30_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_30_2,plain,
    ! [U_231,U_230,U_229,U_228] :
      ( c_Natural_Oevaln(U_228,U_229,hAPP(c_Nat_OSuc,U_230),U_231)
      | ~ c_Natural_Oevaln(U_228,U_229,U_230,U_231) ),
    inference(variable_rename,[status(thm)],[f_30_1]) ).

fof(f_30_3,plain,
    ! [U_231,U_230,U_229,U_228] :
      ( c_Natural_Oevaln(U_228,U_229,hAPP(c_Nat_OSuc,U_230),U_231)
      | ~ c_Natural_Oevaln(U_228,U_229,U_230,U_231) ),
    inference(definitional_conversion,[status(esa)],[f_30_2]) ).

cnf(f_30_4,plain,
    ( c_Natural_Oevaln(U_228,U_229,hAPP(c_Nat_OSuc,U_230),U_231)
    | ~ c_Natural_Oevaln(U_228,U_229,U_230,U_231) ),
    inference(clausify,[status(thm)],[f_30_3]) ).

fof(f_31_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_31_2,plain,
    ! [U_237,U_236,U_235,U_234,U_233,U_232] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_232,U_233,U_234),U_235,U_236,U_237)
        | ( ( ~ c_Natural_Oevaln(U_234,U_235,U_236,U_237)
            | hBOOL(hAPP(U_232,U_235)) )
          & ( ~ c_Natural_Oevaln(U_233,U_235,U_236,U_237)
            | ~ hBOOL(hAPP(U_232,U_235)) ) ) )
      & ( ( c_Natural_Oevaln(U_234,U_235,U_236,U_237)
          & ~ hBOOL(hAPP(U_232,U_235)) )
        | ( c_Natural_Oevaln(U_233,U_235,U_236,U_237)
          & hBOOL(hAPP(U_232,U_235)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_232,U_233,U_234),U_235,U_236,U_237) ) ),
    inference(variable_rename,[status(thm)],[f_31_1]) ).

fof(f_31_3,plain,
    ( ! [U_249,U_247,U_245,U_243,U_241,U_239] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_239,U_241,U_243),U_245,U_247,U_249)
        | ( ( ~ c_Natural_Oevaln(U_243,U_245,U_247,U_249)
            | hBOOL(hAPP(U_239,U_245)) )
          & ( ~ c_Natural_Oevaln(U_241,U_245,U_247,U_249)
            | ~ hBOOL(hAPP(U_239,U_245)) ) ) )
    & ! [U_248,U_246,U_244,U_242,U_240,U_238] :
        ( ( c_Natural_Oevaln(U_242,U_244,U_246,U_248)
          & ~ hBOOL(hAPP(U_238,U_244)) )
        | ( c_Natural_Oevaln(U_240,U_244,U_246,U_248)
          & hBOOL(hAPP(U_238,U_244)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_238,U_240,U_242),U_244,U_246,U_248) ) ),
    inference(miniscope,[status(thm)],[f_31_2]) ).

fof(f_31_4,plain,
    ( ! [U_245,U_241,U_243,U_247,U_239,U_249] :
        ( ~ c_Natural_Oevaln(U_243,U_245,U_247,U_249)
        | hBOOL(hAPP(U_239,U_245))
        | ~ sP15(U_245,U_241,U_243,U_247,U_239,U_249) )
    & ! [U_245,U_241,U_243,U_247,U_239,U_249] :
        ( ~ c_Natural_Oevaln(U_241,U_245,U_247,U_249)
        | ~ hBOOL(hAPP(U_239,U_245))
        | ~ sP15(U_245,U_241,U_243,U_247,U_239,U_249) )
    & ! [U_242,U_248,U_238,U_244,U_246] :
        ( c_Natural_Oevaln(U_242,U_244,U_246,U_248)
        | ~ sP14(U_242,U_248,U_238,U_244,U_246) )
    & ! [U_242,U_248,U_238,U_244,U_246] :
        ( ~ hBOOL(hAPP(U_238,U_244))
        | ~ sP14(U_242,U_248,U_238,U_244,U_246) )
    & ! [U_240,U_248,U_238,U_244,U_246] :
        ( c_Natural_Oevaln(U_240,U_244,U_246,U_248)
        | ~ sP13(U_240,U_248,U_238,U_244,U_246) )
    & ! [U_240,U_248,U_238,U_244,U_246] :
        ( hBOOL(hAPP(U_238,U_244))
        | ~ sP13(U_240,U_248,U_238,U_244,U_246) )
    & ! [U_245,U_241,U_243,U_247,U_239,U_249] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_239,U_241,U_243),U_245,U_247,U_249)
        | sP15(U_245,U_241,U_243,U_247,U_239,U_249) )
    & ! [U_242,U_240,U_248,U_238,U_244,U_246] :
        ( sP14(U_242,U_248,U_238,U_244,U_246)
        | sP13(U_240,U_248,U_238,U_244,U_246)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_238,U_240,U_242),U_244,U_246,U_248) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13,sP14,sP15])],[f_31_3]) ).

cnf(f_31_5,plain,
    ( sP14(U_242,U_248,U_238,U_244,U_246)
    | sP13(U_240,U_248,U_238,U_244,U_246)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_238,U_240,U_242),U_244,U_246,U_248) ),
    inference(clausify,[status(thm)],[f_31_4]) ).

cnf(f_31_6,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_239,U_241,U_243),U_245,U_247,U_249)
    | sP15(U_245,U_241,U_243,U_247,U_239,U_249) ),
    inference(clausify,[status(thm)],[f_31_4]) ).

cnf(f_31_7,plain,
    ( hBOOL(hAPP(U_238,U_244))
    | ~ sP13(U_240,U_248,U_238,U_244,U_246) ),
    inference(clausify,[status(thm)],[f_31_4]) ).

cnf(f_31_8,plain,
    ( c_Natural_Oevaln(U_240,U_244,U_246,U_248)
    | ~ sP13(U_240,U_248,U_238,U_244,U_246) ),
    inference(clausify,[status(thm)],[f_31_4]) ).

cnf(f_31_9,plain,
    ( ~ hBOOL(hAPP(U_238,U_244))
    | ~ sP14(U_242,U_248,U_238,U_244,U_246) ),
    inference(clausify,[status(thm)],[f_31_4]) ).

cnf(f_31_10,plain,
    ( c_Natural_Oevaln(U_242,U_244,U_246,U_248)
    | ~ sP14(U_242,U_248,U_238,U_244,U_246) ),
    inference(clausify,[status(thm)],[f_31_4]) ).

cnf(f_31_11,plain,
    ( ~ c_Natural_Oevaln(U_241,U_245,U_247,U_249)
    | ~ hBOOL(hAPP(U_239,U_245))
    | ~ sP15(U_245,U_241,U_243,U_247,U_239,U_249) ),
    inference(clausify,[status(thm)],[f_31_4]) ).

cnf(f_31_12,plain,
    ( ~ c_Natural_Oevaln(U_243,U_245,U_247,U_249)
    | hBOOL(hAPP(U_239,U_245))
    | ~ sP15(U_245,U_241,U_243,U_247,U_239,U_249) ),
    inference(clausify,[status(thm)],[f_31_4]) ).

fof(f_32_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_32_2,plain,
    ! [U_255,U_254,U_253,U_252,U_251,U_250] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_250,U_251,U_252),U_253,U_254,U_255)
        | ( ( ~ c_Natural_Oevaln(U_252,U_253,U_254,U_255)
            | hBOOL(hAPP(U_250,U_253)) )
          & ( ~ c_Natural_Oevaln(U_251,U_253,U_254,U_255)
            | ~ hBOOL(hAPP(U_250,U_253)) ) ) )
      & ( ( c_Natural_Oevaln(U_252,U_253,U_254,U_255)
          & ~ hBOOL(hAPP(U_250,U_253)) )
        | ( c_Natural_Oevaln(U_251,U_253,U_254,U_255)
          & hBOOL(hAPP(U_250,U_253)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_250,U_251,U_252),U_253,U_254,U_255) ) ),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

fof(f_32_3,plain,
    ( ! [U_267,U_265,U_263,U_261,U_259,U_257] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_257,U_259,U_261),U_263,U_265,U_267)
        | ( ( ~ c_Natural_Oevaln(U_261,U_263,U_265,U_267)
            | hBOOL(hAPP(U_257,U_263)) )
          & ( ~ c_Natural_Oevaln(U_259,U_263,U_265,U_267)
            | ~ hBOOL(hAPP(U_257,U_263)) ) ) )
    & ! [U_266,U_264,U_262,U_260,U_258,U_256] :
        ( ( c_Natural_Oevaln(U_260,U_262,U_264,U_266)
          & ~ hBOOL(hAPP(U_256,U_262)) )
        | ( c_Natural_Oevaln(U_258,U_262,U_264,U_266)
          & hBOOL(hAPP(U_256,U_262)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_256,U_258,U_260),U_262,U_264,U_266) ) ),
    inference(miniscope,[status(thm)],[f_32_2]) ).

fof(f_32_4,plain,
    ( ! [U_263,U_257,U_259,U_265,U_261,U_267] :
        ( ~ c_Natural_Oevaln(U_261,U_263,U_265,U_267)
        | hBOOL(hAPP(U_257,U_263))
        | ~ sP18(U_263,U_257,U_259,U_265,U_261,U_267) )
    & ! [U_263,U_257,U_259,U_265,U_261,U_267] :
        ( ~ c_Natural_Oevaln(U_259,U_263,U_265,U_267)
        | ~ hBOOL(hAPP(U_257,U_263))
        | ~ sP18(U_263,U_257,U_259,U_265,U_261,U_267) )
    & ! [U_266,U_264,U_260,U_262,U_256] :
        ( c_Natural_Oevaln(U_260,U_262,U_264,U_266)
        | ~ sP17(U_266,U_264,U_260,U_262,U_256) )
    & ! [U_266,U_264,U_260,U_262,U_256] :
        ( ~ hBOOL(hAPP(U_256,U_262))
        | ~ sP17(U_266,U_264,U_260,U_262,U_256) )
    & ! [U_258,U_266,U_264,U_262,U_256] :
        ( c_Natural_Oevaln(U_258,U_262,U_264,U_266)
        | ~ sP16(U_258,U_266,U_264,U_262,U_256) )
    & ! [U_258,U_266,U_264,U_262,U_256] :
        ( hBOOL(hAPP(U_256,U_262))
        | ~ sP16(U_258,U_266,U_264,U_262,U_256) )
    & ! [U_263,U_257,U_259,U_265,U_261,U_267] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_257,U_259,U_261),U_263,U_265,U_267)
        | sP18(U_263,U_257,U_259,U_265,U_261,U_267) )
    & ! [U_258,U_266,U_264,U_260,U_262,U_256] :
        ( sP17(U_266,U_264,U_260,U_262,U_256)
        | sP16(U_258,U_266,U_264,U_262,U_256)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_256,U_258,U_260),U_262,U_264,U_266) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16,sP17,sP18])],[f_32_3]) ).

cnf(f_32_5,plain,
    ( sP17(U_266,U_264,U_260,U_262,U_256)
    | sP16(U_258,U_266,U_264,U_262,U_256)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_256,U_258,U_260),U_262,U_264,U_266) ),
    inference(clausify,[status(thm)],[f_32_4]) ).

cnf(f_32_6,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_257,U_259,U_261),U_263,U_265,U_267)
    | sP18(U_263,U_257,U_259,U_265,U_261,U_267) ),
    inference(clausify,[status(thm)],[f_32_4]) ).

cnf(f_32_7,plain,
    ( hBOOL(hAPP(U_256,U_262))
    | ~ sP16(U_258,U_266,U_264,U_262,U_256) ),
    inference(clausify,[status(thm)],[f_32_4]) ).

cnf(f_32_8,plain,
    ( c_Natural_Oevaln(U_258,U_262,U_264,U_266)
    | ~ sP16(U_258,U_266,U_264,U_262,U_256) ),
    inference(clausify,[status(thm)],[f_32_4]) ).

cnf(f_32_9,plain,
    ( ~ hBOOL(hAPP(U_256,U_262))
    | ~ sP17(U_266,U_264,U_260,U_262,U_256) ),
    inference(clausify,[status(thm)],[f_32_4]) ).

cnf(f_32_10,plain,
    ( c_Natural_Oevaln(U_260,U_262,U_264,U_266)
    | ~ sP17(U_266,U_264,U_260,U_262,U_256) ),
    inference(clausify,[status(thm)],[f_32_4]) ).

cnf(f_32_11,plain,
    ( ~ c_Natural_Oevaln(U_259,U_263,U_265,U_267)
    | ~ hBOOL(hAPP(U_257,U_263))
    | ~ sP18(U_263,U_257,U_259,U_265,U_261,U_267) ),
    inference(clausify,[status(thm)],[f_32_4]) ).

cnf(f_32_12,plain,
    ( ~ c_Natural_Oevaln(U_261,U_263,U_265,U_267)
    | hBOOL(hAPP(U_257,U_263))
    | ~ sP18(U_263,U_257,U_259,U_265,U_261,U_267) ),
    inference(clausify,[status(thm)],[f_32_4]) ).

fof(f_33_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_33_2,plain,
    ! [U_274,U_273,U_272,U_271,U_270] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_270,U_271),U_272,U_273,U_274)
        | ! [U_269] :
            ( ~ c_Natural_Oevaln(U_271,U_269,U_273,U_274)
            | ~ c_Natural_Oevaln(U_270,U_272,U_273,U_269) ) )
      & ( ? [U_268] :
            ( c_Natural_Oevaln(U_271,U_268,U_273,U_274)
            & c_Natural_Oevaln(U_270,U_272,U_273,U_268) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_270,U_271),U_272,U_273,U_274) ) ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

fof(f_33_3,plain,
    ( ! [U_284,U_282,U_280,U_278,U_276] :
        ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_276,U_278),U_280,U_282,U_284)
        | ! [U_269] :
            ( ~ c_Natural_Oevaln(U_278,U_269,U_282,U_284)
            | ~ c_Natural_Oevaln(U_276,U_280,U_282,U_269) ) )
    & ! [U_283,U_281,U_279,U_277,U_275] :
        ( ? [U_268] :
            ( c_Natural_Oevaln(U_277,U_268,U_281,U_283)
            & c_Natural_Oevaln(U_275,U_279,U_281,U_268) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_275,U_277),U_279,U_281,U_283) ) ),
    inference(miniscope,[status(thm)],[f_33_2]) ).

fof(f_33_4,plain,
    ( ! [U_284,U_282,U_280,U_278,U_276] :
        ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_276,U_278),U_280,U_282,U_284)
        | ! [U_269] :
            ( ~ c_Natural_Oevaln(U_278,U_269,U_282,U_284)
            | ~ c_Natural_Oevaln(U_276,U_280,U_282,U_269) ) )
    & ! [U_283,U_281,U_279,U_277,U_275] :
        ( ( c_Natural_Oevaln(U_277,sK9(U_283,U_281,U_279,U_277,U_275),U_281,U_283)
          & c_Natural_Oevaln(U_275,U_279,U_281,sK9(U_283,U_281,U_279,U_277,U_275)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_275,U_277),U_279,U_281,U_283) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_268,sK9(U_283,U_281,U_279,U_277,U_275))],[f_33_3]) ).

fof(f_33_5,plain,
    ( ! [U_279,U_277,U_275,U_281,U_283] :
        ( c_Natural_Oevaln(U_277,sK9(U_283,U_281,U_279,U_277,U_275),U_281,U_283)
        | ~ sP19(U_279,U_277,U_275,U_281,U_283) )
    & ! [U_279,U_277,U_275,U_281,U_283] :
        ( c_Natural_Oevaln(U_275,U_279,U_281,sK9(U_283,U_281,U_279,U_277,U_275))
        | ~ sP19(U_279,U_277,U_275,U_281,U_283) )
    & ! [U_280,U_278,U_269,U_276,U_284,U_282] :
        ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_276,U_278),U_280,U_282,U_284)
        | ~ c_Natural_Oevaln(U_278,U_269,U_282,U_284)
        | ~ c_Natural_Oevaln(U_276,U_280,U_282,U_269) )
    & ! [U_279,U_277,U_275,U_281,U_283] :
        ( sP19(U_279,U_277,U_275,U_281,U_283)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_275,U_277),U_279,U_281,U_283) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_33_4]) ).

cnf(f_33_6,plain,
    ( sP19(U_279,U_277,U_275,U_281,U_283)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_275,U_277),U_279,U_281,U_283) ),
    inference(clausify,[status(thm)],[f_33_5]) ).

cnf(f_33_7,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_276,U_278),U_280,U_282,U_284)
    | ~ c_Natural_Oevaln(U_278,U_269,U_282,U_284)
    | ~ c_Natural_Oevaln(U_276,U_280,U_282,U_269) ),
    inference(clausify,[status(thm)],[f_33_5]) ).

cnf(f_33_8,plain,
    ( c_Natural_Oevaln(U_275,U_279,U_281,sK9(U_283,U_281,U_279,U_277,U_275))
    | ~ sP19(U_279,U_277,U_275,U_281,U_283) ),
    inference(clausify,[status(thm)],[f_33_5]) ).

cnf(f_33_9,plain,
    ( c_Natural_Oevaln(U_277,sK9(U_283,U_281,U_279,U_277,U_275),U_281,U_283)
    | ~ sP19(U_279,U_277,U_275,U_281,U_283) ),
    inference(clausify,[status(thm)],[f_33_5]) ).

fof(f_34_1,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I1_J]) ).

fof(f_34_2,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(definitional_conversion,[status(esa)],[f_34_1]) ).

cnf(f_34_3,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(clausify,[status(thm)],[f_34_2]) ).

fof(f_35_1,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(fof_nnf,[status(thm)],[fact_WT_OSkip]) ).

fof(f_35_2,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(definitional_conversion,[status(esa)],[f_35_1]) ).

cnf(f_35_3,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(clausify,[status(thm)],[f_35_2]) ).

fof(f_36_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_36_2,plain,
    ! [U_287,U_286,U_285] : c_Com_Ocom_OCond(U_285,U_286,U_287) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_36_1]) ).

fof(f_36_3,plain,
    ! [U_285,U_287,U_286] : c_Com_Ocom_OCond(U_285,U_286,U_287) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_36_2]) ).

cnf(f_36_4,plain,
    c_Com_Ocom_OCond(U_285,U_286,U_287) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_36_3]) ).

fof(f_37_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_37_2,plain,
    ! [U_290,U_289,U_288] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_288,U_289,U_290),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

fof(f_37_3,plain,
    ! [U_288,U_289,U_290] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_288,U_289,U_290),
    inference(definitional_conversion,[status(esa)],[f_37_2]) ).

cnf(f_37_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_288,U_289,U_290),
    inference(clausify,[status(thm)],[f_37_3]) ).

fof(f_38_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_38_2,plain,
    ! [U_292,U_291] : c_Com_Ocom_OSemi(U_291,U_292) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_38_1]) ).

fof(f_38_3,plain,
    ! [U_291,U_292] : c_Com_Ocom_OSemi(U_291,U_292) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_38_2]) ).

cnf(f_38_4,plain,
    c_Com_Ocom_OSemi(U_291,U_292) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_38_3]) ).

fof(f_39_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_39_2,plain,
    ! [U_294,U_293] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_293,U_294),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

fof(f_39_3,plain,
    ! [U_294,U_293] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_293,U_294),
    inference(definitional_conversion,[status(esa)],[f_39_2]) ).

cnf(f_39_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_293,U_294),
    inference(clausify,[status(thm)],[f_39_3]) ).

fof(f_40_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_40_2,plain,
    ! [U_300,U_299,U_298,U_297,U_296,U_295] : c_Hoare__Mirabelle_Otriple_Otriple__rec(U_295,U_296,U_297,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_295),U_298),U_299),U_300)) = hAPP(hAPP(hAPP(U_297,U_298),U_299),U_300),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

fof(f_40_3,plain,
    ! [U_295,U_296,U_297,U_298,U_299,U_300] : c_Hoare__Mirabelle_Otriple_Otriple__rec(U_295,U_296,U_297,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_295),U_298),U_299),U_300)) = hAPP(hAPP(hAPP(U_297,U_298),U_299),U_300),
    inference(definitional_conversion,[status(esa)],[f_40_2]) ).

cnf(f_40_4,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__rec(U_295,U_296,U_297,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_295),U_298),U_299),U_300)) = hAPP(hAPP(hAPP(U_297,U_298),U_299),U_300),
    inference(clausify,[status(thm)],[f_40_3]) ).

fof(f_41_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_41_2,plain,
    ! [U_306,U_305,U_304,U_303,U_302,U_301] : c_Hoare__Mirabelle_Otriple_Otriple__case(U_301,U_302,U_303,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_301),U_304),U_305),U_306)) = hAPP(hAPP(hAPP(U_303,U_304),U_305),U_306),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

fof(f_41_3,plain,
    ! [U_302,U_301,U_303,U_304,U_305,U_306] : c_Hoare__Mirabelle_Otriple_Otriple__case(U_301,U_302,U_303,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_301),U_304),U_305),U_306)) = hAPP(hAPP(hAPP(U_303,U_304),U_305),U_306),
    inference(definitional_conversion,[status(esa)],[f_41_2]) ).

cnf(f_41_4,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__case(U_301,U_302,U_303,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_301),U_304),U_305),U_306)) = hAPP(hAPP(hAPP(U_303,U_304),U_305),U_306),
    inference(clausify,[status(thm)],[f_41_3]) ).

fof(f_42_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_42_2,plain,
    ! [U_312,U_311,U_310,U_309,U_308] :
      ( ? [U_307] :
          ( c_Natural_Oevaln(U_309,U_307,U_311,U_312)
          & c_Natural_Oevaln(U_308,U_310,U_311,U_307) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_308,U_309),U_310,U_311,U_312) ),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

fof(f_42_3,plain,
    ! [U_312,U_311,U_310,U_309,U_308] :
      ( ( c_Natural_Oevaln(U_309,sK10(U_312,U_311,U_310,U_309,U_308),U_311,U_312)
        & c_Natural_Oevaln(U_308,U_310,U_311,sK10(U_312,U_311,U_310,U_309,U_308)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_308,U_309),U_310,U_311,U_312) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_307,sK10(U_312,U_311,U_310,U_309,U_308))],[f_42_2]) ).

fof(f_42_4,plain,
    ( ! [U_308,U_309,U_310,U_311,U_312] :
        ( c_Natural_Oevaln(U_309,sK10(U_312,U_311,U_310,U_309,U_308),U_311,U_312)
        | ~ sP20(U_308,U_309,U_310,U_311,U_312) )
    & ! [U_308,U_309,U_310,U_311,U_312] :
        ( c_Natural_Oevaln(U_308,U_310,U_311,sK10(U_312,U_311,U_310,U_309,U_308))
        | ~ sP20(U_308,U_309,U_310,U_311,U_312) )
    & ! [U_308,U_309,U_310,U_311,U_312] :
        ( sP20(U_308,U_309,U_310,U_311,U_312)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_308,U_309),U_310,U_311,U_312) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_42_3]) ).

cnf(f_42_5,plain,
    ( sP20(U_308,U_309,U_310,U_311,U_312)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_308,U_309),U_310,U_311,U_312) ),
    inference(clausify,[status(thm)],[f_42_4]) ).

cnf(f_42_6,plain,
    ( c_Natural_Oevaln(U_308,U_310,U_311,sK10(U_312,U_311,U_310,U_309,U_308))
    | ~ sP20(U_308,U_309,U_310,U_311,U_312) ),
    inference(clausify,[status(thm)],[f_42_4]) ).

cnf(f_42_7,plain,
    ( c_Natural_Oevaln(U_309,sK10(U_312,U_311,U_310,U_309,U_308),U_311,U_312)
    | ~ sP20(U_308,U_309,U_310,U_311,U_312) ),
    inference(clausify,[status(thm)],[f_42_4]) ).

fof(f_43_1,plain,
    ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
    inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).

fof(f_43_2,plain,
    ! [U_313] : U_313 != hAPP(c_Nat_OSuc,U_313),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

fof(f_43_3,plain,
    ! [U_313] : U_313 != hAPP(c_Nat_OSuc,U_313),
    inference(definitional_conversion,[status(esa)],[f_43_2]) ).

cnf(f_43_4,plain,
    U_313 != hAPP(c_Nat_OSuc,U_313),
    inference(clausify,[status(thm)],[f_43_3]) ).

fof(f_44_1,plain,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n,
    inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).

fof(f_44_2,plain,
    ! [U_314] : hAPP(c_Nat_OSuc,U_314) != U_314,
    inference(variable_rename,[status(thm)],[f_44_1]) ).

fof(f_44_3,plain,
    ! [U_314] : hAPP(c_Nat_OSuc,U_314) != U_314,
    inference(definitional_conversion,[status(esa)],[f_44_2]) ).

cnf(f_44_4,plain,
    hAPP(c_Nat_OSuc,U_314) != U_314,
    inference(clausify,[status(thm)],[f_44_3]) ).

fof(f_45_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_45_2,plain,
    ! [U_316,U_315] :
      ( ( hAPP(c_Nat_OSuc,U_315) = hAPP(c_Nat_OSuc,U_316)
        | U_315 != U_316 )
      & ( U_315 = U_316
        | hAPP(c_Nat_OSuc,U_315) != hAPP(c_Nat_OSuc,U_316) ) ),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

fof(f_45_3,plain,
    ( ! [U_320,U_318] :
        ( hAPP(c_Nat_OSuc,U_318) = hAPP(c_Nat_OSuc,U_320)
        | U_318 != U_320 )
    & ! [U_319,U_317] :
        ( U_317 = U_319
        | hAPP(c_Nat_OSuc,U_317) != hAPP(c_Nat_OSuc,U_319) ) ),
    inference(miniscope,[status(thm)],[f_45_2]) ).

fof(f_45_4,plain,
    ( ! [U_320,U_318] :
        ( hAPP(c_Nat_OSuc,U_318) = hAPP(c_Nat_OSuc,U_320)
        | U_318 != U_320 )
    & ! [U_317,U_319] :
        ( U_317 = U_319
        | hAPP(c_Nat_OSuc,U_317) != hAPP(c_Nat_OSuc,U_319) ) ),
    inference(definitional_conversion,[status(esa)],[f_45_3]) ).

cnf(f_45_5,plain,
    ( U_317 = U_319
    | hAPP(c_Nat_OSuc,U_317) != hAPP(c_Nat_OSuc,U_319) ),
    inference(clausify,[status(thm)],[f_45_4]) ).

cnf(f_45_6,plain,
    ( hAPP(c_Nat_OSuc,U_318) = hAPP(c_Nat_OSuc,U_320)
    | U_318 != U_320 ),
    inference(clausify,[status(thm)],[f_45_4]) ).

fof(f_46_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_46_2,plain,
    ! [U_322,U_321] :
      ( U_321 = U_322
      | hAPP(c_Nat_OSuc,U_321) != hAPP(c_Nat_OSuc,U_322) ),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

fof(f_46_3,plain,
    ! [U_322,U_321] :
      ( U_321 = U_322
      | hAPP(c_Nat_OSuc,U_321) != hAPP(c_Nat_OSuc,U_322) ),
    inference(definitional_conversion,[status(esa)],[f_46_2]) ).

cnf(f_46_4,plain,
    ( U_321 = U_322
    | hAPP(c_Nat_OSuc,U_321) != hAPP(c_Nat_OSuc,U_322) ),
    inference(clausify,[status(thm)],[f_46_3]) ).

fof(f_47_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_47_2,plain,
    ! [U_325,U_324,U_323] :
      ( hBOOL(hAPP(c_Com_OWT,U_325))
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_323,U_324,U_325))) ),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

fof(f_47_3,plain,
    ! [U_325] :
      ( ! [U_324,U_323] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_323,U_324,U_325)))
      | hBOOL(hAPP(c_Com_OWT,U_325)) ),
    inference(miniscope,[status(thm)],[f_47_2]) ).

fof(f_47_4,plain,
    ! [U_323,U_324,U_325] :
      ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_323,U_324,U_325)))
      | hBOOL(hAPP(c_Com_OWT,U_325)) ),
    inference(definitional_conversion,[status(esa)],[f_47_3]) ).

cnf(f_47_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_323,U_324,U_325)))
    | hBOOL(hAPP(c_Com_OWT,U_325)) ),
    inference(clausify,[status(thm)],[f_47_4]) ).

fof(f_48_1,plain,
    ! [V_fun_2,V_pname_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = hAPP(hAPP(hAPP(V_f8_2,V_vname_2),V_pname_2),V_fun_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I71_J]) ).

fof(f_48_2,plain,
    ! [U_337,U_336,U_335,U_334,U_333,U_332,U_331,U_330,U_329,U_328,U_327,U_326] : c_Com_Ocom_Ocom__case(U_326,U_327,U_328,U_329,U_330,U_331,U_332,U_333,U_334,c_Com_Ocom_OCall(U_335,U_336,U_337)) = hAPP(hAPP(hAPP(U_334,U_335),U_336),U_337),
    inference(variable_rename,[status(thm)],[f_48_1]) ).

fof(f_48_3,plain,
    ! [U_326,U_327,U_328,U_329,U_330,U_331,U_332,U_333,U_334,U_335,U_336,U_337] : c_Com_Ocom_Ocom__case(U_326,U_327,U_328,U_329,U_330,U_331,U_332,U_333,U_334,c_Com_Ocom_OCall(U_335,U_336,U_337)) = hAPP(hAPP(hAPP(U_334,U_335),U_336),U_337),
    inference(definitional_conversion,[status(esa)],[f_48_2]) ).

cnf(f_48_4,plain,
    c_Com_Ocom_Ocom__case(U_326,U_327,U_328,U_329,U_330,U_331,U_332,U_333,U_334,c_Com_Ocom_OCall(U_335,U_336,U_337)) = hAPP(hAPP(hAPP(U_334,U_335),U_336),U_337),
    inference(clausify,[status(thm)],[f_48_3]) ).

fof(f_49_1,plain,
    ! [V_com_2,V_fun_2,V_loc_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(V_f3_2,V_loc_2),V_fun_2),V_com_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I66_J]) ).

fof(f_49_2,plain,
    ! [U_349,U_348,U_347,U_346,U_345,U_344,U_343,U_342,U_341,U_340,U_339,U_338] : c_Com_Ocom_Ocom__case(U_338,U_339,U_340,U_341,U_342,U_343,U_344,U_345,U_346,c_Com_Ocom_OLocal(U_347,U_348,U_349)) = hAPP(hAPP(hAPP(U_341,U_347),U_348),U_349),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

fof(f_49_3,plain,
    ! [U_338,U_343,U_342,U_339,U_341,U_340,U_345,U_344,U_346,U_347,U_348,U_349] : c_Com_Ocom_Ocom__case(U_338,U_339,U_340,U_341,U_342,U_343,U_344,U_345,U_346,c_Com_Ocom_OLocal(U_347,U_348,U_349)) = hAPP(hAPP(hAPP(U_341,U_347),U_348),U_349),
    inference(definitional_conversion,[status(esa)],[f_49_2]) ).

cnf(f_49_4,plain,
    c_Com_Ocom_Ocom__case(U_338,U_339,U_340,U_341,U_342,U_343,U_344,U_345,U_346,c_Com_Ocom_OLocal(U_347,U_348,U_349)) = hAPP(hAPP(hAPP(U_341,U_347),U_348),U_349),
    inference(clausify,[status(thm)],[f_49_3]) ).

fof(f_50_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_50_2,plain,
    ! [U_354,U_353,U_352,U_351,U_350] : c_Com_Ocom_OAss(U_350,U_351) != c_Com_Ocom_OCall(U_352,U_353,U_354),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

fof(f_50_3,plain,
    ! [U_350,U_354,U_353,U_352,U_351] : c_Com_Ocom_OAss(U_350,U_351) != c_Com_Ocom_OCall(U_352,U_353,U_354),
    inference(definitional_conversion,[status(esa)],[f_50_2]) ).

cnf(f_50_4,plain,
    c_Com_Ocom_OAss(U_350,U_351) != c_Com_Ocom_OCall(U_352,U_353,U_354),
    inference(clausify,[status(thm)],[f_50_3]) ).

fof(f_51_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_51_2,plain,
    ! [U_359,U_358,U_357,U_356,U_355] : c_Com_Ocom_OAss(U_355,U_356) != c_Com_Ocom_OLocal(U_357,U_358,U_359),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

fof(f_51_3,plain,
    ! [U_356,U_355,U_357,U_358,U_359] : c_Com_Ocom_OAss(U_355,U_356) != c_Com_Ocom_OLocal(U_357,U_358,U_359),
    inference(definitional_conversion,[status(esa)],[f_51_2]) ).

cnf(f_51_4,plain,
    c_Com_Ocom_OAss(U_355,U_356) != c_Com_Ocom_OLocal(U_357,U_358,U_359),
    inference(clausify,[status(thm)],[f_51_3]) ).

fof(f_52_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_52_2,plain,
    ! [U_364,U_363,U_362,U_361,U_360] : c_Com_Ocom_OCall(U_360,U_361,U_362) != c_Com_Ocom_OAss(U_363,U_364),
    inference(variable_rename,[status(thm)],[f_52_1]) ).

fof(f_52_3,plain,
    ! [U_361,U_360,U_362,U_363,U_364] : c_Com_Ocom_OCall(U_360,U_361,U_362) != c_Com_Ocom_OAss(U_363,U_364),
    inference(definitional_conversion,[status(esa)],[f_52_2]) ).

cnf(f_52_4,plain,
    c_Com_Ocom_OCall(U_360,U_361,U_362) != c_Com_Ocom_OAss(U_363,U_364),
    inference(clausify,[status(thm)],[f_52_3]) ).

fof(f_53_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_53_2,plain,
    ! [U_369,U_368,U_367,U_366,U_365] : c_Com_Ocom_OLocal(U_365,U_366,U_367) != c_Com_Ocom_OAss(U_368,U_369),
    inference(variable_rename,[status(thm)],[f_53_1]) ).

fof(f_53_3,plain,
    ! [U_366,U_365,U_367,U_368,U_369] : c_Com_Ocom_OLocal(U_365,U_366,U_367) != c_Com_Ocom_OAss(U_368,U_369),
    inference(definitional_conversion,[status(esa)],[f_53_2]) ).

cnf(f_53_4,plain,
    c_Com_Ocom_OLocal(U_365,U_366,U_367) != c_Com_Ocom_OAss(U_368,U_369),
    inference(clausify,[status(thm)],[f_53_3]) ).

fof(f_54_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_54_2,plain,
    ! [U_375,U_374,U_373,U_372,U_371,U_370] : c_Com_Ocom_OCall(U_370,U_371,U_372) != c_Com_Ocom_OLocal(U_373,U_374,U_375),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

fof(f_54_3,plain,
    ! [U_371,U_370,U_372,U_373,U_374,U_375] : c_Com_Ocom_OCall(U_370,U_371,U_372) != c_Com_Ocom_OLocal(U_373,U_374,U_375),
    inference(definitional_conversion,[status(esa)],[f_54_2]) ).

cnf(f_54_4,plain,
    c_Com_Ocom_OCall(U_370,U_371,U_372) != c_Com_Ocom_OLocal(U_373,U_374,U_375),
    inference(clausify,[status(thm)],[f_54_3]) ).

fof(f_55_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_55_2,plain,
    ! [U_381,U_380,U_379,U_378,U_377,U_376] : c_Com_Ocom_OLocal(U_376,U_377,U_378) != c_Com_Ocom_OCall(U_379,U_380,U_381),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

fof(f_55_3,plain,
    ! [U_377,U_376,U_378,U_379,U_380,U_381] : c_Com_Ocom_OLocal(U_376,U_377,U_378) != c_Com_Ocom_OCall(U_379,U_380,U_381),
    inference(definitional_conversion,[status(esa)],[f_55_2]) ).

cnf(f_55_4,plain,
    c_Com_Ocom_OLocal(U_376,U_377,U_378) != c_Com_Ocom_OCall(U_379,U_380,U_381),
    inference(clausify,[status(thm)],[f_55_3]) ).

fof(f_56_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_56_2,plain,
    ! [U_385,U_384,U_383,U_382] :
      ( ( c_Com_Ocom_OAss(U_382,U_383) = c_Com_Ocom_OAss(U_384,U_385)
        | U_383 != U_385
        | U_382 != U_384 )
      & ( ( U_383 = U_385
          & U_382 = U_384 )
        | c_Com_Ocom_OAss(U_382,U_383) != c_Com_Ocom_OAss(U_384,U_385) ) ),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

fof(f_56_3,plain,
    ( ! [U_393,U_391,U_389,U_387] :
        ( c_Com_Ocom_OAss(U_387,U_389) = c_Com_Ocom_OAss(U_391,U_393)
        | U_389 != U_393
        | U_387 != U_391 )
    & ! [U_392,U_390,U_388,U_386] :
        ( ( U_388 = U_392
          & U_386 = U_390 )
        | c_Com_Ocom_OAss(U_386,U_388) != c_Com_Ocom_OAss(U_390,U_392) ) ),
    inference(miniscope,[status(thm)],[f_56_2]) ).

fof(f_56_4,plain,
    ( ! [U_392,U_388,U_386,U_390] :
        ( U_388 = U_392
        | ~ sP21(U_392,U_388,U_386,U_390) )
    & ! [U_392,U_388,U_386,U_390] :
        ( U_386 = U_390
        | ~ sP21(U_392,U_388,U_386,U_390) )
    & ! [U_393,U_387,U_389,U_391] :
        ( c_Com_Ocom_OAss(U_387,U_389) = c_Com_Ocom_OAss(U_391,U_393)
        | U_389 != U_393
        | U_387 != U_391 )
    & ! [U_392,U_388,U_386,U_390] :
        ( sP21(U_392,U_388,U_386,U_390)
        | c_Com_Ocom_OAss(U_386,U_388) != c_Com_Ocom_OAss(U_390,U_392) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21])],[f_56_3]) ).

cnf(f_56_5,plain,
    ( sP21(U_392,U_388,U_386,U_390)
    | c_Com_Ocom_OAss(U_386,U_388) != c_Com_Ocom_OAss(U_390,U_392) ),
    inference(clausify,[status(thm)],[f_56_4]) ).

cnf(f_56_6,plain,
    ( c_Com_Ocom_OAss(U_387,U_389) = c_Com_Ocom_OAss(U_391,U_393)
    | U_389 != U_393
    | U_387 != U_391 ),
    inference(clausify,[status(thm)],[f_56_4]) ).

cnf(f_56_7,plain,
    ( U_386 = U_390
    | ~ sP21(U_392,U_388,U_386,U_390) ),
    inference(clausify,[status(thm)],[f_56_4]) ).

cnf(f_56_8,plain,
    ( U_388 = U_392
    | ~ sP21(U_392,U_388,U_386,U_390) ),
    inference(clausify,[status(thm)],[f_56_4]) ).

fof(f_57_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_57_2,plain,
    ! [U_399,U_398,U_397,U_396,U_395,U_394] :
      ( ( c_Com_Ocom_OCall(U_394,U_395,U_396) = c_Com_Ocom_OCall(U_397,U_398,U_399)
        | U_396 != U_399
        | U_395 != U_398
        | U_394 != U_397 )
      & ( ( U_396 = U_399
          & U_395 = U_398
          & U_394 = U_397 )
        | c_Com_Ocom_OCall(U_394,U_395,U_396) != c_Com_Ocom_OCall(U_397,U_398,U_399) ) ),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

fof(f_57_3,plain,
    ( ! [U_411,U_409,U_407,U_405,U_403,U_401] :
        ( c_Com_Ocom_OCall(U_401,U_403,U_405) = c_Com_Ocom_OCall(U_407,U_409,U_411)
        | U_405 != U_411
        | U_403 != U_409
        | U_401 != U_407 )
    & ! [U_410,U_408,U_406,U_404,U_402,U_400] :
        ( ( U_404 = U_410
          & U_402 = U_408
          & U_400 = U_406 )
        | c_Com_Ocom_OCall(U_400,U_402,U_404) != c_Com_Ocom_OCall(U_406,U_408,U_410) ) ),
    inference(miniscope,[status(thm)],[f_57_2]) ).

fof(f_57_4,plain,
    ( ! [U_404,U_410,U_400,U_406,U_402,U_408] :
        ( U_404 = U_410
        | ~ sP22(U_404,U_410,U_400,U_406,U_402,U_408) )
    & ! [U_404,U_410,U_400,U_406,U_402,U_408] :
        ( U_402 = U_408
        | ~ sP22(U_404,U_410,U_400,U_406,U_402,U_408) )
    & ! [U_404,U_410,U_400,U_406,U_402,U_408] :
        ( U_400 = U_406
        | ~ sP22(U_404,U_410,U_400,U_406,U_402,U_408) )
    & ! [U_405,U_403,U_401,U_407,U_409,U_411] :
        ( c_Com_Ocom_OCall(U_401,U_403,U_405) = c_Com_Ocom_OCall(U_407,U_409,U_411)
        | U_405 != U_411
        | U_403 != U_409
        | U_401 != U_407 )
    & ! [U_404,U_410,U_400,U_406,U_402,U_408] :
        ( sP22(U_404,U_410,U_400,U_406,U_402,U_408)
        | c_Com_Ocom_OCall(U_400,U_402,U_404) != c_Com_Ocom_OCall(U_406,U_408,U_410) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22])],[f_57_3]) ).

cnf(f_57_5,plain,
    ( sP22(U_404,U_410,U_400,U_406,U_402,U_408)
    | c_Com_Ocom_OCall(U_400,U_402,U_404) != c_Com_Ocom_OCall(U_406,U_408,U_410) ),
    inference(clausify,[status(thm)],[f_57_4]) ).

cnf(f_57_6,plain,
    ( c_Com_Ocom_OCall(U_401,U_403,U_405) = c_Com_Ocom_OCall(U_407,U_409,U_411)
    | U_405 != U_411
    | U_403 != U_409
    | U_401 != U_407 ),
    inference(clausify,[status(thm)],[f_57_4]) ).

cnf(f_57_7,plain,
    ( U_400 = U_406
    | ~ sP22(U_404,U_410,U_400,U_406,U_402,U_408) ),
    inference(clausify,[status(thm)],[f_57_4]) ).

cnf(f_57_8,plain,
    ( U_402 = U_408
    | ~ sP22(U_404,U_410,U_400,U_406,U_402,U_408) ),
    inference(clausify,[status(thm)],[f_57_4]) ).

cnf(f_57_9,plain,
    ( U_404 = U_410
    | ~ sP22(U_404,U_410,U_400,U_406,U_402,U_408) ),
    inference(clausify,[status(thm)],[f_57_4]) ).

fof(f_58_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_58_2,plain,
    ! [U_417,U_416,U_415,U_414,U_413,U_412] :
      ( ( c_Com_Ocom_OLocal(U_412,U_413,U_414) = c_Com_Ocom_OLocal(U_415,U_416,U_417)
        | U_414 != U_417
        | U_413 != U_416
        | U_412 != U_415 )
      & ( ( U_414 = U_417
          & U_413 = U_416
          & U_412 = U_415 )
        | c_Com_Ocom_OLocal(U_412,U_413,U_414) != c_Com_Ocom_OLocal(U_415,U_416,U_417) ) ),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

fof(f_58_3,plain,
    ( ! [U_429,U_427,U_425,U_423,U_421,U_419] :
        ( c_Com_Ocom_OLocal(U_419,U_421,U_423) = c_Com_Ocom_OLocal(U_425,U_427,U_429)
        | U_423 != U_429
        | U_421 != U_427
        | U_419 != U_425 )
    & ! [U_428,U_426,U_424,U_422,U_420,U_418] :
        ( ( U_422 = U_428
          & U_420 = U_426
          & U_418 = U_424 )
        | c_Com_Ocom_OLocal(U_418,U_420,U_422) != c_Com_Ocom_OLocal(U_424,U_426,U_428) ) ),
    inference(miniscope,[status(thm)],[f_58_2]) ).

fof(f_58_4,plain,
    ( ! [U_428,U_422,U_418,U_424,U_420,U_426] :
        ( U_422 = U_428
        | ~ sP23(U_428,U_422,U_418,U_424,U_420,U_426) )
    & ! [U_428,U_422,U_418,U_424,U_420,U_426] :
        ( U_420 = U_426
        | ~ sP23(U_428,U_422,U_418,U_424,U_420,U_426) )
    & ! [U_428,U_422,U_418,U_424,U_420,U_426] :
        ( U_418 = U_424
        | ~ sP23(U_428,U_422,U_418,U_424,U_420,U_426) )
    & ! [U_421,U_427,U_425,U_423,U_419,U_429] :
        ( c_Com_Ocom_OLocal(U_419,U_421,U_423) = c_Com_Ocom_OLocal(U_425,U_427,U_429)
        | U_423 != U_429
        | U_421 != U_427
        | U_419 != U_425 )
    & ! [U_428,U_422,U_418,U_424,U_420,U_426] :
        ( sP23(U_428,U_422,U_418,U_424,U_420,U_426)
        | c_Com_Ocom_OLocal(U_418,U_420,U_422) != c_Com_Ocom_OLocal(U_424,U_426,U_428) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_58_3]) ).

cnf(f_58_5,plain,
    ( sP23(U_428,U_422,U_418,U_424,U_420,U_426)
    | c_Com_Ocom_OLocal(U_418,U_420,U_422) != c_Com_Ocom_OLocal(U_424,U_426,U_428) ),
    inference(clausify,[status(thm)],[f_58_4]) ).

cnf(f_58_6,plain,
    ( c_Com_Ocom_OLocal(U_419,U_421,U_423) = c_Com_Ocom_OLocal(U_425,U_427,U_429)
    | U_423 != U_429
    | U_421 != U_427
    | U_419 != U_425 ),
    inference(clausify,[status(thm)],[f_58_4]) ).

cnf(f_58_7,plain,
    ( U_418 = U_424
    | ~ sP23(U_428,U_422,U_418,U_424,U_420,U_426) ),
    inference(clausify,[status(thm)],[f_58_4]) ).

cnf(f_58_8,plain,
    ( U_420 = U_426
    | ~ sP23(U_428,U_422,U_418,U_424,U_420,U_426) ),
    inference(clausify,[status(thm)],[f_58_4]) ).

cnf(f_58_9,plain,
    ( U_422 = U_428
    | ~ sP23(U_428,U_422,U_418,U_424,U_420,U_426) ),
    inference(clausify,[status(thm)],[f_58_4]) ).

fof(f_59_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_59_2,plain,
    ! [U_431,U_430] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_430,U_431))),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

fof(f_59_3,plain,
    ! [U_431,U_430] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_430,U_431))),
    inference(definitional_conversion,[status(esa)],[f_59_2]) ).

cnf(f_59_4,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_430,U_431))),
    inference(clausify,[status(thm)],[f_59_3]) ).

fof(f_60_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_60_2,plain,
    ! [U_433,U_432] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_432,U_433))),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

fof(f_60_3,plain,
    ! [U_432,U_433] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_432,U_433))),
    inference(definitional_conversion,[status(esa)],[f_60_2]) ).

cnf(f_60_4,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_432,U_433))),
    inference(clausify,[status(thm)],[f_60_3]) ).

fof(f_61_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_61_2,plain,
    ! [U_436,U_435,U_434] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_435,U_436,U_434)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_434)) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

fof(f_61_3,plain,
    ! [U_436,U_434,U_435] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_435,U_436,U_434)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_434)) ),
    inference(definitional_conversion,[status(esa)],[f_61_2]) ).

cnf(f_61_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_435,U_436,U_434)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_434)) ),
    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_439,U_438,U_437] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_437,U_438,U_439)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_439)) )
      & ( hBOOL(hAPP(c_Com_OWT,U_439))
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_437,U_438,U_439))) ) ),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

fof(f_62_3,plain,
    ( ! [U_445] :
        ( ! [U_443,U_441] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_441,U_443,U_445)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_445)) )
    & ! [U_444] :
        ( ! [U_442,U_440] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_440,U_442,U_444)))
        | hBOOL(hAPP(c_Com_OWT,U_444)) ) ),
    inference(miniscope,[status(thm)],[f_62_2]) ).

fof(f_62_4,plain,
    ( ! [U_441,U_445,U_443] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_441,U_443,U_445)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_445)) )
    & ! [U_442,U_444,U_440] :
        ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_440,U_442,U_444)))
        | hBOOL(hAPP(c_Com_OWT,U_444)) ) ),
    inference(definitional_conversion,[status(esa)],[f_62_3]) ).

cnf(f_62_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_440,U_442,U_444)))
    | hBOOL(hAPP(c_Com_OWT,U_444)) ),
    inference(clausify,[status(thm)],[f_62_4]) ).

cnf(f_62_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_441,U_443,U_445)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_445)) ),
    inference(clausify,[status(thm)],[f_62_4]) ).

fof(f_63_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_63_2,plain,
    ! [U_450,U_449,U_448,U_447,U_446] : c_Com_Ocom_OCond(U_446,U_447,U_448) != c_Com_Ocom_OAss(U_449,U_450),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

fof(f_63_3,plain,
    ! [U_446,U_447,U_448,U_449,U_450] : c_Com_Ocom_OCond(U_446,U_447,U_448) != c_Com_Ocom_OAss(U_449,U_450),
    inference(definitional_conversion,[status(esa)],[f_63_2]) ).

cnf(f_63_4,plain,
    c_Com_Ocom_OCond(U_446,U_447,U_448) != c_Com_Ocom_OAss(U_449,U_450),
    inference(clausify,[status(thm)],[f_63_3]) ).

fof(f_64_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_64_2,plain,
    ! [U_455,U_454,U_453,U_452,U_451] : c_Com_Ocom_OAss(U_451,U_452) != c_Com_Ocom_OCond(U_453,U_454,U_455),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

fof(f_64_3,plain,
    ! [U_451,U_452,U_453,U_454,U_455] : c_Com_Ocom_OAss(U_451,U_452) != c_Com_Ocom_OCond(U_453,U_454,U_455),
    inference(definitional_conversion,[status(esa)],[f_64_2]) ).

cnf(f_64_4,plain,
    c_Com_Ocom_OAss(U_451,U_452) != c_Com_Ocom_OCond(U_453,U_454,U_455),
    inference(clausify,[status(thm)],[f_64_3]) ).

fof(f_65_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_65_2,plain,
    ! [U_461,U_460,U_459,U_458,U_457,U_456] : c_Com_Ocom_OLocal(U_456,U_457,U_458) != c_Com_Ocom_OCond(U_459,U_460,U_461),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

fof(f_65_3,plain,
    ! [U_456,U_457,U_458,U_459,U_460,U_461] : c_Com_Ocom_OLocal(U_456,U_457,U_458) != c_Com_Ocom_OCond(U_459,U_460,U_461),
    inference(definitional_conversion,[status(esa)],[f_65_2]) ).

cnf(f_65_4,plain,
    c_Com_Ocom_OLocal(U_456,U_457,U_458) != c_Com_Ocom_OCond(U_459,U_460,U_461),
    inference(clausify,[status(thm)],[f_65_3]) ).

fof(f_66_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_66_2,plain,
    ! [U_467,U_466,U_465,U_464,U_463,U_462] : c_Com_Ocom_OCond(U_462,U_463,U_464) != c_Com_Ocom_OLocal(U_465,U_466,U_467),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

fof(f_66_3,plain,
    ! [U_465,U_466,U_467,U_463,U_462,U_464] : c_Com_Ocom_OCond(U_462,U_463,U_464) != c_Com_Ocom_OLocal(U_465,U_466,U_467),
    inference(definitional_conversion,[status(esa)],[f_66_2]) ).

cnf(f_66_4,plain,
    c_Com_Ocom_OCond(U_462,U_463,U_464) != c_Com_Ocom_OLocal(U_465,U_466,U_467),
    inference(clausify,[status(thm)],[f_66_3]) ).

fof(f_67_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_67_2,plain,
    ! [U_473,U_472,U_471,U_470,U_469,U_468] : c_Com_Ocom_OCond(U_468,U_469,U_470) != c_Com_Ocom_OCall(U_471,U_472,U_473),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

fof(f_67_3,plain,
    ! [U_469,U_468,U_470,U_471,U_472,U_473] : c_Com_Ocom_OCond(U_468,U_469,U_470) != c_Com_Ocom_OCall(U_471,U_472,U_473),
    inference(definitional_conversion,[status(esa)],[f_67_2]) ).

cnf(f_67_4,plain,
    c_Com_Ocom_OCond(U_468,U_469,U_470) != c_Com_Ocom_OCall(U_471,U_472,U_473),
    inference(clausify,[status(thm)],[f_67_3]) ).

fof(f_68_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_68_2,plain,
    ! [U_479,U_478,U_477,U_476,U_475,U_474] : c_Com_Ocom_OCall(U_474,U_475,U_476) != c_Com_Ocom_OCond(U_477,U_478,U_479),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

fof(f_68_3,plain,
    ! [U_475,U_474,U_476,U_477,U_478,U_479] : c_Com_Ocom_OCall(U_474,U_475,U_476) != c_Com_Ocom_OCond(U_477,U_478,U_479),
    inference(definitional_conversion,[status(esa)],[f_68_2]) ).

cnf(f_68_4,plain,
    c_Com_Ocom_OCall(U_474,U_475,U_476) != c_Com_Ocom_OCond(U_477,U_478,U_479),
    inference(clausify,[status(thm)],[f_68_3]) ).

fof(f_69_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_69_2,plain,
    ! [U_483,U_482,U_481,U_480] : c_Com_Ocom_OSemi(U_480,U_481) != c_Com_Ocom_OAss(U_482,U_483),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

fof(f_69_3,plain,
    ! [U_481,U_480,U_482,U_483] : c_Com_Ocom_OSemi(U_480,U_481) != c_Com_Ocom_OAss(U_482,U_483),
    inference(definitional_conversion,[status(esa)],[f_69_2]) ).

cnf(f_69_4,plain,
    c_Com_Ocom_OSemi(U_480,U_481) != c_Com_Ocom_OAss(U_482,U_483),
    inference(clausify,[status(thm)],[f_69_3]) ).

fof(f_70_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_70_2,plain,
    ! [U_487,U_486,U_485,U_484] : c_Com_Ocom_OAss(U_484,U_485) != c_Com_Ocom_OSemi(U_486,U_487),
    inference(variable_rename,[status(thm)],[f_70_1]) ).

fof(f_70_3,plain,
    ! [U_484,U_485,U_486,U_487] : c_Com_Ocom_OAss(U_484,U_485) != c_Com_Ocom_OSemi(U_486,U_487),
    inference(definitional_conversion,[status(esa)],[f_70_2]) ).

cnf(f_70_4,plain,
    c_Com_Ocom_OAss(U_484,U_485) != c_Com_Ocom_OSemi(U_486,U_487),
    inference(clausify,[status(thm)],[f_70_3]) ).

fof(f_71_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_71_2,plain,
    ! [U_489,U_488] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(U_488,U_489),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

fof(f_71_3,plain,
    ! [U_488,U_489] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(U_488,U_489),
    inference(definitional_conversion,[status(esa)],[f_71_2]) ).

cnf(f_71_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(U_488,U_489),
    inference(clausify,[status(thm)],[f_71_3]) ).

fof(f_72_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_72_2,plain,
    ! [U_491,U_490] : c_Com_Ocom_OAss(U_490,U_491) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_72_1]) ).

fof(f_72_3,plain,
    ! [U_490,U_491] : c_Com_Ocom_OAss(U_490,U_491) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_72_2]) ).

cnf(f_72_4,plain,
    c_Com_Ocom_OAss(U_490,U_491) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_72_3]) ).

fof(f_73_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_73_2,plain,
    ! [U_496,U_495,U_494,U_493,U_492] : c_Com_Ocom_OLocal(U_492,U_493,U_494) != c_Com_Ocom_OSemi(U_495,U_496),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

fof(f_73_3,plain,
    ! [U_492,U_493,U_494,U_495,U_496] : c_Com_Ocom_OLocal(U_492,U_493,U_494) != c_Com_Ocom_OSemi(U_495,U_496),
    inference(definitional_conversion,[status(esa)],[f_73_2]) ).

cnf(f_73_4,plain,
    c_Com_Ocom_OLocal(U_492,U_493,U_494) != c_Com_Ocom_OSemi(U_495,U_496),
    inference(clausify,[status(thm)],[f_73_3]) ).

fof(f_74_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_74_2,plain,
    ! [U_501,U_500,U_499,U_498,U_497] : c_Com_Ocom_OCall(U_497,U_498,U_499) != c_Com_Ocom_OSemi(U_500,U_501),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

fof(f_74_3,plain,
    ! [U_498,U_497,U_499,U_500,U_501] : c_Com_Ocom_OCall(U_497,U_498,U_499) != c_Com_Ocom_OSemi(U_500,U_501),
    inference(definitional_conversion,[status(esa)],[f_74_2]) ).

cnf(f_74_4,plain,
    c_Com_Ocom_OCall(U_497,U_498,U_499) != c_Com_Ocom_OSemi(U_500,U_501),
    inference(clausify,[status(thm)],[f_74_3]) ).

fof(f_75_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_75_2,plain,
    ! [U_506,U_505,U_504,U_503,U_502] : c_Com_Ocom_OSemi(U_502,U_503) != c_Com_Ocom_OLocal(U_504,U_505,U_506),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

fof(f_75_3,plain,
    ! [U_502,U_503,U_504,U_505,U_506] : c_Com_Ocom_OSemi(U_502,U_503) != c_Com_Ocom_OLocal(U_504,U_505,U_506),
    inference(definitional_conversion,[status(esa)],[f_75_2]) ).

cnf(f_75_4,plain,
    c_Com_Ocom_OSemi(U_502,U_503) != c_Com_Ocom_OLocal(U_504,U_505,U_506),
    inference(clausify,[status(thm)],[f_75_3]) ).

fof(f_76_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_76_2,plain,
    ! [U_511,U_510,U_509,U_508,U_507] : c_Com_Ocom_OSemi(U_507,U_508) != c_Com_Ocom_OCall(U_509,U_510,U_511),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

fof(f_76_3,plain,
    ! [U_507,U_508,U_509,U_510,U_511] : c_Com_Ocom_OSemi(U_507,U_508) != c_Com_Ocom_OCall(U_509,U_510,U_511),
    inference(definitional_conversion,[status(esa)],[f_76_2]) ).

cnf(f_76_4,plain,
    c_Com_Ocom_OSemi(U_507,U_508) != c_Com_Ocom_OCall(U_509,U_510,U_511),
    inference(clausify,[status(thm)],[f_76_3]) ).

fof(f_77_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_77_2,plain,
    ! [U_514,U_513,U_512] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(U_512,U_513,U_514),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

fof(f_77_3,plain,
    ! [U_513,U_512,U_514] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(U_512,U_513,U_514),
    inference(definitional_conversion,[status(esa)],[f_77_2]) ).

cnf(f_77_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(U_512,U_513,U_514),
    inference(clausify,[status(thm)],[f_77_3]) ).

fof(f_78_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_78_2,plain,
    ! [U_517,U_516,U_515] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_515,U_516,U_517),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

fof(f_78_3,plain,
    ! [U_516,U_515,U_517] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_515,U_516,U_517),
    inference(definitional_conversion,[status(esa)],[f_78_2]) ).

cnf(f_78_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_515,U_516,U_517),
    inference(clausify,[status(thm)],[f_78_3]) ).

fof(f_79_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_79_2,plain,
    ! [U_520,U_519,U_518] : c_Com_Ocom_OCall(U_518,U_519,U_520) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_79_1]) ).

fof(f_79_3,plain,
    ! [U_518,U_519,U_520] : c_Com_Ocom_OCall(U_518,U_519,U_520) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_79_2]) ).

cnf(f_79_4,plain,
    c_Com_Ocom_OCall(U_518,U_519,U_520) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_79_3]) ).

fof(f_80_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_80_2,plain,
    ! [U_523,U_522,U_521] : c_Com_Ocom_OLocal(U_521,U_522,U_523) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_80_1]) ).

fof(f_80_3,plain,
    ! [U_522,U_521,U_523] : c_Com_Ocom_OLocal(U_521,U_522,U_523) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_80_2]) ).

cnf(f_80_4,plain,
    c_Com_Ocom_OLocal(U_521,U_522,U_523) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_80_3]) ).

fof(f_81_1,plain,
    ! [V_fun_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = hAPP(hAPP(V_f2_2,V_vname_2),V_fun_2),
    inference(fof_nnf,[status(thm)],[fact_com_Orecs_I2_J]) ).

fof(f_81_2,plain,
    ! [U_534,U_533,U_532,U_531,U_530,U_529,U_528,U_527,U_526,U_525,U_524] : c_Com_Ocom_Ocom__rec(U_524,U_525,U_526,U_527,U_528,U_529,U_530,U_531,U_532,c_Com_Ocom_OAss(U_533,U_534)) = hAPP(hAPP(U_526,U_533),U_534),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

fof(f_81_3,plain,
    ! [U_524,U_525,U_526,U_527,U_528,U_529,U_530,U_531,U_532,U_533,U_534] : c_Com_Ocom_Ocom__rec(U_524,U_525,U_526,U_527,U_528,U_529,U_530,U_531,U_532,c_Com_Ocom_OAss(U_533,U_534)) = hAPP(hAPP(U_526,U_533),U_534),
    inference(definitional_conversion,[status(esa)],[f_81_2]) ).

cnf(f_81_4,plain,
    c_Com_Ocom_Ocom__rec(U_524,U_525,U_526,U_527,U_528,U_529,U_530,U_531,U_532,c_Com_Ocom_OAss(U_533,U_534)) = hAPP(hAPP(U_526,U_533),U_534),
    inference(clausify,[status(thm)],[f_81_3]) ).

fof(f_82_1,plain,
    ! [V_com_2,V_fun_2,V_loc_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(hAPP(V_f3_2,V_loc_2),V_fun_2),V_com_2),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com_2)),
    inference(fof_nnf,[status(thm)],[fact_com_Orecs_I3_J]) ).

fof(f_82_2,plain,
    ! [U_546,U_545,U_544,U_543,U_542,U_541,U_540,U_539,U_538,U_537,U_536,U_535] : c_Com_Ocom_Ocom__rec(U_535,U_536,U_537,U_538,U_539,U_540,U_541,U_542,U_543,c_Com_Ocom_OLocal(U_544,U_545,U_546)) = hAPP(hAPP(hAPP(hAPP(U_538,U_544),U_545),U_546),c_Com_Ocom_Ocom__rec(U_535,U_536,U_537,U_538,U_539,U_540,U_541,U_542,U_543,U_546)),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

fof(f_82_3,plain,
    ! [U_535,U_537,U_536,U_538,U_539,U_540,U_541,U_542,U_543,U_544,U_545,U_546] : c_Com_Ocom_Ocom__rec(U_535,U_536,U_537,U_538,U_539,U_540,U_541,U_542,U_543,c_Com_Ocom_OLocal(U_544,U_545,U_546)) = hAPP(hAPP(hAPP(hAPP(U_538,U_544),U_545),U_546),c_Com_Ocom_Ocom__rec(U_535,U_536,U_537,U_538,U_539,U_540,U_541,U_542,U_543,U_546)),
    inference(definitional_conversion,[status(esa)],[f_82_2]) ).

cnf(f_82_4,plain,
    c_Com_Ocom_Ocom__rec(U_535,U_536,U_537,U_538,U_539,U_540,U_541,U_542,U_543,c_Com_Ocom_OLocal(U_544,U_545,U_546)) = hAPP(hAPP(hAPP(hAPP(U_538,U_544),U_545),U_546),c_Com_Ocom_Ocom__rec(U_535,U_536,U_537,U_538,U_539,U_540,U_541,U_542,U_543,U_546)),
    inference(clausify,[status(thm)],[f_82_3]) ).

fof(f_83_1,plain,
    ! [V_fun_2,V_pname_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = hAPP(hAPP(hAPP(V_f8_2,V_vname_2),V_pname_2),V_fun_2),
    inference(fof_nnf,[status(thm)],[fact_com_Orecs_I8_J]) ).

fof(f_83_2,plain,
    ! [U_558,U_557,U_556,U_555,U_554,U_553,U_552,U_551,U_550,U_549,U_548,U_547] : c_Com_Ocom_Ocom__rec(U_547,U_548,U_549,U_550,U_551,U_552,U_553,U_554,U_555,c_Com_Ocom_OCall(U_556,U_557,U_558)) = hAPP(hAPP(hAPP(U_555,U_556),U_557),U_558),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

fof(f_83_3,plain,
    ! [U_547,U_552,U_548,U_551,U_557,U_550,U_549,U_555,U_554,U_553,U_556,U_558] : c_Com_Ocom_Ocom__rec(U_547,U_548,U_549,U_550,U_551,U_552,U_553,U_554,U_555,c_Com_Ocom_OCall(U_556,U_557,U_558)) = hAPP(hAPP(hAPP(U_555,U_556),U_557),U_558),
    inference(definitional_conversion,[status(esa)],[f_83_2]) ).

cnf(f_83_4,plain,
    c_Com_Ocom_Ocom__rec(U_547,U_548,U_549,U_550,U_551,U_552,U_553,U_554,U_555,c_Com_Ocom_OCall(U_556,U_557,U_558)) = hAPP(hAPP(hAPP(U_555,U_556),U_557),U_558),
    inference(clausify,[status(thm)],[f_83_3]) ).

fof(f_84_1,plain,
    ! [V_fun_2,V_vname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OAss(V_vname_2,V_fun_2)) = hAPP(hAPP(V_f2_2,V_vname_2),V_fun_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I65_J]) ).

fof(f_84_2,plain,
    ! [U_569,U_568,U_567,U_566,U_565,U_564,U_563,U_562,U_561,U_560,U_559] : c_Com_Ocom_Ocom__case(U_559,U_560,U_561,U_562,U_563,U_564,U_565,U_566,U_567,c_Com_Ocom_OAss(U_568,U_569)) = hAPP(hAPP(U_561,U_568),U_569),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

fof(f_84_3,plain,
    ! [U_565,U_567,U_559,U_564,U_563,U_562,U_560,U_561,U_566,U_568,U_569] : c_Com_Ocom_Ocom__case(U_559,U_560,U_561,U_562,U_563,U_564,U_565,U_566,U_567,c_Com_Ocom_OAss(U_568,U_569)) = hAPP(hAPP(U_561,U_568),U_569),
    inference(definitional_conversion,[status(esa)],[f_84_2]) ).

cnf(f_84_4,plain,
    c_Com_Ocom_Ocom__case(U_559,U_560,U_561,U_562,U_563,U_564,U_565,U_566,U_567,c_Com_Ocom_OAss(U_568,U_569)) = hAPP(hAPP(U_561,U_568),U_569),
    inference(clausify,[status(thm)],[f_84_3]) ).

fof(f_85_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_85_2,plain,
    ! [U_573,U_572,U_571,U_570] : c_Natural_Oevaln(c_Com_Ocom_OAss(U_570,U_571),U_572,U_573,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_572),U_570),hAPP(U_571,U_572))),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

fof(f_85_3,plain,
    ! [U_572,U_571,U_570,U_573] : c_Natural_Oevaln(c_Com_Ocom_OAss(U_570,U_571),U_572,U_573,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_572),U_570),hAPP(U_571,U_572))),
    inference(definitional_conversion,[status(esa)],[f_85_2]) ).

cnf(f_85_4,plain,
    c_Natural_Oevaln(c_Com_Ocom_OAss(U_570,U_571),U_572,U_573,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_572),U_570),hAPP(U_571,U_572))),
    inference(clausify,[status(thm)],[f_85_3]) ).

fof(f_86_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_86_2,plain,
    ! [U_578,U_577,U_576,U_575,U_574] :
      ( U_578 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_576),U_574),hAPP(U_575,U_576))
      | ~ c_Natural_Oevaln(c_Com_Ocom_OAss(U_574,U_575),U_576,U_577,U_578) ),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

fof(f_86_3,plain,
    ! [U_574,U_575,U_576,U_577,U_578] :
      ( U_578 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_576),U_574),hAPP(U_575,U_576))
      | ~ c_Natural_Oevaln(c_Com_Ocom_OAss(U_574,U_575),U_576,U_577,U_578) ),
    inference(definitional_conversion,[status(esa)],[f_86_2]) ).

cnf(f_86_4,plain,
    ( U_578 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_576),U_574),hAPP(U_575,U_576))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OAss(U_574,U_575),U_576,U_577,U_578) ),
    inference(clausify,[status(thm)],[f_86_3]) ).

fof(f_87_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_87_2,plain,
    ! [U_581,U_580,U_579] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_580)))
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_579,U_580,U_581))) ),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

fof(f_87_3,plain,
    ! [U_581,U_580] :
      ( ! [U_579] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_579,U_580,U_581)))
      | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_580))) ),
    inference(miniscope,[status(thm)],[f_87_2]) ).

fof(f_87_4,plain,
    ! [U_579,U_580,U_581] :
      ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_579,U_580,U_581)))
      | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_580))) ),
    inference(definitional_conversion,[status(esa)],[f_87_3]) ).

cnf(f_87_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_579,U_580,U_581)))
    | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_580))) ),
    inference(clausify,[status(thm)],[f_87_4]) ).

fof(f_88_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_88_2,plain,
    ! [U_585,U_584,U_583,U_582] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_582,U_583,hAPP(c_Nat_OSuc,U_584),U_585) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_582,U_583,U_584,hAPP(U_583,U_585))
      | ~ class_Rings_Osemiring__1(U_582) ),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

fof(f_88_3,plain,
    ! [U_584,U_583,U_582,U_585] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_582,U_583,hAPP(c_Nat_OSuc,U_584),U_585) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_582,U_583,U_584,hAPP(U_583,U_585))
      | ~ class_Rings_Osemiring__1(U_582) ),
    inference(definitional_conversion,[status(esa)],[f_88_2]) ).

cnf(f_88_4,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_582,U_583,hAPP(c_Nat_OSuc,U_584),U_585) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_582,U_583,U_584,hAPP(U_583,U_585))
    | ~ class_Rings_Osemiring__1(U_582) ),
    inference(clausify,[status(thm)],[f_88_3]) ).

fof(f_89_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_89_2,plain,
    ! [U_589,U_588,U_587,U_586] : c_Natural_Oevaln(c_Com_Ocom_OAss(U_586,U_587),U_588,U_589,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_588),U_586),hAPP(U_587,U_588))),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

fof(f_89_3,plain,
    ! [U_586,U_587,U_588,U_589] : c_Natural_Oevaln(c_Com_Ocom_OAss(U_586,U_587),U_588,U_589,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_588),U_586),hAPP(U_587,U_588))),
    inference(definitional_conversion,[status(esa)],[f_89_2]) ).

cnf(f_89_4,plain,
    c_Natural_Oevaln(c_Com_Ocom_OAss(U_586,U_587),U_588,U_589,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_588),U_586),hAPP(U_587,U_588))),
    inference(clausify,[status(thm)],[f_89_3]) ).

fof(f_90_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_90_2,plain,
    ! [U_592,U_591,U_590] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_591,U_590,U_592)))
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_590))) ),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

fof(f_90_3,plain,
    ! [U_590,U_591,U_592] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_591,U_590,U_592)))
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_590))) ),
    inference(definitional_conversion,[status(esa)],[f_90_2]) ).

cnf(f_90_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_591,U_590,U_592)))
    | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_590))) ),
    inference(clausify,[status(thm)],[f_90_3]) ).

fof(f_91_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_91_2,plain,
    ! [U_595,U_594,U_593] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_593,U_594,U_595)))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_594))) )
      & ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_594)))
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_593,U_594,U_595))) ) ),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

fof(f_91_3,plain,
    ( ! [U_601,U_599] :
        ( ! [U_597] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_597,U_599,U_601)))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_599))) )
    & ! [U_600,U_598] :
        ( ! [U_596] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_596,U_598,U_600)))
        | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_598))) ) ),
    inference(miniscope,[status(thm)],[f_91_2]) ).

fof(f_91_4,plain,
    ( ! [U_601,U_597,U_599] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_597,U_599,U_601)))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_599))) )
    & ! [U_596,U_598,U_600] :
        ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_596,U_598,U_600)))
        | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_598))) ) ),
    inference(definitional_conversion,[status(esa)],[f_91_3]) ).

cnf(f_91_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_596,U_598,U_600)))
    | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_598))) ),
    inference(clausify,[status(thm)],[f_91_4]) ).

cnf(f_91_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_597,U_599,U_601)))
    | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_599))) ),
    inference(clausify,[status(thm)],[f_91_4]) ).

fof(f_92_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_92_2,plain,
    ! [U_605,U_604,U_603,U_602] : c_Nat_Onat_Onat__case(U_602,U_603,U_604,hAPP(c_Nat_OSuc,U_605)) = hAPP(U_604,U_605),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

fof(f_92_3,plain,
    ! [U_604,U_603,U_602,U_605] : c_Nat_Onat_Onat__case(U_602,U_603,U_604,hAPP(c_Nat_OSuc,U_605)) = hAPP(U_604,U_605),
    inference(definitional_conversion,[status(esa)],[f_92_2]) ).

cnf(f_92_4,plain,
    c_Nat_Onat_Onat__case(U_602,U_603,U_604,hAPP(c_Nat_OSuc,U_605)) = hAPP(U_604,U_605),
    inference(clausify,[status(thm)],[f_92_3]) ).

fof(f_93_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_93_2,plain,
    ! [U_609,U_608,U_607,U_606] : hAPP(c_Nat_Onat_Onat__rec(U_606,U_607,U_608),hAPP(c_Nat_OSuc,U_609)) = hAPP(hAPP(U_608,U_609),hAPP(c_Nat_Onat_Onat__rec(U_606,U_607,U_608),U_609)),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

fof(f_93_3,plain,
    ! [U_606,U_607,U_608,U_609] : hAPP(c_Nat_Onat_Onat__rec(U_606,U_607,U_608),hAPP(c_Nat_OSuc,U_609)) = hAPP(hAPP(U_608,U_609),hAPP(c_Nat_Onat_Onat__rec(U_606,U_607,U_608),U_609)),
    inference(definitional_conversion,[status(esa)],[f_93_2]) ).

cnf(f_93_4,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_606,U_607,U_608),hAPP(c_Nat_OSuc,U_609)) = hAPP(hAPP(U_608,U_609),hAPP(c_Nat_Onat_Onat__rec(U_606,U_607,U_608),U_609)),
    inference(clausify,[status(thm)],[f_93_3]) ).

fof(f_94_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_94_2,plain,
    ! [U_611,U_610] :
      ( hBOOL(hAPP(c_Com_OWT,U_611))
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_610,U_611))) ),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

fof(f_94_3,plain,
    ! [U_611] :
      ( ! [U_610] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_610,U_611)))
      | hBOOL(hAPP(c_Com_OWT,U_611)) ),
    inference(miniscope,[status(thm)],[f_94_2]) ).

fof(f_94_4,plain,
    ! [U_610,U_611] :
      ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_610,U_611)))
      | hBOOL(hAPP(c_Com_OWT,U_611)) ),
    inference(definitional_conversion,[status(esa)],[f_94_3]) ).

cnf(f_94_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_610,U_611)))
    | hBOOL(hAPP(c_Com_OWT,U_611)) ),
    inference(clausify,[status(thm)],[f_94_4]) ).

fof(f_95_1,plain,
    ! [V_com_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(V_f6_2,V_fun_2),V_com_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I69_J]) ).

fof(f_95_2,plain,
    ! [U_622,U_621,U_620,U_619,U_618,U_617,U_616,U_615,U_614,U_613,U_612] : c_Com_Ocom_Ocom__case(U_612,U_613,U_614,U_615,U_616,U_617,U_618,U_619,U_620,c_Com_Ocom_OWhile(U_621,U_622)) = hAPP(hAPP(U_618,U_621),U_622),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

fof(f_95_3,plain,
    ! [U_612,U_613,U_614,U_615,U_616,U_617,U_618,U_619,U_620,U_621,U_622] : c_Com_Ocom_Ocom__case(U_612,U_613,U_614,U_615,U_616,U_617,U_618,U_619,U_620,c_Com_Ocom_OWhile(U_621,U_622)) = hAPP(hAPP(U_618,U_621),U_622),
    inference(definitional_conversion,[status(esa)],[f_95_2]) ).

cnf(f_95_4,plain,
    c_Com_Ocom_Ocom__case(U_612,U_613,U_614,U_615,U_616,U_617,U_618,U_619,U_620,c_Com_Ocom_OWhile(U_621,U_622)) = hAPP(hAPP(U_618,U_621),U_622),
    inference(clausify,[status(thm)],[f_95_3]) ).

fof(f_96_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_96_2,plain,
    ! [U_626,U_625,U_624,U_623] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_623,U_625),U_624,U_626,U_624)
      | hBOOL(hAPP(U_623,U_624)) ),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

fof(f_96_3,plain,
    ! [U_626,U_625,U_624,U_623] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_623,U_625),U_624,U_626,U_624)
      | hBOOL(hAPP(U_623,U_624)) ),
    inference(definitional_conversion,[status(esa)],[f_96_2]) ).

cnf(f_96_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_623,U_625),U_624,U_626,U_624)
    | hBOOL(hAPP(U_623,U_624)) ),
    inference(clausify,[status(thm)],[f_96_3]) ).

fof(f_97_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_97_2,plain,
    ! [U_632,U_631,U_630,U_629,U_628,U_627] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_627,U_629),U_628,U_630,U_632)
      | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_627,U_629),U_631,U_630,U_632)
      | ~ c_Natural_Oevaln(U_629,U_628,U_630,U_631)
      | ~ hBOOL(hAPP(U_627,U_628)) ),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

fof(f_97_3,plain,
    ! [U_627,U_628,U_629,U_630,U_631,U_632] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_627,U_629),U_628,U_630,U_632)
      | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_627,U_629),U_631,U_630,U_632)
      | ~ c_Natural_Oevaln(U_629,U_628,U_630,U_631)
      | ~ hBOOL(hAPP(U_627,U_628)) ),
    inference(definitional_conversion,[status(esa)],[f_97_2]) ).

cnf(f_97_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_627,U_629),U_628,U_630,U_632)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_627,U_629),U_631,U_630,U_632)
    | ~ c_Natural_Oevaln(U_629,U_628,U_630,U_631)
    | ~ hBOOL(hAPP(U_627,U_628)) ),
    inference(clausify,[status(thm)],[f_97_3]) ).

fof(f_98_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_98_2,plain,
    ! [U_636,U_635,U_634,U_633] :
      ( ( c_Com_Ocom_OWhile(U_633,U_634) = c_Com_Ocom_OWhile(U_635,U_636)
        | U_634 != U_636
        | U_633 != U_635 )
      & ( ( U_634 = U_636
          & U_633 = U_635 )
        | c_Com_Ocom_OWhile(U_633,U_634) != c_Com_Ocom_OWhile(U_635,U_636) ) ),
    inference(variable_rename,[status(thm)],[f_98_1]) ).

fof(f_98_3,plain,
    ( ! [U_644,U_642,U_640,U_638] :
        ( c_Com_Ocom_OWhile(U_638,U_640) = c_Com_Ocom_OWhile(U_642,U_644)
        | U_640 != U_644
        | U_638 != U_642 )
    & ! [U_643,U_641,U_639,U_637] :
        ( ( U_639 = U_643
          & U_637 = U_641 )
        | c_Com_Ocom_OWhile(U_637,U_639) != c_Com_Ocom_OWhile(U_641,U_643) ) ),
    inference(miniscope,[status(thm)],[f_98_2]) ).

fof(f_98_4,plain,
    ( ! [U_637,U_641,U_639,U_643] :
        ( U_639 = U_643
        | ~ sP24(U_637,U_641,U_639,U_643) )
    & ! [U_637,U_641,U_639,U_643] :
        ( U_637 = U_641
        | ~ sP24(U_637,U_641,U_639,U_643) )
    & ! [U_640,U_642,U_638,U_644] :
        ( c_Com_Ocom_OWhile(U_638,U_640) = c_Com_Ocom_OWhile(U_642,U_644)
        | U_640 != U_644
        | U_638 != U_642 )
    & ! [U_637,U_641,U_639,U_643] :
        ( sP24(U_637,U_641,U_639,U_643)
        | c_Com_Ocom_OWhile(U_637,U_639) != c_Com_Ocom_OWhile(U_641,U_643) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24])],[f_98_3]) ).

cnf(f_98_5,plain,
    ( sP24(U_637,U_641,U_639,U_643)
    | c_Com_Ocom_OWhile(U_637,U_639) != c_Com_Ocom_OWhile(U_641,U_643) ),
    inference(clausify,[status(thm)],[f_98_4]) ).

cnf(f_98_6,plain,
    ( c_Com_Ocom_OWhile(U_638,U_640) = c_Com_Ocom_OWhile(U_642,U_644)
    | U_640 != U_644
    | U_638 != U_642 ),
    inference(clausify,[status(thm)],[f_98_4]) ).

cnf(f_98_7,plain,
    ( U_637 = U_641
    | ~ sP24(U_637,U_641,U_639,U_643) ),
    inference(clausify,[status(thm)],[f_98_4]) ).

cnf(f_98_8,plain,
    ( U_639 = U_643
    | ~ sP24(U_637,U_641,U_639,U_643) ),
    inference(clausify,[status(thm)],[f_98_4]) ).

fof(f_99_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_99_2,plain,
    ! [U_646,U_645] :
      ( ( hAPP(c_Com_Ocom_OBODY,U_645) = hAPP(c_Com_Ocom_OBODY,U_646)
        | U_645 != U_646 )
      & ( U_645 = U_646
        | hAPP(c_Com_Ocom_OBODY,U_645) != hAPP(c_Com_Ocom_OBODY,U_646) ) ),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

fof(f_99_3,plain,
    ( ! [U_650,U_648] :
        ( hAPP(c_Com_Ocom_OBODY,U_648) = hAPP(c_Com_Ocom_OBODY,U_650)
        | U_648 != U_650 )
    & ! [U_649,U_647] :
        ( U_647 = U_649
        | hAPP(c_Com_Ocom_OBODY,U_647) != hAPP(c_Com_Ocom_OBODY,U_649) ) ),
    inference(miniscope,[status(thm)],[f_99_2]) ).

fof(f_99_4,plain,
    ( ! [U_650,U_648] :
        ( hAPP(c_Com_Ocom_OBODY,U_648) = hAPP(c_Com_Ocom_OBODY,U_650)
        | U_648 != U_650 )
    & ! [U_649,U_647] :
        ( U_647 = U_649
        | hAPP(c_Com_Ocom_OBODY,U_647) != hAPP(c_Com_Ocom_OBODY,U_649) ) ),
    inference(definitional_conversion,[status(esa)],[f_99_3]) ).

cnf(f_99_5,plain,
    ( U_647 = U_649
    | hAPP(c_Com_Ocom_OBODY,U_647) != hAPP(c_Com_Ocom_OBODY,U_649) ),
    inference(clausify,[status(thm)],[f_99_4]) ).

cnf(f_99_6,plain,
    ( hAPP(c_Com_Ocom_OBODY,U_648) = hAPP(c_Com_Ocom_OBODY,U_650)
    | U_648 != U_650 ),
    inference(clausify,[status(thm)],[f_99_4]) ).

fof(f_100_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_100_2,plain,
    ! [U_653,U_652,U_651] : c_Com_Ocom_OWhile(U_651,U_652) != hAPP(c_Com_Ocom_OBODY,U_653),
    inference(variable_rename,[status(thm)],[f_100_1]) ).

fof(f_100_3,plain,
    ! [U_651,U_652,U_653] : c_Com_Ocom_OWhile(U_651,U_652) != hAPP(c_Com_Ocom_OBODY,U_653),
    inference(definitional_conversion,[status(esa)],[f_100_2]) ).

cnf(f_100_4,plain,
    c_Com_Ocom_OWhile(U_651,U_652) != hAPP(c_Com_Ocom_OBODY,U_653),
    inference(clausify,[status(thm)],[f_100_3]) ).

fof(f_101_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_101_2,plain,
    ! [U_656,U_655,U_654] : hAPP(c_Com_Ocom_OBODY,U_654) != c_Com_Ocom_OWhile(U_655,U_656),
    inference(variable_rename,[status(thm)],[f_101_1]) ).

fof(f_101_3,plain,
    ! [U_654,U_655,U_656] : hAPP(c_Com_Ocom_OBODY,U_654) != c_Com_Ocom_OWhile(U_655,U_656),
    inference(definitional_conversion,[status(esa)],[f_101_2]) ).

cnf(f_101_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_654) != c_Com_Ocom_OWhile(U_655,U_656),
    inference(clausify,[status(thm)],[f_101_3]) ).

fof(f_102_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_102_2,plain,
    ! [U_663,U_662,U_661,U_660,U_659] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_659,U_660),U_661,U_662,U_663)
        | ( ( ! [U_658] :
                ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_659,U_660),U_658,U_662,U_663)
                | ~ c_Natural_Oevaln(U_660,U_661,U_662,U_658) )
            | ~ hBOOL(hAPP(U_659,U_661)) )
          & ( hBOOL(hAPP(U_659,U_661))
            | U_663 != U_661 ) ) )
      & ( ( ? [U_657] :
              ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_659,U_660),U_657,U_662,U_663)
              & c_Natural_Oevaln(U_660,U_661,U_662,U_657) )
          & hBOOL(hAPP(U_659,U_661)) )
        | ( ~ hBOOL(hAPP(U_659,U_661))
          & U_663 = U_661 )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_659,U_660),U_661,U_662,U_663) ) ),
    inference(variable_rename,[status(thm)],[f_102_1]) ).

fof(f_102_3,plain,
    ( ! [U_673,U_671,U_669,U_667,U_665] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_665,U_667),U_669,U_671,U_673)
        | ( ( ! [U_658] :
                ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_665,U_667),U_658,U_671,U_673)
                | ~ c_Natural_Oevaln(U_667,U_669,U_671,U_658) )
            | ~ hBOOL(hAPP(U_665,U_669)) )
          & ( hBOOL(hAPP(U_665,U_669))
            | U_673 != U_669 ) ) )
    & ! [U_672,U_670,U_668,U_666,U_664] :
        ( ( ? [U_657] :
              ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_664,U_666),U_657,U_670,U_672)
              & c_Natural_Oevaln(U_666,U_668,U_670,U_657) )
          & hBOOL(hAPP(U_664,U_668)) )
        | ( ~ hBOOL(hAPP(U_664,U_668))
          & U_672 = U_668 )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_664,U_666),U_668,U_670,U_672) ) ),
    inference(miniscope,[status(thm)],[f_102_2]) ).

fof(f_102_4,plain,
    ( ! [U_673,U_671,U_669,U_667,U_665] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_665,U_667),U_669,U_671,U_673)
        | ( ( ! [U_658] :
                ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_665,U_667),U_658,U_671,U_673)
                | ~ c_Natural_Oevaln(U_667,U_669,U_671,U_658) )
            | ~ hBOOL(hAPP(U_665,U_669)) )
          & ( hBOOL(hAPP(U_665,U_669))
            | U_673 != U_669 ) ) )
    & ! [U_672,U_670,U_668,U_666,U_664] :
        ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_664,U_666),sK11(U_672,U_670,U_668,U_666,U_664),U_670,U_672)
          & c_Natural_Oevaln(U_666,U_668,U_670,sK11(U_672,U_670,U_668,U_666,U_664))
          & hBOOL(hAPP(U_664,U_668)) )
        | ( ~ hBOOL(hAPP(U_664,U_668))
          & U_672 = U_668 )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_664,U_666),U_668,U_670,U_672) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_657,sK11(U_672,U_670,U_668,U_666,U_664))],[f_102_3]) ).

fof(f_102_5,plain,
    ( ! [U_658,U_673,U_671,U_667,U_669,U_665] :
        ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_665,U_667),U_658,U_671,U_673)
        | ~ c_Natural_Oevaln(U_667,U_669,U_671,U_658)
        | ~ hBOOL(hAPP(U_665,U_669))
        | ~ sP27(U_658,U_673,U_671,U_667,U_669,U_665) )
    & ! [U_658,U_673,U_671,U_667,U_669,U_665] :
        ( hBOOL(hAPP(U_665,U_669))
        | U_673 != U_669
        | ~ sP27(U_658,U_673,U_671,U_667,U_669,U_665) )
    & ! [U_668,U_666,U_664,U_670,U_672] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_664,U_666),sK11(U_672,U_670,U_668,U_666,U_664),U_670,U_672)
        | ~ sP26(U_668,U_666,U_664,U_670,U_672) )
    & ! [U_668,U_666,U_664,U_670,U_672] :
        ( c_Natural_Oevaln(U_666,U_668,U_670,sK11(U_672,U_670,U_668,U_666,U_664))
        | ~ sP26(U_668,U_666,U_664,U_670,U_672) )
    & ! [U_668,U_666,U_664,U_670,U_672] :
        ( hBOOL(hAPP(U_664,U_668))
        | ~ sP26(U_668,U_666,U_664,U_670,U_672) )
    & ! [U_668,U_664,U_672] :
        ( ~ hBOOL(hAPP(U_664,U_668))
        | ~ sP25(U_668,U_664,U_672) )
    & ! [U_668,U_664,U_672] :
        ( U_672 = U_668
        | ~ sP25(U_668,U_664,U_672) )
    & ! [U_658,U_673,U_671,U_667,U_669,U_665] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_665,U_667),U_669,U_671,U_673)
        | sP27(U_658,U_673,U_671,U_667,U_669,U_665) )
    & ! [U_668,U_666,U_664,U_670,U_672] :
        ( sP26(U_668,U_666,U_664,U_670,U_672)
        | sP25(U_668,U_664,U_672)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_664,U_666),U_668,U_670,U_672) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25,sP26,sP27])],[f_102_4]) ).

cnf(f_102_6,plain,
    ( sP26(U_668,U_666,U_664,U_670,U_672)
    | sP25(U_668,U_664,U_672)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_664,U_666),U_668,U_670,U_672) ),
    inference(clausify,[status(thm)],[f_102_5]) ).

cnf(f_102_7,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_665,U_667),U_669,U_671,U_673)
    | sP27(U_658,U_673,U_671,U_667,U_669,U_665) ),
    inference(clausify,[status(thm)],[f_102_5]) ).

cnf(f_102_8,plain,
    ( U_672 = U_668
    | ~ sP25(U_668,U_664,U_672) ),
    inference(clausify,[status(thm)],[f_102_5]) ).

cnf(f_102_9,plain,
    ( ~ hBOOL(hAPP(U_664,U_668))
    | ~ sP25(U_668,U_664,U_672) ),
    inference(clausify,[status(thm)],[f_102_5]) ).

cnf(f_102_10,plain,
    ( hBOOL(hAPP(U_664,U_668))
    | ~ sP26(U_668,U_666,U_664,U_670,U_672) ),
    inference(clausify,[status(thm)],[f_102_5]) ).

cnf(f_102_11,plain,
    ( c_Natural_Oevaln(U_666,U_668,U_670,sK11(U_672,U_670,U_668,U_666,U_664))
    | ~ sP26(U_668,U_666,U_664,U_670,U_672) ),
    inference(clausify,[status(thm)],[f_102_5]) ).

cnf(f_102_12,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_664,U_666),sK11(U_672,U_670,U_668,U_666,U_664),U_670,U_672)
    | ~ sP26(U_668,U_666,U_664,U_670,U_672) ),
    inference(clausify,[status(thm)],[f_102_5]) ).

cnf(f_102_13,plain,
    ( hBOOL(hAPP(U_665,U_669))
    | U_673 != U_669
    | ~ sP27(U_658,U_673,U_671,U_667,U_669,U_665) ),
    inference(clausify,[status(thm)],[f_102_5]) ).

cnf(f_102_14,plain,
    ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_665,U_667),U_658,U_671,U_673)
    | ~ c_Natural_Oevaln(U_667,U_669,U_671,U_658)
    | ~ hBOOL(hAPP(U_665,U_669))
    | ~ sP27(U_658,U_673,U_671,U_667,U_669,U_665) ),
    inference(clausify,[status(thm)],[f_102_5]) ).

fof(f_103_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_103_2,plain,
    ! [U_679,U_678,U_677,U_676] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_676,U_677),U_678,U_679,U_678)
        | ( ! [U_675] :
              ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_676,U_677),U_675,U_679,U_678)
              | ~ c_Natural_Oevaln(U_677,U_678,U_679,U_675) )
          & hBOOL(hAPP(U_676,U_678)) ) )
      & ( ? [U_674] :
            ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_676,U_677),U_674,U_679,U_678)
            & c_Natural_Oevaln(U_677,U_678,U_679,U_674) )
        | ~ hBOOL(hAPP(U_676,U_678))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_676,U_677),U_678,U_679,U_678) ) ),
    inference(variable_rename,[status(thm)],[f_103_1]) ).

fof(f_103_3,plain,
    ( ! [U_687,U_685,U_683,U_681] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_681,U_683),U_685,U_687,U_685)
        | ( ! [U_675] :
              ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_681,U_683),U_675,U_687,U_685)
              | ~ c_Natural_Oevaln(U_683,U_685,U_687,U_675) )
          & hBOOL(hAPP(U_681,U_685)) ) )
    & ! [U_686,U_684,U_682,U_680] :
        ( ? [U_674] :
            ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_680,U_682),U_674,U_686,U_684)
            & c_Natural_Oevaln(U_682,U_684,U_686,U_674) )
        | ~ hBOOL(hAPP(U_680,U_684))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_680,U_682),U_684,U_686,U_684) ) ),
    inference(miniscope,[status(thm)],[f_103_2]) ).

fof(f_103_4,plain,
    ( ! [U_687,U_685,U_683,U_681] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_681,U_683),U_685,U_687,U_685)
        | ( ! [U_675] :
              ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_681,U_683),U_675,U_687,U_685)
              | ~ c_Natural_Oevaln(U_683,U_685,U_687,U_675) )
          & hBOOL(hAPP(U_681,U_685)) ) )
    & ! [U_686,U_684,U_682,U_680] :
        ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_680,U_682),sK12(U_686,U_684,U_682,U_680),U_686,U_684)
          & c_Natural_Oevaln(U_682,U_684,U_686,sK12(U_686,U_684,U_682,U_680)) )
        | ~ hBOOL(hAPP(U_680,U_684))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_680,U_682),U_684,U_686,U_684) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_674,sK12(U_686,U_684,U_682,U_680))],[f_103_3]) ).

fof(f_103_5,plain,
    ( ! [U_675,U_685,U_687,U_683,U_681] :
        ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_681,U_683),U_675,U_687,U_685)
        | ~ c_Natural_Oevaln(U_683,U_685,U_687,U_675)
        | ~ sP29(U_675,U_685,U_687,U_683,U_681) )
    & ! [U_675,U_685,U_687,U_683,U_681] :
        ( hBOOL(hAPP(U_681,U_685))
        | ~ sP29(U_675,U_685,U_687,U_683,U_681) )
    & ! [U_684,U_686,U_680,U_682] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_680,U_682),sK12(U_686,U_684,U_682,U_680),U_686,U_684)
        | ~ sP28(U_684,U_686,U_680,U_682) )
    & ! [U_684,U_686,U_680,U_682] :
        ( c_Natural_Oevaln(U_682,U_684,U_686,sK12(U_686,U_684,U_682,U_680))
        | ~ sP28(U_684,U_686,U_680,U_682) )
    & ! [U_675,U_685,U_687,U_683,U_681] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_681,U_683),U_685,U_687,U_685)
        | sP29(U_675,U_685,U_687,U_683,U_681) )
    & ! [U_684,U_686,U_680,U_682] :
        ( sP28(U_684,U_686,U_680,U_682)
        | ~ hBOOL(hAPP(U_680,U_684))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_680,U_682),U_684,U_686,U_684) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28,sP29])],[f_103_4]) ).

cnf(f_103_6,plain,
    ( sP28(U_684,U_686,U_680,U_682)
    | ~ hBOOL(hAPP(U_680,U_684))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_680,U_682),U_684,U_686,U_684) ),
    inference(clausify,[status(thm)],[f_103_5]) ).

cnf(f_103_7,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_681,U_683),U_685,U_687,U_685)
    | sP29(U_675,U_685,U_687,U_683,U_681) ),
    inference(clausify,[status(thm)],[f_103_5]) ).

cnf(f_103_8,plain,
    ( c_Natural_Oevaln(U_682,U_684,U_686,sK12(U_686,U_684,U_682,U_680))
    | ~ sP28(U_684,U_686,U_680,U_682) ),
    inference(clausify,[status(thm)],[f_103_5]) ).

cnf(f_103_9,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_680,U_682),sK12(U_686,U_684,U_682,U_680),U_686,U_684)
    | ~ sP28(U_684,U_686,U_680,U_682) ),
    inference(clausify,[status(thm)],[f_103_5]) ).

cnf(f_103_10,plain,
    ( hBOOL(hAPP(U_681,U_685))
    | ~ sP29(U_675,U_685,U_687,U_683,U_681) ),
    inference(clausify,[status(thm)],[f_103_5]) ).

cnf(f_103_11,plain,
    ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_681,U_683),U_675,U_687,U_685)
    | ~ c_Natural_Oevaln(U_683,U_685,U_687,U_675)
    | ~ sP29(U_675,U_685,U_687,U_683,U_681) ),
    inference(clausify,[status(thm)],[f_103_5]) ).

fof(f_104_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_104_2,plain,
    ! [U_691,U_690,U_689,U_688] : hAPP(c_Com_Ocom_OBODY,U_688) != c_Com_Ocom_OCond(U_689,U_690,U_691),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

fof(f_104_3,plain,
    ! [U_689,U_691,U_690,U_688] : hAPP(c_Com_Ocom_OBODY,U_688) != c_Com_Ocom_OCond(U_689,U_690,U_691),
    inference(definitional_conversion,[status(esa)],[f_104_2]) ).

cnf(f_104_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_688) != c_Com_Ocom_OCond(U_689,U_690,U_691),
    inference(clausify,[status(thm)],[f_104_3]) ).

fof(f_105_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_105_2,plain,
    ! [U_695,U_694,U_693,U_692] : c_Com_Ocom_OCond(U_692,U_693,U_694) != hAPP(c_Com_Ocom_OBODY,U_695),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

fof(f_105_3,plain,
    ! [U_694,U_695,U_692,U_693] : c_Com_Ocom_OCond(U_692,U_693,U_694) != hAPP(c_Com_Ocom_OBODY,U_695),
    inference(definitional_conversion,[status(esa)],[f_105_2]) ).

cnf(f_105_4,plain,
    c_Com_Ocom_OCond(U_692,U_693,U_694) != hAPP(c_Com_Ocom_OBODY,U_695),
    inference(clausify,[status(thm)],[f_105_3]) ).

fof(f_106_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_106_2,plain,
    ! [U_698,U_697,U_696] : c_Com_Ocom_OAss(U_696,U_697) != hAPP(c_Com_Ocom_OBODY,U_698),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

fof(f_106_3,plain,
    ! [U_698,U_696,U_697] : c_Com_Ocom_OAss(U_696,U_697) != hAPP(c_Com_Ocom_OBODY,U_698),
    inference(definitional_conversion,[status(esa)],[f_106_2]) ).

cnf(f_106_4,plain,
    c_Com_Ocom_OAss(U_696,U_697) != hAPP(c_Com_Ocom_OBODY,U_698),
    inference(clausify,[status(thm)],[f_106_3]) ).

fof(f_107_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_107_2,plain,
    ! [U_701,U_700,U_699] : hAPP(c_Com_Ocom_OBODY,U_699) != c_Com_Ocom_OAss(U_700,U_701),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

fof(f_107_3,plain,
    ! [U_699,U_700,U_701] : hAPP(c_Com_Ocom_OBODY,U_699) != c_Com_Ocom_OAss(U_700,U_701),
    inference(definitional_conversion,[status(esa)],[f_107_2]) ).

cnf(f_107_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_699) != c_Com_Ocom_OAss(U_700,U_701),
    inference(clausify,[status(thm)],[f_107_3]) ).

fof(f_108_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_108_2,plain,
    ! [U_703,U_702] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_702,U_703)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_703)) )
      & ( hBOOL(hAPP(c_Com_OWT,U_703))
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_702,U_703))) ) ),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

fof(f_108_3,plain,
    ( ! [U_707] :
        ( ! [U_705] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_705,U_707)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_707)) )
    & ! [U_706] :
        ( ! [U_704] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_704,U_706)))
        | hBOOL(hAPP(c_Com_OWT,U_706)) ) ),
    inference(miniscope,[status(thm)],[f_108_2]) ).

fof(f_108_4,plain,
    ( ! [U_705,U_707] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_705,U_707)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_707)) )
    & ! [U_704,U_706] :
        ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_704,U_706)))
        | hBOOL(hAPP(c_Com_OWT,U_706)) ) ),
    inference(definitional_conversion,[status(esa)],[f_108_3]) ).

cnf(f_108_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_704,U_706)))
    | hBOOL(hAPP(c_Com_OWT,U_706)) ),
    inference(clausify,[status(thm)],[f_108_4]) ).

cnf(f_108_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_705,U_707)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_707)) ),
    inference(clausify,[status(thm)],[f_108_4]) ).

fof(f_109_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_109_2,plain,
    ! [U_709,U_708] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_709,U_708)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_708)) ),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

fof(f_109_3,plain,
    ! [U_708,U_709] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_709,U_708)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_708)) ),
    inference(definitional_conversion,[status(esa)],[f_109_2]) ).

cnf(f_109_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_709,U_708)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_708)) ),
    inference(clausify,[status(thm)],[f_109_3]) ).

fof(f_110_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_110_2,plain,
    ! [U_712,U_711,U_710] : hAPP(c_Com_Ocom_OBODY,U_710) != c_Com_Ocom_OSemi(U_711,U_712),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

fof(f_110_3,plain,
    ! [U_710,U_711,U_712] : hAPP(c_Com_Ocom_OBODY,U_710) != c_Com_Ocom_OSemi(U_711,U_712),
    inference(definitional_conversion,[status(esa)],[f_110_2]) ).

cnf(f_110_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_710) != c_Com_Ocom_OSemi(U_711,U_712),
    inference(clausify,[status(thm)],[f_110_3]) ).

fof(f_111_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_111_2,plain,
    ! [U_715,U_714,U_713] : c_Com_Ocom_OSemi(U_713,U_714) != hAPP(c_Com_Ocom_OBODY,U_715),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

fof(f_111_3,plain,
    ! [U_713,U_714,U_715] : c_Com_Ocom_OSemi(U_713,U_714) != hAPP(c_Com_Ocom_OBODY,U_715),
    inference(definitional_conversion,[status(esa)],[f_111_2]) ).

cnf(f_111_4,plain,
    c_Com_Ocom_OSemi(U_713,U_714) != hAPP(c_Com_Ocom_OBODY,U_715),
    inference(clausify,[status(thm)],[f_111_3]) ).

fof(f_112_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_112_2,plain,
    ! [U_719,U_718,U_717,U_716] : c_Com_Ocom_OLocal(U_716,U_717,U_718) != hAPP(c_Com_Ocom_OBODY,U_719),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

fof(f_112_3,plain,
    ! [U_716,U_717,U_718,U_719] : c_Com_Ocom_OLocal(U_716,U_717,U_718) != hAPP(c_Com_Ocom_OBODY,U_719),
    inference(definitional_conversion,[status(esa)],[f_112_2]) ).

cnf(f_112_4,plain,
    c_Com_Ocom_OLocal(U_716,U_717,U_718) != hAPP(c_Com_Ocom_OBODY,U_719),
    inference(clausify,[status(thm)],[f_112_3]) ).

fof(f_113_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_113_2,plain,
    ! [U_723,U_722,U_721,U_720] : c_Com_Ocom_OCall(U_720,U_721,U_722) != hAPP(c_Com_Ocom_OBODY,U_723),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

fof(f_113_3,plain,
    ! [U_721,U_720,U_722,U_723] : c_Com_Ocom_OCall(U_720,U_721,U_722) != hAPP(c_Com_Ocom_OBODY,U_723),
    inference(definitional_conversion,[status(esa)],[f_113_2]) ).

cnf(f_113_4,plain,
    c_Com_Ocom_OCall(U_720,U_721,U_722) != hAPP(c_Com_Ocom_OBODY,U_723),
    inference(clausify,[status(thm)],[f_113_3]) ).

fof(f_114_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_114_2,plain,
    ! [U_727,U_726,U_725,U_724] : hAPP(c_Com_Ocom_OBODY,U_724) != c_Com_Ocom_OLocal(U_725,U_726,U_727),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

fof(f_114_3,plain,
    ! [U_724,U_725,U_726,U_727] : hAPP(c_Com_Ocom_OBODY,U_724) != c_Com_Ocom_OLocal(U_725,U_726,U_727),
    inference(definitional_conversion,[status(esa)],[f_114_2]) ).

cnf(f_114_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_724) != c_Com_Ocom_OLocal(U_725,U_726,U_727),
    inference(clausify,[status(thm)],[f_114_3]) ).

fof(f_115_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_115_2,plain,
    ! [U_731,U_730,U_729,U_728] : hAPP(c_Com_Ocom_OBODY,U_728) != c_Com_Ocom_OCall(U_729,U_730,U_731),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

fof(f_115_3,plain,
    ! [U_728,U_729,U_730,U_731] : hAPP(c_Com_Ocom_OBODY,U_728) != c_Com_Ocom_OCall(U_729,U_730,U_731),
    inference(definitional_conversion,[status(esa)],[f_115_2]) ).

cnf(f_115_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_728) != c_Com_Ocom_OCall(U_729,U_730,U_731),
    inference(clausify,[status(thm)],[f_115_3]) ).

fof(f_116_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_116_2,plain,
    ! [U_732] : hAPP(c_Com_Ocom_OBODY,U_732) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_116_1]) ).

fof(f_116_3,plain,
    ! [U_732] : hAPP(c_Com_Ocom_OBODY,U_732) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_116_2]) ).

cnf(f_116_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_732) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_116_3]) ).

fof(f_117_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_117_2,plain,
    ! [U_733] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,U_733),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

fof(f_117_3,plain,
    ! [U_733] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,U_733),
    inference(definitional_conversion,[status(esa)],[f_117_2]) ).

cnf(f_117_4,plain,
    c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,U_733),
    inference(clausify,[status(thm)],[f_117_3]) ).

fof(f_118_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_118_2,plain,
    ! [U_738,U_737,U_736,U_735,U_734] : c_Com_Ocom_OWhile(U_734,U_735) != c_Com_Ocom_OCond(U_736,U_737,U_738),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

fof(f_118_3,plain,
    ! [U_734,U_735,U_736,U_737,U_738] : c_Com_Ocom_OWhile(U_734,U_735) != c_Com_Ocom_OCond(U_736,U_737,U_738),
    inference(definitional_conversion,[status(esa)],[f_118_2]) ).

cnf(f_118_4,plain,
    c_Com_Ocom_OWhile(U_734,U_735) != c_Com_Ocom_OCond(U_736,U_737,U_738),
    inference(clausify,[status(thm)],[f_118_3]) ).

fof(f_119_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_119_2,plain,
    ! [U_743,U_742,U_741,U_740,U_739] : c_Com_Ocom_OCond(U_739,U_740,U_741) != c_Com_Ocom_OWhile(U_742,U_743),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

fof(f_119_3,plain,
    ! [U_740,U_739,U_741,U_742,U_743] : c_Com_Ocom_OCond(U_739,U_740,U_741) != c_Com_Ocom_OWhile(U_742,U_743),
    inference(definitional_conversion,[status(esa)],[f_119_2]) ).

cnf(f_119_4,plain,
    c_Com_Ocom_OCond(U_739,U_740,U_741) != c_Com_Ocom_OWhile(U_742,U_743),
    inference(clausify,[status(thm)],[f_119_3]) ).

fof(f_120_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_120_2,plain,
    ! [U_747,U_746,U_745,U_744] : c_Com_Ocom_OWhile(U_744,U_745) != c_Com_Ocom_OAss(U_746,U_747),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

fof(f_120_3,plain,
    ! [U_744,U_745,U_746,U_747] : c_Com_Ocom_OWhile(U_744,U_745) != c_Com_Ocom_OAss(U_746,U_747),
    inference(definitional_conversion,[status(esa)],[f_120_2]) ).

cnf(f_120_4,plain,
    c_Com_Ocom_OWhile(U_744,U_745) != c_Com_Ocom_OAss(U_746,U_747),
    inference(clausify,[status(thm)],[f_120_3]) ).

fof(f_121_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_121_2,plain,
    ! [U_751,U_750,U_749,U_748] : c_Com_Ocom_OAss(U_748,U_749) != c_Com_Ocom_OWhile(U_750,U_751),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

fof(f_121_3,plain,
    ! [U_748,U_749,U_750,U_751] : c_Com_Ocom_OAss(U_748,U_749) != c_Com_Ocom_OWhile(U_750,U_751),
    inference(definitional_conversion,[status(esa)],[f_121_2]) ).

cnf(f_121_4,plain,
    c_Com_Ocom_OAss(U_748,U_749) != c_Com_Ocom_OWhile(U_750,U_751),
    inference(clausify,[status(thm)],[f_121_3]) ).

fof(f_122_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_122_2,plain,
    ! [U_755,U_754,U_753,U_752] : c_Com_Ocom_OSemi(U_752,U_753) != c_Com_Ocom_OWhile(U_754,U_755),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

fof(f_122_3,plain,
    ! [U_752,U_753,U_754,U_755] : c_Com_Ocom_OSemi(U_752,U_753) != c_Com_Ocom_OWhile(U_754,U_755),
    inference(definitional_conversion,[status(esa)],[f_122_2]) ).

cnf(f_122_4,plain,
    c_Com_Ocom_OSemi(U_752,U_753) != c_Com_Ocom_OWhile(U_754,U_755),
    inference(clausify,[status(thm)],[f_122_3]) ).

fof(f_123_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_123_2,plain,
    ! [U_759,U_758,U_757,U_756] : c_Com_Ocom_OWhile(U_756,U_757) != c_Com_Ocom_OSemi(U_758,U_759),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

fof(f_123_3,plain,
    ! [U_756,U_757,U_758,U_759] : c_Com_Ocom_OWhile(U_756,U_757) != c_Com_Ocom_OSemi(U_758,U_759),
    inference(definitional_conversion,[status(esa)],[f_123_2]) ).

cnf(f_123_4,plain,
    c_Com_Ocom_OWhile(U_756,U_757) != c_Com_Ocom_OSemi(U_758,U_759),
    inference(clausify,[status(thm)],[f_123_3]) ).

fof(f_124_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_124_2,plain,
    ! [U_764,U_763,U_762,U_761,U_760] : c_Com_Ocom_OLocal(U_760,U_761,U_762) != c_Com_Ocom_OWhile(U_763,U_764),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

fof(f_124_3,plain,
    ! [U_761,U_760,U_762,U_763,U_764] : c_Com_Ocom_OLocal(U_760,U_761,U_762) != c_Com_Ocom_OWhile(U_763,U_764),
    inference(definitional_conversion,[status(esa)],[f_124_2]) ).

cnf(f_124_4,plain,
    c_Com_Ocom_OLocal(U_760,U_761,U_762) != c_Com_Ocom_OWhile(U_763,U_764),
    inference(clausify,[status(thm)],[f_124_3]) ).

fof(f_125_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_125_2,plain,
    ! [U_769,U_768,U_767,U_766,U_765] : c_Com_Ocom_OCall(U_765,U_766,U_767) != c_Com_Ocom_OWhile(U_768,U_769),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

fof(f_125_3,plain,
    ! [U_766,U_765,U_767,U_768,U_769] : c_Com_Ocom_OCall(U_765,U_766,U_767) != c_Com_Ocom_OWhile(U_768,U_769),
    inference(definitional_conversion,[status(esa)],[f_125_2]) ).

cnf(f_125_4,plain,
    c_Com_Ocom_OCall(U_765,U_766,U_767) != c_Com_Ocom_OWhile(U_768,U_769),
    inference(clausify,[status(thm)],[f_125_3]) ).

fof(f_126_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_126_2,plain,
    ! [U_774,U_773,U_772,U_771,U_770] : c_Com_Ocom_OWhile(U_770,U_771) != c_Com_Ocom_OLocal(U_772,U_773,U_774),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

fof(f_126_3,plain,
    ! [U_770,U_771,U_772,U_773,U_774] : c_Com_Ocom_OWhile(U_770,U_771) != c_Com_Ocom_OLocal(U_772,U_773,U_774),
    inference(definitional_conversion,[status(esa)],[f_126_2]) ).

cnf(f_126_4,plain,
    c_Com_Ocom_OWhile(U_770,U_771) != c_Com_Ocom_OLocal(U_772,U_773,U_774),
    inference(clausify,[status(thm)],[f_126_3]) ).

fof(f_127_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_127_2,plain,
    ! [U_779,U_778,U_777,U_776,U_775] : c_Com_Ocom_OWhile(U_775,U_776) != c_Com_Ocom_OCall(U_777,U_778,U_779),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

fof(f_127_3,plain,
    ! [U_776,U_777,U_778,U_779,U_775] : c_Com_Ocom_OWhile(U_775,U_776) != c_Com_Ocom_OCall(U_777,U_778,U_779),
    inference(definitional_conversion,[status(esa)],[f_127_2]) ).

cnf(f_127_4,plain,
    c_Com_Ocom_OWhile(U_775,U_776) != c_Com_Ocom_OCall(U_777,U_778,U_779),
    inference(clausify,[status(thm)],[f_127_3]) ).

fof(f_128_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_128_2,plain,
    ! [U_781,U_780] : c_Com_Ocom_OWhile(U_780,U_781) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_128_1]) ).

fof(f_128_3,plain,
    ! [U_781,U_780] : c_Com_Ocom_OWhile(U_780,U_781) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_128_2]) ).

cnf(f_128_4,plain,
    c_Com_Ocom_OWhile(U_780,U_781) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_128_3]) ).

fof(f_129_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_129_2,plain,
    ! [U_783,U_782] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_782,U_783),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

fof(f_129_3,plain,
    ! [U_782,U_783] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_782,U_783),
    inference(definitional_conversion,[status(esa)],[f_129_2]) ).

cnf(f_129_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_782,U_783),
    inference(clausify,[status(thm)],[f_129_3]) ).

fof(f_130_1,plain,
    ! [V_pname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,hAPP(c_Com_Ocom_OBODY,V_pname_2)) = hAPP(V_f7_2,V_pname_2),
    inference(fof_nnf,[status(thm)],[fact_com_Orecs_I7_J]) ).

fof(f_130_2,plain,
    ! [U_793,U_792,U_791,U_790,U_789,U_788,U_787,U_786,U_785,U_784] : c_Com_Ocom_Ocom__rec(U_784,U_785,U_786,U_787,U_788,U_789,U_790,U_791,U_792,hAPP(c_Com_Ocom_OBODY,U_793)) = hAPP(U_791,U_793),
    inference(variable_rename,[status(thm)],[f_130_1]) ).

fof(f_130_3,plain,
    ! [U_784,U_785,U_786,U_787,U_788,U_789,U_790,U_791,U_792,U_793] : c_Com_Ocom_Ocom__rec(U_784,U_785,U_786,U_787,U_788,U_789,U_790,U_791,U_792,hAPP(c_Com_Ocom_OBODY,U_793)) = hAPP(U_791,U_793),
    inference(definitional_conversion,[status(esa)],[f_130_2]) ).

cnf(f_130_4,plain,
    c_Com_Ocom_Ocom__rec(U_784,U_785,U_786,U_787,U_788,U_789,U_790,U_791,U_792,hAPP(c_Com_Ocom_OBODY,U_793)) = hAPP(U_791,U_793),
    inference(clausify,[status(thm)],[f_130_3]) ).

fof(f_131_1,plain,
    ! [V_com_2,V_fun_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,c_Com_Ocom_OWhile(V_fun_2,V_com_2)) = hAPP(hAPP(hAPP(V_f6_2,V_fun_2),V_com_2),c_Com_Ocom_Ocom__rec(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,V_com_2)),
    inference(fof_nnf,[status(thm)],[fact_com_Orecs_I6_J]) ).

fof(f_131_2,plain,
    ! [U_804,U_803,U_802,U_801,U_800,U_799,U_798,U_797,U_796,U_795,U_794] : c_Com_Ocom_Ocom__rec(U_794,U_795,U_796,U_797,U_798,U_799,U_800,U_801,U_802,c_Com_Ocom_OWhile(U_803,U_804)) = hAPP(hAPP(hAPP(U_800,U_803),U_804),c_Com_Ocom_Ocom__rec(U_794,U_795,U_796,U_797,U_798,U_799,U_800,U_801,U_802,U_804)),
    inference(variable_rename,[status(thm)],[f_131_1]) ).

fof(f_131_3,plain,
    ! [U_794,U_796,U_795,U_797,U_798,U_799,U_800,U_801,U_802,U_803,U_804] : c_Com_Ocom_Ocom__rec(U_794,U_795,U_796,U_797,U_798,U_799,U_800,U_801,U_802,c_Com_Ocom_OWhile(U_803,U_804)) = hAPP(hAPP(hAPP(U_800,U_803),U_804),c_Com_Ocom_Ocom__rec(U_794,U_795,U_796,U_797,U_798,U_799,U_800,U_801,U_802,U_804)),
    inference(definitional_conversion,[status(esa)],[f_131_2]) ).

cnf(f_131_4,plain,
    c_Com_Ocom_Ocom__rec(U_794,U_795,U_796,U_797,U_798,U_799,U_800,U_801,U_802,c_Com_Ocom_OWhile(U_803,U_804)) = hAPP(hAPP(hAPP(U_800,U_803),U_804),c_Com_Ocom_Ocom__rec(U_794,U_795,U_796,U_797,U_798,U_799,U_800,U_801,U_802,U_804)),
    inference(clausify,[status(thm)],[f_131_3]) ).

fof(f_132_1,plain,
    ! [V_pname_2,V_f8_2,V_f7_2,V_f6_2,V_f5_2,V_f4_2,V_f3_2,V_f2_2,V_f1_2,T_b] : c_Com_Ocom_Ocom__case(T_b,V_f1_2,V_f2_2,V_f3_2,V_f4_2,V_f5_2,V_f6_2,V_f7_2,V_f8_2,hAPP(c_Com_Ocom_OBODY,V_pname_2)) = hAPP(V_f7_2,V_pname_2),
    inference(fof_nnf,[status(thm)],[fact_com_Osimps_I70_J]) ).

fof(f_132_2,plain,
    ! [U_814,U_813,U_812,U_811,U_810,U_809,U_808,U_807,U_806,U_805] : c_Com_Ocom_Ocom__case(U_805,U_806,U_807,U_808,U_809,U_810,U_811,U_812,U_813,hAPP(c_Com_Ocom_OBODY,U_814)) = hAPP(U_812,U_814),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

fof(f_132_3,plain,
    ! [U_805,U_812,U_813,U_814,U_806,U_809,U_808,U_807,U_811,U_810] : c_Com_Ocom_Ocom__case(U_805,U_806,U_807,U_808,U_809,U_810,U_811,U_812,U_813,hAPP(c_Com_Ocom_OBODY,U_814)) = hAPP(U_812,U_814),
    inference(definitional_conversion,[status(esa)],[f_132_2]) ).

cnf(f_132_4,plain,
    c_Com_Ocom_Ocom__case(U_805,U_806,U_807,U_808,U_809,U_810,U_811,U_812,U_813,hAPP(c_Com_Ocom_OBODY,U_814)) = hAPP(U_812,U_814),
    inference(clausify,[status(thm)],[f_132_3]) ).

fof(f_133_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_133_2,plain,
    ! [U_818,U_817,U_816,U_815] : c_Hoare__Mirabelle_Otriple__valid(U_815,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_815),U_816),hAPP(c_Com_Ocom_OBODY,U_817)),U_818)),
    inference(variable_rename,[status(thm)],[f_133_1]) ).

fof(f_133_3,plain,
    ! [U_815,U_818,U_817,U_816] : c_Hoare__Mirabelle_Otriple__valid(U_815,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_815),U_816),hAPP(c_Com_Ocom_OBODY,U_817)),U_818)),
    inference(definitional_conversion,[status(esa)],[f_133_2]) ).

cnf(f_133_4,plain,
    c_Hoare__Mirabelle_Otriple__valid(U_815,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_815),U_816),hAPP(c_Com_Ocom_OBODY,U_817)),U_818)),
    inference(clausify,[status(thm)],[f_133_3]) ).

fof(f_134_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_134_2,plain,
    ! [U_823,U_822,U_821,U_820,U_819] :
      ( ( c_Hoare__Mirabelle_Otriple__valid(U_819,U_820,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_819),U_821),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_822))),U_823))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_819,hAPP(c_Nat_OSuc,U_820),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_819),U_821),hAPP(c_Com_Ocom_OBODY,U_822)),U_823)) )
      & ( c_Hoare__Mirabelle_Otriple__valid(U_819,hAPP(c_Nat_OSuc,U_820),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_819),U_821),hAPP(c_Com_Ocom_OBODY,U_822)),U_823))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_819,U_820,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_819),U_821),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_822))),U_823)) ) ),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

fof(f_134_3,plain,
    ( ! [U_833,U_831,U_829,U_827,U_825] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_825,U_827,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_825),U_829),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_831))),U_833))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_825,hAPP(c_Nat_OSuc,U_827),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_825),U_829),hAPP(c_Com_Ocom_OBODY,U_831)),U_833)) )
    & ! [U_832,U_830,U_828,U_826,U_824] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_824,hAPP(c_Nat_OSuc,U_826),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_824),U_828),hAPP(c_Com_Ocom_OBODY,U_830)),U_832))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_824,U_826,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_824),U_828),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_830))),U_832)) ) ),
    inference(miniscope,[status(thm)],[f_134_2]) ).

fof(f_134_4,plain,
    ( ! [U_827,U_825,U_829,U_831,U_833] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_825,U_827,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_825),U_829),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_831))),U_833))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_825,hAPP(c_Nat_OSuc,U_827),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_825),U_829),hAPP(c_Com_Ocom_OBODY,U_831)),U_833)) )
    & ! [U_830,U_826,U_824,U_828,U_832] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_824,hAPP(c_Nat_OSuc,U_826),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_824),U_828),hAPP(c_Com_Ocom_OBODY,U_830)),U_832))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_824,U_826,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_824),U_828),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_830))),U_832)) ) ),
    inference(definitional_conversion,[status(esa)],[f_134_3]) ).

cnf(f_134_5,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_824,hAPP(c_Nat_OSuc,U_826),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_824),U_828),hAPP(c_Com_Ocom_OBODY,U_830)),U_832))
    | ~ c_Hoare__Mirabelle_Otriple__valid(U_824,U_826,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_824),U_828),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_830))),U_832)) ),
    inference(clausify,[status(thm)],[f_134_4]) ).

cnf(f_134_6,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_825,U_827,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_825),U_829),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_831))),U_833))
    | ~ c_Hoare__Mirabelle_Otriple__valid(U_825,hAPP(c_Nat_OSuc,U_827),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_825),U_829),hAPP(c_Com_Ocom_OBODY,U_831)),U_833)) ),
    inference(clausify,[status(thm)],[f_134_4]) ).

fof(f_135_1,plain,
    ! [V_n_2,V_h_2,V_c_2,T_b,V_f_2] :
      ( hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_h_2,V_n_2),hAPP(V_f_2,V_n_2))
      | ? [B_n] : hAPP(V_f_2,B_n) != hAPP(c_Nat_Onat_Onat__rec(T_b,V_c_2,V_h_2),B_n) ),
    inference(fof_nnf,[status(thm)],[fact_def__nat__rec__Suc]) ).

fof(f_135_2,plain,
    ! [U_839,U_838,U_837,U_836,U_835] :
      ( hAPP(U_835,hAPP(c_Nat_OSuc,U_839)) = hAPP(hAPP(U_838,U_839),hAPP(U_835,U_839))
      | ? [U_834] : hAPP(U_835,U_834) != hAPP(c_Nat_Onat_Onat__rec(U_836,U_837,U_838),U_834) ),
    inference(variable_rename,[status(thm)],[f_135_1]) ).

fof(f_135_3,plain,
    ! [U_839,U_838,U_837,U_836,U_835] :
      ( hAPP(U_835,hAPP(c_Nat_OSuc,U_839)) = hAPP(hAPP(U_838,U_839),hAPP(U_835,U_839))
      | hAPP(U_835,sK13(U_839,U_838,U_837,U_836,U_835)) != hAPP(c_Nat_Onat_Onat__rec(U_836,U_837,U_838),sK13(U_839,U_838,U_837,U_836,U_835)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_834,sK13(U_839,U_838,U_837,U_836,U_835))],[f_135_2]) ).

fof(f_135_4,plain,
    ! [U_837,U_836,U_835,U_838,U_839] :
      ( hAPP(U_835,hAPP(c_Nat_OSuc,U_839)) = hAPP(hAPP(U_838,U_839),hAPP(U_835,U_839))
      | hAPP(U_835,sK13(U_839,U_838,U_837,U_836,U_835)) != hAPP(c_Nat_Onat_Onat__rec(U_836,U_837,U_838),sK13(U_839,U_838,U_837,U_836,U_835)) ),
    inference(definitional_conversion,[status(esa)],[f_135_3]) ).

cnf(f_135_5,plain,
    ( hAPP(U_835,hAPP(c_Nat_OSuc,U_839)) = hAPP(hAPP(U_838,U_839),hAPP(U_835,U_839))
    | hAPP(U_835,sK13(U_839,U_838,U_837,U_836,U_835)) != hAPP(c_Nat_Onat_Onat__rec(U_836,U_837,U_838),sK13(U_839,U_838,U_837,U_836,U_835)) ),
    inference(clausify,[status(thm)],[f_135_4]) ).

fof(f_136_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_136_2,plain,
    ! [U_843,U_842,U_841,U_840] :
      ( U_843 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_842),U_840),hAPP(U_841,U_842))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_840,U_841)),U_842),U_843)) ),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

fof(f_136_3,plain,
    ! [U_840,U_841,U_842,U_843] :
      ( U_843 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_842),U_840),hAPP(U_841,U_842))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_840,U_841)),U_842),U_843)) ),
    inference(definitional_conversion,[status(esa)],[f_136_2]) ).

cnf(f_136_4,plain,
    ( U_843 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_842),U_840),hAPP(U_841,U_842))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_840,U_841)),U_842),U_843)) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

fof(f_137_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_137_2,plain,
    ! [U_846,U_845,U_844] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_844,U_845)),U_846),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_846),U_844),hAPP(U_845,U_846)))),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

fof(f_137_3,plain,
    ! [U_844,U_845,U_846] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_844,U_845)),U_846),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_846),U_844),hAPP(U_845,U_846)))),
    inference(definitional_conversion,[status(esa)],[f_137_2]) ).

cnf(f_137_4,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_844,U_845)),U_846),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_846),U_844),hAPP(U_845,U_846)))),
    inference(clausify,[status(thm)],[f_137_3]) ).

fof(f_138_1,plain,
    ! [V_t_2,V_n_2,V_s_2,V_c_2,V_b_2] :
      ( ( ? [B_s1] :
            ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),B_s1,V_n_2,V_t_2)
            & c_Natural_Oevaln(V_c_2,V_s_2,V_n_2,B_s1) )
        & hBOOL(hAPP(V_b_2,V_s_2)) )
      | ( ~ hBOOL(hAPP(V_b_2,V_s_2))
        & V_t_2 = V_s_2 )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s_2,V_n_2,V_t_2) ),
    inference(fof_nnf,[status(thm)],[fact_evaln__WHILE__case]) ).

fof(f_138_2,plain,
    ! [U_852,U_851,U_850,U_849,U_848] :
      ( ( ? [U_847] :
            ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_848,U_849),U_847,U_851,U_852)
            & c_Natural_Oevaln(U_849,U_850,U_851,U_847) )
        & hBOOL(hAPP(U_848,U_850)) )
      | ( ~ hBOOL(hAPP(U_848,U_850))
        & U_852 = U_850 )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_848,U_849),U_850,U_851,U_852) ),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

fof(f_138_3,plain,
    ! [U_852,U_851,U_850,U_849,U_848] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_848,U_849),sK14(U_852,U_851,U_850,U_849,U_848),U_851,U_852)
        & c_Natural_Oevaln(U_849,U_850,U_851,sK14(U_852,U_851,U_850,U_849,U_848))
        & hBOOL(hAPP(U_848,U_850)) )
      | ( ~ hBOOL(hAPP(U_848,U_850))
        & U_852 = U_850 )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_848,U_849),U_850,U_851,U_852) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_847,sK14(U_852,U_851,U_850,U_849,U_848))],[f_138_2]) ).

fof(f_138_4,plain,
    ( ! [U_848,U_849,U_850,U_851,U_852] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_848,U_849),sK14(U_852,U_851,U_850,U_849,U_848),U_851,U_852)
        | ~ sP31(U_848,U_849,U_850,U_851,U_852) )
    & ! [U_848,U_849,U_850,U_851,U_852] :
        ( c_Natural_Oevaln(U_849,U_850,U_851,sK14(U_852,U_851,U_850,U_849,U_848))
        | ~ sP31(U_848,U_849,U_850,U_851,U_852) )
    & ! [U_848,U_849,U_850,U_851,U_852] :
        ( hBOOL(hAPP(U_848,U_850))
        | ~ sP31(U_848,U_849,U_850,U_851,U_852) )
    & ! [U_848,U_850,U_852] :
        ( ~ hBOOL(hAPP(U_848,U_850))
        | ~ sP30(U_848,U_850,U_852) )
    & ! [U_848,U_850,U_852] :
        ( U_852 = U_850
        | ~ sP30(U_848,U_850,U_852) )
    & ! [U_848,U_849,U_850,U_851,U_852] :
        ( sP31(U_848,U_849,U_850,U_851,U_852)
        | sP30(U_848,U_850,U_852)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_848,U_849),U_850,U_851,U_852) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30,sP31])],[f_138_3]) ).

cnf(f_138_5,plain,
    ( sP31(U_848,U_849,U_850,U_851,U_852)
    | sP30(U_848,U_850,U_852)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_848,U_849),U_850,U_851,U_852) ),
    inference(clausify,[status(thm)],[f_138_4]) ).

cnf(f_138_6,plain,
    ( U_852 = U_850
    | ~ sP30(U_848,U_850,U_852) ),
    inference(clausify,[status(thm)],[f_138_4]) ).

cnf(f_138_7,plain,
    ( ~ hBOOL(hAPP(U_848,U_850))
    | ~ sP30(U_848,U_850,U_852) ),
    inference(clausify,[status(thm)],[f_138_4]) ).

cnf(f_138_8,plain,
    ( hBOOL(hAPP(U_848,U_850))
    | ~ sP31(U_848,U_849,U_850,U_851,U_852) ),
    inference(clausify,[status(thm)],[f_138_4]) ).

cnf(f_138_9,plain,
    ( c_Natural_Oevaln(U_849,U_850,U_851,sK14(U_852,U_851,U_850,U_849,U_848))
    | ~ sP31(U_848,U_849,U_850,U_851,U_852) ),
    inference(clausify,[status(thm)],[f_138_4]) ).

cnf(f_138_10,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_848,U_849),sK14(U_852,U_851,U_850,U_849,U_848),U_851,U_852)
    | ~ sP31(U_848,U_849,U_850,U_851,U_852) ),
    inference(clausify,[status(thm)],[f_138_4]) ).

fof(f_139_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_139_2,plain,
    ! [U_856,U_855,U_854,U_853] :
      ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_853),U_854,hAPP(c_Nat_OSuc,U_855),U_856)
      | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_853)),U_854,U_855,U_856) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

fof(f_139_3,plain,
    ! [U_854,U_855,U_853,U_856] :
      ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_853),U_854,hAPP(c_Nat_OSuc,U_855),U_856)
      | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_853)),U_854,U_855,U_856) ),
    inference(definitional_conversion,[status(esa)],[f_139_2]) ).

cnf(f_139_4,plain,
    ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_853),U_854,hAPP(c_Nat_OSuc,U_855),U_856)
    | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_853)),U_854,U_855,U_856) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

fof(f_140_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_140_2,plain,
    ! [U_859,U_858,U_857] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_857,U_858)),U_859),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_859),U_857),hAPP(U_858,U_859)))),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

fof(f_140_3,plain,
    ! [U_857,U_858,U_859] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_857,U_858)),U_859),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_859),U_857),hAPP(U_858,U_859)))),
    inference(definitional_conversion,[status(esa)],[f_140_2]) ).

cnf(f_140_4,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_857,U_858)),U_859),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_859),U_857),hAPP(U_858,U_859)))),
    inference(clausify,[status(thm)],[f_140_3]) ).

fof(f_141_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_141_2,plain,
    ! [U_865,U_864,U_863,U_862,U_861,U_860] :
      ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_862,U_863,U_860),U_861,U_864,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_865),c_Com_Ovname_OLoc(U_862)),hAPP(hAPP(c_Natural_Ogetlocs,U_861),U_862)))
      | ~ c_Natural_Oevaln(U_860,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_861),c_Com_Ovname_OLoc(U_862)),hAPP(U_863,U_861)),U_864,U_865) ),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

fof(f_141_3,plain,
    ! [U_861,U_860,U_862,U_863,U_864,U_865] :
      ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_862,U_863,U_860),U_861,U_864,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_865),c_Com_Ovname_OLoc(U_862)),hAPP(hAPP(c_Natural_Ogetlocs,U_861),U_862)))
      | ~ c_Natural_Oevaln(U_860,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_861),c_Com_Ovname_OLoc(U_862)),hAPP(U_863,U_861)),U_864,U_865) ),
    inference(definitional_conversion,[status(esa)],[f_141_2]) ).

cnf(f_141_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_862,U_863,U_860),U_861,U_864,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_865),c_Com_Ovname_OLoc(U_862)),hAPP(hAPP(c_Natural_Ogetlocs,U_861),U_862)))
    | ~ c_Natural_Oevaln(U_860,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_861),c_Com_Ovname_OLoc(U_862)),hAPP(U_863,U_861)),U_864,U_865) ),
    inference(clausify,[status(thm)],[f_141_3]) ).

fof(f_142_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_142_2,plain,
    ! [U_869,U_868,U_867,U_866] :
      ( ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_866),U_867,hAPP(c_Nat_OSuc,U_868),U_869)
        | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_866)),U_867,U_868,U_869) )
      & ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_866)),U_867,U_868,U_869)
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_866),U_867,hAPP(c_Nat_OSuc,U_868),U_869) ) ),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

fof(f_142_3,plain,
    ( ! [U_877,U_875,U_873,U_871] :
        ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_871),U_873,hAPP(c_Nat_OSuc,U_875),U_877)
        | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_871)),U_873,U_875,U_877) )
    & ! [U_876,U_874,U_872,U_870] :
        ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_870)),U_872,U_874,U_876)
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_870),U_872,hAPP(c_Nat_OSuc,U_874),U_876) ) ),
    inference(miniscope,[status(thm)],[f_142_2]) ).

fof(f_142_4,plain,
    ( ! [U_875,U_871,U_873,U_877] :
        ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_871),U_873,hAPP(c_Nat_OSuc,U_875),U_877)
        | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_871)),U_873,U_875,U_877) )
    & ! [U_872,U_876,U_870,U_874] :
        ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_870)),U_872,U_874,U_876)
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_870),U_872,hAPP(c_Nat_OSuc,U_874),U_876) ) ),
    inference(definitional_conversion,[status(esa)],[f_142_3]) ).

cnf(f_142_5,plain,
    ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_870)),U_872,U_874,U_876)
    | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_870),U_872,hAPP(c_Nat_OSuc,U_874),U_876) ),
    inference(clausify,[status(thm)],[f_142_4]) ).

cnf(f_142_6,plain,
    ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_871),U_873,hAPP(c_Nat_OSuc,U_875),U_877)
    | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_871)),U_873,U_875,U_877) ),
    inference(clausify,[status(thm)],[f_142_4]) ).

fof(f_143_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_143_2,plain,
    ! [U_885,U_884,U_883,U_882,U_881,U_880] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_880,U_881,U_882),U_883,U_884,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_885),c_Com_Ovname_OLoc(U_880)),hAPP(hAPP(c_Natural_Ogetlocs,U_883),U_880)))
        | ! [U_879] :
            ( ~ c_Natural_Oevaln(U_882,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_883),c_Com_Ovname_OLoc(U_880)),hAPP(U_881,U_883)),U_884,U_879)
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_885),c_Com_Ovname_OLoc(U_880)),hAPP(hAPP(c_Natural_Ogetlocs,U_883),U_880)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_879),c_Com_Ovname_OLoc(U_880)),hAPP(hAPP(c_Natural_Ogetlocs,U_883),U_880)) ) )
      & ( ? [U_878] :
            ( c_Natural_Oevaln(U_882,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_883),c_Com_Ovname_OLoc(U_880)),hAPP(U_881,U_883)),U_884,U_878)
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,U_885),c_Com_Ovname_OLoc(U_880)),hAPP(hAPP(c_Natural_Ogetlocs,U_883),U_880)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_878),c_Com_Ovname_OLoc(U_880)),hAPP(hAPP(c_Natural_Ogetlocs,U_883),U_880)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_880,U_881,U_882),U_883,U_884,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_885),c_Com_Ovname_OLoc(U_880)),hAPP(hAPP(c_Natural_Ogetlocs,U_883),U_880))) ) ),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

fof(f_143_3,plain,
    ( ! [U_897,U_895,U_893,U_891,U_889,U_887] :
        ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_887,U_889,U_891),U_893,U_895,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_897),c_Com_Ovname_OLoc(U_887)),hAPP(hAPP(c_Natural_Ogetlocs,U_893),U_887)))
        | ! [U_879] :
            ( ~ c_Natural_Oevaln(U_891,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_893),c_Com_Ovname_OLoc(U_887)),hAPP(U_889,U_893)),U_895,U_879)
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_897),c_Com_Ovname_OLoc(U_887)),hAPP(hAPP(c_Natural_Ogetlocs,U_893),U_887)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_879),c_Com_Ovname_OLoc(U_887)),hAPP(hAPP(c_Natural_Ogetlocs,U_893),U_887)) ) )
    & ! [U_896,U_894,U_892,U_890,U_888,U_886] :
        ( ? [U_878] :
            ( c_Natural_Oevaln(U_890,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_892),c_Com_Ovname_OLoc(U_886)),hAPP(U_888,U_892)),U_894,U_878)
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,U_896),c_Com_Ovname_OLoc(U_886)),hAPP(hAPP(c_Natural_Ogetlocs,U_892),U_886)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_878),c_Com_Ovname_OLoc(U_886)),hAPP(hAPP(c_Natural_Ogetlocs,U_892),U_886)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_886,U_888,U_890),U_892,U_894,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_896),c_Com_Ovname_OLoc(U_886)),hAPP(hAPP(c_Natural_Ogetlocs,U_892),U_886))) ) ),
    inference(miniscope,[status(thm)],[f_143_2]) ).

fof(f_143_4,plain,
    ( ! [U_897,U_895,U_893,U_891,U_889,U_887] :
        ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_887,U_889,U_891),U_893,U_895,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_897),c_Com_Ovname_OLoc(U_887)),hAPP(hAPP(c_Natural_Ogetlocs,U_893),U_887)))
        | ! [U_879] :
            ( ~ c_Natural_Oevaln(U_891,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_893),c_Com_Ovname_OLoc(U_887)),hAPP(U_889,U_893)),U_895,U_879)
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_897),c_Com_Ovname_OLoc(U_887)),hAPP(hAPP(c_Natural_Ogetlocs,U_893),U_887)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_879),c_Com_Ovname_OLoc(U_887)),hAPP(hAPP(c_Natural_Ogetlocs,U_893),U_887)) ) )
    & ! [U_896,U_894,U_892,U_890,U_888,U_886] :
        ( ( c_Natural_Oevaln(U_890,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_892),c_Com_Ovname_OLoc(U_886)),hAPP(U_888,U_892)),U_894,sK15(U_896,U_894,U_892,U_890,U_888,U_886))
          & hAPP(hAPP(hAPP(c_Natural_Oupdate,U_896),c_Com_Ovname_OLoc(U_886)),hAPP(hAPP(c_Natural_Ogetlocs,U_892),U_886)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK15(U_896,U_894,U_892,U_890,U_888,U_886)),c_Com_Ovname_OLoc(U_886)),hAPP(hAPP(c_Natural_Ogetlocs,U_892),U_886)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_886,U_888,U_890),U_892,U_894,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_896),c_Com_Ovname_OLoc(U_886)),hAPP(hAPP(c_Natural_Ogetlocs,U_892),U_886))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_878,sK15(U_896,U_894,U_892,U_890,U_888,U_886))],[f_143_3]) ).

fof(f_143_5,plain,
    ( ! [U_888,U_894,U_886,U_890,U_892,U_896] :
        ( c_Natural_Oevaln(U_890,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_892),c_Com_Ovname_OLoc(U_886)),hAPP(U_888,U_892)),U_894,sK15(U_896,U_894,U_892,U_890,U_888,U_886))
        | ~ sP32(U_888,U_894,U_886,U_890,U_892,U_896) )
    & ! [U_888,U_894,U_886,U_890,U_892,U_896] :
        ( hAPP(hAPP(hAPP(c_Natural_Oupdate,U_896),c_Com_Ovname_OLoc(U_886)),hAPP(hAPP(c_Natural_Ogetlocs,U_892),U_886)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK15(U_896,U_894,U_892,U_890,U_888,U_886)),c_Com_Ovname_OLoc(U_886)),hAPP(hAPP(c_Natural_Ogetlocs,U_892),U_886))
        | ~ sP32(U_888,U_894,U_886,U_890,U_892,U_896) )
    & ! [U_879,U_889,U_887,U_893,U_897,U_891,U_895] :
        ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_887,U_889,U_891),U_893,U_895,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_897),c_Com_Ovname_OLoc(U_887)),hAPP(hAPP(c_Natural_Ogetlocs,U_893),U_887)))
        | ~ c_Natural_Oevaln(U_891,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_893),c_Com_Ovname_OLoc(U_887)),hAPP(U_889,U_893)),U_895,U_879)
        | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_897),c_Com_Ovname_OLoc(U_887)),hAPP(hAPP(c_Natural_Ogetlocs,U_893),U_887)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_879),c_Com_Ovname_OLoc(U_887)),hAPP(hAPP(c_Natural_Ogetlocs,U_893),U_887)) )
    & ! [U_888,U_894,U_886,U_890,U_892,U_896] :
        ( sP32(U_888,U_894,U_886,U_890,U_892,U_896)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_886,U_888,U_890),U_892,U_894,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_896),c_Com_Ovname_OLoc(U_886)),hAPP(hAPP(c_Natural_Ogetlocs,U_892),U_886))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP32])],[f_143_4]) ).

cnf(f_143_6,plain,
    ( sP32(U_888,U_894,U_886,U_890,U_892,U_896)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_886,U_888,U_890),U_892,U_894,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_896),c_Com_Ovname_OLoc(U_886)),hAPP(hAPP(c_Natural_Ogetlocs,U_892),U_886))) ),
    inference(clausify,[status(thm)],[f_143_5]) ).

cnf(f_143_7,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OLocal(U_887,U_889,U_891),U_893,U_895,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_897),c_Com_Ovname_OLoc(U_887)),hAPP(hAPP(c_Natural_Ogetlocs,U_893),U_887)))
    | ~ c_Natural_Oevaln(U_891,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_893),c_Com_Ovname_OLoc(U_887)),hAPP(U_889,U_893)),U_895,U_879)
    | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_897),c_Com_Ovname_OLoc(U_887)),hAPP(hAPP(c_Natural_Ogetlocs,U_893),U_887)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_879),c_Com_Ovname_OLoc(U_887)),hAPP(hAPP(c_Natural_Ogetlocs,U_893),U_887)) ),
    inference(clausify,[status(thm)],[f_143_5]) ).

cnf(f_143_8,plain,
    ( hAPP(hAPP(hAPP(c_Natural_Oupdate,U_896),c_Com_Ovname_OLoc(U_886)),hAPP(hAPP(c_Natural_Ogetlocs,U_892),U_886)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK15(U_896,U_894,U_892,U_890,U_888,U_886)),c_Com_Ovname_OLoc(U_886)),hAPP(hAPP(c_Natural_Ogetlocs,U_892),U_886))
    | ~ sP32(U_888,U_894,U_886,U_890,U_892,U_896) ),
    inference(clausify,[status(thm)],[f_143_5]) ).

cnf(f_143_9,plain,
    ( c_Natural_Oevaln(U_890,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_892),c_Com_Ovname_OLoc(U_886)),hAPP(U_888,U_892)),U_894,sK15(U_896,U_894,U_892,U_890,U_888,U_886))
    | ~ sP32(U_888,U_894,U_886,U_890,U_892,U_896) ),
    inference(clausify,[status(thm)],[f_143_5]) ).

fof(f_144_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_144_2,plain,
    ! [U_900,U_899,U_898] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_898,U_900)),U_899),U_899))
      | hBOOL(hAPP(U_898,U_899)) ),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

fof(f_144_3,plain,
    ! [U_899,U_898,U_900] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_898,U_900)),U_899),U_899))
      | hBOOL(hAPP(U_898,U_899)) ),
    inference(definitional_conversion,[status(esa)],[f_144_2]) ).

cnf(f_144_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_898,U_900)),U_899),U_899))
    | hBOOL(hAPP(U_898,U_899)) ),
    inference(clausify,[status(thm)],[f_144_3]) ).

fof(f_145_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_145_2,plain,
    ! [U_905,U_904,U_903,U_902,U_901] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_901,U_903)),U_902),U_905))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_901,U_903)),U_904),U_905))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_903),U_902),U_904))
      | ~ hBOOL(hAPP(U_901,U_902)) ),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

fof(f_145_3,plain,
    ! [U_901,U_902,U_903,U_904,U_905] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_901,U_903)),U_902),U_905))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_901,U_903)),U_904),U_905))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_903),U_902),U_904))
      | ~ hBOOL(hAPP(U_901,U_902)) ),
    inference(definitional_conversion,[status(esa)],[f_145_2]) ).

cnf(f_145_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_901,U_903)),U_902),U_905))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_901,U_903)),U_904),U_905))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_903),U_902),U_904))
    | ~ hBOOL(hAPP(U_901,U_902)) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

fof(f_146_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_146_2,plain,
    ! [U_910,U_909,U_908,U_907,U_906] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_908),U_909),U_910))
        & ~ hBOOL(hAPP(U_906,U_909)) )
      | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_907),U_909),U_910))
        & hBOOL(hAPP(U_906,U_909)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_906,U_907,U_908)),U_909),U_910)) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

fof(f_146_3,plain,
    ( ! [U_906,U_908,U_909,U_910] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_908),U_909),U_910))
        | ~ sP34(U_906,U_908,U_909,U_910) )
    & ! [U_906,U_908,U_909,U_910] :
        ( ~ hBOOL(hAPP(U_906,U_909))
        | ~ sP34(U_906,U_908,U_909,U_910) )
    & ! [U_907,U_906,U_909,U_910] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_907),U_909),U_910))
        | ~ sP33(U_907,U_906,U_909,U_910) )
    & ! [U_907,U_906,U_909,U_910] :
        ( hBOOL(hAPP(U_906,U_909))
        | ~ sP33(U_907,U_906,U_909,U_910) )
    & ! [U_907,U_906,U_908,U_909,U_910] :
        ( sP34(U_906,U_908,U_909,U_910)
        | sP33(U_907,U_906,U_909,U_910)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_906,U_907,U_908)),U_909),U_910)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33,sP34])],[f_146_2]) ).

cnf(f_146_4,plain,
    ( sP34(U_906,U_908,U_909,U_910)
    | sP33(U_907,U_906,U_909,U_910)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_906,U_907,U_908)),U_909),U_910)) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

cnf(f_146_5,plain,
    ( hBOOL(hAPP(U_906,U_909))
    | ~ sP33(U_907,U_906,U_909,U_910) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

cnf(f_146_6,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_907),U_909),U_910))
    | ~ sP33(U_907,U_906,U_909,U_910) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

cnf(f_146_7,plain,
    ( ~ hBOOL(hAPP(U_906,U_909))
    | ~ sP34(U_906,U_908,U_909,U_910) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

cnf(f_146_8,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_908),U_909),U_910))
    | ~ sP34(U_906,U_908,U_909,U_910) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

fof(f_147_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_147_2,plain,
    ! [U_915,U_914,U_913,U_912,U_911] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_911,U_913,U_915)),U_912),U_914))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_913),U_912),U_914))
      | ~ hBOOL(hAPP(U_911,U_912)) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

fof(f_147_3,plain,
    ! [U_911,U_912,U_913,U_914,U_915] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_911,U_913,U_915)),U_912),U_914))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_913),U_912),U_914))
      | ~ hBOOL(hAPP(U_911,U_912)) ),
    inference(definitional_conversion,[status(esa)],[f_147_2]) ).

cnf(f_147_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_911,U_913,U_915)),U_912),U_914))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_913),U_912),U_914))
    | ~ hBOOL(hAPP(U_911,U_912)) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

fof(f_148_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_148_2,plain,
    ! [U_920,U_919,U_918,U_917,U_916] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_916,U_920,U_918)),U_917),U_919))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_918),U_917),U_919))
      | hBOOL(hAPP(U_916,U_917)) ),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

fof(f_148_3,plain,
    ! [U_917,U_916,U_918,U_919,U_920] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_916,U_920,U_918)),U_917),U_919))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_918),U_917),U_919))
      | hBOOL(hAPP(U_916,U_917)) ),
    inference(definitional_conversion,[status(esa)],[f_148_2]) ).

cnf(f_148_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_916,U_920,U_918)),U_917),U_919))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_918),U_917),U_919))
    | hBOOL(hAPP(U_916,U_917)) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

fof(f_149_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_149_2,plain,
    ! [U_925,U_924,U_923,U_922,U_921] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_921,U_924)),U_922),U_925))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_924),U_923),U_925))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_921),U_922),U_923)) ),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

fof(f_149_3,plain,
    ! [U_921,U_922,U_923,U_924,U_925] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_921,U_924)),U_922),U_925))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_924),U_923),U_925))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_921),U_922),U_923)) ),
    inference(definitional_conversion,[status(esa)],[f_149_2]) ).

cnf(f_149_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_921,U_924)),U_922),U_925))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_924),U_923),U_925))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_921),U_922),U_923)) ),
    inference(clausify,[status(thm)],[f_149_3]) ).

fof(f_150_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_150_2,plain,
    ! [U_926] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_926),U_926)),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

fof(f_150_3,plain,
    ! [U_926] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_926),U_926)),
    inference(definitional_conversion,[status(esa)],[f_150_2]) ).

cnf(f_150_4,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_926),U_926)),
    inference(clausify,[status(thm)],[f_150_3]) ).

fof(f_151_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_151_2,plain,
    ! [U_928,U_927] :
      ( U_928 = U_927
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_927),U_928)) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

fof(f_151_3,plain,
    ! [U_927,U_928] :
      ( U_928 = U_927
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_927),U_928)) ),
    inference(definitional_conversion,[status(esa)],[f_151_2]) ).

cnf(f_151_4,plain,
    ( U_928 = U_927
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_927),U_928)) ),
    inference(clausify,[status(thm)],[f_151_3]) ).

fof(f_152_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_152_2,plain,
    ! [U_931,U_930,U_929] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_929))),U_930),U_931))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_929)),U_930),U_931)) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

fof(f_152_3,plain,
    ! [U_929,U_930,U_931] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_929))),U_930),U_931))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_929)),U_930),U_931)) ),
    inference(definitional_conversion,[status(esa)],[f_152_2]) ).

cnf(f_152_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_929))),U_930),U_931))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_929)),U_930),U_931)) ),
    inference(clausify,[status(thm)],[f_152_3]) ).

fof(f_153_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_153_2,plain,
    ! [U_934,U_933,U_932] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_932)),U_933),U_934))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_932))),U_933),U_934)) ),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

fof(f_153_3,plain,
    ! [U_932,U_933,U_934] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_932)),U_933),U_934))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_932))),U_933),U_934)) ),
    inference(definitional_conversion,[status(esa)],[f_153_2]) ).

cnf(f_153_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_932)),U_933),U_934))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_932))),U_933),U_934)) ),
    inference(clausify,[status(thm)],[f_153_3]) ).

fof(f_154_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_154_2,plain,
    ! [U_939,U_938,U_937,U_936,U_935] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_937,U_938,U_935)),U_936),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_939),c_Com_Ovname_OLoc(U_937)),hAPP(hAPP(c_Natural_Ogetlocs,U_936),U_937))))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_935),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_936),c_Com_Ovname_OLoc(U_937)),hAPP(U_938,U_936))),U_939)) ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

fof(f_154_3,plain,
    ! [U_935,U_936,U_937,U_938,U_939] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_937,U_938,U_935)),U_936),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_939),c_Com_Ovname_OLoc(U_937)),hAPP(hAPP(c_Natural_Ogetlocs,U_936),U_937))))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_935),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_936),c_Com_Ovname_OLoc(U_937)),hAPP(U_938,U_936))),U_939)) ),
    inference(definitional_conversion,[status(esa)],[f_154_2]) ).

cnf(f_154_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_937,U_938,U_935)),U_936),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_939),c_Com_Ovname_OLoc(U_937)),hAPP(hAPP(c_Natural_Ogetlocs,U_936),U_937))))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_935),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_936),c_Com_Ovname_OLoc(U_937)),hAPP(U_938,U_936))),U_939)) ),
    inference(clausify,[status(thm)],[f_154_3]) ).

fof(f_155_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_155_2,plain,
    ! [U_941,U_940] :
      ( ( c_Com_Ovname_OLoc(U_940) = c_Com_Ovname_OLoc(U_941)
        | U_940 != U_941 )
      & ( U_940 = U_941
        | c_Com_Ovname_OLoc(U_940) != c_Com_Ovname_OLoc(U_941) ) ),
    inference(variable_rename,[status(thm)],[f_155_1]) ).

fof(f_155_3,plain,
    ( ! [U_945,U_943] :
        ( c_Com_Ovname_OLoc(U_943) = c_Com_Ovname_OLoc(U_945)
        | U_943 != U_945 )
    & ! [U_944,U_942] :
        ( U_942 = U_944
        | c_Com_Ovname_OLoc(U_942) != c_Com_Ovname_OLoc(U_944) ) ),
    inference(miniscope,[status(thm)],[f_155_2]) ).

fof(f_155_4,plain,
    ( ! [U_943,U_945] :
        ( c_Com_Ovname_OLoc(U_943) = c_Com_Ovname_OLoc(U_945)
        | U_943 != U_945 )
    & ! [U_944,U_942] :
        ( U_942 = U_944
        | c_Com_Ovname_OLoc(U_942) != c_Com_Ovname_OLoc(U_944) ) ),
    inference(definitional_conversion,[status(esa)],[f_155_3]) ).

cnf(f_155_5,plain,
    ( U_942 = U_944
    | c_Com_Ovname_OLoc(U_942) != c_Com_Ovname_OLoc(U_944) ),
    inference(clausify,[status(thm)],[f_155_4]) ).

cnf(f_155_6,plain,
    ( c_Com_Ovname_OLoc(U_943) = c_Com_Ovname_OLoc(U_945)
    | U_943 != U_945 ),
    inference(clausify,[status(thm)],[f_155_4]) ).

fof(f_156_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_156_2,plain,
    ! [U_949,U_948,U_947,U_946] :
      ( U_949 = U_948
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_946),U_947),U_949))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_946),U_947),U_948)) ),
    inference(variable_rename,[status(thm)],[f_156_1]) ).

fof(f_156_3,plain,
    ! [U_949,U_946,U_947,U_948] :
      ( U_949 = U_948
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_946),U_947),U_949))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_946),U_947),U_948)) ),
    inference(definitional_conversion,[status(esa)],[f_156_2]) ).

cnf(f_156_4,plain,
    ( U_949 = U_948
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_946),U_947),U_949))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_946),U_947),U_948)) ),
    inference(clausify,[status(thm)],[f_156_3]) ).

fof(f_157_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_157_2,plain,
    ! [U_952,U_951,U_950] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_950)),U_951),U_952))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_950))),U_951),U_952)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_950))),U_951),U_952))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_950)),U_951),U_952)) ) ),
    inference(variable_rename,[status(thm)],[f_157_1]) ).

fof(f_157_3,plain,
    ( ! [U_958,U_956,U_954] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_954)),U_956),U_958))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_954))),U_956),U_958)) )
    & ! [U_957,U_955,U_953] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_953))),U_955),U_957))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_953)),U_955),U_957)) ) ),
    inference(miniscope,[status(thm)],[f_157_2]) ).

fof(f_157_4,plain,
    ( ! [U_954,U_956,U_958] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_954)),U_956),U_958))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_954))),U_956),U_958)) )
    & ! [U_955,U_957,U_953] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_953))),U_955),U_957))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_953)),U_955),U_957)) ) ),
    inference(definitional_conversion,[status(esa)],[f_157_3]) ).

cnf(f_157_5,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_953))),U_955),U_957))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_953)),U_955),U_957)) ),
    inference(clausify,[status(thm)],[f_157_4]) ).

cnf(f_157_6,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_954)),U_956),U_958))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_954))),U_956),U_958)) ),
    inference(clausify,[status(thm)],[f_157_4]) ).

fof(f_158_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_158_2,plain,
    ! [U_965,U_964,U_963,U_962,U_961] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_961,U_962,U_963)),U_964),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_965),c_Com_Ovname_OLoc(U_961)),hAPP(hAPP(c_Natural_Ogetlocs,U_964),U_961))))
        | ! [U_960] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_963),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_964),c_Com_Ovname_OLoc(U_961)),hAPP(U_962,U_964))),U_960))
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_965),c_Com_Ovname_OLoc(U_961)),hAPP(hAPP(c_Natural_Ogetlocs,U_964),U_961)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_960),c_Com_Ovname_OLoc(U_961)),hAPP(hAPP(c_Natural_Ogetlocs,U_964),U_961)) ) )
      & ( ? [U_959] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_963),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_964),c_Com_Ovname_OLoc(U_961)),hAPP(U_962,U_964))),U_959))
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,U_965),c_Com_Ovname_OLoc(U_961)),hAPP(hAPP(c_Natural_Ogetlocs,U_964),U_961)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_959),c_Com_Ovname_OLoc(U_961)),hAPP(hAPP(c_Natural_Ogetlocs,U_964),U_961)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_961,U_962,U_963)),U_964),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_965),c_Com_Ovname_OLoc(U_961)),hAPP(hAPP(c_Natural_Ogetlocs,U_964),U_961)))) ) ),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

fof(f_158_3,plain,
    ( ! [U_975,U_973,U_971,U_969,U_967] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_967,U_969,U_971)),U_973),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_975),c_Com_Ovname_OLoc(U_967)),hAPP(hAPP(c_Natural_Ogetlocs,U_973),U_967))))
        | ! [U_960] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_971),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_973),c_Com_Ovname_OLoc(U_967)),hAPP(U_969,U_973))),U_960))
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_975),c_Com_Ovname_OLoc(U_967)),hAPP(hAPP(c_Natural_Ogetlocs,U_973),U_967)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_960),c_Com_Ovname_OLoc(U_967)),hAPP(hAPP(c_Natural_Ogetlocs,U_973),U_967)) ) )
    & ! [U_974,U_972,U_970,U_968,U_966] :
        ( ? [U_959] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_970),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_972),c_Com_Ovname_OLoc(U_966)),hAPP(U_968,U_972))),U_959))
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,U_974),c_Com_Ovname_OLoc(U_966)),hAPP(hAPP(c_Natural_Ogetlocs,U_972),U_966)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_959),c_Com_Ovname_OLoc(U_966)),hAPP(hAPP(c_Natural_Ogetlocs,U_972),U_966)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_966,U_968,U_970)),U_972),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_974),c_Com_Ovname_OLoc(U_966)),hAPP(hAPP(c_Natural_Ogetlocs,U_972),U_966)))) ) ),
    inference(miniscope,[status(thm)],[f_158_2]) ).

fof(f_158_4,plain,
    ( ! [U_975,U_973,U_971,U_969,U_967] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_967,U_969,U_971)),U_973),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_975),c_Com_Ovname_OLoc(U_967)),hAPP(hAPP(c_Natural_Ogetlocs,U_973),U_967))))
        | ! [U_960] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_971),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_973),c_Com_Ovname_OLoc(U_967)),hAPP(U_969,U_973))),U_960))
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_975),c_Com_Ovname_OLoc(U_967)),hAPP(hAPP(c_Natural_Ogetlocs,U_973),U_967)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_960),c_Com_Ovname_OLoc(U_967)),hAPP(hAPP(c_Natural_Ogetlocs,U_973),U_967)) ) )
    & ! [U_974,U_972,U_970,U_968,U_966] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_970),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_972),c_Com_Ovname_OLoc(U_966)),hAPP(U_968,U_972))),sK16(U_974,U_972,U_970,U_968,U_966)))
          & hAPP(hAPP(hAPP(c_Natural_Oupdate,U_974),c_Com_Ovname_OLoc(U_966)),hAPP(hAPP(c_Natural_Ogetlocs,U_972),U_966)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK16(U_974,U_972,U_970,U_968,U_966)),c_Com_Ovname_OLoc(U_966)),hAPP(hAPP(c_Natural_Ogetlocs,U_972),U_966)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_966,U_968,U_970)),U_972),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_974),c_Com_Ovname_OLoc(U_966)),hAPP(hAPP(c_Natural_Ogetlocs,U_972),U_966)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_959,sK16(U_974,U_972,U_970,U_968,U_966))],[f_158_3]) ).

fof(f_158_5,plain,
    ( ! [U_968,U_966,U_970,U_972,U_974] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_970),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_972),c_Com_Ovname_OLoc(U_966)),hAPP(U_968,U_972))),sK16(U_974,U_972,U_970,U_968,U_966)))
        | ~ sP35(U_968,U_966,U_970,U_972,U_974) )
    & ! [U_968,U_966,U_970,U_972,U_974] :
        ( hAPP(hAPP(hAPP(c_Natural_Oupdate,U_974),c_Com_Ovname_OLoc(U_966)),hAPP(hAPP(c_Natural_Ogetlocs,U_972),U_966)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK16(U_974,U_972,U_970,U_968,U_966)),c_Com_Ovname_OLoc(U_966)),hAPP(hAPP(c_Natural_Ogetlocs,U_972),U_966))
        | ~ sP35(U_968,U_966,U_970,U_972,U_974) )
    & ! [U_960,U_967,U_969,U_975,U_971,U_973] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_967,U_969,U_971)),U_973),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_975),c_Com_Ovname_OLoc(U_967)),hAPP(hAPP(c_Natural_Ogetlocs,U_973),U_967))))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_971),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_973),c_Com_Ovname_OLoc(U_967)),hAPP(U_969,U_973))),U_960))
        | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_975),c_Com_Ovname_OLoc(U_967)),hAPP(hAPP(c_Natural_Ogetlocs,U_973),U_967)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_960),c_Com_Ovname_OLoc(U_967)),hAPP(hAPP(c_Natural_Ogetlocs,U_973),U_967)) )
    & ! [U_968,U_966,U_970,U_972,U_974] :
        ( sP35(U_968,U_966,U_970,U_972,U_974)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_966,U_968,U_970)),U_972),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_974),c_Com_Ovname_OLoc(U_966)),hAPP(hAPP(c_Natural_Ogetlocs,U_972),U_966)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35])],[f_158_4]) ).

cnf(f_158_6,plain,
    ( sP35(U_968,U_966,U_970,U_972,U_974)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_966,U_968,U_970)),U_972),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_974),c_Com_Ovname_OLoc(U_966)),hAPP(hAPP(c_Natural_Ogetlocs,U_972),U_966)))) ),
    inference(clausify,[status(thm)],[f_158_5]) ).

cnf(f_158_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_967,U_969,U_971)),U_973),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_975),c_Com_Ovname_OLoc(U_967)),hAPP(hAPP(c_Natural_Ogetlocs,U_973),U_967))))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_971),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_973),c_Com_Ovname_OLoc(U_967)),hAPP(U_969,U_973))),U_960))
    | hAPP(hAPP(hAPP(c_Natural_Oupdate,U_975),c_Com_Ovname_OLoc(U_967)),hAPP(hAPP(c_Natural_Ogetlocs,U_973),U_967)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,U_960),c_Com_Ovname_OLoc(U_967)),hAPP(hAPP(c_Natural_Ogetlocs,U_973),U_967)) ),
    inference(clausify,[status(thm)],[f_158_5]) ).

cnf(f_158_8,plain,
    ( hAPP(hAPP(hAPP(c_Natural_Oupdate,U_974),c_Com_Ovname_OLoc(U_966)),hAPP(hAPP(c_Natural_Ogetlocs,U_972),U_966)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK16(U_974,U_972,U_970,U_968,U_966)),c_Com_Ovname_OLoc(U_966)),hAPP(hAPP(c_Natural_Ogetlocs,U_972),U_966))
    | ~ sP35(U_968,U_966,U_970,U_972,U_974) ),
    inference(clausify,[status(thm)],[f_158_5]) ).

cnf(f_158_9,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_970),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_972),c_Com_Ovname_OLoc(U_966)),hAPP(U_968,U_972))),sK16(U_974,U_972,U_970,U_968,U_966)))
    | ~ sP35(U_968,U_966,U_970,U_972,U_974) ),
    inference(clausify,[status(thm)],[f_158_5]) ).

fof(f_159_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_159_2,plain,
    ! [U_976] : hAPP(c_Nat_OSuc,U_976) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

fof(f_159_3,plain,
    ! [U_976] : hAPP(c_Nat_OSuc,U_976) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_159_2]) ).

cnf(f_159_4,plain,
    hAPP(c_Nat_OSuc,U_976) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_159_3]) ).

fof(f_160_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_160_2,plain,
    ! [U_977] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_977),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

fof(f_160_3,plain,
    ! [U_977] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_977),
    inference(definitional_conversion,[status(esa)],[f_160_2]) ).

cnf(f_160_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_977),
    inference(clausify,[status(thm)],[f_160_3]) ).

fof(f_161_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_161_2,plain,
    ! [U_978] : hAPP(c_Nat_OSuc,U_978) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

fof(f_161_3,plain,
    ! [U_978] : hAPP(c_Nat_OSuc,U_978) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_161_2]) ).

cnf(f_161_4,plain,
    hAPP(c_Nat_OSuc,U_978) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_161_3]) ).

fof(f_162_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_162_2,plain,
    ! [U_979] : hAPP(c_Nat_OSuc,U_979) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

fof(f_162_3,plain,
    ! [U_979] : hAPP(c_Nat_OSuc,U_979) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_162_2]) ).

cnf(f_162_4,plain,
    hAPP(c_Nat_OSuc,U_979) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_162_3]) ).

fof(f_163_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_163_2,plain,
    ! [U_980] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_980),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

fof(f_163_3,plain,
    ! [U_980] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_980),
    inference(definitional_conversion,[status(esa)],[f_163_2]) ).

cnf(f_163_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_980),
    inference(clausify,[status(thm)],[f_163_3]) ).

fof(f_164_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_164_2,plain,
    ! [U_981] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_981),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

fof(f_164_3,plain,
    ! [U_981] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_981),
    inference(definitional_conversion,[status(esa)],[f_164_2]) ).

cnf(f_164_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_981),
    inference(clausify,[status(thm)],[f_164_3]) ).

fof(f_165_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_165_2,plain,
    ! [U_986,U_985,U_984] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_984),U_985),U_986))
        | ! [U_983] : ~ c_Natural_Oevaln(U_984,U_985,U_983,U_986) )
      & ( ? [U_982] : c_Natural_Oevaln(U_984,U_985,U_982,U_986)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_984),U_985),U_986)) ) ),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

fof(f_165_3,plain,
    ( ! [U_992,U_990,U_988] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_988),U_990),U_992))
        | ! [U_983] : ~ c_Natural_Oevaln(U_988,U_990,U_983,U_992) )
    & ! [U_991,U_989,U_987] :
        ( ? [U_982] : c_Natural_Oevaln(U_987,U_989,U_982,U_991)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_987),U_989),U_991)) ) ),
    inference(miniscope,[status(thm)],[f_165_2]) ).

fof(f_165_4,plain,
    ( ! [U_992,U_990,U_988] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_988),U_990),U_992))
        | ! [U_983] : ~ c_Natural_Oevaln(U_988,U_990,U_983,U_992) )
    & ! [U_991,U_989,U_987] :
        ( c_Natural_Oevaln(U_987,U_989,sK17(U_991,U_989,U_987),U_991)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_987),U_989),U_991)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_982,sK17(U_991,U_989,U_987))],[f_165_3]) ).

fof(f_165_5,plain,
    ( ! [U_983,U_990,U_988,U_992] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_988),U_990),U_992))
        | ~ c_Natural_Oevaln(U_988,U_990,U_983,U_992) )
    & ! [U_991,U_989,U_987] :
        ( c_Natural_Oevaln(U_987,U_989,sK17(U_991,U_989,U_987),U_991)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_987),U_989),U_991)) ) ),
    inference(definitional_conversion,[status(esa)],[f_165_4]) ).

cnf(f_165_6,plain,
    ( c_Natural_Oevaln(U_987,U_989,sK17(U_991,U_989,U_987),U_991)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_987),U_989),U_991)) ),
    inference(clausify,[status(thm)],[f_165_5]) ).

cnf(f_165_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_988),U_990),U_992))
    | ~ c_Natural_Oevaln(U_988,U_990,U_983,U_992) ),
    inference(clausify,[status(thm)],[f_165_5]) ).

fof(f_166_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_166_2,plain,
    ! [U_996,U_995,U_994,U_993] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_993),U_994),U_996))
      | ~ c_Natural_Oevaln(U_993,U_994,U_995,U_996) ),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

fof(f_166_3,plain,
    ! [U_994,U_993,U_995,U_996] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_993),U_994),U_996))
      | ~ c_Natural_Oevaln(U_993,U_994,U_995,U_996) ),
    inference(definitional_conversion,[status(esa)],[f_166_2]) ).

cnf(f_166_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_993),U_994),U_996))
    | ~ c_Natural_Oevaln(U_993,U_994,U_995,U_996) ),
    inference(clausify,[status(thm)],[f_166_3]) ).

fof(f_167_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_167_2,plain,
    ! [U_1001,U_1000,U_999] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_999,U_1000)),U_1001),U_1001))
        | ( ! [U_998] :
              ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_999,U_1000)),U_998),U_1001))
              | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1000),U_1001),U_998)) )
          & hBOOL(hAPP(U_999,U_1001)) ) )
      & ( ? [U_997] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_999,U_1000)),U_997),U_1001))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1000),U_1001),U_997)) )
        | ~ hBOOL(hAPP(U_999,U_1001))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_999,U_1000)),U_1001),U_1001)) ) ),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

fof(f_167_3,plain,
    ( ! [U_1007,U_1005,U_1003] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1003,U_1005)),U_1007),U_1007))
        | ( ! [U_998] :
              ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1003,U_1005)),U_998),U_1007))
              | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1005),U_1007),U_998)) )
          & hBOOL(hAPP(U_1003,U_1007)) ) )
    & ! [U_1006,U_1004,U_1002] :
        ( ? [U_997] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1002,U_1004)),U_997),U_1006))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1004),U_1006),U_997)) )
        | ~ hBOOL(hAPP(U_1002,U_1006))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1002,U_1004)),U_1006),U_1006)) ) ),
    inference(miniscope,[status(thm)],[f_167_2]) ).

fof(f_167_4,plain,
    ( ! [U_1007,U_1005,U_1003] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1003,U_1005)),U_1007),U_1007))
        | ( ! [U_998] :
              ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1003,U_1005)),U_998),U_1007))
              | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1005),U_1007),U_998)) )
          & hBOOL(hAPP(U_1003,U_1007)) ) )
    & ! [U_1006,U_1004,U_1002] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1002,U_1004)),sK18(U_1006,U_1004,U_1002)),U_1006))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1004),U_1006),sK18(U_1006,U_1004,U_1002))) )
        | ~ hBOOL(hAPP(U_1002,U_1006))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1002,U_1004)),U_1006),U_1006)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_997,sK18(U_1006,U_1004,U_1002))],[f_167_3]) ).

fof(f_167_5,plain,
    ( ! [U_998,U_1003,U_1005,U_1007] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1003,U_1005)),U_998),U_1007))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1005),U_1007),U_998))
        | ~ sP37(U_998,U_1003,U_1005,U_1007) )
    & ! [U_998,U_1003,U_1005,U_1007] :
        ( hBOOL(hAPP(U_1003,U_1007))
        | ~ sP37(U_998,U_1003,U_1005,U_1007) )
    & ! [U_1004,U_1006,U_1002] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1002,U_1004)),sK18(U_1006,U_1004,U_1002)),U_1006))
        | ~ sP36(U_1004,U_1006,U_1002) )
    & ! [U_1004,U_1006,U_1002] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1004),U_1006),sK18(U_1006,U_1004,U_1002)))
        | ~ sP36(U_1004,U_1006,U_1002) )
    & ! [U_998,U_1003,U_1005,U_1007] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1003,U_1005)),U_1007),U_1007))
        | sP37(U_998,U_1003,U_1005,U_1007) )
    & ! [U_1004,U_1006,U_1002] :
        ( sP36(U_1004,U_1006,U_1002)
        | ~ hBOOL(hAPP(U_1002,U_1006))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1002,U_1004)),U_1006),U_1006)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP36,sP37])],[f_167_4]) ).

cnf(f_167_6,plain,
    ( sP36(U_1004,U_1006,U_1002)
    | ~ hBOOL(hAPP(U_1002,U_1006))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1002,U_1004)),U_1006),U_1006)) ),
    inference(clausify,[status(thm)],[f_167_5]) ).

cnf(f_167_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1003,U_1005)),U_1007),U_1007))
    | sP37(U_998,U_1003,U_1005,U_1007) ),
    inference(clausify,[status(thm)],[f_167_5]) ).

cnf(f_167_8,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1004),U_1006),sK18(U_1006,U_1004,U_1002)))
    | ~ sP36(U_1004,U_1006,U_1002) ),
    inference(clausify,[status(thm)],[f_167_5]) ).

cnf(f_167_9,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1002,U_1004)),sK18(U_1006,U_1004,U_1002)),U_1006))
    | ~ sP36(U_1004,U_1006,U_1002) ),
    inference(clausify,[status(thm)],[f_167_5]) ).

cnf(f_167_10,plain,
    ( hBOOL(hAPP(U_1003,U_1007))
    | ~ sP37(U_998,U_1003,U_1005,U_1007) ),
    inference(clausify,[status(thm)],[f_167_5]) ).

cnf(f_167_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1003,U_1005)),U_998),U_1007))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1005),U_1007),U_998))
    | ~ sP37(U_998,U_1003,U_1005,U_1007) ),
    inference(clausify,[status(thm)],[f_167_5]) ).

fof(f_168_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_168_2,plain,
    ! [U_1013,U_1012,U_1011,U_1010] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1010,U_1011)),U_1012),U_1013))
        | ( ( ! [U_1009] :
                ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1010,U_1011)),U_1009),U_1013))
                | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1011),U_1012),U_1009)) )
            | ~ hBOOL(hAPP(U_1010,U_1012)) )
          & ( hBOOL(hAPP(U_1010,U_1012))
            | U_1013 != U_1012 ) ) )
      & ( ( ? [U_1008] :
              ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1010,U_1011)),U_1008),U_1013))
              & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1011),U_1012),U_1008)) )
          & hBOOL(hAPP(U_1010,U_1012)) )
        | ( ~ hBOOL(hAPP(U_1010,U_1012))
          & U_1013 = U_1012 )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1010,U_1011)),U_1012),U_1013)) ) ),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

fof(f_168_3,plain,
    ( ! [U_1021,U_1019,U_1017,U_1015] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1015,U_1017)),U_1019),U_1021))
        | ( ( ! [U_1009] :
                ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1015,U_1017)),U_1009),U_1021))
                | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1017),U_1019),U_1009)) )
            | ~ hBOOL(hAPP(U_1015,U_1019)) )
          & ( hBOOL(hAPP(U_1015,U_1019))
            | U_1021 != U_1019 ) ) )
    & ! [U_1020,U_1018,U_1016,U_1014] :
        ( ( ? [U_1008] :
              ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1014,U_1016)),U_1008),U_1020))
              & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1016),U_1018),U_1008)) )
          & hBOOL(hAPP(U_1014,U_1018)) )
        | ( ~ hBOOL(hAPP(U_1014,U_1018))
          & U_1020 = U_1018 )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1014,U_1016)),U_1018),U_1020)) ) ),
    inference(miniscope,[status(thm)],[f_168_2]) ).

fof(f_168_4,plain,
    ( ! [U_1021,U_1019,U_1017,U_1015] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1015,U_1017)),U_1019),U_1021))
        | ( ( ! [U_1009] :
                ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1015,U_1017)),U_1009),U_1021))
                | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1017),U_1019),U_1009)) )
            | ~ hBOOL(hAPP(U_1015,U_1019)) )
          & ( hBOOL(hAPP(U_1015,U_1019))
            | U_1021 != U_1019 ) ) )
    & ! [U_1020,U_1018,U_1016,U_1014] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1014,U_1016)),sK19(U_1020,U_1018,U_1016,U_1014)),U_1020))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1016),U_1018),sK19(U_1020,U_1018,U_1016,U_1014)))
          & hBOOL(hAPP(U_1014,U_1018)) )
        | ( ~ hBOOL(hAPP(U_1014,U_1018))
          & U_1020 = U_1018 )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1014,U_1016)),U_1018),U_1020)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_1008,sK19(U_1020,U_1018,U_1016,U_1014))],[f_168_3]) ).

fof(f_168_5,plain,
    ( ! [U_1015,U_1009,U_1019,U_1017,U_1021] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1015,U_1017)),U_1009),U_1021))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1017),U_1019),U_1009))
        | ~ hBOOL(hAPP(U_1015,U_1019))
        | ~ sP40(U_1015,U_1009,U_1019,U_1017,U_1021) )
    & ! [U_1015,U_1009,U_1019,U_1017,U_1021] :
        ( hBOOL(hAPP(U_1015,U_1019))
        | U_1021 != U_1019
        | ~ sP40(U_1015,U_1009,U_1019,U_1017,U_1021) )
    & ! [U_1016,U_1014,U_1018,U_1020] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1014,U_1016)),sK19(U_1020,U_1018,U_1016,U_1014)),U_1020))
        | ~ sP39(U_1016,U_1014,U_1018,U_1020) )
    & ! [U_1016,U_1014,U_1018,U_1020] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1016),U_1018),sK19(U_1020,U_1018,U_1016,U_1014)))
        | ~ sP39(U_1016,U_1014,U_1018,U_1020) )
    & ! [U_1016,U_1014,U_1018,U_1020] :
        ( hBOOL(hAPP(U_1014,U_1018))
        | ~ sP39(U_1016,U_1014,U_1018,U_1020) )
    & ! [U_1014,U_1018,U_1020] :
        ( ~ hBOOL(hAPP(U_1014,U_1018))
        | ~ sP38(U_1014,U_1018,U_1020) )
    & ! [U_1014,U_1018,U_1020] :
        ( U_1020 = U_1018
        | ~ sP38(U_1014,U_1018,U_1020) )
    & ! [U_1015,U_1009,U_1019,U_1017,U_1021] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1015,U_1017)),U_1019),U_1021))
        | sP40(U_1015,U_1009,U_1019,U_1017,U_1021) )
    & ! [U_1016,U_1014,U_1018,U_1020] :
        ( sP39(U_1016,U_1014,U_1018,U_1020)
        | sP38(U_1014,U_1018,U_1020)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1014,U_1016)),U_1018),U_1020)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP38,sP39,sP40])],[f_168_4]) ).

cnf(f_168_6,plain,
    ( sP39(U_1016,U_1014,U_1018,U_1020)
    | sP38(U_1014,U_1018,U_1020)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1014,U_1016)),U_1018),U_1020)) ),
    inference(clausify,[status(thm)],[f_168_5]) ).

cnf(f_168_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1015,U_1017)),U_1019),U_1021))
    | sP40(U_1015,U_1009,U_1019,U_1017,U_1021) ),
    inference(clausify,[status(thm)],[f_168_5]) ).

cnf(f_168_8,plain,
    ( U_1020 = U_1018
    | ~ sP38(U_1014,U_1018,U_1020) ),
    inference(clausify,[status(thm)],[f_168_5]) ).

cnf(f_168_9,plain,
    ( ~ hBOOL(hAPP(U_1014,U_1018))
    | ~ sP38(U_1014,U_1018,U_1020) ),
    inference(clausify,[status(thm)],[f_168_5]) ).

cnf(f_168_10,plain,
    ( hBOOL(hAPP(U_1014,U_1018))
    | ~ sP39(U_1016,U_1014,U_1018,U_1020) ),
    inference(clausify,[status(thm)],[f_168_5]) ).

cnf(f_168_11,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1016),U_1018),sK19(U_1020,U_1018,U_1016,U_1014)))
    | ~ sP39(U_1016,U_1014,U_1018,U_1020) ),
    inference(clausify,[status(thm)],[f_168_5]) ).

cnf(f_168_12,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1014,U_1016)),sK19(U_1020,U_1018,U_1016,U_1014)),U_1020))
    | ~ sP39(U_1016,U_1014,U_1018,U_1020) ),
    inference(clausify,[status(thm)],[f_168_5]) ).

cnf(f_168_13,plain,
    ( hBOOL(hAPP(U_1015,U_1019))
    | U_1021 != U_1019
    | ~ sP40(U_1015,U_1009,U_1019,U_1017,U_1021) ),
    inference(clausify,[status(thm)],[f_168_5]) ).

cnf(f_168_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1015,U_1017)),U_1009),U_1021))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1017),U_1019),U_1009))
    | ~ hBOOL(hAPP(U_1015,U_1019))
    | ~ sP40(U_1015,U_1009,U_1019,U_1017,U_1021) ),
    inference(clausify,[status(thm)],[f_168_5]) ).

fof(f_169_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_169_2,plain,
    ! [U_1026,U_1025,U_1024,U_1023,U_1022] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1022,U_1023,U_1024)),U_1025),U_1026))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1024),U_1025),U_1026))
            | hBOOL(hAPP(U_1022,U_1025)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1023),U_1025),U_1026))
            | ~ hBOOL(hAPP(U_1022,U_1025)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1024),U_1025),U_1026))
          & ~ hBOOL(hAPP(U_1022,U_1025)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1023),U_1025),U_1026))
          & hBOOL(hAPP(U_1022,U_1025)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1022,U_1023,U_1024)),U_1025),U_1026)) ) ),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

fof(f_169_3,plain,
    ( ! [U_1036,U_1034,U_1032,U_1030,U_1028] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1028,U_1030,U_1032)),U_1034),U_1036))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1032),U_1034),U_1036))
            | hBOOL(hAPP(U_1028,U_1034)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1030),U_1034),U_1036))
            | ~ hBOOL(hAPP(U_1028,U_1034)) ) ) )
    & ! [U_1035,U_1033,U_1031,U_1029,U_1027] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1031),U_1033),U_1035))
          & ~ hBOOL(hAPP(U_1027,U_1033)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1029),U_1033),U_1035))
          & hBOOL(hAPP(U_1027,U_1033)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1027,U_1029,U_1031)),U_1033),U_1035)) ) ),
    inference(miniscope,[status(thm)],[f_169_2]) ).

fof(f_169_4,plain,
    ( ! [U_1036,U_1028,U_1032,U_1034,U_1030] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1032),U_1034),U_1036))
        | hBOOL(hAPP(U_1028,U_1034))
        | ~ sP43(U_1036,U_1028,U_1032,U_1034,U_1030) )
    & ! [U_1036,U_1028,U_1032,U_1034,U_1030] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1030),U_1034),U_1036))
        | ~ hBOOL(hAPP(U_1028,U_1034))
        | ~ sP43(U_1036,U_1028,U_1032,U_1034,U_1030) )
    & ! [U_1027,U_1031,U_1035,U_1033] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1031),U_1033),U_1035))
        | ~ sP42(U_1027,U_1031,U_1035,U_1033) )
    & ! [U_1027,U_1031,U_1035,U_1033] :
        ( ~ hBOOL(hAPP(U_1027,U_1033))
        | ~ sP42(U_1027,U_1031,U_1035,U_1033) )
    & ! [U_1027,U_1029,U_1035,U_1033] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1029),U_1033),U_1035))
        | ~ sP41(U_1027,U_1029,U_1035,U_1033) )
    & ! [U_1027,U_1029,U_1035,U_1033] :
        ( hBOOL(hAPP(U_1027,U_1033))
        | ~ sP41(U_1027,U_1029,U_1035,U_1033) )
    & ! [U_1036,U_1028,U_1032,U_1034,U_1030] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1028,U_1030,U_1032)),U_1034),U_1036))
        | sP43(U_1036,U_1028,U_1032,U_1034,U_1030) )
    & ! [U_1027,U_1031,U_1029,U_1035,U_1033] :
        ( sP42(U_1027,U_1031,U_1035,U_1033)
        | sP41(U_1027,U_1029,U_1035,U_1033)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1027,U_1029,U_1031)),U_1033),U_1035)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41,sP42,sP43])],[f_169_3]) ).

cnf(f_169_5,plain,
    ( sP42(U_1027,U_1031,U_1035,U_1033)
    | sP41(U_1027,U_1029,U_1035,U_1033)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1027,U_1029,U_1031)),U_1033),U_1035)) ),
    inference(clausify,[status(thm)],[f_169_4]) ).

cnf(f_169_6,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1028,U_1030,U_1032)),U_1034),U_1036))
    | sP43(U_1036,U_1028,U_1032,U_1034,U_1030) ),
    inference(clausify,[status(thm)],[f_169_4]) ).

cnf(f_169_7,plain,
    ( hBOOL(hAPP(U_1027,U_1033))
    | ~ sP41(U_1027,U_1029,U_1035,U_1033) ),
    inference(clausify,[status(thm)],[f_169_4]) ).

cnf(f_169_8,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1029),U_1033),U_1035))
    | ~ sP41(U_1027,U_1029,U_1035,U_1033) ),
    inference(clausify,[status(thm)],[f_169_4]) ).

cnf(f_169_9,plain,
    ( ~ hBOOL(hAPP(U_1027,U_1033))
    | ~ sP42(U_1027,U_1031,U_1035,U_1033) ),
    inference(clausify,[status(thm)],[f_169_4]) ).

cnf(f_169_10,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1031),U_1033),U_1035))
    | ~ sP42(U_1027,U_1031,U_1035,U_1033) ),
    inference(clausify,[status(thm)],[f_169_4]) ).

cnf(f_169_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1030),U_1034),U_1036))
    | ~ hBOOL(hAPP(U_1028,U_1034))
    | ~ sP43(U_1036,U_1028,U_1032,U_1034,U_1030) ),
    inference(clausify,[status(thm)],[f_169_4]) ).

cnf(f_169_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1032),U_1034),U_1036))
    | hBOOL(hAPP(U_1028,U_1034))
    | ~ sP43(U_1036,U_1028,U_1032,U_1034,U_1030) ),
    inference(clausify,[status(thm)],[f_169_4]) ).

fof(f_170_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_170_2,plain,
    ! [U_1041,U_1040,U_1039,U_1038,U_1037] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1037,U_1038,U_1039)),U_1040),U_1041))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1039),U_1040),U_1041))
            | hBOOL(hAPP(U_1037,U_1040)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1038),U_1040),U_1041))
            | ~ hBOOL(hAPP(U_1037,U_1040)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1039),U_1040),U_1041))
          & ~ hBOOL(hAPP(U_1037,U_1040)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1038),U_1040),U_1041))
          & hBOOL(hAPP(U_1037,U_1040)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1037,U_1038,U_1039)),U_1040),U_1041)) ) ),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

fof(f_170_3,plain,
    ( ! [U_1051,U_1049,U_1047,U_1045,U_1043] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1043,U_1045,U_1047)),U_1049),U_1051))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1047),U_1049),U_1051))
            | hBOOL(hAPP(U_1043,U_1049)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1045),U_1049),U_1051))
            | ~ hBOOL(hAPP(U_1043,U_1049)) ) ) )
    & ! [U_1050,U_1048,U_1046,U_1044,U_1042] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1046),U_1048),U_1050))
          & ~ hBOOL(hAPP(U_1042,U_1048)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1044),U_1048),U_1050))
          & hBOOL(hAPP(U_1042,U_1048)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1042,U_1044,U_1046)),U_1048),U_1050)) ) ),
    inference(miniscope,[status(thm)],[f_170_2]) ).

fof(f_170_4,plain,
    ( ! [U_1045,U_1043,U_1047,U_1051,U_1049] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1047),U_1049),U_1051))
        | hBOOL(hAPP(U_1043,U_1049))
        | ~ sP46(U_1045,U_1043,U_1047,U_1051,U_1049) )
    & ! [U_1045,U_1043,U_1047,U_1051,U_1049] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1045),U_1049),U_1051))
        | ~ hBOOL(hAPP(U_1043,U_1049))
        | ~ sP46(U_1045,U_1043,U_1047,U_1051,U_1049) )
    & ! [U_1050,U_1046,U_1042,U_1048] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1046),U_1048),U_1050))
        | ~ sP45(U_1050,U_1046,U_1042,U_1048) )
    & ! [U_1050,U_1046,U_1042,U_1048] :
        ( ~ hBOOL(hAPP(U_1042,U_1048))
        | ~ sP45(U_1050,U_1046,U_1042,U_1048) )
    & ! [U_1050,U_1042,U_1044,U_1048] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1044),U_1048),U_1050))
        | ~ sP44(U_1050,U_1042,U_1044,U_1048) )
    & ! [U_1050,U_1042,U_1044,U_1048] :
        ( hBOOL(hAPP(U_1042,U_1048))
        | ~ sP44(U_1050,U_1042,U_1044,U_1048) )
    & ! [U_1045,U_1043,U_1047,U_1051,U_1049] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1043,U_1045,U_1047)),U_1049),U_1051))
        | sP46(U_1045,U_1043,U_1047,U_1051,U_1049) )
    & ! [U_1050,U_1046,U_1042,U_1044,U_1048] :
        ( sP45(U_1050,U_1046,U_1042,U_1048)
        | sP44(U_1050,U_1042,U_1044,U_1048)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1042,U_1044,U_1046)),U_1048),U_1050)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44,sP45,sP46])],[f_170_3]) ).

cnf(f_170_5,plain,
    ( sP45(U_1050,U_1046,U_1042,U_1048)
    | sP44(U_1050,U_1042,U_1044,U_1048)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1042,U_1044,U_1046)),U_1048),U_1050)) ),
    inference(clausify,[status(thm)],[f_170_4]) ).

cnf(f_170_6,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_1043,U_1045,U_1047)),U_1049),U_1051))
    | sP46(U_1045,U_1043,U_1047,U_1051,U_1049) ),
    inference(clausify,[status(thm)],[f_170_4]) ).

cnf(f_170_7,plain,
    ( hBOOL(hAPP(U_1042,U_1048))
    | ~ sP44(U_1050,U_1042,U_1044,U_1048) ),
    inference(clausify,[status(thm)],[f_170_4]) ).

cnf(f_170_8,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1044),U_1048),U_1050))
    | ~ sP44(U_1050,U_1042,U_1044,U_1048) ),
    inference(clausify,[status(thm)],[f_170_4]) ).

cnf(f_170_9,plain,
    ( ~ hBOOL(hAPP(U_1042,U_1048))
    | ~ sP45(U_1050,U_1046,U_1042,U_1048) ),
    inference(clausify,[status(thm)],[f_170_4]) ).

cnf(f_170_10,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1046),U_1048),U_1050))
    | ~ sP45(U_1050,U_1046,U_1042,U_1048) ),
    inference(clausify,[status(thm)],[f_170_4]) ).

cnf(f_170_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1045),U_1049),U_1051))
    | ~ hBOOL(hAPP(U_1043,U_1049))
    | ~ sP46(U_1045,U_1043,U_1047,U_1051,U_1049) ),
    inference(clausify,[status(thm)],[f_170_4]) ).

cnf(f_170_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1047),U_1049),U_1051))
    | hBOOL(hAPP(U_1043,U_1049))
    | ~ sP46(U_1045,U_1043,U_1047,U_1051,U_1049) ),
    inference(clausify,[status(thm)],[f_170_4]) ).

fof(f_171_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_171_2,plain,
    ! [U_1057,U_1056,U_1055,U_1054] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1054,U_1055)),U_1056),U_1057))
        | ! [U_1053] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1055),U_1053),U_1057))
            | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1054),U_1056),U_1053)) ) )
      & ( ? [U_1052] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1055),U_1052),U_1057))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1054),U_1056),U_1052)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1054,U_1055)),U_1056),U_1057)) ) ),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

fof(f_171_3,plain,
    ( ! [U_1065,U_1063,U_1061,U_1059] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1059,U_1061)),U_1063),U_1065))
        | ! [U_1053] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1061),U_1053),U_1065))
            | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1059),U_1063),U_1053)) ) )
    & ! [U_1064,U_1062,U_1060,U_1058] :
        ( ? [U_1052] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1060),U_1052),U_1064))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1058),U_1062),U_1052)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1058,U_1060)),U_1062),U_1064)) ) ),
    inference(miniscope,[status(thm)],[f_171_2]) ).

fof(f_171_4,plain,
    ( ! [U_1065,U_1063,U_1061,U_1059] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1059,U_1061)),U_1063),U_1065))
        | ! [U_1053] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1061),U_1053),U_1065))
            | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1059),U_1063),U_1053)) ) )
    & ! [U_1064,U_1062,U_1060,U_1058] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1060),sK20(U_1064,U_1062,U_1060,U_1058)),U_1064))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1058),U_1062),sK20(U_1064,U_1062,U_1060,U_1058))) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1058,U_1060)),U_1062),U_1064)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_1052,sK20(U_1064,U_1062,U_1060,U_1058))],[f_171_3]) ).

fof(f_171_5,plain,
    ( ! [U_1060,U_1064,U_1058,U_1062] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1060),sK20(U_1064,U_1062,U_1060,U_1058)),U_1064))
        | ~ sP47(U_1060,U_1064,U_1058,U_1062) )
    & ! [U_1060,U_1064,U_1058,U_1062] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1058),U_1062),sK20(U_1064,U_1062,U_1060,U_1058)))
        | ~ sP47(U_1060,U_1064,U_1058,U_1062) )
    & ! [U_1053,U_1061,U_1059,U_1065,U_1063] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1059,U_1061)),U_1063),U_1065))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1061),U_1053),U_1065))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1059),U_1063),U_1053)) )
    & ! [U_1060,U_1064,U_1058,U_1062] :
        ( sP47(U_1060,U_1064,U_1058,U_1062)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1058,U_1060)),U_1062),U_1064)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47])],[f_171_4]) ).

cnf(f_171_6,plain,
    ( sP47(U_1060,U_1064,U_1058,U_1062)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1058,U_1060)),U_1062),U_1064)) ),
    inference(clausify,[status(thm)],[f_171_5]) ).

cnf(f_171_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1059,U_1061)),U_1063),U_1065))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1061),U_1053),U_1065))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1059),U_1063),U_1053)) ),
    inference(clausify,[status(thm)],[f_171_5]) ).

cnf(f_171_8,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1058),U_1062),sK20(U_1064,U_1062,U_1060,U_1058)))
    | ~ sP47(U_1060,U_1064,U_1058,U_1062) ),
    inference(clausify,[status(thm)],[f_171_5]) ).

cnf(f_171_9,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1060),sK20(U_1064,U_1062,U_1060,U_1058)),U_1064))
    | ~ sP47(U_1060,U_1064,U_1058,U_1062) ),
    inference(clausify,[status(thm)],[f_171_5]) ).

fof(f_172_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_172_2,plain,
    ! [U_1066] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_1066),U_1066)),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

fof(f_172_3,plain,
    ! [U_1066] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_1066),U_1066)),
    inference(definitional_conversion,[status(esa)],[f_172_2]) ).

cnf(f_172_4,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_1066),U_1066)),
    inference(clausify,[status(thm)],[f_172_3]) ).

fof(f_173_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_173_2,plain,
    ! [U_1069,U_1068,U_1067] : c_Nat_Onat_Onat__case(U_1067,U_1068,U_1069,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1068,
    inference(variable_rename,[status(thm)],[f_173_1]) ).

fof(f_173_3,plain,
    ! [U_1069,U_1067,U_1068] : c_Nat_Onat_Onat__case(U_1067,U_1068,U_1069,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1068,
    inference(definitional_conversion,[status(esa)],[f_173_2]) ).

cnf(f_173_4,plain,
    c_Nat_Onat_Onat__case(U_1067,U_1068,U_1069,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1068,
    inference(clausify,[status(thm)],[f_173_3]) ).

fof(f_174_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_174_2,plain,
    ! [U_1072,U_1071,U_1070] : hAPP(c_Nat_Onat_Onat__rec(U_1070,U_1071,U_1072),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1071,
    inference(variable_rename,[status(thm)],[f_174_1]) ).

fof(f_174_3,plain,
    ! [U_1070,U_1071,U_1072] : hAPP(c_Nat_Onat_Onat__rec(U_1070,U_1071,U_1072),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1071,
    inference(definitional_conversion,[status(esa)],[f_174_2]) ).

cnf(f_174_4,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_1070,U_1071,U_1072),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1071,
    inference(clausify,[status(thm)],[f_174_3]) ).

fof(f_175_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_175_2,plain,
    ! [U_1075,U_1074,U_1073] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_1073,U_1074,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1075) = U_1075
      | ~ class_Rings_Osemiring__1(U_1073) ),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

fof(f_175_3,plain,
    ! [U_1073,U_1074,U_1075] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_1073,U_1074,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1075) = U_1075
      | ~ class_Rings_Osemiring__1(U_1073) ),
    inference(definitional_conversion,[status(esa)],[f_175_2]) ).

cnf(f_175_4,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_1073,U_1074,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1075) = U_1075
    | ~ class_Rings_Osemiring__1(U_1073) ),
    inference(clausify,[status(thm)],[f_175_3]) ).

fof(f_176_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_176_2,plain,
    ! [U_1080,U_1079,U_1078,U_1077,U_1076] : c_Hoare__Mirabelle_Otriple_Otriple__size(U_1076,U_1077,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_1076),U_1078),U_1079),U_1080)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

fof(f_176_3,plain,
    ! [U_1076,U_1077,U_1078,U_1079,U_1080] : c_Hoare__Mirabelle_Otriple_Otriple__size(U_1076,U_1077,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_1076),U_1078),U_1079),U_1080)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_176_2]) ).

cnf(f_176_4,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__size(U_1076,U_1077,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_1076),U_1078),U_1079),U_1080)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_176_3]) ).

fof(f_177_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_177_2,plain,
    ! [U_1081] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(U_1081)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

fof(f_177_3,plain,
    ! [U_1081] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(U_1081)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_177_2]) ).

cnf(f_177_4,plain,
    c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(U_1081)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_177_3]) ).

fof(f_178_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_178_2,plain,
    ! [U_1085,U_1084,U_1083,U_1082] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_1082)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_1082),U_1083),U_1084),U_1085)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

fof(f_178_3,plain,
    ! [U_1082,U_1083,U_1084,U_1085] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_1082)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_1082),U_1083),U_1084),U_1085)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_178_2]) ).

cnf(f_178_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_1082)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_1082),U_1083),U_1084),U_1085)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_178_3]) ).

fof(f_179_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_179_2,plain,
    ! [U_1090,U_1089,U_1088,U_1087] :
      ( ? [U_1086] :
          ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_1087)),U_1088,U_1086,U_1090)
          & U_1089 = hAPP(c_Nat_OSuc,U_1086) )
      | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1087),U_1088,U_1089,U_1090) ),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

fof(f_179_3,plain,
    ! [U_1090,U_1089,U_1088,U_1087] :
      ( ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_1087)),U_1088,sK21(U_1090,U_1089,U_1088,U_1087),U_1090)
        & U_1089 = hAPP(c_Nat_OSuc,sK21(U_1090,U_1089,U_1088,U_1087)) )
      | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1087),U_1088,U_1089,U_1090) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_1086,sK21(U_1090,U_1089,U_1088,U_1087))],[f_179_2]) ).

fof(f_179_4,plain,
    ( ! [U_1087,U_1088,U_1089,U_1090] :
        ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_1087)),U_1088,sK21(U_1090,U_1089,U_1088,U_1087),U_1090)
        | ~ sP48(U_1087,U_1088,U_1089,U_1090) )
    & ! [U_1087,U_1088,U_1089,U_1090] :
        ( U_1089 = hAPP(c_Nat_OSuc,sK21(U_1090,U_1089,U_1088,U_1087))
        | ~ sP48(U_1087,U_1088,U_1089,U_1090) )
    & ! [U_1087,U_1088,U_1089,U_1090] :
        ( sP48(U_1087,U_1088,U_1089,U_1090)
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1087),U_1088,U_1089,U_1090) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_179_3]) ).

cnf(f_179_5,plain,
    ( sP48(U_1087,U_1088,U_1089,U_1090)
    | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1087),U_1088,U_1089,U_1090) ),
    inference(clausify,[status(thm)],[f_179_4]) ).

cnf(f_179_6,plain,
    ( U_1089 = hAPP(c_Nat_OSuc,sK21(U_1090,U_1089,U_1088,U_1087))
    | ~ sP48(U_1087,U_1088,U_1089,U_1090) ),
    inference(clausify,[status(thm)],[f_179_4]) ).

cnf(f_179_7,plain,
    ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_1087)),U_1088,sK21(U_1090,U_1089,U_1088,U_1087),U_1090)
    | ~ sP48(U_1087,U_1088,U_1089,U_1090) ),
    inference(clausify,[status(thm)],[f_179_4]) ).

fof(f_180_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_180_2,plain,
    ! [U_1096,U_1095,U_1094,U_1093,U_1092] :
      ( ? [U_1091] :
          ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1094),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_1095),c_Com_Ovname_OLoc(U_1092)),hAPP(U_1093,U_1095))),U_1091))
          & U_1096 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_1091),c_Com_Ovname_OLoc(U_1092)),hAPP(hAPP(c_Natural_Ogetlocs,U_1095),U_1092)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_1092,U_1093,U_1094)),U_1095),U_1096)) ),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

fof(f_180_3,plain,
    ! [U_1096,U_1095,U_1094,U_1093,U_1092] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1094),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_1095),c_Com_Ovname_OLoc(U_1092)),hAPP(U_1093,U_1095))),sK22(U_1096,U_1095,U_1094,U_1093,U_1092)))
        & U_1096 = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK22(U_1096,U_1095,U_1094,U_1093,U_1092)),c_Com_Ovname_OLoc(U_1092)),hAPP(hAPP(c_Natural_Ogetlocs,U_1095),U_1092)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_1092,U_1093,U_1094)),U_1095),U_1096)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_1091,sK22(U_1096,U_1095,U_1094,U_1093,U_1092))],[f_180_2]) ).

fof(f_180_4,plain,
    ( ! [U_1092,U_1093,U_1094,U_1095,U_1096] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1094),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_1095),c_Com_Ovname_OLoc(U_1092)),hAPP(U_1093,U_1095))),sK22(U_1096,U_1095,U_1094,U_1093,U_1092)))
        | ~ sP49(U_1092,U_1093,U_1094,U_1095,U_1096) )
    & ! [U_1092,U_1093,U_1094,U_1095,U_1096] :
        ( U_1096 = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK22(U_1096,U_1095,U_1094,U_1093,U_1092)),c_Com_Ovname_OLoc(U_1092)),hAPP(hAPP(c_Natural_Ogetlocs,U_1095),U_1092))
        | ~ sP49(U_1092,U_1093,U_1094,U_1095,U_1096) )
    & ! [U_1092,U_1093,U_1094,U_1095,U_1096] :
        ( sP49(U_1092,U_1093,U_1094,U_1095,U_1096)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_1092,U_1093,U_1094)),U_1095),U_1096)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49])],[f_180_3]) ).

cnf(f_180_5,plain,
    ( sP49(U_1092,U_1093,U_1094,U_1095,U_1096)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(U_1092,U_1093,U_1094)),U_1095),U_1096)) ),
    inference(clausify,[status(thm)],[f_180_4]) ).

cnf(f_180_6,plain,
    ( U_1096 = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK22(U_1096,U_1095,U_1094,U_1093,U_1092)),c_Com_Ovname_OLoc(U_1092)),hAPP(hAPP(c_Natural_Ogetlocs,U_1095),U_1092))
    | ~ sP49(U_1092,U_1093,U_1094,U_1095,U_1096) ),
    inference(clausify,[status(thm)],[f_180_4]) ).

cnf(f_180_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1094),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_1095),c_Com_Ovname_OLoc(U_1092)),hAPP(U_1093,U_1095))),sK22(U_1096,U_1095,U_1094,U_1093,U_1092)))
    | ~ sP49(U_1092,U_1093,U_1094,U_1095,U_1096) ),
    inference(clausify,[status(thm)],[f_180_4]) ).

fof(f_181_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_181_2,plain,
    ! [U_1103,U_1102,U_1101,U_1100,U_1099,U_1098] :
      ( ? [U_1097] :
          ( c_Natural_Oevaln(U_1100,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_1101),c_Com_Ovname_OLoc(U_1098)),hAPP(U_1099,U_1101)),U_1102,U_1097)
          & U_1103 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_1097),c_Com_Ovname_OLoc(U_1098)),hAPP(hAPP(c_Natural_Ogetlocs,U_1101),U_1098)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_1098,U_1099,U_1100),U_1101,U_1102,U_1103) ),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

fof(f_181_3,plain,
    ! [U_1103,U_1102,U_1101,U_1100,U_1099,U_1098] :
      ( ( c_Natural_Oevaln(U_1100,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_1101),c_Com_Ovname_OLoc(U_1098)),hAPP(U_1099,U_1101)),U_1102,sK23(U_1103,U_1102,U_1101,U_1100,U_1099,U_1098))
        & U_1103 = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK23(U_1103,U_1102,U_1101,U_1100,U_1099,U_1098)),c_Com_Ovname_OLoc(U_1098)),hAPP(hAPP(c_Natural_Ogetlocs,U_1101),U_1098)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_1098,U_1099,U_1100),U_1101,U_1102,U_1103) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_1097,sK23(U_1103,U_1102,U_1101,U_1100,U_1099,U_1098))],[f_181_2]) ).

fof(f_181_4,plain,
    ( ! [U_1101,U_1102,U_1103,U_1098,U_1099,U_1100] :
        ( c_Natural_Oevaln(U_1100,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_1101),c_Com_Ovname_OLoc(U_1098)),hAPP(U_1099,U_1101)),U_1102,sK23(U_1103,U_1102,U_1101,U_1100,U_1099,U_1098))
        | ~ sP50(U_1101,U_1102,U_1103,U_1098,U_1099,U_1100) )
    & ! [U_1101,U_1102,U_1103,U_1098,U_1099,U_1100] :
        ( U_1103 = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK23(U_1103,U_1102,U_1101,U_1100,U_1099,U_1098)),c_Com_Ovname_OLoc(U_1098)),hAPP(hAPP(c_Natural_Ogetlocs,U_1101),U_1098))
        | ~ sP50(U_1101,U_1102,U_1103,U_1098,U_1099,U_1100) )
    & ! [U_1101,U_1102,U_1103,U_1098,U_1099,U_1100] :
        ( sP50(U_1101,U_1102,U_1103,U_1098,U_1099,U_1100)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_1098,U_1099,U_1100),U_1101,U_1102,U_1103) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP50])],[f_181_3]) ).

cnf(f_181_5,plain,
    ( sP50(U_1101,U_1102,U_1103,U_1098,U_1099,U_1100)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OLocal(U_1098,U_1099,U_1100),U_1101,U_1102,U_1103) ),
    inference(clausify,[status(thm)],[f_181_4]) ).

cnf(f_181_6,plain,
    ( U_1103 = hAPP(hAPP(hAPP(c_Natural_Oupdate,sK23(U_1103,U_1102,U_1101,U_1100,U_1099,U_1098)),c_Com_Ovname_OLoc(U_1098)),hAPP(hAPP(c_Natural_Ogetlocs,U_1101),U_1098))
    | ~ sP50(U_1101,U_1102,U_1103,U_1098,U_1099,U_1100) ),
    inference(clausify,[status(thm)],[f_181_4]) ).

cnf(f_181_7,plain,
    ( c_Natural_Oevaln(U_1100,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_1101),c_Com_Ovname_OLoc(U_1098)),hAPP(U_1099,U_1101)),U_1102,sK23(U_1103,U_1102,U_1101,U_1100,U_1099,U_1098))
    | ~ sP50(U_1101,U_1102,U_1103,U_1098,U_1099,U_1100) ),
    inference(clausify,[status(thm)],[f_181_4]) ).

fof(f_182_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_182_2,plain,
    ! [U_1104] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(U_1104)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

fof(f_182_3,plain,
    ! [U_1104] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(U_1104)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_182_2]) ).

cnf(f_182_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(U_1104)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_182_3]) ).

fof(f_183_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_183_2,plain,
    ! [U_1108,U_1107,U_1106,U_1105] : c_Com_Ovname_Ovname__rec(U_1105,U_1106,U_1107,c_Com_Ovname_OLoc(U_1108)) = hAPP(U_1107,U_1108),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

fof(f_183_3,plain,
    ! [U_1107,U_1108,U_1105,U_1106] : c_Com_Ovname_Ovname__rec(U_1105,U_1106,U_1107,c_Com_Ovname_OLoc(U_1108)) = hAPP(U_1107,U_1108),
    inference(definitional_conversion,[status(esa)],[f_183_2]) ).

cnf(f_183_4,plain,
    c_Com_Ovname_Ovname__rec(U_1105,U_1106,U_1107,c_Com_Ovname_OLoc(U_1108)) = hAPP(U_1107,U_1108),
    inference(clausify,[status(thm)],[f_183_3]) ).

fof(f_184_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_184_2,plain,
    ! [U_1112,U_1111,U_1110,U_1109] : c_Com_Ovname_Ovname__case(U_1109,U_1110,U_1111,c_Com_Ovname_OLoc(U_1112)) = hAPP(U_1111,U_1112),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

fof(f_184_3,plain,
    ! [U_1109,U_1111,U_1110,U_1112] : c_Com_Ovname_Ovname__case(U_1109,U_1110,U_1111,c_Com_Ovname_OLoc(U_1112)) = hAPP(U_1111,U_1112),
    inference(definitional_conversion,[status(esa)],[f_184_2]) ).

cnf(f_184_4,plain,
    c_Com_Ovname_Ovname__case(U_1109,U_1110,U_1111,c_Com_Ovname_OLoc(U_1112)) = hAPP(U_1111,U_1112),
    inference(clausify,[status(thm)],[f_184_3]) ).

fof(f_185_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_185_2,plain,
    ! [U_1117,U_1116,U_1115,U_1114] :
      ( ? [U_1113] :
          ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1115),U_1113),U_1117))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1114),U_1116),U_1113)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1114,U_1115)),U_1116),U_1117)) ),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

fof(f_185_3,plain,
    ! [U_1117,U_1116,U_1115,U_1114] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1115),sK24(U_1117,U_1116,U_1115,U_1114)),U_1117))
        & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1114),U_1116),sK24(U_1117,U_1116,U_1115,U_1114))) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1114,U_1115)),U_1116),U_1117)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_1113,sK24(U_1117,U_1116,U_1115,U_1114))],[f_185_2]) ).

fof(f_185_4,plain,
    ( ! [U_1114,U_1115,U_1116,U_1117] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1115),sK24(U_1117,U_1116,U_1115,U_1114)),U_1117))
        | ~ sP51(U_1114,U_1115,U_1116,U_1117) )
    & ! [U_1114,U_1115,U_1116,U_1117] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1114),U_1116),sK24(U_1117,U_1116,U_1115,U_1114)))
        | ~ sP51(U_1114,U_1115,U_1116,U_1117) )
    & ! [U_1114,U_1115,U_1116,U_1117] :
        ( sP51(U_1114,U_1115,U_1116,U_1117)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1114,U_1115)),U_1116),U_1117)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP51])],[f_185_3]) ).

cnf(f_185_5,plain,
    ( sP51(U_1114,U_1115,U_1116,U_1117)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_1114,U_1115)),U_1116),U_1117)) ),
    inference(clausify,[status(thm)],[f_185_4]) ).

cnf(f_185_6,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1114),U_1116),sK24(U_1117,U_1116,U_1115,U_1114)))
    | ~ sP51(U_1114,U_1115,U_1116,U_1117) ),
    inference(clausify,[status(thm)],[f_185_4]) ).

cnf(f_185_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1115),sK24(U_1117,U_1116,U_1115,U_1114)),U_1117))
    | ~ sP51(U_1114,U_1115,U_1116,U_1117) ),
    inference(clausify,[status(thm)],[f_185_4]) ).

fof(f_186_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_186_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_186_1]) ).

cnf(f_186_3,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_186_2]) ).

fof(f_187_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_187_2,plain,
    ! [U_1118] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,U_1118)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

fof(f_187_3,plain,
    ! [U_1118] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,U_1118)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_187_2]) ).

cnf(f_187_4,plain,
    c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,U_1118)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_187_3]) ).

fof(f_188_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_188_2,plain,
    ! [U_1120,U_1119] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(U_1119,U_1120)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

fof(f_188_3,plain,
    ! [U_1119,U_1120] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(U_1119,U_1120)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_188_2]) ).

cnf(f_188_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(U_1119,U_1120)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_188_3]) ).

fof(f_189_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_189_2,plain,
    ! [U_1123,U_1122,U_1121] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(U_1121,U_1122,U_1123)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

fof(f_189_3,plain,
    ! [U_1121,U_1122,U_1123] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(U_1121,U_1122,U_1123)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_189_2]) ).

cnf(f_189_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(U_1121,U_1122,U_1123)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_189_3]) ).

fof(f_190_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_190_2,plain,
    ! [U_1124] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(U_1124)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_190_1]) ).

fof(f_190_3,plain,
    ! [U_1124] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(U_1124)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_190_2]) ).

cnf(f_190_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(U_1124)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_190_3]) ).

fof(f_191_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_191_2,plain,
    ! [U_1125] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(U_1125)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

fof(f_191_3,plain,
    ! [U_1125] : c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(U_1125)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_191_2]) ).

cnf(f_191_4,plain,
    c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(U_1125)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_191_3]) ).

fof(f_192_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_192_2,plain,
    ! [U_1127,U_1126] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_1126,U_1127)) = 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_1126)),c_Com_Ocom_Ocom__size(U_1127))),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_1126,U_1127] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_1126,U_1127)) = 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_1126)),c_Com_Ocom_Ocom__size(U_1127))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_192_2]) ).

cnf(f_192_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_1126,U_1127)) = 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_1126)),c_Com_Ocom_Ocom__size(U_1127))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_192_3]) ).

fof(f_193_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_193_2,plain,
    ! [U_1130,U_1129,U_1128] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_1128,U_1129,U_1130)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_1130)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

fof(f_193_3,plain,
    ! [U_1128,U_1129,U_1130] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_1128,U_1129,U_1130)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_1130)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_193_2]) ).

cnf(f_193_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_1128,U_1129,U_1130)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_1130)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_193_3]) ).

fof(f_194_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_194_2,plain,
    ! [U_1133,U_1132,U_1131] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_1131,U_1132,U_1133)) = 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_1132)),c_Com_Ocom_Ocom__size(U_1133))),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_1131,U_1132,U_1133] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_1131,U_1132,U_1133)) = 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_1132)),c_Com_Ocom_Ocom__size(U_1133))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_194_2]) ).

cnf(f_194_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_1131,U_1132,U_1133)) = 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_1132)),c_Com_Ocom_Ocom__size(U_1133))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_194_3]) ).

fof(f_195_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_195_2,plain,
    ! [U_1135,U_1134] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_1134,U_1135)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_1135)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

fof(f_195_3,plain,
    ! [U_1134,U_1135] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_1134,U_1135)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_1135)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_195_2]) ).

cnf(f_195_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_1134,U_1135)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_1135)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_195_3]) ).

fof(f_196_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_196_2,plain,
    ! [U_1139,U_1138,U_1137,U_1136] : c_Com_Ovname_Ovname__case(U_1136,U_1137,U_1138,c_Com_Ovname_OGlb(U_1139)) = hAPP(U_1137,U_1139),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

fof(f_196_3,plain,
    ! [U_1136,U_1137,U_1138,U_1139] : c_Com_Ovname_Ovname__case(U_1136,U_1137,U_1138,c_Com_Ovname_OGlb(U_1139)) = hAPP(U_1137,U_1139),
    inference(definitional_conversion,[status(esa)],[f_196_2]) ).

cnf(f_196_4,plain,
    c_Com_Ovname_Ovname__case(U_1136,U_1137,U_1138,c_Com_Ovname_OGlb(U_1139)) = hAPP(U_1137,U_1139),
    inference(clausify,[status(thm)],[f_196_3]) ).

fof(f_197_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_197_2,plain,
    ! [U_1143,U_1142,U_1141,U_1140] : c_Com_Ovname_Ovname__rec(U_1140,U_1141,U_1142,c_Com_Ovname_OGlb(U_1143)) = hAPP(U_1141,U_1143),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

fof(f_197_3,plain,
    ! [U_1140,U_1141,U_1142,U_1143] : c_Com_Ovname_Ovname__rec(U_1140,U_1141,U_1142,c_Com_Ovname_OGlb(U_1143)) = hAPP(U_1141,U_1143),
    inference(definitional_conversion,[status(esa)],[f_197_2]) ).

cnf(f_197_4,plain,
    c_Com_Ovname_Ovname__rec(U_1140,U_1141,U_1142,c_Com_Ovname_OGlb(U_1143)) = hAPP(U_1141,U_1143),
    inference(clausify,[status(thm)],[f_197_3]) ).

fof(f_198_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_198_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_198_1]) ).

cnf(f_198_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_198_2]) ).

fof(f_199_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_199_2,plain,
    ! [U_1146,U_1145,U_1144] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(U_1144,U_1145,U_1146)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

fof(f_199_3,plain,
    ! [U_1144,U_1145,U_1146] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(U_1144,U_1145,U_1146)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_199_2]) ).

cnf(f_199_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(U_1144,U_1145,U_1146)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_199_3]) ).

fof(f_200_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_200_2,plain,
    ! [U_1148,U_1147] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(U_1147,U_1148)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_200_1]) ).

fof(f_200_3,plain,
    ! [U_1147,U_1148] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(U_1147,U_1148)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_200_2]) ).

cnf(f_200_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(U_1147,U_1148)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_200_3]) ).

fof(f_201_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_201_2,plain,
    ! [U_1150,U_1149] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1149),U_1150) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1150),U_1149),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

fof(f_201_3,plain,
    ! [U_1149,U_1150] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1149),U_1150) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1150),U_1149),
    inference(definitional_conversion,[status(esa)],[f_201_2]) ).

cnf(f_201_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1149),U_1150) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1150),U_1149),
    inference(clausify,[status(thm)],[f_201_3]) ).

fof(f_202_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_202_2,plain,
    ! [U_1153,U_1152,U_1151] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1151),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1152),U_1153)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1152),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1151),U_1153)),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

fof(f_202_3,plain,
    ! [U_1151,U_1152,U_1153] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1151),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1152),U_1153)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1152),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1151),U_1153)),
    inference(definitional_conversion,[status(esa)],[f_202_2]) ).

cnf(f_202_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1151),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1152),U_1153)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1152),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1151),U_1153)),
    inference(clausify,[status(thm)],[f_202_3]) ).

fof(f_203_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_203_2,plain,
    ! [U_1156,U_1155,U_1154] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1154),U_1155)),U_1156) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1155),U_1156)),
    inference(variable_rename,[status(thm)],[f_203_1]) ).

fof(f_203_3,plain,
    ! [U_1154,U_1155,U_1156] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1154),U_1155)),U_1156) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1155),U_1156)),
    inference(definitional_conversion,[status(esa)],[f_203_2]) ).

cnf(f_203_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1154),U_1155)),U_1156) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1155),U_1156)),
    inference(clausify,[status(thm)],[f_203_3]) ).

fof(f_204_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_204_2,plain,
    ! [U_1159,U_1158,U_1157] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1157),U_1158) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1157),U_1159)
        | U_1158 != U_1159 )
      & ( U_1158 = U_1159
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1157),U_1158) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1157),U_1159) ) ),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

fof(f_204_3,plain,
    ( ! [U_1165,U_1163] :
        ( ! [U_1161] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1161),U_1163) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1161),U_1165)
        | U_1163 != U_1165 )
    & ! [U_1164,U_1162] :
        ( ! [U_1160] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1160),U_1162) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1160),U_1164)
        | U_1162 = U_1164 ) ),
    inference(miniscope,[status(thm)],[f_204_2]) ).

fof(f_204_4,plain,
    ( ! [U_1161,U_1163,U_1165] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1161),U_1163) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1161),U_1165)
        | U_1163 != U_1165 )
    & ! [U_1160,U_1162,U_1164] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1160),U_1162) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1160),U_1164)
        | U_1162 = U_1164 ) ),
    inference(definitional_conversion,[status(esa)],[f_204_3]) ).

cnf(f_204_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1160),U_1162) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1160),U_1164)
    | U_1162 = U_1164 ),
    inference(clausify,[status(thm)],[f_204_4]) ).

cnf(f_204_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1161),U_1163) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1161),U_1165)
    | U_1163 != U_1165 ),
    inference(clausify,[status(thm)],[f_204_4]) ).

fof(f_205_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_205_2,plain,
    ! [U_1168,U_1167,U_1166] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1166),U_1167) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1168),U_1167)
        | U_1166 != U_1168 )
      & ( U_1166 = U_1168
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1166),U_1167) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1168),U_1167) ) ),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

fof(f_205_3,plain,
    ( ! [U_1174,U_1172,U_1170] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1170),U_1172) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1174),U_1172)
        | U_1170 != U_1174 )
    & ! [U_1173,U_1171,U_1169] :
        ( U_1169 = U_1173
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1169),U_1171) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1173),U_1171) ) ),
    inference(miniscope,[status(thm)],[f_205_2]) ).

fof(f_205_4,plain,
    ( ! [U_1172,U_1170,U_1174] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1170),U_1172) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1174),U_1172)
        | U_1170 != U_1174 )
    & ! [U_1171,U_1173,U_1169] :
        ( U_1169 = U_1173
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1169),U_1171) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1173),U_1171) ) ),
    inference(definitional_conversion,[status(esa)],[f_205_3]) ).

cnf(f_205_5,plain,
    ( U_1169 = U_1173
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1169),U_1171) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1173),U_1171) ),
    inference(clausify,[status(thm)],[f_205_4]) ).

cnf(f_205_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1170),U_1172) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1174),U_1172)
    | U_1170 != U_1174 ),
    inference(clausify,[status(thm)],[f_205_4]) ).

fof(f_206_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_206_2,plain,
    ! [U_1176,U_1175] :
      ( ( c_Com_Ovname_OGlb(U_1175) = c_Com_Ovname_OGlb(U_1176)
        | U_1175 != U_1176 )
      & ( U_1175 = U_1176
        | c_Com_Ovname_OGlb(U_1175) != c_Com_Ovname_OGlb(U_1176) ) ),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

fof(f_206_3,plain,
    ( ! [U_1180,U_1178] :
        ( c_Com_Ovname_OGlb(U_1178) = c_Com_Ovname_OGlb(U_1180)
        | U_1178 != U_1180 )
    & ! [U_1179,U_1177] :
        ( U_1177 = U_1179
        | c_Com_Ovname_OGlb(U_1177) != c_Com_Ovname_OGlb(U_1179) ) ),
    inference(miniscope,[status(thm)],[f_206_2]) ).

fof(f_206_4,plain,
    ( ! [U_1180,U_1178] :
        ( c_Com_Ovname_OGlb(U_1178) = c_Com_Ovname_OGlb(U_1180)
        | U_1178 != U_1180 )
    & ! [U_1177,U_1179] :
        ( U_1177 = U_1179
        | c_Com_Ovname_OGlb(U_1177) != c_Com_Ovname_OGlb(U_1179) ) ),
    inference(definitional_conversion,[status(esa)],[f_206_3]) ).

cnf(f_206_5,plain,
    ( U_1177 = U_1179
    | c_Com_Ovname_OGlb(U_1177) != c_Com_Ovname_OGlb(U_1179) ),
    inference(clausify,[status(thm)],[f_206_4]) ).

cnf(f_206_6,plain,
    ( c_Com_Ovname_OGlb(U_1178) = c_Com_Ovname_OGlb(U_1180)
    | U_1178 != U_1180 ),
    inference(clausify,[status(thm)],[f_206_4]) ).

fof(f_207_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_207_2,plain,
    ! [U_1181] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1181) = U_1181,
    inference(variable_rename,[status(thm)],[f_207_1]) ).

fof(f_207_3,plain,
    ! [U_1181] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1181) = U_1181,
    inference(definitional_conversion,[status(esa)],[f_207_2]) ).

cnf(f_207_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1181) = U_1181,
    inference(clausify,[status(thm)],[f_207_3]) ).

fof(f_208_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_208_2,plain,
    ! [U_1182] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1182),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1182,
    inference(variable_rename,[status(thm)],[f_208_1]) ).

fof(f_208_3,plain,
    ! [U_1182] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1182),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1182,
    inference(definitional_conversion,[status(esa)],[f_208_2]) ).

cnf(f_208_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1182),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1182,
    inference(clausify,[status(thm)],[f_208_3]) ).

fof(f_209_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_209_2,plain,
    ! [U_1184,U_1183] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1183),U_1184) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1184 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1183 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_1184 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1183 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1183),U_1184) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

fof(f_209_3,plain,
    ( ! [U_1188,U_1186] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1186),U_1188) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1188 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1186 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1187,U_1185] :
        ( ( U_1187 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1185),U_1187) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_209_2]) ).

fof(f_209_4,plain,
    ( ! [U_1187,U_1185] :
        ( U_1187 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP52(U_1187,U_1185) )
    & ! [U_1187,U_1185] :
        ( U_1185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP52(U_1187,U_1185) )
    & ! [U_1188,U_1186] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1186),U_1188) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1188 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1186 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1187,U_1185] :
        ( sP52(U_1187,U_1185)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1185),U_1187) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52])],[f_209_3]) ).

cnf(f_209_5,plain,
    ( sP52(U_1187,U_1185)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1185),U_1187) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_209_4]) ).

cnf(f_209_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1186),U_1188) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_1188 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_1186 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_209_4]) ).

cnf(f_209_7,plain,
    ( U_1185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP52(U_1187,U_1185) ),
    inference(clausify,[status(thm)],[f_209_4]) ).

cnf(f_209_8,plain,
    ( U_1187 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP52(U_1187,U_1185) ),
    inference(clausify,[status(thm)],[f_209_4]) ).

fof(f_210_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_210_2,plain,
    ! [U_1190,U_1189] :
      ( U_1190 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1189),U_1190) != U_1189 ),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

fof(f_210_3,plain,
    ! [U_1190] :
      ( ! [U_1189] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1189),U_1190) != U_1189
      | U_1190 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_210_2]) ).

fof(f_210_4,plain,
    ! [U_1190,U_1189] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1189),U_1190) != U_1189
      | U_1190 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_210_3]) ).

cnf(f_210_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1189),U_1190) != U_1189
    | U_1190 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_210_4]) ).

fof(f_211_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_211_2,plain,
    ! [U_1192,U_1191] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1191)),U_1192) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1191),hAPP(c_Nat_OSuc,U_1192)),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

fof(f_211_3,plain,
    ! [U_1191,U_1192] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1191)),U_1192) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1191),hAPP(c_Nat_OSuc,U_1192)),
    inference(definitional_conversion,[status(esa)],[f_211_2]) ).

cnf(f_211_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1191)),U_1192) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1191),hAPP(c_Nat_OSuc,U_1192)),
    inference(clausify,[status(thm)],[f_211_3]) ).

fof(f_212_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_212_2,plain,
    ! [U_1194,U_1193] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1193)),U_1194) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1193),U_1194)),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

fof(f_212_3,plain,
    ! [U_1193,U_1194] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1193)),U_1194) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1193),U_1194)),
    inference(definitional_conversion,[status(esa)],[f_212_2]) ).

cnf(f_212_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1193)),U_1194) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1193),U_1194)),
    inference(clausify,[status(thm)],[f_212_3]) ).

fof(f_213_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_213_2,plain,
    ! [U_1196,U_1195] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1195),hAPP(c_Nat_OSuc,U_1196)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1195),U_1196)),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

fof(f_213_3,plain,
    ! [U_1195,U_1196] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1195),hAPP(c_Nat_OSuc,U_1196)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1195),U_1196)),
    inference(definitional_conversion,[status(esa)],[f_213_2]) ).

cnf(f_213_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1195),hAPP(c_Nat_OSuc,U_1196)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1195),U_1196)),
    inference(clausify,[status(thm)],[f_213_3]) ).

fof(f_214_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_214_2,plain,
    ! [U_1198,U_1197] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(U_1197,U_1198)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_1198)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

fof(f_214_3,plain,
    ! [U_1197,U_1198] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(U_1197,U_1198)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_1198)),hAPP(c_Nat_OSuc,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_Com_Ocom),c_Com_Ocom_OWhile(U_1197,U_1198)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_1198)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_214_3]) ).

fof(f_215_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_215_2,plain,
    ! [U_1201,U_1200,U_1199] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(U_1199,U_1200,U_1201)) = 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_1200)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_1201))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_215_1]) ).

fof(f_215_3,plain,
    ! [U_1199,U_1200,U_1201] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(U_1199,U_1200,U_1201)) = 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_1200)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_1201))),hAPP(c_Nat_OSuc,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_Com_Ocom),c_Com_Ocom_OCond(U_1199,U_1200,U_1201)) = 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_1200)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_1201))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_215_3]) ).

fof(f_216_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_216_2,plain,
    ! [U_1204,U_1203,U_1202] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_1202,U_1203,U_1204)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_1204)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_216_1]) ).

fof(f_216_3,plain,
    ! [U_1202,U_1203,U_1204] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_1202,U_1203,U_1204)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_1204)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_216_2]) ).

cnf(f_216_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_1202,U_1203,U_1204)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_1204)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_216_3]) ).

fof(f_217_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_217_2,plain,
    ! [U_1206,U_1205] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_1205,U_1206)) = 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_1205)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_1206))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_217_1]) ).

fof(f_217_3,plain,
    ! [U_1205,U_1206] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_1205,U_1206)) = 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_1205)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_1206))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_217_2]) ).

cnf(f_217_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_1205,U_1206)) = 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_1205)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_1206))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_217_3]) ).

fof(f_218_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_218_2,plain,
    ! [U_1208,U_1207] :
      ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1207),U_1208)
        | ( ( U_1208 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_1207 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_1208 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_1207 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_1208 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_1207 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_1208 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1207 = 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_1207),U_1208) ) ),
    inference(variable_rename,[status(thm)],[f_218_1]) ).

fof(f_218_3,plain,
    ( ! [U_1212,U_1210] :
        ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1210),U_1212)
        | ( ( U_1212 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_1210 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_1212 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_1210 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_1211,U_1209] :
        ( ( U_1211 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_1209 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_1211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1209 = 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_1209),U_1211) ) ),
    inference(miniscope,[status(thm)],[f_218_2]) ).

fof(f_218_4,plain,
    ( ! [U_1210,U_1212] :
        ( U_1212 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_1210 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP55(U_1210,U_1212) )
    & ! [U_1210,U_1212] :
        ( U_1212 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1210 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP55(U_1210,U_1212) )
    & ! [U_1211,U_1209] :
        ( U_1211 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP54(U_1211,U_1209) )
    & ! [U_1211,U_1209] :
        ( U_1209 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP54(U_1211,U_1209) )
    & ! [U_1211,U_1209] :
        ( U_1211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP53(U_1211,U_1209) )
    & ! [U_1211,U_1209] :
        ( U_1209 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP53(U_1211,U_1209) )
    & ! [U_1210,U_1212] :
        ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1210),U_1212)
        | sP55(U_1210,U_1212) )
    & ! [U_1211,U_1209] :
        ( sP54(U_1211,U_1209)
        | sP53(U_1211,U_1209)
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1209),U_1211) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP53,sP54,sP55])],[f_218_3]) ).

cnf(f_218_5,plain,
    ( sP54(U_1211,U_1209)
    | sP53(U_1211,U_1209)
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1209),U_1211) ),
    inference(clausify,[status(thm)],[f_218_4]) ).

cnf(f_218_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_1210),U_1212)
    | sP55(U_1210,U_1212) ),
    inference(clausify,[status(thm)],[f_218_4]) ).

cnf(f_218_7,plain,
    ( U_1209 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP53(U_1211,U_1209) ),
    inference(clausify,[status(thm)],[f_218_4]) ).

cnf(f_218_8,plain,
    ( U_1211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP53(U_1211,U_1209) ),
    inference(clausify,[status(thm)],[f_218_4]) ).

cnf(f_218_9,plain,
    ( U_1209 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP54(U_1211,U_1209) ),
    inference(clausify,[status(thm)],[f_218_4]) ).

cnf(f_218_10,plain,
    ( U_1211 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP54(U_1211,U_1209) ),
    inference(clausify,[status(thm)],[f_218_4]) ).

cnf(f_218_11,plain,
    ( U_1212 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_1210 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP55(U_1210,U_1212) ),
    inference(clausify,[status(thm)],[f_218_4]) ).

cnf(f_218_12,plain,
    ( U_1212 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_1210 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP55(U_1210,U_1212) ),
    inference(clausify,[status(thm)],[f_218_4]) ).

fof(f_219_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_219_2,plain,
    ! [U_1214,U_1213] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1213),U_1214) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_1214 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_1213 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_1214 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_1213 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_1214 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_1213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_1214 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1213 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1213),U_1214) != 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_1218,U_1216] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1216),U_1218) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_1218 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_1216 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_1218 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_1216 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_1217,U_1215] :
        ( ( U_1217 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_1215 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_1217 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1215 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1215),U_1217) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_219_2]) ).

fof(f_219_4,plain,
    ( ! [U_1216,U_1218] :
        ( U_1218 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_1216 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP58(U_1216,U_1218) )
    & ! [U_1216,U_1218] :
        ( U_1218 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1216 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP58(U_1216,U_1218) )
    & ! [U_1215,U_1217] :
        ( U_1217 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP57(U_1215,U_1217) )
    & ! [U_1215,U_1217] :
        ( U_1215 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP57(U_1215,U_1217) )
    & ! [U_1215,U_1217] :
        ( U_1217 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP56(U_1215,U_1217) )
    & ! [U_1215,U_1217] :
        ( U_1215 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP56(U_1215,U_1217) )
    & ! [U_1216,U_1218] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1216),U_1218) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | sP58(U_1216,U_1218) )
    & ! [U_1215,U_1217] :
        ( sP57(U_1215,U_1217)
        | sP56(U_1215,U_1217)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1215),U_1217) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56,sP57,sP58])],[f_219_3]) ).

cnf(f_219_5,plain,
    ( sP57(U_1215,U_1217)
    | sP56(U_1215,U_1217)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1215),U_1217) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_219_4]) ).

cnf(f_219_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1216),U_1218) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | sP58(U_1216,U_1218) ),
    inference(clausify,[status(thm)],[f_219_4]) ).

cnf(f_219_7,plain,
    ( U_1215 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP56(U_1215,U_1217) ),
    inference(clausify,[status(thm)],[f_219_4]) ).

cnf(f_219_8,plain,
    ( U_1217 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP56(U_1215,U_1217) ),
    inference(clausify,[status(thm)],[f_219_4]) ).

cnf(f_219_9,plain,
    ( U_1215 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP57(U_1215,U_1217) ),
    inference(clausify,[status(thm)],[f_219_4]) ).

cnf(f_219_10,plain,
    ( U_1217 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP57(U_1215,U_1217) ),
    inference(clausify,[status(thm)],[f_219_4]) ).

cnf(f_219_11,plain,
    ( U_1218 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_1216 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP58(U_1216,U_1218) ),
    inference(clausify,[status(thm)],[f_219_4]) ).

cnf(f_219_12,plain,
    ( U_1218 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_1216 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP58(U_1216,U_1218) ),
    inference(clausify,[status(thm)],[f_219_4]) ).

fof(f_220_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_220_2,plain,
    ! [U_1220,U_1219] : c_Com_Ovname_OGlb(U_1219) != c_Com_Ovname_OLoc(U_1220),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

fof(f_220_3,plain,
    ! [U_1220,U_1219] : c_Com_Ovname_OGlb(U_1219) != c_Com_Ovname_OLoc(U_1220),
    inference(definitional_conversion,[status(esa)],[f_220_2]) ).

cnf(f_220_4,plain,
    c_Com_Ovname_OGlb(U_1219) != c_Com_Ovname_OLoc(U_1220),
    inference(clausify,[status(thm)],[f_220_3]) ).

fof(f_221_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_221_2,plain,
    ! [U_1222,U_1221] : c_Com_Ovname_OLoc(U_1221) != c_Com_Ovname_OGlb(U_1222),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

fof(f_221_3,plain,
    ! [U_1222,U_1221] : c_Com_Ovname_OLoc(U_1221) != c_Com_Ovname_OGlb(U_1222),
    inference(definitional_conversion,[status(esa)],[f_221_2]) ).

cnf(f_221_4,plain,
    c_Com_Ovname_OLoc(U_1221) != c_Com_Ovname_OGlb(U_1222),
    inference(clausify,[status(thm)],[f_221_3]) ).

fof(f_222_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_222_2,plain,
    ! [U_1223] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,U_1223)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

fof(f_222_3,plain,
    ! [U_1223] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,U_1223)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_222_2]) ).

cnf(f_222_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,U_1223)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_222_3]) ).

fof(f_223_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_223_2,plain,
    ! [U_1225,U_1224] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1224),U_1225),U_1225) = c_Groups_Ozero__class_Ozero(U_1224)
          | U_1225 != c_Groups_Ozero__class_Ozero(U_1224) )
        & ( U_1225 = c_Groups_Ozero__class_Ozero(U_1224)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1224),U_1225),U_1225) != c_Groups_Ozero__class_Ozero(U_1224) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1224) ),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

fof(f_223_3,plain,
    ( ! [U_1225,U_1224] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1224),U_1225),U_1225) = c_Groups_Ozero__class_Ozero(U_1224)
        | U_1225 != c_Groups_Ozero__class_Ozero(U_1224)
        | ~ sP59(U_1225,U_1224) )
    & ! [U_1225,U_1224] :
        ( U_1225 = c_Groups_Ozero__class_Ozero(U_1224)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1224),U_1225),U_1225) != c_Groups_Ozero__class_Ozero(U_1224)
        | ~ sP59(U_1225,U_1224) )
    & ! [U_1225,U_1224] :
        ( sP59(U_1225,U_1224)
        | ~ class_Groups_Olinordered__ab__group__add(U_1224) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP59])],[f_223_2]) ).

cnf(f_223_4,plain,
    ( sP59(U_1225,U_1224)
    | ~ class_Groups_Olinordered__ab__group__add(U_1224) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

cnf(f_223_5,plain,
    ( U_1225 = c_Groups_Ozero__class_Ozero(U_1224)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1224),U_1225),U_1225) != c_Groups_Ozero__class_Ozero(U_1224)
    | ~ sP59(U_1225,U_1224) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

cnf(f_223_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1224),U_1225),U_1225) = c_Groups_Ozero__class_Ozero(U_1224)
    | U_1225 != c_Groups_Ozero__class_Ozero(U_1224)
    | ~ sP59(U_1225,U_1224) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

fof(f_224_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_224_2,plain,
    ! [U_1228,U_1227,U_1226] :
      ( ( ( U_1227 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1226),U_1227),U_1228)
          | U_1228 != c_Groups_Ozero__class_Ozero(U_1226) )
        & ( U_1228 = c_Groups_Ozero__class_Ozero(U_1226)
          | U_1227 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1226),U_1227),U_1228) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1226) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

fof(f_224_3,plain,
    ( ! [U_1228,U_1227,U_1226] :
        ( U_1227 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1226),U_1227),U_1228)
        | U_1228 != c_Groups_Ozero__class_Ozero(U_1226)
        | ~ sP60(U_1228,U_1227,U_1226) )
    & ! [U_1228,U_1227,U_1226] :
        ( U_1228 = c_Groups_Ozero__class_Ozero(U_1226)
        | U_1227 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1226),U_1227),U_1228)
        | ~ sP60(U_1228,U_1227,U_1226) )
    & ! [U_1228,U_1227,U_1226] :
        ( sP60(U_1228,U_1227,U_1226)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1226) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP60])],[f_224_2]) ).

cnf(f_224_4,plain,
    ( sP60(U_1228,U_1227,U_1226)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1226) ),
    inference(clausify,[status(thm)],[f_224_3]) ).

cnf(f_224_5,plain,
    ( U_1228 = c_Groups_Ozero__class_Ozero(U_1226)
    | U_1227 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1226),U_1227),U_1228)
    | ~ sP60(U_1228,U_1227,U_1226) ),
    inference(clausify,[status(thm)],[f_224_3]) ).

cnf(f_224_6,plain,
    ( U_1227 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1226),U_1227),U_1228)
    | U_1228 != c_Groups_Ozero__class_Ozero(U_1226)
    | ~ sP60(U_1228,U_1227,U_1226) ),
    inference(clausify,[status(thm)],[f_224_3]) ).

fof(f_225_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_225_2,plain,
    ! [U_1230,U_1229] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1229),U_1230),c_Groups_Ozero__class_Ozero(U_1229)) = U_1230
      | ~ class_Groups_Ocomm__monoid__add(U_1229) ),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

fof(f_225_3,plain,
    ! [U_1230,U_1229] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1229),U_1230),c_Groups_Ozero__class_Ozero(U_1229)) = U_1230
      | ~ class_Groups_Ocomm__monoid__add(U_1229) ),
    inference(definitional_conversion,[status(esa)],[f_225_2]) ).

cnf(f_225_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1229),U_1230),c_Groups_Ozero__class_Ozero(U_1229)) = U_1230
    | ~ class_Groups_Ocomm__monoid__add(U_1229) ),
    inference(clausify,[status(thm)],[f_225_3]) ).

fof(f_226_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_226_2,plain,
    ! [U_1232,U_1231] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1231),U_1232),c_Groups_Ozero__class_Ozero(U_1231)) = U_1232
      | ~ class_Rings_Ocomm__semiring__1(U_1231) ),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

fof(f_226_3,plain,
    ! [U_1231,U_1232] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1231),U_1232),c_Groups_Ozero__class_Ozero(U_1231)) = U_1232
      | ~ class_Rings_Ocomm__semiring__1(U_1231) ),
    inference(definitional_conversion,[status(esa)],[f_226_2]) ).

cnf(f_226_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1231),U_1232),c_Groups_Ozero__class_Ozero(U_1231)) = U_1232
    | ~ class_Rings_Ocomm__semiring__1(U_1231) ),
    inference(clausify,[status(thm)],[f_226_3]) ).

fof(f_227_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_227_2,plain,
    ! [U_1234,U_1233] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1233),U_1234),c_Groups_Ozero__class_Ozero(U_1233)) = U_1234
      | ~ class_Groups_Omonoid__add(U_1233) ),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

fof(f_227_3,plain,
    ! [U_1233,U_1234] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1233),U_1234),c_Groups_Ozero__class_Ozero(U_1233)) = U_1234
      | ~ class_Groups_Omonoid__add(U_1233) ),
    inference(definitional_conversion,[status(esa)],[f_227_2]) ).

cnf(f_227_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1233),U_1234),c_Groups_Ozero__class_Ozero(U_1233)) = U_1234
    | ~ class_Groups_Omonoid__add(U_1233) ),
    inference(clausify,[status(thm)],[f_227_3]) ).

fof(f_228_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_228_2,plain,
    ! [U_1236,U_1235] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_1235) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1235),U_1236),U_1236)
          | U_1236 != c_Groups_Ozero__class_Ozero(U_1235) )
        & ( U_1236 = c_Groups_Ozero__class_Ozero(U_1235)
          | c_Groups_Ozero__class_Ozero(U_1235) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1235),U_1236),U_1236) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1235) ),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

fof(f_228_3,plain,
    ( ! [U_1235,U_1236] :
        ( c_Groups_Ozero__class_Ozero(U_1235) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1235),U_1236),U_1236)
        | U_1236 != c_Groups_Ozero__class_Ozero(U_1235)
        | ~ sP61(U_1235,U_1236) )
    & ! [U_1235,U_1236] :
        ( U_1236 = c_Groups_Ozero__class_Ozero(U_1235)
        | c_Groups_Ozero__class_Ozero(U_1235) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1235),U_1236),U_1236)
        | ~ sP61(U_1235,U_1236) )
    & ! [U_1235,U_1236] :
        ( sP61(U_1235,U_1236)
        | ~ class_Groups_Olinordered__ab__group__add(U_1235) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61])],[f_228_2]) ).

cnf(f_228_4,plain,
    ( sP61(U_1235,U_1236)
    | ~ class_Groups_Olinordered__ab__group__add(U_1235) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_5,plain,
    ( U_1236 = c_Groups_Ozero__class_Ozero(U_1235)
    | c_Groups_Ozero__class_Ozero(U_1235) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1235),U_1236),U_1236)
    | ~ sP61(U_1235,U_1236) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_1235) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1235),U_1236),U_1236)
    | U_1236 != c_Groups_Ozero__class_Ozero(U_1235)
    | ~ sP61(U_1235,U_1236) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

fof(f_229_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_229_2,plain,
    ! [U_1238,U_1237] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1237),c_Groups_Ozero__class_Ozero(U_1237)),U_1238) = U_1238
      | ~ class_Groups_Ocomm__monoid__add(U_1237) ),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

fof(f_229_3,plain,
    ! [U_1237,U_1238] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1237),c_Groups_Ozero__class_Ozero(U_1237)),U_1238) = U_1238
      | ~ class_Groups_Ocomm__monoid__add(U_1237) ),
    inference(definitional_conversion,[status(esa)],[f_229_2]) ).

cnf(f_229_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1237),c_Groups_Ozero__class_Ozero(U_1237)),U_1238) = U_1238
    | ~ class_Groups_Ocomm__monoid__add(U_1237) ),
    inference(clausify,[status(thm)],[f_229_3]) ).

fof(f_230_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_230_2,plain,
    ! [U_1240,U_1239] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1239),c_Groups_Ozero__class_Ozero(U_1239)),U_1240) = U_1240
      | ~ class_Rings_Ocomm__semiring__1(U_1239) ),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

fof(f_230_3,plain,
    ! [U_1239,U_1240] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1239),c_Groups_Ozero__class_Ozero(U_1239)),U_1240) = U_1240
      | ~ class_Rings_Ocomm__semiring__1(U_1239) ),
    inference(definitional_conversion,[status(esa)],[f_230_2]) ).

cnf(f_230_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1239),c_Groups_Ozero__class_Ozero(U_1239)),U_1240) = U_1240
    | ~ class_Rings_Ocomm__semiring__1(U_1239) ),
    inference(clausify,[status(thm)],[f_230_3]) ).

fof(f_231_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_231_2,plain,
    ! [U_1242,U_1241] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1241),c_Groups_Ozero__class_Ozero(U_1241)),U_1242) = U_1242
      | ~ class_Groups_Omonoid__add(U_1241) ),
    inference(variable_rename,[status(thm)],[f_231_1]) ).

fof(f_231_3,plain,
    ! [U_1241,U_1242] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1241),c_Groups_Ozero__class_Ozero(U_1241)),U_1242) = U_1242
      | ~ class_Groups_Omonoid__add(U_1241) ),
    inference(definitional_conversion,[status(esa)],[f_231_2]) ).

cnf(f_231_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1241),c_Groups_Ozero__class_Ozero(U_1241)),U_1242) = U_1242
    | ~ class_Groups_Omonoid__add(U_1241) ),
    inference(clausify,[status(thm)],[f_231_3]) ).

fof(f_232_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_232_2,plain,
    ! [U_1243] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_1243)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_1243)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

fof(f_232_3,plain,
    ! [U_1243] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_1243)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_1243)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_232_2]) ).

cnf(f_232_4,plain,
    c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_1243)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_1243)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_232_3]) ).

fof(f_233_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_233_2,plain,
    ! [U_1244] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1244)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_1244)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

fof(f_233_3,plain,
    ! [U_1244] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1244)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_1244)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_233_2]) ).

cnf(f_233_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1244)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_1244)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_233_3]) ).

fof(f_234_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_234_2,plain,
    ! [U_1245] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_1245) = U_1245,
    inference(variable_rename,[status(thm)],[f_234_1]) ).

fof(f_234_3,plain,
    ! [U_1245] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_1245) = U_1245,
    inference(definitional_conversion,[status(esa)],[f_234_2]) ).

cnf(f_234_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_1245) = U_1245,
    inference(clausify,[status(thm)],[f_234_3]) ).

fof(f_235_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_235_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_235_1]) ).

cnf(f_235_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_235_2]) ).

fof(f_236_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_236_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_236_1]) ).

cnf(f_236_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_236_2]) ).

fof(f_237_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_237_2,plain,
    ! [U_1247,U_1246] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_1246) = U_1247
          | U_1247 != c_Groups_Ozero__class_Ozero(U_1246) )
        & ( U_1247 = c_Groups_Ozero__class_Ozero(U_1246)
          | c_Groups_Ozero__class_Ozero(U_1246) != U_1247 ) )
      | ~ class_Groups_Ozero(U_1246) ),
    inference(variable_rename,[status(thm)],[f_237_1]) ).

fof(f_237_3,plain,
    ( ! [U_1246,U_1247] :
        ( c_Groups_Ozero__class_Ozero(U_1246) = U_1247
        | U_1247 != c_Groups_Ozero__class_Ozero(U_1246)
        | ~ sP62(U_1246,U_1247) )
    & ! [U_1246,U_1247] :
        ( U_1247 = c_Groups_Ozero__class_Ozero(U_1246)
        | c_Groups_Ozero__class_Ozero(U_1246) != U_1247
        | ~ sP62(U_1246,U_1247) )
    & ! [U_1246,U_1247] :
        ( sP62(U_1246,U_1247)
        | ~ class_Groups_Ozero(U_1246) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62])],[f_237_2]) ).

cnf(f_237_4,plain,
    ( sP62(U_1246,U_1247)
    | ~ class_Groups_Ozero(U_1246) ),
    inference(clausify,[status(thm)],[f_237_3]) ).

cnf(f_237_5,plain,
    ( U_1247 = c_Groups_Ozero__class_Ozero(U_1246)
    | c_Groups_Ozero__class_Ozero(U_1246) != U_1247
    | ~ sP62(U_1246,U_1247) ),
    inference(clausify,[status(thm)],[f_237_3]) ).

cnf(f_237_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_1246) = U_1247
    | U_1247 != c_Groups_Ozero__class_Ozero(U_1246)
    | ~ sP62(U_1246,U_1247) ),
    inference(clausify,[status(thm)],[f_237_3]) ).

fof(f_238_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_238_2,plain,
    ! [U_1250,U_1249,U_1248] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1248),U_1249),U_1250) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1248),U_1250),U_1249)
      | ~ class_Rings_Ocomm__semiring__1(U_1248) ),
    inference(variable_rename,[status(thm)],[f_238_1]) ).

fof(f_238_3,plain,
    ! [U_1249,U_1250,U_1248] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1248),U_1249),U_1250) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1248),U_1250),U_1249)
      | ~ class_Rings_Ocomm__semiring__1(U_1248) ),
    inference(definitional_conversion,[status(esa)],[f_238_2]) ).

cnf(f_238_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1248),U_1249),U_1250) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1248),U_1250),U_1249)
    | ~ class_Rings_Ocomm__semiring__1(U_1248) ),
    inference(clausify,[status(thm)],[f_238_3]) ).

fof(f_239_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_239_2,plain,
    ! [U_1254,U_1253,U_1252,U_1251] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1251),U_1252),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1251),U_1253),U_1254)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1251),U_1253),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1251),U_1252),U_1254))
      | ~ class_Rings_Ocomm__semiring__1(U_1251) ),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

fof(f_239_3,plain,
    ! [U_1251,U_1252,U_1253,U_1254] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1251),U_1252),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1251),U_1253),U_1254)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1251),U_1253),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1251),U_1252),U_1254))
      | ~ class_Rings_Ocomm__semiring__1(U_1251) ),
    inference(definitional_conversion,[status(esa)],[f_239_2]) ).

cnf(f_239_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1251),U_1252),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1251),U_1253),U_1254)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1251),U_1253),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1251),U_1252),U_1254))
    | ~ class_Rings_Ocomm__semiring__1(U_1251) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

fof(f_240_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_240_2,plain,
    ! [U_1258,U_1257,U_1256,U_1255] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1255),U_1256),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1255),U_1257),U_1258)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1255),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1255),U_1256),U_1257)),U_1258)
      | ~ class_Rings_Ocomm__semiring__1(U_1255) ),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

fof(f_240_3,plain,
    ! [U_1255,U_1256,U_1257,U_1258] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1255),U_1256),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1255),U_1257),U_1258)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1255),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1255),U_1256),U_1257)),U_1258)
      | ~ class_Rings_Ocomm__semiring__1(U_1255) ),
    inference(definitional_conversion,[status(esa)],[f_240_2]) ).

cnf(f_240_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1255),U_1256),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1255),U_1257),U_1258)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1255),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1255),U_1256),U_1257)),U_1258)
    | ~ class_Rings_Ocomm__semiring__1(U_1255) ),
    inference(clausify,[status(thm)],[f_240_3]) ).

fof(f_241_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_241_2,plain,
    ! [U_1262,U_1261,U_1260,U_1259] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1259),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1259),U_1260),U_1261)),U_1262) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1259),U_1260),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1259),U_1261),U_1262))
      | ~ class_Rings_Ocomm__semiring__1(U_1259) ),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

fof(f_241_3,plain,
    ! [U_1259,U_1260,U_1261,U_1262] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1259),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1259),U_1260),U_1261)),U_1262) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1259),U_1260),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1259),U_1261),U_1262))
      | ~ class_Rings_Ocomm__semiring__1(U_1259) ),
    inference(definitional_conversion,[status(esa)],[f_241_2]) ).

cnf(f_241_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1259),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1259),U_1260),U_1261)),U_1262) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1259),U_1260),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1259),U_1261),U_1262))
    | ~ class_Rings_Ocomm__semiring__1(U_1259) ),
    inference(clausify,[status(thm)],[f_241_3]) ).

fof(f_242_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_242_2,plain,
    ! [U_1266,U_1265,U_1264,U_1263] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1263),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1263),U_1264),U_1265)),U_1266) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1263),U_1264),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1263),U_1265),U_1266))
      | ~ class_Groups_Oab__semigroup__add(U_1263) ),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

fof(f_242_3,plain,
    ! [U_1263,U_1264,U_1265,U_1266] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1263),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1263),U_1264),U_1265)),U_1266) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1263),U_1264),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1263),U_1265),U_1266))
      | ~ class_Groups_Oab__semigroup__add(U_1263) ),
    inference(definitional_conversion,[status(esa)],[f_242_2]) ).

cnf(f_242_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1263),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1263),U_1264),U_1265)),U_1266) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1263),U_1264),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1263),U_1265),U_1266))
    | ~ class_Groups_Oab__semigroup__add(U_1263) ),
    inference(clausify,[status(thm)],[f_242_3]) ).

fof(f_243_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_243_2,plain,
    ! [U_1270,U_1269,U_1268,U_1267] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1267),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1267),U_1268),U_1269)),U_1270) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1267),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1267),U_1268),U_1270)),U_1269)
      | ~ class_Rings_Ocomm__semiring__1(U_1267) ),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

fof(f_243_3,plain,
    ! [U_1267,U_1268,U_1269,U_1270] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1267),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1267),U_1268),U_1269)),U_1270) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1267),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1267),U_1268),U_1270)),U_1269)
      | ~ class_Rings_Ocomm__semiring__1(U_1267) ),
    inference(definitional_conversion,[status(esa)],[f_243_2]) ).

cnf(f_243_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1267),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1267),U_1268),U_1269)),U_1270) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1267),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1267),U_1268),U_1270)),U_1269)
    | ~ class_Rings_Ocomm__semiring__1(U_1267) ),
    inference(clausify,[status(thm)],[f_243_3]) ).

fof(f_244_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_244_2,plain,
    ! [U_1274,U_1273,U_1272,U_1271] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1271),U_1272),U_1273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1271),U_1272),U_1274)
          | U_1273 != U_1274 )
        & ( U_1273 = U_1274
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1271),U_1272),U_1273) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1271),U_1272),U_1274) ) )
      | ~ class_Groups_Ocancel__semigroup__add(U_1271) ),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

fof(f_244_3,plain,
    ( ! [U_1271,U_1272,U_1273,U_1274] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1271),U_1272),U_1273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1271),U_1272),U_1274)
        | U_1273 != U_1274
        | ~ sP63(U_1271,U_1272,U_1273,U_1274) )
    & ! [U_1271,U_1272,U_1273,U_1274] :
        ( U_1273 = U_1274
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1271),U_1272),U_1273) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1271),U_1272),U_1274)
        | ~ sP63(U_1271,U_1272,U_1273,U_1274) )
    & ! [U_1271,U_1272,U_1273,U_1274] :
        ( sP63(U_1271,U_1272,U_1273,U_1274)
        | ~ class_Groups_Ocancel__semigroup__add(U_1271) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63])],[f_244_2]) ).

cnf(f_244_4,plain,
    ( sP63(U_1271,U_1272,U_1273,U_1274)
    | ~ class_Groups_Ocancel__semigroup__add(U_1271) ),
    inference(clausify,[status(thm)],[f_244_3]) ).

cnf(f_244_5,plain,
    ( U_1273 = U_1274
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1271),U_1272),U_1273) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1271),U_1272),U_1274)
    | ~ sP63(U_1271,U_1272,U_1273,U_1274) ),
    inference(clausify,[status(thm)],[f_244_3]) ).

cnf(f_244_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1271),U_1272),U_1273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1271),U_1272),U_1274)
    | U_1273 != U_1274
    | ~ sP63(U_1271,U_1272,U_1273,U_1274) ),
    inference(clausify,[status(thm)],[f_244_3]) ).

fof(f_245_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_245_2,plain,
    ! [U_1278,U_1277,U_1276,U_1275] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1275),U_1276),U_1277) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1275),U_1278),U_1277)
          | U_1276 != U_1278 )
        & ( U_1276 = U_1278
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1275),U_1276),U_1277) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1275),U_1278),U_1277) ) )
      | ~ class_Groups_Ocancel__semigroup__add(U_1275) ),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

fof(f_245_3,plain,
    ( ! [U_1277,U_1275,U_1276,U_1278] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1275),U_1276),U_1277) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1275),U_1278),U_1277)
        | U_1276 != U_1278
        | ~ sP64(U_1277,U_1275,U_1276,U_1278) )
    & ! [U_1277,U_1275,U_1276,U_1278] :
        ( U_1276 = U_1278
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1275),U_1276),U_1277) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1275),U_1278),U_1277)
        | ~ sP64(U_1277,U_1275,U_1276,U_1278) )
    & ! [U_1277,U_1275,U_1276,U_1278] :
        ( sP64(U_1277,U_1275,U_1276,U_1278)
        | ~ class_Groups_Ocancel__semigroup__add(U_1275) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64])],[f_245_2]) ).

cnf(f_245_4,plain,
    ( sP64(U_1277,U_1275,U_1276,U_1278)
    | ~ class_Groups_Ocancel__semigroup__add(U_1275) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

cnf(f_245_5,plain,
    ( U_1276 = U_1278
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1275),U_1276),U_1277) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1275),U_1278),U_1277)
    | ~ sP64(U_1277,U_1275,U_1276,U_1278) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

cnf(f_245_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1275),U_1276),U_1277) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1275),U_1278),U_1277)
    | U_1276 != U_1278
    | ~ sP64(U_1277,U_1275,U_1276,U_1278) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

fof(f_246_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_246_2,plain,
    ! [U_1283,U_1282,U_1281,U_1280,U_1279] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),U_1280),U_1281)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),U_1282),U_1283)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),U_1280),U_1282)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),U_1281),U_1283))
      | ~ class_Rings_Ocomm__semiring__1(U_1279) ),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

fof(f_246_3,plain,
    ! [U_1280,U_1279,U_1281,U_1282,U_1283] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),U_1280),U_1281)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),U_1282),U_1283)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),U_1280),U_1282)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),U_1281),U_1283))
      | ~ class_Rings_Ocomm__semiring__1(U_1279) ),
    inference(definitional_conversion,[status(esa)],[f_246_2]) ).

cnf(f_246_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),U_1280),U_1281)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),U_1282),U_1283)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),U_1280),U_1282)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1279),U_1281),U_1283))
    | ~ class_Rings_Ocomm__semiring__1(U_1279) ),
    inference(clausify,[status(thm)],[f_246_3]) ).

fof(f_247_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_247_2,plain,
    ! [U_1287,U_1286,U_1285,U_1284] :
      ( U_1286 = U_1287
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1284),U_1285),U_1286) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1284),U_1285),U_1287)
      | ~ class_Groups_Ocancel__semigroup__add(U_1284) ),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

fof(f_247_3,plain,
    ! [U_1285,U_1284,U_1286,U_1287] :
      ( U_1286 = U_1287
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1284),U_1285),U_1286) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1284),U_1285),U_1287)
      | ~ class_Groups_Ocancel__semigroup__add(U_1284) ),
    inference(definitional_conversion,[status(esa)],[f_247_2]) ).

cnf(f_247_4,plain,
    ( U_1286 = U_1287
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1284),U_1285),U_1286) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1284),U_1285),U_1287)
    | ~ class_Groups_Ocancel__semigroup__add(U_1284) ),
    inference(clausify,[status(thm)],[f_247_3]) ).

fof(f_248_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_248_2,plain,
    ! [U_1291,U_1290,U_1289,U_1288] :
      ( U_1290 = U_1291
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1288),U_1289),U_1290) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1288),U_1289),U_1291)
      | ~ class_Groups_Ocancel__ab__semigroup__add(U_1288) ),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

fof(f_248_3,plain,
    ! [U_1288,U_1289,U_1290,U_1291] :
      ( U_1290 = U_1291
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1288),U_1289),U_1290) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1288),U_1289),U_1291)
      | ~ class_Groups_Ocancel__ab__semigroup__add(U_1288) ),
    inference(definitional_conversion,[status(esa)],[f_248_2]) ).

cnf(f_248_4,plain,
    ( U_1290 = U_1291
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1288),U_1289),U_1290) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1288),U_1289),U_1291)
    | ~ class_Groups_Ocancel__ab__semigroup__add(U_1288) ),
    inference(clausify,[status(thm)],[f_248_3]) ).

fof(f_249_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_249_2,plain,
    ! [U_1295,U_1294,U_1293,U_1292] :
      ( U_1293 = U_1295
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1292),U_1293),U_1294) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1292),U_1295),U_1294)
      | ~ class_Groups_Ocancel__semigroup__add(U_1292) ),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

fof(f_249_3,plain,
    ! [U_1292,U_1293,U_1294,U_1295] :
      ( U_1293 = U_1295
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1292),U_1293),U_1294) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1292),U_1295),U_1294)
      | ~ class_Groups_Ocancel__semigroup__add(U_1292) ),
    inference(definitional_conversion,[status(esa)],[f_249_2]) ).

cnf(f_249_4,plain,
    ( U_1293 = U_1295
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1292),U_1293),U_1294) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1292),U_1295),U_1294)
    | ~ class_Groups_Ocancel__semigroup__add(U_1292) ),
    inference(clausify,[status(thm)],[f_249_3]) ).

fof(f_250_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_250_2,plain,
    c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_250_1]) ).

cnf(f_250_3,plain,
    c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_250_2]) ).

fof(f_251_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_251_2,plain,
    c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_251_1]) ).

cnf(f_251_3,plain,
    c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_251_2]) ).

fof(f_252_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_252_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_252_1]) ).

cnf(f_252_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_252_2]) ).

fof(f_253_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_253_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_253_1]) ).

cnf(f_253_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_253_2]) ).

fof(f_254_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_254_2,plain,
    ! [U_1296] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1296)))
      | hAPP(c_Com_Obody,U_1296) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

fof(f_254_3,plain,
    ! [U_1296] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1296)))
      | hAPP(c_Com_Obody,U_1296) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
    inference(definitional_conversion,[status(esa)],[f_254_2]) ).

cnf(f_254_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1296)))
    | hAPP(c_Com_Obody,U_1296) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
    inference(clausify,[status(thm)],[f_254_3]) ).

fof(f_255_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_255_2,plain,
    ! [U_1299] :
      ( ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1299)))
        | ! [U_1298] : hAPP(c_Com_Obody,U_1299) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_1298) )
      & ( ? [U_1297] : hAPP(c_Com_Obody,U_1299) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_1297)
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1299))) ) ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

fof(f_255_3,plain,
    ( ! [U_1301] :
        ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1301)))
        | ! [U_1298] : hAPP(c_Com_Obody,U_1301) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_1298) )
    & ! [U_1300] :
        ( ? [U_1297] : hAPP(c_Com_Obody,U_1300) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_1297)
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1300))) ) ),
    inference(miniscope,[status(thm)],[f_255_2]) ).

fof(f_255_4,plain,
    ( ! [U_1301] :
        ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1301)))
        | ! [U_1298] : hAPP(c_Com_Obody,U_1301) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_1298) )
    & ! [U_1300] :
        ( hAPP(c_Com_Obody,U_1300) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK25(U_1300))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1300))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_1297,sK25(U_1300))],[f_255_3]) ).

fof(f_255_5,plain,
    ( ! [U_1298,U_1301] :
        ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1301)))
        | hAPP(c_Com_Obody,U_1301) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_1298) )
    & ! [U_1300] :
        ( hAPP(c_Com_Obody,U_1300) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK25(U_1300))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1300))) ) ),
    inference(definitional_conversion,[status(esa)],[f_255_4]) ).

cnf(f_255_6,plain,
    ( hAPP(c_Com_Obody,U_1300) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK25(U_1300))
    | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1300))) ),
    inference(clausify,[status(thm)],[f_255_5]) ).

cnf(f_255_7,plain,
    ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1301)))
    | hAPP(c_Com_Obody,U_1301) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_1298) ),
    inference(clausify,[status(thm)],[f_255_5]) ).

fof(f_256_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_256_2,plain,
    ! [U_1306,U_1305,U_1304,U_1303,U_1302] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1306,U_1302,U_1304)),U_1303),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1305),hAPP(c_Natural_Ogetlocs,U_1303))),U_1306),hAPP(hAPP(c_Natural_Ogetlocs,U_1305),c_Com_ORes))))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1302)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1303),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1304,U_1303))),U_1305)) ),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

fof(f_256_3,plain,
    ! [U_1302,U_1303,U_1304,U_1305,U_1306] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1306,U_1302,U_1304)),U_1303),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1305),hAPP(c_Natural_Ogetlocs,U_1303))),U_1306),hAPP(hAPP(c_Natural_Ogetlocs,U_1305),c_Com_ORes))))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1302)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1303),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1304,U_1303))),U_1305)) ),
    inference(definitional_conversion,[status(esa)],[f_256_2]) ).

cnf(f_256_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1306,U_1302,U_1304)),U_1303),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1305),hAPP(c_Natural_Ogetlocs,U_1303))),U_1306),hAPP(hAPP(c_Natural_Ogetlocs,U_1305),c_Com_ORes))))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1302)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1303),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1304,U_1303))),U_1305)) ),
    inference(clausify,[status(thm)],[f_256_3]) ).

fof(f_257_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_257_2,plain,
    ! [U_1312,U_1311,U_1310,U_1309,U_1308,U_1307] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_1312,U_1307,U_1309),U_1308,U_1310,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1311),hAPP(c_Natural_Ogetlocs,U_1308))),U_1312),hAPP(hAPP(c_Natural_Ogetlocs,U_1311),c_Com_ORes)))
      | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1307),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1308),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1309,U_1308)),U_1310,U_1311) ),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

fof(f_257_3,plain,
    ! [U_1308,U_1307,U_1309,U_1310,U_1311,U_1312] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_1312,U_1307,U_1309),U_1308,U_1310,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1311),hAPP(c_Natural_Ogetlocs,U_1308))),U_1312),hAPP(hAPP(c_Natural_Ogetlocs,U_1311),c_Com_ORes)))
      | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1307),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1308),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1309,U_1308)),U_1310,U_1311) ),
    inference(definitional_conversion,[status(esa)],[f_257_2]) ).

cnf(f_257_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_1312,U_1307,U_1309),U_1308,U_1310,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1311),hAPP(c_Natural_Ogetlocs,U_1308))),U_1312),hAPP(hAPP(c_Natural_Ogetlocs,U_1311),c_Com_ORes)))
    | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1307),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1308),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1309,U_1308)),U_1310,U_1311) ),
    inference(clausify,[status(thm)],[f_257_3]) ).

fof(f_258_1,plain,
    ! [V_h_2,V_c_2,T_b,V_f_2] :
      ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_c_2
      | ? [B_n] : hAPP(V_f_2,B_n) != hAPP(c_Nat_Onat_Onat__rec(T_b,V_c_2,V_h_2),B_n) ),
    inference(fof_nnf,[status(thm)],[fact_def__nat__rec__0]) ).

fof(f_258_2,plain,
    ! [U_1317,U_1316,U_1315,U_1314] :
      ( hAPP(U_1314,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1316
      | ? [U_1313] : hAPP(U_1314,U_1313) != hAPP(c_Nat_Onat_Onat__rec(U_1315,U_1316,U_1317),U_1313) ),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

fof(f_258_3,plain,
    ! [U_1317,U_1316,U_1315,U_1314] :
      ( hAPP(U_1314,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1316
      | hAPP(U_1314,sK26(U_1317,U_1316,U_1315,U_1314)) != hAPP(c_Nat_Onat_Onat__rec(U_1315,U_1316,U_1317),sK26(U_1317,U_1316,U_1315,U_1314)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_1313,sK26(U_1317,U_1316,U_1315,U_1314))],[f_258_2]) ).

fof(f_258_4,plain,
    ! [U_1315,U_1317,U_1314,U_1316] :
      ( hAPP(U_1314,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1316
      | hAPP(U_1314,sK26(U_1317,U_1316,U_1315,U_1314)) != hAPP(c_Nat_Onat_Onat__rec(U_1315,U_1316,U_1317),sK26(U_1317,U_1316,U_1315,U_1314)) ),
    inference(definitional_conversion,[status(esa)],[f_258_3]) ).

cnf(f_258_5,plain,
    ( hAPP(U_1314,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1316
    | hAPP(U_1314,sK26(U_1317,U_1316,U_1315,U_1314)) != hAPP(c_Nat_Onat_Onat__rec(U_1315,U_1316,U_1317),sK26(U_1317,U_1316,U_1315,U_1314)) ),
    inference(clausify,[status(thm)],[f_258_4]) ).

fof(f_259_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_259_2,plain,
    ! [U_1324,U_1323,U_1322,U_1321,U_1320] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1320,U_1321,U_1322)),U_1323),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1324),hAPP(c_Natural_Ogetlocs,U_1323))),U_1320),hAPP(hAPP(c_Natural_Ogetlocs,U_1324),c_Com_ORes))))
        | ! [U_1319] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1321)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1323),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1322,U_1323))),U_1319))
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1324),hAPP(c_Natural_Ogetlocs,U_1323))),U_1320),hAPP(hAPP(c_Natural_Ogetlocs,U_1324),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1319),hAPP(c_Natural_Ogetlocs,U_1323))),U_1320),hAPP(hAPP(c_Natural_Ogetlocs,U_1319),c_Com_ORes)) ) )
      & ( ? [U_1318] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1321)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1323),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1322,U_1323))),U_1318))
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1324),hAPP(c_Natural_Ogetlocs,U_1323))),U_1320),hAPP(hAPP(c_Natural_Ogetlocs,U_1324),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1318),hAPP(c_Natural_Ogetlocs,U_1323))),U_1320),hAPP(hAPP(c_Natural_Ogetlocs,U_1318),c_Com_ORes)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1320,U_1321,U_1322)),U_1323),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1324),hAPP(c_Natural_Ogetlocs,U_1323))),U_1320),hAPP(hAPP(c_Natural_Ogetlocs,U_1324),c_Com_ORes)))) ) ),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

fof(f_259_3,plain,
    ( ! [U_1334,U_1332,U_1330,U_1328,U_1326] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1326,U_1328,U_1330)),U_1332),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1334),hAPP(c_Natural_Ogetlocs,U_1332))),U_1326),hAPP(hAPP(c_Natural_Ogetlocs,U_1334),c_Com_ORes))))
        | ! [U_1319] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1328)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1332),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1330,U_1332))),U_1319))
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1334),hAPP(c_Natural_Ogetlocs,U_1332))),U_1326),hAPP(hAPP(c_Natural_Ogetlocs,U_1334),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1319),hAPP(c_Natural_Ogetlocs,U_1332))),U_1326),hAPP(hAPP(c_Natural_Ogetlocs,U_1319),c_Com_ORes)) ) )
    & ! [U_1333,U_1331,U_1329,U_1327,U_1325] :
        ( ? [U_1318] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1327)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1331),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1329,U_1331))),U_1318))
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1333),hAPP(c_Natural_Ogetlocs,U_1331))),U_1325),hAPP(hAPP(c_Natural_Ogetlocs,U_1333),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1318),hAPP(c_Natural_Ogetlocs,U_1331))),U_1325),hAPP(hAPP(c_Natural_Ogetlocs,U_1318),c_Com_ORes)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1325,U_1327,U_1329)),U_1331),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1333),hAPP(c_Natural_Ogetlocs,U_1331))),U_1325),hAPP(hAPP(c_Natural_Ogetlocs,U_1333),c_Com_ORes)))) ) ),
    inference(miniscope,[status(thm)],[f_259_2]) ).

fof(f_259_4,plain,
    ( ! [U_1334,U_1332,U_1330,U_1328,U_1326] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1326,U_1328,U_1330)),U_1332),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1334),hAPP(c_Natural_Ogetlocs,U_1332))),U_1326),hAPP(hAPP(c_Natural_Ogetlocs,U_1334),c_Com_ORes))))
        | ! [U_1319] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1328)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1332),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1330,U_1332))),U_1319))
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1334),hAPP(c_Natural_Ogetlocs,U_1332))),U_1326),hAPP(hAPP(c_Natural_Ogetlocs,U_1334),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1319),hAPP(c_Natural_Ogetlocs,U_1332))),U_1326),hAPP(hAPP(c_Natural_Ogetlocs,U_1319),c_Com_ORes)) ) )
    & ! [U_1333,U_1331,U_1329,U_1327,U_1325] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1327)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1331),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1329,U_1331))),sK27(U_1333,U_1331,U_1329,U_1327,U_1325)))
          & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1333),hAPP(c_Natural_Ogetlocs,U_1331))),U_1325),hAPP(hAPP(c_Natural_Ogetlocs,U_1333),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK27(U_1333,U_1331,U_1329,U_1327,U_1325)),hAPP(c_Natural_Ogetlocs,U_1331))),U_1325),hAPP(hAPP(c_Natural_Ogetlocs,sK27(U_1333,U_1331,U_1329,U_1327,U_1325)),c_Com_ORes)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1325,U_1327,U_1329)),U_1331),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1333),hAPP(c_Natural_Ogetlocs,U_1331))),U_1325),hAPP(hAPP(c_Natural_Ogetlocs,U_1333),c_Com_ORes)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_1318,sK27(U_1333,U_1331,U_1329,U_1327,U_1325))],[f_259_3]) ).

fof(f_259_5,plain,
    ( ! [U_1327,U_1331,U_1325,U_1329,U_1333] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1327)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1331),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1329,U_1331))),sK27(U_1333,U_1331,U_1329,U_1327,U_1325)))
        | ~ sP65(U_1327,U_1331,U_1325,U_1329,U_1333) )
    & ! [U_1327,U_1331,U_1325,U_1329,U_1333] :
        ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1333),hAPP(c_Natural_Ogetlocs,U_1331))),U_1325),hAPP(hAPP(c_Natural_Ogetlocs,U_1333),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK27(U_1333,U_1331,U_1329,U_1327,U_1325)),hAPP(c_Natural_Ogetlocs,U_1331))),U_1325),hAPP(hAPP(c_Natural_Ogetlocs,sK27(U_1333,U_1331,U_1329,U_1327,U_1325)),c_Com_ORes))
        | ~ sP65(U_1327,U_1331,U_1325,U_1329,U_1333) )
    & ! [U_1319,U_1326,U_1328,U_1330,U_1332,U_1334] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1326,U_1328,U_1330)),U_1332),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1334),hAPP(c_Natural_Ogetlocs,U_1332))),U_1326),hAPP(hAPP(c_Natural_Ogetlocs,U_1334),c_Com_ORes))))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1328)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1332),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1330,U_1332))),U_1319))
        | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1334),hAPP(c_Natural_Ogetlocs,U_1332))),U_1326),hAPP(hAPP(c_Natural_Ogetlocs,U_1334),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1319),hAPP(c_Natural_Ogetlocs,U_1332))),U_1326),hAPP(hAPP(c_Natural_Ogetlocs,U_1319),c_Com_ORes)) )
    & ! [U_1327,U_1331,U_1325,U_1329,U_1333] :
        ( sP65(U_1327,U_1331,U_1325,U_1329,U_1333)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1325,U_1327,U_1329)),U_1331),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1333),hAPP(c_Natural_Ogetlocs,U_1331))),U_1325),hAPP(hAPP(c_Natural_Ogetlocs,U_1333),c_Com_ORes)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP65])],[f_259_4]) ).

cnf(f_259_6,plain,
    ( sP65(U_1327,U_1331,U_1325,U_1329,U_1333)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1325,U_1327,U_1329)),U_1331),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1333),hAPP(c_Natural_Ogetlocs,U_1331))),U_1325),hAPP(hAPP(c_Natural_Ogetlocs,U_1333),c_Com_ORes)))) ),
    inference(clausify,[status(thm)],[f_259_5]) ).

cnf(f_259_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1326,U_1328,U_1330)),U_1332),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1334),hAPP(c_Natural_Ogetlocs,U_1332))),U_1326),hAPP(hAPP(c_Natural_Ogetlocs,U_1334),c_Com_ORes))))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1328)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1332),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1330,U_1332))),U_1319))
    | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1334),hAPP(c_Natural_Ogetlocs,U_1332))),U_1326),hAPP(hAPP(c_Natural_Ogetlocs,U_1334),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1319),hAPP(c_Natural_Ogetlocs,U_1332))),U_1326),hAPP(hAPP(c_Natural_Ogetlocs,U_1319),c_Com_ORes)) ),
    inference(clausify,[status(thm)],[f_259_5]) ).

cnf(f_259_8,plain,
    ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1333),hAPP(c_Natural_Ogetlocs,U_1331))),U_1325),hAPP(hAPP(c_Natural_Ogetlocs,U_1333),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK27(U_1333,U_1331,U_1329,U_1327,U_1325)),hAPP(c_Natural_Ogetlocs,U_1331))),U_1325),hAPP(hAPP(c_Natural_Ogetlocs,sK27(U_1333,U_1331,U_1329,U_1327,U_1325)),c_Com_ORes))
    | ~ sP65(U_1327,U_1331,U_1325,U_1329,U_1333) ),
    inference(clausify,[status(thm)],[f_259_5]) ).

cnf(f_259_9,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1327)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1331),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1329,U_1331))),sK27(U_1333,U_1331,U_1329,U_1327,U_1325)))
    | ~ sP65(U_1327,U_1331,U_1325,U_1329,U_1333) ),
    inference(clausify,[status(thm)],[f_259_5]) ).

fof(f_260_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_260_2,plain,
    ! [U_1342,U_1341,U_1340,U_1339,U_1338,U_1337] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_1337,U_1338,U_1339),U_1340,U_1341,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1342),hAPP(c_Natural_Ogetlocs,U_1340))),U_1337),hAPP(hAPP(c_Natural_Ogetlocs,U_1342),c_Com_ORes)))
        | ! [U_1336] :
            ( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1338),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1340),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1339,U_1340)),U_1341,U_1336)
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1342),hAPP(c_Natural_Ogetlocs,U_1340))),U_1337),hAPP(hAPP(c_Natural_Ogetlocs,U_1342),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1336),hAPP(c_Natural_Ogetlocs,U_1340))),U_1337),hAPP(hAPP(c_Natural_Ogetlocs,U_1336),c_Com_ORes)) ) )
      & ( ? [U_1335] :
            ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1338),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1340),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1339,U_1340)),U_1341,U_1335)
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1342),hAPP(c_Natural_Ogetlocs,U_1340))),U_1337),hAPP(hAPP(c_Natural_Ogetlocs,U_1342),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1335),hAPP(c_Natural_Ogetlocs,U_1340))),U_1337),hAPP(hAPP(c_Natural_Ogetlocs,U_1335),c_Com_ORes)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_1337,U_1338,U_1339),U_1340,U_1341,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1342),hAPP(c_Natural_Ogetlocs,U_1340))),U_1337),hAPP(hAPP(c_Natural_Ogetlocs,U_1342),c_Com_ORes))) ) ),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

fof(f_260_3,plain,
    ( ! [U_1354,U_1352,U_1350,U_1348,U_1346,U_1344] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_1344,U_1346,U_1348),U_1350,U_1352,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1354),hAPP(c_Natural_Ogetlocs,U_1350))),U_1344),hAPP(hAPP(c_Natural_Ogetlocs,U_1354),c_Com_ORes)))
        | ! [U_1336] :
            ( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1346),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1350),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1348,U_1350)),U_1352,U_1336)
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1354),hAPP(c_Natural_Ogetlocs,U_1350))),U_1344),hAPP(hAPP(c_Natural_Ogetlocs,U_1354),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1336),hAPP(c_Natural_Ogetlocs,U_1350))),U_1344),hAPP(hAPP(c_Natural_Ogetlocs,U_1336),c_Com_ORes)) ) )
    & ! [U_1353,U_1351,U_1349,U_1347,U_1345,U_1343] :
        ( ? [U_1335] :
            ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1345),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1349),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1347,U_1349)),U_1351,U_1335)
            & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1353),hAPP(c_Natural_Ogetlocs,U_1349))),U_1343),hAPP(hAPP(c_Natural_Ogetlocs,U_1353),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1335),hAPP(c_Natural_Ogetlocs,U_1349))),U_1343),hAPP(hAPP(c_Natural_Ogetlocs,U_1335),c_Com_ORes)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_1343,U_1345,U_1347),U_1349,U_1351,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1353),hAPP(c_Natural_Ogetlocs,U_1349))),U_1343),hAPP(hAPP(c_Natural_Ogetlocs,U_1353),c_Com_ORes))) ) ),
    inference(miniscope,[status(thm)],[f_260_2]) ).

fof(f_260_4,plain,
    ( ! [U_1354,U_1352,U_1350,U_1348,U_1346,U_1344] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_1344,U_1346,U_1348),U_1350,U_1352,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1354),hAPP(c_Natural_Ogetlocs,U_1350))),U_1344),hAPP(hAPP(c_Natural_Ogetlocs,U_1354),c_Com_ORes)))
        | ! [U_1336] :
            ( ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1346),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1350),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1348,U_1350)),U_1352,U_1336)
            | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1354),hAPP(c_Natural_Ogetlocs,U_1350))),U_1344),hAPP(hAPP(c_Natural_Ogetlocs,U_1354),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1336),hAPP(c_Natural_Ogetlocs,U_1350))),U_1344),hAPP(hAPP(c_Natural_Ogetlocs,U_1336),c_Com_ORes)) ) )
    & ! [U_1353,U_1351,U_1349,U_1347,U_1345,U_1343] :
        ( ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1345),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1349),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1347,U_1349)),U_1351,sK28(U_1353,U_1351,U_1349,U_1347,U_1345,U_1343))
          & hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1353),hAPP(c_Natural_Ogetlocs,U_1349))),U_1343),hAPP(hAPP(c_Natural_Ogetlocs,U_1353),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK28(U_1353,U_1351,U_1349,U_1347,U_1345,U_1343)),hAPP(c_Natural_Ogetlocs,U_1349))),U_1343),hAPP(hAPP(c_Natural_Ogetlocs,sK28(U_1353,U_1351,U_1349,U_1347,U_1345,U_1343)),c_Com_ORes)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_1343,U_1345,U_1347),U_1349,U_1351,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1353),hAPP(c_Natural_Ogetlocs,U_1349))),U_1343),hAPP(hAPP(c_Natural_Ogetlocs,U_1353),c_Com_ORes))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_1335,sK28(U_1353,U_1351,U_1349,U_1347,U_1345,U_1343))],[f_260_3]) ).

fof(f_260_5,plain,
    ( ! [U_1345,U_1347,U_1349,U_1343,U_1351,U_1353] :
        ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1345),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1349),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1347,U_1349)),U_1351,sK28(U_1353,U_1351,U_1349,U_1347,U_1345,U_1343))
        | ~ sP66(U_1345,U_1347,U_1349,U_1343,U_1351,U_1353) )
    & ! [U_1345,U_1347,U_1349,U_1343,U_1351,U_1353] :
        ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1353),hAPP(c_Natural_Ogetlocs,U_1349))),U_1343),hAPP(hAPP(c_Natural_Ogetlocs,U_1353),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK28(U_1353,U_1351,U_1349,U_1347,U_1345,U_1343)),hAPP(c_Natural_Ogetlocs,U_1349))),U_1343),hAPP(hAPP(c_Natural_Ogetlocs,sK28(U_1353,U_1351,U_1349,U_1347,U_1345,U_1343)),c_Com_ORes))
        | ~ sP66(U_1345,U_1347,U_1349,U_1343,U_1351,U_1353) )
    & ! [U_1348,U_1336,U_1346,U_1344,U_1350,U_1352,U_1354] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_1344,U_1346,U_1348),U_1350,U_1352,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1354),hAPP(c_Natural_Ogetlocs,U_1350))),U_1344),hAPP(hAPP(c_Natural_Ogetlocs,U_1354),c_Com_ORes)))
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1346),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1350),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1348,U_1350)),U_1352,U_1336)
        | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1354),hAPP(c_Natural_Ogetlocs,U_1350))),U_1344),hAPP(hAPP(c_Natural_Ogetlocs,U_1354),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1336),hAPP(c_Natural_Ogetlocs,U_1350))),U_1344),hAPP(hAPP(c_Natural_Ogetlocs,U_1336),c_Com_ORes)) )
    & ! [U_1345,U_1347,U_1349,U_1343,U_1351,U_1353] :
        ( sP66(U_1345,U_1347,U_1349,U_1343,U_1351,U_1353)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_1343,U_1345,U_1347),U_1349,U_1351,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1353),hAPP(c_Natural_Ogetlocs,U_1349))),U_1343),hAPP(hAPP(c_Natural_Ogetlocs,U_1353),c_Com_ORes))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66])],[f_260_4]) ).

cnf(f_260_6,plain,
    ( sP66(U_1345,U_1347,U_1349,U_1343,U_1351,U_1353)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_1343,U_1345,U_1347),U_1349,U_1351,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1353),hAPP(c_Natural_Ogetlocs,U_1349))),U_1343),hAPP(hAPP(c_Natural_Ogetlocs,U_1353),c_Com_ORes))) ),
    inference(clausify,[status(thm)],[f_260_5]) ).

cnf(f_260_7,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCall(U_1344,U_1346,U_1348),U_1350,U_1352,hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1354),hAPP(c_Natural_Ogetlocs,U_1350))),U_1344),hAPP(hAPP(c_Natural_Ogetlocs,U_1354),c_Com_ORes)))
    | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1346),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1350),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1348,U_1350)),U_1352,U_1336)
    | hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1354),hAPP(c_Natural_Ogetlocs,U_1350))),U_1344),hAPP(hAPP(c_Natural_Ogetlocs,U_1354),c_Com_ORes)) != hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1336),hAPP(c_Natural_Ogetlocs,U_1350))),U_1344),hAPP(hAPP(c_Natural_Ogetlocs,U_1336),c_Com_ORes)) ),
    inference(clausify,[status(thm)],[f_260_5]) ).

cnf(f_260_8,plain,
    ( hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1353),hAPP(c_Natural_Ogetlocs,U_1349))),U_1343),hAPP(hAPP(c_Natural_Ogetlocs,U_1353),c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK28(U_1353,U_1351,U_1349,U_1347,U_1345,U_1343)),hAPP(c_Natural_Ogetlocs,U_1349))),U_1343),hAPP(hAPP(c_Natural_Ogetlocs,sK28(U_1353,U_1351,U_1349,U_1347,U_1345,U_1343)),c_Com_ORes))
    | ~ sP66(U_1345,U_1347,U_1349,U_1343,U_1351,U_1353) ),
    inference(clausify,[status(thm)],[f_260_5]) ).

cnf(f_260_9,plain,
    ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1345),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1349),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1347,U_1349)),U_1351,sK28(U_1353,U_1351,U_1349,U_1347,U_1345,U_1343))
    | ~ sP66(U_1345,U_1347,U_1349,U_1343,U_1351,U_1353) ),
    inference(clausify,[status(thm)],[f_260_5]) ).

fof(f_261_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_261_2,plain,
    ! [U_1360,U_1359,U_1358,U_1357,U_1356] :
      ( ? [U_1355] :
          ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1357)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1359),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1358,U_1359))),U_1355))
          & U_1360 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1355),hAPP(c_Natural_Ogetlocs,U_1359))),U_1356),hAPP(hAPP(c_Natural_Ogetlocs,U_1355),c_Com_ORes)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1356,U_1357,U_1358)),U_1359),U_1360)) ),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

fof(f_261_3,plain,
    ! [U_1360,U_1359,U_1358,U_1357,U_1356] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1357)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1359),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1358,U_1359))),sK29(U_1360,U_1359,U_1358,U_1357,U_1356)))
        & U_1360 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK29(U_1360,U_1359,U_1358,U_1357,U_1356)),hAPP(c_Natural_Ogetlocs,U_1359))),U_1356),hAPP(hAPP(c_Natural_Ogetlocs,sK29(U_1360,U_1359,U_1358,U_1357,U_1356)),c_Com_ORes)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1356,U_1357,U_1358)),U_1359),U_1360)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_1355,sK29(U_1360,U_1359,U_1358,U_1357,U_1356))],[f_261_2]) ).

fof(f_261_4,plain,
    ( ! [U_1358,U_1359,U_1356,U_1357,U_1360] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1357)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1359),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1358,U_1359))),sK29(U_1360,U_1359,U_1358,U_1357,U_1356)))
        | ~ sP67(U_1358,U_1359,U_1356,U_1357,U_1360) )
    & ! [U_1358,U_1359,U_1356,U_1357,U_1360] :
        ( U_1360 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK29(U_1360,U_1359,U_1358,U_1357,U_1356)),hAPP(c_Natural_Ogetlocs,U_1359))),U_1356),hAPP(hAPP(c_Natural_Ogetlocs,sK29(U_1360,U_1359,U_1358,U_1357,U_1356)),c_Com_ORes))
        | ~ sP67(U_1358,U_1359,U_1356,U_1357,U_1360) )
    & ! [U_1358,U_1359,U_1356,U_1357,U_1360] :
        ( sP67(U_1358,U_1359,U_1356,U_1357,U_1360)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1356,U_1357,U_1358)),U_1359),U_1360)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67])],[f_261_3]) ).

cnf(f_261_5,plain,
    ( sP67(U_1358,U_1359,U_1356,U_1357,U_1360)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(U_1356,U_1357,U_1358)),U_1359),U_1360)) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

cnf(f_261_6,plain,
    ( U_1360 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK29(U_1360,U_1359,U_1358,U_1357,U_1356)),hAPP(c_Natural_Ogetlocs,U_1359))),U_1356),hAPP(hAPP(c_Natural_Ogetlocs,sK29(U_1360,U_1359,U_1358,U_1357,U_1356)),c_Com_ORes))
    | ~ sP67(U_1358,U_1359,U_1356,U_1357,U_1360) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

cnf(f_261_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_1357)),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1359),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1358,U_1359))),sK29(U_1360,U_1359,U_1358,U_1357,U_1356)))
    | ~ sP67(U_1358,U_1359,U_1356,U_1357,U_1360) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

fof(f_262_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_262_2,plain,
    ! [U_1367,U_1366,U_1365,U_1364,U_1363,U_1362] :
      ( ? [U_1361] :
          ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1363),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1365),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1364,U_1365)),U_1366,U_1361)
          & U_1367 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1361),hAPP(c_Natural_Ogetlocs,U_1365))),U_1362),hAPP(hAPP(c_Natural_Ogetlocs,U_1361),c_Com_ORes)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_1362,U_1363,U_1364),U_1365,U_1366,U_1367) ),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

fof(f_262_3,plain,
    ! [U_1367,U_1366,U_1365,U_1364,U_1363,U_1362] :
      ( ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1363),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1365),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1364,U_1365)),U_1366,sK30(U_1367,U_1366,U_1365,U_1364,U_1363,U_1362))
        & U_1367 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK30(U_1367,U_1366,U_1365,U_1364,U_1363,U_1362)),hAPP(c_Natural_Ogetlocs,U_1365))),U_1362),hAPP(hAPP(c_Natural_Ogetlocs,sK30(U_1367,U_1366,U_1365,U_1364,U_1363,U_1362)),c_Com_ORes)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_1362,U_1363,U_1364),U_1365,U_1366,U_1367) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_1361,sK30(U_1367,U_1366,U_1365,U_1364,U_1363,U_1362))],[f_262_2]) ).

fof(f_262_4,plain,
    ( ! [U_1362,U_1363,U_1364,U_1365,U_1366,U_1367] :
        ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1363),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1365),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1364,U_1365)),U_1366,sK30(U_1367,U_1366,U_1365,U_1364,U_1363,U_1362))
        | ~ sP68(U_1362,U_1363,U_1364,U_1365,U_1366,U_1367) )
    & ! [U_1362,U_1363,U_1364,U_1365,U_1366,U_1367] :
        ( U_1367 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK30(U_1367,U_1366,U_1365,U_1364,U_1363,U_1362)),hAPP(c_Natural_Ogetlocs,U_1365))),U_1362),hAPP(hAPP(c_Natural_Ogetlocs,sK30(U_1367,U_1366,U_1365,U_1364,U_1363,U_1362)),c_Com_ORes))
        | ~ sP68(U_1362,U_1363,U_1364,U_1365,U_1366,U_1367) )
    & ! [U_1362,U_1363,U_1364,U_1365,U_1366,U_1367] :
        ( sP68(U_1362,U_1363,U_1364,U_1365,U_1366,U_1367)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_1362,U_1363,U_1364),U_1365,U_1366,U_1367) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP68])],[f_262_3]) ).

cnf(f_262_5,plain,
    ( sP68(U_1362,U_1363,U_1364,U_1365,U_1366,U_1367)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCall(U_1362,U_1363,U_1364),U_1365,U_1366,U_1367) ),
    inference(clausify,[status(thm)],[f_262_4]) ).

cnf(f_262_6,plain,
    ( U_1367 = hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,sK30(U_1367,U_1366,U_1365,U_1364,U_1363,U_1362)),hAPP(c_Natural_Ogetlocs,U_1365))),U_1362),hAPP(hAPP(c_Natural_Ogetlocs,sK30(U_1367,U_1366,U_1365,U_1364,U_1363,U_1362)),c_Com_ORes))
    | ~ sP68(U_1362,U_1363,U_1364,U_1365,U_1366,U_1367) ),
    inference(clausify,[status(thm)],[f_262_4]) ).

cnf(f_262_7,plain,
    ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_1363),hAPP(hAPP(hAPP(c_Natural_Oupdate,hAPP(hAPP(c_Natural_Osetlocs,U_1365),c_Natural_Onewlocs)),c_Com_Ovname_OLoc(c_Com_OArg)),hAPP(U_1364,U_1365)),U_1366,sK30(U_1367,U_1366,U_1365,U_1364,U_1363,U_1362))
    | ~ sP68(U_1362,U_1363,U_1364,U_1365,U_1366,U_1367) ),
    inference(clausify,[status(thm)],[f_262_4]) ).

fof(f_263_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_263_2,plain,
    ! [U_1369,U_1368] :
      ( hBOOL(hAPP(c_Com_OWT,U_1369))
      | hAPP(c_Com_Obody,U_1368) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_1369)
      | ~ c_Com_OWT__bodies ),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

fof(f_263_3,plain,
    ( ! [U_1369] :
        ( ! [U_1368] : hAPP(c_Com_Obody,U_1368) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_1369)
        | hBOOL(hAPP(c_Com_OWT,U_1369)) )
    | ~ c_Com_OWT__bodies ),
    inference(miniscope,[status(thm)],[f_263_2]) ).

fof(f_263_4,plain,
    ! [U_1369,U_1368] :
      ( hAPP(c_Com_Obody,U_1368) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_1369)
      | hBOOL(hAPP(c_Com_OWT,U_1369))
      | ~ c_Com_OWT__bodies ),
    inference(definitional_conversion,[status(esa)],[f_263_3]) ).

cnf(f_263_5,plain,
    ( hAPP(c_Com_Obody,U_1368) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_1369)
    | hBOOL(hAPP(c_Com_OWT,U_1369))
    | ~ c_Com_OWT__bodies ),
    inference(clausify,[status(thm)],[f_263_4]) ).

fof(f_264_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_264_2,plain,
    ! [U_1372,U_1371,U_1370] : c_Option_Ooption_Ooption__size(U_1370,U_1371,hAPP(c_Option_Ooption_OSome(U_1370),U_1372)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_1371,U_1372)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

fof(f_264_3,plain,
    ! [U_1371,U_1370,U_1372] : c_Option_Ooption_Ooption__size(U_1370,U_1371,hAPP(c_Option_Ooption_OSome(U_1370),U_1372)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_1371,U_1372)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_264_2]) ).

cnf(f_264_4,plain,
    c_Option_Ooption_Ooption__size(U_1370,U_1371,hAPP(c_Option_Ooption_OSome(U_1370),U_1372)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_1371,U_1372)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_264_3]) ).

fof(f_265_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_265_2,plain,
    ! [U_1374,U_1373] : c_Option_Ooption_Ooption__size(U_1373,U_1374,c_Option_Ooption_ONone(U_1373)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

fof(f_265_3,plain,
    ! [U_1373,U_1374] : c_Option_Ooption_Ooption__size(U_1373,U_1374,c_Option_Ooption_ONone(U_1373)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_265_2]) ).

cnf(f_265_4,plain,
    c_Option_Ooption_Ooption__size(U_1373,U_1374,c_Option_Ooption_ONone(U_1373)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_265_3]) ).

fof(f_266_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_266_2,plain,
    ! [U_1376] :
      ( ? [U_1375] : hAPP(c_Com_Obody,U_1376) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_1375)
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1376))) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

fof(f_266_3,plain,
    ! [U_1376] :
      ( hAPP(c_Com_Obody,U_1376) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK31(U_1376))
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1376))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_1375,sK31(U_1376))],[f_266_2]) ).

fof(f_266_4,plain,
    ! [U_1376] :
      ( hAPP(c_Com_Obody,U_1376) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK31(U_1376))
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1376))) ),
    inference(definitional_conversion,[status(esa)],[f_266_3]) ).

cnf(f_266_5,plain,
    ( hAPP(c_Com_Obody,U_1376) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK31(U_1376))
    | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_1376))) ),
    inference(clausify,[status(thm)],[f_266_4]) ).

fof(f_267_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_267_2,plain,
    ! [U_1378,U_1377] : hAPP(c_Option_Othe(U_1377),hAPP(c_Option_Ooption_OSome(U_1377),U_1378)) = U_1378,
    inference(variable_rename,[status(thm)],[f_267_1]) ).

fof(f_267_3,plain,
    ! [U_1377,U_1378] : hAPP(c_Option_Othe(U_1377),hAPP(c_Option_Ooption_OSome(U_1377),U_1378)) = U_1378,
    inference(definitional_conversion,[status(esa)],[f_267_2]) ).

cnf(f_267_4,plain,
    hAPP(c_Option_Othe(U_1377),hAPP(c_Option_Ooption_OSome(U_1377),U_1378)) = U_1378,
    inference(clausify,[status(thm)],[f_267_3]) ).

fof(f_268_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_268_2,plain,
    ! [U_1382,U_1381] :
      ( ( U_1381 != c_Option_Ooption_ONone(U_1382)
        | ! [U_1380] : U_1381 != hAPP(c_Option_Ooption_OSome(U_1382),U_1380) )
      & ( ? [U_1379] : U_1381 = hAPP(c_Option_Ooption_OSome(U_1382),U_1379)
        | U_1381 = c_Option_Ooption_ONone(U_1382) ) ),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

fof(f_268_3,plain,
    ( ! [U_1386,U_1384] :
        ( U_1384 != c_Option_Ooption_ONone(U_1386)
        | ! [U_1380] : U_1384 != hAPP(c_Option_Ooption_OSome(U_1386),U_1380) )
    & ! [U_1385,U_1383] :
        ( ? [U_1379] : U_1383 = hAPP(c_Option_Ooption_OSome(U_1385),U_1379)
        | U_1383 = c_Option_Ooption_ONone(U_1385) ) ),
    inference(miniscope,[status(thm)],[f_268_2]) ).

fof(f_268_4,plain,
    ( ! [U_1386,U_1384] :
        ( U_1384 != c_Option_Ooption_ONone(U_1386)
        | ! [U_1380] : U_1384 != hAPP(c_Option_Ooption_OSome(U_1386),U_1380) )
    & ! [U_1385,U_1383] :
        ( U_1383 = hAPP(c_Option_Ooption_OSome(U_1385),sK32(U_1385,U_1383))
        | U_1383 = c_Option_Ooption_ONone(U_1385) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_1379,sK32(U_1385,U_1383))],[f_268_3]) ).

fof(f_268_5,plain,
    ( ! [U_1380,U_1384,U_1386] :
        ( U_1384 != c_Option_Ooption_ONone(U_1386)
        | U_1384 != hAPP(c_Option_Ooption_OSome(U_1386),U_1380) )
    & ! [U_1383,U_1385] :
        ( U_1383 = hAPP(c_Option_Ooption_OSome(U_1385),sK32(U_1385,U_1383))
        | U_1383 = c_Option_Ooption_ONone(U_1385) ) ),
    inference(definitional_conversion,[status(esa)],[f_268_4]) ).

cnf(f_268_6,plain,
    ( U_1383 = hAPP(c_Option_Ooption_OSome(U_1385),sK32(U_1385,U_1383))
    | U_1383 = c_Option_Ooption_ONone(U_1385) ),
    inference(clausify,[status(thm)],[f_268_5]) ).

cnf(f_268_7,plain,
    ( U_1384 != c_Option_Ooption_ONone(U_1386)
    | U_1384 != hAPP(c_Option_Ooption_OSome(U_1386),U_1380) ),
    inference(clausify,[status(thm)],[f_268_5]) ).

fof(f_269_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_269_2,plain,
    ! [U_1390,U_1389] :
      ( ( ! [U_1388] : U_1389 != hAPP(c_Option_Ooption_OSome(U_1390),U_1388)
        | U_1389 != c_Option_Ooption_ONone(U_1390) )
      & ( U_1389 = c_Option_Ooption_ONone(U_1390)
        | ? [U_1387] : U_1389 = hAPP(c_Option_Ooption_OSome(U_1390),U_1387) ) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

fof(f_269_3,plain,
    ( ! [U_1394,U_1392] :
        ( ! [U_1388] : U_1392 != hAPP(c_Option_Ooption_OSome(U_1394),U_1388)
        | U_1392 != c_Option_Ooption_ONone(U_1394) )
    & ! [U_1393,U_1391] :
        ( U_1391 = c_Option_Ooption_ONone(U_1393)
        | ? [U_1387] : U_1391 = hAPP(c_Option_Ooption_OSome(U_1393),U_1387) ) ),
    inference(miniscope,[status(thm)],[f_269_2]) ).

fof(f_269_4,plain,
    ( ! [U_1394,U_1392] :
        ( ! [U_1388] : U_1392 != hAPP(c_Option_Ooption_OSome(U_1394),U_1388)
        | U_1392 != c_Option_Ooption_ONone(U_1394) )
    & ! [U_1393,U_1391] :
        ( U_1391 = c_Option_Ooption_ONone(U_1393)
        | U_1391 = hAPP(c_Option_Ooption_OSome(U_1393),sK33(U_1393,U_1391)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_1387,sK33(U_1393,U_1391))],[f_269_3]) ).

fof(f_269_5,plain,
    ( ! [U_1388,U_1392,U_1394] :
        ( U_1392 != hAPP(c_Option_Ooption_OSome(U_1394),U_1388)
        | U_1392 != c_Option_Ooption_ONone(U_1394) )
    & ! [U_1391,U_1393] :
        ( U_1391 = c_Option_Ooption_ONone(U_1393)
        | U_1391 = hAPP(c_Option_Ooption_OSome(U_1393),sK33(U_1393,U_1391)) ) ),
    inference(definitional_conversion,[status(esa)],[f_269_4]) ).

cnf(f_269_6,plain,
    ( U_1391 = c_Option_Ooption_ONone(U_1393)
    | U_1391 = hAPP(c_Option_Ooption_OSome(U_1393),sK33(U_1393,U_1391)) ),
    inference(clausify,[status(thm)],[f_269_5]) ).

cnf(f_269_7,plain,
    ( U_1392 != hAPP(c_Option_Ooption_OSome(U_1394),U_1388)
    | U_1392 != c_Option_Ooption_ONone(U_1394) ),
    inference(clausify,[status(thm)],[f_269_5]) ).

fof(f_270_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_270_2,plain,
    ! [U_1396,U_1395] : hAPP(c_Option_Ooption_OSome(U_1395),U_1396) != c_Option_Ooption_ONone(U_1395),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

fof(f_270_3,plain,
    ! [U_1395,U_1396] : hAPP(c_Option_Ooption_OSome(U_1395),U_1396) != c_Option_Ooption_ONone(U_1395),
    inference(definitional_conversion,[status(esa)],[f_270_2]) ).

cnf(f_270_4,plain,
    hAPP(c_Option_Ooption_OSome(U_1395),U_1396) != c_Option_Ooption_ONone(U_1395),
    inference(clausify,[status(thm)],[f_270_3]) ).

fof(f_271_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_271_2,plain,
    ! [U_1398,U_1397] : c_Option_Ooption_ONone(U_1397) != hAPP(c_Option_Ooption_OSome(U_1397),U_1398),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

fof(f_271_3,plain,
    ! [U_1397,U_1398] : c_Option_Ooption_ONone(U_1397) != hAPP(c_Option_Ooption_OSome(U_1397),U_1398),
    inference(definitional_conversion,[status(esa)],[f_271_2]) ).

cnf(f_271_4,plain,
    c_Option_Ooption_ONone(U_1397) != hAPP(c_Option_Ooption_OSome(U_1397),U_1398),
    inference(clausify,[status(thm)],[f_271_3]) ).

fof(f_272_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_272_2,plain,
    ! [U_1401,U_1400,U_1399] :
      ( ( hAPP(c_Option_Ooption_OSome(U_1399),U_1400) = hAPP(c_Option_Ooption_OSome(U_1399),U_1401)
        | U_1400 != U_1401 )
      & ( U_1400 = U_1401
        | hAPP(c_Option_Ooption_OSome(U_1399),U_1400) != hAPP(c_Option_Ooption_OSome(U_1399),U_1401) ) ),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

fof(f_272_3,plain,
    ( ! [U_1407,U_1405] :
        ( ! [U_1403] : hAPP(c_Option_Ooption_OSome(U_1403),U_1405) = hAPP(c_Option_Ooption_OSome(U_1403),U_1407)
        | U_1405 != U_1407 )
    & ! [U_1406,U_1404] :
        ( ! [U_1402] : hAPP(c_Option_Ooption_OSome(U_1402),U_1404) != hAPP(c_Option_Ooption_OSome(U_1402),U_1406)
        | U_1404 = U_1406 ) ),
    inference(miniscope,[status(thm)],[f_272_2]) ).

fof(f_272_4,plain,
    ( ! [U_1407,U_1403,U_1405] :
        ( hAPP(c_Option_Ooption_OSome(U_1403),U_1405) = hAPP(c_Option_Ooption_OSome(U_1403),U_1407)
        | U_1405 != U_1407 )
    & ! [U_1406,U_1404,U_1402] :
        ( hAPP(c_Option_Ooption_OSome(U_1402),U_1404) != hAPP(c_Option_Ooption_OSome(U_1402),U_1406)
        | U_1404 = U_1406 ) ),
    inference(definitional_conversion,[status(esa)],[f_272_3]) ).

cnf(f_272_5,plain,
    ( hAPP(c_Option_Ooption_OSome(U_1402),U_1404) != hAPP(c_Option_Ooption_OSome(U_1402),U_1406)
    | U_1404 = U_1406 ),
    inference(clausify,[status(thm)],[f_272_4]) ).

cnf(f_272_6,plain,
    ( hAPP(c_Option_Ooption_OSome(U_1403),U_1405) = hAPP(c_Option_Ooption_OSome(U_1403),U_1407)
    | U_1405 != U_1407 ),
    inference(clausify,[status(thm)],[f_272_4]) ).

fof(f_273_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_273_2,plain,
    ! [U_1409,U_1408] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_1408)),hAPP(c_Option_Ooption_OSome(U_1408),U_1409)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

fof(f_273_3,plain,
    ! [U_1408,U_1409] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_1408)),hAPP(c_Option_Ooption_OSome(U_1408),U_1409)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_273_2]) ).

cnf(f_273_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_1408)),hAPP(c_Option_Ooption_OSome(U_1408),U_1409)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_273_3]) ).

fof(f_274_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_274_2,plain,
    ! [U_1410] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_1410)),c_Option_Ooption_ONone(U_1410)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

fof(f_274_3,plain,
    ! [U_1410] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_1410)),c_Option_Ooption_ONone(U_1410)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_274_2]) ).

cnf(f_274_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_1410)),c_Option_Ooption_ONone(U_1410)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_274_3]) ).

fof(f_275_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_275_2,plain,
    ! [U_1415,U_1414,U_1413,U_1412,U_1411] : c_Option_Ooption_Ooption__rec(U_1411,U_1412,U_1413,U_1414,hAPP(c_Option_Ooption_OSome(U_1412),U_1415)) = hAPP(U_1414,U_1415),
    inference(variable_rename,[status(thm)],[f_275_1]) ).

fof(f_275_3,plain,
    ! [U_1411,U_1412,U_1413,U_1414,U_1415] : c_Option_Ooption_Ooption__rec(U_1411,U_1412,U_1413,U_1414,hAPP(c_Option_Ooption_OSome(U_1412),U_1415)) = hAPP(U_1414,U_1415),
    inference(definitional_conversion,[status(esa)],[f_275_2]) ).

cnf(f_275_4,plain,
    c_Option_Ooption_Ooption__rec(U_1411,U_1412,U_1413,U_1414,hAPP(c_Option_Ooption_OSome(U_1412),U_1415)) = hAPP(U_1414,U_1415),
    inference(clausify,[status(thm)],[f_275_3]) ).

fof(f_276_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_276_2,plain,
    ! [U_1420,U_1419,U_1418,U_1417,U_1416] : hAPP(c_Option_Ooption_Ooption__case(U_1416,U_1417,U_1418,U_1419),hAPP(c_Option_Ooption_OSome(U_1417),U_1420)) = hAPP(U_1419,U_1420),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

fof(f_276_3,plain,
    ! [U_1417,U_1416,U_1418,U_1419,U_1420] : hAPP(c_Option_Ooption_Ooption__case(U_1416,U_1417,U_1418,U_1419),hAPP(c_Option_Ooption_OSome(U_1417),U_1420)) = hAPP(U_1419,U_1420),
    inference(definitional_conversion,[status(esa)],[f_276_2]) ).

cnf(f_276_4,plain,
    hAPP(c_Option_Ooption_Ooption__case(U_1416,U_1417,U_1418,U_1419),hAPP(c_Option_Ooption_OSome(U_1417),U_1420)) = hAPP(U_1419,U_1420),
    inference(clausify,[status(thm)],[f_276_3]) ).

fof(f_277_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_277_2,plain,
    ! [U_1424,U_1423,U_1422,U_1421] : c_Option_Ooption_Ooption__rec(U_1421,U_1422,U_1423,U_1424,c_Option_Ooption_ONone(U_1422)) = U_1423,
    inference(variable_rename,[status(thm)],[f_277_1]) ).

fof(f_277_3,plain,
    ! [U_1421,U_1422,U_1423,U_1424] : c_Option_Ooption_Ooption__rec(U_1421,U_1422,U_1423,U_1424,c_Option_Ooption_ONone(U_1422)) = U_1423,
    inference(definitional_conversion,[status(esa)],[f_277_2]) ).

cnf(f_277_4,plain,
    c_Option_Ooption_Ooption__rec(U_1421,U_1422,U_1423,U_1424,c_Option_Ooption_ONone(U_1422)) = U_1423,
    inference(clausify,[status(thm)],[f_277_3]) ).

fof(f_278_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_278_2,plain,
    ! [U_1428,U_1427,U_1426,U_1425] : hAPP(c_Option_Ooption_Ooption__case(U_1425,U_1426,U_1427,U_1428),c_Option_Ooption_ONone(U_1426)) = U_1427,
    inference(variable_rename,[status(thm)],[f_278_1]) ).

fof(f_278_3,plain,
    ! [U_1425,U_1426,U_1427,U_1428] : hAPP(c_Option_Ooption_Ooption__case(U_1425,U_1426,U_1427,U_1428),c_Option_Ooption_ONone(U_1426)) = U_1427,
    inference(definitional_conversion,[status(esa)],[f_278_2]) ).

cnf(f_278_4,plain,
    hAPP(c_Option_Ooption_Ooption__case(U_1425,U_1426,U_1427,U_1428),c_Option_Ooption_ONone(U_1426)) = U_1427,
    inference(clausify,[status(thm)],[f_278_3]) ).

fof(f_279_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_279_2,plain,
    ! [U_1430,U_1429] : ~ c_Option_Ois__none(U_1429,hAPP(c_Option_Ooption_OSome(U_1429),U_1430)),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

fof(f_279_3,plain,
    ! [U_1429,U_1430] : ~ c_Option_Ois__none(U_1429,hAPP(c_Option_Ooption_OSome(U_1429),U_1430)),
    inference(definitional_conversion,[status(esa)],[f_279_2]) ).

cnf(f_279_4,plain,
    ~ c_Option_Ois__none(U_1429,hAPP(c_Option_Ooption_OSome(U_1429),U_1430)),
    inference(clausify,[status(thm)],[f_279_3]) ).

fof(f_280_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_280_2,plain,
    ! [U_1431] : c_Option_Ois__none(U_1431,c_Option_Ooption_ONone(U_1431)),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

fof(f_280_3,plain,
    ! [U_1431] : c_Option_Ois__none(U_1431,c_Option_Ooption_ONone(U_1431)),
    inference(definitional_conversion,[status(esa)],[f_280_2]) ).

cnf(f_280_4,plain,
    c_Option_Ois__none(U_1431,c_Option_Ooption_ONone(U_1431)),
    inference(clausify,[status(thm)],[f_280_3]) ).

fof(f_281_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_281_2,plain,
    ! [U_1433,U_1432] :
      ( ( c_Option_Ois__none(U_1432,U_1433)
        | U_1433 != c_Option_Ooption_ONone(U_1432) )
      & ( U_1433 = c_Option_Ooption_ONone(U_1432)
        | ~ c_Option_Ois__none(U_1432,U_1433) ) ),
    inference(variable_rename,[status(thm)],[f_281_1]) ).

fof(f_281_3,plain,
    ( ! [U_1437,U_1435] :
        ( c_Option_Ois__none(U_1435,U_1437)
        | U_1437 != c_Option_Ooption_ONone(U_1435) )
    & ! [U_1436,U_1434] :
        ( U_1436 = c_Option_Ooption_ONone(U_1434)
        | ~ c_Option_Ois__none(U_1434,U_1436) ) ),
    inference(miniscope,[status(thm)],[f_281_2]) ).

fof(f_281_4,plain,
    ( ! [U_1435,U_1437] :
        ( c_Option_Ois__none(U_1435,U_1437)
        | U_1437 != c_Option_Ooption_ONone(U_1435) )
    & ! [U_1436,U_1434] :
        ( U_1436 = c_Option_Ooption_ONone(U_1434)
        | ~ c_Option_Ois__none(U_1434,U_1436) ) ),
    inference(definitional_conversion,[status(esa)],[f_281_3]) ).

cnf(f_281_5,plain,
    ( U_1436 = c_Option_Ooption_ONone(U_1434)
    | ~ c_Option_Ois__none(U_1434,U_1436) ),
    inference(clausify,[status(thm)],[f_281_4]) ).

cnf(f_281_6,plain,
    ( c_Option_Ois__none(U_1435,U_1437)
    | U_1437 != c_Option_Ooption_ONone(U_1435) ),
    inference(clausify,[status(thm)],[f_281_4]) ).

fof(f_282_1,plain,
    ! [V_t_2,V_s_2,V_c_2,V_b_2] :
      ( ( ? [B_s1] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),B_s1),V_t_2))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),B_s1)) )
        & hBOOL(hAPP(V_b_2,V_s_2)) )
      | ( ~ hBOOL(hAPP(V_b_2,V_s_2))
        & V_t_2 = V_s_2 )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_t_2)) ),
    inference(fof_nnf,[status(thm)],[fact_evalc__WHILE__case]) ).

fof(f_282_2,plain,
    ! [U_1442,U_1441,U_1440,U_1439] :
      ( ( ? [U_1438] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1439,U_1440)),U_1438),U_1442))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1440),U_1441),U_1438)) )
        & hBOOL(hAPP(U_1439,U_1441)) )
      | ( ~ hBOOL(hAPP(U_1439,U_1441))
        & U_1442 = U_1441 )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1439,U_1440)),U_1441),U_1442)) ),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

fof(f_282_3,plain,
    ! [U_1442,U_1441,U_1440,U_1439] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1439,U_1440)),sK34(U_1442,U_1441,U_1440,U_1439)),U_1442))
        & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1440),U_1441),sK34(U_1442,U_1441,U_1440,U_1439)))
        & hBOOL(hAPP(U_1439,U_1441)) )
      | ( ~ hBOOL(hAPP(U_1439,U_1441))
        & U_1442 = U_1441 )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1439,U_1440)),U_1441),U_1442)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_1438,sK34(U_1442,U_1441,U_1440,U_1439))],[f_282_2]) ).

fof(f_282_4,plain,
    ( ! [U_1439,U_1440,U_1441,U_1442] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1439,U_1440)),sK34(U_1442,U_1441,U_1440,U_1439)),U_1442))
        | ~ sP70(U_1439,U_1440,U_1441,U_1442) )
    & ! [U_1439,U_1440,U_1441,U_1442] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1440),U_1441),sK34(U_1442,U_1441,U_1440,U_1439)))
        | ~ sP70(U_1439,U_1440,U_1441,U_1442) )
    & ! [U_1439,U_1440,U_1441,U_1442] :
        ( hBOOL(hAPP(U_1439,U_1441))
        | ~ sP70(U_1439,U_1440,U_1441,U_1442) )
    & ! [U_1439,U_1441,U_1442] :
        ( ~ hBOOL(hAPP(U_1439,U_1441))
        | ~ sP69(U_1439,U_1441,U_1442) )
    & ! [U_1439,U_1441,U_1442] :
        ( U_1442 = U_1441
        | ~ sP69(U_1439,U_1441,U_1442) )
    & ! [U_1439,U_1440,U_1441,U_1442] :
        ( sP70(U_1439,U_1440,U_1441,U_1442)
        | sP69(U_1439,U_1441,U_1442)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1439,U_1440)),U_1441),U_1442)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP69,sP70])],[f_282_3]) ).

cnf(f_282_5,plain,
    ( sP70(U_1439,U_1440,U_1441,U_1442)
    | sP69(U_1439,U_1441,U_1442)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1439,U_1440)),U_1441),U_1442)) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

cnf(f_282_6,plain,
    ( U_1442 = U_1441
    | ~ sP69(U_1439,U_1441,U_1442) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

cnf(f_282_7,plain,
    ( ~ hBOOL(hAPP(U_1439,U_1441))
    | ~ sP69(U_1439,U_1441,U_1442) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

cnf(f_282_8,plain,
    ( hBOOL(hAPP(U_1439,U_1441))
    | ~ sP70(U_1439,U_1440,U_1441,U_1442) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

cnf(f_282_9,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1440),U_1441),sK34(U_1442,U_1441,U_1440,U_1439)))
    | ~ sP70(U_1439,U_1440,U_1441,U_1442) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

cnf(f_282_10,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_1439,U_1440)),sK34(U_1442,U_1441,U_1440,U_1439)),U_1442))
    | ~ sP70(U_1439,U_1440,U_1441,U_1442) ),
    inference(clausify,[status(thm)],[f_282_4]) ).

fof(f_283_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_283_2,plain,
    ! [U_1448,U_1447,U_1446,U_1445,U_1444,U_1443] : c_Nitpick_Opair__box_Opair__box__size(U_1443,U_1444,U_1445,U_1446,c_Nitpick_Opair__box_OPairBox(U_1443,U_1444,U_1447,U_1448)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_1445,U_1447)),hAPP(U_1446,U_1448))),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_1447,U_1446,U_1445,U_1443,U_1444,U_1448] : c_Nitpick_Opair__box_Opair__box__size(U_1443,U_1444,U_1445,U_1446,c_Nitpick_Opair__box_OPairBox(U_1443,U_1444,U_1447,U_1448)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_1445,U_1447)),hAPP(U_1446,U_1448))),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,
    c_Nitpick_Opair__box_Opair__box__size(U_1443,U_1444,U_1445,U_1446,c_Nitpick_Opair__box_OPairBox(U_1443,U_1444,U_1447,U_1448)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_1445,U_1447)),hAPP(U_1446,U_1448))),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_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_284_2,plain,
    ! [U_1454,U_1453,U_1452,U_1451,U_1450,U_1449] :
      ( ( c_Nitpick_Opair__box_OPairBox(U_1449,U_1450,U_1451,U_1452) = c_Nitpick_Opair__box_OPairBox(U_1449,U_1450,U_1453,U_1454)
        | U_1452 != U_1454
        | U_1451 != U_1453 )
      & ( ( U_1452 = U_1454
          & U_1451 = U_1453 )
        | c_Nitpick_Opair__box_OPairBox(U_1449,U_1450,U_1451,U_1452) != c_Nitpick_Opair__box_OPairBox(U_1449,U_1450,U_1453,U_1454) ) ),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

fof(f_284_3,plain,
    ( ! [U_1466,U_1464,U_1462,U_1460] :
        ( ! [U_1458,U_1456] : c_Nitpick_Opair__box_OPairBox(U_1456,U_1458,U_1460,U_1462) = c_Nitpick_Opair__box_OPairBox(U_1456,U_1458,U_1464,U_1466)
        | U_1462 != U_1466
        | U_1460 != U_1464 )
    & ! [U_1465,U_1463,U_1461,U_1459] :
        ( ! [U_1457,U_1455] : c_Nitpick_Opair__box_OPairBox(U_1455,U_1457,U_1459,U_1461) != c_Nitpick_Opair__box_OPairBox(U_1455,U_1457,U_1463,U_1465)
        | ( U_1461 = U_1465
          & U_1459 = U_1463 ) ) ),
    inference(miniscope,[status(thm)],[f_284_2]) ).

fof(f_284_4,plain,
    ( ! [U_1463,U_1459,U_1465,U_1461] :
        ( U_1461 = U_1465
        | ~ sP71(U_1463,U_1459,U_1465,U_1461) )
    & ! [U_1463,U_1459,U_1465,U_1461] :
        ( U_1459 = U_1463
        | ~ sP71(U_1463,U_1459,U_1465,U_1461) )
    & ! [U_1462,U_1466,U_1464,U_1456,U_1460,U_1458] :
        ( c_Nitpick_Opair__box_OPairBox(U_1456,U_1458,U_1460,U_1462) = c_Nitpick_Opair__box_OPairBox(U_1456,U_1458,U_1464,U_1466)
        | U_1462 != U_1466
        | U_1460 != U_1464 )
    & ! [U_1463,U_1459,U_1465,U_1455,U_1457,U_1461] :
        ( c_Nitpick_Opair__box_OPairBox(U_1455,U_1457,U_1459,U_1461) != c_Nitpick_Opair__box_OPairBox(U_1455,U_1457,U_1463,U_1465)
        | sP71(U_1463,U_1459,U_1465,U_1461) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71])],[f_284_3]) ).

cnf(f_284_5,plain,
    ( c_Nitpick_Opair__box_OPairBox(U_1455,U_1457,U_1459,U_1461) != c_Nitpick_Opair__box_OPairBox(U_1455,U_1457,U_1463,U_1465)
    | sP71(U_1463,U_1459,U_1465,U_1461) ),
    inference(clausify,[status(thm)],[f_284_4]) ).

cnf(f_284_6,plain,
    ( c_Nitpick_Opair__box_OPairBox(U_1456,U_1458,U_1460,U_1462) = c_Nitpick_Opair__box_OPairBox(U_1456,U_1458,U_1464,U_1466)
    | U_1462 != U_1466
    | U_1460 != U_1464 ),
    inference(clausify,[status(thm)],[f_284_4]) ).

cnf(f_284_7,plain,
    ( U_1459 = U_1463
    | ~ sP71(U_1463,U_1459,U_1465,U_1461) ),
    inference(clausify,[status(thm)],[f_284_4]) ).

cnf(f_284_8,plain,
    ( U_1461 = U_1465
    | ~ sP71(U_1463,U_1459,U_1465,U_1461) ),
    inference(clausify,[status(thm)],[f_284_4]) ).

fof(f_285_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_285_2,plain,
    ! [U_1470,U_1469,U_1468,U_1467] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_1467,U_1468)),c_Nitpick_Opair__box_OPairBox(U_1467,U_1468,U_1469,U_1470)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

fof(f_285_3,plain,
    ! [U_1468,U_1467,U_1469,U_1470] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_1467,U_1468)),c_Nitpick_Opair__box_OPairBox(U_1467,U_1468,U_1469,U_1470)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_285_2]) ).

cnf(f_285_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_1467,U_1468)),c_Nitpick_Opair__box_OPairBox(U_1467,U_1468,U_1469,U_1470)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_285_3]) ).

fof(f_286_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_286_2,plain,
    ! [U_1476,U_1475,U_1474,U_1473,U_1472,U_1471] : c_Nitpick_Opair__box_Opair__box__case(U_1471,U_1472,U_1473,U_1474,c_Nitpick_Opair__box_OPairBox(U_1471,U_1472,U_1475,U_1476)) = hAPP(hAPP(U_1474,U_1475),U_1476),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

fof(f_286_3,plain,
    ! [U_1471,U_1472,U_1473,U_1474,U_1475,U_1476] : c_Nitpick_Opair__box_Opair__box__case(U_1471,U_1472,U_1473,U_1474,c_Nitpick_Opair__box_OPairBox(U_1471,U_1472,U_1475,U_1476)) = hAPP(hAPP(U_1474,U_1475),U_1476),
    inference(definitional_conversion,[status(esa)],[f_286_2]) ).

cnf(f_286_4,plain,
    c_Nitpick_Opair__box_Opair__box__case(U_1471,U_1472,U_1473,U_1474,c_Nitpick_Opair__box_OPairBox(U_1471,U_1472,U_1475,U_1476)) = hAPP(hAPP(U_1474,U_1475),U_1476),
    inference(clausify,[status(thm)],[f_286_3]) ).

fof(f_287_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_287_2,plain,
    ! [U_1482,U_1481,U_1480,U_1479,U_1478,U_1477] : c_Nitpick_Opair__box_Opair__box__rec(U_1477,U_1478,U_1479,U_1480,c_Nitpick_Opair__box_OPairBox(U_1477,U_1478,U_1481,U_1482)) = hAPP(hAPP(U_1480,U_1481),U_1482),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

fof(f_287_3,plain,
    ! [U_1478,U_1477,U_1479,U_1480,U_1481,U_1482] : c_Nitpick_Opair__box_Opair__box__rec(U_1477,U_1478,U_1479,U_1480,c_Nitpick_Opair__box_OPairBox(U_1477,U_1478,U_1481,U_1482)) = hAPP(hAPP(U_1480,U_1481),U_1482),
    inference(definitional_conversion,[status(esa)],[f_287_2]) ).

cnf(f_287_4,plain,
    c_Nitpick_Opair__box_Opair__box__rec(U_1477,U_1478,U_1479,U_1480,c_Nitpick_Opair__box_OPairBox(U_1477,U_1478,U_1481,U_1482)) = hAPP(hAPP(U_1480,U_1481),U_1482),
    inference(clausify,[status(thm)],[f_287_3]) ).

fof(f_288_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_288_2,plain,
    ! [U_1486,U_1485,U_1484] :
      ( ? [U_1483] : c_Natural_Oevaln(U_1484,U_1485,U_1483,U_1486)
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1484),U_1485),U_1486)) ),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

fof(f_288_3,plain,
    ! [U_1486,U_1485,U_1484] :
      ( c_Natural_Oevaln(U_1484,U_1485,sK35(U_1486,U_1485,U_1484),U_1486)
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1484),U_1485),U_1486)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_1483,sK35(U_1486,U_1485,U_1484))],[f_288_2]) ).

fof(f_288_4,plain,
    ! [U_1485,U_1484,U_1486] :
      ( c_Natural_Oevaln(U_1484,U_1485,sK35(U_1486,U_1485,U_1484),U_1486)
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1484),U_1485),U_1486)) ),
    inference(definitional_conversion,[status(esa)],[f_288_3]) ).

cnf(f_288_5,plain,
    ( c_Natural_Oevaln(U_1484,U_1485,sK35(U_1486,U_1485,U_1484),U_1486)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_1484),U_1485),U_1486)) ),
    inference(clausify,[status(thm)],[f_288_4]) ).

fof(f_289_1,plain,
    ! [V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Sum__Type_Osum_Osum__size(T_b,T_c,V_fa_2,V_fb_2,hAPP(c_Sum__Type_OInl(T_b,T_c),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_sum_Osize_I1_J]) ).

fof(f_289_2,plain,
    ! [U_1491,U_1490,U_1489,U_1488,U_1487] : c_Sum__Type_Osum_Osum__size(U_1487,U_1488,U_1489,U_1490,hAPP(c_Sum__Type_OInl(U_1487,U_1488),U_1491)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_1489,U_1491)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

fof(f_289_3,plain,
    ! [U_1488,U_1487,U_1489,U_1490,U_1491] : c_Sum__Type_Osum_Osum__size(U_1487,U_1488,U_1489,U_1490,hAPP(c_Sum__Type_OInl(U_1487,U_1488),U_1491)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_1489,U_1491)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_289_2]) ).

cnf(f_289_4,plain,
    c_Sum__Type_Osum_Osum__size(U_1487,U_1488,U_1489,U_1490,hAPP(c_Sum__Type_OInl(U_1487,U_1488),U_1491)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_1489,U_1491)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_289_3]) ).

fof(f_290_1,plain,
    ! [V_b_2,V_fb_2,V_fa_2,T_c,T_b] : c_Sum__Type_Osum_Osum__size(T_b,T_c,V_fa_2,V_fb_2,hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),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_sum_Osize_I2_J]) ).

fof(f_290_2,plain,
    ! [U_1496,U_1495,U_1494,U_1493,U_1492] : c_Sum__Type_Osum_Osum__size(U_1492,U_1493,U_1494,U_1495,hAPP(c_Sum__Type_OInr(U_1493,U_1492),U_1496)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_1495,U_1496)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

fof(f_290_3,plain,
    ! [U_1493,U_1492,U_1494,U_1495,U_1496] : c_Sum__Type_Osum_Osum__size(U_1492,U_1493,U_1494,U_1495,hAPP(c_Sum__Type_OInr(U_1493,U_1492),U_1496)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_1495,U_1496)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_290_2]) ).

cnf(f_290_4,plain,
    c_Sum__Type_Osum_Osum__size(U_1492,U_1493,U_1494,U_1495,hAPP(c_Sum__Type_OInr(U_1493,U_1492),U_1496)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_1495,U_1496)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_290_3]) ).

fof(f_291_1,plain,
    ! [T_a,V_y] :
      ( ? [B_a] : V_y = hAPP(c_Option_Ooption_OSome(T_a),B_a)
      | V_y = c_Option_Ooption_ONone(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_option_Oexhaust]) ).

fof(f_291_2,plain,
    ! [U_1499,U_1498] :
      ( ? [U_1497] : U_1498 = hAPP(c_Option_Ooption_OSome(U_1499),U_1497)
      | U_1498 = c_Option_Ooption_ONone(U_1499) ),
    inference(variable_rename,[status(thm)],[f_291_1]) ).

fof(f_291_3,plain,
    ! [U_1499,U_1498] :
      ( U_1498 = hAPP(c_Option_Ooption_OSome(U_1499),sK36(U_1499,U_1498))
      | U_1498 = c_Option_Ooption_ONone(U_1499) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_1497,sK36(U_1499,U_1498))],[f_291_2]) ).

fof(f_291_4,plain,
    ! [U_1498,U_1499] :
      ( U_1498 = hAPP(c_Option_Ooption_OSome(U_1499),sK36(U_1499,U_1498))
      | U_1498 = c_Option_Ooption_ONone(U_1499) ),
    inference(definitional_conversion,[status(esa)],[f_291_3]) ).

cnf(f_291_5,plain,
    ( U_1498 = hAPP(c_Option_Ooption_OSome(U_1499),sK36(U_1499,U_1498))
    | U_1498 = c_Option_Ooption_ONone(U_1499) ),
    inference(clausify,[status(thm)],[f_291_4]) ).

fof(f_292_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_292_2,plain,
    ! [U_1500] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_1500))),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

fof(f_292_3,plain,
    ! [U_1500] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_1500))),
    inference(definitional_conversion,[status(esa)],[f_292_2]) ).

cnf(f_292_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_1500))),
    inference(clausify,[status(thm)],[f_292_3]) ).

fof(f_293_1,plain,
    ! [V_n] :
      ( ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m)
      | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_not0__implies__Suc]) ).

fof(f_293_2,plain,
    ! [U_1502] :
      ( ? [U_1501] : U_1502 = hAPP(c_Nat_OSuc,U_1501)
      | U_1502 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

fof(f_293_3,plain,
    ! [U_1502] :
      ( U_1502 = hAPP(c_Nat_OSuc,sK37(U_1502))
      | U_1502 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_1501,sK37(U_1502))],[f_293_2]) ).

fof(f_293_4,plain,
    ! [U_1502] :
      ( U_1502 = hAPP(c_Nat_OSuc,sK37(U_1502))
      | U_1502 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_293_3]) ).

cnf(f_293_5,plain,
    ( U_1502 = hAPP(c_Nat_OSuc,sK37(U_1502))
    | U_1502 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_293_4]) ).

fof(f_294_1,plain,
    ! [V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_n_2))
      | ? [B_n] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_n)))
          & hBOOL(hAPP(V_P_2,B_n)) )
      | ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(fof_nnf,[status(thm)],[fact_nat__induct]) ).

fof(f_294_2,plain,
    ! [U_1505,U_1504] :
      ( hBOOL(hAPP(U_1504,U_1505))
      | ? [U_1503] :
          ( ~ hBOOL(hAPP(U_1504,hAPP(c_Nat_OSuc,U_1503)))
          & hBOOL(hAPP(U_1504,U_1503)) )
      | ~ hBOOL(hAPP(U_1504,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_294_1]) ).

fof(f_294_3,plain,
    ! [U_1505,U_1504] :
      ( hBOOL(hAPP(U_1504,U_1505))
      | ( ~ hBOOL(hAPP(U_1504,hAPP(c_Nat_OSuc,sK38(U_1505,U_1504))))
        & hBOOL(hAPP(U_1504,sK38(U_1505,U_1504))) )
      | ~ hBOOL(hAPP(U_1504,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_1503,sK38(U_1505,U_1504))],[f_294_2]) ).

fof(f_294_4,plain,
    ( ! [U_1504,U_1505] :
        ( ~ hBOOL(hAPP(U_1504,hAPP(c_Nat_OSuc,sK38(U_1505,U_1504))))
        | ~ sP72(U_1504,U_1505) )
    & ! [U_1504,U_1505] :
        ( hBOOL(hAPP(U_1504,sK38(U_1505,U_1504)))
        | ~ sP72(U_1504,U_1505) )
    & ! [U_1504,U_1505] :
        ( hBOOL(hAPP(U_1504,U_1505))
        | sP72(U_1504,U_1505)
        | ~ hBOOL(hAPP(U_1504,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72])],[f_294_3]) ).

cnf(f_294_5,plain,
    ( hBOOL(hAPP(U_1504,U_1505))
    | sP72(U_1504,U_1505)
    | ~ hBOOL(hAPP(U_1504,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_294_4]) ).

cnf(f_294_6,plain,
    ( hBOOL(hAPP(U_1504,sK38(U_1505,U_1504)))
    | ~ sP72(U_1504,U_1505) ),
    inference(clausify,[status(thm)],[f_294_4]) ).

cnf(f_294_7,plain,
    ( ~ hBOOL(hAPP(U_1504,hAPP(c_Nat_OSuc,sK38(U_1505,U_1504))))
    | ~ sP72(U_1504,U_1505) ),
    inference(clausify,[status(thm)],[f_294_4]) ).

fof(f_295_1,plain,
    ! [V_k_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ? [B_n] :
          ( ~ hBOOL(hAPP(V_P_2,B_n))
          & hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_n))) )
      | ~ hBOOL(hAPP(V_P_2,V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_zero__induct]) ).

fof(f_295_2,plain,
    ! [U_1508,U_1507] :
      ( hBOOL(hAPP(U_1507,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ? [U_1506] :
          ( ~ hBOOL(hAPP(U_1507,U_1506))
          & hBOOL(hAPP(U_1507,hAPP(c_Nat_OSuc,U_1506))) )
      | ~ hBOOL(hAPP(U_1507,U_1508)) ),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

fof(f_295_3,plain,
    ! [U_1508,U_1507] :
      ( hBOOL(hAPP(U_1507,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ( ~ hBOOL(hAPP(U_1507,sK39(U_1508,U_1507)))
        & hBOOL(hAPP(U_1507,hAPP(c_Nat_OSuc,sK39(U_1508,U_1507)))) )
      | ~ hBOOL(hAPP(U_1507,U_1508)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_1506,sK39(U_1508,U_1507))],[f_295_2]) ).

fof(f_295_4,plain,
    ( ! [U_1507,U_1508] :
        ( ~ hBOOL(hAPP(U_1507,sK39(U_1508,U_1507)))
        | ~ sP73(U_1507,U_1508) )
    & ! [U_1507,U_1508] :
        ( hBOOL(hAPP(U_1507,hAPP(c_Nat_OSuc,sK39(U_1508,U_1507))))
        | ~ sP73(U_1507,U_1508) )
    & ! [U_1507,U_1508] :
        ( hBOOL(hAPP(U_1507,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | sP73(U_1507,U_1508)
        | ~ hBOOL(hAPP(U_1507,U_1508)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73])],[f_295_3]) ).

cnf(f_295_5,plain,
    ( hBOOL(hAPP(U_1507,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | sP73(U_1507,U_1508)
    | ~ hBOOL(hAPP(U_1507,U_1508)) ),
    inference(clausify,[status(thm)],[f_295_4]) ).

cnf(f_295_6,plain,
    ( hBOOL(hAPP(U_1507,hAPP(c_Nat_OSuc,sK39(U_1508,U_1507))))
    | ~ sP73(U_1507,U_1508) ),
    inference(clausify,[status(thm)],[f_295_4]) ).

cnf(f_295_7,plain,
    ( ~ hBOOL(hAPP(U_1507,sK39(U_1508,U_1507)))
    | ~ sP73(U_1507,U_1508) ),
    inference(clausify,[status(thm)],[f_295_4]) ).

fof(f_296_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_296_2,plain,
    ! [U_1509] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1509),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

fof(f_296_3,plain,
    ! [U_1509] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1509),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_296_2]) ).

cnf(f_296_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1509),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_296_3]) ).

fof(f_297_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_297_2,plain,
    ! [U_1510] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1510),hAPP(c_Nat_OSuc,U_1510))),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

fof(f_297_3,plain,
    ! [U_1510] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1510),hAPP(c_Nat_OSuc,U_1510))),
    inference(definitional_conversion,[status(esa)],[f_297_2]) ).

cnf(f_297_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1510),hAPP(c_Nat_OSuc,U_1510))),
    inference(clausify,[status(thm)],[f_297_3]) ).

fof(f_298_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_298_2,plain,
    ! [U_1512,U_1511] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1511)),hAPP(c_Nat_OSuc,U_1512)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1511),U_1512)) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

fof(f_298_3,plain,
    ! [U_1511,U_1512] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1511)),hAPP(c_Nat_OSuc,U_1512)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1511),U_1512)) ),
    inference(definitional_conversion,[status(esa)],[f_298_2]) ).

cnf(f_298_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1511)),hAPP(c_Nat_OSuc,U_1512)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1511),U_1512)) ),
    inference(clausify,[status(thm)],[f_298_3]) ).

fof(f_299_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_299_2,plain,
    ! [U_1515,U_1514,U_1513] :
      ( hBOOL(hAPP(hAPP(U_1515,U_1514),U_1513))
      | ( ~ hBOOL(hAPP(hAPP(U_1515,U_1514),U_1513))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1514),U_1513)) )
      | ( ~ hBOOL(hAPP(hAPP(U_1515,U_1514),U_1513))
        & U_1513 = U_1514 )
      | ( ~ hBOOL(hAPP(hAPP(U_1515,U_1514),U_1513))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1513),U_1514)) ) ),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

fof(f_299_3,plain,
    ( ! [U_1513,U_1514,U_1515] :
        ( ~ hBOOL(hAPP(hAPP(U_1515,U_1514),U_1513))
        | ~ sP76(U_1513,U_1514,U_1515) )
    & ! [U_1513,U_1514,U_1515] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1514),U_1513))
        | ~ sP76(U_1513,U_1514,U_1515) )
    & ! [U_1513,U_1514,U_1515] :
        ( ~ hBOOL(hAPP(hAPP(U_1515,U_1514),U_1513))
        | ~ sP75(U_1513,U_1514,U_1515) )
    & ! [U_1513,U_1514,U_1515] :
        ( U_1513 = U_1514
        | ~ sP75(U_1513,U_1514,U_1515) )
    & ! [U_1513,U_1514,U_1515] :
        ( ~ hBOOL(hAPP(hAPP(U_1515,U_1514),U_1513))
        | ~ sP74(U_1513,U_1514,U_1515) )
    & ! [U_1513,U_1514,U_1515] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1513),U_1514))
        | ~ sP74(U_1513,U_1514,U_1515) )
    & ! [U_1513,U_1514,U_1515] :
        ( hBOOL(hAPP(hAPP(U_1515,U_1514),U_1513))
        | sP76(U_1513,U_1514,U_1515)
        | sP75(U_1513,U_1514,U_1515)
        | sP74(U_1513,U_1514,U_1515) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74,sP75,sP76])],[f_299_2]) ).

cnf(f_299_4,plain,
    ( hBOOL(hAPP(hAPP(U_1515,U_1514),U_1513))
    | sP76(U_1513,U_1514,U_1515)
    | sP75(U_1513,U_1514,U_1515)
    | sP74(U_1513,U_1514,U_1515) ),
    inference(clausify,[status(thm)],[f_299_3]) ).

cnf(f_299_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1513),U_1514))
    | ~ sP74(U_1513,U_1514,U_1515) ),
    inference(clausify,[status(thm)],[f_299_3]) ).

cnf(f_299_6,plain,
    ( ~ hBOOL(hAPP(hAPP(U_1515,U_1514),U_1513))
    | ~ sP74(U_1513,U_1514,U_1515) ),
    inference(clausify,[status(thm)],[f_299_3]) ).

cnf(f_299_7,plain,
    ( U_1513 = U_1514
    | ~ sP75(U_1513,U_1514,U_1515) ),
    inference(clausify,[status(thm)],[f_299_3]) ).

cnf(f_299_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_1515,U_1514),U_1513))
    | ~ sP75(U_1513,U_1514,U_1515) ),
    inference(clausify,[status(thm)],[f_299_3]) ).

cnf(f_299_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1514),U_1513))
    | ~ sP76(U_1513,U_1514,U_1515) ),
    inference(clausify,[status(thm)],[f_299_3]) ).

cnf(f_299_10,plain,
    ( ~ hBOOL(hAPP(hAPP(U_1515,U_1514),U_1513))
    | ~ sP76(U_1513,U_1514,U_1515) ),
    inference(clausify,[status(thm)],[f_299_3]) ).

fof(f_300_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_300_2,plain,
    ! [U_1517,U_1516] :
      ( U_1516 != U_1517
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1516),U_1517)) ),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

fof(f_300_3,plain,
    ! [U_1517,U_1516] :
      ( U_1516 != U_1517
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1516),U_1517)) ),
    inference(definitional_conversion,[status(esa)],[f_300_2]) ).

cnf(f_300_4,plain,
    ( U_1516 != U_1517
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1516),U_1517)) ),
    inference(clausify,[status(thm)],[f_300_3]) ).

fof(f_301_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_301_2,plain,
    ! [U_1519,U_1518] :
      ( U_1519 != U_1518
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1518),U_1519)) ),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

fof(f_301_3,plain,
    ! [U_1518,U_1519] :
      ( U_1519 != U_1518
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1518),U_1519)) ),
    inference(definitional_conversion,[status(esa)],[f_301_2]) ).

cnf(f_301_4,plain,
    ( U_1519 != U_1518
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1518),U_1519)) ),
    inference(clausify,[status(thm)],[f_301_3]) ).

fof(f_302_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_302_2,plain,
    ! [U_1520] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1520),U_1520)),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

fof(f_302_3,plain,
    ! [U_1520] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1520),U_1520)),
    inference(definitional_conversion,[status(esa)],[f_302_2]) ).

cnf(f_302_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1520),U_1520)),
    inference(clausify,[status(thm)],[f_302_3]) ).

fof(f_303_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_303_2,plain,
    ! [U_1522,U_1521] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1522),U_1521))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1521),U_1522))
      | U_1521 = U_1522 ),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

fof(f_303_3,plain,
    ! [U_1522,U_1521] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1522),U_1521))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1521),U_1522))
      | U_1521 = U_1522 ),
    inference(definitional_conversion,[status(esa)],[f_303_2]) ).

cnf(f_303_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1522),U_1521))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1521),U_1522))
    | U_1521 = U_1522 ),
    inference(clausify,[status(thm)],[f_303_3]) ).

fof(f_304_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_304_2,plain,
    ! [U_1524,U_1523] :
      ( ( U_1523 != U_1524
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1524),U_1523))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1523),U_1524)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1524),U_1523))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1523),U_1524))
        | U_1523 = U_1524 ) ),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

fof(f_304_3,plain,
    ( ! [U_1528,U_1526] :
        ( U_1526 != U_1528
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1528),U_1526))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1526),U_1528)) ) )
    & ! [U_1527,U_1525] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1527),U_1525))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1525),U_1527))
        | U_1525 = U_1527 ) ),
    inference(miniscope,[status(thm)],[f_304_2]) ).

fof(f_304_4,plain,
    ( ! [U_1528,U_1526] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1528),U_1526))
        | ~ sP77(U_1528,U_1526) )
    & ! [U_1528,U_1526] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1526),U_1528))
        | ~ sP77(U_1528,U_1526) )
    & ! [U_1528,U_1526] :
        ( U_1526 != U_1528
        | sP77(U_1528,U_1526) )
    & ! [U_1527,U_1525] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1527),U_1525))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1525),U_1527))
        | U_1525 = U_1527 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP77])],[f_304_3]) ).

cnf(f_304_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1527),U_1525))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1525),U_1527))
    | U_1525 = U_1527 ),
    inference(clausify,[status(thm)],[f_304_4]) ).

cnf(f_304_6,plain,
    ( U_1526 != U_1528
    | sP77(U_1528,U_1526) ),
    inference(clausify,[status(thm)],[f_304_4]) ).

cnf(f_304_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1526),U_1528))
    | ~ sP77(U_1528,U_1526) ),
    inference(clausify,[status(thm)],[f_304_4]) ).

cnf(f_304_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1528),U_1526))
    | ~ sP77(U_1528,U_1526) ),
    inference(clausify,[status(thm)],[f_304_4]) ).

fof(f_305_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_305_2,plain,
    ! [U_1529] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1529),U_1529)),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

fof(f_305_3,plain,
    ! [U_1529] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1529),U_1529)),
    inference(definitional_conversion,[status(esa)],[f_305_2]) ).

cnf(f_305_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1529),U_1529)),
    inference(clausify,[status(thm)],[f_305_3]) ).

fof(f_306_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_306_2,plain,
    ! [U_1533,U_1532,U_1531,U_1530] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1530),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1530),U_1531),U_1532)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1530),U_1533),U_1532)))
          | ~ 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_1531),U_1533))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1530),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1530),U_1531),U_1532)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1530),U_1533),U_1532))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1530) ),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

fof(f_306_3,plain,
    ( ! [U_1531,U_1530,U_1532,U_1533] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1530),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1530),U_1531),U_1532)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1530),U_1533),U_1532)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1530),U_1531),U_1533))
        | ~ sP78(U_1531,U_1530,U_1532,U_1533) )
    & ! [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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1530),U_1531),U_1532)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1530),U_1533),U_1532)))
        | ~ sP78(U_1531,U_1530,U_1532,U_1533) )
    & ! [U_1531,U_1530,U_1532,U_1533] :
        ( sP78(U_1531,U_1530,U_1532,U_1533)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1530) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78])],[f_306_2]) ).

cnf(f_306_4,plain,
    ( sP78(U_1531,U_1530,U_1532,U_1533)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1530) ),
    inference(clausify,[status(thm)],[f_306_3]) ).

cnf(f_306_5,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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1530),U_1531),U_1532)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1530),U_1533),U_1532)))
    | ~ sP78(U_1531,U_1530,U_1532,U_1533) ),
    inference(clausify,[status(thm)],[f_306_3]) ).

cnf(f_306_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1530),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1530),U_1531),U_1532)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1530),U_1533),U_1532)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1530),U_1531),U_1533))
    | ~ sP78(U_1531,U_1530,U_1532,U_1533) ),
    inference(clausify,[status(thm)],[f_306_3]) ).

fof(f_307_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_307_2,plain,
    ! [U_1537,U_1536,U_1535,U_1534] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1534),U_1535),U_1536)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1534),U_1535),U_1537)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),U_1536),U_1537)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),U_1536),U_1537))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1534),U_1535),U_1536)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1534),U_1535),U_1537))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1534) ),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

fof(f_307_3,plain,
    ( ! [U_1536,U_1534,U_1535,U_1537] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1534),U_1535),U_1536)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1534),U_1535),U_1537)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),U_1536),U_1537))
        | ~ sP79(U_1536,U_1534,U_1535,U_1537) )
    & ! [U_1536,U_1534,U_1535,U_1537] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),U_1536),U_1537))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1534),U_1535),U_1536)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1534),U_1535),U_1537)))
        | ~ sP79(U_1536,U_1534,U_1535,U_1537) )
    & ! [U_1536,U_1534,U_1535,U_1537] :
        ( sP79(U_1536,U_1534,U_1535,U_1537)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1534) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79])],[f_307_2]) ).

cnf(f_307_4,plain,
    ( sP79(U_1536,U_1534,U_1535,U_1537)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1534) ),
    inference(clausify,[status(thm)],[f_307_3]) ).

cnf(f_307_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),U_1536),U_1537))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1534),U_1535),U_1536)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1534),U_1535),U_1537)))
    | ~ sP79(U_1536,U_1534,U_1535,U_1537) ),
    inference(clausify,[status(thm)],[f_307_3]) ).

cnf(f_307_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1534),U_1535),U_1536)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1534),U_1535),U_1537)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1534),U_1536),U_1537))
    | ~ sP79(U_1536,U_1534,U_1535,U_1537) ),
    inference(clausify,[status(thm)],[f_307_3]) ).

fof(f_308_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_308_2,plain,
    ! [U_1541,U_1540,U_1539,U_1538] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1538),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1538),U_1539),U_1541)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1538),U_1540),U_1541)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1538),U_1539),U_1540))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1538) ),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

fof(f_308_3,plain,
    ! [U_1540,U_1539,U_1538,U_1541] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1538),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1538),U_1539),U_1541)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1538),U_1540),U_1541)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1538),U_1539),U_1540))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1538) ),
    inference(definitional_conversion,[status(esa)],[f_308_2]) ).

cnf(f_308_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1538),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1538),U_1539),U_1541)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1538),U_1540),U_1541)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1538),U_1539),U_1540))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1538) ),
    inference(clausify,[status(thm)],[f_308_3]) ).

fof(f_309_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_309_2,plain,
    ! [U_1545,U_1544,U_1543,U_1542] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1542),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1542),U_1545),U_1543)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1542),U_1545),U_1544)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1542),U_1543),U_1544))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1542) ),
    inference(variable_rename,[status(thm)],[f_309_1]) ).

fof(f_309_3,plain,
    ! [U_1542,U_1543,U_1544,U_1545] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1542),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1542),U_1545),U_1543)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1542),U_1545),U_1544)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1542),U_1543),U_1544))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1542) ),
    inference(definitional_conversion,[status(esa)],[f_309_2]) ).

cnf(f_309_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1542),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1542),U_1545),U_1543)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1542),U_1545),U_1544)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1542),U_1543),U_1544))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1542) ),
    inference(clausify,[status(thm)],[f_309_3]) ).

fof(f_310_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_310_2,plain,
    ! [U_1550,U_1549,U_1548,U_1547,U_1546] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1546),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1546),U_1547),U_1549)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1546),U_1548),U_1550)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1546),U_1549),U_1550))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1546),U_1547),U_1548))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1546) ),
    inference(variable_rename,[status(thm)],[f_310_1]) ).

fof(f_310_3,plain,
    ! [U_1546,U_1547,U_1548,U_1549,U_1550] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1546),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1546),U_1547),U_1549)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1546),U_1548),U_1550)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1546),U_1549),U_1550))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1546),U_1547),U_1548))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1546) ),
    inference(definitional_conversion,[status(esa)],[f_310_2]) ).

cnf(f_310_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1546),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1546),U_1547),U_1549)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1546),U_1548),U_1550)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1546),U_1549),U_1550))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1546),U_1547),U_1548))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1546) ),
    inference(clausify,[status(thm)],[f_310_3]) ).

fof(f_311_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_311_2,plain,
    ! [U_1554,U_1553,U_1552,U_1551] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1551),U_1552),U_1554))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1551),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1551),U_1552),U_1553)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1551),U_1554),U_1553)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1551) ),
    inference(variable_rename,[status(thm)],[f_311_1]) ).

fof(f_311_3,plain,
    ! [U_1551,U_1552,U_1553,U_1554] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1551),U_1552),U_1554))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1551),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1551),U_1552),U_1553)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1551),U_1554),U_1553)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1551) ),
    inference(definitional_conversion,[status(esa)],[f_311_2]) ).

cnf(f_311_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1551),U_1552),U_1554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1551),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1551),U_1552),U_1553)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1551),U_1554),U_1553)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1551) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

fof(f_312_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_312_2,plain,
    ! [U_1558,U_1557,U_1556,U_1555] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1555),U_1557),U_1558))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1555),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1555),U_1556),U_1557)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1555),U_1556),U_1558)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1555) ),
    inference(variable_rename,[status(thm)],[f_312_1]) ).

fof(f_312_3,plain,
    ! [U_1555,U_1556,U_1557,U_1558] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1555),U_1557),U_1558))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1555),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1555),U_1556),U_1557)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1555),U_1556),U_1558)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1555) ),
    inference(definitional_conversion,[status(esa)],[f_312_2]) ).

cnf(f_312_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1555),U_1557),U_1558))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1555),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1555),U_1556),U_1557)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1555),U_1556),U_1558)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1555) ),
    inference(clausify,[status(thm)],[f_312_3]) ).

fof(f_313_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_313_2,plain,
    ! [U_1559] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1559))
      | U_1559 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

fof(f_313_3,plain,
    ! [U_1559] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1559))
      | U_1559 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_313_2]) ).

cnf(f_313_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1559))
    | U_1559 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_313_3]) ).

fof(f_314_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_314_2,plain,
    ! [U_1561,U_1560] :
      ( U_1561 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1560),U_1561)) ),
    inference(variable_rename,[status(thm)],[f_314_1]) ).

fof(f_314_3,plain,
    ! [U_1561] :
      ( ! [U_1560] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1560),U_1561))
      | U_1561 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_314_2]) ).

fof(f_314_4,plain,
    ! [U_1560,U_1561] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1560),U_1561))
      | U_1561 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_314_3]) ).

cnf(f_314_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1560),U_1561))
    | U_1561 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_314_4]) ).

fof(f_315_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_315_2,plain,
    ! [U_1562] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1562),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_315_1]) ).

fof(f_315_3,plain,
    ! [U_1562] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1562),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_315_2]) ).

cnf(f_315_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1562),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_315_3]) ).

fof(f_316_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_316_2,plain,
    ! [U_1563] :
      ( ( U_1563 != 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_1563)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1563))
        | U_1563 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

fof(f_316_3,plain,
    ( ! [U_1565] :
        ( U_1565 != 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_1565)) )
    & ! [U_1564] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1564))
        | U_1564 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_316_2]) ).

fof(f_316_4,plain,
    ( ! [U_1565] :
        ( U_1565 != 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_1565)) )
    & ! [U_1564] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1564))
        | U_1564 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_316_3]) ).

cnf(f_316_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1564))
    | U_1564 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_316_4]) ).

cnf(f_316_6,plain,
    ( U_1565 != 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_1565)) ),
    inference(clausify,[status(thm)],[f_316_4]) ).

fof(f_317_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_317_2,plain,
    ! [U_1566] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1566),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

fof(f_317_3,plain,
    ! [U_1566] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1566),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_317_2]) ).

cnf(f_317_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1566),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_317_3]) ).

fof(f_318_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_318_2,plain,
    ! [U_1568,U_1567] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1567),U_1568))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1568),hAPP(c_Nat_OSuc,U_1567))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1568),hAPP(c_Nat_OSuc,U_1567)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1567),U_1568)) ) ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

fof(f_318_3,plain,
    ( ! [U_1572,U_1570] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1570),U_1572))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1572),hAPP(c_Nat_OSuc,U_1570))) )
    & ! [U_1571,U_1569] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1571),hAPP(c_Nat_OSuc,U_1569)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1569),U_1571)) ) ),
    inference(miniscope,[status(thm)],[f_318_2]) ).

fof(f_318_4,plain,
    ( ! [U_1570,U_1572] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1570),U_1572))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1572),hAPP(c_Nat_OSuc,U_1570))) )
    & ! [U_1571,U_1569] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1571),hAPP(c_Nat_OSuc,U_1569)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1569),U_1571)) ) ),
    inference(definitional_conversion,[status(esa)],[f_318_3]) ).

cnf(f_318_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1571),hAPP(c_Nat_OSuc,U_1569)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1569),U_1571)) ),
    inference(clausify,[status(thm)],[f_318_4]) ).

cnf(f_318_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1570),U_1572))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1572),hAPP(c_Nat_OSuc,U_1570))) ),
    inference(clausify,[status(thm)],[f_318_4]) ).

fof(f_319_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_319_2,plain,
    ! [U_1574,U_1573] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1573),hAPP(c_Nat_OSuc,U_1574)))
        | ( U_1573 != U_1574
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1573),U_1574)) ) )
      & ( U_1573 = U_1574
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1573),U_1574))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1573),hAPP(c_Nat_OSuc,U_1574))) ) ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

fof(f_319_3,plain,
    ( ! [U_1578,U_1576] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1576),hAPP(c_Nat_OSuc,U_1578)))
        | ( U_1576 != U_1578
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1576),U_1578)) ) )
    & ! [U_1577,U_1575] :
        ( U_1575 = U_1577
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1575),U_1577))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1575),hAPP(c_Nat_OSuc,U_1577))) ) ),
    inference(miniscope,[status(thm)],[f_319_2]) ).

fof(f_319_4,plain,
    ( ! [U_1578,U_1576] :
        ( U_1576 != U_1578
        | ~ sP80(U_1578,U_1576) )
    & ! [U_1578,U_1576] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1576),U_1578))
        | ~ sP80(U_1578,U_1576) )
    & ! [U_1578,U_1576] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1576),hAPP(c_Nat_OSuc,U_1578)))
        | sP80(U_1578,U_1576) )
    & ! [U_1577,U_1575] :
        ( U_1575 = U_1577
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1575),U_1577))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1575),hAPP(c_Nat_OSuc,U_1577))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80])],[f_319_3]) ).

cnf(f_319_5,plain,
    ( U_1575 = U_1577
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1575),U_1577))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1575),hAPP(c_Nat_OSuc,U_1577))) ),
    inference(clausify,[status(thm)],[f_319_4]) ).

cnf(f_319_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1576),hAPP(c_Nat_OSuc,U_1578)))
    | sP80(U_1578,U_1576) ),
    inference(clausify,[status(thm)],[f_319_4]) ).

cnf(f_319_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1576),U_1578))
    | ~ sP80(U_1578,U_1576) ),
    inference(clausify,[status(thm)],[f_319_4]) ).

cnf(f_319_8,plain,
    ( U_1576 != U_1578
    | ~ sP80(U_1578,U_1576) ),
    inference(clausify,[status(thm)],[f_319_4]) ).

fof(f_320_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_320_2,plain,
    ! [U_1580,U_1579] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1579)),hAPP(c_Nat_OSuc,U_1580)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1579),U_1580)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1579),U_1580))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1579)),hAPP(c_Nat_OSuc,U_1580))) ) ),
    inference(variable_rename,[status(thm)],[f_320_1]) ).

fof(f_320_3,plain,
    ( ! [U_1584,U_1582] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1582)),hAPP(c_Nat_OSuc,U_1584)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1582),U_1584)) )
    & ! [U_1583,U_1581] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1581),U_1583))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1581)),hAPP(c_Nat_OSuc,U_1583))) ) ),
    inference(miniscope,[status(thm)],[f_320_2]) ).

fof(f_320_4,plain,
    ( ! [U_1582,U_1584] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1582)),hAPP(c_Nat_OSuc,U_1584)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1582),U_1584)) )
    & ! [U_1583,U_1581] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1581),U_1583))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1581)),hAPP(c_Nat_OSuc,U_1583))) ) ),
    inference(definitional_conversion,[status(esa)],[f_320_3]) ).

cnf(f_320_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1581),U_1583))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1581)),hAPP(c_Nat_OSuc,U_1583))) ),
    inference(clausify,[status(thm)],[f_320_4]) ).

cnf(f_320_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1582)),hAPP(c_Nat_OSuc,U_1584)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1582),U_1584)) ),
    inference(clausify,[status(thm)],[f_320_4]) ).

fof(f_321_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_321_2,plain,
    ! [U_1586,U_1585] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1585),hAPP(c_Nat_OSuc,U_1586)))
          | U_1585 != U_1586 )
        & ( U_1585 = U_1586
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1585),hAPP(c_Nat_OSuc,U_1586))) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1585),U_1586)) ),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

fof(f_321_3,plain,
    ( ! [U_1586,U_1585] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1585),hAPP(c_Nat_OSuc,U_1586)))
        | U_1585 != U_1586
        | ~ sP81(U_1586,U_1585) )
    & ! [U_1586,U_1585] :
        ( U_1585 = U_1586
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1585),hAPP(c_Nat_OSuc,U_1586)))
        | ~ sP81(U_1586,U_1585) )
    & ! [U_1586,U_1585] :
        ( sP81(U_1586,U_1585)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1585),U_1586)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81])],[f_321_2]) ).

cnf(f_321_4,plain,
    ( sP81(U_1586,U_1585)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1585),U_1586)) ),
    inference(clausify,[status(thm)],[f_321_3]) ).

cnf(f_321_5,plain,
    ( U_1585 = U_1586
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1585),hAPP(c_Nat_OSuc,U_1586)))
    | ~ sP81(U_1586,U_1585) ),
    inference(clausify,[status(thm)],[f_321_3]) ).

cnf(f_321_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1585),hAPP(c_Nat_OSuc,U_1586)))
    | U_1585 != U_1586
    | ~ sP81(U_1586,U_1585) ),
    inference(clausify,[status(thm)],[f_321_3]) ).

fof(f_322_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_322_2,plain,
    ! [U_1588,U_1587] :
      ( U_1588 = U_1587
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1587),hAPP(c_Nat_OSuc,U_1588)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1587),U_1588)) ),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

fof(f_322_3,plain,
    ! [U_1588,U_1587] :
      ( U_1588 = U_1587
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1587),hAPP(c_Nat_OSuc,U_1588)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1587),U_1588)) ),
    inference(definitional_conversion,[status(esa)],[f_322_2]) ).

cnf(f_322_4,plain,
    ( U_1588 = U_1587
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1587),hAPP(c_Nat_OSuc,U_1588)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1587),U_1588)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

fof(f_323_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_323_2,plain,
    ! [U_1590,U_1589] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1589),hAPP(c_Nat_OSuc,U_1590)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1589),U_1590)) ),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

fof(f_323_3,plain,
    ! [U_1590,U_1589] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1589),hAPP(c_Nat_OSuc,U_1590)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1589),U_1590)) ),
    inference(definitional_conversion,[status(esa)],[f_323_2]) ).

cnf(f_323_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1589),hAPP(c_Nat_OSuc,U_1590)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1589),U_1590)) ),
    inference(clausify,[status(thm)],[f_323_3]) ).

fof(f_324_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_324_2,plain,
    ! [U_1592,U_1591] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1591)),U_1592))
      | hAPP(c_Nat_OSuc,U_1591) = U_1592
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1591),U_1592)) ),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

fof(f_324_3,plain,
    ! [U_1591,U_1592] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1591)),U_1592))
      | hAPP(c_Nat_OSuc,U_1591) = U_1592
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1591),U_1592)) ),
    inference(definitional_conversion,[status(esa)],[f_324_2]) ).

cnf(f_324_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1591)),U_1592))
    | hAPP(c_Nat_OSuc,U_1591) = U_1592
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1591),U_1592)) ),
    inference(clausify,[status(thm)],[f_324_3]) ).

fof(f_325_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_325_2,plain,
    ! [U_1595,U_1594,U_1593] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1593)),U_1595))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1594),U_1595))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1593),U_1594)) ),
    inference(variable_rename,[status(thm)],[f_325_1]) ).

fof(f_325_3,plain,
    ! [U_1593,U_1594,U_1595] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1593)),U_1595))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1594),U_1595))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1593),U_1594)) ),
    inference(definitional_conversion,[status(esa)],[f_325_2]) ).

cnf(f_325_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1593)),U_1595))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1594),U_1595))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1593),U_1594)) ),
    inference(clausify,[status(thm)],[f_325_3]) ).

fof(f_326_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_326_2,plain,
    ! [U_1597,U_1596] :
      ( U_1596 = U_1597
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1596),U_1597))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1596),hAPP(c_Nat_OSuc,U_1597))) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

fof(f_326_3,plain,
    ! [U_1596,U_1597] :
      ( U_1596 = U_1597
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1596),U_1597))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1596),hAPP(c_Nat_OSuc,U_1597))) ),
    inference(definitional_conversion,[status(esa)],[f_326_2]) ).

cnf(f_326_4,plain,
    ( U_1596 = U_1597
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1596),U_1597))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1596),hAPP(c_Nat_OSuc,U_1597))) ),
    inference(clausify,[status(thm)],[f_326_3]) ).

fof(f_327_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_327_2,plain,
    ! [U_1599,U_1598] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1598),U_1599))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1598)),U_1599)) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

fof(f_327_3,plain,
    ! [U_1598,U_1599] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1598),U_1599))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1598)),U_1599)) ),
    inference(definitional_conversion,[status(esa)],[f_327_2]) ).

cnf(f_327_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1598),U_1599))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1598)),U_1599)) ),
    inference(clausify,[status(thm)],[f_327_3]) ).

fof(f_328_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_328_2,plain,
    ! [U_1601,U_1600] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1600),U_1601))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1600)),hAPP(c_Nat_OSuc,U_1601))) ),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

fof(f_328_3,plain,
    ! [U_1600,U_1601] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1600),U_1601))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1600)),hAPP(c_Nat_OSuc,U_1601))) ),
    inference(definitional_conversion,[status(esa)],[f_328_2]) ).

cnf(f_328_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1600),U_1601))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1600)),hAPP(c_Nat_OSuc,U_1601))) ),
    inference(clausify,[status(thm)],[f_328_3]) ).

fof(f_329_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_329_2,plain,
    ! [U_1604,U_1603,U_1602] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1602),U_1604))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1602),U_1603)),U_1604)) ),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

fof(f_329_3,plain,
    ! [U_1602,U_1603,U_1604] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1602),U_1604))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1602),U_1603)),U_1604)) ),
    inference(definitional_conversion,[status(esa)],[f_329_2]) ).

cnf(f_329_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1602),U_1604))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1602),U_1603)),U_1604)) ),
    inference(clausify,[status(thm)],[f_329_3]) ).

fof(f_330_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_330_2,plain,
    ! [U_1608,U_1607,U_1606,U_1605] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1607),U_1608))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1607),U_1606) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1605),U_1608)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1605),U_1606)) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

fof(f_330_3,plain,
    ! [U_1605,U_1606,U_1607,U_1608] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1607),U_1608))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1607),U_1606) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1605),U_1608)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1605),U_1606)) ),
    inference(definitional_conversion,[status(esa)],[f_330_2]) ).

cnf(f_330_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1607),U_1608))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1607),U_1606) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1605),U_1608)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1605),U_1606)) ),
    inference(clausify,[status(thm)],[f_330_3]) ).

fof(f_331_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_331_2,plain,
    ! [U_1612,U_1611,U_1610,U_1609] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1609),U_1611)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1610),U_1612)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1611),U_1612))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1609),U_1610)) ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

fof(f_331_3,plain,
    ! [U_1609,U_1610,U_1611,U_1612] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1609),U_1611)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1610),U_1612)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1611),U_1612))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1609),U_1610)) ),
    inference(definitional_conversion,[status(esa)],[f_331_2]) ).

cnf(f_331_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1609),U_1611)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1610),U_1612)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1611),U_1612))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1609),U_1610)) ),
    inference(clausify,[status(thm)],[f_331_3]) ).

fof(f_332_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_332_2,plain,
    ! [U_1615,U_1614,U_1613] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1613),U_1615)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1614),U_1615)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1613),U_1614)) ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

fof(f_332_3,plain,
    ! [U_1613,U_1614,U_1615] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1613),U_1615)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1614),U_1615)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1613),U_1614)) ),
    inference(definitional_conversion,[status(esa)],[f_332_2]) ).

cnf(f_332_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1613),U_1615)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1614),U_1615)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1613),U_1614)) ),
    inference(clausify,[status(thm)],[f_332_3]) ).

fof(f_333_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_333_2,plain,
    ! [U_1618,U_1617,U_1616] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1618),U_1617)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1616),U_1617)) ),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

fof(f_333_3,plain,
    ! [U_1616,U_1617,U_1618] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1618),U_1617)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1616),U_1617)) ),
    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_1616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1618),U_1617)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1616),U_1617)) ),
    inference(clausify,[status(thm)],[f_333_3]) ).

fof(f_334_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_334_2,plain,
    ! [U_1621,U_1620,U_1619] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1619),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1620),U_1621)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1619),U_1620)) ),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

fof(f_334_3,plain,
    ! [U_1619,U_1620,U_1621] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1619),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1620),U_1621)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1619),U_1620)) ),
    inference(definitional_conversion,[status(esa)],[f_334_2]) ).

cnf(f_334_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1619),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1620),U_1621)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1619),U_1620)) ),
    inference(clausify,[status(thm)],[f_334_3]) ).

fof(f_335_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_335_2,plain,
    ! [U_1624,U_1623,U_1622] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1622),U_1623)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1622),U_1624)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1623),U_1624)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1623),U_1624))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1622),U_1623)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1622),U_1624))) ) ),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

fof(f_335_3,plain,
    ( ! [U_1630,U_1628] :
        ( ! [U_1626] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1626),U_1628)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1626),U_1630)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1628),U_1630)) )
    & ! [U_1629,U_1627] :
        ( ! [U_1625] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1625),U_1627)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1625),U_1629)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1627),U_1629)) ) ),
    inference(miniscope,[status(thm)],[f_335_2]) ).

fof(f_335_4,plain,
    ( ! [U_1630,U_1626,U_1628] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1626),U_1628)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1626),U_1630)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1628),U_1630)) )
    & ! [U_1627,U_1625,U_1629] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1625),U_1627)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1625),U_1629)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1627),U_1629)) ) ),
    inference(definitional_conversion,[status(esa)],[f_335_3]) ).

cnf(f_335_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1625),U_1627)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1625),U_1629)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1627),U_1629)) ),
    inference(clausify,[status(thm)],[f_335_4]) ).

cnf(f_335_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1626),U_1628)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1626),U_1630)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1628),U_1630)) ),
    inference(clausify,[status(thm)],[f_335_4]) ).

fof(f_336_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_336_2,plain,
    ! [U_1632,U_1631] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1631),U_1632)),U_1632)),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

fof(f_336_3,plain,
    ! [U_1632,U_1631] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1631),U_1632)),U_1632)),
    inference(definitional_conversion,[status(esa)],[f_336_2]) ).

cnf(f_336_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1631),U_1632)),U_1632)),
    inference(clausify,[status(thm)],[f_336_3]) ).

fof(f_337_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_337_2,plain,
    ! [U_1634,U_1633] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1633),U_1634)),U_1633)),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

fof(f_337_3,plain,
    ! [U_1633,U_1634] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1633),U_1634)),U_1633)),
    inference(definitional_conversion,[status(esa)],[f_337_2]) ).

cnf(f_337_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1633),U_1634)),U_1633)),
    inference(clausify,[status(thm)],[f_337_3]) ).

fof(f_338_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_338_2,plain,
    ! [U_1637,U_1636,U_1635] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1635),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1635),U_1636),U_1637)),c_Groups_Ozero__class_Ozero(U_1635)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1635),U_1637),c_Groups_Ozero__class_Ozero(U_1635)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1635),U_1636),c_Groups_Ozero__class_Ozero(U_1635)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1635) ),
    inference(variable_rename,[status(thm)],[f_338_1]) ).

fof(f_338_3,plain,
    ! [U_1635,U_1636,U_1637] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1635),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1635),U_1636),U_1637)),c_Groups_Ozero__class_Ozero(U_1635)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1635),U_1637),c_Groups_Ozero__class_Ozero(U_1635)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1635),U_1636),c_Groups_Ozero__class_Ozero(U_1635)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1635) ),
    inference(definitional_conversion,[status(esa)],[f_338_2]) ).

cnf(f_338_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1635),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1635),U_1636),U_1637)),c_Groups_Ozero__class_Ozero(U_1635)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1635),U_1637),c_Groups_Ozero__class_Ozero(U_1635)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1635),U_1636),c_Groups_Ozero__class_Ozero(U_1635)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_1635) ),
    inference(clausify,[status(thm)],[f_338_3]) ).

fof(f_339_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_339_2,plain,
    ! [U_1640,U_1639,U_1638] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1638),c_Groups_Ozero__class_Ozero(U_1638)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1638),U_1639),U_1640)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1638),c_Groups_Ozero__class_Ozero(U_1638)),U_1640))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1638),c_Groups_Ozero__class_Ozero(U_1638)),U_1639))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1638) ),
    inference(variable_rename,[status(thm)],[f_339_1]) ).

fof(f_339_3,plain,
    ! [U_1638,U_1639,U_1640] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1638),c_Groups_Ozero__class_Ozero(U_1638)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1638),U_1639),U_1640)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1638),c_Groups_Ozero__class_Ozero(U_1638)),U_1640))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1638),c_Groups_Ozero__class_Ozero(U_1638)),U_1639))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1638) ),
    inference(definitional_conversion,[status(esa)],[f_339_2]) ).

cnf(f_339_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1638),c_Groups_Ozero__class_Ozero(U_1638)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1638),U_1639),U_1640)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1638),c_Groups_Ozero__class_Ozero(U_1638)),U_1640))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1638),c_Groups_Ozero__class_Ozero(U_1638)),U_1639))
    | ~ class_Groups_Oordered__comm__monoid__add(U_1638) ),
    inference(clausify,[status(thm)],[f_339_3]) ).

fof(f_340_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_340_2,plain,
    ! [U_1642,U_1641] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1641),U_1642),U_1642)),c_Groups_Ozero__class_Ozero(U_1641)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1641),U_1642),c_Groups_Ozero__class_Ozero(U_1641))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1641),U_1642),c_Groups_Ozero__class_Ozero(U_1641)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1641),U_1642),U_1642)),c_Groups_Ozero__class_Ozero(U_1641))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1641) ),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

fof(f_340_3,plain,
    ( ! [U_1641,U_1642] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1641),U_1642),U_1642)),c_Groups_Ozero__class_Ozero(U_1641)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1641),U_1642),c_Groups_Ozero__class_Ozero(U_1641)))
        | ~ sP82(U_1641,U_1642) )
    & ! [U_1641,U_1642] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1641),U_1642),c_Groups_Ozero__class_Ozero(U_1641)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1641),U_1642),U_1642)),c_Groups_Ozero__class_Ozero(U_1641)))
        | ~ sP82(U_1641,U_1642) )
    & ! [U_1641,U_1642] :
        ( sP82(U_1641,U_1642)
        | ~ class_Groups_Olinordered__ab__group__add(U_1641) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP82])],[f_340_2]) ).

cnf(f_340_4,plain,
    ( sP82(U_1641,U_1642)
    | ~ class_Groups_Olinordered__ab__group__add(U_1641) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

cnf(f_340_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1641),U_1642),c_Groups_Ozero__class_Ozero(U_1641)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1641),U_1642),U_1642)),c_Groups_Ozero__class_Ozero(U_1641)))
    | ~ sP82(U_1641,U_1642) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

cnf(f_340_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1641),U_1642),U_1642)),c_Groups_Ozero__class_Ozero(U_1641)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1641),U_1642),c_Groups_Ozero__class_Ozero(U_1641)))
    | ~ sP82(U_1641,U_1642) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

fof(f_341_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_341_2,plain,
    ! [U_1644,U_1643] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),U_1644),U_1644)),c_Groups_Ozero__class_Ozero(U_1643)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),U_1644),c_Groups_Ozero__class_Ozero(U_1643))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),U_1644),c_Groups_Ozero__class_Ozero(U_1643)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),U_1644),U_1644)),c_Groups_Ozero__class_Ozero(U_1643))) ) )
      | ~ class_Rings_Olinordered__idom(U_1643) ),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

fof(f_341_3,plain,
    ( ! [U_1644,U_1643] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),U_1644),U_1644)),c_Groups_Ozero__class_Ozero(U_1643)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),U_1644),c_Groups_Ozero__class_Ozero(U_1643)))
        | ~ sP83(U_1644,U_1643) )
    & ! [U_1644,U_1643] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),U_1644),c_Groups_Ozero__class_Ozero(U_1643)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),U_1644),U_1644)),c_Groups_Ozero__class_Ozero(U_1643)))
        | ~ sP83(U_1644,U_1643) )
    & ! [U_1644,U_1643] :
        ( sP83(U_1644,U_1643)
        | ~ class_Rings_Olinordered__idom(U_1643) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83])],[f_341_2]) ).

cnf(f_341_4,plain,
    ( sP83(U_1644,U_1643)
    | ~ class_Rings_Olinordered__idom(U_1643) ),
    inference(clausify,[status(thm)],[f_341_3]) ).

cnf(f_341_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),U_1644),c_Groups_Ozero__class_Ozero(U_1643)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),U_1644),U_1644)),c_Groups_Ozero__class_Ozero(U_1643)))
    | ~ sP83(U_1644,U_1643) ),
    inference(clausify,[status(thm)],[f_341_3]) ).

cnf(f_341_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),U_1644),U_1644)),c_Groups_Ozero__class_Ozero(U_1643)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1643),U_1644),c_Groups_Ozero__class_Ozero(U_1643)))
    | ~ sP83(U_1644,U_1643) ),
    inference(clausify,[status(thm)],[f_341_3]) ).

fof(f_342_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_342_2,plain,
    ! [U_1646,U_1645] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),c_Groups_Ozero__class_Ozero(U_1645)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1645),U_1646),U_1646)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),c_Groups_Ozero__class_Ozero(U_1645)),U_1646)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),c_Groups_Ozero__class_Ozero(U_1645)),U_1646))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),c_Groups_Ozero__class_Ozero(U_1645)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1645),U_1646),U_1646))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1645) ),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

fof(f_342_3,plain,
    ( ! [U_1646,U_1645] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),c_Groups_Ozero__class_Ozero(U_1645)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1645),U_1646),U_1646)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),c_Groups_Ozero__class_Ozero(U_1645)),U_1646))
        | ~ sP84(U_1646,U_1645) )
    & ! [U_1646,U_1645] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),c_Groups_Ozero__class_Ozero(U_1645)),U_1646))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),c_Groups_Ozero__class_Ozero(U_1645)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1645),U_1646),U_1646)))
        | ~ sP84(U_1646,U_1645) )
    & ! [U_1646,U_1645] :
        ( sP84(U_1646,U_1645)
        | ~ class_Groups_Olinordered__ab__group__add(U_1645) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84])],[f_342_2]) ).

cnf(f_342_4,plain,
    ( sP84(U_1646,U_1645)
    | ~ class_Groups_Olinordered__ab__group__add(U_1645) ),
    inference(clausify,[status(thm)],[f_342_3]) ).

cnf(f_342_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),c_Groups_Ozero__class_Ozero(U_1645)),U_1646))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),c_Groups_Ozero__class_Ozero(U_1645)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1645),U_1646),U_1646)))
    | ~ sP84(U_1646,U_1645) ),
    inference(clausify,[status(thm)],[f_342_3]) ).

cnf(f_342_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),c_Groups_Ozero__class_Ozero(U_1645)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1645),U_1646),U_1646)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1645),c_Groups_Ozero__class_Ozero(U_1645)),U_1646))
    | ~ sP84(U_1646,U_1645) ),
    inference(clausify,[status(thm)],[f_342_3]) ).

fof(f_343_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_343_2,plain,
    ! [U_1650,U_1649] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1649),hAPP(c_Nat_OSuc,U_1650)))
        | ( ! [U_1648] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1648),U_1650))
              | U_1649 != hAPP(c_Nat_OSuc,U_1648) )
          & U_1649 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ? [U_1647] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1647),U_1650))
            & U_1649 = hAPP(c_Nat_OSuc,U_1647) )
        | U_1649 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1649),hAPP(c_Nat_OSuc,U_1650))) ) ),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

fof(f_343_3,plain,
    ( ! [U_1654,U_1652] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1652),hAPP(c_Nat_OSuc,U_1654)))
        | ( ! [U_1648] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1648),U_1654))
              | U_1652 != hAPP(c_Nat_OSuc,U_1648) )
          & U_1652 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_1653,U_1651] :
        ( ? [U_1647] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1647),U_1653))
            & U_1651 = hAPP(c_Nat_OSuc,U_1647) )
        | U_1651 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1651),hAPP(c_Nat_OSuc,U_1653))) ) ),
    inference(miniscope,[status(thm)],[f_343_2]) ).

fof(f_343_4,plain,
    ( ! [U_1654,U_1652] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1652),hAPP(c_Nat_OSuc,U_1654)))
        | ( ! [U_1648] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1648),U_1654))
              | U_1652 != hAPP(c_Nat_OSuc,U_1648) )
          & U_1652 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_1653,U_1651] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK40(U_1653,U_1651)),U_1653))
          & U_1651 = hAPP(c_Nat_OSuc,sK40(U_1653,U_1651)) )
        | U_1651 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1651),hAPP(c_Nat_OSuc,U_1653))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_1647,sK40(U_1653,U_1651))],[f_343_3]) ).

fof(f_343_5,plain,
    ( ! [U_1648,U_1654,U_1652] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1648),U_1654))
        | U_1652 != hAPP(c_Nat_OSuc,U_1648)
        | ~ sP86(U_1648,U_1654,U_1652) )
    & ! [U_1648,U_1654,U_1652] :
        ( U_1652 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP86(U_1648,U_1654,U_1652) )
    & ! [U_1651,U_1653] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK40(U_1653,U_1651)),U_1653))
        | ~ sP85(U_1651,U_1653) )
    & ! [U_1651,U_1653] :
        ( U_1651 = hAPP(c_Nat_OSuc,sK40(U_1653,U_1651))
        | ~ sP85(U_1651,U_1653) )
    & ! [U_1648,U_1654,U_1652] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1652),hAPP(c_Nat_OSuc,U_1654)))
        | sP86(U_1648,U_1654,U_1652) )
    & ! [U_1651,U_1653] :
        ( sP85(U_1651,U_1653)
        | U_1651 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1651),hAPP(c_Nat_OSuc,U_1653))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85,sP86])],[f_343_4]) ).

cnf(f_343_6,plain,
    ( sP85(U_1651,U_1653)
    | U_1651 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1651),hAPP(c_Nat_OSuc,U_1653))) ),
    inference(clausify,[status(thm)],[f_343_5]) ).

cnf(f_343_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1652),hAPP(c_Nat_OSuc,U_1654)))
    | sP86(U_1648,U_1654,U_1652) ),
    inference(clausify,[status(thm)],[f_343_5]) ).

cnf(f_343_8,plain,
    ( U_1651 = hAPP(c_Nat_OSuc,sK40(U_1653,U_1651))
    | ~ sP85(U_1651,U_1653) ),
    inference(clausify,[status(thm)],[f_343_5]) ).

cnf(f_343_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK40(U_1653,U_1651)),U_1653))
    | ~ sP85(U_1651,U_1653) ),
    inference(clausify,[status(thm)],[f_343_5]) ).

cnf(f_343_10,plain,
    ( U_1652 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP86(U_1648,U_1654,U_1652) ),
    inference(clausify,[status(thm)],[f_343_5]) ).

cnf(f_343_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1648),U_1654))
    | U_1652 != hAPP(c_Nat_OSuc,U_1648)
    | ~ sP86(U_1648,U_1654,U_1652) ),
    inference(clausify,[status(thm)],[f_343_5]) ).

fof(f_344_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_344_2,plain,
    ! [U_1655] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1655),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_1655 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_1655 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1655),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

fof(f_344_3,plain,
    ( ! [U_1657] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1657),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_1657 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1656] :
        ( U_1656 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1656),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(miniscope,[status(thm)],[f_344_2]) ).

fof(f_344_4,plain,
    ( ! [U_1657] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1657),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_1657 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1656] :
        ( U_1656 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1656),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_344_3]) ).

cnf(f_344_5,plain,
    ( U_1656 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1656),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(clausify,[status(thm)],[f_344_4]) ).

cnf(f_344_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1657),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | U_1657 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_344_4]) ).

fof(f_345_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_345_2,plain,
    ! [U_1660] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1660))
        | ! [U_1659] : U_1660 != hAPP(c_Nat_OSuc,U_1659) )
      & ( ? [U_1658] : U_1660 = hAPP(c_Nat_OSuc,U_1658)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1660)) ) ),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

fof(f_345_3,plain,
    ( ! [U_1662] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1662))
        | ! [U_1659] : U_1662 != hAPP(c_Nat_OSuc,U_1659) )
    & ! [U_1661] :
        ( ? [U_1658] : U_1661 = hAPP(c_Nat_OSuc,U_1658)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1661)) ) ),
    inference(miniscope,[status(thm)],[f_345_2]) ).

fof(f_345_4,plain,
    ( ! [U_1662] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1662))
        | ! [U_1659] : U_1662 != hAPP(c_Nat_OSuc,U_1659) )
    & ! [U_1661] :
        ( U_1661 = hAPP(c_Nat_OSuc,sK41(U_1661))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1661)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_1658,sK41(U_1661))],[f_345_3]) ).

fof(f_345_5,plain,
    ( ! [U_1662,U_1659] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1662))
        | U_1662 != hAPP(c_Nat_OSuc,U_1659) )
    & ! [U_1661] :
        ( U_1661 = hAPP(c_Nat_OSuc,sK41(U_1661))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1661)) ) ),
    inference(definitional_conversion,[status(esa)],[f_345_4]) ).

cnf(f_345_6,plain,
    ( U_1661 = hAPP(c_Nat_OSuc,sK41(U_1661))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1661)) ),
    inference(clausify,[status(thm)],[f_345_5]) ).

cnf(f_345_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1662))
    | U_1662 != hAPP(c_Nat_OSuc,U_1659) ),
    inference(clausify,[status(thm)],[f_345_5]) ).

fof(f_346_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_346_2,plain,
    ! [U_1664,U_1663] :
      ( ( 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_1663),U_1664)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1664))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1663)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1664))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1663))
        | ~ 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_1663),U_1664))) ) ),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

fof(f_346_3,plain,
    ( ! [U_1668,U_1666] :
        ( 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_1666),U_1668)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1668))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1666)) ) )
    & ! [U_1667,U_1665] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1667))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1665))
        | ~ 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_1665),U_1667))) ) ),
    inference(miniscope,[status(thm)],[f_346_2]) ).

fof(f_346_4,plain,
    ( ! [U_1668,U_1666] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1668))
        | ~ sP87(U_1668,U_1666) )
    & ! [U_1668,U_1666] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1666))
        | ~ sP87(U_1668,U_1666) )
    & ! [U_1668,U_1666] :
        ( 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_1666),U_1668)))
        | sP87(U_1668,U_1666) )
    & ! [U_1667,U_1665] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1667))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1665))
        | ~ 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_1665),U_1667))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87])],[f_346_3]) ).

cnf(f_346_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1667))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1665))
    | ~ 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_1665),U_1667))) ),
    inference(clausify,[status(thm)],[f_346_4]) ).

cnf(f_346_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_1666),U_1668)))
    | sP87(U_1668,U_1666) ),
    inference(clausify,[status(thm)],[f_346_4]) ).

cnf(f_346_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1666))
    | ~ sP87(U_1668,U_1666) ),
    inference(clausify,[status(thm)],[f_346_4]) ).

cnf(f_346_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1668))
    | ~ sP87(U_1668,U_1666) ),
    inference(clausify,[status(thm)],[f_346_4]) ).

fof(f_347_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_347_2,plain,
    ! [U_1672,U_1671] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1671),U_1672))
        | ! [U_1670] : U_1672 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1671),U_1670)) )
      & ( ? [U_1669] : U_1672 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1671),U_1669))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1671),U_1672)) ) ),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

fof(f_347_3,plain,
    ( ! [U_1676,U_1674] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1674),U_1676))
        | ! [U_1670] : U_1676 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1674),U_1670)) )
    & ! [U_1675,U_1673] :
        ( ? [U_1669] : U_1675 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1673),U_1669))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1673),U_1675)) ) ),
    inference(miniscope,[status(thm)],[f_347_2]) ).

fof(f_347_4,plain,
    ( ! [U_1676,U_1674] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1674),U_1676))
        | ! [U_1670] : U_1676 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1674),U_1670)) )
    & ! [U_1675,U_1673] :
        ( U_1675 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1673),sK42(U_1675,U_1673)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1673),U_1675)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_1669,sK42(U_1675,U_1673))],[f_347_3]) ).

fof(f_347_5,plain,
    ( ! [U_1670,U_1676,U_1674] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1674),U_1676))
        | U_1676 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1674),U_1670)) )
    & ! [U_1675,U_1673] :
        ( U_1675 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1673),sK42(U_1675,U_1673)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1673),U_1675)) ) ),
    inference(definitional_conversion,[status(esa)],[f_347_4]) ).

cnf(f_347_6,plain,
    ( U_1675 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1673),sK42(U_1675,U_1673)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1673),U_1675)) ),
    inference(clausify,[status(thm)],[f_347_5]) ).

cnf(f_347_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1674),U_1676))
    | U_1676 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1674),U_1670)) ),
    inference(clausify,[status(thm)],[f_347_5]) ).

fof(f_348_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_348_2,plain,
    ! [U_1678,U_1677] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1677),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1678),U_1677)))),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

fof(f_348_3,plain,
    ! [U_1677,U_1678] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1677),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1678),U_1677)))),
    inference(definitional_conversion,[status(esa)],[f_348_2]) ).

cnf(f_348_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1677),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1678),U_1677)))),
    inference(clausify,[status(thm)],[f_348_3]) ).

fof(f_349_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_349_2,plain,
    ! [U_1680,U_1679] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1679),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1679),U_1680)))),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

fof(f_349_3,plain,
    ! [U_1679,U_1680] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1679),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1679),U_1680)))),
    inference(definitional_conversion,[status(esa)],[f_349_2]) ).

cnf(f_349_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1679),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1679),U_1680)))),
    inference(clausify,[status(thm)],[f_349_3]) ).

fof(f_350_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_350_2,plain,
    ! [U_1684,U_1683,U_1682,U_1681] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),U_1683),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1681),U_1682),U_1684)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),U_1683),U_1684))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),c_Groups_Ozero__class_Ozero(U_1681)),U_1682))
      | ~ class_Rings_Olinordered__semidom(U_1681) ),
    inference(variable_rename,[status(thm)],[f_350_1]) ).

fof(f_350_3,plain,
    ! [U_1681,U_1682,U_1683,U_1684] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),U_1683),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1681),U_1682),U_1684)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),U_1683),U_1684))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),c_Groups_Ozero__class_Ozero(U_1681)),U_1682))
      | ~ class_Rings_Olinordered__semidom(U_1681) ),
    inference(definitional_conversion,[status(esa)],[f_350_2]) ).

cnf(f_350_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),U_1683),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1681),U_1682),U_1684)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),U_1683),U_1684))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1681),c_Groups_Ozero__class_Ozero(U_1681)),U_1682))
    | ~ class_Rings_Olinordered__semidom(U_1681) ),
    inference(clausify,[status(thm)],[f_350_3]) ).

fof(f_351_1,plain,
    ! [V_b,V_a,T_b,T_a] : hAPP(c_Sum__Type_OInl(T_a,T_b),V_a) != hAPP(c_Sum__Type_OInr(T_b,T_a),V_b),
    inference(fof_nnf,[status(thm)],[fact_Inl__not__Inr]) ).

fof(f_351_2,plain,
    ! [U_1688,U_1687,U_1686,U_1685] : hAPP(c_Sum__Type_OInl(U_1685,U_1686),U_1687) != hAPP(c_Sum__Type_OInr(U_1686,U_1685),U_1688),
    inference(variable_rename,[status(thm)],[f_351_1]) ).

fof(f_351_3,plain,
    ! [U_1687,U_1685,U_1686,U_1688] : hAPP(c_Sum__Type_OInl(U_1685,U_1686),U_1687) != hAPP(c_Sum__Type_OInr(U_1686,U_1685),U_1688),
    inference(definitional_conversion,[status(esa)],[f_351_2]) ).

cnf(f_351_4,plain,
    hAPP(c_Sum__Type_OInl(U_1685,U_1686),U_1687) != hAPP(c_Sum__Type_OInr(U_1686,U_1685),U_1688),
    inference(clausify,[status(thm)],[f_351_3]) ).

fof(f_352_1,plain,
    ! [V_b_H,V_a,T_b,T_a] : hAPP(c_Sum__Type_OInl(T_a,T_b),V_a) != hAPP(c_Sum__Type_OInr(T_b,T_a),V_b_H),
    inference(fof_nnf,[status(thm)],[fact_sum_Osimps_I3_J]) ).

fof(f_352_2,plain,
    ! [U_1692,U_1691,U_1690,U_1689] : hAPP(c_Sum__Type_OInl(U_1689,U_1690),U_1691) != hAPP(c_Sum__Type_OInr(U_1690,U_1689),U_1692),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

fof(f_352_3,plain,
    ! [U_1689,U_1690,U_1691,U_1692] : hAPP(c_Sum__Type_OInl(U_1689,U_1690),U_1691) != hAPP(c_Sum__Type_OInr(U_1690,U_1689),U_1692),
    inference(definitional_conversion,[status(esa)],[f_352_2]) ).

cnf(f_352_4,plain,
    hAPP(c_Sum__Type_OInl(U_1689,U_1690),U_1691) != hAPP(c_Sum__Type_OInr(U_1690,U_1689),U_1692),
    inference(clausify,[status(thm)],[f_352_3]) ).

fof(f_353_1,plain,
    ! [V_a,V_b,T_a,T_b] : hAPP(c_Sum__Type_OInr(T_b,T_a),V_b) != hAPP(c_Sum__Type_OInl(T_a,T_b),V_a),
    inference(fof_nnf,[status(thm)],[fact_Inr__not__Inl]) ).

fof(f_353_2,plain,
    ! [U_1696,U_1695,U_1694,U_1693] : hAPP(c_Sum__Type_OInr(U_1693,U_1694),U_1695) != hAPP(c_Sum__Type_OInl(U_1694,U_1693),U_1696),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

fof(f_353_3,plain,
    ! [U_1693,U_1694,U_1695,U_1696] : hAPP(c_Sum__Type_OInr(U_1693,U_1694),U_1695) != hAPP(c_Sum__Type_OInl(U_1694,U_1693),U_1696),
    inference(definitional_conversion,[status(esa)],[f_353_2]) ).

cnf(f_353_4,plain,
    hAPP(c_Sum__Type_OInr(U_1693,U_1694),U_1695) != hAPP(c_Sum__Type_OInl(U_1694,U_1693),U_1696),
    inference(clausify,[status(thm)],[f_353_3]) ).

fof(f_354_1,plain,
    ! [V_a_1,V_b_H_1,T_a_1,T_b_1] : hAPP(c_Sum__Type_OInr(T_b_1,T_a_1),V_b_H_1) != hAPP(c_Sum__Type_OInl(T_a_1,T_b_1),V_a_1),
    inference(fof_nnf,[status(thm)],[fact_sum_Osimps_I4_J]) ).

fof(f_354_2,plain,
    ! [U_1700,U_1699,U_1698,U_1697] : hAPP(c_Sum__Type_OInr(U_1697,U_1698),U_1699) != hAPP(c_Sum__Type_OInl(U_1698,U_1697),U_1700),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

fof(f_354_3,plain,
    ! [U_1697,U_1698,U_1699,U_1700] : hAPP(c_Sum__Type_OInr(U_1697,U_1698),U_1699) != hAPP(c_Sum__Type_OInl(U_1698,U_1697),U_1700),
    inference(definitional_conversion,[status(esa)],[f_354_2]) ).

cnf(f_354_4,plain,
    hAPP(c_Sum__Type_OInr(U_1697,U_1698),U_1699) != hAPP(c_Sum__Type_OInl(U_1698,U_1697),U_1700),
    inference(clausify,[status(thm)],[f_354_3]) ).

fof(f_355_1,plain,
    ! [V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_sum(T_a,T_b)),hAPP(c_Sum__Type_OInl(T_a,T_b),V_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_sum_Osize_I3_J]) ).

fof(f_355_2,plain,
    ! [U_1703,U_1702,U_1701] : hAPP(c_Nat_Osize__class_Osize(tc_sum(U_1701,U_1702)),hAPP(c_Sum__Type_OInl(U_1701,U_1702),U_1703)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

fof(f_355_3,plain,
    ! [U_1701,U_1702,U_1703] : hAPP(c_Nat_Osize__class_Osize(tc_sum(U_1701,U_1702)),hAPP(c_Sum__Type_OInl(U_1701,U_1702),U_1703)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_355_2]) ).

cnf(f_355_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_sum(U_1701,U_1702)),hAPP(c_Sum__Type_OInl(U_1701,U_1702),U_1703)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_355_3]) ).

fof(f_356_1,plain,
    ! [V_b,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_sum(T_a,T_b)),hAPP(c_Sum__Type_OInr(T_b,T_a),V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_sum_Osize_I4_J]) ).

fof(f_356_2,plain,
    ! [U_1706,U_1705,U_1704] : hAPP(c_Nat_Osize__class_Osize(tc_sum(U_1704,U_1705)),hAPP(c_Sum__Type_OInr(U_1705,U_1704),U_1706)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

fof(f_356_3,plain,
    ! [U_1705,U_1706,U_1704] : hAPP(c_Nat_Osize__class_Osize(tc_sum(U_1704,U_1705)),hAPP(c_Sum__Type_OInr(U_1705,U_1704),U_1706)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_356_2]) ).

cnf(f_356_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_sum(U_1704,U_1705)),hAPP(c_Sum__Type_OInr(U_1705,U_1704),U_1706)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_356_3]) ).

fof(f_357_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_357_2,plain,
    ! [U_1709,U_1708,U_1707] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1708),U_1709)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1707),U_1708)) ),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

fof(f_357_3,plain,
    ! [U_1707,U_1708,U_1709] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1708),U_1709)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1707),U_1708)) ),
    inference(definitional_conversion,[status(esa)],[f_357_2]) ).

cnf(f_357_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1708),U_1709)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1707),U_1708)) ),
    inference(clausify,[status(thm)],[f_357_3]) ).

fof(f_358_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_358_2,plain,
    ! [U_1712,U_1711,U_1710] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1710),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1712),U_1711)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1710),U_1711)) ),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

fof(f_358_3,plain,
    ! [U_1710,U_1711,U_1712] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1710),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1712),U_1711)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1710),U_1711)) ),
    inference(definitional_conversion,[status(esa)],[f_358_2]) ).

cnf(f_358_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1710),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1712),U_1711)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1710),U_1711)) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

fof(f_359_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_359_2,plain,
    ! [U_1714,U_1713] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1713),c_Groups_Ozero__class_Ozero(U_1713)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1713),U_1714)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1714)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1714))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1713),c_Groups_Ozero__class_Ozero(U_1713)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1713),U_1714))) ) )
      | ~ class_Rings_Olinordered__semidom(U_1713) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

fof(f_359_3,plain,
    ( ! [U_1714,U_1713] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1713),c_Groups_Ozero__class_Ozero(U_1713)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1713),U_1714)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1714))
        | ~ sP88(U_1714,U_1713) )
    & ! [U_1714,U_1713] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1714))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1713),c_Groups_Ozero__class_Ozero(U_1713)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1713),U_1714)))
        | ~ sP88(U_1714,U_1713) )
    & ! [U_1714,U_1713] :
        ( sP88(U_1714,U_1713)
        | ~ class_Rings_Olinordered__semidom(U_1713) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88])],[f_359_2]) ).

cnf(f_359_4,plain,
    ( sP88(U_1714,U_1713)
    | ~ class_Rings_Olinordered__semidom(U_1713) ),
    inference(clausify,[status(thm)],[f_359_3]) ).

cnf(f_359_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1714))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1713),c_Groups_Ozero__class_Ozero(U_1713)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1713),U_1714)))
    | ~ sP88(U_1714,U_1713) ),
    inference(clausify,[status(thm)],[f_359_3]) ).

cnf(f_359_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1713),c_Groups_Ozero__class_Ozero(U_1713)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1713),U_1714)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1714))
    | ~ sP88(U_1714,U_1713) ),
    inference(clausify,[status(thm)],[f_359_3]) ).

fof(f_360_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_360_2,plain,
    ! [U_1717,U_1716,U_1715] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1715),U_1716) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1715),U_1717)
          | U_1716 != U_1717 )
        & ( U_1716 = U_1717
          | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1715),U_1716) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1715),U_1717) ) )
      | ~ class_Nat_Osemiring__char__0(U_1715) ),
    inference(variable_rename,[status(thm)],[f_360_1]) ).

fof(f_360_3,plain,
    ( ! [U_1716,U_1715,U_1717] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1715),U_1716) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1715),U_1717)
        | U_1716 != U_1717
        | ~ sP89(U_1716,U_1715,U_1717) )
    & ! [U_1716,U_1715,U_1717] :
        ( U_1716 = U_1717
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1715),U_1716) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1715),U_1717)
        | ~ sP89(U_1716,U_1715,U_1717) )
    & ! [U_1716,U_1715,U_1717] :
        ( sP89(U_1716,U_1715,U_1717)
        | ~ class_Nat_Osemiring__char__0(U_1715) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89])],[f_360_2]) ).

cnf(f_360_4,plain,
    ( sP89(U_1716,U_1715,U_1717)
    | ~ class_Nat_Osemiring__char__0(U_1715) ),
    inference(clausify,[status(thm)],[f_360_3]) ).

cnf(f_360_5,plain,
    ( U_1716 = U_1717
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1715),U_1716) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1715),U_1717)
    | ~ sP89(U_1716,U_1715,U_1717) ),
    inference(clausify,[status(thm)],[f_360_3]) ).

cnf(f_360_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1715),U_1716) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1715),U_1717)
    | U_1716 != U_1717
    | ~ sP89(U_1716,U_1715,U_1717) ),
    inference(clausify,[status(thm)],[f_360_3]) ).

fof(f_361_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_361_2,plain,
    ! [U_1721,U_1720] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1720),U_1721))
        | ! [U_1719] : U_1721 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1720),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1719))) )
      & ( ? [U_1718] : U_1721 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1720),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1718)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1720),U_1721)) ) ),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

fof(f_361_3,plain,
    ( ! [U_1725,U_1723] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1723),U_1725))
        | ! [U_1719] : U_1725 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1723),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1719))) )
    & ! [U_1724,U_1722] :
        ( ? [U_1718] : U_1724 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1722),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1718)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1722),U_1724)) ) ),
    inference(miniscope,[status(thm)],[f_361_2]) ).

fof(f_361_4,plain,
    ( ! [U_1725,U_1723] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1723),U_1725))
        | ! [U_1719] : U_1725 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1723),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1719))) )
    & ! [U_1724,U_1722] :
        ( U_1724 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1722),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK43(U_1724,U_1722))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1722),U_1724)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_1718,sK43(U_1724,U_1722))],[f_361_3]) ).

fof(f_361_5,plain,
    ( ! [U_1719,U_1725,U_1723] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1723),U_1725))
        | U_1725 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1723),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1719))) )
    & ! [U_1724,U_1722] :
        ( U_1724 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1722),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK43(U_1724,U_1722))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1722),U_1724)) ) ),
    inference(definitional_conversion,[status(esa)],[f_361_4]) ).

cnf(f_361_6,plain,
    ( U_1724 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1722),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK43(U_1724,U_1722))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1722),U_1724)) ),
    inference(clausify,[status(thm)],[f_361_5]) ).

cnf(f_361_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1723),U_1725))
    | U_1725 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1723),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_1719))) ),
    inference(clausify,[status(thm)],[f_361_5]) ).

fof(f_362_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_362_2,plain,
    ! [U_1727,U_1726] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1726)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1727)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1726),U_1727)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1726),U_1727))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1726)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1727))) ) ),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

fof(f_362_3,plain,
    ( ! [U_1731,U_1729] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1729)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1731)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1729),U_1731)) )
    & ! [U_1730,U_1728] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1728),U_1730))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1728)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1730))) ) ),
    inference(miniscope,[status(thm)],[f_362_2]) ).

fof(f_362_4,plain,
    ( ! [U_1729,U_1731] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1729)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1731)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1729),U_1731)) )
    & ! [U_1728,U_1730] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1728),U_1730))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1728)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1730))) ) ),
    inference(definitional_conversion,[status(esa)],[f_362_3]) ).

cnf(f_362_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1728),U_1730))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1728)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1730))) ),
    inference(clausify,[status(thm)],[f_362_4]) ).

cnf(f_362_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_1729)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1731)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1729),U_1731)) ),
    inference(clausify,[status(thm)],[f_362_4]) ).

fof(f_363_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_363_2,plain,
    ! [U_1732] :
      ( ( 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_1732)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1732)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1732))
        | ~ 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_1732))) ) ),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

fof(f_363_3,plain,
    ( ! [U_1734] :
        ( 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_1734)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1734)) )
    & ! [U_1733] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1733))
        | ~ 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_1733))) ) ),
    inference(miniscope,[status(thm)],[f_363_2]) ).

fof(f_363_4,plain,
    ( ! [U_1734] :
        ( 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_1734)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1734)) )
    & ! [U_1733] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1733))
        | ~ 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_1733))) ) ),
    inference(definitional_conversion,[status(esa)],[f_363_3]) ).

cnf(f_363_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1733))
    | ~ 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_1733))) ),
    inference(clausify,[status(thm)],[f_363_4]) ).

cnf(f_363_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_1734)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1734)) ),
    inference(clausify,[status(thm)],[f_363_4]) ).

fof(f_364_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_364_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_364_1]) ).

cnf(f_364_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_364_2]) ).

fof(f_365_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_365_2,plain,
    ! [U_1735] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1735) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_1735 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_1735 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1735) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

fof(f_365_3,plain,
    ( ! [U_1737] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1737) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_1737 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1736] :
        ( U_1736 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1736) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_365_2]) ).

fof(f_365_4,plain,
    ( ! [U_1737] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1737) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_1737 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1736] :
        ( U_1736 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1736) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_365_3]) ).

cnf(f_365_5,plain,
    ( U_1736 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1736) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_365_4]) ).

cnf(f_365_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1737) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_1737 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_365_4]) ).

fof(f_366_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_366_2,plain,
    ! [U_1739,U_1738] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1738)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1739)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1738),U_1739)),
    inference(variable_rename,[status(thm)],[f_366_1]) ).

fof(f_366_3,plain,
    ! [U_1738,U_1739] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1738)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1739)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1738),U_1739)),
    inference(definitional_conversion,[status(esa)],[f_366_2]) ).

cnf(f_366_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1738)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1739)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1738),U_1739)),
    inference(clausify,[status(thm)],[f_366_3]) ).

fof(f_367_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_367_2,plain,
    ! [U_1742,U_1741,U_1740] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1740)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1741)),U_1742)) = 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_1740),U_1741))),U_1742),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

fof(f_367_3,plain,
    ! [U_1740,U_1741,U_1742] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1740)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1741)),U_1742)) = 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_1740),U_1741))),U_1742),
    inference(definitional_conversion,[status(esa)],[f_367_2]) ).

cnf(f_367_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1740)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1741)),U_1742)) = 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_1740),U_1741))),U_1742),
    inference(clausify,[status(thm)],[f_367_3]) ).

fof(f_368_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_368_2,plain,
    ! [U_1744,U_1743] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1743),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1743),U_1744)),c_Groups_Ozero__class_Ozero(U_1743)))
      | ~ class_Rings_Olinordered__semidom(U_1743) ),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

fof(f_368_3,plain,
    ! [U_1743,U_1744] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1743),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1743),U_1744)),c_Groups_Ozero__class_Ozero(U_1743)))
      | ~ class_Rings_Olinordered__semidom(U_1743) ),
    inference(definitional_conversion,[status(esa)],[f_368_2]) ).

cnf(f_368_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1743),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1743),U_1744)),c_Groups_Ozero__class_Ozero(U_1743)))
    | ~ class_Rings_Olinordered__semidom(U_1743) ),
    inference(clausify,[status(thm)],[f_368_3]) ).

fof(f_369_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_369_2,plain,
    ! [U_1745] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1745),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_1745)
      | ~ class_Rings_Osemiring__1(U_1745) ),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

fof(f_369_3,plain,
    ! [U_1745] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1745),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_1745)
      | ~ class_Rings_Osemiring__1(U_1745) ),
    inference(definitional_conversion,[status(esa)],[f_369_2]) ).

cnf(f_369_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1745),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_1745)
    | ~ class_Rings_Osemiring__1(U_1745) ),
    inference(clausify,[status(thm)],[f_369_3]) ).

fof(f_370_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_370_2,plain,
    ! [U_1748,U_1747,U_1746] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1746),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1746),U_1747)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1746),U_1748)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1747),U_1748)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1747),U_1748))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1746),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1746),U_1747)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1746),U_1748))) ) )
      | ~ class_Rings_Olinordered__semidom(U_1746) ),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

fof(f_370_3,plain,
    ( ! [U_1746,U_1747,U_1748] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1746),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1746),U_1747)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1746),U_1748)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1747),U_1748))
        | ~ sP90(U_1746,U_1747,U_1748) )
    & ! [U_1746,U_1747,U_1748] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1747),U_1748))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1746),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1746),U_1747)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1746),U_1748)))
        | ~ sP90(U_1746,U_1747,U_1748) )
    & ! [U_1746,U_1747,U_1748] :
        ( sP90(U_1746,U_1747,U_1748)
        | ~ class_Rings_Olinordered__semidom(U_1746) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90])],[f_370_2]) ).

cnf(f_370_4,plain,
    ( sP90(U_1746,U_1747,U_1748)
    | ~ class_Rings_Olinordered__semidom(U_1746) ),
    inference(clausify,[status(thm)],[f_370_3]) ).

cnf(f_370_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1747),U_1748))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1746),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1746),U_1747)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1746),U_1748)))
    | ~ sP90(U_1746,U_1747,U_1748) ),
    inference(clausify,[status(thm)],[f_370_3]) ).

cnf(f_370_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1746),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1746),U_1747)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1746),U_1748)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1747),U_1748))
    | ~ sP90(U_1746,U_1747,U_1748) ),
    inference(clausify,[status(thm)],[f_370_3]) ).

fof(f_371_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_371_2,plain,
    ! [U_1751,U_1750,U_1749] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1749),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1749),U_1750)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1749),U_1751)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1750),U_1751))
      | ~ class_Rings_Olinordered__semidom(U_1749) ),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

fof(f_371_3,plain,
    ! [U_1749,U_1751,U_1750] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1749),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1749),U_1750)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1749),U_1751)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1750),U_1751))
      | ~ class_Rings_Olinordered__semidom(U_1749) ),
    inference(definitional_conversion,[status(esa)],[f_371_2]) ).

cnf(f_371_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1749),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1749),U_1750)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1749),U_1751)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1750),U_1751))
    | ~ class_Rings_Olinordered__semidom(U_1749) ),
    inference(clausify,[status(thm)],[f_371_3]) ).

fof(f_372_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_372_2,plain,
    ! [U_1754,U_1753,U_1752] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1753),U_1754))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1752),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1752),U_1753)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1752),U_1754)))
      | ~ class_Rings_Olinordered__semidom(U_1752) ),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

fof(f_372_3,plain,
    ! [U_1752,U_1753,U_1754] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1753),U_1754))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1752),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1752),U_1753)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1752),U_1754)))
      | ~ class_Rings_Olinordered__semidom(U_1752) ),
    inference(definitional_conversion,[status(esa)],[f_372_2]) ).

cnf(f_372_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1753),U_1754))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1752),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1752),U_1753)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1752),U_1754)))
    | ~ class_Rings_Olinordered__semidom(U_1752) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

fof(f_373_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_373_2,plain,
    ! [U_1757,U_1756,U_1755] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1755),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1756),U_1757)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1755),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1755),U_1756)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1755),U_1757))
      | ~ class_Rings_Osemiring__1(U_1755) ),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

fof(f_373_3,plain,
    ! [U_1755,U_1756,U_1757] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1755),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1756),U_1757)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1755),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1755),U_1756)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1755),U_1757))
      | ~ class_Rings_Osemiring__1(U_1755) ),
    inference(definitional_conversion,[status(esa)],[f_373_2]) ).

cnf(f_373_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1755),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1756),U_1757)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1755),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1755),U_1756)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1755),U_1757))
    | ~ class_Rings_Osemiring__1(U_1755) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

fof(f_374_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_374_2,plain,
    ! [U_1760,U_1759,U_1758] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1758),U_1760),U_1759))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1758),U_1759),U_1760))
      | U_1759 = U_1760
      | ~ class_Rings_Olinordered__idom(U_1758) ),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

fof(f_374_3,plain,
    ! [U_1758,U_1759,U_1760] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1758),U_1760),U_1759))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1758),U_1759),U_1760))
      | U_1759 = U_1760
      | ~ class_Rings_Olinordered__idom(U_1758) ),
    inference(definitional_conversion,[status(esa)],[f_374_2]) ).

cnf(f_374_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1758),U_1760),U_1759))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1758),U_1759),U_1760))
    | U_1759 = U_1760
    | ~ class_Rings_Olinordered__idom(U_1758) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

fof(f_375_1,plain,
    ! [V_y,V_x,T_a,T_b] :
      ( V_x = V_y
      | hAPP(c_Sum__Type_OInr(T_b,T_a),V_x) != hAPP(c_Sum__Type_OInr(T_b,T_a),V_y) ),
    inference(fof_nnf,[status(thm)],[fact_Inr__inject]) ).

fof(f_375_2,plain,
    ! [U_1764,U_1763,U_1762,U_1761] :
      ( U_1763 = U_1764
      | hAPP(c_Sum__Type_OInr(U_1761,U_1762),U_1763) != hAPP(c_Sum__Type_OInr(U_1761,U_1762),U_1764) ),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

fof(f_375_3,plain,
    ! [U_1764,U_1763] :
      ( ! [U_1762,U_1761] : hAPP(c_Sum__Type_OInr(U_1761,U_1762),U_1763) != hAPP(c_Sum__Type_OInr(U_1761,U_1762),U_1764)
      | U_1763 = U_1764 ),
    inference(miniscope,[status(thm)],[f_375_2]) ).

fof(f_375_4,plain,
    ! [U_1762,U_1761,U_1763,U_1764] :
      ( hAPP(c_Sum__Type_OInr(U_1761,U_1762),U_1763) != hAPP(c_Sum__Type_OInr(U_1761,U_1762),U_1764)
      | U_1763 = U_1764 ),
    inference(definitional_conversion,[status(esa)],[f_375_3]) ).

cnf(f_375_5,plain,
    ( hAPP(c_Sum__Type_OInr(U_1761,U_1762),U_1763) != hAPP(c_Sum__Type_OInr(U_1761,U_1762),U_1764)
    | U_1763 = U_1764 ),
    inference(clausify,[status(thm)],[f_375_4]) ).

fof(f_376_1,plain,
    ! [V_b_H_2,V_b_2,T_b,T_c] :
      ( ( hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_2) = hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_H_2)
        | V_b_2 != V_b_H_2 )
      & ( V_b_2 = V_b_H_2
        | hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_2) != hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_sum_Osimps_I2_J]) ).

fof(f_376_2,plain,
    ! [U_1768,U_1767,U_1766,U_1765] :
      ( ( hAPP(c_Sum__Type_OInr(U_1765,U_1766),U_1767) = hAPP(c_Sum__Type_OInr(U_1765,U_1766),U_1768)
        | U_1767 != U_1768 )
      & ( U_1767 = U_1768
        | hAPP(c_Sum__Type_OInr(U_1765,U_1766),U_1767) != hAPP(c_Sum__Type_OInr(U_1765,U_1766),U_1768) ) ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

fof(f_376_3,plain,
    ( ! [U_1776,U_1774] :
        ( ! [U_1772,U_1770] : hAPP(c_Sum__Type_OInr(U_1770,U_1772),U_1774) = hAPP(c_Sum__Type_OInr(U_1770,U_1772),U_1776)
        | U_1774 != U_1776 )
    & ! [U_1775,U_1773] :
        ( ! [U_1771,U_1769] : hAPP(c_Sum__Type_OInr(U_1769,U_1771),U_1773) != hAPP(c_Sum__Type_OInr(U_1769,U_1771),U_1775)
        | U_1773 = U_1775 ) ),
    inference(miniscope,[status(thm)],[f_376_2]) ).

fof(f_376_4,plain,
    ( ! [U_1776,U_1774,U_1770,U_1772] :
        ( hAPP(c_Sum__Type_OInr(U_1770,U_1772),U_1774) = hAPP(c_Sum__Type_OInr(U_1770,U_1772),U_1776)
        | U_1774 != U_1776 )
    & ! [U_1773,U_1769,U_1771,U_1775] :
        ( hAPP(c_Sum__Type_OInr(U_1769,U_1771),U_1773) != hAPP(c_Sum__Type_OInr(U_1769,U_1771),U_1775)
        | U_1773 = U_1775 ) ),
    inference(definitional_conversion,[status(esa)],[f_376_3]) ).

cnf(f_376_5,plain,
    ( hAPP(c_Sum__Type_OInr(U_1769,U_1771),U_1773) != hAPP(c_Sum__Type_OInr(U_1769,U_1771),U_1775)
    | U_1773 = U_1775 ),
    inference(clausify,[status(thm)],[f_376_4]) ).

cnf(f_376_6,plain,
    ( hAPP(c_Sum__Type_OInr(U_1770,U_1772),U_1774) = hAPP(c_Sum__Type_OInr(U_1770,U_1772),U_1776)
    | U_1774 != U_1776 ),
    inference(clausify,[status(thm)],[f_376_4]) ).

fof(f_377_1,plain,
    ! [V_y,V_x,T_b,T_a] :
      ( V_x = V_y
      | hAPP(c_Sum__Type_OInl(T_a,T_b),V_x) != hAPP(c_Sum__Type_OInl(T_a,T_b),V_y) ),
    inference(fof_nnf,[status(thm)],[fact_Inl__inject]) ).

fof(f_377_2,plain,
    ! [U_1780,U_1779,U_1778,U_1777] :
      ( U_1779 = U_1780
      | hAPP(c_Sum__Type_OInl(U_1777,U_1778),U_1779) != hAPP(c_Sum__Type_OInl(U_1777,U_1778),U_1780) ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

fof(f_377_3,plain,
    ! [U_1780,U_1779] :
      ( ! [U_1778,U_1777] : hAPP(c_Sum__Type_OInl(U_1777,U_1778),U_1779) != hAPP(c_Sum__Type_OInl(U_1777,U_1778),U_1780)
      | U_1779 = U_1780 ),
    inference(miniscope,[status(thm)],[f_377_2]) ).

fof(f_377_4,plain,
    ! [U_1779,U_1778,U_1777,U_1780] :
      ( hAPP(c_Sum__Type_OInl(U_1777,U_1778),U_1779) != hAPP(c_Sum__Type_OInl(U_1777,U_1778),U_1780)
      | U_1779 = U_1780 ),
    inference(definitional_conversion,[status(esa)],[f_377_3]) ).

cnf(f_377_5,plain,
    ( hAPP(c_Sum__Type_OInl(U_1777,U_1778),U_1779) != hAPP(c_Sum__Type_OInl(U_1777,U_1778),U_1780)
    | U_1779 = U_1780 ),
    inference(clausify,[status(thm)],[f_377_4]) ).

fof(f_378_1,plain,
    ! [V_a_H_2,V_a_2,T_c,T_b] :
      ( ( hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_2) = hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_H_2)
        | V_a_2 != V_a_H_2 )
      & ( V_a_2 = V_a_H_2
        | hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_2) != hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_sum_Osimps_I1_J]) ).

fof(f_378_2,plain,
    ! [U_1784,U_1783,U_1782,U_1781] :
      ( ( hAPP(c_Sum__Type_OInl(U_1781,U_1782),U_1783) = hAPP(c_Sum__Type_OInl(U_1781,U_1782),U_1784)
        | U_1783 != U_1784 )
      & ( U_1783 = U_1784
        | hAPP(c_Sum__Type_OInl(U_1781,U_1782),U_1783) != hAPP(c_Sum__Type_OInl(U_1781,U_1782),U_1784) ) ),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

fof(f_378_3,plain,
    ( ! [U_1792,U_1790] :
        ( ! [U_1788,U_1786] : hAPP(c_Sum__Type_OInl(U_1786,U_1788),U_1790) = hAPP(c_Sum__Type_OInl(U_1786,U_1788),U_1792)
        | U_1790 != U_1792 )
    & ! [U_1791,U_1789] :
        ( ! [U_1787,U_1785] : hAPP(c_Sum__Type_OInl(U_1785,U_1787),U_1789) != hAPP(c_Sum__Type_OInl(U_1785,U_1787),U_1791)
        | U_1789 = U_1791 ) ),
    inference(miniscope,[status(thm)],[f_378_2]) ).

fof(f_378_4,plain,
    ( ! [U_1790,U_1786,U_1792,U_1788] :
        ( hAPP(c_Sum__Type_OInl(U_1786,U_1788),U_1790) = hAPP(c_Sum__Type_OInl(U_1786,U_1788),U_1792)
        | U_1790 != U_1792 )
    & ! [U_1789,U_1785,U_1787,U_1791] :
        ( hAPP(c_Sum__Type_OInl(U_1785,U_1787),U_1789) != hAPP(c_Sum__Type_OInl(U_1785,U_1787),U_1791)
        | U_1789 = U_1791 ) ),
    inference(definitional_conversion,[status(esa)],[f_378_3]) ).

cnf(f_378_5,plain,
    ( hAPP(c_Sum__Type_OInl(U_1785,U_1787),U_1789) != hAPP(c_Sum__Type_OInl(U_1785,U_1787),U_1791)
    | U_1789 = U_1791 ),
    inference(clausify,[status(thm)],[f_378_4]) ).

cnf(f_378_6,plain,
    ( hAPP(c_Sum__Type_OInl(U_1786,U_1788),U_1790) = hAPP(c_Sum__Type_OInl(U_1786,U_1788),U_1792)
    | U_1790 != U_1792 ),
    inference(clausify,[status(thm)],[f_378_4]) ).

fof(f_379_1,plain,
    ! [V_x,T_b,T_a] : c_Sum__Type_OProjl(T_a,T_b,hAPP(c_Sum__Type_OInl(T_a,T_b),V_x)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_Projl_Osimps]) ).

fof(f_379_2,plain,
    ! [U_1795,U_1794,U_1793] : c_Sum__Type_OProjl(U_1793,U_1794,hAPP(c_Sum__Type_OInl(U_1793,U_1794),U_1795)) = U_1795,
    inference(variable_rename,[status(thm)],[f_379_1]) ).

fof(f_379_3,plain,
    ! [U_1793,U_1794,U_1795] : c_Sum__Type_OProjl(U_1793,U_1794,hAPP(c_Sum__Type_OInl(U_1793,U_1794),U_1795)) = U_1795,
    inference(definitional_conversion,[status(esa)],[f_379_2]) ).

cnf(f_379_4,plain,
    c_Sum__Type_OProjl(U_1793,U_1794,hAPP(c_Sum__Type_OInl(U_1793,U_1794),U_1795)) = U_1795,
    inference(clausify,[status(thm)],[f_379_3]) ).

fof(f_380_1,plain,
    ! [V_x,T_b,T_a] : c_Sum__Type_OProjr(T_a,T_b,hAPP(c_Sum__Type_OInr(T_b,T_a),V_x)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_Projr_Osimps]) ).

fof(f_380_2,plain,
    ! [U_1798,U_1797,U_1796] : c_Sum__Type_OProjr(U_1796,U_1797,hAPP(c_Sum__Type_OInr(U_1797,U_1796),U_1798)) = U_1798,
    inference(variable_rename,[status(thm)],[f_380_1]) ).

fof(f_380_3,plain,
    ! [U_1796,U_1797,U_1798] : c_Sum__Type_OProjr(U_1796,U_1797,hAPP(c_Sum__Type_OInr(U_1797,U_1796),U_1798)) = U_1798,
    inference(definitional_conversion,[status(esa)],[f_380_2]) ).

cnf(f_380_4,plain,
    c_Sum__Type_OProjr(U_1796,U_1797,hAPP(c_Sum__Type_OInr(U_1797,U_1796),U_1798)) = U_1798,
    inference(clausify,[status(thm)],[f_380_3]) ).

fof(f_381_1,plain,
    ! [V_a_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : c_Sum__Type_Osum_Osum__rec(T_c,T_b,T_d,V_f1_2,V_f2_2,hAPP(c_Sum__Type_OInl(T_c,T_d),V_a_2)) = hAPP(V_f1_2,V_a_2),
    inference(fof_nnf,[status(thm)],[fact_sum_Orecs_I1_J]) ).

fof(f_381_2,plain,
    ! [U_1804,U_1803,U_1802,U_1801,U_1800,U_1799] : c_Sum__Type_Osum_Osum__rec(U_1799,U_1800,U_1801,U_1802,U_1803,hAPP(c_Sum__Type_OInl(U_1799,U_1801),U_1804)) = hAPP(U_1802,U_1804),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

fof(f_381_3,plain,
    ! [U_1799,U_1800,U_1801,U_1802,U_1803,U_1804] : c_Sum__Type_Osum_Osum__rec(U_1799,U_1800,U_1801,U_1802,U_1803,hAPP(c_Sum__Type_OInl(U_1799,U_1801),U_1804)) = hAPP(U_1802,U_1804),
    inference(definitional_conversion,[status(esa)],[f_381_2]) ).

cnf(f_381_4,plain,
    c_Sum__Type_Osum_Osum__rec(U_1799,U_1800,U_1801,U_1802,U_1803,hAPP(c_Sum__Type_OInl(U_1799,U_1801),U_1804)) = hAPP(U_1802,U_1804),
    inference(clausify,[status(thm)],[f_381_3]) ).

fof(f_382_1,plain,
    ! [V_b_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : c_Sum__Type_Osum_Osum__rec(T_c,T_b,T_d,V_f1_2,V_f2_2,hAPP(c_Sum__Type_OInr(T_d,T_c),V_b_2)) = hAPP(V_f2_2,V_b_2),
    inference(fof_nnf,[status(thm)],[fact_sum_Orecs_I2_J]) ).

fof(f_382_2,plain,
    ! [U_1810,U_1809,U_1808,U_1807,U_1806,U_1805] : c_Sum__Type_Osum_Osum__rec(U_1805,U_1806,U_1807,U_1808,U_1809,hAPP(c_Sum__Type_OInr(U_1807,U_1805),U_1810)) = hAPP(U_1809,U_1810),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

fof(f_382_3,plain,
    ! [U_1805,U_1807,U_1806,U_1808,U_1809,U_1810] : c_Sum__Type_Osum_Osum__rec(U_1805,U_1806,U_1807,U_1808,U_1809,hAPP(c_Sum__Type_OInr(U_1807,U_1805),U_1810)) = hAPP(U_1809,U_1810),
    inference(definitional_conversion,[status(esa)],[f_382_2]) ).

cnf(f_382_4,plain,
    c_Sum__Type_Osum_Osum__rec(U_1805,U_1806,U_1807,U_1808,U_1809,hAPP(c_Sum__Type_OInr(U_1807,U_1805),U_1810)) = hAPP(U_1809,U_1810),
    inference(clausify,[status(thm)],[f_382_3]) ).

fof(f_383_1,plain,
    ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_OSuml(T_c,T_b,T_d,V_f_2),hAPP(c_Sum__Type_OInl(T_c,T_d),V_x_2)) = hAPP(V_f_2,V_x_2),
    inference(fof_nnf,[status(thm)],[fact_Suml_Osimps]) ).

fof(f_383_2,plain,
    ! [U_1815,U_1814,U_1813,U_1812,U_1811] : hAPP(c_Sum__Type_OSuml(U_1811,U_1812,U_1813,U_1814),hAPP(c_Sum__Type_OInl(U_1811,U_1813),U_1815)) = hAPP(U_1814,U_1815),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

fof(f_383_3,plain,
    ! [U_1811,U_1812,U_1813,U_1814,U_1815] : hAPP(c_Sum__Type_OSuml(U_1811,U_1812,U_1813,U_1814),hAPP(c_Sum__Type_OInl(U_1811,U_1813),U_1815)) = hAPP(U_1814,U_1815),
    inference(definitional_conversion,[status(esa)],[f_383_2]) ).

cnf(f_383_4,plain,
    hAPP(c_Sum__Type_OSuml(U_1811,U_1812,U_1813,U_1814),hAPP(c_Sum__Type_OInl(U_1811,U_1813),U_1815)) = hAPP(U_1814,U_1815),
    inference(clausify,[status(thm)],[f_383_3]) ).

fof(f_384_1,plain,
    ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_OSumr(T_c,T_b,T_d,V_f_2),hAPP(c_Sum__Type_OInr(T_c,T_d),V_x_2)) = hAPP(V_f_2,V_x_2),
    inference(fof_nnf,[status(thm)],[fact_Sumr_Osimps]) ).

fof(f_384_2,plain,
    ! [U_1820,U_1819,U_1818,U_1817,U_1816] : hAPP(c_Sum__Type_OSumr(U_1816,U_1817,U_1818,U_1819),hAPP(c_Sum__Type_OInr(U_1816,U_1818),U_1820)) = hAPP(U_1819,U_1820),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

fof(f_384_3,plain,
    ! [U_1816,U_1817,U_1818,U_1819,U_1820] : hAPP(c_Sum__Type_OSumr(U_1816,U_1817,U_1818,U_1819),hAPP(c_Sum__Type_OInr(U_1816,U_1818),U_1820)) = hAPP(U_1819,U_1820),
    inference(definitional_conversion,[status(esa)],[f_384_2]) ).

cnf(f_384_4,plain,
    hAPP(c_Sum__Type_OSumr(U_1816,U_1817,U_1818,U_1819),hAPP(c_Sum__Type_OInr(U_1816,U_1818),U_1820)) = hAPP(U_1819,U_1820),
    inference(clausify,[status(thm)],[f_384_3]) ).

fof(f_385_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_385_2,plain,
    ! [U_1823,U_1822] :
      ( ? [U_1821] : U_1823 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1822),U_1821))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1822),U_1823)) ),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

fof(f_385_3,plain,
    ! [U_1823,U_1822] :
      ( U_1823 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1822),sK44(U_1823,U_1822)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1822),U_1823)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_1821,sK44(U_1823,U_1822))],[f_385_2]) ).

fof(f_385_4,plain,
    ! [U_1822,U_1823] :
      ( U_1823 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1822),sK44(U_1823,U_1822)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1822),U_1823)) ),
    inference(definitional_conversion,[status(esa)],[f_385_3]) ).

cnf(f_385_5,plain,
    ( U_1823 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1822),sK44(U_1823,U_1822)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1822),U_1823)) ),
    inference(clausify,[status(thm)],[f_385_4]) ).

fof(f_386_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_386_2,plain,
    ! [U_1826,U_1825] :
      ( ? [U_1824] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1825),U_1824) = U_1826
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1824)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1825),U_1826)) ),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

fof(f_386_3,plain,
    ! [U_1826,U_1825] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1825),sK45(U_1826,U_1825)) = U_1826
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK45(U_1826,U_1825))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1825),U_1826)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_1824,sK45(U_1826,U_1825))],[f_386_2]) ).

fof(f_386_4,plain,
    ( ! [U_1825,U_1826] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1825),sK45(U_1826,U_1825)) = U_1826
        | ~ sP91(U_1825,U_1826) )
    & ! [U_1825,U_1826] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK45(U_1826,U_1825)))
        | ~ sP91(U_1825,U_1826) )
    & ! [U_1825,U_1826] :
        ( sP91(U_1825,U_1826)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1825),U_1826)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91])],[f_386_3]) ).

cnf(f_386_5,plain,
    ( sP91(U_1825,U_1826)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1825),U_1826)) ),
    inference(clausify,[status(thm)],[f_386_4]) ).

cnf(f_386_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK45(U_1826,U_1825)))
    | ~ sP91(U_1825,U_1826) ),
    inference(clausify,[status(thm)],[f_386_4]) ).

cnf(f_386_7,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1825),sK45(U_1826,U_1825)) = U_1826
    | ~ sP91(U_1825,U_1826) ),
    inference(clausify,[status(thm)],[f_386_4]) ).

fof(f_387_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_387_2,plain,
    ! [U_1828] :
      ( ? [U_1827] : U_1828 = hAPP(c_Nat_OSuc,U_1827)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1828)) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

fof(f_387_3,plain,
    ! [U_1828] :
      ( U_1828 = hAPP(c_Nat_OSuc,sK46(U_1828))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1828)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_1827,sK46(U_1828))],[f_387_2]) ).

fof(f_387_4,plain,
    ! [U_1828] :
      ( U_1828 = hAPP(c_Nat_OSuc,sK46(U_1828))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1828)) ),
    inference(definitional_conversion,[status(esa)],[f_387_3]) ).

cnf(f_387_5,plain,
    ( U_1828 = hAPP(c_Nat_OSuc,sK46(U_1828))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1828)) ),
    inference(clausify,[status(thm)],[f_387_4]) ).

fof(f_388_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_388_2,plain,
    ! [U_1833,U_1832,U_1831,U_1830] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1830),hAPP(U_1831,U_1832)),hAPP(U_1831,U_1833)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1832),U_1833))
      | ? [U_1829] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1830),hAPP(U_1831,U_1829)),hAPP(U_1831,hAPP(c_Nat_OSuc,U_1829))))
      | ~ class_Orderings_Oorder(U_1830) ),
    inference(variable_rename,[status(thm)],[f_388_1]) ).

fof(f_388_3,plain,
    ! [U_1833,U_1832,U_1831,U_1830] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1830),hAPP(U_1831,U_1832)),hAPP(U_1831,U_1833)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1832),U_1833))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1830),hAPP(U_1831,sK47(U_1833,U_1832,U_1831,U_1830))),hAPP(U_1831,hAPP(c_Nat_OSuc,sK47(U_1833,U_1832,U_1831,U_1830)))))
      | ~ class_Orderings_Oorder(U_1830) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_1829,sK47(U_1833,U_1832,U_1831,U_1830))],[f_388_2]) ).

fof(f_388_4,plain,
    ! [U_1830,U_1831,U_1832,U_1833] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1830),hAPP(U_1831,U_1832)),hAPP(U_1831,U_1833)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1832),U_1833))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1830),hAPP(U_1831,sK47(U_1833,U_1832,U_1831,U_1830))),hAPP(U_1831,hAPP(c_Nat_OSuc,sK47(U_1833,U_1832,U_1831,U_1830)))))
      | ~ class_Orderings_Oorder(U_1830) ),
    inference(definitional_conversion,[status(esa)],[f_388_3]) ).

cnf(f_388_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1830),hAPP(U_1831,U_1832)),hAPP(U_1831,U_1833)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1832),U_1833))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1830),hAPP(U_1831,sK47(U_1833,U_1832,U_1831,U_1830))),hAPP(U_1831,hAPP(c_Nat_OSuc,sK47(U_1833,U_1832,U_1831,U_1830)))))
    | ~ class_Orderings_Oorder(U_1830) ),
    inference(clausify,[status(thm)],[f_388_4]) ).

fof(f_389_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_389_2,plain,
    ! [U_1835,U_1834] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1835),U_1834))
      | U_1834 = U_1835
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1834),U_1835)) ),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

fof(f_389_3,plain,
    ! [U_1835,U_1834] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1835),U_1834))
      | U_1834 = U_1835
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1834),U_1835)) ),
    inference(definitional_conversion,[status(esa)],[f_389_2]) ).

cnf(f_389_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1835),U_1834))
    | U_1834 = U_1835
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1834),U_1835)) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

fof(f_390_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_390_2,plain,
    ! [U_1836] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1836)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

fof(f_390_3,plain,
    ! [U_1836] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1836)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_390_2]) ).

cnf(f_390_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_1836)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_390_3]) ).

fof(f_391_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_391_2,plain,
    ! [U_1839,U_1838,U_1837] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1837),U_1839)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1838),U_1839)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1837),U_1838)) ),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

fof(f_391_3,plain,
    ! [U_1837,U_1838,U_1839] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1837),U_1839)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1838),U_1839)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1837),U_1838)) ),
    inference(definitional_conversion,[status(esa)],[f_391_2]) ).

cnf(f_391_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1837),U_1839)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1838),U_1839)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1837),U_1838)) ),
    inference(clausify,[status(thm)],[f_391_3]) ).

fof(f_392_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_392_2,plain,
    ! [U_1841,U_1840] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1840) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1841)
        | U_1840 != U_1841 )
      & ( U_1840 = U_1841
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1840) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1841) ) ),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

fof(f_392_3,plain,
    ( ! [U_1845,U_1843] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1843) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1845)
        | U_1843 != U_1845 )
    & ! [U_1844,U_1842] :
        ( U_1842 = U_1844
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1842) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1844) ) ),
    inference(miniscope,[status(thm)],[f_392_2]) ).

fof(f_392_4,plain,
    ( ! [U_1845,U_1843] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1843) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1845)
        | U_1843 != U_1845 )
    & ! [U_1844,U_1842] :
        ( U_1842 = U_1844
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1842) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1844) ) ),
    inference(definitional_conversion,[status(esa)],[f_392_3]) ).

cnf(f_392_5,plain,
    ( U_1842 = U_1844
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1842) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1844) ),
    inference(clausify,[status(thm)],[f_392_4]) ).

cnf(f_392_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1843) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1845)
    | U_1843 != U_1845 ),
    inference(clausify,[status(thm)],[f_392_4]) ).

fof(f_393_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_393_2,plain,
    ! [U_1846] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1846),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_1846,
    inference(variable_rename,[status(thm)],[f_393_1]) ).

fof(f_393_3,plain,
    ! [U_1846] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1846),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_1846,
    inference(definitional_conversion,[status(esa)],[f_393_2]) ).

cnf(f_393_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1846),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_1846,
    inference(clausify,[status(thm)],[f_393_3]) ).

fof(f_394_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_394_2,plain,
    ! [U_1847] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1847) = U_1847,
    inference(variable_rename,[status(thm)],[f_394_1]) ).

fof(f_394_3,plain,
    ! [U_1847] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1847) = U_1847,
    inference(definitional_conversion,[status(esa)],[f_394_2]) ).

cnf(f_394_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1847) = U_1847,
    inference(clausify,[status(thm)],[f_394_3]) ).

fof(f_395_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_395_2,plain,
    ! [U_1849,U_1848] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1848),U_1849) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1849),U_1848),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

fof(f_395_3,plain,
    ! [U_1848,U_1849] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1848),U_1849) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1849),U_1848),
    inference(definitional_conversion,[status(esa)],[f_395_2]) ).

cnf(f_395_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1848),U_1849) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1849),U_1848),
    inference(clausify,[status(thm)],[f_395_3]) ).

fof(f_396_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_396_2,plain,
    ! [U_1852,U_1851,U_1850] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1850),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1851),U_1852)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1851),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1850),U_1852)),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

fof(f_396_3,plain,
    ! [U_1850,U_1851,U_1852] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1850),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1851),U_1852)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1851),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1850),U_1852)),
    inference(definitional_conversion,[status(esa)],[f_396_2]) ).

cnf(f_396_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1850),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1851),U_1852)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1851),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1850),U_1852)),
    inference(clausify,[status(thm)],[f_396_3]) ).

fof(f_397_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_397_2,plain,
    ! [U_1855,U_1854,U_1853] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1853),U_1854)),U_1855) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1853),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1854),U_1855)),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

fof(f_397_3,plain,
    ! [U_1853,U_1854,U_1855] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1853),U_1854)),U_1855) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1853),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1854),U_1855)),
    inference(definitional_conversion,[status(esa)],[f_397_2]) ).

cnf(f_397_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1853),U_1854)),U_1855) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1853),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1854),U_1855)),
    inference(clausify,[status(thm)],[f_397_3]) ).

fof(f_398_1,plain,
    ! [V_g_2,V_f_2,T_c,T_d,T_b] :
      ( V_f_2 = V_g_2
      | c_Sum__Type_OSuml(T_b,T_d,T_c,V_f_2) != c_Sum__Type_OSuml(T_b,T_d,T_c,V_g_2) ),
    inference(fof_nnf,[status(thm)],[fact_Suml__inject]) ).

fof(f_398_2,plain,
    ! [U_1860,U_1859,U_1858,U_1857,U_1856] :
      ( U_1859 = U_1860
      | c_Sum__Type_OSuml(U_1856,U_1857,U_1858,U_1859) != c_Sum__Type_OSuml(U_1856,U_1857,U_1858,U_1860) ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

fof(f_398_3,plain,
    ! [U_1860,U_1859] :
      ( ! [U_1858,U_1857,U_1856] : c_Sum__Type_OSuml(U_1856,U_1857,U_1858,U_1859) != c_Sum__Type_OSuml(U_1856,U_1857,U_1858,U_1860)
      | U_1859 = U_1860 ),
    inference(miniscope,[status(thm)],[f_398_2]) ).

fof(f_398_4,plain,
    ! [U_1857,U_1858,U_1856,U_1859,U_1860] :
      ( c_Sum__Type_OSuml(U_1856,U_1857,U_1858,U_1859) != c_Sum__Type_OSuml(U_1856,U_1857,U_1858,U_1860)
      | U_1859 = U_1860 ),
    inference(definitional_conversion,[status(esa)],[f_398_3]) ).

cnf(f_398_5,plain,
    ( c_Sum__Type_OSuml(U_1856,U_1857,U_1858,U_1859) != c_Sum__Type_OSuml(U_1856,U_1857,U_1858,U_1860)
    | U_1859 = U_1860 ),
    inference(clausify,[status(thm)],[f_398_4]) ).

fof(f_399_1,plain,
    ! [V_g_2,V_f_2,T_b,T_d,T_c] :
      ( V_f_2 = V_g_2
      | c_Sum__Type_OSumr(T_c,T_d,T_b,V_f_2) != c_Sum__Type_OSumr(T_c,T_d,T_b,V_g_2) ),
    inference(fof_nnf,[status(thm)],[fact_Sumr__inject]) ).

fof(f_399_2,plain,
    ! [U_1865,U_1864,U_1863,U_1862,U_1861] :
      ( U_1864 = U_1865
      | c_Sum__Type_OSumr(U_1861,U_1862,U_1863,U_1864) != c_Sum__Type_OSumr(U_1861,U_1862,U_1863,U_1865) ),
    inference(variable_rename,[status(thm)],[f_399_1]) ).

fof(f_399_3,plain,
    ! [U_1865,U_1864] :
      ( ! [U_1863,U_1862,U_1861] : c_Sum__Type_OSumr(U_1861,U_1862,U_1863,U_1864) != c_Sum__Type_OSumr(U_1861,U_1862,U_1863,U_1865)
      | U_1864 = U_1865 ),
    inference(miniscope,[status(thm)],[f_399_2]) ).

fof(f_399_4,plain,
    ! [U_1862,U_1863,U_1861,U_1864,U_1865] :
      ( c_Sum__Type_OSumr(U_1861,U_1862,U_1863,U_1864) != c_Sum__Type_OSumr(U_1861,U_1862,U_1863,U_1865)
      | U_1864 = U_1865 ),
    inference(definitional_conversion,[status(esa)],[f_399_3]) ).

cnf(f_399_5,plain,
    ( c_Sum__Type_OSumr(U_1861,U_1862,U_1863,U_1864) != c_Sum__Type_OSumr(U_1861,U_1862,U_1863,U_1865)
    | U_1864 = U_1865 ),
    inference(clausify,[status(thm)],[f_399_4]) ).

fof(f_400_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_400_2,plain,
    ! [U_1867,U_1866] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1866)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1867)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1866),U_1867)),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

fof(f_400_3,plain,
    ! [U_1866,U_1867] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1866)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1867)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1866),U_1867)),
    inference(definitional_conversion,[status(esa)],[f_400_2]) ).

cnf(f_400_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1866)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1867)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1866),U_1867)),
    inference(clausify,[status(thm)],[f_400_3]) ).

fof(f_401_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_401_2,plain,
    ! [U_1869,U_1868] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1868)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1869)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1868),U_1869)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1868),U_1869))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1868)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1869))) ) ),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

fof(f_401_3,plain,
    ( ! [U_1873,U_1871] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1871)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1873)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1871),U_1873)) )
    & ! [U_1872,U_1870] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1870),U_1872))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1870)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1872))) ) ),
    inference(miniscope,[status(thm)],[f_401_2]) ).

fof(f_401_4,plain,
    ( ! [U_1871,U_1873] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1871)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1873)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1871),U_1873)) )
    & ! [U_1872,U_1870] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1870),U_1872))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1870)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1872))) ) ),
    inference(definitional_conversion,[status(esa)],[f_401_3]) ).

cnf(f_401_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1870),U_1872))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1870)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1872))) ),
    inference(clausify,[status(thm)],[f_401_4]) ).

cnf(f_401_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_1871)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1873)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1871),U_1873)) ),
    inference(clausify,[status(thm)],[f_401_4]) ).

fof(f_402_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_402_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_402_1]) ).

cnf(f_402_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_402_2]) ).

fof(f_403_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_403_2,plain,
    ! [U_1875] :
      ( ? [U_1874] :
          ( U_1875 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1874)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1874)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1875)) ),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

fof(f_403_3,plain,
    ! [U_1875] :
      ( ( U_1875 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK48(U_1875))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK48(U_1875))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1875)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_1874,sK48(U_1875))],[f_403_2]) ).

fof(f_403_4,plain,
    ( ! [U_1875] :
        ( U_1875 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK48(U_1875))
        | ~ sP92(U_1875) )
    & ! [U_1875] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK48(U_1875)))
        | ~ sP92(U_1875) )
    & ! [U_1875] :
        ( sP92(U_1875)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1875)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92])],[f_403_3]) ).

cnf(f_403_5,plain,
    ( sP92(U_1875)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1875)) ),
    inference(clausify,[status(thm)],[f_403_4]) ).

cnf(f_403_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK48(U_1875)))
    | ~ sP92(U_1875) ),
    inference(clausify,[status(thm)],[f_403_4]) ).

cnf(f_403_7,plain,
    ( U_1875 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK48(U_1875))
    | ~ sP92(U_1875) ),
    inference(clausify,[status(thm)],[f_403_4]) ).

fof(f_404_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_404_2,plain,
    ! [U_1877,U_1876] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1876),c_Groups_Ozero__class_Ozero(U_1876)),hAPP(c_Int_Oring__1__class_Oof__int(U_1876),U_1877)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1877)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1877))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1876),c_Groups_Ozero__class_Ozero(U_1876)),hAPP(c_Int_Oring__1__class_Oof__int(U_1876),U_1877))) ) )
      | ~ class_Rings_Olinordered__idom(U_1876) ),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

fof(f_404_3,plain,
    ( ! [U_1876,U_1877] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1876),c_Groups_Ozero__class_Ozero(U_1876)),hAPP(c_Int_Oring__1__class_Oof__int(U_1876),U_1877)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1877))
        | ~ sP93(U_1876,U_1877) )
    & ! [U_1876,U_1877] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1877))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1876),c_Groups_Ozero__class_Ozero(U_1876)),hAPP(c_Int_Oring__1__class_Oof__int(U_1876),U_1877)))
        | ~ sP93(U_1876,U_1877) )
    & ! [U_1876,U_1877] :
        ( sP93(U_1876,U_1877)
        | ~ class_Rings_Olinordered__idom(U_1876) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP93])],[f_404_2]) ).

cnf(f_404_4,plain,
    ( sP93(U_1876,U_1877)
    | ~ class_Rings_Olinordered__idom(U_1876) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

cnf(f_404_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1877))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1876),c_Groups_Ozero__class_Ozero(U_1876)),hAPP(c_Int_Oring__1__class_Oof__int(U_1876),U_1877)))
    | ~ sP93(U_1876,U_1877) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

cnf(f_404_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1876),c_Groups_Ozero__class_Ozero(U_1876)),hAPP(c_Int_Oring__1__class_Oof__int(U_1876),U_1877)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1877))
    | ~ sP93(U_1876,U_1877) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

fof(f_405_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_405_2,plain,
    ! [U_1879,U_1878] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),hAPP(c_Int_Oring__1__class_Oof__int(U_1878),U_1879)),c_Groups_Ozero__class_Ozero(U_1878)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1879),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1879),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),hAPP(c_Int_Oring__1__class_Oof__int(U_1878),U_1879)),c_Groups_Ozero__class_Ozero(U_1878))) ) )
      | ~ class_Rings_Olinordered__idom(U_1878) ),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

fof(f_405_3,plain,
    ( ! [U_1879,U_1878] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),hAPP(c_Int_Oring__1__class_Oof__int(U_1878),U_1879)),c_Groups_Ozero__class_Ozero(U_1878)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1879),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP94(U_1879,U_1878) )
    & ! [U_1879,U_1878] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1879),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),hAPP(c_Int_Oring__1__class_Oof__int(U_1878),U_1879)),c_Groups_Ozero__class_Ozero(U_1878)))
        | ~ sP94(U_1879,U_1878) )
    & ! [U_1879,U_1878] :
        ( sP94(U_1879,U_1878)
        | ~ class_Rings_Olinordered__idom(U_1878) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94])],[f_405_2]) ).

cnf(f_405_4,plain,
    ( sP94(U_1879,U_1878)
    | ~ class_Rings_Olinordered__idom(U_1878) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

cnf(f_405_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1879),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),hAPP(c_Int_Oring__1__class_Oof__int(U_1878),U_1879)),c_Groups_Ozero__class_Ozero(U_1878)))
    | ~ sP94(U_1879,U_1878) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

cnf(f_405_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1878),hAPP(c_Int_Oring__1__class_Oof__int(U_1878),U_1879)),c_Groups_Ozero__class_Ozero(U_1878)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1879),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP94(U_1879,U_1878) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

fof(f_406_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_406_2,plain,
    ! [U_1882,U_1881,U_1880] :
      ( 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_1882)),U_1880)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1882)),U_1881)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1882))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1880),U_1881)) ),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

fof(f_406_3,plain,
    ! [U_1880,U_1882,U_1881] :
      ( 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_1882)),U_1880)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1882)),U_1881)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1882))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1880),U_1881)) ),
    inference(definitional_conversion,[status(esa)],[f_406_2]) ).

cnf(f_406_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_1882)),U_1880)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1882)),U_1881)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1882))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1880),U_1881)) ),
    inference(clausify,[status(thm)],[f_406_3]) ).

fof(f_407_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_407_2,plain,
    ! [U_1883] : 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_1883)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

fof(f_407_3,plain,
    ! [U_1883] : 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_1883)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_407_2]) ).

cnf(f_407_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_1883)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_407_3]) ).

fof(f_408_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_408_2,plain,
    ! [U_1887,U_1886] :
      ( ( hBOOL(hAPP(U_1886,hAPP(c_Int_Onat,U_1887)))
        | ( ~ hBOOL(hAPP(U_1886,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1887),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ? [U_1885] :
            ( ~ hBOOL(hAPP(U_1886,U_1885))
            & U_1887 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1885) ) )
      & ( ( ( hBOOL(hAPP(U_1886,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1887),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_1884] :
              ( hBOOL(hAPP(U_1886,U_1884))
              | U_1887 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1884) ) )
        | ~ hBOOL(hAPP(U_1886,hAPP(c_Int_Onat,U_1887))) ) ),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

fof(f_408_3,plain,
    ( ! [U_1891,U_1889] :
        ( hBOOL(hAPP(U_1889,hAPP(c_Int_Onat,U_1891)))
        | ( ~ hBOOL(hAPP(U_1889,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1891),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ? [U_1885] :
            ( ~ hBOOL(hAPP(U_1889,U_1885))
            & U_1891 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1885) ) )
    & ! [U_1890,U_1888] :
        ( ( ( hBOOL(hAPP(U_1888,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1890),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_1884] :
              ( hBOOL(hAPP(U_1888,U_1884))
              | U_1890 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1884) ) )
        | ~ hBOOL(hAPP(U_1888,hAPP(c_Int_Onat,U_1890))) ) ),
    inference(miniscope,[status(thm)],[f_408_2]) ).

fof(f_408_4,plain,
    ( ! [U_1891,U_1889] :
        ( hBOOL(hAPP(U_1889,hAPP(c_Int_Onat,U_1891)))
        | ( ~ hBOOL(hAPP(U_1889,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1891),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_1889,sK49(U_1891,U_1889)))
          & U_1891 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK49(U_1891,U_1889)) ) )
    & ! [U_1890,U_1888] :
        ( ( ( hBOOL(hAPP(U_1888,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1890),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_1884] :
              ( hBOOL(hAPP(U_1888,U_1884))
              | U_1890 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1884) ) )
        | ~ hBOOL(hAPP(U_1888,hAPP(c_Int_Onat,U_1890))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_1885,sK49(U_1891,U_1889))],[f_408_3]) ).

fof(f_408_5,plain,
    ( ! [U_1889,U_1891] :
        ( ~ hBOOL(hAPP(U_1889,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP97(U_1889,U_1891) )
    & ! [U_1889,U_1891] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1891),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP97(U_1889,U_1891) )
    & ! [U_1889,U_1891] :
        ( ~ hBOOL(hAPP(U_1889,sK49(U_1891,U_1889)))
        | ~ sP96(U_1889,U_1891) )
    & ! [U_1889,U_1891] :
        ( U_1891 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK49(U_1891,U_1889))
        | ~ sP96(U_1889,U_1891) )
    & ! [U_1884,U_1888,U_1890] :
        ( hBOOL(hAPP(U_1888,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1890),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP95(U_1884,U_1888,U_1890) )
    & ! [U_1884,U_1888,U_1890] :
        ( hBOOL(hAPP(U_1888,U_1884))
        | U_1890 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1884)
        | ~ sP95(U_1884,U_1888,U_1890) )
    & ! [U_1889,U_1891] :
        ( hBOOL(hAPP(U_1889,hAPP(c_Int_Onat,U_1891)))
        | sP97(U_1889,U_1891)
        | sP96(U_1889,U_1891) )
    & ! [U_1884,U_1888,U_1890] :
        ( sP95(U_1884,U_1888,U_1890)
        | ~ hBOOL(hAPP(U_1888,hAPP(c_Int_Onat,U_1890))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP95,sP96,sP97])],[f_408_4]) ).

cnf(f_408_6,plain,
    ( sP95(U_1884,U_1888,U_1890)
    | ~ hBOOL(hAPP(U_1888,hAPP(c_Int_Onat,U_1890))) ),
    inference(clausify,[status(thm)],[f_408_5]) ).

cnf(f_408_7,plain,
    ( hBOOL(hAPP(U_1889,hAPP(c_Int_Onat,U_1891)))
    | sP97(U_1889,U_1891)
    | sP96(U_1889,U_1891) ),
    inference(clausify,[status(thm)],[f_408_5]) ).

cnf(f_408_8,plain,
    ( hBOOL(hAPP(U_1888,U_1884))
    | U_1890 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1884)
    | ~ sP95(U_1884,U_1888,U_1890) ),
    inference(clausify,[status(thm)],[f_408_5]) ).

cnf(f_408_9,plain,
    ( hBOOL(hAPP(U_1888,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1890),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP95(U_1884,U_1888,U_1890) ),
    inference(clausify,[status(thm)],[f_408_5]) ).

cnf(f_408_10,plain,
    ( U_1891 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK49(U_1891,U_1889))
    | ~ sP96(U_1889,U_1891) ),
    inference(clausify,[status(thm)],[f_408_5]) ).

cnf(f_408_11,plain,
    ( ~ hBOOL(hAPP(U_1889,sK49(U_1891,U_1889)))
    | ~ sP96(U_1889,U_1891) ),
    inference(clausify,[status(thm)],[f_408_5]) ).

cnf(f_408_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1891),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP97(U_1889,U_1891) ),
    inference(clausify,[status(thm)],[f_408_5]) ).

cnf(f_408_13,plain,
    ( ~ hBOOL(hAPP(U_1889,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP97(U_1889,U_1891) ),
    inference(clausify,[status(thm)],[f_408_5]) ).

fof(f_409_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_409_2,plain,
    ! [U_1892] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1892)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1892)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1892))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1892))) ) ),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

fof(f_409_3,plain,
    ( ! [U_1894] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1894)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1894)) )
    & ! [U_1893] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1893))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1893))) ) ),
    inference(miniscope,[status(thm)],[f_409_2]) ).

fof(f_409_4,plain,
    ( ! [U_1894] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1894)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1894)) )
    & ! [U_1893] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1893))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1893))) ) ),
    inference(definitional_conversion,[status(esa)],[f_409_3]) ).

cnf(f_409_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1893))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1893))) ),
    inference(clausify,[status(thm)],[f_409_4]) ).

cnf(f_409_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_1894)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1894)) ),
    inference(clausify,[status(thm)],[f_409_4]) ).

fof(f_410_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_410_2,plain,
    ! [U_1896,U_1895] : 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_1895)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1896))),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

fof(f_410_3,plain,
    ! [U_1895,U_1896] : 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_1895)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1896))),
    inference(definitional_conversion,[status(esa)],[f_410_2]) ).

cnf(f_410_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_1895)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1896))),
    inference(clausify,[status(thm)],[f_410_3]) ).

fof(f_411_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_411_2,plain,
    ! [U_1898,U_1897] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1897),hAPP(c_Groups_Ouminus__class_Ouminus(U_1897),U_1898)) = U_1898
      | ~ class_Groups_Ogroup__add(U_1897) ),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

fof(f_411_3,plain,
    ! [U_1897,U_1898] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1897),hAPP(c_Groups_Ouminus__class_Ouminus(U_1897),U_1898)) = U_1898
      | ~ class_Groups_Ogroup__add(U_1897) ),
    inference(definitional_conversion,[status(esa)],[f_411_2]) ).

cnf(f_411_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1897),hAPP(c_Groups_Ouminus__class_Ouminus(U_1897),U_1898)) = U_1898
    | ~ class_Groups_Ogroup__add(U_1897) ),
    inference(clausify,[status(thm)],[f_411_3]) ).

fof(f_412_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_412_2,plain,
    ! [U_1899] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1899)) = U_1899,
    inference(variable_rename,[status(thm)],[f_412_1]) ).

fof(f_412_3,plain,
    ! [U_1899] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1899)) = U_1899,
    inference(definitional_conversion,[status(esa)],[f_412_2]) ).

cnf(f_412_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1899)) = U_1899,
    inference(clausify,[status(thm)],[f_412_3]) ).

fof(f_413_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_413_2,plain,
    ! [U_1901,U_1900] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1900),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1901)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1900),hAPP(c_Int_Oring__1__class_Oof__int(U_1900),U_1901))
      | ~ class_Rings_Oring__1(U_1900) ),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

fof(f_413_3,plain,
    ! [U_1900,U_1901] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1900),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1901)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1900),hAPP(c_Int_Oring__1__class_Oof__int(U_1900),U_1901))
      | ~ class_Rings_Oring__1(U_1900) ),
    inference(definitional_conversion,[status(esa)],[f_413_2]) ).

cnf(f_413_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1900),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1901)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1900),hAPP(c_Int_Oring__1__class_Oof__int(U_1900),U_1901))
    | ~ class_Rings_Oring__1(U_1900) ),
    inference(clausify,[status(thm)],[f_413_3]) ).

fof(f_414_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_414_2,plain,
    ! [U_1904,U_1903,U_1902] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1903),U_1904)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1902),hAPP(c_Int_Oring__1__class_Oof__int(U_1902),U_1903)),hAPP(c_Int_Oring__1__class_Oof__int(U_1902),U_1904))
      | ~ class_Rings_Oring__1(U_1902) ),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

fof(f_414_3,plain,
    ! [U_1902,U_1903,U_1904] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1903),U_1904)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1902),hAPP(c_Int_Oring__1__class_Oof__int(U_1902),U_1903)),hAPP(c_Int_Oring__1__class_Oof__int(U_1902),U_1904))
      | ~ class_Rings_Oring__1(U_1902) ),
    inference(definitional_conversion,[status(esa)],[f_414_2]) ).

cnf(f_414_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1903),U_1904)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1902),hAPP(c_Int_Oring__1__class_Oof__int(U_1902),U_1903)),hAPP(c_Int_Oring__1__class_Oof__int(U_1902),U_1904))
    | ~ class_Rings_Oring__1(U_1902) ),
    inference(clausify,[status(thm)],[f_414_3]) ).

fof(f_415_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_415_2,plain,
    ! [U_1907,U_1906,U_1905] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1906),U_1907) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1907),U_1906)
      | ~ class_Rings_Ocomm__semiring__1(U_1905) ),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

fof(f_415_3,plain,
    ! [U_1905,U_1906,U_1907] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1906),U_1907) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1907),U_1906)
      | ~ class_Rings_Ocomm__semiring__1(U_1905) ),
    inference(definitional_conversion,[status(esa)],[f_415_2]) ).

cnf(f_415_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1906),U_1907) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1905),U_1907),U_1906)
    | ~ class_Rings_Ocomm__semiring__1(U_1905) ),
    inference(clausify,[status(thm)],[f_415_3]) ).

fof(f_416_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_416_2,plain,
    ! [U_1909,U_1908] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1908),U_1909) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1909),U_1908),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

fof(f_416_3,plain,
    ! [U_1908,U_1909] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1908),U_1909) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1909),U_1908),
    inference(definitional_conversion,[status(esa)],[f_416_2]) ).

cnf(f_416_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1908),U_1909) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1909),U_1908),
    inference(clausify,[status(thm)],[f_416_3]) ).

fof(f_417_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_417_2,plain,
    ! [U_1912,U_1911,U_1910] :
      ( ( ( U_1911 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1910),U_1912)
          | U_1912 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1910),U_1911) )
        & ( U_1912 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1910),U_1911)
          | U_1911 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1910),U_1912) ) )
      | ~ class_Groups_Ogroup__add(U_1910) ),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

fof(f_417_3,plain,
    ( ! [U_1910,U_1911,U_1912] :
        ( U_1911 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1910),U_1912)
        | U_1912 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1910),U_1911)
        | ~ sP98(U_1910,U_1911,U_1912) )
    & ! [U_1910,U_1911,U_1912] :
        ( U_1912 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1910),U_1911)
        | U_1911 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1910),U_1912)
        | ~ sP98(U_1910,U_1911,U_1912) )
    & ! [U_1910,U_1911,U_1912] :
        ( sP98(U_1910,U_1911,U_1912)
        | ~ class_Groups_Ogroup__add(U_1910) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98])],[f_417_2]) ).

cnf(f_417_4,plain,
    ( sP98(U_1910,U_1911,U_1912)
    | ~ class_Groups_Ogroup__add(U_1910) ),
    inference(clausify,[status(thm)],[f_417_3]) ).

cnf(f_417_5,plain,
    ( U_1912 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1910),U_1911)
    | U_1911 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1910),U_1912)
    | ~ sP98(U_1910,U_1911,U_1912) ),
    inference(clausify,[status(thm)],[f_417_3]) ).

cnf(f_417_6,plain,
    ( U_1911 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1910),U_1912)
    | U_1912 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1910),U_1911)
    | ~ sP98(U_1910,U_1911,U_1912) ),
    inference(clausify,[status(thm)],[f_417_3]) ).

fof(f_418_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_418_2,plain,
    ! [U_1916,U_1915,U_1914,U_1913] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1915),U_1916)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),U_1916))
      | ~ class_Rings_Ocomm__semiring__1(U_1913) ),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

fof(f_418_3,plain,
    ! [U_1915,U_1913,U_1914,U_1916] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1915),U_1916)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),U_1916))
      | ~ class_Rings_Ocomm__semiring__1(U_1913) ),
    inference(definitional_conversion,[status(esa)],[f_418_2]) ).

cnf(f_418_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1915),U_1916)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1913),U_1914),U_1916))
    | ~ class_Rings_Ocomm__semiring__1(U_1913) ),
    inference(clausify,[status(thm)],[f_418_3]) ).

fof(f_419_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_419_2,plain,
    ! [U_1920,U_1919,U_1918,U_1917] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1919),U_1920)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),U_1919)),U_1920)
      | ~ class_Rings_Ocomm__semiring__1(U_1917) ),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

fof(f_419_3,plain,
    ! [U_1917,U_1918,U_1919,U_1920] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1919),U_1920)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),U_1919)),U_1920)
      | ~ class_Rings_Ocomm__semiring__1(U_1917) ),
    inference(definitional_conversion,[status(esa)],[f_419_2]) ).

cnf(f_419_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1919),U_1920)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1917),U_1918),U_1919)),U_1920)
    | ~ class_Rings_Ocomm__semiring__1(U_1917) ),
    inference(clausify,[status(thm)],[f_419_3]) ).

fof(f_420_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_420_2,plain,
    ! [U_1922,U_1921] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1921)),U_1922) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1921),U_1922)),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

fof(f_420_3,plain,
    ! [U_1921,U_1922] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1921)),U_1922) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1921),U_1922)),
    inference(definitional_conversion,[status(esa)],[f_420_2]) ).

cnf(f_420_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1921)),U_1922) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1921),U_1922)),
    inference(clausify,[status(thm)],[f_420_3]) ).

fof(f_421_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_421_2,plain,
    ! [U_1925,U_1924,U_1923] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1923),U_1924) = U_1925
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_1923),U_1925) != U_1924 )
        & ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1923),U_1925) = U_1924
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_1923),U_1924) != U_1925 ) )
      | ~ class_Groups_Ogroup__add(U_1923) ),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

fof(f_421_3,plain,
    ( ! [U_1923,U_1924,U_1925] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1923),U_1924) = U_1925
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_1923),U_1925) != U_1924
        | ~ sP99(U_1923,U_1924,U_1925) )
    & ! [U_1923,U_1924,U_1925] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1923),U_1925) = U_1924
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_1923),U_1924) != U_1925
        | ~ sP99(U_1923,U_1924,U_1925) )
    & ! [U_1923,U_1924,U_1925] :
        ( sP99(U_1923,U_1924,U_1925)
        | ~ class_Groups_Ogroup__add(U_1923) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99])],[f_421_2]) ).

cnf(f_421_4,plain,
    ( sP99(U_1923,U_1924,U_1925)
    | ~ class_Groups_Ogroup__add(U_1923) ),
    inference(clausify,[status(thm)],[f_421_3]) ).

cnf(f_421_5,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1923),U_1925) = U_1924
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_1923),U_1924) != U_1925
    | ~ sP99(U_1923,U_1924,U_1925) ),
    inference(clausify,[status(thm)],[f_421_3]) ).

cnf(f_421_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1923),U_1924) = U_1925
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_1923),U_1925) != U_1924
    | ~ sP99(U_1923,U_1924,U_1925) ),
    inference(clausify,[status(thm)],[f_421_3]) ).

fof(f_422_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_422_2,plain,
    ! [U_1928,U_1927,U_1926] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_1926),U_1927) = hAPP(c_Int_Oring__1__class_Oof__int(U_1926),U_1928)
          | U_1927 != U_1928 )
        & ( U_1927 = U_1928
          | hAPP(c_Int_Oring__1__class_Oof__int(U_1926),U_1927) != hAPP(c_Int_Oring__1__class_Oof__int(U_1926),U_1928) ) )
      | ~ class_Int_Oring__char__0(U_1926) ),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

fof(f_422_3,plain,
    ( ! [U_1927,U_1928,U_1926] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_1926),U_1927) = hAPP(c_Int_Oring__1__class_Oof__int(U_1926),U_1928)
        | U_1927 != U_1928
        | ~ sP100(U_1927,U_1928,U_1926) )
    & ! [U_1927,U_1928,U_1926] :
        ( U_1927 = U_1928
        | hAPP(c_Int_Oring__1__class_Oof__int(U_1926),U_1927) != hAPP(c_Int_Oring__1__class_Oof__int(U_1926),U_1928)
        | ~ sP100(U_1927,U_1928,U_1926) )
    & ! [U_1927,U_1928,U_1926] :
        ( sP100(U_1927,U_1928,U_1926)
        | ~ class_Int_Oring__char__0(U_1926) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP100])],[f_422_2]) ).

cnf(f_422_4,plain,
    ( sP100(U_1927,U_1928,U_1926)
    | ~ class_Int_Oring__char__0(U_1926) ),
    inference(clausify,[status(thm)],[f_422_3]) ).

cnf(f_422_5,plain,
    ( U_1927 = U_1928
    | hAPP(c_Int_Oring__1__class_Oof__int(U_1926),U_1927) != hAPP(c_Int_Oring__1__class_Oof__int(U_1926),U_1928)
    | ~ sP100(U_1927,U_1928,U_1926) ),
    inference(clausify,[status(thm)],[f_422_3]) ).

cnf(f_422_6,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1926),U_1927) = hAPP(c_Int_Oring__1__class_Oof__int(U_1926),U_1928)
    | U_1927 != U_1928
    | ~ sP100(U_1927,U_1928,U_1926) ),
    inference(clausify,[status(thm)],[f_422_3]) ).

fof(f_423_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_423_2,plain,
    ! [U_1931,U_1930,U_1929] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1929),U_1930) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1929),U_1931)
          | U_1930 != U_1931 )
        & ( U_1930 = U_1931
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_1929),U_1930) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1929),U_1931) ) )
      | ~ class_Groups_Ogroup__add(U_1929) ),
    inference(variable_rename,[status(thm)],[f_423_1]) ).

fof(f_423_3,plain,
    ( ! [U_1930,U_1931,U_1929] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1929),U_1930) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1929),U_1931)
        | U_1930 != U_1931
        | ~ sP101(U_1930,U_1931,U_1929) )
    & ! [U_1930,U_1931,U_1929] :
        ( U_1930 = U_1931
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_1929),U_1930) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1929),U_1931)
        | ~ sP101(U_1930,U_1931,U_1929) )
    & ! [U_1930,U_1931,U_1929] :
        ( sP101(U_1930,U_1931,U_1929)
        | ~ class_Groups_Ogroup__add(U_1929) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101])],[f_423_2]) ).

cnf(f_423_4,plain,
    ( sP101(U_1930,U_1931,U_1929)
    | ~ class_Groups_Ogroup__add(U_1929) ),
    inference(clausify,[status(thm)],[f_423_3]) ).

cnf(f_423_5,plain,
    ( U_1930 = U_1931
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_1929),U_1930) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1929),U_1931)
    | ~ sP101(U_1930,U_1931,U_1929) ),
    inference(clausify,[status(thm)],[f_423_3]) ).

cnf(f_423_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1929),U_1930) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1929),U_1931)
    | U_1930 != U_1931
    | ~ sP101(U_1930,U_1931,U_1929) ),
    inference(clausify,[status(thm)],[f_423_3]) ).

fof(f_424_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_424_2,plain,
    ! [U_1935,U_1934,U_1933,U_1932] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1933),U_1934)),U_1935) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1933),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1934),U_1935))
      | ~ class_Groups_Oab__semigroup__mult(U_1932) ),
    inference(variable_rename,[status(thm)],[f_424_1]) ).

fof(f_424_3,plain,
    ! [U_1933,U_1932,U_1934,U_1935] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1933),U_1934)),U_1935) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1933),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1934),U_1935))
      | ~ class_Groups_Oab__semigroup__mult(U_1932) ),
    inference(definitional_conversion,[status(esa)],[f_424_2]) ).

cnf(f_424_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1933),U_1934)),U_1935) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1933),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1934),U_1935))
    | ~ class_Groups_Oab__semigroup__mult(U_1932) ),
    inference(clausify,[status(thm)],[f_424_3]) ).

fof(f_425_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_425_2,plain,
    ! [U_1939,U_1938,U_1937,U_1936] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),U_1938)),U_1939) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1938),U_1939))
      | ~ class_Rings_Ocomm__semiring__1(U_1936) ),
    inference(variable_rename,[status(thm)],[f_425_1]) ).

fof(f_425_3,plain,
    ! [U_1936,U_1937,U_1938,U_1939] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),U_1938)),U_1939) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1938),U_1939))
      | ~ class_Rings_Ocomm__semiring__1(U_1936) ),
    inference(definitional_conversion,[status(esa)],[f_425_2]) ).

cnf(f_425_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),U_1938)),U_1939) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1936),U_1938),U_1939))
    | ~ class_Rings_Ocomm__semiring__1(U_1936) ),
    inference(clausify,[status(thm)],[f_425_3]) ).

fof(f_426_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_426_2,plain,
    ! [U_1942,U_1941,U_1940] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1940),U_1941)),U_1942) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1941),U_1942)),
    inference(variable_rename,[status(thm)],[f_426_1]) ).

fof(f_426_3,plain,
    ! [U_1940,U_1941,U_1942] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1940),U_1941)),U_1942) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1941),U_1942)),
    inference(definitional_conversion,[status(esa)],[f_426_2]) ).

cnf(f_426_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1940),U_1941)),U_1942) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1941),U_1942)),
    inference(clausify,[status(thm)],[f_426_3]) ).

fof(f_427_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_427_2,plain,
    ! [U_1946,U_1945,U_1944,U_1943] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),U_1944),U_1945)),U_1946) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),U_1944),U_1946)),U_1945)
      | ~ class_Rings_Ocomm__semiring__1(U_1943) ),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

fof(f_427_3,plain,
    ! [U_1943,U_1944,U_1945,U_1946] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),U_1944),U_1945)),U_1946) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),U_1944),U_1946)),U_1945)
      | ~ class_Rings_Ocomm__semiring__1(U_1943) ),
    inference(definitional_conversion,[status(esa)],[f_427_2]) ).

cnf(f_427_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),U_1944),U_1945)),U_1946) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),U_1944),U_1946)),U_1945)
    | ~ class_Rings_Ocomm__semiring__1(U_1943) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

fof(f_428_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_428_2,plain,
    ! [U_1951,U_1950,U_1949,U_1948,U_1947] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1948),U_1949)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1950),U_1951)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1949),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1950),U_1951)))
      | ~ class_Rings_Ocomm__semiring__1(U_1947) ),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

fof(f_428_3,plain,
    ! [U_1948,U_1947,U_1949,U_1950,U_1951] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1948),U_1949)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1950),U_1951)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1949),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1950),U_1951)))
      | ~ class_Rings_Ocomm__semiring__1(U_1947) ),
    inference(definitional_conversion,[status(esa)],[f_428_2]) ).

cnf(f_428_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1948),U_1949)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1950),U_1951)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1949),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1950),U_1951)))
    | ~ class_Rings_Ocomm__semiring__1(U_1947) ),
    inference(clausify,[status(thm)],[f_428_3]) ).

fof(f_429_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_429_2,plain,
    ! [U_1956,U_1955,U_1954,U_1953,U_1952] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),U_1953),U_1954)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),U_1955),U_1956)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),U_1955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),U_1953),U_1954)),U_1956))
      | ~ class_Rings_Ocomm__semiring__1(U_1952) ),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

fof(f_429_3,plain,
    ! [U_1952,U_1953,U_1954,U_1955,U_1956] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),U_1953),U_1954)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),U_1955),U_1956)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),U_1955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),U_1953),U_1954)),U_1956))
      | ~ class_Rings_Ocomm__semiring__1(U_1952) ),
    inference(definitional_conversion,[status(esa)],[f_429_2]) ).

cnf(f_429_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),U_1953),U_1954)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),U_1955),U_1956)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),U_1955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1952),U_1953),U_1954)),U_1956))
    | ~ class_Rings_Ocomm__semiring__1(U_1952) ),
    inference(clausify,[status(thm)],[f_429_3]) ).

fof(f_430_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_430_2,plain,
    ! [U_1961,U_1960,U_1959,U_1958,U_1957] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),U_1958),U_1959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),U_1960),U_1961)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),U_1958),U_1960)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),U_1959),U_1961))
      | ~ class_Rings_Ocomm__semiring__1(U_1957) ),
    inference(variable_rename,[status(thm)],[f_430_1]) ).

fof(f_430_3,plain,
    ! [U_1957,U_1958,U_1959,U_1960,U_1961] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),U_1958),U_1959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),U_1960),U_1961)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),U_1958),U_1960)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),U_1959),U_1961))
      | ~ class_Rings_Ocomm__semiring__1(U_1957) ),
    inference(definitional_conversion,[status(esa)],[f_430_2]) ).

cnf(f_430_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),U_1958),U_1959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),U_1960),U_1961)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),U_1958),U_1960)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),U_1959),U_1961))
    | ~ class_Rings_Ocomm__semiring__1(U_1957) ),
    inference(clausify,[status(thm)],[f_430_3]) ).

fof(f_431_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_431_2,plain,
    ! [U_1964,U_1963,U_1962] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1962),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1962),U_1963),U_1964)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1962),U_1963),hAPP(c_Groups_Ouminus__class_Ouminus(U_1962),U_1964))
      | ~ class_Rings_Oring(U_1962) ),
    inference(variable_rename,[status(thm)],[f_431_1]) ).

fof(f_431_3,plain,
    ! [U_1962,U_1963,U_1964] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1962),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1962),U_1963),U_1964)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1962),U_1963),hAPP(c_Groups_Ouminus__class_Ouminus(U_1962),U_1964))
      | ~ class_Rings_Oring(U_1962) ),
    inference(definitional_conversion,[status(esa)],[f_431_2]) ).

cnf(f_431_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1962),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1962),U_1963),U_1964)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1962),U_1963),hAPP(c_Groups_Ouminus__class_Ouminus(U_1962),U_1964))
    | ~ class_Rings_Oring(U_1962) ),
    inference(clausify,[status(thm)],[f_431_3]) ).

fof(f_432_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_432_2,plain,
    ! [U_1967,U_1966,U_1965] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1965),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1966),U_1967)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),hAPP(c_Groups_Ouminus__class_Ouminus(U_1965),U_1966)),U_1967)
      | ~ class_Rings_Oring(U_1965) ),
    inference(variable_rename,[status(thm)],[f_432_1]) ).

fof(f_432_3,plain,
    ! [U_1965,U_1966,U_1967] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1965),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1966),U_1967)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),hAPP(c_Groups_Ouminus__class_Ouminus(U_1965),U_1966)),U_1967)
      | ~ class_Rings_Oring(U_1965) ),
    inference(definitional_conversion,[status(esa)],[f_432_2]) ).

cnf(f_432_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1965),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1966),U_1967)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),hAPP(c_Groups_Ouminus__class_Ouminus(U_1965),U_1966)),U_1967)
    | ~ class_Rings_Oring(U_1965) ),
    inference(clausify,[status(thm)],[f_432_3]) ).

fof(f_433_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_433_2,plain,
    ! [U_1970,U_1969,U_1968] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1968),hAPP(c_Groups_Ouminus__class_Ouminus(U_1968),U_1969)),U_1970) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1968),U_1969),hAPP(c_Groups_Ouminus__class_Ouminus(U_1968),U_1970))
      | ~ class_Rings_Oring(U_1968) ),
    inference(variable_rename,[status(thm)],[f_433_1]) ).

fof(f_433_3,plain,
    ! [U_1968,U_1969,U_1970] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1968),hAPP(c_Groups_Ouminus__class_Ouminus(U_1968),U_1969)),U_1970) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1968),U_1969),hAPP(c_Groups_Ouminus__class_Ouminus(U_1968),U_1970))
      | ~ class_Rings_Oring(U_1968) ),
    inference(definitional_conversion,[status(esa)],[f_433_2]) ).

cnf(f_433_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1968),hAPP(c_Groups_Ouminus__class_Ouminus(U_1968),U_1969)),U_1970) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1968),U_1969),hAPP(c_Groups_Ouminus__class_Ouminus(U_1968),U_1970))
    | ~ class_Rings_Oring(U_1968) ),
    inference(clausify,[status(thm)],[f_433_3]) ).

fof(f_434_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_434_2,plain,
    ! [U_1973,U_1972,U_1971] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1971),hAPP(c_Groups_Ouminus__class_Ouminus(U_1971),U_1972)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1971),U_1973)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1971),U_1972),U_1973)
      | ~ class_Rings_Oring(U_1971) ),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

fof(f_434_3,plain,
    ! [U_1971,U_1972,U_1973] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1971),hAPP(c_Groups_Ouminus__class_Ouminus(U_1971),U_1972)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1971),U_1973)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1971),U_1972),U_1973)
      | ~ class_Rings_Oring(U_1971) ),
    inference(definitional_conversion,[status(esa)],[f_434_2]) ).

cnf(f_434_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1971),hAPP(c_Groups_Ouminus__class_Ouminus(U_1971),U_1972)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1971),U_1973)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1971),U_1972),U_1973)
    | ~ class_Rings_Oring(U_1971) ),
    inference(clausify,[status(thm)],[f_434_3]) ).

fof(f_435_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_435_2,plain,
    ! [U_1976,U_1975,U_1974] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),U_1975) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1976),U_1976)
          | ( U_1975 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1974),U_1976)
            & U_1975 != U_1976 ) )
        & ( U_1975 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1974),U_1976)
          | U_1975 = U_1976
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),U_1975) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1976),U_1976) ) )
      | ~ class_Rings_Oidom(U_1974) ),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

fof(f_435_3,plain,
    ( ! [U_1974,U_1975,U_1976] :
        ( U_1975 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1974),U_1976)
        | ~ sP102(U_1974,U_1975,U_1976) )
    & ! [U_1974,U_1975,U_1976] :
        ( U_1975 != U_1976
        | ~ sP102(U_1974,U_1975,U_1976) )
    & ! [U_1974,U_1975,U_1976] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),U_1975) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1976),U_1976)
        | sP102(U_1974,U_1975,U_1976)
        | ~ sP103(U_1974,U_1975,U_1976) )
    & ! [U_1974,U_1975,U_1976] :
        ( U_1975 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1974),U_1976)
        | U_1975 = U_1976
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),U_1975) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1976),U_1976)
        | ~ sP103(U_1974,U_1975,U_1976) )
    & ! [U_1974,U_1975,U_1976] :
        ( sP103(U_1974,U_1975,U_1976)
        | ~ class_Rings_Oidom(U_1974) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102,sP103])],[f_435_2]) ).

cnf(f_435_4,plain,
    ( sP103(U_1974,U_1975,U_1976)
    | ~ class_Rings_Oidom(U_1974) ),
    inference(clausify,[status(thm)],[f_435_3]) ).

cnf(f_435_5,plain,
    ( U_1975 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1974),U_1976)
    | U_1975 = U_1976
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),U_1975) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1976),U_1976)
    | ~ sP103(U_1974,U_1975,U_1976) ),
    inference(clausify,[status(thm)],[f_435_3]) ).

cnf(f_435_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),U_1975) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1976),U_1976)
    | sP102(U_1974,U_1975,U_1976)
    | ~ sP103(U_1974,U_1975,U_1976) ),
    inference(clausify,[status(thm)],[f_435_3]) ).

cnf(f_435_7,plain,
    ( U_1975 != U_1976
    | ~ sP102(U_1974,U_1975,U_1976) ),
    inference(clausify,[status(thm)],[f_435_3]) ).

cnf(f_435_8,plain,
    ( U_1975 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1974),U_1976)
    | ~ sP102(U_1974,U_1975,U_1976) ),
    inference(clausify,[status(thm)],[f_435_3]) ).

fof(f_436_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_436_2,plain,
    ! [U_1979,U_1978,U_1977] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1978),U_1979)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1977),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1977),U_1978)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1977),U_1979))
      | ~ class_Rings_Osemiring__1(U_1977) ),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

fof(f_436_3,plain,
    ! [U_1979,U_1978,U_1977] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1978),U_1979)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1977),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1977),U_1978)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1977),U_1979))
      | ~ class_Rings_Osemiring__1(U_1977) ),
    inference(definitional_conversion,[status(esa)],[f_436_2]) ).

cnf(f_436_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1978),U_1979)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1977),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1977),U_1978)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1977),U_1979))
    | ~ class_Rings_Osemiring__1(U_1977) ),
    inference(clausify,[status(thm)],[f_436_3]) ).

fof(f_437_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_437_2,plain,
    ! [U_1981,U_1980] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_1980),U_1981) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1980),hAPP(c_Int_Onat,U_1981))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1981),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(U_1980),U_1981) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1980),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1980),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1981))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1981),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ class_Rings_Oring__1(U_1980) ),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

fof(f_437_3,plain,
    ( ! [U_1980,U_1981] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_1980),U_1981) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1980),hAPP(c_Int_Onat,U_1981))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1981),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP104(U_1980,U_1981) )
    & ! [U_1980,U_1981] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_1980),U_1981) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1980),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1980),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1981))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1981),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP104(U_1980,U_1981) )
    & ! [U_1980,U_1981] :
        ( sP104(U_1980,U_1981)
        | ~ class_Rings_Oring__1(U_1980) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP104])],[f_437_2]) ).

cnf(f_437_4,plain,
    ( sP104(U_1980,U_1981)
    | ~ class_Rings_Oring__1(U_1980) ),
    inference(clausify,[status(thm)],[f_437_3]) ).

cnf(f_437_5,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1980),U_1981) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1980),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1980),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1981))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1981),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP104(U_1980,U_1981) ),
    inference(clausify,[status(thm)],[f_437_3]) ).

cnf(f_437_6,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1980),U_1981) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1980),hAPP(c_Int_Onat,U_1981))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1981),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP104(U_1980,U_1981) ),
    inference(clausify,[status(thm)],[f_437_3]) ).

fof(f_438_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_438_2,plain,
    ! [U_1982] : 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_1982))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_438_1]) ).

fof(f_438_3,plain,
    ! [U_1982] : 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_1982))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_438_2]) ).

cnf(f_438_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_1982))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_438_3]) ).

fof(f_439_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_439_2,plain,
    ! [U_1984,U_1983] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1983),U_1984) = U_1984
          | U_1984 != c_Groups_Ozero__class_Ozero(U_1983) )
        & ( U_1984 = c_Groups_Ozero__class_Ozero(U_1983)
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_1983),U_1984) != U_1984 ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1983) ),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

fof(f_439_3,plain,
    ( ! [U_1983,U_1984] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1983),U_1984) = U_1984
        | U_1984 != c_Groups_Ozero__class_Ozero(U_1983)
        | ~ sP105(U_1983,U_1984) )
    & ! [U_1983,U_1984] :
        ( U_1984 = c_Groups_Ozero__class_Ozero(U_1983)
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_1983),U_1984) != U_1984
        | ~ sP105(U_1983,U_1984) )
    & ! [U_1983,U_1984] :
        ( sP105(U_1983,U_1984)
        | ~ class_Groups_Olinordered__ab__group__add(U_1983) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105])],[f_439_2]) ).

cnf(f_439_4,plain,
    ( sP105(U_1983,U_1984)
    | ~ class_Groups_Olinordered__ab__group__add(U_1983) ),
    inference(clausify,[status(thm)],[f_439_3]) ).

cnf(f_439_5,plain,
    ( U_1984 = c_Groups_Ozero__class_Ozero(U_1983)
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_1983),U_1984) != U_1984
    | ~ sP105(U_1983,U_1984) ),
    inference(clausify,[status(thm)],[f_439_3]) ).

cnf(f_439_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1983),U_1984) = U_1984
    | U_1984 != c_Groups_Ozero__class_Ozero(U_1983)
    | ~ sP105(U_1983,U_1984) ),
    inference(clausify,[status(thm)],[f_439_3]) ).

fof(f_440_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_440_2,plain,
    ! [U_1986,U_1985] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1985),U_1986) = c_Groups_Ozero__class_Ozero(U_1985)
          | U_1986 != c_Groups_Ozero__class_Ozero(U_1985) )
        & ( U_1986 = c_Groups_Ozero__class_Ozero(U_1985)
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_1985),U_1986) != c_Groups_Ozero__class_Ozero(U_1985) ) )
      | ~ class_Groups_Ogroup__add(U_1985) ),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

fof(f_440_3,plain,
    ( ! [U_1986,U_1985] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1985),U_1986) = c_Groups_Ozero__class_Ozero(U_1985)
        | U_1986 != c_Groups_Ozero__class_Ozero(U_1985)
        | ~ sP106(U_1986,U_1985) )
    & ! [U_1986,U_1985] :
        ( U_1986 = c_Groups_Ozero__class_Ozero(U_1985)
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_1985),U_1986) != c_Groups_Ozero__class_Ozero(U_1985)
        | ~ sP106(U_1986,U_1985) )
    & ! [U_1986,U_1985] :
        ( sP106(U_1986,U_1985)
        | ~ class_Groups_Ogroup__add(U_1985) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP106])],[f_440_2]) ).

cnf(f_440_4,plain,
    ( sP106(U_1986,U_1985)
    | ~ class_Groups_Ogroup__add(U_1985) ),
    inference(clausify,[status(thm)],[f_440_3]) ).

cnf(f_440_5,plain,
    ( U_1986 = c_Groups_Ozero__class_Ozero(U_1985)
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_1985),U_1986) != c_Groups_Ozero__class_Ozero(U_1985)
    | ~ sP106(U_1986,U_1985) ),
    inference(clausify,[status(thm)],[f_440_3]) ).

cnf(f_440_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1985),U_1986) = c_Groups_Ozero__class_Ozero(U_1985)
    | U_1986 != c_Groups_Ozero__class_Ozero(U_1985)
    | ~ sP106(U_1986,U_1985) ),
    inference(clausify,[status(thm)],[f_440_3]) ).

fof(f_441_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_441_2,plain,
    ! [U_1988,U_1987] :
      ( ( ( U_1988 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1987),U_1988)
          | U_1988 != c_Groups_Ozero__class_Ozero(U_1987) )
        & ( U_1988 = c_Groups_Ozero__class_Ozero(U_1987)
          | U_1988 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1987),U_1988) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1987) ),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

fof(f_441_3,plain,
    ( ! [U_1988,U_1987] :
        ( U_1988 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1987),U_1988)
        | U_1988 != c_Groups_Ozero__class_Ozero(U_1987)
        | ~ sP107(U_1988,U_1987) )
    & ! [U_1988,U_1987] :
        ( U_1988 = c_Groups_Ozero__class_Ozero(U_1987)
        | U_1988 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1987),U_1988)
        | ~ sP107(U_1988,U_1987) )
    & ! [U_1988,U_1987] :
        ( sP107(U_1988,U_1987)
        | ~ class_Groups_Olinordered__ab__group__add(U_1987) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP107])],[f_441_2]) ).

cnf(f_441_4,plain,
    ( sP107(U_1988,U_1987)
    | ~ class_Groups_Olinordered__ab__group__add(U_1987) ),
    inference(clausify,[status(thm)],[f_441_3]) ).

cnf(f_441_5,plain,
    ( U_1988 = c_Groups_Ozero__class_Ozero(U_1987)
    | U_1988 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1987),U_1988)
    | ~ sP107(U_1988,U_1987) ),
    inference(clausify,[status(thm)],[f_441_3]) ).

cnf(f_441_6,plain,
    ( U_1988 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1987),U_1988)
    | U_1988 != c_Groups_Ozero__class_Ozero(U_1987)
    | ~ sP107(U_1988,U_1987) ),
    inference(clausify,[status(thm)],[f_441_3]) ).

fof(f_442_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_442_2,plain,
    ! [U_1990,U_1989] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_1989) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1989),U_1990)
          | c_Groups_Ozero__class_Ozero(U_1989) != U_1990 )
        & ( c_Groups_Ozero__class_Ozero(U_1989) = U_1990
          | c_Groups_Ozero__class_Ozero(U_1989) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1989),U_1990) ) )
      | ~ class_Groups_Ogroup__add(U_1989) ),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

fof(f_442_3,plain,
    ( ! [U_1990,U_1989] :
        ( c_Groups_Ozero__class_Ozero(U_1989) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1989),U_1990)
        | c_Groups_Ozero__class_Ozero(U_1989) != U_1990
        | ~ sP108(U_1990,U_1989) )
    & ! [U_1990,U_1989] :
        ( c_Groups_Ozero__class_Ozero(U_1989) = U_1990
        | c_Groups_Ozero__class_Ozero(U_1989) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1989),U_1990)
        | ~ sP108(U_1990,U_1989) )
    & ! [U_1990,U_1989] :
        ( sP108(U_1990,U_1989)
        | ~ class_Groups_Ogroup__add(U_1989) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP108])],[f_442_2]) ).

cnf(f_442_4,plain,
    ( sP108(U_1990,U_1989)
    | ~ class_Groups_Ogroup__add(U_1989) ),
    inference(clausify,[status(thm)],[f_442_3]) ).

cnf(f_442_5,plain,
    ( c_Groups_Ozero__class_Ozero(U_1989) = U_1990
    | c_Groups_Ozero__class_Ozero(U_1989) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1989),U_1990)
    | ~ sP108(U_1990,U_1989) ),
    inference(clausify,[status(thm)],[f_442_3]) ).

cnf(f_442_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_1989) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1989),U_1990)
    | c_Groups_Ozero__class_Ozero(U_1989) != U_1990
    | ~ sP108(U_1990,U_1989) ),
    inference(clausify,[status(thm)],[f_442_3]) ).

fof(f_443_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_443_2,plain,
    ! [U_1991] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1991),c_Groups_Ozero__class_Ozero(U_1991)) = c_Groups_Ozero__class_Ozero(U_1991)
      | ~ class_Groups_Ogroup__add(U_1991) ),
    inference(variable_rename,[status(thm)],[f_443_1]) ).

fof(f_443_3,plain,
    ! [U_1991] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1991),c_Groups_Ozero__class_Ozero(U_1991)) = c_Groups_Ozero__class_Ozero(U_1991)
      | ~ class_Groups_Ogroup__add(U_1991) ),
    inference(definitional_conversion,[status(esa)],[f_443_2]) ).

cnf(f_443_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1991),c_Groups_Ozero__class_Ozero(U_1991)) = c_Groups_Ozero__class_Ozero(U_1991)
    | ~ class_Groups_Ogroup__add(U_1991) ),
    inference(clausify,[status(thm)],[f_443_3]) ).

fof(f_444_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_444_2,plain,
    ! [U_1994,U_1993,U_1992] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1992),U_1993),hAPP(c_Groups_Ouminus__class_Ouminus(U_1992),U_1994)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1992),U_1994),hAPP(c_Groups_Ouminus__class_Ouminus(U_1992),U_1993))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1992),U_1994),hAPP(c_Groups_Ouminus__class_Ouminus(U_1992),U_1993)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1992),U_1993),hAPP(c_Groups_Ouminus__class_Ouminus(U_1992),U_1994))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1992) ),
    inference(variable_rename,[status(thm)],[f_444_1]) ).

fof(f_444_3,plain,
    ( ! [U_1993,U_1992,U_1994] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1992),U_1993),hAPP(c_Groups_Ouminus__class_Ouminus(U_1992),U_1994)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1992),U_1994),hAPP(c_Groups_Ouminus__class_Ouminus(U_1992),U_1993)))
        | ~ sP109(U_1993,U_1992,U_1994) )
    & ! [U_1993,U_1992,U_1994] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1992),U_1994),hAPP(c_Groups_Ouminus__class_Ouminus(U_1992),U_1993)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1992),U_1993),hAPP(c_Groups_Ouminus__class_Ouminus(U_1992),U_1994)))
        | ~ sP109(U_1993,U_1992,U_1994) )
    & ! [U_1993,U_1992,U_1994] :
        ( sP109(U_1993,U_1992,U_1994)
        | ~ class_Groups_Oordered__ab__group__add(U_1992) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109])],[f_444_2]) ).

cnf(f_444_4,plain,
    ( sP109(U_1993,U_1992,U_1994)
    | ~ class_Groups_Oordered__ab__group__add(U_1992) ),
    inference(clausify,[status(thm)],[f_444_3]) ).

cnf(f_444_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1992),U_1994),hAPP(c_Groups_Ouminus__class_Ouminus(U_1992),U_1993)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1992),U_1993),hAPP(c_Groups_Ouminus__class_Ouminus(U_1992),U_1994)))
    | ~ sP109(U_1993,U_1992,U_1994) ),
    inference(clausify,[status(thm)],[f_444_3]) ).

cnf(f_444_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1992),U_1993),hAPP(c_Groups_Ouminus__class_Ouminus(U_1992),U_1994)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1992),U_1994),hAPP(c_Groups_Ouminus__class_Ouminus(U_1992),U_1993)))
    | ~ sP109(U_1993,U_1992,U_1994) ),
    inference(clausify,[status(thm)],[f_444_3]) ).

fof(f_445_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_445_2,plain,
    ! [U_1997,U_1996,U_1995] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),hAPP(c_Groups_Ouminus__class_Ouminus(U_1995),U_1996)),U_1997))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),hAPP(c_Groups_Ouminus__class_Ouminus(U_1995),U_1997)),U_1996)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),hAPP(c_Groups_Ouminus__class_Ouminus(U_1995),U_1997)),U_1996))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),hAPP(c_Groups_Ouminus__class_Ouminus(U_1995),U_1996)),U_1997)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1995) ),
    inference(variable_rename,[status(thm)],[f_445_1]) ).

fof(f_445_3,plain,
    ( ! [U_1997,U_1996,U_1995] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),hAPP(c_Groups_Ouminus__class_Ouminus(U_1995),U_1996)),U_1997))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),hAPP(c_Groups_Ouminus__class_Ouminus(U_1995),U_1997)),U_1996))
        | ~ sP110(U_1997,U_1996,U_1995) )
    & ! [U_1997,U_1996,U_1995] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),hAPP(c_Groups_Ouminus__class_Ouminus(U_1995),U_1997)),U_1996))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),hAPP(c_Groups_Ouminus__class_Ouminus(U_1995),U_1996)),U_1997))
        | ~ sP110(U_1997,U_1996,U_1995) )
    & ! [U_1997,U_1996,U_1995] :
        ( sP110(U_1997,U_1996,U_1995)
        | ~ class_Groups_Oordered__ab__group__add(U_1995) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP110])],[f_445_2]) ).

cnf(f_445_4,plain,
    ( sP110(U_1997,U_1996,U_1995)
    | ~ class_Groups_Oordered__ab__group__add(U_1995) ),
    inference(clausify,[status(thm)],[f_445_3]) ).

cnf(f_445_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),hAPP(c_Groups_Ouminus__class_Ouminus(U_1995),U_1997)),U_1996))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),hAPP(c_Groups_Ouminus__class_Ouminus(U_1995),U_1996)),U_1997))
    | ~ sP110(U_1997,U_1996,U_1995) ),
    inference(clausify,[status(thm)],[f_445_3]) ).

cnf(f_445_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),hAPP(c_Groups_Ouminus__class_Ouminus(U_1995),U_1996)),U_1997))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),hAPP(c_Groups_Ouminus__class_Ouminus(U_1995),U_1997)),U_1996))
    | ~ sP110(U_1997,U_1996,U_1995) ),
    inference(clausify,[status(thm)],[f_445_3]) ).

fof(f_446_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_446_2,plain,
    ! [U_2000,U_1999,U_1998] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1998),hAPP(c_Groups_Ouminus__class_Ouminus(U_1998),U_1999)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1998),U_2000)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1998),U_2000),U_1999)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1998),U_2000),U_1999))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1998),hAPP(c_Groups_Ouminus__class_Ouminus(U_1998),U_1999)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1998),U_2000))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1998) ),
    inference(variable_rename,[status(thm)],[f_446_1]) ).

fof(f_446_3,plain,
    ( ! [U_2000,U_1999,U_1998] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1998),hAPP(c_Groups_Ouminus__class_Ouminus(U_1998),U_1999)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1998),U_2000)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1998),U_2000),U_1999))
        | ~ sP111(U_2000,U_1999,U_1998) )
    & ! [U_2000,U_1999,U_1998] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1998),U_2000),U_1999))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1998),hAPP(c_Groups_Ouminus__class_Ouminus(U_1998),U_1999)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1998),U_2000)))
        | ~ sP111(U_2000,U_1999,U_1998) )
    & ! [U_2000,U_1999,U_1998] :
        ( sP111(U_2000,U_1999,U_1998)
        | ~ class_Groups_Oordered__ab__group__add(U_1998) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP111])],[f_446_2]) ).

cnf(f_446_4,plain,
    ( sP111(U_2000,U_1999,U_1998)
    | ~ class_Groups_Oordered__ab__group__add(U_1998) ),
    inference(clausify,[status(thm)],[f_446_3]) ).

cnf(f_446_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1998),U_2000),U_1999))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1998),hAPP(c_Groups_Ouminus__class_Ouminus(U_1998),U_1999)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1998),U_2000)))
    | ~ sP111(U_2000,U_1999,U_1998) ),
    inference(clausify,[status(thm)],[f_446_3]) ).

cnf(f_446_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1998),hAPP(c_Groups_Ouminus__class_Ouminus(U_1998),U_1999)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1998),U_2000)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1998),U_2000),U_1999))
    | ~ sP111(U_2000,U_1999,U_1998) ),
    inference(clausify,[status(thm)],[f_446_3]) ).

fof(f_447_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_447_2,plain,
    ! [U_2003,U_2002,U_2001] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2001),hAPP(c_Groups_Ouminus__class_Ouminus(U_2001),U_2002)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2001),U_2002),U_2003)) = U_2003
      | ~ class_Groups_Ogroup__add(U_2001) ),
    inference(variable_rename,[status(thm)],[f_447_1]) ).

fof(f_447_3,plain,
    ! [U_2003,U_2002,U_2001] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2001),hAPP(c_Groups_Ouminus__class_Ouminus(U_2001),U_2002)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2001),U_2002),U_2003)) = U_2003
      | ~ class_Groups_Ogroup__add(U_2001) ),
    inference(definitional_conversion,[status(esa)],[f_447_2]) ).

cnf(f_447_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2001),hAPP(c_Groups_Ouminus__class_Ouminus(U_2001),U_2002)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2001),U_2002),U_2003)) = U_2003
    | ~ class_Groups_Ogroup__add(U_2001) ),
    inference(clausify,[status(thm)],[f_447_3]) ).

fof(f_448_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_448_2,plain,
    ! [U_2006,U_2005,U_2004] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2004),U_2005),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2004),hAPP(c_Groups_Ouminus__class_Ouminus(U_2004),U_2005)),U_2006)) = U_2006
      | ~ class_Groups_Ogroup__add(U_2004) ),
    inference(variable_rename,[status(thm)],[f_448_1]) ).

fof(f_448_3,plain,
    ! [U_2004,U_2005,U_2006] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2004),U_2005),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2004),hAPP(c_Groups_Ouminus__class_Ouminus(U_2004),U_2005)),U_2006)) = U_2006
      | ~ class_Groups_Ogroup__add(U_2004) ),
    inference(definitional_conversion,[status(esa)],[f_448_2]) ).

cnf(f_448_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2004),U_2005),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2004),hAPP(c_Groups_Ouminus__class_Ouminus(U_2004),U_2005)),U_2006)) = U_2006
    | ~ class_Groups_Ogroup__add(U_2004) ),
    inference(clausify,[status(thm)],[f_448_3]) ).

fof(f_449_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_449_2,plain,
    ! [U_2009,U_2008,U_2007] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2007),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2007),U_2008),U_2009)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2007),hAPP(c_Groups_Ouminus__class_Ouminus(U_2007),U_2009)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2007),U_2008))
      | ~ class_Groups_Ogroup__add(U_2007) ),
    inference(variable_rename,[status(thm)],[f_449_1]) ).

fof(f_449_3,plain,
    ! [U_2007,U_2008,U_2009] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2007),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2007),U_2008),U_2009)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2007),hAPP(c_Groups_Ouminus__class_Ouminus(U_2007),U_2009)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2007),U_2008))
      | ~ class_Groups_Ogroup__add(U_2007) ),
    inference(definitional_conversion,[status(esa)],[f_449_2]) ).

cnf(f_449_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2007),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2007),U_2008),U_2009)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2007),hAPP(c_Groups_Ouminus__class_Ouminus(U_2007),U_2009)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2007),U_2008))
    | ~ class_Groups_Ogroup__add(U_2007) ),
    inference(clausify,[status(thm)],[f_449_3]) ).

fof(f_450_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_450_2,plain,
    ! [U_2012,U_2011,U_2010] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2010),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2010),U_2011),U_2012)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2010),hAPP(c_Groups_Ouminus__class_Ouminus(U_2010),U_2011)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2010),U_2012))
      | ~ class_Groups_Oab__group__add(U_2010) ),
    inference(variable_rename,[status(thm)],[f_450_1]) ).

fof(f_450_3,plain,
    ! [U_2010,U_2011,U_2012] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2010),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2010),U_2011),U_2012)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2010),hAPP(c_Groups_Ouminus__class_Ouminus(U_2010),U_2011)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2010),U_2012))
      | ~ class_Groups_Oab__group__add(U_2010) ),
    inference(definitional_conversion,[status(esa)],[f_450_2]) ).

cnf(f_450_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2010),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2010),U_2011),U_2012)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2010),hAPP(c_Groups_Ouminus__class_Ouminus(U_2010),U_2011)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2010),U_2012))
    | ~ class_Groups_Oab__group__add(U_2010) ),
    inference(clausify,[status(thm)],[f_450_3]) ).

fof(f_451_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_451_2,plain,
    ! [U_2015,U_2014,U_2013] :
      ( U_2015 = c_Groups_Ozero__class_Ozero(U_2013)
      | U_2014 = c_Groups_Ozero__class_Ozero(U_2013)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2013),U_2014),U_2015) != c_Groups_Ozero__class_Ozero(U_2013)
      | ~ class_Rings_Ono__zero__divisors(U_2013) ),
    inference(variable_rename,[status(thm)],[f_451_1]) ).

fof(f_451_3,plain,
    ! [U_2013,U_2014,U_2015] :
      ( U_2015 = c_Groups_Ozero__class_Ozero(U_2013)
      | U_2014 = c_Groups_Ozero__class_Ozero(U_2013)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2013),U_2014),U_2015) != c_Groups_Ozero__class_Ozero(U_2013)
      | ~ class_Rings_Ono__zero__divisors(U_2013) ),
    inference(definitional_conversion,[status(esa)],[f_451_2]) ).

cnf(f_451_4,plain,
    ( U_2015 = c_Groups_Ozero__class_Ozero(U_2013)
    | U_2014 = c_Groups_Ozero__class_Ozero(U_2013)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2013),U_2014),U_2015) != c_Groups_Ozero__class_Ozero(U_2013)
    | ~ class_Rings_Ono__zero__divisors(U_2013) ),
    inference(clausify,[status(thm)],[f_451_3]) ).

fof(f_452_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_452_2,plain,
    ! [U_2018,U_2017,U_2016] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2016),U_2017),U_2018) != c_Groups_Ozero__class_Ozero(U_2016)
      | U_2018 = c_Groups_Ozero__class_Ozero(U_2016)
      | U_2017 = c_Groups_Ozero__class_Ozero(U_2016)
      | ~ class_Rings_Ono__zero__divisors(U_2016) ),
    inference(variable_rename,[status(thm)],[f_452_1]) ).

fof(f_452_3,plain,
    ! [U_2017,U_2016,U_2018] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2016),U_2017),U_2018) != c_Groups_Ozero__class_Ozero(U_2016)
      | U_2018 = c_Groups_Ozero__class_Ozero(U_2016)
      | U_2017 = c_Groups_Ozero__class_Ozero(U_2016)
      | ~ class_Rings_Ono__zero__divisors(U_2016) ),
    inference(definitional_conversion,[status(esa)],[f_452_2]) ).

cnf(f_452_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2016),U_2017),U_2018) != c_Groups_Ozero__class_Ozero(U_2016)
    | U_2018 = c_Groups_Ozero__class_Ozero(U_2016)
    | U_2017 = c_Groups_Ozero__class_Ozero(U_2016)
    | ~ class_Rings_Ono__zero__divisors(U_2016) ),
    inference(clausify,[status(thm)],[f_452_3]) ).

fof(f_453_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_453_2,plain,
    ! [U_2021,U_2020,U_2019] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2019),U_2020),U_2021) = c_Groups_Ozero__class_Ozero(U_2019)
          | ( U_2021 != c_Groups_Ozero__class_Ozero(U_2019)
            & U_2020 != c_Groups_Ozero__class_Ozero(U_2019) ) )
        & ( U_2021 = c_Groups_Ozero__class_Ozero(U_2019)
          | U_2020 = c_Groups_Ozero__class_Ozero(U_2019)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2019),U_2020),U_2021) != c_Groups_Ozero__class_Ozero(U_2019) ) )
      | ~ class_Rings_Oring__no__zero__divisors(U_2019) ),
    inference(variable_rename,[status(thm)],[f_453_1]) ).

fof(f_453_3,plain,
    ( ! [U_2019,U_2020,U_2021] :
        ( U_2021 != c_Groups_Ozero__class_Ozero(U_2019)
        | ~ sP112(U_2019,U_2020,U_2021) )
    & ! [U_2019,U_2020,U_2021] :
        ( U_2020 != c_Groups_Ozero__class_Ozero(U_2019)
        | ~ sP112(U_2019,U_2020,U_2021) )
    & ! [U_2019,U_2020,U_2021] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2019),U_2020),U_2021) = c_Groups_Ozero__class_Ozero(U_2019)
        | sP112(U_2019,U_2020,U_2021)
        | ~ sP113(U_2019,U_2020,U_2021) )
    & ! [U_2019,U_2020,U_2021] :
        ( U_2021 = c_Groups_Ozero__class_Ozero(U_2019)
        | U_2020 = c_Groups_Ozero__class_Ozero(U_2019)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2019),U_2020),U_2021) != c_Groups_Ozero__class_Ozero(U_2019)
        | ~ sP113(U_2019,U_2020,U_2021) )
    & ! [U_2019,U_2020,U_2021] :
        ( sP113(U_2019,U_2020,U_2021)
        | ~ class_Rings_Oring__no__zero__divisors(U_2019) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112,sP113])],[f_453_2]) ).

cnf(f_453_4,plain,
    ( sP113(U_2019,U_2020,U_2021)
    | ~ class_Rings_Oring__no__zero__divisors(U_2019) ),
    inference(clausify,[status(thm)],[f_453_3]) ).

cnf(f_453_5,plain,
    ( U_2021 = c_Groups_Ozero__class_Ozero(U_2019)
    | U_2020 = c_Groups_Ozero__class_Ozero(U_2019)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2019),U_2020),U_2021) != c_Groups_Ozero__class_Ozero(U_2019)
    | ~ sP113(U_2019,U_2020,U_2021) ),
    inference(clausify,[status(thm)],[f_453_3]) ).

cnf(f_453_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2019),U_2020),U_2021) = c_Groups_Ozero__class_Ozero(U_2019)
    | sP112(U_2019,U_2020,U_2021)
    | ~ sP113(U_2019,U_2020,U_2021) ),
    inference(clausify,[status(thm)],[f_453_3]) ).

cnf(f_453_7,plain,
    ( U_2020 != c_Groups_Ozero__class_Ozero(U_2019)
    | ~ sP112(U_2019,U_2020,U_2021) ),
    inference(clausify,[status(thm)],[f_453_3]) ).

cnf(f_453_8,plain,
    ( U_2021 != c_Groups_Ozero__class_Ozero(U_2019)
    | ~ sP112(U_2019,U_2020,U_2021) ),
    inference(clausify,[status(thm)],[f_453_3]) ).

fof(f_454_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_454_2,plain,
    ! [U_2023,U_2022] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2022),U_2023),c_Groups_Ozero__class_Ozero(U_2022)) = c_Groups_Ozero__class_Ozero(U_2022)
      | ~ class_Rings_Omult__zero(U_2022) ),
    inference(variable_rename,[status(thm)],[f_454_1]) ).

fof(f_454_3,plain,
    ! [U_2022,U_2023] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2022),U_2023),c_Groups_Ozero__class_Ozero(U_2022)) = c_Groups_Ozero__class_Ozero(U_2022)
      | ~ class_Rings_Omult__zero(U_2022) ),
    inference(definitional_conversion,[status(esa)],[f_454_2]) ).

cnf(f_454_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2022),U_2023),c_Groups_Ozero__class_Ozero(U_2022)) = c_Groups_Ozero__class_Ozero(U_2022)
    | ~ class_Rings_Omult__zero(U_2022) ),
    inference(clausify,[status(thm)],[f_454_3]) ).

fof(f_455_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_455_2,plain,
    ! [U_2025,U_2024] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2024),c_Groups_Ozero__class_Ozero(U_2024)),U_2025) = c_Groups_Ozero__class_Ozero(U_2024)
      | ~ class_Rings_Omult__zero(U_2024) ),
    inference(variable_rename,[status(thm)],[f_455_1]) ).

fof(f_455_3,plain,
    ! [U_2025,U_2024] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2024),c_Groups_Ozero__class_Ozero(U_2024)),U_2025) = c_Groups_Ozero__class_Ozero(U_2024)
      | ~ class_Rings_Omult__zero(U_2024) ),
    inference(definitional_conversion,[status(esa)],[f_455_2]) ).

cnf(f_455_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2024),c_Groups_Ozero__class_Ozero(U_2024)),U_2025) = c_Groups_Ozero__class_Ozero(U_2024)
    | ~ class_Rings_Omult__zero(U_2024) ),
    inference(clausify,[status(thm)],[f_455_3]) ).

fof(f_456_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_456_2,plain,
    ! [U_2027,U_2026] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2026),U_2027),c_Groups_Ozero__class_Ozero(U_2026)) = c_Groups_Ozero__class_Ozero(U_2026)
      | ~ class_Rings_Ocomm__semiring__1(U_2026) ),
    inference(variable_rename,[status(thm)],[f_456_1]) ).

fof(f_456_3,plain,
    ! [U_2026,U_2027] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2026),U_2027),c_Groups_Ozero__class_Ozero(U_2026)) = c_Groups_Ozero__class_Ozero(U_2026)
      | ~ class_Rings_Ocomm__semiring__1(U_2026) ),
    inference(definitional_conversion,[status(esa)],[f_456_2]) ).

cnf(f_456_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2026),U_2027),c_Groups_Ozero__class_Ozero(U_2026)) = c_Groups_Ozero__class_Ozero(U_2026)
    | ~ class_Rings_Ocomm__semiring__1(U_2026) ),
    inference(clausify,[status(thm)],[f_456_3]) ).

fof(f_457_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_457_2,plain,
    ! [U_2029,U_2028] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2028),c_Groups_Ozero__class_Ozero(U_2028)),U_2029) = c_Groups_Ozero__class_Ozero(U_2028)
      | ~ class_Rings_Ocomm__semiring__1(U_2028) ),
    inference(variable_rename,[status(thm)],[f_457_1]) ).

fof(f_457_3,plain,
    ! [U_2029,U_2028] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2028),c_Groups_Ozero__class_Ozero(U_2028)),U_2029) = c_Groups_Ozero__class_Ozero(U_2028)
      | ~ class_Rings_Ocomm__semiring__1(U_2028) ),
    inference(definitional_conversion,[status(esa)],[f_457_2]) ).

cnf(f_457_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2028),c_Groups_Ozero__class_Ozero(U_2028)),U_2029) = c_Groups_Ozero__class_Ozero(U_2028)
    | ~ class_Rings_Ocomm__semiring__1(U_2028) ),
    inference(clausify,[status(thm)],[f_457_3]) ).

fof(f_458_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_458_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_458_1]) ).

cnf(f_458_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_458_2]) ).

fof(f_459_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_459_2,plain,
    ! [U_2030] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2030)) = U_2030,
    inference(variable_rename,[status(thm)],[f_459_1]) ).

fof(f_459_3,plain,
    ! [U_2030] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2030)) = U_2030,
    inference(definitional_conversion,[status(esa)],[f_459_2]) ).

cnf(f_459_4,plain,
    hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2030)) = U_2030,
    inference(clausify,[status(thm)],[f_459_3]) ).

fof(f_460_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_460_2,plain,
    ! [U_2035,U_2034,U_2033,U_2032,U_2031] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2031),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2031),U_2032),U_2033)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2031),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2031),U_2034),U_2033)),U_2035)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2031),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2031),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2031),U_2032),U_2034)),U_2033)),U_2035)
      | ~ class_Rings_Osemiring(U_2031) ),
    inference(variable_rename,[status(thm)],[f_460_1]) ).

fof(f_460_3,plain,
    ! [U_2031,U_2032,U_2033,U_2034,U_2035] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2031),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2031),U_2032),U_2033)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2031),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2031),U_2034),U_2033)),U_2035)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2031),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2031),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2031),U_2032),U_2034)),U_2033)),U_2035)
      | ~ class_Rings_Osemiring(U_2031) ),
    inference(definitional_conversion,[status(esa)],[f_460_2]) ).

cnf(f_460_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2031),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2031),U_2032),U_2033)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2031),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2031),U_2034),U_2033)),U_2035)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2031),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2031),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2031),U_2032),U_2034)),U_2033)),U_2035)
    | ~ class_Rings_Osemiring(U_2031) ),
    inference(clausify,[status(thm)],[f_460_3]) ).

fof(f_461_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_461_2,plain,
    ! [U_2039,U_2038,U_2037,U_2036] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2036),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2036),U_2037),U_2038)),U_2039) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2036),U_2037),U_2039)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2036),U_2038),U_2039))
      | ~ class_Rings_Ocomm__semiring(U_2036) ),
    inference(variable_rename,[status(thm)],[f_461_1]) ).

fof(f_461_3,plain,
    ! [U_2036,U_2037,U_2038,U_2039] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2036),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2036),U_2037),U_2038)),U_2039) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2036),U_2037),U_2039)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2036),U_2038),U_2039))
      | ~ class_Rings_Ocomm__semiring(U_2036) ),
    inference(definitional_conversion,[status(esa)],[f_461_2]) ).

cnf(f_461_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2036),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2036),U_2037),U_2038)),U_2039) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2036),U_2037),U_2039)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2036),U_2038),U_2039))
    | ~ class_Rings_Ocomm__semiring(U_2036) ),
    inference(clausify,[status(thm)],[f_461_3]) ).

fof(f_462_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_462_2,plain,
    ! [U_2044,U_2043,U_2042,U_2041,U_2040] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2041),U_2042)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2043),U_2044)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2041),U_2044)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2043),U_2042))
          | ( U_2042 != U_2044
            & U_2041 != U_2043 ) )
        & ( U_2042 = U_2044
          | U_2041 = U_2043
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2041),U_2042)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2043),U_2044)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2041),U_2044)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2043),U_2042)) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2040) ),
    inference(variable_rename,[status(thm)],[f_462_1]) ).

fof(f_462_3,plain,
    ( ! [U_2041,U_2042,U_2043,U_2044] :
        ( U_2042 != U_2044
        | ~ sP114(U_2041,U_2042,U_2043,U_2044) )
    & ! [U_2041,U_2042,U_2043,U_2044] :
        ( U_2041 != U_2043
        | ~ sP114(U_2041,U_2042,U_2043,U_2044) )
    & ! [U_2040,U_2041,U_2042,U_2043,U_2044] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2041),U_2042)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2043),U_2044)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2041),U_2044)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2043),U_2042))
        | sP114(U_2041,U_2042,U_2043,U_2044)
        | ~ sP115(U_2040,U_2041,U_2042,U_2043,U_2044) )
    & ! [U_2040,U_2041,U_2042,U_2043,U_2044] :
        ( U_2042 = U_2044
        | U_2041 = U_2043
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2041),U_2042)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2043),U_2044)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2041),U_2044)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2043),U_2042))
        | ~ sP115(U_2040,U_2041,U_2042,U_2043,U_2044) )
    & ! [U_2040,U_2041,U_2042,U_2043,U_2044] :
        ( sP115(U_2040,U_2041,U_2042,U_2043,U_2044)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2040) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP114,sP115])],[f_462_2]) ).

cnf(f_462_4,plain,
    ( sP115(U_2040,U_2041,U_2042,U_2043,U_2044)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2040) ),
    inference(clausify,[status(thm)],[f_462_3]) ).

cnf(f_462_5,plain,
    ( U_2042 = U_2044
    | U_2041 = U_2043
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2041),U_2042)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2043),U_2044)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2041),U_2044)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2043),U_2042))
    | ~ sP115(U_2040,U_2041,U_2042,U_2043,U_2044) ),
    inference(clausify,[status(thm)],[f_462_3]) ).

cnf(f_462_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2041),U_2042)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2043),U_2044)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2041),U_2044)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2040),U_2043),U_2042))
    | sP114(U_2041,U_2042,U_2043,U_2044)
    | ~ sP115(U_2040,U_2041,U_2042,U_2043,U_2044) ),
    inference(clausify,[status(thm)],[f_462_3]) ).

cnf(f_462_7,plain,
    ( U_2041 != U_2043
    | ~ sP114(U_2041,U_2042,U_2043,U_2044) ),
    inference(clausify,[status(thm)],[f_462_3]) ).

cnf(f_462_8,plain,
    ( U_2042 != U_2044
    | ~ sP114(U_2041,U_2042,U_2043,U_2044) ),
    inference(clausify,[status(thm)],[f_462_3]) ).

fof(f_463_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_463_2,plain,
    ! [U_2048,U_2047,U_2046,U_2045] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2045),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2045),U_2046),U_2047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2045),U_2048),U_2047)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2045),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2045),U_2046),U_2048)),U_2047)
      | ~ class_Rings_Ocomm__semiring__1(U_2045) ),
    inference(variable_rename,[status(thm)],[f_463_1]) ).

fof(f_463_3,plain,
    ! [U_2048,U_2046,U_2047,U_2045] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2045),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2045),U_2046),U_2047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2045),U_2048),U_2047)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2045),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2045),U_2046),U_2048)),U_2047)
      | ~ class_Rings_Ocomm__semiring__1(U_2045) ),
    inference(definitional_conversion,[status(esa)],[f_463_2]) ).

cnf(f_463_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2045),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2045),U_2046),U_2047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2045),U_2048),U_2047)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2045),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2045),U_2046),U_2048)),U_2047)
    | ~ class_Rings_Ocomm__semiring__1(U_2045) ),
    inference(clausify,[status(thm)],[f_463_3]) ).

fof(f_464_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_464_2,plain,
    ! [U_2052,U_2051,U_2050,U_2049] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2049),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2049),U_2050),U_2051)),U_2052) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2049),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2049),U_2050),U_2052)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2049),U_2051),U_2052))
      | ~ class_Rings_Ocomm__semiring__1(U_2049) ),
    inference(variable_rename,[status(thm)],[f_464_1]) ).

fof(f_464_3,plain,
    ! [U_2049,U_2050,U_2051,U_2052] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2049),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2049),U_2050),U_2051)),U_2052) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2049),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2049),U_2050),U_2052)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2049),U_2051),U_2052))
      | ~ class_Rings_Ocomm__semiring__1(U_2049) ),
    inference(definitional_conversion,[status(esa)],[f_464_2]) ).

cnf(f_464_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2049),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2049),U_2050),U_2051)),U_2052) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2049),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2049),U_2050),U_2052)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2049),U_2051),U_2052))
    | ~ class_Rings_Ocomm__semiring__1(U_2049) ),
    inference(clausify,[status(thm)],[f_464_3]) ).

fof(f_465_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_465_2,plain,
    ! [U_2057,U_2056,U_2055,U_2054,U_2053] :
      ( ( ( ( U_2056 != U_2057
            & U_2054 != U_2055 )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2054),U_2056)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2055),U_2057)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2054),U_2057)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2055),U_2056)) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2054),U_2056)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2055),U_2057)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2054),U_2057)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2055),U_2056))
          | U_2056 = U_2057
          | U_2054 = U_2055 ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2053) ),
    inference(variable_rename,[status(thm)],[f_465_1]) ).

fof(f_465_3,plain,
    ( ! [U_2054,U_2055,U_2056,U_2057] :
        ( U_2056 != U_2057
        | ~ sP116(U_2054,U_2055,U_2056,U_2057) )
    & ! [U_2054,U_2055,U_2056,U_2057] :
        ( U_2054 != U_2055
        | ~ sP116(U_2054,U_2055,U_2056,U_2057) )
    & ! [U_2053,U_2054,U_2055,U_2056,U_2057] :
        ( sP116(U_2054,U_2055,U_2056,U_2057)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2054),U_2056)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2055),U_2057)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2054),U_2057)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2055),U_2056))
        | ~ sP117(U_2053,U_2054,U_2055,U_2056,U_2057) )
    & ! [U_2053,U_2054,U_2055,U_2056,U_2057] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2054),U_2056)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2055),U_2057)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2054),U_2057)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2055),U_2056))
        | U_2056 = U_2057
        | U_2054 = U_2055
        | ~ sP117(U_2053,U_2054,U_2055,U_2056,U_2057) )
    & ! [U_2053,U_2054,U_2055,U_2056,U_2057] :
        ( sP117(U_2053,U_2054,U_2055,U_2056,U_2057)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2053) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP116,sP117])],[f_465_2]) ).

cnf(f_465_4,plain,
    ( sP117(U_2053,U_2054,U_2055,U_2056,U_2057)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2053) ),
    inference(clausify,[status(thm)],[f_465_3]) ).

cnf(f_465_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2054),U_2056)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2055),U_2057)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2054),U_2057)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2055),U_2056))
    | U_2056 = U_2057
    | U_2054 = U_2055
    | ~ sP117(U_2053,U_2054,U_2055,U_2056,U_2057) ),
    inference(clausify,[status(thm)],[f_465_3]) ).

cnf(f_465_6,plain,
    ( sP116(U_2054,U_2055,U_2056,U_2057)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2054),U_2056)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2055),U_2057)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2054),U_2057)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2055),U_2056))
    | ~ sP117(U_2053,U_2054,U_2055,U_2056,U_2057) ),
    inference(clausify,[status(thm)],[f_465_3]) ).

cnf(f_465_7,plain,
    ( U_2054 != U_2055
    | ~ sP116(U_2054,U_2055,U_2056,U_2057) ),
    inference(clausify,[status(thm)],[f_465_3]) ).

cnf(f_465_8,plain,
    ( U_2056 != U_2057
    | ~ sP116(U_2054,U_2055,U_2056,U_2057) ),
    inference(clausify,[status(thm)],[f_465_3]) ).

fof(f_466_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_466_2,plain,
    ! [U_2061,U_2060,U_2059,U_2058] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2058),U_2059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2058),U_2060),U_2061)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2058),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2058),U_2059),U_2060)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2058),U_2059),U_2061))
      | ~ class_Rings_Ocomm__semiring__1(U_2058) ),
    inference(variable_rename,[status(thm)],[f_466_1]) ).

fof(f_466_3,plain,
    ! [U_2059,U_2061,U_2058,U_2060] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2058),U_2059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2058),U_2060),U_2061)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2058),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2058),U_2059),U_2060)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2058),U_2059),U_2061))
      | ~ class_Rings_Ocomm__semiring__1(U_2058) ),
    inference(definitional_conversion,[status(esa)],[f_466_2]) ).

cnf(f_466_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2058),U_2059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2058),U_2060),U_2061)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2058),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2058),U_2059),U_2060)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2058),U_2059),U_2061))
    | ~ class_Rings_Ocomm__semiring__1(U_2058) ),
    inference(clausify,[status(thm)],[f_466_3]) ).

fof(f_467_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_467_2,plain,
    ! [U_2063,U_2062] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2062),U_2063)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2062)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2063)),
    inference(variable_rename,[status(thm)],[f_467_1]) ).

fof(f_467_3,plain,
    ! [U_2062,U_2063] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2062),U_2063)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2062)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2063)),
    inference(definitional_conversion,[status(esa)],[f_467_2]) ).

cnf(f_467_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2062),U_2063)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2062)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2063)),
    inference(clausify,[status(thm)],[f_467_3]) ).

fof(f_468_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_468_2,plain,
    ! [U_2066,U_2065,U_2064] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2064),U_2065)),U_2066) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2064),U_2066)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2065),U_2066)),
    inference(variable_rename,[status(thm)],[f_468_1]) ).

fof(f_468_3,plain,
    ! [U_2064,U_2065,U_2066] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2064),U_2065)),U_2066) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2064),U_2066)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2065),U_2066)),
    inference(definitional_conversion,[status(esa)],[f_468_2]) ).

cnf(f_468_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2064),U_2065)),U_2066) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2064),U_2066)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2065),U_2066)),
    inference(clausify,[status(thm)],[f_468_3]) ).

fof(f_469_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_469_2,plain,
    ! [U_2069,U_2068,U_2067] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2067),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2068),U_2069)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2067),U_2068)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2067),U_2069)),
    inference(variable_rename,[status(thm)],[f_469_1]) ).

fof(f_469_3,plain,
    ! [U_2067,U_2068,U_2069] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2067),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2068),U_2069)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2067),U_2068)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2067),U_2069)),
    inference(definitional_conversion,[status(esa)],[f_469_2]) ).

cnf(f_469_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2067),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2068),U_2069)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2067),U_2068)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2067),U_2069)),
    inference(clausify,[status(thm)],[f_469_3]) ).

fof(f_470_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_470_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_470_1]) ).

cnf(f_470_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_470_2]) ).

fof(f_471_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_471_2,plain,
    ! [U_2070] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2070)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2070),
    inference(variable_rename,[status(thm)],[f_471_1]) ).

fof(f_471_3,plain,
    ! [U_2070] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2070)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2070),
    inference(definitional_conversion,[status(esa)],[f_471_2]) ).

cnf(f_471_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_2070)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2070),
    inference(clausify,[status(thm)],[f_471_3]) ).

fof(f_472_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_472_2,plain,
    ! [U_2072,U_2071] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2071),U_2072),hAPP(c_Groups_Ouminus__class_Ouminus(U_2071),U_2072)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2071),U_2072),c_Groups_Ozero__class_Ozero(U_2071))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2071),U_2072),c_Groups_Ozero__class_Ozero(U_2071)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2071),U_2072),hAPP(c_Groups_Ouminus__class_Ouminus(U_2071),U_2072))) ) )
      | ~ class_Rings_Olinordered__idom(U_2071) ),
    inference(variable_rename,[status(thm)],[f_472_1]) ).

fof(f_472_3,plain,
    ( ! [U_2071,U_2072] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2071),U_2072),hAPP(c_Groups_Ouminus__class_Ouminus(U_2071),U_2072)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2071),U_2072),c_Groups_Ozero__class_Ozero(U_2071)))
        | ~ sP118(U_2071,U_2072) )
    & ! [U_2071,U_2072] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2071),U_2072),c_Groups_Ozero__class_Ozero(U_2071)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2071),U_2072),hAPP(c_Groups_Ouminus__class_Ouminus(U_2071),U_2072)))
        | ~ sP118(U_2071,U_2072) )
    & ! [U_2071,U_2072] :
        ( sP118(U_2071,U_2072)
        | ~ class_Rings_Olinordered__idom(U_2071) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP118])],[f_472_2]) ).

cnf(f_472_4,plain,
    ( sP118(U_2071,U_2072)
    | ~ class_Rings_Olinordered__idom(U_2071) ),
    inference(clausify,[status(thm)],[f_472_3]) ).

cnf(f_472_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2071),U_2072),c_Groups_Ozero__class_Ozero(U_2071)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2071),U_2072),hAPP(c_Groups_Ouminus__class_Ouminus(U_2071),U_2072)))
    | ~ sP118(U_2071,U_2072) ),
    inference(clausify,[status(thm)],[f_472_3]) ).

cnf(f_472_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2071),U_2072),hAPP(c_Groups_Ouminus__class_Ouminus(U_2071),U_2072)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2071),U_2072),c_Groups_Ozero__class_Ozero(U_2071)))
    | ~ sP118(U_2071,U_2072) ),
    inference(clausify,[status(thm)],[f_472_3]) ).

fof(f_473_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_473_2,plain,
    ! [U_2074,U_2073] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2073),hAPP(c_Groups_Ouminus__class_Ouminus(U_2073),U_2074)),U_2074))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2073),c_Groups_Ozero__class_Ozero(U_2073)),U_2074)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2073),c_Groups_Ozero__class_Ozero(U_2073)),U_2074))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2073),hAPP(c_Groups_Ouminus__class_Ouminus(U_2073),U_2074)),U_2074)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_2073) ),
    inference(variable_rename,[status(thm)],[f_473_1]) ).

fof(f_473_3,plain,
    ( ! [U_2074,U_2073] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2073),hAPP(c_Groups_Ouminus__class_Ouminus(U_2073),U_2074)),U_2074))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2073),c_Groups_Ozero__class_Ozero(U_2073)),U_2074))
        | ~ sP119(U_2074,U_2073) )
    & ! [U_2074,U_2073] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2073),c_Groups_Ozero__class_Ozero(U_2073)),U_2074))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2073),hAPP(c_Groups_Ouminus__class_Ouminus(U_2073),U_2074)),U_2074))
        | ~ sP119(U_2074,U_2073) )
    & ! [U_2074,U_2073] :
        ( sP119(U_2074,U_2073)
        | ~ class_Groups_Olinordered__ab__group__add(U_2073) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP119])],[f_473_2]) ).

cnf(f_473_4,plain,
    ( sP119(U_2074,U_2073)
    | ~ class_Groups_Olinordered__ab__group__add(U_2073) ),
    inference(clausify,[status(thm)],[f_473_3]) ).

cnf(f_473_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2073),c_Groups_Ozero__class_Ozero(U_2073)),U_2074))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2073),hAPP(c_Groups_Ouminus__class_Ouminus(U_2073),U_2074)),U_2074))
    | ~ sP119(U_2074,U_2073) ),
    inference(clausify,[status(thm)],[f_473_3]) ).

cnf(f_473_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2073),hAPP(c_Groups_Ouminus__class_Ouminus(U_2073),U_2074)),U_2074))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2073),c_Groups_Ozero__class_Ozero(U_2073)),U_2074))
    | ~ sP119(U_2074,U_2073) ),
    inference(clausify,[status(thm)],[f_473_3]) ).

fof(f_474_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_474_2,plain,
    ! [U_2076,U_2075] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2075),hAPP(c_Groups_Ouminus__class_Ouminus(U_2075),U_2076)),c_Groups_Ozero__class_Ozero(U_2075)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2075),c_Groups_Ozero__class_Ozero(U_2075)),U_2076)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2075),c_Groups_Ozero__class_Ozero(U_2075)),U_2076))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2075),hAPP(c_Groups_Ouminus__class_Ouminus(U_2075),U_2076)),c_Groups_Ozero__class_Ozero(U_2075))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2075) ),
    inference(variable_rename,[status(thm)],[f_474_1]) ).

fof(f_474_3,plain,
    ( ! [U_2076,U_2075] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2075),hAPP(c_Groups_Ouminus__class_Ouminus(U_2075),U_2076)),c_Groups_Ozero__class_Ozero(U_2075)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2075),c_Groups_Ozero__class_Ozero(U_2075)),U_2076))
        | ~ sP120(U_2076,U_2075) )
    & ! [U_2076,U_2075] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2075),c_Groups_Ozero__class_Ozero(U_2075)),U_2076))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2075),hAPP(c_Groups_Ouminus__class_Ouminus(U_2075),U_2076)),c_Groups_Ozero__class_Ozero(U_2075)))
        | ~ sP120(U_2076,U_2075) )
    & ! [U_2076,U_2075] :
        ( sP120(U_2076,U_2075)
        | ~ class_Groups_Oordered__ab__group__add(U_2075) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP120])],[f_474_2]) ).

cnf(f_474_4,plain,
    ( sP120(U_2076,U_2075)
    | ~ class_Groups_Oordered__ab__group__add(U_2075) ),
    inference(clausify,[status(thm)],[f_474_3]) ).

cnf(f_474_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2075),c_Groups_Ozero__class_Ozero(U_2075)),U_2076))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2075),hAPP(c_Groups_Ouminus__class_Ouminus(U_2075),U_2076)),c_Groups_Ozero__class_Ozero(U_2075)))
    | ~ sP120(U_2076,U_2075) ),
    inference(clausify,[status(thm)],[f_474_3]) ).

cnf(f_474_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2075),hAPP(c_Groups_Ouminus__class_Ouminus(U_2075),U_2076)),c_Groups_Ozero__class_Ozero(U_2075)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2075),c_Groups_Ozero__class_Ozero(U_2075)),U_2076))
    | ~ sP120(U_2076,U_2075) ),
    inference(clausify,[status(thm)],[f_474_3]) ).

fof(f_475_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_475_2,plain,
    ! [U_2078,U_2077] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2077),c_Groups_Ozero__class_Ozero(U_2077)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2077),U_2078)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2077),U_2078),c_Groups_Ozero__class_Ozero(U_2077))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2077),U_2078),c_Groups_Ozero__class_Ozero(U_2077)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2077),c_Groups_Ozero__class_Ozero(U_2077)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2077),U_2078))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2077) ),
    inference(variable_rename,[status(thm)],[f_475_1]) ).

fof(f_475_3,plain,
    ( ! [U_2077,U_2078] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2077),c_Groups_Ozero__class_Ozero(U_2077)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2077),U_2078)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2077),U_2078),c_Groups_Ozero__class_Ozero(U_2077)))
        | ~ sP121(U_2077,U_2078) )
    & ! [U_2077,U_2078] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2077),U_2078),c_Groups_Ozero__class_Ozero(U_2077)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2077),c_Groups_Ozero__class_Ozero(U_2077)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2077),U_2078)))
        | ~ sP121(U_2077,U_2078) )
    & ! [U_2077,U_2078] :
        ( sP121(U_2077,U_2078)
        | ~ class_Groups_Oordered__ab__group__add(U_2077) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP121])],[f_475_2]) ).

cnf(f_475_4,plain,
    ( sP121(U_2077,U_2078)
    | ~ class_Groups_Oordered__ab__group__add(U_2077) ),
    inference(clausify,[status(thm)],[f_475_3]) ).

cnf(f_475_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2077),U_2078),c_Groups_Ozero__class_Ozero(U_2077)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2077),c_Groups_Ozero__class_Ozero(U_2077)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2077),U_2078)))
    | ~ sP121(U_2077,U_2078) ),
    inference(clausify,[status(thm)],[f_475_3]) ).

cnf(f_475_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2077),c_Groups_Ozero__class_Ozero(U_2077)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2077),U_2078)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2077),U_2078),c_Groups_Ozero__class_Ozero(U_2077)))
    | ~ sP121(U_2077,U_2078) ),
    inference(clausify,[status(thm)],[f_475_3]) ).

fof(f_476_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_476_2,plain,
    ! [U_2080,U_2079] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2079),U_2080),hAPP(c_Groups_Ouminus__class_Ouminus(U_2079),U_2080)) = c_Groups_Ozero__class_Ozero(U_2079)
      | ~ class_Groups_Ogroup__add(U_2079) ),
    inference(variable_rename,[status(thm)],[f_476_1]) ).

fof(f_476_3,plain,
    ! [U_2080,U_2079] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2079),U_2080),hAPP(c_Groups_Ouminus__class_Ouminus(U_2079),U_2080)) = c_Groups_Ozero__class_Ozero(U_2079)
      | ~ class_Groups_Ogroup__add(U_2079) ),
    inference(definitional_conversion,[status(esa)],[f_476_2]) ).

cnf(f_476_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2079),U_2080),hAPP(c_Groups_Ouminus__class_Ouminus(U_2079),U_2080)) = c_Groups_Ozero__class_Ozero(U_2079)
    | ~ class_Groups_Ogroup__add(U_2079) ),
    inference(clausify,[status(thm)],[f_476_3]) ).

fof(f_477_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_477_2,plain,
    ! [U_2083,U_2082,U_2081] :
      ( ( ( U_2082 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2081),U_2083)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2081),U_2082),U_2083) != c_Groups_Ozero__class_Ozero(U_2081) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2081),U_2082),U_2083) = c_Groups_Ozero__class_Ozero(U_2081)
          | U_2082 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2081),U_2083) ) )
      | ~ class_Groups_Ogroup__add(U_2081) ),
    inference(variable_rename,[status(thm)],[f_477_1]) ).

fof(f_477_3,plain,
    ( ! [U_2081,U_2082,U_2083] :
        ( U_2082 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2081),U_2083)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2081),U_2082),U_2083) != c_Groups_Ozero__class_Ozero(U_2081)
        | ~ sP122(U_2081,U_2082,U_2083) )
    & ! [U_2081,U_2082,U_2083] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2081),U_2082),U_2083) = c_Groups_Ozero__class_Ozero(U_2081)
        | U_2082 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2081),U_2083)
        | ~ sP122(U_2081,U_2082,U_2083) )
    & ! [U_2081,U_2082,U_2083] :
        ( sP122(U_2081,U_2082,U_2083)
        | ~ class_Groups_Ogroup__add(U_2081) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP122])],[f_477_2]) ).

cnf(f_477_4,plain,
    ( sP122(U_2081,U_2082,U_2083)
    | ~ class_Groups_Ogroup__add(U_2081) ),
    inference(clausify,[status(thm)],[f_477_3]) ).

cnf(f_477_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2081),U_2082),U_2083) = c_Groups_Ozero__class_Ozero(U_2081)
    | U_2082 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2081),U_2083)
    | ~ sP122(U_2081,U_2082,U_2083) ),
    inference(clausify,[status(thm)],[f_477_3]) ).

cnf(f_477_6,plain,
    ( U_2082 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2081),U_2083)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2081),U_2082),U_2083) != c_Groups_Ozero__class_Ozero(U_2081)
    | ~ sP122(U_2081,U_2082,U_2083) ),
    inference(clausify,[status(thm)],[f_477_3]) ).

fof(f_478_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_478_2,plain,
    ! [U_2085,U_2084] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2084),hAPP(c_Groups_Ouminus__class_Ouminus(U_2084),U_2085)),U_2085) = c_Groups_Ozero__class_Ozero(U_2084)
      | ~ class_Groups_Ogroup__add(U_2084) ),
    inference(variable_rename,[status(thm)],[f_478_1]) ).

fof(f_478_3,plain,
    ! [U_2085,U_2084] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2084),hAPP(c_Groups_Ouminus__class_Ouminus(U_2084),U_2085)),U_2085) = c_Groups_Ozero__class_Ozero(U_2084)
      | ~ class_Groups_Ogroup__add(U_2084) ),
    inference(definitional_conversion,[status(esa)],[f_478_2]) ).

cnf(f_478_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2084),hAPP(c_Groups_Ouminus__class_Ouminus(U_2084),U_2085)),U_2085) = c_Groups_Ozero__class_Ozero(U_2084)
    | ~ class_Groups_Ogroup__add(U_2084) ),
    inference(clausify,[status(thm)],[f_478_3]) ).

fof(f_479_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_479_2,plain,
    ! [U_2087,U_2086] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2086),hAPP(c_Groups_Ouminus__class_Ouminus(U_2086),U_2087)),U_2087) = c_Groups_Ozero__class_Ozero(U_2086)
      | ~ class_Groups_Oab__group__add(U_2086) ),
    inference(variable_rename,[status(thm)],[f_479_1]) ).

fof(f_479_3,plain,
    ! [U_2086,U_2087] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2086),hAPP(c_Groups_Ouminus__class_Ouminus(U_2086),U_2087)),U_2087) = c_Groups_Ozero__class_Ozero(U_2086)
      | ~ class_Groups_Oab__group__add(U_2086) ),
    inference(definitional_conversion,[status(esa)],[f_479_2]) ).

cnf(f_479_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2086),hAPP(c_Groups_Ouminus__class_Ouminus(U_2086),U_2087)),U_2087) = c_Groups_Ozero__class_Ozero(U_2086)
    | ~ class_Groups_Oab__group__add(U_2086) ),
    inference(clausify,[status(thm)],[f_479_3]) ).

fof(f_480_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_480_2,plain,
    ! [U_2090,U_2089,U_2088] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2088),U_2089) = U_2090
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2088),U_2089),U_2090) != c_Groups_Ozero__class_Ozero(U_2088)
      | ~ class_Groups_Ogroup__add(U_2088) ),
    inference(variable_rename,[status(thm)],[f_480_1]) ).

fof(f_480_3,plain,
    ! [U_2088,U_2089,U_2090] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2088),U_2089) = U_2090
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2088),U_2089),U_2090) != c_Groups_Ozero__class_Ozero(U_2088)
      | ~ class_Groups_Ogroup__add(U_2088) ),
    inference(definitional_conversion,[status(esa)],[f_480_2]) ).

cnf(f_480_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2088),U_2089) = U_2090
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2088),U_2089),U_2090) != c_Groups_Ozero__class_Ozero(U_2088)
    | ~ class_Groups_Ogroup__add(U_2088) ),
    inference(clausify,[status(thm)],[f_480_3]) ).

fof(f_481_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_481_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_481_1]) ).

cnf(f_481_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_481_2]) ).

fof(f_482_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_482_2,plain,
    ! [U_2094,U_2093,U_2092,U_2091] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2091),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2091),U_2094),U_2093)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2091),U_2094),U_2092)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2091),U_2094),c_Groups_Ozero__class_Ozero(U_2091)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2091),U_2092),U_2093))
      | ~ class_Rings_Olinordered__ring__strict(U_2091) ),
    inference(variable_rename,[status(thm)],[f_482_1]) ).

fof(f_482_3,plain,
    ! [U_2091,U_2092,U_2093,U_2094] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2091),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2091),U_2094),U_2093)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2091),U_2094),U_2092)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2091),U_2094),c_Groups_Ozero__class_Ozero(U_2091)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2091),U_2092),U_2093))
      | ~ class_Rings_Olinordered__ring__strict(U_2091) ),
    inference(definitional_conversion,[status(esa)],[f_482_2]) ).

cnf(f_482_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2091),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2091),U_2094),U_2093)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2091),U_2094),U_2092)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2091),U_2094),c_Groups_Ozero__class_Ozero(U_2091)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2091),U_2092),U_2093))
    | ~ class_Rings_Olinordered__ring__strict(U_2091) ),
    inference(clausify,[status(thm)],[f_482_3]) ).

fof(f_483_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_483_2,plain,
    ! [U_2098,U_2097,U_2096,U_2095] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2095),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2095),U_2097),U_2098)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2095),U_2096),U_2098)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2095),U_2098),c_Groups_Ozero__class_Ozero(U_2095)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2095),U_2096),U_2097))
      | ~ class_Rings_Olinordered__ring__strict(U_2095) ),
    inference(variable_rename,[status(thm)],[f_483_1]) ).

fof(f_483_3,plain,
    ! [U_2095,U_2096,U_2097,U_2098] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2095),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2095),U_2097),U_2098)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2095),U_2096),U_2098)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2095),U_2098),c_Groups_Ozero__class_Ozero(U_2095)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2095),U_2096),U_2097))
      | ~ class_Rings_Olinordered__ring__strict(U_2095) ),
    inference(definitional_conversion,[status(esa)],[f_483_2]) ).

cnf(f_483_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2095),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2095),U_2097),U_2098)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2095),U_2096),U_2098)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2095),U_2098),c_Groups_Ozero__class_Ozero(U_2095)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2095),U_2096),U_2097))
    | ~ class_Rings_Olinordered__ring__strict(U_2095) ),
    inference(clausify,[status(thm)],[f_483_3]) ).

fof(f_484_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_484_2,plain,
    ! [U_2102,U_2101,U_2100,U_2099] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2102),U_2100)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2102),U_2101)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2099),c_Groups_Ozero__class_Ozero(U_2099)),U_2102))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2099),U_2100),U_2101))
      | ~ class_Rings_Olinordered__comm__semiring__strict(U_2099) ),
    inference(variable_rename,[status(thm)],[f_484_1]) ).

fof(f_484_3,plain,
    ! [U_2099,U_2100,U_2101,U_2102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2102),U_2100)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2102),U_2101)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2099),c_Groups_Ozero__class_Ozero(U_2099)),U_2102))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2099),U_2100),U_2101))
      | ~ class_Rings_Olinordered__comm__semiring__strict(U_2099) ),
    inference(definitional_conversion,[status(esa)],[f_484_2]) ).

cnf(f_484_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2102),U_2100)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2099),U_2102),U_2101)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2099),c_Groups_Ozero__class_Ozero(U_2099)),U_2102))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2099),U_2100),U_2101))
    | ~ class_Rings_Olinordered__comm__semiring__strict(U_2099) ),
    inference(clausify,[status(thm)],[f_484_3]) ).

fof(f_485_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_485_2,plain,
    ! [U_2106,U_2105,U_2104,U_2103] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2103),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2106),U_2104)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2106),U_2105)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2103),c_Groups_Ozero__class_Ozero(U_2103)),U_2106))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2103),U_2104),U_2105))
      | ~ class_Rings_Olinordered__semiring__strict(U_2103) ),
    inference(variable_rename,[status(thm)],[f_485_1]) ).

fof(f_485_3,plain,
    ! [U_2103,U_2104,U_2105,U_2106] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2103),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2106),U_2104)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2106),U_2105)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2103),c_Groups_Ozero__class_Ozero(U_2103)),U_2106))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2103),U_2104),U_2105))
      | ~ class_Rings_Olinordered__semiring__strict(U_2103) ),
    inference(definitional_conversion,[status(esa)],[f_485_2]) ).

cnf(f_485_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2103),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2106),U_2104)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2103),U_2106),U_2105)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2103),c_Groups_Ozero__class_Ozero(U_2103)),U_2106))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2103),U_2104),U_2105))
    | ~ class_Rings_Olinordered__semiring__strict(U_2103) ),
    inference(clausify,[status(thm)],[f_485_3]) ).

fof(f_486_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_486_2,plain,
    ! [U_2110,U_2109,U_2108,U_2107] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2107),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2107),U_2108),U_2110)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2107),U_2109),U_2110)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2107),c_Groups_Ozero__class_Ozero(U_2107)),U_2110))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2107),U_2108),U_2109))
      | ~ class_Rings_Olinordered__semiring__strict(U_2107) ),
    inference(variable_rename,[status(thm)],[f_486_1]) ).

fof(f_486_3,plain,
    ! [U_2107,U_2108,U_2109,U_2110] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2107),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2107),U_2108),U_2110)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2107),U_2109),U_2110)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2107),c_Groups_Ozero__class_Ozero(U_2107)),U_2110))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2107),U_2108),U_2109))
      | ~ class_Rings_Olinordered__semiring__strict(U_2107) ),
    inference(definitional_conversion,[status(esa)],[f_486_2]) ).

cnf(f_486_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2107),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2107),U_2108),U_2110)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2107),U_2109),U_2110)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2107),c_Groups_Ozero__class_Ozero(U_2107)),U_2110))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2107),U_2108),U_2109))
    | ~ class_Rings_Olinordered__semiring__strict(U_2107) ),
    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),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_487_2,plain,
    ! [U_2113,U_2112,U_2111] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2111),c_Groups_Ozero__class_Ozero(U_2111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2111),U_2112),U_2113)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2111),U_2113),c_Groups_Ozero__class_Ozero(U_2111)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2111),U_2112),c_Groups_Ozero__class_Ozero(U_2111)))
      | ~ class_Rings_Olinordered__ring__strict(U_2111) ),
    inference(variable_rename,[status(thm)],[f_487_1]) ).

fof(f_487_3,plain,
    ! [U_2112,U_2111,U_2113] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2111),c_Groups_Ozero__class_Ozero(U_2111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2111),U_2112),U_2113)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2111),U_2113),c_Groups_Ozero__class_Ozero(U_2111)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2111),U_2112),c_Groups_Ozero__class_Ozero(U_2111)))
      | ~ class_Rings_Olinordered__ring__strict(U_2111) ),
    inference(definitional_conversion,[status(esa)],[f_487_2]) ).

cnf(f_487_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2111),c_Groups_Ozero__class_Ozero(U_2111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2111),U_2112),U_2113)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2111),U_2113),c_Groups_Ozero__class_Ozero(U_2111)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2111),U_2112),c_Groups_Ozero__class_Ozero(U_2111)))
    | ~ class_Rings_Olinordered__ring__strict(U_2111) ),
    inference(clausify,[status(thm)],[f_487_3]) ).

fof(f_488_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_488_2,plain,
    ! [U_2116,U_2115,U_2114] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2114),U_2115),U_2116)),c_Groups_Ozero__class_Ozero(U_2114)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2114),c_Groups_Ozero__class_Ozero(U_2114)),U_2116))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2114),U_2115),c_Groups_Ozero__class_Ozero(U_2114)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2114) ),
    inference(variable_rename,[status(thm)],[f_488_1]) ).

fof(f_488_3,plain,
    ! [U_2114,U_2116,U_2115] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2114),U_2115),U_2116)),c_Groups_Ozero__class_Ozero(U_2114)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2114),c_Groups_Ozero__class_Ozero(U_2114)),U_2116))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2114),U_2115),c_Groups_Ozero__class_Ozero(U_2114)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2114) ),
    inference(definitional_conversion,[status(esa)],[f_488_2]) ).

cnf(f_488_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2114),U_2115),U_2116)),c_Groups_Ozero__class_Ozero(U_2114)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2114),c_Groups_Ozero__class_Ozero(U_2114)),U_2116))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2114),U_2115),c_Groups_Ozero__class_Ozero(U_2114)))
    | ~ class_Rings_Olinordered__semiring__strict(U_2114) ),
    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_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_489_2,plain,
    ! [U_2120,U_2119,U_2118,U_2117] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2118),U_2119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2118),U_2120)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),U_2120),U_2119)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),U_2120),U_2119))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2118),U_2119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2118),U_2120))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),U_2118),c_Groups_Ozero__class_Ozero(U_2117)))
      | ~ class_Rings_Olinordered__ring__strict(U_2117) ),
    inference(variable_rename,[status(thm)],[f_489_1]) ).

fof(f_489_3,plain,
    ( ! [U_2117,U_2118,U_2119,U_2120] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2118),U_2119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2118),U_2120)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),U_2120),U_2119))
        | ~ sP123(U_2117,U_2118,U_2119,U_2120) )
    & ! [U_2117,U_2118,U_2119,U_2120] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),U_2120),U_2119))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2118),U_2119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2118),U_2120)))
        | ~ sP123(U_2117,U_2118,U_2119,U_2120) )
    & ! [U_2117,U_2118,U_2119,U_2120] :
        ( sP123(U_2117,U_2118,U_2119,U_2120)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),U_2118),c_Groups_Ozero__class_Ozero(U_2117)))
        | ~ class_Rings_Olinordered__ring__strict(U_2117) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP123])],[f_489_2]) ).

cnf(f_489_4,plain,
    ( sP123(U_2117,U_2118,U_2119,U_2120)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),U_2118),c_Groups_Ozero__class_Ozero(U_2117)))
    | ~ class_Rings_Olinordered__ring__strict(U_2117) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

cnf(f_489_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),U_2120),U_2119))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2118),U_2119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2118),U_2120)))
    | ~ sP123(U_2117,U_2118,U_2119,U_2120) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

cnf(f_489_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2118),U_2119)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2117),U_2118),U_2120)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),U_2120),U_2119))
    | ~ sP123(U_2117,U_2118,U_2119,U_2120) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

fof(f_490_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_490_2,plain,
    ! [U_2123,U_2122,U_2121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2121),c_Groups_Ozero__class_Ozero(U_2121)),U_2122))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2121),c_Groups_Ozero__class_Ozero(U_2121)),U_2123))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2121),c_Groups_Ozero__class_Ozero(U_2121)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2121),U_2122),U_2123)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2121) ),
    inference(variable_rename,[status(thm)],[f_490_1]) ).

fof(f_490_3,plain,
    ! [U_2123,U_2121,U_2122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2121),c_Groups_Ozero__class_Ozero(U_2121)),U_2122))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2121),c_Groups_Ozero__class_Ozero(U_2121)),U_2123))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2121),c_Groups_Ozero__class_Ozero(U_2121)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2121),U_2122),U_2123)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2121) ),
    inference(definitional_conversion,[status(esa)],[f_490_2]) ).

cnf(f_490_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2121),c_Groups_Ozero__class_Ozero(U_2121)),U_2122))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2121),c_Groups_Ozero__class_Ozero(U_2121)),U_2123))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2121),c_Groups_Ozero__class_Ozero(U_2121)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2121),U_2122),U_2123)))
    | ~ class_Rings_Olinordered__semiring__strict(U_2121) ),
    inference(clausify,[status(thm)],[f_490_3]) ).

fof(f_491_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_491_2,plain,
    ! [U_2126,U_2125,U_2124] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2124),c_Groups_Ozero__class_Ozero(U_2124)),U_2126))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2124),c_Groups_Ozero__class_Ozero(U_2124)),U_2125))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2124),c_Groups_Ozero__class_Ozero(U_2124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2124),U_2125),U_2126)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2124) ),
    inference(variable_rename,[status(thm)],[f_491_1]) ).

fof(f_491_3,plain,
    ! [U_2124,U_2125,U_2126] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2124),c_Groups_Ozero__class_Ozero(U_2124)),U_2126))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2124),c_Groups_Ozero__class_Ozero(U_2124)),U_2125))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2124),c_Groups_Ozero__class_Ozero(U_2124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2124),U_2125),U_2126)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2124) ),
    inference(definitional_conversion,[status(esa)],[f_491_2]) ).

cnf(f_491_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2124),c_Groups_Ozero__class_Ozero(U_2124)),U_2126))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2124),c_Groups_Ozero__class_Ozero(U_2124)),U_2125))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2124),c_Groups_Ozero__class_Ozero(U_2124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2124),U_2125),U_2126)))
    | ~ class_Rings_Olinordered__semiring__strict(U_2124) ),
    inference(clausify,[status(thm)],[f_491_3]) ).

fof(f_492_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_492_2,plain,
    ! [U_2129,U_2128,U_2127] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2127),U_2129),U_2128)),c_Groups_Ozero__class_Ozero(U_2127)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2127),U_2129),c_Groups_Ozero__class_Ozero(U_2127)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2127),c_Groups_Ozero__class_Ozero(U_2127)),U_2128))
      | ~ class_Rings_Olinordered__semiring__strict(U_2127) ),
    inference(variable_rename,[status(thm)],[f_492_1]) ).

fof(f_492_3,plain,
    ! [U_2127,U_2128,U_2129] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2127),U_2129),U_2128)),c_Groups_Ozero__class_Ozero(U_2127)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2127),U_2129),c_Groups_Ozero__class_Ozero(U_2127)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2127),c_Groups_Ozero__class_Ozero(U_2127)),U_2128))
      | ~ class_Rings_Olinordered__semiring__strict(U_2127) ),
    inference(definitional_conversion,[status(esa)],[f_492_2]) ).

cnf(f_492_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2127),U_2129),U_2128)),c_Groups_Ozero__class_Ozero(U_2127)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2127),U_2129),c_Groups_Ozero__class_Ozero(U_2127)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2127),c_Groups_Ozero__class_Ozero(U_2127)),U_2128))
    | ~ class_Rings_Olinordered__semiring__strict(U_2127) ),
    inference(clausify,[status(thm)],[f_492_3]) ).

fof(f_493_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_493_2,plain,
    ! [U_2132,U_2131,U_2130] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2130),U_2131),U_2132)),c_Groups_Ozero__class_Ozero(U_2130)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2130),U_2132),c_Groups_Ozero__class_Ozero(U_2130)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2130),c_Groups_Ozero__class_Ozero(U_2130)),U_2131))
      | ~ class_Rings_Olinordered__semiring__strict(U_2130) ),
    inference(variable_rename,[status(thm)],[f_493_1]) ).

fof(f_493_3,plain,
    ! [U_2130,U_2131,U_2132] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2130),U_2131),U_2132)),c_Groups_Ozero__class_Ozero(U_2130)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2130),U_2132),c_Groups_Ozero__class_Ozero(U_2130)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2130),c_Groups_Ozero__class_Ozero(U_2130)),U_2131))
      | ~ class_Rings_Olinordered__semiring__strict(U_2130) ),
    inference(definitional_conversion,[status(esa)],[f_493_2]) ).

cnf(f_493_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2130),U_2131),U_2132)),c_Groups_Ozero__class_Ozero(U_2130)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2130),U_2132),c_Groups_Ozero__class_Ozero(U_2130)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2130),c_Groups_Ozero__class_Ozero(U_2130)),U_2131))
    | ~ class_Rings_Olinordered__semiring__strict(U_2130) ),
    inference(clausify,[status(thm)],[f_493_3]) ).

fof(f_494_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_494_2,plain,
    ! [U_2135,U_2134,U_2133] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2133),c_Groups_Ozero__class_Ozero(U_2133)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2133),U_2134),U_2135)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2133),c_Groups_Ozero__class_Ozero(U_2133)),U_2135))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2133),c_Groups_Ozero__class_Ozero(U_2133)),U_2134))
      | ~ class_Rings_Olinordered__semiring__strict(U_2133) ),
    inference(variable_rename,[status(thm)],[f_494_1]) ).

fof(f_494_3,plain,
    ! [U_2134,U_2133,U_2135] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2133),c_Groups_Ozero__class_Ozero(U_2133)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2133),U_2134),U_2135)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2133),c_Groups_Ozero__class_Ozero(U_2133)),U_2135))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2133),c_Groups_Ozero__class_Ozero(U_2133)),U_2134))
      | ~ class_Rings_Olinordered__semiring__strict(U_2133) ),
    inference(definitional_conversion,[status(esa)],[f_494_2]) ).

cnf(f_494_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2133),c_Groups_Ozero__class_Ozero(U_2133)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2133),U_2134),U_2135)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2133),c_Groups_Ozero__class_Ozero(U_2133)),U_2135))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2133),c_Groups_Ozero__class_Ozero(U_2133)),U_2134))
    | ~ class_Rings_Olinordered__semiring__strict(U_2133) ),
    inference(clausify,[status(thm)],[f_494_3]) ).

fof(f_495_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_495_2,plain,
    ! [U_2139,U_2138,U_2137,U_2136] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2136),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2136),U_2137),U_2138)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2136),U_2137),U_2139)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2136),U_2138),U_2139)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2136),U_2138),U_2139))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2136),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2136),U_2137),U_2138)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2136),U_2137),U_2139))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2136),c_Groups_Ozero__class_Ozero(U_2136)),U_2137))
      | ~ class_Rings_Olinordered__ring__strict(U_2136) ),
    inference(variable_rename,[status(thm)],[f_495_1]) ).

fof(f_495_3,plain,
    ( ! [U_2137,U_2136,U_2138,U_2139] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2136),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2136),U_2137),U_2138)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2136),U_2137),U_2139)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2136),U_2138),U_2139))
        | ~ sP124(U_2137,U_2136,U_2138,U_2139) )
    & ! [U_2137,U_2136,U_2138,U_2139] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2136),U_2138),U_2139))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2136),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2136),U_2137),U_2138)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2136),U_2137),U_2139)))
        | ~ sP124(U_2137,U_2136,U_2138,U_2139) )
    & ! [U_2137,U_2136,U_2138,U_2139] :
        ( sP124(U_2137,U_2136,U_2138,U_2139)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2136),c_Groups_Ozero__class_Ozero(U_2136)),U_2137))
        | ~ class_Rings_Olinordered__ring__strict(U_2136) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP124])],[f_495_2]) ).

cnf(f_495_4,plain,
    ( sP124(U_2137,U_2136,U_2138,U_2139)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2136),c_Groups_Ozero__class_Ozero(U_2136)),U_2137))
    | ~ class_Rings_Olinordered__ring__strict(U_2136) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

cnf(f_495_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2136),U_2138),U_2139))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2136),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2136),U_2137),U_2138)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2136),U_2137),U_2139)))
    | ~ sP124(U_2137,U_2136,U_2138,U_2139) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

cnf(f_495_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2136),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2136),U_2137),U_2138)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2136),U_2137),U_2139)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2136),U_2138),U_2139))
    | ~ sP124(U_2137,U_2136,U_2138,U_2139) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

fof(f_496_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_496_2,plain,
    ! [U_2143,U_2142,U_2141,U_2140] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2141),U_2142)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2141),U_2143)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2143),U_2142))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2141),c_Groups_Ozero__class_Ozero(U_2140))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2142),U_2143))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),c_Groups_Ozero__class_Ozero(U_2140)),U_2141)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2143),U_2142))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2141),c_Groups_Ozero__class_Ozero(U_2140))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2142),U_2143))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),c_Groups_Ozero__class_Ozero(U_2140)),U_2141)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2141),U_2142)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2141),U_2143))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_2140) ),
    inference(variable_rename,[status(thm)],[f_496_1]) ).

fof(f_496_3,plain,
    ( ! [U_2141,U_2140,U_2142,U_2143] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2143),U_2142))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2141),c_Groups_Ozero__class_Ozero(U_2140)))
        | ~ sP127(U_2141,U_2140,U_2142,U_2143) )
    & ! [U_2141,U_2140,U_2142,U_2143] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2142),U_2143))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),c_Groups_Ozero__class_Ozero(U_2140)),U_2141))
        | ~ sP127(U_2141,U_2140,U_2142,U_2143) )
    & ! [U_2141,U_2140,U_2142,U_2143] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2143),U_2142))
        | ~ sP126(U_2141,U_2140,U_2142,U_2143) )
    & ! [U_2141,U_2140,U_2142,U_2143] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2141),c_Groups_Ozero__class_Ozero(U_2140)))
        | ~ sP126(U_2141,U_2140,U_2142,U_2143) )
    & ! [U_2141,U_2140,U_2142,U_2143] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2142),U_2143))
        | ~ sP125(U_2141,U_2140,U_2142,U_2143) )
    & ! [U_2141,U_2140,U_2142,U_2143] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),c_Groups_Ozero__class_Ozero(U_2140)),U_2141))
        | ~ sP125(U_2141,U_2140,U_2142,U_2143) )
    & ! [U_2141,U_2140,U_2142,U_2143] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2141),U_2142)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2141),U_2143)))
        | sP127(U_2141,U_2140,U_2142,U_2143)
        | ~ sP128(U_2141,U_2140,U_2142,U_2143) )
    & ! [U_2141,U_2140,U_2142,U_2143] :
        ( sP126(U_2141,U_2140,U_2142,U_2143)
        | sP125(U_2141,U_2140,U_2142,U_2143)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2141),U_2142)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2141),U_2143)))
        | ~ sP128(U_2141,U_2140,U_2142,U_2143) )
    & ! [U_2141,U_2140,U_2142,U_2143] :
        ( sP128(U_2141,U_2140,U_2142,U_2143)
        | ~ class_Rings_Olinordered__ring__strict(U_2140) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP125,sP126,sP127,sP128])],[f_496_2]) ).

cnf(f_496_4,plain,
    ( sP128(U_2141,U_2140,U_2142,U_2143)
    | ~ class_Rings_Olinordered__ring__strict(U_2140) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_5,plain,
    ( sP126(U_2141,U_2140,U_2142,U_2143)
    | sP125(U_2141,U_2140,U_2142,U_2143)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2141),U_2142)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2141),U_2143)))
    | ~ sP128(U_2141,U_2140,U_2142,U_2143) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2141),U_2142)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2141),U_2143)))
    | sP127(U_2141,U_2140,U_2142,U_2143)
    | ~ sP128(U_2141,U_2140,U_2142,U_2143) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),c_Groups_Ozero__class_Ozero(U_2140)),U_2141))
    | ~ sP125(U_2141,U_2140,U_2142,U_2143) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2142),U_2143))
    | ~ sP125(U_2141,U_2140,U_2142,U_2143) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2141),c_Groups_Ozero__class_Ozero(U_2140)))
    | ~ sP126(U_2141,U_2140,U_2142,U_2143) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2143),U_2142))
    | ~ sP126(U_2141,U_2140,U_2142,U_2143) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2142),U_2143))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),c_Groups_Ozero__class_Ozero(U_2140)),U_2141))
    | ~ sP127(U_2141,U_2140,U_2142,U_2143) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2143),U_2142))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),U_2141),c_Groups_Ozero__class_Ozero(U_2140)))
    | ~ sP127(U_2141,U_2140,U_2142,U_2143) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

fof(f_497_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_497_2,plain,
    ! [U_2147,U_2146,U_2145,U_2144] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2145),U_2146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2147),U_2146)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2147),U_2145))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2146),c_Groups_Ozero__class_Ozero(U_2144))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2145),U_2147))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),c_Groups_Ozero__class_Ozero(U_2144)),U_2146)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2147),U_2145))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2146),c_Groups_Ozero__class_Ozero(U_2144))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2145),U_2147))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),c_Groups_Ozero__class_Ozero(U_2144)),U_2146)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2145),U_2146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2147),U_2146))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_2144) ),
    inference(variable_rename,[status(thm)],[f_497_1]) ).

fof(f_497_3,plain,
    ( ! [U_2146,U_2147,U_2144,U_2145] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2147),U_2145))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2146),c_Groups_Ozero__class_Ozero(U_2144)))
        | ~ sP131(U_2146,U_2147,U_2144,U_2145) )
    & ! [U_2146,U_2147,U_2144,U_2145] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2145),U_2147))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),c_Groups_Ozero__class_Ozero(U_2144)),U_2146))
        | ~ sP131(U_2146,U_2147,U_2144,U_2145) )
    & ! [U_2146,U_2147,U_2144,U_2145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2147),U_2145))
        | ~ sP130(U_2146,U_2147,U_2144,U_2145) )
    & ! [U_2146,U_2147,U_2144,U_2145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2146),c_Groups_Ozero__class_Ozero(U_2144)))
        | ~ sP130(U_2146,U_2147,U_2144,U_2145) )
    & ! [U_2146,U_2147,U_2144,U_2145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2145),U_2147))
        | ~ sP129(U_2146,U_2147,U_2144,U_2145) )
    & ! [U_2146,U_2147,U_2144,U_2145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),c_Groups_Ozero__class_Ozero(U_2144)),U_2146))
        | ~ sP129(U_2146,U_2147,U_2144,U_2145) )
    & ! [U_2146,U_2147,U_2144,U_2145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2145),U_2146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2147),U_2146)))
        | sP131(U_2146,U_2147,U_2144,U_2145)
        | ~ sP132(U_2146,U_2147,U_2144,U_2145) )
    & ! [U_2146,U_2147,U_2144,U_2145] :
        ( sP130(U_2146,U_2147,U_2144,U_2145)
        | sP129(U_2146,U_2147,U_2144,U_2145)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2145),U_2146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2147),U_2146)))
        | ~ sP132(U_2146,U_2147,U_2144,U_2145) )
    & ! [U_2146,U_2147,U_2144,U_2145] :
        ( sP132(U_2146,U_2147,U_2144,U_2145)
        | ~ class_Rings_Olinordered__ring__strict(U_2144) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP129,sP130,sP131,sP132])],[f_497_2]) ).

cnf(f_497_4,plain,
    ( sP132(U_2146,U_2147,U_2144,U_2145)
    | ~ class_Rings_Olinordered__ring__strict(U_2144) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_5,plain,
    ( sP130(U_2146,U_2147,U_2144,U_2145)
    | sP129(U_2146,U_2147,U_2144,U_2145)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2145),U_2146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2147),U_2146)))
    | ~ sP132(U_2146,U_2147,U_2144,U_2145) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2145),U_2146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2144),U_2147),U_2146)))
    | sP131(U_2146,U_2147,U_2144,U_2145)
    | ~ sP132(U_2146,U_2147,U_2144,U_2145) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),c_Groups_Ozero__class_Ozero(U_2144)),U_2146))
    | ~ sP129(U_2146,U_2147,U_2144,U_2145) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2145),U_2147))
    | ~ sP129(U_2146,U_2147,U_2144,U_2145) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2146),c_Groups_Ozero__class_Ozero(U_2144)))
    | ~ sP130(U_2146,U_2147,U_2144,U_2145) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2147),U_2145))
    | ~ sP130(U_2146,U_2147,U_2144,U_2145) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2145),U_2147))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),c_Groups_Ozero__class_Ozero(U_2144)),U_2146))
    | ~ sP131(U_2146,U_2147,U_2144,U_2145) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2147),U_2145))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2144),U_2146),c_Groups_Ozero__class_Ozero(U_2144)))
    | ~ sP131(U_2146,U_2147,U_2144,U_2145) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

fof(f_498_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_498_2,plain,
    ! [U_2149,U_2148] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2148),U_2149),U_2149)),c_Groups_Ozero__class_Ozero(U_2148)))
      | ~ class_Rings_Olinordered__ring(U_2148) ),
    inference(variable_rename,[status(thm)],[f_498_1]) ).

fof(f_498_3,plain,
    ! [U_2149,U_2148] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2148),U_2149),U_2149)),c_Groups_Ozero__class_Ozero(U_2148)))
      | ~ class_Rings_Olinordered__ring(U_2148) ),
    inference(definitional_conversion,[status(esa)],[f_498_2]) ).

cnf(f_498_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2148),U_2149),U_2149)),c_Groups_Ozero__class_Ozero(U_2148)))
    | ~ class_Rings_Olinordered__ring(U_2148) ),
    inference(clausify,[status(thm)],[f_498_3]) ).

fof(f_499_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_499_2,plain,
    ! [U_2152,U_2151,U_2150] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2150),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2150),U_2151),U_2151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2150),U_2152),U_2152)) = c_Groups_Ozero__class_Ozero(U_2150)
          | U_2152 != c_Groups_Ozero__class_Ozero(U_2150)
          | U_2151 != c_Groups_Ozero__class_Ozero(U_2150) )
        & ( ( U_2152 = c_Groups_Ozero__class_Ozero(U_2150)
            & U_2151 = c_Groups_Ozero__class_Ozero(U_2150) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2150),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2150),U_2151),U_2151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2150),U_2152),U_2152)) != c_Groups_Ozero__class_Ozero(U_2150) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_2150) ),
    inference(variable_rename,[status(thm)],[f_499_1]) ).

fof(f_499_3,plain,
    ( ! [U_2152,U_2150,U_2151] :
        ( U_2152 = c_Groups_Ozero__class_Ozero(U_2150)
        | ~ sP133(U_2152,U_2150,U_2151) )
    & ! [U_2152,U_2150,U_2151] :
        ( U_2151 = c_Groups_Ozero__class_Ozero(U_2150)
        | ~ sP133(U_2152,U_2150,U_2151) )
    & ! [U_2152,U_2150,U_2151] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2150),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2150),U_2151),U_2151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2150),U_2152),U_2152)) = c_Groups_Ozero__class_Ozero(U_2150)
        | U_2152 != c_Groups_Ozero__class_Ozero(U_2150)
        | U_2151 != c_Groups_Ozero__class_Ozero(U_2150)
        | ~ sP134(U_2152,U_2150,U_2151) )
    & ! [U_2152,U_2150,U_2151] :
        ( sP133(U_2152,U_2150,U_2151)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2150),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2150),U_2151),U_2151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2150),U_2152),U_2152)) != c_Groups_Ozero__class_Ozero(U_2150)
        | ~ sP134(U_2152,U_2150,U_2151) )
    & ! [U_2152,U_2150,U_2151] :
        ( sP134(U_2152,U_2150,U_2151)
        | ~ class_Rings_Olinordered__ring__strict(U_2150) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP133,sP134])],[f_499_2]) ).

cnf(f_499_4,plain,
    ( sP134(U_2152,U_2150,U_2151)
    | ~ class_Rings_Olinordered__ring__strict(U_2150) ),
    inference(clausify,[status(thm)],[f_499_3]) ).

cnf(f_499_5,plain,
    ( sP133(U_2152,U_2150,U_2151)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2150),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2150),U_2151),U_2151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2150),U_2152),U_2152)) != c_Groups_Ozero__class_Ozero(U_2150)
    | ~ sP134(U_2152,U_2150,U_2151) ),
    inference(clausify,[status(thm)],[f_499_3]) ).

cnf(f_499_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2150),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2150),U_2151),U_2151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2150),U_2152),U_2152)) = c_Groups_Ozero__class_Ozero(U_2150)
    | U_2152 != c_Groups_Ozero__class_Ozero(U_2150)
    | U_2151 != c_Groups_Ozero__class_Ozero(U_2150)
    | ~ sP134(U_2152,U_2150,U_2151) ),
    inference(clausify,[status(thm)],[f_499_3]) ).

cnf(f_499_7,plain,
    ( U_2151 = c_Groups_Ozero__class_Ozero(U_2150)
    | ~ sP133(U_2152,U_2150,U_2151) ),
    inference(clausify,[status(thm)],[f_499_3]) ).

cnf(f_499_8,plain,
    ( U_2152 = c_Groups_Ozero__class_Ozero(U_2150)
    | ~ sP133(U_2152,U_2150,U_2151) ),
    inference(clausify,[status(thm)],[f_499_3]) ).

fof(f_500_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_500_2,plain,
    ! [U_2158,U_2157,U_2156,U_2155,U_2154,U_2153] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2153),U_2155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2153),U_2154),U_2157)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2153),U_2156),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2153),U_2154),U_2158))
      | U_2157 = U_2158
      | U_2155 != U_2156
      | U_2154 = c_Groups_Ozero__class_Ozero(U_2153)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2153) ),
    inference(variable_rename,[status(thm)],[f_500_1]) ).

fof(f_500_3,plain,
    ! [U_2156,U_2158,U_2154,U_2155,U_2157,U_2153] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2153),U_2155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2153),U_2154),U_2157)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2153),U_2156),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2153),U_2154),U_2158))
      | U_2157 = U_2158
      | U_2155 != U_2156
      | U_2154 = c_Groups_Ozero__class_Ozero(U_2153)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2153) ),
    inference(definitional_conversion,[status(esa)],[f_500_2]) ).

cnf(f_500_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2153),U_2155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2153),U_2154),U_2157)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2153),U_2156),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2153),U_2154),U_2158))
    | U_2157 = U_2158
    | U_2155 != U_2156
    | U_2154 = c_Groups_Ozero__class_Ozero(U_2153)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2153) ),
    inference(clausify,[status(thm)],[f_500_3]) ).

fof(f_501_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_501_2,plain,
    ! [U_2159] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2159)),U_2159) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_501_1]) ).

fof(f_501_3,plain,
    ! [U_2159] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2159)),U_2159) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_501_2]) ).

cnf(f_501_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2159)),U_2159) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_501_3]) ).

fof(f_502_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_502_2,plain,
    ! [U_2161,U_2160] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2160)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2161)
        | U_2161 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2160 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_2161 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2160 = 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_2160)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2161) ) ),
    inference(variable_rename,[status(thm)],[f_502_1]) ).

fof(f_502_3,plain,
    ( ! [U_2165,U_2163] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2163)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2165)
        | U_2165 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2163 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2164,U_2162] :
        ( ( U_2164 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2162 = 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_2162)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2164) ) ),
    inference(miniscope,[status(thm)],[f_502_2]) ).

fof(f_502_4,plain,
    ( ! [U_2162,U_2164] :
        ( U_2164 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP135(U_2162,U_2164) )
    & ! [U_2162,U_2164] :
        ( U_2162 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP135(U_2162,U_2164) )
    & ! [U_2163,U_2165] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2163)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2165)
        | U_2165 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2163 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2162,U_2164] :
        ( sP135(U_2162,U_2164)
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2162)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2164) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP135])],[f_502_3]) ).

cnf(f_502_5,plain,
    ( sP135(U_2162,U_2164)
    | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2162)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2164) ),
    inference(clausify,[status(thm)],[f_502_4]) ).

cnf(f_502_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2163)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2165)
    | U_2165 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2163 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_502_4]) ).

cnf(f_502_7,plain,
    ( U_2162 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP135(U_2162,U_2164) ),
    inference(clausify,[status(thm)],[f_502_4]) ).

cnf(f_502_8,plain,
    ( U_2164 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP135(U_2162,U_2164) ),
    inference(clausify,[status(thm)],[f_502_4]) ).

fof(f_503_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_503_2,plain,
    ! [U_2167,U_2166] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2166)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2167)))),
    inference(variable_rename,[status(thm)],[f_503_1]) ).

fof(f_503_3,plain,
    ! [U_2166,U_2167] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2166)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2167)))),
    inference(definitional_conversion,[status(esa)],[f_503_2]) ).

cnf(f_503_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_2166)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2167)))),
    inference(clausify,[status(thm)],[f_503_3]) ).

fof(f_504_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_504_2,plain,
    ! [U_2170,U_2169,U_2168] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2170),U_2168)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2170),U_2169)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2170))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2168),U_2169)) ),
    inference(variable_rename,[status(thm)],[f_504_1]) ).

fof(f_504_3,plain,
    ! [U_2169,U_2168,U_2170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2170),U_2168)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2170),U_2169)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2170))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2168),U_2169)) ),
    inference(definitional_conversion,[status(esa)],[f_504_2]) ).

cnf(f_504_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2170),U_2168)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2170),U_2169)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2170))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2168),U_2169)) ),
    inference(clausify,[status(thm)],[f_504_3]) ).

fof(f_505_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_505_2,plain,
    ! [U_2172,U_2171] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_2171),U_2172) = c_Groups_Ozero__class_Ozero(U_2171)
          | U_2172 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( U_2172 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | hAPP(c_Int_Oring__1__class_Oof__int(U_2171),U_2172) != c_Groups_Ozero__class_Ozero(U_2171) ) )
      | ~ class_Int_Oring__char__0(U_2171) ),
    inference(variable_rename,[status(thm)],[f_505_1]) ).

fof(f_505_3,plain,
    ( ! [U_2172,U_2171] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_2171),U_2172) = c_Groups_Ozero__class_Ozero(U_2171)
        | U_2172 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP136(U_2172,U_2171) )
    & ! [U_2172,U_2171] :
        ( U_2172 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(c_Int_Oring__1__class_Oof__int(U_2171),U_2172) != c_Groups_Ozero__class_Ozero(U_2171)
        | ~ sP136(U_2172,U_2171) )
    & ! [U_2172,U_2171] :
        ( sP136(U_2172,U_2171)
        | ~ class_Int_Oring__char__0(U_2171) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP136])],[f_505_2]) ).

cnf(f_505_4,plain,
    ( sP136(U_2172,U_2171)
    | ~ class_Int_Oring__char__0(U_2171) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

cnf(f_505_5,plain,
    ( U_2172 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(c_Int_Oring__1__class_Oof__int(U_2171),U_2172) != c_Groups_Ozero__class_Ozero(U_2171)
    | ~ sP136(U_2172,U_2171) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

cnf(f_505_6,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_2171),U_2172) = c_Groups_Ozero__class_Ozero(U_2171)
    | U_2172 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP136(U_2172,U_2171) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

fof(f_506_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_506_2,plain,
    ! [U_2174,U_2173] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_2173) = hAPP(c_Int_Oring__1__class_Oof__int(U_2173),U_2174)
          | U_2174 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( U_2174 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | c_Groups_Ozero__class_Ozero(U_2173) != hAPP(c_Int_Oring__1__class_Oof__int(U_2173),U_2174) ) )
      | ~ class_Int_Oring__char__0(U_2173) ),
    inference(variable_rename,[status(thm)],[f_506_1]) ).

fof(f_506_3,plain,
    ( ! [U_2174,U_2173] :
        ( c_Groups_Ozero__class_Ozero(U_2173) = hAPP(c_Int_Oring__1__class_Oof__int(U_2173),U_2174)
        | U_2174 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP137(U_2174,U_2173) )
    & ! [U_2174,U_2173] :
        ( U_2174 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Groups_Ozero__class_Ozero(U_2173) != hAPP(c_Int_Oring__1__class_Oof__int(U_2173),U_2174)
        | ~ sP137(U_2174,U_2173) )
    & ! [U_2174,U_2173] :
        ( sP137(U_2174,U_2173)
        | ~ class_Int_Oring__char__0(U_2173) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP137])],[f_506_2]) ).

cnf(f_506_4,plain,
    ( sP137(U_2174,U_2173)
    | ~ class_Int_Oring__char__0(U_2173) ),
    inference(clausify,[status(thm)],[f_506_3]) ).

cnf(f_506_5,plain,
    ( U_2174 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Groups_Ozero__class_Ozero(U_2173) != hAPP(c_Int_Oring__1__class_Oof__int(U_2173),U_2174)
    | ~ sP137(U_2174,U_2173) ),
    inference(clausify,[status(thm)],[f_506_3]) ).

cnf(f_506_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_2173) = hAPP(c_Int_Oring__1__class_Oof__int(U_2173),U_2174)
    | U_2174 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP137(U_2174,U_2173) ),
    inference(clausify,[status(thm)],[f_506_3]) ).

fof(f_507_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_507_2,plain,
    ! [U_2175] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_2175),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_2175)
      | ~ class_Rings_Oring__1(U_2175) ),
    inference(variable_rename,[status(thm)],[f_507_1]) ).

fof(f_507_3,plain,
    ! [U_2175] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_2175),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_2175)
      | ~ class_Rings_Oring__1(U_2175) ),
    inference(definitional_conversion,[status(esa)],[f_507_2]) ).

cnf(f_507_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_2175),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_2175)
    | ~ class_Rings_Oring__1(U_2175) ),
    inference(clausify,[status(thm)],[f_507_3]) ).

fof(f_508_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_508_2,plain,
    ! [U_2178,U_2177,U_2176] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2176),hAPP(c_Int_Oring__1__class_Oof__int(U_2176),U_2177)),hAPP(c_Int_Oring__1__class_Oof__int(U_2176),U_2178)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2177),U_2178)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2177),U_2178))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2176),hAPP(c_Int_Oring__1__class_Oof__int(U_2176),U_2177)),hAPP(c_Int_Oring__1__class_Oof__int(U_2176),U_2178))) ) )
      | ~ class_Rings_Olinordered__idom(U_2176) ),
    inference(variable_rename,[status(thm)],[f_508_1]) ).

fof(f_508_3,plain,
    ( ! [U_2177,U_2176,U_2178] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2176),hAPP(c_Int_Oring__1__class_Oof__int(U_2176),U_2177)),hAPP(c_Int_Oring__1__class_Oof__int(U_2176),U_2178)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2177),U_2178))
        | ~ sP138(U_2177,U_2176,U_2178) )
    & ! [U_2177,U_2176,U_2178] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2177),U_2178))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2176),hAPP(c_Int_Oring__1__class_Oof__int(U_2176),U_2177)),hAPP(c_Int_Oring__1__class_Oof__int(U_2176),U_2178)))
        | ~ sP138(U_2177,U_2176,U_2178) )
    & ! [U_2177,U_2176,U_2178] :
        ( sP138(U_2177,U_2176,U_2178)
        | ~ class_Rings_Olinordered__idom(U_2176) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138])],[f_508_2]) ).

cnf(f_508_4,plain,
    ( sP138(U_2177,U_2176,U_2178)
    | ~ class_Rings_Olinordered__idom(U_2176) ),
    inference(clausify,[status(thm)],[f_508_3]) ).

cnf(f_508_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2177),U_2178))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2176),hAPP(c_Int_Oring__1__class_Oof__int(U_2176),U_2177)),hAPP(c_Int_Oring__1__class_Oof__int(U_2176),U_2178)))
    | ~ sP138(U_2177,U_2176,U_2178) ),
    inference(clausify,[status(thm)],[f_508_3]) ).

cnf(f_508_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2176),hAPP(c_Int_Oring__1__class_Oof__int(U_2176),U_2177)),hAPP(c_Int_Oring__1__class_Oof__int(U_2176),U_2178)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2177),U_2178))
    | ~ sP138(U_2177,U_2176,U_2178) ),
    inference(clausify,[status(thm)],[f_508_3]) ).

fof(f_509_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_509_2,plain,
    ! [U_2181,U_2180,U_2179] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_2179),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2180),U_2181)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2179),hAPP(c_Int_Oring__1__class_Oof__int(U_2179),U_2180)),hAPP(c_Int_Oring__1__class_Oof__int(U_2179),U_2181))
      | ~ class_Rings_Oring__1(U_2179) ),
    inference(variable_rename,[status(thm)],[f_509_1]) ).

fof(f_509_3,plain,
    ! [U_2179,U_2180,U_2181] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_2179),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2180),U_2181)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2179),hAPP(c_Int_Oring__1__class_Oof__int(U_2179),U_2180)),hAPP(c_Int_Oring__1__class_Oof__int(U_2179),U_2181))
      | ~ class_Rings_Oring__1(U_2179) ),
    inference(definitional_conversion,[status(esa)],[f_509_2]) ).

cnf(f_509_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_2179),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2180),U_2181)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2179),hAPP(c_Int_Oring__1__class_Oof__int(U_2179),U_2180)),hAPP(c_Int_Oring__1__class_Oof__int(U_2179),U_2181))
    | ~ class_Rings_Oring__1(U_2179) ),
    inference(clausify,[status(thm)],[f_509_3]) ).

fof(f_510_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_510_2,plain,
    ! [U_2183,U_2182] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_2182),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2183)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2182),U_2183)
      | ~ class_Rings_Oring__1(U_2182) ),
    inference(variable_rename,[status(thm)],[f_510_1]) ).

fof(f_510_3,plain,
    ! [U_2182,U_2183] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_2182),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2183)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2182),U_2183)
      | ~ class_Rings_Oring__1(U_2182) ),
    inference(definitional_conversion,[status(esa)],[f_510_2]) ).

cnf(f_510_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_2182),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2183)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2182),U_2183)
    | ~ class_Rings_Oring__1(U_2182) ),
    inference(clausify,[status(thm)],[f_510_3]) ).

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_2185,U_2184] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2185)),hAPP(c_Int_Onat,U_2184)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2185),U_2184)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2185),U_2184))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2185)),hAPP(c_Int_Onat,U_2184))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2184)) ),
    inference(variable_rename,[status(thm)],[f_511_1]) ).

fof(f_511_3,plain,
    ( ! [U_2185,U_2184] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2185)),hAPP(c_Int_Onat,U_2184)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2185),U_2184))
        | ~ sP139(U_2185,U_2184) )
    & ! [U_2185,U_2184] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2185),U_2184))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2185)),hAPP(c_Int_Onat,U_2184)))
        | ~ sP139(U_2185,U_2184) )
    & ! [U_2185,U_2184] :
        ( sP139(U_2185,U_2184)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2184)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP139])],[f_511_2]) ).

cnf(f_511_4,plain,
    ( sP139(U_2185,U_2184)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2184)) ),
    inference(clausify,[status(thm)],[f_511_3]) ).

cnf(f_511_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2185),U_2184))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2185)),hAPP(c_Int_Onat,U_2184)))
    | ~ sP139(U_2185,U_2184) ),
    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_2185)),hAPP(c_Int_Onat,U_2184)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2185),U_2184))
    | ~ sP139(U_2185,U_2184) ),
    inference(clausify,[status(thm)],[f_511_3]) ).

fof(f_512_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_512_2,plain,
    ! [U_2187,U_2186] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2186)),hAPP(c_Int_Onat,U_2187)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2186),U_2187))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2187)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2186),U_2187))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2187)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2186)),hAPP(c_Int_Onat,U_2187))) ) ),
    inference(variable_rename,[status(thm)],[f_512_1]) ).

fof(f_512_3,plain,
    ( ! [U_2191,U_2189] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2189)),hAPP(c_Int_Onat,U_2191)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2189),U_2191))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2191)) )
    & ! [U_2190,U_2188] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2188),U_2190))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2190)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2188)),hAPP(c_Int_Onat,U_2190))) ) ),
    inference(miniscope,[status(thm)],[f_512_2]) ).

fof(f_512_4,plain,
    ( ! [U_2190,U_2188] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2188),U_2190))
        | ~ sP140(U_2190,U_2188) )
    & ! [U_2190,U_2188] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2190))
        | ~ sP140(U_2190,U_2188) )
    & ! [U_2189,U_2191] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2189)),hAPP(c_Int_Onat,U_2191)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2189),U_2191))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2191)) )
    & ! [U_2190,U_2188] :
        ( sP140(U_2190,U_2188)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2188)),hAPP(c_Int_Onat,U_2190))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP140])],[f_512_3]) ).

cnf(f_512_5,plain,
    ( sP140(U_2190,U_2188)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2188)),hAPP(c_Int_Onat,U_2190))) ),
    inference(clausify,[status(thm)],[f_512_4]) ).

cnf(f_512_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2189)),hAPP(c_Int_Onat,U_2191)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2189),U_2191))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2191)) ),
    inference(clausify,[status(thm)],[f_512_4]) ).

cnf(f_512_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2190))
    | ~ sP140(U_2190,U_2188) ),
    inference(clausify,[status(thm)],[f_512_4]) ).

cnf(f_512_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2188),U_2190))
    | ~ sP140(U_2190,U_2188) ),
    inference(clausify,[status(thm)],[f_512_4]) ).

fof(f_513_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_513_2,plain,
    ! [U_2193,U_2192] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2192),hAPP(c_Int_Onat,U_2193)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2192)),U_2193)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2192)),U_2193))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2192),hAPP(c_Int_Onat,U_2193))) ) ),
    inference(variable_rename,[status(thm)],[f_513_1]) ).

fof(f_513_3,plain,
    ( ! [U_2197,U_2195] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2195),hAPP(c_Int_Onat,U_2197)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2195)),U_2197)) )
    & ! [U_2196,U_2194] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2194)),U_2196))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2194),hAPP(c_Int_Onat,U_2196))) ) ),
    inference(miniscope,[status(thm)],[f_513_2]) ).

fof(f_513_4,plain,
    ( ! [U_2195,U_2197] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2195),hAPP(c_Int_Onat,U_2197)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2195)),U_2197)) )
    & ! [U_2196,U_2194] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2194)),U_2196))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2194),hAPP(c_Int_Onat,U_2196))) ) ),
    inference(definitional_conversion,[status(esa)],[f_513_3]) ).

cnf(f_513_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_2194)),U_2196))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2194),hAPP(c_Int_Onat,U_2196))) ),
    inference(clausify,[status(thm)],[f_513_4]) ).

cnf(f_513_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2195),hAPP(c_Int_Onat,U_2197)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2195)),U_2197)) ),
    inference(clausify,[status(thm)],[f_513_4]) ).

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_2200,U_2199,U_2198] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2198),c_Groups_Ozero__class_Ozero(U_2198)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2198),U_2199),U_2199)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2198),U_2200),U_2200))))
          | ( U_2200 = c_Groups_Ozero__class_Ozero(U_2198)
            & U_2199 = c_Groups_Ozero__class_Ozero(U_2198) ) )
        & ( U_2200 != c_Groups_Ozero__class_Ozero(U_2198)
          | U_2199 != c_Groups_Ozero__class_Ozero(U_2198)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2198),c_Groups_Ozero__class_Ozero(U_2198)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2198),U_2199),U_2199)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2198),U_2200),U_2200)))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_2198) ),
    inference(variable_rename,[status(thm)],[f_514_1]) ).

fof(f_514_3,plain,
    ( ! [U_2199,U_2200,U_2198] :
        ( U_2200 = c_Groups_Ozero__class_Ozero(U_2198)
        | ~ sP141(U_2199,U_2200,U_2198) )
    & ! [U_2199,U_2200,U_2198] :
        ( U_2199 = c_Groups_Ozero__class_Ozero(U_2198)
        | ~ sP141(U_2199,U_2200,U_2198) )
    & ! [U_2199,U_2200,U_2198] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2198),c_Groups_Ozero__class_Ozero(U_2198)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2198),U_2199),U_2199)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2198),U_2200),U_2200))))
        | sP141(U_2199,U_2200,U_2198)
        | ~ sP142(U_2199,U_2200,U_2198) )
    & ! [U_2199,U_2200,U_2198] :
        ( U_2200 != c_Groups_Ozero__class_Ozero(U_2198)
        | U_2199 != c_Groups_Ozero__class_Ozero(U_2198)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2198),c_Groups_Ozero__class_Ozero(U_2198)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2198),U_2199),U_2199)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2198),U_2200),U_2200))))
        | ~ sP142(U_2199,U_2200,U_2198) )
    & ! [U_2199,U_2200,U_2198] :
        ( sP142(U_2199,U_2200,U_2198)
        | ~ class_Rings_Olinordered__ring__strict(U_2198) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP141,sP142])],[f_514_2]) ).

cnf(f_514_4,plain,
    ( sP142(U_2199,U_2200,U_2198)
    | ~ class_Rings_Olinordered__ring__strict(U_2198) ),
    inference(clausify,[status(thm)],[f_514_3]) ).

cnf(f_514_5,plain,
    ( U_2200 != c_Groups_Ozero__class_Ozero(U_2198)
    | U_2199 != c_Groups_Ozero__class_Ozero(U_2198)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2198),c_Groups_Ozero__class_Ozero(U_2198)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2198),U_2199),U_2199)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2198),U_2200),U_2200))))
    | ~ sP142(U_2199,U_2200,U_2198) ),
    inference(clausify,[status(thm)],[f_514_3]) ).

cnf(f_514_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2198),c_Groups_Ozero__class_Ozero(U_2198)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2198),U_2199),U_2199)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2198),U_2200),U_2200))))
    | sP141(U_2199,U_2200,U_2198)
    | ~ sP142(U_2199,U_2200,U_2198) ),
    inference(clausify,[status(thm)],[f_514_3]) ).

cnf(f_514_7,plain,
    ( U_2199 = c_Groups_Ozero__class_Ozero(U_2198)
    | ~ sP141(U_2199,U_2200,U_2198) ),
    inference(clausify,[status(thm)],[f_514_3]) ).

cnf(f_514_8,plain,
    ( U_2200 = c_Groups_Ozero__class_Ozero(U_2198)
    | ~ sP141(U_2199,U_2200,U_2198) ),
    inference(clausify,[status(thm)],[f_514_3]) ).

fof(f_515_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_515_2,plain,
    ! [U_2203,U_2202,U_2201] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2201),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2201),U_2202),U_2202)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2201),U_2203),U_2203))),c_Groups_Ozero__class_Ozero(U_2201)))
      | ~ class_Rings_Olinordered__ring(U_2201) ),
    inference(variable_rename,[status(thm)],[f_515_1]) ).

fof(f_515_3,plain,
    ! [U_2203,U_2201,U_2202] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2201),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2201),U_2202),U_2202)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2201),U_2203),U_2203))),c_Groups_Ozero__class_Ozero(U_2201)))
      | ~ class_Rings_Olinordered__ring(U_2201) ),
    inference(definitional_conversion,[status(esa)],[f_515_2]) ).

cnf(f_515_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2201),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2201),U_2202),U_2202)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2201),U_2203),U_2203))),c_Groups_Ozero__class_Ozero(U_2201)))
    | ~ class_Rings_Olinordered__ring(U_2201) ),
    inference(clausify,[status(thm)],[f_515_3]) ).

fof(f_516_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_516_2,plain,
    ! [U_2205,U_2204] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2204) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2205)
        | U_2204 != U_2205 )
      & ( U_2204 = U_2205
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2204) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2205) ) ),
    inference(variable_rename,[status(thm)],[f_516_1]) ).

fof(f_516_3,plain,
    ( ! [U_2209,U_2207] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2207) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2209)
        | U_2207 != U_2209 )
    & ! [U_2208,U_2206] :
        ( U_2206 = U_2208
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2206) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2208) ) ),
    inference(miniscope,[status(thm)],[f_516_2]) ).

fof(f_516_4,plain,
    ( ! [U_2209,U_2207] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2207) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2209)
        | U_2207 != U_2209 )
    & ! [U_2208,U_2206] :
        ( U_2206 = U_2208
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2206) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2208) ) ),
    inference(definitional_conversion,[status(esa)],[f_516_3]) ).

cnf(f_516_5,plain,
    ( U_2206 = U_2208
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2206) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2208) ),
    inference(clausify,[status(thm)],[f_516_4]) ).

cnf(f_516_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2207) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2209)
    | U_2207 != U_2209 ),
    inference(clausify,[status(thm)],[f_516_4]) ).

fof(f_517_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_517_2,plain,
    ! [U_2211,U_2210] : c_Int_Onat__aux(U_2210,U_2211) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2210)),U_2211),
    inference(variable_rename,[status(thm)],[f_517_1]) ).

fof(f_517_3,plain,
    ! [U_2210,U_2211] : c_Int_Onat__aux(U_2210,U_2211) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2210)),U_2211),
    inference(definitional_conversion,[status(esa)],[f_517_2]) ).

cnf(f_517_4,plain,
    c_Int_Onat__aux(U_2210,U_2211) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2210)),U_2211),
    inference(clausify,[status(thm)],[f_517_3]) ).

fof(f_518_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_518_2,plain,
    ! [U_2213] :
      ( ? [U_2212] : U_2213 = 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_2212)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2213),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_518_1]) ).

fof(f_518_3,plain,
    ! [U_2213] :
      ( U_2213 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK50(U_2213))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2213),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_2212,sK50(U_2213))],[f_518_2]) ).

fof(f_518_4,plain,
    ! [U_2213] :
      ( U_2213 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK50(U_2213))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2213),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_518_3]) ).

cnf(f_518_5,plain,
    ( U_2213 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK50(U_2213))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2213),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_518_4]) ).

fof(f_519_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_519_2,plain,
    ! [U_2215,U_2214] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2214)),U_2215))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2214),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2215))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2214),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2215)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2214)),U_2215)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2214)) ),
    inference(variable_rename,[status(thm)],[f_519_1]) ).

fof(f_519_3,plain,
    ( ! [U_2214,U_2215] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2214)),U_2215))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2214),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2215)))
        | ~ sP143(U_2214,U_2215) )
    & ! [U_2214,U_2215] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2214),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2215)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2214)),U_2215))
        | ~ sP143(U_2214,U_2215) )
    & ! [U_2214,U_2215] :
        ( sP143(U_2214,U_2215)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2214)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP143])],[f_519_2]) ).

cnf(f_519_4,plain,
    ( sP143(U_2214,U_2215)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2214)) ),
    inference(clausify,[status(thm)],[f_519_3]) ).

cnf(f_519_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2214),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2215)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2214)),U_2215))
    | ~ sP143(U_2214,U_2215) ),
    inference(clausify,[status(thm)],[f_519_3]) ).

cnf(f_519_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2214)),U_2215))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2214),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2215)))
    | ~ sP143(U_2214,U_2215) ),
    inference(clausify,[status(thm)],[f_519_3]) ).

fof(f_520_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_520_2,plain,
    ! [U_2216] :
      ( ( 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_2216)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2216)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2216))
        | ~ 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_2216))) ) ),
    inference(variable_rename,[status(thm)],[f_520_1]) ).

fof(f_520_3,plain,
    ( ! [U_2218] :
        ( 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_2218)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2218)) )
    & ! [U_2217] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2217))
        | ~ 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_2217))) ) ),
    inference(miniscope,[status(thm)],[f_520_2]) ).

fof(f_520_4,plain,
    ( ! [U_2218] :
        ( 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_2218)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2218)) )
    & ! [U_2217] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2217))
        | ~ 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_2217))) ) ),
    inference(definitional_conversion,[status(esa)],[f_520_3]) ).

cnf(f_520_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2217))
    | ~ 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_2217))) ),
    inference(clausify,[status(thm)],[f_520_4]) ).

cnf(f_520_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_2218)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2218)) ),
    inference(clausify,[status(thm)],[f_520_4]) ).

fof(f_521_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_521_2,plain,
    ! [U_2220,U_2219] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2219),hAPP(c_Int_Onat,U_2220)) = hAPP(c_Int_Oring__1__class_Oof__int(U_2219),U_2220)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2220))
      | ~ class_Rings_Oring__1(U_2219) ),
    inference(variable_rename,[status(thm)],[f_521_1]) ).

fof(f_521_3,plain,
    ! [U_2219,U_2220] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2219),hAPP(c_Int_Onat,U_2220)) = hAPP(c_Int_Oring__1__class_Oof__int(U_2219),U_2220)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2220))
      | ~ class_Rings_Oring__1(U_2219) ),
    inference(definitional_conversion,[status(esa)],[f_521_2]) ).

cnf(f_521_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2219),hAPP(c_Int_Onat,U_2220)) = hAPP(c_Int_Oring__1__class_Oof__int(U_2219),U_2220)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2220))
    | ~ class_Rings_Oring__1(U_2219) ),
    inference(clausify,[status(thm)],[f_521_3]) ).

fof(f_522_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_522_2,plain,
    ! [U_2221] : ~ 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_2221))))),
    inference(variable_rename,[status(thm)],[f_522_1]) ).

fof(f_522_3,plain,
    ! [U_2221] : ~ 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_2221))))),
    inference(definitional_conversion,[status(esa)],[f_522_2]) ).

cnf(f_522_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_2221))))),
    inference(clausify,[status(thm)],[f_522_3]) ).

fof(f_523_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_523_2,plain,
    ! [U_2223,U_2222] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2222)),hAPP(c_Int_Onat,U_2223)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2222),U_2223))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2223))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2222)) ),
    inference(variable_rename,[status(thm)],[f_523_1]) ).

fof(f_523_3,plain,
    ! [U_2222,U_2223] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2222)),hAPP(c_Int_Onat,U_2223)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2222),U_2223))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2223))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2222)) ),
    inference(definitional_conversion,[status(esa)],[f_523_2]) ).

cnf(f_523_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2222)),hAPP(c_Int_Onat,U_2223)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2222),U_2223))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2223))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2222)) ),
    inference(clausify,[status(thm)],[f_523_3]) ).

fof(f_524_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_524_2,plain,
    ! [U_2225,U_2224] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2224),U_2225)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2224)),hAPP(c_Int_Onat,U_2225))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2225))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2224)) ),
    inference(variable_rename,[status(thm)],[f_524_1]) ).

fof(f_524_3,plain,
    ! [U_2224,U_2225] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2224),U_2225)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2224)),hAPP(c_Int_Onat,U_2225))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2225))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2224)) ),
    inference(definitional_conversion,[status(esa)],[f_524_2]) ).

cnf(f_524_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2224),U_2225)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2224)),hAPP(c_Int_Onat,U_2225))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2225))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2224)) ),
    inference(clausify,[status(thm)],[f_524_3]) ).

fof(f_525_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_525_2,plain,
    ! [U_2227,U_2226] :
      ( ( U_2226 = hAPP(c_Int_Onat,U_2227)
        | ( U_2226 != 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_2227)) )
        | ( U_2227 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2226)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2227)) ) )
      & ( ( ( U_2226 = 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_2227)) )
          & ( U_2227 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2226)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2227)) ) )
        | U_2226 != hAPP(c_Int_Onat,U_2227) ) ),
    inference(variable_rename,[status(thm)],[f_525_1]) ).

fof(f_525_3,plain,
    ( ! [U_2231,U_2229] :
        ( U_2229 = hAPP(c_Int_Onat,U_2231)
        | ( U_2229 != 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_2231)) )
        | ( U_2231 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2229)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2231)) ) )
    & ! [U_2230,U_2228] :
        ( ( ( U_2228 = 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_2230)) )
          & ( U_2230 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2228)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2230)) ) )
        | U_2228 != hAPP(c_Int_Onat,U_2230) ) ),
    inference(miniscope,[status(thm)],[f_525_2]) ).

fof(f_525_4,plain,
    ( ! [U_2229,U_2231] :
        ( U_2229 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP146(U_2229,U_2231) )
    & ! [U_2229,U_2231] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2231))
        | ~ sP146(U_2229,U_2231) )
    & ! [U_2229,U_2231] :
        ( U_2231 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2229)
        | ~ sP145(U_2229,U_2231) )
    & ! [U_2229,U_2231] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2231))
        | ~ sP145(U_2229,U_2231) )
    & ! [U_2228,U_2230] :
        ( U_2228 = 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_2230))
        | ~ sP144(U_2228,U_2230) )
    & ! [U_2228,U_2230] :
        ( U_2230 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2228)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2230))
        | ~ sP144(U_2228,U_2230) )
    & ! [U_2229,U_2231] :
        ( U_2229 = hAPP(c_Int_Onat,U_2231)
        | sP146(U_2229,U_2231)
        | sP145(U_2229,U_2231) )
    & ! [U_2228,U_2230] :
        ( sP144(U_2228,U_2230)
        | U_2228 != hAPP(c_Int_Onat,U_2230) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP144,sP145,sP146])],[f_525_3]) ).

cnf(f_525_5,plain,
    ( sP144(U_2228,U_2230)
    | U_2228 != hAPP(c_Int_Onat,U_2230) ),
    inference(clausify,[status(thm)],[f_525_4]) ).

cnf(f_525_6,plain,
    ( U_2229 = hAPP(c_Int_Onat,U_2231)
    | sP146(U_2229,U_2231)
    | sP145(U_2229,U_2231) ),
    inference(clausify,[status(thm)],[f_525_4]) ).

cnf(f_525_7,plain,
    ( U_2230 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2228)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2230))
    | ~ sP144(U_2228,U_2230) ),
    inference(clausify,[status(thm)],[f_525_4]) ).

cnf(f_525_8,plain,
    ( U_2228 = 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_2230))
    | ~ sP144(U_2228,U_2230) ),
    inference(clausify,[status(thm)],[f_525_4]) ).

cnf(f_525_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2231))
    | ~ sP145(U_2229,U_2231) ),
    inference(clausify,[status(thm)],[f_525_4]) ).

cnf(f_525_10,plain,
    ( U_2231 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2229)
    | ~ sP145(U_2229,U_2231) ),
    inference(clausify,[status(thm)],[f_525_4]) ).

cnf(f_525_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2231))
    | ~ sP146(U_2229,U_2231) ),
    inference(clausify,[status(thm)],[f_525_4]) ).

cnf(f_525_12,plain,
    ( U_2229 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP146(U_2229,U_2231) ),
    inference(clausify,[status(thm)],[f_525_4]) ).

fof(f_526_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_526_2,plain,
    ! [U_2233,U_2232] :
      ( ( hAPP(c_Int_Onat,U_2232) = U_2233
        | ( U_2233 != 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_2232)) )
        | ( U_2232 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2233)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2232)) ) )
      & ( ( ( U_2233 = 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_2232)) )
          & ( U_2232 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2233)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2232)) ) )
        | hAPP(c_Int_Onat,U_2232) != U_2233 ) ),
    inference(variable_rename,[status(thm)],[f_526_1]) ).

fof(f_526_3,plain,
    ( ! [U_2237,U_2235] :
        ( hAPP(c_Int_Onat,U_2235) = U_2237
        | ( U_2237 != 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_2235)) )
        | ( U_2235 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2237)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2235)) ) )
    & ! [U_2236,U_2234] :
        ( ( ( U_2236 = 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_2234)) )
          & ( U_2234 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2236)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2234)) ) )
        | hAPP(c_Int_Onat,U_2234) != U_2236 ) ),
    inference(miniscope,[status(thm)],[f_526_2]) ).

fof(f_526_4,plain,
    ( ! [U_2235,U_2237] :
        ( U_2237 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP149(U_2235,U_2237) )
    & ! [U_2235,U_2237] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2235))
        | ~ sP149(U_2235,U_2237) )
    & ! [U_2235,U_2237] :
        ( U_2235 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2237)
        | ~ sP148(U_2235,U_2237) )
    & ! [U_2235,U_2237] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2235))
        | ~ sP148(U_2235,U_2237) )
    & ! [U_2236,U_2234] :
        ( U_2236 = 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_2234))
        | ~ sP147(U_2236,U_2234) )
    & ! [U_2236,U_2234] :
        ( U_2234 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2236)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2234))
        | ~ sP147(U_2236,U_2234) )
    & ! [U_2235,U_2237] :
        ( hAPP(c_Int_Onat,U_2235) = U_2237
        | sP149(U_2235,U_2237)
        | sP148(U_2235,U_2237) )
    & ! [U_2236,U_2234] :
        ( sP147(U_2236,U_2234)
        | hAPP(c_Int_Onat,U_2234) != U_2236 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP147,sP148,sP149])],[f_526_3]) ).

cnf(f_526_5,plain,
    ( sP147(U_2236,U_2234)
    | hAPP(c_Int_Onat,U_2234) != U_2236 ),
    inference(clausify,[status(thm)],[f_526_4]) ).

cnf(f_526_6,plain,
    ( hAPP(c_Int_Onat,U_2235) = U_2237
    | sP149(U_2235,U_2237)
    | sP148(U_2235,U_2237) ),
    inference(clausify,[status(thm)],[f_526_4]) ).

cnf(f_526_7,plain,
    ( U_2234 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2236)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2234))
    | ~ sP147(U_2236,U_2234) ),
    inference(clausify,[status(thm)],[f_526_4]) ).

cnf(f_526_8,plain,
    ( U_2236 = 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_2234))
    | ~ sP147(U_2236,U_2234) ),
    inference(clausify,[status(thm)],[f_526_4]) ).

cnf(f_526_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2235))
    | ~ sP148(U_2235,U_2237) ),
    inference(clausify,[status(thm)],[f_526_4]) ).

cnf(f_526_10,plain,
    ( U_2235 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2237)
    | ~ sP148(U_2235,U_2237) ),
    inference(clausify,[status(thm)],[f_526_4]) ).

cnf(f_526_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2235))
    | ~ sP149(U_2235,U_2237) ),
    inference(clausify,[status(thm)],[f_526_4]) ).

cnf(f_526_12,plain,
    ( U_2237 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP149(U_2235,U_2237) ),
    inference(clausify,[status(thm)],[f_526_4]) ).

fof(f_527_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_527_2,plain,
    ! [U_2239,U_2238] : 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_2238))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2239))),
    inference(variable_rename,[status(thm)],[f_527_1]) ).

fof(f_527_3,plain,
    ! [U_2238,U_2239] : 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_2238))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2239))),
    inference(definitional_conversion,[status(esa)],[f_527_2]) ).

cnf(f_527_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_2238))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2239))),
    inference(clausify,[status(thm)],[f_527_3]) ).

fof(f_528_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_528_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_528_1]) ).

cnf(f_528_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_528_2]) ).

fof(f_529_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_529_2,plain,
    ! [U_2241,U_2240] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2240),U_2241) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2241),U_2240),
    inference(variable_rename,[status(thm)],[f_529_1]) ).

fof(f_529_3,plain,
    ! [U_2240,U_2241] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2240),U_2241) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2241),U_2240),
    inference(definitional_conversion,[status(esa)],[f_529_2]) ).

cnf(f_529_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2240),U_2241) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2241),U_2240),
    inference(clausify,[status(thm)],[f_529_3]) ).

fof(f_530_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_530_2,plain,
    ! [U_2244,U_2243,U_2242] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2242),U_2243)),U_2244) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2242),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2243),U_2244)),
    inference(variable_rename,[status(thm)],[f_530_1]) ).

fof(f_530_3,plain,
    ! [U_2242,U_2243,U_2244] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2242),U_2243)),U_2244) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2242),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2243),U_2244)),
    inference(definitional_conversion,[status(esa)],[f_530_2]) ).

cnf(f_530_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2242),U_2243)),U_2244) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2242),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2243),U_2244)),
    inference(clausify,[status(thm)],[f_530_3]) ).

fof(f_531_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_531_2,plain,
    ! [U_2246,U_2245] :
      ( U_2245 = U_2246
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2246),U_2245))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2245),U_2246)) ),
    inference(variable_rename,[status(thm)],[f_531_1]) ).

fof(f_531_3,plain,
    ! [U_2245,U_2246] :
      ( U_2245 = U_2246
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2246),U_2245))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2245),U_2246)) ),
    inference(definitional_conversion,[status(esa)],[f_531_2]) ).

cnf(f_531_4,plain,
    ( U_2245 = U_2246
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2246),U_2245))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2245),U_2246)) ),
    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_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_532_2,plain,
    ! [U_2249,U_2248,U_2247] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2247),U_2249))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2248),U_2249))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2247),U_2248)) ),
    inference(variable_rename,[status(thm)],[f_532_1]) ).

fof(f_532_3,plain,
    ! [U_2248,U_2247,U_2249] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2247),U_2249))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2248),U_2249))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2247),U_2248)) ),
    inference(definitional_conversion,[status(esa)],[f_532_2]) ).

cnf(f_532_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2247),U_2249))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2248),U_2249))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2247),U_2248)) ),
    inference(clausify,[status(thm)],[f_532_3]) ).

fof(f_533_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_533_2,plain,
    ! [U_2251,U_2250] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2251),U_2250))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2250),U_2251)) ),
    inference(variable_rename,[status(thm)],[f_533_1]) ).

fof(f_533_3,plain,
    ! [U_2251,U_2250] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2251),U_2250))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2250),U_2251)) ),
    inference(definitional_conversion,[status(esa)],[f_533_2]) ).

cnf(f_533_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2251),U_2250))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2250),U_2251)) ),
    inference(clausify,[status(thm)],[f_533_3]) ).

fof(f_534_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_534_2,plain,
    ! [U_2253,U_2252] :
      ( ( ( c_Groups_Oone__class_Oone(U_2252) = U_2253
          | U_2253 != c_Groups_Oone__class_Oone(U_2252) )
        & ( U_2253 = c_Groups_Oone__class_Oone(U_2252)
          | c_Groups_Oone__class_Oone(U_2252) != U_2253 ) )
      | ~ class_Groups_Oone(U_2252) ),
    inference(variable_rename,[status(thm)],[f_534_1]) ).

fof(f_534_3,plain,
    ( ! [U_2252,U_2253] :
        ( c_Groups_Oone__class_Oone(U_2252) = U_2253
        | U_2253 != c_Groups_Oone__class_Oone(U_2252)
        | ~ sP150(U_2252,U_2253) )
    & ! [U_2252,U_2253] :
        ( U_2253 = c_Groups_Oone__class_Oone(U_2252)
        | c_Groups_Oone__class_Oone(U_2252) != U_2253
        | ~ sP150(U_2252,U_2253) )
    & ! [U_2252,U_2253] :
        ( sP150(U_2252,U_2253)
        | ~ class_Groups_Oone(U_2252) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP150])],[f_534_2]) ).

cnf(f_534_4,plain,
    ( sP150(U_2252,U_2253)
    | ~ class_Groups_Oone(U_2252) ),
    inference(clausify,[status(thm)],[f_534_3]) ).

cnf(f_534_5,plain,
    ( U_2253 = c_Groups_Oone__class_Oone(U_2252)
    | c_Groups_Oone__class_Oone(U_2252) != U_2253
    | ~ sP150(U_2252,U_2253) ),
    inference(clausify,[status(thm)],[f_534_3]) ).

cnf(f_534_6,plain,
    ( c_Groups_Oone__class_Oone(U_2252) = U_2253
    | U_2253 != c_Groups_Oone__class_Oone(U_2252)
    | ~ sP150(U_2252,U_2253) ),
    inference(clausify,[status(thm)],[f_534_3]) ).

fof(f_535_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_535_2,plain,
    ! [U_2254] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2254),U_2254)),
    inference(variable_rename,[status(thm)],[f_535_1]) ).

fof(f_535_3,plain,
    ! [U_2254] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2254),U_2254)),
    inference(definitional_conversion,[status(esa)],[f_535_2]) ).

cnf(f_535_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2254),U_2254)),
    inference(clausify,[status(thm)],[f_535_3]) ).

fof(f_536_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_536_2,plain,
    ! [U_2255] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2255),c_Groups_Oone__class_Oone(U_2255)),c_Groups_Ozero__class_Ozero(U_2255)))
      | ~ class_Rings_Olinordered__semidom(U_2255) ),
    inference(variable_rename,[status(thm)],[f_536_1]) ).

fof(f_536_3,plain,
    ! [U_2255] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2255),c_Groups_Oone__class_Oone(U_2255)),c_Groups_Ozero__class_Ozero(U_2255)))
      | ~ class_Rings_Olinordered__semidom(U_2255) ),
    inference(definitional_conversion,[status(esa)],[f_536_2]) ).

cnf(f_536_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2255),c_Groups_Oone__class_Oone(U_2255)),c_Groups_Ozero__class_Ozero(U_2255)))
    | ~ class_Rings_Olinordered__semidom(U_2255) ),
    inference(clausify,[status(thm)],[f_536_3]) ).

fof(f_537_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_537_2,plain,
    ! [U_2256] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2256),c_Groups_Ozero__class_Ozero(U_2256)),c_Groups_Oone__class_Oone(U_2256)))
      | ~ class_Rings_Olinordered__semidom(U_2256) ),
    inference(variable_rename,[status(thm)],[f_537_1]) ).

fof(f_537_3,plain,
    ! [U_2256] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2256),c_Groups_Ozero__class_Ozero(U_2256)),c_Groups_Oone__class_Oone(U_2256)))
      | ~ class_Rings_Olinordered__semidom(U_2256) ),
    inference(definitional_conversion,[status(esa)],[f_537_2]) ).

cnf(f_537_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2256),c_Groups_Ozero__class_Ozero(U_2256)),c_Groups_Oone__class_Oone(U_2256)))
    | ~ class_Rings_Olinordered__semidom(U_2256) ),
    inference(clausify,[status(thm)],[f_537_3]) ).

fof(f_538_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_538_2,plain,
    ! [U_2257] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2257),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2257)
      | ~ class_Rings_Osemiring__1(U_2257) ),
    inference(variable_rename,[status(thm)],[f_538_1]) ).

fof(f_538_3,plain,
    ! [U_2257] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2257),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2257)
      | ~ class_Rings_Osemiring__1(U_2257) ),
    inference(definitional_conversion,[status(esa)],[f_538_2]) ).

cnf(f_538_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2257),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2257)
    | ~ class_Rings_Osemiring__1(U_2257) ),
    inference(clausify,[status(thm)],[f_538_3]) ).

fof(f_539_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_539_2,plain,
    ! [U_2260,U_2259,U_2258] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2258),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2258),U_2259)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2258),U_2260)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2259),U_2260)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2259),U_2260))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2258),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2258),U_2259)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2258),U_2260))) ) )
      | ~ class_Rings_Olinordered__semidom(U_2258) ),
    inference(variable_rename,[status(thm)],[f_539_1]) ).

fof(f_539_3,plain,
    ( ! [U_2258,U_2259,U_2260] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2258),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2258),U_2259)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2258),U_2260)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2259),U_2260))
        | ~ sP151(U_2258,U_2259,U_2260) )
    & ! [U_2258,U_2259,U_2260] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2259),U_2260))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2258),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2258),U_2259)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2258),U_2260)))
        | ~ sP151(U_2258,U_2259,U_2260) )
    & ! [U_2258,U_2259,U_2260] :
        ( sP151(U_2258,U_2259,U_2260)
        | ~ class_Rings_Olinordered__semidom(U_2258) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP151])],[f_539_2]) ).

cnf(f_539_4,plain,
    ( sP151(U_2258,U_2259,U_2260)
    | ~ class_Rings_Olinordered__semidom(U_2258) ),
    inference(clausify,[status(thm)],[f_539_3]) ).

cnf(f_539_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2259),U_2260))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2258),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2258),U_2259)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2258),U_2260)))
    | ~ sP151(U_2258,U_2259,U_2260) ),
    inference(clausify,[status(thm)],[f_539_3]) ).

cnf(f_539_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2258),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2258),U_2259)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2258),U_2260)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2259),U_2260))
    | ~ sP151(U_2258,U_2259,U_2260) ),
    inference(clausify,[status(thm)],[f_539_3]) ).

fof(f_540_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_540_2,plain,
    ! [U_2263,U_2262,U_2261] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2261),hAPP(c_Int_Oring__1__class_Oof__int(U_2261),U_2262)),hAPP(c_Int_Oring__1__class_Oof__int(U_2261),U_2263)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2262),U_2263)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2262),U_2263))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2261),hAPP(c_Int_Oring__1__class_Oof__int(U_2261),U_2262)),hAPP(c_Int_Oring__1__class_Oof__int(U_2261),U_2263))) ) )
      | ~ class_Rings_Olinordered__idom(U_2261) ),
    inference(variable_rename,[status(thm)],[f_540_1]) ).

fof(f_540_3,plain,
    ( ! [U_2263,U_2261,U_2262] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2261),hAPP(c_Int_Oring__1__class_Oof__int(U_2261),U_2262)),hAPP(c_Int_Oring__1__class_Oof__int(U_2261),U_2263)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2262),U_2263))
        | ~ sP152(U_2263,U_2261,U_2262) )
    & ! [U_2263,U_2261,U_2262] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2262),U_2263))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2261),hAPP(c_Int_Oring__1__class_Oof__int(U_2261),U_2262)),hAPP(c_Int_Oring__1__class_Oof__int(U_2261),U_2263)))
        | ~ sP152(U_2263,U_2261,U_2262) )
    & ! [U_2263,U_2261,U_2262] :
        ( sP152(U_2263,U_2261,U_2262)
        | ~ class_Rings_Olinordered__idom(U_2261) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP152])],[f_540_2]) ).

cnf(f_540_4,plain,
    ( sP152(U_2263,U_2261,U_2262)
    | ~ class_Rings_Olinordered__idom(U_2261) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

cnf(f_540_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2262),U_2263))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2261),hAPP(c_Int_Oring__1__class_Oof__int(U_2261),U_2262)),hAPP(c_Int_Oring__1__class_Oof__int(U_2261),U_2263)))
    | ~ sP152(U_2263,U_2261,U_2262) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

cnf(f_540_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2261),hAPP(c_Int_Oring__1__class_Oof__int(U_2261),U_2262)),hAPP(c_Int_Oring__1__class_Oof__int(U_2261),U_2263)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2262),U_2263))
    | ~ sP152(U_2263,U_2261,U_2262) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

fof(f_541_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_541_2,plain,
    ! [U_2264] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_2264),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_2264)
      | ~ class_Rings_Oring__1(U_2264) ),
    inference(variable_rename,[status(thm)],[f_541_1]) ).

fof(f_541_3,plain,
    ! [U_2264] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_2264),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_2264)
      | ~ class_Rings_Oring__1(U_2264) ),
    inference(definitional_conversion,[status(esa)],[f_541_2]) ).

cnf(f_541_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_2264),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_2264)
    | ~ class_Rings_Oring__1(U_2264) ),
    inference(clausify,[status(thm)],[f_541_3]) ).

fof(f_542_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_542_2,plain,
    ! [U_2267,U_2266,U_2265] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2265),U_2266),U_2267)),U_2266))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),U_2267),c_Groups_Oone__class_Oone(U_2265)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),c_Groups_Ozero__class_Ozero(U_2265)),U_2267))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),c_Groups_Ozero__class_Ozero(U_2265)),U_2266))
      | ~ class_Rings_Olinordered__idom(U_2265) ),
    inference(variable_rename,[status(thm)],[f_542_1]) ).

fof(f_542_3,plain,
    ! [U_2265,U_2266,U_2267] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2265),U_2266),U_2267)),U_2266))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),U_2267),c_Groups_Oone__class_Oone(U_2265)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),c_Groups_Ozero__class_Ozero(U_2265)),U_2267))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),c_Groups_Ozero__class_Ozero(U_2265)),U_2266))
      | ~ class_Rings_Olinordered__idom(U_2265) ),
    inference(definitional_conversion,[status(esa)],[f_542_2]) ).

cnf(f_542_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2265),U_2266),U_2267)),U_2266))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),U_2267),c_Groups_Oone__class_Oone(U_2265)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),c_Groups_Ozero__class_Ozero(U_2265)),U_2267))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),c_Groups_Ozero__class_Ozero(U_2265)),U_2266))
    | ~ class_Rings_Olinordered__idom(U_2265) ),
    inference(clausify,[status(thm)],[f_542_3]) ).

fof(f_543_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_543_2,plain,
    ! [U_2270,U_2269,U_2268] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2268),U_2270),U_2269)),U_2269))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),U_2270),c_Groups_Oone__class_Oone(U_2268)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),c_Groups_Ozero__class_Ozero(U_2268)),U_2270))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),c_Groups_Ozero__class_Ozero(U_2268)),U_2269))
      | ~ class_Rings_Olinordered__idom(U_2268) ),
    inference(variable_rename,[status(thm)],[f_543_1]) ).

fof(f_543_3,plain,
    ! [U_2269,U_2268,U_2270] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2268),U_2270),U_2269)),U_2269))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),U_2270),c_Groups_Oone__class_Oone(U_2268)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),c_Groups_Ozero__class_Ozero(U_2268)),U_2270))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),c_Groups_Ozero__class_Ozero(U_2268)),U_2269))
      | ~ class_Rings_Olinordered__idom(U_2268) ),
    inference(definitional_conversion,[status(esa)],[f_543_2]) ).

cnf(f_543_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2268),U_2270),U_2269)),U_2269))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),U_2270),c_Groups_Oone__class_Oone(U_2268)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),c_Groups_Ozero__class_Ozero(U_2268)),U_2270))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),c_Groups_Ozero__class_Ozero(U_2268)),U_2269))
    | ~ class_Rings_Olinordered__idom(U_2268) ),
    inference(clausify,[status(thm)],[f_543_3]) ).

fof(f_544_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_544_2,plain,
    ! [U_2271] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2271))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2271)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2271))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2271)) ) ),
    inference(variable_rename,[status(thm)],[f_544_1]) ).

fof(f_544_3,plain,
    ( ! [U_2273] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2273))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2273)) )
    & ! [U_2272] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2272))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2272)) ) ),
    inference(miniscope,[status(thm)],[f_544_2]) ).

fof(f_544_4,plain,
    ( ! [U_2273] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2273))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2273)) )
    & ! [U_2272] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2272))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2272)) ) ),
    inference(definitional_conversion,[status(esa)],[f_544_3]) ).

cnf(f_544_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2272))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2272)) ),
    inference(clausify,[status(thm)],[f_544_4]) ).

cnf(f_544_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2273))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2273)) ),
    inference(clausify,[status(thm)],[f_544_4]) ).

fof(f_545_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_545_2,plain,
    ! [U_2275,U_2274] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2274),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2275),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2274),U_2275)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2274),U_2275))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2274),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2275),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_545_1]) ).

fof(f_545_3,plain,
    ( ! [U_2279,U_2277] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2277),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2279),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2277),U_2279)) )
    & ! [U_2278,U_2276] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2276),U_2278))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2278),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_545_2]) ).

fof(f_545_4,plain,
    ( ! [U_2277,U_2279] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2277),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2279),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2277),U_2279)) )
    & ! [U_2276,U_2278] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2276),U_2278))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2278),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_545_3]) ).

cnf(f_545_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2276),U_2278))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2278),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_545_4]) ).

cnf(f_545_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2277),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2279),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2277),U_2279)) ),
    inference(clausify,[status(thm)],[f_545_4]) ).

fof(f_546_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_546_2,plain,
    ! [U_2281,U_2280] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2280),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2281))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2280),U_2281)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2280),U_2281))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2280),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2281)) ) ),
    inference(variable_rename,[status(thm)],[f_546_1]) ).

fof(f_546_3,plain,
    ( ! [U_2285,U_2283] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2283),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2285))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2283),U_2285)) )
    & ! [U_2284,U_2282] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2282),U_2284))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2282),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2284)) ) ),
    inference(miniscope,[status(thm)],[f_546_2]) ).

fof(f_546_4,plain,
    ( ! [U_2283,U_2285] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2283),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2285))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2283),U_2285)) )
    & ! [U_2282,U_2284] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2282),U_2284))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2282),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2284)) ) ),
    inference(definitional_conversion,[status(esa)],[f_546_3]) ).

cnf(f_546_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2282),U_2284))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2282),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2284)) ),
    inference(clausify,[status(thm)],[f_546_4]) ).

cnf(f_546_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_2283),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2285))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2283),U_2285)) ),
    inference(clausify,[status(thm)],[f_546_4]) ).

fof(f_547_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_547_2,plain,
    ! [U_2287,U_2286] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2286),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2287))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2286),U_2287)) ),
    inference(variable_rename,[status(thm)],[f_547_1]) ).

fof(f_547_3,plain,
    ! [U_2287,U_2286] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2286),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2287))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2286),U_2287)) ),
    inference(definitional_conversion,[status(esa)],[f_547_2]) ).

cnf(f_547_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_2286),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2287))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2286),U_2287)) ),
    inference(clausify,[status(thm)],[f_547_3]) ).

fof(f_548_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_548_2,plain,
    ! [U_2288] :
      ( c_Groups_Oone__class_Oone(U_2288) != c_Groups_Ozero__class_Ozero(U_2288)
      | ~ class_Rings_Ozero__neq__one(U_2288) ),
    inference(variable_rename,[status(thm)],[f_548_1]) ).

fof(f_548_3,plain,
    ! [U_2288] :
      ( c_Groups_Oone__class_Oone(U_2288) != c_Groups_Ozero__class_Ozero(U_2288)
      | ~ class_Rings_Ozero__neq__one(U_2288) ),
    inference(definitional_conversion,[status(esa)],[f_548_2]) ).

cnf(f_548_4,plain,
    ( c_Groups_Oone__class_Oone(U_2288) != c_Groups_Ozero__class_Ozero(U_2288)
    | ~ class_Rings_Ozero__neq__one(U_2288) ),
    inference(clausify,[status(thm)],[f_548_3]) ).

fof(f_549_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_549_2,plain,
    ! [U_2289] :
      ( c_Groups_Ozero__class_Ozero(U_2289) != c_Groups_Oone__class_Oone(U_2289)
      | ~ class_Rings_Ozero__neq__one(U_2289) ),
    inference(variable_rename,[status(thm)],[f_549_1]) ).

fof(f_549_3,plain,
    ! [U_2289] :
      ( c_Groups_Ozero__class_Ozero(U_2289) != c_Groups_Oone__class_Oone(U_2289)
      | ~ class_Rings_Ozero__neq__one(U_2289) ),
    inference(definitional_conversion,[status(esa)],[f_549_2]) ).

cnf(f_549_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_2289) != c_Groups_Oone__class_Oone(U_2289)
    | ~ class_Rings_Ozero__neq__one(U_2289) ),
    inference(clausify,[status(thm)],[f_549_3]) ).

fof(f_550_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_550_2,plain,
    ! [U_2291,U_2290] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2290),U_2291),c_Groups_Oone__class_Oone(U_2290)) = U_2291
      | ~ class_Groups_Ocomm__monoid__mult(U_2290) ),
    inference(variable_rename,[status(thm)],[f_550_1]) ).

fof(f_550_3,plain,
    ! [U_2290,U_2291] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2290),U_2291),c_Groups_Oone__class_Oone(U_2290)) = U_2291
      | ~ class_Groups_Ocomm__monoid__mult(U_2290) ),
    inference(definitional_conversion,[status(esa)],[f_550_2]) ).

cnf(f_550_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2290),U_2291),c_Groups_Oone__class_Oone(U_2290)) = U_2291
    | ~ class_Groups_Ocomm__monoid__mult(U_2290) ),
    inference(clausify,[status(thm)],[f_550_3]) ).

fof(f_551_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_551_2,plain,
    ! [U_2293,U_2292] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2292),U_2293),c_Groups_Oone__class_Oone(U_2292)) = U_2293
      | ~ class_Rings_Ocomm__semiring__1(U_2292) ),
    inference(variable_rename,[status(thm)],[f_551_1]) ).

fof(f_551_3,plain,
    ! [U_2292,U_2293] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2292),U_2293),c_Groups_Oone__class_Oone(U_2292)) = U_2293
      | ~ class_Rings_Ocomm__semiring__1(U_2292) ),
    inference(definitional_conversion,[status(esa)],[f_551_2]) ).

cnf(f_551_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2292),U_2293),c_Groups_Oone__class_Oone(U_2292)) = U_2293
    | ~ class_Rings_Ocomm__semiring__1(U_2292) ),
    inference(clausify,[status(thm)],[f_551_3]) ).

fof(f_552_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_552_2,plain,
    ! [U_2295,U_2294] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2294),U_2295),c_Groups_Oone__class_Oone(U_2294)) = U_2295
      | ~ class_Groups_Omonoid__mult(U_2294) ),
    inference(variable_rename,[status(thm)],[f_552_1]) ).

fof(f_552_3,plain,
    ! [U_2294,U_2295] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2294),U_2295),c_Groups_Oone__class_Oone(U_2294)) = U_2295
      | ~ class_Groups_Omonoid__mult(U_2294) ),
    inference(definitional_conversion,[status(esa)],[f_552_2]) ).

cnf(f_552_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2294),U_2295),c_Groups_Oone__class_Oone(U_2294)) = U_2295
    | ~ class_Groups_Omonoid__mult(U_2294) ),
    inference(clausify,[status(thm)],[f_552_3]) ).

fof(f_553_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_553_2,plain,
    ! [U_2297,U_2296] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2296),c_Groups_Oone__class_Oone(U_2296)),U_2297) = U_2297
      | ~ class_Groups_Ocomm__monoid__mult(U_2296) ),
    inference(variable_rename,[status(thm)],[f_553_1]) ).

fof(f_553_3,plain,
    ! [U_2296,U_2297] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2296),c_Groups_Oone__class_Oone(U_2296)),U_2297) = U_2297
      | ~ class_Groups_Ocomm__monoid__mult(U_2296) ),
    inference(definitional_conversion,[status(esa)],[f_553_2]) ).

cnf(f_553_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2296),c_Groups_Oone__class_Oone(U_2296)),U_2297) = U_2297
    | ~ class_Groups_Ocomm__monoid__mult(U_2296) ),
    inference(clausify,[status(thm)],[f_553_3]) ).

fof(f_554_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_554_2,plain,
    ! [U_2299,U_2298] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2298),c_Groups_Oone__class_Oone(U_2298)),U_2299) = U_2299
      | ~ class_Rings_Ocomm__semiring__1(U_2298) ),
    inference(variable_rename,[status(thm)],[f_554_1]) ).

fof(f_554_3,plain,
    ! [U_2298,U_2299] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2298),c_Groups_Oone__class_Oone(U_2298)),U_2299) = U_2299
      | ~ class_Rings_Ocomm__semiring__1(U_2298) ),
    inference(definitional_conversion,[status(esa)],[f_554_2]) ).

cnf(f_554_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2298),c_Groups_Oone__class_Oone(U_2298)),U_2299) = U_2299
    | ~ class_Rings_Ocomm__semiring__1(U_2298) ),
    inference(clausify,[status(thm)],[f_554_3]) ).

fof(f_555_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_555_2,plain,
    ! [U_2301,U_2300] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2300),c_Groups_Oone__class_Oone(U_2300)),U_2301) = U_2301
      | ~ class_Groups_Omonoid__mult(U_2300) ),
    inference(variable_rename,[status(thm)],[f_555_1]) ).

fof(f_555_3,plain,
    ! [U_2300,U_2301] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2300),c_Groups_Oone__class_Oone(U_2300)),U_2301) = U_2301
      | ~ class_Groups_Omonoid__mult(U_2300) ),
    inference(definitional_conversion,[status(esa)],[f_555_2]) ).

cnf(f_555_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2300),c_Groups_Oone__class_Oone(U_2300)),U_2301) = U_2301
    | ~ class_Groups_Omonoid__mult(U_2300) ),
    inference(clausify,[status(thm)],[f_555_3]) ).

fof(f_556_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_556_2,plain,
    ! [U_2305,U_2304,U_2303,U_2302] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2302),U_2303),U_2304)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2302),U_2305),U_2304)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2302),U_2303),U_2305)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2302),U_2303),U_2305))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2302),U_2303),U_2304)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2302),U_2305),U_2304))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2302) ),
    inference(variable_rename,[status(thm)],[f_556_1]) ).

fof(f_556_3,plain,
    ( ! [U_2302,U_2303,U_2304,U_2305] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2302),U_2303),U_2304)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2302),U_2305),U_2304)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2302),U_2303),U_2305))
        | ~ sP153(U_2302,U_2303,U_2304,U_2305) )
    & ! [U_2302,U_2303,U_2304,U_2305] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2302),U_2303),U_2305))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2302),U_2303),U_2304)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2302),U_2305),U_2304)))
        | ~ sP153(U_2302,U_2303,U_2304,U_2305) )
    & ! [U_2302,U_2303,U_2304,U_2305] :
        ( sP153(U_2302,U_2303,U_2304,U_2305)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2302) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP153])],[f_556_2]) ).

cnf(f_556_4,plain,
    ( sP153(U_2302,U_2303,U_2304,U_2305)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2302) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

cnf(f_556_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2302),U_2303),U_2305))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2302),U_2303),U_2304)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2302),U_2305),U_2304)))
    | ~ sP153(U_2302,U_2303,U_2304,U_2305) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

cnf(f_556_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2302),U_2303),U_2304)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2302),U_2305),U_2304)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2302),U_2303),U_2305))
    | ~ sP153(U_2302,U_2303,U_2304,U_2305) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

fof(f_557_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_557_2,plain,
    ! [U_2309,U_2308,U_2307,U_2306] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2306),U_2307),U_2308)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2306),U_2307),U_2309)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2306),U_2308),U_2309)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2306),U_2308),U_2309))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2306),U_2307),U_2308)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2306),U_2307),U_2309))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2306) ),
    inference(variable_rename,[status(thm)],[f_557_1]) ).

fof(f_557_3,plain,
    ( ! [U_2307,U_2306,U_2308,U_2309] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2306),U_2307),U_2308)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2306),U_2307),U_2309)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2306),U_2308),U_2309))
        | ~ sP154(U_2307,U_2306,U_2308,U_2309) )
    & ! [U_2307,U_2306,U_2308,U_2309] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2306),U_2308),U_2309))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2306),U_2307),U_2308)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2306),U_2307),U_2309)))
        | ~ sP154(U_2307,U_2306,U_2308,U_2309) )
    & ! [U_2307,U_2306,U_2308,U_2309] :
        ( sP154(U_2307,U_2306,U_2308,U_2309)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2306) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP154])],[f_557_2]) ).

cnf(f_557_4,plain,
    ( sP154(U_2307,U_2306,U_2308,U_2309)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2306) ),
    inference(clausify,[status(thm)],[f_557_3]) ).

cnf(f_557_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2306),U_2308),U_2309))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2306),U_2307),U_2308)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2306),U_2307),U_2309)))
    | ~ sP154(U_2307,U_2306,U_2308,U_2309) ),
    inference(clausify,[status(thm)],[f_557_3]) ).

cnf(f_557_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2306),U_2307),U_2308)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2306),U_2307),U_2309)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2306),U_2308),U_2309))
    | ~ sP154(U_2307,U_2306,U_2308,U_2309) ),
    inference(clausify,[status(thm)],[f_557_3]) ).

fof(f_558_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_558_2,plain,
    ! [U_2313,U_2312,U_2311,U_2310] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2310),U_2311),U_2313)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2310),U_2312),U_2313)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2310),U_2311),U_2312))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_2310) ),
    inference(variable_rename,[status(thm)],[f_558_1]) ).

fof(f_558_3,plain,
    ! [U_2311,U_2310,U_2312,U_2313] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2310),U_2311),U_2313)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2310),U_2312),U_2313)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2310),U_2311),U_2312))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_2310) ),
    inference(definitional_conversion,[status(esa)],[f_558_2]) ).

cnf(f_558_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2310),U_2311),U_2313)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2310),U_2312),U_2313)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2310),U_2311),U_2312))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_2310) ),
    inference(clausify,[status(thm)],[f_558_3]) ).

fof(f_559_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_559_2,plain,
    ! [U_2317,U_2316,U_2315,U_2314] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2314),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2314),U_2317),U_2315)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2314),U_2317),U_2316)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2314),U_2315),U_2316))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_2314) ),
    inference(variable_rename,[status(thm)],[f_559_1]) ).

fof(f_559_3,plain,
    ! [U_2314,U_2315,U_2316,U_2317] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2314),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2314),U_2317),U_2315)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2314),U_2317),U_2316)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2314),U_2315),U_2316))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_2314) ),
    inference(definitional_conversion,[status(esa)],[f_559_2]) ).

cnf(f_559_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2314),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2314),U_2317),U_2315)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2314),U_2317),U_2316)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2314),U_2315),U_2316))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_2314) ),
    inference(clausify,[status(thm)],[f_559_3]) ).

fof(f_560_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_560_2,plain,
    ! [U_2322,U_2321,U_2320,U_2319,U_2318] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2318),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2318),U_2319),U_2321)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2318),U_2320),U_2322)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2318),U_2321),U_2322))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2318),U_2319),U_2320))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_2318) ),
    inference(variable_rename,[status(thm)],[f_560_1]) ).

fof(f_560_3,plain,
    ! [U_2318,U_2319,U_2320,U_2321,U_2322] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2318),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2318),U_2319),U_2321)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2318),U_2320),U_2322)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2318),U_2321),U_2322))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2318),U_2319),U_2320))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_2318) ),
    inference(definitional_conversion,[status(esa)],[f_560_2]) ).

cnf(f_560_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2318),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2318),U_2319),U_2321)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2318),U_2320),U_2322)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2318),U_2321),U_2322))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2318),U_2319),U_2320))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_2318) ),
    inference(clausify,[status(thm)],[f_560_3]) ).

fof(f_561_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_561_2,plain,
    ! [U_2326,U_2325,U_2324,U_2323] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2323),U_2324),U_2326))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2323),U_2324),U_2325)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2323),U_2326),U_2325)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2323) ),
    inference(variable_rename,[status(thm)],[f_561_1]) ).

fof(f_561_3,plain,
    ! [U_2323,U_2324,U_2325,U_2326] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2323),U_2324),U_2326))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2323),U_2324),U_2325)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2323),U_2326),U_2325)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2323) ),
    inference(definitional_conversion,[status(esa)],[f_561_2]) ).

cnf(f_561_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2323),U_2324),U_2326))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2323),U_2324),U_2325)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2323),U_2326),U_2325)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2323) ),
    inference(clausify,[status(thm)],[f_561_3]) ).

fof(f_562_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_562_2,plain,
    ! [U_2330,U_2329,U_2328,U_2327] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2327),U_2329),U_2330))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2327),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2327),U_2328),U_2329)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2327),U_2328),U_2330)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2327) ),
    inference(variable_rename,[status(thm)],[f_562_1]) ).

fof(f_562_3,plain,
    ! [U_2327,U_2328,U_2329,U_2330] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2327),U_2329),U_2330))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2327),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2327),U_2328),U_2329)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2327),U_2328),U_2330)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2327) ),
    inference(definitional_conversion,[status(esa)],[f_562_2]) ).

cnf(f_562_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2327),U_2329),U_2330))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2327),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2327),U_2328),U_2329)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2327),U_2328),U_2330)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2327) ),
    inference(clausify,[status(thm)],[f_562_3]) ).

fof(f_563_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_563_2,plain,
    ! [U_2333,U_2332,U_2331] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2331),U_2332) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2333),U_2332)
        | ( U_2332 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2331 != U_2333 ) )
      & ( U_2332 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2331 = U_2333
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2331),U_2332) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2333),U_2332) ) ),
    inference(variable_rename,[status(thm)],[f_563_1]) ).

fof(f_563_3,plain,
    ( ! [U_2339,U_2337,U_2335] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2335),U_2337) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2339),U_2337)
        | ( U_2337 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2335 != U_2339 ) )
    & ! [U_2338,U_2336,U_2334] :
        ( U_2336 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2334 = U_2338
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2334),U_2336) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2338),U_2336) ) ),
    inference(miniscope,[status(thm)],[f_563_2]) ).

fof(f_563_4,plain,
    ( ! [U_2339,U_2337,U_2335] :
        ( U_2337 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP155(U_2339,U_2337,U_2335) )
    & ! [U_2339,U_2337,U_2335] :
        ( U_2335 != U_2339
        | ~ sP155(U_2339,U_2337,U_2335) )
    & ! [U_2339,U_2337,U_2335] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2335),U_2337) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2339),U_2337)
        | sP155(U_2339,U_2337,U_2335) )
    & ! [U_2336,U_2334,U_2338] :
        ( U_2336 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2334 = U_2338
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2334),U_2336) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2338),U_2336) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP155])],[f_563_3]) ).

cnf(f_563_5,plain,
    ( U_2336 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2334 = U_2338
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2334),U_2336) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2338),U_2336) ),
    inference(clausify,[status(thm)],[f_563_4]) ).

cnf(f_563_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2335),U_2337) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2339),U_2337)
    | sP155(U_2339,U_2337,U_2335) ),
    inference(clausify,[status(thm)],[f_563_4]) ).

cnf(f_563_7,plain,
    ( U_2335 != U_2339
    | ~ sP155(U_2339,U_2337,U_2335) ),
    inference(clausify,[status(thm)],[f_563_4]) ).

cnf(f_563_8,plain,
    ( U_2337 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP155(U_2339,U_2337,U_2335) ),
    inference(clausify,[status(thm)],[f_563_4]) ).

fof(f_564_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_564_2,plain,
    ! [U_2342,U_2341,U_2340] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2340),U_2341) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2340),U_2342)
        | ( U_2340 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2341 != U_2342 ) )
      & ( U_2340 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2341 = U_2342
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2340),U_2341) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2340),U_2342) ) ),
    inference(variable_rename,[status(thm)],[f_564_1]) ).

fof(f_564_3,plain,
    ( ! [U_2348,U_2346,U_2344] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2344),U_2346) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2344),U_2348)
        | ( U_2344 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2346 != U_2348 ) )
    & ! [U_2347,U_2345,U_2343] :
        ( U_2343 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2345 = U_2347
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2343),U_2345) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2343),U_2347) ) ),
    inference(miniscope,[status(thm)],[f_564_2]) ).

fof(f_564_4,plain,
    ( ! [U_2346,U_2348,U_2344] :
        ( U_2344 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP156(U_2346,U_2348,U_2344) )
    & ! [U_2346,U_2348,U_2344] :
        ( U_2346 != U_2348
        | ~ sP156(U_2346,U_2348,U_2344) )
    & ! [U_2346,U_2348,U_2344] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2344),U_2346) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2344),U_2348)
        | sP156(U_2346,U_2348,U_2344) )
    & ! [U_2345,U_2343,U_2347] :
        ( U_2343 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2345 = U_2347
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2343),U_2345) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2343),U_2347) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP156])],[f_564_3]) ).

cnf(f_564_5,plain,
    ( U_2343 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2345 = U_2347
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2343),U_2345) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2343),U_2347) ),
    inference(clausify,[status(thm)],[f_564_4]) ).

cnf(f_564_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2344),U_2346) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2344),U_2348)
    | sP156(U_2346,U_2348,U_2344) ),
    inference(clausify,[status(thm)],[f_564_4]) ).

cnf(f_564_7,plain,
    ( U_2346 != U_2348
    | ~ sP156(U_2346,U_2348,U_2344) ),
    inference(clausify,[status(thm)],[f_564_4]) ).

cnf(f_564_8,plain,
    ( U_2344 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP156(U_2346,U_2348,U_2344) ),
    inference(clausify,[status(thm)],[f_564_4]) ).

fof(f_565_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_565_2,plain,
    ! [U_2350,U_2349] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2349),U_2350) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_2350 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2349 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_2350 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2349 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2349),U_2350) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_565_1]) ).

fof(f_565_3,plain,
    ( ! [U_2354,U_2352] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2352),U_2354) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_2354 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2352 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_2353,U_2351] :
        ( U_2353 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2351),U_2353) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_565_2]) ).

fof(f_565_4,plain,
    ( ! [U_2354,U_2352] :
        ( U_2354 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP157(U_2354,U_2352) )
    & ! [U_2354,U_2352] :
        ( U_2352 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP157(U_2354,U_2352) )
    & ! [U_2354,U_2352] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2352),U_2354) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP157(U_2354,U_2352) )
    & ! [U_2353,U_2351] :
        ( U_2353 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2351),U_2353) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP157])],[f_565_3]) ).

cnf(f_565_5,plain,
    ( U_2353 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2351),U_2353) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_565_4]) ).

cnf(f_565_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2352),U_2354) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP157(U_2354,U_2352) ),
    inference(clausify,[status(thm)],[f_565_4]) ).

cnf(f_565_7,plain,
    ( U_2352 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP157(U_2354,U_2352) ),
    inference(clausify,[status(thm)],[f_565_4]) ).

cnf(f_565_8,plain,
    ( U_2354 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP157(U_2354,U_2352) ),
    inference(clausify,[status(thm)],[f_565_4]) ).

fof(f_566_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_566_2,plain,
    ! [U_2355] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2355),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_566_1]) ).

fof(f_566_3,plain,
    ! [U_2355] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2355),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_566_2]) ).

cnf(f_566_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2355),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_566_3]) ).

fof(f_567_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_567_2,plain,
    ! [U_2356] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2356) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_567_1]) ).

fof(f_567_3,plain,
    ! [U_2356] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2356) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_567_2]) ).

cnf(f_567_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2356) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_567_3]) ).

fof(f_568_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_568_2,plain,
    ! [U_2359,U_2358,U_2357] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2357)),U_2358) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2357)),U_2359)
        | U_2358 != U_2359 )
      & ( U_2358 = U_2359
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2357)),U_2358) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2357)),U_2359) ) ),
    inference(variable_rename,[status(thm)],[f_568_1]) ).

fof(f_568_3,plain,
    ( ! [U_2365,U_2363] :
        ( ! [U_2361] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2361)),U_2363) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2361)),U_2365)
        | U_2363 != U_2365 )
    & ! [U_2364,U_2362] :
        ( ! [U_2360] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2360)),U_2362) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2360)),U_2364)
        | U_2362 = U_2364 ) ),
    inference(miniscope,[status(thm)],[f_568_2]) ).

fof(f_568_4,plain,
    ( ! [U_2365,U_2361,U_2363] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2361)),U_2363) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2361)),U_2365)
        | U_2363 != U_2365 )
    & ! [U_2360,U_2364,U_2362] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2360)),U_2362) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2360)),U_2364)
        | U_2362 = U_2364 ) ),
    inference(definitional_conversion,[status(esa)],[f_568_3]) ).

cnf(f_568_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2360)),U_2362) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2360)),U_2364)
    | U_2362 = U_2364 ),
    inference(clausify,[status(thm)],[f_568_4]) ).

cnf(f_568_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2361)),U_2363) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2361)),U_2365)
    | U_2363 != U_2365 ),
    inference(clausify,[status(thm)],[f_568_4]) ).

fof(f_569_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_569_2,plain,
    ! [U_2368,U_2367,U_2366] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2366),hAPP(c_Groups_Ouminus__class_Ouminus(U_2366),U_2368)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2366),U_2367)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2366),U_2367),U_2368))
      | ~ class_Groups_Oordered__ab__group__add(U_2366) ),
    inference(variable_rename,[status(thm)],[f_569_1]) ).

fof(f_569_3,plain,
    ! [U_2366,U_2367,U_2368] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2366),hAPP(c_Groups_Ouminus__class_Ouminus(U_2366),U_2368)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2366),U_2367)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2366),U_2367),U_2368))
      | ~ class_Groups_Oordered__ab__group__add(U_2366) ),
    inference(definitional_conversion,[status(esa)],[f_569_2]) ).

cnf(f_569_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2366),hAPP(c_Groups_Ouminus__class_Ouminus(U_2366),U_2368)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2366),U_2367)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2366),U_2367),U_2368))
    | ~ class_Groups_Oordered__ab__group__add(U_2366) ),
    inference(clausify,[status(thm)],[f_569_3]) ).

fof(f_570_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_570_2,plain,
    ! [U_2371,U_2370,U_2369] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2369),hAPP(c_Groups_Ouminus__class_Ouminus(U_2369),U_2370)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2369),U_2371)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2369),U_2371),U_2370)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2369),U_2371),U_2370))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2369),hAPP(c_Groups_Ouminus__class_Ouminus(U_2369),U_2370)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2369),U_2371))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2369) ),
    inference(variable_rename,[status(thm)],[f_570_1]) ).

fof(f_570_3,plain,
    ( ! [U_2370,U_2369,U_2371] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2369),hAPP(c_Groups_Ouminus__class_Ouminus(U_2369),U_2370)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2369),U_2371)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2369),U_2371),U_2370))
        | ~ sP158(U_2370,U_2369,U_2371) )
    & ! [U_2370,U_2369,U_2371] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2369),U_2371),U_2370))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2369),hAPP(c_Groups_Ouminus__class_Ouminus(U_2369),U_2370)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2369),U_2371)))
        | ~ sP158(U_2370,U_2369,U_2371) )
    & ! [U_2370,U_2369,U_2371] :
        ( sP158(U_2370,U_2369,U_2371)
        | ~ class_Groups_Oordered__ab__group__add(U_2369) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP158])],[f_570_2]) ).

cnf(f_570_4,plain,
    ( sP158(U_2370,U_2369,U_2371)
    | ~ class_Groups_Oordered__ab__group__add(U_2369) ),
    inference(clausify,[status(thm)],[f_570_3]) ).

cnf(f_570_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2369),U_2371),U_2370))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2369),hAPP(c_Groups_Ouminus__class_Ouminus(U_2369),U_2370)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2369),U_2371)))
    | ~ sP158(U_2370,U_2369,U_2371) ),
    inference(clausify,[status(thm)],[f_570_3]) ).

cnf(f_570_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2369),hAPP(c_Groups_Ouminus__class_Ouminus(U_2369),U_2370)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2369),U_2371)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2369),U_2371),U_2370))
    | ~ sP158(U_2370,U_2369,U_2371) ),
    inference(clausify,[status(thm)],[f_570_3]) ).

fof(f_571_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_571_2,plain,
    ! [U_2374,U_2373,U_2372] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2372),hAPP(c_Groups_Ouminus__class_Ouminus(U_2372),U_2373)),U_2374))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2372),hAPP(c_Groups_Ouminus__class_Ouminus(U_2372),U_2374)),U_2373)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2372),hAPP(c_Groups_Ouminus__class_Ouminus(U_2372),U_2374)),U_2373))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2372),hAPP(c_Groups_Ouminus__class_Ouminus(U_2372),U_2373)),U_2374)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2372) ),
    inference(variable_rename,[status(thm)],[f_571_1]) ).

fof(f_571_3,plain,
    ( ! [U_2374,U_2373,U_2372] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2372),hAPP(c_Groups_Ouminus__class_Ouminus(U_2372),U_2373)),U_2374))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2372),hAPP(c_Groups_Ouminus__class_Ouminus(U_2372),U_2374)),U_2373))
        | ~ sP159(U_2374,U_2373,U_2372) )
    & ! [U_2374,U_2373,U_2372] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2372),hAPP(c_Groups_Ouminus__class_Ouminus(U_2372),U_2374)),U_2373))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2372),hAPP(c_Groups_Ouminus__class_Ouminus(U_2372),U_2373)),U_2374))
        | ~ sP159(U_2374,U_2373,U_2372) )
    & ! [U_2374,U_2373,U_2372] :
        ( sP159(U_2374,U_2373,U_2372)
        | ~ class_Groups_Oordered__ab__group__add(U_2372) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP159])],[f_571_2]) ).

cnf(f_571_4,plain,
    ( sP159(U_2374,U_2373,U_2372)
    | ~ class_Groups_Oordered__ab__group__add(U_2372) ),
    inference(clausify,[status(thm)],[f_571_3]) ).

cnf(f_571_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2372),hAPP(c_Groups_Ouminus__class_Ouminus(U_2372),U_2374)),U_2373))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2372),hAPP(c_Groups_Ouminus__class_Ouminus(U_2372),U_2373)),U_2374))
    | ~ sP159(U_2374,U_2373,U_2372) ),
    inference(clausify,[status(thm)],[f_571_3]) ).

cnf(f_571_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2372),hAPP(c_Groups_Ouminus__class_Ouminus(U_2372),U_2373)),U_2374))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2372),hAPP(c_Groups_Ouminus__class_Ouminus(U_2372),U_2374)),U_2373))
    | ~ sP159(U_2374,U_2373,U_2372) ),
    inference(clausify,[status(thm)],[f_571_3]) ).

fof(f_572_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_572_2,plain,
    ! [U_2377,U_2376,U_2375] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2375),U_2376),hAPP(c_Groups_Ouminus__class_Ouminus(U_2375),U_2377)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2375),U_2377),hAPP(c_Groups_Ouminus__class_Ouminus(U_2375),U_2376))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2375),U_2377),hAPP(c_Groups_Ouminus__class_Ouminus(U_2375),U_2376)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2375),U_2376),hAPP(c_Groups_Ouminus__class_Ouminus(U_2375),U_2377))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2375) ),
    inference(variable_rename,[status(thm)],[f_572_1]) ).

fof(f_572_3,plain,
    ( ! [U_2377,U_2376,U_2375] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2375),U_2376),hAPP(c_Groups_Ouminus__class_Ouminus(U_2375),U_2377)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2375),U_2377),hAPP(c_Groups_Ouminus__class_Ouminus(U_2375),U_2376)))
        | ~ sP160(U_2377,U_2376,U_2375) )
    & ! [U_2377,U_2376,U_2375] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2375),U_2377),hAPP(c_Groups_Ouminus__class_Ouminus(U_2375),U_2376)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2375),U_2376),hAPP(c_Groups_Ouminus__class_Ouminus(U_2375),U_2377)))
        | ~ sP160(U_2377,U_2376,U_2375) )
    & ! [U_2377,U_2376,U_2375] :
        ( sP160(U_2377,U_2376,U_2375)
        | ~ class_Groups_Oordered__ab__group__add(U_2375) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP160])],[f_572_2]) ).

cnf(f_572_4,plain,
    ( sP160(U_2377,U_2376,U_2375)
    | ~ class_Groups_Oordered__ab__group__add(U_2375) ),
    inference(clausify,[status(thm)],[f_572_3]) ).

cnf(f_572_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2375),U_2377),hAPP(c_Groups_Ouminus__class_Ouminus(U_2375),U_2376)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2375),U_2376),hAPP(c_Groups_Ouminus__class_Ouminus(U_2375),U_2377)))
    | ~ sP160(U_2377,U_2376,U_2375) ),
    inference(clausify,[status(thm)],[f_572_3]) ).

cnf(f_572_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2375),U_2376),hAPP(c_Groups_Ouminus__class_Ouminus(U_2375),U_2377)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2375),U_2377),hAPP(c_Groups_Ouminus__class_Ouminus(U_2375),U_2376)))
    | ~ sP160(U_2377,U_2376,U_2375) ),
    inference(clausify,[status(thm)],[f_572_3]) ).

fof(f_573_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_573_2,plain,
    ! [U_2380,U_2379,U_2378] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2378),U_2379)),U_2380) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2378),U_2380)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2379),U_2380)),
    inference(variable_rename,[status(thm)],[f_573_1]) ).

fof(f_573_3,plain,
    ! [U_2379,U_2380,U_2378] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2378),U_2379)),U_2380) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2378),U_2380)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2379),U_2380)),
    inference(definitional_conversion,[status(esa)],[f_573_2]) ).

cnf(f_573_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2378),U_2379)),U_2380) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2378),U_2380)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2379),U_2380)),
    inference(clausify,[status(thm)],[f_573_3]) ).

fof(f_574_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_574_2,plain,
    ! [U_2383,U_2382,U_2381] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2381),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2382),U_2383)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2381),U_2382)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2381),U_2383)),
    inference(variable_rename,[status(thm)],[f_574_1]) ).

fof(f_574_3,plain,
    ! [U_2381,U_2382,U_2383] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2381),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2382),U_2383)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2381),U_2382)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2381),U_2383)),
    inference(definitional_conversion,[status(esa)],[f_574_2]) ).

cnf(f_574_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2381),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2382),U_2383)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2381),U_2382)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2381),U_2383)),
    inference(clausify,[status(thm)],[f_574_3]) ).

fof(f_575_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_575_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_575_1]) ).

cnf(f_575_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_575_2]) ).

fof(f_576_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_576_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_576_1]) ).

cnf(f_576_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_576_2]) ).

fof(f_577_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_577_2,plain,
    ! [U_2385,U_2384] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2384),U_2385))
        | U_2384 = U_2385
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2384),U_2385)) )
      & ( ( U_2384 != U_2385
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2384),U_2385)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2384),U_2385)) ) ),
    inference(variable_rename,[status(thm)],[f_577_1]) ).

fof(f_577_3,plain,
    ( ! [U_2389,U_2387] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2387),U_2389))
        | U_2387 = U_2389
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2387),U_2389)) )
    & ! [U_2388,U_2386] :
        ( ( U_2386 != U_2388
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2386),U_2388)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2386),U_2388)) ) ),
    inference(miniscope,[status(thm)],[f_577_2]) ).

fof(f_577_4,plain,
    ( ! [U_2388,U_2386] :
        ( U_2386 != U_2388
        | ~ sP161(U_2388,U_2386) )
    & ! [U_2388,U_2386] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2386),U_2388))
        | ~ sP161(U_2388,U_2386) )
    & ! [U_2387,U_2389] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2387),U_2389))
        | U_2387 = U_2389
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2387),U_2389)) )
    & ! [U_2388,U_2386] :
        ( sP161(U_2388,U_2386)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2386),U_2388)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP161])],[f_577_3]) ).

cnf(f_577_5,plain,
    ( sP161(U_2388,U_2386)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2386),U_2388)) ),
    inference(clausify,[status(thm)],[f_577_4]) ).

cnf(f_577_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2387),U_2389))
    | U_2387 = U_2389
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2387),U_2389)) ),
    inference(clausify,[status(thm)],[f_577_4]) ).

cnf(f_577_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2386),U_2388))
    | ~ sP161(U_2388,U_2386) ),
    inference(clausify,[status(thm)],[f_577_4]) ).

cnf(f_577_8,plain,
    ( U_2386 != U_2388
    | ~ sP161(U_2388,U_2386) ),
    inference(clausify,[status(thm)],[f_577_4]) ).

fof(f_578_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_578_2,plain,
    ! [U_2392,U_2391,U_2390] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2392),U_2390)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2392),U_2391)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2390),U_2391)) ),
    inference(variable_rename,[status(thm)],[f_578_1]) ).

fof(f_578_3,plain,
    ! [U_2392,U_2391,U_2390] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2392),U_2390)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2392),U_2391)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2390),U_2391)) ),
    inference(definitional_conversion,[status(esa)],[f_578_2]) ).

cnf(f_578_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_2392),U_2390)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2392),U_2391)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2390),U_2391)) ),
    inference(clausify,[status(thm)],[f_578_3]) ).

fof(f_579_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_579_2,plain,
    ! [U_2393] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2393),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_2393,
    inference(variable_rename,[status(thm)],[f_579_1]) ).

fof(f_579_3,plain,
    ! [U_2393] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2393),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_2393,
    inference(definitional_conversion,[status(esa)],[f_579_2]) ).

cnf(f_579_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2393),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_2393,
    inference(clausify,[status(thm)],[f_579_3]) ).

fof(f_580_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_580_2,plain,
    ! [U_2394] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2394) = U_2394,
    inference(variable_rename,[status(thm)],[f_580_1]) ).

fof(f_580_3,plain,
    ! [U_2394] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2394) = U_2394,
    inference(definitional_conversion,[status(esa)],[f_580_2]) ).

cnf(f_580_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2394) = U_2394,
    inference(clausify,[status(thm)],[f_580_3]) ).

fof(f_581_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_581_2,plain,
    ! [U_2400,U_2399,U_2398,U_2397,U_2396,U_2395] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2395),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2395),U_2399),U_2396)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2395),U_2400),U_2398))),U_2397))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2395),U_2399),U_2400) != c_Groups_Oone__class_Oone(U_2395)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2395),c_Groups_Ozero__class_Ozero(U_2395)),U_2400))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2395),c_Groups_Ozero__class_Ozero(U_2395)),U_2399))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2395),U_2398),U_2397))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2395),U_2396),U_2397))
      | ~ class_Rings_Olinordered__semiring__1(U_2395) ),
    inference(variable_rename,[status(thm)],[f_581_1]) ).

fof(f_581_3,plain,
    ! [U_2395,U_2396,U_2397,U_2398,U_2399,U_2400] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2395),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2395),U_2399),U_2396)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2395),U_2400),U_2398))),U_2397))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2395),U_2399),U_2400) != c_Groups_Oone__class_Oone(U_2395)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2395),c_Groups_Ozero__class_Ozero(U_2395)),U_2400))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2395),c_Groups_Ozero__class_Ozero(U_2395)),U_2399))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2395),U_2398),U_2397))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2395),U_2396),U_2397))
      | ~ class_Rings_Olinordered__semiring__1(U_2395) ),
    inference(definitional_conversion,[status(esa)],[f_581_2]) ).

cnf(f_581_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2395),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2395),U_2399),U_2396)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2395),U_2400),U_2398))),U_2397))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2395),U_2399),U_2400) != c_Groups_Oone__class_Oone(U_2395)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2395),c_Groups_Ozero__class_Ozero(U_2395)),U_2400))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2395),c_Groups_Ozero__class_Ozero(U_2395)),U_2399))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2395),U_2398),U_2397))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2395),U_2396),U_2397))
    | ~ class_Rings_Olinordered__semiring__1(U_2395) ),
    inference(clausify,[status(thm)],[f_581_3]) ).

fof(f_582_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_582_2,plain,
    ! [U_2401] :
      ( 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_2401)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2401)) ),
    inference(variable_rename,[status(thm)],[f_582_1]) ).

fof(f_582_3,plain,
    ! [U_2401] :
      ( 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_2401)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2401)) ),
    inference(definitional_conversion,[status(esa)],[f_582_2]) ).

cnf(f_582_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_2401)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2401)) ),
    inference(clausify,[status(thm)],[f_582_3]) ).

fof(f_583_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_583_2,plain,
    ! [U_2403,U_2402] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_2402)),hAPP(c_Int_Onat,U_2403)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2402),U_2403))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2403))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2402)) ),
    inference(variable_rename,[status(thm)],[f_583_1]) ).

fof(f_583_3,plain,
    ! [U_2403,U_2402] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_2402)),hAPP(c_Int_Onat,U_2403)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2402),U_2403))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2403))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2402)) ),
    inference(definitional_conversion,[status(esa)],[f_583_2]) ).

cnf(f_583_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_2402)),hAPP(c_Int_Onat,U_2403)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2402),U_2403))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2403))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2402)) ),
    inference(clausify,[status(thm)],[f_583_3]) ).

fof(f_584_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_584_2,plain,
    ! [U_2405,U_2404] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2404),U_2405)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_2404)),hAPP(c_Int_Onat,U_2405))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2404)) ),
    inference(variable_rename,[status(thm)],[f_584_1]) ).

fof(f_584_3,plain,
    ! [U_2404,U_2405] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2404),U_2405)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_2404)),hAPP(c_Int_Onat,U_2405))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2404)) ),
    inference(definitional_conversion,[status(esa)],[f_584_2]) ).

cnf(f_584_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2404),U_2405)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_2404)),hAPP(c_Int_Onat,U_2405))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2404)) ),
    inference(clausify,[status(thm)],[f_584_3]) ).

fof(f_585_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_585_2,plain,
    ! [U_2407,U_2406] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2406),c_Groups_Ozero__class_Ozero(U_2406)),hAPP(c_Int_Oring__1__class_Oof__int(U_2406),U_2407)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2407)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2407))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2406),c_Groups_Ozero__class_Ozero(U_2406)),hAPP(c_Int_Oring__1__class_Oof__int(U_2406),U_2407))) ) )
      | ~ class_Rings_Olinordered__idom(U_2406) ),
    inference(variable_rename,[status(thm)],[f_585_1]) ).

fof(f_585_3,plain,
    ( ! [U_2406,U_2407] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2406),c_Groups_Ozero__class_Ozero(U_2406)),hAPP(c_Int_Oring__1__class_Oof__int(U_2406),U_2407)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2407))
        | ~ sP162(U_2406,U_2407) )
    & ! [U_2406,U_2407] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2407))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2406),c_Groups_Ozero__class_Ozero(U_2406)),hAPP(c_Int_Oring__1__class_Oof__int(U_2406),U_2407)))
        | ~ sP162(U_2406,U_2407) )
    & ! [U_2406,U_2407] :
        ( sP162(U_2406,U_2407)
        | ~ class_Rings_Olinordered__idom(U_2406) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP162])],[f_585_2]) ).

cnf(f_585_4,plain,
    ( sP162(U_2406,U_2407)
    | ~ class_Rings_Olinordered__idom(U_2406) ),
    inference(clausify,[status(thm)],[f_585_3]) ).

cnf(f_585_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2407))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2406),c_Groups_Ozero__class_Ozero(U_2406)),hAPP(c_Int_Oring__1__class_Oof__int(U_2406),U_2407)))
    | ~ sP162(U_2406,U_2407) ),
    inference(clausify,[status(thm)],[f_585_3]) ).

cnf(f_585_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2406),c_Groups_Ozero__class_Ozero(U_2406)),hAPP(c_Int_Oring__1__class_Oof__int(U_2406),U_2407)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2407))
    | ~ sP162(U_2406,U_2407) ),
    inference(clausify,[status(thm)],[f_585_3]) ).

fof(f_586_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_586_2,plain,
    ! [U_2409,U_2408] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2408),hAPP(c_Int_Oring__1__class_Oof__int(U_2408),U_2409)),c_Groups_Ozero__class_Ozero(U_2408)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2409),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2409),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2408),hAPP(c_Int_Oring__1__class_Oof__int(U_2408),U_2409)),c_Groups_Ozero__class_Ozero(U_2408))) ) )
      | ~ class_Rings_Olinordered__idom(U_2408) ),
    inference(variable_rename,[status(thm)],[f_586_1]) ).

fof(f_586_3,plain,
    ( ! [U_2409,U_2408] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2408),hAPP(c_Int_Oring__1__class_Oof__int(U_2408),U_2409)),c_Groups_Ozero__class_Ozero(U_2408)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2409),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP163(U_2409,U_2408) )
    & ! [U_2409,U_2408] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2409),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2408),hAPP(c_Int_Oring__1__class_Oof__int(U_2408),U_2409)),c_Groups_Ozero__class_Ozero(U_2408)))
        | ~ sP163(U_2409,U_2408) )
    & ! [U_2409,U_2408] :
        ( sP163(U_2409,U_2408)
        | ~ class_Rings_Olinordered__idom(U_2408) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP163])],[f_586_2]) ).

cnf(f_586_4,plain,
    ( sP163(U_2409,U_2408)
    | ~ class_Rings_Olinordered__idom(U_2408) ),
    inference(clausify,[status(thm)],[f_586_3]) ).

cnf(f_586_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2409),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2408),hAPP(c_Int_Oring__1__class_Oof__int(U_2408),U_2409)),c_Groups_Ozero__class_Ozero(U_2408)))
    | ~ sP163(U_2409,U_2408) ),
    inference(clausify,[status(thm)],[f_586_3]) ).

cnf(f_586_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2408),hAPP(c_Int_Oring__1__class_Oof__int(U_2408),U_2409)),c_Groups_Ozero__class_Ozero(U_2408)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2409),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP163(U_2409,U_2408) ),
    inference(clausify,[status(thm)],[f_586_3]) ).

fof(f_587_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_587_2,plain,
    ! [U_2415,U_2414,U_2413,U_2412,U_2411,U_2410] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2410),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2410),U_2414),U_2411)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2410),U_2415),U_2413))),U_2412))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2410),U_2414),U_2415) != c_Groups_Oone__class_Oone(U_2410)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2410),c_Groups_Ozero__class_Ozero(U_2410)),U_2415))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2410),c_Groups_Ozero__class_Ozero(U_2410)),U_2414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2410),U_2413),U_2412))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2410),U_2411),U_2412))
      | ~ class_Rings_Olinordered__semiring__1__strict(U_2410) ),
    inference(variable_rename,[status(thm)],[f_587_1]) ).

fof(f_587_3,plain,
    ! [U_2410,U_2411,U_2412,U_2413,U_2414,U_2415] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2410),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2410),U_2414),U_2411)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2410),U_2415),U_2413))),U_2412))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2410),U_2414),U_2415) != c_Groups_Oone__class_Oone(U_2410)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2410),c_Groups_Ozero__class_Ozero(U_2410)),U_2415))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2410),c_Groups_Ozero__class_Ozero(U_2410)),U_2414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2410),U_2413),U_2412))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2410),U_2411),U_2412))
      | ~ class_Rings_Olinordered__semiring__1__strict(U_2410) ),
    inference(definitional_conversion,[status(esa)],[f_587_2]) ).

cnf(f_587_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2410),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2410),U_2414),U_2411)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2410),U_2415),U_2413))),U_2412))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2410),U_2414),U_2415) != c_Groups_Oone__class_Oone(U_2410)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2410),c_Groups_Ozero__class_Ozero(U_2410)),U_2415))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2410),c_Groups_Ozero__class_Ozero(U_2410)),U_2414))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2410),U_2413),U_2412))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2410),U_2411),U_2412))
    | ~ class_Rings_Olinordered__semiring__1__strict(U_2410) ),
    inference(clausify,[status(thm)],[f_587_3]) ).

fof(f_588_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_588_2,plain,
    ! [U_2416] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_2416)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2416))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2416)) ),
    inference(variable_rename,[status(thm)],[f_588_1]) ).

fof(f_588_3,plain,
    ! [U_2416] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_2416)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2416))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2416)) ),
    inference(definitional_conversion,[status(esa)],[f_588_2]) ).

cnf(f_588_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_2416)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2416))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2416)) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

fof(f_589_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_589_2,plain,
    ! [U_2417] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2417),c_Groups_Oone__class_Oone(U_2417)),c_Groups_Ozero__class_Ozero(U_2417)))
      | ~ class_Rings_Olinordered__semidom(U_2417) ),
    inference(variable_rename,[status(thm)],[f_589_1]) ).

fof(f_589_3,plain,
    ! [U_2417] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2417),c_Groups_Oone__class_Oone(U_2417)),c_Groups_Ozero__class_Ozero(U_2417)))
      | ~ class_Rings_Olinordered__semidom(U_2417) ),
    inference(definitional_conversion,[status(esa)],[f_589_2]) ).

cnf(f_589_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2417),c_Groups_Oone__class_Oone(U_2417)),c_Groups_Ozero__class_Ozero(U_2417)))
    | ~ class_Rings_Olinordered__semidom(U_2417) ),
    inference(clausify,[status(thm)],[f_589_3]) ).

fof(f_590_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_590_2,plain,
    ! [U_2418] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2418),c_Groups_Ozero__class_Ozero(U_2418)),c_Groups_Oone__class_Oone(U_2418)))
      | ~ class_Rings_Olinordered__semidom(U_2418) ),
    inference(variable_rename,[status(thm)],[f_590_1]) ).

fof(f_590_3,plain,
    ! [U_2418] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2418),c_Groups_Ozero__class_Ozero(U_2418)),c_Groups_Oone__class_Oone(U_2418)))
      | ~ class_Rings_Olinordered__semidom(U_2418) ),
    inference(definitional_conversion,[status(esa)],[f_590_2]) ).

cnf(f_590_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2418),c_Groups_Ozero__class_Ozero(U_2418)),c_Groups_Oone__class_Oone(U_2418)))
    | ~ class_Rings_Olinordered__semidom(U_2418) ),
    inference(clausify,[status(thm)],[f_590_3]) ).

fof(f_591_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_591_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_591_1]) ).

fof(f_591_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_591_2]) ).

cnf(f_591_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_591_3]) ).

fof(f_592_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_592_2,plain,
    ! [U_2422,U_2421] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2421),U_2422),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2421),U_2422),c_Groups_Oone__class_Oone(U_2421))))
      | ~ class_Rings_Olinordered__semidom(U_2421) ),
    inference(variable_rename,[status(thm)],[f_592_1]) ).

fof(f_592_3,plain,
    ! [U_2421,U_2422] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2421),U_2422),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2421),U_2422),c_Groups_Oone__class_Oone(U_2421))))
      | ~ class_Rings_Olinordered__semidom(U_2421) ),
    inference(definitional_conversion,[status(esa)],[f_592_2]) ).

cnf(f_592_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2421),U_2422),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2421),U_2422),c_Groups_Oone__class_Oone(U_2421))))
    | ~ class_Rings_Olinordered__semidom(U_2421) ),
    inference(clausify,[status(thm)],[f_592_3]) ).

fof(f_593_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_593_2,plain,
    ! [U_2425,U_2424,U_2423] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2423),c_Groups_Oone__class_Oone(U_2423)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2423),U_2424),U_2425)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2423),c_Groups_Oone__class_Oone(U_2423)),U_2425))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2423),c_Groups_Oone__class_Oone(U_2423)),U_2424))
      | ~ class_Rings_Olinordered__semidom(U_2423) ),
    inference(variable_rename,[status(thm)],[f_593_1]) ).

fof(f_593_3,plain,
    ! [U_2423,U_2424,U_2425] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2423),c_Groups_Oone__class_Oone(U_2423)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2423),U_2424),U_2425)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2423),c_Groups_Oone__class_Oone(U_2423)),U_2425))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2423),c_Groups_Oone__class_Oone(U_2423)),U_2424))
      | ~ class_Rings_Olinordered__semidom(U_2423) ),
    inference(definitional_conversion,[status(esa)],[f_593_2]) ).

cnf(f_593_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2423),c_Groups_Oone__class_Oone(U_2423)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2423),U_2424),U_2425)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2423),c_Groups_Oone__class_Oone(U_2423)),U_2425))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2423),c_Groups_Oone__class_Oone(U_2423)),U_2424))
    | ~ class_Rings_Olinordered__semidom(U_2423) ),
    inference(clausify,[status(thm)],[f_593_3]) ).

fof(f_594_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_594_2,plain,
    ! [U_2428,U_2427,U_2426] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2426),U_2427),U_2428)),U_2428) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2426),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2426),U_2427),c_Groups_Oone__class_Oone(U_2426))),U_2428)
      | ~ class_Rings_Ocomm__semiring__1(U_2426) ),
    inference(variable_rename,[status(thm)],[f_594_1]) ).

fof(f_594_3,plain,
    ! [U_2426,U_2427,U_2428] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2426),U_2427),U_2428)),U_2428) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2426),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2426),U_2427),c_Groups_Oone__class_Oone(U_2426))),U_2428)
      | ~ class_Rings_Ocomm__semiring__1(U_2426) ),
    inference(definitional_conversion,[status(esa)],[f_594_2]) ).

cnf(f_594_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2426),U_2427),U_2428)),U_2428) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2426),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2426),U_2427),c_Groups_Oone__class_Oone(U_2426))),U_2428)
    | ~ class_Rings_Ocomm__semiring__1(U_2426) ),
    inference(clausify,[status(thm)],[f_594_3]) ).

fof(f_595_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_595_2,plain,
    ! [U_2431,U_2430,U_2429] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),U_2430),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),U_2431),U_2430)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),U_2431),c_Groups_Oone__class_Oone(U_2429))),U_2430)
      | ~ class_Rings_Ocomm__semiring__1(U_2429) ),
    inference(variable_rename,[status(thm)],[f_595_1]) ).

fof(f_595_3,plain,
    ! [U_2429,U_2430,U_2431] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),U_2430),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),U_2431),U_2430)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),U_2431),c_Groups_Oone__class_Oone(U_2429))),U_2430)
      | ~ class_Rings_Ocomm__semiring__1(U_2429) ),
    inference(definitional_conversion,[status(esa)],[f_595_2]) ).

cnf(f_595_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),U_2430),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),U_2431),U_2430)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),U_2431),c_Groups_Oone__class_Oone(U_2429))),U_2430)
    | ~ class_Rings_Ocomm__semiring__1(U_2429) ),
    inference(clausify,[status(thm)],[f_595_3]) ).

fof(f_596_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_596_2,plain,
    ! [U_2433,U_2432] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2432),U_2433),U_2433) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2432),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2432),c_Groups_Oone__class_Oone(U_2432)),c_Groups_Oone__class_Oone(U_2432))),U_2433)
      | ~ class_Rings_Ocomm__semiring__1(U_2432) ),
    inference(variable_rename,[status(thm)],[f_596_1]) ).

fof(f_596_3,plain,
    ! [U_2432,U_2433] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2432),U_2433),U_2433) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2432),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2432),c_Groups_Oone__class_Oone(U_2432)),c_Groups_Oone__class_Oone(U_2432))),U_2433)
      | ~ class_Rings_Ocomm__semiring__1(U_2432) ),
    inference(definitional_conversion,[status(esa)],[f_596_2]) ).

cnf(f_596_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2432),U_2433),U_2433) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2432),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2432),c_Groups_Oone__class_Oone(U_2432)),c_Groups_Oone__class_Oone(U_2432))),U_2433)
    | ~ class_Rings_Ocomm__semiring__1(U_2432) ),
    inference(clausify,[status(thm)],[f_596_3]) ).

fof(f_597_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_597_2,plain,
    ! [U_2436,U_2435,U_2434] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2434),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2434),U_2435),U_2436)),c_Groups_Ozero__class_Ozero(U_2434)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2434),U_2436),c_Groups_Ozero__class_Ozero(U_2434)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2434),U_2435),c_Groups_Ozero__class_Ozero(U_2434)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2434) ),
    inference(variable_rename,[status(thm)],[f_597_1]) ).

fof(f_597_3,plain,
    ! [U_2434,U_2435,U_2436] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2434),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2434),U_2435),U_2436)),c_Groups_Ozero__class_Ozero(U_2434)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2434),U_2436),c_Groups_Ozero__class_Ozero(U_2434)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2434),U_2435),c_Groups_Ozero__class_Ozero(U_2434)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2434) ),
    inference(definitional_conversion,[status(esa)],[f_597_2]) ).

cnf(f_597_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2434),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2434),U_2435),U_2436)),c_Groups_Ozero__class_Ozero(U_2434)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2434),U_2436),c_Groups_Ozero__class_Ozero(U_2434)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2434),U_2435),c_Groups_Ozero__class_Ozero(U_2434)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2434) ),
    inference(clausify,[status(thm)],[f_597_3]) ).

fof(f_598_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_598_2,plain,
    ! [U_2440,U_2439,U_2438,U_2437] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2437),U_2439),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2437),U_2440),U_2438)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2437),U_2439),U_2440))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2437),c_Groups_Ozero__class_Ozero(U_2437)),U_2438))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2437) ),
    inference(variable_rename,[status(thm)],[f_598_1]) ).

fof(f_598_3,plain,
    ! [U_2438,U_2437,U_2439,U_2440] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2437),U_2439),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2437),U_2440),U_2438)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2437),U_2439),U_2440))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2437),c_Groups_Ozero__class_Ozero(U_2437)),U_2438))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2437) ),
    inference(definitional_conversion,[status(esa)],[f_598_2]) ).

cnf(f_598_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2437),U_2439),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2437),U_2440),U_2438)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2437),U_2439),U_2440))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2437),c_Groups_Ozero__class_Ozero(U_2437)),U_2438))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2437) ),
    inference(clausify,[status(thm)],[f_598_3]) ).

fof(f_599_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_599_2,plain,
    ! [U_2444,U_2443,U_2442,U_2441] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2441),U_2443),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2441),U_2442),U_2444)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2441),U_2443),U_2444))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2441),c_Groups_Ozero__class_Ozero(U_2441)),U_2442))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2441) ),
    inference(variable_rename,[status(thm)],[f_599_1]) ).

fof(f_599_3,plain,
    ! [U_2442,U_2441,U_2443,U_2444] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2441),U_2443),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2441),U_2442),U_2444)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2441),U_2443),U_2444))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2441),c_Groups_Ozero__class_Ozero(U_2441)),U_2442))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2441) ),
    inference(definitional_conversion,[status(esa)],[f_599_2]) ).

cnf(f_599_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2441),U_2443),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2441),U_2442),U_2444)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2441),U_2443),U_2444))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2441),c_Groups_Ozero__class_Ozero(U_2441)),U_2442))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2441) ),
    inference(clausify,[status(thm)],[f_599_3]) ).

fof(f_600_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_600_2,plain,
    ! [U_2447,U_2446,U_2445] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2445),U_2446),U_2447) = c_Groups_Ozero__class_Ozero(U_2445)
          | U_2447 != c_Groups_Ozero__class_Ozero(U_2445)
          | U_2446 != c_Groups_Ozero__class_Ozero(U_2445) )
        & ( ( U_2447 = c_Groups_Ozero__class_Ozero(U_2445)
            & U_2446 = c_Groups_Ozero__class_Ozero(U_2445) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2445),U_2446),U_2447) != 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_Groups_Oordered__comm__monoid__add(U_2445) ),
    inference(variable_rename,[status(thm)],[f_600_1]) ).

fof(f_600_3,plain,
    ( ! [U_2445,U_2446,U_2447] :
        ( U_2447 = c_Groups_Ozero__class_Ozero(U_2445)
        | ~ sP164(U_2445,U_2446,U_2447) )
    & ! [U_2445,U_2446,U_2447] :
        ( U_2446 = c_Groups_Ozero__class_Ozero(U_2445)
        | ~ sP164(U_2445,U_2446,U_2447) )
    & ! [U_2445,U_2446,U_2447] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2445),U_2446),U_2447) = c_Groups_Ozero__class_Ozero(U_2445)
        | U_2447 != c_Groups_Ozero__class_Ozero(U_2445)
        | U_2446 != c_Groups_Ozero__class_Ozero(U_2445)
        | ~ sP165(U_2445,U_2446,U_2447) )
    & ! [U_2445,U_2446,U_2447] :
        ( sP164(U_2445,U_2446,U_2447)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2445),U_2446),U_2447) != c_Groups_Ozero__class_Ozero(U_2445)
        | ~ sP165(U_2445,U_2446,U_2447) )
    & ! [U_2445,U_2446,U_2447] :
        ( sP165(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))
        | ~ class_Groups_Oordered__comm__monoid__add(U_2445) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP164,sP165])],[f_600_2]) ).

cnf(f_600_4,plain,
    ( sP165(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))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2445) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

cnf(f_600_5,plain,
    ( sP164(U_2445,U_2446,U_2447)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2445),U_2446),U_2447) != c_Groups_Ozero__class_Ozero(U_2445)
    | ~ sP165(U_2445,U_2446,U_2447) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

cnf(f_600_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2445),U_2446),U_2447) = c_Groups_Ozero__class_Ozero(U_2445)
    | U_2447 != c_Groups_Ozero__class_Ozero(U_2445)
    | U_2446 != c_Groups_Ozero__class_Ozero(U_2445)
    | ~ sP165(U_2445,U_2446,U_2447) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

cnf(f_600_7,plain,
    ( U_2446 = c_Groups_Ozero__class_Ozero(U_2445)
    | ~ sP164(U_2445,U_2446,U_2447) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

cnf(f_600_8,plain,
    ( U_2447 = c_Groups_Ozero__class_Ozero(U_2445)
    | ~ sP164(U_2445,U_2446,U_2447) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

fof(f_601_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_601_2,plain,
    ! [U_2450,U_2449,U_2448] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),c_Groups_Ozero__class_Ozero(U_2448)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2448),U_2449),U_2450)))
      | ~ 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),c_Groups_Ozero__class_Ozero(U_2448)),U_2449))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2448) ),
    inference(variable_rename,[status(thm)],[f_601_1]) ).

fof(f_601_3,plain,
    ! [U_2449,U_2450,U_2448] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),c_Groups_Ozero__class_Ozero(U_2448)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2448),U_2449),U_2450)))
      | ~ 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),c_Groups_Ozero__class_Ozero(U_2448)),U_2449))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2448) ),
    inference(definitional_conversion,[status(esa)],[f_601_2]) ).

cnf(f_601_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2448),c_Groups_Ozero__class_Ozero(U_2448)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2448),U_2449),U_2450)))
    | ~ 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),c_Groups_Ozero__class_Ozero(U_2448)),U_2449))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2448) ),
    inference(clausify,[status(thm)],[f_601_3]) ).

fof(f_602_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_602_2,plain,
    ! [U_2452,U_2451] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2451),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2451),U_2452),U_2452)),c_Groups_Ozero__class_Ozero(U_2451)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2451),U_2452),c_Groups_Ozero__class_Ozero(U_2451))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2451),U_2452),c_Groups_Ozero__class_Ozero(U_2451)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2451),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2451),U_2452),U_2452)),c_Groups_Ozero__class_Ozero(U_2451))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_2451) ),
    inference(variable_rename,[status(thm)],[f_602_1]) ).

fof(f_602_3,plain,
    ( ! [U_2452,U_2451] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2451),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2451),U_2452),U_2452)),c_Groups_Ozero__class_Ozero(U_2451)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2451),U_2452),c_Groups_Ozero__class_Ozero(U_2451)))
        | ~ sP166(U_2452,U_2451) )
    & ! [U_2452,U_2451] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2451),U_2452),c_Groups_Ozero__class_Ozero(U_2451)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2451),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2451),U_2452),U_2452)),c_Groups_Ozero__class_Ozero(U_2451)))
        | ~ sP166(U_2452,U_2451) )
    & ! [U_2452,U_2451] :
        ( sP166(U_2452,U_2451)
        | ~ class_Groups_Olinordered__ab__group__add(U_2451) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166])],[f_602_2]) ).

cnf(f_602_4,plain,
    ( sP166(U_2452,U_2451)
    | ~ class_Groups_Olinordered__ab__group__add(U_2451) ),
    inference(clausify,[status(thm)],[f_602_3]) ).

cnf(f_602_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2451),U_2452),c_Groups_Ozero__class_Ozero(U_2451)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2451),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2451),U_2452),U_2452)),c_Groups_Ozero__class_Ozero(U_2451)))
    | ~ sP166(U_2452,U_2451) ),
    inference(clausify,[status(thm)],[f_602_3]) ).

cnf(f_602_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2451),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2451),U_2452),U_2452)),c_Groups_Ozero__class_Ozero(U_2451)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2451),U_2452),c_Groups_Ozero__class_Ozero(U_2451)))
    | ~ sP166(U_2452,U_2451) ),
    inference(clausify,[status(thm)],[f_602_3]) ).

fof(f_603_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_603_2,plain,
    ! [U_2454,U_2453] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),c_Groups_Ozero__class_Ozero(U_2453)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2453),U_2454),U_2454)))
          | ~ 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),c_Groups_Ozero__class_Ozero(U_2453)),U_2454))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),c_Groups_Ozero__class_Ozero(U_2453)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2453),U_2454),U_2454))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_2453) ),
    inference(variable_rename,[status(thm)],[f_603_1]) ).

fof(f_603_3,plain,
    ( ! [U_2454,U_2453] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),c_Groups_Ozero__class_Ozero(U_2453)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2453),U_2454),U_2454)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),c_Groups_Ozero__class_Ozero(U_2453)),U_2454))
        | ~ sP167(U_2454,U_2453) )
    & ! [U_2454,U_2453] :
        ( 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),c_Groups_Ozero__class_Ozero(U_2453)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2453),U_2454),U_2454)))
        | ~ sP167(U_2454,U_2453) )
    & ! [U_2454,U_2453] :
        ( sP167(U_2454,U_2453)
        | ~ class_Groups_Olinordered__ab__group__add(U_2453) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP167])],[f_603_2]) ).

cnf(f_603_4,plain,
    ( sP167(U_2454,U_2453)
    | ~ class_Groups_Olinordered__ab__group__add(U_2453) ),
    inference(clausify,[status(thm)],[f_603_3]) ).

cnf(f_603_5,plain,
    ( 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),c_Groups_Ozero__class_Ozero(U_2453)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2453),U_2454),U_2454)))
    | ~ sP167(U_2454,U_2453) ),
    inference(clausify,[status(thm)],[f_603_3]) ).

cnf(f_603_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),c_Groups_Ozero__class_Ozero(U_2453)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2453),U_2454),U_2454)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2453),c_Groups_Ozero__class_Ozero(U_2453)),U_2454))
    | ~ sP167(U_2454,U_2453) ),
    inference(clausify,[status(thm)],[f_603_3]) ).

fof(f_604_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_604_2,plain,
    ! [U_2456,U_2455] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2455),c_Groups_Ozero__class_Ozero(U_2455)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2455),U_2456),U_2456)))
      | ~ class_Rings_Olinordered__ring(U_2455) ),
    inference(variable_rename,[status(thm)],[f_604_1]) ).

fof(f_604_3,plain,
    ! [U_2455,U_2456] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2455),c_Groups_Ozero__class_Ozero(U_2455)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2455),U_2456),U_2456)))
      | ~ class_Rings_Olinordered__ring(U_2455) ),
    inference(definitional_conversion,[status(esa)],[f_604_2]) ).

cnf(f_604_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2455),c_Groups_Ozero__class_Ozero(U_2455)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2455),U_2456),U_2456)))
    | ~ class_Rings_Olinordered__ring(U_2455) ),
    inference(clausify,[status(thm)],[f_604_3]) ).

fof(f_605_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_605_2,plain,
    ! [U_2459,U_2458,U_2457] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2457),U_2458),U_2459)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),U_2459),c_Groups_Ozero__class_Ozero(U_2457)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),U_2458),c_Groups_Ozero__class_Ozero(U_2457))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),U_2459))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),U_2458)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),U_2459),c_Groups_Ozero__class_Ozero(U_2457)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),U_2458),c_Groups_Ozero__class_Ozero(U_2457))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),U_2459))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),U_2458)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2457),U_2458),U_2459))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_2457) ),
    inference(variable_rename,[status(thm)],[f_605_1]) ).

fof(f_605_3,plain,
    ( ! [U_2457,U_2458,U_2459] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),U_2459),c_Groups_Ozero__class_Ozero(U_2457)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),U_2458),c_Groups_Ozero__class_Ozero(U_2457)))
        | ~ sP170(U_2457,U_2458,U_2459) )
    & ! [U_2457,U_2458,U_2459] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),U_2459))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),U_2458))
        | ~ sP170(U_2457,U_2458,U_2459) )
    & ! [U_2457,U_2458,U_2459] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),U_2459),c_Groups_Ozero__class_Ozero(U_2457)))
        | ~ sP169(U_2457,U_2458,U_2459) )
    & ! [U_2457,U_2458,U_2459] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),U_2458),c_Groups_Ozero__class_Ozero(U_2457)))
        | ~ sP169(U_2457,U_2458,U_2459) )
    & ! [U_2457,U_2458,U_2459] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),U_2459))
        | ~ sP168(U_2457,U_2458,U_2459) )
    & ! [U_2457,U_2458,U_2459] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),U_2458))
        | ~ sP168(U_2457,U_2458,U_2459) )
    & ! [U_2457,U_2458,U_2459] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2457),U_2458),U_2459)))
        | sP170(U_2457,U_2458,U_2459)
        | ~ sP171(U_2457,U_2458,U_2459) )
    & ! [U_2457,U_2458,U_2459] :
        ( sP169(U_2457,U_2458,U_2459)
        | sP168(U_2457,U_2458,U_2459)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2457),U_2458),U_2459)))
        | ~ sP171(U_2457,U_2458,U_2459) )
    & ! [U_2457,U_2458,U_2459] :
        ( sP171(U_2457,U_2458,U_2459)
        | ~ class_Rings_Olinordered__ring__strict(U_2457) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP168,sP169,sP170,sP171])],[f_605_2]) ).

cnf(f_605_4,plain,
    ( sP171(U_2457,U_2458,U_2459)
    | ~ class_Rings_Olinordered__ring__strict(U_2457) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

cnf(f_605_5,plain,
    ( sP169(U_2457,U_2458,U_2459)
    | sP168(U_2457,U_2458,U_2459)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2457),U_2458),U_2459)))
    | ~ sP171(U_2457,U_2458,U_2459) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

cnf(f_605_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2457),U_2458),U_2459)))
    | sP170(U_2457,U_2458,U_2459)
    | ~ sP171(U_2457,U_2458,U_2459) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

cnf(f_605_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),U_2458))
    | ~ sP168(U_2457,U_2458,U_2459) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

cnf(f_605_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),U_2459))
    | ~ sP168(U_2457,U_2458,U_2459) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

cnf(f_605_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),U_2458),c_Groups_Ozero__class_Ozero(U_2457)))
    | ~ sP169(U_2457,U_2458,U_2459) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

cnf(f_605_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),U_2459),c_Groups_Ozero__class_Ozero(U_2457)))
    | ~ sP169(U_2457,U_2458,U_2459) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

cnf(f_605_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),U_2459))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),c_Groups_Ozero__class_Ozero(U_2457)),U_2458))
    | ~ sP170(U_2457,U_2458,U_2459) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

cnf(f_605_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),U_2459),c_Groups_Ozero__class_Ozero(U_2457)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2457),U_2458),c_Groups_Ozero__class_Ozero(U_2457)))
    | ~ sP170(U_2457,U_2458,U_2459) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

fof(f_606_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_606_2,plain,
    ! [U_2462,U_2461,U_2460] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2461),U_2462)),c_Groups_Ozero__class_Ozero(U_2460)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),c_Groups_Ozero__class_Ozero(U_2460)),U_2462))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),U_2461),c_Groups_Ozero__class_Ozero(U_2460))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),U_2462),c_Groups_Ozero__class_Ozero(U_2460)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),c_Groups_Ozero__class_Ozero(U_2460)),U_2461)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),c_Groups_Ozero__class_Ozero(U_2460)),U_2462))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),U_2461),c_Groups_Ozero__class_Ozero(U_2460))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),U_2462),c_Groups_Ozero__class_Ozero(U_2460)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),c_Groups_Ozero__class_Ozero(U_2460)),U_2461)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2461),U_2462)),c_Groups_Ozero__class_Ozero(U_2460))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_2460) ),
    inference(variable_rename,[status(thm)],[f_606_1]) ).

fof(f_606_3,plain,
    ( ! [U_2461,U_2462,U_2460] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),c_Groups_Ozero__class_Ozero(U_2460)),U_2462))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),U_2461),c_Groups_Ozero__class_Ozero(U_2460)))
        | ~ sP174(U_2461,U_2462,U_2460) )
    & ! [U_2461,U_2462,U_2460] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),U_2462),c_Groups_Ozero__class_Ozero(U_2460)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),c_Groups_Ozero__class_Ozero(U_2460)),U_2461))
        | ~ sP174(U_2461,U_2462,U_2460) )
    & ! [U_2461,U_2462,U_2460] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),c_Groups_Ozero__class_Ozero(U_2460)),U_2462))
        | ~ sP173(U_2461,U_2462,U_2460) )
    & ! [U_2461,U_2462,U_2460] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),U_2461),c_Groups_Ozero__class_Ozero(U_2460)))
        | ~ sP173(U_2461,U_2462,U_2460) )
    & ! [U_2461,U_2462,U_2460] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),U_2462),c_Groups_Ozero__class_Ozero(U_2460)))
        | ~ sP172(U_2461,U_2462,U_2460) )
    & ! [U_2461,U_2462,U_2460] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),c_Groups_Ozero__class_Ozero(U_2460)),U_2461))
        | ~ sP172(U_2461,U_2462,U_2460) )
    & ! [U_2461,U_2462,U_2460] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2461),U_2462)),c_Groups_Ozero__class_Ozero(U_2460)))
        | sP174(U_2461,U_2462,U_2460)
        | ~ sP175(U_2461,U_2462,U_2460) )
    & ! [U_2461,U_2462,U_2460] :
        ( sP173(U_2461,U_2462,U_2460)
        | sP172(U_2461,U_2462,U_2460)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2461),U_2462)),c_Groups_Ozero__class_Ozero(U_2460)))
        | ~ sP175(U_2461,U_2462,U_2460) )
    & ! [U_2461,U_2462,U_2460] :
        ( sP175(U_2461,U_2462,U_2460)
        | ~ class_Rings_Olinordered__ring__strict(U_2460) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP172,sP173,sP174,sP175])],[f_606_2]) ).

cnf(f_606_4,plain,
    ( sP175(U_2461,U_2462,U_2460)
    | ~ class_Rings_Olinordered__ring__strict(U_2460) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

cnf(f_606_5,plain,
    ( sP173(U_2461,U_2462,U_2460)
    | sP172(U_2461,U_2462,U_2460)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2461),U_2462)),c_Groups_Ozero__class_Ozero(U_2460)))
    | ~ sP175(U_2461,U_2462,U_2460) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

cnf(f_606_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2461),U_2462)),c_Groups_Ozero__class_Ozero(U_2460)))
    | sP174(U_2461,U_2462,U_2460)
    | ~ sP175(U_2461,U_2462,U_2460) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

cnf(f_606_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),c_Groups_Ozero__class_Ozero(U_2460)),U_2461))
    | ~ sP172(U_2461,U_2462,U_2460) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

cnf(f_606_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),U_2462),c_Groups_Ozero__class_Ozero(U_2460)))
    | ~ sP172(U_2461,U_2462,U_2460) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

cnf(f_606_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),U_2461),c_Groups_Ozero__class_Ozero(U_2460)))
    | ~ sP173(U_2461,U_2462,U_2460) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

cnf(f_606_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),c_Groups_Ozero__class_Ozero(U_2460)),U_2462))
    | ~ sP173(U_2461,U_2462,U_2460) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

cnf(f_606_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),U_2462),c_Groups_Ozero__class_Ozero(U_2460)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),c_Groups_Ozero__class_Ozero(U_2460)),U_2461))
    | ~ sP174(U_2461,U_2462,U_2460) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

cnf(f_606_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),c_Groups_Ozero__class_Ozero(U_2460)),U_2462))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2460),U_2461),c_Groups_Ozero__class_Ozero(U_2460)))
    | ~ sP174(U_2461,U_2462,U_2460) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

fof(f_607_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_607_2,plain,
    ! [U_2465,U_2464,U_2463] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2463),c_Groups_Ozero__class_Ozero(U_2463)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2463),U_2464),U_2465)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2463),c_Groups_Ozero__class_Ozero(U_2463)),U_2465))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2463),c_Groups_Ozero__class_Ozero(U_2463)),U_2464))
      | ~ class_Rings_Oordered__cancel__semiring(U_2463) ),
    inference(variable_rename,[status(thm)],[f_607_1]) ).

fof(f_607_3,plain,
    ! [U_2464,U_2465,U_2463] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2463),c_Groups_Ozero__class_Ozero(U_2463)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2463),U_2464),U_2465)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2463),c_Groups_Ozero__class_Ozero(U_2463)),U_2465))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2463),c_Groups_Ozero__class_Ozero(U_2463)),U_2464))
      | ~ class_Rings_Oordered__cancel__semiring(U_2463) ),
    inference(definitional_conversion,[status(esa)],[f_607_2]) ).

cnf(f_607_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2463),c_Groups_Ozero__class_Ozero(U_2463)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2463),U_2464),U_2465)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2463),c_Groups_Ozero__class_Ozero(U_2463)),U_2465))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2463),c_Groups_Ozero__class_Ozero(U_2463)),U_2464))
    | ~ class_Rings_Oordered__cancel__semiring(U_2463) ),
    inference(clausify,[status(thm)],[f_607_3]) ).

fof(f_608_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_608_2,plain,
    ! [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_2467),U_2468)),c_Groups_Ozero__class_Ozero(U_2466)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),U_2468),c_Groups_Ozero__class_Ozero(U_2466)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),c_Groups_Ozero__class_Ozero(U_2466)),U_2467))
      | ~ class_Rings_Oordered__cancel__semiring(U_2466) ),
    inference(variable_rename,[status(thm)],[f_608_1]) ).

fof(f_608_3,plain,
    ! [U_2467,U_2466,U_2468] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2466),U_2467),U_2468)),c_Groups_Ozero__class_Ozero(U_2466)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),U_2468),c_Groups_Ozero__class_Ozero(U_2466)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),c_Groups_Ozero__class_Ozero(U_2466)),U_2467))
      | ~ class_Rings_Oordered__cancel__semiring(U_2466) ),
    inference(definitional_conversion,[status(esa)],[f_608_2]) ).

cnf(f_608_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2466),U_2467),U_2468)),c_Groups_Ozero__class_Ozero(U_2466)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),U_2468),c_Groups_Ozero__class_Ozero(U_2466)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2466),c_Groups_Ozero__class_Ozero(U_2466)),U_2467))
    | ~ class_Rings_Oordered__cancel__semiring(U_2466) ),
    inference(clausify,[status(thm)],[f_608_3]) ).

fof(f_609_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_609_2,plain,
    ! [U_2471,U_2470,U_2469] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2469),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2469),U_2471),U_2470)),c_Groups_Ozero__class_Ozero(U_2469)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2469),U_2471),c_Groups_Ozero__class_Ozero(U_2469)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2469),c_Groups_Ozero__class_Ozero(U_2469)),U_2470))
      | ~ class_Rings_Oordered__cancel__semiring(U_2469) ),
    inference(variable_rename,[status(thm)],[f_609_1]) ).

fof(f_609_3,plain,
    ! [U_2469,U_2470,U_2471] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2469),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2469),U_2471),U_2470)),c_Groups_Ozero__class_Ozero(U_2469)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2469),U_2471),c_Groups_Ozero__class_Ozero(U_2469)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2469),c_Groups_Ozero__class_Ozero(U_2469)),U_2470))
      | ~ class_Rings_Oordered__cancel__semiring(U_2469) ),
    inference(definitional_conversion,[status(esa)],[f_609_2]) ).

cnf(f_609_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2469),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2469),U_2471),U_2470)),c_Groups_Ozero__class_Ozero(U_2469)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2469),U_2471),c_Groups_Ozero__class_Ozero(U_2469)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2469),c_Groups_Ozero__class_Ozero(U_2469)),U_2470))
    | ~ class_Rings_Oordered__cancel__semiring(U_2469) ),
    inference(clausify,[status(thm)],[f_609_3]) ).

fof(f_610_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_610_2,plain,
    ! [U_2474,U_2473,U_2472] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2472),U_2473),U_2474)),c_Groups_Ozero__class_Ozero(U_2472)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2472),c_Groups_Ozero__class_Ozero(U_2472)),U_2474))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2472),U_2473),c_Groups_Ozero__class_Ozero(U_2472)))
      | ~ class_Rings_Oordered__cancel__semiring(U_2472) ),
    inference(variable_rename,[status(thm)],[f_610_1]) ).

fof(f_610_3,plain,
    ! [U_2472,U_2473,U_2474] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2472),U_2473),U_2474)),c_Groups_Ozero__class_Ozero(U_2472)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2472),c_Groups_Ozero__class_Ozero(U_2472)),U_2474))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2472),U_2473),c_Groups_Ozero__class_Ozero(U_2472)))
      | ~ class_Rings_Oordered__cancel__semiring(U_2472) ),
    inference(definitional_conversion,[status(esa)],[f_610_2]) ).

cnf(f_610_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2472),U_2473),U_2474)),c_Groups_Ozero__class_Ozero(U_2472)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2472),c_Groups_Ozero__class_Ozero(U_2472)),U_2474))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2472),U_2473),c_Groups_Ozero__class_Ozero(U_2472)))
    | ~ class_Rings_Oordered__cancel__semiring(U_2472) ),
    inference(clausify,[status(thm)],[f_610_3]) ).

fof(f_611_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_611_2,plain,
    ! [U_2477,U_2476,U_2475] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2475),c_Groups_Ozero__class_Ozero(U_2475)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2475),U_2476),U_2477)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2475),U_2477),c_Groups_Ozero__class_Ozero(U_2475)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2475),U_2476),c_Groups_Ozero__class_Ozero(U_2475)))
      | ~ class_Rings_Oordered__ring(U_2475) ),
    inference(variable_rename,[status(thm)],[f_611_1]) ).

fof(f_611_3,plain,
    ! [U_2475,U_2476,U_2477] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2475),c_Groups_Ozero__class_Ozero(U_2475)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2475),U_2476),U_2477)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2475),U_2477),c_Groups_Ozero__class_Ozero(U_2475)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2475),U_2476),c_Groups_Ozero__class_Ozero(U_2475)))
      | ~ class_Rings_Oordered__ring(U_2475) ),
    inference(definitional_conversion,[status(esa)],[f_611_2]) ).

cnf(f_611_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2475),c_Groups_Ozero__class_Ozero(U_2475)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2475),U_2476),U_2477)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2475),U_2477),c_Groups_Ozero__class_Ozero(U_2475)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2475),U_2476),c_Groups_Ozero__class_Ozero(U_2475)))
    | ~ class_Rings_Oordered__ring(U_2475) ),
    inference(clausify,[status(thm)],[f_611_3]) ).

fof(f_612_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_612_2,plain,
    ! [U_2481,U_2480,U_2479,U_2478] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2479),U_2481)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2480),U_2481)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),c_Groups_Ozero__class_Ozero(U_2478)),U_2481))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),U_2479),U_2480))
      | ~ class_Rings_Oordered__semiring(U_2478) ),
    inference(variable_rename,[status(thm)],[f_612_1]) ).

fof(f_612_3,plain,
    ! [U_2478,U_2479,U_2480,U_2481] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2479),U_2481)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2480),U_2481)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),c_Groups_Ozero__class_Ozero(U_2478)),U_2481))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),U_2479),U_2480))
      | ~ class_Rings_Oordered__semiring(U_2478) ),
    inference(definitional_conversion,[status(esa)],[f_612_2]) ).

cnf(f_612_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2479),U_2481)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2480),U_2481)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),c_Groups_Ozero__class_Ozero(U_2478)),U_2481))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),U_2479),U_2480))
    | ~ class_Rings_Oordered__semiring(U_2478) ),
    inference(clausify,[status(thm)],[f_612_3]) ).

fof(f_613_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_613_2,plain,
    ! [U_2485,U_2484,U_2483,U_2482] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2482),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2482),U_2485),U_2483)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2482),U_2485),U_2484)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2482),c_Groups_Ozero__class_Ozero(U_2482)),U_2485))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2482),U_2483),U_2484))
      | ~ class_Rings_Oordered__semiring(U_2482) ),
    inference(variable_rename,[status(thm)],[f_613_1]) ).

fof(f_613_3,plain,
    ! [U_2482,U_2483,U_2484,U_2485] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2482),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2482),U_2485),U_2483)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2482),U_2485),U_2484)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2482),c_Groups_Ozero__class_Ozero(U_2482)),U_2485))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2482),U_2483),U_2484))
      | ~ class_Rings_Oordered__semiring(U_2482) ),
    inference(definitional_conversion,[status(esa)],[f_613_2]) ).

cnf(f_613_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2482),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2482),U_2485),U_2483)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2482),U_2485),U_2484)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2482),c_Groups_Ozero__class_Ozero(U_2482)),U_2485))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2482),U_2483),U_2484))
    | ~ class_Rings_Oordered__semiring(U_2482) ),
    inference(clausify,[status(thm)],[f_613_3]) ).

fof(f_614_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_614_2,plain,
    ! [U_2489,U_2488,U_2487,U_2486] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2486),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2486),U_2489),U_2487)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2486),U_2489),U_2488)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2486),c_Groups_Ozero__class_Ozero(U_2486)),U_2489))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2486),U_2487),U_2488))
      | ~ class_Rings_Oordered__comm__semiring(U_2486) ),
    inference(variable_rename,[status(thm)],[f_614_1]) ).

fof(f_614_3,plain,
    ! [U_2486,U_2487,U_2488,U_2489] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2486),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2486),U_2489),U_2487)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2486),U_2489),U_2488)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2486),c_Groups_Ozero__class_Ozero(U_2486)),U_2489))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2486),U_2487),U_2488))
      | ~ class_Rings_Oordered__comm__semiring(U_2486) ),
    inference(definitional_conversion,[status(esa)],[f_614_2]) ).

cnf(f_614_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2486),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2486),U_2489),U_2487)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2486),U_2489),U_2488)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2486),c_Groups_Ozero__class_Ozero(U_2486)),U_2489))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2486),U_2487),U_2488))
    | ~ class_Rings_Oordered__comm__semiring(U_2486) ),
    inference(clausify,[status(thm)],[f_614_3]) ).

fof(f_615_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_615_2,plain,
    ! [U_2493,U_2492,U_2491,U_2490] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2490),U_2492),U_2493)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2490),U_2491),U_2493)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),U_2493),c_Groups_Ozero__class_Ozero(U_2490)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),U_2491),U_2492))
      | ~ class_Rings_Oordered__ring(U_2490) ),
    inference(variable_rename,[status(thm)],[f_615_1]) ).

fof(f_615_3,plain,
    ! [U_2490,U_2491,U_2492,U_2493] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2490),U_2492),U_2493)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2490),U_2491),U_2493)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),U_2493),c_Groups_Ozero__class_Ozero(U_2490)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),U_2491),U_2492))
      | ~ class_Rings_Oordered__ring(U_2490) ),
    inference(definitional_conversion,[status(esa)],[f_615_2]) ).

cnf(f_615_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2490),U_2492),U_2493)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2490),U_2491),U_2493)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),U_2493),c_Groups_Ozero__class_Ozero(U_2490)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2490),U_2491),U_2492))
    | ~ class_Rings_Oordered__ring(U_2490) ),
    inference(clausify,[status(thm)],[f_615_3]) ).

fof(f_616_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_616_2,plain,
    ! [U_2497,U_2496,U_2495,U_2494] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2494),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2494),U_2497),U_2496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2494),U_2497),U_2495)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2494),U_2497),c_Groups_Ozero__class_Ozero(U_2494)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2494),U_2495),U_2496))
      | ~ class_Rings_Oordered__ring(U_2494) ),
    inference(variable_rename,[status(thm)],[f_616_1]) ).

fof(f_616_3,plain,
    ! [U_2494,U_2495,U_2496,U_2497] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2494),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2494),U_2497),U_2496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2494),U_2497),U_2495)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2494),U_2497),c_Groups_Ozero__class_Ozero(U_2494)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2494),U_2495),U_2496))
      | ~ class_Rings_Oordered__ring(U_2494) ),
    inference(definitional_conversion,[status(esa)],[f_616_2]) ).

cnf(f_616_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2494),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2494),U_2497),U_2496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2494),U_2497),U_2495)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2494),U_2497),c_Groups_Ozero__class_Ozero(U_2494)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2494),U_2495),U_2496))
    | ~ class_Rings_Oordered__ring(U_2494) ),
    inference(clausify,[status(thm)],[f_616_3]) ).

fof(f_617_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_617_2,plain,
    ! [U_2502,U_2501,U_2500,U_2499,U_2498] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2498),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2498),U_2499),U_2501)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2498),U_2500),U_2502)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2498),c_Groups_Ozero__class_Ozero(U_2498)),U_2501))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2498),c_Groups_Ozero__class_Ozero(U_2498)),U_2499))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2498),U_2501),U_2502))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2498),U_2499),U_2500))
      | ~ class_Rings_Oordered__semiring(U_2498) ),
    inference(variable_rename,[status(thm)],[f_617_1]) ).

fof(f_617_3,plain,
    ! [U_2498,U_2499,U_2500,U_2501,U_2502] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2498),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2498),U_2499),U_2501)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2498),U_2500),U_2502)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2498),c_Groups_Ozero__class_Ozero(U_2498)),U_2501))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2498),c_Groups_Ozero__class_Ozero(U_2498)),U_2499))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2498),U_2501),U_2502))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2498),U_2499),U_2500))
      | ~ class_Rings_Oordered__semiring(U_2498) ),
    inference(definitional_conversion,[status(esa)],[f_617_2]) ).

cnf(f_617_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2498),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2498),U_2499),U_2501)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2498),U_2500),U_2502)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2498),c_Groups_Ozero__class_Ozero(U_2498)),U_2501))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2498),c_Groups_Ozero__class_Ozero(U_2498)),U_2499))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2498),U_2501),U_2502))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2498),U_2499),U_2500))
    | ~ class_Rings_Oordered__semiring(U_2498) ),
    inference(clausify,[status(thm)],[f_617_3]) ).

fof(f_618_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_618_2,plain,
    ! [U_2507,U_2506,U_2505,U_2504,U_2503] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2503),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2503),U_2504),U_2506)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2503),U_2505),U_2507)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2503),c_Groups_Ozero__class_Ozero(U_2503)),U_2506))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2503),c_Groups_Ozero__class_Ozero(U_2503)),U_2505))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2503),U_2506),U_2507))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2503),U_2504),U_2505))
      | ~ class_Rings_Oordered__semiring(U_2503) ),
    inference(variable_rename,[status(thm)],[f_618_1]) ).

fof(f_618_3,plain,
    ! [U_2504,U_2505,U_2506,U_2507,U_2503] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2503),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2503),U_2504),U_2506)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2503),U_2505),U_2507)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2503),c_Groups_Ozero__class_Ozero(U_2503)),U_2506))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2503),c_Groups_Ozero__class_Ozero(U_2503)),U_2505))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2503),U_2506),U_2507))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2503),U_2504),U_2505))
      | ~ class_Rings_Oordered__semiring(U_2503) ),
    inference(definitional_conversion,[status(esa)],[f_618_2]) ).

cnf(f_618_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2503),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2503),U_2504),U_2506)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2503),U_2505),U_2507)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2503),c_Groups_Ozero__class_Ozero(U_2503)),U_2506))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2503),c_Groups_Ozero__class_Ozero(U_2503)),U_2505))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2503),U_2506),U_2507))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2503),U_2504),U_2505))
    | ~ class_Rings_Oordered__semiring(U_2503) ),
    inference(clausify,[status(thm)],[f_618_3]) ).

fof(f_619_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_619_2,plain,
    ! [U_2510,U_2509,U_2508] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2508),U_2509),U_2510)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2508),U_2510),c_Groups_Ozero__class_Ozero(U_2508)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2508),U_2509),c_Groups_Ozero__class_Ozero(U_2508))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),U_2510))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),U_2509)) ) )
      | ~ class_Rings_Oordered__ring(U_2508) ),
    inference(variable_rename,[status(thm)],[f_619_1]) ).

fof(f_619_3,plain,
    ( ! [U_2509,U_2508,U_2510] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2508),U_2510),c_Groups_Ozero__class_Ozero(U_2508)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2508),U_2509),c_Groups_Ozero__class_Ozero(U_2508)))
        | ~ sP176(U_2509,U_2508,U_2510) )
    & ! [U_2509,U_2508,U_2510] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),U_2510))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),U_2509))
        | ~ sP176(U_2509,U_2508,U_2510) )
    & ! [U_2509,U_2508,U_2510] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2508),U_2509),U_2510)))
        | sP176(U_2509,U_2508,U_2510)
        | ~ class_Rings_Oordered__ring(U_2508) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP176])],[f_619_2]) ).

cnf(f_619_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2508),U_2509),U_2510)))
    | sP176(U_2509,U_2508,U_2510)
    | ~ class_Rings_Oordered__ring(U_2508) ),
    inference(clausify,[status(thm)],[f_619_3]) ).

cnf(f_619_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),U_2510))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),U_2509))
    | ~ sP176(U_2509,U_2508,U_2510) ),
    inference(clausify,[status(thm)],[f_619_3]) ).

cnf(f_619_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2508),U_2510),c_Groups_Ozero__class_Ozero(U_2508)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2508),U_2509),c_Groups_Ozero__class_Ozero(U_2508)))
    | ~ sP176(U_2509,U_2508,U_2510) ),
    inference(clausify,[status(thm)],[f_619_3]) ).

fof(f_620_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_620_2,plain,
    ! [U_2513,U_2512,U_2511] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2511),U_2512),U_2513)),c_Groups_Ozero__class_Ozero(U_2511)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),c_Groups_Ozero__class_Ozero(U_2511)),U_2513))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),U_2512),c_Groups_Ozero__class_Ozero(U_2511))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),U_2513),c_Groups_Ozero__class_Ozero(U_2511)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),c_Groups_Ozero__class_Ozero(U_2511)),U_2512)) ) )
      | ~ class_Rings_Oordered__cancel__semiring(U_2511) ),
    inference(variable_rename,[status(thm)],[f_620_1]) ).

fof(f_620_3,plain,
    ( ! [U_2511,U_2512,U_2513] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),c_Groups_Ozero__class_Ozero(U_2511)),U_2513))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),U_2512),c_Groups_Ozero__class_Ozero(U_2511)))
        | ~ sP177(U_2511,U_2512,U_2513) )
    & ! [U_2511,U_2512,U_2513] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),U_2513),c_Groups_Ozero__class_Ozero(U_2511)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),c_Groups_Ozero__class_Ozero(U_2511)),U_2512))
        | ~ sP177(U_2511,U_2512,U_2513) )
    & ! [U_2511,U_2512,U_2513] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2511),U_2512),U_2513)),c_Groups_Ozero__class_Ozero(U_2511)))
        | sP177(U_2511,U_2512,U_2513)
        | ~ class_Rings_Oordered__cancel__semiring(U_2511) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP177])],[f_620_2]) ).

cnf(f_620_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2511),U_2512),U_2513)),c_Groups_Ozero__class_Ozero(U_2511)))
    | sP177(U_2511,U_2512,U_2513)
    | ~ class_Rings_Oordered__cancel__semiring(U_2511) ),
    inference(clausify,[status(thm)],[f_620_3]) ).

cnf(f_620_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),U_2513),c_Groups_Ozero__class_Ozero(U_2511)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),c_Groups_Ozero__class_Ozero(U_2511)),U_2512))
    | ~ sP177(U_2511,U_2512,U_2513) ),
    inference(clausify,[status(thm)],[f_620_3]) ).

cnf(f_620_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),c_Groups_Ozero__class_Ozero(U_2511)),U_2513))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2511),U_2512),c_Groups_Ozero__class_Ozero(U_2511)))
    | ~ sP177(U_2511,U_2512,U_2513) ),
    inference(clausify,[status(thm)],[f_620_3]) ).

fof(f_621_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_621_2,plain,
    ! [U_2518,U_2517,U_2516,U_2515,U_2514] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2514),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2514),U_2515),U_2517)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2514),U_2516),U_2518)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2514),U_2517),U_2518))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2514),U_2515),U_2516))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2514) ),
    inference(variable_rename,[status(thm)],[f_621_1]) ).

fof(f_621_3,plain,
    ! [U_2515,U_2517,U_2518,U_2516,U_2514] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2514),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2514),U_2515),U_2517)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2514),U_2516),U_2518)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2514),U_2517),U_2518))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2514),U_2515),U_2516))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2514) ),
    inference(definitional_conversion,[status(esa)],[f_621_2]) ).

cnf(f_621_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2514),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2514),U_2515),U_2517)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2514),U_2516),U_2518)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2514),U_2517),U_2518))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2514),U_2515),U_2516))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2514) ),
    inference(clausify,[status(thm)],[f_621_3]) ).

fof(f_622_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_622_2,plain,
    ! [U_2523,U_2522,U_2521,U_2520,U_2519] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2519),U_2520),U_2522)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2519),U_2521),U_2523)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2519),U_2522),U_2523))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2519),U_2520),U_2521))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2519) ),
    inference(variable_rename,[status(thm)],[f_622_1]) ).

fof(f_622_3,plain,
    ! [U_2519,U_2520,U_2521,U_2522,U_2523] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2519),U_2520),U_2522)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2519),U_2521),U_2523)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2519),U_2522),U_2523))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2519),U_2520),U_2521))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2519) ),
    inference(definitional_conversion,[status(esa)],[f_622_2]) ).

cnf(f_622_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2519),U_2520),U_2522)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2519),U_2521),U_2523)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2519),U_2522),U_2523))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2519),U_2520),U_2521))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2519) ),
    inference(clausify,[status(thm)],[f_622_3]) ).

fof(f_623_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_623_2,plain,
    ! [U_2525,U_2524] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2524),U_2525),U_2525) = c_Groups_Oone__class_Oone(U_2524)
          | ( U_2525 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2524),c_Groups_Oone__class_Oone(U_2524))
            & U_2525 != c_Groups_Oone__class_Oone(U_2524) ) )
        & ( U_2525 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2524),c_Groups_Oone__class_Oone(U_2524))
          | U_2525 = c_Groups_Oone__class_Oone(U_2524)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2524),U_2525),U_2525) != c_Groups_Oone__class_Oone(U_2524) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_2524) ),
    inference(variable_rename,[status(thm)],[f_623_1]) ).

fof(f_623_3,plain,
    ( ! [U_2524,U_2525] :
        ( U_2525 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2524),c_Groups_Oone__class_Oone(U_2524))
        | ~ sP178(U_2524,U_2525) )
    & ! [U_2524,U_2525] :
        ( U_2525 != c_Groups_Oone__class_Oone(U_2524)
        | ~ sP178(U_2524,U_2525) )
    & ! [U_2524,U_2525] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2524),U_2525),U_2525) = c_Groups_Oone__class_Oone(U_2524)
        | sP178(U_2524,U_2525)
        | ~ sP179(U_2524,U_2525) )
    & ! [U_2524,U_2525] :
        ( U_2525 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2524),c_Groups_Oone__class_Oone(U_2524))
        | U_2525 = c_Groups_Oone__class_Oone(U_2524)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2524),U_2525),U_2525) != c_Groups_Oone__class_Oone(U_2524)
        | ~ sP179(U_2524,U_2525) )
    & ! [U_2524,U_2525] :
        ( sP179(U_2524,U_2525)
        | ~ class_Rings_Oring__1__no__zero__divisors(U_2524) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP178,sP179])],[f_623_2]) ).

cnf(f_623_4,plain,
    ( sP179(U_2524,U_2525)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_2524) ),
    inference(clausify,[status(thm)],[f_623_3]) ).

cnf(f_623_5,plain,
    ( U_2525 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2524),c_Groups_Oone__class_Oone(U_2524))
    | U_2525 = c_Groups_Oone__class_Oone(U_2524)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2524),U_2525),U_2525) != c_Groups_Oone__class_Oone(U_2524)
    | ~ sP179(U_2524,U_2525) ),
    inference(clausify,[status(thm)],[f_623_3]) ).

cnf(f_623_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2524),U_2525),U_2525) = c_Groups_Oone__class_Oone(U_2524)
    | sP178(U_2524,U_2525)
    | ~ sP179(U_2524,U_2525) ),
    inference(clausify,[status(thm)],[f_623_3]) ).

cnf(f_623_7,plain,
    ( U_2525 != c_Groups_Oone__class_Oone(U_2524)
    | ~ sP178(U_2524,U_2525) ),
    inference(clausify,[status(thm)],[f_623_3]) ).

cnf(f_623_8,plain,
    ( U_2525 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2524),c_Groups_Oone__class_Oone(U_2524))
    | ~ sP178(U_2524,U_2525) ),
    inference(clausify,[status(thm)],[f_623_3]) ).

fof(f_624_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_624_2,plain,
    ! [U_2527,U_2526] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2526),U_2527) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2526),hAPP(c_Groups_Ouminus__class_Ouminus(U_2526),c_Groups_Oone__class_Oone(U_2526))),U_2527)
      | ~ class_Rings_Ocomm__ring__1(U_2526) ),
    inference(variable_rename,[status(thm)],[f_624_1]) ).

fof(f_624_3,plain,
    ! [U_2527,U_2526] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2526),U_2527) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2526),hAPP(c_Groups_Ouminus__class_Ouminus(U_2526),c_Groups_Oone__class_Oone(U_2526))),U_2527)
      | ~ class_Rings_Ocomm__ring__1(U_2526) ),
    inference(definitional_conversion,[status(esa)],[f_624_2]) ).

cnf(f_624_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2526),U_2527) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2526),hAPP(c_Groups_Ouminus__class_Ouminus(U_2526),c_Groups_Oone__class_Oone(U_2526))),U_2527)
    | ~ class_Rings_Ocomm__ring__1(U_2526) ),
    inference(clausify,[status(thm)],[f_624_3]) ).

fof(f_625_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_625_2,plain,
    ! [U_2529,U_2528] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),hAPP(c_Groups_Ouminus__class_Ouminus(U_2528),U_2529)),U_2529))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),c_Groups_Ozero__class_Ozero(U_2528)),U_2529)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),c_Groups_Ozero__class_Ozero(U_2528)),U_2529))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),hAPP(c_Groups_Ouminus__class_Ouminus(U_2528),U_2529)),U_2529)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_2528) ),
    inference(variable_rename,[status(thm)],[f_625_1]) ).

fof(f_625_3,plain,
    ( ! [U_2528,U_2529] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),hAPP(c_Groups_Ouminus__class_Ouminus(U_2528),U_2529)),U_2529))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),c_Groups_Ozero__class_Ozero(U_2528)),U_2529))
        | ~ sP180(U_2528,U_2529) )
    & ! [U_2528,U_2529] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),c_Groups_Ozero__class_Ozero(U_2528)),U_2529))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),hAPP(c_Groups_Ouminus__class_Ouminus(U_2528),U_2529)),U_2529))
        | ~ sP180(U_2528,U_2529) )
    & ! [U_2528,U_2529] :
        ( sP180(U_2528,U_2529)
        | ~ class_Groups_Olinordered__ab__group__add(U_2528) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP180])],[f_625_2]) ).

cnf(f_625_4,plain,
    ( sP180(U_2528,U_2529)
    | ~ class_Groups_Olinordered__ab__group__add(U_2528) ),
    inference(clausify,[status(thm)],[f_625_3]) ).

cnf(f_625_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),c_Groups_Ozero__class_Ozero(U_2528)),U_2529))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),hAPP(c_Groups_Ouminus__class_Ouminus(U_2528),U_2529)),U_2529))
    | ~ sP180(U_2528,U_2529) ),
    inference(clausify,[status(thm)],[f_625_3]) ).

cnf(f_625_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),hAPP(c_Groups_Ouminus__class_Ouminus(U_2528),U_2529)),U_2529))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),c_Groups_Ozero__class_Ozero(U_2528)),U_2529))
    | ~ sP180(U_2528,U_2529) ),
    inference(clausify,[status(thm)],[f_625_3]) ).

fof(f_626_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_626_2,plain,
    ! [U_2531,U_2530] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2530),hAPP(c_Groups_Ouminus__class_Ouminus(U_2530),U_2531)),c_Groups_Ozero__class_Ozero(U_2530)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2530),c_Groups_Ozero__class_Ozero(U_2530)),U_2531)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2530),c_Groups_Ozero__class_Ozero(U_2530)),U_2531))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2530),hAPP(c_Groups_Ouminus__class_Ouminus(U_2530),U_2531)),c_Groups_Ozero__class_Ozero(U_2530))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2530) ),
    inference(variable_rename,[status(thm)],[f_626_1]) ).

fof(f_626_3,plain,
    ( ! [U_2530,U_2531] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2530),hAPP(c_Groups_Ouminus__class_Ouminus(U_2530),U_2531)),c_Groups_Ozero__class_Ozero(U_2530)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2530),c_Groups_Ozero__class_Ozero(U_2530)),U_2531))
        | ~ sP181(U_2530,U_2531) )
    & ! [U_2530,U_2531] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2530),c_Groups_Ozero__class_Ozero(U_2530)),U_2531))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2530),hAPP(c_Groups_Ouminus__class_Ouminus(U_2530),U_2531)),c_Groups_Ozero__class_Ozero(U_2530)))
        | ~ sP181(U_2530,U_2531) )
    & ! [U_2530,U_2531] :
        ( sP181(U_2530,U_2531)
        | ~ class_Groups_Oordered__ab__group__add(U_2530) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP181])],[f_626_2]) ).

cnf(f_626_4,plain,
    ( sP181(U_2530,U_2531)
    | ~ class_Groups_Oordered__ab__group__add(U_2530) ),
    inference(clausify,[status(thm)],[f_626_3]) ).

cnf(f_626_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2530),c_Groups_Ozero__class_Ozero(U_2530)),U_2531))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2530),hAPP(c_Groups_Ouminus__class_Ouminus(U_2530),U_2531)),c_Groups_Ozero__class_Ozero(U_2530)))
    | ~ sP181(U_2530,U_2531) ),
    inference(clausify,[status(thm)],[f_626_3]) ).

cnf(f_626_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2530),hAPP(c_Groups_Ouminus__class_Ouminus(U_2530),U_2531)),c_Groups_Ozero__class_Ozero(U_2530)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2530),c_Groups_Ozero__class_Ozero(U_2530)),U_2531))
    | ~ sP181(U_2530,U_2531) ),
    inference(clausify,[status(thm)],[f_626_3]) ).

fof(f_627_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_627_2,plain,
    ! [U_2533,U_2532] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2532),U_2533),hAPP(c_Groups_Ouminus__class_Ouminus(U_2532),U_2533)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2532),U_2533),c_Groups_Ozero__class_Ozero(U_2532))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2532),U_2533),c_Groups_Ozero__class_Ozero(U_2532)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2532),U_2533),hAPP(c_Groups_Ouminus__class_Ouminus(U_2532),U_2533))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_2532) ),
    inference(variable_rename,[status(thm)],[f_627_1]) ).

fof(f_627_3,plain,
    ( ! [U_2533,U_2532] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2532),U_2533),hAPP(c_Groups_Ouminus__class_Ouminus(U_2532),U_2533)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2532),U_2533),c_Groups_Ozero__class_Ozero(U_2532)))
        | ~ sP182(U_2533,U_2532) )
    & ! [U_2533,U_2532] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2532),U_2533),c_Groups_Ozero__class_Ozero(U_2532)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2532),U_2533),hAPP(c_Groups_Ouminus__class_Ouminus(U_2532),U_2533)))
        | ~ sP182(U_2533,U_2532) )
    & ! [U_2533,U_2532] :
        ( sP182(U_2533,U_2532)
        | ~ class_Groups_Olinordered__ab__group__add(U_2532) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP182])],[f_627_2]) ).

cnf(f_627_4,plain,
    ( sP182(U_2533,U_2532)
    | ~ class_Groups_Olinordered__ab__group__add(U_2532) ),
    inference(clausify,[status(thm)],[f_627_3]) ).

cnf(f_627_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2532),U_2533),c_Groups_Ozero__class_Ozero(U_2532)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2532),U_2533),hAPP(c_Groups_Ouminus__class_Ouminus(U_2532),U_2533)))
    | ~ sP182(U_2533,U_2532) ),
    inference(clausify,[status(thm)],[f_627_3]) ).

cnf(f_627_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2532),U_2533),hAPP(c_Groups_Ouminus__class_Ouminus(U_2532),U_2533)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2532),U_2533),c_Groups_Ozero__class_Ozero(U_2532)))
    | ~ sP182(U_2533,U_2532) ),
    inference(clausify,[status(thm)],[f_627_3]) ).

fof(f_628_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_628_2,plain,
    ! [U_2535,U_2534] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2534),c_Groups_Ozero__class_Ozero(U_2534)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2534),U_2535)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2534),U_2535),c_Groups_Ozero__class_Ozero(U_2534))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2534),U_2535),c_Groups_Ozero__class_Ozero(U_2534)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2534),c_Groups_Ozero__class_Ozero(U_2534)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2534),U_2535))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2534) ),
    inference(variable_rename,[status(thm)],[f_628_1]) ).

fof(f_628_3,plain,
    ( ! [U_2534,U_2535] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2534),c_Groups_Ozero__class_Ozero(U_2534)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2534),U_2535)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2534),U_2535),c_Groups_Ozero__class_Ozero(U_2534)))
        | ~ sP183(U_2534,U_2535) )
    & ! [U_2534,U_2535] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2534),U_2535),c_Groups_Ozero__class_Ozero(U_2534)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2534),c_Groups_Ozero__class_Ozero(U_2534)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2534),U_2535)))
        | ~ sP183(U_2534,U_2535) )
    & ! [U_2534,U_2535] :
        ( sP183(U_2534,U_2535)
        | ~ class_Groups_Oordered__ab__group__add(U_2534) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP183])],[f_628_2]) ).

cnf(f_628_4,plain,
    ( sP183(U_2534,U_2535)
    | ~ class_Groups_Oordered__ab__group__add(U_2534) ),
    inference(clausify,[status(thm)],[f_628_3]) ).

cnf(f_628_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2534),U_2535),c_Groups_Ozero__class_Ozero(U_2534)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2534),c_Groups_Ozero__class_Ozero(U_2534)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2534),U_2535)))
    | ~ sP183(U_2534,U_2535) ),
    inference(clausify,[status(thm)],[f_628_3]) ).

cnf(f_628_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2534),c_Groups_Ozero__class_Ozero(U_2534)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2534),U_2535)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2534),U_2535),c_Groups_Ozero__class_Ozero(U_2534)))
    | ~ sP183(U_2534,U_2535) ),
    inference(clausify,[status(thm)],[f_628_3]) ).

fof(f_629_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_629_2,plain,
    ! [U_2537,U_2536] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2536),U_2537) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2537 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2536 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( ( U_2537 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2536 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2536),U_2537) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_629_1]) ).

fof(f_629_3,plain,
    ( ! [U_2541,U_2539] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2539),U_2541) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2541 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2539 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_2540,U_2538] :
        ( ( U_2540 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2538 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2538),U_2540) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_629_2]) ).

fof(f_629_4,plain,
    ( ! [U_2540,U_2538] :
        ( U_2540 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP184(U_2540,U_2538) )
    & ! [U_2540,U_2538] :
        ( U_2538 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP184(U_2540,U_2538) )
    & ! [U_2541,U_2539] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2539),U_2541) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2541 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2539 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_2540,U_2538] :
        ( sP184(U_2540,U_2538)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2538),U_2540) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP184])],[f_629_3]) ).

cnf(f_629_5,plain,
    ( sP184(U_2540,U_2538)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2538),U_2540) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_629_4]) ).

cnf(f_629_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2539),U_2541) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_2541 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_2539 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_629_4]) ).

cnf(f_629_7,plain,
    ( U_2538 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP184(U_2540,U_2538) ),
    inference(clausify,[status(thm)],[f_629_4]) ).

cnf(f_629_8,plain,
    ( U_2540 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP184(U_2540,U_2538) ),
    inference(clausify,[status(thm)],[f_629_4]) ).

fof(f_630_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_630_2,plain,
    ! [U_2543,U_2542] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2542),c_Groups_Ozero__class_Ozero(U_2542)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2542),U_2543)))
      | ~ class_Rings_Olinordered__semidom(U_2542) ),
    inference(variable_rename,[status(thm)],[f_630_1]) ).

fof(f_630_3,plain,
    ! [U_2542,U_2543] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2542),c_Groups_Ozero__class_Ozero(U_2542)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2542),U_2543)))
      | ~ class_Rings_Olinordered__semidom(U_2542) ),
    inference(definitional_conversion,[status(esa)],[f_630_2]) ).

cnf(f_630_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2542),c_Groups_Ozero__class_Ozero(U_2542)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2542),U_2543)))
    | ~ class_Rings_Olinordered__semidom(U_2542) ),
    inference(clausify,[status(thm)],[f_630_3]) ).

fof(f_631_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_631_2,plain,
    ! [U_2545,U_2544] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2544),c_Groups_Ozero__class_Ozero(U_2544)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2544),U_2545)))
      | ~ class_Rings_Olinordered__semidom(U_2544) ),
    inference(variable_rename,[status(thm)],[f_631_1]) ).

fof(f_631_3,plain,
    ! [U_2544,U_2545] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2544),c_Groups_Ozero__class_Ozero(U_2544)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2544),U_2545)))
      | ~ class_Rings_Olinordered__semidom(U_2544) ),
    inference(definitional_conversion,[status(esa)],[f_631_2]) ).

cnf(f_631_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2544),c_Groups_Ozero__class_Ozero(U_2544)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2544),U_2545)))
    | ~ class_Rings_Olinordered__semidom(U_2544) ),
    inference(clausify,[status(thm)],[f_631_3]) ).

fof(f_632_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_632_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_2548),U_2546)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2548),U_2547)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2548))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2546),U_2547)) ),
    inference(variable_rename,[status(thm)],[f_632_1]) ).

fof(f_632_3,plain,
    ! [U_2546,U_2547,U_2548] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2548),U_2546)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2548),U_2547)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2548))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2546),U_2547)) ),
    inference(definitional_conversion,[status(esa)],[f_632_2]) ).

cnf(f_632_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2548),U_2546)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2548),U_2547)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2548))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2546),U_2547)) ),
    inference(clausify,[status(thm)],[f_632_3]) ).

fof(f_633_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_633_2,plain,
    ! [U_2551,U_2550,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_2550),U_2551)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2551))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2549),U_2550)) ),
    inference(variable_rename,[status(thm)],[f_633_1]) ).

fof(f_633_3,plain,
    ! [U_2549,U_2550,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_2550),U_2551)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2551))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2549),U_2550)) ),
    inference(definitional_conversion,[status(esa)],[f_633_2]) ).

cnf(f_633_4,plain,
    ( 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_2550),U_2551)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2551))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2549),U_2550)) ),
    inference(clausify,[status(thm)],[f_633_3]) ).

fof(f_634_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_634_2,plain,
    ! [U_2554,U_2553,U_2552] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2552),U_2553)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2554),U_2553)))
        | ~ 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_2553)) )
      & ( ( 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_2553)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2552),U_2553)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2554),U_2553))) ) ),
    inference(variable_rename,[status(thm)],[f_634_1]) ).

fof(f_634_3,plain,
    ( ! [U_2560,U_2558,U_2556] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2556),U_2558)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2558)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2556),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,U_2555] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2555),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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2555),U_2557)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2559),U_2557))) ) ),
    inference(miniscope,[status(thm)],[f_634_2]) ).

fof(f_634_4,plain,
    ( ! [U_2557,U_2555,U_2559] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2555),U_2559))
        | ~ sP185(U_2557,U_2555,U_2559) )
    & ! [U_2557,U_2555,U_2559] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2557))
        | ~ sP185(U_2557,U_2555,U_2559) )
    & ! [U_2558,U_2556,U_2560] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2556),U_2558)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2558)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2556),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_2555,U_2559] :
        ( sP185(U_2557,U_2555,U_2559)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2555),U_2557)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2559),U_2557))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP185])],[f_634_3]) ).

cnf(f_634_5,plain,
    ( sP185(U_2557,U_2555,U_2559)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2555),U_2557)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2559),U_2557))) ),
    inference(clausify,[status(thm)],[f_634_4]) ).

cnf(f_634_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2556),U_2558)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2558)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2556),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_634_4]) ).

cnf(f_634_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2557))
    | ~ sP185(U_2557,U_2555,U_2559) ),
    inference(clausify,[status(thm)],[f_634_4]) ).

cnf(f_634_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2555),U_2559))
    | ~ sP185(U_2557,U_2555,U_2559) ),
    inference(clausify,[status(thm)],[f_634_4]) ).

fof(f_635_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_635_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),U_2561),U_2562)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2561)) )
      & ( ( 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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2561)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2561),U_2562)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2561),U_2563))) ) ),
    inference(variable_rename,[status(thm)],[f_635_1]) ).

fof(f_635_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),U_2565),U_2567)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2565),U_2569)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2567),U_2569))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2565)) )
    & ! [U_2568,U_2566,U_2564] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2566),U_2568))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2564)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2564),U_2566)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2564),U_2568))) ) ),
    inference(miniscope,[status(thm)],[f_635_2]) ).

fof(f_635_4,plain,
    ( ! [U_2564,U_2566,U_2568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2566),U_2568))
        | ~ sP186(U_2564,U_2566,U_2568) )
    & ! [U_2564,U_2566,U_2568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2564))
        | ~ sP186(U_2564,U_2566,U_2568) )
    & ! [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),U_2565),U_2567)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2565),U_2569)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2567),U_2569))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2565)) )
    & ! [U_2564,U_2566,U_2568] :
        ( sP186(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),U_2564),U_2566)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2564),U_2568))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186])],[f_635_3]) ).

cnf(f_635_5,plain,
    ( sP186(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),U_2564),U_2566)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2564),U_2568))) ),
    inference(clausify,[status(thm)],[f_635_4]) ).

cnf(f_635_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2565),U_2567)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2565),U_2569)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2567),U_2569))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2565)) ),
    inference(clausify,[status(thm)],[f_635_4]) ).

cnf(f_635_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2564))
    | ~ sP186(U_2564,U_2566,U_2568) ),
    inference(clausify,[status(thm)],[f_635_4]) ).

cnf(f_635_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2566),U_2568))
    | ~ sP186(U_2564,U_2566,U_2568) ),
    inference(clausify,[status(thm)],[f_635_4]) ).

fof(f_636_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_636_2,plain,
    ! [U_2571,U_2570] :
      ( ( 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_2570),U_2571)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2571))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2570)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2571))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2570)) )
        | ~ 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_2570),U_2571))) ) ),
    inference(variable_rename,[status(thm)],[f_636_1]) ).

fof(f_636_3,plain,
    ( ! [U_2575,U_2573] :
        ( 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_2573),U_2575)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2575))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2573)) )
    & ! [U_2574,U_2572] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2574))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2572)) )
        | ~ 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_2572),U_2574))) ) ),
    inference(miniscope,[status(thm)],[f_636_2]) ).

fof(f_636_4,plain,
    ( ! [U_2572,U_2574] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2574))
        | ~ sP187(U_2572,U_2574) )
    & ! [U_2572,U_2574] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2572))
        | ~ sP187(U_2572,U_2574) )
    & ! [U_2575,U_2573] :
        ( 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_2573),U_2575)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2575))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2573)) )
    & ! [U_2572,U_2574] :
        ( sP187(U_2572,U_2574)
        | ~ 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_2572),U_2574))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP187])],[f_636_3]) ).

cnf(f_636_5,plain,
    ( sP187(U_2572,U_2574)
    | ~ 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_2572),U_2574))) ),
    inference(clausify,[status(thm)],[f_636_4]) ).

cnf(f_636_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_2573),U_2575)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2575))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2573)) ),
    inference(clausify,[status(thm)],[f_636_4]) ).

cnf(f_636_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2572))
    | ~ sP187(U_2572,U_2574) ),
    inference(clausify,[status(thm)],[f_636_4]) ).

cnf(f_636_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2574))
    | ~ sP187(U_2572,U_2574) ),
    inference(clausify,[status(thm)],[f_636_4]) ).

fof(f_637_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_637_2,plain,
    ! [U_2578,U_2577,U_2576] :
      ( ( 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_2576)),U_2577)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2576)),U_2578)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2577),U_2578)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2577),U_2578))
        | ~ 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_2576)),U_2577)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2576)),U_2578))) ) ),
    inference(variable_rename,[status(thm)],[f_637_1]) ).

fof(f_637_3,plain,
    ( ! [U_2584,U_2582] :
        ( ! [U_2580] : 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_2580)),U_2582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2580)),U_2584)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2582),U_2584)) )
    & ! [U_2583,U_2581] :
        ( ! [U_2579] : ~ 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_2579)),U_2581)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2579)),U_2583)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2581),U_2583)) ) ),
    inference(miniscope,[status(thm)],[f_637_2]) ).

fof(f_637_4,plain,
    ( ! [U_2584,U_2580,U_2582] :
        ( 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_2580)),U_2582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2580)),U_2584)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2582),U_2584)) )
    & ! [U_2579,U_2581,U_2583] :
        ( ~ 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_2579)),U_2581)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2579)),U_2583)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2581),U_2583)) ) ),
    inference(definitional_conversion,[status(esa)],[f_637_3]) ).

cnf(f_637_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_2579)),U_2581)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2579)),U_2583)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2581),U_2583)) ),
    inference(clausify,[status(thm)],[f_637_4]) ).

cnf(f_637_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_2580)),U_2582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2580)),U_2584)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2582),U_2584)) ),
    inference(clausify,[status(thm)],[f_637_4]) ).

fof(f_638_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_638_2,plain,
    ! [U_2586,U_2585] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2585)),U_2586) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2585),U_2586)),
    inference(variable_rename,[status(thm)],[f_638_1]) ).

fof(f_638_3,plain,
    ! [U_2585,U_2586] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2585)),U_2586) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2585),U_2586)),
    inference(definitional_conversion,[status(esa)],[f_638_2]) ).

cnf(f_638_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2585)),U_2586) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2585),U_2586)),
    inference(clausify,[status(thm)],[f_638_3]) ).

fof(f_639_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_639_2,plain,
    ! [U_2588,U_2587] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2587),hAPP(c_Nat_OSuc,U_2588)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2587),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2587),U_2588)),
    inference(variable_rename,[status(thm)],[f_639_1]) ).

fof(f_639_3,plain,
    ! [U_2587,U_2588] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2587),hAPP(c_Nat_OSuc,U_2588)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2587),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2587),U_2588)),
    inference(definitional_conversion,[status(esa)],[f_639_2]) ).

cnf(f_639_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2587),hAPP(c_Nat_OSuc,U_2588)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2587),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2587),U_2588)),
    inference(clausify,[status(thm)],[f_639_3]) ).

fof(f_640_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_640_2,plain,
    ! [U_2590,U_2589] :
      ( 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_2589),U_2590)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2590))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2589)) ),
    inference(variable_rename,[status(thm)],[f_640_1]) ).

fof(f_640_3,plain,
    ! [U_2589,U_2590] :
      ( 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_2589),U_2590)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2590))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2589)) ),
    inference(definitional_conversion,[status(esa)],[f_640_2]) ).

cnf(f_640_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_2589),U_2590)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2590))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2589)) ),
    inference(clausify,[status(thm)],[f_640_3]) ).

fof(f_641_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_641_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_641_1]) ).

cnf(f_641_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_641_2]) ).

fof(f_642_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_642_2,plain,
    ! [U_2591] : 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_2591))),
    inference(variable_rename,[status(thm)],[f_642_1]) ).

fof(f_642_3,plain,
    ! [U_2591] : 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_2591))),
    inference(definitional_conversion,[status(esa)],[f_642_2]) ).

cnf(f_642_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_2591))),
    inference(clausify,[status(thm)],[f_642_3]) ).

fof(f_643_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_643_2,plain,
    ! [U_2596] :
      ( ( ! [U_2595] :
            ( hBOOL(hAPP(U_2596,U_2595))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2595)) )
        | ? [U_2594] : ~ hBOOL(hAPP(U_2596,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2594))) )
      & ( ! [U_2593] : hBOOL(hAPP(U_2596,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2593)))
        | ? [U_2592] :
            ( ~ hBOOL(hAPP(U_2596,U_2592))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2592)) ) ) ),
    inference(variable_rename,[status(thm)],[f_643_1]) ).

fof(f_643_3,plain,
    ( ! [U_2598] :
        ( ! [U_2595] :
            ( hBOOL(hAPP(U_2598,U_2595))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2595)) )
        | ? [U_2594] : ~ hBOOL(hAPP(U_2598,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2594))) )
    & ! [U_2597] :
        ( ! [U_2593] : hBOOL(hAPP(U_2597,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2593)))
        | ? [U_2592] :
            ( ~ hBOOL(hAPP(U_2597,U_2592))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2592)) ) ) ),
    inference(miniscope,[status(thm)],[f_643_2]) ).

fof(f_643_4,plain,
    ( ! [U_2598] :
        ( ! [U_2595] :
            ( hBOOL(hAPP(U_2598,U_2595))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2595)) )
        | ? [U_2594] : ~ hBOOL(hAPP(U_2598,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2594))) )
    & ! [U_2597] :
        ( ! [U_2593] : hBOOL(hAPP(U_2597,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2593)))
        | ( ~ hBOOL(hAPP(U_2597,sK51(U_2597)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK51(U_2597))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_2592,sK51(U_2597))],[f_643_3]) ).

fof(f_643_5,plain,
    ( ! [U_2598] :
        ( ! [U_2595] :
            ( hBOOL(hAPP(U_2598,U_2595))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2595)) )
        | ~ hBOOL(hAPP(U_2598,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK52(U_2598)))) )
    & ! [U_2597] :
        ( ! [U_2593] : hBOOL(hAPP(U_2597,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2593)))
        | ( ~ hBOOL(hAPP(U_2597,sK51(U_2597)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK51(U_2597))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_2594,sK52(U_2598))],[f_643_4]) ).

fof(f_643_6,plain,
    ( ! [U_2597] :
        ( ~ hBOOL(hAPP(U_2597,sK51(U_2597)))
        | ~ sP188(U_2597) )
    & ! [U_2597] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK51(U_2597)))
        | ~ sP188(U_2597) )
    & ! [U_2595,U_2598] :
        ( hBOOL(hAPP(U_2598,U_2595))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2595))
        | ~ hBOOL(hAPP(U_2598,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK52(U_2598)))) )
    & ! [U_2593,U_2597] :
        ( hBOOL(hAPP(U_2597,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2593)))
        | sP188(U_2597) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP188])],[f_643_5]) ).

cnf(f_643_7,plain,
    ( hBOOL(hAPP(U_2597,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2593)))
    | sP188(U_2597) ),
    inference(clausify,[status(thm)],[f_643_6]) ).

cnf(f_643_8,plain,
    ( hBOOL(hAPP(U_2598,U_2595))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2595))
    | ~ hBOOL(hAPP(U_2598,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK52(U_2598)))) ),
    inference(clausify,[status(thm)],[f_643_6]) ).

cnf(f_643_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK51(U_2597)))
    | ~ sP188(U_2597) ),
    inference(clausify,[status(thm)],[f_643_6]) ).

cnf(f_643_10,plain,
    ( ~ hBOOL(hAPP(U_2597,sK51(U_2597)))
    | ~ sP188(U_2597) ),
    inference(clausify,[status(thm)],[f_643_6]) ).

fof(f_644_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_644_2,plain,
    ! [U_2603] :
      ( ( ? [U_2602] :
            ( hBOOL(hAPP(U_2603,U_2602))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2602)) )
        | ! [U_2601] : ~ hBOOL(hAPP(U_2603,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2601))) )
      & ( ? [U_2600] : hBOOL(hAPP(U_2603,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2600)))
        | ! [U_2599] :
            ( ~ hBOOL(hAPP(U_2603,U_2599))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2599)) ) ) ),
    inference(variable_rename,[status(thm)],[f_644_1]) ).

fof(f_644_3,plain,
    ( ! [U_2605] :
        ( ? [U_2602] :
            ( hBOOL(hAPP(U_2605,U_2602))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2602)) )
        | ! [U_2601] : ~ hBOOL(hAPP(U_2605,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2601))) )
    & ! [U_2604] :
        ( ? [U_2600] : hBOOL(hAPP(U_2604,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2600)))
        | ! [U_2599] :
            ( ~ hBOOL(hAPP(U_2604,U_2599))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2599)) ) ) ),
    inference(miniscope,[status(thm)],[f_644_2]) ).

fof(f_644_4,plain,
    ( ! [U_2605] :
        ( ? [U_2602] :
            ( hBOOL(hAPP(U_2605,U_2602))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2602)) )
        | ! [U_2601] : ~ hBOOL(hAPP(U_2605,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2601))) )
    & ! [U_2604] :
        ( hBOOL(hAPP(U_2604,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK53(U_2604))))
        | ! [U_2599] :
            ( ~ hBOOL(hAPP(U_2604,U_2599))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2599)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_2600,sK53(U_2604))],[f_644_3]) ).

fof(f_644_5,plain,
    ( ! [U_2605] :
        ( ( hBOOL(hAPP(U_2605,sK54(U_2605)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK54(U_2605))) )
        | ! [U_2601] : ~ hBOOL(hAPP(U_2605,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2601))) )
    & ! [U_2604] :
        ( hBOOL(hAPP(U_2604,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK53(U_2604))))
        | ! [U_2599] :
            ( ~ hBOOL(hAPP(U_2604,U_2599))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2599)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_2602,sK54(U_2605))],[f_644_4]) ).

fof(f_644_6,plain,
    ( ! [U_2605] :
        ( hBOOL(hAPP(U_2605,sK54(U_2605)))
        | ~ sP189(U_2605) )
    & ! [U_2605] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK54(U_2605)))
        | ~ sP189(U_2605) )
    & ! [U_2601,U_2605] :
        ( sP189(U_2605)
        | ~ hBOOL(hAPP(U_2605,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2601))) )
    & ! [U_2599,U_2604] :
        ( hBOOL(hAPP(U_2604,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK53(U_2604))))
        | ~ hBOOL(hAPP(U_2604,U_2599))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2599)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP189])],[f_644_5]) ).

cnf(f_644_7,plain,
    ( hBOOL(hAPP(U_2604,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK53(U_2604))))
    | ~ hBOOL(hAPP(U_2604,U_2599))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2599)) ),
    inference(clausify,[status(thm)],[f_644_6]) ).

cnf(f_644_8,plain,
    ( sP189(U_2605)
    | ~ hBOOL(hAPP(U_2605,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2601))) ),
    inference(clausify,[status(thm)],[f_644_6]) ).

cnf(f_644_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK54(U_2605)))
    | ~ sP189(U_2605) ),
    inference(clausify,[status(thm)],[f_644_6]) ).

cnf(f_644_10,plain,
    ( hBOOL(hAPP(U_2605,sK54(U_2605)))
    | ~ sP189(U_2605) ),
    inference(clausify,[status(thm)],[f_644_6]) ).

fof(f_645_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_645_2,plain,
    ! [U_2606] : 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_2606))),
    inference(variable_rename,[status(thm)],[f_645_1]) ).

fof(f_645_3,plain,
    ! [U_2606] : 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_2606))),
    inference(definitional_conversion,[status(esa)],[f_645_2]) ).

cnf(f_645_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_2606))),
    inference(clausify,[status(thm)],[f_645_3]) ).

fof(f_646_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_646_2,plain,
    ! [U_2608,U_2607] :
      ( ( ( hAPP(c_Int_Onat,U_2607) = hAPP(c_Int_Onat,U_2608)
          | U_2607 != U_2608 )
        & ( U_2607 = U_2608
          | hAPP(c_Int_Onat,U_2607) != hAPP(c_Int_Onat,U_2608) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2608))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2607)) ),
    inference(variable_rename,[status(thm)],[f_646_1]) ).

fof(f_646_3,plain,
    ( ! [U_2607,U_2608] :
        ( hAPP(c_Int_Onat,U_2607) = hAPP(c_Int_Onat,U_2608)
        | U_2607 != U_2608
        | ~ sP190(U_2607,U_2608) )
    & ! [U_2607,U_2608] :
        ( U_2607 = U_2608
        | hAPP(c_Int_Onat,U_2607) != hAPP(c_Int_Onat,U_2608)
        | ~ sP190(U_2607,U_2608) )
    & ! [U_2607,U_2608] :
        ( sP190(U_2607,U_2608)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2608))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2607)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP190])],[f_646_2]) ).

cnf(f_646_4,plain,
    ( sP190(U_2607,U_2608)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2608))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2607)) ),
    inference(clausify,[status(thm)],[f_646_3]) ).

cnf(f_646_5,plain,
    ( U_2607 = U_2608
    | hAPP(c_Int_Onat,U_2607) != hAPP(c_Int_Onat,U_2608)
    | ~ sP190(U_2607,U_2608) ),
    inference(clausify,[status(thm)],[f_646_3]) ).

cnf(f_646_6,plain,
    ( hAPP(c_Int_Onat,U_2607) = hAPP(c_Int_Onat,U_2608)
    | U_2607 != U_2608
    | ~ sP190(U_2607,U_2608) ),
    inference(clausify,[status(thm)],[f_646_3]) ).

fof(f_647_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_647_2,plain,
    ! [U_2610,U_2609] :
      ( ( ( hAPP(c_Int_Onat,U_2609) = hAPP(c_Int_Onat,U_2610)
          | U_2609 != U_2610 )
        & ( U_2609 = U_2610
          | hAPP(c_Int_Onat,U_2609) != hAPP(c_Int_Onat,U_2610) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2610))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2609)) ),
    inference(variable_rename,[status(thm)],[f_647_1]) ).

fof(f_647_3,plain,
    ( ! [U_2610,U_2609] :
        ( hAPP(c_Int_Onat,U_2609) = hAPP(c_Int_Onat,U_2610)
        | U_2609 != U_2610
        | ~ sP191(U_2610,U_2609) )
    & ! [U_2610,U_2609] :
        ( U_2609 = U_2610
        | hAPP(c_Int_Onat,U_2609) != hAPP(c_Int_Onat,U_2610)
        | ~ sP191(U_2610,U_2609) )
    & ! [U_2610,U_2609] :
        ( sP191(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_2610))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2609)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP191])],[f_647_2]) ).

cnf(f_647_4,plain,
    ( sP191(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_2610))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2609)) ),
    inference(clausify,[status(thm)],[f_647_3]) ).

cnf(f_647_5,plain,
    ( U_2609 = U_2610
    | hAPP(c_Int_Onat,U_2609) != hAPP(c_Int_Onat,U_2610)
    | ~ sP191(U_2610,U_2609) ),
    inference(clausify,[status(thm)],[f_647_3]) ).

cnf(f_647_6,plain,
    ( hAPP(c_Int_Onat,U_2609) = hAPP(c_Int_Onat,U_2610)
    | U_2609 != U_2610
    | ~ sP191(U_2610,U_2609) ),
    inference(clausify,[status(thm)],[f_647_3]) ).

fof(f_648_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_648_2,plain,
    ! [U_2615] :
      ( ( ! [U_2614] : hBOOL(hAPP(U_2615,U_2614))
        | ? [U_2613] :
            ( ~ hBOOL(hAPP(U_2615,hAPP(c_Int_Onat,U_2613)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2613)) ) )
      & ( ! [U_2612] :
            ( hBOOL(hAPP(U_2615,hAPP(c_Int_Onat,U_2612)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2612)) )
        | ? [U_2611] : ~ hBOOL(hAPP(U_2615,U_2611)) ) ),
    inference(variable_rename,[status(thm)],[f_648_1]) ).

fof(f_648_3,plain,
    ( ! [U_2617] :
        ( ! [U_2614] : hBOOL(hAPP(U_2617,U_2614))
        | ? [U_2613] :
            ( ~ hBOOL(hAPP(U_2617,hAPP(c_Int_Onat,U_2613)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2613)) ) )
    & ! [U_2616] :
        ( ! [U_2612] :
            ( hBOOL(hAPP(U_2616,hAPP(c_Int_Onat,U_2612)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2612)) )
        | ? [U_2611] : ~ hBOOL(hAPP(U_2616,U_2611)) ) ),
    inference(miniscope,[status(thm)],[f_648_2]) ).

fof(f_648_4,plain,
    ( ! [U_2617] :
        ( ! [U_2614] : hBOOL(hAPP(U_2617,U_2614))
        | ? [U_2613] :
            ( ~ hBOOL(hAPP(U_2617,hAPP(c_Int_Onat,U_2613)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2613)) ) )
    & ! [U_2616] :
        ( ! [U_2612] :
            ( hBOOL(hAPP(U_2616,hAPP(c_Int_Onat,U_2612)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2612)) )
        | ~ hBOOL(hAPP(U_2616,sK55(U_2616))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_2611,sK55(U_2616))],[f_648_3]) ).

fof(f_648_5,plain,
    ( ! [U_2617] :
        ( ! [U_2614] : hBOOL(hAPP(U_2617,U_2614))
        | ( ~ hBOOL(hAPP(U_2617,hAPP(c_Int_Onat,sK56(U_2617))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK56(U_2617))) ) )
    & ! [U_2616] :
        ( ! [U_2612] :
            ( hBOOL(hAPP(U_2616,hAPP(c_Int_Onat,U_2612)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2612)) )
        | ~ hBOOL(hAPP(U_2616,sK55(U_2616))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_2613,sK56(U_2617))],[f_648_4]) ).

fof(f_648_6,plain,
    ( ! [U_2617] :
        ( ~ hBOOL(hAPP(U_2617,hAPP(c_Int_Onat,sK56(U_2617))))
        | ~ sP192(U_2617) )
    & ! [U_2617] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK56(U_2617)))
        | ~ sP192(U_2617) )
    & ! [U_2614,U_2617] :
        ( hBOOL(hAPP(U_2617,U_2614))
        | sP192(U_2617) )
    & ! [U_2612,U_2616] :
        ( hBOOL(hAPP(U_2616,hAPP(c_Int_Onat,U_2612)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2612))
        | ~ hBOOL(hAPP(U_2616,sK55(U_2616))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP192])],[f_648_5]) ).

cnf(f_648_7,plain,
    ( hBOOL(hAPP(U_2616,hAPP(c_Int_Onat,U_2612)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2612))
    | ~ hBOOL(hAPP(U_2616,sK55(U_2616))) ),
    inference(clausify,[status(thm)],[f_648_6]) ).

cnf(f_648_8,plain,
    ( hBOOL(hAPP(U_2617,U_2614))
    | sP192(U_2617) ),
    inference(clausify,[status(thm)],[f_648_6]) ).

cnf(f_648_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK56(U_2617)))
    | ~ sP192(U_2617) ),
    inference(clausify,[status(thm)],[f_648_6]) ).

cnf(f_648_10,plain,
    ( ~ hBOOL(hAPP(U_2617,hAPP(c_Int_Onat,sK56(U_2617))))
    | ~ sP192(U_2617) ),
    inference(clausify,[status(thm)],[f_648_6]) ).

fof(f_649_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_649_2,plain,
    ! [U_2622] :
      ( ( ? [U_2621] : hBOOL(hAPP(U_2622,U_2621))
        | ! [U_2620] :
            ( ~ hBOOL(hAPP(U_2622,hAPP(c_Int_Onat,U_2620)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2620)) ) )
      & ( ? [U_2619] :
            ( hBOOL(hAPP(U_2622,hAPP(c_Int_Onat,U_2619)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2619)) )
        | ! [U_2618] : ~ hBOOL(hAPP(U_2622,U_2618)) ) ),
    inference(variable_rename,[status(thm)],[f_649_1]) ).

fof(f_649_3,plain,
    ( ! [U_2624] :
        ( ? [U_2621] : hBOOL(hAPP(U_2624,U_2621))
        | ! [U_2620] :
            ( ~ hBOOL(hAPP(U_2624,hAPP(c_Int_Onat,U_2620)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2620)) ) )
    & ! [U_2623] :
        ( ? [U_2619] :
            ( hBOOL(hAPP(U_2623,hAPP(c_Int_Onat,U_2619)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2619)) )
        | ! [U_2618] : ~ hBOOL(hAPP(U_2623,U_2618)) ) ),
    inference(miniscope,[status(thm)],[f_649_2]) ).

fof(f_649_4,plain,
    ( ! [U_2624] :
        ( ? [U_2621] : hBOOL(hAPP(U_2624,U_2621))
        | ! [U_2620] :
            ( ~ hBOOL(hAPP(U_2624,hAPP(c_Int_Onat,U_2620)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2620)) ) )
    & ! [U_2623] :
        ( ( hBOOL(hAPP(U_2623,hAPP(c_Int_Onat,sK57(U_2623))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK57(U_2623))) )
        | ! [U_2618] : ~ hBOOL(hAPP(U_2623,U_2618)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_2619,sK57(U_2623))],[f_649_3]) ).

fof(f_649_5,plain,
    ( ! [U_2624] :
        ( hBOOL(hAPP(U_2624,sK58(U_2624)))
        | ! [U_2620] :
            ( ~ hBOOL(hAPP(U_2624,hAPP(c_Int_Onat,U_2620)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2620)) ) )
    & ! [U_2623] :
        ( ( hBOOL(hAPP(U_2623,hAPP(c_Int_Onat,sK57(U_2623))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK57(U_2623))) )
        | ! [U_2618] : ~ hBOOL(hAPP(U_2623,U_2618)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_2621,sK58(U_2624))],[f_649_4]) ).

fof(f_649_6,plain,
    ( ! [U_2623] :
        ( hBOOL(hAPP(U_2623,hAPP(c_Int_Onat,sK57(U_2623))))
        | ~ sP193(U_2623) )
    & ! [U_2623] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK57(U_2623)))
        | ~ sP193(U_2623) )
    & ! [U_2620,U_2624] :
        ( hBOOL(hAPP(U_2624,sK58(U_2624)))
        | ~ hBOOL(hAPP(U_2624,hAPP(c_Int_Onat,U_2620)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2620)) )
    & ! [U_2618,U_2623] :
        ( sP193(U_2623)
        | ~ hBOOL(hAPP(U_2623,U_2618)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP193])],[f_649_5]) ).

cnf(f_649_7,plain,
    ( sP193(U_2623)
    | ~ hBOOL(hAPP(U_2623,U_2618)) ),
    inference(clausify,[status(thm)],[f_649_6]) ).

cnf(f_649_8,plain,
    ( hBOOL(hAPP(U_2624,sK58(U_2624)))
    | ~ hBOOL(hAPP(U_2624,hAPP(c_Int_Onat,U_2620)))
    | ~ 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_649_6]) ).

cnf(f_649_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK57(U_2623)))
    | ~ sP193(U_2623) ),
    inference(clausify,[status(thm)],[f_649_6]) ).

cnf(f_649_10,plain,
    ( hBOOL(hAPP(U_2623,hAPP(c_Int_Onat,sK57(U_2623))))
    | ~ sP193(U_2623) ),
    inference(clausify,[status(thm)],[f_649_6]) ).

fof(f_650_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_650_2,plain,
    ! [U_2628,U_2627,U_2626,U_2625] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2625),U_2627)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2626),U_2628)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2627),U_2628))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2625),U_2626)) ),
    inference(variable_rename,[status(thm)],[f_650_1]) ).

fof(f_650_3,plain,
    ! [U_2626,U_2627,U_2628,U_2625] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2625),U_2627)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2626),U_2628)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2627),U_2628))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2625),U_2626)) ),
    inference(definitional_conversion,[status(esa)],[f_650_2]) ).

cnf(f_650_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2625),U_2627)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2626),U_2628)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2627),U_2628))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2625),U_2626)) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

fof(f_651_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_651_2,plain,
    ! [U_2630,U_2629] :
      ( 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_2629),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(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2629)) ),
    inference(variable_rename,[status(thm)],[f_651_1]) ).

fof(f_651_3,plain,
    ! [U_2629,U_2630] :
      ( 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_2629),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(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2629)) ),
    inference(definitional_conversion,[status(esa)],[f_651_2]) ).

cnf(f_651_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_2629),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(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2629)) ),
    inference(clausify,[status(thm)],[f_651_3]) ).

fof(f_652_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_652_2,plain,
    ! [U_2631] : 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_2631)),U_2631) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_652_1]) ).

fof(f_652_3,plain,
    ! [U_2631] : 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_2631)),U_2631) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_652_2]) ).

cnf(f_652_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_2631)),U_2631) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_652_3]) ).

fof(f_653_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_653_2,plain,
    ! [U_2633,U_2632] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2632),U_2633)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2632)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2633)),
    inference(variable_rename,[status(thm)],[f_653_1]) ).

fof(f_653_3,plain,
    ! [U_2632,U_2633] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2632),U_2633)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2632)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2633)),
    inference(definitional_conversion,[status(esa)],[f_653_2]) ).

cnf(f_653_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2632),U_2633)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2632)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2633)),
    inference(clausify,[status(thm)],[f_653_3]) ).

fof(f_654_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_654_2,plain,
    ! [U_2635,U_2634] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2634)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2635)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2634),U_2635)),
    inference(variable_rename,[status(thm)],[f_654_1]) ).

fof(f_654_3,plain,
    ! [U_2634,U_2635] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2634)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2635)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2634),U_2635)),
    inference(definitional_conversion,[status(esa)],[f_654_2]) ).

cnf(f_654_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2634)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2635)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2634),U_2635)),
    inference(clausify,[status(thm)],[f_654_3]) ).

fof(f_655_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_655_2,plain,
    ! [U_2637,U_2636] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2636)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2637)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2636),U_2637)),
    inference(variable_rename,[status(thm)],[f_655_1]) ).

fof(f_655_3,plain,
    ! [U_2636,U_2637] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2636)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2637)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2636),U_2637)),
    inference(definitional_conversion,[status(esa)],[f_655_2]) ).

cnf(f_655_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2636)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2637)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2636),U_2637)),
    inference(clausify,[status(thm)],[f_655_3]) ).

fof(f_656_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_656_2,plain,
    ! [U_2639,U_2638] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2638),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2639),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ( U_2638 != U_2639
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2638),U_2639)) ) )
      & ( U_2638 = U_2639
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2638),U_2639))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2638),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2639),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_656_1]) ).

fof(f_656_3,plain,
    ( ! [U_2643,U_2641] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2643),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ( U_2641 != U_2643
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2641),U_2643)) ) )
    & ! [U_2642,U_2640] :
        ( U_2640 = U_2642
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2640),U_2642))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2640),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2642),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_656_2]) ).

fof(f_656_4,plain,
    ( ! [U_2643,U_2641] :
        ( U_2641 != U_2643
        | ~ sP194(U_2643,U_2641) )
    & ! [U_2643,U_2641] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2641),U_2643))
        | ~ sP194(U_2643,U_2641) )
    & ! [U_2643,U_2641] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2643),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | sP194(U_2643,U_2641) )
    & ! [U_2642,U_2640] :
        ( U_2640 = U_2642
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2640),U_2642))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2640),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2642),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP194])],[f_656_3]) ).

cnf(f_656_5,plain,
    ( U_2640 = U_2642
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2640),U_2642))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2640),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2642),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_656_4]) ).

cnf(f_656_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2643),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | sP194(U_2643,U_2641) ),
    inference(clausify,[status(thm)],[f_656_4]) ).

cnf(f_656_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2641),U_2643))
    | ~ sP194(U_2643,U_2641) ),
    inference(clausify,[status(thm)],[f_656_4]) ).

cnf(f_656_8,plain,
    ( U_2641 != U_2643
    | ~ sP194(U_2643,U_2641) ),
    inference(clausify,[status(thm)],[f_656_4]) ).

fof(f_657_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_657_2,plain,
    ! [U_2647,U_2646] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2646),U_2647))
        | ! [U_2645] : U_2647 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2646),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2645)) )
      & ( ? [U_2644] : U_2647 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2646),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2644))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2646),U_2647)) ) ),
    inference(variable_rename,[status(thm)],[f_657_1]) ).

fof(f_657_3,plain,
    ( ! [U_2651,U_2649] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2649),U_2651))
        | ! [U_2645] : U_2651 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2649),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2645)) )
    & ! [U_2650,U_2648] :
        ( ? [U_2644] : U_2650 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2648),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2644))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2648),U_2650)) ) ),
    inference(miniscope,[status(thm)],[f_657_2]) ).

fof(f_657_4,plain,
    ( ! [U_2651,U_2649] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2649),U_2651))
        | ! [U_2645] : U_2651 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2649),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2645)) )
    & ! [U_2650,U_2648] :
        ( U_2650 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2648),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK59(U_2650,U_2648)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2648),U_2650)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_2644,sK59(U_2650,U_2648))],[f_657_3]) ).

fof(f_657_5,plain,
    ( ! [U_2645,U_2651,U_2649] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2649),U_2651))
        | U_2651 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2649),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2645)) )
    & ! [U_2650,U_2648] :
        ( U_2650 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2648),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK59(U_2650,U_2648)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2648),U_2650)) ) ),
    inference(definitional_conversion,[status(esa)],[f_657_4]) ).

cnf(f_657_6,plain,
    ( U_2650 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2648),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK59(U_2650,U_2648)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2648),U_2650)) ),
    inference(clausify,[status(thm)],[f_657_5]) ).

cnf(f_657_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2649),U_2651))
    | U_2651 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2649),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2645)) ),
    inference(clausify,[status(thm)],[f_657_5]) ).

fof(f_658_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_658_2,plain,
    ! [U_2652] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2652),c_Groups_Ozero__class_Ozero(U_2652)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2652),c_Groups_Oone__class_Oone(U_2652)),c_Groups_Oone__class_Oone(U_2652))))
      | ~ class_Rings_Olinordered__semidom(U_2652) ),
    inference(variable_rename,[status(thm)],[f_658_1]) ).

fof(f_658_3,plain,
    ! [U_2652] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2652),c_Groups_Ozero__class_Ozero(U_2652)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2652),c_Groups_Oone__class_Oone(U_2652)),c_Groups_Oone__class_Oone(U_2652))))
      | ~ class_Rings_Olinordered__semidom(U_2652) ),
    inference(definitional_conversion,[status(esa)],[f_658_2]) ).

cnf(f_658_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2652),c_Groups_Ozero__class_Ozero(U_2652)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2652),c_Groups_Oone__class_Oone(U_2652)),c_Groups_Oone__class_Oone(U_2652))))
    | ~ class_Rings_Olinordered__semidom(U_2652) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

fof(f_659_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_659_2,plain,
    ! [U_2655,U_2654,U_2653] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2653),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2653),U_2654),U_2655)),c_Groups_Ozero__class_Ozero(U_2653)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2653),U_2655),c_Groups_Ozero__class_Ozero(U_2653)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2653),U_2654),c_Groups_Ozero__class_Ozero(U_2653)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2653) ),
    inference(variable_rename,[status(thm)],[f_659_1]) ).

fof(f_659_3,plain,
    ! [U_2653,U_2654,U_2655] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2653),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2653),U_2654),U_2655)),c_Groups_Ozero__class_Ozero(U_2653)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2653),U_2655),c_Groups_Ozero__class_Ozero(U_2653)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2653),U_2654),c_Groups_Ozero__class_Ozero(U_2653)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2653) ),
    inference(definitional_conversion,[status(esa)],[f_659_2]) ).

cnf(f_659_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2653),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2653),U_2654),U_2655)),c_Groups_Ozero__class_Ozero(U_2653)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2653),U_2655),c_Groups_Ozero__class_Ozero(U_2653)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2653),U_2654),c_Groups_Ozero__class_Ozero(U_2653)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2653) ),
    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(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_660_2,plain,
    ! [U_2658,U_2657,U_2656] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2656),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2656),U_2657),U_2658)),c_Groups_Ozero__class_Ozero(U_2656)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2656),U_2658),c_Groups_Ozero__class_Ozero(U_2656)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2656),U_2657),c_Groups_Ozero__class_Ozero(U_2656)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2656) ),
    inference(variable_rename,[status(thm)],[f_660_1]) ).

fof(f_660_3,plain,
    ! [U_2656,U_2657,U_2658] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2656),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2656),U_2657),U_2658)),c_Groups_Ozero__class_Ozero(U_2656)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2656),U_2658),c_Groups_Ozero__class_Ozero(U_2656)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2656),U_2657),c_Groups_Ozero__class_Ozero(U_2656)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2656) ),
    inference(definitional_conversion,[status(esa)],[f_660_2]) ).

cnf(f_660_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2656),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2656),U_2657),U_2658)),c_Groups_Ozero__class_Ozero(U_2656)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2656),U_2658),c_Groups_Ozero__class_Ozero(U_2656)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2656),U_2657),c_Groups_Ozero__class_Ozero(U_2656)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2656) ),
    inference(clausify,[status(thm)],[f_660_3]) ).

fof(f_661_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_661_2,plain,
    ! [U_2662,U_2661,U_2660,U_2659] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2659),U_2661),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2659),U_2660),U_2662)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2659),U_2661),U_2662))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2659),c_Groups_Ozero__class_Ozero(U_2659)),U_2660))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2659) ),
    inference(variable_rename,[status(thm)],[f_661_1]) ).

fof(f_661_3,plain,
    ! [U_2659,U_2660,U_2661,U_2662] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2659),U_2661),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2659),U_2660),U_2662)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2659),U_2661),U_2662))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2659),c_Groups_Ozero__class_Ozero(U_2659)),U_2660))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2659) ),
    inference(definitional_conversion,[status(esa)],[f_661_2]) ).

cnf(f_661_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2659),U_2661),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2659),U_2660),U_2662)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2659),U_2661),U_2662))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2659),c_Groups_Ozero__class_Ozero(U_2659)),U_2660))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2659) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

fof(f_662_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_662_2,plain,
    ! [U_2666,U_2665,U_2664,U_2663] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2663),U_2665),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2663),U_2664),U_2666)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2663),U_2665),U_2666))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2663),c_Groups_Ozero__class_Ozero(U_2663)),U_2664))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2663) ),
    inference(variable_rename,[status(thm)],[f_662_1]) ).

fof(f_662_3,plain,
    ! [U_2663,U_2664,U_2665,U_2666] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2663),U_2665),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2663),U_2664),U_2666)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2663),U_2665),U_2666))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2663),c_Groups_Ozero__class_Ozero(U_2663)),U_2664))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2663) ),
    inference(definitional_conversion,[status(esa)],[f_662_2]) ).

cnf(f_662_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2663),U_2665),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2663),U_2664),U_2666)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2663),U_2665),U_2666))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2663),c_Groups_Ozero__class_Ozero(U_2663)),U_2664))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2663) ),
    inference(clausify,[status(thm)],[f_662_3]) ).

fof(f_663_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_663_2,plain,
    ! [U_2669,U_2668,U_2667] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2667),c_Groups_Ozero__class_Ozero(U_2667)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2667),U_2668),U_2669)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2667),c_Groups_Ozero__class_Ozero(U_2667)),U_2669))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2667),c_Groups_Ozero__class_Ozero(U_2667)),U_2668))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2667) ),
    inference(variable_rename,[status(thm)],[f_663_1]) ).

fof(f_663_3,plain,
    ! [U_2667,U_2668,U_2669] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2667),c_Groups_Ozero__class_Ozero(U_2667)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2667),U_2668),U_2669)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2667),c_Groups_Ozero__class_Ozero(U_2667)),U_2669))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2667),c_Groups_Ozero__class_Ozero(U_2667)),U_2668))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2667) ),
    inference(definitional_conversion,[status(esa)],[f_663_2]) ).

cnf(f_663_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2667),c_Groups_Ozero__class_Ozero(U_2667)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2667),U_2668),U_2669)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2667),c_Groups_Ozero__class_Ozero(U_2667)),U_2669))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2667),c_Groups_Ozero__class_Ozero(U_2667)),U_2668))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2667) ),
    inference(clausify,[status(thm)],[f_663_3]) ).

fof(f_664_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_664_2,plain,
    ! [U_2672,U_2671,U_2670] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2670),c_Groups_Ozero__class_Ozero(U_2670)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2670),U_2671),U_2672)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2670),c_Groups_Ozero__class_Ozero(U_2670)),U_2672))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2670),c_Groups_Ozero__class_Ozero(U_2670)),U_2671))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2670) ),
    inference(variable_rename,[status(thm)],[f_664_1]) ).

fof(f_664_3,plain,
    ! [U_2670,U_2671,U_2672] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2670),c_Groups_Ozero__class_Ozero(U_2670)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2670),U_2671),U_2672)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2670),c_Groups_Ozero__class_Ozero(U_2670)),U_2672))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2670),c_Groups_Ozero__class_Ozero(U_2670)),U_2671))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2670) ),
    inference(definitional_conversion,[status(esa)],[f_664_2]) ).

cnf(f_664_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2670),c_Groups_Ozero__class_Ozero(U_2670)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2670),U_2671),U_2672)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2670),c_Groups_Ozero__class_Ozero(U_2670)),U_2672))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2670),c_Groups_Ozero__class_Ozero(U_2670)),U_2671))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2670) ),
    inference(clausify,[status(thm)],[f_664_3]) ).

fof(f_665_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_665_2,plain,
    ! [U_2676,U_2675,U_2674,U_2673] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2673),U_2674),U_2675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2673),U_2674),U_2676)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2673),U_2675),U_2676)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2673),U_2675),U_2676))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2673),U_2674),U_2675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2673),U_2674),U_2676))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2673),c_Groups_Ozero__class_Ozero(U_2673)),U_2674))
      | ~ class_Rings_Olinordered__ring__strict(U_2673) ),
    inference(variable_rename,[status(thm)],[f_665_1]) ).

fof(f_665_3,plain,
    ( ! [U_2673,U_2674,U_2675,U_2676] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2673),U_2674),U_2675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2673),U_2674),U_2676)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2673),U_2675),U_2676))
        | ~ sP195(U_2673,U_2674,U_2675,U_2676) )
    & ! [U_2673,U_2674,U_2675,U_2676] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2673),U_2675),U_2676))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2673),U_2674),U_2675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2673),U_2674),U_2676)))
        | ~ sP195(U_2673,U_2674,U_2675,U_2676) )
    & ! [U_2673,U_2674,U_2675,U_2676] :
        ( sP195(U_2673,U_2674,U_2675,U_2676)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2673),c_Groups_Ozero__class_Ozero(U_2673)),U_2674))
        | ~ class_Rings_Olinordered__ring__strict(U_2673) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP195])],[f_665_2]) ).

cnf(f_665_4,plain,
    ( sP195(U_2673,U_2674,U_2675,U_2676)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2673),c_Groups_Ozero__class_Ozero(U_2673)),U_2674))
    | ~ class_Rings_Olinordered__ring__strict(U_2673) ),
    inference(clausify,[status(thm)],[f_665_3]) ).

cnf(f_665_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2673),U_2675),U_2676))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2673),U_2674),U_2675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2673),U_2674),U_2676)))
    | ~ sP195(U_2673,U_2674,U_2675,U_2676) ),
    inference(clausify,[status(thm)],[f_665_3]) ).

cnf(f_665_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2673),U_2674),U_2675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2673),U_2674),U_2676)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2673),U_2675),U_2676))
    | ~ sP195(U_2673,U_2674,U_2675,U_2676) ),
    inference(clausify,[status(thm)],[f_665_3]) ).

fof(f_666_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_666_2,plain,
    ! [U_2680,U_2679,U_2678,U_2677] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2678),U_2679)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2678),U_2680)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2677),U_2680),U_2679)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2677),U_2680),U_2679))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2678),U_2679)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2678),U_2680))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2677),U_2678),c_Groups_Ozero__class_Ozero(U_2677)))
      | ~ class_Rings_Olinordered__ring__strict(U_2677) ),
    inference(variable_rename,[status(thm)],[f_666_1]) ).

fof(f_666_3,plain,
    ( ! [U_2677,U_2678,U_2679,U_2680] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2678),U_2679)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2678),U_2680)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2677),U_2680),U_2679))
        | ~ sP196(U_2677,U_2678,U_2679,U_2680) )
    & ! [U_2677,U_2678,U_2679,U_2680] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2677),U_2680),U_2679))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2678),U_2679)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2678),U_2680)))
        | ~ sP196(U_2677,U_2678,U_2679,U_2680) )
    & ! [U_2677,U_2678,U_2679,U_2680] :
        ( sP196(U_2677,U_2678,U_2679,U_2680)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2677),U_2678),c_Groups_Ozero__class_Ozero(U_2677)))
        | ~ class_Rings_Olinordered__ring__strict(U_2677) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP196])],[f_666_2]) ).

cnf(f_666_4,plain,
    ( sP196(U_2677,U_2678,U_2679,U_2680)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2677),U_2678),c_Groups_Ozero__class_Ozero(U_2677)))
    | ~ class_Rings_Olinordered__ring__strict(U_2677) ),
    inference(clausify,[status(thm)],[f_666_3]) ).

cnf(f_666_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2677),U_2680),U_2679))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2678),U_2679)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2678),U_2680)))
    | ~ sP196(U_2677,U_2678,U_2679,U_2680) ),
    inference(clausify,[status(thm)],[f_666_3]) ).

cnf(f_666_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2678),U_2679)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2678),U_2680)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2677),U_2680),U_2679))
    | ~ sP196(U_2677,U_2678,U_2679,U_2680) ),
    inference(clausify,[status(thm)],[f_666_3]) ).

fof(f_667_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_667_2,plain,
    ! [U_2685,U_2684,U_2683,U_2682,U_2681] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2681),U_2682),U_2684)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2681),U_2683),U_2685)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2681),c_Groups_Ozero__class_Ozero(U_2681)),U_2684))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2681),c_Groups_Ozero__class_Ozero(U_2681)),U_2683))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2681),U_2684),U_2685))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2681),U_2682),U_2683))
      | ~ class_Rings_Olinordered__semiring__strict(U_2681) ),
    inference(variable_rename,[status(thm)],[f_667_1]) ).

fof(f_667_3,plain,
    ! [U_2684,U_2682,U_2683,U_2681,U_2685] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2681),U_2682),U_2684)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2681),U_2683),U_2685)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2681),c_Groups_Ozero__class_Ozero(U_2681)),U_2684))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2681),c_Groups_Ozero__class_Ozero(U_2681)),U_2683))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2681),U_2684),U_2685))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2681),U_2682),U_2683))
      | ~ class_Rings_Olinordered__semiring__strict(U_2681) ),
    inference(definitional_conversion,[status(esa)],[f_667_2]) ).

cnf(f_667_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2681),U_2682),U_2684)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2681),U_2683),U_2685)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2681),c_Groups_Ozero__class_Ozero(U_2681)),U_2684))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2681),c_Groups_Ozero__class_Ozero(U_2681)),U_2683))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2681),U_2684),U_2685))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2681),U_2682),U_2683))
    | ~ class_Rings_Olinordered__semiring__strict(U_2681) ),
    inference(clausify,[status(thm)],[f_667_3]) ).

fof(f_668_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_668_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__eq(U_2686),c_Groups_Ozero__class_Ozero(U_2686)),U_2687))
      | ~ 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_668_1]) ).

fof(f_668_3,plain,
    ! [U_2689,U_2686,U_2688,U_2687,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__eq(U_2686),c_Groups_Ozero__class_Ozero(U_2686)),U_2687))
      | ~ 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_668_2]) ).

cnf(f_668_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__eq(U_2686),c_Groups_Ozero__class_Ozero(U_2686)),U_2687))
    | ~ 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_668_3]) ).

fof(f_669_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_669_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(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__eq(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_669_1]) ).

fof(f_669_3,plain,
    ! [U_2693,U_2692,U_2691,U_2694,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(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__eq(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_669_2]) ).

cnf(f_669_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(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__eq(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_669_3]) ).

fof(f_670_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_670_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__eq(U_2696),c_Groups_Ozero__class_Ozero(U_2696)),U_2699))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2696),c_Groups_Ozero__class_Ozero(U_2696)),U_2697))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2696),U_2699),U_2700))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2696),U_2697),U_2698))
      | ~ class_Rings_Olinordered__semiring__strict(U_2696) ),
    inference(variable_rename,[status(thm)],[f_670_1]) ).

fof(f_670_3,plain,
    ! [U_2698,U_2697,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__eq(U_2696),c_Groups_Ozero__class_Ozero(U_2696)),U_2699))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2696),c_Groups_Ozero__class_Ozero(U_2696)),U_2697))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2696),U_2699),U_2700))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2696),U_2697),U_2698))
      | ~ class_Rings_Olinordered__semiring__strict(U_2696) ),
    inference(definitional_conversion,[status(esa)],[f_670_2]) ).

cnf(f_670_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__eq(U_2696),c_Groups_Ozero__class_Ozero(U_2696)),U_2699))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2696),c_Groups_Ozero__class_Ozero(U_2696)),U_2697))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2696),U_2699),U_2700))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2696),U_2697),U_2698))
    | ~ class_Rings_Olinordered__semiring__strict(U_2696) ),
    inference(clausify,[status(thm)],[f_670_3]) ).

fof(f_671_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_671_2,plain,
    ! [U_2704,U_2703,U_2702,U_2701] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2701),U_2702),U_2704))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2701),c_Groups_Ozero__class_Ozero(U_2701)),U_2703))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2701),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2701),U_2702),U_2703)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2701),U_2704),U_2703)))
      | ~ class_Rings_Olinordered__semiring(U_2701) ),
    inference(variable_rename,[status(thm)],[f_671_1]) ).

fof(f_671_3,plain,
    ! [U_2702,U_2703,U_2704,U_2701] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2701),U_2702),U_2704))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2701),c_Groups_Ozero__class_Ozero(U_2701)),U_2703))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2701),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2701),U_2702),U_2703)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2701),U_2704),U_2703)))
      | ~ class_Rings_Olinordered__semiring(U_2701) ),
    inference(definitional_conversion,[status(esa)],[f_671_2]) ).

cnf(f_671_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2701),U_2702),U_2704))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2701),c_Groups_Ozero__class_Ozero(U_2701)),U_2703))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2701),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2701),U_2702),U_2703)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2701),U_2704),U_2703)))
    | ~ class_Rings_Olinordered__semiring(U_2701) ),
    inference(clausify,[status(thm)],[f_671_3]) ).

fof(f_672_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_672_2,plain,
    ! [U_2708,U_2707,U_2706,U_2705] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2705),U_2706),U_2708))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2705),c_Groups_Ozero__class_Ozero(U_2705)),U_2707))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2705),U_2706),U_2707)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2705),U_2708),U_2707)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2705) ),
    inference(variable_rename,[status(thm)],[f_672_1]) ).

fof(f_672_3,plain,
    ! [U_2705,U_2706,U_2707,U_2708] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2705),U_2706),U_2708))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2705),c_Groups_Ozero__class_Ozero(U_2705)),U_2707))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2705),U_2706),U_2707)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2705),U_2708),U_2707)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2705) ),
    inference(definitional_conversion,[status(esa)],[f_672_2]) ).

cnf(f_672_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2705),U_2706),U_2708))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2705),c_Groups_Ozero__class_Ozero(U_2705)),U_2707))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2705),U_2706),U_2707)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2705),U_2708),U_2707)))
    | ~ class_Rings_Olinordered__semiring__strict(U_2705) ),
    inference(clausify,[status(thm)],[f_672_3]) ).

fof(f_673_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_673_2,plain,
    ! [U_2712,U_2711,U_2710,U_2709] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2709),U_2711),U_2712))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2709),c_Groups_Ozero__class_Ozero(U_2709)),U_2710))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2709),U_2710),U_2711)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2709),U_2710),U_2712)))
      | ~ class_Rings_Olinordered__semiring(U_2709) ),
    inference(variable_rename,[status(thm)],[f_673_1]) ).

fof(f_673_3,plain,
    ! [U_2709,U_2710,U_2711,U_2712] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2709),U_2711),U_2712))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2709),c_Groups_Ozero__class_Ozero(U_2709)),U_2710))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2709),U_2710),U_2711)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2709),U_2710),U_2712)))
      | ~ class_Rings_Olinordered__semiring(U_2709) ),
    inference(definitional_conversion,[status(esa)],[f_673_2]) ).

cnf(f_673_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2709),U_2711),U_2712))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2709),c_Groups_Ozero__class_Ozero(U_2709)),U_2710))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2709),U_2710),U_2711)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2709),U_2710),U_2712)))
    | ~ class_Rings_Olinordered__semiring(U_2709) ),
    inference(clausify,[status(thm)],[f_673_3]) ).

fof(f_674_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_674_2,plain,
    ! [U_2716,U_2715,U_2714,U_2713] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2713),U_2715),U_2716))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2713),c_Groups_Ozero__class_Ozero(U_2713)),U_2714))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2713),U_2714),U_2715)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2713),U_2714),U_2716)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2713) ),
    inference(variable_rename,[status(thm)],[f_674_1]) ).

fof(f_674_3,plain,
    ! [U_2713,U_2714,U_2715,U_2716] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2713),U_2715),U_2716))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2713),c_Groups_Ozero__class_Ozero(U_2713)),U_2714))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2713),U_2714),U_2715)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2713),U_2714),U_2716)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2713) ),
    inference(definitional_conversion,[status(esa)],[f_674_2]) ).

cnf(f_674_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2713),U_2715),U_2716))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2713),c_Groups_Ozero__class_Ozero(U_2713)),U_2714))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2713),U_2714),U_2715)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2713),U_2714),U_2716)))
    | ~ class_Rings_Olinordered__semiring__strict(U_2713) ),
    inference(clausify,[status(thm)],[f_674_3]) ).

fof(f_675_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_675_2,plain,
    ! [U_2720,U_2719,U_2718,U_2717] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2717),U_2718),U_2720))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2717),c_Groups_Ozero__class_Ozero(U_2717)),U_2719))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2717),U_2718),U_2719)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2717),U_2720),U_2719)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2717) ),
    inference(variable_rename,[status(thm)],[f_675_1]) ).

fof(f_675_3,plain,
    ! [U_2717,U_2718,U_2719,U_2720] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2717),U_2718),U_2720))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2717),c_Groups_Ozero__class_Ozero(U_2717)),U_2719))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2717),U_2718),U_2719)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2717),U_2720),U_2719)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2717) ),
    inference(definitional_conversion,[status(esa)],[f_675_2]) ).

cnf(f_675_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2717),U_2718),U_2720))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2717),c_Groups_Ozero__class_Ozero(U_2717)),U_2719))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2717),U_2718),U_2719)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2717),U_2720),U_2719)))
    | ~ class_Rings_Olinordered__semiring__strict(U_2717) ),
    inference(clausify,[status(thm)],[f_675_3]) ).

fof(f_676_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_676_2,plain,
    ! [U_2724,U_2723,U_2722,U_2721] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2721),U_2723),U_2724))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),c_Groups_Ozero__class_Ozero(U_2721)),U_2722))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2721),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2721),U_2722),U_2723)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2721),U_2722),U_2724)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2721) ),
    inference(variable_rename,[status(thm)],[f_676_1]) ).

fof(f_676_3,plain,
    ! [U_2721,U_2722,U_2723,U_2724] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2721),U_2723),U_2724))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),c_Groups_Ozero__class_Ozero(U_2721)),U_2722))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2721),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2721),U_2722),U_2723)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2721),U_2722),U_2724)))
      | ~ class_Rings_Olinordered__semiring__strict(U_2721) ),
    inference(definitional_conversion,[status(esa)],[f_676_2]) ).

cnf(f_676_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2721),U_2723),U_2724))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2721),c_Groups_Ozero__class_Ozero(U_2721)),U_2722))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2721),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2721),U_2722),U_2723)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2721),U_2722),U_2724)))
    | ~ class_Rings_Olinordered__semiring__strict(U_2721) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

fof(f_677_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_677_2,plain,
    ! [U_2727,U_2726,U_2725] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2725),c_Groups_Ozero__class_Ozero(U_2725)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2725),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2725),U_2726),U_2726)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2725),U_2727),U_2727))))
      | ~ class_Rings_Olinordered__ring(U_2725) ),
    inference(variable_rename,[status(thm)],[f_677_1]) ).

fof(f_677_3,plain,
    ! [U_2725,U_2726,U_2727] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2725),c_Groups_Ozero__class_Ozero(U_2725)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2725),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2725),U_2726),U_2726)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2725),U_2727),U_2727))))
      | ~ class_Rings_Olinordered__ring(U_2725) ),
    inference(definitional_conversion,[status(esa)],[f_677_2]) ).

cnf(f_677_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2725),c_Groups_Ozero__class_Ozero(U_2725)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2725),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2725),U_2726),U_2726)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2725),U_2727),U_2727))))
    | ~ class_Rings_Olinordered__ring(U_2725) ),
    inference(clausify,[status(thm)],[f_677_3]) ).

fof(f_678_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_678_2,plain,
    ! [U_2730,U_2729,U_2728] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2728),U_2729),U_2729)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2728),U_2730),U_2730))),c_Groups_Ozero__class_Ozero(U_2728)))
          | U_2730 != c_Groups_Ozero__class_Ozero(U_2728)
          | U_2729 != c_Groups_Ozero__class_Ozero(U_2728) )
        & ( ( U_2730 = c_Groups_Ozero__class_Ozero(U_2728)
            & U_2729 = c_Groups_Ozero__class_Ozero(U_2728) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2728),U_2729),U_2729)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2728),U_2730),U_2730))),c_Groups_Ozero__class_Ozero(U_2728))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_2728) ),
    inference(variable_rename,[status(thm)],[f_678_1]) ).

fof(f_678_3,plain,
    ( ! [U_2728,U_2729,U_2730] :
        ( U_2730 = c_Groups_Ozero__class_Ozero(U_2728)
        | ~ sP197(U_2728,U_2729,U_2730) )
    & ! [U_2728,U_2729,U_2730] :
        ( U_2729 = c_Groups_Ozero__class_Ozero(U_2728)
        | ~ sP197(U_2728,U_2729,U_2730) )
    & ! [U_2728,U_2729,U_2730] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2728),U_2729),U_2729)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2728),U_2730),U_2730))),c_Groups_Ozero__class_Ozero(U_2728)))
        | U_2730 != c_Groups_Ozero__class_Ozero(U_2728)
        | U_2729 != c_Groups_Ozero__class_Ozero(U_2728)
        | ~ sP198(U_2728,U_2729,U_2730) )
    & ! [U_2728,U_2729,U_2730] :
        ( sP197(U_2728,U_2729,U_2730)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2728),U_2729),U_2729)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2728),U_2730),U_2730))),c_Groups_Ozero__class_Ozero(U_2728)))
        | ~ sP198(U_2728,U_2729,U_2730) )
    & ! [U_2728,U_2729,U_2730] :
        ( sP198(U_2728,U_2729,U_2730)
        | ~ class_Rings_Olinordered__ring__strict(U_2728) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP197,sP198])],[f_678_2]) ).

cnf(f_678_4,plain,
    ( sP198(U_2728,U_2729,U_2730)
    | ~ class_Rings_Olinordered__ring__strict(U_2728) ),
    inference(clausify,[status(thm)],[f_678_3]) ).

cnf(f_678_5,plain,
    ( sP197(U_2728,U_2729,U_2730)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2728),U_2729),U_2729)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2728),U_2730),U_2730))),c_Groups_Ozero__class_Ozero(U_2728)))
    | ~ sP198(U_2728,U_2729,U_2730) ),
    inference(clausify,[status(thm)],[f_678_3]) ).

cnf(f_678_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2728),U_2729),U_2729)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2728),U_2730),U_2730))),c_Groups_Ozero__class_Ozero(U_2728)))
    | U_2730 != c_Groups_Ozero__class_Ozero(U_2728)
    | U_2729 != c_Groups_Ozero__class_Ozero(U_2728)
    | ~ sP198(U_2728,U_2729,U_2730) ),
    inference(clausify,[status(thm)],[f_678_3]) ).

cnf(f_678_7,plain,
    ( U_2729 = c_Groups_Ozero__class_Ozero(U_2728)
    | ~ sP197(U_2728,U_2729,U_2730) ),
    inference(clausify,[status(thm)],[f_678_3]) ).

cnf(f_678_8,plain,
    ( U_2730 = c_Groups_Ozero__class_Ozero(U_2728)
    | ~ sP197(U_2728,U_2729,U_2730) ),
    inference(clausify,[status(thm)],[f_678_3]) ).

fof(f_679_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_679_2,plain,
    ! [U_2732,U_2731] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2731),hAPP(c_Nat_OSuc,U_2732)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2731),c_Groups_Oone__class_Oone(U_2731)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2731),U_2732))
      | ~ class_Rings_Osemiring__1(U_2731) ),
    inference(variable_rename,[status(thm)],[f_679_1]) ).

fof(f_679_3,plain,
    ! [U_2732,U_2731] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2731),hAPP(c_Nat_OSuc,U_2732)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2731),c_Groups_Oone__class_Oone(U_2731)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2731),U_2732))
      | ~ class_Rings_Osemiring__1(U_2731) ),
    inference(definitional_conversion,[status(esa)],[f_679_2]) ).

cnf(f_679_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2731),hAPP(c_Nat_OSuc,U_2732)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2731),c_Groups_Oone__class_Oone(U_2731)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2731),U_2732))
    | ~ class_Rings_Osemiring__1(U_2731) ),
    inference(clausify,[status(thm)],[f_679_3]) ).

fof(f_680_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_680_2,plain,
    ! [U_2734,U_2733] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2734),U_2733)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2734))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2733)) ),
    inference(variable_rename,[status(thm)],[f_680_1]) ).

fof(f_680_3,plain,
    ! [U_2734,U_2733] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2734),U_2733)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2734))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2733)) ),
    inference(definitional_conversion,[status(esa)],[f_680_2]) ).

cnf(f_680_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2734),U_2733)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2734))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2733)) ),
    inference(clausify,[status(thm)],[f_680_3]) ).

fof(f_681_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_681_2,plain,
    ! [U_2736,U_2735] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2735),U_2736)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2736))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2735)) ),
    inference(variable_rename,[status(thm)],[f_681_1]) ).

fof(f_681_3,plain,
    ! [U_2735,U_2736] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2735),U_2736)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2736))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2735)) ),
    inference(definitional_conversion,[status(esa)],[f_681_2]) ).

cnf(f_681_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2735),U_2736)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2736))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2735)) ),
    inference(clausify,[status(thm)],[f_681_3]) ).

fof(f_682_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_682_2,plain,
    ! [U_2738,U_2737] :
      ( 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_2738),U_2737)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2738))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2737)) ),
    inference(variable_rename,[status(thm)],[f_682_1]) ).

fof(f_682_3,plain,
    ! [U_2737,U_2738] :
      ( 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_2738),U_2737)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2738))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2737)) ),
    inference(definitional_conversion,[status(esa)],[f_682_2]) ).

cnf(f_682_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_2738),U_2737)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2738))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2737)) ),
    inference(clausify,[status(thm)],[f_682_3]) ).

fof(f_683_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_683_2,plain,
    ! [U_2739] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2739)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_2739 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_2739 = 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_2739)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_683_1]) ).

fof(f_683_3,plain,
    ( ! [U_2741] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2741)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_2741 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2740] :
        ( U_2740 = 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_2740)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_683_2]) ).

fof(f_683_4,plain,
    ( ! [U_2741] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2741)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_2741 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2740] :
        ( U_2740 = 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_2740)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_683_3]) ).

cnf(f_683_5,plain,
    ( U_2740 = 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_2740)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_683_4]) ).

cnf(f_683_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_2741)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_2741 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_683_4]) ).

fof(f_684_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_684_2,plain,
    ! [U_2742] :
      ( ( hAPP(c_Int_Onat,U_2742) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2742),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2742),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,U_2742) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_684_1]) ).

fof(f_684_3,plain,
    ( ! [U_2744] :
        ( hAPP(c_Int_Onat,U_2744) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2744),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_2743] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2743),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,U_2743) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_684_2]) ).

fof(f_684_4,plain,
    ( ! [U_2744] :
        ( hAPP(c_Int_Onat,U_2744) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2744),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_2743] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2743),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,U_2743) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_684_3]) ).

cnf(f_684_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2743),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onat,U_2743) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_684_4]) ).

cnf(f_684_6,plain,
    ( hAPP(c_Int_Onat,U_2744) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2744),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_684_4]) ).

fof(f_685_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_685_2,plain,
    ! [U_2745] :
      ( hAPP(c_Int_Onat,U_2745) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2745),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_685_1]) ).

fof(f_685_3,plain,
    ! [U_2745] :
      ( hAPP(c_Int_Onat,U_2745) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2745),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_685_2]) ).

cnf(f_685_4,plain,
    ( hAPP(c_Int_Onat,U_2745) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2745),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_685_3]) ).

fof(f_686_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_686_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_686_1]) ).

cnf(f_686_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_686_2]) ).

fof(f_687_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_687_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_687_1]) ).

cnf(f_687_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_687_2]) ).

fof(f_688_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_688_2,plain,
    ! [U_2746] :
      ( ( 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_2746)),U_2746)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2746),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2746),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_2746)),U_2746)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_688_1]) ).

fof(f_688_3,plain,
    ( ! [U_2748] :
        ( 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_2748)),U_2748)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2748),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_2747] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2747),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_2747)),U_2747)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_688_2]) ).

fof(f_688_4,plain,
    ( ! [U_2748] :
        ( 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_2748)),U_2748)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2748),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_2747] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2747),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_2747)),U_2747)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_688_3]) ).

cnf(f_688_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2747),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_2747)),U_2747)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_688_4]) ).

cnf(f_688_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_2748)),U_2748)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2748),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_688_4]) ).

fof(f_689_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_689_2,plain,
    ! [U_2749] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2749)) = U_2749
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2749)) ),
    inference(variable_rename,[status(thm)],[f_689_1]) ).

fof(f_689_3,plain,
    ! [U_2749] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2749)) = U_2749
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2749)) ),
    inference(definitional_conversion,[status(esa)],[f_689_2]) ).

cnf(f_689_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2749)) = U_2749
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2749)) ),
    inference(clausify,[status(thm)],[f_689_3]) ).

fof(f_690_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_690_2,plain,
    ! [U_2751,U_2750] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2750) = U_2751
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2751))
        | U_2750 != hAPP(c_Int_Onat,U_2751) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2751))
          & U_2750 = hAPP(c_Int_Onat,U_2751) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2750) != U_2751 ) ),
    inference(variable_rename,[status(thm)],[f_690_1]) ).

fof(f_690_3,plain,
    ( ! [U_2755,U_2753] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2753) = U_2755
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2755))
        | U_2753 != hAPP(c_Int_Onat,U_2755) )
    & ! [U_2754,U_2752] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2754))
          & U_2752 = hAPP(c_Int_Onat,U_2754) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2752) != U_2754 ) ),
    inference(miniscope,[status(thm)],[f_690_2]) ).

fof(f_690_4,plain,
    ( ! [U_2754,U_2752] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2754))
        | ~ sP199(U_2754,U_2752) )
    & ! [U_2754,U_2752] :
        ( U_2752 = hAPP(c_Int_Onat,U_2754)
        | ~ sP199(U_2754,U_2752) )
    & ! [U_2753,U_2755] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2753) = U_2755
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2755))
        | U_2753 != hAPP(c_Int_Onat,U_2755) )
    & ! [U_2754,U_2752] :
        ( sP199(U_2754,U_2752)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2752) != U_2754 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP199])],[f_690_3]) ).

cnf(f_690_5,plain,
    ( sP199(U_2754,U_2752)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2752) != U_2754 ),
    inference(clausify,[status(thm)],[f_690_4]) ).

cnf(f_690_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2753) = U_2755
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2755))
    | U_2753 != hAPP(c_Int_Onat,U_2755) ),
    inference(clausify,[status(thm)],[f_690_4]) ).

cnf(f_690_7,plain,
    ( U_2752 = hAPP(c_Int_Onat,U_2754)
    | ~ sP199(U_2754,U_2752) ),
    inference(clausify,[status(thm)],[f_690_4]) ).

cnf(f_690_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2754))
    | ~ sP199(U_2754,U_2752) ),
    inference(clausify,[status(thm)],[f_690_4]) ).

fof(f_691_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_691_2,plain,
    ! [U_2756] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2756)) = 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_2756)) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2756)) = U_2756
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2756)) ) ),
    inference(variable_rename,[status(thm)],[f_691_1]) ).

fof(f_691_3,plain,
    ( ! [U_2758] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2758)) = 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_2758)) )
    & ! [U_2757] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2757)) = U_2757
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2757)) ) ),
    inference(miniscope,[status(thm)],[f_691_2]) ).

fof(f_691_4,plain,
    ( ! [U_2758] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2758)) = 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_2758)) )
    & ! [U_2757] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2757)) = U_2757
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2757)) ) ),
    inference(definitional_conversion,[status(esa)],[f_691_3]) ).

cnf(f_691_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2757)) = U_2757
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2757)) ),
    inference(clausify,[status(thm)],[f_691_4]) ).

cnf(f_691_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2758)) = 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_2758)) ),
    inference(clausify,[status(thm)],[f_691_4]) ).

fof(f_692_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_692_2,plain,
    ! [U_2760,U_2759] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2759),U_2760) = c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_2760 != c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_2759 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
        & ( ( U_2760 = c_Groups_Oone__class_Oone(tc_Int_Oint)
            & U_2759 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2759),U_2760) != 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_2759)) ),
    inference(variable_rename,[status(thm)],[f_692_1]) ).

fof(f_692_3,plain,
    ( ! [U_2759,U_2760] :
        ( U_2760 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP200(U_2759,U_2760) )
    & ! [U_2759,U_2760] :
        ( U_2759 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP200(U_2759,U_2760) )
    & ! [U_2759,U_2760] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2759),U_2760) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | U_2760 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | U_2759 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP201(U_2759,U_2760) )
    & ! [U_2759,U_2760] :
        ( sP200(U_2759,U_2760)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2759),U_2760) != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP201(U_2759,U_2760) )
    & ! [U_2759,U_2760] :
        ( sP201(U_2759,U_2760)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2759)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP200,sP201])],[f_692_2]) ).

cnf(f_692_4,plain,
    ( sP201(U_2759,U_2760)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2759)) ),
    inference(clausify,[status(thm)],[f_692_3]) ).

cnf(f_692_5,plain,
    ( sP200(U_2759,U_2760)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2759),U_2760) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP201(U_2759,U_2760) ),
    inference(clausify,[status(thm)],[f_692_3]) ).

cnf(f_692_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2759),U_2760) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_2760 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_2759 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP201(U_2759,U_2760) ),
    inference(clausify,[status(thm)],[f_692_3]) ).

cnf(f_692_7,plain,
    ( U_2759 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP200(U_2759,U_2760) ),
    inference(clausify,[status(thm)],[f_692_3]) ).

cnf(f_692_8,plain,
    ( U_2760 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP200(U_2759,U_2760) ),
    inference(clausify,[status(thm)],[f_692_3]) ).

fof(f_693_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_693_2,plain,
    ! [U_2761] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2761)) = 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_2761)),
    inference(variable_rename,[status(thm)],[f_693_1]) ).

fof(f_693_3,plain,
    ! [U_2761] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2761)) = 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_2761)),
    inference(definitional_conversion,[status(esa)],[f_693_2]) ).

cnf(f_693_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2761)) = 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_2761)),
    inference(clausify,[status(thm)],[f_693_3]) ).

fof(f_694_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_694_2,plain,
    ! [U_2763,U_2762] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2762)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2763))))
        | U_2763 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2762 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_2763 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2762 = 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_2762)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2763)))) ) ),
    inference(variable_rename,[status(thm)],[f_694_1]) ).

fof(f_694_3,plain,
    ( ! [U_2767,U_2765] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2765)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2767))))
        | U_2767 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2765 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2766,U_2764] :
        ( ( U_2766 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2764 = 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_2764)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2766)))) ) ),
    inference(miniscope,[status(thm)],[f_694_2]) ).

fof(f_694_4,plain,
    ( ! [U_2764,U_2766] :
        ( U_2766 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP202(U_2764,U_2766) )
    & ! [U_2764,U_2766] :
        ( U_2764 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP202(U_2764,U_2766) )
    & ! [U_2767,U_2765] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2765)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2767))))
        | U_2767 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2765 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2764,U_2766] :
        ( sP202(U_2764,U_2766)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2764)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2766)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP202])],[f_694_3]) ).

cnf(f_694_5,plain,
    ( sP202(U_2764,U_2766)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2764)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2766)))) ),
    inference(clausify,[status(thm)],[f_694_4]) ).

cnf(f_694_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_2765)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2767))))
    | U_2767 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2765 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_694_4]) ).

cnf(f_694_7,plain,
    ( U_2764 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP202(U_2764,U_2766) ),
    inference(clausify,[status(thm)],[f_694_4]) ).

cnf(f_694_8,plain,
    ( U_2766 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP202(U_2764,U_2766) ),
    inference(clausify,[status(thm)],[f_694_4]) ).

fof(f_695_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_695_2,plain,
    ! [U_2768] : 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_2768))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_695_1]) ).

fof(f_695_3,plain,
    ! [U_2768] : 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_2768))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_695_2]) ).

cnf(f_695_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_2768))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_695_3]) ).

fof(f_696_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_696_2,plain,
    ! [U_2770,U_2769] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2769)),hAPP(c_Int_Onat,U_2770)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2769),U_2770)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2769),U_2770))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2769)),hAPP(c_Int_Onat,U_2770))) ) )
      | ~ 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_696_1]) ).

fof(f_696_3,plain,
    ( ! [U_2770,U_2769] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2769)),hAPP(c_Int_Onat,U_2770)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2769),U_2770))
        | ~ sP203(U_2770,U_2769) )
    & ! [U_2770,U_2769] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2769),U_2770))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2769)),hAPP(c_Int_Onat,U_2770)))
        | ~ sP203(U_2770,U_2769) )
    & ! [U_2770,U_2769] :
        ( sP203(U_2770,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(definitional_conversion,[status(esa),new_symbols(definitional,[sP203])],[f_696_2]) ).

cnf(f_696_4,plain,
    ( sP203(U_2770,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(clausify,[status(thm)],[f_696_3]) ).

cnf(f_696_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2769),U_2770))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2769)),hAPP(c_Int_Onat,U_2770)))
    | ~ sP203(U_2770,U_2769) ),
    inference(clausify,[status(thm)],[f_696_3]) ).

cnf(f_696_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2769)),hAPP(c_Int_Onat,U_2770)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2769),U_2770))
    | ~ sP203(U_2770,U_2769) ),
    inference(clausify,[status(thm)],[f_696_3]) ).

fof(f_697_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_697_2,plain,
    ! [U_2772,U_2771] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2771)),hAPP(c_Int_Onat,U_2772)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2771),U_2772)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2771),U_2772))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2771)),hAPP(c_Int_Onat,U_2772))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2772))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2771)) ),
    inference(variable_rename,[status(thm)],[f_697_1]) ).

fof(f_697_3,plain,
    ( ! [U_2771,U_2772] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2771)),hAPP(c_Int_Onat,U_2772)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2771),U_2772))
        | ~ sP204(U_2771,U_2772) )
    & ! [U_2771,U_2772] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2771),U_2772))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2771)),hAPP(c_Int_Onat,U_2772)))
        | ~ sP204(U_2771,U_2772) )
    & ! [U_2771,U_2772] :
        ( sP204(U_2771,U_2772)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2772))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2771)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP204])],[f_697_2]) ).

cnf(f_697_4,plain,
    ( sP204(U_2771,U_2772)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2772))
    | ~ 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_697_3]) ).

cnf(f_697_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2771),U_2772))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2771)),hAPP(c_Int_Onat,U_2772)))
    | ~ sP204(U_2771,U_2772) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

cnf(f_697_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_2771)),hAPP(c_Int_Onat,U_2772)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2771),U_2772))
    | ~ sP204(U_2771,U_2772) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

fof(f_698_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_698_2,plain,
    ! [U_2775,U_2774,U_2773] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2774),U_2773))
      | U_2773 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2774),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2773),U_2775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2773)) ),
    inference(variable_rename,[status(thm)],[f_698_1]) ).

fof(f_698_3,plain,
    ! [U_2774,U_2775,U_2773] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2774),U_2773))
      | U_2773 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2774),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2773),U_2775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2773)) ),
    inference(definitional_conversion,[status(esa)],[f_698_2]) ).

cnf(f_698_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2775))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2774),U_2773))
    | U_2773 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2774),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2773),U_2775))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2773)) ),
    inference(clausify,[status(thm)],[f_698_3]) ).

fof(f_699_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_699_2,plain,
    ! [U_2778,U_2777,U_2776] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2778),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_2777))
      | U_2776 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2777),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2776),U_2778))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2776)) ),
    inference(variable_rename,[status(thm)],[f_699_1]) ).

fof(f_699_3,plain,
    ! [U_2776,U_2778,U_2777] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2778),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_2777))
      | U_2776 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2777),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2776),U_2778))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2776)) ),
    inference(definitional_conversion,[status(esa)],[f_699_2]) ).

cnf(f_699_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2778),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_2777))
    | U_2776 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2777),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2776),U_2778))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2776)) ),
    inference(clausify,[status(thm)],[f_699_3]) ).

fof(f_700_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_700_2,plain,
    ! [U_2784,U_2783,U_2782,U_2781,U_2780,U_2779] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2783),U_2780))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2782),U_2779))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2782))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2784))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2781),U_2779))
      | ~ 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_2782),U_2783)),U_2784)),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_2779),U_2780)),U_2781) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2782),U_2783)),U_2784) ),
    inference(variable_rename,[status(thm)],[f_700_1]) ).

fof(f_700_3,plain,
    ! [U_2780,U_2779,U_2781,U_2782,U_2783,U_2784] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2783),U_2780))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2782),U_2779))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2782))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2784))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2781),U_2779))
      | ~ 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_2782),U_2783)),U_2784)),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_2779),U_2780)),U_2781) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2782),U_2783)),U_2784) ),
    inference(definitional_conversion,[status(esa)],[f_700_2]) ).

cnf(f_700_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2783),U_2780))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2782),U_2779))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2782))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2784))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2781),U_2779))
    | ~ 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_2782),U_2783)),U_2784)),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_2779),U_2780)),U_2781) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2782),U_2783)),U_2784) ),
    inference(clausify,[status(thm)],[f_700_3]) ).

fof(f_701_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_701_2,plain,
    ! [U_2789,U_2788,U_2787,U_2786,U_2785] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2788),U_2786))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2785),U_2787))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2785),U_2789))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2789),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_2785),U_2786)),U_2787)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2785),U_2788)),U_2789))) ),
    inference(variable_rename,[status(thm)],[f_701_1]) ).

fof(f_701_3,plain,
    ! [U_2787,U_2785,U_2786,U_2788,U_2789] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2788),U_2786))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2785),U_2787))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2785),U_2789))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2789),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_2785),U_2786)),U_2787)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2785),U_2788)),U_2789))) ),
    inference(definitional_conversion,[status(esa)],[f_701_2]) ).

cnf(f_701_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2788),U_2786))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2785),U_2787))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2785),U_2789))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2789),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_2785),U_2786)),U_2787)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2785),U_2788)),U_2789))) ),
    inference(clausify,[status(thm)],[f_701_3]) ).

fof(f_702_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_702_2,plain,
    ! [U_2795,U_2794,U_2793,U_2792,U_2791,U_2790] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2791),U_2794))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2793),U_2790))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2793))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2792))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2795),U_2793))
      | ~ 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_2793),U_2794)),U_2795)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2790),U_2791)),U_2792) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2793),U_2794)),U_2795) ),
    inference(variable_rename,[status(thm)],[f_702_1]) ).

fof(f_702_3,plain,
    ! [U_2792,U_2790,U_2793,U_2791,U_2794,U_2795] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2791),U_2794))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2793),U_2790))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2793))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2792))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2795),U_2793))
      | ~ 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_2793),U_2794)),U_2795)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2790),U_2791)),U_2792) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2793),U_2794)),U_2795) ),
    inference(definitional_conversion,[status(esa)],[f_702_2]) ).

cnf(f_702_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2791),U_2794))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2793),U_2790))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2793))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2792))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2795),U_2793))
    | ~ 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_2793),U_2794)),U_2795)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2790),U_2791)),U_2792) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2793),U_2794)),U_2795) ),
    inference(clausify,[status(thm)],[f_702_3]) ).

fof(f_703_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_703_2,plain,
    ! [U_2800,U_2799,U_2798,U_2797,U_2796] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2797),U_2799))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2800),U_2796))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2798),U_2796))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2798))
      | ~ 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_2796),U_2797)),U_2798)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2796),U_2799)),U_2800))) ),
    inference(variable_rename,[status(thm)],[f_703_1]) ).

fof(f_703_3,plain,
    ! [U_2798,U_2797,U_2799,U_2796,U_2800] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2797),U_2799))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2800),U_2796))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2798),U_2796))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2798))
      | ~ 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_2796),U_2797)),U_2798)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2796),U_2799)),U_2800))) ),
    inference(definitional_conversion,[status(esa)],[f_703_2]) ).

cnf(f_703_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2797),U_2799))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2800),U_2796))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2798),U_2796))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2798))
    | ~ 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_2796),U_2797)),U_2798)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2796),U_2799)),U_2800))) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

fof(f_704_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_704_2,plain,
    ! [U_2803,U_2802,U_2801] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2802),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_2801))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2803))
      | ~ 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_2801),U_2802)),U_2803)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_704_1]) ).

fof(f_704_3,plain,
    ! [U_2801,U_2802,U_2803] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2802),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_2801))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2803))
      | ~ 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_2801),U_2802)),U_2803)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_704_2]) ).

cnf(f_704_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2802),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_2801))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2803))
    | ~ 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_2801),U_2802)),U_2803)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_704_3]) ).

fof(f_705_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_705_2,plain,
    ! [U_2806,U_2805,U_2804] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2805))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2804))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2806),U_2804))
      | ~ 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_2804),U_2805)),U_2806))) ),
    inference(variable_rename,[status(thm)],[f_705_1]) ).

fof(f_705_3,plain,
    ! [U_2804,U_2805,U_2806] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2805))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2804))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2806),U_2804))
      | ~ 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_2804),U_2805)),U_2806))) ),
    inference(definitional_conversion,[status(esa)],[f_705_2]) ).

cnf(f_705_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2805))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2804))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2806),U_2804))
    | ~ 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_2804),U_2805)),U_2806))) ),
    inference(clausify,[status(thm)],[f_705_3]) ).

fof(f_706_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_706_2,plain,
    ! [U_2809,U_2808,U_2807] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2807),U_2808) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2807),U_2809)
          | U_2808 != U_2809 )
        & ( U_2808 = U_2809
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2807),U_2808) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2807),U_2809) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2807)) ),
    inference(variable_rename,[status(thm)],[f_706_1]) ).

fof(f_706_3,plain,
    ( ! [U_2807,U_2808,U_2809] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2807),U_2808) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2807),U_2809)
        | U_2808 != U_2809
        | ~ sP205(U_2807,U_2808,U_2809) )
    & ! [U_2807,U_2808,U_2809] :
        ( U_2808 = U_2809
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2807),U_2808) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2807),U_2809)
        | ~ sP205(U_2807,U_2808,U_2809) )
    & ! [U_2807,U_2808,U_2809] :
        ( sP205(U_2807,U_2808,U_2809)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2807)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205])],[f_706_2]) ).

cnf(f_706_4,plain,
    ( sP205(U_2807,U_2808,U_2809)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2807)) ),
    inference(clausify,[status(thm)],[f_706_3]) ).

cnf(f_706_5,plain,
    ( U_2808 = U_2809
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2807),U_2808) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2807),U_2809)
    | ~ sP205(U_2807,U_2808,U_2809) ),
    inference(clausify,[status(thm)],[f_706_3]) ).

cnf(f_706_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2807),U_2808) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2807),U_2809)
    | U_2808 != U_2809
    | ~ sP205(U_2807,U_2808,U_2809) ),
    inference(clausify,[status(thm)],[f_706_3]) ).

fof(f_707_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_707_2,plain,
    ! [U_2810] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2810)),
    inference(variable_rename,[status(thm)],[f_707_1]) ).

fof(f_707_3,plain,
    ! [U_2810] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2810)),
    inference(definitional_conversion,[status(esa)],[f_707_2]) ).

cnf(f_707_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2810)),
    inference(clausify,[status(thm)],[f_707_3]) ).

fof(f_708_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_708_2,plain,
    ! [U_2812,U_2811] :
      ( U_2811 = U_2812
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2812),U_2811))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2811),U_2812)) ),
    inference(variable_rename,[status(thm)],[f_708_1]) ).

fof(f_708_3,plain,
    ! [U_2812,U_2811] :
      ( U_2811 = U_2812
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2812),U_2811))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2811),U_2812)) ),
    inference(definitional_conversion,[status(esa)],[f_708_2]) ).

cnf(f_708_4,plain,
    ( U_2811 = U_2812
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2812),U_2811))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2811),U_2812)) ),
    inference(clausify,[status(thm)],[f_708_3]) ).

fof(f_709_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_709_2,plain,
    ! [U_2815,U_2814,U_2813] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2813),U_2815))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2814),U_2815))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2813),U_2814)) ),
    inference(variable_rename,[status(thm)],[f_709_1]) ).

fof(f_709_3,plain,
    ! [U_2813,U_2814,U_2815] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2813),U_2815))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2814),U_2815))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2813),U_2814)) ),
    inference(definitional_conversion,[status(esa)],[f_709_2]) ).

cnf(f_709_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2813),U_2815))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2814),U_2815))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2813),U_2814)) ),
    inference(clausify,[status(thm)],[f_709_3]) ).

fof(f_710_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_710_2,plain,
    ! [U_2817,U_2816] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2816),U_2817))
      | U_2816 != U_2817 ),
    inference(variable_rename,[status(thm)],[f_710_1]) ).

fof(f_710_3,plain,
    ! [U_2816,U_2817] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2816),U_2817))
      | U_2816 != U_2817 ),
    inference(definitional_conversion,[status(esa)],[f_710_2]) ).

cnf(f_710_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2816),U_2817))
    | U_2816 != U_2817 ),
    inference(clausify,[status(thm)],[f_710_3]) ).

fof(f_711_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_711_2,plain,
    ! [U_2819,U_2818] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2819),U_2818))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2818),U_2819)) ),
    inference(variable_rename,[status(thm)],[f_711_1]) ).

fof(f_711_3,plain,
    ! [U_2818,U_2819] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2819),U_2818))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2818),U_2819)) ),
    inference(definitional_conversion,[status(esa)],[f_711_2]) ).

cnf(f_711_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2819),U_2818))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2818),U_2819)) ),
    inference(clausify,[status(thm)],[f_711_3]) ).

fof(f_712_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_712_2,plain,
    ! [U_2820] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2820),U_2820)),
    inference(variable_rename,[status(thm)],[f_712_1]) ).

fof(f_712_3,plain,
    ! [U_2820] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2820),U_2820)),
    inference(definitional_conversion,[status(esa)],[f_712_2]) ).

cnf(f_712_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2820),U_2820)),
    inference(clausify,[status(thm)],[f_712_3]) ).

fof(f_713_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_713_2,plain,
    ! [U_2821] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2821)),
    inference(variable_rename,[status(thm)],[f_713_1]) ).

fof(f_713_3,plain,
    ! [U_2821] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2821)),
    inference(definitional_conversion,[status(esa)],[f_713_2]) ).

cnf(f_713_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2821)),
    inference(clausify,[status(thm)],[f_713_3]) ).

fof(f_714_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_714_2,plain,
    ! [U_2822] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2822),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_2822 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_2822 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2822),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[f_714_1]) ).

fof(f_714_3,plain,
    ( ! [U_2824] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2824),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_2824 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2823] :
        ( U_2823 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2823),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(miniscope,[status(thm)],[f_714_2]) ).

fof(f_714_4,plain,
    ( ! [U_2824] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2824),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_2824 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2823] :
        ( U_2823 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2823),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_714_3]) ).

cnf(f_714_5,plain,
    ( U_2823 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2823),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_714_4]) ).

cnf(f_714_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2824),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_2824 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_714_4]) ).

fof(f_715_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_715_2,plain,
    ! [U_2826,U_2825] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2825),U_2826))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2825)),U_2826)) ),
    inference(variable_rename,[status(thm)],[f_715_1]) ).

fof(f_715_3,plain,
    ! [U_2825,U_2826] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2825),U_2826))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2825)),U_2826)) ),
    inference(definitional_conversion,[status(esa)],[f_715_2]) ).

cnf(f_715_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2825),U_2826))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2825)),U_2826)) ),
    inference(clausify,[status(thm)],[f_715_3]) ).

fof(f_716_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_716_2,plain,
    ! [U_2828,U_2827] :
      ( U_2827 = hAPP(c_Nat_OSuc,U_2828)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2827),U_2828))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2827),hAPP(c_Nat_OSuc,U_2828))) ),
    inference(variable_rename,[status(thm)],[f_716_1]) ).

fof(f_716_3,plain,
    ! [U_2827,U_2828] :
      ( U_2827 = hAPP(c_Nat_OSuc,U_2828)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2827),U_2828))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2827),hAPP(c_Nat_OSuc,U_2828))) ),
    inference(definitional_conversion,[status(esa)],[f_716_2]) ).

cnf(f_716_4,plain,
    ( U_2827 = hAPP(c_Nat_OSuc,U_2828)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2827),U_2828))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2827),hAPP(c_Nat_OSuc,U_2828))) ),
    inference(clausify,[status(thm)],[f_716_3]) ).

fof(f_717_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_717_2,plain,
    ! [U_2830,U_2829] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2829),hAPP(c_Nat_OSuc,U_2830)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2829),U_2830)) ),
    inference(variable_rename,[status(thm)],[f_717_1]) ).

fof(f_717_3,plain,
    ! [U_2829,U_2830] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2829),hAPP(c_Nat_OSuc,U_2830)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2829),U_2830)) ),
    inference(definitional_conversion,[status(esa)],[f_717_2]) ).

cnf(f_717_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2829),hAPP(c_Nat_OSuc,U_2830)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2829),U_2830)) ),
    inference(clausify,[status(thm)],[f_717_3]) ).

fof(f_718_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_718_2,plain,
    ! [U_2832,U_2831] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2831)),hAPP(c_Nat_OSuc,U_2832)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2831),U_2832)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2831),U_2832))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2831)),hAPP(c_Nat_OSuc,U_2832))) ) ),
    inference(variable_rename,[status(thm)],[f_718_1]) ).

fof(f_718_3,plain,
    ( ! [U_2836,U_2834] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2834)),hAPP(c_Nat_OSuc,U_2836)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2834),U_2836)) )
    & ! [U_2835,U_2833] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2833),U_2835))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2833)),hAPP(c_Nat_OSuc,U_2835))) ) ),
    inference(miniscope,[status(thm)],[f_718_2]) ).

fof(f_718_4,plain,
    ( ! [U_2834,U_2836] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2834)),hAPP(c_Nat_OSuc,U_2836)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2834),U_2836)) )
    & ! [U_2835,U_2833] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2833),U_2835))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2833)),hAPP(c_Nat_OSuc,U_2835))) ) ),
    inference(definitional_conversion,[status(esa)],[f_718_3]) ).

cnf(f_718_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2833),U_2835))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2833)),hAPP(c_Nat_OSuc,U_2835))) ),
    inference(clausify,[status(thm)],[f_718_4]) ).

cnf(f_718_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2834)),hAPP(c_Nat_OSuc,U_2836)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2834),U_2836)) ),
    inference(clausify,[status(thm)],[f_718_4]) ).

fof(f_719_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_719_2,plain,
    ! [U_2838,U_2837] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2837),hAPP(c_Nat_OSuc,U_2838)))
        | ( U_2837 != hAPP(c_Nat_OSuc,U_2838)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2837),U_2838)) ) )
      & ( U_2837 = hAPP(c_Nat_OSuc,U_2838)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2837),U_2838))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2837),hAPP(c_Nat_OSuc,U_2838))) ) ),
    inference(variable_rename,[status(thm)],[f_719_1]) ).

fof(f_719_3,plain,
    ( ! [U_2842,U_2840] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2840),hAPP(c_Nat_OSuc,U_2842)))
        | ( U_2840 != hAPP(c_Nat_OSuc,U_2842)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2840),U_2842)) ) )
    & ! [U_2841,U_2839] :
        ( U_2839 = hAPP(c_Nat_OSuc,U_2841)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2839),U_2841))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2839),hAPP(c_Nat_OSuc,U_2841))) ) ),
    inference(miniscope,[status(thm)],[f_719_2]) ).

fof(f_719_4,plain,
    ( ! [U_2842,U_2840] :
        ( U_2840 != hAPP(c_Nat_OSuc,U_2842)
        | ~ sP206(U_2842,U_2840) )
    & ! [U_2842,U_2840] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2840),U_2842))
        | ~ sP206(U_2842,U_2840) )
    & ! [U_2842,U_2840] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2840),hAPP(c_Nat_OSuc,U_2842)))
        | sP206(U_2842,U_2840) )
    & ! [U_2841,U_2839] :
        ( U_2839 = hAPP(c_Nat_OSuc,U_2841)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2839),U_2841))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2839),hAPP(c_Nat_OSuc,U_2841))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP206])],[f_719_3]) ).

cnf(f_719_5,plain,
    ( U_2839 = hAPP(c_Nat_OSuc,U_2841)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2839),U_2841))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2839),hAPP(c_Nat_OSuc,U_2841))) ),
    inference(clausify,[status(thm)],[f_719_4]) ).

cnf(f_719_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2840),hAPP(c_Nat_OSuc,U_2842)))
    | sP206(U_2842,U_2840) ),
    inference(clausify,[status(thm)],[f_719_4]) ).

cnf(f_719_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2840),U_2842))
    | ~ sP206(U_2842,U_2840) ),
    inference(clausify,[status(thm)],[f_719_4]) ).

cnf(f_719_8,plain,
    ( U_2840 != hAPP(c_Nat_OSuc,U_2842)
    | ~ sP206(U_2842,U_2840) ),
    inference(clausify,[status(thm)],[f_719_4]) ).

fof(f_720_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_720_2,plain,
    ! [U_2844,U_2843] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2843),U_2844))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2844)),U_2843)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2844)),U_2843))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2843),U_2844)) ) ),
    inference(variable_rename,[status(thm)],[f_720_1]) ).

fof(f_720_3,plain,
    ( ! [U_2848,U_2846] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2846),U_2848))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2848)),U_2846)) )
    & ! [U_2847,U_2845] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2847)),U_2845))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2845),U_2847)) ) ),
    inference(miniscope,[status(thm)],[f_720_2]) ).

fof(f_720_4,plain,
    ( ! [U_2846,U_2848] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2846),U_2848))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2848)),U_2846)) )
    & ! [U_2847,U_2845] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2847)),U_2845))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2845),U_2847)) ) ),
    inference(definitional_conversion,[status(esa)],[f_720_3]) ).

cnf(f_720_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2847)),U_2845))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2845),U_2847)) ),
    inference(clausify,[status(thm)],[f_720_4]) ).

cnf(f_720_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2846),U_2848))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2848)),U_2846)) ),
    inference(clausify,[status(thm)],[f_720_4]) ).

fof(f_721_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_721_2,plain,
    ! [U_2849] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2849)),U_2849)),
    inference(variable_rename,[status(thm)],[f_721_1]) ).

fof(f_721_3,plain,
    ! [U_2849] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2849)),U_2849)),
    inference(definitional_conversion,[status(esa)],[f_721_2]) ).

cnf(f_721_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2849)),U_2849)),
    inference(clausify,[status(thm)],[f_721_3]) ).

fof(f_722_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_722_2,plain,
    ! [U_2851,U_2850] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2850),U_2851))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2850),U_2851)) ),
    inference(variable_rename,[status(thm)],[f_722_1]) ).

fof(f_722_3,plain,
    ! [U_2850,U_2851] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2850),U_2851))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2850),U_2851)) ),
    inference(definitional_conversion,[status(esa)],[f_722_2]) ).

cnf(f_722_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2850),U_2851))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2850),U_2851)) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

fof(f_723_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_723_2,plain,
    ! [U_2853,U_2852] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2852),U_2853))
        | U_2852 = U_2853
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2852),U_2853)) )
      & ( ( U_2852 != U_2853
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2852),U_2853)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2852),U_2853)) ) ),
    inference(variable_rename,[status(thm)],[f_723_1]) ).

fof(f_723_3,plain,
    ( ! [U_2857,U_2855] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2855),U_2857))
        | U_2855 = U_2857
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2855),U_2857)) )
    & ! [U_2856,U_2854] :
        ( ( U_2854 != U_2856
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2854),U_2856)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2854),U_2856)) ) ),
    inference(miniscope,[status(thm)],[f_723_2]) ).

fof(f_723_4,plain,
    ( ! [U_2854,U_2856] :
        ( U_2854 != U_2856
        | ~ sP207(U_2854,U_2856) )
    & ! [U_2854,U_2856] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2854),U_2856))
        | ~ sP207(U_2854,U_2856) )
    & ! [U_2857,U_2855] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2855),U_2857))
        | U_2855 = U_2857
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2855),U_2857)) )
    & ! [U_2854,U_2856] :
        ( sP207(U_2854,U_2856)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2854),U_2856)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP207])],[f_723_3]) ).

cnf(f_723_5,plain,
    ( sP207(U_2854,U_2856)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2854),U_2856)) ),
    inference(clausify,[status(thm)],[f_723_4]) ).

cnf(f_723_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2855),U_2857))
    | U_2855 = U_2857
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2855),U_2857)) ),
    inference(clausify,[status(thm)],[f_723_4]) ).

cnf(f_723_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2854),U_2856))
    | ~ sP207(U_2854,U_2856) ),
    inference(clausify,[status(thm)],[f_723_4]) ).

cnf(f_723_8,plain,
    ( U_2854 != U_2856
    | ~ sP207(U_2854,U_2856) ),
    inference(clausify,[status(thm)],[f_723_4]) ).

fof(f_724_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_724_2,plain,
    ! [U_2859,U_2858] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2858),U_2859))
        | ( U_2858 != U_2859
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2858),U_2859)) ) )
      & ( U_2858 = U_2859
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2858),U_2859))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2858),U_2859)) ) ),
    inference(variable_rename,[status(thm)],[f_724_1]) ).

fof(f_724_3,plain,
    ( ! [U_2863,U_2861] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2861),U_2863))
        | ( U_2861 != U_2863
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2861),U_2863)) ) )
    & ! [U_2862,U_2860] :
        ( U_2860 = U_2862
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2860),U_2862))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2860),U_2862)) ) ),
    inference(miniscope,[status(thm)],[f_724_2]) ).

fof(f_724_4,plain,
    ( ! [U_2863,U_2861] :
        ( U_2861 != U_2863
        | ~ sP208(U_2863,U_2861) )
    & ! [U_2863,U_2861] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2861),U_2863))
        | ~ sP208(U_2863,U_2861) )
    & ! [U_2863,U_2861] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2861),U_2863))
        | sP208(U_2863,U_2861) )
    & ! [U_2860,U_2862] :
        ( U_2860 = U_2862
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2860),U_2862))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2860),U_2862)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP208])],[f_724_3]) ).

cnf(f_724_5,plain,
    ( U_2860 = U_2862
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2860),U_2862))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2860),U_2862)) ),
    inference(clausify,[status(thm)],[f_724_4]) ).

cnf(f_724_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2861),U_2863))
    | sP208(U_2863,U_2861) ),
    inference(clausify,[status(thm)],[f_724_4]) ).

cnf(f_724_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2861),U_2863))
    | ~ sP208(U_2863,U_2861) ),
    inference(clausify,[status(thm)],[f_724_4]) ).

cnf(f_724_8,plain,
    ( U_2861 != U_2863
    | ~ sP208(U_2863,U_2861) ),
    inference(clausify,[status(thm)],[f_724_4]) ).

fof(f_725_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_725_2,plain,
    ! [U_2865,U_2864] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2864),U_2865))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2864),U_2865)) ),
    inference(variable_rename,[status(thm)],[f_725_1]) ).

fof(f_725_3,plain,
    ! [U_2865,U_2864] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2864),U_2865))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2864),U_2865)) ),
    inference(definitional_conversion,[status(esa)],[f_725_2]) ).

cnf(f_725_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2864),U_2865))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2864),U_2865)) ),
    inference(clausify,[status(thm)],[f_725_3]) ).

fof(f_726_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_726_2,plain,
    ! [U_2867,U_2866] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2866),U_2867))
      | U_2866 = U_2867
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2866),U_2867)) ),
    inference(variable_rename,[status(thm)],[f_726_1]) ).

fof(f_726_3,plain,
    ! [U_2866,U_2867] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2866),U_2867))
      | U_2866 = U_2867
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2866),U_2867)) ),
    inference(definitional_conversion,[status(esa)],[f_726_2]) ).

cnf(f_726_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2866),U_2867))
    | U_2866 = U_2867
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2866),U_2867)) ),
    inference(clausify,[status(thm)],[f_726_3]) ).

fof(f_727_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_727_2,plain,
    ! [U_2869,U_2868] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2868),U_2869))
      | ( U_2868 != U_2869
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2868),U_2869)) ) ),
    inference(variable_rename,[status(thm)],[f_727_1]) ).

fof(f_727_3,plain,
    ( ! [U_2868,U_2869] :
        ( U_2868 != U_2869
        | ~ sP209(U_2868,U_2869) )
    & ! [U_2868,U_2869] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2868),U_2869))
        | ~ sP209(U_2868,U_2869) )
    & ! [U_2868,U_2869] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2868),U_2869))
        | sP209(U_2868,U_2869) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP209])],[f_727_2]) ).

cnf(f_727_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2868),U_2869))
    | sP209(U_2868,U_2869) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

cnf(f_727_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2868),U_2869))
    | ~ sP209(U_2868,U_2869) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

cnf(f_727_6,plain,
    ( U_2868 != U_2869
    | ~ sP209(U_2868,U_2869) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

fof(f_728_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_728_2,plain,
    ! [U_2872,U_2871,U_2870] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2870),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2872),U_2871)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2870),U_2871)) ),
    inference(variable_rename,[status(thm)],[f_728_1]) ).

fof(f_728_3,plain,
    ! [U_2870,U_2871,U_2872] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2870),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2872),U_2871)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2870),U_2871)) ),
    inference(definitional_conversion,[status(esa)],[f_728_2]) ).

cnf(f_728_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2870),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2872),U_2871)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2870),U_2871)) ),
    inference(clausify,[status(thm)],[f_728_3]) ).

fof(f_729_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_729_2,plain,
    ! [U_2875,U_2874,U_2873] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2873),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2874),U_2875)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2873),U_2874)) ),
    inference(variable_rename,[status(thm)],[f_729_1]) ).

fof(f_729_3,plain,
    ! [U_2873,U_2874,U_2875] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2873),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2874),U_2875)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2873),U_2874)) ),
    inference(definitional_conversion,[status(esa)],[f_729_2]) ).

cnf(f_729_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2873),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2874),U_2875)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2873),U_2874)) ),
    inference(clausify,[status(thm)],[f_729_3]) ).

fof(f_730_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_730_2,plain,
    ! [U_2877,U_2876] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2877),U_2876))),
    inference(variable_rename,[status(thm)],[f_730_1]) ).

fof(f_730_3,plain,
    ! [U_2876,U_2877] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2877),U_2876))),
    inference(definitional_conversion,[status(esa)],[f_730_2]) ).

cnf(f_730_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2877),U_2876))),
    inference(clausify,[status(thm)],[f_730_3]) ).

fof(f_731_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_731_2,plain,
    ! [U_2879,U_2878] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2878),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2878),U_2879))),
    inference(variable_rename,[status(thm)],[f_731_1]) ).

fof(f_731_3,plain,
    ! [U_2878,U_2879] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2878),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2878),U_2879))),
    inference(definitional_conversion,[status(esa)],[f_731_2]) ).

cnf(f_731_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2878),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2878),U_2879))),
    inference(clausify,[status(thm)],[f_731_3]) ).

fof(f_732_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_732_2,plain,
    ! [U_2883,U_2882] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2882),U_2883))
        | ! [U_2881] : U_2883 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2882),U_2881) )
      & ( ? [U_2880] : U_2883 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2882),U_2880)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2882),U_2883)) ) ),
    inference(variable_rename,[status(thm)],[f_732_1]) ).

fof(f_732_3,plain,
    ( ! [U_2887,U_2885] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2885),U_2887))
        | ! [U_2881] : U_2887 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2885),U_2881) )
    & ! [U_2886,U_2884] :
        ( ? [U_2880] : U_2886 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2884),U_2880)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2884),U_2886)) ) ),
    inference(miniscope,[status(thm)],[f_732_2]) ).

fof(f_732_4,plain,
    ( ! [U_2887,U_2885] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2885),U_2887))
        | ! [U_2881] : U_2887 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2885),U_2881) )
    & ! [U_2886,U_2884] :
        ( U_2886 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2884),sK60(U_2886,U_2884))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2884),U_2886)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_2880,sK60(U_2886,U_2884))],[f_732_3]) ).

fof(f_732_5,plain,
    ( ! [U_2881,U_2885,U_2887] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2885),U_2887))
        | U_2887 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2885),U_2881) )
    & ! [U_2886,U_2884] :
        ( U_2886 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2884),sK60(U_2886,U_2884))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2884),U_2886)) ) ),
    inference(definitional_conversion,[status(esa)],[f_732_4]) ).

cnf(f_732_6,plain,
    ( U_2886 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2884),sK60(U_2886,U_2884))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2884),U_2886)) ),
    inference(clausify,[status(thm)],[f_732_5]) ).

cnf(f_732_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2885),U_2887))
    | U_2887 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2885),U_2881) ),
    inference(clausify,[status(thm)],[f_732_5]) ).

fof(f_733_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_733_2,plain,
    ! [U_2890,U_2889,U_2888] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2888),U_2889)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2888),U_2890)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2889),U_2890)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2889),U_2890))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2888),U_2889)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2888),U_2890))) ) ),
    inference(variable_rename,[status(thm)],[f_733_1]) ).

fof(f_733_3,plain,
    ( ! [U_2896,U_2894] :
        ( ! [U_2892] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2892),U_2894)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2892),U_2896)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2894),U_2896)) )
    & ! [U_2895,U_2893] :
        ( ! [U_2891] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2891),U_2893)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2891),U_2895)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2893),U_2895)) ) ),
    inference(miniscope,[status(thm)],[f_733_2]) ).

fof(f_733_4,plain,
    ( ! [U_2896,U_2894,U_2892] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2892),U_2894)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2892),U_2896)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2894),U_2896)) )
    & ! [U_2893,U_2895,U_2891] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2891),U_2893)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2891),U_2895)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2893),U_2895)) ) ),
    inference(definitional_conversion,[status(esa)],[f_733_3]) ).

cnf(f_733_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_2891),U_2893)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2891),U_2895)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2893),U_2895)) ),
    inference(clausify,[status(thm)],[f_733_4]) ).

cnf(f_733_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_2892),U_2894)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2892),U_2896)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2894),U_2896)) ),
    inference(clausify,[status(thm)],[f_733_4]) ).

fof(f_734_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_734_2,plain,
    ! [U_2899,U_2898,U_2897] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2897),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2898),U_2899)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2897),U_2898)) ),
    inference(variable_rename,[status(thm)],[f_734_1]) ).

fof(f_734_3,plain,
    ! [U_2898,U_2897,U_2899] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2897),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2898),U_2899)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2897),U_2898)) ),
    inference(definitional_conversion,[status(esa)],[f_734_2]) ).

cnf(f_734_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2897),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2898),U_2899)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2897),U_2898)) ),
    inference(clausify,[status(thm)],[f_734_3]) ).

fof(f_735_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_735_2,plain,
    ! [U_2902,U_2901,U_2900] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2902),U_2901)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2900),U_2901)) ),
    inference(variable_rename,[status(thm)],[f_735_1]) ).

fof(f_735_3,plain,
    ! [U_2900,U_2901,U_2902] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2902),U_2901)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2900),U_2901)) ),
    inference(definitional_conversion,[status(esa)],[f_735_2]) ).

cnf(f_735_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2902),U_2901)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2900),U_2901)) ),
    inference(clausify,[status(thm)],[f_735_3]) ).

fof(f_736_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_736_2,plain,
    ! [U_2905,U_2904,U_2903] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2903),U_2905)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2904),U_2905)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2903),U_2904)) ),
    inference(variable_rename,[status(thm)],[f_736_1]) ).

fof(f_736_3,plain,
    ! [U_2903,U_2904,U_2905] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2903),U_2905)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2904),U_2905)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2903),U_2904)) ),
    inference(definitional_conversion,[status(esa)],[f_736_2]) ).

cnf(f_736_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_2903),U_2905)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2904),U_2905)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2903),U_2904)) ),
    inference(clausify,[status(thm)],[f_736_3]) ).

fof(f_737_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_737_2,plain,
    ! [U_2909,U_2908,U_2907,U_2906] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2906),U_2908)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2907),U_2909)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2908),U_2909))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2906),U_2907)) ),
    inference(variable_rename,[status(thm)],[f_737_1]) ).

fof(f_737_3,plain,
    ! [U_2906,U_2907,U_2908,U_2909] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2906),U_2908)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2907),U_2909)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2908),U_2909))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2906),U_2907)) ),
    inference(definitional_conversion,[status(esa)],[f_737_2]) ).

cnf(f_737_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_2906),U_2908)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2907),U_2909)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2908),U_2909))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2906),U_2907)) ),
    inference(clausify,[status(thm)],[f_737_3]) ).

fof(f_738_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_738_2,plain,
    ! [U_2912,U_2911,U_2910] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2911),U_2912))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2910),U_2911)),U_2912)) ),
    inference(variable_rename,[status(thm)],[f_738_1]) ).

fof(f_738_3,plain,
    ! [U_2912,U_2911] :
      ( ! [U_2910] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2910),U_2911)),U_2912))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2911),U_2912)) ),
    inference(miniscope,[status(thm)],[f_738_2]) ).

fof(f_738_4,plain,
    ! [U_2910,U_2911,U_2912] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2910),U_2911)),U_2912))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2911),U_2912)) ),
    inference(definitional_conversion,[status(esa)],[f_738_3]) ).

cnf(f_738_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_2910),U_2911)),U_2912))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2911),U_2912)) ),
    inference(clausify,[status(thm)],[f_738_4]) ).

fof(f_739_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_739_2,plain,
    ! [U_2915,U_2914,U_2913] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2913),U_2915))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2913),U_2914)),U_2915)) ),
    inference(variable_rename,[status(thm)],[f_739_1]) ).

fof(f_739_3,plain,
    ! [U_2913,U_2914,U_2915] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2913),U_2915))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2913),U_2914)),U_2915)) ),
    inference(definitional_conversion,[status(esa)],[f_739_2]) ).

cnf(f_739_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2913),U_2915))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2913),U_2914)),U_2915)) ),
    inference(clausify,[status(thm)],[f_739_3]) ).

fof(f_740_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_740_2,plain,
    ! [U_2918,U_2917,U_2916] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2917),U_2918))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2916),U_2918)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2916),U_2917)),U_2918)) ),
    inference(variable_rename,[status(thm)],[f_740_1]) ).

fof(f_740_3,plain,
    ( ! [U_2916,U_2917,U_2918] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2917),U_2918))
        | ~ sP210(U_2916,U_2917,U_2918) )
    & ! [U_2916,U_2917,U_2918] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2916),U_2918))
        | ~ sP210(U_2916,U_2917,U_2918) )
    & ! [U_2916,U_2917,U_2918] :
        ( sP210(U_2916,U_2917,U_2918)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2916),U_2917)),U_2918)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP210])],[f_740_2]) ).

cnf(f_740_4,plain,
    ( sP210(U_2916,U_2917,U_2918)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2916),U_2917)),U_2918)) ),
    inference(clausify,[status(thm)],[f_740_3]) ).

cnf(f_740_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2916),U_2918))
    | ~ sP210(U_2916,U_2917,U_2918) ),
    inference(clausify,[status(thm)],[f_740_3]) ).

cnf(f_740_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2917),U_2918))
    | ~ sP210(U_2916,U_2917,U_2918) ),
    inference(clausify,[status(thm)],[f_740_3]) ).

fof(f_741_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_741_2,plain,
    ! [U_2922,U_2921,U_2920,U_2919] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2919),U_2921)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2920),U_2922)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2921),U_2922))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2919),U_2920)) ),
    inference(variable_rename,[status(thm)],[f_741_1]) ).

fof(f_741_3,plain,
    ! [U_2919,U_2920,U_2921,U_2922] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2919),U_2921)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2920),U_2922)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2921),U_2922))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2919),U_2920)) ),
    inference(definitional_conversion,[status(esa)],[f_741_2]) ).

cnf(f_741_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_2919),U_2921)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2920),U_2922)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2921),U_2922))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2919),U_2920)) ),
    inference(clausify,[status(thm)],[f_741_3]) ).

fof(f_742_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_742_2,plain,
    ! [U_2925,U_2924,U_2923] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2925),U_2923)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2925),U_2924)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2923),U_2924)) ),
    inference(variable_rename,[status(thm)],[f_742_1]) ).

fof(f_742_3,plain,
    ! [U_2923,U_2924,U_2925] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2925),U_2923)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2925),U_2924)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2923),U_2924)) ),
    inference(definitional_conversion,[status(esa)],[f_742_2]) ).

cnf(f_742_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_2925),U_2923)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2925),U_2924)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2923),U_2924)) ),
    inference(clausify,[status(thm)],[f_742_3]) ).

fof(f_743_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_743_2,plain,
    ! [U_2928,U_2927,U_2926] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2926),U_2928)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2927),U_2928)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2926),U_2927)) ),
    inference(variable_rename,[status(thm)],[f_743_1]) ).

fof(f_743_3,plain,
    ! [U_2926,U_2927,U_2928] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2926),U_2928)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2927),U_2928)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2926),U_2927)) ),
    inference(definitional_conversion,[status(esa)],[f_743_2]) ).

cnf(f_743_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_2926),U_2928)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2927),U_2928)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2926),U_2927)) ),
    inference(clausify,[status(thm)],[f_743_3]) ).

fof(f_744_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_744_2,plain,
    ! [U_2929] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2929),U_2929)))),
    inference(variable_rename,[status(thm)],[f_744_1]) ).

fof(f_744_3,plain,
    ! [U_2929] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2929),U_2929)))),
    inference(definitional_conversion,[status(esa)],[f_744_2]) ).

cnf(f_744_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2929),U_2929)))),
    inference(clausify,[status(thm)],[f_744_3]) ).

fof(f_745_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_745_2,plain,
    ! [U_2930] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2930),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2930),U_2930))),
    inference(variable_rename,[status(thm)],[f_745_1]) ).

fof(f_745_3,plain,
    ! [U_2930] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2930),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2930),U_2930))),
    inference(definitional_conversion,[status(esa)],[f_745_2]) ).

cnf(f_745_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2930),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2930),U_2930))),
    inference(clausify,[status(thm)],[f_745_3]) ).

fof(f_746_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_746_2,plain,
    ! [U_2932,U_2931] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2931),U_2932) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2932 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2931 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_2932 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2931 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2931),U_2932) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_746_1]) ).

fof(f_746_3,plain,
    ( ! [U_2936,U_2934] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2934),U_2936) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2936 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2934 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2935,U_2933] :
        ( ( U_2935 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2933 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2933),U_2935) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_746_2]) ).

fof(f_746_4,plain,
    ( ! [U_2933,U_2935] :
        ( U_2935 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP211(U_2933,U_2935) )
    & ! [U_2933,U_2935] :
        ( U_2933 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP211(U_2933,U_2935) )
    & ! [U_2936,U_2934] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2934),U_2936) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2936 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2934 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2933,U_2935] :
        ( sP211(U_2933,U_2935)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2933),U_2935) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP211])],[f_746_3]) ).

cnf(f_746_5,plain,
    ( sP211(U_2933,U_2935)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2933),U_2935) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_746_4]) ).

cnf(f_746_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2934),U_2936) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2936 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2934 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_746_4]) ).

cnf(f_746_7,plain,
    ( U_2933 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP211(U_2933,U_2935) ),
    inference(clausify,[status(thm)],[f_746_4]) ).

cnf(f_746_8,plain,
    ( U_2935 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP211(U_2933,U_2935) ),
    inference(clausify,[status(thm)],[f_746_4]) ).

fof(f_747_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_747_2,plain,
    ! [U_2937] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2937),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2937,
    inference(variable_rename,[status(thm)],[f_747_1]) ).

fof(f_747_3,plain,
    ! [U_2937] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2937),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2937,
    inference(definitional_conversion,[status(esa)],[f_747_2]) ).

cnf(f_747_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2937),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2937,
    inference(clausify,[status(thm)],[f_747_3]) ).

fof(f_748_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_748_2,plain,
    ! [U_2939,U_2938] :
      ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2938),U_2939)
        | U_2939 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2938 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_2939 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2938 = 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_2938),U_2939) ) ),
    inference(variable_rename,[status(thm)],[f_748_1]) ).

fof(f_748_3,plain,
    ( ! [U_2943,U_2941] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2941),U_2943)
        | U_2943 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2941 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2942,U_2940] :
        ( ( U_2942 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2940 = 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_2940),U_2942) ) ),
    inference(miniscope,[status(thm)],[f_748_2]) ).

fof(f_748_4,plain,
    ( ! [U_2940,U_2942] :
        ( U_2942 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP212(U_2940,U_2942) )
    & ! [U_2940,U_2942] :
        ( U_2940 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP212(U_2940,U_2942) )
    & ! [U_2943,U_2941] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2941),U_2943)
        | U_2943 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2941 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2940,U_2942] :
        ( sP212(U_2940,U_2942)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2940),U_2942) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP212])],[f_748_3]) ).

cnf(f_748_5,plain,
    ( sP212(U_2940,U_2942)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2940),U_2942) ),
    inference(clausify,[status(thm)],[f_748_4]) ).

cnf(f_748_6,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2941),U_2943)
    | U_2943 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2941 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_748_4]) ).

cnf(f_748_7,plain,
    ( U_2940 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP212(U_2940,U_2942) ),
    inference(clausify,[status(thm)],[f_748_4]) ).

cnf(f_748_8,plain,
    ( U_2942 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP212(U_2940,U_2942) ),
    inference(clausify,[status(thm)],[f_748_4]) ).

fof(f_749_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_749_2,plain,
    ! [U_2944] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2944) = U_2944,
    inference(variable_rename,[status(thm)],[f_749_1]) ).

fof(f_749_3,plain,
    ! [U_2944] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2944) = U_2944,
    inference(definitional_conversion,[status(esa)],[f_749_2]) ).

cnf(f_749_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2944) = U_2944,
    inference(clausify,[status(thm)],[f_749_3]) ).

fof(f_750_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_750_2,plain,
    ! [U_2949,U_2948,U_2947,U_2946,U_2945] :
      ( c_Natural_Oevaln(U_2945,U_2946,U_2949,U_2948)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2947),U_2949))
      | ~ c_Natural_Oevaln(U_2945,U_2946,U_2947,U_2948) ),
    inference(variable_rename,[status(thm)],[f_750_1]) ).

fof(f_750_3,plain,
    ! [U_2945,U_2946,U_2947,U_2948,U_2949] :
      ( c_Natural_Oevaln(U_2945,U_2946,U_2949,U_2948)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2947),U_2949))
      | ~ c_Natural_Oevaln(U_2945,U_2946,U_2947,U_2948) ),
    inference(definitional_conversion,[status(esa)],[f_750_2]) ).

cnf(f_750_4,plain,
    ( c_Natural_Oevaln(U_2945,U_2946,U_2949,U_2948)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2947),U_2949))
    | ~ c_Natural_Oevaln(U_2945,U_2946,U_2947,U_2948) ),
    inference(clausify,[status(thm)],[f_750_3]) ).

fof(f_751_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_751_2,plain,
    ! [U_2952,U_2951,U_2950] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2950),U_2951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2950),U_2952)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2951),U_2952)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2951),U_2952))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2950),U_2951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2950),U_2952))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2950)) ),
    inference(variable_rename,[status(thm)],[f_751_1]) ).

fof(f_751_3,plain,
    ( ! [U_2951,U_2950,U_2952] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2950),U_2951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2950),U_2952)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2951),U_2952))
        | ~ sP213(U_2951,U_2950,U_2952) )
    & ! [U_2951,U_2950,U_2952] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2951),U_2952))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2950),U_2951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2950),U_2952)))
        | ~ sP213(U_2951,U_2950,U_2952) )
    & ! [U_2951,U_2950,U_2952] :
        ( sP213(U_2951,U_2950,U_2952)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2950)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP213])],[f_751_2]) ).

cnf(f_751_4,plain,
    ( sP213(U_2951,U_2950,U_2952)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2950)) ),
    inference(clausify,[status(thm)],[f_751_3]) ).

cnf(f_751_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2951),U_2952))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2950),U_2951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2950),U_2952)))
    | ~ sP213(U_2951,U_2950,U_2952) ),
    inference(clausify,[status(thm)],[f_751_3]) ).

cnf(f_751_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_2950),U_2951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2950),U_2952)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2951),U_2952))
    | ~ sP213(U_2951,U_2950,U_2952) ),
    inference(clausify,[status(thm)],[f_751_3]) ).

fof(f_752_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_752_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_752_1]) ).

cnf(f_752_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_752_2]) ).

fof(f_753_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_753_2,plain,
    ! [U_2954,U_2953] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2953),U_2954))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2953)),U_2954)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2953)),U_2954))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2953),U_2954)) ) ),
    inference(variable_rename,[status(thm)],[f_753_1]) ).

fof(f_753_3,plain,
    ( ! [U_2958,U_2956] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2956),U_2958))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2956)),U_2958)) )
    & ! [U_2957,U_2955] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2955)),U_2957))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2955),U_2957)) ) ),
    inference(miniscope,[status(thm)],[f_753_2]) ).

fof(f_753_4,plain,
    ( ! [U_2956,U_2958] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2956),U_2958))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2956)),U_2958)) )
    & ! [U_2957,U_2955] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2955)),U_2957))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2955),U_2957)) ) ),
    inference(definitional_conversion,[status(esa)],[f_753_3]) ).

cnf(f_753_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2955)),U_2957))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2955),U_2957)) ),
    inference(clausify,[status(thm)],[f_753_4]) ).

cnf(f_753_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2956),U_2958))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2956)),U_2958)) ),
    inference(clausify,[status(thm)],[f_753_4]) ).

fof(f_754_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_754_2,plain,
    ! [U_2960,U_2959] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2959),hAPP(c_Nat_OSuc,U_2960)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2959),U_2960)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2959),U_2960))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2959),hAPP(c_Nat_OSuc,U_2960))) ) ),
    inference(variable_rename,[status(thm)],[f_754_1]) ).

fof(f_754_3,plain,
    ( ! [U_2964,U_2962] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2962),hAPP(c_Nat_OSuc,U_2964)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2962),U_2964)) )
    & ! [U_2963,U_2961] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2961),U_2963))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2961),hAPP(c_Nat_OSuc,U_2963))) ) ),
    inference(miniscope,[status(thm)],[f_754_2]) ).

fof(f_754_4,plain,
    ( ! [U_2962,U_2964] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2962),hAPP(c_Nat_OSuc,U_2964)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2962),U_2964)) )
    & ! [U_2963,U_2961] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2961),U_2963))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2961),hAPP(c_Nat_OSuc,U_2963))) ) ),
    inference(definitional_conversion,[status(esa)],[f_754_3]) ).

cnf(f_754_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2961),U_2963))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2961),hAPP(c_Nat_OSuc,U_2963))) ),
    inference(clausify,[status(thm)],[f_754_4]) ).

cnf(f_754_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2962),hAPP(c_Nat_OSuc,U_2964)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2962),U_2964)) ),
    inference(clausify,[status(thm)],[f_754_4]) ).

fof(f_755_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_755_2,plain,
    ! [U_2966,U_2965] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2965)),U_2966))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2965),U_2966)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2965),U_2966))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2965)),U_2966)) ) ),
    inference(variable_rename,[status(thm)],[f_755_1]) ).

fof(f_755_3,plain,
    ( ! [U_2970,U_2968] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2968)),U_2970))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2968),U_2970)) )
    & ! [U_2969,U_2967] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2967),U_2969))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2967)),U_2969)) ) ),
    inference(miniscope,[status(thm)],[f_755_2]) ).

fof(f_755_4,plain,
    ( ! [U_2968,U_2970] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2968)),U_2970))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2968),U_2970)) )
    & ! [U_2969,U_2967] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2967),U_2969))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2967)),U_2969)) ) ),
    inference(definitional_conversion,[status(esa)],[f_755_3]) ).

cnf(f_755_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2967),U_2969))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2967)),U_2969)) ),
    inference(clausify,[status(thm)],[f_755_4]) ).

cnf(f_755_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2968)),U_2970))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2968),U_2970)) ),
    inference(clausify,[status(thm)],[f_755_4]) ).

fof(f_756_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_756_2,plain,
    ! [U_2972,U_2971] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2971),hAPP(c_Nat_OSuc,U_2972)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2971),U_2972)) ),
    inference(variable_rename,[status(thm)],[f_756_1]) ).

fof(f_756_3,plain,
    ! [U_2972,U_2971] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2971),hAPP(c_Nat_OSuc,U_2972)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2971),U_2972)) ),
    inference(definitional_conversion,[status(esa)],[f_756_2]) ).

cnf(f_756_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2971),hAPP(c_Nat_OSuc,U_2972)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2971),U_2972)) ),
    inference(clausify,[status(thm)],[f_756_3]) ).

fof(f_757_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_757_2,plain,
    ! [U_2974,U_2973] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2973)),U_2974))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2973),U_2974)) ),
    inference(variable_rename,[status(thm)],[f_757_1]) ).

fof(f_757_3,plain,
    ! [U_2973,U_2974] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2973)),U_2974))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2973),U_2974)) ),
    inference(definitional_conversion,[status(esa)],[f_757_2]) ).

cnf(f_757_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2973)),U_2974))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2973),U_2974)) ),
    inference(clausify,[status(thm)],[f_757_3]) ).

fof(f_758_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_758_2,plain,
    ! [U_2976,U_2975] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2976),hAPP(c_Nat_OSuc,U_2975)))
          | U_2976 != U_2975 )
        & ( U_2976 = U_2975
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2976),hAPP(c_Nat_OSuc,U_2975))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2975),U_2976)) ),
    inference(variable_rename,[status(thm)],[f_758_1]) ).

fof(f_758_3,plain,
    ( ! [U_2975,U_2976] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2976),hAPP(c_Nat_OSuc,U_2975)))
        | U_2976 != U_2975
        | ~ sP214(U_2975,U_2976) )
    & ! [U_2975,U_2976] :
        ( U_2976 = U_2975
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2976),hAPP(c_Nat_OSuc,U_2975)))
        | ~ sP214(U_2975,U_2976) )
    & ! [U_2975,U_2976] :
        ( sP214(U_2975,U_2976)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2975),U_2976)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP214])],[f_758_2]) ).

cnf(f_758_4,plain,
    ( sP214(U_2975,U_2976)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2975),U_2976)) ),
    inference(clausify,[status(thm)],[f_758_3]) ).

cnf(f_758_5,plain,
    ( U_2976 = U_2975
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2976),hAPP(c_Nat_OSuc,U_2975)))
    | ~ sP214(U_2975,U_2976) ),
    inference(clausify,[status(thm)],[f_758_3]) ).

cnf(f_758_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2976),hAPP(c_Nat_OSuc,U_2975)))
    | U_2976 != U_2975
    | ~ sP214(U_2975,U_2976) ),
    inference(clausify,[status(thm)],[f_758_3]) ).

fof(f_759_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_759_2,plain,
    ! [U_2978,U_2977] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2977),U_2978))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2977)),U_2978)) ),
    inference(variable_rename,[status(thm)],[f_759_1]) ).

fof(f_759_3,plain,
    ! [U_2978,U_2977] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2977),U_2978))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2977)),U_2978)) ),
    inference(definitional_conversion,[status(esa)],[f_759_2]) ).

cnf(f_759_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2977),U_2978))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2977)),U_2978)) ),
    inference(clausify,[status(thm)],[f_759_3]) ).

fof(f_760_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_760_2,plain,
    ! [U_2979] : hAPP(c_Nat_OSuc,U_2979) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2979),
    inference(variable_rename,[status(thm)],[f_760_1]) ).

fof(f_760_3,plain,
    ! [U_2979] : hAPP(c_Nat_OSuc,U_2979) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2979),
    inference(definitional_conversion,[status(esa)],[f_760_2]) ).

cnf(f_760_4,plain,
    hAPP(c_Nat_OSuc,U_2979) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2979),
    inference(clausify,[status(thm)],[f_760_3]) ).

fof(f_761_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_761_2,plain,
    ! [U_2980] : hAPP(c_Nat_OSuc,U_2980) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2980),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_761_1]) ).

fof(f_761_3,plain,
    ! [U_2980] : hAPP(c_Nat_OSuc,U_2980) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2980),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_761_2]) ).

cnf(f_761_4,plain,
    hAPP(c_Nat_OSuc,U_2980) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2980),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_761_3]) ).

fof(f_762_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_762_2,plain,
    ! [U_2982,U_2981] :
      ( U_2981 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_2982 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | U_2981 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2981),U_2982) ),
    inference(variable_rename,[status(thm)],[f_762_1]) ).

fof(f_762_3,plain,
    ! [U_2981,U_2982] :
      ( U_2981 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_2982 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | U_2981 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2981),U_2982) ),
    inference(definitional_conversion,[status(esa)],[f_762_2]) ).

cnf(f_762_4,plain,
    ( U_2981 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2982 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2981 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2981),U_2982) ),
    inference(clausify,[status(thm)],[f_762_3]) ).

fof(f_763_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_763_2,plain,
    ! [U_2985,U_2984,U_2983] :
      ( ( 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_2983)),U_2984)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2983)),U_2985)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2984),U_2985)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2984),U_2985))
        | ~ 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_2983)),U_2984)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2983)),U_2985))) ) ),
    inference(variable_rename,[status(thm)],[f_763_1]) ).

fof(f_763_3,plain,
    ( ! [U_2991,U_2989] :
        ( ! [U_2987] : 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_2987)),U_2989)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2987)),U_2991)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2989),U_2991)) )
    & ! [U_2990,U_2988] :
        ( ! [U_2986] : ~ 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_2986)),U_2988)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2986)),U_2990)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2988),U_2990)) ) ),
    inference(miniscope,[status(thm)],[f_763_2]) ).

fof(f_763_4,plain,
    ( ! [U_2991,U_2989,U_2987] :
        ( 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_2987)),U_2989)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2987)),U_2991)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2989),U_2991)) )
    & ! [U_2988,U_2986,U_2990] :
        ( ~ 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_2986)),U_2988)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2986)),U_2990)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2988),U_2990)) ) ),
    inference(definitional_conversion,[status(esa)],[f_763_3]) ).

cnf(f_763_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_2986)),U_2988)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2986)),U_2990)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2988),U_2990)) ),
    inference(clausify,[status(thm)],[f_763_4]) ).

cnf(f_763_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_2987)),U_2989)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2987)),U_2991)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2989),U_2991)) ),
    inference(clausify,[status(thm)],[f_763_4]) ).

fof(f_764_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_764_2,plain,
    ! [U_2993,U_2992] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2992)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2993)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2992),U_2993)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2992),U_2993))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2992)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2993))) ) ),
    inference(variable_rename,[status(thm)],[f_764_1]) ).

fof(f_764_3,plain,
    ( ! [U_2997,U_2995] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2995)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2997)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2995),U_2997)) )
    & ! [U_2996,U_2994] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2994),U_2996))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2994)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2996))) ) ),
    inference(miniscope,[status(thm)],[f_764_2]) ).

fof(f_764_4,plain,
    ( ! [U_2997,U_2995] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2995)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2997)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2995),U_2997)) )
    & ! [U_2994,U_2996] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2994),U_2996))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2994)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2996))) ) ),
    inference(definitional_conversion,[status(esa)],[f_764_3]) ).

cnf(f_764_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2994),U_2996))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2994)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2996))) ),
    inference(clausify,[status(thm)],[f_764_4]) ).

cnf(f_764_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_2995)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2997)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2995),U_2997)) ),
    inference(clausify,[status(thm)],[f_764_4]) ).

fof(f_765_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_765_2,plain,
    ! [U_2999,U_2998] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2998)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2999)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2998),U_2999)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2998),U_2999))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2998)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2999))) ) ),
    inference(variable_rename,[status(thm)],[f_765_1]) ).

fof(f_765_3,plain,
    ( ! [U_3003,U_3001] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3001)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3003)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3001),U_3003)) )
    & ! [U_3002,U_3000] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3000),U_3002))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3000)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3002))) ) ),
    inference(miniscope,[status(thm)],[f_765_2]) ).

fof(f_765_4,plain,
    ( ! [U_3003,U_3001] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3001)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3003)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3001),U_3003)) )
    & ! [U_3000,U_3002] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3000),U_3002))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3000)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3002))) ) ),
    inference(definitional_conversion,[status(esa)],[f_765_3]) ).

cnf(f_765_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3000),U_3002))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3000)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3002))) ),
    inference(clausify,[status(thm)],[f_765_4]) ).

cnf(f_765_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_3001)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3003)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3001),U_3003)) ),
    inference(clausify,[status(thm)],[f_765_4]) ).

fof(f_766_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_766_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_766_1]) ).

cnf(f_766_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_766_2]) ).

fof(f_767_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_767_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_767_1]) ).

cnf(f_767_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_767_2]) ).

fof(f_768_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_768_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_768_1]) ).

cnf(f_768_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_768_2]) ).

fof(f_769_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_769_2,plain,
    ! [U_3005,U_3004] :
      ( ( 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_3004),U_3005)))
        | ~ 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_3005))
        | ~ 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_3004)) )
      & ( ( 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_3005))
          & 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_3004)) )
        | ~ 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_3004),U_3005))) ) ),
    inference(variable_rename,[status(thm)],[f_769_1]) ).

fof(f_769_3,plain,
    ( ! [U_3009,U_3007] :
        ( 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_3007),U_3009)))
        | ~ 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_3009))
        | ~ 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_3007)) )
    & ! [U_3008,U_3006] :
        ( ( 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_3008))
          & 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_3006)) )
        | ~ 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_3006),U_3008))) ) ),
    inference(miniscope,[status(thm)],[f_769_2]) ).

fof(f_769_4,plain,
    ( ! [U_3008,U_3006] :
        ( 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_3008))
        | ~ sP215(U_3008,U_3006) )
    & ! [U_3008,U_3006] :
        ( 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_3006))
        | ~ sP215(U_3008,U_3006) )
    & ! [U_3009,U_3007] :
        ( 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_3007),U_3009)))
        | ~ 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_3009))
        | ~ 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_3007)) )
    & ! [U_3008,U_3006] :
        ( sP215(U_3008,U_3006)
        | ~ 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_3006),U_3008))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP215])],[f_769_3]) ).

cnf(f_769_5,plain,
    ( sP215(U_3008,U_3006)
    | ~ 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_3006),U_3008))) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

cnf(f_769_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_3007),U_3009)))
    | ~ 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_3009))
    | ~ 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_3007)) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

cnf(f_769_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_3006))
    | ~ sP215(U_3008,U_3006) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

cnf(f_769_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_3008))
    | ~ sP215(U_3008,U_3006) ),
    inference(clausify,[status(thm)],[f_769_4]) ).

fof(f_770_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_770_2,plain,
    ! [U_3012,U_3011,U_3010] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3010),U_3011)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3010),U_3012)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3011),U_3012))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3010)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3011),U_3012))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3010))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3010),U_3011)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3010),U_3012))) ) ),
    inference(variable_rename,[status(thm)],[f_770_1]) ).

fof(f_770_3,plain,
    ( ! [U_3018,U_3016,U_3014] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3014),U_3016)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3014),U_3018)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3016),U_3018))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3014)) ) )
    & ! [U_3017,U_3015,U_3013] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3015),U_3017))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3013))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3013),U_3015)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3013),U_3017))) ) ),
    inference(miniscope,[status(thm)],[f_770_2]) ).

fof(f_770_4,plain,
    ( ! [U_3018,U_3014,U_3016] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3016),U_3018))
        | ~ sP216(U_3018,U_3014,U_3016) )
    & ! [U_3018,U_3014,U_3016] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3014))
        | ~ sP216(U_3018,U_3014,U_3016) )
    & ! [U_3018,U_3014,U_3016] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3014),U_3016)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3014),U_3018)))
        | sP216(U_3018,U_3014,U_3016) )
    & ! [U_3013,U_3015,U_3017] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3015),U_3017))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3013))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3013),U_3015)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3013),U_3017))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP216])],[f_770_3]) ).

cnf(f_770_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3015),U_3017))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3013))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3013),U_3015)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3013),U_3017))) ),
    inference(clausify,[status(thm)],[f_770_4]) ).

cnf(f_770_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_3014),U_3016)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3014),U_3018)))
    | sP216(U_3018,U_3014,U_3016) ),
    inference(clausify,[status(thm)],[f_770_4]) ).

cnf(f_770_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3014))
    | ~ sP216(U_3018,U_3014,U_3016) ),
    inference(clausify,[status(thm)],[f_770_4]) ).

cnf(f_770_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3016),U_3018))
    | ~ sP216(U_3018,U_3014,U_3016) ),
    inference(clausify,[status(thm)],[f_770_4]) ).

fof(f_771_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_771_2,plain,
    ! [U_3021,U_3020,U_3019] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3019),U_3020)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3021),U_3020)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3019),U_3021))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3020)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3019),U_3021))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3020))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3019),U_3020)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3021),U_3020))) ) ),
    inference(variable_rename,[status(thm)],[f_771_1]) ).

fof(f_771_3,plain,
    ( ! [U_3027,U_3025,U_3023] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3023),U_3025)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3027),U_3025)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3023),U_3027))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3025)) ) )
    & ! [U_3026,U_3024,U_3022] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3022),U_3026))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3024))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3022),U_3024)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3026),U_3024))) ) ),
    inference(miniscope,[status(thm)],[f_771_2]) ).

fof(f_771_4,plain,
    ( ! [U_3025,U_3027,U_3023] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3023),U_3027))
        | ~ sP217(U_3025,U_3027,U_3023) )
    & ! [U_3025,U_3027,U_3023] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3025))
        | ~ sP217(U_3025,U_3027,U_3023) )
    & ! [U_3025,U_3027,U_3023] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3023),U_3025)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3027),U_3025)))
        | sP217(U_3025,U_3027,U_3023) )
    & ! [U_3022,U_3026,U_3024] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3022),U_3026))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3024))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3022),U_3024)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3026),U_3024))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP217])],[f_771_3]) ).

cnf(f_771_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3022),U_3026))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3024))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3022),U_3024)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3026),U_3024))) ),
    inference(clausify,[status(thm)],[f_771_4]) ).

cnf(f_771_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_3023),U_3025)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3027),U_3025)))
    | sP217(U_3025,U_3027,U_3023) ),
    inference(clausify,[status(thm)],[f_771_4]) ).

cnf(f_771_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3025))
    | ~ sP217(U_3025,U_3027,U_3023) ),
    inference(clausify,[status(thm)],[f_771_4]) ).

cnf(f_771_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3023),U_3027))
    | ~ sP217(U_3025,U_3027,U_3023) ),
    inference(clausify,[status(thm)],[f_771_4]) ).

fof(f_772_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_772_2,plain,
    ! [U_3029,U_3028] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_3028)),hAPP(c_Int_Onat,U_3029)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3028),U_3029)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3028),U_3029))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_3028)),hAPP(c_Int_Onat,U_3029))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3029))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3028)) ),
    inference(variable_rename,[status(thm)],[f_772_1]) ).

fof(f_772_3,plain,
    ( ! [U_3028,U_3029] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_3028)),hAPP(c_Int_Onat,U_3029)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3028),U_3029))
        | ~ sP218(U_3028,U_3029) )
    & ! [U_3028,U_3029] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3028),U_3029))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_3028)),hAPP(c_Int_Onat,U_3029)))
        | ~ sP218(U_3028,U_3029) )
    & ! [U_3028,U_3029] :
        ( sP218(U_3028,U_3029)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3029))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3028)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP218])],[f_772_2]) ).

cnf(f_772_4,plain,
    ( sP218(U_3028,U_3029)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3029))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3028)) ),
    inference(clausify,[status(thm)],[f_772_3]) ).

cnf(f_772_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3028),U_3029))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_3028)),hAPP(c_Int_Onat,U_3029)))
    | ~ sP218(U_3028,U_3029) ),
    inference(clausify,[status(thm)],[f_772_3]) ).

cnf(f_772_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_3028)),hAPP(c_Int_Onat,U_3029)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3028),U_3029))
    | ~ sP218(U_3028,U_3029) ),
    inference(clausify,[status(thm)],[f_772_3]) ).

fof(f_773_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_773_2,plain,
    ! [U_3031,U_3030] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_3030)),hAPP(c_Int_Onat,U_3031)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3030),U_3031)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3030),U_3031))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_3030)),hAPP(c_Int_Onat,U_3031))) ) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3031))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3030)) ) ),
    inference(variable_rename,[status(thm)],[f_773_1]) ).

fof(f_773_3,plain,
    ( ! [U_3031,U_3030] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_3030)),hAPP(c_Int_Onat,U_3031)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3030),U_3031))
        | ~ sP220(U_3031,U_3030) )
    & ! [U_3031,U_3030] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3030),U_3031))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_3030)),hAPP(c_Int_Onat,U_3031)))
        | ~ sP220(U_3031,U_3030) )
    & ! [U_3031,U_3030] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3031))
        | ~ sP219(U_3031,U_3030) )
    & ! [U_3031,U_3030] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3030))
        | ~ sP219(U_3031,U_3030) )
    & ! [U_3031,U_3030] :
        ( sP220(U_3031,U_3030)
        | sP219(U_3031,U_3030) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP219,sP220])],[f_773_2]) ).

cnf(f_773_4,plain,
    ( sP220(U_3031,U_3030)
    | sP219(U_3031,U_3030) ),
    inference(clausify,[status(thm)],[f_773_3]) ).

cnf(f_773_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3030))
    | ~ sP219(U_3031,U_3030) ),
    inference(clausify,[status(thm)],[f_773_3]) ).

cnf(f_773_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3031))
    | ~ sP219(U_3031,U_3030) ),
    inference(clausify,[status(thm)],[f_773_3]) ).

cnf(f_773_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3030),U_3031))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_3030)),hAPP(c_Int_Onat,U_3031)))
    | ~ sP220(U_3031,U_3030) ),
    inference(clausify,[status(thm)],[f_773_3]) ).

cnf(f_773_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_3030)),hAPP(c_Int_Onat,U_3031)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3030),U_3031))
    | ~ sP220(U_3031,U_3030) ),
    inference(clausify,[status(thm)],[f_773_3]) ).

fof(f_774_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_774_2,plain,
    ! [U_3034,U_3033,U_3032] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3032),U_3033) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3032),U_3034)
        | ( U_3033 != U_3034
          & U_3032 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_3033 = U_3034
        | U_3032 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3032),U_3033) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3032),U_3034) ) ),
    inference(variable_rename,[status(thm)],[f_774_1]) ).

fof(f_774_3,plain,
    ( ! [U_3040,U_3038,U_3036] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3036),U_3038) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3036),U_3040)
        | ( U_3038 != U_3040
          & U_3036 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3039,U_3037,U_3035] :
        ( U_3037 = U_3039
        | U_3035 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3035),U_3037) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3035),U_3039) ) ),
    inference(miniscope,[status(thm)],[f_774_2]) ).

fof(f_774_4,plain,
    ( ! [U_3040,U_3038,U_3036] :
        ( U_3038 != U_3040
        | ~ sP221(U_3040,U_3038,U_3036) )
    & ! [U_3040,U_3038,U_3036] :
        ( U_3036 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP221(U_3040,U_3038,U_3036) )
    & ! [U_3040,U_3038,U_3036] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3036),U_3038) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3036),U_3040)
        | sP221(U_3040,U_3038,U_3036) )
    & ! [U_3035,U_3039,U_3037] :
        ( U_3037 = U_3039
        | U_3035 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3035),U_3037) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3035),U_3039) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP221])],[f_774_3]) ).

cnf(f_774_5,plain,
    ( U_3037 = U_3039
    | U_3035 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3035),U_3037) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3035),U_3039) ),
    inference(clausify,[status(thm)],[f_774_4]) ).

cnf(f_774_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3036),U_3038) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3036),U_3040)
    | sP221(U_3040,U_3038,U_3036) ),
    inference(clausify,[status(thm)],[f_774_4]) ).

cnf(f_774_7,plain,
    ( U_3036 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP221(U_3040,U_3038,U_3036) ),
    inference(clausify,[status(thm)],[f_774_4]) ).

cnf(f_774_8,plain,
    ( U_3038 != U_3040
    | ~ sP221(U_3040,U_3038,U_3036) ),
    inference(clausify,[status(thm)],[f_774_4]) ).

fof(f_775_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_775_2,plain,
    ! [U_3044,U_3043,U_3042,U_3041] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3041),U_3042)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3043),U_3042)),U_3044)) = 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_3041),U_3043)),U_3042)),U_3044),
    inference(variable_rename,[status(thm)],[f_775_1]) ).

fof(f_775_3,plain,
    ! [U_3041,U_3042,U_3043,U_3044] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3041),U_3042)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3043),U_3042)),U_3044)) = 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_3041),U_3043)),U_3042)),U_3044),
    inference(definitional_conversion,[status(esa)],[f_775_2]) ).

cnf(f_775_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3041),U_3042)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3043),U_3042)),U_3044)) = 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_3041),U_3043)),U_3042)),U_3044),
    inference(clausify,[status(thm)],[f_775_3]) ).

fof(f_776_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_776_2,plain,
    ! [U_3047,U_3046,U_3045] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3045),U_3046)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3045),U_3047)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3046),U_3047)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3046),U_3047))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3045),U_3046)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3045),U_3047))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3045)) ),
    inference(variable_rename,[status(thm)],[f_776_1]) ).

fof(f_776_3,plain,
    ( ! [U_3045,U_3046,U_3047] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3045),U_3046)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3045),U_3047)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3046),U_3047))
        | ~ sP222(U_3045,U_3046,U_3047) )
    & ! [U_3045,U_3046,U_3047] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3046),U_3047))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3045),U_3046)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3045),U_3047)))
        | ~ sP222(U_3045,U_3046,U_3047) )
    & ! [U_3045,U_3046,U_3047] :
        ( sP222(U_3045,U_3046,U_3047)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3045)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP222])],[f_776_2]) ).

cnf(f_776_4,plain,
    ( sP222(U_3045,U_3046,U_3047)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3045)) ),
    inference(clausify,[status(thm)],[f_776_3]) ).

cnf(f_776_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3046),U_3047))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3045),U_3046)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3045),U_3047)))
    | ~ sP222(U_3045,U_3046,U_3047) ),
    inference(clausify,[status(thm)],[f_776_3]) ).

cnf(f_776_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3045),U_3046)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3045),U_3047)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3046),U_3047))
    | ~ sP222(U_3045,U_3046,U_3047) ),
    inference(clausify,[status(thm)],[f_776_3]) ).

fof(f_777_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_777_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_777_1]) ).

cnf(f_777_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_777_2]) ).

fof(f_778_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_778_2,plain,
    ! [U_3049,U_3048] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3048),U_3049),U_3049))
      | ~ class_Orderings_Opreorder(U_3048) ),
    inference(variable_rename,[status(thm)],[f_778_1]) ).

fof(f_778_3,plain,
    ! [U_3049,U_3048] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3048),U_3049),U_3049))
      | ~ class_Orderings_Opreorder(U_3048) ),
    inference(definitional_conversion,[status(esa)],[f_778_2]) ).

cnf(f_778_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3048),U_3049),U_3049))
    | ~ class_Orderings_Opreorder(U_3048) ),
    inference(clausify,[status(thm)],[f_778_3]) ).

fof(f_779_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_779_2,plain,
    ! [U_3052,U_3051,U_3050] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3050),hAPP(c_Groups_Ouminus__class_Ouminus(U_3050),U_3052)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3050),U_3051)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3050),U_3051),U_3052))
      | ~ class_Lattices_Oboolean__algebra(U_3050) ),
    inference(variable_rename,[status(thm)],[f_779_1]) ).

fof(f_779_3,plain,
    ! [U_3050,U_3051,U_3052] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3050),hAPP(c_Groups_Ouminus__class_Ouminus(U_3050),U_3052)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3050),U_3051)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3050),U_3051),U_3052))
      | ~ class_Lattices_Oboolean__algebra(U_3050) ),
    inference(definitional_conversion,[status(esa)],[f_779_2]) ).

cnf(f_779_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3050),hAPP(c_Groups_Ouminus__class_Ouminus(U_3050),U_3052)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3050),U_3051)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3050),U_3051),U_3052))
    | ~ class_Lattices_Oboolean__algebra(U_3050) ),
    inference(clausify,[status(thm)],[f_779_3]) ).

fof(f_780_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_780_2,plain,
    ! [U_3055,U_3054,U_3053] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3053),hAPP(c_Groups_Ouminus__class_Ouminus(U_3053),U_3054)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3053),U_3055)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3053),U_3055),U_3054)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3053),U_3055),U_3054))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3053),hAPP(c_Groups_Ouminus__class_Ouminus(U_3053),U_3054)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3053),U_3055))) ) )
      | ~ class_Lattices_Oboolean__algebra(U_3053) ),
    inference(variable_rename,[status(thm)],[f_780_1]) ).

fof(f_780_3,plain,
    ( ! [U_3053,U_3054,U_3055] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3053),hAPP(c_Groups_Ouminus__class_Ouminus(U_3053),U_3054)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3053),U_3055)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3053),U_3055),U_3054))
        | ~ sP223(U_3053,U_3054,U_3055) )
    & ! [U_3053,U_3054,U_3055] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3053),U_3055),U_3054))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3053),hAPP(c_Groups_Ouminus__class_Ouminus(U_3053),U_3054)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3053),U_3055)))
        | ~ sP223(U_3053,U_3054,U_3055) )
    & ! [U_3053,U_3054,U_3055] :
        ( sP223(U_3053,U_3054,U_3055)
        | ~ class_Lattices_Oboolean__algebra(U_3053) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP223])],[f_780_2]) ).

cnf(f_780_4,plain,
    ( sP223(U_3053,U_3054,U_3055)
    | ~ class_Lattices_Oboolean__algebra(U_3053) ),
    inference(clausify,[status(thm)],[f_780_3]) ).

cnf(f_780_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3053),U_3055),U_3054))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3053),hAPP(c_Groups_Ouminus__class_Ouminus(U_3053),U_3054)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3053),U_3055)))
    | ~ sP223(U_3053,U_3054,U_3055) ),
    inference(clausify,[status(thm)],[f_780_3]) ).

cnf(f_780_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3053),hAPP(c_Groups_Ouminus__class_Ouminus(U_3053),U_3054)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3053),U_3055)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3053),U_3055),U_3054))
    | ~ sP223(U_3053,U_3054,U_3055) ),
    inference(clausify,[status(thm)],[f_780_3]) ).

fof(f_781_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_781_2,plain,
    ! [U_3059,U_3058,U_3057,U_3056] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3056),U_3059),U_3058))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3056),U_3059),U_3057))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3056),U_3057),U_3058))
      | ~ class_Orderings_Oorder(U_3056) ),
    inference(variable_rename,[status(thm)],[f_781_1]) ).

fof(f_781_3,plain,
    ! [U_3057,U_3056,U_3058,U_3059] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3056),U_3059),U_3058))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3056),U_3059),U_3057))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3056),U_3057),U_3058))
      | ~ class_Orderings_Oorder(U_3056) ),
    inference(definitional_conversion,[status(esa)],[f_781_2]) ).

cnf(f_781_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3056),U_3059),U_3058))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3056),U_3059),U_3057))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3056),U_3057),U_3058))
    | ~ class_Orderings_Oorder(U_3056) ),
    inference(clausify,[status(thm)],[f_781_3]) ).

fof(f_782_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_782_2,plain,
    ! [U_3063,U_3062,U_3061,U_3060] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3060),U_3061),U_3063))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3060),U_3062),U_3063))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3060),U_3061),U_3062))
      | ~ class_Orderings_Opreorder(U_3060) ),
    inference(variable_rename,[status(thm)],[f_782_1]) ).

fof(f_782_3,plain,
    ! [U_3060,U_3061,U_3062,U_3063] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3060),U_3061),U_3063))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3060),U_3062),U_3063))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3060),U_3061),U_3062))
      | ~ class_Orderings_Opreorder(U_3060) ),
    inference(definitional_conversion,[status(esa)],[f_782_2]) ).

cnf(f_782_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3060),U_3061),U_3063))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3060),U_3062),U_3063))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3060),U_3061),U_3062))
    | ~ class_Orderings_Opreorder(U_3060) ),
    inference(clausify,[status(thm)],[f_782_3]) ).

fof(f_783_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_783_2,plain,
    ! [U_3067,U_3066,U_3065,U_3064] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3064),U_3067),U_3066))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3064),U_3067),U_3065))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3064),U_3065),U_3066))
      | ~ class_Orderings_Oorder(U_3064) ),
    inference(variable_rename,[status(thm)],[f_783_1]) ).

fof(f_783_3,plain,
    ! [U_3064,U_3065,U_3066,U_3067] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3064),U_3067),U_3066))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3064),U_3067),U_3065))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3064),U_3065),U_3066))
      | ~ class_Orderings_Oorder(U_3064) ),
    inference(definitional_conversion,[status(esa)],[f_783_2]) ).

cnf(f_783_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3064),U_3067),U_3066))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3064),U_3067),U_3065))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3064),U_3065),U_3066))
    | ~ class_Orderings_Oorder(U_3064) ),
    inference(clausify,[status(thm)],[f_783_3]) ).

fof(f_784_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_784_2,plain,
    ! [U_3071,U_3070,U_3069,U_3068] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3068),U_3069),U_3071))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3068),U_3070),U_3071))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3068),U_3069),U_3070))
      | ~ class_Orderings_Opreorder(U_3068) ),
    inference(variable_rename,[status(thm)],[f_784_1]) ).

fof(f_784_3,plain,
    ! [U_3068,U_3069,U_3070,U_3071] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3068),U_3069),U_3071))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3068),U_3070),U_3071))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3068),U_3069),U_3070))
      | ~ class_Orderings_Opreorder(U_3068) ),
    inference(definitional_conversion,[status(esa)],[f_784_2]) ).

cnf(f_784_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3068),U_3069),U_3071))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3068),U_3070),U_3071))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3068),U_3069),U_3070))
    | ~ class_Orderings_Opreorder(U_3068) ),
    inference(clausify,[status(thm)],[f_784_3]) ).

fof(f_785_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_785_2,plain,
    ! [U_3074,U_3073,U_3072] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3072),U_3073),U_3074))
      | U_3074 = U_3073
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3072),U_3073),U_3074))
      | ~ class_Orderings_Oorder(U_3072) ),
    inference(variable_rename,[status(thm)],[f_785_1]) ).

fof(f_785_3,plain,
    ! [U_3072,U_3073,U_3074] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3072),U_3073),U_3074))
      | U_3074 = U_3073
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3072),U_3073),U_3074))
      | ~ class_Orderings_Oorder(U_3072) ),
    inference(definitional_conversion,[status(esa)],[f_785_2]) ).

cnf(f_785_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3072),U_3073),U_3074))
    | U_3074 = U_3073
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3072),U_3073),U_3074))
    | ~ class_Orderings_Oorder(U_3072) ),
    inference(clausify,[status(thm)],[f_785_3]) ).

fof(f_786_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_786_2,plain,
    ! [U_3080,U_3079,U_3078,U_3077] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3078,U_3077)),U_3079),U_3080))
          | ? [U_3076] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3077),hAPP(U_3079,U_3076)),hAPP(U_3080,U_3076))) )
        & ( ! [U_3075] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3077),hAPP(U_3079,U_3075)),hAPP(U_3080,U_3075)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3078,U_3077)),U_3079),U_3080)) ) )
      | ~ class_Orderings_Oord(U_3077) ),
    inference(variable_rename,[status(thm)],[f_786_1]) ).

fof(f_786_3,plain,
    ! [U_3080,U_3079,U_3078,U_3077] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3078,U_3077)),U_3079),U_3080))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3077),hAPP(U_3079,sK61(U_3080,U_3079,U_3078,U_3077))),hAPP(U_3080,sK61(U_3080,U_3079,U_3078,U_3077)))) )
        & ( ! [U_3075] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3077),hAPP(U_3079,U_3075)),hAPP(U_3080,U_3075)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3078,U_3077)),U_3079),U_3080)) ) )
      | ~ class_Orderings_Oord(U_3077) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_3076,sK61(U_3080,U_3079,U_3078,U_3077))],[f_786_2]) ).

fof(f_786_4,plain,
    ( ! [U_3075,U_3077,U_3078,U_3079,U_3080] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3078,U_3077)),U_3079),U_3080))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3077),hAPP(U_3079,sK61(U_3080,U_3079,U_3078,U_3077))),hAPP(U_3080,sK61(U_3080,U_3079,U_3078,U_3077))))
        | ~ sP224(U_3075,U_3077,U_3078,U_3079,U_3080) )
    & ! [U_3075,U_3077,U_3078,U_3079,U_3080] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3077),hAPP(U_3079,U_3075)),hAPP(U_3080,U_3075)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3078,U_3077)),U_3079),U_3080))
        | ~ sP224(U_3075,U_3077,U_3078,U_3079,U_3080) )
    & ! [U_3075,U_3077,U_3078,U_3079,U_3080] :
        ( sP224(U_3075,U_3077,U_3078,U_3079,U_3080)
        | ~ class_Orderings_Oord(U_3077) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP224])],[f_786_3]) ).

cnf(f_786_5,plain,
    ( sP224(U_3075,U_3077,U_3078,U_3079,U_3080)
    | ~ class_Orderings_Oord(U_3077) ),
    inference(clausify,[status(thm)],[f_786_4]) ).

cnf(f_786_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3077),hAPP(U_3079,U_3075)),hAPP(U_3080,U_3075)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3078,U_3077)),U_3079),U_3080))
    | ~ sP224(U_3075,U_3077,U_3078,U_3079,U_3080) ),
    inference(clausify,[status(thm)],[f_786_4]) ).

cnf(f_786_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3078,U_3077)),U_3079),U_3080))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3077),hAPP(U_3079,sK61(U_3080,U_3079,U_3078,U_3077))),hAPP(U_3080,sK61(U_3080,U_3079,U_3078,U_3077))))
    | ~ sP224(U_3075,U_3077,U_3078,U_3079,U_3080) ),
    inference(clausify,[status(thm)],[f_786_4]) ).

fof(f_787_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_787_2,plain,
    ! [U_3083,U_3082,U_3081] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3081),U_3083),U_3082))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3081),U_3082),U_3083))
      | ~ class_Orderings_Olinorder(U_3081) ),
    inference(variable_rename,[status(thm)],[f_787_1]) ).

fof(f_787_3,plain,
    ! [U_3081,U_3083,U_3082] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3081),U_3083),U_3082))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3081),U_3082),U_3083))
      | ~ class_Orderings_Olinorder(U_3081) ),
    inference(definitional_conversion,[status(esa)],[f_787_2]) ).

cnf(f_787_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3081),U_3083),U_3082))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3081),U_3082),U_3083))
    | ~ class_Orderings_Olinorder(U_3081) ),
    inference(clausify,[status(thm)],[f_787_3]) ).

fof(f_788_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_788_2,plain,
    ! [U_3086,U_3085,U_3084] :
      ( ( ( U_3085 = U_3086
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3084),U_3086),U_3085))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3084),U_3085),U_3086)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3084),U_3086),U_3085))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3084),U_3085),U_3086)) )
          | U_3085 != U_3086 ) )
      | ~ class_Orderings_Oorder(U_3084) ),
    inference(variable_rename,[status(thm)],[f_788_1]) ).

fof(f_788_3,plain,
    ( ! [U_3084,U_3085,U_3086] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3084),U_3086),U_3085))
        | ~ sP225(U_3084,U_3085,U_3086) )
    & ! [U_3084,U_3085,U_3086] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3084),U_3085),U_3086))
        | ~ sP225(U_3084,U_3085,U_3086) )
    & ! [U_3084,U_3085,U_3086] :
        ( U_3085 = U_3086
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3084),U_3086),U_3085))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3084),U_3085),U_3086))
        | ~ sP226(U_3084,U_3085,U_3086) )
    & ! [U_3084,U_3085,U_3086] :
        ( sP225(U_3084,U_3085,U_3086)
        | U_3085 != U_3086
        | ~ sP226(U_3084,U_3085,U_3086) )
    & ! [U_3084,U_3085,U_3086] :
        ( sP226(U_3084,U_3085,U_3086)
        | ~ class_Orderings_Oorder(U_3084) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP225,sP226])],[f_788_2]) ).

cnf(f_788_4,plain,
    ( sP226(U_3084,U_3085,U_3086)
    | ~ class_Orderings_Oorder(U_3084) ),
    inference(clausify,[status(thm)],[f_788_3]) ).

cnf(f_788_5,plain,
    ( sP225(U_3084,U_3085,U_3086)
    | U_3085 != U_3086
    | ~ sP226(U_3084,U_3085,U_3086) ),
    inference(clausify,[status(thm)],[f_788_3]) ).

cnf(f_788_6,plain,
    ( U_3085 = U_3086
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3084),U_3086),U_3085))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3084),U_3085),U_3086))
    | ~ sP226(U_3084,U_3085,U_3086) ),
    inference(clausify,[status(thm)],[f_788_3]) ).

cnf(f_788_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3084),U_3085),U_3086))
    | ~ sP225(U_3084,U_3085,U_3086) ),
    inference(clausify,[status(thm)],[f_788_3]) ).

cnf(f_788_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3084),U_3086),U_3085))
    | ~ sP225(U_3084,U_3085,U_3086) ),
    inference(clausify,[status(thm)],[f_788_3]) ).

fof(f_789_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_789_2,plain,
    ! [U_3089,U_3088,U_3087] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3087),U_3088),U_3089))
      | U_3088 != U_3089
      | ~ class_Orderings_Opreorder(U_3087) ),
    inference(variable_rename,[status(thm)],[f_789_1]) ).

fof(f_789_3,plain,
    ! [U_3089,U_3088,U_3087] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3087),U_3088),U_3089))
      | U_3088 != U_3089
      | ~ class_Orderings_Opreorder(U_3087) ),
    inference(definitional_conversion,[status(esa)],[f_789_2]) ).

cnf(f_789_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3087),U_3088),U_3089))
    | U_3088 != U_3089
    | ~ class_Orderings_Opreorder(U_3087) ),
    inference(clausify,[status(thm)],[f_789_3]) ).

fof(f_790_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_790_2,plain,
    ! [U_3094,U_3093,U_3092,U_3091,U_3090] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3090),hAPP(U_3092,U_3094)),hAPP(U_3093,U_3094)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3091,U_3090)),U_3092),U_3093))
      | ~ class_Orderings_Oord(U_3090) ),
    inference(variable_rename,[status(thm)],[f_790_1]) ).

fof(f_790_3,plain,
    ! [U_3090,U_3091,U_3092,U_3093,U_3094] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3090),hAPP(U_3092,U_3094)),hAPP(U_3093,U_3094)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3091,U_3090)),U_3092),U_3093))
      | ~ class_Orderings_Oord(U_3090) ),
    inference(definitional_conversion,[status(esa)],[f_790_2]) ).

cnf(f_790_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3090),hAPP(U_3092,U_3094)),hAPP(U_3093,U_3094)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3091,U_3090)),U_3092),U_3093))
    | ~ class_Orderings_Oord(U_3090) ),
    inference(clausify,[status(thm)],[f_790_3]) ).

fof(f_791_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_791_2,plain,
    ! [U_3097,U_3096,U_3095] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3095),U_3097),U_3096))
          | U_3097 != U_3096 )
        & ( U_3097 = U_3096
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3095),U_3097),U_3096)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3095),U_3096),U_3097))
      | ~ class_Orderings_Oorder(U_3095) ),
    inference(variable_rename,[status(thm)],[f_791_1]) ).

fof(f_791_3,plain,
    ( ! [U_3095,U_3096,U_3097] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3095),U_3097),U_3096))
        | U_3097 != U_3096
        | ~ sP227(U_3095,U_3096,U_3097) )
    & ! [U_3095,U_3096,U_3097] :
        ( U_3097 = U_3096
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3095),U_3097),U_3096))
        | ~ sP227(U_3095,U_3096,U_3097) )
    & ! [U_3095,U_3096,U_3097] :
        ( sP227(U_3095,U_3096,U_3097)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3095),U_3096),U_3097))
        | ~ class_Orderings_Oorder(U_3095) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP227])],[f_791_2]) ).

cnf(f_791_4,plain,
    ( sP227(U_3095,U_3096,U_3097)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3095),U_3096),U_3097))
    | ~ class_Orderings_Oorder(U_3095) ),
    inference(clausify,[status(thm)],[f_791_3]) ).

cnf(f_791_5,plain,
    ( U_3097 = U_3096
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3095),U_3097),U_3096))
    | ~ sP227(U_3095,U_3096,U_3097) ),
    inference(clausify,[status(thm)],[f_791_3]) ).

cnf(f_791_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3095),U_3097),U_3096))
    | U_3097 != U_3096
    | ~ sP227(U_3095,U_3096,U_3097) ),
    inference(clausify,[status(thm)],[f_791_3]) ).

fof(f_792_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_792_2,plain,
    ! [U_3101,U_3100,U_3099,U_3098] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3098),U_3099),U_3101))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3098),U_3100),U_3101))
      | U_3099 != U_3100
      | ~ class_Orderings_Oord(U_3098) ),
    inference(variable_rename,[status(thm)],[f_792_1]) ).

fof(f_792_3,plain,
    ! [U_3100,U_3101,U_3099,U_3098] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3098),U_3099),U_3101))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3098),U_3100),U_3101))
      | U_3099 != U_3100
      | ~ class_Orderings_Oord(U_3098) ),
    inference(definitional_conversion,[status(esa)],[f_792_2]) ).

cnf(f_792_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3098),U_3099),U_3101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3098),U_3100),U_3101))
    | U_3099 != U_3100
    | ~ class_Orderings_Oord(U_3098) ),
    inference(clausify,[status(thm)],[f_792_3]) ).

fof(f_793_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_793_2,plain,
    ! [U_3105,U_3104,U_3103,U_3102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3102),U_3105),U_3103))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3102),U_3105),U_3104))
      | U_3103 != U_3104
      | ~ class_Orderings_Oorder(U_3102) ),
    inference(variable_rename,[status(thm)],[f_793_1]) ).

fof(f_793_3,plain,
    ! [U_3102,U_3103,U_3104,U_3105] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3102),U_3105),U_3103))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3102),U_3105),U_3104))
      | U_3103 != U_3104
      | ~ class_Orderings_Oorder(U_3102) ),
    inference(definitional_conversion,[status(esa)],[f_793_2]) ).

cnf(f_793_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3102),U_3105),U_3103))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3102),U_3105),U_3104))
    | U_3103 != U_3104
    | ~ class_Orderings_Oorder(U_3102) ),
    inference(clausify,[status(thm)],[f_793_3]) ).

fof(f_794_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_794_2,plain,
    ! [U_3109,U_3108,U_3107,U_3106] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3106),U_3107),U_3109))
      | U_3108 != U_3109
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3106),U_3107),U_3108))
      | ~ class_Orderings_Oord(U_3106) ),
    inference(variable_rename,[status(thm)],[f_794_1]) ).

fof(f_794_3,plain,
    ! [U_3107,U_3106,U_3108,U_3109] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3106),U_3107),U_3109))
      | U_3108 != U_3109
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3106),U_3107),U_3108))
      | ~ class_Orderings_Oord(U_3106) ),
    inference(definitional_conversion,[status(esa)],[f_794_2]) ).

cnf(f_794_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3106),U_3107),U_3109))
    | U_3108 != U_3109
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3106),U_3107),U_3108))
    | ~ class_Orderings_Oord(U_3106) ),
    inference(clausify,[status(thm)],[f_794_3]) ).

fof(f_795_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_795_2,plain,
    ! [U_3113,U_3112,U_3111,U_3110] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3110),U_3113),U_3112))
      | U_3111 != U_3113
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3110),U_3111),U_3112))
      | ~ class_Orderings_Oorder(U_3110) ),
    inference(variable_rename,[status(thm)],[f_795_1]) ).

fof(f_795_3,plain,
    ! [U_3110,U_3111,U_3112,U_3113] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3110),U_3113),U_3112))
      | U_3111 != U_3113
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3110),U_3111),U_3112))
      | ~ class_Orderings_Oorder(U_3110) ),
    inference(definitional_conversion,[status(esa)],[f_795_2]) ).

cnf(f_795_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3110),U_3113),U_3112))
    | U_3111 != U_3113
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3110),U_3111),U_3112))
    | ~ class_Orderings_Oorder(U_3110) ),
    inference(clausify,[status(thm)],[f_795_3]) ).

fof(f_796_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_796_2,plain,
    ! [U_3116,U_3115,U_3114] :
      ( U_3115 = U_3116
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3114),U_3116),U_3115))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3114),U_3115),U_3116))
      | ~ class_Orderings_Oorder(U_3114) ),
    inference(variable_rename,[status(thm)],[f_796_1]) ).

fof(f_796_3,plain,
    ! [U_3114,U_3115,U_3116] :
      ( U_3115 = U_3116
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3114),U_3116),U_3115))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3114),U_3115),U_3116))
      | ~ class_Orderings_Oorder(U_3114) ),
    inference(definitional_conversion,[status(esa)],[f_796_2]) ).

cnf(f_796_4,plain,
    ( U_3115 = U_3116
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3114),U_3116),U_3115))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3114),U_3115),U_3116))
    | ~ class_Orderings_Oorder(U_3114) ),
    inference(clausify,[status(thm)],[f_796_3]) ).

fof(f_797_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_797_2,plain,
    ! [U_3120,U_3119,U_3118,U_3117] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3117),U_3118),U_3120))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3117),U_3119),U_3120))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3117),U_3118),U_3119))
      | ~ class_Orderings_Opreorder(U_3117) ),
    inference(variable_rename,[status(thm)],[f_797_1]) ).

fof(f_797_3,plain,
    ! [U_3117,U_3118,U_3119,U_3120] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3117),U_3118),U_3120))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3117),U_3119),U_3120))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3117),U_3118),U_3119))
      | ~ class_Orderings_Opreorder(U_3117) ),
    inference(definitional_conversion,[status(esa)],[f_797_2]) ).

cnf(f_797_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3117),U_3118),U_3120))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3117),U_3119),U_3120))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3117),U_3118),U_3119))
    | ~ class_Orderings_Opreorder(U_3117) ),
    inference(clausify,[status(thm)],[f_797_3]) ).

fof(f_798_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_798_2,plain,
    ! [U_3123,U_3122,U_3121] :
      ( U_3123 = U_3122
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3121),U_3123),U_3122))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3121),U_3122),U_3123))
      | ~ class_Orderings_Oorder(U_3121) ),
    inference(variable_rename,[status(thm)],[f_798_1]) ).

fof(f_798_3,plain,
    ! [U_3121,U_3122,U_3123] :
      ( U_3123 = U_3122
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3121),U_3123),U_3122))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3121),U_3122),U_3123))
      | ~ class_Orderings_Oorder(U_3121) ),
    inference(definitional_conversion,[status(esa)],[f_798_2]) ).

cnf(f_798_4,plain,
    ( U_3123 = U_3122
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3121),U_3123),U_3122))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3121),U_3122),U_3123))
    | ~ class_Orderings_Oorder(U_3121) ),
    inference(clausify,[status(thm)],[f_798_3]) ).

fof(f_799_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_799_2,plain,
    ! [U_3127,U_3126,U_3125,U_3124] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3124),U_3127),U_3126))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3124),U_3127),U_3125))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3124),U_3125),U_3126))
      | ~ class_Orderings_Oorder(U_3124) ),
    inference(variable_rename,[status(thm)],[f_799_1]) ).

fof(f_799_3,plain,
    ! [U_3124,U_3125,U_3126,U_3127] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3124),U_3127),U_3126))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3124),U_3127),U_3125))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3124),U_3125),U_3126))
      | ~ class_Orderings_Oorder(U_3124) ),
    inference(definitional_conversion,[status(esa)],[f_799_2]) ).

cnf(f_799_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3124),U_3127),U_3126))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3124),U_3127),U_3125))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3124),U_3125),U_3126))
    | ~ class_Orderings_Oorder(U_3124) ),
    inference(clausify,[status(thm)],[f_799_3]) ).

fof(f_800_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_800_2,plain,
    ! [U_3132,U_3131,U_3130,U_3129,U_3128] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3128),hAPP(U_3130,U_3132)),hAPP(U_3131,U_3132)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3129,U_3128)),U_3130),U_3131))
      | ~ class_Orderings_Oord(U_3128) ),
    inference(variable_rename,[status(thm)],[f_800_1]) ).

fof(f_800_3,plain,
    ! [U_3128,U_3129,U_3130,U_3131,U_3132] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3128),hAPP(U_3130,U_3132)),hAPP(U_3131,U_3132)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3129,U_3128)),U_3130),U_3131))
      | ~ class_Orderings_Oord(U_3128) ),
    inference(definitional_conversion,[status(esa)],[f_800_2]) ).

cnf(f_800_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3128),hAPP(U_3130,U_3132)),hAPP(U_3131,U_3132)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3129,U_3128)),U_3130),U_3131))
    | ~ class_Orderings_Oord(U_3128) ),
    inference(clausify,[status(thm)],[f_800_3]) ).

fof(f_801_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_801_2,plain,
    ! [U_3135,U_3134,U_3133] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3133),U_3135),U_3134))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3133),U_3134),U_3135))
      | ~ class_Orderings_Olinorder(U_3133) ),
    inference(variable_rename,[status(thm)],[f_801_1]) ).

fof(f_801_3,plain,
    ! [U_3133,U_3134,U_3135] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3133),U_3135),U_3134))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3133),U_3134),U_3135))
      | ~ class_Orderings_Olinorder(U_3133) ),
    inference(definitional_conversion,[status(esa)],[f_801_2]) ).

cnf(f_801_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3133),U_3135),U_3134))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3133),U_3134),U_3135))
    | ~ class_Orderings_Olinorder(U_3133) ),
    inference(clausify,[status(thm)],[f_801_3]) ).

fof(f_802_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_802_2,plain,
    ! [U_3137,U_3136] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3136),U_3137),U_3137))
      | ~ class_Orderings_Opreorder(U_3136) ),
    inference(variable_rename,[status(thm)],[f_802_1]) ).

fof(f_802_3,plain,
    ! [U_3137,U_3136] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3136),U_3137),U_3137))
      | ~ class_Orderings_Opreorder(U_3136) ),
    inference(definitional_conversion,[status(esa)],[f_802_2]) ).

cnf(f_802_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3136),U_3137),U_3137))
    | ~ class_Orderings_Opreorder(U_3136) ),
    inference(clausify,[status(thm)],[f_802_3]) ).

fof(f_803_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_803_2,plain,
    ! [U_3140,U_3139,U_3138] :
      ( ( ( U_3139 != U_3140
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3138),U_3140),U_3139))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3138),U_3139),U_3140)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3138),U_3140),U_3139))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3138),U_3139),U_3140))
          | U_3139 = U_3140 ) )
      | ~ class_Orderings_Olinorder(U_3138) ),
    inference(variable_rename,[status(thm)],[f_803_1]) ).

fof(f_803_3,plain,
    ( ! [U_3138,U_3139,U_3140] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3138),U_3140),U_3139))
        | ~ sP228(U_3138,U_3139,U_3140) )
    & ! [U_3138,U_3139,U_3140] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3138),U_3139),U_3140))
        | ~ sP228(U_3138,U_3139,U_3140) )
    & ! [U_3138,U_3139,U_3140] :
        ( U_3139 != U_3140
        | sP228(U_3138,U_3139,U_3140)
        | ~ sP229(U_3138,U_3139,U_3140) )
    & ! [U_3138,U_3139,U_3140] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3138),U_3140),U_3139))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3138),U_3139),U_3140))
        | U_3139 = U_3140
        | ~ sP229(U_3138,U_3139,U_3140) )
    & ! [U_3138,U_3139,U_3140] :
        ( sP229(U_3138,U_3139,U_3140)
        | ~ class_Orderings_Olinorder(U_3138) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP228,sP229])],[f_803_2]) ).

cnf(f_803_4,plain,
    ( sP229(U_3138,U_3139,U_3140)
    | ~ class_Orderings_Olinorder(U_3138) ),
    inference(clausify,[status(thm)],[f_803_3]) ).

cnf(f_803_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3138),U_3140),U_3139))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3138),U_3139),U_3140))
    | U_3139 = U_3140
    | ~ sP229(U_3138,U_3139,U_3140) ),
    inference(clausify,[status(thm)],[f_803_3]) ).

cnf(f_803_6,plain,
    ( U_3139 != U_3140
    | sP228(U_3138,U_3139,U_3140)
    | ~ sP229(U_3138,U_3139,U_3140) ),
    inference(clausify,[status(thm)],[f_803_3]) ).

cnf(f_803_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3138),U_3139),U_3140))
    | ~ sP228(U_3138,U_3139,U_3140) ),
    inference(clausify,[status(thm)],[f_803_3]) ).

cnf(f_803_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3138),U_3140),U_3139))
    | ~ sP228(U_3138,U_3139,U_3140) ),
    inference(clausify,[status(thm)],[f_803_3]) ).

fof(f_804_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_804_2,plain,
    ! [U_3143,U_3142,U_3141] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3141),U_3142),U_3143))
          | ( U_3142 != U_3143
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3141),U_3143),U_3142)) ) )
        & ( U_3142 = U_3143
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3141),U_3143),U_3142))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3141),U_3142),U_3143)) ) )
      | ~ class_Orderings_Olinorder(U_3141) ),
    inference(variable_rename,[status(thm)],[f_804_1]) ).

fof(f_804_3,plain,
    ( ! [U_3142,U_3141,U_3143] :
        ( U_3142 != U_3143
        | ~ sP230(U_3142,U_3141,U_3143) )
    & ! [U_3142,U_3141,U_3143] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3141),U_3143),U_3142))
        | ~ sP230(U_3142,U_3141,U_3143) )
    & ! [U_3142,U_3141,U_3143] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3141),U_3142),U_3143))
        | sP230(U_3142,U_3141,U_3143)
        | ~ sP231(U_3142,U_3141,U_3143) )
    & ! [U_3142,U_3141,U_3143] :
        ( U_3142 = U_3143
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3141),U_3143),U_3142))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3141),U_3142),U_3143))
        | ~ sP231(U_3142,U_3141,U_3143) )
    & ! [U_3142,U_3141,U_3143] :
        ( sP231(U_3142,U_3141,U_3143)
        | ~ class_Orderings_Olinorder(U_3141) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP230,sP231])],[f_804_2]) ).

cnf(f_804_4,plain,
    ( sP231(U_3142,U_3141,U_3143)
    | ~ class_Orderings_Olinorder(U_3141) ),
    inference(clausify,[status(thm)],[f_804_3]) ).

cnf(f_804_5,plain,
    ( U_3142 = U_3143
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3141),U_3143),U_3142))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3141),U_3142),U_3143))
    | ~ sP231(U_3142,U_3141,U_3143) ),
    inference(clausify,[status(thm)],[f_804_3]) ).

cnf(f_804_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3141),U_3142),U_3143))
    | sP230(U_3142,U_3141,U_3143)
    | ~ sP231(U_3142,U_3141,U_3143) ),
    inference(clausify,[status(thm)],[f_804_3]) ).

cnf(f_804_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3141),U_3143),U_3142))
    | ~ sP230(U_3142,U_3141,U_3143) ),
    inference(clausify,[status(thm)],[f_804_3]) ).

cnf(f_804_8,plain,
    ( U_3142 != U_3143
    | ~ sP230(U_3142,U_3141,U_3143) ),
    inference(clausify,[status(thm)],[f_804_3]) ).

fof(f_805_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_805_2,plain,
    ! [U_3146,U_3145,U_3144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3144),U_3146),U_3145))
      | U_3145 = U_3146
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3144),U_3145),U_3146))
      | ~ class_Orderings_Olinorder(U_3144) ),
    inference(variable_rename,[status(thm)],[f_805_1]) ).

fof(f_805_3,plain,
    ! [U_3145,U_3146,U_3144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3144),U_3146),U_3145))
      | U_3145 = U_3146
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3144),U_3145),U_3146))
      | ~ class_Orderings_Olinorder(U_3144) ),
    inference(definitional_conversion,[status(esa)],[f_805_2]) ).

cnf(f_805_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3144),U_3146),U_3145))
    | U_3145 = U_3146
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3144),U_3145),U_3146))
    | ~ class_Orderings_Olinorder(U_3144) ),
    inference(clausify,[status(thm)],[f_805_3]) ).

fof(f_806_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_806_2,plain,
    ! [U_3149,U_3148,U_3147] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3147),U_3149),U_3148))
          | U_3149 != U_3148 )
        & ( U_3149 = U_3148
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3147),U_3149),U_3148)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3147),U_3148),U_3149))
      | ~ class_Orderings_Olinorder(U_3147) ),
    inference(variable_rename,[status(thm)],[f_806_1]) ).

fof(f_806_3,plain,
    ( ! [U_3148,U_3147,U_3149] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3147),U_3149),U_3148))
        | U_3149 != U_3148
        | ~ sP232(U_3148,U_3147,U_3149) )
    & ! [U_3148,U_3147,U_3149] :
        ( U_3149 = U_3148
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3147),U_3149),U_3148))
        | ~ sP232(U_3148,U_3147,U_3149) )
    & ! [U_3148,U_3147,U_3149] :
        ( sP232(U_3148,U_3147,U_3149)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3147),U_3148),U_3149))
        | ~ class_Orderings_Olinorder(U_3147) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP232])],[f_806_2]) ).

cnf(f_806_4,plain,
    ( sP232(U_3148,U_3147,U_3149)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3147),U_3148),U_3149))
    | ~ class_Orderings_Olinorder(U_3147) ),
    inference(clausify,[status(thm)],[f_806_3]) ).

cnf(f_806_5,plain,
    ( U_3149 = U_3148
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3147),U_3149),U_3148))
    | ~ sP232(U_3148,U_3147,U_3149) ),
    inference(clausify,[status(thm)],[f_806_3]) ).

cnf(f_806_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3147),U_3149),U_3148))
    | U_3149 != U_3148
    | ~ sP232(U_3148,U_3147,U_3149) ),
    inference(clausify,[status(thm)],[f_806_3]) ).

fof(f_807_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_807_2,plain,
    ! [U_3152,U_3151,U_3150] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3150),U_3152),U_3151))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3150),U_3151),U_3152))
      | U_3151 = U_3152
      | ~ class_Orderings_Olinorder(U_3150) ),
    inference(variable_rename,[status(thm)],[f_807_1]) ).

fof(f_807_3,plain,
    ! [U_3152,U_3151,U_3150] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3150),U_3152),U_3151))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3150),U_3151),U_3152))
      | U_3151 = U_3152
      | ~ class_Orderings_Olinorder(U_3150) ),
    inference(definitional_conversion,[status(esa)],[f_807_2]) ).

cnf(f_807_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3150),U_3152),U_3151))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3150),U_3151),U_3152))
    | U_3151 = U_3152
    | ~ class_Orderings_Olinorder(U_3150) ),
    inference(clausify,[status(thm)],[f_807_3]) ).

fof(f_808_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_808_2,plain,
    ! [U_3155,U_3154,U_3153] :
      ( U_3154 != U_3155
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3153),U_3154),U_3155))
      | ~ class_Orderings_Oorder(U_3153) ),
    inference(variable_rename,[status(thm)],[f_808_1]) ).

fof(f_808_3,plain,
    ! [U_3155,U_3154,U_3153] :
      ( U_3154 != U_3155
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3153),U_3154),U_3155))
      | ~ class_Orderings_Oorder(U_3153) ),
    inference(definitional_conversion,[status(esa)],[f_808_2]) ).

cnf(f_808_4,plain,
    ( U_3154 != U_3155
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3153),U_3154),U_3155))
    | ~ class_Orderings_Oorder(U_3153) ),
    inference(clausify,[status(thm)],[f_808_3]) ).

fof(f_809_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_809_2,plain,
    ! [U_3158,U_3157,U_3156] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3156),U_3158),U_3157))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3156),U_3157),U_3158))
      | ~ class_Orderings_Opreorder(U_3156) ),
    inference(variable_rename,[status(thm)],[f_809_1]) ).

fof(f_809_3,plain,
    ! [U_3156,U_3157,U_3158] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3156),U_3158),U_3157))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3156),U_3157),U_3158))
      | ~ class_Orderings_Opreorder(U_3156) ),
    inference(definitional_conversion,[status(esa)],[f_809_2]) ).

cnf(f_809_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3156),U_3158),U_3157))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3156),U_3157),U_3158))
    | ~ class_Orderings_Opreorder(U_3156) ),
    inference(clausify,[status(thm)],[f_809_3]) ).

fof(f_810_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_810_2,plain,
    ! [U_3161,U_3160,U_3159] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3159),U_3161),U_3160))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3159),U_3160),U_3161))
      | ~ class_Orderings_Opreorder(U_3159) ),
    inference(variable_rename,[status(thm)],[f_810_1]) ).

fof(f_810_3,plain,
    ! [U_3159,U_3160,U_3161] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3159),U_3161),U_3160))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3159),U_3160),U_3161))
      | ~ class_Orderings_Opreorder(U_3159) ),
    inference(definitional_conversion,[status(esa)],[f_810_2]) ).

cnf(f_810_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3159),U_3161),U_3160))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3159),U_3160),U_3161))
    | ~ class_Orderings_Opreorder(U_3159) ),
    inference(clausify,[status(thm)],[f_810_3]) ).

fof(f_811_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_811_2,plain,
    ! [U_3164,U_3163,U_3162] :
      ( U_3163 != U_3164
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3162),U_3163),U_3164))
      | ~ class_Orderings_Oorder(U_3162) ),
    inference(variable_rename,[status(thm)],[f_811_1]) ).

fof(f_811_3,plain,
    ! [U_3163,U_3162,U_3164] :
      ( U_3163 != U_3164
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3162),U_3163),U_3164))
      | ~ class_Orderings_Oorder(U_3162) ),
    inference(definitional_conversion,[status(esa)],[f_811_2]) ).

cnf(f_811_4,plain,
    ( U_3163 != U_3164
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3162),U_3163),U_3164))
    | ~ class_Orderings_Oorder(U_3162) ),
    inference(clausify,[status(thm)],[f_811_3]) ).

fof(f_812_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_812_2,plain,
    ! [U_3167,U_3166,U_3165] :
      ( U_3167 != U_3166
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3165),U_3166),U_3167))
      | ~ class_Orderings_Oorder(U_3165) ),
    inference(variable_rename,[status(thm)],[f_812_1]) ).

fof(f_812_3,plain,
    ! [U_3165,U_3166,U_3167] :
      ( U_3167 != U_3166
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3165),U_3166),U_3167))
      | ~ class_Orderings_Oorder(U_3165) ),
    inference(definitional_conversion,[status(esa)],[f_812_2]) ).

cnf(f_812_4,plain,
    ( U_3167 != U_3166
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3165),U_3166),U_3167))
    | ~ class_Orderings_Oorder(U_3165) ),
    inference(clausify,[status(thm)],[f_812_3]) ).

fof(f_813_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_813_2,plain,
    ! [U_3170,U_3169,U_3168] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3168),U_3170),U_3169))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3168),U_3169),U_3170))
      | ~ class_Orderings_Opreorder(U_3168) ),
    inference(variable_rename,[status(thm)],[f_813_1]) ).

fof(f_813_3,plain,
    ! [U_3168,U_3169,U_3170] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3168),U_3170),U_3169))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3168),U_3169),U_3170))
      | ~ class_Orderings_Opreorder(U_3168) ),
    inference(definitional_conversion,[status(esa)],[f_813_2]) ).

cnf(f_813_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3168),U_3170),U_3169))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3168),U_3169),U_3170))
    | ~ class_Orderings_Opreorder(U_3168) ),
    inference(clausify,[status(thm)],[f_813_3]) ).

fof(f_814_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_814_2,plain,
    ! [U_3173,U_3172,U_3171] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3171),U_3173),U_3172))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3171),U_3172),U_3173))
      | ~ class_Orderings_Oorder(U_3171) ),
    inference(variable_rename,[status(thm)],[f_814_1]) ).

fof(f_814_3,plain,
    ! [U_3171,U_3172,U_3173] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3171),U_3173),U_3172))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3171),U_3172),U_3173))
      | ~ class_Orderings_Oorder(U_3171) ),
    inference(definitional_conversion,[status(esa)],[f_814_2]) ).

cnf(f_814_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3171),U_3173),U_3172))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3171),U_3172),U_3173))
    | ~ class_Orderings_Oorder(U_3171) ),
    inference(clausify,[status(thm)],[f_814_3]) ).

fof(f_815_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_815_2,plain,
    ! [U_3177,U_3176,U_3175,U_3174] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3174),U_3175),U_3177))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3174),U_3176),U_3177))
      | U_3175 != U_3176
      | ~ class_Orderings_Oord(U_3174) ),
    inference(variable_rename,[status(thm)],[f_815_1]) ).

fof(f_815_3,plain,
    ! [U_3174,U_3175,U_3176,U_3177] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3174),U_3175),U_3177))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3174),U_3176),U_3177))
      | U_3175 != U_3176
      | ~ class_Orderings_Oord(U_3174) ),
    inference(definitional_conversion,[status(esa)],[f_815_2]) ).

cnf(f_815_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3174),U_3175),U_3177))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3174),U_3176),U_3177))
    | U_3175 != U_3176
    | ~ class_Orderings_Oord(U_3174) ),
    inference(clausify,[status(thm)],[f_815_3]) ).

fof(f_816_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_816_2,plain,
    ! [U_3181,U_3180,U_3179,U_3178] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3178),U_3181),U_3179))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3178),U_3181),U_3180))
      | U_3179 != U_3180
      | ~ class_Orderings_Oorder(U_3178) ),
    inference(variable_rename,[status(thm)],[f_816_1]) ).

fof(f_816_3,plain,
    ! [U_3179,U_3178,U_3181,U_3180] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3178),U_3181),U_3179))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3178),U_3181),U_3180))
      | U_3179 != U_3180
      | ~ class_Orderings_Oorder(U_3178) ),
    inference(definitional_conversion,[status(esa)],[f_816_2]) ).

cnf(f_816_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3178),U_3181),U_3179))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3178),U_3181),U_3180))
    | U_3179 != U_3180
    | ~ class_Orderings_Oorder(U_3178) ),
    inference(clausify,[status(thm)],[f_816_3]) ).

fof(f_817_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_817_2,plain,
    ! [U_3185,U_3184,U_3183,U_3182] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3182),U_3183),U_3185))
      | U_3184 != U_3185
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3182),U_3183),U_3184))
      | ~ class_Orderings_Oord(U_3182) ),
    inference(variable_rename,[status(thm)],[f_817_1]) ).

fof(f_817_3,plain,
    ! [U_3182,U_3183,U_3184,U_3185] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3182),U_3183),U_3185))
      | U_3184 != U_3185
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3182),U_3183),U_3184))
      | ~ class_Orderings_Oord(U_3182) ),
    inference(definitional_conversion,[status(esa)],[f_817_2]) ).

cnf(f_817_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3182),U_3183),U_3185))
    | U_3184 != U_3185
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3182),U_3183),U_3184))
    | ~ class_Orderings_Oord(U_3182) ),
    inference(clausify,[status(thm)],[f_817_3]) ).

fof(f_818_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_818_2,plain,
    ! [U_3189,U_3188,U_3187,U_3186] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3186),U_3189),U_3188))
      | U_3187 != U_3189
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3186),U_3187),U_3188))
      | ~ class_Orderings_Oorder(U_3186) ),
    inference(variable_rename,[status(thm)],[f_818_1]) ).

fof(f_818_3,plain,
    ! [U_3187,U_3186,U_3188,U_3189] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3186),U_3189),U_3188))
      | U_3187 != U_3189
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3186),U_3187),U_3188))
      | ~ class_Orderings_Oorder(U_3186) ),
    inference(definitional_conversion,[status(esa)],[f_818_2]) ).

cnf(f_818_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3186),U_3189),U_3188))
    | U_3187 != U_3189
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3186),U_3187),U_3188))
    | ~ class_Orderings_Oorder(U_3186) ),
    inference(clausify,[status(thm)],[f_818_3]) ).

fof(f_819_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_819_2,plain,
    ! [U_3193,U_3192,U_3191,U_3190] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3190),U_3191),U_3193))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3190),U_3192),U_3193))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3190),U_3191),U_3192))
      | ~ class_Orderings_Opreorder(U_3190) ),
    inference(variable_rename,[status(thm)],[f_819_1]) ).

fof(f_819_3,plain,
    ! [U_3190,U_3191,U_3192,U_3193] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3190),U_3191),U_3193))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3190),U_3192),U_3193))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3190),U_3191),U_3192))
      | ~ class_Orderings_Opreorder(U_3190) ),
    inference(definitional_conversion,[status(esa)],[f_819_2]) ).

cnf(f_819_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3190),U_3191),U_3193))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3190),U_3192),U_3193))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3190),U_3191),U_3192))
    | ~ class_Orderings_Opreorder(U_3190) ),
    inference(clausify,[status(thm)],[f_819_3]) ).

fof(f_820_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_820_2,plain,
    ! [U_3197,U_3196,U_3195,U_3194] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3194),U_3197),U_3196))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3194),U_3197),U_3195))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3194),U_3195),U_3196))
      | ~ class_Orderings_Oorder(U_3194) ),
    inference(variable_rename,[status(thm)],[f_820_1]) ).

fof(f_820_3,plain,
    ! [U_3195,U_3194,U_3196,U_3197] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3194),U_3197),U_3196))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3194),U_3197),U_3195))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3194),U_3195),U_3196))
      | ~ class_Orderings_Oorder(U_3194) ),
    inference(definitional_conversion,[status(esa)],[f_820_2]) ).

cnf(f_820_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3194),U_3197),U_3196))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3194),U_3197),U_3195))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3194),U_3195),U_3196))
    | ~ class_Orderings_Oorder(U_3194) ),
    inference(clausify,[status(thm)],[f_820_3]) ).

fof(f_821_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_821_2,plain,
    ! [U_3200,U_3199,U_3198] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3198),U_3200),U_3199))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3198),U_3199),U_3200))
      | ~ class_Orderings_Opreorder(U_3198) ),
    inference(variable_rename,[status(thm)],[f_821_1]) ).

fof(f_821_3,plain,
    ! [U_3198,U_3199,U_3200] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3198),U_3200),U_3199))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3198),U_3199),U_3200))
      | ~ class_Orderings_Opreorder(U_3198) ),
    inference(definitional_conversion,[status(esa)],[f_821_2]) ).

cnf(f_821_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3198),U_3200),U_3199))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3198),U_3199),U_3200))
    | ~ class_Orderings_Opreorder(U_3198) ),
    inference(clausify,[status(thm)],[f_821_3]) ).

fof(f_822_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_822_2,plain,
    ! [U_3203,U_3202,U_3201] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3201),U_3203),U_3202))
      | U_3202 = U_3203
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3201),U_3202),U_3203))
      | ~ class_Orderings_Olinorder(U_3201) ),
    inference(variable_rename,[status(thm)],[f_822_1]) ).

fof(f_822_3,plain,
    ! [U_3201,U_3202,U_3203] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3201),U_3203),U_3202))
      | U_3202 = U_3203
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3201),U_3202),U_3203))
      | ~ class_Orderings_Olinorder(U_3201) ),
    inference(definitional_conversion,[status(esa)],[f_822_2]) ).

cnf(f_822_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3201),U_3203),U_3202))
    | U_3202 = U_3203
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3201),U_3202),U_3203))
    | ~ class_Orderings_Olinorder(U_3201) ),
    inference(clausify,[status(thm)],[f_822_3]) ).

fof(f_823_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_823_2,plain,
    ! [U_3205,U_3204] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3204),U_3205),U_3205) = U_3205
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3204) ),
    inference(variable_rename,[status(thm)],[f_823_1]) ).

fof(f_823_3,plain,
    ! [U_3204,U_3205] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3204),U_3205),U_3205) = U_3205
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3204) ),
    inference(definitional_conversion,[status(esa)],[f_823_2]) ).

cnf(f_823_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3204),U_3205),U_3205) = U_3205
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_3204) ),
    inference(clausify,[status(thm)],[f_823_3]) ).

fof(f_824_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_824_2,plain,
    ! [U_3207,U_3206] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3206),U_3207),U_3207) = U_3207
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3206) ),
    inference(variable_rename,[status(thm)],[f_824_1]) ).

fof(f_824_3,plain,
    ! [U_3206,U_3207] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3206),U_3207),U_3207) = U_3207
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3206) ),
    inference(definitional_conversion,[status(esa)],[f_824_2]) ).

cnf(f_824_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3206),U_3207),U_3207) = U_3207
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_3206) ),
    inference(clausify,[status(thm)],[f_824_3]) ).

fof(f_825_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_825_2,plain,
    ! [U_3210,U_3209,U_3208] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3208),U_3209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3208),U_3209),U_3210)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3208),U_3209),U_3210)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3208) ),
    inference(variable_rename,[status(thm)],[f_825_1]) ).

fof(f_825_3,plain,
    ! [U_3208,U_3209,U_3210] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3208),U_3209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3208),U_3209),U_3210)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3208),U_3209),U_3210)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3208) ),
    inference(definitional_conversion,[status(esa)],[f_825_2]) ).

cnf(f_825_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3208),U_3209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3208),U_3209),U_3210)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3208),U_3209),U_3210)
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_3208) ),
    inference(clausify,[status(thm)],[f_825_3]) ).

fof(f_826_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_826_2,plain,
    ! [U_3212,U_3211] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3211),hAPP(c_Groups_Ouminus__class_Ouminus(U_3211),U_3212)) = U_3212
      | ~ class_Lattices_Oboolean__algebra(U_3211) ),
    inference(variable_rename,[status(thm)],[f_826_1]) ).

fof(f_826_3,plain,
    ! [U_3211,U_3212] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3211),hAPP(c_Groups_Ouminus__class_Ouminus(U_3211),U_3212)) = U_3212
      | ~ class_Lattices_Oboolean__algebra(U_3211) ),
    inference(definitional_conversion,[status(esa)],[f_826_2]) ).

cnf(f_826_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3211),hAPP(c_Groups_Ouminus__class_Ouminus(U_3211),U_3212)) = U_3212
    | ~ class_Lattices_Oboolean__algebra(U_3211) ),
    inference(clausify,[status(thm)],[f_826_3]) ).

fof(f_827_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_827_2,plain,
    ! [U_3216,U_3215,U_3214,U_3213] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3214,U_3213)),U_3215),U_3216) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3213),hAPP(U_3215,U_3216))
      | ~ class_Groups_Ouminus(U_3213) ),
    inference(variable_rename,[status(thm)],[f_827_1]) ).

fof(f_827_3,plain,
    ! [U_3213,U_3214,U_3215,U_3216] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3214,U_3213)),U_3215),U_3216) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3213),hAPP(U_3215,U_3216))
      | ~ class_Groups_Ouminus(U_3213) ),
    inference(definitional_conversion,[status(esa)],[f_827_2]) ).

cnf(f_827_4,plain,
    ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_3214,U_3213)),U_3215),U_3216) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3213),hAPP(U_3215,U_3216))
    | ~ class_Groups_Ouminus(U_3213) ),
    inference(clausify,[status(thm)],[f_827_3]) ).

fof(f_828_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_828_2,plain,
    ! [U_3219,U_3218,U_3217] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3217),U_3218) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3217),U_3219)
          | U_3218 != U_3219 )
        & ( U_3218 = U_3219
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_3217),U_3218) != hAPP(c_Groups_Ouminus__class_Ouminus(U_3217),U_3219) ) )
      | ~ class_Lattices_Oboolean__algebra(U_3217) ),
    inference(variable_rename,[status(thm)],[f_828_1]) ).

fof(f_828_3,plain,
    ( ! [U_3217,U_3218,U_3219] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3217),U_3218) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3217),U_3219)
        | U_3218 != U_3219
        | ~ sP233(U_3217,U_3218,U_3219) )
    & ! [U_3217,U_3218,U_3219] :
        ( U_3218 = U_3219
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_3217),U_3218) != hAPP(c_Groups_Ouminus__class_Ouminus(U_3217),U_3219)
        | ~ sP233(U_3217,U_3218,U_3219) )
    & ! [U_3217,U_3218,U_3219] :
        ( sP233(U_3217,U_3218,U_3219)
        | ~ class_Lattices_Oboolean__algebra(U_3217) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP233])],[f_828_2]) ).

cnf(f_828_4,plain,
    ( sP233(U_3217,U_3218,U_3219)
    | ~ class_Lattices_Oboolean__algebra(U_3217) ),
    inference(clausify,[status(thm)],[f_828_3]) ).

cnf(f_828_5,plain,
    ( U_3218 = U_3219
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_3217),U_3218) != hAPP(c_Groups_Ouminus__class_Ouminus(U_3217),U_3219)
    | ~ sP233(U_3217,U_3218,U_3219) ),
    inference(clausify,[status(thm)],[f_828_3]) ).

cnf(f_828_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3217),U_3218) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3217),U_3219)
    | U_3218 != U_3219
    | ~ sP233(U_3217,U_3218,U_3219) ),
    inference(clausify,[status(thm)],[f_828_3]) ).

fof(f_829_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_829_2,plain,
    ! [U_3222,U_3221,U_3220] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3220),U_3221),U_3222))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3220),U_3222),U_3221)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3220),U_3222),U_3221))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3220),U_3221),U_3222)) ) )
      | ~ class_Orderings_Olinorder(U_3220) ),
    inference(variable_rename,[status(thm)],[f_829_1]) ).

fof(f_829_3,plain,
    ( ! [U_3221,U_3222,U_3220] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3220),U_3221),U_3222))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3220),U_3222),U_3221))
        | ~ sP234(U_3221,U_3222,U_3220) )
    & ! [U_3221,U_3222,U_3220] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3220),U_3222),U_3221))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3220),U_3221),U_3222))
        | ~ sP234(U_3221,U_3222,U_3220) )
    & ! [U_3221,U_3222,U_3220] :
        ( sP234(U_3221,U_3222,U_3220)
        | ~ class_Orderings_Olinorder(U_3220) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP234])],[f_829_2]) ).

cnf(f_829_4,plain,
    ( sP234(U_3221,U_3222,U_3220)
    | ~ class_Orderings_Olinorder(U_3220) ),
    inference(clausify,[status(thm)],[f_829_3]) ).

cnf(f_829_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3220),U_3222),U_3221))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3220),U_3221),U_3222))
    | ~ sP234(U_3221,U_3222,U_3220) ),
    inference(clausify,[status(thm)],[f_829_3]) ).

cnf(f_829_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3220),U_3221),U_3222))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3220),U_3222),U_3221))
    | ~ sP234(U_3221,U_3222,U_3220) ),
    inference(clausify,[status(thm)],[f_829_3]) ).

fof(f_830_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_830_2,plain,
    ! [U_3225,U_3224,U_3223] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3223),U_3224),U_3225))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3223),U_3225),U_3224)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3223),U_3225),U_3224))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3223),U_3224),U_3225)) ) )
      | ~ class_Orderings_Olinorder(U_3223) ),
    inference(variable_rename,[status(thm)],[f_830_1]) ).

fof(f_830_3,plain,
    ( ! [U_3224,U_3223,U_3225] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3223),U_3224),U_3225))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3223),U_3225),U_3224))
        | ~ sP235(U_3224,U_3223,U_3225) )
    & ! [U_3224,U_3223,U_3225] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3223),U_3225),U_3224))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3223),U_3224),U_3225))
        | ~ sP235(U_3224,U_3223,U_3225) )
    & ! [U_3224,U_3223,U_3225] :
        ( sP235(U_3224,U_3223,U_3225)
        | ~ class_Orderings_Olinorder(U_3223) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP235])],[f_830_2]) ).

cnf(f_830_4,plain,
    ( sP235(U_3224,U_3223,U_3225)
    | ~ class_Orderings_Olinorder(U_3223) ),
    inference(clausify,[status(thm)],[f_830_3]) ).

cnf(f_830_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3223),U_3225),U_3224))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3223),U_3224),U_3225))
    | ~ sP235(U_3224,U_3223,U_3225) ),
    inference(clausify,[status(thm)],[f_830_3]) ).

cnf(f_830_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3223),U_3224),U_3225))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3223),U_3225),U_3224))
    | ~ sP235(U_3224,U_3223,U_3225) ),
    inference(clausify,[status(thm)],[f_830_3]) ).

fof(f_831_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_831_2,plain,
    ! [U_3228,U_3227,U_3226] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3226),U_3228),U_3227))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3226),U_3227),U_3228))
      | ~ class_Orderings_Olinorder(U_3226) ),
    inference(variable_rename,[status(thm)],[f_831_1]) ).

fof(f_831_3,plain,
    ! [U_3227,U_3228,U_3226] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3226),U_3228),U_3227))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3226),U_3227),U_3228))
      | ~ class_Orderings_Olinorder(U_3226) ),
    inference(definitional_conversion,[status(esa)],[f_831_2]) ).

cnf(f_831_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3226),U_3228),U_3227))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3226),U_3227),U_3228))
    | ~ class_Orderings_Olinorder(U_3226) ),
    inference(clausify,[status(thm)],[f_831_3]) ).

fof(f_832_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_832_2,plain,
    ! [U_3231,U_3230,U_3229] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3229),U_3230),U_3231))
          | U_3230 = U_3231
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3229),U_3230),U_3231)) )
        & ( ( U_3230 != U_3231
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3229),U_3230),U_3231)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3229),U_3230),U_3231)) ) )
      | ~ class_Orderings_Oorder(U_3229) ),
    inference(variable_rename,[status(thm)],[f_832_1]) ).

fof(f_832_3,plain,
    ( ! [U_3229,U_3230,U_3231] :
        ( U_3230 != U_3231
        | ~ sP236(U_3229,U_3230,U_3231) )
    & ! [U_3229,U_3230,U_3231] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3229),U_3230),U_3231))
        | ~ sP236(U_3229,U_3230,U_3231) )
    & ! [U_3229,U_3230,U_3231] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3229),U_3230),U_3231))
        | U_3230 = U_3231
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3229),U_3230),U_3231))
        | ~ sP237(U_3229,U_3230,U_3231) )
    & ! [U_3229,U_3230,U_3231] :
        ( sP236(U_3229,U_3230,U_3231)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3229),U_3230),U_3231))
        | ~ sP237(U_3229,U_3230,U_3231) )
    & ! [U_3229,U_3230,U_3231] :
        ( sP237(U_3229,U_3230,U_3231)
        | ~ class_Orderings_Oorder(U_3229) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP236,sP237])],[f_832_2]) ).

cnf(f_832_4,plain,
    ( sP237(U_3229,U_3230,U_3231)
    | ~ class_Orderings_Oorder(U_3229) ),
    inference(clausify,[status(thm)],[f_832_3]) ).

cnf(f_832_5,plain,
    ( sP236(U_3229,U_3230,U_3231)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3229),U_3230),U_3231))
    | ~ sP237(U_3229,U_3230,U_3231) ),
    inference(clausify,[status(thm)],[f_832_3]) ).

cnf(f_832_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3229),U_3230),U_3231))
    | U_3230 = U_3231
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3229),U_3230),U_3231))
    | ~ sP237(U_3229,U_3230,U_3231) ),
    inference(clausify,[status(thm)],[f_832_3]) ).

cnf(f_832_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3229),U_3230),U_3231))
    | ~ sP236(U_3229,U_3230,U_3231) ),
    inference(clausify,[status(thm)],[f_832_3]) ).

cnf(f_832_8,plain,
    ( U_3230 != U_3231
    | ~ sP236(U_3229,U_3230,U_3231) ),
    inference(clausify,[status(thm)],[f_832_3]) ).

fof(f_833_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_833_2,plain,
    ! [U_3234,U_3233,U_3232] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3232),U_3233),U_3234))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3232),U_3234),U_3233))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3232),U_3233),U_3234)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3232),U_3234),U_3233))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3232),U_3233),U_3234)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3232),U_3233),U_3234)) ) )
      | ~ class_Orderings_Opreorder(U_3232) ),
    inference(variable_rename,[status(thm)],[f_833_1]) ).

fof(f_833_3,plain,
    ( ! [U_3233,U_3232,U_3234] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3232),U_3234),U_3233))
        | ~ sP238(U_3233,U_3232,U_3234) )
    & ! [U_3233,U_3232,U_3234] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3232),U_3233),U_3234))
        | ~ sP238(U_3233,U_3232,U_3234) )
    & ! [U_3233,U_3232,U_3234] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3232),U_3233),U_3234))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3232),U_3234),U_3233))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3232),U_3233),U_3234))
        | ~ sP239(U_3233,U_3232,U_3234) )
    & ! [U_3233,U_3232,U_3234] :
        ( sP238(U_3233,U_3232,U_3234)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3232),U_3233),U_3234))
        | ~ sP239(U_3233,U_3232,U_3234) )
    & ! [U_3233,U_3232,U_3234] :
        ( sP239(U_3233,U_3232,U_3234)
        | ~ class_Orderings_Opreorder(U_3232) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP238,sP239])],[f_833_2]) ).

cnf(f_833_4,plain,
    ( sP239(U_3233,U_3232,U_3234)
    | ~ class_Orderings_Opreorder(U_3232) ),
    inference(clausify,[status(thm)],[f_833_3]) ).

cnf(f_833_5,plain,
    ( sP238(U_3233,U_3232,U_3234)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3232),U_3233),U_3234))
    | ~ sP239(U_3233,U_3232,U_3234) ),
    inference(clausify,[status(thm)],[f_833_3]) ).

cnf(f_833_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3232),U_3233),U_3234))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3232),U_3234),U_3233))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3232),U_3233),U_3234))
    | ~ sP239(U_3233,U_3232,U_3234) ),
    inference(clausify,[status(thm)],[f_833_3]) ).

cnf(f_833_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3232),U_3233),U_3234))
    | ~ sP238(U_3233,U_3232,U_3234) ),
    inference(clausify,[status(thm)],[f_833_3]) ).

cnf(f_833_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3232),U_3234),U_3233))
    | ~ sP238(U_3233,U_3232,U_3234) ),
    inference(clausify,[status(thm)],[f_833_3]) ).

fof(f_834_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_834_2,plain,
    ! [U_3237,U_3236,U_3235] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3235),U_3236),U_3237))
          | ( U_3236 != U_3237
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3235),U_3236),U_3237)) ) )
        & ( U_3236 = U_3237
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3235),U_3236),U_3237))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3235),U_3236),U_3237)) ) )
      | ~ class_Orderings_Oorder(U_3235) ),
    inference(variable_rename,[status(thm)],[f_834_1]) ).

fof(f_834_3,plain,
    ( ! [U_3236,U_3235,U_3237] :
        ( U_3236 != U_3237
        | ~ sP240(U_3236,U_3235,U_3237) )
    & ! [U_3236,U_3235,U_3237] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3235),U_3236),U_3237))
        | ~ sP240(U_3236,U_3235,U_3237) )
    & ! [U_3236,U_3235,U_3237] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3235),U_3236),U_3237))
        | sP240(U_3236,U_3235,U_3237)
        | ~ sP241(U_3236,U_3235,U_3237) )
    & ! [U_3236,U_3235,U_3237] :
        ( U_3236 = U_3237
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3235),U_3236),U_3237))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3235),U_3236),U_3237))
        | ~ sP241(U_3236,U_3235,U_3237) )
    & ! [U_3236,U_3235,U_3237] :
        ( sP241(U_3236,U_3235,U_3237)
        | ~ class_Orderings_Oorder(U_3235) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP240,sP241])],[f_834_2]) ).

cnf(f_834_4,plain,
    ( sP241(U_3236,U_3235,U_3237)
    | ~ class_Orderings_Oorder(U_3235) ),
    inference(clausify,[status(thm)],[f_834_3]) ).

cnf(f_834_5,plain,
    ( U_3236 = U_3237
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3235),U_3236),U_3237))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3235),U_3236),U_3237))
    | ~ sP241(U_3236,U_3235,U_3237) ),
    inference(clausify,[status(thm)],[f_834_3]) ).

cnf(f_834_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3235),U_3236),U_3237))
    | sP240(U_3236,U_3235,U_3237)
    | ~ sP241(U_3236,U_3235,U_3237) ),
    inference(clausify,[status(thm)],[f_834_3]) ).

cnf(f_834_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3235),U_3236),U_3237))
    | ~ sP240(U_3236,U_3235,U_3237) ),
    inference(clausify,[status(thm)],[f_834_3]) ).

cnf(f_834_8,plain,
    ( U_3236 != U_3237
    | ~ sP240(U_3236,U_3235,U_3237) ),
    inference(clausify,[status(thm)],[f_834_3]) ).

fof(f_835_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_835_2,plain,
    ! [U_3240,U_3239,U_3238] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3238),U_3240),U_3239))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3238),U_3239),U_3240))
      | ~ class_Orderings_Olinorder(U_3238) ),
    inference(variable_rename,[status(thm)],[f_835_1]) ).

fof(f_835_3,plain,
    ! [U_3240,U_3238,U_3239] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3238),U_3240),U_3239))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3238),U_3239),U_3240))
      | ~ class_Orderings_Olinorder(U_3238) ),
    inference(definitional_conversion,[status(esa)],[f_835_2]) ).

cnf(f_835_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3238),U_3240),U_3239))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3238),U_3239),U_3240))
    | ~ class_Orderings_Olinorder(U_3238) ),
    inference(clausify,[status(thm)],[f_835_3]) ).

fof(f_836_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_836_2,plain,
    ! [U_3243,U_3242,U_3241] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3241),U_3243),U_3242))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3241),U_3242),U_3243))
      | ~ class_Orderings_Olinorder(U_3241) ),
    inference(variable_rename,[status(thm)],[f_836_1]) ).

fof(f_836_3,plain,
    ! [U_3241,U_3243,U_3242] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3241),U_3243),U_3242))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3241),U_3242),U_3243))
      | ~ class_Orderings_Olinorder(U_3241) ),
    inference(definitional_conversion,[status(esa)],[f_836_2]) ).

cnf(f_836_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3241),U_3243),U_3242))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3241),U_3242),U_3243))
    | ~ class_Orderings_Olinorder(U_3241) ),
    inference(clausify,[status(thm)],[f_836_3]) ).

fof(f_837_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_837_2,plain,
    ! [U_3246,U_3245,U_3244] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3244),U_3245),U_3246))
          | U_3245 != U_3246 )
        & ( U_3245 = U_3246
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3244),U_3245),U_3246)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3244),U_3245),U_3246))
      | ~ class_Orderings_Olinorder(U_3244) ),
    inference(variable_rename,[status(thm)],[f_837_1]) ).

fof(f_837_3,plain,
    ( ! [U_3244,U_3245,U_3246] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3244),U_3245),U_3246))
        | U_3245 != U_3246
        | ~ sP242(U_3244,U_3245,U_3246) )
    & ! [U_3244,U_3245,U_3246] :
        ( U_3245 = U_3246
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3244),U_3245),U_3246))
        | ~ sP242(U_3244,U_3245,U_3246) )
    & ! [U_3244,U_3245,U_3246] :
        ( sP242(U_3244,U_3245,U_3246)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3244),U_3245),U_3246))
        | ~ class_Orderings_Olinorder(U_3244) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP242])],[f_837_2]) ).

cnf(f_837_4,plain,
    ( sP242(U_3244,U_3245,U_3246)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3244),U_3245),U_3246))
    | ~ class_Orderings_Olinorder(U_3244) ),
    inference(clausify,[status(thm)],[f_837_3]) ).

cnf(f_837_5,plain,
    ( U_3245 = U_3246
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3244),U_3245),U_3246))
    | ~ sP242(U_3244,U_3245,U_3246) ),
    inference(clausify,[status(thm)],[f_837_3]) ).

cnf(f_837_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3244),U_3245),U_3246))
    | U_3245 != U_3246
    | ~ sP242(U_3244,U_3245,U_3246) ),
    inference(clausify,[status(thm)],[f_837_3]) ).

fof(f_838_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_838_2,plain,
    ! [U_3249,U_3248,U_3247] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3247),U_3248),U_3249))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3247),U_3248),U_3249))
      | U_3248 = U_3249
      | ~ class_Orderings_Oorder(U_3247) ),
    inference(variable_rename,[status(thm)],[f_838_1]) ).

fof(f_838_3,plain,
    ! [U_3249,U_3248,U_3247] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3247),U_3248),U_3249))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3247),U_3248),U_3249))
      | U_3248 = U_3249
      | ~ class_Orderings_Oorder(U_3247) ),
    inference(definitional_conversion,[status(esa)],[f_838_2]) ).

cnf(f_838_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3247),U_3248),U_3249))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3247),U_3248),U_3249))
    | U_3248 = U_3249
    | ~ class_Orderings_Oorder(U_3247) ),
    inference(clausify,[status(thm)],[f_838_3]) ).

fof(f_839_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_839_2,plain,
    ! [U_3252,U_3251,U_3250] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3250),U_3252),U_3251))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3250),U_3252),U_3251))
      | U_3251 = U_3252
      | ~ class_Orderings_Oorder(U_3250) ),
    inference(variable_rename,[status(thm)],[f_839_1]) ).

fof(f_839_3,plain,
    ! [U_3250,U_3251,U_3252] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3250),U_3252),U_3251))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3250),U_3252),U_3251))
      | U_3251 = U_3252
      | ~ class_Orderings_Oorder(U_3250) ),
    inference(definitional_conversion,[status(esa)],[f_839_2]) ).

cnf(f_839_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3250),U_3252),U_3251))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3250),U_3252),U_3251))
    | U_3251 = U_3252
    | ~ class_Orderings_Oorder(U_3250) ),
    inference(clausify,[status(thm)],[f_839_3]) ).

fof(f_840_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_840_2,plain,
    ! [U_3255,U_3254,U_3253] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3253),U_3255),U_3254))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3253),U_3254),U_3255))
      | ~ class_Orderings_Olinorder(U_3253) ),
    inference(variable_rename,[status(thm)],[f_840_1]) ).

fof(f_840_3,plain,
    ! [U_3253,U_3254,U_3255] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3253),U_3255),U_3254))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3253),U_3254),U_3255))
      | ~ class_Orderings_Olinorder(U_3253) ),
    inference(definitional_conversion,[status(esa)],[f_840_2]) ).

cnf(f_840_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3253),U_3255),U_3254))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3253),U_3254),U_3255))
    | ~ class_Orderings_Olinorder(U_3253) ),
    inference(clausify,[status(thm)],[f_840_3]) ).

fof(f_841_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_841_2,plain,
    ! [U_3258,U_3257,U_3256] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3256),U_3257),U_3258))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3256),U_3257),U_3258))
      | ~ class_Orderings_Opreorder(U_3256) ),
    inference(variable_rename,[status(thm)],[f_841_1]) ).

fof(f_841_3,plain,
    ! [U_3256,U_3257,U_3258] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3256),U_3257),U_3258))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3256),U_3257),U_3258))
      | ~ class_Orderings_Opreorder(U_3256) ),
    inference(definitional_conversion,[status(esa)],[f_841_2]) ).

cnf(f_841_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3256),U_3257),U_3258))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3256),U_3257),U_3258))
    | ~ class_Orderings_Opreorder(U_3256) ),
    inference(clausify,[status(thm)],[f_841_3]) ).

fof(f_842_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_842_2,plain,
    ! [U_3261,U_3260,U_3259] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3259),U_3260),U_3261))
          | U_3260 != U_3261 )
        & ( U_3260 = U_3261
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3259),U_3260),U_3261)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3259),U_3260),U_3261))
      | ~ class_Orderings_Olinorder(U_3259) ),
    inference(variable_rename,[status(thm)],[f_842_1]) ).

fof(f_842_3,plain,
    ( ! [U_3259,U_3260,U_3261] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3259),U_3260),U_3261))
        | U_3260 != U_3261
        | ~ sP243(U_3259,U_3260,U_3261) )
    & ! [U_3259,U_3260,U_3261] :
        ( U_3260 = U_3261
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3259),U_3260),U_3261))
        | ~ sP243(U_3259,U_3260,U_3261) )
    & ! [U_3259,U_3260,U_3261] :
        ( sP243(U_3259,U_3260,U_3261)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3259),U_3260),U_3261))
        | ~ class_Orderings_Olinorder(U_3259) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP243])],[f_842_2]) ).

cnf(f_842_4,plain,
    ( sP243(U_3259,U_3260,U_3261)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3259),U_3260),U_3261))
    | ~ class_Orderings_Olinorder(U_3259) ),
    inference(clausify,[status(thm)],[f_842_3]) ).

cnf(f_842_5,plain,
    ( U_3260 = U_3261
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3259),U_3260),U_3261))
    | ~ sP243(U_3259,U_3260,U_3261) ),
    inference(clausify,[status(thm)],[f_842_3]) ).

cnf(f_842_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3259),U_3260),U_3261))
    | U_3260 != U_3261
    | ~ sP243(U_3259,U_3260,U_3261) ),
    inference(clausify,[status(thm)],[f_842_3]) ).

fof(f_843_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_843_2,plain,
    ! [U_3264,U_3263,U_3262] :
      ( U_3263 = U_3264
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3262),U_3263),U_3264))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3262),U_3263),U_3264))
      | ~ class_Orderings_Oorder(U_3262) ),
    inference(variable_rename,[status(thm)],[f_843_1]) ).

fof(f_843_3,plain,
    ! [U_3264,U_3263,U_3262] :
      ( U_3263 = U_3264
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3262),U_3263),U_3264))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3262),U_3263),U_3264))
      | ~ class_Orderings_Oorder(U_3262) ),
    inference(definitional_conversion,[status(esa)],[f_843_2]) ).

cnf(f_843_4,plain,
    ( U_3263 = U_3264
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3262),U_3263),U_3264))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3262),U_3263),U_3264))
    | ~ class_Orderings_Oorder(U_3262) ),
    inference(clausify,[status(thm)],[f_843_3]) ).

fof(f_844_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_844_2,plain,
    ! [U_3267,U_3266,U_3265] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3265),U_3266),U_3267))
      | U_3266 = U_3267
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3265),U_3266),U_3267))
      | ~ class_Orderings_Oorder(U_3265) ),
    inference(variable_rename,[status(thm)],[f_844_1]) ).

fof(f_844_3,plain,
    ! [U_3265,U_3266,U_3267] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3265),U_3266),U_3267))
      | U_3266 = U_3267
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3265),U_3266),U_3267))
      | ~ class_Orderings_Oorder(U_3265) ),
    inference(definitional_conversion,[status(esa)],[f_844_2]) ).

cnf(f_844_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3265),U_3266),U_3267))
    | U_3266 = U_3267
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3265),U_3266),U_3267))
    | ~ class_Orderings_Oorder(U_3265) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

fof(f_845_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_845_2,plain,
    ! [U_3271,U_3270] :
      ( ? [U_3269] :
          ( hBOOL(hAPP(U_3270,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3269),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          & ! [U_3268] :
              ( ~ hBOOL(hAPP(U_3270,U_3268))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3268),U_3269)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3269),U_3271)) )
      | ~ hBOOL(hAPP(U_3270,U_3271))
      | hBOOL(hAPP(U_3270,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_845_1]) ).

fof(f_845_3,plain,
    ! [U_3271,U_3270] :
      ( ( hBOOL(hAPP(U_3270,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK62(U_3271,U_3270)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        & ! [U_3268] :
            ( ~ hBOOL(hAPP(U_3270,U_3268))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3268),sK62(U_3271,U_3270))) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK62(U_3271,U_3270)),U_3271)) )
      | ~ hBOOL(hAPP(U_3270,U_3271))
      | hBOOL(hAPP(U_3270,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_3269,sK62(U_3271,U_3270))],[f_845_2]) ).

fof(f_845_4,plain,
    ( ! [U_3268,U_3270,U_3271] :
        ( hBOOL(hAPP(U_3270,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK62(U_3271,U_3270)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ sP244(U_3268,U_3270,U_3271) )
    & ! [U_3268,U_3270,U_3271] :
        ( ~ hBOOL(hAPP(U_3270,U_3268))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3268),sK62(U_3271,U_3270)))
        | ~ sP244(U_3268,U_3270,U_3271) )
    & ! [U_3268,U_3270,U_3271] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK62(U_3271,U_3270)),U_3271))
        | ~ sP244(U_3268,U_3270,U_3271) )
    & ! [U_3268,U_3270,U_3271] :
        ( sP244(U_3268,U_3270,U_3271)
        | ~ hBOOL(hAPP(U_3270,U_3271))
        | hBOOL(hAPP(U_3270,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP244])],[f_845_3]) ).

cnf(f_845_5,plain,
    ( sP244(U_3268,U_3270,U_3271)
    | ~ hBOOL(hAPP(U_3270,U_3271))
    | hBOOL(hAPP(U_3270,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_845_4]) ).

cnf(f_845_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK62(U_3271,U_3270)),U_3271))
    | ~ sP244(U_3268,U_3270,U_3271) ),
    inference(clausify,[status(thm)],[f_845_4]) ).

cnf(f_845_7,plain,
    ( ~ hBOOL(hAPP(U_3270,U_3268))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3268),sK62(U_3271,U_3270)))
    | ~ sP244(U_3268,U_3270,U_3271) ),
    inference(clausify,[status(thm)],[f_845_4]) ).

cnf(f_845_8,plain,
    ( hBOOL(hAPP(U_3270,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK62(U_3271,U_3270)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ sP244(U_3268,U_3270,U_3271) ),
    inference(clausify,[status(thm)],[f_845_4]) ).

fof(f_846_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_846_2,plain,
    ! [U_3273,U_3272] :
      ( ( ( ( ( c_Groups_Osgn__class_Osgn(U_3272,U_3273) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3272),c_Groups_Oone__class_Oone(U_3272))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3272),c_Groups_Ozero__class_Ozero(U_3272)),U_3273)) )
            & ( c_Groups_Osgn__class_Osgn(U_3272,U_3273) = c_Groups_Oone__class_Oone(U_3272)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3272),c_Groups_Ozero__class_Ozero(U_3272)),U_3273)) ) )
          | U_3273 = c_Groups_Ozero__class_Ozero(U_3272) )
        & ( c_Groups_Osgn__class_Osgn(U_3272,U_3273) = c_Groups_Ozero__class_Ozero(U_3272)
          | U_3273 != c_Groups_Ozero__class_Ozero(U_3272) ) )
      | ~ class_Groups_Osgn__if(U_3272) ),
    inference(variable_rename,[status(thm)],[f_846_1]) ).

fof(f_846_3,plain,
    ( ! [U_3272,U_3273] :
        ( c_Groups_Osgn__class_Osgn(U_3272,U_3273) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3272),c_Groups_Oone__class_Oone(U_3272))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3272),c_Groups_Ozero__class_Ozero(U_3272)),U_3273))
        | ~ sP245(U_3272,U_3273) )
    & ! [U_3272,U_3273] :
        ( c_Groups_Osgn__class_Osgn(U_3272,U_3273) = c_Groups_Oone__class_Oone(U_3272)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3272),c_Groups_Ozero__class_Ozero(U_3272)),U_3273))
        | ~ sP245(U_3272,U_3273) )
    & ! [U_3272,U_3273] :
        ( sP245(U_3272,U_3273)
        | U_3273 = c_Groups_Ozero__class_Ozero(U_3272)
        | ~ sP246(U_3272,U_3273) )
    & ! [U_3272,U_3273] :
        ( c_Groups_Osgn__class_Osgn(U_3272,U_3273) = c_Groups_Ozero__class_Ozero(U_3272)
        | U_3273 != c_Groups_Ozero__class_Ozero(U_3272)
        | ~ sP246(U_3272,U_3273) )
    & ! [U_3272,U_3273] :
        ( sP246(U_3272,U_3273)
        | ~ class_Groups_Osgn__if(U_3272) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP245,sP246])],[f_846_2]) ).

cnf(f_846_4,plain,
    ( sP246(U_3272,U_3273)
    | ~ class_Groups_Osgn__if(U_3272) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

cnf(f_846_5,plain,
    ( c_Groups_Osgn__class_Osgn(U_3272,U_3273) = c_Groups_Ozero__class_Ozero(U_3272)
    | U_3273 != c_Groups_Ozero__class_Ozero(U_3272)
    | ~ sP246(U_3272,U_3273) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

cnf(f_846_6,plain,
    ( sP245(U_3272,U_3273)
    | U_3273 = c_Groups_Ozero__class_Ozero(U_3272)
    | ~ sP246(U_3272,U_3273) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

cnf(f_846_7,plain,
    ( c_Groups_Osgn__class_Osgn(U_3272,U_3273) = c_Groups_Oone__class_Oone(U_3272)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3272),c_Groups_Ozero__class_Ozero(U_3272)),U_3273))
    | ~ sP245(U_3272,U_3273) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

cnf(f_846_8,plain,
    ( c_Groups_Osgn__class_Osgn(U_3272,U_3273) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3272),c_Groups_Oone__class_Oone(U_3272))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3272),c_Groups_Ozero__class_Ozero(U_3272)),U_3273))
    | ~ sP245(U_3272,U_3273) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

fof(f_847_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_847_2,plain,
    ! [U_3275,U_3274] :
      ( c_Groups_Osgn__class_Osgn(U_3274,U_3275) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3274),c_Groups_Oone__class_Oone(U_3274))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3274),U_3275),c_Groups_Ozero__class_Ozero(U_3274)))
      | ~ class_Rings_Olinordered__idom(U_3274) ),
    inference(variable_rename,[status(thm)],[f_847_1]) ).

fof(f_847_3,plain,
    ! [U_3275,U_3274] :
      ( c_Groups_Osgn__class_Osgn(U_3274,U_3275) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3274),c_Groups_Oone__class_Oone(U_3274))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3274),U_3275),c_Groups_Ozero__class_Ozero(U_3274)))
      | ~ class_Rings_Olinordered__idom(U_3274) ),
    inference(definitional_conversion,[status(esa)],[f_847_2]) ).

cnf(f_847_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_3274,U_3275) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3274),c_Groups_Oone__class_Oone(U_3274))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3274),U_3275),c_Groups_Ozero__class_Ozero(U_3274)))
    | ~ class_Rings_Olinordered__idom(U_3274) ),
    inference(clausify,[status(thm)],[f_847_3]) ).

fof(f_848_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_848_2,plain,
    ! [U_3277,U_3276] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_3276,U_3277) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3276),c_Groups_Oone__class_Oone(U_3276))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3276),U_3277),c_Groups_Ozero__class_Ozero(U_3276))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3276),U_3277),c_Groups_Ozero__class_Ozero(U_3276)))
          | c_Groups_Osgn__class_Osgn(U_3276,U_3277) != hAPP(c_Groups_Ouminus__class_Ouminus(U_3276),c_Groups_Oone__class_Oone(U_3276)) ) )
      | ~ class_Rings_Olinordered__idom(U_3276) ),
    inference(variable_rename,[status(thm)],[f_848_1]) ).

fof(f_848_3,plain,
    ( ! [U_3277,U_3276] :
        ( c_Groups_Osgn__class_Osgn(U_3276,U_3277) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3276),c_Groups_Oone__class_Oone(U_3276))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3276),U_3277),c_Groups_Ozero__class_Ozero(U_3276)))
        | ~ sP247(U_3277,U_3276) )
    & ! [U_3277,U_3276] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3276),U_3277),c_Groups_Ozero__class_Ozero(U_3276)))
        | c_Groups_Osgn__class_Osgn(U_3276,U_3277) != hAPP(c_Groups_Ouminus__class_Ouminus(U_3276),c_Groups_Oone__class_Oone(U_3276))
        | ~ sP247(U_3277,U_3276) )
    & ! [U_3277,U_3276] :
        ( sP247(U_3277,U_3276)
        | ~ class_Rings_Olinordered__idom(U_3276) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP247])],[f_848_2]) ).

cnf(f_848_4,plain,
    ( sP247(U_3277,U_3276)
    | ~ class_Rings_Olinordered__idom(U_3276) ),
    inference(clausify,[status(thm)],[f_848_3]) ).

cnf(f_848_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3276),U_3277),c_Groups_Ozero__class_Ozero(U_3276)))
    | c_Groups_Osgn__class_Osgn(U_3276,U_3277) != hAPP(c_Groups_Ouminus__class_Ouminus(U_3276),c_Groups_Oone__class_Oone(U_3276))
    | ~ sP247(U_3277,U_3276) ),
    inference(clausify,[status(thm)],[f_848_3]) ).

cnf(f_848_6,plain,
    ( c_Groups_Osgn__class_Osgn(U_3276,U_3277) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3276),c_Groups_Oone__class_Oone(U_3276))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3276),U_3277),c_Groups_Ozero__class_Ozero(U_3276)))
    | ~ sP247(U_3277,U_3276) ),
    inference(clausify,[status(thm)],[f_848_3]) ).

fof(f_849_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_849_2,plain,
    ! [U_3278] :
      ( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_3278) = 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_3278)) )
          & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_3278) = 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_3278)) ) )
        | U_3278 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_3278) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_3278 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_849_1]) ).

fof(f_849_3,plain,
    ( ! [U_3280] :
        ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_3280) = 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_3280)) )
          & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_3280) = 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_3280)) ) )
        | U_3280 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_3279] :
        ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_3279) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_3279 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_849_2]) ).

fof(f_849_4,plain,
    ( ! [U_3280] :
        ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_3280) = 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_3280))
        | ~ sP248(U_3280) )
    & ! [U_3280] :
        ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_3280) = 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_3280))
        | ~ sP248(U_3280) )
    & ! [U_3280] :
        ( sP248(U_3280)
        | U_3280 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_3279] :
        ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_3279) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_3279 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP248])],[f_849_3]) ).

cnf(f_849_5,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_3279) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_3279 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_849_4]) ).

cnf(f_849_6,plain,
    ( sP248(U_3280)
    | U_3280 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_849_4]) ).

cnf(f_849_7,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_3280) = 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_3280))
    | ~ sP248(U_3280) ),
    inference(clausify,[status(thm)],[f_849_4]) ).

cnf(f_849_8,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_3280) = 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_3280))
    | ~ sP248(U_3280) ),
    inference(clausify,[status(thm)],[f_849_4]) ).

fof(f_850_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_850_2,plain,
    ! [U_3284,U_3283,U_3282,U_3281] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3281,U_3282) = U_3284
      | U_3282 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3284),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3282),U_3284)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3282)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3284),U_3282))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3284)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3282)) )
      | U_3281 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3282),U_3283)),U_3284) ),
    inference(variable_rename,[status(thm)],[f_850_1]) ).

fof(f_850_3,plain,
    ( ! [U_3282,U_3284] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3284),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3282),U_3284))
        | ~ sP250(U_3282,U_3284) )
    & ! [U_3282,U_3284] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3282))
        | ~ sP250(U_3282,U_3284) )
    & ! [U_3282,U_3284] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3284),U_3282))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3284))
        | ~ sP249(U_3282,U_3284) )
    & ! [U_3282,U_3284] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3282))
        | ~ sP249(U_3282,U_3284) )
    & ! [U_3281,U_3282,U_3283,U_3284] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3281,U_3282) = U_3284
        | U_3282 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | sP250(U_3282,U_3284)
        | sP249(U_3282,U_3284)
        | U_3281 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3282),U_3283)),U_3284) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP249,sP250])],[f_850_2]) ).

cnf(f_850_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3281,U_3282) = U_3284
    | U_3282 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | sP250(U_3282,U_3284)
    | sP249(U_3282,U_3284)
    | U_3281 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3282),U_3283)),U_3284) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

cnf(f_850_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3282))
    | ~ sP249(U_3282,U_3284) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

cnf(f_850_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3284),U_3282))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3284))
    | ~ sP249(U_3282,U_3284) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

cnf(f_850_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3282))
    | ~ sP250(U_3282,U_3284) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

cnf(f_850_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3284),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3282),U_3284))
    | ~ sP250(U_3282,U_3284) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

fof(f_851_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_851_2,plain,
    ! [U_3288,U_3287,U_3286,U_3285] :
      ( 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_3286),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3288,U_3285))),U_3287)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3287),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3286),U_3287))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3285)) ),
    inference(variable_rename,[status(thm)],[f_851_1]) ).

fof(f_851_3,plain,
    ! [U_3285,U_3287,U_3288,U_3286] :
      ( 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_3286),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3288,U_3285))),U_3287)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3287),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3286),U_3287))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3285)) ),
    inference(definitional_conversion,[status(esa)],[f_851_2]) ).

cnf(f_851_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_3286),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3288,U_3285))),U_3287)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3287),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3286),U_3287))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3285)) ),
    inference(clausify,[status(thm)],[f_851_3]) ).

fof(f_852_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_852_2,plain,
    ! [U_3292,U_3291,U_3290,U_3289] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3290),U_3289)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3290),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3292,U_3289))),U_3291)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3291),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3290),U_3291))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3289)) ),
    inference(variable_rename,[status(thm)],[f_852_1]) ).

fof(f_852_3,plain,
    ! [U_3291,U_3292,U_3289,U_3290] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3290),U_3289)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3290),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3292,U_3289))),U_3291)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3291),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3290),U_3291))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3289)) ),
    inference(definitional_conversion,[status(esa)],[f_852_2]) ).

cnf(f_852_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3290),U_3289)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3290),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3292,U_3289))),U_3291)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3291),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3290),U_3291))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3289)) ),
    inference(clausify,[status(thm)],[f_852_3]) ).

fof(f_853_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_853_2,plain,
    ! [U_3296,U_3295,U_3294,U_3293] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_3294,U_3293)),U_3295),U_3296))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3294,U_3293)),U_3296),U_3295))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3294,U_3293)),U_3295),U_3296)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3294,U_3293)),U_3296),U_3295))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3294,U_3293)),U_3295),U_3296)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_3294,U_3293)),U_3295),U_3296)) ) )
      | ~ class_Orderings_Oord(U_3293) ),
    inference(variable_rename,[status(thm)],[f_853_1]) ).

fof(f_853_3,plain,
    ( ! [U_3293,U_3294,U_3295,U_3296] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3294,U_3293)),U_3296),U_3295))
        | ~ sP251(U_3293,U_3294,U_3295,U_3296) )
    & ! [U_3293,U_3294,U_3295,U_3296] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3294,U_3293)),U_3295),U_3296))
        | ~ sP251(U_3293,U_3294,U_3295,U_3296) )
    & ! [U_3293,U_3294,U_3295,U_3296] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_3294,U_3293)),U_3295),U_3296))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3294,U_3293)),U_3296),U_3295))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3294,U_3293)),U_3295),U_3296))
        | ~ sP252(U_3293,U_3294,U_3295,U_3296) )
    & ! [U_3293,U_3294,U_3295,U_3296] :
        ( sP251(U_3293,U_3294,U_3295,U_3296)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_3294,U_3293)),U_3295),U_3296))
        | ~ sP252(U_3293,U_3294,U_3295,U_3296) )
    & ! [U_3293,U_3294,U_3295,U_3296] :
        ( sP252(U_3293,U_3294,U_3295,U_3296)
        | ~ class_Orderings_Oord(U_3293) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP251,sP252])],[f_853_2]) ).

cnf(f_853_4,plain,
    ( sP252(U_3293,U_3294,U_3295,U_3296)
    | ~ class_Orderings_Oord(U_3293) ),
    inference(clausify,[status(thm)],[f_853_3]) ).

cnf(f_853_5,plain,
    ( sP251(U_3293,U_3294,U_3295,U_3296)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_3294,U_3293)),U_3295),U_3296))
    | ~ sP252(U_3293,U_3294,U_3295,U_3296) ),
    inference(clausify,[status(thm)],[f_853_3]) ).

cnf(f_853_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_3294,U_3293)),U_3295),U_3296))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3294,U_3293)),U_3296),U_3295))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3294,U_3293)),U_3295),U_3296))
    | ~ sP252(U_3293,U_3294,U_3295,U_3296) ),
    inference(clausify,[status(thm)],[f_853_3]) ).

cnf(f_853_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3294,U_3293)),U_3295),U_3296))
    | ~ sP251(U_3293,U_3294,U_3295,U_3296) ),
    inference(clausify,[status(thm)],[f_853_3]) ).

cnf(f_853_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3294,U_3293)),U_3296),U_3295))
    | ~ sP251(U_3293,U_3294,U_3295,U_3296) ),
    inference(clausify,[status(thm)],[f_853_3]) ).

fof(f_854_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_854_2,plain,
    ! [U_3298,U_3297] :
      ( c_Groups_Osgn__class_Osgn(U_3297,c_Groups_Osgn__class_Osgn(U_3297,U_3298)) = c_Groups_Osgn__class_Osgn(U_3297,U_3298)
      | ~ class_Rings_Olinordered__idom(U_3297) ),
    inference(variable_rename,[status(thm)],[f_854_1]) ).

fof(f_854_3,plain,
    ! [U_3297,U_3298] :
      ( c_Groups_Osgn__class_Osgn(U_3297,c_Groups_Osgn__class_Osgn(U_3297,U_3298)) = c_Groups_Osgn__class_Osgn(U_3297,U_3298)
      | ~ class_Rings_Olinordered__idom(U_3297) ),
    inference(definitional_conversion,[status(esa)],[f_854_2]) ).

cnf(f_854_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_3297,c_Groups_Osgn__class_Osgn(U_3297,U_3298)) = c_Groups_Osgn__class_Osgn(U_3297,U_3298)
    | ~ class_Rings_Olinordered__idom(U_3297) ),
    inference(clausify,[status(thm)],[f_854_3]) ).

fof(f_855_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_855_2,plain,
    ! [U_3301,U_3300,U_3299] :
      ( c_Divides_Odiv__class_Omod(U_3299,c_Divides_Odiv__class_Omod(U_3299,U_3300,U_3301),U_3301) = c_Divides_Odiv__class_Omod(U_3299,U_3300,U_3301)
      | ~ class_Divides_Osemiring__div(U_3299) ),
    inference(variable_rename,[status(thm)],[f_855_1]) ).

fof(f_855_3,plain,
    ! [U_3300,U_3301,U_3299] :
      ( c_Divides_Odiv__class_Omod(U_3299,c_Divides_Odiv__class_Omod(U_3299,U_3300,U_3301),U_3301) = c_Divides_Odiv__class_Omod(U_3299,U_3300,U_3301)
      | ~ class_Divides_Osemiring__div(U_3299) ),
    inference(definitional_conversion,[status(esa)],[f_855_2]) ).

cnf(f_855_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3299,c_Divides_Odiv__class_Omod(U_3299,U_3300,U_3301),U_3301) = c_Divides_Odiv__class_Omod(U_3299,U_3300,U_3301)
    | ~ class_Divides_Osemiring__div(U_3299) ),
    inference(clausify,[status(thm)],[f_855_3]) ).

fof(f_856_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_856_2,plain,
    ! [U_3303,U_3302] :
      ( c_Divides_Odiv__class_Omod(U_3302,c_Groups_Ozero__class_Ozero(U_3302),U_3303) = c_Groups_Ozero__class_Ozero(U_3302)
      | ~ class_Divides_Osemiring__div(U_3302) ),
    inference(variable_rename,[status(thm)],[f_856_1]) ).

fof(f_856_3,plain,
    ! [U_3303,U_3302] :
      ( c_Divides_Odiv__class_Omod(U_3302,c_Groups_Ozero__class_Ozero(U_3302),U_3303) = c_Groups_Ozero__class_Ozero(U_3302)
      | ~ class_Divides_Osemiring__div(U_3302) ),
    inference(definitional_conversion,[status(esa)],[f_856_2]) ).

cnf(f_856_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3302,c_Groups_Ozero__class_Ozero(U_3302),U_3303) = c_Groups_Ozero__class_Ozero(U_3302)
    | ~ class_Divides_Osemiring__div(U_3302) ),
    inference(clausify,[status(thm)],[f_856_3]) ).

fof(f_857_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_857_2,plain,
    ! [U_3305,U_3304] :
      ( c_Divides_Odiv__class_Omod(U_3304,U_3305,c_Groups_Ozero__class_Ozero(U_3304)) = U_3305
      | ~ class_Divides_Osemiring__div(U_3304) ),
    inference(variable_rename,[status(thm)],[f_857_1]) ).

fof(f_857_3,plain,
    ! [U_3304,U_3305] :
      ( c_Divides_Odiv__class_Omod(U_3304,U_3305,c_Groups_Ozero__class_Ozero(U_3304)) = U_3305
      | ~ class_Divides_Osemiring__div(U_3304) ),
    inference(definitional_conversion,[status(esa)],[f_857_2]) ).

cnf(f_857_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3304,U_3305,c_Groups_Ozero__class_Ozero(U_3304)) = U_3305
    | ~ class_Divides_Osemiring__div(U_3304) ),
    inference(clausify,[status(thm)],[f_857_3]) ).

fof(f_858_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_858_2,plain,
    ! [U_3307,U_3306] :
      ( c_Divides_Odiv__class_Omod(U_3306,U_3307,U_3307) = c_Groups_Ozero__class_Ozero(U_3306)
      | ~ class_Divides_Osemiring__div(U_3306) ),
    inference(variable_rename,[status(thm)],[f_858_1]) ).

fof(f_858_3,plain,
    ! [U_3306,U_3307] :
      ( c_Divides_Odiv__class_Omod(U_3306,U_3307,U_3307) = c_Groups_Ozero__class_Ozero(U_3306)
      | ~ class_Divides_Osemiring__div(U_3306) ),
    inference(definitional_conversion,[status(esa)],[f_858_2]) ).

cnf(f_858_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3306,U_3307,U_3307) = c_Groups_Ozero__class_Ozero(U_3306)
    | ~ class_Divides_Osemiring__div(U_3306) ),
    inference(clausify,[status(thm)],[f_858_3]) ).

fof(f_859_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_859_2,plain,
    ! [U_3310,U_3309,U_3308] :
      ( c_Divides_Odiv__class_Omod(U_3308,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3308),U_3309),U_3310),U_3310) = c_Divides_Odiv__class_Omod(U_3308,U_3309,U_3310)
      | ~ class_Divides_Osemiring__div(U_3308) ),
    inference(variable_rename,[status(thm)],[f_859_1]) ).

fof(f_859_3,plain,
    ! [U_3308,U_3309,U_3310] :
      ( c_Divides_Odiv__class_Omod(U_3308,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3308),U_3309),U_3310),U_3310) = c_Divides_Odiv__class_Omod(U_3308,U_3309,U_3310)
      | ~ class_Divides_Osemiring__div(U_3308) ),
    inference(definitional_conversion,[status(esa)],[f_859_2]) ).

cnf(f_859_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3308,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3308),U_3309),U_3310),U_3310) = c_Divides_Odiv__class_Omod(U_3308,U_3309,U_3310)
    | ~ class_Divides_Osemiring__div(U_3308) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

fof(f_860_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_860_2,plain,
    ! [U_3313,U_3312,U_3311] :
      ( c_Divides_Odiv__class_Omod(U_3311,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3311),U_3312),U_3313),U_3312) = c_Divides_Odiv__class_Omod(U_3311,U_3313,U_3312)
      | ~ class_Divides_Osemiring__div(U_3311) ),
    inference(variable_rename,[status(thm)],[f_860_1]) ).

fof(f_860_3,plain,
    ! [U_3311,U_3312,U_3313] :
      ( c_Divides_Odiv__class_Omod(U_3311,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3311),U_3312),U_3313),U_3312) = c_Divides_Odiv__class_Omod(U_3311,U_3313,U_3312)
      | ~ class_Divides_Osemiring__div(U_3311) ),
    inference(definitional_conversion,[status(esa)],[f_860_2]) ).

cnf(f_860_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3311,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3311),U_3312),U_3313),U_3312) = c_Divides_Odiv__class_Omod(U_3311,U_3313,U_3312)
    | ~ class_Divides_Osemiring__div(U_3311) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

fof(f_861_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_861_2,plain,
    ! [U_3317,U_3316,U_3315,U_3314] :
      ( c_Divides_Odiv__class_Omod(U_3314,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3314),U_3315),U_3316),U_3317) = c_Divides_Odiv__class_Omod(U_3314,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3314),U_3315),c_Divides_Odiv__class_Omod(U_3314,U_3316,U_3317)),U_3317)
      | ~ class_Divides_Osemiring__div(U_3314) ),
    inference(variable_rename,[status(thm)],[f_861_1]) ).

fof(f_861_3,plain,
    ! [U_3314,U_3315,U_3316,U_3317] :
      ( c_Divides_Odiv__class_Omod(U_3314,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3314),U_3315),U_3316),U_3317) = c_Divides_Odiv__class_Omod(U_3314,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3314),U_3315),c_Divides_Odiv__class_Omod(U_3314,U_3316,U_3317)),U_3317)
      | ~ class_Divides_Osemiring__div(U_3314) ),
    inference(definitional_conversion,[status(esa)],[f_861_2]) ).

cnf(f_861_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3314,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3314),U_3315),U_3316),U_3317) = c_Divides_Odiv__class_Omod(U_3314,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3314),U_3315),c_Divides_Odiv__class_Omod(U_3314,U_3316,U_3317)),U_3317)
    | ~ class_Divides_Osemiring__div(U_3314) ),
    inference(clausify,[status(thm)],[f_861_3]) ).

fof(f_862_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_862_2,plain,
    ! [U_3321,U_3320,U_3319,U_3318] :
      ( c_Divides_Odiv__class_Omod(U_3318,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3318),U_3319),U_3320),U_3321) = c_Divides_Odiv__class_Omod(U_3318,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3318),c_Divides_Odiv__class_Omod(U_3318,U_3319,U_3321)),U_3320),U_3321)
      | ~ class_Divides_Osemiring__div(U_3318) ),
    inference(variable_rename,[status(thm)],[f_862_1]) ).

fof(f_862_3,plain,
    ! [U_3318,U_3319,U_3320,U_3321] :
      ( c_Divides_Odiv__class_Omod(U_3318,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3318),U_3319),U_3320),U_3321) = c_Divides_Odiv__class_Omod(U_3318,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3318),c_Divides_Odiv__class_Omod(U_3318,U_3319,U_3321)),U_3320),U_3321)
      | ~ class_Divides_Osemiring__div(U_3318) ),
    inference(definitional_conversion,[status(esa)],[f_862_2]) ).

cnf(f_862_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3318,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3318),U_3319),U_3320),U_3321) = c_Divides_Odiv__class_Omod(U_3318,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3318),c_Divides_Odiv__class_Omod(U_3318,U_3319,U_3321)),U_3320),U_3321)
    | ~ class_Divides_Osemiring__div(U_3318) ),
    inference(clausify,[status(thm)],[f_862_3]) ).

fof(f_863_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_863_2,plain,
    ! [U_3325,U_3324,U_3323,U_3322] :
      ( c_Divides_Odiv__class_Omod(U_3322,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3322),U_3323),U_3324),U_3325) = c_Divides_Odiv__class_Omod(U_3322,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3322),c_Divides_Odiv__class_Omod(U_3322,U_3323,U_3325)),c_Divides_Odiv__class_Omod(U_3322,U_3324,U_3325)),U_3325)
      | ~ class_Divides_Osemiring__div(U_3322) ),
    inference(variable_rename,[status(thm)],[f_863_1]) ).

fof(f_863_3,plain,
    ! [U_3322,U_3323,U_3324,U_3325] :
      ( c_Divides_Odiv__class_Omod(U_3322,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3322),U_3323),U_3324),U_3325) = c_Divides_Odiv__class_Omod(U_3322,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3322),c_Divides_Odiv__class_Omod(U_3322,U_3323,U_3325)),c_Divides_Odiv__class_Omod(U_3322,U_3324,U_3325)),U_3325)
      | ~ class_Divides_Osemiring__div(U_3322) ),
    inference(definitional_conversion,[status(esa)],[f_863_2]) ).

cnf(f_863_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3322,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3322),U_3323),U_3324),U_3325) = c_Divides_Odiv__class_Omod(U_3322,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3322),c_Divides_Odiv__class_Omod(U_3322,U_3323,U_3325)),c_Divides_Odiv__class_Omod(U_3322,U_3324,U_3325)),U_3325)
    | ~ class_Divides_Osemiring__div(U_3322) ),
    inference(clausify,[status(thm)],[f_863_3]) ).

fof(f_864_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_864_2,plain,
    ! [U_3329,U_3328,U_3327,U_3326] :
      ( c_Divides_Odiv__class_Omod(U_3326,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3326),U_3327),c_Divides_Odiv__class_Omod(U_3326,U_3328,U_3329)),U_3329) = c_Divides_Odiv__class_Omod(U_3326,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3326),U_3327),U_3328),U_3329)
      | ~ class_Divides_Osemiring__div(U_3326) ),
    inference(variable_rename,[status(thm)],[f_864_1]) ).

fof(f_864_3,plain,
    ! [U_3326,U_3327,U_3328,U_3329] :
      ( c_Divides_Odiv__class_Omod(U_3326,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3326),U_3327),c_Divides_Odiv__class_Omod(U_3326,U_3328,U_3329)),U_3329) = c_Divides_Odiv__class_Omod(U_3326,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3326),U_3327),U_3328),U_3329)
      | ~ class_Divides_Osemiring__div(U_3326) ),
    inference(definitional_conversion,[status(esa)],[f_864_2]) ).

cnf(f_864_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3326,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3326),U_3327),c_Divides_Odiv__class_Omod(U_3326,U_3328,U_3329)),U_3329) = c_Divides_Odiv__class_Omod(U_3326,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3326),U_3327),U_3328),U_3329)
    | ~ class_Divides_Osemiring__div(U_3326) ),
    inference(clausify,[status(thm)],[f_864_3]) ).

fof(f_865_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_865_2,plain,
    ! [U_3333,U_3332,U_3331,U_3330] :
      ( c_Divides_Odiv__class_Omod(U_3330,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3330),c_Divides_Odiv__class_Omod(U_3330,U_3331,U_3332)),U_3333),U_3332) = c_Divides_Odiv__class_Omod(U_3330,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3330),U_3331),U_3333),U_3332)
      | ~ class_Divides_Osemiring__div(U_3330) ),
    inference(variable_rename,[status(thm)],[f_865_1]) ).

fof(f_865_3,plain,
    ! [U_3330,U_3331,U_3332,U_3333] :
      ( c_Divides_Odiv__class_Omod(U_3330,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3330),c_Divides_Odiv__class_Omod(U_3330,U_3331,U_3332)),U_3333),U_3332) = c_Divides_Odiv__class_Omod(U_3330,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3330),U_3331),U_3333),U_3332)
      | ~ class_Divides_Osemiring__div(U_3330) ),
    inference(definitional_conversion,[status(esa)],[f_865_2]) ).

cnf(f_865_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3330,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3330),c_Divides_Odiv__class_Omod(U_3330,U_3331,U_3332)),U_3333),U_3332) = c_Divides_Odiv__class_Omod(U_3330,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3330),U_3331),U_3333),U_3332)
    | ~ class_Divides_Osemiring__div(U_3330) ),
    inference(clausify,[status(thm)],[f_865_3]) ).

fof(f_866_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_866_2,plain,
    ! [U_3339,U_3338,U_3337,U_3336,U_3335,U_3334] :
      ( c_Divides_Odiv__class_Omod(U_3334,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3334),U_3335),U_3338),U_3336) = c_Divides_Odiv__class_Omod(U_3334,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3334),U_3337),U_3339),U_3336)
      | c_Divides_Odiv__class_Omod(U_3334,U_3338,U_3336) != c_Divides_Odiv__class_Omod(U_3334,U_3339,U_3336)
      | c_Divides_Odiv__class_Omod(U_3334,U_3335,U_3336) != c_Divides_Odiv__class_Omod(U_3334,U_3337,U_3336)
      | ~ class_Divides_Osemiring__div(U_3334) ),
    inference(variable_rename,[status(thm)],[f_866_1]) ).

fof(f_866_3,plain,
    ! [U_3334,U_3335,U_3336,U_3337,U_3338,U_3339] :
      ( c_Divides_Odiv__class_Omod(U_3334,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3334),U_3335),U_3338),U_3336) = c_Divides_Odiv__class_Omod(U_3334,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3334),U_3337),U_3339),U_3336)
      | c_Divides_Odiv__class_Omod(U_3334,U_3338,U_3336) != c_Divides_Odiv__class_Omod(U_3334,U_3339,U_3336)
      | c_Divides_Odiv__class_Omod(U_3334,U_3335,U_3336) != c_Divides_Odiv__class_Omod(U_3334,U_3337,U_3336)
      | ~ class_Divides_Osemiring__div(U_3334) ),
    inference(definitional_conversion,[status(esa)],[f_866_2]) ).

cnf(f_866_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3334,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3334),U_3335),U_3338),U_3336) = c_Divides_Odiv__class_Omod(U_3334,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3334),U_3337),U_3339),U_3336)
    | c_Divides_Odiv__class_Omod(U_3334,U_3338,U_3336) != c_Divides_Odiv__class_Omod(U_3334,U_3339,U_3336)
    | c_Divides_Odiv__class_Omod(U_3334,U_3335,U_3336) != c_Divides_Odiv__class_Omod(U_3334,U_3337,U_3336)
    | ~ class_Divides_Osemiring__div(U_3334) ),
    inference(clausify,[status(thm)],[f_866_3]) ).

fof(f_867_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_867_2,plain,
    ! [U_3343,U_3342,U_3341,U_3340] :
      ( c_Divides_Odiv__class_Omod(U_3340,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3340),U_3341),U_3342),U_3343) = c_Divides_Odiv__class_Omod(U_3340,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3340),U_3341),c_Divides_Odiv__class_Omod(U_3340,U_3342,U_3343)),U_3343)
      | ~ class_Divides_Osemiring__div(U_3340) ),
    inference(variable_rename,[status(thm)],[f_867_1]) ).

fof(f_867_3,plain,
    ! [U_3340,U_3341,U_3342,U_3343] :
      ( c_Divides_Odiv__class_Omod(U_3340,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3340),U_3341),U_3342),U_3343) = c_Divides_Odiv__class_Omod(U_3340,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3340),U_3341),c_Divides_Odiv__class_Omod(U_3340,U_3342,U_3343)),U_3343)
      | ~ class_Divides_Osemiring__div(U_3340) ),
    inference(definitional_conversion,[status(esa)],[f_867_2]) ).

cnf(f_867_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3340,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3340),U_3341),U_3342),U_3343) = c_Divides_Odiv__class_Omod(U_3340,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3340),U_3341),c_Divides_Odiv__class_Omod(U_3340,U_3342,U_3343)),U_3343)
    | ~ class_Divides_Osemiring__div(U_3340) ),
    inference(clausify,[status(thm)],[f_867_3]) ).

fof(f_868_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_868_2,plain,
    ! [U_3347,U_3346,U_3345,U_3344] :
      ( c_Divides_Odiv__class_Omod(U_3344,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3344),U_3345),U_3346),U_3347) = c_Divides_Odiv__class_Omod(U_3344,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3344),c_Divides_Odiv__class_Omod(U_3344,U_3345,U_3347)),U_3346),U_3347)
      | ~ class_Divides_Osemiring__div(U_3344) ),
    inference(variable_rename,[status(thm)],[f_868_1]) ).

fof(f_868_3,plain,
    ! [U_3344,U_3345,U_3346,U_3347] :
      ( c_Divides_Odiv__class_Omod(U_3344,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3344),U_3345),U_3346),U_3347) = c_Divides_Odiv__class_Omod(U_3344,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3344),c_Divides_Odiv__class_Omod(U_3344,U_3345,U_3347)),U_3346),U_3347)
      | ~ class_Divides_Osemiring__div(U_3344) ),
    inference(definitional_conversion,[status(esa)],[f_868_2]) ).

cnf(f_868_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3344,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3344),U_3345),U_3346),U_3347) = c_Divides_Odiv__class_Omod(U_3344,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3344),c_Divides_Odiv__class_Omod(U_3344,U_3345,U_3347)),U_3346),U_3347)
    | ~ class_Divides_Osemiring__div(U_3344) ),
    inference(clausify,[status(thm)],[f_868_3]) ).

fof(f_869_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_869_2,plain,
    ! [U_3351,U_3350,U_3349,U_3348] :
      ( c_Divides_Odiv__class_Omod(U_3348,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3348),U_3349),U_3350),U_3351) = c_Divides_Odiv__class_Omod(U_3348,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3348),c_Divides_Odiv__class_Omod(U_3348,U_3349,U_3351)),c_Divides_Odiv__class_Omod(U_3348,U_3350,U_3351)),U_3351)
      | ~ class_Divides_Osemiring__div(U_3348) ),
    inference(variable_rename,[status(thm)],[f_869_1]) ).

fof(f_869_3,plain,
    ! [U_3348,U_3349,U_3350,U_3351] :
      ( c_Divides_Odiv__class_Omod(U_3348,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3348),U_3349),U_3350),U_3351) = c_Divides_Odiv__class_Omod(U_3348,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3348),c_Divides_Odiv__class_Omod(U_3348,U_3349,U_3351)),c_Divides_Odiv__class_Omod(U_3348,U_3350,U_3351)),U_3351)
      | ~ class_Divides_Osemiring__div(U_3348) ),
    inference(definitional_conversion,[status(esa)],[f_869_2]) ).

cnf(f_869_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3348,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3348),U_3349),U_3350),U_3351) = c_Divides_Odiv__class_Omod(U_3348,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3348),c_Divides_Odiv__class_Omod(U_3348,U_3349,U_3351)),c_Divides_Odiv__class_Omod(U_3348,U_3350,U_3351)),U_3351)
    | ~ class_Divides_Osemiring__div(U_3348) ),
    inference(clausify,[status(thm)],[f_869_3]) ).

fof(f_870_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_870_2,plain,
    ! [U_3355,U_3354,U_3353,U_3352] :
      ( c_Divides_Odiv__class_Omod(U_3352,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3352),U_3353),U_3354),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3352),U_3353),U_3355)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3352),U_3353),c_Divides_Odiv__class_Omod(U_3352,U_3354,U_3355))
      | ~ class_Divides_Osemiring__div(U_3352) ),
    inference(variable_rename,[status(thm)],[f_870_1]) ).

fof(f_870_3,plain,
    ! [U_3352,U_3353,U_3354,U_3355] :
      ( c_Divides_Odiv__class_Omod(U_3352,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3352),U_3353),U_3354),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3352),U_3353),U_3355)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3352),U_3353),c_Divides_Odiv__class_Omod(U_3352,U_3354,U_3355))
      | ~ class_Divides_Osemiring__div(U_3352) ),
    inference(definitional_conversion,[status(esa)],[f_870_2]) ).

cnf(f_870_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3352,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3352),U_3353),U_3354),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3352),U_3353),U_3355)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3352),U_3353),c_Divides_Odiv__class_Omod(U_3352,U_3354,U_3355))
    | ~ class_Divides_Osemiring__div(U_3352) ),
    inference(clausify,[status(thm)],[f_870_3]) ).

fof(f_871_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_871_2,plain,
    ! [U_3359,U_3358,U_3357,U_3356] :
      ( c_Divides_Odiv__class_Omod(U_3356,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3356),U_3357),U_3358),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3356),U_3359),U_3358)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3356),c_Divides_Odiv__class_Omod(U_3356,U_3357,U_3359)),U_3358)
      | ~ class_Divides_Osemiring__div(U_3356) ),
    inference(variable_rename,[status(thm)],[f_871_1]) ).

fof(f_871_3,plain,
    ! [U_3356,U_3357,U_3358,U_3359] :
      ( c_Divides_Odiv__class_Omod(U_3356,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3356),U_3357),U_3358),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3356),U_3359),U_3358)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3356),c_Divides_Odiv__class_Omod(U_3356,U_3357,U_3359)),U_3358)
      | ~ class_Divides_Osemiring__div(U_3356) ),
    inference(definitional_conversion,[status(esa)],[f_871_2]) ).

cnf(f_871_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3356,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3356),U_3357),U_3358),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3356),U_3359),U_3358)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3356),c_Divides_Odiv__class_Omod(U_3356,U_3357,U_3359)),U_3358)
    | ~ class_Divides_Osemiring__div(U_3356) ),
    inference(clausify,[status(thm)],[f_871_3]) ).

fof(f_872_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_872_2,plain,
    ! [U_3363,U_3362,U_3361,U_3360] :
      ( c_Divides_Odiv__class_Omod(U_3360,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3360),c_Divides_Odiv__class_Omod(U_3360,U_3361,U_3362)),U_3363),U_3362) = c_Divides_Odiv__class_Omod(U_3360,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3360),U_3361),U_3363),U_3362)
      | ~ class_Divides_Osemiring__div(U_3360) ),
    inference(variable_rename,[status(thm)],[f_872_1]) ).

fof(f_872_3,plain,
    ! [U_3360,U_3361,U_3362,U_3363] :
      ( c_Divides_Odiv__class_Omod(U_3360,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3360),c_Divides_Odiv__class_Omod(U_3360,U_3361,U_3362)),U_3363),U_3362) = c_Divides_Odiv__class_Omod(U_3360,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3360),U_3361),U_3363),U_3362)
      | ~ class_Divides_Osemiring__div(U_3360) ),
    inference(definitional_conversion,[status(esa)],[f_872_2]) ).

cnf(f_872_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3360,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3360),c_Divides_Odiv__class_Omod(U_3360,U_3361,U_3362)),U_3363),U_3362) = c_Divides_Odiv__class_Omod(U_3360,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3360),U_3361),U_3363),U_3362)
    | ~ class_Divides_Osemiring__div(U_3360) ),
    inference(clausify,[status(thm)],[f_872_3]) ).

fof(f_873_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_873_2,plain,
    ! [U_3369,U_3368,U_3367,U_3366,U_3365,U_3364] :
      ( c_Divides_Odiv__class_Omod(U_3364,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3364),U_3365),U_3368),U_3366) = c_Divides_Odiv__class_Omod(U_3364,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3364),U_3367),U_3369),U_3366)
      | c_Divides_Odiv__class_Omod(U_3364,U_3368,U_3366) != c_Divides_Odiv__class_Omod(U_3364,U_3369,U_3366)
      | c_Divides_Odiv__class_Omod(U_3364,U_3365,U_3366) != c_Divides_Odiv__class_Omod(U_3364,U_3367,U_3366)
      | ~ class_Divides_Osemiring__div(U_3364) ),
    inference(variable_rename,[status(thm)],[f_873_1]) ).

fof(f_873_3,plain,
    ! [U_3364,U_3365,U_3366,U_3367,U_3368,U_3369] :
      ( c_Divides_Odiv__class_Omod(U_3364,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3364),U_3365),U_3368),U_3366) = c_Divides_Odiv__class_Omod(U_3364,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3364),U_3367),U_3369),U_3366)
      | c_Divides_Odiv__class_Omod(U_3364,U_3368,U_3366) != c_Divides_Odiv__class_Omod(U_3364,U_3369,U_3366)
      | c_Divides_Odiv__class_Omod(U_3364,U_3365,U_3366) != c_Divides_Odiv__class_Omod(U_3364,U_3367,U_3366)
      | ~ class_Divides_Osemiring__div(U_3364) ),
    inference(definitional_conversion,[status(esa)],[f_873_2]) ).

cnf(f_873_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3364,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3364),U_3365),U_3368),U_3366) = c_Divides_Odiv__class_Omod(U_3364,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3364),U_3367),U_3369),U_3366)
    | c_Divides_Odiv__class_Omod(U_3364,U_3368,U_3366) != c_Divides_Odiv__class_Omod(U_3364,U_3369,U_3366)
    | c_Divides_Odiv__class_Omod(U_3364,U_3365,U_3366) != c_Divides_Odiv__class_Omod(U_3364,U_3367,U_3366)
    | ~ class_Divides_Osemiring__div(U_3364) ),
    inference(clausify,[status(thm)],[f_873_3]) ).

fof(f_874_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_874_2,plain,
    ! [U_3372,U_3371,U_3370] :
      ( c_Divides_Odiv__class_Omod(U_3370,hAPP(c_Groups_Ouminus__class_Ouminus(U_3370),U_3371),U_3372) = c_Divides_Odiv__class_Omod(U_3370,hAPP(c_Groups_Ouminus__class_Ouminus(U_3370),c_Divides_Odiv__class_Omod(U_3370,U_3371,U_3372)),U_3372)
      | ~ class_Divides_Oring__div(U_3370) ),
    inference(variable_rename,[status(thm)],[f_874_1]) ).

fof(f_874_3,plain,
    ! [U_3371,U_3370,U_3372] :
      ( c_Divides_Odiv__class_Omod(U_3370,hAPP(c_Groups_Ouminus__class_Ouminus(U_3370),U_3371),U_3372) = c_Divides_Odiv__class_Omod(U_3370,hAPP(c_Groups_Ouminus__class_Ouminus(U_3370),c_Divides_Odiv__class_Omod(U_3370,U_3371,U_3372)),U_3372)
      | ~ class_Divides_Oring__div(U_3370) ),
    inference(definitional_conversion,[status(esa)],[f_874_2]) ).

cnf(f_874_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3370,hAPP(c_Groups_Ouminus__class_Ouminus(U_3370),U_3371),U_3372) = c_Divides_Odiv__class_Omod(U_3370,hAPP(c_Groups_Ouminus__class_Ouminus(U_3370),c_Divides_Odiv__class_Omod(U_3370,U_3371,U_3372)),U_3372)
    | ~ class_Divides_Oring__div(U_3370) ),
    inference(clausify,[status(thm)],[f_874_3]) ).

fof(f_875_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_875_2,plain,
    ! [U_3376,U_3375,U_3374,U_3373] :
      ( c_Divides_Odiv__class_Omod(U_3373,hAPP(c_Groups_Ouminus__class_Ouminus(U_3373),U_3374),U_3375) = c_Divides_Odiv__class_Omod(U_3373,hAPP(c_Groups_Ouminus__class_Ouminus(U_3373),U_3376),U_3375)
      | c_Divides_Odiv__class_Omod(U_3373,U_3374,U_3375) != c_Divides_Odiv__class_Omod(U_3373,U_3376,U_3375)
      | ~ class_Divides_Oring__div(U_3373) ),
    inference(variable_rename,[status(thm)],[f_875_1]) ).

fof(f_875_3,plain,
    ! [U_3373,U_3374,U_3375,U_3376] :
      ( c_Divides_Odiv__class_Omod(U_3373,hAPP(c_Groups_Ouminus__class_Ouminus(U_3373),U_3374),U_3375) = c_Divides_Odiv__class_Omod(U_3373,hAPP(c_Groups_Ouminus__class_Ouminus(U_3373),U_3376),U_3375)
      | c_Divides_Odiv__class_Omod(U_3373,U_3374,U_3375) != c_Divides_Odiv__class_Omod(U_3373,U_3376,U_3375)
      | ~ class_Divides_Oring__div(U_3373) ),
    inference(definitional_conversion,[status(esa)],[f_875_2]) ).

cnf(f_875_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3373,hAPP(c_Groups_Ouminus__class_Ouminus(U_3373),U_3374),U_3375) = c_Divides_Odiv__class_Omod(U_3373,hAPP(c_Groups_Ouminus__class_Ouminus(U_3373),U_3376),U_3375)
    | c_Divides_Odiv__class_Omod(U_3373,U_3374,U_3375) != c_Divides_Odiv__class_Omod(U_3373,U_3376,U_3375)
    | ~ class_Divides_Oring__div(U_3373) ),
    inference(clausify,[status(thm)],[f_875_3]) ).

fof(f_876_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_876_2,plain,
    ! [U_3377] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3377,U_3377) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_876_1]) ).

fof(f_876_3,plain,
    ! [U_3377] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3377,U_3377) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_876_2]) ).

cnf(f_876_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3377,U_3377) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_876_3]) ).

fof(f_877_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_877_2,plain,
    ! [U_3378] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3378) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_877_1]) ).

fof(f_877_3,plain,
    ! [U_3378] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3378) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_877_2]) ).

cnf(f_877_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3378) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_877_3]) ).

fof(f_878_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_878_2,plain,
    ! [U_3381,U_3380,U_3379] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3379),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3380,U_3381)),U_3381) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3379),U_3380),U_3381),
    inference(variable_rename,[status(thm)],[f_878_1]) ).

fof(f_878_3,plain,
    ! [U_3379,U_3380,U_3381] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3379),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3380,U_3381)),U_3381) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3379),U_3380),U_3381),
    inference(definitional_conversion,[status(esa)],[f_878_2]) ).

cnf(f_878_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3379),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3380,U_3381)),U_3381) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3379),U_3380),U_3381),
    inference(clausify,[status(thm)],[f_878_3]) ).

fof(f_879_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_879_2,plain,
    ! [U_3384,U_3383,U_3382] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3382),U_3383),U_3384) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3382),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3383,U_3384)),U_3384),
    inference(variable_rename,[status(thm)],[f_879_1]) ).

fof(f_879_3,plain,
    ! [U_3382,U_3383,U_3384] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3382),U_3383),U_3384) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3382),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3383,U_3384)),U_3384),
    inference(definitional_conversion,[status(esa)],[f_879_2]) ).

cnf(f_879_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3382),U_3383),U_3384) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3382),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3383,U_3384)),U_3384),
    inference(clausify,[status(thm)],[f_879_3]) ).

fof(f_880_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_880_2,plain,
    ! [U_3386,U_3385] : 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_3385,U_3386)),U_3386) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3385),U_3386),
    inference(variable_rename,[status(thm)],[f_880_1]) ).

fof(f_880_3,plain,
    ! [U_3385,U_3386] : 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_3385,U_3386)),U_3386) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3385),U_3386),
    inference(definitional_conversion,[status(esa)],[f_880_2]) ).

cnf(f_880_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_3385,U_3386)),U_3386) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3385),U_3386),
    inference(clausify,[status(thm)],[f_880_3]) ).

fof(f_881_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_881_2,plain,
    ! [U_3388,U_3387] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3387),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3388)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3387,U_3388)),
    inference(variable_rename,[status(thm)],[f_881_1]) ).

fof(f_881_3,plain,
    ! [U_3387,U_3388] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3387),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3388)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3387,U_3388)),
    inference(definitional_conversion,[status(esa)],[f_881_2]) ).

cnf(f_881_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3387),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3388)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3387,U_3388)),
    inference(clausify,[status(thm)],[f_881_3]) ).

fof(f_882_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_882_2,plain,
    ! [U_3390,U_3389] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3389,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3390)) = 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_3389),U_3390)),
    inference(variable_rename,[status(thm)],[f_882_1]) ).

fof(f_882_3,plain,
    ! [U_3389,U_3390] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3389,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3390)) = 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_3389),U_3390)),
    inference(definitional_conversion,[status(esa)],[f_882_2]) ).

cnf(f_882_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3389,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3390)) = 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_3389),U_3390)),
    inference(clausify,[status(thm)],[f_882_3]) ).

fof(f_883_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_883_2,plain,
    ! [U_3392,U_3391] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_3391,U_3392) = c_Groups_Ozero__class_Ozero(U_3391)
          | U_3392 != c_Groups_Ozero__class_Ozero(U_3391) )
        & ( U_3392 = c_Groups_Ozero__class_Ozero(U_3391)
          | c_Groups_Osgn__class_Osgn(U_3391,U_3392) != c_Groups_Ozero__class_Ozero(U_3391) ) )
      | ~ class_Rings_Olinordered__idom(U_3391) ),
    inference(variable_rename,[status(thm)],[f_883_1]) ).

fof(f_883_3,plain,
    ( ! [U_3391,U_3392] :
        ( c_Groups_Osgn__class_Osgn(U_3391,U_3392) = c_Groups_Ozero__class_Ozero(U_3391)
        | U_3392 != c_Groups_Ozero__class_Ozero(U_3391)
        | ~ sP253(U_3391,U_3392) )
    & ! [U_3391,U_3392] :
        ( U_3392 = c_Groups_Ozero__class_Ozero(U_3391)
        | c_Groups_Osgn__class_Osgn(U_3391,U_3392) != c_Groups_Ozero__class_Ozero(U_3391)
        | ~ sP253(U_3391,U_3392) )
    & ! [U_3391,U_3392] :
        ( sP253(U_3391,U_3392)
        | ~ class_Rings_Olinordered__idom(U_3391) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP253])],[f_883_2]) ).

cnf(f_883_4,plain,
    ( sP253(U_3391,U_3392)
    | ~ class_Rings_Olinordered__idom(U_3391) ),
    inference(clausify,[status(thm)],[f_883_3]) ).

cnf(f_883_5,plain,
    ( U_3392 = c_Groups_Ozero__class_Ozero(U_3391)
    | c_Groups_Osgn__class_Osgn(U_3391,U_3392) != c_Groups_Ozero__class_Ozero(U_3391)
    | ~ sP253(U_3391,U_3392) ),
    inference(clausify,[status(thm)],[f_883_3]) ).

cnf(f_883_6,plain,
    ( c_Groups_Osgn__class_Osgn(U_3391,U_3392) = c_Groups_Ozero__class_Ozero(U_3391)
    | U_3392 != c_Groups_Ozero__class_Ozero(U_3391)
    | ~ sP253(U_3391,U_3392) ),
    inference(clausify,[status(thm)],[f_883_3]) ).

fof(f_884_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_884_2,plain,
    ! [U_3393] :
      ( c_Groups_Osgn__class_Osgn(U_3393,c_Groups_Ozero__class_Ozero(U_3393)) = c_Groups_Ozero__class_Ozero(U_3393)
      | ~ class_Groups_Osgn__if(U_3393) ),
    inference(variable_rename,[status(thm)],[f_884_1]) ).

fof(f_884_3,plain,
    ! [U_3393] :
      ( c_Groups_Osgn__class_Osgn(U_3393,c_Groups_Ozero__class_Ozero(U_3393)) = c_Groups_Ozero__class_Ozero(U_3393)
      | ~ class_Groups_Osgn__if(U_3393) ),
    inference(definitional_conversion,[status(esa)],[f_884_2]) ).

cnf(f_884_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_3393,c_Groups_Ozero__class_Ozero(U_3393)) = c_Groups_Ozero__class_Ozero(U_3393)
    | ~ class_Groups_Osgn__if(U_3393) ),
    inference(clausify,[status(thm)],[f_884_3]) ).

fof(f_885_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_885_2,plain,
    ! [U_3396,U_3395,U_3394] :
      ( c_Groups_Osgn__class_Osgn(U_3394,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3394),U_3395),U_3396)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3394),c_Groups_Osgn__class_Osgn(U_3394,U_3395)),c_Groups_Osgn__class_Osgn(U_3394,U_3396))
      | ~ class_Rings_Olinordered__idom(U_3394) ),
    inference(variable_rename,[status(thm)],[f_885_1]) ).

fof(f_885_3,plain,
    ! [U_3394,U_3395,U_3396] :
      ( c_Groups_Osgn__class_Osgn(U_3394,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3394),U_3395),U_3396)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3394),c_Groups_Osgn__class_Osgn(U_3394,U_3395)),c_Groups_Osgn__class_Osgn(U_3394,U_3396))
      | ~ class_Rings_Olinordered__idom(U_3394) ),
    inference(definitional_conversion,[status(esa)],[f_885_2]) ).

cnf(f_885_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_3394,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3394),U_3395),U_3396)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3394),c_Groups_Osgn__class_Osgn(U_3394,U_3395)),c_Groups_Osgn__class_Osgn(U_3394,U_3396))
    | ~ class_Rings_Olinordered__idom(U_3394) ),
    inference(clausify,[status(thm)],[f_885_3]) ).

fof(f_886_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_886_2,plain,
    ! [U_3399,U_3398,U_3397] :
      ( c_Divides_Odiv__class_Omod(U_3397,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3397),U_3398),U_3399),U_3399) = c_Groups_Ozero__class_Ozero(U_3397)
      | ~ class_Divides_Osemiring__div(U_3397) ),
    inference(variable_rename,[status(thm)],[f_886_1]) ).

fof(f_886_3,plain,
    ! [U_3397,U_3398,U_3399] :
      ( c_Divides_Odiv__class_Omod(U_3397,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3397),U_3398),U_3399),U_3399) = c_Groups_Ozero__class_Ozero(U_3397)
      | ~ class_Divides_Osemiring__div(U_3397) ),
    inference(definitional_conversion,[status(esa)],[f_886_2]) ).

cnf(f_886_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3397,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3397),U_3398),U_3399),U_3399) = c_Groups_Ozero__class_Ozero(U_3397)
    | ~ class_Divides_Osemiring__div(U_3397) ),
    inference(clausify,[status(thm)],[f_886_3]) ).

fof(f_887_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_887_2,plain,
    ! [U_3402,U_3401,U_3400] :
      ( c_Divides_Odiv__class_Omod(U_3400,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3400),U_3401),U_3402),U_3401) = c_Groups_Ozero__class_Ozero(U_3400)
      | ~ class_Divides_Osemiring__div(U_3400) ),
    inference(variable_rename,[status(thm)],[f_887_1]) ).

fof(f_887_3,plain,
    ! [U_3400,U_3401,U_3402] :
      ( c_Divides_Odiv__class_Omod(U_3400,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3400),U_3401),U_3402),U_3401) = c_Groups_Ozero__class_Ozero(U_3400)
      | ~ class_Divides_Osemiring__div(U_3400) ),
    inference(definitional_conversion,[status(esa)],[f_887_2]) ).

cnf(f_887_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3400,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3400),U_3401),U_3402),U_3401) = c_Groups_Ozero__class_Ozero(U_3400)
    | ~ class_Divides_Osemiring__div(U_3400) ),
    inference(clausify,[status(thm)],[f_887_3]) ).

fof(f_888_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_888_2,plain,
    ! [U_3406,U_3405,U_3404,U_3403] :
      ( c_Divides_Odiv__class_Omod(U_3403,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3403),U_3404),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3403),U_3405),U_3406)),U_3405) = c_Divides_Odiv__class_Omod(U_3403,U_3404,U_3405)
      | ~ class_Divides_Osemiring__div(U_3403) ),
    inference(variable_rename,[status(thm)],[f_888_1]) ).

fof(f_888_3,plain,
    ! [U_3403,U_3404,U_3405,U_3406] :
      ( c_Divides_Odiv__class_Omod(U_3403,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3403),U_3404),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3403),U_3405),U_3406)),U_3405) = c_Divides_Odiv__class_Omod(U_3403,U_3404,U_3405)
      | ~ class_Divides_Osemiring__div(U_3403) ),
    inference(definitional_conversion,[status(esa)],[f_888_2]) ).

cnf(f_888_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3403,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3403),U_3404),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3403),U_3405),U_3406)),U_3405) = c_Divides_Odiv__class_Omod(U_3403,U_3404,U_3405)
    | ~ class_Divides_Osemiring__div(U_3403) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

fof(f_889_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_889_2,plain,
    ! [U_3410,U_3409,U_3408,U_3407] :
      ( c_Divides_Odiv__class_Omod(U_3407,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3407),U_3408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3407),U_3409),U_3410)),U_3410) = c_Divides_Odiv__class_Omod(U_3407,U_3408,U_3410)
      | ~ class_Divides_Osemiring__div(U_3407) ),
    inference(variable_rename,[status(thm)],[f_889_1]) ).

fof(f_889_3,plain,
    ! [U_3407,U_3408,U_3409,U_3410] :
      ( c_Divides_Odiv__class_Omod(U_3407,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3407),U_3408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3407),U_3409),U_3410)),U_3410) = c_Divides_Odiv__class_Omod(U_3407,U_3408,U_3410)
      | ~ class_Divides_Osemiring__div(U_3407) ),
    inference(definitional_conversion,[status(esa)],[f_889_2]) ).

cnf(f_889_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3407,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3407),U_3408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3407),U_3409),U_3410)),U_3410) = c_Divides_Odiv__class_Omod(U_3407,U_3408,U_3410)
    | ~ class_Divides_Osemiring__div(U_3407) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

fof(f_890_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_890_2,plain,
    ! [U_3412,U_3411] :
      ( c_Divides_Odiv__class_Omod(U_3411,U_3412,c_Groups_Oone__class_Oone(U_3411)) = c_Groups_Ozero__class_Ozero(U_3411)
      | ~ class_Divides_Osemiring__div(U_3411) ),
    inference(variable_rename,[status(thm)],[f_890_1]) ).

fof(f_890_3,plain,
    ! [U_3411,U_3412] :
      ( c_Divides_Odiv__class_Omod(U_3411,U_3412,c_Groups_Oone__class_Oone(U_3411)) = c_Groups_Ozero__class_Ozero(U_3411)
      | ~ class_Divides_Osemiring__div(U_3411) ),
    inference(definitional_conversion,[status(esa)],[f_890_2]) ).

cnf(f_890_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3411,U_3412,c_Groups_Oone__class_Oone(U_3411)) = c_Groups_Ozero__class_Ozero(U_3411)
    | ~ class_Divides_Osemiring__div(U_3411) ),
    inference(clausify,[status(thm)],[f_890_3]) ).

fof(f_891_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_891_2,plain,
    ! [U_3414,U_3413] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3413,U_3414)),U_3413))
      | ~ 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_891_1]) ).

fof(f_891_3,plain,
    ! [U_3413,U_3414] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3413,U_3414)),U_3413))
      | ~ 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_891_2]) ).

cnf(f_891_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3413,U_3414)),U_3413))
    | ~ 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_891_3]) ).

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)),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_892_2,plain,
    ! [U_3416,U_3415] :
      ( 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_3415,U_3416)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3416))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3415)) ),
    inference(variable_rename,[status(thm)],[f_892_1]) ).

fof(f_892_3,plain,
    ! [U_3415,U_3416] :
      ( 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_3415,U_3416)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3416))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3415)) ),
    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)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3415,U_3416)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3416))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3415)) ),
    inference(clausify,[status(thm)],[f_892_3]) ).

fof(f_893_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_893_2,plain,
    ! [U_3418,U_3417] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3417),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3418,U_3417)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3417),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_893_1]) ).

fof(f_893_3,plain,
    ! [U_3417,U_3418] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3417),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3418,U_3417)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3417),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_893_2]) ).

cnf(f_893_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3417),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3418,U_3417)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3417),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_893_3]) ).

fof(f_894_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_894_2,plain,
    ! [U_3420,U_3419] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3420,U_3419)),U_3419))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3419)) ),
    inference(variable_rename,[status(thm)],[f_894_1]) ).

fof(f_894_3,plain,
    ! [U_3419,U_3420] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3420,U_3419)),U_3419))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3419)) ),
    inference(definitional_conversion,[status(esa)],[f_894_2]) ).

cnf(f_894_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3420,U_3419)),U_3419))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3419)) ),
    inference(clausify,[status(thm)],[f_894_3]) ).

fof(f_895_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_895_2,plain,
    ! [U_3424,U_3423] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3423,U_3424) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_3422] : U_3423 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3424),U_3422) )
      & ( ? [U_3421] : U_3423 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3424),U_3421)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3423,U_3424) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_895_1]) ).

fof(f_895_3,plain,
    ( ! [U_3428,U_3426] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3426,U_3428) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_3422] : U_3426 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3428),U_3422) )
    & ! [U_3427,U_3425] :
        ( ? [U_3421] : U_3425 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3427),U_3421)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3425,U_3427) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_895_2]) ).

fof(f_895_4,plain,
    ( ! [U_3428,U_3426] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3426,U_3428) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_3422] : U_3426 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3428),U_3422) )
    & ! [U_3427,U_3425] :
        ( U_3425 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3427),sK63(U_3427,U_3425))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3425,U_3427) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_3421,sK63(U_3427,U_3425))],[f_895_3]) ).

fof(f_895_5,plain,
    ( ! [U_3422,U_3426,U_3428] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3426,U_3428) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_3426 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3428),U_3422) )
    & ! [U_3425,U_3427] :
        ( U_3425 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3427),sK63(U_3427,U_3425))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3425,U_3427) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_895_4]) ).

cnf(f_895_6,plain,
    ( U_3425 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3427),sK63(U_3427,U_3425))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3425,U_3427) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_895_5]) ).

cnf(f_895_7,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3426,U_3428) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_3426 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3428),U_3422) ),
    inference(clausify,[status(thm)],[f_895_5]) ).

fof(f_896_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_896_2,plain,
    ! [U_3430,U_3429] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3429,U_3430) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3429,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3430)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_896_1]) ).

fof(f_896_3,plain,
    ! [U_3430,U_3429] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3429,U_3430) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3429,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3430)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_896_2]) ).

cnf(f_896_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3429,U_3430) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3429,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3430)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_896_3]) ).

fof(f_897_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_897_2,plain,
    ! [U_3432,U_3431] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3431,U_3432) != 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_3431),U_3432) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_897_1]) ).

fof(f_897_3,plain,
    ! [U_3431,U_3432] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3431,U_3432) != 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_3431),U_3432) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_897_2]) ).

cnf(f_897_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3431,U_3432) != 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_3431),U_3432) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_897_3]) ).

fof(f_898_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_898_2,plain,
    ! [U_3434,U_3433] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3433,U_3434) = U_3433
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3434),U_3433))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3433),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_898_1]) ).

fof(f_898_3,plain,
    ! [U_3433,U_3434] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3433,U_3434) = U_3433
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3434),U_3433))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3433),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_898_2]) ).

cnf(f_898_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3433,U_3434) = U_3433
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3434),U_3433))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3433),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_898_3]) ).

fof(f_899_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_899_2,plain,
    ! [U_3436,U_3435] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3435),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3436,U_3435)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3436,U_3435)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3435),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_899_1]) ).

fof(f_899_3,plain,
    ( ! [U_3435,U_3436] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3435),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3436,U_3435)))
        | ~ sP254(U_3435,U_3436) )
    & ! [U_3435,U_3436] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3436,U_3435)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP254(U_3435,U_3436) )
    & ! [U_3435,U_3436] :
        ( sP254(U_3435,U_3436)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3435),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP254])],[f_899_2]) ).

cnf(f_899_4,plain,
    ( sP254(U_3435,U_3436)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3435),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_899_3]) ).

cnf(f_899_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3436,U_3435)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP254(U_3435,U_3436) ),
    inference(clausify,[status(thm)],[f_899_3]) ).

cnf(f_899_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3435),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3436,U_3435)))
    | ~ sP254(U_3435,U_3436) ),
    inference(clausify,[status(thm)],[f_899_3]) ).

fof(f_900_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_900_2,plain,
    ! [U_3438,U_3437] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3438,U_3437)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3437),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_900_1]) ).

fof(f_900_3,plain,
    ! [U_3438,U_3437] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3438,U_3437)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3437),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_900_2]) ).

cnf(f_900_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3438,U_3437)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3437),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_900_3]) ).

fof(f_901_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_901_2,plain,
    ! [U_3440,U_3439] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3439,U_3440) = U_3439
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3439),U_3440))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3439)) ),
    inference(variable_rename,[status(thm)],[f_901_1]) ).

fof(f_901_3,plain,
    ! [U_3439,U_3440] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3439,U_3440) = U_3439
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3439),U_3440))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3439)) ),
    inference(definitional_conversion,[status(esa)],[f_901_2]) ).

cnf(f_901_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3439,U_3440) = U_3439
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3439),U_3440))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3439)) ),
    inference(clausify,[status(thm)],[f_901_3]) ).

fof(f_902_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_902_2,plain,
    ! [U_3442,U_3441] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3442,U_3441)),U_3441))
        & 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_3442,U_3441))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3441)) ),
    inference(variable_rename,[status(thm)],[f_902_1]) ).

fof(f_902_3,plain,
    ( ! [U_3441,U_3442] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3442,U_3441)),U_3441))
        | ~ sP255(U_3441,U_3442) )
    & ! [U_3441,U_3442] :
        ( 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_3442,U_3441)))
        | ~ sP255(U_3441,U_3442) )
    & ! [U_3441,U_3442] :
        ( sP255(U_3441,U_3442)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3441)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP255])],[f_902_2]) ).

cnf(f_902_4,plain,
    ( sP255(U_3441,U_3442)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3441)) ),
    inference(clausify,[status(thm)],[f_902_3]) ).

cnf(f_902_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_3442,U_3441)))
    | ~ sP255(U_3441,U_3442) ),
    inference(clausify,[status(thm)],[f_902_3]) ).

cnf(f_902_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3442,U_3441)),U_3441))
    | ~ sP255(U_3441,U_3442) ),
    inference(clausify,[status(thm)],[f_902_3]) ).

fof(f_903_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_903_2,plain,
    ! [U_3444,U_3443] :
      ( 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_3444,U_3443)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3443)) ),
    inference(variable_rename,[status(thm)],[f_903_1]) ).

fof(f_903_3,plain,
    ! [U_3443,U_3444] :
      ( 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_3444,U_3443)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3443)) ),
    inference(definitional_conversion,[status(esa)],[f_903_2]) ).

cnf(f_903_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_3444,U_3443)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3443)) ),
    inference(clausify,[status(thm)],[f_903_3]) ).

fof(f_904_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_904_2,plain,
    ! [U_3446,U_3445] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3445),c_Groups_Osgn__class_Osgn(U_3445,U_3446)),c_Groups_Ozero__class_Ozero(U_3445)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3445),U_3446),c_Groups_Ozero__class_Ozero(U_3445))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3445),U_3446),c_Groups_Ozero__class_Ozero(U_3445)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3445),c_Groups_Osgn__class_Osgn(U_3445,U_3446)),c_Groups_Ozero__class_Ozero(U_3445))) ) )
      | ~ class_Rings_Olinordered__idom(U_3445) ),
    inference(variable_rename,[status(thm)],[f_904_1]) ).

fof(f_904_3,plain,
    ( ! [U_3445,U_3446] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3445),c_Groups_Osgn__class_Osgn(U_3445,U_3446)),c_Groups_Ozero__class_Ozero(U_3445)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3445),U_3446),c_Groups_Ozero__class_Ozero(U_3445)))
        | ~ sP256(U_3445,U_3446) )
    & ! [U_3445,U_3446] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3445),U_3446),c_Groups_Ozero__class_Ozero(U_3445)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3445),c_Groups_Osgn__class_Osgn(U_3445,U_3446)),c_Groups_Ozero__class_Ozero(U_3445)))
        | ~ sP256(U_3445,U_3446) )
    & ! [U_3445,U_3446] :
        ( sP256(U_3445,U_3446)
        | ~ class_Rings_Olinordered__idom(U_3445) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP256])],[f_904_2]) ).

cnf(f_904_4,plain,
    ( sP256(U_3445,U_3446)
    | ~ class_Rings_Olinordered__idom(U_3445) ),
    inference(clausify,[status(thm)],[f_904_3]) ).

cnf(f_904_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3445),U_3446),c_Groups_Ozero__class_Ozero(U_3445)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3445),c_Groups_Osgn__class_Osgn(U_3445,U_3446)),c_Groups_Ozero__class_Ozero(U_3445)))
    | ~ sP256(U_3445,U_3446) ),
    inference(clausify,[status(thm)],[f_904_3]) ).

cnf(f_904_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3445),c_Groups_Osgn__class_Osgn(U_3445,U_3446)),c_Groups_Ozero__class_Ozero(U_3445)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3445),U_3446),c_Groups_Ozero__class_Ozero(U_3445)))
    | ~ sP256(U_3445,U_3446) ),
    inference(clausify,[status(thm)],[f_904_3]) ).

fof(f_905_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_905_2,plain,
    ! [U_3448,U_3447] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3447),c_Groups_Ozero__class_Ozero(U_3447)),c_Groups_Osgn__class_Osgn(U_3447,U_3448)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3447),c_Groups_Ozero__class_Ozero(U_3447)),U_3448)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3447),c_Groups_Ozero__class_Ozero(U_3447)),U_3448))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3447),c_Groups_Ozero__class_Ozero(U_3447)),c_Groups_Osgn__class_Osgn(U_3447,U_3448))) ) )
      | ~ class_Rings_Olinordered__idom(U_3447) ),
    inference(variable_rename,[status(thm)],[f_905_1]) ).

fof(f_905_3,plain,
    ( ! [U_3447,U_3448] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3447),c_Groups_Ozero__class_Ozero(U_3447)),c_Groups_Osgn__class_Osgn(U_3447,U_3448)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3447),c_Groups_Ozero__class_Ozero(U_3447)),U_3448))
        | ~ sP257(U_3447,U_3448) )
    & ! [U_3447,U_3448] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3447),c_Groups_Ozero__class_Ozero(U_3447)),U_3448))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3447),c_Groups_Ozero__class_Ozero(U_3447)),c_Groups_Osgn__class_Osgn(U_3447,U_3448)))
        | ~ sP257(U_3447,U_3448) )
    & ! [U_3447,U_3448] :
        ( sP257(U_3447,U_3448)
        | ~ class_Rings_Olinordered__idom(U_3447) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP257])],[f_905_2]) ).

cnf(f_905_4,plain,
    ( sP257(U_3447,U_3448)
    | ~ class_Rings_Olinordered__idom(U_3447) ),
    inference(clausify,[status(thm)],[f_905_3]) ).

cnf(f_905_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3447),c_Groups_Ozero__class_Ozero(U_3447)),U_3448))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3447),c_Groups_Ozero__class_Ozero(U_3447)),c_Groups_Osgn__class_Osgn(U_3447,U_3448)))
    | ~ sP257(U_3447,U_3448) ),
    inference(clausify,[status(thm)],[f_905_3]) ).

cnf(f_905_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3447),c_Groups_Ozero__class_Ozero(U_3447)),c_Groups_Osgn__class_Osgn(U_3447,U_3448)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3447),c_Groups_Ozero__class_Ozero(U_3447)),U_3448))
    | ~ sP257(U_3447,U_3448) ),
    inference(clausify,[status(thm)],[f_905_3]) ).

fof(f_906_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_906_2,plain,
    ! [U_3450,U_3449] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3449,U_3450) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3449),U_3450)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3449),U_3450)),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_3449)) ),
    inference(variable_rename,[status(thm)],[f_906_1]) ).

fof(f_906_3,plain,
    ! [U_3449,U_3450] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3449,U_3450) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3449),U_3450)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3449),U_3450)),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_3449)) ),
    inference(definitional_conversion,[status(esa)],[f_906_2]) ).

cnf(f_906_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3449,U_3450) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3449),U_3450)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3449),U_3450)),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_3449)) ),
    inference(clausify,[status(thm)],[f_906_3]) ).

fof(f_907_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_907_2,plain,
    ! [U_3452,U_3451] :
      ( c_Groups_Osgn__class_Osgn(U_3451,U_3452) = c_Groups_Oone__class_Oone(U_3451)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3451),c_Groups_Ozero__class_Ozero(U_3451)),U_3452))
      | ~ class_Rings_Olinordered__idom(U_3451) ),
    inference(variable_rename,[status(thm)],[f_907_1]) ).

fof(f_907_3,plain,
    ! [U_3451,U_3452] :
      ( c_Groups_Osgn__class_Osgn(U_3451,U_3452) = c_Groups_Oone__class_Oone(U_3451)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3451),c_Groups_Ozero__class_Ozero(U_3451)),U_3452))
      | ~ class_Rings_Olinordered__idom(U_3451) ),
    inference(definitional_conversion,[status(esa)],[f_907_2]) ).

cnf(f_907_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_3451,U_3452) = c_Groups_Oone__class_Oone(U_3451)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3451),c_Groups_Ozero__class_Ozero(U_3451)),U_3452))
    | ~ class_Rings_Olinordered__idom(U_3451) ),
    inference(clausify,[status(thm)],[f_907_3]) ).

fof(f_908_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_908_2,plain,
    ! [U_3454,U_3453] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_3453,U_3454) = c_Groups_Oone__class_Oone(U_3453)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),c_Groups_Ozero__class_Ozero(U_3453)),U_3454)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),c_Groups_Ozero__class_Ozero(U_3453)),U_3454))
          | c_Groups_Osgn__class_Osgn(U_3453,U_3454) != c_Groups_Oone__class_Oone(U_3453) ) )
      | ~ class_Rings_Olinordered__idom(U_3453) ),
    inference(variable_rename,[status(thm)],[f_908_1]) ).

fof(f_908_3,plain,
    ( ! [U_3453,U_3454] :
        ( c_Groups_Osgn__class_Osgn(U_3453,U_3454) = c_Groups_Oone__class_Oone(U_3453)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),c_Groups_Ozero__class_Ozero(U_3453)),U_3454))
        | ~ sP258(U_3453,U_3454) )
    & ! [U_3453,U_3454] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),c_Groups_Ozero__class_Ozero(U_3453)),U_3454))
        | c_Groups_Osgn__class_Osgn(U_3453,U_3454) != c_Groups_Oone__class_Oone(U_3453)
        | ~ sP258(U_3453,U_3454) )
    & ! [U_3453,U_3454] :
        ( sP258(U_3453,U_3454)
        | ~ class_Rings_Olinordered__idom(U_3453) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP258])],[f_908_2]) ).

cnf(f_908_4,plain,
    ( sP258(U_3453,U_3454)
    | ~ class_Rings_Olinordered__idom(U_3453) ),
    inference(clausify,[status(thm)],[f_908_3]) ).

cnf(f_908_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),c_Groups_Ozero__class_Ozero(U_3453)),U_3454))
    | c_Groups_Osgn__class_Osgn(U_3453,U_3454) != c_Groups_Oone__class_Oone(U_3453)
    | ~ sP258(U_3453,U_3454) ),
    inference(clausify,[status(thm)],[f_908_3]) ).

cnf(f_908_6,plain,
    ( c_Groups_Osgn__class_Osgn(U_3453,U_3454) = c_Groups_Oone__class_Oone(U_3453)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3453),c_Groups_Ozero__class_Ozero(U_3453)),U_3454))
    | ~ sP258(U_3453,U_3454) ),
    inference(clausify,[status(thm)],[f_908_3]) ).

fof(f_909_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_909_2,plain,
    ! [U_3465,U_3464,U_3463] :
      ( ( hBOOL(hAPP(U_3463,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3464,U_3465)))
        | ( ? [U_3462,U_3461] :
              ( ~ hBOOL(hAPP(U_3463,U_3461))
              & U_3464 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3465),U_3462)),U_3461)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3461),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3465),U_3461)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3465),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_3460,U_3459] :
              ( ~ hBOOL(hAPP(U_3463,U_3459))
              & U_3464 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3465),U_3460)),U_3459)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3459),U_3465))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3459)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3465)) )
        | ( ~ hBOOL(hAPP(U_3463,U_3464))
          & U_3465 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [U_3458,U_3457] :
                ( hBOOL(hAPP(U_3463,U_3457))
                | U_3464 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3465),U_3458)),U_3457)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3457),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3465),U_3457)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3465),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3456,U_3455] :
                ( hBOOL(hAPP(U_3463,U_3455))
                | U_3464 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3465),U_3456)),U_3455)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3455),U_3465))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3455)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3465)) )
          & ( hBOOL(hAPP(U_3463,U_3464))
            | U_3465 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3463,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3464,U_3465))) ) ),
    inference(variable_rename,[status(thm)],[f_909_1]) ).

fof(f_909_3,plain,
    ( ! [U_3471,U_3469,U_3467] :
        ( hBOOL(hAPP(U_3467,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3469,U_3471)))
        | ( ? [U_3462,U_3461] :
              ( ~ hBOOL(hAPP(U_3467,U_3461))
              & U_3469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3471),U_3462)),U_3461)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3461),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3471),U_3461)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3471),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_3460,U_3459] :
              ( ~ hBOOL(hAPP(U_3467,U_3459))
              & U_3469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3471),U_3460)),U_3459)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3459),U_3471))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3459)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3471)) )
        | ( ~ hBOOL(hAPP(U_3467,U_3469))
          & U_3471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3470,U_3468,U_3466] :
        ( ( ( ! [U_3458,U_3457] :
                ( hBOOL(hAPP(U_3466,U_3457))
                | U_3468 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3470),U_3458)),U_3457)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3457),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3470),U_3457)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3470),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3456,U_3455] :
                ( hBOOL(hAPP(U_3466,U_3455))
                | U_3468 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3470),U_3456)),U_3455)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3455),U_3470))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3455)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3470)) )
          & ( hBOOL(hAPP(U_3466,U_3468))
            | U_3470 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3466,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3468,U_3470))) ) ),
    inference(miniscope,[status(thm)],[f_909_2]) ).

fof(f_909_4,plain,
    ( ! [U_3471,U_3469,U_3467] :
        ( hBOOL(hAPP(U_3467,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3469,U_3471)))
        | ( ? [U_3462,U_3461] :
              ( ~ hBOOL(hAPP(U_3467,U_3461))
              & U_3469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3471),U_3462)),U_3461)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3461),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3471),U_3461)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3471),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_3459] :
              ( ~ hBOOL(hAPP(U_3467,U_3459))
              & U_3469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3471),sK64(U_3471,U_3469,U_3467))),U_3459)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3459),U_3471))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3459)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3471)) )
        | ( ~ hBOOL(hAPP(U_3467,U_3469))
          & U_3471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3470,U_3468,U_3466] :
        ( ( ( ! [U_3458,U_3457] :
                ( hBOOL(hAPP(U_3466,U_3457))
                | U_3468 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3470),U_3458)),U_3457)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3457),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3470),U_3457)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3470),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3456,U_3455] :
                ( hBOOL(hAPP(U_3466,U_3455))
                | U_3468 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3470),U_3456)),U_3455)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3455),U_3470))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3455)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3470)) )
          & ( hBOOL(hAPP(U_3466,U_3468))
            | U_3470 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3466,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3468,U_3470))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_3460,sK64(U_3471,U_3469,U_3467))],[f_909_3]) ).

fof(f_909_5,plain,
    ( ! [U_3471,U_3469,U_3467] :
        ( hBOOL(hAPP(U_3467,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3469,U_3471)))
        | ( ? [U_3462,U_3461] :
              ( ~ hBOOL(hAPP(U_3467,U_3461))
              & U_3469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3471),U_3462)),U_3461)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3461),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3471),U_3461)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3471),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3467,sK65(U_3471,U_3469,U_3467)))
          & U_3469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3471),sK64(U_3471,U_3469,U_3467))),sK65(U_3471,U_3469,U_3467))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK65(U_3471,U_3469,U_3467)),U_3471))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK65(U_3471,U_3469,U_3467)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3471)) )
        | ( ~ hBOOL(hAPP(U_3467,U_3469))
          & U_3471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3470,U_3468,U_3466] :
        ( ( ( ! [U_3458,U_3457] :
                ( hBOOL(hAPP(U_3466,U_3457))
                | U_3468 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3470),U_3458)),U_3457)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3457),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3470),U_3457)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3470),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3456,U_3455] :
                ( hBOOL(hAPP(U_3466,U_3455))
                | U_3468 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3470),U_3456)),U_3455)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3455),U_3470))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3455)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3470)) )
          & ( hBOOL(hAPP(U_3466,U_3468))
            | U_3470 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3466,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3468,U_3470))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_3459,sK65(U_3471,U_3469,U_3467))],[f_909_4]) ).

fof(f_909_6,plain,
    ( ! [U_3471,U_3469,U_3467] :
        ( hBOOL(hAPP(U_3467,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3469,U_3471)))
        | ( ? [U_3461] :
              ( ~ hBOOL(hAPP(U_3467,U_3461))
              & U_3469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3471),sK66(U_3471,U_3469,U_3467))),U_3461)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3461),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3471),U_3461)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3471),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3467,sK65(U_3471,U_3469,U_3467)))
          & U_3469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3471),sK64(U_3471,U_3469,U_3467))),sK65(U_3471,U_3469,U_3467))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK65(U_3471,U_3469,U_3467)),U_3471))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK65(U_3471,U_3469,U_3467)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3471)) )
        | ( ~ hBOOL(hAPP(U_3467,U_3469))
          & U_3471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3470,U_3468,U_3466] :
        ( ( ( ! [U_3458,U_3457] :
                ( hBOOL(hAPP(U_3466,U_3457))
                | U_3468 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3470),U_3458)),U_3457)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3457),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3470),U_3457)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3470),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3456,U_3455] :
                ( hBOOL(hAPP(U_3466,U_3455))
                | U_3468 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3470),U_3456)),U_3455)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3455),U_3470))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3455)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3470)) )
          & ( hBOOL(hAPP(U_3466,U_3468))
            | U_3470 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3466,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3468,U_3470))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_3462,sK66(U_3471,U_3469,U_3467))],[f_909_5]) ).

fof(f_909_7,plain,
    ( ! [U_3471,U_3469,U_3467] :
        ( hBOOL(hAPP(U_3467,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3469,U_3471)))
        | ( ~ hBOOL(hAPP(U_3467,sK67(U_3471,U_3469,U_3467)))
          & U_3469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3471),sK66(U_3471,U_3469,U_3467))),sK67(U_3471,U_3469,U_3467))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK67(U_3471,U_3469,U_3467)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3471),sK67(U_3471,U_3469,U_3467)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3471),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3467,sK65(U_3471,U_3469,U_3467)))
          & U_3469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3471),sK64(U_3471,U_3469,U_3467))),sK65(U_3471,U_3469,U_3467))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK65(U_3471,U_3469,U_3467)),U_3471))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK65(U_3471,U_3469,U_3467)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3471)) )
        | ( ~ hBOOL(hAPP(U_3467,U_3469))
          & U_3471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3470,U_3468,U_3466] :
        ( ( ( ! [U_3458,U_3457] :
                ( hBOOL(hAPP(U_3466,U_3457))
                | U_3468 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3470),U_3458)),U_3457)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3457),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3470),U_3457)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3470),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3456,U_3455] :
                ( hBOOL(hAPP(U_3466,U_3455))
                | U_3468 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3470),U_3456)),U_3455)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3455),U_3470))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3455)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3470)) )
          & ( hBOOL(hAPP(U_3466,U_3468))
            | U_3470 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3466,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3468,U_3470))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_3461,sK67(U_3471,U_3469,U_3467))],[f_909_6]) ).

fof(f_909_8,plain,
    ( ! [U_3467,U_3471,U_3469] :
        ( ~ hBOOL(hAPP(U_3467,sK67(U_3471,U_3469,U_3467)))
        | ~ sP262(U_3467,U_3471,U_3469) )
    & ! [U_3467,U_3471,U_3469] :
        ( U_3469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3471),sK66(U_3471,U_3469,U_3467))),sK67(U_3471,U_3469,U_3467))
        | ~ sP262(U_3467,U_3471,U_3469) )
    & ! [U_3467,U_3471,U_3469] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK67(U_3471,U_3469,U_3467)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP262(U_3467,U_3471,U_3469) )
    & ! [U_3467,U_3471,U_3469] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3471),sK67(U_3471,U_3469,U_3467)))
        | ~ sP262(U_3467,U_3471,U_3469) )
    & ! [U_3467,U_3471,U_3469] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3471),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP262(U_3467,U_3471,U_3469) )
    & ! [U_3467,U_3471,U_3469] :
        ( ~ hBOOL(hAPP(U_3467,sK65(U_3471,U_3469,U_3467)))
        | ~ sP261(U_3467,U_3471,U_3469) )
    & ! [U_3467,U_3471,U_3469] :
        ( U_3469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3471),sK64(U_3471,U_3469,U_3467))),sK65(U_3471,U_3469,U_3467))
        | ~ sP261(U_3467,U_3471,U_3469) )
    & ! [U_3467,U_3471,U_3469] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK65(U_3471,U_3469,U_3467)),U_3471))
        | ~ sP261(U_3467,U_3471,U_3469) )
    & ! [U_3467,U_3471,U_3469] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK65(U_3471,U_3469,U_3467)))
        | ~ sP261(U_3467,U_3471,U_3469) )
    & ! [U_3467,U_3471,U_3469] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3471))
        | ~ sP261(U_3467,U_3471,U_3469) )
    & ! [U_3467,U_3471,U_3469] :
        ( ~ hBOOL(hAPP(U_3467,U_3469))
        | ~ sP260(U_3467,U_3471,U_3469) )
    & ! [U_3467,U_3471,U_3469] :
        ( U_3471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP260(U_3467,U_3471,U_3469) )
    & ! [U_3456,U_3455,U_3457,U_3458,U_3466,U_3470,U_3468] :
        ( hBOOL(hAPP(U_3466,U_3457))
        | U_3468 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3470),U_3458)),U_3457)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3457),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3470),U_3457))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3470),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP259(U_3456,U_3455,U_3457,U_3458,U_3466,U_3470,U_3468) )
    & ! [U_3456,U_3455,U_3457,U_3458,U_3466,U_3470,U_3468] :
        ( hBOOL(hAPP(U_3466,U_3455))
        | U_3468 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3470),U_3456)),U_3455)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3455),U_3470))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3455))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3470))
        | ~ sP259(U_3456,U_3455,U_3457,U_3458,U_3466,U_3470,U_3468) )
    & ! [U_3456,U_3455,U_3457,U_3458,U_3466,U_3470,U_3468] :
        ( hBOOL(hAPP(U_3466,U_3468))
        | U_3470 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP259(U_3456,U_3455,U_3457,U_3458,U_3466,U_3470,U_3468) )
    & ! [U_3467,U_3471,U_3469] :
        ( hBOOL(hAPP(U_3467,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3469,U_3471)))
        | sP262(U_3467,U_3471,U_3469)
        | sP261(U_3467,U_3471,U_3469)
        | sP260(U_3467,U_3471,U_3469) )
    & ! [U_3456,U_3455,U_3457,U_3458,U_3466,U_3470,U_3468] :
        ( sP259(U_3456,U_3455,U_3457,U_3458,U_3466,U_3470,U_3468)
        | ~ hBOOL(hAPP(U_3466,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3468,U_3470))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP259,sP260,sP261,sP262])],[f_909_7]) ).

cnf(f_909_9,plain,
    ( sP259(U_3456,U_3455,U_3457,U_3458,U_3466,U_3470,U_3468)
    | ~ hBOOL(hAPP(U_3466,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3468,U_3470))) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_10,plain,
    ( hBOOL(hAPP(U_3467,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3469,U_3471)))
    | sP262(U_3467,U_3471,U_3469)
    | sP261(U_3467,U_3471,U_3469)
    | sP260(U_3467,U_3471,U_3469) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_11,plain,
    ( hBOOL(hAPP(U_3466,U_3468))
    | U_3470 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP259(U_3456,U_3455,U_3457,U_3458,U_3466,U_3470,U_3468) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_12,plain,
    ( hBOOL(hAPP(U_3466,U_3455))
    | U_3468 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3470),U_3456)),U_3455)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3455),U_3470))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3455))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3470))
    | ~ sP259(U_3456,U_3455,U_3457,U_3458,U_3466,U_3470,U_3468) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_13,plain,
    ( hBOOL(hAPP(U_3466,U_3457))
    | U_3468 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3470),U_3458)),U_3457)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3457),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3470),U_3457))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3470),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP259(U_3456,U_3455,U_3457,U_3458,U_3466,U_3470,U_3468) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_14,plain,
    ( U_3471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP260(U_3467,U_3471,U_3469) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_15,plain,
    ( ~ hBOOL(hAPP(U_3467,U_3469))
    | ~ sP260(U_3467,U_3471,U_3469) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_16,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3471))
    | ~ sP261(U_3467,U_3471,U_3469) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_17,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK65(U_3471,U_3469,U_3467)))
    | ~ sP261(U_3467,U_3471,U_3469) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_18,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK65(U_3471,U_3469,U_3467)),U_3471))
    | ~ sP261(U_3467,U_3471,U_3469) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_19,plain,
    ( U_3469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3471),sK64(U_3471,U_3469,U_3467))),sK65(U_3471,U_3469,U_3467))
    | ~ sP261(U_3467,U_3471,U_3469) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_20,plain,
    ( ~ hBOOL(hAPP(U_3467,sK65(U_3471,U_3469,U_3467)))
    | ~ sP261(U_3467,U_3471,U_3469) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_21,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3471),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP262(U_3467,U_3471,U_3469) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_22,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3471),sK67(U_3471,U_3469,U_3467)))
    | ~ sP262(U_3467,U_3471,U_3469) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_23,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK67(U_3471,U_3469,U_3467)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP262(U_3467,U_3471,U_3469) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_24,plain,
    ( U_3469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3471),sK66(U_3471,U_3469,U_3467))),sK67(U_3471,U_3469,U_3467))
    | ~ sP262(U_3467,U_3471,U_3469) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

cnf(f_909_25,plain,
    ( ~ hBOOL(hAPP(U_3467,sK67(U_3471,U_3469,U_3467)))
    | ~ sP262(U_3467,U_3471,U_3469) ),
    inference(clausify,[status(thm)],[f_909_8]) ).

fof(f_910_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_910_2,plain,
    ! [U_3475,U_3474,U_3473,U_3472] :
      ( 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_3474),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3475,U_3472))),U_3473)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3473),U_3474))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3473))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3472)) ),
    inference(variable_rename,[status(thm)],[f_910_1]) ).

fof(f_910_3,plain,
    ! [U_3474,U_3475,U_3473,U_3472] :
      ( 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_3474),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3475,U_3472))),U_3473)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3473),U_3474))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3473))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3472)) ),
    inference(definitional_conversion,[status(esa)],[f_910_2]) ).

cnf(f_910_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_3474),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3475,U_3472))),U_3473)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3473),U_3474))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3473))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3472)) ),
    inference(clausify,[status(thm)],[f_910_3]) ).

fof(f_911_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_911_2,plain,
    ! [U_3479,U_3478,U_3477,U_3476] :
      ( 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_3478),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3479,U_3476))),U_3477)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3478),U_3476)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3477),U_3478))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3477))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3476)) ),
    inference(variable_rename,[status(thm)],[f_911_1]) ).

fof(f_911_3,plain,
    ! [U_3477,U_3476,U_3478,U_3479] :
      ( 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_3478),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3479,U_3476))),U_3477)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3478),U_3476)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3477),U_3478))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3477))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3476)) ),
    inference(definitional_conversion,[status(esa)],[f_911_2]) ).

cnf(f_911_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_3478),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3479,U_3476))),U_3477)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3478),U_3476)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3477),U_3478))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3477))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3476)) ),
    inference(clausify,[status(thm)],[f_911_3]) ).

fof(f_912_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_912_2,plain,
    ! [U_3481,U_3480] :
      ( ( c_SMT_Oz3mod(U_3481,U_3480) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3481,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3480))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3480)) )
      & ( c_SMT_Oz3mod(U_3481,U_3480) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3481,U_3480)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3480)) ) ),
    inference(variable_rename,[status(thm)],[f_912_1]) ).

fof(f_912_3,plain,
    ( ! [U_3485,U_3483] :
        ( c_SMT_Oz3mod(U_3485,U_3483) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3485,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3483))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3483)) )
    & ! [U_3484,U_3482] :
        ( c_SMT_Oz3mod(U_3484,U_3482) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3484,U_3482)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3482)) ) ),
    inference(miniscope,[status(thm)],[f_912_2]) ).

fof(f_912_4,plain,
    ( ! [U_3483,U_3485] :
        ( c_SMT_Oz3mod(U_3485,U_3483) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3485,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3483))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3483)) )
    & ! [U_3484,U_3482] :
        ( c_SMT_Oz3mod(U_3484,U_3482) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3484,U_3482)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3482)) ) ),
    inference(definitional_conversion,[status(esa)],[f_912_3]) ).

cnf(f_912_5,plain,
    ( c_SMT_Oz3mod(U_3484,U_3482) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3484,U_3482)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3482)) ),
    inference(clausify,[status(thm)],[f_912_4]) ).

cnf(f_912_6,plain,
    ( c_SMT_Oz3mod(U_3485,U_3483) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3485,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3483))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3483)) ),
    inference(clausify,[status(thm)],[f_912_4]) ).

fof(f_913_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_913_2,plain,
    ! [U_3492,U_3491,U_3490] :
      ( ( ( hBOOL(hAPP(hAPP(U_3491,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3492),U_3490)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3492,U_3490)))
          | ? [U_3489,U_3488] :
              ( ~ hBOOL(hAPP(hAPP(U_3491,U_3489),U_3488))
              & U_3492 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3490),U_3489)),U_3488)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3488),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3490),U_3488)) ) )
        & ( ! [U_3487,U_3486] :
              ( hBOOL(hAPP(hAPP(U_3491,U_3487),U_3486))
              | U_3492 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3490),U_3487)),U_3486)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3486),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3490),U_3486)) )
          | ~ hBOOL(hAPP(hAPP(U_3491,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3492),U_3490)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3492,U_3490))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3490),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_913_1]) ).

fof(f_913_3,plain,
    ! [U_3492,U_3491,U_3490] :
      ( ( ( hBOOL(hAPP(hAPP(U_3491,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3492),U_3490)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3492,U_3490)))
          | ? [U_3488] :
              ( ~ hBOOL(hAPP(hAPP(U_3491,sK68(U_3492,U_3491,U_3490)),U_3488))
              & U_3492 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3490),sK68(U_3492,U_3491,U_3490))),U_3488)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3488),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3490),U_3488)) ) )
        & ( ! [U_3487,U_3486] :
              ( hBOOL(hAPP(hAPP(U_3491,U_3487),U_3486))
              | U_3492 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3490),U_3487)),U_3486)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3486),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3490),U_3486)) )
          | ~ hBOOL(hAPP(hAPP(U_3491,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3492),U_3490)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3492,U_3490))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3490),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_3489,sK68(U_3492,U_3491,U_3490))],[f_913_2]) ).

fof(f_913_4,plain,
    ! [U_3492,U_3491,U_3490] :
      ( ( ( hBOOL(hAPP(hAPP(U_3491,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3492),U_3490)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3492,U_3490)))
          | ( ~ hBOOL(hAPP(hAPP(U_3491,sK68(U_3492,U_3491,U_3490)),sK69(U_3492,U_3491,U_3490)))
            & U_3492 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3490),sK68(U_3492,U_3491,U_3490))),sK69(U_3492,U_3491,U_3490))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK69(U_3492,U_3491,U_3490)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3490),sK69(U_3492,U_3491,U_3490))) ) )
        & ( ! [U_3487,U_3486] :
              ( hBOOL(hAPP(hAPP(U_3491,U_3487),U_3486))
              | U_3492 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3490),U_3487)),U_3486)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3486),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3490),U_3486)) )
          | ~ hBOOL(hAPP(hAPP(U_3491,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3492),U_3490)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3492,U_3490))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3490),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_3488,sK69(U_3492,U_3491,U_3490))],[f_913_3]) ).

fof(f_913_5,plain,
    ( ! [U_3490,U_3491,U_3492] :
        ( ~ hBOOL(hAPP(hAPP(U_3491,sK68(U_3492,U_3491,U_3490)),sK69(U_3492,U_3491,U_3490)))
        | ~ sP263(U_3490,U_3491,U_3492) )
    & ! [U_3490,U_3491,U_3492] :
        ( U_3492 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3490),sK68(U_3492,U_3491,U_3490))),sK69(U_3492,U_3491,U_3490))
        | ~ sP263(U_3490,U_3491,U_3492) )
    & ! [U_3490,U_3491,U_3492] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK69(U_3492,U_3491,U_3490)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP263(U_3490,U_3491,U_3492) )
    & ! [U_3490,U_3491,U_3492] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3490),sK69(U_3492,U_3491,U_3490)))
        | ~ sP263(U_3490,U_3491,U_3492) )
    & ! [U_3490,U_3487,U_3491,U_3492,U_3486] :
        ( hBOOL(hAPP(hAPP(U_3491,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3492),U_3490)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3492,U_3490)))
        | sP263(U_3490,U_3491,U_3492)
        | ~ sP264(U_3490,U_3487,U_3491,U_3492,U_3486) )
    & ! [U_3490,U_3487,U_3491,U_3492,U_3486] :
        ( hBOOL(hAPP(hAPP(U_3491,U_3487),U_3486))
        | U_3492 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3490),U_3487)),U_3486)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3486),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3490),U_3486))
        | ~ hBOOL(hAPP(hAPP(U_3491,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3492),U_3490)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3492,U_3490)))
        | ~ sP264(U_3490,U_3487,U_3491,U_3492,U_3486) )
    & ! [U_3490,U_3487,U_3491,U_3492,U_3486] :
        ( sP264(U_3490,U_3487,U_3491,U_3492,U_3486)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3490),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP263,sP264])],[f_913_4]) ).

cnf(f_913_6,plain,
    ( sP264(U_3490,U_3487,U_3491,U_3492,U_3486)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3490),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_913_5]) ).

cnf(f_913_7,plain,
    ( hBOOL(hAPP(hAPP(U_3491,U_3487),U_3486))
    | U_3492 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3490),U_3487)),U_3486)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3486),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3490),U_3486))
    | ~ hBOOL(hAPP(hAPP(U_3491,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3492),U_3490)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3492,U_3490)))
    | ~ sP264(U_3490,U_3487,U_3491,U_3492,U_3486) ),
    inference(clausify,[status(thm)],[f_913_5]) ).

cnf(f_913_8,plain,
    ( hBOOL(hAPP(hAPP(U_3491,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3492),U_3490)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3492,U_3490)))
    | sP263(U_3490,U_3491,U_3492)
    | ~ sP264(U_3490,U_3487,U_3491,U_3492,U_3486) ),
    inference(clausify,[status(thm)],[f_913_5]) ).

cnf(f_913_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3490),sK69(U_3492,U_3491,U_3490)))
    | ~ sP263(U_3490,U_3491,U_3492) ),
    inference(clausify,[status(thm)],[f_913_5]) ).

cnf(f_913_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK69(U_3492,U_3491,U_3490)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP263(U_3490,U_3491,U_3492) ),
    inference(clausify,[status(thm)],[f_913_5]) ).

cnf(f_913_11,plain,
    ( U_3492 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3490),sK68(U_3492,U_3491,U_3490))),sK69(U_3492,U_3491,U_3490))
    | ~ sP263(U_3490,U_3491,U_3492) ),
    inference(clausify,[status(thm)],[f_913_5]) ).

cnf(f_913_12,plain,
    ( ~ hBOOL(hAPP(hAPP(U_3491,sK68(U_3492,U_3491,U_3490)),sK69(U_3492,U_3491,U_3490)))
    | ~ sP263(U_3490,U_3491,U_3492) ),
    inference(clausify,[status(thm)],[f_913_5]) ).

fof(f_914_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_914_2,plain,
    ! [U_3499,U_3498,U_3497] :
      ( ( ( hBOOL(hAPP(hAPP(U_3498,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3499),U_3497)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3499,U_3497)))
          | ? [U_3496,U_3495] :
              ( ~ hBOOL(hAPP(hAPP(U_3498,U_3496),U_3495))
              & U_3499 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3497),U_3496)),U_3495)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3495),U_3497))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3495)) ) )
        & ( ! [U_3494,U_3493] :
              ( hBOOL(hAPP(hAPP(U_3498,U_3494),U_3493))
              | U_3499 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3497),U_3494)),U_3493)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3493),U_3497))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3493)) )
          | ~ hBOOL(hAPP(hAPP(U_3498,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3499),U_3497)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3499,U_3497))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3497)) ),
    inference(variable_rename,[status(thm)],[f_914_1]) ).

fof(f_914_3,plain,
    ! [U_3499,U_3498,U_3497] :
      ( ( ( hBOOL(hAPP(hAPP(U_3498,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3499),U_3497)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3499,U_3497)))
          | ? [U_3495] :
              ( ~ hBOOL(hAPP(hAPP(U_3498,sK70(U_3499,U_3498,U_3497)),U_3495))
              & U_3499 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3497),sK70(U_3499,U_3498,U_3497))),U_3495)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3495),U_3497))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3495)) ) )
        & ( ! [U_3494,U_3493] :
              ( hBOOL(hAPP(hAPP(U_3498,U_3494),U_3493))
              | U_3499 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3497),U_3494)),U_3493)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3493),U_3497))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3493)) )
          | ~ hBOOL(hAPP(hAPP(U_3498,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3499),U_3497)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3499,U_3497))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3497)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_3496,sK70(U_3499,U_3498,U_3497))],[f_914_2]) ).

fof(f_914_4,plain,
    ! [U_3499,U_3498,U_3497] :
      ( ( ( hBOOL(hAPP(hAPP(U_3498,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3499),U_3497)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3499,U_3497)))
          | ( ~ hBOOL(hAPP(hAPP(U_3498,sK70(U_3499,U_3498,U_3497)),sK71(U_3499,U_3498,U_3497)))
            & U_3499 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3497),sK70(U_3499,U_3498,U_3497))),sK71(U_3499,U_3498,U_3497))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK71(U_3499,U_3498,U_3497)),U_3497))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK71(U_3499,U_3498,U_3497))) ) )
        & ( ! [U_3494,U_3493] :
              ( hBOOL(hAPP(hAPP(U_3498,U_3494),U_3493))
              | U_3499 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3497),U_3494)),U_3493)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3493),U_3497))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3493)) )
          | ~ hBOOL(hAPP(hAPP(U_3498,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3499),U_3497)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3499,U_3497))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3497)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_3495,sK71(U_3499,U_3498,U_3497))],[f_914_3]) ).

fof(f_914_5,plain,
    ( ! [U_3498,U_3499,U_3497] :
        ( ~ hBOOL(hAPP(hAPP(U_3498,sK70(U_3499,U_3498,U_3497)),sK71(U_3499,U_3498,U_3497)))
        | ~ sP265(U_3498,U_3499,U_3497) )
    & ! [U_3498,U_3499,U_3497] :
        ( U_3499 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3497),sK70(U_3499,U_3498,U_3497))),sK71(U_3499,U_3498,U_3497))
        | ~ sP265(U_3498,U_3499,U_3497) )
    & ! [U_3498,U_3499,U_3497] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK71(U_3499,U_3498,U_3497)),U_3497))
        | ~ sP265(U_3498,U_3499,U_3497) )
    & ! [U_3498,U_3499,U_3497] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK71(U_3499,U_3498,U_3497)))
        | ~ sP265(U_3498,U_3499,U_3497) )
    & ! [U_3494,U_3498,U_3499,U_3493,U_3497] :
        ( hBOOL(hAPP(hAPP(U_3498,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3499),U_3497)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3499,U_3497)))
        | sP265(U_3498,U_3499,U_3497)
        | ~ sP266(U_3494,U_3498,U_3499,U_3493,U_3497) )
    & ! [U_3494,U_3498,U_3499,U_3493,U_3497] :
        ( hBOOL(hAPP(hAPP(U_3498,U_3494),U_3493))
        | U_3499 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3497),U_3494)),U_3493)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3493),U_3497))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3493))
        | ~ hBOOL(hAPP(hAPP(U_3498,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3499),U_3497)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3499,U_3497)))
        | ~ sP266(U_3494,U_3498,U_3499,U_3493,U_3497) )
    & ! [U_3494,U_3498,U_3499,U_3493,U_3497] :
        ( sP266(U_3494,U_3498,U_3499,U_3493,U_3497)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3497)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP265,sP266])],[f_914_4]) ).

cnf(f_914_6,plain,
    ( sP266(U_3494,U_3498,U_3499,U_3493,U_3497)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3497)) ),
    inference(clausify,[status(thm)],[f_914_5]) ).

cnf(f_914_7,plain,
    ( hBOOL(hAPP(hAPP(U_3498,U_3494),U_3493))
    | U_3499 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3497),U_3494)),U_3493)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3493),U_3497))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3493))
    | ~ hBOOL(hAPP(hAPP(U_3498,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3499),U_3497)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3499,U_3497)))
    | ~ sP266(U_3494,U_3498,U_3499,U_3493,U_3497) ),
    inference(clausify,[status(thm)],[f_914_5]) ).

cnf(f_914_8,plain,
    ( hBOOL(hAPP(hAPP(U_3498,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3499),U_3497)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3499,U_3497)))
    | sP265(U_3498,U_3499,U_3497)
    | ~ sP266(U_3494,U_3498,U_3499,U_3493,U_3497) ),
    inference(clausify,[status(thm)],[f_914_5]) ).

cnf(f_914_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK71(U_3499,U_3498,U_3497)))
    | ~ sP265(U_3498,U_3499,U_3497) ),
    inference(clausify,[status(thm)],[f_914_5]) ).

cnf(f_914_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK71(U_3499,U_3498,U_3497)),U_3497))
    | ~ sP265(U_3498,U_3499,U_3497) ),
    inference(clausify,[status(thm)],[f_914_5]) ).

cnf(f_914_11,plain,
    ( U_3499 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3497),sK70(U_3499,U_3498,U_3497))),sK71(U_3499,U_3498,U_3497))
    | ~ sP265(U_3498,U_3499,U_3497) ),
    inference(clausify,[status(thm)],[f_914_5]) ).

cnf(f_914_12,plain,
    ( ~ hBOOL(hAPP(hAPP(U_3498,sK70(U_3499,U_3498,U_3497)),sK71(U_3499,U_3498,U_3497)))
    | ~ sP265(U_3498,U_3499,U_3497) ),
    inference(clausify,[status(thm)],[f_914_5]) ).

fof(f_915_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_915_2,plain,
    ! [U_3502,U_3501,U_3500] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3501,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3502),U_3500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3502),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3501),U_3502),U_3500))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3501,U_3502))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3500)) ),
    inference(variable_rename,[status(thm)],[f_915_1]) ).

fof(f_915_3,plain,
    ! [U_3501,U_3500,U_3502] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3501,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3502),U_3500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3502),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3501),U_3502),U_3500))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3501,U_3502))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3500)) ),
    inference(definitional_conversion,[status(esa)],[f_915_2]) ).

cnf(f_915_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3501,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3502),U_3500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3502),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3501),U_3502),U_3500))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3501,U_3502))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3500)) ),
    inference(clausify,[status(thm)],[f_915_3]) ).

fof(f_916_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_916_2,plain,
    ! [U_3504,U_3503] :
      ( 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_3503,U_3504)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3504))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3503)) ),
    inference(variable_rename,[status(thm)],[f_916_1]) ).

fof(f_916_3,plain,
    ! [U_3503,U_3504] :
      ( 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_3503,U_3504)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3504))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3503)) ),
    inference(definitional_conversion,[status(esa)],[f_916_2]) ).

cnf(f_916_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_3503,U_3504)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3504))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3503)) ),
    inference(clausify,[status(thm)],[f_916_3]) ).

fof(f_917_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_917_2,plain,
    ! [U_3515,U_3514,U_3513] :
      ( ( hBOOL(hAPP(U_3513,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3514),U_3515)))
        | ( ? [U_3512] :
              ( ~ hBOOL(hAPP(U_3513,U_3512))
              & ? [U_3511] :
                  ( U_3514 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3515),U_3512)),U_3511)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3511),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3515),U_3511)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3515),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_3510] :
              ( ~ hBOOL(hAPP(U_3513,U_3510))
              & ? [U_3509] :
                  ( U_3514 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3515),U_3510)),U_3509)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3509),U_3515))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3509)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3515)) )
        | ( ~ hBOOL(hAPP(U_3513,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3515 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [U_3508] :
                ( hBOOL(hAPP(U_3513,U_3508))
                | ! [U_3507] :
                    ( U_3514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3515),U_3508)),U_3507)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3507),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3515),U_3507)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3515),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3506] :
                ( hBOOL(hAPP(U_3513,U_3506))
                | ! [U_3505] :
                    ( U_3514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3515),U_3506)),U_3505)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3505),U_3515))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3505)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3515)) )
          & ( hBOOL(hAPP(U_3513,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3515 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3513,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3514),U_3515))) ) ),
    inference(variable_rename,[status(thm)],[f_917_1]) ).

fof(f_917_3,plain,
    ( ! [U_3521,U_3519,U_3517] :
        ( hBOOL(hAPP(U_3517,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3519),U_3521)))
        | ( ? [U_3512] :
              ( ~ hBOOL(hAPP(U_3517,U_3512))
              & ? [U_3511] :
                  ( U_3519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3521),U_3512)),U_3511)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3511),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3521),U_3511)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3521),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_3510] :
              ( ~ hBOOL(hAPP(U_3517,U_3510))
              & ? [U_3509] :
                  ( U_3519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3521),U_3510)),U_3509)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3509),U_3521))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3509)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3521)) )
        | ( ~ hBOOL(hAPP(U_3517,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3521 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3520,U_3518,U_3516] :
        ( ( ( ! [U_3508] :
                ( hBOOL(hAPP(U_3516,U_3508))
                | ! [U_3507] :
                    ( U_3518 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3520),U_3508)),U_3507)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3507),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3520),U_3507)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3520),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3506] :
                ( hBOOL(hAPP(U_3516,U_3506))
                | ! [U_3505] :
                    ( U_3518 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3520),U_3506)),U_3505)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3505),U_3520))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3505)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3520)) )
          & ( hBOOL(hAPP(U_3516,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3520 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3516,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3518),U_3520))) ) ),
    inference(miniscope,[status(thm)],[f_917_2]) ).

fof(f_917_4,plain,
    ( ! [U_3521,U_3519,U_3517] :
        ( hBOOL(hAPP(U_3517,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3519),U_3521)))
        | ( ? [U_3512] :
              ( ~ hBOOL(hAPP(U_3517,U_3512))
              & ? [U_3511] :
                  ( U_3519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3521),U_3512)),U_3511)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3511),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3521),U_3511)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3521),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3517,sK72(U_3521,U_3519,U_3517)))
          & ? [U_3509] :
              ( U_3519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3521),sK72(U_3521,U_3519,U_3517))),U_3509)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3509),U_3521))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3509)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3521)) )
        | ( ~ hBOOL(hAPP(U_3517,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3521 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3520,U_3518,U_3516] :
        ( ( ( ! [U_3508] :
                ( hBOOL(hAPP(U_3516,U_3508))
                | ! [U_3507] :
                    ( U_3518 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3520),U_3508)),U_3507)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3507),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3520),U_3507)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3520),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3506] :
                ( hBOOL(hAPP(U_3516,U_3506))
                | ! [U_3505] :
                    ( U_3518 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3520),U_3506)),U_3505)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3505),U_3520))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3505)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3520)) )
          & ( hBOOL(hAPP(U_3516,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3520 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3516,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3518),U_3520))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_3510,sK72(U_3521,U_3519,U_3517))],[f_917_3]) ).

fof(f_917_5,plain,
    ( ! [U_3521,U_3519,U_3517] :
        ( hBOOL(hAPP(U_3517,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3519),U_3521)))
        | ( ? [U_3512] :
              ( ~ hBOOL(hAPP(U_3517,U_3512))
              & ? [U_3511] :
                  ( U_3519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3521),U_3512)),U_3511)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3511),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3521),U_3511)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3521),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3517,sK72(U_3521,U_3519,U_3517)))
          & U_3519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3521),sK72(U_3521,U_3519,U_3517))),sK73(U_3521,U_3519,U_3517))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK73(U_3521,U_3519,U_3517)),U_3521))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK73(U_3521,U_3519,U_3517)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3521)) )
        | ( ~ hBOOL(hAPP(U_3517,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3521 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3520,U_3518,U_3516] :
        ( ( ( ! [U_3508] :
                ( hBOOL(hAPP(U_3516,U_3508))
                | ! [U_3507] :
                    ( U_3518 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3520),U_3508)),U_3507)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3507),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3520),U_3507)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3520),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3506] :
                ( hBOOL(hAPP(U_3516,U_3506))
                | ! [U_3505] :
                    ( U_3518 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3520),U_3506)),U_3505)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3505),U_3520))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3505)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3520)) )
          & ( hBOOL(hAPP(U_3516,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3520 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3516,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3518),U_3520))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_3509,sK73(U_3521,U_3519,U_3517))],[f_917_4]) ).

fof(f_917_6,plain,
    ( ! [U_3521,U_3519,U_3517] :
        ( hBOOL(hAPP(U_3517,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3519),U_3521)))
        | ( ~ hBOOL(hAPP(U_3517,sK74(U_3521,U_3519,U_3517)))
          & ? [U_3511] :
              ( U_3519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3521),sK74(U_3521,U_3519,U_3517))),U_3511)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3511),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3521),U_3511)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3521),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3517,sK72(U_3521,U_3519,U_3517)))
          & U_3519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3521),sK72(U_3521,U_3519,U_3517))),sK73(U_3521,U_3519,U_3517))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK73(U_3521,U_3519,U_3517)),U_3521))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK73(U_3521,U_3519,U_3517)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3521)) )
        | ( ~ hBOOL(hAPP(U_3517,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3521 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3520,U_3518,U_3516] :
        ( ( ( ! [U_3508] :
                ( hBOOL(hAPP(U_3516,U_3508))
                | ! [U_3507] :
                    ( U_3518 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3520),U_3508)),U_3507)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3507),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3520),U_3507)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3520),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3506] :
                ( hBOOL(hAPP(U_3516,U_3506))
                | ! [U_3505] :
                    ( U_3518 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3520),U_3506)),U_3505)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3505),U_3520))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3505)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3520)) )
          & ( hBOOL(hAPP(U_3516,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3520 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3516,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3518),U_3520))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_3512,sK74(U_3521,U_3519,U_3517))],[f_917_5]) ).

fof(f_917_7,plain,
    ( ! [U_3521,U_3519,U_3517] :
        ( hBOOL(hAPP(U_3517,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3519),U_3521)))
        | ( ~ hBOOL(hAPP(U_3517,sK74(U_3521,U_3519,U_3517)))
          & U_3519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3521),sK74(U_3521,U_3519,U_3517))),sK75(U_3521,U_3519,U_3517))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK75(U_3521,U_3519,U_3517)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3521),sK75(U_3521,U_3519,U_3517)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3521),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3517,sK72(U_3521,U_3519,U_3517)))
          & U_3519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3521),sK72(U_3521,U_3519,U_3517))),sK73(U_3521,U_3519,U_3517))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK73(U_3521,U_3519,U_3517)),U_3521))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK73(U_3521,U_3519,U_3517)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3521)) )
        | ( ~ hBOOL(hAPP(U_3517,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3521 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3520,U_3518,U_3516] :
        ( ( ( ! [U_3508] :
                ( hBOOL(hAPP(U_3516,U_3508))
                | ! [U_3507] :
                    ( U_3518 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3520),U_3508)),U_3507)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3507),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3520),U_3507)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3520),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3506] :
                ( hBOOL(hAPP(U_3516,U_3506))
                | ! [U_3505] :
                    ( U_3518 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3520),U_3506)),U_3505)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3505),U_3520))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3505)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3520)) )
          & ( hBOOL(hAPP(U_3516,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3520 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3516,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3518),U_3520))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_3511,sK75(U_3521,U_3519,U_3517))],[f_917_6]) ).

fof(f_917_8,plain,
    ( ! [U_3519,U_3517,U_3521] :
        ( ~ hBOOL(hAPP(U_3517,sK74(U_3521,U_3519,U_3517)))
        | ~ sP270(U_3519,U_3517,U_3521) )
    & ! [U_3519,U_3517,U_3521] :
        ( U_3519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3521),sK74(U_3521,U_3519,U_3517))),sK75(U_3521,U_3519,U_3517))
        | ~ sP270(U_3519,U_3517,U_3521) )
    & ! [U_3519,U_3517,U_3521] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK75(U_3521,U_3519,U_3517)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP270(U_3519,U_3517,U_3521) )
    & ! [U_3519,U_3517,U_3521] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3521),sK75(U_3521,U_3519,U_3517)))
        | ~ sP270(U_3519,U_3517,U_3521) )
    & ! [U_3519,U_3517,U_3521] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3521),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP270(U_3519,U_3517,U_3521) )
    & ! [U_3519,U_3517,U_3521] :
        ( ~ hBOOL(hAPP(U_3517,sK72(U_3521,U_3519,U_3517)))
        | ~ sP269(U_3519,U_3517,U_3521) )
    & ! [U_3519,U_3517,U_3521] :
        ( U_3519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3521),sK72(U_3521,U_3519,U_3517))),sK73(U_3521,U_3519,U_3517))
        | ~ sP269(U_3519,U_3517,U_3521) )
    & ! [U_3519,U_3517,U_3521] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK73(U_3521,U_3519,U_3517)),U_3521))
        | ~ sP269(U_3519,U_3517,U_3521) )
    & ! [U_3519,U_3517,U_3521] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK73(U_3521,U_3519,U_3517)))
        | ~ sP269(U_3519,U_3517,U_3521) )
    & ! [U_3519,U_3517,U_3521] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3521))
        | ~ sP269(U_3519,U_3517,U_3521) )
    & ! [U_3517,U_3521] :
        ( ~ hBOOL(hAPP(U_3517,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP268(U_3517,U_3521) )
    & ! [U_3517,U_3521] :
        ( U_3521 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP268(U_3517,U_3521) )
    & ! [U_3507,U_3505,U_3506,U_3508,U_3516,U_3518,U_3520] :
        ( hBOOL(hAPP(U_3516,U_3508))
        | U_3518 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3520),U_3508)),U_3507)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3507),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3520),U_3507))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3520),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP267(U_3507,U_3505,U_3506,U_3508,U_3516,U_3518,U_3520) )
    & ! [U_3507,U_3505,U_3506,U_3508,U_3516,U_3518,U_3520] :
        ( hBOOL(hAPP(U_3516,U_3506))
        | U_3518 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3520),U_3506)),U_3505)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3505),U_3520))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3505))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3520))
        | ~ sP267(U_3507,U_3505,U_3506,U_3508,U_3516,U_3518,U_3520) )
    & ! [U_3507,U_3505,U_3506,U_3508,U_3516,U_3518,U_3520] :
        ( hBOOL(hAPP(U_3516,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_3520 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP267(U_3507,U_3505,U_3506,U_3508,U_3516,U_3518,U_3520) )
    & ! [U_3519,U_3517,U_3521] :
        ( hBOOL(hAPP(U_3517,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3519),U_3521)))
        | sP270(U_3519,U_3517,U_3521)
        | sP269(U_3519,U_3517,U_3521)
        | sP268(U_3517,U_3521) )
    & ! [U_3507,U_3505,U_3506,U_3508,U_3516,U_3518,U_3520] :
        ( sP267(U_3507,U_3505,U_3506,U_3508,U_3516,U_3518,U_3520)
        | ~ hBOOL(hAPP(U_3516,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3518),U_3520))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP267,sP268,sP269,sP270])],[f_917_7]) ).

cnf(f_917_9,plain,
    ( sP267(U_3507,U_3505,U_3506,U_3508,U_3516,U_3518,U_3520)
    | ~ hBOOL(hAPP(U_3516,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3518),U_3520))) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_10,plain,
    ( hBOOL(hAPP(U_3517,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3519),U_3521)))
    | sP270(U_3519,U_3517,U_3521)
    | sP269(U_3519,U_3517,U_3521)
    | sP268(U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_11,plain,
    ( hBOOL(hAPP(U_3516,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_3520 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP267(U_3507,U_3505,U_3506,U_3508,U_3516,U_3518,U_3520) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_12,plain,
    ( hBOOL(hAPP(U_3516,U_3506))
    | U_3518 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3520),U_3506)),U_3505)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3505),U_3520))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3505))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3520))
    | ~ sP267(U_3507,U_3505,U_3506,U_3508,U_3516,U_3518,U_3520) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_13,plain,
    ( hBOOL(hAPP(U_3516,U_3508))
    | U_3518 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3520),U_3508)),U_3507)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3507),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3520),U_3507))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3520),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP267(U_3507,U_3505,U_3506,U_3508,U_3516,U_3518,U_3520) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_14,plain,
    ( U_3521 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP268(U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_15,plain,
    ( ~ hBOOL(hAPP(U_3517,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP268(U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_16,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3521))
    | ~ sP269(U_3519,U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_17,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK73(U_3521,U_3519,U_3517)))
    | ~ sP269(U_3519,U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_18,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK73(U_3521,U_3519,U_3517)),U_3521))
    | ~ sP269(U_3519,U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_19,plain,
    ( U_3519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3521),sK72(U_3521,U_3519,U_3517))),sK73(U_3521,U_3519,U_3517))
    | ~ sP269(U_3519,U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_20,plain,
    ( ~ hBOOL(hAPP(U_3517,sK72(U_3521,U_3519,U_3517)))
    | ~ sP269(U_3519,U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_21,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3521),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP270(U_3519,U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_22,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3521),sK75(U_3521,U_3519,U_3517)))
    | ~ sP270(U_3519,U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_23,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK75(U_3521,U_3519,U_3517)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP270(U_3519,U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_24,plain,
    ( U_3519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3521),sK74(U_3521,U_3519,U_3517))),sK75(U_3521,U_3519,U_3517))
    | ~ sP270(U_3519,U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

cnf(f_917_25,plain,
    ( ~ hBOOL(hAPP(U_3517,sK74(U_3521,U_3519,U_3517)))
    | ~ sP270(U_3519,U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_917_8]) ).

fof(f_918_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_918_2,plain,
    ! [U_3525,U_3524,U_3523,U_3522] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3522),U_3523) = U_3524
      | U_3523 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3525),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3523),U_3525)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3523)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3525),U_3523))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3525)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3523)) )
      | U_3522 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3523),U_3524)),U_3525) ),
    inference(variable_rename,[status(thm)],[f_918_1]) ).

fof(f_918_3,plain,
    ( ! [U_3525,U_3523] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3525),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3523),U_3525))
        | ~ sP272(U_3525,U_3523) )
    & ! [U_3525,U_3523] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3523))
        | ~ sP272(U_3525,U_3523) )
    & ! [U_3525,U_3523] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3525),U_3523))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3525))
        | ~ sP271(U_3525,U_3523) )
    & ! [U_3525,U_3523] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3523))
        | ~ sP271(U_3525,U_3523) )
    & ! [U_3525,U_3523,U_3524,U_3522] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3522),U_3523) = U_3524
        | U_3523 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | sP272(U_3525,U_3523)
        | sP271(U_3525,U_3523)
        | U_3522 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3523),U_3524)),U_3525) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP271,sP272])],[f_918_2]) ).

cnf(f_918_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3522),U_3523) = U_3524
    | U_3523 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | sP272(U_3525,U_3523)
    | sP271(U_3525,U_3523)
    | U_3522 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3523),U_3524)),U_3525) ),
    inference(clausify,[status(thm)],[f_918_3]) ).

cnf(f_918_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3523))
    | ~ sP271(U_3525,U_3523) ),
    inference(clausify,[status(thm)],[f_918_3]) ).

cnf(f_918_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3525),U_3523))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3525))
    | ~ sP271(U_3525,U_3523) ),
    inference(clausify,[status(thm)],[f_918_3]) ).

cnf(f_918_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3523))
    | ~ sP272(U_3525,U_3523) ),
    inference(clausify,[status(thm)],[f_918_3]) ).

cnf(f_918_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3525),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3523),U_3525))
    | ~ sP272(U_3525,U_3523) ),
    inference(clausify,[status(thm)],[f_918_3]) ).

fof(f_919_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_919_2,plain,
    ! [U_3530,U_3529,U_3528] :
      ( ( hBOOL(hAPP(U_3528,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3529),U_3530)))
        | ( ! [U_3527] :
              ( ~ hBOOL(hAPP(U_3528,U_3527))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3529),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3530),hAPP(c_Nat_OSuc,U_3527))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3530),U_3527)),U_3529)) )
          & ( ~ hBOOL(hAPP(U_3528,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3530 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
      & ( ? [U_3526] :
            ( hBOOL(hAPP(U_3528,U_3526))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3529),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3530),hAPP(c_Nat_OSuc,U_3526))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3530),U_3526)),U_3529)) )
        | ( hBOOL(hAPP(U_3528,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3530 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_3528,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3529),U_3530))) ) ),
    inference(variable_rename,[status(thm)],[f_919_1]) ).

fof(f_919_3,plain,
    ( ! [U_3536,U_3534,U_3532] :
        ( hBOOL(hAPP(U_3532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3534),U_3536)))
        | ( ! [U_3527] :
              ( ~ hBOOL(hAPP(U_3532,U_3527))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3534),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3536),hAPP(c_Nat_OSuc,U_3527))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3536),U_3527)),U_3534)) )
          & ( ~ hBOOL(hAPP(U_3532,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3536 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
    & ! [U_3535,U_3533,U_3531] :
        ( ? [U_3526] :
            ( hBOOL(hAPP(U_3531,U_3526))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3533),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3535),hAPP(c_Nat_OSuc,U_3526))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3535),U_3526)),U_3533)) )
        | ( hBOOL(hAPP(U_3531,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3535 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_3531,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3533),U_3535))) ) ),
    inference(miniscope,[status(thm)],[f_919_2]) ).

fof(f_919_4,plain,
    ( ! [U_3536,U_3534,U_3532] :
        ( hBOOL(hAPP(U_3532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3534),U_3536)))
        | ( ! [U_3527] :
              ( ~ hBOOL(hAPP(U_3532,U_3527))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3534),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3536),hAPP(c_Nat_OSuc,U_3527))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3536),U_3527)),U_3534)) )
          & ( ~ hBOOL(hAPP(U_3532,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3536 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
    & ! [U_3535,U_3533,U_3531] :
        ( ( hBOOL(hAPP(U_3531,sK76(U_3535,U_3533,U_3531)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3533),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3535),hAPP(c_Nat_OSuc,sK76(U_3535,U_3533,U_3531)))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3535),sK76(U_3535,U_3533,U_3531))),U_3533)) )
        | ( hBOOL(hAPP(U_3531,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3535 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_3531,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3533),U_3535))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_3526,sK76(U_3535,U_3533,U_3531))],[f_919_3]) ).

fof(f_919_5,plain,
    ( ! [U_3527,U_3532,U_3534,U_3536] :
        ( ~ hBOOL(hAPP(U_3532,U_3527))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3534),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3536),hAPP(c_Nat_OSuc,U_3527))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3536),U_3527)),U_3534))
        | ~ sP275(U_3527,U_3532,U_3534,U_3536) )
    & ! [U_3527,U_3532,U_3534,U_3536] :
        ( ~ hBOOL(hAPP(U_3532,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_3536 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP275(U_3527,U_3532,U_3534,U_3536) )
    & ! [U_3535,U_3533,U_3531] :
        ( hBOOL(hAPP(U_3531,sK76(U_3535,U_3533,U_3531)))
        | ~ sP274(U_3535,U_3533,U_3531) )
    & ! [U_3535,U_3533,U_3531] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3533),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3535),hAPP(c_Nat_OSuc,sK76(U_3535,U_3533,U_3531)))))
        | ~ sP274(U_3535,U_3533,U_3531) )
    & ! [U_3535,U_3533,U_3531] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3535),sK76(U_3535,U_3533,U_3531))),U_3533))
        | ~ sP274(U_3535,U_3533,U_3531) )
    & ! [U_3535,U_3531] :
        ( hBOOL(hAPP(U_3531,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP273(U_3535,U_3531) )
    & ! [U_3535,U_3531] :
        ( U_3535 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP273(U_3535,U_3531) )
    & ! [U_3527,U_3532,U_3534,U_3536] :
        ( hBOOL(hAPP(U_3532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3534),U_3536)))
        | sP275(U_3527,U_3532,U_3534,U_3536) )
    & ! [U_3535,U_3533,U_3531] :
        ( sP274(U_3535,U_3533,U_3531)
        | sP273(U_3535,U_3531)
        | ~ hBOOL(hAPP(U_3531,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3533),U_3535))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP273,sP274,sP275])],[f_919_4]) ).

cnf(f_919_6,plain,
    ( sP274(U_3535,U_3533,U_3531)
    | sP273(U_3535,U_3531)
    | ~ hBOOL(hAPP(U_3531,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3533),U_3535))) ),
    inference(clausify,[status(thm)],[f_919_5]) ).

cnf(f_919_7,plain,
    ( hBOOL(hAPP(U_3532,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3534),U_3536)))
    | sP275(U_3527,U_3532,U_3534,U_3536) ),
    inference(clausify,[status(thm)],[f_919_5]) ).

cnf(f_919_8,plain,
    ( U_3535 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP273(U_3535,U_3531) ),
    inference(clausify,[status(thm)],[f_919_5]) ).

cnf(f_919_9,plain,
    ( hBOOL(hAPP(U_3531,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP273(U_3535,U_3531) ),
    inference(clausify,[status(thm)],[f_919_5]) ).

cnf(f_919_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_3535),sK76(U_3535,U_3533,U_3531))),U_3533))
    | ~ sP274(U_3535,U_3533,U_3531) ),
    inference(clausify,[status(thm)],[f_919_5]) ).

cnf(f_919_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3533),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3535),hAPP(c_Nat_OSuc,sK76(U_3535,U_3533,U_3531)))))
    | ~ sP274(U_3535,U_3533,U_3531) ),
    inference(clausify,[status(thm)],[f_919_5]) ).

cnf(f_919_12,plain,
    ( hBOOL(hAPP(U_3531,sK76(U_3535,U_3533,U_3531)))
    | ~ sP274(U_3535,U_3533,U_3531) ),
    inference(clausify,[status(thm)],[f_919_5]) ).

cnf(f_919_13,plain,
    ( ~ hBOOL(hAPP(U_3532,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_3536 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP275(U_3527,U_3532,U_3534,U_3536) ),
    inference(clausify,[status(thm)],[f_919_5]) ).

cnf(f_919_14,plain,
    ( ~ hBOOL(hAPP(U_3532,U_3527))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3534),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3536),hAPP(c_Nat_OSuc,U_3527))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3536),U_3527)),U_3534))
    | ~ sP275(U_3527,U_3532,U_3534,U_3536) ),
    inference(clausify,[status(thm)],[f_919_5]) ).

fof(f_920_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_920_2,plain,
    ! [U_3539,U_3538,U_3537] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3537),U_3538)),U_3539) = 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_3537),U_3539)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3538),U_3539))),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_3537,U_3539)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3538,U_3539))),U_3539)),
    inference(variable_rename,[status(thm)],[f_920_1]) ).

fof(f_920_3,plain,
    ! [U_3537,U_3539,U_3538] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3537),U_3538)),U_3539) = 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_3537),U_3539)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3538),U_3539))),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_3537,U_3539)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3538,U_3539))),U_3539)),
    inference(definitional_conversion,[status(esa)],[f_920_2]) ).

cnf(f_920_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3537),U_3538)),U_3539) = 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_3537),U_3539)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3538),U_3539))),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_3537,U_3539)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3538,U_3539))),U_3539)),
    inference(clausify,[status(thm)],[f_920_3]) ).

fof(f_921_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_921_2,plain,
    ! [U_3541,U_3540] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3540)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3541)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3540),U_3541)),
    inference(variable_rename,[status(thm)],[f_921_1]) ).

fof(f_921_3,plain,
    ! [U_3541,U_3540] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3540)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3541)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3540),U_3541)),
    inference(definitional_conversion,[status(esa)],[f_921_2]) ).

cnf(f_921_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3540)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3541)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3540),U_3541)),
    inference(clausify,[status(thm)],[f_921_3]) ).

fof(f_922_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_922_2,plain,
    ! [U_3543,U_3542] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3542),U_3543)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3542)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3543)),
    inference(variable_rename,[status(thm)],[f_922_1]) ).

fof(f_922_3,plain,
    ! [U_3542,U_3543] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3542),U_3543)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3542)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3543)),
    inference(definitional_conversion,[status(esa)],[f_922_2]) ).

cnf(f_922_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3542),U_3543)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3542)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3543)),
    inference(clausify,[status(thm)],[f_922_3]) ).

fof(f_923_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_923_2,plain,
    ! [U_3546,U_3545,U_3544] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3544,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3545),U_3546)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3545),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3544),U_3545),U_3546))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3544,U_3545)),
    inference(variable_rename,[status(thm)],[f_923_1]) ).

fof(f_923_3,plain,
    ! [U_3544,U_3545,U_3546] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3544,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3545),U_3546)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3545),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3544),U_3545),U_3546))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3544,U_3545)),
    inference(definitional_conversion,[status(esa)],[f_923_2]) ).

cnf(f_923_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3544,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3545),U_3546)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3545),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3544),U_3545),U_3546))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3544,U_3545)),
    inference(clausify,[status(thm)],[f_923_3]) ).

fof(f_924_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_924_2,plain,
    ! [U_3549,U_3548,U_3547] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3547),U_3548)),U_3549) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3547),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3548),U_3549))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3547),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3548,U_3549))),U_3549)),
    inference(variable_rename,[status(thm)],[f_924_1]) ).

fof(f_924_3,plain,
    ! [U_3547,U_3548,U_3549] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3547),U_3548)),U_3549) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3547),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3548),U_3549))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3547),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3548,U_3549))),U_3549)),
    inference(definitional_conversion,[status(esa)],[f_924_2]) ).

cnf(f_924_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3547),U_3548)),U_3549) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3547),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3548),U_3549))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3547),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3548,U_3549))),U_3549)),
    inference(clausify,[status(thm)],[f_924_3]) ).

fof(f_925_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_925_2,plain,
    ! [U_3552,U_3551,U_3550] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3550),U_3552)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3551),U_3552)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3550),U_3551)) ),
    inference(variable_rename,[status(thm)],[f_925_1]) ).

fof(f_925_3,plain,
    ! [U_3550,U_3551,U_3552] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3550),U_3552)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3551),U_3552)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3550),U_3551)) ),
    inference(definitional_conversion,[status(esa)],[f_925_2]) ).

cnf(f_925_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_3550),U_3552)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3551),U_3552)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3550),U_3551)) ),
    inference(clausify,[status(thm)],[f_925_3]) ).

fof(f_926_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_926_2,plain,
    ! [U_3554,U_3553] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3553),U_3554)),U_3553)),
    inference(variable_rename,[status(thm)],[f_926_1]) ).

fof(f_926_3,plain,
    ! [U_3553,U_3554] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3553),U_3554)),U_3553)),
    inference(definitional_conversion,[status(esa)],[f_926_2]) ).

cnf(f_926_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_3553),U_3554)),U_3553)),
    inference(clausify,[status(thm)],[f_926_3]) ).

fof(f_927_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_927_2,plain,
    ! [U_3555] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3555) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_927_1]) ).

fof(f_927_3,plain,
    ! [U_3555] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3555) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_927_2]) ).

cnf(f_927_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3555) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_927_3]) ).

fof(f_928_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_928_2,plain,
    ! [U_3557,U_3556] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3556),U_3557) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3556,U_3557)),U_3557),
    inference(variable_rename,[status(thm)],[f_928_1]) ).

fof(f_928_3,plain,
    ! [U_3556,U_3557] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3556),U_3557) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3556,U_3557)),U_3557),
    inference(definitional_conversion,[status(esa)],[f_928_2]) ).

cnf(f_928_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3556),U_3557) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3556,U_3557)),U_3557),
    inference(clausify,[status(thm)],[f_928_3]) ).

fof(f_929_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_929_2,plain,
    ! [U_3560,U_3559,U_3558] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3558),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3559),U_3560)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3558),U_3559)),U_3560),
    inference(variable_rename,[status(thm)],[f_929_1]) ).

fof(f_929_3,plain,
    ! [U_3558,U_3559,U_3560] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3558),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3559),U_3560)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3558),U_3559)),U_3560),
    inference(definitional_conversion,[status(esa)],[f_929_2]) ).

cnf(f_929_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3558),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3559),U_3560)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3558),U_3559)),U_3560),
    inference(clausify,[status(thm)],[f_929_3]) ).

fof(f_930_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_930_2,plain,
    ! [U_3562,U_3561] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3561,U_3562) = U_3561
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3561),U_3562)) ),
    inference(variable_rename,[status(thm)],[f_930_1]) ).

fof(f_930_3,plain,
    ! [U_3561,U_3562] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3561,U_3562) = U_3561
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3561),U_3562)) ),
    inference(definitional_conversion,[status(esa)],[f_930_2]) ).

cnf(f_930_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3561,U_3562) = U_3561
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3561),U_3562)) ),
    inference(clausify,[status(thm)],[f_930_3]) ).

fof(f_931_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_931_2,plain,
    ! [U_3564,U_3563] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3563,U_3564)),U_3563)),
    inference(variable_rename,[status(thm)],[f_931_1]) ).

fof(f_931_3,plain,
    ! [U_3563,U_3564] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3563,U_3564)),U_3563)),
    inference(definitional_conversion,[status(esa)],[f_931_2]) ).

cnf(f_931_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3563,U_3564)),U_3563)),
    inference(clausify,[status(thm)],[f_931_3]) ).

fof(f_932_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_932_2,plain,
    ! [U_3567,U_3566,U_3565] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3565,U_3566)),U_3567) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3565),U_3567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3566),U_3567)),
    inference(variable_rename,[status(thm)],[f_932_1]) ).

fof(f_932_3,plain,
    ! [U_3565,U_3566,U_3567] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3565,U_3566)),U_3567) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3565),U_3567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3566),U_3567)),
    inference(definitional_conversion,[status(esa)],[f_932_2]) ).

cnf(f_932_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3565,U_3566)),U_3567) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3565),U_3567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3566),U_3567)),
    inference(clausify,[status(thm)],[f_932_3]) ).

fof(f_933_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_933_2,plain,
    ! [U_3570,U_3569,U_3568] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3568),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3569,U_3570)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3568),U_3569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3568),U_3570)),
    inference(variable_rename,[status(thm)],[f_933_1]) ).

fof(f_933_3,plain,
    ! [U_3568,U_3569,U_3570] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3568),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3569,U_3570)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3568),U_3569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3568),U_3570)),
    inference(definitional_conversion,[status(esa)],[f_933_2]) ).

cnf(f_933_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3568),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3569,U_3570)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3568),U_3569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3568),U_3570)),
    inference(clausify,[status(thm)],[f_933_3]) ).

fof(f_934_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_934_2,plain,
    ! [U_3572,U_3571] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3571),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3572)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3571)),U_3572),
    inference(variable_rename,[status(thm)],[f_934_1]) ).

fof(f_934_3,plain,
    ! [U_3571,U_3572] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3571),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3572)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3571)),U_3572),
    inference(definitional_conversion,[status(esa)],[f_934_2]) ).

cnf(f_934_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3571),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3572)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3571)),U_3572),
    inference(clausify,[status(thm)],[f_934_3]) ).

fof(f_935_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_935_2,plain,
    ! [U_3574,U_3573] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3573)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3574)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3573),U_3574),
    inference(variable_rename,[status(thm)],[f_935_1]) ).

fof(f_935_3,plain,
    ! [U_3573,U_3574] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3573)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3574)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3573),U_3574),
    inference(definitional_conversion,[status(esa)],[f_935_2]) ).

cnf(f_935_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3573)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3574)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3573),U_3574),
    inference(clausify,[status(thm)],[f_935_3]) ).

fof(f_936_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_936_2,plain,
    ! [U_3576,U_3575] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3575),c_Groups_Ozero__class_Ozero(U_3575)),U_3576) = c_Groups_Ozero__class_Ozero(U_3575)
      | ~ class_Divides_Osemiring__div(U_3575) ),
    inference(variable_rename,[status(thm)],[f_936_1]) ).

fof(f_936_3,plain,
    ! [U_3575,U_3576] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3575),c_Groups_Ozero__class_Ozero(U_3575)),U_3576) = c_Groups_Ozero__class_Ozero(U_3575)
      | ~ class_Divides_Osemiring__div(U_3575) ),
    inference(definitional_conversion,[status(esa)],[f_936_2]) ).

cnf(f_936_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3575),c_Groups_Ozero__class_Ozero(U_3575)),U_3576) = c_Groups_Ozero__class_Ozero(U_3575)
    | ~ class_Divides_Osemiring__div(U_3575) ),
    inference(clausify,[status(thm)],[f_936_3]) ).

fof(f_937_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_937_2,plain,
    ! [U_3578,U_3577] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3577),U_3578),c_Groups_Ozero__class_Ozero(U_3577)) = c_Groups_Ozero__class_Ozero(U_3577)
      | ~ class_Divides_Osemiring__div(U_3577) ),
    inference(variable_rename,[status(thm)],[f_937_1]) ).

fof(f_937_3,plain,
    ! [U_3577,U_3578] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3577),U_3578),c_Groups_Ozero__class_Ozero(U_3577)) = c_Groups_Ozero__class_Ozero(U_3577)
      | ~ class_Divides_Osemiring__div(U_3577) ),
    inference(definitional_conversion,[status(esa)],[f_937_2]) ).

cnf(f_937_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3577),U_3578),c_Groups_Ozero__class_Ozero(U_3577)) = c_Groups_Ozero__class_Ozero(U_3577)
    | ~ class_Divides_Osemiring__div(U_3577) ),
    inference(clausify,[status(thm)],[f_937_3]) ).

fof(f_938_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_938_2,plain,
    ! [U_3580,U_3579] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3579),U_3580),c_Groups_Oone__class_Oone(U_3579)) = U_3580
      | ~ class_Divides_Osemiring__div(U_3579) ),
    inference(variable_rename,[status(thm)],[f_938_1]) ).

fof(f_938_3,plain,
    ! [U_3579,U_3580] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3579),U_3580),c_Groups_Oone__class_Oone(U_3579)) = U_3580
      | ~ class_Divides_Osemiring__div(U_3579) ),
    inference(definitional_conversion,[status(esa)],[f_938_2]) ).

cnf(f_938_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3579),U_3580),c_Groups_Oone__class_Oone(U_3579)) = U_3580
    | ~ class_Divides_Osemiring__div(U_3579) ),
    inference(clausify,[status(thm)],[f_938_3]) ).

fof(f_939_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_939_2,plain,
    ! [U_3582,U_3581] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3581),U_3582)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3581)),hAPP(c_Int_Onat,U_3582))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3581)) ),
    inference(variable_rename,[status(thm)],[f_939_1]) ).

fof(f_939_3,plain,
    ! [U_3581,U_3582] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3581),U_3582)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3581)),hAPP(c_Int_Onat,U_3582))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3581)) ),
    inference(definitional_conversion,[status(esa)],[f_939_2]) ).

cnf(f_939_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3581),U_3582)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3581)),hAPP(c_Int_Onat,U_3582))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3581)) ),
    inference(clausify,[status(thm)],[f_939_3]) ).

fof(f_940_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_940_2,plain,
    ! [U_3584,U_3583] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3583)),hAPP(c_Int_Onat,U_3584)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3583),U_3584))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3584))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3583)) ),
    inference(variable_rename,[status(thm)],[f_940_1]) ).

fof(f_940_3,plain,
    ! [U_3583,U_3584] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3583)),hAPP(c_Int_Onat,U_3584)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3583),U_3584))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3584))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3583)) ),
    inference(definitional_conversion,[status(esa)],[f_940_2]) ).

cnf(f_940_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3583)),hAPP(c_Int_Onat,U_3584)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3583),U_3584))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3584))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3583)) ),
    inference(clausify,[status(thm)],[f_940_3]) ).

fof(f_941_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_941_2,plain,
    ! [U_3585] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3585),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3585,
    inference(variable_rename,[status(thm)],[f_941_1]) ).

fof(f_941_3,plain,
    ! [U_3585] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3585),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3585,
    inference(definitional_conversion,[status(esa)],[f_941_2]) ).

cnf(f_941_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3585),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3585,
    inference(clausify,[status(thm)],[f_941_3]) ).

fof(f_942_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_942_2,plain,
    ! [U_3587,U_3586] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3586),U_3587) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3586),U_3587)) ),
    inference(variable_rename,[status(thm)],[f_942_1]) ).

fof(f_942_3,plain,
    ! [U_3586,U_3587] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3586),U_3587) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3586),U_3587)) ),
    inference(definitional_conversion,[status(esa)],[f_942_2]) ).

cnf(f_942_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3586),U_3587) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3586),U_3587)) ),
    inference(clausify,[status(thm)],[f_942_3]) ).

fof(f_943_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_943_2,plain,
    ! [U_3590,U_3589,U_3588] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3588),U_3589)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3588),U_3590)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3589),U_3590)
        | U_3588 = 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_3588),U_3589)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3588),U_3590)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3588 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_943_1]) ).

fof(f_943_3,plain,
    ( ! [U_3596,U_3594,U_3592] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3592),U_3594)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3592),U_3596)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3594),U_3596)
        | U_3592 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3595,U_3593,U_3591] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3591),U_3593)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3591),U_3595)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3591 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_943_2]) ).

fof(f_943_4,plain,
    ( ! [U_3592,U_3594,U_3596] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3592),U_3594)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3592),U_3596)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3594),U_3596)
        | U_3592 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3595,U_3591,U_3593] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3591),U_3593)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3591),U_3595)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3591 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_943_3]) ).

cnf(f_943_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3591),U_3593)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3591),U_3595)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3591 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

cnf(f_943_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3592),U_3594)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3592),U_3596)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3594),U_3596)
    | U_3592 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_943_4]) ).

fof(f_944_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_944_2,plain,
    ! [U_3598,U_3597] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3597),U_3598) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3597,U_3598))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3597,U_3598)) = U_3598 )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3597),U_3598) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3597,U_3598)) != U_3598 ) ),
    inference(variable_rename,[status(thm)],[f_944_1]) ).

fof(f_944_3,plain,
    ( ! [U_3602,U_3600] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3600),U_3602) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3600,U_3602))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3600,U_3602)) = U_3602 )
    & ! [U_3601,U_3599] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3599),U_3601) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3599,U_3601)) != U_3601 ) ),
    inference(miniscope,[status(thm)],[f_944_2]) ).

fof(f_944_4,plain,
    ( ! [U_3602,U_3600] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3600),U_3602) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3600,U_3602))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3600,U_3602)) = U_3602 )
    & ! [U_3599,U_3601] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3599),U_3601) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3599,U_3601)) != U_3601 ) ),
    inference(definitional_conversion,[status(esa)],[f_944_3]) ).

cnf(f_944_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3599),U_3601) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3599,U_3601)) != U_3601 ),
    inference(clausify,[status(thm)],[f_944_4]) ).

cnf(f_944_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3600),U_3602) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3600,U_3602))
    | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3600,U_3602)) = U_3602 ),
    inference(clausify,[status(thm)],[f_944_4]) ).

fof(f_945_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_945_2,plain,
    ! [U_3603] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3603,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_945_1]) ).

fof(f_945_3,plain,
    ! [U_3603] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3603,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_945_2]) ).

cnf(f_945_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3603,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_945_3]) ).

fof(f_946_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_946_2,plain,
    ! [U_3605,U_3604] :
      ( 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_3604),U_3605)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3605))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3604)) ),
    inference(variable_rename,[status(thm)],[f_946_1]) ).

fof(f_946_3,plain,
    ! [U_3604,U_3605] :
      ( 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_3604),U_3605)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3605))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3604)) ),
    inference(definitional_conversion,[status(esa)],[f_946_2]) ).

cnf(f_946_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_3604),U_3605)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3605))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3604)) ),
    inference(clausify,[status(thm)],[f_946_3]) ).

fof(f_947_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_947_2,plain,
    ! [U_3607,U_3606] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3607,U_3606)),U_3606))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3606)) ),
    inference(variable_rename,[status(thm)],[f_947_1]) ).

fof(f_947_3,plain,
    ! [U_3606,U_3607] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3607,U_3606)),U_3606))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3606)) ),
    inference(definitional_conversion,[status(esa)],[f_947_2]) ).

cnf(f_947_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3607,U_3606)),U_3606))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3606)) ),
    inference(clausify,[status(thm)],[f_947_3]) ).

fof(f_948_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_948_2,plain,
    ! [U_3609,U_3608] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3609),U_3608)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3609),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3609),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_3609),U_3608)),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_3608)) ),
    inference(variable_rename,[status(thm)],[f_948_1]) ).

fof(f_948_3,plain,
    ( ! [U_3608,U_3609] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3609),U_3608)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3609),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP276(U_3608,U_3609) )
    & ! [U_3608,U_3609] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3609),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_3609),U_3608)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP276(U_3608,U_3609) )
    & ! [U_3608,U_3609] :
        ( sP276(U_3608,U_3609)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3608)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP276])],[f_948_2]) ).

cnf(f_948_4,plain,
    ( sP276(U_3608,U_3609)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3608)) ),
    inference(clausify,[status(thm)],[f_948_3]) ).

cnf(f_948_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3609),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_3609),U_3608)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP276(U_3608,U_3609) ),
    inference(clausify,[status(thm)],[f_948_3]) ).

cnf(f_948_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3609),U_3608)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3609),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP276(U_3608,U_3609) ),
    inference(clausify,[status(thm)],[f_948_3]) ).

fof(f_949_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_949_2,plain,
    ! [U_3611,U_3610] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3611),U_3610)),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_3611)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3611))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3611),U_3610)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3610),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_949_1]) ).

fof(f_949_3,plain,
    ( ! [U_3611,U_3610] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3611),U_3610)),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_3611))
        | ~ sP277(U_3611,U_3610) )
    & ! [U_3611,U_3610] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3611))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3611),U_3610)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP277(U_3611,U_3610) )
    & ! [U_3611,U_3610] :
        ( sP277(U_3611,U_3610)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3610),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP277])],[f_949_2]) ).

cnf(f_949_4,plain,
    ( sP277(U_3611,U_3610)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3610),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_949_3]) ).

cnf(f_949_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3611))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3611),U_3610)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP277(U_3611,U_3610) ),
    inference(clausify,[status(thm)],[f_949_3]) ).

cnf(f_949_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3611),U_3610)),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_3611))
    | ~ sP277(U_3611,U_3610) ),
    inference(clausify,[status(thm)],[f_949_3]) ).

fof(f_950_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_950_2,plain,
    ! [U_3613,U_3612] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3612),U_3613)),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_3613))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3612),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_950_1]) ).

fof(f_950_3,plain,
    ! [U_3612,U_3613] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3612),U_3613)),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_3613))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3612),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_950_2]) ).

cnf(f_950_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3612),U_3613)),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_3613))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3612),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_950_3]) ).

fof(f_951_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_951_2,plain,
    ! [U_3614] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3614),U_3614) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_3614 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_951_1]) ).

fof(f_951_3,plain,
    ! [U_3614] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3614),U_3614) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_3614 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_951_2]) ).

cnf(f_951_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3614),U_3614) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_3614 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_951_3]) ).

fof(f_952_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_952_2,plain,
    ! [U_3618,U_3617] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3617,U_3618) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_3616] : U_3617 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3618),U_3616) )
      & ( ? [U_3615] : U_3617 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3618),U_3615)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3617,U_3618) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_952_1]) ).

fof(f_952_3,plain,
    ( ! [U_3622,U_3620] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3620,U_3622) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_3616] : U_3620 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3622),U_3616) )
    & ! [U_3621,U_3619] :
        ( ? [U_3615] : U_3619 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3621),U_3615)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3619,U_3621) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_952_2]) ).

fof(f_952_4,plain,
    ( ! [U_3622,U_3620] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3620,U_3622) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_3616] : U_3620 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3622),U_3616) )
    & ! [U_3621,U_3619] :
        ( U_3619 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3621),sK77(U_3621,U_3619))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3619,U_3621) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_3615,sK77(U_3621,U_3619))],[f_952_3]) ).

fof(f_952_5,plain,
    ( ! [U_3616,U_3620,U_3622] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3620,U_3622) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3620 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3622),U_3616) )
    & ! [U_3619,U_3621] :
        ( U_3619 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3621),sK77(U_3621,U_3619))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3619,U_3621) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_952_4]) ).

cnf(f_952_6,plain,
    ( U_3619 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3621),sK77(U_3621,U_3619))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3619,U_3621) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_952_5]) ).

cnf(f_952_7,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3620,U_3622) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3620 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3622),U_3616) ),
    inference(clausify,[status(thm)],[f_952_5]) ).

fof(f_953_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_953_2,plain,
    ! [U_3623] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3623,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3623
      & hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3623),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_953_1]) ).

fof(f_953_3,plain,
    ( ! [U_3625] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3625,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3625
    & ! [U_3624] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3624),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(miniscope,[status(thm)],[f_953_2]) ).

fof(f_953_4,plain,
    ( ! [U_3625] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3625,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3625
    & ! [U_3624] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3624),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_953_3]) ).

cnf(f_953_5,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3624),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_953_4]) ).

cnf(f_953_6,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3625,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3625,
    inference(clausify,[status(thm)],[f_953_4]) ).

fof(f_954_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_954_2,plain,
    ! [U_3627,U_3626] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3626,U_3627)),U_3627) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_954_1]) ).

fof(f_954_3,plain,
    ! [U_3626,U_3627] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3626,U_3627)),U_3627) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_954_2]) ).

cnf(f_954_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3626,U_3627)),U_3627) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_954_3]) ).

fof(f_955_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_955_2,plain,
    ! [U_3630,U_3629,U_3628] : 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_3628),U_3629)),U_3630),U_3629) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3630,U_3629),
    inference(variable_rename,[status(thm)],[f_955_1]) ).

fof(f_955_3,plain,
    ! [U_3628,U_3629,U_3630] : 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_3628),U_3629)),U_3630),U_3629) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3630,U_3629),
    inference(definitional_conversion,[status(esa)],[f_955_2]) ).

cnf(f_955_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_3628),U_3629)),U_3630),U_3629) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3630,U_3629),
    inference(clausify,[status(thm)],[f_955_3]) ).

fof(f_956_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_956_2,plain,
    ! [U_3633,U_3632,U_3631] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3631),U_3632)),U_3633) = 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_3631),U_3633)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3632),U_3633))),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_3631,U_3633)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3632,U_3633))),U_3633)),
    inference(variable_rename,[status(thm)],[f_956_1]) ).

fof(f_956_3,plain,
    ! [U_3631,U_3632,U_3633] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3631),U_3632)),U_3633) = 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_3631),U_3633)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3632),U_3633))),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_3631,U_3633)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3632,U_3633))),U_3633)),
    inference(definitional_conversion,[status(esa)],[f_956_2]) ).

cnf(f_956_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3631),U_3632)),U_3633) = 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_3631),U_3633)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3632),U_3633))),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_3631,U_3633)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3632,U_3633))),U_3633)),
    inference(clausify,[status(thm)],[f_956_3]) ).

fof(f_957_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_957_2,plain,
    ! [U_3635,U_3634] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3634),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3635)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3634,U_3635)),
    inference(variable_rename,[status(thm)],[f_957_1]) ).

fof(f_957_3,plain,
    ! [U_3635,U_3634] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3634),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3635)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3634,U_3635)),
    inference(definitional_conversion,[status(esa)],[f_957_2]) ).

cnf(f_957_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3634),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3635)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3634,U_3635)),
    inference(clausify,[status(thm)],[f_957_3]) ).

fof(f_958_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_958_2,plain,
    ! [U_3637,U_3636] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3636,U_3637)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3636),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3637)),
    inference(variable_rename,[status(thm)],[f_958_1]) ).

fof(f_958_3,plain,
    ! [U_3636,U_3637] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3636,U_3637)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3636),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3637)),
    inference(definitional_conversion,[status(esa)],[f_958_2]) ).

cnf(f_958_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3636,U_3637)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3636),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3637)),
    inference(clausify,[status(thm)],[f_958_3]) ).

fof(f_959_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_959_2,plain,
    ! [U_3641,U_3640,U_3639,U_3638] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3638),U_3639),U_3640)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3638),U_3639),U_3641)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3638),U_3640),U_3641)
      | U_3639 = c_Groups_Ozero__class_Ozero(U_3638)
      | ~ class_Divides_Osemiring__div(U_3638) ),
    inference(variable_rename,[status(thm)],[f_959_1]) ).

fof(f_959_3,plain,
    ! [U_3638,U_3639,U_3640,U_3641] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3638),U_3639),U_3640)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3638),U_3639),U_3641)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3638),U_3640),U_3641)
      | U_3639 = c_Groups_Ozero__class_Ozero(U_3638)
      | ~ class_Divides_Osemiring__div(U_3638) ),
    inference(definitional_conversion,[status(esa)],[f_959_2]) ).

cnf(f_959_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3638),U_3639),U_3640)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3638),U_3639),U_3641)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3638),U_3640),U_3641)
    | U_3639 = c_Groups_Ozero__class_Ozero(U_3638)
    | ~ class_Divides_Osemiring__div(U_3638) ),
    inference(clausify,[status(thm)],[f_959_3]) ).

fof(f_960_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_960_2,plain,
    ! [U_3645,U_3644,U_3643,U_3642] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3642),U_3644),U_3643)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3642),U_3645),U_3643)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3642),U_3644),U_3645)
      | U_3643 = c_Groups_Ozero__class_Ozero(U_3642)
      | ~ class_Divides_Osemiring__div(U_3642) ),
    inference(variable_rename,[status(thm)],[f_960_1]) ).

fof(f_960_3,plain,
    ! [U_3642,U_3643,U_3644,U_3645] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3642),U_3644),U_3643)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3642),U_3645),U_3643)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3642),U_3644),U_3645)
      | U_3643 = c_Groups_Ozero__class_Ozero(U_3642)
      | ~ class_Divides_Osemiring__div(U_3642) ),
    inference(definitional_conversion,[status(esa)],[f_960_2]) ).

cnf(f_960_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3642),U_3644),U_3643)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3642),U_3645),U_3643)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3642),U_3644),U_3645)
    | U_3643 = c_Groups_Ozero__class_Ozero(U_3642)
    | ~ class_Divides_Osemiring__div(U_3642) ),
    inference(clausify,[status(thm)],[f_960_3]) ).

fof(f_961_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_961_2,plain,
    ! [U_3648,U_3647,U_3646] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3646),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3646),U_3647),U_3648)),U_3647) = U_3648
      | U_3647 = c_Groups_Ozero__class_Ozero(U_3646)
      | ~ class_Divides_Osemiring__div(U_3646) ),
    inference(variable_rename,[status(thm)],[f_961_1]) ).

fof(f_961_3,plain,
    ! [U_3646,U_3647,U_3648] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3646),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3646),U_3647),U_3648)),U_3647) = U_3648
      | U_3647 = c_Groups_Ozero__class_Ozero(U_3646)
      | ~ class_Divides_Osemiring__div(U_3646) ),
    inference(definitional_conversion,[status(esa)],[f_961_2]) ).

cnf(f_961_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3646),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3646),U_3647),U_3648)),U_3647) = U_3648
    | U_3647 = c_Groups_Ozero__class_Ozero(U_3646)
    | ~ class_Divides_Osemiring__div(U_3646) ),
    inference(clausify,[status(thm)],[f_961_3]) ).

fof(f_962_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_962_2,plain,
    ! [U_3651,U_3650,U_3649] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3649),U_3651),U_3650)),U_3650) = U_3651
      | U_3650 = c_Groups_Ozero__class_Ozero(U_3649)
      | ~ class_Divides_Osemiring__div(U_3649) ),
    inference(variable_rename,[status(thm)],[f_962_1]) ).

fof(f_962_3,plain,
    ! [U_3649,U_3650,U_3651] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3649),U_3651),U_3650)),U_3650) = U_3651
      | U_3650 = c_Groups_Ozero__class_Ozero(U_3649)
      | ~ class_Divides_Osemiring__div(U_3649) ),
    inference(definitional_conversion,[status(esa)],[f_962_2]) ).

cnf(f_962_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3649),U_3651),U_3650)),U_3650) = U_3651
    | U_3650 = c_Groups_Ozero__class_Ozero(U_3649)
    | ~ class_Divides_Osemiring__div(U_3649) ),
    inference(clausify,[status(thm)],[f_962_3]) ).

fof(f_963_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_963_2,plain,
    ! [U_3655,U_3654,U_3653,U_3652] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3652),U_3653),U_3654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3652),U_3653),U_3655)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3652),U_3654),U_3655)
          | U_3653 = c_Groups_Ozero__class_Ozero(U_3652) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3652),U_3653),U_3654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3652),U_3653),U_3655)) = c_Groups_Ozero__class_Ozero(U_3652)
          | U_3653 != c_Groups_Ozero__class_Ozero(U_3652) ) )
      | ~ class_Divides_Osemiring__div(U_3652) ),
    inference(variable_rename,[status(thm)],[f_963_1]) ).

fof(f_963_3,plain,
    ( ! [U_3652,U_3653,U_3654,U_3655] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3652),U_3653),U_3654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3652),U_3653),U_3655)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3652),U_3654),U_3655)
        | U_3653 = c_Groups_Ozero__class_Ozero(U_3652)
        | ~ sP278(U_3652,U_3653,U_3654,U_3655) )
    & ! [U_3652,U_3653,U_3654,U_3655] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3652),U_3653),U_3654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3652),U_3653),U_3655)) = c_Groups_Ozero__class_Ozero(U_3652)
        | U_3653 != c_Groups_Ozero__class_Ozero(U_3652)
        | ~ sP278(U_3652,U_3653,U_3654,U_3655) )
    & ! [U_3652,U_3653,U_3654,U_3655] :
        ( sP278(U_3652,U_3653,U_3654,U_3655)
        | ~ class_Divides_Osemiring__div(U_3652) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP278])],[f_963_2]) ).

cnf(f_963_4,plain,
    ( sP278(U_3652,U_3653,U_3654,U_3655)
    | ~ class_Divides_Osemiring__div(U_3652) ),
    inference(clausify,[status(thm)],[f_963_3]) ).

cnf(f_963_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3652),U_3653),U_3654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3652),U_3653),U_3655)) = c_Groups_Ozero__class_Ozero(U_3652)
    | U_3653 != c_Groups_Ozero__class_Ozero(U_3652)
    | ~ sP278(U_3652,U_3653,U_3654,U_3655) ),
    inference(clausify,[status(thm)],[f_963_3]) ).

cnf(f_963_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3652),U_3653),U_3654)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3652),U_3653),U_3655)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3652),U_3654),U_3655)
    | U_3653 = c_Groups_Ozero__class_Ozero(U_3652)
    | ~ sP278(U_3652,U_3653,U_3654,U_3655) ),
    inference(clausify,[status(thm)],[f_963_3]) ).

fof(f_964_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_964_2,plain,
    ! [U_3657,U_3656] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3656),U_3657),U_3657) = c_Groups_Oone__class_Oone(U_3656)
      | U_3657 = c_Groups_Ozero__class_Ozero(U_3656)
      | ~ class_Divides_Osemiring__div(U_3656) ),
    inference(variable_rename,[status(thm)],[f_964_1]) ).

fof(f_964_3,plain,
    ! [U_3657,U_3656] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3656),U_3657),U_3657) = c_Groups_Oone__class_Oone(U_3656)
      | U_3657 = c_Groups_Ozero__class_Ozero(U_3656)
      | ~ class_Divides_Osemiring__div(U_3656) ),
    inference(definitional_conversion,[status(esa)],[f_964_2]) ).

cnf(f_964_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3656),U_3657),U_3657) = c_Groups_Oone__class_Oone(U_3656)
    | U_3657 = c_Groups_Ozero__class_Ozero(U_3656)
    | ~ class_Divides_Osemiring__div(U_3656) ),
    inference(clausify,[status(thm)],[f_964_3]) ).

fof(f_965_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_965_2,plain,
    ! [U_3660,U_3659,U_3658] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3658),c_Divides_Odiv__class_Omod(U_3658,U_3659,U_3660)),U_3660) = c_Groups_Ozero__class_Ozero(U_3658)
      | ~ class_Divides_Osemiring__div(U_3658) ),
    inference(variable_rename,[status(thm)],[f_965_1]) ).

fof(f_965_3,plain,
    ! [U_3658,U_3659,U_3660] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3658),c_Divides_Odiv__class_Omod(U_3658,U_3659,U_3660)),U_3660) = c_Groups_Ozero__class_Ozero(U_3658)
      | ~ class_Divides_Osemiring__div(U_3658) ),
    inference(definitional_conversion,[status(esa)],[f_965_2]) ).

cnf(f_965_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3658),c_Divides_Odiv__class_Omod(U_3658,U_3659,U_3660)),U_3660) = c_Groups_Ozero__class_Ozero(U_3658)
    | ~ class_Divides_Osemiring__div(U_3658) ),
    inference(clausify,[status(thm)],[f_965_3]) ).

fof(f_966_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_966_2,plain,
    ! [U_3663,U_3662,U_3661] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3663),U_3662)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3663),U_3661)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3661),U_3662))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3661)) ),
    inference(variable_rename,[status(thm)],[f_966_1]) ).

fof(f_966_3,plain,
    ! [U_3661,U_3662,U_3663] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3663),U_3662)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3663),U_3661)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3661),U_3662))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3661)) ),
    inference(definitional_conversion,[status(esa)],[f_966_2]) ).

cnf(f_966_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_3663),U_3662)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3663),U_3661)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3661),U_3662))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3661)) ),
    inference(clausify,[status(thm)],[f_966_3]) ).

fof(f_967_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_967_2,plain,
    ! [U_3665,U_3664] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3665),U_3664)),U_3664) = U_3665
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3664)) ),
    inference(variable_rename,[status(thm)],[f_967_1]) ).

fof(f_967_3,plain,
    ! [U_3665,U_3664] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3665),U_3664)),U_3664) = U_3665
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3664)) ),
    inference(definitional_conversion,[status(esa)],[f_967_2]) ).

cnf(f_967_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3665),U_3664)),U_3664) = U_3665
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3664)) ),
    inference(clausify,[status(thm)],[f_967_3]) ).

fof(f_968_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_968_2,plain,
    ! [U_3667,U_3666] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3666),U_3667)),U_3666) = U_3667
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3666)) ),
    inference(variable_rename,[status(thm)],[f_968_1]) ).

fof(f_968_3,plain,
    ! [U_3666,U_3667] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3666),U_3667)),U_3666) = U_3667
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3666)) ),
    inference(definitional_conversion,[status(esa)],[f_968_2]) ).

cnf(f_968_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3666),U_3667)),U_3666) = U_3667
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3666)) ),
    inference(clausify,[status(thm)],[f_968_3]) ).

fof(f_969_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_969_2,plain,
    ! [U_3670,U_3669,U_3668] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3668),U_3669)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3668),U_3670)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3669),U_3670)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3668)) ),
    inference(variable_rename,[status(thm)],[f_969_1]) ).

fof(f_969_3,plain,
    ! [U_3668,U_3669,U_3670] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3668),U_3669)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3668),U_3670)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3669),U_3670)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3668)) ),
    inference(definitional_conversion,[status(esa)],[f_969_2]) ).

cnf(f_969_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3668),U_3669)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3668),U_3670)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3669),U_3670)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3668)) ),
    inference(clausify,[status(thm)],[f_969_3]) ).

fof(f_970_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_970_2,plain,
    ! [U_3672,U_3671] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3672),U_3671)),U_3672))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3672))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3671)) ),
    inference(variable_rename,[status(thm)],[f_970_1]) ).

fof(f_970_3,plain,
    ! [U_3671,U_3672] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3672),U_3671)),U_3672))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3672))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3671)) ),
    inference(definitional_conversion,[status(esa)],[f_970_2]) ).

cnf(f_970_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3672),U_3671)),U_3672))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3672))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3671)) ),
    inference(clausify,[status(thm)],[f_970_3]) ).

fof(f_971_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_971_2,plain,
    ! [U_3674,U_3673] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3673),U_3674) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3674),U_3673))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3673),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3673),U_3674))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3673)) )
          & U_3674 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3674),U_3673))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3673),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3673),U_3674))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3673)) )
        | U_3674 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3673),U_3674) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_971_1]) ).

fof(f_971_3,plain,
    ( ! [U_3678,U_3676] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3676),U_3678) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3678),U_3676))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3676),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3676),U_3678))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3676)) )
          & U_3678 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3677,U_3675] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3677),U_3675))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3675),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3675),U_3677))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3675)) )
        | U_3677 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3675),U_3677) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_971_2]) ).

fof(f_971_4,plain,
    ( ! [U_3678,U_3676] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3678),U_3676))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3676),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP281(U_3678,U_3676) )
    & ! [U_3678,U_3676] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3676),U_3678))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3676))
        | ~ sP281(U_3678,U_3676) )
    & ! [U_3678,U_3676] :
        ( U_3678 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP281(U_3678,U_3676) )
    & ! [U_3675,U_3677] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3677),U_3675))
        | ~ sP280(U_3675,U_3677) )
    & ! [U_3675,U_3677] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3675),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP280(U_3675,U_3677) )
    & ! [U_3675,U_3677] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3675),U_3677))
        | ~ sP279(U_3675,U_3677) )
    & ! [U_3675,U_3677] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3675))
        | ~ sP279(U_3675,U_3677) )
    & ! [U_3678,U_3676] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3676),U_3678) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | sP281(U_3678,U_3676) )
    & ! [U_3675,U_3677] :
        ( sP280(U_3675,U_3677)
        | sP279(U_3675,U_3677)
        | U_3677 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3675),U_3677) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP279,sP280,sP281])],[f_971_3]) ).

cnf(f_971_5,plain,
    ( sP280(U_3675,U_3677)
    | sP279(U_3675,U_3677)
    | U_3677 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3675),U_3677) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_971_4]) ).

cnf(f_971_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3676),U_3678) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | sP281(U_3678,U_3676) ),
    inference(clausify,[status(thm)],[f_971_4]) ).

cnf(f_971_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3675))
    | ~ sP279(U_3675,U_3677) ),
    inference(clausify,[status(thm)],[f_971_4]) ).

cnf(f_971_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3675),U_3677))
    | ~ sP279(U_3675,U_3677) ),
    inference(clausify,[status(thm)],[f_971_4]) ).

cnf(f_971_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3675),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP280(U_3675,U_3677) ),
    inference(clausify,[status(thm)],[f_971_4]) ).

cnf(f_971_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3677),U_3675))
    | ~ sP280(U_3675,U_3677) ),
    inference(clausify,[status(thm)],[f_971_4]) ).

cnf(f_971_11,plain,
    ( U_3678 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP281(U_3678,U_3676) ),
    inference(clausify,[status(thm)],[f_971_4]) ).

cnf(f_971_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3676),U_3678))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3676))
    | ~ sP281(U_3678,U_3676) ),
    inference(clausify,[status(thm)],[f_971_4]) ).

cnf(f_971_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3678),U_3676))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3676),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP281(U_3678,U_3676) ),
    inference(clausify,[status(thm)],[f_971_4]) ).

fof(f_972_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_972_2,plain,
    ! [U_3680,U_3679] :
      ( ( ( 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_3680),U_3679)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3680)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3680))
          | ~ 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_3680),U_3679))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3679)) ),
    inference(variable_rename,[status(thm)],[f_972_1]) ).

fof(f_972_3,plain,
    ( ! [U_3679,U_3680] :
        ( 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_3680),U_3679)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3680))
        | ~ sP282(U_3679,U_3680) )
    & ! [U_3679,U_3680] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3680))
        | ~ 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_3680),U_3679)))
        | ~ sP282(U_3679,U_3680) )
    & ! [U_3679,U_3680] :
        ( sP282(U_3679,U_3680)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3679)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP282])],[f_972_2]) ).

cnf(f_972_4,plain,
    ( sP282(U_3679,U_3680)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3679)) ),
    inference(clausify,[status(thm)],[f_972_3]) ).

cnf(f_972_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3680))
    | ~ 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_3680),U_3679)))
    | ~ sP282(U_3679,U_3680) ),
    inference(clausify,[status(thm)],[f_972_3]) ).

cnf(f_972_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_3680),U_3679)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3680))
    | ~ sP282(U_3679,U_3680) ),
    inference(clausify,[status(thm)],[f_972_3]) ).

fof(f_973_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_973_2,plain,
    ! [U_3682,U_3681] :
      ( ( ( 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_3682),U_3681)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3681),U_3682)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3681),U_3682))
          | ~ 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_3682),U_3681))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3681)) ),
    inference(variable_rename,[status(thm)],[f_973_1]) ).

fof(f_973_3,plain,
    ( ! [U_3681,U_3682] :
        ( 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_3682),U_3681)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3681),U_3682))
        | ~ sP283(U_3681,U_3682) )
    & ! [U_3681,U_3682] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3681),U_3682))
        | ~ 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_3682),U_3681)))
        | ~ sP283(U_3681,U_3682) )
    & ! [U_3681,U_3682] :
        ( sP283(U_3681,U_3682)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3681)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP283])],[f_973_2]) ).

cnf(f_973_4,plain,
    ( sP283(U_3681,U_3682)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3681)) ),
    inference(clausify,[status(thm)],[f_973_3]) ).

cnf(f_973_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3681),U_3682))
    | ~ 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_3682),U_3681)))
    | ~ sP283(U_3681,U_3682) ),
    inference(clausify,[status(thm)],[f_973_3]) ).

cnf(f_973_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_3682),U_3681)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3681),U_3682))
    | ~ sP283(U_3681,U_3682) ),
    inference(clausify,[status(thm)],[f_973_3]) ).

fof(f_974_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_974_2,plain,
    ! [U_3684,U_3683] :
      ( ( ( 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_3683),U_3684)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3684))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3684),U_3683)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3684))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3684),U_3683)) )
          | ~ 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_3683),U_3684))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3683)) ),
    inference(variable_rename,[status(thm)],[f_974_1]) ).

fof(f_974_3,plain,
    ( ! [U_3684,U_3683] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3684))
        | ~ sP284(U_3684,U_3683) )
    & ! [U_3684,U_3683] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3684),U_3683))
        | ~ sP284(U_3684,U_3683) )
    & ! [U_3684,U_3683] :
        ( 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_3683),U_3684)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3684))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3684),U_3683))
        | ~ sP285(U_3684,U_3683) )
    & ! [U_3684,U_3683] :
        ( sP284(U_3684,U_3683)
        | ~ 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_3683),U_3684)))
        | ~ sP285(U_3684,U_3683) )
    & ! [U_3684,U_3683] :
        ( sP285(U_3684,U_3683)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3683)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP284,sP285])],[f_974_2]) ).

cnf(f_974_4,plain,
    ( sP285(U_3684,U_3683)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3683)) ),
    inference(clausify,[status(thm)],[f_974_3]) ).

cnf(f_974_5,plain,
    ( sP284(U_3684,U_3683)
    | ~ 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_3683),U_3684)))
    | ~ sP285(U_3684,U_3683) ),
    inference(clausify,[status(thm)],[f_974_3]) ).

cnf(f_974_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_3683),U_3684)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3684))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3684),U_3683))
    | ~ sP285(U_3684,U_3683) ),
    inference(clausify,[status(thm)],[f_974_3]) ).

cnf(f_974_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3684),U_3683))
    | ~ sP284(U_3684,U_3683) ),
    inference(clausify,[status(thm)],[f_974_3]) ).

cnf(f_974_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3684))
    | ~ sP284(U_3684,U_3683) ),
    inference(clausify,[status(thm)],[f_974_3]) ).

fof(f_975_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_975_2,plain,
    ! [U_3687,U_3686,U_3685] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3685),U_3687)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3685),U_3686)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3686),U_3687))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3686))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3685)) ),
    inference(variable_rename,[status(thm)],[f_975_1]) ).

fof(f_975_3,plain,
    ! [U_3686,U_3687,U_3685] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3685),U_3687)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3685),U_3686)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3686),U_3687))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3686))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3685)) ),
    inference(definitional_conversion,[status(esa)],[f_975_2]) ).

cnf(f_975_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_3685),U_3687)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3685),U_3686)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3686),U_3687))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3686))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3685)) ),
    inference(clausify,[status(thm)],[f_975_3]) ).

fof(f_976_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_976_2,plain,
    ! [U_3689,U_3688] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3688),U_3689)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3689),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_3688)) ),
    inference(variable_rename,[status(thm)],[f_976_1]) ).

fof(f_976_3,plain,
    ! [U_3689,U_3688] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3688),U_3689)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3689),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_3688)) ),
    inference(definitional_conversion,[status(esa)],[f_976_2]) ).

cnf(f_976_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_3688),U_3689)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3689),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_3688)) ),
    inference(clausify,[status(thm)],[f_976_3]) ).

fof(f_977_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_977_2,plain,
    ! [U_3691,U_3690] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3690),U_3691) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3690),U_3691))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3690)) ),
    inference(variable_rename,[status(thm)],[f_977_1]) ).

fof(f_977_3,plain,
    ! [U_3690,U_3691] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3690),U_3691) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3690),U_3691))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3690)) ),
    inference(definitional_conversion,[status(esa)],[f_977_2]) ).

cnf(f_977_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3690),U_3691) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3690),U_3691))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3690)) ),
    inference(clausify,[status(thm)],[f_977_3]) ).

fof(f_978_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_978_2,plain,
    ! [U_3693,U_3692] :
      ( ( ( 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_3693),U_3692)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3693),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3693),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_3693),U_3692))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3692),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_978_1]) ).

fof(f_978_3,plain,
    ( ! [U_3693,U_3692] :
        ( 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_3693),U_3692)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3693),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP286(U_3693,U_3692) )
    & ! [U_3693,U_3692] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3693),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_3693),U_3692)))
        | ~ sP286(U_3693,U_3692) )
    & ! [U_3693,U_3692] :
        ( sP286(U_3693,U_3692)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3692),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP286])],[f_978_2]) ).

cnf(f_978_4,plain,
    ( sP286(U_3693,U_3692)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3692),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_978_3]) ).

cnf(f_978_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3693),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_3693),U_3692)))
    | ~ sP286(U_3693,U_3692) ),
    inference(clausify,[status(thm)],[f_978_3]) ).

cnf(f_978_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_3693),U_3692)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3693),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP286(U_3693,U_3692) ),
    inference(clausify,[status(thm)],[f_978_3]) ).

fof(f_979_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_979_2,plain,
    ! [U_3695,U_3694] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3694),U_3695)),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_3695))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3694),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_979_1]) ).

fof(f_979_3,plain,
    ! [U_3694,U_3695] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3694),U_3695)),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_3695))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3694),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_979_2]) ).

cnf(f_979_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_3694),U_3695)),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_3695))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3694),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_979_3]) ).

fof(f_980_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_980_2,plain,
    ! [U_3698,U_3697,U_3696] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3696),U_3697)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3696),U_3698)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3697),U_3698))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3697))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3696),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_980_1]) ).

fof(f_980_3,plain,
    ! [U_3696,U_3697,U_3698] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3696),U_3697)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3696),U_3698)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3697),U_3698))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3697))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3696),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_980_2]) ).

cnf(f_980_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_3696),U_3697)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3696),U_3698)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3697),U_3698))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3697))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3696),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_980_3]) ).

fof(f_981_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_981_2,plain,
    ! [U_3700,U_3699] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3699),U_3700) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3700),U_3699))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3699),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_981_1]) ).

fof(f_981_3,plain,
    ! [U_3700,U_3699] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3699),U_3700) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3700),U_3699))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3699),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_981_2]) ).

cnf(f_981_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3699),U_3700) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3700),U_3699))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3699),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_981_3]) ).

fof(f_982_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_982_2,plain,
    ! [U_3703,U_3702,U_3701] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3701),U_3703)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3702),U_3703)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3703))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3701),U_3702)) ),
    inference(variable_rename,[status(thm)],[f_982_1]) ).

fof(f_982_3,plain,
    ! [U_3701,U_3702,U_3703] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3701),U_3703)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3702),U_3703)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3703))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3701),U_3702)) ),
    inference(definitional_conversion,[status(esa)],[f_982_2]) ).

cnf(f_982_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_3701),U_3703)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3702),U_3703)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3703))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3701),U_3702)) ),
    inference(clausify,[status(thm)],[f_982_3]) ).

fof(f_983_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_983_2,plain,
    ! [U_3706,U_3705,U_3704] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3705),U_3706)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3704),U_3706)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3706),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3704),U_3705)) ),
    inference(variable_rename,[status(thm)],[f_983_1]) ).

fof(f_983_3,plain,
    ! [U_3704,U_3705,U_3706] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3705),U_3706)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3704),U_3706)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3706),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3704),U_3705)) ),
    inference(definitional_conversion,[status(esa)],[f_983_2]) ).

cnf(f_983_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_3705),U_3706)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3704),U_3706)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3706),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3704),U_3705)) ),
    inference(clausify,[status(thm)],[f_983_3]) ).

fof(f_984_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_984_2,plain,
    ! [U_3708,U_3707] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3708,U_3707)),U_3707))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3707)) ),
    inference(variable_rename,[status(thm)],[f_984_1]) ).

fof(f_984_3,plain,
    ! [U_3707,U_3708] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3708,U_3707)),U_3707))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3707)) ),
    inference(definitional_conversion,[status(esa)],[f_984_2]) ).

cnf(f_984_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3708,U_3707)),U_3707))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3707)) ),
    inference(clausify,[status(thm)],[f_984_3]) ).

fof(f_985_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_985_2,plain,
    ! [U_3710,U_3709] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3709),U_3710)),U_3709))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_3710))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3709)) ),
    inference(variable_rename,[status(thm)],[f_985_1]) ).

fof(f_985_3,plain,
    ! [U_3709,U_3710] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3709),U_3710)),U_3709))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_3710))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3709)) ),
    inference(definitional_conversion,[status(esa)],[f_985_2]) ).

cnf(f_985_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3709),U_3710)),U_3709))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_3710))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3709)) ),
    inference(clausify,[status(thm)],[f_985_3]) ).

fof(f_986_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_986_2,plain,
    ! [U_3713,U_3712,U_3711] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3713),U_3711)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3712),U_3713)),U_3711)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3711)) ),
    inference(variable_rename,[status(thm)],[f_986_1]) ).

fof(f_986_3,plain,
    ! [U_3711,U_3712,U_3713] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3713),U_3711)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3712),U_3713)),U_3711)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3711)) ),
    inference(definitional_conversion,[status(esa)],[f_986_2]) ).

cnf(f_986_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3713),U_3711)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3712),U_3713)),U_3711)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3711)) ),
    inference(clausify,[status(thm)],[f_986_3]) ).

fof(f_987_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_987_2,plain,
    ! [U_3716,U_3715,U_3714] : 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_3714),U_3715)),U_3716)),U_3715) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3716),U_3715),
    inference(variable_rename,[status(thm)],[f_987_1]) ).

fof(f_987_3,plain,
    ! [U_3714,U_3715,U_3716] : 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_3714),U_3715)),U_3716)),U_3715) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3716),U_3715),
    inference(definitional_conversion,[status(esa)],[f_987_2]) ).

cnf(f_987_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_3714),U_3715)),U_3716)),U_3715) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3716),U_3715),
    inference(clausify,[status(thm)],[f_987_3]) ).

fof(f_988_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_988_2,plain,
    ! [U_3719,U_3718,U_3717] : 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_3717),U_3718)),U_3718)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3717,U_3718))),U_3719) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3717),U_3719),
    inference(variable_rename,[status(thm)],[f_988_1]) ).

fof(f_988_3,plain,
    ! [U_3717,U_3718,U_3719] : 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_3717),U_3718)),U_3718)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3717,U_3718))),U_3719) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3717),U_3719),
    inference(definitional_conversion,[status(esa)],[f_988_2]) ).

cnf(f_988_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_3717),U_3718)),U_3718)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3717,U_3718))),U_3719) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3717),U_3719),
    inference(clausify,[status(thm)],[f_988_3]) ).

fof(f_989_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_989_2,plain,
    ! [U_3722,U_3721,U_3720] : 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_3720),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3721),U_3720))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3721,U_3720))),U_3722) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3721),U_3722),
    inference(variable_rename,[status(thm)],[f_989_1]) ).

fof(f_989_3,plain,
    ! [U_3720,U_3721,U_3722] : 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_3720),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3721),U_3720))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3721,U_3720))),U_3722) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3721),U_3722),
    inference(definitional_conversion,[status(esa)],[f_989_2]) ).

cnf(f_989_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_3720),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3721),U_3720))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3721,U_3720))),U_3722) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3721),U_3722),
    inference(clausify,[status(thm)],[f_989_3]) ).

fof(f_990_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_990_2,plain,
    ! [U_3725,U_3724,U_3723] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3723),U_3724)),U_3725) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3723),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3724),U_3725))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3723),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3724,U_3725))),U_3725)),
    inference(variable_rename,[status(thm)],[f_990_1]) ).

fof(f_990_3,plain,
    ! [U_3723,U_3724,U_3725] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3723),U_3724)),U_3725) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3723),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3724),U_3725))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3723),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3724,U_3725))),U_3725)),
    inference(definitional_conversion,[status(esa)],[f_990_2]) ).

cnf(f_990_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3723),U_3724)),U_3725) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3723),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3724),U_3725))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3723),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3724,U_3725))),U_3725)),
    inference(clausify,[status(thm)],[f_990_3]) ).

fof(f_991_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_991_2,plain,
    ! [U_3727,U_3726] : U_3726 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3727),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3726),U_3727))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3726,U_3727)),
    inference(variable_rename,[status(thm)],[f_991_1]) ).

fof(f_991_3,plain,
    ! [U_3727,U_3726] : U_3726 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3727),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3726),U_3727))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3726,U_3727)),
    inference(definitional_conversion,[status(esa)],[f_991_2]) ).

cnf(f_991_4,plain,
    U_3726 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3727),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3726),U_3727))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3726,U_3727)),
    inference(clausify,[status(thm)],[f_991_3]) ).

fof(f_992_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_992_2,plain,
    ! [U_3731,U_3730,U_3729,U_3728] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3728),U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3728),U_3731),U_3729))),U_3729) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3728),U_3731),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3728),U_3730),U_3729))
      | U_3729 = c_Groups_Ozero__class_Ozero(U_3728)
      | ~ class_Divides_Osemiring__div(U_3728) ),
    inference(variable_rename,[status(thm)],[f_992_1]) ).

fof(f_992_3,plain,
    ! [U_3728,U_3729,U_3730,U_3731] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3728),U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3728),U_3731),U_3729))),U_3729) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3728),U_3731),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3728),U_3730),U_3729))
      | U_3729 = c_Groups_Ozero__class_Ozero(U_3728)
      | ~ class_Divides_Osemiring__div(U_3728) ),
    inference(definitional_conversion,[status(esa)],[f_992_2]) ).

cnf(f_992_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3728),U_3730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3728),U_3731),U_3729))),U_3729) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3728),U_3731),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3728),U_3730),U_3729))
    | U_3729 = c_Groups_Ozero__class_Ozero(U_3728)
    | ~ class_Divides_Osemiring__div(U_3728) ),
    inference(clausify,[status(thm)],[f_992_3]) ).

fof(f_993_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_993_2,plain,
    ! [U_3735,U_3734,U_3733,U_3732] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3732),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3732),U_3734),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3732),U_3733),U_3735))),U_3733) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3732),U_3735),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3732),U_3734),U_3733))
      | U_3733 = c_Groups_Ozero__class_Ozero(U_3732)
      | ~ class_Divides_Osemiring__div(U_3732) ),
    inference(variable_rename,[status(thm)],[f_993_1]) ).

fof(f_993_3,plain,
    ! [U_3732,U_3733,U_3734,U_3735] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3732),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3732),U_3734),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3732),U_3733),U_3735))),U_3733) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3732),U_3735),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3732),U_3734),U_3733))
      | U_3733 = c_Groups_Ozero__class_Ozero(U_3732)
      | ~ class_Divides_Osemiring__div(U_3732) ),
    inference(definitional_conversion,[status(esa)],[f_993_2]) ).

cnf(f_993_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3732),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3732),U_3734),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3732),U_3733),U_3735))),U_3733) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3732),U_3735),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3732),U_3734),U_3733))
    | U_3733 = c_Groups_Ozero__class_Ozero(U_3732)
    | ~ class_Divides_Osemiring__div(U_3732) ),
    inference(clausify,[status(thm)],[f_993_3]) ).

fof(f_994_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_994_2,plain,
    ! [U_3738,U_3737,U_3736] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),U_3737),U_3738)),U_3737) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3736),U_3738),U_3737)),c_Groups_Oone__class_Oone(U_3736))
      | U_3737 = c_Groups_Ozero__class_Ozero(U_3736)
      | ~ class_Divides_Osemiring__div(U_3736) ),
    inference(variable_rename,[status(thm)],[f_994_1]) ).

fof(f_994_3,plain,
    ! [U_3736,U_3737,U_3738] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),U_3737),U_3738)),U_3737) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3736),U_3738),U_3737)),c_Groups_Oone__class_Oone(U_3736))
      | U_3737 = c_Groups_Ozero__class_Ozero(U_3736)
      | ~ class_Divides_Osemiring__div(U_3736) ),
    inference(definitional_conversion,[status(esa)],[f_994_2]) ).

cnf(f_994_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),U_3737),U_3738)),U_3737) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3736),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3736),U_3738),U_3737)),c_Groups_Oone__class_Oone(U_3736))
    | U_3737 = c_Groups_Ozero__class_Ozero(U_3736)
    | ~ class_Divides_Osemiring__div(U_3736) ),
    inference(clausify,[status(thm)],[f_994_3]) ).

fof(f_995_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_995_2,plain,
    ! [U_3741,U_3740,U_3739] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3739),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3739),U_3741),U_3740)),U_3740) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3739),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3739),U_3741),U_3740)),c_Groups_Oone__class_Oone(U_3739))
      | U_3740 = c_Groups_Ozero__class_Ozero(U_3739)
      | ~ class_Divides_Osemiring__div(U_3739) ),
    inference(variable_rename,[status(thm)],[f_995_1]) ).

fof(f_995_3,plain,
    ! [U_3739,U_3740,U_3741] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3739),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3739),U_3741),U_3740)),U_3740) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3739),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3739),U_3741),U_3740)),c_Groups_Oone__class_Oone(U_3739))
      | U_3740 = c_Groups_Ozero__class_Ozero(U_3739)
      | ~ class_Divides_Osemiring__div(U_3739) ),
    inference(definitional_conversion,[status(esa)],[f_995_2]) ).

cnf(f_995_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3739),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3739),U_3741),U_3740)),U_3740) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3739),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3739),U_3741),U_3740)),c_Groups_Oone__class_Oone(U_3739))
    | U_3740 = c_Groups_Ozero__class_Ozero(U_3739)
    | ~ class_Divides_Osemiring__div(U_3739) ),
    inference(clausify,[status(thm)],[f_995_3]) ).

fof(f_996_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_996_2,plain,
    ! [U_3745,U_3744,U_3743,U_3742] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3742),U_3743),U_3744)),U_3744)),c_Divides_Odiv__class_Omod(U_3742,U_3743,U_3744))),U_3745) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),U_3743),U_3745)
      | ~ class_Divides_Osemiring__div(U_3742) ),
    inference(variable_rename,[status(thm)],[f_996_1]) ).

fof(f_996_3,plain,
    ! [U_3742,U_3743,U_3744,U_3745] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3742),U_3743),U_3744)),U_3744)),c_Divides_Odiv__class_Omod(U_3742,U_3743,U_3744))),U_3745) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),U_3743),U_3745)
      | ~ class_Divides_Osemiring__div(U_3742) ),
    inference(definitional_conversion,[status(esa)],[f_996_2]) ).

cnf(f_996_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3742),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3742),U_3743),U_3744)),U_3744)),c_Divides_Odiv__class_Omod(U_3742,U_3743,U_3744))),U_3745) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3742),U_3743),U_3745)
    | ~ class_Divides_Osemiring__div(U_3742) ),
    inference(clausify,[status(thm)],[f_996_3]) ).

fof(f_997_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_997_2,plain,
    ! [U_3749,U_3748,U_3747,U_3746] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3746),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3746),U_3747),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3746),U_3748),U_3747))),c_Divides_Odiv__class_Omod(U_3746,U_3748,U_3747))),U_3749) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3746),U_3748),U_3749)
      | ~ class_Divides_Osemiring__div(U_3746) ),
    inference(variable_rename,[status(thm)],[f_997_1]) ).

fof(f_997_3,plain,
    ! [U_3746,U_3747,U_3748,U_3749] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3746),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3746),U_3747),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3746),U_3748),U_3747))),c_Divides_Odiv__class_Omod(U_3746,U_3748,U_3747))),U_3749) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3746),U_3748),U_3749)
      | ~ class_Divides_Osemiring__div(U_3746) ),
    inference(definitional_conversion,[status(esa)],[f_997_2]) ).

cnf(f_997_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3746),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3746),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3746),U_3747),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3746),U_3748),U_3747))),c_Divides_Odiv__class_Omod(U_3746,U_3748,U_3747))),U_3749) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3746),U_3748),U_3749)
    | ~ class_Divides_Osemiring__div(U_3746) ),
    inference(clausify,[status(thm)],[f_997_3]) ).

fof(f_998_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_998_2,plain,
    ! [U_3752,U_3751,U_3750] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3750),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3750),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3750),U_3751),U_3752)),U_3752)),c_Divides_Odiv__class_Omod(U_3750,U_3751,U_3752)) = U_3751
      | ~ class_Divides_Osemiring__div(U_3750) ),
    inference(variable_rename,[status(thm)],[f_998_1]) ).

fof(f_998_3,plain,
    ! [U_3750,U_3751,U_3752] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3750),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3750),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3750),U_3751),U_3752)),U_3752)),c_Divides_Odiv__class_Omod(U_3750,U_3751,U_3752)) = U_3751
      | ~ class_Divides_Osemiring__div(U_3750) ),
    inference(definitional_conversion,[status(esa)],[f_998_2]) ).

cnf(f_998_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3750),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3750),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3750),U_3751),U_3752)),U_3752)),c_Divides_Odiv__class_Omod(U_3750,U_3751,U_3752)) = U_3751
    | ~ class_Divides_Osemiring__div(U_3750) ),
    inference(clausify,[status(thm)],[f_998_3]) ).

fof(f_999_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_999_2,plain,
    ! [U_3755,U_3754,U_3753] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3753),U_3754),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3753),U_3755),U_3754))),c_Divides_Odiv__class_Omod(U_3753,U_3755,U_3754)) = U_3755
      | ~ class_Divides_Osemiring__div(U_3753) ),
    inference(variable_rename,[status(thm)],[f_999_1]) ).

fof(f_999_3,plain,
    ! [U_3753,U_3754,U_3755] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3753),U_3754),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3753),U_3755),U_3754))),c_Divides_Odiv__class_Omod(U_3753,U_3755,U_3754)) = U_3755
      | ~ class_Divides_Osemiring__div(U_3753) ),
    inference(definitional_conversion,[status(esa)],[f_999_2]) ).

cnf(f_999_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3753),U_3754),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3753),U_3755),U_3754))),c_Divides_Odiv__class_Omod(U_3753,U_3755,U_3754)) = U_3755
    | ~ class_Divides_Osemiring__div(U_3753) ),
    inference(clausify,[status(thm)],[f_999_3]) ).

fof(f_1000_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_1000_2,plain,
    ! [U_3758,U_3757,U_3756] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3756),c_Divides_Odiv__class_Omod(U_3756,U_3757,U_3758)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3756),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3756),U_3757),U_3758)),U_3758)) = U_3757
      | ~ class_Divides_Osemiring__div(U_3756) ),
    inference(variable_rename,[status(thm)],[f_1000_1]) ).

fof(f_1000_3,plain,
    ! [U_3756,U_3757,U_3758] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3756),c_Divides_Odiv__class_Omod(U_3756,U_3757,U_3758)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3756),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3756),U_3757),U_3758)),U_3758)) = U_3757
      | ~ class_Divides_Osemiring__div(U_3756) ),
    inference(definitional_conversion,[status(esa)],[f_1000_2]) ).

cnf(f_1000_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3756),c_Divides_Odiv__class_Omod(U_3756,U_3757,U_3758)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3756),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3756),U_3757),U_3758)),U_3758)) = U_3757
    | ~ class_Divides_Osemiring__div(U_3756) ),
    inference(clausify,[status(thm)],[f_1000_3]) ).

fof(f_1001_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_1001_2,plain,
    ! [U_3765,U_3764,U_3763] :
      ( ( hBOOL(hAPP(U_3763,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3764),U_3765)))
        | ( ? [U_3762,U_3761] :
              ( ~ hBOOL(hAPP(U_3763,U_3762))
              & U_3764 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3765),U_3762)),U_3761)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3761),U_3765)) )
          & U_3765 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3765 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [U_3760,U_3759] :
                ( hBOOL(hAPP(U_3763,U_3760))
                | U_3764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3765),U_3760)),U_3759)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3759),U_3765)) )
            | U_3765 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3763,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3765 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3763,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3764),U_3765))) ) ),
    inference(variable_rename,[status(thm)],[f_1001_1]) ).

fof(f_1001_3,plain,
    ( ! [U_3771,U_3769,U_3767] :
        ( hBOOL(hAPP(U_3767,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3769),U_3771)))
        | ( ? [U_3762,U_3761] :
              ( ~ hBOOL(hAPP(U_3767,U_3762))
              & U_3769 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3771),U_3762)),U_3761)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3761),U_3771)) )
          & U_3771 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3767,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3770,U_3768,U_3766] :
        ( ( ( ! [U_3760,U_3759] :
                ( hBOOL(hAPP(U_3766,U_3760))
                | U_3768 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3770),U_3760)),U_3759)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3759),U_3770)) )
            | U_3770 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3766,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3770 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3766,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3768),U_3770))) ) ),
    inference(miniscope,[status(thm)],[f_1001_2]) ).

fof(f_1001_4,plain,
    ( ! [U_3771,U_3769,U_3767] :
        ( hBOOL(hAPP(U_3767,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3769),U_3771)))
        | ( ? [U_3761] :
              ( ~ hBOOL(hAPP(U_3767,sK78(U_3771,U_3769,U_3767)))
              & U_3769 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3771),sK78(U_3771,U_3769,U_3767))),U_3761)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3761),U_3771)) )
          & U_3771 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3767,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3770,U_3768,U_3766] :
        ( ( ( ! [U_3760,U_3759] :
                ( hBOOL(hAPP(U_3766,U_3760))
                | U_3768 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3770),U_3760)),U_3759)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3759),U_3770)) )
            | U_3770 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3766,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3770 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3766,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3768),U_3770))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_3762,sK78(U_3771,U_3769,U_3767))],[f_1001_3]) ).

fof(f_1001_5,plain,
    ( ! [U_3771,U_3769,U_3767] :
        ( hBOOL(hAPP(U_3767,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3769),U_3771)))
        | ( ~ hBOOL(hAPP(U_3767,sK78(U_3771,U_3769,U_3767)))
          & U_3769 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3771),sK78(U_3771,U_3769,U_3767))),sK79(U_3771,U_3769,U_3767))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK79(U_3771,U_3769,U_3767)),U_3771))
          & U_3771 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3767,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3770,U_3768,U_3766] :
        ( ( ( ! [U_3760,U_3759] :
                ( hBOOL(hAPP(U_3766,U_3760))
                | U_3768 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3770),U_3760)),U_3759)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3759),U_3770)) )
            | U_3770 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3766,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3770 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3766,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3768),U_3770))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_3761,sK79(U_3771,U_3769,U_3767))],[f_1001_4]) ).

fof(f_1001_6,plain,
    ( ! [U_3769,U_3771,U_3767] :
        ( ~ hBOOL(hAPP(U_3767,sK78(U_3771,U_3769,U_3767)))
        | ~ sP289(U_3769,U_3771,U_3767) )
    & ! [U_3769,U_3771,U_3767] :
        ( U_3769 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3771),sK78(U_3771,U_3769,U_3767))),sK79(U_3771,U_3769,U_3767))
        | ~ sP289(U_3769,U_3771,U_3767) )
    & ! [U_3769,U_3771,U_3767] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK79(U_3771,U_3769,U_3767)),U_3771))
        | ~ sP289(U_3769,U_3771,U_3767) )
    & ! [U_3769,U_3771,U_3767] :
        ( U_3771 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP289(U_3769,U_3771,U_3767) )
    & ! [U_3771,U_3767] :
        ( ~ hBOOL(hAPP(U_3767,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP288(U_3771,U_3767) )
    & ! [U_3771,U_3767] :
        ( U_3771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP288(U_3771,U_3767) )
    & ! [U_3766,U_3770,U_3768,U_3760,U_3759] :
        ( hBOOL(hAPP(U_3766,U_3760))
        | U_3768 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3770),U_3760)),U_3759)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3759),U_3770))
        | U_3770 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP287(U_3766,U_3770,U_3768,U_3760,U_3759) )
    & ! [U_3766,U_3770,U_3768,U_3760,U_3759] :
        ( hBOOL(hAPP(U_3766,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_3770 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP287(U_3766,U_3770,U_3768,U_3760,U_3759) )
    & ! [U_3769,U_3771,U_3767] :
        ( hBOOL(hAPP(U_3767,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3769),U_3771)))
        | sP289(U_3769,U_3771,U_3767)
        | sP288(U_3771,U_3767) )
    & ! [U_3766,U_3770,U_3768,U_3760,U_3759] :
        ( sP287(U_3766,U_3770,U_3768,U_3760,U_3759)
        | ~ hBOOL(hAPP(U_3766,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3768),U_3770))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP287,sP288,sP289])],[f_1001_5]) ).

cnf(f_1001_7,plain,
    ( sP287(U_3766,U_3770,U_3768,U_3760,U_3759)
    | ~ hBOOL(hAPP(U_3766,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3768),U_3770))) ),
    inference(clausify,[status(thm)],[f_1001_6]) ).

cnf(f_1001_8,plain,
    ( hBOOL(hAPP(U_3767,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3769),U_3771)))
    | sP289(U_3769,U_3771,U_3767)
    | sP288(U_3771,U_3767) ),
    inference(clausify,[status(thm)],[f_1001_6]) ).

cnf(f_1001_9,plain,
    ( hBOOL(hAPP(U_3766,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_3770 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP287(U_3766,U_3770,U_3768,U_3760,U_3759) ),
    inference(clausify,[status(thm)],[f_1001_6]) ).

cnf(f_1001_10,plain,
    ( hBOOL(hAPP(U_3766,U_3760))
    | U_3768 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3770),U_3760)),U_3759)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3759),U_3770))
    | U_3770 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP287(U_3766,U_3770,U_3768,U_3760,U_3759) ),
    inference(clausify,[status(thm)],[f_1001_6]) ).

cnf(f_1001_11,plain,
    ( U_3771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP288(U_3771,U_3767) ),
    inference(clausify,[status(thm)],[f_1001_6]) ).

cnf(f_1001_12,plain,
    ( ~ hBOOL(hAPP(U_3767,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP288(U_3771,U_3767) ),
    inference(clausify,[status(thm)],[f_1001_6]) ).

cnf(f_1001_13,plain,
    ( U_3771 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP289(U_3769,U_3771,U_3767) ),
    inference(clausify,[status(thm)],[f_1001_6]) ).

cnf(f_1001_14,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK79(U_3771,U_3769,U_3767)),U_3771))
    | ~ sP289(U_3769,U_3771,U_3767) ),
    inference(clausify,[status(thm)],[f_1001_6]) ).

cnf(f_1001_15,plain,
    ( U_3769 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3771),sK78(U_3771,U_3769,U_3767))),sK79(U_3771,U_3769,U_3767))
    | ~ sP289(U_3769,U_3771,U_3767) ),
    inference(clausify,[status(thm)],[f_1001_6]) ).

cnf(f_1001_16,plain,
    ( ~ hBOOL(hAPP(U_3767,sK78(U_3771,U_3769,U_3767)))
    | ~ sP289(U_3769,U_3771,U_3767) ),
    inference(clausify,[status(thm)],[f_1001_6]) ).

fof(f_1002_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_1002_2,plain,
    ! [U_3775,U_3774,U_3773,U_3772] :
      ( 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_3774),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3775,U_3772))),U_3773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3774),U_3772)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3773),U_3774))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3772)) ),
    inference(variable_rename,[status(thm)],[f_1002_1]) ).

fof(f_1002_3,plain,
    ! [U_3774,U_3775,U_3772,U_3773] :
      ( 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_3774),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3775,U_3772))),U_3773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3774),U_3772)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3773),U_3774))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3772)) ),
    inference(definitional_conversion,[status(esa)],[f_1002_2]) ).

cnf(f_1002_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_3774),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3775,U_3772))),U_3773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3774),U_3772)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3773),U_3774))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3772)) ),
    inference(clausify,[status(thm)],[f_1002_3]) ).

fof(f_1003_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_1003_2,plain,
    ! [U_3782,U_3781,U_3780] :
      ( ( hBOOL(hAPP(U_3780,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3781,U_3782)))
        | ( ? [U_3779,U_3778] :
              ( ~ hBOOL(hAPP(U_3780,U_3778))
              & U_3781 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3782),U_3779)),U_3778)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3778),U_3782)) )
          & U_3782 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3780,U_3781))
          & U_3782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [U_3777,U_3776] :
                ( hBOOL(hAPP(U_3780,U_3776))
                | U_3781 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3782),U_3777)),U_3776)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3776),U_3782)) )
            | U_3782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3780,U_3781))
            | U_3782 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3780,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3781,U_3782))) ) ),
    inference(variable_rename,[status(thm)],[f_1003_1]) ).

fof(f_1003_3,plain,
    ( ! [U_3788,U_3786,U_3784] :
        ( hBOOL(hAPP(U_3784,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3786,U_3788)))
        | ( ? [U_3779,U_3778] :
              ( ~ hBOOL(hAPP(U_3784,U_3778))
              & U_3786 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3788),U_3779)),U_3778)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3778),U_3788)) )
          & U_3788 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3784,U_3786))
          & U_3788 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3787,U_3785,U_3783] :
        ( ( ( ! [U_3777,U_3776] :
                ( hBOOL(hAPP(U_3783,U_3776))
                | U_3785 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3787),U_3777)),U_3776)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3776),U_3787)) )
            | U_3787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3783,U_3785))
            | U_3787 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3783,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3785,U_3787))) ) ),
    inference(miniscope,[status(thm)],[f_1003_2]) ).

fof(f_1003_4,plain,
    ( ! [U_3788,U_3786,U_3784] :
        ( hBOOL(hAPP(U_3784,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3786,U_3788)))
        | ( ? [U_3778] :
              ( ~ hBOOL(hAPP(U_3784,U_3778))
              & U_3786 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3788),sK80(U_3788,U_3786,U_3784))),U_3778)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3778),U_3788)) )
          & U_3788 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3784,U_3786))
          & U_3788 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3787,U_3785,U_3783] :
        ( ( ( ! [U_3777,U_3776] :
                ( hBOOL(hAPP(U_3783,U_3776))
                | U_3785 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3787),U_3777)),U_3776)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3776),U_3787)) )
            | U_3787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3783,U_3785))
            | U_3787 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3783,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3785,U_3787))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_3779,sK80(U_3788,U_3786,U_3784))],[f_1003_3]) ).

fof(f_1003_5,plain,
    ( ! [U_3788,U_3786,U_3784] :
        ( hBOOL(hAPP(U_3784,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3786,U_3788)))
        | ( ~ hBOOL(hAPP(U_3784,sK81(U_3788,U_3786,U_3784)))
          & U_3786 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3788),sK80(U_3788,U_3786,U_3784))),sK81(U_3788,U_3786,U_3784))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK81(U_3788,U_3786,U_3784)),U_3788))
          & U_3788 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3784,U_3786))
          & U_3788 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3787,U_3785,U_3783] :
        ( ( ( ! [U_3777,U_3776] :
                ( hBOOL(hAPP(U_3783,U_3776))
                | U_3785 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3787),U_3777)),U_3776)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3776),U_3787)) )
            | U_3787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3783,U_3785))
            | U_3787 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3783,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3785,U_3787))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_3778,sK81(U_3788,U_3786,U_3784))],[f_1003_4]) ).

fof(f_1003_6,plain,
    ( ! [U_3788,U_3784,U_3786] :
        ( ~ hBOOL(hAPP(U_3784,sK81(U_3788,U_3786,U_3784)))
        | ~ sP292(U_3788,U_3784,U_3786) )
    & ! [U_3788,U_3784,U_3786] :
        ( U_3786 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3788),sK80(U_3788,U_3786,U_3784))),sK81(U_3788,U_3786,U_3784))
        | ~ sP292(U_3788,U_3784,U_3786) )
    & ! [U_3788,U_3784,U_3786] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK81(U_3788,U_3786,U_3784)),U_3788))
        | ~ sP292(U_3788,U_3784,U_3786) )
    & ! [U_3788,U_3784,U_3786] :
        ( U_3788 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP292(U_3788,U_3784,U_3786) )
    & ! [U_3788,U_3784,U_3786] :
        ( ~ hBOOL(hAPP(U_3784,U_3786))
        | ~ sP291(U_3788,U_3784,U_3786) )
    & ! [U_3788,U_3784,U_3786] :
        ( U_3788 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP291(U_3788,U_3784,U_3786) )
    & ! [U_3787,U_3776,U_3777,U_3783,U_3785] :
        ( hBOOL(hAPP(U_3783,U_3776))
        | U_3785 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3787),U_3777)),U_3776)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3776),U_3787))
        | U_3787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP290(U_3787,U_3776,U_3777,U_3783,U_3785) )
    & ! [U_3787,U_3776,U_3777,U_3783,U_3785] :
        ( hBOOL(hAPP(U_3783,U_3785))
        | U_3787 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP290(U_3787,U_3776,U_3777,U_3783,U_3785) )
    & ! [U_3788,U_3784,U_3786] :
        ( hBOOL(hAPP(U_3784,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3786,U_3788)))
        | sP292(U_3788,U_3784,U_3786)
        | sP291(U_3788,U_3784,U_3786) )
    & ! [U_3787,U_3776,U_3777,U_3783,U_3785] :
        ( sP290(U_3787,U_3776,U_3777,U_3783,U_3785)
        | ~ hBOOL(hAPP(U_3783,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3785,U_3787))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP290,sP291,sP292])],[f_1003_5]) ).

cnf(f_1003_7,plain,
    ( sP290(U_3787,U_3776,U_3777,U_3783,U_3785)
    | ~ hBOOL(hAPP(U_3783,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3785,U_3787))) ),
    inference(clausify,[status(thm)],[f_1003_6]) ).

cnf(f_1003_8,plain,
    ( hBOOL(hAPP(U_3784,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3786,U_3788)))
    | sP292(U_3788,U_3784,U_3786)
    | sP291(U_3788,U_3784,U_3786) ),
    inference(clausify,[status(thm)],[f_1003_6]) ).

cnf(f_1003_9,plain,
    ( hBOOL(hAPP(U_3783,U_3785))
    | U_3787 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP290(U_3787,U_3776,U_3777,U_3783,U_3785) ),
    inference(clausify,[status(thm)],[f_1003_6]) ).

cnf(f_1003_10,plain,
    ( hBOOL(hAPP(U_3783,U_3776))
    | U_3785 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3787),U_3777)),U_3776)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3776),U_3787))
    | U_3787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP290(U_3787,U_3776,U_3777,U_3783,U_3785) ),
    inference(clausify,[status(thm)],[f_1003_6]) ).

cnf(f_1003_11,plain,
    ( U_3788 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP291(U_3788,U_3784,U_3786) ),
    inference(clausify,[status(thm)],[f_1003_6]) ).

cnf(f_1003_12,plain,
    ( ~ hBOOL(hAPP(U_3784,U_3786))
    | ~ sP291(U_3788,U_3784,U_3786) ),
    inference(clausify,[status(thm)],[f_1003_6]) ).

cnf(f_1003_13,plain,
    ( U_3788 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP292(U_3788,U_3784,U_3786) ),
    inference(clausify,[status(thm)],[f_1003_6]) ).

cnf(f_1003_14,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK81(U_3788,U_3786,U_3784)),U_3788))
    | ~ sP292(U_3788,U_3784,U_3786) ),
    inference(clausify,[status(thm)],[f_1003_6]) ).

cnf(f_1003_15,plain,
    ( U_3786 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3788),sK80(U_3788,U_3786,U_3784))),sK81(U_3788,U_3786,U_3784))
    | ~ sP292(U_3788,U_3784,U_3786) ),
    inference(clausify,[status(thm)],[f_1003_6]) ).

cnf(f_1003_16,plain,
    ( ~ hBOOL(hAPP(U_3784,sK81(U_3788,U_3786,U_3784)))
    | ~ sP292(U_3788,U_3784,U_3786) ),
    inference(clausify,[status(thm)],[f_1003_6]) ).

fof(f_1004_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_1004_2,plain,
    ! [U_3790,U_3789] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3789),U_3790)),U_3789) = 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_3789)) ),
    inference(variable_rename,[status(thm)],[f_1004_1]) ).

fof(f_1004_3,plain,
    ! [U_3790,U_3789] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3789),U_3790)),U_3789) = 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_3789)) ),
    inference(definitional_conversion,[status(esa)],[f_1004_2]) ).

cnf(f_1004_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_3789),U_3790)),U_3789) = 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_3789)) ),
    inference(clausify,[status(thm)],[f_1004_3]) ).

fof(f_1005_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_1005_2,plain,
    ! [U_3792,U_3791] :
      ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3791,U_3792)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3791),hAPP(c_Int_Onat,U_3792))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3792))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3791)) ),
    inference(variable_rename,[status(thm)],[f_1005_1]) ).

fof(f_1005_3,plain,
    ! [U_3791,U_3792] :
      ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3791,U_3792)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3791),hAPP(c_Int_Onat,U_3792))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3792))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3791)) ),
    inference(definitional_conversion,[status(esa)],[f_1005_2]) ).

cnf(f_1005_4,plain,
    ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3791,U_3792)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3791),hAPP(c_Int_Onat,U_3792))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3792))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3791)) ),
    inference(clausify,[status(thm)],[f_1005_3]) ).

fof(f_1006_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_1006_2,plain,
    ! [U_3794,U_3793] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3793),hAPP(c_Int_Onat,U_3794)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3793,U_3794))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3794))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3793)) ),
    inference(variable_rename,[status(thm)],[f_1006_1]) ).

fof(f_1006_3,plain,
    ! [U_3793,U_3794] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3793),hAPP(c_Int_Onat,U_3794)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3793,U_3794))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3794))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3793)) ),
    inference(definitional_conversion,[status(esa)],[f_1006_2]) ).

cnf(f_1006_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3793),hAPP(c_Int_Onat,U_3794)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3793,U_3794))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3794))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3793)) ),
    inference(clausify,[status(thm)],[f_1006_3]) ).

fof(f_1007_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_1007_2,plain,
    ! [U_3797,U_3796,U_3795] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3795),hAPP(c_Nat_OSuc,U_3796))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3795),U_3796)),U_3797)) )
          | U_3796 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3797),U_3795) )
        & ( U_3796 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3797),U_3795)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3795),hAPP(c_Nat_OSuc,U_3796))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3795),U_3796)),U_3797)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3795)) ),
    inference(variable_rename,[status(thm)],[f_1007_1]) ).

fof(f_1007_3,plain,
    ( ! [U_3797,U_3796,U_3795] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3795),hAPP(c_Nat_OSuc,U_3796))))
        | ~ sP293(U_3797,U_3796,U_3795) )
    & ! [U_3797,U_3796,U_3795] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3795),U_3796)),U_3797))
        | ~ sP293(U_3797,U_3796,U_3795) )
    & ! [U_3797,U_3796,U_3795] :
        ( sP293(U_3797,U_3796,U_3795)
        | U_3796 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3797),U_3795)
        | ~ sP294(U_3797,U_3796,U_3795) )
    & ! [U_3797,U_3796,U_3795] :
        ( U_3796 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3797),U_3795)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3795),hAPP(c_Nat_OSuc,U_3796))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3795),U_3796)),U_3797))
        | ~ sP294(U_3797,U_3796,U_3795) )
    & ! [U_3797,U_3796,U_3795] :
        ( sP294(U_3797,U_3796,U_3795)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3795)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP293,sP294])],[f_1007_2]) ).

cnf(f_1007_4,plain,
    ( sP294(U_3797,U_3796,U_3795)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3795)) ),
    inference(clausify,[status(thm)],[f_1007_3]) ).

cnf(f_1007_5,plain,
    ( U_3796 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3797),U_3795)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3795),hAPP(c_Nat_OSuc,U_3796))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3795),U_3796)),U_3797))
    | ~ sP294(U_3797,U_3796,U_3795) ),
    inference(clausify,[status(thm)],[f_1007_3]) ).

cnf(f_1007_6,plain,
    ( sP293(U_3797,U_3796,U_3795)
    | U_3796 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3797),U_3795)
    | ~ sP294(U_3797,U_3796,U_3795) ),
    inference(clausify,[status(thm)],[f_1007_3]) ).

cnf(f_1007_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_3795),U_3796)),U_3797))
    | ~ sP293(U_3797,U_3796,U_3795) ),
    inference(clausify,[status(thm)],[f_1007_3]) ).

cnf(f_1007_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3795),hAPP(c_Nat_OSuc,U_3796))))
    | ~ sP293(U_3797,U_3796,U_3795) ),
    inference(clausify,[status(thm)],[f_1007_3]) ).

fof(f_1008_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_1008_2,plain,
    ! [U_3799,U_3798] :
      ( ( c_SMT_Oz3div(U_3799,U_3798) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3799),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3798)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3798)) )
      & ( c_SMT_Oz3div(U_3799,U_3798) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3799),U_3798)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3798)) ) ),
    inference(variable_rename,[status(thm)],[f_1008_1]) ).

fof(f_1008_3,plain,
    ( ! [U_3803,U_3801] :
        ( c_SMT_Oz3div(U_3803,U_3801) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3803),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3801)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3801)) )
    & ! [U_3802,U_3800] :
        ( c_SMT_Oz3div(U_3802,U_3800) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3802),U_3800)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3800)) ) ),
    inference(miniscope,[status(thm)],[f_1008_2]) ).

fof(f_1008_4,plain,
    ( ! [U_3801,U_3803] :
        ( c_SMT_Oz3div(U_3803,U_3801) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3803),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3801)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3801)) )
    & ! [U_3802,U_3800] :
        ( c_SMT_Oz3div(U_3802,U_3800) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3802),U_3800)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3800)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1008_3]) ).

cnf(f_1008_5,plain,
    ( c_SMT_Oz3div(U_3802,U_3800) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3802),U_3800)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3800)) ),
    inference(clausify,[status(thm)],[f_1008_4]) ).

cnf(f_1008_6,plain,
    ( c_SMT_Oz3div(U_3803,U_3801) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3803),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3801)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3801)) ),
    inference(clausify,[status(thm)],[f_1008_4]) ).

fof(f_1009_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_1009_2,plain,
    ! [U_3805,U_3804] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3805),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3804)) = 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_3805),U_3804))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3805,U_3804) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3805),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3804)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3805),U_3804))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3805,U_3804) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | U_3804 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1009_1]) ).

fof(f_1009_3,plain,
    ( ! [U_3804,U_3805] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3805),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3804)) = 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_3805),U_3804))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3805,U_3804) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP295(U_3804,U_3805) )
    & ! [U_3804,U_3805] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3805),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3804)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3805),U_3804))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3805,U_3804) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP295(U_3804,U_3805) )
    & ! [U_3804,U_3805] :
        ( sP295(U_3804,U_3805)
        | U_3804 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP295])],[f_1009_2]) ).

cnf(f_1009_4,plain,
    ( sP295(U_3804,U_3805)
    | U_3804 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1009_3]) ).

cnf(f_1009_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3805),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3804)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3805),U_3804))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3805,U_3804) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP295(U_3804,U_3805) ),
    inference(clausify,[status(thm)],[f_1009_3]) ).

cnf(f_1009_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3805),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3804)) = 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_3805),U_3804))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3805,U_3804) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP295(U_3804,U_3805) ),
    inference(clausify,[status(thm)],[f_1009_3]) ).

fof(f_1010_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_1010_2,plain,
    ! [U_3807,U_3806] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3807)),U_3806) = 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_3807),U_3806))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3807,U_3806) = 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_3807)),U_3806) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3807),U_3806))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3807,U_3806) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | U_3806 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1010_1]) ).

fof(f_1010_3,plain,
    ( ! [U_3807,U_3806] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3807)),U_3806) = 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_3807),U_3806))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3807,U_3806) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP296(U_3807,U_3806) )
    & ! [U_3807,U_3806] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3807)),U_3806) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3807),U_3806))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3807,U_3806) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP296(U_3807,U_3806) )
    & ! [U_3807,U_3806] :
        ( sP296(U_3807,U_3806)
        | U_3806 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP296])],[f_1010_2]) ).

cnf(f_1010_4,plain,
    ( sP296(U_3807,U_3806)
    | U_3806 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1010_3]) ).

cnf(f_1010_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3807)),U_3806) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3807),U_3806))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3807,U_3806) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP296(U_3807,U_3806) ),
    inference(clausify,[status(thm)],[f_1010_3]) ).

cnf(f_1010_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3807)),U_3806) = 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_3807),U_3806))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3807,U_3806) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP296(U_3807,U_3806) ),
    inference(clausify,[status(thm)],[f_1010_3]) ).

fof(f_1011_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_1011_2,plain,
    ! [U_3809,U_3808] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3809),U_3808) = 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_3809),U_3808)),U_3808))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3808),U_3809))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3808)) ),
    inference(variable_rename,[status(thm)],[f_1011_1]) ).

fof(f_1011_3,plain,
    ! [U_3809,U_3808] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3809),U_3808) = 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_3809),U_3808)),U_3808))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3808),U_3809))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3808)) ),
    inference(definitional_conversion,[status(esa)],[f_1011_2]) ).

cnf(f_1011_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3809),U_3808) = 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_3809),U_3808)),U_3808))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3808),U_3809))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3808)) ),
    inference(clausify,[status(thm)],[f_1011_3]) ).

fof(f_1012_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_1012_2,plain,
    ! [U_3812,U_3811,U_3810] :
      ( U_3811 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3810),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3810),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3810),U_3811),U_3812)),U_3812)),c_Divides_Odiv__class_Omod(U_3810,U_3811,U_3812))
      | ~ class_Divides_Osemiring__div(U_3810) ),
    inference(variable_rename,[status(thm)],[f_1012_1]) ).

fof(f_1012_3,plain,
    ! [U_3810,U_3811,U_3812] :
      ( U_3811 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3810),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3810),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3810),U_3811),U_3812)),U_3812)),c_Divides_Odiv__class_Omod(U_3810,U_3811,U_3812))
      | ~ class_Divides_Osemiring__div(U_3810) ),
    inference(definitional_conversion,[status(esa)],[f_1012_2]) ).

cnf(f_1012_4,plain,
    ( U_3811 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3810),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3810),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3810),U_3811),U_3812)),U_3812)),c_Divides_Odiv__class_Omod(U_3810,U_3811,U_3812))
    | ~ class_Divides_Osemiring__div(U_3810) ),
    inference(clausify,[status(thm)],[f_1012_3]) ).

fof(f_1013_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_1013_2,plain,
    ! [U_3814,U_3813] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3813)),hAPP(c_Int_Onat,U_3814)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_3813,U_3814))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3814))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3813)) ),
    inference(variable_rename,[status(thm)],[f_1013_1]) ).

fof(f_1013_3,plain,
    ! [U_3813,U_3814] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3813)),hAPP(c_Int_Onat,U_3814)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_3813,U_3814))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3814))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3813)) ),
    inference(definitional_conversion,[status(esa)],[f_1013_2]) ).

cnf(f_1013_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3813)),hAPP(c_Int_Onat,U_3814)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_3813,U_3814))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3814))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3813)) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

fof(f_1014_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_1014_2,plain,
    ! [U_3819,U_3818,U_3817] :
      ( ! [U_3816] :
          ( hBOOL(hAPP(U_3818,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3816),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3819),U_3817))))
          | ~ hBOOL(hAPP(U_3818,U_3816)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3819))
      | ? [U_3815] :
          ( ~ hBOOL(hAPP(U_3818,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3815),U_3817)))
          & hBOOL(hAPP(U_3818,U_3815)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3817)) ),
    inference(variable_rename,[status(thm)],[f_1014_1]) ).

fof(f_1014_3,plain,
    ! [U_3819,U_3818,U_3817] :
      ( ! [U_3816] :
          ( hBOOL(hAPP(U_3818,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3816),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3819),U_3817))))
          | ~ hBOOL(hAPP(U_3818,U_3816)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3819))
      | ( ~ hBOOL(hAPP(U_3818,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK82(U_3819,U_3818,U_3817)),U_3817)))
        & hBOOL(hAPP(U_3818,sK82(U_3819,U_3818,U_3817))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3817)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_3815,sK82(U_3819,U_3818,U_3817))],[f_1014_2]) ).

fof(f_1014_4,plain,
    ( ! [U_3817,U_3818,U_3819] :
        ( ~ hBOOL(hAPP(U_3818,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK82(U_3819,U_3818,U_3817)),U_3817)))
        | ~ sP297(U_3817,U_3818,U_3819) )
    & ! [U_3817,U_3818,U_3819] :
        ( hBOOL(hAPP(U_3818,sK82(U_3819,U_3818,U_3817)))
        | ~ sP297(U_3817,U_3818,U_3819) )
    & ! [U_3816,U_3817,U_3818,U_3819] :
        ( hBOOL(hAPP(U_3818,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3816),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3819),U_3817))))
        | ~ hBOOL(hAPP(U_3818,U_3816))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3819))
        | sP297(U_3817,U_3818,U_3819)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3817)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP297])],[f_1014_3]) ).

cnf(f_1014_5,plain,
    ( hBOOL(hAPP(U_3818,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3816),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3819),U_3817))))
    | ~ hBOOL(hAPP(U_3818,U_3816))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3819))
    | sP297(U_3817,U_3818,U_3819)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3817)) ),
    inference(clausify,[status(thm)],[f_1014_4]) ).

cnf(f_1014_6,plain,
    ( hBOOL(hAPP(U_3818,sK82(U_3819,U_3818,U_3817)))
    | ~ sP297(U_3817,U_3818,U_3819) ),
    inference(clausify,[status(thm)],[f_1014_4]) ).

cnf(f_1014_7,plain,
    ( ~ hBOOL(hAPP(U_3818,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK82(U_3819,U_3818,U_3817)),U_3817)))
    | ~ sP297(U_3817,U_3818,U_3819) ),
    inference(clausify,[status(thm)],[f_1014_4]) ).

fof(f_1015_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_1015_2,plain,
    ! [U_3823,U_3822,U_3821] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3821),U_3822),U_3823))
      | ? [U_3820] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3821),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3821),U_3820),U_3822)),U_3823))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3821),U_3820),c_Groups_Oone__class_Oone(U_3821)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3821),c_Groups_Ozero__class_Ozero(U_3821)),U_3820)) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_3821) ),
    inference(variable_rename,[status(thm)],[f_1015_1]) ).

fof(f_1015_3,plain,
    ! [U_3823,U_3822,U_3821] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3821),U_3822),U_3823))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3821),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3821),sK83(U_3823,U_3822,U_3821)),U_3822)),U_3823))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3821),sK83(U_3823,U_3822,U_3821)),c_Groups_Oone__class_Oone(U_3821)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3821),c_Groups_Ozero__class_Ozero(U_3821)),sK83(U_3823,U_3822,U_3821))) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_3821) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_3820,sK83(U_3823,U_3822,U_3821))],[f_1015_2]) ).

fof(f_1015_4,plain,
    ( ! [U_3821,U_3822,U_3823] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3821),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3821),sK83(U_3823,U_3822,U_3821)),U_3822)),U_3823))
        | ~ sP298(U_3821,U_3822,U_3823) )
    & ! [U_3821,U_3822,U_3823] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3821),sK83(U_3823,U_3822,U_3821)),c_Groups_Oone__class_Oone(U_3821)))
        | ~ sP298(U_3821,U_3822,U_3823) )
    & ! [U_3821,U_3822,U_3823] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3821),c_Groups_Ozero__class_Ozero(U_3821)),sK83(U_3823,U_3822,U_3821)))
        | ~ sP298(U_3821,U_3822,U_3823) )
    & ! [U_3821,U_3822,U_3823] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3821),U_3822),U_3823))
        | sP298(U_3821,U_3822,U_3823)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_3821) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP298])],[f_1015_3]) ).

cnf(f_1015_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3821),U_3822),U_3823))
    | sP298(U_3821,U_3822,U_3823)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_3821) ),
    inference(clausify,[status(thm)],[f_1015_4]) ).

cnf(f_1015_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3821),c_Groups_Ozero__class_Ozero(U_3821)),sK83(U_3823,U_3822,U_3821)))
    | ~ sP298(U_3821,U_3822,U_3823) ),
    inference(clausify,[status(thm)],[f_1015_4]) ).

cnf(f_1015_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3821),sK83(U_3823,U_3822,U_3821)),c_Groups_Oone__class_Oone(U_3821)))
    | ~ sP298(U_3821,U_3822,U_3823) ),
    inference(clausify,[status(thm)],[f_1015_4]) ).

cnf(f_1015_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3821),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3821),sK83(U_3823,U_3822,U_3821)),U_3822)),U_3823))
    | ~ sP298(U_3821,U_3822,U_3823) ),
    inference(clausify,[status(thm)],[f_1015_4]) ).

fof(f_1016_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_1016_2,plain,
    ! [U_3828,U_3827,U_3826,U_3825,U_3824] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3825,U_3824)),U_3826),U_3827),U_3828) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3824),hAPP(U_3826,U_3828)),hAPP(U_3827,U_3828))
      | ~ class_Groups_Ominus(U_3824) ),
    inference(variable_rename,[status(thm)],[f_1016_1]) ).

fof(f_1016_3,plain,
    ! [U_3826,U_3825,U_3824,U_3827,U_3828] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3825,U_3824)),U_3826),U_3827),U_3828) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3824),hAPP(U_3826,U_3828)),hAPP(U_3827,U_3828))
      | ~ class_Groups_Ominus(U_3824) ),
    inference(definitional_conversion,[status(esa)],[f_1016_2]) ).

cnf(f_1016_4,plain,
    ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3825,U_3824)),U_3826),U_3827),U_3828) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3824),hAPP(U_3826,U_3828)),hAPP(U_3827,U_3828))
    | ~ class_Groups_Ominus(U_3824) ),
    inference(clausify,[status(thm)],[f_1016_3]) ).

fof(f_1017_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_1017_2,plain,
    ! [U_3831,U_3830,U_3829] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_3829),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3830),U_3831)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3829),hAPP(c_Int_Oring__1__class_Oof__int(U_3829),U_3830)),hAPP(c_Int_Oring__1__class_Oof__int(U_3829),U_3831))
      | ~ class_Rings_Oring__1(U_3829) ),
    inference(variable_rename,[status(thm)],[f_1017_1]) ).

fof(f_1017_3,plain,
    ! [U_3829,U_3830,U_3831] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_3829),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3830),U_3831)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3829),hAPP(c_Int_Oring__1__class_Oof__int(U_3829),U_3830)),hAPP(c_Int_Oring__1__class_Oof__int(U_3829),U_3831))
      | ~ class_Rings_Oring__1(U_3829) ),
    inference(definitional_conversion,[status(esa)],[f_1017_2]) ).

cnf(f_1017_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_3829),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3830),U_3831)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3829),hAPP(c_Int_Oring__1__class_Oof__int(U_3829),U_3830)),hAPP(c_Int_Oring__1__class_Oof__int(U_3829),U_3831))
    | ~ class_Rings_Oring__1(U_3829) ),
    inference(clausify,[status(thm)],[f_1017_3]) ).

fof(f_1018_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_1018_2,plain,
    ! [U_3836,U_3835,U_3834,U_3833,U_3832] :
      ( ( ( U_3833 = U_3834
          | U_3835 != U_3836 )
        & ( U_3835 = U_3836
          | U_3833 != U_3834 ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3832),U_3833),U_3834) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3832),U_3835),U_3836)
      | ~ class_Groups_Oab__group__add(U_3832) ),
    inference(variable_rename,[status(thm)],[f_1018_1]) ).

fof(f_1018_3,plain,
    ( ! [U_3833,U_3834,U_3835,U_3836] :
        ( U_3833 = U_3834
        | U_3835 != U_3836
        | ~ sP299(U_3833,U_3834,U_3835,U_3836) )
    & ! [U_3833,U_3834,U_3835,U_3836] :
        ( U_3835 = U_3836
        | U_3833 != U_3834
        | ~ sP299(U_3833,U_3834,U_3835,U_3836) )
    & ! [U_3832,U_3833,U_3834,U_3835,U_3836] :
        ( sP299(U_3833,U_3834,U_3835,U_3836)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3832),U_3833),U_3834) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3832),U_3835),U_3836)
        | ~ class_Groups_Oab__group__add(U_3832) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP299])],[f_1018_2]) ).

cnf(f_1018_4,plain,
    ( sP299(U_3833,U_3834,U_3835,U_3836)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3832),U_3833),U_3834) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3832),U_3835),U_3836)
    | ~ class_Groups_Oab__group__add(U_3832) ),
    inference(clausify,[status(thm)],[f_1018_3]) ).

cnf(f_1018_5,plain,
    ( U_3835 = U_3836
    | U_3833 != U_3834
    | ~ sP299(U_3833,U_3834,U_3835,U_3836) ),
    inference(clausify,[status(thm)],[f_1018_3]) ).

cnf(f_1018_6,plain,
    ( U_3833 = U_3834
    | U_3835 != U_3836
    | ~ sP299(U_3833,U_3834,U_3835,U_3836) ),
    inference(clausify,[status(thm)],[f_1018_3]) ).

fof(f_1019_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_1019_2,plain,
    ! [U_3839,U_3838,U_3837] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3837),U_3838)),U_3839) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3837),U_3839)),U_3838),
    inference(variable_rename,[status(thm)],[f_1019_1]) ).

fof(f_1019_3,plain,
    ! [U_3839,U_3838,U_3837] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3837),U_3838)),U_3839) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3837),U_3839)),U_3838),
    inference(definitional_conversion,[status(esa)],[f_1019_2]) ).

cnf(f_1019_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3837),U_3838)),U_3839) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3837),U_3839)),U_3838),
    inference(clausify,[status(thm)],[f_1019_3]) ).

fof(f_1020_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_1020_2,plain,
    ! [U_3842,U_3841,U_3840] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3840),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3842),U_3841)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3840),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3840),U_3842)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3840),U_3841))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3841),U_3842))
      | ~ class_Rings_Oring__1(U_3840) ),
    inference(variable_rename,[status(thm)],[f_1020_1]) ).

fof(f_1020_3,plain,
    ! [U_3840,U_3841,U_3842] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3840),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3842),U_3841)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3840),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3840),U_3842)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3840),U_3841))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3841),U_3842))
      | ~ class_Rings_Oring__1(U_3840) ),
    inference(definitional_conversion,[status(esa)],[f_1020_2]) ).

cnf(f_1020_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3840),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3842),U_3841)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3840),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3840),U_3842)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3840),U_3841))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3841),U_3842))
    | ~ class_Rings_Oring__1(U_3840) ),
    inference(clausify,[status(thm)],[f_1020_3]) ).

fof(f_1021_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_1021_2,plain,
    ! [U_3844,U_3843] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3844)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3843)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3844),U_3843))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3843),U_3844)) ),
    inference(variable_rename,[status(thm)],[f_1021_1]) ).

fof(f_1021_3,plain,
    ! [U_3843,U_3844] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3844)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3843)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3844),U_3843))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3843),U_3844)) ),
    inference(definitional_conversion,[status(esa)],[f_1021_2]) ).

cnf(f_1021_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3844)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3843)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3844),U_3843))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3843),U_3844)) ),
    inference(clausify,[status(thm)],[f_1021_3]) ).

fof(f_1022_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_1022_2,plain,
    ! [U_3849,U_3848,U_3847,U_3846,U_3845] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3845),U_3846),U_3847))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3845),U_3848),U_3849)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3845),U_3848),U_3849))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3845),U_3846),U_3847)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3845),U_3846),U_3847) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3845),U_3848),U_3849)
      | ~ class_Groups_Oordered__ab__group__add(U_3845) ),
    inference(variable_rename,[status(thm)],[f_1022_1]) ).

fof(f_1022_3,plain,
    ( ! [U_3845,U_3846,U_3847,U_3848,U_3849] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3845),U_3846),U_3847))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3845),U_3848),U_3849))
        | ~ sP300(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__eq(U_3845),U_3848),U_3849))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3845),U_3846),U_3847))
        | ~ sP300(U_3845,U_3846,U_3847,U_3848,U_3849) )
    & ! [U_3845,U_3846,U_3847,U_3848,U_3849] :
        ( sP300(U_3845,U_3846,U_3847,U_3848,U_3849)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3845),U_3846),U_3847) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3845),U_3848),U_3849)
        | ~ class_Groups_Oordered__ab__group__add(U_3845) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP300])],[f_1022_2]) ).

cnf(f_1022_4,plain,
    ( sP300(U_3845,U_3846,U_3847,U_3848,U_3849)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3845),U_3846),U_3847) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3845),U_3848),U_3849)
    | ~ class_Groups_Oordered__ab__group__add(U_3845) ),
    inference(clausify,[status(thm)],[f_1022_3]) ).

cnf(f_1022_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3845),U_3848),U_3849))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3845),U_3846),U_3847))
    | ~ sP300(U_3845,U_3846,U_3847,U_3848,U_3849) ),
    inference(clausify,[status(thm)],[f_1022_3]) ).

cnf(f_1022_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3845),U_3846),U_3847))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3845),U_3848),U_3849))
    | ~ sP300(U_3845,U_3846,U_3847,U_3848,U_3849) ),
    inference(clausify,[status(thm)],[f_1022_3]) ).

fof(f_1023_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_1023_2,plain,
    ! [U_3852,U_3851,U_3850] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3850),U_3851),U_3852) = c_Groups_Ozero__class_Ozero(U_3850)
          | U_3851 != U_3852 )
        & ( U_3851 = U_3852
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3850),U_3851),U_3852) != c_Groups_Ozero__class_Ozero(U_3850) ) )
      | ~ class_Groups_Ogroup__add(U_3850) ),
    inference(variable_rename,[status(thm)],[f_1023_1]) ).

fof(f_1023_3,plain,
    ( ! [U_3850,U_3851,U_3852] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3850),U_3851),U_3852) = c_Groups_Ozero__class_Ozero(U_3850)
        | U_3851 != U_3852
        | ~ sP301(U_3850,U_3851,U_3852) )
    & ! [U_3850,U_3851,U_3852] :
        ( U_3851 = U_3852
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3850),U_3851),U_3852) != c_Groups_Ozero__class_Ozero(U_3850)
        | ~ sP301(U_3850,U_3851,U_3852) )
    & ! [U_3850,U_3851,U_3852] :
        ( sP301(U_3850,U_3851,U_3852)
        | ~ class_Groups_Ogroup__add(U_3850) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP301])],[f_1023_2]) ).

cnf(f_1023_4,plain,
    ( sP301(U_3850,U_3851,U_3852)
    | ~ class_Groups_Ogroup__add(U_3850) ),
    inference(clausify,[status(thm)],[f_1023_3]) ).

cnf(f_1023_5,plain,
    ( U_3851 = U_3852
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3850),U_3851),U_3852) != c_Groups_Ozero__class_Ozero(U_3850)
    | ~ sP301(U_3850,U_3851,U_3852) ),
    inference(clausify,[status(thm)],[f_1023_3]) ).

cnf(f_1023_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3850),U_3851),U_3852) = c_Groups_Ozero__class_Ozero(U_3850)
    | U_3851 != U_3852
    | ~ sP301(U_3850,U_3851,U_3852) ),
    inference(clausify,[status(thm)],[f_1023_3]) ).

fof(f_1024_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_1024_2,plain,
    ! [U_3855,U_3854,U_3853] :
      ( ( ( U_3854 = U_3855
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3853),U_3854),U_3855) != c_Groups_Ozero__class_Ozero(U_3853) )
        & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3853),U_3854),U_3855) = c_Groups_Ozero__class_Ozero(U_3853)
          | U_3854 != U_3855 ) )
      | ~ class_Groups_Oab__group__add(U_3853) ),
    inference(variable_rename,[status(thm)],[f_1024_1]) ).

fof(f_1024_3,plain,
    ( ! [U_3854,U_3853,U_3855] :
        ( U_3854 = U_3855
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3853),U_3854),U_3855) != c_Groups_Ozero__class_Ozero(U_3853)
        | ~ sP302(U_3854,U_3853,U_3855) )
    & ! [U_3854,U_3853,U_3855] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3853),U_3854),U_3855) = c_Groups_Ozero__class_Ozero(U_3853)
        | U_3854 != U_3855
        | ~ sP302(U_3854,U_3853,U_3855) )
    & ! [U_3854,U_3853,U_3855] :
        ( sP302(U_3854,U_3853,U_3855)
        | ~ class_Groups_Oab__group__add(U_3853) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP302])],[f_1024_2]) ).

cnf(f_1024_4,plain,
    ( sP302(U_3854,U_3853,U_3855)
    | ~ class_Groups_Oab__group__add(U_3853) ),
    inference(clausify,[status(thm)],[f_1024_3]) ).

cnf(f_1024_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3853),U_3854),U_3855) = c_Groups_Ozero__class_Ozero(U_3853)
    | U_3854 != U_3855
    | ~ sP302(U_3854,U_3853,U_3855) ),
    inference(clausify,[status(thm)],[f_1024_3]) ).

cnf(f_1024_6,plain,
    ( U_3854 = U_3855
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3853),U_3854),U_3855) != c_Groups_Ozero__class_Ozero(U_3853)
    | ~ sP302(U_3854,U_3853,U_3855) ),
    inference(clausify,[status(thm)],[f_1024_3]) ).

fof(f_1025_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_1025_2,plain,
    ! [U_3857,U_3856] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3856),U_3857),U_3857) = c_Groups_Ozero__class_Ozero(U_3856)
      | ~ class_Groups_Ogroup__add(U_3856) ),
    inference(variable_rename,[status(thm)],[f_1025_1]) ).

fof(f_1025_3,plain,
    ! [U_3857,U_3856] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3856),U_3857),U_3857) = c_Groups_Ozero__class_Ozero(U_3856)
      | ~ class_Groups_Ogroup__add(U_3856) ),
    inference(definitional_conversion,[status(esa)],[f_1025_2]) ).

cnf(f_1025_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3856),U_3857),U_3857) = c_Groups_Ozero__class_Ozero(U_3856)
    | ~ class_Groups_Ogroup__add(U_3856) ),
    inference(clausify,[status(thm)],[f_1025_3]) ).

fof(f_1026_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_1026_2,plain,
    ! [U_3859,U_3858] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3858),U_3859),c_Groups_Ozero__class_Ozero(U_3858)) = U_3859
      | ~ class_Groups_Ogroup__add(U_3858) ),
    inference(variable_rename,[status(thm)],[f_1026_1]) ).

fof(f_1026_3,plain,
    ! [U_3859,U_3858] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3858),U_3859),c_Groups_Ozero__class_Ozero(U_3858)) = U_3859
      | ~ class_Groups_Ogroup__add(U_3858) ),
    inference(definitional_conversion,[status(esa)],[f_1026_2]) ).

cnf(f_1026_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3858),U_3859),c_Groups_Ozero__class_Ozero(U_3858)) = U_3859
    | ~ class_Groups_Ogroup__add(U_3858) ),
    inference(clausify,[status(thm)],[f_1026_3]) ).

fof(f_1027_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_1027_2,plain,
    ! [U_3864,U_3863,U_3862,U_3861,U_3860] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3860),U_3861),U_3862))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3860),U_3863),U_3864)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3860),U_3863),U_3864))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3860),U_3861),U_3862)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3860),U_3861),U_3862) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3860),U_3863),U_3864)
      | ~ class_Groups_Oordered__ab__group__add(U_3860) ),
    inference(variable_rename,[status(thm)],[f_1027_1]) ).

fof(f_1027_3,plain,
    ( ! [U_3861,U_3862,U_3863,U_3864,U_3860] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3860),U_3861),U_3862))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3860),U_3863),U_3864))
        | ~ sP303(U_3861,U_3862,U_3863,U_3864,U_3860) )
    & ! [U_3861,U_3862,U_3863,U_3864,U_3860] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3860),U_3863),U_3864))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3860),U_3861),U_3862))
        | ~ sP303(U_3861,U_3862,U_3863,U_3864,U_3860) )
    & ! [U_3861,U_3862,U_3863,U_3864,U_3860] :
        ( sP303(U_3861,U_3862,U_3863,U_3864,U_3860)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3860),U_3861),U_3862) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3860),U_3863),U_3864)
        | ~ class_Groups_Oordered__ab__group__add(U_3860) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP303])],[f_1027_2]) ).

cnf(f_1027_4,plain,
    ( sP303(U_3861,U_3862,U_3863,U_3864,U_3860)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3860),U_3861),U_3862) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3860),U_3863),U_3864)
    | ~ class_Groups_Oordered__ab__group__add(U_3860) ),
    inference(clausify,[status(thm)],[f_1027_3]) ).

cnf(f_1027_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3860),U_3863),U_3864))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3860),U_3861),U_3862))
    | ~ sP303(U_3861,U_3862,U_3863,U_3864,U_3860) ),
    inference(clausify,[status(thm)],[f_1027_3]) ).

cnf(f_1027_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3860),U_3861),U_3862))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3860),U_3863),U_3864))
    | ~ sP303(U_3861,U_3862,U_3863,U_3864,U_3860) ),
    inference(clausify,[status(thm)],[f_1027_3]) ).

fof(f_1028_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_1028_2,plain,
    ! [U_3867,U_3866,U_3865] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3865),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3865),U_3866),U_3867)),U_3867) = U_3866
      | ~ class_Groups_Ogroup__add(U_3865) ),
    inference(variable_rename,[status(thm)],[f_1028_1]) ).

fof(f_1028_3,plain,
    ! [U_3867,U_3865,U_3866] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3865),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3865),U_3866),U_3867)),U_3867) = U_3866
      | ~ class_Groups_Ogroup__add(U_3865) ),
    inference(definitional_conversion,[status(esa)],[f_1028_2]) ).

cnf(f_1028_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3865),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3865),U_3866),U_3867)),U_3867) = U_3866
    | ~ class_Groups_Ogroup__add(U_3865) ),
    inference(clausify,[status(thm)],[f_1028_3]) ).

fof(f_1029_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_1029_2,plain,
    ! [U_3870,U_3869,U_3868] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3868),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3868),U_3869),U_3870)),U_3870) = U_3869
      | ~ class_Groups_Ogroup__add(U_3868) ),
    inference(variable_rename,[status(thm)],[f_1029_1]) ).

fof(f_1029_3,plain,
    ! [U_3869,U_3870,U_3868] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3868),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3868),U_3869),U_3870)),U_3870) = U_3869
      | ~ class_Groups_Ogroup__add(U_3868) ),
    inference(definitional_conversion,[status(esa)],[f_1029_2]) ).

cnf(f_1029_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3868),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3868),U_3869),U_3870)),U_3870) = U_3869
    | ~ class_Groups_Ogroup__add(U_3868) ),
    inference(clausify,[status(thm)],[f_1029_3]) ).

fof(f_1030_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_1030_2,plain,
    ! [U_3873,U_3872,U_3871] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3871),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3871),U_3872),U_3873)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3871),U_3873),U_3872)
      | ~ class_Groups_Oab__group__add(U_3871) ),
    inference(variable_rename,[status(thm)],[f_1030_1]) ).

fof(f_1030_3,plain,
    ! [U_3871,U_3872,U_3873] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3871),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3871),U_3872),U_3873)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3871),U_3873),U_3872)
      | ~ class_Groups_Oab__group__add(U_3871) ),
    inference(definitional_conversion,[status(esa)],[f_1030_2]) ).

cnf(f_1030_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3871),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3871),U_3872),U_3873)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3871),U_3873),U_3872)
    | ~ class_Groups_Oab__group__add(U_3871) ),
    inference(clausify,[status(thm)],[f_1030_3]) ).

fof(f_1031_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_1031_2,plain,
    ! [U_3877,U_3876,U_3875,U_3874] :
      ( c_Divides_Odiv__class_Omod(U_3874,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3874),U_3875),U_3876),U_3877) = c_Divides_Odiv__class_Omod(U_3874,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3874),U_3875),c_Divides_Odiv__class_Omod(U_3874,U_3876,U_3877)),U_3877)
      | ~ class_Divides_Oring__div(U_3874) ),
    inference(variable_rename,[status(thm)],[f_1031_1]) ).

fof(f_1031_3,plain,
    ! [U_3874,U_3875,U_3876,U_3877] :
      ( c_Divides_Odiv__class_Omod(U_3874,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3874),U_3875),U_3876),U_3877) = c_Divides_Odiv__class_Omod(U_3874,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3874),U_3875),c_Divides_Odiv__class_Omod(U_3874,U_3876,U_3877)),U_3877)
      | ~ class_Divides_Oring__div(U_3874) ),
    inference(definitional_conversion,[status(esa)],[f_1031_2]) ).

cnf(f_1031_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3874,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3874),U_3875),U_3876),U_3877) = c_Divides_Odiv__class_Omod(U_3874,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3874),U_3875),c_Divides_Odiv__class_Omod(U_3874,U_3876,U_3877)),U_3877)
    | ~ class_Divides_Oring__div(U_3874) ),
    inference(clausify,[status(thm)],[f_1031_3]) ).

fof(f_1032_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_1032_2,plain,
    ! [U_3881,U_3880,U_3879,U_3878] :
      ( c_Divides_Odiv__class_Omod(U_3878,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3878),U_3879),U_3880),U_3881) = c_Divides_Odiv__class_Omod(U_3878,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3878),c_Divides_Odiv__class_Omod(U_3878,U_3879,U_3881)),U_3880),U_3881)
      | ~ class_Divides_Oring__div(U_3878) ),
    inference(variable_rename,[status(thm)],[f_1032_1]) ).

fof(f_1032_3,plain,
    ! [U_3878,U_3879,U_3880,U_3881] :
      ( c_Divides_Odiv__class_Omod(U_3878,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3878),U_3879),U_3880),U_3881) = c_Divides_Odiv__class_Omod(U_3878,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3878),c_Divides_Odiv__class_Omod(U_3878,U_3879,U_3881)),U_3880),U_3881)
      | ~ class_Divides_Oring__div(U_3878) ),
    inference(definitional_conversion,[status(esa)],[f_1032_2]) ).

cnf(f_1032_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3878,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3878),U_3879),U_3880),U_3881) = c_Divides_Odiv__class_Omod(U_3878,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3878),c_Divides_Odiv__class_Omod(U_3878,U_3879,U_3881)),U_3880),U_3881)
    | ~ class_Divides_Oring__div(U_3878) ),
    inference(clausify,[status(thm)],[f_1032_3]) ).

fof(f_1033_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_1033_2,plain,
    ! [U_3885,U_3884,U_3883,U_3882] :
      ( c_Divides_Odiv__class_Omod(U_3882,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3882),U_3883),U_3884),U_3885) = c_Divides_Odiv__class_Omod(U_3882,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3882),c_Divides_Odiv__class_Omod(U_3882,U_3883,U_3885)),c_Divides_Odiv__class_Omod(U_3882,U_3884,U_3885)),U_3885)
      | ~ class_Divides_Oring__div(U_3882) ),
    inference(variable_rename,[status(thm)],[f_1033_1]) ).

fof(f_1033_3,plain,
    ! [U_3882,U_3883,U_3884,U_3885] :
      ( c_Divides_Odiv__class_Omod(U_3882,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3882),U_3883),U_3884),U_3885) = c_Divides_Odiv__class_Omod(U_3882,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3882),c_Divides_Odiv__class_Omod(U_3882,U_3883,U_3885)),c_Divides_Odiv__class_Omod(U_3882,U_3884,U_3885)),U_3885)
      | ~ class_Divides_Oring__div(U_3882) ),
    inference(definitional_conversion,[status(esa)],[f_1033_2]) ).

cnf(f_1033_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3882,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3882),U_3883),U_3884),U_3885) = c_Divides_Odiv__class_Omod(U_3882,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3882),c_Divides_Odiv__class_Omod(U_3882,U_3883,U_3885)),c_Divides_Odiv__class_Omod(U_3882,U_3884,U_3885)),U_3885)
    | ~ class_Divides_Oring__div(U_3882) ),
    inference(clausify,[status(thm)],[f_1033_3]) ).

fof(f_1034_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_1034_2,plain,
    ! [U_3891,U_3890,U_3889,U_3888,U_3887,U_3886] :
      ( c_Divides_Odiv__class_Omod(U_3886,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3886),U_3887),U_3890),U_3888) = c_Divides_Odiv__class_Omod(U_3886,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3886),U_3889),U_3891),U_3888)
      | c_Divides_Odiv__class_Omod(U_3886,U_3890,U_3888) != c_Divides_Odiv__class_Omod(U_3886,U_3891,U_3888)
      | c_Divides_Odiv__class_Omod(U_3886,U_3887,U_3888) != c_Divides_Odiv__class_Omod(U_3886,U_3889,U_3888)
      | ~ class_Divides_Oring__div(U_3886) ),
    inference(variable_rename,[status(thm)],[f_1034_1]) ).

fof(f_1034_3,plain,
    ! [U_3886,U_3887,U_3888,U_3889,U_3890,U_3891] :
      ( c_Divides_Odiv__class_Omod(U_3886,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3886),U_3887),U_3890),U_3888) = c_Divides_Odiv__class_Omod(U_3886,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3886),U_3889),U_3891),U_3888)
      | c_Divides_Odiv__class_Omod(U_3886,U_3890,U_3888) != c_Divides_Odiv__class_Omod(U_3886,U_3891,U_3888)
      | c_Divides_Odiv__class_Omod(U_3886,U_3887,U_3888) != c_Divides_Odiv__class_Omod(U_3886,U_3889,U_3888)
      | ~ class_Divides_Oring__div(U_3886) ),
    inference(definitional_conversion,[status(esa)],[f_1034_2]) ).

cnf(f_1034_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3886,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3886),U_3887),U_3890),U_3888) = c_Divides_Odiv__class_Omod(U_3886,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3886),U_3889),U_3891),U_3888)
    | c_Divides_Odiv__class_Omod(U_3886,U_3890,U_3888) != c_Divides_Odiv__class_Omod(U_3886,U_3891,U_3888)
    | c_Divides_Odiv__class_Omod(U_3886,U_3887,U_3888) != c_Divides_Odiv__class_Omod(U_3886,U_3889,U_3888)
    | ~ class_Divides_Oring__div(U_3886) ),
    inference(clausify,[status(thm)],[f_1034_3]) ).

fof(f_1035_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_1035_2,plain,
    ! [U_3892] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3892) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1035_1]) ).

fof(f_1035_3,plain,
    ! [U_3892] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3892) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1035_2]) ).

cnf(f_1035_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3892) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1035_3]) ).

fof(f_1036_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_1036_2,plain,
    ! [U_3893] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3893),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3893,
    inference(variable_rename,[status(thm)],[f_1036_1]) ).

fof(f_1036_3,plain,
    ! [U_3893] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3893),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3893,
    inference(definitional_conversion,[status(esa)],[f_1036_2]) ).

cnf(f_1036_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3893),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3893,
    inference(clausify,[status(thm)],[f_1036_3]) ).

fof(f_1037_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_1037_2,plain,
    ! [U_3894] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3894),U_3894) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1037_1]) ).

fof(f_1037_3,plain,
    ! [U_3894] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3894),U_3894) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1037_2]) ).

cnf(f_1037_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3894),U_3894) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1037_3]) ).

fof(f_1038_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_1038_2,plain,
    ! [U_3896,U_3895] :
      ( U_3895 = U_3896
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3896),U_3895) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3895),U_3896) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_1038_1]) ).

fof(f_1038_3,plain,
    ! [U_3895,U_3896] :
      ( U_3895 = U_3896
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3896),U_3895) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3895),U_3896) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_1038_2]) ).

cnf(f_1038_4,plain,
    ( U_3895 = U_3896
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3896),U_3895) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3895),U_3896) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1038_3]) ).

fof(f_1039_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_1039_2,plain,
    ! [U_3899,U_3898,U_3897] : 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_3897)),U_3898)),hAPP(c_Nat_OSuc,U_3899)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3897),U_3898)),U_3899),
    inference(variable_rename,[status(thm)],[f_1039_1]) ).

fof(f_1039_3,plain,
    ! [U_3897,U_3898,U_3899] : 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_3897)),U_3898)),hAPP(c_Nat_OSuc,U_3899)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3897),U_3898)),U_3899),
    inference(definitional_conversion,[status(esa)],[f_1039_2]) ).

cnf(f_1039_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_3897)),U_3898)),hAPP(c_Nat_OSuc,U_3899)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3897),U_3898)),U_3899),
    inference(clausify,[status(thm)],[f_1039_3]) ).

fof(f_1040_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_1040_2,plain,
    ! [U_3901,U_3900] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3900)),hAPP(c_Nat_OSuc,U_3901)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3900),U_3901),
    inference(variable_rename,[status(thm)],[f_1040_1]) ).

fof(f_1040_3,plain,
    ! [U_3900,U_3901] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3900)),hAPP(c_Nat_OSuc,U_3901)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3900),U_3901),
    inference(definitional_conversion,[status(esa)],[f_1040_2]) ).

cnf(f_1040_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3900)),hAPP(c_Nat_OSuc,U_3901)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3900),U_3901),
    inference(clausify,[status(thm)],[f_1040_3]) ).

fof(f_1041_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_1041_2,plain,
    ! [U_3904,U_3903,U_3902] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3902),U_3904)),U_3903))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3902),U_3903)) ),
    inference(variable_rename,[status(thm)],[f_1041_1]) ).

fof(f_1041_3,plain,
    ! [U_3902,U_3903,U_3904] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3902),U_3904)),U_3903))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3902),U_3903)) ),
    inference(definitional_conversion,[status(esa)],[f_1041_2]) ).

cnf(f_1041_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3902),U_3904)),U_3903))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3902),U_3903)) ),
    inference(clausify,[status(thm)],[f_1041_3]) ).

fof(f_1042_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_1042_2,plain,
    ! [U_3907,U_3906,U_3905] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3907),U_3906)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3907),U_3905)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3905),U_3907))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3905),U_3906)) ),
    inference(variable_rename,[status(thm)],[f_1042_1]) ).

fof(f_1042_3,plain,
    ! [U_3905,U_3906,U_3907] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3907),U_3906)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3907),U_3905)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3905),U_3907))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3905),U_3906)) ),
    inference(definitional_conversion,[status(esa)],[f_1042_2]) ).

cnf(f_1042_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3907),U_3906)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3907),U_3905)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3905),U_3907))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3905),U_3906)) ),
    inference(clausify,[status(thm)],[f_1042_3]) ).

fof(f_1043_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_1043_2,plain,
    ! [U_3909,U_3908] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3908,U_3909) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3908),U_3909),U_3909)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3908),U_3909)) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3908,U_3909) = U_3908
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3908),U_3909)) ) ),
    inference(variable_rename,[status(thm)],[f_1043_1]) ).

fof(f_1043_3,plain,
    ( ! [U_3913,U_3911] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3911,U_3913) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3911),U_3913),U_3913)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3911),U_3913)) )
    & ! [U_3912,U_3910] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3910,U_3912) = U_3910
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3910),U_3912)) ) ),
    inference(miniscope,[status(thm)],[f_1043_2]) ).

fof(f_1043_4,plain,
    ( ! [U_3913,U_3911] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3911,U_3913) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3911),U_3913),U_3913)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3911),U_3913)) )
    & ! [U_3910,U_3912] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3910,U_3912) = U_3910
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3910),U_3912)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1043_3]) ).

cnf(f_1043_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3910,U_3912) = U_3910
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3910),U_3912)) ),
    inference(clausify,[status(thm)],[f_1043_4]) ).

cnf(f_1043_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3911,U_3913) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3911),U_3913),U_3913)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3911),U_3913)) ),
    inference(clausify,[status(thm)],[f_1043_4]) ).

fof(f_1044_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_1044_2,plain,
    ! [U_3915,U_3914] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3914,U_3915) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3914),U_3915),U_3915)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3914),U_3915)) ),
    inference(variable_rename,[status(thm)],[f_1044_1]) ).

fof(f_1044_3,plain,
    ! [U_3915,U_3914] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3914,U_3915) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3914),U_3915),U_3915)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3914),U_3915)) ),
    inference(definitional_conversion,[status(esa)],[f_1044_2]) ).

cnf(f_1044_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3914,U_3915) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3914),U_3915),U_3915)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3914),U_3915)) ),
    inference(clausify,[status(thm)],[f_1044_3]) ).

fof(f_1045_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_1045_2,plain,
    ! [U_3917,U_3916] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3916),U_3917)),U_3917) = U_3916,
    inference(variable_rename,[status(thm)],[f_1045_1]) ).

fof(f_1045_3,plain,
    ! [U_3916,U_3917] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3916),U_3917)),U_3917) = U_3916,
    inference(definitional_conversion,[status(esa)],[f_1045_2]) ).

cnf(f_1045_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3916),U_3917)),U_3917) = U_3916,
    inference(clausify,[status(thm)],[f_1045_3]) ).

fof(f_1046_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_1046_2,plain,
    ! [U_3919,U_3918] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3918),U_3919)),U_3918) = U_3919,
    inference(variable_rename,[status(thm)],[f_1046_1]) ).

fof(f_1046_3,plain,
    ! [U_3918,U_3919] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3918),U_3919)),U_3918) = U_3919,
    inference(definitional_conversion,[status(esa)],[f_1046_2]) ).

cnf(f_1046_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3918),U_3919)),U_3918) = U_3919,
    inference(clausify,[status(thm)],[f_1046_3]) ).

fof(f_1047_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_1047_2,plain,
    ! [U_3922,U_3921,U_3920] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3920),U_3921)),U_3922) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3921),U_3922)),
    inference(variable_rename,[status(thm)],[f_1047_1]) ).

fof(f_1047_3,plain,
    ! [U_3920,U_3921,U_3922] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3920),U_3921)),U_3922) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3921),U_3922)),
    inference(definitional_conversion,[status(esa)],[f_1047_2]) ).

cnf(f_1047_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3920),U_3921)),U_3922) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3921),U_3922)),
    inference(clausify,[status(thm)],[f_1047_3]) ).

fof(f_1048_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_1048_2,plain,
    ! [U_3925,U_3924,U_3923] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3923),U_3924)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3923),U_3925)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3924),U_3925),
    inference(variable_rename,[status(thm)],[f_1048_1]) ).

fof(f_1048_3,plain,
    ! [U_3923,U_3924,U_3925] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3923),U_3924)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3923),U_3925)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3924),U_3925),
    inference(definitional_conversion,[status(esa)],[f_1048_2]) ).

cnf(f_1048_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3923),U_3924)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3923),U_3925)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3924),U_3925),
    inference(clausify,[status(thm)],[f_1048_3]) ).

fof(f_1049_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_1049_2,plain,
    ! [U_3928,U_3927,U_3926] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3926),U_3927)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3928),U_3927)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3926),U_3928),
    inference(variable_rename,[status(thm)],[f_1049_1]) ).

fof(f_1049_3,plain,
    ! [U_3926,U_3927,U_3928] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3926),U_3927)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3928),U_3927)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3926),U_3928),
    inference(definitional_conversion,[status(esa)],[f_1049_2]) ).

cnf(f_1049_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3926),U_3927)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3928),U_3927)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3926),U_3928),
    inference(clausify,[status(thm)],[f_1049_3]) ).

fof(f_1050_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_1050_2,plain,
    ! [U_3931,U_3930,U_3929] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3930),U_3929)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3931),U_3929)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3930),U_3931)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3930),U_3931))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3930),U_3929)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3931),U_3929))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3929),U_3931))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3929),U_3930)) ),
    inference(variable_rename,[status(thm)],[f_1050_1]) ).

fof(f_1050_3,plain,
    ( ! [U_3929,U_3930,U_3931] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3930),U_3929)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3931),U_3929)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3930),U_3931))
        | ~ sP304(U_3929,U_3930,U_3931) )
    & ! [U_3929,U_3930,U_3931] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3930),U_3931))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3930),U_3929)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3931),U_3929)))
        | ~ sP304(U_3929,U_3930,U_3931) )
    & ! [U_3929,U_3930,U_3931] :
        ( sP304(U_3929,U_3930,U_3931)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3929),U_3931))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3929),U_3930)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP304])],[f_1050_2]) ).

cnf(f_1050_4,plain,
    ( sP304(U_3929,U_3930,U_3931)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3929),U_3931))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3929),U_3930)) ),
    inference(clausify,[status(thm)],[f_1050_3]) ).

cnf(f_1050_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3930),U_3931))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3930),U_3929)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3931),U_3929)))
    | ~ sP304(U_3929,U_3930,U_3931) ),
    inference(clausify,[status(thm)],[f_1050_3]) ).

cnf(f_1050_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_3930),U_3929)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3931),U_3929)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3930),U_3931))
    | ~ sP304(U_3929,U_3930,U_3931) ),
    inference(clausify,[status(thm)],[f_1050_3]) ).

fof(f_1051_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_1051_2,plain,
    ! [U_3934,U_3933,U_3932] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3933),U_3932)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3934),U_3932)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3933),U_3934)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3932),U_3934))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3932),U_3933)) ),
    inference(variable_rename,[status(thm)],[f_1051_1]) ).

fof(f_1051_3,plain,
    ! [U_3934,U_3933,U_3932] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3933),U_3932)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3934),U_3932)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3933),U_3934)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3932),U_3934))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3932),U_3933)) ),
    inference(definitional_conversion,[status(esa)],[f_1051_2]) ).

cnf(f_1051_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3933),U_3932)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3934),U_3932)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3933),U_3934)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3932),U_3934))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3932),U_3933)) ),
    inference(clausify,[status(thm)],[f_1051_3]) ).

fof(f_1052_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_1052_2,plain,
    ! [U_3937,U_3936,U_3935] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3936),U_3935) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3937),U_3935)
          | U_3936 != U_3937 )
        & ( U_3936 = U_3937
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3936),U_3935) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3937),U_3935) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3935),U_3937))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3935),U_3936)) ),
    inference(variable_rename,[status(thm)],[f_1052_1]) ).

fof(f_1052_3,plain,
    ( ! [U_3935,U_3936,U_3937] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3936),U_3935) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3937),U_3935)
        | U_3936 != U_3937
        | ~ sP305(U_3935,U_3936,U_3937) )
    & ! [U_3935,U_3936,U_3937] :
        ( U_3936 = U_3937
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3936),U_3935) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3937),U_3935)
        | ~ sP305(U_3935,U_3936,U_3937) )
    & ! [U_3935,U_3936,U_3937] :
        ( sP305(U_3935,U_3936,U_3937)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3935),U_3937))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3935),U_3936)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP305])],[f_1052_2]) ).

cnf(f_1052_4,plain,
    ( sP305(U_3935,U_3936,U_3937)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3935),U_3937))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3935),U_3936)) ),
    inference(clausify,[status(thm)],[f_1052_3]) ).

cnf(f_1052_5,plain,
    ( U_3936 = U_3937
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3936),U_3935) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3937),U_3935)
    | ~ sP305(U_3935,U_3936,U_3937) ),
    inference(clausify,[status(thm)],[f_1052_3]) ).

cnf(f_1052_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3936),U_3935) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3937),U_3935)
    | U_3936 != U_3937
    | ~ sP305(U_3935,U_3936,U_3937) ),
    inference(clausify,[status(thm)],[f_1052_3]) ).

fof(f_1053_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_1053_2,plain,
    ! [U_3939,U_3938] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3939),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3939),U_3938)) = U_3938
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3938),U_3939)) ),
    inference(variable_rename,[status(thm)],[f_1053_1]) ).

fof(f_1053_3,plain,
    ! [U_3939,U_3938] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3939),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3939),U_3938)) = U_3938
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3938),U_3939)) ),
    inference(definitional_conversion,[status(esa)],[f_1053_2]) ).

cnf(f_1053_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3939),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3939),U_3938)) = U_3938
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3938),U_3939)) ),
    inference(clausify,[status(thm)],[f_1053_3]) ).

fof(f_1054_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_1054_2,plain,
    ! [U_3942,U_3941,U_3940] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3940),U_3942)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3941),U_3942)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3940),U_3941)) ),
    inference(variable_rename,[status(thm)],[f_1054_1]) ).

fof(f_1054_3,plain,
    ! [U_3940,U_3941,U_3942] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3940),U_3942)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3941),U_3942)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3940),U_3941)) ),
    inference(definitional_conversion,[status(esa)],[f_1054_2]) ).

cnf(f_1054_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_3940),U_3942)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3941),U_3942)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3940),U_3941)) ),
    inference(clausify,[status(thm)],[f_1054_3]) ).

fof(f_1055_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_1055_2,plain,
    ! [U_3945,U_3944,U_3943] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3945),U_3944)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3945),U_3943)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3943),U_3944)) ),
    inference(variable_rename,[status(thm)],[f_1055_1]) ).

fof(f_1055_3,plain,
    ! [U_3943,U_3944,U_3945] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3945),U_3944)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3945),U_3943)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3943),U_3944)) ),
    inference(definitional_conversion,[status(esa)],[f_1055_2]) ).

cnf(f_1055_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_3945),U_3944)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3945),U_3943)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3943),U_3944)) ),
    inference(clausify,[status(thm)],[f_1055_3]) ).

fof(f_1056_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_1056_2,plain,
    ! [U_3947,U_3946] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3946),U_3947)),U_3946)),
    inference(variable_rename,[status(thm)],[f_1056_1]) ).

fof(f_1056_3,plain,
    ! [U_3946,U_3947] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3946),U_3947)),U_3946)),
    inference(definitional_conversion,[status(esa)],[f_1056_2]) ).

cnf(f_1056_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_3946),U_3947)),U_3946)),
    inference(clausify,[status(thm)],[f_1056_3]) ).

fof(f_1057_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_1057_2,plain,
    ! [U_3949,U_3948] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3949,U_3948) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3949),U_3948),U_3948)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3948),U_3949)) ),
    inference(variable_rename,[status(thm)],[f_1057_1]) ).

fof(f_1057_3,plain,
    ! [U_3948,U_3949] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3949,U_3948) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3949),U_3948),U_3948)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3948),U_3949)) ),
    inference(definitional_conversion,[status(esa)],[f_1057_2]) ).

cnf(f_1057_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3949,U_3948) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3949),U_3948),U_3948)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3948),U_3949)) ),
    inference(clausify,[status(thm)],[f_1057_3]) ).

fof(f_1058_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_1058_2,plain,
    ! [U_3952,U_3951,U_3950] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3950),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3951),U_3952)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3950),U_3951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3950),U_3952)),
    inference(variable_rename,[status(thm)],[f_1058_1]) ).

fof(f_1058_3,plain,
    ! [U_3950,U_3951,U_3952] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3950),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3951),U_3952)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3950),U_3951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3950),U_3952)),
    inference(definitional_conversion,[status(esa)],[f_1058_2]) ).

cnf(f_1058_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3950),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3951),U_3952)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3950),U_3951)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3950),U_3952)),
    inference(clausify,[status(thm)],[f_1058_3]) ).

fof(f_1059_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_1059_2,plain,
    ! [U_3955,U_3954,U_3953] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3953),U_3954)),U_3955) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3953),U_3955)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3954),U_3955)),
    inference(variable_rename,[status(thm)],[f_1059_1]) ).

fof(f_1059_3,plain,
    ! [U_3953,U_3954,U_3955] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3953),U_3954)),U_3955) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3953),U_3955)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3954),U_3955)),
    inference(definitional_conversion,[status(esa)],[f_1059_2]) ).

cnf(f_1059_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3953),U_3954)),U_3955) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3953),U_3955)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3954),U_3955)),
    inference(clausify,[status(thm)],[f_1059_3]) ).

fof(f_1060_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_1060_2,plain,
    ! [U_3958,U_3957,U_3956] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3956),U_3957)),U_3958) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3956),U_3958)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3957),U_3958)),
    inference(variable_rename,[status(thm)],[f_1060_1]) ).

fof(f_1060_3,plain,
    ! [U_3958,U_3957,U_3956] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3956),U_3957)),U_3958) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3956),U_3958)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3957),U_3958)),
    inference(definitional_conversion,[status(esa)],[f_1060_2]) ).

cnf(f_1060_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3956),U_3957)),U_3958) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3956),U_3958)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3957),U_3958)),
    inference(clausify,[status(thm)],[f_1060_3]) ).

fof(f_1061_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_1061_2,plain,
    ! [U_3961,U_3960,U_3959] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3959),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3960),U_3961)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3959),U_3960)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3959),U_3961)),
    inference(variable_rename,[status(thm)],[f_1061_1]) ).

fof(f_1061_3,plain,
    ! [U_3959,U_3960,U_3961] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3959),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3960),U_3961)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3959),U_3960)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3959),U_3961)),
    inference(definitional_conversion,[status(esa)],[f_1061_2]) ).

cnf(f_1061_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3959),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3960),U_3961)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3959),U_3960)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3959),U_3961)),
    inference(clausify,[status(thm)],[f_1061_3]) ).

fof(f_1062_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_1062_2,plain,
    ! [U_3964,U_3963,U_3962] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3962),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3963,U_3964)),U_3964) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3962),U_3963),U_3964),
    inference(variable_rename,[status(thm)],[f_1062_1]) ).

fof(f_1062_3,plain,
    ! [U_3962,U_3963,U_3964] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3962),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3963,U_3964)),U_3964) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3962),U_3963),U_3964),
    inference(definitional_conversion,[status(esa)],[f_1062_2]) ).

cnf(f_1062_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3962),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3963,U_3964)),U_3964) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3962),U_3963),U_3964),
    inference(clausify,[status(thm)],[f_1062_3]) ).

fof(f_1063_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_1063_2,plain,
    ! [U_3967,U_3966,U_3965] : 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_3965,U_3966)),U_3967),U_3966) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3965),U_3967),U_3966),
    inference(variable_rename,[status(thm)],[f_1063_1]) ).

fof(f_1063_3,plain,
    ! [U_3965,U_3966,U_3967] : 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_3965,U_3966)),U_3967),U_3966) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3965),U_3967),U_3966),
    inference(definitional_conversion,[status(esa)],[f_1063_2]) ).

cnf(f_1063_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_3965,U_3966)),U_3967),U_3966) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3965),U_3967),U_3966),
    inference(clausify,[status(thm)],[f_1063_3]) ).

fof(f_1064_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_1064_2,plain,
    ! [U_3969,U_3968] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3969),U_3968)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3969)),hAPP(c_Int_Onat,U_3968))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3968),U_3969))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3968)) ),
    inference(variable_rename,[status(thm)],[f_1064_1]) ).

fof(f_1064_3,plain,
    ! [U_3968,U_3969] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3969),U_3968)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3969)),hAPP(c_Int_Onat,U_3968))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3968),U_3969))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3968)) ),
    inference(definitional_conversion,[status(esa)],[f_1064_2]) ).

cnf(f_1064_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3969),U_3968)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3969)),hAPP(c_Int_Onat,U_3968))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3968),U_3969))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3968)) ),
    inference(clausify,[status(thm)],[f_1064_3]) ).

fof(f_1065_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_1065_2,plain,
    ! [U_3972,U_3971,U_3970] :
      ( ( hBOOL(hAPP(U_3970,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3971),U_3972))))
        | ( ~ hBOOL(hAPP(U_3970,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3971),U_3972)) )
        | ( ~ hBOOL(hAPP(U_3970,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3971)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3972))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3972),U_3971)) ) )
      & ( ( ( hBOOL(hAPP(U_3970,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3971),U_3972)) )
          & ( hBOOL(hAPP(U_3970,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3971)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3972))))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3972),U_3971)) ) )
        | ~ hBOOL(hAPP(U_3970,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3971),U_3972)))) ) ),
    inference(variable_rename,[status(thm)],[f_1065_1]) ).

fof(f_1065_3,plain,
    ( ! [U_3978,U_3976,U_3974] :
        ( hBOOL(hAPP(U_3974,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3976),U_3978))))
        | ( ~ hBOOL(hAPP(U_3974,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3976),U_3978)) )
        | ( ~ hBOOL(hAPP(U_3974,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3976)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3978))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3978),U_3976)) ) )
    & ! [U_3977,U_3975,U_3973] :
        ( ( ( hBOOL(hAPP(U_3973,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3975),U_3977)) )
          & ( hBOOL(hAPP(U_3973,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3975)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3977))))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3977),U_3975)) ) )
        | ~ hBOOL(hAPP(U_3973,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3975),U_3977)))) ) ),
    inference(miniscope,[status(thm)],[f_1065_2]) ).

fof(f_1065_4,plain,
    ( ! [U_3974,U_3978,U_3976] :
        ( ~ hBOOL(hAPP(U_3974,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP308(U_3974,U_3978,U_3976) )
    & ! [U_3974,U_3978,U_3976] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3976),U_3978))
        | ~ sP308(U_3974,U_3978,U_3976) )
    & ! [U_3974,U_3978,U_3976] :
        ( ~ hBOOL(hAPP(U_3974,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3976)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3978))))
        | ~ sP307(U_3974,U_3978,U_3976) )
    & ! [U_3974,U_3978,U_3976] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3978),U_3976))
        | ~ sP307(U_3974,U_3978,U_3976) )
    & ! [U_3975,U_3973,U_3977] :
        ( hBOOL(hAPP(U_3973,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3975),U_3977))
        | ~ sP306(U_3975,U_3973,U_3977) )
    & ! [U_3975,U_3973,U_3977] :
        ( hBOOL(hAPP(U_3973,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3975)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3977))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3977),U_3975))
        | ~ sP306(U_3975,U_3973,U_3977) )
    & ! [U_3974,U_3978,U_3976] :
        ( hBOOL(hAPP(U_3974,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3976),U_3978))))
        | sP308(U_3974,U_3978,U_3976)
        | sP307(U_3974,U_3978,U_3976) )
    & ! [U_3975,U_3973,U_3977] :
        ( sP306(U_3975,U_3973,U_3977)
        | ~ hBOOL(hAPP(U_3973,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3975),U_3977)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP306,sP307,sP308])],[f_1065_3]) ).

cnf(f_1065_5,plain,
    ( sP306(U_3975,U_3973,U_3977)
    | ~ hBOOL(hAPP(U_3973,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3975),U_3977)))) ),
    inference(clausify,[status(thm)],[f_1065_4]) ).

cnf(f_1065_6,plain,
    ( hBOOL(hAPP(U_3974,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3976),U_3978))))
    | sP308(U_3974,U_3978,U_3976)
    | sP307(U_3974,U_3978,U_3976) ),
    inference(clausify,[status(thm)],[f_1065_4]) ).

cnf(f_1065_7,plain,
    ( hBOOL(hAPP(U_3973,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3975)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3977))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3977),U_3975))
    | ~ sP306(U_3975,U_3973,U_3977) ),
    inference(clausify,[status(thm)],[f_1065_4]) ).

cnf(f_1065_8,plain,
    ( hBOOL(hAPP(U_3973,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3975),U_3977))
    | ~ sP306(U_3975,U_3973,U_3977) ),
    inference(clausify,[status(thm)],[f_1065_4]) ).

cnf(f_1065_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3978),U_3976))
    | ~ sP307(U_3974,U_3978,U_3976) ),
    inference(clausify,[status(thm)],[f_1065_4]) ).

cnf(f_1065_10,plain,
    ( ~ hBOOL(hAPP(U_3974,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3976)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3978))))
    | ~ sP307(U_3974,U_3978,U_3976) ),
    inference(clausify,[status(thm)],[f_1065_4]) ).

cnf(f_1065_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3976),U_3978))
    | ~ sP308(U_3974,U_3978,U_3976) ),
    inference(clausify,[status(thm)],[f_1065_4]) ).

cnf(f_1065_12,plain,
    ( ~ hBOOL(hAPP(U_3974,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP308(U_3974,U_3978,U_3976) ),
    inference(clausify,[status(thm)],[f_1065_4]) ).

fof(f_1066_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_1066_2,plain,
    ! [U_3981,U_3980,U_3979] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3979),U_3980),U_3981))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3979),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3979),U_3980),U_3981)),c_Groups_Ozero__class_Ozero(U_3979))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3979),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3979),U_3980),U_3981)),c_Groups_Ozero__class_Ozero(U_3979)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3979),U_3980),U_3981)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_3979) ),
    inference(variable_rename,[status(thm)],[f_1066_1]) ).

fof(f_1066_3,plain,
    ( ! [U_3980,U_3981,U_3979] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3979),U_3980),U_3981))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3979),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3979),U_3980),U_3981)),c_Groups_Ozero__class_Ozero(U_3979)))
        | ~ sP309(U_3980,U_3981,U_3979) )
    & ! [U_3980,U_3981,U_3979] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3979),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3979),U_3980),U_3981)),c_Groups_Ozero__class_Ozero(U_3979)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3979),U_3980),U_3981))
        | ~ sP309(U_3980,U_3981,U_3979) )
    & ! [U_3980,U_3981,U_3979] :
        ( sP309(U_3980,U_3981,U_3979)
        | ~ class_Groups_Oordered__ab__group__add(U_3979) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP309])],[f_1066_2]) ).

cnf(f_1066_4,plain,
    ( sP309(U_3980,U_3981,U_3979)
    | ~ class_Groups_Oordered__ab__group__add(U_3979) ),
    inference(clausify,[status(thm)],[f_1066_3]) ).

cnf(f_1066_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3979),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3979),U_3980),U_3981)),c_Groups_Ozero__class_Ozero(U_3979)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3979),U_3980),U_3981))
    | ~ sP309(U_3980,U_3981,U_3979) ),
    inference(clausify,[status(thm)],[f_1066_3]) ).

cnf(f_1066_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3979),U_3980),U_3981))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3979),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3979),U_3980),U_3981)),c_Groups_Ozero__class_Ozero(U_3979)))
    | ~ sP309(U_3980,U_3981,U_3979) ),
    inference(clausify,[status(thm)],[f_1066_3]) ).

fof(f_1067_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_1067_2,plain,
    ! [U_3984,U_3983,U_3982] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3982),U_3983),U_3984))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3982),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3982),U_3983),U_3984)),c_Groups_Ozero__class_Ozero(U_3982))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3982),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3982),U_3983),U_3984)),c_Groups_Ozero__class_Ozero(U_3982)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3982),U_3983),U_3984)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_3982) ),
    inference(variable_rename,[status(thm)],[f_1067_1]) ).

fof(f_1067_3,plain,
    ( ! [U_3982,U_3983,U_3984] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3982),U_3983),U_3984))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3982),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3982),U_3983),U_3984)),c_Groups_Ozero__class_Ozero(U_3982)))
        | ~ sP310(U_3982,U_3983,U_3984) )
    & ! [U_3982,U_3983,U_3984] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3982),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3982),U_3983),U_3984)),c_Groups_Ozero__class_Ozero(U_3982)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3982),U_3983),U_3984))
        | ~ sP310(U_3982,U_3983,U_3984) )
    & ! [U_3982,U_3983,U_3984] :
        ( sP310(U_3982,U_3983,U_3984)
        | ~ class_Groups_Oordered__ab__group__add(U_3982) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP310])],[f_1067_2]) ).

cnf(f_1067_4,plain,
    ( sP310(U_3982,U_3983,U_3984)
    | ~ class_Groups_Oordered__ab__group__add(U_3982) ),
    inference(clausify,[status(thm)],[f_1067_3]) ).

cnf(f_1067_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3982),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3982),U_3983),U_3984)),c_Groups_Ozero__class_Ozero(U_3982)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3982),U_3983),U_3984))
    | ~ sP310(U_3982,U_3983,U_3984) ),
    inference(clausify,[status(thm)],[f_1067_3]) ).

cnf(f_1067_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3982),U_3983),U_3984))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3982),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3982),U_3983),U_3984)),c_Groups_Ozero__class_Ozero(U_3982)))
    | ~ sP310(U_3982,U_3983,U_3984) ),
    inference(clausify,[status(thm)],[f_1067_3]) ).

fof(f_1068_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_1068_2,plain,
    ! [U_3990,U_3989,U_3988,U_3987,U_3986,U_3985] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3986),U_3987)),U_3988) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3989),U_3987)),U_3990)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3985),U_3986),U_3989)),U_3987)),U_3988) != U_3990 )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3985),U_3986),U_3989)),U_3987)),U_3988) = U_3990
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3986),U_3987)),U_3988) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3989),U_3987)),U_3990) ) )
      | ~ class_Rings_Oring(U_3985) ),
    inference(variable_rename,[status(thm)],[f_1068_1]) ).

fof(f_1068_3,plain,
    ( ! [U_3986,U_3985,U_3987,U_3988,U_3989,U_3990] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3986),U_3987)),U_3988) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3989),U_3987)),U_3990)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3985),U_3986),U_3989)),U_3987)),U_3988) != U_3990
        | ~ sP311(U_3986,U_3985,U_3987,U_3988,U_3989,U_3990) )
    & ! [U_3986,U_3985,U_3987,U_3988,U_3989,U_3990] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3985),U_3986),U_3989)),U_3987)),U_3988) = U_3990
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3986),U_3987)),U_3988) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3989),U_3987)),U_3990)
        | ~ sP311(U_3986,U_3985,U_3987,U_3988,U_3989,U_3990) )
    & ! [U_3986,U_3985,U_3987,U_3988,U_3989,U_3990] :
        ( sP311(U_3986,U_3985,U_3987,U_3988,U_3989,U_3990)
        | ~ class_Rings_Oring(U_3985) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP311])],[f_1068_2]) ).

cnf(f_1068_4,plain,
    ( sP311(U_3986,U_3985,U_3987,U_3988,U_3989,U_3990)
    | ~ class_Rings_Oring(U_3985) ),
    inference(clausify,[status(thm)],[f_1068_3]) ).

cnf(f_1068_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3985),U_3986),U_3989)),U_3987)),U_3988) = U_3990
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3986),U_3987)),U_3988) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3989),U_3987)),U_3990)
    | ~ sP311(U_3986,U_3985,U_3987,U_3988,U_3989,U_3990) ),
    inference(clausify,[status(thm)],[f_1068_3]) ).

cnf(f_1068_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3986),U_3987)),U_3988) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3989),U_3987)),U_3990)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3985),U_3986),U_3989)),U_3987)),U_3988) != U_3990
    | ~ sP311(U_3986,U_3985,U_3987,U_3988,U_3989,U_3990) ),
    inference(clausify,[status(thm)],[f_1068_3]) ).

fof(f_1069_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_1069_2,plain,
    ! [U_3996,U_3995,U_3994,U_3993,U_3992,U_3991] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),U_3992),U_3993)),U_3994) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),U_3995),U_3993)),U_3996)
          | U_3994 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3991),U_3995),U_3992)),U_3993)),U_3996) )
        & ( U_3994 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3991),U_3995),U_3992)),U_3993)),U_3996)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),U_3992),U_3993)),U_3994) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),U_3995),U_3993)),U_3996) ) )
      | ~ class_Rings_Oring(U_3991) ),
    inference(variable_rename,[status(thm)],[f_1069_1]) ).

fof(f_1069_3,plain,
    ( ! [U_3993,U_3992,U_3991,U_3994,U_3995,U_3996] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),U_3992),U_3993)),U_3994) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),U_3995),U_3993)),U_3996)
        | U_3994 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3991),U_3995),U_3992)),U_3993)),U_3996)
        | ~ sP312(U_3993,U_3992,U_3991,U_3994,U_3995,U_3996) )
    & ! [U_3993,U_3992,U_3991,U_3994,U_3995,U_3996] :
        ( U_3994 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3991),U_3995),U_3992)),U_3993)),U_3996)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),U_3992),U_3993)),U_3994) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),U_3995),U_3993)),U_3996)
        | ~ sP312(U_3993,U_3992,U_3991,U_3994,U_3995,U_3996) )
    & ! [U_3993,U_3992,U_3991,U_3994,U_3995,U_3996] :
        ( sP312(U_3993,U_3992,U_3991,U_3994,U_3995,U_3996)
        | ~ class_Rings_Oring(U_3991) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP312])],[f_1069_2]) ).

cnf(f_1069_4,plain,
    ( sP312(U_3993,U_3992,U_3991,U_3994,U_3995,U_3996)
    | ~ class_Rings_Oring(U_3991) ),
    inference(clausify,[status(thm)],[f_1069_3]) ).

cnf(f_1069_5,plain,
    ( U_3994 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3991),U_3995),U_3992)),U_3993)),U_3996)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),U_3992),U_3993)),U_3994) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),U_3995),U_3993)),U_3996)
    | ~ sP312(U_3993,U_3992,U_3991,U_3994,U_3995,U_3996) ),
    inference(clausify,[status(thm)],[f_1069_3]) ).

cnf(f_1069_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),U_3992),U_3993)),U_3994) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),U_3995),U_3993)),U_3996)
    | U_3994 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3991),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3991),U_3995),U_3992)),U_3993)),U_3996)
    | ~ sP312(U_3993,U_3992,U_3991,U_3994,U_3995,U_3996) ),
    inference(clausify,[status(thm)],[f_1069_3]) ).

fof(f_1070_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_1070_2,plain,
    ! [U_3998,U_3997] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3997),c_Groups_Ozero__class_Ozero(U_3997)),U_3998) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3997),U_3998)
      | ~ class_Groups_Ogroup__add(U_3997) ),
    inference(variable_rename,[status(thm)],[f_1070_1]) ).

fof(f_1070_3,plain,
    ! [U_3998,U_3997] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3997),c_Groups_Ozero__class_Ozero(U_3997)),U_3998) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3997),U_3998)
      | ~ class_Groups_Ogroup__add(U_3997) ),
    inference(definitional_conversion,[status(esa)],[f_1070_2]) ).

cnf(f_1070_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3997),c_Groups_Ozero__class_Ozero(U_3997)),U_3998) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3997),U_3998)
    | ~ class_Groups_Ogroup__add(U_3997) ),
    inference(clausify,[status(thm)],[f_1070_3]) ).

fof(f_1071_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_1071_2,plain,
    ! [U_4001,U_4000,U_3999] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3999),U_4000),U_4001) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3999),U_4000),hAPP(c_Groups_Ouminus__class_Ouminus(U_3999),U_4001))
      | ~ class_Groups_Ogroup__add(U_3999) ),
    inference(variable_rename,[status(thm)],[f_1071_1]) ).

fof(f_1071_3,plain,
    ! [U_3999,U_4000,U_4001] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3999),U_4000),U_4001) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3999),U_4000),hAPP(c_Groups_Ouminus__class_Ouminus(U_3999),U_4001))
      | ~ class_Groups_Ogroup__add(U_3999) ),
    inference(definitional_conversion,[status(esa)],[f_1071_2]) ).

cnf(f_1071_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3999),U_4000),U_4001) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3999),U_4000),hAPP(c_Groups_Ouminus__class_Ouminus(U_3999),U_4001))
    | ~ class_Groups_Ogroup__add(U_3999) ),
    inference(clausify,[status(thm)],[f_1071_3]) ).

fof(f_1072_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_1072_2,plain,
    ! [U_4004,U_4003,U_4002] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4002),U_4003),U_4004) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4002),U_4003),hAPP(c_Groups_Ouminus__class_Ouminus(U_4002),U_4004))
      | ~ class_Groups_Oab__group__add(U_4002) ),
    inference(variable_rename,[status(thm)],[f_1072_1]) ).

fof(f_1072_3,plain,
    ! [U_4002,U_4003,U_4004] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4002),U_4003),U_4004) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4002),U_4003),hAPP(c_Groups_Ouminus__class_Ouminus(U_4002),U_4004))
      | ~ class_Groups_Oab__group__add(U_4002) ),
    inference(definitional_conversion,[status(esa)],[f_1072_2]) ).

cnf(f_1072_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4002),U_4003),U_4004) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4002),U_4003),hAPP(c_Groups_Ouminus__class_Ouminus(U_4002),U_4004))
    | ~ class_Groups_Oab__group__add(U_4002) ),
    inference(clausify,[status(thm)],[f_1072_3]) ).

fof(f_1073_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_1073_2,plain,
    ! [U_4007,U_4006,U_4005] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4005),U_4006),U_4007) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4005),U_4006),hAPP(c_Groups_Ouminus__class_Ouminus(U_4005),U_4007))
      | ~ class_Rings_Ocomm__ring__1(U_4005) ),
    inference(variable_rename,[status(thm)],[f_1073_1]) ).

fof(f_1073_3,plain,
    ! [U_4005,U_4006,U_4007] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4005),U_4006),U_4007) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4005),U_4006),hAPP(c_Groups_Ouminus__class_Ouminus(U_4005),U_4007))
      | ~ class_Rings_Ocomm__ring__1(U_4005) ),
    inference(definitional_conversion,[status(esa)],[f_1073_2]) ).

cnf(f_1073_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4005),U_4006),U_4007) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4005),U_4006),hAPP(c_Groups_Ouminus__class_Ouminus(U_4005),U_4007))
    | ~ class_Rings_Ocomm__ring__1(U_4005) ),
    inference(clausify,[status(thm)],[f_1073_3]) ).

fof(f_1074_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_1074_2,plain,
    ! [U_4010,U_4009,U_4008] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4008),U_4009),hAPP(c_Groups_Ouminus__class_Ouminus(U_4008),U_4010)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4008),U_4009),U_4010)
      | ~ class_Groups_Ogroup__add(U_4008) ),
    inference(variable_rename,[status(thm)],[f_1074_1]) ).

fof(f_1074_3,plain,
    ! [U_4008,U_4009,U_4010] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4008),U_4009),hAPP(c_Groups_Ouminus__class_Ouminus(U_4008),U_4010)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4008),U_4009),U_4010)
      | ~ class_Groups_Ogroup__add(U_4008) ),
    inference(definitional_conversion,[status(esa)],[f_1074_2]) ).

cnf(f_1074_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4008),U_4009),hAPP(c_Groups_Ouminus__class_Ouminus(U_4008),U_4010)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4008),U_4009),U_4010)
    | ~ class_Groups_Ogroup__add(U_4008) ),
    inference(clausify,[status(thm)],[f_1074_3]) ).

fof(f_1075_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_1075_2,plain,
    ! [U_4012,U_4011] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4011),U_4012))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4011),U_4012)),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_4011),U_4012)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4011),U_4012)) ) ),
    inference(variable_rename,[status(thm)],[f_1075_1]) ).

fof(f_1075_3,plain,
    ( ! [U_4016,U_4014] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4014),U_4016))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4014),U_4016)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4015,U_4013] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4013),U_4015)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4013),U_4015)) ) ),
    inference(miniscope,[status(thm)],[f_1075_2]) ).

fof(f_1075_4,plain,
    ( ! [U_4014,U_4016] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4014),U_4016))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4014),U_4016)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4015,U_4013] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4013),U_4015)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4013),U_4015)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1075_3]) ).

cnf(f_1075_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4013),U_4015)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4013),U_4015)) ),
    inference(clausify,[status(thm)],[f_1075_4]) ).

cnf(f_1075_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4014),U_4016))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4014),U_4016)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1075_4]) ).

fof(f_1076_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_1076_2,plain,
    ! [U_4018,U_4017] :
      ( ( 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_4017),U_4018)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4018),U_4017)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4018),U_4017))
        | ~ 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_4017),U_4018))) ) ),
    inference(variable_rename,[status(thm)],[f_1076_1]) ).

fof(f_1076_3,plain,
    ( ! [U_4022,U_4020] :
        ( 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_4020),U_4022)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4022),U_4020)) )
    & ! [U_4021,U_4019] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4021),U_4019))
        | ~ 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_4019),U_4021))) ) ),
    inference(miniscope,[status(thm)],[f_1076_2]) ).

fof(f_1076_4,plain,
    ( ! [U_4020,U_4022] :
        ( 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_4020),U_4022)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4022),U_4020)) )
    & ! [U_4019,U_4021] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4021),U_4019))
        | ~ 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_4019),U_4021))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1076_3]) ).

cnf(f_1076_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4021),U_4019))
    | ~ 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_4019),U_4021))) ),
    inference(clausify,[status(thm)],[f_1076_4]) ).

cnf(f_1076_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_4020),U_4022)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4022),U_4020)) ),
    inference(clausify,[status(thm)],[f_1076_4]) ).

fof(f_1077_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_1077_2,plain,
    ! [U_4024,U_4023] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4024),U_4023)),U_4024))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4024))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4023)) ),
    inference(variable_rename,[status(thm)],[f_1077_1]) ).

fof(f_1077_3,plain,
    ! [U_4023,U_4024] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4024),U_4023)),U_4024))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4024))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4023)) ),
    inference(definitional_conversion,[status(esa)],[f_1077_2]) ).

cnf(f_1077_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4024),U_4023)),U_4024))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4024))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4023)) ),
    inference(clausify,[status(thm)],[f_1077_3]) ).

fof(f_1078_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_1078_2,plain,
    ! [U_4026,U_4025] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4025),U_4026)),hAPP(c_Nat_OSuc,U_4025))),
    inference(variable_rename,[status(thm)],[f_1078_1]) ).

fof(f_1078_3,plain,
    ! [U_4026,U_4025] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4025),U_4026)),hAPP(c_Nat_OSuc,U_4025))),
    inference(definitional_conversion,[status(esa)],[f_1078_2]) ).

cnf(f_1078_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4025),U_4026)),hAPP(c_Nat_OSuc,U_4025))),
    inference(clausify,[status(thm)],[f_1078_3]) ).

fof(f_1079_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_1079_2,plain,
    ! [U_4028,U_4027] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4027),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4027),U_4028)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1079_1]) ).

fof(f_1079_3,plain,
    ! [U_4027,U_4028] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4027),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4027),U_4028)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1079_2]) ).

cnf(f_1079_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4027),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4027),U_4028)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1079_3]) ).

fof(f_1080_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_1080_2,plain,
    ! [U_4030,U_4029] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4029),U_4030) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4029),U_4030)) ),
    inference(variable_rename,[status(thm)],[f_1080_1]) ).

fof(f_1080_3,plain,
    ! [U_4029,U_4030] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4029),U_4030) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4029),U_4030)) ),
    inference(definitional_conversion,[status(esa)],[f_1080_2]) ).

cnf(f_1080_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4029),U_4030) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4029),U_4030)) ),
    inference(clausify,[status(thm)],[f_1080_3]) ).

fof(f_1081_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_1081_2,plain,
    ! [U_4032,U_4031] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4031),U_4032) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4031),U_4032)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4031),U_4032))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4031),U_4032) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1081_1]) ).

fof(f_1081_3,plain,
    ( ! [U_4036,U_4034] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4034),U_4036) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4034),U_4036)) )
    & ! [U_4035,U_4033] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4033),U_4035))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4033),U_4035) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1081_2]) ).

fof(f_1081_4,plain,
    ( ! [U_4034,U_4036] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4034),U_4036) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4034),U_4036)) )
    & ! [U_4035,U_4033] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4033),U_4035))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4033),U_4035) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1081_3]) ).

cnf(f_1081_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4033),U_4035))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4033),U_4035) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1081_4]) ).

cnf(f_1081_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4034),U_4036) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4034),U_4036)) ),
    inference(clausify,[status(thm)],[f_1081_4]) ).

fof(f_1082_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_1082_2,plain,
    ! [U_4039,U_4038,U_4037] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4037),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4038),U_4039)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4037),U_4039)),U_4038)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4037),U_4039)),U_4038))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4037),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4038),U_4039))) ) ),
    inference(variable_rename,[status(thm)],[f_1082_1]) ).

fof(f_1082_3,plain,
    ( ! [U_4045,U_4043,U_4041] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4041),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4043),U_4045)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4041),U_4045)),U_4043)) )
    & ! [U_4044,U_4042,U_4040] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4040),U_4044)),U_4042))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4040),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4042),U_4044))) ) ),
    inference(miniscope,[status(thm)],[f_1082_2]) ).

fof(f_1082_4,plain,
    ( ! [U_4041,U_4043,U_4045] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4041),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4043),U_4045)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4041),U_4045)),U_4043)) )
    & ! [U_4042,U_4040,U_4044] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4040),U_4044)),U_4042))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4040),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4042),U_4044))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1082_3]) ).

cnf(f_1082_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4040),U_4044)),U_4042))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4040),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4042),U_4044))) ),
    inference(clausify,[status(thm)],[f_1082_4]) ).

cnf(f_1082_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4041),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4043),U_4045)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4041),U_4045)),U_4043)) ),
    inference(clausify,[status(thm)],[f_1082_4]) ).

fof(f_1083_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_1083_2,plain,
    ! [U_4047,U_4046] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4047),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4046),U_4047)) = U_4046
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4046),U_4047)) ),
    inference(variable_rename,[status(thm)],[f_1083_1]) ).

fof(f_1083_3,plain,
    ! [U_4047,U_4046] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4047),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4046),U_4047)) = U_4046
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4046),U_4047)) ),
    inference(definitional_conversion,[status(esa)],[f_1083_2]) ).

cnf(f_1083_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4047),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4046),U_4047)) = U_4046
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4046),U_4047)) ),
    inference(clausify,[status(thm)],[f_1083_3]) ).

fof(f_1084_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_1084_2,plain,
    ! [U_4049,U_4048] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4049)),U_4048) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4049),U_4048))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4048),U_4049)) ),
    inference(variable_rename,[status(thm)],[f_1084_1]) ).

fof(f_1084_3,plain,
    ! [U_4048,U_4049] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4049)),U_4048) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4049),U_4048))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4048),U_4049)) ),
    inference(definitional_conversion,[status(esa)],[f_1084_2]) ).

cnf(f_1084_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4049)),U_4048) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4049),U_4048))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4048),U_4049)) ),
    inference(clausify,[status(thm)],[f_1084_3]) ).

fof(f_1085_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_1085_2,plain,
    ! [U_4052,U_4051,U_4050] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4051),U_4050)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4052),U_4050)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4051),U_4052)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4051),U_4052))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4051),U_4050)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4052),U_4050))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4050),U_4052))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4050),U_4051)) ),
    inference(variable_rename,[status(thm)],[f_1085_1]) ).

fof(f_1085_3,plain,
    ( ! [U_4050,U_4051,U_4052] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4051),U_4050)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4052),U_4050)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4051),U_4052))
        | ~ sP313(U_4050,U_4051,U_4052) )
    & ! [U_4050,U_4051,U_4052] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4051),U_4052))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4051),U_4050)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4052),U_4050)))
        | ~ sP313(U_4050,U_4051,U_4052) )
    & ! [U_4050,U_4051,U_4052] :
        ( sP313(U_4050,U_4051,U_4052)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4050),U_4052))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4050),U_4051)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP313])],[f_1085_2]) ).

cnf(f_1085_4,plain,
    ( sP313(U_4050,U_4051,U_4052)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4050),U_4052))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4050),U_4051)) ),
    inference(clausify,[status(thm)],[f_1085_3]) ).

cnf(f_1085_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4051),U_4052))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4051),U_4050)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4052),U_4050)))
    | ~ sP313(U_4050,U_4051,U_4052) ),
    inference(clausify,[status(thm)],[f_1085_3]) ).

cnf(f_1085_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4051),U_4050)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4052),U_4050)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4051),U_4052))
    | ~ sP313(U_4050,U_4051,U_4052) ),
    inference(clausify,[status(thm)],[f_1085_3]) ).

fof(f_1086_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_1086_2,plain,
    ! [U_4055,U_4054,U_4053] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4053),U_4055)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4054),U_4055)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4055),U_4053))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4053),U_4054)) ),
    inference(variable_rename,[status(thm)],[f_1086_1]) ).

fof(f_1086_3,plain,
    ! [U_4054,U_4053,U_4055] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4053),U_4055)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4054),U_4055)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4055),U_4053))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4053),U_4054)) ),
    inference(definitional_conversion,[status(esa)],[f_1086_2]) ).

cnf(f_1086_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4053),U_4055)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4054),U_4055)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4055),U_4053))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4053),U_4054)) ),
    inference(clausify,[status(thm)],[f_1086_3]) ).

fof(f_1087_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_1087_2,plain,
    ! [U_4058,U_4057,U_4056] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4058),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4057),U_4056)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4058),U_4056)),U_4057)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4056),U_4057)) ),
    inference(variable_rename,[status(thm)],[f_1087_1]) ).

fof(f_1087_3,plain,
    ! [U_4056,U_4057,U_4058] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4058),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4057),U_4056)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4058),U_4056)),U_4057)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4056),U_4057)) ),
    inference(definitional_conversion,[status(esa)],[f_1087_2]) ).

cnf(f_1087_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4058),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4057),U_4056)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4058),U_4056)),U_4057)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4056),U_4057)) ),
    inference(clausify,[status(thm)],[f_1087_3]) ).

fof(f_1088_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_1088_2,plain,
    ! [U_4061,U_4060,U_4059] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4059),U_4060)),U_4061))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4061),U_4060))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4061),U_4060)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4059),U_4060)),U_4061)) ) ),
    inference(variable_rename,[status(thm)],[f_1088_1]) ).

fof(f_1088_3,plain,
    ( ! [U_4067,U_4065,U_4063] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4063),U_4065)),U_4067))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4063),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4067),U_4065))) )
    & ! [U_4066,U_4064,U_4062] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4062),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4066),U_4064)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4062),U_4064)),U_4066)) ) ),
    inference(miniscope,[status(thm)],[f_1088_2]) ).

fof(f_1088_4,plain,
    ( ! [U_4063,U_4065,U_4067] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4063),U_4065)),U_4067))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4063),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4067),U_4065))) )
    & ! [U_4064,U_4062,U_4066] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4062),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4066),U_4064)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4062),U_4064)),U_4066)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1088_3]) ).

cnf(f_1088_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4062),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4066),U_4064)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4062),U_4064)),U_4066)) ),
    inference(clausify,[status(thm)],[f_1088_4]) ).

cnf(f_1088_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_4063),U_4065)),U_4067))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4063),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4067),U_4065))) ),
    inference(clausify,[status(thm)],[f_1088_4]) ).

fof(f_1089_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_1089_2,plain,
    ! [U_4070,U_4069,U_4068] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4070),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4069),U_4070)),U_4068)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4068),U_4069)) ),
    inference(variable_rename,[status(thm)],[f_1089_1]) ).

fof(f_1089_3,plain,
    ! [U_4068,U_4069,U_4070] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4070),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4069),U_4070)),U_4068)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4068),U_4069)) ),
    inference(definitional_conversion,[status(esa)],[f_1089_2]) ).

cnf(f_1089_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4070),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4069),U_4070)),U_4068)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4068),U_4069)) ),
    inference(clausify,[status(thm)],[f_1089_3]) ).

fof(f_1090_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_1090_2,plain,
    ! [U_4072,U_4071] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4071),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4072),U_4071)) = U_4072
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4071),U_4072)) ),
    inference(variable_rename,[status(thm)],[f_1090_1]) ).

fof(f_1090_3,plain,
    ! [U_4071,U_4072] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4071),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4072),U_4071)) = U_4072
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4071),U_4072)) ),
    inference(definitional_conversion,[status(esa)],[f_1090_2]) ).

cnf(f_1090_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4071),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4072),U_4071)) = U_4072
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4071),U_4072)) ),
    inference(clausify,[status(thm)],[f_1090_3]) ).

fof(f_1091_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_1091_2,plain,
    ! [U_4075,U_4074,U_4073] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4075),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4074),U_4073)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4075),U_4074)),U_4073)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4073),U_4074)) ),
    inference(variable_rename,[status(thm)],[f_1091_1]) ).

fof(f_1091_3,plain,
    ! [U_4073,U_4074,U_4075] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4075),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4074),U_4073)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4075),U_4074)),U_4073)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4073),U_4074)) ),
    inference(definitional_conversion,[status(esa)],[f_1091_2]) ).

cnf(f_1091_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4075),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4074),U_4073)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4075),U_4074)),U_4073)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4073),U_4074)) ),
    inference(clausify,[status(thm)],[f_1091_3]) ).

fof(f_1092_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_1092_2,plain,
    ! [U_4078,U_4077,U_4076] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4078),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4077),U_4076)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4078),U_4076)),U_4077)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4078),U_4076)),U_4077))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4078),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4077),U_4076))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4076),U_4077)) ),
    inference(variable_rename,[status(thm)],[f_1092_1]) ).

fof(f_1092_3,plain,
    ( ! [U_4076,U_4077,U_4078] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4078),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4077),U_4076)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4078),U_4076)),U_4077))
        | ~ sP314(U_4076,U_4077,U_4078) )
    & ! [U_4076,U_4077,U_4078] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4078),U_4076)),U_4077))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4078),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4077),U_4076)))
        | ~ sP314(U_4076,U_4077,U_4078) )
    & ! [U_4076,U_4077,U_4078] :
        ( sP314(U_4076,U_4077,U_4078)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4076),U_4077)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP314])],[f_1092_2]) ).

cnf(f_1092_4,plain,
    ( sP314(U_4076,U_4077,U_4078)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4076),U_4077)) ),
    inference(clausify,[status(thm)],[f_1092_3]) ).

cnf(f_1092_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_4078),U_4076)),U_4077))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4078),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4077),U_4076)))
    | ~ sP314(U_4076,U_4077,U_4078) ),
    inference(clausify,[status(thm)],[f_1092_3]) ).

cnf(f_1092_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4078),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4077),U_4076)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4078),U_4076)),U_4077))
    | ~ sP314(U_4076,U_4077,U_4078) ),
    inference(clausify,[status(thm)],[f_1092_3]) ).

fof(f_1093_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_1093_2,plain,
    ! [U_4080,U_4079] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4080),U_4079)),U_4079) = U_4080
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4079),U_4080)) ),
    inference(variable_rename,[status(thm)],[f_1093_1]) ).

fof(f_1093_3,plain,
    ! [U_4080,U_4079] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4080),U_4079)),U_4079) = U_4080
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4079),U_4080)) ),
    inference(definitional_conversion,[status(esa)],[f_1093_2]) ).

cnf(f_1093_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4080),U_4079)),U_4079) = U_4080
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4079),U_4080)) ),
    inference(clausify,[status(thm)],[f_1093_3]) ).

fof(f_1094_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_1094_2,plain,
    ! [U_4083,U_4082,U_4081] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4082),U_4081) = U_4083
          | U_4082 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4083),U_4081) )
        & ( U_4082 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4083),U_4081)
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4082),U_4081) != U_4083 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4081),U_4082)) ),
    inference(variable_rename,[status(thm)],[f_1094_1]) ).

fof(f_1094_3,plain,
    ( ! [U_4081,U_4082,U_4083] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4082),U_4081) = U_4083
        | U_4082 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4083),U_4081)
        | ~ sP315(U_4081,U_4082,U_4083) )
    & ! [U_4081,U_4082,U_4083] :
        ( U_4082 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4083),U_4081)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4082),U_4081) != U_4083
        | ~ sP315(U_4081,U_4082,U_4083) )
    & ! [U_4081,U_4082,U_4083] :
        ( sP315(U_4081,U_4082,U_4083)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4081),U_4082)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP315])],[f_1094_2]) ).

cnf(f_1094_4,plain,
    ( sP315(U_4081,U_4082,U_4083)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4081),U_4082)) ),
    inference(clausify,[status(thm)],[f_1094_3]) ).

cnf(f_1094_5,plain,
    ( U_4082 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4083),U_4081)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4082),U_4081) != U_4083
    | ~ sP315(U_4081,U_4082,U_4083) ),
    inference(clausify,[status(thm)],[f_1094_3]) ).

cnf(f_1094_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4082),U_4081) = U_4083
    | U_4082 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4083),U_4081)
    | ~ sP315(U_4081,U_4082,U_4083) ),
    inference(clausify,[status(thm)],[f_1094_3]) ).

fof(f_1095_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_1095_2,plain,
    ! [U_4086,U_4085,U_4084] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4086),U_4085)),U_4084) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4085),U_4084))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4084),U_4085)) ),
    inference(variable_rename,[status(thm)],[f_1095_1]) ).

fof(f_1095_3,plain,
    ! [U_4085,U_4086,U_4084] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4086),U_4085)),U_4084) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4085),U_4084))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4084),U_4085)) ),
    inference(definitional_conversion,[status(esa)],[f_1095_2]) ).

cnf(f_1095_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4086),U_4085)),U_4084) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4085),U_4084))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4084),U_4085)) ),
    inference(clausify,[status(thm)],[f_1095_3]) ).

fof(f_1096_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_1096_2,plain,
    ! [U_4089,U_4088,U_4087] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4088),U_4087)),U_4089) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4088),U_4089)),U_4087)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4087),U_4088)) ),
    inference(variable_rename,[status(thm)],[f_1096_1]) ).

fof(f_1096_3,plain,
    ! [U_4087,U_4088,U_4089] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4088),U_4087)),U_4089) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4088),U_4089)),U_4087)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4087),U_4088)) ),
    inference(definitional_conversion,[status(esa)],[f_1096_2]) ).

cnf(f_1096_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4088),U_4087)),U_4089) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4088),U_4089)),U_4087)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4087),U_4088)) ),
    inference(clausify,[status(thm)],[f_1096_3]) ).

fof(f_1097_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_1097_2,plain,
    ! [U_4092,U_4091,U_4090] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4091),U_4092)),U_4090) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4091),U_4090)),U_4092)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4090),U_4091)) ),
    inference(variable_rename,[status(thm)],[f_1097_1]) ).

fof(f_1097_3,plain,
    ! [U_4090,U_4091,U_4092] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4091),U_4092)),U_4090) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4091),U_4090)),U_4092)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4090),U_4091)) ),
    inference(definitional_conversion,[status(esa)],[f_1097_2]) ).

cnf(f_1097_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4091),U_4092)),U_4090) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4091),U_4090)),U_4092)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4090),U_4091)) ),
    inference(clausify,[status(thm)],[f_1097_3]) ).

fof(f_1098_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_1098_2,plain,
    ! [U_4094,U_4093] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4093),U_4094) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4093),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4094)),
    inference(variable_rename,[status(thm)],[f_1098_1]) ).

fof(f_1098_3,plain,
    ! [U_4093,U_4094] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4093),U_4094) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4093),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4094)),
    inference(definitional_conversion,[status(esa)],[f_1098_2]) ).

cnf(f_1098_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4093),U_4094) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4093),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4094)),
    inference(clausify,[status(thm)],[f_1098_3]) ).

fof(f_1099_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_1099_2,plain,
    ! [U_4096,U_4095] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4095),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4096)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4095),U_4096),
    inference(variable_rename,[status(thm)],[f_1099_1]) ).

fof(f_1099_3,plain,
    ! [U_4095,U_4096] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4095),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4096)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4095),U_4096),
    inference(definitional_conversion,[status(esa)],[f_1099_2]) ).

cnf(f_1099_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4095),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4096)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4095),U_4096),
    inference(clausify,[status(thm)],[f_1099_3]) ).

fof(f_1100_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_1100_2,plain,
    ! [U_4098,U_4097] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4097),hAPP(c_Nat_OSuc,U_4098)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4097),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4098),
    inference(variable_rename,[status(thm)],[f_1100_1]) ).

fof(f_1100_3,plain,
    ! [U_4097,U_4098] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4097),hAPP(c_Nat_OSuc,U_4098)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4097),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4098),
    inference(definitional_conversion,[status(esa)],[f_1100_2]) ).

cnf(f_1100_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4097),hAPP(c_Nat_OSuc,U_4098)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4097),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4098),
    inference(clausify,[status(thm)],[f_1100_3]) ).

fof(f_1101_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_1101_2,plain,
    ! [U_4099] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4099)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4099,
    inference(variable_rename,[status(thm)],[f_1101_1]) ).

fof(f_1101_3,plain,
    ! [U_4099] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4099)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4099,
    inference(definitional_conversion,[status(esa)],[f_1101_2]) ).

cnf(f_1101_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4099)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4099,
    inference(clausify,[status(thm)],[f_1101_3]) ).

fof(f_1102_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_1102_2,plain,
    ! [U_4101,U_4100] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4100),U_4101)),U_4101) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4100),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4100,U_4101)),
    inference(variable_rename,[status(thm)],[f_1102_1]) ).

fof(f_1102_3,plain,
    ! [U_4100,U_4101] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4100),U_4101)),U_4101) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4100),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4100,U_4101)),
    inference(definitional_conversion,[status(esa)],[f_1102_2]) ).

cnf(f_1102_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4100),U_4101)),U_4101) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4100),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4100,U_4101)),
    inference(clausify,[status(thm)],[f_1102_3]) ).

fof(f_1103_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_1103_2,plain,
    ! [U_4103,U_4102] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4102),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4103),U_4102)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4103),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4103,U_4102)),
    inference(variable_rename,[status(thm)],[f_1103_1]) ).

fof(f_1103_3,plain,
    ! [U_4102,U_4103] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4102),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4103),U_4102)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4103),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4103,U_4102)),
    inference(definitional_conversion,[status(esa)],[f_1103_2]) ).

cnf(f_1103_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4102),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4103),U_4102)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4103),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4103,U_4102)),
    inference(clausify,[status(thm)],[f_1103_3]) ).

fof(f_1104_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_1104_2,plain,
    ! [U_4105,U_4104] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4104,U_4105) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4104),U_4105)),U_4105)),
    inference(variable_rename,[status(thm)],[f_1104_1]) ).

fof(f_1104_3,plain,
    ! [U_4104,U_4105] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4104,U_4105) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4104),U_4105)),U_4105)),
    inference(definitional_conversion,[status(esa)],[f_1104_2]) ).

cnf(f_1104_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4104,U_4105) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4104),U_4105)),U_4105)),
    inference(clausify,[status(thm)],[f_1104_3]) ).

fof(f_1105_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_1105_2,plain,
    ! [U_4107,U_4106] :
      ( c_Nat__Transfer_Otsub(U_4107,U_4106) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4107),U_4106)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4106),U_4107)) ),
    inference(variable_rename,[status(thm)],[f_1105_1]) ).

fof(f_1105_3,plain,
    ! [U_4106,U_4107] :
      ( c_Nat__Transfer_Otsub(U_4107,U_4106) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4107),U_4106)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4106),U_4107)) ),
    inference(definitional_conversion,[status(esa)],[f_1105_2]) ).

cnf(f_1105_4,plain,
    ( c_Nat__Transfer_Otsub(U_4107,U_4106) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4107),U_4106)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4106),U_4107)) ),
    inference(clausify,[status(thm)],[f_1105_3]) ).

fof(f_1106_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_1106_2,plain,
    ! [U_4109,U_4108] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4108),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4109)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4108),U_4109)),
    inference(variable_rename,[status(thm)],[f_1106_1]) ).

fof(f_1106_3,plain,
    ! [U_4108,U_4109] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4108),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4109)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4108),U_4109)),
    inference(definitional_conversion,[status(esa)],[f_1106_2]) ).

cnf(f_1106_4,plain,
    c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4108),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4109)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4108),U_4109)),
    inference(clausify,[status(thm)],[f_1106_3]) ).

fof(f_1107_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_1107_2,plain,
    ! [U_4115,U_4114,U_4113,U_4112,U_4111,U_4110] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4111),U_4112)),U_4113)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4114),U_4112)),U_4115)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4110),U_4111),U_4114)),U_4112)),U_4113)),U_4115)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4110),U_4111),U_4114)),U_4112)),U_4113)),U_4115))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4111),U_4112)),U_4113)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4114),U_4112)),U_4115))) ) )
      | ~ class_Rings_Oordered__ring(U_4110) ),
    inference(variable_rename,[status(thm)],[f_1107_1]) ).

fof(f_1107_3,plain,
    ( ! [U_4110,U_4111,U_4112,U_4113,U_4114,U_4115] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4111),U_4112)),U_4113)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4114),U_4112)),U_4115)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4110),U_4111),U_4114)),U_4112)),U_4113)),U_4115))
        | ~ sP316(U_4110,U_4111,U_4112,U_4113,U_4114,U_4115) )
    & ! [U_4110,U_4111,U_4112,U_4113,U_4114,U_4115] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4110),U_4111),U_4114)),U_4112)),U_4113)),U_4115))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4111),U_4112)),U_4113)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4114),U_4112)),U_4115)))
        | ~ sP316(U_4110,U_4111,U_4112,U_4113,U_4114,U_4115) )
    & ! [U_4110,U_4111,U_4112,U_4113,U_4114,U_4115] :
        ( sP316(U_4110,U_4111,U_4112,U_4113,U_4114,U_4115)
        | ~ class_Rings_Oordered__ring(U_4110) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP316])],[f_1107_2]) ).

cnf(f_1107_4,plain,
    ( sP316(U_4110,U_4111,U_4112,U_4113,U_4114,U_4115)
    | ~ class_Rings_Oordered__ring(U_4110) ),
    inference(clausify,[status(thm)],[f_1107_3]) ).

cnf(f_1107_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4110),U_4111),U_4114)),U_4112)),U_4113)),U_4115))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4111),U_4112)),U_4113)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4114),U_4112)),U_4115)))
    | ~ sP316(U_4110,U_4111,U_4112,U_4113,U_4114,U_4115) ),
    inference(clausify,[status(thm)],[f_1107_3]) ).

cnf(f_1107_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4111),U_4112)),U_4113)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),U_4114),U_4112)),U_4115)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4110),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4110),U_4111),U_4114)),U_4112)),U_4113)),U_4115))
    | ~ sP316(U_4110,U_4111,U_4112,U_4113,U_4114,U_4115) ),
    inference(clausify,[status(thm)],[f_1107_3]) ).

fof(f_1108_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_1108_2,plain,
    ! [U_4121,U_4120,U_4119,U_4118,U_4117,U_4116] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),U_4117),U_4118)),U_4119)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),U_4120),U_4118)),U_4121)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4116),U_4119),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4116),U_4120),U_4117)),U_4118)),U_4121))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4116),U_4119),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4116),U_4120),U_4117)),U_4118)),U_4121)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),U_4117),U_4118)),U_4119)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),U_4120),U_4118)),U_4121))) ) )
      | ~ class_Rings_Oordered__ring(U_4116) ),
    inference(variable_rename,[status(thm)],[f_1108_1]) ).

fof(f_1108_3,plain,
    ( ! [U_4116,U_4117,U_4118,U_4119,U_4120,U_4121] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),U_4117),U_4118)),U_4119)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),U_4120),U_4118)),U_4121)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4116),U_4119),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4116),U_4120),U_4117)),U_4118)),U_4121)))
        | ~ sP317(U_4116,U_4117,U_4118,U_4119,U_4120,U_4121) )
    & ! [U_4116,U_4117,U_4118,U_4119,U_4120,U_4121] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4116),U_4119),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4116),U_4120),U_4117)),U_4118)),U_4121)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),U_4117),U_4118)),U_4119)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),U_4120),U_4118)),U_4121)))
        | ~ sP317(U_4116,U_4117,U_4118,U_4119,U_4120,U_4121) )
    & ! [U_4116,U_4117,U_4118,U_4119,U_4120,U_4121] :
        ( sP317(U_4116,U_4117,U_4118,U_4119,U_4120,U_4121)
        | ~ class_Rings_Oordered__ring(U_4116) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP317])],[f_1108_2]) ).

cnf(f_1108_4,plain,
    ( sP317(U_4116,U_4117,U_4118,U_4119,U_4120,U_4121)
    | ~ class_Rings_Oordered__ring(U_4116) ),
    inference(clausify,[status(thm)],[f_1108_3]) ).

cnf(f_1108_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4116),U_4119),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4116),U_4120),U_4117)),U_4118)),U_4121)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),U_4117),U_4118)),U_4119)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),U_4120),U_4118)),U_4121)))
    | ~ sP317(U_4116,U_4117,U_4118,U_4119,U_4120,U_4121) ),
    inference(clausify,[status(thm)],[f_1108_3]) ).

cnf(f_1108_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4116),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),U_4117),U_4118)),U_4119)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),U_4120),U_4118)),U_4121)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4116),U_4119),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4116),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4116),U_4120),U_4117)),U_4118)),U_4121)))
    | ~ sP317(U_4116,U_4117,U_4118,U_4119,U_4120,U_4121) ),
    inference(clausify,[status(thm)],[f_1108_3]) ).

fof(f_1109_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_1109_2,plain,
    ! [U_4127,U_4126,U_4125,U_4124,U_4123,U_4122] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4124)),U_4125)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4126),U_4124)),U_4127)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4122),U_4123),U_4126)),U_4124)),U_4125)),U_4127)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4122),U_4123),U_4126)),U_4124)),U_4125)),U_4127))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4124)),U_4125)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4126),U_4124)),U_4127))) ) )
      | ~ class_Rings_Oordered__ring(U_4122) ),
    inference(variable_rename,[status(thm)],[f_1109_1]) ).

fof(f_1109_3,plain,
    ( ! [U_4122,U_4123,U_4124,U_4125,U_4126,U_4127] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4124)),U_4125)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4126),U_4124)),U_4127)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4122),U_4123),U_4126)),U_4124)),U_4125)),U_4127))
        | ~ sP318(U_4122,U_4123,U_4124,U_4125,U_4126,U_4127) )
    & ! [U_4122,U_4123,U_4124,U_4125,U_4126,U_4127] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4122),U_4123),U_4126)),U_4124)),U_4125)),U_4127))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4124)),U_4125)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4126),U_4124)),U_4127)))
        | ~ sP318(U_4122,U_4123,U_4124,U_4125,U_4126,U_4127) )
    & ! [U_4122,U_4123,U_4124,U_4125,U_4126,U_4127] :
        ( sP318(U_4122,U_4123,U_4124,U_4125,U_4126,U_4127)
        | ~ class_Rings_Oordered__ring(U_4122) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP318])],[f_1109_2]) ).

cnf(f_1109_4,plain,
    ( sP318(U_4122,U_4123,U_4124,U_4125,U_4126,U_4127)
    | ~ class_Rings_Oordered__ring(U_4122) ),
    inference(clausify,[status(thm)],[f_1109_3]) ).

cnf(f_1109_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4122),U_4123),U_4126)),U_4124)),U_4125)),U_4127))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4124)),U_4125)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4126),U_4124)),U_4127)))
    | ~ sP318(U_4122,U_4123,U_4124,U_4125,U_4126,U_4127) ),
    inference(clausify,[status(thm)],[f_1109_3]) ).

cnf(f_1109_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4123),U_4124)),U_4125)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),U_4126),U_4124)),U_4127)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4122),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4122),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4122),U_4123),U_4126)),U_4124)),U_4125)),U_4127))
    | ~ sP318(U_4122,U_4123,U_4124,U_4125,U_4126,U_4127) ),
    inference(clausify,[status(thm)],[f_1109_3]) ).

fof(f_1110_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_1110_2,plain,
    ! [U_4133,U_4132,U_4131,U_4130,U_4129,U_4128] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4128),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),U_4129),U_4130)),U_4131)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),U_4132),U_4130)),U_4133)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4128),U_4131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4128),U_4132),U_4129)),U_4130)),U_4133))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4128),U_4131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4128),U_4132),U_4129)),U_4130)),U_4133)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4128),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),U_4129),U_4130)),U_4131)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),U_4132),U_4130)),U_4133))) ) )
      | ~ class_Rings_Oordered__ring(U_4128) ),
    inference(variable_rename,[status(thm)],[f_1110_1]) ).

fof(f_1110_3,plain,
    ( ! [U_4128,U_4129,U_4130,U_4131,U_4132,U_4133] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4128),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),U_4129),U_4130)),U_4131)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),U_4132),U_4130)),U_4133)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4128),U_4131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4128),U_4132),U_4129)),U_4130)),U_4133)))
        | ~ sP319(U_4128,U_4129,U_4130,U_4131,U_4132,U_4133) )
    & ! [U_4128,U_4129,U_4130,U_4131,U_4132,U_4133] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4128),U_4131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4128),U_4132),U_4129)),U_4130)),U_4133)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4128),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),U_4129),U_4130)),U_4131)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),U_4132),U_4130)),U_4133)))
        | ~ sP319(U_4128,U_4129,U_4130,U_4131,U_4132,U_4133) )
    & ! [U_4128,U_4129,U_4130,U_4131,U_4132,U_4133] :
        ( sP319(U_4128,U_4129,U_4130,U_4131,U_4132,U_4133)
        | ~ class_Rings_Oordered__ring(U_4128) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP319])],[f_1110_2]) ).

cnf(f_1110_4,plain,
    ( sP319(U_4128,U_4129,U_4130,U_4131,U_4132,U_4133)
    | ~ class_Rings_Oordered__ring(U_4128) ),
    inference(clausify,[status(thm)],[f_1110_3]) ).

cnf(f_1110_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4128),U_4131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4128),U_4132),U_4129)),U_4130)),U_4133)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4128),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),U_4129),U_4130)),U_4131)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),U_4132),U_4130)),U_4133)))
    | ~ sP319(U_4128,U_4129,U_4130,U_4131,U_4132,U_4133) ),
    inference(clausify,[status(thm)],[f_1110_3]) ).

cnf(f_1110_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4128),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),U_4129),U_4130)),U_4131)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),U_4132),U_4130)),U_4133)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4128),U_4131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4128),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4128),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4128),U_4132),U_4129)),U_4130)),U_4133)))
    | ~ sP319(U_4128,U_4129,U_4130,U_4131,U_4132,U_4133) ),
    inference(clausify,[status(thm)],[f_1110_3]) ).

fof(f_1111_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_1111_2,plain,
    ! [U_4135,U_4134] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4134),hAPP(c_Nat_OSuc,U_4135))),U_4134))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4134)) ),
    inference(variable_rename,[status(thm)],[f_1111_1]) ).

fof(f_1111_3,plain,
    ! [U_4134,U_4135] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4134),hAPP(c_Nat_OSuc,U_4135))),U_4134))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4134)) ),
    inference(definitional_conversion,[status(esa)],[f_1111_2]) ).

cnf(f_1111_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4134),hAPP(c_Nat_OSuc,U_4135))),U_4134))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4134)) ),
    inference(clausify,[status(thm)],[f_1111_3]) ).

fof(f_1112_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_1112_2,plain,
    ! [U_4136] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4136),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_4136
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4136)) ),
    inference(variable_rename,[status(thm)],[f_1112_1]) ).

fof(f_1112_3,plain,
    ! [U_4136] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4136),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_4136
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4136)) ),
    inference(definitional_conversion,[status(esa)],[f_1112_2]) ).

cnf(f_1112_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4136),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_4136
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4136)) ),
    inference(clausify,[status(thm)],[f_1112_3]) ).

fof(f_1113_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_1113_2,plain,
    ! [U_4141,U_4140,U_4139] :
      ( ( hBOOL(hAPP(U_4139,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4140),U_4141)))
        | ? [U_4138] :
            ( ~ hBOOL(hAPP(U_4139,U_4138))
            & U_4140 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4141),U_4138) )
        | ( ~ hBOOL(hAPP(U_4139,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4140),U_4141)) ) )
      & ( ( ! [U_4137] :
              ( hBOOL(hAPP(U_4139,U_4137))
              | U_4140 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4141),U_4137) )
          & ( hBOOL(hAPP(U_4139,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4140),U_4141)) ) )
        | ~ hBOOL(hAPP(U_4139,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4140),U_4141))) ) ),
    inference(variable_rename,[status(thm)],[f_1113_1]) ).

fof(f_1113_3,plain,
    ( ! [U_4147,U_4145,U_4143] :
        ( hBOOL(hAPP(U_4143,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4145),U_4147)))
        | ? [U_4138] :
            ( ~ hBOOL(hAPP(U_4143,U_4138))
            & U_4145 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4147),U_4138) )
        | ( ~ hBOOL(hAPP(U_4143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4145),U_4147)) ) )
    & ! [U_4146,U_4144,U_4142] :
        ( ( ! [U_4137] :
              ( hBOOL(hAPP(U_4142,U_4137))
              | U_4144 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4146),U_4137) )
          & ( hBOOL(hAPP(U_4142,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4144),U_4146)) ) )
        | ~ hBOOL(hAPP(U_4142,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4144),U_4146))) ) ),
    inference(miniscope,[status(thm)],[f_1113_2]) ).

fof(f_1113_4,plain,
    ( ! [U_4147,U_4145,U_4143] :
        ( hBOOL(hAPP(U_4143,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4145),U_4147)))
        | ( ~ hBOOL(hAPP(U_4143,sK84(U_4147,U_4145,U_4143)))
          & U_4145 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4147),sK84(U_4147,U_4145,U_4143)) )
        | ( ~ hBOOL(hAPP(U_4143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4145),U_4147)) ) )
    & ! [U_4146,U_4144,U_4142] :
        ( ( ! [U_4137] :
              ( hBOOL(hAPP(U_4142,U_4137))
              | U_4144 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4146),U_4137) )
          & ( hBOOL(hAPP(U_4142,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4144),U_4146)) ) )
        | ~ hBOOL(hAPP(U_4142,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4144),U_4146))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_4138,sK84(U_4147,U_4145,U_4143))],[f_1113_3]) ).

fof(f_1113_5,plain,
    ( ! [U_4143,U_4145,U_4147] :
        ( ~ hBOOL(hAPP(U_4143,sK84(U_4147,U_4145,U_4143)))
        | ~ sP322(U_4143,U_4145,U_4147) )
    & ! [U_4143,U_4145,U_4147] :
        ( U_4145 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4147),sK84(U_4147,U_4145,U_4143))
        | ~ sP322(U_4143,U_4145,U_4147) )
    & ! [U_4143,U_4145,U_4147] :
        ( ~ hBOOL(hAPP(U_4143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP321(U_4143,U_4145,U_4147) )
    & ! [U_4143,U_4145,U_4147] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4145),U_4147))
        | ~ sP321(U_4143,U_4145,U_4147) )
    & ! [U_4137,U_4142,U_4144,U_4146] :
        ( hBOOL(hAPP(U_4142,U_4137))
        | U_4144 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4146),U_4137)
        | ~ sP320(U_4137,U_4142,U_4144,U_4146) )
    & ! [U_4137,U_4142,U_4144,U_4146] :
        ( hBOOL(hAPP(U_4142,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4144),U_4146))
        | ~ sP320(U_4137,U_4142,U_4144,U_4146) )
    & ! [U_4143,U_4145,U_4147] :
        ( hBOOL(hAPP(U_4143,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4145),U_4147)))
        | sP322(U_4143,U_4145,U_4147)
        | sP321(U_4143,U_4145,U_4147) )
    & ! [U_4137,U_4142,U_4144,U_4146] :
        ( sP320(U_4137,U_4142,U_4144,U_4146)
        | ~ hBOOL(hAPP(U_4142,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4144),U_4146))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP320,sP321,sP322])],[f_1113_4]) ).

cnf(f_1113_6,plain,
    ( sP320(U_4137,U_4142,U_4144,U_4146)
    | ~ hBOOL(hAPP(U_4142,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4144),U_4146))) ),
    inference(clausify,[status(thm)],[f_1113_5]) ).

cnf(f_1113_7,plain,
    ( hBOOL(hAPP(U_4143,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4145),U_4147)))
    | sP322(U_4143,U_4145,U_4147)
    | sP321(U_4143,U_4145,U_4147) ),
    inference(clausify,[status(thm)],[f_1113_5]) ).

cnf(f_1113_8,plain,
    ( hBOOL(hAPP(U_4142,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4144),U_4146))
    | ~ sP320(U_4137,U_4142,U_4144,U_4146) ),
    inference(clausify,[status(thm)],[f_1113_5]) ).

cnf(f_1113_9,plain,
    ( hBOOL(hAPP(U_4142,U_4137))
    | U_4144 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4146),U_4137)
    | ~ sP320(U_4137,U_4142,U_4144,U_4146) ),
    inference(clausify,[status(thm)],[f_1113_5]) ).

cnf(f_1113_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4145),U_4147))
    | ~ sP321(U_4143,U_4145,U_4147) ),
    inference(clausify,[status(thm)],[f_1113_5]) ).

cnf(f_1113_11,plain,
    ( ~ hBOOL(hAPP(U_4143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP321(U_4143,U_4145,U_4147) ),
    inference(clausify,[status(thm)],[f_1113_5]) ).

cnf(f_1113_12,plain,
    ( U_4145 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4147),sK84(U_4147,U_4145,U_4143))
    | ~ sP322(U_4143,U_4145,U_4147) ),
    inference(clausify,[status(thm)],[f_1113_5]) ).

cnf(f_1113_13,plain,
    ( ~ hBOOL(hAPP(U_4143,sK84(U_4147,U_4145,U_4143)))
    | ~ sP322(U_4143,U_4145,U_4147) ),
    inference(clausify,[status(thm)],[f_1113_5]) ).

fof(f_1114_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_1114_2,plain,
    ! [U_4152,U_4151,U_4150] :
      ( ( hBOOL(hAPP(U_4150,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4151),U_4152)))
        | ? [U_4149] :
            ( ~ hBOOL(hAPP(U_4150,U_4149))
            & U_4151 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4152),U_4149) )
        | ( ~ hBOOL(hAPP(U_4150,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4151),U_4152)) ) )
      & ( ( ! [U_4148] :
              ( hBOOL(hAPP(U_4150,U_4148))
              | U_4151 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4152),U_4148) )
          & ( hBOOL(hAPP(U_4150,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4151),U_4152)) ) )
        | ~ hBOOL(hAPP(U_4150,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4151),U_4152))) ) ),
    inference(variable_rename,[status(thm)],[f_1114_1]) ).

fof(f_1114_3,plain,
    ( ! [U_4158,U_4156,U_4154] :
        ( hBOOL(hAPP(U_4154,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4156),U_4158)))
        | ? [U_4149] :
            ( ~ hBOOL(hAPP(U_4154,U_4149))
            & U_4156 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4158),U_4149) )
        | ( ~ hBOOL(hAPP(U_4154,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4156),U_4158)) ) )
    & ! [U_4157,U_4155,U_4153] :
        ( ( ! [U_4148] :
              ( hBOOL(hAPP(U_4153,U_4148))
              | U_4155 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4157),U_4148) )
          & ( hBOOL(hAPP(U_4153,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4155),U_4157)) ) )
        | ~ hBOOL(hAPP(U_4153,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4155),U_4157))) ) ),
    inference(miniscope,[status(thm)],[f_1114_2]) ).

fof(f_1114_4,plain,
    ( ! [U_4158,U_4156,U_4154] :
        ( hBOOL(hAPP(U_4154,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4156),U_4158)))
        | ( ~ hBOOL(hAPP(U_4154,sK85(U_4158,U_4156,U_4154)))
          & U_4156 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4158),sK85(U_4158,U_4156,U_4154)) )
        | ( ~ hBOOL(hAPP(U_4154,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4156),U_4158)) ) )
    & ! [U_4157,U_4155,U_4153] :
        ( ( ! [U_4148] :
              ( hBOOL(hAPP(U_4153,U_4148))
              | U_4155 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4157),U_4148) )
          & ( hBOOL(hAPP(U_4153,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4155),U_4157)) ) )
        | ~ hBOOL(hAPP(U_4153,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4155),U_4157))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_4149,sK85(U_4158,U_4156,U_4154))],[f_1114_3]) ).

fof(f_1114_5,plain,
    ( ! [U_4156,U_4154,U_4158] :
        ( ~ hBOOL(hAPP(U_4154,sK85(U_4158,U_4156,U_4154)))
        | ~ sP325(U_4156,U_4154,U_4158) )
    & ! [U_4156,U_4154,U_4158] :
        ( U_4156 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4158),sK85(U_4158,U_4156,U_4154))
        | ~ sP325(U_4156,U_4154,U_4158) )
    & ! [U_4156,U_4154,U_4158] :
        ( ~ hBOOL(hAPP(U_4154,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP324(U_4156,U_4154,U_4158) )
    & ! [U_4156,U_4154,U_4158] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4156),U_4158))
        | ~ sP324(U_4156,U_4154,U_4158) )
    & ! [U_4157,U_4148,U_4153,U_4155] :
        ( hBOOL(hAPP(U_4153,U_4148))
        | U_4155 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4157),U_4148)
        | ~ sP323(U_4157,U_4148,U_4153,U_4155) )
    & ! [U_4157,U_4148,U_4153,U_4155] :
        ( hBOOL(hAPP(U_4153,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4155),U_4157))
        | ~ sP323(U_4157,U_4148,U_4153,U_4155) )
    & ! [U_4156,U_4154,U_4158] :
        ( hBOOL(hAPP(U_4154,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4156),U_4158)))
        | sP325(U_4156,U_4154,U_4158)
        | sP324(U_4156,U_4154,U_4158) )
    & ! [U_4157,U_4148,U_4153,U_4155] :
        ( sP323(U_4157,U_4148,U_4153,U_4155)
        | ~ hBOOL(hAPP(U_4153,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4155),U_4157))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP323,sP324,sP325])],[f_1114_4]) ).

cnf(f_1114_6,plain,
    ( sP323(U_4157,U_4148,U_4153,U_4155)
    | ~ hBOOL(hAPP(U_4153,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4155),U_4157))) ),
    inference(clausify,[status(thm)],[f_1114_5]) ).

cnf(f_1114_7,plain,
    ( hBOOL(hAPP(U_4154,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4156),U_4158)))
    | sP325(U_4156,U_4154,U_4158)
    | sP324(U_4156,U_4154,U_4158) ),
    inference(clausify,[status(thm)],[f_1114_5]) ).

cnf(f_1114_8,plain,
    ( hBOOL(hAPP(U_4153,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4155),U_4157))
    | ~ sP323(U_4157,U_4148,U_4153,U_4155) ),
    inference(clausify,[status(thm)],[f_1114_5]) ).

cnf(f_1114_9,plain,
    ( hBOOL(hAPP(U_4153,U_4148))
    | U_4155 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4157),U_4148)
    | ~ sP323(U_4157,U_4148,U_4153,U_4155) ),
    inference(clausify,[status(thm)],[f_1114_5]) ).

cnf(f_1114_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4156),U_4158))
    | ~ sP324(U_4156,U_4154,U_4158) ),
    inference(clausify,[status(thm)],[f_1114_5]) ).

cnf(f_1114_11,plain,
    ( ~ hBOOL(hAPP(U_4154,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP324(U_4156,U_4154,U_4158) ),
    inference(clausify,[status(thm)],[f_1114_5]) ).

cnf(f_1114_12,plain,
    ( U_4156 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4158),sK85(U_4158,U_4156,U_4154))
    | ~ sP325(U_4156,U_4154,U_4158) ),
    inference(clausify,[status(thm)],[f_1114_5]) ).

cnf(f_1114_13,plain,
    ( ~ hBOOL(hAPP(U_4154,sK85(U_4158,U_4156,U_4154)))
    | ~ sP325(U_4156,U_4154,U_4158) ),
    inference(clausify,[status(thm)],[f_1114_5]) ).

fof(f_1115_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_1115_2,plain,
    ! [U_4160,U_4159] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4159),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4160),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4159),U_4160)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4159),U_4160))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4159),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4160),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_1115_1]) ).

fof(f_1115_3,plain,
    ( ! [U_4164,U_4162] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4162),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4164),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4162),U_4164)) )
    & ! [U_4163,U_4161] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4161),U_4163))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4161),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4163),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_1115_2]) ).

fof(f_1115_4,plain,
    ( ! [U_4164,U_4162] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4162),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4164),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4162),U_4164)) )
    & ! [U_4163,U_4161] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4161),U_4163))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4161),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4163),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1115_3]) ).

cnf(f_1115_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4161),U_4163))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4161),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4163),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1115_4]) ).

cnf(f_1115_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4162),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4164),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4162),U_4164)) ),
    inference(clausify,[status(thm)],[f_1115_4]) ).

fof(f_1116_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_1116_2,plain,
    ! [U_4167,U_4166,U_4165] :
      ( 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_4166),U_4165))),U_4167) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4166)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4165),U_4167))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4165),U_4166)) ),
    inference(variable_rename,[status(thm)],[f_1116_1]) ).

fof(f_1116_3,plain,
    ! [U_4166,U_4165,U_4167] :
      ( 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_4166),U_4165))),U_4167) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4166)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4165),U_4167))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4165),U_4166)) ),
    inference(definitional_conversion,[status(esa)],[f_1116_2]) ).

cnf(f_1116_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_4166),U_4165))),U_4167) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4166)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4165),U_4167))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4165),U_4166)) ),
    inference(clausify,[status(thm)],[f_1116_3]) ).

fof(f_1117_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_1117_2,plain,
    ! [U_4170,U_4169,U_4168] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4170),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4169),U_4168))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4170),U_4168)),hAPP(c_Nat_OSuc,U_4169))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4168),U_4169)) ),
    inference(variable_rename,[status(thm)],[f_1117_1]) ).

fof(f_1117_3,plain,
    ! [U_4168,U_4169,U_4170] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4170),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4169),U_4168))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4170),U_4168)),hAPP(c_Nat_OSuc,U_4169))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4168),U_4169)) ),
    inference(definitional_conversion,[status(esa)],[f_1117_2]) ).

cnf(f_1117_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4170),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4169),U_4168))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4170),U_4168)),hAPP(c_Nat_OSuc,U_4169))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4168),U_4169)) ),
    inference(clausify,[status(thm)],[f_1117_3]) ).

fof(f_1118_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_1118_2,plain,
    ! [U_4175,U_4174,U_4173,U_4172,U_4171] :
      ( ( ( 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_4172),U_4173)),U_4174)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4171),U_4173)),U_4175)))
          | ~ 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_4172),U_4171)),U_4173)),U_4174)),U_4175)) )
        & ( 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_4172),U_4171)),U_4173)),U_4174)),U_4175))
          | ~ 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_4172),U_4173)),U_4174)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4171),U_4173)),U_4175))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4171),U_4172)) ),
    inference(variable_rename,[status(thm)],[f_1118_1]) ).

fof(f_1118_3,plain,
    ( ! [U_4171,U_4172,U_4173,U_4174,U_4175] :
        ( 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_4172),U_4173)),U_4174)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4171),U_4173)),U_4175)))
        | ~ 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_4172),U_4171)),U_4173)),U_4174)),U_4175))
        | ~ sP326(U_4171,U_4172,U_4173,U_4174,U_4175) )
    & ! [U_4171,U_4172,U_4173,U_4174,U_4175] :
        ( 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_4172),U_4171)),U_4173)),U_4174)),U_4175))
        | ~ 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_4172),U_4173)),U_4174)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4171),U_4173)),U_4175)))
        | ~ sP326(U_4171,U_4172,U_4173,U_4174,U_4175) )
    & ! [U_4171,U_4172,U_4173,U_4174,U_4175] :
        ( sP326(U_4171,U_4172,U_4173,U_4174,U_4175)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4171),U_4172)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP326])],[f_1118_2]) ).

cnf(f_1118_4,plain,
    ( sP326(U_4171,U_4172,U_4173,U_4174,U_4175)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4171),U_4172)) ),
    inference(clausify,[status(thm)],[f_1118_3]) ).

cnf(f_1118_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_4172),U_4171)),U_4173)),U_4174)),U_4175))
    | ~ 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_4172),U_4173)),U_4174)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4171),U_4173)),U_4175)))
    | ~ sP326(U_4171,U_4172,U_4173,U_4174,U_4175) ),
    inference(clausify,[status(thm)],[f_1118_3]) ).

cnf(f_1118_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_4172),U_4173)),U_4174)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4171),U_4173)),U_4175)))
    | ~ 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_4172),U_4171)),U_4173)),U_4174)),U_4175))
    | ~ sP326(U_4171,U_4172,U_4173,U_4174,U_4175) ),
    inference(clausify,[status(thm)],[f_1118_3]) ).

fof(f_1119_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_1119_2,plain,
    ! [U_4180,U_4179,U_4178,U_4177,U_4176] :
      ( 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_4177),U_4178)),U_4179)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4176),U_4178)),U_4180)) = 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_4177),U_4176)),U_4178)),U_4179)),U_4180)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4176),U_4177)) ),
    inference(variable_rename,[status(thm)],[f_1119_1]) ).

fof(f_1119_3,plain,
    ! [U_4177,U_4178,U_4176,U_4179,U_4180] :
      ( 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_4177),U_4178)),U_4179)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4176),U_4178)),U_4180)) = 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_4177),U_4176)),U_4178)),U_4179)),U_4180)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4176),U_4177)) ),
    inference(definitional_conversion,[status(esa)],[f_1119_2]) ).

cnf(f_1119_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_4177),U_4178)),U_4179)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4176),U_4178)),U_4180)) = 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_4177),U_4176)),U_4178)),U_4179)),U_4180)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4176),U_4177)) ),
    inference(clausify,[status(thm)],[f_1119_3]) ).

fof(f_1120_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_1120_2,plain,
    ! [U_4185,U_4184,U_4183,U_4182,U_4181] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4182),U_4183)),U_4184) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4181),U_4183)),U_4185)
          | 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_4182),U_4181)),U_4183)),U_4184) != U_4185 )
        & ( 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_4182),U_4181)),U_4183)),U_4184) = U_4185
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4182),U_4183)),U_4184) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4181),U_4183)),U_4185) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4181),U_4182)) ),
    inference(variable_rename,[status(thm)],[f_1120_1]) ).

fof(f_1120_3,plain,
    ( ! [U_4181,U_4182,U_4183,U_4184,U_4185] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4182),U_4183)),U_4184) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4181),U_4183)),U_4185)
        | 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_4182),U_4181)),U_4183)),U_4184) != U_4185
        | ~ sP327(U_4181,U_4182,U_4183,U_4184,U_4185) )
    & ! [U_4181,U_4182,U_4183,U_4184,U_4185] :
        ( 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_4182),U_4181)),U_4183)),U_4184) = U_4185
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4182),U_4183)),U_4184) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4181),U_4183)),U_4185)
        | ~ sP327(U_4181,U_4182,U_4183,U_4184,U_4185) )
    & ! [U_4181,U_4182,U_4183,U_4184,U_4185] :
        ( sP327(U_4181,U_4182,U_4183,U_4184,U_4185)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4181),U_4182)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP327])],[f_1120_2]) ).

cnf(f_1120_4,plain,
    ( sP327(U_4181,U_4182,U_4183,U_4184,U_4185)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4181),U_4182)) ),
    inference(clausify,[status(thm)],[f_1120_3]) ).

cnf(f_1120_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_4182),U_4181)),U_4183)),U_4184) = U_4185
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4182),U_4183)),U_4184) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4181),U_4183)),U_4185)
    | ~ sP327(U_4181,U_4182,U_4183,U_4184,U_4185) ),
    inference(clausify,[status(thm)],[f_1120_3]) ).

cnf(f_1120_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4182),U_4183)),U_4184) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4181),U_4183)),U_4185)
    | 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_4182),U_4181)),U_4183)),U_4184) != U_4185
    | ~ sP327(U_4181,U_4182,U_4183,U_4184,U_4185) ),
    inference(clausify,[status(thm)],[f_1120_3]) ).

fof(f_1121_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_1121_2,plain,
    ! [U_4190,U_4189,U_4188,U_4187,U_4186] :
      ( ( ( 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_4186),U_4188)),U_4189)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4187),U_4188)),U_4190)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4189),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_4187),U_4186)),U_4188)),U_4190))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4189),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_4187),U_4186)),U_4188)),U_4190)))
          | ~ 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_4186),U_4188)),U_4189)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4187),U_4188)),U_4190))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4186),U_4187)) ),
    inference(variable_rename,[status(thm)],[f_1121_1]) ).

fof(f_1121_3,plain,
    ( ! [U_4186,U_4187,U_4189,U_4188,U_4190] :
        ( 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_4186),U_4188)),U_4189)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4187),U_4188)),U_4190)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4189),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_4187),U_4186)),U_4188)),U_4190)))
        | ~ sP328(U_4186,U_4187,U_4189,U_4188,U_4190) )
    & ! [U_4186,U_4187,U_4189,U_4188,U_4190] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4189),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_4187),U_4186)),U_4188)),U_4190)))
        | ~ 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_4186),U_4188)),U_4189)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4187),U_4188)),U_4190)))
        | ~ sP328(U_4186,U_4187,U_4189,U_4188,U_4190) )
    & ! [U_4186,U_4187,U_4189,U_4188,U_4190] :
        ( sP328(U_4186,U_4187,U_4189,U_4188,U_4190)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4186),U_4187)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP328])],[f_1121_2]) ).

cnf(f_1121_4,plain,
    ( sP328(U_4186,U_4187,U_4189,U_4188,U_4190)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4186),U_4187)) ),
    inference(clausify,[status(thm)],[f_1121_3]) ).

cnf(f_1121_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4189),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_4187),U_4186)),U_4188)),U_4190)))
    | ~ 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_4186),U_4188)),U_4189)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4187),U_4188)),U_4190)))
    | ~ sP328(U_4186,U_4187,U_4189,U_4188,U_4190) ),
    inference(clausify,[status(thm)],[f_1121_3]) ).

cnf(f_1121_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_4186),U_4188)),U_4189)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4187),U_4188)),U_4190)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4189),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_4187),U_4186)),U_4188)),U_4190)))
    | ~ sP328(U_4186,U_4187,U_4189,U_4188,U_4190) ),
    inference(clausify,[status(thm)],[f_1121_3]) ).

fof(f_1122_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_1122_2,plain,
    ! [U_4195,U_4194,U_4193,U_4192,U_4191] :
      ( 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_4191),U_4193)),U_4194)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4192),U_4193)),U_4195)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4194),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_4192),U_4191)),U_4193)),U_4195))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4191),U_4192)) ),
    inference(variable_rename,[status(thm)],[f_1122_1]) ).

fof(f_1122_3,plain,
    ! [U_4193,U_4192,U_4191,U_4194,U_4195] :
      ( 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_4191),U_4193)),U_4194)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4192),U_4193)),U_4195)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4194),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_4192),U_4191)),U_4193)),U_4195))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4191),U_4192)) ),
    inference(definitional_conversion,[status(esa)],[f_1122_2]) ).

cnf(f_1122_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_4191),U_4193)),U_4194)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4192),U_4193)),U_4195)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4194),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_4192),U_4191)),U_4193)),U_4195))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4191),U_4192)) ),
    inference(clausify,[status(thm)],[f_1122_3]) ).

fof(f_1123_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_1123_2,plain,
    ! [U_4200,U_4199,U_4198,U_4197,U_4196] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4196),U_4198)),U_4199) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4197),U_4198)),U_4200)
          | U_4199 != 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_4197),U_4196)),U_4198)),U_4200) )
        & ( U_4199 = 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_4197),U_4196)),U_4198)),U_4200)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4196),U_4198)),U_4199) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4197),U_4198)),U_4200) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4196),U_4197)) ),
    inference(variable_rename,[status(thm)],[f_1123_1]) ).

fof(f_1123_3,plain,
    ( ! [U_4196,U_4197,U_4198,U_4199,U_4200] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4196),U_4198)),U_4199) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4197),U_4198)),U_4200)
        | U_4199 != 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_4197),U_4196)),U_4198)),U_4200)
        | ~ sP329(U_4196,U_4197,U_4198,U_4199,U_4200) )
    & ! [U_4196,U_4197,U_4198,U_4199,U_4200] :
        ( U_4199 = 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_4197),U_4196)),U_4198)),U_4200)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4196),U_4198)),U_4199) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4197),U_4198)),U_4200)
        | ~ sP329(U_4196,U_4197,U_4198,U_4199,U_4200) )
    & ! [U_4196,U_4197,U_4198,U_4199,U_4200] :
        ( sP329(U_4196,U_4197,U_4198,U_4199,U_4200)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4196),U_4197)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP329])],[f_1123_2]) ).

cnf(f_1123_4,plain,
    ( sP329(U_4196,U_4197,U_4198,U_4199,U_4200)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4196),U_4197)) ),
    inference(clausify,[status(thm)],[f_1123_3]) ).

cnf(f_1123_5,plain,
    ( U_4199 = 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_4197),U_4196)),U_4198)),U_4200)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4196),U_4198)),U_4199) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4197),U_4198)),U_4200)
    | ~ sP329(U_4196,U_4197,U_4198,U_4199,U_4200) ),
    inference(clausify,[status(thm)],[f_1123_3]) ).

cnf(f_1123_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4196),U_4198)),U_4199) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4197),U_4198)),U_4200)
    | U_4199 != 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_4197),U_4196)),U_4198)),U_4200)
    | ~ sP329(U_4196,U_4197,U_4198,U_4199,U_4200) ),
    inference(clausify,[status(thm)],[f_1123_3]) ).

fof(f_1124_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_1124_2,plain,
    ! [U_4202,U_4201] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4201,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4202)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4201,U_4202)),U_4202)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4201,U_4202) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4201,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4202)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4201,U_4202) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1124_1]) ).

fof(f_1124_3,plain,
    ( ! [U_4206,U_4204] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4204,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4206)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4204,U_4206)),U_4206)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4204,U_4206) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_4205,U_4203] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4203,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4205)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4203,U_4205) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1124_2]) ).

fof(f_1124_4,plain,
    ( ! [U_4204,U_4206] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4204,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4206)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4204,U_4206)),U_4206)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4204,U_4206) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_4203,U_4205] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4203,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4205)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4203,U_4205) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_1124_3]) ).

cnf(f_1124_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4203,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4205)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4203,U_4205) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1124_4]) ).

cnf(f_1124_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4204,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4206)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4204,U_4206)),U_4206)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4204,U_4206) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1124_4]) ).

fof(f_1125_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_1125_2,plain,
    ! [U_4208,U_4207] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4207),U_4208) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4208),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4207,U_4208))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4207,U_4208) = 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_4207),U_4208) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4207,U_4208) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1125_1]) ).

fof(f_1125_3,plain,
    ( ! [U_4212,U_4210] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4210),U_4212) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4212),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4210,U_4212))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4210,U_4212) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_4211,U_4209] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4209),U_4211) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4209,U_4211) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1125_2]) ).

fof(f_1125_4,plain,
    ( ! [U_4212,U_4210] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4210),U_4212) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4212),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4210,U_4212))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4210,U_4212) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_4209,U_4211] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4209),U_4211) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4209,U_4211) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_1125_3]) ).

cnf(f_1125_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4209),U_4211) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4209,U_4211) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1125_4]) ).

cnf(f_1125_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4210),U_4212) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4212),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4210,U_4212))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4210,U_4212) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1125_4]) ).

fof(f_1126_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_1126_2,plain,
    ! [U_4214,U_4213] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4213,U_4214) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4213),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4213),U_4214)),U_4214)),
    inference(variable_rename,[status(thm)],[f_1126_1]) ).

fof(f_1126_3,plain,
    ! [U_4213,U_4214] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4213,U_4214) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4213),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4213),U_4214)),U_4214)),
    inference(definitional_conversion,[status(esa)],[f_1126_2]) ).

cnf(f_1126_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4213,U_4214) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4213),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4213),U_4214)),U_4214)),
    inference(clausify,[status(thm)],[f_1126_3]) ).

fof(f_1127_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_1127_2,plain,
    ! [U_4216,U_4215] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4215),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4216),U_4215)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4216),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4216,U_4215)),
    inference(variable_rename,[status(thm)],[f_1127_1]) ).

fof(f_1127_3,plain,
    ! [U_4215,U_4216] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4215),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4216),U_4215)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4216),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4216,U_4215)),
    inference(definitional_conversion,[status(esa)],[f_1127_2]) ).

cnf(f_1127_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4215),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4216),U_4215)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4216),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4216,U_4215)),
    inference(clausify,[status(thm)],[f_1127_3]) ).

fof(f_1128_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_1128_2,plain,
    ! [U_4218,U_4217] :
      ( ( c_Nat__Transfer_Otsub(U_4218,U_4217) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4217),U_4218)) )
      & ( c_Nat__Transfer_Otsub(U_4218,U_4217) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4218),U_4217)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4217),U_4218)) ) ),
    inference(variable_rename,[status(thm)],[f_1128_1]) ).

fof(f_1128_3,plain,
    ( ! [U_4222,U_4220] :
        ( c_Nat__Transfer_Otsub(U_4222,U_4220) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4220),U_4222)) )
    & ! [U_4221,U_4219] :
        ( c_Nat__Transfer_Otsub(U_4221,U_4219) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4221),U_4219)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4219),U_4221)) ) ),
    inference(miniscope,[status(thm)],[f_1128_2]) ).

fof(f_1128_4,plain,
    ( ! [U_4220,U_4222] :
        ( c_Nat__Transfer_Otsub(U_4222,U_4220) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4220),U_4222)) )
    & ! [U_4221,U_4219] :
        ( c_Nat__Transfer_Otsub(U_4221,U_4219) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4221),U_4219)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4219),U_4221)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1128_3]) ).

cnf(f_1128_5,plain,
    ( c_Nat__Transfer_Otsub(U_4221,U_4219) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4221),U_4219)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4219),U_4221)) ),
    inference(clausify,[status(thm)],[f_1128_4]) ).

cnf(f_1128_6,plain,
    ( c_Nat__Transfer_Otsub(U_4222,U_4220) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4220),U_4222)) ),
    inference(clausify,[status(thm)],[f_1128_4]) ).

fof(f_1129_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_1129_2,plain,
    ! [U_4223] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4223),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_4223
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4223)) ),
    inference(variable_rename,[status(thm)],[f_1129_1]) ).

fof(f_1129_3,plain,
    ! [U_4223] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4223),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_4223
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4223)) ),
    inference(definitional_conversion,[status(esa)],[f_1129_2]) ).

cnf(f_1129_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4223),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_4223
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4223)) ),
    inference(clausify,[status(thm)],[f_1129_3]) ).

fof(f_1130_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_1130_2,plain,
    ! [U_4224] :
      ( U_4224 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4224),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_4224)) ),
    inference(variable_rename,[status(thm)],[f_1130_1]) ).

fof(f_1130_3,plain,
    ! [U_4224] :
      ( U_4224 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4224),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_4224)) ),
    inference(definitional_conversion,[status(esa)],[f_1130_2]) ).

cnf(f_1130_4,plain,
    ( U_4224 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4224),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_4224)) ),
    inference(clausify,[status(thm)],[f_1130_3]) ).

fof(f_1131_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_1131_2,plain,
    ! [U_4229,U_4228,U_4227,U_4226,U_4225] :
      ( ( ( 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_4226),U_4227)),U_4228)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4225),U_4227)),U_4229)))
          | ~ 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_4226),U_4225)),U_4227)),U_4228)),U_4229)) )
        & ( 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_4226),U_4225)),U_4227)),U_4228)),U_4229))
          | ~ 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_4226),U_4227)),U_4228)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4225),U_4227)),U_4229))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4225),U_4226)) ),
    inference(variable_rename,[status(thm)],[f_1131_1]) ).

fof(f_1131_3,plain,
    ( ! [U_4225,U_4226,U_4227,U_4228,U_4229] :
        ( 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_4226),U_4227)),U_4228)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4225),U_4227)),U_4229)))
        | ~ 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_4226),U_4225)),U_4227)),U_4228)),U_4229))
        | ~ sP330(U_4225,U_4226,U_4227,U_4228,U_4229) )
    & ! [U_4225,U_4226,U_4227,U_4228,U_4229] :
        ( 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_4226),U_4225)),U_4227)),U_4228)),U_4229))
        | ~ 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_4226),U_4227)),U_4228)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4225),U_4227)),U_4229)))
        | ~ sP330(U_4225,U_4226,U_4227,U_4228,U_4229) )
    & ! [U_4225,U_4226,U_4227,U_4228,U_4229] :
        ( sP330(U_4225,U_4226,U_4227,U_4228,U_4229)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4225),U_4226)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP330])],[f_1131_2]) ).

cnf(f_1131_4,plain,
    ( sP330(U_4225,U_4226,U_4227,U_4228,U_4229)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4225),U_4226)) ),
    inference(clausify,[status(thm)],[f_1131_3]) ).

cnf(f_1131_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_4226),U_4225)),U_4227)),U_4228)),U_4229))
    | ~ 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_4226),U_4227)),U_4228)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4225),U_4227)),U_4229)))
    | ~ sP330(U_4225,U_4226,U_4227,U_4228,U_4229) ),
    inference(clausify,[status(thm)],[f_1131_3]) ).

cnf(f_1131_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_4226),U_4227)),U_4228)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4225),U_4227)),U_4229)))
    | ~ 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_4226),U_4225)),U_4227)),U_4228)),U_4229))
    | ~ sP330(U_4225,U_4226,U_4227,U_4228,U_4229) ),
    inference(clausify,[status(thm)],[f_1131_3]) ).

fof(f_1132_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_1132_2,plain,
    ! [U_4234,U_4233,U_4232,U_4231,U_4230] :
      ( ( ( 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_4230),U_4232)),U_4233)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4231),U_4232)),U_4234)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4233),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_4231),U_4230)),U_4232)),U_4234))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4233),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_4231),U_4230)),U_4232)),U_4234)))
          | ~ 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_4230),U_4232)),U_4233)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4231),U_4232)),U_4234))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4230),U_4231)) ),
    inference(variable_rename,[status(thm)],[f_1132_1]) ).

fof(f_1132_3,plain,
    ( ! [U_4231,U_4230,U_4233,U_4232,U_4234] :
        ( 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_4230),U_4232)),U_4233)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4231),U_4232)),U_4234)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4233),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_4231),U_4230)),U_4232)),U_4234)))
        | ~ sP331(U_4231,U_4230,U_4233,U_4232,U_4234) )
    & ! [U_4231,U_4230,U_4233,U_4232,U_4234] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4233),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_4231),U_4230)),U_4232)),U_4234)))
        | ~ 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_4230),U_4232)),U_4233)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4231),U_4232)),U_4234)))
        | ~ sP331(U_4231,U_4230,U_4233,U_4232,U_4234) )
    & ! [U_4231,U_4230,U_4233,U_4232,U_4234] :
        ( sP331(U_4231,U_4230,U_4233,U_4232,U_4234)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4230),U_4231)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP331])],[f_1132_2]) ).

cnf(f_1132_4,plain,
    ( sP331(U_4231,U_4230,U_4233,U_4232,U_4234)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4230),U_4231)) ),
    inference(clausify,[status(thm)],[f_1132_3]) ).

cnf(f_1132_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4233),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_4231),U_4230)),U_4232)),U_4234)))
    | ~ 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_4230),U_4232)),U_4233)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4231),U_4232)),U_4234)))
    | ~ sP331(U_4231,U_4230,U_4233,U_4232,U_4234) ),
    inference(clausify,[status(thm)],[f_1132_3]) ).

cnf(f_1132_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_4230),U_4232)),U_4233)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4231),U_4232)),U_4234)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4233),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_4231),U_4230)),U_4232)),U_4234)))
    | ~ sP331(U_4231,U_4230,U_4233,U_4232,U_4234) ),
    inference(clausify,[status(thm)],[f_1132_3]) ).

fof(f_1133_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_1133_2,plain,
    ! [U_4236,U_4235] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4235),U_4236) = 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_4235),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4236))
        | U_4235 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4235),U_4236) = U_4236
        | U_4235 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1133_1]) ).

fof(f_1133_3,plain,
    ( ! [U_4240,U_4238] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4238),U_4240) = 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_4238),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4240))
        | U_4238 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4239,U_4237] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4237),U_4239) = U_4239
        | U_4237 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1133_2]) ).

fof(f_1133_4,plain,
    ( ! [U_4238,U_4240] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4238),U_4240) = 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_4238),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4240))
        | U_4238 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4239,U_4237] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4237),U_4239) = U_4239
        | U_4237 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1133_3]) ).

cnf(f_1133_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4237),U_4239) = U_4239
    | U_4237 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1133_4]) ).

cnf(f_1133_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4238),U_4240) = 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_4238),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4240))
    | U_4238 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1133_4]) ).

fof(f_1134_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_1134_2,plain,
    ! [U_4242,U_4241] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4242),U_4241) = 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_4242),U_4241)),U_4241))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4242),U_4241)) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4242),U_4241) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4242),U_4241)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4241)) ),
    inference(variable_rename,[status(thm)],[f_1134_1]) ).

fof(f_1134_3,plain,
    ( ! [U_4241,U_4242] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4242),U_4241) = 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_4242),U_4241)),U_4241))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4242),U_4241))
        | ~ sP332(U_4241,U_4242) )
    & ! [U_4241,U_4242] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4242),U_4241) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4242),U_4241))
        | ~ sP332(U_4241,U_4242) )
    & ! [U_4241,U_4242] :
        ( sP332(U_4241,U_4242)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4241)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP332])],[f_1134_2]) ).

cnf(f_1134_4,plain,
    ( sP332(U_4241,U_4242)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4241)) ),
    inference(clausify,[status(thm)],[f_1134_3]) ).

cnf(f_1134_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4242),U_4241) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4242),U_4241))
    | ~ sP332(U_4241,U_4242) ),
    inference(clausify,[status(thm)],[f_1134_3]) ).

cnf(f_1134_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4242),U_4241) = 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_4242),U_4241)),U_4241))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4242),U_4241))
    | ~ sP332(U_4241,U_4242) ),
    inference(clausify,[status(thm)],[f_1134_3]) ).

fof(f_1135_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_1135_2,plain,
    ! [U_4244,U_4243] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4244),U_4243) = 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_4244),U_4243)),U_4243))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4244),U_4243))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4243)) ),
    inference(variable_rename,[status(thm)],[f_1135_1]) ).

fof(f_1135_3,plain,
    ! [U_4243,U_4244] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4244),U_4243) = 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_4244),U_4243)),U_4243))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4244),U_4243))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4243)) ),
    inference(definitional_conversion,[status(esa)],[f_1135_2]) ).

cnf(f_1135_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4244),U_4243) = 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_4244),U_4243)),U_4243))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4244),U_4243))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4243)) ),
    inference(clausify,[status(thm)],[f_1135_3]) ).

fof(f_1136_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_1136_2,plain,
    ! [U_4246,U_4245] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4245),U_4246) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4246),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4245),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4246))
        | U_4245 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4245),U_4246) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4245 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1136_1]) ).

fof(f_1136_3,plain,
    ( ! [U_4250,U_4248] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4248),U_4250) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4248),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4250))
        | U_4248 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4249,U_4247] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4247),U_4249) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4247 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1136_2]) ).

fof(f_1136_4,plain,
    ( ! [U_4250,U_4248] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4248),U_4250) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4248),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4250))
        | U_4248 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4249,U_4247] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4247),U_4249) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4247 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1136_3]) ).

cnf(f_1136_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4247),U_4249) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4247 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1136_4]) ).

cnf(f_1136_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4248),U_4250) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4250),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4248),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4250))
    | U_4248 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1136_4]) ).

fof(f_1137_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_1137_2,plain,
    ! [U_4252,U_4251] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4252),U_4251)),U_4252) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4252),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4251),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_4252))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4251)) ),
    inference(variable_rename,[status(thm)],[f_1137_1]) ).

fof(f_1137_3,plain,
    ! [U_4251,U_4252] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4252),U_4251)),U_4252) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4252),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4251),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_4252))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4251)) ),
    inference(definitional_conversion,[status(esa)],[f_1137_2]) ).

cnf(f_1137_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4252),U_4251)),U_4252) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4252),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4251),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_4252))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4251)) ),
    inference(clausify,[status(thm)],[f_1137_3]) ).

fof(f_1138_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_1138_2,plain,
    ! [U_4257,U_4256,U_4255] :
      ( ! [U_4254] :
          ( hBOOL(hAPP(U_4256,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4257),U_4255))))
          | ~ hBOOL(hAPP(U_4256,U_4254)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4257))
      | ? [U_4253] :
          ( ~ hBOOL(hAPP(U_4256,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4253),U_4255)))
          & hBOOL(hAPP(U_4256,U_4253)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4255)) ),
    inference(variable_rename,[status(thm)],[f_1138_1]) ).

fof(f_1138_3,plain,
    ! [U_4257,U_4256,U_4255] :
      ( ! [U_4254] :
          ( hBOOL(hAPP(U_4256,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4257),U_4255))))
          | ~ hBOOL(hAPP(U_4256,U_4254)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4257))
      | ( ~ hBOOL(hAPP(U_4256,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK86(U_4257,U_4256,U_4255)),U_4255)))
        & hBOOL(hAPP(U_4256,sK86(U_4257,U_4256,U_4255))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4255)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_4253,sK86(U_4257,U_4256,U_4255))],[f_1138_2]) ).

fof(f_1138_4,plain,
    ( ! [U_4255,U_4256,U_4257] :
        ( ~ hBOOL(hAPP(U_4256,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK86(U_4257,U_4256,U_4255)),U_4255)))
        | ~ sP333(U_4255,U_4256,U_4257) )
    & ! [U_4255,U_4256,U_4257] :
        ( hBOOL(hAPP(U_4256,sK86(U_4257,U_4256,U_4255)))
        | ~ sP333(U_4255,U_4256,U_4257) )
    & ! [U_4254,U_4255,U_4256,U_4257] :
        ( hBOOL(hAPP(U_4256,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4257),U_4255))))
        | ~ hBOOL(hAPP(U_4256,U_4254))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4257))
        | sP333(U_4255,U_4256,U_4257)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4255)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP333])],[f_1138_3]) ).

cnf(f_1138_5,plain,
    ( hBOOL(hAPP(U_4256,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4254),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4257),U_4255))))
    | ~ hBOOL(hAPP(U_4256,U_4254))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4257))
    | sP333(U_4255,U_4256,U_4257)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4255)) ),
    inference(clausify,[status(thm)],[f_1138_4]) ).

cnf(f_1138_6,plain,
    ( hBOOL(hAPP(U_4256,sK86(U_4257,U_4256,U_4255)))
    | ~ sP333(U_4255,U_4256,U_4257) ),
    inference(clausify,[status(thm)],[f_1138_4]) ).

cnf(f_1138_7,plain,
    ( ~ hBOOL(hAPP(U_4256,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK86(U_4257,U_4256,U_4255)),U_4255)))
    | ~ sP333(U_4255,U_4256,U_4257) ),
    inference(clausify,[status(thm)],[f_1138_4]) ).

fof(f_1139_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_1139_2,plain,
    ! [U_4260,U_4259,U_4258] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4259),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4260),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_4260),U_4259))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4258))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4258)) ),
    inference(variable_rename,[status(thm)],[f_1139_1]) ).

fof(f_1139_3,plain,
    ! [U_4260,U_4259,U_4258] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4259),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4260),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_4260),U_4259))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4258))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4258)) ),
    inference(definitional_conversion,[status(esa)],[f_1139_2]) ).

cnf(f_1139_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4259),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4260),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_4260),U_4259))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4258))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4258)) ),
    inference(clausify,[status(thm)],[f_1139_3]) ).

fof(f_1140_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_1140_2,plain,
    ! [U_4263,U_4262,U_4261] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4262),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_4262),U_4263))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4261))),U_4263))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4261)) ),
    inference(variable_rename,[status(thm)],[f_1140_1]) ).

fof(f_1140_3,plain,
    ! [U_4261,U_4262,U_4263] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4262),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_4262),U_4263))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4261))),U_4263))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4261)) ),
    inference(definitional_conversion,[status(esa)],[f_1140_2]) ).

cnf(f_1140_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4262),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_4262),U_4263))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_4261))),U_4263))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4261)) ),
    inference(clausify,[status(thm)],[f_1140_3]) ).

fof(f_1141_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_1141_2,plain,
    ! [U_4267,U_4266,U_4265] :
      ( ? [U_4264] : U_4265 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4267),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4266),U_4264))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4267),U_4265))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4265,U_4266) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4267,U_4266) ),
    inference(variable_rename,[status(thm)],[f_1141_1]) ).

fof(f_1141_3,plain,
    ! [U_4267,U_4266,U_4265] :
      ( U_4265 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4267),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4266),sK87(U_4267,U_4266,U_4265)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4267),U_4265))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4265,U_4266) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4267,U_4266) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_4264,sK87(U_4267,U_4266,U_4265))],[f_1141_2]) ).

fof(f_1141_4,plain,
    ! [U_4265,U_4266,U_4267] :
      ( U_4265 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4267),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4266),sK87(U_4267,U_4266,U_4265)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4267),U_4265))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4265,U_4266) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4267,U_4266) ),
    inference(definitional_conversion,[status(esa)],[f_1141_3]) ).

cnf(f_1141_5,plain,
    ( U_4265 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4267),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4266),sK87(U_4267,U_4266,U_4265)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4267),U_4265))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4265,U_4266) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4267,U_4266) ),
    inference(clausify,[status(thm)],[f_1141_4]) ).

fof(f_1142_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_1142_2,plain,
    ! [U_4271,U_4270,U_4269] :
      ( hBOOL(hAPP(U_4270,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4271),U_4269))
      | ~ hBOOL(hAPP(U_4270,U_4271))
      | ? [U_4268] :
          ( ~ hBOOL(hAPP(U_4270,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4268),U_4269)))
          & hBOOL(hAPP(U_4270,U_4268))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4268),U_4269)) ) ),
    inference(variable_rename,[status(thm)],[f_1142_1]) ).

fof(f_1142_3,plain,
    ! [U_4271,U_4270,U_4269] :
      ( hBOOL(hAPP(U_4270,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4271),U_4269))
      | ~ hBOOL(hAPP(U_4270,U_4271))
      | ( ~ hBOOL(hAPP(U_4270,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK88(U_4271,U_4270,U_4269)),U_4269)))
        & hBOOL(hAPP(U_4270,sK88(U_4271,U_4270,U_4269)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK88(U_4271,U_4270,U_4269)),U_4269)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_4268,sK88(U_4271,U_4270,U_4269))],[f_1142_2]) ).

fof(f_1142_4,plain,
    ( ! [U_4269,U_4270,U_4271] :
        ( ~ hBOOL(hAPP(U_4270,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK88(U_4271,U_4270,U_4269)),U_4269)))
        | ~ sP334(U_4269,U_4270,U_4271) )
    & ! [U_4269,U_4270,U_4271] :
        ( hBOOL(hAPP(U_4270,sK88(U_4271,U_4270,U_4269)))
        | ~ sP334(U_4269,U_4270,U_4271) )
    & ! [U_4269,U_4270,U_4271] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK88(U_4271,U_4270,U_4269)),U_4269))
        | ~ sP334(U_4269,U_4270,U_4271) )
    & ! [U_4269,U_4270,U_4271] :
        ( hBOOL(hAPP(U_4270,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4271),U_4269))
        | ~ hBOOL(hAPP(U_4270,U_4271))
        | sP334(U_4269,U_4270,U_4271) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP334])],[f_1142_3]) ).

cnf(f_1142_5,plain,
    ( hBOOL(hAPP(U_4270,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4271),U_4269))
    | ~ hBOOL(hAPP(U_4270,U_4271))
    | sP334(U_4269,U_4270,U_4271) ),
    inference(clausify,[status(thm)],[f_1142_4]) ).

cnf(f_1142_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK88(U_4271,U_4270,U_4269)),U_4269))
    | ~ sP334(U_4269,U_4270,U_4271) ),
    inference(clausify,[status(thm)],[f_1142_4]) ).

cnf(f_1142_7,plain,
    ( hBOOL(hAPP(U_4270,sK88(U_4271,U_4270,U_4269)))
    | ~ sP334(U_4269,U_4270,U_4271) ),
    inference(clausify,[status(thm)],[f_1142_4]) ).

cnf(f_1142_8,plain,
    ( ~ hBOOL(hAPP(U_4270,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK88(U_4271,U_4270,U_4269)),U_4269)))
    | ~ sP334(U_4269,U_4270,U_4271) ),
    inference(clausify,[status(thm)],[f_1142_4]) ).

fof(f_1143_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_1143_2,plain,
    ! [U_4272] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4272) = 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_4272)),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_4272))) ),
    inference(variable_rename,[status(thm)],[f_1143_1]) ).

fof(f_1143_3,plain,
    ! [U_4272] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4272) = 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_4272)),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_4272))) ),
    inference(definitional_conversion,[status(esa)],[f_1143_2]) ).

cnf(f_1143_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4272) = 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_4272)),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_4272))) ),
    inference(clausify,[status(thm)],[f_1143_3]) ).

fof(f_1144_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_1144_2,plain,
    ! [U_4275,U_4274,U_4273] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4273),U_4274) = hAPP(c_Int_Onumber__class_Onumber__of(U_4273),U_4275)
          | U_4274 != U_4275 )
        & ( U_4274 = U_4275
          | hAPP(c_Int_Onumber__class_Onumber__of(U_4273),U_4274) != hAPP(c_Int_Onumber__class_Onumber__of(U_4273),U_4275) ) )
      | ~ class_Int_Oring__char__0(U_4273)
      | ~ class_Int_Onumber__ring(U_4273) ),
    inference(variable_rename,[status(thm)],[f_1144_1]) ).

fof(f_1144_3,plain,
    ( ! [U_4274,U_4275,U_4273] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_4273),U_4274) = hAPP(c_Int_Onumber__class_Onumber__of(U_4273),U_4275)
        | U_4274 != U_4275
        | ~ sP335(U_4274,U_4275,U_4273) )
    & ! [U_4274,U_4275,U_4273] :
        ( U_4274 = U_4275
        | hAPP(c_Int_Onumber__class_Onumber__of(U_4273),U_4274) != hAPP(c_Int_Onumber__class_Onumber__of(U_4273),U_4275)
        | ~ sP335(U_4274,U_4275,U_4273) )
    & ! [U_4274,U_4275,U_4273] :
        ( sP335(U_4274,U_4275,U_4273)
        | ~ class_Int_Oring__char__0(U_4273)
        | ~ class_Int_Onumber__ring(U_4273) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP335])],[f_1144_2]) ).

cnf(f_1144_4,plain,
    ( sP335(U_4274,U_4275,U_4273)
    | ~ class_Int_Oring__char__0(U_4273)
    | ~ class_Int_Onumber__ring(U_4273) ),
    inference(clausify,[status(thm)],[f_1144_3]) ).

cnf(f_1144_5,plain,
    ( U_4274 = U_4275
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4273),U_4274) != hAPP(c_Int_Onumber__class_Onumber__of(U_4273),U_4275)
    | ~ sP335(U_4274,U_4275,U_4273) ),
    inference(clausify,[status(thm)],[f_1144_3]) ).

cnf(f_1144_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4273),U_4274) = hAPP(c_Int_Onumber__class_Onumber__of(U_4273),U_4275)
    | U_4274 != U_4275
    | ~ sP335(U_4274,U_4275,U_4273) ),
    inference(clausify,[status(thm)],[f_1144_3]) ).

fof(f_1145_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_1145_2,plain,
    ! [U_4278,U_4277,U_4276] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4276),U_4277) = U_4278
          | U_4278 != hAPP(c_Int_Onumber__class_Onumber__of(U_4276),U_4277) )
        & ( U_4278 = hAPP(c_Int_Onumber__class_Onumber__of(U_4276),U_4277)
          | hAPP(c_Int_Onumber__class_Onumber__of(U_4276),U_4277) != U_4278 ) )
      | ~ class_Int_Onumber(U_4276) ),
    inference(variable_rename,[status(thm)],[f_1145_1]) ).

fof(f_1145_3,plain,
    ( ! [U_4277,U_4278,U_4276] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_4276),U_4277) = U_4278
        | U_4278 != hAPP(c_Int_Onumber__class_Onumber__of(U_4276),U_4277)
        | ~ sP336(U_4277,U_4278,U_4276) )
    & ! [U_4277,U_4278,U_4276] :
        ( U_4278 = hAPP(c_Int_Onumber__class_Onumber__of(U_4276),U_4277)
        | hAPP(c_Int_Onumber__class_Onumber__of(U_4276),U_4277) != U_4278
        | ~ sP336(U_4277,U_4278,U_4276) )
    & ! [U_4277,U_4278,U_4276] :
        ( sP336(U_4277,U_4278,U_4276)
        | ~ class_Int_Onumber(U_4276) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP336])],[f_1145_2]) ).

cnf(f_1145_4,plain,
    ( sP336(U_4277,U_4278,U_4276)
    | ~ class_Int_Onumber(U_4276) ),
    inference(clausify,[status(thm)],[f_1145_3]) ).

cnf(f_1145_5,plain,
    ( U_4278 = hAPP(c_Int_Onumber__class_Onumber__of(U_4276),U_4277)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4276),U_4277) != U_4278
    | ~ sP336(U_4277,U_4278,U_4276) ),
    inference(clausify,[status(thm)],[f_1145_3]) ).

cnf(f_1145_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4276),U_4277) = U_4278
    | U_4278 != hAPP(c_Int_Onumber__class_Onumber__of(U_4276),U_4277)
    | ~ sP336(U_4277,U_4278,U_4276) ),
    inference(clausify,[status(thm)],[f_1145_3]) ).

fof(f_1146_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_1146_2,plain,
    ! [U_4280,U_4279] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4279),hAPP(c_Groups_Oabs__class_Oabs(U_4279),U_4280)) = hAPP(c_Groups_Oabs__class_Oabs(U_4279),U_4280)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4279) ),
    inference(variable_rename,[status(thm)],[f_1146_1]) ).

fof(f_1146_3,plain,
    ! [U_4280,U_4279] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4279),hAPP(c_Groups_Oabs__class_Oabs(U_4279),U_4280)) = hAPP(c_Groups_Oabs__class_Oabs(U_4279),U_4280)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4279) ),
    inference(definitional_conversion,[status(esa)],[f_1146_2]) ).

cnf(f_1146_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4279),hAPP(c_Groups_Oabs__class_Oabs(U_4279),U_4280)) = hAPP(c_Groups_Oabs__class_Oabs(U_4279),U_4280)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4279) ),
    inference(clausify,[status(thm)],[f_1146_3]) ).

fof(f_1147_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_1147_2,plain,
    ! [U_4282,U_4281] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_4281),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4282)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4281),U_4282)
      | ~ class_Int_Onumber__ring(U_4281) ),
    inference(variable_rename,[status(thm)],[f_1147_1]) ).

fof(f_1147_3,plain,
    ! [U_4281,U_4282] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_4281),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4282)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4281),U_4282)
      | ~ class_Int_Onumber__ring(U_4281) ),
    inference(definitional_conversion,[status(esa)],[f_1147_2]) ).

cnf(f_1147_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_4281),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4282)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4281),U_4282)
    | ~ class_Int_Onumber__ring(U_4281) ),
    inference(clausify,[status(thm)],[f_1147_3]) ).

fof(f_1148_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_1148_2,plain,
    ! [U_4285,U_4284,U_4283] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_4283),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4284),U_4285)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4283),hAPP(c_Int_Oring__1__class_Oof__int(U_4283),U_4284)),U_4285)
      | ~ class_Rings_Oring__1(U_4283) ),
    inference(variable_rename,[status(thm)],[f_1148_1]) ).

fof(f_1148_3,plain,
    ! [U_4283,U_4284,U_4285] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_4283),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4284),U_4285)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4283),hAPP(c_Int_Oring__1__class_Oof__int(U_4283),U_4284)),U_4285)
      | ~ class_Rings_Oring__1(U_4283) ),
    inference(definitional_conversion,[status(esa)],[f_1148_2]) ).

cnf(f_1148_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_4283),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4284),U_4285)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4283),hAPP(c_Int_Oring__1__class_Oof__int(U_4283),U_4284)),U_4285)
    | ~ class_Rings_Oring__1(U_4283) ),
    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),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_1149_2,plain,
    ! [U_4287,U_4286] : 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_4286)),U_4287))),
    inference(variable_rename,[status(thm)],[f_1149_1]) ).

fof(f_1149_3,plain,
    ! [U_4286,U_4287] : 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_4286)),U_4287))),
    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),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4286)),U_4287))),
    inference(clausify,[status(thm)],[f_1149_3]) ).

fof(f_1150_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_1150_2,plain,
    ! [U_4290,U_4289,U_4288] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4288),U_4289),U_4290))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4288),hAPP(c_Groups_Oabs__class_Oabs(U_4288),U_4289)),U_4290))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4288) ),
    inference(variable_rename,[status(thm)],[f_1150_1]) ).

fof(f_1150_3,plain,
    ! [U_4288,U_4289,U_4290] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4288),U_4289),U_4290))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4288),hAPP(c_Groups_Oabs__class_Oabs(U_4288),U_4289)),U_4290))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4288) ),
    inference(definitional_conversion,[status(esa)],[f_1150_2]) ).

cnf(f_1150_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4288),U_4289),U_4290))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4288),hAPP(c_Groups_Oabs__class_Oabs(U_4288),U_4289)),U_4290))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4288) ),
    inference(clausify,[status(thm)],[f_1150_3]) ).

fof(f_1151_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_1151_2,plain,
    ! [U_4292,U_4291] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4291),U_4292),hAPP(c_Groups_Oabs__class_Oabs(U_4291),U_4292)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4291) ),
    inference(variable_rename,[status(thm)],[f_1151_1]) ).

fof(f_1151_3,plain,
    ! [U_4291,U_4292] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4291),U_4292),hAPP(c_Groups_Oabs__class_Oabs(U_4291),U_4292)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4291) ),
    inference(definitional_conversion,[status(esa)],[f_1151_2]) ).

cnf(f_1151_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4291),U_4292),hAPP(c_Groups_Oabs__class_Oabs(U_4291),U_4292)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4291) ),
    inference(clausify,[status(thm)],[f_1151_3]) ).

fof(f_1152_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_1152_2,plain,
    ! [U_4293] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4293),c_Groups_Ozero__class_Ozero(U_4293)) = c_Groups_Ozero__class_Ozero(U_4293)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4293) ),
    inference(variable_rename,[status(thm)],[f_1152_1]) ).

fof(f_1152_3,plain,
    ! [U_4293] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4293),c_Groups_Ozero__class_Ozero(U_4293)) = c_Groups_Ozero__class_Ozero(U_4293)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4293) ),
    inference(definitional_conversion,[status(esa)],[f_1152_2]) ).

cnf(f_1152_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4293),c_Groups_Ozero__class_Ozero(U_4293)) = c_Groups_Ozero__class_Ozero(U_4293)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4293) ),
    inference(clausify,[status(thm)],[f_1152_3]) ).

fof(f_1153_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_1153_2,plain,
    ! [U_4295,U_4294] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_4294),U_4295) = c_Groups_Ozero__class_Ozero(U_4294)
          | U_4295 != c_Groups_Ozero__class_Ozero(U_4294) )
        & ( U_4295 = c_Groups_Ozero__class_Ozero(U_4294)
          | hAPP(c_Groups_Oabs__class_Oabs(U_4294),U_4295) != c_Groups_Ozero__class_Ozero(U_4294) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4294) ),
    inference(variable_rename,[status(thm)],[f_1153_1]) ).

fof(f_1153_3,plain,
    ( ! [U_4294,U_4295] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_4294),U_4295) = c_Groups_Ozero__class_Ozero(U_4294)
        | U_4295 != c_Groups_Ozero__class_Ozero(U_4294)
        | ~ sP337(U_4294,U_4295) )
    & ! [U_4294,U_4295] :
        ( U_4295 = c_Groups_Ozero__class_Ozero(U_4294)
        | hAPP(c_Groups_Oabs__class_Oabs(U_4294),U_4295) != c_Groups_Ozero__class_Ozero(U_4294)
        | ~ sP337(U_4294,U_4295) )
    & ! [U_4294,U_4295] :
        ( sP337(U_4294,U_4295)
        | ~ class_Groups_Oordered__ab__group__add__abs(U_4294) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP337])],[f_1153_2]) ).

cnf(f_1153_4,plain,
    ( sP337(U_4294,U_4295)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4294) ),
    inference(clausify,[status(thm)],[f_1153_3]) ).

cnf(f_1153_5,plain,
    ( U_4295 = c_Groups_Ozero__class_Ozero(U_4294)
    | hAPP(c_Groups_Oabs__class_Oabs(U_4294),U_4295) != c_Groups_Ozero__class_Ozero(U_4294)
    | ~ sP337(U_4294,U_4295) ),
    inference(clausify,[status(thm)],[f_1153_3]) ).

cnf(f_1153_6,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4294),U_4295) = c_Groups_Ozero__class_Ozero(U_4294)
    | U_4295 != c_Groups_Ozero__class_Ozero(U_4294)
    | ~ sP337(U_4294,U_4295) ),
    inference(clausify,[status(thm)],[f_1153_3]) ).

fof(f_1154_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_1154_2,plain,
    ! [U_4298,U_4297,U_4296] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4296),hAPP(c_Groups_Oabs__class_Oabs(U_4296),U_4297)),hAPP(c_Groups_Oabs__class_Oabs(U_4296),U_4298))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4296),hAPP(c_Groups_Oabs__class_Oabs(U_4296),U_4297)),hAPP(c_Groups_Oabs__class_Oabs(U_4296),U_4298))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4296) ),
    inference(variable_rename,[status(thm)],[f_1154_1]) ).

fof(f_1154_3,plain,
    ! [U_4297,U_4296,U_4298] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4296),hAPP(c_Groups_Oabs__class_Oabs(U_4296),U_4297)),hAPP(c_Groups_Oabs__class_Oabs(U_4296),U_4298))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4296),hAPP(c_Groups_Oabs__class_Oabs(U_4296),U_4297)),hAPP(c_Groups_Oabs__class_Oabs(U_4296),U_4298))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4296) ),
    inference(definitional_conversion,[status(esa)],[f_1154_2]) ).

cnf(f_1154_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4296),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4296),hAPP(c_Groups_Oabs__class_Oabs(U_4296),U_4297)),hAPP(c_Groups_Oabs__class_Oabs(U_4296),U_4298))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4296),hAPP(c_Groups_Oabs__class_Oabs(U_4296),U_4297)),hAPP(c_Groups_Oabs__class_Oabs(U_4296),U_4298))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4296) ),
    inference(clausify,[status(thm)],[f_1154_3]) ).

fof(f_1155_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_1155_2,plain,
    ! [U_4300,U_4299] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4299),hAPP(c_Groups_Oabs__class_Oabs(U_4299),U_4300)),hAPP(c_Groups_Oabs__class_Oabs(U_4299),U_4300)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4299),U_4300),U_4300)
      | ~ class_Rings_Olinordered__idom(U_4299) ),
    inference(variable_rename,[status(thm)],[f_1155_1]) ).

fof(f_1155_3,plain,
    ! [U_4299,U_4300] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4299),hAPP(c_Groups_Oabs__class_Oabs(U_4299),U_4300)),hAPP(c_Groups_Oabs__class_Oabs(U_4299),U_4300)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4299),U_4300),U_4300)
      | ~ class_Rings_Olinordered__idom(U_4299) ),
    inference(definitional_conversion,[status(esa)],[f_1155_2]) ).

cnf(f_1155_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4299),hAPP(c_Groups_Oabs__class_Oabs(U_4299),U_4300)),hAPP(c_Groups_Oabs__class_Oabs(U_4299),U_4300)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4299),U_4300),U_4300)
    | ~ class_Rings_Olinordered__idom(U_4299) ),
    inference(clausify,[status(thm)],[f_1155_3]) ).

fof(f_1156_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_1156_2,plain,
    ! [U_4303,U_4302,U_4301] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4301),U_4302),U_4303)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4301),hAPP(c_Groups_Oabs__class_Oabs(U_4301),U_4302)),hAPP(c_Groups_Oabs__class_Oabs(U_4301),U_4303))
      | ~ class_Rings_Olinordered__idom(U_4301) ),
    inference(variable_rename,[status(thm)],[f_1156_1]) ).

fof(f_1156_3,plain,
    ! [U_4301,U_4302,U_4303] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4301),U_4302),U_4303)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4301),hAPP(c_Groups_Oabs__class_Oabs(U_4301),U_4302)),hAPP(c_Groups_Oabs__class_Oabs(U_4301),U_4303))
      | ~ class_Rings_Olinordered__idom(U_4301) ),
    inference(definitional_conversion,[status(esa)],[f_1156_2]) ).

cnf(f_1156_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4301),U_4302),U_4303)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4301),hAPP(c_Groups_Oabs__class_Oabs(U_4301),U_4302)),hAPP(c_Groups_Oabs__class_Oabs(U_4301),U_4303))
    | ~ class_Rings_Olinordered__idom(U_4301) ),
    inference(clausify,[status(thm)],[f_1156_3]) ).

fof(f_1157_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_1157_2,plain,
    ! [U_4306,U_4305,U_4304] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4304),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4304),U_4305),U_4306)) = hAPP(c_Groups_Oabs__class_Oabs(U_4304),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4304),U_4306),U_4305))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4304) ),
    inference(variable_rename,[status(thm)],[f_1157_1]) ).

fof(f_1157_3,plain,
    ! [U_4304,U_4305,U_4306] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4304),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4304),U_4305),U_4306)) = hAPP(c_Groups_Oabs__class_Oabs(U_4304),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4304),U_4306),U_4305))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4304) ),
    inference(definitional_conversion,[status(esa)],[f_1157_2]) ).

cnf(f_1157_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4304),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4304),U_4305),U_4306)) = hAPP(c_Groups_Oabs__class_Oabs(U_4304),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4304),U_4306),U_4305))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4304) ),
    inference(clausify,[status(thm)],[f_1157_3]) ).

fof(f_1158_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_1158_2,plain,
    ! [U_4307] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4307),c_Groups_Oone__class_Oone(U_4307)) = c_Groups_Oone__class_Oone(U_4307)
      | ~ class_Rings_Olinordered__idom(U_4307) ),
    inference(variable_rename,[status(thm)],[f_1158_1]) ).

fof(f_1158_3,plain,
    ! [U_4307] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4307),c_Groups_Oone__class_Oone(U_4307)) = c_Groups_Oone__class_Oone(U_4307)
      | ~ class_Rings_Olinordered__idom(U_4307) ),
    inference(definitional_conversion,[status(esa)],[f_1158_2]) ).

cnf(f_1158_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4307),c_Groups_Oone__class_Oone(U_4307)) = c_Groups_Oone__class_Oone(U_4307)
    | ~ class_Rings_Olinordered__idom(U_4307) ),
    inference(clausify,[status(thm)],[f_1158_3]) ).

fof(f_1159_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_1159_2,plain,
    ! [U_4309,U_4308] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4308),hAPP(c_Groups_Ouminus__class_Ouminus(U_4308),U_4309)) = hAPP(c_Groups_Oabs__class_Oabs(U_4308),U_4309)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4308) ),
    inference(variable_rename,[status(thm)],[f_1159_1]) ).

fof(f_1159_3,plain,
    ! [U_4308,U_4309] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4308),hAPP(c_Groups_Ouminus__class_Ouminus(U_4308),U_4309)) = hAPP(c_Groups_Oabs__class_Oabs(U_4308),U_4309)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4308) ),
    inference(definitional_conversion,[status(esa)],[f_1159_2]) ).

cnf(f_1159_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4308),hAPP(c_Groups_Ouminus__class_Ouminus(U_4308),U_4309)) = hAPP(c_Groups_Oabs__class_Oabs(U_4308),U_4309)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4308) ),
    inference(clausify,[status(thm)],[f_1159_3]) ).

fof(f_1160_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_1160_2,plain,
    ! [U_4313,U_4312,U_4311,U_4310] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4310),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4310),U_4311),U_4312)),U_4313) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4310),hAPP(hAPP(c_Power_Opower__class_Opower(U_4310),U_4311),U_4313)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4310),U_4312),U_4313))
      | ~ class_Rings_Ocomm__semiring__1(U_4310) ),
    inference(variable_rename,[status(thm)],[f_1160_1]) ).

fof(f_1160_3,plain,
    ! [U_4310,U_4311,U_4312,U_4313] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4310),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4310),U_4311),U_4312)),U_4313) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4310),hAPP(hAPP(c_Power_Opower__class_Opower(U_4310),U_4311),U_4313)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4310),U_4312),U_4313))
      | ~ class_Rings_Ocomm__semiring__1(U_4310) ),
    inference(definitional_conversion,[status(esa)],[f_1160_2]) ).

cnf(f_1160_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4310),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4310),U_4311),U_4312)),U_4313) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4310),hAPP(hAPP(c_Power_Opower__class_Opower(U_4310),U_4311),U_4313)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4310),U_4312),U_4313))
    | ~ class_Rings_Ocomm__semiring__1(U_4310) ),
    inference(clausify,[status(thm)],[f_1160_3]) ).

fof(f_1161_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_1161_2,plain,
    ! [U_4315,U_4314] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4314),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4314),U_4315)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4314),U_4315)
      | ~ class_Rings_Olinordered__idom(U_4314) ),
    inference(variable_rename,[status(thm)],[f_1161_1]) ).

fof(f_1161_3,plain,
    ! [U_4315,U_4314] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4314),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4314),U_4315)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4314),U_4315)
      | ~ class_Rings_Olinordered__idom(U_4314) ),
    inference(definitional_conversion,[status(esa)],[f_1161_2]) ).

cnf(f_1161_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4314),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4314),U_4315)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4314),U_4315)
    | ~ class_Rings_Olinordered__idom(U_4314) ),
    inference(clausify,[status(thm)],[f_1161_3]) ).

fof(f_1162_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_1162_2,plain,
    ! [U_4316] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4316)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4316),
    inference(variable_rename,[status(thm)],[f_1162_1]) ).

fof(f_1162_3,plain,
    ! [U_4316] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4316)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4316),
    inference(definitional_conversion,[status(esa)],[f_1162_2]) ).

cnf(f_1162_4,plain,
    hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4316)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4316),
    inference(clausify,[status(thm)],[f_1162_3]) ).

fof(f_1163_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_1163_2,plain,
    ! [U_4320,U_4319,U_4318,U_4317] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4317),hAPP(hAPP(c_Power_Opower__class_Opower(U_4317),U_4318),U_4319)),U_4320) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4317),U_4318),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4319),U_4320))
      | ~ class_Rings_Ocomm__semiring__1(U_4317) ),
    inference(variable_rename,[status(thm)],[f_1163_1]) ).

fof(f_1163_3,plain,
    ! [U_4317,U_4318,U_4319,U_4320] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4317),hAPP(hAPP(c_Power_Opower__class_Opower(U_4317),U_4318),U_4319)),U_4320) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4317),U_4318),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4319),U_4320))
      | ~ class_Rings_Ocomm__semiring__1(U_4317) ),
    inference(definitional_conversion,[status(esa)],[f_1163_2]) ).

cnf(f_1163_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4317),hAPP(hAPP(c_Power_Opower__class_Opower(U_4317),U_4318),U_4319)),U_4320) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4317),U_4318),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4319),U_4320))
    | ~ class_Rings_Ocomm__semiring__1(U_4317) ),
    inference(clausify,[status(thm)],[f_1163_3]) ).

fof(f_1164_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_1164_2,plain,
    ! [U_4323,U_4322,U_4321] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4321),U_4322)),U_4323) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4322),U_4323)),
    inference(variable_rename,[status(thm)],[f_1164_1]) ).

fof(f_1164_3,plain,
    ! [U_4321,U_4322,U_4323] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4321),U_4322)),U_4323) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4322),U_4323)),
    inference(definitional_conversion,[status(esa)],[f_1164_2]) ).

cnf(f_1164_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4321),U_4322)),U_4323) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4322),U_4323)),
    inference(clausify,[status(thm)],[f_1164_3]) ).

fof(f_1165_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_1165_2,plain,
    ! [U_4325,U_4324] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4324),U_4325),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4325
      | ~ class_Rings_Ocomm__semiring__1(U_4324) ),
    inference(variable_rename,[status(thm)],[f_1165_1]) ).

fof(f_1165_3,plain,
    ! [U_4324,U_4325] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4324),U_4325),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4325
      | ~ class_Rings_Ocomm__semiring__1(U_4324) ),
    inference(definitional_conversion,[status(esa)],[f_1165_2]) ).

cnf(f_1165_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4324),U_4325),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4325
    | ~ class_Rings_Ocomm__semiring__1(U_4324) ),
    inference(clausify,[status(thm)],[f_1165_3]) ).

fof(f_1166_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_1166_2,plain,
    ! [U_4328,U_4327,U_4326] : 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_4326,U_4327)),U_4328),U_4327) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4326),U_4328),U_4327),
    inference(variable_rename,[status(thm)],[f_1166_1]) ).

fof(f_1166_3,plain,
    ! [U_4326,U_4327,U_4328] : 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_4326,U_4327)),U_4328),U_4327) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4326),U_4328),U_4327),
    inference(definitional_conversion,[status(esa)],[f_1166_2]) ).

cnf(f_1166_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_4326,U_4327)),U_4328),U_4327) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4326),U_4328),U_4327),
    inference(clausify,[status(thm)],[f_1166_3]) ).

fof(f_1167_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_1167_2,plain,
    ! [U_4330,U_4329] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4329),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4330)) = c_Groups_Ozero__class_Ozero(U_4329)
          | 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_4330))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4329),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4330)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4329),U_4330)
          | ~ 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_4330))) ) )
      | ~ class_Int_Onumber__ring(U_4329) ),
    inference(variable_rename,[status(thm)],[f_1167_1]) ).

fof(f_1167_3,plain,
    ( ! [U_4329,U_4330] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4329),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4330)) = c_Groups_Ozero__class_Ozero(U_4329)
        | 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_4330)))
        | ~ sP338(U_4329,U_4330) )
    & ! [U_4329,U_4330] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4329),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4330)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4329),U_4330)
        | ~ 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_4330)))
        | ~ sP338(U_4329,U_4330) )
    & ! [U_4329,U_4330] :
        ( sP338(U_4329,U_4330)
        | ~ class_Int_Onumber__ring(U_4329) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP338])],[f_1167_2]) ).

cnf(f_1167_4,plain,
    ( sP338(U_4329,U_4330)
    | ~ class_Int_Onumber__ring(U_4329) ),
    inference(clausify,[status(thm)],[f_1167_3]) ).

cnf(f_1167_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4329),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4330)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4329),U_4330)
    | ~ 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_4330)))
    | ~ sP338(U_4329,U_4330) ),
    inference(clausify,[status(thm)],[f_1167_3]) ).

cnf(f_1167_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4329),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4330)) = c_Groups_Ozero__class_Ozero(U_4329)
    | 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_4330)))
    | ~ sP338(U_4329,U_4330) ),
    inference(clausify,[status(thm)],[f_1167_3]) ).

fof(f_1168_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_1168_2,plain,
    ! [U_4332,U_4331] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4331),U_4332) = hAPP(c_Int_Oring__1__class_Oof__int(U_4331),U_4332)
      | ~ class_Int_Onumber__ring(U_4331) ),
    inference(variable_rename,[status(thm)],[f_1168_1]) ).

fof(f_1168_3,plain,
    ! [U_4331,U_4332] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4331),U_4332) = hAPP(c_Int_Oring__1__class_Oof__int(U_4331),U_4332)
      | ~ class_Int_Onumber__ring(U_4331) ),
    inference(definitional_conversion,[status(esa)],[f_1168_2]) ).

cnf(f_1168_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4331),U_4332) = hAPP(c_Int_Oring__1__class_Oof__int(U_4331),U_4332)
    | ~ class_Int_Onumber__ring(U_4331) ),
    inference(clausify,[status(thm)],[f_1168_3]) ).

fof(f_1169_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_1169_2,plain,
    ! [U_4334,U_4333] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_4333),hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334)),c_Groups_Ozero__class_Ozero(U_4333))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(U_4333),hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4333),hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334)),c_Groups_Ozero__class_Ozero(U_4333))) ) )
      | ~ class_Rings_Olinordered__idom(U_4333)
      | ~ class_Int_Onumber__ring(U_4333) ),
    inference(variable_rename,[status(thm)],[f_1169_1]) ).

fof(f_1169_3,plain,
    ( ! [U_4333,U_4334] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_4333),hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334)),c_Groups_Ozero__class_Ozero(U_4333)))
        | ~ sP339(U_4333,U_4334) )
    & ! [U_4333,U_4334] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_4333),hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4333),hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334)),c_Groups_Ozero__class_Ozero(U_4333)))
        | ~ sP339(U_4333,U_4334) )
    & ! [U_4333,U_4334] :
        ( sP339(U_4333,U_4334)
        | ~ class_Rings_Olinordered__idom(U_4333)
        | ~ class_Int_Onumber__ring(U_4333) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP339])],[f_1169_2]) ).

cnf(f_1169_4,plain,
    ( sP339(U_4333,U_4334)
    | ~ class_Rings_Olinordered__idom(U_4333)
    | ~ class_Int_Onumber__ring(U_4333) ),
    inference(clausify,[status(thm)],[f_1169_3]) ).

cnf(f_1169_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4333),hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4333),hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334)),c_Groups_Ozero__class_Ozero(U_4333)))
    | ~ sP339(U_4333,U_4334) ),
    inference(clausify,[status(thm)],[f_1169_3]) ).

cnf(f_1169_6,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4333),hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4333),hAPP(c_Int_Onumber__class_Onumber__of(U_4333),U_4334)),c_Groups_Ozero__class_Ozero(U_4333)))
    | ~ sP339(U_4333,U_4334) ),
    inference(clausify,[status(thm)],[f_1169_3]) ).

fof(f_1170_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_1170_2,plain,
    ! [U_4336,U_4335] :
      ( ( 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_4335)),U_4336)))
        | ( U_4336 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4335 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( U_4336 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4335 != 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_4335)),U_4336))) ) ),
    inference(variable_rename,[status(thm)],[f_1170_1]) ).

fof(f_1170_3,plain,
    ( ! [U_4340,U_4338] :
        ( 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_4338)),U_4340)))
        | ( U_4340 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4338 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_4339,U_4337] :
        ( U_4339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4337 != 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_4337)),U_4339))) ) ),
    inference(miniscope,[status(thm)],[f_1170_2]) ).

fof(f_1170_4,plain,
    ( ! [U_4340,U_4338] :
        ( U_4340 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP340(U_4340,U_4338) )
    & ! [U_4340,U_4338] :
        ( U_4338 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP340(U_4340,U_4338) )
    & ! [U_4340,U_4338] :
        ( 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_4338)),U_4340)))
        | sP340(U_4340,U_4338) )
    & ! [U_4337,U_4339] :
        ( U_4339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4337 != 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_4337)),U_4339))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP340])],[f_1170_3]) ).

cnf(f_1170_5,plain,
    ( U_4339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4337 != 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_4337)),U_4339))) ),
    inference(clausify,[status(thm)],[f_1170_4]) ).

cnf(f_1170_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_4338)),U_4340)))
    | sP340(U_4340,U_4338) ),
    inference(clausify,[status(thm)],[f_1170_4]) ).

cnf(f_1170_7,plain,
    ( U_4338 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP340(U_4340,U_4338) ),
    inference(clausify,[status(thm)],[f_1170_4]) ).

cnf(f_1170_8,plain,
    ( U_4340 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP340(U_4340,U_4338) ),
    inference(clausify,[status(thm)],[f_1170_4]) ).

fof(f_1171_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_1171_2,plain,
    ! [U_4342,U_4341] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4341),U_4342) = U_4342
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4341),c_Groups_Ozero__class_Ozero(U_4341)),U_4342))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4341) ),
    inference(variable_rename,[status(thm)],[f_1171_1]) ).

fof(f_1171_3,plain,
    ! [U_4342,U_4341] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4341),U_4342) = U_4342
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4341),c_Groups_Ozero__class_Ozero(U_4341)),U_4342))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4341) ),
    inference(definitional_conversion,[status(esa)],[f_1171_2]) ).

cnf(f_1171_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4341),U_4342) = U_4342
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4341),c_Groups_Ozero__class_Ozero(U_4341)),U_4342))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4341) ),
    inference(clausify,[status(thm)],[f_1171_3]) ).

fof(f_1172_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_1172_2,plain,
    ! [U_4344,U_4343] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4343),hAPP(c_Groups_Oabs__class_Oabs(U_4343),U_4344)),c_Groups_Ozero__class_Ozero(U_4343)))
          | U_4344 != c_Groups_Ozero__class_Ozero(U_4343) )
        & ( U_4344 = c_Groups_Ozero__class_Ozero(U_4343)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4343),hAPP(c_Groups_Oabs__class_Oabs(U_4343),U_4344)),c_Groups_Ozero__class_Ozero(U_4343))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4343) ),
    inference(variable_rename,[status(thm)],[f_1172_1]) ).

fof(f_1172_3,plain,
    ( ! [U_4343,U_4344] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4343),hAPP(c_Groups_Oabs__class_Oabs(U_4343),U_4344)),c_Groups_Ozero__class_Ozero(U_4343)))
        | U_4344 != c_Groups_Ozero__class_Ozero(U_4343)
        | ~ sP341(U_4343,U_4344) )
    & ! [U_4343,U_4344] :
        ( U_4344 = c_Groups_Ozero__class_Ozero(U_4343)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4343),hAPP(c_Groups_Oabs__class_Oabs(U_4343),U_4344)),c_Groups_Ozero__class_Ozero(U_4343)))
        | ~ sP341(U_4343,U_4344) )
    & ! [U_4343,U_4344] :
        ( sP341(U_4343,U_4344)
        | ~ class_Groups_Oordered__ab__group__add__abs(U_4343) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP341])],[f_1172_2]) ).

cnf(f_1172_4,plain,
    ( sP341(U_4343,U_4344)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4343) ),
    inference(clausify,[status(thm)],[f_1172_3]) ).

cnf(f_1172_5,plain,
    ( U_4344 = c_Groups_Ozero__class_Ozero(U_4343)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4343),hAPP(c_Groups_Oabs__class_Oabs(U_4343),U_4344)),c_Groups_Ozero__class_Ozero(U_4343)))
    | ~ sP341(U_4343,U_4344) ),
    inference(clausify,[status(thm)],[f_1172_3]) ).

cnf(f_1172_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4343),hAPP(c_Groups_Oabs__class_Oabs(U_4343),U_4344)),c_Groups_Ozero__class_Ozero(U_4343)))
    | U_4344 != c_Groups_Ozero__class_Ozero(U_4343)
    | ~ sP341(U_4343,U_4344) ),
    inference(clausify,[status(thm)],[f_1172_3]) ).

fof(f_1173_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_1173_2,plain,
    ! [U_4346,U_4345] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4345),c_Groups_Ozero__class_Ozero(U_4345)),hAPP(c_Groups_Oabs__class_Oabs(U_4345),U_4346)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4345) ),
    inference(variable_rename,[status(thm)],[f_1173_1]) ).

fof(f_1173_3,plain,
    ! [U_4345,U_4346] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4345),c_Groups_Ozero__class_Ozero(U_4345)),hAPP(c_Groups_Oabs__class_Oabs(U_4345),U_4346)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4345) ),
    inference(definitional_conversion,[status(esa)],[f_1173_2]) ).

cnf(f_1173_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4345),c_Groups_Ozero__class_Ozero(U_4345)),hAPP(c_Groups_Oabs__class_Oabs(U_4345),U_4346)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4345) ),
    inference(clausify,[status(thm)],[f_1173_3]) ).

fof(f_1174_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_1174_2,plain,
    ! [U_4348,U_4347] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4347),hAPP(c_Groups_Oabs__class_Oabs(U_4347),U_4348)),c_Groups_Ozero__class_Ozero(U_4347)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4347) ),
    inference(variable_rename,[status(thm)],[f_1174_1]) ).

fof(f_1174_3,plain,
    ! [U_4347,U_4348] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4347),hAPP(c_Groups_Oabs__class_Oabs(U_4347),U_4348)),c_Groups_Ozero__class_Ozero(U_4347)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4347) ),
    inference(definitional_conversion,[status(esa)],[f_1174_2]) ).

cnf(f_1174_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4347),hAPP(c_Groups_Oabs__class_Oabs(U_4347),U_4348)),c_Groups_Ozero__class_Ozero(U_4347)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4347) ),
    inference(clausify,[status(thm)],[f_1174_3]) ).

fof(f_1175_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_1175_2,plain,
    ! [U_4350,U_4349] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4349),c_Groups_Ozero__class_Ozero(U_4349)),hAPP(c_Groups_Oabs__class_Oabs(U_4349),U_4350)))
          | U_4350 = c_Groups_Ozero__class_Ozero(U_4349) )
        & ( U_4350 != c_Groups_Ozero__class_Ozero(U_4349)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4349),c_Groups_Ozero__class_Ozero(U_4349)),hAPP(c_Groups_Oabs__class_Oabs(U_4349),U_4350))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4349) ),
    inference(variable_rename,[status(thm)],[f_1175_1]) ).

fof(f_1175_3,plain,
    ( ! [U_4349,U_4350] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4349),c_Groups_Ozero__class_Ozero(U_4349)),hAPP(c_Groups_Oabs__class_Oabs(U_4349),U_4350)))
        | U_4350 = c_Groups_Ozero__class_Ozero(U_4349)
        | ~ sP342(U_4349,U_4350) )
    & ! [U_4349,U_4350] :
        ( U_4350 != c_Groups_Ozero__class_Ozero(U_4349)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4349),c_Groups_Ozero__class_Ozero(U_4349)),hAPP(c_Groups_Oabs__class_Oabs(U_4349),U_4350)))
        | ~ sP342(U_4349,U_4350) )
    & ! [U_4349,U_4350] :
        ( sP342(U_4349,U_4350)
        | ~ class_Groups_Oordered__ab__group__add__abs(U_4349) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP342])],[f_1175_2]) ).

cnf(f_1175_4,plain,
    ( sP342(U_4349,U_4350)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4349) ),
    inference(clausify,[status(thm)],[f_1175_3]) ).

cnf(f_1175_5,plain,
    ( U_4350 != c_Groups_Ozero__class_Ozero(U_4349)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4349),c_Groups_Ozero__class_Ozero(U_4349)),hAPP(c_Groups_Oabs__class_Oabs(U_4349),U_4350)))
    | ~ sP342(U_4349,U_4350) ),
    inference(clausify,[status(thm)],[f_1175_3]) ).

cnf(f_1175_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4349),c_Groups_Ozero__class_Ozero(U_4349)),hAPP(c_Groups_Oabs__class_Oabs(U_4349),U_4350)))
    | U_4350 = c_Groups_Ozero__class_Ozero(U_4349)
    | ~ sP342(U_4349,U_4350) ),
    inference(clausify,[status(thm)],[f_1175_3]) ).

fof(f_1176_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_1176_2,plain,
    ! [U_4352,U_4351] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4351),U_4352) = U_4352
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4351),c_Groups_Ozero__class_Ozero(U_4351)),U_4352))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4351) ),
    inference(variable_rename,[status(thm)],[f_1176_1]) ).

fof(f_1176_3,plain,
    ! [U_4352,U_4351] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4351),U_4352) = U_4352
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4351),c_Groups_Ozero__class_Ozero(U_4351)),U_4352))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4351) ),
    inference(definitional_conversion,[status(esa)],[f_1176_2]) ).

cnf(f_1176_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4351),U_4352) = U_4352
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4351),c_Groups_Ozero__class_Ozero(U_4351)),U_4352))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4351) ),
    inference(clausify,[status(thm)],[f_1176_3]) ).

fof(f_1177_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_1177_2,plain,
    ! [U_4355,U_4354,U_4353] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4353),hAPP(c_Groups_Oabs__class_Oabs(U_4353),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4353),U_4354),U_4355))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4353),hAPP(c_Groups_Oabs__class_Oabs(U_4353),U_4354)),hAPP(c_Groups_Oabs__class_Oabs(U_4353),U_4355))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4353) ),
    inference(variable_rename,[status(thm)],[f_1177_1]) ).

fof(f_1177_3,plain,
    ! [U_4353,U_4354,U_4355] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4353),hAPP(c_Groups_Oabs__class_Oabs(U_4353),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4353),U_4354),U_4355))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4353),hAPP(c_Groups_Oabs__class_Oabs(U_4353),U_4354)),hAPP(c_Groups_Oabs__class_Oabs(U_4353),U_4355))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4353) ),
    inference(definitional_conversion,[status(esa)],[f_1177_2]) ).

cnf(f_1177_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4353),hAPP(c_Groups_Oabs__class_Oabs(U_4353),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4353),U_4354),U_4355))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4353),hAPP(c_Groups_Oabs__class_Oabs(U_4353),U_4354)),hAPP(c_Groups_Oabs__class_Oabs(U_4353),U_4355))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4353) ),
    inference(clausify,[status(thm)],[f_1177_3]) ).

fof(f_1178_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_1178_2,plain,
    ! [U_4360,U_4359,U_4358,U_4357,U_4356] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),hAPP(c_Groups_Oabs__class_Oabs(U_4356),U_4357)),hAPP(c_Groups_Oabs__class_Oabs(U_4356),U_4359))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),U_4358),U_4360)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4356),hAPP(c_Groups_Oabs__class_Oabs(U_4356),U_4359)),U_4360))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4356),hAPP(c_Groups_Oabs__class_Oabs(U_4356),U_4357)),U_4358))
      | ~ class_Rings_Olinordered__idom(U_4356) ),
    inference(variable_rename,[status(thm)],[f_1178_1]) ).

fof(f_1178_3,plain,
    ! [U_4356,U_4357,U_4358,U_4359,U_4360] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),hAPP(c_Groups_Oabs__class_Oabs(U_4356),U_4357)),hAPP(c_Groups_Oabs__class_Oabs(U_4356),U_4359))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),U_4358),U_4360)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4356),hAPP(c_Groups_Oabs__class_Oabs(U_4356),U_4359)),U_4360))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4356),hAPP(c_Groups_Oabs__class_Oabs(U_4356),U_4357)),U_4358))
      | ~ class_Rings_Olinordered__idom(U_4356) ),
    inference(definitional_conversion,[status(esa)],[f_1178_2]) ).

cnf(f_1178_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),hAPP(c_Groups_Oabs__class_Oabs(U_4356),U_4357)),hAPP(c_Groups_Oabs__class_Oabs(U_4356),U_4359))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),U_4358),U_4360)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4356),hAPP(c_Groups_Oabs__class_Oabs(U_4356),U_4359)),U_4360))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4356),hAPP(c_Groups_Oabs__class_Oabs(U_4356),U_4357)),U_4358))
    | ~ class_Rings_Olinordered__idom(U_4356) ),
    inference(clausify,[status(thm)],[f_1178_3]) ).

fof(f_1179_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_1179_2,plain,
    ! [U_4363,U_4362,U_4361] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4361),hAPP(c_Groups_Oabs__class_Oabs(U_4361),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4361),hAPP(c_Groups_Oabs__class_Oabs(U_4361),U_4362)),hAPP(c_Groups_Oabs__class_Oabs(U_4361),U_4363)))),hAPP(c_Groups_Oabs__class_Oabs(U_4361),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4361),U_4362),U_4363))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4361) ),
    inference(variable_rename,[status(thm)],[f_1179_1]) ).

fof(f_1179_3,plain,
    ! [U_4362,U_4361,U_4363] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4361),hAPP(c_Groups_Oabs__class_Oabs(U_4361),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4361),hAPP(c_Groups_Oabs__class_Oabs(U_4361),U_4362)),hAPP(c_Groups_Oabs__class_Oabs(U_4361),U_4363)))),hAPP(c_Groups_Oabs__class_Oabs(U_4361),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4361),U_4362),U_4363))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4361) ),
    inference(definitional_conversion,[status(esa)],[f_1179_2]) ).

cnf(f_1179_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4361),hAPP(c_Groups_Oabs__class_Oabs(U_4361),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4361),hAPP(c_Groups_Oabs__class_Oabs(U_4361),U_4362)),hAPP(c_Groups_Oabs__class_Oabs(U_4361),U_4363)))),hAPP(c_Groups_Oabs__class_Oabs(U_4361),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4361),U_4362),U_4363))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4361) ),
    inference(clausify,[status(thm)],[f_1179_3]) ).

fof(f_1180_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_1180_2,plain,
    ! [U_4366,U_4365,U_4364] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4364),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4364),hAPP(c_Groups_Oabs__class_Oabs(U_4364),U_4365)),hAPP(c_Groups_Oabs__class_Oabs(U_4364),U_4366))),hAPP(c_Groups_Oabs__class_Oabs(U_4364),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4364),U_4365),U_4366))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4364) ),
    inference(variable_rename,[status(thm)],[f_1180_1]) ).

fof(f_1180_3,plain,
    ! [U_4364,U_4365,U_4366] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4364),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4364),hAPP(c_Groups_Oabs__class_Oabs(U_4364),U_4365)),hAPP(c_Groups_Oabs__class_Oabs(U_4364),U_4366))),hAPP(c_Groups_Oabs__class_Oabs(U_4364),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4364),U_4365),U_4366))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4364) ),
    inference(definitional_conversion,[status(esa)],[f_1180_2]) ).

cnf(f_1180_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4364),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4364),hAPP(c_Groups_Oabs__class_Oabs(U_4364),U_4365)),hAPP(c_Groups_Oabs__class_Oabs(U_4364),U_4366))),hAPP(c_Groups_Oabs__class_Oabs(U_4364),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4364),U_4365),U_4366))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4364) ),
    inference(clausify,[status(thm)],[f_1180_3]) ).

fof(f_1181_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_1181_2,plain,
    ! [U_4369,U_4368,U_4367] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4367),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4367),hAPP(c_Groups_Oabs__class_Oabs(U_4367),U_4368)),hAPP(c_Groups_Oabs__class_Oabs(U_4367),U_4369))),hAPP(c_Groups_Oabs__class_Oabs(U_4367),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4367),U_4369),U_4368))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4367) ),
    inference(variable_rename,[status(thm)],[f_1181_1]) ).

fof(f_1181_3,plain,
    ! [U_4367,U_4368,U_4369] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4367),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4367),hAPP(c_Groups_Oabs__class_Oabs(U_4367),U_4368)),hAPP(c_Groups_Oabs__class_Oabs(U_4367),U_4369))),hAPP(c_Groups_Oabs__class_Oabs(U_4367),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4367),U_4369),U_4368))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4367) ),
    inference(definitional_conversion,[status(esa)],[f_1181_2]) ).

cnf(f_1181_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4367),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4367),hAPP(c_Groups_Oabs__class_Oabs(U_4367),U_4368)),hAPP(c_Groups_Oabs__class_Oabs(U_4367),U_4369))),hAPP(c_Groups_Oabs__class_Oabs(U_4367),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4367),U_4369),U_4368))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4367) ),
    inference(clausify,[status(thm)],[f_1181_3]) ).

fof(f_1182_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_1182_2,plain,
    ! [U_4371,U_4370] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4370),hAPP(c_Groups_Ouminus__class_Ouminus(U_4370),U_4371)),hAPP(c_Groups_Oabs__class_Oabs(U_4370),U_4371)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4370) ),
    inference(variable_rename,[status(thm)],[f_1182_1]) ).

fof(f_1182_3,plain,
    ! [U_4370,U_4371] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4370),hAPP(c_Groups_Ouminus__class_Ouminus(U_4370),U_4371)),hAPP(c_Groups_Oabs__class_Oabs(U_4370),U_4371)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4370) ),
    inference(definitional_conversion,[status(esa)],[f_1182_2]) ).

cnf(f_1182_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4370),hAPP(c_Groups_Ouminus__class_Ouminus(U_4370),U_4371)),hAPP(c_Groups_Oabs__class_Oabs(U_4370),U_4371)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4370) ),
    inference(clausify,[status(thm)],[f_1182_3]) ).

fof(f_1183_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_1183_2,plain,
    ! [U_4374,U_4373,U_4372] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(c_Groups_Oabs__class_Oabs(U_4372),U_4373)),U_4374))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(c_Groups_Ouminus__class_Ouminus(U_4372),U_4373)),U_4374))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),U_4373),U_4374)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(c_Groups_Ouminus__class_Ouminus(U_4372),U_4373)),U_4374))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),U_4373),U_4374)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(c_Groups_Oabs__class_Oabs(U_4372),U_4373)),U_4374)) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4372) ),
    inference(variable_rename,[status(thm)],[f_1183_1]) ).

fof(f_1183_3,plain,
    ( ! [U_4372,U_4373,U_4374] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(c_Groups_Ouminus__class_Ouminus(U_4372),U_4373)),U_4374))
        | ~ sP343(U_4372,U_4373,U_4374) )
    & ! [U_4372,U_4373,U_4374] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),U_4373),U_4374))
        | ~ sP343(U_4372,U_4373,U_4374) )
    & ! [U_4372,U_4373,U_4374] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(c_Groups_Oabs__class_Oabs(U_4372),U_4373)),U_4374))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(c_Groups_Ouminus__class_Ouminus(U_4372),U_4373)),U_4374))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),U_4373),U_4374))
        | ~ sP344(U_4372,U_4373,U_4374) )
    & ! [U_4372,U_4373,U_4374] :
        ( sP343(U_4372,U_4373,U_4374)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(c_Groups_Oabs__class_Oabs(U_4372),U_4373)),U_4374))
        | ~ sP344(U_4372,U_4373,U_4374) )
    & ! [U_4372,U_4373,U_4374] :
        ( sP344(U_4372,U_4373,U_4374)
        | ~ class_Groups_Oordered__ab__group__add__abs(U_4372) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP343,sP344])],[f_1183_2]) ).

cnf(f_1183_4,plain,
    ( sP344(U_4372,U_4373,U_4374)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4372) ),
    inference(clausify,[status(thm)],[f_1183_3]) ).

cnf(f_1183_5,plain,
    ( sP343(U_4372,U_4373,U_4374)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(c_Groups_Oabs__class_Oabs(U_4372),U_4373)),U_4374))
    | ~ sP344(U_4372,U_4373,U_4374) ),
    inference(clausify,[status(thm)],[f_1183_3]) ).

cnf(f_1183_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(c_Groups_Oabs__class_Oabs(U_4372),U_4373)),U_4374))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(c_Groups_Ouminus__class_Ouminus(U_4372),U_4373)),U_4374))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),U_4373),U_4374))
    | ~ sP344(U_4372,U_4373,U_4374) ),
    inference(clausify,[status(thm)],[f_1183_3]) ).

cnf(f_1183_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),U_4373),U_4374))
    | ~ sP343(U_4372,U_4373,U_4374) ),
    inference(clausify,[status(thm)],[f_1183_3]) ).

cnf(f_1183_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(c_Groups_Ouminus__class_Ouminus(U_4372),U_4373)),U_4374))
    | ~ sP343(U_4372,U_4373,U_4374) ),
    inference(clausify,[status(thm)],[f_1183_3]) ).

fof(f_1184_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_1184_2,plain,
    ! [U_4377,U_4376,U_4375] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4375),hAPP(c_Groups_Oabs__class_Oabs(U_4375),U_4376)),U_4377))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4375),hAPP(c_Groups_Ouminus__class_Ouminus(U_4375),U_4376)),U_4377))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4375),U_4376),U_4377))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4375) ),
    inference(variable_rename,[status(thm)],[f_1184_1]) ).

fof(f_1184_3,plain,
    ! [U_4375,U_4377,U_4376] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4375),hAPP(c_Groups_Oabs__class_Oabs(U_4375),U_4376)),U_4377))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4375),hAPP(c_Groups_Ouminus__class_Ouminus(U_4375),U_4376)),U_4377))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4375),U_4376),U_4377))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4375) ),
    inference(definitional_conversion,[status(esa)],[f_1184_2]) ).

cnf(f_1184_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4375),hAPP(c_Groups_Oabs__class_Oabs(U_4375),U_4376)),U_4377))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4375),hAPP(c_Groups_Ouminus__class_Ouminus(U_4375),U_4376)),U_4377))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4375),U_4376),U_4377))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4375) ),
    inference(clausify,[status(thm)],[f_1184_3]) ).

fof(f_1185_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_1185_2,plain,
    ! [U_4380,U_4379,U_4378] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4378),hAPP(c_Groups_Ouminus__class_Ouminus(U_4378),U_4379)),U_4380))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4378),hAPP(c_Groups_Oabs__class_Oabs(U_4378),U_4379)),U_4380))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4378) ),
    inference(variable_rename,[status(thm)],[f_1185_1]) ).

fof(f_1185_3,plain,
    ! [U_4378,U_4379,U_4380] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4378),hAPP(c_Groups_Ouminus__class_Ouminus(U_4378),U_4379)),U_4380))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4378),hAPP(c_Groups_Oabs__class_Oabs(U_4378),U_4379)),U_4380))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4378) ),
    inference(definitional_conversion,[status(esa)],[f_1185_2]) ).

cnf(f_1185_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4378),hAPP(c_Groups_Ouminus__class_Ouminus(U_4378),U_4379)),U_4380))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4378),hAPP(c_Groups_Oabs__class_Oabs(U_4378),U_4379)),U_4380))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4378) ),
    inference(clausify,[status(thm)],[f_1185_3]) ).

fof(f_1186_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_1186_2,plain,
    ! [U_4383,U_4382,U_4381] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),hAPP(c_Groups_Oabs__class_Oabs(U_4381),U_4382)),U_4383))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),hAPP(c_Groups_Ouminus__class_Ouminus(U_4381),U_4382)),U_4383))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),U_4382),U_4383)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),hAPP(c_Groups_Ouminus__class_Ouminus(U_4381),U_4382)),U_4383))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),U_4382),U_4383)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),hAPP(c_Groups_Oabs__class_Oabs(U_4381),U_4382)),U_4383)) ) )
      | ~ class_Rings_Olinordered__idom(U_4381) ),
    inference(variable_rename,[status(thm)],[f_1186_1]) ).

fof(f_1186_3,plain,
    ( ! [U_4381,U_4382,U_4383] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),hAPP(c_Groups_Ouminus__class_Ouminus(U_4381),U_4382)),U_4383))
        | ~ sP345(U_4381,U_4382,U_4383) )
    & ! [U_4381,U_4382,U_4383] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),U_4382),U_4383))
        | ~ sP345(U_4381,U_4382,U_4383) )
    & ! [U_4381,U_4382,U_4383] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),hAPP(c_Groups_Oabs__class_Oabs(U_4381),U_4382)),U_4383))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),hAPP(c_Groups_Ouminus__class_Ouminus(U_4381),U_4382)),U_4383))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),U_4382),U_4383))
        | ~ sP346(U_4381,U_4382,U_4383) )
    & ! [U_4381,U_4382,U_4383] :
        ( sP345(U_4381,U_4382,U_4383)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),hAPP(c_Groups_Oabs__class_Oabs(U_4381),U_4382)),U_4383))
        | ~ sP346(U_4381,U_4382,U_4383) )
    & ! [U_4381,U_4382,U_4383] :
        ( sP346(U_4381,U_4382,U_4383)
        | ~ class_Rings_Olinordered__idom(U_4381) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP345,sP346])],[f_1186_2]) ).

cnf(f_1186_4,plain,
    ( sP346(U_4381,U_4382,U_4383)
    | ~ class_Rings_Olinordered__idom(U_4381) ),
    inference(clausify,[status(thm)],[f_1186_3]) ).

cnf(f_1186_5,plain,
    ( sP345(U_4381,U_4382,U_4383)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),hAPP(c_Groups_Oabs__class_Oabs(U_4381),U_4382)),U_4383))
    | ~ sP346(U_4381,U_4382,U_4383) ),
    inference(clausify,[status(thm)],[f_1186_3]) ).

cnf(f_1186_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),hAPP(c_Groups_Oabs__class_Oabs(U_4381),U_4382)),U_4383))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),hAPP(c_Groups_Ouminus__class_Ouminus(U_4381),U_4382)),U_4383))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),U_4382),U_4383))
    | ~ sP346(U_4381,U_4382,U_4383) ),
    inference(clausify,[status(thm)],[f_1186_3]) ).

cnf(f_1186_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),U_4382),U_4383))
    | ~ sP345(U_4381,U_4382,U_4383) ),
    inference(clausify,[status(thm)],[f_1186_3]) ).

cnf(f_1186_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4381),hAPP(c_Groups_Ouminus__class_Ouminus(U_4381),U_4382)),U_4383))
    | ~ sP345(U_4381,U_4382,U_4383) ),
    inference(clausify,[status(thm)],[f_1186_3]) ).

fof(f_1187_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_1187_2,plain,
    ! [U_4386,U_4385,U_4384] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4386)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4386)),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4386)),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4386))) ) )
      | ~ class_Orderings_Olinorder(U_4384)
      | ~ class_Int_Onumber(U_4384) ),
    inference(variable_rename,[status(thm)],[f_1187_1]) ).

fof(f_1187_3,plain,
    ( ! [U_4386,U_4385,U_4384] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4386)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4386)),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)))
        | ~ sP347(U_4386,U_4385,U_4384) )
    & ! [U_4386,U_4385,U_4384] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4386)),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4386)))
        | ~ sP347(U_4386,U_4385,U_4384) )
    & ! [U_4386,U_4385,U_4384] :
        ( sP347(U_4386,U_4385,U_4384)
        | ~ class_Orderings_Olinorder(U_4384)
        | ~ class_Int_Onumber(U_4384) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP347])],[f_1187_2]) ).

cnf(f_1187_4,plain,
    ( sP347(U_4386,U_4385,U_4384)
    | ~ class_Orderings_Olinorder(U_4384)
    | ~ class_Int_Onumber(U_4384) ),
    inference(clausify,[status(thm)],[f_1187_3]) ).

cnf(f_1187_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4386)),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4386)))
    | ~ sP347(U_4386,U_4385,U_4384) ),
    inference(clausify,[status(thm)],[f_1187_3]) ).

cnf(f_1187_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4386)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4386)),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)))
    | ~ sP347(U_4386,U_4385,U_4384) ),
    inference(clausify,[status(thm)],[f_1187_3]) ).

fof(f_1188_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_1188_2,plain,
    ! [U_4390,U_4389,U_4388,U_4387] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4387),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4387),U_4388),U_4389)),hAPP(c_Int_Onumber__class_Onumber__of(U_4387),U_4390)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4387),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4387),U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4387),U_4390))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4387),U_4389),hAPP(c_Int_Onumber__class_Onumber__of(U_4387),U_4390)))
      | ~ class_Rings_Osemiring(U_4387)
      | ~ class_Int_Onumber(U_4387) ),
    inference(variable_rename,[status(thm)],[f_1188_1]) ).

fof(f_1188_3,plain,
    ! [U_4388,U_4389,U_4387,U_4390] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4387),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4387),U_4388),U_4389)),hAPP(c_Int_Onumber__class_Onumber__of(U_4387),U_4390)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4387),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4387),U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4387),U_4390))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4387),U_4389),hAPP(c_Int_Onumber__class_Onumber__of(U_4387),U_4390)))
      | ~ class_Rings_Osemiring(U_4387)
      | ~ class_Int_Onumber(U_4387) ),
    inference(definitional_conversion,[status(esa)],[f_1188_2]) ).

cnf(f_1188_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4387),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4387),U_4388),U_4389)),hAPP(c_Int_Onumber__class_Onumber__of(U_4387),U_4390)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4387),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4387),U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4387),U_4390))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4387),U_4389),hAPP(c_Int_Onumber__class_Onumber__of(U_4387),U_4390)))
    | ~ class_Rings_Osemiring(U_4387)
    | ~ class_Int_Onumber(U_4387) ),
    inference(clausify,[status(thm)],[f_1188_3]) ).

fof(f_1189_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_1189_2,plain,
    ! [U_4394,U_4393,U_4392,U_4391] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4391),hAPP(c_Int_Onumber__class_Onumber__of(U_4391),U_4392)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4391),U_4393),U_4394)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4391),hAPP(c_Int_Onumber__class_Onumber__of(U_4391),U_4392)),U_4393)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4391),hAPP(c_Int_Onumber__class_Onumber__of(U_4391),U_4392)),U_4394))
      | ~ class_Rings_Osemiring(U_4391)
      | ~ class_Int_Onumber(U_4391) ),
    inference(variable_rename,[status(thm)],[f_1189_1]) ).

fof(f_1189_3,plain,
    ! [U_4392,U_4391,U_4393,U_4394] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4391),hAPP(c_Int_Onumber__class_Onumber__of(U_4391),U_4392)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4391),U_4393),U_4394)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4391),hAPP(c_Int_Onumber__class_Onumber__of(U_4391),U_4392)),U_4393)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4391),hAPP(c_Int_Onumber__class_Onumber__of(U_4391),U_4392)),U_4394))
      | ~ class_Rings_Osemiring(U_4391)
      | ~ class_Int_Onumber(U_4391) ),
    inference(definitional_conversion,[status(esa)],[f_1189_2]) ).

cnf(f_1189_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4391),hAPP(c_Int_Onumber__class_Onumber__of(U_4391),U_4392)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4391),U_4393),U_4394)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4391),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4391),hAPP(c_Int_Onumber__class_Onumber__of(U_4391),U_4392)),U_4393)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4391),hAPP(c_Int_Onumber__class_Onumber__of(U_4391),U_4392)),U_4394))
    | ~ class_Rings_Osemiring(U_4391)
    | ~ class_Int_Onumber(U_4391) ),
    inference(clausify,[status(thm)],[f_1189_3]) ).

fof(f_1190_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_1190_2,plain,
    ! [U_4397,U_4396,U_4395] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4395),U_4396),hAPP(c_Nat_OSuc,U_4397)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4395),U_4396),hAPP(hAPP(c_Power_Opower__class_Opower(U_4395),U_4396),U_4397))
      | ~ class_Rings_Ocomm__semiring__1(U_4395) ),
    inference(variable_rename,[status(thm)],[f_1190_1]) ).

fof(f_1190_3,plain,
    ! [U_4396,U_4397,U_4395] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4395),U_4396),hAPP(c_Nat_OSuc,U_4397)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4395),U_4396),hAPP(hAPP(c_Power_Opower__class_Opower(U_4395),U_4396),U_4397))
      | ~ class_Rings_Ocomm__semiring__1(U_4395) ),
    inference(definitional_conversion,[status(esa)],[f_1190_2]) ).

cnf(f_1190_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4395),U_4396),hAPP(c_Nat_OSuc,U_4397)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4395),U_4396),hAPP(hAPP(c_Power_Opower__class_Opower(U_4395),U_4396),U_4397))
    | ~ class_Rings_Ocomm__semiring__1(U_4395) ),
    inference(clausify,[status(thm)],[f_1190_3]) ).

fof(f_1191_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_1191_2,plain,
    ! [U_4400,U_4399,U_4398] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4399),hAPP(hAPP(c_Power_Opower__class_Opower(U_4398),U_4399),U_4400)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4398),U_4399),hAPP(c_Nat_OSuc,U_4400))
      | ~ class_Rings_Ocomm__semiring__1(U_4398) ),
    inference(variable_rename,[status(thm)],[f_1191_1]) ).

fof(f_1191_3,plain,
    ! [U_4398,U_4399,U_4400] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4399),hAPP(hAPP(c_Power_Opower__class_Opower(U_4398),U_4399),U_4400)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4398),U_4399),hAPP(c_Nat_OSuc,U_4400))
      | ~ class_Rings_Ocomm__semiring__1(U_4398) ),
    inference(definitional_conversion,[status(esa)],[f_1191_2]) ).

cnf(f_1191_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4398),U_4399),hAPP(hAPP(c_Power_Opower__class_Opower(U_4398),U_4399),U_4400)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4398),U_4399),hAPP(c_Nat_OSuc,U_4400))
    | ~ class_Rings_Ocomm__semiring__1(U_4398) ),
    inference(clausify,[status(thm)],[f_1191_3]) ).

fof(f_1192_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_1192_2,plain,
    ! [U_4403,U_4402,U_4401] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4401),hAPP(hAPP(c_Power_Opower__class_Opower(U_4401),U_4402),U_4403)),U_4402) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4401),U_4402),hAPP(c_Nat_OSuc,U_4403))
      | ~ class_Rings_Ocomm__semiring__1(U_4401) ),
    inference(variable_rename,[status(thm)],[f_1192_1]) ).

fof(f_1192_3,plain,
    ! [U_4401,U_4402,U_4403] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4401),hAPP(hAPP(c_Power_Opower__class_Opower(U_4401),U_4402),U_4403)),U_4402) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4401),U_4402),hAPP(c_Nat_OSuc,U_4403))
      | ~ class_Rings_Ocomm__semiring__1(U_4401) ),
    inference(definitional_conversion,[status(esa)],[f_1192_2]) ).

cnf(f_1192_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4401),hAPP(hAPP(c_Power_Opower__class_Opower(U_4401),U_4402),U_4403)),U_4402) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4401),U_4402),hAPP(c_Nat_OSuc,U_4403))
    | ~ class_Rings_Ocomm__semiring__1(U_4401) ),
    inference(clausify,[status(thm)],[f_1192_3]) ).

fof(f_1193_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_1193_2,plain,
    ! [U_4407,U_4406,U_4405,U_4404] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4404),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4404),U_4405),U_4406)),hAPP(c_Int_Onumber__class_Onumber__of(U_4404),U_4407)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4404),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4404),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4404),U_4407))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4404),U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4404),U_4407)))
      | ~ class_Rings_Oring(U_4404)
      | ~ class_Int_Onumber(U_4404) ),
    inference(variable_rename,[status(thm)],[f_1193_1]) ).

fof(f_1193_3,plain,
    ! [U_4404,U_4405,U_4406,U_4407] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4404),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4404),U_4405),U_4406)),hAPP(c_Int_Onumber__class_Onumber__of(U_4404),U_4407)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4404),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4404),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4404),U_4407))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4404),U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4404),U_4407)))
      | ~ class_Rings_Oring(U_4404)
      | ~ class_Int_Onumber(U_4404) ),
    inference(definitional_conversion,[status(esa)],[f_1193_2]) ).

cnf(f_1193_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4404),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4404),U_4405),U_4406)),hAPP(c_Int_Onumber__class_Onumber__of(U_4404),U_4407)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4404),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4404),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4404),U_4407))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4404),U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4404),U_4407)))
    | ~ class_Rings_Oring(U_4404)
    | ~ class_Int_Onumber(U_4404) ),
    inference(clausify,[status(thm)],[f_1193_3]) ).

fof(f_1194_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_1194_2,plain,
    ! [U_4411,U_4410,U_4409,U_4408] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4408),hAPP(c_Int_Onumber__class_Onumber__of(U_4408),U_4409)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4408),U_4410),U_4411)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4408),hAPP(c_Int_Onumber__class_Onumber__of(U_4408),U_4409)),U_4410)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4408),hAPP(c_Int_Onumber__class_Onumber__of(U_4408),U_4409)),U_4411))
      | ~ class_Rings_Oring(U_4408)
      | ~ class_Int_Onumber(U_4408) ),
    inference(variable_rename,[status(thm)],[f_1194_1]) ).

fof(f_1194_3,plain,
    ! [U_4409,U_4408,U_4410,U_4411] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4408),hAPP(c_Int_Onumber__class_Onumber__of(U_4408),U_4409)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4408),U_4410),U_4411)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4408),hAPP(c_Int_Onumber__class_Onumber__of(U_4408),U_4409)),U_4410)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4408),hAPP(c_Int_Onumber__class_Onumber__of(U_4408),U_4409)),U_4411))
      | ~ class_Rings_Oring(U_4408)
      | ~ class_Int_Onumber(U_4408) ),
    inference(definitional_conversion,[status(esa)],[f_1194_2]) ).

cnf(f_1194_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4408),hAPP(c_Int_Onumber__class_Onumber__of(U_4408),U_4409)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4408),U_4410),U_4411)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4408),hAPP(c_Int_Onumber__class_Onumber__of(U_4408),U_4409)),U_4410)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4408),hAPP(c_Int_Onumber__class_Onumber__of(U_4408),U_4409)),U_4411))
    | ~ class_Rings_Oring(U_4408)
    | ~ class_Int_Onumber(U_4408) ),
    inference(clausify,[status(thm)],[f_1194_3]) ).

fof(f_1195_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_1195_2,plain,
    ! [U_4414,U_4413,U_4412] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4412),U_4413)),hAPP(c_Int_Onumber__class_Onumber__of(U_4412),U_4414)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4413),U_4414)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4413),U_4414))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4412),U_4413)),hAPP(c_Int_Onumber__class_Onumber__of(U_4412),U_4414))) ) )
      | ~ class_Rings_Olinordered__idom(U_4412)
      | ~ class_Int_Onumber__ring(U_4412) ),
    inference(variable_rename,[status(thm)],[f_1195_1]) ).

fof(f_1195_3,plain,
    ( ! [U_4412,U_4413,U_4414] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4412),U_4413)),hAPP(c_Int_Onumber__class_Onumber__of(U_4412),U_4414)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4413),U_4414))
        | ~ sP348(U_4412,U_4413,U_4414) )
    & ! [U_4412,U_4413,U_4414] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4413),U_4414))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4412),U_4413)),hAPP(c_Int_Onumber__class_Onumber__of(U_4412),U_4414)))
        | ~ sP348(U_4412,U_4413,U_4414) )
    & ! [U_4412,U_4413,U_4414] :
        ( sP348(U_4412,U_4413,U_4414)
        | ~ class_Rings_Olinordered__idom(U_4412)
        | ~ class_Int_Onumber__ring(U_4412) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP348])],[f_1195_2]) ).

cnf(f_1195_4,plain,
    ( sP348(U_4412,U_4413,U_4414)
    | ~ class_Rings_Olinordered__idom(U_4412)
    | ~ class_Int_Onumber__ring(U_4412) ),
    inference(clausify,[status(thm)],[f_1195_3]) ).

cnf(f_1195_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4413),U_4414))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4412),U_4413)),hAPP(c_Int_Onumber__class_Onumber__of(U_4412),U_4414)))
    | ~ sP348(U_4412,U_4413,U_4414) ),
    inference(clausify,[status(thm)],[f_1195_3]) ).

cnf(f_1195_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4412),hAPP(c_Int_Onumber__class_Onumber__of(U_4412),U_4413)),hAPP(c_Int_Onumber__class_Onumber__of(U_4412),U_4414)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4413),U_4414))
    | ~ sP348(U_4412,U_4413,U_4414) ),
    inference(clausify,[status(thm)],[f_1195_3]) ).

fof(f_1196_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_1196_2,plain,
    ! [U_4416,U_4415] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4415),U_4416),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4415)
      | ~ class_Rings_Ocomm__semiring__1(U_4415) ),
    inference(variable_rename,[status(thm)],[f_1196_1]) ).

fof(f_1196_3,plain,
    ! [U_4415,U_4416] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4415),U_4416),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4415)
      | ~ class_Rings_Ocomm__semiring__1(U_4415) ),
    inference(definitional_conversion,[status(esa)],[f_1196_2]) ).

cnf(f_1196_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4415),U_4416),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4415)
    | ~ class_Rings_Ocomm__semiring__1(U_4415) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

fof(f_1197_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_1197_2,plain,
    ! [U_4420,U_4419,U_4418,U_4417] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4417),hAPP(hAPP(c_Power_Opower__class_Opower(U_4417),U_4418),U_4419)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4417),U_4418),U_4420)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4417),U_4418),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4419),U_4420))
      | ~ class_Rings_Ocomm__semiring__1(U_4417) ),
    inference(variable_rename,[status(thm)],[f_1197_1]) ).

fof(f_1197_3,plain,
    ! [U_4417,U_4418,U_4419,U_4420] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4417),hAPP(hAPP(c_Power_Opower__class_Opower(U_4417),U_4418),U_4419)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4417),U_4418),U_4420)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4417),U_4418),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4419),U_4420))
      | ~ class_Rings_Ocomm__semiring__1(U_4417) ),
    inference(definitional_conversion,[status(esa)],[f_1197_2]) ).

cnf(f_1197_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4417),hAPP(hAPP(c_Power_Opower__class_Opower(U_4417),U_4418),U_4419)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4417),U_4418),U_4420)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4417),U_4418),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4419),U_4420))
    | ~ class_Rings_Ocomm__semiring__1(U_4417) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

fof(f_1198_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_1198_2,plain,
    ! [U_4423,U_4422,U_4421] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4421),hAPP(c_Int_Onumber__class_Onumber__of(U_4421),U_4422)),hAPP(c_Int_Onumber__class_Onumber__of(U_4421),U_4423)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4422),U_4423)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4422),U_4423))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4421),hAPP(c_Int_Onumber__class_Onumber__of(U_4421),U_4422)),hAPP(c_Int_Onumber__class_Onumber__of(U_4421),U_4423))) ) )
      | ~ class_Rings_Olinordered__idom(U_4421)
      | ~ class_Int_Onumber__ring(U_4421) ),
    inference(variable_rename,[status(thm)],[f_1198_1]) ).

fof(f_1198_3,plain,
    ( ! [U_4421,U_4422,U_4423] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4421),hAPP(c_Int_Onumber__class_Onumber__of(U_4421),U_4422)),hAPP(c_Int_Onumber__class_Onumber__of(U_4421),U_4423)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4422),U_4423))
        | ~ sP349(U_4421,U_4422,U_4423) )
    & ! [U_4421,U_4422,U_4423] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4422),U_4423))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4421),hAPP(c_Int_Onumber__class_Onumber__of(U_4421),U_4422)),hAPP(c_Int_Onumber__class_Onumber__of(U_4421),U_4423)))
        | ~ sP349(U_4421,U_4422,U_4423) )
    & ! [U_4421,U_4422,U_4423] :
        ( sP349(U_4421,U_4422,U_4423)
        | ~ class_Rings_Olinordered__idom(U_4421)
        | ~ class_Int_Onumber__ring(U_4421) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP349])],[f_1198_2]) ).

cnf(f_1198_4,plain,
    ( sP349(U_4421,U_4422,U_4423)
    | ~ class_Rings_Olinordered__idom(U_4421)
    | ~ class_Int_Onumber__ring(U_4421) ),
    inference(clausify,[status(thm)],[f_1198_3]) ).

cnf(f_1198_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4422),U_4423))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4421),hAPP(c_Int_Onumber__class_Onumber__of(U_4421),U_4422)),hAPP(c_Int_Onumber__class_Onumber__of(U_4421),U_4423)))
    | ~ sP349(U_4421,U_4422,U_4423) ),
    inference(clausify,[status(thm)],[f_1198_3]) ).

cnf(f_1198_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4421),hAPP(c_Int_Onumber__class_Onumber__of(U_4421),U_4422)),hAPP(c_Int_Onumber__class_Onumber__of(U_4421),U_4423)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4422),U_4423))
    | ~ sP349(U_4421,U_4422,U_4423) ),
    inference(clausify,[status(thm)],[f_1198_3]) ).

fof(f_1199_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_1199_2,plain,
    ! [U_4426,U_4425,U_4424] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4424),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4425),U_4426)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4424),hAPP(c_Int_Onumber__class_Onumber__of(U_4424),U_4425)),hAPP(c_Int_Onumber__class_Onumber__of(U_4424),U_4426))
      | ~ class_Int_Onumber__ring(U_4424) ),
    inference(variable_rename,[status(thm)],[f_1199_1]) ).

fof(f_1199_3,plain,
    ! [U_4426,U_4425,U_4424] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4424),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4425),U_4426)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4424),hAPP(c_Int_Onumber__class_Onumber__of(U_4424),U_4425)),hAPP(c_Int_Onumber__class_Onumber__of(U_4424),U_4426))
      | ~ class_Int_Onumber__ring(U_4424) ),
    inference(definitional_conversion,[status(esa)],[f_1199_2]) ).

cnf(f_1199_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4424),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4425),U_4426)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4424),hAPP(c_Int_Onumber__class_Onumber__of(U_4424),U_4425)),hAPP(c_Int_Onumber__class_Onumber__of(U_4424),U_4426))
    | ~ class_Int_Onumber__ring(U_4424) ),
    inference(clausify,[status(thm)],[f_1199_3]) ).

fof(f_1200_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_1200_2,plain,
    ! [U_4429,U_4428,U_4427] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4427),hAPP(c_Int_Onumber__class_Onumber__of(U_4427),U_4428)),hAPP(c_Int_Onumber__class_Onumber__of(U_4427),U_4429)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4427),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4428),U_4429))
      | ~ class_Int_Onumber__ring(U_4427) ),
    inference(variable_rename,[status(thm)],[f_1200_1]) ).

fof(f_1200_3,plain,
    ! [U_4427,U_4428,U_4429] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4427),hAPP(c_Int_Onumber__class_Onumber__of(U_4427),U_4428)),hAPP(c_Int_Onumber__class_Onumber__of(U_4427),U_4429)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4427),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4428),U_4429))
      | ~ class_Int_Onumber__ring(U_4427) ),
    inference(definitional_conversion,[status(esa)],[f_1200_2]) ).

cnf(f_1200_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4427),hAPP(c_Int_Onumber__class_Onumber__of(U_4427),U_4428)),hAPP(c_Int_Onumber__class_Onumber__of(U_4427),U_4429)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4427),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4428),U_4429))
    | ~ class_Int_Onumber__ring(U_4427) ),
    inference(clausify,[status(thm)],[f_1200_3]) ).

fof(f_1201_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_1201_2,plain,
    ! [U_4433,U_4432,U_4431,U_4430] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4430),hAPP(c_Int_Onumber__class_Onumber__of(U_4430),U_4431)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4430),hAPP(c_Int_Onumber__class_Onumber__of(U_4430),U_4432)),U_4433)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4430),hAPP(c_Int_Onumber__class_Onumber__of(U_4430),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4431),U_4432))),U_4433)
      | ~ class_Int_Onumber__ring(U_4430) ),
    inference(variable_rename,[status(thm)],[f_1201_1]) ).

fof(f_1201_3,plain,
    ! [U_4430,U_4431,U_4432,U_4433] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4430),hAPP(c_Int_Onumber__class_Onumber__of(U_4430),U_4431)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4430),hAPP(c_Int_Onumber__class_Onumber__of(U_4430),U_4432)),U_4433)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4430),hAPP(c_Int_Onumber__class_Onumber__of(U_4430),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4431),U_4432))),U_4433)
      | ~ class_Int_Onumber__ring(U_4430) ),
    inference(definitional_conversion,[status(esa)],[f_1201_2]) ).

cnf(f_1201_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4430),hAPP(c_Int_Onumber__class_Onumber__of(U_4430),U_4431)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4430),hAPP(c_Int_Onumber__class_Onumber__of(U_4430),U_4432)),U_4433)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4430),hAPP(c_Int_Onumber__class_Onumber__of(U_4430),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4431),U_4432))),U_4433)
    | ~ class_Int_Onumber__ring(U_4430) ),
    inference(clausify,[status(thm)],[f_1201_3]) ).

fof(f_1202_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_1202_2,plain,
    ! [U_4435,U_4434] :
      ( 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_4434),U_4435)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4434)) ),
    inference(variable_rename,[status(thm)],[f_1202_1]) ).

fof(f_1202_3,plain,
    ! [U_4434,U_4435] :
      ( 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_4434),U_4435)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4434)) ),
    inference(definitional_conversion,[status(esa)],[f_1202_2]) ).

cnf(f_1202_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_4434),U_4435)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4434)) ),
    inference(clausify,[status(thm)],[f_1202_3]) ).

fof(f_1203_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_1203_2,plain,
    ! [U_4439,U_4438,U_4437,U_4436] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4436),hAPP(c_Int_Onumber__class_Onumber__of(U_4436),U_4437)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4436),hAPP(c_Int_Onumber__class_Onumber__of(U_4436),U_4438)),U_4439)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4436),hAPP(c_Int_Onumber__class_Onumber__of(U_4436),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4437),U_4438))),U_4439)
      | ~ class_Int_Onumber__ring(U_4436) ),
    inference(variable_rename,[status(thm)],[f_1203_1]) ).

fof(f_1203_3,plain,
    ! [U_4436,U_4437,U_4438,U_4439] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4436),hAPP(c_Int_Onumber__class_Onumber__of(U_4436),U_4437)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4436),hAPP(c_Int_Onumber__class_Onumber__of(U_4436),U_4438)),U_4439)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4436),hAPP(c_Int_Onumber__class_Onumber__of(U_4436),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4437),U_4438))),U_4439)
      | ~ class_Int_Onumber__ring(U_4436) ),
    inference(definitional_conversion,[status(esa)],[f_1203_2]) ).

cnf(f_1203_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4436),hAPP(c_Int_Onumber__class_Onumber__of(U_4436),U_4437)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4436),hAPP(c_Int_Onumber__class_Onumber__of(U_4436),U_4438)),U_4439)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4436),hAPP(c_Int_Onumber__class_Onumber__of(U_4436),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4437),U_4438))),U_4439)
    | ~ class_Int_Onumber__ring(U_4436) ),
    inference(clausify,[status(thm)],[f_1203_3]) ).

fof(f_1204_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_1204_2,plain,
    ! [U_4442,U_4441,U_4440] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4440),hAPP(c_Int_Onumber__class_Onumber__of(U_4440),U_4441)),hAPP(c_Int_Onumber__class_Onumber__of(U_4440),U_4442)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4440),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4441),U_4442))
      | ~ class_Int_Onumber__ring(U_4440) ),
    inference(variable_rename,[status(thm)],[f_1204_1]) ).

fof(f_1204_3,plain,
    ! [U_4440,U_4441,U_4442] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4440),hAPP(c_Int_Onumber__class_Onumber__of(U_4440),U_4441)),hAPP(c_Int_Onumber__class_Onumber__of(U_4440),U_4442)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4440),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4441),U_4442))
      | ~ class_Int_Onumber__ring(U_4440) ),
    inference(definitional_conversion,[status(esa)],[f_1204_2]) ).

cnf(f_1204_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4440),hAPP(c_Int_Onumber__class_Onumber__of(U_4440),U_4441)),hAPP(c_Int_Onumber__class_Onumber__of(U_4440),U_4442)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4440),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4441),U_4442))
    | ~ class_Int_Onumber__ring(U_4440) ),
    inference(clausify,[status(thm)],[f_1204_3]) ).

fof(f_1205_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_1205_2,plain,
    ! [U_4445,U_4444,U_4443] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4444),U_4445)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4443),hAPP(c_Int_Onumber__class_Onumber__of(U_4443),U_4444)),hAPP(c_Int_Onumber__class_Onumber__of(U_4443),U_4445))
      | ~ class_Int_Onumber__ring(U_4443) ),
    inference(variable_rename,[status(thm)],[f_1205_1]) ).

fof(f_1205_3,plain,
    ! [U_4443,U_4444,U_4445] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4444),U_4445)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4443),hAPP(c_Int_Onumber__class_Onumber__of(U_4443),U_4444)),hAPP(c_Int_Onumber__class_Onumber__of(U_4443),U_4445))
      | ~ class_Int_Onumber__ring(U_4443) ),
    inference(definitional_conversion,[status(esa)],[f_1205_2]) ).

cnf(f_1205_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4444),U_4445)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4443),hAPP(c_Int_Onumber__class_Onumber__of(U_4443),U_4444)),hAPP(c_Int_Onumber__class_Onumber__of(U_4443),U_4445))
    | ~ class_Int_Onumber__ring(U_4443) ),
    inference(clausify,[status(thm)],[f_1205_3]) ).

fof(f_1206_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_1206_2,plain,
    ! [U_4447,U_4446] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4446) = 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_4446),U_4447)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1206_1]) ).

fof(f_1206_3,plain,
    ! [U_4446,U_4447] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4446) = 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_4446),U_4447)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_1206_2]) ).

cnf(f_1206_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4446) = 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_4446),U_4447)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1206_3]) ).

fof(f_1207_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_1207_2,plain,
    ! [U_4450,U_4449,U_4448] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4449),U_4450)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4448),hAPP(c_Int_Onumber__class_Onumber__of(U_4448),U_4449)),hAPP(c_Int_Onumber__class_Onumber__of(U_4448),U_4450))
      | ~ class_Int_Onumber__ring(U_4448) ),
    inference(variable_rename,[status(thm)],[f_1207_1]) ).

fof(f_1207_3,plain,
    ! [U_4448,U_4449,U_4450] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4449),U_4450)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4448),hAPP(c_Int_Onumber__class_Onumber__of(U_4448),U_4449)),hAPP(c_Int_Onumber__class_Onumber__of(U_4448),U_4450))
      | ~ class_Int_Onumber__ring(U_4448) ),
    inference(definitional_conversion,[status(esa)],[f_1207_2]) ).

cnf(f_1207_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4449),U_4450)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4448),hAPP(c_Int_Onumber__class_Onumber__of(U_4448),U_4449)),hAPP(c_Int_Onumber__class_Onumber__of(U_4448),U_4450))
    | ~ class_Int_Onumber__ring(U_4448) ),
    inference(clausify,[status(thm)],[f_1207_3]) ).

fof(f_1208_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_1208_2,plain,
    ! [U_4453,U_4452,U_4451] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4451),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4452),U_4453)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4451),U_4452)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4451),U_4453)),
    inference(variable_rename,[status(thm)],[f_1208_1]) ).

fof(f_1208_3,plain,
    ! [U_4451,U_4452,U_4453] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4451),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4452),U_4453)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4451),U_4452)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4451),U_4453)),
    inference(definitional_conversion,[status(esa)],[f_1208_2]) ).

cnf(f_1208_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4451),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4452),U_4453)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4451),U_4452)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4451),U_4453)),
    inference(clausify,[status(thm)],[f_1208_3]) ).

fof(f_1209_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_1209_2,plain,
    ! [U_4455,U_4454] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4454),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4455)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4454),hAPP(c_Int_Onumber__class_Onumber__of(U_4454),U_4455))
      | ~ class_Int_Onumber__ring(U_4454) ),
    inference(variable_rename,[status(thm)],[f_1209_1]) ).

fof(f_1209_3,plain,
    ! [U_4454,U_4455] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4454),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4455)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4454),hAPP(c_Int_Onumber__class_Onumber__of(U_4454),U_4455))
      | ~ class_Int_Onumber__ring(U_4454) ),
    inference(definitional_conversion,[status(esa)],[f_1209_2]) ).

cnf(f_1209_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4454),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4455)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4454),hAPP(c_Int_Onumber__class_Onumber__of(U_4454),U_4455))
    | ~ class_Int_Onumber__ring(U_4454) ),
    inference(clausify,[status(thm)],[f_1209_3]) ).

fof(f_1210_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_1210_2,plain,
    ! [U_4457,U_4456] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4456),hAPP(c_Int_Onumber__class_Onumber__of(U_4456),U_4457)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4456),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4457))
      | ~ class_Int_Onumber__ring(U_4456) ),
    inference(variable_rename,[status(thm)],[f_1210_1]) ).

fof(f_1210_3,plain,
    ! [U_4456,U_4457] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4456),hAPP(c_Int_Onumber__class_Onumber__of(U_4456),U_4457)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4456),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4457))
      | ~ class_Int_Onumber__ring(U_4456) ),
    inference(definitional_conversion,[status(esa)],[f_1210_2]) ).

cnf(f_1210_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4456),hAPP(c_Int_Onumber__class_Onumber__of(U_4456),U_4457)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4456),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4457))
    | ~ class_Int_Onumber__ring(U_4456) ),
    inference(clausify,[status(thm)],[f_1210_3]) ).

fof(f_1211_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_1211_2,plain,
    ! [U_4459,U_4458] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4458),U_4459) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4458),U_4459),c_Groups_Osgn__class_Osgn(U_4458,U_4459))
      | ~ class_Rings_Olinordered__idom(U_4458) ),
    inference(variable_rename,[status(thm)],[f_1211_1]) ).

fof(f_1211_3,plain,
    ! [U_4458,U_4459] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4458),U_4459) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4458),U_4459),c_Groups_Osgn__class_Osgn(U_4458,U_4459))
      | ~ class_Rings_Olinordered__idom(U_4458) ),
    inference(definitional_conversion,[status(esa)],[f_1211_2]) ).

cnf(f_1211_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4458),U_4459) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4458),U_4459),c_Groups_Osgn__class_Osgn(U_4458,U_4459))
    | ~ class_Rings_Olinordered__idom(U_4458) ),
    inference(clausify,[status(thm)],[f_1211_3]) ).

fof(f_1212_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_1212_2,plain,
    ! [U_4461,U_4460] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4460),c_Groups_Osgn__class_Osgn(U_4460,U_4461)),hAPP(c_Groups_Oabs__class_Oabs(U_4460),U_4461)) = U_4461
      | ~ class_Rings_Olinordered__idom(U_4460) ),
    inference(variable_rename,[status(thm)],[f_1212_1]) ).

fof(f_1212_3,plain,
    ! [U_4460,U_4461] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4460),c_Groups_Osgn__class_Osgn(U_4460,U_4461)),hAPP(c_Groups_Oabs__class_Oabs(U_4460),U_4461)) = U_4461
      | ~ class_Rings_Olinordered__idom(U_4460) ),
    inference(definitional_conversion,[status(esa)],[f_1212_2]) ).

cnf(f_1212_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4460),c_Groups_Osgn__class_Osgn(U_4460,U_4461)),hAPP(c_Groups_Oabs__class_Oabs(U_4460),U_4461)) = U_4461
    | ~ class_Rings_Olinordered__idom(U_4460) ),
    inference(clausify,[status(thm)],[f_1212_3]) ).

fof(f_1213_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_1213_2,plain,
    ! [U_4464,U_4463,U_4462] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4462),hAPP(c_Groups_Oabs__class_Oabs(U_4462),U_4464)),U_4463) = hAPP(c_Groups_Oabs__class_Oabs(U_4462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4462),U_4464),U_4463))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4462),c_Groups_Ozero__class_Ozero(U_4462)),U_4463))
      | ~ class_Rings_Olinordered__idom(U_4462) ),
    inference(variable_rename,[status(thm)],[f_1213_1]) ).

fof(f_1213_3,plain,
    ! [U_4462,U_4463,U_4464] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4462),hAPP(c_Groups_Oabs__class_Oabs(U_4462),U_4464)),U_4463) = hAPP(c_Groups_Oabs__class_Oabs(U_4462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4462),U_4464),U_4463))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4462),c_Groups_Ozero__class_Ozero(U_4462)),U_4463))
      | ~ class_Rings_Olinordered__idom(U_4462) ),
    inference(definitional_conversion,[status(esa)],[f_1213_2]) ).

cnf(f_1213_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4462),hAPP(c_Groups_Oabs__class_Oabs(U_4462),U_4464)),U_4463) = hAPP(c_Groups_Oabs__class_Oabs(U_4462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4462),U_4464),U_4463))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4462),c_Groups_Ozero__class_Ozero(U_4462)),U_4463))
    | ~ class_Rings_Olinordered__idom(U_4462) ),
    inference(clausify,[status(thm)],[f_1213_3]) ).

fof(f_1214_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_1214_2,plain,
    ! [U_4467,U_4466,U_4465] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4465),U_4466),U_4467)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4465),hAPP(c_Groups_Oabs__class_Oabs(U_4465),U_4466)),hAPP(c_Groups_Oabs__class_Oabs(U_4465),U_4467))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4465),U_4467),c_Groups_Ozero__class_Ozero(U_4465)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4465),c_Groups_Ozero__class_Ozero(U_4465)),U_4467)) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4465),U_4466),c_Groups_Ozero__class_Ozero(U_4465)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4465),c_Groups_Ozero__class_Ozero(U_4465)),U_4466)) )
      | ~ class_Rings_Oordered__ring__abs(U_4465) ),
    inference(variable_rename,[status(thm)],[f_1214_1]) ).

fof(f_1214_3,plain,
    ( ! [U_4465,U_4467] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4465),U_4467),c_Groups_Ozero__class_Ozero(U_4465)))
        | ~ sP351(U_4465,U_4467) )
    & ! [U_4465,U_4467] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4465),c_Groups_Ozero__class_Ozero(U_4465)),U_4467))
        | ~ sP351(U_4465,U_4467) )
    & ! [U_4465,U_4466] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4465),U_4466),c_Groups_Ozero__class_Ozero(U_4465)))
        | ~ sP350(U_4465,U_4466) )
    & ! [U_4465,U_4466] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4465),c_Groups_Ozero__class_Ozero(U_4465)),U_4466))
        | ~ sP350(U_4465,U_4466) )
    & ! [U_4465,U_4466,U_4467] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_4465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4465),U_4466),U_4467)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4465),hAPP(c_Groups_Oabs__class_Oabs(U_4465),U_4466)),hAPP(c_Groups_Oabs__class_Oabs(U_4465),U_4467))
        | sP351(U_4465,U_4467)
        | sP350(U_4465,U_4466)
        | ~ class_Rings_Oordered__ring__abs(U_4465) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP350,sP351])],[f_1214_2]) ).

cnf(f_1214_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4465),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4465),U_4466),U_4467)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4465),hAPP(c_Groups_Oabs__class_Oabs(U_4465),U_4466)),hAPP(c_Groups_Oabs__class_Oabs(U_4465),U_4467))
    | sP351(U_4465,U_4467)
    | sP350(U_4465,U_4466)
    | ~ class_Rings_Oordered__ring__abs(U_4465) ),
    inference(clausify,[status(thm)],[f_1214_3]) ).

cnf(f_1214_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4465),c_Groups_Ozero__class_Ozero(U_4465)),U_4466))
    | ~ sP350(U_4465,U_4466) ),
    inference(clausify,[status(thm)],[f_1214_3]) ).

cnf(f_1214_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4465),U_4466),c_Groups_Ozero__class_Ozero(U_4465)))
    | ~ sP350(U_4465,U_4466) ),
    inference(clausify,[status(thm)],[f_1214_3]) ).

cnf(f_1214_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4465),c_Groups_Ozero__class_Ozero(U_4465)),U_4467))
    | ~ sP351(U_4465,U_4467) ),
    inference(clausify,[status(thm)],[f_1214_3]) ).

cnf(f_1214_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4465),U_4467),c_Groups_Ozero__class_Ozero(U_4465)))
    | ~ sP351(U_4465,U_4467) ),
    inference(clausify,[status(thm)],[f_1214_3]) ).

fof(f_1215_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_1215_2,plain,
    ! [U_4472,U_4471,U_4470,U_4469,U_4468] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4468),hAPP(c_Groups_Oabs__class_Oabs(U_4468),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4468),U_4469),U_4470)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4468),U_4471),U_4472)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4468),hAPP(c_Groups_Oabs__class_Oabs(U_4468),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4468),U_4469),U_4471))),hAPP(c_Groups_Oabs__class_Oabs(U_4468),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4468),U_4470),U_4472)))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4468) ),
    inference(variable_rename,[status(thm)],[f_1215_1]) ).

fof(f_1215_3,plain,
    ! [U_4468,U_4469,U_4470,U_4471,U_4472] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4468),hAPP(c_Groups_Oabs__class_Oabs(U_4468),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4468),U_4469),U_4470)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4468),U_4471),U_4472)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4468),hAPP(c_Groups_Oabs__class_Oabs(U_4468),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4468),U_4469),U_4471))),hAPP(c_Groups_Oabs__class_Oabs(U_4468),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4468),U_4470),U_4472)))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4468) ),
    inference(definitional_conversion,[status(esa)],[f_1215_2]) ).

cnf(f_1215_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4468),hAPP(c_Groups_Oabs__class_Oabs(U_4468),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4468),U_4469),U_4470)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4468),U_4471),U_4472)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4468),hAPP(c_Groups_Oabs__class_Oabs(U_4468),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4468),U_4469),U_4471))),hAPP(c_Groups_Oabs__class_Oabs(U_4468),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4468),U_4470),U_4472)))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4468) ),
    inference(clausify,[status(thm)],[f_1215_3]) ).

fof(f_1216_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_1216_2,plain,
    ! [U_4475,U_4474,U_4473] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4473),hAPP(c_Groups_Oabs__class_Oabs(U_4473),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4473),U_4474),U_4475))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4473),hAPP(c_Groups_Oabs__class_Oabs(U_4473),U_4474)),hAPP(c_Groups_Oabs__class_Oabs(U_4473),U_4475))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4473) ),
    inference(variable_rename,[status(thm)],[f_1216_1]) ).

fof(f_1216_3,plain,
    ! [U_4473,U_4474,U_4475] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4473),hAPP(c_Groups_Oabs__class_Oabs(U_4473),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4473),U_4474),U_4475))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4473),hAPP(c_Groups_Oabs__class_Oabs(U_4473),U_4474)),hAPP(c_Groups_Oabs__class_Oabs(U_4473),U_4475))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4473) ),
    inference(definitional_conversion,[status(esa)],[f_1216_2]) ).

cnf(f_1216_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4473),hAPP(c_Groups_Oabs__class_Oabs(U_4473),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4473),U_4474),U_4475))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4473),hAPP(c_Groups_Oabs__class_Oabs(U_4473),U_4474)),hAPP(c_Groups_Oabs__class_Oabs(U_4473),U_4475))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4473) ),
    inference(clausify,[status(thm)],[f_1216_3]) ).

fof(f_1217_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_1217_2,plain,
    ! [U_4477,U_4476] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4476),U_4477) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4476),U_4477)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4476),U_4477),c_Groups_Ozero__class_Ozero(U_4476)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4476) ),
    inference(variable_rename,[status(thm)],[f_1217_1]) ).

fof(f_1217_3,plain,
    ! [U_4476,U_4477] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4476),U_4477) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4476),U_4477)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4476),U_4477),c_Groups_Ozero__class_Ozero(U_4476)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4476) ),
    inference(definitional_conversion,[status(esa)],[f_1217_2]) ).

cnf(f_1217_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4476),U_4477) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4476),U_4477)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4476),U_4477),c_Groups_Ozero__class_Ozero(U_4476)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4476) ),
    inference(clausify,[status(thm)],[f_1217_3]) ).

fof(f_1218_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_1218_2,plain,
    ! [U_4479,U_4478] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4478),hAPP(c_Groups_Ouminus__class_Ouminus(U_4478),hAPP(c_Groups_Oabs__class_Oabs(U_4478),U_4479))),c_Groups_Ozero__class_Ozero(U_4478)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4478) ),
    inference(variable_rename,[status(thm)],[f_1218_1]) ).

fof(f_1218_3,plain,
    ! [U_4478,U_4479] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4478),hAPP(c_Groups_Ouminus__class_Ouminus(U_4478),hAPP(c_Groups_Oabs__class_Oabs(U_4478),U_4479))),c_Groups_Ozero__class_Ozero(U_4478)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4478) ),
    inference(definitional_conversion,[status(esa)],[f_1218_2]) ).

cnf(f_1218_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4478),hAPP(c_Groups_Ouminus__class_Ouminus(U_4478),hAPP(c_Groups_Oabs__class_Oabs(U_4478),U_4479))),c_Groups_Ozero__class_Ozero(U_4478)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4478) ),
    inference(clausify,[status(thm)],[f_1218_3]) ).

fof(f_1219_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_1219_2,plain,
    ! [U_4481,U_4480] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_4480),U_4481) = U_4481
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4480),U_4481),c_Groups_Ozero__class_Ozero(U_4480))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(U_4480),U_4481) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4480),U_4481)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4480),U_4481),c_Groups_Ozero__class_Ozero(U_4480))) ) )
      | ~ class_Groups_Oabs__if(U_4480) ),
    inference(variable_rename,[status(thm)],[f_1219_1]) ).

fof(f_1219_3,plain,
    ( ! [U_4480,U_4481] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_4480),U_4481) = U_4481
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4480),U_4481),c_Groups_Ozero__class_Ozero(U_4480)))
        | ~ sP352(U_4480,U_4481) )
    & ! [U_4480,U_4481] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_4480),U_4481) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4480),U_4481)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4480),U_4481),c_Groups_Ozero__class_Ozero(U_4480)))
        | ~ sP352(U_4480,U_4481) )
    & ! [U_4480,U_4481] :
        ( sP352(U_4480,U_4481)
        | ~ class_Groups_Oabs__if(U_4480) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP352])],[f_1219_2]) ).

cnf(f_1219_4,plain,
    ( sP352(U_4480,U_4481)
    | ~ class_Groups_Oabs__if(U_4480) ),
    inference(clausify,[status(thm)],[f_1219_3]) ).

cnf(f_1219_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4480),U_4481) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4480),U_4481)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4480),U_4481),c_Groups_Ozero__class_Ozero(U_4480)))
    | ~ sP352(U_4480,U_4481) ),
    inference(clausify,[status(thm)],[f_1219_3]) ).

cnf(f_1219_6,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4480),U_4481) = U_4481
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4480),U_4481),c_Groups_Ozero__class_Ozero(U_4480)))
    | ~ sP352(U_4480,U_4481) ),
    inference(clausify,[status(thm)],[f_1219_3]) ).

fof(f_1220_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_1220_2,plain,
    ! [U_4483,U_4482] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4482),U_4483) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4482),U_4483)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4482),U_4483),c_Groups_Ozero__class_Ozero(U_4482)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4482) ),
    inference(variable_rename,[status(thm)],[f_1220_1]) ).

fof(f_1220_3,plain,
    ! [U_4483,U_4482] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4482),U_4483) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4482),U_4483)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4482),U_4483),c_Groups_Ozero__class_Ozero(U_4482)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4482) ),
    inference(definitional_conversion,[status(esa)],[f_1220_2]) ).

cnf(f_1220_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4482),U_4483) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4482),U_4483)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4482),U_4483),c_Groups_Ozero__class_Ozero(U_4482)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4482) ),
    inference(clausify,[status(thm)],[f_1220_3]) ).

fof(f_1221_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_1221_2,plain,
    ! [U_4484] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4484)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | U_4484 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( U_4484 = 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_4484)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1221_1]) ).

fof(f_1221_3,plain,
    ( ! [U_4486] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4486)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | U_4486 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_4485] :
        ( U_4485 = 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_4485)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1221_2]) ).

fof(f_1221_4,plain,
    ( ! [U_4486] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4486)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | U_4486 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_4485] :
        ( U_4485 = 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_4485)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1221_3]) ).

cnf(f_1221_5,plain,
    ( U_4485 = 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_4485)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1221_4]) ).

cnf(f_1221_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4486)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | U_4486 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1221_4]) ).

fof(f_1222_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_1222_2,plain,
    ! [U_4490,U_4489,U_4488,U_4487] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4487),hAPP(c_Int_Onumber__class_Onumber__of(U_4487),U_4488)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4487),hAPP(c_Int_Onumber__class_Onumber__of(U_4487),U_4489)),U_4490)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4487),hAPP(c_Int_Onumber__class_Onumber__of(U_4487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4488),U_4489))),U_4490)
      | ~ class_Int_Onumber__ring(U_4487) ),
    inference(variable_rename,[status(thm)],[f_1222_1]) ).

fof(f_1222_3,plain,
    ! [U_4487,U_4488,U_4489,U_4490] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4487),hAPP(c_Int_Onumber__class_Onumber__of(U_4487),U_4488)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4487),hAPP(c_Int_Onumber__class_Onumber__of(U_4487),U_4489)),U_4490)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4487),hAPP(c_Int_Onumber__class_Onumber__of(U_4487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4488),U_4489))),U_4490)
      | ~ class_Int_Onumber__ring(U_4487) ),
    inference(definitional_conversion,[status(esa)],[f_1222_2]) ).

cnf(f_1222_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4487),hAPP(c_Int_Onumber__class_Onumber__of(U_4487),U_4488)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4487),hAPP(c_Int_Onumber__class_Onumber__of(U_4487),U_4489)),U_4490)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4487),hAPP(c_Int_Onumber__class_Onumber__of(U_4487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4488),U_4489))),U_4490)
    | ~ class_Int_Onumber__ring(U_4487) ),
    inference(clausify,[status(thm)],[f_1222_3]) ).

fof(f_1223_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_1223_2,plain,
    ! [U_4491] :
      ( ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4491) = U_4491
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4491),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4491) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4491)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4491),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1223_1]) ).

fof(f_1223_3,plain,
    ( ! [U_4493] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4493) = U_4493
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4493),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4492] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4492) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4492)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4492),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1223_2]) ).

fof(f_1223_4,plain,
    ( ! [U_4493] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4493) = U_4493
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4493),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4492] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4492) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4492)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4492),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1223_3]) ).

cnf(f_1223_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4492) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4492)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4492),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1223_4]) ).

cnf(f_1223_6,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4493) = U_4493
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4493),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1223_4]) ).

fof(f_1224_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_1224_2,plain,
    ! [U_4496,U_4495,U_4494] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4494),hAPP(c_Groups_Ouminus__class_Ouminus(U_4494),hAPP(c_Int_Onumber__class_Onumber__of(U_4494),U_4495))),U_4496) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4494),hAPP(c_Int_Onumber__class_Onumber__of(U_4494),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4495))),U_4496)
      | ~ class_Int_Onumber__ring(U_4494) ),
    inference(variable_rename,[status(thm)],[f_1224_1]) ).

fof(f_1224_3,plain,
    ! [U_4494,U_4495,U_4496] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4494),hAPP(c_Groups_Ouminus__class_Ouminus(U_4494),hAPP(c_Int_Onumber__class_Onumber__of(U_4494),U_4495))),U_4496) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4494),hAPP(c_Int_Onumber__class_Onumber__of(U_4494),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4495))),U_4496)
      | ~ class_Int_Onumber__ring(U_4494) ),
    inference(definitional_conversion,[status(esa)],[f_1224_2]) ).

cnf(f_1224_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4494),hAPP(c_Groups_Ouminus__class_Ouminus(U_4494),hAPP(c_Int_Onumber__class_Onumber__of(U_4494),U_4495))),U_4496) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4494),hAPP(c_Int_Onumber__class_Onumber__of(U_4494),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4495))),U_4496)
    | ~ class_Int_Onumber__ring(U_4494) ),
    inference(clausify,[status(thm)],[f_1224_3]) ).

fof(f_1225_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_1225_2,plain,
    ! [U_4498,U_4497] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4497),U_4498))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4497))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4498))),
    inference(variable_rename,[status(thm)],[f_1225_1]) ).

fof(f_1225_3,plain,
    ! [U_4497,U_4498] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4497),U_4498))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4497))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4498))),
    inference(definitional_conversion,[status(esa)],[f_1225_2]) ).

cnf(f_1225_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_4497),U_4498))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4497))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4498))),
    inference(clausify,[status(thm)],[f_1225_3]) ).

fof(f_1226_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_1226_2,plain,
    ! [U_4501,U_4500,U_4499] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4499),hAPP(c_Int_Onumber__class_Onumber__of(U_4499),U_4500)),hAPP(c_Int_Onumber__class_Onumber__of(U_4499),U_4501)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4499),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4500),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4501)))
      | ~ class_Int_Onumber__ring(U_4499) ),
    inference(variable_rename,[status(thm)],[f_1226_1]) ).

fof(f_1226_3,plain,
    ! [U_4499,U_4500,U_4501] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4499),hAPP(c_Int_Onumber__class_Onumber__of(U_4499),U_4500)),hAPP(c_Int_Onumber__class_Onumber__of(U_4499),U_4501)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4499),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4500),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4501)))
      | ~ class_Int_Onumber__ring(U_4499) ),
    inference(definitional_conversion,[status(esa)],[f_1226_2]) ).

cnf(f_1226_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4499),hAPP(c_Int_Onumber__class_Onumber__of(U_4499),U_4500)),hAPP(c_Int_Onumber__class_Onumber__of(U_4499),U_4501)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4499),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4500),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4501)))
    | ~ class_Int_Onumber__ring(U_4499) ),
    inference(clausify,[status(thm)],[f_1226_3]) ).

fof(f_1227_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_1227_2,plain,
    ! [U_4505,U_4504,U_4503,U_4502] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4502),hAPP(c_Int_Onumber__class_Onumber__of(U_4502),U_4503)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4502),U_4504),hAPP(c_Int_Onumber__class_Onumber__of(U_4502),U_4505))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4502),hAPP(c_Int_Onumber__class_Onumber__of(U_4502),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4503),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4505)))),U_4504)
      | ~ class_Int_Onumber__ring(U_4502) ),
    inference(variable_rename,[status(thm)],[f_1227_1]) ).

fof(f_1227_3,plain,
    ! [U_4502,U_4503,U_4504,U_4505] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4502),hAPP(c_Int_Onumber__class_Onumber__of(U_4502),U_4503)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4502),U_4504),hAPP(c_Int_Onumber__class_Onumber__of(U_4502),U_4505))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4502),hAPP(c_Int_Onumber__class_Onumber__of(U_4502),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4503),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4505)))),U_4504)
      | ~ class_Int_Onumber__ring(U_4502) ),
    inference(definitional_conversion,[status(esa)],[f_1227_2]) ).

cnf(f_1227_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4502),hAPP(c_Int_Onumber__class_Onumber__of(U_4502),U_4503)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4502),U_4504),hAPP(c_Int_Onumber__class_Onumber__of(U_4502),U_4505))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4502),hAPP(c_Int_Onumber__class_Onumber__of(U_4502),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4503),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4505)))),U_4504)
    | ~ class_Int_Onumber__ring(U_4502) ),
    inference(clausify,[status(thm)],[f_1227_3]) ).

fof(f_1228_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_1228_2,plain,
    ! [U_4509,U_4508,U_4507,U_4506] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4506),hAPP(hAPP(c_Power_Opower__class_Opower(U_4506),U_4507),U_4509)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4506),U_4508),U_4509)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4509))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4506),c_Groups_Ozero__class_Ozero(U_4506)),U_4507))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4506),U_4507),U_4508))
      | ~ class_Rings_Olinordered__semidom(U_4506) ),
    inference(variable_rename,[status(thm)],[f_1228_1]) ).

fof(f_1228_3,plain,
    ! [U_4506,U_4507,U_4508,U_4509] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4506),hAPP(hAPP(c_Power_Opower__class_Opower(U_4506),U_4507),U_4509)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4506),U_4508),U_4509)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4509))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4506),c_Groups_Ozero__class_Ozero(U_4506)),U_4507))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4506),U_4507),U_4508))
      | ~ class_Rings_Olinordered__semidom(U_4506) ),
    inference(definitional_conversion,[status(esa)],[f_1228_2]) ).

cnf(f_1228_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4506),hAPP(hAPP(c_Power_Opower__class_Opower(U_4506),U_4507),U_4509)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4506),U_4508),U_4509)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4509))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4506),c_Groups_Ozero__class_Ozero(U_4506)),U_4507))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4506),U_4507),U_4508))
    | ~ class_Rings_Olinordered__semidom(U_4506) ),
    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),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_1229_2,plain,
    ! [U_4512,U_4511,U_4510] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4510),c_Groups_Oone__class_Oone(U_4510)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4510),U_4511),U_4512)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4512))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4510),c_Groups_Oone__class_Oone(U_4510)),U_4511))
      | ~ class_Rings_Olinordered__semidom(U_4510) ),
    inference(variable_rename,[status(thm)],[f_1229_1]) ).

fof(f_1229_3,plain,
    ! [U_4511,U_4512,U_4510] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4510),c_Groups_Oone__class_Oone(U_4510)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4510),U_4511),U_4512)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4512))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4510),c_Groups_Oone__class_Oone(U_4510)),U_4511))
      | ~ class_Rings_Olinordered__semidom(U_4510) ),
    inference(definitional_conversion,[status(esa)],[f_1229_2]) ).

cnf(f_1229_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4510),c_Groups_Oone__class_Oone(U_4510)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4510),U_4511),U_4512)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4512))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4510),c_Groups_Oone__class_Oone(U_4510)),U_4511))
    | ~ class_Rings_Olinordered__semidom(U_4510) ),
    inference(clausify,[status(thm)],[f_1229_3]) ).

fof(f_1230_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_1230_2,plain,
    ! [U_4516,U_4515,U_4514,U_4513] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4515),U_4516))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4513),hAPP(hAPP(c_Power_Opower__class_Opower(U_4513),U_4514),U_4515)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4513),U_4514),U_4516)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4513),c_Groups_Oone__class_Oone(U_4513)),U_4514))
      | ~ class_Rings_Olinordered__semidom(U_4513) ),
    inference(variable_rename,[status(thm)],[f_1230_1]) ).

fof(f_1230_3,plain,
    ! [U_4513,U_4514,U_4515,U_4516] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4515),U_4516))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4513),hAPP(hAPP(c_Power_Opower__class_Opower(U_4513),U_4514),U_4515)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4513),U_4514),U_4516)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4513),c_Groups_Oone__class_Oone(U_4513)),U_4514))
      | ~ class_Rings_Olinordered__semidom(U_4513) ),
    inference(definitional_conversion,[status(esa)],[f_1230_2]) ).

cnf(f_1230_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4515),U_4516))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4513),hAPP(hAPP(c_Power_Opower__class_Opower(U_4513),U_4514),U_4515)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4513),U_4514),U_4516)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4513),c_Groups_Oone__class_Oone(U_4513)),U_4514))
    | ~ class_Rings_Olinordered__semidom(U_4513) ),
    inference(clausify,[status(thm)],[f_1230_3]) ).

fof(f_1231_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_1231_2,plain,
    ! [U_4520,U_4519,U_4518,U_4517] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4517),hAPP(hAPP(c_Power_Opower__class_Opower(U_4517),U_4518),U_4519)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4517),U_4518),U_4520)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4519),U_4520)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4519),U_4520))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4517),hAPP(hAPP(c_Power_Opower__class_Opower(U_4517),U_4518),U_4519)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4517),U_4518),U_4520))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4517),c_Groups_Oone__class_Oone(U_4517)),U_4518))
      | ~ class_Rings_Olinordered__semidom(U_4517) ),
    inference(variable_rename,[status(thm)],[f_1231_1]) ).

fof(f_1231_3,plain,
    ( ! [U_4518,U_4517,U_4519,U_4520] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4517),hAPP(hAPP(c_Power_Opower__class_Opower(U_4517),U_4518),U_4519)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4517),U_4518),U_4520)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4519),U_4520))
        | ~ sP353(U_4518,U_4517,U_4519,U_4520) )
    & ! [U_4518,U_4517,U_4519,U_4520] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4519),U_4520))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4517),hAPP(hAPP(c_Power_Opower__class_Opower(U_4517),U_4518),U_4519)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4517),U_4518),U_4520)))
        | ~ sP353(U_4518,U_4517,U_4519,U_4520) )
    & ! [U_4518,U_4517,U_4519,U_4520] :
        ( sP353(U_4518,U_4517,U_4519,U_4520)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4517),c_Groups_Oone__class_Oone(U_4517)),U_4518))
        | ~ class_Rings_Olinordered__semidom(U_4517) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP353])],[f_1231_2]) ).

cnf(f_1231_4,plain,
    ( sP353(U_4518,U_4517,U_4519,U_4520)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4517),c_Groups_Oone__class_Oone(U_4517)),U_4518))
    | ~ class_Rings_Olinordered__semidom(U_4517) ),
    inference(clausify,[status(thm)],[f_1231_3]) ).

cnf(f_1231_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4519),U_4520))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4517),hAPP(hAPP(c_Power_Opower__class_Opower(U_4517),U_4518),U_4519)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4517),U_4518),U_4520)))
    | ~ sP353(U_4518,U_4517,U_4519,U_4520) ),
    inference(clausify,[status(thm)],[f_1231_3]) ).

cnf(f_1231_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4517),hAPP(hAPP(c_Power_Opower__class_Opower(U_4517),U_4518),U_4519)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4517),U_4518),U_4520)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4519),U_4520))
    | ~ sP353(U_4518,U_4517,U_4519,U_4520) ),
    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__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_1232_2,plain,
    ! [U_4524,U_4523,U_4522,U_4521] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4521),hAPP(hAPP(c_Power_Opower__class_Opower(U_4521),U_4524),U_4523)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4521),U_4524),U_4522)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4521),U_4524),c_Groups_Oone__class_Oone(U_4521)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4521),c_Groups_Ozero__class_Ozero(U_4521)),U_4524))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4522),U_4523))
      | ~ class_Rings_Olinordered__semidom(U_4521) ),
    inference(variable_rename,[status(thm)],[f_1232_1]) ).

fof(f_1232_3,plain,
    ! [U_4523,U_4522,U_4524,U_4521] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4521),hAPP(hAPP(c_Power_Opower__class_Opower(U_4521),U_4524),U_4523)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4521),U_4524),U_4522)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4521),U_4524),c_Groups_Oone__class_Oone(U_4521)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4521),c_Groups_Ozero__class_Ozero(U_4521)),U_4524))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4522),U_4523))
      | ~ class_Rings_Olinordered__semidom(U_4521) ),
    inference(definitional_conversion,[status(esa)],[f_1232_2]) ).

cnf(f_1232_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4521),hAPP(hAPP(c_Power_Opower__class_Opower(U_4521),U_4524),U_4523)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4521),U_4524),U_4522)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4521),U_4524),c_Groups_Oone__class_Oone(U_4521)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4521),c_Groups_Ozero__class_Ozero(U_4521)),U_4524))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4522),U_4523))
    | ~ class_Rings_Olinordered__semidom(U_4521) ),
    inference(clausify,[status(thm)],[f_1232_3]) ).

fof(f_1233_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_1233_2,plain,
    ! [U_4528,U_4527,U_4526,U_4525] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4525),hAPP(hAPP(c_Power_Opower__class_Opower(U_4525),U_4528),U_4527)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4525),U_4528),U_4526)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4525),U_4528),c_Groups_Oone__class_Oone(U_4525)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4525),c_Groups_Ozero__class_Ozero(U_4525)),U_4528))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4526),U_4527))
      | ~ class_Rings_Olinordered__semidom(U_4525) ),
    inference(variable_rename,[status(thm)],[f_1233_1]) ).

fof(f_1233_3,plain,
    ! [U_4526,U_4527,U_4525,U_4528] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4525),hAPP(hAPP(c_Power_Opower__class_Opower(U_4525),U_4528),U_4527)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4525),U_4528),U_4526)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4525),U_4528),c_Groups_Oone__class_Oone(U_4525)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4525),c_Groups_Ozero__class_Ozero(U_4525)),U_4528))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4526),U_4527))
      | ~ class_Rings_Olinordered__semidom(U_4525) ),
    inference(definitional_conversion,[status(esa)],[f_1233_2]) ).

cnf(f_1233_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4525),hAPP(hAPP(c_Power_Opower__class_Opower(U_4525),U_4528),U_4527)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4525),U_4528),U_4526)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4525),U_4528),c_Groups_Oone__class_Oone(U_4525)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4525),c_Groups_Ozero__class_Ozero(U_4525)),U_4528))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4526),U_4527))
    | ~ class_Rings_Olinordered__semidom(U_4525) ),
    inference(clausify,[status(thm)],[f_1233_3]) ).

fof(f_1234_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_1234_2,plain,
    ! [U_4531,U_4530,U_4529] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4529),hAPP(hAPP(c_Power_Opower__class_Opower(U_4529),U_4530),hAPP(c_Nat_OSuc,U_4531))),c_Groups_Oone__class_Oone(U_4529)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4529),U_4530),c_Groups_Oone__class_Oone(U_4529)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4529),c_Groups_Ozero__class_Ozero(U_4529)),U_4530))
      | ~ class_Rings_Olinordered__semidom(U_4529) ),
    inference(variable_rename,[status(thm)],[f_1234_1]) ).

fof(f_1234_3,plain,
    ! [U_4531,U_4530,U_4529] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4529),hAPP(hAPP(c_Power_Opower__class_Opower(U_4529),U_4530),hAPP(c_Nat_OSuc,U_4531))),c_Groups_Oone__class_Oone(U_4529)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4529),U_4530),c_Groups_Oone__class_Oone(U_4529)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4529),c_Groups_Ozero__class_Ozero(U_4529)),U_4530))
      | ~ class_Rings_Olinordered__semidom(U_4529) ),
    inference(definitional_conversion,[status(esa)],[f_1234_2]) ).

cnf(f_1234_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4529),hAPP(hAPP(c_Power_Opower__class_Opower(U_4529),U_4530),hAPP(c_Nat_OSuc,U_4531))),c_Groups_Oone__class_Oone(U_4529)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4529),U_4530),c_Groups_Oone__class_Oone(U_4529)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4529),c_Groups_Ozero__class_Ozero(U_4529)),U_4530))
    | ~ class_Rings_Olinordered__semidom(U_4529) ),
    inference(clausify,[status(thm)],[f_1234_3]) ).

fof(f_1235_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_1235_2,plain,
    ! [U_4532] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4532) = U_4532,
    inference(variable_rename,[status(thm)],[f_1235_1]) ).

fof(f_1235_3,plain,
    ! [U_4532] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4532) = U_4532,
    inference(definitional_conversion,[status(esa)],[f_1235_2]) ).

cnf(f_1235_4,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4532) = U_4532,
    inference(clausify,[status(thm)],[f_1235_3]) ).

fof(f_1236_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_1236_2,plain,
    ! [U_4534,U_4533] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4533)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4534)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4533),U_4534)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4533),U_4534))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4533)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4534))) ) ),
    inference(variable_rename,[status(thm)],[f_1236_1]) ).

fof(f_1236_3,plain,
    ( ! [U_4538,U_4536] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4536)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4538)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4536),U_4538)) )
    & ! [U_4537,U_4535] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4535),U_4537))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4535)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4537))) ) ),
    inference(miniscope,[status(thm)],[f_1236_2]) ).

fof(f_1236_4,plain,
    ( ! [U_4536,U_4538] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4536)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4538)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4536),U_4538)) )
    & ! [U_4537,U_4535] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4535),U_4537))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4535)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4537))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1236_3]) ).

cnf(f_1236_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4535),U_4537))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4535)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4537))) ),
    inference(clausify,[status(thm)],[f_1236_4]) ).

cnf(f_1236_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_4536)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4538)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4536),U_4538)) ),
    inference(clausify,[status(thm)],[f_1236_4]) ).

fof(f_1237_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_1237_2,plain,
    ! [U_4540,U_4539] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4539)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4540)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4539),U_4540)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4539),U_4540))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4539)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4540))) ) ),
    inference(variable_rename,[status(thm)],[f_1237_1]) ).

fof(f_1237_3,plain,
    ( ! [U_4544,U_4542] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4542)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4544)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4542),U_4544)) )
    & ! [U_4543,U_4541] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4541),U_4543))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4541)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4543))) ) ),
    inference(miniscope,[status(thm)],[f_1237_2]) ).

fof(f_1237_4,plain,
    ( ! [U_4542,U_4544] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4542)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4544)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4542),U_4544)) )
    & ! [U_4541,U_4543] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4541),U_4543))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4541)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4543))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1237_3]) ).

cnf(f_1237_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4541),U_4543))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4541)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4543))) ),
    inference(clausify,[status(thm)],[f_1237_4]) ).

cnf(f_1237_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4542)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4544)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4542),U_4544)) ),
    inference(clausify,[status(thm)],[f_1237_4]) ).

fof(f_1238_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_1238_2,plain,
    ! [U_4546,U_4545] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4546)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4545),U_4546)),
    inference(variable_rename,[status(thm)],[f_1238_1]) ).

fof(f_1238_3,plain,
    ! [U_4546,U_4545] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4546)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4545),U_4546)),
    inference(definitional_conversion,[status(esa)],[f_1238_2]) ).

cnf(f_1238_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4546)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4545),U_4546)),
    inference(clausify,[status(thm)],[f_1238_3]) ).

fof(f_1239_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_1239_2,plain,
    ! [U_4548,U_4547] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4547)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4548)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4547),U_4548)),
    inference(variable_rename,[status(thm)],[f_1239_1]) ).

fof(f_1239_3,plain,
    ! [U_4547,U_4548] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4547)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4548)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4547),U_4548)),
    inference(definitional_conversion,[status(esa)],[f_1239_2]) ).

cnf(f_1239_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4547)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4548)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4547),U_4548)),
    inference(clausify,[status(thm)],[f_1239_3]) ).

fof(f_1240_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_1240_2,plain,
    ! [U_4549] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4549)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4549)),
    inference(variable_rename,[status(thm)],[f_1240_1]) ).

fof(f_1240_3,plain,
    ! [U_4549] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4549)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4549)),
    inference(definitional_conversion,[status(esa)],[f_1240_2]) ).

cnf(f_1240_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4549)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4549)),
    inference(clausify,[status(thm)],[f_1240_3]) ).

fof(f_1241_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_1241_2,plain,
    ! [U_4550] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4550) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_1241_1]) ).

fof(f_1241_3,plain,
    ! [U_4550] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4550) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_1241_2]) ).

cnf(f_1241_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_4550) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_1241_3]) ).

fof(f_1242_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_1242_2,plain,
    ! [U_4552,U_4551] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4551),U_4552) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_4551 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_4552 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_4551 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_4552 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4551),U_4552) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_1242_1]) ).

fof(f_1242_3,plain,
    ( ! [U_4556,U_4554] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4554),U_4556) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_4554 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_4556 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_4555,U_4553] :
        ( U_4553 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_4555 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4553),U_4555) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_1242_2]) ).

fof(f_1242_4,plain,
    ( ! [U_4556,U_4554] :
        ( U_4554 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP354(U_4556,U_4554) )
    & ! [U_4556,U_4554] :
        ( U_4556 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP354(U_4556,U_4554) )
    & ! [U_4556,U_4554] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4554),U_4556) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | sP354(U_4556,U_4554) )
    & ! [U_4555,U_4553] :
        ( U_4553 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_4555 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4553),U_4555) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP354])],[f_1242_3]) ).

cnf(f_1242_5,plain,
    ( U_4553 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_4555 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4553),U_4555) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1242_4]) ).

cnf(f_1242_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4554),U_4556) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | sP354(U_4556,U_4554) ),
    inference(clausify,[status(thm)],[f_1242_4]) ).

cnf(f_1242_7,plain,
    ( U_4556 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP354(U_4556,U_4554) ),
    inference(clausify,[status(thm)],[f_1242_4]) ).

cnf(f_1242_8,plain,
    ( U_4554 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP354(U_4556,U_4554) ),
    inference(clausify,[status(thm)],[f_1242_4]) ).

fof(f_1243_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_1243_2,plain,
    ! [U_4559,U_4558,U_4557] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4558),U_4559))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4557),U_4558)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4557),U_4559)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4557)) ),
    inference(variable_rename,[status(thm)],[f_1243_1]) ).

fof(f_1243_3,plain,
    ! [U_4558,U_4557,U_4559] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4558),U_4559))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4557),U_4558)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4557),U_4559)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4557)) ),
    inference(definitional_conversion,[status(esa)],[f_1243_2]) ).

cnf(f_1243_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4558),U_4559))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4557),U_4558)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4557),U_4559)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4557)) ),
    inference(clausify,[status(thm)],[f_1243_3]) ).

fof(f_1244_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_1244_2,plain,
    ! [U_4561,U_4560] :
      ( ( 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_4560),U_4561)))
        | ( U_4561 != 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_4560)) ) )
      & ( U_4561 = 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_4560))
        | ~ 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_4560),U_4561))) ) ),
    inference(variable_rename,[status(thm)],[f_1244_1]) ).

fof(f_1244_3,plain,
    ( ! [U_4565,U_4563] :
        ( 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_4563),U_4565)))
        | ( U_4565 != 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_4563)) ) )
    & ! [U_4564,U_4562] :
        ( U_4564 = 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_4562))
        | ~ 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_4562),U_4564))) ) ),
    inference(miniscope,[status(thm)],[f_1244_2]) ).

fof(f_1244_4,plain,
    ( ! [U_4565,U_4563] :
        ( U_4565 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP355(U_4565,U_4563) )
    & ! [U_4565,U_4563] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4563))
        | ~ sP355(U_4565,U_4563) )
    & ! [U_4565,U_4563] :
        ( 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_4563),U_4565)))
        | sP355(U_4565,U_4563) )
    & ! [U_4564,U_4562] :
        ( U_4564 = 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_4562))
        | ~ 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_4562),U_4564))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP355])],[f_1244_3]) ).

cnf(f_1244_5,plain,
    ( U_4564 = 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_4562))
    | ~ 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_4562),U_4564))) ),
    inference(clausify,[status(thm)],[f_1244_4]) ).

cnf(f_1244_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_4563),U_4565)))
    | sP355(U_4565,U_4563) ),
    inference(clausify,[status(thm)],[f_1244_4]) ).

cnf(f_1244_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4563))
    | ~ sP355(U_4565,U_4563) ),
    inference(clausify,[status(thm)],[f_1244_4]) ).

cnf(f_1244_8,plain,
    ( U_4565 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP355(U_4565,U_4563) ),
    inference(clausify,[status(thm)],[f_1244_4]) ).

fof(f_1245_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_1245_2,plain,
    ! [U_4566] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4566) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_4566),
    inference(variable_rename,[status(thm)],[f_1245_1]) ).

fof(f_1245_3,plain,
    ! [U_4566] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4566) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_4566),
    inference(definitional_conversion,[status(esa)],[f_1245_2]) ).

cnf(f_1245_4,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4566) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_4566),
    inference(clausify,[status(thm)],[f_1245_3]) ).

fof(f_1246_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_1246_2,plain,
    ! [U_4568,U_4567] :
      ( 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_4567),U_4568)))
      | ~ 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_4567)) ),
    inference(variable_rename,[status(thm)],[f_1246_1]) ).

fof(f_1246_3,plain,
    ! [U_4568,U_4567] :
      ( 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_4567),U_4568)))
      | ~ 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_4567)) ),
    inference(definitional_conversion,[status(esa)],[f_1246_2]) ).

cnf(f_1246_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_4567),U_4568)))
    | ~ 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_4567)) ),
    inference(clausify,[status(thm)],[f_1246_3]) ).

fof(f_1247_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_1247_2,plain,
    ! [U_4569] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4569)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4569),
    inference(variable_rename,[status(thm)],[f_1247_1]) ).

fof(f_1247_3,plain,
    ! [U_4569] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4569)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4569),
    inference(definitional_conversion,[status(esa)],[f_1247_2]) ).

cnf(f_1247_4,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4569)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4569),
    inference(clausify,[status(thm)],[f_1247_3]) ).

fof(f_1248_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_1248_2,plain,
    ! [U_4570] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4570) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4570)),
    inference(variable_rename,[status(thm)],[f_1248_1]) ).

fof(f_1248_3,plain,
    ! [U_4570] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4570) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4570)),
    inference(definitional_conversion,[status(esa)],[f_1248_2]) ).

cnf(f_1248_4,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4570) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4570)),
    inference(clausify,[status(thm)],[f_1248_3]) ).

fof(f_1249_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_1249_2,plain,
    ! [U_4572,U_4571] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4571),U_4572)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4571)),U_4572),
    inference(variable_rename,[status(thm)],[f_1249_1]) ).

fof(f_1249_3,plain,
    ! [U_4571,U_4572] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4571),U_4572)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4571)),U_4572),
    inference(definitional_conversion,[status(esa)],[f_1249_2]) ).

cnf(f_1249_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4571),U_4572)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4571)),U_4572),
    inference(clausify,[status(thm)],[f_1249_3]) ).

fof(f_1250_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_1250_2,plain,
    ! [U_4574,U_4573] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4573)),U_4574) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4573),U_4574)),
    inference(variable_rename,[status(thm)],[f_1250_1]) ).

fof(f_1250_3,plain,
    ! [U_4573,U_4574] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4573)),U_4574) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4573),U_4574)),
    inference(definitional_conversion,[status(esa)],[f_1250_2]) ).

cnf(f_1250_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4573)),U_4574) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4573),U_4574)),
    inference(clausify,[status(thm)],[f_1250_3]) ).

fof(f_1251_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_1251_2,plain,
    ! [U_4576,U_4575] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4575)),U_4576) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4575),U_4576)),
    inference(variable_rename,[status(thm)],[f_1251_1]) ).

fof(f_1251_3,plain,
    ! [U_4575,U_4576] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4575)),U_4576) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4575),U_4576)),
    inference(definitional_conversion,[status(esa)],[f_1251_2]) ).

cnf(f_1251_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4575)),U_4576) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4575),U_4576)),
    inference(clausify,[status(thm)],[f_1251_3]) ).

fof(f_1252_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_1252_2,plain,
    ! [U_4578,U_4577] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4577)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4578)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4577),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4578))),
    inference(variable_rename,[status(thm)],[f_1252_1]) ).

fof(f_1252_3,plain,
    ! [U_4577,U_4578] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4577)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4578)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4577),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4578))),
    inference(definitional_conversion,[status(esa)],[f_1252_2]) ).

cnf(f_1252_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4577)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4578)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4577),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4578))),
    inference(clausify,[status(thm)],[f_1252_3]) ).

fof(f_1253_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_1253_2,plain,
    ! [U_4580,U_4579] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4580),U_4579) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4580),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4580),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4579),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_4579 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4580),U_4579) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4579 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1253_1]) ).

fof(f_1253_3,plain,
    ( ! [U_4584,U_4582] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4584),U_4582) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4584),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4584),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4582),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_4582 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4583,U_4581] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4583),U_4581) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4581 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1253_2]) ).

fof(f_1253_4,plain,
    ( ! [U_4582,U_4584] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4584),U_4582) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4584),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4584),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4582),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_4582 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4581,U_4583] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4583),U_4581) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4581 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1253_3]) ).

cnf(f_1253_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4583),U_4581) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_4581 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1253_4]) ).

cnf(f_1253_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4584),U_4582) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4584),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4584),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4582),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | U_4582 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1253_4]) ).

fof(f_1254_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_1254_2,plain,
    ! [U_4586,U_4585] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4585) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4586)
        | ~ 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_4586)))
        | U_4585 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4586)) )
      & ( ( 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_4586)))
          & U_4585 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4586)) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4585) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4586) ) ),
    inference(variable_rename,[status(thm)],[f_1254_1]) ).

fof(f_1254_3,plain,
    ( ! [U_4590,U_4588] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4588) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4590)
        | ~ 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_4590)))
        | U_4588 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4590)) )
    & ! [U_4589,U_4587] :
        ( ( 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_4589)))
          & U_4587 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4589)) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4587) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4589) ) ),
    inference(miniscope,[status(thm)],[f_1254_2]) ).

fof(f_1254_4,plain,
    ( ! [U_4587,U_4589] :
        ( 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_4589)))
        | ~ sP356(U_4587,U_4589) )
    & ! [U_4587,U_4589] :
        ( U_4587 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4589))
        | ~ sP356(U_4587,U_4589) )
    & ! [U_4588,U_4590] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4588) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4590)
        | ~ 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_4590)))
        | U_4588 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4590)) )
    & ! [U_4587,U_4589] :
        ( sP356(U_4587,U_4589)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4587) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4589) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP356])],[f_1254_3]) ).

cnf(f_1254_5,plain,
    ( sP356(U_4587,U_4589)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4587) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4589) ),
    inference(clausify,[status(thm)],[f_1254_4]) ).

cnf(f_1254_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4588) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4590)
    | ~ 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_4590)))
    | U_4588 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4590)) ),
    inference(clausify,[status(thm)],[f_1254_4]) ).

cnf(f_1254_7,plain,
    ( U_4587 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4589))
    | ~ sP356(U_4587,U_4589) ),
    inference(clausify,[status(thm)],[f_1254_4]) ).

cnf(f_1254_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_4589)))
    | ~ sP356(U_4587,U_4589) ),
    inference(clausify,[status(thm)],[f_1254_4]) ).

fof(f_1255_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_1255_2,plain,
    ! [U_4592,U_4591] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4591),U_4592)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4591)),U_4592)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4591)) ),
    inference(variable_rename,[status(thm)],[f_1255_1]) ).

fof(f_1255_3,plain,
    ! [U_4591,U_4592] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4591),U_4592)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4591)),U_4592)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4591)) ),
    inference(definitional_conversion,[status(esa)],[f_1255_2]) ).

cnf(f_1255_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4591),U_4592)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4591)),U_4592)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4591)) ),
    inference(clausify,[status(thm)],[f_1255_3]) ).

fof(f_1256_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_1256_2,plain,
    ! [U_4594,U_4593] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4593)),U_4594) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4593),U_4594))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4593)) ),
    inference(variable_rename,[status(thm)],[f_1256_1]) ).

fof(f_1256_3,plain,
    ! [U_4593,U_4594] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4593)),U_4594) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4593),U_4594))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4593)) ),
    inference(definitional_conversion,[status(esa)],[f_1256_2]) ).

cnf(f_1256_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4593)),U_4594) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4593),U_4594))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4593)) ),
    inference(clausify,[status(thm)],[f_1256_3]) ).

fof(f_1257_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_1257_2,plain,
    ! [U_4597,U_4596,U_4595] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4595),U_4596),U_4597) != c_Groups_Ozero__class_Ozero(U_4595)
      | U_4596 = c_Groups_Ozero__class_Ozero(U_4595)
      | ~ class_Rings_Oring__1__no__zero__divisors(U_4595) ),
    inference(variable_rename,[status(thm)],[f_1257_1]) ).

fof(f_1257_3,plain,
    ! [U_4595,U_4596,U_4597] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4595),U_4596),U_4597) != c_Groups_Ozero__class_Ozero(U_4595)
      | U_4596 = c_Groups_Ozero__class_Ozero(U_4595)
      | ~ class_Rings_Oring__1__no__zero__divisors(U_4595) ),
    inference(definitional_conversion,[status(esa)],[f_1257_2]) ).

cnf(f_1257_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4595),U_4596),U_4597) != c_Groups_Ozero__class_Ozero(U_4595)
    | U_4596 = c_Groups_Ozero__class_Ozero(U_4595)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_4595) ),
    inference(clausify,[status(thm)],[f_1257_3]) ).

fof(f_1258_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_1258_2,plain,
    ! [U_4600,U_4599,U_4598] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4598),hAPP(hAPP(c_Power_Opower__class_Opower(U_4598),U_4599),U_4600)),U_4599) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4598),U_4599),hAPP(hAPP(c_Power_Opower__class_Opower(U_4598),U_4599),U_4600))
      | ~ class_Groups_Omonoid__mult(U_4598) ),
    inference(variable_rename,[status(thm)],[f_1258_1]) ).

fof(f_1258_3,plain,
    ! [U_4598,U_4599,U_4600] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4598),hAPP(hAPP(c_Power_Opower__class_Opower(U_4598),U_4599),U_4600)),U_4599) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4598),U_4599),hAPP(hAPP(c_Power_Opower__class_Opower(U_4598),U_4599),U_4600))
      | ~ class_Groups_Omonoid__mult(U_4598) ),
    inference(definitional_conversion,[status(esa)],[f_1258_2]) ).

cnf(f_1258_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4598),hAPP(hAPP(c_Power_Opower__class_Opower(U_4598),U_4599),U_4600)),U_4599) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4598),U_4599),hAPP(hAPP(c_Power_Opower__class_Opower(U_4598),U_4599),U_4600))
    | ~ class_Groups_Omonoid__mult(U_4598) ),
    inference(clausify,[status(thm)],[f_1258_3]) ).

fof(f_1259_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_1259_2,plain,
    ! [U_4604,U_4603,U_4602,U_4601] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4601),U_4602),U_4603)),U_4604) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4601),hAPP(hAPP(c_Power_Opower__class_Opower(U_4601),U_4602),U_4604)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4601),U_4603),U_4604))
      | ~ class_Groups_Ocomm__monoid__mult(U_4601) ),
    inference(variable_rename,[status(thm)],[f_1259_1]) ).

fof(f_1259_3,plain,
    ! [U_4601,U_4602,U_4603,U_4604] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4601),U_4602),U_4603)),U_4604) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4601),hAPP(hAPP(c_Power_Opower__class_Opower(U_4601),U_4602),U_4604)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4601),U_4603),U_4604))
      | ~ class_Groups_Ocomm__monoid__mult(U_4601) ),
    inference(definitional_conversion,[status(esa)],[f_1259_2]) ).

cnf(f_1259_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4601),U_4602),U_4603)),U_4604) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4601),hAPP(hAPP(c_Power_Opower__class_Opower(U_4601),U_4602),U_4604)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4601),U_4603),U_4604))
    | ~ class_Groups_Ocomm__monoid__mult(U_4601) ),
    inference(clausify,[status(thm)],[f_1259_3]) ).

fof(f_1260_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_1260_2,plain,
    ! [U_4606,U_4605] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4605),c_Groups_Oone__class_Oone(U_4605)),U_4606) = c_Groups_Oone__class_Oone(U_4605)
      | ~ class_Groups_Omonoid__mult(U_4605) ),
    inference(variable_rename,[status(thm)],[f_1260_1]) ).

fof(f_1260_3,plain,
    ! [U_4606,U_4605] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4605),c_Groups_Oone__class_Oone(U_4605)),U_4606) = c_Groups_Oone__class_Oone(U_4605)
      | ~ class_Groups_Omonoid__mult(U_4605) ),
    inference(definitional_conversion,[status(esa)],[f_1260_2]) ).

cnf(f_1260_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4605),c_Groups_Oone__class_Oone(U_4605)),U_4606) = c_Groups_Oone__class_Oone(U_4605)
    | ~ class_Groups_Omonoid__mult(U_4605) ),
    inference(clausify,[status(thm)],[f_1260_3]) ).

fof(f_1261_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_1261_2,plain,
    ! [U_4609,U_4608,U_4607] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4607),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4608),U_4609)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4607),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4607),U_4608)),U_4609)
      | ~ class_Rings_Osemiring__1(U_4607) ),
    inference(variable_rename,[status(thm)],[f_1261_1]) ).

fof(f_1261_3,plain,
    ! [U_4607,U_4608,U_4609] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4607),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4608),U_4609)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4607),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4607),U_4608)),U_4609)
      | ~ class_Rings_Osemiring__1(U_4607) ),
    inference(definitional_conversion,[status(esa)],[f_1261_2]) ).

cnf(f_1261_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4607),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4608),U_4609)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4607),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4607),U_4608)),U_4609)
    | ~ class_Rings_Osemiring__1(U_4607) ),
    inference(clausify,[status(thm)],[f_1261_3]) ).

fof(f_1262_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_1262_2,plain,
    ! [U_4613,U_4612,U_4611,U_4610] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4610),U_4611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4612),U_4613)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4610),hAPP(hAPP(c_Power_Opower__class_Opower(U_4610),U_4611),U_4612)),U_4613)
      | ~ class_Groups_Omonoid__mult(U_4610) ),
    inference(variable_rename,[status(thm)],[f_1262_1]) ).

fof(f_1262_3,plain,
    ! [U_4610,U_4611,U_4612,U_4613] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4610),U_4611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4612),U_4613)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4610),hAPP(hAPP(c_Power_Opower__class_Opower(U_4610),U_4611),U_4612)),U_4613)
      | ~ class_Groups_Omonoid__mult(U_4610) ),
    inference(definitional_conversion,[status(esa)],[f_1262_2]) ).

cnf(f_1262_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4610),U_4611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4612),U_4613)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4610),hAPP(hAPP(c_Power_Opower__class_Opower(U_4610),U_4611),U_4612)),U_4613)
    | ~ class_Groups_Omonoid__mult(U_4610) ),
    inference(clausify,[status(thm)],[f_1262_3]) ).

fof(f_1263_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_1263_2,plain,
    ! [U_4614] : 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_4614)) = 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_4614))),
    inference(variable_rename,[status(thm)],[f_1263_1]) ).

fof(f_1263_3,plain,
    ! [U_4614] : 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_4614)) = 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_4614))),
    inference(definitional_conversion,[status(esa)],[f_1263_2]) ).

cnf(f_1263_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_4614)) = 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_4614))),
    inference(clausify,[status(thm)],[f_1263_3]) ).

fof(f_1264_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_1264_2,plain,
    ! [U_4617,U_4616,U_4615] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4615),hAPP(hAPP(c_Power_Opower__class_Opower(U_4615),U_4616),U_4617)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4615),hAPP(c_Groups_Oabs__class_Oabs(U_4615),U_4616)),U_4617)
      | ~ class_Rings_Olinordered__idom(U_4615) ),
    inference(variable_rename,[status(thm)],[f_1264_1]) ).

fof(f_1264_3,plain,
    ! [U_4615,U_4616,U_4617] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4615),hAPP(hAPP(c_Power_Opower__class_Opower(U_4615),U_4616),U_4617)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4615),hAPP(c_Groups_Oabs__class_Oabs(U_4615),U_4616)),U_4617)
      | ~ class_Rings_Olinordered__idom(U_4615) ),
    inference(definitional_conversion,[status(esa)],[f_1264_2]) ).

cnf(f_1264_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4615),hAPP(hAPP(c_Power_Opower__class_Opower(U_4615),U_4616),U_4617)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4615),hAPP(c_Groups_Oabs__class_Oabs(U_4615),U_4616)),U_4617)
    | ~ class_Rings_Olinordered__idom(U_4615) ),
    inference(clausify,[status(thm)],[f_1264_3]) ).

fof(f_1265_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_1265_2,plain,
    ! [U_4619,U_4618] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4618),U_4619),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4619
      | ~ class_Groups_Omonoid__mult(U_4618) ),
    inference(variable_rename,[status(thm)],[f_1265_1]) ).

fof(f_1265_3,plain,
    ! [U_4618,U_4619] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4618),U_4619),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4619
      | ~ class_Groups_Omonoid__mult(U_4618) ),
    inference(definitional_conversion,[status(esa)],[f_1265_2]) ).

cnf(f_1265_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4618),U_4619),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4619
    | ~ class_Groups_Omonoid__mult(U_4618) ),
    inference(clausify,[status(thm)],[f_1265_3]) ).

fof(f_1266_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_1266_2,plain,
    ! [U_4622,U_4621,U_4620] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4620),c_Groups_Ozero__class_Ozero(U_4620)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4620),U_4621),U_4622)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4620),c_Groups_Ozero__class_Ozero(U_4620)),U_4621))
      | ~ class_Rings_Olinordered__semidom(U_4620) ),
    inference(variable_rename,[status(thm)],[f_1266_1]) ).

fof(f_1266_3,plain,
    ! [U_4620,U_4621,U_4622] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4620),c_Groups_Ozero__class_Ozero(U_4620)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4620),U_4621),U_4622)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4620),c_Groups_Ozero__class_Ozero(U_4620)),U_4621))
      | ~ class_Rings_Olinordered__semidom(U_4620) ),
    inference(definitional_conversion,[status(esa)],[f_1266_2]) ).

cnf(f_1266_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4620),c_Groups_Ozero__class_Ozero(U_4620)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4620),U_4621),U_4622)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4620),c_Groups_Ozero__class_Ozero(U_4620)),U_4621))
    | ~ class_Rings_Olinordered__semidom(U_4620) ),
    inference(clausify,[status(thm)],[f_1266_3]) ).

fof(f_1267_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_1267_2,plain,
    ! [U_4626,U_4625,U_4624,U_4623] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4623),hAPP(hAPP(c_Power_Opower__class_Opower(U_4623),U_4624),U_4626)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4623),U_4625),U_4626)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4623),c_Groups_Ozero__class_Ozero(U_4623)),U_4624))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4623),U_4624),U_4625))
      | ~ class_Rings_Olinordered__semidom(U_4623) ),
    inference(variable_rename,[status(thm)],[f_1267_1]) ).

fof(f_1267_3,plain,
    ! [U_4623,U_4624,U_4625,U_4626] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4623),hAPP(hAPP(c_Power_Opower__class_Opower(U_4623),U_4624),U_4626)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4623),U_4625),U_4626)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4623),c_Groups_Ozero__class_Ozero(U_4623)),U_4624))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4623),U_4624),U_4625))
      | ~ class_Rings_Olinordered__semidom(U_4623) ),
    inference(definitional_conversion,[status(esa)],[f_1267_2]) ).

cnf(f_1267_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4623),hAPP(hAPP(c_Power_Opower__class_Opower(U_4623),U_4624),U_4626)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4623),U_4625),U_4626)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4623),c_Groups_Ozero__class_Ozero(U_4623)),U_4624))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4623),U_4624),U_4625))
    | ~ class_Rings_Olinordered__semidom(U_4623) ),
    inference(clausify,[status(thm)],[f_1267_3]) ).

fof(f_1268_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_1268_2,plain,
    ! [U_4629,U_4628,U_4627] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4627),c_Groups_Ozero__class_Ozero(U_4627)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4627),U_4628),U_4629)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4627),c_Groups_Ozero__class_Ozero(U_4627)),U_4628))
      | ~ class_Rings_Olinordered__semidom(U_4627) ),
    inference(variable_rename,[status(thm)],[f_1268_1]) ).

fof(f_1268_3,plain,
    ! [U_4628,U_4627,U_4629] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4627),c_Groups_Ozero__class_Ozero(U_4627)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4627),U_4628),U_4629)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4627),c_Groups_Ozero__class_Ozero(U_4627)),U_4628))
      | ~ class_Rings_Olinordered__semidom(U_4627) ),
    inference(definitional_conversion,[status(esa)],[f_1268_2]) ).

cnf(f_1268_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4627),c_Groups_Ozero__class_Ozero(U_4627)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4627),U_4628),U_4629)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4627),c_Groups_Ozero__class_Ozero(U_4627)),U_4628))
    | ~ class_Rings_Olinordered__semidom(U_4627) ),
    inference(clausify,[status(thm)],[f_1268_3]) ).

fof(f_1269_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_1269_2,plain,
    ! [U_4632,U_4631,U_4630] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4630),U_4631),U_4632) = c_Groups_Ozero__class_Ozero(U_4630)
          | U_4632 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_4631 != c_Groups_Ozero__class_Ozero(U_4630) )
        & ( ( U_4632 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & U_4631 = c_Groups_Ozero__class_Ozero(U_4630) )
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_4630),U_4631),U_4632) != c_Groups_Ozero__class_Ozero(U_4630) ) )
      | ~ class_Rings_Ozero__neq__one(U_4630)
      | ~ class_Rings_Ono__zero__divisors(U_4630)
      | ~ class_Rings_Omult__zero(U_4630)
      | ~ class_Power_Opower(U_4630) ),
    inference(variable_rename,[status(thm)],[f_1269_1]) ).

fof(f_1269_3,plain,
    ( ! [U_4630,U_4631,U_4632] :
        ( U_4632 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP357(U_4630,U_4631,U_4632) )
    & ! [U_4630,U_4631,U_4632] :
        ( U_4631 = c_Groups_Ozero__class_Ozero(U_4630)
        | ~ sP357(U_4630,U_4631,U_4632) )
    & ! [U_4630,U_4631,U_4632] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4630),U_4631),U_4632) = c_Groups_Ozero__class_Ozero(U_4630)
        | U_4632 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4631 != c_Groups_Ozero__class_Ozero(U_4630)
        | ~ sP358(U_4630,U_4631,U_4632) )
    & ! [U_4630,U_4631,U_4632] :
        ( sP357(U_4630,U_4631,U_4632)
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_4630),U_4631),U_4632) != c_Groups_Ozero__class_Ozero(U_4630)
        | ~ sP358(U_4630,U_4631,U_4632) )
    & ! [U_4630,U_4631,U_4632] :
        ( sP358(U_4630,U_4631,U_4632)
        | ~ class_Rings_Ozero__neq__one(U_4630)
        | ~ class_Rings_Ono__zero__divisors(U_4630)
        | ~ class_Rings_Omult__zero(U_4630)
        | ~ class_Power_Opower(U_4630) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP357,sP358])],[f_1269_2]) ).

cnf(f_1269_4,plain,
    ( sP358(U_4630,U_4631,U_4632)
    | ~ class_Rings_Ozero__neq__one(U_4630)
    | ~ class_Rings_Ono__zero__divisors(U_4630)
    | ~ class_Rings_Omult__zero(U_4630)
    | ~ class_Power_Opower(U_4630) ),
    inference(clausify,[status(thm)],[f_1269_3]) ).

cnf(f_1269_5,plain,
    ( sP357(U_4630,U_4631,U_4632)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_4630),U_4631),U_4632) != c_Groups_Ozero__class_Ozero(U_4630)
    | ~ sP358(U_4630,U_4631,U_4632) ),
    inference(clausify,[status(thm)],[f_1269_3]) ).

cnf(f_1269_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4630),U_4631),U_4632) = c_Groups_Ozero__class_Ozero(U_4630)
    | U_4632 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4631 != c_Groups_Ozero__class_Ozero(U_4630)
    | ~ sP358(U_4630,U_4631,U_4632) ),
    inference(clausify,[status(thm)],[f_1269_3]) ).

cnf(f_1269_7,plain,
    ( U_4631 = c_Groups_Ozero__class_Ozero(U_4630)
    | ~ sP357(U_4630,U_4631,U_4632) ),
    inference(clausify,[status(thm)],[f_1269_3]) ).

cnf(f_1269_8,plain,
    ( U_4632 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP357(U_4630,U_4631,U_4632) ),
    inference(clausify,[status(thm)],[f_1269_3]) ).

fof(f_1270_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_1270_2,plain,
    ! [U_4635,U_4634,U_4633] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4633),c_Groups_Oone__class_Oone(U_4633)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4633),U_4634),U_4635)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4633),c_Groups_Oone__class_Oone(U_4633)),U_4634))
      | ~ class_Rings_Olinordered__semidom(U_4633) ),
    inference(variable_rename,[status(thm)],[f_1270_1]) ).

fof(f_1270_3,plain,
    ! [U_4635,U_4634,U_4633] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4633),c_Groups_Oone__class_Oone(U_4633)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4633),U_4634),U_4635)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4633),c_Groups_Oone__class_Oone(U_4633)),U_4634))
      | ~ class_Rings_Olinordered__semidom(U_4633) ),
    inference(definitional_conversion,[status(esa)],[f_1270_2]) ).

cnf(f_1270_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4633),c_Groups_Oone__class_Oone(U_4633)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4633),U_4634),U_4635)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4633),c_Groups_Oone__class_Oone(U_4633)),U_4634))
    | ~ class_Rings_Olinordered__semidom(U_4633) ),
    inference(clausify,[status(thm)],[f_1270_3]) ).

fof(f_1271_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_1271_2,plain,
    ! [U_4637,U_4636] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4636),c_Groups_Ozero__class_Ozero(U_4636)),hAPP(c_Nat_OSuc,U_4637)) = c_Groups_Ozero__class_Ozero(U_4636)
      | ~ class_Rings_Osemiring__0(U_4636)
      | ~ class_Power_Opower(U_4636) ),
    inference(variable_rename,[status(thm)],[f_1271_1]) ).

fof(f_1271_3,plain,
    ! [U_4636,U_4637] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4636),c_Groups_Ozero__class_Ozero(U_4636)),hAPP(c_Nat_OSuc,U_4637)) = c_Groups_Ozero__class_Ozero(U_4636)
      | ~ class_Rings_Osemiring__0(U_4636)
      | ~ class_Power_Opower(U_4636) ),
    inference(definitional_conversion,[status(esa)],[f_1271_2]) ).

cnf(f_1271_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4636),c_Groups_Ozero__class_Ozero(U_4636)),hAPP(c_Nat_OSuc,U_4637)) = c_Groups_Ozero__class_Ozero(U_4636)
    | ~ class_Rings_Osemiring__0(U_4636)
    | ~ class_Power_Opower(U_4636) ),
    inference(clausify,[status(thm)],[f_1271_3]) ).

fof(f_1272_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_1272_2,plain,
    ! [U_4641,U_4640,U_4639,U_4638] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4638),U_4639),U_4640) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4638),U_4639),U_4641)
          | U_4640 != U_4641 )
        & ( U_4640 = U_4641
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_4638),U_4639),U_4640) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4638),U_4639),U_4641) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4638),c_Groups_Oone__class_Oone(U_4638)),U_4639))
      | ~ class_Rings_Olinordered__semidom(U_4638) ),
    inference(variable_rename,[status(thm)],[f_1272_1]) ).

fof(f_1272_3,plain,
    ( ! [U_4638,U_4639,U_4640,U_4641] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4638),U_4639),U_4640) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4638),U_4639),U_4641)
        | U_4640 != U_4641
        | ~ sP359(U_4638,U_4639,U_4640,U_4641) )
    & ! [U_4638,U_4639,U_4640,U_4641] :
        ( U_4640 = U_4641
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_4638),U_4639),U_4640) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4638),U_4639),U_4641)
        | ~ sP359(U_4638,U_4639,U_4640,U_4641) )
    & ! [U_4638,U_4639,U_4640,U_4641] :
        ( sP359(U_4638,U_4639,U_4640,U_4641)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4638),c_Groups_Oone__class_Oone(U_4638)),U_4639))
        | ~ class_Rings_Olinordered__semidom(U_4638) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP359])],[f_1272_2]) ).

cnf(f_1272_4,plain,
    ( sP359(U_4638,U_4639,U_4640,U_4641)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4638),c_Groups_Oone__class_Oone(U_4638)),U_4639))
    | ~ class_Rings_Olinordered__semidom(U_4638) ),
    inference(clausify,[status(thm)],[f_1272_3]) ).

cnf(f_1272_5,plain,
    ( U_4640 = U_4641
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_4638),U_4639),U_4640) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4638),U_4639),U_4641)
    | ~ sP359(U_4638,U_4639,U_4640,U_4641) ),
    inference(clausify,[status(thm)],[f_1272_3]) ).

cnf(f_1272_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4638),U_4639),U_4640) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4638),U_4639),U_4641)
    | U_4640 != U_4641
    | ~ sP359(U_4638,U_4639,U_4640,U_4641) ),
    inference(clausify,[status(thm)],[f_1272_3]) ).

fof(f_1273_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_1273_2,plain,
    ! [U_4644,U_4643,U_4642] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4642),U_4643),hAPP(c_Nat_OSuc,U_4644)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4642),U_4643),hAPP(hAPP(c_Power_Opower__class_Opower(U_4642),U_4643),U_4644))
      | ~ class_Power_Opower(U_4642) ),
    inference(variable_rename,[status(thm)],[f_1273_1]) ).

fof(f_1273_3,plain,
    ! [U_4644,U_4643,U_4642] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4642),U_4643),hAPP(c_Nat_OSuc,U_4644)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4642),U_4643),hAPP(hAPP(c_Power_Opower__class_Opower(U_4642),U_4643),U_4644))
      | ~ class_Power_Opower(U_4642) ),
    inference(definitional_conversion,[status(esa)],[f_1273_2]) ).

cnf(f_1273_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4642),U_4643),hAPP(c_Nat_OSuc,U_4644)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4642),U_4643),hAPP(hAPP(c_Power_Opower__class_Opower(U_4642),U_4643),U_4644))
    | ~ class_Power_Opower(U_4642) ),
    inference(clausify,[status(thm)],[f_1273_3]) ).

fof(f_1274_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_1274_2,plain,
    ! [U_4647,U_4646,U_4645] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4645),U_4646),hAPP(c_Nat_OSuc,U_4647)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4645),hAPP(hAPP(c_Power_Opower__class_Opower(U_4645),U_4646),U_4647)),U_4646)
      | ~ class_Groups_Omonoid__mult(U_4645) ),
    inference(variable_rename,[status(thm)],[f_1274_1]) ).

fof(f_1274_3,plain,
    ! [U_4645,U_4646,U_4647] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4645),U_4646),hAPP(c_Nat_OSuc,U_4647)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4645),hAPP(hAPP(c_Power_Opower__class_Opower(U_4645),U_4646),U_4647)),U_4646)
      | ~ class_Groups_Omonoid__mult(U_4645) ),
    inference(definitional_conversion,[status(esa)],[f_1274_2]) ).

cnf(f_1274_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4645),U_4646),hAPP(c_Nat_OSuc,U_4647)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4645),hAPP(hAPP(c_Power_Opower__class_Opower(U_4645),U_4646),U_4647)),U_4646)
    | ~ class_Groups_Omonoid__mult(U_4645) ),
    inference(clausify,[status(thm)],[f_1274_3]) ).

fof(f_1275_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_1275_2,plain,
    ! [U_4649,U_4648] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4648),U_4649),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4648)
      | ~ class_Power_Opower(U_4648) ),
    inference(variable_rename,[status(thm)],[f_1275_1]) ).

fof(f_1275_3,plain,
    ! [U_4648,U_4649] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4648),U_4649),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4648)
      | ~ class_Power_Opower(U_4648) ),
    inference(definitional_conversion,[status(esa)],[f_1275_2]) ).

cnf(f_1275_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4648),U_4649),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4648)
    | ~ class_Power_Opower(U_4648) ),
    inference(clausify,[status(thm)],[f_1275_3]) ).

fof(f_1276_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_1276_2,plain,
    ! [U_4653,U_4652,U_4651,U_4650] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4650),U_4651),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4652),U_4653)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4650),hAPP(hAPP(c_Power_Opower__class_Opower(U_4650),U_4651),U_4652)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4650),U_4651),U_4653))
      | ~ class_Groups_Omonoid__mult(U_4650) ),
    inference(variable_rename,[status(thm)],[f_1276_1]) ).

fof(f_1276_3,plain,
    ! [U_4650,U_4651,U_4652,U_4653] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4650),U_4651),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4652),U_4653)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4650),hAPP(hAPP(c_Power_Opower__class_Opower(U_4650),U_4651),U_4652)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4650),U_4651),U_4653))
      | ~ class_Groups_Omonoid__mult(U_4650) ),
    inference(definitional_conversion,[status(esa)],[f_1276_2]) ).

cnf(f_1276_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4650),U_4651),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4652),U_4653)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4650),hAPP(hAPP(c_Power_Opower__class_Opower(U_4650),U_4651),U_4652)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4650),U_4651),U_4653))
    | ~ class_Groups_Omonoid__mult(U_4650) ),
    inference(clausify,[status(thm)],[f_1276_3]) ).

fof(f_1277_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_1277_2,plain,
    ! [U_4656,U_4655,U_4654] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4654),hAPP(hAPP(c_Power_Opower__class_Opower(U_4654),hAPP(c_Groups_Ouminus__class_Ouminus(U_4654),U_4655)),U_4656)) = hAPP(c_Groups_Oabs__class_Oabs(U_4654),hAPP(hAPP(c_Power_Opower__class_Opower(U_4654),U_4655),U_4656))
      | ~ class_Rings_Olinordered__idom(U_4654) ),
    inference(variable_rename,[status(thm)],[f_1277_1]) ).

fof(f_1277_3,plain,
    ! [U_4654,U_4655,U_4656] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4654),hAPP(hAPP(c_Power_Opower__class_Opower(U_4654),hAPP(c_Groups_Ouminus__class_Ouminus(U_4654),U_4655)),U_4656)) = hAPP(c_Groups_Oabs__class_Oabs(U_4654),hAPP(hAPP(c_Power_Opower__class_Opower(U_4654),U_4655),U_4656))
      | ~ class_Rings_Olinordered__idom(U_4654) ),
    inference(definitional_conversion,[status(esa)],[f_1277_2]) ).

cnf(f_1277_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4654),hAPP(hAPP(c_Power_Opower__class_Opower(U_4654),hAPP(c_Groups_Ouminus__class_Ouminus(U_4654),U_4655)),U_4656)) = hAPP(c_Groups_Oabs__class_Oabs(U_4654),hAPP(hAPP(c_Power_Opower__class_Opower(U_4654),U_4655),U_4656))
    | ~ class_Rings_Olinordered__idom(U_4654) ),
    inference(clausify,[status(thm)],[f_1277_3]) ).

fof(f_1278_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_1278_2,plain,
    ! [U_4660,U_4659,U_4658,U_4657] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4658),U_4660))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4657),c_Groups_Ozero__class_Ozero(U_4657)),U_4660))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),hAPP(hAPP(c_Power_Opower__class_Opower(U_4657),U_4658),U_4659)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4657),U_4660),U_4659)))
      | ~ class_Rings_Olinordered__semidom(U_4657) ),
    inference(variable_rename,[status(thm)],[f_1278_1]) ).

fof(f_1278_3,plain,
    ! [U_4657,U_4658,U_4659,U_4660] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4658),U_4660))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4657),c_Groups_Ozero__class_Ozero(U_4657)),U_4660))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),hAPP(hAPP(c_Power_Opower__class_Opower(U_4657),U_4658),U_4659)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4657),U_4660),U_4659)))
      | ~ class_Rings_Olinordered__semidom(U_4657) ),
    inference(definitional_conversion,[status(esa)],[f_1278_2]) ).

cnf(f_1278_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),U_4658),U_4660))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4657),c_Groups_Ozero__class_Ozero(U_4657)),U_4660))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4657),hAPP(hAPP(c_Power_Opower__class_Opower(U_4657),U_4658),U_4659)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4657),U_4660),U_4659)))
    | ~ class_Rings_Olinordered__semidom(U_4657) ),
    inference(clausify,[status(thm)],[f_1278_3]) ).

fof(f_1279_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_1279_2,plain,
    ! [U_4664,U_4663,U_4662,U_4661] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),U_4662),U_4664))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),c_Groups_Ozero__class_Ozero(U_4661)),U_4664))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),hAPP(hAPP(c_Power_Opower__class_Opower(U_4661),U_4662),hAPP(c_Nat_OSuc,U_4663))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4661),U_4664),hAPP(c_Nat_OSuc,U_4663))))
      | ~ class_Rings_Olinordered__semidom(U_4661) ),
    inference(variable_rename,[status(thm)],[f_1279_1]) ).

fof(f_1279_3,plain,
    ! [U_4661,U_4662,U_4663,U_4664] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),U_4662),U_4664))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),c_Groups_Ozero__class_Ozero(U_4661)),U_4664))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),hAPP(hAPP(c_Power_Opower__class_Opower(U_4661),U_4662),hAPP(c_Nat_OSuc,U_4663))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4661),U_4664),hAPP(c_Nat_OSuc,U_4663))))
      | ~ class_Rings_Olinordered__semidom(U_4661) ),
    inference(definitional_conversion,[status(esa)],[f_1279_2]) ).

cnf(f_1279_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),U_4662),U_4664))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),c_Groups_Ozero__class_Ozero(U_4661)),U_4664))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4661),hAPP(hAPP(c_Power_Opower__class_Opower(U_4661),U_4662),hAPP(c_Nat_OSuc,U_4663))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4661),U_4664),hAPP(c_Nat_OSuc,U_4663))))
    | ~ class_Rings_Olinordered__semidom(U_4661) ),
    inference(clausify,[status(thm)],[f_1279_3]) ).

fof(f_1280_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_1280_2,plain,
    ! [U_4668,U_4667,U_4666,U_4665] :
      ( U_4666 = U_4668
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4665),c_Groups_Ozero__class_Ozero(U_4665)),U_4668))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4665),c_Groups_Ozero__class_Ozero(U_4665)),U_4666))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_4665),U_4666),hAPP(c_Nat_OSuc,U_4667)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4665),U_4668),hAPP(c_Nat_OSuc,U_4667))
      | ~ class_Rings_Olinordered__semidom(U_4665) ),
    inference(variable_rename,[status(thm)],[f_1280_1]) ).

fof(f_1280_3,plain,
    ! [U_4665,U_4666,U_4667,U_4668] :
      ( U_4666 = U_4668
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4665),c_Groups_Ozero__class_Ozero(U_4665)),U_4668))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4665),c_Groups_Ozero__class_Ozero(U_4665)),U_4666))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_4665),U_4666),hAPP(c_Nat_OSuc,U_4667)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4665),U_4668),hAPP(c_Nat_OSuc,U_4667))
      | ~ class_Rings_Olinordered__semidom(U_4665) ),
    inference(definitional_conversion,[status(esa)],[f_1280_2]) ).

cnf(f_1280_4,plain,
    ( U_4666 = U_4668
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4665),c_Groups_Ozero__class_Ozero(U_4665)),U_4668))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4665),c_Groups_Ozero__class_Ozero(U_4665)),U_4666))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_4665),U_4666),hAPP(c_Nat_OSuc,U_4667)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4665),U_4668),hAPP(c_Nat_OSuc,U_4667))
    | ~ class_Rings_Olinordered__semidom(U_4665) ),
    inference(clausify,[status(thm)],[f_1280_3]) ).

fof(f_1281_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_1281_2,plain,
    ! [U_4671,U_4670,U_4669] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),c_Groups_Oone__class_Oone(U_4669)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4669),U_4670),hAPP(hAPP(c_Power_Opower__class_Opower(U_4669),U_4670),U_4671))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),c_Groups_Oone__class_Oone(U_4669)),U_4670))
      | ~ class_Rings_Olinordered__semidom(U_4669) ),
    inference(variable_rename,[status(thm)],[f_1281_1]) ).

fof(f_1281_3,plain,
    ! [U_4669,U_4670,U_4671] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),c_Groups_Oone__class_Oone(U_4669)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4669),U_4670),hAPP(hAPP(c_Power_Opower__class_Opower(U_4669),U_4670),U_4671))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),c_Groups_Oone__class_Oone(U_4669)),U_4670))
      | ~ class_Rings_Olinordered__semidom(U_4669) ),
    inference(definitional_conversion,[status(esa)],[f_1281_2]) ).

cnf(f_1281_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),c_Groups_Oone__class_Oone(U_4669)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4669),U_4670),hAPP(hAPP(c_Power_Opower__class_Opower(U_4669),U_4670),U_4671))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4669),c_Groups_Oone__class_Oone(U_4669)),U_4670))
    | ~ class_Rings_Olinordered__semidom(U_4669) ),
    inference(clausify,[status(thm)],[f_1281_3]) ).

fof(f_1282_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_1282_2,plain,
    ! [U_4674,U_4673,U_4672] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4672),hAPP(hAPP(c_Power_Opower__class_Opower(U_4672),U_4673),U_4674)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4672),U_4673),hAPP(hAPP(c_Power_Opower__class_Opower(U_4672),U_4673),U_4674))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4672),c_Groups_Oone__class_Oone(U_4672)),U_4673))
      | ~ class_Rings_Olinordered__semidom(U_4672) ),
    inference(variable_rename,[status(thm)],[f_1282_1]) ).

fof(f_1282_3,plain,
    ! [U_4672,U_4673,U_4674] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4672),hAPP(hAPP(c_Power_Opower__class_Opower(U_4672),U_4673),U_4674)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4672),U_4673),hAPP(hAPP(c_Power_Opower__class_Opower(U_4672),U_4673),U_4674))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4672),c_Groups_Oone__class_Oone(U_4672)),U_4673))
      | ~ class_Rings_Olinordered__semidom(U_4672) ),
    inference(definitional_conversion,[status(esa)],[f_1282_2]) ).

cnf(f_1282_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4672),hAPP(hAPP(c_Power_Opower__class_Opower(U_4672),U_4673),U_4674)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4672),U_4673),hAPP(hAPP(c_Power_Opower__class_Opower(U_4672),U_4673),U_4674))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4672),c_Groups_Oone__class_Oone(U_4672)),U_4673))
    | ~ class_Rings_Olinordered__semidom(U_4672) ),
    inference(clausify,[status(thm)],[f_1282_3]) ).

fof(f_1283_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_1283_2,plain,
    ! [U_4676,U_4675] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4675),c_Groups_Ozero__class_Ozero(U_4675)),U_4676) = c_Groups_Ozero__class_Ozero(U_4675)
          | U_4676 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4675),c_Groups_Ozero__class_Ozero(U_4675)),U_4676) = c_Groups_Oone__class_Oone(U_4675)
          | U_4676 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Rings_Osemiring__0(U_4675)
      | ~ class_Power_Opower(U_4675) ),
    inference(variable_rename,[status(thm)],[f_1283_1]) ).

fof(f_1283_3,plain,
    ( ! [U_4676,U_4675] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4675),c_Groups_Ozero__class_Ozero(U_4675)),U_4676) = c_Groups_Ozero__class_Ozero(U_4675)
        | U_4676 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP360(U_4676,U_4675) )
    & ! [U_4676,U_4675] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4675),c_Groups_Ozero__class_Ozero(U_4675)),U_4676) = c_Groups_Oone__class_Oone(U_4675)
        | U_4676 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP360(U_4676,U_4675) )
    & ! [U_4676,U_4675] :
        ( sP360(U_4676,U_4675)
        | ~ class_Rings_Osemiring__0(U_4675)
        | ~ class_Power_Opower(U_4675) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP360])],[f_1283_2]) ).

cnf(f_1283_4,plain,
    ( sP360(U_4676,U_4675)
    | ~ class_Rings_Osemiring__0(U_4675)
    | ~ class_Power_Opower(U_4675) ),
    inference(clausify,[status(thm)],[f_1283_3]) ).

cnf(f_1283_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4675),c_Groups_Ozero__class_Ozero(U_4675)),U_4676) = c_Groups_Oone__class_Oone(U_4675)
    | U_4676 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP360(U_4676,U_4675) ),
    inference(clausify,[status(thm)],[f_1283_3]) ).

cnf(f_1283_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4675),c_Groups_Ozero__class_Ozero(U_4675)),U_4676) = c_Groups_Ozero__class_Ozero(U_4675)
    | U_4676 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP360(U_4676,U_4675) ),
    inference(clausify,[status(thm)],[f_1283_3]) ).

fof(f_1284_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_1284_2,plain,
    ! [U_4679,U_4678,U_4677] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4677),c_Groups_Oone__class_Oone(U_4677)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4677),U_4678),hAPP(c_Nat_OSuc,U_4679))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4677),c_Groups_Oone__class_Oone(U_4677)),U_4678))
      | ~ class_Rings_Olinordered__semidom(U_4677) ),
    inference(variable_rename,[status(thm)],[f_1284_1]) ).

fof(f_1284_3,plain,
    ! [U_4677,U_4679,U_4678] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4677),c_Groups_Oone__class_Oone(U_4677)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4677),U_4678),hAPP(c_Nat_OSuc,U_4679))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4677),c_Groups_Oone__class_Oone(U_4677)),U_4678))
      | ~ class_Rings_Olinordered__semidom(U_4677) ),
    inference(definitional_conversion,[status(esa)],[f_1284_2]) ).

cnf(f_1284_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4677),c_Groups_Oone__class_Oone(U_4677)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4677),U_4678),hAPP(c_Nat_OSuc,U_4679))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4677),c_Groups_Oone__class_Oone(U_4677)),U_4678))
    | ~ class_Rings_Olinordered__semidom(U_4677) ),
    inference(clausify,[status(thm)],[f_1284_3]) ).

fof(f_1285_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_1285_2,plain,
    ! [U_4683,U_4682,U_4681,U_4680] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4680),hAPP(hAPP(c_Power_Opower__class_Opower(U_4680),U_4683),U_4681)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4680),U_4683),U_4682)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4680),c_Groups_Oone__class_Oone(U_4680)),U_4683))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4681),U_4682))
      | ~ class_Rings_Olinordered__semidom(U_4680) ),
    inference(variable_rename,[status(thm)],[f_1285_1]) ).

fof(f_1285_3,plain,
    ! [U_4680,U_4681,U_4682,U_4683] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4680),hAPP(hAPP(c_Power_Opower__class_Opower(U_4680),U_4683),U_4681)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4680),U_4683),U_4682)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4680),c_Groups_Oone__class_Oone(U_4680)),U_4683))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4681),U_4682))
      | ~ class_Rings_Olinordered__semidom(U_4680) ),
    inference(definitional_conversion,[status(esa)],[f_1285_2]) ).

cnf(f_1285_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4680),hAPP(hAPP(c_Power_Opower__class_Opower(U_4680),U_4683),U_4681)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4680),U_4683),U_4682)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4680),c_Groups_Oone__class_Oone(U_4680)),U_4683))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4681),U_4682))
    | ~ class_Rings_Olinordered__semidom(U_4680) ),
    inference(clausify,[status(thm)],[f_1285_3]) ).

fof(f_1286_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_1286_2,plain,
    ! [U_4687,U_4686,U_4685,U_4684] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4686),U_4687))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4684),hAPP(hAPP(c_Power_Opower__class_Opower(U_4684),U_4685),U_4686)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4684),U_4685),U_4687)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4684),c_Groups_Oone__class_Oone(U_4684)),U_4685))
      | ~ class_Rings_Olinordered__semidom(U_4684) ),
    inference(variable_rename,[status(thm)],[f_1286_1]) ).

fof(f_1286_3,plain,
    ! [U_4684,U_4685,U_4686,U_4687] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4686),U_4687))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4684),hAPP(hAPP(c_Power_Opower__class_Opower(U_4684),U_4685),U_4686)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4684),U_4685),U_4687)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4684),c_Groups_Oone__class_Oone(U_4684)),U_4685))
      | ~ class_Rings_Olinordered__semidom(U_4684) ),
    inference(definitional_conversion,[status(esa)],[f_1286_2]) ).

cnf(f_1286_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4686),U_4687))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4684),hAPP(hAPP(c_Power_Opower__class_Opower(U_4684),U_4685),U_4686)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4684),U_4685),U_4687)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4684),c_Groups_Oone__class_Oone(U_4684)),U_4685))
    | ~ class_Rings_Olinordered__semidom(U_4684) ),
    inference(clausify,[status(thm)],[f_1286_3]) ).

fof(f_1287_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_1287_2,plain,
    ! [U_4691,U_4690,U_4689,U_4688] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),hAPP(hAPP(c_Power_Opower__class_Opower(U_4688),U_4689),U_4690)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4688),U_4689),U_4691)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4690),U_4691)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4690),U_4691))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),hAPP(hAPP(c_Power_Opower__class_Opower(U_4688),U_4689),U_4690)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4688),U_4689),U_4691))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),c_Groups_Oone__class_Oone(U_4688)),U_4689))
      | ~ class_Rings_Olinordered__semidom(U_4688) ),
    inference(variable_rename,[status(thm)],[f_1287_1]) ).

fof(f_1287_3,plain,
    ( ! [U_4689,U_4688,U_4690,U_4691] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),hAPP(hAPP(c_Power_Opower__class_Opower(U_4688),U_4689),U_4690)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4688),U_4689),U_4691)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4690),U_4691))
        | ~ sP361(U_4689,U_4688,U_4690,U_4691) )
    & ! [U_4689,U_4688,U_4690,U_4691] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4690),U_4691))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),hAPP(hAPP(c_Power_Opower__class_Opower(U_4688),U_4689),U_4690)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4688),U_4689),U_4691)))
        | ~ sP361(U_4689,U_4688,U_4690,U_4691) )
    & ! [U_4689,U_4688,U_4690,U_4691] :
        ( sP361(U_4689,U_4688,U_4690,U_4691)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),c_Groups_Oone__class_Oone(U_4688)),U_4689))
        | ~ class_Rings_Olinordered__semidom(U_4688) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP361])],[f_1287_2]) ).

cnf(f_1287_4,plain,
    ( sP361(U_4689,U_4688,U_4690,U_4691)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),c_Groups_Oone__class_Oone(U_4688)),U_4689))
    | ~ class_Rings_Olinordered__semidom(U_4688) ),
    inference(clausify,[status(thm)],[f_1287_3]) ).

cnf(f_1287_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4690),U_4691))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),hAPP(hAPP(c_Power_Opower__class_Opower(U_4688),U_4689),U_4690)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4688),U_4689),U_4691)))
    | ~ sP361(U_4689,U_4688,U_4690,U_4691) ),
    inference(clausify,[status(thm)],[f_1287_3]) ).

cnf(f_1287_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4688),hAPP(hAPP(c_Power_Opower__class_Opower(U_4688),U_4689),U_4690)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4688),U_4689),U_4691)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4690),U_4691))
    | ~ sP361(U_4689,U_4688,U_4690,U_4691) ),
    inference(clausify,[status(thm)],[f_1287_3]) ).

fof(f_1288_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_1288_2,plain,
    ! [U_4694,U_4693,U_4692] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4692),c_Groups_Ozero__class_Ozero(U_4692)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4692),hAPP(c_Groups_Oabs__class_Oabs(U_4692),U_4693)),U_4694)))
      | ~ class_Rings_Olinordered__idom(U_4692) ),
    inference(variable_rename,[status(thm)],[f_1288_1]) ).

fof(f_1288_3,plain,
    ! [U_4692,U_4693,U_4694] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4692),c_Groups_Ozero__class_Ozero(U_4692)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4692),hAPP(c_Groups_Oabs__class_Oabs(U_4692),U_4693)),U_4694)))
      | ~ class_Rings_Olinordered__idom(U_4692) ),
    inference(definitional_conversion,[status(esa)],[f_1288_2]) ).

cnf(f_1288_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4692),c_Groups_Ozero__class_Ozero(U_4692)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4692),hAPP(c_Groups_Oabs__class_Oabs(U_4692),U_4693)),U_4694)))
    | ~ class_Rings_Olinordered__idom(U_4692) ),
    inference(clausify,[status(thm)],[f_1288_3]) ).

fof(f_1289_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_1289_2,plain,
    ! [U_4698,U_4697,U_4696,U_4695] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4695),hAPP(hAPP(c_Power_Opower__class_Opower(U_4695),U_4698),U_4696)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4695),U_4698),U_4697)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4695),c_Groups_Oone__class_Oone(U_4695)),U_4698))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4696),U_4697))
      | ~ class_Rings_Olinordered__semidom(U_4695) ),
    inference(variable_rename,[status(thm)],[f_1289_1]) ).

fof(f_1289_3,plain,
    ! [U_4695,U_4696,U_4697,U_4698] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4695),hAPP(hAPP(c_Power_Opower__class_Opower(U_4695),U_4698),U_4696)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4695),U_4698),U_4697)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4695),c_Groups_Oone__class_Oone(U_4695)),U_4698))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4696),U_4697))
      | ~ class_Rings_Olinordered__semidom(U_4695) ),
    inference(definitional_conversion,[status(esa)],[f_1289_2]) ).

cnf(f_1289_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4695),hAPP(hAPP(c_Power_Opower__class_Opower(U_4695),U_4698),U_4696)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4695),U_4698),U_4697)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4695),c_Groups_Oone__class_Oone(U_4695)),U_4698))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4696),U_4697))
    | ~ class_Rings_Olinordered__semidom(U_4695) ),
    inference(clausify,[status(thm)],[f_1289_3]) ).

fof(f_1290_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_1290_2,plain,
    ! [U_4701,U_4700,U_4699] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4699),hAPP(c_Groups_Ouminus__class_Ouminus(U_4699),U_4700)),U_4701) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4699),hAPP(hAPP(c_Power_Opower__class_Opower(U_4699),hAPP(c_Groups_Ouminus__class_Ouminus(U_4699),c_Groups_Oone__class_Oone(U_4699))),U_4701)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4699),U_4700),U_4701))
      | ~ class_Rings_Oring__1(U_4699) ),
    inference(variable_rename,[status(thm)],[f_1290_1]) ).

fof(f_1290_3,plain,
    ! [U_4699,U_4700,U_4701] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4699),hAPP(c_Groups_Ouminus__class_Ouminus(U_4699),U_4700)),U_4701) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4699),hAPP(hAPP(c_Power_Opower__class_Opower(U_4699),hAPP(c_Groups_Ouminus__class_Ouminus(U_4699),c_Groups_Oone__class_Oone(U_4699))),U_4701)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4699),U_4700),U_4701))
      | ~ class_Rings_Oring__1(U_4699) ),
    inference(definitional_conversion,[status(esa)],[f_1290_2]) ).

cnf(f_1290_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4699),hAPP(c_Groups_Ouminus__class_Ouminus(U_4699),U_4700)),U_4701) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4699),hAPP(hAPP(c_Power_Opower__class_Opower(U_4699),hAPP(c_Groups_Ouminus__class_Ouminus(U_4699),c_Groups_Oone__class_Oone(U_4699))),U_4701)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4699),U_4700),U_4701))
    | ~ class_Rings_Oring__1(U_4699) ),
    inference(clausify,[status(thm)],[f_1290_3]) ).

fof(f_1291_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_1291_2,plain,
    ! [U_4704,U_4703,U_4702] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4702),U_4703),hAPP(hAPP(c_Power_Opower__class_Opower(U_4702),U_4703),U_4704))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4702),U_4703),U_4704)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4702),U_4703),c_Groups_Oone__class_Oone(U_4702)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4702),c_Groups_Ozero__class_Ozero(U_4702)),U_4703))
      | ~ class_Rings_Olinordered__semidom(U_4702) ),
    inference(variable_rename,[status(thm)],[f_1291_1]) ).

fof(f_1291_3,plain,
    ! [U_4702,U_4703,U_4704] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4702),U_4703),hAPP(hAPP(c_Power_Opower__class_Opower(U_4702),U_4703),U_4704))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4702),U_4703),U_4704)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4702),U_4703),c_Groups_Oone__class_Oone(U_4702)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4702),c_Groups_Ozero__class_Ozero(U_4702)),U_4703))
      | ~ class_Rings_Olinordered__semidom(U_4702) ),
    inference(definitional_conversion,[status(esa)],[f_1291_2]) ).

cnf(f_1291_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4702),U_4703),hAPP(hAPP(c_Power_Opower__class_Opower(U_4702),U_4703),U_4704))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4702),U_4703),U_4704)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4702),U_4703),c_Groups_Oone__class_Oone(U_4702)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4702),c_Groups_Ozero__class_Ozero(U_4702)),U_4703))
    | ~ class_Rings_Olinordered__semidom(U_4702) ),
    inference(clausify,[status(thm)],[f_1291_3]) ).

fof(f_1292_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_1292_2,plain,
    ! [U_4708,U_4707,U_4706,U_4705] :
      ( U_4706 = U_4708
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4707))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4705),c_Groups_Ozero__class_Ozero(U_4705)),U_4708))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4705),c_Groups_Ozero__class_Ozero(U_4705)),U_4706))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_4705),U_4706),U_4707) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4705),U_4708),U_4707)
      | ~ class_Rings_Olinordered__semidom(U_4705) ),
    inference(variable_rename,[status(thm)],[f_1292_1]) ).

fof(f_1292_3,plain,
    ! [U_4705,U_4706,U_4707,U_4708] :
      ( U_4706 = U_4708
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4707))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4705),c_Groups_Ozero__class_Ozero(U_4705)),U_4708))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4705),c_Groups_Ozero__class_Ozero(U_4705)),U_4706))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_4705),U_4706),U_4707) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4705),U_4708),U_4707)
      | ~ class_Rings_Olinordered__semidom(U_4705) ),
    inference(definitional_conversion,[status(esa)],[f_1292_2]) ).

cnf(f_1292_4,plain,
    ( U_4706 = U_4708
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4707))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4705),c_Groups_Ozero__class_Ozero(U_4705)),U_4708))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4705),c_Groups_Ozero__class_Ozero(U_4705)),U_4706))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_4705),U_4706),U_4707) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4705),U_4708),U_4707)
    | ~ class_Rings_Olinordered__semidom(U_4705) ),
    inference(clausify,[status(thm)],[f_1292_3]) ).

fof(f_1293_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_1293_2,plain,
    ! [U_4709] :
      ( ( 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_4709)) = 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_4709)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4709))) )
      & ( 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_4709)) = 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_4709))) ) ),
    inference(variable_rename,[status(thm)],[f_1293_1]) ).

fof(f_1293_3,plain,
    ( ! [U_4711] :
        ( 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_4711)) = 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_4711)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4711))) )
    & ! [U_4710] :
        ( 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_4710)) = 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_4710))) ) ),
    inference(miniscope,[status(thm)],[f_1293_2]) ).

fof(f_1293_4,plain,
    ( ! [U_4711] :
        ( 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_4711)) = 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_4711)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4711))) )
    & ! [U_4710] :
        ( 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_4710)) = 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_4710))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1293_3]) ).

cnf(f_1293_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_4710)) = 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_4710))) ),
    inference(clausify,[status(thm)],[f_1293_4]) ).

cnf(f_1293_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_4711)) = 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_4711)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4711))) ),
    inference(clausify,[status(thm)],[f_1293_4]) ).

fof(f_1294_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_1294_2,plain,
    ! [U_4712] :
      ( c_Power_Opower__class_Opower(U_4712) = c_Power_Opower_Opower(U_4712,c_Groups_Oone__class_Oone(U_4712),c_Groups_Otimes__class_Otimes(U_4712))
      | ~ class_Power_Opower(U_4712) ),
    inference(variable_rename,[status(thm)],[f_1294_1]) ).

fof(f_1294_3,plain,
    ! [U_4712] :
      ( c_Power_Opower__class_Opower(U_4712) = c_Power_Opower_Opower(U_4712,c_Groups_Oone__class_Oone(U_4712),c_Groups_Otimes__class_Otimes(U_4712))
      | ~ class_Power_Opower(U_4712) ),
    inference(definitional_conversion,[status(esa)],[f_1294_2]) ).

cnf(f_1294_4,plain,
    ( c_Power_Opower__class_Opower(U_4712) = c_Power_Opower_Opower(U_4712,c_Groups_Oone__class_Oone(U_4712),c_Groups_Otimes__class_Otimes(U_4712))
    | ~ class_Power_Opower(U_4712) ),
    inference(clausify,[status(thm)],[f_1294_3]) ).

fof(f_1295_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_1295_2,plain,
    ! [U_4714,U_4713] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4713)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4714)) = 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_4713)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4714)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4713))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4713)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4714)) = 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_4713))) ) ),
    inference(variable_rename,[status(thm)],[f_1295_1]) ).

fof(f_1295_3,plain,
    ( ! [U_4718,U_4716] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4716)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4718)) = 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_4716)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4718)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4716))) )
    & ! [U_4717,U_4715] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4715)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4717)) = 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_4715))) ) ),
    inference(miniscope,[status(thm)],[f_1295_2]) ).

fof(f_1295_4,plain,
    ( ! [U_4716,U_4718] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4716)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4718)) = 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_4716)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4718)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4716))) )
    & ! [U_4717,U_4715] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4715)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4717)) = 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_4715))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1295_3]) ).

cnf(f_1295_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4715)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4717)) = 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_4715))) ),
    inference(clausify,[status(thm)],[f_1295_4]) ).

cnf(f_1295_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4716)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4718)) = 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_4716)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4718)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4716))) ),
    inference(clausify,[status(thm)],[f_1295_4]) ).

fof(f_1296_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_1296_2,plain,
    ! [U_4720,U_4719] :
      ( ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4719),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4720)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4719),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4720)))
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4720))) )
          & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4719),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4720)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4719)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4720))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4719))) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4719),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4720)) = 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_4719))) ) ),
    inference(variable_rename,[status(thm)],[f_1296_1]) ).

fof(f_1296_3,plain,
    ( ! [U_4724,U_4722] :
        ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4722),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4724)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4722),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4724)))
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4724))) )
          & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4722),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4724)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4722)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4724))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4722))) )
    & ! [U_4723,U_4721] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4721),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4723)) = 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_4721))) ) ),
    inference(miniscope,[status(thm)],[f_1296_2]) ).

fof(f_1296_4,plain,
    ( ! [U_4724,U_4722] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4722),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4724)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4722),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4724)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4724)))
        | ~ sP362(U_4724,U_4722) )
    & ! [U_4724,U_4722] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4722),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4724)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4722)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4724)))
        | ~ sP362(U_4724,U_4722) )
    & ! [U_4724,U_4722] :
        ( sP362(U_4724,U_4722)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4722))) )
    & ! [U_4723,U_4721] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4721),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4723)) = 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_4721))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP362])],[f_1296_3]) ).

cnf(f_1296_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4721),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4723)) = 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_4721))) ),
    inference(clausify,[status(thm)],[f_1296_4]) ).

cnf(f_1296_6,plain,
    ( sP362(U_4724,U_4722)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4722))) ),
    inference(clausify,[status(thm)],[f_1296_4]) ).

cnf(f_1296_7,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4722),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4724)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4722)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4724)))
    | ~ sP362(U_4724,U_4722) ),
    inference(clausify,[status(thm)],[f_1296_4]) ).

cnf(f_1296_8,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4722),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4724)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4722),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4724)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4724)))
    | ~ sP362(U_4724,U_4722) ),
    inference(clausify,[status(thm)],[f_1296_4]) ).

fof(f_1297_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_1297_2,plain,
    ! [U_4726,U_4725] : c_Nitpick_Oint__lcm(U_4725,U_4726) = 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_4725)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4726)))),
    inference(variable_rename,[status(thm)],[f_1297_1]) ).

fof(f_1297_3,plain,
    ! [U_4725,U_4726] : c_Nitpick_Oint__lcm(U_4725,U_4726) = 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_4725)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4726)))),
    inference(definitional_conversion,[status(esa)],[f_1297_2]) ).

cnf(f_1297_4,plain,
    c_Nitpick_Oint__lcm(U_4725,U_4726) = 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_4725)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4726)))),
    inference(clausify,[status(thm)],[f_1297_3]) ).

fof(f_1298_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_1298_2,plain,
    ! [U_4728,U_4727] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4727)),U_4728) = 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_4727)),U_4728))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4727))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4727)),U_4728) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4728)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4727))) ) ),
    inference(variable_rename,[status(thm)],[f_1298_1]) ).

fof(f_1298_3,plain,
    ( ! [U_4732,U_4730] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4730)),U_4732) = 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_4730)),U_4732))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4730))) )
    & ! [U_4731,U_4729] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4729)),U_4731) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4731)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4729))) ) ),
    inference(miniscope,[status(thm)],[f_1298_2]) ).

fof(f_1298_4,plain,
    ( ! [U_4730,U_4732] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4730)),U_4732) = 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_4730)),U_4732))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4730))) )
    & ! [U_4731,U_4729] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4729)),U_4731) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4731)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4729))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1298_3]) ).

cnf(f_1298_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4729)),U_4731) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4731)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4729))) ),
    inference(clausify,[status(thm)],[f_1298_4]) ).

cnf(f_1298_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4730)),U_4732) = 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_4730)),U_4732))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4730))) ),
    inference(clausify,[status(thm)],[f_1298_4]) ).

fof(f_1299_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_1299_2,plain,
    ! [U_4734,U_4733] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4733)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4734)) = 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_4733)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4734)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4733))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4733)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4734)) = 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_4734))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4733))) ) ),
    inference(variable_rename,[status(thm)],[f_1299_1]) ).

fof(f_1299_3,plain,
    ( ! [U_4738,U_4736] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4736)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4738)) = 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_4736)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4738)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4736))) )
    & ! [U_4737,U_4735] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4735)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4737)) = 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_4737))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4735))) ) ),
    inference(miniscope,[status(thm)],[f_1299_2]) ).

fof(f_1299_4,plain,
    ( ! [U_4736,U_4738] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4736)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4738)) = 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_4736)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4738)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4736))) )
    & ! [U_4737,U_4735] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4735)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4737)) = 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_4737))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4735))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1299_3]) ).

cnf(f_1299_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4735)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4737)) = 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_4737))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4735))) ),
    inference(clausify,[status(thm)],[f_1299_4]) ).

cnf(f_1299_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4736)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4738)) = 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_4736)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4738)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4736))) ),
    inference(clausify,[status(thm)],[f_1299_4]) ).

fof(f_1300_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_1300_2,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1300_1]) ).

cnf(f_1300_3,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1300_2]) ).

fof(f_1301_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_1301_2,plain,
    ! [U_4739] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4739))),
    inference(variable_rename,[status(thm)],[f_1301_1]) ).

fof(f_1301_3,plain,
    ! [U_4739] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4739))),
    inference(definitional_conversion,[status(esa)],[f_1301_2]) ).

cnf(f_1301_4,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4739))),
    inference(clausify,[status(thm)],[f_1301_3]) ).

fof(f_1302_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_1302_2,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1302_1]) ).

cnf(f_1302_3,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1302_2]) ).

fof(f_1303_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_1303_2,plain,
    ! [U_4740] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4740))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4740)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4740))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4740)) ) ),
    inference(variable_rename,[status(thm)],[f_1303_1]) ).

fof(f_1303_3,plain,
    ( ! [U_4742] :
        ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4742))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4742)) )
    & ! [U_4741] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4741))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4741)) ) ),
    inference(miniscope,[status(thm)],[f_1303_2]) ).

fof(f_1303_4,plain,
    ( ! [U_4742] :
        ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4742))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4742)) )
    & ! [U_4741] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4741))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4741)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1303_3]) ).

cnf(f_1303_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4741))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4741)) ),
    inference(clausify,[status(thm)],[f_1303_4]) ).

cnf(f_1303_6,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4742))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4742)) ),
    inference(clausify,[status(thm)],[f_1303_4]) ).

fof(f_1304_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_1304_2,plain,
    ! [U_4743] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4743))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4743),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4743),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4743)) ) ),
    inference(variable_rename,[status(thm)],[f_1304_1]) ).

fof(f_1304_3,plain,
    ( ! [U_4745] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4745))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4745),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4744] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4744),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4744)) ) ),
    inference(miniscope,[status(thm)],[f_1304_2]) ).

fof(f_1304_4,plain,
    ( ! [U_4745] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4745))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4745),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4744] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4744),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4744)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1304_3]) ).

cnf(f_1304_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4744),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4744)) ),
    inference(clausify,[status(thm)],[f_1304_4]) ).

cnf(f_1304_6,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4745))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4745),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1304_4]) ).

fof(f_1305_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_1305_2,plain,
    ! [U_4746] :
      ( hAPP(c_Int_Onat,U_4746) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4746)) ),
    inference(variable_rename,[status(thm)],[f_1305_1]) ).

fof(f_1305_3,plain,
    ! [U_4746] :
      ( hAPP(c_Int_Onat,U_4746) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4746)) ),
    inference(definitional_conversion,[status(esa)],[f_1305_2]) ).

cnf(f_1305_4,plain,
    ( hAPP(c_Int_Onat,U_4746) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4746)) ),
    inference(clausify,[status(thm)],[f_1305_3]) ).

fof(f_1306_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_1306_2,plain,
    ! [U_4747] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_4747)) = U_4747
      | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4747)) ),
    inference(variable_rename,[status(thm)],[f_1306_1]) ).

fof(f_1306_3,plain,
    ! [U_4747] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_4747)) = U_4747
      | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4747)) ),
    inference(definitional_conversion,[status(esa)],[f_1306_2]) ).

cnf(f_1306_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_4747)) = U_4747
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4747)) ),
    inference(clausify,[status(thm)],[f_1306_3]) ).

fof(f_1307_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_1307_2,plain,
    ! [U_4751,U_4750,U_4749,U_4748] : hAPP(hAPP(c_Power_Opower_Opower(U_4748,U_4749,U_4750),U_4751),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4749,
    inference(variable_rename,[status(thm)],[f_1307_1]) ).

fof(f_1307_3,plain,
    ! [U_4748,U_4749,U_4750,U_4751] : hAPP(hAPP(c_Power_Opower_Opower(U_4748,U_4749,U_4750),U_4751),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4749,
    inference(definitional_conversion,[status(esa)],[f_1307_2]) ).

cnf(f_1307_4,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_4748,U_4749,U_4750),U_4751),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4749,
    inference(clausify,[status(thm)],[f_1307_3]) ).

fof(f_1308_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_1308_2,plain,
    ! [U_4756,U_4755,U_4754,U_4753,U_4752] : hAPP(hAPP(c_Power_Opower_Opower(U_4752,U_4753,U_4754),U_4755),hAPP(c_Nat_OSuc,U_4756)) = hAPP(hAPP(U_4754,U_4755),hAPP(hAPP(c_Power_Opower_Opower(U_4752,U_4753,U_4754),U_4755),U_4756)),
    inference(variable_rename,[status(thm)],[f_1308_1]) ).

fof(f_1308_3,plain,
    ! [U_4754,U_4755,U_4756,U_4753,U_4752] : hAPP(hAPP(c_Power_Opower_Opower(U_4752,U_4753,U_4754),U_4755),hAPP(c_Nat_OSuc,U_4756)) = hAPP(hAPP(U_4754,U_4755),hAPP(hAPP(c_Power_Opower_Opower(U_4752,U_4753,U_4754),U_4755),U_4756)),
    inference(definitional_conversion,[status(esa)],[f_1308_2]) ).

cnf(f_1308_4,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_4752,U_4753,U_4754),U_4755),hAPP(c_Nat_OSuc,U_4756)) = hAPP(hAPP(U_4754,U_4755),hAPP(hAPP(c_Power_Opower_Opower(U_4752,U_4753,U_4754),U_4755),U_4756)),
    inference(clausify,[status(thm)],[f_1308_3]) ).

fof(f_1309_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_1309_2,plain,
    ! [U_4757] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4757) = 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_4757))) ),
    inference(variable_rename,[status(thm)],[f_1309_1]) ).

fof(f_1309_3,plain,
    ! [U_4757] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4757) = 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_4757))) ),
    inference(definitional_conversion,[status(esa)],[f_1309_2]) ).

cnf(f_1309_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4757) = 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_4757))) ),
    inference(clausify,[status(thm)],[f_1309_3]) ).

fof(f_1310_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_1310_2,plain,
    ! [U_4758] : 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_4758))))),
    inference(variable_rename,[status(thm)],[f_1310_1]) ).

fof(f_1310_3,plain,
    ! [U_4758] : 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_4758))))),
    inference(definitional_conversion,[status(esa)],[f_1310_2]) ).

cnf(f_1310_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_4758))))),
    inference(clausify,[status(thm)],[f_1310_3]) ).

fof(f_1311_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_1311_2,plain,
    ! [U_4760,U_4759] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4759) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4760)
        | ( ( ( U_4759 != U_4760
              & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4760))) )
            | ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4759) != 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_4760))) ) )
          & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4759))) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4760)),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_4759))) ) )
      & ( ( ( ( ( U_4759 = U_4760
                | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4760))) )
              & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4759) = 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_4760))) ) )
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4759))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4760)),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_4759))) ) )
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4759) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4760) ) ),
    inference(variable_rename,[status(thm)],[f_1311_1]) ).

fof(f_1311_3,plain,
    ( ! [U_4764,U_4762] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4762) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4764)
        | ( ( ( U_4762 != U_4764
              & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4764))) )
            | ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4762) != 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_4764))) ) )
          & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4762))) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4764)),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_4762))) ) )
    & ! [U_4763,U_4761] :
        ( ( ( ( ( U_4761 = U_4763
                | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4763))) )
              & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4761) = 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_4763))) ) )
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4761))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4763)),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_4761))) ) )
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4761) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4763) ) ),
    inference(miniscope,[status(thm)],[f_1311_2]) ).

fof(f_1311_4,plain,
    ( ! [U_4762,U_4764] :
        ( U_4762 != U_4764
        | ~ sP367(U_4762,U_4764) )
    & ! [U_4762,U_4764] :
        ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4764)))
        | ~ sP367(U_4762,U_4764) )
    & ! [U_4762,U_4764] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4762) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP366(U_4762,U_4764) )
    & ! [U_4762,U_4764] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4764)))
        | ~ sP366(U_4762,U_4764) )
    & ! [U_4762,U_4764] :
        ( sP367(U_4762,U_4764)
        | sP366(U_4762,U_4764)
        | ~ sP368(U_4762,U_4764) )
    & ! [U_4762,U_4764] :
        ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4762)))
        | ~ sP368(U_4762,U_4764) )
    & ! [U_4762,U_4764] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4764)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP365(U_4762,U_4764) )
    & ! [U_4762,U_4764] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4762)))
        | ~ sP365(U_4762,U_4764) )
    & ! [U_4761,U_4763] :
        ( U_4761 = U_4763
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4763)))
        | ~ sP363(U_4761,U_4763) )
    & ! [U_4761,U_4763] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4761) = 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_4763)))
        | ~ sP363(U_4761,U_4763) )
    & ! [U_4761,U_4763] :
        ( sP363(U_4761,U_4763)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4761)))
        | ~ sP364(U_4761,U_4763) )
    & ! [U_4761,U_4763] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4763)),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_4761)))
        | ~ sP364(U_4761,U_4763) )
    & ! [U_4762,U_4764] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4762) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4764)
        | sP368(U_4762,U_4764)
        | sP365(U_4762,U_4764) )
    & ! [U_4761,U_4763] :
        ( sP364(U_4761,U_4763)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4761) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4763) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP363,sP364,sP365,sP366,sP367,sP368])],[f_1311_3]) ).

cnf(f_1311_5,plain,
    ( sP364(U_4761,U_4763)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4761) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4763) ),
    inference(clausify,[status(thm)],[f_1311_4]) ).

cnf(f_1311_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4762) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4764)
    | sP368(U_4762,U_4764)
    | sP365(U_4762,U_4764) ),
    inference(clausify,[status(thm)],[f_1311_4]) ).

cnf(f_1311_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_4763)),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_4761)))
    | ~ sP364(U_4761,U_4763) ),
    inference(clausify,[status(thm)],[f_1311_4]) ).

cnf(f_1311_8,plain,
    ( sP363(U_4761,U_4763)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4761)))
    | ~ sP364(U_4761,U_4763) ),
    inference(clausify,[status(thm)],[f_1311_4]) ).

cnf(f_1311_9,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4761) = 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_4763)))
    | ~ sP363(U_4761,U_4763) ),
    inference(clausify,[status(thm)],[f_1311_4]) ).

cnf(f_1311_10,plain,
    ( U_4761 = U_4763
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4763)))
    | ~ sP363(U_4761,U_4763) ),
    inference(clausify,[status(thm)],[f_1311_4]) ).

cnf(f_1311_11,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4762)))
    | ~ sP365(U_4762,U_4764) ),
    inference(clausify,[status(thm)],[f_1311_4]) ).

cnf(f_1311_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_4764)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP365(U_4762,U_4764) ),
    inference(clausify,[status(thm)],[f_1311_4]) ).

cnf(f_1311_13,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4762)))
    | ~ sP368(U_4762,U_4764) ),
    inference(clausify,[status(thm)],[f_1311_4]) ).

cnf(f_1311_14,plain,
    ( sP367(U_4762,U_4764)
    | sP366(U_4762,U_4764)
    | ~ sP368(U_4762,U_4764) ),
    inference(clausify,[status(thm)],[f_1311_4]) ).

cnf(f_1311_15,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4764)))
    | ~ sP366(U_4762,U_4764) ),
    inference(clausify,[status(thm)],[f_1311_4]) ).

cnf(f_1311_16,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4762) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP366(U_4762,U_4764) ),
    inference(clausify,[status(thm)],[f_1311_4]) ).

cnf(f_1311_17,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4764)))
    | ~ sP367(U_4762,U_4764) ),
    inference(clausify,[status(thm)],[f_1311_4]) ).

cnf(f_1311_18,plain,
    ( U_4762 != U_4764
    | ~ sP367(U_4762,U_4764) ),
    inference(clausify,[status(thm)],[f_1311_4]) ).

fof(f_1312_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_1312_2,plain,
    ! [U_4767,U_4766,U_4765] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4765)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4766)),U_4767)) = 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_4765),U_4766))),U_4767)
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4766))) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4765)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4766)),U_4767)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4765)),U_4767)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4766))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4765))) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4765)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4766)),U_4767)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4766)),U_4767)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4765))) ) ),
    inference(variable_rename,[status(thm)],[f_1312_1]) ).

fof(f_1312_3,plain,
    ( ! [U_4773,U_4771,U_4769] :
        ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4769)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4771)),U_4773)) = 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_4769),U_4771))),U_4773)
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4771))) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4769)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4771)),U_4773)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4769)),U_4773)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4771))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4769))) )
    & ! [U_4772,U_4770,U_4768] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4768)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4770)),U_4772)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4770)),U_4772)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4768))) ) ),
    inference(miniscope,[status(thm)],[f_1312_2]) ).

fof(f_1312_4,plain,
    ( ! [U_4769,U_4773,U_4771] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4769)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4771)),U_4773)) = 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_4769),U_4771))),U_4773)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4771)))
        | ~ sP369(U_4769,U_4773,U_4771) )
    & ! [U_4769,U_4773,U_4771] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4769)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4771)),U_4773)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4769)),U_4773)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4771)))
        | ~ sP369(U_4769,U_4773,U_4771) )
    & ! [U_4769,U_4773,U_4771] :
        ( sP369(U_4769,U_4773,U_4771)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4769))) )
    & ! [U_4768,U_4770,U_4772] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4768)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4770)),U_4772)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4770)),U_4772)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4768))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP369])],[f_1312_3]) ).

cnf(f_1312_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4768)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4770)),U_4772)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4770)),U_4772)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4768))) ),
    inference(clausify,[status(thm)],[f_1312_4]) ).

cnf(f_1312_6,plain,
    ( sP369(U_4769,U_4773,U_4771)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4769))) ),
    inference(clausify,[status(thm)],[f_1312_4]) ).

cnf(f_1312_7,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4769)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4771)),U_4773)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4769)),U_4773)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4771)))
    | ~ sP369(U_4769,U_4773,U_4771) ),
    inference(clausify,[status(thm)],[f_1312_4]) ).

cnf(f_1312_8,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4769)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4771)),U_4773)) = 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_4769),U_4771))),U_4773)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4771)))
    | ~ sP369(U_4769,U_4773,U_4771) ),
    inference(clausify,[status(thm)],[f_1312_4]) ).

fof(f_1313_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_1313_2,plain,
    ! [U_4774] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4774)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4774)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4774))) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4774)) = 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_4774))) ) ),
    inference(variable_rename,[status(thm)],[f_1313_1]) ).

fof(f_1313_3,plain,
    ( ! [U_4776] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4776)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4776)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4776))) )
    & ! [U_4775] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4775)) = 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_4775))) ) ),
    inference(miniscope,[status(thm)],[f_1313_2]) ).

fof(f_1313_4,plain,
    ( ! [U_4776] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4776)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4776)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4776))) )
    & ! [U_4775] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4775)) = 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_4775))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1313_3]) ).

cnf(f_1313_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4775)) = 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_4775))) ),
    inference(clausify,[status(thm)],[f_1313_4]) ).

cnf(f_1313_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4776)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4776)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4776))) ),
    inference(clausify,[status(thm)],[f_1313_4]) ).

fof(f_1314_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_1314_2,plain,
    ! [U_4778,U_4777] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4777),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4778)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4777),U_4778)
          | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4778))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4777),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4778)) = c_Groups_Ozero__class_Ozero(U_4777)
          | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4778))) ) )
      | ~ class_Int_Onumber__ring(U_4777) ),
    inference(variable_rename,[status(thm)],[f_1314_1]) ).

fof(f_1314_3,plain,
    ( ! [U_4777,U_4778] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4777),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4778)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4777),U_4778)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4778)))
        | ~ sP370(U_4777,U_4778) )
    & ! [U_4777,U_4778] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4777),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4778)) = c_Groups_Ozero__class_Ozero(U_4777)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4778)))
        | ~ sP370(U_4777,U_4778) )
    & ! [U_4777,U_4778] :
        ( sP370(U_4777,U_4778)
        | ~ class_Int_Onumber__ring(U_4777) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP370])],[f_1314_2]) ).

cnf(f_1314_4,plain,
    ( sP370(U_4777,U_4778)
    | ~ class_Int_Onumber__ring(U_4777) ),
    inference(clausify,[status(thm)],[f_1314_3]) ).

cnf(f_1314_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4777),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4778)) = c_Groups_Ozero__class_Ozero(U_4777)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4778)))
    | ~ sP370(U_4777,U_4778) ),
    inference(clausify,[status(thm)],[f_1314_3]) ).

cnf(f_1314_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4777),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4778)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4777),U_4778)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4778)))
    | ~ sP370(U_4777,U_4778) ),
    inference(clausify,[status(thm)],[f_1314_3]) ).

fof(f_1315_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_1315_2,plain,
    ! [U_4780,U_4779] :
      ( ( 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_4779)),U_4780)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4779))),U_4780)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4779))) )
      & ( 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_4779)),U_4780)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4780)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4779))) ) ),
    inference(variable_rename,[status(thm)],[f_1315_1]) ).

fof(f_1315_3,plain,
    ( ! [U_4784,U_4782] :
        ( 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_4782)),U_4784)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4782))),U_4784)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4782))) )
    & ! [U_4783,U_4781] :
        ( 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_4781)),U_4783)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4783)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4781))) ) ),
    inference(miniscope,[status(thm)],[f_1315_2]) ).

fof(f_1315_4,plain,
    ( ! [U_4782,U_4784] :
        ( 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_4782)),U_4784)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4782))),U_4784)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4782))) )
    & ! [U_4781,U_4783] :
        ( 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_4781)),U_4783)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4783)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4781))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1315_3]) ).

cnf(f_1315_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_4781)),U_4783)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4783)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4781))) ),
    inference(clausify,[status(thm)],[f_1315_4]) ).

cnf(f_1315_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_4782)),U_4784)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4782))),U_4784)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4782))) ),
    inference(clausify,[status(thm)],[f_1315_4]) ).

fof(f_1316_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_1316_2,plain,
    ! [U_4786,U_4785] : c_Nitpick_Onat__lcm(U_4785,U_4786) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4785),U_4786)),c_Nitpick_Onat__gcd(U_4785,U_4786)),
    inference(variable_rename,[status(thm)],[f_1316_1]) ).

fof(f_1316_3,plain,
    ! [U_4785,U_4786] : c_Nitpick_Onat__lcm(U_4785,U_4786) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4785),U_4786)),c_Nitpick_Onat__gcd(U_4785,U_4786)),
    inference(definitional_conversion,[status(esa)],[f_1316_2]) ).

cnf(f_1316_4,plain,
    c_Nitpick_Onat__lcm(U_4785,U_4786) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4785),U_4786)),c_Nitpick_Onat__gcd(U_4785,U_4786)),
    inference(clausify,[status(thm)],[f_1316_3]) ).

fof(f_1317_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_1317_2,plain,
    ! [U_4787] :
      ( ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4787)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4787))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4787))) )
      & ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4787)) = 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_4787))) ) ),
    inference(variable_rename,[status(thm)],[f_1317_1]) ).

fof(f_1317_3,plain,
    ( ! [U_4789] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4789)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4789))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4789))) )
    & ! [U_4788] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4788)) = 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_4788))) ) ),
    inference(miniscope,[status(thm)],[f_1317_2]) ).

fof(f_1317_4,plain,
    ( ! [U_4789] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4789)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4789))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4789))) )
    & ! [U_4788] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4788)) = 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_4788))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1317_3]) ).

cnf(f_1317_5,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4788)) = 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_4788))) ),
    inference(clausify,[status(thm)],[f_1317_4]) ).

cnf(f_1317_6,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4789)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4789))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4789))) ),
    inference(clausify,[status(thm)],[f_1317_4]) ).

fof(f_1318_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_1318_2,plain,
    ! [U_4790] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_4790) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4790),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_4790)) ),
    inference(variable_rename,[status(thm)],[f_1318_1]) ).

fof(f_1318_3,plain,
    ! [U_4790] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_4790) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4790),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_4790)) ),
    inference(definitional_conversion,[status(esa)],[f_1318_2]) ).

cnf(f_1318_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_4790) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4790),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_4790)) ),
    inference(clausify,[status(thm)],[f_1318_3]) ).

fof(f_1319_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_1319_2,plain,
    ! [U_4792,U_4791] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4791),U_4792) = 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_4791),U_4792)),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_4791)) ),
    inference(variable_rename,[status(thm)],[f_1319_1]) ).

fof(f_1319_3,plain,
    ! [U_4791,U_4792] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4791),U_4792) = 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_4791),U_4792)),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_4791)) ),
    inference(definitional_conversion,[status(esa)],[f_1319_2]) ).

cnf(f_1319_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4791),U_4792) = 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_4791),U_4792)),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_4791)) ),
    inference(clausify,[status(thm)],[f_1319_3]) ).

fof(f_1320_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_1320_2,plain,
    ! [U_4797,U_4796,U_4795] :
      ( ? [U_4794] :
          ( hAPP(U_4796,U_4794) = U_4797
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4794),U_4795)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4797),hAPP(U_4796,U_4795)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4796,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4797))
      | ? [U_4793] :
          ( ~ 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_4796,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4793),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4796,U_4793)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4793),U_4795)) ) ),
    inference(variable_rename,[status(thm)],[f_1320_1]) ).

fof(f_1320_3,plain,
    ! [U_4797,U_4796,U_4795] :
      ( ? [U_4794] :
          ( hAPP(U_4796,U_4794) = U_4797
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4794),U_4795)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4797),hAPP(U_4796,U_4795)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4796,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4797))
      | ( ~ 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_4796,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK89(U_4797,U_4796,U_4795)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4796,sK89(U_4797,U_4796,U_4795))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK89(U_4797,U_4796,U_4795)),U_4795)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_4793,sK89(U_4797,U_4796,U_4795))],[f_1320_2]) ).

fof(f_1320_4,plain,
    ! [U_4797,U_4796,U_4795] :
      ( ( hAPP(U_4796,sK90(U_4797,U_4796,U_4795)) = U_4797
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK90(U_4797,U_4796,U_4795)),U_4795)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4797),hAPP(U_4796,U_4795)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4796,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4797))
      | ( ~ 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_4796,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK89(U_4797,U_4796,U_4795)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4796,sK89(U_4797,U_4796,U_4795))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK89(U_4797,U_4796,U_4795)),U_4795)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_4794,sK90(U_4797,U_4796,U_4795))],[f_1320_3]) ).

fof(f_1320_5,plain,
    ( ! [U_4795,U_4796,U_4797] :
        ( hAPP(U_4796,sK90(U_4797,U_4796,U_4795)) = U_4797
        | ~ sP372(U_4795,U_4796,U_4797) )
    & ! [U_4795,U_4796,U_4797] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK90(U_4797,U_4796,U_4795)),U_4795))
        | ~ sP372(U_4795,U_4796,U_4797) )
    & ! [U_4795,U_4796,U_4797] :
        ( ~ 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_4796,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK89(U_4797,U_4796,U_4795)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4796,sK89(U_4797,U_4796,U_4795))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ sP371(U_4795,U_4796,U_4797) )
    & ! [U_4795,U_4796,U_4797] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK89(U_4797,U_4796,U_4795)),U_4795))
        | ~ sP371(U_4795,U_4796,U_4797) )
    & ! [U_4795,U_4796,U_4797] :
        ( sP372(U_4795,U_4796,U_4797)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4797),hAPP(U_4796,U_4795)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4796,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4797))
        | sP371(U_4795,U_4796,U_4797) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP371,sP372])],[f_1320_4]) ).

cnf(f_1320_6,plain,
    ( sP372(U_4795,U_4796,U_4797)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4797),hAPP(U_4796,U_4795)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4796,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4797))
    | sP371(U_4795,U_4796,U_4797) ),
    inference(clausify,[status(thm)],[f_1320_5]) ).

cnf(f_1320_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK89(U_4797,U_4796,U_4795)),U_4795))
    | ~ sP371(U_4795,U_4796,U_4797) ),
    inference(clausify,[status(thm)],[f_1320_5]) ).

cnf(f_1320_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_4796,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK89(U_4797,U_4796,U_4795)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4796,sK89(U_4797,U_4796,U_4795))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ sP371(U_4795,U_4796,U_4797) ),
    inference(clausify,[status(thm)],[f_1320_5]) ).

cnf(f_1320_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK90(U_4797,U_4796,U_4795)),U_4795))
    | ~ sP372(U_4795,U_4796,U_4797) ),
    inference(clausify,[status(thm)],[f_1320_5]) ).

cnf(f_1320_10,plain,
    ( hAPP(U_4796,sK90(U_4797,U_4796,U_4795)) = U_4797
    | ~ sP372(U_4795,U_4796,U_4797) ),
    inference(clausify,[status(thm)],[f_1320_5]) ).

fof(f_1321_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_1321_2,plain,
    ! [U_4802,U_4801,U_4800] :
      ( ? [U_4799] :
          ( hAPP(U_4801,U_4799) = U_4802
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4799),U_4800)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4802),hAPP(U_4801,U_4800)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4801,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4802))
      | ? [U_4798] :
          ( ~ 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_4801,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4798),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4801,U_4798)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4798),U_4800)) ) ),
    inference(variable_rename,[status(thm)],[f_1321_1]) ).

fof(f_1321_3,plain,
    ! [U_4802,U_4801,U_4800] :
      ( ? [U_4799] :
          ( hAPP(U_4801,U_4799) = U_4802
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4799),U_4800)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4802),hAPP(U_4801,U_4800)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4801,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4802))
      | ( ~ 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_4801,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK91(U_4802,U_4801,U_4800)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4801,sK91(U_4802,U_4801,U_4800))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK91(U_4802,U_4801,U_4800)),U_4800)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_4798,sK91(U_4802,U_4801,U_4800))],[f_1321_2]) ).

fof(f_1321_4,plain,
    ! [U_4802,U_4801,U_4800] :
      ( ( hAPP(U_4801,sK92(U_4802,U_4801,U_4800)) = U_4802
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK92(U_4802,U_4801,U_4800)),U_4800)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4802),hAPP(U_4801,U_4800)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4801,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4802))
      | ( ~ 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_4801,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK91(U_4802,U_4801,U_4800)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4801,sK91(U_4802,U_4801,U_4800))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK91(U_4802,U_4801,U_4800)),U_4800)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_4799,sK92(U_4802,U_4801,U_4800))],[f_1321_3]) ).

fof(f_1321_5,plain,
    ( ! [U_4801,U_4800,U_4802] :
        ( hAPP(U_4801,sK92(U_4802,U_4801,U_4800)) = U_4802
        | ~ sP374(U_4801,U_4800,U_4802) )
    & ! [U_4801,U_4800,U_4802] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK92(U_4802,U_4801,U_4800)),U_4800))
        | ~ sP374(U_4801,U_4800,U_4802) )
    & ! [U_4801,U_4800,U_4802] :
        ( ~ 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_4801,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK91(U_4802,U_4801,U_4800)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4801,sK91(U_4802,U_4801,U_4800))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ sP373(U_4801,U_4800,U_4802) )
    & ! [U_4801,U_4800,U_4802] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK91(U_4802,U_4801,U_4800)),U_4800))
        | ~ sP373(U_4801,U_4800,U_4802) )
    & ! [U_4801,U_4800,U_4802] :
        ( sP374(U_4801,U_4800,U_4802)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4802),hAPP(U_4801,U_4800)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4801,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4802))
        | sP373(U_4801,U_4800,U_4802) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP373,sP374])],[f_1321_4]) ).

cnf(f_1321_6,plain,
    ( sP374(U_4801,U_4800,U_4802)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4802),hAPP(U_4801,U_4800)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4801,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4802))
    | sP373(U_4801,U_4800,U_4802) ),
    inference(clausify,[status(thm)],[f_1321_5]) ).

cnf(f_1321_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK91(U_4802,U_4801,U_4800)),U_4800))
    | ~ sP373(U_4801,U_4800,U_4802) ),
    inference(clausify,[status(thm)],[f_1321_5]) ).

cnf(f_1321_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_4801,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK91(U_4802,U_4801,U_4800)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4801,sK91(U_4802,U_4801,U_4800))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ sP373(U_4801,U_4800,U_4802) ),
    inference(clausify,[status(thm)],[f_1321_5]) ).

cnf(f_1321_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK92(U_4802,U_4801,U_4800)),U_4800))
    | ~ sP374(U_4801,U_4800,U_4802) ),
    inference(clausify,[status(thm)],[f_1321_5]) ).

cnf(f_1321_10,plain,
    ( hAPP(U_4801,sK92(U_4802,U_4801,U_4800)) = U_4802
    | ~ sP374(U_4801,U_4800,U_4802) ),
    inference(clausify,[status(thm)],[f_1321_5]) ).

fof(f_1322_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_1322_2,plain,
    ! [U_4803] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4803),c_Int_OMin) = c_Int_Osucc(U_4803),
    inference(variable_rename,[status(thm)],[f_1322_1]) ).

fof(f_1322_3,plain,
    ! [U_4803] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4803),c_Int_OMin) = c_Int_Osucc(U_4803),
    inference(definitional_conversion,[status(esa)],[f_1322_2]) ).

cnf(f_1322_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4803),c_Int_OMin) = c_Int_Osucc(U_4803),
    inference(clausify,[status(thm)],[f_1322_3]) ).

fof(f_1323_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_1323_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_1323_1]) ).

cnf(f_1323_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_1323_2]) ).

fof(f_1324_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_1324_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_1324_1]) ).

cnf(f_1324_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_1324_2]) ).

fof(f_1325_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_1325_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_1325_1]) ).

cnf(f_1325_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_1325_2]) ).

fof(f_1326_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_1326_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_1326_1]) ).

cnf(f_1326_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_1326_2]) ).

fof(f_1327_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_1327_2,plain,
    ! [U_4804] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_4804) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4804),
    inference(variable_rename,[status(thm)],[f_1327_1]) ).

fof(f_1327_3,plain,
    ! [U_4804] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_4804) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4804),
    inference(definitional_conversion,[status(esa)],[f_1327_2]) ).

cnf(f_1327_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_4804) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4804),
    inference(clausify,[status(thm)],[f_1327_3]) ).

fof(f_1328_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_1328_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_1328_1]) ).

cnf(f_1328_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_1328_2]) ).

fof(f_1329_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_1329_2,plain,
    ! [U_4806,U_4805] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4805),U_4806),hAPP(c_Int_Onumber__class_Onumber__of(U_4805),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4805),U_4806)
      | ~ class_Int_Onumber__ring(U_4805) ),
    inference(variable_rename,[status(thm)],[f_1329_1]) ).

fof(f_1329_3,plain,
    ! [U_4805,U_4806] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4805),U_4806),hAPP(c_Int_Onumber__class_Onumber__of(U_4805),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4805),U_4806)
      | ~ class_Int_Onumber__ring(U_4805) ),
    inference(definitional_conversion,[status(esa)],[f_1329_2]) ).

cnf(f_1329_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4805),U_4806),hAPP(c_Int_Onumber__class_Onumber__of(U_4805),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4805),U_4806)
    | ~ class_Int_Onumber__ring(U_4805) ),
    inference(clausify,[status(thm)],[f_1329_3]) ).

fof(f_1330_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_1330_2,plain,
    ! [U_4808,U_4807] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4807),hAPP(c_Int_Onumber__class_Onumber__of(U_4807),c_Int_OMin)),U_4808) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4807),U_4808)
      | ~ class_Int_Onumber__ring(U_4807) ),
    inference(variable_rename,[status(thm)],[f_1330_1]) ).

fof(f_1330_3,plain,
    ! [U_4807,U_4808] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4807),hAPP(c_Int_Onumber__class_Onumber__of(U_4807),c_Int_OMin)),U_4808) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4807),U_4808)
      | ~ class_Int_Onumber__ring(U_4807) ),
    inference(definitional_conversion,[status(esa)],[f_1330_2]) ).

cnf(f_1330_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4807),hAPP(c_Int_Onumber__class_Onumber__of(U_4807),c_Int_OMin)),U_4808) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4807),U_4808)
    | ~ class_Int_Onumber__ring(U_4807) ),
    inference(clausify,[status(thm)],[f_1330_3]) ).

fof(f_1331_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_1331_2,plain,
    ! [U_4809] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4809),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4809),c_Groups_Oone__class_Oone(U_4809))
      | ~ class_Int_Onumber__ring(U_4809) ),
    inference(variable_rename,[status(thm)],[f_1331_1]) ).

fof(f_1331_3,plain,
    ! [U_4809] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4809),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4809),c_Groups_Oone__class_Oone(U_4809))
      | ~ class_Int_Onumber__ring(U_4809) ),
    inference(definitional_conversion,[status(esa)],[f_1331_2]) ).

cnf(f_1331_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4809),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4809),c_Groups_Oone__class_Oone(U_4809))
    | ~ class_Int_Onumber__ring(U_4809) ),
    inference(clausify,[status(thm)],[f_1331_3]) ).

fof(f_1332_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_1332_2,plain,
    ! [U_4810] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4810),c_Groups_Oone__class_Oone(U_4810)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4810),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_4810) ),
    inference(variable_rename,[status(thm)],[f_1332_1]) ).

fof(f_1332_3,plain,
    ! [U_4810] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4810),c_Groups_Oone__class_Oone(U_4810)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4810),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_4810) ),
    inference(definitional_conversion,[status(esa)],[f_1332_2]) ).

cnf(f_1332_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4810),c_Groups_Oone__class_Oone(U_4810)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4810),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_4810) ),
    inference(clausify,[status(thm)],[f_1332_3]) ).

fof(f_1333_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_1333_2,plain,
    ! [U_4811] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4811),hAPP(c_Int_Onumber__class_Onumber__of(U_4811),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_4811)
      | ~ class_Rings_Olinordered__idom(U_4811)
      | ~ class_Int_Onumber__ring(U_4811) ),
    inference(variable_rename,[status(thm)],[f_1333_1]) ).

fof(f_1333_3,plain,
    ! [U_4811] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4811),hAPP(c_Int_Onumber__class_Onumber__of(U_4811),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_4811)
      | ~ class_Rings_Olinordered__idom(U_4811)
      | ~ class_Int_Onumber__ring(U_4811) ),
    inference(definitional_conversion,[status(esa)],[f_1333_2]) ).

cnf(f_1333_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4811),hAPP(c_Int_Onumber__class_Onumber__of(U_4811),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_4811)
    | ~ class_Rings_Olinordered__idom(U_4811)
    | ~ class_Int_Onumber__ring(U_4811) ),
    inference(clausify,[status(thm)],[f_1333_3]) ).

fof(f_1334_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_1334_2,plain,
    ! [U_4812] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4812,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_1334_1]) ).

fof(f_1334_3,plain,
    ! [U_4812] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4812,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_1334_2]) ).

cnf(f_1334_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4812,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_1334_3]) ).

fof(f_1335_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_1335_2,plain,
    ! [U_4814,U_4813] :
      ( U_4813 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | U_4813 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4813),U_4814) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1335_1]) ).

fof(f_1335_3,plain,
    ! [U_4813,U_4814] :
      ( U_4813 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | U_4813 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4813),U_4814) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_1335_2]) ).

cnf(f_1335_4,plain,
    ( U_4813 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_4813 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4813),U_4814) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1335_3]) ).

fof(f_1336_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_1336_2,plain,
    ! [U_4816,U_4815] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4815),U_4816) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ( ( U_4816 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
            | U_4815 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
          & ( U_4816 != c_Groups_Oone__class_Oone(tc_Int_Oint)
            | U_4815 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
      & ( ( U_4816 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & U_4815 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( U_4816 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & U_4815 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4815),U_4816) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1336_1]) ).

fof(f_1336_3,plain,
    ( ! [U_4820,U_4818] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4818),U_4820) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ( ( U_4820 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
            | U_4818 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
          & ( U_4820 != c_Groups_Oone__class_Oone(tc_Int_Oint)
            | U_4818 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
    & ! [U_4819,U_4817] :
        ( ( U_4819 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & U_4817 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( U_4819 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & U_4817 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4817),U_4819) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1336_2]) ).

fof(f_1336_4,plain,
    ( ! [U_4818,U_4820] :
        ( U_4820 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | U_4818 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | ~ sP377(U_4818,U_4820) )
    & ! [U_4818,U_4820] :
        ( U_4820 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | U_4818 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP377(U_4818,U_4820) )
    & ! [U_4817,U_4819] :
        ( U_4819 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | ~ sP376(U_4817,U_4819) )
    & ! [U_4817,U_4819] :
        ( U_4817 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | ~ sP376(U_4817,U_4819) )
    & ! [U_4817,U_4819] :
        ( U_4819 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP375(U_4817,U_4819) )
    & ! [U_4817,U_4819] :
        ( U_4817 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP375(U_4817,U_4819) )
    & ! [U_4818,U_4820] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4818),U_4820) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | sP377(U_4818,U_4820) )
    & ! [U_4817,U_4819] :
        ( sP376(U_4817,U_4819)
        | sP375(U_4817,U_4819)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4817),U_4819) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP375,sP376,sP377])],[f_1336_3]) ).

cnf(f_1336_5,plain,
    ( sP376(U_4817,U_4819)
    | sP375(U_4817,U_4819)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4817),U_4819) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1336_4]) ).

cnf(f_1336_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4818),U_4820) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | sP377(U_4818,U_4820) ),
    inference(clausify,[status(thm)],[f_1336_4]) ).

cnf(f_1336_7,plain,
    ( U_4817 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP375(U_4817,U_4819) ),
    inference(clausify,[status(thm)],[f_1336_4]) ).

cnf(f_1336_8,plain,
    ( U_4819 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP375(U_4817,U_4819) ),
    inference(clausify,[status(thm)],[f_1336_4]) ).

cnf(f_1336_9,plain,
    ( U_4817 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | ~ sP376(U_4817,U_4819) ),
    inference(clausify,[status(thm)],[f_1336_4]) ).

cnf(f_1336_10,plain,
    ( U_4819 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | ~ sP376(U_4817,U_4819) ),
    inference(clausify,[status(thm)],[f_1336_4]) ).

cnf(f_1336_11,plain,
    ( U_4820 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_4818 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP377(U_4818,U_4820) ),
    inference(clausify,[status(thm)],[f_1336_4]) ).

cnf(f_1336_12,plain,
    ( U_4820 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_4818 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | ~ sP377(U_4818,U_4820) ),
    inference(clausify,[status(thm)],[f_1336_4]) ).

fof(f_1337_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_1337_2,plain,
    ! [U_4821] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_4821),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4821),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_4821) ),
    inference(variable_rename,[status(thm)],[f_1337_1]) ).

fof(f_1337_3,plain,
    ! [U_4821] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_4821),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4821),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_4821) ),
    inference(definitional_conversion,[status(esa)],[f_1337_2]) ).

cnf(f_1337_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_4821),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4821),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_4821) ),
    inference(clausify,[status(thm)],[f_1337_3]) ).

fof(f_1338_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_1338_2,plain,
    ! [U_4822] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4822),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4822),
    inference(variable_rename,[status(thm)],[f_1338_1]) ).

fof(f_1338_3,plain,
    ! [U_4822] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4822),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4822),
    inference(definitional_conversion,[status(esa)],[f_1338_2]) ).

cnf(f_1338_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4822),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4822),
    inference(clausify,[status(thm)],[f_1338_3]) ).

fof(f_1339_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_1339_2,plain,
    ! [U_4823] : c_Int_Osucc(U_4823) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4823),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_1339_1]) ).

fof(f_1339_3,plain,
    ! [U_4823] : c_Int_Osucc(U_4823) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4823),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_1339_2]) ).

cnf(f_1339_4,plain,
    c_Int_Osucc(U_4823) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4823),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1339_3]) ).

fof(f_1340_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_1340_2,plain,
    ! [U_4825,U_4824] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4824),hAPP(hAPP(c_Power_Opower__class_Opower(U_4824),hAPP(c_Int_Onumber__class_Onumber__of(U_4824),c_Int_OMin)),U_4825)) = c_Groups_Oone__class_Oone(U_4824)
      | ~ class_Rings_Olinordered__idom(U_4824)
      | ~ class_Int_Onumber__ring(U_4824) ),
    inference(variable_rename,[status(thm)],[f_1340_1]) ).

fof(f_1340_3,plain,
    ! [U_4824,U_4825] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4824),hAPP(hAPP(c_Power_Opower__class_Opower(U_4824),hAPP(c_Int_Onumber__class_Onumber__of(U_4824),c_Int_OMin)),U_4825)) = c_Groups_Oone__class_Oone(U_4824)
      | ~ class_Rings_Olinordered__idom(U_4824)
      | ~ class_Int_Onumber__ring(U_4824) ),
    inference(definitional_conversion,[status(esa)],[f_1340_2]) ).

cnf(f_1340_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4824),hAPP(hAPP(c_Power_Opower__class_Opower(U_4824),hAPP(c_Int_Onumber__class_Onumber__of(U_4824),c_Int_OMin)),U_4825)) = c_Groups_Oone__class_Oone(U_4824)
    | ~ class_Rings_Olinordered__idom(U_4824)
    | ~ class_Int_Onumber__ring(U_4824) ),
    inference(clausify,[status(thm)],[f_1340_3]) ).

fof(f_1341_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_1341_2,plain,
    ! [U_4826] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_4826) = 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_4826)) ),
    inference(variable_rename,[status(thm)],[f_1341_1]) ).

fof(f_1341_3,plain,
    ! [U_4826] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_4826) = 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_4826)) ),
    inference(definitional_conversion,[status(esa)],[f_1341_2]) ).

cnf(f_1341_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_4826) = 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_4826)) ),
    inference(clausify,[status(thm)],[f_1341_3]) ).

fof(f_1342_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_1342_2,plain,
    ! [U_4828,U_4827] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4827),c_Int_Osucc(U_4828)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4827),c_Groups_Oone__class_Oone(U_4827)),hAPP(c_Int_Onumber__class_Onumber__of(U_4827),U_4828))
      | ~ class_Int_Onumber__ring(U_4827) ),
    inference(variable_rename,[status(thm)],[f_1342_1]) ).

fof(f_1342_3,plain,
    ! [U_4827,U_4828] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4827),c_Int_Osucc(U_4828)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4827),c_Groups_Oone__class_Oone(U_4827)),hAPP(c_Int_Onumber__class_Onumber__of(U_4827),U_4828))
      | ~ class_Int_Onumber__ring(U_4827) ),
    inference(definitional_conversion,[status(esa)],[f_1342_2]) ).

cnf(f_1342_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4827),c_Int_Osucc(U_4828)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4827),c_Groups_Oone__class_Oone(U_4827)),hAPP(c_Int_Onumber__class_Onumber__of(U_4827),U_4828))
    | ~ class_Int_Onumber__ring(U_4827) ),
    inference(clausify,[status(thm)],[f_1342_3]) ).

fof(f_1343_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_1343_2,plain,
    ! [U_4830,U_4829] :
      ( ( c_Nitpick_Onat__gcd(U_4830,U_4829) = c_Nitpick_Onat__gcd(U_4829,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4830,U_4829))
        | U_4829 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Nitpick_Onat__gcd(U_4830,U_4829) = U_4830
        | U_4829 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1343_1]) ).

fof(f_1343_3,plain,
    ( ! [U_4834,U_4832] :
        ( c_Nitpick_Onat__gcd(U_4834,U_4832) = c_Nitpick_Onat__gcd(U_4832,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4834,U_4832))
        | U_4832 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4833,U_4831] :
        ( c_Nitpick_Onat__gcd(U_4833,U_4831) = U_4833
        | U_4831 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1343_2]) ).

fof(f_1343_4,plain,
    ( ! [U_4832,U_4834] :
        ( c_Nitpick_Onat__gcd(U_4834,U_4832) = c_Nitpick_Onat__gcd(U_4832,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4834,U_4832))
        | U_4832 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4833,U_4831] :
        ( c_Nitpick_Onat__gcd(U_4833,U_4831) = U_4833
        | U_4831 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1343_3]) ).

cnf(f_1343_5,plain,
    ( c_Nitpick_Onat__gcd(U_4833,U_4831) = U_4833
    | U_4831 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1343_4]) ).

cnf(f_1343_6,plain,
    ( c_Nitpick_Onat__gcd(U_4834,U_4832) = c_Nitpick_Onat__gcd(U_4832,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4834,U_4832))
    | U_4832 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1343_4]) ).

fof(f_1344_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_1344_2,plain,
    ! [U_4836,U_4835] : hAPP(hAPP(c_Nitpick_Oint__gcd,U_4835),U_4836) = 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_4835)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4836)))),
    inference(variable_rename,[status(thm)],[f_1344_1]) ).

fof(f_1344_3,plain,
    ! [U_4836,U_4835] : hAPP(hAPP(c_Nitpick_Oint__gcd,U_4835),U_4836) = 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_4835)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4836)))),
    inference(definitional_conversion,[status(esa)],[f_1344_2]) ).

cnf(f_1344_4,plain,
    hAPP(hAPP(c_Nitpick_Oint__gcd,U_4835),U_4836) = 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_4835)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4836)))),
    inference(clausify,[status(thm)],[f_1344_3]) ).

fof(f_1345_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_1345_2,plain,
    ! [U_4837] :
      ( ( 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_4837)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4837))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4837),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_4837)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4837),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1345_1]) ).

fof(f_1345_3,plain,
    ( ! [U_4839] :
        ( 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_4839)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4839))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4839),c_Int_OPls)) )
    & ! [U_4838] :
        ( 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_4838)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4838),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1345_2]) ).

fof(f_1345_4,plain,
    ( ! [U_4839] :
        ( 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_4839)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4839))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4839),c_Int_OPls)) )
    & ! [U_4838] :
        ( 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_4838)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4838),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1345_3]) ).

cnf(f_1345_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_4838)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4838),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1345_4]) ).

cnf(f_1345_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_4839)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4839))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4839),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1345_4]) ).

fof(f_1346_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_1346_2,plain,
    ! [U_4840] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4840)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4840))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4840),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4840)),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_4840),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1346_1]) ).

fof(f_1346_3,plain,
    ( ! [U_4842] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4842)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4842))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4842),c_Int_OPls)) )
    & ! [U_4841] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4841)),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_4841),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1346_2]) ).

fof(f_1346_4,plain,
    ( ! [U_4842] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4842)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4842))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4842),c_Int_OPls)) )
    & ! [U_4841] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4841)),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_4841),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1346_3]) ).

cnf(f_1346_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4841)),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_4841),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1346_4]) ).

cnf(f_1346_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4842)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4842))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4842),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1346_4]) ).

fof(f_1347_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_1347_2,plain,
    ! [U_4845,U_4844,U_4843] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4843),U_4844) = hAPP(c_Int_Onumber__class_Onumber__of(U_4843),U_4845)
          | ~ c_Int_Oiszero(U_4843,hAPP(c_Int_Onumber__class_Onumber__of(U_4843),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4844),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4845)))) )
        & ( c_Int_Oiszero(U_4843,hAPP(c_Int_Onumber__class_Onumber__of(U_4843),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4844),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4845))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_4843),U_4844) != hAPP(c_Int_Onumber__class_Onumber__of(U_4843),U_4845) ) )
      | ~ class_Int_Onumber__ring(U_4843) ),
    inference(variable_rename,[status(thm)],[f_1347_1]) ).

fof(f_1347_3,plain,
    ( ! [U_4843,U_4844,U_4845] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_4843),U_4844) = hAPP(c_Int_Onumber__class_Onumber__of(U_4843),U_4845)
        | ~ c_Int_Oiszero(U_4843,hAPP(c_Int_Onumber__class_Onumber__of(U_4843),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4844),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4845))))
        | ~ sP378(U_4843,U_4844,U_4845) )
    & ! [U_4843,U_4844,U_4845] :
        ( c_Int_Oiszero(U_4843,hAPP(c_Int_Onumber__class_Onumber__of(U_4843),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4844),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4845))))
        | hAPP(c_Int_Onumber__class_Onumber__of(U_4843),U_4844) != hAPP(c_Int_Onumber__class_Onumber__of(U_4843),U_4845)
        | ~ sP378(U_4843,U_4844,U_4845) )
    & ! [U_4843,U_4844,U_4845] :
        ( sP378(U_4843,U_4844,U_4845)
        | ~ class_Int_Onumber__ring(U_4843) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP378])],[f_1347_2]) ).

cnf(f_1347_4,plain,
    ( sP378(U_4843,U_4844,U_4845)
    | ~ class_Int_Onumber__ring(U_4843) ),
    inference(clausify,[status(thm)],[f_1347_3]) ).

cnf(f_1347_5,plain,
    ( c_Int_Oiszero(U_4843,hAPP(c_Int_Onumber__class_Onumber__of(U_4843),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4844),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4845))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4843),U_4844) != hAPP(c_Int_Onumber__class_Onumber__of(U_4843),U_4845)
    | ~ sP378(U_4843,U_4844,U_4845) ),
    inference(clausify,[status(thm)],[f_1347_3]) ).

cnf(f_1347_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4843),U_4844) = hAPP(c_Int_Onumber__class_Onumber__of(U_4843),U_4845)
    | ~ c_Int_Oiszero(U_4843,hAPP(c_Int_Onumber__class_Onumber__of(U_4843),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4844),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4845))))
    | ~ sP378(U_4843,U_4844,U_4845) ),
    inference(clausify,[status(thm)],[f_1347_3]) ).

fof(f_1348_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_1348_2,plain,
    ! [U_4846] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4846))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4846) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4846) = 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_4846)))) ) ),
    inference(variable_rename,[status(thm)],[f_1348_1]) ).

fof(f_1348_3,plain,
    ( ! [U_4848] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4848))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4848) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4847] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4847) = 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_4847)))) ) ),
    inference(miniscope,[status(thm)],[f_1348_2]) ).

fof(f_1348_4,plain,
    ( ! [U_4848] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4848))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4848) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4847] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4847) = 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_4847)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1348_3]) ).

cnf(f_1348_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4847) = 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_4847)))) ),
    inference(clausify,[status(thm)],[f_1348_4]) ).

cnf(f_1348_6,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4848))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4848) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1348_4]) ).

fof(f_1349_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_1349_2,plain,
    ! [U_4851,U_4850,U_4849] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4849)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4850)),U_4851)) = 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_4849),U_4850))),U_4851)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4849),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4849)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4850)),U_4851)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4849),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1349_1]) ).

fof(f_1349_3,plain,
    ( ! [U_4857,U_4855,U_4853] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4853)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4855)),U_4857)) = 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_4853),U_4855))),U_4857)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4853),c_Int_OPls)) )
    & ! [U_4856,U_4854,U_4852] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4852)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4854)),U_4856)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4852),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1349_2]) ).

fof(f_1349_4,plain,
    ( ! [U_4853,U_4855,U_4857] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4853)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4855)),U_4857)) = 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_4853),U_4855))),U_4857)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4853),c_Int_OPls)) )
    & ! [U_4852,U_4856,U_4854] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4852)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4854)),U_4856)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4852),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1349_3]) ).

cnf(f_1349_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4852)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4854)),U_4856)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4852),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1349_4]) ).

cnf(f_1349_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4853)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4855)),U_4857)) = 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_4853),U_4855))),U_4857)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4853),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1349_4]) ).

fof(f_1350_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_1350_2,plain,
    ! [U_4859,U_4858] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4858)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4859)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4858),U_4859))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4858),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4858)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4859)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4858),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1350_1]) ).

fof(f_1350_3,plain,
    ( ! [U_4863,U_4861] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4861)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4863)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4861),U_4863))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4861),c_Int_OPls)) )
    & ! [U_4862,U_4860] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4860)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4862)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4860),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1350_2]) ).

fof(f_1350_4,plain,
    ( ! [U_4863,U_4861] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4861)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4863)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4861),U_4863))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4861),c_Int_OPls)) )
    & ! [U_4862,U_4860] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4860)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4862)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4860),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1350_3]) ).

cnf(f_1350_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4860)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4862)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4860),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1350_4]) ).

cnf(f_1350_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4861)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4863)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4861),U_4863))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4861),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1350_4]) ).

fof(f_1351_1,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_pred__Pls]) ).

fof(f_1351_2,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(definitional_conversion,[status(esa)],[f_1351_1]) ).

cnf(f_1351_3,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(clausify,[status(thm)],[f_1351_2]) ).

fof(f_1352_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_1352_2,plain,
    ! [U_4864] :
      ( c_Int_Oiszero(U_4864,hAPP(c_Int_Onumber__class_Onumber__of(U_4864),c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_4864) ),
    inference(variable_rename,[status(thm)],[f_1352_1]) ).

fof(f_1352_3,plain,
    ! [U_4864] :
      ( c_Int_Oiszero(U_4864,hAPP(c_Int_Onumber__class_Onumber__of(U_4864),c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_4864) ),
    inference(definitional_conversion,[status(esa)],[f_1352_2]) ).

cnf(f_1352_4,plain,
    ( c_Int_Oiszero(U_4864,hAPP(c_Int_Onumber__class_Onumber__of(U_4864),c_Int_OPls))
    | ~ class_Int_Onumber__ring(U_4864) ),
    inference(clausify,[status(thm)],[f_1352_3]) ).

fof(f_1353_1,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_Pls__def]) ).

fof(f_1353_2,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1353_1]) ).

cnf(f_1353_3,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1353_2]) ).

fof(f_1354_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_1354_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_1354_1]) ).

cnf(f_1354_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_1354_2]) ).

fof(f_1355_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_1355_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_1355_1]) ).

cnf(f_1355_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_1355_2]) ).

fof(f_1356_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_1356_2,plain,
    ! [U_4865] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_4865) = U_4865,
    inference(variable_rename,[status(thm)],[f_1356_1]) ).

fof(f_1356_3,plain,
    ! [U_4865] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_4865) = U_4865,
    inference(definitional_conversion,[status(esa)],[f_1356_2]) ).

cnf(f_1356_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_4865) = U_4865,
    inference(clausify,[status(thm)],[f_1356_3]) ).

fof(f_1357_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_1357_2,plain,
    ! [U_4866] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4866),c_Int_OPls) = U_4866,
    inference(variable_rename,[status(thm)],[f_1357_1]) ).

fof(f_1357_3,plain,
    ! [U_4866] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4866),c_Int_OPls) = U_4866,
    inference(definitional_conversion,[status(esa)],[f_1357_2]) ).

cnf(f_1357_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4866),c_Int_OPls) = U_4866,
    inference(clausify,[status(thm)],[f_1357_3]) ).

fof(f_1358_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_1358_2,plain,
    ! [U_4867] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_4867) = c_Int_OPls,
    inference(variable_rename,[status(thm)],[f_1358_1]) ).

fof(f_1358_3,plain,
    ! [U_4867] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_4867) = c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1358_2]) ).

cnf(f_1358_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_4867) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1358_3]) ).

fof(f_1359_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_1359_2,plain,
    ! [U_4868] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4868),c_Int_OPls) = U_4868,
    inference(variable_rename,[status(thm)],[f_1359_1]) ).

fof(f_1359_3,plain,
    ! [U_4868] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4868),c_Int_OPls) = U_4868,
    inference(definitional_conversion,[status(esa)],[f_1359_2]) ).

cnf(f_1359_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4868),c_Int_OPls) = U_4868,
    inference(clausify,[status(thm)],[f_1359_3]) ).

fof(f_1360_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_1360_2,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1360_1]) ).

cnf(f_1360_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1360_2]) ).

fof(f_1361_1,plain,
    c_Int_OPls != c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I37_J]) ).

fof(f_1361_2,plain,
    c_Int_OPls != c_Int_OMin,
    inference(definitional_conversion,[status(esa)],[f_1361_1]) ).

cnf(f_1361_3,plain,
    c_Int_OPls != c_Int_OMin,
    inference(clausify,[status(thm)],[f_1361_2]) ).

fof(f_1362_1,plain,
    c_Int_OMin != c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I40_J]) ).

fof(f_1362_2,plain,
    c_Int_OMin != c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1362_1]) ).

cnf(f_1362_3,plain,
    c_Int_OMin != c_Int_OPls,
    inference(clausify,[status(thm)],[f_1362_2]) ).

fof(f_1363_1,plain,
    ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_succ__pred]) ).

fof(f_1363_2,plain,
    ! [U_4869] : c_Int_Osucc(c_Int_Opred(U_4869)) = U_4869,
    inference(variable_rename,[status(thm)],[f_1363_1]) ).

fof(f_1363_3,plain,
    ! [U_4869] : c_Int_Osucc(c_Int_Opred(U_4869)) = U_4869,
    inference(definitional_conversion,[status(esa)],[f_1363_2]) ).

cnf(f_1363_4,plain,
    c_Int_Osucc(c_Int_Opred(U_4869)) = U_4869,
    inference(clausify,[status(thm)],[f_1363_3]) ).

fof(f_1364_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_1364_2,plain,
    ! [U_4870] :
      ( c_Int_Oiszero(U_4870,c_Groups_Ozero__class_Ozero(U_4870))
      | ~ class_Rings_Osemiring__1(U_4870) ),
    inference(variable_rename,[status(thm)],[f_1364_1]) ).

fof(f_1364_3,plain,
    ! [U_4870] :
      ( c_Int_Oiszero(U_4870,c_Groups_Ozero__class_Ozero(U_4870))
      | ~ class_Rings_Osemiring__1(U_4870) ),
    inference(definitional_conversion,[status(esa)],[f_1364_2]) ).

cnf(f_1364_4,plain,
    ( c_Int_Oiszero(U_4870,c_Groups_Ozero__class_Ozero(U_4870))
    | ~ class_Rings_Osemiring__1(U_4870) ),
    inference(clausify,[status(thm)],[f_1364_3]) ).

fof(f_1365_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_1365_2,plain,
    ! [U_4872,U_4871] :
      ( ( ( c_Int_Oiszero(U_4871,U_4872)
          | U_4872 != c_Groups_Ozero__class_Ozero(U_4871) )
        & ( U_4872 = c_Groups_Ozero__class_Ozero(U_4871)
          | ~ c_Int_Oiszero(U_4871,U_4872) ) )
      | ~ class_Rings_Osemiring__1(U_4871) ),
    inference(variable_rename,[status(thm)],[f_1365_1]) ).

fof(f_1365_3,plain,
    ( ! [U_4871,U_4872] :
        ( c_Int_Oiszero(U_4871,U_4872)
        | U_4872 != c_Groups_Ozero__class_Ozero(U_4871)
        | ~ sP379(U_4871,U_4872) )
    & ! [U_4871,U_4872] :
        ( U_4872 = c_Groups_Ozero__class_Ozero(U_4871)
        | ~ c_Int_Oiszero(U_4871,U_4872)
        | ~ sP379(U_4871,U_4872) )
    & ! [U_4871,U_4872] :
        ( sP379(U_4871,U_4872)
        | ~ class_Rings_Osemiring__1(U_4871) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP379])],[f_1365_2]) ).

cnf(f_1365_4,plain,
    ( sP379(U_4871,U_4872)
    | ~ class_Rings_Osemiring__1(U_4871) ),
    inference(clausify,[status(thm)],[f_1365_3]) ).

cnf(f_1365_5,plain,
    ( U_4872 = c_Groups_Ozero__class_Ozero(U_4871)
    | ~ c_Int_Oiszero(U_4871,U_4872)
    | ~ sP379(U_4871,U_4872) ),
    inference(clausify,[status(thm)],[f_1365_3]) ).

cnf(f_1365_6,plain,
    ( c_Int_Oiszero(U_4871,U_4872)
    | U_4872 != c_Groups_Ozero__class_Ozero(U_4871)
    | ~ sP379(U_4871,U_4872) ),
    inference(clausify,[status(thm)],[f_1365_3]) ).

fof(f_1366_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_1366_2,plain,
    ! [U_4873] :
      ( ~ c_Int_Oiszero(U_4873,c_Groups_Oone__class_Oone(U_4873))
      | ~ class_Rings_Osemiring__1(U_4873) ),
    inference(variable_rename,[status(thm)],[f_1366_1]) ).

fof(f_1366_3,plain,
    ! [U_4873] :
      ( ~ c_Int_Oiszero(U_4873,c_Groups_Oone__class_Oone(U_4873))
      | ~ class_Rings_Osemiring__1(U_4873) ),
    inference(definitional_conversion,[status(esa)],[f_1366_2]) ).

cnf(f_1366_4,plain,
    ( ~ c_Int_Oiszero(U_4873,c_Groups_Oone__class_Oone(U_4873))
    | ~ class_Rings_Osemiring__1(U_4873) ),
    inference(clausify,[status(thm)],[f_1366_3]) ).

fof(f_1367_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_1367_2,plain,
    ! [U_4874] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4874),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_4874)
      | ~ class_Int_Onumber__ring(U_4874) ),
    inference(variable_rename,[status(thm)],[f_1367_1]) ).

fof(f_1367_3,plain,
    ! [U_4874] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4874),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_4874)
      | ~ class_Int_Onumber__ring(U_4874) ),
    inference(definitional_conversion,[status(esa)],[f_1367_2]) ).

cnf(f_1367_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4874),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_4874)
    | ~ class_Int_Onumber__ring(U_4874) ),
    inference(clausify,[status(thm)],[f_1367_3]) ).

fof(f_1368_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_1368_2,plain,
    ! [U_4875] :
      ( c_Groups_Ozero__class_Ozero(U_4875) = hAPP(c_Int_Onumber__class_Onumber__of(U_4875),c_Int_OPls)
      | ~ class_Int_Onumber__ring(U_4875) ),
    inference(variable_rename,[status(thm)],[f_1368_1]) ).

fof(f_1368_3,plain,
    ! [U_4875] :
      ( c_Groups_Ozero__class_Ozero(U_4875) = hAPP(c_Int_Onumber__class_Onumber__of(U_4875),c_Int_OPls)
      | ~ class_Int_Onumber__ring(U_4875) ),
    inference(definitional_conversion,[status(esa)],[f_1368_2]) ).

cnf(f_1368_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_4875) = hAPP(c_Int_Onumber__class_Onumber__of(U_4875),c_Int_OPls)
    | ~ class_Int_Onumber__ring(U_4875) ),
    inference(clausify,[status(thm)],[f_1368_3]) ).

fof(f_1369_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_1369_2,plain,
    ! [U_4877,U_4876] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4876),hAPP(c_Int_Onumber__class_Onumber__of(U_4876),c_Int_OPls)),U_4877) = U_4877
      | ~ class_Int_Onumber__ring(U_4876) ),
    inference(variable_rename,[status(thm)],[f_1369_1]) ).

fof(f_1369_3,plain,
    ! [U_4876,U_4877] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4876),hAPP(c_Int_Onumber__class_Onumber__of(U_4876),c_Int_OPls)),U_4877) = U_4877
      | ~ class_Int_Onumber__ring(U_4876) ),
    inference(definitional_conversion,[status(esa)],[f_1369_2]) ).

cnf(f_1369_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4876),hAPP(c_Int_Onumber__class_Onumber__of(U_4876),c_Int_OPls)),U_4877) = U_4877
    | ~ class_Int_Onumber__ring(U_4876) ),
    inference(clausify,[status(thm)],[f_1369_3]) ).

fof(f_1370_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_1370_2,plain,
    ! [U_4879,U_4878] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4878),U_4879),hAPP(c_Int_Onumber__class_Onumber__of(U_4878),c_Int_OPls)) = U_4879
      | ~ class_Int_Onumber__ring(U_4878) ),
    inference(variable_rename,[status(thm)],[f_1370_1]) ).

fof(f_1370_3,plain,
    ! [U_4878,U_4879] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4878),U_4879),hAPP(c_Int_Onumber__class_Onumber__of(U_4878),c_Int_OPls)) = U_4879
      | ~ class_Int_Onumber__ring(U_4878) ),
    inference(definitional_conversion,[status(esa)],[f_1370_2]) ).

cnf(f_1370_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4878),U_4879),hAPP(c_Int_Onumber__class_Onumber__of(U_4878),c_Int_OPls)) = U_4879
    | ~ class_Int_Onumber__ring(U_4878) ),
    inference(clausify,[status(thm)],[f_1370_3]) ).

fof(f_1371_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_1371_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_1371_1]) ).

cnf(f_1371_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_1371_2]) ).

fof(f_1372_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_1372_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_1372_1]) ).

cnf(f_1372_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_1372_2]) ).

fof(f_1373_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_1373_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_1373_1]) ).

cnf(f_1373_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_1373_2]) ).

fof(f_1374_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_1374_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_1374_1]) ).

cnf(f_1374_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_1374_2]) ).

fof(f_1375_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_1375_2,plain,
    ! [U_4881,U_4880] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4881)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4880)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4881),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4880)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4880)) ),
    inference(variable_rename,[status(thm)],[f_1375_1]) ).

fof(f_1375_3,plain,
    ! [U_4880,U_4881] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4881)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4880)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4881),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4880)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4880)) ),
    inference(definitional_conversion,[status(esa)],[f_1375_2]) ).

cnf(f_1375_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4881)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4880)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4881),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4880)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4880)) ),
    inference(clausify,[status(thm)],[f_1375_3]) ).

fof(f_1376_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_1376_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_1376_1]) ).

cnf(f_1376_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_1376_2]) ).

fof(f_1377_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_1377_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_1377_1]) ).

cnf(f_1377_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_1377_2]) ).

fof(f_1378_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_1378_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_1378_1]) ).

cnf(f_1378_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_1378_2]) ).

fof(f_1379_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_1379_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_1379_1]) ).

cnf(f_1379_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_1379_2]) ).

fof(f_1380_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_1380_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_1380_1]) ).

cnf(f_1380_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_1380_2]) ).

fof(f_1381_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_1381_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_1381_1]) ).

cnf(f_1381_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_1381_2]) ).

fof(f_1382_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_1382_2,plain,
    ! [U_4883,U_4882] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_4882) = hAPP(c_Int_Onumber__class_Onumber__of(U_4882),U_4883)
          | ~ c_Int_Oiszero(U_4882,hAPP(c_Int_Onumber__class_Onumber__of(U_4882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4883)))) )
        & ( c_Int_Oiszero(U_4882,hAPP(c_Int_Onumber__class_Onumber__of(U_4882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4883))))
          | c_Groups_Ozero__class_Ozero(U_4882) != hAPP(c_Int_Onumber__class_Onumber__of(U_4882),U_4883) ) )
      | ~ class_Int_Onumber__ring(U_4882) ),
    inference(variable_rename,[status(thm)],[f_1382_1]) ).

fof(f_1382_3,plain,
    ( ! [U_4882,U_4883] :
        ( c_Groups_Ozero__class_Ozero(U_4882) = hAPP(c_Int_Onumber__class_Onumber__of(U_4882),U_4883)
        | ~ c_Int_Oiszero(U_4882,hAPP(c_Int_Onumber__class_Onumber__of(U_4882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4883))))
        | ~ sP380(U_4882,U_4883) )
    & ! [U_4882,U_4883] :
        ( c_Int_Oiszero(U_4882,hAPP(c_Int_Onumber__class_Onumber__of(U_4882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4883))))
        | c_Groups_Ozero__class_Ozero(U_4882) != hAPP(c_Int_Onumber__class_Onumber__of(U_4882),U_4883)
        | ~ sP380(U_4882,U_4883) )
    & ! [U_4882,U_4883] :
        ( sP380(U_4882,U_4883)
        | ~ class_Int_Onumber__ring(U_4882) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP380])],[f_1382_2]) ).

cnf(f_1382_4,plain,
    ( sP380(U_4882,U_4883)
    | ~ class_Int_Onumber__ring(U_4882) ),
    inference(clausify,[status(thm)],[f_1382_3]) ).

cnf(f_1382_5,plain,
    ( c_Int_Oiszero(U_4882,hAPP(c_Int_Onumber__class_Onumber__of(U_4882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4883))))
    | c_Groups_Ozero__class_Ozero(U_4882) != hAPP(c_Int_Onumber__class_Onumber__of(U_4882),U_4883)
    | ~ sP380(U_4882,U_4883) ),
    inference(clausify,[status(thm)],[f_1382_3]) ).

cnf(f_1382_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_4882) = hAPP(c_Int_Onumber__class_Onumber__of(U_4882),U_4883)
    | ~ c_Int_Oiszero(U_4882,hAPP(c_Int_Onumber__class_Onumber__of(U_4882),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4883))))
    | ~ sP380(U_4882,U_4883) ),
    inference(clausify,[status(thm)],[f_1382_3]) ).

fof(f_1383_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_1383_2,plain,
    ! [U_4885,U_4884] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4884),U_4885) = c_Groups_Ozero__class_Ozero(U_4884)
          | ~ c_Int_Oiszero(U_4884,hAPP(c_Int_Onumber__class_Onumber__of(U_4884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4885),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) )
        & ( c_Int_Oiszero(U_4884,hAPP(c_Int_Onumber__class_Onumber__of(U_4884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4885),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_4884),U_4885) != c_Groups_Ozero__class_Ozero(U_4884) ) )
      | ~ class_Int_Onumber__ring(U_4884) ),
    inference(variable_rename,[status(thm)],[f_1383_1]) ).

fof(f_1383_3,plain,
    ( ! [U_4885,U_4884] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_4884),U_4885) = c_Groups_Ozero__class_Ozero(U_4884)
        | ~ c_Int_Oiszero(U_4884,hAPP(c_Int_Onumber__class_Onumber__of(U_4884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4885),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
        | ~ sP381(U_4885,U_4884) )
    & ! [U_4885,U_4884] :
        ( c_Int_Oiszero(U_4884,hAPP(c_Int_Onumber__class_Onumber__of(U_4884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4885),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
        | hAPP(c_Int_Onumber__class_Onumber__of(U_4884),U_4885) != c_Groups_Ozero__class_Ozero(U_4884)
        | ~ sP381(U_4885,U_4884) )
    & ! [U_4885,U_4884] :
        ( sP381(U_4885,U_4884)
        | ~ class_Int_Onumber__ring(U_4884) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP381])],[f_1383_2]) ).

cnf(f_1383_4,plain,
    ( sP381(U_4885,U_4884)
    | ~ class_Int_Onumber__ring(U_4884) ),
    inference(clausify,[status(thm)],[f_1383_3]) ).

cnf(f_1383_5,plain,
    ( c_Int_Oiszero(U_4884,hAPP(c_Int_Onumber__class_Onumber__of(U_4884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4885),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4884),U_4885) != c_Groups_Ozero__class_Ozero(U_4884)
    | ~ sP381(U_4885,U_4884) ),
    inference(clausify,[status(thm)],[f_1383_3]) ).

cnf(f_1383_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4884),U_4885) = c_Groups_Ozero__class_Ozero(U_4884)
    | ~ c_Int_Oiszero(U_4884,hAPP(c_Int_Onumber__class_Onumber__of(U_4884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4885),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
    | ~ sP381(U_4885,U_4884) ),
    inference(clausify,[status(thm)],[f_1383_3]) ).

fof(f_1384_1,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_succ__Min]) ).

fof(f_1384_2,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1384_1]) ).

cnf(f_1384_3,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1384_2]) ).

fof(f_1385_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_1385_2,plain,
    ! [U_4887,U_4886] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4886),U_4887))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4886)),U_4887)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4886)),U_4887))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4886),U_4887)) ) ),
    inference(variable_rename,[status(thm)],[f_1385_1]) ).

fof(f_1385_3,plain,
    ( ! [U_4891,U_4889] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4889),U_4891))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4889)),U_4891)) )
    & ! [U_4890,U_4888] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4888)),U_4890))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4888),U_4890)) ) ),
    inference(miniscope,[status(thm)],[f_1385_2]) ).

fof(f_1385_4,plain,
    ( ! [U_4891,U_4889] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4889),U_4891))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4889)),U_4891)) )
    & ! [U_4890,U_4888] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4888)),U_4890))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4888),U_4890)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1385_3]) ).

cnf(f_1385_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4888)),U_4890))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4888),U_4890)) ),
    inference(clausify,[status(thm)],[f_1385_4]) ).

cnf(f_1385_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4889),U_4891))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_4889)),U_4891)) ),
    inference(clausify,[status(thm)],[f_1385_4]) ).

fof(f_1386_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_1386_2,plain,
    ! [U_4892] : c_Int_Opred(U_4892) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4892),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_1386_1]) ).

fof(f_1386_3,plain,
    ! [U_4892] : c_Int_Opred(U_4892) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4892),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_1386_2]) ).

cnf(f_1386_4,plain,
    c_Int_Opred(U_4892) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4892),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1386_3]) ).

fof(f_1387_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_1387_2,plain,
    ! [U_4893] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4893),c_Int_OMin) = c_Int_Opred(U_4893),
    inference(variable_rename,[status(thm)],[f_1387_1]) ).

fof(f_1387_3,plain,
    ! [U_4893] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4893),c_Int_OMin) = c_Int_Opred(U_4893),
    inference(definitional_conversion,[status(esa)],[f_1387_2]) ).

cnf(f_1387_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4893),c_Int_OMin) = c_Int_Opred(U_4893),
    inference(clausify,[status(thm)],[f_1387_3]) ).

fof(f_1388_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_1388_2,plain,
    ! [U_4894] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_4894) = c_Int_Opred(U_4894),
    inference(variable_rename,[status(thm)],[f_1388_1]) ).

fof(f_1388_3,plain,
    ! [U_4894] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_4894) = c_Int_Opred(U_4894),
    inference(definitional_conversion,[status(esa)],[f_1388_2]) ).

cnf(f_1388_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_4894) = c_Int_Opred(U_4894),
    inference(clausify,[status(thm)],[f_1388_3]) ).

fof(f_1389_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_1389_2,plain,
    ! [U_4895] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4895)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4895))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4895),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4895)),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_4895),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1389_1]) ).

fof(f_1389_3,plain,
    ( ! [U_4897] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4897)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4897))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4897),c_Int_OPls)) )
    & ! [U_4896] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4896)),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_4896),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1389_2]) ).

fof(f_1389_4,plain,
    ( ! [U_4897] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4897)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4897))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4897),c_Int_OPls)) )
    & ! [U_4896] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4896)),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_4896),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1389_3]) ).

cnf(f_1389_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4896)),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_4896),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1389_4]) ).

cnf(f_1389_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4897)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4897))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4897),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1389_4]) ).

fof(f_1390_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_1390_2,plain,
    ! [U_4898] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4898)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4898),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4898),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4898) ) ),
    inference(variable_rename,[status(thm)],[f_1390_1]) ).

fof(f_1390_3,plain,
    ( ! [U_4900] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4900)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4900),c_Int_OPls)) )
    & ! [U_4899] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4899),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4899) ) ),
    inference(miniscope,[status(thm)],[f_1390_2]) ).

fof(f_1390_4,plain,
    ( ! [U_4900] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4900)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4900),c_Int_OPls)) )
    & ! [U_4899] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4899),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4899) ) ),
    inference(definitional_conversion,[status(esa)],[f_1390_3]) ).

cnf(f_1390_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4899),c_Int_OPls))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4899) ),
    inference(clausify,[status(thm)],[f_1390_4]) ).

cnf(f_1390_6,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4900)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4900),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1390_4]) ).

fof(f_1391_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_1391_2,plain,
    ! [U_4901] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4901) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4901),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4901),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4901) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1391_1]) ).

fof(f_1391_3,plain,
    ( ! [U_4903] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4903) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4903),c_Int_OPls)) )
    & ! [U_4902] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4902),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4902) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1391_2]) ).

fof(f_1391_4,plain,
    ( ! [U_4903] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4903) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4903),c_Int_OPls)) )
    & ! [U_4902] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4902),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4902) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1391_3]) ).

cnf(f_1391_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4902),c_Int_OPls))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4902) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1391_4]) ).

cnf(f_1391_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4903) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4903),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1391_4]) ).

fof(f_1392_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_1392_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_1392_1]) ).

cnf(f_1392_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_1392_2]) ).

fof(f_1393_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_1393_2,plain,
    ! [U_4905,U_4904] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4904)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4905)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4904),U_4905))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4905))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4904),U_4905)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4904),U_4905))
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4905))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4904),U_4905)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4904)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4905))) ) ),
    inference(variable_rename,[status(thm)],[f_1393_1]) ).

fof(f_1393_3,plain,
    ( ! [U_4909,U_4907] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4907)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4909)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4907),U_4909))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4909))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4907),U_4909)) ) )
    & ! [U_4908,U_4906] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4906),U_4908))
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4908))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4906),U_4908)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4906)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4908))) ) ),
    inference(miniscope,[status(thm)],[f_1393_2]) ).

fof(f_1393_4,plain,
    ( ! [U_4909,U_4907] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4909))
        | ~ sP383(U_4909,U_4907) )
    & ! [U_4909,U_4907] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4907),U_4909))
        | ~ sP383(U_4909,U_4907) )
    & ! [U_4908,U_4906] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4906),U_4908))
        | ~ sP382(U_4908,U_4906) )
    & ! [U_4908,U_4906] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4908))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4906),U_4908))
        | ~ sP382(U_4908,U_4906) )
    & ! [U_4909,U_4907] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4907)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4909)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4907),U_4909))
        | sP383(U_4909,U_4907) )
    & ! [U_4908,U_4906] :
        ( sP382(U_4908,U_4906)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4906)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4908))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP382,sP383])],[f_1393_3]) ).

cnf(f_1393_5,plain,
    ( sP382(U_4908,U_4906)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4906)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4908))) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4907)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4909)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4907),U_4909))
    | sP383(U_4909,U_4907) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4908))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4906),U_4908))
    | ~ sP382(U_4908,U_4906) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4906),U_4908))
    | ~ sP382(U_4908,U_4906) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4907),U_4909))
    | ~ sP383(U_4909,U_4907) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4909))
    | ~ sP383(U_4909,U_4907) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

fof(f_1394_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_1394_2,plain,
    ! [U_4911,U_4910] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4910)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4911)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4910),c_Int_OPls))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4910),U_4911)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4910),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4910),U_4911))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4910)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4911))) ) ),
    inference(variable_rename,[status(thm)],[f_1394_1]) ).

fof(f_1394_3,plain,
    ( ! [U_4915,U_4913] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4913)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4915)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4913),c_Int_OPls))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4913),U_4915)) ) )
    & ! [U_4914,U_4912] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4912),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4912),U_4914))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4912)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4914))) ) ),
    inference(miniscope,[status(thm)],[f_1394_2]) ).

fof(f_1394_4,plain,
    ( ! [U_4915,U_4913] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4913),c_Int_OPls))
        | ~ sP384(U_4915,U_4913) )
    & ! [U_4915,U_4913] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4913),U_4915))
        | ~ sP384(U_4915,U_4913) )
    & ! [U_4915,U_4913] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4913)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4915)))
        | sP384(U_4915,U_4913) )
    & ! [U_4912,U_4914] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4912),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4912),U_4914))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4912)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4914))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP384])],[f_1394_3]) ).

cnf(f_1394_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4912),c_Int_OPls))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4912),U_4914))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4912)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4914))) ),
    inference(clausify,[status(thm)],[f_1394_4]) ).

cnf(f_1394_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_4913)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4915)))
    | sP384(U_4915,U_4913) ),
    inference(clausify,[status(thm)],[f_1394_4]) ).

cnf(f_1394_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4913),U_4915))
    | ~ sP384(U_4915,U_4913) ),
    inference(clausify,[status(thm)],[f_1394_4]) ).

cnf(f_1394_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4913),c_Int_OPls))
    | ~ sP384(U_4915,U_4913) ),
    inference(clausify,[status(thm)],[f_1394_4]) ).

fof(f_1395_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_1395_2,plain,
    ! [U_4916] :
      ( ~ c_Int_Oiszero(U_4916,hAPP(c_Int_Onumber__class_Onumber__of(U_4916),c_Int_OMin))
      | ~ class_Int_Onumber__ring(U_4916) ),
    inference(variable_rename,[status(thm)],[f_1395_1]) ).

fof(f_1395_3,plain,
    ! [U_4916] :
      ( ~ c_Int_Oiszero(U_4916,hAPP(c_Int_Onumber__class_Onumber__of(U_4916),c_Int_OMin))
      | ~ class_Int_Onumber__ring(U_4916) ),
    inference(definitional_conversion,[status(esa)],[f_1395_2]) ).

cnf(f_1395_4,plain,
    ( ~ c_Int_Oiszero(U_4916,hAPP(c_Int_Onumber__class_Onumber__of(U_4916),c_Int_OMin))
    | ~ class_Int_Onumber__ring(U_4916) ),
    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_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_1396_2,plain,
    ! [U_4918,U_4917] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4917),hAPP(c_Int_Onumber__class_Onumber__of(U_4917),U_4918)),c_Groups_Ozero__class_Ozero(U_4917)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4918),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4918),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4917),hAPP(c_Int_Onumber__class_Onumber__of(U_4917),U_4918)),c_Groups_Ozero__class_Ozero(U_4917))) ) )
      | ~ class_Rings_Olinordered__idom(U_4917)
      | ~ class_Int_Onumber__ring(U_4917) ),
    inference(variable_rename,[status(thm)],[f_1396_1]) ).

fof(f_1396_3,plain,
    ( ! [U_4918,U_4917] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4917),hAPP(c_Int_Onumber__class_Onumber__of(U_4917),U_4918)),c_Groups_Ozero__class_Ozero(U_4917)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4918),c_Int_OPls))
        | ~ sP385(U_4918,U_4917) )
    & ! [U_4918,U_4917] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4918),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4917),hAPP(c_Int_Onumber__class_Onumber__of(U_4917),U_4918)),c_Groups_Ozero__class_Ozero(U_4917)))
        | ~ sP385(U_4918,U_4917) )
    & ! [U_4918,U_4917] :
        ( sP385(U_4918,U_4917)
        | ~ class_Rings_Olinordered__idom(U_4917)
        | ~ class_Int_Onumber__ring(U_4917) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP385])],[f_1396_2]) ).

cnf(f_1396_4,plain,
    ( sP385(U_4918,U_4917)
    | ~ class_Rings_Olinordered__idom(U_4917)
    | ~ class_Int_Onumber__ring(U_4917) ),
    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_4918),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4917),hAPP(c_Int_Onumber__class_Onumber__of(U_4917),U_4918)),c_Groups_Ozero__class_Ozero(U_4917)))
    | ~ sP385(U_4918,U_4917) ),
    inference(clausify,[status(thm)],[f_1396_3]) ).

cnf(f_1396_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4917),hAPP(c_Int_Onumber__class_Onumber__of(U_4917),U_4918)),c_Groups_Ozero__class_Ozero(U_4917)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4918),c_Int_OPls))
    | ~ sP385(U_4918,U_4917) ),
    inference(clausify,[status(thm)],[f_1396_3]) ).

fof(f_1397_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_1397_2,plain,
    ! [U_4920,U_4919] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),c_Groups_Ozero__class_Ozero(U_4919)),hAPP(c_Int_Onumber__class_Onumber__of(U_4919),U_4920)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4920)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4920))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),c_Groups_Ozero__class_Ozero(U_4919)),hAPP(c_Int_Onumber__class_Onumber__of(U_4919),U_4920))) ) )
      | ~ class_Rings_Olinordered__idom(U_4919)
      | ~ class_Int_Onumber__ring(U_4919) ),
    inference(variable_rename,[status(thm)],[f_1397_1]) ).

fof(f_1397_3,plain,
    ( ! [U_4919,U_4920] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),c_Groups_Ozero__class_Ozero(U_4919)),hAPP(c_Int_Onumber__class_Onumber__of(U_4919),U_4920)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4920))
        | ~ sP386(U_4919,U_4920) )
    & ! [U_4919,U_4920] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4920))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),c_Groups_Ozero__class_Ozero(U_4919)),hAPP(c_Int_Onumber__class_Onumber__of(U_4919),U_4920)))
        | ~ sP386(U_4919,U_4920) )
    & ! [U_4919,U_4920] :
        ( sP386(U_4919,U_4920)
        | ~ class_Rings_Olinordered__idom(U_4919)
        | ~ class_Int_Onumber__ring(U_4919) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP386])],[f_1397_2]) ).

cnf(f_1397_4,plain,
    ( sP386(U_4919,U_4920)
    | ~ class_Rings_Olinordered__idom(U_4919)
    | ~ class_Int_Onumber__ring(U_4919) ),
    inference(clausify,[status(thm)],[f_1397_3]) ).

cnf(f_1397_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4920))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),c_Groups_Ozero__class_Ozero(U_4919)),hAPP(c_Int_Onumber__class_Onumber__of(U_4919),U_4920)))
    | ~ sP386(U_4919,U_4920) ),
    inference(clausify,[status(thm)],[f_1397_3]) ).

cnf(f_1397_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4919),c_Groups_Ozero__class_Ozero(U_4919)),hAPP(c_Int_Onumber__class_Onumber__of(U_4919),U_4920)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4920))
    | ~ sP386(U_4919,U_4920) ),
    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_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_1398_2,plain,
    ! [U_4922,U_4921] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4921),c_Groups_Ozero__class_Ozero(U_4921)),hAPP(c_Int_Onumber__class_Onumber__of(U_4921),U_4922)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4922)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4922))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4921),c_Groups_Ozero__class_Ozero(U_4921)),hAPP(c_Int_Onumber__class_Onumber__of(U_4921),U_4922))) ) )
      | ~ class_Rings_Olinordered__idom(U_4921)
      | ~ class_Int_Onumber__ring(U_4921) ),
    inference(variable_rename,[status(thm)],[f_1398_1]) ).

fof(f_1398_3,plain,
    ( ! [U_4921,U_4922] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4921),c_Groups_Ozero__class_Ozero(U_4921)),hAPP(c_Int_Onumber__class_Onumber__of(U_4921),U_4922)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4922))
        | ~ sP387(U_4921,U_4922) )
    & ! [U_4921,U_4922] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4922))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4921),c_Groups_Ozero__class_Ozero(U_4921)),hAPP(c_Int_Onumber__class_Onumber__of(U_4921),U_4922)))
        | ~ sP387(U_4921,U_4922) )
    & ! [U_4921,U_4922] :
        ( sP387(U_4921,U_4922)
        | ~ class_Rings_Olinordered__idom(U_4921)
        | ~ class_Int_Onumber__ring(U_4921) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP387])],[f_1398_2]) ).

cnf(f_1398_4,plain,
    ( sP387(U_4921,U_4922)
    | ~ class_Rings_Olinordered__idom(U_4921)
    | ~ class_Int_Onumber__ring(U_4921) ),
    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_OPls),U_4922))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4921),c_Groups_Ozero__class_Ozero(U_4921)),hAPP(c_Int_Onumber__class_Onumber__of(U_4921),U_4922)))
    | ~ sP387(U_4921,U_4922) ),
    inference(clausify,[status(thm)],[f_1398_3]) ).

cnf(f_1398_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4921),c_Groups_Ozero__class_Ozero(U_4921)),hAPP(c_Int_Onumber__class_Onumber__of(U_4921),U_4922)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4922))
    | ~ sP387(U_4921,U_4922) ),
    inference(clausify,[status(thm)],[f_1398_3]) ).

fof(f_1399_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_1399_2,plain,
    ! [U_4924,U_4923] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4923),hAPP(c_Int_Onumber__class_Onumber__of(U_4923),U_4924)),c_Groups_Ozero__class_Ozero(U_4923)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4924),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4924),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4923),hAPP(c_Int_Onumber__class_Onumber__of(U_4923),U_4924)),c_Groups_Ozero__class_Ozero(U_4923))) ) )
      | ~ class_Rings_Olinordered__idom(U_4923)
      | ~ class_Int_Onumber__ring(U_4923) ),
    inference(variable_rename,[status(thm)],[f_1399_1]) ).

fof(f_1399_3,plain,
    ( ! [U_4924,U_4923] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4923),hAPP(c_Int_Onumber__class_Onumber__of(U_4923),U_4924)),c_Groups_Ozero__class_Ozero(U_4923)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4924),c_Int_OPls))
        | ~ sP388(U_4924,U_4923) )
    & ! [U_4924,U_4923] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4924),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4923),hAPP(c_Int_Onumber__class_Onumber__of(U_4923),U_4924)),c_Groups_Ozero__class_Ozero(U_4923)))
        | ~ sP388(U_4924,U_4923) )
    & ! [U_4924,U_4923] :
        ( sP388(U_4924,U_4923)
        | ~ class_Rings_Olinordered__idom(U_4923)
        | ~ class_Int_Onumber__ring(U_4923) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP388])],[f_1399_2]) ).

cnf(f_1399_4,plain,
    ( sP388(U_4924,U_4923)
    | ~ class_Rings_Olinordered__idom(U_4923)
    | ~ class_Int_Onumber__ring(U_4923) ),
    inference(clausify,[status(thm)],[f_1399_3]) ).

cnf(f_1399_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4924),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4923),hAPP(c_Int_Onumber__class_Onumber__of(U_4923),U_4924)),c_Groups_Ozero__class_Ozero(U_4923)))
    | ~ sP388(U_4924,U_4923) ),
    inference(clausify,[status(thm)],[f_1399_3]) ).

cnf(f_1399_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4923),hAPP(c_Int_Onumber__class_Onumber__of(U_4923),U_4924)),c_Groups_Ozero__class_Ozero(U_4923)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4924),c_Int_OPls))
    | ~ sP388(U_4924,U_4923) ),
    inference(clausify,[status(thm)],[f_1399_3]) ).

fof(f_1400_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_1400_2,plain,
    ! [U_4925] :
      ( ( 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_4925)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4925)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4925))
        | ~ 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_4925))) ) ),
    inference(variable_rename,[status(thm)],[f_1400_1]) ).

fof(f_1400_3,plain,
    ( ! [U_4927] :
        ( 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_4927)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4927)) )
    & ! [U_4926] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4926))
        | ~ 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_4926))) ) ),
    inference(miniscope,[status(thm)],[f_1400_2]) ).

fof(f_1400_4,plain,
    ( ! [U_4927] :
        ( 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_4927)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4927)) )
    & ! [U_4926] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4926))
        | ~ 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_4926))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1400_3]) ).

cnf(f_1400_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4926))
    | ~ 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_4926))) ),
    inference(clausify,[status(thm)],[f_1400_4]) ).

cnf(f_1400_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_4927)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4927)) ),
    inference(clausify,[status(thm)],[f_1400_4]) ).

fof(f_1401_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_1401_2,plain,
    ! [U_4929,U_4928] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4928)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4929)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4928),U_4929))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4929),c_Int_OPls)) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4928)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4929)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4928)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4929),c_Int_OPls)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4928),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4928)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4929)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4929)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4928),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1401_1]) ).

fof(f_1401_3,plain,
    ( ! [U_4933,U_4931] :
        ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4931)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4933)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4931),U_4933))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4933),c_Int_OPls)) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4931)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4933)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4931)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4933),c_Int_OPls)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4931),c_Int_OPls)) )
    & ! [U_4932,U_4930] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4930)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4932)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4932)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4930),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1401_2]) ).

fof(f_1401_4,plain,
    ( ! [U_4933,U_4931] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4931)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4933)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4931),U_4933))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4933),c_Int_OPls))
        | ~ sP389(U_4933,U_4931) )
    & ! [U_4933,U_4931] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4931)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4933)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4931)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4933),c_Int_OPls))
        | ~ sP389(U_4933,U_4931) )
    & ! [U_4933,U_4931] :
        ( sP389(U_4933,U_4931)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4931),c_Int_OPls)) )
    & ! [U_4930,U_4932] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4930)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4932)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4932)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4930),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP389])],[f_1401_3]) ).

cnf(f_1401_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4930)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4932)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4932)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4930),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1401_4]) ).

cnf(f_1401_6,plain,
    ( sP389(U_4933,U_4931)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4931),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1401_4]) ).

cnf(f_1401_7,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4931)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4933)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4931)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4933),c_Int_OPls))
    | ~ sP389(U_4933,U_4931) ),
    inference(clausify,[status(thm)],[f_1401_4]) ).

cnf(f_1401_8,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4931)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4933)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4931),U_4933))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4933),c_Int_OPls))
    | ~ sP389(U_4933,U_4931) ),
    inference(clausify,[status(thm)],[f_1401_4]) ).

fof(f_1402_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_1402_2,plain,
    ! [U_4935,U_4934] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4934),c_Int_Opred(U_4935)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4934),hAPP(c_Groups_Ouminus__class_Ouminus(U_4934),c_Groups_Oone__class_Oone(U_4934))),hAPP(c_Int_Onumber__class_Onumber__of(U_4934),U_4935))
      | ~ class_Int_Onumber__ring(U_4934) ),
    inference(variable_rename,[status(thm)],[f_1402_1]) ).

fof(f_1402_3,plain,
    ! [U_4935,U_4934] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4934),c_Int_Opred(U_4935)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4934),hAPP(c_Groups_Ouminus__class_Ouminus(U_4934),c_Groups_Oone__class_Oone(U_4934))),hAPP(c_Int_Onumber__class_Onumber__of(U_4934),U_4935))
      | ~ class_Int_Onumber__ring(U_4934) ),
    inference(definitional_conversion,[status(esa)],[f_1402_2]) ).

cnf(f_1402_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4934),c_Int_Opred(U_4935)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4934),hAPP(c_Groups_Ouminus__class_Ouminus(U_4934),c_Groups_Oone__class_Oone(U_4934))),hAPP(c_Int_Onumber__class_Onumber__of(U_4934),U_4935))
    | ~ class_Int_Onumber__ring(U_4934) ),
    inference(clausify,[status(thm)],[f_1402_3]) ).

fof(f_1403_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_1403_2,plain,
    ! [U_4937,U_4936] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4936),U_4937) = c_Groups_Oone__class_Oone(U_4936)
          | ~ c_Int_Oiszero(U_4936,hAPP(c_Int_Onumber__class_Onumber__of(U_4936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4937),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) )
        & ( c_Int_Oiszero(U_4936,hAPP(c_Int_Onumber__class_Onumber__of(U_4936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4937),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_4936),U_4937) != c_Groups_Oone__class_Oone(U_4936) ) )
      | ~ class_Int_Onumber__ring(U_4936) ),
    inference(variable_rename,[status(thm)],[f_1403_1]) ).

fof(f_1403_3,plain,
    ( ! [U_4936,U_4937] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_4936),U_4937) = c_Groups_Oone__class_Oone(U_4936)
        | ~ c_Int_Oiszero(U_4936,hAPP(c_Int_Onumber__class_Onumber__of(U_4936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4937),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
        | ~ sP390(U_4936,U_4937) )
    & ! [U_4936,U_4937] :
        ( c_Int_Oiszero(U_4936,hAPP(c_Int_Onumber__class_Onumber__of(U_4936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4937),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(U_4936),U_4937) != c_Groups_Oone__class_Oone(U_4936)
        | ~ sP390(U_4936,U_4937) )
    & ! [U_4936,U_4937] :
        ( sP390(U_4936,U_4937)
        | ~ class_Int_Onumber__ring(U_4936) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP390])],[f_1403_2]) ).

cnf(f_1403_4,plain,
    ( sP390(U_4936,U_4937)
    | ~ class_Int_Onumber__ring(U_4936) ),
    inference(clausify,[status(thm)],[f_1403_3]) ).

cnf(f_1403_5,plain,
    ( c_Int_Oiszero(U_4936,hAPP(c_Int_Onumber__class_Onumber__of(U_4936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4937),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4936),U_4937) != c_Groups_Oone__class_Oone(U_4936)
    | ~ sP390(U_4936,U_4937) ),
    inference(clausify,[status(thm)],[f_1403_3]) ).

cnf(f_1403_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4936),U_4937) = c_Groups_Oone__class_Oone(U_4936)
    | ~ c_Int_Oiszero(U_4936,hAPP(c_Int_Onumber__class_Onumber__of(U_4936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4937),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
    | ~ sP390(U_4936,U_4937) ),
    inference(clausify,[status(thm)],[f_1403_3]) ).

fof(f_1404_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_1404_2,plain,
    ! [U_4939,U_4938] :
      ( ( ( c_Groups_Oone__class_Oone(U_4938) = hAPP(c_Int_Onumber__class_Onumber__of(U_4938),U_4939)
          | ~ c_Int_Oiszero(U_4938,hAPP(c_Int_Onumber__class_Onumber__of(U_4938),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_4939)))) )
        & ( c_Int_Oiszero(U_4938,hAPP(c_Int_Onumber__class_Onumber__of(U_4938),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_4939))))
          | c_Groups_Oone__class_Oone(U_4938) != hAPP(c_Int_Onumber__class_Onumber__of(U_4938),U_4939) ) )
      | ~ class_Int_Onumber__ring(U_4938) ),
    inference(variable_rename,[status(thm)],[f_1404_1]) ).

fof(f_1404_3,plain,
    ( ! [U_4939,U_4938] :
        ( c_Groups_Oone__class_Oone(U_4938) = hAPP(c_Int_Onumber__class_Onumber__of(U_4938),U_4939)
        | ~ c_Int_Oiszero(U_4938,hAPP(c_Int_Onumber__class_Onumber__of(U_4938),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_4939))))
        | ~ sP391(U_4939,U_4938) )
    & ! [U_4939,U_4938] :
        ( c_Int_Oiszero(U_4938,hAPP(c_Int_Onumber__class_Onumber__of(U_4938),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_4939))))
        | c_Groups_Oone__class_Oone(U_4938) != hAPP(c_Int_Onumber__class_Onumber__of(U_4938),U_4939)
        | ~ sP391(U_4939,U_4938) )
    & ! [U_4939,U_4938] :
        ( sP391(U_4939,U_4938)
        | ~ class_Int_Onumber__ring(U_4938) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP391])],[f_1404_2]) ).

cnf(f_1404_4,plain,
    ( sP391(U_4939,U_4938)
    | ~ class_Int_Onumber__ring(U_4938) ),
    inference(clausify,[status(thm)],[f_1404_3]) ).

cnf(f_1404_5,plain,
    ( c_Int_Oiszero(U_4938,hAPP(c_Int_Onumber__class_Onumber__of(U_4938),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_4939))))
    | c_Groups_Oone__class_Oone(U_4938) != hAPP(c_Int_Onumber__class_Onumber__of(U_4938),U_4939)
    | ~ sP391(U_4939,U_4938) ),
    inference(clausify,[status(thm)],[f_1404_3]) ).

cnf(f_1404_6,plain,
    ( c_Groups_Oone__class_Oone(U_4938) = hAPP(c_Int_Onumber__class_Onumber__of(U_4938),U_4939)
    | ~ c_Int_Oiszero(U_4938,hAPP(c_Int_Onumber__class_Onumber__of(U_4938),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_4939))))
    | ~ sP391(U_4939,U_4938) ),
    inference(clausify,[status(thm)],[f_1404_3]) ).

fof(f_1405_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_1405_2,plain,
    ! [U_4941,U_4940] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4940),c_Groups_Oone__class_Oone(U_4940)),hAPP(c_Int_Onumber__class_Onumber__of(U_4940),U_4941)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4940),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_4941)))
      | ~ class_Int_Onumber__ring(U_4940) ),
    inference(variable_rename,[status(thm)],[f_1405_1]) ).

fof(f_1405_3,plain,
    ! [U_4940,U_4941] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4940),c_Groups_Oone__class_Oone(U_4940)),hAPP(c_Int_Onumber__class_Onumber__of(U_4940),U_4941)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4940),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_4941)))
      | ~ class_Int_Onumber__ring(U_4940) ),
    inference(definitional_conversion,[status(esa)],[f_1405_2]) ).

cnf(f_1405_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4940),c_Groups_Oone__class_Oone(U_4940)),hAPP(c_Int_Onumber__class_Onumber__of(U_4940),U_4941)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4940),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_4941)))
    | ~ class_Int_Onumber__ring(U_4940) ),
    inference(clausify,[status(thm)],[f_1405_3]) ).

fof(f_1406_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_1406_2,plain,
    ! [U_4943,U_4942] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4942),hAPP(c_Int_Onumber__class_Onumber__of(U_4942),U_4943)),c_Groups_Oone__class_Oone(U_4942)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4942),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4943),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
      | ~ class_Int_Onumber__ring(U_4942) ),
    inference(variable_rename,[status(thm)],[f_1406_1]) ).

fof(f_1406_3,plain,
    ! [U_4942,U_4943] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4942),hAPP(c_Int_Onumber__class_Onumber__of(U_4942),U_4943)),c_Groups_Oone__class_Oone(U_4942)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4942),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4943),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
      | ~ class_Int_Onumber__ring(U_4942) ),
    inference(definitional_conversion,[status(esa)],[f_1406_2]) ).

cnf(f_1406_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4942),hAPP(c_Int_Onumber__class_Onumber__of(U_4942),U_4943)),c_Groups_Oone__class_Oone(U_4942)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4942),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4943),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
    | ~ class_Int_Onumber__ring(U_4942) ),
    inference(clausify,[status(thm)],[f_1406_3]) ).

fof(f_1407_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_1407_2,plain,
    ! [U_4945,U_4944] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4944)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4945)) = 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_4944)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4945)),
    inference(variable_rename,[status(thm)],[f_1407_1]) ).

fof(f_1407_3,plain,
    ! [U_4944,U_4945] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4944)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4945)) = 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_4944)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4945)),
    inference(definitional_conversion,[status(esa)],[f_1407_2]) ).

cnf(f_1407_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_4944)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4945)) = 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_4944)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4945)),
    inference(clausify,[status(thm)],[f_1407_3]) ).

fof(f_1408_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_1408_2,plain,
    ! [U_4947,U_4946] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4946)))),U_4947) = 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_4946)),U_4947),
    inference(variable_rename,[status(thm)],[f_1408_1]) ).

fof(f_1408_3,plain,
    ! [U_4946,U_4947] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_4946)))),U_4947) = 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_4946)),U_4947),
    inference(definitional_conversion,[status(esa)],[f_1408_2]) ).

cnf(f_1408_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_4946)))),U_4947) = 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_4946)),U_4947),
    inference(clausify,[status(thm)],[f_1408_3]) ).

fof(f_1409_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_1409_2,plain,
    ! [U_4949,U_4948] :
      ( ( c_Int_OBit1(U_4948) = c_Int_OBit1(U_4949)
        | U_4948 != U_4949 )
      & ( U_4948 = U_4949
        | c_Int_OBit1(U_4948) != c_Int_OBit1(U_4949) ) ),
    inference(variable_rename,[status(thm)],[f_1409_1]) ).

fof(f_1409_3,plain,
    ( ! [U_4953,U_4951] :
        ( c_Int_OBit1(U_4951) = c_Int_OBit1(U_4953)
        | U_4951 != U_4953 )
    & ! [U_4952,U_4950] :
        ( U_4950 = U_4952
        | c_Int_OBit1(U_4950) != c_Int_OBit1(U_4952) ) ),
    inference(miniscope,[status(thm)],[f_1409_2]) ).

fof(f_1409_4,plain,
    ( ! [U_4953,U_4951] :
        ( c_Int_OBit1(U_4951) = c_Int_OBit1(U_4953)
        | U_4951 != U_4953 )
    & ! [U_4952,U_4950] :
        ( U_4950 = U_4952
        | c_Int_OBit1(U_4950) != c_Int_OBit1(U_4952) ) ),
    inference(definitional_conversion,[status(esa)],[f_1409_3]) ).

cnf(f_1409_5,plain,
    ( U_4950 = U_4952
    | c_Int_OBit1(U_4950) != c_Int_OBit1(U_4952) ),
    inference(clausify,[status(thm)],[f_1409_4]) ).

cnf(f_1409_6,plain,
    ( c_Int_OBit1(U_4951) = c_Int_OBit1(U_4953)
    | U_4951 != U_4953 ),
    inference(clausify,[status(thm)],[f_1409_4]) ).

fof(f_1410_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_1410_2,plain,
    ! [U_4955,U_4954] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4954)),c_Int_OBit1(U_4955)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4954),U_4955)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4954),U_4955))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4954)),c_Int_OBit1(U_4955))) ) ),
    inference(variable_rename,[status(thm)],[f_1410_1]) ).

fof(f_1410_3,plain,
    ( ! [U_4959,U_4957] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4957)),c_Int_OBit1(U_4959)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4957),U_4959)) )
    & ! [U_4958,U_4956] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4956),U_4958))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4956)),c_Int_OBit1(U_4958))) ) ),
    inference(miniscope,[status(thm)],[f_1410_2]) ).

fof(f_1410_4,plain,
    ( ! [U_4957,U_4959] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4957)),c_Int_OBit1(U_4959)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4957),U_4959)) )
    & ! [U_4958,U_4956] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4956),U_4958))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4956)),c_Int_OBit1(U_4958))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1410_3]) ).

cnf(f_1410_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4956),U_4958))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4956)),c_Int_OBit1(U_4958))) ),
    inference(clausify,[status(thm)],[f_1410_4]) ).

cnf(f_1410_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4957)),c_Int_OBit1(U_4959)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4957),U_4959)) ),
    inference(clausify,[status(thm)],[f_1410_4]) ).

fof(f_1411_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_1411_2,plain,
    ! [U_4961,U_4960] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4960)),c_Int_OBit1(U_4961)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4960),U_4961)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4960),U_4961))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4960)),c_Int_OBit1(U_4961))) ) ),
    inference(variable_rename,[status(thm)],[f_1411_1]) ).

fof(f_1411_3,plain,
    ( ! [U_4965,U_4963] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4963)),c_Int_OBit1(U_4965)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4963),U_4965)) )
    & ! [U_4964,U_4962] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4962),U_4964))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4962)),c_Int_OBit1(U_4964))) ) ),
    inference(miniscope,[status(thm)],[f_1411_2]) ).

fof(f_1411_4,plain,
    ( ! [U_4963,U_4965] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4963)),c_Int_OBit1(U_4965)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4963),U_4965)) )
    & ! [U_4964,U_4962] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4962),U_4964))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4962)),c_Int_OBit1(U_4964))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1411_3]) ).

cnf(f_1411_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4962),U_4964))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4962)),c_Int_OBit1(U_4964))) ),
    inference(clausify,[status(thm)],[f_1411_4]) ).

cnf(f_1411_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4963)),c_Int_OBit1(U_4965)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4963),U_4965)) ),
    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(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_1412_2,plain,
    ! [U_4967,U_4966] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4966)),c_Int_OBit1(U_4967)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4966),U_4967)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4966),U_4967))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4966)),c_Int_OBit1(U_4967))) ) ),
    inference(variable_rename,[status(thm)],[f_1412_1]) ).

fof(f_1412_3,plain,
    ( ! [U_4971,U_4969] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4969)),c_Int_OBit1(U_4971)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4969),U_4971)) )
    & ! [U_4970,U_4968] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4968),U_4970))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4968)),c_Int_OBit1(U_4970))) ) ),
    inference(miniscope,[status(thm)],[f_1412_2]) ).

fof(f_1412_4,plain,
    ( ! [U_4971,U_4969] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4969)),c_Int_OBit1(U_4971)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4969),U_4971)) )
    & ! [U_4970,U_4968] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4968),U_4970))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4968)),c_Int_OBit1(U_4970))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1412_3]) ).

cnf(f_1412_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4968),U_4970))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4968)),c_Int_OBit1(U_4970))) ),
    inference(clausify,[status(thm)],[f_1412_4]) ).

cnf(f_1412_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4969)),c_Int_OBit1(U_4971)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4969),U_4971)) ),
    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(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_1413_2,plain,
    ! [U_4973,U_4972] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4972)),c_Int_OBit1(U_4973)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4972),U_4973)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4972),U_4973))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4972)),c_Int_OBit1(U_4973))) ) ),
    inference(variable_rename,[status(thm)],[f_1413_1]) ).

fof(f_1413_3,plain,
    ( ! [U_4977,U_4975] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4975)),c_Int_OBit1(U_4977)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4975),U_4977)) )
    & ! [U_4976,U_4974] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4974),U_4976))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4974)),c_Int_OBit1(U_4976))) ) ),
    inference(miniscope,[status(thm)],[f_1413_2]) ).

fof(f_1413_4,plain,
    ( ! [U_4975,U_4977] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4975)),c_Int_OBit1(U_4977)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4975),U_4977)) )
    & ! [U_4976,U_4974] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4974),U_4976))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4974)),c_Int_OBit1(U_4976))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1413_3]) ).

cnf(f_1413_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4974),U_4976))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4974)),c_Int_OBit1(U_4976))) ),
    inference(clausify,[status(thm)],[f_1413_4]) ).

cnf(f_1413_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4975)),c_Int_OBit1(U_4977)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4975),U_4977)) ),
    inference(clausify,[status(thm)],[f_1413_4]) ).

fof(f_1414_1,plain,
    ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I39_J]) ).

fof(f_1414_2,plain,
    ! [U_4978] : c_Int_OPls != c_Int_OBit1(U_4978),
    inference(variable_rename,[status(thm)],[f_1414_1]) ).

fof(f_1414_3,plain,
    ! [U_4978] : c_Int_OPls != c_Int_OBit1(U_4978),
    inference(definitional_conversion,[status(esa)],[f_1414_2]) ).

cnf(f_1414_4,plain,
    c_Int_OPls != c_Int_OBit1(U_4978),
    inference(clausify,[status(thm)],[f_1414_3]) ).

fof(f_1415_1,plain,
    ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I46_J]) ).

fof(f_1415_2,plain,
    ! [U_4979] : c_Int_OBit1(U_4979) != c_Int_OPls,
    inference(variable_rename,[status(thm)],[f_1415_1]) ).

fof(f_1415_3,plain,
    ! [U_4979] : c_Int_OBit1(U_4979) != c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1415_2]) ).

cnf(f_1415_4,plain,
    c_Int_OBit1(U_4979) != c_Int_OPls,
    inference(clausify,[status(thm)],[f_1415_3]) ).

fof(f_1416_1,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_Bit1__Min]) ).

fof(f_1416_2,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(definitional_conversion,[status(esa)],[f_1416_1]) ).

cnf(f_1416_3,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(clausify,[status(thm)],[f_1416_2]) ).

fof(f_1417_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_1417_2,plain,
    ! [U_4980] :
      ( ( c_Int_OMin = c_Int_OBit1(U_4980)
        | c_Int_OMin != U_4980 )
      & ( c_Int_OMin = U_4980
        | c_Int_OMin != c_Int_OBit1(U_4980) ) ),
    inference(variable_rename,[status(thm)],[f_1417_1]) ).

fof(f_1417_3,plain,
    ( ! [U_4982] :
        ( c_Int_OMin = c_Int_OBit1(U_4982)
        | c_Int_OMin != U_4982 )
    & ! [U_4981] :
        ( c_Int_OMin = U_4981
        | c_Int_OMin != c_Int_OBit1(U_4981) ) ),
    inference(miniscope,[status(thm)],[f_1417_2]) ).

fof(f_1417_4,plain,
    ( ! [U_4982] :
        ( c_Int_OMin = c_Int_OBit1(U_4982)
        | c_Int_OMin != U_4982 )
    & ! [U_4981] :
        ( c_Int_OMin = U_4981
        | c_Int_OMin != c_Int_OBit1(U_4981) ) ),
    inference(definitional_conversion,[status(esa)],[f_1417_3]) ).

cnf(f_1417_5,plain,
    ( c_Int_OMin = U_4981
    | c_Int_OMin != c_Int_OBit1(U_4981) ),
    inference(clausify,[status(thm)],[f_1417_4]) ).

cnf(f_1417_6,plain,
    ( c_Int_OMin = c_Int_OBit1(U_4982)
    | c_Int_OMin != U_4982 ),
    inference(clausify,[status(thm)],[f_1417_4]) ).

fof(f_1418_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_1418_2,plain,
    ! [U_4983] :
      ( ( c_Int_OBit1(U_4983) = c_Int_OMin
        | U_4983 != c_Int_OMin )
      & ( U_4983 = c_Int_OMin
        | c_Int_OBit1(U_4983) != c_Int_OMin ) ),
    inference(variable_rename,[status(thm)],[f_1418_1]) ).

fof(f_1418_3,plain,
    ( ! [U_4985] :
        ( c_Int_OBit1(U_4985) = c_Int_OMin
        | U_4985 != c_Int_OMin )
    & ! [U_4984] :
        ( U_4984 = c_Int_OMin
        | c_Int_OBit1(U_4984) != c_Int_OMin ) ),
    inference(miniscope,[status(thm)],[f_1418_2]) ).

fof(f_1418_4,plain,
    ( ! [U_4985] :
        ( c_Int_OBit1(U_4985) = c_Int_OMin
        | U_4985 != c_Int_OMin )
    & ! [U_4984] :
        ( U_4984 = c_Int_OMin
        | c_Int_OBit1(U_4984) != c_Int_OMin ) ),
    inference(definitional_conversion,[status(esa)],[f_1418_3]) ).

cnf(f_1418_5,plain,
    ( U_4984 = c_Int_OMin
    | c_Int_OBit1(U_4984) != c_Int_OMin ),
    inference(clausify,[status(thm)],[f_1418_4]) ).

cnf(f_1418_6,plain,
    ( c_Int_OBit1(U_4985) = c_Int_OMin
    | U_4985 != c_Int_OMin ),
    inference(clausify,[status(thm)],[f_1418_4]) ).

fof(f_1419_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_1419_2,plain,
    ! [U_4986] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4986)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4986),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4986),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4986)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1419_1]) ).

fof(f_1419_3,plain,
    ( ! [U_4988] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4988)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4988),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4987] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4987),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4987)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1419_2]) ).

fof(f_1419_4,plain,
    ( ! [U_4988] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4988)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4988),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4987] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4987),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4987)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1419_3]) ).

cnf(f_1419_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4987),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4987)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1419_4]) ).

cnf(f_1419_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4988)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4988),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1419_4]) ).

fof(f_1420_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_1420_2,plain,
    ! [U_4989] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4989)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4989)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4989))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4989))) ) ),
    inference(variable_rename,[status(thm)],[f_1420_1]) ).

fof(f_1420_3,plain,
    ( ! [U_4991] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4991)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4991)) )
    & ! [U_4990] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4990))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4990))) ) ),
    inference(miniscope,[status(thm)],[f_1420_2]) ).

fof(f_1420_4,plain,
    ( ! [U_4991] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4991)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4991)) )
    & ! [U_4990] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4990))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4990))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1420_3]) ).

cnf(f_1420_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4990))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4990))) ),
    inference(clausify,[status(thm)],[f_1420_4]) ).

cnf(f_1420_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_4991)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4991)) ),
    inference(clausify,[status(thm)],[f_1420_4]) ).

fof(f_1421_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_1421_2,plain,
    ! [U_4992] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4992)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4992),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4992),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4992)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1421_1]) ).

fof(f_1421_3,plain,
    ( ! [U_4994] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4994)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4994),c_Int_OPls)) )
    & ! [U_4993] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4993),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4993)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1421_2]) ).

fof(f_1421_4,plain,
    ( ! [U_4994] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4994)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4994),c_Int_OPls)) )
    & ! [U_4993] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4993),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4993)),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1421_3]) ).

cnf(f_1421_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4993),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4993)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1421_4]) ).

cnf(f_1421_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_4994)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4994),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1421_4]) ).

fof(f_1422_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_1422_2,plain,
    ! [U_4995] : c_Int_OBit1(U_4995) = 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_4995)),U_4995),
    inference(variable_rename,[status(thm)],[f_1422_1]) ).

fof(f_1422_3,plain,
    ! [U_4995] : c_Int_OBit1(U_4995) = 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_4995)),U_4995),
    inference(definitional_conversion,[status(esa)],[f_1422_2]) ).

cnf(f_1422_4,plain,
    c_Int_OBit1(U_4995) = 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_4995)),U_4995),
    inference(clausify,[status(thm)],[f_1422_3]) ).

fof(f_1423_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_1423_2,plain,
    ! [U_4996] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4996)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4996),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4996),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4996)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1423_1]) ).

fof(f_1423_3,plain,
    ( ! [U_4998] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4998)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4998),c_Int_OMin)) )
    & ! [U_4997] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4997),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4997)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1423_2]) ).

fof(f_1423_4,plain,
    ( ! [U_4998] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4998)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4998),c_Int_OMin)) )
    & ! [U_4997] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4997),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4997)),c_Int_OMin)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1423_3]) ).

cnf(f_1423_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4997),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4997)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1423_4]) ).

cnf(f_1423_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_4998)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4998),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1423_4]) ).

fof(f_1424_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_1424_2,plain,
    ! [U_4999] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4999)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_4999)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_4999))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_4999))) ) ),
    inference(variable_rename,[status(thm)],[f_1424_1]) ).

fof(f_1424_3,plain,
    ( ! [U_5001] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5001)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5001)) )
    & ! [U_5000] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5000))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5000))) ) ),
    inference(miniscope,[status(thm)],[f_1424_2]) ).

fof(f_1424_4,plain,
    ( ! [U_5001] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5001)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5001)) )
    & ! [U_5000] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5000))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5000))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1424_3]) ).

cnf(f_1424_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5000))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5000))) ),
    inference(clausify,[status(thm)],[f_1424_4]) ).

cnf(f_1424_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5001)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5001)) ),
    inference(clausify,[status(thm)],[f_1424_4]) ).

fof(f_1425_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_1425_2,plain,
    ! [U_5002] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5002)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5002)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5002))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5002))) ) ),
    inference(variable_rename,[status(thm)],[f_1425_1]) ).

fof(f_1425_3,plain,
    ( ! [U_5004] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5004)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5004)) )
    & ! [U_5003] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5003))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5003))) ) ),
    inference(miniscope,[status(thm)],[f_1425_2]) ).

fof(f_1425_4,plain,
    ( ! [U_5004] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5004)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5004)) )
    & ! [U_5003] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5003))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5003))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1425_3]) ).

cnf(f_1425_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5003))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5003))) ),
    inference(clausify,[status(thm)],[f_1425_4]) ).

cnf(f_1425_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5004)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5004)) ),
    inference(clausify,[status(thm)],[f_1425_4]) ).

fof(f_1426_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_1426_2,plain,
    ! [U_5005] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5005)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5005),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5005),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5005)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1426_1]) ).

fof(f_1426_3,plain,
    ( ! [U_5007] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5007)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5007),c_Int_OMin)) )
    & ! [U_5006] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5006),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5006)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1426_2]) ).

fof(f_1426_4,plain,
    ( ! [U_5007] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5007)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5007),c_Int_OMin)) )
    & ! [U_5006] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5006),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5006)),c_Int_OMin)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1426_3]) ).

cnf(f_1426_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5006),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5006)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1426_4]) ).

cnf(f_1426_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5007)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5007),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1426_4]) ).

fof(f_1427_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_1427_2,plain,
    ! [U_5008] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5008))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5008))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5008)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5008)))) ) ),
    inference(variable_rename,[status(thm)],[f_1427_1]) ).

fof(f_1427_3,plain,
    ( ! [U_5010] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5010))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5010))) )
    & ! [U_5009] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5009)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5009)))) ) ),
    inference(miniscope,[status(thm)],[f_1427_2]) ).

fof(f_1427_4,plain,
    ( ! [U_5010] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5010))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5010))) )
    & ! [U_5009] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5009)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5009)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1427_3]) ).

cnf(f_1427_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5009)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5009)))) ),
    inference(clausify,[status(thm)],[f_1427_4]) ).

cnf(f_1427_6,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5010))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5010))) ),
    inference(clausify,[status(thm)],[f_1427_4]) ).

fof(f_1428_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_1428_2,plain,
    ! [U_5011] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_5011)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5011))),
    inference(variable_rename,[status(thm)],[f_1428_1]) ).

fof(f_1428_3,plain,
    ! [U_5011] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_5011)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5011))),
    inference(definitional_conversion,[status(esa)],[f_1428_2]) ).

cnf(f_1428_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_5011)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5011))),
    inference(clausify,[status(thm)],[f_1428_3]) ).

fof(f_1429_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_1429_2,plain,
    ! [U_5013,U_5012] :
      ( ~ c_Int_Oiszero(U_5012,hAPP(c_Int_Onumber__class_Onumber__of(U_5012),c_Int_OBit1(U_5013)))
      | ~ class_Int_Oring__char__0(U_5012)
      | ~ class_Int_Onumber__ring(U_5012) ),
    inference(variable_rename,[status(thm)],[f_1429_1]) ).

fof(f_1429_3,plain,
    ! [U_5012,U_5013] :
      ( ~ c_Int_Oiszero(U_5012,hAPP(c_Int_Onumber__class_Onumber__of(U_5012),c_Int_OBit1(U_5013)))
      | ~ class_Int_Oring__char__0(U_5012)
      | ~ class_Int_Onumber__ring(U_5012) ),
    inference(definitional_conversion,[status(esa)],[f_1429_2]) ).

cnf(f_1429_4,plain,
    ( ~ c_Int_Oiszero(U_5012,hAPP(c_Int_Onumber__class_Onumber__of(U_5012),c_Int_OBit1(U_5013)))
    | ~ class_Int_Oring__char__0(U_5012)
    | ~ class_Int_Onumber__ring(U_5012) ),
    inference(clausify,[status(thm)],[f_1429_3]) ).

fof(f_1430_1,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_succ__Pls]) ).

fof(f_1430_2,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(definitional_conversion,[status(esa)],[f_1430_1]) ).

cnf(f_1430_3,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(clausify,[status(thm)],[f_1430_2]) ).

fof(f_1431_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_1431_2,plain,
    ! [U_5015,U_5014] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5014),c_Int_OBit1(U_5015)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5014),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5014),c_Groups_Oone__class_Oone(U_5014)),hAPP(c_Int_Onumber__class_Onumber__of(U_5014),U_5015))),hAPP(c_Int_Onumber__class_Onumber__of(U_5014),U_5015))
      | ~ class_Int_Onumber__ring(U_5014) ),
    inference(variable_rename,[status(thm)],[f_1431_1]) ).

fof(f_1431_3,plain,
    ! [U_5014,U_5015] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5014),c_Int_OBit1(U_5015)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5014),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5014),c_Groups_Oone__class_Oone(U_5014)),hAPP(c_Int_Onumber__class_Onumber__of(U_5014),U_5015))),hAPP(c_Int_Onumber__class_Onumber__of(U_5014),U_5015))
      | ~ class_Int_Onumber__ring(U_5014) ),
    inference(definitional_conversion,[status(esa)],[f_1431_2]) ).

cnf(f_1431_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5014),c_Int_OBit1(U_5015)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5014),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5014),c_Groups_Oone__class_Oone(U_5014)),hAPP(c_Int_Onumber__class_Onumber__of(U_5014),U_5015))),hAPP(c_Int_Onumber__class_Onumber__of(U_5014),U_5015))
    | ~ class_Int_Onumber__ring(U_5014) ),
    inference(clausify,[status(thm)],[f_1431_3]) ).

fof(f_1432_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_1432_2,plain,
    ! [U_5017,U_5016] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5016),U_5017),hAPP(c_Int_Onumber__class_Onumber__of(U_5016),c_Int_OBit1(c_Int_OPls))) = U_5017
      | ~ class_Int_Onumber__ring(U_5016) ),
    inference(variable_rename,[status(thm)],[f_1432_1]) ).

fof(f_1432_3,plain,
    ! [U_5016,U_5017] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5016),U_5017),hAPP(c_Int_Onumber__class_Onumber__of(U_5016),c_Int_OBit1(c_Int_OPls))) = U_5017
      | ~ class_Int_Onumber__ring(U_5016) ),
    inference(definitional_conversion,[status(esa)],[f_1432_2]) ).

cnf(f_1432_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5016),U_5017),hAPP(c_Int_Onumber__class_Onumber__of(U_5016),c_Int_OBit1(c_Int_OPls))) = U_5017
    | ~ class_Int_Onumber__ring(U_5016) ),
    inference(clausify,[status(thm)],[f_1432_3]) ).

fof(f_1433_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_1433_2,plain,
    ! [U_5019,U_5018] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5018),hAPP(c_Int_Onumber__class_Onumber__of(U_5018),c_Int_OBit1(c_Int_OPls))),U_5019) = U_5019
      | ~ class_Int_Onumber__ring(U_5018) ),
    inference(variable_rename,[status(thm)],[f_1433_1]) ).

fof(f_1433_3,plain,
    ! [U_5018,U_5019] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5018),hAPP(c_Int_Onumber__class_Onumber__of(U_5018),c_Int_OBit1(c_Int_OPls))),U_5019) = U_5019
      | ~ class_Int_Onumber__ring(U_5018) ),
    inference(definitional_conversion,[status(esa)],[f_1433_2]) ).

cnf(f_1433_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5018),hAPP(c_Int_Onumber__class_Onumber__of(U_5018),c_Int_OBit1(c_Int_OPls))),U_5019) = U_5019
    | ~ class_Int_Onumber__ring(U_5018) ),
    inference(clausify,[status(thm)],[f_1433_3]) ).

fof(f_1434_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_1434_2,plain,
    ! [U_5020] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5020),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_5020)
      | ~ class_Int_Onumber__ring(U_5020) ),
    inference(variable_rename,[status(thm)],[f_1434_1]) ).

fof(f_1434_3,plain,
    ! [U_5020] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5020),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_5020)
      | ~ class_Int_Onumber__ring(U_5020) ),
    inference(definitional_conversion,[status(esa)],[f_1434_2]) ).

cnf(f_1434_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5020),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_5020)
    | ~ class_Int_Onumber__ring(U_5020) ),
    inference(clausify,[status(thm)],[f_1434_3]) ).

fof(f_1435_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_1435_2,plain,
    ! [U_5021] :
      ( c_Groups_Oone__class_Oone(U_5021) = hAPP(c_Int_Onumber__class_Onumber__of(U_5021),c_Int_OBit1(c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_5021) ),
    inference(variable_rename,[status(thm)],[f_1435_1]) ).

fof(f_1435_3,plain,
    ! [U_5021] :
      ( c_Groups_Oone__class_Oone(U_5021) = hAPP(c_Int_Onumber__class_Onumber__of(U_5021),c_Int_OBit1(c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_5021) ),
    inference(definitional_conversion,[status(esa)],[f_1435_2]) ).

cnf(f_1435_4,plain,
    ( c_Groups_Oone__class_Oone(U_5021) = hAPP(c_Int_Onumber__class_Onumber__of(U_5021),c_Int_OBit1(c_Int_OPls))
    | ~ class_Int_Onumber__ring(U_5021) ),
    inference(clausify,[status(thm)],[f_1435_3]) ).

fof(f_1436_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_1436_2,plain,
    ! [U_5022] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5022)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5022),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5022),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5022)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1436_1]) ).

fof(f_1436_3,plain,
    ( ! [U_5024] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5024)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5024),c_Int_OPls)) )
    & ! [U_5023] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5023),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5023)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1436_2]) ).

fof(f_1436_4,plain,
    ( ! [U_5024] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5024)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5024),c_Int_OPls)) )
    & ! [U_5023] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5023),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5023)),c_Int_OPls)) ) ),
    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_5023),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5023)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1436_4]) ).

cnf(f_1436_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5024)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5024),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1436_4]) ).

fof(f_1437_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_1437_2,plain,
    ! [U_5025] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5025)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5025)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5025))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5025))) ) ),
    inference(variable_rename,[status(thm)],[f_1437_1]) ).

fof(f_1437_3,plain,
    ( ! [U_5027] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5027)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5027)) )
    & ! [U_5026] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5026))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5026))) ) ),
    inference(miniscope,[status(thm)],[f_1437_2]) ).

fof(f_1437_4,plain,
    ( ! [U_5027] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5027)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5027)) )
    & ! [U_5026] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5026))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5026))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1437_3]) ).

cnf(f_1437_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5026))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5026))) ),
    inference(clausify,[status(thm)],[f_1437_4]) ).

cnf(f_1437_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5027)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5027)) ),
    inference(clausify,[status(thm)],[f_1437_4]) ).

fof(f_1438_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_1438_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_1438_1]) ).

cnf(f_1438_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_1438_2]) ).

fof(f_1439_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_1439_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_1439_1]) ).

cnf(f_1439_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_1439_2]) ).

fof(f_1440_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_1440_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_1440_1]) ).

cnf(f_1440_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_1440_2]) ).

fof(f_1441_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_1441_2,plain,
    ! [U_5028] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5028)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5028)),
    inference(variable_rename,[status(thm)],[f_1441_1]) ).

fof(f_1441_3,plain,
    ! [U_5028] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5028)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5028)),
    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_OPls),c_Int_OBit1(U_5028)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5028)),
    inference(clausify,[status(thm)],[f_1441_3]) ).

fof(f_1442_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_1442_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_1442_1]) ).

cnf(f_1442_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_1442_2]) ).

fof(f_1443_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_1443_2,plain,
    ! [U_5029] :
      ( ~ c_Int_Oiszero(U_5029,hAPP(c_Int_Onumber__class_Onumber__of(U_5029),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_5029) ),
    inference(variable_rename,[status(thm)],[f_1443_1]) ).

fof(f_1443_3,plain,
    ! [U_5029] :
      ( ~ c_Int_Oiszero(U_5029,hAPP(c_Int_Onumber__class_Onumber__of(U_5029),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_5029) ),
    inference(definitional_conversion,[status(esa)],[f_1443_2]) ).

cnf(f_1443_4,plain,
    ( ~ c_Int_Oiszero(U_5029,hAPP(c_Int_Onumber__class_Onumber__of(U_5029),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_5029) ),
    inference(clausify,[status(thm)],[f_1443_3]) ).

fof(f_1444_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_1444_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_1444_1]) ).

cnf(f_1444_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_1444_2]) ).

fof(f_1445_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_1445_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_1445_1]) ).

cnf(f_1445_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_1445_2]) ).

fof(f_1446_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_1446_2,plain,
    ! [U_5031,U_5030] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5030),U_5031),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_5030),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5030),U_5031),U_5031)),U_5031)
      | ~ class_Groups_Omonoid__mult(U_5030) ),
    inference(variable_rename,[status(thm)],[f_1446_1]) ).

fof(f_1446_3,plain,
    ! [U_5030,U_5031] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5030),U_5031),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_5030),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5030),U_5031),U_5031)),U_5031)
      | ~ class_Groups_Omonoid__mult(U_5030) ),
    inference(definitional_conversion,[status(esa)],[f_1446_2]) ).

cnf(f_1446_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5030),U_5031),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_5030),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5030),U_5031),U_5031)),U_5031)
    | ~ class_Groups_Omonoid__mult(U_5030) ),
    inference(clausify,[status(thm)],[f_1446_3]) ).

fof(f_1447_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_1447_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_1447_1]) ).

cnf(f_1447_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_1447_2]) ).

fof(f_1448_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_1448_2,plain,
    ! [U_5032] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5032))) = 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_5032),
    inference(variable_rename,[status(thm)],[f_1448_1]) ).

fof(f_1448_3,plain,
    ! [U_5032] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5032))) = 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_5032),
    inference(definitional_conversion,[status(esa)],[f_1448_2]) ).

cnf(f_1448_4,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5032))) = 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_5032),
    inference(clausify,[status(thm)],[f_1448_3]) ).

fof(f_1449_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_1449_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_1449_1]) ).

cnf(f_1449_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_1449_2]) ).

fof(f_1450_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_1450_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_1450_1]) ).

cnf(f_1450_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_1450_2]) ).

fof(f_1451_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_1451_2,plain,
    ! [U_5034,U_5033] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5033),c_Groups_Oone__class_Oone(U_5033)),hAPP(c_Int_Onumber__class_Onumber__of(U_5033),U_5034)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5034)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5034))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5033),c_Groups_Oone__class_Oone(U_5033)),hAPP(c_Int_Onumber__class_Onumber__of(U_5033),U_5034))) ) )
      | ~ class_Rings_Olinordered__idom(U_5033)
      | ~ class_Int_Onumber__ring(U_5033) ),
    inference(variable_rename,[status(thm)],[f_1451_1]) ).

fof(f_1451_3,plain,
    ( ! [U_5033,U_5034] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5033),c_Groups_Oone__class_Oone(U_5033)),hAPP(c_Int_Onumber__class_Onumber__of(U_5033),U_5034)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5034))
        | ~ sP392(U_5033,U_5034) )
    & ! [U_5033,U_5034] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5034))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5033),c_Groups_Oone__class_Oone(U_5033)),hAPP(c_Int_Onumber__class_Onumber__of(U_5033),U_5034)))
        | ~ sP392(U_5033,U_5034) )
    & ! [U_5033,U_5034] :
        ( sP392(U_5033,U_5034)
        | ~ class_Rings_Olinordered__idom(U_5033)
        | ~ class_Int_Onumber__ring(U_5033) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP392])],[f_1451_2]) ).

cnf(f_1451_4,plain,
    ( sP392(U_5033,U_5034)
    | ~ class_Rings_Olinordered__idom(U_5033)
    | ~ class_Int_Onumber__ring(U_5033) ),
    inference(clausify,[status(thm)],[f_1451_3]) ).

cnf(f_1451_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5034))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5033),c_Groups_Oone__class_Oone(U_5033)),hAPP(c_Int_Onumber__class_Onumber__of(U_5033),U_5034)))
    | ~ sP392(U_5033,U_5034) ),
    inference(clausify,[status(thm)],[f_1451_3]) ).

cnf(f_1451_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5033),c_Groups_Oone__class_Oone(U_5033)),hAPP(c_Int_Onumber__class_Onumber__of(U_5033),U_5034)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5034))
    | ~ sP392(U_5033,U_5034) ),
    inference(clausify,[status(thm)],[f_1451_3]) ).

fof(f_1452_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_1452_2,plain,
    ! [U_5036,U_5035] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5035),hAPP(c_Int_Onumber__class_Onumber__of(U_5035),U_5036)),c_Groups_Oone__class_Oone(U_5035)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5036),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5036),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5035),hAPP(c_Int_Onumber__class_Onumber__of(U_5035),U_5036)),c_Groups_Oone__class_Oone(U_5035))) ) )
      | ~ class_Rings_Olinordered__idom(U_5035)
      | ~ class_Int_Onumber__ring(U_5035) ),
    inference(variable_rename,[status(thm)],[f_1452_1]) ).

fof(f_1452_3,plain,
    ( ! [U_5036,U_5035] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5035),hAPP(c_Int_Onumber__class_Onumber__of(U_5035),U_5036)),c_Groups_Oone__class_Oone(U_5035)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5036),c_Int_OBit1(c_Int_OPls)))
        | ~ sP393(U_5036,U_5035) )
    & ! [U_5036,U_5035] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5036),c_Int_OBit1(c_Int_OPls)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5035),hAPP(c_Int_Onumber__class_Onumber__of(U_5035),U_5036)),c_Groups_Oone__class_Oone(U_5035)))
        | ~ sP393(U_5036,U_5035) )
    & ! [U_5036,U_5035] :
        ( sP393(U_5036,U_5035)
        | ~ class_Rings_Olinordered__idom(U_5035)
        | ~ class_Int_Onumber__ring(U_5035) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP393])],[f_1452_2]) ).

cnf(f_1452_4,plain,
    ( sP393(U_5036,U_5035)
    | ~ class_Rings_Olinordered__idom(U_5035)
    | ~ class_Int_Onumber__ring(U_5035) ),
    inference(clausify,[status(thm)],[f_1452_3]) ).

cnf(f_1452_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5036),c_Int_OBit1(c_Int_OPls)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5035),hAPP(c_Int_Onumber__class_Onumber__of(U_5035),U_5036)),c_Groups_Oone__class_Oone(U_5035)))
    | ~ sP393(U_5036,U_5035) ),
    inference(clausify,[status(thm)],[f_1452_3]) ).

cnf(f_1452_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5035),hAPP(c_Int_Onumber__class_Onumber__of(U_5035),U_5036)),c_Groups_Oone__class_Oone(U_5035)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5036),c_Int_OBit1(c_Int_OPls)))
    | ~ sP393(U_5036,U_5035) ),
    inference(clausify,[status(thm)],[f_1452_3]) ).

fof(f_1453_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_1453_2,plain,
    ! [U_5038,U_5037] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5037),hAPP(c_Int_Onumber__class_Onumber__of(U_5037),U_5038)),c_Groups_Oone__class_Oone(U_5037)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5038),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5038),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5037),hAPP(c_Int_Onumber__class_Onumber__of(U_5037),U_5038)),c_Groups_Oone__class_Oone(U_5037))) ) )
      | ~ class_Rings_Olinordered__idom(U_5037)
      | ~ class_Int_Onumber__ring(U_5037) ),
    inference(variable_rename,[status(thm)],[f_1453_1]) ).

fof(f_1453_3,plain,
    ( ! [U_5037,U_5038] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5037),hAPP(c_Int_Onumber__class_Onumber__of(U_5037),U_5038)),c_Groups_Oone__class_Oone(U_5037)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5038),c_Int_OBit1(c_Int_OPls)))
        | ~ sP394(U_5037,U_5038) )
    & ! [U_5037,U_5038] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5038),c_Int_OBit1(c_Int_OPls)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5037),hAPP(c_Int_Onumber__class_Onumber__of(U_5037),U_5038)),c_Groups_Oone__class_Oone(U_5037)))
        | ~ sP394(U_5037,U_5038) )
    & ! [U_5037,U_5038] :
        ( sP394(U_5037,U_5038)
        | ~ class_Rings_Olinordered__idom(U_5037)
        | ~ class_Int_Onumber__ring(U_5037) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP394])],[f_1453_2]) ).

cnf(f_1453_4,plain,
    ( sP394(U_5037,U_5038)
    | ~ class_Rings_Olinordered__idom(U_5037)
    | ~ class_Int_Onumber__ring(U_5037) ),
    inference(clausify,[status(thm)],[f_1453_3]) ).

cnf(f_1453_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5038),c_Int_OBit1(c_Int_OPls)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5037),hAPP(c_Int_Onumber__class_Onumber__of(U_5037),U_5038)),c_Groups_Oone__class_Oone(U_5037)))
    | ~ sP394(U_5037,U_5038) ),
    inference(clausify,[status(thm)],[f_1453_3]) ).

cnf(f_1453_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5037),hAPP(c_Int_Onumber__class_Onumber__of(U_5037),U_5038)),c_Groups_Oone__class_Oone(U_5037)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5038),c_Int_OBit1(c_Int_OPls)))
    | ~ sP394(U_5037,U_5038) ),
    inference(clausify,[status(thm)],[f_1453_3]) ).

fof(f_1454_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_1454_2,plain,
    ! [U_5040,U_5039] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5039),c_Groups_Oone__class_Oone(U_5039)),hAPP(c_Int_Onumber__class_Onumber__of(U_5039),U_5040)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5040)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5040))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5039),c_Groups_Oone__class_Oone(U_5039)),hAPP(c_Int_Onumber__class_Onumber__of(U_5039),U_5040))) ) )
      | ~ class_Rings_Olinordered__idom(U_5039)
      | ~ class_Int_Onumber__ring(U_5039) ),
    inference(variable_rename,[status(thm)],[f_1454_1]) ).

fof(f_1454_3,plain,
    ( ! [U_5040,U_5039] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5039),c_Groups_Oone__class_Oone(U_5039)),hAPP(c_Int_Onumber__class_Onumber__of(U_5039),U_5040)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5040))
        | ~ sP395(U_5040,U_5039) )
    & ! [U_5040,U_5039] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5040))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5039),c_Groups_Oone__class_Oone(U_5039)),hAPP(c_Int_Onumber__class_Onumber__of(U_5039),U_5040)))
        | ~ sP395(U_5040,U_5039) )
    & ! [U_5040,U_5039] :
        ( sP395(U_5040,U_5039)
        | ~ class_Rings_Olinordered__idom(U_5039)
        | ~ class_Int_Onumber__ring(U_5039) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP395])],[f_1454_2]) ).

cnf(f_1454_4,plain,
    ( sP395(U_5040,U_5039)
    | ~ class_Rings_Olinordered__idom(U_5039)
    | ~ class_Int_Onumber__ring(U_5039) ),
    inference(clausify,[status(thm)],[f_1454_3]) ).

cnf(f_1454_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5040))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5039),c_Groups_Oone__class_Oone(U_5039)),hAPP(c_Int_Onumber__class_Onumber__of(U_5039),U_5040)))
    | ~ sP395(U_5040,U_5039) ),
    inference(clausify,[status(thm)],[f_1454_3]) ).

cnf(f_1454_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5039),c_Groups_Oone__class_Oone(U_5039)),hAPP(c_Int_Onumber__class_Onumber__of(U_5039),U_5040)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5040))
    | ~ sP395(U_5040,U_5039) ),
    inference(clausify,[status(thm)],[f_1454_3]) ).

fof(f_1455_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_1455_2,plain,
    ! [U_5042,U_5041] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5041),c_Groups_Oone__class_Oone(U_5041)),hAPP(c_Int_Onumber__class_Onumber__of(U_5041),U_5042)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5041),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5042))
      | ~ class_Int_Onumber__ring(U_5041) ),
    inference(variable_rename,[status(thm)],[f_1455_1]) ).

fof(f_1455_3,plain,
    ! [U_5041,U_5042] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5041),c_Groups_Oone__class_Oone(U_5041)),hAPP(c_Int_Onumber__class_Onumber__of(U_5041),U_5042)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5041),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5042))
      | ~ class_Int_Onumber__ring(U_5041) ),
    inference(definitional_conversion,[status(esa)],[f_1455_2]) ).

cnf(f_1455_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5041),c_Groups_Oone__class_Oone(U_5041)),hAPP(c_Int_Onumber__class_Onumber__of(U_5041),U_5042)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5041),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5042))
    | ~ class_Int_Onumber__ring(U_5041) ),
    inference(clausify,[status(thm)],[f_1455_3]) ).

fof(f_1456_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_1456_2,plain,
    ! [U_5044,U_5043] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5043),hAPP(c_Int_Onumber__class_Onumber__of(U_5043),U_5044)),c_Groups_Oone__class_Oone(U_5043)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5044),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_5043) ),
    inference(variable_rename,[status(thm)],[f_1456_1]) ).

fof(f_1456_3,plain,
    ! [U_5043,U_5044] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5043),hAPP(c_Int_Onumber__class_Onumber__of(U_5043),U_5044)),c_Groups_Oone__class_Oone(U_5043)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5044),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_5043) ),
    inference(definitional_conversion,[status(esa)],[f_1456_2]) ).

cnf(f_1456_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5043),hAPP(c_Int_Onumber__class_Onumber__of(U_5043),U_5044)),c_Groups_Oone__class_Oone(U_5043)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5044),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_5043) ),
    inference(clausify,[status(thm)],[f_1456_3]) ).

fof(f_1457_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_1457_2,plain,
    ! [U_5046,U_5045] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5046)),U_5045) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5046),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5045),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_5045)) ),
    inference(variable_rename,[status(thm)],[f_1457_1]) ).

fof(f_1457_3,plain,
    ! [U_5045,U_5046] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5046)),U_5045) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5046),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5045),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_5045)) ),
    inference(definitional_conversion,[status(esa)],[f_1457_2]) ).

cnf(f_1457_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5046)),U_5045) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5046),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5045),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_5045)) ),
    inference(clausify,[status(thm)],[f_1457_3]) ).

fof(f_1458_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_1458_2,plain,
    ! [U_5048,U_5047] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5047,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5048)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5047,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_5048)),
    inference(variable_rename,[status(thm)],[f_1458_1]) ).

fof(f_1458_3,plain,
    ! [U_5048,U_5047] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5047,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5048)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5047,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_5048)),
    inference(definitional_conversion,[status(esa)],[f_1458_2]) ).

cnf(f_1458_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5047,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5048)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5047,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_5048)),
    inference(clausify,[status(thm)],[f_1458_3]) ).

fof(f_1459_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_1459_2,plain,
    ! [U_5050,U_5049] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5049))),U_5050) = 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_5049),U_5050),
    inference(variable_rename,[status(thm)],[f_1459_1]) ).

fof(f_1459_3,plain,
    ! [U_5049,U_5050] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5049))),U_5050) = 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_5049),U_5050),
    inference(definitional_conversion,[status(esa)],[f_1459_2]) ).

cnf(f_1459_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5049))),U_5050) = 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_5049),U_5050),
    inference(clausify,[status(thm)],[f_1459_3]) ).

fof(f_1460_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_1460_2,plain,
    ! [U_5052,U_5051] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5051))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5052)) = 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_5051),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5052)),
    inference(variable_rename,[status(thm)],[f_1460_1]) ).

fof(f_1460_3,plain,
    ! [U_5051,U_5052] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5051))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5052)) = 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_5051),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5052)),
    inference(definitional_conversion,[status(esa)],[f_1460_2]) ).

cnf(f_1460_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5051))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5052)) = 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_5051),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5052)),
    inference(clausify,[status(thm)],[f_1460_3]) ).

fof(f_1461_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_1461_2,plain,
    ! [U_5054,U_5053] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5053),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5054)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5053),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_5054)),
    inference(variable_rename,[status(thm)],[f_1461_1]) ).

fof(f_1461_3,plain,
    ! [U_5053,U_5054] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5053),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5054)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5053),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_5054)),
    inference(definitional_conversion,[status(esa)],[f_1461_2]) ).

cnf(f_1461_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5053),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5054)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5053),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_5054)),
    inference(clausify,[status(thm)],[f_1461_3]) ).

fof(f_1462_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_1462_2,plain,
    ! [U_5056,U_5055] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5056)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5055))) = 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_5056)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5055)))),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_5055))) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5056)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5055))) = 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_5056),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5055)))),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_5055))) ) ),
    inference(variable_rename,[status(thm)],[f_1462_1]) ).

fof(f_1462_3,plain,
    ( ! [U_5060,U_5058] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5060)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5058))) = 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_5060)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5058)))),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_5058))) )
    & ! [U_5059,U_5057] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5059)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5057))) = 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_5059),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5057)))),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_5057))) ) ),
    inference(miniscope,[status(thm)],[f_1462_2]) ).

fof(f_1462_4,plain,
    ( ! [U_5058,U_5060] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5060)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5058))) = 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_5060)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5058)))),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_5058))) )
    & ! [U_5059,U_5057] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5059)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5057))) = 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_5059),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5057)))),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_5057))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1462_3]) ).

cnf(f_1462_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5059)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5057))) = 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_5059),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5057)))),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_5057))) ),
    inference(clausify,[status(thm)],[f_1462_4]) ).

cnf(f_1462_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5060)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5058))) = 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_5060)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5058)))),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_5058))) ),
    inference(clausify,[status(thm)],[f_1462_4]) ).

fof(f_1463_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_1463_2,plain,
    ! [U_5062,U_5061] :
      ( 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_5062)),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_5061)) = 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_5062),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5061))),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5061),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1463_1]) ).

fof(f_1463_3,plain,
    ! [U_5061,U_5062] :
      ( 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_5062)),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_5061)) = 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_5062),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5061))),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5061),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1463_2]) ).

cnf(f_1463_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_5062)),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_5061)) = 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_5062),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5061))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5061),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1463_3]) ).

fof(f_1464_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_1464_2,plain,
    ! [U_5064,U_5063] :
      ( 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_5064))),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_5063)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5064),U_5063)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5063)) ),
    inference(variable_rename,[status(thm)],[f_1464_1]) ).

fof(f_1464_3,plain,
    ! [U_5063,U_5064] :
      ( 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_5064))),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_5063)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5064),U_5063)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5063)) ),
    inference(definitional_conversion,[status(esa)],[f_1464_2]) ).

cnf(f_1464_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_5064))),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_5063)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5064),U_5063)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5063)) ),
    inference(clausify,[status(thm)],[f_1464_3]) ).

fof(f_1465_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_1465_2,plain,
    ! [U_5066,U_5065] :
      ( 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_5066))),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_5065)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5066),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5065)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5065),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1465_1]) ).

fof(f_1465_3,plain,
    ! [U_5065,U_5066] :
      ( 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_5066))),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_5065)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5066),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5065)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5065),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1465_2]) ).

cnf(f_1465_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_5066))),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_5065)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5066),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5065)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5065),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1465_3]) ).

fof(f_1466_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_1466_2,plain,
    ! [U_5068,U_5067] :
      ( 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_5068)),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_5067)) = 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_5068,U_5067)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5067)) ),
    inference(variable_rename,[status(thm)],[f_1466_1]) ).

fof(f_1466_3,plain,
    ! [U_5067,U_5068] :
      ( 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_5068)),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_5067)) = 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_5068,U_5067)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5067)) ),
    inference(definitional_conversion,[status(esa)],[f_1466_2]) ).

cnf(f_1466_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_5068)),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_5067)) = 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_5068,U_5067)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5067)) ),
    inference(clausify,[status(thm)],[f_1466_3]) ).

fof(f_1467_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_1467_2,plain,
    ! [U_5070,U_5069] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5069),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_5070))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5069),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5069),hAPP(c_Int_Onat,U_5070))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5069),hAPP(c_Int_Onat,U_5070)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5070))
      | ~ class_Rings_Osemiring__1(U_5069) ),
    inference(variable_rename,[status(thm)],[f_1467_1]) ).

fof(f_1467_3,plain,
    ! [U_5069,U_5070] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5069),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_5070))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5069),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5069),hAPP(c_Int_Onat,U_5070))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5069),hAPP(c_Int_Onat,U_5070)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5070))
      | ~ class_Rings_Osemiring__1(U_5069) ),
    inference(definitional_conversion,[status(esa)],[f_1467_2]) ).

cnf(f_1467_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5069),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_5070))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5069),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5069),hAPP(c_Int_Onat,U_5070))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5069),hAPP(c_Int_Onat,U_5070)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5070))
    | ~ class_Rings_Osemiring__1(U_5069) ),
    inference(clausify,[status(thm)],[f_1467_3]) ).

fof(f_1468_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_1468_2,plain,
    ! [U_5072,U_5071] :
      ( ( c_Int_OBit0(U_5071) = c_Int_OBit0(U_5072)
        | U_5071 != U_5072 )
      & ( U_5071 = U_5072
        | c_Int_OBit0(U_5071) != c_Int_OBit0(U_5072) ) ),
    inference(variable_rename,[status(thm)],[f_1468_1]) ).

fof(f_1468_3,plain,
    ( ! [U_5076,U_5074] :
        ( c_Int_OBit0(U_5074) = c_Int_OBit0(U_5076)
        | U_5074 != U_5076 )
    & ! [U_5075,U_5073] :
        ( U_5073 = U_5075
        | c_Int_OBit0(U_5073) != c_Int_OBit0(U_5075) ) ),
    inference(miniscope,[status(thm)],[f_1468_2]) ).

fof(f_1468_4,plain,
    ( ! [U_5074,U_5076] :
        ( c_Int_OBit0(U_5074) = c_Int_OBit0(U_5076)
        | U_5074 != U_5076 )
    & ! [U_5073,U_5075] :
        ( U_5073 = U_5075
        | c_Int_OBit0(U_5073) != c_Int_OBit0(U_5075) ) ),
    inference(definitional_conversion,[status(esa)],[f_1468_3]) ).

cnf(f_1468_5,plain,
    ( U_5073 = U_5075
    | c_Int_OBit0(U_5073) != c_Int_OBit0(U_5075) ),
    inference(clausify,[status(thm)],[f_1468_4]) ).

cnf(f_1468_6,plain,
    ( c_Int_OBit0(U_5074) = c_Int_OBit0(U_5076)
    | U_5074 != U_5076 ),
    inference(clausify,[status(thm)],[f_1468_4]) ).

fof(f_1469_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_1469_2,plain,
    ! [U_5078,U_5077] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5077)),c_Int_OBit0(U_5078)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5077),U_5078)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5077),U_5078))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5077)),c_Int_OBit0(U_5078))) ) ),
    inference(variable_rename,[status(thm)],[f_1469_1]) ).

fof(f_1469_3,plain,
    ( ! [U_5082,U_5080] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5080)),c_Int_OBit0(U_5082)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5080),U_5082)) )
    & ! [U_5081,U_5079] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5079),U_5081))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5079)),c_Int_OBit0(U_5081))) ) ),
    inference(miniscope,[status(thm)],[f_1469_2]) ).

fof(f_1469_4,plain,
    ( ! [U_5080,U_5082] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5080)),c_Int_OBit0(U_5082)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5080),U_5082)) )
    & ! [U_5081,U_5079] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5079),U_5081))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5079)),c_Int_OBit0(U_5081))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1469_3]) ).

cnf(f_1469_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5079),U_5081))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5079)),c_Int_OBit0(U_5081))) ),
    inference(clausify,[status(thm)],[f_1469_4]) ).

cnf(f_1469_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5080)),c_Int_OBit0(U_5082)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5080),U_5082)) ),
    inference(clausify,[status(thm)],[f_1469_4]) ).

fof(f_1470_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_1470_2,plain,
    ! [U_5084,U_5083] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5083)),c_Int_OBit0(U_5084)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5083),U_5084)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5083),U_5084))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5083)),c_Int_OBit0(U_5084))) ) ),
    inference(variable_rename,[status(thm)],[f_1470_1]) ).

fof(f_1470_3,plain,
    ( ! [U_5088,U_5086] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5086)),c_Int_OBit0(U_5088)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5086),U_5088)) )
    & ! [U_5087,U_5085] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5085),U_5087))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5085)),c_Int_OBit0(U_5087))) ) ),
    inference(miniscope,[status(thm)],[f_1470_2]) ).

fof(f_1470_4,plain,
    ( ! [U_5086,U_5088] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5086)),c_Int_OBit0(U_5088)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5086),U_5088)) )
    & ! [U_5087,U_5085] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5085),U_5087))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5085)),c_Int_OBit0(U_5087))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1470_3]) ).

cnf(f_1470_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5085),U_5087))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5085)),c_Int_OBit0(U_5087))) ),
    inference(clausify,[status(thm)],[f_1470_4]) ).

cnf(f_1470_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5086)),c_Int_OBit0(U_5088)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5086),U_5088)) ),
    inference(clausify,[status(thm)],[f_1470_4]) ).

fof(f_1471_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_1471_2,plain,
    ! [U_5090,U_5089] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5089)),c_Int_OBit0(U_5090)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5089),U_5090)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5089),U_5090))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5089)),c_Int_OBit0(U_5090))) ) ),
    inference(variable_rename,[status(thm)],[f_1471_1]) ).

fof(f_1471_3,plain,
    ( ! [U_5094,U_5092] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5092)),c_Int_OBit0(U_5094)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5092),U_5094)) )
    & ! [U_5093,U_5091] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5091),U_5093))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5091)),c_Int_OBit0(U_5093))) ) ),
    inference(miniscope,[status(thm)],[f_1471_2]) ).

fof(f_1471_4,plain,
    ( ! [U_5092,U_5094] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5092)),c_Int_OBit0(U_5094)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5092),U_5094)) )
    & ! [U_5093,U_5091] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5091),U_5093))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5091)),c_Int_OBit0(U_5093))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1471_3]) ).

cnf(f_1471_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5091),U_5093))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5091)),c_Int_OBit0(U_5093))) ),
    inference(clausify,[status(thm)],[f_1471_4]) ).

cnf(f_1471_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5092)),c_Int_OBit0(U_5094)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5092),U_5094)) ),
    inference(clausify,[status(thm)],[f_1471_4]) ).

fof(f_1472_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_1472_2,plain,
    ! [U_5096,U_5095] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5095)),c_Int_OBit0(U_5096)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5095),U_5096)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5095),U_5096))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5095)),c_Int_OBit0(U_5096))) ) ),
    inference(variable_rename,[status(thm)],[f_1472_1]) ).

fof(f_1472_3,plain,
    ( ! [U_5100,U_5098] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5098)),c_Int_OBit0(U_5100)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5098),U_5100)) )
    & ! [U_5099,U_5097] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5097),U_5099))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5097)),c_Int_OBit0(U_5099))) ) ),
    inference(miniscope,[status(thm)],[f_1472_2]) ).

fof(f_1472_4,plain,
    ( ! [U_5098,U_5100] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5098)),c_Int_OBit0(U_5100)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5098),U_5100)) )
    & ! [U_5099,U_5097] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5097),U_5099))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5097)),c_Int_OBit0(U_5099))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1472_3]) ).

cnf(f_1472_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5097),U_5099))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5097)),c_Int_OBit0(U_5099))) ),
    inference(clausify,[status(thm)],[f_1472_4]) ).

cnf(f_1472_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5098)),c_Int_OBit0(U_5100)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5098),U_5100)) ),
    inference(clausify,[status(thm)],[f_1472_4]) ).

fof(f_1473_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_1473_2,plain,
    ! [U_5101] :
      ( ( c_Int_OBit0(U_5101) = c_Int_OPls
        | U_5101 != c_Int_OPls )
      & ( U_5101 = c_Int_OPls
        | c_Int_OBit0(U_5101) != c_Int_OPls ) ),
    inference(variable_rename,[status(thm)],[f_1473_1]) ).

fof(f_1473_3,plain,
    ( ! [U_5103] :
        ( c_Int_OBit0(U_5103) = c_Int_OPls
        | U_5103 != c_Int_OPls )
    & ! [U_5102] :
        ( U_5102 = c_Int_OPls
        | c_Int_OBit0(U_5102) != c_Int_OPls ) ),
    inference(miniscope,[status(thm)],[f_1473_2]) ).

fof(f_1473_4,plain,
    ( ! [U_5103] :
        ( c_Int_OBit0(U_5103) = c_Int_OPls
        | U_5103 != c_Int_OPls )
    & ! [U_5102] :
        ( U_5102 = c_Int_OPls
        | c_Int_OBit0(U_5102) != c_Int_OPls ) ),
    inference(definitional_conversion,[status(esa)],[f_1473_3]) ).

cnf(f_1473_5,plain,
    ( U_5102 = c_Int_OPls
    | c_Int_OBit0(U_5102) != c_Int_OPls ),
    inference(clausify,[status(thm)],[f_1473_4]) ).

cnf(f_1473_6,plain,
    ( c_Int_OBit0(U_5103) = c_Int_OPls
    | U_5103 != c_Int_OPls ),
    inference(clausify,[status(thm)],[f_1473_4]) ).

fof(f_1474_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_1474_2,plain,
    ! [U_5104] :
      ( ( c_Int_OPls = c_Int_OBit0(U_5104)
        | c_Int_OPls != U_5104 )
      & ( c_Int_OPls = U_5104
        | c_Int_OPls != c_Int_OBit0(U_5104) ) ),
    inference(variable_rename,[status(thm)],[f_1474_1]) ).

fof(f_1474_3,plain,
    ( ! [U_5106] :
        ( c_Int_OPls = c_Int_OBit0(U_5106)
        | c_Int_OPls != U_5106 )
    & ! [U_5105] :
        ( c_Int_OPls = U_5105
        | c_Int_OPls != c_Int_OBit0(U_5105) ) ),
    inference(miniscope,[status(thm)],[f_1474_2]) ).

fof(f_1474_4,plain,
    ( ! [U_5106] :
        ( c_Int_OPls = c_Int_OBit0(U_5106)
        | c_Int_OPls != U_5106 )
    & ! [U_5105] :
        ( c_Int_OPls = U_5105
        | c_Int_OPls != c_Int_OBit0(U_5105) ) ),
    inference(definitional_conversion,[status(esa)],[f_1474_3]) ).

cnf(f_1474_5,plain,
    ( c_Int_OPls = U_5105
    | c_Int_OPls != c_Int_OBit0(U_5105) ),
    inference(clausify,[status(thm)],[f_1474_4]) ).

cnf(f_1474_6,plain,
    ( c_Int_OPls = c_Int_OBit0(U_5106)
    | c_Int_OPls != U_5106 ),
    inference(clausify,[status(thm)],[f_1474_4]) ).

fof(f_1475_1,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_Bit0__Pls]) ).

fof(f_1475_2,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1475_1]) ).

cnf(f_1475_3,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1475_2]) ).

fof(f_1476_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_1476_2,plain,
    ! [U_5108,U_5107] : c_Int_OBit1(U_5107) != c_Int_OBit0(U_5108),
    inference(variable_rename,[status(thm)],[f_1476_1]) ).

fof(f_1476_3,plain,
    ! [U_5107,U_5108] : c_Int_OBit1(U_5107) != c_Int_OBit0(U_5108),
    inference(definitional_conversion,[status(esa)],[f_1476_2]) ).

cnf(f_1476_4,plain,
    c_Int_OBit1(U_5107) != c_Int_OBit0(U_5108),
    inference(clausify,[status(thm)],[f_1476_3]) ).

fof(f_1477_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_1477_2,plain,
    ! [U_5110,U_5109] : c_Int_OBit0(U_5109) != c_Int_OBit1(U_5110),
    inference(variable_rename,[status(thm)],[f_1477_1]) ).

fof(f_1477_3,plain,
    ! [U_5109,U_5110] : c_Int_OBit0(U_5109) != c_Int_OBit1(U_5110),
    inference(definitional_conversion,[status(esa)],[f_1477_2]) ).

cnf(f_1477_4,plain,
    c_Int_OBit0(U_5109) != c_Int_OBit1(U_5110),
    inference(clausify,[status(thm)],[f_1477_3]) ).

fof(f_1478_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_1478_2,plain,
    ! [U_5111] : c_Int_OBit0(U_5111) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5111),U_5111),
    inference(variable_rename,[status(thm)],[f_1478_1]) ).

fof(f_1478_3,plain,
    ! [U_5111] : c_Int_OBit0(U_5111) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5111),U_5111),
    inference(definitional_conversion,[status(esa)],[f_1478_2]) ).

cnf(f_1478_4,plain,
    c_Int_OBit0(U_5111) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5111),U_5111),
    inference(clausify,[status(thm)],[f_1478_3]) ).

fof(f_1479_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_1479_2,plain,
    ! [U_5113,U_5112] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5112)),c_Int_OBit0(U_5113)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5112),U_5113)),
    inference(variable_rename,[status(thm)],[f_1479_1]) ).

fof(f_1479_3,plain,
    ! [U_5112,U_5113] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5112)),c_Int_OBit0(U_5113)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5112),U_5113)),
    inference(definitional_conversion,[status(esa)],[f_1479_2]) ).

cnf(f_1479_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5112)),c_Int_OBit0(U_5113)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5112),U_5113)),
    inference(clausify,[status(thm)],[f_1479_3]) ).

fof(f_1480_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_1480_2,plain,
    ! [U_5115,U_5114] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_5114)),U_5115) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5114),U_5115)),
    inference(variable_rename,[status(thm)],[f_1480_1]) ).

fof(f_1480_3,plain,
    ! [U_5114,U_5115] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_5114)),U_5115) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5114),U_5115)),
    inference(definitional_conversion,[status(esa)],[f_1480_2]) ).

cnf(f_1480_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_5114)),U_5115) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5114),U_5115)),
    inference(clausify,[status(thm)],[f_1480_3]) ).

fof(f_1481_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_1481_2,plain,
    ! [U_5117,U_5116] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5116)),c_Int_OBit0(U_5117)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5116),U_5117)),
    inference(variable_rename,[status(thm)],[f_1481_1]) ).

fof(f_1481_3,plain,
    ! [U_5116,U_5117] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5116)),c_Int_OBit0(U_5117)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5116),U_5117)),
    inference(definitional_conversion,[status(esa)],[f_1481_2]) ).

cnf(f_1481_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5116)),c_Int_OBit0(U_5117)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5116),U_5117)),
    inference(clausify,[status(thm)],[f_1481_3]) ).

fof(f_1482_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_1482_2,plain,
    ! [U_5118] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_5118)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5118)),
    inference(variable_rename,[status(thm)],[f_1482_1]) ).

fof(f_1482_3,plain,
    ! [U_5118] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_5118)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5118)),
    inference(definitional_conversion,[status(esa)],[f_1482_2]) ).

cnf(f_1482_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_5118)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5118)),
    inference(clausify,[status(thm)],[f_1482_3]) ).

fof(f_1483_1,plain,
    ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I45_J]) ).

fof(f_1483_2,plain,
    ! [U_5119] : c_Int_OBit0(U_5119) != c_Int_OMin,
    inference(variable_rename,[status(thm)],[f_1483_1]) ).

fof(f_1483_3,plain,
    ! [U_5119] : c_Int_OBit0(U_5119) != c_Int_OMin,
    inference(definitional_conversion,[status(esa)],[f_1483_2]) ).

cnf(f_1483_4,plain,
    c_Int_OBit0(U_5119) != c_Int_OMin,
    inference(clausify,[status(thm)],[f_1483_3]) ).

fof(f_1484_1,plain,
    ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I42_J]) ).

fof(f_1484_2,plain,
    ! [U_5120] : c_Int_OMin != c_Int_OBit0(U_5120),
    inference(variable_rename,[status(thm)],[f_1484_1]) ).

fof(f_1484_3,plain,
    ! [U_5120] : c_Int_OMin != c_Int_OBit0(U_5120),
    inference(definitional_conversion,[status(esa)],[f_1484_2]) ).

cnf(f_1484_4,plain,
    c_Int_OMin != c_Int_OBit0(U_5120),
    inference(clausify,[status(thm)],[f_1484_3]) ).

fof(f_1485_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_1485_2,plain,
    ! [U_5121] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5121)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5121),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5121),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5121)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1485_1]) ).

fof(f_1485_3,plain,
    ( ! [U_5123] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5123)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5123),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_5122] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5122),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5122)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1485_2]) ).

fof(f_1485_4,plain,
    ( ! [U_5123] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5123)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5123),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_5122] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5122),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5122)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1485_3]) ).

cnf(f_1485_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5122),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5122)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1485_4]) ).

cnf(f_1485_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5123)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5123),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1485_4]) ).

fof(f_1486_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_1486_2,plain,
    ! [U_5124] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5124)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5124)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5124))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5124))) ) ),
    inference(variable_rename,[status(thm)],[f_1486_1]) ).

fof(f_1486_3,plain,
    ( ! [U_5126] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5126)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5126)) )
    & ! [U_5125] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5125))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5125))) ) ),
    inference(miniscope,[status(thm)],[f_1486_2]) ).

fof(f_1486_4,plain,
    ( ! [U_5126] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5126)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5126)) )
    & ! [U_5125] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5125))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5125))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1486_3]) ).

cnf(f_1486_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5125))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5125))) ),
    inference(clausify,[status(thm)],[f_1486_4]) ).

cnf(f_1486_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5126)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5126)) ),
    inference(clausify,[status(thm)],[f_1486_4]) ).

fof(f_1487_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_1487_2,plain,
    ! [U_5127] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5127)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5127),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5127),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5127)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1487_1]) ).

fof(f_1487_3,plain,
    ( ! [U_5129] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5129)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5129),c_Int_OPls)) )
    & ! [U_5128] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5128),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5128)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1487_2]) ).

fof(f_1487_4,plain,
    ( ! [U_5129] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5129)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5129),c_Int_OPls)) )
    & ! [U_5128] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5128),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5128)),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1487_3]) ).

cnf(f_1487_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5128),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5128)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1487_4]) ).

cnf(f_1487_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5129)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5129),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1487_4]) ).

fof(f_1488_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_1488_2,plain,
    ! [U_5131,U_5130] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5130)),c_Int_OBit1(U_5131)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5130),U_5131)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5130),U_5131))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5130)),c_Int_OBit1(U_5131))) ) ),
    inference(variable_rename,[status(thm)],[f_1488_1]) ).

fof(f_1488_3,plain,
    ( ! [U_5135,U_5133] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5133)),c_Int_OBit1(U_5135)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5133),U_5135)) )
    & ! [U_5134,U_5132] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5132),U_5134))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5132)),c_Int_OBit1(U_5134))) ) ),
    inference(miniscope,[status(thm)],[f_1488_2]) ).

fof(f_1488_4,plain,
    ( ! [U_5133,U_5135] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5133)),c_Int_OBit1(U_5135)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5133),U_5135)) )
    & ! [U_5134,U_5132] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5132),U_5134))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5132)),c_Int_OBit1(U_5134))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1488_3]) ).

cnf(f_1488_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5132),U_5134))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5132)),c_Int_OBit1(U_5134))) ),
    inference(clausify,[status(thm)],[f_1488_4]) ).

cnf(f_1488_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5133)),c_Int_OBit1(U_5135)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5133),U_5135)) ),
    inference(clausify,[status(thm)],[f_1488_4]) ).

fof(f_1489_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_1489_2,plain,
    ! [U_5137,U_5136] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5136)),c_Int_OBit1(U_5137)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5136),U_5137)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5136),U_5137))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5136)),c_Int_OBit1(U_5137))) ) ),
    inference(variable_rename,[status(thm)],[f_1489_1]) ).

fof(f_1489_3,plain,
    ( ! [U_5141,U_5139] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5139)),c_Int_OBit1(U_5141)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5139),U_5141)) )
    & ! [U_5140,U_5138] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5138),U_5140))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5138)),c_Int_OBit1(U_5140))) ) ),
    inference(miniscope,[status(thm)],[f_1489_2]) ).

fof(f_1489_4,plain,
    ( ! [U_5139,U_5141] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5139)),c_Int_OBit1(U_5141)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5139),U_5141)) )
    & ! [U_5140,U_5138] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5138),U_5140))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5138)),c_Int_OBit1(U_5140))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1489_3]) ).

cnf(f_1489_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5138),U_5140))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5138)),c_Int_OBit1(U_5140))) ),
    inference(clausify,[status(thm)],[f_1489_4]) ).

cnf(f_1489_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5139)),c_Int_OBit1(U_5141)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5139),U_5141)) ),
    inference(clausify,[status(thm)],[f_1489_4]) ).

fof(f_1490_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_1490_2,plain,
    ! [U_5142] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5142)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5142),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5142),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5142)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1490_1]) ).

fof(f_1490_3,plain,
    ( ! [U_5144] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5144)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5144),c_Int_OPls)) )
    & ! [U_5143] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5143),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5143)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1490_2]) ).

fof(f_1490_4,plain,
    ( ! [U_5144] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5144)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5144),c_Int_OPls)) )
    & ! [U_5143] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5143),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5143)),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1490_3]) ).

cnf(f_1490_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5143),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5143)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1490_4]) ).

cnf(f_1490_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5144)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5144),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1490_4]) ).

fof(f_1491_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_1491_2,plain,
    ! [U_5145] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5145)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5145)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5145))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5145))) ) ),
    inference(variable_rename,[status(thm)],[f_1491_1]) ).

fof(f_1491_3,plain,
    ( ! [U_5147] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5147)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5147)) )
    & ! [U_5146] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5146))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5146))) ) ),
    inference(miniscope,[status(thm)],[f_1491_2]) ).

fof(f_1491_4,plain,
    ( ! [U_5147] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5147)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5147)) )
    & ! [U_5146] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5146))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5146))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1491_3]) ).

cnf(f_1491_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5146))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5146))) ),
    inference(clausify,[status(thm)],[f_1491_4]) ).

cnf(f_1491_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5147)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5147)) ),
    inference(clausify,[status(thm)],[f_1491_4]) ).

fof(f_1492_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_1492_2,plain,
    ! [U_5149,U_5148] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5148)),c_Int_OBit0(U_5149)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5148),U_5149)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5148),U_5149))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5148)),c_Int_OBit0(U_5149))) ) ),
    inference(variable_rename,[status(thm)],[f_1492_1]) ).

fof(f_1492_3,plain,
    ( ! [U_5153,U_5151] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5151)),c_Int_OBit0(U_5153)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5151),U_5153)) )
    & ! [U_5152,U_5150] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5150),U_5152))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5150)),c_Int_OBit0(U_5152))) ) ),
    inference(miniscope,[status(thm)],[f_1492_2]) ).

fof(f_1492_4,plain,
    ( ! [U_5151,U_5153] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5151)),c_Int_OBit0(U_5153)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5151),U_5153)) )
    & ! [U_5152,U_5150] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5150),U_5152))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5150)),c_Int_OBit0(U_5152))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1492_3]) ).

cnf(f_1492_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5150),U_5152))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5150)),c_Int_OBit0(U_5152))) ),
    inference(clausify,[status(thm)],[f_1492_4]) ).

cnf(f_1492_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5151)),c_Int_OBit0(U_5153)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5151),U_5153)) ),
    inference(clausify,[status(thm)],[f_1492_4]) ).

fof(f_1493_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_1493_2,plain,
    ! [U_5155,U_5154] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5154)),c_Int_OBit0(U_5155)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5154),U_5155)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5154),U_5155))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5154)),c_Int_OBit0(U_5155))) ) ),
    inference(variable_rename,[status(thm)],[f_1493_1]) ).

fof(f_1493_3,plain,
    ( ! [U_5159,U_5157] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5157)),c_Int_OBit0(U_5159)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5157),U_5159)) )
    & ! [U_5158,U_5156] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5156),U_5158))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5156)),c_Int_OBit0(U_5158))) ) ),
    inference(miniscope,[status(thm)],[f_1493_2]) ).

fof(f_1493_4,plain,
    ( ! [U_5157,U_5159] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5157)),c_Int_OBit0(U_5159)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5157),U_5159)) )
    & ! [U_5158,U_5156] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5156),U_5158))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5156)),c_Int_OBit0(U_5158))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1493_3]) ).

cnf(f_1493_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5156),U_5158))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5156)),c_Int_OBit0(U_5158))) ),
    inference(clausify,[status(thm)],[f_1493_4]) ).

cnf(f_1493_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5157)),c_Int_OBit0(U_5159)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5157),U_5159)) ),
    inference(clausify,[status(thm)],[f_1493_4]) ).

fof(f_1494_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_1494_2,plain,
    ! [U_5161,U_5160] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5160)),c_Int_OBit0(U_5161)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5160),U_5161)),
    inference(variable_rename,[status(thm)],[f_1494_1]) ).

fof(f_1494_3,plain,
    ! [U_5161,U_5160] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5160)),c_Int_OBit0(U_5161)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5160),U_5161)),
    inference(definitional_conversion,[status(esa)],[f_1494_2]) ).

cnf(f_1494_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5160)),c_Int_OBit0(U_5161)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5160),U_5161)),
    inference(clausify,[status(thm)],[f_1494_3]) ).

fof(f_1495_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_1495_2,plain,
    ! [U_5163,U_5162] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5162)),c_Int_OBit1(U_5163)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5162),U_5163)),
    inference(variable_rename,[status(thm)],[f_1495_1]) ).

fof(f_1495_3,plain,
    ! [U_5162,U_5163] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5162)),c_Int_OBit1(U_5163)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5162),U_5163)),
    inference(definitional_conversion,[status(esa)],[f_1495_2]) ).

cnf(f_1495_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5162)),c_Int_OBit1(U_5163)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5162),U_5163)),
    inference(clausify,[status(thm)],[f_1495_3]) ).

fof(f_1496_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_1496_2,plain,
    ! [U_5164] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5164)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_5164)),
    inference(variable_rename,[status(thm)],[f_1496_1]) ).

fof(f_1496_3,plain,
    ! [U_5164] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5164)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_5164)),
    inference(definitional_conversion,[status(esa)],[f_1496_2]) ).

cnf(f_1496_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5164)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_5164)),
    inference(clausify,[status(thm)],[f_1496_3]) ).

fof(f_1497_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_1497_2,plain,
    ! [U_5166,U_5165] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5165)),c_Int_OBit1(U_5166)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5165),U_5166)),
    inference(variable_rename,[status(thm)],[f_1497_1]) ).

fof(f_1497_3,plain,
    ! [U_5165,U_5166] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5165)),c_Int_OBit1(U_5166)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5165),U_5166)),
    inference(definitional_conversion,[status(esa)],[f_1497_2]) ).

cnf(f_1497_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5165)),c_Int_OBit1(U_5166)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5165),U_5166)),
    inference(clausify,[status(thm)],[f_1497_3]) ).

fof(f_1498_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_1498_2,plain,
    ! [U_5168,U_5167] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5167)),c_Int_OBit0(U_5168)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5167),U_5168)),
    inference(variable_rename,[status(thm)],[f_1498_1]) ).

fof(f_1498_3,plain,
    ! [U_5167,U_5168] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5167)),c_Int_OBit0(U_5168)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5167),U_5168)),
    inference(definitional_conversion,[status(esa)],[f_1498_2]) ).

cnf(f_1498_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5167)),c_Int_OBit0(U_5168)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5167),U_5168)),
    inference(clausify,[status(thm)],[f_1498_3]) ).

fof(f_1499_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_1499_2,plain,
    ! [U_5169] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5169)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5169),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5169),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5169)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1499_1]) ).

fof(f_1499_3,plain,
    ( ! [U_5171] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5171)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5171),c_Int_OMin)) )
    & ! [U_5170] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5170),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5170)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1499_2]) ).

fof(f_1499_4,plain,
    ( ! [U_5171] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5171)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5171),c_Int_OMin)) )
    & ! [U_5170] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5170),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5170)),c_Int_OMin)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1499_3]) ).

cnf(f_1499_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5170),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5170)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1499_4]) ).

cnf(f_1499_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5171)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5171),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1499_4]) ).

fof(f_1500_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_1500_2,plain,
    ! [U_5172] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5172)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5172)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5172))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5172))) ) ),
    inference(variable_rename,[status(thm)],[f_1500_1]) ).

fof(f_1500_3,plain,
    ( ! [U_5174] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5174)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5174)) )
    & ! [U_5173] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5173))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5173))) ) ),
    inference(miniscope,[status(thm)],[f_1500_2]) ).

fof(f_1500_4,plain,
    ( ! [U_5174] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5174)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5174)) )
    & ! [U_5173] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5173))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5173))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1500_3]) ).

cnf(f_1500_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5173))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5173))) ),
    inference(clausify,[status(thm)],[f_1500_4]) ).

cnf(f_1500_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5174)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5174)) ),
    inference(clausify,[status(thm)],[f_1500_4]) ).

fof(f_1501_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_1501_2,plain,
    ! [U_5176,U_5175] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5175))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5176))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5175)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5176)),
    inference(variable_rename,[status(thm)],[f_1501_1]) ).

fof(f_1501_3,plain,
    ! [U_5175,U_5176] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5175))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5176))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5175)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5176)),
    inference(definitional_conversion,[status(esa)],[f_1501_2]) ).

cnf(f_1501_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_5175))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5176))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5175)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5176)),
    inference(clausify,[status(thm)],[f_1501_3]) ).

fof(f_1502_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_1502_2,plain,
    ! [U_5177] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5177))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5177))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5177)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5177)))) ) ),
    inference(variable_rename,[status(thm)],[f_1502_1]) ).

fof(f_1502_3,plain,
    ( ! [U_5179] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5179))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5179))) )
    & ! [U_5178] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5178)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5178)))) ) ),
    inference(miniscope,[status(thm)],[f_1502_2]) ).

fof(f_1502_4,plain,
    ( ! [U_5179] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5179))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5179))) )
    & ! [U_5178] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5178)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5178)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1502_3]) ).

cnf(f_1502_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5178)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5178)))) ),
    inference(clausify,[status(thm)],[f_1502_4]) ).

cnf(f_1502_6,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5179))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5179))) ),
    inference(clausify,[status(thm)],[f_1502_4]) ).

fof(f_1503_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_1503_2,plain,
    ! [U_5180] : c_Int_Opred(c_Int_OBit1(U_5180)) = c_Int_OBit0(U_5180),
    inference(variable_rename,[status(thm)],[f_1503_1]) ).

fof(f_1503_3,plain,
    ! [U_5180] : c_Int_Opred(c_Int_OBit1(U_5180)) = c_Int_OBit0(U_5180),
    inference(definitional_conversion,[status(esa)],[f_1503_2]) ).

cnf(f_1503_4,plain,
    c_Int_Opred(c_Int_OBit1(U_5180)) = c_Int_OBit0(U_5180),
    inference(clausify,[status(thm)],[f_1503_3]) ).

fof(f_1504_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_1504_2,plain,
    ! [U_5181] : c_Int_Opred(c_Int_OBit0(U_5181)) = c_Int_OBit1(c_Int_Opred(U_5181)),
    inference(variable_rename,[status(thm)],[f_1504_1]) ).

fof(f_1504_3,plain,
    ! [U_5181] : c_Int_Opred(c_Int_OBit0(U_5181)) = c_Int_OBit1(c_Int_Opred(U_5181)),
    inference(definitional_conversion,[status(esa)],[f_1504_2]) ).

cnf(f_1504_4,plain,
    c_Int_Opred(c_Int_OBit0(U_5181)) = c_Int_OBit1(c_Int_Opred(U_5181)),
    inference(clausify,[status(thm)],[f_1504_3]) ).

fof(f_1505_1,plain,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    inference(fof_nnf,[status(thm)],[fact_pred__Min]) ).

fof(f_1505_2,plain,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    inference(definitional_conversion,[status(esa)],[f_1505_1]) ).

cnf(f_1505_3,plain,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    inference(clausify,[status(thm)],[f_1505_2]) ).

fof(f_1506_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_1506_2,plain,
    ! [U_5183,U_5182] :
      ( ( ( c_Int_Oiszero(U_5182,hAPP(c_Int_Onumber__class_Onumber__of(U_5182),c_Int_OBit0(U_5183)))
          | ~ c_Int_Oiszero(U_5182,hAPP(c_Int_Onumber__class_Onumber__of(U_5182),U_5183)) )
        & ( c_Int_Oiszero(U_5182,hAPP(c_Int_Onumber__class_Onumber__of(U_5182),U_5183))
          | ~ c_Int_Oiszero(U_5182,hAPP(c_Int_Onumber__class_Onumber__of(U_5182),c_Int_OBit0(U_5183))) ) )
      | ~ class_Int_Oring__char__0(U_5182)
      | ~ class_Int_Onumber__ring(U_5182) ),
    inference(variable_rename,[status(thm)],[f_1506_1]) ).

fof(f_1506_3,plain,
    ( ! [U_5182,U_5183] :
        ( c_Int_Oiszero(U_5182,hAPP(c_Int_Onumber__class_Onumber__of(U_5182),c_Int_OBit0(U_5183)))
        | ~ c_Int_Oiszero(U_5182,hAPP(c_Int_Onumber__class_Onumber__of(U_5182),U_5183))
        | ~ sP396(U_5182,U_5183) )
    & ! [U_5182,U_5183] :
        ( c_Int_Oiszero(U_5182,hAPP(c_Int_Onumber__class_Onumber__of(U_5182),U_5183))
        | ~ c_Int_Oiszero(U_5182,hAPP(c_Int_Onumber__class_Onumber__of(U_5182),c_Int_OBit0(U_5183)))
        | ~ sP396(U_5182,U_5183) )
    & ! [U_5182,U_5183] :
        ( sP396(U_5182,U_5183)
        | ~ class_Int_Oring__char__0(U_5182)
        | ~ class_Int_Onumber__ring(U_5182) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP396])],[f_1506_2]) ).

cnf(f_1506_4,plain,
    ( sP396(U_5182,U_5183)
    | ~ class_Int_Oring__char__0(U_5182)
    | ~ class_Int_Onumber__ring(U_5182) ),
    inference(clausify,[status(thm)],[f_1506_3]) ).

cnf(f_1506_5,plain,
    ( c_Int_Oiszero(U_5182,hAPP(c_Int_Onumber__class_Onumber__of(U_5182),U_5183))
    | ~ c_Int_Oiszero(U_5182,hAPP(c_Int_Onumber__class_Onumber__of(U_5182),c_Int_OBit0(U_5183)))
    | ~ sP396(U_5182,U_5183) ),
    inference(clausify,[status(thm)],[f_1506_3]) ).

cnf(f_1506_6,plain,
    ( c_Int_Oiszero(U_5182,hAPP(c_Int_Onumber__class_Onumber__of(U_5182),c_Int_OBit0(U_5183)))
    | ~ c_Int_Oiszero(U_5182,hAPP(c_Int_Onumber__class_Onumber__of(U_5182),U_5183))
    | ~ sP396(U_5182,U_5183) ),
    inference(clausify,[status(thm)],[f_1506_3]) ).

fof(f_1507_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_1507_2,plain,
    ! [U_5184] : c_Int_Osucc(c_Int_OBit0(U_5184)) = c_Int_OBit1(U_5184),
    inference(variable_rename,[status(thm)],[f_1507_1]) ).

fof(f_1507_3,plain,
    ! [U_5184] : c_Int_Osucc(c_Int_OBit0(U_5184)) = c_Int_OBit1(U_5184),
    inference(definitional_conversion,[status(esa)],[f_1507_2]) ).

cnf(f_1507_4,plain,
    c_Int_Osucc(c_Int_OBit0(U_5184)) = c_Int_OBit1(U_5184),
    inference(clausify,[status(thm)],[f_1507_3]) ).

fof(f_1508_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_1508_2,plain,
    ! [U_5185] : c_Int_Osucc(c_Int_OBit1(U_5185)) = c_Int_OBit0(c_Int_Osucc(U_5185)),
    inference(variable_rename,[status(thm)],[f_1508_1]) ).

fof(f_1508_3,plain,
    ! [U_5185] : c_Int_Osucc(c_Int_OBit1(U_5185)) = c_Int_OBit0(c_Int_Osucc(U_5185)),
    inference(definitional_conversion,[status(esa)],[f_1508_2]) ).

cnf(f_1508_4,plain,
    c_Int_Osucc(c_Int_OBit1(U_5185)) = c_Int_OBit0(c_Int_Osucc(U_5185)),
    inference(clausify,[status(thm)],[f_1508_3]) ).

fof(f_1509_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_1509_2,plain,
    ! [U_5187,U_5186] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5186),c_Int_OBit0(U_5187)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5186),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5186),c_Groups_Ozero__class_Ozero(U_5186)),hAPP(c_Int_Onumber__class_Onumber__of(U_5186),U_5187))),hAPP(c_Int_Onumber__class_Onumber__of(U_5186),U_5187))
      | ~ class_Int_Onumber__ring(U_5186) ),
    inference(variable_rename,[status(thm)],[f_1509_1]) ).

fof(f_1509_3,plain,
    ! [U_5186,U_5187] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5186),c_Int_OBit0(U_5187)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5186),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5186),c_Groups_Ozero__class_Ozero(U_5186)),hAPP(c_Int_Onumber__class_Onumber__of(U_5186),U_5187))),hAPP(c_Int_Onumber__class_Onumber__of(U_5186),U_5187))
      | ~ class_Int_Onumber__ring(U_5186) ),
    inference(definitional_conversion,[status(esa)],[f_1509_2]) ).

cnf(f_1509_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5186),c_Int_OBit0(U_5187)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5186),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5186),c_Groups_Ozero__class_Ozero(U_5186)),hAPP(c_Int_Onumber__class_Onumber__of(U_5186),U_5187))),hAPP(c_Int_Onumber__class_Onumber__of(U_5186),U_5187))
    | ~ class_Int_Onumber__ring(U_5186) ),
    inference(clausify,[status(thm)],[f_1509_3]) ).

fof(f_1510_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_1510_2,plain,
    ! [U_5189,U_5188] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5188)),c_Int_OBit1(U_5189)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5188),U_5189)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5188),U_5189))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5188)),c_Int_OBit1(U_5189))) ) ),
    inference(variable_rename,[status(thm)],[f_1510_1]) ).

fof(f_1510_3,plain,
    ( ! [U_5193,U_5191] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5191)),c_Int_OBit1(U_5193)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5191),U_5193)) )
    & ! [U_5192,U_5190] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5190),U_5192))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5190)),c_Int_OBit1(U_5192))) ) ),
    inference(miniscope,[status(thm)],[f_1510_2]) ).

fof(f_1510_4,plain,
    ( ! [U_5191,U_5193] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5191)),c_Int_OBit1(U_5193)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5191),U_5193)) )
    & ! [U_5192,U_5190] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5190),U_5192))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5190)),c_Int_OBit1(U_5192))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1510_3]) ).

cnf(f_1510_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5190),U_5192))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5190)),c_Int_OBit1(U_5192))) ),
    inference(clausify,[status(thm)],[f_1510_4]) ).

cnf(f_1510_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5191)),c_Int_OBit1(U_5193)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5191),U_5193)) ),
    inference(clausify,[status(thm)],[f_1510_4]) ).

fof(f_1511_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_1511_2,plain,
    ! [U_5195,U_5194] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5194)),c_Int_OBit1(U_5195)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5194),U_5195)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5194),U_5195))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5194)),c_Int_OBit1(U_5195))) ) ),
    inference(variable_rename,[status(thm)],[f_1511_1]) ).

fof(f_1511_3,plain,
    ( ! [U_5199,U_5197] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5197)),c_Int_OBit1(U_5199)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5197),U_5199)) )
    & ! [U_5198,U_5196] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5196),U_5198))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5196)),c_Int_OBit1(U_5198))) ) ),
    inference(miniscope,[status(thm)],[f_1511_2]) ).

fof(f_1511_4,plain,
    ( ! [U_5197,U_5199] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5197)),c_Int_OBit1(U_5199)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5197),U_5199)) )
    & ! [U_5198,U_5196] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5196),U_5198))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5196)),c_Int_OBit1(U_5198))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1511_3]) ).

cnf(f_1511_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5196),U_5198))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5196)),c_Int_OBit1(U_5198))) ),
    inference(clausify,[status(thm)],[f_1511_4]) ).

cnf(f_1511_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5197)),c_Int_OBit1(U_5199)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5197),U_5199)) ),
    inference(clausify,[status(thm)],[f_1511_4]) ).

fof(f_1512_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_1512_2,plain,
    ! [U_5201,U_5200] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5200)),c_Int_OBit0(U_5201)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5200),U_5201)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5200),U_5201))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5200)),c_Int_OBit0(U_5201))) ) ),
    inference(variable_rename,[status(thm)],[f_1512_1]) ).

fof(f_1512_3,plain,
    ( ! [U_5205,U_5203] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5203)),c_Int_OBit0(U_5205)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5203),U_5205)) )
    & ! [U_5204,U_5202] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5202),U_5204))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5202)),c_Int_OBit0(U_5204))) ) ),
    inference(miniscope,[status(thm)],[f_1512_2]) ).

fof(f_1512_4,plain,
    ( ! [U_5203,U_5205] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5203)),c_Int_OBit0(U_5205)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5203),U_5205)) )
    & ! [U_5204,U_5202] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5202),U_5204))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5202)),c_Int_OBit0(U_5204))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1512_3]) ).

cnf(f_1512_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5202),U_5204))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5202)),c_Int_OBit0(U_5204))) ),
    inference(clausify,[status(thm)],[f_1512_4]) ).

cnf(f_1512_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5203)),c_Int_OBit0(U_5205)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5203),U_5205)) ),
    inference(clausify,[status(thm)],[f_1512_4]) ).

fof(f_1513_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_1513_2,plain,
    ! [U_5207,U_5206] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5206)),c_Int_OBit0(U_5207)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5206),U_5207)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5206),U_5207))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5206)),c_Int_OBit0(U_5207))) ) ),
    inference(variable_rename,[status(thm)],[f_1513_1]) ).

fof(f_1513_3,plain,
    ( ! [U_5211,U_5209] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5209)),c_Int_OBit0(U_5211)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5209),U_5211)) )
    & ! [U_5210,U_5208] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5208),U_5210))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5208)),c_Int_OBit0(U_5210))) ) ),
    inference(miniscope,[status(thm)],[f_1513_2]) ).

fof(f_1513_4,plain,
    ( ! [U_5209,U_5211] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5209)),c_Int_OBit0(U_5211)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5209),U_5211)) )
    & ! [U_5210,U_5208] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5208),U_5210))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5208)),c_Int_OBit0(U_5210))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1513_3]) ).

cnf(f_1513_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5208),U_5210))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5208)),c_Int_OBit0(U_5210))) ),
    inference(clausify,[status(thm)],[f_1513_4]) ).

cnf(f_1513_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5209)),c_Int_OBit0(U_5211)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5209),U_5211)) ),
    inference(clausify,[status(thm)],[f_1513_4]) ).

fof(f_1514_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_1514_2,plain,
    ! [U_5213,U_5212] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_5212)),U_5213) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5212),U_5213))),U_5213),
    inference(variable_rename,[status(thm)],[f_1514_1]) ).

fof(f_1514_3,plain,
    ! [U_5212,U_5213] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_5212)),U_5213) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5212),U_5213))),U_5213),
    inference(definitional_conversion,[status(esa)],[f_1514_2]) ).

cnf(f_1514_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_5212)),U_5213) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5212),U_5213))),U_5213),
    inference(clausify,[status(thm)],[f_1514_3]) ).

fof(f_1515_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_1515_2,plain,
    ! [U_5214] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5214)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5214)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5214))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5214))) ) ),
    inference(variable_rename,[status(thm)],[f_1515_1]) ).

fof(f_1515_3,plain,
    ( ! [U_5216] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5216)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5216)) )
    & ! [U_5215] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5215))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5215))) ) ),
    inference(miniscope,[status(thm)],[f_1515_2]) ).

fof(f_1515_4,plain,
    ( ! [U_5216] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5216)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5216)) )
    & ! [U_5215] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5215))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5215))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1515_3]) ).

cnf(f_1515_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5215))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5215))) ),
    inference(clausify,[status(thm)],[f_1515_4]) ).

cnf(f_1515_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5216)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5216)) ),
    inference(clausify,[status(thm)],[f_1515_4]) ).

fof(f_1516_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_1516_2,plain,
    ! [U_5217] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5217)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5217),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5217),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5217)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1516_1]) ).

fof(f_1516_3,plain,
    ( ! [U_5219] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5219)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5219),c_Int_OMin)) )
    & ! [U_5218] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5218),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5218)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1516_2]) ).

fof(f_1516_4,plain,
    ( ! [U_5219] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5219)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5219),c_Int_OMin)) )
    & ! [U_5218] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5218),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5218)),c_Int_OMin)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1516_3]) ).

cnf(f_1516_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5218),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5218)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1516_4]) ).

cnf(f_1516_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5219)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5219),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1516_4]) ).

fof(f_1517_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_1517_2,plain,
    ! [U_5220] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5220)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5220)),
    inference(variable_rename,[status(thm)],[f_1517_1]) ).

fof(f_1517_3,plain,
    ! [U_5220] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5220)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5220)),
    inference(definitional_conversion,[status(esa)],[f_1517_2]) ).

cnf(f_1517_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5220)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5220)),
    inference(clausify,[status(thm)],[f_1517_3]) ).

fof(f_1518_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_1518_2,plain,
    ! [U_5221] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5221)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5221)),
    inference(variable_rename,[status(thm)],[f_1518_1]) ).

fof(f_1518_3,plain,
    ! [U_5221] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5221)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5221)),
    inference(definitional_conversion,[status(esa)],[f_1518_2]) ).

cnf(f_1518_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5221)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5221)),
    inference(clausify,[status(thm)],[f_1518_3]) ).

fof(f_1519_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_1519_2,plain,
    ! [U_5223,U_5222] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5222)),c_Int_OBit1(U_5223)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_5222)),U_5223)),
    inference(variable_rename,[status(thm)],[f_1519_1]) ).

fof(f_1519_3,plain,
    ! [U_5222,U_5223] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5222)),c_Int_OBit1(U_5223)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_5222)),U_5223)),
    inference(definitional_conversion,[status(esa)],[f_1519_2]) ).

cnf(f_1519_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5222)),c_Int_OBit1(U_5223)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_5222)),U_5223)),
    inference(clausify,[status(thm)],[f_1519_3]) ).

fof(f_1520_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_1520_2,plain,
    ! [U_5225,U_5224] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5224)),c_Int_OBit1(U_5225)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5224),c_Int_Osucc(U_5225))),
    inference(variable_rename,[status(thm)],[f_1520_1]) ).

fof(f_1520_3,plain,
    ! [U_5224,U_5225] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5224)),c_Int_OBit1(U_5225)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5224),c_Int_Osucc(U_5225))),
    inference(definitional_conversion,[status(esa)],[f_1520_2]) ).

cnf(f_1520_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5224)),c_Int_OBit1(U_5225)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5224),c_Int_Osucc(U_5225))),
    inference(clausify,[status(thm)],[f_1520_3]) ).

fof(f_1521_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_1521_2,plain,
    ! [U_5227,U_5226] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5226),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5226),c_Groups_Oone__class_Oone(U_5226)),c_Groups_Oone__class_Oone(U_5226))),hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5226),c_Int_OBit0(U_5227))
      | ~ class_Int_Onumber__ring(U_5226) ),
    inference(variable_rename,[status(thm)],[f_1521_1]) ).

fof(f_1521_3,plain,
    ! [U_5226,U_5227] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5226),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5226),c_Groups_Oone__class_Oone(U_5226)),c_Groups_Oone__class_Oone(U_5226))),hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5226),c_Int_OBit0(U_5227))
      | ~ class_Int_Onumber__ring(U_5226) ),
    inference(definitional_conversion,[status(esa)],[f_1521_2]) ).

cnf(f_1521_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5226),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5226),c_Groups_Oone__class_Oone(U_5226)),c_Groups_Oone__class_Oone(U_5226))),hAPP(c_Int_Onumber__class_Onumber__of(U_5226),U_5227)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5226),c_Int_OBit0(U_5227))
    | ~ class_Int_Onumber__ring(U_5226) ),
    inference(clausify,[status(thm)],[f_1521_3]) ).

fof(f_1522_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_1522_2,plain,
    ! [U_5228] :
      ( ( 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_5228))))
        & 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_5228)))) )
      | ~ 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_5228))) ),
    inference(variable_rename,[status(thm)],[f_1522_1]) ).

fof(f_1522_3,plain,
    ( ! [U_5228] :
        ( 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_5228))))
        | ~ sP397(U_5228) )
    & ! [U_5228] :
        ( 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_5228))))
        | ~ sP397(U_5228) )
    & ! [U_5228] :
        ( sP397(U_5228)
        | ~ 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_5228))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP397])],[f_1522_2]) ).

cnf(f_1522_4,plain,
    ( sP397(U_5228)
    | ~ 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_5228))) ),
    inference(clausify,[status(thm)],[f_1522_3]) ).

cnf(f_1522_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_5228))))
    | ~ sP397(U_5228) ),
    inference(clausify,[status(thm)],[f_1522_3]) ).

cnf(f_1522_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_5228))))
    | ~ sP397(U_5228) ),
    inference(clausify,[status(thm)],[f_1522_3]) ).

fof(f_1523_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_1523_2,plain,
    ! [U_5230,U_5229] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5229),U_5230),hAPP(c_Int_Onumber__class_Onumber__of(U_5229),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5229),U_5230),U_5230)
      | ~ class_Int_Onumber__ring(U_5229) ),
    inference(variable_rename,[status(thm)],[f_1523_1]) ).

fof(f_1523_3,plain,
    ! [U_5229,U_5230] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5229),U_5230),hAPP(c_Int_Onumber__class_Onumber__of(U_5229),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5229),U_5230),U_5230)
      | ~ class_Int_Onumber__ring(U_5229) ),
    inference(definitional_conversion,[status(esa)],[f_1523_2]) ).

cnf(f_1523_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5229),U_5230),hAPP(c_Int_Onumber__class_Onumber__of(U_5229),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5229),U_5230),U_5230)
    | ~ class_Int_Onumber__ring(U_5229) ),
    inference(clausify,[status(thm)],[f_1523_3]) ).

fof(f_1524_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_1524_2,plain,
    ! [U_5232,U_5231] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5231),hAPP(c_Int_Onumber__class_Onumber__of(U_5231),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5232) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5231),U_5232),U_5232)
      | ~ class_Int_Onumber__ring(U_5231) ),
    inference(variable_rename,[status(thm)],[f_1524_1]) ).

fof(f_1524_3,plain,
    ! [U_5231,U_5232] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5231),hAPP(c_Int_Onumber__class_Onumber__of(U_5231),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5232) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5231),U_5232),U_5232)
      | ~ class_Int_Onumber__ring(U_5231) ),
    inference(definitional_conversion,[status(esa)],[f_1524_2]) ).

cnf(f_1524_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5231),hAPP(c_Int_Onumber__class_Onumber__of(U_5231),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5232) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5231),U_5232),U_5232)
    | ~ class_Int_Onumber__ring(U_5231) ),
    inference(clausify,[status(thm)],[f_1524_3]) ).

fof(f_1525_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_1525_2,plain,
    ! [U_5233] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5233),c_Groups_Oone__class_Oone(U_5233)),c_Groups_Oone__class_Oone(U_5233)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5233),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_5233) ),
    inference(variable_rename,[status(thm)],[f_1525_1]) ).

fof(f_1525_3,plain,
    ! [U_5233] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5233),c_Groups_Oone__class_Oone(U_5233)),c_Groups_Oone__class_Oone(U_5233)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5233),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_5233) ),
    inference(definitional_conversion,[status(esa)],[f_1525_2]) ).

cnf(f_1525_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5233),c_Groups_Oone__class_Oone(U_5233)),c_Groups_Oone__class_Oone(U_5233)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5233),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_5233) ),
    inference(clausify,[status(thm)],[f_1525_3]) ).

fof(f_1526_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_1526_2,plain,
    ! [U_5234] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5234),c_Groups_Ozero__class_Ozero(U_5234)),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_5234)
      | ~ class_Rings_Osemiring__1(U_5234) ),
    inference(variable_rename,[status(thm)],[f_1526_1]) ).

fof(f_1526_3,plain,
    ! [U_5234] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5234),c_Groups_Ozero__class_Ozero(U_5234)),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_5234)
      | ~ class_Rings_Osemiring__1(U_5234) ),
    inference(definitional_conversion,[status(esa)],[f_1526_2]) ).

cnf(f_1526_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5234),c_Groups_Ozero__class_Ozero(U_5234)),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_5234)
    | ~ class_Rings_Osemiring__1(U_5234) ),
    inference(clausify,[status(thm)],[f_1526_3]) ).

fof(f_1527_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_1527_2,plain,
    ! [U_5236,U_5235] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5235),U_5236),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_5235)
          | U_5236 != c_Groups_Ozero__class_Ozero(U_5235) )
        & ( U_5236 = c_Groups_Ozero__class_Ozero(U_5235)
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_5235),U_5236),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_5235) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_5235) ),
    inference(variable_rename,[status(thm)],[f_1527_1]) ).

fof(f_1527_3,plain,
    ( ! [U_5235,U_5236] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5235),U_5236),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_5235)
        | U_5236 != c_Groups_Ozero__class_Ozero(U_5235)
        | ~ sP398(U_5235,U_5236) )
    & ! [U_5235,U_5236] :
        ( U_5236 = c_Groups_Ozero__class_Ozero(U_5235)
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_5235),U_5236),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_5235)
        | ~ sP398(U_5235,U_5236) )
    & ! [U_5235,U_5236] :
        ( sP398(U_5235,U_5236)
        | ~ class_Rings_Oring__1__no__zero__divisors(U_5235) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP398])],[f_1527_2]) ).

cnf(f_1527_4,plain,
    ( sP398(U_5235,U_5236)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_5235) ),
    inference(clausify,[status(thm)],[f_1527_3]) ).

cnf(f_1527_5,plain,
    ( U_5236 = c_Groups_Ozero__class_Ozero(U_5235)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_5235),U_5236),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_5235)
    | ~ sP398(U_5235,U_5236) ),
    inference(clausify,[status(thm)],[f_1527_3]) ).

cnf(f_1527_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5235),U_5236),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_5235)
    | U_5236 != c_Groups_Ozero__class_Ozero(U_5235)
    | ~ sP398(U_5235,U_5236) ),
    inference(clausify,[status(thm)],[f_1527_3]) ).

fof(f_1528_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_1528_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_1528_1]) ).

cnf(f_1528_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_1528_2]) ).

fof(f_1529_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_1529_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_1529_1]) ).

cnf(f_1529_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_1529_2]) ).

fof(f_1530_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_1530_2,plain,
    ! [U_5238,U_5237] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5237),U_5238),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_5237),U_5238),U_5238)
      | ~ class_Groups_Omonoid__mult(U_5237) ),
    inference(variable_rename,[status(thm)],[f_1530_1]) ).

fof(f_1530_3,plain,
    ! [U_5237,U_5238] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5237),U_5238),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_5237),U_5238),U_5238)
      | ~ class_Groups_Omonoid__mult(U_5237) ),
    inference(definitional_conversion,[status(esa)],[f_1530_2]) ).

cnf(f_1530_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5237),U_5238),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_5237),U_5238),U_5238)
    | ~ class_Groups_Omonoid__mult(U_5237) ),
    inference(clausify,[status(thm)],[f_1530_3]) ).

fof(f_1531_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_1531_2,plain,
    ! [U_5240,U_5239] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5239),U_5240),U_5240) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5239),U_5240),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_5239) ),
    inference(variable_rename,[status(thm)],[f_1531_1]) ).

fof(f_1531_3,plain,
    ! [U_5239,U_5240] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5239),U_5240),U_5240) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5239),U_5240),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_5239) ),
    inference(definitional_conversion,[status(esa)],[f_1531_2]) ).

cnf(f_1531_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5239),U_5240),U_5240) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5239),U_5240),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_5239) ),
    inference(clausify,[status(thm)],[f_1531_3]) ).

fof(f_1532_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_1532_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_1532_1]) ).

cnf(f_1532_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_1532_2]) ).

fof(f_1533_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_1533_2,plain,
    ! [U_5241] : 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_5241) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5241)),
    inference(variable_rename,[status(thm)],[f_1533_1]) ).

fof(f_1533_3,plain,
    ! [U_5241] : 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_5241) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5241)),
    inference(definitional_conversion,[status(esa)],[f_1533_2]) ).

cnf(f_1533_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_5241) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5241)),
    inference(clausify,[status(thm)],[f_1533_3]) ).

fof(f_1534_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_1534_2,plain,
    ! [U_5242] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5242),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_5242)),
    inference(variable_rename,[status(thm)],[f_1534_1]) ).

fof(f_1534_3,plain,
    ! [U_5242] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5242),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_5242)),
    inference(definitional_conversion,[status(esa)],[f_1534_2]) ).

cnf(f_1534_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5242),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_5242)),
    inference(clausify,[status(thm)],[f_1534_3]) ).

fof(f_1535_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_1535_2,plain,
    ! [U_5243] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5243),c_Groups_Oone__class_Oone(U_5243)),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_5243)
      | ~ class_Rings_Osemiring__1(U_5243) ),
    inference(variable_rename,[status(thm)],[f_1535_1]) ).

fof(f_1535_3,plain,
    ! [U_5243] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5243),c_Groups_Oone__class_Oone(U_5243)),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_5243)
      | ~ class_Rings_Osemiring__1(U_5243) ),
    inference(definitional_conversion,[status(esa)],[f_1535_2]) ).

cnf(f_1535_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5243),c_Groups_Oone__class_Oone(U_5243)),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_5243)
    | ~ class_Rings_Osemiring__1(U_5243) ),
    inference(clausify,[status(thm)],[f_1535_3]) ).

fof(f_1536_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_1536_2,plain,
    ! [U_5245,U_5244] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5244),hAPP(c_Groups_Ouminus__class_Ouminus(U_5244),U_5245)),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_5244),U_5245),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Oring__1(U_5244) ),
    inference(variable_rename,[status(thm)],[f_1536_1]) ).

fof(f_1536_3,plain,
    ! [U_5244,U_5245] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5244),hAPP(c_Groups_Ouminus__class_Ouminus(U_5244),U_5245)),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_5244),U_5245),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Oring__1(U_5244) ),
    inference(definitional_conversion,[status(esa)],[f_1536_2]) ).

cnf(f_1536_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5244),hAPP(c_Groups_Ouminus__class_Ouminus(U_5244),U_5245)),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_5244),U_5245),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Oring__1(U_5244) ),
    inference(clausify,[status(thm)],[f_1536_3]) ).

fof(f_1537_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_1537_2,plain,
    ! [U_5246] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5246),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_5246),U_5246),
    inference(variable_rename,[status(thm)],[f_1537_1]) ).

fof(f_1537_3,plain,
    ! [U_5246] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5246),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_5246),U_5246),
    inference(definitional_conversion,[status(esa)],[f_1537_2]) ).

cnf(f_1537_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5246),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_5246),U_5246),
    inference(clausify,[status(thm)],[f_1537_3]) ).

fof(f_1538_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_1538_2,plain,
    ! [U_5247] : 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_5247) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5247),U_5247),
    inference(variable_rename,[status(thm)],[f_1538_1]) ).

fof(f_1538_3,plain,
    ! [U_5247] : 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_5247) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5247),U_5247),
    inference(definitional_conversion,[status(esa)],[f_1538_2]) ).

cnf(f_1538_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_5247) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5247),U_5247),
    inference(clausify,[status(thm)],[f_1538_3]) ).

fof(f_1539_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_1539_2,plain,
    ! [U_5250,U_5249,U_5248] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5248),U_5249),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_5250)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5248),hAPP(hAPP(c_Power_Opower__class_Opower(U_5248),U_5249),U_5250)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Groups_Omonoid__mult(U_5248) ),
    inference(variable_rename,[status(thm)],[f_1539_1]) ).

fof(f_1539_3,plain,
    ! [U_5248,U_5249,U_5250] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5248),U_5249),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_5250)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5248),hAPP(hAPP(c_Power_Opower__class_Opower(U_5248),U_5249),U_5250)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Groups_Omonoid__mult(U_5248) ),
    inference(definitional_conversion,[status(esa)],[f_1539_2]) ).

cnf(f_1539_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5248),U_5249),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_5250)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5248),hAPP(hAPP(c_Power_Opower__class_Opower(U_5248),U_5249),U_5250)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Groups_Omonoid__mult(U_5248) ),
    inference(clausify,[status(thm)],[f_1539_3]) ).

fof(f_1540_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_1540_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_1540_1]) ).

cnf(f_1540_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_1540_2]) ).

fof(f_1541_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_1541_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_1541_1]) ).

cnf(f_1541_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_1541_2]) ).

fof(f_1542_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_1542_2,plain,
    ! [U_5252,U_5251] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5251),hAPP(c_Groups_Oabs__class_Oabs(U_5251),U_5252)),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_5251),U_5252),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_5251) ),
    inference(variable_rename,[status(thm)],[f_1542_1]) ).

fof(f_1542_3,plain,
    ! [U_5251,U_5252] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5251),hAPP(c_Groups_Oabs__class_Oabs(U_5251),U_5252)),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_5251),U_5252),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_5251) ),
    inference(definitional_conversion,[status(esa)],[f_1542_2]) ).

cnf(f_1542_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5251),hAPP(c_Groups_Oabs__class_Oabs(U_5251),U_5252)),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_5251),U_5252),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(U_5251) ),
    inference(clausify,[status(thm)],[f_1542_3]) ).

fof(f_1543_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_1543_2,plain,
    ! [U_5254,U_5253] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5253),hAPP(hAPP(c_Power_Opower__class_Opower(U_5253),U_5254),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_5253),U_5254),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_5253) ),
    inference(variable_rename,[status(thm)],[f_1543_1]) ).

fof(f_1543_3,plain,
    ! [U_5253,U_5254] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5253),hAPP(hAPP(c_Power_Opower__class_Opower(U_5253),U_5254),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_5253),U_5254),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_5253) ),
    inference(definitional_conversion,[status(esa)],[f_1543_2]) ).

cnf(f_1543_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5253),hAPP(hAPP(c_Power_Opower__class_Opower(U_5253),U_5254),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_5253),U_5254),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(U_5253) ),
    inference(clausify,[status(thm)],[f_1543_3]) ).

fof(f_1544_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_1544_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_1544_1]) ).

cnf(f_1544_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_1544_2]) ).

fof(f_1545_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_1545_2,plain,
    ! [U_5255] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5255)),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_5255,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_1545_1]) ).

fof(f_1545_3,plain,
    ! [U_5255] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5255)),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_5255,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_1545_2]) ).

cnf(f_1545_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5255)),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_5255,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_1545_3]) ).

fof(f_1546_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_1546_2,plain,
    ! [U_5256] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5256))),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_5256),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_1546_1]) ).

fof(f_1546_3,plain,
    ! [U_5256] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5256))),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_5256),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_1546_2]) ).

cnf(f_1546_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5256))),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_5256),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(clausify,[status(thm)],[f_1546_3]) ).

fof(f_1547_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_1547_2,plain,
    ! [U_5258,U_5257] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5257)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5258))) = 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_5257),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5258))),
    inference(variable_rename,[status(thm)],[f_1547_1]) ).

fof(f_1547_3,plain,
    ! [U_5257,U_5258] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5257)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5258))) = 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_5257),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5258))),
    inference(definitional_conversion,[status(esa)],[f_1547_2]) ).

cnf(f_1547_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5257)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5258))) = 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_5257),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5258))),
    inference(clausify,[status(thm)],[f_1547_3]) ).

fof(f_1548_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_1548_2,plain,
    ! [U_5259] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5259),U_5259)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_5259,
    inference(variable_rename,[status(thm)],[f_1548_1]) ).

fof(f_1548_3,plain,
    ! [U_5259] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5259),U_5259)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_5259,
    inference(definitional_conversion,[status(esa)],[f_1548_2]) ).

cnf(f_1548_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5259),U_5259)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_5259,
    inference(clausify,[status(thm)],[f_1548_3]) ).

fof(f_1549_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_1549_2,plain,
    ! [U_5262,U_5261,U_5260] :
      ( U_5261 = U_5262
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5260),c_Groups_Ozero__class_Ozero(U_5260)),U_5262))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5260),c_Groups_Ozero__class_Ozero(U_5260)),U_5261))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_5260),U_5261),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_5260),U_5262),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__semidom(U_5260) ),
    inference(variable_rename,[status(thm)],[f_1549_1]) ).

fof(f_1549_3,plain,
    ! [U_5260,U_5261,U_5262] :
      ( U_5261 = U_5262
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5260),c_Groups_Ozero__class_Ozero(U_5260)),U_5262))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5260),c_Groups_Ozero__class_Ozero(U_5260)),U_5261))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_5260),U_5261),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_5260),U_5262),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__semidom(U_5260) ),
    inference(definitional_conversion,[status(esa)],[f_1549_2]) ).

cnf(f_1549_4,plain,
    ( U_5261 = U_5262
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5260),c_Groups_Ozero__class_Ozero(U_5260)),U_5262))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5260),c_Groups_Ozero__class_Ozero(U_5260)),U_5261))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_5260),U_5261),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_5260),U_5262),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__semidom(U_5260) ),
    inference(clausify,[status(thm)],[f_1549_3]) ).

fof(f_1550_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_1550_2,plain,
    ! [U_5265,U_5264,U_5263] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),U_5264),U_5265))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),c_Groups_Ozero__class_Ozero(U_5263)),U_5265))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),hAPP(hAPP(c_Power_Opower__class_Opower(U_5263),U_5264),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_5263),U_5265),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_5263) ),
    inference(variable_rename,[status(thm)],[f_1550_1]) ).

fof(f_1550_3,plain,
    ! [U_5264,U_5263,U_5265] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),U_5264),U_5265))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),c_Groups_Ozero__class_Ozero(U_5263)),U_5265))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),hAPP(hAPP(c_Power_Opower__class_Opower(U_5263),U_5264),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_5263),U_5265),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_5263) ),
    inference(definitional_conversion,[status(esa)],[f_1550_2]) ).

cnf(f_1550_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),U_5264),U_5265))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),c_Groups_Ozero__class_Ozero(U_5263)),U_5265))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5263),hAPP(hAPP(c_Power_Opower__class_Opower(U_5263),U_5264),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_5263),U_5265),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__semidom(U_5263) ),
    inference(clausify,[status(thm)],[f_1550_3]) ).

fof(f_1551_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_1551_2,plain,
    ! [U_5267,U_5266] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5266),c_Groups_Ozero__class_Ozero(U_5266)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5266),U_5267),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__idom(U_5266) ),
    inference(variable_rename,[status(thm)],[f_1551_1]) ).

fof(f_1551_3,plain,
    ! [U_5267,U_5266] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5266),c_Groups_Ozero__class_Ozero(U_5266)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5266),U_5267),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__idom(U_5266) ),
    inference(definitional_conversion,[status(esa)],[f_1551_2]) ).

cnf(f_1551_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5266),c_Groups_Ozero__class_Ozero(U_5266)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5266),U_5267),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(U_5266) ),
    inference(clausify,[status(thm)],[f_1551_3]) ).

fof(f_1552_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_1552_2,plain,
    ! [U_5269,U_5268] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5268),c_Groups_Ozero__class_Ozero(U_5268)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5268),U_5269),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | U_5269 = c_Groups_Ozero__class_Ozero(U_5268) )
        & ( U_5269 != c_Groups_Ozero__class_Ozero(U_5268)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5268),c_Groups_Ozero__class_Ozero(U_5268)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5268),U_5269),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Rings_Olinordered__idom(U_5268) ),
    inference(variable_rename,[status(thm)],[f_1552_1]) ).

fof(f_1552_3,plain,
    ( ! [U_5268,U_5269] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5268),c_Groups_Ozero__class_Ozero(U_5268)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5268),U_5269),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | U_5269 = c_Groups_Ozero__class_Ozero(U_5268)
        | ~ sP399(U_5268,U_5269) )
    & ! [U_5268,U_5269] :
        ( U_5269 != c_Groups_Ozero__class_Ozero(U_5268)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5268),c_Groups_Ozero__class_Ozero(U_5268)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5268),U_5269),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ sP399(U_5268,U_5269) )
    & ! [U_5268,U_5269] :
        ( sP399(U_5268,U_5269)
        | ~ class_Rings_Olinordered__idom(U_5268) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP399])],[f_1552_2]) ).

cnf(f_1552_4,plain,
    ( sP399(U_5268,U_5269)
    | ~ class_Rings_Olinordered__idom(U_5268) ),
    inference(clausify,[status(thm)],[f_1552_3]) ).

cnf(f_1552_5,plain,
    ( U_5269 != c_Groups_Ozero__class_Ozero(U_5268)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5268),c_Groups_Ozero__class_Ozero(U_5268)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5268),U_5269),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ sP399(U_5268,U_5269) ),
    inference(clausify,[status(thm)],[f_1552_3]) ).

cnf(f_1552_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5268),c_Groups_Ozero__class_Ozero(U_5268)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5268),U_5269),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | U_5269 = c_Groups_Ozero__class_Ozero(U_5268)
    | ~ sP399(U_5268,U_5269) ),
    inference(clausify,[status(thm)],[f_1552_3]) ).

fof(f_1553_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_1553_2,plain,
    ! [U_5271,U_5270] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5270),hAPP(hAPP(c_Power_Opower__class_Opower(U_5270),U_5271),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_5270)))
      | ~ class_Rings_Olinordered__idom(U_5270) ),
    inference(variable_rename,[status(thm)],[f_1553_1]) ).

fof(f_1553_3,plain,
    ! [U_5270,U_5271] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5270),hAPP(hAPP(c_Power_Opower__class_Opower(U_5270),U_5271),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_5270)))
      | ~ class_Rings_Olinordered__idom(U_5270) ),
    inference(definitional_conversion,[status(esa)],[f_1553_2]) ).

cnf(f_1553_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5270),hAPP(hAPP(c_Power_Opower__class_Opower(U_5270),U_5271),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_5270)))
    | ~ class_Rings_Olinordered__idom(U_5270) ),
    inference(clausify,[status(thm)],[f_1553_3]) ).

fof(f_1554_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_1554_2,plain,
    ! [U_5274,U_5273,U_5272] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5272),hAPP(hAPP(c_Power_Opower__class_Opower(U_5272),U_5273),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_5272),U_5274),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_5272)
          | U_5274 != c_Groups_Ozero__class_Ozero(U_5272)
          | U_5273 != c_Groups_Ozero__class_Ozero(U_5272) )
        & ( ( U_5274 = c_Groups_Ozero__class_Ozero(U_5272)
            & U_5273 = c_Groups_Ozero__class_Ozero(U_5272) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5272),hAPP(hAPP(c_Power_Opower__class_Opower(U_5272),U_5273),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_5272),U_5274),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_5272) ) )
      | ~ class_Rings_Olinordered__idom(U_5272) ),
    inference(variable_rename,[status(thm)],[f_1554_1]) ).

fof(f_1554_3,plain,
    ( ! [U_5272,U_5273,U_5274] :
        ( U_5274 = c_Groups_Ozero__class_Ozero(U_5272)
        | ~ sP400(U_5272,U_5273,U_5274) )
    & ! [U_5272,U_5273,U_5274] :
        ( U_5273 = c_Groups_Ozero__class_Ozero(U_5272)
        | ~ sP400(U_5272,U_5273,U_5274) )
    & ! [U_5272,U_5273,U_5274] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5272),hAPP(hAPP(c_Power_Opower__class_Opower(U_5272),U_5273),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_5272),U_5274),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_5272)
        | U_5274 != c_Groups_Ozero__class_Ozero(U_5272)
        | U_5273 != c_Groups_Ozero__class_Ozero(U_5272)
        | ~ sP401(U_5272,U_5273,U_5274) )
    & ! [U_5272,U_5273,U_5274] :
        ( sP400(U_5272,U_5273,U_5274)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5272),hAPP(hAPP(c_Power_Opower__class_Opower(U_5272),U_5273),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_5272),U_5274),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_5272)
        | ~ sP401(U_5272,U_5273,U_5274) )
    & ! [U_5272,U_5273,U_5274] :
        ( sP401(U_5272,U_5273,U_5274)
        | ~ class_Rings_Olinordered__idom(U_5272) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP400,sP401])],[f_1554_2]) ).

cnf(f_1554_4,plain,
    ( sP401(U_5272,U_5273,U_5274)
    | ~ class_Rings_Olinordered__idom(U_5272) ),
    inference(clausify,[status(thm)],[f_1554_3]) ).

cnf(f_1554_5,plain,
    ( sP400(U_5272,U_5273,U_5274)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5272),hAPP(hAPP(c_Power_Opower__class_Opower(U_5272),U_5273),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_5272),U_5274),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_5272)
    | ~ sP401(U_5272,U_5273,U_5274) ),
    inference(clausify,[status(thm)],[f_1554_3]) ).

cnf(f_1554_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5272),hAPP(hAPP(c_Power_Opower__class_Opower(U_5272),U_5273),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_5272),U_5274),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_5272)
    | U_5274 != c_Groups_Ozero__class_Ozero(U_5272)
    | U_5273 != c_Groups_Ozero__class_Ozero(U_5272)
    | ~ sP401(U_5272,U_5273,U_5274) ),
    inference(clausify,[status(thm)],[f_1554_3]) ).

cnf(f_1554_7,plain,
    ( U_5273 = c_Groups_Ozero__class_Ozero(U_5272)
    | ~ sP400(U_5272,U_5273,U_5274) ),
    inference(clausify,[status(thm)],[f_1554_3]) ).

cnf(f_1554_8,plain,
    ( U_5274 = c_Groups_Ozero__class_Ozero(U_5272)
    | ~ sP400(U_5272,U_5273,U_5274) ),
    inference(clausify,[status(thm)],[f_1554_3]) ).

fof(f_1555_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_1555_2,plain,
    ! [U_5276,U_5275] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5275),hAPP(c_Int_Onumber__class_Onumber__of(U_5275),U_5276)),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_5275),hAPP(c_Int_Onumber__class_Onumber__of(U_5275),U_5276)),hAPP(c_Int_Onumber__class_Onumber__of(U_5275),U_5276))
      | ~ class_Int_Onumber(U_5275)
      | ~ class_Groups_Omonoid__mult(U_5275) ),
    inference(variable_rename,[status(thm)],[f_1555_1]) ).

fof(f_1555_3,plain,
    ! [U_5275,U_5276] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5275),hAPP(c_Int_Onumber__class_Onumber__of(U_5275),U_5276)),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_5275),hAPP(c_Int_Onumber__class_Onumber__of(U_5275),U_5276)),hAPP(c_Int_Onumber__class_Onumber__of(U_5275),U_5276))
      | ~ class_Int_Onumber(U_5275)
      | ~ class_Groups_Omonoid__mult(U_5275) ),
    inference(definitional_conversion,[status(esa)],[f_1555_2]) ).

cnf(f_1555_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5275),hAPP(c_Int_Onumber__class_Onumber__of(U_5275),U_5276)),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_5275),hAPP(c_Int_Onumber__class_Onumber__of(U_5275),U_5276)),hAPP(c_Int_Onumber__class_Onumber__of(U_5275),U_5276))
    | ~ class_Int_Onumber(U_5275)
    | ~ class_Groups_Omonoid__mult(U_5275) ),
    inference(clausify,[status(thm)],[f_1555_3]) ).

fof(f_1556_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_1556_2,plain,
    ! [U_5277] :
      ( U_5277 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_5277 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5277),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_1556_1]) ).

fof(f_1556_3,plain,
    ! [U_5277] :
      ( U_5277 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_5277 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5277),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_1556_2]) ).

cnf(f_1556_4,plain,
    ( U_5277 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_5277 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5277),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(clausify,[status(thm)],[f_1556_3]) ).

fof(f_1557_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_1557_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_1557_1]) ).

cnf(f_1557_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_1557_2]) ).

fof(f_1558_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_1558_2,plain,
    ! [U_5279,U_5278] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5278),U_5279),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_5278)
          | ( U_5279 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5278),c_Groups_Oone__class_Oone(U_5278))
            & U_5279 != c_Groups_Oone__class_Oone(U_5278) ) )
        & ( U_5279 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5278),c_Groups_Oone__class_Oone(U_5278))
          | U_5279 = c_Groups_Oone__class_Oone(U_5278)
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_5278),U_5279),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_5278) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_5278) ),
    inference(variable_rename,[status(thm)],[f_1558_1]) ).

fof(f_1558_3,plain,
    ( ! [U_5278,U_5279] :
        ( U_5279 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5278),c_Groups_Oone__class_Oone(U_5278))
        | ~ sP402(U_5278,U_5279) )
    & ! [U_5278,U_5279] :
        ( U_5279 != c_Groups_Oone__class_Oone(U_5278)
        | ~ sP402(U_5278,U_5279) )
    & ! [U_5278,U_5279] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5278),U_5279),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_5278)
        | sP402(U_5278,U_5279)
        | ~ sP403(U_5278,U_5279) )
    & ! [U_5278,U_5279] :
        ( U_5279 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5278),c_Groups_Oone__class_Oone(U_5278))
        | U_5279 = c_Groups_Oone__class_Oone(U_5278)
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_5278),U_5279),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_5278)
        | ~ sP403(U_5278,U_5279) )
    & ! [U_5278,U_5279] :
        ( sP403(U_5278,U_5279)
        | ~ class_Rings_Oring__1__no__zero__divisors(U_5278) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP402,sP403])],[f_1558_2]) ).

cnf(f_1558_4,plain,
    ( sP403(U_5278,U_5279)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_5278) ),
    inference(clausify,[status(thm)],[f_1558_3]) ).

cnf(f_1558_5,plain,
    ( U_5279 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5278),c_Groups_Oone__class_Oone(U_5278))
    | U_5279 = c_Groups_Oone__class_Oone(U_5278)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_5278),U_5279),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_5278)
    | ~ sP403(U_5278,U_5279) ),
    inference(clausify,[status(thm)],[f_1558_3]) ).

cnf(f_1558_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5278),U_5279),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_5278)
    | sP402(U_5278,U_5279)
    | ~ sP403(U_5278,U_5279) ),
    inference(clausify,[status(thm)],[f_1558_3]) ).

cnf(f_1558_7,plain,
    ( U_5279 != c_Groups_Oone__class_Oone(U_5278)
    | ~ sP402(U_5278,U_5279) ),
    inference(clausify,[status(thm)],[f_1558_3]) ).

cnf(f_1558_8,plain,
    ( U_5279 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5278),c_Groups_Oone__class_Oone(U_5278))
    | ~ sP402(U_5278,U_5279) ),
    inference(clausify,[status(thm)],[f_1558_3]) ).

fof(f_1559_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_1559_2,plain,
    ! [U_5282,U_5281,U_5280] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5280),U_5281),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_5282)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5280),hAPP(hAPP(c_Power_Opower__class_Opower(U_5280),U_5281),U_5282)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5280),U_5281),U_5282))
      | ~ class_Rings_Ocomm__semiring__1(U_5280) ),
    inference(variable_rename,[status(thm)],[f_1559_1]) ).

fof(f_1559_3,plain,
    ! [U_5281,U_5282,U_5280] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5280),U_5281),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_5282)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5280),hAPP(hAPP(c_Power_Opower__class_Opower(U_5280),U_5281),U_5282)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5280),U_5281),U_5282))
      | ~ class_Rings_Ocomm__semiring__1(U_5280) ),
    inference(definitional_conversion,[status(esa)],[f_1559_2]) ).

cnf(f_1559_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5280),U_5281),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_5282)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5280),hAPP(hAPP(c_Power_Opower__class_Opower(U_5280),U_5281),U_5282)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5280),U_5281),U_5282))
    | ~ class_Rings_Ocomm__semiring__1(U_5280) ),
    inference(clausify,[status(thm)],[f_1559_3]) ).

fof(f_1560_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_1560_2,plain,
    ! [U_5285,U_5284,U_5283] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5283),hAPP(c_Groups_Ouminus__class_Ouminus(U_5283),U_5284)),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_5285)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5283),U_5284),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_5285))
      | ~ class_Rings_Oring__1(U_5283) ),
    inference(variable_rename,[status(thm)],[f_1560_1]) ).

fof(f_1560_3,plain,
    ! [U_5283,U_5284,U_5285] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5283),hAPP(c_Groups_Ouminus__class_Ouminus(U_5283),U_5284)),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_5285)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5283),U_5284),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_5285))
      | ~ class_Rings_Oring__1(U_5283) ),
    inference(definitional_conversion,[status(esa)],[f_1560_2]) ).

cnf(f_1560_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5283),hAPP(c_Groups_Ouminus__class_Ouminus(U_5283),U_5284)),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_5285)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5283),U_5284),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_5285))
    | ~ class_Rings_Oring__1(U_5283) ),
    inference(clausify,[status(thm)],[f_1560_3]) ).

fof(f_1561_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_1561_2,plain,
    ! [U_5288,U_5287,U_5286] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5286),U_5287),U_5288))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5286),c_Groups_Ozero__class_Ozero(U_5286)),U_5288))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5286),hAPP(hAPP(c_Power_Opower__class_Opower(U_5286),U_5287),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_5286),U_5288),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_5286) ),
    inference(variable_rename,[status(thm)],[f_1561_1]) ).

fof(f_1561_3,plain,
    ! [U_5286,U_5287,U_5288] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5286),U_5287),U_5288))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5286),c_Groups_Ozero__class_Ozero(U_5286)),U_5288))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5286),hAPP(hAPP(c_Power_Opower__class_Opower(U_5286),U_5287),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_5286),U_5288),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_5286) ),
    inference(definitional_conversion,[status(esa)],[f_1561_2]) ).

cnf(f_1561_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5286),U_5287),U_5288))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5286),c_Groups_Ozero__class_Ozero(U_5286)),U_5288))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5286),hAPP(hAPP(c_Power_Opower__class_Opower(U_5286),U_5287),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_5286),U_5288),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__semidom(U_5286) ),
    inference(clausify,[status(thm)],[f_1561_3]) ).

fof(f_1562_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_1562_2,plain,
    ! [U_5291,U_5290,U_5289] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5289),c_Groups_Ozero__class_Ozero(U_5289)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5289),hAPP(hAPP(c_Power_Opower__class_Opower(U_5289),U_5290),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_5289),U_5291),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      | ~ class_Rings_Olinordered__idom(U_5289) ),
    inference(variable_rename,[status(thm)],[f_1562_1]) ).

fof(f_1562_3,plain,
    ! [U_5290,U_5289,U_5291] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5289),c_Groups_Ozero__class_Ozero(U_5289)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5289),hAPP(hAPP(c_Power_Opower__class_Opower(U_5289),U_5290),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_5289),U_5291),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      | ~ class_Rings_Olinordered__idom(U_5289) ),
    inference(definitional_conversion,[status(esa)],[f_1562_2]) ).

cnf(f_1562_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5289),c_Groups_Ozero__class_Ozero(U_5289)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5289),hAPP(hAPP(c_Power_Opower__class_Opower(U_5289),U_5290),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_5289),U_5291),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(U_5289) ),
    inference(clausify,[status(thm)],[f_1562_3]) ).

fof(f_1563_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_1563_2,plain,
    ! [U_5294,U_5293,U_5292] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5292),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5292),hAPP(hAPP(c_Power_Opower__class_Opower(U_5292),U_5293),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_5292),U_5294),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_5292)))
          | U_5294 != c_Groups_Ozero__class_Ozero(U_5292)
          | U_5293 != c_Groups_Ozero__class_Ozero(U_5292) )
        & ( ( U_5294 = c_Groups_Ozero__class_Ozero(U_5292)
            & U_5293 = c_Groups_Ozero__class_Ozero(U_5292) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5292),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5292),hAPP(hAPP(c_Power_Opower__class_Opower(U_5292),U_5293),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_5292),U_5294),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_5292))) ) )
      | ~ class_Rings_Olinordered__idom(U_5292) ),
    inference(variable_rename,[status(thm)],[f_1563_1]) ).

fof(f_1563_3,plain,
    ( ! [U_5292,U_5293,U_5294] :
        ( U_5294 = c_Groups_Ozero__class_Ozero(U_5292)
        | ~ sP404(U_5292,U_5293,U_5294) )
    & ! [U_5292,U_5293,U_5294] :
        ( U_5293 = c_Groups_Ozero__class_Ozero(U_5292)
        | ~ sP404(U_5292,U_5293,U_5294) )
    & ! [U_5292,U_5293,U_5294] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5292),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5292),hAPP(hAPP(c_Power_Opower__class_Opower(U_5292),U_5293),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_5292),U_5294),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_5292)))
        | U_5294 != c_Groups_Ozero__class_Ozero(U_5292)
        | U_5293 != c_Groups_Ozero__class_Ozero(U_5292)
        | ~ sP405(U_5292,U_5293,U_5294) )
    & ! [U_5292,U_5293,U_5294] :
        ( sP404(U_5292,U_5293,U_5294)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5292),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5292),hAPP(hAPP(c_Power_Opower__class_Opower(U_5292),U_5293),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_5292),U_5294),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_5292)))
        | ~ sP405(U_5292,U_5293,U_5294) )
    & ! [U_5292,U_5293,U_5294] :
        ( sP405(U_5292,U_5293,U_5294)
        | ~ class_Rings_Olinordered__idom(U_5292) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP404,sP405])],[f_1563_2]) ).

cnf(f_1563_4,plain,
    ( sP405(U_5292,U_5293,U_5294)
    | ~ class_Rings_Olinordered__idom(U_5292) ),
    inference(clausify,[status(thm)],[f_1563_3]) ).

cnf(f_1563_5,plain,
    ( sP404(U_5292,U_5293,U_5294)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5292),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5292),hAPP(hAPP(c_Power_Opower__class_Opower(U_5292),U_5293),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_5292),U_5294),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_5292)))
    | ~ sP405(U_5292,U_5293,U_5294) ),
    inference(clausify,[status(thm)],[f_1563_3]) ).

cnf(f_1563_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5292),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5292),hAPP(hAPP(c_Power_Opower__class_Opower(U_5292),U_5293),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_5292),U_5294),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_5292)))
    | U_5294 != c_Groups_Ozero__class_Ozero(U_5292)
    | U_5293 != c_Groups_Ozero__class_Ozero(U_5292)
    | ~ sP405(U_5292,U_5293,U_5294) ),
    inference(clausify,[status(thm)],[f_1563_3]) ).

cnf(f_1563_7,plain,
    ( U_5293 = c_Groups_Ozero__class_Ozero(U_5292)
    | ~ sP404(U_5292,U_5293,U_5294) ),
    inference(clausify,[status(thm)],[f_1563_3]) ).

cnf(f_1563_8,plain,
    ( U_5294 = c_Groups_Ozero__class_Ozero(U_5292)
    | ~ sP404(U_5292,U_5293,U_5294) ),
    inference(clausify,[status(thm)],[f_1563_3]) ).

fof(f_1564_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_1564_2,plain,
    ! [U_5297,U_5296,U_5295] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5295),hAPP(hAPP(c_Power_Opower__class_Opower(U_5295),U_5296),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_5295),U_5297),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_5295)))
      | ~ class_Rings_Olinordered__idom(U_5295) ),
    inference(variable_rename,[status(thm)],[f_1564_1]) ).

fof(f_1564_3,plain,
    ! [U_5296,U_5297,U_5295] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5295),hAPP(hAPP(c_Power_Opower__class_Opower(U_5295),U_5296),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_5295),U_5297),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_5295)))
      | ~ class_Rings_Olinordered__idom(U_5295) ),
    inference(definitional_conversion,[status(esa)],[f_1564_2]) ).

cnf(f_1564_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5295),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5295),hAPP(hAPP(c_Power_Opower__class_Opower(U_5295),U_5296),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_5295),U_5297),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_5295)))
    | ~ class_Rings_Olinordered__idom(U_5295) ),
    inference(clausify,[status(thm)],[f_1564_3]) ).

fof(f_1565_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_1565_2,plain,
    ! [U_5300,U_5299,U_5298] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5298),c_Groups_Ozero__class_Ozero(U_5298)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5298),hAPP(hAPP(c_Power_Opower__class_Opower(U_5298),U_5299),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_5298),U_5300),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
          | ( U_5300 = c_Groups_Ozero__class_Ozero(U_5298)
            & U_5299 = c_Groups_Ozero__class_Ozero(U_5298) ) )
        & ( U_5300 != c_Groups_Ozero__class_Ozero(U_5298)
          | U_5299 != c_Groups_Ozero__class_Ozero(U_5298)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5298),c_Groups_Ozero__class_Ozero(U_5298)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5298),hAPP(hAPP(c_Power_Opower__class_Opower(U_5298),U_5299),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_5298),U_5300),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) )
      | ~ class_Rings_Olinordered__idom(U_5298) ),
    inference(variable_rename,[status(thm)],[f_1565_1]) ).

fof(f_1565_3,plain,
    ( ! [U_5298,U_5299,U_5300] :
        ( U_5300 = c_Groups_Ozero__class_Ozero(U_5298)
        | ~ sP406(U_5298,U_5299,U_5300) )
    & ! [U_5298,U_5299,U_5300] :
        ( U_5299 = c_Groups_Ozero__class_Ozero(U_5298)
        | ~ sP406(U_5298,U_5299,U_5300) )
    & ! [U_5298,U_5299,U_5300] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5298),c_Groups_Ozero__class_Ozero(U_5298)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5298),hAPP(hAPP(c_Power_Opower__class_Opower(U_5298),U_5299),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_5298),U_5300),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | sP406(U_5298,U_5299,U_5300)
        | ~ sP407(U_5298,U_5299,U_5300) )
    & ! [U_5298,U_5299,U_5300] :
        ( U_5300 != c_Groups_Ozero__class_Ozero(U_5298)
        | U_5299 != c_Groups_Ozero__class_Ozero(U_5298)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5298),c_Groups_Ozero__class_Ozero(U_5298)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5298),hAPP(hAPP(c_Power_Opower__class_Opower(U_5298),U_5299),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_5298),U_5300),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | ~ sP407(U_5298,U_5299,U_5300) )
    & ! [U_5298,U_5299,U_5300] :
        ( sP407(U_5298,U_5299,U_5300)
        | ~ class_Rings_Olinordered__idom(U_5298) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP406,sP407])],[f_1565_2]) ).

cnf(f_1565_4,plain,
    ( sP407(U_5298,U_5299,U_5300)
    | ~ class_Rings_Olinordered__idom(U_5298) ),
    inference(clausify,[status(thm)],[f_1565_3]) ).

cnf(f_1565_5,plain,
    ( U_5300 != c_Groups_Ozero__class_Ozero(U_5298)
    | U_5299 != c_Groups_Ozero__class_Ozero(U_5298)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5298),c_Groups_Ozero__class_Ozero(U_5298)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5298),hAPP(hAPP(c_Power_Opower__class_Opower(U_5298),U_5299),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_5298),U_5300),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ sP407(U_5298,U_5299,U_5300) ),
    inference(clausify,[status(thm)],[f_1565_3]) ).

cnf(f_1565_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5298),c_Groups_Ozero__class_Ozero(U_5298)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5298),hAPP(hAPP(c_Power_Opower__class_Opower(U_5298),U_5299),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_5298),U_5300),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | sP406(U_5298,U_5299,U_5300)
    | ~ sP407(U_5298,U_5299,U_5300) ),
    inference(clausify,[status(thm)],[f_1565_3]) ).

cnf(f_1565_7,plain,
    ( U_5299 = c_Groups_Ozero__class_Ozero(U_5298)
    | ~ sP406(U_5298,U_5299,U_5300) ),
    inference(clausify,[status(thm)],[f_1565_3]) ).

cnf(f_1565_8,plain,
    ( U_5300 = c_Groups_Ozero__class_Ozero(U_5298)
    | ~ sP406(U_5298,U_5299,U_5300) ),
    inference(clausify,[status(thm)],[f_1565_3]) ).

fof(f_1566_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_1566_2,plain,
    ! [U_5303,U_5302,U_5301] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5301),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5301),U_5302),U_5303)),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_5301),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5301),hAPP(hAPP(c_Power_Opower__class_Opower(U_5301),U_5302),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_5301),U_5303),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_5301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5301),hAPP(c_Int_Onumber__class_Onumber__of(U_5301),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5302)),U_5303))
      | ~ class_Int_Onumber__ring(U_5301) ),
    inference(variable_rename,[status(thm)],[f_1566_1]) ).

fof(f_1566_3,plain,
    ! [U_5303,U_5301,U_5302] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5301),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5301),U_5302),U_5303)),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_5301),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5301),hAPP(hAPP(c_Power_Opower__class_Opower(U_5301),U_5302),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_5301),U_5303),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_5301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5301),hAPP(c_Int_Onumber__class_Onumber__of(U_5301),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5302)),U_5303))
      | ~ class_Int_Onumber__ring(U_5301) ),
    inference(definitional_conversion,[status(esa)],[f_1566_2]) ).

cnf(f_1566_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5301),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5301),U_5302),U_5303)),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_5301),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5301),hAPP(hAPP(c_Power_Opower__class_Opower(U_5301),U_5302),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_5301),U_5303),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_5301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5301),hAPP(c_Int_Onumber__class_Onumber__of(U_5301),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5302)),U_5303))
    | ~ class_Int_Onumber__ring(U_5301) ),
    inference(clausify,[status(thm)],[f_1566_3]) ).

fof(f_1567_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_1567_2,plain,
    ! [U_5306,U_5305,U_5304] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5304),c_Groups_Ozero__class_Ozero(U_5304)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5304),U_5305),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_5306))))
      | ~ class_Rings_Olinordered__idom(U_5304) ),
    inference(variable_rename,[status(thm)],[f_1567_1]) ).

fof(f_1567_3,plain,
    ! [U_5305,U_5306,U_5304] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5304),c_Groups_Ozero__class_Ozero(U_5304)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5304),U_5305),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_5306))))
      | ~ class_Rings_Olinordered__idom(U_5304) ),
    inference(definitional_conversion,[status(esa)],[f_1567_2]) ).

cnf(f_1567_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5304),c_Groups_Ozero__class_Ozero(U_5304)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5304),U_5305),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_5306))))
    | ~ class_Rings_Olinordered__idom(U_5304) ),
    inference(clausify,[status(thm)],[f_1567_3]) ).

fof(f_1568_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_1568_2,plain,
    ! [U_5309,U_5308,U_5307] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5307),U_5308),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_5309))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5307),U_5308),hAPP(hAPP(c_Power_Opower__class_Opower(U_5307),hAPP(hAPP(c_Power_Opower__class_Opower(U_5307),U_5308),U_5309)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | ~ class_Groups_Omonoid__mult(U_5307) ),
    inference(variable_rename,[status(thm)],[f_1568_1]) ).

fof(f_1568_3,plain,
    ! [U_5307,U_5308,U_5309] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5307),U_5308),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_5309))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5307),U_5308),hAPP(hAPP(c_Power_Opower__class_Opower(U_5307),hAPP(hAPP(c_Power_Opower__class_Opower(U_5307),U_5308),U_5309)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | ~ class_Groups_Omonoid__mult(U_5307) ),
    inference(definitional_conversion,[status(esa)],[f_1568_2]) ).

cnf(f_1568_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5307),U_5308),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_5309))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5307),U_5308),hAPP(hAPP(c_Power_Opower__class_Opower(U_5307),hAPP(hAPP(c_Power_Opower__class_Opower(U_5307),U_5308),U_5309)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Groups_Omonoid__mult(U_5307) ),
    inference(clausify,[status(thm)],[f_1568_3]) ).

fof(f_1569_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_1569_2,plain,
    ! [U_5312,U_5311,U_5310] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5310),U_5311),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_5312))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5310),U_5311),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5310),hAPP(hAPP(c_Power_Opower__class_Opower(U_5310),U_5311),U_5312)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5310),U_5311),U_5312)))
      | ~ class_Rings_Ocomm__semiring__1(U_5310) ),
    inference(variable_rename,[status(thm)],[f_1569_1]) ).

fof(f_1569_3,plain,
    ! [U_5310,U_5311,U_5312] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5310),U_5311),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_5312))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5310),U_5311),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5310),hAPP(hAPP(c_Power_Opower__class_Opower(U_5310),U_5311),U_5312)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5310),U_5311),U_5312)))
      | ~ class_Rings_Ocomm__semiring__1(U_5310) ),
    inference(definitional_conversion,[status(esa)],[f_1569_2]) ).

cnf(f_1569_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5310),U_5311),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_5312))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5310),U_5311),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5310),hAPP(hAPP(c_Power_Opower__class_Opower(U_5310),U_5311),U_5312)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5310),U_5311),U_5312)))
    | ~ class_Rings_Ocomm__semiring__1(U_5310) ),
    inference(clausify,[status(thm)],[f_1569_3]) ).

fof(f_1570_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_1570_2,plain,
    ! [U_5314,U_5313] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5313),hAPP(c_Groups_Ouminus__class_Ouminus(U_5313),c_Groups_Oone__class_Oone(U_5313))),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_5314)) = c_Groups_Oone__class_Oone(U_5313)
      | ~ class_Rings_Oring__1(U_5313) ),
    inference(variable_rename,[status(thm)],[f_1570_1]) ).

fof(f_1570_3,plain,
    ! [U_5313,U_5314] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5313),hAPP(c_Groups_Ouminus__class_Ouminus(U_5313),c_Groups_Oone__class_Oone(U_5313))),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_5314)) = c_Groups_Oone__class_Oone(U_5313)
      | ~ class_Rings_Oring__1(U_5313) ),
    inference(definitional_conversion,[status(esa)],[f_1570_2]) ).

cnf(f_1570_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5313),hAPP(c_Groups_Ouminus__class_Ouminus(U_5313),c_Groups_Oone__class_Oone(U_5313))),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_5314)) = c_Groups_Oone__class_Oone(U_5313)
    | ~ class_Rings_Oring__1(U_5313) ),
    inference(clausify,[status(thm)],[f_1570_3]) ).

fof(f_1571_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_1571_2,plain,
    ! [U_5316,U_5315] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5316))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5315))) = 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_5316)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5315))
        | 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_5315))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5316))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5315))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5316)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5315))
        | ~ 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_5315))) ) ),
    inference(variable_rename,[status(thm)],[f_1571_1]) ).

fof(f_1571_3,plain,
    ( ! [U_5320,U_5318] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5320))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5318))) = 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_5320)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5318))
        | 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_5318))) )
    & ! [U_5319,U_5317] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5319))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5317))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5319)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5317))
        | ~ 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_5317))) ) ),
    inference(miniscope,[status(thm)],[f_1571_2]) ).

fof(f_1571_4,plain,
    ( ! [U_5318,U_5320] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5320))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5318))) = 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_5320)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5318))
        | 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_5318))) )
    & ! [U_5319,U_5317] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5319))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5317))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5319)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5317))
        | ~ 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_5317))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1571_3]) ).

cnf(f_1571_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_5319))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5317))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5319)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5317))
    | ~ 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_5317))) ),
    inference(clausify,[status(thm)],[f_1571_4]) ).

cnf(f_1571_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_5320))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5318))) = 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_5320)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5318))
    | 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_5318))) ),
    inference(clausify,[status(thm)],[f_1571_4]) ).

fof(f_1572_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_1572_2,plain,
    ! [U_5321] :
      ( ( 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_5321,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_5321,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_5321,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_5321,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_1572_1]) ).

fof(f_1572_3,plain,
    ( ! [U_5323] :
        ( 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_5323,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_5323,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_5322] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5322,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_5322,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    inference(miniscope,[status(thm)],[f_1572_2]) ).

fof(f_1572_4,plain,
    ( ! [U_5323] :
        ( 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_5323,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_5323,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_5322] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5322,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_5322,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_1572_3]) ).

cnf(f_1572_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5322,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_5322,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(clausify,[status(thm)],[f_1572_4]) ).

cnf(f_1572_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_5323,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_5323,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_1572_4]) ).

fof(f_1573_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_1573_2,plain,
    ! [U_5324] :
      ( 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_5324),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_5324)) ),
    inference(variable_rename,[status(thm)],[f_1573_1]) ).

fof(f_1573_3,plain,
    ! [U_5324] :
      ( 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_5324),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_5324)) ),
    inference(definitional_conversion,[status(esa)],[f_1573_2]) ).

cnf(f_1573_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_5324),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_5324)) ),
    inference(clausify,[status(thm)],[f_1573_3]) ).

fof(f_1574_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_1574_2,plain,
    ! [U_5327,U_5326,U_5325] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5325),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5325),U_5326),U_5327)),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_5325),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5325),hAPP(hAPP(c_Power_Opower__class_Opower(U_5325),U_5326),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_5325),U_5327),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_5325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5325),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5326)),U_5327))
      | ~ class_Int_Onumber__ring(U_5325) ),
    inference(variable_rename,[status(thm)],[f_1574_1]) ).

fof(f_1574_3,plain,
    ! [U_5325,U_5326,U_5327] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5325),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5325),U_5326),U_5327)),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_5325),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5325),hAPP(hAPP(c_Power_Opower__class_Opower(U_5325),U_5326),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_5325),U_5327),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_5325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5325),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5326)),U_5327))
      | ~ class_Int_Onumber__ring(U_5325) ),
    inference(definitional_conversion,[status(esa)],[f_1574_2]) ).

cnf(f_1574_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5325),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5325),U_5326),U_5327)),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_5325),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5325),hAPP(hAPP(c_Power_Opower__class_Opower(U_5325),U_5326),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_5325),U_5327),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_5325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5325),hAPP(c_Int_Onumber__class_Onumber__of(U_5325),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5326)),U_5327))
    | ~ class_Int_Onumber__ring(U_5325) ),
    inference(clausify,[status(thm)],[f_1574_3]) ).

fof(f_1575_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_1575_2,plain,
    ! [U_5330,U_5329,U_5328] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),c_Groups_Ozero__class_Ozero(U_5328)),U_5329))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),c_Groups_Ozero__class_Ozero(U_5328)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5328),U_5329),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_5330)))))
      | ~ class_Rings_Olinordered__idom(U_5328) ),
    inference(variable_rename,[status(thm)],[f_1575_1]) ).

fof(f_1575_3,plain,
    ! [U_5328,U_5329,U_5330] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),c_Groups_Ozero__class_Ozero(U_5328)),U_5329))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),c_Groups_Ozero__class_Ozero(U_5328)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5328),U_5329),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_5330)))))
      | ~ class_Rings_Olinordered__idom(U_5328) ),
    inference(definitional_conversion,[status(esa)],[f_1575_2]) ).

cnf(f_1575_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),c_Groups_Ozero__class_Ozero(U_5328)),U_5329))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),c_Groups_Ozero__class_Ozero(U_5328)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5328),U_5329),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_5330)))))
    | ~ class_Rings_Olinordered__idom(U_5328) ),
    inference(clausify,[status(thm)],[f_1575_3]) ).

fof(f_1576_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_1576_2,plain,
    ! [U_5333,U_5332,U_5331] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5331),hAPP(hAPP(c_Power_Opower__class_Opower(U_5331),U_5332),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_5333)))),c_Groups_Ozero__class_Ozero(U_5331)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5331),U_5332),c_Groups_Ozero__class_Ozero(U_5331)))
      | ~ class_Rings_Olinordered__idom(U_5331) ),
    inference(variable_rename,[status(thm)],[f_1576_1]) ).

fof(f_1576_3,plain,
    ! [U_5331,U_5332,U_5333] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5331),hAPP(hAPP(c_Power_Opower__class_Opower(U_5331),U_5332),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_5333)))),c_Groups_Ozero__class_Ozero(U_5331)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5331),U_5332),c_Groups_Ozero__class_Ozero(U_5331)))
      | ~ class_Rings_Olinordered__idom(U_5331) ),
    inference(definitional_conversion,[status(esa)],[f_1576_2]) ).

cnf(f_1576_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5331),hAPP(hAPP(c_Power_Opower__class_Opower(U_5331),U_5332),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_5333)))),c_Groups_Ozero__class_Ozero(U_5331)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5331),U_5332),c_Groups_Ozero__class_Ozero(U_5331)))
    | ~ class_Rings_Olinordered__idom(U_5331) ),
    inference(clausify,[status(thm)],[f_1576_3]) ).

fof(f_1577_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_1577_2,plain,
    ! [U_5335,U_5334] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5334),hAPP(c_Groups_Ouminus__class_Ouminus(U_5334),c_Groups_Oone__class_Oone(U_5334))),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_5335))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5334),c_Groups_Oone__class_Oone(U_5334))
      | ~ class_Rings_Oring__1(U_5334) ),
    inference(variable_rename,[status(thm)],[f_1577_1]) ).

fof(f_1577_3,plain,
    ! [U_5334,U_5335] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5334),hAPP(c_Groups_Ouminus__class_Ouminus(U_5334),c_Groups_Oone__class_Oone(U_5334))),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_5335))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5334),c_Groups_Oone__class_Oone(U_5334))
      | ~ class_Rings_Oring__1(U_5334) ),
    inference(definitional_conversion,[status(esa)],[f_1577_2]) ).

cnf(f_1577_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5334),hAPP(c_Groups_Ouminus__class_Ouminus(U_5334),c_Groups_Oone__class_Oone(U_5334))),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_5335))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5334),c_Groups_Oone__class_Oone(U_5334))
    | ~ class_Rings_Oring__1(U_5334) ),
    inference(clausify,[status(thm)],[f_1577_3]) ).

fof(f_1578_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_1578_2,plain,
    ! [U_5337,U_5336] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5336),hAPP(c_Int_Onumber__class_Onumber__of(U_5336),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_5337)) = c_Groups_Oone__class_Oone(U_5336)
      | ~ class_Int_Onumber__ring(U_5336) ),
    inference(variable_rename,[status(thm)],[f_1578_1]) ).

fof(f_1578_3,plain,
    ! [U_5336,U_5337] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5336),hAPP(c_Int_Onumber__class_Onumber__of(U_5336),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_5337)) = c_Groups_Oone__class_Oone(U_5336)
      | ~ class_Int_Onumber__ring(U_5336) ),
    inference(definitional_conversion,[status(esa)],[f_1578_2]) ).

cnf(f_1578_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5336),hAPP(c_Int_Onumber__class_Onumber__of(U_5336),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_5337)) = c_Groups_Oone__class_Oone(U_5336)
    | ~ class_Int_Onumber__ring(U_5336) ),
    inference(clausify,[status(thm)],[f_1578_3]) ).

fof(f_1579_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_1579_2,plain,
    ! [U_5339,U_5338] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5338),hAPP(c_Int_Onumber__class_Onumber__of(U_5338),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_5339))) = hAPP(c_Int_Onumber__class_Onumber__of(U_5338),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_5338) ),
    inference(variable_rename,[status(thm)],[f_1579_1]) ).

fof(f_1579_3,plain,
    ! [U_5338,U_5339] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5338),hAPP(c_Int_Onumber__class_Onumber__of(U_5338),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_5339))) = hAPP(c_Int_Onumber__class_Onumber__of(U_5338),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_5338) ),
    inference(definitional_conversion,[status(esa)],[f_1579_2]) ).

cnf(f_1579_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5338),hAPP(c_Int_Onumber__class_Onumber__of(U_5338),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_5339))) = hAPP(c_Int_Onumber__class_Onumber__of(U_5338),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_5338) ),
    inference(clausify,[status(thm)],[f_1579_3]) ).

fof(f_1580_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_1580_2,plain,
    ! [U_5340] :
      ( 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_5340),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_5340)) ),
    inference(variable_rename,[status(thm)],[f_1580_1]) ).

fof(f_1580_3,plain,
    ! [U_5340] :
      ( 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_5340),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_5340)) ),
    inference(definitional_conversion,[status(esa)],[f_1580_2]) ).

cnf(f_1580_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_5340),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_5340)) ),
    inference(clausify,[status(thm)],[f_1580_3]) ).

fof(f_1581_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_1581_2,plain,
    ! [U_5341] :
      ( ( ( ( hAPP(c_Code__Numeral_Oint__of,U_5341) = 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_5341),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_5341,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_5341) = 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_5341),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_5341,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_5341 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Code__Numeral_Oint__of,U_5341) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_5341 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_1581_1]) ).

fof(f_1581_3,plain,
    ( ! [U_5343] :
        ( ( ( hAPP(c_Code__Numeral_Oint__of,U_5343) = 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_5343),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_5343,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_5343) = 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_5343),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_5343,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_5343 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_5342] :
        ( hAPP(c_Code__Numeral_Oint__of,U_5342) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_5342 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_1581_2]) ).

fof(f_1581_4,plain,
    ( ! [U_5343] :
        ( hAPP(c_Code__Numeral_Oint__of,U_5343) = 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_5343),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_5343,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)
        | ~ sP408(U_5343) )
    & ! [U_5343] :
        ( hAPP(c_Code__Numeral_Oint__of,U_5343) = 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_5343),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_5343,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)
        | ~ sP408(U_5343) )
    & ! [U_5343] :
        ( sP408(U_5343)
        | U_5343 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_5342] :
        ( hAPP(c_Code__Numeral_Oint__of,U_5342) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_5342 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP408])],[f_1581_3]) ).

cnf(f_1581_5,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_5342) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_5342 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1581_4]) ).

cnf(f_1581_6,plain,
    ( sP408(U_5343)
    | U_5343 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1581_4]) ).

cnf(f_1581_7,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_5343) = 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_5343),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_5343,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)
    | ~ sP408(U_5343) ),
    inference(clausify,[status(thm)],[f_1581_4]) ).

cnf(f_1581_8,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_5343) = 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_5343),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_5343,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)
    | ~ sP408(U_5343) ),
    inference(clausify,[status(thm)],[f_1581_4]) ).

fof(f_1582_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_1582_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_1582_1]) ).

cnf(f_1582_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_1582_2]) ).

fof(f_1583_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_1583_2,plain,
    ! [U_5345,U_5344] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),c_Groups_Ozero__class_Ozero(U_5344)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5344),U_5345),hAPP(c_Int_Onumber__class_Onumber__of(U_5344),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),c_Groups_Ozero__class_Ozero(U_5344)),U_5345)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),c_Groups_Ozero__class_Ozero(U_5344)),U_5345))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),c_Groups_Ozero__class_Ozero(U_5344)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5344),U_5345),hAPP(c_Int_Onumber__class_Onumber__of(U_5344),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Int_Onumber__ring(U_5344)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5344) ),
    inference(variable_rename,[status(thm)],[f_1583_1]) ).

fof(f_1583_3,plain,
    ( ! [U_5345,U_5344] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),c_Groups_Ozero__class_Ozero(U_5344)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5344),U_5345),hAPP(c_Int_Onumber__class_Onumber__of(U_5344),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),c_Groups_Ozero__class_Ozero(U_5344)),U_5345))
        | ~ sP409(U_5345,U_5344) )
    & ! [U_5345,U_5344] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),c_Groups_Ozero__class_Ozero(U_5344)),U_5345))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),c_Groups_Ozero__class_Ozero(U_5344)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5344),U_5345),hAPP(c_Int_Onumber__class_Onumber__of(U_5344),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ sP409(U_5345,U_5344) )
    & ! [U_5345,U_5344] :
        ( sP409(U_5345,U_5344)
        | ~ class_Int_Onumber__ring(U_5344)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5344) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP409])],[f_1583_2]) ).

cnf(f_1583_4,plain,
    ( sP409(U_5345,U_5344)
    | ~ class_Int_Onumber__ring(U_5344)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5344) ),
    inference(clausify,[status(thm)],[f_1583_3]) ).

cnf(f_1583_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),c_Groups_Ozero__class_Ozero(U_5344)),U_5345))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),c_Groups_Ozero__class_Ozero(U_5344)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5344),U_5345),hAPP(c_Int_Onumber__class_Onumber__of(U_5344),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ sP409(U_5345,U_5344) ),
    inference(clausify,[status(thm)],[f_1583_3]) ).

cnf(f_1583_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),c_Groups_Ozero__class_Ozero(U_5344)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5344),U_5345),hAPP(c_Int_Onumber__class_Onumber__of(U_5344),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),c_Groups_Ozero__class_Ozero(U_5344)),U_5345))
    | ~ sP409(U_5345,U_5344) ),
    inference(clausify,[status(thm)],[f_1583_3]) ).

fof(f_1584_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_1584_2,plain,
    ! [U_5347,U_5346] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5346),c_Groups_Ozero__class_Ozero(U_5346)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5346),U_5347),hAPP(c_Int_Onumber__class_Onumber__of(U_5346),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5346),c_Groups_Ozero__class_Ozero(U_5346)),U_5347))
      | ~ class_Int_Onumber__ring(U_5346)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5346) ),
    inference(variable_rename,[status(thm)],[f_1584_1]) ).

fof(f_1584_3,plain,
    ! [U_5346,U_5347] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5346),c_Groups_Ozero__class_Ozero(U_5346)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5346),U_5347),hAPP(c_Int_Onumber__class_Onumber__of(U_5346),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5346),c_Groups_Ozero__class_Ozero(U_5346)),U_5347))
      | ~ class_Int_Onumber__ring(U_5346)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5346) ),
    inference(definitional_conversion,[status(esa)],[f_1584_2]) ).

cnf(f_1584_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5346),c_Groups_Ozero__class_Ozero(U_5346)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5346),U_5347),hAPP(c_Int_Onumber__class_Onumber__of(U_5346),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5346),c_Groups_Ozero__class_Ozero(U_5346)),U_5347))
    | ~ class_Int_Onumber__ring(U_5346)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5346) ),
    inference(clausify,[status(thm)],[f_1584_3]) ).

fof(f_1585_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_1585_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_1585_1]) ).

cnf(f_1585_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_1585_2]) ).

fof(f_1586_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_1586_2,plain,
    ! [U_5353,U_5352,U_5351,U_5350] :
      ( ? [U_5349] :
          ( hAPP(U_5352,U_5349) = U_5353
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5349),U_5351))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5350),U_5349)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5353),hAPP(U_5352,U_5351)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5352,U_5350)),U_5353))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5350),U_5351))
      | ? [U_5348] :
          ( ~ 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_5352,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5348),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5352,U_5348)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5348),U_5351))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5350),U_5348)) ) ),
    inference(variable_rename,[status(thm)],[f_1586_1]) ).

fof(f_1586_3,plain,
    ! [U_5353,U_5352,U_5351,U_5350] :
      ( ? [U_5349] :
          ( hAPP(U_5352,U_5349) = U_5353
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5349),U_5351))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5350),U_5349)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5353),hAPP(U_5352,U_5351)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5352,U_5350)),U_5353))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5350),U_5351))
      | ( ~ 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_5352,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK93(U_5353,U_5352,U_5351,U_5350)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5352,sK93(U_5353,U_5352,U_5351,U_5350))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK93(U_5353,U_5352,U_5351,U_5350)),U_5351))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5350),sK93(U_5353,U_5352,U_5351,U_5350))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_5348,sK93(U_5353,U_5352,U_5351,U_5350))],[f_1586_2]) ).

fof(f_1586_4,plain,
    ! [U_5353,U_5352,U_5351,U_5350] :
      ( ( hAPP(U_5352,sK94(U_5353,U_5352,U_5351,U_5350)) = U_5353
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK94(U_5353,U_5352,U_5351,U_5350)),U_5351))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5350),sK94(U_5353,U_5352,U_5351,U_5350))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5353),hAPP(U_5352,U_5351)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5352,U_5350)),U_5353))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5350),U_5351))
      | ( ~ 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_5352,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK93(U_5353,U_5352,U_5351,U_5350)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5352,sK93(U_5353,U_5352,U_5351,U_5350))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK93(U_5353,U_5352,U_5351,U_5350)),U_5351))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5350),sK93(U_5353,U_5352,U_5351,U_5350))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_5349,sK94(U_5353,U_5352,U_5351,U_5350))],[f_1586_3]) ).

fof(f_1586_5,plain,
    ( ! [U_5350,U_5351,U_5352,U_5353] :
        ( hAPP(U_5352,sK94(U_5353,U_5352,U_5351,U_5350)) = U_5353
        | ~ sP411(U_5350,U_5351,U_5352,U_5353) )
    & ! [U_5350,U_5351,U_5352,U_5353] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK94(U_5353,U_5352,U_5351,U_5350)),U_5351))
        | ~ sP411(U_5350,U_5351,U_5352,U_5353) )
    & ! [U_5350,U_5351,U_5352,U_5353] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5350),sK94(U_5353,U_5352,U_5351,U_5350)))
        | ~ sP411(U_5350,U_5351,U_5352,U_5353) )
    & ! [U_5350,U_5351,U_5352,U_5353] :
        ( ~ 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_5352,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK93(U_5353,U_5352,U_5351,U_5350)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5352,sK93(U_5353,U_5352,U_5351,U_5350))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ sP410(U_5350,U_5351,U_5352,U_5353) )
    & ! [U_5350,U_5351,U_5352,U_5353] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK93(U_5353,U_5352,U_5351,U_5350)),U_5351))
        | ~ sP410(U_5350,U_5351,U_5352,U_5353) )
    & ! [U_5350,U_5351,U_5352,U_5353] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5350),sK93(U_5353,U_5352,U_5351,U_5350)))
        | ~ sP410(U_5350,U_5351,U_5352,U_5353) )
    & ! [U_5350,U_5351,U_5352,U_5353] :
        ( sP411(U_5350,U_5351,U_5352,U_5353)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5353),hAPP(U_5352,U_5351)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5352,U_5350)),U_5353))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5350),U_5351))
        | sP410(U_5350,U_5351,U_5352,U_5353) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP410,sP411])],[f_1586_4]) ).

cnf(f_1586_6,plain,
    ( sP411(U_5350,U_5351,U_5352,U_5353)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5353),hAPP(U_5352,U_5351)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_5352,U_5350)),U_5353))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5350),U_5351))
    | sP410(U_5350,U_5351,U_5352,U_5353) ),
    inference(clausify,[status(thm)],[f_1586_5]) ).

cnf(f_1586_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5350),sK93(U_5353,U_5352,U_5351,U_5350)))
    | ~ sP410(U_5350,U_5351,U_5352,U_5353) ),
    inference(clausify,[status(thm)],[f_1586_5]) ).

cnf(f_1586_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK93(U_5353,U_5352,U_5351,U_5350)),U_5351))
    | ~ sP410(U_5350,U_5351,U_5352,U_5353) ),
    inference(clausify,[status(thm)],[f_1586_5]) ).

cnf(f_1586_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_5352,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK93(U_5353,U_5352,U_5351,U_5350)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_5352,sK93(U_5353,U_5352,U_5351,U_5350))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ sP410(U_5350,U_5351,U_5352,U_5353) ),
    inference(clausify,[status(thm)],[f_1586_5]) ).

cnf(f_1586_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5350),sK94(U_5353,U_5352,U_5351,U_5350)))
    | ~ sP411(U_5350,U_5351,U_5352,U_5353) ),
    inference(clausify,[status(thm)],[f_1586_5]) ).

cnf(f_1586_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK94(U_5353,U_5352,U_5351,U_5350)),U_5351))
    | ~ sP411(U_5350,U_5351,U_5352,U_5353) ),
    inference(clausify,[status(thm)],[f_1586_5]) ).

cnf(f_1586_12,plain,
    ( hAPP(U_5352,sK94(U_5353,U_5352,U_5351,U_5350)) = U_5353
    | ~ sP411(U_5350,U_5351,U_5352,U_5353) ),
    inference(clausify,[status(thm)],[f_1586_5]) ).

fof(f_1587_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_1587_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_1587_1]) ).

cnf(f_1587_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_1587_2]) ).

fof(f_1588_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_1588_2,plain,
    ! [U_5355,U_5354] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5354),U_5355),c_Groups_Ozero__class_Ozero(U_5354)) = c_Groups_Ozero__class_Ozero(U_5354)
      | ~ class_Rings_Odivision__ring__inverse__zero(U_5354) ),
    inference(variable_rename,[status(thm)],[f_1588_1]) ).

fof(f_1588_3,plain,
    ! [U_5354,U_5355] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5354),U_5355),c_Groups_Ozero__class_Ozero(U_5354)) = c_Groups_Ozero__class_Ozero(U_5354)
      | ~ class_Rings_Odivision__ring__inverse__zero(U_5354) ),
    inference(definitional_conversion,[status(esa)],[f_1588_2]) ).

cnf(f_1588_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5354),U_5355),c_Groups_Ozero__class_Ozero(U_5354)) = c_Groups_Ozero__class_Ozero(U_5354)
    | ~ class_Rings_Odivision__ring__inverse__zero(U_5354) ),
    inference(clausify,[status(thm)],[f_1588_3]) ).

fof(f_1589_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_1589_2,plain,
    ! [U_5357,U_5356] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5356),c_Groups_Ozero__class_Ozero(U_5356)),U_5357) = c_Groups_Ozero__class_Ozero(U_5356)
      | ~ class_Rings_Odivision__ring(U_5356) ),
    inference(variable_rename,[status(thm)],[f_1589_1]) ).

fof(f_1589_3,plain,
    ! [U_5357,U_5356] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5356),c_Groups_Ozero__class_Ozero(U_5356)),U_5357) = c_Groups_Ozero__class_Ozero(U_5356)
      | ~ class_Rings_Odivision__ring(U_5356) ),
    inference(definitional_conversion,[status(esa)],[f_1589_2]) ).

cnf(f_1589_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5356),c_Groups_Ozero__class_Ozero(U_5356)),U_5357) = c_Groups_Ozero__class_Ozero(U_5356)
    | ~ class_Rings_Odivision__ring(U_5356) ),
    inference(clausify,[status(thm)],[f_1589_3]) ).

fof(f_1590_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_1590_2,plain,
    ! [U_5361,U_5360,U_5359,U_5358] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5358),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5358),U_5359),U_5360)),U_5361) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5358),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5358),U_5359),U_5361)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5358),U_5360),U_5361))
      | ~ class_Rings_Odivision__ring(U_5358) ),
    inference(variable_rename,[status(thm)],[f_1590_1]) ).

fof(f_1590_3,plain,
    ! [U_5358,U_5359,U_5360,U_5361] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5358),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5358),U_5359),U_5360)),U_5361) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5358),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5358),U_5359),U_5361)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5358),U_5360),U_5361))
      | ~ class_Rings_Odivision__ring(U_5358) ),
    inference(definitional_conversion,[status(esa)],[f_1590_2]) ).

cnf(f_1590_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5358),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5358),U_5359),U_5360)),U_5361) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5358),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5358),U_5359),U_5361)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5358),U_5360),U_5361))
    | ~ class_Rings_Odivision__ring(U_5358) ),
    inference(clausify,[status(thm)],[f_1590_3]) ).

fof(f_1591_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_1591_2,plain,
    ! [U_5366,U_5365,U_5364,U_5363,U_5362] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5362),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5362),U_5363),U_5364)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5362),U_5365),U_5366)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5362),U_5363),U_5365)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5362),U_5364),U_5366))
      | ~ class_Fields_Ofield__inverse__zero(U_5362) ),
    inference(variable_rename,[status(thm)],[f_1591_1]) ).

fof(f_1591_3,plain,
    ! [U_5362,U_5363,U_5364,U_5365,U_5366] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5362),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5362),U_5363),U_5364)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5362),U_5365),U_5366)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5362),U_5363),U_5365)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5362),U_5364),U_5366))
      | ~ class_Fields_Ofield__inverse__zero(U_5362) ),
    inference(definitional_conversion,[status(esa)],[f_1591_2]) ).

cnf(f_1591_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5362),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5362),U_5363),U_5364)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5362),U_5365),U_5366)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5362),U_5363),U_5365)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5362),U_5364),U_5366))
    | ~ class_Fields_Ofield__inverse__zero(U_5362) ),
    inference(clausify,[status(thm)],[f_1591_3]) ).

fof(f_1592_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_1592_2,plain,
    ! [U_5370,U_5369,U_5368,U_5367] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5367),U_5368),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5367),U_5369),U_5370)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5367),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5367),U_5368),U_5369)),U_5370)
      | ~ class_Rings_Odivision__ring(U_5367) ),
    inference(variable_rename,[status(thm)],[f_1592_1]) ).

fof(f_1592_3,plain,
    ! [U_5367,U_5368,U_5369,U_5370] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5367),U_5368),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5367),U_5369),U_5370)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5367),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5367),U_5368),U_5369)),U_5370)
      | ~ class_Rings_Odivision__ring(U_5367) ),
    inference(definitional_conversion,[status(esa)],[f_1592_2]) ).

cnf(f_1592_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5367),U_5368),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5367),U_5369),U_5370)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5367),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5367),U_5368),U_5369)),U_5370)
    | ~ class_Rings_Odivision__ring(U_5367) ),
    inference(clausify,[status(thm)],[f_1592_3]) ).

fof(f_1593_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_1593_2,plain,
    ! [U_5374,U_5373,U_5372,U_5371] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5371),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5371),U_5372),U_5373)),U_5374) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5371),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5371),U_5372),U_5374)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5371),U_5373),U_5374))
      | ~ class_Rings_Odivision__ring(U_5371) ),
    inference(variable_rename,[status(thm)],[f_1593_1]) ).

fof(f_1593_3,plain,
    ! [U_5371,U_5372,U_5373,U_5374] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5371),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5371),U_5372),U_5373)),U_5374) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5371),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5371),U_5372),U_5374)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5371),U_5373),U_5374))
      | ~ class_Rings_Odivision__ring(U_5371) ),
    inference(definitional_conversion,[status(esa)],[f_1593_2]) ).

cnf(f_1593_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5371),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5371),U_5372),U_5373)),U_5374) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5371),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5371),U_5372),U_5374)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5371),U_5373),U_5374))
    | ~ class_Rings_Odivision__ring(U_5371) ),
    inference(clausify,[status(thm)],[f_1593_3]) ).

fof(f_1594_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_1594_2,plain,
    ! [U_5376,U_5375] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5375),U_5376),c_Groups_Oone__class_Oone(U_5375)) = U_5376
      | ~ class_Rings_Odivision__ring(U_5375) ),
    inference(variable_rename,[status(thm)],[f_1594_1]) ).

fof(f_1594_3,plain,
    ! [U_5376,U_5375] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5375),U_5376),c_Groups_Oone__class_Oone(U_5375)) = U_5376
      | ~ class_Rings_Odivision__ring(U_5375) ),
    inference(definitional_conversion,[status(esa)],[f_1594_2]) ).

cnf(f_1594_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5375),U_5376),c_Groups_Oone__class_Oone(U_5375)) = U_5376
    | ~ class_Rings_Odivision__ring(U_5375) ),
    inference(clausify,[status(thm)],[f_1594_3]) ).

fof(f_1595_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_1595_2,plain,
    ! [U_5379,U_5378,U_5377] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5377),hAPP(c_Groups_Ouminus__class_Ouminus(U_5377),U_5378)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5377),U_5379)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5377),U_5378),U_5379)
      | ~ class_Fields_Ofield__inverse__zero(U_5377) ),
    inference(variable_rename,[status(thm)],[f_1595_1]) ).

fof(f_1595_3,plain,
    ! [U_5377,U_5378,U_5379] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5377),hAPP(c_Groups_Ouminus__class_Ouminus(U_5377),U_5378)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5377),U_5379)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5377),U_5378),U_5379)
      | ~ class_Fields_Ofield__inverse__zero(U_5377) ),
    inference(definitional_conversion,[status(esa)],[f_1595_2]) ).

cnf(f_1595_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5377),hAPP(c_Groups_Ouminus__class_Ouminus(U_5377),U_5378)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5377),U_5379)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5377),U_5378),U_5379)
    | ~ class_Fields_Ofield__inverse__zero(U_5377) ),
    inference(clausify,[status(thm)],[f_1595_3]) ).

fof(f_1596_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_1596_2,plain,
    ! [U_5382,U_5381,U_5380] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5380),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5380),U_5381),U_5382)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5380),U_5381),hAPP(c_Groups_Ouminus__class_Ouminus(U_5380),U_5382))
      | ~ class_Fields_Ofield__inverse__zero(U_5380) ),
    inference(variable_rename,[status(thm)],[f_1596_1]) ).

fof(f_1596_3,plain,
    ! [U_5380,U_5381,U_5382] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5380),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5380),U_5381),U_5382)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5380),U_5381),hAPP(c_Groups_Ouminus__class_Ouminus(U_5380),U_5382))
      | ~ class_Fields_Ofield__inverse__zero(U_5380) ),
    inference(definitional_conversion,[status(esa)],[f_1596_2]) ).

cnf(f_1596_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5380),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5380),U_5381),U_5382)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5380),U_5381),hAPP(c_Groups_Ouminus__class_Ouminus(U_5380),U_5382))
    | ~ class_Fields_Ofield__inverse__zero(U_5380) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

fof(f_1597_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_1597_2,plain,
    ! [U_5385,U_5384,U_5383] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5383),U_5384),U_5385)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5383),hAPP(c_Groups_Ouminus__class_Ouminus(U_5383),U_5384)),U_5385)
      | ~ class_Rings_Odivision__ring(U_5383) ),
    inference(variable_rename,[status(thm)],[f_1597_1]) ).

fof(f_1597_3,plain,
    ! [U_5383,U_5384,U_5385] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5383),U_5384),U_5385)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5383),hAPP(c_Groups_Ouminus__class_Ouminus(U_5383),U_5384)),U_5385)
      | ~ class_Rings_Odivision__ring(U_5383) ),
    inference(definitional_conversion,[status(esa)],[f_1597_2]) ).

cnf(f_1597_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5383),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5383),U_5384),U_5385)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5383),hAPP(c_Groups_Ouminus__class_Ouminus(U_5383),U_5384)),U_5385)
    | ~ class_Rings_Odivision__ring(U_5383) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

fof(f_1598_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_1598_2,plain,
    ! [U_5389,U_5388,U_5387,U_5386] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5386),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5386),U_5387),U_5388)),U_5389) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5386),hAPP(hAPP(c_Power_Opower__class_Opower(U_5386),U_5387),U_5389)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5386),U_5388),U_5389))
      | ~ class_Fields_Ofield__inverse__zero(U_5386) ),
    inference(variable_rename,[status(thm)],[f_1598_1]) ).

fof(f_1598_3,plain,
    ! [U_5386,U_5387,U_5388,U_5389] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5386),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5386),U_5387),U_5388)),U_5389) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5386),hAPP(hAPP(c_Power_Opower__class_Opower(U_5386),U_5387),U_5389)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5386),U_5388),U_5389))
      | ~ class_Fields_Ofield__inverse__zero(U_5386) ),
    inference(definitional_conversion,[status(esa)],[f_1598_2]) ).

cnf(f_1598_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5386),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5386),U_5387),U_5388)),U_5389) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5386),hAPP(hAPP(c_Power_Opower__class_Opower(U_5386),U_5387),U_5389)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5386),U_5388),U_5389))
    | ~ class_Fields_Ofield__inverse__zero(U_5386) ),
    inference(clausify,[status(thm)],[f_1598_3]) ).

fof(f_1599_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_1599_2,plain,
    ! [U_5392,U_5391,U_5390] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5390),U_5391),U_5392)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5390),hAPP(c_Groups_Oabs__class_Oabs(U_5390),U_5391)),hAPP(c_Groups_Oabs__class_Oabs(U_5390),U_5392))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5390) ),
    inference(variable_rename,[status(thm)],[f_1599_1]) ).

fof(f_1599_3,plain,
    ! [U_5390,U_5391,U_5392] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5390),U_5391),U_5392)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5390),hAPP(c_Groups_Oabs__class_Oabs(U_5390),U_5391)),hAPP(c_Groups_Oabs__class_Oabs(U_5390),U_5392))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5390) ),
    inference(definitional_conversion,[status(esa)],[f_1599_2]) ).

cnf(f_1599_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5390),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5390),U_5391),U_5392)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5390),hAPP(c_Groups_Oabs__class_Oabs(U_5390),U_5391)),hAPP(c_Groups_Oabs__class_Oabs(U_5390),U_5392))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5390) ),
    inference(clausify,[status(thm)],[f_1599_3]) ).

fof(f_1600_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_1600_2,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_1600_1]) ).

cnf(f_1600_3,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1600_2]) ).

fof(f_1601_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_1601_2,plain,
    ! [U_5394,U_5393] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5393),U_5394))
      | ~ c_Nat__Transfer_Ois__nat(U_5394)
      | ~ c_Nat__Transfer_Ois__nat(U_5393) ),
    inference(variable_rename,[status(thm)],[f_1601_1]) ).

fof(f_1601_3,plain,
    ! [U_5393,U_5394] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5393),U_5394))
      | ~ c_Nat__Transfer_Ois__nat(U_5394)
      | ~ c_Nat__Transfer_Ois__nat(U_5393) ),
    inference(definitional_conversion,[status(esa)],[f_1601_2]) ).

cnf(f_1601_4,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5393),U_5394))
    | ~ c_Nat__Transfer_Ois__nat(U_5394)
    | ~ c_Nat__Transfer_Ois__nat(U_5393) ),
    inference(clausify,[status(thm)],[f_1601_3]) ).

fof(f_1602_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_1602_2,plain,
    ! [U_5395] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5395)),
    inference(variable_rename,[status(thm)],[f_1602_1]) ).

fof(f_1602_3,plain,
    ! [U_5395] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5395)),
    inference(definitional_conversion,[status(esa)],[f_1602_2]) ).

cnf(f_1602_4,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_5395)),
    inference(clausify,[status(thm)],[f_1602_3]) ).

fof(f_1603_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_1603_2,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_1603_1]) ).

cnf(f_1603_3,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1603_2]) ).

fof(f_1604_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_1604_2,plain,
    ! [U_5397,U_5396] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5396),U_5397))
      | ~ c_Nat__Transfer_Ois__nat(U_5397)
      | ~ c_Nat__Transfer_Ois__nat(U_5396) ),
    inference(variable_rename,[status(thm)],[f_1604_1]) ).

fof(f_1604_3,plain,
    ! [U_5396,U_5397] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5396),U_5397))
      | ~ c_Nat__Transfer_Ois__nat(U_5397)
      | ~ c_Nat__Transfer_Ois__nat(U_5396) ),
    inference(definitional_conversion,[status(esa)],[f_1604_2]) ).

cnf(f_1604_4,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5396),U_5397))
    | ~ c_Nat__Transfer_Ois__nat(U_5397)
    | ~ c_Nat__Transfer_Ois__nat(U_5396) ),
    inference(clausify,[status(thm)],[f_1604_3]) ).

fof(f_1605_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_1605_2,plain,
    ! [U_5399,U_5398] :
      ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5398,U_5399))
      | ~ c_Nat__Transfer_Ois__nat(U_5399)
      | ~ c_Nat__Transfer_Ois__nat(U_5398) ),
    inference(variable_rename,[status(thm)],[f_1605_1]) ).

fof(f_1605_3,plain,
    ! [U_5399,U_5398] :
      ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5398,U_5399))
      | ~ c_Nat__Transfer_Ois__nat(U_5399)
      | ~ c_Nat__Transfer_Ois__nat(U_5398) ),
    inference(definitional_conversion,[status(esa)],[f_1605_2]) ).

cnf(f_1605_4,plain,
    ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5398,U_5399))
    | ~ c_Nat__Transfer_Ois__nat(U_5399)
    | ~ c_Nat__Transfer_Ois__nat(U_5398) ),
    inference(clausify,[status(thm)],[f_1605_3]) ).

fof(f_1606_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_1606_2,plain,
    ! [U_5401,U_5400] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5400),U_5401))
      | ~ c_Nat__Transfer_Ois__nat(U_5401)
      | ~ c_Nat__Transfer_Ois__nat(U_5400) ),
    inference(variable_rename,[status(thm)],[f_1606_1]) ).

fof(f_1606_3,plain,
    ! [U_5401,U_5400] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5400),U_5401))
      | ~ c_Nat__Transfer_Ois__nat(U_5401)
      | ~ c_Nat__Transfer_Ois__nat(U_5400) ),
    inference(definitional_conversion,[status(esa)],[f_1606_2]) ).

cnf(f_1606_4,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5400),U_5401))
    | ~ c_Nat__Transfer_Ois__nat(U_5401)
    | ~ c_Nat__Transfer_Ois__nat(U_5400) ),
    inference(clausify,[status(thm)],[f_1606_3]) ).

fof(f_1607_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_1607_2,plain,
    ! [U_5403,U_5402] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5402),U_5403))
      | ~ c_Nat__Transfer_Ois__nat(U_5402) ),
    inference(variable_rename,[status(thm)],[f_1607_1]) ).

fof(f_1607_3,plain,
    ! [U_5402,U_5403] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5402),U_5403))
      | ~ c_Nat__Transfer_Ois__nat(U_5402) ),
    inference(definitional_conversion,[status(esa)],[f_1607_2]) ).

cnf(f_1607_4,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5402),U_5403))
    | ~ c_Nat__Transfer_Ois__nat(U_5402) ),
    inference(clausify,[status(thm)],[f_1607_3]) ).

fof(f_1608_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_1608_2,plain,
    ! [U_5406,U_5405,U_5404] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5404),U_5405),U_5406)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),U_5406),c_Groups_Ozero__class_Ozero(U_5404)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),U_5405),c_Groups_Ozero__class_Ozero(U_5404))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),U_5406))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),U_5405)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),U_5406),c_Groups_Ozero__class_Ozero(U_5404)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),U_5405),c_Groups_Ozero__class_Ozero(U_5404))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),U_5406))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),U_5405)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5404),U_5405),U_5406))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5404) ),
    inference(variable_rename,[status(thm)],[f_1608_1]) ).

fof(f_1608_3,plain,
    ( ! [U_5404,U_5405,U_5406] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),U_5406),c_Groups_Ozero__class_Ozero(U_5404)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),U_5405),c_Groups_Ozero__class_Ozero(U_5404)))
        | ~ sP414(U_5404,U_5405,U_5406) )
    & ! [U_5404,U_5405,U_5406] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),U_5406))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),U_5405))
        | ~ sP414(U_5404,U_5405,U_5406) )
    & ! [U_5404,U_5405,U_5406] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),U_5406),c_Groups_Ozero__class_Ozero(U_5404)))
        | ~ sP413(U_5404,U_5405,U_5406) )
    & ! [U_5404,U_5405,U_5406] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),U_5405),c_Groups_Ozero__class_Ozero(U_5404)))
        | ~ sP413(U_5404,U_5405,U_5406) )
    & ! [U_5404,U_5405,U_5406] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),U_5406))
        | ~ sP412(U_5404,U_5405,U_5406) )
    & ! [U_5404,U_5405,U_5406] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),U_5405))
        | ~ sP412(U_5404,U_5405,U_5406) )
    & ! [U_5404,U_5405,U_5406] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5404),U_5405),U_5406)))
        | sP414(U_5404,U_5405,U_5406)
        | ~ sP415(U_5404,U_5405,U_5406) )
    & ! [U_5404,U_5405,U_5406] :
        ( sP413(U_5404,U_5405,U_5406)
        | sP412(U_5404,U_5405,U_5406)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5404),U_5405),U_5406)))
        | ~ sP415(U_5404,U_5405,U_5406) )
    & ! [U_5404,U_5405,U_5406] :
        ( sP415(U_5404,U_5405,U_5406)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5404) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP412,sP413,sP414,sP415])],[f_1608_2]) ).

cnf(f_1608_4,plain,
    ( sP415(U_5404,U_5405,U_5406)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5404) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_5,plain,
    ( sP413(U_5404,U_5405,U_5406)
    | sP412(U_5404,U_5405,U_5406)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5404),U_5405),U_5406)))
    | ~ sP415(U_5404,U_5405,U_5406) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5404),U_5405),U_5406)))
    | sP414(U_5404,U_5405,U_5406)
    | ~ sP415(U_5404,U_5405,U_5406) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),U_5405))
    | ~ sP412(U_5404,U_5405,U_5406) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),U_5406))
    | ~ sP412(U_5404,U_5405,U_5406) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),U_5405),c_Groups_Ozero__class_Ozero(U_5404)))
    | ~ sP413(U_5404,U_5405,U_5406) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),U_5406),c_Groups_Ozero__class_Ozero(U_5404)))
    | ~ sP413(U_5404,U_5405,U_5406) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),U_5406))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),U_5405))
    | ~ sP414(U_5404,U_5405,U_5406) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

cnf(f_1608_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),U_5406),c_Groups_Ozero__class_Ozero(U_5404)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),U_5405),c_Groups_Ozero__class_Ozero(U_5404)))
    | ~ sP414(U_5404,U_5405,U_5406) ),
    inference(clausify,[status(thm)],[f_1608_3]) ).

fof(f_1609_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_1609_2,plain,
    ! [U_5409,U_5408,U_5407] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5408),U_5409)),c_Groups_Ozero__class_Ozero(U_5407)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),c_Groups_Ozero__class_Ozero(U_5407)),U_5409))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),U_5408),c_Groups_Ozero__class_Ozero(U_5407))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),U_5409),c_Groups_Ozero__class_Ozero(U_5407)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),c_Groups_Ozero__class_Ozero(U_5407)),U_5408)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),c_Groups_Ozero__class_Ozero(U_5407)),U_5409))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),U_5408),c_Groups_Ozero__class_Ozero(U_5407))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),U_5409),c_Groups_Ozero__class_Ozero(U_5407)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),c_Groups_Ozero__class_Ozero(U_5407)),U_5408)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5408),U_5409)),c_Groups_Ozero__class_Ozero(U_5407))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5407) ),
    inference(variable_rename,[status(thm)],[f_1609_1]) ).

fof(f_1609_3,plain,
    ( ! [U_5409,U_5407,U_5408] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),c_Groups_Ozero__class_Ozero(U_5407)),U_5409))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),U_5408),c_Groups_Ozero__class_Ozero(U_5407)))
        | ~ sP418(U_5409,U_5407,U_5408) )
    & ! [U_5409,U_5407,U_5408] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),U_5409),c_Groups_Ozero__class_Ozero(U_5407)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),c_Groups_Ozero__class_Ozero(U_5407)),U_5408))
        | ~ sP418(U_5409,U_5407,U_5408) )
    & ! [U_5409,U_5407,U_5408] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),c_Groups_Ozero__class_Ozero(U_5407)),U_5409))
        | ~ sP417(U_5409,U_5407,U_5408) )
    & ! [U_5409,U_5407,U_5408] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),U_5408),c_Groups_Ozero__class_Ozero(U_5407)))
        | ~ sP417(U_5409,U_5407,U_5408) )
    & ! [U_5409,U_5407,U_5408] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),U_5409),c_Groups_Ozero__class_Ozero(U_5407)))
        | ~ sP416(U_5409,U_5407,U_5408) )
    & ! [U_5409,U_5407,U_5408] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),c_Groups_Ozero__class_Ozero(U_5407)),U_5408))
        | ~ sP416(U_5409,U_5407,U_5408) )
    & ! [U_5409,U_5407,U_5408] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5408),U_5409)),c_Groups_Ozero__class_Ozero(U_5407)))
        | sP418(U_5409,U_5407,U_5408)
        | ~ sP419(U_5409,U_5407,U_5408) )
    & ! [U_5409,U_5407,U_5408] :
        ( sP417(U_5409,U_5407,U_5408)
        | sP416(U_5409,U_5407,U_5408)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5408),U_5409)),c_Groups_Ozero__class_Ozero(U_5407)))
        | ~ sP419(U_5409,U_5407,U_5408) )
    & ! [U_5409,U_5407,U_5408] :
        ( sP419(U_5409,U_5407,U_5408)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5407) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP416,sP417,sP418,sP419])],[f_1609_2]) ).

cnf(f_1609_4,plain,
    ( sP419(U_5409,U_5407,U_5408)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5407) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_5,plain,
    ( sP417(U_5409,U_5407,U_5408)
    | sP416(U_5409,U_5407,U_5408)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5408),U_5409)),c_Groups_Ozero__class_Ozero(U_5407)))
    | ~ sP419(U_5409,U_5407,U_5408) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5407),U_5408),U_5409)),c_Groups_Ozero__class_Ozero(U_5407)))
    | sP418(U_5409,U_5407,U_5408)
    | ~ sP419(U_5409,U_5407,U_5408) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),c_Groups_Ozero__class_Ozero(U_5407)),U_5408))
    | ~ sP416(U_5409,U_5407,U_5408) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),U_5409),c_Groups_Ozero__class_Ozero(U_5407)))
    | ~ sP416(U_5409,U_5407,U_5408) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),U_5408),c_Groups_Ozero__class_Ozero(U_5407)))
    | ~ sP417(U_5409,U_5407,U_5408) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),c_Groups_Ozero__class_Ozero(U_5407)),U_5409))
    | ~ sP417(U_5409,U_5407,U_5408) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),U_5409),c_Groups_Ozero__class_Ozero(U_5407)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),c_Groups_Ozero__class_Ozero(U_5407)),U_5408))
    | ~ sP418(U_5409,U_5407,U_5408) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

cnf(f_1609_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),c_Groups_Ozero__class_Ozero(U_5407)),U_5409))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5407),U_5408),c_Groups_Ozero__class_Ozero(U_5407)))
    | ~ sP418(U_5409,U_5407,U_5408) ),
    inference(clausify,[status(thm)],[f_1609_3]) ).

fof(f_1610_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_1610_2,plain,
    ! [U_5413,U_5412,U_5411,U_5410] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5410),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5410),U_5411),U_5413)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5410),U_5412),U_5413)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5410),c_Groups_Ozero__class_Ozero(U_5410)),U_5413))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5410),U_5411),U_5412))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5410) ),
    inference(variable_rename,[status(thm)],[f_1610_1]) ).

fof(f_1610_3,plain,
    ! [U_5413,U_5412,U_5411,U_5410] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5410),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5410),U_5411),U_5413)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5410),U_5412),U_5413)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5410),c_Groups_Ozero__class_Ozero(U_5410)),U_5413))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5410),U_5411),U_5412))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5410) ),
    inference(definitional_conversion,[status(esa)],[f_1610_2]) ).

cnf(f_1610_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5410),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5410),U_5411),U_5413)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5410),U_5412),U_5413)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5410),c_Groups_Ozero__class_Ozero(U_5410)),U_5413))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5410),U_5411),U_5412))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5410) ),
    inference(clausify,[status(thm)],[f_1610_3]) ).

fof(f_1611_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_1611_2,plain,
    ! [U_5417,U_5416,U_5415,U_5414] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5414),U_5416),U_5417)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5414),U_5415),U_5417)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),U_5417),c_Groups_Ozero__class_Ozero(U_5414)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),U_5415),U_5416))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5414) ),
    inference(variable_rename,[status(thm)],[f_1611_1]) ).

fof(f_1611_3,plain,
    ! [U_5415,U_5414,U_5416,U_5417] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5414),U_5416),U_5417)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5414),U_5415),U_5417)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),U_5417),c_Groups_Ozero__class_Ozero(U_5414)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),U_5415),U_5416))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5414) ),
    inference(definitional_conversion,[status(esa)],[f_1611_2]) ).

cnf(f_1611_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5414),U_5416),U_5417)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5414),U_5415),U_5417)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),U_5417),c_Groups_Ozero__class_Ozero(U_5414)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),U_5415),U_5416))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5414) ),
    inference(clausify,[status(thm)],[f_1611_3]) ).

fof(f_1612_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_1612_2,plain,
    ! [U_5421,U_5420,U_5419,U_5418] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5418),U_5420),U_5421)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5418),U_5419),U_5421)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),U_5421),c_Groups_Ozero__class_Ozero(U_5418)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),U_5419),U_5420))
      | ~ class_Fields_Olinordered__field(U_5418) ),
    inference(variable_rename,[status(thm)],[f_1612_1]) ).

fof(f_1612_3,plain,
    ! [U_5418,U_5419,U_5420,U_5421] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5418),U_5420),U_5421)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5418),U_5419),U_5421)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),U_5421),c_Groups_Ozero__class_Ozero(U_5418)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),U_5419),U_5420))
      | ~ class_Fields_Olinordered__field(U_5418) ),
    inference(definitional_conversion,[status(esa)],[f_1612_2]) ).

cnf(f_1612_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5418),U_5420),U_5421)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5418),U_5419),U_5421)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),U_5421),c_Groups_Ozero__class_Ozero(U_5418)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),U_5419),U_5420))
    | ~ class_Fields_Olinordered__field(U_5418) ),
    inference(clausify,[status(thm)],[f_1612_3]) ).

fof(f_1613_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_1613_2,plain,
    ! [U_5425,U_5424,U_5423,U_5422] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5422),U_5423),U_5425)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5422),U_5424),U_5425)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),c_Groups_Ozero__class_Ozero(U_5422)),U_5425))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),U_5423),U_5424))
      | ~ class_Fields_Olinordered__field(U_5422) ),
    inference(variable_rename,[status(thm)],[f_1613_1]) ).

fof(f_1613_3,plain,
    ! [U_5422,U_5423,U_5424,U_5425] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5422),U_5423),U_5425)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5422),U_5424),U_5425)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),c_Groups_Ozero__class_Ozero(U_5422)),U_5425))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),U_5423),U_5424))
      | ~ class_Fields_Olinordered__field(U_5422) ),
    inference(definitional_conversion,[status(esa)],[f_1613_2]) ).

cnf(f_1613_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5422),U_5423),U_5425)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5422),U_5424),U_5425)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),c_Groups_Ozero__class_Ozero(U_5422)),U_5425))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),U_5423),U_5424))
    | ~ class_Fields_Olinordered__field(U_5422) ),
    inference(clausify,[status(thm)],[f_1613_3]) ).

fof(f_1614_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_1614_2,plain,
    ! [U_5428,U_5427,U_5426] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5426),c_Groups_Ozero__class_Ozero(U_5426)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5426),U_5427),U_5428)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5426),U_5428),c_Groups_Ozero__class_Ozero(U_5426)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5426),U_5427),c_Groups_Ozero__class_Ozero(U_5426)))
      | ~ class_Fields_Olinordered__field(U_5426) ),
    inference(variable_rename,[status(thm)],[f_1614_1]) ).

fof(f_1614_3,plain,
    ! [U_5427,U_5426,U_5428] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5426),c_Groups_Ozero__class_Ozero(U_5426)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5426),U_5427),U_5428)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5426),U_5428),c_Groups_Ozero__class_Ozero(U_5426)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5426),U_5427),c_Groups_Ozero__class_Ozero(U_5426)))
      | ~ class_Fields_Olinordered__field(U_5426) ),
    inference(definitional_conversion,[status(esa)],[f_1614_2]) ).

cnf(f_1614_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5426),c_Groups_Ozero__class_Ozero(U_5426)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5426),U_5427),U_5428)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5426),U_5428),c_Groups_Ozero__class_Ozero(U_5426)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5426),U_5427),c_Groups_Ozero__class_Ozero(U_5426)))
    | ~ class_Fields_Olinordered__field(U_5426) ),
    inference(clausify,[status(thm)],[f_1614_3]) ).

fof(f_1615_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_1615_2,plain,
    ! [U_5431,U_5430,U_5429] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5429),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5429),U_5430),U_5431)),c_Groups_Ozero__class_Ozero(U_5429)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5429),c_Groups_Ozero__class_Ozero(U_5429)),U_5431))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5429),U_5430),c_Groups_Ozero__class_Ozero(U_5429)))
      | ~ class_Fields_Olinordered__field(U_5429) ),
    inference(variable_rename,[status(thm)],[f_1615_1]) ).

fof(f_1615_3,plain,
    ! [U_5429,U_5430,U_5431] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5429),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5429),U_5430),U_5431)),c_Groups_Ozero__class_Ozero(U_5429)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5429),c_Groups_Ozero__class_Ozero(U_5429)),U_5431))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5429),U_5430),c_Groups_Ozero__class_Ozero(U_5429)))
      | ~ class_Fields_Olinordered__field(U_5429) ),
    inference(definitional_conversion,[status(esa)],[f_1615_2]) ).

cnf(f_1615_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5429),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5429),U_5430),U_5431)),c_Groups_Ozero__class_Ozero(U_5429)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5429),c_Groups_Ozero__class_Ozero(U_5429)),U_5431))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5429),U_5430),c_Groups_Ozero__class_Ozero(U_5429)))
    | ~ class_Fields_Olinordered__field(U_5429) ),
    inference(clausify,[status(thm)],[f_1615_3]) ).

fof(f_1616_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_1616_2,plain,
    ! [U_5434,U_5433,U_5432] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5432),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5432),U_5433),U_5434)),c_Groups_Ozero__class_Ozero(U_5432)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5432),U_5434),c_Groups_Ozero__class_Ozero(U_5432)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5432),c_Groups_Ozero__class_Ozero(U_5432)),U_5433))
      | ~ class_Fields_Olinordered__field(U_5432) ),
    inference(variable_rename,[status(thm)],[f_1616_1]) ).

fof(f_1616_3,plain,
    ! [U_5432,U_5433,U_5434] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5432),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5432),U_5433),U_5434)),c_Groups_Ozero__class_Ozero(U_5432)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5432),U_5434),c_Groups_Ozero__class_Ozero(U_5432)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5432),c_Groups_Ozero__class_Ozero(U_5432)),U_5433))
      | ~ class_Fields_Olinordered__field(U_5432) ),
    inference(definitional_conversion,[status(esa)],[f_1616_2]) ).

cnf(f_1616_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5432),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5432),U_5433),U_5434)),c_Groups_Ozero__class_Ozero(U_5432)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5432),U_5434),c_Groups_Ozero__class_Ozero(U_5432)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5432),c_Groups_Ozero__class_Ozero(U_5432)),U_5433))
    | ~ class_Fields_Olinordered__field(U_5432) ),
    inference(clausify,[status(thm)],[f_1616_3]) ).

fof(f_1617_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_1617_2,plain,
    ! [U_5437,U_5436,U_5435] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5435),c_Groups_Ozero__class_Ozero(U_5435)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5435),U_5436),U_5437)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5435),c_Groups_Ozero__class_Ozero(U_5435)),U_5437))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5435),c_Groups_Ozero__class_Ozero(U_5435)),U_5436))
      | ~ class_Fields_Olinordered__field(U_5435) ),
    inference(variable_rename,[status(thm)],[f_1617_1]) ).

fof(f_1617_3,plain,
    ! [U_5436,U_5435,U_5437] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5435),c_Groups_Ozero__class_Ozero(U_5435)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5435),U_5436),U_5437)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5435),c_Groups_Ozero__class_Ozero(U_5435)),U_5437))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5435),c_Groups_Ozero__class_Ozero(U_5435)),U_5436))
      | ~ class_Fields_Olinordered__field(U_5435) ),
    inference(definitional_conversion,[status(esa)],[f_1617_2]) ).

cnf(f_1617_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5435),c_Groups_Ozero__class_Ozero(U_5435)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5435),U_5436),U_5437)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5435),c_Groups_Ozero__class_Ozero(U_5435)),U_5437))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5435),c_Groups_Ozero__class_Ozero(U_5435)),U_5436))
    | ~ class_Fields_Olinordered__field(U_5435) ),
    inference(clausify,[status(thm)],[f_1617_3]) ).

fof(f_1618_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_1618_2,plain,
    ! [U_5440,U_5439,U_5438] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5438),U_5439),U_5440)),c_Groups_Ozero__class_Ozero(U_5438)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),U_5440))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),U_5439),c_Groups_Ozero__class_Ozero(U_5438))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),U_5440),c_Groups_Ozero__class_Ozero(U_5438)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),U_5439)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),U_5440))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),U_5439),c_Groups_Ozero__class_Ozero(U_5438))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),U_5440),c_Groups_Ozero__class_Ozero(U_5438)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),U_5439)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5438),U_5439),U_5440)),c_Groups_Ozero__class_Ozero(U_5438))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5438) ),
    inference(variable_rename,[status(thm)],[f_1618_1]) ).

fof(f_1618_3,plain,
    ( ! [U_5438,U_5439,U_5440] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),U_5440))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),U_5439),c_Groups_Ozero__class_Ozero(U_5438)))
        | ~ sP422(U_5438,U_5439,U_5440) )
    & ! [U_5438,U_5439,U_5440] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),U_5440),c_Groups_Ozero__class_Ozero(U_5438)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),U_5439))
        | ~ sP422(U_5438,U_5439,U_5440) )
    & ! [U_5438,U_5439,U_5440] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),U_5440))
        | ~ sP421(U_5438,U_5439,U_5440) )
    & ! [U_5438,U_5439,U_5440] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),U_5439),c_Groups_Ozero__class_Ozero(U_5438)))
        | ~ sP421(U_5438,U_5439,U_5440) )
    & ! [U_5438,U_5439,U_5440] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),U_5440),c_Groups_Ozero__class_Ozero(U_5438)))
        | ~ sP420(U_5438,U_5439,U_5440) )
    & ! [U_5438,U_5439,U_5440] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),U_5439))
        | ~ sP420(U_5438,U_5439,U_5440) )
    & ! [U_5438,U_5439,U_5440] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5438),U_5439),U_5440)),c_Groups_Ozero__class_Ozero(U_5438)))
        | sP422(U_5438,U_5439,U_5440)
        | ~ sP423(U_5438,U_5439,U_5440) )
    & ! [U_5438,U_5439,U_5440] :
        ( sP421(U_5438,U_5439,U_5440)
        | sP420(U_5438,U_5439,U_5440)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5438),U_5439),U_5440)),c_Groups_Ozero__class_Ozero(U_5438)))
        | ~ sP423(U_5438,U_5439,U_5440) )
    & ! [U_5438,U_5439,U_5440] :
        ( sP423(U_5438,U_5439,U_5440)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5438) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP420,sP421,sP422,sP423])],[f_1618_2]) ).

cnf(f_1618_4,plain,
    ( sP423(U_5438,U_5439,U_5440)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5438) ),
    inference(clausify,[status(thm)],[f_1618_3]) ).

cnf(f_1618_5,plain,
    ( sP421(U_5438,U_5439,U_5440)
    | sP420(U_5438,U_5439,U_5440)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5438),U_5439),U_5440)),c_Groups_Ozero__class_Ozero(U_5438)))
    | ~ sP423(U_5438,U_5439,U_5440) ),
    inference(clausify,[status(thm)],[f_1618_3]) ).

cnf(f_1618_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5438),U_5439),U_5440)),c_Groups_Ozero__class_Ozero(U_5438)))
    | sP422(U_5438,U_5439,U_5440)
    | ~ sP423(U_5438,U_5439,U_5440) ),
    inference(clausify,[status(thm)],[f_1618_3]) ).

cnf(f_1618_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),U_5439))
    | ~ sP420(U_5438,U_5439,U_5440) ),
    inference(clausify,[status(thm)],[f_1618_3]) ).

cnf(f_1618_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),U_5440),c_Groups_Ozero__class_Ozero(U_5438)))
    | ~ sP420(U_5438,U_5439,U_5440) ),
    inference(clausify,[status(thm)],[f_1618_3]) ).

cnf(f_1618_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),U_5439),c_Groups_Ozero__class_Ozero(U_5438)))
    | ~ sP421(U_5438,U_5439,U_5440) ),
    inference(clausify,[status(thm)],[f_1618_3]) ).

cnf(f_1618_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),U_5440))
    | ~ sP421(U_5438,U_5439,U_5440) ),
    inference(clausify,[status(thm)],[f_1618_3]) ).

cnf(f_1618_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),U_5440),c_Groups_Ozero__class_Ozero(U_5438)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),U_5439))
    | ~ sP422(U_5438,U_5439,U_5440) ),
    inference(clausify,[status(thm)],[f_1618_3]) ).

cnf(f_1618_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),U_5440))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),U_5439),c_Groups_Ozero__class_Ozero(U_5438)))
    | ~ sP422(U_5438,U_5439,U_5440) ),
    inference(clausify,[status(thm)],[f_1618_3]) ).

fof(f_1619_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_1619_2,plain,
    ! [U_5443,U_5442,U_5441] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5441),U_5442),U_5443)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),U_5443),c_Groups_Ozero__class_Ozero(U_5441)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),U_5442),c_Groups_Ozero__class_Ozero(U_5441))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),U_5443))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),U_5442)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),U_5443),c_Groups_Ozero__class_Ozero(U_5441)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),U_5442),c_Groups_Ozero__class_Ozero(U_5441))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),U_5443))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),U_5442)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5441),U_5442),U_5443))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5441) ),
    inference(variable_rename,[status(thm)],[f_1619_1]) ).

fof(f_1619_3,plain,
    ( ! [U_5443,U_5442,U_5441] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),U_5443),c_Groups_Ozero__class_Ozero(U_5441)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),U_5442),c_Groups_Ozero__class_Ozero(U_5441)))
        | ~ sP426(U_5443,U_5442,U_5441) )
    & ! [U_5443,U_5442,U_5441] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),U_5443))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),U_5442))
        | ~ sP426(U_5443,U_5442,U_5441) )
    & ! [U_5443,U_5442,U_5441] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),U_5443),c_Groups_Ozero__class_Ozero(U_5441)))
        | ~ sP425(U_5443,U_5442,U_5441) )
    & ! [U_5443,U_5442,U_5441] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),U_5442),c_Groups_Ozero__class_Ozero(U_5441)))
        | ~ sP425(U_5443,U_5442,U_5441) )
    & ! [U_5443,U_5442,U_5441] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),U_5443))
        | ~ sP424(U_5443,U_5442,U_5441) )
    & ! [U_5443,U_5442,U_5441] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),U_5442))
        | ~ sP424(U_5443,U_5442,U_5441) )
    & ! [U_5443,U_5442,U_5441] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5441),U_5442),U_5443)))
        | sP426(U_5443,U_5442,U_5441)
        | ~ sP427(U_5443,U_5442,U_5441) )
    & ! [U_5443,U_5442,U_5441] :
        ( sP425(U_5443,U_5442,U_5441)
        | sP424(U_5443,U_5442,U_5441)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5441),U_5442),U_5443)))
        | ~ sP427(U_5443,U_5442,U_5441) )
    & ! [U_5443,U_5442,U_5441] :
        ( sP427(U_5443,U_5442,U_5441)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5441) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP424,sP425,sP426,sP427])],[f_1619_2]) ).

cnf(f_1619_4,plain,
    ( sP427(U_5443,U_5442,U_5441)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5441) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_5,plain,
    ( sP425(U_5443,U_5442,U_5441)
    | sP424(U_5443,U_5442,U_5441)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5441),U_5442),U_5443)))
    | ~ sP427(U_5443,U_5442,U_5441) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5441),U_5442),U_5443)))
    | sP426(U_5443,U_5442,U_5441)
    | ~ sP427(U_5443,U_5442,U_5441) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),U_5442))
    | ~ sP424(U_5443,U_5442,U_5441) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),U_5443))
    | ~ sP424(U_5443,U_5442,U_5441) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),U_5442),c_Groups_Ozero__class_Ozero(U_5441)))
    | ~ sP425(U_5443,U_5442,U_5441) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),U_5443),c_Groups_Ozero__class_Ozero(U_5441)))
    | ~ sP425(U_5443,U_5442,U_5441) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),U_5443))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),c_Groups_Ozero__class_Ozero(U_5441)),U_5442))
    | ~ sP426(U_5443,U_5442,U_5441) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),U_5443),c_Groups_Ozero__class_Ozero(U_5441)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5441),U_5442),c_Groups_Ozero__class_Ozero(U_5441)))
    | ~ sP426(U_5443,U_5442,U_5441) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

fof(f_1620_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_1620_2,plain,
    ! [U_5447,U_5446,U_5445,U_5444] :
      ( ( ( U_5445 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5444),U_5446),U_5447)
          | ( U_5445 != c_Groups_Ozero__class_Ozero(U_5444)
            & U_5447 = c_Groups_Ozero__class_Ozero(U_5444) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5444),U_5445),U_5447) != U_5446
            & U_5447 != c_Groups_Ozero__class_Ozero(U_5444) ) )
        & ( ( ( U_5445 = c_Groups_Ozero__class_Ozero(U_5444)
              | U_5447 != c_Groups_Ozero__class_Ozero(U_5444) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5444),U_5445),U_5447) = U_5446
              | U_5447 = c_Groups_Ozero__class_Ozero(U_5444) ) )
          | U_5445 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5444),U_5446),U_5447) ) )
      | ~ class_Fields_Ofield__inverse__zero(U_5444) ),
    inference(variable_rename,[status(thm)],[f_1620_1]) ).

fof(f_1620_3,plain,
    ( ! [U_5444,U_5447,U_5445] :
        ( U_5445 != c_Groups_Ozero__class_Ozero(U_5444)
        | ~ sP430(U_5444,U_5447,U_5445) )
    & ! [U_5444,U_5447,U_5445] :
        ( U_5447 = c_Groups_Ozero__class_Ozero(U_5444)
        | ~ sP430(U_5444,U_5447,U_5445) )
    & ! [U_5446,U_5444,U_5447,U_5445] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5444),U_5445),U_5447) != U_5446
        | ~ sP429(U_5446,U_5444,U_5447,U_5445) )
    & ! [U_5446,U_5444,U_5447,U_5445] :
        ( U_5447 != c_Groups_Ozero__class_Ozero(U_5444)
        | ~ sP429(U_5446,U_5444,U_5447,U_5445) )
    & ! [U_5446,U_5444,U_5447,U_5445] :
        ( U_5445 = c_Groups_Ozero__class_Ozero(U_5444)
        | U_5447 != c_Groups_Ozero__class_Ozero(U_5444)
        | ~ sP428(U_5446,U_5444,U_5447,U_5445) )
    & ! [U_5446,U_5444,U_5447,U_5445] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5444),U_5445),U_5447) = U_5446
        | U_5447 = c_Groups_Ozero__class_Ozero(U_5444)
        | ~ sP428(U_5446,U_5444,U_5447,U_5445) )
    & ! [U_5446,U_5444,U_5447,U_5445] :
        ( U_5445 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5444),U_5446),U_5447)
        | sP430(U_5444,U_5447,U_5445)
        | sP429(U_5446,U_5444,U_5447,U_5445)
        | ~ sP431(U_5446,U_5444,U_5447,U_5445) )
    & ! [U_5446,U_5444,U_5447,U_5445] :
        ( sP428(U_5446,U_5444,U_5447,U_5445)
        | U_5445 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5444),U_5446),U_5447)
        | ~ sP431(U_5446,U_5444,U_5447,U_5445) )
    & ! [U_5446,U_5444,U_5447,U_5445] :
        ( sP431(U_5446,U_5444,U_5447,U_5445)
        | ~ class_Fields_Ofield__inverse__zero(U_5444) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP428,sP429,sP430,sP431])],[f_1620_2]) ).

cnf(f_1620_4,plain,
    ( sP431(U_5446,U_5444,U_5447,U_5445)
    | ~ class_Fields_Ofield__inverse__zero(U_5444) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_5,plain,
    ( sP428(U_5446,U_5444,U_5447,U_5445)
    | U_5445 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5444),U_5446),U_5447)
    | ~ sP431(U_5446,U_5444,U_5447,U_5445) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_6,plain,
    ( U_5445 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5444),U_5446),U_5447)
    | sP430(U_5444,U_5447,U_5445)
    | sP429(U_5446,U_5444,U_5447,U_5445)
    | ~ sP431(U_5446,U_5444,U_5447,U_5445) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_7,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5444),U_5445),U_5447) = U_5446
    | U_5447 = c_Groups_Ozero__class_Ozero(U_5444)
    | ~ sP428(U_5446,U_5444,U_5447,U_5445) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_8,plain,
    ( U_5445 = c_Groups_Ozero__class_Ozero(U_5444)
    | U_5447 != c_Groups_Ozero__class_Ozero(U_5444)
    | ~ sP428(U_5446,U_5444,U_5447,U_5445) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_9,plain,
    ( U_5447 != c_Groups_Ozero__class_Ozero(U_5444)
    | ~ sP429(U_5446,U_5444,U_5447,U_5445) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_10,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5444),U_5445),U_5447) != U_5446
    | ~ sP429(U_5446,U_5444,U_5447,U_5445) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_11,plain,
    ( U_5447 = c_Groups_Ozero__class_Ozero(U_5444)
    | ~ sP430(U_5444,U_5447,U_5445) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

cnf(f_1620_12,plain,
    ( U_5445 != c_Groups_Ozero__class_Ozero(U_5444)
    | ~ sP430(U_5444,U_5447,U_5445) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

fof(f_1621_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_1621_2,plain,
    ! [U_5451,U_5450,U_5449,U_5448] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5448),U_5449),U_5450) = U_5451
          | ( U_5451 != c_Groups_Ozero__class_Ozero(U_5448)
            & U_5450 = c_Groups_Ozero__class_Ozero(U_5448) )
          | ( U_5449 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5448),U_5451),U_5450)
            & U_5450 != c_Groups_Ozero__class_Ozero(U_5448) ) )
        & ( ( ( U_5451 = c_Groups_Ozero__class_Ozero(U_5448)
              | U_5450 != c_Groups_Ozero__class_Ozero(U_5448) )
            & ( U_5449 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5448),U_5451),U_5450)
              | U_5450 = c_Groups_Ozero__class_Ozero(U_5448) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5448),U_5449),U_5450) != U_5451 ) )
      | ~ class_Fields_Ofield__inverse__zero(U_5448) ),
    inference(variable_rename,[status(thm)],[f_1621_1]) ).

fof(f_1621_3,plain,
    ( ! [U_5451,U_5450,U_5448] :
        ( U_5451 != c_Groups_Ozero__class_Ozero(U_5448)
        | ~ sP434(U_5451,U_5450,U_5448) )
    & ! [U_5451,U_5450,U_5448] :
        ( U_5450 = c_Groups_Ozero__class_Ozero(U_5448)
        | ~ sP434(U_5451,U_5450,U_5448) )
    & ! [U_5451,U_5449,U_5450,U_5448] :
        ( U_5449 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5448),U_5451),U_5450)
        | ~ sP433(U_5451,U_5449,U_5450,U_5448) )
    & ! [U_5451,U_5449,U_5450,U_5448] :
        ( U_5450 != c_Groups_Ozero__class_Ozero(U_5448)
        | ~ sP433(U_5451,U_5449,U_5450,U_5448) )
    & ! [U_5451,U_5449,U_5450,U_5448] :
        ( U_5451 = c_Groups_Ozero__class_Ozero(U_5448)
        | U_5450 != c_Groups_Ozero__class_Ozero(U_5448)
        | ~ sP432(U_5451,U_5449,U_5450,U_5448) )
    & ! [U_5451,U_5449,U_5450,U_5448] :
        ( U_5449 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5448),U_5451),U_5450)
        | U_5450 = c_Groups_Ozero__class_Ozero(U_5448)
        | ~ sP432(U_5451,U_5449,U_5450,U_5448) )
    & ! [U_5451,U_5449,U_5450,U_5448] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5448),U_5449),U_5450) = U_5451
        | sP434(U_5451,U_5450,U_5448)
        | sP433(U_5451,U_5449,U_5450,U_5448)
        | ~ sP435(U_5451,U_5449,U_5450,U_5448) )
    & ! [U_5451,U_5449,U_5450,U_5448] :
        ( sP432(U_5451,U_5449,U_5450,U_5448)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5448),U_5449),U_5450) != U_5451
        | ~ sP435(U_5451,U_5449,U_5450,U_5448) )
    & ! [U_5451,U_5449,U_5450,U_5448] :
        ( sP435(U_5451,U_5449,U_5450,U_5448)
        | ~ class_Fields_Ofield__inverse__zero(U_5448) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP432,sP433,sP434,sP435])],[f_1621_2]) ).

cnf(f_1621_4,plain,
    ( sP435(U_5451,U_5449,U_5450,U_5448)
    | ~ class_Fields_Ofield__inverse__zero(U_5448) ),
    inference(clausify,[status(thm)],[f_1621_3]) ).

cnf(f_1621_5,plain,
    ( sP432(U_5451,U_5449,U_5450,U_5448)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5448),U_5449),U_5450) != U_5451
    | ~ sP435(U_5451,U_5449,U_5450,U_5448) ),
    inference(clausify,[status(thm)],[f_1621_3]) ).

cnf(f_1621_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5448),U_5449),U_5450) = U_5451
    | sP434(U_5451,U_5450,U_5448)
    | sP433(U_5451,U_5449,U_5450,U_5448)
    | ~ sP435(U_5451,U_5449,U_5450,U_5448) ),
    inference(clausify,[status(thm)],[f_1621_3]) ).

cnf(f_1621_7,plain,
    ( U_5449 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5448),U_5451),U_5450)
    | U_5450 = c_Groups_Ozero__class_Ozero(U_5448)
    | ~ sP432(U_5451,U_5449,U_5450,U_5448) ),
    inference(clausify,[status(thm)],[f_1621_3]) ).

cnf(f_1621_8,plain,
    ( U_5451 = c_Groups_Ozero__class_Ozero(U_5448)
    | U_5450 != c_Groups_Ozero__class_Ozero(U_5448)
    | ~ sP432(U_5451,U_5449,U_5450,U_5448) ),
    inference(clausify,[status(thm)],[f_1621_3]) ).

cnf(f_1621_9,plain,
    ( U_5450 != c_Groups_Ozero__class_Ozero(U_5448)
    | ~ sP433(U_5451,U_5449,U_5450,U_5448) ),
    inference(clausify,[status(thm)],[f_1621_3]) ).

cnf(f_1621_10,plain,
    ( U_5449 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5448),U_5451),U_5450)
    | ~ sP433(U_5451,U_5449,U_5450,U_5448) ),
    inference(clausify,[status(thm)],[f_1621_3]) ).

cnf(f_1621_11,plain,
    ( U_5450 = c_Groups_Ozero__class_Ozero(U_5448)
    | ~ sP434(U_5451,U_5450,U_5448) ),
    inference(clausify,[status(thm)],[f_1621_3]) ).

cnf(f_1621_12,plain,
    ( U_5451 != c_Groups_Ozero__class_Ozero(U_5448)
    | ~ sP434(U_5451,U_5450,U_5448) ),
    inference(clausify,[status(thm)],[f_1621_3]) ).

fof(f_1622_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_1622_2,plain,
    ! [U_5455,U_5454,U_5453,U_5452] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5452),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5452),U_5454),U_5453)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5452),U_5455),U_5453)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5452),U_5454),U_5455)
      | U_5453 = c_Groups_Ozero__class_Ozero(U_5452)
      | ~ class_Fields_Ofield__inverse__zero(U_5452) ),
    inference(variable_rename,[status(thm)],[f_1622_1]) ).

fof(f_1622_3,plain,
    ! [U_5454,U_5453,U_5455,U_5452] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5452),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5452),U_5454),U_5453)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5452),U_5455),U_5453)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5452),U_5454),U_5455)
      | U_5453 = c_Groups_Ozero__class_Ozero(U_5452)
      | ~ class_Fields_Ofield__inverse__zero(U_5452) ),
    inference(definitional_conversion,[status(esa)],[f_1622_2]) ).

cnf(f_1622_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5452),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5452),U_5454),U_5453)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5452),U_5455),U_5453)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5452),U_5454),U_5455)
    | U_5453 = c_Groups_Ozero__class_Ozero(U_5452)
    | ~ class_Fields_Ofield__inverse__zero(U_5452) ),
    inference(clausify,[status(thm)],[f_1622_3]) ).

fof(f_1623_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_1623_2,plain,
    ! [U_5459,U_5458,U_5457,U_5456] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5456),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5456),U_5457),U_5458)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5456),U_5457),U_5459)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5456),U_5458),U_5459)
      | U_5457 = c_Groups_Ozero__class_Ozero(U_5456)
      | ~ class_Fields_Ofield__inverse__zero(U_5456) ),
    inference(variable_rename,[status(thm)],[f_1623_1]) ).

fof(f_1623_3,plain,
    ! [U_5458,U_5457,U_5456,U_5459] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5456),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5456),U_5457),U_5458)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5456),U_5457),U_5459)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5456),U_5458),U_5459)
      | U_5457 = c_Groups_Ozero__class_Ozero(U_5456)
      | ~ class_Fields_Ofield__inverse__zero(U_5456) ),
    inference(definitional_conversion,[status(esa)],[f_1623_2]) ).

cnf(f_1623_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5456),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5456),U_5457),U_5458)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5456),U_5457),U_5459)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5456),U_5458),U_5459)
    | U_5457 = c_Groups_Ozero__class_Ozero(U_5456)
    | ~ class_Fields_Ofield__inverse__zero(U_5456) ),
    inference(clausify,[status(thm)],[f_1623_3]) ).

fof(f_1624_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_1624_2,plain,
    ! [U_5464,U_5463,U_5462,U_5461,U_5460] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5460),U_5463),U_5461) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5460),U_5464),U_5462)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5460),U_5463),U_5462) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5460),U_5464),U_5461) )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5460),U_5463),U_5462) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5460),U_5464),U_5461)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5460),U_5463),U_5461) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5460),U_5464),U_5462) ) )
      | U_5462 = c_Groups_Ozero__class_Ozero(U_5460)
      | U_5461 = c_Groups_Ozero__class_Ozero(U_5460)
      | ~ class_Fields_Ofield(U_5460) ),
    inference(variable_rename,[status(thm)],[f_1624_1]) ).

fof(f_1624_3,plain,
    ( ! [U_5460,U_5461,U_5462,U_5463,U_5464] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5460),U_5463),U_5461) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5460),U_5464),U_5462)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5460),U_5463),U_5462) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5460),U_5464),U_5461)
        | ~ sP436(U_5460,U_5461,U_5462,U_5463,U_5464) )
    & ! [U_5460,U_5461,U_5462,U_5463,U_5464] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5460),U_5463),U_5462) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5460),U_5464),U_5461)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5460),U_5463),U_5461) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5460),U_5464),U_5462)
        | ~ sP436(U_5460,U_5461,U_5462,U_5463,U_5464) )
    & ! [U_5460,U_5461,U_5462,U_5463,U_5464] :
        ( sP436(U_5460,U_5461,U_5462,U_5463,U_5464)
        | U_5462 = c_Groups_Ozero__class_Ozero(U_5460)
        | U_5461 = c_Groups_Ozero__class_Ozero(U_5460)
        | ~ class_Fields_Ofield(U_5460) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP436])],[f_1624_2]) ).

cnf(f_1624_4,plain,
    ( sP436(U_5460,U_5461,U_5462,U_5463,U_5464)
    | U_5462 = c_Groups_Ozero__class_Ozero(U_5460)
    | U_5461 = c_Groups_Ozero__class_Ozero(U_5460)
    | ~ class_Fields_Ofield(U_5460) ),
    inference(clausify,[status(thm)],[f_1624_3]) ).

cnf(f_1624_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5460),U_5463),U_5462) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5460),U_5464),U_5461)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5460),U_5463),U_5461) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5460),U_5464),U_5462)
    | ~ sP436(U_5460,U_5461,U_5462,U_5463,U_5464) ),
    inference(clausify,[status(thm)],[f_1624_3]) ).

cnf(f_1624_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5460),U_5463),U_5461) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5460),U_5464),U_5462)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5460),U_5463),U_5462) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5460),U_5464),U_5461)
    | ~ sP436(U_5460,U_5461,U_5462,U_5463,U_5464) ),
    inference(clausify,[status(thm)],[f_1624_3]) ).

fof(f_1625_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_1625_2,plain,
    ! [U_5468,U_5467,U_5466,U_5465] :
      ( U_5467 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5465),U_5468),U_5466)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5465),U_5467),U_5466) != U_5468
      | U_5466 = c_Groups_Ozero__class_Ozero(U_5465)
      | ~ class_Rings_Odivision__ring(U_5465) ),
    inference(variable_rename,[status(thm)],[f_1625_1]) ).

fof(f_1625_3,plain,
    ! [U_5466,U_5467,U_5468,U_5465] :
      ( U_5467 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5465),U_5468),U_5466)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5465),U_5467),U_5466) != U_5468
      | U_5466 = c_Groups_Ozero__class_Ozero(U_5465)
      | ~ class_Rings_Odivision__ring(U_5465) ),
    inference(definitional_conversion,[status(esa)],[f_1625_2]) ).

cnf(f_1625_4,plain,
    ( U_5467 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5465),U_5468),U_5466)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5465),U_5467),U_5466) != U_5468
    | U_5466 = c_Groups_Ozero__class_Ozero(U_5465)
    | ~ class_Rings_Odivision__ring(U_5465) ),
    inference(clausify,[status(thm)],[f_1625_3]) ).

fof(f_1626_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_1626_2,plain,
    ! [U_5472,U_5471,U_5470,U_5469] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5469),U_5471),U_5470) = U_5472
      | U_5471 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5469),U_5472),U_5470)
      | U_5470 = c_Groups_Ozero__class_Ozero(U_5469)
      | ~ class_Rings_Odivision__ring(U_5469) ),
    inference(variable_rename,[status(thm)],[f_1626_1]) ).

fof(f_1626_3,plain,
    ! [U_5470,U_5469,U_5471,U_5472] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5469),U_5471),U_5470) = U_5472
      | U_5471 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5469),U_5472),U_5470)
      | U_5470 = c_Groups_Ozero__class_Ozero(U_5469)
      | ~ class_Rings_Odivision__ring(U_5469) ),
    inference(definitional_conversion,[status(esa)],[f_1626_2]) ).

cnf(f_1626_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5469),U_5471),U_5470) = U_5472
    | U_5471 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5469),U_5472),U_5470)
    | U_5470 = c_Groups_Ozero__class_Ozero(U_5469)
    | ~ class_Rings_Odivision__ring(U_5469) ),
    inference(clausify,[status(thm)],[f_1626_3]) ).

fof(f_1627_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_1627_2,plain,
    ! [U_5476,U_5475,U_5474,U_5473] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5473),U_5475),U_5474) = U_5476
          | U_5475 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5473),U_5476),U_5474) )
        & ( U_5475 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5473),U_5476),U_5474)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5473),U_5475),U_5474) != U_5476 ) )
      | U_5474 = c_Groups_Ozero__class_Ozero(U_5473)
      | ~ class_Rings_Odivision__ring(U_5473) ),
    inference(variable_rename,[status(thm)],[f_1627_1]) ).

fof(f_1627_3,plain,
    ( ! [U_5473,U_5474,U_5475,U_5476] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5473),U_5475),U_5474) = U_5476
        | U_5475 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5473),U_5476),U_5474)
        | ~ sP437(U_5473,U_5474,U_5475,U_5476) )
    & ! [U_5473,U_5474,U_5475,U_5476] :
        ( U_5475 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5473),U_5476),U_5474)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5473),U_5475),U_5474) != U_5476
        | ~ sP437(U_5473,U_5474,U_5475,U_5476) )
    & ! [U_5473,U_5474,U_5475,U_5476] :
        ( sP437(U_5473,U_5474,U_5475,U_5476)
        | U_5474 = c_Groups_Ozero__class_Ozero(U_5473)
        | ~ class_Rings_Odivision__ring(U_5473) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP437])],[f_1627_2]) ).

cnf(f_1627_4,plain,
    ( sP437(U_5473,U_5474,U_5475,U_5476)
    | U_5474 = c_Groups_Ozero__class_Ozero(U_5473)
    | ~ class_Rings_Odivision__ring(U_5473) ),
    inference(clausify,[status(thm)],[f_1627_3]) ).

cnf(f_1627_5,plain,
    ( U_5475 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5473),U_5476),U_5474)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5473),U_5475),U_5474) != U_5476
    | ~ sP437(U_5473,U_5474,U_5475,U_5476) ),
    inference(clausify,[status(thm)],[f_1627_3]) ).

cnf(f_1627_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5473),U_5475),U_5474) = U_5476
    | U_5475 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5473),U_5476),U_5474)
    | ~ sP437(U_5473,U_5474,U_5475,U_5476) ),
    inference(clausify,[status(thm)],[f_1627_3]) ).

fof(f_1628_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_1628_2,plain,
    ! [U_5480,U_5479,U_5478,U_5477] :
      ( ( ( U_5479 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5477),U_5480),U_5478)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5477),U_5479),U_5478) != U_5480 )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5477),U_5479),U_5478) = U_5480
          | U_5479 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5477),U_5480),U_5478) ) )
      | U_5478 = c_Groups_Ozero__class_Ozero(U_5477)
      | ~ class_Rings_Odivision__ring(U_5477) ),
    inference(variable_rename,[status(thm)],[f_1628_1]) ).

fof(f_1628_3,plain,
    ( ! [U_5477,U_5478,U_5479,U_5480] :
        ( U_5479 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5477),U_5480),U_5478)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5477),U_5479),U_5478) != U_5480
        | ~ sP438(U_5477,U_5478,U_5479,U_5480) )
    & ! [U_5477,U_5478,U_5479,U_5480] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5477),U_5479),U_5478) = U_5480
        | U_5479 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5477),U_5480),U_5478)
        | ~ sP438(U_5477,U_5478,U_5479,U_5480) )
    & ! [U_5477,U_5478,U_5479,U_5480] :
        ( sP438(U_5477,U_5478,U_5479,U_5480)
        | U_5478 = c_Groups_Ozero__class_Ozero(U_5477)
        | ~ class_Rings_Odivision__ring(U_5477) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP438])],[f_1628_2]) ).

cnf(f_1628_4,plain,
    ( sP438(U_5477,U_5478,U_5479,U_5480)
    | U_5478 = c_Groups_Ozero__class_Ozero(U_5477)
    | ~ class_Rings_Odivision__ring(U_5477) ),
    inference(clausify,[status(thm)],[f_1628_3]) ).

cnf(f_1628_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5477),U_5479),U_5478) = U_5480
    | U_5479 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5477),U_5480),U_5478)
    | ~ sP438(U_5477,U_5478,U_5479,U_5480) ),
    inference(clausify,[status(thm)],[f_1628_3]) ).

cnf(f_1628_6,plain,
    ( U_5479 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5477),U_5480),U_5478)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5477),U_5479),U_5478) != U_5480
    | ~ sP438(U_5477,U_5478,U_5479,U_5480) ),
    inference(clausify,[status(thm)],[f_1628_3]) ).

fof(f_1629_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_1629_2,plain,
    ! [U_5483,U_5482,U_5481] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5481),U_5483),U_5482) = c_Groups_Oone__class_Oone(U_5481)
          | U_5483 != U_5482 )
        & ( U_5483 = U_5482
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5481),U_5483),U_5482) != c_Groups_Oone__class_Oone(U_5481) ) )
      | U_5482 = c_Groups_Ozero__class_Ozero(U_5481)
      | ~ class_Rings_Odivision__ring(U_5481) ),
    inference(variable_rename,[status(thm)],[f_1629_1]) ).

fof(f_1629_3,plain,
    ( ! [U_5481,U_5482,U_5483] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5481),U_5483),U_5482) = c_Groups_Oone__class_Oone(U_5481)
        | U_5483 != U_5482
        | ~ sP439(U_5481,U_5482,U_5483) )
    & ! [U_5481,U_5482,U_5483] :
        ( U_5483 = U_5482
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5481),U_5483),U_5482) != c_Groups_Oone__class_Oone(U_5481)
        | ~ sP439(U_5481,U_5482,U_5483) )
    & ! [U_5481,U_5482,U_5483] :
        ( sP439(U_5481,U_5482,U_5483)
        | U_5482 = c_Groups_Ozero__class_Ozero(U_5481)
        | ~ class_Rings_Odivision__ring(U_5481) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP439])],[f_1629_2]) ).

cnf(f_1629_4,plain,
    ( sP439(U_5481,U_5482,U_5483)
    | U_5482 = c_Groups_Ozero__class_Ozero(U_5481)
    | ~ class_Rings_Odivision__ring(U_5481) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_5,plain,
    ( U_5483 = U_5482
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5481),U_5483),U_5482) != c_Groups_Oone__class_Oone(U_5481)
    | ~ sP439(U_5481,U_5482,U_5483) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5481),U_5483),U_5482) = c_Groups_Oone__class_Oone(U_5481)
    | U_5483 != U_5482
    | ~ sP439(U_5481,U_5482,U_5483) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

fof(f_1630_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_1630_2,plain,
    ! [U_5485,U_5484] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5484),U_5485),U_5485) = c_Groups_Oone__class_Oone(U_5484)
      | U_5485 = c_Groups_Ozero__class_Ozero(U_5484)
      | ~ class_Rings_Odivision__ring(U_5484) ),
    inference(variable_rename,[status(thm)],[f_1630_1]) ).

fof(f_1630_3,plain,
    ! [U_5485,U_5484] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5484),U_5485),U_5485) = c_Groups_Oone__class_Oone(U_5484)
      | U_5485 = c_Groups_Ozero__class_Ozero(U_5484)
      | ~ class_Rings_Odivision__ring(U_5484) ),
    inference(definitional_conversion,[status(esa)],[f_1630_2]) ).

cnf(f_1630_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5484),U_5485),U_5485) = c_Groups_Oone__class_Oone(U_5484)
    | U_5485 = c_Groups_Ozero__class_Ozero(U_5484)
    | ~ class_Rings_Odivision__ring(U_5484) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

fof(f_1631_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_1631_2,plain,
    ! [U_5487,U_5486] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5486),U_5487),U_5487) = c_Groups_Oone__class_Oone(U_5486)
          | U_5487 = c_Groups_Ozero__class_Ozero(U_5486) )
        & ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5486),U_5487),U_5487) = c_Groups_Ozero__class_Ozero(U_5486)
          | U_5487 != c_Groups_Ozero__class_Ozero(U_5486) ) )
      | ~ class_Rings_Odivision__ring__inverse__zero(U_5486) ),
    inference(variable_rename,[status(thm)],[f_1631_1]) ).

fof(f_1631_3,plain,
    ( ! [U_5486,U_5487] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5486),U_5487),U_5487) = c_Groups_Oone__class_Oone(U_5486)
        | U_5487 = c_Groups_Ozero__class_Ozero(U_5486)
        | ~ sP440(U_5486,U_5487) )
    & ! [U_5486,U_5487] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5486),U_5487),U_5487) = c_Groups_Ozero__class_Ozero(U_5486)
        | U_5487 != c_Groups_Ozero__class_Ozero(U_5486)
        | ~ sP440(U_5486,U_5487) )
    & ! [U_5486,U_5487] :
        ( sP440(U_5486,U_5487)
        | ~ class_Rings_Odivision__ring__inverse__zero(U_5486) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP440])],[f_1631_2]) ).

cnf(f_1631_4,plain,
    ( sP440(U_5486,U_5487)
    | ~ class_Rings_Odivision__ring__inverse__zero(U_5486) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_5,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5486),U_5487),U_5487) = c_Groups_Ozero__class_Ozero(U_5486)
    | U_5487 != c_Groups_Ozero__class_Ozero(U_5486)
    | ~ sP440(U_5486,U_5487) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5486),U_5487),U_5487) = c_Groups_Oone__class_Oone(U_5486)
    | U_5487 = c_Groups_Ozero__class_Ozero(U_5486)
    | ~ sP440(U_5486,U_5487) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

fof(f_1632_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_1632_2,plain,
    ! [U_5490,U_5489,U_5488] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5488),hAPP(c_Groups_Ouminus__class_Ouminus(U_5488),U_5490)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5488),U_5489)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5488),U_5490),U_5489)
      | U_5489 = c_Groups_Ozero__class_Ozero(U_5488)
      | ~ class_Rings_Odivision__ring(U_5488) ),
    inference(variable_rename,[status(thm)],[f_1632_1]) ).

fof(f_1632_3,plain,
    ! [U_5490,U_5489,U_5488] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5488),hAPP(c_Groups_Ouminus__class_Ouminus(U_5488),U_5490)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5488),U_5489)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5488),U_5490),U_5489)
      | U_5489 = c_Groups_Ozero__class_Ozero(U_5488)
      | ~ class_Rings_Odivision__ring(U_5488) ),
    inference(definitional_conversion,[status(esa)],[f_1632_2]) ).

cnf(f_1632_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5488),hAPP(c_Groups_Ouminus__class_Ouminus(U_5488),U_5490)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5488),U_5489)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5488),U_5490),U_5489)
    | U_5489 = c_Groups_Ozero__class_Ozero(U_5488)
    | ~ class_Rings_Odivision__ring(U_5488) ),
    inference(clausify,[status(thm)],[f_1632_3]) ).

fof(f_1633_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_1633_2,plain,
    ! [U_5493,U_5492,U_5491] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5491),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5491),U_5493),U_5492)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5491),U_5493),hAPP(c_Groups_Ouminus__class_Ouminus(U_5491),U_5492))
      | U_5492 = c_Groups_Ozero__class_Ozero(U_5491)
      | ~ class_Rings_Odivision__ring(U_5491) ),
    inference(variable_rename,[status(thm)],[f_1633_1]) ).

fof(f_1633_3,plain,
    ! [U_5491,U_5492,U_5493] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5491),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5491),U_5493),U_5492)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5491),U_5493),hAPP(c_Groups_Ouminus__class_Ouminus(U_5491),U_5492))
      | U_5492 = c_Groups_Ozero__class_Ozero(U_5491)
      | ~ class_Rings_Odivision__ring(U_5491) ),
    inference(definitional_conversion,[status(esa)],[f_1633_2]) ).

cnf(f_1633_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5491),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5491),U_5493),U_5492)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5491),U_5493),hAPP(c_Groups_Ouminus__class_Ouminus(U_5491),U_5492))
    | U_5492 = c_Groups_Ozero__class_Ozero(U_5491)
    | ~ class_Rings_Odivision__ring(U_5491) ),
    inference(clausify,[status(thm)],[f_1633_3]) ).

fof(f_1634_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_1634_2,plain,
    ! [U_5497,U_5496,U_5495,U_5494] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5494),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5494),U_5496),U_5495)),U_5497) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5494),hAPP(hAPP(c_Power_Opower__class_Opower(U_5494),U_5496),U_5497)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5494),U_5495),U_5497))
      | U_5495 = c_Groups_Ozero__class_Ozero(U_5494)
      | ~ class_Fields_Ofield(U_5494) ),
    inference(variable_rename,[status(thm)],[f_1634_1]) ).

fof(f_1634_3,plain,
    ! [U_5494,U_5495,U_5496,U_5497] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5494),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5494),U_5496),U_5495)),U_5497) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5494),hAPP(hAPP(c_Power_Opower__class_Opower(U_5494),U_5496),U_5497)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5494),U_5495),U_5497))
      | U_5495 = c_Groups_Ozero__class_Ozero(U_5494)
      | ~ class_Fields_Ofield(U_5494) ),
    inference(definitional_conversion,[status(esa)],[f_1634_2]) ).

cnf(f_1634_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5494),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5494),U_5496),U_5495)),U_5497) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5494),hAPP(hAPP(c_Power_Opower__class_Opower(U_5494),U_5496),U_5497)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5494),U_5495),U_5497))
    | U_5495 = c_Groups_Ozero__class_Ozero(U_5494)
    | ~ class_Fields_Ofield(U_5494) ),
    inference(clausify,[status(thm)],[f_1634_3]) ).

fof(f_1635_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_1635_2,plain,
    ! [U_5500,U_5499,U_5498] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5498),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5498),U_5500),U_5499)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5498),hAPP(c_Groups_Oabs__class_Oabs(U_5498),U_5500)),hAPP(c_Groups_Oabs__class_Oabs(U_5498),U_5499))
      | U_5499 = c_Groups_Ozero__class_Ozero(U_5498)
      | ~ class_Fields_Olinordered__field(U_5498) ),
    inference(variable_rename,[status(thm)],[f_1635_1]) ).

fof(f_1635_3,plain,
    ! [U_5498,U_5499,U_5500] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5498),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5498),U_5500),U_5499)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5498),hAPP(c_Groups_Oabs__class_Oabs(U_5498),U_5500)),hAPP(c_Groups_Oabs__class_Oabs(U_5498),U_5499))
      | U_5499 = c_Groups_Ozero__class_Ozero(U_5498)
      | ~ class_Fields_Olinordered__field(U_5498) ),
    inference(definitional_conversion,[status(esa)],[f_1635_2]) ).

cnf(f_1635_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5498),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5498),U_5500),U_5499)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5498),hAPP(c_Groups_Oabs__class_Oabs(U_5498),U_5500)),hAPP(c_Groups_Oabs__class_Oabs(U_5498),U_5499))
    | U_5499 = c_Groups_Ozero__class_Ozero(U_5498)
    | ~ class_Fields_Olinordered__field(U_5498) ),
    inference(clausify,[status(thm)],[f_1635_3]) ).

fof(f_1636_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_1636_2,plain,
    ! [U_5503,U_5502,U_5501] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5501),c_Groups_Oone__class_Oone(U_5501)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5501),U_5502),U_5503)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5501),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5501),c_Groups_Oone__class_Oone(U_5501)),U_5502)),U_5503)
      | ~ class_Fields_Ofield__inverse__zero(U_5501) ),
    inference(variable_rename,[status(thm)],[f_1636_1]) ).

fof(f_1636_3,plain,
    ! [U_5501,U_5502,U_5503] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5501),c_Groups_Oone__class_Oone(U_5501)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5501),U_5502),U_5503)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5501),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5501),c_Groups_Oone__class_Oone(U_5501)),U_5502)),U_5503)
      | ~ class_Fields_Ofield__inverse__zero(U_5501) ),
    inference(definitional_conversion,[status(esa)],[f_1636_2]) ).

cnf(f_1636_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5501),c_Groups_Oone__class_Oone(U_5501)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5501),U_5502),U_5503)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5501),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5501),c_Groups_Oone__class_Oone(U_5501)),U_5502)),U_5503)
    | ~ class_Fields_Ofield__inverse__zero(U_5501) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

fof(f_1637_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_1637_2,plain,
    ! [U_5505,U_5504] :
      ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_5504,U_5505))
      | ~ c_Nat__Transfer_Ois__nat(U_5505)
      | ~ c_Nat__Transfer_Ois__nat(U_5504) ),
    inference(variable_rename,[status(thm)],[f_1637_1]) ).

fof(f_1637_3,plain,
    ! [U_5504,U_5505] :
      ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_5504,U_5505))
      | ~ c_Nat__Transfer_Ois__nat(U_5505)
      | ~ c_Nat__Transfer_Ois__nat(U_5504) ),
    inference(definitional_conversion,[status(esa)],[f_1637_2]) ).

cnf(f_1637_4,plain,
    ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_5504,U_5505))
    | ~ c_Nat__Transfer_Ois__nat(U_5505)
    | ~ c_Nat__Transfer_Ois__nat(U_5504) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

fof(f_1638_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_1638_2,plain,
    ! [U_5508,U_5507,U_5506] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5506),c_Groups_Ozero__class_Ozero(U_5506)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5506),U_5507),U_5508)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5506),U_5508),c_Groups_Ozero__class_Ozero(U_5506)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5506),U_5507),c_Groups_Ozero__class_Ozero(U_5506)))
      | ~ class_Fields_Olinordered__field(U_5506) ),
    inference(variable_rename,[status(thm)],[f_1638_1]) ).

fof(f_1638_3,plain,
    ! [U_5506,U_5507,U_5508] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5506),c_Groups_Ozero__class_Ozero(U_5506)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5506),U_5507),U_5508)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5506),U_5508),c_Groups_Ozero__class_Ozero(U_5506)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5506),U_5507),c_Groups_Ozero__class_Ozero(U_5506)))
      | ~ class_Fields_Olinordered__field(U_5506) ),
    inference(definitional_conversion,[status(esa)],[f_1638_2]) ).

cnf(f_1638_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5506),c_Groups_Ozero__class_Ozero(U_5506)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5506),U_5507),U_5508)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5506),U_5508),c_Groups_Ozero__class_Ozero(U_5506)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5506),U_5507),c_Groups_Ozero__class_Ozero(U_5506)))
    | ~ class_Fields_Olinordered__field(U_5506) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

fof(f_1639_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_1639_2,plain,
    ! [U_5511,U_5510,U_5509] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5509),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5509),U_5510),U_5511)),c_Groups_Ozero__class_Ozero(U_5509)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5509),c_Groups_Ozero__class_Ozero(U_5509)),U_5511))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5509),U_5510),c_Groups_Ozero__class_Ozero(U_5509)))
      | ~ class_Fields_Olinordered__field(U_5509) ),
    inference(variable_rename,[status(thm)],[f_1639_1]) ).

fof(f_1639_3,plain,
    ! [U_5509,U_5510,U_5511] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5509),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5509),U_5510),U_5511)),c_Groups_Ozero__class_Ozero(U_5509)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5509),c_Groups_Ozero__class_Ozero(U_5509)),U_5511))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5509),U_5510),c_Groups_Ozero__class_Ozero(U_5509)))
      | ~ class_Fields_Olinordered__field(U_5509) ),
    inference(definitional_conversion,[status(esa)],[f_1639_2]) ).

cnf(f_1639_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5509),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5509),U_5510),U_5511)),c_Groups_Ozero__class_Ozero(U_5509)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5509),c_Groups_Ozero__class_Ozero(U_5509)),U_5511))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5509),U_5510),c_Groups_Ozero__class_Ozero(U_5509)))
    | ~ class_Fields_Olinordered__field(U_5509) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

fof(f_1640_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_1640_2,plain,
    ! [U_5516,U_5515,U_5514,U_5513,U_5512] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5512),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5512),U_5513),U_5516)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5512),U_5514),U_5515)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5512),U_5515),U_5516))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5512),c_Groups_Ozero__class_Ozero(U_5512)),U_5515))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5512),U_5513),U_5514))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5512),c_Groups_Ozero__class_Ozero(U_5512)),U_5513))
      | ~ class_Fields_Olinordered__field(U_5512) ),
    inference(variable_rename,[status(thm)],[f_1640_1]) ).

fof(f_1640_3,plain,
    ! [U_5512,U_5513,U_5514,U_5515,U_5516] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5512),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5512),U_5513),U_5516)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5512),U_5514),U_5515)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5512),U_5515),U_5516))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5512),c_Groups_Ozero__class_Ozero(U_5512)),U_5515))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5512),U_5513),U_5514))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5512),c_Groups_Ozero__class_Ozero(U_5512)),U_5513))
      | ~ class_Fields_Olinordered__field(U_5512) ),
    inference(definitional_conversion,[status(esa)],[f_1640_2]) ).

cnf(f_1640_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5512),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5512),U_5513),U_5516)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5512),U_5514),U_5515)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5512),U_5515),U_5516))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5512),c_Groups_Ozero__class_Ozero(U_5512)),U_5515))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5512),U_5513),U_5514))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5512),c_Groups_Ozero__class_Ozero(U_5512)),U_5513))
    | ~ class_Fields_Olinordered__field(U_5512) ),
    inference(clausify,[status(thm)],[f_1640_3]) ).

fof(f_1641_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_1641_2,plain,
    ! [U_5521,U_5520,U_5519,U_5518,U_5517] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5517),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5517),U_5518),U_5521)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5517),U_5519),U_5520)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5517),U_5520),U_5521))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5517),c_Groups_Ozero__class_Ozero(U_5517)),U_5520))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5517),U_5518),U_5519))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5517),c_Groups_Ozero__class_Ozero(U_5517)),U_5518))
      | ~ class_Fields_Olinordered__field(U_5517) ),
    inference(variable_rename,[status(thm)],[f_1641_1]) ).

fof(f_1641_3,plain,
    ! [U_5517,U_5519,U_5518,U_5520,U_5521] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5517),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5517),U_5518),U_5521)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5517),U_5519),U_5520)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5517),U_5520),U_5521))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5517),c_Groups_Ozero__class_Ozero(U_5517)),U_5520))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5517),U_5518),U_5519))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5517),c_Groups_Ozero__class_Ozero(U_5517)),U_5518))
      | ~ class_Fields_Olinordered__field(U_5517) ),
    inference(definitional_conversion,[status(esa)],[f_1641_2]) ).

cnf(f_1641_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5517),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5517),U_5518),U_5521)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5517),U_5519),U_5520)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5517),U_5520),U_5521))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5517),c_Groups_Ozero__class_Ozero(U_5517)),U_5520))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5517),U_5518),U_5519))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5517),c_Groups_Ozero__class_Ozero(U_5517)),U_5518))
    | ~ class_Fields_Olinordered__field(U_5517) ),
    inference(clausify,[status(thm)],[f_1641_3]) ).

fof(f_1642_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_1642_2,plain,
    ! [U_5526,U_5525,U_5524,U_5523,U_5522] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5522),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5522),U_5523),U_5526)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5522),U_5524),U_5525)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5522),U_5525),U_5526))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5522),c_Groups_Ozero__class_Ozero(U_5522)),U_5525))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5522),U_5523),U_5524))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5522),c_Groups_Ozero__class_Ozero(U_5522)),U_5523))
      | ~ class_Fields_Olinordered__field(U_5522) ),
    inference(variable_rename,[status(thm)],[f_1642_1]) ).

fof(f_1642_3,plain,
    ! [U_5523,U_5524,U_5522,U_5525,U_5526] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5522),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5522),U_5523),U_5526)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5522),U_5524),U_5525)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5522),U_5525),U_5526))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5522),c_Groups_Ozero__class_Ozero(U_5522)),U_5525))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5522),U_5523),U_5524))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5522),c_Groups_Ozero__class_Ozero(U_5522)),U_5523))
      | ~ class_Fields_Olinordered__field(U_5522) ),
    inference(definitional_conversion,[status(esa)],[f_1642_2]) ).

cnf(f_1642_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5522),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5522),U_5523),U_5526)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5522),U_5524),U_5525)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5522),U_5525),U_5526))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5522),c_Groups_Ozero__class_Ozero(U_5522)),U_5525))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5522),U_5523),U_5524))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5522),c_Groups_Ozero__class_Ozero(U_5522)),U_5523))
    | ~ class_Fields_Olinordered__field(U_5522) ),
    inference(clausify,[status(thm)],[f_1642_3]) ).

fof(f_1643_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_1643_2,plain,
    ! [U_5529,U_5528,U_5527] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5527),U_5528),U_5529)),c_Groups_Ozero__class_Ozero(U_5527)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5527),U_5529),c_Groups_Ozero__class_Ozero(U_5527)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),c_Groups_Ozero__class_Ozero(U_5527)),U_5528))
      | ~ class_Fields_Olinordered__field(U_5527) ),
    inference(variable_rename,[status(thm)],[f_1643_1]) ).

fof(f_1643_3,plain,
    ! [U_5528,U_5529,U_5527] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5527),U_5528),U_5529)),c_Groups_Ozero__class_Ozero(U_5527)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5527),U_5529),c_Groups_Ozero__class_Ozero(U_5527)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),c_Groups_Ozero__class_Ozero(U_5527)),U_5528))
      | ~ class_Fields_Olinordered__field(U_5527) ),
    inference(definitional_conversion,[status(esa)],[f_1643_2]) ).

cnf(f_1643_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5527),U_5528),U_5529)),c_Groups_Ozero__class_Ozero(U_5527)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5527),U_5529),c_Groups_Ozero__class_Ozero(U_5527)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5527),c_Groups_Ozero__class_Ozero(U_5527)),U_5528))
    | ~ class_Fields_Olinordered__field(U_5527) ),
    inference(clausify,[status(thm)],[f_1643_3]) ).

fof(f_1644_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_1644_2,plain,
    ! [U_5532,U_5531,U_5530] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5530),c_Groups_Ozero__class_Ozero(U_5530)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5530),U_5531),U_5532)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5530),c_Groups_Ozero__class_Ozero(U_5530)),U_5532))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5530),c_Groups_Ozero__class_Ozero(U_5530)),U_5531))
      | ~ class_Fields_Olinordered__field(U_5530) ),
    inference(variable_rename,[status(thm)],[f_1644_1]) ).

fof(f_1644_3,plain,
    ! [U_5530,U_5531,U_5532] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5530),c_Groups_Ozero__class_Ozero(U_5530)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5530),U_5531),U_5532)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5530),c_Groups_Ozero__class_Ozero(U_5530)),U_5532))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5530),c_Groups_Ozero__class_Ozero(U_5530)),U_5531))
      | ~ class_Fields_Olinordered__field(U_5530) ),
    inference(definitional_conversion,[status(esa)],[f_1644_2]) ).

cnf(f_1644_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5530),c_Groups_Ozero__class_Ozero(U_5530)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5530),U_5531),U_5532)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5530),c_Groups_Ozero__class_Ozero(U_5530)),U_5532))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5530),c_Groups_Ozero__class_Ozero(U_5530)),U_5531))
    | ~ class_Fields_Olinordered__field(U_5530) ),
    inference(clausify,[status(thm)],[f_1644_3]) ).

fof(f_1645_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_1645_2,plain,
    ! [U_5536,U_5535,U_5534,U_5533] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5533),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5533),U_5536),U_5534)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5533),U_5536),U_5535)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5533),c_Groups_Ozero__class_Ozero(U_5533)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5533),U_5534),U_5535)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5533),U_5536),c_Groups_Ozero__class_Ozero(U_5533)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5533),U_5534),U_5535))
      | ~ class_Fields_Olinordered__field(U_5533) ),
    inference(variable_rename,[status(thm)],[f_1645_1]) ).

fof(f_1645_3,plain,
    ! [U_5533,U_5534,U_5535,U_5536] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5533),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5533),U_5536),U_5534)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5533),U_5536),U_5535)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5533),c_Groups_Ozero__class_Ozero(U_5533)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5533),U_5534),U_5535)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5533),U_5536),c_Groups_Ozero__class_Ozero(U_5533)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5533),U_5534),U_5535))
      | ~ class_Fields_Olinordered__field(U_5533) ),
    inference(definitional_conversion,[status(esa)],[f_1645_2]) ).

cnf(f_1645_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5533),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5533),U_5536),U_5534)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5533),U_5536),U_5535)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5533),c_Groups_Ozero__class_Ozero(U_5533)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5533),U_5534),U_5535)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5533),U_5536),c_Groups_Ozero__class_Ozero(U_5533)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5533),U_5534),U_5535))
    | ~ class_Fields_Olinordered__field(U_5533) ),
    inference(clausify,[status(thm)],[f_1645_3]) ).

fof(f_1646_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_1646_2,plain,
    ! [U_5540,U_5539,U_5538,U_5537] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5537),U_5540),U_5539)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5537),U_5540),U_5538)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),c_Groups_Ozero__class_Ozero(U_5537)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5537),U_5539),U_5538)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),c_Groups_Ozero__class_Ozero(U_5537)),U_5540))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),U_5538),U_5539))
      | ~ class_Fields_Olinordered__field(U_5537) ),
    inference(variable_rename,[status(thm)],[f_1646_1]) ).

fof(f_1646_3,plain,
    ! [U_5538,U_5539,U_5537,U_5540] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5537),U_5540),U_5539)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5537),U_5540),U_5538)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),c_Groups_Ozero__class_Ozero(U_5537)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5537),U_5539),U_5538)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),c_Groups_Ozero__class_Ozero(U_5537)),U_5540))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),U_5538),U_5539))
      | ~ class_Fields_Olinordered__field(U_5537) ),
    inference(definitional_conversion,[status(esa)],[f_1646_2]) ).

cnf(f_1646_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5537),U_5540),U_5539)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5537),U_5540),U_5538)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),c_Groups_Ozero__class_Ozero(U_5537)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5537),U_5539),U_5538)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),c_Groups_Ozero__class_Ozero(U_5537)),U_5540))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5537),U_5538),U_5539))
    | ~ class_Fields_Olinordered__field(U_5537) ),
    inference(clausify,[status(thm)],[f_1646_3]) ).

fof(f_1647_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_1647_2,plain,
    ! [U_5544,U_5543,U_5542,U_5541] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5541),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5541),U_5543),U_5542)),U_5544))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5541),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5541),U_5544),U_5542)),U_5543)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5541),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5541),U_5544),U_5542)),U_5543))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5541),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5541),U_5543),U_5542)),U_5544)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5541),U_5542),c_Groups_Ozero__class_Ozero(U_5541)))
      | ~ class_Fields_Olinordered__field(U_5541) ),
    inference(variable_rename,[status(thm)],[f_1647_1]) ).

fof(f_1647_3,plain,
    ( ! [U_5543,U_5542,U_5541,U_5544] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5541),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5541),U_5543),U_5542)),U_5544))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5541),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5541),U_5544),U_5542)),U_5543))
        | ~ sP441(U_5543,U_5542,U_5541,U_5544) )
    & ! [U_5543,U_5542,U_5541,U_5544] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5541),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5541),U_5544),U_5542)),U_5543))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5541),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5541),U_5543),U_5542)),U_5544))
        | ~ sP441(U_5543,U_5542,U_5541,U_5544) )
    & ! [U_5543,U_5542,U_5541,U_5544] :
        ( sP441(U_5543,U_5542,U_5541,U_5544)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5541),U_5542),c_Groups_Ozero__class_Ozero(U_5541)))
        | ~ class_Fields_Olinordered__field(U_5541) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP441])],[f_1647_2]) ).

cnf(f_1647_4,plain,
    ( sP441(U_5543,U_5542,U_5541,U_5544)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5541),U_5542),c_Groups_Ozero__class_Ozero(U_5541)))
    | ~ class_Fields_Olinordered__field(U_5541) ),
    inference(clausify,[status(thm)],[f_1647_3]) ).

cnf(f_1647_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5541),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5541),U_5544),U_5542)),U_5543))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5541),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5541),U_5543),U_5542)),U_5544))
    | ~ sP441(U_5543,U_5542,U_5541,U_5544) ),
    inference(clausify,[status(thm)],[f_1647_3]) ).

cnf(f_1647_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5541),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5541),U_5543),U_5542)),U_5544))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5541),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5541),U_5544),U_5542)),U_5543))
    | ~ sP441(U_5543,U_5542,U_5541,U_5544) ),
    inference(clausify,[status(thm)],[f_1647_3]) ).

fof(f_1648_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_1648_2,plain,
    ! [U_5548,U_5547,U_5546,U_5545] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5545),U_5547),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5545),U_5548),U_5546)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5545),U_5548),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5545),U_5547),U_5546))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5545),U_5548),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5545),U_5547),U_5546)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5545),U_5547),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5545),U_5548),U_5546))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5545),U_5546),c_Groups_Ozero__class_Ozero(U_5545)))
      | ~ class_Fields_Olinordered__field(U_5545) ),
    inference(variable_rename,[status(thm)],[f_1648_1]) ).

fof(f_1648_3,plain,
    ( ! [U_5546,U_5548,U_5547,U_5545] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5545),U_5547),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5545),U_5548),U_5546)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5545),U_5548),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5545),U_5547),U_5546)))
        | ~ sP442(U_5546,U_5548,U_5547,U_5545) )
    & ! [U_5546,U_5548,U_5547,U_5545] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5545),U_5548),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5545),U_5547),U_5546)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5545),U_5547),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5545),U_5548),U_5546)))
        | ~ sP442(U_5546,U_5548,U_5547,U_5545) )
    & ! [U_5546,U_5548,U_5547,U_5545] :
        ( sP442(U_5546,U_5548,U_5547,U_5545)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5545),U_5546),c_Groups_Ozero__class_Ozero(U_5545)))
        | ~ class_Fields_Olinordered__field(U_5545) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP442])],[f_1648_2]) ).

cnf(f_1648_4,plain,
    ( sP442(U_5546,U_5548,U_5547,U_5545)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5545),U_5546),c_Groups_Ozero__class_Ozero(U_5545)))
    | ~ class_Fields_Olinordered__field(U_5545) ),
    inference(clausify,[status(thm)],[f_1648_3]) ).

cnf(f_1648_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5545),U_5548),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5545),U_5547),U_5546)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5545),U_5547),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5545),U_5548),U_5546)))
    | ~ sP442(U_5546,U_5548,U_5547,U_5545) ),
    inference(clausify,[status(thm)],[f_1648_3]) ).

cnf(f_1648_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5545),U_5547),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5545),U_5548),U_5546)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5545),U_5548),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5545),U_5547),U_5546)))
    | ~ sP442(U_5546,U_5548,U_5547,U_5545) ),
    inference(clausify,[status(thm)],[f_1648_3]) ).

fof(f_1649_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_1649_2,plain,
    ! [U_5552,U_5551,U_5550,U_5549] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5549),U_5551),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5549),U_5552),U_5550)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5549),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5549),U_5551),U_5550)),U_5552))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5549),c_Groups_Ozero__class_Ozero(U_5549)),U_5550))
      | ~ class_Fields_Olinordered__field(U_5549) ),
    inference(variable_rename,[status(thm)],[f_1649_1]) ).

fof(f_1649_3,plain,
    ! [U_5549,U_5550,U_5551,U_5552] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5549),U_5551),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5549),U_5552),U_5550)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5549),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5549),U_5551),U_5550)),U_5552))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5549),c_Groups_Ozero__class_Ozero(U_5549)),U_5550))
      | ~ class_Fields_Olinordered__field(U_5549) ),
    inference(definitional_conversion,[status(esa)],[f_1649_2]) ).

cnf(f_1649_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5549),U_5551),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5549),U_5552),U_5550)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5549),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5549),U_5551),U_5550)),U_5552))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5549),c_Groups_Ozero__class_Ozero(U_5549)),U_5550))
    | ~ class_Fields_Olinordered__field(U_5549) ),
    inference(clausify,[status(thm)],[f_1649_3]) ).

fof(f_1650_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_1650_2,plain,
    ! [U_5556,U_5555,U_5554,U_5553] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5553),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5553),U_5555),U_5554)),U_5556))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5553),U_5555),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5553),U_5556),U_5554)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5553),c_Groups_Ozero__class_Ozero(U_5553)),U_5554))
      | ~ class_Fields_Olinordered__field(U_5553) ),
    inference(variable_rename,[status(thm)],[f_1650_1]) ).

fof(f_1650_3,plain,
    ! [U_5553,U_5554,U_5555,U_5556] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5553),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5553),U_5555),U_5554)),U_5556))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5553),U_5555),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5553),U_5556),U_5554)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5553),c_Groups_Ozero__class_Ozero(U_5553)),U_5554))
      | ~ class_Fields_Olinordered__field(U_5553) ),
    inference(definitional_conversion,[status(esa)],[f_1650_2]) ).

cnf(f_1650_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5553),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5553),U_5555),U_5554)),U_5556))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5553),U_5555),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5553),U_5556),U_5554)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5553),c_Groups_Ozero__class_Ozero(U_5553)),U_5554))
    | ~ class_Fields_Olinordered__field(U_5553) ),
    inference(clausify,[status(thm)],[f_1650_3]) ).

fof(f_1651_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_1651_2,plain,
    ! [U_5560,U_5559,U_5558,U_5557] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5557),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5557),U_5559),U_5558)),U_5560))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5557),U_5559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5557),U_5560),U_5558))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5557),U_5559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5557),U_5560),U_5558)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5557),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5557),U_5559),U_5558)),U_5560)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5557),c_Groups_Ozero__class_Ozero(U_5557)),U_5558))
      | ~ class_Fields_Olinordered__field(U_5557) ),
    inference(variable_rename,[status(thm)],[f_1651_1]) ).

fof(f_1651_3,plain,
    ( ! [U_5558,U_5557,U_5559,U_5560] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5557),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5557),U_5559),U_5558)),U_5560))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5557),U_5559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5557),U_5560),U_5558)))
        | ~ sP443(U_5558,U_5557,U_5559,U_5560) )
    & ! [U_5558,U_5557,U_5559,U_5560] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5557),U_5559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5557),U_5560),U_5558)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5557),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5557),U_5559),U_5558)),U_5560))
        | ~ sP443(U_5558,U_5557,U_5559,U_5560) )
    & ! [U_5558,U_5557,U_5559,U_5560] :
        ( sP443(U_5558,U_5557,U_5559,U_5560)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5557),c_Groups_Ozero__class_Ozero(U_5557)),U_5558))
        | ~ class_Fields_Olinordered__field(U_5557) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP443])],[f_1651_2]) ).

cnf(f_1651_4,plain,
    ( sP443(U_5558,U_5557,U_5559,U_5560)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5557),c_Groups_Ozero__class_Ozero(U_5557)),U_5558))
    | ~ class_Fields_Olinordered__field(U_5557) ),
    inference(clausify,[status(thm)],[f_1651_3]) ).

cnf(f_1651_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5557),U_5559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5557),U_5560),U_5558)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5557),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5557),U_5559),U_5558)),U_5560))
    | ~ sP443(U_5558,U_5557,U_5559,U_5560) ),
    inference(clausify,[status(thm)],[f_1651_3]) ).

cnf(f_1651_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5557),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5557),U_5559),U_5558)),U_5560))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5557),U_5559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5557),U_5560),U_5558)))
    | ~ sP443(U_5558,U_5557,U_5559,U_5560) ),
    inference(clausify,[status(thm)],[f_1651_3]) ).

fof(f_1652_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_1652_2,plain,
    ! [U_5564,U_5563,U_5562,U_5561] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5561),U_5563),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5561),U_5564),U_5562)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5561),U_5563),U_5562)),U_5564)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5561),U_5563),U_5562)),U_5564))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5561),U_5563),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5561),U_5564),U_5562))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5561),c_Groups_Ozero__class_Ozero(U_5561)),U_5562))
      | ~ class_Fields_Olinordered__field(U_5561) ),
    inference(variable_rename,[status(thm)],[f_1652_1]) ).

fof(f_1652_3,plain,
    ( ! [U_5562,U_5563,U_5561,U_5564] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5561),U_5563),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5561),U_5564),U_5562)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5561),U_5563),U_5562)),U_5564))
        | ~ sP444(U_5562,U_5563,U_5561,U_5564) )
    & ! [U_5562,U_5563,U_5561,U_5564] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5561),U_5563),U_5562)),U_5564))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5561),U_5563),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5561),U_5564),U_5562)))
        | ~ sP444(U_5562,U_5563,U_5561,U_5564) )
    & ! [U_5562,U_5563,U_5561,U_5564] :
        ( sP444(U_5562,U_5563,U_5561,U_5564)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5561),c_Groups_Ozero__class_Ozero(U_5561)),U_5562))
        | ~ class_Fields_Olinordered__field(U_5561) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP444])],[f_1652_2]) ).

cnf(f_1652_4,plain,
    ( sP444(U_5562,U_5563,U_5561,U_5564)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5561),c_Groups_Ozero__class_Ozero(U_5561)),U_5562))
    | ~ class_Fields_Olinordered__field(U_5561) ),
    inference(clausify,[status(thm)],[f_1652_3]) ).

cnf(f_1652_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5561),U_5563),U_5562)),U_5564))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5561),U_5563),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5561),U_5564),U_5562)))
    | ~ sP444(U_5562,U_5563,U_5561,U_5564) ),
    inference(clausify,[status(thm)],[f_1652_3]) ).

cnf(f_1652_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5561),U_5563),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5561),U_5564),U_5562)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5561),U_5563),U_5562)),U_5564))
    | ~ sP444(U_5562,U_5563,U_5561,U_5564) ),
    inference(clausify,[status(thm)],[f_1652_3]) ).

fof(f_1653_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_1653_2,plain,
    ! [U_5568,U_5567,U_5566,U_5565] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5565),U_5566),U_5567)),U_5568))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5568))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5567),c_Groups_Ozero__class_Ozero(U_5565))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5565),U_5568),U_5567)),U_5566))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5567),c_Groups_Ozero__class_Ozero(U_5565))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5567)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5566),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5565),U_5568),U_5567)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5567)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5568))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5567),c_Groups_Ozero__class_Ozero(U_5565))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5565),U_5568),U_5567)),U_5566))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5567),c_Groups_Ozero__class_Ozero(U_5565))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5567)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5566),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5565),U_5568),U_5567)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5567)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5565),U_5566),U_5567)),U_5568)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5565) ),
    inference(variable_rename,[status(thm)],[f_1653_1]) ).

fof(f_1653_3,plain,
    ( ! [U_5565,U_5567,U_5568] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5568))
        | ~ sP449(U_5565,U_5567,U_5568) )
    & ! [U_5565,U_5567,U_5568] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5567),c_Groups_Ozero__class_Ozero(U_5565)))
        | ~ sP449(U_5565,U_5567,U_5568) )
    & ! [U_5565,U_5566,U_5567,U_5568] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5565),U_5568),U_5567)),U_5566))
        | ~ sP448(U_5565,U_5566,U_5567,U_5568) )
    & ! [U_5565,U_5566,U_5567,U_5568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5567),c_Groups_Ozero__class_Ozero(U_5565)))
        | ~ sP448(U_5565,U_5566,U_5567,U_5568) )
    & ! [U_5565,U_5566,U_5567,U_5568] :
        ( sP449(U_5565,U_5567,U_5568)
        | sP448(U_5565,U_5566,U_5567,U_5568)
        | ~ sP450(U_5565,U_5566,U_5567,U_5568) )
    & ! [U_5565,U_5566,U_5567,U_5568] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5567))
        | ~ sP450(U_5565,U_5566,U_5567,U_5568) )
    & ! [U_5565,U_5566,U_5567,U_5568] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5566),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5565),U_5568),U_5567)))
        | ~ sP447(U_5565,U_5566,U_5567,U_5568) )
    & ! [U_5565,U_5566,U_5567,U_5568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5567))
        | ~ sP447(U_5565,U_5566,U_5567,U_5568) )
    & ! [U_5565,U_5566,U_5567,U_5568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5568))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5567),c_Groups_Ozero__class_Ozero(U_5565)))
        | ~ sP445(U_5565,U_5566,U_5567,U_5568) )
    & ! [U_5565,U_5566,U_5567,U_5568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5565),U_5568),U_5567)),U_5566))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5567),c_Groups_Ozero__class_Ozero(U_5565)))
        | ~ sP445(U_5565,U_5566,U_5567,U_5568) )
    & ! [U_5565,U_5566,U_5567,U_5568] :
        ( sP445(U_5565,U_5566,U_5567,U_5568)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5567))
        | ~ sP446(U_5565,U_5566,U_5567,U_5568) )
    & ! [U_5565,U_5566,U_5567,U_5568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5566),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5565),U_5568),U_5567)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5567))
        | ~ sP446(U_5565,U_5566,U_5567,U_5568) )
    & ! [U_5565,U_5566,U_5567,U_5568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5565),U_5566),U_5567)),U_5568))
        | sP450(U_5565,U_5566,U_5567,U_5568)
        | sP447(U_5565,U_5566,U_5567,U_5568)
        | ~ sP451(U_5565,U_5566,U_5567,U_5568) )
    & ! [U_5565,U_5566,U_5567,U_5568] :
        ( sP446(U_5565,U_5566,U_5567,U_5568)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5565),U_5566),U_5567)),U_5568))
        | ~ sP451(U_5565,U_5566,U_5567,U_5568) )
    & ! [U_5565,U_5566,U_5567,U_5568] :
        ( sP451(U_5565,U_5566,U_5567,U_5568)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5565) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP445,sP446,sP447,sP448,sP449,sP450,sP451])],[f_1653_2]) ).

cnf(f_1653_4,plain,
    ( sP451(U_5565,U_5566,U_5567,U_5568)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5565) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_5,plain,
    ( sP446(U_5565,U_5566,U_5567,U_5568)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5565),U_5566),U_5567)),U_5568))
    | ~ sP451(U_5565,U_5566,U_5567,U_5568) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5565),U_5566),U_5567)),U_5568))
    | sP450(U_5565,U_5566,U_5567,U_5568)
    | sP447(U_5565,U_5566,U_5567,U_5568)
    | ~ sP451(U_5565,U_5566,U_5567,U_5568) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5566),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5565),U_5568),U_5567)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5567))
    | ~ sP446(U_5565,U_5566,U_5567,U_5568) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_8,plain,
    ( sP445(U_5565,U_5566,U_5567,U_5568)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5567))
    | ~ sP446(U_5565,U_5566,U_5567,U_5568) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5565),U_5568),U_5567)),U_5566))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5567),c_Groups_Ozero__class_Ozero(U_5565)))
    | ~ sP445(U_5565,U_5566,U_5567,U_5568) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5568))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5567),c_Groups_Ozero__class_Ozero(U_5565)))
    | ~ sP445(U_5565,U_5566,U_5567,U_5568) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5567))
    | ~ sP447(U_5565,U_5566,U_5567,U_5568) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5566),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5565),U_5568),U_5567)))
    | ~ sP447(U_5565,U_5566,U_5567,U_5568) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5567))
    | ~ sP450(U_5565,U_5566,U_5567,U_5568) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_14,plain,
    ( sP449(U_5565,U_5567,U_5568)
    | sP448(U_5565,U_5566,U_5567,U_5568)
    | ~ sP450(U_5565,U_5566,U_5567,U_5568) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5567),c_Groups_Ozero__class_Ozero(U_5565)))
    | ~ sP448(U_5565,U_5566,U_5567,U_5568) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5565),U_5568),U_5567)),U_5566))
    | ~ sP448(U_5565,U_5566,U_5567,U_5568) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),U_5567),c_Groups_Ozero__class_Ozero(U_5565)))
    | ~ sP449(U_5565,U_5567,U_5568) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

cnf(f_1653_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5565),c_Groups_Ozero__class_Ozero(U_5565)),U_5568))
    | ~ sP449(U_5565,U_5567,U_5568) ),
    inference(clausify,[status(thm)],[f_1653_3]) ).

fof(f_1654_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_1654_2,plain,
    ! [U_5572,U_5571,U_5570,U_5569] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5570),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5569),U_5571),U_5572)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5570),c_Groups_Ozero__class_Ozero(U_5569)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5572),c_Groups_Ozero__class_Ozero(U_5569))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5569),U_5570),U_5572)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5572),c_Groups_Ozero__class_Ozero(U_5569))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),c_Groups_Ozero__class_Ozero(U_5569)),U_5572)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5569),U_5570),U_5572)),U_5571))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),c_Groups_Ozero__class_Ozero(U_5569)),U_5572)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5570),c_Groups_Ozero__class_Ozero(U_5569)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5572),c_Groups_Ozero__class_Ozero(U_5569))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5569),U_5570),U_5572)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5572),c_Groups_Ozero__class_Ozero(U_5569))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),c_Groups_Ozero__class_Ozero(U_5569)),U_5572)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5569),U_5570),U_5572)),U_5571))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),c_Groups_Ozero__class_Ozero(U_5569)),U_5572)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5570),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5569),U_5571),U_5572))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5569) ),
    inference(variable_rename,[status(thm)],[f_1654_1]) ).

fof(f_1654_3,plain,
    ( ! [U_5570,U_5572,U_5569] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5570),c_Groups_Ozero__class_Ozero(U_5569)))
        | ~ sP456(U_5570,U_5572,U_5569) )
    & ! [U_5570,U_5572,U_5569] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5572),c_Groups_Ozero__class_Ozero(U_5569)))
        | ~ sP456(U_5570,U_5572,U_5569) )
    & ! [U_5570,U_5572,U_5569,U_5571] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5569),U_5570),U_5572)))
        | ~ sP455(U_5570,U_5572,U_5569,U_5571) )
    & ! [U_5570,U_5572,U_5569,U_5571] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5572),c_Groups_Ozero__class_Ozero(U_5569)))
        | ~ sP455(U_5570,U_5572,U_5569,U_5571) )
    & ! [U_5570,U_5572,U_5569,U_5571] :
        ( sP456(U_5570,U_5572,U_5569)
        | sP455(U_5570,U_5572,U_5569,U_5571)
        | ~ sP457(U_5570,U_5572,U_5569,U_5571) )
    & ! [U_5570,U_5572,U_5569,U_5571] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),c_Groups_Ozero__class_Ozero(U_5569)),U_5572))
        | ~ sP457(U_5570,U_5572,U_5569,U_5571) )
    & ! [U_5570,U_5572,U_5569,U_5571] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5569),U_5570),U_5572)),U_5571))
        | ~ sP454(U_5570,U_5572,U_5569,U_5571) )
    & ! [U_5570,U_5572,U_5569,U_5571] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),c_Groups_Ozero__class_Ozero(U_5569)),U_5572))
        | ~ sP454(U_5570,U_5572,U_5569,U_5571) )
    & ! [U_5570,U_5572,U_5569,U_5571] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5570),c_Groups_Ozero__class_Ozero(U_5569)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5572),c_Groups_Ozero__class_Ozero(U_5569)))
        | ~ sP452(U_5570,U_5572,U_5569,U_5571) )
    & ! [U_5570,U_5572,U_5569,U_5571] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5569),U_5570),U_5572)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5572),c_Groups_Ozero__class_Ozero(U_5569)))
        | ~ sP452(U_5570,U_5572,U_5569,U_5571) )
    & ! [U_5570,U_5572,U_5569,U_5571] :
        ( sP452(U_5570,U_5572,U_5569,U_5571)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),c_Groups_Ozero__class_Ozero(U_5569)),U_5572))
        | ~ sP453(U_5570,U_5572,U_5569,U_5571) )
    & ! [U_5570,U_5572,U_5569,U_5571] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5569),U_5570),U_5572)),U_5571))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),c_Groups_Ozero__class_Ozero(U_5569)),U_5572))
        | ~ sP453(U_5570,U_5572,U_5569,U_5571) )
    & ! [U_5570,U_5572,U_5569,U_5571] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5570),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5569),U_5571),U_5572)))
        | sP457(U_5570,U_5572,U_5569,U_5571)
        | sP454(U_5570,U_5572,U_5569,U_5571)
        | ~ sP458(U_5570,U_5572,U_5569,U_5571) )
    & ! [U_5570,U_5572,U_5569,U_5571] :
        ( sP453(U_5570,U_5572,U_5569,U_5571)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5570),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5569),U_5571),U_5572)))
        | ~ sP458(U_5570,U_5572,U_5569,U_5571) )
    & ! [U_5570,U_5572,U_5569,U_5571] :
        ( sP458(U_5570,U_5572,U_5569,U_5571)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5569) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP452,sP453,sP454,sP455,sP456,sP457,sP458])],[f_1654_2]) ).

cnf(f_1654_4,plain,
    ( sP458(U_5570,U_5572,U_5569,U_5571)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5569) ),
    inference(clausify,[status(thm)],[f_1654_3]) ).

cnf(f_1654_5,plain,
    ( sP453(U_5570,U_5572,U_5569,U_5571)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5570),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5569),U_5571),U_5572)))
    | ~ sP458(U_5570,U_5572,U_5569,U_5571) ),
    inference(clausify,[status(thm)],[f_1654_3]) ).

cnf(f_1654_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5570),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5569),U_5571),U_5572)))
    | sP457(U_5570,U_5572,U_5569,U_5571)
    | sP454(U_5570,U_5572,U_5569,U_5571)
    | ~ sP458(U_5570,U_5572,U_5569,U_5571) ),
    inference(clausify,[status(thm)],[f_1654_3]) ).

cnf(f_1654_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5569),U_5570),U_5572)),U_5571))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),c_Groups_Ozero__class_Ozero(U_5569)),U_5572))
    | ~ sP453(U_5570,U_5572,U_5569,U_5571) ),
    inference(clausify,[status(thm)],[f_1654_3]) ).

cnf(f_1654_8,plain,
    ( sP452(U_5570,U_5572,U_5569,U_5571)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),c_Groups_Ozero__class_Ozero(U_5569)),U_5572))
    | ~ sP453(U_5570,U_5572,U_5569,U_5571) ),
    inference(clausify,[status(thm)],[f_1654_3]) ).

cnf(f_1654_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5569),U_5570),U_5572)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5572),c_Groups_Ozero__class_Ozero(U_5569)))
    | ~ sP452(U_5570,U_5572,U_5569,U_5571) ),
    inference(clausify,[status(thm)],[f_1654_3]) ).

cnf(f_1654_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5570),c_Groups_Ozero__class_Ozero(U_5569)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5572),c_Groups_Ozero__class_Ozero(U_5569)))
    | ~ sP452(U_5570,U_5572,U_5569,U_5571) ),
    inference(clausify,[status(thm)],[f_1654_3]) ).

cnf(f_1654_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),c_Groups_Ozero__class_Ozero(U_5569)),U_5572))
    | ~ sP454(U_5570,U_5572,U_5569,U_5571) ),
    inference(clausify,[status(thm)],[f_1654_3]) ).

cnf(f_1654_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5569),U_5570),U_5572)),U_5571))
    | ~ sP454(U_5570,U_5572,U_5569,U_5571) ),
    inference(clausify,[status(thm)],[f_1654_3]) ).

cnf(f_1654_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),c_Groups_Ozero__class_Ozero(U_5569)),U_5572))
    | ~ sP457(U_5570,U_5572,U_5569,U_5571) ),
    inference(clausify,[status(thm)],[f_1654_3]) ).

cnf(f_1654_14,plain,
    ( sP456(U_5570,U_5572,U_5569)
    | sP455(U_5570,U_5572,U_5569,U_5571)
    | ~ sP457(U_5570,U_5572,U_5569,U_5571) ),
    inference(clausify,[status(thm)],[f_1654_3]) ).

cnf(f_1654_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5572),c_Groups_Ozero__class_Ozero(U_5569)))
    | ~ sP455(U_5570,U_5572,U_5569,U_5571) ),
    inference(clausify,[status(thm)],[f_1654_3]) ).

cnf(f_1654_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5569),U_5570),U_5572)))
    | ~ sP455(U_5570,U_5572,U_5569,U_5571) ),
    inference(clausify,[status(thm)],[f_1654_3]) ).

cnf(f_1654_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5572),c_Groups_Ozero__class_Ozero(U_5569)))
    | ~ sP456(U_5570,U_5572,U_5569) ),
    inference(clausify,[status(thm)],[f_1654_3]) ).

cnf(f_1654_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5569),U_5570),c_Groups_Ozero__class_Ozero(U_5569)))
    | ~ sP456(U_5570,U_5572,U_5569) ),
    inference(clausify,[status(thm)],[f_1654_3]) ).

fof(f_1655_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_1655_2,plain,
    ! [U_5573] :
      ( ( c_Nat__Transfer_Ois__nat(U_5573)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5573)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5573))
        | ~ c_Nat__Transfer_Ois__nat(U_5573) ) ),
    inference(variable_rename,[status(thm)],[f_1655_1]) ).

fof(f_1655_3,plain,
    ( ! [U_5575] :
        ( c_Nat__Transfer_Ois__nat(U_5575)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5575)) )
    & ! [U_5574] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5574))
        | ~ c_Nat__Transfer_Ois__nat(U_5574) ) ),
    inference(miniscope,[status(thm)],[f_1655_2]) ).

fof(f_1655_4,plain,
    ( ! [U_5575] :
        ( c_Nat__Transfer_Ois__nat(U_5575)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5575)) )
    & ! [U_5574] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5574))
        | ~ c_Nat__Transfer_Ois__nat(U_5574) ) ),
    inference(definitional_conversion,[status(esa)],[f_1655_3]) ).

cnf(f_1655_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5574))
    | ~ c_Nat__Transfer_Ois__nat(U_5574) ),
    inference(clausify,[status(thm)],[f_1655_4]) ).

cnf(f_1655_6,plain,
    ( c_Nat__Transfer_Ois__nat(U_5575)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5575)) ),
    inference(clausify,[status(thm)],[f_1655_4]) ).

fof(f_1656_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_1656_2,plain,
    ! [U_5579,U_5578,U_5577,U_5576] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5576),U_5578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5576),U_5579),U_5577)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5576),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5576),U_5579),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5576),U_5578),U_5577))),U_5577)
      | U_5577 = c_Groups_Ozero__class_Ozero(U_5576)
      | ~ class_Fields_Ofield__inverse__zero(U_5576) ),
    inference(variable_rename,[status(thm)],[f_1656_1]) ).

fof(f_1656_3,plain,
    ! [U_5579,U_5578,U_5576,U_5577] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5576),U_5578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5576),U_5579),U_5577)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5576),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5576),U_5579),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5576),U_5578),U_5577))),U_5577)
      | U_5577 = c_Groups_Ozero__class_Ozero(U_5576)
      | ~ class_Fields_Ofield__inverse__zero(U_5576) ),
    inference(definitional_conversion,[status(esa)],[f_1656_2]) ).

cnf(f_1656_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5576),U_5578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5576),U_5579),U_5577)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5576),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5576),U_5579),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5576),U_5578),U_5577))),U_5577)
    | U_5577 = c_Groups_Ozero__class_Ozero(U_5576)
    | ~ class_Fields_Ofield__inverse__zero(U_5576) ),
    inference(clausify,[status(thm)],[f_1656_3]) ).

fof(f_1657_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_1657_2,plain,
    ! [U_5583,U_5582,U_5581,U_5580] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5580),U_5582),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5580),U_5583),U_5581)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),U_5581),U_5582)),U_5583)),U_5581)
      | U_5581 = c_Groups_Ozero__class_Ozero(U_5580)
      | ~ class_Fields_Ofield(U_5580) ),
    inference(variable_rename,[status(thm)],[f_1657_1]) ).

fof(f_1657_3,plain,
    ! [U_5583,U_5580,U_5582,U_5581] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5580),U_5582),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5580),U_5583),U_5581)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),U_5581),U_5582)),U_5583)),U_5581)
      | U_5581 = c_Groups_Ozero__class_Ozero(U_5580)
      | ~ class_Fields_Ofield(U_5580) ),
    inference(definitional_conversion,[status(esa)],[f_1657_2]) ).

cnf(f_1657_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5580),U_5582),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5580),U_5583),U_5581)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5580),U_5581),U_5582)),U_5583)),U_5581)
    | U_5581 = c_Groups_Ozero__class_Ozero(U_5580)
    | ~ class_Fields_Ofield(U_5580) ),
    inference(clausify,[status(thm)],[f_1657_3]) ).

fof(f_1658_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_1658_2,plain,
    ! [U_5587,U_5586,U_5585,U_5584] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5584),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5584),U_5586),U_5585)),U_5587) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5584),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5584),U_5586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5584),U_5587),U_5585))),U_5585)
      | U_5585 = c_Groups_Ozero__class_Ozero(U_5584)
      | ~ class_Fields_Ofield__inverse__zero(U_5584) ),
    inference(variable_rename,[status(thm)],[f_1658_1]) ).

fof(f_1658_3,plain,
    ! [U_5584,U_5585,U_5586,U_5587] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5584),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5584),U_5586),U_5585)),U_5587) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5584),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5584),U_5586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5584),U_5587),U_5585))),U_5585)
      | U_5585 = c_Groups_Ozero__class_Ozero(U_5584)
      | ~ class_Fields_Ofield__inverse__zero(U_5584) ),
    inference(definitional_conversion,[status(esa)],[f_1658_2]) ).

cnf(f_1658_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5584),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5584),U_5586),U_5585)),U_5587) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5584),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5584),U_5586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5584),U_5587),U_5585))),U_5585)
    | U_5585 = c_Groups_Ozero__class_Ozero(U_5584)
    | ~ class_Fields_Ofield__inverse__zero(U_5584) ),
    inference(clausify,[status(thm)],[f_1658_3]) ).

fof(f_1659_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_1659_2,plain,
    ! [U_5591,U_5590,U_5589,U_5588] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5588),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5588),U_5590),U_5589)),U_5591) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5588),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5588),U_5590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5588),U_5589),U_5591))),U_5589)
      | U_5589 = c_Groups_Ozero__class_Ozero(U_5588)
      | ~ class_Fields_Ofield(U_5588) ),
    inference(variable_rename,[status(thm)],[f_1659_1]) ).

fof(f_1659_3,plain,
    ! [U_5588,U_5589,U_5590,U_5591] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5588),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5588),U_5590),U_5589)),U_5591) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5588),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5588),U_5590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5588),U_5589),U_5591))),U_5589)
      | U_5589 = c_Groups_Ozero__class_Ozero(U_5588)
      | ~ class_Fields_Ofield(U_5588) ),
    inference(definitional_conversion,[status(esa)],[f_1659_2]) ).

cnf(f_1659_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5588),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5588),U_5590),U_5589)),U_5591) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5588),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5588),U_5590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5588),U_5589),U_5591))),U_5589)
    | U_5589 = c_Groups_Ozero__class_Ozero(U_5588)
    | ~ class_Fields_Ofield(U_5588) ),
    inference(clausify,[status(thm)],[f_1659_3]) ).

fof(f_1660_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_1660_2,plain,
    ! [U_5596,U_5595,U_5594,U_5593,U_5592] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5592),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5592),U_5595),U_5593)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5592),U_5596),U_5594)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5592),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5592),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5592),U_5595),U_5594)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5592),U_5596),U_5593))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5592),U_5593),U_5594))
      | U_5594 = c_Groups_Ozero__class_Ozero(U_5592)
      | U_5593 = c_Groups_Ozero__class_Ozero(U_5592)
      | ~ class_Fields_Ofield(U_5592) ),
    inference(variable_rename,[status(thm)],[f_1660_1]) ).

fof(f_1660_3,plain,
    ! [U_5593,U_5592,U_5594,U_5595,U_5596] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5592),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5592),U_5595),U_5593)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5592),U_5596),U_5594)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5592),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5592),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5592),U_5595),U_5594)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5592),U_5596),U_5593))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5592),U_5593),U_5594))
      | U_5594 = c_Groups_Ozero__class_Ozero(U_5592)
      | U_5593 = c_Groups_Ozero__class_Ozero(U_5592)
      | ~ class_Fields_Ofield(U_5592) ),
    inference(definitional_conversion,[status(esa)],[f_1660_2]) ).

cnf(f_1660_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5592),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5592),U_5595),U_5593)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5592),U_5596),U_5594)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5592),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5592),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5592),U_5595),U_5594)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5592),U_5596),U_5593))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5592),U_5593),U_5594))
    | U_5594 = c_Groups_Ozero__class_Ozero(U_5592)
    | U_5593 = c_Groups_Ozero__class_Ozero(U_5592)
    | ~ class_Fields_Ofield(U_5592) ),
    inference(clausify,[status(thm)],[f_1660_3]) ).

fof(f_1661_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_1661_2,plain,
    ! [U_5601,U_5600,U_5599,U_5598,U_5597] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5597),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5597),U_5600),U_5598)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5597),U_5601),U_5599)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5597),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5597),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5600),U_5599)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5601),U_5598))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5598),U_5599))
      | U_5599 = c_Groups_Ozero__class_Ozero(U_5597)
      | U_5598 = c_Groups_Ozero__class_Ozero(U_5597)
      | ~ class_Fields_Ofield(U_5597) ),
    inference(variable_rename,[status(thm)],[f_1661_1]) ).

fof(f_1661_3,plain,
    ! [U_5597,U_5598,U_5599,U_5600,U_5601] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5597),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5597),U_5600),U_5598)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5597),U_5601),U_5599)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5597),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5597),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5600),U_5599)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5601),U_5598))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5598),U_5599))
      | U_5599 = c_Groups_Ozero__class_Ozero(U_5597)
      | U_5598 = c_Groups_Ozero__class_Ozero(U_5597)
      | ~ class_Fields_Ofield(U_5597) ),
    inference(definitional_conversion,[status(esa)],[f_1661_2]) ).

cnf(f_1661_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5597),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5597),U_5600),U_5598)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5597),U_5601),U_5599)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5597),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5597),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5600),U_5599)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5601),U_5598))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5597),U_5598),U_5599))
    | U_5599 = c_Groups_Ozero__class_Ozero(U_5597)
    | U_5598 = c_Groups_Ozero__class_Ozero(U_5597)
    | ~ class_Fields_Ofield(U_5597) ),
    inference(clausify,[status(thm)],[f_1661_3]) ).

fof(f_1662_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_1662_2,plain,
    ! [U_5605,U_5604,U_5603,U_5602] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5602),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5602),U_5604),U_5603)),U_5605) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5602),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5602),U_5604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5602),U_5603),U_5605))),U_5603)
      | U_5603 = c_Groups_Ozero__class_Ozero(U_5602)
      | ~ class_Fields_Ofield(U_5602) ),
    inference(variable_rename,[status(thm)],[f_1662_1]) ).

fof(f_1662_3,plain,
    ! [U_5602,U_5603,U_5604,U_5605] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5602),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5602),U_5604),U_5603)),U_5605) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5602),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5602),U_5604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5602),U_5603),U_5605))),U_5603)
      | U_5603 = c_Groups_Ozero__class_Ozero(U_5602)
      | ~ class_Fields_Ofield(U_5602) ),
    inference(definitional_conversion,[status(esa)],[f_1662_2]) ).

cnf(f_1662_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5602),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5602),U_5604),U_5603)),U_5605) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5602),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5602),U_5604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5602),U_5603),U_5605))),U_5603)
    | U_5603 = c_Groups_Ozero__class_Ozero(U_5602)
    | ~ class_Fields_Ofield(U_5602) ),
    inference(clausify,[status(thm)],[f_1662_3]) ).

fof(f_1663_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_1663_2,plain,
    ! [U_5609,U_5608,U_5607,U_5606] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5606),U_5608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5606),U_5609),U_5607)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5606),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5606),U_5607),U_5608)),U_5609)),U_5607)
      | U_5607 = c_Groups_Ozero__class_Ozero(U_5606)
      | ~ class_Fields_Ofield(U_5606) ),
    inference(variable_rename,[status(thm)],[f_1663_1]) ).

fof(f_1663_3,plain,
    ! [U_5606,U_5607,U_5608,U_5609] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5606),U_5608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5606),U_5609),U_5607)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5606),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5606),U_5607),U_5608)),U_5609)),U_5607)
      | U_5607 = c_Groups_Ozero__class_Ozero(U_5606)
      | ~ class_Fields_Ofield(U_5606) ),
    inference(definitional_conversion,[status(esa)],[f_1663_2]) ).

cnf(f_1663_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5606),U_5608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5606),U_5609),U_5607)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5606),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5606),U_5607),U_5608)),U_5609)),U_5607)
    | U_5607 = c_Groups_Ozero__class_Ozero(U_5606)
    | ~ class_Fields_Ofield(U_5606) ),
    inference(clausify,[status(thm)],[f_1663_3]) ).

fof(f_1664_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_1664_2,plain,
    ! [U_5613,U_5612,U_5611,U_5610] :
      ( ( ( U_5611 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5610),U_5612),hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613))
          | ( U_5611 != c_Groups_Ozero__class_Ozero(U_5610)
            & hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613) = c_Groups_Ozero__class_Ozero(U_5610) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5610),U_5611),hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613)) != U_5612
            & hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613) != c_Groups_Ozero__class_Ozero(U_5610) ) )
        & ( ( ( U_5611 = c_Groups_Ozero__class_Ozero(U_5610)
              | hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613) != c_Groups_Ozero__class_Ozero(U_5610) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5610),U_5611),hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613)) = U_5612
              | hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613) = c_Groups_Ozero__class_Ozero(U_5610) ) )
          | U_5611 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5610),U_5612),hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613)) ) )
      | ~ class_Int_Onumber(U_5610)
      | ~ class_Fields_Ofield__inverse__zero(U_5610) ),
    inference(variable_rename,[status(thm)],[f_1664_1]) ).

fof(f_1664_3,plain,
    ( ! [U_5610,U_5611,U_5613] :
        ( U_5611 != c_Groups_Ozero__class_Ozero(U_5610)
        | ~ sP461(U_5610,U_5611,U_5613) )
    & ! [U_5610,U_5611,U_5613] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613) = c_Groups_Ozero__class_Ozero(U_5610)
        | ~ sP461(U_5610,U_5611,U_5613) )
    & ! [U_5610,U_5611,U_5612,U_5613] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5610),U_5611),hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613)) != U_5612
        | ~ sP460(U_5610,U_5611,U_5612,U_5613) )
    & ! [U_5610,U_5611,U_5612,U_5613] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613) != c_Groups_Ozero__class_Ozero(U_5610)
        | ~ sP460(U_5610,U_5611,U_5612,U_5613) )
    & ! [U_5610,U_5611,U_5612,U_5613] :
        ( U_5611 = c_Groups_Ozero__class_Ozero(U_5610)
        | hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613) != c_Groups_Ozero__class_Ozero(U_5610)
        | ~ sP459(U_5610,U_5611,U_5612,U_5613) )
    & ! [U_5610,U_5611,U_5612,U_5613] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5610),U_5611),hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613)) = U_5612
        | hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613) = c_Groups_Ozero__class_Ozero(U_5610)
        | ~ sP459(U_5610,U_5611,U_5612,U_5613) )
    & ! [U_5610,U_5611,U_5612,U_5613] :
        ( U_5611 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5610),U_5612),hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613))
        | sP461(U_5610,U_5611,U_5613)
        | sP460(U_5610,U_5611,U_5612,U_5613)
        | ~ sP462(U_5610,U_5611,U_5612,U_5613) )
    & ! [U_5610,U_5611,U_5612,U_5613] :
        ( sP459(U_5610,U_5611,U_5612,U_5613)
        | U_5611 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5610),U_5612),hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613))
        | ~ sP462(U_5610,U_5611,U_5612,U_5613) )
    & ! [U_5610,U_5611,U_5612,U_5613] :
        ( sP462(U_5610,U_5611,U_5612,U_5613)
        | ~ class_Int_Onumber(U_5610)
        | ~ class_Fields_Ofield__inverse__zero(U_5610) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP459,sP460,sP461,sP462])],[f_1664_2]) ).

cnf(f_1664_4,plain,
    ( sP462(U_5610,U_5611,U_5612,U_5613)
    | ~ class_Int_Onumber(U_5610)
    | ~ class_Fields_Ofield__inverse__zero(U_5610) ),
    inference(clausify,[status(thm)],[f_1664_3]) ).

cnf(f_1664_5,plain,
    ( sP459(U_5610,U_5611,U_5612,U_5613)
    | U_5611 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5610),U_5612),hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613))
    | ~ sP462(U_5610,U_5611,U_5612,U_5613) ),
    inference(clausify,[status(thm)],[f_1664_3]) ).

cnf(f_1664_6,plain,
    ( U_5611 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5610),U_5612),hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613))
    | sP461(U_5610,U_5611,U_5613)
    | sP460(U_5610,U_5611,U_5612,U_5613)
    | ~ sP462(U_5610,U_5611,U_5612,U_5613) ),
    inference(clausify,[status(thm)],[f_1664_3]) ).

cnf(f_1664_7,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5610),U_5611),hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613)) = U_5612
    | hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613) = c_Groups_Ozero__class_Ozero(U_5610)
    | ~ sP459(U_5610,U_5611,U_5612,U_5613) ),
    inference(clausify,[status(thm)],[f_1664_3]) ).

cnf(f_1664_8,plain,
    ( U_5611 = c_Groups_Ozero__class_Ozero(U_5610)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613) != c_Groups_Ozero__class_Ozero(U_5610)
    | ~ sP459(U_5610,U_5611,U_5612,U_5613) ),
    inference(clausify,[status(thm)],[f_1664_3]) ).

cnf(f_1664_9,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613) != c_Groups_Ozero__class_Ozero(U_5610)
    | ~ sP460(U_5610,U_5611,U_5612,U_5613) ),
    inference(clausify,[status(thm)],[f_1664_3]) ).

cnf(f_1664_10,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5610),U_5611),hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613)) != U_5612
    | ~ sP460(U_5610,U_5611,U_5612,U_5613) ),
    inference(clausify,[status(thm)],[f_1664_3]) ).

cnf(f_1664_11,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5610),U_5613) = c_Groups_Ozero__class_Ozero(U_5610)
    | ~ sP461(U_5610,U_5611,U_5613) ),
    inference(clausify,[status(thm)],[f_1664_3]) ).

cnf(f_1664_12,plain,
    ( U_5611 != c_Groups_Ozero__class_Ozero(U_5610)
    | ~ sP461(U_5610,U_5611,U_5613) ),
    inference(clausify,[status(thm)],[f_1664_3]) ).

fof(f_1665_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_1665_2,plain,
    ! [U_5617,U_5616,U_5615,U_5614] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5614),U_5616),U_5617)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615) != c_Groups_Ozero__class_Ozero(U_5614)
            & U_5617 = c_Groups_Ozero__class_Ozero(U_5614) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615)),U_5617) != U_5616
            & U_5617 != c_Groups_Ozero__class_Ozero(U_5614) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615) = c_Groups_Ozero__class_Ozero(U_5614)
              | U_5617 != c_Groups_Ozero__class_Ozero(U_5614) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615)),U_5617) = U_5616
              | U_5617 = c_Groups_Ozero__class_Ozero(U_5614) ) )
          | hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5614),U_5616),U_5617) ) )
      | ~ class_Int_Onumber(U_5614)
      | ~ class_Fields_Ofield__inverse__zero(U_5614) ),
    inference(variable_rename,[status(thm)],[f_1665_1]) ).

fof(f_1665_3,plain,
    ( ! [U_5615,U_5614,U_5617] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615) != c_Groups_Ozero__class_Ozero(U_5614)
        | ~ sP465(U_5615,U_5614,U_5617) )
    & ! [U_5615,U_5614,U_5617] :
        ( U_5617 = c_Groups_Ozero__class_Ozero(U_5614)
        | ~ sP465(U_5615,U_5614,U_5617) )
    & ! [U_5615,U_5614,U_5616,U_5617] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615)),U_5617) != U_5616
        | ~ sP464(U_5615,U_5614,U_5616,U_5617) )
    & ! [U_5615,U_5614,U_5616,U_5617] :
        ( U_5617 != c_Groups_Ozero__class_Ozero(U_5614)
        | ~ sP464(U_5615,U_5614,U_5616,U_5617) )
    & ! [U_5615,U_5614,U_5616,U_5617] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615) = c_Groups_Ozero__class_Ozero(U_5614)
        | U_5617 != c_Groups_Ozero__class_Ozero(U_5614)
        | ~ sP463(U_5615,U_5614,U_5616,U_5617) )
    & ! [U_5615,U_5614,U_5616,U_5617] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615)),U_5617) = U_5616
        | U_5617 = c_Groups_Ozero__class_Ozero(U_5614)
        | ~ sP463(U_5615,U_5614,U_5616,U_5617) )
    & ! [U_5615,U_5614,U_5616,U_5617] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5614),U_5616),U_5617)
        | sP465(U_5615,U_5614,U_5617)
        | sP464(U_5615,U_5614,U_5616,U_5617)
        | ~ sP466(U_5615,U_5614,U_5616,U_5617) )
    & ! [U_5615,U_5614,U_5616,U_5617] :
        ( sP463(U_5615,U_5614,U_5616,U_5617)
        | hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5614),U_5616),U_5617)
        | ~ sP466(U_5615,U_5614,U_5616,U_5617) )
    & ! [U_5615,U_5614,U_5616,U_5617] :
        ( sP466(U_5615,U_5614,U_5616,U_5617)
        | ~ class_Int_Onumber(U_5614)
        | ~ class_Fields_Ofield__inverse__zero(U_5614) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP463,sP464,sP465,sP466])],[f_1665_2]) ).

cnf(f_1665_4,plain,
    ( sP466(U_5615,U_5614,U_5616,U_5617)
    | ~ class_Int_Onumber(U_5614)
    | ~ class_Fields_Ofield__inverse__zero(U_5614) ),
    inference(clausify,[status(thm)],[f_1665_3]) ).

cnf(f_1665_5,plain,
    ( sP463(U_5615,U_5614,U_5616,U_5617)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5614),U_5616),U_5617)
    | ~ sP466(U_5615,U_5614,U_5616,U_5617) ),
    inference(clausify,[status(thm)],[f_1665_3]) ).

cnf(f_1665_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5614),U_5616),U_5617)
    | sP465(U_5615,U_5614,U_5617)
    | sP464(U_5615,U_5614,U_5616,U_5617)
    | ~ sP466(U_5615,U_5614,U_5616,U_5617) ),
    inference(clausify,[status(thm)],[f_1665_3]) ).

cnf(f_1665_7,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615)),U_5617) = U_5616
    | U_5617 = c_Groups_Ozero__class_Ozero(U_5614)
    | ~ sP463(U_5615,U_5614,U_5616,U_5617) ),
    inference(clausify,[status(thm)],[f_1665_3]) ).

cnf(f_1665_8,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615) = c_Groups_Ozero__class_Ozero(U_5614)
    | U_5617 != c_Groups_Ozero__class_Ozero(U_5614)
    | ~ sP463(U_5615,U_5614,U_5616,U_5617) ),
    inference(clausify,[status(thm)],[f_1665_3]) ).

cnf(f_1665_9,plain,
    ( U_5617 != c_Groups_Ozero__class_Ozero(U_5614)
    | ~ sP464(U_5615,U_5614,U_5616,U_5617) ),
    inference(clausify,[status(thm)],[f_1665_3]) ).

cnf(f_1665_10,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615)),U_5617) != U_5616
    | ~ sP464(U_5615,U_5614,U_5616,U_5617) ),
    inference(clausify,[status(thm)],[f_1665_3]) ).

cnf(f_1665_11,plain,
    ( U_5617 = c_Groups_Ozero__class_Ozero(U_5614)
    | ~ sP465(U_5615,U_5614,U_5617) ),
    inference(clausify,[status(thm)],[f_1665_3]) ).

cnf(f_1665_12,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5614),U_5615) != c_Groups_Ozero__class_Ozero(U_5614)
    | ~ sP465(U_5615,U_5614,U_5617) ),
    inference(clausify,[status(thm)],[f_1665_3]) ).

fof(f_1666_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_1666_2,plain,
    ! [U_5621,U_5620,U_5619,U_5618] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5618),U_5619),U_5620) = hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621) != c_Groups_Ozero__class_Ozero(U_5618)
            & U_5620 = c_Groups_Ozero__class_Ozero(U_5618) )
          | ( U_5619 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5618),hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621)),U_5620)
            & U_5620 != c_Groups_Ozero__class_Ozero(U_5618) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621) = c_Groups_Ozero__class_Ozero(U_5618)
              | U_5620 != c_Groups_Ozero__class_Ozero(U_5618) )
            & ( U_5619 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5618),hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621)),U_5620)
              | U_5620 = c_Groups_Ozero__class_Ozero(U_5618) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5618),U_5619),U_5620) != hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621) ) )
      | ~ class_Int_Onumber(U_5618)
      | ~ class_Fields_Ofield__inverse__zero(U_5618) ),
    inference(variable_rename,[status(thm)],[f_1666_1]) ).

fof(f_1666_3,plain,
    ( ! [U_5618,U_5620,U_5621] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621) != c_Groups_Ozero__class_Ozero(U_5618)
        | ~ sP469(U_5618,U_5620,U_5621) )
    & ! [U_5618,U_5620,U_5621] :
        ( U_5620 = c_Groups_Ozero__class_Ozero(U_5618)
        | ~ sP469(U_5618,U_5620,U_5621) )
    & ! [U_5618,U_5619,U_5620,U_5621] :
        ( U_5619 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5618),hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621)),U_5620)
        | ~ sP468(U_5618,U_5619,U_5620,U_5621) )
    & ! [U_5618,U_5619,U_5620,U_5621] :
        ( U_5620 != c_Groups_Ozero__class_Ozero(U_5618)
        | ~ sP468(U_5618,U_5619,U_5620,U_5621) )
    & ! [U_5618,U_5619,U_5620,U_5621] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621) = c_Groups_Ozero__class_Ozero(U_5618)
        | U_5620 != c_Groups_Ozero__class_Ozero(U_5618)
        | ~ sP467(U_5618,U_5619,U_5620,U_5621) )
    & ! [U_5618,U_5619,U_5620,U_5621] :
        ( U_5619 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5618),hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621)),U_5620)
        | U_5620 = c_Groups_Ozero__class_Ozero(U_5618)
        | ~ sP467(U_5618,U_5619,U_5620,U_5621) )
    & ! [U_5618,U_5619,U_5620,U_5621] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5618),U_5619),U_5620) = hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621)
        | sP469(U_5618,U_5620,U_5621)
        | sP468(U_5618,U_5619,U_5620,U_5621)
        | ~ sP470(U_5618,U_5619,U_5620,U_5621) )
    & ! [U_5618,U_5619,U_5620,U_5621] :
        ( sP467(U_5618,U_5619,U_5620,U_5621)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5618),U_5619),U_5620) != hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621)
        | ~ sP470(U_5618,U_5619,U_5620,U_5621) )
    & ! [U_5618,U_5619,U_5620,U_5621] :
        ( sP470(U_5618,U_5619,U_5620,U_5621)
        | ~ class_Int_Onumber(U_5618)
        | ~ class_Fields_Ofield__inverse__zero(U_5618) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP467,sP468,sP469,sP470])],[f_1666_2]) ).

cnf(f_1666_4,plain,
    ( sP470(U_5618,U_5619,U_5620,U_5621)
    | ~ class_Int_Onumber(U_5618)
    | ~ class_Fields_Ofield__inverse__zero(U_5618) ),
    inference(clausify,[status(thm)],[f_1666_3]) ).

cnf(f_1666_5,plain,
    ( sP467(U_5618,U_5619,U_5620,U_5621)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5618),U_5619),U_5620) != hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621)
    | ~ sP470(U_5618,U_5619,U_5620,U_5621) ),
    inference(clausify,[status(thm)],[f_1666_3]) ).

cnf(f_1666_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5618),U_5619),U_5620) = hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621)
    | sP469(U_5618,U_5620,U_5621)
    | sP468(U_5618,U_5619,U_5620,U_5621)
    | ~ sP470(U_5618,U_5619,U_5620,U_5621) ),
    inference(clausify,[status(thm)],[f_1666_3]) ).

cnf(f_1666_7,plain,
    ( U_5619 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5618),hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621)),U_5620)
    | U_5620 = c_Groups_Ozero__class_Ozero(U_5618)
    | ~ sP467(U_5618,U_5619,U_5620,U_5621) ),
    inference(clausify,[status(thm)],[f_1666_3]) ).

cnf(f_1666_8,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621) = c_Groups_Ozero__class_Ozero(U_5618)
    | U_5620 != c_Groups_Ozero__class_Ozero(U_5618)
    | ~ sP467(U_5618,U_5619,U_5620,U_5621) ),
    inference(clausify,[status(thm)],[f_1666_3]) ).

cnf(f_1666_9,plain,
    ( U_5620 != c_Groups_Ozero__class_Ozero(U_5618)
    | ~ sP468(U_5618,U_5619,U_5620,U_5621) ),
    inference(clausify,[status(thm)],[f_1666_3]) ).

cnf(f_1666_10,plain,
    ( U_5619 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5618),hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621)),U_5620)
    | ~ sP468(U_5618,U_5619,U_5620,U_5621) ),
    inference(clausify,[status(thm)],[f_1666_3]) ).

cnf(f_1666_11,plain,
    ( U_5620 = c_Groups_Ozero__class_Ozero(U_5618)
    | ~ sP469(U_5618,U_5620,U_5621) ),
    inference(clausify,[status(thm)],[f_1666_3]) ).

cnf(f_1666_12,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5618),U_5621) != c_Groups_Ozero__class_Ozero(U_5618)
    | ~ sP469(U_5618,U_5620,U_5621) ),
    inference(clausify,[status(thm)],[f_1666_3]) ).

fof(f_1667_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_1667_2,plain,
    ! [U_5625,U_5624,U_5623,U_5622] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5622),U_5623),hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624)) = U_5625
          | ( U_5625 != c_Groups_Ozero__class_Ozero(U_5622)
            & hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624) = c_Groups_Ozero__class_Ozero(U_5622) )
          | ( U_5623 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5622),U_5625),hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624))
            & hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624) != c_Groups_Ozero__class_Ozero(U_5622) ) )
        & ( ( ( U_5625 = c_Groups_Ozero__class_Ozero(U_5622)
              | hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624) != c_Groups_Ozero__class_Ozero(U_5622) )
            & ( U_5623 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5622),U_5625),hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624))
              | hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624) = c_Groups_Ozero__class_Ozero(U_5622) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5622),U_5623),hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624)) != U_5625 ) )
      | ~ class_Int_Onumber(U_5622)
      | ~ class_Fields_Ofield__inverse__zero(U_5622) ),
    inference(variable_rename,[status(thm)],[f_1667_1]) ).

fof(f_1667_3,plain,
    ( ! [U_5622,U_5625,U_5624] :
        ( U_5625 != c_Groups_Ozero__class_Ozero(U_5622)
        | ~ sP473(U_5622,U_5625,U_5624) )
    & ! [U_5622,U_5625,U_5624] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624) = c_Groups_Ozero__class_Ozero(U_5622)
        | ~ sP473(U_5622,U_5625,U_5624) )
    & ! [U_5622,U_5623,U_5625,U_5624] :
        ( U_5623 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5622),U_5625),hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624))
        | ~ sP472(U_5622,U_5623,U_5625,U_5624) )
    & ! [U_5622,U_5623,U_5625,U_5624] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624) != c_Groups_Ozero__class_Ozero(U_5622)
        | ~ sP472(U_5622,U_5623,U_5625,U_5624) )
    & ! [U_5622,U_5623,U_5625,U_5624] :
        ( U_5625 = c_Groups_Ozero__class_Ozero(U_5622)
        | hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624) != c_Groups_Ozero__class_Ozero(U_5622)
        | ~ sP471(U_5622,U_5623,U_5625,U_5624) )
    & ! [U_5622,U_5623,U_5625,U_5624] :
        ( U_5623 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5622),U_5625),hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624))
        | hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624) = c_Groups_Ozero__class_Ozero(U_5622)
        | ~ sP471(U_5622,U_5623,U_5625,U_5624) )
    & ! [U_5622,U_5623,U_5625,U_5624] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5622),U_5623),hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624)) = U_5625
        | sP473(U_5622,U_5625,U_5624)
        | sP472(U_5622,U_5623,U_5625,U_5624)
        | ~ sP474(U_5622,U_5623,U_5625,U_5624) )
    & ! [U_5622,U_5623,U_5625,U_5624] :
        ( sP471(U_5622,U_5623,U_5625,U_5624)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5622),U_5623),hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624)) != U_5625
        | ~ sP474(U_5622,U_5623,U_5625,U_5624) )
    & ! [U_5622,U_5623,U_5625,U_5624] :
        ( sP474(U_5622,U_5623,U_5625,U_5624)
        | ~ class_Int_Onumber(U_5622)
        | ~ class_Fields_Ofield__inverse__zero(U_5622) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP471,sP472,sP473,sP474])],[f_1667_2]) ).

cnf(f_1667_4,plain,
    ( sP474(U_5622,U_5623,U_5625,U_5624)
    | ~ class_Int_Onumber(U_5622)
    | ~ class_Fields_Ofield__inverse__zero(U_5622) ),
    inference(clausify,[status(thm)],[f_1667_3]) ).

cnf(f_1667_5,plain,
    ( sP471(U_5622,U_5623,U_5625,U_5624)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5622),U_5623),hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624)) != U_5625
    | ~ sP474(U_5622,U_5623,U_5625,U_5624) ),
    inference(clausify,[status(thm)],[f_1667_3]) ).

cnf(f_1667_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5622),U_5623),hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624)) = U_5625
    | sP473(U_5622,U_5625,U_5624)
    | sP472(U_5622,U_5623,U_5625,U_5624)
    | ~ sP474(U_5622,U_5623,U_5625,U_5624) ),
    inference(clausify,[status(thm)],[f_1667_3]) ).

cnf(f_1667_7,plain,
    ( U_5623 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5622),U_5625),hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624) = c_Groups_Ozero__class_Ozero(U_5622)
    | ~ sP471(U_5622,U_5623,U_5625,U_5624) ),
    inference(clausify,[status(thm)],[f_1667_3]) ).

cnf(f_1667_8,plain,
    ( U_5625 = c_Groups_Ozero__class_Ozero(U_5622)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624) != c_Groups_Ozero__class_Ozero(U_5622)
    | ~ sP471(U_5622,U_5623,U_5625,U_5624) ),
    inference(clausify,[status(thm)],[f_1667_3]) ).

cnf(f_1667_9,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624) != c_Groups_Ozero__class_Ozero(U_5622)
    | ~ sP472(U_5622,U_5623,U_5625,U_5624) ),
    inference(clausify,[status(thm)],[f_1667_3]) ).

cnf(f_1667_10,plain,
    ( U_5623 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5622),U_5625),hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624))
    | ~ sP472(U_5622,U_5623,U_5625,U_5624) ),
    inference(clausify,[status(thm)],[f_1667_3]) ).

cnf(f_1667_11,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5622),U_5624) = c_Groups_Ozero__class_Ozero(U_5622)
    | ~ sP473(U_5622,U_5625,U_5624) ),
    inference(clausify,[status(thm)],[f_1667_3]) ).

cnf(f_1667_12,plain,
    ( U_5625 != c_Groups_Ozero__class_Ozero(U_5622)
    | ~ sP473(U_5622,U_5625,U_5624) ),
    inference(clausify,[status(thm)],[f_1667_3]) ).

fof(f_1668_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_1668_2,plain,
    ! [U_5628,U_5627,U_5626] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5626),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5626),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5626),U_5627),U_5628)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5626),c_Groups_Oone__class_Oone(U_5626)),c_Groups_Oone__class_Oone(U_5626)))),U_5628))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5626),U_5627),U_5628))
      | ~ class_Fields_Olinordered__field(U_5626) ),
    inference(variable_rename,[status(thm)],[f_1668_1]) ).

fof(f_1668_3,plain,
    ! [U_5627,U_5628,U_5626] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5626),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5626),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5626),U_5627),U_5628)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5626),c_Groups_Oone__class_Oone(U_5626)),c_Groups_Oone__class_Oone(U_5626)))),U_5628))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5626),U_5627),U_5628))
      | ~ class_Fields_Olinordered__field(U_5626) ),
    inference(definitional_conversion,[status(esa)],[f_1668_2]) ).

cnf(f_1668_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5626),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5626),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5626),U_5627),U_5628)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5626),c_Groups_Oone__class_Oone(U_5626)),c_Groups_Oone__class_Oone(U_5626)))),U_5628))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5626),U_5627),U_5628))
    | ~ class_Fields_Olinordered__field(U_5626) ),
    inference(clausify,[status(thm)],[f_1668_3]) ).

fof(f_1669_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_1669_2,plain,
    ! [U_5631,U_5630,U_5629] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5629),U_5630),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5629),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5629),U_5630),U_5631)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5629),c_Groups_Oone__class_Oone(U_5629)),c_Groups_Oone__class_Oone(U_5629)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5629),U_5630),U_5631))
      | ~ class_Fields_Olinordered__field(U_5629) ),
    inference(variable_rename,[status(thm)],[f_1669_1]) ).

fof(f_1669_3,plain,
    ! [U_5630,U_5629,U_5631] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5629),U_5630),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5629),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5629),U_5630),U_5631)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5629),c_Groups_Oone__class_Oone(U_5629)),c_Groups_Oone__class_Oone(U_5629)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5629),U_5630),U_5631))
      | ~ class_Fields_Olinordered__field(U_5629) ),
    inference(definitional_conversion,[status(esa)],[f_1669_2]) ).

cnf(f_1669_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5629),U_5630),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5629),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5629),U_5630),U_5631)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5629),c_Groups_Oone__class_Oone(U_5629)),c_Groups_Oone__class_Oone(U_5629)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5629),U_5630),U_5631))
    | ~ class_Fields_Olinordered__field(U_5629) ),
    inference(clausify,[status(thm)],[f_1669_3]) ).

fof(f_1670_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_1670_2,plain,
    ! [U_5633,U_5632] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5632),U_5633),hAPP(c_Int_Onumber__class_Onumber__of(U_5632),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_5632)
      | ~ class_Int_Onumber__ring(U_5632)
      | ~ class_Fields_Ofield__inverse__zero(U_5632) ),
    inference(variable_rename,[status(thm)],[f_1670_1]) ).

fof(f_1670_3,plain,
    ! [U_5632,U_5633] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5632),U_5633),hAPP(c_Int_Onumber__class_Onumber__of(U_5632),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_5632)
      | ~ class_Int_Onumber__ring(U_5632)
      | ~ class_Fields_Ofield__inverse__zero(U_5632) ),
    inference(definitional_conversion,[status(esa)],[f_1670_2]) ).

cnf(f_1670_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5632),U_5633),hAPP(c_Int_Onumber__class_Onumber__of(U_5632),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_5632)
    | ~ class_Int_Onumber__ring(U_5632)
    | ~ class_Fields_Ofield__inverse__zero(U_5632) ),
    inference(clausify,[status(thm)],[f_1670_3]) ).

fof(f_1671_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_1671_2,plain,
    ! [U_5636,U_5635,U_5634] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5634),hAPP(c_Groups_Oabs__class_Oabs(U_5634),U_5636)),U_5635) = hAPP(c_Groups_Oabs__class_Oabs(U_5634),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5634),U_5636),U_5635))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5634),c_Groups_Ozero__class_Ozero(U_5634)),U_5635))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5634) ),
    inference(variable_rename,[status(thm)],[f_1671_1]) ).

fof(f_1671_3,plain,
    ! [U_5634,U_5635,U_5636] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5634),hAPP(c_Groups_Oabs__class_Oabs(U_5634),U_5636)),U_5635) = hAPP(c_Groups_Oabs__class_Oabs(U_5634),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5634),U_5636),U_5635))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5634),c_Groups_Ozero__class_Ozero(U_5634)),U_5635))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5634) ),
    inference(definitional_conversion,[status(esa)],[f_1671_2]) ).

cnf(f_1671_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5634),hAPP(c_Groups_Oabs__class_Oabs(U_5634),U_5636)),U_5635) = hAPP(c_Groups_Oabs__class_Oabs(U_5634),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5634),U_5636),U_5635))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5634),c_Groups_Ozero__class_Ozero(U_5634)),U_5635))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5634) ),
    inference(clausify,[status(thm)],[f_1671_3]) ).

fof(f_1672_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_1672_2,plain,
    ! [U_5638,U_5637] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5637),U_5638),hAPP(c_Int_Onumber__class_Onumber__of(U_5637),c_Int_OBit1(c_Int_OPls))) = U_5638
      | ~ class_Int_Onumber__ring(U_5637)
      | ~ class_Fields_Ofield(U_5637) ),
    inference(variable_rename,[status(thm)],[f_1672_1]) ).

fof(f_1672_3,plain,
    ! [U_5638,U_5637] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5637),U_5638),hAPP(c_Int_Onumber__class_Onumber__of(U_5637),c_Int_OBit1(c_Int_OPls))) = U_5638
      | ~ class_Int_Onumber__ring(U_5637)
      | ~ class_Fields_Ofield(U_5637) ),
    inference(definitional_conversion,[status(esa)],[f_1672_2]) ).

cnf(f_1672_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5637),U_5638),hAPP(c_Int_Onumber__class_Onumber__of(U_5637),c_Int_OBit1(c_Int_OPls))) = U_5638
    | ~ class_Int_Onumber__ring(U_5637)
    | ~ class_Fields_Ofield(U_5637) ),
    inference(clausify,[status(thm)],[f_1672_3]) ).

fof(f_1673_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_1673_2,plain,
    ! [U_5640,U_5639] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5639),U_5640),hAPP(c_Int_Onumber__class_Onumber__of(U_5639),c_Int_OBit1(c_Int_OPls))) = U_5640
      | ~ class_Int_Onumber__ring(U_5639)
      | ~ class_Fields_Ofield(U_5639) ),
    inference(variable_rename,[status(thm)],[f_1673_1]) ).

fof(f_1673_3,plain,
    ! [U_5639,U_5640] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5639),U_5640),hAPP(c_Int_Onumber__class_Onumber__of(U_5639),c_Int_OBit1(c_Int_OPls))) = U_5640
      | ~ class_Int_Onumber__ring(U_5639)
      | ~ class_Fields_Ofield(U_5639) ),
    inference(definitional_conversion,[status(esa)],[f_1673_2]) ).

cnf(f_1673_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5639),U_5640),hAPP(c_Int_Onumber__class_Onumber__of(U_5639),c_Int_OBit1(c_Int_OPls))) = U_5640
    | ~ class_Int_Onumber__ring(U_5639)
    | ~ class_Fields_Ofield(U_5639) ),
    inference(clausify,[status(thm)],[f_1673_3]) ).

fof(f_1674_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_1674_2,plain,
    ! [U_5642,U_5641] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5641),U_5642),hAPP(c_Int_Onumber__class_Onumber__of(U_5641),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5641),U_5642)
      | ~ class_Int_Onumber__ring(U_5641)
      | ~ class_Fields_Ofield__inverse__zero(U_5641) ),
    inference(variable_rename,[status(thm)],[f_1674_1]) ).

fof(f_1674_3,plain,
    ! [U_5641,U_5642] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5641),U_5642),hAPP(c_Int_Onumber__class_Onumber__of(U_5641),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5641),U_5642)
      | ~ class_Int_Onumber__ring(U_5641)
      | ~ class_Fields_Ofield__inverse__zero(U_5641) ),
    inference(definitional_conversion,[status(esa)],[f_1674_2]) ).

cnf(f_1674_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5641),U_5642),hAPP(c_Int_Onumber__class_Onumber__of(U_5641),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5641),U_5642)
    | ~ class_Int_Onumber__ring(U_5641)
    | ~ class_Fields_Ofield__inverse__zero(U_5641) ),
    inference(clausify,[status(thm)],[f_1674_3]) ).

fof(f_1675_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_1675_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_1675_1]) ).

cnf(f_1675_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_1675_2]) ).

fof(f_1676_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_1676_2,plain,
    ! [U_5646,U_5645,U_5644,U_5643] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5644),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5643),U_5645),U_5646)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5644),c_Groups_Ozero__class_Ozero(U_5643)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),U_5646),c_Groups_Ozero__class_Ozero(U_5643))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5643),U_5644),U_5646)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),U_5646),c_Groups_Ozero__class_Ozero(U_5643))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),c_Groups_Ozero__class_Ozero(U_5643)),U_5646)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5643),U_5644),U_5646)),U_5645))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),c_Groups_Ozero__class_Ozero(U_5643)),U_5646)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5644),c_Groups_Ozero__class_Ozero(U_5643)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),U_5646),c_Groups_Ozero__class_Ozero(U_5643))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5643),U_5644),U_5646)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),U_5646),c_Groups_Ozero__class_Ozero(U_5643))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),c_Groups_Ozero__class_Ozero(U_5643)),U_5646)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5643),U_5644),U_5646)),U_5645))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),c_Groups_Ozero__class_Ozero(U_5643)),U_5646)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5644),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5643),U_5645),U_5646))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5643) ),
    inference(variable_rename,[status(thm)],[f_1676_1]) ).

fof(f_1676_3,plain,
    ( ! [U_5643,U_5644,U_5646] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5644),c_Groups_Ozero__class_Ozero(U_5643)))
        | ~ sP479(U_5643,U_5644,U_5646) )
    & ! [U_5643,U_5644,U_5646] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),U_5646),c_Groups_Ozero__class_Ozero(U_5643)))
        | ~ sP479(U_5643,U_5644,U_5646) )
    & ! [U_5643,U_5644,U_5645,U_5646] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5643),U_5644),U_5646)))
        | ~ sP478(U_5643,U_5644,U_5645,U_5646) )
    & ! [U_5643,U_5644,U_5645,U_5646] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),U_5646),c_Groups_Ozero__class_Ozero(U_5643)))
        | ~ sP478(U_5643,U_5644,U_5645,U_5646) )
    & ! [U_5643,U_5644,U_5645,U_5646] :
        ( sP479(U_5643,U_5644,U_5646)
        | sP478(U_5643,U_5644,U_5645,U_5646)
        | ~ sP480(U_5643,U_5644,U_5645,U_5646) )
    & ! [U_5643,U_5644,U_5645,U_5646] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),c_Groups_Ozero__class_Ozero(U_5643)),U_5646))
        | ~ sP480(U_5643,U_5644,U_5645,U_5646) )
    & ! [U_5643,U_5644,U_5645,U_5646] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5643),U_5644),U_5646)),U_5645))
        | ~ sP477(U_5643,U_5644,U_5645,U_5646) )
    & ! [U_5643,U_5644,U_5645,U_5646] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),c_Groups_Ozero__class_Ozero(U_5643)),U_5646))
        | ~ sP477(U_5643,U_5644,U_5645,U_5646) )
    & ! [U_5643,U_5644,U_5645,U_5646] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5644),c_Groups_Ozero__class_Ozero(U_5643)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),U_5646),c_Groups_Ozero__class_Ozero(U_5643)))
        | ~ sP475(U_5643,U_5644,U_5645,U_5646) )
    & ! [U_5643,U_5644,U_5645,U_5646] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5643),U_5644),U_5646)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),U_5646),c_Groups_Ozero__class_Ozero(U_5643)))
        | ~ sP475(U_5643,U_5644,U_5645,U_5646) )
    & ! [U_5643,U_5644,U_5645,U_5646] :
        ( sP475(U_5643,U_5644,U_5645,U_5646)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),c_Groups_Ozero__class_Ozero(U_5643)),U_5646))
        | ~ sP476(U_5643,U_5644,U_5645,U_5646) )
    & ! [U_5643,U_5644,U_5645,U_5646] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5643),U_5644),U_5646)),U_5645))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),c_Groups_Ozero__class_Ozero(U_5643)),U_5646))
        | ~ sP476(U_5643,U_5644,U_5645,U_5646) )
    & ! [U_5643,U_5644,U_5645,U_5646] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5644),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5643),U_5645),U_5646)))
        | sP480(U_5643,U_5644,U_5645,U_5646)
        | sP477(U_5643,U_5644,U_5645,U_5646)
        | ~ sP481(U_5643,U_5644,U_5645,U_5646) )
    & ! [U_5643,U_5644,U_5645,U_5646] :
        ( sP476(U_5643,U_5644,U_5645,U_5646)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5644),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5643),U_5645),U_5646)))
        | ~ sP481(U_5643,U_5644,U_5645,U_5646) )
    & ! [U_5643,U_5644,U_5645,U_5646] :
        ( sP481(U_5643,U_5644,U_5645,U_5646)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5643) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP475,sP476,sP477,sP478,sP479,sP480,sP481])],[f_1676_2]) ).

cnf(f_1676_4,plain,
    ( sP481(U_5643,U_5644,U_5645,U_5646)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5643) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

cnf(f_1676_5,plain,
    ( sP476(U_5643,U_5644,U_5645,U_5646)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5644),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5643),U_5645),U_5646)))
    | ~ sP481(U_5643,U_5644,U_5645,U_5646) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

cnf(f_1676_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5644),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5643),U_5645),U_5646)))
    | sP480(U_5643,U_5644,U_5645,U_5646)
    | sP477(U_5643,U_5644,U_5645,U_5646)
    | ~ sP481(U_5643,U_5644,U_5645,U_5646) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

cnf(f_1676_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5643),U_5644),U_5646)),U_5645))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),c_Groups_Ozero__class_Ozero(U_5643)),U_5646))
    | ~ sP476(U_5643,U_5644,U_5645,U_5646) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

cnf(f_1676_8,plain,
    ( sP475(U_5643,U_5644,U_5645,U_5646)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),c_Groups_Ozero__class_Ozero(U_5643)),U_5646))
    | ~ sP476(U_5643,U_5644,U_5645,U_5646) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

cnf(f_1676_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5643),U_5644),U_5646)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),U_5646),c_Groups_Ozero__class_Ozero(U_5643)))
    | ~ sP475(U_5643,U_5644,U_5645,U_5646) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

cnf(f_1676_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5644),c_Groups_Ozero__class_Ozero(U_5643)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),U_5646),c_Groups_Ozero__class_Ozero(U_5643)))
    | ~ sP475(U_5643,U_5644,U_5645,U_5646) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

cnf(f_1676_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),c_Groups_Ozero__class_Ozero(U_5643)),U_5646))
    | ~ sP477(U_5643,U_5644,U_5645,U_5646) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

cnf(f_1676_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5643),U_5644),U_5646)),U_5645))
    | ~ sP477(U_5643,U_5644,U_5645,U_5646) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

cnf(f_1676_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),c_Groups_Ozero__class_Ozero(U_5643)),U_5646))
    | ~ sP480(U_5643,U_5644,U_5645,U_5646) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

cnf(f_1676_14,plain,
    ( sP479(U_5643,U_5644,U_5646)
    | sP478(U_5643,U_5644,U_5645,U_5646)
    | ~ sP480(U_5643,U_5644,U_5645,U_5646) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

cnf(f_1676_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),U_5646),c_Groups_Ozero__class_Ozero(U_5643)))
    | ~ sP478(U_5643,U_5644,U_5645,U_5646) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

cnf(f_1676_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5643),U_5644),U_5646)))
    | ~ sP478(U_5643,U_5644,U_5645,U_5646) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

cnf(f_1676_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5643),U_5646),c_Groups_Ozero__class_Ozero(U_5643)))
    | ~ sP479(U_5643,U_5644,U_5646) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

cnf(f_1676_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5643),U_5644),c_Groups_Ozero__class_Ozero(U_5643)))
    | ~ sP479(U_5643,U_5644,U_5646) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

fof(f_1677_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_1677_2,plain,
    ! [U_5650,U_5649,U_5648,U_5647] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5647),U_5648),U_5649)),U_5650))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5650))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),U_5649),c_Groups_Ozero__class_Ozero(U_5647))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5650),U_5649)),U_5648))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),U_5649),c_Groups_Ozero__class_Ozero(U_5647))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5649)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),U_5648),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5650),U_5649)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5649)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5650))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),U_5649),c_Groups_Ozero__class_Ozero(U_5647))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5650),U_5649)),U_5648))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),U_5649),c_Groups_Ozero__class_Ozero(U_5647))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5649)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),U_5648),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5650),U_5649)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5649)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5647),U_5648),U_5649)),U_5650)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5647) ),
    inference(variable_rename,[status(thm)],[f_1677_1]) ).

fof(f_1677_3,plain,
    ( ! [U_5649,U_5650,U_5647] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5650))
        | ~ sP486(U_5649,U_5650,U_5647) )
    & ! [U_5649,U_5650,U_5647] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),U_5649),c_Groups_Ozero__class_Ozero(U_5647)))
        | ~ sP486(U_5649,U_5650,U_5647) )
    & ! [U_5649,U_5648,U_5650,U_5647] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5650),U_5649)),U_5648))
        | ~ sP485(U_5649,U_5648,U_5650,U_5647) )
    & ! [U_5649,U_5648,U_5650,U_5647] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),U_5649),c_Groups_Ozero__class_Ozero(U_5647)))
        | ~ sP485(U_5649,U_5648,U_5650,U_5647) )
    & ! [U_5649,U_5648,U_5650,U_5647] :
        ( sP486(U_5649,U_5650,U_5647)
        | sP485(U_5649,U_5648,U_5650,U_5647)
        | ~ sP487(U_5649,U_5648,U_5650,U_5647) )
    & ! [U_5649,U_5648,U_5650,U_5647] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5649))
        | ~ sP487(U_5649,U_5648,U_5650,U_5647) )
    & ! [U_5649,U_5648,U_5650,U_5647] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),U_5648),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5650),U_5649)))
        | ~ sP484(U_5649,U_5648,U_5650,U_5647) )
    & ! [U_5649,U_5648,U_5650,U_5647] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5649))
        | ~ sP484(U_5649,U_5648,U_5650,U_5647) )
    & ! [U_5649,U_5648,U_5650,U_5647] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5650))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),U_5649),c_Groups_Ozero__class_Ozero(U_5647)))
        | ~ sP482(U_5649,U_5648,U_5650,U_5647) )
    & ! [U_5649,U_5648,U_5650,U_5647] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5650),U_5649)),U_5648))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),U_5649),c_Groups_Ozero__class_Ozero(U_5647)))
        | ~ sP482(U_5649,U_5648,U_5650,U_5647) )
    & ! [U_5649,U_5648,U_5650,U_5647] :
        ( sP482(U_5649,U_5648,U_5650,U_5647)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5649))
        | ~ sP483(U_5649,U_5648,U_5650,U_5647) )
    & ! [U_5649,U_5648,U_5650,U_5647] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),U_5648),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5650),U_5649)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5649))
        | ~ sP483(U_5649,U_5648,U_5650,U_5647) )
    & ! [U_5649,U_5648,U_5650,U_5647] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5647),U_5648),U_5649)),U_5650))
        | sP487(U_5649,U_5648,U_5650,U_5647)
        | sP484(U_5649,U_5648,U_5650,U_5647)
        | ~ sP488(U_5649,U_5648,U_5650,U_5647) )
    & ! [U_5649,U_5648,U_5650,U_5647] :
        ( sP483(U_5649,U_5648,U_5650,U_5647)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5647),U_5648),U_5649)),U_5650))
        | ~ sP488(U_5649,U_5648,U_5650,U_5647) )
    & ! [U_5649,U_5648,U_5650,U_5647] :
        ( sP488(U_5649,U_5648,U_5650,U_5647)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5647) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP482,sP483,sP484,sP485,sP486,sP487,sP488])],[f_1677_2]) ).

cnf(f_1677_4,plain,
    ( sP488(U_5649,U_5648,U_5650,U_5647)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5647) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

cnf(f_1677_5,plain,
    ( sP483(U_5649,U_5648,U_5650,U_5647)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5647),U_5648),U_5649)),U_5650))
    | ~ sP488(U_5649,U_5648,U_5650,U_5647) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

cnf(f_1677_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5647),U_5648),U_5649)),U_5650))
    | sP487(U_5649,U_5648,U_5650,U_5647)
    | sP484(U_5649,U_5648,U_5650,U_5647)
    | ~ sP488(U_5649,U_5648,U_5650,U_5647) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

cnf(f_1677_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),U_5648),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5650),U_5649)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5649))
    | ~ sP483(U_5649,U_5648,U_5650,U_5647) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

cnf(f_1677_8,plain,
    ( sP482(U_5649,U_5648,U_5650,U_5647)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5649))
    | ~ sP483(U_5649,U_5648,U_5650,U_5647) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

cnf(f_1677_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5650),U_5649)),U_5648))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),U_5649),c_Groups_Ozero__class_Ozero(U_5647)))
    | ~ sP482(U_5649,U_5648,U_5650,U_5647) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

cnf(f_1677_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5650))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),U_5649),c_Groups_Ozero__class_Ozero(U_5647)))
    | ~ sP482(U_5649,U_5648,U_5650,U_5647) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

cnf(f_1677_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5649))
    | ~ sP484(U_5649,U_5648,U_5650,U_5647) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

cnf(f_1677_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),U_5648),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5650),U_5649)))
    | ~ sP484(U_5649,U_5648,U_5650,U_5647) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

cnf(f_1677_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5649))
    | ~ sP487(U_5649,U_5648,U_5650,U_5647) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

cnf(f_1677_14,plain,
    ( sP486(U_5649,U_5650,U_5647)
    | sP485(U_5649,U_5648,U_5650,U_5647)
    | ~ sP487(U_5649,U_5648,U_5650,U_5647) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

cnf(f_1677_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),U_5649),c_Groups_Ozero__class_Ozero(U_5647)))
    | ~ sP485(U_5649,U_5648,U_5650,U_5647) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

cnf(f_1677_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5647),U_5650),U_5649)),U_5648))
    | ~ sP485(U_5649,U_5648,U_5650,U_5647) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

cnf(f_1677_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5647),U_5649),c_Groups_Ozero__class_Ozero(U_5647)))
    | ~ sP486(U_5649,U_5650,U_5647) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

cnf(f_1677_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5647),c_Groups_Ozero__class_Ozero(U_5647)),U_5650))
    | ~ sP486(U_5649,U_5650,U_5647) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

fof(f_1678_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_1678_2,plain,
    ! [U_5654,U_5653,U_5652,U_5651] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5651),U_5653),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5651),U_5654),U_5652)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5651),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5651),U_5653),U_5652)),U_5654)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5651),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5651),U_5653),U_5652)),U_5654))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5651),U_5653),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5651),U_5654),U_5652))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5651),c_Groups_Ozero__class_Ozero(U_5651)),U_5652))
      | ~ class_Fields_Olinordered__field(U_5651) ),
    inference(variable_rename,[status(thm)],[f_1678_1]) ).

fof(f_1678_3,plain,
    ( ! [U_5653,U_5652,U_5654,U_5651] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5651),U_5653),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5651),U_5654),U_5652)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5651),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5651),U_5653),U_5652)),U_5654))
        | ~ sP489(U_5653,U_5652,U_5654,U_5651) )
    & ! [U_5653,U_5652,U_5654,U_5651] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5651),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5651),U_5653),U_5652)),U_5654))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5651),U_5653),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5651),U_5654),U_5652)))
        | ~ sP489(U_5653,U_5652,U_5654,U_5651) )
    & ! [U_5653,U_5652,U_5654,U_5651] :
        ( sP489(U_5653,U_5652,U_5654,U_5651)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5651),c_Groups_Ozero__class_Ozero(U_5651)),U_5652))
        | ~ class_Fields_Olinordered__field(U_5651) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP489])],[f_1678_2]) ).

cnf(f_1678_4,plain,
    ( sP489(U_5653,U_5652,U_5654,U_5651)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5651),c_Groups_Ozero__class_Ozero(U_5651)),U_5652))
    | ~ class_Fields_Olinordered__field(U_5651) ),
    inference(clausify,[status(thm)],[f_1678_3]) ).

cnf(f_1678_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5651),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5651),U_5653),U_5652)),U_5654))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5651),U_5653),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5651),U_5654),U_5652)))
    | ~ sP489(U_5653,U_5652,U_5654,U_5651) ),
    inference(clausify,[status(thm)],[f_1678_3]) ).

cnf(f_1678_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5651),U_5653),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5651),U_5654),U_5652)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5651),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5651),U_5653),U_5652)),U_5654))
    | ~ sP489(U_5653,U_5652,U_5654,U_5651) ),
    inference(clausify,[status(thm)],[f_1678_3]) ).

fof(f_1679_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_1679_2,plain,
    ! [U_5658,U_5657,U_5656,U_5655] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5655),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5655),U_5657),U_5656)),U_5658))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5655),U_5657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5655),U_5658),U_5656))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5655),U_5657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5655),U_5658),U_5656)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5655),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5655),U_5657),U_5656)),U_5658)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5655),c_Groups_Ozero__class_Ozero(U_5655)),U_5656))
      | ~ class_Fields_Olinordered__field(U_5655) ),
    inference(variable_rename,[status(thm)],[f_1679_1]) ).

fof(f_1679_3,plain,
    ( ! [U_5658,U_5656,U_5655,U_5657] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5655),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5655),U_5657),U_5656)),U_5658))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5655),U_5657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5655),U_5658),U_5656)))
        | ~ sP490(U_5658,U_5656,U_5655,U_5657) )
    & ! [U_5658,U_5656,U_5655,U_5657] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5655),U_5657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5655),U_5658),U_5656)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5655),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5655),U_5657),U_5656)),U_5658))
        | ~ sP490(U_5658,U_5656,U_5655,U_5657) )
    & ! [U_5658,U_5656,U_5655,U_5657] :
        ( sP490(U_5658,U_5656,U_5655,U_5657)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5655),c_Groups_Ozero__class_Ozero(U_5655)),U_5656))
        | ~ class_Fields_Olinordered__field(U_5655) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP490])],[f_1679_2]) ).

cnf(f_1679_4,plain,
    ( sP490(U_5658,U_5656,U_5655,U_5657)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5655),c_Groups_Ozero__class_Ozero(U_5655)),U_5656))
    | ~ class_Fields_Olinordered__field(U_5655) ),
    inference(clausify,[status(thm)],[f_1679_3]) ).

cnf(f_1679_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5655),U_5657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5655),U_5658),U_5656)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5655),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5655),U_5657),U_5656)),U_5658))
    | ~ sP490(U_5658,U_5656,U_5655,U_5657) ),
    inference(clausify,[status(thm)],[f_1679_3]) ).

cnf(f_1679_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5655),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5655),U_5657),U_5656)),U_5658))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5655),U_5657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5655),U_5658),U_5656)))
    | ~ sP490(U_5658,U_5656,U_5655,U_5657) ),
    inference(clausify,[status(thm)],[f_1679_3]) ).

fof(f_1680_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_1680_2,plain,
    ! [U_5662,U_5661,U_5660,U_5659] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5659),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5659),U_5661),U_5660)),U_5662))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5659),U_5661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5659),U_5662),U_5660)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5659),c_Groups_Ozero__class_Ozero(U_5659)),U_5660))
      | ~ class_Fields_Olinordered__field(U_5659) ),
    inference(variable_rename,[status(thm)],[f_1680_1]) ).

fof(f_1680_3,plain,
    ! [U_5660,U_5661,U_5659,U_5662] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5659),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5659),U_5661),U_5660)),U_5662))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5659),U_5661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5659),U_5662),U_5660)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5659),c_Groups_Ozero__class_Ozero(U_5659)),U_5660))
      | ~ class_Fields_Olinordered__field(U_5659) ),
    inference(definitional_conversion,[status(esa)],[f_1680_2]) ).

cnf(f_1680_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5659),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5659),U_5661),U_5660)),U_5662))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5659),U_5661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5659),U_5662),U_5660)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5659),c_Groups_Ozero__class_Ozero(U_5659)),U_5660))
    | ~ class_Fields_Olinordered__field(U_5659) ),
    inference(clausify,[status(thm)],[f_1680_3]) ).

fof(f_1681_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_1681_2,plain,
    ! [U_5666,U_5665,U_5664,U_5663] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5663),U_5665),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5663),U_5666),U_5664)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5665),U_5664)),U_5666))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5663),c_Groups_Ozero__class_Ozero(U_5663)),U_5664))
      | ~ class_Fields_Olinordered__field(U_5663) ),
    inference(variable_rename,[status(thm)],[f_1681_1]) ).

fof(f_1681_3,plain,
    ! [U_5665,U_5663,U_5664,U_5666] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5663),U_5665),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5663),U_5666),U_5664)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5665),U_5664)),U_5666))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5663),c_Groups_Ozero__class_Ozero(U_5663)),U_5664))
      | ~ class_Fields_Olinordered__field(U_5663) ),
    inference(definitional_conversion,[status(esa)],[f_1681_2]) ).

cnf(f_1681_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5663),U_5665),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5663),U_5666),U_5664)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5663),U_5665),U_5664)),U_5666))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5663),c_Groups_Ozero__class_Ozero(U_5663)),U_5664))
    | ~ class_Fields_Olinordered__field(U_5663) ),
    inference(clausify,[status(thm)],[f_1681_3]) ).

fof(f_1682_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_1682_2,plain,
    ! [U_5670,U_5669,U_5668,U_5667] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),U_5669),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5667),U_5670),U_5668)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),U_5670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5667),U_5669),U_5668))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),U_5670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5667),U_5669),U_5668)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),U_5669),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5667),U_5670),U_5668))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5667),U_5668),c_Groups_Ozero__class_Ozero(U_5667)))
      | ~ class_Fields_Olinordered__field(U_5667) ),
    inference(variable_rename,[status(thm)],[f_1682_1]) ).

fof(f_1682_3,plain,
    ( ! [U_5667,U_5668,U_5669,U_5670] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),U_5669),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5667),U_5670),U_5668)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),U_5670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5667),U_5669),U_5668)))
        | ~ sP491(U_5667,U_5668,U_5669,U_5670) )
    & ! [U_5667,U_5668,U_5669,U_5670] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),U_5670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5667),U_5669),U_5668)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),U_5669),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5667),U_5670),U_5668)))
        | ~ sP491(U_5667,U_5668,U_5669,U_5670) )
    & ! [U_5667,U_5668,U_5669,U_5670] :
        ( sP491(U_5667,U_5668,U_5669,U_5670)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5667),U_5668),c_Groups_Ozero__class_Ozero(U_5667)))
        | ~ class_Fields_Olinordered__field(U_5667) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP491])],[f_1682_2]) ).

cnf(f_1682_4,plain,
    ( sP491(U_5667,U_5668,U_5669,U_5670)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5667),U_5668),c_Groups_Ozero__class_Ozero(U_5667)))
    | ~ class_Fields_Olinordered__field(U_5667) ),
    inference(clausify,[status(thm)],[f_1682_3]) ).

cnf(f_1682_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),U_5670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5667),U_5669),U_5668)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),U_5669),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5667),U_5670),U_5668)))
    | ~ sP491(U_5667,U_5668,U_5669,U_5670) ),
    inference(clausify,[status(thm)],[f_1682_3]) ).

cnf(f_1682_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),U_5669),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5667),U_5670),U_5668)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),U_5670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5667),U_5669),U_5668)))
    | ~ sP491(U_5667,U_5668,U_5669,U_5670) ),
    inference(clausify,[status(thm)],[f_1682_3]) ).

fof(f_1683_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_1683_2,plain,
    ! [U_5674,U_5673,U_5672,U_5671] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5671),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5671),U_5673),U_5672)),U_5674))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5671),U_5674),U_5672)),U_5673)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5671),U_5674),U_5672)),U_5673))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5671),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5671),U_5673),U_5672)),U_5674)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5671),U_5672),c_Groups_Ozero__class_Ozero(U_5671)))
      | ~ class_Fields_Olinordered__field(U_5671) ),
    inference(variable_rename,[status(thm)],[f_1683_1]) ).

fof(f_1683_3,plain,
    ( ! [U_5672,U_5673,U_5671,U_5674] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5671),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5671),U_5673),U_5672)),U_5674))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5671),U_5674),U_5672)),U_5673))
        | ~ sP492(U_5672,U_5673,U_5671,U_5674) )
    & ! [U_5672,U_5673,U_5671,U_5674] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5671),U_5674),U_5672)),U_5673))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5671),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5671),U_5673),U_5672)),U_5674))
        | ~ sP492(U_5672,U_5673,U_5671,U_5674) )
    & ! [U_5672,U_5673,U_5671,U_5674] :
        ( sP492(U_5672,U_5673,U_5671,U_5674)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5671),U_5672),c_Groups_Ozero__class_Ozero(U_5671)))
        | ~ class_Fields_Olinordered__field(U_5671) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP492])],[f_1683_2]) ).

cnf(f_1683_4,plain,
    ( sP492(U_5672,U_5673,U_5671,U_5674)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5671),U_5672),c_Groups_Ozero__class_Ozero(U_5671)))
    | ~ class_Fields_Olinordered__field(U_5671) ),
    inference(clausify,[status(thm)],[f_1683_3]) ).

cnf(f_1683_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5671),U_5674),U_5672)),U_5673))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5671),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5671),U_5673),U_5672)),U_5674))
    | ~ sP492(U_5672,U_5673,U_5671,U_5674) ),
    inference(clausify,[status(thm)],[f_1683_3]) ).

cnf(f_1683_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5671),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5671),U_5673),U_5672)),U_5674))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5671),U_5674),U_5672)),U_5673))
    | ~ sP492(U_5672,U_5673,U_5671,U_5674) ),
    inference(clausify,[status(thm)],[f_1683_3]) ).

fof(f_1684_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_1684_2,plain,
    ! [U_5678,U_5677,U_5676,U_5675] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5675),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5675),U_5678),U_5677)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5675),U_5678),U_5676)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5675),c_Groups_Ozero__class_Ozero(U_5675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5675),U_5677),U_5676)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5675),c_Groups_Ozero__class_Ozero(U_5675)),U_5678))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5675),U_5676),U_5677))
      | ~ class_Fields_Olinordered__field(U_5675) ),
    inference(variable_rename,[status(thm)],[f_1684_1]) ).

fof(f_1684_3,plain,
    ! [U_5675,U_5677,U_5676,U_5678] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5675),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5675),U_5678),U_5677)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5675),U_5678),U_5676)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5675),c_Groups_Ozero__class_Ozero(U_5675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5675),U_5677),U_5676)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5675),c_Groups_Ozero__class_Ozero(U_5675)),U_5678))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5675),U_5676),U_5677))
      | ~ class_Fields_Olinordered__field(U_5675) ),
    inference(definitional_conversion,[status(esa)],[f_1684_2]) ).

cnf(f_1684_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5675),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5675),U_5678),U_5677)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5675),U_5678),U_5676)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5675),c_Groups_Ozero__class_Ozero(U_5675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5675),U_5677),U_5676)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5675),c_Groups_Ozero__class_Ozero(U_5675)),U_5678))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5675),U_5676),U_5677))
    | ~ class_Fields_Olinordered__field(U_5675) ),
    inference(clausify,[status(thm)],[f_1684_3]) ).

fof(f_1685_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_1685_2,plain,
    ! [U_5682,U_5681,U_5680,U_5679] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5679),U_5682),U_5680)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5679),U_5682),U_5681)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5679),c_Groups_Ozero__class_Ozero(U_5679)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5679),U_5680),U_5681)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),U_5682),c_Groups_Ozero__class_Ozero(U_5679)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),U_5680),U_5681))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5679) ),
    inference(variable_rename,[status(thm)],[f_1685_1]) ).

fof(f_1685_3,plain,
    ! [U_5680,U_5679,U_5681,U_5682] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5679),U_5682),U_5680)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5679),U_5682),U_5681)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5679),c_Groups_Ozero__class_Ozero(U_5679)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5679),U_5680),U_5681)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),U_5682),c_Groups_Ozero__class_Ozero(U_5679)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),U_5680),U_5681))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5679) ),
    inference(definitional_conversion,[status(esa)],[f_1685_2]) ).

cnf(f_1685_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5679),U_5682),U_5680)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5679),U_5682),U_5681)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5679),c_Groups_Ozero__class_Ozero(U_5679)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5679),U_5680),U_5681)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),U_5682),c_Groups_Ozero__class_Ozero(U_5679)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5679),U_5680),U_5681))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5679) ),
    inference(clausify,[status(thm)],[f_1685_3]) ).

fof(f_1686_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_1686_2,plain,
    ! [U_5686,U_5685,U_5684,U_5683] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5683),U_5684),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))),U_5686))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),U_5686))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)),c_Groups_Ozero__class_Ozero(U_5683))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5683),U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))),U_5684))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)),c_Groups_Ozero__class_Ozero(U_5683))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),U_5684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5683),U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),U_5686))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)),c_Groups_Ozero__class_Ozero(U_5683))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5683),U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))),U_5684))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)),c_Groups_Ozero__class_Ozero(U_5683))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),U_5684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5683),U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5683),U_5684),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))),U_5686)) ) )
      | ~ class_Int_Onumber(U_5683)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5683) ),
    inference(variable_rename,[status(thm)],[f_1686_1]) ).

fof(f_1686_3,plain,
    ( ! [U_5683,U_5685,U_5686] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),U_5686))
        | ~ sP497(U_5683,U_5685,U_5686) )
    & ! [U_5683,U_5685,U_5686] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)),c_Groups_Ozero__class_Ozero(U_5683)))
        | ~ sP497(U_5683,U_5685,U_5686) )
    & ! [U_5683,U_5684,U_5685,U_5686] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5683),U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))),U_5684))
        | ~ sP496(U_5683,U_5684,U_5685,U_5686) )
    & ! [U_5683,U_5684,U_5685,U_5686] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)),c_Groups_Ozero__class_Ozero(U_5683)))
        | ~ sP496(U_5683,U_5684,U_5685,U_5686) )
    & ! [U_5683,U_5684,U_5685,U_5686] :
        ( sP497(U_5683,U_5685,U_5686)
        | sP496(U_5683,U_5684,U_5685,U_5686)
        | ~ sP498(U_5683,U_5684,U_5685,U_5686) )
    & ! [U_5683,U_5684,U_5685,U_5686] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)))
        | ~ sP498(U_5683,U_5684,U_5685,U_5686) )
    & ! [U_5683,U_5684,U_5685,U_5686] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),U_5684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5683),U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))))
        | ~ sP495(U_5683,U_5684,U_5685,U_5686) )
    & ! [U_5683,U_5684,U_5685,U_5686] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)))
        | ~ sP495(U_5683,U_5684,U_5685,U_5686) )
    & ! [U_5683,U_5684,U_5685,U_5686] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),U_5686))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)),c_Groups_Ozero__class_Ozero(U_5683)))
        | ~ sP493(U_5683,U_5684,U_5685,U_5686) )
    & ! [U_5683,U_5684,U_5685,U_5686] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5683),U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))),U_5684))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)),c_Groups_Ozero__class_Ozero(U_5683)))
        | ~ sP493(U_5683,U_5684,U_5685,U_5686) )
    & ! [U_5683,U_5684,U_5685,U_5686] :
        ( sP493(U_5683,U_5684,U_5685,U_5686)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)))
        | ~ sP494(U_5683,U_5684,U_5685,U_5686) )
    & ! [U_5683,U_5684,U_5685,U_5686] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),U_5684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5683),U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)))
        | ~ sP494(U_5683,U_5684,U_5685,U_5686) )
    & ! [U_5683,U_5684,U_5685,U_5686] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5683),U_5684),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))),U_5686))
        | sP498(U_5683,U_5684,U_5685,U_5686)
        | sP495(U_5683,U_5684,U_5685,U_5686)
        | ~ sP499(U_5683,U_5684,U_5685,U_5686) )
    & ! [U_5683,U_5684,U_5685,U_5686] :
        ( sP494(U_5683,U_5684,U_5685,U_5686)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5683),U_5684),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))),U_5686))
        | ~ sP499(U_5683,U_5684,U_5685,U_5686) )
    & ! [U_5683,U_5684,U_5685,U_5686] :
        ( sP499(U_5683,U_5684,U_5685,U_5686)
        | ~ class_Int_Onumber(U_5683)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5683) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP493,sP494,sP495,sP496,sP497,sP498,sP499])],[f_1686_2]) ).

cnf(f_1686_4,plain,
    ( sP499(U_5683,U_5684,U_5685,U_5686)
    | ~ class_Int_Onumber(U_5683)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5683) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

cnf(f_1686_5,plain,
    ( sP494(U_5683,U_5684,U_5685,U_5686)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5683),U_5684),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))),U_5686))
    | ~ sP499(U_5683,U_5684,U_5685,U_5686) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

cnf(f_1686_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5683),U_5684),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))),U_5686))
    | sP498(U_5683,U_5684,U_5685,U_5686)
    | sP495(U_5683,U_5684,U_5685,U_5686)
    | ~ sP499(U_5683,U_5684,U_5685,U_5686) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

cnf(f_1686_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),U_5684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5683),U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)))
    | ~ sP494(U_5683,U_5684,U_5685,U_5686) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

cnf(f_1686_8,plain,
    ( sP493(U_5683,U_5684,U_5685,U_5686)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)))
    | ~ sP494(U_5683,U_5684,U_5685,U_5686) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

cnf(f_1686_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5683),U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))),U_5684))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)),c_Groups_Ozero__class_Ozero(U_5683)))
    | ~ sP493(U_5683,U_5684,U_5685,U_5686) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

cnf(f_1686_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),U_5686))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)),c_Groups_Ozero__class_Ozero(U_5683)))
    | ~ sP493(U_5683,U_5684,U_5685,U_5686) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

cnf(f_1686_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)))
    | ~ sP495(U_5683,U_5684,U_5685,U_5686) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

cnf(f_1686_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),U_5684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5683),U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))))
    | ~ sP495(U_5683,U_5684,U_5685,U_5686) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

cnf(f_1686_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)))
    | ~ sP498(U_5683,U_5684,U_5685,U_5686) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

cnf(f_1686_14,plain,
    ( sP497(U_5683,U_5685,U_5686)
    | sP496(U_5683,U_5684,U_5685,U_5686)
    | ~ sP498(U_5683,U_5684,U_5685,U_5686) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

cnf(f_1686_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)),c_Groups_Ozero__class_Ozero(U_5683)))
    | ~ sP496(U_5683,U_5684,U_5685,U_5686) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

cnf(f_1686_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5683),U_5686),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685))),U_5684))
    | ~ sP496(U_5683,U_5684,U_5685,U_5686) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

cnf(f_1686_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),hAPP(c_Int_Onumber__class_Onumber__of(U_5683),U_5685)),c_Groups_Ozero__class_Ozero(U_5683)))
    | ~ sP497(U_5683,U_5685,U_5686) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

cnf(f_1686_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5683),c_Groups_Ozero__class_Ozero(U_5683)),U_5686))
    | ~ sP497(U_5683,U_5685,U_5686) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

fof(f_1687_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_1687_2,plain,
    ! [U_5690,U_5689,U_5688,U_5687] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5687),U_5688),U_5689)),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5689),c_Groups_Ozero__class_Ozero(U_5687))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5687),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)),U_5689)),U_5688))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5689),c_Groups_Ozero__class_Ozero(U_5687))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),U_5689)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5688),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5687),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)),U_5689)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),U_5689)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5689),c_Groups_Ozero__class_Ozero(U_5687))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5687),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)),U_5689)),U_5688))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5689),c_Groups_Ozero__class_Ozero(U_5687))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),U_5689)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5688),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5687),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)),U_5689)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),U_5689)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5687),U_5688),U_5689)),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690))) ) )
      | ~ class_Int_Onumber(U_5687)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5687) ),
    inference(variable_rename,[status(thm)],[f_1687_1]) ).

fof(f_1687_3,plain,
    ( ! [U_5689,U_5687,U_5690] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)))
        | ~ sP504(U_5689,U_5687,U_5690) )
    & ! [U_5689,U_5687,U_5690] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5689),c_Groups_Ozero__class_Ozero(U_5687)))
        | ~ sP504(U_5689,U_5687,U_5690) )
    & ! [U_5689,U_5687,U_5688,U_5690] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5687),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)),U_5689)),U_5688))
        | ~ sP503(U_5689,U_5687,U_5688,U_5690) )
    & ! [U_5689,U_5687,U_5688,U_5690] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5689),c_Groups_Ozero__class_Ozero(U_5687)))
        | ~ sP503(U_5689,U_5687,U_5688,U_5690) )
    & ! [U_5689,U_5687,U_5688,U_5690] :
        ( sP504(U_5689,U_5687,U_5690)
        | sP503(U_5689,U_5687,U_5688,U_5690)
        | ~ sP505(U_5689,U_5687,U_5688,U_5690) )
    & ! [U_5689,U_5687,U_5688,U_5690] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),U_5689))
        | ~ sP505(U_5689,U_5687,U_5688,U_5690) )
    & ! [U_5689,U_5687,U_5688,U_5690] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5688),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5687),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)),U_5689)))
        | ~ sP502(U_5689,U_5687,U_5688,U_5690) )
    & ! [U_5689,U_5687,U_5688,U_5690] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),U_5689))
        | ~ sP502(U_5689,U_5687,U_5688,U_5690) )
    & ! [U_5689,U_5687,U_5688,U_5690] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5689),c_Groups_Ozero__class_Ozero(U_5687)))
        | ~ sP500(U_5689,U_5687,U_5688,U_5690) )
    & ! [U_5689,U_5687,U_5688,U_5690] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5687),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)),U_5689)),U_5688))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5689),c_Groups_Ozero__class_Ozero(U_5687)))
        | ~ sP500(U_5689,U_5687,U_5688,U_5690) )
    & ! [U_5689,U_5687,U_5688,U_5690] :
        ( sP500(U_5689,U_5687,U_5688,U_5690)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),U_5689))
        | ~ sP501(U_5689,U_5687,U_5688,U_5690) )
    & ! [U_5689,U_5687,U_5688,U_5690] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5688),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5687),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)),U_5689)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),U_5689))
        | ~ sP501(U_5689,U_5687,U_5688,U_5690) )
    & ! [U_5689,U_5687,U_5688,U_5690] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5687),U_5688),U_5689)),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)))
        | sP505(U_5689,U_5687,U_5688,U_5690)
        | sP502(U_5689,U_5687,U_5688,U_5690)
        | ~ sP506(U_5689,U_5687,U_5688,U_5690) )
    & ! [U_5689,U_5687,U_5688,U_5690] :
        ( sP501(U_5689,U_5687,U_5688,U_5690)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5687),U_5688),U_5689)),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)))
        | ~ sP506(U_5689,U_5687,U_5688,U_5690) )
    & ! [U_5689,U_5687,U_5688,U_5690] :
        ( sP506(U_5689,U_5687,U_5688,U_5690)
        | ~ class_Int_Onumber(U_5687)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5687) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP500,sP501,sP502,sP503,sP504,sP505,sP506])],[f_1687_2]) ).

cnf(f_1687_4,plain,
    ( sP506(U_5689,U_5687,U_5688,U_5690)
    | ~ class_Int_Onumber(U_5687)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5687) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

cnf(f_1687_5,plain,
    ( sP501(U_5689,U_5687,U_5688,U_5690)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5687),U_5688),U_5689)),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)))
    | ~ sP506(U_5689,U_5687,U_5688,U_5690) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

cnf(f_1687_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5687),U_5688),U_5689)),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)))
    | sP505(U_5689,U_5687,U_5688,U_5690)
    | sP502(U_5689,U_5687,U_5688,U_5690)
    | ~ sP506(U_5689,U_5687,U_5688,U_5690) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

cnf(f_1687_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5688),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5687),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)),U_5689)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),U_5689))
    | ~ sP501(U_5689,U_5687,U_5688,U_5690) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

cnf(f_1687_8,plain,
    ( sP500(U_5689,U_5687,U_5688,U_5690)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),U_5689))
    | ~ sP501(U_5689,U_5687,U_5688,U_5690) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

cnf(f_1687_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5687),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)),U_5689)),U_5688))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5689),c_Groups_Ozero__class_Ozero(U_5687)))
    | ~ sP500(U_5689,U_5687,U_5688,U_5690) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

cnf(f_1687_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5689),c_Groups_Ozero__class_Ozero(U_5687)))
    | ~ sP500(U_5689,U_5687,U_5688,U_5690) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

cnf(f_1687_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),U_5689))
    | ~ sP502(U_5689,U_5687,U_5688,U_5690) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

cnf(f_1687_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5688),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5687),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)),U_5689)))
    | ~ sP502(U_5689,U_5687,U_5688,U_5690) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

cnf(f_1687_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),U_5689))
    | ~ sP505(U_5689,U_5687,U_5688,U_5690) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

cnf(f_1687_14,plain,
    ( sP504(U_5689,U_5687,U_5690)
    | sP503(U_5689,U_5687,U_5688,U_5690)
    | ~ sP505(U_5689,U_5687,U_5688,U_5690) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

cnf(f_1687_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5689),c_Groups_Ozero__class_Ozero(U_5687)))
    | ~ sP503(U_5689,U_5687,U_5688,U_5690) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

cnf(f_1687_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5687),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)),U_5689)),U_5688))
    | ~ sP503(U_5689,U_5687,U_5688,U_5690) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

cnf(f_1687_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),U_5689),c_Groups_Ozero__class_Ozero(U_5687)))
    | ~ sP504(U_5689,U_5687,U_5690) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

cnf(f_1687_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5687),c_Groups_Ozero__class_Ozero(U_5687)),hAPP(c_Int_Onumber__class_Onumber__of(U_5687),U_5690)))
    | ~ sP504(U_5689,U_5687,U_5690) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

fof(f_1688_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_1688_2,plain,
    ! [U_5694,U_5693,U_5692,U_5691] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5691),U_5693),U_5694)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),c_Groups_Ozero__class_Ozero(U_5691)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5694),c_Groups_Ozero__class_Ozero(U_5691))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),U_5694)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5694),c_Groups_Ozero__class_Ozero(U_5691))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),c_Groups_Ozero__class_Ozero(U_5691)),U_5694)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),U_5694)),U_5693))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),c_Groups_Ozero__class_Ozero(U_5691)),U_5694)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),c_Groups_Ozero__class_Ozero(U_5691)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5694),c_Groups_Ozero__class_Ozero(U_5691))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),U_5694)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5694),c_Groups_Ozero__class_Ozero(U_5691))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),c_Groups_Ozero__class_Ozero(U_5691)),U_5694)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),U_5694)),U_5693))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),c_Groups_Ozero__class_Ozero(U_5691)),U_5694)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5691),U_5693),U_5694))) ) )
      | ~ class_Int_Onumber(U_5691)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5691) ),
    inference(variable_rename,[status(thm)],[f_1688_1]) ).

fof(f_1688_3,plain,
    ( ! [U_5692,U_5694,U_5691] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),c_Groups_Ozero__class_Ozero(U_5691)))
        | ~ sP511(U_5692,U_5694,U_5691) )
    & ! [U_5692,U_5694,U_5691] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5694),c_Groups_Ozero__class_Ozero(U_5691)))
        | ~ sP511(U_5692,U_5694,U_5691) )
    & ! [U_5692,U_5694,U_5691,U_5693] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),U_5694)))
        | ~ sP510(U_5692,U_5694,U_5691,U_5693) )
    & ! [U_5692,U_5694,U_5691,U_5693] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5694),c_Groups_Ozero__class_Ozero(U_5691)))
        | ~ sP510(U_5692,U_5694,U_5691,U_5693) )
    & ! [U_5692,U_5694,U_5691,U_5693] :
        ( sP511(U_5692,U_5694,U_5691)
        | sP510(U_5692,U_5694,U_5691,U_5693)
        | ~ sP512(U_5692,U_5694,U_5691,U_5693) )
    & ! [U_5692,U_5694,U_5691,U_5693] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),c_Groups_Ozero__class_Ozero(U_5691)),U_5694))
        | ~ sP512(U_5692,U_5694,U_5691,U_5693) )
    & ! [U_5692,U_5694,U_5691,U_5693] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),U_5694)),U_5693))
        | ~ sP509(U_5692,U_5694,U_5691,U_5693) )
    & ! [U_5692,U_5694,U_5691,U_5693] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),c_Groups_Ozero__class_Ozero(U_5691)),U_5694))
        | ~ sP509(U_5692,U_5694,U_5691,U_5693) )
    & ! [U_5692,U_5694,U_5691,U_5693] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),c_Groups_Ozero__class_Ozero(U_5691)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5694),c_Groups_Ozero__class_Ozero(U_5691)))
        | ~ sP507(U_5692,U_5694,U_5691,U_5693) )
    & ! [U_5692,U_5694,U_5691,U_5693] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),U_5694)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5694),c_Groups_Ozero__class_Ozero(U_5691)))
        | ~ sP507(U_5692,U_5694,U_5691,U_5693) )
    & ! [U_5692,U_5694,U_5691,U_5693] :
        ( sP507(U_5692,U_5694,U_5691,U_5693)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),c_Groups_Ozero__class_Ozero(U_5691)),U_5694))
        | ~ sP508(U_5692,U_5694,U_5691,U_5693) )
    & ! [U_5692,U_5694,U_5691,U_5693] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),U_5694)),U_5693))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),c_Groups_Ozero__class_Ozero(U_5691)),U_5694))
        | ~ sP508(U_5692,U_5694,U_5691,U_5693) )
    & ! [U_5692,U_5694,U_5691,U_5693] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5691),U_5693),U_5694)))
        | sP512(U_5692,U_5694,U_5691,U_5693)
        | sP509(U_5692,U_5694,U_5691,U_5693)
        | ~ sP513(U_5692,U_5694,U_5691,U_5693) )
    & ! [U_5692,U_5694,U_5691,U_5693] :
        ( sP508(U_5692,U_5694,U_5691,U_5693)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5691),U_5693),U_5694)))
        | ~ sP513(U_5692,U_5694,U_5691,U_5693) )
    & ! [U_5692,U_5694,U_5691,U_5693] :
        ( sP513(U_5692,U_5694,U_5691,U_5693)
        | ~ class_Int_Onumber(U_5691)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5691) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP507,sP508,sP509,sP510,sP511,sP512,sP513])],[f_1688_2]) ).

cnf(f_1688_4,plain,
    ( sP513(U_5692,U_5694,U_5691,U_5693)
    | ~ class_Int_Onumber(U_5691)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5691) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

cnf(f_1688_5,plain,
    ( sP508(U_5692,U_5694,U_5691,U_5693)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5691),U_5693),U_5694)))
    | ~ sP513(U_5692,U_5694,U_5691,U_5693) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

cnf(f_1688_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5691),U_5693),U_5694)))
    | sP512(U_5692,U_5694,U_5691,U_5693)
    | sP509(U_5692,U_5694,U_5691,U_5693)
    | ~ sP513(U_5692,U_5694,U_5691,U_5693) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

cnf(f_1688_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),U_5694)),U_5693))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),c_Groups_Ozero__class_Ozero(U_5691)),U_5694))
    | ~ sP508(U_5692,U_5694,U_5691,U_5693) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

cnf(f_1688_8,plain,
    ( sP507(U_5692,U_5694,U_5691,U_5693)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),c_Groups_Ozero__class_Ozero(U_5691)),U_5694))
    | ~ sP508(U_5692,U_5694,U_5691,U_5693) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

cnf(f_1688_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),U_5694)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5694),c_Groups_Ozero__class_Ozero(U_5691)))
    | ~ sP507(U_5692,U_5694,U_5691,U_5693) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

cnf(f_1688_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),c_Groups_Ozero__class_Ozero(U_5691)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5694),c_Groups_Ozero__class_Ozero(U_5691)))
    | ~ sP507(U_5692,U_5694,U_5691,U_5693) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

cnf(f_1688_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),c_Groups_Ozero__class_Ozero(U_5691)),U_5694))
    | ~ sP509(U_5692,U_5694,U_5691,U_5693) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

cnf(f_1688_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),U_5694)),U_5693))
    | ~ sP509(U_5692,U_5694,U_5691,U_5693) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

cnf(f_1688_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),c_Groups_Ozero__class_Ozero(U_5691)),U_5694))
    | ~ sP512(U_5692,U_5694,U_5691,U_5693) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

cnf(f_1688_14,plain,
    ( sP511(U_5692,U_5694,U_5691)
    | sP510(U_5692,U_5694,U_5691,U_5693)
    | ~ sP512(U_5692,U_5694,U_5691,U_5693) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

cnf(f_1688_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5694),c_Groups_Ozero__class_Ozero(U_5691)))
    | ~ sP510(U_5692,U_5694,U_5691,U_5693) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

cnf(f_1688_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),U_5694)))
    | ~ sP510(U_5692,U_5694,U_5691,U_5693) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

cnf(f_1688_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),U_5694),c_Groups_Ozero__class_Ozero(U_5691)))
    | ~ sP511(U_5692,U_5694,U_5691) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

cnf(f_1688_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),U_5692)),c_Groups_Ozero__class_Ozero(U_5691)))
    | ~ sP511(U_5692,U_5694,U_5691) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

fof(f_1689_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_1689_2,plain,
    ! [U_5698,U_5697,U_5696,U_5695] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5696),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5695),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5696),c_Groups_Ozero__class_Ozero(U_5695)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)),c_Groups_Ozero__class_Ozero(U_5695))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5695),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)),c_Groups_Ozero__class_Ozero(U_5695))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),c_Groups_Ozero__class_Ozero(U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5695),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))),U_5697))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),c_Groups_Ozero__class_Ozero(U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5696),c_Groups_Ozero__class_Ozero(U_5695)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)),c_Groups_Ozero__class_Ozero(U_5695))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5695),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)),c_Groups_Ozero__class_Ozero(U_5695))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),c_Groups_Ozero__class_Ozero(U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5695),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))),U_5697))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),c_Groups_Ozero__class_Ozero(U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5696),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5695),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)))) ) )
      | ~ class_Int_Onumber(U_5695)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5695) ),
    inference(variable_rename,[status(thm)],[f_1689_1]) ).

fof(f_1689_3,plain,
    ( ! [U_5698,U_5695,U_5696] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5696),c_Groups_Ozero__class_Ozero(U_5695)))
        | ~ sP518(U_5698,U_5695,U_5696) )
    & ! [U_5698,U_5695,U_5696] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)),c_Groups_Ozero__class_Ozero(U_5695)))
        | ~ sP518(U_5698,U_5695,U_5696) )
    & ! [U_5698,U_5695,U_5696,U_5697] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5695),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))))
        | ~ sP517(U_5698,U_5695,U_5696,U_5697) )
    & ! [U_5698,U_5695,U_5696,U_5697] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)),c_Groups_Ozero__class_Ozero(U_5695)))
        | ~ sP517(U_5698,U_5695,U_5696,U_5697) )
    & ! [U_5698,U_5695,U_5696,U_5697] :
        ( sP518(U_5698,U_5695,U_5696)
        | sP517(U_5698,U_5695,U_5696,U_5697)
        | ~ sP519(U_5698,U_5695,U_5696,U_5697) )
    & ! [U_5698,U_5695,U_5696,U_5697] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),c_Groups_Ozero__class_Ozero(U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)))
        | ~ sP519(U_5698,U_5695,U_5696,U_5697) )
    & ! [U_5698,U_5695,U_5696,U_5697] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5695),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))),U_5697))
        | ~ sP516(U_5698,U_5695,U_5696,U_5697) )
    & ! [U_5698,U_5695,U_5696,U_5697] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),c_Groups_Ozero__class_Ozero(U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)))
        | ~ sP516(U_5698,U_5695,U_5696,U_5697) )
    & ! [U_5698,U_5695,U_5696,U_5697] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5696),c_Groups_Ozero__class_Ozero(U_5695)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)),c_Groups_Ozero__class_Ozero(U_5695)))
        | ~ sP514(U_5698,U_5695,U_5696,U_5697) )
    & ! [U_5698,U_5695,U_5696,U_5697] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5695),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)),c_Groups_Ozero__class_Ozero(U_5695)))
        | ~ sP514(U_5698,U_5695,U_5696,U_5697) )
    & ! [U_5698,U_5695,U_5696,U_5697] :
        ( sP514(U_5698,U_5695,U_5696,U_5697)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),c_Groups_Ozero__class_Ozero(U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)))
        | ~ sP515(U_5698,U_5695,U_5696,U_5697) )
    & ! [U_5698,U_5695,U_5696,U_5697] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5695),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))),U_5697))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),c_Groups_Ozero__class_Ozero(U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)))
        | ~ sP515(U_5698,U_5695,U_5696,U_5697) )
    & ! [U_5698,U_5695,U_5696,U_5697] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5696),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5695),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))))
        | sP519(U_5698,U_5695,U_5696,U_5697)
        | sP516(U_5698,U_5695,U_5696,U_5697)
        | ~ sP520(U_5698,U_5695,U_5696,U_5697) )
    & ! [U_5698,U_5695,U_5696,U_5697] :
        ( sP515(U_5698,U_5695,U_5696,U_5697)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5696),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5695),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))))
        | ~ sP520(U_5698,U_5695,U_5696,U_5697) )
    & ! [U_5698,U_5695,U_5696,U_5697] :
        ( sP520(U_5698,U_5695,U_5696,U_5697)
        | ~ class_Int_Onumber(U_5695)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5695) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP514,sP515,sP516,sP517,sP518,sP519,sP520])],[f_1689_2]) ).

cnf(f_1689_4,plain,
    ( sP520(U_5698,U_5695,U_5696,U_5697)
    | ~ class_Int_Onumber(U_5695)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5695) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

cnf(f_1689_5,plain,
    ( sP515(U_5698,U_5695,U_5696,U_5697)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5696),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5695),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))))
    | ~ sP520(U_5698,U_5695,U_5696,U_5697) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

cnf(f_1689_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5696),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5695),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))))
    | sP519(U_5698,U_5695,U_5696,U_5697)
    | sP516(U_5698,U_5695,U_5696,U_5697)
    | ~ sP520(U_5698,U_5695,U_5696,U_5697) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

cnf(f_1689_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5695),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))),U_5697))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),c_Groups_Ozero__class_Ozero(U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)))
    | ~ sP515(U_5698,U_5695,U_5696,U_5697) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

cnf(f_1689_8,plain,
    ( sP514(U_5698,U_5695,U_5696,U_5697)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),c_Groups_Ozero__class_Ozero(U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)))
    | ~ sP515(U_5698,U_5695,U_5696,U_5697) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

cnf(f_1689_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5695),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)),c_Groups_Ozero__class_Ozero(U_5695)))
    | ~ sP514(U_5698,U_5695,U_5696,U_5697) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

cnf(f_1689_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5696),c_Groups_Ozero__class_Ozero(U_5695)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)),c_Groups_Ozero__class_Ozero(U_5695)))
    | ~ sP514(U_5698,U_5695,U_5696,U_5697) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

cnf(f_1689_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),c_Groups_Ozero__class_Ozero(U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)))
    | ~ sP516(U_5698,U_5695,U_5696,U_5697) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

cnf(f_1689_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5695),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))),U_5697))
    | ~ sP516(U_5698,U_5695,U_5696,U_5697) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

cnf(f_1689_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),c_Groups_Ozero__class_Ozero(U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)))
    | ~ sP519(U_5698,U_5695,U_5696,U_5697) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

cnf(f_1689_14,plain,
    ( sP518(U_5698,U_5695,U_5696)
    | sP517(U_5698,U_5695,U_5696,U_5697)
    | ~ sP519(U_5698,U_5695,U_5696,U_5697) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

cnf(f_1689_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)),c_Groups_Ozero__class_Ozero(U_5695)))
    | ~ sP517(U_5698,U_5695,U_5696,U_5697) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

cnf(f_1689_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5695),U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698))))
    | ~ sP517(U_5698,U_5695,U_5696,U_5697) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

cnf(f_1689_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),hAPP(c_Int_Onumber__class_Onumber__of(U_5695),U_5698)),c_Groups_Ozero__class_Ozero(U_5695)))
    | ~ sP518(U_5698,U_5695,U_5696) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

cnf(f_1689_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5695),U_5696),c_Groups_Ozero__class_Ozero(U_5695)))
    | ~ sP518(U_5698,U_5695,U_5696) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

fof(f_1690_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_1690_2,plain,
    ! [U_5702,U_5701,U_5700,U_5699] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5699),U_5700),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5702),U_5701)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5699),hAPP(hAPP(c_Power_Opower__class_Opower(U_5699),U_5700),U_5702)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5699),U_5700),U_5701))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5701),U_5702))
      | U_5700 = c_Groups_Ozero__class_Ozero(U_5699)
      | ~ class_Fields_Ofield(U_5699) ),
    inference(variable_rename,[status(thm)],[f_1690_1]) ).

fof(f_1690_3,plain,
    ! [U_5700,U_5699,U_5701,U_5702] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5699),U_5700),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5702),U_5701)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5699),hAPP(hAPP(c_Power_Opower__class_Opower(U_5699),U_5700),U_5702)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5699),U_5700),U_5701))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5701),U_5702))
      | U_5700 = c_Groups_Ozero__class_Ozero(U_5699)
      | ~ class_Fields_Ofield(U_5699) ),
    inference(definitional_conversion,[status(esa)],[f_1690_2]) ).

cnf(f_1690_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5699),U_5700),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5702),U_5701)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5699),hAPP(hAPP(c_Power_Opower__class_Opower(U_5699),U_5700),U_5702)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5699),U_5700),U_5701))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5701),U_5702))
    | U_5700 = c_Groups_Ozero__class_Ozero(U_5699)
    | ~ class_Fields_Ofield(U_5699) ),
    inference(clausify,[status(thm)],[f_1690_3]) ).

fof(f_1691_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_1691_2,plain,
    ! [U_5704,U_5703] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5703),hAPP(c_Int_Onumber__class_Onumber__of(U_5703),c_Int_OMin)),U_5704) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5703),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5703),c_Groups_Oone__class_Oone(U_5703)),U_5704))
      | ~ class_Int_Onumber__ring(U_5703)
      | ~ class_Fields_Ofield__inverse__zero(U_5703) ),
    inference(variable_rename,[status(thm)],[f_1691_1]) ).

fof(f_1691_3,plain,
    ! [U_5704,U_5703] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5703),hAPP(c_Int_Onumber__class_Onumber__of(U_5703),c_Int_OMin)),U_5704) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5703),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5703),c_Groups_Oone__class_Oone(U_5703)),U_5704))
      | ~ class_Int_Onumber__ring(U_5703)
      | ~ class_Fields_Ofield__inverse__zero(U_5703) ),
    inference(definitional_conversion,[status(esa)],[f_1691_2]) ).

cnf(f_1691_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5703),hAPP(c_Int_Onumber__class_Onumber__of(U_5703),c_Int_OMin)),U_5704) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5703),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5703),c_Groups_Oone__class_Oone(U_5703)),U_5704))
    | ~ class_Int_Onumber__ring(U_5703)
    | ~ class_Fields_Ofield__inverse__zero(U_5703) ),
    inference(clausify,[status(thm)],[f_1691_3]) ).

fof(f_1692_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_1692_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_1692_1]) ).

cnf(f_1692_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_1692_2]) ).

fof(f_1693_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_1693_2,plain,
    ! [U_5708,U_5707,U_5706,U_5705] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5706),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5705),U_5707),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5706),c_Groups_Ozero__class_Ozero(U_5705)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)),c_Groups_Ozero__class_Ozero(U_5705))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5707),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5705),U_5706),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)),c_Groups_Ozero__class_Ozero(U_5705))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),c_Groups_Ozero__class_Ozero(U_5705)),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5705),U_5706),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))),U_5707))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),c_Groups_Ozero__class_Ozero(U_5705)),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5706),c_Groups_Ozero__class_Ozero(U_5705)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)),c_Groups_Ozero__class_Ozero(U_5705))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5707),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5705),U_5706),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)),c_Groups_Ozero__class_Ozero(U_5705))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),c_Groups_Ozero__class_Ozero(U_5705)),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5705),U_5706),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))),U_5707))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),c_Groups_Ozero__class_Ozero(U_5705)),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5706),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5705),U_5707),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)))) ) )
      | ~ class_Int_Onumber(U_5705)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5705) ),
    inference(variable_rename,[status(thm)],[f_1693_1]) ).

fof(f_1693_3,plain,
    ( ! [U_5706,U_5705,U_5708] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5706),c_Groups_Ozero__class_Ozero(U_5705)))
        | ~ sP525(U_5706,U_5705,U_5708) )
    & ! [U_5706,U_5705,U_5708] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)),c_Groups_Ozero__class_Ozero(U_5705)))
        | ~ sP525(U_5706,U_5705,U_5708) )
    & ! [U_5706,U_5705,U_5708,U_5707] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5707),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5705),U_5706),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))))
        | ~ sP524(U_5706,U_5705,U_5708,U_5707) )
    & ! [U_5706,U_5705,U_5708,U_5707] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)),c_Groups_Ozero__class_Ozero(U_5705)))
        | ~ sP524(U_5706,U_5705,U_5708,U_5707) )
    & ! [U_5706,U_5705,U_5708,U_5707] :
        ( sP525(U_5706,U_5705,U_5708)
        | sP524(U_5706,U_5705,U_5708,U_5707)
        | ~ sP526(U_5706,U_5705,U_5708,U_5707) )
    & ! [U_5706,U_5705,U_5708,U_5707] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),c_Groups_Ozero__class_Ozero(U_5705)),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)))
        | ~ sP526(U_5706,U_5705,U_5708,U_5707) )
    & ! [U_5706,U_5705,U_5708,U_5707] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5705),U_5706),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))),U_5707))
        | ~ sP523(U_5706,U_5705,U_5708,U_5707) )
    & ! [U_5706,U_5705,U_5708,U_5707] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),c_Groups_Ozero__class_Ozero(U_5705)),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)))
        | ~ sP523(U_5706,U_5705,U_5708,U_5707) )
    & ! [U_5706,U_5705,U_5708,U_5707] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5706),c_Groups_Ozero__class_Ozero(U_5705)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)),c_Groups_Ozero__class_Ozero(U_5705)))
        | ~ sP521(U_5706,U_5705,U_5708,U_5707) )
    & ! [U_5706,U_5705,U_5708,U_5707] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5707),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5705),U_5706),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)),c_Groups_Ozero__class_Ozero(U_5705)))
        | ~ sP521(U_5706,U_5705,U_5708,U_5707) )
    & ! [U_5706,U_5705,U_5708,U_5707] :
        ( sP521(U_5706,U_5705,U_5708,U_5707)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),c_Groups_Ozero__class_Ozero(U_5705)),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)))
        | ~ sP522(U_5706,U_5705,U_5708,U_5707) )
    & ! [U_5706,U_5705,U_5708,U_5707] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5705),U_5706),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))),U_5707))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),c_Groups_Ozero__class_Ozero(U_5705)),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)))
        | ~ sP522(U_5706,U_5705,U_5708,U_5707) )
    & ! [U_5706,U_5705,U_5708,U_5707] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5706),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5705),U_5707),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))))
        | sP526(U_5706,U_5705,U_5708,U_5707)
        | sP523(U_5706,U_5705,U_5708,U_5707)
        | ~ sP527(U_5706,U_5705,U_5708,U_5707) )
    & ! [U_5706,U_5705,U_5708,U_5707] :
        ( sP522(U_5706,U_5705,U_5708,U_5707)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5706),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5705),U_5707),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))))
        | ~ sP527(U_5706,U_5705,U_5708,U_5707) )
    & ! [U_5706,U_5705,U_5708,U_5707] :
        ( sP527(U_5706,U_5705,U_5708,U_5707)
        | ~ class_Int_Onumber(U_5705)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5705) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP521,sP522,sP523,sP524,sP525,sP526,sP527])],[f_1693_2]) ).

cnf(f_1693_4,plain,
    ( sP527(U_5706,U_5705,U_5708,U_5707)
    | ~ class_Int_Onumber(U_5705)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5705) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_5,plain,
    ( sP522(U_5706,U_5705,U_5708,U_5707)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5706),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5705),U_5707),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))))
    | ~ sP527(U_5706,U_5705,U_5708,U_5707) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5706),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5705),U_5707),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))))
    | sP526(U_5706,U_5705,U_5708,U_5707)
    | sP523(U_5706,U_5705,U_5708,U_5707)
    | ~ sP527(U_5706,U_5705,U_5708,U_5707) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5705),U_5706),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))),U_5707))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),c_Groups_Ozero__class_Ozero(U_5705)),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)))
    | ~ sP522(U_5706,U_5705,U_5708,U_5707) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_8,plain,
    ( sP521(U_5706,U_5705,U_5708,U_5707)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),c_Groups_Ozero__class_Ozero(U_5705)),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)))
    | ~ sP522(U_5706,U_5705,U_5708,U_5707) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5707),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5705),U_5706),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)),c_Groups_Ozero__class_Ozero(U_5705)))
    | ~ sP521(U_5706,U_5705,U_5708,U_5707) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5706),c_Groups_Ozero__class_Ozero(U_5705)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)),c_Groups_Ozero__class_Ozero(U_5705)))
    | ~ sP521(U_5706,U_5705,U_5708,U_5707) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),c_Groups_Ozero__class_Ozero(U_5705)),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)))
    | ~ sP523(U_5706,U_5705,U_5708,U_5707) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5705),U_5706),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))),U_5707))
    | ~ sP523(U_5706,U_5705,U_5708,U_5707) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),c_Groups_Ozero__class_Ozero(U_5705)),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)))
    | ~ sP526(U_5706,U_5705,U_5708,U_5707) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_14,plain,
    ( sP525(U_5706,U_5705,U_5708)
    | sP524(U_5706,U_5705,U_5708,U_5707)
    | ~ sP526(U_5706,U_5705,U_5708,U_5707) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)),c_Groups_Ozero__class_Ozero(U_5705)))
    | ~ sP524(U_5706,U_5705,U_5708,U_5707) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5707),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5705),U_5706),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708))))
    | ~ sP524(U_5706,U_5705,U_5708,U_5707) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5705),hAPP(c_Int_Onumber__class_Onumber__of(U_5705),U_5708)),c_Groups_Ozero__class_Ozero(U_5705)))
    | ~ sP525(U_5706,U_5705,U_5708) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5705),U_5706),c_Groups_Ozero__class_Ozero(U_5705)))
    | ~ sP525(U_5706,U_5705,U_5708) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

fof(f_1694_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_1694_2,plain,
    ! [U_5712,U_5711,U_5710,U_5709] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5709),U_5711),U_5712)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),c_Groups_Ozero__class_Ozero(U_5709)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),U_5712),c_Groups_Ozero__class_Ozero(U_5709))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),U_5711),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),U_5712)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),U_5712),c_Groups_Ozero__class_Ozero(U_5709))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),c_Groups_Ozero__class_Ozero(U_5709)),U_5712)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),U_5712)),U_5711))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),c_Groups_Ozero__class_Ozero(U_5709)),U_5712)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),c_Groups_Ozero__class_Ozero(U_5709)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),U_5712),c_Groups_Ozero__class_Ozero(U_5709))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),U_5711),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),U_5712)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),U_5712),c_Groups_Ozero__class_Ozero(U_5709))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),c_Groups_Ozero__class_Ozero(U_5709)),U_5712)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),U_5712)),U_5711))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),c_Groups_Ozero__class_Ozero(U_5709)),U_5712)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5709),U_5711),U_5712))) ) )
      | ~ class_Int_Onumber(U_5709)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5709) ),
    inference(variable_rename,[status(thm)],[f_1694_1]) ).

fof(f_1694_3,plain,
    ( ! [U_5712,U_5710,U_5709] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),c_Groups_Ozero__class_Ozero(U_5709)))
        | ~ sP532(U_5712,U_5710,U_5709) )
    & ! [U_5712,U_5710,U_5709] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),U_5712),c_Groups_Ozero__class_Ozero(U_5709)))
        | ~ sP532(U_5712,U_5710,U_5709) )
    & ! [U_5711,U_5712,U_5710,U_5709] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),U_5711),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),U_5712)))
        | ~ sP531(U_5711,U_5712,U_5710,U_5709) )
    & ! [U_5711,U_5712,U_5710,U_5709] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),U_5712),c_Groups_Ozero__class_Ozero(U_5709)))
        | ~ sP531(U_5711,U_5712,U_5710,U_5709) )
    & ! [U_5711,U_5712,U_5710,U_5709] :
        ( sP532(U_5712,U_5710,U_5709)
        | sP531(U_5711,U_5712,U_5710,U_5709)
        | ~ sP533(U_5711,U_5712,U_5710,U_5709) )
    & ! [U_5711,U_5712,U_5710,U_5709] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),c_Groups_Ozero__class_Ozero(U_5709)),U_5712))
        | ~ sP533(U_5711,U_5712,U_5710,U_5709) )
    & ! [U_5711,U_5712,U_5710,U_5709] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),U_5712)),U_5711))
        | ~ sP530(U_5711,U_5712,U_5710,U_5709) )
    & ! [U_5711,U_5712,U_5710,U_5709] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),c_Groups_Ozero__class_Ozero(U_5709)),U_5712))
        | ~ sP530(U_5711,U_5712,U_5710,U_5709) )
    & ! [U_5711,U_5712,U_5710,U_5709] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),c_Groups_Ozero__class_Ozero(U_5709)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),U_5712),c_Groups_Ozero__class_Ozero(U_5709)))
        | ~ sP528(U_5711,U_5712,U_5710,U_5709) )
    & ! [U_5711,U_5712,U_5710,U_5709] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),U_5711),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),U_5712)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),U_5712),c_Groups_Ozero__class_Ozero(U_5709)))
        | ~ sP528(U_5711,U_5712,U_5710,U_5709) )
    & ! [U_5711,U_5712,U_5710,U_5709] :
        ( sP528(U_5711,U_5712,U_5710,U_5709)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),c_Groups_Ozero__class_Ozero(U_5709)),U_5712))
        | ~ sP529(U_5711,U_5712,U_5710,U_5709) )
    & ! [U_5711,U_5712,U_5710,U_5709] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),U_5712)),U_5711))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),c_Groups_Ozero__class_Ozero(U_5709)),U_5712))
        | ~ sP529(U_5711,U_5712,U_5710,U_5709) )
    & ! [U_5711,U_5712,U_5710,U_5709] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5709),U_5711),U_5712)))
        | sP533(U_5711,U_5712,U_5710,U_5709)
        | sP530(U_5711,U_5712,U_5710,U_5709)
        | ~ sP534(U_5711,U_5712,U_5710,U_5709) )
    & ! [U_5711,U_5712,U_5710,U_5709] :
        ( sP529(U_5711,U_5712,U_5710,U_5709)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5709),U_5711),U_5712)))
        | ~ sP534(U_5711,U_5712,U_5710,U_5709) )
    & ! [U_5711,U_5712,U_5710,U_5709] :
        ( sP534(U_5711,U_5712,U_5710,U_5709)
        | ~ class_Int_Onumber(U_5709)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5709) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP528,sP529,sP530,sP531,sP532,sP533,sP534])],[f_1694_2]) ).

cnf(f_1694_4,plain,
    ( sP534(U_5711,U_5712,U_5710,U_5709)
    | ~ class_Int_Onumber(U_5709)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5709) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_5,plain,
    ( sP529(U_5711,U_5712,U_5710,U_5709)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5709),U_5711),U_5712)))
    | ~ sP534(U_5711,U_5712,U_5710,U_5709) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5709),U_5711),U_5712)))
    | sP533(U_5711,U_5712,U_5710,U_5709)
    | sP530(U_5711,U_5712,U_5710,U_5709)
    | ~ sP534(U_5711,U_5712,U_5710,U_5709) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),U_5712)),U_5711))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),c_Groups_Ozero__class_Ozero(U_5709)),U_5712))
    | ~ sP529(U_5711,U_5712,U_5710,U_5709) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_8,plain,
    ( sP528(U_5711,U_5712,U_5710,U_5709)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),c_Groups_Ozero__class_Ozero(U_5709)),U_5712))
    | ~ sP529(U_5711,U_5712,U_5710,U_5709) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),U_5711),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),U_5712)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),U_5712),c_Groups_Ozero__class_Ozero(U_5709)))
    | ~ sP528(U_5711,U_5712,U_5710,U_5709) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),c_Groups_Ozero__class_Ozero(U_5709)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),U_5712),c_Groups_Ozero__class_Ozero(U_5709)))
    | ~ sP528(U_5711,U_5712,U_5710,U_5709) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),c_Groups_Ozero__class_Ozero(U_5709)),U_5712))
    | ~ sP530(U_5711,U_5712,U_5710,U_5709) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),U_5712)),U_5711))
    | ~ sP530(U_5711,U_5712,U_5710,U_5709) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),c_Groups_Ozero__class_Ozero(U_5709)),U_5712))
    | ~ sP533(U_5711,U_5712,U_5710,U_5709) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_14,plain,
    ( sP532(U_5712,U_5710,U_5709)
    | sP531(U_5711,U_5712,U_5710,U_5709)
    | ~ sP533(U_5711,U_5712,U_5710,U_5709) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),U_5712),c_Groups_Ozero__class_Ozero(U_5709)))
    | ~ sP531(U_5711,U_5712,U_5710,U_5709) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),U_5711),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),U_5712)))
    | ~ sP531(U_5711,U_5712,U_5710,U_5709) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5709),U_5712),c_Groups_Ozero__class_Ozero(U_5709)))
    | ~ sP532(U_5712,U_5710,U_5709) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5709),U_5710)),c_Groups_Ozero__class_Ozero(U_5709)))
    | ~ sP532(U_5712,U_5710,U_5709) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

fof(f_1695_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_1695_2,plain,
    ! [U_5716,U_5715,U_5714,U_5713] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5713),U_5714),U_5715)),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),U_5715),c_Groups_Ozero__class_Ozero(U_5713))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5713),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)),U_5715)),U_5714))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),U_5715),c_Groups_Ozero__class_Ozero(U_5713))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),U_5715)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),U_5714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5713),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)),U_5715)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),U_5715)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),U_5715),c_Groups_Ozero__class_Ozero(U_5713))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5713),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)),U_5715)),U_5714))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),U_5715),c_Groups_Ozero__class_Ozero(U_5713))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),U_5715)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),U_5714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5713),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)),U_5715)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),U_5715)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5713),U_5714),U_5715)),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716))) ) )
      | ~ class_Int_Onumber(U_5713)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5713) ),
    inference(variable_rename,[status(thm)],[f_1695_1]) ).

fof(f_1695_3,plain,
    ( ! [U_5716,U_5713,U_5715] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)))
        | ~ sP539(U_5716,U_5713,U_5715) )
    & ! [U_5716,U_5713,U_5715] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),U_5715),c_Groups_Ozero__class_Ozero(U_5713)))
        | ~ sP539(U_5716,U_5713,U_5715) )
    & ! [U_5714,U_5716,U_5713,U_5715] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5713),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)),U_5715)),U_5714))
        | ~ sP538(U_5714,U_5716,U_5713,U_5715) )
    & ! [U_5714,U_5716,U_5713,U_5715] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),U_5715),c_Groups_Ozero__class_Ozero(U_5713)))
        | ~ sP538(U_5714,U_5716,U_5713,U_5715) )
    & ! [U_5714,U_5716,U_5713,U_5715] :
        ( sP539(U_5716,U_5713,U_5715)
        | sP538(U_5714,U_5716,U_5713,U_5715)
        | ~ sP540(U_5714,U_5716,U_5713,U_5715) )
    & ! [U_5714,U_5716,U_5713,U_5715] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),U_5715))
        | ~ sP540(U_5714,U_5716,U_5713,U_5715) )
    & ! [U_5714,U_5716,U_5713,U_5715] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),U_5714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5713),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)),U_5715)))
        | ~ sP537(U_5714,U_5716,U_5713,U_5715) )
    & ! [U_5714,U_5716,U_5713,U_5715] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),U_5715))
        | ~ sP537(U_5714,U_5716,U_5713,U_5715) )
    & ! [U_5714,U_5716,U_5713,U_5715] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),U_5715),c_Groups_Ozero__class_Ozero(U_5713)))
        | ~ sP535(U_5714,U_5716,U_5713,U_5715) )
    & ! [U_5714,U_5716,U_5713,U_5715] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5713),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)),U_5715)),U_5714))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),U_5715),c_Groups_Ozero__class_Ozero(U_5713)))
        | ~ sP535(U_5714,U_5716,U_5713,U_5715) )
    & ! [U_5714,U_5716,U_5713,U_5715] :
        ( sP535(U_5714,U_5716,U_5713,U_5715)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),U_5715))
        | ~ sP536(U_5714,U_5716,U_5713,U_5715) )
    & ! [U_5714,U_5716,U_5713,U_5715] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),U_5714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5713),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)),U_5715)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),U_5715))
        | ~ sP536(U_5714,U_5716,U_5713,U_5715) )
    & ! [U_5714,U_5716,U_5713,U_5715] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5713),U_5714),U_5715)),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)))
        | sP540(U_5714,U_5716,U_5713,U_5715)
        | sP537(U_5714,U_5716,U_5713,U_5715)
        | ~ sP541(U_5714,U_5716,U_5713,U_5715) )
    & ! [U_5714,U_5716,U_5713,U_5715] :
        ( sP536(U_5714,U_5716,U_5713,U_5715)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5713),U_5714),U_5715)),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)))
        | ~ sP541(U_5714,U_5716,U_5713,U_5715) )
    & ! [U_5714,U_5716,U_5713,U_5715] :
        ( sP541(U_5714,U_5716,U_5713,U_5715)
        | ~ class_Int_Onumber(U_5713)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5713) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP535,sP536,sP537,sP538,sP539,sP540,sP541])],[f_1695_2]) ).

cnf(f_1695_4,plain,
    ( sP541(U_5714,U_5716,U_5713,U_5715)
    | ~ class_Int_Onumber(U_5713)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5713) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_5,plain,
    ( sP536(U_5714,U_5716,U_5713,U_5715)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5713),U_5714),U_5715)),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)))
    | ~ sP541(U_5714,U_5716,U_5713,U_5715) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5713),U_5714),U_5715)),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)))
    | sP540(U_5714,U_5716,U_5713,U_5715)
    | sP537(U_5714,U_5716,U_5713,U_5715)
    | ~ sP541(U_5714,U_5716,U_5713,U_5715) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),U_5714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5713),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)),U_5715)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),U_5715))
    | ~ sP536(U_5714,U_5716,U_5713,U_5715) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_8,plain,
    ( sP535(U_5714,U_5716,U_5713,U_5715)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),U_5715))
    | ~ sP536(U_5714,U_5716,U_5713,U_5715) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5713),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)),U_5715)),U_5714))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),U_5715),c_Groups_Ozero__class_Ozero(U_5713)))
    | ~ sP535(U_5714,U_5716,U_5713,U_5715) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),U_5715),c_Groups_Ozero__class_Ozero(U_5713)))
    | ~ sP535(U_5714,U_5716,U_5713,U_5715) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),U_5715))
    | ~ sP537(U_5714,U_5716,U_5713,U_5715) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),U_5714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5713),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)),U_5715)))
    | ~ sP537(U_5714,U_5716,U_5713,U_5715) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),U_5715))
    | ~ sP540(U_5714,U_5716,U_5713,U_5715) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_14,plain,
    ( sP539(U_5716,U_5713,U_5715)
    | sP538(U_5714,U_5716,U_5713,U_5715)
    | ~ sP540(U_5714,U_5716,U_5713,U_5715) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),U_5715),c_Groups_Ozero__class_Ozero(U_5713)))
    | ~ sP538(U_5714,U_5716,U_5713,U_5715) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5713),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)),U_5715)),U_5714))
    | ~ sP538(U_5714,U_5716,U_5713,U_5715) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5713),U_5715),c_Groups_Ozero__class_Ozero(U_5713)))
    | ~ sP539(U_5716,U_5713,U_5715) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5713),c_Groups_Ozero__class_Ozero(U_5713)),hAPP(c_Int_Onumber__class_Onumber__of(U_5713),U_5716)))
    | ~ sP539(U_5716,U_5713,U_5715) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

fof(f_1696_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_1696_2,plain,
    ! [U_5720,U_5719,U_5718,U_5717] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5717),U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))),U_5720))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),U_5720))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)),c_Groups_Ozero__class_Ozero(U_5717))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5717),U_5720),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))),U_5718))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)),c_Groups_Ozero__class_Ozero(U_5717))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),U_5718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5717),U_5720),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),U_5720))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)),c_Groups_Ozero__class_Ozero(U_5717))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5717),U_5720),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))),U_5718))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)),c_Groups_Ozero__class_Ozero(U_5717))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),U_5718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5717),U_5720),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5717),U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))),U_5720)) ) )
      | ~ class_Int_Onumber(U_5717)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5717) ),
    inference(variable_rename,[status(thm)],[f_1696_1]) ).

fof(f_1696_3,plain,
    ( ! [U_5719,U_5717,U_5720] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),U_5720))
        | ~ sP546(U_5719,U_5717,U_5720) )
    & ! [U_5719,U_5717,U_5720] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)),c_Groups_Ozero__class_Ozero(U_5717)))
        | ~ sP546(U_5719,U_5717,U_5720) )
    & ! [U_5718,U_5719,U_5717,U_5720] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5717),U_5720),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))),U_5718))
        | ~ sP545(U_5718,U_5719,U_5717,U_5720) )
    & ! [U_5718,U_5719,U_5717,U_5720] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)),c_Groups_Ozero__class_Ozero(U_5717)))
        | ~ sP545(U_5718,U_5719,U_5717,U_5720) )
    & ! [U_5718,U_5719,U_5717,U_5720] :
        ( sP546(U_5719,U_5717,U_5720)
        | sP545(U_5718,U_5719,U_5717,U_5720)
        | ~ sP547(U_5718,U_5719,U_5717,U_5720) )
    & ! [U_5718,U_5719,U_5717,U_5720] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)))
        | ~ sP547(U_5718,U_5719,U_5717,U_5720) )
    & ! [U_5718,U_5719,U_5717,U_5720] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),U_5718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5717),U_5720),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))))
        | ~ sP544(U_5718,U_5719,U_5717,U_5720) )
    & ! [U_5718,U_5719,U_5717,U_5720] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)))
        | ~ sP544(U_5718,U_5719,U_5717,U_5720) )
    & ! [U_5718,U_5719,U_5717,U_5720] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),U_5720))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)),c_Groups_Ozero__class_Ozero(U_5717)))
        | ~ sP542(U_5718,U_5719,U_5717,U_5720) )
    & ! [U_5718,U_5719,U_5717,U_5720] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5717),U_5720),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))),U_5718))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)),c_Groups_Ozero__class_Ozero(U_5717)))
        | ~ sP542(U_5718,U_5719,U_5717,U_5720) )
    & ! [U_5718,U_5719,U_5717,U_5720] :
        ( sP542(U_5718,U_5719,U_5717,U_5720)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)))
        | ~ sP543(U_5718,U_5719,U_5717,U_5720) )
    & ! [U_5718,U_5719,U_5717,U_5720] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),U_5718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5717),U_5720),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)))
        | ~ sP543(U_5718,U_5719,U_5717,U_5720) )
    & ! [U_5718,U_5719,U_5717,U_5720] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5717),U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))),U_5720))
        | sP547(U_5718,U_5719,U_5717,U_5720)
        | sP544(U_5718,U_5719,U_5717,U_5720)
        | ~ sP548(U_5718,U_5719,U_5717,U_5720) )
    & ! [U_5718,U_5719,U_5717,U_5720] :
        ( sP543(U_5718,U_5719,U_5717,U_5720)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5717),U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))),U_5720))
        | ~ sP548(U_5718,U_5719,U_5717,U_5720) )
    & ! [U_5718,U_5719,U_5717,U_5720] :
        ( sP548(U_5718,U_5719,U_5717,U_5720)
        | ~ class_Int_Onumber(U_5717)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5717) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP542,sP543,sP544,sP545,sP546,sP547,sP548])],[f_1696_2]) ).

cnf(f_1696_4,plain,
    ( sP548(U_5718,U_5719,U_5717,U_5720)
    | ~ class_Int_Onumber(U_5717)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5717) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_5,plain,
    ( sP543(U_5718,U_5719,U_5717,U_5720)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5717),U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))),U_5720))
    | ~ sP548(U_5718,U_5719,U_5717,U_5720) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5717),U_5718),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))),U_5720))
    | sP547(U_5718,U_5719,U_5717,U_5720)
    | sP544(U_5718,U_5719,U_5717,U_5720)
    | ~ sP548(U_5718,U_5719,U_5717,U_5720) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),U_5718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5717),U_5720),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)))
    | ~ sP543(U_5718,U_5719,U_5717,U_5720) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_8,plain,
    ( sP542(U_5718,U_5719,U_5717,U_5720)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)))
    | ~ sP543(U_5718,U_5719,U_5717,U_5720) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5717),U_5720),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))),U_5718))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)),c_Groups_Ozero__class_Ozero(U_5717)))
    | ~ sP542(U_5718,U_5719,U_5717,U_5720) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),U_5720))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)),c_Groups_Ozero__class_Ozero(U_5717)))
    | ~ sP542(U_5718,U_5719,U_5717,U_5720) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)))
    | ~ sP544(U_5718,U_5719,U_5717,U_5720) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),U_5718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5717),U_5720),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))))
    | ~ sP544(U_5718,U_5719,U_5717,U_5720) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)))
    | ~ sP547(U_5718,U_5719,U_5717,U_5720) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_14,plain,
    ( sP546(U_5719,U_5717,U_5720)
    | sP545(U_5718,U_5719,U_5717,U_5720)
    | ~ sP547(U_5718,U_5719,U_5717,U_5720) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)),c_Groups_Ozero__class_Ozero(U_5717)))
    | ~ sP545(U_5718,U_5719,U_5717,U_5720) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5717),U_5720),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719))),U_5718))
    | ~ sP545(U_5718,U_5719,U_5717,U_5720) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5717),hAPP(c_Int_Onumber__class_Onumber__of(U_5717),U_5719)),c_Groups_Ozero__class_Ozero(U_5717)))
    | ~ sP546(U_5719,U_5717,U_5720) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5717),c_Groups_Ozero__class_Ozero(U_5717)),U_5720))
    | ~ sP546(U_5719,U_5717,U_5720) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

fof(f_1697_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_1697_2,plain,
    ! [U_5722,U_5721] :
      ( ( c_Code__Numeral_Onat__of__aux(U_5721,U_5722) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5721),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_5722))
        | U_5721 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( c_Code__Numeral_Onat__of__aux(U_5721,U_5722) = U_5722
        | U_5721 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_1697_1]) ).

fof(f_1697_3,plain,
    ( ! [U_5726,U_5724] :
        ( c_Code__Numeral_Onat__of__aux(U_5724,U_5726) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5724),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_5726))
        | U_5724 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_5725,U_5723] :
        ( c_Code__Numeral_Onat__of__aux(U_5723,U_5725) = U_5725
        | U_5723 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_1697_2]) ).

fof(f_1697_4,plain,
    ( ! [U_5724,U_5726] :
        ( c_Code__Numeral_Onat__of__aux(U_5724,U_5726) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5724),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_5726))
        | U_5724 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_5725,U_5723] :
        ( c_Code__Numeral_Onat__of__aux(U_5723,U_5725) = U_5725
        | U_5723 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa)],[f_1697_3]) ).

cnf(f_1697_5,plain,
    ( c_Code__Numeral_Onat__of__aux(U_5723,U_5725) = U_5725
    | U_5723 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1697_4]) ).

cnf(f_1697_6,plain,
    ( c_Code__Numeral_Onat__of__aux(U_5724,U_5726) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5724),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_5726))
    | U_5724 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1697_4]) ).

fof(f_1698_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_1698_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_1698_1]) ).

cnf(f_1698_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_1698_2]) ).

fof(f_1699_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_1699_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_1699_1]) ).

cnf(f_1699_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_1699_2]) ).

fof(f_1700_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_1700_2,plain,
    ! [U_5729,U_5728,U_5727] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_5727,U_5728,U_5729,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_5728,
    inference(variable_rename,[status(thm)],[f_1700_1]) ).

fof(f_1700_3,plain,
    ! [U_5729,U_5727,U_5728] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_5727,U_5728,U_5729,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_5728,
    inference(definitional_conversion,[status(esa)],[f_1700_2]) ).

cnf(f_1700_4,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_5727,U_5728,U_5729,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_5728,
    inference(clausify,[status(thm)],[f_1700_3]) ).

fof(f_1701_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_1701_2,plain,
    ! [U_5731,U_5730] :
      ( ( c_Random_Olog(U_5730,U_5731) = 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_5730,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_5731),U_5730)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5731),U_5730))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5730),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
      & ( c_Random_Olog(U_5730,U_5731) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5731),U_5730))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5730),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
    inference(variable_rename,[status(thm)],[f_1701_1]) ).

fof(f_1701_3,plain,
    ( ! [U_5735,U_5733] :
        ( c_Random_Olog(U_5733,U_5735) = 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_5733,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_5735),U_5733)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5735),U_5733))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5733),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_5734,U_5732] :
        ( c_Random_Olog(U_5732,U_5734) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5734),U_5732))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5732),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
    inference(miniscope,[status(thm)],[f_1701_2]) ).

fof(f_1701_4,plain,
    ( ! [U_5732,U_5734] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5734),U_5732))
        | ~ sP549(U_5732,U_5734) )
    & ! [U_5732,U_5734] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5732),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
        | ~ sP549(U_5732,U_5734) )
    & ! [U_5735,U_5733] :
        ( c_Random_Olog(U_5733,U_5735) = 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_5733,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_5735),U_5733)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5735),U_5733))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5733),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_5732,U_5734] :
        ( c_Random_Olog(U_5732,U_5734) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | sP549(U_5732,U_5734) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP549])],[f_1701_3]) ).

cnf(f_1701_5,plain,
    ( c_Random_Olog(U_5732,U_5734) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
    | sP549(U_5732,U_5734) ),
    inference(clausify,[status(thm)],[f_1701_4]) ).

cnf(f_1701_6,plain,
    ( c_Random_Olog(U_5733,U_5735) = 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_5733,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_5735),U_5733)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5735),U_5733))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5733),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_1701_4]) ).

cnf(f_1701_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5732),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
    | ~ sP549(U_5732,U_5734) ),
    inference(clausify,[status(thm)],[f_1701_4]) ).

cnf(f_1701_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5734),U_5732))
    | ~ sP549(U_5732,U_5734) ),
    inference(clausify,[status(thm)],[f_1701_4]) ).

fof(f_1702_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_1702_2,plain,
    ! [U_5739,U_5738,U_5737] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5737),U_5738),U_5739))
      | ? [U_5736] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5737),U_5738),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5737),U_5739),U_5736)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5737),c_Groups_Ozero__class_Ozero(U_5737)),U_5736)) )
      | ~ class_Fields_Olinordered__field(U_5737) ),
    inference(variable_rename,[status(thm)],[f_1702_1]) ).

fof(f_1702_3,plain,
    ! [U_5739,U_5738,U_5737] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5737),U_5738),U_5739))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5737),U_5738),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5737),U_5739),sK95(U_5739,U_5738,U_5737))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5737),c_Groups_Ozero__class_Ozero(U_5737)),sK95(U_5739,U_5738,U_5737))) )
      | ~ class_Fields_Olinordered__field(U_5737) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_5736,sK95(U_5739,U_5738,U_5737))],[f_1702_2]) ).

fof(f_1702_4,plain,
    ( ! [U_5737,U_5739,U_5738] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5737),U_5738),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5737),U_5739),sK95(U_5739,U_5738,U_5737))))
        | ~ sP550(U_5737,U_5739,U_5738) )
    & ! [U_5737,U_5739,U_5738] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5737),c_Groups_Ozero__class_Ozero(U_5737)),sK95(U_5739,U_5738,U_5737)))
        | ~ sP550(U_5737,U_5739,U_5738) )
    & ! [U_5737,U_5739,U_5738] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5737),U_5738),U_5739))
        | sP550(U_5737,U_5739,U_5738)
        | ~ class_Fields_Olinordered__field(U_5737) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP550])],[f_1702_3]) ).

cnf(f_1702_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5737),U_5738),U_5739))
    | sP550(U_5737,U_5739,U_5738)
    | ~ class_Fields_Olinordered__field(U_5737) ),
    inference(clausify,[status(thm)],[f_1702_4]) ).

cnf(f_1702_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5737),c_Groups_Ozero__class_Ozero(U_5737)),sK95(U_5739,U_5738,U_5737)))
    | ~ sP550(U_5737,U_5739,U_5738) ),
    inference(clausify,[status(thm)],[f_1702_4]) ).

cnf(f_1702_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5737),U_5738),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5737),U_5739),sK95(U_5739,U_5738,U_5737))))
    | ~ sP550(U_5737,U_5739,U_5738) ),
    inference(clausify,[status(thm)],[f_1702_4]) ).

fof(f_1703_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_1703_2,plain,
    ! [U_5742,U_5741,U_5740] :
      ( ( c_Random_Ominus__shift(U_5742,U_5740,U_5741) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5740),U_5741)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5740),U_5741)) )
      & ( c_Random_Ominus__shift(U_5742,U_5740,U_5741) = 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_5742),U_5740)),U_5741)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5740),U_5741)) ) ),
    inference(variable_rename,[status(thm)],[f_1703_1]) ).

fof(f_1703_3,plain,
    ( ! [U_5748,U_5746,U_5744] :
        ( c_Random_Ominus__shift(U_5748,U_5744,U_5746) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5744),U_5746)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5744),U_5746)) )
    & ! [U_5747,U_5745,U_5743] :
        ( c_Random_Ominus__shift(U_5747,U_5743,U_5745) = 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_5747),U_5743)),U_5745)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5743),U_5745)) ) ),
    inference(miniscope,[status(thm)],[f_1703_2]) ).

fof(f_1703_4,plain,
    ( ! [U_5746,U_5744,U_5748] :
        ( c_Random_Ominus__shift(U_5748,U_5744,U_5746) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5744),U_5746)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5744),U_5746)) )
    & ! [U_5747,U_5745,U_5743] :
        ( c_Random_Ominus__shift(U_5747,U_5743,U_5745) = 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_5747),U_5743)),U_5745)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5743),U_5745)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1703_3]) ).

cnf(f_1703_5,plain,
    ( c_Random_Ominus__shift(U_5747,U_5743,U_5745) = 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_5747),U_5743)),U_5745)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5743),U_5745)) ),
    inference(clausify,[status(thm)],[f_1703_4]) ).

cnf(f_1703_6,plain,
    ( c_Random_Ominus__shift(U_5748,U_5744,U_5746) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5744),U_5746)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5744),U_5746)) ),
    inference(clausify,[status(thm)],[f_1703_4]) ).

fof(f_1704_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_1704_2,plain,
    ! [U_5750,U_5749] :
      ( ( c_Random_Oinc__shift(U_5749,U_5750) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_5750),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | U_5749 = U_5750 )
      & ( c_Random_Oinc__shift(U_5749,U_5750) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | U_5749 != U_5750 ) ),
    inference(variable_rename,[status(thm)],[f_1704_1]) ).

fof(f_1704_3,plain,
    ( ! [U_5754,U_5752] :
        ( c_Random_Oinc__shift(U_5752,U_5754) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_5754),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | U_5752 = U_5754 )
    & ! [U_5753,U_5751] :
        ( c_Random_Oinc__shift(U_5751,U_5753) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | U_5751 != U_5753 ) ),
    inference(miniscope,[status(thm)],[f_1704_2]) ).

fof(f_1704_4,plain,
    ( ! [U_5752,U_5754] :
        ( c_Random_Oinc__shift(U_5752,U_5754) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_5754),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | U_5752 = U_5754 )
    & ! [U_5753,U_5751] :
        ( c_Random_Oinc__shift(U_5751,U_5753) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | U_5751 != U_5753 ) ),
    inference(definitional_conversion,[status(esa)],[f_1704_3]) ).

cnf(f_1704_5,plain,
    ( c_Random_Oinc__shift(U_5751,U_5753) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
    | U_5751 != U_5753 ),
    inference(clausify,[status(thm)],[f_1704_4]) ).

cnf(f_1704_6,plain,
    ( c_Random_Oinc__shift(U_5752,U_5754) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_5754),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
    | U_5752 = U_5754 ),
    inference(clausify,[status(thm)],[f_1704_4]) ).

fof(f_1705_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_1705_2,plain,
    ! [U_5755] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_5755)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_5755)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1705_1]) ).

fof(f_1705_3,plain,
    ! [U_5755] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_5755)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_5755)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1705_2]) ).

cnf(f_1705_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_5755)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_5755)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1705_3]) ).

fof(f_1706_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_1706_2,plain,
    ! [U_5756] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_5756)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_5756)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1706_1]) ).

fof(f_1706_3,plain,
    ! [U_5756] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_5756)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_5756)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1706_2]) ).

cnf(f_1706_4,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_5756)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_5756)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1706_3]) ).

fof(f_1707_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_1707_2,plain,
    ! [U_5758,U_5757] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5757),U_5758) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_5757),U_5758),
    inference(variable_rename,[status(thm)],[f_1707_1]) ).

fof(f_1707_3,plain,
    ! [U_5757,U_5758] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5757),U_5758) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_5757),U_5758),
    inference(definitional_conversion,[status(esa)],[f_1707_2]) ).

cnf(f_1707_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5757),U_5758) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_5757),U_5758),
    inference(clausify,[status(thm)],[f_1707_3]) ).

fof(f_1708_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_1708_2,plain,
    ! [U_5760,U_5759] :
      ( ( c_Code__Numeral_OSuc__code__numeral(U_5759) = c_Code__Numeral_OSuc__code__numeral(U_5760)
        | U_5759 != U_5760 )
      & ( U_5759 = U_5760
        | c_Code__Numeral_OSuc__code__numeral(U_5759) != c_Code__Numeral_OSuc__code__numeral(U_5760) ) ),
    inference(variable_rename,[status(thm)],[f_1708_1]) ).

fof(f_1708_3,plain,
    ( ! [U_5764,U_5762] :
        ( c_Code__Numeral_OSuc__code__numeral(U_5762) = c_Code__Numeral_OSuc__code__numeral(U_5764)
        | U_5762 != U_5764 )
    & ! [U_5763,U_5761] :
        ( U_5761 = U_5763
        | c_Code__Numeral_OSuc__code__numeral(U_5761) != c_Code__Numeral_OSuc__code__numeral(U_5763) ) ),
    inference(miniscope,[status(thm)],[f_1708_2]) ).

fof(f_1708_4,plain,
    ( ! [U_5762,U_5764] :
        ( c_Code__Numeral_OSuc__code__numeral(U_5762) = c_Code__Numeral_OSuc__code__numeral(U_5764)
        | U_5762 != U_5764 )
    & ! [U_5763,U_5761] :
        ( U_5761 = U_5763
        | c_Code__Numeral_OSuc__code__numeral(U_5761) != c_Code__Numeral_OSuc__code__numeral(U_5763) ) ),
    inference(definitional_conversion,[status(esa)],[f_1708_3]) ).

cnf(f_1708_5,plain,
    ( U_5761 = U_5763
    | c_Code__Numeral_OSuc__code__numeral(U_5761) != c_Code__Numeral_OSuc__code__numeral(U_5763) ),
    inference(clausify,[status(thm)],[f_1708_4]) ).

cnf(f_1708_6,plain,
    ( c_Code__Numeral_OSuc__code__numeral(U_5762) = c_Code__Numeral_OSuc__code__numeral(U_5764)
    | U_5762 != U_5764 ),
    inference(clausify,[status(thm)],[f_1708_4]) ).

fof(f_1709_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_1709_2,plain,
    ! [U_5765] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_5765),
    inference(variable_rename,[status(thm)],[f_1709_1]) ).

fof(f_1709_3,plain,
    ! [U_5765] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_5765),
    inference(definitional_conversion,[status(esa)],[f_1709_2]) ).

cnf(f_1709_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_5765),
    inference(clausify,[status(thm)],[f_1709_3]) ).

fof(f_1710_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_1710_2,plain,
    ! [U_5766] : c_Code__Numeral_OSuc__code__numeral(U_5766) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(variable_rename,[status(thm)],[f_1710_1]) ).

fof(f_1710_3,plain,
    ! [U_5766] : c_Code__Numeral_OSuc__code__numeral(U_5766) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_1710_2]) ).

cnf(f_1710_4,plain,
    c_Code__Numeral_OSuc__code__numeral(U_5766) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_1710_3]) ).

fof(f_1711_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_1711_2,plain,
    ! [U_5770,U_5769,U_5768,U_5767] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_5767,U_5768,U_5769,c_Code__Numeral_OSuc__code__numeral(U_5770)) = hAPP(U_5769,U_5770),
    inference(variable_rename,[status(thm)],[f_1711_1]) ).

fof(f_1711_3,plain,
    ! [U_5769,U_5767,U_5768,U_5770] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_5767,U_5768,U_5769,c_Code__Numeral_OSuc__code__numeral(U_5770)) = hAPP(U_5769,U_5770),
    inference(definitional_conversion,[status(esa)],[f_1711_2]) ).

cnf(f_1711_4,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_5767,U_5768,U_5769,c_Code__Numeral_OSuc__code__numeral(U_5770)) = hAPP(U_5769,U_5770),
    inference(clausify,[status(thm)],[f_1711_3]) ).

fof(f_1712_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_1712_2,plain,
    ! [U_5771] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_5771)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_5771,
    inference(variable_rename,[status(thm)],[f_1712_1]) ).

fof(f_1712_3,plain,
    ! [U_5771] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_5771)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_5771,
    inference(definitional_conversion,[status(esa)],[f_1712_2]) ).

cnf(f_1712_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_5771)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_5771,
    inference(clausify,[status(thm)],[f_1712_3]) ).

fof(f_1713_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_1713_2,plain,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_1713_1]) ).

cnf(f_1713_3,plain,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_1713_2]) ).

fof(f_1714_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_1714_2,plain,
    ! [U_5772] :
      ( ( ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5772)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5772)),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_5772))))
          | 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_5772)))) )
        & ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5772)) = 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_5772)))
          | ~ 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_5772)))) ) )
      | ~ 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_5772))) ),
    inference(variable_rename,[status(thm)],[f_1714_1]) ).

fof(f_1714_3,plain,
    ( ! [U_5772] :
        ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5772)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5772)),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_5772))))
        | 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_5772))))
        | ~ sP551(U_5772) )
    & ! [U_5772] :
        ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5772)) = 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_5772)))
        | ~ 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_5772))))
        | ~ sP551(U_5772) )
    & ! [U_5772] :
        ( sP551(U_5772)
        | ~ 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_5772))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP551])],[f_1714_2]) ).

cnf(f_1714_4,plain,
    ( sP551(U_5772)
    | ~ 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_5772))) ),
    inference(clausify,[status(thm)],[f_1714_3]) ).

cnf(f_1714_5,plain,
    ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5772)) = 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_5772)))
    | ~ 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_5772))))
    | ~ sP551(U_5772) ),
    inference(clausify,[status(thm)],[f_1714_3]) ).

cnf(f_1714_6,plain,
    ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5772)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5772)),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_5772))))
    | 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_5772))))
    | ~ sP551(U_5772) ),
    inference(clausify,[status(thm)],[f_1714_3]) ).

fof(f_1715_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_1715_2,plain,
    ! [U_5774,U_5773] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5774)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5773)) = 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_5774),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5773)))),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_5773),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5774)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5773)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5774)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5773),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1715_1]) ).

fof(f_1715_3,plain,
    ( ! [U_5778,U_5776] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5778)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5776)) = 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_5778),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5776)))),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_5776),c_Int_OPls)) )
    & ! [U_5777,U_5775] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5777)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5775)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5777)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5775),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1715_2]) ).

fof(f_1715_4,plain,
    ( ! [U_5776,U_5778] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5778)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5776)) = 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_5778),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5776)))),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_5776),c_Int_OPls)) )
    & ! [U_5775,U_5777] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5777)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5775)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5777)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5775),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1715_3]) ).

cnf(f_1715_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5777)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5775)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5777)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5775),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1715_4]) ).

cnf(f_1715_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5778)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5776)) = 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_5778),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5776)))),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_5776),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1715_4]) ).

fof(f_1716_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_1716_2,plain,
    ! [U_5782,U_5781,U_5780,U_5779] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_5779,U_5780,U_5781,c_Code__Numeral_OSuc__code__numeral(U_5782)) = hAPP(hAPP(U_5781,U_5782),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_5779,U_5780,U_5781,U_5782)),
    inference(variable_rename,[status(thm)],[f_1716_1]) ).

fof(f_1716_3,plain,
    ! [U_5779,U_5781,U_5780,U_5782] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_5779,U_5780,U_5781,c_Code__Numeral_OSuc__code__numeral(U_5782)) = hAPP(hAPP(U_5781,U_5782),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_5779,U_5780,U_5781,U_5782)),
    inference(definitional_conversion,[status(esa)],[f_1716_2]) ).

cnf(f_1716_4,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_5779,U_5780,U_5781,c_Code__Numeral_OSuc__code__numeral(U_5782)) = hAPP(hAPP(U_5781,U_5782),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_5779,U_5780,U_5781,U_5782)),
    inference(clausify,[status(thm)],[f_1716_3]) ).

fof(f_1717_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_1717_2,plain,
    ! [U_5784,U_5783] :
      ( c_Divides_Odivmod__nat(U_5784,U_5783) = 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_5784),U_5783)),U_5783))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5784),U_5783),U_5783))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5783),U_5784))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5783)) ),
    inference(variable_rename,[status(thm)],[f_1717_1]) ).

fof(f_1717_3,plain,
    ! [U_5783,U_5784] :
      ( c_Divides_Odivmod__nat(U_5784,U_5783) = 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_5784),U_5783)),U_5783))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5784),U_5783),U_5783))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5783),U_5784))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5783)) ),
    inference(definitional_conversion,[status(esa)],[f_1717_2]) ).

cnf(f_1717_4,plain,
    ( c_Divides_Odivmod__nat(U_5784,U_5783) = 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_5784),U_5783)),U_5783))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5784),U_5783),U_5783))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5783),U_5784))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5783)) ),
    inference(clausify,[status(thm)],[f_1717_3]) ).

fof(f_1718_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_1718_2,plain,
    ! [U_5785] :
      ( ( U_5785 != 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_5785)) )
      & ( 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_5785))
        | U_5785 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_1718_1]) ).

fof(f_1718_3,plain,
    ( ! [U_5787] :
        ( U_5787 != 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_5787)) )
    & ! [U_5786] :
        ( 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_5786))
        | U_5786 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_1718_2]) ).

fof(f_1718_4,plain,
    ( ! [U_5787] :
        ( U_5787 != 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_5787)) )
    & ! [U_5786] :
        ( 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_5786))
        | U_5786 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1718_3]) ).

cnf(f_1718_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_5786))
    | U_5786 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1718_4]) ).

cnf(f_1718_6,plain,
    ( U_5787 != 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_5787)) ),
    inference(clausify,[status(thm)],[f_1718_4]) ).

fof(f_1719_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_1719_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_1719_1]) ).

cnf(f_1719_3,plain,
    c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_1719_2]) ).

fof(f_1720_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_1720_2,plain,
    ! [U_5789,U_5788] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,U_5788) = hAPP(c_Code__Numeral_Oof__nat,U_5789)
        | U_5788 != U_5789 )
      & ( U_5788 = U_5789
        | hAPP(c_Code__Numeral_Oof__nat,U_5788) != hAPP(c_Code__Numeral_Oof__nat,U_5789) ) ),
    inference(variable_rename,[status(thm)],[f_1720_1]) ).

fof(f_1720_3,plain,
    ( ! [U_5793,U_5791] :
        ( hAPP(c_Code__Numeral_Oof__nat,U_5791) = hAPP(c_Code__Numeral_Oof__nat,U_5793)
        | U_5791 != U_5793 )
    & ! [U_5792,U_5790] :
        ( U_5790 = U_5792
        | hAPP(c_Code__Numeral_Oof__nat,U_5790) != hAPP(c_Code__Numeral_Oof__nat,U_5792) ) ),
    inference(miniscope,[status(thm)],[f_1720_2]) ).

fof(f_1720_4,plain,
    ( ! [U_5793,U_5791] :
        ( hAPP(c_Code__Numeral_Oof__nat,U_5791) = hAPP(c_Code__Numeral_Oof__nat,U_5793)
        | U_5791 != U_5793 )
    & ! [U_5792,U_5790] :
        ( U_5790 = U_5792
        | hAPP(c_Code__Numeral_Oof__nat,U_5790) != hAPP(c_Code__Numeral_Oof__nat,U_5792) ) ),
    inference(definitional_conversion,[status(esa)],[f_1720_3]) ).

cnf(f_1720_5,plain,
    ( U_5790 = U_5792
    | hAPP(c_Code__Numeral_Oof__nat,U_5790) != hAPP(c_Code__Numeral_Oof__nat,U_5792) ),
    inference(clausify,[status(thm)],[f_1720_4]) ).

cnf(f_1720_6,plain,
    ( hAPP(c_Code__Numeral_Oof__nat,U_5791) = hAPP(c_Code__Numeral_Oof__nat,U_5793)
    | U_5791 != U_5793 ),
    inference(clausify,[status(thm)],[f_1720_4]) ).

fof(f_1721_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_1721_2,plain,
    ! [U_5794] : c_Divides_Odivmod__nat(U_5794,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_5794),
    inference(variable_rename,[status(thm)],[f_1721_1]) ).

fof(f_1721_3,plain,
    ! [U_5794] : c_Divides_Odivmod__nat(U_5794,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_5794),
    inference(definitional_conversion,[status(esa)],[f_1721_2]) ).

cnf(f_1721_4,plain,
    c_Divides_Odivmod__nat(U_5794,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_5794),
    inference(clausify,[status(thm)],[f_1721_3]) ).

fof(f_1722_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_1722_2,plain,
    ! [U_5798,U_5797,U_5796,U_5795] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5796,U_5795)),U_5797),U_5798) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5795),hAPP(U_5797,U_5798))
      | ~ class_Groups_Ouminus(U_5795) ),
    inference(variable_rename,[status(thm)],[f_1722_1]) ).

fof(f_1722_3,plain,
    ! [U_5795,U_5796,U_5797,U_5798] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5796,U_5795)),U_5797),U_5798) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5795),hAPP(U_5797,U_5798))
      | ~ class_Groups_Ouminus(U_5795) ),
    inference(definitional_conversion,[status(esa)],[f_1722_2]) ).

cnf(f_1722_4,plain,
    ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5796,U_5795)),U_5797),U_5798) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5795),hAPP(U_5797,U_5798))
    | ~ class_Groups_Ouminus(U_5795) ),
    inference(clausify,[status(thm)],[f_1722_3]) ).

fof(f_1723_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_1723_2,plain,
    ! [U_5803,U_5802,U_5801,U_5800,U_5799] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5800,U_5799)),U_5801),U_5802),U_5803) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5799),hAPP(U_5801,U_5803)),hAPP(U_5802,U_5803))
      | ~ class_Groups_Ominus(U_5799) ),
    inference(variable_rename,[status(thm)],[f_1723_1]) ).

fof(f_1723_3,plain,
    ! [U_5799,U_5800,U_5801,U_5802,U_5803] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5800,U_5799)),U_5801),U_5802),U_5803) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5799),hAPP(U_5801,U_5803)),hAPP(U_5802,U_5803))
      | ~ class_Groups_Ominus(U_5799) ),
    inference(definitional_conversion,[status(esa)],[f_1723_2]) ).

cnf(f_1723_4,plain,
    ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5800,U_5799)),U_5801),U_5802),U_5803) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5799),hAPP(U_5801,U_5803)),hAPP(U_5802,U_5803))
    | ~ class_Groups_Ominus(U_5799) ),
    inference(clausify,[status(thm)],[f_1723_3]) ).

fof(f_1724_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_1724_2,plain,
    ! [U_5805,U_5804] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5804)),U_5805))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5804),U_5805)) )
      & ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5804),U_5805))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5804)),U_5805)) ) ),
    inference(variable_rename,[status(thm)],[f_1724_1]) ).

fof(f_1724_3,plain,
    ( ! [U_5809,U_5807] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5807)),U_5809))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5807),U_5809)) )
    & ! [U_5808,U_5806] :
        ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5806),U_5808))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5806)),U_5808)) ) ),
    inference(miniscope,[status(thm)],[f_1724_2]) ).

fof(f_1724_4,plain,
    ( ! [U_5809,U_5807] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5807)),U_5809))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5807),U_5809)) )
    & ! [U_5808,U_5806] :
        ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5806),U_5808))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5806)),U_5808)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1724_3]) ).

cnf(f_1724_5,plain,
    ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5806),U_5808))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5806)),U_5808)) ),
    inference(clausify,[status(thm)],[f_1724_4]) ).

cnf(f_1724_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5807)),U_5809))
    | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5807),U_5809)) ),
    inference(clausify,[status(thm)],[f_1724_4]) ).

fof(f_1725_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_1725_2,plain,
    ! [U_5811,U_5810] :
      ( c_Divides_Odivmod__nat(U_5810,U_5811) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5810)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5810),U_5811)) ),
    inference(variable_rename,[status(thm)],[f_1725_1]) ).

fof(f_1725_3,plain,
    ! [U_5810,U_5811] :
      ( c_Divides_Odivmod__nat(U_5810,U_5811) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5810)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5810),U_5811)) ),
    inference(definitional_conversion,[status(esa)],[f_1725_2]) ).

cnf(f_1725_4,plain,
    ( c_Divides_Odivmod__nat(U_5810,U_5811) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5810)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5810),U_5811)) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

fof(f_1726_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_1726_2,plain,
    ! [U_5812] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5812) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5812)),
    inference(variable_rename,[status(thm)],[f_1726_1]) ).

fof(f_1726_3,plain,
    ! [U_5812] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5812) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5812)),
    inference(definitional_conversion,[status(esa)],[f_1726_2]) ).

cnf(f_1726_4,plain,
    hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5812) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5812)),
    inference(clausify,[status(thm)],[f_1726_3]) ).

fof(f_1727_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_1727_2,plain,
    ! [U_5814,U_5813] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5813),hAPP(c_Nat_OSuc,U_5814)) = 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_5813),U_5814)),
    inference(variable_rename,[status(thm)],[f_1727_1]) ).

fof(f_1727_3,plain,
    ! [U_5813,U_5814] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5813),hAPP(c_Nat_OSuc,U_5814)) = 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_5813),U_5814)),
    inference(definitional_conversion,[status(esa)],[f_1727_2]) ).

cnf(f_1727_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5813),hAPP(c_Nat_OSuc,U_5814)) = 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_5813),U_5814)),
    inference(clausify,[status(thm)],[f_1727_3]) ).

fof(f_1728_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_1728_2,plain,
    ! [U_5815] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5815)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5815)),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_1728_1]) ).

fof(f_1728_3,plain,
    ! [U_5815] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5815)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5815)),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_1728_2]) ).

cnf(f_1728_4,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5815)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5815)),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_1728_3]) ).

fof(f_1729_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_1729_2,plain,
    ! [U_5817,U_5816] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5816)),hAPP(c_Code__Numeral_Oof__nat,U_5817)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5816),U_5817)),
    inference(variable_rename,[status(thm)],[f_1729_1]) ).

fof(f_1729_3,plain,
    ! [U_5816,U_5817] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5816)),hAPP(c_Code__Numeral_Oof__nat,U_5817)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5816),U_5817)),
    inference(definitional_conversion,[status(esa)],[f_1729_2]) ).

cnf(f_1729_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5816)),hAPP(c_Code__Numeral_Oof__nat,U_5817)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5816),U_5817)),
    inference(clausify,[status(thm)],[f_1729_3]) ).

fof(f_1730_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_1730_2,plain,
    ! [U_5819,U_5818] : c_Divides_Odivmod__nat(U_5818,U_5819) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5818),U_5819)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5818,U_5819)),
    inference(variable_rename,[status(thm)],[f_1730_1]) ).

fof(f_1730_3,plain,
    ! [U_5818,U_5819] : c_Divides_Odivmod__nat(U_5818,U_5819) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5818),U_5819)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5818,U_5819)),
    inference(definitional_conversion,[status(esa)],[f_1730_2]) ).

cnf(f_1730_4,plain,
    c_Divides_Odivmod__nat(U_5818,U_5819) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5818),U_5819)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5818,U_5819)),
    inference(clausify,[status(thm)],[f_1730_3]) ).

fof(f_1731_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_1731_2,plain,
    ! [U_5822,U_5821,U_5820] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5820),U_5821),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5822))) = hAPP(hAPP(c_HOL_OLet(U_5820,U_5820),hAPP(hAPP(c_Power_Opower__class_Opower(U_5820),U_5821),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5822))),hAPP(hAPP(c_COMBS(U_5820,U_5820,U_5820),c_Groups_Otimes__class_Otimes(U_5820)),c_COMBI(U_5820)))
      | ~ class_Int_Onumber__ring(U_5820) ),
    inference(variable_rename,[status(thm)],[f_1731_1]) ).

fof(f_1731_3,plain,
    ! [U_5820,U_5821,U_5822] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5820),U_5821),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5822))) = hAPP(hAPP(c_HOL_OLet(U_5820,U_5820),hAPP(hAPP(c_Power_Opower__class_Opower(U_5820),U_5821),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5822))),hAPP(hAPP(c_COMBS(U_5820,U_5820,U_5820),c_Groups_Otimes__class_Otimes(U_5820)),c_COMBI(U_5820)))
      | ~ class_Int_Onumber__ring(U_5820) ),
    inference(definitional_conversion,[status(esa)],[f_1731_2]) ).

cnf(f_1731_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5820),U_5821),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5822))) = hAPP(hAPP(c_HOL_OLet(U_5820,U_5820),hAPP(hAPP(c_Power_Opower__class_Opower(U_5820),U_5821),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5822))),hAPP(hAPP(c_COMBS(U_5820,U_5820,U_5820),c_Groups_Otimes__class_Otimes(U_5820)),c_COMBI(U_5820)))
    | ~ class_Int_Onumber__ring(U_5820) ),
    inference(clausify,[status(thm)],[f_1731_3]) ).

fof(f_1732_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_1732_2,plain,
    ! [U_5824,U_5823] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5823),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5824))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5823),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5824))),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_1732_1]) ).

fof(f_1732_3,plain,
    ! [U_5823,U_5824] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5823),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5824))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5823),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5824))),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_1732_2]) ).

cnf(f_1732_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5823),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5824))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5823),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5824))),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_1732_3]) ).

fof(f_1733_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_1733_2,plain,
    ! [U_5827,U_5826,U_5825] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5825),hAPP(c_Int_Onumber__class_Onumber__of(U_5825),U_5826)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5827))) = hAPP(hAPP(c_HOL_OLet(U_5825,U_5825),hAPP(hAPP(c_Power_Opower__class_Opower(U_5825),hAPP(c_Int_Onumber__class_Onumber__of(U_5825),U_5826)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5827))),hAPP(hAPP(c_COMBS(U_5825,U_5825,U_5825),c_Groups_Otimes__class_Otimes(U_5825)),c_COMBI(U_5825)))
      | ~ class_Int_Onumber__ring(U_5825) ),
    inference(variable_rename,[status(thm)],[f_1733_1]) ).

fof(f_1733_3,plain,
    ! [U_5825,U_5826,U_5827] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5825),hAPP(c_Int_Onumber__class_Onumber__of(U_5825),U_5826)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5827))) = hAPP(hAPP(c_HOL_OLet(U_5825,U_5825),hAPP(hAPP(c_Power_Opower__class_Opower(U_5825),hAPP(c_Int_Onumber__class_Onumber__of(U_5825),U_5826)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5827))),hAPP(hAPP(c_COMBS(U_5825,U_5825,U_5825),c_Groups_Otimes__class_Otimes(U_5825)),c_COMBI(U_5825)))
      | ~ class_Int_Onumber__ring(U_5825) ),
    inference(definitional_conversion,[status(esa)],[f_1733_2]) ).

cnf(f_1733_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5825),hAPP(c_Int_Onumber__class_Onumber__of(U_5825),U_5826)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5827))) = hAPP(hAPP(c_HOL_OLet(U_5825,U_5825),hAPP(hAPP(c_Power_Opower__class_Opower(U_5825),hAPP(c_Int_Onumber__class_Onumber__of(U_5825),U_5826)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5827))),hAPP(hAPP(c_COMBS(U_5825,U_5825,U_5825),c_Groups_Otimes__class_Otimes(U_5825)),c_COMBI(U_5825)))
    | ~ class_Int_Onumber__ring(U_5825) ),
    inference(clausify,[status(thm)],[f_1733_3]) ).

fof(f_1734_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_1734_2,plain,
    ! [U_5829,U_5828] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5829)),hAPP(c_Int_Onat,U_5828)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5829),U_5828)),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_5828)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5829)),hAPP(c_Int_Onat,U_5828)) = hAPP(c_Int_Onat,U_5829)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5828)) ) ),
    inference(variable_rename,[status(thm)],[f_1734_1]) ).

fof(f_1734_3,plain,
    ( ! [U_5833,U_5831] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5833)),hAPP(c_Int_Onat,U_5831)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5833),U_5831)),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_5831)) )
    & ! [U_5832,U_5830] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5832)),hAPP(c_Int_Onat,U_5830)) = hAPP(c_Int_Onat,U_5832)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5830)) ) ),
    inference(miniscope,[status(thm)],[f_1734_2]) ).

fof(f_1734_4,plain,
    ( ! [U_5831,U_5833] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5833)),hAPP(c_Int_Onat,U_5831)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5833),U_5831)),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_5831)) )
    & ! [U_5832,U_5830] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5832)),hAPP(c_Int_Onat,U_5830)) = hAPP(c_Int_Onat,U_5832)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5830)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1734_3]) ).

cnf(f_1734_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5832)),hAPP(c_Int_Onat,U_5830)) = hAPP(c_Int_Onat,U_5832)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5830)) ),
    inference(clausify,[status(thm)],[f_1734_4]) ).

cnf(f_1734_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5833)),hAPP(c_Int_Onat,U_5831)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5833),U_5831)),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_5831)) ),
    inference(clausify,[status(thm)],[f_1734_4]) ).

fof(f_1735_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_1735_2,plain,
    ! [U_5835,U_5834] :
      ( c_Divides_OnegDivAlg(U_5834,U_5835) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5834),U_5835)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5834,U_5835))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5835))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5834),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1735_1]) ).

fof(f_1735_3,plain,
    ! [U_5834,U_5835] :
      ( c_Divides_OnegDivAlg(U_5834,U_5835) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5834),U_5835)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5834,U_5835))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5835))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5834),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1735_2]) ).

cnf(f_1735_4,plain,
    ( c_Divides_OnegDivAlg(U_5834,U_5835) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5834),U_5835)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5834,U_5835))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5835))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5834),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1735_3]) ).

fof(f_1736_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_1736_2,plain,
    ! [U_5836] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_5836) = 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_5836),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1736_1]) ).

fof(f_1736_3,plain,
    ! [U_5836] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_5836) = 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_5836),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1736_2]) ).

cnf(f_1736_4,plain,
    c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_5836) = 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_5836),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1736_3]) ).

fof(f_1737_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_1737_2,plain,
    ! [U_5838,U_5837] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5837),U_5838) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_5837,hAPP(hAPP(c_COMBC(U_5837,U_5837,U_5837),c_Groups_Oplus__class_Oplus(U_5837)),c_Groups_Oone__class_Oone(U_5837)),U_5838,c_Groups_Ozero__class_Ozero(U_5837))
      | ~ class_Rings_Osemiring__1(U_5837) ),
    inference(variable_rename,[status(thm)],[f_1737_1]) ).

fof(f_1737_3,plain,
    ! [U_5837,U_5838] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5837),U_5838) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_5837,hAPP(hAPP(c_COMBC(U_5837,U_5837,U_5837),c_Groups_Oplus__class_Oplus(U_5837)),c_Groups_Oone__class_Oone(U_5837)),U_5838,c_Groups_Ozero__class_Ozero(U_5837))
      | ~ class_Rings_Osemiring__1(U_5837) ),
    inference(definitional_conversion,[status(esa)],[f_1737_2]) ).

cnf(f_1737_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5837),U_5838) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_5837,hAPP(hAPP(c_COMBC(U_5837,U_5837,U_5837),c_Groups_Oplus__class_Oplus(U_5837)),c_Groups_Oone__class_Oone(U_5837)),U_5838,c_Groups_Ozero__class_Ozero(U_5837))
    | ~ class_Rings_Osemiring__1(U_5837) ),
    inference(clausify,[status(thm)],[f_1737_3]) ).

fof(f_1738_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_1738_2,plain,
    ! [U_5841,U_5840,U_5839] : hAPP(c_Divides_Oadjust(U_5839),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5840),U_5841)) = 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_5841),U_5839)),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_5840)),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_5840)),U_5841))),
    inference(variable_rename,[status(thm)],[f_1738_1]) ).

fof(f_1738_3,plain,
    ! [U_5839,U_5840,U_5841] : hAPP(c_Divides_Oadjust(U_5839),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5840),U_5841)) = 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_5841),U_5839)),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_5840)),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_5840)),U_5841))),
    inference(definitional_conversion,[status(esa)],[f_1738_2]) ).

cnf(f_1738_4,plain,
    hAPP(c_Divides_Oadjust(U_5839),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5840),U_5841)) = 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_5841),U_5839)),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_5840)),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_5840)),U_5841))),
    inference(clausify,[status(thm)],[f_1738_3]) ).

fof(f_1739_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_1739_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_1739_1]) ).

cnf(f_1739_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_1739_2]) ).

fof(f_1740_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_1740_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_1740_1]) ).

cnf(f_1740_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_1740_2]) ).

fof(f_1741_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_1741_2,plain,
    ! [U_5843,U_5842] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5842)),hAPP(c_Code__Numeral_Oof__nat,U_5843)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5842),U_5843)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5842),U_5843))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5842)),hAPP(c_Code__Numeral_Oof__nat,U_5843))) ) ),
    inference(variable_rename,[status(thm)],[f_1741_1]) ).

fof(f_1741_3,plain,
    ( ! [U_5847,U_5845] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5845)),hAPP(c_Code__Numeral_Oof__nat,U_5847)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5845),U_5847)) )
    & ! [U_5846,U_5844] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5844),U_5846))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5844)),hAPP(c_Code__Numeral_Oof__nat,U_5846))) ) ),
    inference(miniscope,[status(thm)],[f_1741_2]) ).

fof(f_1741_4,plain,
    ( ! [U_5845,U_5847] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5845)),hAPP(c_Code__Numeral_Oof__nat,U_5847)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5845),U_5847)) )
    & ! [U_5846,U_5844] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5844),U_5846))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5844)),hAPP(c_Code__Numeral_Oof__nat,U_5846))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1741_3]) ).

cnf(f_1741_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5844),U_5846))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5844)),hAPP(c_Code__Numeral_Oof__nat,U_5846))) ),
    inference(clausify,[status(thm)],[f_1741_4]) ).

cnf(f_1741_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5845)),hAPP(c_Code__Numeral_Oof__nat,U_5847)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5845),U_5847)) ),
    inference(clausify,[status(thm)],[f_1741_4]) ).

fof(f_1742_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_1742_2,plain,
    ! [U_5849,U_5848] :
      ( ( hAPP(c_Nat_OSuc,U_5848) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5849)
        | ~ 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_5849))),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_5848))))) )
      & ( 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_5849))),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_5848)))))
        | hAPP(c_Nat_OSuc,U_5848) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5849) ) ),
    inference(variable_rename,[status(thm)],[f_1742_1]) ).

fof(f_1742_3,plain,
    ( ! [U_5853,U_5851] :
        ( hAPP(c_Nat_OSuc,U_5851) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5853)
        | ~ 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_5853))),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_5851))))) )
    & ! [U_5852,U_5850] :
        ( 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_5852))),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_5850)))))
        | hAPP(c_Nat_OSuc,U_5850) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5852) ) ),
    inference(miniscope,[status(thm)],[f_1742_2]) ).

fof(f_1742_4,plain,
    ( ! [U_5853,U_5851] :
        ( hAPP(c_Nat_OSuc,U_5851) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5853)
        | ~ 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_5853))),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_5851))))) )
    & ! [U_5850,U_5852] :
        ( 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_5852))),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_5850)))))
        | hAPP(c_Nat_OSuc,U_5850) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5852) ) ),
    inference(definitional_conversion,[status(esa)],[f_1742_3]) ).

cnf(f_1742_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_5852))),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_5850)))))
    | hAPP(c_Nat_OSuc,U_5850) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5852) ),
    inference(clausify,[status(thm)],[f_1742_4]) ).

cnf(f_1742_6,plain,
    ( hAPP(c_Nat_OSuc,U_5851) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5853)
    | ~ 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_5853))),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_5851))))) ),
    inference(clausify,[status(thm)],[f_1742_4]) ).

fof(f_1743_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_1743_2,plain,
    ! [U_5855,U_5854] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5854) = hAPP(c_Nat_OSuc,U_5855)
        | ~ 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_5854))),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_5855))))) )
      & ( 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_5854))),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_5855)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5854) != hAPP(c_Nat_OSuc,U_5855) ) ),
    inference(variable_rename,[status(thm)],[f_1743_1]) ).

fof(f_1743_3,plain,
    ( ! [U_5859,U_5857] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5857) = hAPP(c_Nat_OSuc,U_5859)
        | ~ 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_5857))),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_5859))))) )
    & ! [U_5858,U_5856] :
        ( 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_5856))),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_5858)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5856) != hAPP(c_Nat_OSuc,U_5858) ) ),
    inference(miniscope,[status(thm)],[f_1743_2]) ).

fof(f_1743_4,plain,
    ( ! [U_5859,U_5857] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5857) = hAPP(c_Nat_OSuc,U_5859)
        | ~ 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_5857))),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_5859))))) )
    & ! [U_5858,U_5856] :
        ( 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_5856))),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_5858)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5856) != hAPP(c_Nat_OSuc,U_5858) ) ),
    inference(definitional_conversion,[status(esa)],[f_1743_3]) ).

cnf(f_1743_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_5856))),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_5858)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5856) != hAPP(c_Nat_OSuc,U_5858) ),
    inference(clausify,[status(thm)],[f_1743_4]) ).

cnf(f_1743_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5857) = hAPP(c_Nat_OSuc,U_5859)
    | ~ 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_5857))),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_5859))))) ),
    inference(clausify,[status(thm)],[f_1743_4]) ).

fof(f_1744_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_1744_2,plain,
    ! [U_5863,U_5862,U_5861,U_5860] : c_Nat_Onat_Onat__case(U_5860,U_5861,U_5862,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5863)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5860),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5863))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5860,U_5860),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5860,tc_fun(U_5860,U_5860)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5860,tc_fun(U_5860,U_5860)),tc_Int_Oint),c_If(U_5860)),c_Nat__Numeral_Oneg)),U_5861)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5860,tc_Int_Oint),U_5862),c_Int_Onat))),
    inference(variable_rename,[status(thm)],[f_1744_1]) ).

fof(f_1744_3,plain,
    ! [U_5860,U_5861,U_5862,U_5863] : c_Nat_Onat_Onat__case(U_5860,U_5861,U_5862,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5863)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5860),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5863))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5860,U_5860),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5860,tc_fun(U_5860,U_5860)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5860,tc_fun(U_5860,U_5860)),tc_Int_Oint),c_If(U_5860)),c_Nat__Numeral_Oneg)),U_5861)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5860,tc_Int_Oint),U_5862),c_Int_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1744_2]) ).

cnf(f_1744_4,plain,
    c_Nat_Onat_Onat__case(U_5860,U_5861,U_5862,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5863)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5860),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5863))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5860,U_5860),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5860,tc_fun(U_5860,U_5860)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5860,tc_fun(U_5860,U_5860)),tc_Int_Oint),c_If(U_5860)),c_Nat__Numeral_Oneg)),U_5861)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5860,tc_Int_Oint),U_5862),c_Int_Onat))),
    inference(clausify,[status(thm)],[f_1744_3]) ).

fof(f_1745_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_1745_2,plain,
    ! [U_5867,U_5866,U_5865,U_5864] : hAPP(c_Nat_Onat_Onat__rec(U_5864,U_5865,U_5866),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5867)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5864),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5867))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5864,U_5864),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5864,tc_fun(U_5864,U_5864)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5864,tc_fun(U_5864,U_5864)),tc_Int_Oint),c_If(U_5864)),c_Nat__Numeral_Oneg)),U_5865)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5864,U_5864),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_5864,U_5864),tc_Int_Oint),U_5866),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5864,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_5864,U_5865,U_5866)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_1745_1]) ).

fof(f_1745_3,plain,
    ! [U_5864,U_5865,U_5866,U_5867] : hAPP(c_Nat_Onat_Onat__rec(U_5864,U_5865,U_5866),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5867)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5864),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5867))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5864,U_5864),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5864,tc_fun(U_5864,U_5864)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5864,tc_fun(U_5864,U_5864)),tc_Int_Oint),c_If(U_5864)),c_Nat__Numeral_Oneg)),U_5865)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5864,U_5864),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_5864,U_5864),tc_Int_Oint),U_5866),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5864,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_5864,U_5865,U_5866)),c_Int_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_1745_2]) ).

cnf(f_1745_4,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_5864,U_5865,U_5866),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5867)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5864),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5867))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5864,U_5864),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5864,tc_fun(U_5864,U_5864)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5864,tc_fun(U_5864,U_5864)),tc_Int_Oint),c_If(U_5864)),c_Nat__Numeral_Oneg)),U_5865)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5864,U_5864),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_5864,U_5864),tc_Int_Oint),U_5866),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5864,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_5864,U_5865,U_5866)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_1745_3]) ).

fof(f_1746_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_1746_2,plain,
    ! [U_5869,U_5868] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5868)),hAPP(c_Code__Numeral_Oof__nat,U_5869)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5868),U_5869)),
    inference(variable_rename,[status(thm)],[f_1746_1]) ).

fof(f_1746_3,plain,
    ! [U_5869,U_5868] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5868)),hAPP(c_Code__Numeral_Oof__nat,U_5869)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5868),U_5869)),
    inference(definitional_conversion,[status(esa)],[f_1746_2]) ).

cnf(f_1746_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5868)),hAPP(c_Code__Numeral_Oof__nat,U_5869)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5868),U_5869)),
    inference(clausify,[status(thm)],[f_1746_3]) ).

fof(f_1747_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_1747_2,plain,
    ! [U_5871,U_5870] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5870)),hAPP(c_Code__Numeral_Oof__nat,U_5871)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5870),U_5871)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5870),U_5871))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5870)),hAPP(c_Code__Numeral_Oof__nat,U_5871))) ) ),
    inference(variable_rename,[status(thm)],[f_1747_1]) ).

fof(f_1747_3,plain,
    ( ! [U_5875,U_5873] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5873)),hAPP(c_Code__Numeral_Oof__nat,U_5875)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5873),U_5875)) )
    & ! [U_5874,U_5872] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5872),U_5874))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5872)),hAPP(c_Code__Numeral_Oof__nat,U_5874))) ) ),
    inference(miniscope,[status(thm)],[f_1747_2]) ).

fof(f_1747_4,plain,
    ( ! [U_5873,U_5875] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5873)),hAPP(c_Code__Numeral_Oof__nat,U_5875)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5873),U_5875)) )
    & ! [U_5874,U_5872] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5872),U_5874))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5872)),hAPP(c_Code__Numeral_Oof__nat,U_5874))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1747_3]) ).

cnf(f_1747_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5872),U_5874))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5872)),hAPP(c_Code__Numeral_Oof__nat,U_5874))) ),
    inference(clausify,[status(thm)],[f_1747_4]) ).

cnf(f_1747_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5873)),hAPP(c_Code__Numeral_Oof__nat,U_5875)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5873),U_5875)) ),
    inference(clausify,[status(thm)],[f_1747_4]) ).

fof(f_1748_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_1748_2,plain,
    ! [U_5876] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5876)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5876)),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_5876))) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5876)) = 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_5876))) ) ),
    inference(variable_rename,[status(thm)],[f_1748_1]) ).

fof(f_1748_3,plain,
    ( ! [U_5878] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5878)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5878)),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_5878))) )
    & ! [U_5877] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5877)) = 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_5877))) ) ),
    inference(miniscope,[status(thm)],[f_1748_2]) ).

fof(f_1748_4,plain,
    ( ! [U_5878] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5878)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5878)),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_5878))) )
    & ! [U_5877] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5877)) = 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_5877))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1748_3]) ).

cnf(f_1748_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5877)) = 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_5877))) ),
    inference(clausify,[status(thm)],[f_1748_4]) ).

cnf(f_1748_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5878)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5878)),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_5878))) ),
    inference(clausify,[status(thm)],[f_1748_4]) ).

fof(f_1749_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_1749_2,plain,
    ! [U_5880,U_5879] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5879)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5880)))
        | ~ 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_5880))),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_5879)),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_5880))),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_5879)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5879)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5880))) ) ),
    inference(variable_rename,[status(thm)],[f_1749_1]) ).

fof(f_1749_3,plain,
    ( ! [U_5884,U_5882] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5882)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5884)))
        | ~ 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_5884))),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_5882)),c_Int_Onat))))) )
    & ! [U_5883,U_5881] :
        ( 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_5883))),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_5881)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5881)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5883))) ) ),
    inference(miniscope,[status(thm)],[f_1749_2]) ).

fof(f_1749_4,plain,
    ( ! [U_5882,U_5884] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5882)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5884)))
        | ~ 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_5884))),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_5882)),c_Int_Onat))))) )
    & ! [U_5883,U_5881] :
        ( 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_5883))),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_5881)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5881)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5883))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1749_3]) ).

cnf(f_1749_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_5883))),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_5881)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5881)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5883))) ),
    inference(clausify,[status(thm)],[f_1749_4]) ).

cnf(f_1749_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5882)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5884)))
    | ~ 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_5884))),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_5882)),c_Int_Onat))))) ),
    inference(clausify,[status(thm)],[f_1749_4]) ).

fof(f_1750_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_1750_2,plain,
    ! [U_5886,U_5885] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),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_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_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_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_5886))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5885)),hAPP(c_Nat_OSuc,U_5886))) ) ),
    inference(variable_rename,[status(thm)],[f_1750_1]) ).

fof(f_1750_3,plain,
    ( ! [U_5890,U_5888] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),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_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_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_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_5889))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5887)),hAPP(c_Nat_OSuc,U_5889))) ) ),
    inference(miniscope,[status(thm)],[f_1750_2]) ).

fof(f_1750_4,plain,
    ( ! [U_5890,U_5888] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),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_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_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_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_5889))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5887)),hAPP(c_Nat_OSuc,U_5889))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1750_3]) ).

cnf(f_1750_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_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_5889))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5887)),hAPP(c_Nat_OSuc,U_5889))) ),
    inference(clausify,[status(thm)],[f_1750_4]) ).

cnf(f_1750_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),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_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_5890)))) ),
    inference(clausify,[status(thm)],[f_1750_4]) ).

fof(f_1751_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_1751_2,plain,
    ! [U_5892,U_5891] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5891)),hAPP(c_Nat_OSuc,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_5891))),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_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_5891))),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_5892))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5891)),hAPP(c_Nat_OSuc,U_5892))) ) ),
    inference(variable_rename,[status(thm)],[f_1751_1]) ).

fof(f_1751_3,plain,
    ( ! [U_5896,U_5894] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5894)),hAPP(c_Nat_OSuc,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_5894))),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_5896)))) )
    & ! [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_5893))),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_5895))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5893)),hAPP(c_Nat_OSuc,U_5895))) ) ),
    inference(miniscope,[status(thm)],[f_1751_2]) ).

fof(f_1751_4,plain,
    ( ! [U_5894,U_5896] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5894)),hAPP(c_Nat_OSuc,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_5894))),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_5896)))) )
    & ! [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_5893))),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_5895))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5893)),hAPP(c_Nat_OSuc,U_5895))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1751_3]) ).

cnf(f_1751_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_5893))),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_5895))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5893)),hAPP(c_Nat_OSuc,U_5895))) ),
    inference(clausify,[status(thm)],[f_1751_4]) ).

cnf(f_1751_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_5894)),hAPP(c_Nat_OSuc,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_5894))),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_5896)))) ),
    inference(clausify,[status(thm)],[f_1751_4]) ).

fof(f_1752_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_1752_2,plain,
    ! [U_5898,U_5897] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5897)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5898)))
        | ~ 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_5898))),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_5897)),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_5898))),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_5897)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5897)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5898))) ) ),
    inference(variable_rename,[status(thm)],[f_1752_1]) ).

fof(f_1752_3,plain,
    ( ! [U_5902,U_5900] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5900)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),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_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_5900)),c_Int_Onat))))) )
    & ! [U_5901,U_5899] :
        ( 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_5901))),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_5899)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5899)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5901))) ) ),
    inference(miniscope,[status(thm)],[f_1752_2]) ).

fof(f_1752_4,plain,
    ( ! [U_5900,U_5902] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5900)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),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_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_5900)),c_Int_Onat))))) )
    & ! [U_5901,U_5899] :
        ( 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_5901))),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_5899)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5899)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5901))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1752_3]) ).

cnf(f_1752_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_5901))),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_5899)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5899)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5901))) ),
    inference(clausify,[status(thm)],[f_1752_4]) ).

cnf(f_1752_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5900)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),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_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_5900)),c_Int_Onat))))) ),
    inference(clausify,[status(thm)],[f_1752_4]) ).

fof(f_1753_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_1753_2,plain,
    ! [U_5904,U_5903] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_5903)),hAPP(c_Code__Numeral_Oof__nat,U_5904)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5903),U_5904)),
    inference(variable_rename,[status(thm)],[f_1753_1]) ).

fof(f_1753_3,plain,
    ! [U_5904,U_5903] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_5903)),hAPP(c_Code__Numeral_Oof__nat,U_5904)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5903),U_5904)),
    inference(definitional_conversion,[status(esa)],[f_1753_2]) ).

cnf(f_1753_4,plain,
    hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_5903)),hAPP(c_Code__Numeral_Oof__nat,U_5904)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5903),U_5904)),
    inference(clausify,[status(thm)],[f_1753_3]) ).

fof(f_1754_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_1754_2,plain,
    ! [U_5909,U_5908,U_5907,U_5906,U_5905] : c_Nat_Onat_Onat__case(U_5905,U_5906,U_5907,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5908)),U_5909)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5905),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5908))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5905,U_5905),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5905,tc_fun(U_5905,U_5905)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5905,tc_fun(U_5905,U_5905)),tc_Int_Oint),c_If(U_5905)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_5905,U_5906,U_5907,U_5909))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5905,tc_Int_Oint),U_5907),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_5909)))),
    inference(variable_rename,[status(thm)],[f_1754_1]) ).

fof(f_1754_3,plain,
    ! [U_5905,U_5906,U_5907,U_5908,U_5909] : c_Nat_Onat_Onat__case(U_5905,U_5906,U_5907,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5908)),U_5909)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5905),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5908))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5905,U_5905),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5905,tc_fun(U_5905,U_5905)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5905,tc_fun(U_5905,U_5905)),tc_Int_Oint),c_If(U_5905)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_5905,U_5906,U_5907,U_5909))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5905,tc_Int_Oint),U_5907),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_5909)))),
    inference(definitional_conversion,[status(esa)],[f_1754_2]) ).

cnf(f_1754_4,plain,
    c_Nat_Onat_Onat__case(U_5905,U_5906,U_5907,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5908)),U_5909)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5905),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5908))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5905,U_5905),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5905,tc_fun(U_5905,U_5905)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5905,tc_fun(U_5905,U_5905)),tc_Int_Oint),c_If(U_5905)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_5905,U_5906,U_5907,U_5909))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5905,tc_Int_Oint),U_5907),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_5909)))),
    inference(clausify,[status(thm)],[f_1754_3]) ).

fof(f_1755_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_1755_2,plain,
    ! [U_5914,U_5913,U_5912,U_5911,U_5910] : hAPP(c_Nat_Onat_Onat__rec(U_5910,U_5911,U_5912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5913)),U_5914)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5910),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5913))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5910,U_5910),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5910,tc_fun(U_5910,U_5910)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5910,tc_fun(U_5910,U_5910)),tc_Int_Oint),c_If(U_5910)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_5910,U_5911,U_5912),U_5914))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5910,U_5910),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_5910,U_5910),tc_Int_Oint),U_5912),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_5914))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5910,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_5910,U_5911,U_5912)),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_5914))))),
    inference(variable_rename,[status(thm)],[f_1755_1]) ).

fof(f_1755_3,plain,
    ! [U_5910,U_5911,U_5912,U_5913,U_5914] : hAPP(c_Nat_Onat_Onat__rec(U_5910,U_5911,U_5912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5913)),U_5914)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5910),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5913))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5910,U_5910),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5910,tc_fun(U_5910,U_5910)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5910,tc_fun(U_5910,U_5910)),tc_Int_Oint),c_If(U_5910)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_5910,U_5911,U_5912),U_5914))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5910,U_5910),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_5910,U_5910),tc_Int_Oint),U_5912),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_5914))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5910,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_5910,U_5911,U_5912)),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_5914))))),
    inference(definitional_conversion,[status(esa)],[f_1755_2]) ).

cnf(f_1755_4,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_5910,U_5911,U_5912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5913)),U_5914)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5910),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5913))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5910,U_5910),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5910,tc_fun(U_5910,U_5910)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5910,tc_fun(U_5910,U_5910)),tc_Int_Oint),c_If(U_5910)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_5910,U_5911,U_5912),U_5914))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5910,U_5910),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_5910,U_5910),tc_Int_Oint),U_5912),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_5914))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5910,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_5910,U_5911,U_5912)),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_5914))))),
    inference(clausify,[status(thm)],[f_1755_3]) ).

fof(f_1756_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_1756_2,plain,
    ! [U_5917,U_5916,U_5915] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5915),U_5917),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5916))) = c_Groups_Oone__class_Oone(U_5915)
          | 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_5916))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5915),U_5917),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5916))) = hAPP(hAPP(c_HOL_OLet(U_5915,U_5915),hAPP(hAPP(c_Power_Opower__class_Opower(U_5915),U_5917),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5916))),hAPP(hAPP(c_COMBS(U_5915,U_5915,U_5915),hAPP(hAPP(c_COMBB(U_5915,tc_fun(U_5915,U_5915),U_5915),c_Groups_Otimes__class_Otimes(U_5915)),hAPP(c_Groups_Otimes__class_Otimes(U_5915),U_5917))),c_COMBI(U_5915)))
          | ~ 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_5916))) ) )
      | ~ class_Int_Onumber__ring(U_5915) ),
    inference(variable_rename,[status(thm)],[f_1756_1]) ).

fof(f_1756_3,plain,
    ( ! [U_5915,U_5916,U_5917] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5915),U_5917),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5916))) = c_Groups_Oone__class_Oone(U_5915)
        | 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_5916)))
        | ~ sP552(U_5915,U_5916,U_5917) )
    & ! [U_5915,U_5916,U_5917] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5915),U_5917),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5916))) = hAPP(hAPP(c_HOL_OLet(U_5915,U_5915),hAPP(hAPP(c_Power_Opower__class_Opower(U_5915),U_5917),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5916))),hAPP(hAPP(c_COMBS(U_5915,U_5915,U_5915),hAPP(hAPP(c_COMBB(U_5915,tc_fun(U_5915,U_5915),U_5915),c_Groups_Otimes__class_Otimes(U_5915)),hAPP(c_Groups_Otimes__class_Otimes(U_5915),U_5917))),c_COMBI(U_5915)))
        | ~ 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_5916)))
        | ~ sP552(U_5915,U_5916,U_5917) )
    & ! [U_5915,U_5916,U_5917] :
        ( sP552(U_5915,U_5916,U_5917)
        | ~ class_Int_Onumber__ring(U_5915) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP552])],[f_1756_2]) ).

cnf(f_1756_4,plain,
    ( sP552(U_5915,U_5916,U_5917)
    | ~ class_Int_Onumber__ring(U_5915) ),
    inference(clausify,[status(thm)],[f_1756_3]) ).

cnf(f_1756_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5915),U_5917),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5916))) = hAPP(hAPP(c_HOL_OLet(U_5915,U_5915),hAPP(hAPP(c_Power_Opower__class_Opower(U_5915),U_5917),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5916))),hAPP(hAPP(c_COMBS(U_5915,U_5915,U_5915),hAPP(hAPP(c_COMBB(U_5915,tc_fun(U_5915,U_5915),U_5915),c_Groups_Otimes__class_Otimes(U_5915)),hAPP(c_Groups_Otimes__class_Otimes(U_5915),U_5917))),c_COMBI(U_5915)))
    | ~ 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_5916)))
    | ~ sP552(U_5915,U_5916,U_5917) ),
    inference(clausify,[status(thm)],[f_1756_3]) ).

cnf(f_1756_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5915),U_5917),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5916))) = c_Groups_Oone__class_Oone(U_5915)
    | 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_5916)))
    | ~ sP552(U_5915,U_5916,U_5917) ),
    inference(clausify,[status(thm)],[f_1756_3]) ).

fof(f_1757_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_1757_2,plain,
    ! [U_5919,U_5918] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5919),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5918))) = 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_5918))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5919),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5918))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5919),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5918))),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_5919))),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_5918))) ) ),
    inference(variable_rename,[status(thm)],[f_1757_1]) ).

fof(f_1757_3,plain,
    ( ! [U_5923,U_5921] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5923),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5921))) = 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_5921))) )
    & ! [U_5922,U_5920] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5922),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5920))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5922),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5920))),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_5922))),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_5920))) ) ),
    inference(miniscope,[status(thm)],[f_1757_2]) ).

fof(f_1757_4,plain,
    ( ! [U_5921,U_5923] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5923),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5921))) = 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_5921))) )
    & ! [U_5920,U_5922] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5922),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5920))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5922),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5920))),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_5922))),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_5920))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1757_3]) ).

cnf(f_1757_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5922),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5920))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5922),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5920))),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_5922))),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_5920))) ),
    inference(clausify,[status(thm)],[f_1757_4]) ).

cnf(f_1757_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5923),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5921))) = 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_5921))) ),
    inference(clausify,[status(thm)],[f_1757_4]) ).

fof(f_1758_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_1758_2,plain,
    ! [U_5925,U_5924] :
      ( ( c_Divides_OnegDivAlg(U_5924,U_5925) = hAPP(c_Divides_Oadjust(U_5925),c_Divides_OnegDivAlg(U_5924,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_5925)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5925),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_5924),U_5925))) )
      & ( c_Divides_OnegDivAlg(U_5924,U_5925) = 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_5924),U_5925))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5925),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_5924),U_5925))) ) ) ),
    inference(variable_rename,[status(thm)],[f_1758_1]) ).

fof(f_1758_3,plain,
    ( ! [U_5929,U_5927] :
        ( c_Divides_OnegDivAlg(U_5927,U_5929) = hAPP(c_Divides_Oadjust(U_5929),c_Divides_OnegDivAlg(U_5927,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_5929)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5929),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_5927),U_5929))) )
    & ! [U_5928,U_5926] :
        ( c_Divides_OnegDivAlg(U_5926,U_5928) = 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_5926),U_5928))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5928),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_5926),U_5928))) ) ) ),
    inference(miniscope,[status(thm)],[f_1758_2]) ).

fof(f_1758_4,plain,
    ( ! [U_5928,U_5926] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5928),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP553(U_5928,U_5926) )
    & ! [U_5928,U_5926] :
        ( ~ 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_5926),U_5928)))
        | ~ sP553(U_5928,U_5926) )
    & ! [U_5929,U_5927] :
        ( c_Divides_OnegDivAlg(U_5927,U_5929) = hAPP(c_Divides_Oadjust(U_5929),c_Divides_OnegDivAlg(U_5927,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_5929)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5929),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_5927),U_5929))) )
    & ! [U_5928,U_5926] :
        ( c_Divides_OnegDivAlg(U_5926,U_5928) = 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_5926),U_5928))
        | sP553(U_5928,U_5926) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP553])],[f_1758_3]) ).

cnf(f_1758_5,plain,
    ( c_Divides_OnegDivAlg(U_5926,U_5928) = 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_5926),U_5928))
    | sP553(U_5928,U_5926) ),
    inference(clausify,[status(thm)],[f_1758_4]) ).

cnf(f_1758_6,plain,
    ( c_Divides_OnegDivAlg(U_5927,U_5929) = hAPP(c_Divides_Oadjust(U_5929),c_Divides_OnegDivAlg(U_5927,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_5929)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5929),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_5927),U_5929))) ),
    inference(clausify,[status(thm)],[f_1758_4]) ).

cnf(f_1758_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_5926),U_5928)))
    | ~ sP553(U_5928,U_5926) ),
    inference(clausify,[status(thm)],[f_1758_4]) ).

cnf(f_1758_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5928),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP553(U_5928,U_5926) ),
    inference(clausify,[status(thm)],[f_1758_4]) ).

fof(f_1759_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_1759_2,plain,
    ! [U_5932,U_5931,U_5930] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5930),hAPP(c_Int_Onumber__class_Onumber__of(U_5930),U_5932)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5931))) = c_Groups_Oone__class_Oone(U_5930)
          | 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_5931))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5930),hAPP(c_Int_Onumber__class_Onumber__of(U_5930),U_5932)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5931))) = hAPP(hAPP(c_HOL_OLet(U_5930,U_5930),hAPP(hAPP(c_Power_Opower__class_Opower(U_5930),hAPP(c_Int_Onumber__class_Onumber__of(U_5930),U_5932)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5931))),hAPP(hAPP(c_COMBS(U_5930,U_5930,U_5930),hAPP(hAPP(c_COMBB(U_5930,tc_fun(U_5930,U_5930),U_5930),c_Groups_Otimes__class_Otimes(U_5930)),hAPP(c_Groups_Otimes__class_Otimes(U_5930),hAPP(c_Int_Onumber__class_Onumber__of(U_5930),U_5932)))),c_COMBI(U_5930)))
          | ~ 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_5931))) ) )
      | ~ class_Int_Onumber__ring(U_5930) ),
    inference(variable_rename,[status(thm)],[f_1759_1]) ).

fof(f_1759_3,plain,
    ( ! [U_5931,U_5930,U_5932] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5930),hAPP(c_Int_Onumber__class_Onumber__of(U_5930),U_5932)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5931))) = c_Groups_Oone__class_Oone(U_5930)
        | 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_5931)))
        | ~ sP554(U_5931,U_5930,U_5932) )
    & ! [U_5931,U_5930,U_5932] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5930),hAPP(c_Int_Onumber__class_Onumber__of(U_5930),U_5932)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5931))) = hAPP(hAPP(c_HOL_OLet(U_5930,U_5930),hAPP(hAPP(c_Power_Opower__class_Opower(U_5930),hAPP(c_Int_Onumber__class_Onumber__of(U_5930),U_5932)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5931))),hAPP(hAPP(c_COMBS(U_5930,U_5930,U_5930),hAPP(hAPP(c_COMBB(U_5930,tc_fun(U_5930,U_5930),U_5930),c_Groups_Otimes__class_Otimes(U_5930)),hAPP(c_Groups_Otimes__class_Otimes(U_5930),hAPP(c_Int_Onumber__class_Onumber__of(U_5930),U_5932)))),c_COMBI(U_5930)))
        | ~ 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_5931)))
        | ~ sP554(U_5931,U_5930,U_5932) )
    & ! [U_5931,U_5930,U_5932] :
        ( sP554(U_5931,U_5930,U_5932)
        | ~ class_Int_Onumber__ring(U_5930) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP554])],[f_1759_2]) ).

cnf(f_1759_4,plain,
    ( sP554(U_5931,U_5930,U_5932)
    | ~ class_Int_Onumber__ring(U_5930) ),
    inference(clausify,[status(thm)],[f_1759_3]) ).

cnf(f_1759_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5930),hAPP(c_Int_Onumber__class_Onumber__of(U_5930),U_5932)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5931))) = hAPP(hAPP(c_HOL_OLet(U_5930,U_5930),hAPP(hAPP(c_Power_Opower__class_Opower(U_5930),hAPP(c_Int_Onumber__class_Onumber__of(U_5930),U_5932)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5931))),hAPP(hAPP(c_COMBS(U_5930,U_5930,U_5930),hAPP(hAPP(c_COMBB(U_5930,tc_fun(U_5930,U_5930),U_5930),c_Groups_Otimes__class_Otimes(U_5930)),hAPP(c_Groups_Otimes__class_Otimes(U_5930),hAPP(c_Int_Onumber__class_Onumber__of(U_5930),U_5932)))),c_COMBI(U_5930)))
    | ~ 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_5931)))
    | ~ sP554(U_5931,U_5930,U_5932) ),
    inference(clausify,[status(thm)],[f_1759_3]) ).

cnf(f_1759_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5930),hAPP(c_Int_Onumber__class_Onumber__of(U_5930),U_5932)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5931))) = c_Groups_Oone__class_Oone(U_5930)
    | 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_5931)))
    | ~ sP554(U_5931,U_5930,U_5932) ),
    inference(clausify,[status(thm)],[f_1759_3]) ).

fof(f_1760_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_1760_2,plain,
    ! [U_5935,U_5934,U_5933] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_5933,U_5934,U_5935,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_5934,
    inference(variable_rename,[status(thm)],[f_1760_1]) ).

fof(f_1760_3,plain,
    ! [U_5934,U_5935,U_5933] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_5933,U_5934,U_5935,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_5934,
    inference(definitional_conversion,[status(esa)],[f_1760_2]) ).

cnf(f_1760_4,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_5933,U_5934,U_5935,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_5934,
    inference(clausify,[status(thm)],[f_1760_3]) ).

fof(f_1761_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_1761_2,plain,
    ! [U_5937,U_5936] :
      ( ( ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5937),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5937),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_5936))))
          | 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_5937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936)))) )
        & ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5937),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936)) = 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_5937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936)))
          | ~ 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_5937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936)))) ) )
      | ~ 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_5936))) ),
    inference(variable_rename,[status(thm)],[f_1761_1]) ).

fof(f_1761_3,plain,
    ( ! [U_5937,U_5936] :
        ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5937),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5937),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_5936))))
        | 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_5937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936))))
        | ~ sP555(U_5937,U_5936) )
    & ! [U_5937,U_5936] :
        ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5937),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936)) = 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_5937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936)))
        | ~ 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_5937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936))))
        | ~ sP555(U_5937,U_5936) )
    & ! [U_5937,U_5936] :
        ( sP555(U_5937,U_5936)
        | ~ 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_5936))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP555])],[f_1761_2]) ).

cnf(f_1761_4,plain,
    ( sP555(U_5937,U_5936)
    | ~ 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_5936))) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_5,plain,
    ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5937),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936)) = 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_5937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936)))
    | ~ 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_5937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936))))
    | ~ sP555(U_5937,U_5936) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_6,plain,
    ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5937),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5937),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_5936))))
    | 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_5937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5936))))
    | ~ sP555(U_5937,U_5936) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

fof(f_1762_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_1762_2,plain,
    ! [U_5939,U_5938] :
      ( ( ( c_Divides_OnegDivAlg(U_5939,U_5938) = hAPP(c_Divides_Oadjust(U_5938),c_Divides_OnegDivAlg(U_5939,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_5938)))
          | 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_5939),U_5938))) )
        & ( c_Divides_OnegDivAlg(U_5939,U_5938) = 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_5939),U_5938))
          | ~ 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_5939),U_5938))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5938)) ),
    inference(variable_rename,[status(thm)],[f_1762_1]) ).

fof(f_1762_3,plain,
    ( ! [U_5938,U_5939] :
        ( c_Divides_OnegDivAlg(U_5939,U_5938) = hAPP(c_Divides_Oadjust(U_5938),c_Divides_OnegDivAlg(U_5939,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_5938)))
        | 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_5939),U_5938)))
        | ~ sP556(U_5938,U_5939) )
    & ! [U_5938,U_5939] :
        ( c_Divides_OnegDivAlg(U_5939,U_5938) = 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_5939),U_5938))
        | ~ 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_5939),U_5938)))
        | ~ sP556(U_5938,U_5939) )
    & ! [U_5938,U_5939] :
        ( sP556(U_5938,U_5939)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5938)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP556])],[f_1762_2]) ).

cnf(f_1762_4,plain,
    ( sP556(U_5938,U_5939)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5938)) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_5,plain,
    ( c_Divides_OnegDivAlg(U_5939,U_5938) = 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_5939),U_5938))
    | ~ 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_5939),U_5938)))
    | ~ sP556(U_5938,U_5939) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_6,plain,
    ( c_Divides_OnegDivAlg(U_5939,U_5938) = hAPP(c_Divides_Oadjust(U_5938),c_Divides_OnegDivAlg(U_5939,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_5938)))
    | 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_5939),U_5938)))
    | ~ sP556(U_5938,U_5939) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

fof(f_1763_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_1763_2,plain,
    ! [U_5941,U_5940] :
      ( ( ( ( c_Nitpick_Onorm__frac(U_5941,U_5940) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_5941),U_5940)),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_5941))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5940)))
            | U_5940 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
            | U_5941 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Nitpick_Onorm__frac(U_5941,U_5940) = 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_5940 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & U_5941 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5940),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( c_Nitpick_Onorm__frac(U_5941,U_5940) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5941),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5940))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5940),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1763_1]) ).

fof(f_1763_3,plain,
    ( ! [U_5945,U_5943] :
        ( ( ( c_Nitpick_Onorm__frac(U_5945,U_5943) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_5945),U_5943)),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_5945))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5943)))
            | U_5943 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
            | U_5945 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Nitpick_Onorm__frac(U_5945,U_5943) = 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_5943 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & U_5945 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5943),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_5944,U_5942] :
        ( c_Nitpick_Onorm__frac(U_5944,U_5942) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5944),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5942))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5942),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1763_2]) ).

fof(f_1763_4,plain,
    ( ! [U_5945,U_5943] :
        ( U_5943 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP557(U_5945,U_5943) )
    & ! [U_5945,U_5943] :
        ( U_5945 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP557(U_5945,U_5943) )
    & ! [U_5945,U_5943] :
        ( c_Nitpick_Onorm__frac(U_5945,U_5943) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_5945),U_5943)),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_5945))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5943)))
        | U_5943 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_5945 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP558(U_5945,U_5943) )
    & ! [U_5945,U_5943] :
        ( c_Nitpick_Onorm__frac(U_5945,U_5943) = 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))
        | sP557(U_5945,U_5943)
        | ~ sP558(U_5945,U_5943) )
    & ! [U_5945,U_5943] :
        ( sP558(U_5945,U_5943)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5943),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_5942,U_5944] :
        ( c_Nitpick_Onorm__frac(U_5944,U_5942) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5944),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5942))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5942),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP557,sP558])],[f_1763_3]) ).

cnf(f_1763_5,plain,
    ( c_Nitpick_Onorm__frac(U_5944,U_5942) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5944),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5942))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5942),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1763_4]) ).

cnf(f_1763_6,plain,
    ( sP558(U_5945,U_5943)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5943),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1763_4]) ).

cnf(f_1763_7,plain,
    ( c_Nitpick_Onorm__frac(U_5945,U_5943) = 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))
    | sP557(U_5945,U_5943)
    | ~ sP558(U_5945,U_5943) ),
    inference(clausify,[status(thm)],[f_1763_4]) ).

cnf(f_1763_8,plain,
    ( c_Nitpick_Onorm__frac(U_5945,U_5943) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_5945),U_5943)),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_5945))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5943)))
    | U_5943 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_5945 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP558(U_5945,U_5943) ),
    inference(clausify,[status(thm)],[f_1763_4]) ).

cnf(f_1763_9,plain,
    ( U_5945 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP557(U_5945,U_5943) ),
    inference(clausify,[status(thm)],[f_1763_4]) ).

cnf(f_1763_10,plain,
    ( U_5943 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP557(U_5945,U_5943) ),
    inference(clausify,[status(thm)],[f_1763_4]) ).

fof(f_1764_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_1764_2,plain,
    ! [U_5946] :
      ( ( ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5946)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5946)),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_5946))))
          | 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_5946))) )
        & ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5946)) = 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_5946))) ) )
      | ~ 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_5946))) ),
    inference(variable_rename,[status(thm)],[f_1764_1]) ).

fof(f_1764_3,plain,
    ( ! [U_5946] :
        ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5946)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5946)),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_5946))))
        | 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_5946)))
        | ~ sP559(U_5946) )
    & ! [U_5946] :
        ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5946)) = 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_5946)))
        | ~ sP559(U_5946) )
    & ! [U_5946] :
        ( sP559(U_5946)
        | ~ 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_5946))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP559])],[f_1764_2]) ).

cnf(f_1764_4,plain,
    ( sP559(U_5946)
    | ~ 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_5946))) ),
    inference(clausify,[status(thm)],[f_1764_3]) ).

cnf(f_1764_5,plain,
    ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5946)) = 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_5946)))
    | ~ sP559(U_5946) ),
    inference(clausify,[status(thm)],[f_1764_3]) ).

cnf(f_1764_6,plain,
    ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5946)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5946)),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_5946))))
    | 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_5946)))
    | ~ sP559(U_5946) ),
    inference(clausify,[status(thm)],[f_1764_3]) ).

fof(f_1765_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_1765_2,plain,
    ! [U_5948,U_5947] :
      ( ( c_Divides_OposDivAlg(U_5947,U_5948) = hAPP(c_Divides_Oadjust(U_5948),c_Divides_OposDivAlg(U_5947,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_5948)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5948),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5947),U_5948)) )
      & ( c_Divides_OposDivAlg(U_5947,U_5948) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5947)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5948),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5947),U_5948)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1765_1]) ).

fof(f_1765_3,plain,
    ( ! [U_5952,U_5950] :
        ( c_Divides_OposDivAlg(U_5950,U_5952) = hAPP(c_Divides_Oadjust(U_5952),c_Divides_OposDivAlg(U_5950,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_5952)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5952),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5950),U_5952)) )
    & ! [U_5951,U_5949] :
        ( c_Divides_OposDivAlg(U_5949,U_5951) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5949)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5951),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5949),U_5951)) ) ) ),
    inference(miniscope,[status(thm)],[f_1765_2]) ).

fof(f_1765_4,plain,
    ( ! [U_5951,U_5949] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5951),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP560(U_5951,U_5949) )
    & ! [U_5951,U_5949] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5949),U_5951))
        | ~ sP560(U_5951,U_5949) )
    & ! [U_5950,U_5952] :
        ( c_Divides_OposDivAlg(U_5950,U_5952) = hAPP(c_Divides_Oadjust(U_5952),c_Divides_OposDivAlg(U_5950,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_5952)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5952),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5950),U_5952)) )
    & ! [U_5951,U_5949] :
        ( c_Divides_OposDivAlg(U_5949,U_5951) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5949)
        | sP560(U_5951,U_5949) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP560])],[f_1765_3]) ).

cnf(f_1765_5,plain,
    ( c_Divides_OposDivAlg(U_5949,U_5951) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5949)
    | sP560(U_5951,U_5949) ),
    inference(clausify,[status(thm)],[f_1765_4]) ).

cnf(f_1765_6,plain,
    ( c_Divides_OposDivAlg(U_5950,U_5952) = hAPP(c_Divides_Oadjust(U_5952),c_Divides_OposDivAlg(U_5950,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_5952)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5952),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5950),U_5952)) ),
    inference(clausify,[status(thm)],[f_1765_4]) ).

cnf(f_1765_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5949),U_5951))
    | ~ sP560(U_5951,U_5949) ),
    inference(clausify,[status(thm)],[f_1765_4]) ).

cnf(f_1765_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5951),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP560(U_5951,U_5949) ),
    inference(clausify,[status(thm)],[f_1765_4]) ).

fof(f_1766_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_1766_2,plain,
    ! [U_5953] : c_Divides_Oadjust(U_5953) = 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_5953))))),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_5953))))),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_1766_1]) ).

fof(f_1766_3,plain,
    ! [U_5953] : c_Divides_Oadjust(U_5953) = 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_5953))))),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_5953))))),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_1766_2]) ).

cnf(f_1766_4,plain,
    c_Divides_Oadjust(U_5953) = 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_5953))))),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_5953))))),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_1766_3]) ).

fof(f_1767_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_1767_2,plain,
    ! [U_5955,U_5954] :
      ( ( ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5955),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5954)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5954)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5955),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_5954))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5955)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5954))) )
        & ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5955),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5954)) = 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_5955))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5955)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5954))) ) )
      | ~ 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_5954))) ),
    inference(variable_rename,[status(thm)],[f_1767_1]) ).

fof(f_1767_3,plain,
    ( ! [U_5954,U_5955] :
        ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5955),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5954)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5954)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5955),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_5954))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5955)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5954)))
        | ~ sP561(U_5954,U_5955) )
    & ! [U_5954,U_5955] :
        ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5955),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5954)) = 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_5955))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5955)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5954)))
        | ~ sP561(U_5954,U_5955) )
    & ! [U_5954,U_5955] :
        ( sP561(U_5954,U_5955)
        | ~ 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_5954))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP561])],[f_1767_2]) ).

cnf(f_1767_4,plain,
    ( sP561(U_5954,U_5955)
    | ~ 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_5954))) ),
    inference(clausify,[status(thm)],[f_1767_3]) ).

cnf(f_1767_5,plain,
    ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5955),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5954)) = 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_5955))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5955)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5954)))
    | ~ sP561(U_5954,U_5955) ),
    inference(clausify,[status(thm)],[f_1767_3]) ).

cnf(f_1767_6,plain,
    ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5955),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5954)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5954)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5955),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_5954))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5955)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5954)))
    | ~ sP561(U_5954,U_5955) ),
    inference(clausify,[status(thm)],[f_1767_3]) ).

fof(f_1768_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_1768_2,plain,
    ! [U_5956] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_5956) = 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_1768_1]) ).

fof(f_1768_3,plain,
    ! [U_5956] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_5956) = 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_1768_2]) ).

cnf(f_1768_4,plain,
    c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_5956) = 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_1768_3]) ).

fof(f_1769_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_1769_2,plain,
    ! [U_5958,U_5957] :
      ( c_Divides_OposDivAlg(U_5957,U_5958) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5957),U_5958)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5957,U_5958))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5958))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5957)) ),
    inference(variable_rename,[status(thm)],[f_1769_1]) ).

fof(f_1769_3,plain,
    ! [U_5957,U_5958] :
      ( c_Divides_OposDivAlg(U_5957,U_5958) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5957),U_5958)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5957,U_5958))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5958))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5957)) ),
    inference(definitional_conversion,[status(esa)],[f_1769_2]) ).

cnf(f_1769_4,plain,
    ( c_Divides_OposDivAlg(U_5957,U_5958) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5957),U_5958)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5957,U_5958))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5958))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5957)) ),
    inference(clausify,[status(thm)],[f_1769_3]) ).

fof(f_1770_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_1770_2,plain,
    ! [U_5960,U_5959] :
      ( ( ( c_Divides_OposDivAlg(U_5960,U_5959) = hAPP(c_Divides_Oadjust(U_5959),c_Divides_OposDivAlg(U_5960,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_5959)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5960),U_5959)) )
        & ( c_Divides_OposDivAlg(U_5960,U_5959) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5960)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5960),U_5959)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5959)) ),
    inference(variable_rename,[status(thm)],[f_1770_1]) ).

fof(f_1770_3,plain,
    ( ! [U_5959,U_5960] :
        ( c_Divides_OposDivAlg(U_5960,U_5959) = hAPP(c_Divides_Oadjust(U_5959),c_Divides_OposDivAlg(U_5960,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_5959)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5960),U_5959))
        | ~ sP562(U_5959,U_5960) )
    & ! [U_5959,U_5960] :
        ( c_Divides_OposDivAlg(U_5960,U_5959) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5960)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5960),U_5959))
        | ~ sP562(U_5959,U_5960) )
    & ! [U_5959,U_5960] :
        ( sP562(U_5959,U_5960)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5959)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP562])],[f_1770_2]) ).

cnf(f_1770_4,plain,
    ( sP562(U_5959,U_5960)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5959)) ),
    inference(clausify,[status(thm)],[f_1770_3]) ).

cnf(f_1770_5,plain,
    ( c_Divides_OposDivAlg(U_5960,U_5959) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5960)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5960),U_5959))
    | ~ sP562(U_5959,U_5960) ),
    inference(clausify,[status(thm)],[f_1770_3]) ).

cnf(f_1770_6,plain,
    ( c_Divides_OposDivAlg(U_5960,U_5959) = hAPP(c_Divides_Oadjust(U_5959),c_Divides_OposDivAlg(U_5960,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_5959)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5960),U_5959))
    | ~ sP562(U_5959,U_5960) ),
    inference(clausify,[status(thm)],[f_1770_3]) ).

fof(f_1771_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_1771_2,plain,
    ! [U_5962,U_5961] :
      ( ( ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_5961),U_5962) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_5961),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_5961,U_5961)),tc_fun(tc_Int_Oint,U_5961)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5961,U_5961),U_5961),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_5961,U_5961)),tc_fun(tc_Int_Oint,U_5961)),tc_Int_Oint),c_COMBB(tc_fun(U_5961,U_5961),U_5961,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_5961,tc_fun(tc_fun(U_5961,U_5961),U_5961),tc_Int_Oint),c_HOL_OLet(U_5961,U_5961)),c_Int_Oring__1__class_Oof__int(U_5961)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5961,U_5961),tc_fun(U_5961,U_5961)),hAPP(hAPP(c_COMBB(tc_fun(U_5961,tc_fun(U_5961,U_5961)),tc_fun(tc_fun(U_5961,U_5961),tc_fun(U_5961,U_5961)),tc_Int_Oint),c_COMBS(U_5961,U_5961,U_5961)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5961,U_5961),tc_fun(U_5961,tc_fun(U_5961,U_5961))),hAPP(hAPP(c_COMBB(tc_fun(U_5961,tc_fun(U_5961,U_5961)),tc_fun(tc_fun(U_5961,U_5961),tc_fun(U_5961,tc_fun(U_5961,U_5961))),tc_Int_Oint),c_COMBB(U_5961,tc_fun(U_5961,U_5961),U_5961)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5961,tc_fun(U_5961,U_5961)),tc_Int_Oint),c_If(U_5961)),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_5961,U_5961,U_5961),c_Groups_Oplus__class_Oplus(U_5961)),c_COMBI(U_5961))))),hAPP(hAPP(c_COMBC(U_5961,U_5961,U_5961),hAPP(hAPP(c_COMBB(U_5961,tc_fun(U_5961,U_5961),U_5961),c_Groups_Oplus__class_Oplus(U_5961)),hAPP(hAPP(c_COMBS(U_5961,U_5961,U_5961),c_Groups_Oplus__class_Oplus(U_5961)),c_COMBI(U_5961)))),c_Groups_Oone__class_Oone(U_5961))))),c_Divides_Odivmod__int(U_5962,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_5962),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
            & ( hAPP(c_Int_Oring__1__class_Oof__int(U_5961),U_5962) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5961),hAPP(c_Int_Oring__1__class_Oof__int(U_5961),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5962)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5962),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
          | U_5962 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(U_5961),U_5962) = c_Groups_Ozero__class_Ozero(U_5961)
          | U_5962 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | ~ class_Rings_Oring__1(U_5961) ),
    inference(variable_rename,[status(thm)],[f_1771_1]) ).

fof(f_1771_3,plain,
    ( ! [U_5961,U_5962] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_5961),U_5962) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_5961),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_5961,U_5961)),tc_fun(tc_Int_Oint,U_5961)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5961,U_5961),U_5961),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_5961,U_5961)),tc_fun(tc_Int_Oint,U_5961)),tc_Int_Oint),c_COMBB(tc_fun(U_5961,U_5961),U_5961,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_5961,tc_fun(tc_fun(U_5961,U_5961),U_5961),tc_Int_Oint),c_HOL_OLet(U_5961,U_5961)),c_Int_Oring__1__class_Oof__int(U_5961)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5961,U_5961),tc_fun(U_5961,U_5961)),hAPP(hAPP(c_COMBB(tc_fun(U_5961,tc_fun(U_5961,U_5961)),tc_fun(tc_fun(U_5961,U_5961),tc_fun(U_5961,U_5961)),tc_Int_Oint),c_COMBS(U_5961,U_5961,U_5961)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5961,U_5961),tc_fun(U_5961,tc_fun(U_5961,U_5961))),hAPP(hAPP(c_COMBB(tc_fun(U_5961,tc_fun(U_5961,U_5961)),tc_fun(tc_fun(U_5961,U_5961),tc_fun(U_5961,tc_fun(U_5961,U_5961))),tc_Int_Oint),c_COMBB(U_5961,tc_fun(U_5961,U_5961),U_5961)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5961,tc_fun(U_5961,U_5961)),tc_Int_Oint),c_If(U_5961)),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_5961,U_5961,U_5961),c_Groups_Oplus__class_Oplus(U_5961)),c_COMBI(U_5961))))),hAPP(hAPP(c_COMBC(U_5961,U_5961,U_5961),hAPP(hAPP(c_COMBB(U_5961,tc_fun(U_5961,U_5961),U_5961),c_Groups_Oplus__class_Oplus(U_5961)),hAPP(hAPP(c_COMBS(U_5961,U_5961,U_5961),c_Groups_Oplus__class_Oplus(U_5961)),c_COMBI(U_5961)))),c_Groups_Oone__class_Oone(U_5961))))),c_Divides_Odivmod__int(U_5962,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_5962),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP563(U_5961,U_5962) )
    & ! [U_5961,U_5962] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_5961),U_5962) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5961),hAPP(c_Int_Oring__1__class_Oof__int(U_5961),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5962)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5962),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP563(U_5961,U_5962) )
    & ! [U_5961,U_5962] :
        ( sP563(U_5961,U_5962)
        | U_5962 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP564(U_5961,U_5962) )
    & ! [U_5961,U_5962] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_5961),U_5962) = c_Groups_Ozero__class_Ozero(U_5961)
        | U_5962 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP564(U_5961,U_5962) )
    & ! [U_5961,U_5962] :
        ( sP564(U_5961,U_5962)
        | ~ class_Rings_Oring__1(U_5961) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP563,sP564])],[f_1771_2]) ).

cnf(f_1771_4,plain,
    ( sP564(U_5961,U_5962)
    | ~ class_Rings_Oring__1(U_5961) ),
    inference(clausify,[status(thm)],[f_1771_3]) ).

cnf(f_1771_5,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_5961),U_5962) = c_Groups_Ozero__class_Ozero(U_5961)
    | U_5962 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP564(U_5961,U_5962) ),
    inference(clausify,[status(thm)],[f_1771_3]) ).

cnf(f_1771_6,plain,
    ( sP563(U_5961,U_5962)
    | U_5962 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP564(U_5961,U_5962) ),
    inference(clausify,[status(thm)],[f_1771_3]) ).

cnf(f_1771_7,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_5961),U_5962) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5961),hAPP(c_Int_Oring__1__class_Oof__int(U_5961),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5962)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5962),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP563(U_5961,U_5962) ),
    inference(clausify,[status(thm)],[f_1771_3]) ).

cnf(f_1771_8,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_5961),U_5962) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_5961),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_5961,U_5961)),tc_fun(tc_Int_Oint,U_5961)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5961,U_5961),U_5961),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_5961,U_5961)),tc_fun(tc_Int_Oint,U_5961)),tc_Int_Oint),c_COMBB(tc_fun(U_5961,U_5961),U_5961,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_5961,tc_fun(tc_fun(U_5961,U_5961),U_5961),tc_Int_Oint),c_HOL_OLet(U_5961,U_5961)),c_Int_Oring__1__class_Oof__int(U_5961)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5961,U_5961),tc_fun(U_5961,U_5961)),hAPP(hAPP(c_COMBB(tc_fun(U_5961,tc_fun(U_5961,U_5961)),tc_fun(tc_fun(U_5961,U_5961),tc_fun(U_5961,U_5961)),tc_Int_Oint),c_COMBS(U_5961,U_5961,U_5961)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5961,U_5961),tc_fun(U_5961,tc_fun(U_5961,U_5961))),hAPP(hAPP(c_COMBB(tc_fun(U_5961,tc_fun(U_5961,U_5961)),tc_fun(tc_fun(U_5961,U_5961),tc_fun(U_5961,tc_fun(U_5961,U_5961))),tc_Int_Oint),c_COMBB(U_5961,tc_fun(U_5961,U_5961),U_5961)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5961,tc_fun(U_5961,U_5961)),tc_Int_Oint),c_If(U_5961)),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_5961,U_5961,U_5961),c_Groups_Oplus__class_Oplus(U_5961)),c_COMBI(U_5961))))),hAPP(hAPP(c_COMBC(U_5961,U_5961,U_5961),hAPP(hAPP(c_COMBB(U_5961,tc_fun(U_5961,U_5961),U_5961),c_Groups_Oplus__class_Oplus(U_5961)),hAPP(hAPP(c_COMBS(U_5961,U_5961,U_5961),c_Groups_Oplus__class_Oplus(U_5961)),c_COMBI(U_5961)))),c_Groups_Oone__class_Oone(U_5961))))),c_Divides_Odivmod__int(U_5962,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_5962),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP563(U_5961,U_5962) ),
    inference(clausify,[status(thm)],[f_1771_3]) ).

fof(f_1772_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_1772_2,plain,
    ! [U_5963] : c_Hoare__Mirabelle_OMGT(U_5963) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),U_5963),c_Natural_Oevalc(U_5963)),
    inference(variable_rename,[status(thm)],[f_1772_1]) ).

fof(f_1772_3,plain,
    ! [U_5963] : c_Hoare__Mirabelle_OMGT(U_5963) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),U_5963),c_Natural_Oevalc(U_5963)),
    inference(definitional_conversion,[status(esa)],[f_1772_2]) ).

cnf(f_1772_4,plain,
    c_Hoare__Mirabelle_OMGT(U_5963) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),U_5963),c_Natural_Oevalc(U_5963)),
    inference(clausify,[status(thm)],[f_1772_3]) ).

fof(f_1773_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_1773_2,plain,
    ! [U_5968,U_5967,U_5966,U_5965,U_5964] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5968),U_5964),U_5965),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_5968),U_5966)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5968),U_5967)),U_5965))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5968),U_5967),U_5965))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5965))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5964,U_5965),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5966),U_5967))) ),
    inference(variable_rename,[status(thm)],[f_1773_1]) ).

fof(f_1773_3,plain,
    ! [U_5968,U_5964,U_5965,U_5967,U_5966] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5968),U_5964),U_5965),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_5968),U_5966)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5968),U_5967)),U_5965))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5968),U_5967),U_5965))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5965))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5964,U_5965),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5966),U_5967))) ),
    inference(definitional_conversion,[status(esa)],[f_1773_2]) ).

cnf(f_1773_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5968),U_5964),U_5965),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_5968),U_5966)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5968),U_5967)),U_5965))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5968),U_5967),U_5965))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5965))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5964,U_5965),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5966),U_5967))) ),
    inference(clausify,[status(thm)],[f_1773_3]) ).

fof(f_1774_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_1774_2,plain,
    ! [U_5973,U_5972,U_5971,U_5970,U_5969] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5969,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5970),U_5973)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5971),U_5973)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5970),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5971,U_5973))),U_5972))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5973))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5970))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5969,U_5970),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5971),U_5972))) ),
    inference(variable_rename,[status(thm)],[f_1774_1]) ).

fof(f_1774_3,plain,
    ! [U_5969,U_5970,U_5971,U_5972,U_5973] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5969,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5970),U_5973)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5971),U_5973)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5970),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5971,U_5973))),U_5972))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5973))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5970))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5969,U_5970),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5971),U_5972))) ),
    inference(definitional_conversion,[status(esa)],[f_1774_2]) ).

cnf(f_1774_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5969,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5970),U_5973)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5971),U_5973)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5970),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5971,U_5973))),U_5972))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5973))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5970))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5969,U_5970),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5971),U_5972))) ),
    inference(clausify,[status(thm)],[f_1774_3]) ).

fof(f_1775_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_1775_2,plain,
    ! [U_5975,U_5974] :
      ( ( ( c_Divides_OnegDivAlg(U_5974,U_5975) = hAPP(c_Divides_Oadjust(U_5975),c_Divides_OnegDivAlg(U_5974,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_5975)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5975),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_5974),U_5975))) )
        & ( c_Divides_OnegDivAlg(U_5974,U_5975) = 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_5974),U_5975))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5975),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_5974),U_5975))) ) ) )
      | ~ 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_5974),U_5975))) ),
    inference(variable_rename,[status(thm)],[f_1775_1]) ).

fof(f_1775_3,plain,
    ( ! [U_5974,U_5975] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5975),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP565(U_5974,U_5975) )
    & ! [U_5974,U_5975] :
        ( ~ 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_5974),U_5975)))
        | ~ sP565(U_5974,U_5975) )
    & ! [U_5974,U_5975] :
        ( c_Divides_OnegDivAlg(U_5974,U_5975) = hAPP(c_Divides_Oadjust(U_5975),c_Divides_OnegDivAlg(U_5974,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_5975)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5975),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_5974),U_5975)))
        | ~ sP566(U_5974,U_5975) )
    & ! [U_5974,U_5975] :
        ( c_Divides_OnegDivAlg(U_5974,U_5975) = 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_5974),U_5975))
        | sP565(U_5974,U_5975)
        | ~ sP566(U_5974,U_5975) )
    & ! [U_5974,U_5975] :
        ( sP566(U_5974,U_5975)
        | ~ 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_5974),U_5975))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP565,sP566])],[f_1775_2]) ).

cnf(f_1775_4,plain,
    ( sP566(U_5974,U_5975)
    | ~ 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_5974),U_5975))) ),
    inference(clausify,[status(thm)],[f_1775_3]) ).

cnf(f_1775_5,plain,
    ( c_Divides_OnegDivAlg(U_5974,U_5975) = 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_5974),U_5975))
    | sP565(U_5974,U_5975)
    | ~ sP566(U_5974,U_5975) ),
    inference(clausify,[status(thm)],[f_1775_3]) ).

cnf(f_1775_6,plain,
    ( c_Divides_OnegDivAlg(U_5974,U_5975) = hAPP(c_Divides_Oadjust(U_5975),c_Divides_OnegDivAlg(U_5974,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_5975)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5975),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_5974),U_5975)))
    | ~ sP566(U_5974,U_5975) ),
    inference(clausify,[status(thm)],[f_1775_3]) ).

cnf(f_1775_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_5974),U_5975)))
    | ~ sP565(U_5974,U_5975) ),
    inference(clausify,[status(thm)],[f_1775_3]) ).

cnf(f_1775_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5975),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP565(U_5974,U_5975) ),
    inference(clausify,[status(thm)],[f_1775_3]) ).

fof(f_1776_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_1776_2,plain,
    ! [U_5979,U_5978,U_5977,U_5976] :
      ( U_5978 = U_5979
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5976,U_5977),U_5979))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5976,U_5977),U_5978)) ),
    inference(variable_rename,[status(thm)],[f_1776_1]) ).

fof(f_1776_3,plain,
    ! [U_5977,U_5979,U_5978,U_5976] :
      ( U_5978 = U_5979
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5976,U_5977),U_5979))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5976,U_5977),U_5978)) ),
    inference(definitional_conversion,[status(esa)],[f_1776_2]) ).

cnf(f_1776_4,plain,
    ( U_5978 = U_5979
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5976,U_5977),U_5979))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5976,U_5977),U_5978)) ),
    inference(clausify,[status(thm)],[f_1776_3]) ).

fof(f_1777_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_1777_2,plain,
    ! [U_5983,U_5982,U_5981,U_5980] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5980,U_5981),U_5983))
      | ~ hBOOL(hAPP(hAPP(U_5981,U_5983),U_5982))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5980,U_5981),U_5982)) ),
    inference(variable_rename,[status(thm)],[f_1777_1]) ).

fof(f_1777_3,plain,
    ! [U_5980,U_5981,U_5983,U_5982] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5980,U_5981),U_5983))
      | ~ hBOOL(hAPP(hAPP(U_5981,U_5983),U_5982))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5980,U_5981),U_5982)) ),
    inference(definitional_conversion,[status(esa)],[f_1777_2]) ).

cnf(f_1777_4,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5980,U_5981),U_5983))
    | ~ hBOOL(hAPP(hAPP(U_5981,U_5983),U_5982))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5980,U_5981),U_5982)) ),
    inference(clausify,[status(thm)],[f_1777_3]) ).

fof(f_1778_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_1778_2,plain,
    ! [U_5988,U_5987,U_5986] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5986,U_5987),U_5988))
        | ? [U_5985] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5986,U_5987),U_5985))
            & hBOOL(hAPP(hAPP(U_5987,U_5985),U_5988)) ) )
      & ( ! [U_5984] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5986,U_5987),U_5984))
            | ~ hBOOL(hAPP(hAPP(U_5987,U_5984),U_5988)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5986,U_5987),U_5988)) ) ),
    inference(variable_rename,[status(thm)],[f_1778_1]) ).

fof(f_1778_3,plain,
    ( ! [U_5994,U_5992,U_5990] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5990,U_5992),U_5994))
        | ? [U_5985] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5990,U_5992),U_5985))
            & hBOOL(hAPP(hAPP(U_5992,U_5985),U_5994)) ) )
    & ! [U_5993,U_5991,U_5989] :
        ( ! [U_5984] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5989,U_5991),U_5984))
            | ~ hBOOL(hAPP(hAPP(U_5991,U_5984),U_5993)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5989,U_5991),U_5993)) ) ),
    inference(miniscope,[status(thm)],[f_1778_2]) ).

fof(f_1778_4,plain,
    ( ! [U_5994,U_5992,U_5990] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5990,U_5992),U_5994))
        | ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5990,U_5992),sK96(U_5994,U_5992,U_5990)))
          & hBOOL(hAPP(hAPP(U_5992,sK96(U_5994,U_5992,U_5990)),U_5994)) ) )
    & ! [U_5993,U_5991,U_5989] :
        ( ! [U_5984] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5989,U_5991),U_5984))
            | ~ hBOOL(hAPP(hAPP(U_5991,U_5984),U_5993)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5989,U_5991),U_5993)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_5985,sK96(U_5994,U_5992,U_5990))],[f_1778_3]) ).

fof(f_1778_5,plain,
    ( ! [U_5994,U_5990,U_5992] :
        ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5990,U_5992),sK96(U_5994,U_5992,U_5990)))
        | ~ sP567(U_5994,U_5990,U_5992) )
    & ! [U_5994,U_5990,U_5992] :
        ( hBOOL(hAPP(hAPP(U_5992,sK96(U_5994,U_5992,U_5990)),U_5994))
        | ~ sP567(U_5994,U_5990,U_5992) )
    & ! [U_5994,U_5990,U_5992] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5990,U_5992),U_5994))
        | sP567(U_5994,U_5990,U_5992) )
    & ! [U_5991,U_5984,U_5989,U_5993] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5989,U_5991),U_5984))
        | ~ hBOOL(hAPP(hAPP(U_5991,U_5984),U_5993))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5989,U_5991),U_5993)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP567])],[f_1778_4]) ).

cnf(f_1778_6,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5989,U_5991),U_5984))
    | ~ hBOOL(hAPP(hAPP(U_5991,U_5984),U_5993))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5989,U_5991),U_5993)) ),
    inference(clausify,[status(thm)],[f_1778_5]) ).

cnf(f_1778_7,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5990,U_5992),U_5994))
    | sP567(U_5994,U_5990,U_5992) ),
    inference(clausify,[status(thm)],[f_1778_5]) ).

cnf(f_1778_8,plain,
    ( hBOOL(hAPP(hAPP(U_5992,sK96(U_5994,U_5992,U_5990)),U_5994))
    | ~ sP567(U_5994,U_5990,U_5992) ),
    inference(clausify,[status(thm)],[f_1778_5]) ).

cnf(f_1778_9,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5990,U_5992),sK96(U_5994,U_5992,U_5990)))
    | ~ sP567(U_5994,U_5990,U_5992) ),
    inference(clausify,[status(thm)],[f_1778_5]) ).

fof(f_1779_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_1779_2,plain,
    ! [U_5999,U_5998,U_5997] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5997,U_5998),U_5999))
        | ? [U_5996] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5997,U_5998),U_5996))
            & hBOOL(hAPP(hAPP(U_5998,U_5996),U_5999)) ) )
      & ( ! [U_5995] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5997,U_5998),U_5995))
            | ~ hBOOL(hAPP(hAPP(U_5998,U_5995),U_5999)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5997,U_5998),U_5999)) ) ),
    inference(variable_rename,[status(thm)],[f_1779_1]) ).

fof(f_1779_3,plain,
    ( ! [U_6005,U_6003,U_6001] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_6001,U_6003),U_6005))
        | ? [U_5996] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_6001,U_6003),U_5996))
            & hBOOL(hAPP(hAPP(U_6003,U_5996),U_6005)) ) )
    & ! [U_6004,U_6002,U_6000] :
        ( ! [U_5995] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_6000,U_6002),U_5995))
            | ~ hBOOL(hAPP(hAPP(U_6002,U_5995),U_6004)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_6000,U_6002),U_6004)) ) ),
    inference(miniscope,[status(thm)],[f_1779_2]) ).

fof(f_1779_4,plain,
    ( ! [U_6005,U_6003,U_6001] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_6001,U_6003),U_6005))
        | ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_6001,U_6003),sK97(U_6005,U_6003,U_6001)))
          & hBOOL(hAPP(hAPP(U_6003,sK97(U_6005,U_6003,U_6001)),U_6005)) ) )
    & ! [U_6004,U_6002,U_6000] :
        ( ! [U_5995] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_6000,U_6002),U_5995))
            | ~ hBOOL(hAPP(hAPP(U_6002,U_5995),U_6004)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_6000,U_6002),U_6004)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_5996,sK97(U_6005,U_6003,U_6001))],[f_1779_3]) ).

fof(f_1779_5,plain,
    ( ! [U_6003,U_6005,U_6001] :
        ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_6001,U_6003),sK97(U_6005,U_6003,U_6001)))
        | ~ sP568(U_6003,U_6005,U_6001) )
    & ! [U_6003,U_6005,U_6001] :
        ( hBOOL(hAPP(hAPP(U_6003,sK97(U_6005,U_6003,U_6001)),U_6005))
        | ~ sP568(U_6003,U_6005,U_6001) )
    & ! [U_6003,U_6005,U_6001] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_6001,U_6003),U_6005))
        | sP568(U_6003,U_6005,U_6001) )
    & ! [U_6004,U_5995,U_6002,U_6000] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_6000,U_6002),U_5995))
        | ~ hBOOL(hAPP(hAPP(U_6002,U_5995),U_6004))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_6000,U_6002),U_6004)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP568])],[f_1779_4]) ).

cnf(f_1779_6,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_6000,U_6002),U_5995))
    | ~ hBOOL(hAPP(hAPP(U_6002,U_5995),U_6004))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_6000,U_6002),U_6004)) ),
    inference(clausify,[status(thm)],[f_1779_5]) ).

cnf(f_1779_7,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_6001,U_6003),U_6005))
    | sP568(U_6003,U_6005,U_6001) ),
    inference(clausify,[status(thm)],[f_1779_5]) ).

cnf(f_1779_8,plain,
    ( hBOOL(hAPP(hAPP(U_6003,sK97(U_6005,U_6003,U_6001)),U_6005))
    | ~ sP568(U_6003,U_6005,U_6001) ),
    inference(clausify,[status(thm)],[f_1779_5]) ).

cnf(f_1779_9,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_6001,U_6003),sK97(U_6005,U_6003,U_6001)))
    | ~ sP568(U_6003,U_6005,U_6001) ),
    inference(clausify,[status(thm)],[f_1779_5]) ).

fof(f_1780_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_1780_2,plain,
    ! [U_6008,U_6007,U_6006] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6006,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_6006,U_6008)),c_Wellfounded_Oaccp(U_6006,U_6007)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6006,tc_fun(U_6006,tc_HOL_Obool))),U_6007),U_6008)) ),
    inference(variable_rename,[status(thm)],[f_1780_1]) ).

fof(f_1780_3,plain,
    ! [U_6008,U_6006,U_6007] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6006,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_6006,U_6008)),c_Wellfounded_Oaccp(U_6006,U_6007)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6006,tc_fun(U_6006,tc_HOL_Obool))),U_6007),U_6008)) ),
    inference(definitional_conversion,[status(esa)],[f_1780_2]) ).

cnf(f_1780_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6006,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_6006,U_6008)),c_Wellfounded_Oaccp(U_6006,U_6007)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6006,tc_fun(U_6006,tc_HOL_Obool))),U_6007),U_6008)) ),
    inference(clausify,[status(thm)],[f_1780_3]) ).

fof(f_1781_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_1781_2,plain,
    ! [U_6011,U_6010,U_6009] :
      ( c_Divides_Odivmod__nat(U_6009,U_6010) = U_6011
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6009,U_6010),U_6011)) ),
    inference(variable_rename,[status(thm)],[f_1781_1]) ).

fof(f_1781_3,plain,
    ! [U_6009,U_6010,U_6011] :
      ( c_Divides_Odivmod__nat(U_6009,U_6010) = U_6011
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6009,U_6010),U_6011)) ),
    inference(definitional_conversion,[status(esa)],[f_1781_2]) ).

cnf(f_1781_4,plain,
    ( c_Divides_Odivmod__nat(U_6009,U_6010) = U_6011
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6009,U_6010),U_6011)) ),
    inference(clausify,[status(thm)],[f_1781_3]) ).

fof(f_1782_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_1782_2,plain,
    ! [U_6013,U_6012] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6012,U_6013),c_Divides_Odivmod__nat(U_6012,U_6013))),
    inference(variable_rename,[status(thm)],[f_1782_1]) ).

fof(f_1782_3,plain,
    ! [U_6012,U_6013] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6012,U_6013),c_Divides_Odivmod__nat(U_6012,U_6013))),
    inference(definitional_conversion,[status(esa)],[f_1782_2]) ).

cnf(f_1782_4,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6012,U_6013),c_Divides_Odivmod__nat(U_6012,U_6013))),
    inference(clausify,[status(thm)],[f_1782_3]) ).

fof(f_1783_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_1783_2,plain,
    ! [U_6017,U_6016,U_6015,U_6014] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6014,U_6015) = U_6017
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6014,U_6015),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6016),U_6017))) ),
    inference(variable_rename,[status(thm)],[f_1783_1]) ).

fof(f_1783_3,plain,
    ! [U_6014,U_6015,U_6016,U_6017] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6014,U_6015) = U_6017
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6014,U_6015),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6016),U_6017))) ),
    inference(definitional_conversion,[status(esa)],[f_1783_2]) ).

cnf(f_1783_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6014,U_6015) = U_6017
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6014,U_6015),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6016),U_6017))) ),
    inference(clausify,[status(thm)],[f_1783_3]) ).

fof(f_1784_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_1784_2,plain,
    ! [U_6021,U_6020,U_6019,U_6018] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6018),U_6019) = U_6020
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6018,U_6019),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6020),U_6021))) ),
    inference(variable_rename,[status(thm)],[f_1784_1]) ).

fof(f_1784_3,plain,
    ! [U_6018,U_6019,U_6020,U_6021] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6018),U_6019) = U_6020
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6018,U_6019),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6020),U_6021))) ),
    inference(definitional_conversion,[status(esa)],[f_1784_2]) ).

cnf(f_1784_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6018),U_6019) = U_6020
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6018,U_6019),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6020),U_6021))) ),
    inference(clausify,[status(thm)],[f_1784_3]) ).

fof(f_1785_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_1785_2,plain,
    ! [U_6023,U_6022] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6022,U_6023),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6022),U_6023)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6022,U_6023)))),
    inference(variable_rename,[status(thm)],[f_1785_1]) ).

fof(f_1785_3,plain,
    ! [U_6022,U_6023] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6022,U_6023),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6022),U_6023)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6022,U_6023)))),
    inference(definitional_conversion,[status(esa)],[f_1785_2]) ).

cnf(f_1785_4,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6022,U_6023),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6022),U_6023)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6022,U_6023)))),
    inference(clausify,[status(thm)],[f_1785_3]) ).

fof(f_1786_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_1786_2,plain,
    ! [U_6025,U_6024] : c_Divides_Odivmod__int(U_6024,U_6025) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6024),U_6025)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6024,U_6025)),
    inference(variable_rename,[status(thm)],[f_1786_1]) ).

fof(f_1786_3,plain,
    ! [U_6024,U_6025] : c_Divides_Odivmod__int(U_6024,U_6025) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6024),U_6025)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6024,U_6025)),
    inference(definitional_conversion,[status(esa)],[f_1786_2]) ).

cnf(f_1786_4,plain,
    c_Divides_Odivmod__int(U_6024,U_6025) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6024),U_6025)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6024,U_6025)),
    inference(clausify,[status(thm)],[f_1786_3]) ).

fof(f_1787_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_1787_2,plain,
    ! [U_6032,U_6031,U_6030,U_6029,U_6028,U_6027,U_6026] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6026),U_6030),U_6027),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_6028),U_6031)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6029),U_6032)),U_6027))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6029),U_6032),U_6027))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6027))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6030,U_6027),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6031),U_6032)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6026,U_6027),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6028),U_6029))) ),
    inference(variable_rename,[status(thm)],[f_1787_1]) ).

fof(f_1787_3,plain,
    ! [U_6027,U_6026,U_6028,U_6029,U_6030,U_6031,U_6032] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6026),U_6030),U_6027),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_6028),U_6031)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6029),U_6032)),U_6027))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6029),U_6032),U_6027))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6027))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6030,U_6027),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6031),U_6032)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6026,U_6027),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6028),U_6029))) ),
    inference(definitional_conversion,[status(esa)],[f_1787_2]) ).

cnf(f_1787_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6026),U_6030),U_6027),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_6028),U_6031)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6029),U_6032)),U_6027))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6029),U_6032),U_6027))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6027))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6030,U_6027),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6031),U_6032)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6026,U_6027),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_6028),U_6029))) ),
    inference(clausify,[status(thm)],[f_1787_3]) ).

fof(f_1788_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_1788_2,plain,
    ! [U_6034,U_6033] :
      ( ( ( c_Divides_OposDivAlg(U_6033,U_6034) = hAPP(c_Divides_Oadjust(U_6034),c_Divides_OposDivAlg(U_6033,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_6034)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6034),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6033),U_6034)) )
        & ( c_Divides_OposDivAlg(U_6033,U_6034) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6033)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6034),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6033),U_6034)) ) ) )
      | ~ 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_6033),U_6034))) ),
    inference(variable_rename,[status(thm)],[f_1788_1]) ).

fof(f_1788_3,plain,
    ( ! [U_6034,U_6033] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6034),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP569(U_6034,U_6033) )
    & ! [U_6034,U_6033] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6033),U_6034))
        | ~ sP569(U_6034,U_6033) )
    & ! [U_6034,U_6033] :
        ( c_Divides_OposDivAlg(U_6033,U_6034) = hAPP(c_Divides_Oadjust(U_6034),c_Divides_OposDivAlg(U_6033,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_6034)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6034),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6033),U_6034))
        | ~ sP570(U_6034,U_6033) )
    & ! [U_6034,U_6033] :
        ( c_Divides_OposDivAlg(U_6033,U_6034) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6033)
        | sP569(U_6034,U_6033)
        | ~ sP570(U_6034,U_6033) )
    & ! [U_6034,U_6033] :
        ( sP570(U_6034,U_6033)
        | ~ 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_6033),U_6034))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP569,sP570])],[f_1788_2]) ).

cnf(f_1788_4,plain,
    ( sP570(U_6034,U_6033)
    | ~ 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_6033),U_6034))) ),
    inference(clausify,[status(thm)],[f_1788_3]) ).

cnf(f_1788_5,plain,
    ( c_Divides_OposDivAlg(U_6033,U_6034) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6033)
    | sP569(U_6034,U_6033)
    | ~ sP570(U_6034,U_6033) ),
    inference(clausify,[status(thm)],[f_1788_3]) ).

cnf(f_1788_6,plain,
    ( c_Divides_OposDivAlg(U_6033,U_6034) = hAPP(c_Divides_Oadjust(U_6034),c_Divides_OposDivAlg(U_6033,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_6034)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6034),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6033),U_6034))
    | ~ sP570(U_6034,U_6033) ),
    inference(clausify,[status(thm)],[f_1788_3]) ).

cnf(f_1788_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6033),U_6034))
    | ~ sP569(U_6034,U_6033) ),
    inference(clausify,[status(thm)],[f_1788_3]) ).

cnf(f_1788_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6034),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP569(U_6034,U_6033) ),
    inference(clausify,[status(thm)],[f_1788_3]) ).

fof(f_1789_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_1789_2,plain,
    ! [U_6036,U_6035] :
      ( ( ( ( ( c_Nitpick_Onorm__frac(U_6035,U_6036) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6035),U_6036)),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_6035))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6036)))
              | U_6036 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | U_6035 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( c_Nitpick_Onorm__frac(U_6035,U_6036) = 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_6036 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                & U_6035 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6036),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( c_Nitpick_Onorm__frac(U_6035,U_6036) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6035),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6036))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6036),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_6035),U_6036))) ),
    inference(variable_rename,[status(thm)],[f_1789_1]) ).

fof(f_1789_3,plain,
    ( ! [U_6036,U_6035] :
        ( U_6036 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP571(U_6036,U_6035) )
    & ! [U_6036,U_6035] :
        ( U_6035 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP571(U_6036,U_6035) )
    & ! [U_6036,U_6035] :
        ( c_Nitpick_Onorm__frac(U_6035,U_6036) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6035),U_6036)),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_6035))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6036)))
        | U_6036 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_6035 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP572(U_6036,U_6035) )
    & ! [U_6036,U_6035] :
        ( c_Nitpick_Onorm__frac(U_6035,U_6036) = 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))
        | sP571(U_6036,U_6035)
        | ~ sP572(U_6036,U_6035) )
    & ! [U_6036,U_6035] :
        ( sP572(U_6036,U_6035)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6036),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP573(U_6036,U_6035) )
    & ! [U_6036,U_6035] :
        ( c_Nitpick_Onorm__frac(U_6035,U_6036) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6035),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6036))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6036),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP573(U_6036,U_6035) )
    & ! [U_6036,U_6035] :
        ( sP573(U_6036,U_6035)
        | ~ 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_6035),U_6036))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP571,sP572,sP573])],[f_1789_2]) ).

cnf(f_1789_4,plain,
    ( sP573(U_6036,U_6035)
    | ~ 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_6035),U_6036))) ),
    inference(clausify,[status(thm)],[f_1789_3]) ).

cnf(f_1789_5,plain,
    ( c_Nitpick_Onorm__frac(U_6035,U_6036) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6035),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6036))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6036),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP573(U_6036,U_6035) ),
    inference(clausify,[status(thm)],[f_1789_3]) ).

cnf(f_1789_6,plain,
    ( sP572(U_6036,U_6035)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6036),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP573(U_6036,U_6035) ),
    inference(clausify,[status(thm)],[f_1789_3]) ).

cnf(f_1789_7,plain,
    ( c_Nitpick_Onorm__frac(U_6035,U_6036) = 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))
    | sP571(U_6036,U_6035)
    | ~ sP572(U_6036,U_6035) ),
    inference(clausify,[status(thm)],[f_1789_3]) ).

cnf(f_1789_8,plain,
    ( c_Nitpick_Onorm__frac(U_6035,U_6036) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6035),U_6036)),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_6035))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6036)))
    | U_6036 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6035 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP572(U_6036,U_6035) ),
    inference(clausify,[status(thm)],[f_1789_3]) ).

cnf(f_1789_9,plain,
    ( U_6035 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP571(U_6036,U_6035) ),
    inference(clausify,[status(thm)],[f_1789_3]) ).

cnf(f_1789_10,plain,
    ( U_6036 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP571(U_6036,U_6035) ),
    inference(clausify,[status(thm)],[f_1789_3]) ).

fof(f_1790_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_1790_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_1790_1]) ).

cnf(f_1790_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_1790_2]) ).

fof(f_1791_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_1791_2,plain,
    ! [U_6038,U_6037] :
      ( ( ( ( c_Divides_Odivmod__int(U_6037,U_6038) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6037),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6038)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6038)) )
          & ( c_Divides_Odivmod__int(U_6037,U_6038) = c_Divides_OnegDivAlg(U_6037,U_6038)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6038)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6037)) )
      & ( ( ( ( ( c_Divides_Odivmod__int(U_6037,U_6038) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6037),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6038)))
                | U_6037 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
              & ( c_Divides_Odivmod__int(U_6037,U_6038) = 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_6037 != 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_6038)) )
          & ( c_Divides_Odivmod__int(U_6037,U_6038) = c_Divides_OposDivAlg(U_6037,U_6038)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6038)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6037)) ) ),
    inference(variable_rename,[status(thm)],[f_1791_1]) ).

fof(f_1791_3,plain,
    ( ! [U_6042,U_6040] :
        ( ( ( c_Divides_Odivmod__int(U_6040,U_6042) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6040),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6042)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6042)) )
          & ( c_Divides_Odivmod__int(U_6040,U_6042) = c_Divides_OnegDivAlg(U_6040,U_6042)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6042)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6040)) )
    & ! [U_6041,U_6039] :
        ( ( ( ( ( c_Divides_Odivmod__int(U_6039,U_6041) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6039),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6041)))
                | U_6039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
              & ( c_Divides_Odivmod__int(U_6039,U_6041) = 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_6039 != 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_6041)) )
          & ( c_Divides_Odivmod__int(U_6039,U_6041) = c_Divides_OposDivAlg(U_6039,U_6041)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6041)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6039)) ) ),
    inference(miniscope,[status(thm)],[f_1791_2]) ).

fof(f_1791_4,plain,
    ( ! [U_6042,U_6040] :
        ( c_Divides_Odivmod__int(U_6040,U_6042) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6040),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6042)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6042))
        | ~ sP576(U_6042,U_6040) )
    & ! [U_6042,U_6040] :
        ( c_Divides_Odivmod__int(U_6040,U_6042) = c_Divides_OnegDivAlg(U_6040,U_6042)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6042))
        | ~ sP576(U_6042,U_6040) )
    & ! [U_6039,U_6041] :
        ( c_Divides_Odivmod__int(U_6039,U_6041) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6039),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6041)))
        | U_6039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP574(U_6039,U_6041) )
    & ! [U_6039,U_6041] :
        ( c_Divides_Odivmod__int(U_6039,U_6041) = 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_6039 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP574(U_6039,U_6041) )
    & ! [U_6039,U_6041] :
        ( sP574(U_6039,U_6041)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6041))
        | ~ sP575(U_6039,U_6041) )
    & ! [U_6039,U_6041] :
        ( c_Divides_Odivmod__int(U_6039,U_6041) = c_Divides_OposDivAlg(U_6039,U_6041)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6041))
        | ~ sP575(U_6039,U_6041) )
    & ! [U_6042,U_6040] :
        ( sP576(U_6042,U_6040)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6040)) )
    & ! [U_6039,U_6041] :
        ( sP575(U_6039,U_6041)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6039)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP574,sP575,sP576])],[f_1791_3]) ).

cnf(f_1791_5,plain,
    ( sP575(U_6039,U_6041)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6039)) ),
    inference(clausify,[status(thm)],[f_1791_4]) ).

cnf(f_1791_6,plain,
    ( sP576(U_6042,U_6040)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6040)) ),
    inference(clausify,[status(thm)],[f_1791_4]) ).

cnf(f_1791_7,plain,
    ( c_Divides_Odivmod__int(U_6039,U_6041) = c_Divides_OposDivAlg(U_6039,U_6041)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6041))
    | ~ sP575(U_6039,U_6041) ),
    inference(clausify,[status(thm)],[f_1791_4]) ).

cnf(f_1791_8,plain,
    ( sP574(U_6039,U_6041)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6041))
    | ~ sP575(U_6039,U_6041) ),
    inference(clausify,[status(thm)],[f_1791_4]) ).

cnf(f_1791_9,plain,
    ( c_Divides_Odivmod__int(U_6039,U_6041) = 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_6039 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP574(U_6039,U_6041) ),
    inference(clausify,[status(thm)],[f_1791_4]) ).

cnf(f_1791_10,plain,
    ( c_Divides_Odivmod__int(U_6039,U_6041) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6039),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6041)))
    | U_6039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP574(U_6039,U_6041) ),
    inference(clausify,[status(thm)],[f_1791_4]) ).

cnf(f_1791_11,plain,
    ( c_Divides_Odivmod__int(U_6040,U_6042) = c_Divides_OnegDivAlg(U_6040,U_6042)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6042))
    | ~ sP576(U_6042,U_6040) ),
    inference(clausify,[status(thm)],[f_1791_4]) ).

cnf(f_1791_12,plain,
    ( c_Divides_Odivmod__int(U_6040,U_6042) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6040),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6042)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6042))
    | ~ sP576(U_6042,U_6040) ),
    inference(clausify,[status(thm)],[f_1791_4]) ).

fof(f_1792_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_1792_2,plain,
    ! [U_6047,U_6046,U_6045] :
      ( hBOOL(hAPP(hAPP(U_6047,U_6045),U_6046))
      | ? [U_6044,U_6043] :
          ( ~ hBOOL(hAPP(hAPP(U_6047,U_6044),U_6043))
          & ( hBOOL(hAPP(hAPP(U_6047,U_6044),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_6043)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6043),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_6044),U_6043))) )
          & 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_6044),U_6043))) )
      | ~ 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_6045),U_6046))) ),
    inference(variable_rename,[status(thm)],[f_1792_1]) ).

fof(f_1792_3,plain,
    ! [U_6047,U_6046,U_6045] :
      ( hBOOL(hAPP(hAPP(U_6047,U_6045),U_6046))
      | ? [U_6043] :
          ( ~ hBOOL(hAPP(hAPP(U_6047,sK98(U_6047,U_6046,U_6045)),U_6043))
          & ( hBOOL(hAPP(hAPP(U_6047,sK98(U_6047,U_6046,U_6045)),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_6043)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6043),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),sK98(U_6047,U_6046,U_6045)),U_6043))) )
          & 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),sK98(U_6047,U_6046,U_6045)),U_6043))) )
      | ~ 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_6045),U_6046))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_6044,sK98(U_6047,U_6046,U_6045))],[f_1792_2]) ).

fof(f_1792_4,plain,
    ! [U_6047,U_6046,U_6045] :
      ( hBOOL(hAPP(hAPP(U_6047,U_6045),U_6046))
      | ( ~ hBOOL(hAPP(hAPP(U_6047,sK98(U_6047,U_6046,U_6045)),sK99(U_6047,U_6046,U_6045)))
        & ( hBOOL(hAPP(hAPP(U_6047,sK98(U_6047,U_6046,U_6045)),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)))),sK99(U_6047,U_6046,U_6045))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK99(U_6047,U_6046,U_6045)),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),sK98(U_6047,U_6046,U_6045)),sK99(U_6047,U_6046,U_6045)))) )
        & 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),sK98(U_6047,U_6046,U_6045)),sK99(U_6047,U_6046,U_6045)))) )
      | ~ 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_6045),U_6046))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_6043,sK99(U_6047,U_6046,U_6045))],[f_1792_3]) ).

fof(f_1792_5,plain,
    ( ! [U_6046,U_6045,U_6047] :
        ( ~ hBOOL(hAPP(hAPP(U_6047,sK98(U_6047,U_6046,U_6045)),sK99(U_6047,U_6046,U_6045)))
        | ~ sP577(U_6046,U_6045,U_6047) )
    & ! [U_6046,U_6045,U_6047] :
        ( hBOOL(hAPP(hAPP(U_6047,sK98(U_6047,U_6046,U_6045)),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)))),sK99(U_6047,U_6046,U_6045))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK99(U_6047,U_6046,U_6045)),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),sK98(U_6047,U_6046,U_6045)),sK99(U_6047,U_6046,U_6045))))
        | ~ sP577(U_6046,U_6045,U_6047) )
    & ! [U_6046,U_6045,U_6047] :
        ( 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),sK98(U_6047,U_6046,U_6045)),sK99(U_6047,U_6046,U_6045))))
        | ~ sP577(U_6046,U_6045,U_6047) )
    & ! [U_6046,U_6045,U_6047] :
        ( hBOOL(hAPP(hAPP(U_6047,U_6045),U_6046))
        | sP577(U_6046,U_6045,U_6047)
        | ~ 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_6045),U_6046))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP577])],[f_1792_4]) ).

cnf(f_1792_6,plain,
    ( hBOOL(hAPP(hAPP(U_6047,U_6045),U_6046))
    | sP577(U_6046,U_6045,U_6047)
    | ~ 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_6045),U_6046))) ),
    inference(clausify,[status(thm)],[f_1792_5]) ).

cnf(f_1792_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),sK98(U_6047,U_6046,U_6045)),sK99(U_6047,U_6046,U_6045))))
    | ~ sP577(U_6046,U_6045,U_6047) ),
    inference(clausify,[status(thm)],[f_1792_5]) ).

cnf(f_1792_8,plain,
    ( hBOOL(hAPP(hAPP(U_6047,sK98(U_6047,U_6046,U_6045)),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)))),sK99(U_6047,U_6046,U_6045))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK99(U_6047,U_6046,U_6045)),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),sK98(U_6047,U_6046,U_6045)),sK99(U_6047,U_6046,U_6045))))
    | ~ sP577(U_6046,U_6045,U_6047) ),
    inference(clausify,[status(thm)],[f_1792_5]) ).

cnf(f_1792_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_6047,sK98(U_6047,U_6046,U_6045)),sK99(U_6047,U_6046,U_6045)))
    | ~ sP577(U_6046,U_6045,U_6047) ),
    inference(clausify,[status(thm)],[f_1792_5]) ).

fof(f_1793_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_1793_2,plain,
    ! [U_6049,U_6048] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6048),U_6049)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6048),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6049)),
    inference(variable_rename,[status(thm)],[f_1793_1]) ).

fof(f_1793_3,plain,
    ! [U_6049,U_6048] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6048),U_6049)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6048),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6049)),
    inference(definitional_conversion,[status(esa)],[f_1793_2]) ).

cnf(f_1793_4,plain,
    hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6048),U_6049)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6048),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6049)),
    inference(clausify,[status(thm)],[f_1793_3]) ).

fof(f_1794_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_1794_2,plain,
    ! [U_6054,U_6053,U_6052,U_6051,U_6050] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6053,U_6054,tc_HOL_Obool),U_6050),hAPP(hAPP(c_Product__Type_OPair(U_6053,U_6054),U_6051),U_6052)))
      | ~ hBOOL(hAPP(hAPP(U_6050,U_6051),U_6052)) ),
    inference(variable_rename,[status(thm)],[f_1794_1]) ).

fof(f_1794_3,plain,
    ! [U_6050,U_6051,U_6052,U_6053,U_6054] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6053,U_6054,tc_HOL_Obool),U_6050),hAPP(hAPP(c_Product__Type_OPair(U_6053,U_6054),U_6051),U_6052)))
      | ~ hBOOL(hAPP(hAPP(U_6050,U_6051),U_6052)) ),
    inference(definitional_conversion,[status(esa)],[f_1794_2]) ).

cnf(f_1794_4,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6053,U_6054,tc_HOL_Obool),U_6050),hAPP(hAPP(c_Product__Type_OPair(U_6053,U_6054),U_6051),U_6052)))
    | ~ hBOOL(hAPP(hAPP(U_6050,U_6051),U_6052)) ),
    inference(clausify,[status(thm)],[f_1794_3]) ).

fof(f_1795_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_1795_2,plain,
    ! [U_6059,U_6058,U_6057,U_6056,U_6055] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6058,U_6059,tc_HOL_Obool),U_6055),hAPP(hAPP(c_Product__Type_OPair(U_6058,U_6059),U_6056),U_6057)))
      | ~ hBOOL(hAPP(hAPP(U_6055,U_6056),U_6057)) ),
    inference(variable_rename,[status(thm)],[f_1795_1]) ).

fof(f_1795_3,plain,
    ! [U_6056,U_6055,U_6057,U_6058,U_6059] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6058,U_6059,tc_HOL_Obool),U_6055),hAPP(hAPP(c_Product__Type_OPair(U_6058,U_6059),U_6056),U_6057)))
      | ~ hBOOL(hAPP(hAPP(U_6055,U_6056),U_6057)) ),
    inference(definitional_conversion,[status(esa)],[f_1795_2]) ).

cnf(f_1795_4,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6058,U_6059,tc_HOL_Obool),U_6055),hAPP(hAPP(c_Product__Type_OPair(U_6058,U_6059),U_6056),U_6057)))
    | ~ hBOOL(hAPP(hAPP(U_6055,U_6056),U_6057)) ),
    inference(clausify,[status(thm)],[f_1795_3]) ).

fof(f_1796_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_1796_2,plain,
    ! [U_6064,U_6063,U_6062] :
      ( hBOOL(hAPP(hAPP(U_6064,U_6062),U_6063))
      | ? [U_6061,U_6060] :
          ( ~ hBOOL(hAPP(hAPP(U_6064,U_6061),U_6060))
          & ( hBOOL(hAPP(hAPP(U_6064,U_6061),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_6060)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6060),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6061),U_6060)) )
          & 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_6061),U_6060))) )
      | ~ 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_6062),U_6063))) ),
    inference(variable_rename,[status(thm)],[f_1796_1]) ).

fof(f_1796_3,plain,
    ! [U_6064,U_6063,U_6062] :
      ( hBOOL(hAPP(hAPP(U_6064,U_6062),U_6063))
      | ? [U_6060] :
          ( ~ hBOOL(hAPP(hAPP(U_6064,sK100(U_6064,U_6063,U_6062)),U_6060))
          & ( hBOOL(hAPP(hAPP(U_6064,sK100(U_6064,U_6063,U_6062)),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_6060)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6060),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK100(U_6064,U_6063,U_6062)),U_6060)) )
          & 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),sK100(U_6064,U_6063,U_6062)),U_6060))) )
      | ~ 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_6062),U_6063))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_6061,sK100(U_6064,U_6063,U_6062))],[f_1796_2]) ).

fof(f_1796_4,plain,
    ! [U_6064,U_6063,U_6062] :
      ( hBOOL(hAPP(hAPP(U_6064,U_6062),U_6063))
      | ( ~ hBOOL(hAPP(hAPP(U_6064,sK100(U_6064,U_6063,U_6062)),sK101(U_6064,U_6063,U_6062)))
        & ( hBOOL(hAPP(hAPP(U_6064,sK100(U_6064,U_6063,U_6062)),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)))),sK101(U_6064,U_6063,U_6062))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK101(U_6064,U_6063,U_6062)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK100(U_6064,U_6063,U_6062)),sK101(U_6064,U_6063,U_6062))) )
        & 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),sK100(U_6064,U_6063,U_6062)),sK101(U_6064,U_6063,U_6062)))) )
      | ~ 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_6062),U_6063))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_6060,sK101(U_6064,U_6063,U_6062))],[f_1796_3]) ).

fof(f_1796_5,plain,
    ( ! [U_6062,U_6063,U_6064] :
        ( ~ hBOOL(hAPP(hAPP(U_6064,sK100(U_6064,U_6063,U_6062)),sK101(U_6064,U_6063,U_6062)))
        | ~ sP578(U_6062,U_6063,U_6064) )
    & ! [U_6062,U_6063,U_6064] :
        ( hBOOL(hAPP(hAPP(U_6064,sK100(U_6064,U_6063,U_6062)),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)))),sK101(U_6064,U_6063,U_6062))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK101(U_6064,U_6063,U_6062)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK100(U_6064,U_6063,U_6062)),sK101(U_6064,U_6063,U_6062)))
        | ~ sP578(U_6062,U_6063,U_6064) )
    & ! [U_6062,U_6063,U_6064] :
        ( 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),sK100(U_6064,U_6063,U_6062)),sK101(U_6064,U_6063,U_6062))))
        | ~ sP578(U_6062,U_6063,U_6064) )
    & ! [U_6062,U_6063,U_6064] :
        ( hBOOL(hAPP(hAPP(U_6064,U_6062),U_6063))
        | sP578(U_6062,U_6063,U_6064)
        | ~ 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_6062),U_6063))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP578])],[f_1796_4]) ).

cnf(f_1796_6,plain,
    ( hBOOL(hAPP(hAPP(U_6064,U_6062),U_6063))
    | sP578(U_6062,U_6063,U_6064)
    | ~ 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_6062),U_6063))) ),
    inference(clausify,[status(thm)],[f_1796_5]) ).

cnf(f_1796_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),sK100(U_6064,U_6063,U_6062)),sK101(U_6064,U_6063,U_6062))))
    | ~ sP578(U_6062,U_6063,U_6064) ),
    inference(clausify,[status(thm)],[f_1796_5]) ).

cnf(f_1796_8,plain,
    ( hBOOL(hAPP(hAPP(U_6064,sK100(U_6064,U_6063,U_6062)),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)))),sK101(U_6064,U_6063,U_6062))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK101(U_6064,U_6063,U_6062)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK100(U_6064,U_6063,U_6062)),sK101(U_6064,U_6063,U_6062)))
    | ~ sP578(U_6062,U_6063,U_6064) ),
    inference(clausify,[status(thm)],[f_1796_5]) ).

cnf(f_1796_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_6064,sK100(U_6064,U_6063,U_6062)),sK101(U_6064,U_6063,U_6062)))
    | ~ sP578(U_6062,U_6063,U_6064) ),
    inference(clausify,[status(thm)],[f_1796_5]) ).

fof(f_1797_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_1797_2,plain,
    ! [U_6066,U_6065] :
      ( ( ( c_Nitpick_Onat__gcd(U_6065,U_6066) = c_Nitpick_Onat__gcd(U_6066,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6065,U_6066))
          | U_6066 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( c_Nitpick_Onat__gcd(U_6065,U_6066) = U_6065
          | U_6066 != 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_6065),U_6066))) ),
    inference(variable_rename,[status(thm)],[f_1797_1]) ).

fof(f_1797_3,plain,
    ( ! [U_6066,U_6065] :
        ( c_Nitpick_Onat__gcd(U_6065,U_6066) = c_Nitpick_Onat__gcd(U_6066,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6065,U_6066))
        | U_6066 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP579(U_6066,U_6065) )
    & ! [U_6066,U_6065] :
        ( c_Nitpick_Onat__gcd(U_6065,U_6066) = U_6065
        | U_6066 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP579(U_6066,U_6065) )
    & ! [U_6066,U_6065] :
        ( sP579(U_6066,U_6065)
        | ~ 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_6065),U_6066))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP579])],[f_1797_2]) ).

cnf(f_1797_4,plain,
    ( sP579(U_6066,U_6065)
    | ~ 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_6065),U_6066))) ),
    inference(clausify,[status(thm)],[f_1797_3]) ).

cnf(f_1797_5,plain,
    ( c_Nitpick_Onat__gcd(U_6065,U_6066) = U_6065
    | U_6066 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP579(U_6066,U_6065) ),
    inference(clausify,[status(thm)],[f_1797_3]) ).

cnf(f_1797_6,plain,
    ( c_Nitpick_Onat__gcd(U_6065,U_6066) = c_Nitpick_Onat__gcd(U_6066,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6065,U_6066))
    | U_6066 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP579(U_6066,U_6065) ),
    inference(clausify,[status(thm)],[f_1797_3]) ).

fof(f_1798_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_1798_2,plain,
    ! [U_6068,U_6067] :
      ( ( ( ( c_Divides_Odivmod__int(U_6067,U_6068) = 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_6068))),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_6068)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6067))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6068),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6067),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_6067,U_6068)),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_6068))))),c_Divides_Opdivmod(U_6067,U_6068))))
            | U_6068 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_6067,U_6068) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6067)
            | U_6068 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_6067 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(U_6067,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_6067 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1798_1]) ).

fof(f_1798_3,plain,
    ( ! [U_6072,U_6070] :
        ( ( ( c_Divides_Odivmod__int(U_6070,U_6072) = 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_6072))),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_6072)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6070))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6072),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6070),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_6070,U_6072)),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_6072))))),c_Divides_Opdivmod(U_6070,U_6072))))
            | U_6072 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_6070,U_6072) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6070)
            | U_6072 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_6070 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6071,U_6069] :
        ( c_Divides_Odivmod__int(U_6069,U_6071) = 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_6069 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1798_2]) ).

fof(f_1798_4,plain,
    ( ! [U_6070,U_6072] :
        ( c_Divides_Odivmod__int(U_6070,U_6072) = 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_6072))),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_6072)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6070))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6072),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6070),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_6070,U_6072)),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_6072))))),c_Divides_Opdivmod(U_6070,U_6072))))
        | U_6072 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP580(U_6070,U_6072) )
    & ! [U_6070,U_6072] :
        ( c_Divides_Odivmod__int(U_6070,U_6072) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6070)
        | U_6072 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP580(U_6070,U_6072) )
    & ! [U_6070,U_6072] :
        ( sP580(U_6070,U_6072)
        | U_6070 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6069,U_6071] :
        ( c_Divides_Odivmod__int(U_6069,U_6071) = 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_6069 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP580])],[f_1798_3]) ).

cnf(f_1798_5,plain,
    ( c_Divides_Odivmod__int(U_6069,U_6071) = 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_6069 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1798_4]) ).

cnf(f_1798_6,plain,
    ( sP580(U_6070,U_6072)
    | U_6070 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1798_4]) ).

cnf(f_1798_7,plain,
    ( c_Divides_Odivmod__int(U_6070,U_6072) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6070)
    | U_6072 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP580(U_6070,U_6072) ),
    inference(clausify,[status(thm)],[f_1798_4]) ).

cnf(f_1798_8,plain,
    ( c_Divides_Odivmod__int(U_6070,U_6072) = 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_6072))),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_6072)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6070))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6072),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6070),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_6070,U_6072)),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_6072))))),c_Divides_Opdivmod(U_6070,U_6072))))
    | U_6072 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP580(U_6070,U_6072) ),
    inference(clausify,[status(thm)],[f_1798_4]) ).

fof(f_1799_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_1799_2,plain,
    ! [U_6078,U_6077,U_6076,U_6075,U_6074,U_6073] : hAPP(c_Product__Type_Oapsnd(U_6073,U_6074,U_6075,U_6076),hAPP(hAPP(c_Product__Type_OPair(U_6075,U_6073),U_6077),U_6078)) = hAPP(hAPP(c_Product__Type_OPair(U_6075,U_6074),U_6077),hAPP(U_6076,U_6078)),
    inference(variable_rename,[status(thm)],[f_1799_1]) ).

fof(f_1799_3,plain,
    ! [U_6075,U_6076,U_6078,U_6077,U_6074,U_6073] : hAPP(c_Product__Type_Oapsnd(U_6073,U_6074,U_6075,U_6076),hAPP(hAPP(c_Product__Type_OPair(U_6075,U_6073),U_6077),U_6078)) = hAPP(hAPP(c_Product__Type_OPair(U_6075,U_6074),U_6077),hAPP(U_6076,U_6078)),
    inference(definitional_conversion,[status(esa)],[f_1799_2]) ).

cnf(f_1799_4,plain,
    hAPP(c_Product__Type_Oapsnd(U_6073,U_6074,U_6075,U_6076),hAPP(hAPP(c_Product__Type_OPair(U_6075,U_6073),U_6077),U_6078)) = hAPP(hAPP(c_Product__Type_OPair(U_6075,U_6074),U_6077),hAPP(U_6076,U_6078)),
    inference(clausify,[status(thm)],[f_1799_3]) ).

fof(f_1800_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_1800_2,plain,
    ! [U_6087,U_6086,U_6085] :
      ( ( ! [U_6084] : hBOOL(hAPP(U_6085,U_6084))
        | ? [U_6083,U_6082] : ~ hBOOL(hAPP(U_6085,hAPP(hAPP(c_Product__Type_OPair(U_6086,U_6087),U_6083),U_6082))) )
      & ( ! [U_6081,U_6080] : hBOOL(hAPP(U_6085,hAPP(hAPP(c_Product__Type_OPair(U_6086,U_6087),U_6081),U_6080)))
        | ? [U_6079] : ~ hBOOL(hAPP(U_6085,U_6079)) ) ),
    inference(variable_rename,[status(thm)],[f_1800_1]) ).

fof(f_1800_3,plain,
    ( ! [U_6093,U_6091,U_6089] :
        ( ! [U_6084] : hBOOL(hAPP(U_6089,U_6084))
        | ? [U_6083,U_6082] : ~ hBOOL(hAPP(U_6089,hAPP(hAPP(c_Product__Type_OPair(U_6091,U_6093),U_6083),U_6082))) )
    & ! [U_6092,U_6090,U_6088] :
        ( ! [U_6081,U_6080] : hBOOL(hAPP(U_6088,hAPP(hAPP(c_Product__Type_OPair(U_6090,U_6092),U_6081),U_6080)))
        | ? [U_6079] : ~ hBOOL(hAPP(U_6088,U_6079)) ) ),
    inference(miniscope,[status(thm)],[f_1800_2]) ).

fof(f_1800_4,plain,
    ( ! [U_6093,U_6091,U_6089] :
        ( ! [U_6084] : hBOOL(hAPP(U_6089,U_6084))
        | ? [U_6083,U_6082] : ~ hBOOL(hAPP(U_6089,hAPP(hAPP(c_Product__Type_OPair(U_6091,U_6093),U_6083),U_6082))) )
    & ! [U_6092,U_6090,U_6088] :
        ( ! [U_6081,U_6080] : hBOOL(hAPP(U_6088,hAPP(hAPP(c_Product__Type_OPair(U_6090,U_6092),U_6081),U_6080)))
        | ~ hBOOL(hAPP(U_6088,sK102(U_6092,U_6090,U_6088))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_6079,sK102(U_6092,U_6090,U_6088))],[f_1800_3]) ).

fof(f_1800_5,plain,
    ( ! [U_6093,U_6091,U_6089] :
        ( ! [U_6084] : hBOOL(hAPP(U_6089,U_6084))
        | ? [U_6082] : ~ hBOOL(hAPP(U_6089,hAPP(hAPP(c_Product__Type_OPair(U_6091,U_6093),sK103(U_6093,U_6091,U_6089)),U_6082))) )
    & ! [U_6092,U_6090,U_6088] :
        ( ! [U_6081,U_6080] : hBOOL(hAPP(U_6088,hAPP(hAPP(c_Product__Type_OPair(U_6090,U_6092),U_6081),U_6080)))
        | ~ hBOOL(hAPP(U_6088,sK102(U_6092,U_6090,U_6088))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_6083,sK103(U_6093,U_6091,U_6089))],[f_1800_4]) ).

fof(f_1800_6,plain,
    ( ! [U_6093,U_6091,U_6089] :
        ( ! [U_6084] : hBOOL(hAPP(U_6089,U_6084))
        | ~ hBOOL(hAPP(U_6089,hAPP(hAPP(c_Product__Type_OPair(U_6091,U_6093),sK103(U_6093,U_6091,U_6089)),sK104(U_6093,U_6091,U_6089)))) )
    & ! [U_6092,U_6090,U_6088] :
        ( ! [U_6081,U_6080] : hBOOL(hAPP(U_6088,hAPP(hAPP(c_Product__Type_OPair(U_6090,U_6092),U_6081),U_6080)))
        | ~ hBOOL(hAPP(U_6088,sK102(U_6092,U_6090,U_6088))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_6082,sK104(U_6093,U_6091,U_6089))],[f_1800_5]) ).

fof(f_1800_7,plain,
    ( ! [U_6084,U_6089,U_6091,U_6093] :
        ( hBOOL(hAPP(U_6089,U_6084))
        | ~ hBOOL(hAPP(U_6089,hAPP(hAPP(c_Product__Type_OPair(U_6091,U_6093),sK103(U_6093,U_6091,U_6089)),sK104(U_6093,U_6091,U_6089)))) )
    & ! [U_6090,U_6080,U_6081,U_6088,U_6092] :
        ( hBOOL(hAPP(U_6088,hAPP(hAPP(c_Product__Type_OPair(U_6090,U_6092),U_6081),U_6080)))
        | ~ hBOOL(hAPP(U_6088,sK102(U_6092,U_6090,U_6088))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1800_6]) ).

cnf(f_1800_8,plain,
    ( hBOOL(hAPP(U_6088,hAPP(hAPP(c_Product__Type_OPair(U_6090,U_6092),U_6081),U_6080)))
    | ~ hBOOL(hAPP(U_6088,sK102(U_6092,U_6090,U_6088))) ),
    inference(clausify,[status(thm)],[f_1800_7]) ).

cnf(f_1800_9,plain,
    ( hBOOL(hAPP(U_6089,U_6084))
    | ~ hBOOL(hAPP(U_6089,hAPP(hAPP(c_Product__Type_OPair(U_6091,U_6093),sK103(U_6093,U_6091,U_6089)),sK104(U_6093,U_6091,U_6089)))) ),
    inference(clausify,[status(thm)],[f_1800_7]) ).

fof(f_1801_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_1801_2,plain,
    ! [U_6099,U_6098,U_6097,U_6096,U_6095,U_6094] :
      ( ( hAPP(hAPP(c_Product__Type_OPair(U_6094,U_6095),U_6096),U_6097) = hAPP(hAPP(c_Product__Type_OPair(U_6094,U_6095),U_6098),U_6099)
        | U_6097 != U_6099
        | U_6096 != U_6098 )
      & ( ( U_6097 = U_6099
          & U_6096 = U_6098 )
        | hAPP(hAPP(c_Product__Type_OPair(U_6094,U_6095),U_6096),U_6097) != hAPP(hAPP(c_Product__Type_OPair(U_6094,U_6095),U_6098),U_6099) ) ),
    inference(variable_rename,[status(thm)],[f_1801_1]) ).

fof(f_1801_3,plain,
    ( ! [U_6111,U_6109,U_6107,U_6105] :
        ( ! [U_6103,U_6101] : hAPP(hAPP(c_Product__Type_OPair(U_6101,U_6103),U_6105),U_6107) = hAPP(hAPP(c_Product__Type_OPair(U_6101,U_6103),U_6109),U_6111)
        | U_6107 != U_6111
        | U_6105 != U_6109 )
    & ! [U_6110,U_6108,U_6106,U_6104] :
        ( ! [U_6102,U_6100] : hAPP(hAPP(c_Product__Type_OPair(U_6100,U_6102),U_6104),U_6106) != hAPP(hAPP(c_Product__Type_OPair(U_6100,U_6102),U_6108),U_6110)
        | ( U_6106 = U_6110
          & U_6104 = U_6108 ) ) ),
    inference(miniscope,[status(thm)],[f_1801_2]) ).

fof(f_1801_4,plain,
    ( ! [U_6108,U_6106,U_6104,U_6110] :
        ( U_6106 = U_6110
        | ~ sP581(U_6108,U_6106,U_6104,U_6110) )
    & ! [U_6108,U_6106,U_6104,U_6110] :
        ( U_6104 = U_6108
        | ~ sP581(U_6108,U_6106,U_6104,U_6110) )
    & ! [U_6105,U_6107,U_6101,U_6103,U_6111,U_6109] :
        ( hAPP(hAPP(c_Product__Type_OPair(U_6101,U_6103),U_6105),U_6107) = hAPP(hAPP(c_Product__Type_OPair(U_6101,U_6103),U_6109),U_6111)
        | U_6107 != U_6111
        | U_6105 != U_6109 )
    & ! [U_6102,U_6108,U_6106,U_6100,U_6104,U_6110] :
        ( hAPP(hAPP(c_Product__Type_OPair(U_6100,U_6102),U_6104),U_6106) != hAPP(hAPP(c_Product__Type_OPair(U_6100,U_6102),U_6108),U_6110)
        | sP581(U_6108,U_6106,U_6104,U_6110) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP581])],[f_1801_3]) ).

cnf(f_1801_5,plain,
    ( hAPP(hAPP(c_Product__Type_OPair(U_6100,U_6102),U_6104),U_6106) != hAPP(hAPP(c_Product__Type_OPair(U_6100,U_6102),U_6108),U_6110)
    | sP581(U_6108,U_6106,U_6104,U_6110) ),
    inference(clausify,[status(thm)],[f_1801_4]) ).

cnf(f_1801_6,plain,
    ( hAPP(hAPP(c_Product__Type_OPair(U_6101,U_6103),U_6105),U_6107) = hAPP(hAPP(c_Product__Type_OPair(U_6101,U_6103),U_6109),U_6111)
    | U_6107 != U_6111
    | U_6105 != U_6109 ),
    inference(clausify,[status(thm)],[f_1801_4]) ).

cnf(f_1801_7,plain,
    ( U_6104 = U_6108
    | ~ sP581(U_6108,U_6106,U_6104,U_6110) ),
    inference(clausify,[status(thm)],[f_1801_4]) ).

cnf(f_1801_8,plain,
    ( U_6106 = U_6110
    | ~ sP581(U_6108,U_6106,U_6104,U_6110) ),
    inference(clausify,[status(thm)],[f_1801_4]) ).

fof(f_1802_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_1802_2,plain,
    ! [U_6117,U_6116,U_6115,U_6114,U_6113,U_6112] :
      ( ( U_6115 = U_6117
        & U_6114 = U_6116 )
      | hAPP(hAPP(c_Product__Type_OPair(U_6112,U_6113),U_6114),U_6115) != hAPP(hAPP(c_Product__Type_OPair(U_6112,U_6113),U_6116),U_6117) ),
    inference(variable_rename,[status(thm)],[f_1802_1]) ).

fof(f_1802_3,plain,
    ! [U_6117,U_6116,U_6115,U_6114] :
      ( ! [U_6113,U_6112] : hAPP(hAPP(c_Product__Type_OPair(U_6112,U_6113),U_6114),U_6115) != hAPP(hAPP(c_Product__Type_OPair(U_6112,U_6113),U_6116),U_6117)
      | ( U_6115 = U_6117
        & U_6114 = U_6116 ) ),
    inference(miniscope,[status(thm)],[f_1802_2]) ).

fof(f_1802_4,plain,
    ( ! [U_6116,U_6117,U_6115,U_6114] :
        ( U_6115 = U_6117
        | ~ sP582(U_6116,U_6117,U_6115,U_6114) )
    & ! [U_6116,U_6117,U_6115,U_6114] :
        ( U_6114 = U_6116
        | ~ sP582(U_6116,U_6117,U_6115,U_6114) )
    & ! [U_6116,U_6117,U_6115,U_6113,U_6114,U_6112] :
        ( hAPP(hAPP(c_Product__Type_OPair(U_6112,U_6113),U_6114),U_6115) != hAPP(hAPP(c_Product__Type_OPair(U_6112,U_6113),U_6116),U_6117)
        | sP582(U_6116,U_6117,U_6115,U_6114) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP582])],[f_1802_3]) ).

cnf(f_1802_5,plain,
    ( hAPP(hAPP(c_Product__Type_OPair(U_6112,U_6113),U_6114),U_6115) != hAPP(hAPP(c_Product__Type_OPair(U_6112,U_6113),U_6116),U_6117)
    | sP582(U_6116,U_6117,U_6115,U_6114) ),
    inference(clausify,[status(thm)],[f_1802_4]) ).

cnf(f_1802_6,plain,
    ( U_6114 = U_6116
    | ~ sP582(U_6116,U_6117,U_6115,U_6114) ),
    inference(clausify,[status(thm)],[f_1802_4]) ).

cnf(f_1802_7,plain,
    ( U_6115 = U_6117
    | ~ sP582(U_6116,U_6117,U_6115,U_6114) ),
    inference(clausify,[status(thm)],[f_1802_4]) ).

fof(f_1803_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_1803_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_1803_1]) ).

cnf(f_1803_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_1803_2]) ).

fof(f_1804_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_1804_2,plain,
    ! [U_6123,U_6122,U_6121,U_6120,U_6119,U_6118] :
      ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6120,U_6121,U_6122),U_6123),U_6118) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6120,U_6121,U_6122),U_6123),U_6119)
      | U_6118 != U_6119 ),
    inference(variable_rename,[status(thm)],[f_1804_1]) ).

fof(f_1804_3,plain,
    ! [U_6120,U_6118,U_6119,U_6121,U_6122,U_6123] :
      ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6120,U_6121,U_6122),U_6123),U_6118) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6120,U_6121,U_6122),U_6123),U_6119)
      | U_6118 != U_6119 ),
    inference(definitional_conversion,[status(esa)],[f_1804_2]) ).

cnf(f_1804_4,plain,
    ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6120,U_6121,U_6122),U_6123),U_6118) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6120,U_6121,U_6122),U_6123),U_6119)
    | U_6118 != U_6119 ),
    inference(clausify,[status(thm)],[f_1804_3]) ).

fof(f_1805_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_1805_2,plain,
    ! [U_6129,U_6128,U_6127,U_6126,U_6125,U_6124] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6124,U_6125,U_6126),U_6127),hAPP(hAPP(c_Product__Type_OPair(U_6124,U_6125),U_6128),U_6129)) = hAPP(hAPP(U_6127,U_6128),U_6129),
    inference(variable_rename,[status(thm)],[f_1805_1]) ).

fof(f_1805_3,plain,
    ! [U_6125,U_6124,U_6126,U_6127,U_6128,U_6129] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6124,U_6125,U_6126),U_6127),hAPP(hAPP(c_Product__Type_OPair(U_6124,U_6125),U_6128),U_6129)) = hAPP(hAPP(U_6127,U_6128),U_6129),
    inference(definitional_conversion,[status(esa)],[f_1805_2]) ).

cnf(f_1805_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6124,U_6125,U_6126),U_6127),hAPP(hAPP(c_Product__Type_OPair(U_6124,U_6125),U_6128),U_6129)) = hAPP(hAPP(U_6127,U_6128),U_6129),
    inference(clausify,[status(thm)],[f_1805_3]) ).

fof(f_1806_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_1806_2,plain,
    ! [U_6135,U_6134,U_6133,U_6132,U_6131,U_6130] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6130,U_6131,U_6132),U_6133),hAPP(hAPP(c_Product__Type_OPair(U_6130,U_6131),U_6134),U_6135)) = hAPP(hAPP(U_6133,U_6134),U_6135),
    inference(variable_rename,[status(thm)],[f_1806_1]) ).

fof(f_1806_3,plain,
    ! [U_6130,U_6131,U_6132,U_6133,U_6134,U_6135] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6130,U_6131,U_6132),U_6133),hAPP(hAPP(c_Product__Type_OPair(U_6130,U_6131),U_6134),U_6135)) = hAPP(hAPP(U_6133,U_6134),U_6135),
    inference(definitional_conversion,[status(esa)],[f_1806_2]) ).

cnf(f_1806_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6130,U_6131,U_6132),U_6133),hAPP(hAPP(c_Product__Type_OPair(U_6130,U_6131),U_6134),U_6135)) = hAPP(hAPP(U_6133,U_6134),U_6135),
    inference(clausify,[status(thm)],[f_1806_3]) ).

fof(f_1807_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_1807_2,plain,
    ! [U_6140,U_6139,U_6138,U_6137,U_6136] :
      ( hBOOL(hAPP(hAPP(U_6138,U_6139),U_6140))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6136,U_6137,tc_HOL_Obool),U_6138),hAPP(hAPP(c_Product__Type_OPair(U_6136,U_6137),U_6139),U_6140))) ),
    inference(variable_rename,[status(thm)],[f_1807_1]) ).

fof(f_1807_3,plain,
    ! [U_6140,U_6139,U_6138] :
      ( ! [U_6137,U_6136] : ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6136,U_6137,tc_HOL_Obool),U_6138),hAPP(hAPP(c_Product__Type_OPair(U_6136,U_6137),U_6139),U_6140)))
      | hBOOL(hAPP(hAPP(U_6138,U_6139),U_6140)) ),
    inference(miniscope,[status(thm)],[f_1807_2]) ).

fof(f_1807_4,plain,
    ! [U_6136,U_6137,U_6138,U_6139,U_6140] :
      ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6136,U_6137,tc_HOL_Obool),U_6138),hAPP(hAPP(c_Product__Type_OPair(U_6136,U_6137),U_6139),U_6140)))
      | hBOOL(hAPP(hAPP(U_6138,U_6139),U_6140)) ),
    inference(definitional_conversion,[status(esa)],[f_1807_3]) ).

cnf(f_1807_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6136,U_6137,tc_HOL_Obool),U_6138),hAPP(hAPP(c_Product__Type_OPair(U_6136,U_6137),U_6139),U_6140)))
    | hBOOL(hAPP(hAPP(U_6138,U_6139),U_6140)) ),
    inference(clausify,[status(thm)],[f_1807_4]) ).

fof(f_1808_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_1808_2,plain,
    ! [U_6144,U_6143,U_6142,U_6141] : hAPP(c_Product__Type_Oprod_Oprod__case(U_6141,U_6142,U_6143),hAPP(hAPP(c_COMBB(tc_fun(U_6142,tc_prod(U_6141,U_6142)),tc_fun(U_6142,U_6143),U_6141),hAPP(c_COMBB(tc_prod(U_6141,U_6142),U_6143,U_6142),U_6144)),c_Product__Type_OPair(U_6141,U_6142))) = U_6144,
    inference(variable_rename,[status(thm)],[f_1808_1]) ).

fof(f_1808_3,plain,
    ! [U_6141,U_6142,U_6143,U_6144] : hAPP(c_Product__Type_Oprod_Oprod__case(U_6141,U_6142,U_6143),hAPP(hAPP(c_COMBB(tc_fun(U_6142,tc_prod(U_6141,U_6142)),tc_fun(U_6142,U_6143),U_6141),hAPP(c_COMBB(tc_prod(U_6141,U_6142),U_6143,U_6142),U_6144)),c_Product__Type_OPair(U_6141,U_6142))) = U_6144,
    inference(definitional_conversion,[status(esa)],[f_1808_2]) ).

cnf(f_1808_4,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_6141,U_6142,U_6143),hAPP(hAPP(c_COMBB(tc_fun(U_6142,tc_prod(U_6141,U_6142)),tc_fun(U_6142,U_6143),U_6141),hAPP(c_COMBB(tc_prod(U_6141,U_6142),U_6143,U_6142),U_6144)),c_Product__Type_OPair(U_6141,U_6142))) = U_6144,
    inference(clausify,[status(thm)],[f_1808_3]) ).

fof(f_1809_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_1809_2,plain,
    ! [U_6152,U_6151,U_6150,U_6149,U_6148,U_6147,U_6146,U_6145] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6145,U_6146,U_6147),U_6148),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6149,U_6150,tc_prod(U_6145,U_6146)),U_6151),U_6152)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6149,U_6150,U_6147),hAPP(hAPP(c_COMBB(tc_fun(U_6150,tc_prod(U_6145,U_6146)),tc_fun(U_6150,U_6147),U_6149),hAPP(c_COMBB(tc_prod(U_6145,U_6146),U_6147,U_6150),hAPP(c_Product__Type_Oprod_Oprod__case(U_6145,U_6146,U_6147),U_6148))),U_6151)),U_6152),
    inference(variable_rename,[status(thm)],[f_1809_1]) ).

fof(f_1809_3,plain,
    ! [U_6145,U_6146,U_6147,U_6148,U_6149,U_6150,U_6151,U_6152] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6145,U_6146,U_6147),U_6148),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6149,U_6150,tc_prod(U_6145,U_6146)),U_6151),U_6152)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6149,U_6150,U_6147),hAPP(hAPP(c_COMBB(tc_fun(U_6150,tc_prod(U_6145,U_6146)),tc_fun(U_6150,U_6147),U_6149),hAPP(c_COMBB(tc_prod(U_6145,U_6146),U_6147,U_6150),hAPP(c_Product__Type_Oprod_Oprod__case(U_6145,U_6146,U_6147),U_6148))),U_6151)),U_6152),
    inference(definitional_conversion,[status(esa)],[f_1809_2]) ).

cnf(f_1809_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6145,U_6146,U_6147),U_6148),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6149,U_6150,tc_prod(U_6145,U_6146)),U_6151),U_6152)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6149,U_6150,U_6147),hAPP(hAPP(c_COMBB(tc_fun(U_6150,tc_prod(U_6145,U_6146)),tc_fun(U_6150,U_6147),U_6149),hAPP(c_COMBB(tc_prod(U_6145,U_6146),U_6147,U_6150),hAPP(c_Product__Type_Oprod_Oprod__case(U_6145,U_6146,U_6147),U_6148))),U_6151)),U_6152),
    inference(clausify,[status(thm)],[f_1809_3]) ).

fof(f_1810_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_1810_2,plain,
    ! [U_6154,U_6153] : c_Divides_Opdivmod(U_6153,U_6154) = 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_6153)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6154))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6153),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6154))),
    inference(variable_rename,[status(thm)],[f_1810_1]) ).

fof(f_1810_3,plain,
    ! [U_6154,U_6153] : c_Divides_Opdivmod(U_6153,U_6154) = 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_6153)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6154))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6153),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6154))),
    inference(definitional_conversion,[status(esa)],[f_1810_2]) ).

cnf(f_1810_4,plain,
    c_Divides_Opdivmod(U_6153,U_6154) = 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_6153)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6154))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6153),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6154))),
    inference(clausify,[status(thm)],[f_1810_3]) ).

fof(f_1811_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_1811_2,plain,
    ! [U_6156,U_6155] :
      ( ( c_Divides_Opdivmod(U_6156,U_6155) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6156),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6155))
        | U_6155 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Opdivmod(U_6156,U_6155) = 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_6156))
        | U_6155 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1811_1]) ).

fof(f_1811_3,plain,
    ( ! [U_6160,U_6158] :
        ( c_Divides_Opdivmod(U_6160,U_6158) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6160),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6158))
        | U_6158 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6159,U_6157] :
        ( c_Divides_Opdivmod(U_6159,U_6157) = 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_6159))
        | U_6157 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1811_2]) ).

fof(f_1811_4,plain,
    ( ! [U_6158,U_6160] :
        ( c_Divides_Opdivmod(U_6160,U_6158) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6160),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6158))
        | U_6158 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6159,U_6157] :
        ( c_Divides_Opdivmod(U_6159,U_6157) = 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_6159))
        | U_6157 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_1811_3]) ).

cnf(f_1811_5,plain,
    ( c_Divides_Opdivmod(U_6159,U_6157) = 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_6159))
    | U_6157 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1811_4]) ).

cnf(f_1811_6,plain,
    ( c_Divides_Opdivmod(U_6160,U_6158) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6160),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6158))
    | U_6158 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1811_4]) ).

fof(f_1812_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_1812_2,plain,
    ! [U_6162,U_6161] :
      ( ( ( ( c_Divides_Odivmod__int(U_6161,U_6162) = 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_6162))),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_6161)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6162))),c_Divides_Opdivmod(U_6161,U_6162)),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_6162))))),c_Divides_Opdivmod(U_6161,U_6162))))
            | U_6162 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_6161,U_6162) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6161)
            | U_6162 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_6161 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(U_6161,U_6162) = 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_6161 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1812_1]) ).

fof(f_1812_3,plain,
    ( ! [U_6166,U_6164] :
        ( ( ( c_Divides_Odivmod__int(U_6164,U_6166) = 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_6166))),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_6164)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6166))),c_Divides_Opdivmod(U_6164,U_6166)),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_6166))))),c_Divides_Opdivmod(U_6164,U_6166))))
            | U_6166 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_6164,U_6166) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6164)
            | U_6166 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_6164 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6165,U_6163] :
        ( c_Divides_Odivmod__int(U_6163,U_6165) = 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_6163 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1812_2]) ).

fof(f_1812_4,plain,
    ( ! [U_6164,U_6166] :
        ( c_Divides_Odivmod__int(U_6164,U_6166) = 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_6166))),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_6164)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6166))),c_Divides_Opdivmod(U_6164,U_6166)),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_6166))))),c_Divides_Opdivmod(U_6164,U_6166))))
        | U_6166 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP583(U_6164,U_6166) )
    & ! [U_6164,U_6166] :
        ( c_Divides_Odivmod__int(U_6164,U_6166) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6164)
        | U_6166 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP583(U_6164,U_6166) )
    & ! [U_6164,U_6166] :
        ( sP583(U_6164,U_6166)
        | U_6164 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6165,U_6163] :
        ( c_Divides_Odivmod__int(U_6163,U_6165) = 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_6163 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP583])],[f_1812_3]) ).

cnf(f_1812_5,plain,
    ( c_Divides_Odivmod__int(U_6163,U_6165) = 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_6163 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1812_4]) ).

cnf(f_1812_6,plain,
    ( sP583(U_6164,U_6166)
    | U_6164 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1812_4]) ).

cnf(f_1812_7,plain,
    ( c_Divides_Odivmod__int(U_6164,U_6166) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6164)
    | U_6166 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP583(U_6164,U_6166) ),
    inference(clausify,[status(thm)],[f_1812_4]) ).

cnf(f_1812_8,plain,
    ( c_Divides_Odivmod__int(U_6164,U_6166) = 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_6166))),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_6164)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6166))),c_Divides_Opdivmod(U_6164,U_6166)),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_6166))))),c_Divides_Opdivmod(U_6164,U_6166))))
    | U_6166 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP583(U_6164,U_6166) ),
    inference(clausify,[status(thm)],[f_1812_4]) ).

fof(f_1813_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_1813_2,plain,
    ! [U_6168,U_6167] : c_Code__Numeral_Odiv__mod__code__numeral(U_6167,U_6168) = 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_6167),U_6168)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_6167,U_6168)),
    inference(variable_rename,[status(thm)],[f_1813_1]) ).

fof(f_1813_3,plain,
    ! [U_6168,U_6167] : c_Code__Numeral_Odiv__mod__code__numeral(U_6167,U_6168) = 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_6167),U_6168)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_6167,U_6168)),
    inference(definitional_conversion,[status(esa)],[f_1813_2]) ).

cnf(f_1813_4,plain,
    c_Code__Numeral_Odiv__mod__code__numeral(U_6167,U_6168) = 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_6167),U_6168)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_6167,U_6168)),
    inference(clausify,[status(thm)],[f_1813_3]) ).

fof(f_1814_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_1814_2,plain,
    ! [U_6173,U_6172,U_6171,U_6170,U_6169] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6170),U_6173)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6171),U_6173)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6170),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6171,U_6173))),U_6172))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6173))
      | U_6170 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6169,U_6170),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6171),U_6172))) ),
    inference(variable_rename,[status(thm)],[f_1814_1]) ).

fof(f_1814_3,plain,
    ! [U_6170,U_6169,U_6171,U_6172,U_6173] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6170),U_6173)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6171),U_6173)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6170),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6171,U_6173))),U_6172))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6173))
      | U_6170 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6169,U_6170),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6171),U_6172))) ),
    inference(definitional_conversion,[status(esa)],[f_1814_2]) ).

cnf(f_1814_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6170),U_6173)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6171),U_6173)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6170),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6171,U_6173))),U_6172))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6173))
    | U_6170 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6169,U_6170),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6171),U_6172))) ),
    inference(clausify,[status(thm)],[f_1814_3]) ).

fof(f_1815_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_1815_2,plain,
    ! [U_6174] :
      ( 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_6174)) = 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_6174)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6174)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1815_1]) ).

fof(f_1815_3,plain,
    ! [U_6174] :
      ( 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_6174)) = 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_6174)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6174)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1815_2]) ).

cnf(f_1815_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_6174)) = 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_6174)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6174)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    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_6176,U_6175] : c_Divides_Odivmod__int__rel(U_6175,U_6176) = 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_6175))),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_6176)))))),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_6176))),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_6176))))),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_6176)))),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_6176))),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_6175,U_6176] : c_Divides_Odivmod__int__rel(U_6175,U_6176) = 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_6175))),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_6176)))))),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_6176))),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_6176))))),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_6176)))),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_6176))),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_6175,U_6176) = 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_6175))),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_6176)))))),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_6176))),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_6176))))),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_6176)))),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_6176))),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_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_1817_2,plain,
    ! [U_6181,U_6180,U_6179] :
      ( hBOOL(hAPP(hAPP(U_6181,U_6179),U_6180))
      | ? [U_6178,U_6177] :
          ( ~ hBOOL(hAPP(hAPP(U_6181,U_6178),U_6177))
          & ( hBOOL(hAPP(hAPP(U_6181,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6178)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6177)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6177),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_6178),U_6177))) )
      | ~ 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_6179),U_6180))) ),
    inference(variable_rename,[status(thm)],[f_1817_1]) ).

fof(f_1817_3,plain,
    ! [U_6181,U_6180,U_6179] :
      ( hBOOL(hAPP(hAPP(U_6181,U_6179),U_6180))
      | ? [U_6177] :
          ( ~ hBOOL(hAPP(hAPP(U_6181,sK105(U_6181,U_6180,U_6179)),U_6177))
          & ( hBOOL(hAPP(hAPP(U_6181,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK105(U_6181,U_6180,U_6179))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6177)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6177),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),sK105(U_6181,U_6180,U_6179)),U_6177))) )
      | ~ 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_6179),U_6180))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_6178,sK105(U_6181,U_6180,U_6179))],[f_1817_2]) ).

fof(f_1817_4,plain,
    ! [U_6181,U_6180,U_6179] :
      ( hBOOL(hAPP(hAPP(U_6181,U_6179),U_6180))
      | ( ~ hBOOL(hAPP(hAPP(U_6181,sK105(U_6181,U_6180,U_6179)),sK106(U_6181,U_6180,U_6179)))
        & ( hBOOL(hAPP(hAPP(U_6181,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK105(U_6181,U_6180,U_6179))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK106(U_6181,U_6180,U_6179))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK106(U_6181,U_6180,U_6179)),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),sK105(U_6181,U_6180,U_6179)),sK106(U_6181,U_6180,U_6179)))) )
      | ~ 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_6179),U_6180))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_6177,sK106(U_6181,U_6180,U_6179))],[f_1817_3]) ).

fof(f_1817_5,plain,
    ( ! [U_6179,U_6180,U_6181] :
        ( ~ hBOOL(hAPP(hAPP(U_6181,sK105(U_6181,U_6180,U_6179)),sK106(U_6181,U_6180,U_6179)))
        | ~ sP584(U_6179,U_6180,U_6181) )
    & ! [U_6179,U_6180,U_6181] :
        ( hBOOL(hAPP(hAPP(U_6181,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK105(U_6181,U_6180,U_6179))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK106(U_6181,U_6180,U_6179))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK106(U_6181,U_6180,U_6179)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP584(U_6179,U_6180,U_6181) )
    & ! [U_6179,U_6180,U_6181] :
        ( 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),sK105(U_6181,U_6180,U_6179)),sK106(U_6181,U_6180,U_6179))))
        | ~ sP584(U_6179,U_6180,U_6181) )
    & ! [U_6179,U_6180,U_6181] :
        ( hBOOL(hAPP(hAPP(U_6181,U_6179),U_6180))
        | sP584(U_6179,U_6180,U_6181)
        | ~ 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_6179),U_6180))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP584])],[f_1817_4]) ).

cnf(f_1817_6,plain,
    ( hBOOL(hAPP(hAPP(U_6181,U_6179),U_6180))
    | sP584(U_6179,U_6180,U_6181)
    | ~ 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_6179),U_6180))) ),
    inference(clausify,[status(thm)],[f_1817_5]) ).

cnf(f_1817_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),sK105(U_6181,U_6180,U_6179)),sK106(U_6181,U_6180,U_6179))))
    | ~ sP584(U_6179,U_6180,U_6181) ),
    inference(clausify,[status(thm)],[f_1817_5]) ).

cnf(f_1817_8,plain,
    ( hBOOL(hAPP(hAPP(U_6181,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK105(U_6181,U_6180,U_6179))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK106(U_6181,U_6180,U_6179))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK106(U_6181,U_6180,U_6179)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP584(U_6179,U_6180,U_6181) ),
    inference(clausify,[status(thm)],[f_1817_5]) ).

cnf(f_1817_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_6181,sK105(U_6181,U_6180,U_6179)),sK106(U_6181,U_6180,U_6179)))
    | ~ sP584(U_6179,U_6180,U_6181) ),
    inference(clausify,[status(thm)],[f_1817_5]) ).

fof(f_1818_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_1818_2,plain,
    ! [U_6188,U_6187,U_6186,U_6185,U_6184,U_6183,U_6182] :
      ( hBOOL(hAPP(hAPP(hAPP(U_6185,U_6186),U_6187),U_6188))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6182,U_6183,tc_fun(U_6184,tc_HOL_Obool)),U_6185),hAPP(hAPP(c_Product__Type_OPair(U_6182,U_6183),U_6186),U_6187)),U_6188)) ),
    inference(variable_rename,[status(thm)],[f_1818_1]) ).

fof(f_1818_3,plain,
    ! [U_6188,U_6187,U_6186,U_6185] :
      ( ! [U_6184,U_6183,U_6182] : ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6182,U_6183,tc_fun(U_6184,tc_HOL_Obool)),U_6185),hAPP(hAPP(c_Product__Type_OPair(U_6182,U_6183),U_6186),U_6187)),U_6188))
      | hBOOL(hAPP(hAPP(hAPP(U_6185,U_6186),U_6187),U_6188)) ),
    inference(miniscope,[status(thm)],[f_1818_2]) ).

fof(f_1818_4,plain,
    ! [U_6183,U_6184,U_6182,U_6185,U_6186,U_6187,U_6188] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6182,U_6183,tc_fun(U_6184,tc_HOL_Obool)),U_6185),hAPP(hAPP(c_Product__Type_OPair(U_6182,U_6183),U_6186),U_6187)),U_6188))
      | hBOOL(hAPP(hAPP(hAPP(U_6185,U_6186),U_6187),U_6188)) ),
    inference(definitional_conversion,[status(esa)],[f_1818_3]) ).

cnf(f_1818_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6182,U_6183,tc_fun(U_6184,tc_HOL_Obool)),U_6185),hAPP(hAPP(c_Product__Type_OPair(U_6182,U_6183),U_6186),U_6187)),U_6188))
    | hBOOL(hAPP(hAPP(hAPP(U_6185,U_6186),U_6187),U_6188)) ),
    inference(clausify,[status(thm)],[f_1818_4]) ).

fof(f_1819_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_1819_2,plain,
    ! [U_6192,U_6191,U_6190,U_6189] : hAPP(c_Product__Type_Osnd(U_6189,U_6190),hAPP(hAPP(c_Product__Type_OPair(U_6189,U_6190),U_6191),U_6192)) = U_6192,
    inference(variable_rename,[status(thm)],[f_1819_1]) ).

fof(f_1819_3,plain,
    ! [U_6190,U_6189,U_6191,U_6192] : hAPP(c_Product__Type_Osnd(U_6189,U_6190),hAPP(hAPP(c_Product__Type_OPair(U_6189,U_6190),U_6191),U_6192)) = U_6192,
    inference(definitional_conversion,[status(esa)],[f_1819_2]) ).

cnf(f_1819_4,plain,
    hAPP(c_Product__Type_Osnd(U_6189,U_6190),hAPP(hAPP(c_Product__Type_OPair(U_6189,U_6190),U_6191),U_6192)) = U_6192,
    inference(clausify,[status(thm)],[f_1819_3]) ).

fof(f_1820_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_1820_2,plain,
    ! [U_6197,U_6196,U_6195,U_6194,U_6193] :
      ( U_6196 = U_6197
      | hAPP(c_Product__Type_Osnd(U_6193,U_6194),hAPP(hAPP(c_Product__Type_OPair(U_6193,U_6194),U_6195),U_6196)) != U_6197 ),
    inference(variable_rename,[status(thm)],[f_1820_1]) ).

fof(f_1820_3,plain,
    ! [U_6197,U_6196] :
      ( ! [U_6195,U_6194,U_6193] : hAPP(c_Product__Type_Osnd(U_6193,U_6194),hAPP(hAPP(c_Product__Type_OPair(U_6193,U_6194),U_6195),U_6196)) != U_6197
      | U_6196 = U_6197 ),
    inference(miniscope,[status(thm)],[f_1820_2]) ).

fof(f_1820_4,plain,
    ! [U_6193,U_6194,U_6195,U_6196,U_6197] :
      ( hAPP(c_Product__Type_Osnd(U_6193,U_6194),hAPP(hAPP(c_Product__Type_OPair(U_6193,U_6194),U_6195),U_6196)) != U_6197
      | U_6196 = U_6197 ),
    inference(definitional_conversion,[status(esa)],[f_1820_3]) ).

cnf(f_1820_5,plain,
    ( hAPP(c_Product__Type_Osnd(U_6193,U_6194),hAPP(hAPP(c_Product__Type_OPair(U_6193,U_6194),U_6195),U_6196)) != U_6197
    | U_6196 = U_6197 ),
    inference(clausify,[status(thm)],[f_1820_4]) ).

fof(f_1821_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_1821_2,plain,
    ! [U_6203,U_6202,U_6201,U_6200,U_6199,U_6198] :
      ( ( hAPP(c_Product__Type_Oapsnd(U_6198,U_6199,U_6200,U_6201),U_6202) = hAPP(c_Product__Type_Oapsnd(U_6198,U_6199,U_6200,U_6203),U_6202)
        | hAPP(U_6201,hAPP(c_Product__Type_Osnd(U_6200,U_6198),U_6202)) != hAPP(U_6203,hAPP(c_Product__Type_Osnd(U_6200,U_6198),U_6202)) )
      & ( hAPP(U_6201,hAPP(c_Product__Type_Osnd(U_6200,U_6198),U_6202)) = hAPP(U_6203,hAPP(c_Product__Type_Osnd(U_6200,U_6198),U_6202))
        | hAPP(c_Product__Type_Oapsnd(U_6198,U_6199,U_6200,U_6201),U_6202) != hAPP(c_Product__Type_Oapsnd(U_6198,U_6199,U_6200,U_6203),U_6202) ) ),
    inference(variable_rename,[status(thm)],[f_1821_1]) ).

fof(f_1821_3,plain,
    ( ! [U_6215,U_6213,U_6211,U_6209,U_6207,U_6205] :
        ( hAPP(c_Product__Type_Oapsnd(U_6205,U_6207,U_6209,U_6211),U_6213) = hAPP(c_Product__Type_Oapsnd(U_6205,U_6207,U_6209,U_6215),U_6213)
        | hAPP(U_6211,hAPP(c_Product__Type_Osnd(U_6209,U_6205),U_6213)) != hAPP(U_6215,hAPP(c_Product__Type_Osnd(U_6209,U_6205),U_6213)) )
    & ! [U_6214,U_6212,U_6210,U_6208,U_6206,U_6204] :
        ( hAPP(U_6210,hAPP(c_Product__Type_Osnd(U_6208,U_6204),U_6212)) = hAPP(U_6214,hAPP(c_Product__Type_Osnd(U_6208,U_6204),U_6212))
        | hAPP(c_Product__Type_Oapsnd(U_6204,U_6206,U_6208,U_6210),U_6212) != hAPP(c_Product__Type_Oapsnd(U_6204,U_6206,U_6208,U_6214),U_6212) ) ),
    inference(miniscope,[status(thm)],[f_1821_2]) ).

fof(f_1821_4,plain,
    ( ! [U_6207,U_6205,U_6209,U_6211,U_6213,U_6215] :
        ( hAPP(c_Product__Type_Oapsnd(U_6205,U_6207,U_6209,U_6211),U_6213) = hAPP(c_Product__Type_Oapsnd(U_6205,U_6207,U_6209,U_6215),U_6213)
        | hAPP(U_6211,hAPP(c_Product__Type_Osnd(U_6209,U_6205),U_6213)) != hAPP(U_6215,hAPP(c_Product__Type_Osnd(U_6209,U_6205),U_6213)) )
    & ! [U_6210,U_6206,U_6204,U_6208,U_6214,U_6212] :
        ( hAPP(U_6210,hAPP(c_Product__Type_Osnd(U_6208,U_6204),U_6212)) = hAPP(U_6214,hAPP(c_Product__Type_Osnd(U_6208,U_6204),U_6212))
        | hAPP(c_Product__Type_Oapsnd(U_6204,U_6206,U_6208,U_6210),U_6212) != hAPP(c_Product__Type_Oapsnd(U_6204,U_6206,U_6208,U_6214),U_6212) ) ),
    inference(definitional_conversion,[status(esa)],[f_1821_3]) ).

cnf(f_1821_5,plain,
    ( hAPP(U_6210,hAPP(c_Product__Type_Osnd(U_6208,U_6204),U_6212)) = hAPP(U_6214,hAPP(c_Product__Type_Osnd(U_6208,U_6204),U_6212))
    | hAPP(c_Product__Type_Oapsnd(U_6204,U_6206,U_6208,U_6210),U_6212) != hAPP(c_Product__Type_Oapsnd(U_6204,U_6206,U_6208,U_6214),U_6212) ),
    inference(clausify,[status(thm)],[f_1821_4]) ).

cnf(f_1821_6,plain,
    ( hAPP(c_Product__Type_Oapsnd(U_6205,U_6207,U_6209,U_6211),U_6213) = hAPP(c_Product__Type_Oapsnd(U_6205,U_6207,U_6209,U_6215),U_6213)
    | hAPP(U_6211,hAPP(c_Product__Type_Osnd(U_6209,U_6205),U_6213)) != hAPP(U_6215,hAPP(c_Product__Type_Osnd(U_6209,U_6205),U_6213)) ),
    inference(clausify,[status(thm)],[f_1821_4]) ).

fof(f_1822_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_1822_2,plain,
    ! [U_6220,U_6219,U_6218,U_6217,U_6216] : hAPP(c_Product__Type_Osnd(U_6216,U_6217),hAPP(c_Product__Type_Oapsnd(U_6218,U_6217,U_6216,U_6219),U_6220)) = hAPP(U_6219,hAPP(c_Product__Type_Osnd(U_6216,U_6218),U_6220)),
    inference(variable_rename,[status(thm)],[f_1822_1]) ).

fof(f_1822_3,plain,
    ! [U_6218,U_6217,U_6216,U_6219,U_6220] : hAPP(c_Product__Type_Osnd(U_6216,U_6217),hAPP(c_Product__Type_Oapsnd(U_6218,U_6217,U_6216,U_6219),U_6220)) = hAPP(U_6219,hAPP(c_Product__Type_Osnd(U_6216,U_6218),U_6220)),
    inference(definitional_conversion,[status(esa)],[f_1822_2]) ).

cnf(f_1822_4,plain,
    hAPP(c_Product__Type_Osnd(U_6216,U_6217),hAPP(c_Product__Type_Oapsnd(U_6218,U_6217,U_6216,U_6219),U_6220)) = hAPP(U_6219,hAPP(c_Product__Type_Osnd(U_6216,U_6218),U_6220)),
    inference(clausify,[status(thm)],[f_1822_3]) ).

fof(f_1823_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_1823_2,plain,
    ! [U_6223,U_6222,U_6221] : hAPP(c_Product__Type_Osnd(U_6221,U_6222),U_6223) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6221,U_6222,U_6222),hAPP(c_COMBK(tc_fun(U_6222,U_6222),U_6221),c_COMBI(U_6222))),U_6223),
    inference(variable_rename,[status(thm)],[f_1823_1]) ).

fof(f_1823_3,plain,
    ! [U_6221,U_6222,U_6223] : hAPP(c_Product__Type_Osnd(U_6221,U_6222),U_6223) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6221,U_6222,U_6222),hAPP(c_COMBK(tc_fun(U_6222,U_6222),U_6221),c_COMBI(U_6222))),U_6223),
    inference(definitional_conversion,[status(esa)],[f_1823_2]) ).

cnf(f_1823_4,plain,
    hAPP(c_Product__Type_Osnd(U_6221,U_6222),U_6223) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6221,U_6222,U_6222),hAPP(c_COMBK(tc_fun(U_6222,U_6222),U_6221),c_COMBI(U_6222))),U_6223),
    inference(clausify,[status(thm)],[f_1823_3]) ).

fof(f_1824_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_1824_2,plain,
    ! [U_6225,U_6224] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6224,U_6225) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_6224,U_6225)),
    inference(variable_rename,[status(thm)],[f_1824_1]) ).

fof(f_1824_3,plain,
    ! [U_6224,U_6225] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6224,U_6225) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_6224,U_6225)),
    inference(definitional_conversion,[status(esa)],[f_1824_2]) ).

cnf(f_1824_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6224,U_6225) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_6224,U_6225)),
    inference(clausify,[status(thm)],[f_1824_3]) ).

fof(f_1825_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_1825_2,plain,
    ! [U_6226] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_6226),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_6226 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1825_1]) ).

fof(f_1825_3,plain,
    ! [U_6226] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_6226),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_6226 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_1825_2]) ).

cnf(f_1825_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_6226),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_6226 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1825_3]) ).

fof(f_1826_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_1826_2,plain,
    ! [U_6229,U_6228,U_6227] :
      ( U_6229 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | U_6227 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6227,U_6227),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6228),U_6229))) ),
    inference(variable_rename,[status(thm)],[f_1826_1]) ).

fof(f_1826_3,plain,
    ! [U_6227,U_6228,U_6229] :
      ( U_6229 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | U_6227 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6227,U_6227),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6228),U_6229))) ),
    inference(definitional_conversion,[status(esa)],[f_1826_2]) ).

cnf(f_1826_4,plain,
    ( U_6229 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6227 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6227,U_6227),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6228),U_6229))) ),
    inference(clausify,[status(thm)],[f_1826_3]) ).

fof(f_1827_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_1827_2,plain,
    ! [U_6235,U_6234,U_6233,U_6232,U_6231,U_6230] :
      ( U_6232 = U_6234
      | U_6231 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6230,U_6231),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6234),U_6235)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6230,U_6231),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6232),U_6233))) ),
    inference(variable_rename,[status(thm)],[f_1827_1]) ).

fof(f_1827_3,plain,
    ! [U_6231,U_6230,U_6232,U_6233,U_6234,U_6235] :
      ( U_6232 = U_6234
      | U_6231 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6230,U_6231),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6234),U_6235)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6230,U_6231),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6232),U_6233))) ),
    inference(definitional_conversion,[status(esa)],[f_1827_2]) ).

cnf(f_1827_4,plain,
    ( U_6232 = U_6234
    | U_6231 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6230,U_6231),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6234),U_6235)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6230,U_6231),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6232),U_6233))) ),
    inference(clausify,[status(thm)],[f_1827_3]) ).

fof(f_1828_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_1828_2,plain,
    ! [U_6241,U_6240,U_6239,U_6238,U_6237,U_6236] :
      ( U_6239 = U_6241
      | U_6237 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6236,U_6237),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6240),U_6241)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6236,U_6237),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6238),U_6239))) ),
    inference(variable_rename,[status(thm)],[f_1828_1]) ).

fof(f_1828_3,plain,
    ! [U_6238,U_6236,U_6237,U_6239,U_6240,U_6241] :
      ( U_6239 = U_6241
      | U_6237 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6236,U_6237),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6240),U_6241)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6236,U_6237),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6238),U_6239))) ),
    inference(definitional_conversion,[status(esa)],[f_1828_2]) ).

cnf(f_1828_4,plain,
    ( U_6239 = U_6241
    | U_6237 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6236,U_6237),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6240),U_6241)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6236,U_6237),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6238),U_6239))) ),
    inference(clausify,[status(thm)],[f_1828_3]) ).

fof(f_1829_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_1829_2,plain,
    ! [U_6244,U_6243,U_6242] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6242,U_6243),hAPP(c_Divides_OnegateSnd,U_6244)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6242),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6243)),U_6244)) ),
    inference(variable_rename,[status(thm)],[f_1829_1]) ).

fof(f_1829_3,plain,
    ! [U_6244,U_6243,U_6242] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6242,U_6243),hAPP(c_Divides_OnegateSnd,U_6244)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6242),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6243)),U_6244)) ),
    inference(definitional_conversion,[status(esa)],[f_1829_2]) ).

cnf(f_1829_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6242,U_6243),hAPP(c_Divides_OnegateSnd,U_6244)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6242),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6243)),U_6244)) ),
    inference(clausify,[status(thm)],[f_1829_3]) ).

fof(f_1830_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_1830_2,plain,
    ! [U_6246,U_6245] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6246,U_6245),c_Divides_Odivmod__int(U_6246,U_6245)))
      | U_6245 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1830_1]) ).

fof(f_1830_3,plain,
    ! [U_6245,U_6246] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6246,U_6245),c_Divides_Odivmod__int(U_6246,U_6245)))
      | U_6245 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_1830_2]) ).

cnf(f_1830_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6246,U_6245),c_Divides_Odivmod__int(U_6246,U_6245)))
    | U_6245 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1830_3]) ).

fof(f_1831_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_1831_2,plain,
    ! [U_6249,U_6248,U_6247] :
      ( U_6248 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_6247 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6247,U_6247),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6248),U_6249))) ),
    inference(variable_rename,[status(thm)],[f_1831_1]) ).

fof(f_1831_3,plain,
    ! [U_6247,U_6248,U_6249] :
      ( U_6248 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_6247 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6247,U_6247),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6248),U_6249))) ),
    inference(definitional_conversion,[status(esa)],[f_1831_2]) ).

cnf(f_1831_4,plain,
    ( U_6248 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_6247 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6247,U_6247),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6248),U_6249))) ),
    inference(clausify,[status(thm)],[f_1831_3]) ).

fof(f_1832_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_1832_2,plain,
    ! [U_6253,U_6252,U_6251,U_6250] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6250,U_6251) = U_6253
      | U_6251 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6250,U_6251),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6252),U_6253))) ),
    inference(variable_rename,[status(thm)],[f_1832_1]) ).

fof(f_1832_3,plain,
    ! [U_6251,U_6250,U_6252,U_6253] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6250,U_6251) = U_6253
      | U_6251 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6250,U_6251),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6252),U_6253))) ),
    inference(definitional_conversion,[status(esa)],[f_1832_2]) ).

cnf(f_1832_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6250,U_6251) = U_6253
    | U_6251 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6250,U_6251),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6252),U_6253))) ),
    inference(clausify,[status(thm)],[f_1832_3]) ).

fof(f_1833_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_1833_2,plain,
    ! [U_6257,U_6256,U_6255,U_6254] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6254),U_6255) = U_6256
      | U_6255 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6254,U_6255),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6256),U_6257))) ),
    inference(variable_rename,[status(thm)],[f_1833_1]) ).

fof(f_1833_3,plain,
    ! [U_6254,U_6255,U_6256,U_6257] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6254),U_6255) = U_6256
      | U_6255 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6254,U_6255),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6256),U_6257))) ),
    inference(definitional_conversion,[status(esa)],[f_1833_2]) ).

cnf(f_1833_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6254),U_6255) = U_6256
    | U_6255 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6254,U_6255),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6256),U_6257))) ),
    inference(clausify,[status(thm)],[f_1833_3]) ).

fof(f_1834_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_1834_2,plain,
    ! [U_6259,U_6258] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6258,U_6259),c_Divides_OnegDivAlg(U_6258,U_6259)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6259))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6258),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1834_1]) ).

fof(f_1834_3,plain,
    ! [U_6258,U_6259] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6258,U_6259),c_Divides_OnegDivAlg(U_6258,U_6259)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6259))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6258),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1834_2]) ).

cnf(f_1834_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6258,U_6259),c_Divides_OnegDivAlg(U_6258,U_6259)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6259))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6258),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1834_3]) ).

fof(f_1835_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_1835_2,plain,
    ! [U_6261,U_6260] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6260,U_6261) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_6260,U_6261))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6261))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6260),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1835_1]) ).

fof(f_1835_3,plain,
    ! [U_6260,U_6261] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6260,U_6261) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_6260,U_6261))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6261))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6260),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1835_2]) ).

cnf(f_1835_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6260,U_6261) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_6260,U_6261))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6261))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6260),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1835_3]) ).

fof(f_1836_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_1836_2,plain,
    ! [U_6263,U_6262] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6263,U_6262),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6263),U_6262)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6263,U_6262))))
      | U_6262 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1836_1]) ).

fof(f_1836_3,plain,
    ! [U_6262,U_6263] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6263,U_6262),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6263),U_6262)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6263,U_6262))))
      | U_6262 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_1836_2]) ).

cnf(f_1836_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6263,U_6262),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6263),U_6262)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6263,U_6262))))
    | U_6262 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1836_3]) ).

fof(f_1837_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_1837_2,plain,
    ! [U_6265,U_6264] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6264,U_6265),c_Divides_OposDivAlg(U_6264,U_6265)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6265))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6264)) ),
    inference(variable_rename,[status(thm)],[f_1837_1]) ).

fof(f_1837_3,plain,
    ! [U_6264,U_6265] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6264,U_6265),c_Divides_OposDivAlg(U_6264,U_6265)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6265))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6264)) ),
    inference(definitional_conversion,[status(esa)],[f_1837_2]) ).

cnf(f_1837_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6264,U_6265),c_Divides_OposDivAlg(U_6264,U_6265)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6265))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6264)) ),
    inference(clausify,[status(thm)],[f_1837_3]) ).

fof(f_1838_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_1838_2,plain,
    ! [U_6267,U_6266] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6266,U_6267) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_6266,U_6267))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6267))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6266)) ),
    inference(variable_rename,[status(thm)],[f_1838_1]) ).

fof(f_1838_3,plain,
    ! [U_6267,U_6266] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6266,U_6267) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_6266,U_6267))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6267))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6266)) ),
    inference(definitional_conversion,[status(esa)],[f_1838_2]) ).

cnf(f_1838_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6266,U_6267) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_6266,U_6267))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6267))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6266)) ),
    inference(clausify,[status(thm)],[f_1838_3]) ).

fof(f_1839_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_1839_2,plain,
    ! [U_6268] :
      ( 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_6268)) = 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_6268)))
      | ~ 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_6268))) ),
    inference(variable_rename,[status(thm)],[f_1839_1]) ).

fof(f_1839_3,plain,
    ! [U_6268] :
      ( 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_6268)) = 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_6268)))
      | ~ 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_6268))) ),
    inference(definitional_conversion,[status(esa)],[f_1839_2]) ).

cnf(f_1839_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_6268)) = 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_6268)))
    | ~ 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_6268))) ),
    inference(clausify,[status(thm)],[f_1839_3]) ).

fof(f_1840_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_1840_2,plain,
    ! [U_6275,U_6274,U_6273,U_6272,U_6271,U_6270,U_6269] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6269),U_6273),U_6270),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_6271),U_6274)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6272),U_6275)),U_6270))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6272),U_6275),U_6270))))
      | U_6270 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6273,U_6270),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6274),U_6275)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6269,U_6270),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6271),U_6272))) ),
    inference(variable_rename,[status(thm)],[f_1840_1]) ).

fof(f_1840_3,plain,
    ! [U_6269,U_6270,U_6271,U_6272,U_6273,U_6274,U_6275] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6269),U_6273),U_6270),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_6271),U_6274)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6272),U_6275)),U_6270))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6272),U_6275),U_6270))))
      | U_6270 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6273,U_6270),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6274),U_6275)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6269,U_6270),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6271),U_6272))) ),
    inference(definitional_conversion,[status(esa)],[f_1840_2]) ).

cnf(f_1840_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6269),U_6273),U_6270),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_6271),U_6274)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6272),U_6275)),U_6270))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6272),U_6275),U_6270))))
    | U_6270 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6273,U_6270),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6274),U_6275)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6269,U_6270),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6271),U_6272))) ),
    inference(clausify,[status(thm)],[f_1840_3]) ).

fof(f_1841_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_1841_2,plain,
    ! [U_6279,U_6278,U_6277,U_6276] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6276),U_6277),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_6279),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6278)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6278)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_6279),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_6277),U_6279)))))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6276,U_6277),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6278),U_6279))) ),
    inference(variable_rename,[status(thm)],[f_1841_1]) ).

fof(f_1841_3,plain,
    ! [U_6277,U_6278,U_6276,U_6279] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6276),U_6277),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_6279),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6278)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6278)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_6279),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_6277),U_6279)))))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6276,U_6277),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6278),U_6279))) ),
    inference(definitional_conversion,[status(esa)],[f_1841_2]) ).

cnf(f_1841_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6276),U_6277),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_6279),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6278)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6278)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_6279),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_6277),U_6279)))))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6276,U_6277),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6278),U_6279))) ),
    inference(clausify,[status(thm)],[f_1841_3]) ).

fof(f_1842_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_1842_2,plain,
    ! [U_6281,U_6280] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6280,U_6281) = 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_6280),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6281))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6281),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_6280)) ),
    inference(variable_rename,[status(thm)],[f_1842_1]) ).

fof(f_1842_3,plain,
    ! [U_6280,U_6281] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6280,U_6281) = 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_6280),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6281))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6281),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_6280)) ),
    inference(definitional_conversion,[status(esa)],[f_1842_2]) ).

cnf(f_1842_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6280,U_6281) = 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_6280),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6281))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6281),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_6280)) ),
    inference(clausify,[status(thm)],[f_1842_3]) ).

fof(f_1843_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_1843_2,plain,
    ! [U_6283,U_6282] :
      ( ( c_Divides_Odivmod__nat(U_6283,U_6282) = 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_6283),U_6282),U_6282))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6283),U_6282))
        | U_6282 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Divides_Odivmod__nat(U_6283,U_6282) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6283)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6283),U_6282))
          & U_6282 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(variable_rename,[status(thm)],[f_1843_1]) ).

fof(f_1843_3,plain,
    ( ! [U_6287,U_6285] :
        ( c_Divides_Odivmod__nat(U_6287,U_6285) = 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_6287),U_6285),U_6285))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6287),U_6285))
        | U_6285 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6286,U_6284] :
        ( c_Divides_Odivmod__nat(U_6286,U_6284) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6286)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6286),U_6284))
          & U_6284 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(miniscope,[status(thm)],[f_1843_2]) ).

fof(f_1843_4,plain,
    ( ! [U_6286,U_6284] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6286),U_6284))
        | ~ sP585(U_6286,U_6284) )
    & ! [U_6286,U_6284] :
        ( U_6284 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP585(U_6286,U_6284) )
    & ! [U_6285,U_6287] :
        ( c_Divides_Odivmod__nat(U_6287,U_6285) = 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_6287),U_6285),U_6285))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6287),U_6285))
        | U_6285 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6286,U_6284] :
        ( c_Divides_Odivmod__nat(U_6286,U_6284) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6286)
        | sP585(U_6286,U_6284) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP585])],[f_1843_3]) ).

cnf(f_1843_5,plain,
    ( c_Divides_Odivmod__nat(U_6286,U_6284) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6286)
    | sP585(U_6286,U_6284) ),
    inference(clausify,[status(thm)],[f_1843_4]) ).

cnf(f_1843_6,plain,
    ( c_Divides_Odivmod__nat(U_6287,U_6285) = 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_6287),U_6285),U_6285))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6287),U_6285))
    | U_6285 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1843_4]) ).

cnf(f_1843_7,plain,
    ( U_6284 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP585(U_6286,U_6284) ),
    inference(clausify,[status(thm)],[f_1843_4]) ).

cnf(f_1843_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6286),U_6284))
    | ~ sP585(U_6286,U_6284) ),
    inference(clausify,[status(thm)],[f_1843_4]) ).

fof(f_1844_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_1844_2,plain,
    ! [U_6291,U_6290,U_6289,U_6288] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6288,U_6289),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6290),U_6291)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6291),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6289),U_6291)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6289)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6291),U_6289))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6291)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6289)) )
      | U_6288 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6289),U_6290)),U_6291) ),
    inference(variable_rename,[status(thm)],[f_1844_1]) ).

fof(f_1844_3,plain,
    ( ! [U_6289,U_6291] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6291),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6289),U_6291))
        | ~ sP587(U_6289,U_6291) )
    & ! [U_6289,U_6291] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6289))
        | ~ sP587(U_6289,U_6291) )
    & ! [U_6289,U_6291] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6291),U_6289))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6291))
        | ~ sP586(U_6289,U_6291) )
    & ! [U_6289,U_6291] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6289))
        | ~ sP586(U_6289,U_6291) )
    & ! [U_6288,U_6289,U_6290,U_6291] :
        ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6288,U_6289),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6290),U_6291)))
        | sP587(U_6289,U_6291)
        | sP586(U_6289,U_6291)
        | U_6288 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6289),U_6290)),U_6291) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP586,sP587])],[f_1844_2]) ).

cnf(f_1844_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6288,U_6289),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6290),U_6291)))
    | sP587(U_6289,U_6291)
    | sP586(U_6289,U_6291)
    | U_6288 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6289),U_6290)),U_6291) ),
    inference(clausify,[status(thm)],[f_1844_3]) ).

cnf(f_1844_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6289))
    | ~ sP586(U_6289,U_6291) ),
    inference(clausify,[status(thm)],[f_1844_3]) ).

cnf(f_1844_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6291),U_6289))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6291))
    | ~ sP586(U_6289,U_6291) ),
    inference(clausify,[status(thm)],[f_1844_3]) ).

cnf(f_1844_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6289))
    | ~ sP587(U_6289,U_6291) ),
    inference(clausify,[status(thm)],[f_1844_3]) ).

cnf(f_1844_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6291),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6289),U_6291))
    | ~ sP587(U_6289,U_6291) ),
    inference(clausify,[status(thm)],[f_1844_3]) ).

fof(f_1845_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_1845_2,plain,
    ! [U_6293,U_6292] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6292,U_6293) = 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_6292),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6293))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6293),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6292),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1845_1]) ).

fof(f_1845_3,plain,
    ! [U_6293,U_6292] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6292,U_6293) = 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_6292),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6293))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6293),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6292),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1845_2]) ).

cnf(f_1845_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6292,U_6293) = 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_6292),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6293))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6293),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6292),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1845_3]) ).

fof(f_1846_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_1846_2,plain,
    ! [U_6298,U_6297,U_6296,U_6295,U_6294] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6298),U_6294),U_6295),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_6298),U_6296)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6298),U_6297)),U_6295))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6298),U_6297),U_6295))))
      | U_6295 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6294,U_6295),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6296),U_6297))) ),
    inference(variable_rename,[status(thm)],[f_1846_1]) ).

fof(f_1846_3,plain,
    ! [U_6295,U_6294,U_6296,U_6297,U_6298] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6298),U_6294),U_6295),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_6298),U_6296)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6298),U_6297)),U_6295))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6298),U_6297),U_6295))))
      | U_6295 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6294,U_6295),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6296),U_6297))) ),
    inference(definitional_conversion,[status(esa)],[f_1846_2]) ).

cnf(f_1846_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6298),U_6294),U_6295),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_6298),U_6296)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6298),U_6297)),U_6295))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6298),U_6297),U_6295))))
    | U_6295 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_6294,U_6295),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6296),U_6297))) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

fof(f_1847_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_1847_2,plain,
    ! [U_6301,U_6300,U_6299] :
      ( U_6300 = U_6301
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6299,tc_HOL_Obool)),U_6301),U_6300))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6299,tc_HOL_Obool)),U_6300),U_6301)) ),
    inference(variable_rename,[status(thm)],[f_1847_1]) ).

fof(f_1847_3,plain,
    ! [U_6300,U_6299,U_6301] :
      ( U_6300 = U_6301
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6299,tc_HOL_Obool)),U_6301),U_6300))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6299,tc_HOL_Obool)),U_6300),U_6301)) ),
    inference(definitional_conversion,[status(esa)],[f_1847_2]) ).

cnf(f_1847_4,plain,
    ( U_6300 = U_6301
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6299,tc_HOL_Obool)),U_6301),U_6300))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6299,tc_HOL_Obool)),U_6300),U_6301)) ),
    inference(clausify,[status(thm)],[f_1847_3]) ).

fof(f_1848_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_1848_2,plain,
    ! [U_6302] :
      ( 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_6302)) = 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_6302)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6302)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1848_1]) ).

fof(f_1848_3,plain,
    ! [U_6302] :
      ( 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_6302)) = 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_6302)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6302)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1848_2]) ).

cnf(f_1848_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_6302)) = 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_6302)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6302)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1848_3]) ).

fof(f_1849_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_1849_2,plain,
    ! [U_6307,U_6306,U_6305] :
      ( hBOOL(hAPP(hAPP(U_6307,U_6305),U_6306))
      | ? [U_6304,U_6303] :
          ( ~ hBOOL(hAPP(hAPP(U_6307,U_6304),U_6303))
          & ( hBOOL(hAPP(hAPP(U_6307,U_6303),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6304,U_6303)))
            | U_6303 = 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_6304),U_6303))) )
      | ~ 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_6305),U_6306))) ),
    inference(variable_rename,[status(thm)],[f_1849_1]) ).

fof(f_1849_3,plain,
    ! [U_6307,U_6306,U_6305] :
      ( hBOOL(hAPP(hAPP(U_6307,U_6305),U_6306))
      | ? [U_6303] :
          ( ~ hBOOL(hAPP(hAPP(U_6307,sK107(U_6307,U_6306,U_6305)),U_6303))
          & ( hBOOL(hAPP(hAPP(U_6307,U_6303),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK107(U_6307,U_6306,U_6305),U_6303)))
            | U_6303 = 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),sK107(U_6307,U_6306,U_6305)),U_6303))) )
      | ~ 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_6305),U_6306))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_6304,sK107(U_6307,U_6306,U_6305))],[f_1849_2]) ).

fof(f_1849_4,plain,
    ! [U_6307,U_6306,U_6305] :
      ( hBOOL(hAPP(hAPP(U_6307,U_6305),U_6306))
      | ( ~ hBOOL(hAPP(hAPP(U_6307,sK107(U_6307,U_6306,U_6305)),sK108(U_6307,U_6306,U_6305)))
        & ( hBOOL(hAPP(hAPP(U_6307,sK108(U_6307,U_6306,U_6305)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK107(U_6307,U_6306,U_6305),sK108(U_6307,U_6306,U_6305))))
          | sK108(U_6307,U_6306,U_6305) = 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),sK107(U_6307,U_6306,U_6305)),sK108(U_6307,U_6306,U_6305)))) )
      | ~ 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_6305),U_6306))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_6303,sK108(U_6307,U_6306,U_6305))],[f_1849_3]) ).

fof(f_1849_5,plain,
    ( ! [U_6305,U_6306,U_6307] :
        ( ~ hBOOL(hAPP(hAPP(U_6307,sK107(U_6307,U_6306,U_6305)),sK108(U_6307,U_6306,U_6305)))
        | ~ sP588(U_6305,U_6306,U_6307) )
    & ! [U_6305,U_6306,U_6307] :
        ( hBOOL(hAPP(hAPP(U_6307,sK108(U_6307,U_6306,U_6305)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK107(U_6307,U_6306,U_6305),sK108(U_6307,U_6306,U_6305))))
        | sK108(U_6307,U_6306,U_6305) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP588(U_6305,U_6306,U_6307) )
    & ! [U_6305,U_6306,U_6307] :
        ( 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),sK107(U_6307,U_6306,U_6305)),sK108(U_6307,U_6306,U_6305))))
        | ~ sP588(U_6305,U_6306,U_6307) )
    & ! [U_6305,U_6306,U_6307] :
        ( hBOOL(hAPP(hAPP(U_6307,U_6305),U_6306))
        | sP588(U_6305,U_6306,U_6307)
        | ~ 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_6305),U_6306))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP588])],[f_1849_4]) ).

cnf(f_1849_6,plain,
    ( hBOOL(hAPP(hAPP(U_6307,U_6305),U_6306))
    | sP588(U_6305,U_6306,U_6307)
    | ~ 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_6305),U_6306))) ),
    inference(clausify,[status(thm)],[f_1849_5]) ).

cnf(f_1849_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),sK107(U_6307,U_6306,U_6305)),sK108(U_6307,U_6306,U_6305))))
    | ~ sP588(U_6305,U_6306,U_6307) ),
    inference(clausify,[status(thm)],[f_1849_5]) ).

cnf(f_1849_8,plain,
    ( hBOOL(hAPP(hAPP(U_6307,sK108(U_6307,U_6306,U_6305)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK107(U_6307,U_6306,U_6305),sK108(U_6307,U_6306,U_6305))))
    | sK108(U_6307,U_6306,U_6305) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP588(U_6305,U_6306,U_6307) ),
    inference(clausify,[status(thm)],[f_1849_5]) ).

cnf(f_1849_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_6307,sK107(U_6307,U_6306,U_6305)),sK108(U_6307,U_6306,U_6305)))
    | ~ sP588(U_6305,U_6306,U_6307) ),
    inference(clausify,[status(thm)],[f_1849_5]) ).

fof(f_1850_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_1850_2,plain,
    ! [U_6309,U_6308] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6308),U_6309) = 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_6308),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6309))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6309),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6308),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1850_1]) ).

fof(f_1850_3,plain,
    ! [U_6308,U_6309] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6308),U_6309) = 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_6308),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6309))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6309),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6308),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1850_2]) ).

cnf(f_1850_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6308),U_6309) = 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_6308),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6309))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6309),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6308),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1850_3]) ).

fof(f_1851_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_1851_2,plain,
    ! [U_6311,U_6310] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6310)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6311)) = 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_6311))),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_6310)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_1851_1]) ).

fof(f_1851_3,plain,
    ! [U_6310,U_6311] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6310)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6311)) = 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_6311))),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_6310)),c_Int_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_1851_2]) ).

cnf(f_1851_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6310)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6311)) = 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_6311))),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_6310)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_1851_3]) ).

fof(f_1852_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_1852_2,plain,
    ! [U_6314,U_6313,U_6312] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6312),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6312),U_6313),U_6314)),U_6313))
      | ~ class_Orderings_Olinorder(U_6312) ),
    inference(variable_rename,[status(thm)],[f_1852_1]) ).

fof(f_1852_3,plain,
    ! [U_6312,U_6313,U_6314] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6312),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6312),U_6313),U_6314)),U_6313))
      | ~ class_Orderings_Olinorder(U_6312) ),
    inference(definitional_conversion,[status(esa)],[f_1852_2]) ).

cnf(f_1852_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6312),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6312),U_6313),U_6314)),U_6313))
    | ~ class_Orderings_Olinorder(U_6312) ),
    inference(clausify,[status(thm)],[f_1852_3]) ).

fof(f_1853_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_1853_2,plain,
    ! [U_6317,U_6316,U_6315] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6315),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6315),U_6316),U_6317)),U_6317))
      | ~ class_Orderings_Olinorder(U_6315) ),
    inference(variable_rename,[status(thm)],[f_1853_1]) ).

fof(f_1853_3,plain,
    ! [U_6315,U_6316,U_6317] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6315),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6315),U_6316),U_6317)),U_6317))
      | ~ class_Orderings_Olinorder(U_6315) ),
    inference(definitional_conversion,[status(esa)],[f_1853_2]) ).

cnf(f_1853_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6315),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6315),U_6316),U_6317)),U_6317))
    | ~ class_Orderings_Olinorder(U_6315) ),
    inference(clausify,[status(thm)],[f_1853_3]) ).

fof(f_1854_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_1854_2,plain,
    ! [U_6320,U_6319,U_6318] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6318),U_6319),U_6320))
          | hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6318),U_6319),U_6320) != U_6319 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6318),U_6319),U_6320) = U_6319
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6318),U_6319),U_6320)) ) )
      | ~ class_Orderings_Olinorder(U_6318) ),
    inference(variable_rename,[status(thm)],[f_1854_1]) ).

fof(f_1854_3,plain,
    ( ! [U_6318,U_6319,U_6320] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6318),U_6319),U_6320))
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6318),U_6319),U_6320) != U_6319
        | ~ sP589(U_6318,U_6319,U_6320) )
    & ! [U_6318,U_6319,U_6320] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6318),U_6319),U_6320) = U_6319
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6318),U_6319),U_6320))
        | ~ sP589(U_6318,U_6319,U_6320) )
    & ! [U_6318,U_6319,U_6320] :
        ( sP589(U_6318,U_6319,U_6320)
        | ~ class_Orderings_Olinorder(U_6318) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP589])],[f_1854_2]) ).

cnf(f_1854_4,plain,
    ( sP589(U_6318,U_6319,U_6320)
    | ~ class_Orderings_Olinorder(U_6318) ),
    inference(clausify,[status(thm)],[f_1854_3]) ).

cnf(f_1854_5,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6318),U_6319),U_6320) = U_6319
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6318),U_6319),U_6320))
    | ~ sP589(U_6318,U_6319,U_6320) ),
    inference(clausify,[status(thm)],[f_1854_3]) ).

cnf(f_1854_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6318),U_6319),U_6320))
    | hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6318),U_6319),U_6320) != U_6319
    | ~ sP589(U_6318,U_6319,U_6320) ),
    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__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_1855_2,plain,
    ! [U_6324,U_6323,U_6322,U_6321] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6321),U_6323),U_6324)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),U_6324))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),U_6323)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),U_6324))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),U_6323)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6321),U_6323),U_6324))) ) )
      | ~ class_Orderings_Olinorder(U_6321) ),
    inference(variable_rename,[status(thm)],[f_1855_1]) ).

fof(f_1855_3,plain,
    ( ! [U_6322,U_6321,U_6323,U_6324] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),U_6324))
        | ~ sP590(U_6322,U_6321,U_6323,U_6324) )
    & ! [U_6322,U_6321,U_6323,U_6324] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),U_6323))
        | ~ sP590(U_6322,U_6321,U_6323,U_6324) )
    & ! [U_6322,U_6321,U_6323,U_6324] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6321),U_6323),U_6324)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),U_6324))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),U_6323))
        | ~ sP591(U_6322,U_6321,U_6323,U_6324) )
    & ! [U_6322,U_6321,U_6323,U_6324] :
        ( sP590(U_6322,U_6321,U_6323,U_6324)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6321),U_6323),U_6324)))
        | ~ sP591(U_6322,U_6321,U_6323,U_6324) )
    & ! [U_6322,U_6321,U_6323,U_6324] :
        ( sP591(U_6322,U_6321,U_6323,U_6324)
        | ~ class_Orderings_Olinorder(U_6321) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP590,sP591])],[f_1855_2]) ).

cnf(f_1855_4,plain,
    ( sP591(U_6322,U_6321,U_6323,U_6324)
    | ~ class_Orderings_Olinorder(U_6321) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

cnf(f_1855_5,plain,
    ( sP590(U_6322,U_6321,U_6323,U_6324)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6321),U_6323),U_6324)))
    | ~ sP591(U_6322,U_6321,U_6323,U_6324) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

cnf(f_1855_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6321),U_6323),U_6324)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),U_6324))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),U_6323))
    | ~ sP591(U_6322,U_6321,U_6323,U_6324) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

cnf(f_1855_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),U_6323))
    | ~ sP590(U_6322,U_6321,U_6323,U_6324) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

cnf(f_1855_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6321),U_6322),U_6324))
    | ~ sP590(U_6322,U_6321,U_6323,U_6324) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

fof(f_1856_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_1856_2,plain,
    ! [U_6328,U_6327,U_6326,U_6325] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6325),U_6326),U_6327)),U_6328))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),U_6327),U_6328))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),U_6326),U_6328)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),U_6327),U_6328))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),U_6326),U_6328))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6325),U_6326),U_6327)),U_6328)) ) )
      | ~ class_Orderings_Olinorder(U_6325) ),
    inference(variable_rename,[status(thm)],[f_1856_1]) ).

fof(f_1856_3,plain,
    ( ! [U_6328,U_6326,U_6325,U_6327] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),U_6327),U_6328))
        | ~ sP592(U_6328,U_6326,U_6325,U_6327) )
    & ! [U_6328,U_6326,U_6325,U_6327] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),U_6326),U_6328))
        | ~ sP592(U_6328,U_6326,U_6325,U_6327) )
    & ! [U_6328,U_6326,U_6325,U_6327] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6325),U_6326),U_6327)),U_6328))
        | sP592(U_6328,U_6326,U_6325,U_6327)
        | ~ sP593(U_6328,U_6326,U_6325,U_6327) )
    & ! [U_6328,U_6326,U_6325,U_6327] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),U_6327),U_6328))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),U_6326),U_6328))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6325),U_6326),U_6327)),U_6328))
        | ~ sP593(U_6328,U_6326,U_6325,U_6327) )
    & ! [U_6328,U_6326,U_6325,U_6327] :
        ( sP593(U_6328,U_6326,U_6325,U_6327)
        | ~ class_Orderings_Olinorder(U_6325) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP592,sP593])],[f_1856_2]) ).

cnf(f_1856_4,plain,
    ( sP593(U_6328,U_6326,U_6325,U_6327)
    | ~ class_Orderings_Olinorder(U_6325) ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

cnf(f_1856_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),U_6327),U_6328))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),U_6326),U_6328))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6325),U_6326),U_6327)),U_6328))
    | ~ sP593(U_6328,U_6326,U_6325,U_6327) ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

cnf(f_1856_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6325),U_6326),U_6327)),U_6328))
    | sP592(U_6328,U_6326,U_6325,U_6327)
    | ~ sP593(U_6328,U_6326,U_6325,U_6327) ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

cnf(f_1856_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),U_6326),U_6328))
    | ~ sP592(U_6328,U_6326,U_6325,U_6327) ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

cnf(f_1856_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6325),U_6327),U_6328))
    | ~ sP592(U_6328,U_6326,U_6325,U_6327) ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

fof(f_1857_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_1857_2,plain,
    ! [U_6332,U_6331,U_6330,U_6329] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6329),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6329),U_6330),U_6332)),U_6331))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6329),U_6330),U_6331))
      | ~ class_Orderings_Olinorder(U_6329) ),
    inference(variable_rename,[status(thm)],[f_1857_1]) ).

fof(f_1857_3,plain,
    ! [U_6331,U_6332,U_6330,U_6329] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6329),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6329),U_6330),U_6332)),U_6331))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6329),U_6330),U_6331))
      | ~ class_Orderings_Olinorder(U_6329) ),
    inference(definitional_conversion,[status(esa)],[f_1857_2]) ).

cnf(f_1857_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6329),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6329),U_6330),U_6332)),U_6331))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6329),U_6330),U_6331))
    | ~ class_Orderings_Olinorder(U_6329) ),
    inference(clausify,[status(thm)],[f_1857_3]) ).

fof(f_1858_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_1858_2,plain,
    ! [U_6336,U_6335,U_6334,U_6333] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6333),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6333),U_6336),U_6334)),U_6335))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6333),U_6334),U_6335))
      | ~ class_Orderings_Olinorder(U_6333) ),
    inference(variable_rename,[status(thm)],[f_1858_1]) ).

fof(f_1858_3,plain,
    ! [U_6333,U_6334,U_6335,U_6336] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6333),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6333),U_6336),U_6334)),U_6335))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6333),U_6334),U_6335))
      | ~ class_Orderings_Olinorder(U_6333) ),
    inference(definitional_conversion,[status(esa)],[f_1858_2]) ).

cnf(f_1858_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6333),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6333),U_6336),U_6334)),U_6335))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6333),U_6334),U_6335))
    | ~ class_Orderings_Olinorder(U_6333) ),
    inference(clausify,[status(thm)],[f_1858_3]) ).

fof(f_1859_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_1859_2,plain,
    ! [U_6339,U_6338,U_6337] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6337),U_6338),U_6339) = U_6338
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6337),U_6338),U_6339))
      | ~ class_Orderings_Olinorder(U_6337) ),
    inference(variable_rename,[status(thm)],[f_1859_1]) ).

fof(f_1859_3,plain,
    ! [U_6337,U_6338,U_6339] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6337),U_6338),U_6339) = U_6338
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6337),U_6338),U_6339))
      | ~ class_Orderings_Olinorder(U_6337) ),
    inference(definitional_conversion,[status(esa)],[f_1859_2]) ).

cnf(f_1859_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6337),U_6338),U_6339) = U_6338
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6337),U_6338),U_6339))
    | ~ class_Orderings_Olinorder(U_6337) ),
    inference(clausify,[status(thm)],[f_1859_3]) ).

fof(f_1860_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_1860_2,plain,
    ! [U_6342,U_6341,U_6340] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6340),U_6342),U_6341) = U_6341
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6340),U_6341),U_6342))
      | ~ class_Orderings_Olinorder(U_6340) ),
    inference(variable_rename,[status(thm)],[f_1860_1]) ).

fof(f_1860_3,plain,
    ! [U_6340,U_6341,U_6342] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6340),U_6342),U_6341) = U_6341
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6340),U_6341),U_6342))
      | ~ class_Orderings_Olinorder(U_6340) ),
    inference(definitional_conversion,[status(esa)],[f_1860_2]) ).

cnf(f_1860_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6340),U_6342),U_6341) = U_6341
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6340),U_6341),U_6342))
    | ~ class_Orderings_Olinorder(U_6340) ),
    inference(clausify,[status(thm)],[f_1860_3]) ).

fof(f_1861_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_1861_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_Omin(U_6343),U_6345),U_6346)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6343),U_6344),U_6346))
      | ~ 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_1861_1]) ).

fof(f_1861_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_Omin(U_6343),U_6345),U_6346)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6343),U_6344),U_6346))
      | ~ 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_1861_2]) ).

cnf(f_1861_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6343),U_6344),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6343),U_6345),U_6346)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6343),U_6344),U_6346))
    | ~ 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_1861_3]) ).

fof(f_1862_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_1862_2,plain,
    ! [U_6350,U_6349,U_6348,U_6347] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6347),U_6348),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6347),U_6349),U_6350)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6347),U_6348),U_6350))
      | ~ 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_1862_1]) ).

fof(f_1862_3,plain,
    ! [U_6347,U_6348,U_6349,U_6350] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6347),U_6348),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6347),U_6349),U_6350)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6347),U_6348),U_6350))
      | ~ 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_1862_2]) ).

cnf(f_1862_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6347),U_6348),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6347),U_6349),U_6350)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6347),U_6348),U_6350))
    | ~ 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_1862_3]) ).

fof(f_1863_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_1863_2,plain,
    ! [U_6355,U_6354,U_6353,U_6352,U_6351] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6351),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6351),U_6352),U_6354)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6351),U_6353),U_6355)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6351),U_6354),U_6355))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6351),U_6352),U_6353))
      | ~ class_Orderings_Olinorder(U_6351) ),
    inference(variable_rename,[status(thm)],[f_1863_1]) ).

fof(f_1863_3,plain,
    ! [U_6353,U_6351,U_6352,U_6354,U_6355] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6351),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6351),U_6352),U_6354)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6351),U_6353),U_6355)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6351),U_6354),U_6355))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6351),U_6352),U_6353))
      | ~ class_Orderings_Olinorder(U_6351) ),
    inference(definitional_conversion,[status(esa)],[f_1863_2]) ).

cnf(f_1863_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6351),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6351),U_6352),U_6354)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6351),U_6353),U_6355)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6351),U_6354),U_6355))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6351),U_6352),U_6353))
    | ~ class_Orderings_Olinorder(U_6351) ),
    inference(clausify,[status(thm)],[f_1863_3]) ).

fof(f_1864_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_1864_2,plain,
    ! [U_6359,U_6358,U_6357,U_6356] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6356),U_6357),U_6359))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6356),U_6357),U_6358)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6356),U_6357),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6356),U_6358),U_6359)))
      | ~ class_Orderings_Olinorder(U_6356) ),
    inference(variable_rename,[status(thm)],[f_1864_1]) ).

fof(f_1864_3,plain,
    ( ! [U_6356,U_6357,U_6358,U_6359] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6356),U_6357),U_6359))
        | ~ sP594(U_6356,U_6357,U_6358,U_6359) )
    & ! [U_6356,U_6357,U_6358,U_6359] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6356),U_6357),U_6358))
        | ~ sP594(U_6356,U_6357,U_6358,U_6359) )
    & ! [U_6356,U_6357,U_6358,U_6359] :
        ( sP594(U_6356,U_6357,U_6358,U_6359)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6356),U_6357),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6356),U_6358),U_6359)))
        | ~ class_Orderings_Olinorder(U_6356) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP594])],[f_1864_2]) ).

cnf(f_1864_4,plain,
    ( sP594(U_6356,U_6357,U_6358,U_6359)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6356),U_6357),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6356),U_6358),U_6359)))
    | ~ class_Orderings_Olinorder(U_6356) ),
    inference(clausify,[status(thm)],[f_1864_3]) ).

cnf(f_1864_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6356),U_6357),U_6358))
    | ~ sP594(U_6356,U_6357,U_6358,U_6359) ),
    inference(clausify,[status(thm)],[f_1864_3]) ).

cnf(f_1864_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6356),U_6357),U_6359))
    | ~ sP594(U_6356,U_6357,U_6358,U_6359) ),
    inference(clausify,[status(thm)],[f_1864_3]) ).

fof(f_1865_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_1865_2,plain,
    ! [U_6360] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6360) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1865_1]) ).

fof(f_1865_3,plain,
    ! [U_6360] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6360) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1865_2]) ).

cnf(f_1865_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6360) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1865_3]) ).

fof(f_1866_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_1866_2,plain,
    ! [U_6361] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6361),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1866_1]) ).

fof(f_1866_3,plain,
    ! [U_6361] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6361),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1866_2]) ).

cnf(f_1866_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6361),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1866_3]) ).

fof(f_1867_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_1867_2,plain,
    ! [U_6365,U_6364,U_6363,U_6362] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6362),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6362),U_6363),U_6364)),U_6365) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6362),U_6363),U_6365)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6362),U_6364),U_6365))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6362) ),
    inference(variable_rename,[status(thm)],[f_1867_1]) ).

fof(f_1867_3,plain,
    ! [U_6362,U_6363,U_6364,U_6365] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6362),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6362),U_6363),U_6364)),U_6365) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6362),U_6363),U_6365)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6362),U_6364),U_6365))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6362) ),
    inference(definitional_conversion,[status(esa)],[f_1867_2]) ).

cnf(f_1867_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6362),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6362),U_6363),U_6364)),U_6365) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6362),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6362),U_6363),U_6365)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6362),U_6364),U_6365))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6362) ),
    inference(clausify,[status(thm)],[f_1867_3]) ).

fof(f_1868_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_1868_2,plain,
    ! [U_6369,U_6368,U_6367,U_6366] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6366),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6366),U_6367),U_6368)),U_6369) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6366),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6366),U_6367),U_6369)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6366),U_6368),U_6369))
      | ~ class_Groups_Oordered__ab__group__add(U_6366) ),
    inference(variable_rename,[status(thm)],[f_1868_1]) ).

fof(f_1868_3,plain,
    ! [U_6366,U_6367,U_6368,U_6369] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6366),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6366),U_6367),U_6368)),U_6369) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6366),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6366),U_6367),U_6369)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6366),U_6368),U_6369))
      | ~ class_Groups_Oordered__ab__group__add(U_6366) ),
    inference(definitional_conversion,[status(esa)],[f_1868_2]) ).

cnf(f_1868_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6366),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6366),U_6367),U_6368)),U_6369) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6366),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6366),U_6367),U_6369)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6366),U_6368),U_6369))
    | ~ class_Groups_Oordered__ab__group__add(U_6366) ),
    inference(clausify,[status(thm)],[f_1868_3]) ).

fof(f_1869_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_1869_2,plain,
    ! [U_6373,U_6372,U_6371,U_6370] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6370),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6370),U_6371),U_6372)),U_6373) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6370),U_6371),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6370),U_6372),U_6373))
      | ~ class_Orderings_Olinorder(U_6370) ),
    inference(variable_rename,[status(thm)],[f_1869_1]) ).

fof(f_1869_3,plain,
    ! [U_6370,U_6371,U_6372,U_6373] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6370),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6370),U_6371),U_6372)),U_6373) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6370),U_6371),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6370),U_6372),U_6373))
      | ~ class_Orderings_Olinorder(U_6370) ),
    inference(definitional_conversion,[status(esa)],[f_1869_2]) ).

cnf(f_1869_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6370),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6370),U_6371),U_6372)),U_6373) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6370),U_6371),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6370),U_6372),U_6373))
    | ~ class_Orderings_Olinorder(U_6370) ),
    inference(clausify,[status(thm)],[f_1869_3]) ).

fof(f_1870_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_1870_2,plain,
    ! [U_6377,U_6376,U_6375,U_6374] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6374),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6374),U_6375),U_6376)),U_6377) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6374),U_6375),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6374),U_6376),U_6377))
      | ~ class_Orderings_Olinorder(U_6374) ),
    inference(variable_rename,[status(thm)],[f_1870_1]) ).

fof(f_1870_3,plain,
    ! [U_6374,U_6375,U_6376,U_6377] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6374),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6374),U_6375),U_6376)),U_6377) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6374),U_6375),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6374),U_6376),U_6377))
      | ~ class_Orderings_Olinorder(U_6374) ),
    inference(definitional_conversion,[status(esa)],[f_1870_2]) ).

cnf(f_1870_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6374),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6374),U_6375),U_6376)),U_6377) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6374),U_6375),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6374),U_6376),U_6377))
    | ~ class_Orderings_Olinorder(U_6374) ),
    inference(clausify,[status(thm)],[f_1870_3]) ).

fof(f_1871_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_1871_2,plain,
    ! [U_6381,U_6380,U_6379,U_6378] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6378),U_6379),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6378),U_6380),U_6381)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6378),U_6380),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6378),U_6379),U_6381))
      | ~ class_Orderings_Olinorder(U_6378) ),
    inference(variable_rename,[status(thm)],[f_1871_1]) ).

fof(f_1871_3,plain,
    ! [U_6378,U_6379,U_6380,U_6381] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6378),U_6379),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6378),U_6380),U_6381)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6378),U_6380),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6378),U_6379),U_6381))
      | ~ class_Orderings_Olinorder(U_6378) ),
    inference(definitional_conversion,[status(esa)],[f_1871_2]) ).

cnf(f_1871_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6378),U_6379),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6378),U_6380),U_6381)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6378),U_6380),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6378),U_6379),U_6381))
    | ~ class_Orderings_Olinorder(U_6378) ),
    inference(clausify,[status(thm)],[f_1871_3]) ).

fof(f_1872_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_1872_2,plain,
    ! [U_6385,U_6384,U_6383,U_6382] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6382),U_6383),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6382),U_6384),U_6385)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6382),U_6384),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6382),U_6383),U_6385))
      | ~ class_Orderings_Olinorder(U_6382) ),
    inference(variable_rename,[status(thm)],[f_1872_1]) ).

fof(f_1872_3,plain,
    ! [U_6382,U_6383,U_6384,U_6385] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6382),U_6383),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6382),U_6384),U_6385)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6382),U_6384),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6382),U_6383),U_6385))
      | ~ class_Orderings_Olinorder(U_6382) ),
    inference(definitional_conversion,[status(esa)],[f_1872_2]) ).

cnf(f_1872_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6382),U_6383),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6382),U_6384),U_6385)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6382),U_6384),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6382),U_6383),U_6385))
    | ~ class_Orderings_Olinorder(U_6382) ),
    inference(clausify,[status(thm)],[f_1872_3]) ).

fof(f_1873_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_1873_2,plain,
    ! [U_6388,U_6387,U_6386] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6386),U_6387),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6386),U_6387),U_6388)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6386),U_6387),U_6388)
      | ~ class_Orderings_Olinorder(U_6386) ),
    inference(variable_rename,[status(thm)],[f_1873_1]) ).

fof(f_1873_3,plain,
    ! [U_6386,U_6387,U_6388] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6386),U_6387),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6386),U_6387),U_6388)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6386),U_6387),U_6388)
      | ~ class_Orderings_Olinorder(U_6386) ),
    inference(definitional_conversion,[status(esa)],[f_1873_2]) ).

cnf(f_1873_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6386),U_6387),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6386),U_6387),U_6388)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6386),U_6387),U_6388)
    | ~ class_Orderings_Olinorder(U_6386) ),
    inference(clausify,[status(thm)],[f_1873_3]) ).

fof(f_1874_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_1874_2,plain,
    ! [U_6391,U_6390,U_6389] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6389),U_6390),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6389),U_6390),U_6391)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6389),U_6390),U_6391)
      | ~ class_Orderings_Olinorder(U_6389) ),
    inference(variable_rename,[status(thm)],[f_1874_1]) ).

fof(f_1874_3,plain,
    ! [U_6389,U_6390,U_6391] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6389),U_6390),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6389),U_6390),U_6391)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6389),U_6390),U_6391)
      | ~ class_Orderings_Olinorder(U_6389) ),
    inference(definitional_conversion,[status(esa)],[f_1874_2]) ).

cnf(f_1874_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6389),U_6390),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6389),U_6390),U_6391)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6389),U_6390),U_6391)
    | ~ class_Orderings_Olinorder(U_6389) ),
    inference(clausify,[status(thm)],[f_1874_3]) ).

fof(f_1875_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_1875_2,plain,
    ! [U_6394,U_6393,U_6392] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),U_6393),U_6394) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),U_6394),U_6393)
      | ~ class_Orderings_Olinorder(U_6392) ),
    inference(variable_rename,[status(thm)],[f_1875_1]) ).

fof(f_1875_3,plain,
    ! [U_6392,U_6393,U_6394] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),U_6393),U_6394) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),U_6394),U_6393)
      | ~ class_Orderings_Olinorder(U_6392) ),
    inference(definitional_conversion,[status(esa)],[f_1875_2]) ).

cnf(f_1875_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),U_6393),U_6394) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),U_6394),U_6393)
    | ~ class_Orderings_Olinorder(U_6392) ),
    inference(clausify,[status(thm)],[f_1875_3]) ).

fof(f_1876_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_1876_2,plain,
    ! [U_6397,U_6396,U_6395] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6395),U_6396),U_6397) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6395),U_6397),U_6396)
      | ~ class_Orderings_Olinorder(U_6395) ),
    inference(variable_rename,[status(thm)],[f_1876_1]) ).

fof(f_1876_3,plain,
    ! [U_6395,U_6396,U_6397] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6395),U_6396),U_6397) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6395),U_6397),U_6396)
      | ~ class_Orderings_Olinorder(U_6395) ),
    inference(definitional_conversion,[status(esa)],[f_1876_2]) ).

cnf(f_1876_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6395),U_6396),U_6397) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6395),U_6397),U_6396)
    | ~ class_Orderings_Olinorder(U_6395) ),
    inference(clausify,[status(thm)],[f_1876_3]) ).

fof(f_1877_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_1877_2,plain,
    ! [U_6399,U_6398] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6398),U_6399),U_6399) = U_6399
      | ~ class_Orderings_Olinorder(U_6398) ),
    inference(variable_rename,[status(thm)],[f_1877_1]) ).

fof(f_1877_3,plain,
    ! [U_6398,U_6399] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6398),U_6399),U_6399) = U_6399
      | ~ class_Orderings_Olinorder(U_6398) ),
    inference(definitional_conversion,[status(esa)],[f_1877_2]) ).

cnf(f_1877_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6398),U_6399),U_6399) = U_6399
    | ~ class_Orderings_Olinorder(U_6398) ),
    inference(clausify,[status(thm)],[f_1877_3]) ).

fof(f_1878_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_1878_2,plain,
    ! [U_6403,U_6402,U_6401,U_6400] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6400),U_6402),U_6403)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),U_6403))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),U_6402)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),U_6403))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),U_6402)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6400),U_6402),U_6403))) ) )
      | ~ class_Orderings_Olinorder(U_6400) ),
    inference(variable_rename,[status(thm)],[f_1878_1]) ).

fof(f_1878_3,plain,
    ( ! [U_6400,U_6401,U_6402,U_6403] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),U_6403))
        | ~ sP595(U_6400,U_6401,U_6402,U_6403) )
    & ! [U_6400,U_6401,U_6402,U_6403] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),U_6402))
        | ~ sP595(U_6400,U_6401,U_6402,U_6403) )
    & ! [U_6400,U_6401,U_6402,U_6403] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6400),U_6402),U_6403)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),U_6403))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),U_6402))
        | ~ sP596(U_6400,U_6401,U_6402,U_6403) )
    & ! [U_6400,U_6401,U_6402,U_6403] :
        ( sP595(U_6400,U_6401,U_6402,U_6403)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6400),U_6402),U_6403)))
        | ~ sP596(U_6400,U_6401,U_6402,U_6403) )
    & ! [U_6400,U_6401,U_6402,U_6403] :
        ( sP596(U_6400,U_6401,U_6402,U_6403)
        | ~ class_Orderings_Olinorder(U_6400) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP595,sP596])],[f_1878_2]) ).

cnf(f_1878_4,plain,
    ( sP596(U_6400,U_6401,U_6402,U_6403)
    | ~ class_Orderings_Olinorder(U_6400) ),
    inference(clausify,[status(thm)],[f_1878_3]) ).

cnf(f_1878_5,plain,
    ( sP595(U_6400,U_6401,U_6402,U_6403)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6400),U_6402),U_6403)))
    | ~ sP596(U_6400,U_6401,U_6402,U_6403) ),
    inference(clausify,[status(thm)],[f_1878_3]) ).

cnf(f_1878_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6400),U_6402),U_6403)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),U_6403))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),U_6402))
    | ~ sP596(U_6400,U_6401,U_6402,U_6403) ),
    inference(clausify,[status(thm)],[f_1878_3]) ).

cnf(f_1878_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),U_6402))
    | ~ sP595(U_6400,U_6401,U_6402,U_6403) ),
    inference(clausify,[status(thm)],[f_1878_3]) ).

cnf(f_1878_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6400),U_6401),U_6403))
    | ~ sP595(U_6400,U_6401,U_6402,U_6403) ),
    inference(clausify,[status(thm)],[f_1878_3]) ).

fof(f_1879_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_1879_2,plain,
    ! [U_6407,U_6406,U_6405,U_6404] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6404),U_6405),U_6406)),U_6407))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),U_6406),U_6407))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),U_6405),U_6407)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),U_6406),U_6407))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),U_6405),U_6407))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6404),U_6405),U_6406)),U_6407)) ) )
      | ~ class_Orderings_Olinorder(U_6404) ),
    inference(variable_rename,[status(thm)],[f_1879_1]) ).

fof(f_1879_3,plain,
    ( ! [U_6406,U_6405,U_6404,U_6407] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),U_6406),U_6407))
        | ~ sP597(U_6406,U_6405,U_6404,U_6407) )
    & ! [U_6406,U_6405,U_6404,U_6407] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),U_6405),U_6407))
        | ~ sP597(U_6406,U_6405,U_6404,U_6407) )
    & ! [U_6406,U_6405,U_6404,U_6407] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6404),U_6405),U_6406)),U_6407))
        | sP597(U_6406,U_6405,U_6404,U_6407)
        | ~ sP598(U_6406,U_6405,U_6404,U_6407) )
    & ! [U_6406,U_6405,U_6404,U_6407] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),U_6406),U_6407))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),U_6405),U_6407))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6404),U_6405),U_6406)),U_6407))
        | ~ sP598(U_6406,U_6405,U_6404,U_6407) )
    & ! [U_6406,U_6405,U_6404,U_6407] :
        ( sP598(U_6406,U_6405,U_6404,U_6407)
        | ~ class_Orderings_Olinorder(U_6404) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP597,sP598])],[f_1879_2]) ).

cnf(f_1879_4,plain,
    ( sP598(U_6406,U_6405,U_6404,U_6407)
    | ~ class_Orderings_Olinorder(U_6404) ),
    inference(clausify,[status(thm)],[f_1879_3]) ).

cnf(f_1879_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),U_6406),U_6407))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),U_6405),U_6407))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6404),U_6405),U_6406)),U_6407))
    | ~ sP598(U_6406,U_6405,U_6404,U_6407) ),
    inference(clausify,[status(thm)],[f_1879_3]) ).

cnf(f_1879_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6404),U_6405),U_6406)),U_6407))
    | sP597(U_6406,U_6405,U_6404,U_6407)
    | ~ sP598(U_6406,U_6405,U_6404,U_6407) ),
    inference(clausify,[status(thm)],[f_1879_3]) ).

cnf(f_1879_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),U_6405),U_6407))
    | ~ sP597(U_6406,U_6405,U_6404,U_6407) ),
    inference(clausify,[status(thm)],[f_1879_3]) ).

cnf(f_1879_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),U_6406),U_6407))
    | ~ sP597(U_6406,U_6405,U_6404,U_6407) ),
    inference(clausify,[status(thm)],[f_1879_3]) ).

fof(f_1880_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_1880_2,plain,
    ! [U_6411,U_6410,U_6409,U_6408] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6408),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6408),U_6409),U_6411)),U_6410))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6408),U_6409),U_6410))
      | ~ class_Orderings_Olinorder(U_6408) ),
    inference(variable_rename,[status(thm)],[f_1880_1]) ).

fof(f_1880_3,plain,
    ! [U_6411,U_6410,U_6409,U_6408] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6408),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6408),U_6409),U_6411)),U_6410))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6408),U_6409),U_6410))
      | ~ class_Orderings_Olinorder(U_6408) ),
    inference(definitional_conversion,[status(esa)],[f_1880_2]) ).

cnf(f_1880_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6408),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6408),U_6409),U_6411)),U_6410))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6408),U_6409),U_6410))
    | ~ class_Orderings_Olinorder(U_6408) ),
    inference(clausify,[status(thm)],[f_1880_3]) ).

fof(f_1881_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_1881_2,plain,
    ! [U_6415,U_6414,U_6413,U_6412] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6412),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6412),U_6415),U_6413)),U_6414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6412),U_6413),U_6414))
      | ~ class_Orderings_Olinorder(U_6412) ),
    inference(variable_rename,[status(thm)],[f_1881_1]) ).

fof(f_1881_3,plain,
    ! [U_6415,U_6412,U_6413,U_6414] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6412),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6412),U_6415),U_6413)),U_6414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6412),U_6413),U_6414))
      | ~ class_Orderings_Olinorder(U_6412) ),
    inference(definitional_conversion,[status(esa)],[f_1881_2]) ).

cnf(f_1881_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6412),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6412),U_6415),U_6413)),U_6414))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6412),U_6413),U_6414))
    | ~ class_Orderings_Olinorder(U_6412) ),
    inference(clausify,[status(thm)],[f_1881_3]) ).

fof(f_1882_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_1882_2,plain,
    ! [U_6417,U_6416] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6416)),hAPP(c_Nat_OSuc,U_6417)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6416),U_6417)),
    inference(variable_rename,[status(thm)],[f_1882_1]) ).

fof(f_1882_3,plain,
    ! [U_6416,U_6417] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6416)),hAPP(c_Nat_OSuc,U_6417)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6416),U_6417)),
    inference(definitional_conversion,[status(esa)],[f_1882_2]) ).

cnf(f_1882_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6416)),hAPP(c_Nat_OSuc,U_6417)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6416),U_6417)),
    inference(clausify,[status(thm)],[f_1882_3]) ).

fof(f_1883_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_1883_2,plain,
    ! [U_6420,U_6419,U_6418] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6418),U_6419)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6420),U_6419)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6418),U_6420)),U_6419),
    inference(variable_rename,[status(thm)],[f_1883_1]) ).

fof(f_1883_3,plain,
    ! [U_6418,U_6419,U_6420] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6418),U_6419)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6420),U_6419)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6418),U_6420)),U_6419),
    inference(definitional_conversion,[status(esa)],[f_1883_2]) ).

cnf(f_1883_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6418),U_6419)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6420),U_6419)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6418),U_6420)),U_6419),
    inference(clausify,[status(thm)],[f_1883_3]) ).

fof(f_1884_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_1884_2,plain,
    ! [U_6425,U_6424,U_6423,U_6422,U_6421] :
      ( U_6423 = U_6425
      | hAPP(c_Product__Type_Ofst(U_6421,U_6422),hAPP(hAPP(c_Product__Type_OPair(U_6421,U_6422),U_6423),U_6424)) != U_6425 ),
    inference(variable_rename,[status(thm)],[f_1884_1]) ).

fof(f_1884_3,plain,
    ! [U_6425,U_6424,U_6423] :
      ( ! [U_6422,U_6421] : hAPP(c_Product__Type_Ofst(U_6421,U_6422),hAPP(hAPP(c_Product__Type_OPair(U_6421,U_6422),U_6423),U_6424)) != U_6425
      | U_6423 = U_6425 ),
    inference(miniscope,[status(thm)],[f_1884_2]) ).

fof(f_1884_4,plain,
    ! [U_6421,U_6422,U_6423,U_6424,U_6425] :
      ( hAPP(c_Product__Type_Ofst(U_6421,U_6422),hAPP(hAPP(c_Product__Type_OPair(U_6421,U_6422),U_6423),U_6424)) != U_6425
      | U_6423 = U_6425 ),
    inference(definitional_conversion,[status(esa)],[f_1884_3]) ).

cnf(f_1884_5,plain,
    ( hAPP(c_Product__Type_Ofst(U_6421,U_6422),hAPP(hAPP(c_Product__Type_OPair(U_6421,U_6422),U_6423),U_6424)) != U_6425
    | U_6423 = U_6425 ),
    inference(clausify,[status(thm)],[f_1884_4]) ).

fof(f_1885_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_1885_2,plain,
    ! [U_6429,U_6428,U_6427,U_6426] : hAPP(c_Product__Type_Ofst(U_6426,U_6427),hAPP(hAPP(c_Product__Type_OPair(U_6426,U_6427),U_6428),U_6429)) = U_6428,
    inference(variable_rename,[status(thm)],[f_1885_1]) ).

fof(f_1885_3,plain,
    ! [U_6428,U_6429,U_6426,U_6427] : hAPP(c_Product__Type_Ofst(U_6426,U_6427),hAPP(hAPP(c_Product__Type_OPair(U_6426,U_6427),U_6428),U_6429)) = U_6428,
    inference(definitional_conversion,[status(esa)],[f_1885_2]) ).

cnf(f_1885_4,plain,
    hAPP(c_Product__Type_Ofst(U_6426,U_6427),hAPP(hAPP(c_Product__Type_OPair(U_6426,U_6427),U_6428),U_6429)) = U_6428,
    inference(clausify,[status(thm)],[f_1885_3]) ).

fof(f_1886_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_1886_2,plain,
    ! [U_6433,U_6432,U_6431,U_6430] :
      ( U_6432 = U_6433
      | hAPP(c_Product__Type_Osnd(U_6430,U_6431),U_6432) != hAPP(c_Product__Type_Osnd(U_6430,U_6431),U_6433)
      | hAPP(c_Product__Type_Ofst(U_6430,U_6431),U_6432) != hAPP(c_Product__Type_Ofst(U_6430,U_6431),U_6433) ),
    inference(variable_rename,[status(thm)],[f_1886_1]) ).

fof(f_1886_3,plain,
    ! [U_6430,U_6431,U_6432,U_6433] :
      ( U_6432 = U_6433
      | hAPP(c_Product__Type_Osnd(U_6430,U_6431),U_6432) != hAPP(c_Product__Type_Osnd(U_6430,U_6431),U_6433)
      | hAPP(c_Product__Type_Ofst(U_6430,U_6431),U_6432) != hAPP(c_Product__Type_Ofst(U_6430,U_6431),U_6433) ),
    inference(definitional_conversion,[status(esa)],[f_1886_2]) ).

cnf(f_1886_4,plain,
    ( U_6432 = U_6433
    | hAPP(c_Product__Type_Osnd(U_6430,U_6431),U_6432) != hAPP(c_Product__Type_Osnd(U_6430,U_6431),U_6433)
    | hAPP(c_Product__Type_Ofst(U_6430,U_6431),U_6432) != hAPP(c_Product__Type_Ofst(U_6430,U_6431),U_6433) ),
    inference(clausify,[status(thm)],[f_1886_3]) ).

fof(f_1887_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_1887_2,plain,
    ! [U_6437,U_6436,U_6435,U_6434] :
      ( ( U_6434 = U_6435
        | hAPP(c_Product__Type_Osnd(U_6436,U_6437),U_6434) != hAPP(c_Product__Type_Osnd(U_6436,U_6437),U_6435)
        | hAPP(c_Product__Type_Ofst(U_6436,U_6437),U_6434) != hAPP(c_Product__Type_Ofst(U_6436,U_6437),U_6435) )
      & ( ( hAPP(c_Product__Type_Osnd(U_6436,U_6437),U_6434) = hAPP(c_Product__Type_Osnd(U_6436,U_6437),U_6435)
          & hAPP(c_Product__Type_Ofst(U_6436,U_6437),U_6434) = hAPP(c_Product__Type_Ofst(U_6436,U_6437),U_6435) )
        | U_6434 != U_6435 ) ),
    inference(variable_rename,[status(thm)],[f_1887_1]) ).

fof(f_1887_3,plain,
    ( ! [U_6445,U_6443,U_6441,U_6439] :
        ( U_6439 = U_6441
        | hAPP(c_Product__Type_Osnd(U_6443,U_6445),U_6439) != hAPP(c_Product__Type_Osnd(U_6443,U_6445),U_6441)
        | hAPP(c_Product__Type_Ofst(U_6443,U_6445),U_6439) != hAPP(c_Product__Type_Ofst(U_6443,U_6445),U_6441) )
    & ! [U_6444,U_6442,U_6440,U_6438] :
        ( ( hAPP(c_Product__Type_Osnd(U_6442,U_6444),U_6438) = hAPP(c_Product__Type_Osnd(U_6442,U_6444),U_6440)
          & hAPP(c_Product__Type_Ofst(U_6442,U_6444),U_6438) = hAPP(c_Product__Type_Ofst(U_6442,U_6444),U_6440) )
        | U_6438 != U_6440 ) ),
    inference(miniscope,[status(thm)],[f_1887_2]) ).

fof(f_1887_4,plain,
    ( ! [U_6440,U_6438,U_6442,U_6444] :
        ( hAPP(c_Product__Type_Osnd(U_6442,U_6444),U_6438) = hAPP(c_Product__Type_Osnd(U_6442,U_6444),U_6440)
        | ~ sP599(U_6440,U_6438,U_6442,U_6444) )
    & ! [U_6440,U_6438,U_6442,U_6444] :
        ( hAPP(c_Product__Type_Ofst(U_6442,U_6444),U_6438) = hAPP(c_Product__Type_Ofst(U_6442,U_6444),U_6440)
        | ~ sP599(U_6440,U_6438,U_6442,U_6444) )
    & ! [U_6441,U_6439,U_6443,U_6445] :
        ( U_6439 = U_6441
        | hAPP(c_Product__Type_Osnd(U_6443,U_6445),U_6439) != hAPP(c_Product__Type_Osnd(U_6443,U_6445),U_6441)
        | hAPP(c_Product__Type_Ofst(U_6443,U_6445),U_6439) != hAPP(c_Product__Type_Ofst(U_6443,U_6445),U_6441) )
    & ! [U_6440,U_6438,U_6442,U_6444] :
        ( sP599(U_6440,U_6438,U_6442,U_6444)
        | U_6438 != U_6440 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP599])],[f_1887_3]) ).

cnf(f_1887_5,plain,
    ( sP599(U_6440,U_6438,U_6442,U_6444)
    | U_6438 != U_6440 ),
    inference(clausify,[status(thm)],[f_1887_4]) ).

cnf(f_1887_6,plain,
    ( U_6439 = U_6441
    | hAPP(c_Product__Type_Osnd(U_6443,U_6445),U_6439) != hAPP(c_Product__Type_Osnd(U_6443,U_6445),U_6441)
    | hAPP(c_Product__Type_Ofst(U_6443,U_6445),U_6439) != hAPP(c_Product__Type_Ofst(U_6443,U_6445),U_6441) ),
    inference(clausify,[status(thm)],[f_1887_4]) ).

cnf(f_1887_7,plain,
    ( hAPP(c_Product__Type_Ofst(U_6442,U_6444),U_6438) = hAPP(c_Product__Type_Ofst(U_6442,U_6444),U_6440)
    | ~ sP599(U_6440,U_6438,U_6442,U_6444) ),
    inference(clausify,[status(thm)],[f_1887_4]) ).

cnf(f_1887_8,plain,
    ( hAPP(c_Product__Type_Osnd(U_6442,U_6444),U_6438) = hAPP(c_Product__Type_Osnd(U_6442,U_6444),U_6440)
    | ~ sP599(U_6440,U_6438,U_6442,U_6444) ),
    inference(clausify,[status(thm)],[f_1887_4]) ).

fof(f_1888_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_1888_2,plain,
    ! [U_6450,U_6449,U_6448,U_6447,U_6446] : hAPP(c_Product__Type_Ofst(U_6446,U_6447),hAPP(c_Product__Type_Oapsnd(U_6448,U_6447,U_6446,U_6449),U_6450)) = hAPP(c_Product__Type_Ofst(U_6446,U_6448),U_6450),
    inference(variable_rename,[status(thm)],[f_1888_1]) ).

fof(f_1888_3,plain,
    ! [U_6446,U_6447,U_6448,U_6449,U_6450] : hAPP(c_Product__Type_Ofst(U_6446,U_6447),hAPP(c_Product__Type_Oapsnd(U_6448,U_6447,U_6446,U_6449),U_6450)) = hAPP(c_Product__Type_Ofst(U_6446,U_6448),U_6450),
    inference(definitional_conversion,[status(esa)],[f_1888_2]) ).

cnf(f_1888_4,plain,
    hAPP(c_Product__Type_Ofst(U_6446,U_6447),hAPP(c_Product__Type_Oapsnd(U_6448,U_6447,U_6446,U_6449),U_6450)) = hAPP(c_Product__Type_Ofst(U_6446,U_6448),U_6450),
    inference(clausify,[status(thm)],[f_1888_3]) ).

fof(f_1889_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_1889_2,plain,
    ! [U_6453,U_6452,U_6451] : hAPP(c_Product__Type_Ofst(U_6451,U_6452),U_6453) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6451,U_6452,U_6451),c_COMBK(U_6451,U_6452)),U_6453),
    inference(variable_rename,[status(thm)],[f_1889_1]) ).

fof(f_1889_3,plain,
    ! [U_6451,U_6452,U_6453] : hAPP(c_Product__Type_Ofst(U_6451,U_6452),U_6453) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6451,U_6452,U_6451),c_COMBK(U_6451,U_6452)),U_6453),
    inference(definitional_conversion,[status(esa)],[f_1889_2]) ).

cnf(f_1889_4,plain,
    hAPP(c_Product__Type_Ofst(U_6451,U_6452),U_6453) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6451,U_6452,U_6451),c_COMBK(U_6451,U_6452)),U_6453),
    inference(clausify,[status(thm)],[f_1889_3]) ).

fof(f_1890_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_1890_2,plain,
    ! [U_6456,U_6455,U_6454] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6454),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6455)),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6456)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6456)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6454),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6455)),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6456))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6454),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6455)),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6456)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6455)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6454),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6455)),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6456))) ) )
      | ~ class_Orderings_Oord(U_6454)
      | ~ class_Int_Onumber(U_6454) ),
    inference(variable_rename,[status(thm)],[f_1890_1]) ).

fof(f_1890_3,plain,
    ( ! [U_6454,U_6455,U_6456] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6454),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6455)),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6456)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6456)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6454),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6455)),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6456)))
        | ~ sP600(U_6454,U_6455,U_6456) )
    & ! [U_6454,U_6455,U_6456] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6454),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6455)),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6456)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6455)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6454),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6455)),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6456)))
        | ~ sP600(U_6454,U_6455,U_6456) )
    & ! [U_6454,U_6455,U_6456] :
        ( sP600(U_6454,U_6455,U_6456)
        | ~ class_Orderings_Oord(U_6454)
        | ~ class_Int_Onumber(U_6454) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP600])],[f_1890_2]) ).

cnf(f_1890_4,plain,
    ( sP600(U_6454,U_6455,U_6456)
    | ~ class_Orderings_Oord(U_6454)
    | ~ class_Int_Onumber(U_6454) ),
    inference(clausify,[status(thm)],[f_1890_3]) ).

cnf(f_1890_5,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6454),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6455)),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6456)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6455)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6454),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6455)),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6456)))
    | ~ sP600(U_6454,U_6455,U_6456) ),
    inference(clausify,[status(thm)],[f_1890_3]) ).

cnf(f_1890_6,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6454),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6455)),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6456)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6456)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6454),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6455)),hAPP(c_Int_Onumber__class_Onumber__of(U_6454),U_6456)))
    | ~ sP600(U_6454,U_6455,U_6456) ),
    inference(clausify,[status(thm)],[f_1890_3]) ).

fof(f_1891_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_1891_2,plain,
    ! [U_6459,U_6458,U_6457] : U_6457 = hAPP(hAPP(c_Product__Type_OPair(U_6458,U_6459),hAPP(c_Product__Type_Ofst(U_6458,U_6459),U_6457)),hAPP(c_Product__Type_Osnd(U_6458,U_6459),U_6457)),
    inference(variable_rename,[status(thm)],[f_1891_1]) ).

fof(f_1891_3,plain,
    ! [U_6458,U_6457,U_6459] : U_6457 = hAPP(hAPP(c_Product__Type_OPair(U_6458,U_6459),hAPP(c_Product__Type_Ofst(U_6458,U_6459),U_6457)),hAPP(c_Product__Type_Osnd(U_6458,U_6459),U_6457)),
    inference(definitional_conversion,[status(esa)],[f_1891_2]) ).

cnf(f_1891_4,plain,
    U_6457 = hAPP(hAPP(c_Product__Type_OPair(U_6458,U_6459),hAPP(c_Product__Type_Ofst(U_6458,U_6459),U_6457)),hAPP(c_Product__Type_Osnd(U_6458,U_6459),U_6457)),
    inference(clausify,[status(thm)],[f_1891_3]) ).

fof(f_1892_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_1892_2,plain,
    ! [U_6462,U_6461,U_6460] : hAPP(hAPP(c_Product__Type_OPair(U_6460,U_6461),hAPP(c_Product__Type_Ofst(U_6460,U_6461),U_6462)),hAPP(c_Product__Type_Osnd(U_6460,U_6461),U_6462)) = U_6462,
    inference(variable_rename,[status(thm)],[f_1892_1]) ).

fof(f_1892_3,plain,
    ! [U_6460,U_6461,U_6462] : hAPP(hAPP(c_Product__Type_OPair(U_6460,U_6461),hAPP(c_Product__Type_Ofst(U_6460,U_6461),U_6462)),hAPP(c_Product__Type_Osnd(U_6460,U_6461),U_6462)) = U_6462,
    inference(definitional_conversion,[status(esa)],[f_1892_2]) ).

cnf(f_1892_4,plain,
    hAPP(hAPP(c_Product__Type_OPair(U_6460,U_6461),hAPP(c_Product__Type_Ofst(U_6460,U_6461),U_6462)),hAPP(c_Product__Type_Osnd(U_6460,U_6461),U_6462)) = U_6462,
    inference(clausify,[status(thm)],[f_1892_3]) ).

fof(f_1893_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_1893_2,plain,
    ! [U_6467,U_6466,U_6465,U_6464,U_6463] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6463,U_6464,U_6465),U_6466),U_6467) = hAPP(hAPP(U_6466,hAPP(c_Product__Type_Ofst(U_6463,U_6464),U_6467)),hAPP(c_Product__Type_Osnd(U_6463,U_6464),U_6467)),
    inference(variable_rename,[status(thm)],[f_1893_1]) ).

fof(f_1893_3,plain,
    ! [U_6463,U_6464,U_6465,U_6466,U_6467] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6463,U_6464,U_6465),U_6466),U_6467) = hAPP(hAPP(U_6466,hAPP(c_Product__Type_Ofst(U_6463,U_6464),U_6467)),hAPP(c_Product__Type_Osnd(U_6463,U_6464),U_6467)),
    inference(definitional_conversion,[status(esa)],[f_1893_2]) ).

cnf(f_1893_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6463,U_6464,U_6465),U_6466),U_6467) = hAPP(hAPP(U_6466,hAPP(c_Product__Type_Ofst(U_6463,U_6464),U_6467)),hAPP(c_Product__Type_Osnd(U_6463,U_6464),U_6467)),
    inference(clausify,[status(thm)],[f_1893_3]) ).

fof(f_1894_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_1894_2,plain,
    ! [U_6469,U_6468] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6468),U_6469) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_6468,U_6469)),
    inference(variable_rename,[status(thm)],[f_1894_1]) ).

fof(f_1894_3,plain,
    ! [U_6468,U_6469] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6468),U_6469) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_6468,U_6469)),
    inference(definitional_conversion,[status(esa)],[f_1894_2]) ).

cnf(f_1894_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6468),U_6469) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_6468,U_6469)),
    inference(clausify,[status(thm)],[f_1894_3]) ).

fof(f_1895_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_1895_2,plain,
    ! [U_6471,U_6470] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6470,U_6471) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_6470,U_6471)),
    inference(variable_rename,[status(thm)],[f_1895_1]) ).

fof(f_1895_3,plain,
    ! [U_6470,U_6471] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6470,U_6471) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_6470,U_6471)),
    inference(definitional_conversion,[status(esa)],[f_1895_2]) ).

cnf(f_1895_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6470,U_6471) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_6470,U_6471)),
    inference(clausify,[status(thm)],[f_1895_3]) ).

fof(f_1896_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_1896_2,plain,
    ! [U_6476,U_6475,U_6474,U_6473,U_6472] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6472,U_6473,U_6474),U_6475),U_6476) = hAPP(hAPP(U_6475,hAPP(c_Product__Type_Ofst(U_6472,U_6473),U_6476)),hAPP(c_Product__Type_Osnd(U_6472,U_6473),U_6476)),
    inference(variable_rename,[status(thm)],[f_1896_1]) ).

fof(f_1896_3,plain,
    ! [U_6472,U_6473,U_6474,U_6475,U_6476] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6472,U_6473,U_6474),U_6475),U_6476) = hAPP(hAPP(U_6475,hAPP(c_Product__Type_Ofst(U_6472,U_6473),U_6476)),hAPP(c_Product__Type_Osnd(U_6472,U_6473),U_6476)),
    inference(definitional_conversion,[status(esa)],[f_1896_2]) ).

cnf(f_1896_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6472,U_6473,U_6474),U_6475),U_6476) = hAPP(hAPP(U_6475,hAPP(c_Product__Type_Ofst(U_6472,U_6473),U_6476)),hAPP(c_Product__Type_Osnd(U_6472,U_6473),U_6476)),
    inference(clausify,[status(thm)],[f_1896_3]) ).

fof(f_1897_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_1897_2,plain,
    ! [U_6482,U_6481,U_6480,U_6479,U_6478,U_6477] : hAPP(hAPP(c_COMBS(tc_prod(U_6477,U_6478),U_6478,U_6479),hAPP(hAPP(c_COMBB(U_6480,tc_fun(U_6478,U_6479),tc_prod(U_6477,U_6478)),U_6481),hAPP(hAPP(c_COMBB(U_6477,U_6480,tc_prod(U_6477,U_6478)),U_6482),c_Product__Type_Ofst(U_6477,U_6478)))),c_Product__Type_Osnd(U_6477,U_6478)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_6477,U_6478,U_6479),hAPP(hAPP(c_COMBB(U_6480,tc_fun(U_6478,U_6479),U_6477),U_6481),U_6482)),
    inference(variable_rename,[status(thm)],[f_1897_1]) ).

fof(f_1897_3,plain,
    ! [U_6477,U_6478,U_6479,U_6480,U_6481,U_6482] : hAPP(hAPP(c_COMBS(tc_prod(U_6477,U_6478),U_6478,U_6479),hAPP(hAPP(c_COMBB(U_6480,tc_fun(U_6478,U_6479),tc_prod(U_6477,U_6478)),U_6481),hAPP(hAPP(c_COMBB(U_6477,U_6480,tc_prod(U_6477,U_6478)),U_6482),c_Product__Type_Ofst(U_6477,U_6478)))),c_Product__Type_Osnd(U_6477,U_6478)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_6477,U_6478,U_6479),hAPP(hAPP(c_COMBB(U_6480,tc_fun(U_6478,U_6479),U_6477),U_6481),U_6482)),
    inference(definitional_conversion,[status(esa)],[f_1897_2]) ).

cnf(f_1897_4,plain,
    hAPP(hAPP(c_COMBS(tc_prod(U_6477,U_6478),U_6478,U_6479),hAPP(hAPP(c_COMBB(U_6480,tc_fun(U_6478,U_6479),tc_prod(U_6477,U_6478)),U_6481),hAPP(hAPP(c_COMBB(U_6477,U_6480,tc_prod(U_6477,U_6478)),U_6482),c_Product__Type_Ofst(U_6477,U_6478)))),c_Product__Type_Osnd(U_6477,U_6478)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_6477,U_6478,U_6479),hAPP(hAPP(c_COMBB(U_6480,tc_fun(U_6478,U_6479),U_6477),U_6481),U_6482)),
    inference(clausify,[status(thm)],[f_1897_3]) ).

fof(f_1898_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_1898_2,plain,
    ! [U_6487,U_6486,U_6485,U_6484,U_6483] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6483,U_6484,U_6485),U_6486),U_6487) = hAPP(hAPP(U_6486,hAPP(c_Product__Type_Ofst(U_6483,U_6484),U_6487)),hAPP(c_Product__Type_Osnd(U_6483,U_6484),U_6487)),
    inference(variable_rename,[status(thm)],[f_1898_1]) ).

fof(f_1898_3,plain,
    ! [U_6483,U_6484,U_6485,U_6486,U_6487] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6483,U_6484,U_6485),U_6486),U_6487) = hAPP(hAPP(U_6486,hAPP(c_Product__Type_Ofst(U_6483,U_6484),U_6487)),hAPP(c_Product__Type_Osnd(U_6483,U_6484),U_6487)),
    inference(definitional_conversion,[status(esa)],[f_1898_2]) ).

cnf(f_1898_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6483,U_6484,U_6485),U_6486),U_6487) = hAPP(hAPP(U_6486,hAPP(c_Product__Type_Ofst(U_6483,U_6484),U_6487)),hAPP(c_Product__Type_Osnd(U_6483,U_6484),U_6487)),
    inference(clausify,[status(thm)],[f_1898_3]) ).

fof(f_1899_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_1899_2,plain,
    ! [U_6490,U_6489,U_6488] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6488,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6488,tc_HOL_Obool)),U_6489),U_6490)),U_6489)),
    inference(variable_rename,[status(thm)],[f_1899_1]) ).

fof(f_1899_3,plain,
    ! [U_6488,U_6489,U_6490] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6488,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6488,tc_HOL_Obool)),U_6489),U_6490)),U_6489)),
    inference(definitional_conversion,[status(esa)],[f_1899_2]) ).

cnf(f_1899_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6488,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6488,tc_HOL_Obool)),U_6489),U_6490)),U_6489)),
    inference(clausify,[status(thm)],[f_1899_3]) ).

fof(f_1900_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_1900_2,plain,
    ! [U_6495,U_6494,U_6493,U_6492,U_6491] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6491,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6491,tc_HOL_Obool)),U_6492),U_6495)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6491,tc_HOL_Obool)),U_6493),U_6494)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6491,tc_HOL_Obool)),U_6494),U_6495))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6491,tc_HOL_Obool)),U_6492),U_6493)) ),
    inference(variable_rename,[status(thm)],[f_1900_1]) ).

fof(f_1900_3,plain,
    ! [U_6491,U_6492,U_6493,U_6494,U_6495] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6491,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6491,tc_HOL_Obool)),U_6492),U_6495)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6491,tc_HOL_Obool)),U_6493),U_6494)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6491,tc_HOL_Obool)),U_6494),U_6495))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6491,tc_HOL_Obool)),U_6492),U_6493)) ),
    inference(definitional_conversion,[status(esa)],[f_1900_2]) ).

cnf(f_1900_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6491,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6491,tc_HOL_Obool)),U_6492),U_6495)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6491,tc_HOL_Obool)),U_6493),U_6494)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6491,tc_HOL_Obool)),U_6494),U_6495))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6491,tc_HOL_Obool)),U_6492),U_6493)) ),
    inference(clausify,[status(thm)],[f_1900_3]) ).

fof(f_1901_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_1901_2,plain,
    ! [U_6499,U_6498,U_6497,U_6496] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6496,tc_HOL_Obool)),U_6498),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6496,tc_HOL_Obool)),U_6499),U_6497)) = U_6497
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6496,tc_HOL_Obool)),U_6498),U_6499))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6496,tc_HOL_Obool)),U_6497),U_6498)) ),
    inference(variable_rename,[status(thm)],[f_1901_1]) ).

fof(f_1901_3,plain,
    ! [U_6497,U_6496,U_6498,U_6499] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6496,tc_HOL_Obool)),U_6498),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6496,tc_HOL_Obool)),U_6499),U_6497)) = U_6497
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6496,tc_HOL_Obool)),U_6498),U_6499))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6496,tc_HOL_Obool)),U_6497),U_6498)) ),
    inference(definitional_conversion,[status(esa)],[f_1901_2]) ).

cnf(f_1901_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6496,tc_HOL_Obool)),U_6498),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6496,tc_HOL_Obool)),U_6499),U_6497)) = U_6497
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6496,tc_HOL_Obool)),U_6498),U_6499))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6496,tc_HOL_Obool)),U_6497),U_6498)) ),
    inference(clausify,[status(thm)],[f_1901_3]) ).

fof(f_1902_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_1902_2,plain,
    ! [U_6502,U_6501,U_6500] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6500,tc_HOL_Obool)),U_6501),U_6502))
        | U_6501 = U_6502
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6500,tc_HOL_Obool)),U_6501),U_6502)) )
      & ( ( U_6501 != U_6502
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6500,tc_HOL_Obool)),U_6501),U_6502)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6500,tc_HOL_Obool)),U_6501),U_6502)) ) ),
    inference(variable_rename,[status(thm)],[f_1902_1]) ).

fof(f_1902_3,plain,
    ( ! [U_6508,U_6506,U_6504] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6504,tc_HOL_Obool)),U_6506),U_6508))
        | U_6506 = U_6508
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6504,tc_HOL_Obool)),U_6506),U_6508)) )
    & ! [U_6507,U_6505,U_6503] :
        ( ( U_6505 != U_6507
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6503,tc_HOL_Obool)),U_6505),U_6507)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6503,tc_HOL_Obool)),U_6505),U_6507)) ) ),
    inference(miniscope,[status(thm)],[f_1902_2]) ).

fof(f_1902_4,plain,
    ( ! [U_6505,U_6503,U_6507] :
        ( U_6505 != U_6507
        | ~ sP601(U_6505,U_6503,U_6507) )
    & ! [U_6505,U_6503,U_6507] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6503,tc_HOL_Obool)),U_6505),U_6507))
        | ~ sP601(U_6505,U_6503,U_6507) )
    & ! [U_6506,U_6504,U_6508] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6504,tc_HOL_Obool)),U_6506),U_6508))
        | U_6506 = U_6508
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6504,tc_HOL_Obool)),U_6506),U_6508)) )
    & ! [U_6505,U_6503,U_6507] :
        ( sP601(U_6505,U_6503,U_6507)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6503,tc_HOL_Obool)),U_6505),U_6507)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP601])],[f_1902_3]) ).

cnf(f_1902_5,plain,
    ( sP601(U_6505,U_6503,U_6507)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6503,tc_HOL_Obool)),U_6505),U_6507)) ),
    inference(clausify,[status(thm)],[f_1902_4]) ).

cnf(f_1902_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6504,tc_HOL_Obool)),U_6506),U_6508))
    | U_6506 = U_6508
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6504,tc_HOL_Obool)),U_6506),U_6508)) ),
    inference(clausify,[status(thm)],[f_1902_4]) ).

cnf(f_1902_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6503,tc_HOL_Obool)),U_6505),U_6507))
    | ~ sP601(U_6505,U_6503,U_6507) ),
    inference(clausify,[status(thm)],[f_1902_4]) ).

cnf(f_1902_8,plain,
    ( U_6505 != U_6507
    | ~ sP601(U_6505,U_6503,U_6507) ),
    inference(clausify,[status(thm)],[f_1902_4]) ).

fof(f_1903_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_1903_2,plain,
    ! [U_6511,U_6510,U_6509] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6509,tc_HOL_Obool)),U_6510),U_6511))
        | ( U_6510 != U_6511
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6509,tc_HOL_Obool)),U_6510),U_6511)) ) )
      & ( U_6510 = U_6511
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6509,tc_HOL_Obool)),U_6510),U_6511))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6509,tc_HOL_Obool)),U_6510),U_6511)) ) ),
    inference(variable_rename,[status(thm)],[f_1903_1]) ).

fof(f_1903_3,plain,
    ( ! [U_6517,U_6515,U_6513] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6513,tc_HOL_Obool)),U_6515),U_6517))
        | ( U_6515 != U_6517
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6513,tc_HOL_Obool)),U_6515),U_6517)) ) )
    & ! [U_6516,U_6514,U_6512] :
        ( U_6514 = U_6516
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6512,tc_HOL_Obool)),U_6514),U_6516))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6512,tc_HOL_Obool)),U_6514),U_6516)) ) ),
    inference(miniscope,[status(thm)],[f_1903_2]) ).

fof(f_1903_4,plain,
    ( ! [U_6515,U_6517,U_6513] :
        ( U_6515 != U_6517
        | ~ sP602(U_6515,U_6517,U_6513) )
    & ! [U_6515,U_6517,U_6513] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6513,tc_HOL_Obool)),U_6515),U_6517))
        | ~ sP602(U_6515,U_6517,U_6513) )
    & ! [U_6515,U_6517,U_6513] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6513,tc_HOL_Obool)),U_6515),U_6517))
        | sP602(U_6515,U_6517,U_6513) )
    & ! [U_6514,U_6512,U_6516] :
        ( U_6514 = U_6516
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6512,tc_HOL_Obool)),U_6514),U_6516))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6512,tc_HOL_Obool)),U_6514),U_6516)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP602])],[f_1903_3]) ).

cnf(f_1903_5,plain,
    ( U_6514 = U_6516
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6512,tc_HOL_Obool)),U_6514),U_6516))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6512,tc_HOL_Obool)),U_6514),U_6516)) ),
    inference(clausify,[status(thm)],[f_1903_4]) ).

cnf(f_1903_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6513,tc_HOL_Obool)),U_6515),U_6517))
    | sP602(U_6515,U_6517,U_6513) ),
    inference(clausify,[status(thm)],[f_1903_4]) ).

cnf(f_1903_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6513,tc_HOL_Obool)),U_6515),U_6517))
    | ~ sP602(U_6515,U_6517,U_6513) ),
    inference(clausify,[status(thm)],[f_1903_4]) ).

cnf(f_1903_8,plain,
    ( U_6515 != U_6517
    | ~ sP602(U_6515,U_6517,U_6513) ),
    inference(clausify,[status(thm)],[f_1903_4]) ).

fof(f_1904_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_1904_2,plain,
    ! [U_6520,U_6519,U_6518] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6518,tc_HOL_Obool)),U_6519),U_6520))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6518,tc_HOL_Obool)),U_6519),U_6520)) ),
    inference(variable_rename,[status(thm)],[f_1904_1]) ).

fof(f_1904_3,plain,
    ! [U_6519,U_6518,U_6520] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6518,tc_HOL_Obool)),U_6519),U_6520))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6518,tc_HOL_Obool)),U_6519),U_6520)) ),
    inference(definitional_conversion,[status(esa)],[f_1904_2]) ).

cnf(f_1904_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6518,tc_HOL_Obool)),U_6519),U_6520))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6518,tc_HOL_Obool)),U_6519),U_6520)) ),
    inference(clausify,[status(thm)],[f_1904_3]) ).

fof(f_1905_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_1905_2,plain,
    ! [U_6524,U_6523,U_6522,U_6521] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6521,tc_HOL_Obool)),U_6522),U_6524))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6521,tc_HOL_Obool)),U_6523),U_6524))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6521,tc_HOL_Obool)),U_6522),U_6523)) ),
    inference(variable_rename,[status(thm)],[f_1905_1]) ).

fof(f_1905_3,plain,
    ! [U_6521,U_6522,U_6523,U_6524] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6521,tc_HOL_Obool)),U_6522),U_6524))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6521,tc_HOL_Obool)),U_6523),U_6524))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6521,tc_HOL_Obool)),U_6522),U_6523)) ),
    inference(definitional_conversion,[status(esa)],[f_1905_2]) ).

cnf(f_1905_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6521,tc_HOL_Obool)),U_6522),U_6524))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6521,tc_HOL_Obool)),U_6523),U_6524))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6521,tc_HOL_Obool)),U_6522),U_6523)) ),
    inference(clausify,[status(thm)],[f_1905_3]) ).

fof(f_1906_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_1906_2,plain,
    ! [U_6528,U_6527,U_6526,U_6525] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6525,tc_HOL_Obool)),U_6526),U_6528))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6525,tc_HOL_Obool)),U_6527),U_6528))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6525,tc_HOL_Obool)),U_6526),U_6527)) ),
    inference(variable_rename,[status(thm)],[f_1906_1]) ).

fof(f_1906_3,plain,
    ! [U_6525,U_6526,U_6527,U_6528] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6525,tc_HOL_Obool)),U_6526),U_6528))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6525,tc_HOL_Obool)),U_6527),U_6528))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6525,tc_HOL_Obool)),U_6526),U_6527)) ),
    inference(definitional_conversion,[status(esa)],[f_1906_2]) ).

cnf(f_1906_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6525,tc_HOL_Obool)),U_6526),U_6528))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6525,tc_HOL_Obool)),U_6527),U_6528))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6525,tc_HOL_Obool)),U_6526),U_6527)) ),
    inference(clausify,[status(thm)],[f_1906_3]) ).

fof(f_1907_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_1907_2,plain,
    ! [U_6531,U_6530,U_6529] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6529,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6529,tc_HOL_Obool)),U_6531)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6529,tc_HOL_Obool)),U_6530)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6529,tc_HOL_Obool)),U_6530),U_6531)) ),
    inference(variable_rename,[status(thm)],[f_1907_1]) ).

fof(f_1907_3,plain,
    ! [U_6529,U_6530,U_6531] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6529,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6529,tc_HOL_Obool)),U_6531)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6529,tc_HOL_Obool)),U_6530)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6529,tc_HOL_Obool)),U_6530),U_6531)) ),
    inference(definitional_conversion,[status(esa)],[f_1907_2]) ).

cnf(f_1907_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6529,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6529,tc_HOL_Obool)),U_6531)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6529,tc_HOL_Obool)),U_6530)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6529,tc_HOL_Obool)),U_6530),U_6531)) ),
    inference(clausify,[status(thm)],[f_1907_3]) ).

fof(f_1908_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_1908_2,plain,
    ! [U_6534,U_6533,U_6532] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6532,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6532,tc_HOL_Obool)),U_6533)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6532,tc_HOL_Obool)),U_6534)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6532,tc_HOL_Obool)),U_6534),U_6533)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6532,tc_HOL_Obool)),U_6534),U_6533))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6532,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6532,tc_HOL_Obool)),U_6533)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6532,tc_HOL_Obool)),U_6534))) ) ),
    inference(variable_rename,[status(thm)],[f_1908_1]) ).

fof(f_1908_3,plain,
    ( ! [U_6540,U_6538,U_6536] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6536,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6536,tc_HOL_Obool)),U_6538)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6536,tc_HOL_Obool)),U_6540)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6536,tc_HOL_Obool)),U_6540),U_6538)) )
    & ! [U_6539,U_6537,U_6535] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6535,tc_HOL_Obool)),U_6539),U_6537))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6535,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6535,tc_HOL_Obool)),U_6537)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6535,tc_HOL_Obool)),U_6539))) ) ),
    inference(miniscope,[status(thm)],[f_1908_2]) ).

fof(f_1908_4,plain,
    ( ! [U_6536,U_6538,U_6540] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6536,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6536,tc_HOL_Obool)),U_6538)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6536,tc_HOL_Obool)),U_6540)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6536,tc_HOL_Obool)),U_6540),U_6538)) )
    & ! [U_6537,U_6535,U_6539] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6535,tc_HOL_Obool)),U_6539),U_6537))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6535,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6535,tc_HOL_Obool)),U_6537)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6535,tc_HOL_Obool)),U_6539))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1908_3]) ).

cnf(f_1908_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6535,tc_HOL_Obool)),U_6539),U_6537))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6535,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6535,tc_HOL_Obool)),U_6537)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6535,tc_HOL_Obool)),U_6539))) ),
    inference(clausify,[status(thm)],[f_1908_4]) ).

cnf(f_1908_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6536,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6536,tc_HOL_Obool)),U_6538)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6536,tc_HOL_Obool)),U_6540)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6536,tc_HOL_Obool)),U_6540),U_6538)) ),
    inference(clausify,[status(thm)],[f_1908_4]) ).

fof(f_1909_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_1909_2,plain,
    ! [U_6542,U_6541] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6541,tc_HOL_Obool)),U_6542),U_6542)),
    inference(variable_rename,[status(thm)],[f_1909_1]) ).

fof(f_1909_3,plain,
    ! [U_6542,U_6541] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6541,tc_HOL_Obool)),U_6542),U_6542)),
    inference(definitional_conversion,[status(esa)],[f_1909_2]) ).

cnf(f_1909_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6541,tc_HOL_Obool)),U_6542),U_6542)),
    inference(clausify,[status(thm)],[f_1909_3]) ).

fof(f_1910_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_1910_2,plain,
    ! [U_6545,U_6544,U_6543] :
      ( ( U_6543 = U_6544
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6545,tc_HOL_Obool)),U_6544),U_6543))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6545,tc_HOL_Obool)),U_6543),U_6544)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6545,tc_HOL_Obool)),U_6544),U_6543))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6545,tc_HOL_Obool)),U_6543),U_6544)) )
        | U_6543 != U_6544 ) ),
    inference(variable_rename,[status(thm)],[f_1910_1]) ).

fof(f_1910_3,plain,
    ( ! [U_6551,U_6549,U_6547] :
        ( U_6547 = U_6549
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6551,tc_HOL_Obool)),U_6549),U_6547))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6551,tc_HOL_Obool)),U_6547),U_6549)) )
    & ! [U_6550,U_6548,U_6546] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6550,tc_HOL_Obool)),U_6548),U_6546))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6550,tc_HOL_Obool)),U_6546),U_6548)) )
        | U_6546 != U_6548 ) ),
    inference(miniscope,[status(thm)],[f_1910_2]) ).

fof(f_1910_4,plain,
    ( ! [U_6548,U_6546,U_6550] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6550,tc_HOL_Obool)),U_6548),U_6546))
        | ~ sP603(U_6548,U_6546,U_6550) )
    & ! [U_6548,U_6546,U_6550] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6550,tc_HOL_Obool)),U_6546),U_6548))
        | ~ sP603(U_6548,U_6546,U_6550) )
    & ! [U_6549,U_6547,U_6551] :
        ( U_6547 = U_6549
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6551,tc_HOL_Obool)),U_6549),U_6547))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6551,tc_HOL_Obool)),U_6547),U_6549)) )
    & ! [U_6548,U_6546,U_6550] :
        ( sP603(U_6548,U_6546,U_6550)
        | U_6546 != U_6548 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP603])],[f_1910_3]) ).

cnf(f_1910_5,plain,
    ( sP603(U_6548,U_6546,U_6550)
    | U_6546 != U_6548 ),
    inference(clausify,[status(thm)],[f_1910_4]) ).

cnf(f_1910_6,plain,
    ( U_6547 = U_6549
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6551,tc_HOL_Obool)),U_6549),U_6547))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6551,tc_HOL_Obool)),U_6547),U_6549)) ),
    inference(clausify,[status(thm)],[f_1910_4]) ).

cnf(f_1910_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6550,tc_HOL_Obool)),U_6546),U_6548))
    | ~ sP603(U_6548,U_6546,U_6550) ),
    inference(clausify,[status(thm)],[f_1910_4]) ).

cnf(f_1910_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6550,tc_HOL_Obool)),U_6548),U_6546))
    | ~ sP603(U_6548,U_6546,U_6550) ),
    inference(clausify,[status(thm)],[f_1910_4]) ).

fof(f_1911_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_1911_2,plain,
    ! [U_6554,U_6553,U_6552] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6554,tc_HOL_Obool)),U_6552),U_6553))
      | U_6552 != U_6553 ),
    inference(variable_rename,[status(thm)],[f_1911_1]) ).

fof(f_1911_3,plain,
    ! [U_6552,U_6554,U_6553] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6554,tc_HOL_Obool)),U_6552),U_6553))
      | U_6552 != U_6553 ),
    inference(definitional_conversion,[status(esa)],[f_1911_2]) ).

cnf(f_1911_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6554,tc_HOL_Obool)),U_6552),U_6553))
    | U_6552 != U_6553 ),
    inference(clausify,[status(thm)],[f_1911_3]) ).

fof(f_1912_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_1912_2,plain,
    ! [U_6557,U_6556,U_6555] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6557,tc_HOL_Obool)),U_6556),U_6555))
      | U_6555 != U_6556 ),
    inference(variable_rename,[status(thm)],[f_1912_1]) ).

fof(f_1912_3,plain,
    ! [U_6555,U_6556,U_6557] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6557,tc_HOL_Obool)),U_6556),U_6555))
      | U_6555 != U_6556 ),
    inference(definitional_conversion,[status(esa)],[f_1912_2]) ).

cnf(f_1912_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6557,tc_HOL_Obool)),U_6556),U_6555))
    | U_6555 != U_6556 ),
    inference(clausify,[status(thm)],[f_1912_3]) ).

fof(f_1913_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_1913_2,plain,
    ! [U_6561,U_6560,U_6559,U_6558] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6558,tc_HOL_Obool)),U_6559),U_6561))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6558,tc_HOL_Obool)),U_6560),U_6561))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6558,tc_HOL_Obool)),U_6559),U_6560)) ),
    inference(variable_rename,[status(thm)],[f_1913_1]) ).

fof(f_1913_3,plain,
    ! [U_6558,U_6559,U_6560,U_6561] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6558,tc_HOL_Obool)),U_6559),U_6561))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6558,tc_HOL_Obool)),U_6560),U_6561))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6558,tc_HOL_Obool)),U_6559),U_6560)) ),
    inference(definitional_conversion,[status(esa)],[f_1913_2]) ).

cnf(f_1913_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6558,tc_HOL_Obool)),U_6559),U_6561))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6558,tc_HOL_Obool)),U_6560),U_6561))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6558,tc_HOL_Obool)),U_6559),U_6560)) ),
    inference(clausify,[status(thm)],[f_1913_3]) ).

fof(f_1914_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_1914_2,plain,
    ! [U_6564,U_6563,U_6562] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6564,tc_HOL_Obool)),U_6563),U_6562))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6564,tc_HOL_Obool)),U_6562),U_6563)) )
      | U_6562 != U_6563 ),
    inference(variable_rename,[status(thm)],[f_1914_1]) ).

fof(f_1914_3,plain,
    ( ! [U_6562,U_6563,U_6564] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6564,tc_HOL_Obool)),U_6563),U_6562))
        | ~ sP604(U_6562,U_6563,U_6564) )
    & ! [U_6562,U_6563,U_6564] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6564,tc_HOL_Obool)),U_6562),U_6563))
        | ~ sP604(U_6562,U_6563,U_6564) )
    & ! [U_6562,U_6563,U_6564] :
        ( sP604(U_6562,U_6563,U_6564)
        | U_6562 != U_6563 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP604])],[f_1914_2]) ).

cnf(f_1914_4,plain,
    ( sP604(U_6562,U_6563,U_6564)
    | U_6562 != U_6563 ),
    inference(clausify,[status(thm)],[f_1914_3]) ).

cnf(f_1914_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6564,tc_HOL_Obool)),U_6562),U_6563))
    | ~ sP604(U_6562,U_6563,U_6564) ),
    inference(clausify,[status(thm)],[f_1914_3]) ).

cnf(f_1914_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6564,tc_HOL_Obool)),U_6563),U_6562))
    | ~ sP604(U_6562,U_6563,U_6564) ),
    inference(clausify,[status(thm)],[f_1914_3]) ).

fof(f_1915_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_1915_2,plain,
    ! [U_6566,U_6565] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6565)),U_6566) = 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_6565)),U_6566),
    inference(variable_rename,[status(thm)],[f_1915_1]) ).

fof(f_1915_3,plain,
    ! [U_6566,U_6565] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6565)),U_6566) = 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_6565)),U_6566),
    inference(definitional_conversion,[status(esa)],[f_1915_2]) ).

cnf(f_1915_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6565)),U_6566) = 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_6565)),U_6566),
    inference(clausify,[status(thm)],[f_1915_3]) ).

fof(f_1916_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_1916_2,plain,
    ! [U_6568,U_6567] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6567),hAPP(c_Nat_OSuc,U_6568)) = 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_6568)),U_6567),
    inference(variable_rename,[status(thm)],[f_1916_1]) ).

fof(f_1916_3,plain,
    ! [U_6567,U_6568] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6567),hAPP(c_Nat_OSuc,U_6568)) = 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_6568)),U_6567),
    inference(definitional_conversion,[status(esa)],[f_1916_2]) ).

cnf(f_1916_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6567),hAPP(c_Nat_OSuc,U_6568)) = 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_6568)),U_6567),
    inference(clausify,[status(thm)],[f_1916_3]) ).

fof(f_1917_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_1917_2,plain,
    ! [U_6570,U_6569] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6569),U_6570) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_6569,U_6570))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6570))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6569),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1917_1]) ).

fof(f_1917_3,plain,
    ! [U_6569,U_6570] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6569),U_6570) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_6569,U_6570))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6570))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6569),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1917_2]) ).

cnf(f_1917_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6569),U_6570) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_6569,U_6570))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6570))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6569),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1917_3]) ).

fof(f_1918_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_1918_2,plain,
    ! [U_6572,U_6571] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6571),U_6572) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_6571,U_6572))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6572))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6571)) ),
    inference(variable_rename,[status(thm)],[f_1918_1]) ).

fof(f_1918_3,plain,
    ! [U_6571,U_6572] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6571),U_6572) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_6571,U_6572))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6572))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6571)) ),
    inference(definitional_conversion,[status(esa)],[f_1918_2]) ).

cnf(f_1918_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6571),U_6572) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_6571,U_6572))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6572))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6571)) ),
    inference(clausify,[status(thm)],[f_1918_3]) ).

fof(f_1919_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_1919_2,plain,
    ! [U_6573] :
      ( 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_6573)) = 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_6573)))
      | ~ 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_6573))) ),
    inference(variable_rename,[status(thm)],[f_1919_1]) ).

fof(f_1919_3,plain,
    ! [U_6573] :
      ( 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_6573)) = 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_6573)))
      | ~ 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_6573))) ),
    inference(definitional_conversion,[status(esa)],[f_1919_2]) ).

cnf(f_1919_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_6573)) = 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_6573)))
    | ~ 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_6573))) ),
    inference(clausify,[status(thm)],[f_1919_3]) ).

fof(f_1920_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_1920_2,plain,
    ! [U_6575,U_6574] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6574),U_6575) = 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_6574),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6575))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6575),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_6574)) ),
    inference(variable_rename,[status(thm)],[f_1920_1]) ).

fof(f_1920_3,plain,
    ! [U_6574,U_6575] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6574),U_6575) = 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_6574),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6575))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6575),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_6574)) ),
    inference(definitional_conversion,[status(esa)],[f_1920_2]) ).

cnf(f_1920_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6574),U_6575) = 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_6574),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6575))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6575),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_6574)) ),
    inference(clausify,[status(thm)],[f_1920_3]) ).

fof(f_1921_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_1921_2,plain,
    ! [U_6577,U_6576] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6576)),hAPP(c_Nat_OSuc,U_6577)) = 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_6576))),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_6577)))),
    inference(variable_rename,[status(thm)],[f_1921_1]) ).

fof(f_1921_3,plain,
    ! [U_6577,U_6576] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6576)),hAPP(c_Nat_OSuc,U_6577)) = 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_6576))),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_6577)))),
    inference(definitional_conversion,[status(esa)],[f_1921_2]) ).

cnf(f_1921_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6576)),hAPP(c_Nat_OSuc,U_6577)) = 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_6576))),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_6577)))),
    inference(clausify,[status(thm)],[f_1921_3]) ).

fof(f_1922_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_1922_2,plain,
    ! [U_6582,U_6581,U_6580,U_6579,U_6578] : c_Product__Type_Oprod_Oprod__size(U_6578,U_6579,U_6580,U_6581,U_6582) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_6580,hAPP(c_Product__Type_Ofst(U_6578,U_6579),U_6582))),hAPP(U_6581,hAPP(c_Product__Type_Osnd(U_6578,U_6579),U_6582)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1922_1]) ).

fof(f_1922_3,plain,
    ! [U_6578,U_6579,U_6580,U_6581,U_6582] : c_Product__Type_Oprod_Oprod__size(U_6578,U_6579,U_6580,U_6581,U_6582) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_6580,hAPP(c_Product__Type_Ofst(U_6578,U_6579),U_6582))),hAPP(U_6581,hAPP(c_Product__Type_Osnd(U_6578,U_6579),U_6582)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1922_2]) ).

cnf(f_1922_4,plain,
    c_Product__Type_Oprod_Oprod__size(U_6578,U_6579,U_6580,U_6581,U_6582) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_6580,hAPP(c_Product__Type_Ofst(U_6578,U_6579),U_6582))),hAPP(U_6581,hAPP(c_Product__Type_Osnd(U_6578,U_6579),U_6582)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1922_3]) ).

fof(f_1923_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_1923_2,plain,
    ! [U_6588,U_6587,U_6586,U_6585,U_6584,U_6583] :
      ( ( hBOOL(hAPP(U_6585,hAPP(c_Product__Type_Osnd(U_6587,U_6588),hAPP(hAPP(c_Product__Type_OPair(U_6587,U_6588),U_6584),U_6586))))
        & hBOOL(hAPP(U_6583,hAPP(c_Product__Type_Ofst(U_6587,U_6588),hAPP(hAPP(c_Product__Type_OPair(U_6587,U_6588),U_6584),U_6586)))) )
      | ~ hBOOL(hAPP(U_6585,U_6586))
      | ~ hBOOL(hAPP(U_6583,U_6584)) ),
    inference(variable_rename,[status(thm)],[f_1923_1]) ).

fof(f_1923_3,plain,
    ( ! [U_6584,U_6583,U_6585,U_6586,U_6587,U_6588] :
        ( hBOOL(hAPP(U_6585,hAPP(c_Product__Type_Osnd(U_6587,U_6588),hAPP(hAPP(c_Product__Type_OPair(U_6587,U_6588),U_6584),U_6586))))
        | ~ sP605(U_6584,U_6583,U_6585,U_6586,U_6587,U_6588) )
    & ! [U_6584,U_6583,U_6585,U_6586,U_6587,U_6588] :
        ( hBOOL(hAPP(U_6583,hAPP(c_Product__Type_Ofst(U_6587,U_6588),hAPP(hAPP(c_Product__Type_OPair(U_6587,U_6588),U_6584),U_6586))))
        | ~ sP605(U_6584,U_6583,U_6585,U_6586,U_6587,U_6588) )
    & ! [U_6584,U_6583,U_6585,U_6586,U_6587,U_6588] :
        ( sP605(U_6584,U_6583,U_6585,U_6586,U_6587,U_6588)
        | ~ hBOOL(hAPP(U_6585,U_6586))
        | ~ hBOOL(hAPP(U_6583,U_6584)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP605])],[f_1923_2]) ).

cnf(f_1923_4,plain,
    ( sP605(U_6584,U_6583,U_6585,U_6586,U_6587,U_6588)
    | ~ hBOOL(hAPP(U_6585,U_6586))
    | ~ hBOOL(hAPP(U_6583,U_6584)) ),
    inference(clausify,[status(thm)],[f_1923_3]) ).

cnf(f_1923_5,plain,
    ( hBOOL(hAPP(U_6583,hAPP(c_Product__Type_Ofst(U_6587,U_6588),hAPP(hAPP(c_Product__Type_OPair(U_6587,U_6588),U_6584),U_6586))))
    | ~ sP605(U_6584,U_6583,U_6585,U_6586,U_6587,U_6588) ),
    inference(clausify,[status(thm)],[f_1923_3]) ).

cnf(f_1923_6,plain,
    ( hBOOL(hAPP(U_6585,hAPP(c_Product__Type_Osnd(U_6587,U_6588),hAPP(hAPP(c_Product__Type_OPair(U_6587,U_6588),U_6584),U_6586))))
    | ~ sP605(U_6584,U_6583,U_6585,U_6586,U_6587,U_6588) ),
    inference(clausify,[status(thm)],[f_1923_3]) ).

fof(f_1924_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_1924_2,plain,
    ! [U_6593,U_6592,U_6591,U_6590,U_6589] :
      ( hBOOL(hAPP(hAPP(U_6589,hAPP(c_Product__Type_Osnd(U_6592,U_6593),hAPP(hAPP(c_Product__Type_OPair(U_6592,U_6593),U_6591),U_6590))),hAPP(c_Product__Type_Ofst(U_6592,U_6593),hAPP(hAPP(c_Product__Type_OPair(U_6592,U_6593),U_6591),U_6590))))
      | ~ hBOOL(hAPP(hAPP(U_6589,U_6590),U_6591)) ),
    inference(variable_rename,[status(thm)],[f_1924_1]) ).

fof(f_1924_3,plain,
    ! [U_6589,U_6591,U_6590,U_6592,U_6593] :
      ( hBOOL(hAPP(hAPP(U_6589,hAPP(c_Product__Type_Osnd(U_6592,U_6593),hAPP(hAPP(c_Product__Type_OPair(U_6592,U_6593),U_6591),U_6590))),hAPP(c_Product__Type_Ofst(U_6592,U_6593),hAPP(hAPP(c_Product__Type_OPair(U_6592,U_6593),U_6591),U_6590))))
      | ~ hBOOL(hAPP(hAPP(U_6589,U_6590),U_6591)) ),
    inference(definitional_conversion,[status(esa)],[f_1924_2]) ).

cnf(f_1924_4,plain,
    ( hBOOL(hAPP(hAPP(U_6589,hAPP(c_Product__Type_Osnd(U_6592,U_6593),hAPP(hAPP(c_Product__Type_OPair(U_6592,U_6593),U_6591),U_6590))),hAPP(c_Product__Type_Ofst(U_6592,U_6593),hAPP(hAPP(c_Product__Type_OPair(U_6592,U_6593),U_6591),U_6590))))
    | ~ hBOOL(hAPP(hAPP(U_6589,U_6590),U_6591)) ),
    inference(clausify,[status(thm)],[f_1924_3]) ).

fof(f_1925_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_1925_2,plain,
    ! [U_6594] :
      ( c_Orderings_Oord__class_Omin(U_6594) = c_Orderings_Oord_Omin(U_6594,c_Orderings_Oord__class_Oless__eq(U_6594))
      | ~ class_Orderings_Oord(U_6594) ),
    inference(variable_rename,[status(thm)],[f_1925_1]) ).

fof(f_1925_3,plain,
    ! [U_6594] :
      ( c_Orderings_Oord__class_Omin(U_6594) = c_Orderings_Oord_Omin(U_6594,c_Orderings_Oord__class_Oless__eq(U_6594))
      | ~ class_Orderings_Oord(U_6594) ),
    inference(definitional_conversion,[status(esa)],[f_1925_2]) ).

cnf(f_1925_4,plain,
    ( c_Orderings_Oord__class_Omin(U_6594) = c_Orderings_Oord_Omin(U_6594,c_Orderings_Oord__class_Oless__eq(U_6594))
    | ~ class_Orderings_Oord(U_6594) ),
    inference(clausify,[status(thm)],[f_1925_3]) ).

fof(f_1926_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_1926_2,plain,
    ! [U_6600,U_6599,U_6598,U_6597,U_6596,U_6595] : c_Product__Type_Oprod_Oprod__rec(U_6595,U_6596,U_6597,U_6598,hAPP(hAPP(c_Product__Type_OPair(U_6595,U_6596),U_6599),U_6600)) = hAPP(hAPP(U_6598,U_6599),U_6600),
    inference(variable_rename,[status(thm)],[f_1926_1]) ).

fof(f_1926_3,plain,
    ! [U_6596,U_6595,U_6597,U_6598,U_6599,U_6600] : c_Product__Type_Oprod_Oprod__rec(U_6595,U_6596,U_6597,U_6598,hAPP(hAPP(c_Product__Type_OPair(U_6595,U_6596),U_6599),U_6600)) = hAPP(hAPP(U_6598,U_6599),U_6600),
    inference(definitional_conversion,[status(esa)],[f_1926_2]) ).

cnf(f_1926_4,plain,
    c_Product__Type_Oprod_Oprod__rec(U_6595,U_6596,U_6597,U_6598,hAPP(hAPP(c_Product__Type_OPair(U_6595,U_6596),U_6599),U_6600)) = hAPP(hAPP(U_6598,U_6599),U_6600),
    inference(clausify,[status(thm)],[f_1926_3]) ).

fof(f_1927_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_1927_2,plain,
    ! [U_6603,U_6602,U_6601] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6601,tc_HOL_Obool)),U_6602) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6601,tc_HOL_Obool)),U_6603)
        | U_6602 != U_6603 )
      & ( U_6602 = U_6603
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6601,tc_HOL_Obool)),U_6602) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6601,tc_HOL_Obool)),U_6603) ) ),
    inference(variable_rename,[status(thm)],[f_1927_1]) ).

fof(f_1927_3,plain,
    ( ! [U_6609,U_6607] :
        ( ! [U_6605] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6605,tc_HOL_Obool)),U_6607) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6605,tc_HOL_Obool)),U_6609)
        | U_6607 != U_6609 )
    & ! [U_6608,U_6606] :
        ( ! [U_6604] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6604,tc_HOL_Obool)),U_6606) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6604,tc_HOL_Obool)),U_6608)
        | U_6606 = U_6608 ) ),
    inference(miniscope,[status(thm)],[f_1927_2]) ).

fof(f_1927_4,plain,
    ( ! [U_6609,U_6605,U_6607] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6605,tc_HOL_Obool)),U_6607) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6605,tc_HOL_Obool)),U_6609)
        | U_6607 != U_6609 )
    & ! [U_6606,U_6608,U_6604] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6604,tc_HOL_Obool)),U_6606) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6604,tc_HOL_Obool)),U_6608)
        | U_6606 = U_6608 ) ),
    inference(definitional_conversion,[status(esa)],[f_1927_3]) ).

cnf(f_1927_5,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6604,tc_HOL_Obool)),U_6606) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6604,tc_HOL_Obool)),U_6608)
    | U_6606 = U_6608 ),
    inference(clausify,[status(thm)],[f_1927_4]) ).

cnf(f_1927_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6605,tc_HOL_Obool)),U_6607) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6605,tc_HOL_Obool)),U_6609)
    | U_6607 != U_6609 ),
    inference(clausify,[status(thm)],[f_1927_4]) ).

fof(f_1928_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_1928_2,plain,
    ! [U_6611,U_6610] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6610,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6610,tc_HOL_Obool)),U_6611)) = U_6611,
    inference(variable_rename,[status(thm)],[f_1928_1]) ).

fof(f_1928_3,plain,
    ! [U_6610,U_6611] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6610,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6610,tc_HOL_Obool)),U_6611)) = U_6611,
    inference(definitional_conversion,[status(esa)],[f_1928_2]) ).

cnf(f_1928_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6610,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6610,tc_HOL_Obool)),U_6611)) = U_6611,
    inference(clausify,[status(thm)],[f_1928_3]) ).

fof(f_1929_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_1929_2,plain,
    ! [U_6614,U_6613,U_6612] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6612,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6612,tc_HOL_Obool)),U_6613),U_6614)),U_6614) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6612,tc_HOL_Obool)),U_6613),U_6614),
    inference(variable_rename,[status(thm)],[f_1929_1]) ).

fof(f_1929_3,plain,
    ! [U_6612,U_6613,U_6614] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6612,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6612,tc_HOL_Obool)),U_6613),U_6614)),U_6614) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6612,tc_HOL_Obool)),U_6613),U_6614),
    inference(definitional_conversion,[status(esa)],[f_1929_2]) ).

cnf(f_1929_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6612,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6612,tc_HOL_Obool)),U_6613),U_6614)),U_6614) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6612,tc_HOL_Obool)),U_6613),U_6614),
    inference(clausify,[status(thm)],[f_1929_3]) ).

fof(f_1930_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_1930_2,plain,
    ! [U_6618,U_6617,U_6616,U_6615] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6615,tc_HOL_Obool)),U_6616),U_6618))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6615,tc_HOL_Obool)),U_6617),U_6618))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6615,tc_HOL_Obool)),U_6616),U_6617)) ),
    inference(variable_rename,[status(thm)],[f_1930_1]) ).

fof(f_1930_3,plain,
    ! [U_6615,U_6616,U_6617,U_6618] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6615,tc_HOL_Obool)),U_6616),U_6618))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6615,tc_HOL_Obool)),U_6617),U_6618))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6615,tc_HOL_Obool)),U_6616),U_6617)) ),
    inference(definitional_conversion,[status(esa)],[f_1930_2]) ).

cnf(f_1930_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6615,tc_HOL_Obool)),U_6616),U_6618))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6615,tc_HOL_Obool)),U_6617),U_6618))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6615,tc_HOL_Obool)),U_6616),U_6617)) ),
    inference(clausify,[status(thm)],[f_1930_3]) ).

fof(f_1931_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_1931_2,plain,
    ! [U_6620,U_6619] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6619),U_6620) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_6619,U_6620)),
    inference(variable_rename,[status(thm)],[f_1931_1]) ).

fof(f_1931_3,plain,
    ! [U_6620,U_6619] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6619),U_6620) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_6619,U_6620)),
    inference(definitional_conversion,[status(esa)],[f_1931_2]) ).

cnf(f_1931_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_6619),U_6620) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_6619,U_6620)),
    inference(clausify,[status(thm)],[f_1931_3]) ).

fof(f_1932_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_1932_2,plain,
    ! [U_6623,U_6622,U_6621] :
      ( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6621,U_6622),U_6623))
        | ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6623)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6622),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6623))) )
              & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6622)) )
            | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6623)),U_6622))
                | ~ 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_6623))) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6622)) ) )
          & U_6622 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_6623) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_6622 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_6621 != 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_6623)),U_6622)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6623)) )
      & ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6623)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6622),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6623))) )
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6622)) )
              & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6623)),U_6622))
                  & 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_6623))) )
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6622)) ) )
            | U_6622 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_6623) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_6622 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_6621 = 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_6623)),U_6622)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6623)) )
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6621,U_6622),U_6623)) ) ),
    inference(variable_rename,[status(thm)],[f_1932_1]) ).

fof(f_1932_3,plain,
    ( ! [U_6629,U_6627,U_6625] :
        ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6625,U_6627),U_6629))
        | ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6629)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6627),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6629))) )
              & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6627)) )
            | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6629)),U_6627))
                | ~ 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_6629))) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6627)) ) )
          & U_6627 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_6629) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_6627 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_6625 != 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_6629)),U_6627)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6629)) )
    & ! [U_6628,U_6626,U_6624] :
        ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6628)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6626),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6628))) )
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6626)) )
              & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6628)),U_6626))
                  & 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_6628))) )
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6626)) ) )
            | U_6626 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_6628) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_6626 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_6624 = 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_6628)),U_6626)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6628)) )
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6624,U_6626),U_6628)) ) ),
    inference(miniscope,[status(thm)],[f_1932_2]) ).

fof(f_1932_4,plain,
    ( ! [U_6627,U_6629] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6629)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6627),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6629)))
        | ~ sP612(U_6627,U_6629) )
    & ! [U_6627,U_6629] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6627))
        | ~ sP612(U_6627,U_6629) )
    & ! [U_6627,U_6629] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6629)),U_6627))
        | ~ 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_6629)))
        | ~ sP611(U_6627,U_6629) )
    & ! [U_6627,U_6629] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6627))
        | ~ sP611(U_6627,U_6629) )
    & ! [U_6627,U_6629] :
        ( sP612(U_6627,U_6629)
        | sP611(U_6627,U_6629)
        | ~ sP613(U_6627,U_6629) )
    & ! [U_6627,U_6629] :
        ( U_6627 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP613(U_6627,U_6629) )
    & ! [U_6627,U_6629] :
        ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_6629) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP610(U_6627,U_6629) )
    & ! [U_6627,U_6629] :
        ( U_6627 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP610(U_6627,U_6629) )
    & ! [U_6626,U_6628] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6628)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP607(U_6626,U_6628) )
    & ! [U_6626,U_6628] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6626),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6628)))
        | ~ sP607(U_6626,U_6628) )
    & ! [U_6626,U_6628] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6628)),U_6626))
        | ~ sP606(U_6626,U_6628) )
    & ! [U_6626,U_6628] :
        ( 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_6628)))
        | ~ sP606(U_6626,U_6628) )
    & ! [U_6626,U_6628] :
        ( sP607(U_6626,U_6628)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6626))
        | ~ sP608(U_6626,U_6628) )
    & ! [U_6626,U_6628] :
        ( sP606(U_6626,U_6628)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6626))
        | ~ sP608(U_6626,U_6628) )
    & ! [U_6626,U_6624,U_6628] :
        ( sP608(U_6626,U_6628)
        | U_6626 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP609(U_6626,U_6624,U_6628) )
    & ! [U_6626,U_6624,U_6628] :
        ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_6628) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_6626 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP609(U_6626,U_6624,U_6628) )
    & ! [U_6626,U_6624,U_6628] :
        ( U_6624 = 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_6628)),U_6626)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6628))
        | ~ sP609(U_6626,U_6624,U_6628) )
    & ! [U_6627,U_6625,U_6629] :
        ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6625,U_6627),U_6629))
        | sP613(U_6627,U_6629)
        | sP610(U_6627,U_6629)
        | U_6625 != 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_6629)),U_6627)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6629)) )
    & ! [U_6626,U_6624,U_6628] :
        ( sP609(U_6626,U_6624,U_6628)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6624,U_6626),U_6628)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP606,sP607,sP608,sP609,sP610,sP611,sP612,sP613])],[f_1932_3]) ).

cnf(f_1932_5,plain,
    ( sP609(U_6626,U_6624,U_6628)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6624,U_6626),U_6628)) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_6,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_6625,U_6627),U_6629))
    | sP613(U_6627,U_6629)
    | sP610(U_6627,U_6629)
    | U_6625 != 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_6629)),U_6627)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6629)) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_7,plain,
    ( U_6624 = 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_6628)),U_6626)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6628))
    | ~ sP609(U_6626,U_6624,U_6628) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_8,plain,
    ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_6628) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_6626 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP609(U_6626,U_6624,U_6628) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_9,plain,
    ( sP608(U_6626,U_6628)
    | U_6626 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP609(U_6626,U_6624,U_6628) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_10,plain,
    ( sP606(U_6626,U_6628)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6626))
    | ~ sP608(U_6626,U_6628) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_11,plain,
    ( sP607(U_6626,U_6628)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6626))
    | ~ sP608(U_6626,U_6628) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_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_6628)))
    | ~ sP606(U_6626,U_6628) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_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_6628)),U_6626))
    | ~ sP606(U_6626,U_6628) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_14,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6626),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6628)))
    | ~ sP607(U_6626,U_6628) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_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_6628)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP607(U_6626,U_6628) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_16,plain,
    ( U_6627 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP610(U_6627,U_6629) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_17,plain,
    ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_6629) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP610(U_6627,U_6629) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_18,plain,
    ( U_6627 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP613(U_6627,U_6629) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_19,plain,
    ( sP612(U_6627,U_6629)
    | sP611(U_6627,U_6629)
    | ~ sP613(U_6627,U_6629) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_20,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6627))
    | ~ sP611(U_6627,U_6629) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_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_6629)),U_6627))
    | ~ 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_6629)))
    | ~ sP611(U_6627,U_6629) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_22,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6627))
    | ~ sP612(U_6627,U_6629) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

cnf(f_1932_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_6629)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6627),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_6629)))
    | ~ sP612(U_6627,U_6629) ),
    inference(clausify,[status(thm)],[f_1932_4]) ).

fof(f_1933_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_1933_2,plain,
    ! [U_6631,U_6630] :
      ( 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_6630),U_6631))),U_6630))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_6630)) ),
    inference(variable_rename,[status(thm)],[f_1933_1]) ).

fof(f_1933_3,plain,
    ! [U_6630,U_6631] :
      ( 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_6630),U_6631))),U_6630))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_6630)) ),
    inference(definitional_conversion,[status(esa)],[f_1933_2]) ).

cnf(f_1933_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_6630),U_6631))),U_6630))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_6630)) ),
    inference(clausify,[status(thm)],[f_1933_3]) ).

fof(f_1934_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_1934_2,plain,
    ! [U_6633,U_6632] : hAPP(c_New__DSequence_Opos__not__seq(U_6632),U_6633) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_6632,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_6633))),
    inference(variable_rename,[status(thm)],[f_1934_1]) ).

fof(f_1934_3,plain,
    ! [U_6633,U_6632] : hAPP(c_New__DSequence_Opos__not__seq(U_6632),U_6633) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_6632,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_6633))),
    inference(definitional_conversion,[status(esa)],[f_1934_2]) ).

cnf(f_1934_4,plain,
    hAPP(c_New__DSequence_Opos__not__seq(U_6632),U_6633) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_6632,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_6633))),
    inference(clausify,[status(thm)],[f_1934_3]) ).

fof(f_1935_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_1935_2,plain,
    ! [U_6635,U_6634] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6634)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6635)) = 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_6635))),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_6634))),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_6634)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_1935_1]) ).

fof(f_1935_3,plain,
    ! [U_6635,U_6634] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6634)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6635)) = 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_6635))),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_6634))),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_6634)),c_Int_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_1935_2]) ).

cnf(f_1935_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6634)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6635)) = 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_6635))),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_6634))),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_6634)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_1935_3]) ).

fof(f_1936_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_1936_2,plain,
    ! [U_6637,U_6636] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6636)),hAPP(c_Nat_OSuc,U_6637)) = 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_6636))),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_6637))),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_6637)))),
    inference(variable_rename,[status(thm)],[f_1936_1]) ).

fof(f_1936_3,plain,
    ! [U_6637,U_6636] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6636)),hAPP(c_Nat_OSuc,U_6637)) = 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_6636))),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_6637))),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_6637)))),
    inference(definitional_conversion,[status(esa)],[f_1936_2]) ).

cnf(f_1936_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6636)),hAPP(c_Nat_OSuc,U_6637)) = 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_6636))),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_6637))),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_6637)))),
    inference(clausify,[status(thm)],[f_1936_3]) ).

fof(f_1937_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_1937_2,plain,
    ! [U_6644,U_6643,U_6642,U_6641,U_6640,U_6639,U_6638] : hAPP(c_Product__Type_Oapsnd(U_6638,U_6639,U_6640,U_6641),hAPP(c_Product__Type_Oapfst(U_6642,U_6640,U_6638,U_6643),U_6644)) = hAPP(hAPP(c_Product__Type_OPair(U_6640,U_6639),hAPP(U_6643,hAPP(c_Product__Type_Ofst(U_6642,U_6638),U_6644))),hAPP(U_6641,hAPP(c_Product__Type_Osnd(U_6642,U_6638),U_6644))),
    inference(variable_rename,[status(thm)],[f_1937_1]) ).

fof(f_1937_3,plain,
    ! [U_6643,U_6644,U_6638,U_6639,U_6640,U_6641,U_6642] : hAPP(c_Product__Type_Oapsnd(U_6638,U_6639,U_6640,U_6641),hAPP(c_Product__Type_Oapfst(U_6642,U_6640,U_6638,U_6643),U_6644)) = hAPP(hAPP(c_Product__Type_OPair(U_6640,U_6639),hAPP(U_6643,hAPP(c_Product__Type_Ofst(U_6642,U_6638),U_6644))),hAPP(U_6641,hAPP(c_Product__Type_Osnd(U_6642,U_6638),U_6644))),
    inference(definitional_conversion,[status(esa)],[f_1937_2]) ).

cnf(f_1937_4,plain,
    hAPP(c_Product__Type_Oapsnd(U_6638,U_6639,U_6640,U_6641),hAPP(c_Product__Type_Oapfst(U_6642,U_6640,U_6638,U_6643),U_6644)) = hAPP(hAPP(c_Product__Type_OPair(U_6640,U_6639),hAPP(U_6643,hAPP(c_Product__Type_Ofst(U_6642,U_6638),U_6644))),hAPP(U_6641,hAPP(c_Product__Type_Osnd(U_6642,U_6638),U_6644))),
    inference(clausify,[status(thm)],[f_1937_3]) ).

fof(f_1938_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_1938_2,plain,
    ! [U_6648,U_6647,U_6646,U_6645] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6645),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6645),U_6646),U_6647)),U_6648) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6645),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6645),U_6646),U_6648)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6645),U_6647),U_6648))
      | ~ class_Orderings_Olinorder(U_6645) ),
    inference(variable_rename,[status(thm)],[f_1938_1]) ).

fof(f_1938_3,plain,
    ! [U_6645,U_6646,U_6647,U_6648] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6645),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6645),U_6646),U_6647)),U_6648) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6645),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6645),U_6646),U_6648)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6645),U_6647),U_6648))
      | ~ class_Orderings_Olinorder(U_6645) ),
    inference(definitional_conversion,[status(esa)],[f_1938_2]) ).

cnf(f_1938_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6645),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6645),U_6646),U_6647)),U_6648) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6645),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6645),U_6646),U_6648)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6645),U_6647),U_6648))
    | ~ class_Orderings_Olinorder(U_6645) ),
    inference(clausify,[status(thm)],[f_1938_3]) ).

fof(f_1939_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_1939_2,plain,
    ! [U_6652,U_6651,U_6650,U_6649] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6649),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6649),U_6650),U_6651)),U_6652) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6649),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6649),U_6650),U_6652)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6649),U_6651),U_6652))
      | ~ class_Orderings_Olinorder(U_6649) ),
    inference(variable_rename,[status(thm)],[f_1939_1]) ).

fof(f_1939_3,plain,
    ! [U_6649,U_6650,U_6651,U_6652] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6649),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6649),U_6650),U_6651)),U_6652) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6649),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6649),U_6650),U_6652)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6649),U_6651),U_6652))
      | ~ class_Orderings_Olinorder(U_6649) ),
    inference(definitional_conversion,[status(esa)],[f_1939_2]) ).

cnf(f_1939_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6649),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6649),U_6650),U_6651)),U_6652) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6649),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6649),U_6650),U_6652)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6649),U_6651),U_6652))
    | ~ class_Orderings_Olinorder(U_6649) ),
    inference(clausify,[status(thm)],[f_1939_3]) ).

fof(f_1940_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_1940_2,plain,
    ! [U_6656,U_6655,U_6654,U_6653] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6653),U_6654),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6653),U_6655),U_6656)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6653),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6653),U_6654),U_6655)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6653),U_6654),U_6656))
      | ~ class_Orderings_Olinorder(U_6653) ),
    inference(variable_rename,[status(thm)],[f_1940_1]) ).

fof(f_1940_3,plain,
    ! [U_6653,U_6654,U_6655,U_6656] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6653),U_6654),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6653),U_6655),U_6656)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6653),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6653),U_6654),U_6655)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6653),U_6654),U_6656))
      | ~ class_Orderings_Olinorder(U_6653) ),
    inference(definitional_conversion,[status(esa)],[f_1940_2]) ).

cnf(f_1940_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6653),U_6654),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6653),U_6655),U_6656)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6653),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6653),U_6654),U_6655)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6653),U_6654),U_6656))
    | ~ class_Orderings_Olinorder(U_6653) ),
    inference(clausify,[status(thm)],[f_1940_3]) ).

fof(f_1941_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_1941_2,plain,
    ! [U_6660,U_6659,U_6658,U_6657] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6657),U_6658),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6657),U_6659),U_6660)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6657),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6657),U_6658),U_6659)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6657),U_6658),U_6660))
      | ~ class_Orderings_Olinorder(U_6657) ),
    inference(variable_rename,[status(thm)],[f_1941_1]) ).

fof(f_1941_3,plain,
    ! [U_6657,U_6658,U_6659,U_6660] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6657),U_6658),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6657),U_6659),U_6660)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6657),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6657),U_6658),U_6659)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6657),U_6658),U_6660))
      | ~ class_Orderings_Olinorder(U_6657) ),
    inference(definitional_conversion,[status(esa)],[f_1941_2]) ).

cnf(f_1941_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6657),U_6658),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6657),U_6659),U_6660)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6657),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6657),U_6658),U_6659)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6657),U_6658),U_6660))
    | ~ class_Orderings_Olinorder(U_6657) ),
    inference(clausify,[status(thm)],[f_1941_3]) ).

fof(f_1942_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_1942_2,plain,
    ! [U_6663,U_6662,U_6661] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6661),U_6662),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6661),U_6662),U_6663)) = U_6662
      | ~ class_Orderings_Olinorder(U_6661) ),
    inference(variable_rename,[status(thm)],[f_1942_1]) ).

fof(f_1942_3,plain,
    ! [U_6661,U_6662,U_6663] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6661),U_6662),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6661),U_6662),U_6663)) = U_6662
      | ~ class_Orderings_Olinorder(U_6661) ),
    inference(definitional_conversion,[status(esa)],[f_1942_2]) ).

cnf(f_1942_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6661),U_6662),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6661),U_6662),U_6663)) = U_6662
    | ~ class_Orderings_Olinorder(U_6661) ),
    inference(clausify,[status(thm)],[f_1942_3]) ).

fof(f_1943_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_1943_2,plain,
    ! [U_6666,U_6665,U_6664] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6664),U_6665),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6664),U_6665),U_6666)) = U_6665
      | ~ class_Orderings_Olinorder(U_6664) ),
    inference(variable_rename,[status(thm)],[f_1943_1]) ).

fof(f_1943_3,plain,
    ! [U_6664,U_6665,U_6666] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6664),U_6665),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6664),U_6665),U_6666)) = U_6665
      | ~ class_Orderings_Olinorder(U_6664) ),
    inference(definitional_conversion,[status(esa)],[f_1943_2]) ).

cnf(f_1943_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6664),U_6665),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6664),U_6665),U_6666)) = U_6665
    | ~ class_Orderings_Olinorder(U_6664) ),
    inference(clausify,[status(thm)],[f_1943_3]) ).

fof(f_1944_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_1944_2,plain,
    ! [U_6670,U_6669,U_6668,U_6667] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6667),U_6668),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6667),U_6670),U_6669)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6667),U_6668),U_6669))
      | ~ class_Orderings_Olinorder(U_6667) ),
    inference(variable_rename,[status(thm)],[f_1944_1]) ).

fof(f_1944_3,plain,
    ! [U_6667,U_6668,U_6669,U_6670] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6667),U_6668),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6667),U_6670),U_6669)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6667),U_6668),U_6669))
      | ~ class_Orderings_Olinorder(U_6667) ),
    inference(definitional_conversion,[status(esa)],[f_1944_2]) ).

cnf(f_1944_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6667),U_6668),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6667),U_6670),U_6669)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6667),U_6668),U_6669))
    | ~ class_Orderings_Olinorder(U_6667) ),
    inference(clausify,[status(thm)],[f_1944_3]) ).

fof(f_1945_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_1945_2,plain,
    ! [U_6674,U_6673,U_6672,U_6671] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6671),U_6672),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6671),U_6673),U_6674)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6671),U_6672),U_6673))
      | ~ class_Orderings_Olinorder(U_6671) ),
    inference(variable_rename,[status(thm)],[f_1945_1]) ).

fof(f_1945_3,plain,
    ! [U_6671,U_6672,U_6673,U_6674] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6671),U_6672),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6671),U_6673),U_6674)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6671),U_6672),U_6673))
      | ~ class_Orderings_Olinorder(U_6671) ),
    inference(definitional_conversion,[status(esa)],[f_1945_2]) ).

cnf(f_1945_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6671),U_6672),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6671),U_6673),U_6674)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6671),U_6672),U_6673))
    | ~ class_Orderings_Olinorder(U_6671) ),
    inference(clausify,[status(thm)],[f_1945_3]) ).

fof(f_1946_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_1946_2,plain,
    ! [U_6678,U_6677,U_6676,U_6675] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6675),U_6676),U_6677)),U_6678))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),U_6677),U_6678))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),U_6676),U_6678)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),U_6677),U_6678))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),U_6676),U_6678)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6675),U_6676),U_6677)),U_6678)) ) )
      | ~ class_Orderings_Olinorder(U_6675) ),
    inference(variable_rename,[status(thm)],[f_1946_1]) ).

fof(f_1946_3,plain,
    ( ! [U_6675,U_6676,U_6677,U_6678] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),U_6677),U_6678))
        | ~ sP614(U_6675,U_6676,U_6677,U_6678) )
    & ! [U_6675,U_6676,U_6677,U_6678] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),U_6676),U_6678))
        | ~ sP614(U_6675,U_6676,U_6677,U_6678) )
    & ! [U_6675,U_6676,U_6677,U_6678] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6675),U_6676),U_6677)),U_6678))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),U_6677),U_6678))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),U_6676),U_6678))
        | ~ sP615(U_6675,U_6676,U_6677,U_6678) )
    & ! [U_6675,U_6676,U_6677,U_6678] :
        ( sP614(U_6675,U_6676,U_6677,U_6678)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6675),U_6676),U_6677)),U_6678))
        | ~ sP615(U_6675,U_6676,U_6677,U_6678) )
    & ! [U_6675,U_6676,U_6677,U_6678] :
        ( sP615(U_6675,U_6676,U_6677,U_6678)
        | ~ class_Orderings_Olinorder(U_6675) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP614,sP615])],[f_1946_2]) ).

cnf(f_1946_4,plain,
    ( sP615(U_6675,U_6676,U_6677,U_6678)
    | ~ class_Orderings_Olinorder(U_6675) ),
    inference(clausify,[status(thm)],[f_1946_3]) ).

cnf(f_1946_5,plain,
    ( sP614(U_6675,U_6676,U_6677,U_6678)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6675),U_6676),U_6677)),U_6678))
    | ~ sP615(U_6675,U_6676,U_6677,U_6678) ),
    inference(clausify,[status(thm)],[f_1946_3]) ).

cnf(f_1946_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6675),U_6676),U_6677)),U_6678))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),U_6677),U_6678))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),U_6676),U_6678))
    | ~ sP615(U_6675,U_6676,U_6677,U_6678) ),
    inference(clausify,[status(thm)],[f_1946_3]) ).

cnf(f_1946_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),U_6676),U_6678))
    | ~ sP614(U_6675,U_6676,U_6677,U_6678) ),
    inference(clausify,[status(thm)],[f_1946_3]) ).

cnf(f_1946_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6675),U_6677),U_6678))
    | ~ sP614(U_6675,U_6676,U_6677,U_6678) ),
    inference(clausify,[status(thm)],[f_1946_3]) ).

fof(f_1947_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_1947_2,plain,
    ! [U_6682,U_6681,U_6680,U_6679] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6679),U_6681),U_6682)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),U_6682))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),U_6681)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),U_6682))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),U_6681))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6679),U_6681),U_6682))) ) )
      | ~ class_Orderings_Olinorder(U_6679) ),
    inference(variable_rename,[status(thm)],[f_1947_1]) ).

fof(f_1947_3,plain,
    ( ! [U_6679,U_6682,U_6680,U_6681] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),U_6682))
        | ~ sP616(U_6679,U_6682,U_6680,U_6681) )
    & ! [U_6679,U_6682,U_6680,U_6681] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),U_6681))
        | ~ sP616(U_6679,U_6682,U_6680,U_6681) )
    & ! [U_6679,U_6682,U_6680,U_6681] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6679),U_6681),U_6682)))
        | sP616(U_6679,U_6682,U_6680,U_6681)
        | ~ sP617(U_6679,U_6682,U_6680,U_6681) )
    & ! [U_6679,U_6682,U_6680,U_6681] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),U_6682))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),U_6681))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6679),U_6681),U_6682)))
        | ~ sP617(U_6679,U_6682,U_6680,U_6681) )
    & ! [U_6679,U_6682,U_6680,U_6681] :
        ( sP617(U_6679,U_6682,U_6680,U_6681)
        | ~ class_Orderings_Olinorder(U_6679) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP616,sP617])],[f_1947_2]) ).

cnf(f_1947_4,plain,
    ( sP617(U_6679,U_6682,U_6680,U_6681)
    | ~ class_Orderings_Olinorder(U_6679) ),
    inference(clausify,[status(thm)],[f_1947_3]) ).

cnf(f_1947_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),U_6682))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),U_6681))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6679),U_6681),U_6682)))
    | ~ sP617(U_6679,U_6682,U_6680,U_6681) ),
    inference(clausify,[status(thm)],[f_1947_3]) ).

cnf(f_1947_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6679),U_6681),U_6682)))
    | sP616(U_6679,U_6682,U_6680,U_6681)
    | ~ sP617(U_6679,U_6682,U_6680,U_6681) ),
    inference(clausify,[status(thm)],[f_1947_3]) ).

cnf(f_1947_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),U_6681))
    | ~ sP616(U_6679,U_6682,U_6680,U_6681) ),
    inference(clausify,[status(thm)],[f_1947_3]) ).

cnf(f_1947_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6679),U_6680),U_6682))
    | ~ sP616(U_6679,U_6682,U_6680,U_6681) ),
    inference(clausify,[status(thm)],[f_1947_3]) ).

fof(f_1948_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_1948_2,plain,
    ! [U_6686,U_6685,U_6684,U_6683] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6683),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6683),U_6684),U_6685)),U_6686) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6683),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6683),U_6684),U_6686)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6683),U_6685),U_6686))
      | ~ class_Groups_Oordered__ab__group__add(U_6683) ),
    inference(variable_rename,[status(thm)],[f_1948_1]) ).

fof(f_1948_3,plain,
    ! [U_6684,U_6685,U_6686,U_6683] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6683),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6683),U_6684),U_6685)),U_6686) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6683),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6683),U_6684),U_6686)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6683),U_6685),U_6686))
      | ~ class_Groups_Oordered__ab__group__add(U_6683) ),
    inference(definitional_conversion,[status(esa)],[f_1948_2]) ).

cnf(f_1948_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6683),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6683),U_6684),U_6685)),U_6686) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6683),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6683),U_6684),U_6686)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6683),U_6685),U_6686))
    | ~ class_Groups_Oordered__ab__group__add(U_6683) ),
    inference(clausify,[status(thm)],[f_1948_3]) ).

fof(f_1949_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_1949_2,plain,
    ! [U_6689,U_6688,U_6687] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6687),U_6688),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6687),U_6688),U_6689)))
      | ~ class_Orderings_Olinorder(U_6687) ),
    inference(variable_rename,[status(thm)],[f_1949_1]) ).

fof(f_1949_3,plain,
    ! [U_6687,U_6688,U_6689] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6687),U_6688),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6687),U_6688),U_6689)))
      | ~ class_Orderings_Olinorder(U_6687) ),
    inference(definitional_conversion,[status(esa)],[f_1949_2]) ).

cnf(f_1949_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6687),U_6688),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6687),U_6688),U_6689)))
    | ~ class_Orderings_Olinorder(U_6687) ),
    inference(clausify,[status(thm)],[f_1949_3]) ).

fof(f_1950_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_1950_2,plain,
    ! [U_6692,U_6691,U_6690] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6690),U_6691),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6690),U_6692),U_6691)))
      | ~ class_Orderings_Olinorder(U_6690) ),
    inference(variable_rename,[status(thm)],[f_1950_1]) ).

fof(f_1950_3,plain,
    ! [U_6690,U_6691,U_6692] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6690),U_6691),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6690),U_6692),U_6691)))
      | ~ class_Orderings_Olinorder(U_6690) ),
    inference(definitional_conversion,[status(esa)],[f_1950_2]) ).

cnf(f_1950_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6690),U_6691),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6690),U_6692),U_6691)))
    | ~ class_Orderings_Olinorder(U_6690) ),
    inference(clausify,[status(thm)],[f_1950_3]) ).

fof(f_1951_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_1951_2,plain,
    ! [U_6695,U_6694,U_6693] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6693),U_6694),U_6695))
          | hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6693),U_6694),U_6695) != U_6695 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6693),U_6694),U_6695) = U_6695
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6693),U_6694),U_6695)) ) )
      | ~ class_Orderings_Olinorder(U_6693) ),
    inference(variable_rename,[status(thm)],[f_1951_1]) ).

fof(f_1951_3,plain,
    ( ! [U_6693,U_6694,U_6695] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6693),U_6694),U_6695))
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6693),U_6694),U_6695) != U_6695
        | ~ sP618(U_6693,U_6694,U_6695) )
    & ! [U_6693,U_6694,U_6695] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6693),U_6694),U_6695) = U_6695
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6693),U_6694),U_6695))
        | ~ sP618(U_6693,U_6694,U_6695) )
    & ! [U_6693,U_6694,U_6695] :
        ( sP618(U_6693,U_6694,U_6695)
        | ~ class_Orderings_Olinorder(U_6693) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP618])],[f_1951_2]) ).

cnf(f_1951_4,plain,
    ( sP618(U_6693,U_6694,U_6695)
    | ~ class_Orderings_Olinorder(U_6693) ),
    inference(clausify,[status(thm)],[f_1951_3]) ).

cnf(f_1951_5,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6693),U_6694),U_6695) = U_6695
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6693),U_6694),U_6695))
    | ~ sP618(U_6693,U_6694,U_6695) ),
    inference(clausify,[status(thm)],[f_1951_3]) ).

cnf(f_1951_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6693),U_6694),U_6695))
    | hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6693),U_6694),U_6695) != U_6695
    | ~ sP618(U_6693,U_6694,U_6695) ),
    inference(clausify,[status(thm)],[f_1951_3]) ).

fof(f_1952_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_1952_2,plain,
    ! [U_6699,U_6698,U_6697,U_6696] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6696),U_6698),U_6699)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),U_6699))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),U_6698)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),U_6699))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),U_6698))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6696),U_6698),U_6699))) ) )
      | ~ class_Orderings_Olinorder(U_6696) ),
    inference(variable_rename,[status(thm)],[f_1952_1]) ).

fof(f_1952_3,plain,
    ( ! [U_6698,U_6696,U_6697,U_6699] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),U_6699))
        | ~ sP619(U_6698,U_6696,U_6697,U_6699) )
    & ! [U_6698,U_6696,U_6697,U_6699] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),U_6698))
        | ~ sP619(U_6698,U_6696,U_6697,U_6699) )
    & ! [U_6698,U_6696,U_6697,U_6699] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6696),U_6698),U_6699)))
        | sP619(U_6698,U_6696,U_6697,U_6699)
        | ~ sP620(U_6698,U_6696,U_6697,U_6699) )
    & ! [U_6698,U_6696,U_6697,U_6699] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),U_6699))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),U_6698))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6696),U_6698),U_6699)))
        | ~ sP620(U_6698,U_6696,U_6697,U_6699) )
    & ! [U_6698,U_6696,U_6697,U_6699] :
        ( sP620(U_6698,U_6696,U_6697,U_6699)
        | ~ class_Orderings_Olinorder(U_6696) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP619,sP620])],[f_1952_2]) ).

cnf(f_1952_4,plain,
    ( sP620(U_6698,U_6696,U_6697,U_6699)
    | ~ class_Orderings_Olinorder(U_6696) ),
    inference(clausify,[status(thm)],[f_1952_3]) ).

cnf(f_1952_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),U_6699))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),U_6698))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6696),U_6698),U_6699)))
    | ~ sP620(U_6698,U_6696,U_6697,U_6699) ),
    inference(clausify,[status(thm)],[f_1952_3]) ).

cnf(f_1952_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6696),U_6698),U_6699)))
    | sP619(U_6698,U_6696,U_6697,U_6699)
    | ~ sP620(U_6698,U_6696,U_6697,U_6699) ),
    inference(clausify,[status(thm)],[f_1952_3]) ).

cnf(f_1952_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),U_6698))
    | ~ sP619(U_6698,U_6696,U_6697,U_6699) ),
    inference(clausify,[status(thm)],[f_1952_3]) ).

cnf(f_1952_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6696),U_6697),U_6699))
    | ~ sP619(U_6698,U_6696,U_6697,U_6699) ),
    inference(clausify,[status(thm)],[f_1952_3]) ).

fof(f_1953_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_1953_2,plain,
    ! [U_6703,U_6702,U_6701,U_6700] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6700),U_6701),U_6702)),U_6703))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),U_6702),U_6703))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),U_6701),U_6703)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),U_6702),U_6703))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),U_6701),U_6703)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6700),U_6701),U_6702)),U_6703)) ) )
      | ~ class_Orderings_Olinorder(U_6700) ),
    inference(variable_rename,[status(thm)],[f_1953_1]) ).

fof(f_1953_3,plain,
    ( ! [U_6701,U_6703,U_6700,U_6702] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),U_6702),U_6703))
        | ~ sP621(U_6701,U_6703,U_6700,U_6702) )
    & ! [U_6701,U_6703,U_6700,U_6702] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),U_6701),U_6703))
        | ~ sP621(U_6701,U_6703,U_6700,U_6702) )
    & ! [U_6701,U_6703,U_6700,U_6702] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6700),U_6701),U_6702)),U_6703))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),U_6702),U_6703))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),U_6701),U_6703))
        | ~ sP622(U_6701,U_6703,U_6700,U_6702) )
    & ! [U_6701,U_6703,U_6700,U_6702] :
        ( sP621(U_6701,U_6703,U_6700,U_6702)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6700),U_6701),U_6702)),U_6703))
        | ~ sP622(U_6701,U_6703,U_6700,U_6702) )
    & ! [U_6701,U_6703,U_6700,U_6702] :
        ( sP622(U_6701,U_6703,U_6700,U_6702)
        | ~ class_Orderings_Olinorder(U_6700) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP621,sP622])],[f_1953_2]) ).

cnf(f_1953_4,plain,
    ( sP622(U_6701,U_6703,U_6700,U_6702)
    | ~ class_Orderings_Olinorder(U_6700) ),
    inference(clausify,[status(thm)],[f_1953_3]) ).

cnf(f_1953_5,plain,
    ( sP621(U_6701,U_6703,U_6700,U_6702)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6700),U_6701),U_6702)),U_6703))
    | ~ sP622(U_6701,U_6703,U_6700,U_6702) ),
    inference(clausify,[status(thm)],[f_1953_3]) ).

cnf(f_1953_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6700),U_6701),U_6702)),U_6703))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),U_6702),U_6703))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),U_6701),U_6703))
    | ~ sP622(U_6701,U_6703,U_6700,U_6702) ),
    inference(clausify,[status(thm)],[f_1953_3]) ).

cnf(f_1953_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),U_6701),U_6703))
    | ~ sP621(U_6701,U_6703,U_6700,U_6702) ),
    inference(clausify,[status(thm)],[f_1953_3]) ).

cnf(f_1953_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6700),U_6702),U_6703))
    | ~ sP621(U_6701,U_6703,U_6700,U_6702) ),
    inference(clausify,[status(thm)],[f_1953_3]) ).

fof(f_1954_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_1954_2,plain,
    ! [U_6707,U_6706,U_6705,U_6704] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6704),U_6705),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6704),U_6706),U_6707)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6704),U_6705),U_6706))
      | ~ class_Orderings_Olinorder(U_6704) ),
    inference(variable_rename,[status(thm)],[f_1954_1]) ).

fof(f_1954_3,plain,
    ! [U_6707,U_6706,U_6705,U_6704] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6704),U_6705),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6704),U_6706),U_6707)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6704),U_6705),U_6706))
      | ~ class_Orderings_Olinorder(U_6704) ),
    inference(definitional_conversion,[status(esa)],[f_1954_2]) ).

cnf(f_1954_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6704),U_6705),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6704),U_6706),U_6707)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6704),U_6705),U_6706))
    | ~ class_Orderings_Olinorder(U_6704) ),
    inference(clausify,[status(thm)],[f_1954_3]) ).

fof(f_1955_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_1955_2,plain,
    ! [U_6711,U_6710,U_6709,U_6708] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6708),U_6709),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6708),U_6711),U_6710)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6708),U_6709),U_6710))
      | ~ class_Orderings_Olinorder(U_6708) ),
    inference(variable_rename,[status(thm)],[f_1955_1]) ).

fof(f_1955_3,plain,
    ! [U_6708,U_6709,U_6710,U_6711] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6708),U_6709),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6708),U_6711),U_6710)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6708),U_6709),U_6710))
      | ~ class_Orderings_Olinorder(U_6708) ),
    inference(definitional_conversion,[status(esa)],[f_1955_2]) ).

cnf(f_1955_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6708),U_6709),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6708),U_6711),U_6710)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6708),U_6709),U_6710))
    | ~ class_Orderings_Olinorder(U_6708) ),
    inference(clausify,[status(thm)],[f_1955_3]) ).

fof(f_1956_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_1956_2,plain,
    ! [U_6714,U_6713,U_6712] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6712),U_6713),U_6714) = U_6714
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6712),U_6713),U_6714))
      | ~ class_Orderings_Olinorder(U_6712) ),
    inference(variable_rename,[status(thm)],[f_1956_1]) ).

fof(f_1956_3,plain,
    ! [U_6712,U_6713,U_6714] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6712),U_6713),U_6714) = U_6714
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6712),U_6713),U_6714))
      | ~ class_Orderings_Olinorder(U_6712) ),
    inference(definitional_conversion,[status(esa)],[f_1956_2]) ).

cnf(f_1956_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6712),U_6713),U_6714) = U_6714
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6712),U_6713),U_6714))
    | ~ class_Orderings_Olinorder(U_6712) ),
    inference(clausify,[status(thm)],[f_1956_3]) ).

fof(f_1957_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_1957_2,plain,
    ! [U_6717,U_6716,U_6715] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6715),U_6717),U_6716) = U_6717
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6715),U_6716),U_6717))
      | ~ class_Orderings_Olinorder(U_6715) ),
    inference(variable_rename,[status(thm)],[f_1957_1]) ).

fof(f_1957_3,plain,
    ! [U_6715,U_6716,U_6717] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6715),U_6717),U_6716) = U_6717
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6715),U_6716),U_6717))
      | ~ class_Orderings_Olinorder(U_6715) ),
    inference(definitional_conversion,[status(esa)],[f_1957_2]) ).

cnf(f_1957_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6715),U_6717),U_6716) = U_6717
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6715),U_6716),U_6717))
    | ~ class_Orderings_Olinorder(U_6715) ),
    inference(clausify,[status(thm)],[f_1957_3]) ).

fof(f_1958_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_1958_2,plain,
    ! [U_6721,U_6720,U_6719,U_6718] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6718),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6718),U_6719),U_6721)),U_6720))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6718),U_6721),U_6720))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6718),U_6719),U_6720))
      | ~ class_Orderings_Olinorder(U_6718) ),
    inference(variable_rename,[status(thm)],[f_1958_1]) ).

fof(f_1958_3,plain,
    ! [U_6718,U_6719,U_6720,U_6721] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6718),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6718),U_6719),U_6721)),U_6720))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6718),U_6721),U_6720))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6718),U_6719),U_6720))
      | ~ class_Orderings_Olinorder(U_6718) ),
    inference(definitional_conversion,[status(esa)],[f_1958_2]) ).

cnf(f_1958_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6718),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6718),U_6719),U_6721)),U_6720))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6718),U_6721),U_6720))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6718),U_6719),U_6720))
    | ~ class_Orderings_Olinorder(U_6718) ),
    inference(clausify,[status(thm)],[f_1958_3]) ).

fof(f_1959_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_1959_2,plain,
    ! [U_6725,U_6724,U_6723,U_6722] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6722),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6722),U_6723),U_6725)),U_6724))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6722),U_6725),U_6724))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6722),U_6723),U_6724))
      | ~ class_Orderings_Olinorder(U_6722) ),
    inference(variable_rename,[status(thm)],[f_1959_1]) ).

fof(f_1959_3,plain,
    ! [U_6722,U_6723,U_6724,U_6725] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6722),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6722),U_6723),U_6725)),U_6724))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6722),U_6725),U_6724))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6722),U_6723),U_6724))
      | ~ class_Orderings_Olinorder(U_6722) ),
    inference(definitional_conversion,[status(esa)],[f_1959_2]) ).

cnf(f_1959_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6722),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6722),U_6723),U_6725)),U_6724))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6722),U_6725),U_6724))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6722),U_6723),U_6724))
    | ~ class_Orderings_Olinorder(U_6722) ),
    inference(clausify,[status(thm)],[f_1959_3]) ).

fof(f_1960_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_1960_2,plain,
    ! [U_6730,U_6729,U_6728,U_6727,U_6726] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6726),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6726),U_6727),U_6729)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6726),U_6728),U_6730)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6726),U_6729),U_6730))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6726),U_6727),U_6728))
      | ~ class_Orderings_Olinorder(U_6726) ),
    inference(variable_rename,[status(thm)],[f_1960_1]) ).

fof(f_1960_3,plain,
    ! [U_6726,U_6727,U_6728,U_6729,U_6730] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6726),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6726),U_6727),U_6729)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6726),U_6728),U_6730)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6726),U_6729),U_6730))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6726),U_6727),U_6728))
      | ~ class_Orderings_Olinorder(U_6726) ),
    inference(definitional_conversion,[status(esa)],[f_1960_2]) ).

cnf(f_1960_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6726),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6726),U_6727),U_6729)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6726),U_6728),U_6730)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6726),U_6729),U_6730))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6726),U_6727),U_6728))
    | ~ class_Orderings_Olinorder(U_6726) ),
    inference(clausify,[status(thm)],[f_1960_3]) ).

fof(f_1961_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_1961_2,plain,
    ! [U_6734,U_6733,U_6732,U_6731] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6731),U_6733),U_6734))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6731),U_6732),U_6734)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6731),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6731),U_6732),U_6733)),U_6734))
      | ~ class_Orderings_Olinorder(U_6731) ),
    inference(variable_rename,[status(thm)],[f_1961_1]) ).

fof(f_1961_3,plain,
    ( ! [U_6732,U_6731,U_6733,U_6734] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6731),U_6733),U_6734))
        | ~ sP623(U_6732,U_6731,U_6733,U_6734) )
    & ! [U_6732,U_6731,U_6733,U_6734] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6731),U_6732),U_6734))
        | ~ sP623(U_6732,U_6731,U_6733,U_6734) )
    & ! [U_6732,U_6731,U_6733,U_6734] :
        ( sP623(U_6732,U_6731,U_6733,U_6734)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6731),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6731),U_6732),U_6733)),U_6734))
        | ~ class_Orderings_Olinorder(U_6731) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP623])],[f_1961_2]) ).

cnf(f_1961_4,plain,
    ( sP623(U_6732,U_6731,U_6733,U_6734)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6731),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6731),U_6732),U_6733)),U_6734))
    | ~ class_Orderings_Olinorder(U_6731) ),
    inference(clausify,[status(thm)],[f_1961_3]) ).

cnf(f_1961_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6731),U_6732),U_6734))
    | ~ sP623(U_6732,U_6731,U_6733,U_6734) ),
    inference(clausify,[status(thm)],[f_1961_3]) ).

cnf(f_1961_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6731),U_6733),U_6734))
    | ~ sP623(U_6732,U_6731,U_6733,U_6734) ),
    inference(clausify,[status(thm)],[f_1961_3]) ).

fof(f_1962_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_1962_2,plain,
    ! [U_6735] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6735) = U_6735,
    inference(variable_rename,[status(thm)],[f_1962_1]) ).

fof(f_1962_3,plain,
    ! [U_6735] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6735) = U_6735,
    inference(definitional_conversion,[status(esa)],[f_1962_2]) ).

cnf(f_1962_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6735) = U_6735,
    inference(clausify,[status(thm)],[f_1962_3]) ).

fof(f_1963_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_1963_2,plain,
    ! [U_6736] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6736),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6736,
    inference(variable_rename,[status(thm)],[f_1963_1]) ).

fof(f_1963_3,plain,
    ! [U_6736] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6736),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6736,
    inference(definitional_conversion,[status(esa)],[f_1963_2]) ).

cnf(f_1963_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6736),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6736,
    inference(clausify,[status(thm)],[f_1963_3]) ).

fof(f_1964_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_1964_2,plain,
    ! [U_6738,U_6737] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6737)),hAPP(c_Nat_OSuc,U_6738)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6737),U_6738)),
    inference(variable_rename,[status(thm)],[f_1964_1]) ).

fof(f_1964_3,plain,
    ! [U_6737,U_6738] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6737)),hAPP(c_Nat_OSuc,U_6738)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6737),U_6738)),
    inference(definitional_conversion,[status(esa)],[f_1964_2]) ).

cnf(f_1964_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6737)),hAPP(c_Nat_OSuc,U_6738)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6737),U_6738)),
    inference(clausify,[status(thm)],[f_1964_3]) ).

fof(f_1965_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_1965_2,plain,
    ! [U_6742,U_6741,U_6740,U_6739] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6739),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6739),U_6740),U_6741)),U_6742) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6739),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6739),U_6740),U_6742)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6739),U_6741),U_6742))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6739) ),
    inference(variable_rename,[status(thm)],[f_1965_1]) ).

fof(f_1965_3,plain,
    ! [U_6739,U_6740,U_6741,U_6742] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6739),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6739),U_6740),U_6741)),U_6742) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6739),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6739),U_6740),U_6742)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6739),U_6741),U_6742))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6739) ),
    inference(definitional_conversion,[status(esa)],[f_1965_2]) ).

cnf(f_1965_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6739),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6739),U_6740),U_6741)),U_6742) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6739),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6739),U_6740),U_6742)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6739),U_6741),U_6742))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6739) ),
    inference(clausify,[status(thm)],[f_1965_3]) ).

fof(f_1966_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_1966_2,plain,
    ! [U_6746,U_6745,U_6744,U_6743] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6743),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6743),U_6744),U_6745)),U_6746) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6743),U_6744),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6743),U_6745),U_6746))
      | ~ class_Orderings_Olinorder(U_6743) ),
    inference(variable_rename,[status(thm)],[f_1966_1]) ).

fof(f_1966_3,plain,
    ! [U_6743,U_6744,U_6745,U_6746] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6743),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6743),U_6744),U_6745)),U_6746) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6743),U_6744),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6743),U_6745),U_6746))
      | ~ class_Orderings_Olinorder(U_6743) ),
    inference(definitional_conversion,[status(esa)],[f_1966_2]) ).

cnf(f_1966_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6743),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6743),U_6744),U_6745)),U_6746) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6743),U_6744),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6743),U_6745),U_6746))
    | ~ class_Orderings_Olinorder(U_6743) ),
    inference(clausify,[status(thm)],[f_1966_3]) ).

fof(f_1967_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_1967_2,plain,
    ! [U_6750,U_6749,U_6748,U_6747] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6747),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6747),U_6748),U_6749)),U_6750) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6747),U_6748),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6747),U_6749),U_6750))
      | ~ class_Orderings_Olinorder(U_6747) ),
    inference(variable_rename,[status(thm)],[f_1967_1]) ).

fof(f_1967_3,plain,
    ! [U_6747,U_6748,U_6749,U_6750] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6747),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6747),U_6748),U_6749)),U_6750) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6747),U_6748),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6747),U_6749),U_6750))
      | ~ class_Orderings_Olinorder(U_6747) ),
    inference(definitional_conversion,[status(esa)],[f_1967_2]) ).

cnf(f_1967_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6747),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6747),U_6748),U_6749)),U_6750) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6747),U_6748),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6747),U_6749),U_6750))
    | ~ class_Orderings_Olinorder(U_6747) ),
    inference(clausify,[status(thm)],[f_1967_3]) ).

fof(f_1968_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_1968_2,plain,
    ! [U_6754,U_6753,U_6752,U_6751] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6751),U_6752),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6751),U_6753),U_6754)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6751),U_6753),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6751),U_6752),U_6754))
      | ~ class_Orderings_Olinorder(U_6751) ),
    inference(variable_rename,[status(thm)],[f_1968_1]) ).

fof(f_1968_3,plain,
    ! [U_6751,U_6752,U_6753,U_6754] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6751),U_6752),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6751),U_6753),U_6754)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6751),U_6753),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6751),U_6752),U_6754))
      | ~ class_Orderings_Olinorder(U_6751) ),
    inference(definitional_conversion,[status(esa)],[f_1968_2]) ).

cnf(f_1968_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6751),U_6752),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6751),U_6753),U_6754)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6751),U_6753),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6751),U_6752),U_6754))
    | ~ class_Orderings_Olinorder(U_6751) ),
    inference(clausify,[status(thm)],[f_1968_3]) ).

fof(f_1969_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_1969_2,plain,
    ! [U_6758,U_6757,U_6756,U_6755] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6755),U_6756),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6755),U_6757),U_6758)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6755),U_6757),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6755),U_6756),U_6758))
      | ~ class_Orderings_Olinorder(U_6755) ),
    inference(variable_rename,[status(thm)],[f_1969_1]) ).

fof(f_1969_3,plain,
    ! [U_6755,U_6756,U_6757,U_6758] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6755),U_6756),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6755),U_6757),U_6758)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6755),U_6757),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6755),U_6756),U_6758))
      | ~ class_Orderings_Olinorder(U_6755) ),
    inference(definitional_conversion,[status(esa)],[f_1969_2]) ).

cnf(f_1969_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6755),U_6756),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6755),U_6757),U_6758)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6755),U_6757),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6755),U_6756),U_6758))
    | ~ class_Orderings_Olinorder(U_6755) ),
    inference(clausify,[status(thm)],[f_1969_3]) ).

fof(f_1970_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_1970_2,plain,
    ! [U_6761,U_6760,U_6759] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6759),U_6760),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6759),U_6760),U_6761)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6759),U_6760),U_6761)
      | ~ class_Orderings_Olinorder(U_6759) ),
    inference(variable_rename,[status(thm)],[f_1970_1]) ).

fof(f_1970_3,plain,
    ! [U_6759,U_6760,U_6761] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6759),U_6760),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6759),U_6760),U_6761)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6759),U_6760),U_6761)
      | ~ class_Orderings_Olinorder(U_6759) ),
    inference(definitional_conversion,[status(esa)],[f_1970_2]) ).

cnf(f_1970_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6759),U_6760),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6759),U_6760),U_6761)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6759),U_6760),U_6761)
    | ~ class_Orderings_Olinorder(U_6759) ),
    inference(clausify,[status(thm)],[f_1970_3]) ).

fof(f_1971_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_1971_2,plain,
    ! [U_6764,U_6763,U_6762] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6762),U_6763),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6762),U_6763),U_6764)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6762),U_6763),U_6764)
      | ~ class_Orderings_Olinorder(U_6762) ),
    inference(variable_rename,[status(thm)],[f_1971_1]) ).

fof(f_1971_3,plain,
    ! [U_6762,U_6763,U_6764] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6762),U_6763),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6762),U_6763),U_6764)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6762),U_6763),U_6764)
      | ~ class_Orderings_Olinorder(U_6762) ),
    inference(definitional_conversion,[status(esa)],[f_1971_2]) ).

cnf(f_1971_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6762),U_6763),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6762),U_6763),U_6764)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6762),U_6763),U_6764)
    | ~ class_Orderings_Olinorder(U_6762) ),
    inference(clausify,[status(thm)],[f_1971_3]) ).

fof(f_1972_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_1972_2,plain,
    ! [U_6767,U_6766,U_6765] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6765),U_6766),U_6767) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6765),U_6767),U_6766)
      | ~ class_Orderings_Olinorder(U_6765) ),
    inference(variable_rename,[status(thm)],[f_1972_1]) ).

fof(f_1972_3,plain,
    ! [U_6765,U_6766,U_6767] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6765),U_6766),U_6767) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6765),U_6767),U_6766)
      | ~ class_Orderings_Olinorder(U_6765) ),
    inference(definitional_conversion,[status(esa)],[f_1972_2]) ).

cnf(f_1972_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6765),U_6766),U_6767) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6765),U_6767),U_6766)
    | ~ class_Orderings_Olinorder(U_6765) ),
    inference(clausify,[status(thm)],[f_1972_3]) ).

fof(f_1973_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_1973_2,plain,
    ! [U_6770,U_6769,U_6768] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6768),U_6769),U_6770) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6768),U_6770),U_6769)
      | ~ class_Orderings_Olinorder(U_6768) ),
    inference(variable_rename,[status(thm)],[f_1973_1]) ).

fof(f_1973_3,plain,
    ! [U_6768,U_6769,U_6770] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6768),U_6769),U_6770) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6768),U_6770),U_6769)
      | ~ class_Orderings_Olinorder(U_6768) ),
    inference(definitional_conversion,[status(esa)],[f_1973_2]) ).

cnf(f_1973_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6768),U_6769),U_6770) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6768),U_6770),U_6769)
    | ~ class_Orderings_Olinorder(U_6768) ),
    inference(clausify,[status(thm)],[f_1973_3]) ).

fof(f_1974_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_1974_2,plain,
    ! [U_6772,U_6771] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6771),U_6772),U_6772) = U_6772
      | ~ class_Orderings_Olinorder(U_6771) ),
    inference(variable_rename,[status(thm)],[f_1974_1]) ).

fof(f_1974_3,plain,
    ! [U_6771,U_6772] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6771),U_6772),U_6772) = U_6772
      | ~ class_Orderings_Olinorder(U_6771) ),
    inference(definitional_conversion,[status(esa)],[f_1974_2]) ).

cnf(f_1974_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6771),U_6772),U_6772) = U_6772
    | ~ class_Orderings_Olinorder(U_6771) ),
    inference(clausify,[status(thm)],[f_1974_3]) ).

fof(f_1975_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_1975_2,plain,
    ! [U_6778,U_6777,U_6776,U_6775,U_6774,U_6773] : hAPP(c_Product__Type_Oapfst(U_6773,U_6774,U_6775,U_6776),hAPP(hAPP(c_Product__Type_OPair(U_6773,U_6775),U_6777),U_6778)) = hAPP(hAPP(c_Product__Type_OPair(U_6774,U_6775),hAPP(U_6776,U_6777)),U_6778),
    inference(variable_rename,[status(thm)],[f_1975_1]) ).

fof(f_1975_3,plain,
    ! [U_6773,U_6774,U_6775,U_6776,U_6777,U_6778] : hAPP(c_Product__Type_Oapfst(U_6773,U_6774,U_6775,U_6776),hAPP(hAPP(c_Product__Type_OPair(U_6773,U_6775),U_6777),U_6778)) = hAPP(hAPP(c_Product__Type_OPair(U_6774,U_6775),hAPP(U_6776,U_6777)),U_6778),
    inference(definitional_conversion,[status(esa)],[f_1975_2]) ).

cnf(f_1975_4,plain,
    hAPP(c_Product__Type_Oapfst(U_6773,U_6774,U_6775,U_6776),hAPP(hAPP(c_Product__Type_OPair(U_6773,U_6775),U_6777),U_6778)) = hAPP(hAPP(c_Product__Type_OPair(U_6774,U_6775),hAPP(U_6776,U_6777)),U_6778),
    inference(clausify,[status(thm)],[f_1975_3]) ).

fof(f_1976_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_1976_2,plain,
    ! [U_6784,U_6783,U_6782,U_6781,U_6780,U_6779] :
      ( ( hAPP(c_Product__Type_Oapfst(U_6779,U_6780,U_6781,U_6782),U_6783) = hAPP(c_Product__Type_Oapfst(U_6779,U_6780,U_6781,U_6784),U_6783)
        | hAPP(U_6782,hAPP(c_Product__Type_Ofst(U_6779,U_6781),U_6783)) != hAPP(U_6784,hAPP(c_Product__Type_Ofst(U_6779,U_6781),U_6783)) )
      & ( hAPP(U_6782,hAPP(c_Product__Type_Ofst(U_6779,U_6781),U_6783)) = hAPP(U_6784,hAPP(c_Product__Type_Ofst(U_6779,U_6781),U_6783))
        | hAPP(c_Product__Type_Oapfst(U_6779,U_6780,U_6781,U_6782),U_6783) != hAPP(c_Product__Type_Oapfst(U_6779,U_6780,U_6781,U_6784),U_6783) ) ),
    inference(variable_rename,[status(thm)],[f_1976_1]) ).

fof(f_1976_3,plain,
    ( ! [U_6796,U_6794,U_6792,U_6790,U_6788,U_6786] :
        ( hAPP(c_Product__Type_Oapfst(U_6786,U_6788,U_6790,U_6792),U_6794) = hAPP(c_Product__Type_Oapfst(U_6786,U_6788,U_6790,U_6796),U_6794)
        | hAPP(U_6792,hAPP(c_Product__Type_Ofst(U_6786,U_6790),U_6794)) != hAPP(U_6796,hAPP(c_Product__Type_Ofst(U_6786,U_6790),U_6794)) )
    & ! [U_6795,U_6793,U_6791,U_6789,U_6787,U_6785] :
        ( hAPP(U_6791,hAPP(c_Product__Type_Ofst(U_6785,U_6789),U_6793)) = hAPP(U_6795,hAPP(c_Product__Type_Ofst(U_6785,U_6789),U_6793))
        | hAPP(c_Product__Type_Oapfst(U_6785,U_6787,U_6789,U_6791),U_6793) != hAPP(c_Product__Type_Oapfst(U_6785,U_6787,U_6789,U_6795),U_6793) ) ),
    inference(miniscope,[status(thm)],[f_1976_2]) ).

fof(f_1976_4,plain,
    ( ! [U_6786,U_6788,U_6790,U_6792,U_6794,U_6796] :
        ( hAPP(c_Product__Type_Oapfst(U_6786,U_6788,U_6790,U_6792),U_6794) = hAPP(c_Product__Type_Oapfst(U_6786,U_6788,U_6790,U_6796),U_6794)
        | hAPP(U_6792,hAPP(c_Product__Type_Ofst(U_6786,U_6790),U_6794)) != hAPP(U_6796,hAPP(c_Product__Type_Ofst(U_6786,U_6790),U_6794)) )
    & ! [U_6791,U_6785,U_6787,U_6789,U_6795,U_6793] :
        ( hAPP(U_6791,hAPP(c_Product__Type_Ofst(U_6785,U_6789),U_6793)) = hAPP(U_6795,hAPP(c_Product__Type_Ofst(U_6785,U_6789),U_6793))
        | hAPP(c_Product__Type_Oapfst(U_6785,U_6787,U_6789,U_6791),U_6793) != hAPP(c_Product__Type_Oapfst(U_6785,U_6787,U_6789,U_6795),U_6793) ) ),
    inference(definitional_conversion,[status(esa)],[f_1976_3]) ).

cnf(f_1976_5,plain,
    ( hAPP(U_6791,hAPP(c_Product__Type_Ofst(U_6785,U_6789),U_6793)) = hAPP(U_6795,hAPP(c_Product__Type_Ofst(U_6785,U_6789),U_6793))
    | hAPP(c_Product__Type_Oapfst(U_6785,U_6787,U_6789,U_6791),U_6793) != hAPP(c_Product__Type_Oapfst(U_6785,U_6787,U_6789,U_6795),U_6793) ),
    inference(clausify,[status(thm)],[f_1976_4]) ).

cnf(f_1976_6,plain,
    ( hAPP(c_Product__Type_Oapfst(U_6786,U_6788,U_6790,U_6792),U_6794) = hAPP(c_Product__Type_Oapfst(U_6786,U_6788,U_6790,U_6796),U_6794)
    | hAPP(U_6792,hAPP(c_Product__Type_Ofst(U_6786,U_6790),U_6794)) != hAPP(U_6796,hAPP(c_Product__Type_Ofst(U_6786,U_6790),U_6794)) ),
    inference(clausify,[status(thm)],[f_1976_4]) ).

fof(f_1977_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_1977_2,plain,
    ! [U_6801,U_6800,U_6799,U_6798,U_6797] : hAPP(c_Product__Type_Ofst(U_6797,U_6798),hAPP(c_Product__Type_Oapfst(U_6799,U_6797,U_6798,U_6800),U_6801)) = hAPP(U_6800,hAPP(c_Product__Type_Ofst(U_6799,U_6798),U_6801)),
    inference(variable_rename,[status(thm)],[f_1977_1]) ).

fof(f_1977_3,plain,
    ! [U_6798,U_6797,U_6799,U_6800,U_6801] : hAPP(c_Product__Type_Ofst(U_6797,U_6798),hAPP(c_Product__Type_Oapfst(U_6799,U_6797,U_6798,U_6800),U_6801)) = hAPP(U_6800,hAPP(c_Product__Type_Ofst(U_6799,U_6798),U_6801)),
    inference(definitional_conversion,[status(esa)],[f_1977_2]) ).

cnf(f_1977_4,plain,
    hAPP(c_Product__Type_Ofst(U_6797,U_6798),hAPP(c_Product__Type_Oapfst(U_6799,U_6797,U_6798,U_6800),U_6801)) = hAPP(U_6800,hAPP(c_Product__Type_Ofst(U_6799,U_6798),U_6801)),
    inference(clausify,[status(thm)],[f_1977_3]) ).

fof(f_1978_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_1978_2,plain,
    ! [U_6806,U_6805,U_6804,U_6803,U_6802] : hAPP(c_Product__Type_Osnd(U_6802,U_6803),hAPP(c_Product__Type_Oapfst(U_6804,U_6802,U_6803,U_6805),U_6806)) = hAPP(c_Product__Type_Osnd(U_6804,U_6803),U_6806),
    inference(variable_rename,[status(thm)],[f_1978_1]) ).

fof(f_1978_3,plain,
    ! [U_6802,U_6803,U_6804,U_6805,U_6806] : hAPP(c_Product__Type_Osnd(U_6802,U_6803),hAPP(c_Product__Type_Oapfst(U_6804,U_6802,U_6803,U_6805),U_6806)) = hAPP(c_Product__Type_Osnd(U_6804,U_6803),U_6806),
    inference(definitional_conversion,[status(esa)],[f_1978_2]) ).

cnf(f_1978_4,plain,
    hAPP(c_Product__Type_Osnd(U_6802,U_6803),hAPP(c_Product__Type_Oapfst(U_6804,U_6802,U_6803,U_6805),U_6806)) = hAPP(c_Product__Type_Osnd(U_6804,U_6803),U_6806),
    inference(clausify,[status(thm)],[f_1978_3]) ).

fof(f_1979_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_1979_2,plain,
    ! [U_6809,U_6808,U_6807] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6807),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6808)),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6809)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6808)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6807),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6808)),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6809))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6807),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6808)),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6809)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6809)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6807),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6808)),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6809))) ) )
      | ~ class_Orderings_Oord(U_6807)
      | ~ class_Int_Onumber(U_6807) ),
    inference(variable_rename,[status(thm)],[f_1979_1]) ).

fof(f_1979_3,plain,
    ( ! [U_6807,U_6808,U_6809] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6807),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6808)),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6809)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6808)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6807),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6808)),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6809)))
        | ~ sP624(U_6807,U_6808,U_6809) )
    & ! [U_6807,U_6808,U_6809] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6807),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6808)),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6809)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6809)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6807),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6808)),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6809)))
        | ~ sP624(U_6807,U_6808,U_6809) )
    & ! [U_6807,U_6808,U_6809] :
        ( sP624(U_6807,U_6808,U_6809)
        | ~ class_Orderings_Oord(U_6807)
        | ~ class_Int_Onumber(U_6807) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP624])],[f_1979_2]) ).

cnf(f_1979_4,plain,
    ( sP624(U_6807,U_6808,U_6809)
    | ~ class_Orderings_Oord(U_6807)
    | ~ class_Int_Onumber(U_6807) ),
    inference(clausify,[status(thm)],[f_1979_3]) ).

cnf(f_1979_5,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6807),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6808)),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6809)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6809)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6807),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6808)),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6809)))
    | ~ sP624(U_6807,U_6808,U_6809) ),
    inference(clausify,[status(thm)],[f_1979_3]) ).

cnf(f_1979_6,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6807),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6808)),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6809)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6808)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6807),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6808)),hAPP(c_Int_Onumber__class_Onumber__of(U_6807),U_6809)))
    | ~ sP624(U_6807,U_6808,U_6809) ),
    inference(clausify,[status(thm)],[f_1979_3]) ).

fof(f_1980_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_1980_2,plain,
    ! [U_6813,U_6812,U_6811,U_6810] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6810),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6810),U_6811),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6810),U_6812),U_6813))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6810),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6810),U_6811),U_6812)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6810),U_6811),U_6813))))
      | ~ class_Orderings_Olinorder(U_6810) ),
    inference(variable_rename,[status(thm)],[f_1980_1]) ).

fof(f_1980_3,plain,
    ! [U_6811,U_6810,U_6812,U_6813] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6810),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6810),U_6811),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6810),U_6812),U_6813))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6810),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6810),U_6811),U_6812)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6810),U_6811),U_6813))))
      | ~ class_Orderings_Olinorder(U_6810) ),
    inference(definitional_conversion,[status(esa)],[f_1980_2]) ).

cnf(f_1980_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6810),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6810),U_6811),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6810),U_6812),U_6813))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6810),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6810),U_6811),U_6812)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6810),U_6811),U_6813))))
    | ~ class_Orderings_Olinorder(U_6810) ),
    inference(clausify,[status(thm)],[f_1980_3]) ).

fof(f_1981_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_1981_2,plain,
    ! [U_6817,U_6816,U_6815,U_6814] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6814),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6814),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6814),U_6815),U_6816)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6814),U_6815),U_6817))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6814),U_6815),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6814),U_6816),U_6817))))
      | ~ class_Orderings_Olinorder(U_6814) ),
    inference(variable_rename,[status(thm)],[f_1981_1]) ).

fof(f_1981_3,plain,
    ! [U_6814,U_6815,U_6816,U_6817] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6814),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6814),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6814),U_6815),U_6816)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6814),U_6815),U_6817))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6814),U_6815),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6814),U_6816),U_6817))))
      | ~ class_Orderings_Olinorder(U_6814) ),
    inference(definitional_conversion,[status(esa)],[f_1981_2]) ).

cnf(f_1981_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6814),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6814),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6814),U_6815),U_6816)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6814),U_6815),U_6817))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6814),U_6815),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6814),U_6816),U_6817))))
    | ~ class_Orderings_Olinorder(U_6814) ),
    inference(clausify,[status(thm)],[f_1981_3]) ).

fof(f_1982_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_1982_2,plain,
    ! [U_6820,U_6819,U_6818] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6818),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6818),U_6819),U_6820)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6818),hAPP(c_Groups_Ouminus__class_Ouminus(U_6818),U_6819)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6818),U_6820))
      | ~ class_Groups_Olinordered__ab__group__add(U_6818) ),
    inference(variable_rename,[status(thm)],[f_1982_1]) ).

fof(f_1982_3,plain,
    ! [U_6818,U_6819,U_6820] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6818),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6818),U_6819),U_6820)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6818),hAPP(c_Groups_Ouminus__class_Ouminus(U_6818),U_6819)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6818),U_6820))
      | ~ class_Groups_Olinordered__ab__group__add(U_6818) ),
    inference(definitional_conversion,[status(esa)],[f_1982_2]) ).

cnf(f_1982_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6818),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6818),U_6819),U_6820)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6818),hAPP(c_Groups_Ouminus__class_Ouminus(U_6818),U_6819)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6818),U_6820))
    | ~ class_Groups_Olinordered__ab__group__add(U_6818) ),
    inference(clausify,[status(thm)],[f_1982_3]) ).

fof(f_1983_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_1983_2,plain,
    ! [U_6823,U_6822,U_6821] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6821),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6821),U_6822),U_6823)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6821),hAPP(c_Groups_Ouminus__class_Ouminus(U_6821),U_6822)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6821),U_6823))
      | ~ class_Groups_Olinordered__ab__group__add(U_6821) ),
    inference(variable_rename,[status(thm)],[f_1983_1]) ).

fof(f_1983_3,plain,
    ! [U_6821,U_6822,U_6823] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6821),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6821),U_6822),U_6823)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6821),hAPP(c_Groups_Ouminus__class_Ouminus(U_6821),U_6822)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6821),U_6823))
      | ~ class_Groups_Olinordered__ab__group__add(U_6821) ),
    inference(definitional_conversion,[status(esa)],[f_1983_2]) ).

cnf(f_1983_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6821),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6821),U_6822),U_6823)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6821),hAPP(c_Groups_Ouminus__class_Ouminus(U_6821),U_6822)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6821),U_6823))
    | ~ class_Groups_Olinordered__ab__group__add(U_6821) ),
    inference(clausify,[status(thm)],[f_1983_3]) ).

fof(f_1984_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_1984_2,plain,
    ! [U_6825,U_6824] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6824),U_6825)),U_6825) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6824),U_6825),
    inference(variable_rename,[status(thm)],[f_1984_1]) ).

fof(f_1984_3,plain,
    ! [U_6824,U_6825] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6824),U_6825)),U_6825) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6824),U_6825),
    inference(definitional_conversion,[status(esa)],[f_1984_2]) ).

cnf(f_1984_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6824),U_6825)),U_6825) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6824),U_6825),
    inference(clausify,[status(thm)],[f_1984_3]) ).

fof(f_1985_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_1985_2,plain,
    ! [U_6832,U_6831,U_6830,U_6829,U_6828,U_6827,U_6826] : hAPP(c_Product__Type_Oapsnd(U_6826,U_6827,U_6828,U_6829),hAPP(c_Product__Type_Oapfst(U_6830,U_6828,U_6826,U_6831),U_6832)) = hAPP(c_Product__Type_Oapfst(U_6830,U_6828,U_6827,U_6831),hAPP(c_Product__Type_Oapsnd(U_6826,U_6827,U_6830,U_6829),U_6832)),
    inference(variable_rename,[status(thm)],[f_1985_1]) ).

fof(f_1985_3,plain,
    ! [U_6826,U_6827,U_6828,U_6829,U_6830,U_6831,U_6832] : hAPP(c_Product__Type_Oapsnd(U_6826,U_6827,U_6828,U_6829),hAPP(c_Product__Type_Oapfst(U_6830,U_6828,U_6826,U_6831),U_6832)) = hAPP(c_Product__Type_Oapfst(U_6830,U_6828,U_6827,U_6831),hAPP(c_Product__Type_Oapsnd(U_6826,U_6827,U_6830,U_6829),U_6832)),
    inference(definitional_conversion,[status(esa)],[f_1985_2]) ).

cnf(f_1985_4,plain,
    hAPP(c_Product__Type_Oapsnd(U_6826,U_6827,U_6828,U_6829),hAPP(c_Product__Type_Oapfst(U_6830,U_6828,U_6826,U_6831),U_6832)) = hAPP(c_Product__Type_Oapfst(U_6830,U_6828,U_6827,U_6831),hAPP(c_Product__Type_Oapsnd(U_6826,U_6827,U_6830,U_6829),U_6832)),
    inference(clausify,[status(thm)],[f_1985_3]) ).

fof(f_1986_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_1986_2,plain,
    ! [U_6834,U_6833] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6833)),U_6834) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6833),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_6833)),U_6834),
    inference(variable_rename,[status(thm)],[f_1986_1]) ).

fof(f_1986_3,plain,
    ! [U_6834,U_6833] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6833)),U_6834) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6833),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_6833)),U_6834),
    inference(definitional_conversion,[status(esa)],[f_1986_2]) ).

cnf(f_1986_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6833)),U_6834) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6833),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_6833)),U_6834),
    inference(clausify,[status(thm)],[f_1986_3]) ).

fof(f_1987_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_1987_2,plain,
    ! [U_6836,U_6835] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6835),hAPP(c_Nat_OSuc,U_6836)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6836),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_6836)),U_6835),
    inference(variable_rename,[status(thm)],[f_1987_1]) ).

fof(f_1987_3,plain,
    ! [U_6835,U_6836] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6835),hAPP(c_Nat_OSuc,U_6836)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6836),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_6836)),U_6835),
    inference(definitional_conversion,[status(esa)],[f_1987_2]) ).

cnf(f_1987_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6835),hAPP(c_Nat_OSuc,U_6836)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6836),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_6836)),U_6835),
    inference(clausify,[status(thm)],[f_1987_3]) ).

fof(f_1988_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_1988_2,plain,
    ! [U_6843,U_6842,U_6841,U_6840,U_6839,U_6838,U_6837] : hAPP(c_Product__Type_Oapfst(U_6837,U_6838,U_6839,U_6840),hAPP(c_Product__Type_Oapsnd(U_6841,U_6839,U_6837,U_6842),U_6843)) = hAPP(hAPP(c_Product__Type_OPair(U_6838,U_6839),hAPP(U_6840,hAPP(c_Product__Type_Ofst(U_6837,U_6841),U_6843))),hAPP(U_6842,hAPP(c_Product__Type_Osnd(U_6837,U_6841),U_6843))),
    inference(variable_rename,[status(thm)],[f_1988_1]) ).

fof(f_1988_3,plain,
    ! [U_6837,U_6838,U_6839,U_6840,U_6841,U_6842,U_6843] : hAPP(c_Product__Type_Oapfst(U_6837,U_6838,U_6839,U_6840),hAPP(c_Product__Type_Oapsnd(U_6841,U_6839,U_6837,U_6842),U_6843)) = hAPP(hAPP(c_Product__Type_OPair(U_6838,U_6839),hAPP(U_6840,hAPP(c_Product__Type_Ofst(U_6837,U_6841),U_6843))),hAPP(U_6842,hAPP(c_Product__Type_Osnd(U_6837,U_6841),U_6843))),
    inference(definitional_conversion,[status(esa)],[f_1988_2]) ).

cnf(f_1988_4,plain,
    hAPP(c_Product__Type_Oapfst(U_6837,U_6838,U_6839,U_6840),hAPP(c_Product__Type_Oapsnd(U_6841,U_6839,U_6837,U_6842),U_6843)) = hAPP(hAPP(c_Product__Type_OPair(U_6838,U_6839),hAPP(U_6840,hAPP(c_Product__Type_Ofst(U_6837,U_6841),U_6843))),hAPP(U_6842,hAPP(c_Product__Type_Osnd(U_6837,U_6841),U_6843))),
    inference(clausify,[status(thm)],[f_1988_3]) ).

fof(f_1989_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_1989_2,plain,
    ! [U_6844] :
      ( c_Orderings_Oord_Omin(U_6844,hAPP(c_COMBC(U_6844,U_6844,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6844))) = c_Orderings_Oord__class_Omax(U_6844)
      | ~ class_Orderings_Olinorder(U_6844) ),
    inference(variable_rename,[status(thm)],[f_1989_1]) ).

fof(f_1989_3,plain,
    ! [U_6844] :
      ( c_Orderings_Oord_Omin(U_6844,hAPP(c_COMBC(U_6844,U_6844,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6844))) = c_Orderings_Oord__class_Omax(U_6844)
      | ~ class_Orderings_Olinorder(U_6844) ),
    inference(definitional_conversion,[status(esa)],[f_1989_2]) ).

cnf(f_1989_4,plain,
    ( c_Orderings_Oord_Omin(U_6844,hAPP(c_COMBC(U_6844,U_6844,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6844))) = c_Orderings_Oord__class_Omax(U_6844)
    | ~ class_Orderings_Olinorder(U_6844) ),
    inference(clausify,[status(thm)],[f_1989_3]) ).

fof(f_1990_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_1990_2,plain,
    ! [U_6845] :
      ( c_Orderings_Oord__class_Omax(U_6845) = c_Orderings_Oord_Omax(U_6845,c_Orderings_Oord__class_Oless__eq(U_6845))
      | ~ class_Orderings_Oord(U_6845) ),
    inference(variable_rename,[status(thm)],[f_1990_1]) ).

fof(f_1990_3,plain,
    ! [U_6845] :
      ( c_Orderings_Oord__class_Omax(U_6845) = c_Orderings_Oord_Omax(U_6845,c_Orderings_Oord__class_Oless__eq(U_6845))
      | ~ class_Orderings_Oord(U_6845) ),
    inference(definitional_conversion,[status(esa)],[f_1990_2]) ).

cnf(f_1990_4,plain,
    ( c_Orderings_Oord__class_Omax(U_6845) = c_Orderings_Oord_Omax(U_6845,c_Orderings_Oord__class_Oless__eq(U_6845))
    | ~ class_Orderings_Oord(U_6845) ),
    inference(clausify,[status(thm)],[f_1990_3]) ).

fof(f_1991_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_1991_2,plain,
    ! [U_6846] :
      ( 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_6846)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_6846)))
      | U_6846 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[f_1991_1]) ).

fof(f_1991_3,plain,
    ! [U_6846] :
      ( 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_6846)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_6846)))
      | U_6846 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(definitional_conversion,[status(esa)],[f_1991_2]) ).

cnf(f_1991_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_6846)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_6846)))
    | U_6846 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1991_3]) ).

fof(f_1992_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_1992_2,plain,
    ! [U_6847] : c_Nitpick_Ozero__frac(U_6847) = c_Nitpick_OAbs__Frac(U_6847,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_1992_1]) ).

fof(f_1992_3,plain,
    ! [U_6847] : c_Nitpick_Ozero__frac(U_6847) = c_Nitpick_OAbs__Frac(U_6847,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_1992_2]) ).

cnf(f_1992_4,plain,
    c_Nitpick_Ozero__frac(U_6847) = c_Nitpick_OAbs__Frac(U_6847,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_1992_3]) ).

fof(f_1993_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_1993_2,plain,
    ! [U_6851,U_6850,U_6849,U_6848] : c_New__Random__Sequence_Opos__not__random__dseq(U_6848,U_6849,U_6850,U_6851) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_6848,U_6849),U_6850),U_6851)),
    inference(variable_rename,[status(thm)],[f_1993_1]) ).

fof(f_1993_3,plain,
    ! [U_6850,U_6848,U_6849,U_6851] : c_New__Random__Sequence_Opos__not__random__dseq(U_6848,U_6849,U_6850,U_6851) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_6848,U_6849),U_6850),U_6851)),
    inference(definitional_conversion,[status(esa)],[f_1993_2]) ).

cnf(f_1993_4,plain,
    c_New__Random__Sequence_Opos__not__random__dseq(U_6848,U_6849,U_6850,U_6851) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_6848,U_6849),U_6850),U_6851)),
    inference(clausify,[status(thm)],[f_1993_3]) ).

fof(f_1994_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_1994_2,plain,
    ! [U_6853,U_6852] :
      ( ( hAPP(c_Code__Numeral_Onat__of,U_6852) = hAPP(c_Code__Numeral_Onat__of,U_6853)
        | U_6852 != U_6853 )
      & ( U_6852 = U_6853
        | hAPP(c_Code__Numeral_Onat__of,U_6852) != hAPP(c_Code__Numeral_Onat__of,U_6853) ) ),
    inference(variable_rename,[status(thm)],[f_1994_1]) ).

fof(f_1994_3,plain,
    ( ! [U_6857,U_6855] :
        ( hAPP(c_Code__Numeral_Onat__of,U_6855) = hAPP(c_Code__Numeral_Onat__of,U_6857)
        | U_6855 != U_6857 )
    & ! [U_6856,U_6854] :
        ( U_6854 = U_6856
        | hAPP(c_Code__Numeral_Onat__of,U_6854) != hAPP(c_Code__Numeral_Onat__of,U_6856) ) ),
    inference(miniscope,[status(thm)],[f_1994_2]) ).

fof(f_1994_4,plain,
    ( ! [U_6855,U_6857] :
        ( hAPP(c_Code__Numeral_Onat__of,U_6855) = hAPP(c_Code__Numeral_Onat__of,U_6857)
        | U_6855 != U_6857 )
    & ! [U_6856,U_6854] :
        ( U_6854 = U_6856
        | hAPP(c_Code__Numeral_Onat__of,U_6854) != hAPP(c_Code__Numeral_Onat__of,U_6856) ) ),
    inference(definitional_conversion,[status(esa)],[f_1994_3]) ).

cnf(f_1994_5,plain,
    ( U_6854 = U_6856
    | hAPP(c_Code__Numeral_Onat__of,U_6854) != hAPP(c_Code__Numeral_Onat__of,U_6856) ),
    inference(clausify,[status(thm)],[f_1994_4]) ).

cnf(f_1994_6,plain,
    ( hAPP(c_Code__Numeral_Onat__of,U_6855) = hAPP(c_Code__Numeral_Onat__of,U_6857)
    | U_6855 != U_6857 ),
    inference(clausify,[status(thm)],[f_1994_4]) ).

fof(f_1995_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_1995_2,plain,
    ! [U_6859,U_6858] :
      ( ( hAPP(c_Code__Numeral_Onat__of,U_6858) = hAPP(c_Code__Numeral_Onat__of,U_6859)
        | U_6858 != U_6859 )
      & ( U_6858 = U_6859
        | hAPP(c_Code__Numeral_Onat__of,U_6858) != hAPP(c_Code__Numeral_Onat__of,U_6859) ) ),
    inference(variable_rename,[status(thm)],[f_1995_1]) ).

fof(f_1995_3,plain,
    ( ! [U_6863,U_6861] :
        ( hAPP(c_Code__Numeral_Onat__of,U_6861) = hAPP(c_Code__Numeral_Onat__of,U_6863)
        | U_6861 != U_6863 )
    & ! [U_6862,U_6860] :
        ( U_6860 = U_6862
        | hAPP(c_Code__Numeral_Onat__of,U_6860) != hAPP(c_Code__Numeral_Onat__of,U_6862) ) ),
    inference(miniscope,[status(thm)],[f_1995_2]) ).

fof(f_1995_4,plain,
    ( ! [U_6861,U_6863] :
        ( hAPP(c_Code__Numeral_Onat__of,U_6861) = hAPP(c_Code__Numeral_Onat__of,U_6863)
        | U_6861 != U_6863 )
    & ! [U_6862,U_6860] :
        ( U_6860 = U_6862
        | hAPP(c_Code__Numeral_Onat__of,U_6860) != hAPP(c_Code__Numeral_Onat__of,U_6862) ) ),
    inference(definitional_conversion,[status(esa)],[f_1995_3]) ).

cnf(f_1995_5,plain,
    ( U_6860 = U_6862
    | hAPP(c_Code__Numeral_Onat__of,U_6860) != hAPP(c_Code__Numeral_Onat__of,U_6862) ),
    inference(clausify,[status(thm)],[f_1995_4]) ).

cnf(f_1995_6,plain,
    ( hAPP(c_Code__Numeral_Onat__of,U_6861) = hAPP(c_Code__Numeral_Onat__of,U_6863)
    | U_6861 != U_6863 ),
    inference(clausify,[status(thm)],[f_1995_4]) ).

fof(f_1996_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_1996_2,plain,
    ! [U_6864] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_6864)) = U_6864,
    inference(variable_rename,[status(thm)],[f_1996_1]) ).

fof(f_1996_3,plain,
    ! [U_6864] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_6864)) = U_6864,
    inference(definitional_conversion,[status(esa)],[f_1996_2]) ).

cnf(f_1996_4,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_6864)) = U_6864,
    inference(clausify,[status(thm)],[f_1996_3]) ).

fof(f_1997_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_1997_2,plain,
    ! [U_6865] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_6865)) = U_6865,
    inference(variable_rename,[status(thm)],[f_1997_1]) ).

fof(f_1997_3,plain,
    ! [U_6865] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_6865)) = U_6865,
    inference(definitional_conversion,[status(esa)],[f_1997_2]) ).

cnf(f_1997_4,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_6865)) = U_6865,
    inference(clausify,[status(thm)],[f_1997_3]) ).

fof(f_1998_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_1998_2,plain,
    ! [U_6866] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_6866)) = U_6866,
    inference(variable_rename,[status(thm)],[f_1998_1]) ).

fof(f_1998_3,plain,
    ! [U_6866] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_6866)) = U_6866,
    inference(definitional_conversion,[status(esa)],[f_1998_2]) ).

cnf(f_1998_4,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_6866)) = U_6866,
    inference(clausify,[status(thm)],[f_1998_3]) ).

fof(f_1999_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_1999_2,plain,
    ! [U_6868,U_6867] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6867),U_6868))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6867)),hAPP(c_Code__Numeral_Onat__of,U_6868))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6867)),hAPP(c_Code__Numeral_Onat__of,U_6868)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6867),U_6868)) ) ),
    inference(variable_rename,[status(thm)],[f_1999_1]) ).

fof(f_1999_3,plain,
    ( ! [U_6872,U_6870] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6870),U_6872))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6870)),hAPP(c_Code__Numeral_Onat__of,U_6872))) )
    & ! [U_6871,U_6869] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6869)),hAPP(c_Code__Numeral_Onat__of,U_6871)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6869),U_6871)) ) ),
    inference(miniscope,[status(thm)],[f_1999_2]) ).

fof(f_1999_4,plain,
    ( ! [U_6870,U_6872] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6870),U_6872))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6870)),hAPP(c_Code__Numeral_Onat__of,U_6872))) )
    & ! [U_6871,U_6869] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6869)),hAPP(c_Code__Numeral_Onat__of,U_6871)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6869),U_6871)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1999_3]) ).

cnf(f_1999_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6869)),hAPP(c_Code__Numeral_Onat__of,U_6871)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6869),U_6871)) ),
    inference(clausify,[status(thm)],[f_1999_4]) ).

cnf(f_1999_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6870),U_6872))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6870)),hAPP(c_Code__Numeral_Onat__of,U_6872))) ),
    inference(clausify,[status(thm)],[f_1999_4]) ).

fof(f_2000_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_2000_2,plain,
    ! [U_6873] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_6873)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6873),
    inference(variable_rename,[status(thm)],[f_2000_1]) ).

fof(f_2000_3,plain,
    ! [U_6873] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_6873)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6873),
    inference(definitional_conversion,[status(esa)],[f_2000_2]) ).

cnf(f_2000_4,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_6873)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6873),
    inference(clausify,[status(thm)],[f_2000_3]) ).

fof(f_2001_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_2001_2,plain,
    ! [U_6875,U_6874] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6874),U_6875))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6874)),hAPP(c_Code__Numeral_Onat__of,U_6875))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6874)),hAPP(c_Code__Numeral_Onat__of,U_6875)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6874),U_6875)) ) ),
    inference(variable_rename,[status(thm)],[f_2001_1]) ).

fof(f_2001_3,plain,
    ( ! [U_6879,U_6877] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6877),U_6879))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6877)),hAPP(c_Code__Numeral_Onat__of,U_6879))) )
    & ! [U_6878,U_6876] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6876)),hAPP(c_Code__Numeral_Onat__of,U_6878)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6876),U_6878)) ) ),
    inference(miniscope,[status(thm)],[f_2001_2]) ).

fof(f_2001_4,plain,
    ( ! [U_6877,U_6879] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6877),U_6879))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6877)),hAPP(c_Code__Numeral_Onat__of,U_6879))) )
    & ! [U_6878,U_6876] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6876)),hAPP(c_Code__Numeral_Onat__of,U_6878)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6876),U_6878)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2001_3]) ).

cnf(f_2001_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6876)),hAPP(c_Code__Numeral_Onat__of,U_6878)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6876),U_6878)) ),
    inference(clausify,[status(thm)],[f_2001_4]) ).

cnf(f_2001_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6877),U_6879))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6877)),hAPP(c_Code__Numeral_Onat__of,U_6879))) ),
    inference(clausify,[status(thm)],[f_2001_4]) ).

fof(f_2002_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_2002_2,plain,
    ! [U_6880] : hAPP(c_Code__Numeral_Onat__of,U_6880) = c_Code__Numeral_Onat__of__aux(U_6880,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_2002_1]) ).

fof(f_2002_3,plain,
    ! [U_6880] : hAPP(c_Code__Numeral_Onat__of,U_6880) = c_Code__Numeral_Onat__of__aux(U_6880,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_2002_2]) ).

cnf(f_2002_4,plain,
    hAPP(c_Code__Numeral_Onat__of,U_6880) = c_Code__Numeral_Onat__of__aux(U_6880,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_2002_3]) ).

fof(f_2003_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_2003_2,plain,
    ! [U_6882,U_6881] : c_Code__Numeral_Onat__of__aux(U_6881,U_6882) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6881)),U_6882),
    inference(variable_rename,[status(thm)],[f_2003_1]) ).

fof(f_2003_3,plain,
    ! [U_6882,U_6881] : c_Code__Numeral_Onat__of__aux(U_6881,U_6882) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6881)),U_6882),
    inference(definitional_conversion,[status(esa)],[f_2003_2]) ).

cnf(f_2003_4,plain,
    c_Code__Numeral_Onat__of__aux(U_6881,U_6882) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6881)),U_6882),
    inference(clausify,[status(thm)],[f_2003_3]) ).

fof(f_2004_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_2004_2,plain,
    ! [U_6884,U_6883] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6883),U_6884),U_6884) = U_6884
      | ~ class_Orderings_Olinorder(U_6883) ),
    inference(variable_rename,[status(thm)],[f_2004_1]) ).

fof(f_2004_3,plain,
    ! [U_6883,U_6884] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6883),U_6884),U_6884) = U_6884
      | ~ class_Orderings_Olinorder(U_6883) ),
    inference(definitional_conversion,[status(esa)],[f_2004_2]) ).

cnf(f_2004_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6883),U_6884),U_6884) = U_6884
    | ~ class_Orderings_Olinorder(U_6883) ),
    inference(clausify,[status(thm)],[f_2004_3]) ).

fof(f_2005_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_2005_2,plain,
    ! [U_6886,U_6885] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6885),U_6886),U_6886) = U_6886
      | ~ class_Orderings_Olinorder(U_6885) ),
    inference(variable_rename,[status(thm)],[f_2005_1]) ).

fof(f_2005_3,plain,
    ! [U_6885,U_6886] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6885),U_6886),U_6886) = U_6886
      | ~ class_Orderings_Olinorder(U_6885) ),
    inference(definitional_conversion,[status(esa)],[f_2005_2]) ).

cnf(f_2005_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6885),U_6886),U_6886) = U_6886
    | ~ class_Orderings_Olinorder(U_6885) ),
    inference(clausify,[status(thm)],[f_2005_3]) ).

fof(f_2006_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_2006_2,plain,
    ! [U_6887] :
      ( c_Orderings_Oord_Omax(U_6887,hAPP(c_COMBC(U_6887,U_6887,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6887))) = c_Orderings_Oord__class_Omin(U_6887)
      | ~ class_Orderings_Olinorder(U_6887) ),
    inference(variable_rename,[status(thm)],[f_2006_1]) ).

fof(f_2006_3,plain,
    ! [U_6887] :
      ( c_Orderings_Oord_Omax(U_6887,hAPP(c_COMBC(U_6887,U_6887,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6887))) = c_Orderings_Oord__class_Omin(U_6887)
      | ~ class_Orderings_Olinorder(U_6887) ),
    inference(definitional_conversion,[status(esa)],[f_2006_2]) ).

cnf(f_2006_4,plain,
    ( c_Orderings_Oord_Omax(U_6887,hAPP(c_COMBC(U_6887,U_6887,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6887))) = c_Orderings_Oord__class_Omin(U_6887)
    | ~ class_Orderings_Olinorder(U_6887) ),
    inference(clausify,[status(thm)],[f_2006_3]) ).

fof(f_2007_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_2007_2,plain,
    ! [U_6888] : c_Code__Numeral_OSuc__code__numeral(U_6888) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_6888))),
    inference(variable_rename,[status(thm)],[f_2007_1]) ).

fof(f_2007_3,plain,
    ! [U_6888] : c_Code__Numeral_OSuc__code__numeral(U_6888) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_6888))),
    inference(definitional_conversion,[status(esa)],[f_2007_2]) ).

cnf(f_2007_4,plain,
    c_Code__Numeral_OSuc__code__numeral(U_6888) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_6888))),
    inference(clausify,[status(thm)],[f_2007_3]) ).

fof(f_2008_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_2008_2,plain,
    ! [U_6890,U_6889] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6889),U_6890) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6889)),hAPP(c_Code__Numeral_Onat__of,U_6890))),
    inference(variable_rename,[status(thm)],[f_2008_1]) ).

fof(f_2008_3,plain,
    ! [U_6889,U_6890] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6889),U_6890) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6889)),hAPP(c_Code__Numeral_Onat__of,U_6890))),
    inference(definitional_conversion,[status(esa)],[f_2008_2]) ).

cnf(f_2008_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6889),U_6890) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6889)),hAPP(c_Code__Numeral_Onat__of,U_6890))),
    inference(clausify,[status(thm)],[f_2008_3]) ).

fof(f_2009_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_2009_2,plain,
    ! [U_6892,U_6891] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_6891),U_6892) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6891)),hAPP(c_Code__Numeral_Onat__of,U_6892))),
    inference(variable_rename,[status(thm)],[f_2009_1]) ).

fof(f_2009_3,plain,
    ! [U_6891,U_6892] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_6891),U_6892) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6891)),hAPP(c_Code__Numeral_Onat__of,U_6892))),
    inference(definitional_conversion,[status(esa)],[f_2009_2]) ).

cnf(f_2009_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_6891),U_6892) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6891)),hAPP(c_Code__Numeral_Onat__of,U_6892))),
    inference(clausify,[status(thm)],[f_2009_3]) ).

fof(f_2010_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_2010_2,plain,
    ! [U_6894,U_6893] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_6893),U_6894) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6893)),hAPP(c_Code__Numeral_Onat__of,U_6894))),
    inference(variable_rename,[status(thm)],[f_2010_1]) ).

fof(f_2010_3,plain,
    ! [U_6893,U_6894] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_6893),U_6894) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6893)),hAPP(c_Code__Numeral_Onat__of,U_6894))),
    inference(definitional_conversion,[status(esa)],[f_2010_2]) ).

cnf(f_2010_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_6893),U_6894) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6893)),hAPP(c_Code__Numeral_Onat__of,U_6894))),
    inference(clausify,[status(thm)],[f_2010_3]) ).

fof(f_2011_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_2011_2,plain,
    ! [U_6896,U_6895] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_6895),U_6896) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6895)),hAPP(c_Code__Numeral_Onat__of,U_6896))),
    inference(variable_rename,[status(thm)],[f_2011_1]) ).

fof(f_2011_3,plain,
    ! [U_6895,U_6896] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_6895),U_6896) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6895)),hAPP(c_Code__Numeral_Onat__of,U_6896))),
    inference(definitional_conversion,[status(esa)],[f_2011_2]) ).

cnf(f_2011_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_6895),U_6896) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_6895)),hAPP(c_Code__Numeral_Onat__of,U_6896))),
    inference(clausify,[status(thm)],[f_2011_3]) ).

fof(f_2012_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_2012_2,plain,
    ! [U_6898,U_6897] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_6897,U_6898) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_6897),hAPP(c_Code__Numeral_Onat__of,U_6898))),
    inference(variable_rename,[status(thm)],[f_2012_1]) ).

fof(f_2012_3,plain,
    ! [U_6897,U_6898] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_6897,U_6898) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_6897),hAPP(c_Code__Numeral_Onat__of,U_6898))),
    inference(definitional_conversion,[status(esa)],[f_2012_2]) ).

cnf(f_2012_4,plain,
    c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_6897,U_6898) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_6897),hAPP(c_Code__Numeral_Onat__of,U_6898))),
    inference(clausify,[status(thm)],[f_2012_3]) ).

fof(f_2013_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_2013_2,plain,
    ! [U_6899] : c_Nitpick_Oone__frac(U_6899) = c_Nitpick_OAbs__Frac(U_6899,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_2013_1]) ).

fof(f_2013_3,plain,
    ! [U_6899] : c_Nitpick_Oone__frac(U_6899) = c_Nitpick_OAbs__Frac(U_6899,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_2013_2]) ).

cnf(f_2013_4,plain,
    c_Nitpick_Oone__frac(U_6899) = c_Nitpick_OAbs__Frac(U_6899,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_2013_3]) ).

fof(f_2014_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_2014_2,plain,
    ! [U_6901,U_6900] : c_Nitpick_Onumber__of__frac(U_6900,U_6901) = c_Nitpick_OAbs__Frac(U_6900,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6901),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_2014_1]) ).

fof(f_2014_3,plain,
    ! [U_6900,U_6901] : c_Nitpick_Onumber__of__frac(U_6900,U_6901) = c_Nitpick_OAbs__Frac(U_6900,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6901),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_2014_2]) ).

cnf(f_2014_4,plain,
    c_Nitpick_Onumber__of__frac(U_6900,U_6901) = c_Nitpick_OAbs__Frac(U_6900,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6901),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_2014_3]) ).

fof(f_2015_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_2015_2,plain,
    ! [U_6904,U_6903,U_6902] : hAPP(hAPP(c_Nitpick_Ofrac(U_6902),U_6903),U_6904) = c_Nitpick_OAbs__Frac(U_6902,c_Nitpick_Onorm__frac(U_6903,U_6904)),
    inference(variable_rename,[status(thm)],[f_2015_1]) ).

fof(f_2015_3,plain,
    ! [U_6902,U_6903,U_6904] : hAPP(hAPP(c_Nitpick_Ofrac(U_6902),U_6903),U_6904) = c_Nitpick_OAbs__Frac(U_6902,c_Nitpick_Onorm__frac(U_6903,U_6904)),
    inference(definitional_conversion,[status(esa)],[f_2015_2]) ).

cnf(f_2015_4,plain,
    hAPP(hAPP(c_Nitpick_Ofrac(U_6902),U_6903),U_6904) = c_Nitpick_OAbs__Frac(U_6902,c_Nitpick_Onorm__frac(U_6903,U_6904)),
    inference(clausify,[status(thm)],[f_2015_3]) ).

fof(f_2016_1,plain,
    ! [V_f_2,T_c,T_d,T_b] : c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,hAPP(hAPP(c_COMBB(tc_sum(T_b,T_c),T_d,T_b),V_f_2),c_Sum__Type_OInl(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_sum(T_b,T_c),T_d,T_c),V_f_2),c_Sum__Type_OInr(T_c,T_b))) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_surjective__sum]) ).

fof(f_2016_2,plain,
    ! [U_6908,U_6907,U_6906,U_6905] : c_Sum__Type_Osum_Osum__case(U_6905,U_6906,U_6907,hAPP(hAPP(c_COMBB(tc_sum(U_6905,U_6907),U_6906,U_6905),U_6908),c_Sum__Type_OInl(U_6905,U_6907)),hAPP(hAPP(c_COMBB(tc_sum(U_6905,U_6907),U_6906,U_6907),U_6908),c_Sum__Type_OInr(U_6907,U_6905))) = U_6908,
    inference(variable_rename,[status(thm)],[f_2016_1]) ).

fof(f_2016_3,plain,
    ! [U_6905,U_6906,U_6907,U_6908] : c_Sum__Type_Osum_Osum__case(U_6905,U_6906,U_6907,hAPP(hAPP(c_COMBB(tc_sum(U_6905,U_6907),U_6906,U_6905),U_6908),c_Sum__Type_OInl(U_6905,U_6907)),hAPP(hAPP(c_COMBB(tc_sum(U_6905,U_6907),U_6906,U_6907),U_6908),c_Sum__Type_OInr(U_6907,U_6905))) = U_6908,
    inference(definitional_conversion,[status(esa)],[f_2016_2]) ).

cnf(f_2016_4,plain,
    c_Sum__Type_Osum_Osum__case(U_6905,U_6906,U_6907,hAPP(hAPP(c_COMBB(tc_sum(U_6905,U_6907),U_6906,U_6905),U_6908),c_Sum__Type_OInl(U_6905,U_6907)),hAPP(hAPP(c_COMBB(tc_sum(U_6905,U_6907),U_6906,U_6907),U_6908),c_Sum__Type_OInr(U_6907,U_6905))) = U_6908,
    inference(clausify,[status(thm)],[f_2016_3]) ).

fof(f_2017_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_2017_2,plain,
    ! [U_6913,U_6912,U_6911,U_6910,U_6909] :
      ( ( hAPP(c_Random_Oiterate(U_6910,U_6911,U_6909,U_6912),U_6913) = hAPP(hAPP(c_Product__Type_Oscomp(U_6911,U_6910,U_6911,tc_prod(U_6910,U_6911)),hAPP(U_6912,U_6913)),c_Random_Oiterate(U_6910,U_6911,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6909),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6912))
        | U_6909 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Random_Oiterate(U_6910,U_6911,U_6909,U_6912),U_6913) = hAPP(c_Product__Type_OPair(U_6910,U_6911),U_6913)
        | U_6909 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_2017_1]) ).

fof(f_2017_3,plain,
    ( ! [U_6923,U_6921,U_6919,U_6917,U_6915] :
        ( hAPP(c_Random_Oiterate(U_6917,U_6919,U_6915,U_6921),U_6923) = hAPP(hAPP(c_Product__Type_Oscomp(U_6919,U_6917,U_6919,tc_prod(U_6917,U_6919)),hAPP(U_6921,U_6923)),c_Random_Oiterate(U_6917,U_6919,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6915),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6921))
        | U_6915 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_6922,U_6920,U_6918,U_6916,U_6914] :
        ( hAPP(c_Random_Oiterate(U_6916,U_6918,U_6914,U_6920),U_6922) = hAPP(c_Product__Type_OPair(U_6916,U_6918),U_6922)
        | U_6914 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_2017_2]) ).

fof(f_2017_4,plain,
    ( ! [U_6915,U_6923,U_6917,U_6919,U_6921] :
        ( hAPP(c_Random_Oiterate(U_6917,U_6919,U_6915,U_6921),U_6923) = hAPP(hAPP(c_Product__Type_Oscomp(U_6919,U_6917,U_6919,tc_prod(U_6917,U_6919)),hAPP(U_6921,U_6923)),c_Random_Oiterate(U_6917,U_6919,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6915),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6921))
        | U_6915 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_6914,U_6916,U_6920,U_6918,U_6922] :
        ( hAPP(c_Random_Oiterate(U_6916,U_6918,U_6914,U_6920),U_6922) = hAPP(c_Product__Type_OPair(U_6916,U_6918),U_6922)
        | U_6914 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa)],[f_2017_3]) ).

cnf(f_2017_5,plain,
    ( hAPP(c_Random_Oiterate(U_6916,U_6918,U_6914,U_6920),U_6922) = hAPP(c_Product__Type_OPair(U_6916,U_6918),U_6922)
    | U_6914 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2017_4]) ).

cnf(f_2017_6,plain,
    ( hAPP(c_Random_Oiterate(U_6917,U_6919,U_6915,U_6921),U_6923) = hAPP(hAPP(c_Product__Type_Oscomp(U_6919,U_6917,U_6919,tc_prod(U_6917,U_6919)),hAPP(U_6921,U_6923)),c_Random_Oiterate(U_6917,U_6919,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6915),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6921))
    | U_6915 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2017_4]) ).

fof(f_2018_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_2018_2,plain,
    ! [U_6932,U_6931,U_6930,U_6929,U_6928,U_6927,U_6926,U_6925,U_6924] : hAPP(hAPP(c_Product__Type_Oscomp(U_6924,U_6925,U_6926,U_6927),hAPP(hAPP(c_Product__Type_Oscomp(U_6924,U_6928,U_6929,tc_prod(U_6925,U_6926)),U_6930),U_6931)),U_6932) = hAPP(hAPP(c_Product__Type_Oscomp(U_6924,U_6928,U_6929,U_6927),U_6930),hAPP(hAPP(c_COMBC(U_6928,tc_fun(U_6925,tc_fun(U_6926,U_6927)),tc_fun(U_6929,U_6927)),hAPP(hAPP(c_COMBB(tc_fun(U_6929,tc_prod(U_6925,U_6926)),tc_fun(tc_fun(U_6925,tc_fun(U_6926,U_6927)),tc_fun(U_6929,U_6927)),U_6928),c_Product__Type_Oscomp(U_6929,U_6925,U_6926,U_6927)),U_6931)),U_6932)),
    inference(variable_rename,[status(thm)],[f_2018_1]) ).

fof(f_2018_3,plain,
    ! [U_6929,U_6924,U_6925,U_6926,U_6927,U_6928,U_6930,U_6931,U_6932] : hAPP(hAPP(c_Product__Type_Oscomp(U_6924,U_6925,U_6926,U_6927),hAPP(hAPP(c_Product__Type_Oscomp(U_6924,U_6928,U_6929,tc_prod(U_6925,U_6926)),U_6930),U_6931)),U_6932) = hAPP(hAPP(c_Product__Type_Oscomp(U_6924,U_6928,U_6929,U_6927),U_6930),hAPP(hAPP(c_COMBC(U_6928,tc_fun(U_6925,tc_fun(U_6926,U_6927)),tc_fun(U_6929,U_6927)),hAPP(hAPP(c_COMBB(tc_fun(U_6929,tc_prod(U_6925,U_6926)),tc_fun(tc_fun(U_6925,tc_fun(U_6926,U_6927)),tc_fun(U_6929,U_6927)),U_6928),c_Product__Type_Oscomp(U_6929,U_6925,U_6926,U_6927)),U_6931)),U_6932)),
    inference(definitional_conversion,[status(esa)],[f_2018_2]) ).

cnf(f_2018_4,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_6924,U_6925,U_6926,U_6927),hAPP(hAPP(c_Product__Type_Oscomp(U_6924,U_6928,U_6929,tc_prod(U_6925,U_6926)),U_6930),U_6931)),U_6932) = hAPP(hAPP(c_Product__Type_Oscomp(U_6924,U_6928,U_6929,U_6927),U_6930),hAPP(hAPP(c_COMBC(U_6928,tc_fun(U_6925,tc_fun(U_6926,U_6927)),tc_fun(U_6929,U_6927)),hAPP(hAPP(c_COMBB(tc_fun(U_6929,tc_prod(U_6925,U_6926)),tc_fun(tc_fun(U_6925,tc_fun(U_6926,U_6927)),tc_fun(U_6929,U_6927)),U_6928),c_Product__Type_Oscomp(U_6929,U_6925,U_6926,U_6927)),U_6931)),U_6932)),
    inference(clausify,[status(thm)],[f_2018_3]) ).

fof(f_2019_1,plain,
    ! [V_x_2,V_a_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_a_2),hAPP(c_COMBK(T_b,T_d),V_a_2)),V_x_2) = V_a_2,
    inference(fof_nnf,[status(thm)],[fact_sum__case__KK]) ).

fof(f_2019_2,plain,
    ! [U_6937,U_6936,U_6935,U_6934,U_6933] : hAPP(c_Sum__Type_Osum_Osum__case(U_6933,U_6934,U_6935,hAPP(c_COMBK(U_6934,U_6933),U_6936),hAPP(c_COMBK(U_6934,U_6935),U_6936)),U_6937) = U_6936,
    inference(variable_rename,[status(thm)],[f_2019_1]) ).

fof(f_2019_3,plain,
    ! [U_6933,U_6934,U_6935,U_6936,U_6937] : hAPP(c_Sum__Type_Osum_Osum__case(U_6933,U_6934,U_6935,hAPP(c_COMBK(U_6934,U_6933),U_6936),hAPP(c_COMBK(U_6934,U_6935),U_6936)),U_6937) = U_6936,
    inference(definitional_conversion,[status(esa)],[f_2019_2]) ).

cnf(f_2019_4,plain,
    hAPP(c_Sum__Type_Osum_Osum__case(U_6933,U_6934,U_6935,hAPP(c_COMBK(U_6934,U_6933),U_6936),hAPP(c_COMBK(U_6934,U_6935),U_6936)),U_6937) = U_6936,
    inference(clausify,[status(thm)],[f_2019_3]) ).

fof(f_2020_1,plain,
    ! [V_g2_2,V_g1_2,V_f2_2,V_f1_2,T_c,T_d,T_b] :
      ( ( V_f2_2 = V_g2_2
        & V_f1_2 = V_g1_2 )
      | c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f1_2,V_f2_2) != c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_g1_2,V_g2_2) ),
    inference(fof_nnf,[status(thm)],[fact_sum__case__inject]) ).

fof(f_2020_2,plain,
    ! [U_6944,U_6943,U_6942,U_6941,U_6940,U_6939,U_6938] :
      ( ( U_6942 = U_6944
        & U_6941 = U_6943 )
      | c_Sum__Type_Osum_Osum__case(U_6938,U_6939,U_6940,U_6941,U_6942) != c_Sum__Type_Osum_Osum__case(U_6938,U_6939,U_6940,U_6943,U_6944) ),
    inference(variable_rename,[status(thm)],[f_2020_1]) ).

fof(f_2020_3,plain,
    ! [U_6944,U_6943,U_6942,U_6941] :
      ( ! [U_6940,U_6939,U_6938] : c_Sum__Type_Osum_Osum__case(U_6938,U_6939,U_6940,U_6941,U_6942) != c_Sum__Type_Osum_Osum__case(U_6938,U_6939,U_6940,U_6943,U_6944)
      | ( U_6942 = U_6944
        & U_6941 = U_6943 ) ),
    inference(miniscope,[status(thm)],[f_2020_2]) ).

fof(f_2020_4,plain,
    ( ! [U_6941,U_6942,U_6943,U_6944] :
        ( U_6942 = U_6944
        | ~ sP625(U_6941,U_6942,U_6943,U_6944) )
    & ! [U_6941,U_6942,U_6943,U_6944] :
        ( U_6941 = U_6943
        | ~ sP625(U_6941,U_6942,U_6943,U_6944) )
    & ! [U_6939,U_6938,U_6940,U_6941,U_6942,U_6943,U_6944] :
        ( c_Sum__Type_Osum_Osum__case(U_6938,U_6939,U_6940,U_6941,U_6942) != c_Sum__Type_Osum_Osum__case(U_6938,U_6939,U_6940,U_6943,U_6944)
        | sP625(U_6941,U_6942,U_6943,U_6944) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP625])],[f_2020_3]) ).

cnf(f_2020_5,plain,
    ( c_Sum__Type_Osum_Osum__case(U_6938,U_6939,U_6940,U_6941,U_6942) != c_Sum__Type_Osum_Osum__case(U_6938,U_6939,U_6940,U_6943,U_6944)
    | sP625(U_6941,U_6942,U_6943,U_6944) ),
    inference(clausify,[status(thm)],[f_2020_4]) ).

cnf(f_2020_6,plain,
    ( U_6941 = U_6943
    | ~ sP625(U_6941,U_6942,U_6943,U_6944) ),
    inference(clausify,[status(thm)],[f_2020_4]) ).

cnf(f_2020_7,plain,
    ( U_6942 = U_6944
    | ~ sP625(U_6941,U_6942,U_6943,U_6944) ),
    inference(clausify,[status(thm)],[f_2020_4]) ).

fof(f_2021_1,plain,
    ! [V_g_2,V_f_2,T_c,T_d,T_b,V_t_2,V_s_2] :
      ( hAPP(c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f_2,V_g_2),V_s_2) = hAPP(c_Sum__Type_Osum_Osum__case(T_b,T_d,T_c,V_f_2,V_g_2),V_t_2)
      | V_s_2 != V_t_2 ),
    inference(fof_nnf,[status(thm)],[fact_sum__case__weak__cong]) ).

fof(f_2021_2,plain,
    ! [U_6951,U_6950,U_6949,U_6948,U_6947,U_6946,U_6945] :
      ( hAPP(c_Sum__Type_Osum_Osum__case(U_6947,U_6948,U_6949,U_6950,U_6951),U_6945) = hAPP(c_Sum__Type_Osum_Osum__case(U_6947,U_6948,U_6949,U_6950,U_6951),U_6946)
      | U_6945 != U_6946 ),
    inference(variable_rename,[status(thm)],[f_2021_1]) ).

fof(f_2021_3,plain,
    ! [U_6946,U_6945,U_6947,U_6948,U_6949,U_6950,U_6951] :
      ( hAPP(c_Sum__Type_Osum_Osum__case(U_6947,U_6948,U_6949,U_6950,U_6951),U_6945) = hAPP(c_Sum__Type_Osum_Osum__case(U_6947,U_6948,U_6949,U_6950,U_6951),U_6946)
      | U_6945 != U_6946 ),
    inference(definitional_conversion,[status(esa)],[f_2021_2]) ).

cnf(f_2021_4,plain,
    ( hAPP(c_Sum__Type_Osum_Osum__case(U_6947,U_6948,U_6949,U_6950,U_6951),U_6945) = hAPP(c_Sum__Type_Osum_Osum__case(U_6947,U_6948,U_6949,U_6950,U_6951),U_6946)
    | U_6945 != U_6946 ),
    inference(clausify,[status(thm)],[f_2021_3]) ).

fof(f_2022_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_2022_2,plain,
    ! [U_6955,U_6954,U_6953,U_6952] : hAPP(hAPP(c_Product__Type_Oscomp(U_6952,U_6953,U_6954,tc_prod(U_6953,U_6954)),U_6955),c_Product__Type_OPair(U_6953,U_6954)) = U_6955,
    inference(variable_rename,[status(thm)],[f_2022_1]) ).

fof(f_2022_3,plain,
    ! [U_6953,U_6952,U_6954,U_6955] : hAPP(hAPP(c_Product__Type_Oscomp(U_6952,U_6953,U_6954,tc_prod(U_6953,U_6954)),U_6955),c_Product__Type_OPair(U_6953,U_6954)) = U_6955,
    inference(definitional_conversion,[status(esa)],[f_2022_2]) ).

cnf(f_2022_4,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_6952,U_6953,U_6954,tc_prod(U_6953,U_6954)),U_6955),c_Product__Type_OPair(U_6953,U_6954)) = U_6955,
    inference(clausify,[status(thm)],[f_2022_3]) ).

fof(f_2023_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_2023_2,plain,
    ! [U_6960,U_6959,U_6958,U_6957,U_6956] : hAPP(hAPP(c_Product__Type_Oscomp(U_6956,U_6957,U_6956,U_6958),hAPP(c_Product__Type_OPair(U_6957,U_6956),U_6959)),U_6960) = hAPP(U_6960,U_6959),
    inference(variable_rename,[status(thm)],[f_2023_1]) ).

fof(f_2023_3,plain,
    ! [U_6956,U_6957,U_6958,U_6959,U_6960] : hAPP(hAPP(c_Product__Type_Oscomp(U_6956,U_6957,U_6956,U_6958),hAPP(c_Product__Type_OPair(U_6957,U_6956),U_6959)),U_6960) = hAPP(U_6960,U_6959),
    inference(definitional_conversion,[status(esa)],[f_2023_2]) ).

cnf(f_2023_4,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_6956,U_6957,U_6956,U_6958),hAPP(c_Product__Type_OPair(U_6957,U_6956),U_6959)),U_6960) = hAPP(U_6960,U_6959),
    inference(clausify,[status(thm)],[f_2023_3]) ).

fof(f_2024_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_2024_2,plain,
    ! [U_6967,U_6966,U_6965,U_6964,U_6963,U_6962,U_6961] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6961,U_6962,U_6963,U_6964),U_6965),U_6966),U_6967) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6962,U_6963,U_6964),U_6966),hAPP(U_6965,U_6967)),
    inference(variable_rename,[status(thm)],[f_2024_1]) ).

fof(f_2024_3,plain,
    ! [U_6961,U_6962,U_6963,U_6964,U_6965,U_6966,U_6967] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6961,U_6962,U_6963,U_6964),U_6965),U_6966),U_6967) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6962,U_6963,U_6964),U_6966),hAPP(U_6965,U_6967)),
    inference(definitional_conversion,[status(esa)],[f_2024_2]) ).

cnf(f_2024_4,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6961,U_6962,U_6963,U_6964),U_6965),U_6966),U_6967) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6962,U_6963,U_6964),U_6966),hAPP(U_6965,U_6967)),
    inference(clausify,[status(thm)],[f_2024_3]) ).

fof(f_2025_1,plain,
    ! [V_b_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,V_f1_2,V_f2_2),hAPP(c_Sum__Type_OInr(T_d,T_c),V_b_2)) = hAPP(V_f2_2,V_b_2),
    inference(fof_nnf,[status(thm)],[fact_sum_Osimps_I6_J]) ).

fof(f_2025_2,plain,
    ! [U_6973,U_6972,U_6971,U_6970,U_6969,U_6968] : hAPP(c_Sum__Type_Osum_Osum__case(U_6968,U_6969,U_6970,U_6971,U_6972),hAPP(c_Sum__Type_OInr(U_6970,U_6968),U_6973)) = hAPP(U_6972,U_6973),
    inference(variable_rename,[status(thm)],[f_2025_1]) ).

fof(f_2025_3,plain,
    ! [U_6968,U_6969,U_6970,U_6971,U_6972,U_6973] : hAPP(c_Sum__Type_Osum_Osum__case(U_6968,U_6969,U_6970,U_6971,U_6972),hAPP(c_Sum__Type_OInr(U_6970,U_6968),U_6973)) = hAPP(U_6972,U_6973),
    inference(definitional_conversion,[status(esa)],[f_2025_2]) ).

cnf(f_2025_4,plain,
    hAPP(c_Sum__Type_Osum_Osum__case(U_6968,U_6969,U_6970,U_6971,U_6972),hAPP(c_Sum__Type_OInr(U_6970,U_6968),U_6973)) = hAPP(U_6972,U_6973),
    inference(clausify,[status(thm)],[f_2025_3]) ).

fof(f_2026_1,plain,
    ! [V_a_2,V_f2_2,V_f1_2,T_d,T_b,T_c] : hAPP(c_Sum__Type_Osum_Osum__case(T_c,T_b,T_d,V_f1_2,V_f2_2),hAPP(c_Sum__Type_OInl(T_c,T_d),V_a_2)) = hAPP(V_f1_2,V_a_2),
    inference(fof_nnf,[status(thm)],[fact_sum_Osimps_I5_J]) ).

fof(f_2026_2,plain,
    ! [U_6979,U_6978,U_6977,U_6976,U_6975,U_6974] : hAPP(c_Sum__Type_Osum_Osum__case(U_6974,U_6975,U_6976,U_6977,U_6978),hAPP(c_Sum__Type_OInl(U_6974,U_6976),U_6979)) = hAPP(U_6977,U_6979),
    inference(variable_rename,[status(thm)],[f_2026_1]) ).

fof(f_2026_3,plain,
    ! [U_6974,U_6975,U_6976,U_6977,U_6978,U_6979] : hAPP(c_Sum__Type_Osum_Osum__case(U_6974,U_6975,U_6976,U_6977,U_6978),hAPP(c_Sum__Type_OInl(U_6974,U_6976),U_6979)) = hAPP(U_6977,U_6979),
    inference(definitional_conversion,[status(esa)],[f_2026_2]) ).

cnf(f_2026_4,plain,
    hAPP(c_Sum__Type_Osum_Osum__case(U_6974,U_6975,U_6976,U_6977,U_6978),hAPP(c_Sum__Type_OInl(U_6974,U_6976),U_6979)) = hAPP(U_6977,U_6979),
    inference(clausify,[status(thm)],[f_2026_3]) ).

fof(f_2027_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_2027_2,plain,
    ! [U_6986,U_6985,U_6984,U_6983,U_6982,U_6981,U_6980] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6980,U_6981,U_6982,U_6983),U_6984),U_6985),U_6986) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6981,U_6982,U_6983),U_6985),hAPP(U_6984,U_6986)),
    inference(variable_rename,[status(thm)],[f_2027_1]) ).

fof(f_2027_3,plain,
    ! [U_6980,U_6981,U_6982,U_6983,U_6984,U_6985,U_6986] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6980,U_6981,U_6982,U_6983),U_6984),U_6985),U_6986) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6981,U_6982,U_6983),U_6985),hAPP(U_6984,U_6986)),
    inference(definitional_conversion,[status(esa)],[f_2027_2]) ).

cnf(f_2027_4,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6980,U_6981,U_6982,U_6983),U_6984),U_6985),U_6986) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6981,U_6982,U_6983),U_6985),hAPP(U_6984,U_6986)),
    inference(clausify,[status(thm)],[f_2027_3]) ).

fof(f_2028_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_2028_2,plain,
    ! [U_6993,U_6992,U_6991,U_6990,U_6989,U_6988,U_6987] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6987,U_6988,U_6989,U_6990),U_6991),U_6992),U_6993) = hAPP(hAPP(U_6992,hAPP(c_Product__Type_Ofst(U_6988,U_6989),hAPP(U_6991,U_6993))),hAPP(c_Product__Type_Osnd(U_6988,U_6989),hAPP(U_6991,U_6993))),
    inference(variable_rename,[status(thm)],[f_2028_1]) ).

fof(f_2028_3,plain,
    ! [U_6987,U_6988,U_6989,U_6990,U_6991,U_6992,U_6993] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6987,U_6988,U_6989,U_6990),U_6991),U_6992),U_6993) = hAPP(hAPP(U_6992,hAPP(c_Product__Type_Ofst(U_6988,U_6989),hAPP(U_6991,U_6993))),hAPP(c_Product__Type_Osnd(U_6988,U_6989),hAPP(U_6991,U_6993))),
    inference(definitional_conversion,[status(esa)],[f_2028_2]) ).

cnf(f_2028_4,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6987,U_6988,U_6989,U_6990),U_6991),U_6992),U_6993) = hAPP(hAPP(U_6992,hAPP(c_Product__Type_Ofst(U_6988,U_6989),hAPP(U_6991,U_6993))),hAPP(c_Product__Type_Osnd(U_6988,U_6989),hAPP(U_6991,U_6993))),
    inference(clausify,[status(thm)],[f_2028_3]) ).

fof(f_2029_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_2029_2,plain,
    ! [U_6996,U_6995,U_6994] : c_Nitpick_Oplus__frac(U_6994,U_6995,U_6996) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6994),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_6994),U_6995),hAPP(c_Nitpick_Odenom(U_6994),U_6996))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_6994),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_6994),tc_Int_Oint),c_Nitpick_Ofrac(U_6994)),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_6994),U_6995))),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_6994),U_6995))))),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_6994),U_6996))),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_6994),U_6996)))))),c_COMBI(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_2029_1]) ).

fof(f_2029_3,plain,
    ! [U_6994,U_6995,U_6996] : c_Nitpick_Oplus__frac(U_6994,U_6995,U_6996) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6994),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_6994),U_6995),hAPP(c_Nitpick_Odenom(U_6994),U_6996))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_6994),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_6994),tc_Int_Oint),c_Nitpick_Ofrac(U_6994)),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_6994),U_6995))),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_6994),U_6995))))),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_6994),U_6996))),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_6994),U_6996)))))),c_COMBI(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_2029_2]) ).

cnf(f_2029_4,plain,
    c_Nitpick_Oplus__frac(U_6994,U_6995,U_6996) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6994),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_6994),U_6995),hAPP(c_Nitpick_Odenom(U_6994),U_6996))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_6994),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_6994),tc_Int_Oint),c_Nitpick_Ofrac(U_6994)),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_6994),U_6995))),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_6994),U_6995))))),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_6994),U_6996))),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_6994),U_6996)))))),c_COMBI(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_2029_3]) ).

fof(f_2030_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_2030_2,plain,
    ! [U_6999,U_6998,U_6997] : c_Product__Type_Ointernal__split(U_6997,U_6998,U_6999) = c_Product__Type_Oprod_Oprod__case(U_6997,U_6998,U_6999),
    inference(variable_rename,[status(thm)],[f_2030_1]) ).

fof(f_2030_3,plain,
    ! [U_6997,U_6998,U_6999] : c_Product__Type_Ointernal__split(U_6997,U_6998,U_6999) = c_Product__Type_Oprod_Oprod__case(U_6997,U_6998,U_6999),
    inference(definitional_conversion,[status(esa)],[f_2030_2]) ).

cnf(f_2030_4,plain,
    c_Product__Type_Ointernal__split(U_6997,U_6998,U_6999) = c_Product__Type_Oprod_Oprod__case(U_6997,U_6998,U_6999),
    inference(clausify,[status(thm)],[f_2030_3]) ).

fof(f_2031_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_2031_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_2031_1]) ).

cnf(f_2031_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_2031_2]) ).

fof(f_2032_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_2032_2,plain,
    ! [U_7004,U_7003,U_7002,U_7001,U_7000] :
      ( ( hAPP(c_New__DSequence_Opos__decr__bind(U_7001,U_7002,U_7003,U_7004),U_7000) = c_Lazy__Sequence_Obind(U_7001,U_7002,hAPP(U_7003,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7000),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7001,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_7002)),U_7004),U_7000))
        | U_7000 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Opos__decr__bind(U_7001,U_7002,U_7003,U_7004),U_7000) = c_Lazy__Sequence_Oempty(U_7002)
        | U_7000 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_2032_1]) ).

fof(f_2032_3,plain,
    ( ! [U_7014,U_7012,U_7010,U_7008,U_7006] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_7008,U_7010,U_7012,U_7014),U_7006) = c_Lazy__Sequence_Obind(U_7008,U_7010,hAPP(U_7012,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7006),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7008,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_7010)),U_7014),U_7006))
        | U_7006 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_7013,U_7011,U_7009,U_7007,U_7005] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_7007,U_7009,U_7011,U_7013),U_7005) = c_Lazy__Sequence_Oempty(U_7009)
        | U_7005 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_2032_2]) ).

fof(f_2032_4,plain,
    ( ! [U_7012,U_7006,U_7008,U_7010,U_7014] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_7008,U_7010,U_7012,U_7014),U_7006) = c_Lazy__Sequence_Obind(U_7008,U_7010,hAPP(U_7012,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7006),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7008,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_7010)),U_7014),U_7006))
        | U_7006 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_7005,U_7007,U_7009,U_7011,U_7013] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_7007,U_7009,U_7011,U_7013),U_7005) = c_Lazy__Sequence_Oempty(U_7009)
        | U_7005 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa)],[f_2032_3]) ).

cnf(f_2032_5,plain,
    ( hAPP(c_New__DSequence_Opos__decr__bind(U_7007,U_7009,U_7011,U_7013),U_7005) = c_Lazy__Sequence_Oempty(U_7009)
    | U_7005 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2032_4]) ).

cnf(f_2032_6,plain,
    ( hAPP(c_New__DSequence_Opos__decr__bind(U_7008,U_7010,U_7012,U_7014),U_7006) = c_Lazy__Sequence_Obind(U_7008,U_7010,hAPP(U_7012,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7006),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7008,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_7010)),U_7014),U_7006))
    | U_7006 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2032_4]) ).

fof(f_2033_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_2033_2,plain,
    ! [U_7019,U_7018,U_7017,U_7016,U_7015] :
      ( ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7016,U_7017,U_7018,U_7019),U_7015) = c_Lazy__Sequence_Ohb__bind(U_7016,U_7017,hAPP(U_7018,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7015),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7016,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7017))),U_7019),U_7015))
        | U_7015 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7016,U_7017,U_7018,U_7019),U_7015) = c_Lazy__Sequence_Ohit__bound(U_7017)
        | U_7015 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_2033_1]) ).

fof(f_2033_3,plain,
    ( ! [U_7029,U_7027,U_7025,U_7023,U_7021] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7023,U_7025,U_7027,U_7029),U_7021) = c_Lazy__Sequence_Ohb__bind(U_7023,U_7025,hAPP(U_7027,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7021),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7023,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7025))),U_7029),U_7021))
        | U_7021 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_7028,U_7026,U_7024,U_7022,U_7020] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7022,U_7024,U_7026,U_7028),U_7020) = c_Lazy__Sequence_Ohit__bound(U_7024)
        | U_7020 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_2033_2]) ).

fof(f_2033_4,plain,
    ( ! [U_7023,U_7027,U_7021,U_7025,U_7029] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7023,U_7025,U_7027,U_7029),U_7021) = c_Lazy__Sequence_Ohb__bind(U_7023,U_7025,hAPP(U_7027,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7021),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7023,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7025))),U_7029),U_7021))
        | U_7021 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_7020,U_7022,U_7024,U_7026,U_7028] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7022,U_7024,U_7026,U_7028),U_7020) = c_Lazy__Sequence_Ohit__bound(U_7024)
        | U_7020 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa)],[f_2033_3]) ).

cnf(f_2033_5,plain,
    ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7022,U_7024,U_7026,U_7028),U_7020) = c_Lazy__Sequence_Ohit__bound(U_7024)
    | U_7020 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2033_4]) ).

cnf(f_2033_6,plain,
    ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7023,U_7025,U_7027,U_7029),U_7021) = c_Lazy__Sequence_Ohb__bind(U_7023,U_7025,hAPP(U_7027,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7021),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7023,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7025))),U_7029),U_7021))
    | U_7021 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2033_4]) ).

fof(f_2034_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_2034_2,plain,
    ! [U_7035,U_7034,U_7033,U_7032,U_7031,U_7030] : hAPP(hAPP(c_Product__Type_Ointernal__split(U_7030,U_7031,U_7032),U_7033),hAPP(hAPP(c_Product__Type_OPair(U_7030,U_7031),U_7034),U_7035)) = hAPP(hAPP(U_7033,U_7034),U_7035),
    inference(variable_rename,[status(thm)],[f_2034_1]) ).

fof(f_2034_3,plain,
    ! [U_7031,U_7032,U_7033,U_7030,U_7034,U_7035] : hAPP(hAPP(c_Product__Type_Ointernal__split(U_7030,U_7031,U_7032),U_7033),hAPP(hAPP(c_Product__Type_OPair(U_7030,U_7031),U_7034),U_7035)) = hAPP(hAPP(U_7033,U_7034),U_7035),
    inference(definitional_conversion,[status(esa)],[f_2034_2]) ).

cnf(f_2034_4,plain,
    hAPP(hAPP(c_Product__Type_Ointernal__split(U_7030,U_7031,U_7032),U_7033),hAPP(hAPP(c_Product__Type_OPair(U_7030,U_7031),U_7034),U_7035)) = hAPP(hAPP(U_7033,U_7034),U_7035),
    inference(clausify,[status(thm)],[f_2034_3]) ).

fof(f_2035_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_2035_2,plain,
    ! [U_7038,U_7037,U_7036] : c_Nitpick_Otimes__frac(U_7036,U_7037,U_7038) = hAPP(hAPP(c_Nitpick_Ofrac(U_7036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7036),U_7037)),hAPP(c_Nitpick_Onum(U_7036),U_7038))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_7036),U_7037)),hAPP(c_Nitpick_Odenom(U_7036),U_7038))),
    inference(variable_rename,[status(thm)],[f_2035_1]) ).

fof(f_2035_3,plain,
    ! [U_7036,U_7037,U_7038] : c_Nitpick_Otimes__frac(U_7036,U_7037,U_7038) = hAPP(hAPP(c_Nitpick_Ofrac(U_7036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7036),U_7037)),hAPP(c_Nitpick_Onum(U_7036),U_7038))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_7036),U_7037)),hAPP(c_Nitpick_Odenom(U_7036),U_7038))),
    inference(definitional_conversion,[status(esa)],[f_2035_2]) ).

cnf(f_2035_4,plain,
    c_Nitpick_Otimes__frac(U_7036,U_7037,U_7038) = hAPP(hAPP(c_Nitpick_Ofrac(U_7036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7036),U_7037)),hAPP(c_Nitpick_Onum(U_7036),U_7038))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_7036),U_7037)),hAPP(c_Nitpick_Odenom(U_7036),U_7038))),
    inference(clausify,[status(thm)],[f_2035_3]) ).

fof(f_2036_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_2036_2,plain,
    ! [U_7041,U_7040,U_7039] :
      ( c_Nitpick_Oof__frac(U_7040,U_7039,U_7041) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7039),hAPP(c_Int_Oring__1__class_Oof__int(U_7039),hAPP(c_Nitpick_Onum(U_7040),U_7041))),hAPP(c_Int_Oring__1__class_Oof__int(U_7039),hAPP(c_Nitpick_Odenom(U_7040),U_7041)))
      | ~ class_Rings_Oring__1(U_7039)
      | ~ class_Rings_Oinverse(U_7039) ),
    inference(variable_rename,[status(thm)],[f_2036_1]) ).

fof(f_2036_3,plain,
    ! [U_7039,U_7040,U_7041] :
      ( c_Nitpick_Oof__frac(U_7040,U_7039,U_7041) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7039),hAPP(c_Int_Oring__1__class_Oof__int(U_7039),hAPP(c_Nitpick_Onum(U_7040),U_7041))),hAPP(c_Int_Oring__1__class_Oof__int(U_7039),hAPP(c_Nitpick_Odenom(U_7040),U_7041)))
      | ~ class_Rings_Oring__1(U_7039)
      | ~ class_Rings_Oinverse(U_7039) ),
    inference(definitional_conversion,[status(esa)],[f_2036_2]) ).

cnf(f_2036_4,plain,
    ( c_Nitpick_Oof__frac(U_7040,U_7039,U_7041) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7039),hAPP(c_Int_Oring__1__class_Oof__int(U_7039),hAPP(c_Nitpick_Onum(U_7040),U_7041))),hAPP(c_Int_Oring__1__class_Oof__int(U_7039),hAPP(c_Nitpick_Odenom(U_7040),U_7041)))
    | ~ class_Rings_Oring__1(U_7039)
    | ~ class_Rings_Oinverse(U_7039) ),
    inference(clausify,[status(thm)],[f_2036_3]) ).

fof(f_2037_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_2037_2,plain,
    ! [U_7043,U_7042] : c_Nitpick_Oinverse__frac(U_7042,U_7043) = hAPP(hAPP(c_Nitpick_Ofrac(U_7042),hAPP(c_Nitpick_Odenom(U_7042),U_7043)),hAPP(c_Nitpick_Onum(U_7042),U_7043)),
    inference(variable_rename,[status(thm)],[f_2037_1]) ).

fof(f_2037_3,plain,
    ! [U_7042,U_7043] : c_Nitpick_Oinverse__frac(U_7042,U_7043) = hAPP(hAPP(c_Nitpick_Ofrac(U_7042),hAPP(c_Nitpick_Odenom(U_7042),U_7043)),hAPP(c_Nitpick_Onum(U_7042),U_7043)),
    inference(definitional_conversion,[status(esa)],[f_2037_2]) ).

cnf(f_2037_4,plain,
    c_Nitpick_Oinverse__frac(U_7042,U_7043) = hAPP(hAPP(c_Nitpick_Ofrac(U_7042),hAPP(c_Nitpick_Odenom(U_7042),U_7043)),hAPP(c_Nitpick_Onum(U_7042),U_7043)),
    inference(clausify,[status(thm)],[f_2037_3]) ).

fof(f_2038_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_2038_2,plain,
    ! [U_7045,U_7044] : c_Nitpick_Ouminus__frac(U_7044,U_7045) = c_Nitpick_OAbs__Frac(U_7044,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_7044),U_7045))),hAPP(c_Nitpick_Odenom(U_7044),U_7045))),
    inference(variable_rename,[status(thm)],[f_2038_1]) ).

fof(f_2038_3,plain,
    ! [U_7044,U_7045] : c_Nitpick_Ouminus__frac(U_7044,U_7045) = c_Nitpick_OAbs__Frac(U_7044,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_7044),U_7045))),hAPP(c_Nitpick_Odenom(U_7044),U_7045))),
    inference(definitional_conversion,[status(esa)],[f_2038_2]) ).

cnf(f_2038_4,plain,
    c_Nitpick_Ouminus__frac(U_7044,U_7045) = c_Nitpick_OAbs__Frac(U_7044,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_7044),U_7045))),hAPP(c_Nitpick_Odenom(U_7044),U_7045))),
    inference(clausify,[status(thm)],[f_2038_3]) ).

fof(f_2039_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_2039_2,plain,
    ! [U_7052,U_7051,U_7050,U_7049,U_7048,U_7047,U_7046] : c_New__Random__Sequence_Opos__decr__bind(U_7046,U_7047,U_7048,U_7049,U_7050,U_7051,U_7052) = c_New__DSequence_Opos__decr__bind(U_7046,U_7047,hAPP(hAPP(hAPP(U_7048,U_7050),U_7051),U_7052),hAPP(hAPP(c_COMBC(U_7046,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_7047))),hAPP(hAPP(c_COMBC(U_7046,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_7047)))),hAPP(hAPP(c_COMBC(U_7046,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_7047))))),U_7049),U_7050)),U_7051)),U_7052)),
    inference(variable_rename,[status(thm)],[f_2039_1]) ).

fof(f_2039_3,plain,
    ! [U_7047,U_7046,U_7048,U_7049,U_7050,U_7051,U_7052] : c_New__Random__Sequence_Opos__decr__bind(U_7046,U_7047,U_7048,U_7049,U_7050,U_7051,U_7052) = c_New__DSequence_Opos__decr__bind(U_7046,U_7047,hAPP(hAPP(hAPP(U_7048,U_7050),U_7051),U_7052),hAPP(hAPP(c_COMBC(U_7046,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_7047))),hAPP(hAPP(c_COMBC(U_7046,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_7047)))),hAPP(hAPP(c_COMBC(U_7046,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_7047))))),U_7049),U_7050)),U_7051)),U_7052)),
    inference(definitional_conversion,[status(esa)],[f_2039_2]) ).

cnf(f_2039_4,plain,
    c_New__Random__Sequence_Opos__decr__bind(U_7046,U_7047,U_7048,U_7049,U_7050,U_7051,U_7052) = c_New__DSequence_Opos__decr__bind(U_7046,U_7047,hAPP(hAPP(hAPP(U_7048,U_7050),U_7051),U_7052),hAPP(hAPP(c_COMBC(U_7046,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_7047))),hAPP(hAPP(c_COMBC(U_7046,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_7047)))),hAPP(hAPP(c_COMBC(U_7046,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_7047))))),U_7049),U_7050)),U_7051)),U_7052)),
    inference(clausify,[status(thm)],[f_2039_3]) ).

fof(f_2040_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_2040_2,plain,
    ! [U_7055,U_7054,U_7053] :
      ( ( c_Nitpick_Oless__frac(U_7053,U_7054,U_7055)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7053),c_Nitpick_Oplus__frac(U_7053,U_7054,c_Nitpick_Ouminus__frac(U_7053,U_7055)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7053),c_Nitpick_Oplus__frac(U_7053,U_7054,c_Nitpick_Ouminus__frac(U_7053,U_7055)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(U_7053,U_7054,U_7055) ) ),
    inference(variable_rename,[status(thm)],[f_2040_1]) ).

fof(f_2040_3,plain,
    ( ! [U_7061,U_7059,U_7057] :
        ( c_Nitpick_Oless__frac(U_7057,U_7059,U_7061)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7057),c_Nitpick_Oplus__frac(U_7057,U_7059,c_Nitpick_Ouminus__frac(U_7057,U_7061)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_7060,U_7058,U_7056] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7056),c_Nitpick_Oplus__frac(U_7056,U_7058,c_Nitpick_Ouminus__frac(U_7056,U_7060)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(U_7056,U_7058,U_7060) ) ),
    inference(miniscope,[status(thm)],[f_2040_2]) ).

fof(f_2040_4,plain,
    ( ! [U_7057,U_7059,U_7061] :
        ( c_Nitpick_Oless__frac(U_7057,U_7059,U_7061)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7057),c_Nitpick_Oplus__frac(U_7057,U_7059,c_Nitpick_Ouminus__frac(U_7057,U_7061)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_7058,U_7056,U_7060] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7056),c_Nitpick_Oplus__frac(U_7056,U_7058,c_Nitpick_Ouminus__frac(U_7056,U_7060)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(U_7056,U_7058,U_7060) ) ),
    inference(definitional_conversion,[status(esa)],[f_2040_3]) ).

cnf(f_2040_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7056),c_Nitpick_Oplus__frac(U_7056,U_7058,c_Nitpick_Ouminus__frac(U_7056,U_7060)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__frac(U_7056,U_7058,U_7060) ),
    inference(clausify,[status(thm)],[f_2040_4]) ).

cnf(f_2040_6,plain,
    ( c_Nitpick_Oless__frac(U_7057,U_7059,U_7061)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7057),c_Nitpick_Oplus__frac(U_7057,U_7059,c_Nitpick_Ouminus__frac(U_7057,U_7061)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2040_4]) ).

fof(f_2041_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_2041_2,plain,
    ! [U_7064,U_7063,U_7062] :
      ( ( c_Nitpick_Oless__eq__frac(U_7062,U_7063,U_7064)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7062),c_Nitpick_Oplus__frac(U_7062,U_7063,c_Nitpick_Ouminus__frac(U_7062,U_7064)))),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_7062),c_Nitpick_Oplus__frac(U_7062,U_7063,c_Nitpick_Ouminus__frac(U_7062,U_7064)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(U_7062,U_7063,U_7064) ) ),
    inference(variable_rename,[status(thm)],[f_2041_1]) ).

fof(f_2041_3,plain,
    ( ! [U_7070,U_7068,U_7066] :
        ( c_Nitpick_Oless__eq__frac(U_7066,U_7068,U_7070)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7066),c_Nitpick_Oplus__frac(U_7066,U_7068,c_Nitpick_Ouminus__frac(U_7066,U_7070)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_7069,U_7067,U_7065] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7065),c_Nitpick_Oplus__frac(U_7065,U_7067,c_Nitpick_Ouminus__frac(U_7065,U_7069)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(U_7065,U_7067,U_7069) ) ),
    inference(miniscope,[status(thm)],[f_2041_2]) ).

fof(f_2041_4,plain,
    ( ! [U_7066,U_7068,U_7070] :
        ( c_Nitpick_Oless__eq__frac(U_7066,U_7068,U_7070)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7066),c_Nitpick_Oplus__frac(U_7066,U_7068,c_Nitpick_Ouminus__frac(U_7066,U_7070)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_7067,U_7065,U_7069] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7065),c_Nitpick_Oplus__frac(U_7065,U_7067,c_Nitpick_Ouminus__frac(U_7065,U_7069)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(U_7065,U_7067,U_7069) ) ),
    inference(definitional_conversion,[status(esa)],[f_2041_3]) ).

cnf(f_2041_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7065),c_Nitpick_Oplus__frac(U_7065,U_7067,c_Nitpick_Ouminus__frac(U_7065,U_7069)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__eq__frac(U_7065,U_7067,U_7069) ),
    inference(clausify,[status(thm)],[f_2041_4]) ).

cnf(f_2041_6,plain,
    ( c_Nitpick_Oless__eq__frac(U_7066,U_7068,U_7070)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_7066),c_Nitpick_Oplus__frac(U_7066,U_7068,c_Nitpick_Ouminus__frac(U_7066,U_7070)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2041_4]) ).

fof(f_2042_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_2042_2,plain,
    ! [U_7077,U_7076,U_7075,U_7074,U_7073,U_7072,U_7071] : c_New__Random__Sequence_Oneg__decr__bind(U_7071,U_7072,U_7073,U_7074,U_7075,U_7076,U_7077) = c_New__DSequence_Oneg__decr__bind(U_7071,U_7072,hAPP(hAPP(hAPP(U_7073,U_7075),U_7076),U_7077),hAPP(hAPP(c_COMBC(U_7071,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_7072)))),hAPP(hAPP(c_COMBC(U_7071,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_7072))))),hAPP(hAPP(c_COMBC(U_7071,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_7072)))))),U_7074),U_7075)),U_7076)),U_7077)),
    inference(variable_rename,[status(thm)],[f_2042_1]) ).

fof(f_2042_3,plain,
    ! [U_7072,U_7071,U_7073,U_7074,U_7075,U_7076,U_7077] : c_New__Random__Sequence_Oneg__decr__bind(U_7071,U_7072,U_7073,U_7074,U_7075,U_7076,U_7077) = c_New__DSequence_Oneg__decr__bind(U_7071,U_7072,hAPP(hAPP(hAPP(U_7073,U_7075),U_7076),U_7077),hAPP(hAPP(c_COMBC(U_7071,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_7072)))),hAPP(hAPP(c_COMBC(U_7071,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_7072))))),hAPP(hAPP(c_COMBC(U_7071,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_7072)))))),U_7074),U_7075)),U_7076)),U_7077)),
    inference(definitional_conversion,[status(esa)],[f_2042_2]) ).

cnf(f_2042_4,plain,
    c_New__Random__Sequence_Oneg__decr__bind(U_7071,U_7072,U_7073,U_7074,U_7075,U_7076,U_7077) = c_New__DSequence_Oneg__decr__bind(U_7071,U_7072,hAPP(hAPP(hAPP(U_7073,U_7075),U_7076),U_7077),hAPP(hAPP(c_COMBC(U_7071,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_7072)))),hAPP(hAPP(c_COMBC(U_7071,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_7072))))),hAPP(hAPP(c_COMBC(U_7071,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_7072)))))),U_7074),U_7075)),U_7076)),U_7077)),
    inference(clausify,[status(thm)],[f_2042_3]) ).

fof(f_2043_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_2043_2,plain,
    ! [U_7082,U_7081,U_7080,U_7079,U_7078] : hAPP(c_New__DSequence_Oneg__bind(U_7078,U_7079,U_7080,U_7081),U_7082) = c_Lazy__Sequence_Ohb__bind(U_7078,U_7079,hAPP(U_7080,U_7082),hAPP(hAPP(c_COMBC(U_7078,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7079))),U_7081),U_7082)),
    inference(variable_rename,[status(thm)],[f_2043_1]) ).

fof(f_2043_3,plain,
    ! [U_7079,U_7078,U_7080,U_7081,U_7082] : hAPP(c_New__DSequence_Oneg__bind(U_7078,U_7079,U_7080,U_7081),U_7082) = c_Lazy__Sequence_Ohb__bind(U_7078,U_7079,hAPP(U_7080,U_7082),hAPP(hAPP(c_COMBC(U_7078,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7079))),U_7081),U_7082)),
    inference(definitional_conversion,[status(esa)],[f_2043_2]) ).

cnf(f_2043_4,plain,
    hAPP(c_New__DSequence_Oneg__bind(U_7078,U_7079,U_7080,U_7081),U_7082) = c_Lazy__Sequence_Ohb__bind(U_7078,U_7079,hAPP(U_7080,U_7082),hAPP(hAPP(c_COMBC(U_7078,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7079))),U_7081),U_7082)),
    inference(clausify,[status(thm)],[f_2043_3]) ).

fof(f_2044_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_2044_2,plain,
    ! [U_7084,U_7083] : hAPP(c_New__DSequence_Opos__empty(U_7083),U_7084) = c_Lazy__Sequence_Oempty(U_7083),
    inference(variable_rename,[status(thm)],[f_2044_1]) ).

fof(f_2044_3,plain,
    ! [U_7084,U_7083] : hAPP(c_New__DSequence_Opos__empty(U_7083),U_7084) = c_Lazy__Sequence_Oempty(U_7083),
    inference(definitional_conversion,[status(esa)],[f_2044_2]) ).

cnf(f_2044_4,plain,
    hAPP(c_New__DSequence_Opos__empty(U_7083),U_7084) = c_Lazy__Sequence_Oempty(U_7083),
    inference(clausify,[status(thm)],[f_2044_3]) ).

fof(f_2045_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_2045_2,plain,
    ! [U_7088,U_7087,U_7086,U_7085] : c_New__Random__Sequence_Opos__empty(U_7085,U_7086,U_7087,U_7088) = c_New__DSequence_Opos__empty(U_7085),
    inference(variable_rename,[status(thm)],[f_2045_1]) ).

fof(f_2045_3,plain,
    ! [U_7085,U_7086,U_7087,U_7088] : c_New__Random__Sequence_Opos__empty(U_7085,U_7086,U_7087,U_7088) = c_New__DSequence_Opos__empty(U_7085),
    inference(definitional_conversion,[status(esa)],[f_2045_2]) ).

cnf(f_2045_4,plain,
    c_New__Random__Sequence_Opos__empty(U_7085,U_7086,U_7087,U_7088) = c_New__DSequence_Opos__empty(U_7085),
    inference(clausify,[status(thm)],[f_2045_3]) ).

fof(f_2046_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_2046_2,plain,
    ! [U_7095,U_7094,U_7093,U_7092,U_7091,U_7090,U_7089] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_7089,U_7090,U_7091,U_7092),U_7093),U_7094),U_7095) = c_New__DSequence_Oneg__bind(U_7089,U_7090,hAPP(hAPP(hAPP(U_7091,U_7093),U_7094),U_7095),hAPP(hAPP(c_COMBC(U_7089,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_7090)))),hAPP(hAPP(c_COMBC(U_7089,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_7090))))),hAPP(hAPP(c_COMBC(U_7089,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_7090)))))),U_7092),U_7093)),U_7094)),U_7095)),
    inference(variable_rename,[status(thm)],[f_2046_1]) ).

fof(f_2046_3,plain,
    ! [U_7089,U_7090,U_7091,U_7092,U_7093,U_7094,U_7095] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_7089,U_7090,U_7091,U_7092),U_7093),U_7094),U_7095) = c_New__DSequence_Oneg__bind(U_7089,U_7090,hAPP(hAPP(hAPP(U_7091,U_7093),U_7094),U_7095),hAPP(hAPP(c_COMBC(U_7089,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_7090)))),hAPP(hAPP(c_COMBC(U_7089,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_7090))))),hAPP(hAPP(c_COMBC(U_7089,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_7090)))))),U_7092),U_7093)),U_7094)),U_7095)),
    inference(definitional_conversion,[status(esa)],[f_2046_2]) ).

cnf(f_2046_4,plain,
    hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_7089,U_7090,U_7091,U_7092),U_7093),U_7094),U_7095) = c_New__DSequence_Oneg__bind(U_7089,U_7090,hAPP(hAPP(hAPP(U_7091,U_7093),U_7094),U_7095),hAPP(hAPP(c_COMBC(U_7089,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_7090)))),hAPP(hAPP(c_COMBC(U_7089,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_7090))))),hAPP(hAPP(c_COMBC(U_7089,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_7090)))))),U_7092),U_7093)),U_7094)),U_7095)),
    inference(clausify,[status(thm)],[f_2046_3]) ).

fof(f_2047_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_2047_2,plain,
    ! [U_7100,U_7099,U_7098,U_7097,U_7096] : hAPP(c_New__DSequence_Opos__bind(U_7096,U_7097,U_7098,U_7099),U_7100) = c_Lazy__Sequence_Obind(U_7096,U_7097,hAPP(U_7098,U_7100),hAPP(hAPP(c_COMBC(U_7096,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_7097)),U_7099),U_7100)),
    inference(variable_rename,[status(thm)],[f_2047_1]) ).

fof(f_2047_3,plain,
    ! [U_7096,U_7097,U_7098,U_7099,U_7100] : hAPP(c_New__DSequence_Opos__bind(U_7096,U_7097,U_7098,U_7099),U_7100) = c_Lazy__Sequence_Obind(U_7096,U_7097,hAPP(U_7098,U_7100),hAPP(hAPP(c_COMBC(U_7096,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_7097)),U_7099),U_7100)),
    inference(definitional_conversion,[status(esa)],[f_2047_2]) ).

cnf(f_2047_4,plain,
    hAPP(c_New__DSequence_Opos__bind(U_7096,U_7097,U_7098,U_7099),U_7100) = c_Lazy__Sequence_Obind(U_7096,U_7097,hAPP(U_7098,U_7100),hAPP(hAPP(c_COMBC(U_7096,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_7097)),U_7099),U_7100)),
    inference(clausify,[status(thm)],[f_2047_3]) ).

fof(f_2048_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_2048_2,plain,
    ! [U_7106,U_7105,U_7104,U_7103,U_7102,U_7101] :
      ( hBOOL(hAPP(hAPP(U_7106,U_7102),U_7103))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7104,tc_fun(U_7105,tc_HOL_Obool))),U_7101),U_7106))
      | ~ hBOOL(hAPP(hAPP(U_7101,U_7102),U_7103)) ),
    inference(variable_rename,[status(thm)],[f_2048_1]) ).

fof(f_2048_3,plain,
    ! [U_7102,U_7101,U_7103,U_7104,U_7105,U_7106] :
      ( hBOOL(hAPP(hAPP(U_7106,U_7102),U_7103))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7104,tc_fun(U_7105,tc_HOL_Obool))),U_7101),U_7106))
      | ~ hBOOL(hAPP(hAPP(U_7101,U_7102),U_7103)) ),
    inference(definitional_conversion,[status(esa)],[f_2048_2]) ).

cnf(f_2048_4,plain,
    ( hBOOL(hAPP(hAPP(U_7106,U_7102),U_7103))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7104,tc_fun(U_7105,tc_HOL_Obool))),U_7101),U_7106))
    | ~ hBOOL(hAPP(hAPP(U_7101,U_7102),U_7103)) ),
    inference(clausify,[status(thm)],[f_2048_3]) ).

fof(f_2049_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_2049_2,plain,
    ! [U_7112,U_7111,U_7110,U_7109,U_7108,U_7107] :
      ( hBOOL(hAPP(hAPP(U_7110,U_7111),U_7112))
      | ~ hBOOL(hAPP(hAPP(U_7109,U_7111),U_7112))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7107,tc_fun(U_7108,tc_HOL_Obool))),U_7109),U_7110)) ),
    inference(variable_rename,[status(thm)],[f_2049_1]) ).

fof(f_2049_3,plain,
    ! [U_7112,U_7111,U_7110,U_7109] :
      ( ! [U_7108,U_7107] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7107,tc_fun(U_7108,tc_HOL_Obool))),U_7109),U_7110))
      | hBOOL(hAPP(hAPP(U_7110,U_7111),U_7112))
      | ~ hBOOL(hAPP(hAPP(U_7109,U_7111),U_7112)) ),
    inference(miniscope,[status(thm)],[f_2049_2]) ).

fof(f_2049_4,plain,
    ! [U_7107,U_7108,U_7109,U_7110,U_7111,U_7112] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7107,tc_fun(U_7108,tc_HOL_Obool))),U_7109),U_7110))
      | hBOOL(hAPP(hAPP(U_7110,U_7111),U_7112))
      | ~ hBOOL(hAPP(hAPP(U_7109,U_7111),U_7112)) ),
    inference(definitional_conversion,[status(esa)],[f_2049_3]) ).

cnf(f_2049_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7107,tc_fun(U_7108,tc_HOL_Obool))),U_7109),U_7110))
    | hBOOL(hAPP(hAPP(U_7110,U_7111),U_7112))
    | ~ hBOOL(hAPP(hAPP(U_7109,U_7111),U_7112)) ),
    inference(clausify,[status(thm)],[f_2049_4]) ).

fof(f_2050_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_2050_2,plain,
    ! [U_7116,U_7115,U_7114,U_7113] :
      ( hBOOL(hAPP(U_7116,U_7114))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7115,tc_HOL_Obool)),U_7113),U_7116))
      | ~ hBOOL(hAPP(U_7113,U_7114)) ),
    inference(variable_rename,[status(thm)],[f_2050_1]) ).

fof(f_2050_3,plain,
    ! [U_7114,U_7115,U_7116,U_7113] :
      ( hBOOL(hAPP(U_7116,U_7114))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7115,tc_HOL_Obool)),U_7113),U_7116))
      | ~ hBOOL(hAPP(U_7113,U_7114)) ),
    inference(definitional_conversion,[status(esa)],[f_2050_2]) ).

cnf(f_2050_4,plain,
    ( hBOOL(hAPP(U_7116,U_7114))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7115,tc_HOL_Obool)),U_7113),U_7116))
    | ~ hBOOL(hAPP(U_7113,U_7114)) ),
    inference(clausify,[status(thm)],[f_2050_3]) ).

fof(f_2051_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_2051_2,plain,
    ! [U_7120,U_7119,U_7118,U_7117] :
      ( hBOOL(hAPP(U_7119,U_7120))
      | ~ hBOOL(hAPP(U_7118,U_7120))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7117,tc_HOL_Obool)),U_7118),U_7119)) ),
    inference(variable_rename,[status(thm)],[f_2051_1]) ).

fof(f_2051_3,plain,
    ! [U_7120,U_7119,U_7118] :
      ( ! [U_7117] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7117,tc_HOL_Obool)),U_7118),U_7119))
      | hBOOL(hAPP(U_7119,U_7120))
      | ~ hBOOL(hAPP(U_7118,U_7120)) ),
    inference(miniscope,[status(thm)],[f_2051_2]) ).

fof(f_2051_4,plain,
    ! [U_7117,U_7118,U_7119,U_7120] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7117,tc_HOL_Obool)),U_7118),U_7119))
      | hBOOL(hAPP(U_7119,U_7120))
      | ~ hBOOL(hAPP(U_7118,U_7120)) ),
    inference(definitional_conversion,[status(esa)],[f_2051_3]) ).

cnf(f_2051_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7117,tc_HOL_Obool)),U_7118),U_7119))
    | hBOOL(hAPP(U_7119,U_7120))
    | ~ hBOOL(hAPP(U_7118,U_7120)) ),
    inference(clausify,[status(thm)],[f_2051_4]) ).

fof(f_2052_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_2052_2,plain,
    ! [U_7127,U_7126,U_7125,U_7124,U_7123,U_7122,U_7121] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_7121,U_7122,U_7123,U_7124),U_7125),U_7126),U_7127) = c_New__DSequence_Opos__bind(U_7121,U_7122,hAPP(hAPP(hAPP(U_7123,U_7125),U_7126),U_7127),hAPP(hAPP(c_COMBC(U_7121,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_7122))),hAPP(hAPP(c_COMBC(U_7121,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_7122)))),hAPP(hAPP(c_COMBC(U_7121,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_7122))))),U_7124),U_7125)),U_7126)),U_7127)),
    inference(variable_rename,[status(thm)],[f_2052_1]) ).

fof(f_2052_3,plain,
    ! [U_7121,U_7122,U_7123,U_7124,U_7125,U_7126,U_7127] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_7121,U_7122,U_7123,U_7124),U_7125),U_7126),U_7127) = c_New__DSequence_Opos__bind(U_7121,U_7122,hAPP(hAPP(hAPP(U_7123,U_7125),U_7126),U_7127),hAPP(hAPP(c_COMBC(U_7121,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_7122))),hAPP(hAPP(c_COMBC(U_7121,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_7122)))),hAPP(hAPP(c_COMBC(U_7121,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_7122))))),U_7124),U_7125)),U_7126)),U_7127)),
    inference(definitional_conversion,[status(esa)],[f_2052_2]) ).

cnf(f_2052_4,plain,
    hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_7121,U_7122,U_7123,U_7124),U_7125),U_7126),U_7127) = c_New__DSequence_Opos__bind(U_7121,U_7122,hAPP(hAPP(hAPP(U_7123,U_7125),U_7126),U_7127),hAPP(hAPP(c_COMBC(U_7121,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_7122))),hAPP(hAPP(c_COMBC(U_7121,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_7122)))),hAPP(hAPP(c_COMBC(U_7121,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_7122))))),U_7124),U_7125)),U_7126)),U_7127)),
    inference(clausify,[status(thm)],[f_2052_3]) ).

fof(f_2053_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_2053_2,plain,
    ! [U_7130,U_7129,U_7128] : c_HOL_OThe(tc_prod(U_7128,U_7129),hAPP(c_Product__Type_Oprod_Oprod__case(U_7128,U_7129,tc_HOL_Obool),U_7130)) = c_HOL_OThe(tc_prod(U_7128,U_7129),hAPP(hAPP(c_COMBS(tc_prod(U_7128,U_7129),U_7129,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_7128,tc_fun(U_7129,tc_HOL_Obool),tc_prod(U_7128,U_7129)),U_7130),c_Product__Type_Ofst(U_7128,U_7129))),c_Product__Type_Osnd(U_7128,U_7129))),
    inference(variable_rename,[status(thm)],[f_2053_1]) ).

fof(f_2053_3,plain,
    ! [U_7128,U_7130,U_7129] : c_HOL_OThe(tc_prod(U_7128,U_7129),hAPP(c_Product__Type_Oprod_Oprod__case(U_7128,U_7129,tc_HOL_Obool),U_7130)) = c_HOL_OThe(tc_prod(U_7128,U_7129),hAPP(hAPP(c_COMBS(tc_prod(U_7128,U_7129),U_7129,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_7128,tc_fun(U_7129,tc_HOL_Obool),tc_prod(U_7128,U_7129)),U_7130),c_Product__Type_Ofst(U_7128,U_7129))),c_Product__Type_Osnd(U_7128,U_7129))),
    inference(definitional_conversion,[status(esa)],[f_2053_2]) ).

cnf(f_2053_4,plain,
    c_HOL_OThe(tc_prod(U_7128,U_7129),hAPP(c_Product__Type_Oprod_Oprod__case(U_7128,U_7129,tc_HOL_Obool),U_7130)) = c_HOL_OThe(tc_prod(U_7128,U_7129),hAPP(hAPP(c_COMBS(tc_prod(U_7128,U_7129),U_7129,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_7128,tc_fun(U_7129,tc_HOL_Obool),tc_prod(U_7128,U_7129)),U_7130),c_Product__Type_Ofst(U_7128,U_7129))),c_Product__Type_Osnd(U_7128,U_7129))),
    inference(clausify,[status(thm)],[f_2053_3]) ).

fof(f_2054_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_2054_2,plain,
    ! [U_7134,U_7133,U_7132,U_7131] :
      ( ( c_Random__Sequence_ORandom(U_7132,U_7133,U_7131,U_7134) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_7132,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_7132)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_7133,U_7134)),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_7132)))),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_7132)))),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_7132)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_7132,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_7132)))),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_7132)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_7132,U_7133,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7131),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_7134))),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_7132)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7132))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7132)))),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_7132)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_7132,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_7132)))),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_7132)))),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_7132))))),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_7132)))),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_7132)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7132)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7132))))),tc_prod(U_7132,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_7132)),hAPP(hAPP(c_COMBB(U_7132,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7132)))),tc_prod(U_7132,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_7132)),c_Product__Type_Ofst(U_7132,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_7131),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
      & ( c_Random__Sequence_ORandom(U_7132,U_7133,U_7131,U_7134) = 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_7132)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_7132))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7131),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
    inference(variable_rename,[status(thm)],[f_2054_1]) ).

fof(f_2054_3,plain,
    ( ! [U_7142,U_7140,U_7138,U_7136] :
        ( c_Random__Sequence_ORandom(U_7138,U_7140,U_7136,U_7142) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_7138,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_7138)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_7140,U_7142)),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_7138)))),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_7138)))),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_7138)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_7138,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_7138)))),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_7138)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_7138,U_7140,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7136),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_7142))),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_7138)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7138))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7138)))),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_7138)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_7138,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_7138)))),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_7138)))),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_7138))))),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_7138)))),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_7138)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7138)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7138))))),tc_prod(U_7138,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_7138)),hAPP(hAPP(c_COMBB(U_7138,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7138)))),tc_prod(U_7138,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_7138)),c_Product__Type_Ofst(U_7138,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_7136),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_7141,U_7139,U_7137,U_7135] :
        ( c_Random__Sequence_ORandom(U_7137,U_7139,U_7135,U_7141) = 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_7137)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_7137))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7135),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
    inference(miniscope,[status(thm)],[f_2054_2]) ).

fof(f_2054_4,plain,
    ( ! [U_7136,U_7142,U_7140,U_7138] :
        ( c_Random__Sequence_ORandom(U_7138,U_7140,U_7136,U_7142) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_7138,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_7138)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_7140,U_7142)),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_7138)))),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_7138)))),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_7138)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_7138,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_7138)))),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_7138)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_7138,U_7140,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7136),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_7142))),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_7138)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7138))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7138)))),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_7138)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_7138,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_7138)))),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_7138)))),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_7138))))),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_7138)))),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_7138)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7138)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7138))))),tc_prod(U_7138,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_7138)),hAPP(hAPP(c_COMBB(U_7138,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7138)))),tc_prod(U_7138,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_7138)),c_Product__Type_Ofst(U_7138,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_7136),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_7135,U_7139,U_7141,U_7137] :
        ( c_Random__Sequence_ORandom(U_7137,U_7139,U_7135,U_7141) = 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_7137)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_7137))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7135),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2054_3]) ).

cnf(f_2054_5,plain,
    ( c_Random__Sequence_ORandom(U_7137,U_7139,U_7135,U_7141) = 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_7137)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_7137))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7135),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_2054_4]) ).

cnf(f_2054_6,plain,
    ( c_Random__Sequence_ORandom(U_7138,U_7140,U_7136,U_7142) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_7138,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_7138)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_7140,U_7142)),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_7138)))),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_7138)))),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_7138)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_7138,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_7138)))),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_7138)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_7138,U_7140,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7136),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_7142))),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_7138)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7138))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7138)))),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_7138)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_7138,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_7138)))),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_7138)))),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_7138))))),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_7138)))),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_7138)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7138)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7138))))),tc_prod(U_7138,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_7138)),hAPP(hAPP(c_COMBB(U_7138,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_7138)))),tc_prod(U_7138,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_7138)),c_Product__Type_Ofst(U_7138,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_7136),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_2054_4]) ).

fof(f_2055_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_2055_2,plain,
    ! [U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145] :
      ( hBOOL(hAPP(U_7149,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_7146,U_7147,U_7151),U_7150),U_7148)))
      | ? [U_7144,U_7143] :
          ( ~ hBOOL(hAPP(U_7149,hAPP(hAPP(U_7150,U_7144),U_7143)))
          & hBOOL(hAPP(hAPP(U_7145,U_7143),U_7144)) )
      | ~ hBOOL(hAPP(hAPP(U_7145,hAPP(c_Product__Type_Osnd(U_7146,U_7147),U_7148)),hAPP(c_Product__Type_Ofst(U_7146,U_7147),U_7148))) ),
    inference(variable_rename,[status(thm)],[f_2055_1]) ).

fof(f_2055_3,plain,
    ! [U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145] :
      ( hBOOL(hAPP(U_7149,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_7146,U_7147,U_7151),U_7150),U_7148)))
      | ? [U_7143] :
          ( ~ hBOOL(hAPP(U_7149,hAPP(hAPP(U_7150,sK109(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145)),U_7143)))
          & hBOOL(hAPP(hAPP(U_7145,U_7143),sK109(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145))) )
      | ~ hBOOL(hAPP(hAPP(U_7145,hAPP(c_Product__Type_Osnd(U_7146,U_7147),U_7148)),hAPP(c_Product__Type_Ofst(U_7146,U_7147),U_7148))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_7144,sK109(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145))],[f_2055_2]) ).

fof(f_2055_4,plain,
    ! [U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145] :
      ( hBOOL(hAPP(U_7149,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_7146,U_7147,U_7151),U_7150),U_7148)))
      | ( ~ hBOOL(hAPP(U_7149,hAPP(hAPP(U_7150,sK109(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145)),sK110(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145))))
        & hBOOL(hAPP(hAPP(U_7145,sK110(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145)),sK109(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145))) )
      | ~ hBOOL(hAPP(hAPP(U_7145,hAPP(c_Product__Type_Osnd(U_7146,U_7147),U_7148)),hAPP(c_Product__Type_Ofst(U_7146,U_7147),U_7148))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_7143,sK110(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145))],[f_2055_3]) ).

fof(f_2055_5,plain,
    ( ! [U_7145,U_7146,U_7147,U_7148,U_7149,U_7150,U_7151] :
        ( ~ hBOOL(hAPP(U_7149,hAPP(hAPP(U_7150,sK109(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145)),sK110(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145))))
        | ~ sP626(U_7145,U_7146,U_7147,U_7148,U_7149,U_7150,U_7151) )
    & ! [U_7145,U_7146,U_7147,U_7148,U_7149,U_7150,U_7151] :
        ( hBOOL(hAPP(hAPP(U_7145,sK110(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145)),sK109(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145)))
        | ~ sP626(U_7145,U_7146,U_7147,U_7148,U_7149,U_7150,U_7151) )
    & ! [U_7145,U_7146,U_7147,U_7148,U_7149,U_7150,U_7151] :
        ( hBOOL(hAPP(U_7149,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_7146,U_7147,U_7151),U_7150),U_7148)))
        | sP626(U_7145,U_7146,U_7147,U_7148,U_7149,U_7150,U_7151)
        | ~ hBOOL(hAPP(hAPP(U_7145,hAPP(c_Product__Type_Osnd(U_7146,U_7147),U_7148)),hAPP(c_Product__Type_Ofst(U_7146,U_7147),U_7148))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP626])],[f_2055_4]) ).

cnf(f_2055_6,plain,
    ( hBOOL(hAPP(U_7149,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_7146,U_7147,U_7151),U_7150),U_7148)))
    | sP626(U_7145,U_7146,U_7147,U_7148,U_7149,U_7150,U_7151)
    | ~ hBOOL(hAPP(hAPP(U_7145,hAPP(c_Product__Type_Osnd(U_7146,U_7147),U_7148)),hAPP(c_Product__Type_Ofst(U_7146,U_7147),U_7148))) ),
    inference(clausify,[status(thm)],[f_2055_5]) ).

cnf(f_2055_7,plain,
    ( hBOOL(hAPP(hAPP(U_7145,sK110(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145)),sK109(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145)))
    | ~ sP626(U_7145,U_7146,U_7147,U_7148,U_7149,U_7150,U_7151) ),
    inference(clausify,[status(thm)],[f_2055_5]) ).

cnf(f_2055_8,plain,
    ( ~ hBOOL(hAPP(U_7149,hAPP(hAPP(U_7150,sK109(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145)),sK110(U_7151,U_7150,U_7149,U_7148,U_7147,U_7146,U_7145))))
    | ~ sP626(U_7145,U_7146,U_7147,U_7148,U_7149,U_7150,U_7151) ),
    inference(clausify,[status(thm)],[f_2055_5]) ).

fof(f_2056_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_2056_2,plain,
    ! [U_7153,U_7152] :
      ( ( c_Quickcheck_Obeyond(U_7152,U_7153) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7152),U_7153)) )
      & ( c_Quickcheck_Obeyond(U_7152,U_7153) = U_7153
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7152),U_7153)) ) ),
    inference(variable_rename,[status(thm)],[f_2056_1]) ).

fof(f_2056_3,plain,
    ( ! [U_7157,U_7155] :
        ( c_Quickcheck_Obeyond(U_7155,U_7157) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7155),U_7157)) )
    & ! [U_7156,U_7154] :
        ( c_Quickcheck_Obeyond(U_7154,U_7156) = U_7156
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7154),U_7156)) ) ),
    inference(miniscope,[status(thm)],[f_2056_2]) ).

fof(f_2056_4,plain,
    ( ! [U_7155,U_7157] :
        ( c_Quickcheck_Obeyond(U_7155,U_7157) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7155),U_7157)) )
    & ! [U_7156,U_7154] :
        ( c_Quickcheck_Obeyond(U_7154,U_7156) = U_7156
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7154),U_7156)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2056_3]) ).

cnf(f_2056_5,plain,
    ( c_Quickcheck_Obeyond(U_7154,U_7156) = U_7156
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7154),U_7156)) ),
    inference(clausify,[status(thm)],[f_2056_4]) ).

cnf(f_2056_6,plain,
    ( c_Quickcheck_Obeyond(U_7155,U_7157) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7155),U_7157)) ),
    inference(clausify,[status(thm)],[f_2056_4]) ).

fof(f_2057_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_2057_2,plain,
    ! [U_7158] : c_Quickcheck_Obeyond(U_7158,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_2057_1]) ).

fof(f_2057_3,plain,
    ! [U_7158] : c_Quickcheck_Obeyond(U_7158,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_2057_2]) ).

cnf(f_2057_4,plain,
    c_Quickcheck_Obeyond(U_7158,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_2057_3]) ).

fof(f_2058_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_2058_2,plain,
    ! [U_7161,U_7160,U_7159] : c_HOL_OThe(tc_prod(U_7159,U_7160),U_7161) = c_HOL_OThe(tc_prod(U_7159,U_7160),hAPP(c_Product__Type_Oprod_Oprod__case(U_7159,U_7160,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_7160,tc_prod(U_7159,U_7160)),tc_fun(U_7160,tc_HOL_Obool),U_7159),hAPP(c_COMBB(tc_prod(U_7159,U_7160),tc_HOL_Obool,U_7160),U_7161)),c_Product__Type_OPair(U_7159,U_7160)))),
    inference(variable_rename,[status(thm)],[f_2058_1]) ).

fof(f_2058_3,plain,
    ! [U_7159,U_7160,U_7161] : c_HOL_OThe(tc_prod(U_7159,U_7160),U_7161) = c_HOL_OThe(tc_prod(U_7159,U_7160),hAPP(c_Product__Type_Oprod_Oprod__case(U_7159,U_7160,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_7160,tc_prod(U_7159,U_7160)),tc_fun(U_7160,tc_HOL_Obool),U_7159),hAPP(c_COMBB(tc_prod(U_7159,U_7160),tc_HOL_Obool,U_7160),U_7161)),c_Product__Type_OPair(U_7159,U_7160)))),
    inference(definitional_conversion,[status(esa)],[f_2058_2]) ).

cnf(f_2058_4,plain,
    c_HOL_OThe(tc_prod(U_7159,U_7160),U_7161) = c_HOL_OThe(tc_prod(U_7159,U_7160),hAPP(c_Product__Type_Oprod_Oprod__case(U_7159,U_7160,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_7160,tc_prod(U_7159,U_7160)),tc_fun(U_7160,tc_HOL_Obool),U_7159),hAPP(c_COMBB(tc_prod(U_7159,U_7160),tc_HOL_Obool,U_7160),U_7161)),c_Product__Type_OPair(U_7159,U_7160)))),
    inference(clausify,[status(thm)],[f_2058_3]) ).

fof(f_2059_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_2059_2,plain,
    ! [U_7165,U_7164,U_7163,U_7162] : c_HOL_OThe(tc_prod(U_7162,U_7163),hAPP(c_Product__Type_Oprod_Oprod__case(U_7162,U_7163,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7162,tc_fun(U_7163,tc_HOL_Obool),tc_fun(U_7163,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_7163,tc_HOL_Obool),tc_fun(U_7163,tc_HOL_Obool)),U_7162),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_7163)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_7162),c_fconj),hAPP(c_fequal,U_7164)))),hAPP(c_fequal,U_7165)))) = hAPP(hAPP(c_Product__Type_OPair(U_7162,U_7163),U_7164),U_7165),
    inference(variable_rename,[status(thm)],[f_2059_1]) ).

fof(f_2059_3,plain,
    ! [U_7162,U_7163,U_7164,U_7165] : c_HOL_OThe(tc_prod(U_7162,U_7163),hAPP(c_Product__Type_Oprod_Oprod__case(U_7162,U_7163,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7162,tc_fun(U_7163,tc_HOL_Obool),tc_fun(U_7163,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_7163,tc_HOL_Obool),tc_fun(U_7163,tc_HOL_Obool)),U_7162),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_7163)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_7162),c_fconj),hAPP(c_fequal,U_7164)))),hAPP(c_fequal,U_7165)))) = hAPP(hAPP(c_Product__Type_OPair(U_7162,U_7163),U_7164),U_7165),
    inference(definitional_conversion,[status(esa)],[f_2059_2]) ).

cnf(f_2059_4,plain,
    c_HOL_OThe(tc_prod(U_7162,U_7163),hAPP(c_Product__Type_Oprod_Oprod__case(U_7162,U_7163,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7162,tc_fun(U_7163,tc_HOL_Obool),tc_fun(U_7163,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_7163,tc_HOL_Obool),tc_fun(U_7163,tc_HOL_Obool)),U_7162),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_7163)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_7162),c_fconj),hAPP(c_fequal,U_7164)))),hAPP(c_fequal,U_7165)))) = hAPP(hAPP(c_Product__Type_OPair(U_7162,U_7163),U_7164),U_7165),
    inference(clausify,[status(thm)],[f_2059_3]) ).

fof(f_2060_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_2060_2,plain,
    ! [U_7167,U_7166] : c_Divides_Odivmod__nat(U_7166,U_7167) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_7166,U_7167)),
    inference(variable_rename,[status(thm)],[f_2060_1]) ).

fof(f_2060_3,plain,
    ! [U_7167,U_7166] : c_Divides_Odivmod__nat(U_7166,U_7167) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_7166,U_7167)),
    inference(definitional_conversion,[status(esa)],[f_2060_2]) ).

cnf(f_2060_4,plain,
    c_Divides_Odivmod__nat(U_7166,U_7167) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_7166,U_7167)),
    inference(clausify,[status(thm)],[f_2060_3]) ).

fof(f_2061_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_2061_2,plain,
    ! [U_7170,U_7169,U_7168] : c_Random__Sequence_Oempty(U_7168,U_7169,U_7170) = 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_7168)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_7168)),
    inference(variable_rename,[status(thm)],[f_2061_1]) ).

fof(f_2061_3,plain,
    ! [U_7168,U_7169,U_7170] : c_Random__Sequence_Oempty(U_7168,U_7169,U_7170) = 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_7168)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_7168)),
    inference(definitional_conversion,[status(esa)],[f_2061_2]) ).

cnf(f_2061_4,plain,
    c_Random__Sequence_Oempty(U_7168,U_7169,U_7170) = 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_7168)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_7168)),
    inference(clausify,[status(thm)],[f_2061_3]) ).

fof(f_2062_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_2062_2,plain,
    ! [U_7174,U_7173,U_7172,U_7171] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(U_7171),U_7172),U_7173),U_7174) = 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_7171)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(U_7171),U_7172)),
    inference(variable_rename,[status(thm)],[f_2062_1]) ).

fof(f_2062_3,plain,
    ! [U_7171,U_7172,U_7173,U_7174] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(U_7171),U_7172),U_7173),U_7174) = 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_7171)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(U_7171),U_7172)),
    inference(definitional_conversion,[status(esa)],[f_2062_2]) ).

cnf(f_2062_4,plain,
    hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(U_7171),U_7172),U_7173),U_7174) = 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_7171)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(U_7171),U_7172)),
    inference(clausify,[status(thm)],[f_2062_3]) ).

fof(f_2063_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_2063_2,plain,
    ! [U_7176,U_7175] : c_HOL_OThe(U_7175,hAPP(hAPP(c_COMBC(U_7175,U_7175,tc_HOL_Obool),c_fequal),U_7176)) = U_7176,
    inference(variable_rename,[status(thm)],[f_2063_1]) ).

fof(f_2063_3,plain,
    ! [U_7175,U_7176] : c_HOL_OThe(U_7175,hAPP(hAPP(c_COMBC(U_7175,U_7175,tc_HOL_Obool),c_fequal),U_7176)) = U_7176,
    inference(definitional_conversion,[status(esa)],[f_2063_2]) ).

cnf(f_2063_4,plain,
    c_HOL_OThe(U_7175,hAPP(hAPP(c_COMBC(U_7175,U_7175,tc_HOL_Obool),c_fequal),U_7176)) = U_7176,
    inference(clausify,[status(thm)],[f_2063_3]) ).

fof(f_2064_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_2064_2,plain,
    ! [U_7178,U_7177] : c_HOL_OThe(U_7177,hAPP(c_fequal,U_7178)) = U_7178,
    inference(variable_rename,[status(thm)],[f_2064_1]) ).

fof(f_2064_3,plain,
    ! [U_7177,U_7178] : c_HOL_OThe(U_7177,hAPP(c_fequal,U_7178)) = U_7178,
    inference(definitional_conversion,[status(esa)],[f_2064_2]) ).

cnf(f_2064_4,plain,
    c_HOL_OThe(U_7177,hAPP(c_fequal,U_7178)) = U_7178,
    inference(clausify,[status(thm)],[f_2064_3]) ).

fof(f_2065_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_2065_2,plain,
    ! [U_7184,U_7183,U_7182,U_7181,U_7180,U_7179] : hAPP(hAPP(c_Product__Type_Ocurry(U_7179,U_7180,U_7181,U_7182),U_7183),U_7184) = hAPP(U_7182,hAPP(hAPP(c_Product__Type_OPair(U_7179,U_7180),U_7183),U_7184)),
    inference(variable_rename,[status(thm)],[f_2065_1]) ).

fof(f_2065_3,plain,
    ! [U_7179,U_7180,U_7181,U_7182,U_7183,U_7184] : hAPP(hAPP(c_Product__Type_Ocurry(U_7179,U_7180,U_7181,U_7182),U_7183),U_7184) = hAPP(U_7182,hAPP(hAPP(c_Product__Type_OPair(U_7179,U_7180),U_7183),U_7184)),
    inference(definitional_conversion,[status(esa)],[f_2065_2]) ).

cnf(f_2065_4,plain,
    hAPP(hAPP(c_Product__Type_Ocurry(U_7179,U_7180,U_7181,U_7182),U_7183),U_7184) = hAPP(U_7182,hAPP(hAPP(c_Product__Type_OPair(U_7179,U_7180),U_7183),U_7184)),
    inference(clausify,[status(thm)],[f_2065_3]) ).

fof(f_2066_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_2066_2,plain,
    ! [U_7189,U_7188,U_7187,U_7186,U_7185] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_7186,U_7187,tc_HOL_Obool,U_7185),U_7188),U_7189))
      | ~ hBOOL(hAPP(U_7185,hAPP(hAPP(c_Product__Type_OPair(U_7186,U_7187),U_7188),U_7189))) ),
    inference(variable_rename,[status(thm)],[f_2066_1]) ).

fof(f_2066_3,plain,
    ! [U_7186,U_7185,U_7187,U_7188,U_7189] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_7186,U_7187,tc_HOL_Obool,U_7185),U_7188),U_7189))
      | ~ hBOOL(hAPP(U_7185,hAPP(hAPP(c_Product__Type_OPair(U_7186,U_7187),U_7188),U_7189))) ),
    inference(definitional_conversion,[status(esa)],[f_2066_2]) ).

cnf(f_2066_4,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_7186,U_7187,tc_HOL_Obool,U_7185),U_7188),U_7189))
    | ~ hBOOL(hAPP(U_7185,hAPP(hAPP(c_Product__Type_OPair(U_7186,U_7187),U_7188),U_7189))) ),
    inference(clausify,[status(thm)],[f_2066_3]) ).

fof(f_2067_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_2067_2,plain,
    ! [U_7194,U_7193,U_7192,U_7191,U_7190] :
      ( hBOOL(hAPP(U_7192,hAPP(hAPP(c_Product__Type_OPair(U_7190,U_7191),U_7193),U_7194)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_7190,U_7191,tc_HOL_Obool,U_7192),U_7193),U_7194)) ),
    inference(variable_rename,[status(thm)],[f_2067_1]) ).

fof(f_2067_3,plain,
    ! [U_7190,U_7191,U_7192,U_7193,U_7194] :
      ( hBOOL(hAPP(U_7192,hAPP(hAPP(c_Product__Type_OPair(U_7190,U_7191),U_7193),U_7194)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_7190,U_7191,tc_HOL_Obool,U_7192),U_7193),U_7194)) ),
    inference(definitional_conversion,[status(esa)],[f_2067_2]) ).

cnf(f_2067_4,plain,
    ( hBOOL(hAPP(U_7192,hAPP(hAPP(c_Product__Type_OPair(U_7190,U_7191),U_7193),U_7194)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_7190,U_7191,tc_HOL_Obool,U_7192),U_7193),U_7194)) ),
    inference(clausify,[status(thm)],[f_2067_3]) ).

fof(f_2068_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_2068_2,plain,
    ! [U_7199,U_7198,U_7197,U_7196,U_7195] :
      ( hBOOL(hAPP(U_7197,hAPP(hAPP(c_Product__Type_OPair(U_7195,U_7196),U_7198),U_7199)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_7195,U_7196,tc_HOL_Obool,U_7197),U_7198),U_7199)) ),
    inference(variable_rename,[status(thm)],[f_2068_1]) ).

fof(f_2068_3,plain,
    ! [U_7195,U_7196,U_7197,U_7198,U_7199] :
      ( hBOOL(hAPP(U_7197,hAPP(hAPP(c_Product__Type_OPair(U_7195,U_7196),U_7198),U_7199)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_7195,U_7196,tc_HOL_Obool,U_7197),U_7198),U_7199)) ),
    inference(definitional_conversion,[status(esa)],[f_2068_2]) ).

cnf(f_2068_4,plain,
    ( hBOOL(hAPP(U_7197,hAPP(hAPP(c_Product__Type_OPair(U_7195,U_7196),U_7198),U_7199)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_7195,U_7196,tc_HOL_Obool,U_7197),U_7198),U_7199)) ),
    inference(clausify,[status(thm)],[f_2068_3]) ).

fof(f_2069_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_2069_2,plain,
    ! [U_7205,U_7204,U_7203,U_7202,U_7201,U_7200] : hAPP(hAPP(c_Product__Type_Ocurry(U_7200,U_7201,U_7202,U_7203),U_7204),U_7205) = hAPP(U_7203,hAPP(hAPP(c_Product__Type_OPair(U_7200,U_7201),U_7204),U_7205)),
    inference(variable_rename,[status(thm)],[f_2069_1]) ).

fof(f_2069_3,plain,
    ! [U_7200,U_7201,U_7202,U_7203,U_7204,U_7205] : hAPP(hAPP(c_Product__Type_Ocurry(U_7200,U_7201,U_7202,U_7203),U_7204),U_7205) = hAPP(U_7203,hAPP(hAPP(c_Product__Type_OPair(U_7200,U_7201),U_7204),U_7205)),
    inference(definitional_conversion,[status(esa)],[f_2069_2]) ).

cnf(f_2069_4,plain,
    hAPP(hAPP(c_Product__Type_Ocurry(U_7200,U_7201,U_7202,U_7203),U_7204),U_7205) = hAPP(U_7203,hAPP(hAPP(c_Product__Type_OPair(U_7200,U_7201),U_7204),U_7205)),
    inference(clausify,[status(thm)],[f_2069_3]) ).

fof(f_2070_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_2070_2,plain,
    ! [U_7209,U_7208,U_7207,U_7206] : c_Product__Type_Ocurry(U_7206,U_7207,U_7208,hAPP(c_Product__Type_Oprod_Oprod__case(U_7206,U_7207,U_7208),U_7209)) = U_7209,
    inference(variable_rename,[status(thm)],[f_2070_1]) ).

fof(f_2070_3,plain,
    ! [U_7206,U_7208,U_7207,U_7209] : c_Product__Type_Ocurry(U_7206,U_7207,U_7208,hAPP(c_Product__Type_Oprod_Oprod__case(U_7206,U_7207,U_7208),U_7209)) = U_7209,
    inference(definitional_conversion,[status(esa)],[f_2070_2]) ).

cnf(f_2070_4,plain,
    c_Product__Type_Ocurry(U_7206,U_7207,U_7208,hAPP(c_Product__Type_Oprod_Oprod__case(U_7206,U_7207,U_7208),U_7209)) = U_7209,
    inference(clausify,[status(thm)],[f_2070_3]) ).

fof(f_2071_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_2071_2,plain,
    ! [U_7213,U_7212,U_7211,U_7210] : hAPP(c_Product__Type_Oprod_Oprod__case(U_7210,U_7211,U_7212),c_Product__Type_Ocurry(U_7210,U_7211,U_7212,U_7213)) = U_7213,
    inference(variable_rename,[status(thm)],[f_2071_1]) ).

fof(f_2071_3,plain,
    ! [U_7210,U_7211,U_7212,U_7213] : hAPP(c_Product__Type_Oprod_Oprod__case(U_7210,U_7211,U_7212),c_Product__Type_Ocurry(U_7210,U_7211,U_7212,U_7213)) = U_7213,
    inference(definitional_conversion,[status(esa)],[f_2071_2]) ).

cnf(f_2071_4,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_7210,U_7211,U_7212),c_Product__Type_Ocurry(U_7210,U_7211,U_7212,U_7213)) = U_7213,
    inference(clausify,[status(thm)],[f_2071_3]) ).

fof(f_2072_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_2072_2,plain,
    ! [U_7218,U_7217,U_7216] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(U_7216,U_7217),U_7218))
        | ? [U_7215] :
            ( ~ hBOOL(hAPP(U_7217,U_7215))
            & hBOOL(hAPP(hAPP(c_member(U_7216),U_7215),U_7218)) ) )
      & ( ! [U_7214] :
            ( hBOOL(hAPP(U_7217,U_7214))
            | ~ hBOOL(hAPP(hAPP(c_member(U_7216),U_7214),U_7218)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_7216,U_7217),U_7218)) ) ),
    inference(variable_rename,[status(thm)],[f_2072_1]) ).

fof(f_2072_3,plain,
    ( ! [U_7224,U_7222,U_7220] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_7220,U_7222),U_7224))
        | ? [U_7215] :
            ( ~ hBOOL(hAPP(U_7222,U_7215))
            & hBOOL(hAPP(hAPP(c_member(U_7220),U_7215),U_7224)) ) )
    & ! [U_7223,U_7221,U_7219] :
        ( ! [U_7214] :
            ( hBOOL(hAPP(U_7221,U_7214))
            | ~ hBOOL(hAPP(hAPP(c_member(U_7219),U_7214),U_7223)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_7219,U_7221),U_7223)) ) ),
    inference(miniscope,[status(thm)],[f_2072_2]) ).

fof(f_2072_4,plain,
    ( ! [U_7224,U_7222,U_7220] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_7220,U_7222),U_7224))
        | ( ~ hBOOL(hAPP(U_7222,sK111(U_7224,U_7222,U_7220)))
          & hBOOL(hAPP(hAPP(c_member(U_7220),sK111(U_7224,U_7222,U_7220)),U_7224)) ) )
    & ! [U_7223,U_7221,U_7219] :
        ( ! [U_7214] :
            ( hBOOL(hAPP(U_7221,U_7214))
            | ~ hBOOL(hAPP(hAPP(c_member(U_7219),U_7214),U_7223)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_7219,U_7221),U_7223)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_7215,sK111(U_7224,U_7222,U_7220))],[f_2072_3]) ).

fof(f_2072_5,plain,
    ( ! [U_7222,U_7220,U_7224] :
        ( ~ hBOOL(hAPP(U_7222,sK111(U_7224,U_7222,U_7220)))
        | ~ sP627(U_7222,U_7220,U_7224) )
    & ! [U_7222,U_7220,U_7224] :
        ( hBOOL(hAPP(hAPP(c_member(U_7220),sK111(U_7224,U_7222,U_7220)),U_7224))
        | ~ sP627(U_7222,U_7220,U_7224) )
    & ! [U_7222,U_7220,U_7224] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_7220,U_7222),U_7224))
        | sP627(U_7222,U_7220,U_7224) )
    & ! [U_7214,U_7221,U_7223,U_7219] :
        ( hBOOL(hAPP(U_7221,U_7214))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7219),U_7214),U_7223))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_7219,U_7221),U_7223)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP627])],[f_2072_4]) ).

cnf(f_2072_6,plain,
    ( hBOOL(hAPP(U_7221,U_7214))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7219),U_7214),U_7223))
    | ~ hBOOL(hAPP(c_Predicate_OPowp(U_7219,U_7221),U_7223)) ),
    inference(clausify,[status(thm)],[f_2072_5]) ).

cnf(f_2072_7,plain,
    ( hBOOL(hAPP(c_Predicate_OPowp(U_7220,U_7222),U_7224))
    | sP627(U_7222,U_7220,U_7224) ),
    inference(clausify,[status(thm)],[f_2072_5]) ).

cnf(f_2072_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7220),sK111(U_7224,U_7222,U_7220)),U_7224))
    | ~ sP627(U_7222,U_7220,U_7224) ),
    inference(clausify,[status(thm)],[f_2072_5]) ).

cnf(f_2072_9,plain,
    ( ~ hBOOL(hAPP(U_7222,sK111(U_7224,U_7222,U_7220)))
    | ~ sP627(U_7222,U_7220,U_7224) ),
    inference(clausify,[status(thm)],[f_2072_5]) ).

fof(f_2073_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_2073_2,plain,
    ! [U_7227,U_7226,U_7225] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7226),U_7227))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7225))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7225),U_7226)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7225),U_7227))) ),
    inference(variable_rename,[status(thm)],[f_2073_1]) ).

fof(f_2073_3,plain,
    ! [U_7227,U_7226,U_7225] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7226),U_7227))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7225))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7225),U_7226)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7225),U_7227))) ),
    inference(definitional_conversion,[status(esa)],[f_2073_2]) ).

cnf(f_2073_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7226),U_7227))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7225))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7225),U_7226)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7225),U_7227))) ),
    inference(clausify,[status(thm)],[f_2073_3]) ).

fof(f_2074_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_2074_2,plain,
    ! [U_7235,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),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7228),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_7233)))),hAPP(hAPP(c_COMBC(U_7228,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_7228),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7230)),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_7235)))),c_Com_Ocom_OCall(U_7234,U_7231,U_7235)),U_7232)),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),hAPP(c_Com_Ocom_OBODY,U_7231)),hAPP(hAPP(c_COMBC(U_7228,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_7228),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7232)),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_7233)))),U_7234)),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_7228),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2074_1]) ).

fof(f_2074_3,plain,
    ! [U_7228,U_7229,U_7230,U_7231,U_7232,U_7233,U_7234,U_7235] :
      ( 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),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7228),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_7233)))),hAPP(hAPP(c_COMBC(U_7228,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_7228),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7230)),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_7235)))),c_Com_Ocom_OCall(U_7234,U_7231,U_7235)),U_7232)),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),hAPP(c_Com_Ocom_OBODY,U_7231)),hAPP(hAPP(c_COMBC(U_7228,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_7228),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7232)),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_7233)))),U_7234)),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_7228),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2074_2]) ).

cnf(f_2074_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),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7228),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_7233)))),hAPP(hAPP(c_COMBC(U_7228,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_7228),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7230)),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_7235)))),c_Com_Ocom_OCall(U_7234,U_7231,U_7235)),U_7232)),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),hAPP(c_Com_Ocom_OBODY,U_7231)),hAPP(hAPP(c_COMBC(U_7228,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_7228),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7232)),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_7233)))),U_7234)),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_7228),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2074_3]) ).

fof(f_2075_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_2075_2,plain,
    ! [U_7237,U_7236] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7237),U_7236)),U_7236))
          | U_7237 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        & ( U_7237 = 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_7237),U_7236)),U_7236)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7236)) ),
    inference(variable_rename,[status(thm)],[f_2075_1]) ).

fof(f_2075_3,plain,
    ( ! [U_7236,U_7237] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7237),U_7236)),U_7236))
        | U_7237 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP628(U_7236,U_7237) )
    & ! [U_7236,U_7237] :
        ( U_7237 = 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_7237),U_7236)),U_7236))
        | ~ sP628(U_7236,U_7237) )
    & ! [U_7236,U_7237] :
        ( sP628(U_7236,U_7237)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7236)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP628])],[f_2075_2]) ).

cnf(f_2075_4,plain,
    ( sP628(U_7236,U_7237)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7236)) ),
    inference(clausify,[status(thm)],[f_2075_3]) ).

cnf(f_2075_5,plain,
    ( U_7237 = 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_7237),U_7236)),U_7236))
    | ~ sP628(U_7236,U_7237) ),
    inference(clausify,[status(thm)],[f_2075_3]) ).

cnf(f_2075_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7237),U_7236)),U_7236))
    | U_7237 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP628(U_7236,U_7237) ),
    inference(clausify,[status(thm)],[f_2075_3]) ).

fof(f_2076_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_2076_2,plain,
    ! [U_7239,U_7238] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7238),U_7239)),U_7238))
          | U_7239 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        & ( U_7239 = 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_7238),U_7239)),U_7238)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7238)) ),
    inference(variable_rename,[status(thm)],[f_2076_1]) ).

fof(f_2076_3,plain,
    ( ! [U_7239,U_7238] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7238),U_7239)),U_7238))
        | U_7239 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP629(U_7239,U_7238) )
    & ! [U_7239,U_7238] :
        ( U_7239 = 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_7238),U_7239)),U_7238))
        | ~ sP629(U_7239,U_7238) )
    & ! [U_7239,U_7238] :
        ( sP629(U_7239,U_7238)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7238)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP629])],[f_2076_2]) ).

cnf(f_2076_4,plain,
    ( sP629(U_7239,U_7238)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7238)) ),
    inference(clausify,[status(thm)],[f_2076_3]) ).

cnf(f_2076_5,plain,
    ( U_7239 = 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_7238),U_7239)),U_7238))
    | ~ sP629(U_7239,U_7238) ),
    inference(clausify,[status(thm)],[f_2076_3]) ).

cnf(f_2076_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7238),U_7239)),U_7238))
    | U_7239 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP629(U_7239,U_7238) ),
    inference(clausify,[status(thm)],[f_2076_3]) ).

fof(f_2077_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_2077_2,plain,
    ! [U_7240] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7240),U_7240)),
    inference(variable_rename,[status(thm)],[f_2077_1]) ).

fof(f_2077_3,plain,
    ! [U_7240] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7240),U_7240)),
    inference(definitional_conversion,[status(esa)],[f_2077_2]) ).

cnf(f_2077_4,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7240),U_7240)),
    inference(clausify,[status(thm)],[f_2077_3]) ).

fof(f_2078_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_2078_2,plain,
    ! [U_7242,U_7241] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7241),U_7242),c_Groups_Ozero__class_Ozero(U_7241)))
      | ~ class_Rings_Ocomm__semiring__1(U_7241) ),
    inference(variable_rename,[status(thm)],[f_2078_1]) ).

fof(f_2078_3,plain,
    ! [U_7242,U_7241] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7241),U_7242),c_Groups_Ozero__class_Ozero(U_7241)))
      | ~ class_Rings_Ocomm__semiring__1(U_7241) ),
    inference(definitional_conversion,[status(esa)],[f_2078_2]) ).

cnf(f_2078_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7241),U_7242),c_Groups_Ozero__class_Ozero(U_7241)))
    | ~ class_Rings_Ocomm__semiring__1(U_7241) ),
    inference(clausify,[status(thm)],[f_2078_3]) ).

fof(f_2079_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_2079_2,plain,
    ! [U_7244,U_7243] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7243,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7243,tc_HOL_Obool))),U_7244)),
    inference(variable_rename,[status(thm)],[f_2079_1]) ).

fof(f_2079_3,plain,
    ! [U_7243,U_7244] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7243,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7243,tc_HOL_Obool))),U_7244)),
    inference(definitional_conversion,[status(esa)],[f_2079_2]) ).

cnf(f_2079_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7243,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7243,tc_HOL_Obool))),U_7244)),
    inference(clausify,[status(thm)],[f_2079_3]) ).

fof(f_2080_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_2080_2,plain,
    ! [U_7245] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_7245)),
    inference(variable_rename,[status(thm)],[f_2080_1]) ).

fof(f_2080_3,plain,
    ! [U_7245] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_7245)),
    inference(definitional_conversion,[status(esa)],[f_2080_2]) ).

cnf(f_2080_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_7245)),
    inference(clausify,[status(thm)],[f_2080_3]) ).

fof(f_2081_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_2081_2,plain,
    ! [U_7248,U_7247,U_7246] :
      ( hBOOL(hAPP(U_7248,U_7246))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7247),U_7246),c_Orderings_Obot__class_Obot(tc_fun(U_7247,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2081_1]) ).

fof(f_2081_3,plain,
    ! [U_7246,U_7247,U_7248] :
      ( hBOOL(hAPP(U_7248,U_7246))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7247),U_7246),c_Orderings_Obot__class_Obot(tc_fun(U_7247,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2081_2]) ).

cnf(f_2081_4,plain,
    ( hBOOL(hAPP(U_7248,U_7246))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7247),U_7246),c_Orderings_Obot__class_Obot(tc_fun(U_7247,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2081_3]) ).

fof(f_2082_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_2082_2,plain,
    ! [U_7253,U_7252,U_7251,U_7250,U_7249] : c_Hoare__Mirabelle_Ohoare__derivs(U_7249,U_7250,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7249)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7249),hAPP(hAPP(c_COMBC(U_7249,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_7249),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7251)),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_7252)),U_7253))),c_Com_Ocom_OAss(U_7252,U_7253)),U_7251)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7249),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2082_1]) ).

fof(f_2082_3,plain,
    ! [U_7249,U_7250,U_7251,U_7252,U_7253] : c_Hoare__Mirabelle_Ohoare__derivs(U_7249,U_7250,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7249)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7249),hAPP(hAPP(c_COMBC(U_7249,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_7249),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7251)),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_7252)),U_7253))),c_Com_Ocom_OAss(U_7252,U_7253)),U_7251)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7249),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2082_2]) ).

cnf(f_2082_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_7249,U_7250,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7249)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7249),hAPP(hAPP(c_COMBC(U_7249,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_7249),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7251)),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_7252)),U_7253))),c_Com_Ocom_OAss(U_7252,U_7253)),U_7251)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7249),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2082_3]) ).

fof(f_2083_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_2083_2,plain,
    ! [U_7258,U_7257,U_7256,U_7255,U_7254] : c_Hoare__Mirabelle_Ohoare__derivs(U_7254,U_7255,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7254)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7254),hAPP(hAPP(c_COMBC(U_7254,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_7254),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7256)),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_7257)),U_7258))),c_Com_Ocom_OAss(U_7257,U_7258)),U_7256)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7254),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2083_1]) ).

fof(f_2083_3,plain,
    ! [U_7254,U_7255,U_7256,U_7257,U_7258] : c_Hoare__Mirabelle_Ohoare__derivs(U_7254,U_7255,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7254)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7254),hAPP(hAPP(c_COMBC(U_7254,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_7254),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7256)),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_7257)),U_7258))),c_Com_Ocom_OAss(U_7257,U_7258)),U_7256)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7254),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2083_2]) ).

cnf(f_2083_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_7254,U_7255,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7254)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7254),hAPP(hAPP(c_COMBC(U_7254,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_7254),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7256)),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_7257)),U_7258))),c_Com_Ocom_OAss(U_7257,U_7258)),U_7256)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7254),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2083_3]) ).

fof(f_2084_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_2084_2,plain,
    ! [U_7261,U_7260,U_7259] :
      ( U_7260 = hAPP(hAPP(c_Set_Oinsert(U_7259),U_7261),c_Orderings_Obot__class_Obot(tc_fun(U_7259,tc_HOL_Obool)))
      | U_7260 = c_Orderings_Obot__class_Obot(tc_fun(U_7259,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7259,tc_HOL_Obool)),U_7260),hAPP(hAPP(c_Set_Oinsert(U_7259),U_7261),c_Orderings_Obot__class_Obot(tc_fun(U_7259,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_2084_1]) ).

fof(f_2084_3,plain,
    ! [U_7259,U_7260,U_7261] :
      ( U_7260 = hAPP(hAPP(c_Set_Oinsert(U_7259),U_7261),c_Orderings_Obot__class_Obot(tc_fun(U_7259,tc_HOL_Obool)))
      | U_7260 = c_Orderings_Obot__class_Obot(tc_fun(U_7259,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7259,tc_HOL_Obool)),U_7260),hAPP(hAPP(c_Set_Oinsert(U_7259),U_7261),c_Orderings_Obot__class_Obot(tc_fun(U_7259,tc_HOL_Obool))))) ),
    inference(definitional_conversion,[status(esa)],[f_2084_2]) ).

cnf(f_2084_4,plain,
    ( U_7260 = hAPP(hAPP(c_Set_Oinsert(U_7259),U_7261),c_Orderings_Obot__class_Obot(tc_fun(U_7259,tc_HOL_Obool)))
    | U_7260 = c_Orderings_Obot__class_Obot(tc_fun(U_7259,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7259,tc_HOL_Obool)),U_7260),hAPP(hAPP(c_Set_Oinsert(U_7259),U_7261),c_Orderings_Obot__class_Obot(tc_fun(U_7259,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_2084_3]) ).

fof(f_2085_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_2085_2,plain,
    ! [U_7264,U_7263,U_7262] : c_Orderings_Obot__class_Obot(tc_fun(U_7262,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_7262),U_7263),U_7264),
    inference(variable_rename,[status(thm)],[f_2085_1]) ).

fof(f_2085_3,plain,
    ! [U_7262,U_7263,U_7264] : c_Orderings_Obot__class_Obot(tc_fun(U_7262,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_7262),U_7263),U_7264),
    inference(definitional_conversion,[status(esa)],[f_2085_2]) ).

cnf(f_2085_4,plain,
    c_Orderings_Obot__class_Obot(tc_fun(U_7262,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_7262),U_7263),U_7264),
    inference(clausify,[status(thm)],[f_2085_3]) ).

fof(f_2086_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_2086_2,plain,
    ! [U_7267,U_7266,U_7265] : hAPP(hAPP(c_Set_Oinsert(U_7265),U_7266),U_7267) != c_Orderings_Obot__class_Obot(tc_fun(U_7265,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2086_1]) ).

fof(f_2086_3,plain,
    ! [U_7265,U_7266,U_7267] : hAPP(hAPP(c_Set_Oinsert(U_7265),U_7266),U_7267) != c_Orderings_Obot__class_Obot(tc_fun(U_7265,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2086_2]) ).

cnf(f_2086_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_7265),U_7266),U_7267) != c_Orderings_Obot__class_Obot(tc_fun(U_7265,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2086_3]) ).

fof(f_2087_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_2087_2,plain,
    ! [U_7270,U_7269,U_7268] : hAPP(hAPP(c_Set_Oinsert(U_7268),U_7269),hAPP(hAPP(c_Set_Oinsert(U_7268),U_7269),U_7270)) = hAPP(hAPP(c_Set_Oinsert(U_7268),U_7269),U_7270),
    inference(variable_rename,[status(thm)],[f_2087_1]) ).

fof(f_2087_3,plain,
    ! [U_7268,U_7269,U_7270] : hAPP(hAPP(c_Set_Oinsert(U_7268),U_7269),hAPP(hAPP(c_Set_Oinsert(U_7268),U_7269),U_7270)) = hAPP(hAPP(c_Set_Oinsert(U_7268),U_7269),U_7270),
    inference(definitional_conversion,[status(esa)],[f_2087_2]) ).

cnf(f_2087_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_7268),U_7269),hAPP(hAPP(c_Set_Oinsert(U_7268),U_7269),U_7270)) = hAPP(hAPP(c_Set_Oinsert(U_7268),U_7269),U_7270),
    inference(clausify,[status(thm)],[f_2087_3]) ).

fof(f_2088_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_2088_2,plain,
    ! [U_7274,U_7273,U_7272,U_7271] : hAPP(hAPP(c_Set_Oinsert(U_7271),U_7272),hAPP(hAPP(c_Set_Oinsert(U_7271),U_7273),U_7274)) = hAPP(hAPP(c_Set_Oinsert(U_7271),U_7273),hAPP(hAPP(c_Set_Oinsert(U_7271),U_7272),U_7274)),
    inference(variable_rename,[status(thm)],[f_2088_1]) ).

fof(f_2088_3,plain,
    ! [U_7271,U_7272,U_7273,U_7274] : hAPP(hAPP(c_Set_Oinsert(U_7271),U_7272),hAPP(hAPP(c_Set_Oinsert(U_7271),U_7273),U_7274)) = hAPP(hAPP(c_Set_Oinsert(U_7271),U_7273),hAPP(hAPP(c_Set_Oinsert(U_7271),U_7272),U_7274)),
    inference(definitional_conversion,[status(esa)],[f_2088_2]) ).

cnf(f_2088_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_7271),U_7272),hAPP(hAPP(c_Set_Oinsert(U_7271),U_7273),U_7274)) = hAPP(hAPP(c_Set_Oinsert(U_7271),U_7273),hAPP(hAPP(c_Set_Oinsert(U_7271),U_7272),U_7274)),
    inference(clausify,[status(thm)],[f_2088_3]) ).

fof(f_2089_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_2089_2,plain,
    ! [U_7279,U_7278,U_7277,U_7276,U_7275] :
      ( ( hAPP(hAPP(c_Set_Oinsert(U_7275),U_7276),hAPP(hAPP(c_Set_Oinsert(U_7275),U_7277),c_Orderings_Obot__class_Obot(tc_fun(U_7275,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_7275),U_7278),hAPP(hAPP(c_Set_Oinsert(U_7275),U_7279),c_Orderings_Obot__class_Obot(tc_fun(U_7275,tc_HOL_Obool))))
        | ( ( U_7277 != U_7278
            | U_7276 != U_7279 )
          & ( U_7277 != U_7279
            | U_7276 != U_7278 ) ) )
      & ( ( U_7277 = U_7278
          & U_7276 = U_7279 )
        | ( U_7277 = U_7279
          & U_7276 = U_7278 )
        | hAPP(hAPP(c_Set_Oinsert(U_7275),U_7276),hAPP(hAPP(c_Set_Oinsert(U_7275),U_7277),c_Orderings_Obot__class_Obot(tc_fun(U_7275,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_7275),U_7278),hAPP(hAPP(c_Set_Oinsert(U_7275),U_7279),c_Orderings_Obot__class_Obot(tc_fun(U_7275,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_2089_1]) ).

fof(f_2089_3,plain,
    ( ! [U_7289,U_7287,U_7285,U_7283] :
        ( ! [U_7281] : hAPP(hAPP(c_Set_Oinsert(U_7281),U_7283),hAPP(hAPP(c_Set_Oinsert(U_7281),U_7285),c_Orderings_Obot__class_Obot(tc_fun(U_7281,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_7281),U_7287),hAPP(hAPP(c_Set_Oinsert(U_7281),U_7289),c_Orderings_Obot__class_Obot(tc_fun(U_7281,tc_HOL_Obool))))
        | ( ( U_7285 != U_7287
            | U_7283 != U_7289 )
          & ( U_7285 != U_7289
            | U_7283 != U_7287 ) ) )
    & ! [U_7288,U_7286,U_7284,U_7282] :
        ( ! [U_7280] : hAPP(hAPP(c_Set_Oinsert(U_7280),U_7282),hAPP(hAPP(c_Set_Oinsert(U_7280),U_7284),c_Orderings_Obot__class_Obot(tc_fun(U_7280,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_7280),U_7286),hAPP(hAPP(c_Set_Oinsert(U_7280),U_7288),c_Orderings_Obot__class_Obot(tc_fun(U_7280,tc_HOL_Obool))))
        | ( U_7284 = U_7286
          & U_7282 = U_7288 )
        | ( U_7284 = U_7288
          & U_7282 = U_7286 ) ) ),
    inference(miniscope,[status(thm)],[f_2089_2]) ).

fof(f_2089_4,plain,
    ( ! [U_7285,U_7287,U_7283,U_7289] :
        ( U_7285 != U_7287
        | U_7283 != U_7289
        | ~ sP632(U_7285,U_7287,U_7283,U_7289) )
    & ! [U_7285,U_7287,U_7283,U_7289] :
        ( U_7285 != U_7289
        | U_7283 != U_7287
        | ~ sP632(U_7285,U_7287,U_7283,U_7289) )
    & ! [U_7284,U_7282,U_7288,U_7286] :
        ( U_7284 = U_7286
        | ~ sP631(U_7284,U_7282,U_7288,U_7286) )
    & ! [U_7284,U_7282,U_7288,U_7286] :
        ( U_7282 = U_7288
        | ~ sP631(U_7284,U_7282,U_7288,U_7286) )
    & ! [U_7284,U_7282,U_7288,U_7286] :
        ( U_7284 = U_7288
        | ~ sP630(U_7284,U_7282,U_7288,U_7286) )
    & ! [U_7284,U_7282,U_7288,U_7286] :
        ( U_7282 = U_7286
        | ~ sP630(U_7284,U_7282,U_7288,U_7286) )
    & ! [U_7285,U_7281,U_7287,U_7283,U_7289] :
        ( hAPP(hAPP(c_Set_Oinsert(U_7281),U_7283),hAPP(hAPP(c_Set_Oinsert(U_7281),U_7285),c_Orderings_Obot__class_Obot(tc_fun(U_7281,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_7281),U_7287),hAPP(hAPP(c_Set_Oinsert(U_7281),U_7289),c_Orderings_Obot__class_Obot(tc_fun(U_7281,tc_HOL_Obool))))
        | sP632(U_7285,U_7287,U_7283,U_7289) )
    & ! [U_7284,U_7280,U_7282,U_7288,U_7286] :
        ( hAPP(hAPP(c_Set_Oinsert(U_7280),U_7282),hAPP(hAPP(c_Set_Oinsert(U_7280),U_7284),c_Orderings_Obot__class_Obot(tc_fun(U_7280,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_7280),U_7286),hAPP(hAPP(c_Set_Oinsert(U_7280),U_7288),c_Orderings_Obot__class_Obot(tc_fun(U_7280,tc_HOL_Obool))))
        | sP631(U_7284,U_7282,U_7288,U_7286)
        | sP630(U_7284,U_7282,U_7288,U_7286) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP630,sP631,sP632])],[f_2089_3]) ).

cnf(f_2089_5,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_7280),U_7282),hAPP(hAPP(c_Set_Oinsert(U_7280),U_7284),c_Orderings_Obot__class_Obot(tc_fun(U_7280,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_7280),U_7286),hAPP(hAPP(c_Set_Oinsert(U_7280),U_7288),c_Orderings_Obot__class_Obot(tc_fun(U_7280,tc_HOL_Obool))))
    | sP631(U_7284,U_7282,U_7288,U_7286)
    | sP630(U_7284,U_7282,U_7288,U_7286) ),
    inference(clausify,[status(thm)],[f_2089_4]) ).

cnf(f_2089_6,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_7281),U_7283),hAPP(hAPP(c_Set_Oinsert(U_7281),U_7285),c_Orderings_Obot__class_Obot(tc_fun(U_7281,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_7281),U_7287),hAPP(hAPP(c_Set_Oinsert(U_7281),U_7289),c_Orderings_Obot__class_Obot(tc_fun(U_7281,tc_HOL_Obool))))
    | sP632(U_7285,U_7287,U_7283,U_7289) ),
    inference(clausify,[status(thm)],[f_2089_4]) ).

cnf(f_2089_7,plain,
    ( U_7282 = U_7286
    | ~ sP630(U_7284,U_7282,U_7288,U_7286) ),
    inference(clausify,[status(thm)],[f_2089_4]) ).

cnf(f_2089_8,plain,
    ( U_7284 = U_7288
    | ~ sP630(U_7284,U_7282,U_7288,U_7286) ),
    inference(clausify,[status(thm)],[f_2089_4]) ).

cnf(f_2089_9,plain,
    ( U_7282 = U_7288
    | ~ sP631(U_7284,U_7282,U_7288,U_7286) ),
    inference(clausify,[status(thm)],[f_2089_4]) ).

cnf(f_2089_10,plain,
    ( U_7284 = U_7286
    | ~ sP631(U_7284,U_7282,U_7288,U_7286) ),
    inference(clausify,[status(thm)],[f_2089_4]) ).

cnf(f_2089_11,plain,
    ( U_7285 != U_7289
    | U_7283 != U_7287
    | ~ sP632(U_7285,U_7287,U_7283,U_7289) ),
    inference(clausify,[status(thm)],[f_2089_4]) ).

cnf(f_2089_12,plain,
    ( U_7285 != U_7287
    | U_7283 != U_7289
    | ~ sP632(U_7285,U_7287,U_7283,U_7289) ),
    inference(clausify,[status(thm)],[f_2089_4]) ).

fof(f_2090_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_2090_2,plain,
    ! [U_7293,U_7292,U_7291,U_7290] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7290),U_7291),U_7292),U_7293))
        | ( ~ hBOOL(hAPP(U_7292,U_7293))
          & U_7291 != U_7293 ) )
      & ( hBOOL(hAPP(U_7292,U_7293))
        | U_7291 = U_7293
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7290),U_7291),U_7292),U_7293)) ) ),
    inference(variable_rename,[status(thm)],[f_2090_1]) ).

fof(f_2090_3,plain,
    ( ! [U_7301,U_7299,U_7297] :
        ( ! [U_7295] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7295),U_7297),U_7299),U_7301))
        | ( ~ hBOOL(hAPP(U_7299,U_7301))
          & U_7297 != U_7301 ) )
    & ! [U_7300,U_7298,U_7296] :
        ( ! [U_7294] : ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7294),U_7296),U_7298),U_7300))
        | hBOOL(hAPP(U_7298,U_7300))
        | U_7296 = U_7300 ) ),
    inference(miniscope,[status(thm)],[f_2090_2]) ).

fof(f_2090_4,plain,
    ( ! [U_7299,U_7301,U_7297] :
        ( ~ hBOOL(hAPP(U_7299,U_7301))
        | ~ sP633(U_7299,U_7301,U_7297) )
    & ! [U_7299,U_7301,U_7297] :
        ( U_7297 != U_7301
        | ~ sP633(U_7299,U_7301,U_7297) )
    & ! [U_7299,U_7295,U_7301,U_7297] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7295),U_7297),U_7299),U_7301))
        | sP633(U_7299,U_7301,U_7297) )
    & ! [U_7294,U_7300,U_7298,U_7296] :
        ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7294),U_7296),U_7298),U_7300))
        | hBOOL(hAPP(U_7298,U_7300))
        | U_7296 = U_7300 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP633])],[f_2090_3]) ).

cnf(f_2090_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7294),U_7296),U_7298),U_7300))
    | hBOOL(hAPP(U_7298,U_7300))
    | U_7296 = U_7300 ),
    inference(clausify,[status(thm)],[f_2090_4]) ).

cnf(f_2090_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7295),U_7297),U_7299),U_7301))
    | sP633(U_7299,U_7301,U_7297) ),
    inference(clausify,[status(thm)],[f_2090_4]) ).

cnf(f_2090_7,plain,
    ( U_7297 != U_7301
    | ~ sP633(U_7299,U_7301,U_7297) ),
    inference(clausify,[status(thm)],[f_2090_4]) ).

cnf(f_2090_8,plain,
    ( ~ hBOOL(hAPP(U_7299,U_7301))
    | ~ sP633(U_7299,U_7301,U_7297) ),
    inference(clausify,[status(thm)],[f_2090_4]) ).

fof(f_2091_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_2091_2,plain,
    ! [U_7304,U_7303,U_7302] :
      ( U_7303 = U_7304
      | hAPP(hAPP(c_Set_Oinsert(U_7302),U_7303),c_Orderings_Obot__class_Obot(tc_fun(U_7302,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_7302),U_7304),c_Orderings_Obot__class_Obot(tc_fun(U_7302,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_2091_1]) ).

fof(f_2091_3,plain,
    ! [U_7304,U_7303] :
      ( ! [U_7302] : hAPP(hAPP(c_Set_Oinsert(U_7302),U_7303),c_Orderings_Obot__class_Obot(tc_fun(U_7302,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_7302),U_7304),c_Orderings_Obot__class_Obot(tc_fun(U_7302,tc_HOL_Obool)))
      | U_7303 = U_7304 ),
    inference(miniscope,[status(thm)],[f_2091_2]) ).

fof(f_2091_4,plain,
    ! [U_7303,U_7302,U_7304] :
      ( hAPP(hAPP(c_Set_Oinsert(U_7302),U_7303),c_Orderings_Obot__class_Obot(tc_fun(U_7302,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_7302),U_7304),c_Orderings_Obot__class_Obot(tc_fun(U_7302,tc_HOL_Obool)))
      | U_7303 = U_7304 ),
    inference(definitional_conversion,[status(esa)],[f_2091_3]) ).

cnf(f_2091_5,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_7302),U_7303),c_Orderings_Obot__class_Obot(tc_fun(U_7302,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_7302),U_7304),c_Orderings_Obot__class_Obot(tc_fun(U_7302,tc_HOL_Obool)))
    | U_7303 = U_7304 ),
    inference(clausify,[status(thm)],[f_2091_4]) ).

fof(f_2092_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_2092_2,plain,
    ! [U_7307,U_7306,U_7305] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7305),U_7306),U_7307))
      | hAPP(c_Groups_Oabs__class_Oabs(U_7305),U_7306) != hAPP(c_Groups_Oabs__class_Oabs(U_7305),U_7307)
      | ~ class_Rings_Olinordered__idom(U_7305) ),
    inference(variable_rename,[status(thm)],[f_2092_1]) ).

fof(f_2092_3,plain,
    ! [U_7305,U_7306,U_7307] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7305),U_7306),U_7307))
      | hAPP(c_Groups_Oabs__class_Oabs(U_7305),U_7306) != hAPP(c_Groups_Oabs__class_Oabs(U_7305),U_7307)
      | ~ class_Rings_Olinordered__idom(U_7305) ),
    inference(definitional_conversion,[status(esa)],[f_2092_2]) ).

cnf(f_2092_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7305),U_7306),U_7307))
    | hAPP(c_Groups_Oabs__class_Oabs(U_7305),U_7306) != hAPP(c_Groups_Oabs__class_Oabs(U_7305),U_7307)
    | ~ class_Rings_Olinordered__idom(U_7305) ),
    inference(clausify,[status(thm)],[f_2092_3]) ).

fof(f_2093_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_2093_2,plain,
    ! [U_7310,U_7309,U_7308] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7308),hAPP(c_Groups_Oabs__class_Oabs(U_7308),U_7309)),U_7310))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7308),U_7309),U_7310)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7308),U_7309),U_7310))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7308),hAPP(c_Groups_Oabs__class_Oabs(U_7308),U_7309)),U_7310)) ) )
      | ~ class_Rings_Olinordered__idom(U_7308) ),
    inference(variable_rename,[status(thm)],[f_2093_1]) ).

fof(f_2093_3,plain,
    ( ! [U_7308,U_7309,U_7310] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7308),hAPP(c_Groups_Oabs__class_Oabs(U_7308),U_7309)),U_7310))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7308),U_7309),U_7310))
        | ~ sP634(U_7308,U_7309,U_7310) )
    & ! [U_7308,U_7309,U_7310] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7308),U_7309),U_7310))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7308),hAPP(c_Groups_Oabs__class_Oabs(U_7308),U_7309)),U_7310))
        | ~ sP634(U_7308,U_7309,U_7310) )
    & ! [U_7308,U_7309,U_7310] :
        ( sP634(U_7308,U_7309,U_7310)
        | ~ class_Rings_Olinordered__idom(U_7308) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP634])],[f_2093_2]) ).

cnf(f_2093_4,plain,
    ( sP634(U_7308,U_7309,U_7310)
    | ~ class_Rings_Olinordered__idom(U_7308) ),
    inference(clausify,[status(thm)],[f_2093_3]) ).

cnf(f_2093_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7308),U_7309),U_7310))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7308),hAPP(c_Groups_Oabs__class_Oabs(U_7308),U_7309)),U_7310))
    | ~ sP634(U_7308,U_7309,U_7310) ),
    inference(clausify,[status(thm)],[f_2093_3]) ).

cnf(f_2093_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7308),hAPP(c_Groups_Oabs__class_Oabs(U_7308),U_7309)),U_7310))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7308),U_7309),U_7310))
    | ~ sP634(U_7308,U_7309,U_7310) ),
    inference(clausify,[status(thm)],[f_2093_3]) ).

fof(f_2094_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_2094_2,plain,
    ! [U_7313,U_7312,U_7311] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7311),U_7312),hAPP(c_Groups_Oabs__class_Oabs(U_7311),U_7313)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7311),U_7312),U_7313)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7311),U_7312),U_7313))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7311),U_7312),hAPP(c_Groups_Oabs__class_Oabs(U_7311),U_7313))) ) )
      | ~ class_Rings_Olinordered__idom(U_7311) ),
    inference(variable_rename,[status(thm)],[f_2094_1]) ).

fof(f_2094_3,plain,
    ( ! [U_7312,U_7311,U_7313] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7311),U_7312),hAPP(c_Groups_Oabs__class_Oabs(U_7311),U_7313)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7311),U_7312),U_7313))
        | ~ sP635(U_7312,U_7311,U_7313) )
    & ! [U_7312,U_7311,U_7313] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7311),U_7312),U_7313))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7311),U_7312),hAPP(c_Groups_Oabs__class_Oabs(U_7311),U_7313)))
        | ~ sP635(U_7312,U_7311,U_7313) )
    & ! [U_7312,U_7311,U_7313] :
        ( sP635(U_7312,U_7311,U_7313)
        | ~ class_Rings_Olinordered__idom(U_7311) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP635])],[f_2094_2]) ).

cnf(f_2094_4,plain,
    ( sP635(U_7312,U_7311,U_7313)
    | ~ class_Rings_Olinordered__idom(U_7311) ),
    inference(clausify,[status(thm)],[f_2094_3]) ).

cnf(f_2094_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7311),U_7312),U_7313))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7311),U_7312),hAPP(c_Groups_Oabs__class_Oabs(U_7311),U_7313)))
    | ~ sP635(U_7312,U_7311,U_7313) ),
    inference(clausify,[status(thm)],[f_2094_3]) ).

cnf(f_2094_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7311),U_7312),hAPP(c_Groups_Oabs__class_Oabs(U_7311),U_7313)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7311),U_7312),U_7313))
    | ~ sP635(U_7312,U_7311,U_7313) ),
    inference(clausify,[status(thm)],[f_2094_3]) ).

fof(f_2095_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_2095_2,plain,
    ! [U_7320,U_7319,U_7318,U_7317,U_7316,U_7315,U_7314] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7314,U_7315,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7314)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7314),U_7316),c_Com_Ocom_OSemi(U_7317,U_7319)),U_7320)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7314),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7314,U_7315,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7314)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7314),U_7318),U_7319),U_7320)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7314),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7314,U_7315,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7314)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7314),U_7316),U_7317),U_7318)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7314),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2095_1]) ).

fof(f_2095_3,plain,
    ! [U_7316,U_7315,U_7314,U_7317,U_7318,U_7319,U_7320] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7314,U_7315,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7314)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7314),U_7316),c_Com_Ocom_OSemi(U_7317,U_7319)),U_7320)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7314),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7314,U_7315,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7314)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7314),U_7318),U_7319),U_7320)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7314),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7314,U_7315,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7314)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7314),U_7316),U_7317),U_7318)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7314),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2095_2]) ).

cnf(f_2095_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7314,U_7315,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7314)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7314),U_7316),c_Com_Ocom_OSemi(U_7317,U_7319)),U_7320)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7314),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7314,U_7315,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7314)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7314),U_7318),U_7319),U_7320)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7314),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7314,U_7315,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7314)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7314),U_7316),U_7317),U_7318)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7314),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2095_3]) ).

fof(f_2096_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_2096_2,plain,
    ! [U_7323,U_7322,U_7321] : c_Hoare__Mirabelle_Ohoare__derivs(U_7321,U_7322,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7321)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7321),U_7323),c_Com_Ocom_OSKIP),U_7323)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7321),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2096_1]) ).

fof(f_2096_3,plain,
    ! [U_7322,U_7323,U_7321] : c_Hoare__Mirabelle_Ohoare__derivs(U_7321,U_7322,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7321)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7321),U_7323),c_Com_Ocom_OSKIP),U_7323)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7321),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2096_2]) ).

cnf(f_2096_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_7321,U_7322,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7321)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7321),U_7323),c_Com_Ocom_OSKIP),U_7323)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7321),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2096_3]) ).

fof(f_2097_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_2097_2,plain,
    ! [U_7326,U_7325,U_7324] : c_Hoare__Mirabelle_Ohoare__derivs(U_7324,U_7325,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7324)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7324),U_7326),c_Com_Ocom_OSKIP),U_7326)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7324),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2097_1]) ).

fof(f_2097_3,plain,
    ! [U_7324,U_7325,U_7326] : c_Hoare__Mirabelle_Ohoare__derivs(U_7324,U_7325,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7324)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7324),U_7326),c_Com_Ocom_OSKIP),U_7326)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7324),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2097_2]) ).

cnf(f_2097_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_7324,U_7325,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7324)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7324),U_7326),c_Com_Ocom_OSKIP),U_7326)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7324),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2097_3]) ).

fof(f_2098_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_2098_2,plain,
    ! [U_7328,U_7327] :
      ( U_7328 = c_Groups_Ozero__class_Ozero(U_7327)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7327),c_Groups_Ozero__class_Ozero(U_7327)),U_7328))
      | ~ class_Rings_Ocomm__semiring__1(U_7327) ),
    inference(variable_rename,[status(thm)],[f_2098_1]) ).

fof(f_2098_3,plain,
    ! [U_7327,U_7328] :
      ( U_7328 = c_Groups_Ozero__class_Ozero(U_7327)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7327),c_Groups_Ozero__class_Ozero(U_7327)),U_7328))
      | ~ class_Rings_Ocomm__semiring__1(U_7327) ),
    inference(definitional_conversion,[status(esa)],[f_2098_2]) ).

cnf(f_2098_4,plain,
    ( U_7328 = c_Groups_Ozero__class_Ozero(U_7327)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7327),c_Groups_Ozero__class_Ozero(U_7327)),U_7328))
    | ~ class_Rings_Ocomm__semiring__1(U_7327) ),
    inference(clausify,[status(thm)],[f_2098_3]) ).

fof(f_2099_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_2099_2,plain,
    ! [U_7332,U_7331,U_7330,U_7329] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7329),U_7330),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7329),U_7331),U_7332)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7329),U_7330),U_7332))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7329),U_7330),U_7331))
      | ~ class_Rings_Ocomm__semiring__1(U_7329) ),
    inference(variable_rename,[status(thm)],[f_2099_1]) ).

fof(f_2099_3,plain,
    ! [U_7329,U_7330,U_7331,U_7332] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7329),U_7330),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7329),U_7331),U_7332)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7329),U_7330),U_7332))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7329),U_7330),U_7331))
      | ~ class_Rings_Ocomm__semiring__1(U_7329) ),
    inference(definitional_conversion,[status(esa)],[f_2099_2]) ).

cnf(f_2099_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7329),U_7330),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7329),U_7331),U_7332)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7329),U_7330),U_7332))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7329),U_7330),U_7331))
    | ~ class_Rings_Ocomm__semiring__1(U_7329) ),
    inference(clausify,[status(thm)],[f_2099_3]) ).

fof(f_2100_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_2100_2,plain,
    ! [U_7334,U_7333] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7333),c_Groups_Oone__class_Oone(U_7333)),U_7334))
      | ~ class_Rings_Ocomm__semiring__1(U_7333) ),
    inference(variable_rename,[status(thm)],[f_2100_1]) ).

fof(f_2100_3,plain,
    ! [U_7334,U_7333] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7333),c_Groups_Oone__class_Oone(U_7333)),U_7334))
      | ~ class_Rings_Ocomm__semiring__1(U_7333) ),
    inference(definitional_conversion,[status(esa)],[f_2100_2]) ).

cnf(f_2100_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7333),c_Groups_Oone__class_Oone(U_7333)),U_7334))
    | ~ class_Rings_Ocomm__semiring__1(U_7333) ),
    inference(clausify,[status(thm)],[f_2100_3]) ).

fof(f_2101_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_2101_2,plain,
    ! [U_7337,U_7336,U_7335] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7336,U_7335)),U_7337) = c_Orderings_Obot__class_Obot(U_7335)
      | ~ class_Orderings_Obot(U_7335) ),
    inference(variable_rename,[status(thm)],[f_2101_1]) ).

fof(f_2101_3,plain,
    ! [U_7335,U_7336,U_7337] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7336,U_7335)),U_7337) = c_Orderings_Obot__class_Obot(U_7335)
      | ~ class_Orderings_Obot(U_7335) ),
    inference(definitional_conversion,[status(esa)],[f_2101_2]) ).

cnf(f_2101_4,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7336,U_7335)),U_7337) = c_Orderings_Obot__class_Obot(U_7335)
    | ~ class_Orderings_Obot(U_7335) ),
    inference(clausify,[status(thm)],[f_2101_3]) ).

fof(f_2102_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_2102_2,plain,
    ! [U_7341,U_7340,U_7339,U_7338] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs(U_7338,U_7339,U_7341)
        & c_Hoare__Mirabelle_Ohoare__derivs(U_7338,U_7339,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7338)),U_7340),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7338),tc_HOL_Obool)))) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7338,U_7339,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7338)),U_7340),U_7341)) ),
    inference(variable_rename,[status(thm)],[f_2102_1]) ).

fof(f_2102_3,plain,
    ( ! [U_7338,U_7339,U_7340,U_7341] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_7338,U_7339,U_7341)
        | ~ sP636(U_7338,U_7339,U_7340,U_7341) )
    & ! [U_7338,U_7339,U_7340,U_7341] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_7338,U_7339,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7338)),U_7340),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7338),tc_HOL_Obool))))
        | ~ sP636(U_7338,U_7339,U_7340,U_7341) )
    & ! [U_7338,U_7339,U_7340,U_7341] :
        ( sP636(U_7338,U_7339,U_7340,U_7341)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7338,U_7339,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7338)),U_7340),U_7341)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP636])],[f_2102_2]) ).

cnf(f_2102_4,plain,
    ( sP636(U_7338,U_7339,U_7340,U_7341)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7338,U_7339,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7338)),U_7340),U_7341)) ),
    inference(clausify,[status(thm)],[f_2102_3]) ).

cnf(f_2102_5,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7338,U_7339,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7338)),U_7340),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7338),tc_HOL_Obool))))
    | ~ sP636(U_7338,U_7339,U_7340,U_7341) ),
    inference(clausify,[status(thm)],[f_2102_3]) ).

cnf(f_2102_6,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7338,U_7339,U_7341)
    | ~ sP636(U_7338,U_7339,U_7340,U_7341) ),
    inference(clausify,[status(thm)],[f_2102_3]) ).

fof(f_2103_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_2103_2,plain,
    ! [U_7345,U_7344,U_7343,U_7342] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7342,U_7343,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7342)),U_7344),U_7345))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7342,U_7343,U_7345)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7342,U_7343,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7342)),U_7344),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7342),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2103_1]) ).

fof(f_2103_3,plain,
    ! [U_7342,U_7343,U_7344,U_7345] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7342,U_7343,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7342)),U_7344),U_7345))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7342,U_7343,U_7345)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7342,U_7343,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7342)),U_7344),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7342),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2103_2]) ).

cnf(f_2103_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7342,U_7343,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7342)),U_7344),U_7345))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7342,U_7343,U_7345)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7342,U_7343,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7342)),U_7344),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7342),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2103_3]) ).

fof(f_2104_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_2104_2,plain,
    ! [U_7349,U_7348,U_7347,U_7346] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7346,U_7349,U_7348)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7346,U_7349,U_7347)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7346,U_7347,U_7348) ),
    inference(variable_rename,[status(thm)],[f_2104_1]) ).

fof(f_2104_3,plain,
    ! [U_7348,U_7346,U_7349,U_7347] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7346,U_7349,U_7348)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7346,U_7349,U_7347)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7346,U_7347,U_7348) ),
    inference(definitional_conversion,[status(esa)],[f_2104_2]) ).

cnf(f_2104_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7346,U_7349,U_7348)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7346,U_7349,U_7347)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7346,U_7347,U_7348) ),
    inference(clausify,[status(thm)],[f_2104_3]) ).

fof(f_2105_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_2105_2,plain,
    ! [U_7351,U_7350] : c_Hoare__Mirabelle_Ohoare__derivs(U_7350,U_7351,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7350),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2105_1]) ).

fof(f_2105_3,plain,
    ! [U_7351,U_7350] : c_Hoare__Mirabelle_Ohoare__derivs(U_7350,U_7351,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7350),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2105_2]) ).

cnf(f_2105_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_7350,U_7351,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7350),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2105_3]) ).

fof(f_2106_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_2106_2,plain,
    ! [U_7353,U_7352] : c_Hoare__Mirabelle_Ohoare__derivs(U_7352,U_7353,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7352),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2106_1]) ).

fof(f_2106_3,plain,
    ! [U_7352,U_7353] : c_Hoare__Mirabelle_Ohoare__derivs(U_7352,U_7353,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7352),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2106_2]) ).

cnf(f_2106_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_7352,U_7353,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7352),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2106_3]) ).

fof(f_2107_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_2107_2,plain,
    ! [U_7355,U_7354] :
      ( ( U_7354 = U_7355
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7355),U_7354))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7354),U_7355)) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7355),U_7354))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7354),U_7355)) )
        | U_7354 != U_7355 ) ),
    inference(variable_rename,[status(thm)],[f_2107_1]) ).

fof(f_2107_3,plain,
    ( ! [U_7359,U_7357] :
        ( U_7357 = U_7359
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7359),U_7357))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7357),U_7359)) )
    & ! [U_7358,U_7356] :
        ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7358),U_7356))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7356),U_7358)) )
        | U_7356 != U_7358 ) ),
    inference(miniscope,[status(thm)],[f_2107_2]) ).

fof(f_2107_4,plain,
    ( ! [U_7358,U_7356] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7358),U_7356))
        | ~ sP637(U_7358,U_7356) )
    & ! [U_7358,U_7356] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7356),U_7358))
        | ~ sP637(U_7358,U_7356) )
    & ! [U_7359,U_7357] :
        ( U_7357 = U_7359
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7359),U_7357))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7357),U_7359)) )
    & ! [U_7358,U_7356] :
        ( sP637(U_7358,U_7356)
        | U_7356 != U_7358 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP637])],[f_2107_3]) ).

cnf(f_2107_5,plain,
    ( sP637(U_7358,U_7356)
    | U_7356 != U_7358 ),
    inference(clausify,[status(thm)],[f_2107_4]) ).

cnf(f_2107_6,plain,
    ( U_7357 = U_7359
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7359),U_7357))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7357),U_7359)) ),
    inference(clausify,[status(thm)],[f_2107_4]) ).

cnf(f_2107_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7356),U_7358))
    | ~ sP637(U_7358,U_7356) ),
    inference(clausify,[status(thm)],[f_2107_4]) ).

cnf(f_2107_8,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7358),U_7356))
    | ~ sP637(U_7358,U_7356) ),
    inference(clausify,[status(thm)],[f_2107_4]) ).

fof(f_2108_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_2108_2,plain,
    ! [U_7361,U_7360] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7360),U_7361))
        | ( U_7360 != U_7361
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7361),U_7360))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7360),U_7361)) ) ) )
      & ( U_7360 = U_7361
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7361),U_7360))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7360),U_7361)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7360),U_7361)) ) ),
    inference(variable_rename,[status(thm)],[f_2108_1]) ).

fof(f_2108_3,plain,
    ( ! [U_7365,U_7363] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7363),U_7365))
        | ( U_7363 != U_7365
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7365),U_7363))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7363),U_7365)) ) ) )
    & ! [U_7364,U_7362] :
        ( U_7362 = U_7364
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7364),U_7362))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7362),U_7364)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7362),U_7364)) ) ),
    inference(miniscope,[status(thm)],[f_2108_2]) ).

fof(f_2108_4,plain,
    ( ! [U_7365,U_7363] :
        ( U_7363 != U_7365
        | ~ sP639(U_7365,U_7363) )
    & ! [U_7365,U_7363] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7365),U_7363))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7363),U_7365))
        | ~ sP639(U_7365,U_7363) )
    & ! [U_7364,U_7362] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7364),U_7362))
        | ~ sP638(U_7364,U_7362) )
    & ! [U_7364,U_7362] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7362),U_7364))
        | ~ sP638(U_7364,U_7362) )
    & ! [U_7365,U_7363] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7363),U_7365))
        | sP639(U_7365,U_7363) )
    & ! [U_7364,U_7362] :
        ( U_7362 = U_7364
        | sP638(U_7364,U_7362)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7362),U_7364)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP638,sP639])],[f_2108_3]) ).

cnf(f_2108_5,plain,
    ( U_7362 = U_7364
    | sP638(U_7364,U_7362)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7362),U_7364)) ),
    inference(clausify,[status(thm)],[f_2108_4]) ).

cnf(f_2108_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7363),U_7365))
    | sP639(U_7365,U_7363) ),
    inference(clausify,[status(thm)],[f_2108_4]) ).

cnf(f_2108_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7362),U_7364))
    | ~ sP638(U_7364,U_7362) ),
    inference(clausify,[status(thm)],[f_2108_4]) ).

cnf(f_2108_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7364),U_7362))
    | ~ sP638(U_7364,U_7362) ),
    inference(clausify,[status(thm)],[f_2108_4]) ).

cnf(f_2108_9,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7365),U_7363))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7363),U_7365))
    | ~ sP639(U_7365,U_7363) ),
    inference(clausify,[status(thm)],[f_2108_4]) ).

cnf(f_2108_10,plain,
    ( U_7363 != U_7365
    | ~ sP639(U_7365,U_7363) ),
    inference(clausify,[status(thm)],[f_2108_4]) ).

fof(f_2109_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_2109_2,plain,
    ! [U_7367,U_7366] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7367),U_7366))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7366),U_7367)) )
        | U_7366 = U_7367
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7366),U_7367)) )
      & ( ( U_7366 != U_7367
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7366),U_7367)) )
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7367),U_7366))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7366),U_7367)) ) ),
    inference(variable_rename,[status(thm)],[f_2109_1]) ).

fof(f_2109_3,plain,
    ( ! [U_7371,U_7369] :
        ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7371),U_7369))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7369),U_7371)) )
        | U_7369 = U_7371
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7369),U_7371)) )
    & ! [U_7370,U_7368] :
        ( ( U_7368 != U_7370
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7368),U_7370)) )
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7370),U_7368))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7368),U_7370)) ) ),
    inference(miniscope,[status(thm)],[f_2109_2]) ).

fof(f_2109_4,plain,
    ( ! [U_7369,U_7371] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7371),U_7369))
        | ~ sP641(U_7369,U_7371) )
    & ! [U_7369,U_7371] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7369),U_7371))
        | ~ sP641(U_7369,U_7371) )
    & ! [U_7368,U_7370] :
        ( U_7368 != U_7370
        | ~ sP640(U_7368,U_7370) )
    & ! [U_7368,U_7370] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7368),U_7370))
        | ~ sP640(U_7368,U_7370) )
    & ! [U_7369,U_7371] :
        ( sP641(U_7369,U_7371)
        | U_7369 = U_7371
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7369),U_7371)) )
    & ! [U_7368,U_7370] :
        ( sP640(U_7368,U_7370)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7370),U_7368))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7368),U_7370)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP640,sP641])],[f_2109_3]) ).

cnf(f_2109_5,plain,
    ( sP640(U_7368,U_7370)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7370),U_7368))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7368),U_7370)) ),
    inference(clausify,[status(thm)],[f_2109_4]) ).

cnf(f_2109_6,plain,
    ( sP641(U_7369,U_7371)
    | U_7369 = U_7371
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7369),U_7371)) ),
    inference(clausify,[status(thm)],[f_2109_4]) ).

cnf(f_2109_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7368),U_7370))
    | ~ sP640(U_7368,U_7370) ),
    inference(clausify,[status(thm)],[f_2109_4]) ).

cnf(f_2109_8,plain,
    ( U_7368 != U_7370
    | ~ sP640(U_7368,U_7370) ),
    inference(clausify,[status(thm)],[f_2109_4]) ).

cnf(f_2109_9,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7369),U_7371))
    | ~ sP641(U_7369,U_7371) ),
    inference(clausify,[status(thm)],[f_2109_4]) ).

cnf(f_2109_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7371),U_7369))
    | ~ sP641(U_7369,U_7371) ),
    inference(clausify,[status(thm)],[f_2109_4]) ).

fof(f_2110_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_2110_2,plain,
    ! [U_7373,U_7372] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7373),U_7372))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7372),U_7373)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7372),U_7373))
      | U_7372 = U_7373 ),
    inference(variable_rename,[status(thm)],[f_2110_1]) ).

fof(f_2110_3,plain,
    ( ! [U_7372,U_7373] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7373),U_7372))
        | ~ sP642(U_7372,U_7373) )
    & ! [U_7372,U_7373] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7372),U_7373))
        | ~ sP642(U_7372,U_7373) )
    & ! [U_7372,U_7373] :
        ( sP642(U_7372,U_7373)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7372),U_7373))
        | U_7372 = U_7373 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP642])],[f_2110_2]) ).

cnf(f_2110_4,plain,
    ( sP642(U_7372,U_7373)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7372),U_7373))
    | U_7372 = U_7373 ),
    inference(clausify,[status(thm)],[f_2110_3]) ).

cnf(f_2110_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7372),U_7373))
    | ~ sP642(U_7372,U_7373) ),
    inference(clausify,[status(thm)],[f_2110_3]) ).

cnf(f_2110_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7373),U_7372))
    | ~ sP642(U_7372,U_7373) ),
    inference(clausify,[status(thm)],[f_2110_3]) ).

fof(f_2111_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_2111_2,plain,
    ! [U_7375,U_7374] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7374),U_7375))
      | U_7374 != U_7375 ),
    inference(variable_rename,[status(thm)],[f_2111_1]) ).

fof(f_2111_3,plain,
    ! [U_7374,U_7375] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7374),U_7375))
      | U_7374 != U_7375 ),
    inference(definitional_conversion,[status(esa)],[f_2111_2]) ).

cnf(f_2111_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7374),U_7375))
    | U_7374 != U_7375 ),
    inference(clausify,[status(thm)],[f_2111_3]) ).

fof(f_2112_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_2112_2,plain,
    ! [U_7377,U_7376] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7377),U_7376))
          | U_7377 != U_7376 )
        & ( U_7377 = U_7376
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7377),U_7376)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7376),U_7377)) ),
    inference(variable_rename,[status(thm)],[f_2112_1]) ).

fof(f_2112_3,plain,
    ( ! [U_7376,U_7377] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7377),U_7376))
        | U_7377 != U_7376
        | ~ sP643(U_7376,U_7377) )
    & ! [U_7376,U_7377] :
        ( U_7377 = U_7376
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7377),U_7376))
        | ~ sP643(U_7376,U_7377) )
    & ! [U_7376,U_7377] :
        ( sP643(U_7376,U_7377)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7376),U_7377)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP643])],[f_2112_2]) ).

cnf(f_2112_4,plain,
    ( sP643(U_7376,U_7377)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7376),U_7377)) ),
    inference(clausify,[status(thm)],[f_2112_3]) ).

cnf(f_2112_5,plain,
    ( U_7377 = U_7376
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7377),U_7376))
    | ~ sP643(U_7376,U_7377) ),
    inference(clausify,[status(thm)],[f_2112_3]) ).

cnf(f_2112_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7377),U_7376))
    | U_7377 != U_7376
    | ~ sP643(U_7376,U_7377) ),
    inference(clausify,[status(thm)],[f_2112_3]) ).

fof(f_2113_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_2113_2,plain,
    ! [U_7379,U_7378] :
      ( U_7378 = U_7379
      | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7379),U_7378))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7378),U_7379)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7378),U_7379)) ),
    inference(variable_rename,[status(thm)],[f_2113_1]) ).

fof(f_2113_3,plain,
    ( ! [U_7379,U_7378] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7379),U_7378))
        | ~ sP644(U_7379,U_7378) )
    & ! [U_7379,U_7378] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7378),U_7379))
        | ~ sP644(U_7379,U_7378) )
    & ! [U_7379,U_7378] :
        ( U_7378 = U_7379
        | sP644(U_7379,U_7378)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7378),U_7379)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP644])],[f_2113_2]) ).

cnf(f_2113_4,plain,
    ( U_7378 = U_7379
    | sP644(U_7379,U_7378)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7378),U_7379)) ),
    inference(clausify,[status(thm)],[f_2113_3]) ).

cnf(f_2113_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7378),U_7379))
    | ~ sP644(U_7379,U_7378) ),
    inference(clausify,[status(thm)],[f_2113_3]) ).

cnf(f_2113_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7379),U_7378))
    | ~ sP644(U_7379,U_7378) ),
    inference(clausify,[status(thm)],[f_2113_3]) ).

fof(f_2114_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_2114_2,plain,
    ! [U_7381,U_7380] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7381),U_7380))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7380),U_7381)) )
      | U_7380 = U_7381
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7380),U_7381)) ),
    inference(variable_rename,[status(thm)],[f_2114_1]) ).

fof(f_2114_3,plain,
    ( ! [U_7380,U_7381] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7381),U_7380))
        | ~ sP645(U_7380,U_7381) )
    & ! [U_7380,U_7381] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7380),U_7381))
        | ~ sP645(U_7380,U_7381) )
    & ! [U_7380,U_7381] :
        ( sP645(U_7380,U_7381)
        | U_7380 = U_7381
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7380),U_7381)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP645])],[f_2114_2]) ).

cnf(f_2114_4,plain,
    ( sP645(U_7380,U_7381)
    | U_7380 = U_7381
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7380),U_7381)) ),
    inference(clausify,[status(thm)],[f_2114_3]) ).

cnf(f_2114_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7380),U_7381))
    | ~ sP645(U_7380,U_7381) ),
    inference(clausify,[status(thm)],[f_2114_3]) ).

cnf(f_2114_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7381),U_7380))
    | ~ sP645(U_7380,U_7381) ),
    inference(clausify,[status(thm)],[f_2114_3]) ).

fof(f_2115_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_2115_2,plain,
    ! [U_7384,U_7383,U_7382] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7382),U_7384))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7383),U_7384))
      | U_7382 != U_7383 ),
    inference(variable_rename,[status(thm)],[f_2115_1]) ).

fof(f_2115_3,plain,
    ! [U_7382,U_7383,U_7384] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7382),U_7384))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7383),U_7384))
      | U_7382 != U_7383 ),
    inference(definitional_conversion,[status(esa)],[f_2115_2]) ).

cnf(f_2115_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7382),U_7384))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7383),U_7384))
    | U_7382 != U_7383 ),
    inference(clausify,[status(thm)],[f_2115_3]) ).

fof(f_2116_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_2116_2,plain,
    ! [U_7387,U_7386,U_7385] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7385),U_7387))
      | U_7386 != U_7387
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7385),U_7386)) ),
    inference(variable_rename,[status(thm)],[f_2116_1]) ).

fof(f_2116_3,plain,
    ! [U_7386,U_7385,U_7387] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7385),U_7387))
      | U_7386 != U_7387
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7385),U_7386)) ),
    inference(definitional_conversion,[status(esa)],[f_2116_2]) ).

cnf(f_2116_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7385),U_7387))
    | U_7386 != U_7387
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7385),U_7386)) ),
    inference(clausify,[status(thm)],[f_2116_3]) ).

fof(f_2117_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_2117_2,plain,
    ! [U_7389,U_7388] :
      ( U_7388 = U_7389
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7389),U_7388))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7388),U_7389)) ),
    inference(variable_rename,[status(thm)],[f_2117_1]) ).

fof(f_2117_3,plain,
    ! [U_7388,U_7389] :
      ( U_7388 = U_7389
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7389),U_7388))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7388),U_7389)) ),
    inference(definitional_conversion,[status(esa)],[f_2117_2]) ).

cnf(f_2117_4,plain,
    ( U_7388 = U_7389
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7389),U_7388))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7388),U_7389)) ),
    inference(clausify,[status(thm)],[f_2117_3]) ).

fof(f_2118_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_2118_2,plain,
    ! [U_7391,U_7390] :
      ( U_7390 = U_7391
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7391),U_7390))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7390),U_7391)) ),
    inference(variable_rename,[status(thm)],[f_2118_1]) ).

fof(f_2118_3,plain,
    ! [U_7390,U_7391] :
      ( U_7390 = U_7391
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7391),U_7390))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7390),U_7391)) ),
    inference(definitional_conversion,[status(esa)],[f_2118_2]) ).

cnf(f_2118_4,plain,
    ( U_7390 = U_7391
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7391),U_7390))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7390),U_7391)) ),
    inference(clausify,[status(thm)],[f_2118_3]) ).

fof(f_2119_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_2119_2,plain,
    ! [U_7394,U_7393,U_7392] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7392),U_7394))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7393),U_7394))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7392),U_7393)) ),
    inference(variable_rename,[status(thm)],[f_2119_1]) ).

fof(f_2119_3,plain,
    ! [U_7392,U_7393,U_7394] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7392),U_7394))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7393),U_7394))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7392),U_7393)) ),
    inference(definitional_conversion,[status(esa)],[f_2119_2]) ).

cnf(f_2119_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7392),U_7394))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7393),U_7394))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7392),U_7393)) ),
    inference(clausify,[status(thm)],[f_2119_3]) ).

fof(f_2120_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_2120_2,plain,
    ! [U_7397,U_7396,U_7395] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7397),U_7395))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7395),U_7397)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7397),U_7396))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7396),U_7397))
      | U_7395 != U_7396 ),
    inference(variable_rename,[status(thm)],[f_2120_1]) ).

fof(f_2120_3,plain,
    ( ! [U_7395,U_7397] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7397),U_7395))
        | ~ sP646(U_7395,U_7397) )
    & ! [U_7395,U_7397] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7395),U_7397))
        | ~ sP646(U_7395,U_7397) )
    & ! [U_7395,U_7396,U_7397] :
        ( sP646(U_7395,U_7397)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7397),U_7396))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7396),U_7397))
        | U_7395 != U_7396 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP646])],[f_2120_2]) ).

cnf(f_2120_4,plain,
    ( sP646(U_7395,U_7397)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7397),U_7396))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7396),U_7397))
    | U_7395 != U_7396 ),
    inference(clausify,[status(thm)],[f_2120_3]) ).

cnf(f_2120_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7395),U_7397))
    | ~ sP646(U_7395,U_7397) ),
    inference(clausify,[status(thm)],[f_2120_3]) ).

cnf(f_2120_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7397),U_7395))
    | ~ sP646(U_7395,U_7397) ),
    inference(clausify,[status(thm)],[f_2120_3]) ).

fof(f_2121_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_2121_2,plain,
    ! [U_7400,U_7399,U_7398] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7400),U_7398))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7398),U_7400)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7400),U_7399))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7399),U_7400))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7398),U_7399)) ),
    inference(variable_rename,[status(thm)],[f_2121_1]) ).

fof(f_2121_3,plain,
    ( ! [U_7398,U_7400] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7400),U_7398))
        | ~ sP647(U_7398,U_7400) )
    & ! [U_7398,U_7400] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7398),U_7400))
        | ~ sP647(U_7398,U_7400) )
    & ! [U_7398,U_7399,U_7400] :
        ( sP647(U_7398,U_7400)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7400),U_7399))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7399),U_7400))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7398),U_7399)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP647])],[f_2121_2]) ).

cnf(f_2121_4,plain,
    ( sP647(U_7398,U_7400)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7400),U_7399))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7399),U_7400))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7398),U_7399)) ),
    inference(clausify,[status(thm)],[f_2121_3]) ).

cnf(f_2121_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7398),U_7400))
    | ~ sP647(U_7398,U_7400) ),
    inference(clausify,[status(thm)],[f_2121_3]) ).

cnf(f_2121_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7400),U_7398))
    | ~ sP647(U_7398,U_7400) ),
    inference(clausify,[status(thm)],[f_2121_3]) ).

fof(f_2122_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_2122_2,plain,
    ! [U_7402,U_7401] :
      ( U_7401 != U_7402
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7402),U_7401))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7401),U_7402)) ),
    inference(variable_rename,[status(thm)],[f_2122_1]) ).

fof(f_2122_3,plain,
    ! [U_7402,U_7401] :
      ( U_7401 != U_7402
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7402),U_7401))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7401),U_7402)) ),
    inference(definitional_conversion,[status(esa)],[f_2122_2]) ).

cnf(f_2122_4,plain,
    ( U_7401 != U_7402
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7402),U_7401))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7401),U_7402)) ),
    inference(clausify,[status(thm)],[f_2122_3]) ).

fof(f_2123_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_2123_2,plain,
    ! [U_7404,U_7403] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7403),U_7404))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7404),U_7403))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7404),U_7403))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7403),U_7404)) ),
    inference(variable_rename,[status(thm)],[f_2123_1]) ).

fof(f_2123_3,plain,
    ! [U_7403,U_7404] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7403),U_7404))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7404),U_7403))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7404),U_7403))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7403),U_7404)) ),
    inference(definitional_conversion,[status(esa)],[f_2123_2]) ).

cnf(f_2123_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7403),U_7404))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7404),U_7403))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7404),U_7403))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7403),U_7404)) ),
    inference(clausify,[status(thm)],[f_2123_3]) ).

fof(f_2124_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_2124_2,plain,
    ! [U_7406,U_7405] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7405),U_7406))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7406),U_7405))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7405),U_7406)) ),
    inference(variable_rename,[status(thm)],[f_2124_1]) ).

fof(f_2124_3,plain,
    ! [U_7406,U_7405] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7405),U_7406))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7406),U_7405))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7405),U_7406)) ),
    inference(definitional_conversion,[status(esa)],[f_2124_2]) ).

cnf(f_2124_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7405),U_7406))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7406),U_7405))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7405),U_7406)) ),
    inference(clausify,[status(thm)],[f_2124_3]) ).

fof(f_2125_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_2125_2,plain,
    ! [U_7408,U_7407] :
      ( 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_7408),U_7407))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7408),U_7407))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7407),U_7408)) ),
    inference(variable_rename,[status(thm)],[f_2125_1]) ).

fof(f_2125_3,plain,
    ! [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_Nat_Onat),U_7408),U_7407))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7408),U_7407))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7407),U_7408)) ),
    inference(definitional_conversion,[status(esa)],[f_2125_2]) ).

cnf(f_2125_4,plain,
    ( 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_7408),U_7407))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7408),U_7407))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7407),U_7408)) ),
    inference(clausify,[status(thm)],[f_2125_3]) ).

fof(f_2126_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_2126_2,plain,
    ! [U_7410,U_7409] :
      ( U_7409 != U_7410
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7410),U_7409))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7409),U_7410)) ),
    inference(variable_rename,[status(thm)],[f_2126_1]) ).

fof(f_2126_3,plain,
    ! [U_7409,U_7410] :
      ( U_7409 != U_7410
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7410),U_7409))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7409),U_7410)) ),
    inference(definitional_conversion,[status(esa)],[f_2126_2]) ).

cnf(f_2126_4,plain,
    ( U_7409 != U_7410
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7410),U_7409))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7409),U_7410)) ),
    inference(clausify,[status(thm)],[f_2126_3]) ).

fof(f_2127_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_2127_2,plain,
    ! [U_7412,U_7411] :
      ( U_7412 != U_7411
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7412),U_7411))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7411),U_7412)) ),
    inference(variable_rename,[status(thm)],[f_2127_1]) ).

fof(f_2127_3,plain,
    ! [U_7411,U_7412] :
      ( U_7412 != U_7411
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7412),U_7411))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7411),U_7412)) ),
    inference(definitional_conversion,[status(esa)],[f_2127_2]) ).

cnf(f_2127_4,plain,
    ( U_7412 != U_7411
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7412),U_7411))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7411),U_7412)) ),
    inference(clausify,[status(thm)],[f_2127_3]) ).

fof(f_2128_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_2128_2,plain,
    ! [U_7415,U_7414,U_7413] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7415),U_7413))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7413),U_7415)) )
      | U_7414 != U_7415
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7414),U_7413))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7413),U_7414)) ),
    inference(variable_rename,[status(thm)],[f_2128_1]) ).

fof(f_2128_3,plain,
    ( ! [U_7413,U_7415] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7415),U_7413))
        | ~ sP648(U_7413,U_7415) )
    & ! [U_7413,U_7415] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7413),U_7415))
        | ~ sP648(U_7413,U_7415) )
    & ! [U_7413,U_7414,U_7415] :
        ( sP648(U_7413,U_7415)
        | U_7414 != U_7415
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7414),U_7413))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7413),U_7414)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP648])],[f_2128_2]) ).

cnf(f_2128_4,plain,
    ( sP648(U_7413,U_7415)
    | U_7414 != U_7415
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7414),U_7413))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7413),U_7414)) ),
    inference(clausify,[status(thm)],[f_2128_3]) ).

cnf(f_2128_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7413),U_7415))
    | ~ sP648(U_7413,U_7415) ),
    inference(clausify,[status(thm)],[f_2128_3]) ).

cnf(f_2128_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7415),U_7413))
    | ~ sP648(U_7413,U_7415) ),
    inference(clausify,[status(thm)],[f_2128_3]) ).

fof(f_2129_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_2129_2,plain,
    ! [U_7418,U_7417,U_7416] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7418),U_7416))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7416),U_7418)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7417),U_7418))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7417),U_7416))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7416),U_7417)) ),
    inference(variable_rename,[status(thm)],[f_2129_1]) ).

fof(f_2129_3,plain,
    ( ! [U_7416,U_7418] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7418),U_7416))
        | ~ sP649(U_7416,U_7418) )
    & ! [U_7416,U_7418] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7416),U_7418))
        | ~ sP649(U_7416,U_7418) )
    & ! [U_7416,U_7417,U_7418] :
        ( sP649(U_7416,U_7418)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7417),U_7418))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7417),U_7416))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7416),U_7417)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP649])],[f_2129_2]) ).

cnf(f_2129_4,plain,
    ( sP649(U_7416,U_7418)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7417),U_7418))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7417),U_7416))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7416),U_7417)) ),
    inference(clausify,[status(thm)],[f_2129_3]) ).

cnf(f_2129_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7416),U_7418))
    | ~ sP649(U_7416,U_7418) ),
    inference(clausify,[status(thm)],[f_2129_3]) ).

cnf(f_2129_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7418),U_7416))
    | ~ sP649(U_7416,U_7418) ),
    inference(clausify,[status(thm)],[f_2129_3]) ).

fof(f_2130_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_2130_2,plain,
    ! [U_7420,U_7419] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7419),U_7420))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7420),U_7419))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7420),U_7419))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7419),U_7420)) ),
    inference(variable_rename,[status(thm)],[f_2130_1]) ).

fof(f_2130_3,plain,
    ! [U_7420,U_7419] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7419),U_7420))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7420),U_7419))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7420),U_7419))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7419),U_7420)) ),
    inference(definitional_conversion,[status(esa)],[f_2130_2]) ).

cnf(f_2130_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7419),U_7420))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7420),U_7419))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7420),U_7419))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7419),U_7420)) ),
    inference(clausify,[status(thm)],[f_2130_3]) ).

fof(f_2131_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_2131_2,plain,
    ! [U_7423,U_7422,U_7421] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7423),U_7421))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7421),U_7423)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7423),U_7422))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7422),U_7423))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7422),U_7421))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7421),U_7422)) ),
    inference(variable_rename,[status(thm)],[f_2131_1]) ).

fof(f_2131_3,plain,
    ( ! [U_7421,U_7423] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7423),U_7421))
        | ~ sP650(U_7421,U_7423) )
    & ! [U_7421,U_7423] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7421),U_7423))
        | ~ sP650(U_7421,U_7423) )
    & ! [U_7421,U_7422,U_7423] :
        ( sP650(U_7421,U_7423)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7423),U_7422))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7422),U_7423))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7422),U_7421))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7421),U_7422)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP650])],[f_2131_2]) ).

cnf(f_2131_4,plain,
    ( sP650(U_7421,U_7423)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7423),U_7422))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7422),U_7423))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7422),U_7421))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7421),U_7422)) ),
    inference(clausify,[status(thm)],[f_2131_3]) ).

cnf(f_2131_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7421),U_7423))
    | ~ sP650(U_7421,U_7423) ),
    inference(clausify,[status(thm)],[f_2131_3]) ).

cnf(f_2131_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7423),U_7421))
    | ~ sP650(U_7421,U_7423) ),
    inference(clausify,[status(thm)],[f_2131_3]) ).

fof(f_2132_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_2132_2,plain,
    ! [U_7425,U_7424] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7424),U_7425))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7425),U_7424))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7425),U_7424))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7424),U_7425)) ),
    inference(variable_rename,[status(thm)],[f_2132_1]) ).

fof(f_2132_3,plain,
    ! [U_7425,U_7424] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7424),U_7425))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7425),U_7424))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7425),U_7424))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7424),U_7425)) ),
    inference(definitional_conversion,[status(esa)],[f_2132_2]) ).

cnf(f_2132_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7424),U_7425))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7425),U_7424))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7425),U_7424))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7424),U_7425)) ),
    inference(clausify,[status(thm)],[f_2132_3]) ).

fof(f_2133_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_2133_2,plain,
    ! [U_7427,U_7426] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7426),U_7427),U_7427))
      | ~ class_Rings_Ocomm__semiring__1(U_7426) ),
    inference(variable_rename,[status(thm)],[f_2133_1]) ).

fof(f_2133_3,plain,
    ! [U_7427,U_7426] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7426),U_7427),U_7427))
      | ~ class_Rings_Ocomm__semiring__1(U_7426) ),
    inference(definitional_conversion,[status(esa)],[f_2133_2]) ).

cnf(f_2133_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7426),U_7427),U_7427))
    | ~ class_Rings_Ocomm__semiring__1(U_7426) ),
    inference(clausify,[status(thm)],[f_2133_3]) ).

fof(f_2134_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_2134_2,plain,
    ! [U_7431,U_7430,U_7429,U_7428] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7428),U_7429),U_7431))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7428),U_7430),U_7431))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7428),U_7429),U_7430))
      | ~ class_Rings_Ocomm__semiring__1(U_7428) ),
    inference(variable_rename,[status(thm)],[f_2134_1]) ).

fof(f_2134_3,plain,
    ! [U_7428,U_7429,U_7430,U_7431] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7428),U_7429),U_7431))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7428),U_7430),U_7431))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7428),U_7429),U_7430))
      | ~ class_Rings_Ocomm__semiring__1(U_7428) ),
    inference(definitional_conversion,[status(esa)],[f_2134_2]) ).

cnf(f_2134_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7428),U_7429),U_7431))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7428),U_7430),U_7431))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7428),U_7429),U_7430))
    | ~ class_Rings_Ocomm__semiring__1(U_7428) ),
    inference(clausify,[status(thm)],[f_2134_3]) ).

fof(f_2135_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_2135_2,plain,
    ! [U_7435,U_7434,U_7433,U_7432] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7432),U_7434),U_7433)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7432),U_7435),U_7433)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),U_7434),U_7435)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),U_7434),U_7435))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7432),U_7434),U_7433)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7432),U_7435),U_7433))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),U_7433),U_7435))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),U_7433),U_7434))
      | ~ class_Divides_Osemiring__div(U_7432) ),
    inference(variable_rename,[status(thm)],[f_2135_1]) ).

fof(f_2135_3,plain,
    ( ! [U_7432,U_7433,U_7434,U_7435] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7432),U_7434),U_7433)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7432),U_7435),U_7433)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),U_7434),U_7435))
        | ~ sP651(U_7432,U_7433,U_7434,U_7435) )
    & ! [U_7432,U_7433,U_7434,U_7435] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),U_7434),U_7435))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7432),U_7434),U_7433)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7432),U_7435),U_7433)))
        | ~ sP651(U_7432,U_7433,U_7434,U_7435) )
    & ! [U_7432,U_7433,U_7434,U_7435] :
        ( sP651(U_7432,U_7433,U_7434,U_7435)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),U_7433),U_7435))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),U_7433),U_7434))
        | ~ class_Divides_Osemiring__div(U_7432) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP651])],[f_2135_2]) ).

cnf(f_2135_4,plain,
    ( sP651(U_7432,U_7433,U_7434,U_7435)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),U_7433),U_7435))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),U_7433),U_7434))
    | ~ class_Divides_Osemiring__div(U_7432) ),
    inference(clausify,[status(thm)],[f_2135_3]) ).

cnf(f_2135_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),U_7434),U_7435))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7432),U_7434),U_7433)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7432),U_7435),U_7433)))
    | ~ sP651(U_7432,U_7433,U_7434,U_7435) ),
    inference(clausify,[status(thm)],[f_2135_3]) ).

cnf(f_2135_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7432),U_7434),U_7433)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7432),U_7435),U_7433)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7432),U_7434),U_7435))
    | ~ sP651(U_7432,U_7433,U_7434,U_7435) ),
    inference(clausify,[status(thm)],[f_2135_3]) ).

fof(f_2136_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_2136_2,plain,
    ! [U_7439,U_7438,U_7437,U_7436] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7436),hAPP(hAPP(c_Power_Opower__class_Opower(U_7436),U_7437),U_7439)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7436),U_7438),U_7439)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7436),U_7437),U_7438))
      | ~ class_Rings_Ocomm__semiring__1(U_7436) ),
    inference(variable_rename,[status(thm)],[f_2136_1]) ).

fof(f_2136_3,plain,
    ! [U_7438,U_7437,U_7439,U_7436] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7436),hAPP(hAPP(c_Power_Opower__class_Opower(U_7436),U_7437),U_7439)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7436),U_7438),U_7439)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7436),U_7437),U_7438))
      | ~ class_Rings_Ocomm__semiring__1(U_7436) ),
    inference(definitional_conversion,[status(esa)],[f_2136_2]) ).

cnf(f_2136_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7436),hAPP(hAPP(c_Power_Opower__class_Opower(U_7436),U_7437),U_7439)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7436),U_7438),U_7439)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7436),U_7437),U_7438))
    | ~ class_Rings_Ocomm__semiring__1(U_7436) ),
    inference(clausify,[status(thm)],[f_2136_3]) ).

fof(f_2137_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_2137_2,plain,
    ! [U_7443,U_7442,U_7441,U_7440] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7440),U_7441),U_7442))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7440),U_7441),U_7443))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7440),U_7441),c_Divides_Odiv__class_Omod(U_7440,U_7442,U_7443)))
      | ~ class_Divides_Osemiring__div(U_7440) ),
    inference(variable_rename,[status(thm)],[f_2137_1]) ).

fof(f_2137_3,plain,
    ! [U_7440,U_7441,U_7442,U_7443] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7440),U_7441),U_7442))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7440),U_7441),U_7443))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7440),U_7441),c_Divides_Odiv__class_Omod(U_7440,U_7442,U_7443)))
      | ~ class_Divides_Osemiring__div(U_7440) ),
    inference(definitional_conversion,[status(esa)],[f_2137_2]) ).

cnf(f_2137_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7440),U_7441),U_7442))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7440),U_7441),U_7443))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7440),U_7441),c_Divides_Odiv__class_Omod(U_7440,U_7442,U_7443)))
    | ~ class_Divides_Osemiring__div(U_7440) ),
    inference(clausify,[status(thm)],[f_2137_3]) ).

fof(f_2138_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_2138_2,plain,
    ! [U_7447,U_7446,U_7445,U_7444] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7444),U_7445),c_Divides_Odiv__class_Omod(U_7444,U_7446,U_7447)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7444),U_7445),U_7447))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7444),U_7445),U_7446))
      | ~ class_Divides_Osemiring__div(U_7444) ),
    inference(variable_rename,[status(thm)],[f_2138_1]) ).

fof(f_2138_3,plain,
    ! [U_7444,U_7445,U_7446,U_7447] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7444),U_7445),c_Divides_Odiv__class_Omod(U_7444,U_7446,U_7447)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7444),U_7445),U_7447))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7444),U_7445),U_7446))
      | ~ class_Divides_Osemiring__div(U_7444) ),
    inference(definitional_conversion,[status(esa)],[f_2138_2]) ).

cnf(f_2138_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7444),U_7445),c_Divides_Odiv__class_Omod(U_7444,U_7446,U_7447)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7444),U_7445),U_7447))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7444),U_7445),U_7446))
    | ~ class_Divides_Osemiring__div(U_7444) ),
    inference(clausify,[status(thm)],[f_2138_3]) ).

fof(f_2139_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_2139_2,plain,
    ! [U_7451,U_7450,U_7449,U_7448] :
      ( c_Divides_Odiv__class_Omod(U_7448,c_Divides_Odiv__class_Omod(U_7448,U_7451,U_7450),U_7449) = c_Divides_Odiv__class_Omod(U_7448,U_7451,U_7449)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7448),U_7449),U_7450))
      | ~ class_Divides_Osemiring__div(U_7448) ),
    inference(variable_rename,[status(thm)],[f_2139_1]) ).

fof(f_2139_3,plain,
    ! [U_7450,U_7449,U_7448,U_7451] :
      ( c_Divides_Odiv__class_Omod(U_7448,c_Divides_Odiv__class_Omod(U_7448,U_7451,U_7450),U_7449) = c_Divides_Odiv__class_Omod(U_7448,U_7451,U_7449)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7448),U_7449),U_7450))
      | ~ class_Divides_Osemiring__div(U_7448) ),
    inference(definitional_conversion,[status(esa)],[f_2139_2]) ).

cnf(f_2139_4,plain,
    ( c_Divides_Odiv__class_Omod(U_7448,c_Divides_Odiv__class_Omod(U_7448,U_7451,U_7450),U_7449) = c_Divides_Odiv__class_Omod(U_7448,U_7451,U_7449)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7448),U_7449),U_7450))
    | ~ class_Divides_Osemiring__div(U_7448) ),
    inference(clausify,[status(thm)],[f_2139_3]) ).

fof(f_2140_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_2140_2,plain,
    ! [U_7455,U_7454,U_7453,U_7452] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7452),U_7453),c_Divides_Odiv__class_Omod(U_7452,U_7455,U_7454)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7452),U_7453),U_7455)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7452),U_7453),U_7455))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7452),U_7453),c_Divides_Odiv__class_Omod(U_7452,U_7455,U_7454))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7452),U_7453),U_7454))
      | ~ class_Divides_Osemiring__div(U_7452) ),
    inference(variable_rename,[status(thm)],[f_2140_1]) ).

fof(f_2140_3,plain,
    ( ! [U_7452,U_7453,U_7454,U_7455] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7452),U_7453),c_Divides_Odiv__class_Omod(U_7452,U_7455,U_7454)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7452),U_7453),U_7455))
        | ~ sP652(U_7452,U_7453,U_7454,U_7455) )
    & ! [U_7452,U_7453,U_7454,U_7455] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7452),U_7453),U_7455))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7452),U_7453),c_Divides_Odiv__class_Omod(U_7452,U_7455,U_7454)))
        | ~ sP652(U_7452,U_7453,U_7454,U_7455) )
    & ! [U_7452,U_7453,U_7454,U_7455] :
        ( sP652(U_7452,U_7453,U_7454,U_7455)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7452),U_7453),U_7454))
        | ~ class_Divides_Osemiring__div(U_7452) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP652])],[f_2140_2]) ).

cnf(f_2140_4,plain,
    ( sP652(U_7452,U_7453,U_7454,U_7455)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7452),U_7453),U_7454))
    | ~ class_Divides_Osemiring__div(U_7452) ),
    inference(clausify,[status(thm)],[f_2140_3]) ).

cnf(f_2140_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7452),U_7453),U_7455))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7452),U_7453),c_Divides_Odiv__class_Omod(U_7452,U_7455,U_7454)))
    | ~ sP652(U_7452,U_7453,U_7454,U_7455) ),
    inference(clausify,[status(thm)],[f_2140_3]) ).

cnf(f_2140_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7452),U_7453),c_Divides_Odiv__class_Omod(U_7452,U_7455,U_7454)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7452),U_7453),U_7455))
    | ~ sP652(U_7452,U_7453,U_7454,U_7455) ),
    inference(clausify,[status(thm)],[f_2140_3]) ).

fof(f_2141_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_2141_2,plain,
    ! [U_7458,U_7457,U_7456] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7456),U_7457),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7456),U_7457),U_7458)))
      | ~ class_Rings_Ocomm__semiring__1(U_7456) ),
    inference(variable_rename,[status(thm)],[f_2141_1]) ).

fof(f_2141_3,plain,
    ! [U_7456,U_7457,U_7458] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7456),U_7457),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7456),U_7457),U_7458)))
      | ~ class_Rings_Ocomm__semiring__1(U_7456) ),
    inference(definitional_conversion,[status(esa)],[f_2141_2]) ).

cnf(f_2141_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7456),U_7457),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7456),U_7457),U_7458)))
    | ~ class_Rings_Ocomm__semiring__1(U_7456) ),
    inference(clausify,[status(thm)],[f_2141_3]) ).

fof(f_2142_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_2142_2,plain,
    ! [U_7461,U_7460,U_7459] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7459),U_7460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7459),U_7461),U_7460)))
      | ~ class_Rings_Ocomm__semiring__1(U_7459) ),
    inference(variable_rename,[status(thm)],[f_2142_1]) ).

fof(f_2142_3,plain,
    ! [U_7459,U_7460,U_7461] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7459),U_7460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7459),U_7461),U_7460)))
      | ~ class_Rings_Ocomm__semiring__1(U_7459) ),
    inference(definitional_conversion,[status(esa)],[f_2142_2]) ).

cnf(f_2142_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7459),U_7460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7459),U_7461),U_7460)))
    | ~ class_Rings_Ocomm__semiring__1(U_7459) ),
    inference(clausify,[status(thm)],[f_2142_3]) ).

fof(f_2143_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_2143_2,plain,
    ! [U_7465,U_7464,U_7463,U_7462] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),U_7465)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7463),U_7464))
      | ~ class_Rings_Ocomm__semiring__1(U_7462) ),
    inference(variable_rename,[status(thm)],[f_2143_1]) ).

fof(f_2143_3,plain,
    ! [U_7462,U_7463,U_7464,U_7465] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),U_7465)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7463),U_7464))
      | ~ class_Rings_Ocomm__semiring__1(U_7462) ),
    inference(definitional_conversion,[status(esa)],[f_2143_2]) ).

cnf(f_2143_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),U_7465)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7463),U_7464))
    | ~ class_Rings_Ocomm__semiring__1(U_7462) ),
    inference(clausify,[status(thm)],[f_2143_3]) ).

fof(f_2144_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_2144_2,plain,
    ! [U_7469,U_7468,U_7467,U_7466] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7466),U_7467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7466),U_7469),U_7468)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7466),U_7467),U_7468))
      | ~ class_Rings_Ocomm__semiring__1(U_7466) ),
    inference(variable_rename,[status(thm)],[f_2144_1]) ).

fof(f_2144_3,plain,
    ! [U_7466,U_7467,U_7468,U_7469] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7466),U_7467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7466),U_7469),U_7468)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7466),U_7467),U_7468))
      | ~ class_Rings_Ocomm__semiring__1(U_7466) ),
    inference(definitional_conversion,[status(esa)],[f_2144_2]) ).

cnf(f_2144_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7466),U_7467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7466),U_7469),U_7468)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7466),U_7467),U_7468))
    | ~ class_Rings_Ocomm__semiring__1(U_7466) ),
    inference(clausify,[status(thm)],[f_2144_3]) ).

fof(f_2145_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_2145_2,plain,
    ! [U_7474,U_7473,U_7472,U_7471,U_7470] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7470),U_7471),U_7473)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7470),U_7472),U_7474)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7470),U_7473),U_7474))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7470),U_7471),U_7472))
      | ~ class_Rings_Ocomm__semiring__1(U_7470) ),
    inference(variable_rename,[status(thm)],[f_2145_1]) ).

fof(f_2145_3,plain,
    ! [U_7470,U_7471,U_7472,U_7473,U_7474] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7470),U_7471),U_7473)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7470),U_7472),U_7474)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7470),U_7473),U_7474))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7470),U_7471),U_7472))
      | ~ class_Rings_Ocomm__semiring__1(U_7470) ),
    inference(definitional_conversion,[status(esa)],[f_2145_2]) ).

cnf(f_2145_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7470),U_7471),U_7473)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7470),U_7472),U_7474)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7470),U_7473),U_7474))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7470),U_7471),U_7472))
    | ~ class_Rings_Ocomm__semiring__1(U_7470) ),
    inference(clausify,[status(thm)],[f_2145_3]) ).

fof(f_2146_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_2146_2,plain,
    ! [U_7478,U_7477,U_7476,U_7475] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7475),U_7477),U_7476))
      | U_7476 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7475),U_7477),U_7478)
      | ~ class_Rings_Odvd(U_7475) ),
    inference(variable_rename,[status(thm)],[f_2146_1]) ).

fof(f_2146_3,plain,
    ! [U_7477,U_7476,U_7475,U_7478] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7475),U_7477),U_7476))
      | U_7476 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7475),U_7477),U_7478)
      | ~ class_Rings_Odvd(U_7475) ),
    inference(definitional_conversion,[status(esa)],[f_2146_2]) ).

cnf(f_2146_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7475),U_7477),U_7476))
    | U_7476 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7475),U_7477),U_7478)
    | ~ class_Rings_Odvd(U_7475) ),
    inference(clausify,[status(thm)],[f_2146_3]) ).

fof(f_2147_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_2147_2,plain,
    ! [U_7482,U_7481,U_7480,U_7479] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7479),U_7480),U_7482))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7479),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7479),U_7480),U_7481)),U_7482))
      | ~ class_Rings_Ocomm__semiring__1(U_7479) ),
    inference(variable_rename,[status(thm)],[f_2147_1]) ).

fof(f_2147_3,plain,
    ! [U_7479,U_7480,U_7481,U_7482] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7479),U_7480),U_7482))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7479),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7479),U_7480),U_7481)),U_7482))
      | ~ class_Rings_Ocomm__semiring__1(U_7479) ),
    inference(definitional_conversion,[status(esa)],[f_2147_2]) ).

cnf(f_2147_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7479),U_7480),U_7482))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7479),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7479),U_7480),U_7481)),U_7482))
    | ~ class_Rings_Ocomm__semiring__1(U_7479) ),
    inference(clausify,[status(thm)],[f_2147_3]) ).

fof(f_2148_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_2148_2,plain,
    ! [U_7486,U_7485,U_7484,U_7483] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7483),U_7485),U_7486))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7483),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7483),U_7484),U_7485)),U_7486))
      | ~ class_Rings_Ocomm__semiring__1(U_7483) ),
    inference(variable_rename,[status(thm)],[f_2148_1]) ).

fof(f_2148_3,plain,
    ! [U_7483,U_7484,U_7485,U_7486] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7483),U_7485),U_7486))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7483),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7483),U_7484),U_7485)),U_7486))
      | ~ class_Rings_Ocomm__semiring__1(U_7483) ),
    inference(definitional_conversion,[status(esa)],[f_2148_2]) ).

cnf(f_2148_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7483),U_7485),U_7486))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7483),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7483),U_7484),U_7485)),U_7486))
    | ~ class_Rings_Ocomm__semiring__1(U_7483) ),
    inference(clausify,[status(thm)],[f_2148_3]) ).

fof(f_2149_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_2149_2,plain,
    ! [U_7489,U_7488,U_7487] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7487,U_7489,U_7488)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7487),tc_HOL_Obool)),U_7488),U_7489)) ),
    inference(variable_rename,[status(thm)],[f_2149_1]) ).

fof(f_2149_3,plain,
    ! [U_7487,U_7488,U_7489] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7487,U_7489,U_7488)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7487),tc_HOL_Obool)),U_7488),U_7489)) ),
    inference(definitional_conversion,[status(esa)],[f_2149_2]) ).

cnf(f_2149_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7487,U_7489,U_7488)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7487),tc_HOL_Obool)),U_7488),U_7489)) ),
    inference(clausify,[status(thm)],[f_2149_3]) ).

fof(f_2150_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_2150_2,plain,
    ! [U_7493,U_7492,U_7491,U_7490] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7490,U_7491,U_7493)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7490),tc_HOL_Obool)),U_7493),U_7492))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7490,U_7491,U_7492) ),
    inference(variable_rename,[status(thm)],[f_2150_1]) ).

fof(f_2150_3,plain,
    ! [U_7490,U_7491,U_7492,U_7493] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7490,U_7491,U_7493)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7490),tc_HOL_Obool)),U_7493),U_7492))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7490,U_7491,U_7492) ),
    inference(definitional_conversion,[status(esa)],[f_2150_2]) ).

cnf(f_2150_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7490,U_7491,U_7493)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7490),tc_HOL_Obool)),U_7493),U_7492))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7490,U_7491,U_7492) ),
    inference(clausify,[status(thm)],[f_2150_3]) ).

fof(f_2151_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_2151_2,plain,
    ! [U_7497,U_7496,U_7495,U_7494] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7494,U_7497,U_7496)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7494),tc_HOL_Obool)),U_7495),U_7497))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7494,U_7495,U_7496) ),
    inference(variable_rename,[status(thm)],[f_2151_1]) ).

fof(f_2151_3,plain,
    ! [U_7495,U_7494,U_7496,U_7497] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7494,U_7497,U_7496)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7494),tc_HOL_Obool)),U_7495),U_7497))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7494,U_7495,U_7496) ),
    inference(definitional_conversion,[status(esa)],[f_2151_2]) ).

cnf(f_2151_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7494,U_7497,U_7496)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7494),tc_HOL_Obool)),U_7495),U_7497))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7494,U_7495,U_7496) ),
    inference(clausify,[status(thm)],[f_2151_3]) ).

fof(f_2152_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_2152_2,plain,
    ! [U_7500,U_7499,U_7498] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7498),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7499),U_7500)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7498),U_7500))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7498),U_7499)) ),
    inference(variable_rename,[status(thm)],[f_2152_1]) ).

fof(f_2152_3,plain,
    ! [U_7498,U_7499,U_7500] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7498),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7499),U_7500)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7498),U_7500))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7498),U_7499)) ),
    inference(definitional_conversion,[status(esa)],[f_2152_2]) ).

cnf(f_2152_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7498),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7499),U_7500)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7498),U_7500))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7498),U_7499)) ),
    inference(clausify,[status(thm)],[f_2152_3]) ).

fof(f_2153_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_2153_2,plain,
    ! [U_7504,U_7503,U_7502,U_7501] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7501,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7501),U_7504),U_7502)),hAPP(hAPP(c_Set_Oinsert(U_7501),U_7504),U_7503)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7501,tc_HOL_Obool)),U_7502),U_7503)) ),
    inference(variable_rename,[status(thm)],[f_2153_1]) ).

fof(f_2153_3,plain,
    ! [U_7501,U_7502,U_7503,U_7504] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7501,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7501),U_7504),U_7502)),hAPP(hAPP(c_Set_Oinsert(U_7501),U_7504),U_7503)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7501,tc_HOL_Obool)),U_7502),U_7503)) ),
    inference(definitional_conversion,[status(esa)],[f_2153_2]) ).

cnf(f_2153_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7501,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7501),U_7504),U_7502)),hAPP(hAPP(c_Set_Oinsert(U_7501),U_7504),U_7503)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7501,tc_HOL_Obool)),U_7502),U_7503)) ),
    inference(clausify,[status(thm)],[f_2153_3]) ).

fof(f_2154_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_2154_2,plain,
    ! [U_7508,U_7507,U_7506,U_7505] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7505,tc_HOL_Obool)),U_7506),hAPP(hAPP(c_Set_Oinsert(U_7505),U_7508),U_7507)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7505,tc_HOL_Obool)),U_7506),U_7507)) ),
    inference(variable_rename,[status(thm)],[f_2154_1]) ).

fof(f_2154_3,plain,
    ! [U_7505,U_7506,U_7507,U_7508] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7505,tc_HOL_Obool)),U_7506),hAPP(hAPP(c_Set_Oinsert(U_7505),U_7508),U_7507)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7505,tc_HOL_Obool)),U_7506),U_7507)) ),
    inference(definitional_conversion,[status(esa)],[f_2154_2]) ).

cnf(f_2154_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7505,tc_HOL_Obool)),U_7506),hAPP(hAPP(c_Set_Oinsert(U_7505),U_7508),U_7507)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7505,tc_HOL_Obool)),U_7506),U_7507)) ),
    inference(clausify,[status(thm)],[f_2154_3]) ).

fof(f_2155_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_2155_2,plain,
    ! [U_7511,U_7510,U_7509] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7509,tc_HOL_Obool)),U_7510),hAPP(hAPP(c_Set_Oinsert(U_7509),U_7511),U_7510))),
    inference(variable_rename,[status(thm)],[f_2155_1]) ).

fof(f_2155_3,plain,
    ! [U_7509,U_7510,U_7511] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7509,tc_HOL_Obool)),U_7510),hAPP(hAPP(c_Set_Oinsert(U_7509),U_7511),U_7510))),
    inference(definitional_conversion,[status(esa)],[f_2155_2]) ).

cnf(f_2155_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7509,tc_HOL_Obool)),U_7510),hAPP(hAPP(c_Set_Oinsert(U_7509),U_7511),U_7510))),
    inference(clausify,[status(thm)],[f_2155_3]) ).

fof(f_2156_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_2156_2,plain,
    ! [U_7513,U_7512] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7512),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7513),U_7512)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7512),U_7513)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7512),U_7513))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7512),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7513),U_7512))) ) ),
    inference(variable_rename,[status(thm)],[f_2156_1]) ).

fof(f_2156_3,plain,
    ( ! [U_7517,U_7515] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7515),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7517),U_7515)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7515),U_7517)) )
    & ! [U_7516,U_7514] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7514),U_7516))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7514),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7516),U_7514))) ) ),
    inference(miniscope,[status(thm)],[f_2156_2]) ).

fof(f_2156_4,plain,
    ( ! [U_7515,U_7517] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7515),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7517),U_7515)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7515),U_7517)) )
    & ! [U_7516,U_7514] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7514),U_7516))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7514),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7516),U_7514))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2156_3]) ).

cnf(f_2156_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7514),U_7516))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7514),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7516),U_7514))) ),
    inference(clausify,[status(thm)],[f_2156_4]) ).

cnf(f_2156_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7515),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7517),U_7515)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7515),U_7517)) ),
    inference(clausify,[status(thm)],[f_2156_4]) ).

fof(f_2157_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_2157_2,plain,
    ! [U_7521,U_7520,U_7519,U_7518] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7518),U_7519),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7518),U_7520),U_7521)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7518),U_7519),U_7521))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7518),U_7519),U_7520))
      | ~ class_Rings_Ocomm__ring__1(U_7518) ),
    inference(variable_rename,[status(thm)],[f_2157_1]) ).

fof(f_2157_3,plain,
    ! [U_7518,U_7519,U_7520,U_7521] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7518),U_7519),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7518),U_7520),U_7521)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7518),U_7519),U_7521))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7518),U_7519),U_7520))
      | ~ class_Rings_Ocomm__ring__1(U_7518) ),
    inference(definitional_conversion,[status(esa)],[f_2157_2]) ).

cnf(f_2157_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7518),U_7519),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7518),U_7520),U_7521)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7518),U_7519),U_7521))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7518),U_7519),U_7520))
    | ~ class_Rings_Ocomm__ring__1(U_7518) ),
    inference(clausify,[status(thm)],[f_2157_3]) ).

fof(f_2158_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_2158_2,plain,
    ! [U_7524,U_7523,U_7522] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7522),U_7523),hAPP(c_Groups_Ouminus__class_Ouminus(U_7522),U_7524)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7522),U_7523),U_7524)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7522),U_7523),U_7524))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7522),U_7523),hAPP(c_Groups_Ouminus__class_Ouminus(U_7522),U_7524))) ) )
      | ~ class_Rings_Ocomm__ring__1(U_7522) ),
    inference(variable_rename,[status(thm)],[f_2158_1]) ).

fof(f_2158_3,plain,
    ( ! [U_7522,U_7523,U_7524] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7522),U_7523),hAPP(c_Groups_Ouminus__class_Ouminus(U_7522),U_7524)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7522),U_7523),U_7524))
        | ~ sP653(U_7522,U_7523,U_7524) )
    & ! [U_7522,U_7523,U_7524] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7522),U_7523),U_7524))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7522),U_7523),hAPP(c_Groups_Ouminus__class_Ouminus(U_7522),U_7524)))
        | ~ sP653(U_7522,U_7523,U_7524) )
    & ! [U_7522,U_7523,U_7524] :
        ( sP653(U_7522,U_7523,U_7524)
        | ~ class_Rings_Ocomm__ring__1(U_7522) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP653])],[f_2158_2]) ).

cnf(f_2158_4,plain,
    ( sP653(U_7522,U_7523,U_7524)
    | ~ class_Rings_Ocomm__ring__1(U_7522) ),
    inference(clausify,[status(thm)],[f_2158_3]) ).

cnf(f_2158_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7522),U_7523),U_7524))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7522),U_7523),hAPP(c_Groups_Ouminus__class_Ouminus(U_7522),U_7524)))
    | ~ sP653(U_7522,U_7523,U_7524) ),
    inference(clausify,[status(thm)],[f_2158_3]) ).

cnf(f_2158_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7522),U_7523),hAPP(c_Groups_Ouminus__class_Ouminus(U_7522),U_7524)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7522),U_7523),U_7524))
    | ~ sP653(U_7522,U_7523,U_7524) ),
    inference(clausify,[status(thm)],[f_2158_3]) ).

fof(f_2159_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_2159_2,plain,
    ! [U_7527,U_7526,U_7525] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7525),hAPP(c_Groups_Ouminus__class_Ouminus(U_7525),U_7526)),U_7527))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7525),U_7526),U_7527)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7525),U_7526),U_7527))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7525),hAPP(c_Groups_Ouminus__class_Ouminus(U_7525),U_7526)),U_7527)) ) )
      | ~ class_Rings_Ocomm__ring__1(U_7525) ),
    inference(variable_rename,[status(thm)],[f_2159_1]) ).

fof(f_2159_3,plain,
    ( ! [U_7525,U_7526,U_7527] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7525),hAPP(c_Groups_Ouminus__class_Ouminus(U_7525),U_7526)),U_7527))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7525),U_7526),U_7527))
        | ~ sP654(U_7525,U_7526,U_7527) )
    & ! [U_7525,U_7526,U_7527] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7525),U_7526),U_7527))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7525),hAPP(c_Groups_Ouminus__class_Ouminus(U_7525),U_7526)),U_7527))
        | ~ sP654(U_7525,U_7526,U_7527) )
    & ! [U_7525,U_7526,U_7527] :
        ( sP654(U_7525,U_7526,U_7527)
        | ~ class_Rings_Ocomm__ring__1(U_7525) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP654])],[f_2159_2]) ).

cnf(f_2159_4,plain,
    ( sP654(U_7525,U_7526,U_7527)
    | ~ class_Rings_Ocomm__ring__1(U_7525) ),
    inference(clausify,[status(thm)],[f_2159_3]) ).

cnf(f_2159_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7525),U_7526),U_7527))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7525),hAPP(c_Groups_Ouminus__class_Ouminus(U_7525),U_7526)),U_7527))
    | ~ sP654(U_7525,U_7526,U_7527) ),
    inference(clausify,[status(thm)],[f_2159_3]) ).

cnf(f_2159_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7525),hAPP(c_Groups_Ouminus__class_Ouminus(U_7525),U_7526)),U_7527))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7525),U_7526),U_7527))
    | ~ sP654(U_7525,U_7526,U_7527) ),
    inference(clausify,[status(thm)],[f_2159_3]) ).

fof(f_2160_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_2160_2,plain,
    ! [U_7530,U_7529,U_7528] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7529,U_7528)),U_7530) = c_Orderings_Obot__class_Obot(U_7528)
      | ~ class_Orderings_Obot(U_7528) ),
    inference(variable_rename,[status(thm)],[f_2160_1]) ).

fof(f_2160_3,plain,
    ! [U_7529,U_7530,U_7528] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7529,U_7528)),U_7530) = c_Orderings_Obot__class_Obot(U_7528)
      | ~ class_Orderings_Obot(U_7528) ),
    inference(definitional_conversion,[status(esa)],[f_2160_2]) ).

cnf(f_2160_4,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7529,U_7528)),U_7530) = c_Orderings_Obot__class_Obot(U_7528)
    | ~ class_Orderings_Obot(U_7528) ),
    inference(clausify,[status(thm)],[f_2160_3]) ).

fof(f_2161_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_2161_2,plain,
    ! [U_7535,U_7534,U_7533,U_7532,U_7531] : c_Hoare__Mirabelle_Ohoare__derivs(U_7531,U_7532,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7531)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7531),hAPP(hAPP(c_COMBC(U_7531,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_7531),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_7531),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),U_7533))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),U_7534))),c_Com_Ocom_OWhile(U_7534,U_7535)),U_7533)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7531),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2161_1]) ).

fof(f_2161_3,plain,
    ! [U_7531,U_7532,U_7533,U_7534,U_7535] : c_Hoare__Mirabelle_Ohoare__derivs(U_7531,U_7532,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7531)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7531),hAPP(hAPP(c_COMBC(U_7531,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_7531),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_7531),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),U_7533))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),U_7534))),c_Com_Ocom_OWhile(U_7534,U_7535)),U_7533)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7531),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2161_2]) ).

cnf(f_2161_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_7531,U_7532,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7531)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7531),hAPP(hAPP(c_COMBC(U_7531,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_7531),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_7531),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),U_7533))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),U_7534))),c_Com_Ocom_OWhile(U_7534,U_7535)),U_7533)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7531),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2161_3]) ).

fof(f_2162_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_2162_2,plain,
    ! [U_7539,U_7538,U_7537,U_7536] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7536,tc_HOL_Obool)),U_7537),hAPP(hAPP(c_Set_Oinsert(U_7536),U_7538),U_7539)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7536,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7536,tc_HOL_Obool)),U_7537),U_7539)),hAPP(hAPP(c_Set_Oinsert(U_7536),U_7538),c_Orderings_Obot__class_Obot(tc_fun(U_7536,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2162_1]) ).

fof(f_2162_3,plain,
    ! [U_7536,U_7537,U_7538,U_7539] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7536,tc_HOL_Obool)),U_7537),hAPP(hAPP(c_Set_Oinsert(U_7536),U_7538),U_7539)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7536,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7536,tc_HOL_Obool)),U_7537),U_7539)),hAPP(hAPP(c_Set_Oinsert(U_7536),U_7538),c_Orderings_Obot__class_Obot(tc_fun(U_7536,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2162_2]) ).

cnf(f_2162_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7536,tc_HOL_Obool)),U_7537),hAPP(hAPP(c_Set_Oinsert(U_7536),U_7538),U_7539)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7536,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7536,tc_HOL_Obool)),U_7537),U_7539)),hAPP(hAPP(c_Set_Oinsert(U_7536),U_7538),c_Orderings_Obot__class_Obot(tc_fun(U_7536,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2162_3]) ).

fof(f_2163_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_2163_2,plain,
    ! [U_7543,U_7542,U_7541,U_7540] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7540,tc_HOL_Obool)),U_7541),hAPP(hAPP(c_Set_Oinsert(U_7540),U_7542),U_7543)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7540,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7540,tc_HOL_Obool)),U_7541),hAPP(hAPP(c_Set_Oinsert(U_7540),U_7542),c_Orderings_Obot__class_Obot(tc_fun(U_7540,tc_HOL_Obool))))),U_7543),
    inference(variable_rename,[status(thm)],[f_2163_1]) ).

fof(f_2163_3,plain,
    ! [U_7540,U_7541,U_7542,U_7543] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7540,tc_HOL_Obool)),U_7541),hAPP(hAPP(c_Set_Oinsert(U_7540),U_7542),U_7543)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7540,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7540,tc_HOL_Obool)),U_7541),hAPP(hAPP(c_Set_Oinsert(U_7540),U_7542),c_Orderings_Obot__class_Obot(tc_fun(U_7540,tc_HOL_Obool))))),U_7543),
    inference(definitional_conversion,[status(esa)],[f_2163_2]) ).

cnf(f_2163_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7540,tc_HOL_Obool)),U_7541),hAPP(hAPP(c_Set_Oinsert(U_7540),U_7542),U_7543)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7540,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7540,tc_HOL_Obool)),U_7541),hAPP(hAPP(c_Set_Oinsert(U_7540),U_7542),c_Orderings_Obot__class_Obot(tc_fun(U_7540,tc_HOL_Obool))))),U_7543),
    inference(clausify,[status(thm)],[f_2163_3]) ).

fof(f_2164_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_2164_2,plain,
    ! [U_7546,U_7545,U_7544] : hAPP(hAPP(c_Set_Oinsert(U_7544),U_7545),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7544,tc_HOL_Obool)),U_7546),hAPP(hAPP(c_Set_Oinsert(U_7544),U_7545),c_Orderings_Obot__class_Obot(tc_fun(U_7544,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_7544),U_7545),U_7546),
    inference(variable_rename,[status(thm)],[f_2164_1]) ).

fof(f_2164_3,plain,
    ! [U_7544,U_7545,U_7546] : hAPP(hAPP(c_Set_Oinsert(U_7544),U_7545),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7544,tc_HOL_Obool)),U_7546),hAPP(hAPP(c_Set_Oinsert(U_7544),U_7545),c_Orderings_Obot__class_Obot(tc_fun(U_7544,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_7544),U_7545),U_7546),
    inference(definitional_conversion,[status(esa)],[f_2164_2]) ).

cnf(f_2164_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_7544),U_7545),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7544,tc_HOL_Obool)),U_7546),hAPP(hAPP(c_Set_Oinsert(U_7544),U_7545),c_Orderings_Obot__class_Obot(tc_fun(U_7544,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_7544),U_7545),U_7546),
    inference(clausify,[status(thm)],[f_2164_3]) ).

fof(f_2165_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_2165_2,plain,
    ! [U_7547] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7547),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_7547 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( U_7547 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7547),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[f_2165_1]) ).

fof(f_2165_3,plain,
    ( ! [U_7549] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7549),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_7549 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_7548] :
        ( U_7548 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7548),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(miniscope,[status(thm)],[f_2165_2]) ).

fof(f_2165_4,plain,
    ( ! [U_7549] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7549),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_7549 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_7548] :
        ( U_7548 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7548),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2165_3]) ).

cnf(f_2165_5,plain,
    ( U_7548 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7548),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_2165_4]) ).

cnf(f_2165_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7549),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_7549 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2165_4]) ).

fof(f_2166_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_2166_2,plain,
    ! [U_7551,U_7550] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7550,tc_HOL_Obool)),U_7551),c_Orderings_Obot__class_Obot(tc_fun(U_7550,tc_HOL_Obool))))
        | U_7551 != c_Orderings_Obot__class_Obot(tc_fun(U_7550,tc_HOL_Obool)) )
      & ( U_7551 = c_Orderings_Obot__class_Obot(tc_fun(U_7550,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7550,tc_HOL_Obool)),U_7551),c_Orderings_Obot__class_Obot(tc_fun(U_7550,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_2166_1]) ).

fof(f_2166_3,plain,
    ( ! [U_7555,U_7553] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7553,tc_HOL_Obool)),U_7555),c_Orderings_Obot__class_Obot(tc_fun(U_7553,tc_HOL_Obool))))
        | U_7555 != c_Orderings_Obot__class_Obot(tc_fun(U_7553,tc_HOL_Obool)) )
    & ! [U_7554,U_7552] :
        ( U_7554 = c_Orderings_Obot__class_Obot(tc_fun(U_7552,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7552,tc_HOL_Obool)),U_7554),c_Orderings_Obot__class_Obot(tc_fun(U_7552,tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_2166_2]) ).

fof(f_2166_4,plain,
    ( ! [U_7553,U_7555] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7553,tc_HOL_Obool)),U_7555),c_Orderings_Obot__class_Obot(tc_fun(U_7553,tc_HOL_Obool))))
        | U_7555 != c_Orderings_Obot__class_Obot(tc_fun(U_7553,tc_HOL_Obool)) )
    & ! [U_7554,U_7552] :
        ( U_7554 = c_Orderings_Obot__class_Obot(tc_fun(U_7552,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7552,tc_HOL_Obool)),U_7554),c_Orderings_Obot__class_Obot(tc_fun(U_7552,tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2166_3]) ).

cnf(f_2166_5,plain,
    ( U_7554 = c_Orderings_Obot__class_Obot(tc_fun(U_7552,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7552,tc_HOL_Obool)),U_7554),c_Orderings_Obot__class_Obot(tc_fun(U_7552,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2166_4]) ).

cnf(f_2166_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7553,tc_HOL_Obool)),U_7555),c_Orderings_Obot__class_Obot(tc_fun(U_7553,tc_HOL_Obool))))
    | U_7555 != c_Orderings_Obot__class_Obot(tc_fun(U_7553,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2166_4]) ).

fof(f_2167_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_2167_2,plain,
    ! [U_7557,U_7556] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7556,tc_HOL_Obool)),U_7557),U_7557) = c_Orderings_Obot__class_Obot(tc_fun(U_7556,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2167_1]) ).

fof(f_2167_3,plain,
    ! [U_7556,U_7557] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7556,tc_HOL_Obool)),U_7557),U_7557) = c_Orderings_Obot__class_Obot(tc_fun(U_7556,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2167_2]) ).

cnf(f_2167_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7556,tc_HOL_Obool)),U_7557),U_7557) = c_Orderings_Obot__class_Obot(tc_fun(U_7556,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2167_3]) ).

fof(f_2168_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_2168_2,plain,
    ! [U_7559,U_7558] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7558,tc_HOL_Obool)),U_7559),c_Orderings_Obot__class_Obot(tc_fun(U_7558,tc_HOL_Obool))) = U_7559,
    inference(variable_rename,[status(thm)],[f_2168_1]) ).

fof(f_2168_3,plain,
    ! [U_7558,U_7559] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7558,tc_HOL_Obool)),U_7559),c_Orderings_Obot__class_Obot(tc_fun(U_7558,tc_HOL_Obool))) = U_7559,
    inference(definitional_conversion,[status(esa)],[f_2168_2]) ).

cnf(f_2168_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7558,tc_HOL_Obool)),U_7559),c_Orderings_Obot__class_Obot(tc_fun(U_7558,tc_HOL_Obool))) = U_7559,
    inference(clausify,[status(thm)],[f_2168_3]) ).

fof(f_2169_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_2169_2,plain,
    ! [U_7561,U_7560] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7560,tc_HOL_Obool)),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)),
    inference(variable_rename,[status(thm)],[f_2169_1]) ).

fof(f_2169_3,plain,
    ! [U_7560,U_7561] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7560,tc_HOL_Obool)),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)),
    inference(definitional_conversion,[status(esa)],[f_2169_2]) ).

cnf(f_2169_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7560,tc_HOL_Obool)),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)),
    inference(clausify,[status(thm)],[f_2169_3]) ).

fof(f_2170_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_2170_2,plain,
    ! [U_7563,U_7562] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7562,tc_HOL_Obool)),U_7563),c_Orderings_Obot__class_Obot(tc_fun(U_7562,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2170_1]) ).

fof(f_2170_3,plain,
    ! [U_7562,U_7563] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7562,tc_HOL_Obool)),U_7563),c_Orderings_Obot__class_Obot(tc_fun(U_7562,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2170_2]) ).

cnf(f_2170_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7562,tc_HOL_Obool)),U_7563),c_Orderings_Obot__class_Obot(tc_fun(U_7562,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2170_3]) ).

fof(f_2171_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_2171_2,plain,
    ! [U_7568,U_7567,U_7566,U_7565,U_7564] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7564,U_7565,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7564)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7564),U_7566),hAPP(c_Com_Ocom_OBODY,U_7567)),U_7568)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7564),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7564,U_7565,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7564)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7564),U_7566),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_7567))),U_7568)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7564),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2171_1]) ).

fof(f_2171_3,plain,
    ! [U_7564,U_7565,U_7566,U_7567,U_7568] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7564,U_7565,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7564)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7564),U_7566),hAPP(c_Com_Ocom_OBODY,U_7567)),U_7568)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7564),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7564,U_7565,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7564)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7564),U_7566),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_7567))),U_7568)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7564),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2171_2]) ).

cnf(f_2171_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7564,U_7565,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7564)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7564),U_7566),hAPP(c_Com_Ocom_OBODY,U_7567)),U_7568)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7564),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7564,U_7565,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7564)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7564),U_7566),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_7567))),U_7568)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7564),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2171_3]) ).

fof(f_2172_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_2172_2,plain,
    ! [U_7573,U_7572,U_7571,U_7570,U_7569] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7569,U_7573,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7569)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7569),U_7570),hAPP(c_Com_Ocom_OBODY,U_7571)),U_7572)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7569),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7569,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7569)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7569),U_7570),hAPP(c_Com_Ocom_OBODY,U_7571)),U_7572)),U_7573),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7569)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7569),U_7570),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_7571))),U_7572)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7569),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2172_1]) ).

fof(f_2172_3,plain,
    ! [U_7569,U_7570,U_7571,U_7572,U_7573] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7569,U_7573,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7569)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7569),U_7570),hAPP(c_Com_Ocom_OBODY,U_7571)),U_7572)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7569),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7569,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7569)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7569),U_7570),hAPP(c_Com_Ocom_OBODY,U_7571)),U_7572)),U_7573),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7569)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7569),U_7570),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_7571))),U_7572)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7569),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2172_2]) ).

cnf(f_2172_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7569,U_7573,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7569)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7569),U_7570),hAPP(c_Com_Ocom_OBODY,U_7571)),U_7572)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7569),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7569,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7569)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7569),U_7570),hAPP(c_Com_Ocom_OBODY,U_7571)),U_7572)),U_7573),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7569)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7569),U_7570),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_7571))),U_7572)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7569),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2172_3]) ).

fof(f_2173_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_2173_2,plain,
    ! [U_7575,U_7574] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7574),c_Orderings_Obot__class_Obot(U_7574)),U_7575))
      | ~ class_Orderings_Obot(U_7574) ),
    inference(variable_rename,[status(thm)],[f_2173_1]) ).

fof(f_2173_3,plain,
    ! [U_7574,U_7575] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7574),c_Orderings_Obot__class_Obot(U_7574)),U_7575))
      | ~ class_Orderings_Obot(U_7574) ),
    inference(definitional_conversion,[status(esa)],[f_2173_2]) ).

cnf(f_2173_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7574),c_Orderings_Obot__class_Obot(U_7574)),U_7575))
    | ~ class_Orderings_Obot(U_7574) ),
    inference(clausify,[status(thm)],[f_2173_3]) ).

fof(f_2174_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_2174_2,plain,
    ! [U_7579,U_7578,U_7577,U_7576] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7576),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7576),U_7577),U_7578)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7576),U_7577),U_7579)))
          | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7576),U_7578),U_7579))
            & U_7577 != c_Groups_Ozero__class_Ozero(U_7576) ) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7576),U_7578),U_7579))
          | U_7577 = c_Groups_Ozero__class_Ozero(U_7576)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7576),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7576),U_7577),U_7578)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7576),U_7577),U_7579))) ) )
      | ~ class_Rings_Oidom(U_7576) ),
    inference(variable_rename,[status(thm)],[f_2174_1]) ).

fof(f_2174_3,plain,
    ( ! [U_7576,U_7577,U_7578,U_7579] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7576),U_7578),U_7579))
        | ~ sP655(U_7576,U_7577,U_7578,U_7579) )
    & ! [U_7576,U_7577,U_7578,U_7579] :
        ( U_7577 != c_Groups_Ozero__class_Ozero(U_7576)
        | ~ sP655(U_7576,U_7577,U_7578,U_7579) )
    & ! [U_7576,U_7577,U_7578,U_7579] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7576),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7576),U_7577),U_7578)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7576),U_7577),U_7579)))
        | sP655(U_7576,U_7577,U_7578,U_7579)
        | ~ sP656(U_7576,U_7577,U_7578,U_7579) )
    & ! [U_7576,U_7577,U_7578,U_7579] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7576),U_7578),U_7579))
        | U_7577 = c_Groups_Ozero__class_Ozero(U_7576)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7576),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7576),U_7577),U_7578)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7576),U_7577),U_7579)))
        | ~ sP656(U_7576,U_7577,U_7578,U_7579) )
    & ! [U_7576,U_7577,U_7578,U_7579] :
        ( sP656(U_7576,U_7577,U_7578,U_7579)
        | ~ class_Rings_Oidom(U_7576) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP655,sP656])],[f_2174_2]) ).

cnf(f_2174_4,plain,
    ( sP656(U_7576,U_7577,U_7578,U_7579)
    | ~ class_Rings_Oidom(U_7576) ),
    inference(clausify,[status(thm)],[f_2174_3]) ).

cnf(f_2174_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7576),U_7578),U_7579))
    | U_7577 = c_Groups_Ozero__class_Ozero(U_7576)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7576),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7576),U_7577),U_7578)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7576),U_7577),U_7579)))
    | ~ sP656(U_7576,U_7577,U_7578,U_7579) ),
    inference(clausify,[status(thm)],[f_2174_3]) ).

cnf(f_2174_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7576),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7576),U_7577),U_7578)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7576),U_7577),U_7579)))
    | sP655(U_7576,U_7577,U_7578,U_7579)
    | ~ sP656(U_7576,U_7577,U_7578,U_7579) ),
    inference(clausify,[status(thm)],[f_2174_3]) ).

cnf(f_2174_7,plain,
    ( U_7577 != c_Groups_Ozero__class_Ozero(U_7576)
    | ~ sP655(U_7576,U_7577,U_7578,U_7579) ),
    inference(clausify,[status(thm)],[f_2174_3]) ).

cnf(f_2174_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7576),U_7578),U_7579))
    | ~ sP655(U_7576,U_7577,U_7578,U_7579) ),
    inference(clausify,[status(thm)],[f_2174_3]) ).

fof(f_2175_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_2175_2,plain,
    ! [U_7583,U_7582,U_7581,U_7580] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7580),U_7581),U_7582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7580),U_7583),U_7582)))
          | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7580),U_7581),U_7583))
            & U_7582 != c_Groups_Ozero__class_Ozero(U_7580) ) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7580),U_7581),U_7583))
          | U_7582 = c_Groups_Ozero__class_Ozero(U_7580)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7580),U_7581),U_7582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7580),U_7583),U_7582))) ) )
      | ~ class_Rings_Oidom(U_7580) ),
    inference(variable_rename,[status(thm)],[f_2175_1]) ).

fof(f_2175_3,plain,
    ( ! [U_7581,U_7582,U_7583,U_7580] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7580),U_7581),U_7583))
        | ~ sP657(U_7581,U_7582,U_7583,U_7580) )
    & ! [U_7581,U_7582,U_7583,U_7580] :
        ( U_7582 != c_Groups_Ozero__class_Ozero(U_7580)
        | ~ sP657(U_7581,U_7582,U_7583,U_7580) )
    & ! [U_7581,U_7582,U_7583,U_7580] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7580),U_7581),U_7582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7580),U_7583),U_7582)))
        | sP657(U_7581,U_7582,U_7583,U_7580)
        | ~ sP658(U_7581,U_7582,U_7583,U_7580) )
    & ! [U_7581,U_7582,U_7583,U_7580] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7580),U_7581),U_7583))
        | U_7582 = c_Groups_Ozero__class_Ozero(U_7580)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7580),U_7581),U_7582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7580),U_7583),U_7582)))
        | ~ sP658(U_7581,U_7582,U_7583,U_7580) )
    & ! [U_7581,U_7582,U_7583,U_7580] :
        ( sP658(U_7581,U_7582,U_7583,U_7580)
        | ~ class_Rings_Oidom(U_7580) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP657,sP658])],[f_2175_2]) ).

cnf(f_2175_4,plain,
    ( sP658(U_7581,U_7582,U_7583,U_7580)
    | ~ class_Rings_Oidom(U_7580) ),
    inference(clausify,[status(thm)],[f_2175_3]) ).

cnf(f_2175_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7580),U_7581),U_7583))
    | U_7582 = c_Groups_Ozero__class_Ozero(U_7580)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7580),U_7581),U_7582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7580),U_7583),U_7582)))
    | ~ sP658(U_7581,U_7582,U_7583,U_7580) ),
    inference(clausify,[status(thm)],[f_2175_3]) ).

cnf(f_2175_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7580),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7580),U_7581),U_7582)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7580),U_7583),U_7582)))
    | sP657(U_7581,U_7582,U_7583,U_7580)
    | ~ sP658(U_7581,U_7582,U_7583,U_7580) ),
    inference(clausify,[status(thm)],[f_2175_3]) ).

cnf(f_2175_7,plain,
    ( U_7582 != c_Groups_Ozero__class_Ozero(U_7580)
    | ~ sP657(U_7581,U_7582,U_7583,U_7580) ),
    inference(clausify,[status(thm)],[f_2175_3]) ).

cnf(f_2175_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7580),U_7581),U_7583))
    | ~ sP657(U_7581,U_7582,U_7583,U_7580) ),
    inference(clausify,[status(thm)],[f_2175_3]) ).

fof(f_2176_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_2176_2,plain,
    ! [U_7586,U_7585,U_7584] :
      ( c_Divides_Odiv__class_Omod(U_7584,U_7586,U_7585) = c_Groups_Ozero__class_Ozero(U_7584)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7584),U_7585),U_7586))
      | ~ class_Divides_Osemiring__div(U_7584) ),
    inference(variable_rename,[status(thm)],[f_2176_1]) ).

fof(f_2176_3,plain,
    ! [U_7586,U_7585,U_7584] :
      ( c_Divides_Odiv__class_Omod(U_7584,U_7586,U_7585) = c_Groups_Ozero__class_Ozero(U_7584)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7584),U_7585),U_7586))
      | ~ class_Divides_Osemiring__div(U_7584) ),
    inference(definitional_conversion,[status(esa)],[f_2176_2]) ).

cnf(f_2176_4,plain,
    ( c_Divides_Odiv__class_Omod(U_7584,U_7586,U_7585) = c_Groups_Ozero__class_Ozero(U_7584)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7584),U_7585),U_7586))
    | ~ class_Divides_Osemiring__div(U_7584) ),
    inference(clausify,[status(thm)],[f_2176_3]) ).

fof(f_2177_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_2177_2,plain,
    ! [U_7589,U_7588,U_7587] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7587),U_7588),U_7589))
          | c_Divides_Odiv__class_Omod(U_7587,U_7589,U_7588) != c_Groups_Ozero__class_Ozero(U_7587) )
        & ( c_Divides_Odiv__class_Omod(U_7587,U_7589,U_7588) = c_Groups_Ozero__class_Ozero(U_7587)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7587),U_7588),U_7589)) ) )
      | ~ class_Divides_Osemiring__div(U_7587) ),
    inference(variable_rename,[status(thm)],[f_2177_1]) ).

fof(f_2177_3,plain,
    ( ! [U_7587,U_7589,U_7588] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7587),U_7588),U_7589))
        | c_Divides_Odiv__class_Omod(U_7587,U_7589,U_7588) != c_Groups_Ozero__class_Ozero(U_7587)
        | ~ sP659(U_7587,U_7589,U_7588) )
    & ! [U_7587,U_7589,U_7588] :
        ( c_Divides_Odiv__class_Omod(U_7587,U_7589,U_7588) = c_Groups_Ozero__class_Ozero(U_7587)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7587),U_7588),U_7589))
        | ~ sP659(U_7587,U_7589,U_7588) )
    & ! [U_7587,U_7589,U_7588] :
        ( sP659(U_7587,U_7589,U_7588)
        | ~ class_Divides_Osemiring__div(U_7587) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP659])],[f_2177_2]) ).

cnf(f_2177_4,plain,
    ( sP659(U_7587,U_7589,U_7588)
    | ~ class_Divides_Osemiring__div(U_7587) ),
    inference(clausify,[status(thm)],[f_2177_3]) ).

cnf(f_2177_5,plain,
    ( c_Divides_Odiv__class_Omod(U_7587,U_7589,U_7588) = c_Groups_Ozero__class_Ozero(U_7587)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7587),U_7588),U_7589))
    | ~ sP659(U_7587,U_7589,U_7588) ),
    inference(clausify,[status(thm)],[f_2177_3]) ).

cnf(f_2177_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7587),U_7588),U_7589))
    | c_Divides_Odiv__class_Omod(U_7587,U_7589,U_7588) != c_Groups_Ozero__class_Ozero(U_7587)
    | ~ sP659(U_7587,U_7589,U_7588) ),
    inference(clausify,[status(thm)],[f_2177_3]) ).

fof(f_2178_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_2178_2,plain,
    ! [U_7593,U_7592,U_7591,U_7590] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7590),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7590),U_7592),U_7593)),U_7591) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7590),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7590),U_7592),U_7591)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7590),U_7593),U_7591))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7590),U_7591),U_7593))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7590),U_7591),U_7592))
      | ~ class_Divides_Osemiring__div(U_7590) ),
    inference(variable_rename,[status(thm)],[f_2178_1]) ).

fof(f_2178_3,plain,
    ! [U_7590,U_7591,U_7592,U_7593] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7590),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7590),U_7592),U_7593)),U_7591) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7590),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7590),U_7592),U_7591)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7590),U_7593),U_7591))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7590),U_7591),U_7593))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7590),U_7591),U_7592))
      | ~ class_Divides_Osemiring__div(U_7590) ),
    inference(definitional_conversion,[status(esa)],[f_2178_2]) ).

cnf(f_2178_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7590),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7590),U_7592),U_7593)),U_7591) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7590),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7590),U_7592),U_7591)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7590),U_7593),U_7591))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7590),U_7591),U_7593))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7590),U_7591),U_7592))
    | ~ class_Divides_Osemiring__div(U_7590) ),
    inference(clausify,[status(thm)],[f_2178_3]) ).

fof(f_2179_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_2179_2,plain,
    ! [U_7596,U_7595,U_7594] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7594),U_7595),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7594),U_7596),U_7595)) = U_7596
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7594),U_7595),U_7596))
      | ~ class_Divides_Osemiring__div(U_7594) ),
    inference(variable_rename,[status(thm)],[f_2179_1]) ).

fof(f_2179_3,plain,
    ! [U_7595,U_7594,U_7596] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7594),U_7595),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7594),U_7596),U_7595)) = U_7596
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7594),U_7595),U_7596))
      | ~ class_Divides_Osemiring__div(U_7594) ),
    inference(definitional_conversion,[status(esa)],[f_2179_2]) ).

cnf(f_2179_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7594),U_7595),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7594),U_7596),U_7595)) = U_7596
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7594),U_7595),U_7596))
    | ~ class_Divides_Osemiring__div(U_7594) ),
    inference(clausify,[status(thm)],[f_2179_3]) ).

fof(f_2180_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_2180_2,plain,
    ! [U_7600,U_7599,U_7598,U_7597] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7597),U_7600),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7597),U_7599),U_7598)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7597),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7597),U_7600),U_7599)),U_7598)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7597),U_7598),U_7599))
      | ~ class_Divides_Osemiring__div(U_7597) ),
    inference(variable_rename,[status(thm)],[f_2180_1]) ).

fof(f_2180_3,plain,
    ! [U_7597,U_7598,U_7599,U_7600] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7597),U_7600),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7597),U_7599),U_7598)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7597),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7597),U_7600),U_7599)),U_7598)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7597),U_7598),U_7599))
      | ~ class_Divides_Osemiring__div(U_7597) ),
    inference(definitional_conversion,[status(esa)],[f_2180_2]) ).

cnf(f_2180_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7597),U_7600),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7597),U_7599),U_7598)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7597),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7597),U_7600),U_7599)),U_7598)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7597),U_7598),U_7599))
    | ~ class_Divides_Osemiring__div(U_7597) ),
    inference(clausify,[status(thm)],[f_2180_3]) ).

fof(f_2181_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_2181_2,plain,
    ! [U_7603,U_7602,U_7601] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7601),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7601),U_7603),U_7602)),U_7602) = U_7603
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7601),U_7602),U_7603))
      | ~ class_Divides_Osemiring__div(U_7601) ),
    inference(variable_rename,[status(thm)],[f_2181_1]) ).

fof(f_2181_3,plain,
    ! [U_7601,U_7602,U_7603] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7601),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7601),U_7603),U_7602)),U_7602) = U_7603
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7601),U_7602),U_7603))
      | ~ class_Divides_Osemiring__div(U_7601) ),
    inference(definitional_conversion,[status(esa)],[f_2181_2]) ).

cnf(f_2181_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7601),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7601),U_7603),U_7602)),U_7602) = U_7603
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7601),U_7602),U_7603))
    | ~ class_Divides_Osemiring__div(U_7601) ),
    inference(clausify,[status(thm)],[f_2181_3]) ).

fof(f_2182_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_2182_2,plain,
    ! [U_7607,U_7606,U_7605,U_7604] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7604),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7604),U_7606),U_7605)),U_7607) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7604),U_7606),U_7607)),U_7605)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7604),U_7605),U_7606))
      | ~ class_Divides_Osemiring__div(U_7604) ),
    inference(variable_rename,[status(thm)],[f_2182_1]) ).

fof(f_2182_3,plain,
    ! [U_7604,U_7605,U_7606,U_7607] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7604),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7604),U_7606),U_7605)),U_7607) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7604),U_7606),U_7607)),U_7605)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7604),U_7605),U_7606))
      | ~ class_Divides_Osemiring__div(U_7604) ),
    inference(definitional_conversion,[status(esa)],[f_2182_2]) ).

cnf(f_2182_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7604),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7604),U_7606),U_7605)),U_7607) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7604),U_7606),U_7607)),U_7605)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7604),U_7605),U_7606))
    | ~ class_Divides_Osemiring__div(U_7604) ),
    inference(clausify,[status(thm)],[f_2182_3]) ).

fof(f_2183_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_2183_2,plain,
    ! [U_7612,U_7611,U_7610,U_7609,U_7608] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7608),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7608),U_7610),U_7609)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7608),U_7612),U_7611)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7608),U_7610),U_7612)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7608),U_7609),U_7611))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7608),U_7611),U_7612))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7608),U_7609),U_7610))
      | ~ class_Divides_Osemiring__div(U_7608) ),
    inference(variable_rename,[status(thm)],[f_2183_1]) ).

fof(f_2183_3,plain,
    ! [U_7608,U_7609,U_7610,U_7611,U_7612] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7608),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7608),U_7610),U_7609)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7608),U_7612),U_7611)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7608),U_7610),U_7612)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7608),U_7609),U_7611))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7608),U_7611),U_7612))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7608),U_7609),U_7610))
      | ~ class_Divides_Osemiring__div(U_7608) ),
    inference(definitional_conversion,[status(esa)],[f_2183_2]) ).

cnf(f_2183_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7608),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7608),U_7610),U_7609)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7608),U_7612),U_7611)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7608),U_7610),U_7612)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7608),U_7609),U_7611))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7608),U_7611),U_7612))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7608),U_7609),U_7610))
    | ~ class_Divides_Osemiring__div(U_7608) ),
    inference(clausify,[status(thm)],[f_2183_3]) ).

fof(f_2184_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_2184_2,plain,
    ! [U_7615,U_7614,U_7613] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7613),hAPP(c_Groups_Ouminus__class_Ouminus(U_7613),U_7615)),U_7614) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7613),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7613),U_7615),U_7614))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7613),U_7614),U_7615))
      | ~ class_Divides_Oring__div(U_7613) ),
    inference(variable_rename,[status(thm)],[f_2184_1]) ).

fof(f_2184_3,plain,
    ! [U_7614,U_7613,U_7615] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7613),hAPP(c_Groups_Ouminus__class_Ouminus(U_7613),U_7615)),U_7614) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7613),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7613),U_7615),U_7614))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7613),U_7614),U_7615))
      | ~ class_Divides_Oring__div(U_7613) ),
    inference(definitional_conversion,[status(esa)],[f_2184_2]) ).

cnf(f_2184_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7613),hAPP(c_Groups_Ouminus__class_Ouminus(U_7613),U_7615)),U_7614) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7613),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7613),U_7615),U_7614))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7613),U_7614),U_7615))
    | ~ class_Divides_Oring__div(U_7613) ),
    inference(clausify,[status(thm)],[f_2184_3]) ).

fof(f_2185_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_2185_2,plain,
    ! [U_7618,U_7617,U_7616] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7616),U_7618),hAPP(c_Groups_Ouminus__class_Ouminus(U_7616),U_7617)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7616),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7616),U_7618),U_7617))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7616),U_7617),U_7618))
      | ~ class_Divides_Oring__div(U_7616) ),
    inference(variable_rename,[status(thm)],[f_2185_1]) ).

fof(f_2185_3,plain,
    ! [U_7616,U_7617,U_7618] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7616),U_7618),hAPP(c_Groups_Ouminus__class_Ouminus(U_7616),U_7617)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7616),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7616),U_7618),U_7617))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7616),U_7617),U_7618))
      | ~ class_Divides_Oring__div(U_7616) ),
    inference(definitional_conversion,[status(esa)],[f_2185_2]) ).

cnf(f_2185_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7616),U_7618),hAPP(c_Groups_Ouminus__class_Ouminus(U_7616),U_7617)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7616),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7616),U_7618),U_7617))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7616),U_7617),U_7618))
    | ~ class_Divides_Oring__div(U_7616) ),
    inference(clausify,[status(thm)],[f_2185_3]) ).

fof(f_2186_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_2186_2,plain,
    ! [U_7622,U_7621,U_7620,U_7619] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7619),hAPP(hAPP(c_Power_Opower__class_Opower(U_7619),U_7622),U_7620)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7619),U_7622),U_7621)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7620),U_7621))
      | ~ class_Rings_Ocomm__semiring__1(U_7619) ),
    inference(variable_rename,[status(thm)],[f_2186_1]) ).

fof(f_2186_3,plain,
    ! [U_7619,U_7620,U_7621,U_7622] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7619),hAPP(hAPP(c_Power_Opower__class_Opower(U_7619),U_7622),U_7620)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7619),U_7622),U_7621)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7620),U_7621))
      | ~ class_Rings_Ocomm__semiring__1(U_7619) ),
    inference(definitional_conversion,[status(esa)],[f_2186_2]) ).

cnf(f_2186_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7619),hAPP(hAPP(c_Power_Opower__class_Opower(U_7619),U_7622),U_7620)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7619),U_7622),U_7621)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7620),U_7621))
    | ~ class_Rings_Ocomm__semiring__1(U_7619) ),
    inference(clausify,[status(thm)],[f_2186_3]) ).

fof(f_2187_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_2187_2,plain,
    ! [U_7627,U_7626,U_7625,U_7624,U_7623] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7623),hAPP(hAPP(c_Power_Opower__class_Opower(U_7623),U_7624),U_7626)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7623),U_7625),U_7627)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7626),U_7627))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7623),U_7624),U_7625))
      | ~ class_Rings_Ocomm__semiring__1(U_7623) ),
    inference(variable_rename,[status(thm)],[f_2187_1]) ).

fof(f_2187_3,plain,
    ! [U_7623,U_7624,U_7625,U_7626,U_7627] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7623),hAPP(hAPP(c_Power_Opower__class_Opower(U_7623),U_7624),U_7626)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7623),U_7625),U_7627)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7626),U_7627))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7623),U_7624),U_7625))
      | ~ class_Rings_Ocomm__semiring__1(U_7623) ),
    inference(definitional_conversion,[status(esa)],[f_2187_2]) ).

cnf(f_2187_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7623),hAPP(hAPP(c_Power_Opower__class_Opower(U_7623),U_7624),U_7626)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7623),U_7625),U_7627)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7626),U_7627))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7623),U_7624),U_7625))
    | ~ class_Rings_Ocomm__semiring__1(U_7623) ),
    inference(clausify,[status(thm)],[f_2187_3]) ).

fof(f_2188_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_2188_2,plain,
    ! [U_7632,U_7631,U_7630,U_7629,U_7628] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7628),hAPP(hAPP(c_Power_Opower__class_Opower(U_7628),U_7629),U_7632)),U_7631))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7632),U_7630))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7628),hAPP(hAPP(c_Power_Opower__class_Opower(U_7628),U_7629),U_7630)),U_7631))
      | ~ class_Rings_Ocomm__semiring__1(U_7628) ),
    inference(variable_rename,[status(thm)],[f_2188_1]) ).

fof(f_2188_3,plain,
    ! [U_7629,U_7628,U_7630,U_7631,U_7632] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7628),hAPP(hAPP(c_Power_Opower__class_Opower(U_7628),U_7629),U_7632)),U_7631))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7632),U_7630))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7628),hAPP(hAPP(c_Power_Opower__class_Opower(U_7628),U_7629),U_7630)),U_7631))
      | ~ class_Rings_Ocomm__semiring__1(U_7628) ),
    inference(definitional_conversion,[status(esa)],[f_2188_2]) ).

cnf(f_2188_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7628),hAPP(hAPP(c_Power_Opower__class_Opower(U_7628),U_7629),U_7632)),U_7631))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7632),U_7630))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7628),hAPP(hAPP(c_Power_Opower__class_Opower(U_7628),U_7629),U_7630)),U_7631))
    | ~ class_Rings_Ocomm__semiring__1(U_7628) ),
    inference(clausify,[status(thm)],[f_2188_3]) ).

fof(f_2189_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_2189_2,plain,
    ! [U_7636,U_7635,U_7634,U_7633] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7633),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7633),U_7635),U_7634)),U_7636) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7633),hAPP(hAPP(c_Power_Opower__class_Opower(U_7633),U_7635),U_7636)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7633),U_7634),U_7636))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7633),U_7634),U_7635))
      | ~ class_Divides_Osemiring__div(U_7633) ),
    inference(variable_rename,[status(thm)],[f_2189_1]) ).

fof(f_2189_3,plain,
    ! [U_7633,U_7634,U_7635,U_7636] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7633),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7633),U_7635),U_7634)),U_7636) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7633),hAPP(hAPP(c_Power_Opower__class_Opower(U_7633),U_7635),U_7636)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7633),U_7634),U_7636))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7633),U_7634),U_7635))
      | ~ class_Divides_Osemiring__div(U_7633) ),
    inference(definitional_conversion,[status(esa)],[f_2189_2]) ).

cnf(f_2189_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7633),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7633),U_7635),U_7634)),U_7636) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7633),hAPP(hAPP(c_Power_Opower__class_Opower(U_7633),U_7635),U_7636)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7633),U_7634),U_7636))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7633),U_7634),U_7635))
    | ~ class_Divides_Osemiring__div(U_7633) ),
    inference(clausify,[status(thm)],[f_2189_3]) ).

fof(f_2190_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_2190_2,plain,
    ! [U_7644,U_7643,U_7642,U_7641,U_7640,U_7639,U_7638,U_7637] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7637,U_7638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7637),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7637),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_7643)))),hAPP(hAPP(c_COMBC(U_7637,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_7637),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7639)),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_7642))),U_7644)))),c_Com_Ocom_OLocal(U_7642,U_7644,U_7640)),U_7641)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7637),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7637,U_7638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7637),U_7639),U_7640),hAPP(hAPP(c_COMBC(U_7637,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_7637),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7641)),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_7642))),hAPP(hAPP(c_Natural_Ogetlocs,U_7643),U_7642))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7637),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2190_1]) ).

fof(f_2190_3,plain,
    ! [U_7637,U_7638,U_7639,U_7640,U_7641,U_7642,U_7643,U_7644] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7637,U_7638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7637),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7637),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_7643)))),hAPP(hAPP(c_COMBC(U_7637,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_7637),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7639)),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_7642))),U_7644)))),c_Com_Ocom_OLocal(U_7642,U_7644,U_7640)),U_7641)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7637),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7637,U_7638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7637),U_7639),U_7640),hAPP(hAPP(c_COMBC(U_7637,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_7637),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7641)),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_7642))),hAPP(hAPP(c_Natural_Ogetlocs,U_7643),U_7642))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7637),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2190_2]) ).

cnf(f_2190_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7637,U_7638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7637),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7637),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_7643)))),hAPP(hAPP(c_COMBC(U_7637,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_7637),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7639)),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_7642))),U_7644)))),c_Com_Ocom_OLocal(U_7642,U_7644,U_7640)),U_7641)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7637),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7637,U_7638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7637),U_7639),U_7640),hAPP(hAPP(c_COMBC(U_7637,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_7637),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_7641)),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_7642))),hAPP(hAPP(c_Natural_Ogetlocs,U_7643),U_7642))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7637),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2190_3]) ).

fof(f_2191_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_2191_2,plain,
    ! [U_7645] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7645),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_7645 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( U_7645 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7645),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[f_2191_1]) ).

fof(f_2191_3,plain,
    ( ! [U_7647] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7647),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_7647 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_7646] :
        ( U_7646 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7646),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(miniscope,[status(thm)],[f_2191_2]) ).

fof(f_2191_4,plain,
    ( ! [U_7647] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7647),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_7647 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_7646] :
        ( U_7646 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7646),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2191_3]) ).

cnf(f_2191_5,plain,
    ( U_7646 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7646),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(clausify,[status(thm)],[f_2191_4]) ).

cnf(f_2191_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7647),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | U_7647 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_2191_4]) ).

fof(f_2192_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_2192_2,plain,
    ! [U_7649,U_7648] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7649),U_7648))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7648),U_7649))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7648)) ),
    inference(variable_rename,[status(thm)],[f_2192_1]) ).

fof(f_2192_3,plain,
    ! [U_7648,U_7649] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7649),U_7648))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7648),U_7649))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7648)) ),
    inference(definitional_conversion,[status(esa)],[f_2192_2]) ).

cnf(f_2192_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7649),U_7648))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7648),U_7649))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7648)) ),
    inference(clausify,[status(thm)],[f_2192_3]) ).

fof(f_2193_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_2193_2,plain,
    ! [U_7652,U_7651,U_7650] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7650),U_7651)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7650),U_7652)))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7651),U_7652))
          & U_7650 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7651),U_7652))
        | U_7650 = 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_7650),U_7651)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7650),U_7652))) ) ),
    inference(variable_rename,[status(thm)],[f_2193_1]) ).

fof(f_2193_3,plain,
    ( ! [U_7658,U_7656,U_7654] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7654),U_7656)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7654),U_7658)))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7656),U_7658))
          & U_7654 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_7657,U_7655,U_7653] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7655),U_7657))
        | U_7653 = 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_7653),U_7655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7653),U_7657))) ) ),
    inference(miniscope,[status(thm)],[f_2193_2]) ).

fof(f_2193_4,plain,
    ( ! [U_7658,U_7656,U_7654] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7656),U_7658))
        | ~ sP660(U_7658,U_7656,U_7654) )
    & ! [U_7658,U_7656,U_7654] :
        ( U_7654 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP660(U_7658,U_7656,U_7654) )
    & ! [U_7658,U_7656,U_7654] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7654),U_7656)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7654),U_7658)))
        | sP660(U_7658,U_7656,U_7654) )
    & ! [U_7655,U_7653,U_7657] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7655),U_7657))
        | U_7653 = 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_7653),U_7655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7653),U_7657))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP660])],[f_2193_3]) ).

cnf(f_2193_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7655),U_7657))
    | U_7653 = 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_7653),U_7655)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7653),U_7657))) ),
    inference(clausify,[status(thm)],[f_2193_4]) ).

cnf(f_2193_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7654),U_7656)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7654),U_7658)))
    | sP660(U_7658,U_7656,U_7654) ),
    inference(clausify,[status(thm)],[f_2193_4]) ).

cnf(f_2193_7,plain,
    ( U_7654 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP660(U_7658,U_7656,U_7654) ),
    inference(clausify,[status(thm)],[f_2193_4]) ).

cnf(f_2193_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7656),U_7658))
    | ~ sP660(U_7658,U_7656,U_7654) ),
    inference(clausify,[status(thm)],[f_2193_4]) ).

fof(f_2194_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_2194_2,plain,
    ! [U_7661,U_7660,U_7659] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7659),U_7660))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7661),U_7660))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7659),U_7661))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7659),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7660),U_7661))) ),
    inference(variable_rename,[status(thm)],[f_2194_1]) ).

fof(f_2194_3,plain,
    ! [U_7660,U_7659,U_7661] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7659),U_7660))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7661),U_7660))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7659),U_7661))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7659),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7660),U_7661))) ),
    inference(definitional_conversion,[status(esa)],[f_2194_2]) ).

cnf(f_2194_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7659),U_7660))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7661),U_7660))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7659),U_7661))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7659),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7660),U_7661))) ),
    inference(clausify,[status(thm)],[f_2194_3]) ).

fof(f_2195_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_2195_2,plain,
    ! [U_7664,U_7663,U_7662] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7662),U_7664))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7664),U_7663))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7662),U_7663))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7662),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7663),U_7664))) ),
    inference(variable_rename,[status(thm)],[f_2195_1]) ).

fof(f_2195_3,plain,
    ! [U_7662,U_7663,U_7664] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7662),U_7664))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7664),U_7663))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7662),U_7663))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7662),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7663),U_7664))) ),
    inference(definitional_conversion,[status(esa)],[f_2195_2]) ).

cnf(f_2195_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7662),U_7664))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7664),U_7663))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7662),U_7663))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7662),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7663),U_7664))) ),
    inference(clausify,[status(thm)],[f_2195_3]) ).

fof(f_2196_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_2196_2,plain,
    ! [U_7666,U_7665] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7665,tc_HOL_Obool)),U_7666),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7665,tc_HOL_Obool)),U_7666)))
        | U_7666 != c_Orderings_Obot__class_Obot(tc_fun(U_7665,tc_HOL_Obool)) )
      & ( U_7666 = c_Orderings_Obot__class_Obot(tc_fun(U_7665,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7665,tc_HOL_Obool)),U_7666),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7665,tc_HOL_Obool)),U_7666))) ) ),
    inference(variable_rename,[status(thm)],[f_2196_1]) ).

fof(f_2196_3,plain,
    ( ! [U_7670,U_7668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7668,tc_HOL_Obool)),U_7670),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7668,tc_HOL_Obool)),U_7670)))
        | U_7670 != c_Orderings_Obot__class_Obot(tc_fun(U_7668,tc_HOL_Obool)) )
    & ! [U_7669,U_7667] :
        ( U_7669 = c_Orderings_Obot__class_Obot(tc_fun(U_7667,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7667,tc_HOL_Obool)),U_7669),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7667,tc_HOL_Obool)),U_7669))) ) ),
    inference(miniscope,[status(thm)],[f_2196_2]) ).

fof(f_2196_4,plain,
    ( ! [U_7668,U_7670] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7668,tc_HOL_Obool)),U_7670),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7668,tc_HOL_Obool)),U_7670)))
        | U_7670 != c_Orderings_Obot__class_Obot(tc_fun(U_7668,tc_HOL_Obool)) )
    & ! [U_7669,U_7667] :
        ( U_7669 = c_Orderings_Obot__class_Obot(tc_fun(U_7667,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7667,tc_HOL_Obool)),U_7669),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7667,tc_HOL_Obool)),U_7669))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2196_3]) ).

cnf(f_2196_5,plain,
    ( U_7669 = c_Orderings_Obot__class_Obot(tc_fun(U_7667,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7667,tc_HOL_Obool)),U_7669),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7667,tc_HOL_Obool)),U_7669))) ),
    inference(clausify,[status(thm)],[f_2196_4]) ).

cnf(f_2196_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7668,tc_HOL_Obool)),U_7670),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7668,tc_HOL_Obool)),U_7670)))
    | U_7670 != c_Orderings_Obot__class_Obot(tc_fun(U_7668,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2196_4]) ).

fof(f_2197_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_2197_2,plain,
    ! [U_7677,U_7676,U_7675] :
      ( ( ( ? [U_7674] : hBOOL(hAPP(U_7676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7675),U_7677),U_7674)))
          | ! [U_7673] :
              ( ~ hBOOL(hAPP(U_7676,U_7673))
              | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7675),U_7677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7675),U_7673),c_Groups_Ozero__class_Ozero(U_7675)))) ) )
        & ( ? [U_7672] :
              ( hBOOL(hAPP(U_7676,U_7672))
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7675),U_7677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7675),U_7672),c_Groups_Ozero__class_Ozero(U_7675)))) )
          | ! [U_7671] : ~ hBOOL(hAPP(U_7676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7675),U_7677),U_7671))) ) )
      | ~ class_Rings_Osemiring__0(U_7675)
      | ~ class_Rings_Odvd(U_7675) ),
    inference(variable_rename,[status(thm)],[f_2197_1]) ).

fof(f_2197_3,plain,
    ! [U_7677,U_7676,U_7675] :
      ( ( ( ? [U_7674] : hBOOL(hAPP(U_7676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7675),U_7677),U_7674)))
          | ! [U_7673] :
              ( ~ hBOOL(hAPP(U_7676,U_7673))
              | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7675),U_7677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7675),U_7673),c_Groups_Ozero__class_Ozero(U_7675)))) ) )
        & ( ( hBOOL(hAPP(U_7676,sK112(U_7677,U_7676,U_7675)))
            & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7675),U_7677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7675),sK112(U_7677,U_7676,U_7675)),c_Groups_Ozero__class_Ozero(U_7675)))) )
          | ! [U_7671] : ~ hBOOL(hAPP(U_7676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7675),U_7677),U_7671))) ) )
      | ~ class_Rings_Osemiring__0(U_7675)
      | ~ class_Rings_Odvd(U_7675) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_7672,sK112(U_7677,U_7676,U_7675))],[f_2197_2]) ).

fof(f_2197_4,plain,
    ! [U_7677,U_7676,U_7675] :
      ( ( ( hBOOL(hAPP(U_7676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7675),U_7677),sK113(U_7677,U_7676,U_7675))))
          | ! [U_7673] :
              ( ~ hBOOL(hAPP(U_7676,U_7673))
              | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7675),U_7677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7675),U_7673),c_Groups_Ozero__class_Ozero(U_7675)))) ) )
        & ( ( hBOOL(hAPP(U_7676,sK112(U_7677,U_7676,U_7675)))
            & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7675),U_7677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7675),sK112(U_7677,U_7676,U_7675)),c_Groups_Ozero__class_Ozero(U_7675)))) )
          | ! [U_7671] : ~ hBOOL(hAPP(U_7676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7675),U_7677),U_7671))) ) )
      | ~ class_Rings_Osemiring__0(U_7675)
      | ~ class_Rings_Odvd(U_7675) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_7674,sK113(U_7677,U_7676,U_7675))],[f_2197_3]) ).

fof(f_2197_5,plain,
    ( ! [U_7675,U_7676,U_7677] :
        ( hBOOL(hAPP(U_7676,sK112(U_7677,U_7676,U_7675)))
        | ~ sP661(U_7675,U_7676,U_7677) )
    & ! [U_7675,U_7676,U_7677] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7675),U_7677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7675),sK112(U_7677,U_7676,U_7675)),c_Groups_Ozero__class_Ozero(U_7675))))
        | ~ sP661(U_7675,U_7676,U_7677) )
    & ! [U_7671,U_7673,U_7675,U_7676,U_7677] :
        ( hBOOL(hAPP(U_7676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7675),U_7677),sK113(U_7677,U_7676,U_7675))))
        | ~ hBOOL(hAPP(U_7676,U_7673))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7675),U_7677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7675),U_7673),c_Groups_Ozero__class_Ozero(U_7675))))
        | ~ sP662(U_7671,U_7673,U_7675,U_7676,U_7677) )
    & ! [U_7671,U_7673,U_7675,U_7676,U_7677] :
        ( sP661(U_7675,U_7676,U_7677)
        | ~ hBOOL(hAPP(U_7676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7675),U_7677),U_7671)))
        | ~ sP662(U_7671,U_7673,U_7675,U_7676,U_7677) )
    & ! [U_7671,U_7673,U_7675,U_7676,U_7677] :
        ( sP662(U_7671,U_7673,U_7675,U_7676,U_7677)
        | ~ class_Rings_Osemiring__0(U_7675)
        | ~ class_Rings_Odvd(U_7675) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP661,sP662])],[f_2197_4]) ).

cnf(f_2197_6,plain,
    ( sP662(U_7671,U_7673,U_7675,U_7676,U_7677)
    | ~ class_Rings_Osemiring__0(U_7675)
    | ~ class_Rings_Odvd(U_7675) ),
    inference(clausify,[status(thm)],[f_2197_5]) ).

cnf(f_2197_7,plain,
    ( sP661(U_7675,U_7676,U_7677)
    | ~ hBOOL(hAPP(U_7676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7675),U_7677),U_7671)))
    | ~ sP662(U_7671,U_7673,U_7675,U_7676,U_7677) ),
    inference(clausify,[status(thm)],[f_2197_5]) ).

cnf(f_2197_8,plain,
    ( hBOOL(hAPP(U_7676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7675),U_7677),sK113(U_7677,U_7676,U_7675))))
    | ~ hBOOL(hAPP(U_7676,U_7673))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7675),U_7677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7675),U_7673),c_Groups_Ozero__class_Ozero(U_7675))))
    | ~ sP662(U_7671,U_7673,U_7675,U_7676,U_7677) ),
    inference(clausify,[status(thm)],[f_2197_5]) ).

cnf(f_2197_9,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7675),U_7677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7675),sK112(U_7677,U_7676,U_7675)),c_Groups_Ozero__class_Ozero(U_7675))))
    | ~ sP661(U_7675,U_7676,U_7677) ),
    inference(clausify,[status(thm)],[f_2197_5]) ).

cnf(f_2197_10,plain,
    ( hBOOL(hAPP(U_7676,sK112(U_7677,U_7676,U_7675)))
    | ~ sP661(U_7675,U_7676,U_7677) ),
    inference(clausify,[status(thm)],[f_2197_5]) ).

fof(f_2198_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_2198_2,plain,
    ! [U_7683,U_7682,U_7681,U_7680] :
      ( ! [U_7679,U_7678] :
          ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),U_7679),U_7683)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7680),U_7679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7680),U_7678),U_7682))),U_7683))) )
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7680),U_7679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7680),U_7678),U_7682))),U_7683)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),U_7679),U_7683))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),U_7682))
      | ~ class_Rings_Odvd(U_7680)
      | ~ class_Rings_Ocomm__ring(U_7680) ),
    inference(variable_rename,[status(thm)],[f_2198_1]) ).

fof(f_2198_3,plain,
    ! [U_7683,U_7682,U_7681,U_7680] :
      ( ( ! [U_7687] :
            ( ! [U_7685] : ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7680),U_7687),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7680),U_7685),U_7682))),U_7683)))
            | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),U_7687),U_7683))) )
        & ! [U_7686] :
            ( ! [U_7684] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7680),U_7686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7680),U_7684),U_7682))),U_7683)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),U_7686),U_7683))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),U_7682))
      | ~ class_Rings_Odvd(U_7680)
      | ~ class_Rings_Ocomm__ring(U_7680) ),
    inference(miniscope,[status(thm)],[f_2198_2]) ).

fof(f_2198_4,plain,
    ( ! [U_7680,U_7683,U_7686,U_7681,U_7682,U_7684,U_7685,U_7687] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7680),U_7687),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7680),U_7685),U_7682))),U_7683)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),U_7687),U_7683)))
        | ~ sP663(U_7680,U_7683,U_7686,U_7681,U_7682,U_7684,U_7685,U_7687) )
    & ! [U_7680,U_7683,U_7686,U_7681,U_7682,U_7684,U_7685,U_7687] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7680),U_7686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7680),U_7684),U_7682))),U_7683)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),U_7686),U_7683)))
        | ~ sP663(U_7680,U_7683,U_7686,U_7681,U_7682,U_7684,U_7685,U_7687) )
    & ! [U_7680,U_7683,U_7686,U_7681,U_7682,U_7684,U_7685,U_7687] :
        ( sP663(U_7680,U_7683,U_7686,U_7681,U_7682,U_7684,U_7685,U_7687)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),U_7682))
        | ~ class_Rings_Odvd(U_7680)
        | ~ class_Rings_Ocomm__ring(U_7680) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP663])],[f_2198_3]) ).

cnf(f_2198_5,plain,
    ( sP663(U_7680,U_7683,U_7686,U_7681,U_7682,U_7684,U_7685,U_7687)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),U_7682))
    | ~ class_Rings_Odvd(U_7680)
    | ~ class_Rings_Ocomm__ring(U_7680) ),
    inference(clausify,[status(thm)],[f_2198_4]) ).

cnf(f_2198_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7680),U_7686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7680),U_7684),U_7682))),U_7683)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),U_7686),U_7683)))
    | ~ sP663(U_7680,U_7683,U_7686,U_7681,U_7682,U_7684,U_7685,U_7687) ),
    inference(clausify,[status(thm)],[f_2198_4]) ).

cnf(f_2198_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7680),U_7687),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7680),U_7685),U_7682))),U_7683)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7680),U_7681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7680),U_7687),U_7683)))
    | ~ sP663(U_7680,U_7683,U_7686,U_7681,U_7682,U_7684,U_7685,U_7687) ),
    inference(clausify,[status(thm)],[f_2198_4]) ).

fof(f_2199_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_2199_2,plain,
    ! [U_7693,U_7692,U_7691,U_7690] :
      ( ! [U_7689,U_7688] :
          ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),U_7689),U_7693)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7690),U_7689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7690),U_7688),U_7692))),U_7693))) )
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7690),U_7689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7690),U_7688),U_7692))),U_7693)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),U_7689),U_7693))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),U_7692))
      | ~ class_Rings_Odvd(U_7690)
      | ~ class_Rings_Ocomm__ring(U_7690) ),
    inference(variable_rename,[status(thm)],[f_2199_1]) ).

fof(f_2199_3,plain,
    ! [U_7693,U_7692,U_7691,U_7690] :
      ( ( ! [U_7697] :
            ( ! [U_7695] : ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7690),U_7697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7690),U_7695),U_7692))),U_7693)))
            | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),U_7697),U_7693))) )
        & ! [U_7696] :
            ( ! [U_7694] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7690),U_7696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7690),U_7694),U_7692))),U_7693)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),U_7696),U_7693))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),U_7692))
      | ~ class_Rings_Odvd(U_7690)
      | ~ class_Rings_Ocomm__ring(U_7690) ),
    inference(miniscope,[status(thm)],[f_2199_2]) ).

fof(f_2199_4,plain,
    ( ! [U_7691,U_7696,U_7694,U_7692,U_7693,U_7690,U_7695,U_7697] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7690),U_7697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7690),U_7695),U_7692))),U_7693)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),U_7697),U_7693)))
        | ~ sP664(U_7691,U_7696,U_7694,U_7692,U_7693,U_7690,U_7695,U_7697) )
    & ! [U_7691,U_7696,U_7694,U_7692,U_7693,U_7690,U_7695,U_7697] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7690),U_7696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7690),U_7694),U_7692))),U_7693)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),U_7696),U_7693)))
        | ~ sP664(U_7691,U_7696,U_7694,U_7692,U_7693,U_7690,U_7695,U_7697) )
    & ! [U_7691,U_7696,U_7694,U_7692,U_7693,U_7690,U_7695,U_7697] :
        ( sP664(U_7691,U_7696,U_7694,U_7692,U_7693,U_7690,U_7695,U_7697)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),U_7692))
        | ~ class_Rings_Odvd(U_7690)
        | ~ class_Rings_Ocomm__ring(U_7690) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP664])],[f_2199_3]) ).

cnf(f_2199_5,plain,
    ( sP664(U_7691,U_7696,U_7694,U_7692,U_7693,U_7690,U_7695,U_7697)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),U_7692))
    | ~ class_Rings_Odvd(U_7690)
    | ~ class_Rings_Ocomm__ring(U_7690) ),
    inference(clausify,[status(thm)],[f_2199_4]) ).

cnf(f_2199_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7690),U_7696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7690),U_7694),U_7692))),U_7693)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),U_7696),U_7693)))
    | ~ sP664(U_7691,U_7696,U_7694,U_7692,U_7693,U_7690,U_7695,U_7697) ),
    inference(clausify,[status(thm)],[f_2199_4]) ).

cnf(f_2199_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7690),U_7697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7690),U_7695),U_7692))),U_7693)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7690),U_7691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7690),U_7697),U_7693)))
    | ~ sP664(U_7691,U_7696,U_7694,U_7692,U_7693,U_7690,U_7695,U_7697) ),
    inference(clausify,[status(thm)],[f_2199_4]) ).

fof(f_2200_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_2200_2,plain,
    ! [U_7700,U_7699,U_7698] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7698),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7699)),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7700)))
          | c_Divides_Odiv__class_Omod(U_7698,hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7700),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7699)) != c_Groups_Ozero__class_Ozero(U_7698) )
        & ( c_Divides_Odiv__class_Omod(U_7698,hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7700),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7699)) = c_Groups_Ozero__class_Ozero(U_7698)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7698),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7699)),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7700))) ) )
      | ~ class_Int_Onumber(U_7698)
      | ~ class_Divides_Osemiring__div(U_7698) ),
    inference(variable_rename,[status(thm)],[f_2200_1]) ).

fof(f_2200_3,plain,
    ( ! [U_7698,U_7699,U_7700] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7698),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7699)),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7700)))
        | c_Divides_Odiv__class_Omod(U_7698,hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7700),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7699)) != c_Groups_Ozero__class_Ozero(U_7698)
        | ~ sP665(U_7698,U_7699,U_7700) )
    & ! [U_7698,U_7699,U_7700] :
        ( c_Divides_Odiv__class_Omod(U_7698,hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7700),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7699)) = c_Groups_Ozero__class_Ozero(U_7698)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7698),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7699)),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7700)))
        | ~ sP665(U_7698,U_7699,U_7700) )
    & ! [U_7698,U_7699,U_7700] :
        ( sP665(U_7698,U_7699,U_7700)
        | ~ class_Int_Onumber(U_7698)
        | ~ class_Divides_Osemiring__div(U_7698) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP665])],[f_2200_2]) ).

cnf(f_2200_4,plain,
    ( sP665(U_7698,U_7699,U_7700)
    | ~ class_Int_Onumber(U_7698)
    | ~ class_Divides_Osemiring__div(U_7698) ),
    inference(clausify,[status(thm)],[f_2200_3]) ).

cnf(f_2200_5,plain,
    ( c_Divides_Odiv__class_Omod(U_7698,hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7700),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7699)) = c_Groups_Ozero__class_Ozero(U_7698)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7698),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7699)),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7700)))
    | ~ sP665(U_7698,U_7699,U_7700) ),
    inference(clausify,[status(thm)],[f_2200_3]) ).

cnf(f_2200_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7698),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7699)),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7700)))
    | c_Divides_Odiv__class_Omod(U_7698,hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7700),hAPP(c_Int_Onumber__class_Onumber__of(U_7698),U_7699)) != c_Groups_Ozero__class_Ozero(U_7698)
    | ~ sP665(U_7698,U_7699,U_7700) ),
    inference(clausify,[status(thm)],[f_2200_3]) ).

fof(f_2201_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_2201_2,plain,
    ! [U_7705,U_7704,U_7703,U_7702,U_7701] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7701),U_7704),U_7702) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7701),U_7705),U_7703)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7701),U_7704),U_7703) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7701),U_7702),U_7705) )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7701),U_7704),U_7703) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7701),U_7702),U_7705)
          | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7701),U_7704),U_7702) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7701),U_7705),U_7703) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7701),U_7703),U_7705))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7701),U_7702),U_7704))
      | U_7703 = c_Groups_Ozero__class_Ozero(U_7701)
      | U_7702 = c_Groups_Ozero__class_Ozero(U_7701)
      | ~ class_Divides_Osemiring__div(U_7701) ),
    inference(variable_rename,[status(thm)],[f_2201_1]) ).

fof(f_2201_3,plain,
    ( ! [U_7703,U_7701,U_7702,U_7704,U_7705] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7701),U_7704),U_7702) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7701),U_7705),U_7703)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7701),U_7704),U_7703) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7701),U_7702),U_7705)
        | ~ sP666(U_7703,U_7701,U_7702,U_7704,U_7705) )
    & ! [U_7703,U_7701,U_7702,U_7704,U_7705] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7701),U_7704),U_7703) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7701),U_7702),U_7705)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7701),U_7704),U_7702) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7701),U_7705),U_7703)
        | ~ sP666(U_7703,U_7701,U_7702,U_7704,U_7705) )
    & ! [U_7703,U_7701,U_7702,U_7704,U_7705] :
        ( sP666(U_7703,U_7701,U_7702,U_7704,U_7705)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7701),U_7703),U_7705))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7701),U_7702),U_7704))
        | U_7703 = c_Groups_Ozero__class_Ozero(U_7701)
        | U_7702 = c_Groups_Ozero__class_Ozero(U_7701)
        | ~ class_Divides_Osemiring__div(U_7701) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP666])],[f_2201_2]) ).

cnf(f_2201_4,plain,
    ( sP666(U_7703,U_7701,U_7702,U_7704,U_7705)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7701),U_7703),U_7705))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7701),U_7702),U_7704))
    | U_7703 = c_Groups_Ozero__class_Ozero(U_7701)
    | U_7702 = c_Groups_Ozero__class_Ozero(U_7701)
    | ~ class_Divides_Osemiring__div(U_7701) ),
    inference(clausify,[status(thm)],[f_2201_3]) ).

cnf(f_2201_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7701),U_7704),U_7703) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7701),U_7702),U_7705)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7701),U_7704),U_7702) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7701),U_7705),U_7703)
    | ~ sP666(U_7703,U_7701,U_7702,U_7704,U_7705) ),
    inference(clausify,[status(thm)],[f_2201_3]) ).

cnf(f_2201_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7701),U_7704),U_7702) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7701),U_7705),U_7703)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7701),U_7704),U_7703) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7701),U_7702),U_7705)
    | ~ sP666(U_7703,U_7701,U_7702,U_7704,U_7705) ),
    inference(clausify,[status(thm)],[f_2201_3]) ).

fof(f_2202_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_2202_2,plain,
    ! [U_7709,U_7708,U_7707,U_7706] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7706),U_7708),U_7707) = U_7709
          | U_7708 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7706),U_7709),U_7707) )
        & ( U_7708 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7706),U_7709),U_7707)
          | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7706),U_7708),U_7707) != U_7709 ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7706),U_7707),U_7708))
      | U_7707 = c_Groups_Ozero__class_Ozero(U_7706)
      | ~ class_Divides_Osemiring__div(U_7706) ),
    inference(variable_rename,[status(thm)],[f_2202_1]) ).

fof(f_2202_3,plain,
    ( ! [U_7708,U_7709,U_7707,U_7706] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7706),U_7708),U_7707) = U_7709
        | U_7708 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7706),U_7709),U_7707)
        | ~ sP667(U_7708,U_7709,U_7707,U_7706) )
    & ! [U_7708,U_7709,U_7707,U_7706] :
        ( U_7708 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7706),U_7709),U_7707)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7706),U_7708),U_7707) != U_7709
        | ~ sP667(U_7708,U_7709,U_7707,U_7706) )
    & ! [U_7708,U_7709,U_7707,U_7706] :
        ( sP667(U_7708,U_7709,U_7707,U_7706)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7706),U_7707),U_7708))
        | U_7707 = c_Groups_Ozero__class_Ozero(U_7706)
        | ~ class_Divides_Osemiring__div(U_7706) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP667])],[f_2202_2]) ).

cnf(f_2202_4,plain,
    ( sP667(U_7708,U_7709,U_7707,U_7706)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7706),U_7707),U_7708))
    | U_7707 = c_Groups_Ozero__class_Ozero(U_7706)
    | ~ class_Divides_Osemiring__div(U_7706) ),
    inference(clausify,[status(thm)],[f_2202_3]) ).

cnf(f_2202_5,plain,
    ( U_7708 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7706),U_7709),U_7707)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7706),U_7708),U_7707) != U_7709
    | ~ sP667(U_7708,U_7709,U_7707,U_7706) ),
    inference(clausify,[status(thm)],[f_2202_3]) ).

cnf(f_2202_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7706),U_7708),U_7707) = U_7709
    | U_7708 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7706),U_7709),U_7707)
    | ~ sP667(U_7708,U_7709,U_7707,U_7706) ),
    inference(clausify,[status(thm)],[f_2202_3]) ).

fof(f_2203_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_2203_2,plain,
    ! [U_7711,U_7710] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7710),U_7711))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7711))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7710),U_7711)) ),
    inference(variable_rename,[status(thm)],[f_2203_1]) ).

fof(f_2203_3,plain,
    ! [U_7710,U_7711] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7710),U_7711))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7711))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7710),U_7711)) ),
    inference(definitional_conversion,[status(esa)],[f_2203_2]) ).

cnf(f_2203_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7710),U_7711))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7711))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7710),U_7711)) ),
    inference(clausify,[status(thm)],[f_2203_3]) ).

fof(f_2204_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_2204_2,plain,
    ! [U_7714,U_7713,U_7712] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7713)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7714)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7713),U_7714)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7713),U_7714))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7713)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7714))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7712)) ),
    inference(variable_rename,[status(thm)],[f_2204_1]) ).

fof(f_2204_3,plain,
    ( ! [U_7713,U_7712,U_7714] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7713)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7714)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7713),U_7714))
        | ~ sP668(U_7713,U_7712,U_7714) )
    & ! [U_7713,U_7712,U_7714] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7713),U_7714))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7713)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7714)))
        | ~ sP668(U_7713,U_7712,U_7714) )
    & ! [U_7713,U_7712,U_7714] :
        ( sP668(U_7713,U_7712,U_7714)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7712)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP668])],[f_2204_2]) ).

cnf(f_2204_4,plain,
    ( sP668(U_7713,U_7712,U_7714)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7712)) ),
    inference(clausify,[status(thm)],[f_2204_3]) ).

cnf(f_2204_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7713),U_7714))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7713)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7714)))
    | ~ sP668(U_7713,U_7712,U_7714) ),
    inference(clausify,[status(thm)],[f_2204_3]) ).

cnf(f_2204_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7713)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7712),U_7714)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7713),U_7714))
    | ~ sP668(U_7713,U_7712,U_7714) ),
    inference(clausify,[status(thm)],[f_2204_3]) ).

fof(f_2205_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_2205_2,plain,
    ! [U_7717,U_7716,U_7715] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7716),U_7717))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7715))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7715),U_7716)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7715),U_7717))) ),
    inference(variable_rename,[status(thm)],[f_2205_1]) ).

fof(f_2205_3,plain,
    ! [U_7717,U_7716,U_7715] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7716),U_7717))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7715))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7715),U_7716)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7715),U_7717))) ),
    inference(definitional_conversion,[status(esa)],[f_2205_2]) ).

cnf(f_2205_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7716),U_7717))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7715))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7715),U_7716)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7715),U_7717))) ),
    inference(clausify,[status(thm)],[f_2205_3]) ).

fof(f_2206_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_2206_2,plain,
    ! [U_7720,U_7719,U_7718] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_7718,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_7718,U_7719)),c_Predicate_OPowp(U_7718,U_7720)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7718,tc_HOL_Obool)),U_7719),U_7720)) ),
    inference(variable_rename,[status(thm)],[f_2206_1]) ).

fof(f_2206_3,plain,
    ! [U_7718,U_7719,U_7720] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_7718,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_7718,U_7719)),c_Predicate_OPowp(U_7718,U_7720)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7718,tc_HOL_Obool)),U_7719),U_7720)) ),
    inference(definitional_conversion,[status(esa)],[f_2206_2]) ).

cnf(f_2206_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_7718,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_7718,U_7719)),c_Predicate_OPowp(U_7718,U_7720)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7718,tc_HOL_Obool)),U_7719),U_7720)) ),
    inference(clausify,[status(thm)],[f_2206_3]) ).

fof(f_2207_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_2207_2,plain,
    ! [U_7723,U_7722,U_7721] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7721),U_7723),hAPP(hAPP(c_Power_Opower__class_Opower(U_7721),U_7723),U_7722)))
      | ( U_7723 != c_Groups_Oone__class_Oone(U_7721)
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7722)) )
      | ~ class_Rings_Ocomm__semiring__1(U_7721) ),
    inference(variable_rename,[status(thm)],[f_2207_1]) ).

fof(f_2207_3,plain,
    ( ! [U_7721,U_7722,U_7723] :
        ( U_7723 != c_Groups_Oone__class_Oone(U_7721)
        | ~ sP669(U_7721,U_7722,U_7723) )
    & ! [U_7721,U_7722,U_7723] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7722))
        | ~ sP669(U_7721,U_7722,U_7723) )
    & ! [U_7721,U_7722,U_7723] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7721),U_7723),hAPP(hAPP(c_Power_Opower__class_Opower(U_7721),U_7723),U_7722)))
        | sP669(U_7721,U_7722,U_7723)
        | ~ class_Rings_Ocomm__semiring__1(U_7721) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP669])],[f_2207_2]) ).

cnf(f_2207_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7721),U_7723),hAPP(hAPP(c_Power_Opower__class_Opower(U_7721),U_7723),U_7722)))
    | sP669(U_7721,U_7722,U_7723)
    | ~ class_Rings_Ocomm__semiring__1(U_7721) ),
    inference(clausify,[status(thm)],[f_2207_3]) ).

cnf(f_2207_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7722))
    | ~ sP669(U_7721,U_7722,U_7723) ),
    inference(clausify,[status(thm)],[f_2207_3]) ).

cnf(f_2207_6,plain,
    ( U_7723 != c_Groups_Oone__class_Oone(U_7721)
    | ~ sP669(U_7721,U_7722,U_7723) ),
    inference(clausify,[status(thm)],[f_2207_3]) ).

fof(f_2208_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_2208_2,plain,
    ! [U_7725,U_7724] : c_Set_Othe__elem(U_7724,U_7725) = c_HOL_OThe(U_7724,hAPP(hAPP(c_COMBB(tc_fun(U_7724,tc_HOL_Obool),tc_HOL_Obool,U_7724),hAPP(c_fequal,U_7725)),hAPP(hAPP(c_COMBC(U_7724,tc_fun(U_7724,tc_HOL_Obool),tc_fun(U_7724,tc_HOL_Obool)),c_Set_Oinsert(U_7724)),c_Orderings_Obot__class_Obot(tc_fun(U_7724,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2208_1]) ).

fof(f_2208_3,plain,
    ! [U_7724,U_7725] : c_Set_Othe__elem(U_7724,U_7725) = c_HOL_OThe(U_7724,hAPP(hAPP(c_COMBB(tc_fun(U_7724,tc_HOL_Obool),tc_HOL_Obool,U_7724),hAPP(c_fequal,U_7725)),hAPP(hAPP(c_COMBC(U_7724,tc_fun(U_7724,tc_HOL_Obool),tc_fun(U_7724,tc_HOL_Obool)),c_Set_Oinsert(U_7724)),c_Orderings_Obot__class_Obot(tc_fun(U_7724,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2208_2]) ).

cnf(f_2208_4,plain,
    c_Set_Othe__elem(U_7724,U_7725) = c_HOL_OThe(U_7724,hAPP(hAPP(c_COMBB(tc_fun(U_7724,tc_HOL_Obool),tc_HOL_Obool,U_7724),hAPP(c_fequal,U_7725)),hAPP(hAPP(c_COMBC(U_7724,tc_fun(U_7724,tc_HOL_Obool),tc_fun(U_7724,tc_HOL_Obool)),c_Set_Oinsert(U_7724)),c_Orderings_Obot__class_Obot(tc_fun(U_7724,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2208_3]) ).

fof(f_2209_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_2209_2,plain,
    ! [U_7727,U_7726] : c_Set_Othe__elem(U_7726,hAPP(hAPP(c_Set_Oinsert(U_7726),U_7727),c_Orderings_Obot__class_Obot(tc_fun(U_7726,tc_HOL_Obool)))) = U_7727,
    inference(variable_rename,[status(thm)],[f_2209_1]) ).

fof(f_2209_3,plain,
    ! [U_7726,U_7727] : c_Set_Othe__elem(U_7726,hAPP(hAPP(c_Set_Oinsert(U_7726),U_7727),c_Orderings_Obot__class_Obot(tc_fun(U_7726,tc_HOL_Obool)))) = U_7727,
    inference(definitional_conversion,[status(esa)],[f_2209_2]) ).

cnf(f_2209_4,plain,
    c_Set_Othe__elem(U_7726,hAPP(hAPP(c_Set_Oinsert(U_7726),U_7727),c_Orderings_Obot__class_Obot(tc_fun(U_7726,tc_HOL_Obool)))) = U_7727,
    inference(clausify,[status(thm)],[f_2209_3]) ).

fof(f_2210_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_2210_2,plain,
    ! [U_7729,U_7728] : c_Option_Oset(U_7728,hAPP(c_Option_Ooption_OSome(U_7728),U_7729)) = hAPP(hAPP(c_Set_Oinsert(U_7728),U_7729),c_Orderings_Obot__class_Obot(tc_fun(U_7728,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2210_1]) ).

fof(f_2210_3,plain,
    ! [U_7728,U_7729] : c_Option_Oset(U_7728,hAPP(c_Option_Ooption_OSome(U_7728),U_7729)) = hAPP(hAPP(c_Set_Oinsert(U_7728),U_7729),c_Orderings_Obot__class_Obot(tc_fun(U_7728,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2210_2]) ).

cnf(f_2210_4,plain,
    c_Option_Oset(U_7728,hAPP(c_Option_Ooption_OSome(U_7728),U_7729)) = hAPP(hAPP(c_Set_Oinsert(U_7728),U_7729),c_Orderings_Obot__class_Obot(tc_fun(U_7728,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2210_3]) ).

fof(f_2211_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_2211_2,plain,
    ! [U_7733,U_7732,U_7731,U_7730] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7730),hAPP(U_7731,U_7732)),hAPP(U_7731,U_7733)))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7733),U_7732))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7732),U_7733))
      | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7730,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_7731)
      | ~ class_Orderings_Oorder(U_7730) ),
    inference(variable_rename,[status(thm)],[f_2211_1]) ).

fof(f_2211_3,plain,
    ! [U_7731,U_7732,U_7730,U_7733] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7730),hAPP(U_7731,U_7732)),hAPP(U_7731,U_7733)))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7733),U_7732))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7732),U_7733))
      | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7730,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_7731)
      | ~ class_Orderings_Oorder(U_7730) ),
    inference(definitional_conversion,[status(esa)],[f_2211_2]) ).

cnf(f_2211_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7730),hAPP(U_7731,U_7732)),hAPP(U_7731,U_7733)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7733),U_7732))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7732),U_7733))
    | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7730,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_7731)
    | ~ class_Orderings_Oorder(U_7730) ),
    inference(clausify,[status(thm)],[f_2211_3]) ).

fof(f_2212_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_2212_2,plain,
    ! [U_7737,U_7736,U_7735,U_7734] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7734),hAPP(U_7735,U_7736)),hAPP(U_7735,U_7737)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7736),U_7737))
      | ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7734,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7735)
      | ~ class_Orderings_Oorder(U_7734) ),
    inference(variable_rename,[status(thm)],[f_2212_1]) ).

fof(f_2212_3,plain,
    ! [U_7735,U_7734,U_7736,U_7737] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7734),hAPP(U_7735,U_7736)),hAPP(U_7735,U_7737)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7736),U_7737))
      | ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7734,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7735)
      | ~ class_Orderings_Oorder(U_7734) ),
    inference(definitional_conversion,[status(esa)],[f_2212_2]) ).

cnf(f_2212_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7734),hAPP(U_7735,U_7736)),hAPP(U_7735,U_7737)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7736),U_7737))
    | ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7734,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7735)
    | ~ class_Orderings_Oorder(U_7734) ),
    inference(clausify,[status(thm)],[f_2212_3]) ).

fof(f_2213_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_2213_2,plain,
    ! [U_7740,U_7739,U_7738] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7738),U_7739))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7738),U_7740))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7738),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7739,U_7740))) ),
    inference(variable_rename,[status(thm)],[f_2213_1]) ).

fof(f_2213_3,plain,
    ! [U_7738,U_7739,U_7740] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7738),U_7739))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7738),U_7740))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7738),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7739,U_7740))) ),
    inference(definitional_conversion,[status(esa)],[f_2213_2]) ).

cnf(f_2213_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7738),U_7739))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7738),U_7740))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7738),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7739,U_7740))) ),
    inference(clausify,[status(thm)],[f_2213_3]) ).

fof(f_2214_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_2214_2,plain,
    ! [U_7743,U_7742,U_7741] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7741),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7742,U_7743)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7741),U_7743))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7741),U_7742)) ),
    inference(variable_rename,[status(thm)],[f_2214_1]) ).

fof(f_2214_3,plain,
    ! [U_7741,U_7742,U_7743] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7741),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7742,U_7743)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7741),U_7743))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7741),U_7742)) ),
    inference(definitional_conversion,[status(esa)],[f_2214_2]) ).

cnf(f_2214_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7741),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7742,U_7743)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7741),U_7743))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7741),U_7742)) ),
    inference(clausify,[status(thm)],[f_2214_3]) ).

fof(f_2215_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_2215_2,plain,
    ! [U_7745,U_7744] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7744),U_7745))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7744),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7745))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7744),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7745)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7744),U_7745)) ) ),
    inference(variable_rename,[status(thm)],[f_2215_1]) ).

fof(f_2215_3,plain,
    ( ! [U_7749,U_7747] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7747),U_7749))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7747),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7749))) )
    & ! [U_7748,U_7746] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7746),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7748)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7746),U_7748)) ) ),
    inference(miniscope,[status(thm)],[f_2215_2]) ).

fof(f_2215_4,plain,
    ( ! [U_7747,U_7749] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7747),U_7749))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7747),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7749))) )
    & ! [U_7748,U_7746] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7746),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7748)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7746),U_7748)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2215_3]) ).

cnf(f_2215_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7746),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7748)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7746),U_7748)) ),
    inference(clausify,[status(thm)],[f_2215_4]) ).

cnf(f_2215_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7747),U_7749))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7747),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7749))) ),
    inference(clausify,[status(thm)],[f_2215_4]) ).

fof(f_2216_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_2216_2,plain,
    ! [U_7751,U_7750] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7750),U_7751))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7750)),U_7751)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7750)),U_7751))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7750),U_7751)) ) ),
    inference(variable_rename,[status(thm)],[f_2216_1]) ).

fof(f_2216_3,plain,
    ( ! [U_7755,U_7753] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7753),U_7755))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7753)),U_7755)) )
    & ! [U_7754,U_7752] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7752)),U_7754))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7752),U_7754)) ) ),
    inference(miniscope,[status(thm)],[f_2216_2]) ).

fof(f_2216_4,plain,
    ( ! [U_7753,U_7755] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7753),U_7755))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7753)),U_7755)) )
    & ! [U_7754,U_7752] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7752)),U_7754))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7752),U_7754)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2216_3]) ).

cnf(f_2216_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7752)),U_7754))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7752),U_7754)) ),
    inference(clausify,[status(thm)],[f_2216_4]) ).

cnf(f_2216_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7753),U_7755))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7753)),U_7755)) ),
    inference(clausify,[status(thm)],[f_2216_4]) ).

fof(f_2217_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_2217_2,plain,
    ! [U_7758,U_7757,U_7756] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7756),U_7757))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7756),U_7758))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7756),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7757),U_7758))) ),
    inference(variable_rename,[status(thm)],[f_2217_1]) ).

fof(f_2217_3,plain,
    ! [U_7756,U_7757,U_7758] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7756),U_7757))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7756),U_7758))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7756),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7757),U_7758))) ),
    inference(definitional_conversion,[status(esa)],[f_2217_2]) ).

cnf(f_2217_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7756),U_7757))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7756),U_7758))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7756),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7757),U_7758))) ),
    inference(clausify,[status(thm)],[f_2217_3]) ).

fof(f_2218_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_2218_2,plain,
    ! [U_7760,U_7759] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7759) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7760)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7760),U_7759))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7759),U_7760)) ),
    inference(variable_rename,[status(thm)],[f_2218_1]) ).

fof(f_2218_3,plain,
    ! [U_7759,U_7760] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7759) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7760)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7760),U_7759))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7759),U_7760)) ),
    inference(definitional_conversion,[status(esa)],[f_2218_2]) ).

cnf(f_2218_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7759) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7760)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7760),U_7759))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7759),U_7760)) ),
    inference(clausify,[status(thm)],[f_2218_3]) ).

fof(f_2219_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_2219_2,plain,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_2219_1]) ).

cnf(f_2219_3,plain,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2219_2]) ).

fof(f_2220_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_2220_2,plain,
    ! [U_7762,U_7761] :
      ( U_7761 = U_7762
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7762),U_7761))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7761),U_7762))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7762))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7761)) ),
    inference(variable_rename,[status(thm)],[f_2220_1]) ).

fof(f_2220_3,plain,
    ! [U_7761,U_7762] :
      ( U_7761 = U_7762
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7762),U_7761))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7761),U_7762))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7762))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7761)) ),
    inference(definitional_conversion,[status(esa)],[f_2220_2]) ).

cnf(f_2220_4,plain,
    ( U_7761 = U_7762
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7762),U_7761))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7761),U_7762))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7762))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7761)) ),
    inference(clausify,[status(thm)],[f_2220_3]) ).

fof(f_2221_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_2221_2,plain,
    ! [U_7764,U_7763] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7764),U_7763))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7763),U_7764))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7763)) ),
    inference(variable_rename,[status(thm)],[f_2221_1]) ).

fof(f_2221_3,plain,
    ! [U_7764,U_7763] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7764),U_7763))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7763),U_7764))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7763)) ),
    inference(definitional_conversion,[status(esa)],[f_2221_2]) ).

cnf(f_2221_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7764),U_7763))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7763),U_7764))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7763)) ),
    inference(clausify,[status(thm)],[f_2221_3]) ).

fof(f_2222_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_2222_2,plain,
    ! [U_7767,U_7766,U_7765] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7766),U_7767))
      | U_7765 = 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_7765),U_7766)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7765),U_7767))) ),
    inference(variable_rename,[status(thm)],[f_2222_1]) ).

fof(f_2222_3,plain,
    ! [U_7765,U_7766,U_7767] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7766),U_7767))
      | U_7765 = 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_7765),U_7766)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7765),U_7767))) ),
    inference(definitional_conversion,[status(esa)],[f_2222_2]) ).

cnf(f_2222_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7766),U_7767))
    | U_7765 = 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_7765),U_7766)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7765),U_7767))) ),
    inference(clausify,[status(thm)],[f_2222_3]) ).

fof(f_2223_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_2223_2,plain,
    ! [U_7770,U_7769,U_7768] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7769),U_7770))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7768),U_7769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7768),U_7770))) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7768),U_7769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7768),U_7770)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7769),U_7770)) ) )
      | U_7768 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2223_1]) ).

fof(f_2223_3,plain,
    ( ! [U_7769,U_7770,U_7768] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7769),U_7770))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7768),U_7769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7768),U_7770)))
        | ~ sP670(U_7769,U_7770,U_7768) )
    & ! [U_7769,U_7770,U_7768] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7768),U_7769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7768),U_7770)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7769),U_7770))
        | ~ sP670(U_7769,U_7770,U_7768) )
    & ! [U_7769,U_7770,U_7768] :
        ( sP670(U_7769,U_7770,U_7768)
        | U_7768 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP670])],[f_2223_2]) ).

cnf(f_2223_4,plain,
    ( sP670(U_7769,U_7770,U_7768)
    | U_7768 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2223_3]) ).

cnf(f_2223_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7768),U_7769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7768),U_7770)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7769),U_7770))
    | ~ sP670(U_7769,U_7770,U_7768) ),
    inference(clausify,[status(thm)],[f_2223_3]) ).

cnf(f_2223_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7769),U_7770))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7768),U_7769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7768),U_7770)))
    | ~ sP670(U_7769,U_7770,U_7768) ),
    inference(clausify,[status(thm)],[f_2223_3]) ).

fof(f_2224_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_2224_2,plain,
    ! [U_7775,U_7774,U_7773,U_7772,U_7771] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7773),U_7774)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7773),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7775),U_7772))),U_7774))) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7773),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7775),U_7772))),U_7774)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7773),U_7774))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7771),U_7772)) ),
    inference(variable_rename,[status(thm)],[f_2224_1]) ).

fof(f_2224_3,plain,
    ( ! [U_7772,U_7774,U_7771,U_7773,U_7775] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7773),U_7774)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7773),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7775),U_7772))),U_7774)))
        | ~ sP671(U_7772,U_7774,U_7771,U_7773,U_7775) )
    & ! [U_7772,U_7774,U_7771,U_7773,U_7775] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7773),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7775),U_7772))),U_7774)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7773),U_7774)))
        | ~ sP671(U_7772,U_7774,U_7771,U_7773,U_7775) )
    & ! [U_7772,U_7774,U_7771,U_7773,U_7775] :
        ( sP671(U_7772,U_7774,U_7771,U_7773,U_7775)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7771),U_7772)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP671])],[f_2224_2]) ).

cnf(f_2224_4,plain,
    ( sP671(U_7772,U_7774,U_7771,U_7773,U_7775)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7771),U_7772)) ),
    inference(clausify,[status(thm)],[f_2224_3]) ).

cnf(f_2224_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7773),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7775),U_7772))),U_7774)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7773),U_7774)))
    | ~ sP671(U_7772,U_7774,U_7771,U_7773,U_7775) ),
    inference(clausify,[status(thm)],[f_2224_3]) ).

cnf(f_2224_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7773),U_7774)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7771),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7773),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7775),U_7772))),U_7774)))
    | ~ sP671(U_7772,U_7774,U_7771,U_7773,U_7775) ),
    inference(clausify,[status(thm)],[f_2224_3]) ).

fof(f_2225_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_2225_2,plain,
    ! [U_7778,U_7777,U_7776] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7777),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7776),U_7778))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7776),U_7777)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7776),U_7777))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7777),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7776),U_7778)))) ) ),
    inference(variable_rename,[status(thm)],[f_2225_1]) ).

fof(f_2225_3,plain,
    ( ! [U_7784,U_7782,U_7780] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7780),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7782),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7780),U_7784))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7780),U_7782)) )
    & ! [U_7783,U_7781,U_7779] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7779),U_7781))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7779),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7779),U_7783)))) ) ),
    inference(miniscope,[status(thm)],[f_2225_2]) ).

fof(f_2225_4,plain,
    ( ! [U_7780,U_7782,U_7784] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7780),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7782),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7780),U_7784))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7780),U_7782)) )
    & ! [U_7779,U_7783,U_7781] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7779),U_7781))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7779),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7779),U_7783)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2225_3]) ).

cnf(f_2225_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7779),U_7781))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7779),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7779),U_7783)))) ),
    inference(clausify,[status(thm)],[f_2225_4]) ).

cnf(f_2225_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7780),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7782),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7780),U_7784))))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7780),U_7782)) ),
    inference(clausify,[status(thm)],[f_2225_4]) ).

fof(f_2226_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_2226_2,plain,
    ! [U_7786,U_7785] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7785),U_7786))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7785)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7786))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7785)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7786)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7785),U_7786)) ) ),
    inference(variable_rename,[status(thm)],[f_2226_1]) ).

fof(f_2226_3,plain,
    ( ! [U_7790,U_7788] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7788),U_7790))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7788)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7790))) )
    & ! [U_7789,U_7787] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7787)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7789)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7787),U_7789)) ) ),
    inference(miniscope,[status(thm)],[f_2226_2]) ).

fof(f_2226_4,plain,
    ( ! [U_7788,U_7790] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7788),U_7790))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7788)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7790))) )
    & ! [U_7789,U_7787] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7787)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7789)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7787),U_7789)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2226_3]) ).

cnf(f_2226_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_7787)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7789)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7787),U_7789)) ),
    inference(clausify,[status(thm)],[f_2226_4]) ).

cnf(f_2226_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7788),U_7790))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7788)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7790))) ),
    inference(clausify,[status(thm)],[f_2226_4]) ).

fof(f_2227_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_2227_2,plain,
    ! [U_7792,U_7791] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7791)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7792)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7791),U_7792)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7791),U_7792))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7791)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7792))) ) ),
    inference(variable_rename,[status(thm)],[f_2227_1]) ).

fof(f_2227_3,plain,
    ( ! [U_7796,U_7794] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7794)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7796)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7794),U_7796)) )
    & ! [U_7795,U_7793] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7793),U_7795))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7793)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7795))) ) ),
    inference(miniscope,[status(thm)],[f_2227_2]) ).

fof(f_2227_4,plain,
    ( ! [U_7794,U_7796] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7794)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7796)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7794),U_7796)) )
    & ! [U_7795,U_7793] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7793),U_7795))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7793)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7795))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2227_3]) ).

cnf(f_2227_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7793),U_7795))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7793)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7795))) ),
    inference(clausify,[status(thm)],[f_2227_4]) ).

cnf(f_2227_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_7794)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7796)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7794),U_7796)) ),
    inference(clausify,[status(thm)],[f_2227_4]) ).

fof(f_2228_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_2228_2,plain,
    ! [U_7798,U_7797] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7797),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7798),U_7797)) = U_7798
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7797),U_7798)) ),
    inference(variable_rename,[status(thm)],[f_2228_1]) ).

fof(f_2228_3,plain,
    ! [U_7798,U_7797] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7797),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7798),U_7797)) = U_7798
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7797),U_7798)) ),
    inference(definitional_conversion,[status(esa)],[f_2228_2]) ).

cnf(f_2228_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7797),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7798),U_7797)) = U_7798
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7797),U_7798)) ),
    inference(clausify,[status(thm)],[f_2228_3]) ).

fof(f_2229_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_2229_2,plain,
    ! [U_7801,U_7800,U_7799] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7799,U_7800) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7801,U_7800)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7800),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7799),U_7801))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7800),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7799),U_7801)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7799,U_7800) != c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7801,U_7800) ) ),
    inference(variable_rename,[status(thm)],[f_2229_1]) ).

fof(f_2229_3,plain,
    ( ! [U_7807,U_7805,U_7803] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7803,U_7805) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7807,U_7805)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7805),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7803),U_7807))) )
    & ! [U_7806,U_7804,U_7802] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7804),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7802),U_7806)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7802,U_7804) != c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7806,U_7804) ) ),
    inference(miniscope,[status(thm)],[f_2229_2]) ).

fof(f_2229_4,plain,
    ( ! [U_7803,U_7805,U_7807] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7803,U_7805) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7807,U_7805)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7805),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7803),U_7807))) )
    & ! [U_7802,U_7804,U_7806] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7804),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7802),U_7806)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7802,U_7804) != c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7806,U_7804) ) ),
    inference(definitional_conversion,[status(esa)],[f_2229_3]) ).

cnf(f_2229_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7804),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7802),U_7806)))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7802,U_7804) != c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7806,U_7804) ),
    inference(clausify,[status(thm)],[f_2229_4]) ).

cnf(f_2229_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7803,U_7805) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7807,U_7805)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7805),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7803),U_7807))) ),
    inference(clausify,[status(thm)],[f_2229_4]) ).

fof(f_2230_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_2230_2,plain,
    ! [U_7808] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7808),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7808) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7808) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7808),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_2230_1]) ).

fof(f_2230_3,plain,
    ( ! [U_7810] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7810),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7810) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
    & ! [U_7809] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7809) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7809),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_2230_2]) ).

fof(f_2230_4,plain,
    ( ! [U_7810] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7810),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7810) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
    & ! [U_7809] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7809) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7809),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2230_3]) ).

cnf(f_2230_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7809) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7809),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2230_4]) ).

cnf(f_2230_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7810),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7810) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2230_4]) ).

fof(f_2231_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_2231_2,plain,
    ! [U_7812,U_7811] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7812),U_7811)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7812)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7811))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7811),U_7812)) ),
    inference(variable_rename,[status(thm)],[f_2231_1]) ).

fof(f_2231_3,plain,
    ! [U_7811,U_7812] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7812),U_7811)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7812)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7811))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7811),U_7812)) ),
    inference(definitional_conversion,[status(esa)],[f_2231_2]) ).

cnf(f_2231_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7812),U_7811)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7812)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7811))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7811),U_7812)) ),
    inference(clausify,[status(thm)],[f_2231_3]) ).

fof(f_2232_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_2232_2,plain,
    ! [U_7814,U_7813] :
      ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7813,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7814)
      | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7813,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_7814)
      | ~ class_Orderings_Oorder(U_7813) ),
    inference(variable_rename,[status(thm)],[f_2232_1]) ).

fof(f_2232_3,plain,
    ! [U_7814,U_7813] :
      ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7813,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7814)
      | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7813,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_7814)
      | ~ class_Orderings_Oorder(U_7813) ),
    inference(definitional_conversion,[status(esa)],[f_2232_2]) ).

cnf(f_2232_4,plain,
    ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7813,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7814)
    | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7813,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_7814)
    | ~ class_Orderings_Oorder(U_7813) ),
    inference(clausify,[status(thm)],[f_2232_3]) ).

fof(f_2233_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_2233_2,plain,
    ! [U_7816,U_7815] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7815),U_7816))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7816))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7815),U_7816)) ),
    inference(variable_rename,[status(thm)],[f_2233_1]) ).

fof(f_2233_3,plain,
    ! [U_7815,U_7816] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7815),U_7816))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7816))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7815),U_7816)) ),
    inference(definitional_conversion,[status(esa)],[f_2233_2]) ).

cnf(f_2233_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7815),U_7816))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7816))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7815),U_7816)) ),
    inference(clausify,[status(thm)],[f_2233_3]) ).

fof(f_2234_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_2234_2,plain,
    ! [U_7818,U_7817] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7817)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7818)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7818),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7817)) != 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_7818),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7817)) = 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_7817)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7818))) ) ),
    inference(variable_rename,[status(thm)],[f_2234_1]) ).

fof(f_2234_3,plain,
    ( ! [U_7822,U_7820] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7820)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7822)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7822),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7820)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_7821,U_7819] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7821),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7819)) = 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_7819)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7821))) ) ),
    inference(miniscope,[status(thm)],[f_2234_2]) ).

fof(f_2234_4,plain,
    ( ! [U_7820,U_7822] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7820)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7822)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7822),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7820)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_7821,U_7819] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7821),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7819)) = 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_7819)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7821))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2234_3]) ).

cnf(f_2234_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7821),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7819)) = 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_7819)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7821))) ),
    inference(clausify,[status(thm)],[f_2234_4]) ).

cnf(f_2234_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7820)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7822)))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7822),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7820)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2234_4]) ).

fof(f_2235_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_2235_2,plain,
    ! [U_7824,U_7823] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7824)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7823)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7824),U_7823))
      | U_7823 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2235_1]) ).

fof(f_2235_3,plain,
    ! [U_7823,U_7824] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7824)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7823)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7824),U_7823))
      | U_7823 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_2235_2]) ).

cnf(f_2235_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7824)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7823)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7824),U_7823))
    | U_7823 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2235_3]) ).

fof(f_2236_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_2236_2,plain,
    ! [U_7826,U_7825] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7825)),hAPP(c_Int_Onat,U_7826)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7825),U_7826)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7825),U_7826))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7825)),hAPP(c_Int_Onat,U_7826))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7826))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7825)) ),
    inference(variable_rename,[status(thm)],[f_2236_1]) ).

fof(f_2236_3,plain,
    ( ! [U_7825,U_7826] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7825)),hAPP(c_Int_Onat,U_7826)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7825),U_7826))
        | ~ sP672(U_7825,U_7826) )
    & ! [U_7825,U_7826] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7825),U_7826))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7825)),hAPP(c_Int_Onat,U_7826)))
        | ~ sP672(U_7825,U_7826) )
    & ! [U_7825,U_7826] :
        ( sP672(U_7825,U_7826)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7826))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7825)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP672])],[f_2236_2]) ).

cnf(f_2236_4,plain,
    ( sP672(U_7825,U_7826)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7826))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7825)) ),
    inference(clausify,[status(thm)],[f_2236_3]) ).

cnf(f_2236_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7825),U_7826))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7825)),hAPP(c_Int_Onat,U_7826)))
    | ~ sP672(U_7825,U_7826) ),
    inference(clausify,[status(thm)],[f_2236_3]) ).

cnf(f_2236_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7825)),hAPP(c_Int_Onat,U_7826)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7825),U_7826))
    | ~ sP672(U_7825,U_7826) ),
    inference(clausify,[status(thm)],[f_2236_3]) ).

fof(f_2237_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_2237_2,plain,
    ! [U_7828,U_7827] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7827),U_7828)),U_7827))
          | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7828) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7828) = 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_7827),U_7828)),U_7827)) ) )
      | U_7827 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2237_1]) ).

fof(f_2237_3,plain,
    ( ! [U_7827,U_7828] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7827),U_7828)),U_7827))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7828) != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP673(U_7827,U_7828) )
    & ! [U_7827,U_7828] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7828) = 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_7827),U_7828)),U_7827))
        | ~ sP673(U_7827,U_7828) )
    & ! [U_7827,U_7828] :
        ( sP673(U_7827,U_7828)
        | U_7827 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP673])],[f_2237_2]) ).

cnf(f_2237_4,plain,
    ( sP673(U_7827,U_7828)
    | U_7827 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2237_3]) ).

cnf(f_2237_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7828) = 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_7827),U_7828)),U_7827))
    | ~ sP673(U_7827,U_7828) ),
    inference(clausify,[status(thm)],[f_2237_3]) ).

cnf(f_2237_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7827),U_7828)),U_7827))
    | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7828) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP673(U_7827,U_7828) ),
    inference(clausify,[status(thm)],[f_2237_3]) ).

fof(f_2238_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_2238_2,plain,
    ! [U_7830,U_7829] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7829),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7830)))
        | ~ 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_7829))),U_7830)) )
      & ( 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_7829))),U_7830))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7829),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7830))) ) ),
    inference(variable_rename,[status(thm)],[f_2238_1]) ).

fof(f_2238_3,plain,
    ( ! [U_7834,U_7832] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7832),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7834)))
        | ~ 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_7832))),U_7834)) )
    & ! [U_7833,U_7831] :
        ( 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_7831))),U_7833))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7831),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7833))) ) ),
    inference(miniscope,[status(thm)],[f_2238_2]) ).

fof(f_2238_4,plain,
    ( ! [U_7832,U_7834] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7832),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7834)))
        | ~ 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_7832))),U_7834)) )
    & ! [U_7831,U_7833] :
        ( 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_7831))),U_7833))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7831),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7833))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2238_3]) ).

cnf(f_2238_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_7831))),U_7833))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7831),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7833))) ),
    inference(clausify,[status(thm)],[f_2238_4]) ).

cnf(f_2238_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7832),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7834)))
    | ~ 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_7832))),U_7834)) ),
    inference(clausify,[status(thm)],[f_2238_4]) ).

fof(f_2239_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_2239_2,plain,
    ! [U_7836,U_7835] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7835)),U_7836))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7835),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7836)))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7835),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7836))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7835)),U_7836)) ) ),
    inference(variable_rename,[status(thm)],[f_2239_1]) ).

fof(f_2239_3,plain,
    ( ! [U_7840,U_7838] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7838)),U_7840))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7838),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7840)))) )
    & ! [U_7839,U_7837] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7837),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7839))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7837)),U_7839)) ) ),
    inference(miniscope,[status(thm)],[f_2239_2]) ).

fof(f_2239_4,plain,
    ( ! [U_7838,U_7840] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7838)),U_7840))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7838),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7840)))) )
    & ! [U_7837,U_7839] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7837),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7839))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7837)),U_7839)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2239_3]) ).

cnf(f_2239_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7837),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7839))))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7837)),U_7839)) ),
    inference(clausify,[status(thm)],[f_2239_4]) ).

cnf(f_2239_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_7838)),U_7840))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7838),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7840)))) ),
    inference(clausify,[status(thm)],[f_2239_4]) ).

fof(f_2240_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_2240_2,plain,
    ! [U_7841] : c_Option_Oset(U_7841,c_Option_Ooption_ONone(U_7841)) = c_Orderings_Obot__class_Obot(tc_fun(U_7841,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2240_1]) ).

fof(f_2240_3,plain,
    ! [U_7841] : c_Option_Oset(U_7841,c_Option_Ooption_ONone(U_7841)) = c_Orderings_Obot__class_Obot(tc_fun(U_7841,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2240_2]) ).

cnf(f_2240_4,plain,
    c_Option_Oset(U_7841,c_Option_Ooption_ONone(U_7841)) = c_Orderings_Obot__class_Obot(tc_fun(U_7841,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2240_3]) ).

fof(f_2241_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_2241_2,plain,
    ! [U_7843,U_7842] :
      ( ( c_Option_Oset(U_7842,U_7843) = c_Orderings_Obot__class_Obot(tc_fun(U_7842,tc_HOL_Obool))
        | U_7843 != c_Option_Ooption_ONone(U_7842) )
      & ( U_7843 = c_Option_Ooption_ONone(U_7842)
        | c_Option_Oset(U_7842,U_7843) != c_Orderings_Obot__class_Obot(tc_fun(U_7842,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2241_1]) ).

fof(f_2241_3,plain,
    ( ! [U_7847,U_7845] :
        ( c_Option_Oset(U_7845,U_7847) = c_Orderings_Obot__class_Obot(tc_fun(U_7845,tc_HOL_Obool))
        | U_7847 != c_Option_Ooption_ONone(U_7845) )
    & ! [U_7846,U_7844] :
        ( U_7846 = c_Option_Ooption_ONone(U_7844)
        | c_Option_Oset(U_7844,U_7846) != c_Orderings_Obot__class_Obot(tc_fun(U_7844,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2241_2]) ).

fof(f_2241_4,plain,
    ( ! [U_7847,U_7845] :
        ( c_Option_Oset(U_7845,U_7847) = c_Orderings_Obot__class_Obot(tc_fun(U_7845,tc_HOL_Obool))
        | U_7847 != c_Option_Ooption_ONone(U_7845) )
    & ! [U_7846,U_7844] :
        ( U_7846 = c_Option_Ooption_ONone(U_7844)
        | c_Option_Oset(U_7844,U_7846) != c_Orderings_Obot__class_Obot(tc_fun(U_7844,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2241_3]) ).

cnf(f_2241_5,plain,
    ( U_7846 = c_Option_Ooption_ONone(U_7844)
    | c_Option_Oset(U_7844,U_7846) != c_Orderings_Obot__class_Obot(tc_fun(U_7844,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2241_4]) ).

cnf(f_2241_6,plain,
    ( c_Option_Oset(U_7845,U_7847) = c_Orderings_Obot__class_Obot(tc_fun(U_7845,tc_HOL_Obool))
    | U_7847 != c_Option_Ooption_ONone(U_7845) ),
    inference(clausify,[status(thm)],[f_2241_4]) ).

fof(f_2242_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_2242_2,plain,
    ! [U_7849,U_7848] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7848)),U_7849))
        | ( U_7849 != 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_7848)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7848),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7849)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7848)) ) )
      & ( ( ( U_7849 = 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_7848)) )
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7848),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7849)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7848)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7848)),U_7849)) ) ),
    inference(variable_rename,[status(thm)],[f_2242_1]) ).

fof(f_2242_3,plain,
    ( ! [U_7853,U_7851] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7851)),U_7853))
        | ( U_7853 != 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_7851)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7851),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7853)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7851)) ) )
    & ! [U_7852,U_7850] :
        ( ( ( U_7852 = 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_7850)) )
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7850),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7852)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7850)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7850)),U_7852)) ) ),
    inference(miniscope,[status(thm)],[f_2242_2]) ).

fof(f_2242_4,plain,
    ( ! [U_7851,U_7853] :
        ( U_7853 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP676(U_7851,U_7853) )
    & ! [U_7851,U_7853] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7851))
        | ~ sP676(U_7851,U_7853) )
    & ! [U_7851,U_7853] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7851),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7853)))
        | ~ sP675(U_7851,U_7853) )
    & ! [U_7851,U_7853] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7851))
        | ~ sP675(U_7851,U_7853) )
    & ! [U_7852,U_7850] :
        ( U_7852 = 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_7850))
        | ~ sP674(U_7852,U_7850) )
    & ! [U_7852,U_7850] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7850),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7852)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7850))
        | ~ sP674(U_7852,U_7850) )
    & ! [U_7851,U_7853] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7851)),U_7853))
        | sP676(U_7851,U_7853)
        | sP675(U_7851,U_7853) )
    & ! [U_7852,U_7850] :
        ( sP674(U_7852,U_7850)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7850)),U_7852)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP674,sP675,sP676])],[f_2242_3]) ).

cnf(f_2242_5,plain,
    ( sP674(U_7852,U_7850)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7850)),U_7852)) ),
    inference(clausify,[status(thm)],[f_2242_4]) ).

cnf(f_2242_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7851)),U_7853))
    | sP676(U_7851,U_7853)
    | sP675(U_7851,U_7853) ),
    inference(clausify,[status(thm)],[f_2242_4]) ).

cnf(f_2242_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7850),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7852)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7850))
    | ~ sP674(U_7852,U_7850) ),
    inference(clausify,[status(thm)],[f_2242_4]) ).

cnf(f_2242_8,plain,
    ( U_7852 = 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_7850))
    | ~ sP674(U_7852,U_7850) ),
    inference(clausify,[status(thm)],[f_2242_4]) ).

cnf(f_2242_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7851))
    | ~ sP675(U_7851,U_7853) ),
    inference(clausify,[status(thm)],[f_2242_4]) ).

cnf(f_2242_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7851),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7853)))
    | ~ sP675(U_7851,U_7853) ),
    inference(clausify,[status(thm)],[f_2242_4]) ).

cnf(f_2242_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7851))
    | ~ sP676(U_7851,U_7853) ),
    inference(clausify,[status(thm)],[f_2242_4]) ).

cnf(f_2242_12,plain,
    ( U_7853 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP676(U_7851,U_7853) ),
    inference(clausify,[status(thm)],[f_2242_4]) ).

fof(f_2243_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_2243_2,plain,
    ! [U_7860,U_7859,U_7858,U_7857,U_7856] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7857,U_7858,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7857)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7857),U_7856),U_7859),U_7860)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7857),tc_HOL_Obool))))
      | ? [U_7855,U_7854] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7857,U_7858,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7857)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7857),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7857),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),U_7854))),U_7859),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7857),hAPP(U_7860,U_7855)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7857),tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(U_7856,U_7855),U_7854)) ) ),
    inference(variable_rename,[status(thm)],[f_2243_1]) ).

fof(f_2243_3,plain,
    ! [U_7860,U_7859,U_7858,U_7857,U_7856] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7857,U_7858,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7857)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7857),U_7856),U_7859),U_7860)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7857),tc_HOL_Obool))))
      | ? [U_7854] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7857,U_7858,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7857)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7857),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7857),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),U_7854))),U_7859),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7857),hAPP(U_7860,sK114(U_7860,U_7859,U_7858,U_7857,U_7856))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7857),tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(U_7856,sK114(U_7860,U_7859,U_7858,U_7857,U_7856)),U_7854)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_7855,sK114(U_7860,U_7859,U_7858,U_7857,U_7856))],[f_2243_2]) ).

fof(f_2243_4,plain,
    ! [U_7860,U_7859,U_7858,U_7857,U_7856] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7857,U_7858,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7857)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7857),U_7856),U_7859),U_7860)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7857),tc_HOL_Obool))))
      | ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7857,U_7858,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7857)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7857),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7857),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK115(U_7860,U_7859,U_7858,U_7857,U_7856)))),U_7859),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7857),hAPP(U_7860,sK114(U_7860,U_7859,U_7858,U_7857,U_7856))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7857),tc_HOL_Obool))))
        & hBOOL(hAPP(hAPP(U_7856,sK114(U_7860,U_7859,U_7858,U_7857,U_7856)),sK115(U_7860,U_7859,U_7858,U_7857,U_7856))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_7854,sK115(U_7860,U_7859,U_7858,U_7857,U_7856))],[f_2243_3]) ).

fof(f_2243_5,plain,
    ( ! [U_7860,U_7859,U_7858,U_7856,U_7857] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7857,U_7858,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7857)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7857),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7857),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK115(U_7860,U_7859,U_7858,U_7857,U_7856)))),U_7859),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7857),hAPP(U_7860,sK114(U_7860,U_7859,U_7858,U_7857,U_7856))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7857),tc_HOL_Obool))))
        | ~ sP677(U_7860,U_7859,U_7858,U_7856,U_7857) )
    & ! [U_7860,U_7859,U_7858,U_7856,U_7857] :
        ( hBOOL(hAPP(hAPP(U_7856,sK114(U_7860,U_7859,U_7858,U_7857,U_7856)),sK115(U_7860,U_7859,U_7858,U_7857,U_7856)))
        | ~ sP677(U_7860,U_7859,U_7858,U_7856,U_7857) )
    & ! [U_7860,U_7859,U_7858,U_7856,U_7857] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_7857,U_7858,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7857)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7857),U_7856),U_7859),U_7860)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7857),tc_HOL_Obool))))
        | sP677(U_7860,U_7859,U_7858,U_7856,U_7857) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP677])],[f_2243_4]) ).

cnf(f_2243_6,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7857,U_7858,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7857)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7857),U_7856),U_7859),U_7860)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7857),tc_HOL_Obool))))
    | sP677(U_7860,U_7859,U_7858,U_7856,U_7857) ),
    inference(clausify,[status(thm)],[f_2243_5]) ).

cnf(f_2243_7,plain,
    ( hBOOL(hAPP(hAPP(U_7856,sK114(U_7860,U_7859,U_7858,U_7857,U_7856)),sK115(U_7860,U_7859,U_7858,U_7857,U_7856)))
    | ~ sP677(U_7860,U_7859,U_7858,U_7856,U_7857) ),
    inference(clausify,[status(thm)],[f_2243_5]) ).

cnf(f_2243_8,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7857,U_7858,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7857)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7857),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7857),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK115(U_7860,U_7859,U_7858,U_7857,U_7856)))),U_7859),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_7857),hAPP(U_7860,sK114(U_7860,U_7859,U_7858,U_7857,U_7856))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7857),tc_HOL_Obool))))
    | ~ sP677(U_7860,U_7859,U_7858,U_7856,U_7857) ),
    inference(clausify,[status(thm)],[f_2243_5]) ).

fof(f_2244_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_2244_2,plain,
    ! [U_7868,U_7867,U_7866,U_7865,U_7864,U_7863] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7863,U_7864,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7863)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7863),U_7865),U_7866),U_7868)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7863),tc_HOL_Obool))))
      | ? [U_7862,U_7861] :
          ( ~ hBOOL(hAPP(hAPP(U_7868,U_7862),U_7861))
          & hBOOL(hAPP(hAPP(U_7867,U_7862),U_7861)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7863,U_7864,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7863)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7863),U_7865),U_7866),U_7867)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7863),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2244_1]) ).

fof(f_2244_3,plain,
    ! [U_7868,U_7867,U_7866,U_7865,U_7864,U_7863] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7863,U_7864,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7863)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7863),U_7865),U_7866),U_7868)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7863),tc_HOL_Obool))))
      | ? [U_7861] :
          ( ~ hBOOL(hAPP(hAPP(U_7868,sK116(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863)),U_7861))
          & hBOOL(hAPP(hAPP(U_7867,sK116(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863)),U_7861)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7863,U_7864,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7863)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7863),U_7865),U_7866),U_7867)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7863),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_7862,sK116(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863))],[f_2244_2]) ).

fof(f_2244_4,plain,
    ! [U_7868,U_7867,U_7866,U_7865,U_7864,U_7863] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7863,U_7864,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7863)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7863),U_7865),U_7866),U_7868)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7863),tc_HOL_Obool))))
      | ( ~ hBOOL(hAPP(hAPP(U_7868,sK116(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863)),sK117(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863)))
        & hBOOL(hAPP(hAPP(U_7867,sK116(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863)),sK117(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863))) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7863,U_7864,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7863)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7863),U_7865),U_7866),U_7867)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7863),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_7861,sK117(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863))],[f_2244_3]) ).

fof(f_2244_5,plain,
    ( ! [U_7863,U_7864,U_7865,U_7866,U_7867,U_7868] :
        ( ~ hBOOL(hAPP(hAPP(U_7868,sK116(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863)),sK117(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863)))
        | ~ sP678(U_7863,U_7864,U_7865,U_7866,U_7867,U_7868) )
    & ! [U_7863,U_7864,U_7865,U_7866,U_7867,U_7868] :
        ( hBOOL(hAPP(hAPP(U_7867,sK116(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863)),sK117(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863)))
        | ~ sP678(U_7863,U_7864,U_7865,U_7866,U_7867,U_7868) )
    & ! [U_7863,U_7864,U_7865,U_7866,U_7867,U_7868] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_7863,U_7864,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7863)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7863),U_7865),U_7866),U_7868)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7863),tc_HOL_Obool))))
        | sP678(U_7863,U_7864,U_7865,U_7866,U_7867,U_7868)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7863,U_7864,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7863)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7863),U_7865),U_7866),U_7867)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7863),tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP678])],[f_2244_4]) ).

cnf(f_2244_6,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7863,U_7864,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7863)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7863),U_7865),U_7866),U_7868)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7863),tc_HOL_Obool))))
    | sP678(U_7863,U_7864,U_7865,U_7866,U_7867,U_7868)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7863,U_7864,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7863)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7863),U_7865),U_7866),U_7867)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7863),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2244_5]) ).

cnf(f_2244_7,plain,
    ( hBOOL(hAPP(hAPP(U_7867,sK116(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863)),sK117(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863)))
    | ~ sP678(U_7863,U_7864,U_7865,U_7866,U_7867,U_7868) ),
    inference(clausify,[status(thm)],[f_2244_5]) ).

cnf(f_2244_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_7868,sK116(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863)),sK117(U_7868,U_7867,U_7866,U_7865,U_7864,U_7863)))
    | ~ sP678(U_7863,U_7864,U_7865,U_7866,U_7867,U_7868) ),
    inference(clausify,[status(thm)],[f_2244_5]) ).

fof(f_2245_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_2245_2,plain,
    ! [U_7876,U_7875,U_7874,U_7873,U_7872,U_7871] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7871,U_7872,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7871)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7871),U_7876),U_7874),U_7875)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7871),tc_HOL_Obool))))
      | ? [U_7870,U_7869] :
          ( ~ hBOOL(hAPP(hAPP(U_7873,U_7870),U_7869))
          & hBOOL(hAPP(hAPP(U_7876,U_7870),U_7869)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7871,U_7872,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7871)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7871),U_7873),U_7874),U_7875)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7871),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2245_1]) ).

fof(f_2245_3,plain,
    ! [U_7876,U_7875,U_7874,U_7873,U_7872,U_7871] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7871,U_7872,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7871)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7871),U_7876),U_7874),U_7875)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7871),tc_HOL_Obool))))
      | ? [U_7869] :
          ( ~ hBOOL(hAPP(hAPP(U_7873,sK118(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871)),U_7869))
          & hBOOL(hAPP(hAPP(U_7876,sK118(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871)),U_7869)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7871,U_7872,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7871)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7871),U_7873),U_7874),U_7875)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7871),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_7870,sK118(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871))],[f_2245_2]) ).

fof(f_2245_4,plain,
    ! [U_7876,U_7875,U_7874,U_7873,U_7872,U_7871] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_7871,U_7872,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7871)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7871),U_7876),U_7874),U_7875)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7871),tc_HOL_Obool))))
      | ( ~ hBOOL(hAPP(hAPP(U_7873,sK118(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871)),sK119(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871)))
        & hBOOL(hAPP(hAPP(U_7876,sK118(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871)),sK119(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871))) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7871,U_7872,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7871)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7871),U_7873),U_7874),U_7875)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7871),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_7869,sK119(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871))],[f_2245_3]) ).

fof(f_2245_5,plain,
    ( ! [U_7871,U_7874,U_7875,U_7876,U_7872,U_7873] :
        ( ~ hBOOL(hAPP(hAPP(U_7873,sK118(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871)),sK119(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871)))
        | ~ sP679(U_7871,U_7874,U_7875,U_7876,U_7872,U_7873) )
    & ! [U_7871,U_7874,U_7875,U_7876,U_7872,U_7873] :
        ( hBOOL(hAPP(hAPP(U_7876,sK118(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871)),sK119(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871)))
        | ~ sP679(U_7871,U_7874,U_7875,U_7876,U_7872,U_7873) )
    & ! [U_7871,U_7874,U_7875,U_7876,U_7872,U_7873] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_7871,U_7872,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7871)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7871),U_7876),U_7874),U_7875)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7871),tc_HOL_Obool))))
        | sP679(U_7871,U_7874,U_7875,U_7876,U_7872,U_7873)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7871,U_7872,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7871)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7871),U_7873),U_7874),U_7875)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7871),tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP679])],[f_2245_4]) ).

cnf(f_2245_6,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_7871,U_7872,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7871)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7871),U_7876),U_7874),U_7875)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7871),tc_HOL_Obool))))
    | sP679(U_7871,U_7874,U_7875,U_7876,U_7872,U_7873)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_7871,U_7872,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_7871)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_7871),U_7873),U_7874),U_7875)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_7871),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2245_5]) ).

cnf(f_2245_7,plain,
    ( hBOOL(hAPP(hAPP(U_7876,sK118(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871)),sK119(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871)))
    | ~ sP679(U_7871,U_7874,U_7875,U_7876,U_7872,U_7873) ),
    inference(clausify,[status(thm)],[f_2245_5]) ).

cnf(f_2245_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_7873,sK118(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871)),sK119(U_7876,U_7875,U_7874,U_7873,U_7872,U_7871)))
    | ~ sP679(U_7871,U_7874,U_7875,U_7876,U_7872,U_7873) ),
    inference(clausify,[status(thm)],[f_2245_5]) ).

fof(f_2246_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_2246_2,plain,
    ! [U_7880,U_7879,U_7878,U_7877] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7877,tc_HOL_Obool)),U_7878),hAPP(hAPP(c_Set_Oinsert(U_7877),U_7879),U_7880)))
        | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7877,tc_HOL_Obool)),U_7878),U_7880))
              & ~ hBOOL(hAPP(hAPP(c_member(U_7877),U_7879),U_7878)) )
            | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7877,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7877,tc_HOL_Obool)),U_7878),hAPP(hAPP(c_Set_Oinsert(U_7877),U_7879),c_Orderings_Obot__class_Obot(tc_fun(U_7877,tc_HOL_Obool))))),U_7880))
              & hBOOL(hAPP(hAPP(c_member(U_7877),U_7879),U_7878)) ) )
          & ~ hBOOL(hAPP(hAPP(c_member(U_7877),U_7879),U_7880)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7877,tc_HOL_Obool)),U_7878),U_7880))
          & hBOOL(hAPP(hAPP(c_member(U_7877),U_7879),U_7880)) ) )
      & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7877,tc_HOL_Obool)),U_7878),U_7880))
                | hBOOL(hAPP(hAPP(c_member(U_7877),U_7879),U_7878)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7877,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7877,tc_HOL_Obool)),U_7878),hAPP(hAPP(c_Set_Oinsert(U_7877),U_7879),c_Orderings_Obot__class_Obot(tc_fun(U_7877,tc_HOL_Obool))))),U_7880))
                | ~ hBOOL(hAPP(hAPP(c_member(U_7877),U_7879),U_7878)) ) )
            | hBOOL(hAPP(hAPP(c_member(U_7877),U_7879),U_7880)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7877,tc_HOL_Obool)),U_7878),U_7880))
            | ~ hBOOL(hAPP(hAPP(c_member(U_7877),U_7879),U_7880)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7877,tc_HOL_Obool)),U_7878),hAPP(hAPP(c_Set_Oinsert(U_7877),U_7879),U_7880))) ) ),
    inference(variable_rename,[status(thm)],[f_2246_1]) ).

fof(f_2246_3,plain,
    ( ! [U_7888,U_7886,U_7884,U_7882] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7882,tc_HOL_Obool)),U_7884),hAPP(hAPP(c_Set_Oinsert(U_7882),U_7886),U_7888)))
        | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7882,tc_HOL_Obool)),U_7884),U_7888))
              & ~ hBOOL(hAPP(hAPP(c_member(U_7882),U_7886),U_7884)) )
            | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7882,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7882,tc_HOL_Obool)),U_7884),hAPP(hAPP(c_Set_Oinsert(U_7882),U_7886),c_Orderings_Obot__class_Obot(tc_fun(U_7882,tc_HOL_Obool))))),U_7888))
              & hBOOL(hAPP(hAPP(c_member(U_7882),U_7886),U_7884)) ) )
          & ~ hBOOL(hAPP(hAPP(c_member(U_7882),U_7886),U_7888)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7882,tc_HOL_Obool)),U_7884),U_7888))
          & hBOOL(hAPP(hAPP(c_member(U_7882),U_7886),U_7888)) ) )
    & ! [U_7887,U_7885,U_7883,U_7881] :
        ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7881,tc_HOL_Obool)),U_7883),U_7887))
                | hBOOL(hAPP(hAPP(c_member(U_7881),U_7885),U_7883)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7881,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7881,tc_HOL_Obool)),U_7883),hAPP(hAPP(c_Set_Oinsert(U_7881),U_7885),c_Orderings_Obot__class_Obot(tc_fun(U_7881,tc_HOL_Obool))))),U_7887))
                | ~ hBOOL(hAPP(hAPP(c_member(U_7881),U_7885),U_7883)) ) )
            | hBOOL(hAPP(hAPP(c_member(U_7881),U_7885),U_7887)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7881,tc_HOL_Obool)),U_7883),U_7887))
            | ~ hBOOL(hAPP(hAPP(c_member(U_7881),U_7885),U_7887)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7881,tc_HOL_Obool)),U_7883),hAPP(hAPP(c_Set_Oinsert(U_7881),U_7885),U_7887))) ) ),
    inference(miniscope,[status(thm)],[f_2246_2]) ).

fof(f_2246_4,plain,
    ( ! [U_7884,U_7882,U_7888,U_7886] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7882,tc_HOL_Obool)),U_7884),U_7888))
        | ~ sP684(U_7884,U_7882,U_7888,U_7886) )
    & ! [U_7884,U_7882,U_7888,U_7886] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7882),U_7886),U_7884))
        | ~ sP684(U_7884,U_7882,U_7888,U_7886) )
    & ! [U_7884,U_7882,U_7888,U_7886] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7882,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7882,tc_HOL_Obool)),U_7884),hAPP(hAPP(c_Set_Oinsert(U_7882),U_7886),c_Orderings_Obot__class_Obot(tc_fun(U_7882,tc_HOL_Obool))))),U_7888))
        | ~ sP683(U_7884,U_7882,U_7888,U_7886) )
    & ! [U_7884,U_7882,U_7888,U_7886] :
        ( hBOOL(hAPP(hAPP(c_member(U_7882),U_7886),U_7884))
        | ~ sP683(U_7884,U_7882,U_7888,U_7886) )
    & ! [U_7884,U_7882,U_7888,U_7886] :
        ( sP684(U_7884,U_7882,U_7888,U_7886)
        | sP683(U_7884,U_7882,U_7888,U_7886)
        | ~ sP685(U_7884,U_7882,U_7888,U_7886) )
    & ! [U_7884,U_7882,U_7888,U_7886] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7882),U_7886),U_7888))
        | ~ sP685(U_7884,U_7882,U_7888,U_7886) )
    & ! [U_7884,U_7882,U_7888,U_7886] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7882,tc_HOL_Obool)),U_7884),U_7888))
        | ~ sP682(U_7884,U_7882,U_7888,U_7886) )
    & ! [U_7884,U_7882,U_7888,U_7886] :
        ( hBOOL(hAPP(hAPP(c_member(U_7882),U_7886),U_7888))
        | ~ sP682(U_7884,U_7882,U_7888,U_7886) )
    & ! [U_7881,U_7883,U_7885,U_7887] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7881,tc_HOL_Obool)),U_7883),U_7887))
        | hBOOL(hAPP(hAPP(c_member(U_7881),U_7885),U_7883))
        | ~ sP680(U_7881,U_7883,U_7885,U_7887) )
    & ! [U_7881,U_7883,U_7885,U_7887] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7881,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7881,tc_HOL_Obool)),U_7883),hAPP(hAPP(c_Set_Oinsert(U_7881),U_7885),c_Orderings_Obot__class_Obot(tc_fun(U_7881,tc_HOL_Obool))))),U_7887))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7881),U_7885),U_7883))
        | ~ sP680(U_7881,U_7883,U_7885,U_7887) )
    & ! [U_7881,U_7883,U_7885,U_7887] :
        ( sP680(U_7881,U_7883,U_7885,U_7887)
        | hBOOL(hAPP(hAPP(c_member(U_7881),U_7885),U_7887))
        | ~ sP681(U_7881,U_7883,U_7885,U_7887) )
    & ! [U_7881,U_7883,U_7885,U_7887] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7881,tc_HOL_Obool)),U_7883),U_7887))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7881),U_7885),U_7887))
        | ~ sP681(U_7881,U_7883,U_7885,U_7887) )
    & ! [U_7884,U_7882,U_7888,U_7886] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7882,tc_HOL_Obool)),U_7884),hAPP(hAPP(c_Set_Oinsert(U_7882),U_7886),U_7888)))
        | sP685(U_7884,U_7882,U_7888,U_7886)
        | sP682(U_7884,U_7882,U_7888,U_7886) )
    & ! [U_7881,U_7883,U_7885,U_7887] :
        ( sP681(U_7881,U_7883,U_7885,U_7887)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7881,tc_HOL_Obool)),U_7883),hAPP(hAPP(c_Set_Oinsert(U_7881),U_7885),U_7887))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP680,sP681,sP682,sP683,sP684,sP685])],[f_2246_3]) ).

cnf(f_2246_5,plain,
    ( sP681(U_7881,U_7883,U_7885,U_7887)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7881,tc_HOL_Obool)),U_7883),hAPP(hAPP(c_Set_Oinsert(U_7881),U_7885),U_7887))) ),
    inference(clausify,[status(thm)],[f_2246_4]) ).

cnf(f_2246_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7882,tc_HOL_Obool)),U_7884),hAPP(hAPP(c_Set_Oinsert(U_7882),U_7886),U_7888)))
    | sP685(U_7884,U_7882,U_7888,U_7886)
    | sP682(U_7884,U_7882,U_7888,U_7886) ),
    inference(clausify,[status(thm)],[f_2246_4]) ).

cnf(f_2246_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7881,tc_HOL_Obool)),U_7883),U_7887))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7881),U_7885),U_7887))
    | ~ sP681(U_7881,U_7883,U_7885,U_7887) ),
    inference(clausify,[status(thm)],[f_2246_4]) ).

cnf(f_2246_8,plain,
    ( sP680(U_7881,U_7883,U_7885,U_7887)
    | hBOOL(hAPP(hAPP(c_member(U_7881),U_7885),U_7887))
    | ~ sP681(U_7881,U_7883,U_7885,U_7887) ),
    inference(clausify,[status(thm)],[f_2246_4]) ).

cnf(f_2246_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7881,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7881,tc_HOL_Obool)),U_7883),hAPP(hAPP(c_Set_Oinsert(U_7881),U_7885),c_Orderings_Obot__class_Obot(tc_fun(U_7881,tc_HOL_Obool))))),U_7887))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7881),U_7885),U_7883))
    | ~ sP680(U_7881,U_7883,U_7885,U_7887) ),
    inference(clausify,[status(thm)],[f_2246_4]) ).

cnf(f_2246_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7881,tc_HOL_Obool)),U_7883),U_7887))
    | hBOOL(hAPP(hAPP(c_member(U_7881),U_7885),U_7883))
    | ~ sP680(U_7881,U_7883,U_7885,U_7887) ),
    inference(clausify,[status(thm)],[f_2246_4]) ).

cnf(f_2246_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7882),U_7886),U_7888))
    | ~ sP682(U_7884,U_7882,U_7888,U_7886) ),
    inference(clausify,[status(thm)],[f_2246_4]) ).

cnf(f_2246_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7882,tc_HOL_Obool)),U_7884),U_7888))
    | ~ sP682(U_7884,U_7882,U_7888,U_7886) ),
    inference(clausify,[status(thm)],[f_2246_4]) ).

cnf(f_2246_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7882),U_7886),U_7888))
    | ~ sP685(U_7884,U_7882,U_7888,U_7886) ),
    inference(clausify,[status(thm)],[f_2246_4]) ).

cnf(f_2246_14,plain,
    ( sP684(U_7884,U_7882,U_7888,U_7886)
    | sP683(U_7884,U_7882,U_7888,U_7886)
    | ~ sP685(U_7884,U_7882,U_7888,U_7886) ),
    inference(clausify,[status(thm)],[f_2246_4]) ).

cnf(f_2246_15,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7882),U_7886),U_7884))
    | ~ sP683(U_7884,U_7882,U_7888,U_7886) ),
    inference(clausify,[status(thm)],[f_2246_4]) ).

cnf(f_2246_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7882,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7882,tc_HOL_Obool)),U_7884),hAPP(hAPP(c_Set_Oinsert(U_7882),U_7886),c_Orderings_Obot__class_Obot(tc_fun(U_7882,tc_HOL_Obool))))),U_7888))
    | ~ sP683(U_7884,U_7882,U_7888,U_7886) ),
    inference(clausify,[status(thm)],[f_2246_4]) ).

cnf(f_2246_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7882),U_7886),U_7884))
    | ~ sP684(U_7884,U_7882,U_7888,U_7886) ),
    inference(clausify,[status(thm)],[f_2246_4]) ).

cnf(f_2246_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7882,tc_HOL_Obool)),U_7884),U_7888))
    | ~ sP684(U_7884,U_7882,U_7888,U_7886) ),
    inference(clausify,[status(thm)],[f_2246_4]) ).

fof(f_2247_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_2247_2,plain,
    ! [U_7892,U_7891,U_7890,U_7889] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_7891),U_7892),U_7890))
        & ~ hBOOL(hAPP(hAPP(c_member(U_7891),U_7892),U_7889)) )
      | ( hBOOL(hAPP(hAPP(c_member(U_7891),U_7892),U_7890))
        & hBOOL(hAPP(hAPP(c_member(U_7891),U_7892),U_7889)) )
      | U_7889 != U_7890 ),
    inference(variable_rename,[status(thm)],[f_2247_1]) ).

fof(f_2247_3,plain,
    ( ! [U_7889,U_7892,U_7891,U_7890] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7891),U_7892),U_7890))
        | ~ sP687(U_7889,U_7892,U_7891,U_7890) )
    & ! [U_7889,U_7892,U_7891,U_7890] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7891),U_7892),U_7889))
        | ~ sP687(U_7889,U_7892,U_7891,U_7890) )
    & ! [U_7889,U_7892,U_7891,U_7890] :
        ( hBOOL(hAPP(hAPP(c_member(U_7891),U_7892),U_7890))
        | ~ sP686(U_7889,U_7892,U_7891,U_7890) )
    & ! [U_7889,U_7892,U_7891,U_7890] :
        ( hBOOL(hAPP(hAPP(c_member(U_7891),U_7892),U_7889))
        | ~ sP686(U_7889,U_7892,U_7891,U_7890) )
    & ! [U_7889,U_7892,U_7891,U_7890] :
        ( sP687(U_7889,U_7892,U_7891,U_7890)
        | sP686(U_7889,U_7892,U_7891,U_7890)
        | U_7889 != U_7890 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP686,sP687])],[f_2247_2]) ).

cnf(f_2247_4,plain,
    ( sP687(U_7889,U_7892,U_7891,U_7890)
    | sP686(U_7889,U_7892,U_7891,U_7890)
    | U_7889 != U_7890 ),
    inference(clausify,[status(thm)],[f_2247_3]) ).

cnf(f_2247_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7891),U_7892),U_7889))
    | ~ sP686(U_7889,U_7892,U_7891,U_7890) ),
    inference(clausify,[status(thm)],[f_2247_3]) ).

cnf(f_2247_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7891),U_7892),U_7890))
    | ~ sP686(U_7889,U_7892,U_7891,U_7890) ),
    inference(clausify,[status(thm)],[f_2247_3]) ).

cnf(f_2247_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7891),U_7892),U_7889))
    | ~ sP687(U_7889,U_7892,U_7891,U_7890) ),
    inference(clausify,[status(thm)],[f_2247_3]) ).

cnf(f_2247_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7891),U_7892),U_7890))
    | ~ sP687(U_7889,U_7892,U_7891,U_7890) ),
    inference(clausify,[status(thm)],[f_2247_3]) ).

fof(f_2248_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_2248_2,plain,
    ! [U_7894,U_7893] : ~ hBOOL(hAPP(hAPP(c_member(U_7893),U_7894),c_Orderings_Obot__class_Obot(tc_fun(U_7893,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2248_1]) ).

fof(f_2248_3,plain,
    ! [U_7893,U_7894] : ~ hBOOL(hAPP(hAPP(c_member(U_7893),U_7894),c_Orderings_Obot__class_Obot(tc_fun(U_7893,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2248_2]) ).

cnf(f_2248_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(U_7893),U_7894),c_Orderings_Obot__class_Obot(tc_fun(U_7893,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2248_3]) ).

fof(f_2249_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_2249_2,plain,
    ! [U_7898,U_7897,U_7896,U_7895] :
      ( hBOOL(hAPP(hAPP(c_member(U_7895),U_7896),U_7898))
      | U_7896 = U_7897
      | ~ hBOOL(hAPP(hAPP(c_member(U_7895),U_7896),hAPP(hAPP(c_Set_Oinsert(U_7895),U_7897),U_7898))) ),
    inference(variable_rename,[status(thm)],[f_2249_1]) ).

fof(f_2249_3,plain,
    ! [U_7898,U_7896,U_7897,U_7895] :
      ( hBOOL(hAPP(hAPP(c_member(U_7895),U_7896),U_7898))
      | U_7896 = U_7897
      | ~ hBOOL(hAPP(hAPP(c_member(U_7895),U_7896),hAPP(hAPP(c_Set_Oinsert(U_7895),U_7897),U_7898))) ),
    inference(definitional_conversion,[status(esa)],[f_2249_2]) ).

cnf(f_2249_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7895),U_7896),U_7898))
    | U_7896 = U_7897
    | ~ hBOOL(hAPP(hAPP(c_member(U_7895),U_7896),hAPP(hAPP(c_Set_Oinsert(U_7895),U_7897),U_7898))) ),
    inference(clausify,[status(thm)],[f_2249_3]) ).

fof(f_2250_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_2250_2,plain,
    ! [U_7902,U_7901,U_7900,U_7899] :
      ( hBOOL(hAPP(hAPP(c_member(U_7899),U_7900),hAPP(hAPP(c_Set_Oinsert(U_7899),U_7902),U_7901)))
      | ( U_7900 != U_7902
        & ~ hBOOL(hAPP(hAPP(c_member(U_7899),U_7900),U_7901)) ) ),
    inference(variable_rename,[status(thm)],[f_2250_1]) ).

fof(f_2250_3,plain,
    ( ! [U_7899,U_7900,U_7902,U_7901] :
        ( U_7900 != U_7902
        | ~ sP688(U_7899,U_7900,U_7902,U_7901) )
    & ! [U_7899,U_7900,U_7902,U_7901] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7899),U_7900),U_7901))
        | ~ sP688(U_7899,U_7900,U_7902,U_7901) )
    & ! [U_7899,U_7900,U_7902,U_7901] :
        ( hBOOL(hAPP(hAPP(c_member(U_7899),U_7900),hAPP(hAPP(c_Set_Oinsert(U_7899),U_7902),U_7901)))
        | sP688(U_7899,U_7900,U_7902,U_7901) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP688])],[f_2250_2]) ).

cnf(f_2250_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7899),U_7900),hAPP(hAPP(c_Set_Oinsert(U_7899),U_7902),U_7901)))
    | sP688(U_7899,U_7900,U_7902,U_7901) ),
    inference(clausify,[status(thm)],[f_2250_3]) ).

cnf(f_2250_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7899),U_7900),U_7901))
    | ~ sP688(U_7899,U_7900,U_7902,U_7901) ),
    inference(clausify,[status(thm)],[f_2250_3]) ).

cnf(f_2250_6,plain,
    ( U_7900 != U_7902
    | ~ sP688(U_7899,U_7900,U_7902,U_7901) ),
    inference(clausify,[status(thm)],[f_2250_3]) ).

fof(f_2251_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_2251_2,plain,
    ! [U_7906,U_7905,U_7904,U_7903] :
      ( hBOOL(hAPP(hAPP(c_member(U_7903),U_7906),U_7905))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7903),U_7906),U_7904))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7903,tc_HOL_Obool)),U_7904),U_7905)) ),
    inference(variable_rename,[status(thm)],[f_2251_1]) ).

fof(f_2251_3,plain,
    ! [U_7903,U_7904,U_7905,U_7906] :
      ( hBOOL(hAPP(hAPP(c_member(U_7903),U_7906),U_7905))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7903),U_7906),U_7904))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7903,tc_HOL_Obool)),U_7904),U_7905)) ),
    inference(definitional_conversion,[status(esa)],[f_2251_2]) ).

cnf(f_2251_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7903),U_7906),U_7905))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7903),U_7906),U_7904))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7903,tc_HOL_Obool)),U_7904),U_7905)) ),
    inference(clausify,[status(thm)],[f_2251_3]) ).

fof(f_2252_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_2252_2,plain,
    ! [U_7910,U_7909,U_7908,U_7907] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_7907),U_7908),U_7910))
        & hBOOL(hAPP(hAPP(c_member(U_7907),U_7908),U_7909)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_7907),U_7908),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7907,tc_HOL_Obool)),U_7909),U_7910))) ),
    inference(variable_rename,[status(thm)],[f_2252_1]) ).

fof(f_2252_3,plain,
    ( ! [U_7907,U_7908,U_7909,U_7910] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7907),U_7908),U_7910))
        | ~ sP689(U_7907,U_7908,U_7909,U_7910) )
    & ! [U_7907,U_7908,U_7909,U_7910] :
        ( hBOOL(hAPP(hAPP(c_member(U_7907),U_7908),U_7909))
        | ~ sP689(U_7907,U_7908,U_7909,U_7910) )
    & ! [U_7907,U_7908,U_7909,U_7910] :
        ( sP689(U_7907,U_7908,U_7909,U_7910)
        | ~ hBOOL(hAPP(hAPP(c_member(U_7907),U_7908),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7907,tc_HOL_Obool)),U_7909),U_7910))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP689])],[f_2252_2]) ).

cnf(f_2252_4,plain,
    ( sP689(U_7907,U_7908,U_7909,U_7910)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7907),U_7908),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7907,tc_HOL_Obool)),U_7909),U_7910))) ),
    inference(clausify,[status(thm)],[f_2252_3]) ).

cnf(f_2252_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7907),U_7908),U_7909))
    | ~ sP689(U_7907,U_7908,U_7909,U_7910) ),
    inference(clausify,[status(thm)],[f_2252_3]) ).

cnf(f_2252_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7907),U_7908),U_7910))
    | ~ sP689(U_7907,U_7908,U_7909,U_7910) ),
    inference(clausify,[status(thm)],[f_2252_3]) ).

fof(f_2253_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_2253_2,plain,
    ! [U_7914,U_7913,U_7912,U_7911] :
      ( hBOOL(hAPP(hAPP(c_member(U_7911),U_7912),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7911,tc_HOL_Obool)),U_7913),U_7914)))
      | hBOOL(hAPP(hAPP(c_member(U_7911),U_7912),U_7914))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7911),U_7912),U_7913)) ),
    inference(variable_rename,[status(thm)],[f_2253_1]) ).

fof(f_2253_3,plain,
    ! [U_7911,U_7912,U_7913,U_7914] :
      ( hBOOL(hAPP(hAPP(c_member(U_7911),U_7912),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7911,tc_HOL_Obool)),U_7913),U_7914)))
      | hBOOL(hAPP(hAPP(c_member(U_7911),U_7912),U_7914))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7911),U_7912),U_7913)) ),
    inference(definitional_conversion,[status(esa)],[f_2253_2]) ).

cnf(f_2253_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7911),U_7912),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7911,tc_HOL_Obool)),U_7913),U_7914)))
    | hBOOL(hAPP(hAPP(c_member(U_7911),U_7912),U_7914))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7911),U_7912),U_7913)) ),
    inference(clausify,[status(thm)],[f_2253_3]) ).

fof(f_2254_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_2254_2,plain,
    ! [U_7917,U_7916,U_7915] :
      ( hBOOL(hAPP(hAPP(c_member(U_7915),U_7916),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7915,tc_HOL_Obool)),U_7917)))
      | hBOOL(hAPP(hAPP(c_member(U_7915),U_7916),U_7917)) ),
    inference(variable_rename,[status(thm)],[f_2254_1]) ).

fof(f_2254_3,plain,
    ! [U_7915,U_7916,U_7917] :
      ( hBOOL(hAPP(hAPP(c_member(U_7915),U_7916),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7915,tc_HOL_Obool)),U_7917)))
      | hBOOL(hAPP(hAPP(c_member(U_7915),U_7916),U_7917)) ),
    inference(definitional_conversion,[status(esa)],[f_2254_2]) ).

cnf(f_2254_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7915),U_7916),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7915,tc_HOL_Obool)),U_7917)))
    | hBOOL(hAPP(hAPP(c_member(U_7915),U_7916),U_7917)) ),
    inference(clausify,[status(thm)],[f_2254_3]) ).

fof(f_2255_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_2255_2,plain,
    ! [U_7924,U_7923,U_7922,U_7921,U_7920,U_7919,U_7918] :
      ( hBOOL(hAPP(hAPP(c_member(U_7918),U_7919),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_7923,U_7924,tc_fun(U_7918,tc_HOL_Obool)),U_7920),hAPP(hAPP(c_Product__Type_OPair(U_7923,U_7924),U_7921),U_7922))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7918),U_7919),hAPP(hAPP(U_7920,U_7921),U_7922))) ),
    inference(variable_rename,[status(thm)],[f_2255_1]) ).

fof(f_2255_3,plain,
    ! [U_7918,U_7919,U_7920,U_7921,U_7922,U_7923,U_7924] :
      ( hBOOL(hAPP(hAPP(c_member(U_7918),U_7919),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_7923,U_7924,tc_fun(U_7918,tc_HOL_Obool)),U_7920),hAPP(hAPP(c_Product__Type_OPair(U_7923,U_7924),U_7921),U_7922))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7918),U_7919),hAPP(hAPP(U_7920,U_7921),U_7922))) ),
    inference(definitional_conversion,[status(esa)],[f_2255_2]) ).

cnf(f_2255_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7918),U_7919),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_7923,U_7924,tc_fun(U_7918,tc_HOL_Obool)),U_7920),hAPP(hAPP(c_Product__Type_OPair(U_7923,U_7924),U_7921),U_7922))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7918),U_7919),hAPP(hAPP(U_7920,U_7921),U_7922))) ),
    inference(clausify,[status(thm)],[f_2255_3]) ).

fof(f_2256_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_2256_2,plain,
    ! [U_7927,U_7926,U_7925] : hBOOL(hAPP(hAPP(c_member(U_7925),U_7926),hAPP(hAPP(c_Set_Oinsert(U_7925),U_7926),U_7927))),
    inference(variable_rename,[status(thm)],[f_2256_1]) ).

fof(f_2256_3,plain,
    ! [U_7927,U_7926,U_7925] : hBOOL(hAPP(hAPP(c_member(U_7925),U_7926),hAPP(hAPP(c_Set_Oinsert(U_7925),U_7926),U_7927))),
    inference(definitional_conversion,[status(esa)],[f_2256_2]) ).

cnf(f_2256_4,plain,
    hBOOL(hAPP(hAPP(c_member(U_7925),U_7926),hAPP(hAPP(c_Set_Oinsert(U_7925),U_7926),U_7927))),
    inference(clausify,[status(thm)],[f_2256_3]) ).

fof(f_2257_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_2257_2,plain,
    ! [U_7931,U_7930] :
      ( ( ! [U_7929] : ~ hBOOL(hAPP(hAPP(c_member(U_7930),U_7929),U_7931))
        | U_7931 != c_Orderings_Obot__class_Obot(tc_fun(U_7930,tc_HOL_Obool)) )
      & ( U_7931 = c_Orderings_Obot__class_Obot(tc_fun(U_7930,tc_HOL_Obool))
        | ? [U_7928] : hBOOL(hAPP(hAPP(c_member(U_7930),U_7928),U_7931)) ) ),
    inference(variable_rename,[status(thm)],[f_2257_1]) ).

fof(f_2257_3,plain,
    ( ! [U_7935,U_7933] :
        ( ! [U_7929] : ~ hBOOL(hAPP(hAPP(c_member(U_7933),U_7929),U_7935))
        | U_7935 != c_Orderings_Obot__class_Obot(tc_fun(U_7933,tc_HOL_Obool)) )
    & ! [U_7934,U_7932] :
        ( U_7934 = c_Orderings_Obot__class_Obot(tc_fun(U_7932,tc_HOL_Obool))
        | ? [U_7928] : hBOOL(hAPP(hAPP(c_member(U_7932),U_7928),U_7934)) ) ),
    inference(miniscope,[status(thm)],[f_2257_2]) ).

fof(f_2257_4,plain,
    ( ! [U_7935,U_7933] :
        ( ! [U_7929] : ~ hBOOL(hAPP(hAPP(c_member(U_7933),U_7929),U_7935))
        | U_7935 != c_Orderings_Obot__class_Obot(tc_fun(U_7933,tc_HOL_Obool)) )
    & ! [U_7934,U_7932] :
        ( U_7934 = c_Orderings_Obot__class_Obot(tc_fun(U_7932,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_7932),sK120(U_7934,U_7932)),U_7934)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_7928,sK120(U_7934,U_7932))],[f_2257_3]) ).

fof(f_2257_5,plain,
    ( ! [U_7929,U_7933,U_7935] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7933),U_7929),U_7935))
        | U_7935 != c_Orderings_Obot__class_Obot(tc_fun(U_7933,tc_HOL_Obool)) )
    & ! [U_7934,U_7932] :
        ( U_7934 = c_Orderings_Obot__class_Obot(tc_fun(U_7932,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_7932),sK120(U_7934,U_7932)),U_7934)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2257_4]) ).

cnf(f_2257_6,plain,
    ( U_7934 = c_Orderings_Obot__class_Obot(tc_fun(U_7932,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_7932),sK120(U_7934,U_7932)),U_7934)) ),
    inference(clausify,[status(thm)],[f_2257_5]) ).

cnf(f_2257_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7933),U_7929),U_7935))
    | U_7935 != c_Orderings_Obot__class_Obot(tc_fun(U_7933,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2257_5]) ).

fof(f_2258_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_2258_2,plain,
    ! [U_7939,U_7938] :
      ( ( ? [U_7937] : hBOOL(hAPP(hAPP(c_member(U_7938),U_7937),U_7939))
        | U_7939 = c_Orderings_Obot__class_Obot(tc_fun(U_7938,tc_HOL_Obool)) )
      & ( U_7939 != c_Orderings_Obot__class_Obot(tc_fun(U_7938,tc_HOL_Obool))
        | ! [U_7936] : ~ hBOOL(hAPP(hAPP(c_member(U_7938),U_7936),U_7939)) ) ),
    inference(variable_rename,[status(thm)],[f_2258_1]) ).

fof(f_2258_3,plain,
    ( ! [U_7943,U_7941] :
        ( ? [U_7937] : hBOOL(hAPP(hAPP(c_member(U_7941),U_7937),U_7943))
        | U_7943 = c_Orderings_Obot__class_Obot(tc_fun(U_7941,tc_HOL_Obool)) )
    & ! [U_7942,U_7940] :
        ( U_7942 != c_Orderings_Obot__class_Obot(tc_fun(U_7940,tc_HOL_Obool))
        | ! [U_7936] : ~ hBOOL(hAPP(hAPP(c_member(U_7940),U_7936),U_7942)) ) ),
    inference(miniscope,[status(thm)],[f_2258_2]) ).

fof(f_2258_4,plain,
    ( ! [U_7943,U_7941] :
        ( hBOOL(hAPP(hAPP(c_member(U_7941),sK121(U_7943,U_7941)),U_7943))
        | U_7943 = c_Orderings_Obot__class_Obot(tc_fun(U_7941,tc_HOL_Obool)) )
    & ! [U_7942,U_7940] :
        ( U_7942 != c_Orderings_Obot__class_Obot(tc_fun(U_7940,tc_HOL_Obool))
        | ! [U_7936] : ~ hBOOL(hAPP(hAPP(c_member(U_7940),U_7936),U_7942)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_7937,sK121(U_7943,U_7941))],[f_2258_3]) ).

fof(f_2258_5,plain,
    ( ! [U_7941,U_7943] :
        ( hBOOL(hAPP(hAPP(c_member(U_7941),sK121(U_7943,U_7941)),U_7943))
        | U_7943 = c_Orderings_Obot__class_Obot(tc_fun(U_7941,tc_HOL_Obool)) )
    & ! [U_7936,U_7942,U_7940] :
        ( U_7942 != c_Orderings_Obot__class_Obot(tc_fun(U_7940,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7940),U_7936),U_7942)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2258_4]) ).

cnf(f_2258_6,plain,
    ( U_7942 != c_Orderings_Obot__class_Obot(tc_fun(U_7940,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7940),U_7936),U_7942)) ),
    inference(clausify,[status(thm)],[f_2258_5]) ).

cnf(f_2258_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7941),sK121(U_7943,U_7941)),U_7943))
    | U_7943 = c_Orderings_Obot__class_Obot(tc_fun(U_7941,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2258_5]) ).

fof(f_2259_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_2259_2,plain,
    ! [U_7945,U_7944] : ~ hBOOL(hAPP(hAPP(c_member(U_7944),U_7945),c_Orderings_Obot__class_Obot(tc_fun(U_7944,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2259_1]) ).

fof(f_2259_3,plain,
    ! [U_7944,U_7945] : ~ hBOOL(hAPP(hAPP(c_member(U_7944),U_7945),c_Orderings_Obot__class_Obot(tc_fun(U_7944,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2259_2]) ).

cnf(f_2259_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(U_7944),U_7945),c_Orderings_Obot__class_Obot(tc_fun(U_7944,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2259_3]) ).

fof(f_2260_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_2260_2,plain,
    ! [U_7949,U_7948,U_7947,U_7946] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7946),U_7947),hAPP(hAPP(c_Set_Oinsert(U_7946),U_7948),U_7949)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_7946),U_7947),U_7949))
          & U_7947 != U_7948 ) )
      & ( hBOOL(hAPP(hAPP(c_member(U_7946),U_7947),U_7949))
        | U_7947 = U_7948
        | ~ hBOOL(hAPP(hAPP(c_member(U_7946),U_7947),hAPP(hAPP(c_Set_Oinsert(U_7946),U_7948),U_7949))) ) ),
    inference(variable_rename,[status(thm)],[f_2260_1]) ).

fof(f_2260_3,plain,
    ( ! [U_7957,U_7955,U_7953,U_7951] :
        ( hBOOL(hAPP(hAPP(c_member(U_7951),U_7953),hAPP(hAPP(c_Set_Oinsert(U_7951),U_7955),U_7957)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_7951),U_7953),U_7957))
          & U_7953 != U_7955 ) )
    & ! [U_7956,U_7954,U_7952,U_7950] :
        ( hBOOL(hAPP(hAPP(c_member(U_7950),U_7952),U_7956))
        | U_7952 = U_7954
        | ~ hBOOL(hAPP(hAPP(c_member(U_7950),U_7952),hAPP(hAPP(c_Set_Oinsert(U_7950),U_7954),U_7956))) ) ),
    inference(miniscope,[status(thm)],[f_2260_2]) ).

fof(f_2260_4,plain,
    ( ! [U_7955,U_7953,U_7957,U_7951] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7951),U_7953),U_7957))
        | ~ sP690(U_7955,U_7953,U_7957,U_7951) )
    & ! [U_7955,U_7953,U_7957,U_7951] :
        ( U_7953 != U_7955
        | ~ sP690(U_7955,U_7953,U_7957,U_7951) )
    & ! [U_7955,U_7953,U_7957,U_7951] :
        ( hBOOL(hAPP(hAPP(c_member(U_7951),U_7953),hAPP(hAPP(c_Set_Oinsert(U_7951),U_7955),U_7957)))
        | sP690(U_7955,U_7953,U_7957,U_7951) )
    & ! [U_7952,U_7950,U_7954,U_7956] :
        ( hBOOL(hAPP(hAPP(c_member(U_7950),U_7952),U_7956))
        | U_7952 = U_7954
        | ~ hBOOL(hAPP(hAPP(c_member(U_7950),U_7952),hAPP(hAPP(c_Set_Oinsert(U_7950),U_7954),U_7956))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP690])],[f_2260_3]) ).

cnf(f_2260_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7950),U_7952),U_7956))
    | U_7952 = U_7954
    | ~ hBOOL(hAPP(hAPP(c_member(U_7950),U_7952),hAPP(hAPP(c_Set_Oinsert(U_7950),U_7954),U_7956))) ),
    inference(clausify,[status(thm)],[f_2260_4]) ).

cnf(f_2260_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7951),U_7953),hAPP(hAPP(c_Set_Oinsert(U_7951),U_7955),U_7957)))
    | sP690(U_7955,U_7953,U_7957,U_7951) ),
    inference(clausify,[status(thm)],[f_2260_4]) ).

cnf(f_2260_7,plain,
    ( U_7953 != U_7955
    | ~ sP690(U_7955,U_7953,U_7957,U_7951) ),
    inference(clausify,[status(thm)],[f_2260_4]) ).

cnf(f_2260_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7951),U_7953),U_7957))
    | ~ sP690(U_7955,U_7953,U_7957,U_7951) ),
    inference(clausify,[status(thm)],[f_2260_4]) ).

fof(f_2261_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_2261_2,plain,
    ! [U_7961,U_7960,U_7959,U_7958] :
      ( ( ( hAPP(hAPP(c_Set_Oinsert(U_7958),U_7959),U_7960) = hAPP(hAPP(c_Set_Oinsert(U_7958),U_7959),U_7961)
          | U_7960 != U_7961 )
        & ( U_7960 = U_7961
          | hAPP(hAPP(c_Set_Oinsert(U_7958),U_7959),U_7960) != hAPP(hAPP(c_Set_Oinsert(U_7958),U_7959),U_7961) ) )
      | hBOOL(hAPP(hAPP(c_member(U_7958),U_7959),U_7961))
      | hBOOL(hAPP(hAPP(c_member(U_7958),U_7959),U_7960)) ),
    inference(variable_rename,[status(thm)],[f_2261_1]) ).

fof(f_2261_3,plain,
    ( ! [U_7958,U_7959,U_7960,U_7961] :
        ( hAPP(hAPP(c_Set_Oinsert(U_7958),U_7959),U_7960) = hAPP(hAPP(c_Set_Oinsert(U_7958),U_7959),U_7961)
        | U_7960 != U_7961
        | ~ sP691(U_7958,U_7959,U_7960,U_7961) )
    & ! [U_7958,U_7959,U_7960,U_7961] :
        ( U_7960 = U_7961
        | hAPP(hAPP(c_Set_Oinsert(U_7958),U_7959),U_7960) != hAPP(hAPP(c_Set_Oinsert(U_7958),U_7959),U_7961)
        | ~ sP691(U_7958,U_7959,U_7960,U_7961) )
    & ! [U_7958,U_7959,U_7960,U_7961] :
        ( sP691(U_7958,U_7959,U_7960,U_7961)
        | hBOOL(hAPP(hAPP(c_member(U_7958),U_7959),U_7961))
        | hBOOL(hAPP(hAPP(c_member(U_7958),U_7959),U_7960)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP691])],[f_2261_2]) ).

cnf(f_2261_4,plain,
    ( sP691(U_7958,U_7959,U_7960,U_7961)
    | hBOOL(hAPP(hAPP(c_member(U_7958),U_7959),U_7961))
    | hBOOL(hAPP(hAPP(c_member(U_7958),U_7959),U_7960)) ),
    inference(clausify,[status(thm)],[f_2261_3]) ).

cnf(f_2261_5,plain,
    ( U_7960 = U_7961
    | hAPP(hAPP(c_Set_Oinsert(U_7958),U_7959),U_7960) != hAPP(hAPP(c_Set_Oinsert(U_7958),U_7959),U_7961)
    | ~ sP691(U_7958,U_7959,U_7960,U_7961) ),
    inference(clausify,[status(thm)],[f_2261_3]) ).

cnf(f_2261_6,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_7958),U_7959),U_7960) = hAPP(hAPP(c_Set_Oinsert(U_7958),U_7959),U_7961)
    | U_7960 != U_7961
    | ~ sP691(U_7958,U_7959,U_7960,U_7961) ),
    inference(clausify,[status(thm)],[f_2261_3]) ).

fof(f_2262_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_2262_2,plain,
    ! [U_7964,U_7963,U_7962] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7963),U_7964),U_7962))
      | U_7962 != c_Orderings_Obot__class_Obot(tc_fun(U_7963,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2262_1]) ).

fof(f_2262_3,plain,
    ! [U_7962,U_7964,U_7963] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7963),U_7964),U_7962))
      | U_7962 != c_Orderings_Obot__class_Obot(tc_fun(U_7963,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_2262_2]) ).

cnf(f_2262_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7963),U_7964),U_7962))
    | U_7962 != c_Orderings_Obot__class_Obot(tc_fun(U_7963,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2262_3]) ).

fof(f_2263_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_2263_2,plain,
    ! [U_7968,U_7967,U_7966,U_7965] :
      ( hBOOL(hAPP(hAPP(c_member(U_7965),U_7966),hAPP(hAPP(c_Set_Oinsert(U_7965),U_7968),U_7967)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7965),U_7966),U_7967)) ),
    inference(variable_rename,[status(thm)],[f_2263_1]) ).

fof(f_2263_3,plain,
    ! [U_7966,U_7965,U_7967,U_7968] :
      ( hBOOL(hAPP(hAPP(c_member(U_7965),U_7966),hAPP(hAPP(c_Set_Oinsert(U_7965),U_7968),U_7967)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7965),U_7966),U_7967)) ),
    inference(definitional_conversion,[status(esa)],[f_2263_2]) ).

cnf(f_2263_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7965),U_7966),hAPP(hAPP(c_Set_Oinsert(U_7965),U_7968),U_7967)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7965),U_7966),U_7967)) ),
    inference(clausify,[status(thm)],[f_2263_3]) ).

fof(f_2264_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_2264_2,plain,
    ! [U_7971,U_7970,U_7969] :
      ( hAPP(hAPP(c_Set_Oinsert(U_7969),U_7970),U_7971) = U_7971
      | ~ hBOOL(hAPP(hAPP(c_member(U_7969),U_7970),U_7971)) ),
    inference(variable_rename,[status(thm)],[f_2264_1]) ).

fof(f_2264_3,plain,
    ! [U_7969,U_7970,U_7971] :
      ( hAPP(hAPP(c_Set_Oinsert(U_7969),U_7970),U_7971) = U_7971
      | ~ hBOOL(hAPP(hAPP(c_member(U_7969),U_7970),U_7971)) ),
    inference(definitional_conversion,[status(esa)],[f_2264_2]) ).

cnf(f_2264_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_7969),U_7970),U_7971) = U_7971
    | ~ hBOOL(hAPP(hAPP(c_member(U_7969),U_7970),U_7971)) ),
    inference(clausify,[status(thm)],[f_2264_3]) ).

fof(f_2265_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_2265_2,plain,
    ! [U_7975,U_7974,U_7973,U_7972] :
      ( hBOOL(hAPP(hAPP(c_member(U_7972),U_7975),U_7974))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7972),U_7975),U_7973))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7972,tc_HOL_Obool)),U_7973),U_7974)) ),
    inference(variable_rename,[status(thm)],[f_2265_1]) ).

fof(f_2265_3,plain,
    ! [U_7972,U_7973,U_7974,U_7975] :
      ( hBOOL(hAPP(hAPP(c_member(U_7972),U_7975),U_7974))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7972),U_7975),U_7973))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7972,tc_HOL_Obool)),U_7973),U_7974)) ),
    inference(definitional_conversion,[status(esa)],[f_2265_2]) ).

cnf(f_2265_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7972),U_7975),U_7974))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7972),U_7975),U_7973))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7972,tc_HOL_Obool)),U_7973),U_7974)) ),
    inference(clausify,[status(thm)],[f_2265_3]) ).

fof(f_2266_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_2266_2,plain,
    ! [U_7979,U_7978,U_7977,U_7976] :
      ( hBOOL(hAPP(hAPP(c_member(U_7976),U_7977),U_7979))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7976,tc_HOL_Obool)),U_7978),U_7979))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7976),U_7977),U_7978)) ),
    inference(variable_rename,[status(thm)],[f_2266_1]) ).

fof(f_2266_3,plain,
    ! [U_7976,U_7977,U_7978,U_7979] :
      ( hBOOL(hAPP(hAPP(c_member(U_7976),U_7977),U_7979))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7976,tc_HOL_Obool)),U_7978),U_7979))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7976),U_7977),U_7978)) ),
    inference(definitional_conversion,[status(esa)],[f_2266_2]) ).

cnf(f_2266_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7976),U_7977),U_7979))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7976,tc_HOL_Obool)),U_7978),U_7979))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7976),U_7977),U_7978)) ),
    inference(clausify,[status(thm)],[f_2266_3]) ).

fof(f_2267_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_2267_2,plain,
    ! [U_7983,U_7982,U_7981,U_7980] :
      ( hBOOL(hAPP(hAPP(c_member(U_7980),U_7983),U_7982))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7980),U_7983),U_7981))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7980,tc_HOL_Obool)),U_7981),U_7982)) ),
    inference(variable_rename,[status(thm)],[f_2267_1]) ).

fof(f_2267_3,plain,
    ! [U_7980,U_7981,U_7982,U_7983] :
      ( hBOOL(hAPP(hAPP(c_member(U_7980),U_7983),U_7982))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7980),U_7983),U_7981))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7980,tc_HOL_Obool)),U_7981),U_7982)) ),
    inference(definitional_conversion,[status(esa)],[f_2267_2]) ).

cnf(f_2267_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7980),U_7983),U_7982))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7980),U_7983),U_7981))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7980,tc_HOL_Obool)),U_7981),U_7982)) ),
    inference(clausify,[status(thm)],[f_2267_3]) ).

fof(f_2268_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_2268_2,plain,
    ! [U_7986,U_7985,U_7984] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7984),U_7985),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7984,tc_HOL_Obool)),U_7986)))
        | hBOOL(hAPP(hAPP(c_member(U_7984),U_7985),U_7986)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(U_7984),U_7985),U_7986))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7984),U_7985),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7984,tc_HOL_Obool)),U_7986))) ) ),
    inference(variable_rename,[status(thm)],[f_2268_1]) ).

fof(f_2268_3,plain,
    ( ! [U_7992,U_7990,U_7988] :
        ( hBOOL(hAPP(hAPP(c_member(U_7988),U_7990),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7988,tc_HOL_Obool)),U_7992)))
        | hBOOL(hAPP(hAPP(c_member(U_7988),U_7990),U_7992)) )
    & ! [U_7991,U_7989,U_7987] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7987),U_7989),U_7991))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7987),U_7989),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7987,tc_HOL_Obool)),U_7991))) ) ),
    inference(miniscope,[status(thm)],[f_2268_2]) ).

fof(f_2268_4,plain,
    ( ! [U_7988,U_7990,U_7992] :
        ( hBOOL(hAPP(hAPP(c_member(U_7988),U_7990),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7988,tc_HOL_Obool)),U_7992)))
        | hBOOL(hAPP(hAPP(c_member(U_7988),U_7990),U_7992)) )
    & ! [U_7991,U_7989,U_7987] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7987),U_7989),U_7991))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7987),U_7989),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7987,tc_HOL_Obool)),U_7991))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2268_3]) ).

cnf(f_2268_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7987),U_7989),U_7991))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7987),U_7989),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7987,tc_HOL_Obool)),U_7991))) ),
    inference(clausify,[status(thm)],[f_2268_4]) ).

cnf(f_2268_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7988),U_7990),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7988,tc_HOL_Obool)),U_7992)))
    | hBOOL(hAPP(hAPP(c_member(U_7988),U_7990),U_7992)) ),
    inference(clausify,[status(thm)],[f_2268_4]) ).

fof(f_2269_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_2269_2,plain,
    ! [U_7995,U_7994,U_7993] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7993),U_7994),U_7995))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7993),U_7994),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7993,tc_HOL_Obool)),U_7995))) ),
    inference(variable_rename,[status(thm)],[f_2269_1]) ).

fof(f_2269_3,plain,
    ! [U_7995,U_7994,U_7993] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7993),U_7994),U_7995))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7993),U_7994),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7993,tc_HOL_Obool)),U_7995))) ),
    inference(definitional_conversion,[status(esa)],[f_2269_2]) ).

cnf(f_2269_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7993),U_7994),U_7995))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7993),U_7994),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7993,tc_HOL_Obool)),U_7995))) ),
    inference(clausify,[status(thm)],[f_2269_3]) ).

fof(f_2270_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_2270_2,plain,
    ! [U_7998,U_7997,U_7996] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7996),U_7997),U_7998))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7996),U_7997),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7996,tc_HOL_Obool)),U_7998))) ),
    inference(variable_rename,[status(thm)],[f_2270_1]) ).

fof(f_2270_3,plain,
    ! [U_7996,U_7997,U_7998] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7996),U_7997),U_7998))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7996),U_7997),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7996,tc_HOL_Obool)),U_7998))) ),
    inference(definitional_conversion,[status(esa)],[f_2270_2]) ).

cnf(f_2270_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7996),U_7997),U_7998))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7996),U_7997),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7996,tc_HOL_Obool)),U_7998))) ),
    inference(clausify,[status(thm)],[f_2270_3]) ).

fof(f_2271_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_2271_2,plain,
    ! [U_8001,U_8000,U_7999] :
      ( ( hAPP(hAPP(c_COMBC(U_7999,tc_fun(U_7999,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7999)),U_8000) = hAPP(hAPP(c_COMBC(U_7999,tc_fun(U_7999,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7999)),U_8001)
        | U_8000 != U_8001 )
      & ( U_8000 = U_8001
        | hAPP(hAPP(c_COMBC(U_7999,tc_fun(U_7999,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7999)),U_8000) != hAPP(hAPP(c_COMBC(U_7999,tc_fun(U_7999,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7999)),U_8001) ) ),
    inference(variable_rename,[status(thm)],[f_2271_1]) ).

fof(f_2271_3,plain,
    ( ! [U_8007,U_8005] :
        ( ! [U_8003] : hAPP(hAPP(c_COMBC(U_8003,tc_fun(U_8003,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8003)),U_8005) = hAPP(hAPP(c_COMBC(U_8003,tc_fun(U_8003,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8003)),U_8007)
        | U_8005 != U_8007 )
    & ! [U_8006,U_8004] :
        ( ! [U_8002] : hAPP(hAPP(c_COMBC(U_8002,tc_fun(U_8002,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8002)),U_8004) != hAPP(hAPP(c_COMBC(U_8002,tc_fun(U_8002,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8002)),U_8006)
        | U_8004 = U_8006 ) ),
    inference(miniscope,[status(thm)],[f_2271_2]) ).

fof(f_2271_4,plain,
    ( ! [U_8003,U_8007,U_8005] :
        ( hAPP(hAPP(c_COMBC(U_8003,tc_fun(U_8003,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8003)),U_8005) = hAPP(hAPP(c_COMBC(U_8003,tc_fun(U_8003,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8003)),U_8007)
        | U_8005 != U_8007 )
    & ! [U_8002,U_8006,U_8004] :
        ( hAPP(hAPP(c_COMBC(U_8002,tc_fun(U_8002,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8002)),U_8004) != hAPP(hAPP(c_COMBC(U_8002,tc_fun(U_8002,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8002)),U_8006)
        | U_8004 = U_8006 ) ),
    inference(definitional_conversion,[status(esa)],[f_2271_3]) ).

cnf(f_2271_5,plain,
    ( hAPP(hAPP(c_COMBC(U_8002,tc_fun(U_8002,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8002)),U_8004) != hAPP(hAPP(c_COMBC(U_8002,tc_fun(U_8002,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8002)),U_8006)
    | U_8004 = U_8006 ),
    inference(clausify,[status(thm)],[f_2271_4]) ).

cnf(f_2271_6,plain,
    ( hAPP(hAPP(c_COMBC(U_8003,tc_fun(U_8003,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8003)),U_8005) = hAPP(hAPP(c_COMBC(U_8003,tc_fun(U_8003,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8003)),U_8007)
    | U_8005 != U_8007 ),
    inference(clausify,[status(thm)],[f_2271_4]) ).

fof(f_2272_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_2272_2,plain,
    ! [U_8010,U_8009,U_8008] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8008),U_8009),hAPP(c_fequal,U_8010)))
        | U_8009 != U_8010 )
      & ( U_8009 = U_8010
        | ~ hBOOL(hAPP(hAPP(c_member(U_8008),U_8009),hAPP(c_fequal,U_8010))) ) ),
    inference(variable_rename,[status(thm)],[f_2272_1]) ).

fof(f_2272_3,plain,
    ( ! [U_8016,U_8014] :
        ( ! [U_8012] : hBOOL(hAPP(hAPP(c_member(U_8012),U_8014),hAPP(c_fequal,U_8016)))
        | U_8014 != U_8016 )
    & ! [U_8015,U_8013] :
        ( ! [U_8011] : ~ hBOOL(hAPP(hAPP(c_member(U_8011),U_8013),hAPP(c_fequal,U_8015)))
        | U_8013 = U_8015 ) ),
    inference(miniscope,[status(thm)],[f_2272_2]) ).

fof(f_2272_4,plain,
    ( ! [U_8016,U_8012,U_8014] :
        ( hBOOL(hAPP(hAPP(c_member(U_8012),U_8014),hAPP(c_fequal,U_8016)))
        | U_8014 != U_8016 )
    & ! [U_8015,U_8013,U_8011] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8011),U_8013),hAPP(c_fequal,U_8015)))
        | U_8013 = U_8015 ) ),
    inference(definitional_conversion,[status(esa)],[f_2272_3]) ).

cnf(f_2272_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8011),U_8013),hAPP(c_fequal,U_8015)))
    | U_8013 = U_8015 ),
    inference(clausify,[status(thm)],[f_2272_4]) ).

cnf(f_2272_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8012),U_8014),hAPP(c_fequal,U_8016)))
    | U_8014 != U_8016 ),
    inference(clausify,[status(thm)],[f_2272_4]) ).

fof(f_2273_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_2273_2,plain,
    ! [U_8020,U_8019,U_8018,U_8017] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8017),U_8018),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8017,tc_HOL_Obool)),U_8019),U_8020)))
        | hBOOL(hAPP(hAPP(c_member(U_8017),U_8018),U_8020))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8017),U_8018),U_8019)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(U_8017),U_8018),U_8020))
          & hBOOL(hAPP(hAPP(c_member(U_8017),U_8018),U_8019)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8017),U_8018),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8017,tc_HOL_Obool)),U_8019),U_8020))) ) ),
    inference(variable_rename,[status(thm)],[f_2273_1]) ).

fof(f_2273_3,plain,
    ( ! [U_8028,U_8026,U_8024,U_8022] :
        ( hBOOL(hAPP(hAPP(c_member(U_8022),U_8024),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8022,tc_HOL_Obool)),U_8026),U_8028)))
        | hBOOL(hAPP(hAPP(c_member(U_8022),U_8024),U_8028))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8022),U_8024),U_8026)) )
    & ! [U_8027,U_8025,U_8023,U_8021] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_8021),U_8023),U_8027))
          & hBOOL(hAPP(hAPP(c_member(U_8021),U_8023),U_8025)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8021),U_8023),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8021,tc_HOL_Obool)),U_8025),U_8027))) ) ),
    inference(miniscope,[status(thm)],[f_2273_2]) ).

fof(f_2273_4,plain,
    ( ! [U_8027,U_8023,U_8021,U_8025] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8021),U_8023),U_8027))
        | ~ sP692(U_8027,U_8023,U_8021,U_8025) )
    & ! [U_8027,U_8023,U_8021,U_8025] :
        ( hBOOL(hAPP(hAPP(c_member(U_8021),U_8023),U_8025))
        | ~ sP692(U_8027,U_8023,U_8021,U_8025) )
    & ! [U_8024,U_8022,U_8028,U_8026] :
        ( hBOOL(hAPP(hAPP(c_member(U_8022),U_8024),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8022,tc_HOL_Obool)),U_8026),U_8028)))
        | hBOOL(hAPP(hAPP(c_member(U_8022),U_8024),U_8028))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8022),U_8024),U_8026)) )
    & ! [U_8027,U_8023,U_8021,U_8025] :
        ( sP692(U_8027,U_8023,U_8021,U_8025)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8021),U_8023),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8021,tc_HOL_Obool)),U_8025),U_8027))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP692])],[f_2273_3]) ).

cnf(f_2273_5,plain,
    ( sP692(U_8027,U_8023,U_8021,U_8025)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8021),U_8023),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8021,tc_HOL_Obool)),U_8025),U_8027))) ),
    inference(clausify,[status(thm)],[f_2273_4]) ).

cnf(f_2273_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8022),U_8024),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8022,tc_HOL_Obool)),U_8026),U_8028)))
    | hBOOL(hAPP(hAPP(c_member(U_8022),U_8024),U_8028))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8022),U_8024),U_8026)) ),
    inference(clausify,[status(thm)],[f_2273_4]) ).

cnf(f_2273_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8021),U_8023),U_8025))
    | ~ sP692(U_8027,U_8023,U_8021,U_8025) ),
    inference(clausify,[status(thm)],[f_2273_4]) ).

cnf(f_2273_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8021),U_8023),U_8027))
    | ~ sP692(U_8027,U_8023,U_8021,U_8025) ),
    inference(clausify,[status(thm)],[f_2273_4]) ).

fof(f_2274_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_2274_2,plain,
    ! [U_8032,U_8031,U_8030,U_8029] :
      ( hBOOL(hAPP(hAPP(c_member(U_8029),U_8030),U_8031))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8029),U_8030),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8029,tc_HOL_Obool)),U_8031),U_8032))) ),
    inference(variable_rename,[status(thm)],[f_2274_1]) ).

fof(f_2274_3,plain,
    ! [U_8030,U_8031,U_8032,U_8029] :
      ( hBOOL(hAPP(hAPP(c_member(U_8029),U_8030),U_8031))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8029),U_8030),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8029,tc_HOL_Obool)),U_8031),U_8032))) ),
    inference(definitional_conversion,[status(esa)],[f_2274_2]) ).

cnf(f_2274_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8029),U_8030),U_8031))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8029),U_8030),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8029,tc_HOL_Obool)),U_8031),U_8032))) ),
    inference(clausify,[status(thm)],[f_2274_3]) ).

fof(f_2275_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_2275_2,plain,
    ! [U_8036,U_8035,U_8034,U_8033] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_8033),U_8034),U_8036))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8033),U_8034),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8033,tc_HOL_Obool)),U_8035),U_8036))) ),
    inference(variable_rename,[status(thm)],[f_2275_1]) ).

fof(f_2275_3,plain,
    ! [U_8033,U_8034,U_8035,U_8036] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_8033),U_8034),U_8036))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8033),U_8034),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8033,tc_HOL_Obool)),U_8035),U_8036))) ),
    inference(definitional_conversion,[status(esa)],[f_2275_2]) ).

cnf(f_2275_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8033),U_8034),U_8036))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8033),U_8034),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8033,tc_HOL_Obool)),U_8035),U_8036))) ),
    inference(clausify,[status(thm)],[f_2275_3]) ).

fof(f_2276_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_2276_2,plain,
    ! [U_8039,U_8038,U_8037] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8037),U_8038),U_8039))
        | ~ hBOOL(hAPP(U_8039,U_8038)) )
      & ( hBOOL(hAPP(U_8039,U_8038))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8037),U_8038),U_8039)) ) ),
    inference(variable_rename,[status(thm)],[f_2276_1]) ).

fof(f_2276_3,plain,
    ( ! [U_8045,U_8043] :
        ( ! [U_8041] : hBOOL(hAPP(hAPP(c_member(U_8041),U_8043),U_8045))
        | ~ hBOOL(hAPP(U_8045,U_8043)) )
    & ! [U_8044,U_8042] :
        ( ! [U_8040] : ~ hBOOL(hAPP(hAPP(c_member(U_8040),U_8042),U_8044))
        | hBOOL(hAPP(U_8044,U_8042)) ) ),
    inference(miniscope,[status(thm)],[f_2276_2]) ).

fof(f_2276_4,plain,
    ( ! [U_8045,U_8041,U_8043] :
        ( hBOOL(hAPP(hAPP(c_member(U_8041),U_8043),U_8045))
        | ~ hBOOL(hAPP(U_8045,U_8043)) )
    & ! [U_8044,U_8042,U_8040] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8040),U_8042),U_8044))
        | hBOOL(hAPP(U_8044,U_8042)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2276_3]) ).

cnf(f_2276_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8040),U_8042),U_8044))
    | hBOOL(hAPP(U_8044,U_8042)) ),
    inference(clausify,[status(thm)],[f_2276_4]) ).

cnf(f_2276_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8041),U_8043),U_8045))
    | ~ hBOOL(hAPP(U_8045,U_8043)) ),
    inference(clausify,[status(thm)],[f_2276_4]) ).

fof(f_2277_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_2277_2,plain,
    ! [U_8049,U_8048,U_8047,U_8046] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_8048),U_8049),U_8046))
          | ~ hBOOL(hAPP(hAPP(c_member(U_8048),U_8049),U_8047)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_8048),U_8049),U_8047))
          | ~ hBOOL(hAPP(hAPP(c_member(U_8048),U_8049),U_8046)) ) )
      | U_8046 != U_8047 ),
    inference(variable_rename,[status(thm)],[f_2277_1]) ).

fof(f_2277_3,plain,
    ( ! [U_8046,U_8048,U_8047,U_8049] :
        ( hBOOL(hAPP(hAPP(c_member(U_8048),U_8049),U_8046))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8048),U_8049),U_8047))
        | ~ sP693(U_8046,U_8048,U_8047,U_8049) )
    & ! [U_8046,U_8048,U_8047,U_8049] :
        ( hBOOL(hAPP(hAPP(c_member(U_8048),U_8049),U_8047))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8048),U_8049),U_8046))
        | ~ sP693(U_8046,U_8048,U_8047,U_8049) )
    & ! [U_8046,U_8048,U_8047,U_8049] :
        ( sP693(U_8046,U_8048,U_8047,U_8049)
        | U_8046 != U_8047 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP693])],[f_2277_2]) ).

cnf(f_2277_4,plain,
    ( sP693(U_8046,U_8048,U_8047,U_8049)
    | U_8046 != U_8047 ),
    inference(clausify,[status(thm)],[f_2277_3]) ).

cnf(f_2277_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8048),U_8049),U_8047))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8048),U_8049),U_8046))
    | ~ sP693(U_8046,U_8048,U_8047,U_8049) ),
    inference(clausify,[status(thm)],[f_2277_3]) ).

cnf(f_2277_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8048),U_8049),U_8046))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8048),U_8049),U_8047))
    | ~ sP693(U_8046,U_8048,U_8047,U_8049) ),
    inference(clausify,[status(thm)],[f_2277_3]) ).

fof(f_2278_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_2278_2,plain,
    ! [U_8053,U_8052,U_8051,U_8050] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_8052),U_8050),U_8053))
          | ~ hBOOL(hAPP(hAPP(c_member(U_8052),U_8051),U_8053)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_8052),U_8051),U_8053))
          | ~ hBOOL(hAPP(hAPP(c_member(U_8052),U_8050),U_8053)) ) )
      | U_8050 != U_8051 ),
    inference(variable_rename,[status(thm)],[f_2278_1]) ).

fof(f_2278_3,plain,
    ( ! [U_8053,U_8051,U_8050,U_8052] :
        ( hBOOL(hAPP(hAPP(c_member(U_8052),U_8050),U_8053))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8052),U_8051),U_8053))
        | ~ sP694(U_8053,U_8051,U_8050,U_8052) )
    & ! [U_8053,U_8051,U_8050,U_8052] :
        ( hBOOL(hAPP(hAPP(c_member(U_8052),U_8051),U_8053))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8052),U_8050),U_8053))
        | ~ sP694(U_8053,U_8051,U_8050,U_8052) )
    & ! [U_8053,U_8051,U_8050,U_8052] :
        ( sP694(U_8053,U_8051,U_8050,U_8052)
        | U_8050 != U_8051 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP694])],[f_2278_2]) ).

cnf(f_2278_4,plain,
    ( sP694(U_8053,U_8051,U_8050,U_8052)
    | U_8050 != U_8051 ),
    inference(clausify,[status(thm)],[f_2278_3]) ).

cnf(f_2278_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8052),U_8051),U_8053))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8052),U_8050),U_8053))
    | ~ sP694(U_8053,U_8051,U_8050,U_8052) ),
    inference(clausify,[status(thm)],[f_2278_3]) ).

cnf(f_2278_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8052),U_8050),U_8053))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8052),U_8051),U_8053))
    | ~ sP694(U_8053,U_8051,U_8050,U_8052) ),
    inference(clausify,[status(thm)],[f_2278_3]) ).

fof(f_2279_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_2279_2,plain,
    ! [U_8057,U_8056,U_8055,U_8054] :
      ( hBOOL(hAPP(hAPP(c_member(U_8056),U_8054),U_8057))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8056),U_8055),U_8057))
      | U_8054 != U_8055 ),
    inference(variable_rename,[status(thm)],[f_2279_1]) ).

fof(f_2279_3,plain,
    ! [U_8055,U_8057,U_8054,U_8056] :
      ( hBOOL(hAPP(hAPP(c_member(U_8056),U_8054),U_8057))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8056),U_8055),U_8057))
      | U_8054 != U_8055 ),
    inference(definitional_conversion,[status(esa)],[f_2279_2]) ).

cnf(f_2279_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8056),U_8054),U_8057))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8056),U_8055),U_8057))
    | U_8054 != U_8055 ),
    inference(clausify,[status(thm)],[f_2279_3]) ).

fof(f_2280_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_2280_2,plain,
    ! [U_8061,U_8060,U_8059,U_8058] :
      ( hBOOL(hAPP(hAPP(c_member(U_8058),U_8061),U_8060))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8058),U_8061),U_8059))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8058,tc_HOL_Obool)),U_8059),U_8060)) ),
    inference(variable_rename,[status(thm)],[f_2280_1]) ).

fof(f_2280_3,plain,
    ! [U_8058,U_8059,U_8060,U_8061] :
      ( hBOOL(hAPP(hAPP(c_member(U_8058),U_8061),U_8060))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8058),U_8061),U_8059))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8058,tc_HOL_Obool)),U_8059),U_8060)) ),
    inference(definitional_conversion,[status(esa)],[f_2280_2]) ).

cnf(f_2280_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8058),U_8061),U_8060))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8058),U_8061),U_8059))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8058,tc_HOL_Obool)),U_8059),U_8060)) ),
    inference(clausify,[status(thm)],[f_2280_3]) ).

fof(f_2281_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_2281_2,plain,
    ! [U_8063,U_8062] :
      ( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8062,tc_HOL_Obool)),U_8063))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8062),U_8063),c_Orderings_Obot__class_Obot(tc_fun(U_8062,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_8062),U_8063),c_Orderings_Obot__class_Obot(tc_fun(U_8062,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8062,tc_HOL_Obool)),U_8063)) ) ),
    inference(variable_rename,[status(thm)],[f_2281_1]) ).

fof(f_2281_3,plain,
    ( ! [U_8067,U_8065] :
        ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8065,tc_HOL_Obool)),U_8067))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8065),U_8067),c_Orderings_Obot__class_Obot(tc_fun(U_8065,tc_HOL_Obool)))) )
    & ! [U_8066,U_8064] :
        ( hBOOL(hAPP(hAPP(c_member(U_8064),U_8066),c_Orderings_Obot__class_Obot(tc_fun(U_8064,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8064,tc_HOL_Obool)),U_8066)) ) ),
    inference(miniscope,[status(thm)],[f_2281_2]) ).

fof(f_2281_4,plain,
    ( ! [U_8067,U_8065] :
        ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8065,tc_HOL_Obool)),U_8067))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8065),U_8067),c_Orderings_Obot__class_Obot(tc_fun(U_8065,tc_HOL_Obool)))) )
    & ! [U_8066,U_8064] :
        ( hBOOL(hAPP(hAPP(c_member(U_8064),U_8066),c_Orderings_Obot__class_Obot(tc_fun(U_8064,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8064,tc_HOL_Obool)),U_8066)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2281_3]) ).

cnf(f_2281_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8064),U_8066),c_Orderings_Obot__class_Obot(tc_fun(U_8064,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8064,tc_HOL_Obool)),U_8066)) ),
    inference(clausify,[status(thm)],[f_2281_4]) ).

cnf(f_2281_6,plain,
    ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8065,tc_HOL_Obool)),U_8067))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8065),U_8067),c_Orderings_Obot__class_Obot(tc_fun(U_8065,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2281_4]) ).

fof(f_2282_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_2282_2,plain,
    ! [U_8071,U_8070,U_8069,U_8068] :
      ( ( hAPP(hAPP(c_COMBC(U_8068,tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_fun(U_8069,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8069,tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_fun(U_8069,tc_HOL_Obool)),U_8068),c_COMBC(U_8069,tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8069,tc_prod(U_8068,U_8069)),tc_fun(U_8069,tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool)),U_8068),hAPP(c_COMBB(tc_prod(U_8068,U_8069),tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool),U_8069),c_member(tc_prod(U_8068,U_8069)))),c_Product__Type_OPair(U_8068,U_8069)))),U_8070) = hAPP(hAPP(c_COMBC(U_8068,tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_fun(U_8069,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8069,tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_fun(U_8069,tc_HOL_Obool)),U_8068),c_COMBC(U_8069,tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8069,tc_prod(U_8068,U_8069)),tc_fun(U_8069,tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool)),U_8068),hAPP(c_COMBB(tc_prod(U_8068,U_8069),tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool),U_8069),c_member(tc_prod(U_8068,U_8069)))),c_Product__Type_OPair(U_8068,U_8069)))),U_8071)
        | U_8070 != U_8071 )
      & ( U_8070 = U_8071
        | hAPP(hAPP(c_COMBC(U_8068,tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_fun(U_8069,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8069,tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_fun(U_8069,tc_HOL_Obool)),U_8068),c_COMBC(U_8069,tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8069,tc_prod(U_8068,U_8069)),tc_fun(U_8069,tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool)),U_8068),hAPP(c_COMBB(tc_prod(U_8068,U_8069),tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool),U_8069),c_member(tc_prod(U_8068,U_8069)))),c_Product__Type_OPair(U_8068,U_8069)))),U_8070) != hAPP(hAPP(c_COMBC(U_8068,tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_fun(U_8069,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8069,tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_fun(U_8069,tc_HOL_Obool)),U_8068),c_COMBC(U_8069,tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8069,tc_prod(U_8068,U_8069)),tc_fun(U_8069,tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool)),U_8068),hAPP(c_COMBB(tc_prod(U_8068,U_8069),tc_fun(tc_fun(tc_prod(U_8068,U_8069),tc_HOL_Obool),tc_HOL_Obool),U_8069),c_member(tc_prod(U_8068,U_8069)))),c_Product__Type_OPair(U_8068,U_8069)))),U_8071) ) ),
    inference(variable_rename,[status(thm)],[f_2282_1]) ).

fof(f_2282_3,plain,
    ( ! [U_8079,U_8077] :
        ( ! [U_8075,U_8073] : hAPP(hAPP(c_COMBC(U_8073,tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_fun(U_8075,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8075,tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_fun(U_8075,tc_HOL_Obool)),U_8073),c_COMBC(U_8075,tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8075,tc_prod(U_8073,U_8075)),tc_fun(U_8075,tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),U_8073),hAPP(c_COMBB(tc_prod(U_8073,U_8075),tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool),U_8075),c_member(tc_prod(U_8073,U_8075)))),c_Product__Type_OPair(U_8073,U_8075)))),U_8077) = hAPP(hAPP(c_COMBC(U_8073,tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_fun(U_8075,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8075,tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_fun(U_8075,tc_HOL_Obool)),U_8073),c_COMBC(U_8075,tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8075,tc_prod(U_8073,U_8075)),tc_fun(U_8075,tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),U_8073),hAPP(c_COMBB(tc_prod(U_8073,U_8075),tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool),U_8075),c_member(tc_prod(U_8073,U_8075)))),c_Product__Type_OPair(U_8073,U_8075)))),U_8079)
        | U_8077 != U_8079 )
    & ! [U_8078,U_8076] :
        ( ! [U_8074,U_8072] : hAPP(hAPP(c_COMBC(U_8072,tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_fun(U_8074,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8074,tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_fun(U_8074,tc_HOL_Obool)),U_8072),c_COMBC(U_8074,tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8074,tc_prod(U_8072,U_8074)),tc_fun(U_8074,tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),U_8072),hAPP(c_COMBB(tc_prod(U_8072,U_8074),tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool),U_8074),c_member(tc_prod(U_8072,U_8074)))),c_Product__Type_OPair(U_8072,U_8074)))),U_8076) != hAPP(hAPP(c_COMBC(U_8072,tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_fun(U_8074,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8074,tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_fun(U_8074,tc_HOL_Obool)),U_8072),c_COMBC(U_8074,tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8074,tc_prod(U_8072,U_8074)),tc_fun(U_8074,tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),U_8072),hAPP(c_COMBB(tc_prod(U_8072,U_8074),tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool),U_8074),c_member(tc_prod(U_8072,U_8074)))),c_Product__Type_OPair(U_8072,U_8074)))),U_8078)
        | U_8076 = U_8078 ) ),
    inference(miniscope,[status(thm)],[f_2282_2]) ).

fof(f_2282_4,plain,
    ( ! [U_8077,U_8079,U_8073,U_8075] :
        ( hAPP(hAPP(c_COMBC(U_8073,tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_fun(U_8075,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8075,tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_fun(U_8075,tc_HOL_Obool)),U_8073),c_COMBC(U_8075,tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8075,tc_prod(U_8073,U_8075)),tc_fun(U_8075,tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),U_8073),hAPP(c_COMBB(tc_prod(U_8073,U_8075),tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool),U_8075),c_member(tc_prod(U_8073,U_8075)))),c_Product__Type_OPair(U_8073,U_8075)))),U_8077) = hAPP(hAPP(c_COMBC(U_8073,tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_fun(U_8075,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8075,tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_fun(U_8075,tc_HOL_Obool)),U_8073),c_COMBC(U_8075,tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8075,tc_prod(U_8073,U_8075)),tc_fun(U_8075,tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),U_8073),hAPP(c_COMBB(tc_prod(U_8073,U_8075),tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool),U_8075),c_member(tc_prod(U_8073,U_8075)))),c_Product__Type_OPair(U_8073,U_8075)))),U_8079)
        | U_8077 != U_8079 )
    & ! [U_8072,U_8076,U_8074,U_8078] :
        ( hAPP(hAPP(c_COMBC(U_8072,tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_fun(U_8074,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8074,tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_fun(U_8074,tc_HOL_Obool)),U_8072),c_COMBC(U_8074,tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8074,tc_prod(U_8072,U_8074)),tc_fun(U_8074,tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),U_8072),hAPP(c_COMBB(tc_prod(U_8072,U_8074),tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool),U_8074),c_member(tc_prod(U_8072,U_8074)))),c_Product__Type_OPair(U_8072,U_8074)))),U_8076) != hAPP(hAPP(c_COMBC(U_8072,tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_fun(U_8074,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8074,tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_fun(U_8074,tc_HOL_Obool)),U_8072),c_COMBC(U_8074,tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8074,tc_prod(U_8072,U_8074)),tc_fun(U_8074,tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),U_8072),hAPP(c_COMBB(tc_prod(U_8072,U_8074),tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool),U_8074),c_member(tc_prod(U_8072,U_8074)))),c_Product__Type_OPair(U_8072,U_8074)))),U_8078)
        | U_8076 = U_8078 ) ),
    inference(definitional_conversion,[status(esa)],[f_2282_3]) ).

cnf(f_2282_5,plain,
    ( hAPP(hAPP(c_COMBC(U_8072,tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_fun(U_8074,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8074,tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_fun(U_8074,tc_HOL_Obool)),U_8072),c_COMBC(U_8074,tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8074,tc_prod(U_8072,U_8074)),tc_fun(U_8074,tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),U_8072),hAPP(c_COMBB(tc_prod(U_8072,U_8074),tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool),U_8074),c_member(tc_prod(U_8072,U_8074)))),c_Product__Type_OPair(U_8072,U_8074)))),U_8076) != hAPP(hAPP(c_COMBC(U_8072,tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_fun(U_8074,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8074,tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_fun(U_8074,tc_HOL_Obool)),U_8072),c_COMBC(U_8074,tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8074,tc_prod(U_8072,U_8074)),tc_fun(U_8074,tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool)),U_8072),hAPP(c_COMBB(tc_prod(U_8072,U_8074),tc_fun(tc_fun(tc_prod(U_8072,U_8074),tc_HOL_Obool),tc_HOL_Obool),U_8074),c_member(tc_prod(U_8072,U_8074)))),c_Product__Type_OPair(U_8072,U_8074)))),U_8078)
    | U_8076 = U_8078 ),
    inference(clausify,[status(thm)],[f_2282_4]) ).

cnf(f_2282_6,plain,
    ( hAPP(hAPP(c_COMBC(U_8073,tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_fun(U_8075,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8075,tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_fun(U_8075,tc_HOL_Obool)),U_8073),c_COMBC(U_8075,tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8075,tc_prod(U_8073,U_8075)),tc_fun(U_8075,tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),U_8073),hAPP(c_COMBB(tc_prod(U_8073,U_8075),tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool),U_8075),c_member(tc_prod(U_8073,U_8075)))),c_Product__Type_OPair(U_8073,U_8075)))),U_8077) = hAPP(hAPP(c_COMBC(U_8073,tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_fun(U_8075,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8075,tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_fun(U_8075,tc_HOL_Obool)),U_8073),c_COMBC(U_8075,tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8075,tc_prod(U_8073,U_8075)),tc_fun(U_8075,tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool)),U_8073),hAPP(c_COMBB(tc_prod(U_8073,U_8075),tc_fun(tc_fun(tc_prod(U_8073,U_8075),tc_HOL_Obool),tc_HOL_Obool),U_8075),c_member(tc_prod(U_8073,U_8075)))),c_Product__Type_OPair(U_8073,U_8075)))),U_8079)
    | U_8077 != U_8079 ),
    inference(clausify,[status(thm)],[f_2282_4]) ).

fof(f_2283_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_2283_2,plain,
    ! [U_8083,U_8082,U_8081,U_8080] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8080,tc_fun(U_8081,tc_HOL_Obool))),U_8082),U_8083))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8080,U_8081)),hAPP(hAPP(c_Product__Type_OPair(U_8080,U_8081),U_8082),U_8083)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8080,U_8081),tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8080,U_8081)),hAPP(hAPP(c_Product__Type_OPair(U_8080,U_8081),U_8082),U_8083)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8080,U_8081),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8080,tc_fun(U_8081,tc_HOL_Obool))),U_8082),U_8083)) ) ),
    inference(variable_rename,[status(thm)],[f_2283_1]) ).

fof(f_2283_3,plain,
    ( ! [U_8091,U_8089,U_8087,U_8085] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8085,tc_fun(U_8087,tc_HOL_Obool))),U_8089),U_8091))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8085,U_8087)),hAPP(hAPP(c_Product__Type_OPair(U_8085,U_8087),U_8089),U_8091)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8085,U_8087),tc_HOL_Obool)))) )
    & ! [U_8090,U_8088,U_8086,U_8084] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8084,U_8086)),hAPP(hAPP(c_Product__Type_OPair(U_8084,U_8086),U_8088),U_8090)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8084,U_8086),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8084,tc_fun(U_8086,tc_HOL_Obool))),U_8088),U_8090)) ) ),
    inference(miniscope,[status(thm)],[f_2283_2]) ).

fof(f_2283_4,plain,
    ( ! [U_8085,U_8087,U_8089,U_8091] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8085,tc_fun(U_8087,tc_HOL_Obool))),U_8089),U_8091))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8085,U_8087)),hAPP(hAPP(c_Product__Type_OPair(U_8085,U_8087),U_8089),U_8091)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8085,U_8087),tc_HOL_Obool)))) )
    & ! [U_8088,U_8086,U_8090,U_8084] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8084,U_8086)),hAPP(hAPP(c_Product__Type_OPair(U_8084,U_8086),U_8088),U_8090)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8084,U_8086),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8084,tc_fun(U_8086,tc_HOL_Obool))),U_8088),U_8090)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2283_3]) ).

cnf(f_2283_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8084,U_8086)),hAPP(hAPP(c_Product__Type_OPair(U_8084,U_8086),U_8088),U_8090)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8084,U_8086),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8084,tc_fun(U_8086,tc_HOL_Obool))),U_8088),U_8090)) ),
    inference(clausify,[status(thm)],[f_2283_4]) ).

cnf(f_2283_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8085,tc_fun(U_8087,tc_HOL_Obool))),U_8089),U_8091))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8085,U_8087)),hAPP(hAPP(c_Product__Type_OPair(U_8085,U_8087),U_8089),U_8091)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8085,U_8087),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2283_4]) ).

fof(f_2284_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_2284_2,plain,
    ! [U_8094,U_8093,U_8092] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8092,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8092,tc_fun(U_8092,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8092)),U_8093)),hAPP(hAPP(c_COMBC(U_8092,tc_fun(U_8092,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8092)),U_8094)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8092,tc_HOL_Obool)),U_8093),U_8094)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8092,tc_HOL_Obool)),U_8093),U_8094))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8092,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8092,tc_fun(U_8092,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8092)),U_8093)),hAPP(hAPP(c_COMBC(U_8092,tc_fun(U_8092,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8092)),U_8094))) ) ),
    inference(variable_rename,[status(thm)],[f_2284_1]) ).

fof(f_2284_3,plain,
    ( ! [U_8100,U_8098,U_8096] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8096,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8096,tc_fun(U_8096,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8096)),U_8098)),hAPP(hAPP(c_COMBC(U_8096,tc_fun(U_8096,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8096)),U_8100)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8096,tc_HOL_Obool)),U_8098),U_8100)) )
    & ! [U_8099,U_8097,U_8095] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8095,tc_HOL_Obool)),U_8097),U_8099))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8095,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8095,tc_fun(U_8095,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8095)),U_8097)),hAPP(hAPP(c_COMBC(U_8095,tc_fun(U_8095,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8095)),U_8099))) ) ),
    inference(miniscope,[status(thm)],[f_2284_2]) ).

fof(f_2284_4,plain,
    ( ! [U_8098,U_8100,U_8096] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8096,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8096,tc_fun(U_8096,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8096)),U_8098)),hAPP(hAPP(c_COMBC(U_8096,tc_fun(U_8096,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8096)),U_8100)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8096,tc_HOL_Obool)),U_8098),U_8100)) )
    & ! [U_8099,U_8097,U_8095] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8095,tc_HOL_Obool)),U_8097),U_8099))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8095,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8095,tc_fun(U_8095,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8095)),U_8097)),hAPP(hAPP(c_COMBC(U_8095,tc_fun(U_8095,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8095)),U_8099))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2284_3]) ).

cnf(f_2284_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8095,tc_HOL_Obool)),U_8097),U_8099))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8095,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8095,tc_fun(U_8095,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8095)),U_8097)),hAPP(hAPP(c_COMBC(U_8095,tc_fun(U_8095,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8095)),U_8099))) ),
    inference(clausify,[status(thm)],[f_2284_4]) ).

cnf(f_2284_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8096,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8096,tc_fun(U_8096,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8096)),U_8098)),hAPP(hAPP(c_COMBC(U_8096,tc_fun(U_8096,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8096)),U_8100)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8096,tc_HOL_Obool)),U_8098),U_8100)) ),
    inference(clausify,[status(thm)],[f_2284_4]) ).

fof(f_2285_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_2285_2,plain,
    ! [U_8103,U_8102,U_8101] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8101),U_8102),hAPP(hAPP(c_Set_Oinsert(U_8101),U_8103),c_Orderings_Obot__class_Obot(tc_fun(U_8101,tc_HOL_Obool)))))
        | U_8102 != U_8103 )
      & ( U_8102 = U_8103
        | ~ hBOOL(hAPP(hAPP(c_member(U_8101),U_8102),hAPP(hAPP(c_Set_Oinsert(U_8101),U_8103),c_Orderings_Obot__class_Obot(tc_fun(U_8101,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[f_2285_1]) ).

fof(f_2285_3,plain,
    ( ! [U_8109,U_8107] :
        ( ! [U_8105] : hBOOL(hAPP(hAPP(c_member(U_8105),U_8107),hAPP(hAPP(c_Set_Oinsert(U_8105),U_8109),c_Orderings_Obot__class_Obot(tc_fun(U_8105,tc_HOL_Obool)))))
        | U_8107 != U_8109 )
    & ! [U_8108,U_8106] :
        ( ! [U_8104] : ~ hBOOL(hAPP(hAPP(c_member(U_8104),U_8106),hAPP(hAPP(c_Set_Oinsert(U_8104),U_8108),c_Orderings_Obot__class_Obot(tc_fun(U_8104,tc_HOL_Obool)))))
        | U_8106 = U_8108 ) ),
    inference(miniscope,[status(thm)],[f_2285_2]) ).

fof(f_2285_4,plain,
    ( ! [U_8109,U_8105,U_8107] :
        ( hBOOL(hAPP(hAPP(c_member(U_8105),U_8107),hAPP(hAPP(c_Set_Oinsert(U_8105),U_8109),c_Orderings_Obot__class_Obot(tc_fun(U_8105,tc_HOL_Obool)))))
        | U_8107 != U_8109 )
    & ! [U_8106,U_8104,U_8108] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8104),U_8106),hAPP(hAPP(c_Set_Oinsert(U_8104),U_8108),c_Orderings_Obot__class_Obot(tc_fun(U_8104,tc_HOL_Obool)))))
        | U_8106 = U_8108 ) ),
    inference(definitional_conversion,[status(esa)],[f_2285_3]) ).

cnf(f_2285_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8104),U_8106),hAPP(hAPP(c_Set_Oinsert(U_8104),U_8108),c_Orderings_Obot__class_Obot(tc_fun(U_8104,tc_HOL_Obool)))))
    | U_8106 = U_8108 ),
    inference(clausify,[status(thm)],[f_2285_4]) ).

cnf(f_2285_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8105),U_8107),hAPP(hAPP(c_Set_Oinsert(U_8105),U_8109),c_Orderings_Obot__class_Obot(tc_fun(U_8105,tc_HOL_Obool)))))
    | U_8107 != U_8109 ),
    inference(clausify,[status(thm)],[f_2285_4]) ).

fof(f_2286_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_2286_2,plain,
    ! [U_8112,U_8111,U_8110] :
      ( U_8111 = U_8112
      | ~ hBOOL(hAPP(hAPP(c_member(U_8110),U_8111),hAPP(hAPP(c_Set_Oinsert(U_8110),U_8112),c_Orderings_Obot__class_Obot(tc_fun(U_8110,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_2286_1]) ).

fof(f_2286_3,plain,
    ! [U_8112,U_8111] :
      ( ! [U_8110] : ~ hBOOL(hAPP(hAPP(c_member(U_8110),U_8111),hAPP(hAPP(c_Set_Oinsert(U_8110),U_8112),c_Orderings_Obot__class_Obot(tc_fun(U_8110,tc_HOL_Obool)))))
      | U_8111 = U_8112 ),
    inference(miniscope,[status(thm)],[f_2286_2]) ).

fof(f_2286_4,plain,
    ! [U_8110,U_8111,U_8112] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_8110),U_8111),hAPP(hAPP(c_Set_Oinsert(U_8110),U_8112),c_Orderings_Obot__class_Obot(tc_fun(U_8110,tc_HOL_Obool)))))
      | U_8111 = U_8112 ),
    inference(definitional_conversion,[status(esa)],[f_2286_3]) ).

cnf(f_2286_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8110),U_8111),hAPP(hAPP(c_Set_Oinsert(U_8110),U_8112),c_Orderings_Obot__class_Obot(tc_fun(U_8110,tc_HOL_Obool)))))
    | U_8111 = U_8112 ),
    inference(clausify,[status(thm)],[f_2286_4]) ).

fof(f_2287_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_2287_2,plain,
    ! [U_8116,U_8115,U_8114,U_8113] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8113,tc_HOL_Obool)),U_8115),hAPP(hAPP(c_Set_Oinsert(U_8113),U_8114),U_8116)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8113,tc_HOL_Obool)),U_8115),U_8116)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8113,tc_HOL_Obool)),U_8115),U_8116))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8113,tc_HOL_Obool)),U_8115),hAPP(hAPP(c_Set_Oinsert(U_8113),U_8114),U_8116))) ) )
      | hBOOL(hAPP(hAPP(c_member(U_8113),U_8114),U_8115)) ),
    inference(variable_rename,[status(thm)],[f_2287_1]) ).

fof(f_2287_3,plain,
    ( ! [U_8113,U_8114,U_8115,U_8116] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8113,tc_HOL_Obool)),U_8115),hAPP(hAPP(c_Set_Oinsert(U_8113),U_8114),U_8116)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8113,tc_HOL_Obool)),U_8115),U_8116))
        | ~ sP695(U_8113,U_8114,U_8115,U_8116) )
    & ! [U_8113,U_8114,U_8115,U_8116] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8113,tc_HOL_Obool)),U_8115),U_8116))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8113,tc_HOL_Obool)),U_8115),hAPP(hAPP(c_Set_Oinsert(U_8113),U_8114),U_8116)))
        | ~ sP695(U_8113,U_8114,U_8115,U_8116) )
    & ! [U_8113,U_8114,U_8115,U_8116] :
        ( sP695(U_8113,U_8114,U_8115,U_8116)
        | hBOOL(hAPP(hAPP(c_member(U_8113),U_8114),U_8115)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP695])],[f_2287_2]) ).

cnf(f_2287_4,plain,
    ( sP695(U_8113,U_8114,U_8115,U_8116)
    | hBOOL(hAPP(hAPP(c_member(U_8113),U_8114),U_8115)) ),
    inference(clausify,[status(thm)],[f_2287_3]) ).

cnf(f_2287_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8113,tc_HOL_Obool)),U_8115),U_8116))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8113,tc_HOL_Obool)),U_8115),hAPP(hAPP(c_Set_Oinsert(U_8113),U_8114),U_8116)))
    | ~ sP695(U_8113,U_8114,U_8115,U_8116) ),
    inference(clausify,[status(thm)],[f_2287_3]) ).

cnf(f_2287_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8113,tc_HOL_Obool)),U_8115),hAPP(hAPP(c_Set_Oinsert(U_8113),U_8114),U_8116)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8113,tc_HOL_Obool)),U_8115),U_8116))
    | ~ sP695(U_8113,U_8114,U_8115,U_8116) ),
    inference(clausify,[status(thm)],[f_2287_3]) ).

fof(f_2288_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_2288_2,plain,
    ! [U_8120,U_8119,U_8118,U_8117] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8117,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8117),U_8118),U_8119)),U_8120))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8117,tc_HOL_Obool)),U_8119),U_8120))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8117),U_8118),U_8120)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8117,tc_HOL_Obool)),U_8119),U_8120))
          & hBOOL(hAPP(hAPP(c_member(U_8117),U_8118),U_8120)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8117,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8117),U_8118),U_8119)),U_8120)) ) ),
    inference(variable_rename,[status(thm)],[f_2288_1]) ).

fof(f_2288_3,plain,
    ( ! [U_8128,U_8126,U_8124,U_8122] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8122,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8122),U_8124),U_8126)),U_8128))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8122,tc_HOL_Obool)),U_8126),U_8128))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8122),U_8124),U_8128)) )
    & ! [U_8127,U_8125,U_8123,U_8121] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8121,tc_HOL_Obool)),U_8125),U_8127))
          & hBOOL(hAPP(hAPP(c_member(U_8121),U_8123),U_8127)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8121,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8121),U_8123),U_8125)),U_8127)) ) ),
    inference(miniscope,[status(thm)],[f_2288_2]) ).

fof(f_2288_4,plain,
    ( ! [U_8125,U_8127,U_8121,U_8123] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8121,tc_HOL_Obool)),U_8125),U_8127))
        | ~ sP696(U_8125,U_8127,U_8121,U_8123) )
    & ! [U_8125,U_8127,U_8121,U_8123] :
        ( hBOOL(hAPP(hAPP(c_member(U_8121),U_8123),U_8127))
        | ~ sP696(U_8125,U_8127,U_8121,U_8123) )
    & ! [U_8126,U_8124,U_8128,U_8122] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8122,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8122),U_8124),U_8126)),U_8128))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8122,tc_HOL_Obool)),U_8126),U_8128))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8122),U_8124),U_8128)) )
    & ! [U_8125,U_8127,U_8121,U_8123] :
        ( sP696(U_8125,U_8127,U_8121,U_8123)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8121,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8121),U_8123),U_8125)),U_8127)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP696])],[f_2288_3]) ).

cnf(f_2288_5,plain,
    ( sP696(U_8125,U_8127,U_8121,U_8123)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8121,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8121),U_8123),U_8125)),U_8127)) ),
    inference(clausify,[status(thm)],[f_2288_4]) ).

cnf(f_2288_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8122,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8122),U_8124),U_8126)),U_8128))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8122,tc_HOL_Obool)),U_8126),U_8128))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8122),U_8124),U_8128)) ),
    inference(clausify,[status(thm)],[f_2288_4]) ).

cnf(f_2288_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8121),U_8123),U_8127))
    | ~ sP696(U_8125,U_8127,U_8121,U_8123) ),
    inference(clausify,[status(thm)],[f_2288_4]) ).

cnf(f_2288_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8121,tc_HOL_Obool)),U_8125),U_8127))
    | ~ sP696(U_8125,U_8127,U_8121,U_8123) ),
    inference(clausify,[status(thm)],[f_2288_4]) ).

fof(f_2289_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_2289_2,plain,
    ! [U_8132,U_8131,U_8130,U_8129] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8129,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8129),U_8130),U_8132)),U_8131) = hAPP(hAPP(c_Set_Oinsert(U_8129),U_8130),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8129,tc_HOL_Obool)),U_8132),U_8131))
        | hBOOL(hAPP(hAPP(c_member(U_8129),U_8130),U_8131)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8129,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8129),U_8130),U_8132)),U_8131) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8129,tc_HOL_Obool)),U_8132),U_8131)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8129),U_8130),U_8131)) ) ),
    inference(variable_rename,[status(thm)],[f_2289_1]) ).

fof(f_2289_3,plain,
    ( ! [U_8140,U_8138,U_8136,U_8134] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8134,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8134),U_8136),U_8140)),U_8138) = hAPP(hAPP(c_Set_Oinsert(U_8134),U_8136),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8134,tc_HOL_Obool)),U_8140),U_8138))
        | hBOOL(hAPP(hAPP(c_member(U_8134),U_8136),U_8138)) )
    & ! [U_8139,U_8137,U_8135,U_8133] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8133,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8133),U_8135),U_8139)),U_8137) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8133,tc_HOL_Obool)),U_8139),U_8137)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8133),U_8135),U_8137)) ) ),
    inference(miniscope,[status(thm)],[f_2289_2]) ).

fof(f_2289_4,plain,
    ( ! [U_8134,U_8136,U_8138,U_8140] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8134,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8134),U_8136),U_8140)),U_8138) = hAPP(hAPP(c_Set_Oinsert(U_8134),U_8136),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8134,tc_HOL_Obool)),U_8140),U_8138))
        | hBOOL(hAPP(hAPP(c_member(U_8134),U_8136),U_8138)) )
    & ! [U_8137,U_8139,U_8135,U_8133] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8133,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8133),U_8135),U_8139)),U_8137) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8133,tc_HOL_Obool)),U_8139),U_8137)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8133),U_8135),U_8137)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2289_3]) ).

cnf(f_2289_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8133,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8133),U_8135),U_8139)),U_8137) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8133,tc_HOL_Obool)),U_8139),U_8137)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8133),U_8135),U_8137)) ),
    inference(clausify,[status(thm)],[f_2289_4]) ).

cnf(f_2289_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8134,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8134),U_8136),U_8140)),U_8138) = hAPP(hAPP(c_Set_Oinsert(U_8134),U_8136),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8134,tc_HOL_Obool)),U_8140),U_8138))
    | hBOOL(hAPP(hAPP(c_member(U_8134),U_8136),U_8138)) ),
    inference(clausify,[status(thm)],[f_2289_4]) ).

fof(f_2290_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_2290_2,plain,
    ! [U_8144,U_8143,U_8142,U_8141] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8141,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8141),U_8142),U_8144)),U_8143) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8141,tc_HOL_Obool)),U_8144),U_8143)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8141),U_8142),U_8143)) ),
    inference(variable_rename,[status(thm)],[f_2290_1]) ).

fof(f_2290_3,plain,
    ! [U_8141,U_8142,U_8143,U_8144] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8141,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8141),U_8142),U_8144)),U_8143) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8141,tc_HOL_Obool)),U_8144),U_8143)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8141),U_8142),U_8143)) ),
    inference(definitional_conversion,[status(esa)],[f_2290_2]) ).

cnf(f_2290_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8141,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8141),U_8142),U_8144)),U_8143) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8141,tc_HOL_Obool)),U_8144),U_8143)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8141),U_8142),U_8143)) ),
    inference(clausify,[status(thm)],[f_2290_3]) ).

fof(f_2291_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_2291_2,plain,
    ! [U_8147,U_8146,U_8145] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8145),U_8146),c_Option_Oset(U_8145,U_8147)))
        | U_8147 != hAPP(c_Option_Ooption_OSome(U_8145),U_8146) )
      & ( U_8147 = hAPP(c_Option_Ooption_OSome(U_8145),U_8146)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8145),U_8146),c_Option_Oset(U_8145,U_8147))) ) ),
    inference(variable_rename,[status(thm)],[f_2291_1]) ).

fof(f_2291_3,plain,
    ( ! [U_8153,U_8151,U_8149] :
        ( hBOOL(hAPP(hAPP(c_member(U_8149),U_8151),c_Option_Oset(U_8149,U_8153)))
        | U_8153 != hAPP(c_Option_Ooption_OSome(U_8149),U_8151) )
    & ! [U_8152,U_8150,U_8148] :
        ( U_8152 = hAPP(c_Option_Ooption_OSome(U_8148),U_8150)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8148),U_8150),c_Option_Oset(U_8148,U_8152))) ) ),
    inference(miniscope,[status(thm)],[f_2291_2]) ).

fof(f_2291_4,plain,
    ( ! [U_8149,U_8151,U_8153] :
        ( hBOOL(hAPP(hAPP(c_member(U_8149),U_8151),c_Option_Oset(U_8149,U_8153)))
        | U_8153 != hAPP(c_Option_Ooption_OSome(U_8149),U_8151) )
    & ! [U_8150,U_8148,U_8152] :
        ( U_8152 = hAPP(c_Option_Ooption_OSome(U_8148),U_8150)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8148),U_8150),c_Option_Oset(U_8148,U_8152))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2291_3]) ).

cnf(f_2291_5,plain,
    ( U_8152 = hAPP(c_Option_Ooption_OSome(U_8148),U_8150)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8148),U_8150),c_Option_Oset(U_8148,U_8152))) ),
    inference(clausify,[status(thm)],[f_2291_4]) ).

cnf(f_2291_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8149),U_8151),c_Option_Oset(U_8149,U_8153)))
    | U_8153 != hAPP(c_Option_Ooption_OSome(U_8149),U_8151) ),
    inference(clausify,[status(thm)],[f_2291_4]) ).

fof(f_2292_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_2292_2,plain,
    ! [U_8157,U_8156,U_8155,U_8154] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8154,tc_fun(U_8155,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8154,tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_fun(U_8155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8155,tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_fun(U_8155,tc_HOL_Obool)),U_8154),c_COMBC(U_8155,tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8155,tc_prod(U_8154,U_8155)),tc_fun(U_8155,tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool)),U_8154),hAPP(c_COMBB(tc_prod(U_8154,U_8155),tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool),U_8155),c_member(tc_prod(U_8154,U_8155)))),c_Product__Type_OPair(U_8154,U_8155)))),U_8156)),hAPP(hAPP(c_COMBC(U_8154,tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_fun(U_8155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8155,tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_fun(U_8155,tc_HOL_Obool)),U_8154),c_COMBC(U_8155,tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8155,tc_prod(U_8154,U_8155)),tc_fun(U_8155,tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool)),U_8154),hAPP(c_COMBB(tc_prod(U_8154,U_8155),tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool),U_8155),c_member(tc_prod(U_8154,U_8155)))),c_Product__Type_OPair(U_8154,U_8155)))),U_8157)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool)),U_8156),U_8157)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool)),U_8156),U_8157))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8154,tc_fun(U_8155,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8154,tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_fun(U_8155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8155,tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_fun(U_8155,tc_HOL_Obool)),U_8154),c_COMBC(U_8155,tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8155,tc_prod(U_8154,U_8155)),tc_fun(U_8155,tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool)),U_8154),hAPP(c_COMBB(tc_prod(U_8154,U_8155),tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool),U_8155),c_member(tc_prod(U_8154,U_8155)))),c_Product__Type_OPair(U_8154,U_8155)))),U_8156)),hAPP(hAPP(c_COMBC(U_8154,tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_fun(U_8155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8155,tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_fun(U_8155,tc_HOL_Obool)),U_8154),c_COMBC(U_8155,tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8155,tc_prod(U_8154,U_8155)),tc_fun(U_8155,tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool)),U_8154),hAPP(c_COMBB(tc_prod(U_8154,U_8155),tc_fun(tc_fun(tc_prod(U_8154,U_8155),tc_HOL_Obool),tc_HOL_Obool),U_8155),c_member(tc_prod(U_8154,U_8155)))),c_Product__Type_OPair(U_8154,U_8155)))),U_8157))) ) ),
    inference(variable_rename,[status(thm)],[f_2292_1]) ).

fof(f_2292_3,plain,
    ( ! [U_8165,U_8163,U_8161,U_8159] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8159,tc_fun(U_8161,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8159,tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_fun(U_8161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8161,tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_fun(U_8161,tc_HOL_Obool)),U_8159),c_COMBC(U_8161,tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8161,tc_prod(U_8159,U_8161)),tc_fun(U_8161,tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),U_8159),hAPP(c_COMBB(tc_prod(U_8159,U_8161),tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool),U_8161),c_member(tc_prod(U_8159,U_8161)))),c_Product__Type_OPair(U_8159,U_8161)))),U_8163)),hAPP(hAPP(c_COMBC(U_8159,tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_fun(U_8161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8161,tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_fun(U_8161,tc_HOL_Obool)),U_8159),c_COMBC(U_8161,tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8161,tc_prod(U_8159,U_8161)),tc_fun(U_8161,tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),U_8159),hAPP(c_COMBB(tc_prod(U_8159,U_8161),tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool),U_8161),c_member(tc_prod(U_8159,U_8161)))),c_Product__Type_OPair(U_8159,U_8161)))),U_8165)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool)),U_8163),U_8165)) )
    & ! [U_8164,U_8162,U_8160,U_8158] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool)),U_8162),U_8164))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8158,tc_fun(U_8160,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8158,tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_fun(U_8160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8160,tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_fun(U_8160,tc_HOL_Obool)),U_8158),c_COMBC(U_8160,tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8160,tc_prod(U_8158,U_8160)),tc_fun(U_8160,tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),U_8158),hAPP(c_COMBB(tc_prod(U_8158,U_8160),tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool),U_8160),c_member(tc_prod(U_8158,U_8160)))),c_Product__Type_OPair(U_8158,U_8160)))),U_8162)),hAPP(hAPP(c_COMBC(U_8158,tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_fun(U_8160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8160,tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_fun(U_8160,tc_HOL_Obool)),U_8158),c_COMBC(U_8160,tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8160,tc_prod(U_8158,U_8160)),tc_fun(U_8160,tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),U_8158),hAPP(c_COMBB(tc_prod(U_8158,U_8160),tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool),U_8160),c_member(tc_prod(U_8158,U_8160)))),c_Product__Type_OPair(U_8158,U_8160)))),U_8164))) ) ),
    inference(miniscope,[status(thm)],[f_2292_2]) ).

fof(f_2292_4,plain,
    ( ! [U_8159,U_8161,U_8163,U_8165] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8159,tc_fun(U_8161,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8159,tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_fun(U_8161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8161,tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_fun(U_8161,tc_HOL_Obool)),U_8159),c_COMBC(U_8161,tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8161,tc_prod(U_8159,U_8161)),tc_fun(U_8161,tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),U_8159),hAPP(c_COMBB(tc_prod(U_8159,U_8161),tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool),U_8161),c_member(tc_prod(U_8159,U_8161)))),c_Product__Type_OPair(U_8159,U_8161)))),U_8163)),hAPP(hAPP(c_COMBC(U_8159,tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_fun(U_8161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8161,tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_fun(U_8161,tc_HOL_Obool)),U_8159),c_COMBC(U_8161,tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8161,tc_prod(U_8159,U_8161)),tc_fun(U_8161,tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),U_8159),hAPP(c_COMBB(tc_prod(U_8159,U_8161),tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool),U_8161),c_member(tc_prod(U_8159,U_8161)))),c_Product__Type_OPair(U_8159,U_8161)))),U_8165)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool)),U_8163),U_8165)) )
    & ! [U_8164,U_8160,U_8162,U_8158] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool)),U_8162),U_8164))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8158,tc_fun(U_8160,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8158,tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_fun(U_8160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8160,tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_fun(U_8160,tc_HOL_Obool)),U_8158),c_COMBC(U_8160,tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8160,tc_prod(U_8158,U_8160)),tc_fun(U_8160,tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),U_8158),hAPP(c_COMBB(tc_prod(U_8158,U_8160),tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool),U_8160),c_member(tc_prod(U_8158,U_8160)))),c_Product__Type_OPair(U_8158,U_8160)))),U_8162)),hAPP(hAPP(c_COMBC(U_8158,tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_fun(U_8160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8160,tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_fun(U_8160,tc_HOL_Obool)),U_8158),c_COMBC(U_8160,tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8160,tc_prod(U_8158,U_8160)),tc_fun(U_8160,tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),U_8158),hAPP(c_COMBB(tc_prod(U_8158,U_8160),tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool),U_8160),c_member(tc_prod(U_8158,U_8160)))),c_Product__Type_OPair(U_8158,U_8160)))),U_8164))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2292_3]) ).

cnf(f_2292_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool)),U_8162),U_8164))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8158,tc_fun(U_8160,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8158,tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_fun(U_8160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8160,tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_fun(U_8160,tc_HOL_Obool)),U_8158),c_COMBC(U_8160,tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8160,tc_prod(U_8158,U_8160)),tc_fun(U_8160,tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),U_8158),hAPP(c_COMBB(tc_prod(U_8158,U_8160),tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool),U_8160),c_member(tc_prod(U_8158,U_8160)))),c_Product__Type_OPair(U_8158,U_8160)))),U_8162)),hAPP(hAPP(c_COMBC(U_8158,tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_fun(U_8160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8160,tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_fun(U_8160,tc_HOL_Obool)),U_8158),c_COMBC(U_8160,tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8160,tc_prod(U_8158,U_8160)),tc_fun(U_8160,tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool)),U_8158),hAPP(c_COMBB(tc_prod(U_8158,U_8160),tc_fun(tc_fun(tc_prod(U_8158,U_8160),tc_HOL_Obool),tc_HOL_Obool),U_8160),c_member(tc_prod(U_8158,U_8160)))),c_Product__Type_OPair(U_8158,U_8160)))),U_8164))) ),
    inference(clausify,[status(thm)],[f_2292_4]) ).

cnf(f_2292_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8159,tc_fun(U_8161,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8159,tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_fun(U_8161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8161,tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_fun(U_8161,tc_HOL_Obool)),U_8159),c_COMBC(U_8161,tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8161,tc_prod(U_8159,U_8161)),tc_fun(U_8161,tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),U_8159),hAPP(c_COMBB(tc_prod(U_8159,U_8161),tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool),U_8161),c_member(tc_prod(U_8159,U_8161)))),c_Product__Type_OPair(U_8159,U_8161)))),U_8163)),hAPP(hAPP(c_COMBC(U_8159,tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_fun(U_8161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8161,tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_fun(U_8161,tc_HOL_Obool)),U_8159),c_COMBC(U_8161,tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8161,tc_prod(U_8159,U_8161)),tc_fun(U_8161,tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool)),U_8159),hAPP(c_COMBB(tc_prod(U_8159,U_8161),tc_fun(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool),tc_HOL_Obool),U_8161),c_member(tc_prod(U_8159,U_8161)))),c_Product__Type_OPair(U_8159,U_8161)))),U_8165)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8159,U_8161),tc_HOL_Obool)),U_8163),U_8165)) ),
    inference(clausify,[status(thm)],[f_2292_4]) ).

fof(f_2293_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_2293_2,plain,
    ! [U_8168,U_8167,U_8166] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8166,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8166),U_8167),U_8168)),hAPP(hAPP(c_Set_Oinsert(U_8166),U_8167),c_Orderings_Obot__class_Obot(tc_fun(U_8166,tc_HOL_Obool)))) = U_8168
      | hBOOL(hAPP(hAPP(c_member(U_8166),U_8167),U_8168)) ),
    inference(variable_rename,[status(thm)],[f_2293_1]) ).

fof(f_2293_3,plain,
    ! [U_8166,U_8167,U_8168] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8166,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8166),U_8167),U_8168)),hAPP(hAPP(c_Set_Oinsert(U_8166),U_8167),c_Orderings_Obot__class_Obot(tc_fun(U_8166,tc_HOL_Obool)))) = U_8168
      | hBOOL(hAPP(hAPP(c_member(U_8166),U_8167),U_8168)) ),
    inference(definitional_conversion,[status(esa)],[f_2293_2]) ).

cnf(f_2293_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8166,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8166),U_8167),U_8168)),hAPP(hAPP(c_Set_Oinsert(U_8166),U_8167),c_Orderings_Obot__class_Obot(tc_fun(U_8166,tc_HOL_Obool)))) = U_8168
    | hBOOL(hAPP(hAPP(c_member(U_8166),U_8167),U_8168)) ),
    inference(clausify,[status(thm)],[f_2293_3]) ).

fof(f_2294_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_2294_2,plain,
    ! [U_8171,U_8170,U_8169] :
      ( hAPP(hAPP(c_Set_Oinsert(U_8169),U_8170),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8169,tc_HOL_Obool)),U_8171),hAPP(hAPP(c_Set_Oinsert(U_8169),U_8170),c_Orderings_Obot__class_Obot(tc_fun(U_8169,tc_HOL_Obool))))) = U_8171
      | ~ hBOOL(hAPP(hAPP(c_member(U_8169),U_8170),U_8171)) ),
    inference(variable_rename,[status(thm)],[f_2294_1]) ).

fof(f_2294_3,plain,
    ! [U_8169,U_8170,U_8171] :
      ( hAPP(hAPP(c_Set_Oinsert(U_8169),U_8170),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8169,tc_HOL_Obool)),U_8171),hAPP(hAPP(c_Set_Oinsert(U_8169),U_8170),c_Orderings_Obot__class_Obot(tc_fun(U_8169,tc_HOL_Obool))))) = U_8171
      | ~ hBOOL(hAPP(hAPP(c_member(U_8169),U_8170),U_8171)) ),
    inference(definitional_conversion,[status(esa)],[f_2294_2]) ).

cnf(f_2294_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_8169),U_8170),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8169,tc_HOL_Obool)),U_8171),hAPP(hAPP(c_Set_Oinsert(U_8169),U_8170),c_Orderings_Obot__class_Obot(tc_fun(U_8169,tc_HOL_Obool))))) = U_8171
    | ~ hBOOL(hAPP(hAPP(c_member(U_8169),U_8170),U_8171)) ),
    inference(clausify,[status(thm)],[f_2294_3]) ).

fof(f_2295_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_2295_2,plain,
    ! [U_8175,U_8174,U_8173,U_8172] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8172,tc_HOL_Obool)),U_8173),hAPP(hAPP(c_Set_Oinsert(U_8172),U_8174),U_8175)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8172,tc_HOL_Obool)),U_8173),U_8175))
          & ~ hBOOL(hAPP(hAPP(c_member(U_8172),U_8174),U_8173)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8172,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8172,tc_HOL_Obool)),U_8173),hAPP(hAPP(c_Set_Oinsert(U_8172),U_8174),c_Orderings_Obot__class_Obot(tc_fun(U_8172,tc_HOL_Obool))))),U_8175))
          & hBOOL(hAPP(hAPP(c_member(U_8172),U_8174),U_8173)) ) )
      & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8172,tc_HOL_Obool)),U_8173),U_8175))
            | hBOOL(hAPP(hAPP(c_member(U_8172),U_8174),U_8173)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8172,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8172,tc_HOL_Obool)),U_8173),hAPP(hAPP(c_Set_Oinsert(U_8172),U_8174),c_Orderings_Obot__class_Obot(tc_fun(U_8172,tc_HOL_Obool))))),U_8175))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8172),U_8174),U_8173)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8172,tc_HOL_Obool)),U_8173),hAPP(hAPP(c_Set_Oinsert(U_8172),U_8174),U_8175))) ) ),
    inference(variable_rename,[status(thm)],[f_2295_1]) ).

fof(f_2295_3,plain,
    ( ! [U_8183,U_8181,U_8179,U_8177] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8177,tc_HOL_Obool)),U_8179),hAPP(hAPP(c_Set_Oinsert(U_8177),U_8181),U_8183)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8177,tc_HOL_Obool)),U_8179),U_8183))
          & ~ hBOOL(hAPP(hAPP(c_member(U_8177),U_8181),U_8179)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8177,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8177,tc_HOL_Obool)),U_8179),hAPP(hAPP(c_Set_Oinsert(U_8177),U_8181),c_Orderings_Obot__class_Obot(tc_fun(U_8177,tc_HOL_Obool))))),U_8183))
          & hBOOL(hAPP(hAPP(c_member(U_8177),U_8181),U_8179)) ) )
    & ! [U_8182,U_8180,U_8178,U_8176] :
        ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8176,tc_HOL_Obool)),U_8178),U_8182))
            | hBOOL(hAPP(hAPP(c_member(U_8176),U_8180),U_8178)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8176,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8176,tc_HOL_Obool)),U_8178),hAPP(hAPP(c_Set_Oinsert(U_8176),U_8180),c_Orderings_Obot__class_Obot(tc_fun(U_8176,tc_HOL_Obool))))),U_8182))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8176),U_8180),U_8178)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8176,tc_HOL_Obool)),U_8178),hAPP(hAPP(c_Set_Oinsert(U_8176),U_8180),U_8182))) ) ),
    inference(miniscope,[status(thm)],[f_2295_2]) ).

fof(f_2295_4,plain,
    ( ! [U_8179,U_8177,U_8181,U_8183] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8177,tc_HOL_Obool)),U_8179),U_8183))
        | ~ sP699(U_8179,U_8177,U_8181,U_8183) )
    & ! [U_8179,U_8177,U_8181,U_8183] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8177),U_8181),U_8179))
        | ~ sP699(U_8179,U_8177,U_8181,U_8183) )
    & ! [U_8179,U_8177,U_8181,U_8183] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8177,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8177,tc_HOL_Obool)),U_8179),hAPP(hAPP(c_Set_Oinsert(U_8177),U_8181),c_Orderings_Obot__class_Obot(tc_fun(U_8177,tc_HOL_Obool))))),U_8183))
        | ~ sP698(U_8179,U_8177,U_8181,U_8183) )
    & ! [U_8179,U_8177,U_8181,U_8183] :
        ( hBOOL(hAPP(hAPP(c_member(U_8177),U_8181),U_8179))
        | ~ sP698(U_8179,U_8177,U_8181,U_8183) )
    & ! [U_8182,U_8176,U_8178,U_8180] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8176,tc_HOL_Obool)),U_8178),U_8182))
        | hBOOL(hAPP(hAPP(c_member(U_8176),U_8180),U_8178))
        | ~ sP697(U_8182,U_8176,U_8178,U_8180) )
    & ! [U_8182,U_8176,U_8178,U_8180] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8176,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8176,tc_HOL_Obool)),U_8178),hAPP(hAPP(c_Set_Oinsert(U_8176),U_8180),c_Orderings_Obot__class_Obot(tc_fun(U_8176,tc_HOL_Obool))))),U_8182))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8176),U_8180),U_8178))
        | ~ sP697(U_8182,U_8176,U_8178,U_8180) )
    & ! [U_8179,U_8177,U_8181,U_8183] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8177,tc_HOL_Obool)),U_8179),hAPP(hAPP(c_Set_Oinsert(U_8177),U_8181),U_8183)))
        | sP699(U_8179,U_8177,U_8181,U_8183)
        | sP698(U_8179,U_8177,U_8181,U_8183) )
    & ! [U_8182,U_8176,U_8178,U_8180] :
        ( sP697(U_8182,U_8176,U_8178,U_8180)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8176,tc_HOL_Obool)),U_8178),hAPP(hAPP(c_Set_Oinsert(U_8176),U_8180),U_8182))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP697,sP698,sP699])],[f_2295_3]) ).

cnf(f_2295_5,plain,
    ( sP697(U_8182,U_8176,U_8178,U_8180)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8176,tc_HOL_Obool)),U_8178),hAPP(hAPP(c_Set_Oinsert(U_8176),U_8180),U_8182))) ),
    inference(clausify,[status(thm)],[f_2295_4]) ).

cnf(f_2295_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8177,tc_HOL_Obool)),U_8179),hAPP(hAPP(c_Set_Oinsert(U_8177),U_8181),U_8183)))
    | sP699(U_8179,U_8177,U_8181,U_8183)
    | sP698(U_8179,U_8177,U_8181,U_8183) ),
    inference(clausify,[status(thm)],[f_2295_4]) ).

cnf(f_2295_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8176,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8176,tc_HOL_Obool)),U_8178),hAPP(hAPP(c_Set_Oinsert(U_8176),U_8180),c_Orderings_Obot__class_Obot(tc_fun(U_8176,tc_HOL_Obool))))),U_8182))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8176),U_8180),U_8178))
    | ~ sP697(U_8182,U_8176,U_8178,U_8180) ),
    inference(clausify,[status(thm)],[f_2295_4]) ).

cnf(f_2295_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8176,tc_HOL_Obool)),U_8178),U_8182))
    | hBOOL(hAPP(hAPP(c_member(U_8176),U_8180),U_8178))
    | ~ sP697(U_8182,U_8176,U_8178,U_8180) ),
    inference(clausify,[status(thm)],[f_2295_4]) ).

cnf(f_2295_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8177),U_8181),U_8179))
    | ~ sP698(U_8179,U_8177,U_8181,U_8183) ),
    inference(clausify,[status(thm)],[f_2295_4]) ).

cnf(f_2295_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8177,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8177,tc_HOL_Obool)),U_8179),hAPP(hAPP(c_Set_Oinsert(U_8177),U_8181),c_Orderings_Obot__class_Obot(tc_fun(U_8177,tc_HOL_Obool))))),U_8183))
    | ~ sP698(U_8179,U_8177,U_8181,U_8183) ),
    inference(clausify,[status(thm)],[f_2295_4]) ).

cnf(f_2295_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8177),U_8181),U_8179))
    | ~ sP699(U_8179,U_8177,U_8181,U_8183) ),
    inference(clausify,[status(thm)],[f_2295_4]) ).

cnf(f_2295_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8177,tc_HOL_Obool)),U_8179),U_8183))
    | ~ sP699(U_8179,U_8177,U_8181,U_8183) ),
    inference(clausify,[status(thm)],[f_2295_4]) ).

fof(f_2296_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_2296_2,plain,
    ! [U_8187,U_8186,U_8185,U_8184] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8184,tc_HOL_Obool)),U_8185),hAPP(hAPP(c_Set_Oinsert(U_8184),U_8186),U_8187)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8184),U_8186),U_8185))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8184,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8184,tc_HOL_Obool)),U_8185),hAPP(hAPP(c_Set_Oinsert(U_8184),U_8186),c_Orderings_Obot__class_Obot(tc_fun(U_8184,tc_HOL_Obool))))),U_8187)) ),
    inference(variable_rename,[status(thm)],[f_2296_1]) ).

fof(f_2296_3,plain,
    ! [U_8184,U_8187,U_8185,U_8186] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8184,tc_HOL_Obool)),U_8185),hAPP(hAPP(c_Set_Oinsert(U_8184),U_8186),U_8187)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8184),U_8186),U_8185))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8184,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8184,tc_HOL_Obool)),U_8185),hAPP(hAPP(c_Set_Oinsert(U_8184),U_8186),c_Orderings_Obot__class_Obot(tc_fun(U_8184,tc_HOL_Obool))))),U_8187)) ),
    inference(definitional_conversion,[status(esa)],[f_2296_2]) ).

cnf(f_2296_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8184,tc_HOL_Obool)),U_8185),hAPP(hAPP(c_Set_Oinsert(U_8184),U_8186),U_8187)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8184),U_8186),U_8185))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8184,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8184,tc_HOL_Obool)),U_8185),hAPP(hAPP(c_Set_Oinsert(U_8184),U_8186),c_Orderings_Obot__class_Obot(tc_fun(U_8184,tc_HOL_Obool))))),U_8187)) ),
    inference(clausify,[status(thm)],[f_2296_3]) ).

fof(f_2297_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_2297_2,plain,
    ! [U_8192,U_8191,U_8190,U_8189,U_8188] :
      ( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_8188,U_8189,U_8190),U_8191),U_8192))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8188,U_8189)),hAPP(hAPP(c_Product__Type_OPair(U_8188,U_8189),U_8191),U_8192)),U_8190)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8188,U_8189)),hAPP(hAPP(c_Product__Type_OPair(U_8188,U_8189),U_8191),U_8192)),U_8190))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_8188,U_8189,U_8190),U_8191),U_8192)) ) ),
    inference(variable_rename,[status(thm)],[f_2297_1]) ).

fof(f_2297_3,plain,
    ( ! [U_8202,U_8200,U_8198,U_8196,U_8194] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_8194,U_8196,U_8198),U_8200),U_8202))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8194,U_8196)),hAPP(hAPP(c_Product__Type_OPair(U_8194,U_8196),U_8200),U_8202)),U_8198)) )
    & ! [U_8201,U_8199,U_8197,U_8195,U_8193] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8193,U_8195)),hAPP(hAPP(c_Product__Type_OPair(U_8193,U_8195),U_8199),U_8201)),U_8197))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_8193,U_8195,U_8197),U_8199),U_8201)) ) ),
    inference(miniscope,[status(thm)],[f_2297_2]) ).

fof(f_2297_4,plain,
    ( ! [U_8194,U_8196,U_8198,U_8200,U_8202] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_8194,U_8196,U_8198),U_8200),U_8202))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8194,U_8196)),hAPP(hAPP(c_Product__Type_OPair(U_8194,U_8196),U_8200),U_8202)),U_8198)) )
    & ! [U_8193,U_8195,U_8199,U_8197,U_8201] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8193,U_8195)),hAPP(hAPP(c_Product__Type_OPair(U_8193,U_8195),U_8199),U_8201)),U_8197))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_8193,U_8195,U_8197),U_8199),U_8201)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2297_3]) ).

cnf(f_2297_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8193,U_8195)),hAPP(hAPP(c_Product__Type_OPair(U_8193,U_8195),U_8199),U_8201)),U_8197))
    | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_8193,U_8195,U_8197),U_8199),U_8201)) ),
    inference(clausify,[status(thm)],[f_2297_4]) ).

cnf(f_2297_6,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_8194,U_8196,U_8198),U_8200),U_8202))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8194,U_8196)),hAPP(hAPP(c_Product__Type_OPair(U_8194,U_8196),U_8200),U_8202)),U_8198)) ),
    inference(clausify,[status(thm)],[f_2297_4]) ).

fof(f_2298_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_2298_2,plain,
    ! [U_8209,U_8208,U_8207,U_8206,U_8205,U_8204,U_8203] :
      ( c_Nitpick_Ofold__graph_H(U_8203,U_8206,U_8207,U_8208,U_8205,hAPP(hAPP(U_8207,U_8204),U_8209))
      | ~ c_Nitpick_Ofold__graph_H(U_8203,U_8206,U_8207,U_8208,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8203,tc_HOL_Obool)),U_8205),hAPP(hAPP(c_Set_Oinsert(U_8203),U_8204),c_Orderings_Obot__class_Obot(tc_fun(U_8203,tc_HOL_Obool)))),U_8209)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8203),U_8204),U_8205)) ),
    inference(variable_rename,[status(thm)],[f_2298_1]) ).

fof(f_2298_3,plain,
    ! [U_8203,U_8204,U_8205,U_8206,U_8207,U_8208,U_8209] :
      ( c_Nitpick_Ofold__graph_H(U_8203,U_8206,U_8207,U_8208,U_8205,hAPP(hAPP(U_8207,U_8204),U_8209))
      | ~ c_Nitpick_Ofold__graph_H(U_8203,U_8206,U_8207,U_8208,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8203,tc_HOL_Obool)),U_8205),hAPP(hAPP(c_Set_Oinsert(U_8203),U_8204),c_Orderings_Obot__class_Obot(tc_fun(U_8203,tc_HOL_Obool)))),U_8209)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8203),U_8204),U_8205)) ),
    inference(definitional_conversion,[status(esa)],[f_2298_2]) ).

cnf(f_2298_4,plain,
    ( c_Nitpick_Ofold__graph_H(U_8203,U_8206,U_8207,U_8208,U_8205,hAPP(hAPP(U_8207,U_8204),U_8209))
    | ~ c_Nitpick_Ofold__graph_H(U_8203,U_8206,U_8207,U_8208,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8203,tc_HOL_Obool)),U_8205),hAPP(hAPP(c_Set_Oinsert(U_8203),U_8204),c_Orderings_Obot__class_Obot(tc_fun(U_8203,tc_HOL_Obool)))),U_8209)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8203),U_8204),U_8205)) ),
    inference(clausify,[status(thm)],[f_2298_3]) ).

fof(f_2299_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_2299_2,plain,
    ! [U_8213,U_8212] :
      ( ( c_Nitpick_Orefl_H(U_8212,U_8213)
        | ? [U_8211] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8212,U_8212)),hAPP(hAPP(c_Product__Type_OPair(U_8212,U_8212),U_8211),U_8211)),U_8213)) )
      & ( ! [U_8210] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8212,U_8212)),hAPP(hAPP(c_Product__Type_OPair(U_8212,U_8212),U_8210),U_8210)),U_8213))
        | ~ c_Nitpick_Orefl_H(U_8212,U_8213) ) ),
    inference(variable_rename,[status(thm)],[f_2299_1]) ).

fof(f_2299_3,plain,
    ( ! [U_8217,U_8215] :
        ( c_Nitpick_Orefl_H(U_8215,U_8217)
        | ? [U_8211] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8215,U_8215)),hAPP(hAPP(c_Product__Type_OPair(U_8215,U_8215),U_8211),U_8211)),U_8217)) )
    & ! [U_8216,U_8214] :
        ( ! [U_8210] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8214,U_8214)),hAPP(hAPP(c_Product__Type_OPair(U_8214,U_8214),U_8210),U_8210)),U_8216))
        | ~ c_Nitpick_Orefl_H(U_8214,U_8216) ) ),
    inference(miniscope,[status(thm)],[f_2299_2]) ).

fof(f_2299_4,plain,
    ( ! [U_8217,U_8215] :
        ( c_Nitpick_Orefl_H(U_8215,U_8217)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8215,U_8215)),hAPP(hAPP(c_Product__Type_OPair(U_8215,U_8215),sK122(U_8217,U_8215)),sK122(U_8217,U_8215))),U_8217)) )
    & ! [U_8216,U_8214] :
        ( ! [U_8210] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8214,U_8214)),hAPP(hAPP(c_Product__Type_OPair(U_8214,U_8214),U_8210),U_8210)),U_8216))
        | ~ c_Nitpick_Orefl_H(U_8214,U_8216) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_8211,sK122(U_8217,U_8215))],[f_2299_3]) ).

fof(f_2299_5,plain,
    ( ! [U_8217,U_8215] :
        ( c_Nitpick_Orefl_H(U_8215,U_8217)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8215,U_8215)),hAPP(hAPP(c_Product__Type_OPair(U_8215,U_8215),sK122(U_8217,U_8215)),sK122(U_8217,U_8215))),U_8217)) )
    & ! [U_8216,U_8210,U_8214] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8214,U_8214)),hAPP(hAPP(c_Product__Type_OPair(U_8214,U_8214),U_8210),U_8210)),U_8216))
        | ~ c_Nitpick_Orefl_H(U_8214,U_8216) ) ),
    inference(definitional_conversion,[status(esa)],[f_2299_4]) ).

cnf(f_2299_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8214,U_8214)),hAPP(hAPP(c_Product__Type_OPair(U_8214,U_8214),U_8210),U_8210)),U_8216))
    | ~ c_Nitpick_Orefl_H(U_8214,U_8216) ),
    inference(clausify,[status(thm)],[f_2299_5]) ).

cnf(f_2299_7,plain,
    ( c_Nitpick_Orefl_H(U_8215,U_8217)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8215,U_8215)),hAPP(hAPP(c_Product__Type_OPair(U_8215,U_8215),sK122(U_8217,U_8215)),sK122(U_8217,U_8215))),U_8217)) ),
    inference(clausify,[status(thm)],[f_2299_5]) ).

fof(f_2300_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_2300_2,plain,
    ! [U_8220,U_8219,U_8218] :
      ( ( c_Partial__Function_Oflat__lub(U_8218,U_8220,U_8219) = c_HOL_OThe(U_8218,hAPP(hAPP(c_COMBC(U_8218,tc_fun(U_8218,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8218)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8218,tc_HOL_Obool)),U_8219),hAPP(hAPP(c_Set_Oinsert(U_8218),U_8220),c_Orderings_Obot__class_Obot(tc_fun(U_8218,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8218,tc_HOL_Obool)),U_8219),hAPP(hAPP(c_Set_Oinsert(U_8218),U_8220),c_Orderings_Obot__class_Obot(tc_fun(U_8218,tc_HOL_Obool))))) )
      & ( c_Partial__Function_Oflat__lub(U_8218,U_8220,U_8219) = U_8220
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8218,tc_HOL_Obool)),U_8219),hAPP(hAPP(c_Set_Oinsert(U_8218),U_8220),c_Orderings_Obot__class_Obot(tc_fun(U_8218,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[f_2300_1]) ).

fof(f_2300_3,plain,
    ( ! [U_8226,U_8224,U_8222] :
        ( c_Partial__Function_Oflat__lub(U_8222,U_8226,U_8224) = c_HOL_OThe(U_8222,hAPP(hAPP(c_COMBC(U_8222,tc_fun(U_8222,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8222)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8222,tc_HOL_Obool)),U_8224),hAPP(hAPP(c_Set_Oinsert(U_8222),U_8226),c_Orderings_Obot__class_Obot(tc_fun(U_8222,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8222,tc_HOL_Obool)),U_8224),hAPP(hAPP(c_Set_Oinsert(U_8222),U_8226),c_Orderings_Obot__class_Obot(tc_fun(U_8222,tc_HOL_Obool))))) )
    & ! [U_8225,U_8223,U_8221] :
        ( c_Partial__Function_Oflat__lub(U_8221,U_8225,U_8223) = U_8225
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8221,tc_HOL_Obool)),U_8223),hAPP(hAPP(c_Set_Oinsert(U_8221),U_8225),c_Orderings_Obot__class_Obot(tc_fun(U_8221,tc_HOL_Obool))))) ) ),
    inference(miniscope,[status(thm)],[f_2300_2]) ).

fof(f_2300_4,plain,
    ( ! [U_8224,U_8222,U_8226] :
        ( c_Partial__Function_Oflat__lub(U_8222,U_8226,U_8224) = c_HOL_OThe(U_8222,hAPP(hAPP(c_COMBC(U_8222,tc_fun(U_8222,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8222)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8222,tc_HOL_Obool)),U_8224),hAPP(hAPP(c_Set_Oinsert(U_8222),U_8226),c_Orderings_Obot__class_Obot(tc_fun(U_8222,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8222,tc_HOL_Obool)),U_8224),hAPP(hAPP(c_Set_Oinsert(U_8222),U_8226),c_Orderings_Obot__class_Obot(tc_fun(U_8222,tc_HOL_Obool))))) )
    & ! [U_8225,U_8223,U_8221] :
        ( c_Partial__Function_Oflat__lub(U_8221,U_8225,U_8223) = U_8225
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8221,tc_HOL_Obool)),U_8223),hAPP(hAPP(c_Set_Oinsert(U_8221),U_8225),c_Orderings_Obot__class_Obot(tc_fun(U_8221,tc_HOL_Obool))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2300_3]) ).

cnf(f_2300_5,plain,
    ( c_Partial__Function_Oflat__lub(U_8221,U_8225,U_8223) = U_8225
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8221,tc_HOL_Obool)),U_8223),hAPP(hAPP(c_Set_Oinsert(U_8221),U_8225),c_Orderings_Obot__class_Obot(tc_fun(U_8221,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_2300_4]) ).

cnf(f_2300_6,plain,
    ( c_Partial__Function_Oflat__lub(U_8222,U_8226,U_8224) = c_HOL_OThe(U_8222,hAPP(hAPP(c_COMBC(U_8222,tc_fun(U_8222,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8222)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8222,tc_HOL_Obool)),U_8224),hAPP(hAPP(c_Set_Oinsert(U_8222),U_8226),c_Orderings_Obot__class_Obot(tc_fun(U_8222,tc_HOL_Obool))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8222,tc_HOL_Obool)),U_8224),hAPP(hAPP(c_Set_Oinsert(U_8222),U_8226),c_Orderings_Obot__class_Obot(tc_fun(U_8222,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_2300_4]) ).

fof(f_2301_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_2301_2,plain,
    ! [U_8230,U_8229,U_8228,U_8227] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8227,tc_fun(U_8228,tc_HOL_Obool))),U_8229),U_8230)),
    inference(variable_rename,[status(thm)],[f_2301_1]) ).

fof(f_2301_3,plain,
    ! [U_8227,U_8228,U_8230,U_8229] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8227,tc_fun(U_8228,tc_HOL_Obool))),U_8229),U_8230)),
    inference(definitional_conversion,[status(esa)],[f_2301_2]) ).

cnf(f_2301_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8227,tc_fun(U_8228,tc_HOL_Obool))),U_8229),U_8230)),
    inference(clausify,[status(thm)],[f_2301_3]) ).

fof(f_2302_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_2302_2,plain,
    ! [U_8233,U_8232,U_8231] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8232,U_8232),tc_HOL_Obool)),U_8231),U_8233))
      | U_8231 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8232,U_8232),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2302_1]) ).

fof(f_2302_3,plain,
    ! [U_8231,U_8232,U_8233] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8232,U_8232),tc_HOL_Obool)),U_8231),U_8233))
      | U_8231 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8232,U_8232),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_2302_2]) ).

cnf(f_2302_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8232,U_8232),tc_HOL_Obool)),U_8231),U_8233))
    | U_8231 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8232,U_8232),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2302_3]) ).

fof(f_2303_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_2303_2,plain,
    ! [U_8237,U_8236,U_8235,U_8234] : c_Nitpick_Ofold__graph_H(U_8234,U_8235,U_8236,U_8237,c_Orderings_Obot__class_Obot(tc_fun(U_8234,tc_HOL_Obool)),U_8237),
    inference(variable_rename,[status(thm)],[f_2303_1]) ).

fof(f_2303_3,plain,
    ! [U_8234,U_8235,U_8236,U_8237] : c_Nitpick_Ofold__graph_H(U_8234,U_8235,U_8236,U_8237,c_Orderings_Obot__class_Obot(tc_fun(U_8234,tc_HOL_Obool)),U_8237),
    inference(definitional_conversion,[status(esa)],[f_2303_2]) ).

cnf(f_2303_4,plain,
    c_Nitpick_Ofold__graph_H(U_8234,U_8235,U_8236,U_8237,c_Orderings_Obot__class_Obot(tc_fun(U_8234,tc_HOL_Obool)),U_8237),
    inference(clausify,[status(thm)],[f_2303_3]) ).

fof(f_2304_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_2304_2,plain,
    ! [U_8241,U_8240,U_8239,U_8238] : c_Nitpick_Ofold__graph_H(U_8238,U_8239,U_8240,U_8241,c_Orderings_Obot__class_Obot(tc_fun(U_8238,tc_HOL_Obool)),U_8241),
    inference(variable_rename,[status(thm)],[f_2304_1]) ).

fof(f_2304_3,plain,
    ! [U_8238,U_8239,U_8240,U_8241] : c_Nitpick_Ofold__graph_H(U_8238,U_8239,U_8240,U_8241,c_Orderings_Obot__class_Obot(tc_fun(U_8238,tc_HOL_Obool)),U_8241),
    inference(definitional_conversion,[status(esa)],[f_2304_2]) ).

cnf(f_2304_4,plain,
    c_Nitpick_Ofold__graph_H(U_8238,U_8239,U_8240,U_8241,c_Orderings_Obot__class_Obot(tc_fun(U_8238,tc_HOL_Obool)),U_8241),
    inference(clausify,[status(thm)],[f_2304_3]) ).

fof(f_2305_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_2305_2,plain,
    ! [U_8245,U_8244,U_8243,U_8242] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8242,U_8242)),hAPP(hAPP(c_Product__Type_OPair(U_8242,U_8242),U_8243),U_8244)),hAPP(c_Wellfounded_Omeasure(U_8242),U_8245)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8245,U_8243)),hAPP(U_8245,U_8244))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8245,U_8243)),hAPP(U_8245,U_8244)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8242,U_8242)),hAPP(hAPP(c_Product__Type_OPair(U_8242,U_8242),U_8243),U_8244)),hAPP(c_Wellfounded_Omeasure(U_8242),U_8245))) ) ),
    inference(variable_rename,[status(thm)],[f_2305_1]) ).

fof(f_2305_3,plain,
    ( ! [U_8253,U_8251,U_8249] :
        ( ! [U_8247] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8247,U_8247)),hAPP(hAPP(c_Product__Type_OPair(U_8247,U_8247),U_8249),U_8251)),hAPP(c_Wellfounded_Omeasure(U_8247),U_8253)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8253,U_8249)),hAPP(U_8253,U_8251))) )
    & ! [U_8252,U_8250,U_8248] :
        ( ! [U_8246] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8246,U_8246)),hAPP(hAPP(c_Product__Type_OPair(U_8246,U_8246),U_8248),U_8250)),hAPP(c_Wellfounded_Omeasure(U_8246),U_8252)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8252,U_8248)),hAPP(U_8252,U_8250))) ) ),
    inference(miniscope,[status(thm)],[f_2305_2]) ).

fof(f_2305_4,plain,
    ( ! [U_8247,U_8249,U_8251,U_8253] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8247,U_8247)),hAPP(hAPP(c_Product__Type_OPair(U_8247,U_8247),U_8249),U_8251)),hAPP(c_Wellfounded_Omeasure(U_8247),U_8253)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8253,U_8249)),hAPP(U_8253,U_8251))) )
    & ! [U_8246,U_8248,U_8252,U_8250] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8246,U_8246)),hAPP(hAPP(c_Product__Type_OPair(U_8246,U_8246),U_8248),U_8250)),hAPP(c_Wellfounded_Omeasure(U_8246),U_8252)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8252,U_8248)),hAPP(U_8252,U_8250))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2305_3]) ).

cnf(f_2305_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8246,U_8246)),hAPP(hAPP(c_Product__Type_OPair(U_8246,U_8246),U_8248),U_8250)),hAPP(c_Wellfounded_Omeasure(U_8246),U_8252)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8252,U_8248)),hAPP(U_8252,U_8250))) ),
    inference(clausify,[status(thm)],[f_2305_4]) ).

cnf(f_2305_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8247,U_8247)),hAPP(hAPP(c_Product__Type_OPair(U_8247,U_8247),U_8249),U_8251)),hAPP(c_Wellfounded_Omeasure(U_8247),U_8253)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8253,U_8249)),hAPP(U_8253,U_8251))) ),
    inference(clausify,[status(thm)],[f_2305_4]) ).

fof(f_2306_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_2306_2,plain,
    ! [U_8258,U_8257,U_8256,U_8255,U_8254] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8257,U_8257)),hAPP(hAPP(c_Product__Type_OPair(U_8257,U_8257),U_8255),U_8256)),c_Wellfounded_Omlex__prod(U_8257,U_8254,U_8258)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8257,U_8257)),hAPP(hAPP(c_Product__Type_OPair(U_8257,U_8257),U_8255),U_8256)),U_8258))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_8254,U_8255)),hAPP(U_8254,U_8256))) ),
    inference(variable_rename,[status(thm)],[f_2306_1]) ).

fof(f_2306_3,plain,
    ! [U_8255,U_8254,U_8256,U_8257,U_8258] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8257,U_8257)),hAPP(hAPP(c_Product__Type_OPair(U_8257,U_8257),U_8255),U_8256)),c_Wellfounded_Omlex__prod(U_8257,U_8254,U_8258)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8257,U_8257)),hAPP(hAPP(c_Product__Type_OPair(U_8257,U_8257),U_8255),U_8256)),U_8258))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_8254,U_8255)),hAPP(U_8254,U_8256))) ),
    inference(definitional_conversion,[status(esa)],[f_2306_2]) ).

cnf(f_2306_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8257,U_8257)),hAPP(hAPP(c_Product__Type_OPair(U_8257,U_8257),U_8255),U_8256)),c_Wellfounded_Omlex__prod(U_8257,U_8254,U_8258)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8257,U_8257)),hAPP(hAPP(c_Product__Type_OPair(U_8257,U_8257),U_8255),U_8256)),U_8258))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_8254,U_8255)),hAPP(U_8254,U_8256))) ),
    inference(clausify,[status(thm)],[f_2306_3]) ).

fof(f_2307_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_2307_2,plain,
    ! [U_8263,U_8262,U_8261,U_8260,U_8259] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8262,U_8262)),hAPP(hAPP(c_Product__Type_OPair(U_8262,U_8262),U_8260),U_8261)),c_Wellfounded_Omlex__prod(U_8262,U_8259,U_8263)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8259,U_8260)),hAPP(U_8259,U_8261))) ),
    inference(variable_rename,[status(thm)],[f_2307_1]) ).

fof(f_2307_3,plain,
    ! [U_8260,U_8259,U_8261,U_8262,U_8263] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8262,U_8262)),hAPP(hAPP(c_Product__Type_OPair(U_8262,U_8262),U_8260),U_8261)),c_Wellfounded_Omlex__prod(U_8262,U_8259,U_8263)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8259,U_8260)),hAPP(U_8259,U_8261))) ),
    inference(definitional_conversion,[status(esa)],[f_2307_2]) ).

cnf(f_2307_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8262,U_8262)),hAPP(hAPP(c_Product__Type_OPair(U_8262,U_8262),U_8260),U_8261)),c_Wellfounded_Omlex__prod(U_8262,U_8259,U_8263)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8259,U_8260)),hAPP(U_8259,U_8261))) ),
    inference(clausify,[status(thm)],[f_2307_3]) ).

fof(f_2308_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_2308_2,plain,
    ! [U_8265,U_8264] :
      ( hBOOL(hAPP(hAPP(c_member(U_8264),hAPP(c_Int_Onumber__class_Onumber__of(U_8264),U_8265)),c_Nat_Osemiring__1__class_ONats(U_8264)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_8265))
      | ~ class_Int_Onumber__ring(U_8264) ),
    inference(variable_rename,[status(thm)],[f_2308_1]) ).

fof(f_2308_3,plain,
    ! [U_8264,U_8265] :
      ( hBOOL(hAPP(hAPP(c_member(U_8264),hAPP(c_Int_Onumber__class_Onumber__of(U_8264),U_8265)),c_Nat_Osemiring__1__class_ONats(U_8264)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_8265))
      | ~ class_Int_Onumber__ring(U_8264) ),
    inference(definitional_conversion,[status(esa)],[f_2308_2]) ).

cnf(f_2308_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8264),hAPP(c_Int_Onumber__class_Onumber__of(U_8264),U_8265)),c_Nat_Osemiring__1__class_ONats(U_8264)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_8265))
    | ~ class_Int_Onumber__ring(U_8264) ),
    inference(clausify,[status(thm)],[f_2308_3]) ).

fof(f_2309_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_2309_2,plain,
    ! [U_8266] :
      ( hBOOL(hAPP(hAPP(c_member(U_8266),c_Groups_Ozero__class_Ozero(U_8266)),c_Nat_Osemiring__1__class_ONats(U_8266)))
      | ~ class_Rings_Osemiring__1(U_8266) ),
    inference(variable_rename,[status(thm)],[f_2309_1]) ).

fof(f_2309_3,plain,
    ! [U_8266] :
      ( hBOOL(hAPP(hAPP(c_member(U_8266),c_Groups_Ozero__class_Ozero(U_8266)),c_Nat_Osemiring__1__class_ONats(U_8266)))
      | ~ class_Rings_Osemiring__1(U_8266) ),
    inference(definitional_conversion,[status(esa)],[f_2309_2]) ).

cnf(f_2309_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8266),c_Groups_Ozero__class_Ozero(U_8266)),c_Nat_Osemiring__1__class_ONats(U_8266)))
    | ~ class_Rings_Osemiring__1(U_8266) ),
    inference(clausify,[status(thm)],[f_2309_3]) ).

fof(f_2310_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_2310_2,plain,
    ! [U_8269,U_8268,U_8267] :
      ( hBOOL(hAPP(hAPP(c_member(U_8267),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8267),U_8268),U_8269)),c_Nat_Osemiring__1__class_ONats(U_8267)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8267),U_8269),c_Nat_Osemiring__1__class_ONats(U_8267)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8267),U_8268),c_Nat_Osemiring__1__class_ONats(U_8267)))
      | ~ class_Rings_Osemiring__1(U_8267) ),
    inference(variable_rename,[status(thm)],[f_2310_1]) ).

fof(f_2310_3,plain,
    ! [U_8267,U_8268,U_8269] :
      ( hBOOL(hAPP(hAPP(c_member(U_8267),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8267),U_8268),U_8269)),c_Nat_Osemiring__1__class_ONats(U_8267)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8267),U_8269),c_Nat_Osemiring__1__class_ONats(U_8267)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8267),U_8268),c_Nat_Osemiring__1__class_ONats(U_8267)))
      | ~ class_Rings_Osemiring__1(U_8267) ),
    inference(definitional_conversion,[status(esa)],[f_2310_2]) ).

cnf(f_2310_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8267),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8267),U_8268),U_8269)),c_Nat_Osemiring__1__class_ONats(U_8267)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8267),U_8269),c_Nat_Osemiring__1__class_ONats(U_8267)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8267),U_8268),c_Nat_Osemiring__1__class_ONats(U_8267)))
    | ~ class_Rings_Osemiring__1(U_8267) ),
    inference(clausify,[status(thm)],[f_2310_3]) ).

fof(f_2311_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_2311_2,plain,
    ! [U_8272,U_8271,U_8270] :
      ( hBOOL(hAPP(hAPP(c_member(U_8270),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8270),U_8271),U_8272)),c_Nat_Osemiring__1__class_ONats(U_8270)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8270),U_8272),c_Nat_Osemiring__1__class_ONats(U_8270)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8270),U_8271),c_Nat_Osemiring__1__class_ONats(U_8270)))
      | ~ class_Rings_Osemiring__1(U_8270) ),
    inference(variable_rename,[status(thm)],[f_2311_1]) ).

fof(f_2311_3,plain,
    ! [U_8270,U_8271,U_8272] :
      ( hBOOL(hAPP(hAPP(c_member(U_8270),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8270),U_8271),U_8272)),c_Nat_Osemiring__1__class_ONats(U_8270)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8270),U_8272),c_Nat_Osemiring__1__class_ONats(U_8270)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8270),U_8271),c_Nat_Osemiring__1__class_ONats(U_8270)))
      | ~ class_Rings_Osemiring__1(U_8270) ),
    inference(definitional_conversion,[status(esa)],[f_2311_2]) ).

cnf(f_2311_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8270),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8270),U_8271),U_8272)),c_Nat_Osemiring__1__class_ONats(U_8270)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8270),U_8272),c_Nat_Osemiring__1__class_ONats(U_8270)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8270),U_8271),c_Nat_Osemiring__1__class_ONats(U_8270)))
    | ~ class_Rings_Osemiring__1(U_8270) ),
    inference(clausify,[status(thm)],[f_2311_3]) ).

fof(f_2312_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_2312_2,plain,
    ! [U_8273] :
      ( hBOOL(hAPP(hAPP(c_member(U_8273),c_Groups_Oone__class_Oone(U_8273)),c_Nat_Osemiring__1__class_ONats(U_8273)))
      | ~ class_Rings_Osemiring__1(U_8273) ),
    inference(variable_rename,[status(thm)],[f_2312_1]) ).

fof(f_2312_3,plain,
    ! [U_8273] :
      ( hBOOL(hAPP(hAPP(c_member(U_8273),c_Groups_Oone__class_Oone(U_8273)),c_Nat_Osemiring__1__class_ONats(U_8273)))
      | ~ class_Rings_Osemiring__1(U_8273) ),
    inference(definitional_conversion,[status(esa)],[f_2312_2]) ).

cnf(f_2312_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8273),c_Groups_Oone__class_Oone(U_8273)),c_Nat_Osemiring__1__class_ONats(U_8273)))
    | ~ class_Rings_Osemiring__1(U_8273) ),
    inference(clausify,[status(thm)],[f_2312_3]) ).

fof(f_2313_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_2313_2,plain,
    ! [U_8275,U_8274] :
      ( hBOOL(hAPP(hAPP(c_member(U_8274),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8274),U_8275)),c_Nat_Osemiring__1__class_ONats(U_8274)))
      | ~ class_Rings_Osemiring__1(U_8274) ),
    inference(variable_rename,[status(thm)],[f_2313_1]) ).

fof(f_2313_3,plain,
    ! [U_8274,U_8275] :
      ( hBOOL(hAPP(hAPP(c_member(U_8274),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8274),U_8275)),c_Nat_Osemiring__1__class_ONats(U_8274)))
      | ~ class_Rings_Osemiring__1(U_8274) ),
    inference(definitional_conversion,[status(esa)],[f_2313_2]) ).

cnf(f_2313_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8274),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8274),U_8275)),c_Nat_Osemiring__1__class_ONats(U_8274)))
    | ~ class_Rings_Osemiring__1(U_8274) ),
    inference(clausify,[status(thm)],[f_2313_3]) ).

fof(f_2314_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_2314_2,plain,
    ! [U_8277,U_8276] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8276),c_Groups_Oone__class_Oone(U_8276)),U_8277)),U_8277)),c_Groups_Ozero__class_Ozero(U_8276)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8276),U_8277),c_Groups_Ozero__class_Ozero(U_8276))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8276),U_8277),c_Groups_Ozero__class_Ozero(U_8276)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8276),c_Groups_Oone__class_Oone(U_8276)),U_8277)),U_8277)),c_Groups_Ozero__class_Ozero(U_8276))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_8276),U_8277),c_Int_Oring__1__class_OInts(U_8276)))
      | ~ class_Rings_Olinordered__idom(U_8276) ),
    inference(variable_rename,[status(thm)],[f_2314_1]) ).

fof(f_2314_3,plain,
    ( ! [U_8276,U_8277] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8276),c_Groups_Oone__class_Oone(U_8276)),U_8277)),U_8277)),c_Groups_Ozero__class_Ozero(U_8276)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8276),U_8277),c_Groups_Ozero__class_Ozero(U_8276)))
        | ~ sP700(U_8276,U_8277) )
    & ! [U_8276,U_8277] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8276),U_8277),c_Groups_Ozero__class_Ozero(U_8276)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8276),c_Groups_Oone__class_Oone(U_8276)),U_8277)),U_8277)),c_Groups_Ozero__class_Ozero(U_8276)))
        | ~ sP700(U_8276,U_8277) )
    & ! [U_8276,U_8277] :
        ( sP700(U_8276,U_8277)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8276),U_8277),c_Int_Oring__1__class_OInts(U_8276)))
        | ~ class_Rings_Olinordered__idom(U_8276) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP700])],[f_2314_2]) ).

cnf(f_2314_4,plain,
    ( sP700(U_8276,U_8277)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8276),U_8277),c_Int_Oring__1__class_OInts(U_8276)))
    | ~ class_Rings_Olinordered__idom(U_8276) ),
    inference(clausify,[status(thm)],[f_2314_3]) ).

cnf(f_2314_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8276),U_8277),c_Groups_Ozero__class_Ozero(U_8276)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8276),c_Groups_Oone__class_Oone(U_8276)),U_8277)),U_8277)),c_Groups_Ozero__class_Ozero(U_8276)))
    | ~ sP700(U_8276,U_8277) ),
    inference(clausify,[status(thm)],[f_2314_3]) ).

cnf(f_2314_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8276),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8276),c_Groups_Oone__class_Oone(U_8276)),U_8277)),U_8277)),c_Groups_Ozero__class_Ozero(U_8276)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8276),U_8277),c_Groups_Ozero__class_Ozero(U_8276)))
    | ~ sP700(U_8276,U_8277) ),
    inference(clausify,[status(thm)],[f_2314_3]) ).

fof(f_2315_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_2315_2,plain,
    ! [U_8288,U_8287,U_8286,U_8285,U_8284,U_8283,U_8282] :
      ( ( c_Nitpick_Ofold__graph_H(U_8282,U_8283,U_8284,U_8285,U_8286,hAPP(hAPP(U_8284,U_8287),U_8288))
        | ( ! [U_8281,U_8280] :
              ( ~ c_Nitpick_Ofold__graph_H(U_8282,U_8283,U_8284,U_8285,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8282,tc_HOL_Obool)),U_8286),hAPP(hAPP(c_Set_Oinsert(U_8282),U_8281),c_Orderings_Obot__class_Obot(tc_fun(U_8282,tc_HOL_Obool)))),U_8280)
              | ~ hBOOL(hAPP(hAPP(c_member(U_8282),U_8281),U_8286))
              | hAPP(hAPP(U_8284,U_8287),U_8288) != hAPP(hAPP(U_8284,U_8281),U_8280) )
          & ( hAPP(hAPP(U_8284,U_8287),U_8288) != U_8285
            | U_8286 != c_Orderings_Obot__class_Obot(tc_fun(U_8282,tc_HOL_Obool)) ) ) )
      & ( ? [U_8279,U_8278] :
            ( c_Nitpick_Ofold__graph_H(U_8282,U_8283,U_8284,U_8285,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8282,tc_HOL_Obool)),U_8286),hAPP(hAPP(c_Set_Oinsert(U_8282),U_8279),c_Orderings_Obot__class_Obot(tc_fun(U_8282,tc_HOL_Obool)))),U_8278)
            & hBOOL(hAPP(hAPP(c_member(U_8282),U_8279),U_8286))
            & hAPP(hAPP(U_8284,U_8287),U_8288) = hAPP(hAPP(U_8284,U_8279),U_8278) )
        | ( hAPP(hAPP(U_8284,U_8287),U_8288) = U_8285
          & U_8286 = c_Orderings_Obot__class_Obot(tc_fun(U_8282,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_8282,U_8283,U_8284,U_8285,U_8286,hAPP(hAPP(U_8284,U_8287),U_8288)) ) ),
    inference(variable_rename,[status(thm)],[f_2315_1]) ).

fof(f_2315_3,plain,
    ( ! [U_8302,U_8300,U_8298,U_8296,U_8294,U_8292,U_8290] :
        ( c_Nitpick_Ofold__graph_H(U_8290,U_8292,U_8294,U_8296,U_8298,hAPP(hAPP(U_8294,U_8300),U_8302))
        | ( ! [U_8281] :
              ( ! [U_8280] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_8290,U_8292,U_8294,U_8296,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8290,tc_HOL_Obool)),U_8298),hAPP(hAPP(c_Set_Oinsert(U_8290),U_8281),c_Orderings_Obot__class_Obot(tc_fun(U_8290,tc_HOL_Obool)))),U_8280)
                  | hAPP(hAPP(U_8294,U_8300),U_8302) != hAPP(hAPP(U_8294,U_8281),U_8280) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_8290),U_8281),U_8298)) )
          & ( hAPP(hAPP(U_8294,U_8300),U_8302) != U_8296
            | U_8298 != c_Orderings_Obot__class_Obot(tc_fun(U_8290,tc_HOL_Obool)) ) ) )
    & ! [U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289] :
        ( ? [U_8279] :
            ( ? [U_8278] :
                ( c_Nitpick_Ofold__graph_H(U_8289,U_8291,U_8293,U_8295,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8289,tc_HOL_Obool)),U_8297),hAPP(hAPP(c_Set_Oinsert(U_8289),U_8279),c_Orderings_Obot__class_Obot(tc_fun(U_8289,tc_HOL_Obool)))),U_8278)
                & hAPP(hAPP(U_8293,U_8299),U_8301) = hAPP(hAPP(U_8293,U_8279),U_8278) )
            & hBOOL(hAPP(hAPP(c_member(U_8289),U_8279),U_8297)) )
        | ( hAPP(hAPP(U_8293,U_8299),U_8301) = U_8295
          & U_8297 = c_Orderings_Obot__class_Obot(tc_fun(U_8289,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_8289,U_8291,U_8293,U_8295,U_8297,hAPP(hAPP(U_8293,U_8299),U_8301)) ) ),
    inference(miniscope,[status(thm)],[f_2315_2]) ).

fof(f_2315_4,plain,
    ( ! [U_8302,U_8300,U_8298,U_8296,U_8294,U_8292,U_8290] :
        ( c_Nitpick_Ofold__graph_H(U_8290,U_8292,U_8294,U_8296,U_8298,hAPP(hAPP(U_8294,U_8300),U_8302))
        | ( ! [U_8281] :
              ( ! [U_8280] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_8290,U_8292,U_8294,U_8296,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8290,tc_HOL_Obool)),U_8298),hAPP(hAPP(c_Set_Oinsert(U_8290),U_8281),c_Orderings_Obot__class_Obot(tc_fun(U_8290,tc_HOL_Obool)))),U_8280)
                  | hAPP(hAPP(U_8294,U_8300),U_8302) != hAPP(hAPP(U_8294,U_8281),U_8280) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_8290),U_8281),U_8298)) )
          & ( hAPP(hAPP(U_8294,U_8300),U_8302) != U_8296
            | U_8298 != c_Orderings_Obot__class_Obot(tc_fun(U_8290,tc_HOL_Obool)) ) ) )
    & ! [U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289] :
        ( ( ? [U_8278] :
              ( c_Nitpick_Ofold__graph_H(U_8289,U_8291,U_8293,U_8295,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8289,tc_HOL_Obool)),U_8297),hAPP(hAPP(c_Set_Oinsert(U_8289),sK123(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289)),c_Orderings_Obot__class_Obot(tc_fun(U_8289,tc_HOL_Obool)))),U_8278)
              & hAPP(hAPP(U_8293,U_8299),U_8301) = hAPP(hAPP(U_8293,sK123(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289)),U_8278) )
          & hBOOL(hAPP(hAPP(c_member(U_8289),sK123(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289)),U_8297)) )
        | ( hAPP(hAPP(U_8293,U_8299),U_8301) = U_8295
          & U_8297 = c_Orderings_Obot__class_Obot(tc_fun(U_8289,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_8289,U_8291,U_8293,U_8295,U_8297,hAPP(hAPP(U_8293,U_8299),U_8301)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_8279,sK123(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289))],[f_2315_3]) ).

fof(f_2315_5,plain,
    ( ! [U_8302,U_8300,U_8298,U_8296,U_8294,U_8292,U_8290] :
        ( c_Nitpick_Ofold__graph_H(U_8290,U_8292,U_8294,U_8296,U_8298,hAPP(hAPP(U_8294,U_8300),U_8302))
        | ( ! [U_8281] :
              ( ! [U_8280] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_8290,U_8292,U_8294,U_8296,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8290,tc_HOL_Obool)),U_8298),hAPP(hAPP(c_Set_Oinsert(U_8290),U_8281),c_Orderings_Obot__class_Obot(tc_fun(U_8290,tc_HOL_Obool)))),U_8280)
                  | hAPP(hAPP(U_8294,U_8300),U_8302) != hAPP(hAPP(U_8294,U_8281),U_8280) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_8290),U_8281),U_8298)) )
          & ( hAPP(hAPP(U_8294,U_8300),U_8302) != U_8296
            | U_8298 != c_Orderings_Obot__class_Obot(tc_fun(U_8290,tc_HOL_Obool)) ) ) )
    & ! [U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289] :
        ( ( c_Nitpick_Ofold__graph_H(U_8289,U_8291,U_8293,U_8295,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8289,tc_HOL_Obool)),U_8297),hAPP(hAPP(c_Set_Oinsert(U_8289),sK123(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289)),c_Orderings_Obot__class_Obot(tc_fun(U_8289,tc_HOL_Obool)))),sK124(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289))
          & hAPP(hAPP(U_8293,U_8299),U_8301) = hAPP(hAPP(U_8293,sK123(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289)),sK124(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289))
          & hBOOL(hAPP(hAPP(c_member(U_8289),sK123(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289)),U_8297)) )
        | ( hAPP(hAPP(U_8293,U_8299),U_8301) = U_8295
          & U_8297 = c_Orderings_Obot__class_Obot(tc_fun(U_8289,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_8289,U_8291,U_8293,U_8295,U_8297,hAPP(hAPP(U_8293,U_8299),U_8301)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_8278,sK124(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289))],[f_2315_4]) ).

fof(f_2315_6,plain,
    ( ! [U_8294,U_8302,U_8281,U_8280,U_8296,U_8292,U_8298,U_8290,U_8300] :
        ( ~ c_Nitpick_Ofold__graph_H(U_8290,U_8292,U_8294,U_8296,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8290,tc_HOL_Obool)),U_8298),hAPP(hAPP(c_Set_Oinsert(U_8290),U_8281),c_Orderings_Obot__class_Obot(tc_fun(U_8290,tc_HOL_Obool)))),U_8280)
        | hAPP(hAPP(U_8294,U_8300),U_8302) != hAPP(hAPP(U_8294,U_8281),U_8280)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8290),U_8281),U_8298))
        | ~ sP703(U_8294,U_8302,U_8281,U_8280,U_8296,U_8292,U_8298,U_8290,U_8300) )
    & ! [U_8294,U_8302,U_8281,U_8280,U_8296,U_8292,U_8298,U_8290,U_8300] :
        ( hAPP(hAPP(U_8294,U_8300),U_8302) != U_8296
        | U_8298 != c_Orderings_Obot__class_Obot(tc_fun(U_8290,tc_HOL_Obool))
        | ~ sP703(U_8294,U_8302,U_8281,U_8280,U_8296,U_8292,U_8298,U_8290,U_8300) )
    & ! [U_8291,U_8289,U_8295,U_8293,U_8297,U_8299,U_8301] :
        ( c_Nitpick_Ofold__graph_H(U_8289,U_8291,U_8293,U_8295,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8289,tc_HOL_Obool)),U_8297),hAPP(hAPP(c_Set_Oinsert(U_8289),sK123(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289)),c_Orderings_Obot__class_Obot(tc_fun(U_8289,tc_HOL_Obool)))),sK124(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289))
        | ~ sP702(U_8291,U_8289,U_8295,U_8293,U_8297,U_8299,U_8301) )
    & ! [U_8291,U_8289,U_8295,U_8293,U_8297,U_8299,U_8301] :
        ( hAPP(hAPP(U_8293,U_8299),U_8301) = hAPP(hAPP(U_8293,sK123(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289)),sK124(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289))
        | ~ sP702(U_8291,U_8289,U_8295,U_8293,U_8297,U_8299,U_8301) )
    & ! [U_8291,U_8289,U_8295,U_8293,U_8297,U_8299,U_8301] :
        ( hBOOL(hAPP(hAPP(c_member(U_8289),sK123(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289)),U_8297))
        | ~ sP702(U_8291,U_8289,U_8295,U_8293,U_8297,U_8299,U_8301) )
    & ! [U_8289,U_8295,U_8293,U_8297,U_8299,U_8301] :
        ( hAPP(hAPP(U_8293,U_8299),U_8301) = U_8295
        | ~ sP701(U_8289,U_8295,U_8293,U_8297,U_8299,U_8301) )
    & ! [U_8289,U_8295,U_8293,U_8297,U_8299,U_8301] :
        ( U_8297 = c_Orderings_Obot__class_Obot(tc_fun(U_8289,tc_HOL_Obool))
        | ~ sP701(U_8289,U_8295,U_8293,U_8297,U_8299,U_8301) )
    & ! [U_8294,U_8302,U_8281,U_8280,U_8296,U_8292,U_8298,U_8290,U_8300] :
        ( c_Nitpick_Ofold__graph_H(U_8290,U_8292,U_8294,U_8296,U_8298,hAPP(hAPP(U_8294,U_8300),U_8302))
        | sP703(U_8294,U_8302,U_8281,U_8280,U_8296,U_8292,U_8298,U_8290,U_8300) )
    & ! [U_8291,U_8289,U_8295,U_8293,U_8297,U_8299,U_8301] :
        ( sP702(U_8291,U_8289,U_8295,U_8293,U_8297,U_8299,U_8301)
        | sP701(U_8289,U_8295,U_8293,U_8297,U_8299,U_8301)
        | ~ c_Nitpick_Ofold__graph_H(U_8289,U_8291,U_8293,U_8295,U_8297,hAPP(hAPP(U_8293,U_8299),U_8301)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP701,sP702,sP703])],[f_2315_5]) ).

cnf(f_2315_7,plain,
    ( sP702(U_8291,U_8289,U_8295,U_8293,U_8297,U_8299,U_8301)
    | sP701(U_8289,U_8295,U_8293,U_8297,U_8299,U_8301)
    | ~ c_Nitpick_Ofold__graph_H(U_8289,U_8291,U_8293,U_8295,U_8297,hAPP(hAPP(U_8293,U_8299),U_8301)) ),
    inference(clausify,[status(thm)],[f_2315_6]) ).

cnf(f_2315_8,plain,
    ( c_Nitpick_Ofold__graph_H(U_8290,U_8292,U_8294,U_8296,U_8298,hAPP(hAPP(U_8294,U_8300),U_8302))
    | sP703(U_8294,U_8302,U_8281,U_8280,U_8296,U_8292,U_8298,U_8290,U_8300) ),
    inference(clausify,[status(thm)],[f_2315_6]) ).

cnf(f_2315_9,plain,
    ( U_8297 = c_Orderings_Obot__class_Obot(tc_fun(U_8289,tc_HOL_Obool))
    | ~ sP701(U_8289,U_8295,U_8293,U_8297,U_8299,U_8301) ),
    inference(clausify,[status(thm)],[f_2315_6]) ).

cnf(f_2315_10,plain,
    ( hAPP(hAPP(U_8293,U_8299),U_8301) = U_8295
    | ~ sP701(U_8289,U_8295,U_8293,U_8297,U_8299,U_8301) ),
    inference(clausify,[status(thm)],[f_2315_6]) ).

cnf(f_2315_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8289),sK123(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289)),U_8297))
    | ~ sP702(U_8291,U_8289,U_8295,U_8293,U_8297,U_8299,U_8301) ),
    inference(clausify,[status(thm)],[f_2315_6]) ).

cnf(f_2315_12,plain,
    ( hAPP(hAPP(U_8293,U_8299),U_8301) = hAPP(hAPP(U_8293,sK123(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289)),sK124(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289))
    | ~ sP702(U_8291,U_8289,U_8295,U_8293,U_8297,U_8299,U_8301) ),
    inference(clausify,[status(thm)],[f_2315_6]) ).

cnf(f_2315_13,plain,
    ( c_Nitpick_Ofold__graph_H(U_8289,U_8291,U_8293,U_8295,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8289,tc_HOL_Obool)),U_8297),hAPP(hAPP(c_Set_Oinsert(U_8289),sK123(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289)),c_Orderings_Obot__class_Obot(tc_fun(U_8289,tc_HOL_Obool)))),sK124(U_8301,U_8299,U_8297,U_8295,U_8293,U_8291,U_8289))
    | ~ sP702(U_8291,U_8289,U_8295,U_8293,U_8297,U_8299,U_8301) ),
    inference(clausify,[status(thm)],[f_2315_6]) ).

cnf(f_2315_14,plain,
    ( hAPP(hAPP(U_8294,U_8300),U_8302) != U_8296
    | U_8298 != c_Orderings_Obot__class_Obot(tc_fun(U_8290,tc_HOL_Obool))
    | ~ sP703(U_8294,U_8302,U_8281,U_8280,U_8296,U_8292,U_8298,U_8290,U_8300) ),
    inference(clausify,[status(thm)],[f_2315_6]) ).

cnf(f_2315_15,plain,
    ( ~ c_Nitpick_Ofold__graph_H(U_8290,U_8292,U_8294,U_8296,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8290,tc_HOL_Obool)),U_8298),hAPP(hAPP(c_Set_Oinsert(U_8290),U_8281),c_Orderings_Obot__class_Obot(tc_fun(U_8290,tc_HOL_Obool)))),U_8280)
    | hAPP(hAPP(U_8294,U_8300),U_8302) != hAPP(hAPP(U_8294,U_8281),U_8280)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8290),U_8281),U_8298))
    | ~ sP703(U_8294,U_8302,U_8281,U_8280,U_8296,U_8292,U_8298,U_8290,U_8300) ),
    inference(clausify,[status(thm)],[f_2315_6]) ).

fof(f_2316_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_2316_2,plain,
    ! [U_8310,U_8309,U_8308,U_8307,U_8306,U_8305,U_8304,U_8303] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8303,U_8304),tc_prod(U_8303,U_8304))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8303,U_8304),tc_prod(U_8303,U_8304)),hAPP(hAPP(c_Product__Type_OPair(U_8303,U_8304),U_8305),U_8306)),hAPP(hAPP(c_Product__Type_OPair(U_8303,U_8304),U_8307),U_8308))),c_Wellfounded_Olex__prod(U_8303,U_8304,U_8309,U_8310)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8304,U_8304)),hAPP(hAPP(c_Product__Type_OPair(U_8304,U_8304),U_8306),U_8308)),U_8310))
            | U_8305 != U_8307 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8303,U_8303)),hAPP(hAPP(c_Product__Type_OPair(U_8303,U_8303),U_8305),U_8307)),U_8309)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8304,U_8304)),hAPP(hAPP(c_Product__Type_OPair(U_8304,U_8304),U_8306),U_8308)),U_8310))
          & U_8305 = U_8307 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8303,U_8303)),hAPP(hAPP(c_Product__Type_OPair(U_8303,U_8303),U_8305),U_8307)),U_8309))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8303,U_8304),tc_prod(U_8303,U_8304))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8303,U_8304),tc_prod(U_8303,U_8304)),hAPP(hAPP(c_Product__Type_OPair(U_8303,U_8304),U_8305),U_8306)),hAPP(hAPP(c_Product__Type_OPair(U_8303,U_8304),U_8307),U_8308))),c_Wellfounded_Olex__prod(U_8303,U_8304,U_8309,U_8310))) ) ),
    inference(variable_rename,[status(thm)],[f_2316_1]) ).

fof(f_2316_3,plain,
    ( ! [U_8326,U_8324,U_8322,U_8320,U_8318,U_8316,U_8314,U_8312] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8312,U_8314),tc_prod(U_8312,U_8314))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8312,U_8314),tc_prod(U_8312,U_8314)),hAPP(hAPP(c_Product__Type_OPair(U_8312,U_8314),U_8316),U_8318)),hAPP(hAPP(c_Product__Type_OPair(U_8312,U_8314),U_8320),U_8322))),c_Wellfounded_Olex__prod(U_8312,U_8314,U_8324,U_8326)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8314,U_8314)),hAPP(hAPP(c_Product__Type_OPair(U_8314,U_8314),U_8318),U_8322)),U_8326))
            | U_8316 != U_8320 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8312,U_8312)),hAPP(hAPP(c_Product__Type_OPair(U_8312,U_8312),U_8316),U_8320)),U_8324)) ) )
    & ! [U_8325,U_8323,U_8321,U_8319,U_8317,U_8315,U_8313,U_8311] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8313,U_8313)),hAPP(hAPP(c_Product__Type_OPair(U_8313,U_8313),U_8317),U_8321)),U_8325))
          & U_8315 = U_8319 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8311,U_8311)),hAPP(hAPP(c_Product__Type_OPair(U_8311,U_8311),U_8315),U_8319)),U_8323))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8311,U_8313),tc_prod(U_8311,U_8313))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8311,U_8313),tc_prod(U_8311,U_8313)),hAPP(hAPP(c_Product__Type_OPair(U_8311,U_8313),U_8315),U_8317)),hAPP(hAPP(c_Product__Type_OPair(U_8311,U_8313),U_8319),U_8321))),c_Wellfounded_Olex__prod(U_8311,U_8313,U_8323,U_8325))) ) ),
    inference(miniscope,[status(thm)],[f_2316_2]) ).

fof(f_2316_4,plain,
    ( ! [U_8312,U_8314,U_8320,U_8316,U_8318,U_8322,U_8324,U_8326] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8314,U_8314)),hAPP(hAPP(c_Product__Type_OPair(U_8314,U_8314),U_8318),U_8322)),U_8326))
        | U_8316 != U_8320
        | ~ sP705(U_8312,U_8314,U_8320,U_8316,U_8318,U_8322,U_8324,U_8326) )
    & ! [U_8312,U_8314,U_8320,U_8316,U_8318,U_8322,U_8324,U_8326] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8312,U_8312)),hAPP(hAPP(c_Product__Type_OPair(U_8312,U_8312),U_8316),U_8320)),U_8324))
        | ~ sP705(U_8312,U_8314,U_8320,U_8316,U_8318,U_8322,U_8324,U_8326) )
    & ! [U_8313,U_8315,U_8317,U_8319,U_8321,U_8325] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8313,U_8313)),hAPP(hAPP(c_Product__Type_OPair(U_8313,U_8313),U_8317),U_8321)),U_8325))
        | ~ sP704(U_8313,U_8315,U_8317,U_8319,U_8321,U_8325) )
    & ! [U_8313,U_8315,U_8317,U_8319,U_8321,U_8325] :
        ( U_8315 = U_8319
        | ~ sP704(U_8313,U_8315,U_8317,U_8319,U_8321,U_8325) )
    & ! [U_8312,U_8314,U_8320,U_8316,U_8318,U_8322,U_8324,U_8326] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8312,U_8314),tc_prod(U_8312,U_8314))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8312,U_8314),tc_prod(U_8312,U_8314)),hAPP(hAPP(c_Product__Type_OPair(U_8312,U_8314),U_8316),U_8318)),hAPP(hAPP(c_Product__Type_OPair(U_8312,U_8314),U_8320),U_8322))),c_Wellfounded_Olex__prod(U_8312,U_8314,U_8324,U_8326)))
        | sP705(U_8312,U_8314,U_8320,U_8316,U_8318,U_8322,U_8324,U_8326) )
    & ! [U_8311,U_8313,U_8315,U_8317,U_8319,U_8321,U_8325,U_8323] :
        ( sP704(U_8313,U_8315,U_8317,U_8319,U_8321,U_8325)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8311,U_8311)),hAPP(hAPP(c_Product__Type_OPair(U_8311,U_8311),U_8315),U_8319)),U_8323))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8311,U_8313),tc_prod(U_8311,U_8313))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8311,U_8313),tc_prod(U_8311,U_8313)),hAPP(hAPP(c_Product__Type_OPair(U_8311,U_8313),U_8315),U_8317)),hAPP(hAPP(c_Product__Type_OPair(U_8311,U_8313),U_8319),U_8321))),c_Wellfounded_Olex__prod(U_8311,U_8313,U_8323,U_8325))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP704,sP705])],[f_2316_3]) ).

cnf(f_2316_5,plain,
    ( sP704(U_8313,U_8315,U_8317,U_8319,U_8321,U_8325)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8311,U_8311)),hAPP(hAPP(c_Product__Type_OPair(U_8311,U_8311),U_8315),U_8319)),U_8323))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8311,U_8313),tc_prod(U_8311,U_8313))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8311,U_8313),tc_prod(U_8311,U_8313)),hAPP(hAPP(c_Product__Type_OPair(U_8311,U_8313),U_8315),U_8317)),hAPP(hAPP(c_Product__Type_OPair(U_8311,U_8313),U_8319),U_8321))),c_Wellfounded_Olex__prod(U_8311,U_8313,U_8323,U_8325))) ),
    inference(clausify,[status(thm)],[f_2316_4]) ).

cnf(f_2316_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8312,U_8314),tc_prod(U_8312,U_8314))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8312,U_8314),tc_prod(U_8312,U_8314)),hAPP(hAPP(c_Product__Type_OPair(U_8312,U_8314),U_8316),U_8318)),hAPP(hAPP(c_Product__Type_OPair(U_8312,U_8314),U_8320),U_8322))),c_Wellfounded_Olex__prod(U_8312,U_8314,U_8324,U_8326)))
    | sP705(U_8312,U_8314,U_8320,U_8316,U_8318,U_8322,U_8324,U_8326) ),
    inference(clausify,[status(thm)],[f_2316_4]) ).

cnf(f_2316_7,plain,
    ( U_8315 = U_8319
    | ~ sP704(U_8313,U_8315,U_8317,U_8319,U_8321,U_8325) ),
    inference(clausify,[status(thm)],[f_2316_4]) ).

cnf(f_2316_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8313,U_8313)),hAPP(hAPP(c_Product__Type_OPair(U_8313,U_8313),U_8317),U_8321)),U_8325))
    | ~ sP704(U_8313,U_8315,U_8317,U_8319,U_8321,U_8325) ),
    inference(clausify,[status(thm)],[f_2316_4]) ).

cnf(f_2316_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8312,U_8312)),hAPP(hAPP(c_Product__Type_OPair(U_8312,U_8312),U_8316),U_8320)),U_8324))
    | ~ sP705(U_8312,U_8314,U_8320,U_8316,U_8318,U_8322,U_8324,U_8326) ),
    inference(clausify,[status(thm)],[f_2316_4]) ).

cnf(f_2316_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8314,U_8314)),hAPP(hAPP(c_Product__Type_OPair(U_8314,U_8314),U_8318),U_8322)),U_8326))
    | U_8316 != U_8320
    | ~ sP705(U_8312,U_8314,U_8320,U_8316,U_8318,U_8322,U_8324,U_8326) ),
    inference(clausify,[status(thm)],[f_2316_4]) ).

fof(f_2317_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_2317_2,plain,
    ! [U_8330,U_8329,U_8328,U_8327] :
      ( 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_8327),U_8329)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8328),U_8330))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8329),U_8330))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8327),U_8328)) ),
    inference(variable_rename,[status(thm)],[f_2317_1]) ).

fof(f_2317_3,plain,
    ! [U_8328,U_8330,U_8329,U_8327] :
      ( 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_8327),U_8329)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8328),U_8330))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8329),U_8330))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8327),U_8328)) ),
    inference(definitional_conversion,[status(esa)],[f_2317_2]) ).

cnf(f_2317_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_8327),U_8329)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8328),U_8330))),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8329),U_8330))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8327),U_8328)) ),
    inference(clausify,[status(thm)],[f_2317_3]) ).

fof(f_2318_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_2318_2,plain,
    ! [U_8331] :
      ( hBOOL(hAPP(hAPP(c_member(U_8331),c_Groups_Ozero__class_Ozero(U_8331)),c_Int_Oring__1__class_OInts(U_8331)))
      | ~ class_Rings_Oring__1(U_8331) ),
    inference(variable_rename,[status(thm)],[f_2318_1]) ).

fof(f_2318_3,plain,
    ! [U_8331] :
      ( hBOOL(hAPP(hAPP(c_member(U_8331),c_Groups_Ozero__class_Ozero(U_8331)),c_Int_Oring__1__class_OInts(U_8331)))
      | ~ class_Rings_Oring__1(U_8331) ),
    inference(definitional_conversion,[status(esa)],[f_2318_2]) ).

cnf(f_2318_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8331),c_Groups_Ozero__class_Ozero(U_8331)),c_Int_Oring__1__class_OInts(U_8331)))
    | ~ class_Rings_Oring__1(U_8331) ),
    inference(clausify,[status(thm)],[f_2318_3]) ).

fof(f_2319_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_2319_2,plain,
    ! [U_8334,U_8333,U_8332] :
      ( hBOOL(hAPP(hAPP(c_member(U_8332),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8332),U_8333),U_8334)),c_Int_Oring__1__class_OInts(U_8332)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8332),U_8334),c_Int_Oring__1__class_OInts(U_8332)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8332),U_8333),c_Int_Oring__1__class_OInts(U_8332)))
      | ~ class_Rings_Oring__1(U_8332) ),
    inference(variable_rename,[status(thm)],[f_2319_1]) ).

fof(f_2319_3,plain,
    ! [U_8332,U_8333,U_8334] :
      ( hBOOL(hAPP(hAPP(c_member(U_8332),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8332),U_8333),U_8334)),c_Int_Oring__1__class_OInts(U_8332)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8332),U_8334),c_Int_Oring__1__class_OInts(U_8332)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8332),U_8333),c_Int_Oring__1__class_OInts(U_8332)))
      | ~ class_Rings_Oring__1(U_8332) ),
    inference(definitional_conversion,[status(esa)],[f_2319_2]) ).

cnf(f_2319_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8332),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8332),U_8333),U_8334)),c_Int_Oring__1__class_OInts(U_8332)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8332),U_8334),c_Int_Oring__1__class_OInts(U_8332)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8332),U_8333),c_Int_Oring__1__class_OInts(U_8332)))
    | ~ class_Rings_Oring__1(U_8332) ),
    inference(clausify,[status(thm)],[f_2319_3]) ).

fof(f_2320_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_2320_2,plain,
    ! [U_8337,U_8336,U_8335] :
      ( hBOOL(hAPP(hAPP(c_member(U_8335),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8335),U_8336),U_8337)),c_Int_Oring__1__class_OInts(U_8335)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8335),U_8337),c_Int_Oring__1__class_OInts(U_8335)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8335),U_8336),c_Int_Oring__1__class_OInts(U_8335)))
      | ~ class_Rings_Oring__1(U_8335) ),
    inference(variable_rename,[status(thm)],[f_2320_1]) ).

fof(f_2320_3,plain,
    ! [U_8335,U_8336,U_8337] :
      ( hBOOL(hAPP(hAPP(c_member(U_8335),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8335),U_8336),U_8337)),c_Int_Oring__1__class_OInts(U_8335)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8335),U_8337),c_Int_Oring__1__class_OInts(U_8335)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8335),U_8336),c_Int_Oring__1__class_OInts(U_8335)))
      | ~ class_Rings_Oring__1(U_8335) ),
    inference(definitional_conversion,[status(esa)],[f_2320_2]) ).

cnf(f_2320_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8335),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8335),U_8336),U_8337)),c_Int_Oring__1__class_OInts(U_8335)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8335),U_8337),c_Int_Oring__1__class_OInts(U_8335)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8335),U_8336),c_Int_Oring__1__class_OInts(U_8335)))
    | ~ class_Rings_Oring__1(U_8335) ),
    inference(clausify,[status(thm)],[f_2320_3]) ).

fof(f_2321_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_2321_2,plain,
    ! [U_8340,U_8339,U_8338] :
      ( hBOOL(hAPP(hAPP(c_member(U_8338),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8338),U_8339),U_8340)),c_Int_Oring__1__class_OInts(U_8338)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8338),U_8340),c_Int_Oring__1__class_OInts(U_8338)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8338),U_8339),c_Int_Oring__1__class_OInts(U_8338)))
      | ~ class_Rings_Oring__1(U_8338) ),
    inference(variable_rename,[status(thm)],[f_2321_1]) ).

fof(f_2321_3,plain,
    ! [U_8338,U_8339,U_8340] :
      ( hBOOL(hAPP(hAPP(c_member(U_8338),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8338),U_8339),U_8340)),c_Int_Oring__1__class_OInts(U_8338)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8338),U_8340),c_Int_Oring__1__class_OInts(U_8338)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8338),U_8339),c_Int_Oring__1__class_OInts(U_8338)))
      | ~ class_Rings_Oring__1(U_8338) ),
    inference(definitional_conversion,[status(esa)],[f_2321_2]) ).

cnf(f_2321_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8338),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8338),U_8339),U_8340)),c_Int_Oring__1__class_OInts(U_8338)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8338),U_8340),c_Int_Oring__1__class_OInts(U_8338)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8338),U_8339),c_Int_Oring__1__class_OInts(U_8338)))
    | ~ class_Rings_Oring__1(U_8338) ),
    inference(clausify,[status(thm)],[f_2321_3]) ).

fof(f_2322_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_2322_2,plain,
    ! [U_8342,U_8341] :
      ( hBOOL(hAPP(hAPP(c_member(U_8341),hAPP(c_Int_Onumber__class_Onumber__of(U_8341),U_8342)),c_Int_Oring__1__class_OInts(U_8341)))
      | ~ class_Int_Onumber__ring(U_8341) ),
    inference(variable_rename,[status(thm)],[f_2322_1]) ).

fof(f_2322_3,plain,
    ! [U_8342,U_8341] :
      ( hBOOL(hAPP(hAPP(c_member(U_8341),hAPP(c_Int_Onumber__class_Onumber__of(U_8341),U_8342)),c_Int_Oring__1__class_OInts(U_8341)))
      | ~ class_Int_Onumber__ring(U_8341) ),
    inference(definitional_conversion,[status(esa)],[f_2322_2]) ).

cnf(f_2322_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8341),hAPP(c_Int_Onumber__class_Onumber__of(U_8341),U_8342)),c_Int_Oring__1__class_OInts(U_8341)))
    | ~ class_Int_Onumber__ring(U_8341) ),
    inference(clausify,[status(thm)],[f_2322_3]) ).

fof(f_2323_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_2323_2,plain,
    ! [U_8343] :
      ( hBOOL(hAPP(hAPP(c_member(U_8343),c_Groups_Oone__class_Oone(U_8343)),c_Int_Oring__1__class_OInts(U_8343)))
      | ~ class_Rings_Oring__1(U_8343) ),
    inference(variable_rename,[status(thm)],[f_2323_1]) ).

fof(f_2323_3,plain,
    ! [U_8343] :
      ( hBOOL(hAPP(hAPP(c_member(U_8343),c_Groups_Oone__class_Oone(U_8343)),c_Int_Oring__1__class_OInts(U_8343)))
      | ~ class_Rings_Oring__1(U_8343) ),
    inference(definitional_conversion,[status(esa)],[f_2323_2]) ).

cnf(f_2323_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8343),c_Groups_Oone__class_Oone(U_8343)),c_Int_Oring__1__class_OInts(U_8343)))
    | ~ class_Rings_Oring__1(U_8343) ),
    inference(clausify,[status(thm)],[f_2323_3]) ).

fof(f_2324_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_2324_2,plain,
    ! [U_8345,U_8344] :
      ( hBOOL(hAPP(hAPP(c_member(U_8344),hAPP(c_Groups_Ouminus__class_Ouminus(U_8344),U_8345)),c_Int_Oring__1__class_OInts(U_8344)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8344),U_8345),c_Int_Oring__1__class_OInts(U_8344)))
      | ~ class_Rings_Oring__1(U_8344) ),
    inference(variable_rename,[status(thm)],[f_2324_1]) ).

fof(f_2324_3,plain,
    ! [U_8344,U_8345] :
      ( hBOOL(hAPP(hAPP(c_member(U_8344),hAPP(c_Groups_Ouminus__class_Ouminus(U_8344),U_8345)),c_Int_Oring__1__class_OInts(U_8344)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8344),U_8345),c_Int_Oring__1__class_OInts(U_8344)))
      | ~ class_Rings_Oring__1(U_8344) ),
    inference(definitional_conversion,[status(esa)],[f_2324_2]) ).

cnf(f_2324_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8344),hAPP(c_Groups_Ouminus__class_Ouminus(U_8344),U_8345)),c_Int_Oring__1__class_OInts(U_8344)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8344),U_8345),c_Int_Oring__1__class_OInts(U_8344)))
    | ~ class_Rings_Oring__1(U_8344) ),
    inference(clausify,[status(thm)],[f_2324_3]) ).

fof(f_2325_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_2325_2,plain,
    ! [U_8347,U_8346] :
      ( hBOOL(hAPP(hAPP(c_member(U_8346),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8346),U_8347)),c_Int_Oring__1__class_OInts(U_8346)))
      | ~ class_Rings_Oring__1(U_8346) ),
    inference(variable_rename,[status(thm)],[f_2325_1]) ).

fof(f_2325_3,plain,
    ! [U_8346,U_8347] :
      ( hBOOL(hAPP(hAPP(c_member(U_8346),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8346),U_8347)),c_Int_Oring__1__class_OInts(U_8346)))
      | ~ class_Rings_Oring__1(U_8346) ),
    inference(definitional_conversion,[status(esa)],[f_2325_2]) ).

cnf(f_2325_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8346),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8346),U_8347)),c_Int_Oring__1__class_OInts(U_8346)))
    | ~ class_Rings_Oring__1(U_8346) ),
    inference(clausify,[status(thm)],[f_2325_3]) ).

fof(f_2326_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_2326_2,plain,
    ! [U_8350,U_8349,U_8348] :
      ( hBOOL(hAPP(hAPP(c_member(U_8348),hAPP(hAPP(c_Power_Opower__class_Opower(U_8348),U_8349),U_8350)),c_Int_Oring__1__class_OInts(U_8348)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8348),U_8349),c_Int_Oring__1__class_OInts(U_8348)))
      | ~ class_Rings_Oring__1(U_8348) ),
    inference(variable_rename,[status(thm)],[f_2326_1]) ).

fof(f_2326_3,plain,
    ! [U_8348,U_8349,U_8350] :
      ( hBOOL(hAPP(hAPP(c_member(U_8348),hAPP(hAPP(c_Power_Opower__class_Opower(U_8348),U_8349),U_8350)),c_Int_Oring__1__class_OInts(U_8348)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8348),U_8349),c_Int_Oring__1__class_OInts(U_8348)))
      | ~ class_Rings_Oring__1(U_8348) ),
    inference(definitional_conversion,[status(esa)],[f_2326_2]) ).

cnf(f_2326_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8348),hAPP(hAPP(c_Power_Opower__class_Opower(U_8348),U_8349),U_8350)),c_Int_Oring__1__class_OInts(U_8348)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8348),U_8349),c_Int_Oring__1__class_OInts(U_8348)))
    | ~ class_Rings_Oring__1(U_8348) ),
    inference(clausify,[status(thm)],[f_2326_3]) ).

fof(f_2327_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_2327_2,plain,
    ! [U_8352,U_8351] :
      ( hBOOL(hAPP(hAPP(c_member(U_8351),hAPP(c_Int_Oring__1__class_Oof__int(U_8351),U_8352)),c_Int_Oring__1__class_OInts(U_8351)))
      | ~ class_Rings_Oring__1(U_8351) ),
    inference(variable_rename,[status(thm)],[f_2327_1]) ).

fof(f_2327_3,plain,
    ! [U_8351,U_8352] :
      ( hBOOL(hAPP(hAPP(c_member(U_8351),hAPP(c_Int_Oring__1__class_Oof__int(U_8351),U_8352)),c_Int_Oring__1__class_OInts(U_8351)))
      | ~ class_Rings_Oring__1(U_8351) ),
    inference(definitional_conversion,[status(esa)],[f_2327_2]) ).

cnf(f_2327_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8351),hAPP(c_Int_Oring__1__class_Oof__int(U_8351),U_8352)),c_Int_Oring__1__class_OInts(U_8351)))
    | ~ class_Rings_Oring__1(U_8351) ),
    inference(clausify,[status(thm)],[f_2327_3]) ).

fof(f_2328_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_2328_2,plain,
    ! [U_8354,U_8353] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8353),U_8354),U_8354) = c_Groups_Ozero__class_Ozero(U_8353)
          | U_8354 != c_Groups_Ozero__class_Ozero(U_8353) )
        & ( U_8354 = c_Groups_Ozero__class_Ozero(U_8353)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8353),U_8354),U_8354) != c_Groups_Ozero__class_Ozero(U_8353) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_8353),U_8354),c_Int_Oring__1__class_OInts(U_8353)))
      | ~ class_Int_Oring__char__0(U_8353) ),
    inference(variable_rename,[status(thm)],[f_2328_1]) ).

fof(f_2328_3,plain,
    ( ! [U_8353,U_8354] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8353),U_8354),U_8354) = c_Groups_Ozero__class_Ozero(U_8353)
        | U_8354 != c_Groups_Ozero__class_Ozero(U_8353)
        | ~ sP706(U_8353,U_8354) )
    & ! [U_8353,U_8354] :
        ( U_8354 = c_Groups_Ozero__class_Ozero(U_8353)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8353),U_8354),U_8354) != c_Groups_Ozero__class_Ozero(U_8353)
        | ~ sP706(U_8353,U_8354) )
    & ! [U_8353,U_8354] :
        ( sP706(U_8353,U_8354)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8353),U_8354),c_Int_Oring__1__class_OInts(U_8353)))
        | ~ class_Int_Oring__char__0(U_8353) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP706])],[f_2328_2]) ).

cnf(f_2328_4,plain,
    ( sP706(U_8353,U_8354)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8353),U_8354),c_Int_Oring__1__class_OInts(U_8353)))
    | ~ class_Int_Oring__char__0(U_8353) ),
    inference(clausify,[status(thm)],[f_2328_3]) ).

cnf(f_2328_5,plain,
    ( U_8354 = c_Groups_Ozero__class_Ozero(U_8353)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8353),U_8354),U_8354) != c_Groups_Ozero__class_Ozero(U_8353)
    | ~ sP706(U_8353,U_8354) ),
    inference(clausify,[status(thm)],[f_2328_3]) ).

cnf(f_2328_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8353),U_8354),U_8354) = c_Groups_Ozero__class_Ozero(U_8353)
    | U_8354 != c_Groups_Ozero__class_Ozero(U_8353)
    | ~ sP706(U_8353,U_8354) ),
    inference(clausify,[status(thm)],[f_2328_3]) ).

fof(f_2329_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_2329_2,plain,
    ! [U_8358,U_8357,U_8356,U_8355] :
      ( 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_8355),U_8357)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8356),U_8358))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8355),U_8356)) ),
    inference(variable_rename,[status(thm)],[f_2329_1]) ).

fof(f_2329_3,plain,
    ! [U_8356,U_8355,U_8357,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_8355),U_8357)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8356),U_8358))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8355),U_8356)) ),
    inference(definitional_conversion,[status(esa)],[f_2329_2]) ).

cnf(f_2329_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_8355),U_8357)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8356),U_8358))),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8355),U_8356)) ),
    inference(clausify,[status(thm)],[f_2329_3]) ).

fof(f_2330_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_2330_2,plain,
    ! [U_8360,U_8359] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8359),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8359),c_Groups_Oone__class_Oone(U_8359)),U_8360)),U_8360) != c_Groups_Ozero__class_Ozero(U_8359)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8359),U_8360),c_Int_Oring__1__class_OInts(U_8359)))
      | ~ class_Int_Oring__char__0(U_8359) ),
    inference(variable_rename,[status(thm)],[f_2330_1]) ).

fof(f_2330_3,plain,
    ! [U_8359,U_8360] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8359),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8359),c_Groups_Oone__class_Oone(U_8359)),U_8360)),U_8360) != c_Groups_Ozero__class_Ozero(U_8359)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8359),U_8360),c_Int_Oring__1__class_OInts(U_8359)))
      | ~ class_Int_Oring__char__0(U_8359) ),
    inference(definitional_conversion,[status(esa)],[f_2330_2]) ).

cnf(f_2330_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8359),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8359),c_Groups_Oone__class_Oone(U_8359)),U_8360)),U_8360) != c_Groups_Ozero__class_Ozero(U_8359)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8359),U_8360),c_Int_Oring__1__class_OInts(U_8359)))
    | ~ class_Int_Oring__char__0(U_8359) ),
    inference(clausify,[status(thm)],[f_2330_3]) ).

fof(f_2331_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_2331_2,plain,
    ! [U_8367,U_8366,U_8365,U_8364,U_8363,U_8362,U_8361] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8367,U_8363),tc_prod(U_8367,U_8363))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8367,U_8363),tc_prod(U_8367,U_8363)),hAPP(hAPP(c_Product__Type_OPair(U_8367,U_8363),U_8362),U_8364)),hAPP(hAPP(c_Product__Type_OPair(U_8367,U_8363),U_8362),U_8365))),c_Recdef_Osame__fst(U_8367,U_8363,U_8361,U_8366)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8363,U_8363)),hAPP(hAPP(c_Product__Type_OPair(U_8363,U_8363),U_8364),U_8365)),hAPP(U_8366,U_8362)))
      | ~ hBOOL(hAPP(U_8361,U_8362)) ),
    inference(variable_rename,[status(thm)],[f_2331_1]) ).

fof(f_2331_3,plain,
    ! [U_8361,U_8362,U_8363,U_8364,U_8365,U_8366,U_8367] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8367,U_8363),tc_prod(U_8367,U_8363))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8367,U_8363),tc_prod(U_8367,U_8363)),hAPP(hAPP(c_Product__Type_OPair(U_8367,U_8363),U_8362),U_8364)),hAPP(hAPP(c_Product__Type_OPair(U_8367,U_8363),U_8362),U_8365))),c_Recdef_Osame__fst(U_8367,U_8363,U_8361,U_8366)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8363,U_8363)),hAPP(hAPP(c_Product__Type_OPair(U_8363,U_8363),U_8364),U_8365)),hAPP(U_8366,U_8362)))
      | ~ hBOOL(hAPP(U_8361,U_8362)) ),
    inference(definitional_conversion,[status(esa)],[f_2331_2]) ).

cnf(f_2331_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_8367,U_8363),tc_prod(U_8367,U_8363))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_8367,U_8363),tc_prod(U_8367,U_8363)),hAPP(hAPP(c_Product__Type_OPair(U_8367,U_8363),U_8362),U_8364)),hAPP(hAPP(c_Product__Type_OPair(U_8367,U_8363),U_8362),U_8365))),c_Recdef_Osame__fst(U_8367,U_8363,U_8361,U_8366)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8363,U_8363)),hAPP(hAPP(c_Product__Type_OPair(U_8363,U_8363),U_8364),U_8365)),hAPP(U_8366,U_8362)))
    | ~ hBOOL(hAPP(U_8361,U_8362)) ),
    inference(clausify,[status(thm)],[f_2331_3]) ).

fof(f_2332_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_2332_2,plain,
    ! [U_8371,U_8370,U_8369,U_8368] :
      ( 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_8368),U_8370)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8369),U_8371))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8370),U_8371))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8368),U_8369)) ),
    inference(variable_rename,[status(thm)],[f_2332_1]) ).

fof(f_2332_3,plain,
    ! [U_8368,U_8369,U_8370,U_8371] :
      ( 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_8368),U_8370)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8369),U_8371))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8370),U_8371))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8368),U_8369)) ),
    inference(definitional_conversion,[status(esa)],[f_2332_2]) ).

cnf(f_2332_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_8368),U_8370)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8369),U_8371))),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8370),U_8371))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8368),U_8369)) ),
    inference(clausify,[status(thm)],[f_2332_3]) ).

fof(f_2333_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_2333_2,plain,
    ! [U_8375,U_8374,U_8373,U_8372] :
      ( 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_8374),U_8375)),U_8373)),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_8375),U_8373)),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_8374),U_8372)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8372),U_8373)) ),
    inference(variable_rename,[status(thm)],[f_2333_1]) ).

fof(f_2333_3,plain,
    ! [U_8374,U_8373,U_8372,U_8375] :
      ( 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_8374),U_8375)),U_8373)),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_8375),U_8373)),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_8374),U_8372)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8372),U_8373)) ),
    inference(definitional_conversion,[status(esa)],[f_2333_2]) ).

cnf(f_2333_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_8374),U_8375)),U_8373)),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_8375),U_8373)),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_8374),U_8372)),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8372),U_8373)) ),
    inference(clausify,[status(thm)],[f_2333_3]) ).

fof(f_2334_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_2334_2,plain,
    ! [U_8379,U_8378,U_8377,U_8376] :
      ( 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_8377),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8378),U_8379))),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_8377),U_8379)),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_8376),U_8378)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8376),U_8377)) ),
    inference(variable_rename,[status(thm)],[f_2334_1]) ).

fof(f_2334_3,plain,
    ! [U_8377,U_8378,U_8376,U_8379] :
      ( 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_8377),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8378),U_8379))),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_8377),U_8379)),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_8376),U_8378)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8376),U_8377)) ),
    inference(definitional_conversion,[status(esa)],[f_2334_2]) ).

cnf(f_2334_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_8377),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8378),U_8379))),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_8377),U_8379)),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_8376),U_8378)),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8376),U_8377)) ),
    inference(clausify,[status(thm)],[f_2334_3]) ).

fof(f_2335_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_2335_2,plain,
    ! [U_8380] :
      ( 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_8380),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
      | U_8380 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2335_1]) ).

fof(f_2335_3,plain,
    ! [U_8380] :
      ( 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_8380),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
      | U_8380 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_2335_2]) ).

cnf(f_2335_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_8380),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
    | U_8380 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2335_3]) ).

fof(f_2336_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_2336_2,plain,
    ! [U_8384,U_8383,U_8382,U_8381] :
      ( 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_8381),U_8383)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8382),U_8384))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8381),U_8382)) ),
    inference(variable_rename,[status(thm)],[f_2336_1]) ).

fof(f_2336_3,plain,
    ! [U_8383,U_8382,U_8381,U_8384] :
      ( 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_8381),U_8383)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8382),U_8384))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8381),U_8382)) ),
    inference(definitional_conversion,[status(esa)],[f_2336_2]) ).

cnf(f_2336_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_8381),U_8383)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8382),U_8384))),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8381),U_8382)) ),
    inference(clausify,[status(thm)],[f_2336_3]) ).

fof(f_2337_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_2337_2,plain,
    ! [U_8388,U_8387,U_8386,U_8385] :
      ( 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_8386),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8387),U_8388))),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_8386),U_8388)),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_8385),U_8387)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8385),U_8386)) ),
    inference(variable_rename,[status(thm)],[f_2337_1]) ).

fof(f_2337_3,plain,
    ! [U_8385,U_8386,U_8387,U_8388] :
      ( 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_8386),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8387),U_8388))),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_8386),U_8388)),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_8385),U_8387)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8385),U_8386)) ),
    inference(definitional_conversion,[status(esa)],[f_2337_2]) ).

cnf(f_2337_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_8386),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8387),U_8388))),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_8386),U_8388)),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_8385),U_8387)),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8385),U_8386)) ),
    inference(clausify,[status(thm)],[f_2337_3]) ).

fof(f_2338_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_2338_2,plain,
    ! [U_8392,U_8391,U_8390,U_8389] :
      ( 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_8391),U_8392)),U_8390)),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_8392),U_8390)),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_8391),U_8389)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8389),U_8390)) ),
    inference(variable_rename,[status(thm)],[f_2338_1]) ).

fof(f_2338_3,plain,
    ! [U_8391,U_8390,U_8389,U_8392] :
      ( 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_8391),U_8392)),U_8390)),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_8392),U_8390)),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_8391),U_8389)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8389),U_8390)) ),
    inference(definitional_conversion,[status(esa)],[f_2338_2]) ).

cnf(f_2338_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_8391),U_8392)),U_8390)),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_8392),U_8390)),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_8391),U_8389)),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_8389),U_8390)) ),
    inference(clausify,[status(thm)],[f_2338_3]) ).

fof(f_2339_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_2339_2,plain,
    ! [U_8393] : 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_8393),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_2339_1]) ).

fof(f_2339_3,plain,
    ! [U_8393] : 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_8393),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_2339_2]) ).

cnf(f_2339_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_8393),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_2339_3]) ).

fof(f_2340_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_2340_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_2340_1]) ).

cnf(f_2340_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_2340_2]) ).

fof(f_2341_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_2341_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_2341_1]) ).

cnf(f_2341_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_2341_2]) ).

fof(f_2342_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_2342_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_2342_1]) ).

cnf(f_2342_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_2342_2]) ).

fof(f_2343_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_2343_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_2343_1]) ).

cnf(f_2343_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_2343_2]) ).

fof(f_2344_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_2344_2,plain,
    ! [U_8395,U_8394] :
      ( ( 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_8394),U_8395)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8394),U_8395)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8394),U_8395))
        | ~ 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_8394),U_8395)),c_Wellfounded_Oless__than)) ) ),
    inference(variable_rename,[status(thm)],[f_2344_1]) ).

fof(f_2344_3,plain,
    ( ! [U_8399,U_8397] :
        ( 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_8397),U_8399)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8397),U_8399)) )
    & ! [U_8398,U_8396] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8396),U_8398))
        | ~ 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_8396),U_8398)),c_Wellfounded_Oless__than)) ) ),
    inference(miniscope,[status(thm)],[f_2344_2]) ).

fof(f_2344_4,plain,
    ( ! [U_8397,U_8399] :
        ( 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_8397),U_8399)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8397),U_8399)) )
    & ! [U_8398,U_8396] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8396),U_8398))
        | ~ 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_8396),U_8398)),c_Wellfounded_Oless__than)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2344_3]) ).

cnf(f_2344_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8396),U_8398))
    | ~ 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_8396),U_8398)),c_Wellfounded_Oless__than)) ),
    inference(clausify,[status(thm)],[f_2344_4]) ).

cnf(f_2344_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_8397),U_8399)),c_Wellfounded_Oless__than))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8397),U_8399)) ),
    inference(clausify,[status(thm)],[f_2344_4]) ).

fof(f_2345_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_2345_2,plain,
    ! [U_8403,U_8402,U_8401,U_8400] :
      ( hBOOL(hAPP(U_8402,U_8403))
      | hBOOL(hAPP(U_8401,U_8403))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8400,tc_HOL_Obool)),U_8401),U_8402),U_8403)) ),
    inference(variable_rename,[status(thm)],[f_2345_1]) ).

fof(f_2345_3,plain,
    ! [U_8403,U_8402,U_8401] :
      ( ! [U_8400] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8400,tc_HOL_Obool)),U_8401),U_8402),U_8403))
      | hBOOL(hAPP(U_8402,U_8403))
      | hBOOL(hAPP(U_8401,U_8403)) ),
    inference(miniscope,[status(thm)],[f_2345_2]) ).

fof(f_2345_4,plain,
    ! [U_8400,U_8402,U_8401,U_8403] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8400,tc_HOL_Obool)),U_8401),U_8402),U_8403))
      | hBOOL(hAPP(U_8402,U_8403))
      | hBOOL(hAPP(U_8401,U_8403)) ),
    inference(definitional_conversion,[status(esa)],[f_2345_3]) ).

cnf(f_2345_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8400,tc_HOL_Obool)),U_8401),U_8402),U_8403))
    | hBOOL(hAPP(U_8402,U_8403))
    | hBOOL(hAPP(U_8401,U_8403)) ),
    inference(clausify,[status(thm)],[f_2345_4]) ).

fof(f_2346_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_2346_2,plain,
    ! [U_8407,U_8406,U_8405,U_8404] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8407,tc_HOL_Obool)),U_8406),U_8404),U_8405))
      | ( ~ hBOOL(hAPP(U_8406,U_8405))
        & ~ hBOOL(hAPP(U_8404,U_8405)) ) ),
    inference(variable_rename,[status(thm)],[f_2346_1]) ).

fof(f_2346_3,plain,
    ( ! [U_8404,U_8405,U_8406] :
        ( ~ hBOOL(hAPP(U_8406,U_8405))
        | ~ sP707(U_8404,U_8405,U_8406) )
    & ! [U_8404,U_8405,U_8406] :
        ( ~ hBOOL(hAPP(U_8404,U_8405))
        | ~ sP707(U_8404,U_8405,U_8406) )
    & ! [U_8404,U_8405,U_8406,U_8407] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8407,tc_HOL_Obool)),U_8406),U_8404),U_8405))
        | sP707(U_8404,U_8405,U_8406) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP707])],[f_2346_2]) ).

cnf(f_2346_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8407,tc_HOL_Obool)),U_8406),U_8404),U_8405))
    | sP707(U_8404,U_8405,U_8406) ),
    inference(clausify,[status(thm)],[f_2346_3]) ).

cnf(f_2346_5,plain,
    ( ~ hBOOL(hAPP(U_8404,U_8405))
    | ~ sP707(U_8404,U_8405,U_8406) ),
    inference(clausify,[status(thm)],[f_2346_3]) ).

cnf(f_2346_6,plain,
    ( ~ hBOOL(hAPP(U_8406,U_8405))
    | ~ sP707(U_8404,U_8405,U_8406) ),
    inference(clausify,[status(thm)],[f_2346_3]) ).

fof(f_2347_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_2347_2,plain,
    ! [U_8411,U_8410,U_8409,U_8408] :
      ( hBOOL(hAPP(hAPP(c_member(U_8408),U_8409),U_8411))
      | hBOOL(hAPP(hAPP(c_member(U_8408),U_8409),U_8410))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8408),U_8409),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8408,tc_HOL_Obool)),U_8410),U_8411))) ),
    inference(variable_rename,[status(thm)],[f_2347_1]) ).

fof(f_2347_3,plain,
    ! [U_8408,U_8409,U_8410,U_8411] :
      ( hBOOL(hAPP(hAPP(c_member(U_8408),U_8409),U_8411))
      | hBOOL(hAPP(hAPP(c_member(U_8408),U_8409),U_8410))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8408),U_8409),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8408,tc_HOL_Obool)),U_8410),U_8411))) ),
    inference(definitional_conversion,[status(esa)],[f_2347_2]) ).

cnf(f_2347_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8408),U_8409),U_8411))
    | hBOOL(hAPP(hAPP(c_member(U_8408),U_8409),U_8410))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8408),U_8409),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8408,tc_HOL_Obool)),U_8410),U_8411))) ),
    inference(clausify,[status(thm)],[f_2347_3]) ).

fof(f_2348_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_2348_2,plain,
    ! [U_8415,U_8414,U_8413,U_8412] :
      ( hBOOL(hAPP(hAPP(c_member(U_8412),U_8413),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8412,tc_HOL_Obool)),U_8415),U_8414)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_8412),U_8413),U_8415))
        & ~ hBOOL(hAPP(hAPP(c_member(U_8412),U_8413),U_8414)) ) ),
    inference(variable_rename,[status(thm)],[f_2348_1]) ).

fof(f_2348_3,plain,
    ( ! [U_8412,U_8413,U_8414,U_8415] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8412),U_8413),U_8415))
        | ~ sP708(U_8412,U_8413,U_8414,U_8415) )
    & ! [U_8412,U_8413,U_8414,U_8415] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8412),U_8413),U_8414))
        | ~ sP708(U_8412,U_8413,U_8414,U_8415) )
    & ! [U_8412,U_8413,U_8414,U_8415] :
        ( hBOOL(hAPP(hAPP(c_member(U_8412),U_8413),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8412,tc_HOL_Obool)),U_8415),U_8414)))
        | sP708(U_8412,U_8413,U_8414,U_8415) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP708])],[f_2348_2]) ).

cnf(f_2348_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8412),U_8413),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8412,tc_HOL_Obool)),U_8415),U_8414)))
    | sP708(U_8412,U_8413,U_8414,U_8415) ),
    inference(clausify,[status(thm)],[f_2348_3]) ).

cnf(f_2348_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8412),U_8413),U_8414))
    | ~ sP708(U_8412,U_8413,U_8414,U_8415) ),
    inference(clausify,[status(thm)],[f_2348_3]) ).

cnf(f_2348_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8412),U_8413),U_8415))
    | ~ sP708(U_8412,U_8413,U_8414,U_8415) ),
    inference(clausify,[status(thm)],[f_2348_3]) ).

fof(f_2349_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_2349_2,plain,
    ! [U_8418,U_8417,U_8416] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8416),U_8417),U_8418) = c_Orderings_Obot__class_Obot(U_8416)
          | U_8418 != c_Orderings_Obot__class_Obot(U_8416)
          | U_8417 != c_Orderings_Obot__class_Obot(U_8416) )
        & ( ( U_8418 = c_Orderings_Obot__class_Obot(U_8416)
            & U_8417 = c_Orderings_Obot__class_Obot(U_8416) )
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8416),U_8417),U_8418) != c_Orderings_Obot__class_Obot(U_8416) ) )
      | ~ class_Lattices_Obounded__lattice__bot(U_8416) ),
    inference(variable_rename,[status(thm)],[f_2349_1]) ).

fof(f_2349_3,plain,
    ( ! [U_8416,U_8418,U_8417] :
        ( U_8418 = c_Orderings_Obot__class_Obot(U_8416)
        | ~ sP709(U_8416,U_8418,U_8417) )
    & ! [U_8416,U_8418,U_8417] :
        ( U_8417 = c_Orderings_Obot__class_Obot(U_8416)
        | ~ sP709(U_8416,U_8418,U_8417) )
    & ! [U_8416,U_8418,U_8417] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8416),U_8417),U_8418) = c_Orderings_Obot__class_Obot(U_8416)
        | U_8418 != c_Orderings_Obot__class_Obot(U_8416)
        | U_8417 != c_Orderings_Obot__class_Obot(U_8416)
        | ~ sP710(U_8416,U_8418,U_8417) )
    & ! [U_8416,U_8418,U_8417] :
        ( sP709(U_8416,U_8418,U_8417)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8416),U_8417),U_8418) != c_Orderings_Obot__class_Obot(U_8416)
        | ~ sP710(U_8416,U_8418,U_8417) )
    & ! [U_8416,U_8418,U_8417] :
        ( sP710(U_8416,U_8418,U_8417)
        | ~ class_Lattices_Obounded__lattice__bot(U_8416) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP709,sP710])],[f_2349_2]) ).

cnf(f_2349_4,plain,
    ( sP710(U_8416,U_8418,U_8417)
    | ~ class_Lattices_Obounded__lattice__bot(U_8416) ),
    inference(clausify,[status(thm)],[f_2349_3]) ).

cnf(f_2349_5,plain,
    ( sP709(U_8416,U_8418,U_8417)
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8416),U_8417),U_8418) != c_Orderings_Obot__class_Obot(U_8416)
    | ~ sP710(U_8416,U_8418,U_8417) ),
    inference(clausify,[status(thm)],[f_2349_3]) ).

cnf(f_2349_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8416),U_8417),U_8418) = c_Orderings_Obot__class_Obot(U_8416)
    | U_8418 != c_Orderings_Obot__class_Obot(U_8416)
    | U_8417 != c_Orderings_Obot__class_Obot(U_8416)
    | ~ sP710(U_8416,U_8418,U_8417) ),
    inference(clausify,[status(thm)],[f_2349_3]) ).

cnf(f_2349_7,plain,
    ( U_8417 = c_Orderings_Obot__class_Obot(U_8416)
    | ~ sP709(U_8416,U_8418,U_8417) ),
    inference(clausify,[status(thm)],[f_2349_3]) ).

cnf(f_2349_8,plain,
    ( U_8418 = c_Orderings_Obot__class_Obot(U_8416)
    | ~ sP709(U_8416,U_8418,U_8417) ),
    inference(clausify,[status(thm)],[f_2349_3]) ).

fof(f_2350_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_2350_2,plain,
    ! [U_8420,U_8419] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8419),U_8420),c_Orderings_Obot__class_Obot(U_8419)) = U_8420
      | ~ class_Lattices_Obounded__lattice__bot(U_8419) ),
    inference(variable_rename,[status(thm)],[f_2350_1]) ).

fof(f_2350_3,plain,
    ! [U_8419,U_8420] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8419),U_8420),c_Orderings_Obot__class_Obot(U_8419)) = U_8420
      | ~ class_Lattices_Obounded__lattice__bot(U_8419) ),
    inference(definitional_conversion,[status(esa)],[f_2350_2]) ).

cnf(f_2350_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8419),U_8420),c_Orderings_Obot__class_Obot(U_8419)) = U_8420
    | ~ class_Lattices_Obounded__lattice__bot(U_8419) ),
    inference(clausify,[status(thm)],[f_2350_3]) ).

fof(f_2351_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_2351_2,plain,
    ! [U_8422,U_8421] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8421),c_Orderings_Obot__class_Obot(U_8421)),U_8422) = U_8422
      | ~ class_Lattices_Obounded__lattice__bot(U_8421) ),
    inference(variable_rename,[status(thm)],[f_2351_1]) ).

fof(f_2351_3,plain,
    ! [U_8422,U_8421] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8421),c_Orderings_Obot__class_Obot(U_8421)),U_8422) = U_8422
      | ~ class_Lattices_Obounded__lattice__bot(U_8421) ),
    inference(definitional_conversion,[status(esa)],[f_2351_2]) ).

cnf(f_2351_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8421),c_Orderings_Obot__class_Obot(U_8421)),U_8422) = U_8422
    | ~ class_Lattices_Obounded__lattice__bot(U_8421) ),
    inference(clausify,[status(thm)],[f_2351_3]) ).

fof(f_2352_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_2352_2,plain,
    ! [U_8425,U_8424,U_8423] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8423,tc_HOL_Obool)),U_8424),U_8425) = c_Orderings_Obot__class_Obot(tc_fun(U_8423,tc_HOL_Obool))
        | U_8425 != c_Orderings_Obot__class_Obot(tc_fun(U_8423,tc_HOL_Obool))
        | U_8424 != c_Orderings_Obot__class_Obot(tc_fun(U_8423,tc_HOL_Obool)) )
      & ( ( U_8425 = c_Orderings_Obot__class_Obot(tc_fun(U_8423,tc_HOL_Obool))
          & U_8424 = c_Orderings_Obot__class_Obot(tc_fun(U_8423,tc_HOL_Obool)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8423,tc_HOL_Obool)),U_8424),U_8425) != c_Orderings_Obot__class_Obot(tc_fun(U_8423,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2352_1]) ).

fof(f_2352_3,plain,
    ( ! [U_8431,U_8429,U_8427] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8427,tc_HOL_Obool)),U_8429),U_8431) = c_Orderings_Obot__class_Obot(tc_fun(U_8427,tc_HOL_Obool))
        | U_8431 != c_Orderings_Obot__class_Obot(tc_fun(U_8427,tc_HOL_Obool))
        | U_8429 != c_Orderings_Obot__class_Obot(tc_fun(U_8427,tc_HOL_Obool)) )
    & ! [U_8430,U_8428,U_8426] :
        ( ( U_8430 = c_Orderings_Obot__class_Obot(tc_fun(U_8426,tc_HOL_Obool))
          & U_8428 = c_Orderings_Obot__class_Obot(tc_fun(U_8426,tc_HOL_Obool)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8426,tc_HOL_Obool)),U_8428),U_8430) != c_Orderings_Obot__class_Obot(tc_fun(U_8426,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2352_2]) ).

fof(f_2352_4,plain,
    ( ! [U_8428,U_8430,U_8426] :
        ( U_8430 = c_Orderings_Obot__class_Obot(tc_fun(U_8426,tc_HOL_Obool))
        | ~ sP711(U_8428,U_8430,U_8426) )
    & ! [U_8428,U_8430,U_8426] :
        ( U_8428 = c_Orderings_Obot__class_Obot(tc_fun(U_8426,tc_HOL_Obool))
        | ~ sP711(U_8428,U_8430,U_8426) )
    & ! [U_8429,U_8431,U_8427] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8427,tc_HOL_Obool)),U_8429),U_8431) = c_Orderings_Obot__class_Obot(tc_fun(U_8427,tc_HOL_Obool))
        | U_8431 != c_Orderings_Obot__class_Obot(tc_fun(U_8427,tc_HOL_Obool))
        | U_8429 != c_Orderings_Obot__class_Obot(tc_fun(U_8427,tc_HOL_Obool)) )
    & ! [U_8428,U_8430,U_8426] :
        ( sP711(U_8428,U_8430,U_8426)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8426,tc_HOL_Obool)),U_8428),U_8430) != c_Orderings_Obot__class_Obot(tc_fun(U_8426,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP711])],[f_2352_3]) ).

cnf(f_2352_5,plain,
    ( sP711(U_8428,U_8430,U_8426)
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8426,tc_HOL_Obool)),U_8428),U_8430) != c_Orderings_Obot__class_Obot(tc_fun(U_8426,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2352_4]) ).

cnf(f_2352_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8427,tc_HOL_Obool)),U_8429),U_8431) = c_Orderings_Obot__class_Obot(tc_fun(U_8427,tc_HOL_Obool))
    | U_8431 != c_Orderings_Obot__class_Obot(tc_fun(U_8427,tc_HOL_Obool))
    | U_8429 != c_Orderings_Obot__class_Obot(tc_fun(U_8427,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2352_4]) ).

cnf(f_2352_7,plain,
    ( U_8428 = c_Orderings_Obot__class_Obot(tc_fun(U_8426,tc_HOL_Obool))
    | ~ sP711(U_8428,U_8430,U_8426) ),
    inference(clausify,[status(thm)],[f_2352_4]) ).

cnf(f_2352_8,plain,
    ( U_8430 = c_Orderings_Obot__class_Obot(tc_fun(U_8426,tc_HOL_Obool))
    | ~ sP711(U_8428,U_8430,U_8426) ),
    inference(clausify,[status(thm)],[f_2352_4]) ).

fof(f_2353_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_2353_2,plain,
    ! [U_8433,U_8432] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8432,tc_HOL_Obool)),U_8433),c_Orderings_Obot__class_Obot(tc_fun(U_8432,tc_HOL_Obool))) = U_8433,
    inference(variable_rename,[status(thm)],[f_2353_1]) ).

fof(f_2353_3,plain,
    ! [U_8433,U_8432] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8432,tc_HOL_Obool)),U_8433),c_Orderings_Obot__class_Obot(tc_fun(U_8432,tc_HOL_Obool))) = U_8433,
    inference(definitional_conversion,[status(esa)],[f_2353_2]) ).

cnf(f_2353_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8432,tc_HOL_Obool)),U_8433),c_Orderings_Obot__class_Obot(tc_fun(U_8432,tc_HOL_Obool))) = U_8433,
    inference(clausify,[status(thm)],[f_2353_3]) ).

fof(f_2354_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_2354_2,plain,
    ! [U_8435,U_8434] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8434,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8434,tc_HOL_Obool))),U_8435) = U_8435,
    inference(variable_rename,[status(thm)],[f_2354_1]) ).

fof(f_2354_3,plain,
    ! [U_8434,U_8435] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8434,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8434,tc_HOL_Obool))),U_8435) = U_8435,
    inference(definitional_conversion,[status(esa)],[f_2354_2]) ).

cnf(f_2354_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8434,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8434,tc_HOL_Obool))),U_8435) = U_8435,
    inference(clausify,[status(thm)],[f_2354_3]) ).

fof(f_2355_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_2355_2,plain,
    ! [U_8439,U_8438,U_8437,U_8436] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8436),U_8438),U_8439))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8436),U_8437),U_8439)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8436),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8436),U_8437),U_8438)),U_8439))
      | ~ class_Lattices_Osemilattice__sup(U_8436) ),
    inference(variable_rename,[status(thm)],[f_2355_1]) ).

fof(f_2355_3,plain,
    ( ! [U_8436,U_8437,U_8438,U_8439] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8436),U_8438),U_8439))
        | ~ sP712(U_8436,U_8437,U_8438,U_8439) )
    & ! [U_8436,U_8437,U_8438,U_8439] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8436),U_8437),U_8439))
        | ~ sP712(U_8436,U_8437,U_8438,U_8439) )
    & ! [U_8436,U_8437,U_8438,U_8439] :
        ( sP712(U_8436,U_8437,U_8438,U_8439)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8436),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8436),U_8437),U_8438)),U_8439))
        | ~ class_Lattices_Osemilattice__sup(U_8436) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP712])],[f_2355_2]) ).

cnf(f_2355_4,plain,
    ( sP712(U_8436,U_8437,U_8438,U_8439)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8436),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8436),U_8437),U_8438)),U_8439))
    | ~ class_Lattices_Osemilattice__sup(U_8436) ),
    inference(clausify,[status(thm)],[f_2355_3]) ).

cnf(f_2355_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8436),U_8437),U_8439))
    | ~ sP712(U_8436,U_8437,U_8438,U_8439) ),
    inference(clausify,[status(thm)],[f_2355_3]) ).

cnf(f_2355_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8436),U_8438),U_8439))
    | ~ sP712(U_8436,U_8437,U_8438,U_8439) ),
    inference(clausify,[status(thm)],[f_2355_3]) ).

fof(f_2356_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_2356_2,plain,
    ! [U_8444,U_8443,U_8442,U_8441,U_8440] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8440),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8440),U_8441),U_8443)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8440),U_8442),U_8444)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8440),U_8443),U_8444))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8440),U_8441),U_8442))
      | ~ class_Lattices_Osemilattice__sup(U_8440) ),
    inference(variable_rename,[status(thm)],[f_2356_1]) ).

fof(f_2356_3,plain,
    ! [U_8441,U_8440,U_8442,U_8443,U_8444] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8440),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8440),U_8441),U_8443)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8440),U_8442),U_8444)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8440),U_8443),U_8444))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8440),U_8441),U_8442))
      | ~ class_Lattices_Osemilattice__sup(U_8440) ),
    inference(definitional_conversion,[status(esa)],[f_2356_2]) ).

cnf(f_2356_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8440),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8440),U_8441),U_8443)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8440),U_8442),U_8444)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8440),U_8443),U_8444))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8440),U_8441),U_8442))
    | ~ class_Lattices_Osemilattice__sup(U_8440) ),
    inference(clausify,[status(thm)],[f_2356_3]) ).

fof(f_2357_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_2357_2,plain,
    ! [U_8448,U_8447,U_8446,U_8445] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8445),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8445),U_8446),U_8448)),U_8447))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8445),U_8448),U_8447))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8445),U_8446),U_8447))
      | ~ class_Lattices_Osemilattice__sup(U_8445) ),
    inference(variable_rename,[status(thm)],[f_2357_1]) ).

fof(f_2357_3,plain,
    ! [U_8445,U_8446,U_8447,U_8448] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8445),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8445),U_8446),U_8448)),U_8447))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8445),U_8448),U_8447))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8445),U_8446),U_8447))
      | ~ class_Lattices_Osemilattice__sup(U_8445) ),
    inference(definitional_conversion,[status(esa)],[f_2357_2]) ).

cnf(f_2357_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8445),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8445),U_8446),U_8448)),U_8447))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8445),U_8448),U_8447))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8445),U_8446),U_8447))
    | ~ class_Lattices_Osemilattice__sup(U_8445) ),
    inference(clausify,[status(thm)],[f_2357_3]) ).

fof(f_2358_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_2358_2,plain,
    ! [U_8452,U_8451,U_8450,U_8449] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8449),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8449),U_8450),U_8452)),U_8451))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8449),U_8452),U_8451))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8449),U_8450),U_8451))
      | ~ class_Lattices_Osemilattice__sup(U_8449) ),
    inference(variable_rename,[status(thm)],[f_2358_1]) ).

fof(f_2358_3,plain,
    ! [U_8449,U_8450,U_8451,U_8452] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8449),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8449),U_8450),U_8452)),U_8451))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8449),U_8452),U_8451))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8449),U_8450),U_8451))
      | ~ class_Lattices_Osemilattice__sup(U_8449) ),
    inference(definitional_conversion,[status(esa)],[f_2358_2]) ).

cnf(f_2358_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8449),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8449),U_8450),U_8452)),U_8451))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8449),U_8452),U_8451))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8449),U_8450),U_8451))
    | ~ class_Lattices_Osemilattice__sup(U_8449) ),
    inference(clausify,[status(thm)],[f_2358_3]) ).

fof(f_2359_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_2359_2,plain,
    ! [U_8455,U_8454,U_8453] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8453),U_8455),U_8454) = U_8455
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8453),U_8454),U_8455))
      | ~ class_Lattices_Osemilattice__sup(U_8453) ),
    inference(variable_rename,[status(thm)],[f_2359_1]) ).

fof(f_2359_3,plain,
    ! [U_8453,U_8454,U_8455] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8453),U_8455),U_8454) = U_8455
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8453),U_8454),U_8455))
      | ~ class_Lattices_Osemilattice__sup(U_8453) ),
    inference(definitional_conversion,[status(esa)],[f_2359_2]) ).

cnf(f_2359_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8453),U_8455),U_8454) = U_8455
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8453),U_8454),U_8455))
    | ~ class_Lattices_Osemilattice__sup(U_8453) ),
    inference(clausify,[status(thm)],[f_2359_3]) ).

fof(f_2360_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_2360_2,plain,
    ! [U_8458,U_8457,U_8456] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8456),U_8457),U_8458) = U_8458
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8456),U_8457),U_8458))
      | ~ class_Lattices_Osemilattice__sup(U_8456) ),
    inference(variable_rename,[status(thm)],[f_2360_1]) ).

fof(f_2360_3,plain,
    ! [U_8456,U_8457,U_8458] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8456),U_8457),U_8458) = U_8458
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8456),U_8457),U_8458))
      | ~ class_Lattices_Osemilattice__sup(U_8456) ),
    inference(definitional_conversion,[status(esa)],[f_2360_2]) ).

cnf(f_2360_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8456),U_8457),U_8458) = U_8458
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8456),U_8457),U_8458))
    | ~ class_Lattices_Osemilattice__sup(U_8456) ),
    inference(clausify,[status(thm)],[f_2360_3]) ).

fof(f_2361_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_2361_2,plain,
    ! [U_8462,U_8461,U_8460,U_8459] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8459),U_8460),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8459),U_8462),U_8461)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8459),U_8460),U_8461))
      | ~ class_Lattices_Osemilattice__sup(U_8459) ),
    inference(variable_rename,[status(thm)],[f_2361_1]) ).

fof(f_2361_3,plain,
    ! [U_8459,U_8460,U_8461,U_8462] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8459),U_8460),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8459),U_8462),U_8461)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8459),U_8460),U_8461))
      | ~ class_Lattices_Osemilattice__sup(U_8459) ),
    inference(definitional_conversion,[status(esa)],[f_2361_2]) ).

cnf(f_2361_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8459),U_8460),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8459),U_8462),U_8461)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8459),U_8460),U_8461))
    | ~ class_Lattices_Osemilattice__sup(U_8459) ),
    inference(clausify,[status(thm)],[f_2361_3]) ).

fof(f_2362_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_2362_2,plain,
    ! [U_8466,U_8465,U_8464,U_8463] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8463),U_8464),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8463),U_8465),U_8466)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8463),U_8464),U_8465))
      | ~ class_Lattices_Osemilattice__sup(U_8463) ),
    inference(variable_rename,[status(thm)],[f_2362_1]) ).

fof(f_2362_3,plain,
    ! [U_8463,U_8464,U_8465,U_8466] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8463),U_8464),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8463),U_8465),U_8466)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8463),U_8464),U_8465))
      | ~ class_Lattices_Osemilattice__sup(U_8463) ),
    inference(definitional_conversion,[status(esa)],[f_2362_2]) ).

cnf(f_2362_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8463),U_8464),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8463),U_8465),U_8466)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8463),U_8464),U_8465))
    | ~ class_Lattices_Osemilattice__sup(U_8463) ),
    inference(clausify,[status(thm)],[f_2362_3]) ).

fof(f_2363_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_2363_2,plain,
    ! [U_8470,U_8469,U_8468,U_8467] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8467),U_8468),U_8469)),U_8470))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8469),U_8470))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8468),U_8470)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8469),U_8470))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8468),U_8470)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8467),U_8468),U_8469)),U_8470)) ) )
      | ~ class_Lattices_Osemilattice__sup(U_8467) ),
    inference(variable_rename,[status(thm)],[f_2363_1]) ).

fof(f_2363_3,plain,
    ( ! [U_8467,U_8468,U_8469,U_8470] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8469),U_8470))
        | ~ sP713(U_8467,U_8468,U_8469,U_8470) )
    & ! [U_8467,U_8468,U_8469,U_8470] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8468),U_8470))
        | ~ sP713(U_8467,U_8468,U_8469,U_8470) )
    & ! [U_8467,U_8468,U_8469,U_8470] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8467),U_8468),U_8469)),U_8470))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8469),U_8470))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8468),U_8470))
        | ~ sP714(U_8467,U_8468,U_8469,U_8470) )
    & ! [U_8467,U_8468,U_8469,U_8470] :
        ( sP713(U_8467,U_8468,U_8469,U_8470)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8467),U_8468),U_8469)),U_8470))
        | ~ sP714(U_8467,U_8468,U_8469,U_8470) )
    & ! [U_8467,U_8468,U_8469,U_8470] :
        ( sP714(U_8467,U_8468,U_8469,U_8470)
        | ~ class_Lattices_Osemilattice__sup(U_8467) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP713,sP714])],[f_2363_2]) ).

cnf(f_2363_4,plain,
    ( sP714(U_8467,U_8468,U_8469,U_8470)
    | ~ class_Lattices_Osemilattice__sup(U_8467) ),
    inference(clausify,[status(thm)],[f_2363_3]) ).

cnf(f_2363_5,plain,
    ( sP713(U_8467,U_8468,U_8469,U_8470)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8467),U_8468),U_8469)),U_8470))
    | ~ sP714(U_8467,U_8468,U_8469,U_8470) ),
    inference(clausify,[status(thm)],[f_2363_3]) ).

cnf(f_2363_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8467),U_8468),U_8469)),U_8470))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8469),U_8470))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8468),U_8470))
    | ~ sP714(U_8467,U_8468,U_8469,U_8470) ),
    inference(clausify,[status(thm)],[f_2363_3]) ).

cnf(f_2363_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8468),U_8470))
    | ~ sP713(U_8467,U_8468,U_8469,U_8470) ),
    inference(clausify,[status(thm)],[f_2363_3]) ).

cnf(f_2363_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8467),U_8469),U_8470))
    | ~ sP713(U_8467,U_8468,U_8469,U_8470) ),
    inference(clausify,[status(thm)],[f_2363_3]) ).

fof(f_2364_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_2364_2,plain,
    ! [U_8473,U_8472,U_8471] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8471),U_8472),U_8473))
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8471),U_8472),U_8473) != U_8473 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8471),U_8472),U_8473) = U_8473
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8471),U_8472),U_8473)) ) )
      | ~ class_Lattices_Osemilattice__sup(U_8471) ),
    inference(variable_rename,[status(thm)],[f_2364_1]) ).

fof(f_2364_3,plain,
    ( ! [U_8473,U_8472,U_8471] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8471),U_8472),U_8473))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8471),U_8472),U_8473) != U_8473
        | ~ sP715(U_8473,U_8472,U_8471) )
    & ! [U_8473,U_8472,U_8471] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8471),U_8472),U_8473) = U_8473
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8471),U_8472),U_8473))
        | ~ sP715(U_8473,U_8472,U_8471) )
    & ! [U_8473,U_8472,U_8471] :
        ( sP715(U_8473,U_8472,U_8471)
        | ~ class_Lattices_Osemilattice__sup(U_8471) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP715])],[f_2364_2]) ).

cnf(f_2364_4,plain,
    ( sP715(U_8473,U_8472,U_8471)
    | ~ class_Lattices_Osemilattice__sup(U_8471) ),
    inference(clausify,[status(thm)],[f_2364_3]) ).

cnf(f_2364_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8471),U_8472),U_8473) = U_8473
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8471),U_8472),U_8473))
    | ~ sP715(U_8473,U_8472,U_8471) ),
    inference(clausify,[status(thm)],[f_2364_3]) ).

cnf(f_2364_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8471),U_8472),U_8473))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8471),U_8472),U_8473) != U_8473
    | ~ sP715(U_8473,U_8472,U_8471) ),
    inference(clausify,[status(thm)],[f_2364_3]) ).

fof(f_2365_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_2365_2,plain,
    ! [U_8476,U_8475,U_8474] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8474),U_8475),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8474),U_8476),U_8475)))
      | ~ class_Lattices_Osemilattice__sup(U_8474) ),
    inference(variable_rename,[status(thm)],[f_2365_1]) ).

fof(f_2365_3,plain,
    ! [U_8475,U_8474,U_8476] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8474),U_8475),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8474),U_8476),U_8475)))
      | ~ class_Lattices_Osemilattice__sup(U_8474) ),
    inference(definitional_conversion,[status(esa)],[f_2365_2]) ).

cnf(f_2365_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8474),U_8475),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8474),U_8476),U_8475)))
    | ~ class_Lattices_Osemilattice__sup(U_8474) ),
    inference(clausify,[status(thm)],[f_2365_3]) ).

fof(f_2366_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_2366_2,plain,
    ! [U_8479,U_8478,U_8477] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8478),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8477),U_8479),U_8478)))
      | ~ class_Lattices_Olattice(U_8477) ),
    inference(variable_rename,[status(thm)],[f_2366_1]) ).

fof(f_2366_3,plain,
    ! [U_8477,U_8478,U_8479] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8478),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8477),U_8479),U_8478)))
      | ~ class_Lattices_Olattice(U_8477) ),
    inference(definitional_conversion,[status(esa)],[f_2366_2]) ).

cnf(f_2366_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8477),U_8478),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8477),U_8479),U_8478)))
    | ~ class_Lattices_Olattice(U_8477) ),
    inference(clausify,[status(thm)],[f_2366_3]) ).

fof(f_2367_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_2367_2,plain,
    ! [U_8482,U_8481,U_8480] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8480),U_8481),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8480),U_8481),U_8482)))
      | ~ class_Lattices_Osemilattice__sup(U_8480) ),
    inference(variable_rename,[status(thm)],[f_2367_1]) ).

fof(f_2367_3,plain,
    ! [U_8480,U_8481,U_8482] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8480),U_8481),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8480),U_8481),U_8482)))
      | ~ class_Lattices_Osemilattice__sup(U_8480) ),
    inference(definitional_conversion,[status(esa)],[f_2367_2]) ).

cnf(f_2367_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8480),U_8481),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8480),U_8481),U_8482)))
    | ~ class_Lattices_Osemilattice__sup(U_8480) ),
    inference(clausify,[status(thm)],[f_2367_3]) ).

fof(f_2368_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_2368_2,plain,
    ! [U_8485,U_8484,U_8483] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8483),U_8484),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8483),U_8484),U_8485)))
      | ~ class_Lattices_Olattice(U_8483) ),
    inference(variable_rename,[status(thm)],[f_2368_1]) ).

fof(f_2368_3,plain,
    ! [U_8483,U_8484,U_8485] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8483),U_8484),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8483),U_8484),U_8485)))
      | ~ class_Lattices_Olattice(U_8483) ),
    inference(definitional_conversion,[status(esa)],[f_2368_2]) ).

cnf(f_2368_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8483),U_8484),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8483),U_8484),U_8485)))
    | ~ class_Lattices_Olattice(U_8483) ),
    inference(clausify,[status(thm)],[f_2368_3]) ).

fof(f_2369_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_2369_2,plain,
    ! [U_8490,U_8489,U_8488,U_8487,U_8486] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8486,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8486,tc_HOL_Obool)),U_8487),U_8489)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8486,tc_HOL_Obool)),U_8488),U_8490)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8486,tc_HOL_Obool)),U_8489),U_8490))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8486,tc_HOL_Obool)),U_8487),U_8488)) ),
    inference(variable_rename,[status(thm)],[f_2369_1]) ).

fof(f_2369_3,plain,
    ! [U_8486,U_8487,U_8488,U_8489,U_8490] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8486,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8486,tc_HOL_Obool)),U_8487),U_8489)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8486,tc_HOL_Obool)),U_8488),U_8490)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8486,tc_HOL_Obool)),U_8489),U_8490))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8486,tc_HOL_Obool)),U_8487),U_8488)) ),
    inference(definitional_conversion,[status(esa)],[f_2369_2]) ).

cnf(f_2369_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8486,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8486,tc_HOL_Obool)),U_8487),U_8489)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8486,tc_HOL_Obool)),U_8488),U_8490)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8486,tc_HOL_Obool)),U_8489),U_8490))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8486,tc_HOL_Obool)),U_8487),U_8488)) ),
    inference(clausify,[status(thm)],[f_2369_3]) ).

fof(f_2370_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_2370_2,plain,
    ! [U_8494,U_8493,U_8492,U_8491] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8491,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8491,tc_HOL_Obool)),U_8492),U_8494)),U_8493))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8491,tc_HOL_Obool)),U_8494),U_8493))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8491,tc_HOL_Obool)),U_8492),U_8493)) ),
    inference(variable_rename,[status(thm)],[f_2370_1]) ).

fof(f_2370_3,plain,
    ! [U_8491,U_8492,U_8493,U_8494] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8491,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8491,tc_HOL_Obool)),U_8492),U_8494)),U_8493))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8491,tc_HOL_Obool)),U_8494),U_8493))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8491,tc_HOL_Obool)),U_8492),U_8493)) ),
    inference(definitional_conversion,[status(esa)],[f_2370_2]) ).

cnf(f_2370_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8491,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8491,tc_HOL_Obool)),U_8492),U_8494)),U_8493))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8491,tc_HOL_Obool)),U_8494),U_8493))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8491,tc_HOL_Obool)),U_8492),U_8493)) ),
    inference(clausify,[status(thm)],[f_2370_3]) ).

fof(f_2371_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_2371_2,plain,
    ! [U_8497,U_8496,U_8495] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8495,tc_HOL_Obool)),U_8497),U_8496) = U_8497
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8495,tc_HOL_Obool)),U_8496),U_8497)) ),
    inference(variable_rename,[status(thm)],[f_2371_1]) ).

fof(f_2371_3,plain,
    ! [U_8495,U_8496,U_8497] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8495,tc_HOL_Obool)),U_8497),U_8496) = U_8497
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8495,tc_HOL_Obool)),U_8496),U_8497)) ),
    inference(definitional_conversion,[status(esa)],[f_2371_2]) ).

cnf(f_2371_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8495,tc_HOL_Obool)),U_8497),U_8496) = U_8497
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8495,tc_HOL_Obool)),U_8496),U_8497)) ),
    inference(clausify,[status(thm)],[f_2371_3]) ).

fof(f_2372_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_2372_2,plain,
    ! [U_8500,U_8499,U_8498] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8498,tc_HOL_Obool)),U_8499),U_8500) = U_8500
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8498,tc_HOL_Obool)),U_8499),U_8500)) ),
    inference(variable_rename,[status(thm)],[f_2372_1]) ).

fof(f_2372_3,plain,
    ! [U_8498,U_8499,U_8500] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8498,tc_HOL_Obool)),U_8499),U_8500) = U_8500
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8498,tc_HOL_Obool)),U_8499),U_8500)) ),
    inference(definitional_conversion,[status(esa)],[f_2372_2]) ).

cnf(f_2372_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8498,tc_HOL_Obool)),U_8499),U_8500) = U_8500
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8498,tc_HOL_Obool)),U_8499),U_8500)) ),
    inference(clausify,[status(thm)],[f_2372_3]) ).

fof(f_2373_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_2373_2,plain,
    ! [U_8503,U_8502,U_8501] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8501,tc_HOL_Obool)),U_8502),U_8503))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8501,tc_HOL_Obool)),U_8502),U_8503) != U_8503 )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8501,tc_HOL_Obool)),U_8502),U_8503) = U_8503
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8501,tc_HOL_Obool)),U_8502),U_8503)) ) ),
    inference(variable_rename,[status(thm)],[f_2373_1]) ).

fof(f_2373_3,plain,
    ( ! [U_8509,U_8507,U_8505] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8505,tc_HOL_Obool)),U_8507),U_8509))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8505,tc_HOL_Obool)),U_8507),U_8509) != U_8509 )
    & ! [U_8508,U_8506,U_8504] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8504,tc_HOL_Obool)),U_8506),U_8508) = U_8508
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8504,tc_HOL_Obool)),U_8506),U_8508)) ) ),
    inference(miniscope,[status(thm)],[f_2373_2]) ).

fof(f_2373_4,plain,
    ( ! [U_8507,U_8505,U_8509] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8505,tc_HOL_Obool)),U_8507),U_8509))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8505,tc_HOL_Obool)),U_8507),U_8509) != U_8509 )
    & ! [U_8506,U_8508,U_8504] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8504,tc_HOL_Obool)),U_8506),U_8508) = U_8508
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8504,tc_HOL_Obool)),U_8506),U_8508)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2373_3]) ).

cnf(f_2373_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8504,tc_HOL_Obool)),U_8506),U_8508) = U_8508
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8504,tc_HOL_Obool)),U_8506),U_8508)) ),
    inference(clausify,[status(thm)],[f_2373_4]) ).

cnf(f_2373_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8505,tc_HOL_Obool)),U_8507),U_8509))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8505,tc_HOL_Obool)),U_8507),U_8509) != U_8509 ),
    inference(clausify,[status(thm)],[f_2373_4]) ).

fof(f_2374_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_2374_2,plain,
    ! [U_8512,U_8511,U_8510] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8510,tc_HOL_Obool)),U_8511),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8510,tc_HOL_Obool)),U_8512),U_8511))),
    inference(variable_rename,[status(thm)],[f_2374_1]) ).

fof(f_2374_3,plain,
    ! [U_8510,U_8511,U_8512] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8510,tc_HOL_Obool)),U_8511),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8510,tc_HOL_Obool)),U_8512),U_8511))),
    inference(definitional_conversion,[status(esa)],[f_2374_2]) ).

cnf(f_2374_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8510,tc_HOL_Obool)),U_8511),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8510,tc_HOL_Obool)),U_8512),U_8511))),
    inference(clausify,[status(thm)],[f_2374_3]) ).

fof(f_2375_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_2375_2,plain,
    ! [U_8515,U_8514,U_8513] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8513,tc_HOL_Obool)),U_8514),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8513,tc_HOL_Obool)),U_8514),U_8515))),
    inference(variable_rename,[status(thm)],[f_2375_1]) ).

fof(f_2375_3,plain,
    ! [U_8513,U_8514,U_8515] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8513,tc_HOL_Obool)),U_8514),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8513,tc_HOL_Obool)),U_8514),U_8515))),
    inference(definitional_conversion,[status(esa)],[f_2375_2]) ).

cnf(f_2375_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8513,tc_HOL_Obool)),U_8514),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8513,tc_HOL_Obool)),U_8514),U_8515))),
    inference(clausify,[status(thm)],[f_2375_3]) ).

fof(f_2376_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_2376_2,plain,
    ! [U_8519,U_8518,U_8517,U_8516] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8518,tc_HOL_Obool)),U_8516),U_8519),U_8517))
      | ~ hBOOL(hAPP(U_8516,U_8517)) ),
    inference(variable_rename,[status(thm)],[f_2376_1]) ).

fof(f_2376_3,plain,
    ! [U_8516,U_8517,U_8518,U_8519] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8518,tc_HOL_Obool)),U_8516),U_8519),U_8517))
      | ~ hBOOL(hAPP(U_8516,U_8517)) ),
    inference(definitional_conversion,[status(esa)],[f_2376_2]) ).

cnf(f_2376_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8518,tc_HOL_Obool)),U_8516),U_8519),U_8517))
    | ~ hBOOL(hAPP(U_8516,U_8517)) ),
    inference(clausify,[status(thm)],[f_2376_3]) ).

fof(f_2377_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_2377_2,plain,
    ! [U_8523,U_8522,U_8521,U_8520] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8522,tc_HOL_Obool)),U_8523),U_8520),U_8521))
      | ~ hBOOL(hAPP(U_8520,U_8521)) ),
    inference(variable_rename,[status(thm)],[f_2377_1]) ).

fof(f_2377_3,plain,
    ! [U_8520,U_8521,U_8522,U_8523] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8522,tc_HOL_Obool)),U_8523),U_8520),U_8521))
      | ~ hBOOL(hAPP(U_8520,U_8521)) ),
    inference(definitional_conversion,[status(esa)],[f_2377_2]) ).

cnf(f_2377_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8522,tc_HOL_Obool)),U_8523),U_8520),U_8521))
    | ~ hBOOL(hAPP(U_8520,U_8521)) ),
    inference(clausify,[status(thm)],[f_2377_3]) ).

fof(f_2378_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_2378_2,plain,
    ! [U_8526,U_8525,U_8524] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8524,tc_HOL_Obool)),U_8525),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8524,tc_HOL_Obool)),U_8526),U_8525)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8524,tc_HOL_Obool)),U_8525),U_8526),
    inference(variable_rename,[status(thm)],[f_2378_1]) ).

fof(f_2378_3,plain,
    ! [U_8524,U_8525,U_8526] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8524,tc_HOL_Obool)),U_8525),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8524,tc_HOL_Obool)),U_8526),U_8525)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8524,tc_HOL_Obool)),U_8525),U_8526),
    inference(definitional_conversion,[status(esa)],[f_2378_2]) ).

cnf(f_2378_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8524,tc_HOL_Obool)),U_8525),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8524,tc_HOL_Obool)),U_8526),U_8525)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8524,tc_HOL_Obool)),U_8525),U_8526),
    inference(clausify,[status(thm)],[f_2378_3]) ).

fof(f_2379_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_2379_2,plain,
    ! [U_8529,U_8528,U_8527] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8527,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8527,tc_HOL_Obool)),U_8528),U_8529)),U_8529) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8527,tc_HOL_Obool)),U_8528),U_8529),
    inference(variable_rename,[status(thm)],[f_2379_1]) ).

fof(f_2379_3,plain,
    ! [U_8527,U_8528,U_8529] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8527,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8527,tc_HOL_Obool)),U_8528),U_8529)),U_8529) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8527,tc_HOL_Obool)),U_8528),U_8529),
    inference(definitional_conversion,[status(esa)],[f_2379_2]) ).

cnf(f_2379_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8527,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8527,tc_HOL_Obool)),U_8528),U_8529)),U_8529) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8527,tc_HOL_Obool)),U_8528),U_8529),
    inference(clausify,[status(thm)],[f_2379_3]) ).

fof(f_2380_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_2380_2,plain,
    ! [U_8533,U_8532,U_8531,U_8530] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8530,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8530,tc_HOL_Obool)),U_8531),U_8532)),U_8533) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8530,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8530,tc_HOL_Obool)),U_8531),U_8533)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8530,tc_HOL_Obool)),U_8532),U_8533)),
    inference(variable_rename,[status(thm)],[f_2380_1]) ).

fof(f_2380_3,plain,
    ! [U_8530,U_8531,U_8532,U_8533] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8530,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8530,tc_HOL_Obool)),U_8531),U_8532)),U_8533) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8530,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8530,tc_HOL_Obool)),U_8531),U_8533)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8530,tc_HOL_Obool)),U_8532),U_8533)),
    inference(definitional_conversion,[status(esa)],[f_2380_2]) ).

cnf(f_2380_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8530,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8530,tc_HOL_Obool)),U_8531),U_8532)),U_8533) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8530,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8530,tc_HOL_Obool)),U_8531),U_8533)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8530,tc_HOL_Obool)),U_8532),U_8533)),
    inference(clausify,[status(thm)],[f_2380_3]) ).

fof(f_2381_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_2381_2,plain,
    ! [U_8535,U_8534] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8534,tc_HOL_Obool)),U_8535),U_8535) = U_8535,
    inference(variable_rename,[status(thm)],[f_2381_1]) ).

fof(f_2381_3,plain,
    ! [U_8535,U_8534] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8534,tc_HOL_Obool)),U_8535),U_8535) = U_8535,
    inference(definitional_conversion,[status(esa)],[f_2381_2]) ).

cnf(f_2381_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8534,tc_HOL_Obool)),U_8535),U_8535) = U_8535,
    inference(clausify,[status(thm)],[f_2381_3]) ).

fof(f_2382_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_2382_2,plain,
    ! [U_8538,U_8537,U_8536] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8536,tc_HOL_Obool)),U_8537),U_8538) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8536,tc_HOL_Obool)),U_8538),U_8537),
    inference(variable_rename,[status(thm)],[f_2382_1]) ).

fof(f_2382_3,plain,
    ! [U_8536,U_8537,U_8538] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8536,tc_HOL_Obool)),U_8537),U_8538) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8536,tc_HOL_Obool)),U_8538),U_8537),
    inference(definitional_conversion,[status(esa)],[f_2382_2]) ).

cnf(f_2382_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8536,tc_HOL_Obool)),U_8537),U_8538) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8536,tc_HOL_Obool)),U_8538),U_8537),
    inference(clausify,[status(thm)],[f_2382_3]) ).

fof(f_2383_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_2383_2,plain,
    ! [U_8541,U_8540,U_8539] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8539,tc_HOL_Obool)),U_8540),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8539,tc_HOL_Obool)),U_8540),U_8541)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8539,tc_HOL_Obool)),U_8540),U_8541),
    inference(variable_rename,[status(thm)],[f_2383_1]) ).

fof(f_2383_3,plain,
    ! [U_8539,U_8540,U_8541] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8539,tc_HOL_Obool)),U_8540),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8539,tc_HOL_Obool)),U_8540),U_8541)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8539,tc_HOL_Obool)),U_8540),U_8541),
    inference(definitional_conversion,[status(esa)],[f_2383_2]) ).

cnf(f_2383_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8539,tc_HOL_Obool)),U_8540),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8539,tc_HOL_Obool)),U_8540),U_8541)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8539,tc_HOL_Obool)),U_8540),U_8541),
    inference(clausify,[status(thm)],[f_2383_3]) ).

fof(f_2384_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_2384_2,plain,
    ! [U_8545,U_8544,U_8543,U_8542] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8542,tc_HOL_Obool)),U_8543),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8542,tc_HOL_Obool)),U_8544),U_8545)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8542,tc_HOL_Obool)),U_8544),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8542,tc_HOL_Obool)),U_8543),U_8545)),
    inference(variable_rename,[status(thm)],[f_2384_1]) ).

fof(f_2384_3,plain,
    ! [U_8542,U_8543,U_8544,U_8545] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8542,tc_HOL_Obool)),U_8543),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8542,tc_HOL_Obool)),U_8544),U_8545)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8542,tc_HOL_Obool)),U_8544),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8542,tc_HOL_Obool)),U_8543),U_8545)),
    inference(definitional_conversion,[status(esa)],[f_2384_2]) ).

cnf(f_2384_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8542,tc_HOL_Obool)),U_8543),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8542,tc_HOL_Obool)),U_8544),U_8545)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8542,tc_HOL_Obool)),U_8544),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8542,tc_HOL_Obool)),U_8543),U_8545)),
    inference(clausify,[status(thm)],[f_2384_3]) ).

fof(f_2385_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_2385_2,plain,
    ! [U_8549,U_8548,U_8547,U_8546] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8546,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8546,tc_HOL_Obool)),U_8547),U_8548)),U_8549) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8546,tc_HOL_Obool)),U_8547),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8546,tc_HOL_Obool)),U_8548),U_8549)),
    inference(variable_rename,[status(thm)],[f_2385_1]) ).

fof(f_2385_3,plain,
    ! [U_8546,U_8547,U_8548,U_8549] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8546,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8546,tc_HOL_Obool)),U_8547),U_8548)),U_8549) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8546,tc_HOL_Obool)),U_8547),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8546,tc_HOL_Obool)),U_8548),U_8549)),
    inference(definitional_conversion,[status(esa)],[f_2385_2]) ).

cnf(f_2385_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8546,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8546,tc_HOL_Obool)),U_8547),U_8548)),U_8549) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8546,tc_HOL_Obool)),U_8547),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8546,tc_HOL_Obool)),U_8548),U_8549)),
    inference(clausify,[status(thm)],[f_2385_3]) ).

fof(f_2386_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_2386_2,plain,
    ! [U_8559,U_8558,U_8557,U_8556] :
      ( ( ? [U_8555] :
            ( hBOOL(hAPP(U_8559,U_8555))
            & hBOOL(hAPP(hAPP(c_member(U_8556),U_8555),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8556,tc_HOL_Obool)),U_8557),U_8558))) )
        | ( ! [U_8554] :
              ( ~ hBOOL(hAPP(U_8559,U_8554))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8556),U_8554),U_8558)) )
          & ! [U_8553] :
              ( ~ hBOOL(hAPP(U_8559,U_8553))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8556),U_8553),U_8557)) ) ) )
      & ( ? [U_8552] :
            ( hBOOL(hAPP(U_8559,U_8552))
            & hBOOL(hAPP(hAPP(c_member(U_8556),U_8552),U_8558)) )
        | ? [U_8551] :
            ( hBOOL(hAPP(U_8559,U_8551))
            & hBOOL(hAPP(hAPP(c_member(U_8556),U_8551),U_8557)) )
        | ! [U_8550] :
            ( ~ hBOOL(hAPP(U_8559,U_8550))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8556),U_8550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8556,tc_HOL_Obool)),U_8557),U_8558))) ) ) ),
    inference(variable_rename,[status(thm)],[f_2386_1]) ).

fof(f_2386_3,plain,
    ( ! [U_8567,U_8565,U_8563,U_8561] :
        ( ? [U_8555] :
            ( hBOOL(hAPP(U_8567,U_8555))
            & hBOOL(hAPP(hAPP(c_member(U_8561),U_8555),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8561,tc_HOL_Obool)),U_8563),U_8565))) )
        | ( ! [U_8554] :
              ( ~ hBOOL(hAPP(U_8567,U_8554))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8561),U_8554),U_8565)) )
          & ! [U_8553] :
              ( ~ hBOOL(hAPP(U_8567,U_8553))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8561),U_8553),U_8563)) ) ) )
    & ! [U_8566,U_8564,U_8562,U_8560] :
        ( ? [U_8552] :
            ( hBOOL(hAPP(U_8566,U_8552))
            & hBOOL(hAPP(hAPP(c_member(U_8560),U_8552),U_8564)) )
        | ? [U_8551] :
            ( hBOOL(hAPP(U_8566,U_8551))
            & hBOOL(hAPP(hAPP(c_member(U_8560),U_8551),U_8562)) )
        | ! [U_8550] :
            ( ~ hBOOL(hAPP(U_8566,U_8550))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8560),U_8550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8560,tc_HOL_Obool)),U_8562),U_8564))) ) ) ),
    inference(miniscope,[status(thm)],[f_2386_2]) ).

fof(f_2386_4,plain,
    ( ! [U_8567,U_8565,U_8563,U_8561] :
        ( ? [U_8555] :
            ( hBOOL(hAPP(U_8567,U_8555))
            & hBOOL(hAPP(hAPP(c_member(U_8561),U_8555),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8561,tc_HOL_Obool)),U_8563),U_8565))) )
        | ( ! [U_8554] :
              ( ~ hBOOL(hAPP(U_8567,U_8554))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8561),U_8554),U_8565)) )
          & ! [U_8553] :
              ( ~ hBOOL(hAPP(U_8567,U_8553))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8561),U_8553),U_8563)) ) ) )
    & ! [U_8566,U_8564,U_8562,U_8560] :
        ( ? [U_8552] :
            ( hBOOL(hAPP(U_8566,U_8552))
            & hBOOL(hAPP(hAPP(c_member(U_8560),U_8552),U_8564)) )
        | ( hBOOL(hAPP(U_8566,sK125(U_8566,U_8564,U_8562,U_8560)))
          & hBOOL(hAPP(hAPP(c_member(U_8560),sK125(U_8566,U_8564,U_8562,U_8560)),U_8562)) )
        | ! [U_8550] :
            ( ~ hBOOL(hAPP(U_8566,U_8550))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8560),U_8550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8560,tc_HOL_Obool)),U_8562),U_8564))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_8551,sK125(U_8566,U_8564,U_8562,U_8560))],[f_2386_3]) ).

fof(f_2386_5,plain,
    ( ! [U_8567,U_8565,U_8563,U_8561] :
        ( ? [U_8555] :
            ( hBOOL(hAPP(U_8567,U_8555))
            & hBOOL(hAPP(hAPP(c_member(U_8561),U_8555),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8561,tc_HOL_Obool)),U_8563),U_8565))) )
        | ( ! [U_8554] :
              ( ~ hBOOL(hAPP(U_8567,U_8554))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8561),U_8554),U_8565)) )
          & ! [U_8553] :
              ( ~ hBOOL(hAPP(U_8567,U_8553))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8561),U_8553),U_8563)) ) ) )
    & ! [U_8566,U_8564,U_8562,U_8560] :
        ( ( hBOOL(hAPP(U_8566,sK126(U_8566,U_8564,U_8562,U_8560)))
          & hBOOL(hAPP(hAPP(c_member(U_8560),sK126(U_8566,U_8564,U_8562,U_8560)),U_8564)) )
        | ( hBOOL(hAPP(U_8566,sK125(U_8566,U_8564,U_8562,U_8560)))
          & hBOOL(hAPP(hAPP(c_member(U_8560),sK125(U_8566,U_8564,U_8562,U_8560)),U_8562)) )
        | ! [U_8550] :
            ( ~ hBOOL(hAPP(U_8566,U_8550))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8560),U_8550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8560,tc_HOL_Obool)),U_8562),U_8564))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_8552,sK126(U_8566,U_8564,U_8562,U_8560))],[f_2386_4]) ).

fof(f_2386_6,plain,
    ( ! [U_8567,U_8565,U_8563,U_8561] :
        ( ( hBOOL(hAPP(U_8567,sK127(U_8567,U_8565,U_8563,U_8561)))
          & hBOOL(hAPP(hAPP(c_member(U_8561),sK127(U_8567,U_8565,U_8563,U_8561)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8561,tc_HOL_Obool)),U_8563),U_8565))) )
        | ( ! [U_8554] :
              ( ~ hBOOL(hAPP(U_8567,U_8554))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8561),U_8554),U_8565)) )
          & ! [U_8553] :
              ( ~ hBOOL(hAPP(U_8567,U_8553))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8561),U_8553),U_8563)) ) ) )
    & ! [U_8566,U_8564,U_8562,U_8560] :
        ( ( hBOOL(hAPP(U_8566,sK126(U_8566,U_8564,U_8562,U_8560)))
          & hBOOL(hAPP(hAPP(c_member(U_8560),sK126(U_8566,U_8564,U_8562,U_8560)),U_8564)) )
        | ( hBOOL(hAPP(U_8566,sK125(U_8566,U_8564,U_8562,U_8560)))
          & hBOOL(hAPP(hAPP(c_member(U_8560),sK125(U_8566,U_8564,U_8562,U_8560)),U_8562)) )
        | ! [U_8550] :
            ( ~ hBOOL(hAPP(U_8566,U_8550))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8560),U_8550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8560,tc_HOL_Obool)),U_8562),U_8564))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_8555,sK127(U_8567,U_8565,U_8563,U_8561))],[f_2386_5]) ).

fof(f_2386_7,plain,
    ( ! [U_8561,U_8565,U_8563,U_8567] :
        ( hBOOL(hAPP(U_8567,sK127(U_8567,U_8565,U_8563,U_8561)))
        | ~ sP719(U_8561,U_8565,U_8563,U_8567) )
    & ! [U_8561,U_8565,U_8563,U_8567] :
        ( hBOOL(hAPP(hAPP(c_member(U_8561),sK127(U_8567,U_8565,U_8563,U_8561)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8561,tc_HOL_Obool)),U_8563),U_8565)))
        | ~ sP719(U_8561,U_8565,U_8563,U_8567) )
    & ! [U_8561,U_8565,U_8553,U_8554,U_8563,U_8567] :
        ( ~ hBOOL(hAPP(U_8567,U_8554))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8561),U_8554),U_8565))
        | ~ sP718(U_8561,U_8565,U_8553,U_8554,U_8563,U_8567) )
    & ! [U_8561,U_8565,U_8553,U_8554,U_8563,U_8567] :
        ( ~ hBOOL(hAPP(U_8567,U_8553))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8561),U_8553),U_8563))
        | ~ sP718(U_8561,U_8565,U_8553,U_8554,U_8563,U_8567) )
    & ! [U_8562,U_8566,U_8560,U_8564] :
        ( hBOOL(hAPP(U_8566,sK126(U_8566,U_8564,U_8562,U_8560)))
        | ~ sP717(U_8562,U_8566,U_8560,U_8564) )
    & ! [U_8562,U_8566,U_8560,U_8564] :
        ( hBOOL(hAPP(hAPP(c_member(U_8560),sK126(U_8566,U_8564,U_8562,U_8560)),U_8564))
        | ~ sP717(U_8562,U_8566,U_8560,U_8564) )
    & ! [U_8562,U_8566,U_8560,U_8564] :
        ( hBOOL(hAPP(U_8566,sK125(U_8566,U_8564,U_8562,U_8560)))
        | ~ sP716(U_8562,U_8566,U_8560,U_8564) )
    & ! [U_8562,U_8566,U_8560,U_8564] :
        ( hBOOL(hAPP(hAPP(c_member(U_8560),sK125(U_8566,U_8564,U_8562,U_8560)),U_8562))
        | ~ sP716(U_8562,U_8566,U_8560,U_8564) )
    & ! [U_8561,U_8565,U_8553,U_8554,U_8563,U_8567] :
        ( sP719(U_8561,U_8565,U_8563,U_8567)
        | sP718(U_8561,U_8565,U_8553,U_8554,U_8563,U_8567) )
    & ! [U_8562,U_8550,U_8566,U_8560,U_8564] :
        ( sP717(U_8562,U_8566,U_8560,U_8564)
        | sP716(U_8562,U_8566,U_8560,U_8564)
        | ~ hBOOL(hAPP(U_8566,U_8550))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8560),U_8550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8560,tc_HOL_Obool)),U_8562),U_8564))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP716,sP717,sP718,sP719])],[f_2386_6]) ).

cnf(f_2386_8,plain,
    ( sP717(U_8562,U_8566,U_8560,U_8564)
    | sP716(U_8562,U_8566,U_8560,U_8564)
    | ~ hBOOL(hAPP(U_8566,U_8550))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8560),U_8550),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8560,tc_HOL_Obool)),U_8562),U_8564))) ),
    inference(clausify,[status(thm)],[f_2386_7]) ).

cnf(f_2386_9,plain,
    ( sP719(U_8561,U_8565,U_8563,U_8567)
    | sP718(U_8561,U_8565,U_8553,U_8554,U_8563,U_8567) ),
    inference(clausify,[status(thm)],[f_2386_7]) ).

cnf(f_2386_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8560),sK125(U_8566,U_8564,U_8562,U_8560)),U_8562))
    | ~ sP716(U_8562,U_8566,U_8560,U_8564) ),
    inference(clausify,[status(thm)],[f_2386_7]) ).

cnf(f_2386_11,plain,
    ( hBOOL(hAPP(U_8566,sK125(U_8566,U_8564,U_8562,U_8560)))
    | ~ sP716(U_8562,U_8566,U_8560,U_8564) ),
    inference(clausify,[status(thm)],[f_2386_7]) ).

cnf(f_2386_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8560),sK126(U_8566,U_8564,U_8562,U_8560)),U_8564))
    | ~ sP717(U_8562,U_8566,U_8560,U_8564) ),
    inference(clausify,[status(thm)],[f_2386_7]) ).

cnf(f_2386_13,plain,
    ( hBOOL(hAPP(U_8566,sK126(U_8566,U_8564,U_8562,U_8560)))
    | ~ sP717(U_8562,U_8566,U_8560,U_8564) ),
    inference(clausify,[status(thm)],[f_2386_7]) ).

cnf(f_2386_14,plain,
    ( ~ hBOOL(hAPP(U_8567,U_8553))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8561),U_8553),U_8563))
    | ~ sP718(U_8561,U_8565,U_8553,U_8554,U_8563,U_8567) ),
    inference(clausify,[status(thm)],[f_2386_7]) ).

cnf(f_2386_15,plain,
    ( ~ hBOOL(hAPP(U_8567,U_8554))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8561),U_8554),U_8565))
    | ~ sP718(U_8561,U_8565,U_8553,U_8554,U_8563,U_8567) ),
    inference(clausify,[status(thm)],[f_2386_7]) ).

cnf(f_2386_16,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8561),sK127(U_8567,U_8565,U_8563,U_8561)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8561,tc_HOL_Obool)),U_8563),U_8565)))
    | ~ sP719(U_8561,U_8565,U_8563,U_8567) ),
    inference(clausify,[status(thm)],[f_2386_7]) ).

cnf(f_2386_17,plain,
    ( hBOOL(hAPP(U_8567,sK127(U_8567,U_8565,U_8563,U_8561)))
    | ~ sP719(U_8561,U_8565,U_8563,U_8567) ),
    inference(clausify,[status(thm)],[f_2386_7]) ).

fof(f_2387_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_2387_2,plain,
    ! [U_8577,U_8576,U_8575,U_8574] :
      ( ( ! [U_8573] :
            ( hBOOL(hAPP(U_8577,U_8573))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8574),U_8573),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8574,tc_HOL_Obool)),U_8575),U_8576))) )
        | ? [U_8572] :
            ( ~ hBOOL(hAPP(U_8577,U_8572))
            & hBOOL(hAPP(hAPP(c_member(U_8574),U_8572),U_8576)) )
        | ? [U_8571] :
            ( ~ hBOOL(hAPP(U_8577,U_8571))
            & hBOOL(hAPP(hAPP(c_member(U_8574),U_8571),U_8575)) ) )
      & ( ( ! [U_8570] :
              ( hBOOL(hAPP(U_8577,U_8570))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8574),U_8570),U_8576)) )
          & ! [U_8569] :
              ( hBOOL(hAPP(U_8577,U_8569))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8574),U_8569),U_8575)) ) )
        | ? [U_8568] :
            ( ~ hBOOL(hAPP(U_8577,U_8568))
            & hBOOL(hAPP(hAPP(c_member(U_8574),U_8568),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8574,tc_HOL_Obool)),U_8575),U_8576))) ) ) ),
    inference(variable_rename,[status(thm)],[f_2387_1]) ).

fof(f_2387_3,plain,
    ( ! [U_8585,U_8583,U_8581,U_8579] :
        ( ! [U_8573] :
            ( hBOOL(hAPP(U_8585,U_8573))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8579),U_8573),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8579,tc_HOL_Obool)),U_8581),U_8583))) )
        | ? [U_8572] :
            ( ~ hBOOL(hAPP(U_8585,U_8572))
            & hBOOL(hAPP(hAPP(c_member(U_8579),U_8572),U_8583)) )
        | ? [U_8571] :
            ( ~ hBOOL(hAPP(U_8585,U_8571))
            & hBOOL(hAPP(hAPP(c_member(U_8579),U_8571),U_8581)) ) )
    & ! [U_8584,U_8582,U_8580,U_8578] :
        ( ( ! [U_8570] :
              ( hBOOL(hAPP(U_8584,U_8570))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8578),U_8570),U_8582)) )
          & ! [U_8569] :
              ( hBOOL(hAPP(U_8584,U_8569))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8578),U_8569),U_8580)) ) )
        | ? [U_8568] :
            ( ~ hBOOL(hAPP(U_8584,U_8568))
            & hBOOL(hAPP(hAPP(c_member(U_8578),U_8568),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8578,tc_HOL_Obool)),U_8580),U_8582))) ) ) ),
    inference(miniscope,[status(thm)],[f_2387_2]) ).

fof(f_2387_4,plain,
    ( ! [U_8585,U_8583,U_8581,U_8579] :
        ( ! [U_8573] :
            ( hBOOL(hAPP(U_8585,U_8573))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8579),U_8573),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8579,tc_HOL_Obool)),U_8581),U_8583))) )
        | ? [U_8572] :
            ( ~ hBOOL(hAPP(U_8585,U_8572))
            & hBOOL(hAPP(hAPP(c_member(U_8579),U_8572),U_8583)) )
        | ? [U_8571] :
            ( ~ hBOOL(hAPP(U_8585,U_8571))
            & hBOOL(hAPP(hAPP(c_member(U_8579),U_8571),U_8581)) ) )
    & ! [U_8584,U_8582,U_8580,U_8578] :
        ( ( ! [U_8570] :
              ( hBOOL(hAPP(U_8584,U_8570))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8578),U_8570),U_8582)) )
          & ! [U_8569] :
              ( hBOOL(hAPP(U_8584,U_8569))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8578),U_8569),U_8580)) ) )
        | ( ~ hBOOL(hAPP(U_8584,sK128(U_8584,U_8582,U_8580,U_8578)))
          & hBOOL(hAPP(hAPP(c_member(U_8578),sK128(U_8584,U_8582,U_8580,U_8578)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8578,tc_HOL_Obool)),U_8580),U_8582))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_8568,sK128(U_8584,U_8582,U_8580,U_8578))],[f_2387_3]) ).

fof(f_2387_5,plain,
    ( ! [U_8585,U_8583,U_8581,U_8579] :
        ( ! [U_8573] :
            ( hBOOL(hAPP(U_8585,U_8573))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8579),U_8573),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8579,tc_HOL_Obool)),U_8581),U_8583))) )
        | ? [U_8572] :
            ( ~ hBOOL(hAPP(U_8585,U_8572))
            & hBOOL(hAPP(hAPP(c_member(U_8579),U_8572),U_8583)) )
        | ( ~ hBOOL(hAPP(U_8585,sK129(U_8585,U_8583,U_8581,U_8579)))
          & hBOOL(hAPP(hAPP(c_member(U_8579),sK129(U_8585,U_8583,U_8581,U_8579)),U_8581)) ) )
    & ! [U_8584,U_8582,U_8580,U_8578] :
        ( ( ! [U_8570] :
              ( hBOOL(hAPP(U_8584,U_8570))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8578),U_8570),U_8582)) )
          & ! [U_8569] :
              ( hBOOL(hAPP(U_8584,U_8569))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8578),U_8569),U_8580)) ) )
        | ( ~ hBOOL(hAPP(U_8584,sK128(U_8584,U_8582,U_8580,U_8578)))
          & hBOOL(hAPP(hAPP(c_member(U_8578),sK128(U_8584,U_8582,U_8580,U_8578)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8578,tc_HOL_Obool)),U_8580),U_8582))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_8571,sK129(U_8585,U_8583,U_8581,U_8579))],[f_2387_4]) ).

fof(f_2387_6,plain,
    ( ! [U_8585,U_8583,U_8581,U_8579] :
        ( ! [U_8573] :
            ( hBOOL(hAPP(U_8585,U_8573))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8579),U_8573),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8579,tc_HOL_Obool)),U_8581),U_8583))) )
        | ( ~ hBOOL(hAPP(U_8585,sK130(U_8585,U_8583,U_8581,U_8579)))
          & hBOOL(hAPP(hAPP(c_member(U_8579),sK130(U_8585,U_8583,U_8581,U_8579)),U_8583)) )
        | ( ~ hBOOL(hAPP(U_8585,sK129(U_8585,U_8583,U_8581,U_8579)))
          & hBOOL(hAPP(hAPP(c_member(U_8579),sK129(U_8585,U_8583,U_8581,U_8579)),U_8581)) ) )
    & ! [U_8584,U_8582,U_8580,U_8578] :
        ( ( ! [U_8570] :
              ( hBOOL(hAPP(U_8584,U_8570))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8578),U_8570),U_8582)) )
          & ! [U_8569] :
              ( hBOOL(hAPP(U_8584,U_8569))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8578),U_8569),U_8580)) ) )
        | ( ~ hBOOL(hAPP(U_8584,sK128(U_8584,U_8582,U_8580,U_8578)))
          & hBOOL(hAPP(hAPP(c_member(U_8578),sK128(U_8584,U_8582,U_8580,U_8578)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8578,tc_HOL_Obool)),U_8580),U_8582))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_8572,sK130(U_8585,U_8583,U_8581,U_8579))],[f_2387_5]) ).

fof(f_2387_7,plain,
    ( ! [U_8583,U_8579,U_8581,U_8585] :
        ( ~ hBOOL(hAPP(U_8585,sK130(U_8585,U_8583,U_8581,U_8579)))
        | ~ sP723(U_8583,U_8579,U_8581,U_8585) )
    & ! [U_8583,U_8579,U_8581,U_8585] :
        ( hBOOL(hAPP(hAPP(c_member(U_8579),sK130(U_8585,U_8583,U_8581,U_8579)),U_8583))
        | ~ sP723(U_8583,U_8579,U_8581,U_8585) )
    & ! [U_8583,U_8579,U_8581,U_8585] :
        ( ~ hBOOL(hAPP(U_8585,sK129(U_8585,U_8583,U_8581,U_8579)))
        | ~ sP722(U_8583,U_8579,U_8581,U_8585) )
    & ! [U_8583,U_8579,U_8581,U_8585] :
        ( hBOOL(hAPP(hAPP(c_member(U_8579),sK129(U_8585,U_8583,U_8581,U_8579)),U_8581))
        | ~ sP722(U_8583,U_8579,U_8581,U_8585) )
    & ! [U_8569,U_8570,U_8578,U_8582,U_8580,U_8584] :
        ( hBOOL(hAPP(U_8584,U_8570))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8578),U_8570),U_8582))
        | ~ sP721(U_8569,U_8570,U_8578,U_8582,U_8580,U_8584) )
    & ! [U_8569,U_8570,U_8578,U_8582,U_8580,U_8584] :
        ( hBOOL(hAPP(U_8584,U_8569))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8578),U_8569),U_8580))
        | ~ sP721(U_8569,U_8570,U_8578,U_8582,U_8580,U_8584) )
    & ! [U_8578,U_8582,U_8580,U_8584] :
        ( ~ hBOOL(hAPP(U_8584,sK128(U_8584,U_8582,U_8580,U_8578)))
        | ~ sP720(U_8578,U_8582,U_8580,U_8584) )
    & ! [U_8578,U_8582,U_8580,U_8584] :
        ( hBOOL(hAPP(hAPP(c_member(U_8578),sK128(U_8584,U_8582,U_8580,U_8578)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8578,tc_HOL_Obool)),U_8580),U_8582)))
        | ~ sP720(U_8578,U_8582,U_8580,U_8584) )
    & ! [U_8583,U_8573,U_8579,U_8581,U_8585] :
        ( hBOOL(hAPP(U_8585,U_8573))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8579),U_8573),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8579,tc_HOL_Obool)),U_8581),U_8583)))
        | sP723(U_8583,U_8579,U_8581,U_8585)
        | sP722(U_8583,U_8579,U_8581,U_8585) )
    & ! [U_8569,U_8570,U_8578,U_8582,U_8580,U_8584] :
        ( sP721(U_8569,U_8570,U_8578,U_8582,U_8580,U_8584)
        | sP720(U_8578,U_8582,U_8580,U_8584) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP720,sP721,sP722,sP723])],[f_2387_6]) ).

cnf(f_2387_8,plain,
    ( sP721(U_8569,U_8570,U_8578,U_8582,U_8580,U_8584)
    | sP720(U_8578,U_8582,U_8580,U_8584) ),
    inference(clausify,[status(thm)],[f_2387_7]) ).

cnf(f_2387_9,plain,
    ( hBOOL(hAPP(U_8585,U_8573))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8579),U_8573),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8579,tc_HOL_Obool)),U_8581),U_8583)))
    | sP723(U_8583,U_8579,U_8581,U_8585)
    | sP722(U_8583,U_8579,U_8581,U_8585) ),
    inference(clausify,[status(thm)],[f_2387_7]) ).

cnf(f_2387_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8578),sK128(U_8584,U_8582,U_8580,U_8578)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8578,tc_HOL_Obool)),U_8580),U_8582)))
    | ~ sP720(U_8578,U_8582,U_8580,U_8584) ),
    inference(clausify,[status(thm)],[f_2387_7]) ).

cnf(f_2387_11,plain,
    ( ~ hBOOL(hAPP(U_8584,sK128(U_8584,U_8582,U_8580,U_8578)))
    | ~ sP720(U_8578,U_8582,U_8580,U_8584) ),
    inference(clausify,[status(thm)],[f_2387_7]) ).

cnf(f_2387_12,plain,
    ( hBOOL(hAPP(U_8584,U_8569))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8578),U_8569),U_8580))
    | ~ sP721(U_8569,U_8570,U_8578,U_8582,U_8580,U_8584) ),
    inference(clausify,[status(thm)],[f_2387_7]) ).

cnf(f_2387_13,plain,
    ( hBOOL(hAPP(U_8584,U_8570))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8578),U_8570),U_8582))
    | ~ sP721(U_8569,U_8570,U_8578,U_8582,U_8580,U_8584) ),
    inference(clausify,[status(thm)],[f_2387_7]) ).

cnf(f_2387_14,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8579),sK129(U_8585,U_8583,U_8581,U_8579)),U_8581))
    | ~ sP722(U_8583,U_8579,U_8581,U_8585) ),
    inference(clausify,[status(thm)],[f_2387_7]) ).

cnf(f_2387_15,plain,
    ( ~ hBOOL(hAPP(U_8585,sK129(U_8585,U_8583,U_8581,U_8579)))
    | ~ sP722(U_8583,U_8579,U_8581,U_8585) ),
    inference(clausify,[status(thm)],[f_2387_7]) ).

cnf(f_2387_16,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8579),sK130(U_8585,U_8583,U_8581,U_8579)),U_8583))
    | ~ sP723(U_8583,U_8579,U_8581,U_8585) ),
    inference(clausify,[status(thm)],[f_2387_7]) ).

cnf(f_2387_17,plain,
    ( ~ hBOOL(hAPP(U_8585,sK130(U_8585,U_8583,U_8581,U_8579)))
    | ~ sP723(U_8583,U_8579,U_8581,U_8585) ),
    inference(clausify,[status(thm)],[f_2387_7]) ).

fof(f_2388_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_2388_2,plain,
    ! [U_8587,U_8586] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8586),U_8587),U_8587) = U_8587
      | ~ class_Lattices_Osemilattice__sup(U_8586) ),
    inference(variable_rename,[status(thm)],[f_2388_1]) ).

fof(f_2388_3,plain,
    ! [U_8586,U_8587] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8586),U_8587),U_8587) = U_8587
      | ~ class_Lattices_Osemilattice__sup(U_8586) ),
    inference(definitional_conversion,[status(esa)],[f_2388_2]) ).

cnf(f_2388_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8586),U_8587),U_8587) = U_8587
    | ~ class_Lattices_Osemilattice__sup(U_8586) ),
    inference(clausify,[status(thm)],[f_2388_3]) ).

fof(f_2389_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_2389_2,plain,
    ! [U_8589,U_8588] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8588),U_8589),U_8589) = U_8589
      | ~ class_Lattices_Osemilattice__sup(U_8588) ),
    inference(variable_rename,[status(thm)],[f_2389_1]) ).

fof(f_2389_3,plain,
    ! [U_8589,U_8588] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8588),U_8589),U_8589) = U_8589
      | ~ class_Lattices_Osemilattice__sup(U_8588) ),
    inference(definitional_conversion,[status(esa)],[f_2389_2]) ).

cnf(f_2389_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8588),U_8589),U_8589) = U_8589
    | ~ class_Lattices_Osemilattice__sup(U_8588) ),
    inference(clausify,[status(thm)],[f_2389_3]) ).

fof(f_2390_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_2390_2,plain,
    ! [U_8592,U_8591,U_8590] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8590),U_8591),U_8592) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8590),U_8592),U_8591)
      | ~ class_Lattices_Osemilattice__sup(U_8590) ),
    inference(variable_rename,[status(thm)],[f_2390_1]) ).

fof(f_2390_3,plain,
    ! [U_8591,U_8592,U_8590] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8590),U_8591),U_8592) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8590),U_8592),U_8591)
      | ~ class_Lattices_Osemilattice__sup(U_8590) ),
    inference(definitional_conversion,[status(esa)],[f_2390_2]) ).

cnf(f_2390_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8590),U_8591),U_8592) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8590),U_8592),U_8591)
    | ~ class_Lattices_Osemilattice__sup(U_8590) ),
    inference(clausify,[status(thm)],[f_2390_3]) ).

fof(f_2391_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_2391_2,plain,
    ! [U_8595,U_8594,U_8593] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8593),U_8594),U_8595) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8593),U_8595),U_8594)
      | ~ class_Lattices_Olattice(U_8593) ),
    inference(variable_rename,[status(thm)],[f_2391_1]) ).

fof(f_2391_3,plain,
    ! [U_8593,U_8594,U_8595] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8593),U_8594),U_8595) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8593),U_8595),U_8594)
      | ~ class_Lattices_Olattice(U_8593) ),
    inference(definitional_conversion,[status(esa)],[f_2391_2]) ).

cnf(f_2391_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8593),U_8594),U_8595) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8593),U_8595),U_8594)
    | ~ class_Lattices_Olattice(U_8593) ),
    inference(clausify,[status(thm)],[f_2391_3]) ).

fof(f_2392_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_2392_2,plain,
    ! [U_8598,U_8597,U_8596] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8596),U_8597),U_8598) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8596),U_8598),U_8597)
      | ~ class_Lattices_Osemilattice__sup(U_8596) ),
    inference(variable_rename,[status(thm)],[f_2392_1]) ).

fof(f_2392_3,plain,
    ! [U_8596,U_8597,U_8598] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8596),U_8597),U_8598) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8596),U_8598),U_8597)
      | ~ class_Lattices_Osemilattice__sup(U_8596) ),
    inference(definitional_conversion,[status(esa)],[f_2392_2]) ).

cnf(f_2392_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8596),U_8597),U_8598) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8596),U_8598),U_8597)
    | ~ class_Lattices_Osemilattice__sup(U_8596) ),
    inference(clausify,[status(thm)],[f_2392_3]) ).

fof(f_2393_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_2393_2,plain,
    ! [U_8601,U_8600,U_8599] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8599),U_8600),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8599),U_8600),U_8601)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8599),U_8600),U_8601)
      | ~ class_Lattices_Osemilattice__sup(U_8599) ),
    inference(variable_rename,[status(thm)],[f_2393_1]) ).

fof(f_2393_3,plain,
    ! [U_8599,U_8600,U_8601] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8599),U_8600),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8599),U_8600),U_8601)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8599),U_8600),U_8601)
      | ~ class_Lattices_Osemilattice__sup(U_8599) ),
    inference(definitional_conversion,[status(esa)],[f_2393_2]) ).

cnf(f_2393_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8599),U_8600),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8599),U_8600),U_8601)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8599),U_8600),U_8601)
    | ~ class_Lattices_Osemilattice__sup(U_8599) ),
    inference(clausify,[status(thm)],[f_2393_3]) ).

fof(f_2394_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_2394_2,plain,
    ! [U_8604,U_8603,U_8602] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8602),U_8603),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8602),U_8603),U_8604)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8602),U_8603),U_8604)
      | ~ class_Lattices_Olattice(U_8602) ),
    inference(variable_rename,[status(thm)],[f_2394_1]) ).

fof(f_2394_3,plain,
    ! [U_8602,U_8603,U_8604] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8602),U_8603),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8602),U_8603),U_8604)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8602),U_8603),U_8604)
      | ~ class_Lattices_Olattice(U_8602) ),
    inference(definitional_conversion,[status(esa)],[f_2394_2]) ).

cnf(f_2394_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8602),U_8603),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8602),U_8603),U_8604)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8602),U_8603),U_8604)
    | ~ class_Lattices_Olattice(U_8602) ),
    inference(clausify,[status(thm)],[f_2394_3]) ).

fof(f_2395_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_2395_2,plain,
    ! [U_8607,U_8606,U_8605] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8605),U_8606),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8605),U_8606),U_8607)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8605),U_8606),U_8607)
      | ~ class_Lattices_Osemilattice__sup(U_8605) ),
    inference(variable_rename,[status(thm)],[f_2395_1]) ).

fof(f_2395_3,plain,
    ! [U_8605,U_8606,U_8607] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8605),U_8606),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8605),U_8606),U_8607)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8605),U_8606),U_8607)
      | ~ class_Lattices_Osemilattice__sup(U_8605) ),
    inference(definitional_conversion,[status(esa)],[f_2395_2]) ).

cnf(f_2395_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8605),U_8606),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8605),U_8606),U_8607)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8605),U_8606),U_8607)
    | ~ class_Lattices_Osemilattice__sup(U_8605) ),
    inference(clausify,[status(thm)],[f_2395_3]) ).

fof(f_2396_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_2396_2,plain,
    ! [U_8611,U_8610,U_8609,U_8608] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8608),U_8609),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8608),U_8610),U_8611)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8608),U_8610),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8608),U_8609),U_8611))
      | ~ class_Lattices_Osemilattice__sup(U_8608) ),
    inference(variable_rename,[status(thm)],[f_2396_1]) ).

fof(f_2396_3,plain,
    ! [U_8608,U_8609,U_8610,U_8611] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8608),U_8609),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8608),U_8610),U_8611)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8608),U_8610),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8608),U_8609),U_8611))
      | ~ class_Lattices_Osemilattice__sup(U_8608) ),
    inference(definitional_conversion,[status(esa)],[f_2396_2]) ).

cnf(f_2396_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8608),U_8609),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8608),U_8610),U_8611)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8608),U_8610),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8608),U_8609),U_8611))
    | ~ class_Lattices_Osemilattice__sup(U_8608) ),
    inference(clausify,[status(thm)],[f_2396_3]) ).

fof(f_2397_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_2397_2,plain,
    ! [U_8615,U_8614,U_8613,U_8612] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8612),U_8613),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8612),U_8614),U_8615)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8612),U_8614),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8612),U_8613),U_8615))
      | ~ class_Lattices_Olattice(U_8612) ),
    inference(variable_rename,[status(thm)],[f_2397_1]) ).

fof(f_2397_3,plain,
    ! [U_8612,U_8613,U_8614,U_8615] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8612),U_8613),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8612),U_8614),U_8615)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8612),U_8614),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8612),U_8613),U_8615))
      | ~ class_Lattices_Olattice(U_8612) ),
    inference(definitional_conversion,[status(esa)],[f_2397_2]) ).

cnf(f_2397_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8612),U_8613),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8612),U_8614),U_8615)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8612),U_8614),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8612),U_8613),U_8615))
    | ~ class_Lattices_Olattice(U_8612) ),
    inference(clausify,[status(thm)],[f_2397_3]) ).

fof(f_2398_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_2398_2,plain,
    ! [U_8619,U_8618,U_8617,U_8616] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8616),U_8617),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8616),U_8618),U_8619)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8616),U_8618),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8616),U_8617),U_8619))
      | ~ class_Lattices_Osemilattice__sup(U_8616) ),
    inference(variable_rename,[status(thm)],[f_2398_1]) ).

fof(f_2398_3,plain,
    ! [U_8616,U_8617,U_8618,U_8619] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8616),U_8617),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8616),U_8618),U_8619)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8616),U_8618),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8616),U_8617),U_8619))
      | ~ class_Lattices_Osemilattice__sup(U_8616) ),
    inference(definitional_conversion,[status(esa)],[f_2398_2]) ).

cnf(f_2398_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8616),U_8617),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8616),U_8618),U_8619)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8616),U_8618),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8616),U_8617),U_8619))
    | ~ class_Lattices_Osemilattice__sup(U_8616) ),
    inference(clausify,[status(thm)],[f_2398_3]) ).

fof(f_2399_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_2399_2,plain,
    ! [U_8623,U_8622,U_8621,U_8620] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8620),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8620),U_8621),U_8622)),U_8623) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8620),U_8621),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8620),U_8622),U_8623))
      | ~ class_Lattices_Osemilattice__sup(U_8620) ),
    inference(variable_rename,[status(thm)],[f_2399_1]) ).

fof(f_2399_3,plain,
    ! [U_8620,U_8621,U_8622,U_8623] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8620),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8620),U_8621),U_8622)),U_8623) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8620),U_8621),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8620),U_8622),U_8623))
      | ~ class_Lattices_Osemilattice__sup(U_8620) ),
    inference(definitional_conversion,[status(esa)],[f_2399_2]) ).

cnf(f_2399_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8620),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8620),U_8621),U_8622)),U_8623) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8620),U_8621),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8620),U_8622),U_8623))
    | ~ class_Lattices_Osemilattice__sup(U_8620) ),
    inference(clausify,[status(thm)],[f_2399_3]) ).

fof(f_2400_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_2400_2,plain,
    ! [U_8627,U_8626,U_8625,U_8624] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8624),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8624),U_8625),U_8626)),U_8627) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8624),U_8625),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8624),U_8626),U_8627))
      | ~ class_Lattices_Olattice(U_8624) ),
    inference(variable_rename,[status(thm)],[f_2400_1]) ).

fof(f_2400_3,plain,
    ! [U_8624,U_8625,U_8626,U_8627] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8624),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8624),U_8625),U_8626)),U_8627) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8624),U_8625),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8624),U_8626),U_8627))
      | ~ class_Lattices_Olattice(U_8624) ),
    inference(definitional_conversion,[status(esa)],[f_2400_2]) ).

cnf(f_2400_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8624),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8624),U_8625),U_8626)),U_8627) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8624),U_8625),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8624),U_8626),U_8627))
    | ~ class_Lattices_Olattice(U_8624) ),
    inference(clausify,[status(thm)],[f_2400_3]) ).

fof(f_2401_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_2401_2,plain,
    ! [U_8631,U_8630,U_8629,U_8628] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8628),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8628),U_8629),U_8630)),U_8631) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8628),U_8629),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8628),U_8630),U_8631))
      | ~ class_Lattices_Osemilattice__sup(U_8628) ),
    inference(variable_rename,[status(thm)],[f_2401_1]) ).

fof(f_2401_3,plain,
    ! [U_8628,U_8629,U_8630,U_8631] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8628),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8628),U_8629),U_8630)),U_8631) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8628),U_8629),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8628),U_8630),U_8631))
      | ~ class_Lattices_Osemilattice__sup(U_8628) ),
    inference(definitional_conversion,[status(esa)],[f_2401_2]) ).

cnf(f_2401_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8628),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8628),U_8629),U_8630)),U_8631) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8628),U_8629),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8628),U_8630),U_8631))
    | ~ class_Lattices_Osemilattice__sup(U_8628) ),
    inference(clausify,[status(thm)],[f_2401_3]) ).

fof(f_2402_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_2402_2,plain,
    ! [U_8636,U_8635,U_8634,U_8633,U_8632] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8633,U_8632)),U_8634),U_8635),U_8636) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8632),hAPP(U_8634,U_8636)),hAPP(U_8635,U_8636))
      | ~ class_Lattices_Olattice(U_8632) ),
    inference(variable_rename,[status(thm)],[f_2402_1]) ).

fof(f_2402_3,plain,
    ! [U_8632,U_8633,U_8634,U_8635,U_8636] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8633,U_8632)),U_8634),U_8635),U_8636) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8632),hAPP(U_8634,U_8636)),hAPP(U_8635,U_8636))
      | ~ class_Lattices_Olattice(U_8632) ),
    inference(definitional_conversion,[status(esa)],[f_2402_2]) ).

cnf(f_2402_4,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8633,U_8632)),U_8634),U_8635),U_8636) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8632),hAPP(U_8634,U_8636)),hAPP(U_8635,U_8636))
    | ~ class_Lattices_Olattice(U_8632) ),
    inference(clausify,[status(thm)],[f_2402_3]) ).

fof(f_2403_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_2403_2,plain,
    ! [U_8640,U_8639,U_8638,U_8637] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8637),U_8638),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8637),U_8639),U_8640)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8637),U_8638),U_8639))
      | ~ class_Lattices_Osemilattice__sup(U_8637) ),
    inference(variable_rename,[status(thm)],[f_2403_1]) ).

fof(f_2403_3,plain,
    ! [U_8637,U_8638,U_8639,U_8640] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8637),U_8638),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8637),U_8639),U_8640)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8637),U_8638),U_8639))
      | ~ class_Lattices_Osemilattice__sup(U_8637) ),
    inference(definitional_conversion,[status(esa)],[f_2403_2]) ).

cnf(f_2403_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8637),U_8638),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8637),U_8639),U_8640)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8637),U_8638),U_8639))
    | ~ class_Lattices_Osemilattice__sup(U_8637) ),
    inference(clausify,[status(thm)],[f_2403_3]) ).

fof(f_2404_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_2404_2,plain,
    ! [U_8644,U_8643,U_8642,U_8641] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8641),U_8642),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8641),U_8644),U_8643)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8641),U_8642),U_8643))
      | ~ class_Lattices_Osemilattice__sup(U_8641) ),
    inference(variable_rename,[status(thm)],[f_2404_1]) ).

fof(f_2404_3,plain,
    ! [U_8641,U_8642,U_8643,U_8644] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8641),U_8642),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8641),U_8644),U_8643)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8641),U_8642),U_8643))
      | ~ class_Lattices_Osemilattice__sup(U_8641) ),
    inference(definitional_conversion,[status(esa)],[f_2404_2]) ).

cnf(f_2404_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8641),U_8642),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8641),U_8644),U_8643)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8641),U_8642),U_8643))
    | ~ class_Lattices_Osemilattice__sup(U_8641) ),
    inference(clausify,[status(thm)],[f_2404_3]) ).

fof(f_2405_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_2405_2,plain,
    ! [U_8649,U_8648,U_8647,U_8646,U_8645] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8646,U_8645)),U_8647),U_8648),U_8649) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8645),hAPP(U_8647,U_8649)),hAPP(U_8648,U_8649))
      | ~ class_Lattices_Olattice(U_8645) ),
    inference(variable_rename,[status(thm)],[f_2405_1]) ).

fof(f_2405_3,plain,
    ! [U_8645,U_8646,U_8647,U_8648,U_8649] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8646,U_8645)),U_8647),U_8648),U_8649) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8645),hAPP(U_8647,U_8649)),hAPP(U_8648,U_8649))
      | ~ class_Lattices_Olattice(U_8645) ),
    inference(definitional_conversion,[status(esa)],[f_2405_2]) ).

cnf(f_2405_4,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8646,U_8645)),U_8647),U_8648),U_8649) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8645),hAPP(U_8647,U_8649)),hAPP(U_8648,U_8649))
    | ~ class_Lattices_Olattice(U_8645) ),
    inference(clausify,[status(thm)],[f_2405_3]) ).

fof(f_2406_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_2406_2,plain,
    ! [U_8651,U_8650] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8650),U_8651),U_8651) = U_8651
      | ~ class_Lattices_Olattice(U_8650) ),
    inference(variable_rename,[status(thm)],[f_2406_1]) ).

fof(f_2406_3,plain,
    ! [U_8651,U_8650] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8650),U_8651),U_8651) = U_8651
      | ~ class_Lattices_Olattice(U_8650) ),
    inference(definitional_conversion,[status(esa)],[f_2406_2]) ).

cnf(f_2406_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8650),U_8651),U_8651) = U_8651
    | ~ class_Lattices_Olattice(U_8650) ),
    inference(clausify,[status(thm)],[f_2406_3]) ).

fof(f_2407_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_2407_2,plain,
    ! [U_8652] :
      ( c_Lattices_Osemilattice__sup__class_Osup(U_8652) = c_Orderings_Oord__class_Omax(U_8652)
      | ~ class_Orderings_Olinorder(U_8652)
      | ~ class_Lattices_Osemilattice__sup(U_8652) ),
    inference(variable_rename,[status(thm)],[f_2407_1]) ).

fof(f_2407_3,plain,
    ! [U_8652] :
      ( c_Lattices_Osemilattice__sup__class_Osup(U_8652) = c_Orderings_Oord__class_Omax(U_8652)
      | ~ class_Orderings_Olinorder(U_8652)
      | ~ class_Lattices_Osemilattice__sup(U_8652) ),
    inference(definitional_conversion,[status(esa)],[f_2407_2]) ).

cnf(f_2407_4,plain,
    ( c_Lattices_Osemilattice__sup__class_Osup(U_8652) = c_Orderings_Oord__class_Omax(U_8652)
    | ~ class_Orderings_Olinorder(U_8652)
    | ~ class_Lattices_Osemilattice__sup(U_8652) ),
    inference(clausify,[status(thm)],[f_2407_3]) ).

fof(f_2408_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_2408_2,plain,
    ! [U_8656,U_8655,U_8654,U_8653] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8653,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8653),U_8654),U_8655)),U_8656) = hAPP(hAPP(c_Set_Oinsert(U_8653),U_8654),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8653,tc_HOL_Obool)),U_8655),U_8656)),
    inference(variable_rename,[status(thm)],[f_2408_1]) ).

fof(f_2408_3,plain,
    ! [U_8653,U_8654,U_8655,U_8656] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8653,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8653),U_8654),U_8655)),U_8656) = hAPP(hAPP(c_Set_Oinsert(U_8653),U_8654),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8653,tc_HOL_Obool)),U_8655),U_8656)),
    inference(definitional_conversion,[status(esa)],[f_2408_2]) ).

cnf(f_2408_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8653,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8653),U_8654),U_8655)),U_8656) = hAPP(hAPP(c_Set_Oinsert(U_8653),U_8654),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8653,tc_HOL_Obool)),U_8655),U_8656)),
    inference(clausify,[status(thm)],[f_2408_3]) ).

fof(f_2409_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_2409_2,plain,
    ! [U_8660,U_8659,U_8658,U_8657] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8657,tc_HOL_Obool)),U_8658),hAPP(hAPP(c_Set_Oinsert(U_8657),U_8659),U_8660)) = hAPP(hAPP(c_Set_Oinsert(U_8657),U_8659),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8657,tc_HOL_Obool)),U_8658),U_8660)),
    inference(variable_rename,[status(thm)],[f_2409_1]) ).

fof(f_2409_3,plain,
    ! [U_8657,U_8658,U_8659,U_8660] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8657,tc_HOL_Obool)),U_8658),hAPP(hAPP(c_Set_Oinsert(U_8657),U_8659),U_8660)) = hAPP(hAPP(c_Set_Oinsert(U_8657),U_8659),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8657,tc_HOL_Obool)),U_8658),U_8660)),
    inference(definitional_conversion,[status(esa)],[f_2409_2]) ).

cnf(f_2409_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8657,tc_HOL_Obool)),U_8658),hAPP(hAPP(c_Set_Oinsert(U_8657),U_8659),U_8660)) = hAPP(hAPP(c_Set_Oinsert(U_8657),U_8659),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8657,tc_HOL_Obool)),U_8658),U_8660)),
    inference(clausify,[status(thm)],[f_2409_3]) ).

fof(f_2410_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_2410_2,plain,
    ! [U_8664,U_8663,U_8662,U_8661] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8661),U_8662),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8661,tc_HOL_Obool)),U_8663),U_8664)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_8661),U_8662),U_8664))
          & ~ hBOOL(hAPP(hAPP(c_member(U_8661),U_8662),U_8663)) ) )
      & ( hBOOL(hAPP(hAPP(c_member(U_8661),U_8662),U_8664))
        | hBOOL(hAPP(hAPP(c_member(U_8661),U_8662),U_8663))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8661),U_8662),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8661,tc_HOL_Obool)),U_8663),U_8664))) ) ),
    inference(variable_rename,[status(thm)],[f_2410_1]) ).

fof(f_2410_3,plain,
    ( ! [U_8672,U_8670,U_8668,U_8666] :
        ( hBOOL(hAPP(hAPP(c_member(U_8666),U_8668),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8666,tc_HOL_Obool)),U_8670),U_8672)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_8666),U_8668),U_8672))
          & ~ hBOOL(hAPP(hAPP(c_member(U_8666),U_8668),U_8670)) ) )
    & ! [U_8671,U_8669,U_8667,U_8665] :
        ( hBOOL(hAPP(hAPP(c_member(U_8665),U_8667),U_8671))
        | hBOOL(hAPP(hAPP(c_member(U_8665),U_8667),U_8669))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8665),U_8667),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8665,tc_HOL_Obool)),U_8669),U_8671))) ) ),
    inference(miniscope,[status(thm)],[f_2410_2]) ).

fof(f_2410_4,plain,
    ( ! [U_8668,U_8666,U_8672,U_8670] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8666),U_8668),U_8672))
        | ~ sP724(U_8668,U_8666,U_8672,U_8670) )
    & ! [U_8668,U_8666,U_8672,U_8670] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8666),U_8668),U_8670))
        | ~ sP724(U_8668,U_8666,U_8672,U_8670) )
    & ! [U_8668,U_8666,U_8672,U_8670] :
        ( hBOOL(hAPP(hAPP(c_member(U_8666),U_8668),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8666,tc_HOL_Obool)),U_8670),U_8672)))
        | sP724(U_8668,U_8666,U_8672,U_8670) )
    & ! [U_8671,U_8669,U_8665,U_8667] :
        ( hBOOL(hAPP(hAPP(c_member(U_8665),U_8667),U_8671))
        | hBOOL(hAPP(hAPP(c_member(U_8665),U_8667),U_8669))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8665),U_8667),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8665,tc_HOL_Obool)),U_8669),U_8671))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP724])],[f_2410_3]) ).

cnf(f_2410_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8665),U_8667),U_8671))
    | hBOOL(hAPP(hAPP(c_member(U_8665),U_8667),U_8669))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8665),U_8667),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8665,tc_HOL_Obool)),U_8669),U_8671))) ),
    inference(clausify,[status(thm)],[f_2410_4]) ).

cnf(f_2410_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8666),U_8668),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8666,tc_HOL_Obool)),U_8670),U_8672)))
    | sP724(U_8668,U_8666,U_8672,U_8670) ),
    inference(clausify,[status(thm)],[f_2410_4]) ).

cnf(f_2410_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8666),U_8668),U_8670))
    | ~ sP724(U_8668,U_8666,U_8672,U_8670) ),
    inference(clausify,[status(thm)],[f_2410_4]) ).

cnf(f_2410_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8666),U_8668),U_8672))
    | ~ sP724(U_8668,U_8666,U_8672,U_8670) ),
    inference(clausify,[status(thm)],[f_2410_4]) ).

fof(f_2411_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_2411_2,plain,
    ! [U_8676,U_8675,U_8674,U_8673] :
      ( hBOOL(hAPP(hAPP(c_member(U_8673),U_8674),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8673,tc_HOL_Obool)),U_8675),U_8676)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8673),U_8674),U_8675)) ),
    inference(variable_rename,[status(thm)],[f_2411_1]) ).

fof(f_2411_3,plain,
    ! [U_8674,U_8673,U_8675,U_8676] :
      ( hBOOL(hAPP(hAPP(c_member(U_8673),U_8674),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8673,tc_HOL_Obool)),U_8675),U_8676)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8673),U_8674),U_8675)) ),
    inference(definitional_conversion,[status(esa)],[f_2411_2]) ).

cnf(f_2411_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8673),U_8674),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8673,tc_HOL_Obool)),U_8675),U_8676)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8673),U_8674),U_8675)) ),
    inference(clausify,[status(thm)],[f_2411_3]) ).

fof(f_2412_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_2412_2,plain,
    ! [U_8680,U_8679,U_8678,U_8677] :
      ( hBOOL(hAPP(hAPP(c_member(U_8677),U_8678),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8677,tc_HOL_Obool)),U_8680),U_8679)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8677),U_8678),U_8679)) ),
    inference(variable_rename,[status(thm)],[f_2412_1]) ).

fof(f_2412_3,plain,
    ! [U_8677,U_8678,U_8679,U_8680] :
      ( hBOOL(hAPP(hAPP(c_member(U_8677),U_8678),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8677,tc_HOL_Obool)),U_8680),U_8679)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8677),U_8678),U_8679)) ),
    inference(definitional_conversion,[status(esa)],[f_2412_2]) ).

cnf(f_2412_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8677),U_8678),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8677,tc_HOL_Obool)),U_8680),U_8679)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8677),U_8678),U_8679)) ),
    inference(clausify,[status(thm)],[f_2412_3]) ).

fof(f_2413_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_2413_2,plain,
    ! [U_8684,U_8683,U_8682,U_8681] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8681,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8681,tc_fun(U_8681,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8681)),U_8682)),hAPP(hAPP(c_COMBC(U_8681,tc_fun(U_8681,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8681)),U_8683)),U_8684))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8681),U_8684),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8681,tc_HOL_Obool)),U_8682),U_8683))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_8681),U_8684),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8681,tc_HOL_Obool)),U_8682),U_8683)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8681,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8681,tc_fun(U_8681,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8681)),U_8682)),hAPP(hAPP(c_COMBC(U_8681,tc_fun(U_8681,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8681)),U_8683)),U_8684)) ) ),
    inference(variable_rename,[status(thm)],[f_2413_1]) ).

fof(f_2413_3,plain,
    ( ! [U_8692,U_8690,U_8688,U_8686] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8686,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8686,tc_fun(U_8686,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8686)),U_8688)),hAPP(hAPP(c_COMBC(U_8686,tc_fun(U_8686,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8686)),U_8690)),U_8692))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8686),U_8692),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8686,tc_HOL_Obool)),U_8688),U_8690))) )
    & ! [U_8691,U_8689,U_8687,U_8685] :
        ( hBOOL(hAPP(hAPP(c_member(U_8685),U_8691),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8685,tc_HOL_Obool)),U_8687),U_8689)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8685,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8685,tc_fun(U_8685,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8685)),U_8687)),hAPP(hAPP(c_COMBC(U_8685,tc_fun(U_8685,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8685)),U_8689)),U_8691)) ) ),
    inference(miniscope,[status(thm)],[f_2413_2]) ).

fof(f_2413_4,plain,
    ( ! [U_8686,U_8688,U_8690,U_8692] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8686,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8686,tc_fun(U_8686,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8686)),U_8688)),hAPP(hAPP(c_COMBC(U_8686,tc_fun(U_8686,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8686)),U_8690)),U_8692))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8686),U_8692),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8686,tc_HOL_Obool)),U_8688),U_8690))) )
    & ! [U_8687,U_8689,U_8691,U_8685] :
        ( hBOOL(hAPP(hAPP(c_member(U_8685),U_8691),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8685,tc_HOL_Obool)),U_8687),U_8689)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8685,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8685,tc_fun(U_8685,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8685)),U_8687)),hAPP(hAPP(c_COMBC(U_8685,tc_fun(U_8685,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8685)),U_8689)),U_8691)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2413_3]) ).

cnf(f_2413_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8685),U_8691),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8685,tc_HOL_Obool)),U_8687),U_8689)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8685,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8685,tc_fun(U_8685,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8685)),U_8687)),hAPP(hAPP(c_COMBC(U_8685,tc_fun(U_8685,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8685)),U_8689)),U_8691)) ),
    inference(clausify,[status(thm)],[f_2413_4]) ).

cnf(f_2413_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8686,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8686,tc_fun(U_8686,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8686)),U_8688)),hAPP(hAPP(c_COMBC(U_8686,tc_fun(U_8686,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8686)),U_8690)),U_8692))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8686),U_8692),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8686,tc_HOL_Obool)),U_8688),U_8690))) ),
    inference(clausify,[status(thm)],[f_2413_4]) ).

fof(f_2414_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_2414_2,plain,
    ! [U_8695,U_8694,U_8693] : hAPP(hAPP(c_Set_Oinsert(U_8693),U_8694),U_8695) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8693,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8693),U_8694),c_Orderings_Obot__class_Obot(tc_fun(U_8693,tc_HOL_Obool)))),U_8695),
    inference(variable_rename,[status(thm)],[f_2414_1]) ).

fof(f_2414_3,plain,
    ! [U_8693,U_8694,U_8695] : hAPP(hAPP(c_Set_Oinsert(U_8693),U_8694),U_8695) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8693,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8693),U_8694),c_Orderings_Obot__class_Obot(tc_fun(U_8693,tc_HOL_Obool)))),U_8695),
    inference(definitional_conversion,[status(esa)],[f_2414_2]) ).

cnf(f_2414_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_8693),U_8694),U_8695) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8693,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8693),U_8694),c_Orderings_Obot__class_Obot(tc_fun(U_8693,tc_HOL_Obool)))),U_8695),
    inference(clausify,[status(thm)],[f_2414_3]) ).

fof(f_2415_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_2415_2,plain,
    ! [U_8699,U_8698,U_8697,U_8696] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8696,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8696,tc_HOL_Obool)),U_8697),U_8698)),U_8699))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8696,tc_HOL_Obool)),U_8697),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8696,tc_HOL_Obool)),U_8698),U_8699))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8696,tc_HOL_Obool)),U_8697),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8696,tc_HOL_Obool)),U_8698),U_8699)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8696,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8696,tc_HOL_Obool)),U_8697),U_8698)),U_8699)) ) ),
    inference(variable_rename,[status(thm)],[f_2415_1]) ).

fof(f_2415_3,plain,
    ( ! [U_8707,U_8705,U_8703,U_8701] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8701,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8701,tc_HOL_Obool)),U_8703),U_8705)),U_8707))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8701,tc_HOL_Obool)),U_8703),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8701,tc_HOL_Obool)),U_8705),U_8707))) )
    & ! [U_8706,U_8704,U_8702,U_8700] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8700,tc_HOL_Obool)),U_8702),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8700,tc_HOL_Obool)),U_8704),U_8706)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8700,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8700,tc_HOL_Obool)),U_8702),U_8704)),U_8706)) ) ),
    inference(miniscope,[status(thm)],[f_2415_2]) ).

fof(f_2415_4,plain,
    ( ! [U_8701,U_8703,U_8705,U_8707] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8701,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8701,tc_HOL_Obool)),U_8703),U_8705)),U_8707))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8701,tc_HOL_Obool)),U_8703),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8701,tc_HOL_Obool)),U_8705),U_8707))) )
    & ! [U_8706,U_8702,U_8700,U_8704] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8700,tc_HOL_Obool)),U_8702),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8700,tc_HOL_Obool)),U_8704),U_8706)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8700,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8700,tc_HOL_Obool)),U_8702),U_8704)),U_8706)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2415_3]) ).

cnf(f_2415_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8700,tc_HOL_Obool)),U_8702),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8700,tc_HOL_Obool)),U_8704),U_8706)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8700,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8700,tc_HOL_Obool)),U_8702),U_8704)),U_8706)) ),
    inference(clausify,[status(thm)],[f_2415_4]) ).

cnf(f_2415_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8701,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8701,tc_HOL_Obool)),U_8703),U_8705)),U_8707))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8701,tc_HOL_Obool)),U_8703),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8701,tc_HOL_Obool)),U_8705),U_8707))) ),
    inference(clausify,[status(thm)],[f_2415_4]) ).

fof(f_2416_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_2416_2,plain,
    ! [U_8710,U_8709,U_8708] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8708,tc_HOL_Obool)),U_8709),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8708,tc_HOL_Obool)),U_8710),U_8709)) = U_8710
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8708,tc_HOL_Obool)),U_8709),U_8710)) ),
    inference(variable_rename,[status(thm)],[f_2416_1]) ).

fof(f_2416_3,plain,
    ! [U_8708,U_8709,U_8710] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8708,tc_HOL_Obool)),U_8709),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8708,tc_HOL_Obool)),U_8710),U_8709)) = U_8710
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8708,tc_HOL_Obool)),U_8709),U_8710)) ),
    inference(definitional_conversion,[status(esa)],[f_2416_2]) ).

cnf(f_2416_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8708,tc_HOL_Obool)),U_8709),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8708,tc_HOL_Obool)),U_8710),U_8709)) = U_8710
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8708,tc_HOL_Obool)),U_8709),U_8710)) ),
    inference(clausify,[status(thm)],[f_2416_3]) ).

fof(f_2417_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_2417_2,plain,
    ! [U_8713,U_8712,U_8711] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8711,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8711,tc_HOL_Obool)),U_8712),U_8713)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8711,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8711,tc_HOL_Obool)),U_8712)),U_8713),
    inference(variable_rename,[status(thm)],[f_2417_1]) ).

fof(f_2417_3,plain,
    ! [U_8711,U_8712,U_8713] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8711,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8711,tc_HOL_Obool)),U_8712),U_8713)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8711,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8711,tc_HOL_Obool)),U_8712)),U_8713),
    inference(definitional_conversion,[status(esa)],[f_2417_2]) ).

cnf(f_2417_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8711,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8711,tc_HOL_Obool)),U_8712),U_8713)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8711,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8711,tc_HOL_Obool)),U_8712)),U_8713),
    inference(clausify,[status(thm)],[f_2417_3]) ).

fof(f_2418_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_2418_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_2418_1]) ).

cnf(f_2418_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_2418_2]) ).

fof(f_2419_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_2419_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_2419_1]) ).

cnf(f_2419_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_2419_2]) ).

fof(f_2420_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_2420_2,plain,
    ! [U_8716,U_8715,U_8714] : c_Wellfounded_Omlex__prod(U_8714,U_8715,U_8716) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_8714),U_8714),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_8714,c_Wellfounded_Oless__than,U_8716)),hAPP(hAPP(c_COMBS(U_8714,U_8714,tc_prod(tc_Nat_Onat,U_8714)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_8714,tc_prod(tc_Nat_Onat,U_8714)),U_8714),c_Product__Type_OPair(tc_Nat_Onat,U_8714)),U_8715)),c_COMBI(U_8714))),
    inference(variable_rename,[status(thm)],[f_2420_1]) ).

fof(f_2420_3,plain,
    ! [U_8714,U_8715,U_8716] : c_Wellfounded_Omlex__prod(U_8714,U_8715,U_8716) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_8714),U_8714),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_8714,c_Wellfounded_Oless__than,U_8716)),hAPP(hAPP(c_COMBS(U_8714,U_8714,tc_prod(tc_Nat_Onat,U_8714)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_8714,tc_prod(tc_Nat_Onat,U_8714)),U_8714),c_Product__Type_OPair(tc_Nat_Onat,U_8714)),U_8715)),c_COMBI(U_8714))),
    inference(definitional_conversion,[status(esa)],[f_2420_2]) ).

cnf(f_2420_4,plain,
    c_Wellfounded_Omlex__prod(U_8714,U_8715,U_8716) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_8714),U_8714),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_8714,c_Wellfounded_Oless__than,U_8716)),hAPP(hAPP(c_COMBS(U_8714,U_8714,tc_prod(tc_Nat_Onat,U_8714)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_8714,tc_prod(tc_Nat_Onat,U_8714)),U_8714),c_Product__Type_OPair(tc_Nat_Onat,U_8714)),U_8715)),c_COMBI(U_8714))),
    inference(clausify,[status(thm)],[f_2420_3]) ).

fof(f_2421_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_2421_2,plain,
    ! [U_8720,U_8719,U_8718,U_8717] :
      ( ( 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_8717),U_8718)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8719),U_8720))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8717),U_8720) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8719),U_8718) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8717),U_8720) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8719),U_8718)
        | ~ 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_8717),U_8718)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8719),U_8720))),c_Int_Ointrel)) ) ),
    inference(variable_rename,[status(thm)],[f_2421_1]) ).

fof(f_2421_3,plain,
    ( ! [U_8728,U_8726,U_8724,U_8722] :
        ( 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_8722),U_8724)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8726),U_8728))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8722),U_8728) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8726),U_8724) )
    & ! [U_8727,U_8725,U_8723,U_8721] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8721),U_8727) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8725),U_8723)
        | ~ 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_8721),U_8723)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8725),U_8727))),c_Int_Ointrel)) ) ),
    inference(miniscope,[status(thm)],[f_2421_2]) ).

fof(f_2421_4,plain,
    ( ! [U_8722,U_8724,U_8726,U_8728] :
        ( 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_8722),U_8724)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8726),U_8728))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8722),U_8728) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8726),U_8724) )
    & ! [U_8727,U_8723,U_8721,U_8725] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8721),U_8727) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8725),U_8723)
        | ~ 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_8721),U_8723)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8725),U_8727))),c_Int_Ointrel)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2421_3]) ).

cnf(f_2421_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8721),U_8727) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8725),U_8723)
    | ~ 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_8721),U_8723)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8725),U_8727))),c_Int_Ointrel)) ),
    inference(clausify,[status(thm)],[f_2421_4]) ).

cnf(f_2421_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_8722),U_8724)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_8726),U_8728))),c_Int_Ointrel))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8722),U_8728) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8726),U_8724) ),
    inference(clausify,[status(thm)],[f_2421_4]) ).

fof(f_2422_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_2422_2,plain,
    ! [U_8732,U_8731,U_8730,U_8729] :
      ( c_FunDef_Oreduction__pair(U_8731,hAPP(hAPP(c_FunDef_Orp__inv__image(U_8729,U_8731),U_8730),U_8732))
      | ~ c_FunDef_Oreduction__pair(U_8729,U_8730) ),
    inference(variable_rename,[status(thm)],[f_2422_1]) ).

fof(f_2422_3,plain,
    ! [U_8729,U_8731,U_8730,U_8732] :
      ( c_FunDef_Oreduction__pair(U_8731,hAPP(hAPP(c_FunDef_Orp__inv__image(U_8729,U_8731),U_8730),U_8732))
      | ~ c_FunDef_Oreduction__pair(U_8729,U_8730) ),
    inference(definitional_conversion,[status(esa)],[f_2422_2]) ).

cnf(f_2422_4,plain,
    ( c_FunDef_Oreduction__pair(U_8731,hAPP(hAPP(c_FunDef_Orp__inv__image(U_8729,U_8731),U_8730),U_8732))
    | ~ c_FunDef_Oreduction__pair(U_8729,U_8730) ),
    inference(clausify,[status(thm)],[f_2422_3]) ).

fof(f_2423_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_2423_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_2423_1]) ).

cnf(f_2423_3,plain,
    c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2423_2]) ).

fof(f_2424_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_2424_2,plain,
    ! [U_8734,U_8733] : c_FunDef_Orp__inv__image(U_8733,U_8734) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))))),tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))),tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool)),c_COMBS(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)),tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))),tc_fun(U_8734,U_8733)),c_Product__Type_OPair(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),c_Relation_Oinv__image(U_8733,U_8734))))),c_Relation_Oinv__image(U_8733,U_8734))),
    inference(variable_rename,[status(thm)],[f_2424_1]) ).

fof(f_2424_3,plain,
    ! [U_8733,U_8734] : c_FunDef_Orp__inv__image(U_8733,U_8734) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))))),tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))),tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool)),c_COMBS(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)),tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))),tc_fun(U_8734,U_8733)),c_Product__Type_OPair(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),c_Relation_Oinv__image(U_8733,U_8734))))),c_Relation_Oinv__image(U_8733,U_8734))),
    inference(definitional_conversion,[status(esa)],[f_2424_2]) ).

cnf(f_2424_4,plain,
    c_FunDef_Orp__inv__image(U_8733,U_8734) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))))),tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))),tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)),tc_fun(tc_fun(U_8734,U_8733),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool)),c_COMBS(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)),tc_fun(tc_fun(U_8734,U_8733),tc_fun(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),tc_fun(tc_prod(U_8733,U_8733),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool))),tc_fun(U_8734,U_8733)),c_Product__Type_OPair(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool),tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)))),c_Relation_Oinv__image(U_8733,U_8734))))),c_Relation_Oinv__image(U_8733,U_8734))),
    inference(clausify,[status(thm)],[f_2424_3]) ).

fof(f_2425_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_2425_2,plain,
    ! [U_8740,U_8739,U_8738,U_8737,U_8736,U_8735] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8735,tc_fun(U_8736,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8735,tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_fun(U_8736,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8736,tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_fun(U_8736,tc_HOL_Obool)),U_8735),c_COMBC(U_8736,tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8736,tc_prod(U_8735,U_8736)),tc_fun(U_8736,tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool)),U_8735),hAPP(c_COMBB(tc_prod(U_8735,U_8736),tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool),U_8736),c_member(tc_prod(U_8735,U_8736)))),c_Product__Type_OPair(U_8735,U_8736)))),U_8737)),hAPP(hAPP(c_COMBC(U_8735,tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_fun(U_8736,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8736,tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_fun(U_8736,tc_HOL_Obool)),U_8735),c_COMBC(U_8736,tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8736,tc_prod(U_8735,U_8736)),tc_fun(U_8736,tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool)),U_8735),hAPP(c_COMBB(tc_prod(U_8735,U_8736),tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool),U_8736),c_member(tc_prod(U_8735,U_8736)))),c_Product__Type_OPair(U_8735,U_8736)))),U_8738)),U_8739),U_8740))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8735,U_8736)),hAPP(hAPP(c_Product__Type_OPair(U_8735,U_8736),U_8739),U_8740)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool)),U_8737),U_8738))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8735,U_8736)),hAPP(hAPP(c_Product__Type_OPair(U_8735,U_8736),U_8739),U_8740)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool)),U_8737),U_8738)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8735,tc_fun(U_8736,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8735,tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_fun(U_8736,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8736,tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_fun(U_8736,tc_HOL_Obool)),U_8735),c_COMBC(U_8736,tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8736,tc_prod(U_8735,U_8736)),tc_fun(U_8736,tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool)),U_8735),hAPP(c_COMBB(tc_prod(U_8735,U_8736),tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool),U_8736),c_member(tc_prod(U_8735,U_8736)))),c_Product__Type_OPair(U_8735,U_8736)))),U_8737)),hAPP(hAPP(c_COMBC(U_8735,tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_fun(U_8736,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8736,tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_fun(U_8736,tc_HOL_Obool)),U_8735),c_COMBC(U_8736,tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8736,tc_prod(U_8735,U_8736)),tc_fun(U_8736,tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool)),U_8735),hAPP(c_COMBB(tc_prod(U_8735,U_8736),tc_fun(tc_fun(tc_prod(U_8735,U_8736),tc_HOL_Obool),tc_HOL_Obool),U_8736),c_member(tc_prod(U_8735,U_8736)))),c_Product__Type_OPair(U_8735,U_8736)))),U_8738)),U_8739),U_8740)) ) ),
    inference(variable_rename,[status(thm)],[f_2425_1]) ).

fof(f_2425_3,plain,
    ( ! [U_8752,U_8750,U_8748,U_8746,U_8744,U_8742] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8742,tc_fun(U_8744,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8742,tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_fun(U_8744,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8744,tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_fun(U_8744,tc_HOL_Obool)),U_8742),c_COMBC(U_8744,tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8744,tc_prod(U_8742,U_8744)),tc_fun(U_8744,tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),U_8742),hAPP(c_COMBB(tc_prod(U_8742,U_8744),tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool),U_8744),c_member(tc_prod(U_8742,U_8744)))),c_Product__Type_OPair(U_8742,U_8744)))),U_8746)),hAPP(hAPP(c_COMBC(U_8742,tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_fun(U_8744,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8744,tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_fun(U_8744,tc_HOL_Obool)),U_8742),c_COMBC(U_8744,tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8744,tc_prod(U_8742,U_8744)),tc_fun(U_8744,tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),U_8742),hAPP(c_COMBB(tc_prod(U_8742,U_8744),tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool),U_8744),c_member(tc_prod(U_8742,U_8744)))),c_Product__Type_OPair(U_8742,U_8744)))),U_8748)),U_8750),U_8752))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8742,U_8744)),hAPP(hAPP(c_Product__Type_OPair(U_8742,U_8744),U_8750),U_8752)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool)),U_8746),U_8748))) )
    & ! [U_8751,U_8749,U_8747,U_8745,U_8743,U_8741] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8741,U_8743)),hAPP(hAPP(c_Product__Type_OPair(U_8741,U_8743),U_8749),U_8751)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool)),U_8745),U_8747)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8741,tc_fun(U_8743,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8741,tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_fun(U_8743,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8743,tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_fun(U_8743,tc_HOL_Obool)),U_8741),c_COMBC(U_8743,tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8743,tc_prod(U_8741,U_8743)),tc_fun(U_8743,tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),U_8741),hAPP(c_COMBB(tc_prod(U_8741,U_8743),tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool),U_8743),c_member(tc_prod(U_8741,U_8743)))),c_Product__Type_OPair(U_8741,U_8743)))),U_8745)),hAPP(hAPP(c_COMBC(U_8741,tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_fun(U_8743,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8743,tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_fun(U_8743,tc_HOL_Obool)),U_8741),c_COMBC(U_8743,tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8743,tc_prod(U_8741,U_8743)),tc_fun(U_8743,tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),U_8741),hAPP(c_COMBB(tc_prod(U_8741,U_8743),tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool),U_8743),c_member(tc_prod(U_8741,U_8743)))),c_Product__Type_OPair(U_8741,U_8743)))),U_8747)),U_8749),U_8751)) ) ),
    inference(miniscope,[status(thm)],[f_2425_2]) ).

fof(f_2425_4,plain,
    ( ! [U_8742,U_8744,U_8746,U_8748,U_8750,U_8752] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8742,tc_fun(U_8744,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8742,tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_fun(U_8744,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8744,tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_fun(U_8744,tc_HOL_Obool)),U_8742),c_COMBC(U_8744,tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8744,tc_prod(U_8742,U_8744)),tc_fun(U_8744,tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),U_8742),hAPP(c_COMBB(tc_prod(U_8742,U_8744),tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool),U_8744),c_member(tc_prod(U_8742,U_8744)))),c_Product__Type_OPair(U_8742,U_8744)))),U_8746)),hAPP(hAPP(c_COMBC(U_8742,tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_fun(U_8744,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8744,tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_fun(U_8744,tc_HOL_Obool)),U_8742),c_COMBC(U_8744,tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8744,tc_prod(U_8742,U_8744)),tc_fun(U_8744,tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),U_8742),hAPP(c_COMBB(tc_prod(U_8742,U_8744),tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool),U_8744),c_member(tc_prod(U_8742,U_8744)))),c_Product__Type_OPair(U_8742,U_8744)))),U_8748)),U_8750),U_8752))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8742,U_8744)),hAPP(hAPP(c_Product__Type_OPair(U_8742,U_8744),U_8750),U_8752)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool)),U_8746),U_8748))) )
    & ! [U_8747,U_8743,U_8741,U_8745,U_8749,U_8751] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8741,U_8743)),hAPP(hAPP(c_Product__Type_OPair(U_8741,U_8743),U_8749),U_8751)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool)),U_8745),U_8747)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8741,tc_fun(U_8743,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8741,tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_fun(U_8743,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8743,tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_fun(U_8743,tc_HOL_Obool)),U_8741),c_COMBC(U_8743,tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8743,tc_prod(U_8741,U_8743)),tc_fun(U_8743,tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),U_8741),hAPP(c_COMBB(tc_prod(U_8741,U_8743),tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool),U_8743),c_member(tc_prod(U_8741,U_8743)))),c_Product__Type_OPair(U_8741,U_8743)))),U_8745)),hAPP(hAPP(c_COMBC(U_8741,tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_fun(U_8743,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8743,tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_fun(U_8743,tc_HOL_Obool)),U_8741),c_COMBC(U_8743,tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8743,tc_prod(U_8741,U_8743)),tc_fun(U_8743,tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),U_8741),hAPP(c_COMBB(tc_prod(U_8741,U_8743),tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool),U_8743),c_member(tc_prod(U_8741,U_8743)))),c_Product__Type_OPair(U_8741,U_8743)))),U_8747)),U_8749),U_8751)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2425_3]) ).

cnf(f_2425_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8741,U_8743)),hAPP(hAPP(c_Product__Type_OPair(U_8741,U_8743),U_8749),U_8751)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool)),U_8745),U_8747)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8741,tc_fun(U_8743,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8741,tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_fun(U_8743,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8743,tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_fun(U_8743,tc_HOL_Obool)),U_8741),c_COMBC(U_8743,tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8743,tc_prod(U_8741,U_8743)),tc_fun(U_8743,tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),U_8741),hAPP(c_COMBB(tc_prod(U_8741,U_8743),tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool),U_8743),c_member(tc_prod(U_8741,U_8743)))),c_Product__Type_OPair(U_8741,U_8743)))),U_8745)),hAPP(hAPP(c_COMBC(U_8741,tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_fun(U_8743,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8743,tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_fun(U_8743,tc_HOL_Obool)),U_8741),c_COMBC(U_8743,tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8743,tc_prod(U_8741,U_8743)),tc_fun(U_8743,tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool)),U_8741),hAPP(c_COMBB(tc_prod(U_8741,U_8743),tc_fun(tc_fun(tc_prod(U_8741,U_8743),tc_HOL_Obool),tc_HOL_Obool),U_8743),c_member(tc_prod(U_8741,U_8743)))),c_Product__Type_OPair(U_8741,U_8743)))),U_8747)),U_8749),U_8751)) ),
    inference(clausify,[status(thm)],[f_2425_4]) ).

cnf(f_2425_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8742,tc_fun(U_8744,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8742,tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_fun(U_8744,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8744,tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_fun(U_8744,tc_HOL_Obool)),U_8742),c_COMBC(U_8744,tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8744,tc_prod(U_8742,U_8744)),tc_fun(U_8744,tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),U_8742),hAPP(c_COMBB(tc_prod(U_8742,U_8744),tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool),U_8744),c_member(tc_prod(U_8742,U_8744)))),c_Product__Type_OPair(U_8742,U_8744)))),U_8746)),hAPP(hAPP(c_COMBC(U_8742,tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_fun(U_8744,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8744,tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_fun(U_8744,tc_HOL_Obool)),U_8742),c_COMBC(U_8744,tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8744,tc_prod(U_8742,U_8744)),tc_fun(U_8744,tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool)),U_8742),hAPP(c_COMBB(tc_prod(U_8742,U_8744),tc_fun(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool),tc_HOL_Obool),U_8744),c_member(tc_prod(U_8742,U_8744)))),c_Product__Type_OPair(U_8742,U_8744)))),U_8748)),U_8750),U_8752))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8742,U_8744)),hAPP(hAPP(c_Product__Type_OPair(U_8742,U_8744),U_8750),U_8752)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8742,U_8744),tc_HOL_Obool)),U_8746),U_8748))) ),
    inference(clausify,[status(thm)],[f_2425_4]) ).

fof(f_2426_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_2426_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_2426_1]) ).

cnf(f_2426_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_2426_2]) ).

fof(f_2427_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_2427_2,plain,
    ! [U_8758,U_8757,U_8756,U_8755,U_8754,U_8753] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8753,tc_HOL_Obool)),U_8754),U_8757)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8753,tc_HOL_Obool)),U_8755),U_8758))),c_Wellfounded_Omax__ext(U_8753,U_8756)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool)),U_8757),U_8758)),c_Wellfounded_Omax__ext(U_8753,U_8756)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool)),U_8754),U_8755)),c_Wellfounded_Omax__ext(U_8753,U_8756))) ),
    inference(variable_rename,[status(thm)],[f_2427_1]) ).

fof(f_2427_3,plain,
    ! [U_8753,U_8755,U_8756,U_8757,U_8754,U_8758] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8753,tc_HOL_Obool)),U_8754),U_8757)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8753,tc_HOL_Obool)),U_8755),U_8758))),c_Wellfounded_Omax__ext(U_8753,U_8756)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool)),U_8757),U_8758)),c_Wellfounded_Omax__ext(U_8753,U_8756)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool)),U_8754),U_8755)),c_Wellfounded_Omax__ext(U_8753,U_8756))) ),
    inference(definitional_conversion,[status(esa)],[f_2427_2]) ).

cnf(f_2427_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8753,tc_HOL_Obool)),U_8754),U_8757)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8753,tc_HOL_Obool)),U_8755),U_8758))),c_Wellfounded_Omax__ext(U_8753,U_8756)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool)),U_8757),U_8758)),c_Wellfounded_Omax__ext(U_8753,U_8756)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8753,tc_HOL_Obool),tc_fun(U_8753,tc_HOL_Obool)),U_8754),U_8755)),c_Wellfounded_Omax__ext(U_8753,U_8756))) ),
    inference(clausify,[status(thm)],[f_2427_3]) ).

fof(f_2428_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_2428_2,plain,
    ! [U_8762,U_8761,U_8760,U_8759] :
      ( ( c_Wellfounded_Omax__extp(U_8759,hAPP(hAPP(c_COMBC(U_8759,tc_fun(tc_prod(U_8759,U_8759),tc_HOL_Obool),tc_fun(U_8759,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8759,tc_fun(tc_fun(tc_prod(U_8759,U_8759),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8759,U_8759),tc_HOL_Obool),tc_fun(U_8759,tc_HOL_Obool)),U_8759),c_COMBC(U_8759,tc_fun(tc_prod(U_8759,U_8759),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8759,tc_prod(U_8759,U_8759)),tc_fun(U_8759,tc_fun(tc_fun(tc_prod(U_8759,U_8759),tc_HOL_Obool),tc_HOL_Obool)),U_8759),hAPP(c_COMBB(tc_prod(U_8759,U_8759),tc_fun(tc_fun(tc_prod(U_8759,U_8759),tc_HOL_Obool),tc_HOL_Obool),U_8759),c_member(tc_prod(U_8759,U_8759)))),c_Product__Type_OPair(U_8759,U_8759)))),U_8760),U_8761,U_8762)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8759,tc_HOL_Obool),tc_fun(U_8759,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8759,tc_HOL_Obool),tc_fun(U_8759,tc_HOL_Obool)),U_8761),U_8762)),c_Wellfounded_Omax__ext(U_8759,U_8760))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8759,tc_HOL_Obool),tc_fun(U_8759,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8759,tc_HOL_Obool),tc_fun(U_8759,tc_HOL_Obool)),U_8761),U_8762)),c_Wellfounded_Omax__ext(U_8759,U_8760)))
        | ~ c_Wellfounded_Omax__extp(U_8759,hAPP(hAPP(c_COMBC(U_8759,tc_fun(tc_prod(U_8759,U_8759),tc_HOL_Obool),tc_fun(U_8759,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8759,tc_fun(tc_fun(tc_prod(U_8759,U_8759),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8759,U_8759),tc_HOL_Obool),tc_fun(U_8759,tc_HOL_Obool)),U_8759),c_COMBC(U_8759,tc_fun(tc_prod(U_8759,U_8759),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8759,tc_prod(U_8759,U_8759)),tc_fun(U_8759,tc_fun(tc_fun(tc_prod(U_8759,U_8759),tc_HOL_Obool),tc_HOL_Obool)),U_8759),hAPP(c_COMBB(tc_prod(U_8759,U_8759),tc_fun(tc_fun(tc_prod(U_8759,U_8759),tc_HOL_Obool),tc_HOL_Obool),U_8759),c_member(tc_prod(U_8759,U_8759)))),c_Product__Type_OPair(U_8759,U_8759)))),U_8760),U_8761,U_8762) ) ),
    inference(variable_rename,[status(thm)],[f_2428_1]) ).

fof(f_2428_3,plain,
    ( ! [U_8770,U_8768,U_8766,U_8764] :
        ( c_Wellfounded_Omax__extp(U_8764,hAPP(hAPP(c_COMBC(U_8764,tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_fun(U_8764,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8764,tc_fun(tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_fun(U_8764,tc_HOL_Obool)),U_8764),c_COMBC(U_8764,tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8764,tc_prod(U_8764,U_8764)),tc_fun(U_8764,tc_fun(tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_HOL_Obool)),U_8764),hAPP(c_COMBB(tc_prod(U_8764,U_8764),tc_fun(tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_HOL_Obool),U_8764),c_member(tc_prod(U_8764,U_8764)))),c_Product__Type_OPair(U_8764,U_8764)))),U_8766),U_8768,U_8770)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8764,tc_HOL_Obool),tc_fun(U_8764,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8764,tc_HOL_Obool),tc_fun(U_8764,tc_HOL_Obool)),U_8768),U_8770)),c_Wellfounded_Omax__ext(U_8764,U_8766))) )
    & ! [U_8769,U_8767,U_8765,U_8763] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8763,tc_HOL_Obool),tc_fun(U_8763,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8763,tc_HOL_Obool),tc_fun(U_8763,tc_HOL_Obool)),U_8767),U_8769)),c_Wellfounded_Omax__ext(U_8763,U_8765)))
        | ~ c_Wellfounded_Omax__extp(U_8763,hAPP(hAPP(c_COMBC(U_8763,tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_fun(U_8763,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8763,tc_fun(tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_fun(U_8763,tc_HOL_Obool)),U_8763),c_COMBC(U_8763,tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8763,tc_prod(U_8763,U_8763)),tc_fun(U_8763,tc_fun(tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_HOL_Obool)),U_8763),hAPP(c_COMBB(tc_prod(U_8763,U_8763),tc_fun(tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_HOL_Obool),U_8763),c_member(tc_prod(U_8763,U_8763)))),c_Product__Type_OPair(U_8763,U_8763)))),U_8765),U_8767,U_8769) ) ),
    inference(miniscope,[status(thm)],[f_2428_2]) ).

fof(f_2428_4,plain,
    ( ! [U_8766,U_8764,U_8768,U_8770] :
        ( c_Wellfounded_Omax__extp(U_8764,hAPP(hAPP(c_COMBC(U_8764,tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_fun(U_8764,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8764,tc_fun(tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_fun(U_8764,tc_HOL_Obool)),U_8764),c_COMBC(U_8764,tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8764,tc_prod(U_8764,U_8764)),tc_fun(U_8764,tc_fun(tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_HOL_Obool)),U_8764),hAPP(c_COMBB(tc_prod(U_8764,U_8764),tc_fun(tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_HOL_Obool),U_8764),c_member(tc_prod(U_8764,U_8764)))),c_Product__Type_OPair(U_8764,U_8764)))),U_8766),U_8768,U_8770)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8764,tc_HOL_Obool),tc_fun(U_8764,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8764,tc_HOL_Obool),tc_fun(U_8764,tc_HOL_Obool)),U_8768),U_8770)),c_Wellfounded_Omax__ext(U_8764,U_8766))) )
    & ! [U_8765,U_8763,U_8767,U_8769] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8763,tc_HOL_Obool),tc_fun(U_8763,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8763,tc_HOL_Obool),tc_fun(U_8763,tc_HOL_Obool)),U_8767),U_8769)),c_Wellfounded_Omax__ext(U_8763,U_8765)))
        | ~ c_Wellfounded_Omax__extp(U_8763,hAPP(hAPP(c_COMBC(U_8763,tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_fun(U_8763,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8763,tc_fun(tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_fun(U_8763,tc_HOL_Obool)),U_8763),c_COMBC(U_8763,tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8763,tc_prod(U_8763,U_8763)),tc_fun(U_8763,tc_fun(tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_HOL_Obool)),U_8763),hAPP(c_COMBB(tc_prod(U_8763,U_8763),tc_fun(tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_HOL_Obool),U_8763),c_member(tc_prod(U_8763,U_8763)))),c_Product__Type_OPair(U_8763,U_8763)))),U_8765),U_8767,U_8769) ) ),
    inference(definitional_conversion,[status(esa)],[f_2428_3]) ).

cnf(f_2428_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8763,tc_HOL_Obool),tc_fun(U_8763,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8763,tc_HOL_Obool),tc_fun(U_8763,tc_HOL_Obool)),U_8767),U_8769)),c_Wellfounded_Omax__ext(U_8763,U_8765)))
    | ~ c_Wellfounded_Omax__extp(U_8763,hAPP(hAPP(c_COMBC(U_8763,tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_fun(U_8763,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8763,tc_fun(tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_fun(U_8763,tc_HOL_Obool)),U_8763),c_COMBC(U_8763,tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8763,tc_prod(U_8763,U_8763)),tc_fun(U_8763,tc_fun(tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_HOL_Obool)),U_8763),hAPP(c_COMBB(tc_prod(U_8763,U_8763),tc_fun(tc_fun(tc_prod(U_8763,U_8763),tc_HOL_Obool),tc_HOL_Obool),U_8763),c_member(tc_prod(U_8763,U_8763)))),c_Product__Type_OPair(U_8763,U_8763)))),U_8765),U_8767,U_8769) ),
    inference(clausify,[status(thm)],[f_2428_4]) ).

cnf(f_2428_6,plain,
    ( c_Wellfounded_Omax__extp(U_8764,hAPP(hAPP(c_COMBC(U_8764,tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_fun(U_8764,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8764,tc_fun(tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_fun(U_8764,tc_HOL_Obool)),U_8764),c_COMBC(U_8764,tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8764,tc_prod(U_8764,U_8764)),tc_fun(U_8764,tc_fun(tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_HOL_Obool)),U_8764),hAPP(c_COMBB(tc_prod(U_8764,U_8764),tc_fun(tc_fun(tc_prod(U_8764,U_8764),tc_HOL_Obool),tc_HOL_Obool),U_8764),c_member(tc_prod(U_8764,U_8764)))),c_Product__Type_OPair(U_8764,U_8764)))),U_8766),U_8768,U_8770)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_8764,tc_HOL_Obool),tc_fun(U_8764,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_8764,tc_HOL_Obool),tc_fun(U_8764,tc_HOL_Obool)),U_8768),U_8770)),c_Wellfounded_Omax__ext(U_8764,U_8766))) ),
    inference(clausify,[status(thm)],[f_2428_4]) ).

fof(f_2429_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_2429_2,plain,
    ! [U_8776,U_8775,U_8774,U_8773,U_8772,U_8771] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8771,U_8771)),hAPP(hAPP(c_Product__Type_OPair(U_8771,U_8771),U_8772),U_8773)),hAPP(hAPP(c_Relation_Oinv__image(U_8774,U_8771),U_8775),U_8776)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8774,U_8774)),hAPP(hAPP(c_Product__Type_OPair(U_8774,U_8774),hAPP(U_8776,U_8772)),hAPP(U_8776,U_8773))),U_8775)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8774,U_8774)),hAPP(hAPP(c_Product__Type_OPair(U_8774,U_8774),hAPP(U_8776,U_8772)),hAPP(U_8776,U_8773))),U_8775))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8771,U_8771)),hAPP(hAPP(c_Product__Type_OPair(U_8771,U_8771),U_8772),U_8773)),hAPP(hAPP(c_Relation_Oinv__image(U_8774,U_8771),U_8775),U_8776))) ) ),
    inference(variable_rename,[status(thm)],[f_2429_1]) ).

fof(f_2429_3,plain,
    ( ! [U_8788,U_8786,U_8784,U_8782,U_8780] :
        ( ! [U_8778] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8778,U_8778)),hAPP(hAPP(c_Product__Type_OPair(U_8778,U_8778),U_8780),U_8782)),hAPP(hAPP(c_Relation_Oinv__image(U_8784,U_8778),U_8786),U_8788)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8784,U_8784)),hAPP(hAPP(c_Product__Type_OPair(U_8784,U_8784),hAPP(U_8788,U_8780)),hAPP(U_8788,U_8782))),U_8786)) )
    & ! [U_8787,U_8785,U_8783,U_8781,U_8779] :
        ( ! [U_8777] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8777,U_8777)),hAPP(hAPP(c_Product__Type_OPair(U_8777,U_8777),U_8779),U_8781)),hAPP(hAPP(c_Relation_Oinv__image(U_8783,U_8777),U_8785),U_8787)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8783,U_8783)),hAPP(hAPP(c_Product__Type_OPair(U_8783,U_8783),hAPP(U_8787,U_8779)),hAPP(U_8787,U_8781))),U_8785)) ) ),
    inference(miniscope,[status(thm)],[f_2429_2]) ).

fof(f_2429_4,plain,
    ( ! [U_8778,U_8780,U_8782,U_8784,U_8786,U_8788] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8778,U_8778)),hAPP(hAPP(c_Product__Type_OPair(U_8778,U_8778),U_8780),U_8782)),hAPP(hAPP(c_Relation_Oinv__image(U_8784,U_8778),U_8786),U_8788)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8784,U_8784)),hAPP(hAPP(c_Product__Type_OPair(U_8784,U_8784),hAPP(U_8788,U_8780)),hAPP(U_8788,U_8782))),U_8786)) )
    & ! [U_8783,U_8779,U_8777,U_8781,U_8785,U_8787] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8777,U_8777)),hAPP(hAPP(c_Product__Type_OPair(U_8777,U_8777),U_8779),U_8781)),hAPP(hAPP(c_Relation_Oinv__image(U_8783,U_8777),U_8785),U_8787)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8783,U_8783)),hAPP(hAPP(c_Product__Type_OPair(U_8783,U_8783),hAPP(U_8787,U_8779)),hAPP(U_8787,U_8781))),U_8785)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2429_3]) ).

cnf(f_2429_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8777,U_8777)),hAPP(hAPP(c_Product__Type_OPair(U_8777,U_8777),U_8779),U_8781)),hAPP(hAPP(c_Relation_Oinv__image(U_8783,U_8777),U_8785),U_8787)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8783,U_8783)),hAPP(hAPP(c_Product__Type_OPair(U_8783,U_8783),hAPP(U_8787,U_8779)),hAPP(U_8787,U_8781))),U_8785)) ),
    inference(clausify,[status(thm)],[f_2429_4]) ).

cnf(f_2429_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8778,U_8778)),hAPP(hAPP(c_Product__Type_OPair(U_8778,U_8778),U_8780),U_8782)),hAPP(hAPP(c_Relation_Oinv__image(U_8784,U_8778),U_8786),U_8788)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8784,U_8784)),hAPP(hAPP(c_Product__Type_OPair(U_8784,U_8784),hAPP(U_8788,U_8780)),hAPP(U_8788,U_8782))),U_8786)) ),
    inference(clausify,[status(thm)],[f_2429_4]) ).

fof(f_2430_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_2430_2,plain,
    ! [U_8794,U_8793,U_8792,U_8791,U_8790,U_8789] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8789,U_8790,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8789)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8789),hAPP(U_8791,U_8794)),hAPP(c_Com_Ocom_OBODY,U_8794)),hAPP(U_8792,U_8794))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8789),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_8794),U_8793))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8789,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8789),tc_HOL_Obool)),U_8790),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8789),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789))),hAPP(hAPP(c_COMBB(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8789)),U_8791)),c_Com_Ocom_OBODY)),U_8792)),U_8793)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8789),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789))),hAPP(hAPP(c_COMBB(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8789)),U_8791)),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_8792)),U_8793)) ),
    inference(variable_rename,[status(thm)],[f_2430_1]) ).

fof(f_2430_3,plain,
    ! [U_8789,U_8790,U_8791,U_8792,U_8793,U_8794] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8789,U_8790,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8789)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8789),hAPP(U_8791,U_8794)),hAPP(c_Com_Ocom_OBODY,U_8794)),hAPP(U_8792,U_8794))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8789),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_8794),U_8793))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8789,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8789),tc_HOL_Obool)),U_8790),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8789),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789))),hAPP(hAPP(c_COMBB(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8789)),U_8791)),c_Com_Ocom_OBODY)),U_8792)),U_8793)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8789),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789))),hAPP(hAPP(c_COMBB(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8789)),U_8791)),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_8792)),U_8793)) ),
    inference(definitional_conversion,[status(esa)],[f_2430_2]) ).

cnf(f_2430_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_8789,U_8790,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8789)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8789),hAPP(U_8791,U_8794)),hAPP(c_Com_Ocom_OBODY,U_8794)),hAPP(U_8792,U_8794))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8789),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_8794),U_8793))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8789,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8789),tc_HOL_Obool)),U_8790),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8789),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789))),hAPP(hAPP(c_COMBB(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8789)),U_8791)),c_Com_Ocom_OBODY)),U_8792)),U_8793)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8789),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789))),hAPP(hAPP(c_COMBB(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8789,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8789))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8789)),U_8791)),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_8792)),U_8793)) ),
    inference(clausify,[status(thm)],[f_2430_3]) ).

fof(f_2431_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_2431_2,plain,
    ! [U_8799,U_8798,U_8797,U_8796,U_8795] :
      ( c_Hoare__Mirabelle_Ohoare__valids(U_8795,U_8796,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8795),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),hAPP(hAPP(c_COMBB(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8795)),U_8797)),c_Com_Ocom_OBODY)),U_8798)),U_8799))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(U_8795,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8795),tc_HOL_Obool)),U_8796),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8795),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),hAPP(hAPP(c_COMBB(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8795)),U_8797)),c_Com_Ocom_OBODY)),U_8798)),U_8799)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8795),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),hAPP(hAPP(c_COMBB(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8795)),U_8797)),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_8798)),U_8799)) ),
    inference(variable_rename,[status(thm)],[f_2431_1]) ).

fof(f_2431_3,plain,
    ! [U_8795,U_8798,U_8799,U_8796,U_8797] :
      ( c_Hoare__Mirabelle_Ohoare__valids(U_8795,U_8796,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8795),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),hAPP(hAPP(c_COMBB(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8795)),U_8797)),c_Com_Ocom_OBODY)),U_8798)),U_8799))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(U_8795,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8795),tc_HOL_Obool)),U_8796),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8795),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),hAPP(hAPP(c_COMBB(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8795)),U_8797)),c_Com_Ocom_OBODY)),U_8798)),U_8799)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8795),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),hAPP(hAPP(c_COMBB(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8795)),U_8797)),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_8798)),U_8799)) ),
    inference(definitional_conversion,[status(esa)],[f_2431_2]) ).

cnf(f_2431_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__valids(U_8795,U_8796,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8795),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),hAPP(hAPP(c_COMBB(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8795)),U_8797)),c_Com_Ocom_OBODY)),U_8798)),U_8799))
    | ~ c_Hoare__Mirabelle_Ohoare__valids(U_8795,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8795),tc_HOL_Obool)),U_8796),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8795),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),hAPP(hAPP(c_COMBB(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8795)),U_8797)),c_Com_Ocom_OBODY)),U_8798)),U_8799)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8795),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),hAPP(hAPP(c_COMBB(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8795,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8795))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8795)),U_8797)),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_8798)),U_8799)) ),
    inference(clausify,[status(thm)],[f_2431_3]) ).

fof(f_2432_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_2432_2,plain,
    ! [U_8805,U_8804,U_8803,U_8802,U_8801,U_8800] :
      ( hBOOL(hAPP(hAPP(U_8803,U_8804),U_8805))
      | hBOOL(hAPP(hAPP(U_8802,U_8804),U_8805))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8800,tc_fun(U_8801,tc_HOL_Obool))),U_8802),U_8803),U_8804),U_8805)) ),
    inference(variable_rename,[status(thm)],[f_2432_1]) ).

fof(f_2432_3,plain,
    ! [U_8805,U_8804,U_8803,U_8802] :
      ( ! [U_8801,U_8800] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8800,tc_fun(U_8801,tc_HOL_Obool))),U_8802),U_8803),U_8804),U_8805))
      | hBOOL(hAPP(hAPP(U_8803,U_8804),U_8805))
      | hBOOL(hAPP(hAPP(U_8802,U_8804),U_8805)) ),
    inference(miniscope,[status(thm)],[f_2432_2]) ).

fof(f_2432_4,plain,
    ! [U_8800,U_8801,U_8802,U_8803,U_8804,U_8805] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8800,tc_fun(U_8801,tc_HOL_Obool))),U_8802),U_8803),U_8804),U_8805))
      | hBOOL(hAPP(hAPP(U_8803,U_8804),U_8805))
      | hBOOL(hAPP(hAPP(U_8802,U_8804),U_8805)) ),
    inference(definitional_conversion,[status(esa)],[f_2432_3]) ).

cnf(f_2432_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8800,tc_fun(U_8801,tc_HOL_Obool))),U_8802),U_8803),U_8804),U_8805))
    | hBOOL(hAPP(hAPP(U_8803,U_8804),U_8805))
    | hBOOL(hAPP(hAPP(U_8802,U_8804),U_8805)) ),
    inference(clausify,[status(thm)],[f_2432_4]) ).

fof(f_2433_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_2433_2,plain,
    ! [U_8811,U_8810,U_8809,U_8808,U_8807,U_8806] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8810,tc_fun(U_8811,tc_HOL_Obool))),U_8809),U_8806),U_8807),U_8808))
      | ( ~ hBOOL(hAPP(hAPP(U_8809,U_8807),U_8808))
        & ~ hBOOL(hAPP(hAPP(U_8806,U_8807),U_8808)) ) ),
    inference(variable_rename,[status(thm)],[f_2433_1]) ).

fof(f_2433_3,plain,
    ( ! [U_8806,U_8807,U_8808,U_8809] :
        ( ~ hBOOL(hAPP(hAPP(U_8809,U_8807),U_8808))
        | ~ sP725(U_8806,U_8807,U_8808,U_8809) )
    & ! [U_8806,U_8807,U_8808,U_8809] :
        ( ~ hBOOL(hAPP(hAPP(U_8806,U_8807),U_8808))
        | ~ sP725(U_8806,U_8807,U_8808,U_8809) )
    & ! [U_8806,U_8807,U_8808,U_8809,U_8810,U_8811] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8810,tc_fun(U_8811,tc_HOL_Obool))),U_8809),U_8806),U_8807),U_8808))
        | sP725(U_8806,U_8807,U_8808,U_8809) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP725])],[f_2433_2]) ).

cnf(f_2433_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8810,tc_fun(U_8811,tc_HOL_Obool))),U_8809),U_8806),U_8807),U_8808))
    | sP725(U_8806,U_8807,U_8808,U_8809) ),
    inference(clausify,[status(thm)],[f_2433_3]) ).

cnf(f_2433_5,plain,
    ( ~ hBOOL(hAPP(hAPP(U_8806,U_8807),U_8808))
    | ~ sP725(U_8806,U_8807,U_8808,U_8809) ),
    inference(clausify,[status(thm)],[f_2433_3]) ).

cnf(f_2433_6,plain,
    ( ~ hBOOL(hAPP(hAPP(U_8809,U_8807),U_8808))
    | ~ sP725(U_8806,U_8807,U_8808,U_8809) ),
    inference(clausify,[status(thm)],[f_2433_3]) ).

fof(f_2434_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_2434_2,plain,
    ! [U_8817,U_8816,U_8815,U_8814,U_8813,U_8812] :
      ( hBOOL(hAPP(hAPP(c_member(U_8817),U_8812),hAPP(c_Set_Oimage(U_8815,U_8817,U_8813),U_8816)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8815),U_8814),U_8816))
      | U_8812 != hAPP(U_8813,U_8814) ),
    inference(variable_rename,[status(thm)],[f_2434_1]) ).

fof(f_2434_3,plain,
    ! [U_8813,U_8812,U_8815,U_8814,U_8816,U_8817] :
      ( hBOOL(hAPP(hAPP(c_member(U_8817),U_8812),hAPP(c_Set_Oimage(U_8815,U_8817,U_8813),U_8816)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8815),U_8814),U_8816))
      | U_8812 != hAPP(U_8813,U_8814) ),
    inference(definitional_conversion,[status(esa)],[f_2434_2]) ).

cnf(f_2434_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8817),U_8812),hAPP(c_Set_Oimage(U_8815,U_8817,U_8813),U_8816)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8815),U_8814),U_8816))
    | U_8812 != hAPP(U_8813,U_8814) ),
    inference(clausify,[status(thm)],[f_2434_3]) ).

fof(f_2435_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_2435_2,plain,
    ! [U_8823,U_8822,U_8821,U_8820,U_8819,U_8818] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8821,tc_fun(U_8822,tc_HOL_Obool))),U_8818),U_8823),U_8819),U_8820))
      | ~ hBOOL(hAPP(hAPP(U_8818,U_8819),U_8820)) ),
    inference(variable_rename,[status(thm)],[f_2435_1]) ).

fof(f_2435_3,plain,
    ! [U_8819,U_8818,U_8820,U_8821,U_8822,U_8823] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8821,tc_fun(U_8822,tc_HOL_Obool))),U_8818),U_8823),U_8819),U_8820))
      | ~ hBOOL(hAPP(hAPP(U_8818,U_8819),U_8820)) ),
    inference(definitional_conversion,[status(esa)],[f_2435_2]) ).

cnf(f_2435_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8821,tc_fun(U_8822,tc_HOL_Obool))),U_8818),U_8823),U_8819),U_8820))
    | ~ hBOOL(hAPP(hAPP(U_8818,U_8819),U_8820)) ),
    inference(clausify,[status(thm)],[f_2435_3]) ).

fof(f_2436_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_2436_2,plain,
    ! [U_8829,U_8828,U_8827,U_8826,U_8825,U_8824] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8827,tc_fun(U_8828,tc_HOL_Obool))),U_8829),U_8824),U_8825),U_8826))
      | ~ hBOOL(hAPP(hAPP(U_8824,U_8825),U_8826)) ),
    inference(variable_rename,[status(thm)],[f_2436_1]) ).

fof(f_2436_3,plain,
    ! [U_8825,U_8824,U_8826,U_8827,U_8828,U_8829] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8827,tc_fun(U_8828,tc_HOL_Obool))),U_8829),U_8824),U_8825),U_8826))
      | ~ hBOOL(hAPP(hAPP(U_8824,U_8825),U_8826)) ),
    inference(definitional_conversion,[status(esa)],[f_2436_2]) ).

cnf(f_2436_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8827,tc_fun(U_8828,tc_HOL_Obool))),U_8829),U_8824),U_8825),U_8826))
    | ~ hBOOL(hAPP(hAPP(U_8824,U_8825),U_8826)) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

fof(f_2437_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_2437_2,plain,
    ! [U_8834,U_8833,U_8832,U_8831,U_8830] : hAPP(c_Set_Oimage(U_8830,U_8831,U_8832),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8830,tc_HOL_Obool)),U_8833),U_8834)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8831,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8830,U_8831,U_8832),U_8833)),hAPP(c_Set_Oimage(U_8830,U_8831,U_8832),U_8834)),
    inference(variable_rename,[status(thm)],[f_2437_1]) ).

fof(f_2437_3,plain,
    ! [U_8830,U_8831,U_8832,U_8833,U_8834] : hAPP(c_Set_Oimage(U_8830,U_8831,U_8832),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8830,tc_HOL_Obool)),U_8833),U_8834)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8831,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8830,U_8831,U_8832),U_8833)),hAPP(c_Set_Oimage(U_8830,U_8831,U_8832),U_8834)),
    inference(definitional_conversion,[status(esa)],[f_2437_2]) ).

cnf(f_2437_4,plain,
    hAPP(c_Set_Oimage(U_8830,U_8831,U_8832),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8830,tc_HOL_Obool)),U_8833),U_8834)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8831,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8830,U_8831,U_8832),U_8833)),hAPP(c_Set_Oimage(U_8830,U_8831,U_8832),U_8834)),
    inference(clausify,[status(thm)],[f_2437_3]) ).

fof(f_2438_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_2438_2,plain,
    ! [U_8839,U_8838,U_8837,U_8836,U_8835] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8838,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8835,U_8838,U_8839),U_8836)),hAPP(c_Set_Oimage(U_8835,U_8838,U_8839),U_8837)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8835,tc_HOL_Obool)),U_8836),U_8837)) ),
    inference(variable_rename,[status(thm)],[f_2438_1]) ).

fof(f_2438_3,plain,
    ! [U_8835,U_8836,U_8837,U_8838,U_8839] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8838,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8835,U_8838,U_8839),U_8836)),hAPP(c_Set_Oimage(U_8835,U_8838,U_8839),U_8837)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8835,tc_HOL_Obool)),U_8836),U_8837)) ),
    inference(definitional_conversion,[status(esa)],[f_2438_2]) ).

cnf(f_2438_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8838,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8835,U_8838,U_8839),U_8836)),hAPP(c_Set_Oimage(U_8835,U_8838,U_8839),U_8837)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8835,tc_HOL_Obool)),U_8836),U_8837)) ),
    inference(clausify,[status(thm)],[f_2438_3]) ).

fof(f_2439_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_2439_2,plain,
    ! [U_8846,U_8845,U_8844,U_8843,U_8842] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8842,tc_HOL_Obool)),U_8843),hAPP(c_Set_Oimage(U_8844,U_8842,U_8845),U_8846)))
        | ! [U_8841] :
            ( U_8843 != hAPP(c_Set_Oimage(U_8844,U_8842,U_8845),U_8841)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8844,tc_HOL_Obool)),U_8841),U_8846)) ) )
      & ( ? [U_8840] :
            ( U_8843 = hAPP(c_Set_Oimage(U_8844,U_8842,U_8845),U_8840)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8844,tc_HOL_Obool)),U_8840),U_8846)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8842,tc_HOL_Obool)),U_8843),hAPP(c_Set_Oimage(U_8844,U_8842,U_8845),U_8846))) ) ),
    inference(variable_rename,[status(thm)],[f_2439_1]) ).

fof(f_2439_3,plain,
    ( ! [U_8856,U_8854,U_8852,U_8850,U_8848] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8848,tc_HOL_Obool)),U_8850),hAPP(c_Set_Oimage(U_8852,U_8848,U_8854),U_8856)))
        | ! [U_8841] :
            ( U_8850 != hAPP(c_Set_Oimage(U_8852,U_8848,U_8854),U_8841)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8852,tc_HOL_Obool)),U_8841),U_8856)) ) )
    & ! [U_8855,U_8853,U_8851,U_8849,U_8847] :
        ( ? [U_8840] :
            ( U_8849 = hAPP(c_Set_Oimage(U_8851,U_8847,U_8853),U_8840)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8851,tc_HOL_Obool)),U_8840),U_8855)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8847,tc_HOL_Obool)),U_8849),hAPP(c_Set_Oimage(U_8851,U_8847,U_8853),U_8855))) ) ),
    inference(miniscope,[status(thm)],[f_2439_2]) ).

fof(f_2439_4,plain,
    ( ! [U_8856,U_8854,U_8852,U_8850,U_8848] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8848,tc_HOL_Obool)),U_8850),hAPP(c_Set_Oimage(U_8852,U_8848,U_8854),U_8856)))
        | ! [U_8841] :
            ( U_8850 != hAPP(c_Set_Oimage(U_8852,U_8848,U_8854),U_8841)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8852,tc_HOL_Obool)),U_8841),U_8856)) ) )
    & ! [U_8855,U_8853,U_8851,U_8849,U_8847] :
        ( ( U_8849 = hAPP(c_Set_Oimage(U_8851,U_8847,U_8853),sK131(U_8855,U_8853,U_8851,U_8849,U_8847))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8851,tc_HOL_Obool)),sK131(U_8855,U_8853,U_8851,U_8849,U_8847)),U_8855)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8847,tc_HOL_Obool)),U_8849),hAPP(c_Set_Oimage(U_8851,U_8847,U_8853),U_8855))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_8840,sK131(U_8855,U_8853,U_8851,U_8849,U_8847))],[f_2439_3]) ).

fof(f_2439_5,plain,
    ( ! [U_8849,U_8851,U_8847,U_8855,U_8853] :
        ( U_8849 = hAPP(c_Set_Oimage(U_8851,U_8847,U_8853),sK131(U_8855,U_8853,U_8851,U_8849,U_8847))
        | ~ sP726(U_8849,U_8851,U_8847,U_8855,U_8853) )
    & ! [U_8849,U_8851,U_8847,U_8855,U_8853] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8851,tc_HOL_Obool)),sK131(U_8855,U_8853,U_8851,U_8849,U_8847)),U_8855))
        | ~ sP726(U_8849,U_8851,U_8847,U_8855,U_8853) )
    & ! [U_8856,U_8841,U_8848,U_8850,U_8854,U_8852] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8848,tc_HOL_Obool)),U_8850),hAPP(c_Set_Oimage(U_8852,U_8848,U_8854),U_8856)))
        | U_8850 != hAPP(c_Set_Oimage(U_8852,U_8848,U_8854),U_8841)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8852,tc_HOL_Obool)),U_8841),U_8856)) )
    & ! [U_8849,U_8851,U_8847,U_8855,U_8853] :
        ( sP726(U_8849,U_8851,U_8847,U_8855,U_8853)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8847,tc_HOL_Obool)),U_8849),hAPP(c_Set_Oimage(U_8851,U_8847,U_8853),U_8855))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP726])],[f_2439_4]) ).

cnf(f_2439_6,plain,
    ( sP726(U_8849,U_8851,U_8847,U_8855,U_8853)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8847,tc_HOL_Obool)),U_8849),hAPP(c_Set_Oimage(U_8851,U_8847,U_8853),U_8855))) ),
    inference(clausify,[status(thm)],[f_2439_5]) ).

cnf(f_2439_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8848,tc_HOL_Obool)),U_8850),hAPP(c_Set_Oimage(U_8852,U_8848,U_8854),U_8856)))
    | U_8850 != hAPP(c_Set_Oimage(U_8852,U_8848,U_8854),U_8841)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8852,tc_HOL_Obool)),U_8841),U_8856)) ),
    inference(clausify,[status(thm)],[f_2439_5]) ).

cnf(f_2439_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8851,tc_HOL_Obool)),sK131(U_8855,U_8853,U_8851,U_8849,U_8847)),U_8855))
    | ~ sP726(U_8849,U_8851,U_8847,U_8855,U_8853) ),
    inference(clausify,[status(thm)],[f_2439_5]) ).

cnf(f_2439_9,plain,
    ( U_8849 = hAPP(c_Set_Oimage(U_8851,U_8847,U_8853),sK131(U_8855,U_8853,U_8851,U_8849,U_8847))
    | ~ sP726(U_8849,U_8851,U_8847,U_8855,U_8853) ),
    inference(clausify,[status(thm)],[f_2439_5]) ).

fof(f_2440_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_2440_2,plain,
    ! [U_8862,U_8861,U_8860,U_8859,U_8858,U_8857] : hAPP(c_Set_Oimage(U_8857,U_8858,U_8859),hAPP(c_Set_Oimage(U_8860,U_8857,U_8861),U_8862)) = hAPP(c_Set_Oimage(U_8860,U_8858,hAPP(hAPP(c_COMBB(U_8857,U_8858,U_8860),U_8859),U_8861)),U_8862),
    inference(variable_rename,[status(thm)],[f_2440_1]) ).

fof(f_2440_3,plain,
    ! [U_8858,U_8857,U_8860,U_8859,U_8861,U_8862] : hAPP(c_Set_Oimage(U_8857,U_8858,U_8859),hAPP(c_Set_Oimage(U_8860,U_8857,U_8861),U_8862)) = hAPP(c_Set_Oimage(U_8860,U_8858,hAPP(hAPP(c_COMBB(U_8857,U_8858,U_8860),U_8859),U_8861)),U_8862),
    inference(definitional_conversion,[status(esa)],[f_2440_2]) ).

cnf(f_2440_4,plain,
    hAPP(c_Set_Oimage(U_8857,U_8858,U_8859),hAPP(c_Set_Oimage(U_8860,U_8857,U_8861),U_8862)) = hAPP(c_Set_Oimage(U_8860,U_8858,hAPP(hAPP(c_COMBB(U_8857,U_8858,U_8860),U_8859),U_8861)),U_8862),
    inference(clausify,[status(thm)],[f_2440_3]) ).

fof(f_2441_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_2441_2,plain,
    ! [U_8869,U_8868,U_8867,U_8866,U_8865] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8865),U_8866),hAPP(c_Set_Oimage(U_8867,U_8865,U_8868),U_8869)))
        | ! [U_8864] :
            ( U_8866 != hAPP(U_8868,U_8864)
            | ~ hBOOL(hAPP(hAPP(c_member(U_8867),U_8864),U_8869)) ) )
      & ( ? [U_8863] :
            ( U_8866 = hAPP(U_8868,U_8863)
            & hBOOL(hAPP(hAPP(c_member(U_8867),U_8863),U_8869)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_8865),U_8866),hAPP(c_Set_Oimage(U_8867,U_8865,U_8868),U_8869))) ) ),
    inference(variable_rename,[status(thm)],[f_2441_1]) ).

fof(f_2441_3,plain,
    ( ! [U_8879,U_8877,U_8875,U_8873] :
        ( ! [U_8871] : hBOOL(hAPP(hAPP(c_member(U_8871),U_8873),hAPP(c_Set_Oimage(U_8875,U_8871,U_8877),U_8879)))
        | ! [U_8864] :
            ( U_8873 != hAPP(U_8877,U_8864)
            | ~ hBOOL(hAPP(hAPP(c_member(U_8875),U_8864),U_8879)) ) )
    & ! [U_8878,U_8876,U_8874,U_8872] :
        ( ! [U_8870] : ~ hBOOL(hAPP(hAPP(c_member(U_8870),U_8872),hAPP(c_Set_Oimage(U_8874,U_8870,U_8876),U_8878)))
        | ? [U_8863] :
            ( U_8872 = hAPP(U_8876,U_8863)
            & hBOOL(hAPP(hAPP(c_member(U_8874),U_8863),U_8878)) ) ) ),
    inference(miniscope,[status(thm)],[f_2441_2]) ).

fof(f_2441_4,plain,
    ( ! [U_8879,U_8877,U_8875,U_8873] :
        ( ! [U_8871] : hBOOL(hAPP(hAPP(c_member(U_8871),U_8873),hAPP(c_Set_Oimage(U_8875,U_8871,U_8877),U_8879)))
        | ! [U_8864] :
            ( U_8873 != hAPP(U_8877,U_8864)
            | ~ hBOOL(hAPP(hAPP(c_member(U_8875),U_8864),U_8879)) ) )
    & ! [U_8878,U_8876,U_8874,U_8872] :
        ( ! [U_8870] : ~ hBOOL(hAPP(hAPP(c_member(U_8870),U_8872),hAPP(c_Set_Oimage(U_8874,U_8870,U_8876),U_8878)))
        | ( U_8872 = hAPP(U_8876,sK132(U_8878,U_8876,U_8874,U_8872))
          & hBOOL(hAPP(hAPP(c_member(U_8874),sK132(U_8878,U_8876,U_8874,U_8872)),U_8878)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_8863,sK132(U_8878,U_8876,U_8874,U_8872))],[f_2441_3]) ).

fof(f_2441_5,plain,
    ( ! [U_8876,U_8874,U_8872,U_8878] :
        ( U_8872 = hAPP(U_8876,sK132(U_8878,U_8876,U_8874,U_8872))
        | ~ sP727(U_8876,U_8874,U_8872,U_8878) )
    & ! [U_8876,U_8874,U_8872,U_8878] :
        ( hBOOL(hAPP(hAPP(c_member(U_8874),sK132(U_8878,U_8876,U_8874,U_8872)),U_8878))
        | ~ sP727(U_8876,U_8874,U_8872,U_8878) )
    & ! [U_8864,U_8879,U_8873,U_8871,U_8877,U_8875] :
        ( hBOOL(hAPP(hAPP(c_member(U_8871),U_8873),hAPP(c_Set_Oimage(U_8875,U_8871,U_8877),U_8879)))
        | U_8873 != hAPP(U_8877,U_8864)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8875),U_8864),U_8879)) )
    & ! [U_8876,U_8874,U_8870,U_8872,U_8878] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8870),U_8872),hAPP(c_Set_Oimage(U_8874,U_8870,U_8876),U_8878)))
        | sP727(U_8876,U_8874,U_8872,U_8878) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP727])],[f_2441_4]) ).

cnf(f_2441_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8870),U_8872),hAPP(c_Set_Oimage(U_8874,U_8870,U_8876),U_8878)))
    | sP727(U_8876,U_8874,U_8872,U_8878) ),
    inference(clausify,[status(thm)],[f_2441_5]) ).

cnf(f_2441_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8871),U_8873),hAPP(c_Set_Oimage(U_8875,U_8871,U_8877),U_8879)))
    | U_8873 != hAPP(U_8877,U_8864)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8875),U_8864),U_8879)) ),
    inference(clausify,[status(thm)],[f_2441_5]) ).

cnf(f_2441_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8874),sK132(U_8878,U_8876,U_8874,U_8872)),U_8878))
    | ~ sP727(U_8876,U_8874,U_8872,U_8878) ),
    inference(clausify,[status(thm)],[f_2441_5]) ).

cnf(f_2441_9,plain,
    ( U_8872 = hAPP(U_8876,sK132(U_8878,U_8876,U_8874,U_8872))
    | ~ sP727(U_8876,U_8874,U_8872,U_8878) ),
    inference(clausify,[status(thm)],[f_2441_5]) ).

fof(f_2442_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_2442_2,plain,
    ! [U_8884,U_8883,U_8882,U_8881,U_8880] :
      ( hBOOL(hAPP(hAPP(c_member(U_8883),hAPP(U_8884,U_8881)),hAPP(c_Set_Oimage(U_8880,U_8883,U_8884),U_8882)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8880),U_8881),U_8882)) ),
    inference(variable_rename,[status(thm)],[f_2442_1]) ).

fof(f_2442_3,plain,
    ! [U_8882,U_8881,U_8880,U_8883,U_8884] :
      ( hBOOL(hAPP(hAPP(c_member(U_8883),hAPP(U_8884,U_8881)),hAPP(c_Set_Oimage(U_8880,U_8883,U_8884),U_8882)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8880),U_8881),U_8882)) ),
    inference(definitional_conversion,[status(esa)],[f_2442_2]) ).

cnf(f_2442_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8883),hAPP(U_8884,U_8881)),hAPP(c_Set_Oimage(U_8880,U_8883,U_8884),U_8882)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8880),U_8881),U_8882)) ),
    inference(clausify,[status(thm)],[f_2442_3]) ).

fof(f_2443_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_2443_2,plain,
    ! [U_8890,U_8889,U_8888,U_8887,U_8886,U_8885] :
      ( hBOOL(hAPP(hAPP(c_member(U_8890),U_8888),hAPP(c_Set_Oimage(U_8885,U_8890,U_8889),U_8887)))
      | U_8888 != hAPP(U_8889,U_8886)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8885),U_8886),U_8887)) ),
    inference(variable_rename,[status(thm)],[f_2443_1]) ).

fof(f_2443_3,plain,
    ! [U_8885,U_8886,U_8887,U_8888,U_8889,U_8890] :
      ( hBOOL(hAPP(hAPP(c_member(U_8890),U_8888),hAPP(c_Set_Oimage(U_8885,U_8890,U_8889),U_8887)))
      | U_8888 != hAPP(U_8889,U_8886)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8885),U_8886),U_8887)) ),
    inference(definitional_conversion,[status(esa)],[f_2443_2]) ).

cnf(f_2443_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8890),U_8888),hAPP(c_Set_Oimage(U_8885,U_8890,U_8889),U_8887)))
    | U_8888 != hAPP(U_8889,U_8886)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8885),U_8886),U_8887)) ),
    inference(clausify,[status(thm)],[f_2443_3]) ).

fof(f_2444_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_2444_2,plain,
    ! [U_8895,U_8894,U_8893,U_8892,U_8891] : hAPP(c_Set_Oimage(U_8891,U_8892,U_8893),hAPP(hAPP(c_Set_Oinsert(U_8891),U_8894),U_8895)) = hAPP(hAPP(c_Set_Oinsert(U_8892),hAPP(U_8893,U_8894)),hAPP(c_Set_Oimage(U_8891,U_8892,U_8893),U_8895)),
    inference(variable_rename,[status(thm)],[f_2444_1]) ).

fof(f_2444_3,plain,
    ! [U_8891,U_8892,U_8893,U_8894,U_8895] : hAPP(c_Set_Oimage(U_8891,U_8892,U_8893),hAPP(hAPP(c_Set_Oinsert(U_8891),U_8894),U_8895)) = hAPP(hAPP(c_Set_Oinsert(U_8892),hAPP(U_8893,U_8894)),hAPP(c_Set_Oimage(U_8891,U_8892,U_8893),U_8895)),
    inference(definitional_conversion,[status(esa)],[f_2444_2]) ).

cnf(f_2444_4,plain,
    hAPP(c_Set_Oimage(U_8891,U_8892,U_8893),hAPP(hAPP(c_Set_Oinsert(U_8891),U_8894),U_8895)) = hAPP(hAPP(c_Set_Oinsert(U_8892),hAPP(U_8893,U_8894)),hAPP(c_Set_Oimage(U_8891,U_8892,U_8893),U_8895)),
    inference(clausify,[status(thm)],[f_2444_3]) ).

fof(f_2445_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_2445_2,plain,
    ! [U_8899,U_8898,U_8897,U_8896] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_8896,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_8897,U_8896,U_8898),U_8899)
        | U_8899 != c_Orderings_Obot__class_Obot(tc_fun(U_8897,tc_HOL_Obool)) )
      & ( U_8899 = c_Orderings_Obot__class_Obot(tc_fun(U_8897,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(U_8896,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_8897,U_8896,U_8898),U_8899) ) ),
    inference(variable_rename,[status(thm)],[f_2445_1]) ).

fof(f_2445_3,plain,
    ( ! [U_8907,U_8905,U_8903] :
        ( ! [U_8901] : c_Orderings_Obot__class_Obot(tc_fun(U_8901,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_8903,U_8901,U_8905),U_8907)
        | U_8907 != c_Orderings_Obot__class_Obot(tc_fun(U_8903,tc_HOL_Obool)) )
    & ! [U_8906,U_8904,U_8902] :
        ( ! [U_8900] : c_Orderings_Obot__class_Obot(tc_fun(U_8900,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_8902,U_8900,U_8904),U_8906)
        | U_8906 = c_Orderings_Obot__class_Obot(tc_fun(U_8902,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2445_2]) ).

fof(f_2445_4,plain,
    ( ! [U_8907,U_8905,U_8901,U_8903] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_8901,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_8903,U_8901,U_8905),U_8907)
        | U_8907 != c_Orderings_Obot__class_Obot(tc_fun(U_8903,tc_HOL_Obool)) )
    & ! [U_8904,U_8902,U_8906,U_8900] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_8900,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_8902,U_8900,U_8904),U_8906)
        | U_8906 = c_Orderings_Obot__class_Obot(tc_fun(U_8902,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2445_3]) ).

cnf(f_2445_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_8900,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_8902,U_8900,U_8904),U_8906)
    | U_8906 = c_Orderings_Obot__class_Obot(tc_fun(U_8902,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2445_4]) ).

cnf(f_2445_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_8901,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_8903,U_8901,U_8905),U_8907)
    | U_8907 != c_Orderings_Obot__class_Obot(tc_fun(U_8903,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2445_4]) ).

fof(f_2446_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_2446_2,plain,
    ! [U_8910,U_8909,U_8908] : hAPP(c_Set_Oimage(U_8908,U_8909,U_8910),c_Orderings_Obot__class_Obot(tc_fun(U_8908,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8909,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2446_1]) ).

fof(f_2446_3,plain,
    ! [U_8908,U_8909,U_8910] : hAPP(c_Set_Oimage(U_8908,U_8909,U_8910),c_Orderings_Obot__class_Obot(tc_fun(U_8908,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8909,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2446_2]) ).

cnf(f_2446_4,plain,
    hAPP(c_Set_Oimage(U_8908,U_8909,U_8910),c_Orderings_Obot__class_Obot(tc_fun(U_8908,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8909,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2446_3]) ).

fof(f_2447_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_2447_2,plain,
    ! [U_8914,U_8913,U_8912,U_8911] :
      ( ( hAPP(c_Set_Oimage(U_8911,U_8912,U_8913),U_8914) = c_Orderings_Obot__class_Obot(tc_fun(U_8912,tc_HOL_Obool))
        | U_8914 != c_Orderings_Obot__class_Obot(tc_fun(U_8911,tc_HOL_Obool)) )
      & ( U_8914 = c_Orderings_Obot__class_Obot(tc_fun(U_8911,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(U_8911,U_8912,U_8913),U_8914) != c_Orderings_Obot__class_Obot(tc_fun(U_8912,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2447_1]) ).

fof(f_2447_3,plain,
    ( ! [U_8922,U_8920,U_8918,U_8916] :
        ( hAPP(c_Set_Oimage(U_8916,U_8918,U_8920),U_8922) = c_Orderings_Obot__class_Obot(tc_fun(U_8918,tc_HOL_Obool))
        | U_8922 != c_Orderings_Obot__class_Obot(tc_fun(U_8916,tc_HOL_Obool)) )
    & ! [U_8921,U_8919,U_8917,U_8915] :
        ( U_8921 = c_Orderings_Obot__class_Obot(tc_fun(U_8915,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(U_8915,U_8917,U_8919),U_8921) != c_Orderings_Obot__class_Obot(tc_fun(U_8917,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2447_2]) ).

fof(f_2447_4,plain,
    ( ! [U_8916,U_8922,U_8918,U_8920] :
        ( hAPP(c_Set_Oimage(U_8916,U_8918,U_8920),U_8922) = c_Orderings_Obot__class_Obot(tc_fun(U_8918,tc_HOL_Obool))
        | U_8922 != c_Orderings_Obot__class_Obot(tc_fun(U_8916,tc_HOL_Obool)) )
    & ! [U_8917,U_8919,U_8921,U_8915] :
        ( U_8921 = c_Orderings_Obot__class_Obot(tc_fun(U_8915,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(U_8915,U_8917,U_8919),U_8921) != c_Orderings_Obot__class_Obot(tc_fun(U_8917,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2447_3]) ).

cnf(f_2447_5,plain,
    ( U_8921 = c_Orderings_Obot__class_Obot(tc_fun(U_8915,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_8915,U_8917,U_8919),U_8921) != c_Orderings_Obot__class_Obot(tc_fun(U_8917,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2447_4]) ).

cnf(f_2447_6,plain,
    ( hAPP(c_Set_Oimage(U_8916,U_8918,U_8920),U_8922) = c_Orderings_Obot__class_Obot(tc_fun(U_8918,tc_HOL_Obool))
    | U_8922 != c_Orderings_Obot__class_Obot(tc_fun(U_8916,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2447_4]) ).

fof(f_2448_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_2448_2,plain,
    ! [U_8927,U_8926,U_8925,U_8924,U_8923] :
      ( hAPP(hAPP(c_Set_Oinsert(U_8926),hAPP(U_8927,U_8924)),hAPP(c_Set_Oimage(U_8923,U_8926,U_8927),U_8925)) = hAPP(c_Set_Oimage(U_8923,U_8926,U_8927),U_8925)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8923),U_8924),U_8925)) ),
    inference(variable_rename,[status(thm)],[f_2448_1]) ).

fof(f_2448_3,plain,
    ! [U_8923,U_8924,U_8925,U_8926,U_8927] :
      ( hAPP(hAPP(c_Set_Oinsert(U_8926),hAPP(U_8927,U_8924)),hAPP(c_Set_Oimage(U_8923,U_8926,U_8927),U_8925)) = hAPP(c_Set_Oimage(U_8923,U_8926,U_8927),U_8925)
      | ~ hBOOL(hAPP(hAPP(c_member(U_8923),U_8924),U_8925)) ),
    inference(definitional_conversion,[status(esa)],[f_2448_2]) ).

cnf(f_2448_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_8926),hAPP(U_8927,U_8924)),hAPP(c_Set_Oimage(U_8923,U_8926,U_8927),U_8925)) = hAPP(c_Set_Oimage(U_8923,U_8926,U_8927),U_8925)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8923),U_8924),U_8925)) ),
    inference(clausify,[status(thm)],[f_2448_3]) ).

fof(f_2449_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_2449_2,plain,
    ! [U_8932,U_8931,U_8930,U_8929,U_8928] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8928,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8928,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8929,U_8928,U_8930),U_8931)),hAPP(c_Set_Oimage(U_8929,U_8928,U_8930),U_8932))),hAPP(c_Set_Oimage(U_8929,U_8928,U_8930),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8929,tc_HOL_Obool)),U_8931),U_8932)))),
    inference(variable_rename,[status(thm)],[f_2449_1]) ).

fof(f_2449_3,plain,
    ! [U_8928,U_8929,U_8930,U_8931,U_8932] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8928,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8928,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8929,U_8928,U_8930),U_8931)),hAPP(c_Set_Oimage(U_8929,U_8928,U_8930),U_8932))),hAPP(c_Set_Oimage(U_8929,U_8928,U_8930),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8929,tc_HOL_Obool)),U_8931),U_8932)))),
    inference(definitional_conversion,[status(esa)],[f_2449_2]) ).

cnf(f_2449_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8928,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8928,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8929,U_8928,U_8930),U_8931)),hAPP(c_Set_Oimage(U_8929,U_8928,U_8930),U_8932))),hAPP(c_Set_Oimage(U_8929,U_8928,U_8930),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8929,tc_HOL_Obool)),U_8931),U_8932)))),
    inference(clausify,[status(thm)],[f_2449_3]) ).

fof(f_2450_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_2450_2,plain,
    ! [U_8936,U_8935,U_8934,U_8933] :
      ( ( hAPP(c_Set_Oimage(U_8934,U_8935,hAPP(c_COMBK(U_8935,U_8934),U_8936)),U_8933) = hAPP(hAPP(c_Set_Oinsert(U_8935),U_8936),c_Orderings_Obot__class_Obot(tc_fun(U_8935,tc_HOL_Obool)))
        | U_8933 = c_Orderings_Obot__class_Obot(tc_fun(U_8934,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(U_8934,U_8935,hAPP(c_COMBK(U_8935,U_8934),U_8936)),U_8933) = c_Orderings_Obot__class_Obot(tc_fun(U_8935,tc_HOL_Obool))
        | U_8933 != c_Orderings_Obot__class_Obot(tc_fun(U_8934,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2450_1]) ).

fof(f_2450_3,plain,
    ( ! [U_8944,U_8942,U_8940,U_8938] :
        ( hAPP(c_Set_Oimage(U_8940,U_8942,hAPP(c_COMBK(U_8942,U_8940),U_8944)),U_8938) = hAPP(hAPP(c_Set_Oinsert(U_8942),U_8944),c_Orderings_Obot__class_Obot(tc_fun(U_8942,tc_HOL_Obool)))
        | U_8938 = c_Orderings_Obot__class_Obot(tc_fun(U_8940,tc_HOL_Obool)) )
    & ! [U_8943,U_8941,U_8939,U_8937] :
        ( hAPP(c_Set_Oimage(U_8939,U_8941,hAPP(c_COMBK(U_8941,U_8939),U_8943)),U_8937) = c_Orderings_Obot__class_Obot(tc_fun(U_8941,tc_HOL_Obool))
        | U_8937 != c_Orderings_Obot__class_Obot(tc_fun(U_8939,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2450_2]) ).

fof(f_2450_4,plain,
    ( ! [U_8944,U_8938,U_8940,U_8942] :
        ( hAPP(c_Set_Oimage(U_8940,U_8942,hAPP(c_COMBK(U_8942,U_8940),U_8944)),U_8938) = hAPP(hAPP(c_Set_Oinsert(U_8942),U_8944),c_Orderings_Obot__class_Obot(tc_fun(U_8942,tc_HOL_Obool)))
        | U_8938 = c_Orderings_Obot__class_Obot(tc_fun(U_8940,tc_HOL_Obool)) )
    & ! [U_8939,U_8943,U_8941,U_8937] :
        ( hAPP(c_Set_Oimage(U_8939,U_8941,hAPP(c_COMBK(U_8941,U_8939),U_8943)),U_8937) = c_Orderings_Obot__class_Obot(tc_fun(U_8941,tc_HOL_Obool))
        | U_8937 != c_Orderings_Obot__class_Obot(tc_fun(U_8939,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2450_3]) ).

cnf(f_2450_5,plain,
    ( hAPP(c_Set_Oimage(U_8939,U_8941,hAPP(c_COMBK(U_8941,U_8939),U_8943)),U_8937) = c_Orderings_Obot__class_Obot(tc_fun(U_8941,tc_HOL_Obool))
    | U_8937 != c_Orderings_Obot__class_Obot(tc_fun(U_8939,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2450_4]) ).

cnf(f_2450_6,plain,
    ( hAPP(c_Set_Oimage(U_8940,U_8942,hAPP(c_COMBK(U_8942,U_8940),U_8944)),U_8938) = hAPP(hAPP(c_Set_Oinsert(U_8942),U_8944),c_Orderings_Obot__class_Obot(tc_fun(U_8942,tc_HOL_Obool)))
    | U_8938 = c_Orderings_Obot__class_Obot(tc_fun(U_8940,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2450_4]) ).

fof(f_2451_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_2451_2,plain,
    ! [U_8949,U_8948,U_8947,U_8946,U_8945] :
      ( hAPP(c_Set_Oimage(U_8945,U_8948,hAPP(c_COMBK(U_8948,U_8945),U_8949)),U_8947) = hAPP(hAPP(c_Set_Oinsert(U_8948),U_8949),c_Orderings_Obot__class_Obot(tc_fun(U_8948,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8945),U_8946),U_8947)) ),
    inference(variable_rename,[status(thm)],[f_2451_1]) ).

fof(f_2451_3,plain,
    ! [U_8947,U_8945,U_8946,U_8948,U_8949] :
      ( hAPP(c_Set_Oimage(U_8945,U_8948,hAPP(c_COMBK(U_8948,U_8945),U_8949)),U_8947) = hAPP(hAPP(c_Set_Oinsert(U_8948),U_8949),c_Orderings_Obot__class_Obot(tc_fun(U_8948,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8945),U_8946),U_8947)) ),
    inference(definitional_conversion,[status(esa)],[f_2451_2]) ).

cnf(f_2451_4,plain,
    ( hAPP(c_Set_Oimage(U_8945,U_8948,hAPP(c_COMBK(U_8948,U_8945),U_8949)),U_8947) = hAPP(hAPP(c_Set_Oinsert(U_8948),U_8949),c_Orderings_Obot__class_Obot(tc_fun(U_8948,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8945),U_8946),U_8947)) ),
    inference(clausify,[status(thm)],[f_2451_3]) ).

fof(f_2452_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_2452_2,plain,
    ! [U_8950] : c_Wellfounded_Omeasure(U_8950) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_8950),c_Wellfounded_Oless__than),
    inference(variable_rename,[status(thm)],[f_2452_1]) ).

fof(f_2452_3,plain,
    ! [U_8950] : c_Wellfounded_Omeasure(U_8950) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_8950),c_Wellfounded_Oless__than),
    inference(definitional_conversion,[status(esa)],[f_2452_2]) ).

cnf(f_2452_4,plain,
    c_Wellfounded_Omeasure(U_8950) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_8950),c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_2452_3]) ).

fof(f_2453_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_2453_2,plain,
    ! [U_8955,U_8954,U_8953,U_8952,U_8951] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8951,U_8952,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8951),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),hAPP(hAPP(c_COMBB(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8951)),U_8953)),c_Com_Ocom_OBODY)),U_8954)),U_8955))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8951,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8951),tc_HOL_Obool)),U_8952),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8951),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),hAPP(hAPP(c_COMBB(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8951)),U_8953)),c_Com_Ocom_OBODY)),U_8954)),U_8955)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8951),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),hAPP(hAPP(c_COMBB(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8951)),U_8953)),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_8954)),U_8955)) ),
    inference(variable_rename,[status(thm)],[f_2453_1]) ).

fof(f_2453_3,plain,
    ! [U_8951,U_8952,U_8953,U_8954,U_8955] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8951,U_8952,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8951),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),hAPP(hAPP(c_COMBB(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8951)),U_8953)),c_Com_Ocom_OBODY)),U_8954)),U_8955))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8951,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8951),tc_HOL_Obool)),U_8952),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8951),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),hAPP(hAPP(c_COMBB(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8951)),U_8953)),c_Com_Ocom_OBODY)),U_8954)),U_8955)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8951),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),hAPP(hAPP(c_COMBB(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8951)),U_8953)),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_8954)),U_8955)) ),
    inference(definitional_conversion,[status(esa)],[f_2453_2]) ).

cnf(f_2453_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_8951,U_8952,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8951),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),hAPP(hAPP(c_COMBB(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8951)),U_8953)),c_Com_Ocom_OBODY)),U_8954)),U_8955))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8951,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8951),tc_HOL_Obool)),U_8952),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8951),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),hAPP(hAPP(c_COMBB(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8951)),U_8953)),c_Com_Ocom_OBODY)),U_8954)),U_8955)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8951),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),hAPP(hAPP(c_COMBB(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8951,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8951))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8951)),U_8953)),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_8954)),U_8955)) ),
    inference(clausify,[status(thm)],[f_2453_3]) ).

fof(f_2454_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_2454_2,plain,
    ! [U_8959,U_8958] :
      ( ( c_Relation_Oirrefl(U_8958,U_8959)
        | ? [U_8957] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8958,U_8958)),hAPP(hAPP(c_Product__Type_OPair(U_8958,U_8958),U_8957),U_8957)),U_8959)) )
      & ( ! [U_8956] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8958,U_8958)),hAPP(hAPP(c_Product__Type_OPair(U_8958,U_8958),U_8956),U_8956)),U_8959))
        | ~ c_Relation_Oirrefl(U_8958,U_8959) ) ),
    inference(variable_rename,[status(thm)],[f_2454_1]) ).

fof(f_2454_3,plain,
    ( ! [U_8963,U_8961] :
        ( c_Relation_Oirrefl(U_8961,U_8963)
        | ? [U_8957] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8961,U_8961)),hAPP(hAPP(c_Product__Type_OPair(U_8961,U_8961),U_8957),U_8957)),U_8963)) )
    & ! [U_8962,U_8960] :
        ( ! [U_8956] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8960,U_8960)),hAPP(hAPP(c_Product__Type_OPair(U_8960,U_8960),U_8956),U_8956)),U_8962))
        | ~ c_Relation_Oirrefl(U_8960,U_8962) ) ),
    inference(miniscope,[status(thm)],[f_2454_2]) ).

fof(f_2454_4,plain,
    ( ! [U_8963,U_8961] :
        ( c_Relation_Oirrefl(U_8961,U_8963)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8961,U_8961)),hAPP(hAPP(c_Product__Type_OPair(U_8961,U_8961),sK133(U_8963,U_8961)),sK133(U_8963,U_8961))),U_8963)) )
    & ! [U_8962,U_8960] :
        ( ! [U_8956] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8960,U_8960)),hAPP(hAPP(c_Product__Type_OPair(U_8960,U_8960),U_8956),U_8956)),U_8962))
        | ~ c_Relation_Oirrefl(U_8960,U_8962) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_8957,sK133(U_8963,U_8961))],[f_2454_3]) ).

fof(f_2454_5,plain,
    ( ! [U_8963,U_8961] :
        ( c_Relation_Oirrefl(U_8961,U_8963)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8961,U_8961)),hAPP(hAPP(c_Product__Type_OPair(U_8961,U_8961),sK133(U_8963,U_8961)),sK133(U_8963,U_8961))),U_8963)) )
    & ! [U_8962,U_8956,U_8960] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8960,U_8960)),hAPP(hAPP(c_Product__Type_OPair(U_8960,U_8960),U_8956),U_8956)),U_8962))
        | ~ c_Relation_Oirrefl(U_8960,U_8962) ) ),
    inference(definitional_conversion,[status(esa)],[f_2454_4]) ).

cnf(f_2454_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8960,U_8960)),hAPP(hAPP(c_Product__Type_OPair(U_8960,U_8960),U_8956),U_8956)),U_8962))
    | ~ c_Relation_Oirrefl(U_8960,U_8962) ),
    inference(clausify,[status(thm)],[f_2454_5]) ).

cnf(f_2454_7,plain,
    ( c_Relation_Oirrefl(U_8961,U_8963)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8961,U_8961)),hAPP(hAPP(c_Product__Type_OPair(U_8961,U_8961),sK133(U_8963,U_8961)),sK133(U_8963,U_8961))),U_8963)) ),
    inference(clausify,[status(thm)],[f_2454_5]) ).

fof(f_2455_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_2455_2,plain,
    ! [U_8967,U_8966,U_8965,U_8964] : hAPP(c_Relation_OField(U_8964),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_8964,U_8964)),hAPP(hAPP(c_Product__Type_OPair(U_8964,U_8964),U_8965),U_8966)),U_8967)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8964,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8964),U_8965),hAPP(hAPP(c_Set_Oinsert(U_8964),U_8966),c_Orderings_Obot__class_Obot(tc_fun(U_8964,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_8964),U_8967)),
    inference(variable_rename,[status(thm)],[f_2455_1]) ).

fof(f_2455_3,plain,
    ! [U_8964,U_8965,U_8966,U_8967] : hAPP(c_Relation_OField(U_8964),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_8964,U_8964)),hAPP(hAPP(c_Product__Type_OPair(U_8964,U_8964),U_8965),U_8966)),U_8967)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8964,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8964),U_8965),hAPP(hAPP(c_Set_Oinsert(U_8964),U_8966),c_Orderings_Obot__class_Obot(tc_fun(U_8964,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_8964),U_8967)),
    inference(definitional_conversion,[status(esa)],[f_2455_2]) ).

cnf(f_2455_4,plain,
    hAPP(c_Relation_OField(U_8964),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_8964,U_8964)),hAPP(hAPP(c_Product__Type_OPair(U_8964,U_8964),U_8965),U_8966)),U_8967)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8964,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8964),U_8965),hAPP(hAPP(c_Set_Oinsert(U_8964),U_8966),c_Orderings_Obot__class_Obot(tc_fun(U_8964,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_8964),U_8967)),
    inference(clausify,[status(thm)],[f_2455_3]) ).

fof(f_2456_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_2456_2,plain,
    ! [U_8969,U_8968] :
      ( ( 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_8968),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_8969),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_8968),U_8969)),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_8968),U_8969)),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_8968),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_8969),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_2456_1]) ).

fof(f_2456_3,plain,
    ( ! [U_8973,U_8971] :
        ( 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_8971),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_8973),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_8971),U_8973)),c_Int_Ointrel)) )
    & ! [U_8972,U_8970] :
        ( 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_8970),U_8972)),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_8970),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_8972),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_2456_2]) ).

fof(f_2456_4,plain,
    ( ! [U_8971,U_8973] :
        ( 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_8971),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_8973),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_8971),U_8973)),c_Int_Ointrel)) )
    & ! [U_8970,U_8972] :
        ( 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_8970),U_8972)),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_8970),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_8972),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2456_3]) ).

cnf(f_2456_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_8970),U_8972)),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_8970),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_8972),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2456_4]) ).

cnf(f_2456_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_8971),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_8973),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_8971),U_8973)),c_Int_Ointrel)) ),
    inference(clausify,[status(thm)],[f_2456_4]) ).

fof(f_2457_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_2457_2,plain,
    ! [U_8976,U_8975,U_8974] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8974,hAPP(hAPP(c_COMBC(U_8974,tc_fun(tc_prod(U_8974,U_8974),tc_HOL_Obool),tc_fun(U_8974,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8974,tc_fun(tc_fun(tc_prod(U_8974,U_8974),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8974,U_8974),tc_HOL_Obool),tc_fun(U_8974,tc_HOL_Obool)),U_8974),c_COMBC(U_8974,tc_fun(tc_prod(U_8974,U_8974),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8974,tc_prod(U_8974,U_8974)),tc_fun(U_8974,tc_fun(tc_fun(tc_prod(U_8974,U_8974),tc_HOL_Obool),tc_HOL_Obool)),U_8974),hAPP(c_COMBB(tc_prod(U_8974,U_8974),tc_fun(tc_fun(tc_prod(U_8974,U_8974),tc_HOL_Obool),tc_HOL_Obool),U_8974),c_member(tc_prod(U_8974,U_8974)))),c_Product__Type_OPair(U_8974,U_8974)))),U_8975)),U_8976))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8974),U_8976),c_Wellfounded_Oacc(U_8974,U_8975))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_8974),U_8976),c_Wellfounded_Oacc(U_8974,U_8975)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8974,hAPP(hAPP(c_COMBC(U_8974,tc_fun(tc_prod(U_8974,U_8974),tc_HOL_Obool),tc_fun(U_8974,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8974,tc_fun(tc_fun(tc_prod(U_8974,U_8974),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8974,U_8974),tc_HOL_Obool),tc_fun(U_8974,tc_HOL_Obool)),U_8974),c_COMBC(U_8974,tc_fun(tc_prod(U_8974,U_8974),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8974,tc_prod(U_8974,U_8974)),tc_fun(U_8974,tc_fun(tc_fun(tc_prod(U_8974,U_8974),tc_HOL_Obool),tc_HOL_Obool)),U_8974),hAPP(c_COMBB(tc_prod(U_8974,U_8974),tc_fun(tc_fun(tc_prod(U_8974,U_8974),tc_HOL_Obool),tc_HOL_Obool),U_8974),c_member(tc_prod(U_8974,U_8974)))),c_Product__Type_OPair(U_8974,U_8974)))),U_8975)),U_8976)) ) ),
    inference(variable_rename,[status(thm)],[f_2457_1]) ).

fof(f_2457_3,plain,
    ( ! [U_8982,U_8980,U_8978] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8978,hAPP(hAPP(c_COMBC(U_8978,tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_fun(U_8978,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8978,tc_fun(tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_fun(U_8978,tc_HOL_Obool)),U_8978),c_COMBC(U_8978,tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8978,tc_prod(U_8978,U_8978)),tc_fun(U_8978,tc_fun(tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_HOL_Obool)),U_8978),hAPP(c_COMBB(tc_prod(U_8978,U_8978),tc_fun(tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_HOL_Obool),U_8978),c_member(tc_prod(U_8978,U_8978)))),c_Product__Type_OPair(U_8978,U_8978)))),U_8980)),U_8982))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8978),U_8982),c_Wellfounded_Oacc(U_8978,U_8980))) )
    & ! [U_8981,U_8979,U_8977] :
        ( hBOOL(hAPP(hAPP(c_member(U_8977),U_8981),c_Wellfounded_Oacc(U_8977,U_8979)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8977,hAPP(hAPP(c_COMBC(U_8977,tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_fun(U_8977,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8977,tc_fun(tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_fun(U_8977,tc_HOL_Obool)),U_8977),c_COMBC(U_8977,tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8977,tc_prod(U_8977,U_8977)),tc_fun(U_8977,tc_fun(tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_HOL_Obool)),U_8977),hAPP(c_COMBB(tc_prod(U_8977,U_8977),tc_fun(tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_HOL_Obool),U_8977),c_member(tc_prod(U_8977,U_8977)))),c_Product__Type_OPair(U_8977,U_8977)))),U_8979)),U_8981)) ) ),
    inference(miniscope,[status(thm)],[f_2457_2]) ).

fof(f_2457_4,plain,
    ( ! [U_8978,U_8980,U_8982] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8978,hAPP(hAPP(c_COMBC(U_8978,tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_fun(U_8978,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8978,tc_fun(tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_fun(U_8978,tc_HOL_Obool)),U_8978),c_COMBC(U_8978,tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8978,tc_prod(U_8978,U_8978)),tc_fun(U_8978,tc_fun(tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_HOL_Obool)),U_8978),hAPP(c_COMBB(tc_prod(U_8978,U_8978),tc_fun(tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_HOL_Obool),U_8978),c_member(tc_prod(U_8978,U_8978)))),c_Product__Type_OPair(U_8978,U_8978)))),U_8980)),U_8982))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8978),U_8982),c_Wellfounded_Oacc(U_8978,U_8980))) )
    & ! [U_8979,U_8977,U_8981] :
        ( hBOOL(hAPP(hAPP(c_member(U_8977),U_8981),c_Wellfounded_Oacc(U_8977,U_8979)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8977,hAPP(hAPP(c_COMBC(U_8977,tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_fun(U_8977,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8977,tc_fun(tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_fun(U_8977,tc_HOL_Obool)),U_8977),c_COMBC(U_8977,tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8977,tc_prod(U_8977,U_8977)),tc_fun(U_8977,tc_fun(tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_HOL_Obool)),U_8977),hAPP(c_COMBB(tc_prod(U_8977,U_8977),tc_fun(tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_HOL_Obool),U_8977),c_member(tc_prod(U_8977,U_8977)))),c_Product__Type_OPair(U_8977,U_8977)))),U_8979)),U_8981)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2457_3]) ).

cnf(f_2457_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8977),U_8981),c_Wellfounded_Oacc(U_8977,U_8979)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8977,hAPP(hAPP(c_COMBC(U_8977,tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_fun(U_8977,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8977,tc_fun(tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_fun(U_8977,tc_HOL_Obool)),U_8977),c_COMBC(U_8977,tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8977,tc_prod(U_8977,U_8977)),tc_fun(U_8977,tc_fun(tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_HOL_Obool)),U_8977),hAPP(c_COMBB(tc_prod(U_8977,U_8977),tc_fun(tc_fun(tc_prod(U_8977,U_8977),tc_HOL_Obool),tc_HOL_Obool),U_8977),c_member(tc_prod(U_8977,U_8977)))),c_Product__Type_OPair(U_8977,U_8977)))),U_8979)),U_8981)) ),
    inference(clausify,[status(thm)],[f_2457_4]) ).

cnf(f_2457_6,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8978,hAPP(hAPP(c_COMBC(U_8978,tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_fun(U_8978,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8978,tc_fun(tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_fun(U_8978,tc_HOL_Obool)),U_8978),c_COMBC(U_8978,tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8978,tc_prod(U_8978,U_8978)),tc_fun(U_8978,tc_fun(tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_HOL_Obool)),U_8978),hAPP(c_COMBB(tc_prod(U_8978,U_8978),tc_fun(tc_fun(tc_prod(U_8978,U_8978),tc_HOL_Obool),tc_HOL_Obool),U_8978),c_member(tc_prod(U_8978,U_8978)))),c_Product__Type_OPair(U_8978,U_8978)))),U_8980)),U_8982))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8978),U_8982),c_Wellfounded_Oacc(U_8978,U_8980))) ),
    inference(clausify,[status(thm)],[f_2457_4]) ).

fof(f_2458_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_2458_2,plain,
    ! [U_8989,U_8988,U_8987,U_8986,U_8985,U_8984,U_8983] :
      ( hBOOL(hAPP(hAPP(c_member(U_8988),hAPP(hAPP(U_8989,U_8985),U_8986)),hAPP(c_Set_Oimage(tc_prod(U_8983,U_8984),U_8988,hAPP(c_Product__Type_Oprod_Oprod__case(U_8983,U_8984,U_8988),U_8989)),U_8987)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8983,U_8984)),hAPP(hAPP(c_Product__Type_OPair(U_8983,U_8984),U_8985),U_8986)),U_8987)) ),
    inference(variable_rename,[status(thm)],[f_2458_1]) ).

fof(f_2458_3,plain,
    ! [U_8983,U_8984,U_8985,U_8986,U_8987,U_8988,U_8989] :
      ( hBOOL(hAPP(hAPP(c_member(U_8988),hAPP(hAPP(U_8989,U_8985),U_8986)),hAPP(c_Set_Oimage(tc_prod(U_8983,U_8984),U_8988,hAPP(c_Product__Type_Oprod_Oprod__case(U_8983,U_8984,U_8988),U_8989)),U_8987)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8983,U_8984)),hAPP(hAPP(c_Product__Type_OPair(U_8983,U_8984),U_8985),U_8986)),U_8987)) ),
    inference(definitional_conversion,[status(esa)],[f_2458_2]) ).

cnf(f_2458_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8988),hAPP(hAPP(U_8989,U_8985),U_8986)),hAPP(c_Set_Oimage(tc_prod(U_8983,U_8984),U_8988,hAPP(c_Product__Type_Oprod_Oprod__case(U_8983,U_8984,U_8988),U_8989)),U_8987)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8983,U_8984)),hAPP(hAPP(c_Product__Type_OPair(U_8983,U_8984),U_8985),U_8986)),U_8987)) ),
    inference(clausify,[status(thm)],[f_2458_3]) ).

fof(f_2459_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_2459_2,plain,
    ! [U_8994,U_8993,U_8992,U_8991,U_8990] : hAPP(c_Relation_OImage(U_8990,U_8991,U_8992),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8990,tc_HOL_Obool)),U_8993),U_8994)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8991,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8990,U_8991,U_8992),U_8993)),hAPP(c_Relation_OImage(U_8990,U_8991,U_8992),U_8994)),
    inference(variable_rename,[status(thm)],[f_2459_1]) ).

fof(f_2459_3,plain,
    ! [U_8991,U_8990,U_8992,U_8993,U_8994] : hAPP(c_Relation_OImage(U_8990,U_8991,U_8992),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8990,tc_HOL_Obool)),U_8993),U_8994)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8991,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8990,U_8991,U_8992),U_8993)),hAPP(c_Relation_OImage(U_8990,U_8991,U_8992),U_8994)),
    inference(definitional_conversion,[status(esa)],[f_2459_2]) ).

cnf(f_2459_4,plain,
    hAPP(c_Relation_OImage(U_8990,U_8991,U_8992),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8990,tc_HOL_Obool)),U_8993),U_8994)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8991,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_8990,U_8991,U_8992),U_8993)),hAPP(c_Relation_OImage(U_8990,U_8991,U_8992),U_8994)),
    inference(clausify,[status(thm)],[f_2459_3]) ).

fof(f_2460_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_2460_2,plain,
    ! [U_8996,U_8995] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8995),U_8996) = 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_8995)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8996))),
    inference(variable_rename,[status(thm)],[f_2460_1]) ).

fof(f_2460_3,plain,
    ! [U_8995,U_8996] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8995),U_8996) = 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_8995)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8996))),
    inference(definitional_conversion,[status(esa)],[f_2460_2]) ).

cnf(f_2460_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8995),U_8996) = 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_8995)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8996))),
    inference(clausify,[status(thm)],[f_2460_3]) ).

fof(f_2461_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_2461_2,plain,
    ! [U_8998,U_8997] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8997),U_8998))
        | ~ 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_8997)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8998))) )
      & ( 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_8997)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8998)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8997),U_8998)) ) ),
    inference(variable_rename,[status(thm)],[f_2461_1]) ).

fof(f_2461_3,plain,
    ( ! [U_9002,U_9000] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9000),U_9002))
        | ~ 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_9000)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9002))) )
    & ! [U_9001,U_8999] :
        ( 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_8999)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9001)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8999),U_9001)) ) ),
    inference(miniscope,[status(thm)],[f_2461_2]) ).

fof(f_2461_4,plain,
    ( ! [U_9000,U_9002] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9000),U_9002))
        | ~ 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_9000)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9002))) )
    & ! [U_9001,U_8999] :
        ( 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_8999)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9001)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8999),U_9001)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2461_3]) ).

cnf(f_2461_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_8999)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9001)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8999),U_9001)) ),
    inference(clausify,[status(thm)],[f_2461_4]) ).

cnf(f_2461_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9000),U_9002))
    | ~ 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_9000)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9002))) ),
    inference(clausify,[status(thm)],[f_2461_4]) ).

fof(f_2462_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_2462_2,plain,
    ! [U_9003] : 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_9003)) = U_9003,
    inference(variable_rename,[status(thm)],[f_2462_1]) ).

fof(f_2462_3,plain,
    ! [U_9003] : 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_9003)) = U_9003,
    inference(definitional_conversion,[status(esa)],[f_2462_2]) ).

cnf(f_2462_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_9003)) = U_9003,
    inference(clausify,[status(thm)],[f_2462_3]) ).

fof(f_2463_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_2463_2,plain,
    ! [U_9005,U_9004] :
      ( ( U_9004 = U_9005
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9004) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9005) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9004) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9005)
        | U_9004 != U_9005 ) ),
    inference(variable_rename,[status(thm)],[f_2463_1]) ).

fof(f_2463_3,plain,
    ( ! [U_9009,U_9007] :
        ( U_9007 = U_9009
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9007) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9009) )
    & ! [U_9008,U_9006] :
        ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9006) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9008)
        | U_9006 != U_9008 ) ),
    inference(miniscope,[status(thm)],[f_2463_2]) ).

fof(f_2463_4,plain,
    ( ! [U_9007,U_9009] :
        ( U_9007 = U_9009
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9007) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9009) )
    & ! [U_9006,U_9008] :
        ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9006) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9008)
        | U_9006 != U_9008 ) ),
    inference(definitional_conversion,[status(esa)],[f_2463_3]) ).

cnf(f_2463_5,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9006) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9008)
    | U_9006 != U_9008 ),
    inference(clausify,[status(thm)],[f_2463_4]) ).

cnf(f_2463_6,plain,
    ( U_9007 = U_9009
    | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9007) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9009) ),
    inference(clausify,[status(thm)],[f_2463_4]) ).

fof(f_2464_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_2464_2,plain,
    ! [U_9011,U_9010] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9010),U_9011))
        | ~ 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_9010)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9011))) )
      & ( 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_9010)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9011)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9010),U_9011)) ) ),
    inference(variable_rename,[status(thm)],[f_2464_1]) ).

fof(f_2464_3,plain,
    ( ! [U_9015,U_9013] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9013),U_9015))
        | ~ 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_9013)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9015))) )
    & ! [U_9014,U_9012] :
        ( 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_9012)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9014)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9012),U_9014)) ) ),
    inference(miniscope,[status(thm)],[f_2464_2]) ).

fof(f_2464_4,plain,
    ( ! [U_9015,U_9013] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9013),U_9015))
        | ~ 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_9013)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9015))) )
    & ! [U_9014,U_9012] :
        ( 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_9012)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9014)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9012),U_9014)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2464_3]) ).

cnf(f_2464_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_9012)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9014)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9012),U_9014)) ),
    inference(clausify,[status(thm)],[f_2464_4]) ).

cnf(f_2464_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9013),U_9015))
    | ~ 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_9013)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9015))) ),
    inference(clausify,[status(thm)],[f_2464_4]) ).

fof(f_2465_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_2465_2,plain,
    ! [U_9017,U_9016] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9016),U_9017))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9016)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9017))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9016)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9017)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9016),U_9017)) ) ),
    inference(variable_rename,[status(thm)],[f_2465_1]) ).

fof(f_2465_3,plain,
    ( ! [U_9021,U_9019] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9019),U_9021))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9019)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9021))) )
    & ! [U_9020,U_9018] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9018)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9020)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9018),U_9020)) ) ),
    inference(miniscope,[status(thm)],[f_2465_2]) ).

fof(f_2465_4,plain,
    ( ! [U_9021,U_9019] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9019),U_9021))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9019)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9021))) )
    & ! [U_9018,U_9020] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9018)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9020)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9018),U_9020)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2465_3]) ).

cnf(f_2465_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9018)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9020)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9018),U_9020)) ),
    inference(clausify,[status(thm)],[f_2465_4]) ).

cnf(f_2465_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9019),U_9021))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9019)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9021))) ),
    inference(clausify,[status(thm)],[f_2465_4]) ).

fof(f_2466_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_2466_2,plain,
    ! [U_9024,U_9023,U_9022] : hAPP(c_Relation_OImage(U_9022,U_9023,U_9024),c_Orderings_Obot__class_Obot(tc_fun(U_9022,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9023,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2466_1]) ).

fof(f_2466_3,plain,
    ! [U_9023,U_9022,U_9024] : hAPP(c_Relation_OImage(U_9022,U_9023,U_9024),c_Orderings_Obot__class_Obot(tc_fun(U_9022,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9023,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2466_2]) ).

cnf(f_2466_4,plain,
    hAPP(c_Relation_OImage(U_9022,U_9023,U_9024),c_Orderings_Obot__class_Obot(tc_fun(U_9022,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9023,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2466_3]) ).

fof(f_2467_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_2467_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_2467_1]) ).

cnf(f_2467_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_2467_2]) ).

fof(f_2468_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_2468_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_2468_1]) ).

cnf(f_2468_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_2468_2]) ).

fof(f_2469_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_2469_2,plain,
    ! [U_9030,U_9029,U_9028,U_9027,U_9026,U_9025] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9026,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9025,U_9026,U_9027),U_9029)),hAPP(c_Relation_OImage(U_9025,U_9026,U_9028),U_9030)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9025,tc_HOL_Obool)),U_9029),U_9030))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9025,U_9026),tc_HOL_Obool)),U_9027),U_9028)) ),
    inference(variable_rename,[status(thm)],[f_2469_1]) ).

fof(f_2469_3,plain,
    ! [U_9025,U_9026,U_9027,U_9028,U_9029,U_9030] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9026,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9025,U_9026,U_9027),U_9029)),hAPP(c_Relation_OImage(U_9025,U_9026,U_9028),U_9030)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9025,tc_HOL_Obool)),U_9029),U_9030))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9025,U_9026),tc_HOL_Obool)),U_9027),U_9028)) ),
    inference(definitional_conversion,[status(esa)],[f_2469_2]) ).

cnf(f_2469_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9026,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9025,U_9026,U_9027),U_9029)),hAPP(c_Relation_OImage(U_9025,U_9026,U_9028),U_9030)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9025,tc_HOL_Obool)),U_9029),U_9030))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9025,U_9026),tc_HOL_Obool)),U_9027),U_9028)) ),
    inference(clausify,[status(thm)],[f_2469_3]) ).

fof(f_2470_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_2470_2,plain,
    ! [U_9035,U_9034,U_9033,U_9032,U_9031] : hAPP(c_Relation_OImage(U_9031,U_9032,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9031,U_9032),tc_HOL_Obool)),U_9033),U_9034)),U_9035) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9032,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9031,U_9032,U_9033),U_9035)),hAPP(c_Relation_OImage(U_9031,U_9032,U_9034),U_9035)),
    inference(variable_rename,[status(thm)],[f_2470_1]) ).

fof(f_2470_3,plain,
    ! [U_9031,U_9032,U_9033,U_9034,U_9035] : hAPP(c_Relation_OImage(U_9031,U_9032,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9031,U_9032),tc_HOL_Obool)),U_9033),U_9034)),U_9035) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9032,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9031,U_9032,U_9033),U_9035)),hAPP(c_Relation_OImage(U_9031,U_9032,U_9034),U_9035)),
    inference(definitional_conversion,[status(esa)],[f_2470_2]) ).

cnf(f_2470_4,plain,
    hAPP(c_Relation_OImage(U_9031,U_9032,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9031,U_9032),tc_HOL_Obool)),U_9033),U_9034)),U_9035) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9032,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9031,U_9032,U_9033),U_9035)),hAPP(c_Relation_OImage(U_9031,U_9032,U_9034),U_9035)),
    inference(clausify,[status(thm)],[f_2470_3]) ).

fof(f_2471_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_2471_2,plain,
    ! [U_9038,U_9037,U_9036] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9036,tc_HOL_Obool)),c_Wellfounded_Oacc(U_9036,U_9038)),c_Wellfounded_Oacc(U_9036,U_9037)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9036,U_9036),tc_HOL_Obool)),U_9037),U_9038)) ),
    inference(variable_rename,[status(thm)],[f_2471_1]) ).

fof(f_2471_3,plain,
    ! [U_9036,U_9037,U_9038] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9036,tc_HOL_Obool)),c_Wellfounded_Oacc(U_9036,U_9038)),c_Wellfounded_Oacc(U_9036,U_9037)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9036,U_9036),tc_HOL_Obool)),U_9037),U_9038)) ),
    inference(definitional_conversion,[status(esa)],[f_2471_2]) ).

cnf(f_2471_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9036,tc_HOL_Obool)),c_Wellfounded_Oacc(U_9036,U_9038)),c_Wellfounded_Oacc(U_9036,U_9037)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9036,U_9036),tc_HOL_Obool)),U_9037),U_9038)) ),
    inference(clausify,[status(thm)],[f_2471_3]) ).

fof(f_2472_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_2472_2,plain,
    ! [U_9044,U_9043,U_9042,U_9041,U_9040,U_9039] :
      ( hBOOL(hAPP(hAPP(c_member(U_9042),U_9043),hAPP(c_Relation_OImage(U_9039,U_9042,U_9044),U_9041)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9039,U_9042)),hAPP(hAPP(c_Product__Type_OPair(U_9039,U_9042),U_9040),U_9043)),U_9044))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9039),U_9040),U_9041)) ),
    inference(variable_rename,[status(thm)],[f_2472_1]) ).

fof(f_2472_3,plain,
    ! [U_9039,U_9040,U_9041,U_9042,U_9043,U_9044] :
      ( hBOOL(hAPP(hAPP(c_member(U_9042),U_9043),hAPP(c_Relation_OImage(U_9039,U_9042,U_9044),U_9041)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9039,U_9042)),hAPP(hAPP(c_Product__Type_OPair(U_9039,U_9042),U_9040),U_9043)),U_9044))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9039),U_9040),U_9041)) ),
    inference(definitional_conversion,[status(esa)],[f_2472_2]) ).

cnf(f_2472_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9042),U_9043),hAPP(c_Relation_OImage(U_9039,U_9042,U_9044),U_9041)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9039,U_9042)),hAPP(hAPP(c_Product__Type_OPair(U_9039,U_9042),U_9040),U_9043)),U_9044))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9039),U_9040),U_9041)) ),
    inference(clausify,[status(thm)],[f_2472_3]) ).

fof(f_2473_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_2473_2,plain,
    ! [U_9051,U_9050,U_9049,U_9048,U_9047] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9047),U_9048),hAPP(c_Relation_OImage(U_9049,U_9047,U_9050),U_9051)))
        | ! [U_9046] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9049,U_9047)),hAPP(hAPP(c_Product__Type_OPair(U_9049,U_9047),U_9046),U_9048)),U_9050))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9049),U_9046),U_9051)) ) )
      & ( ? [U_9045] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9049,U_9047)),hAPP(hAPP(c_Product__Type_OPair(U_9049,U_9047),U_9045),U_9048)),U_9050))
            & hBOOL(hAPP(hAPP(c_member(U_9049),U_9045),U_9051)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9047),U_9048),hAPP(c_Relation_OImage(U_9049,U_9047,U_9050),U_9051))) ) ),
    inference(variable_rename,[status(thm)],[f_2473_1]) ).

fof(f_2473_3,plain,
    ( ! [U_9061,U_9059,U_9057,U_9055,U_9053] :
        ( hBOOL(hAPP(hAPP(c_member(U_9053),U_9055),hAPP(c_Relation_OImage(U_9057,U_9053,U_9059),U_9061)))
        | ! [U_9046] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9057,U_9053)),hAPP(hAPP(c_Product__Type_OPair(U_9057,U_9053),U_9046),U_9055)),U_9059))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9057),U_9046),U_9061)) ) )
    & ! [U_9060,U_9058,U_9056,U_9054,U_9052] :
        ( ? [U_9045] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9056,U_9052)),hAPP(hAPP(c_Product__Type_OPair(U_9056,U_9052),U_9045),U_9054)),U_9058))
            & hBOOL(hAPP(hAPP(c_member(U_9056),U_9045),U_9060)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9052),U_9054),hAPP(c_Relation_OImage(U_9056,U_9052,U_9058),U_9060))) ) ),
    inference(miniscope,[status(thm)],[f_2473_2]) ).

fof(f_2473_4,plain,
    ( ! [U_9061,U_9059,U_9057,U_9055,U_9053] :
        ( hBOOL(hAPP(hAPP(c_member(U_9053),U_9055),hAPP(c_Relation_OImage(U_9057,U_9053,U_9059),U_9061)))
        | ! [U_9046] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9057,U_9053)),hAPP(hAPP(c_Product__Type_OPair(U_9057,U_9053),U_9046),U_9055)),U_9059))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9057),U_9046),U_9061)) ) )
    & ! [U_9060,U_9058,U_9056,U_9054,U_9052] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9056,U_9052)),hAPP(hAPP(c_Product__Type_OPair(U_9056,U_9052),sK134(U_9060,U_9058,U_9056,U_9054,U_9052)),U_9054)),U_9058))
          & hBOOL(hAPP(hAPP(c_member(U_9056),sK134(U_9060,U_9058,U_9056,U_9054,U_9052)),U_9060)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9052),U_9054),hAPP(c_Relation_OImage(U_9056,U_9052,U_9058),U_9060))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_9045,sK134(U_9060,U_9058,U_9056,U_9054,U_9052))],[f_2473_3]) ).

fof(f_2473_5,plain,
    ( ! [U_9054,U_9052,U_9060,U_9056,U_9058] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9056,U_9052)),hAPP(hAPP(c_Product__Type_OPair(U_9056,U_9052),sK134(U_9060,U_9058,U_9056,U_9054,U_9052)),U_9054)),U_9058))
        | ~ sP728(U_9054,U_9052,U_9060,U_9056,U_9058) )
    & ! [U_9054,U_9052,U_9060,U_9056,U_9058] :
        ( hBOOL(hAPP(hAPP(c_member(U_9056),sK134(U_9060,U_9058,U_9056,U_9054,U_9052)),U_9060))
        | ~ sP728(U_9054,U_9052,U_9060,U_9056,U_9058) )
    & ! [U_9055,U_9046,U_9061,U_9053,U_9059,U_9057] :
        ( hBOOL(hAPP(hAPP(c_member(U_9053),U_9055),hAPP(c_Relation_OImage(U_9057,U_9053,U_9059),U_9061)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9057,U_9053)),hAPP(hAPP(c_Product__Type_OPair(U_9057,U_9053),U_9046),U_9055)),U_9059))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9057),U_9046),U_9061)) )
    & ! [U_9054,U_9052,U_9060,U_9056,U_9058] :
        ( sP728(U_9054,U_9052,U_9060,U_9056,U_9058)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9052),U_9054),hAPP(c_Relation_OImage(U_9056,U_9052,U_9058),U_9060))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP728])],[f_2473_4]) ).

cnf(f_2473_6,plain,
    ( sP728(U_9054,U_9052,U_9060,U_9056,U_9058)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9052),U_9054),hAPP(c_Relation_OImage(U_9056,U_9052,U_9058),U_9060))) ),
    inference(clausify,[status(thm)],[f_2473_5]) ).

cnf(f_2473_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9053),U_9055),hAPP(c_Relation_OImage(U_9057,U_9053,U_9059),U_9061)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9057,U_9053)),hAPP(hAPP(c_Product__Type_OPair(U_9057,U_9053),U_9046),U_9055)),U_9059))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9057),U_9046),U_9061)) ),
    inference(clausify,[status(thm)],[f_2473_5]) ).

cnf(f_2473_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9056),sK134(U_9060,U_9058,U_9056,U_9054,U_9052)),U_9060))
    | ~ sP728(U_9054,U_9052,U_9060,U_9056,U_9058) ),
    inference(clausify,[status(thm)],[f_2473_5]) ).

cnf(f_2473_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9056,U_9052)),hAPP(hAPP(c_Product__Type_OPair(U_9056,U_9052),sK134(U_9060,U_9058,U_9056,U_9054,U_9052)),U_9054)),U_9058))
    | ~ sP728(U_9054,U_9052,U_9060,U_9056,U_9058) ),
    inference(clausify,[status(thm)],[f_2473_5]) ).

fof(f_2474_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_2474_2,plain,
    ! [U_9062] : hAPP(c_Relation_OField(U_9062),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9062,U_9062),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9062,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2474_1]) ).

fof(f_2474_3,plain,
    ! [U_9062] : hAPP(c_Relation_OField(U_9062),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9062,U_9062),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9062,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2474_2]) ).

cnf(f_2474_4,plain,
    hAPP(c_Relation_OField(U_9062),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9062,U_9062),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9062,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2474_3]) ).

fof(f_2475_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_2475_2,plain,
    ! [U_9065,U_9064,U_9063] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9063,tc_HOL_Obool)),hAPP(c_Relation_OField(U_9063),U_9064)),hAPP(c_Relation_OField(U_9063),U_9065)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9063,U_9063),tc_HOL_Obool)),U_9064),U_9065)) ),
    inference(variable_rename,[status(thm)],[f_2475_1]) ).

fof(f_2475_3,plain,
    ! [U_9063,U_9064,U_9065] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9063,tc_HOL_Obool)),hAPP(c_Relation_OField(U_9063),U_9064)),hAPP(c_Relation_OField(U_9063),U_9065)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9063,U_9063),tc_HOL_Obool)),U_9064),U_9065)) ),
    inference(definitional_conversion,[status(esa)],[f_2475_2]) ).

cnf(f_2475_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9063,tc_HOL_Obool)),hAPP(c_Relation_OField(U_9063),U_9064)),hAPP(c_Relation_OField(U_9063),U_9065)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9063,U_9063),tc_HOL_Obool)),U_9064),U_9065)) ),
    inference(clausify,[status(thm)],[f_2475_3]) ).

fof(f_2476_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_2476_2,plain,
    ! [U_9068,U_9067,U_9066] : hAPP(c_Relation_OField(U_9066),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9066,U_9066),tc_HOL_Obool)),U_9067),U_9068)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9066,tc_HOL_Obool)),hAPP(c_Relation_OField(U_9066),U_9067)),hAPP(c_Relation_OField(U_9066),U_9068)),
    inference(variable_rename,[status(thm)],[f_2476_1]) ).

fof(f_2476_3,plain,
    ! [U_9066,U_9067,U_9068] : hAPP(c_Relation_OField(U_9066),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9066,U_9066),tc_HOL_Obool)),U_9067),U_9068)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9066,tc_HOL_Obool)),hAPP(c_Relation_OField(U_9066),U_9067)),hAPP(c_Relation_OField(U_9066),U_9068)),
    inference(definitional_conversion,[status(esa)],[f_2476_2]) ).

cnf(f_2476_4,plain,
    hAPP(c_Relation_OField(U_9066),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9066,U_9066),tc_HOL_Obool)),U_9067),U_9068)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9066,tc_HOL_Obool)),hAPP(c_Relation_OField(U_9066),U_9067)),hAPP(c_Relation_OField(U_9066),U_9068)),
    inference(clausify,[status(thm)],[f_2476_3]) ).

fof(f_2477_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_2477_2,plain,
    ! [U_9072,U_9071,U_9070,U_9069] :
      ( hBOOL(hAPP(hAPP(c_member(U_9069),U_9072),c_Wellfounded_Oacc(U_9069,U_9071)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9069,U_9069)),hAPP(hAPP(c_Product__Type_OPair(U_9069,U_9069),U_9072),U_9070)),U_9071))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9069),U_9070),c_Wellfounded_Oacc(U_9069,U_9071))) ),
    inference(variable_rename,[status(thm)],[f_2477_1]) ).

fof(f_2477_3,plain,
    ! [U_9069,U_9070,U_9071,U_9072] :
      ( hBOOL(hAPP(hAPP(c_member(U_9069),U_9072),c_Wellfounded_Oacc(U_9069,U_9071)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9069,U_9069)),hAPP(hAPP(c_Product__Type_OPair(U_9069,U_9069),U_9072),U_9070)),U_9071))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9069),U_9070),c_Wellfounded_Oacc(U_9069,U_9071))) ),
    inference(definitional_conversion,[status(esa)],[f_2477_2]) ).

cnf(f_2477_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9069),U_9072),c_Wellfounded_Oacc(U_9069,U_9071)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9069,U_9069)),hAPP(hAPP(c_Product__Type_OPair(U_9069,U_9069),U_9072),U_9070)),U_9071))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9069),U_9070),c_Wellfounded_Oacc(U_9069,U_9071))) ),
    inference(clausify,[status(thm)],[f_2477_3]) ).

fof(f_2478_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_2478_2,plain,
    ! [U_9077,U_9076,U_9075] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9075),U_9076),c_Wellfounded_Oacc(U_9075,U_9077)))
        | ? [U_9074] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_9075),U_9074),c_Wellfounded_Oacc(U_9075,U_9077)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_9075,U_9075)),hAPP(hAPP(c_Product__Type_OPair(U_9075,U_9075),U_9074),U_9076)),U_9077)) ) )
      & ( ! [U_9073] :
            ( hBOOL(hAPP(hAPP(c_member(U_9075),U_9073),c_Wellfounded_Oacc(U_9075,U_9077)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9075,U_9075)),hAPP(hAPP(c_Product__Type_OPair(U_9075,U_9075),U_9073),U_9076)),U_9077)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9075),U_9076),c_Wellfounded_Oacc(U_9075,U_9077))) ) ),
    inference(variable_rename,[status(thm)],[f_2478_1]) ).

fof(f_2478_3,plain,
    ( ! [U_9083,U_9081,U_9079] :
        ( hBOOL(hAPP(hAPP(c_member(U_9079),U_9081),c_Wellfounded_Oacc(U_9079,U_9083)))
        | ? [U_9074] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_9079),U_9074),c_Wellfounded_Oacc(U_9079,U_9083)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_9079,U_9079)),hAPP(hAPP(c_Product__Type_OPair(U_9079,U_9079),U_9074),U_9081)),U_9083)) ) )
    & ! [U_9082,U_9080,U_9078] :
        ( ! [U_9073] :
            ( hBOOL(hAPP(hAPP(c_member(U_9078),U_9073),c_Wellfounded_Oacc(U_9078,U_9082)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9078,U_9078)),hAPP(hAPP(c_Product__Type_OPair(U_9078,U_9078),U_9073),U_9080)),U_9082)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9078),U_9080),c_Wellfounded_Oacc(U_9078,U_9082))) ) ),
    inference(miniscope,[status(thm)],[f_2478_2]) ).

fof(f_2478_4,plain,
    ( ! [U_9083,U_9081,U_9079] :
        ( hBOOL(hAPP(hAPP(c_member(U_9079),U_9081),c_Wellfounded_Oacc(U_9079,U_9083)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_9079),sK135(U_9083,U_9081,U_9079)),c_Wellfounded_Oacc(U_9079,U_9083)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_9079,U_9079)),hAPP(hAPP(c_Product__Type_OPair(U_9079,U_9079),sK135(U_9083,U_9081,U_9079)),U_9081)),U_9083)) ) )
    & ! [U_9082,U_9080,U_9078] :
        ( ! [U_9073] :
            ( hBOOL(hAPP(hAPP(c_member(U_9078),U_9073),c_Wellfounded_Oacc(U_9078,U_9082)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9078,U_9078)),hAPP(hAPP(c_Product__Type_OPair(U_9078,U_9078),U_9073),U_9080)),U_9082)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9078),U_9080),c_Wellfounded_Oacc(U_9078,U_9082))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_9074,sK135(U_9083,U_9081,U_9079))],[f_2478_3]) ).

fof(f_2478_5,plain,
    ( ! [U_9083,U_9081,U_9079] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9079),sK135(U_9083,U_9081,U_9079)),c_Wellfounded_Oacc(U_9079,U_9083)))
        | ~ sP729(U_9083,U_9081,U_9079) )
    & ! [U_9083,U_9081,U_9079] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9079,U_9079)),hAPP(hAPP(c_Product__Type_OPair(U_9079,U_9079),sK135(U_9083,U_9081,U_9079)),U_9081)),U_9083))
        | ~ sP729(U_9083,U_9081,U_9079) )
    & ! [U_9083,U_9081,U_9079] :
        ( hBOOL(hAPP(hAPP(c_member(U_9079),U_9081),c_Wellfounded_Oacc(U_9079,U_9083)))
        | sP729(U_9083,U_9081,U_9079) )
    & ! [U_9080,U_9073,U_9082,U_9078] :
        ( hBOOL(hAPP(hAPP(c_member(U_9078),U_9073),c_Wellfounded_Oacc(U_9078,U_9082)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9078,U_9078)),hAPP(hAPP(c_Product__Type_OPair(U_9078,U_9078),U_9073),U_9080)),U_9082))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9078),U_9080),c_Wellfounded_Oacc(U_9078,U_9082))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP729])],[f_2478_4]) ).

cnf(f_2478_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9078),U_9073),c_Wellfounded_Oacc(U_9078,U_9082)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9078,U_9078)),hAPP(hAPP(c_Product__Type_OPair(U_9078,U_9078),U_9073),U_9080)),U_9082))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9078),U_9080),c_Wellfounded_Oacc(U_9078,U_9082))) ),
    inference(clausify,[status(thm)],[f_2478_5]) ).

cnf(f_2478_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9079),U_9081),c_Wellfounded_Oacc(U_9079,U_9083)))
    | sP729(U_9083,U_9081,U_9079) ),
    inference(clausify,[status(thm)],[f_2478_5]) ).

cnf(f_2478_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9079,U_9079)),hAPP(hAPP(c_Product__Type_OPair(U_9079,U_9079),sK135(U_9083,U_9081,U_9079)),U_9081)),U_9083))
    | ~ sP729(U_9083,U_9081,U_9079) ),
    inference(clausify,[status(thm)],[f_2478_5]) ).

cnf(f_2478_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9079),sK135(U_9083,U_9081,U_9079)),c_Wellfounded_Oacc(U_9079,U_9083)))
    | ~ sP729(U_9083,U_9081,U_9079) ),
    inference(clausify,[status(thm)],[f_2478_5]) ).

fof(f_2479_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_2479_2,plain,
    ! [U_9088,U_9087,U_9086,U_9085,U_9084] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9084),U_9085),hAPP(c_Relation_OImage(U_9086,U_9084,U_9087),hAPP(hAPP(c_Set_Oinsert(U_9086),U_9088),c_Orderings_Obot__class_Obot(tc_fun(U_9086,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9086,U_9084)),hAPP(hAPP(c_Product__Type_OPair(U_9086,U_9084),U_9088),U_9085)),U_9087)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9086,U_9084)),hAPP(hAPP(c_Product__Type_OPair(U_9086,U_9084),U_9088),U_9085)),U_9087))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9084),U_9085),hAPP(c_Relation_OImage(U_9086,U_9084,U_9087),hAPP(hAPP(c_Set_Oinsert(U_9086),U_9088),c_Orderings_Obot__class_Obot(tc_fun(U_9086,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[f_2479_1]) ).

fof(f_2479_3,plain,
    ( ! [U_9098,U_9096,U_9094,U_9092,U_9090] :
        ( hBOOL(hAPP(hAPP(c_member(U_9090),U_9092),hAPP(c_Relation_OImage(U_9094,U_9090,U_9096),hAPP(hAPP(c_Set_Oinsert(U_9094),U_9098),c_Orderings_Obot__class_Obot(tc_fun(U_9094,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9094,U_9090)),hAPP(hAPP(c_Product__Type_OPair(U_9094,U_9090),U_9098),U_9092)),U_9096)) )
    & ! [U_9097,U_9095,U_9093,U_9091,U_9089] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9093,U_9089)),hAPP(hAPP(c_Product__Type_OPair(U_9093,U_9089),U_9097),U_9091)),U_9095))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9089),U_9091),hAPP(c_Relation_OImage(U_9093,U_9089,U_9095),hAPP(hAPP(c_Set_Oinsert(U_9093),U_9097),c_Orderings_Obot__class_Obot(tc_fun(U_9093,tc_HOL_Obool)))))) ) ),
    inference(miniscope,[status(thm)],[f_2479_2]) ).

fof(f_2479_4,plain,
    ( ! [U_9090,U_9092,U_9094,U_9096,U_9098] :
        ( hBOOL(hAPP(hAPP(c_member(U_9090),U_9092),hAPP(c_Relation_OImage(U_9094,U_9090,U_9096),hAPP(hAPP(c_Set_Oinsert(U_9094),U_9098),c_Orderings_Obot__class_Obot(tc_fun(U_9094,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9094,U_9090)),hAPP(hAPP(c_Product__Type_OPair(U_9094,U_9090),U_9098),U_9092)),U_9096)) )
    & ! [U_9091,U_9093,U_9095,U_9089,U_9097] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9093,U_9089)),hAPP(hAPP(c_Product__Type_OPair(U_9093,U_9089),U_9097),U_9091)),U_9095))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9089),U_9091),hAPP(c_Relation_OImage(U_9093,U_9089,U_9095),hAPP(hAPP(c_Set_Oinsert(U_9093),U_9097),c_Orderings_Obot__class_Obot(tc_fun(U_9093,tc_HOL_Obool)))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2479_3]) ).

cnf(f_2479_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9093,U_9089)),hAPP(hAPP(c_Product__Type_OPair(U_9093,U_9089),U_9097),U_9091)),U_9095))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9089),U_9091),hAPP(c_Relation_OImage(U_9093,U_9089,U_9095),hAPP(hAPP(c_Set_Oinsert(U_9093),U_9097),c_Orderings_Obot__class_Obot(tc_fun(U_9093,tc_HOL_Obool)))))) ),
    inference(clausify,[status(thm)],[f_2479_4]) ).

cnf(f_2479_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9090),U_9092),hAPP(c_Relation_OImage(U_9094,U_9090,U_9096),hAPP(hAPP(c_Set_Oinsert(U_9094),U_9098),c_Orderings_Obot__class_Obot(tc_fun(U_9094,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9094,U_9090)),hAPP(hAPP(c_Product__Type_OPair(U_9094,U_9090),U_9098),U_9092)),U_9096)) ),
    inference(clausify,[status(thm)],[f_2479_4]) ).

fof(f_2480_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_2480_2,plain,
    ! [U_9101,U_9100,U_9099] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_9099),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_9100),U_9101)),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_9099),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9099),U_9100)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9099),U_9101))
      | ~ class_Rings_Oring__1(U_9099) ),
    inference(variable_rename,[status(thm)],[f_2480_1]) ).

fof(f_2480_3,plain,
    ! [U_9099,U_9100,U_9101] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_9099),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_9100),U_9101)),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_9099),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9099),U_9100)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9099),U_9101))
      | ~ class_Rings_Oring__1(U_9099) ),
    inference(definitional_conversion,[status(esa)],[f_2480_2]) ).

cnf(f_2480_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_9099),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_9100),U_9101)),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_9099),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9099),U_9100)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9099),U_9101))
    | ~ class_Rings_Oring__1(U_9099) ),
    inference(clausify,[status(thm)],[f_2480_3]) ).

fof(f_2481_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_2481_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_2481_1]) ).

cnf(f_2481_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_2481_2]) ).

fof(f_2482_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_2482_2,plain,
    ! [U_9105,U_9104,U_9103,U_9102] : 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_9102),U_9103)),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_9104),U_9105)),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_9102),U_9104)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9103),U_9105))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9102),U_9105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9103),U_9104)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2482_1]) ).

fof(f_2482_3,plain,
    ! [U_9102,U_9103,U_9104,U_9105] : 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_9102),U_9103)),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_9104),U_9105)),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_9102),U_9104)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9103),U_9105))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9102),U_9105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9103),U_9104)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2482_2]) ).

cnf(f_2482_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_9102),U_9103)),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_9104),U_9105)),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_9102),U_9104)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9103),U_9105))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9102),U_9105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_9103),U_9104)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2482_3]) ).

fof(f_2483_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_2483_2,plain,
    ! [U_9109,U_9108,U_9107,U_9106] :
      ( ( 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_9106),U_9107)),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_9108),U_9109)),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_9106),U_9109)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9108),U_9107))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9106),U_9109)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9108),U_9107)))
        | ~ 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_9106),U_9107)),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_9108),U_9109)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(variable_rename,[status(thm)],[f_2483_1]) ).

fof(f_2483_3,plain,
    ( ! [U_9117,U_9115,U_9113,U_9111] :
        ( 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_9111),U_9113)),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_9115),U_9117)),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_9111),U_9117)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9115),U_9113))) )
    & ! [U_9116,U_9114,U_9112,U_9110] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9110),U_9116)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9114),U_9112)))
        | ~ 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_9110),U_9112)),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_9114),U_9116)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(miniscope,[status(thm)],[f_2483_2]) ).

fof(f_2483_4,plain,
    ( ! [U_9111,U_9113,U_9115,U_9117] :
        ( 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_9111),U_9113)),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_9115),U_9117)),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_9111),U_9117)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9115),U_9113))) )
    & ! [U_9116,U_9112,U_9110,U_9114] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9110),U_9116)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9114),U_9112)))
        | ~ 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_9110),U_9112)),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_9114),U_9116)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2483_3]) ).

cnf(f_2483_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_9110),U_9116)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9114),U_9112)))
    | ~ 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_9110),U_9112)),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_9114),U_9116)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
    inference(clausify,[status(thm)],[f_2483_4]) ).

cnf(f_2483_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_9111),U_9113)),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_9115),U_9117)),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_9111),U_9117)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9115),U_9113))) ),
    inference(clausify,[status(thm)],[f_2483_4]) ).

fof(f_2484_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_2484_2,plain,
    ! [U_9119,U_9118] : 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_9118),U_9119)),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_9119),U_9118)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2484_1]) ).

fof(f_2484_3,plain,
    ! [U_9118,U_9119] : 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_9118),U_9119)),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_9119),U_9118)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2484_2]) ).

cnf(f_2484_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_9118),U_9119)),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_9119),U_9118)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2484_3]) ).

fof(f_2485_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_2485_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_2485_1]) ).

cnf(f_2485_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_2485_2]) ).

fof(f_2486_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_2486_2,plain,
    ! [U_9120] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9120) = 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_9120),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_2486_1]) ).

fof(f_2486_3,plain,
    ! [U_9120] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9120) = 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_9120),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_2486_2]) ).

cnf(f_2486_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_9120) = 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_9120),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_2486_3]) ).

fof(f_2487_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_2487_2,plain,
    ! [U_9124,U_9123,U_9122,U_9121] : 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_9121),U_9122)),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_9123),U_9124)),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_9121),U_9123)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9122),U_9124))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2487_1]) ).

fof(f_2487_3,plain,
    ! [U_9121,U_9122,U_9123,U_9124] : 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_9121),U_9122)),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_9123),U_9124)),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_9121),U_9123)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9122),U_9124))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2487_2]) ).

cnf(f_2487_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_9121),U_9122)),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_9123),U_9124)),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_9121),U_9123)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9122),U_9124))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2487_3]) ).

fof(f_2488_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_2488_2,plain,
    ! [U_9126,U_9125] : 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_9125),U_9126)),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_9125),U_9126),
    inference(variable_rename,[status(thm)],[f_2488_1]) ).

fof(f_2488_3,plain,
    ! [U_9125,U_9126] : 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_9125),U_9126)),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_9125),U_9126),
    inference(definitional_conversion,[status(esa)],[f_2488_2]) ).

cnf(f_2488_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_9125),U_9126)),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_9125),U_9126),
    inference(clausify,[status(thm)],[f_2488_3]) ).

fof(f_2489_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_2489_2,plain,
    ! [U_9130,U_9129,U_9128,U_9127] :
      ( ( 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_9127),U_9128)),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_9129),U_9130)),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_9127),U_9130)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9129),U_9128))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9127),U_9130)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9129),U_9128)))
        | ~ 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_9127),U_9128)),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_9129),U_9130)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(variable_rename,[status(thm)],[f_2489_1]) ).

fof(f_2489_3,plain,
    ( ! [U_9138,U_9136,U_9134,U_9132] :
        ( 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_9132),U_9134)),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_9136),U_9138)),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_9132),U_9138)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9136),U_9134))) )
    & ! [U_9137,U_9135,U_9133,U_9131] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9131),U_9137)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9135),U_9133)))
        | ~ 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_9131),U_9133)),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_9135),U_9137)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(miniscope,[status(thm)],[f_2489_2]) ).

fof(f_2489_4,plain,
    ( ! [U_9132,U_9134,U_9136,U_9138] :
        ( 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_9132),U_9134)),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_9136),U_9138)),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_9132),U_9138)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9136),U_9134))) )
    & ! [U_9133,U_9137,U_9131,U_9135] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9131),U_9137)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9135),U_9133)))
        | ~ 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_9131),U_9133)),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_9135),U_9137)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2489_3]) ).

cnf(f_2489_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9131),U_9137)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9135),U_9133)))
    | ~ 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_9131),U_9133)),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_9135),U_9137)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
    inference(clausify,[status(thm)],[f_2489_4]) ).

cnf(f_2489_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_9132),U_9134)),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_9136),U_9138)),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_9132),U_9138)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9136),U_9134))) ),
    inference(clausify,[status(thm)],[f_2489_4]) ).

fof(f_2490_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_2490_2,plain,
    ! [U_9140,U_9139] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9139),U_9140) = 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_9139)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9140)))
      | ~ c_Nat__Transfer_Onat__set(U_9140)
      | ~ c_Nat__Transfer_Onat__set(U_9139) ),
    inference(variable_rename,[status(thm)],[f_2490_1]) ).

fof(f_2490_3,plain,
    ! [U_9139,U_9140] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9139),U_9140) = 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_9139)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9140)))
      | ~ c_Nat__Transfer_Onat__set(U_9140)
      | ~ c_Nat__Transfer_Onat__set(U_9139) ),
    inference(definitional_conversion,[status(esa)],[f_2490_2]) ).

cnf(f_2490_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9139),U_9140) = 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_9139)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9140)))
    | ~ c_Nat__Transfer_Onat__set(U_9140)
    | ~ c_Nat__Transfer_Onat__set(U_9139) ),
    inference(clausify,[status(thm)],[f_2490_3]) ).

fof(f_2491_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_2491_2,plain,
    ! [U_9143] :
    ? [U_9142,U_9141] : U_9143 = 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_9142),U_9141)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2491_1]) ).

fof(f_2491_3,plain,
    ! [U_9143] :
    ? [U_9141] : U_9143 = 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),sK136(U_9143)),U_9141)),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,[sK136]),skolemize(U_9142,sK136(U_9143))],[f_2491_2]) ).

fof(f_2491_4,plain,
    ! [U_9143] : U_9143 = 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),sK136(U_9143)),sK137(U_9143))),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,[sK137]),skolemize(U_9141,sK137(U_9143))],[f_2491_3]) ).

fof(f_2491_5,plain,
    ! [U_9143] : U_9143 = 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),sK136(U_9143)),sK137(U_9143))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2491_4]) ).

cnf(f_2491_6,plain,
    U_9143 = 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),sK136(U_9143)),sK137(U_9143))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2491_5]) ).

fof(f_2492_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_2492_2,plain,
    ! [U_9145,U_9144] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9144),U_9145))
          | ~ 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_9144)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9145))) )
        & ( 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_9144)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9145)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9144),U_9145)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_9145)
      | ~ c_Nat__Transfer_Onat__set(U_9144) ),
    inference(variable_rename,[status(thm)],[f_2492_1]) ).

fof(f_2492_3,plain,
    ( ! [U_9144,U_9145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9144),U_9145))
        | ~ 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_9144)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9145)))
        | ~ sP730(U_9144,U_9145) )
    & ! [U_9144,U_9145] :
        ( 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_9144)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9145)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9144),U_9145))
        | ~ sP730(U_9144,U_9145) )
    & ! [U_9144,U_9145] :
        ( sP730(U_9144,U_9145)
        | ~ c_Nat__Transfer_Onat__set(U_9145)
        | ~ c_Nat__Transfer_Onat__set(U_9144) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP730])],[f_2492_2]) ).

cnf(f_2492_4,plain,
    ( sP730(U_9144,U_9145)
    | ~ c_Nat__Transfer_Onat__set(U_9145)
    | ~ c_Nat__Transfer_Onat__set(U_9144) ),
    inference(clausify,[status(thm)],[f_2492_3]) ).

cnf(f_2492_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_9144)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9145)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9144),U_9145))
    | ~ sP730(U_9144,U_9145) ),
    inference(clausify,[status(thm)],[f_2492_3]) ).

cnf(f_2492_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9144),U_9145))
    | ~ 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_9144)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9145)))
    | ~ sP730(U_9144,U_9145) ),
    inference(clausify,[status(thm)],[f_2492_3]) ).

fof(f_2493_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_2493_2,plain,
    ! [U_9147,U_9146] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9146),U_9147))
          | ~ 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_9146)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9147))) )
        & ( 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_9146)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9147)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9146),U_9147)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_9147)
      | ~ c_Nat__Transfer_Onat__set(U_9146) ),
    inference(variable_rename,[status(thm)],[f_2493_1]) ).

fof(f_2493_3,plain,
    ( ! [U_9146,U_9147] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9146),U_9147))
        | ~ 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_9146)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9147)))
        | ~ sP731(U_9146,U_9147) )
    & ! [U_9146,U_9147] :
        ( 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_9146)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9147)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9146),U_9147))
        | ~ sP731(U_9146,U_9147) )
    & ! [U_9146,U_9147] :
        ( sP731(U_9146,U_9147)
        | ~ c_Nat__Transfer_Onat__set(U_9147)
        | ~ c_Nat__Transfer_Onat__set(U_9146) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP731])],[f_2493_2]) ).

cnf(f_2493_4,plain,
    ( sP731(U_9146,U_9147)
    | ~ c_Nat__Transfer_Onat__set(U_9147)
    | ~ c_Nat__Transfer_Onat__set(U_9146) ),
    inference(clausify,[status(thm)],[f_2493_3]) ).

cnf(f_2493_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_9146)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9147)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9146),U_9147))
    | ~ sP731(U_9146,U_9147) ),
    inference(clausify,[status(thm)],[f_2493_3]) ).

cnf(f_2493_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9146),U_9147))
    | ~ 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_9146)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9147)))
    | ~ sP731(U_9146,U_9147) ),
    inference(clausify,[status(thm)],[f_2493_3]) ).

fof(f_2494_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_2494_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_2494_1]) ).

cnf(f_2494_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_2494_2]) ).

fof(f_2495_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_2495_2,plain,
    ! [U_9149,U_9148] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9148),U_9149))
      | ~ c_Nat__Transfer_Onat__set(U_9149)
      | ~ c_Nat__Transfer_Onat__set(U_9148) ),
    inference(variable_rename,[status(thm)],[f_2495_1]) ).

fof(f_2495_3,plain,
    ! [U_9148,U_9149] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9148),U_9149))
      | ~ c_Nat__Transfer_Onat__set(U_9149)
      | ~ c_Nat__Transfer_Onat__set(U_9148) ),
    inference(definitional_conversion,[status(esa)],[f_2495_2]) ).

cnf(f_2495_4,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9148),U_9149))
    | ~ c_Nat__Transfer_Onat__set(U_9149)
    | ~ c_Nat__Transfer_Onat__set(U_9148) ),
    inference(clausify,[status(thm)],[f_2495_3]) ).

fof(f_2496_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_2496_2,plain,
    ! [U_9152] :
      ( ( c_Nat__Transfer_Onat__set(U_9152)
        | ? [U_9151] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9151))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9151),U_9152)) ) )
      & ( ! [U_9150] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9150))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9150),U_9152)) )
        | ~ c_Nat__Transfer_Onat__set(U_9152) ) ),
    inference(variable_rename,[status(thm)],[f_2496_1]) ).

fof(f_2496_3,plain,
    ( ! [U_9154] :
        ( c_Nat__Transfer_Onat__set(U_9154)
        | ? [U_9151] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9151))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9151),U_9154)) ) )
    & ! [U_9153] :
        ( ! [U_9150] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9150))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9150),U_9153)) )
        | ~ c_Nat__Transfer_Onat__set(U_9153) ) ),
    inference(miniscope,[status(thm)],[f_2496_2]) ).

fof(f_2496_4,plain,
    ( ! [U_9154] :
        ( c_Nat__Transfer_Onat__set(U_9154)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_9154)))
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK138(U_9154)),U_9154)) ) )
    & ! [U_9153] :
        ( ! [U_9150] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9150))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9150),U_9153)) )
        | ~ c_Nat__Transfer_Onat__set(U_9153) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_9151,sK138(U_9154))],[f_2496_3]) ).

fof(f_2496_5,plain,
    ( ! [U_9154] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_9154)))
        | ~ sP732(U_9154) )
    & ! [U_9154] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK138(U_9154)),U_9154))
        | ~ sP732(U_9154) )
    & ! [U_9154] :
        ( c_Nat__Transfer_Onat__set(U_9154)
        | sP732(U_9154) )
    & ! [U_9150,U_9153] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9150))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9150),U_9153))
        | ~ c_Nat__Transfer_Onat__set(U_9153) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP732])],[f_2496_4]) ).

cnf(f_2496_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9150))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9150),U_9153))
    | ~ c_Nat__Transfer_Onat__set(U_9153) ),
    inference(clausify,[status(thm)],[f_2496_5]) ).

cnf(f_2496_7,plain,
    ( c_Nat__Transfer_Onat__set(U_9154)
    | sP732(U_9154) ),
    inference(clausify,[status(thm)],[f_2496_5]) ).

cnf(f_2496_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK138(U_9154)),U_9154))
    | ~ sP732(U_9154) ),
    inference(clausify,[status(thm)],[f_2496_5]) ).

cnf(f_2496_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK138(U_9154)))
    | ~ sP732(U_9154) ),
    inference(clausify,[status(thm)],[f_2496_5]) ).

fof(f_2497_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_2497_2,plain,
    ! [U_9155] : 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_9155)),
    inference(variable_rename,[status(thm)],[f_2497_1]) ).

fof(f_2497_3,plain,
    ! [U_9155] : 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_9155)),
    inference(definitional_conversion,[status(esa)],[f_2497_2]) ).

cnf(f_2497_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_9155)),
    inference(clausify,[status(thm)],[f_2497_3]) ).

fof(f_2498_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_2498_2,plain,
    ! [U_9157,U_9156] :
      ( ( ( U_9156 = U_9157
          | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9156) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9157) )
        & ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9156) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9157)
          | U_9156 != U_9157 ) )
      | ~ c_Nat__Transfer_Onat__set(U_9157)
      | ~ c_Nat__Transfer_Onat__set(U_9156) ),
    inference(variable_rename,[status(thm)],[f_2498_1]) ).

fof(f_2498_3,plain,
    ( ! [U_9156,U_9157] :
        ( U_9156 = U_9157
        | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9156) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9157)
        | ~ sP733(U_9156,U_9157) )
    & ! [U_9156,U_9157] :
        ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9156) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9157)
        | U_9156 != U_9157
        | ~ sP733(U_9156,U_9157) )
    & ! [U_9156,U_9157] :
        ( sP733(U_9156,U_9157)
        | ~ c_Nat__Transfer_Onat__set(U_9157)
        | ~ c_Nat__Transfer_Onat__set(U_9156) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP733])],[f_2498_2]) ).

cnf(f_2498_4,plain,
    ( sP733(U_9156,U_9157)
    | ~ c_Nat__Transfer_Onat__set(U_9157)
    | ~ c_Nat__Transfer_Onat__set(U_9156) ),
    inference(clausify,[status(thm)],[f_2498_3]) ).

cnf(f_2498_5,plain,
    ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9156) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9157)
    | U_9156 != U_9157
    | ~ sP733(U_9156,U_9157) ),
    inference(clausify,[status(thm)],[f_2498_3]) ).

cnf(f_2498_6,plain,
    ( U_9156 = U_9157
    | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9156) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9157)
    | ~ sP733(U_9156,U_9157) ),
    inference(clausify,[status(thm)],[f_2498_3]) ).

fof(f_2499_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_2499_2,plain,
    ! [U_9159,U_9158] :
      ( c_Nat__Transfer_Ois__nat(U_9159)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9159),U_9158))
      | ~ c_Nat__Transfer_Onat__set(U_9158) ),
    inference(variable_rename,[status(thm)],[f_2499_1]) ).

fof(f_2499_3,plain,
    ! [U_9158,U_9159] :
      ( c_Nat__Transfer_Ois__nat(U_9159)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9159),U_9158))
      | ~ c_Nat__Transfer_Onat__set(U_9158) ),
    inference(definitional_conversion,[status(esa)],[f_2499_2]) ).

cnf(f_2499_4,plain,
    ( c_Nat__Transfer_Ois__nat(U_9159)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9159),U_9158))
    | ~ c_Nat__Transfer_Onat__set(U_9158) ),
    inference(clausify,[status(thm)],[f_2499_3]) ).

fof(f_2500_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_2500_2,plain,
    ! [U_9161,U_9160] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9161))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9161),U_9160))
      | ~ c_Nat__Transfer_Onat__set(U_9160) ),
    inference(variable_rename,[status(thm)],[f_2500_1]) ).

fof(f_2500_3,plain,
    ! [U_9161,U_9160] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9161))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9161),U_9160))
      | ~ c_Nat__Transfer_Onat__set(U_9160) ),
    inference(definitional_conversion,[status(esa)],[f_2500_2]) ).

cnf(f_2500_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9161))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9161),U_9160))
    | ~ c_Nat__Transfer_Onat__set(U_9160) ),
    inference(clausify,[status(thm)],[f_2500_3]) ).

fof(f_2501_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_2501_2,plain,
    ! [U_9162] :
      ( 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_9162)) = U_9162
      | ~ c_Nat__Transfer_Onat__set(U_9162) ),
    inference(variable_rename,[status(thm)],[f_2501_1]) ).

fof(f_2501_3,plain,
    ! [U_9162] :
      ( 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_9162)) = U_9162
      | ~ c_Nat__Transfer_Onat__set(U_9162) ),
    inference(definitional_conversion,[status(esa)],[f_2501_2]) ).

cnf(f_2501_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_9162)) = U_9162
    | ~ c_Nat__Transfer_Onat__set(U_9162) ),
    inference(clausify,[status(thm)],[f_2501_3]) ).

fof(f_2502_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_2502_2,plain,
    ! [U_9164,U_9163] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9163),U_9164))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_9163)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9164))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_9163)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9164)))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9163),U_9164)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_9164)
      | ~ c_Nat__Transfer_Ois__nat(U_9163) ),
    inference(variable_rename,[status(thm)],[f_2502_1]) ).

fof(f_2502_3,plain,
    ( ! [U_9163,U_9164] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9163),U_9164))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_9163)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9164)))
        | ~ sP734(U_9163,U_9164) )
    & ! [U_9163,U_9164] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_9163)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9164)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9163),U_9164))
        | ~ sP734(U_9163,U_9164) )
    & ! [U_9163,U_9164] :
        ( sP734(U_9163,U_9164)
        | ~ c_Nat__Transfer_Onat__set(U_9164)
        | ~ c_Nat__Transfer_Ois__nat(U_9163) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP734])],[f_2502_2]) ).

cnf(f_2502_4,plain,
    ( sP734(U_9163,U_9164)
    | ~ c_Nat__Transfer_Onat__set(U_9164)
    | ~ c_Nat__Transfer_Ois__nat(U_9163) ),
    inference(clausify,[status(thm)],[f_2502_3]) ).

cnf(f_2502_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_9163)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9164)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9163),U_9164))
    | ~ sP734(U_9163,U_9164) ),
    inference(clausify,[status(thm)],[f_2502_3]) ).

cnf(f_2502_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9163),U_9164))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_9163)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9164)))
    | ~ sP734(U_9163,U_9164) ),
    inference(clausify,[status(thm)],[f_2502_3]) ).

fof(f_2503_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_2503_2,plain,
    ! [U_9170,U_9169,U_9168,U_9167,U_9166] :
      ( ? [U_9165] :
          ( hBOOL(hAPP(hAPP(c_member(U_9168),U_9165),U_9170))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_9168,U_9166)),hAPP(hAPP(c_Product__Type_OPair(U_9168,U_9166),U_9165),U_9167)),U_9169)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9166),U_9167),hAPP(c_Relation_OImage(U_9168,U_9166,U_9169),U_9170))) ),
    inference(variable_rename,[status(thm)],[f_2503_1]) ).

fof(f_2503_3,plain,
    ! [U_9170,U_9169,U_9168,U_9167,U_9166] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9168),sK139(U_9170,U_9169,U_9168,U_9167,U_9166)),U_9170))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_9168,U_9166)),hAPP(hAPP(c_Product__Type_OPair(U_9168,U_9166),sK139(U_9170,U_9169,U_9168,U_9167,U_9166)),U_9167)),U_9169)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9166),U_9167),hAPP(c_Relation_OImage(U_9168,U_9166,U_9169),U_9170))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_9165,sK139(U_9170,U_9169,U_9168,U_9167,U_9166))],[f_2503_2]) ).

fof(f_2503_4,plain,
    ( ! [U_9167,U_9166,U_9168,U_9169,U_9170] :
        ( hBOOL(hAPP(hAPP(c_member(U_9168),sK139(U_9170,U_9169,U_9168,U_9167,U_9166)),U_9170))
        | ~ sP735(U_9167,U_9166,U_9168,U_9169,U_9170) )
    & ! [U_9167,U_9166,U_9168,U_9169,U_9170] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9168,U_9166)),hAPP(hAPP(c_Product__Type_OPair(U_9168,U_9166),sK139(U_9170,U_9169,U_9168,U_9167,U_9166)),U_9167)),U_9169))
        | ~ sP735(U_9167,U_9166,U_9168,U_9169,U_9170) )
    & ! [U_9167,U_9166,U_9168,U_9169,U_9170] :
        ( sP735(U_9167,U_9166,U_9168,U_9169,U_9170)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9166),U_9167),hAPP(c_Relation_OImage(U_9168,U_9166,U_9169),U_9170))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP735])],[f_2503_3]) ).

cnf(f_2503_5,plain,
    ( sP735(U_9167,U_9166,U_9168,U_9169,U_9170)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9166),U_9167),hAPP(c_Relation_OImage(U_9168,U_9166,U_9169),U_9170))) ),
    inference(clausify,[status(thm)],[f_2503_4]) ).

cnf(f_2503_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9168,U_9166)),hAPP(hAPP(c_Product__Type_OPair(U_9168,U_9166),sK139(U_9170,U_9169,U_9168,U_9167,U_9166)),U_9167)),U_9169))
    | ~ sP735(U_9167,U_9166,U_9168,U_9169,U_9170) ),
    inference(clausify,[status(thm)],[f_2503_4]) ).

cnf(f_2503_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9168),sK139(U_9170,U_9169,U_9168,U_9167,U_9166)),U_9170))
    | ~ sP735(U_9167,U_9166,U_9168,U_9169,U_9170) ),
    inference(clausify,[status(thm)],[f_2503_4]) ).

fof(f_2504_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_2504_2,plain,
    ! [U_9175,U_9174,U_9173,U_9172,U_9171] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9171,U_9171)),hAPP(hAPP(c_Product__Type_OPair(U_9171,U_9171),U_9175),U_9174)),U_9173))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9171),U_9174),U_9172))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9171,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9171,U_9171,U_9173),hAPP(hAPP(c_Set_Oinsert(U_9171),U_9174),c_Orderings_Obot__class_Obot(tc_fun(U_9171,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_9171,U_9171,U_9173),hAPP(hAPP(c_Set_Oinsert(U_9171),U_9175),c_Orderings_Obot__class_Obot(tc_fun(U_9171,tc_HOL_Obool))))))
      | ~ c_Equiv__Relations_Oequiv(U_9171,U_9172,U_9173) ),
    inference(variable_rename,[status(thm)],[f_2504_1]) ).

fof(f_2504_3,plain,
    ! [U_9171,U_9172,U_9173,U_9174,U_9175] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9171,U_9171)),hAPP(hAPP(c_Product__Type_OPair(U_9171,U_9171),U_9175),U_9174)),U_9173))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9171),U_9174),U_9172))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9171,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9171,U_9171,U_9173),hAPP(hAPP(c_Set_Oinsert(U_9171),U_9174),c_Orderings_Obot__class_Obot(tc_fun(U_9171,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_9171,U_9171,U_9173),hAPP(hAPP(c_Set_Oinsert(U_9171),U_9175),c_Orderings_Obot__class_Obot(tc_fun(U_9171,tc_HOL_Obool))))))
      | ~ c_Equiv__Relations_Oequiv(U_9171,U_9172,U_9173) ),
    inference(definitional_conversion,[status(esa)],[f_2504_2]) ).

cnf(f_2504_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9171,U_9171)),hAPP(hAPP(c_Product__Type_OPair(U_9171,U_9171),U_9175),U_9174)),U_9173))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9171),U_9174),U_9172))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9171,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9171,U_9171,U_9173),hAPP(hAPP(c_Set_Oinsert(U_9171),U_9174),c_Orderings_Obot__class_Obot(tc_fun(U_9171,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_9171,U_9171,U_9173),hAPP(hAPP(c_Set_Oinsert(U_9171),U_9175),c_Orderings_Obot__class_Obot(tc_fun(U_9171,tc_HOL_Obool))))))
    | ~ c_Equiv__Relations_Oequiv(U_9171,U_9172,U_9173) ),
    inference(clausify,[status(thm)],[f_2504_3]) ).

fof(f_2505_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_2505_2,plain,
    ! [U_9176] :
      ( 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_9176)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9176)) ),
    inference(variable_rename,[status(thm)],[f_2505_1]) ).

fof(f_2505_3,plain,
    ! [U_9176] :
      ( 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_9176)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9176)) ),
    inference(definitional_conversion,[status(esa)],[f_2505_2]) ).

cnf(f_2505_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_9176)),c_FunDef_Omax__weak))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9176)) ),
    inference(clausify,[status(thm)],[f_2505_3]) ).

fof(f_2506_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_2506_2,plain,
    ! [U_9177] :
      ( 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_9177)),c_FunDef_Omax__strict))
      | U_9177 = 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_9177)) ),
    inference(variable_rename,[status(thm)],[f_2506_1]) ).

fof(f_2506_3,plain,
    ! [U_9177] :
      ( 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_9177)),c_FunDef_Omax__strict))
      | U_9177 = 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_9177)) ),
    inference(definitional_conversion,[status(esa)],[f_2506_2]) ).

cnf(f_2506_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_9177)),c_FunDef_Omax__strict))
    | U_9177 = 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_9177)) ),
    inference(clausify,[status(thm)],[f_2506_3]) ).

fof(f_2507_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_2507_2,plain,
    ! [U_9179,U_9178] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9178),hAPP(c_Relation_OField(U_9178),U_9179)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9178,U_9178)),U_9179)) ),
    inference(variable_rename,[status(thm)],[f_2507_1]) ).

fof(f_2507_3,plain,
    ! [U_9178,U_9179] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9178),hAPP(c_Relation_OField(U_9178),U_9179)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9178,U_9178)),U_9179)) ),
    inference(definitional_conversion,[status(esa)],[f_2507_2]) ).

cnf(f_2507_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9178),hAPP(c_Relation_OField(U_9178),U_9179)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9178,U_9178)),U_9179)) ),
    inference(clausify,[status(thm)],[f_2507_3]) ).

fof(f_2508_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_2508_2,plain,
    ! [U_9183,U_9182,U_9181,U_9180] :
      ( hBOOL(hAPP(hAPP(c_member(U_9180),U_9183),hAPP(c_Relation_OImage(U_9180,U_9180,U_9182),hAPP(hAPP(c_Set_Oinsert(U_9180),U_9183),c_Orderings_Obot__class_Obot(tc_fun(U_9180,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9180),U_9183),U_9181))
      | ~ c_Equiv__Relations_Oequiv(U_9180,U_9181,U_9182) ),
    inference(variable_rename,[status(thm)],[f_2508_1]) ).

fof(f_2508_3,plain,
    ! [U_9180,U_9181,U_9182,U_9183] :
      ( hBOOL(hAPP(hAPP(c_member(U_9180),U_9183),hAPP(c_Relation_OImage(U_9180,U_9180,U_9182),hAPP(hAPP(c_Set_Oinsert(U_9180),U_9183),c_Orderings_Obot__class_Obot(tc_fun(U_9180,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9180),U_9183),U_9181))
      | ~ c_Equiv__Relations_Oequiv(U_9180,U_9181,U_9182) ),
    inference(definitional_conversion,[status(esa)],[f_2508_2]) ).

cnf(f_2508_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9180),U_9183),hAPP(c_Relation_OImage(U_9180,U_9180,U_9182),hAPP(hAPP(c_Set_Oinsert(U_9180),U_9183),c_Orderings_Obot__class_Obot(tc_fun(U_9180,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9180),U_9183),U_9181))
    | ~ c_Equiv__Relations_Oequiv(U_9180,U_9181,U_9182) ),
    inference(clausify,[status(thm)],[f_2508_3]) ).

fof(f_2509_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_2509_2,plain,
    ! [U_9188,U_9187,U_9186,U_9185,U_9184] :
      ( hAPP(c_Relation_OImage(U_9184,U_9184,U_9186),hAPP(hAPP(c_Set_Oinsert(U_9184),U_9187),c_Orderings_Obot__class_Obot(tc_fun(U_9184,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_9184,U_9184,U_9186),hAPP(hAPP(c_Set_Oinsert(U_9184),U_9188),c_Orderings_Obot__class_Obot(tc_fun(U_9184,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9184,U_9184)),hAPP(hAPP(c_Product__Type_OPair(U_9184,U_9184),U_9187),U_9188)),U_9186))
      | ~ c_Equiv__Relations_Oequiv(U_9184,U_9185,U_9186) ),
    inference(variable_rename,[status(thm)],[f_2509_1]) ).

fof(f_2509_3,plain,
    ! [U_9184,U_9185,U_9186,U_9187,U_9188] :
      ( hAPP(c_Relation_OImage(U_9184,U_9184,U_9186),hAPP(hAPP(c_Set_Oinsert(U_9184),U_9187),c_Orderings_Obot__class_Obot(tc_fun(U_9184,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_9184,U_9184,U_9186),hAPP(hAPP(c_Set_Oinsert(U_9184),U_9188),c_Orderings_Obot__class_Obot(tc_fun(U_9184,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9184,U_9184)),hAPP(hAPP(c_Product__Type_OPair(U_9184,U_9184),U_9187),U_9188)),U_9186))
      | ~ c_Equiv__Relations_Oequiv(U_9184,U_9185,U_9186) ),
    inference(definitional_conversion,[status(esa)],[f_2509_2]) ).

cnf(f_2509_4,plain,
    ( hAPP(c_Relation_OImage(U_9184,U_9184,U_9186),hAPP(hAPP(c_Set_Oinsert(U_9184),U_9187),c_Orderings_Obot__class_Obot(tc_fun(U_9184,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_9184,U_9184,U_9186),hAPP(hAPP(c_Set_Oinsert(U_9184),U_9188),c_Orderings_Obot__class_Obot(tc_fun(U_9184,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9184,U_9184)),hAPP(hAPP(c_Product__Type_OPair(U_9184,U_9184),U_9187),U_9188)),U_9186))
    | ~ c_Equiv__Relations_Oequiv(U_9184,U_9185,U_9186) ),
    inference(clausify,[status(thm)],[f_2509_3]) ).

fof(f_2510_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_2510_2,plain,
    ! [U_9193,U_9192,U_9191,U_9190,U_9189] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9189,U_9189)),hAPP(hAPP(c_Product__Type_OPair(U_9189,U_9189),U_9192),U_9193)),U_9191))
          | ~ hBOOL(hAPP(hAPP(c_member(U_9189),U_9193),U_9190))
          | ~ hBOOL(hAPP(hAPP(c_member(U_9189),U_9192),U_9190))
          | hAPP(c_Relation_OImage(U_9189,U_9189,U_9191),hAPP(hAPP(c_Set_Oinsert(U_9189),U_9192),c_Orderings_Obot__class_Obot(tc_fun(U_9189,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_9189,U_9189,U_9191),hAPP(hAPP(c_Set_Oinsert(U_9189),U_9193),c_Orderings_Obot__class_Obot(tc_fun(U_9189,tc_HOL_Obool)))) )
        & ( ( hBOOL(hAPP(hAPP(c_member(U_9189),U_9193),U_9190))
            & hBOOL(hAPP(hAPP(c_member(U_9189),U_9192),U_9190))
            & hAPP(c_Relation_OImage(U_9189,U_9189,U_9191),hAPP(hAPP(c_Set_Oinsert(U_9189),U_9192),c_Orderings_Obot__class_Obot(tc_fun(U_9189,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_9189,U_9189,U_9191),hAPP(hAPP(c_Set_Oinsert(U_9189),U_9193),c_Orderings_Obot__class_Obot(tc_fun(U_9189,tc_HOL_Obool)))) )
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9189,U_9189)),hAPP(hAPP(c_Product__Type_OPair(U_9189,U_9189),U_9192),U_9193)),U_9191)) ) )
      | ~ c_Equiv__Relations_Oequiv(U_9189,U_9190,U_9191) ),
    inference(variable_rename,[status(thm)],[f_2510_1]) ).

fof(f_2510_3,plain,
    ( ! [U_9189,U_9190,U_9191,U_9192,U_9193] :
        ( hBOOL(hAPP(hAPP(c_member(U_9189),U_9193),U_9190))
        | ~ sP736(U_9189,U_9190,U_9191,U_9192,U_9193) )
    & ! [U_9189,U_9190,U_9191,U_9192,U_9193] :
        ( hBOOL(hAPP(hAPP(c_member(U_9189),U_9192),U_9190))
        | ~ sP736(U_9189,U_9190,U_9191,U_9192,U_9193) )
    & ! [U_9189,U_9190,U_9191,U_9192,U_9193] :
        ( hAPP(c_Relation_OImage(U_9189,U_9189,U_9191),hAPP(hAPP(c_Set_Oinsert(U_9189),U_9192),c_Orderings_Obot__class_Obot(tc_fun(U_9189,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_9189,U_9189,U_9191),hAPP(hAPP(c_Set_Oinsert(U_9189),U_9193),c_Orderings_Obot__class_Obot(tc_fun(U_9189,tc_HOL_Obool))))
        | ~ sP736(U_9189,U_9190,U_9191,U_9192,U_9193) )
    & ! [U_9189,U_9190,U_9191,U_9192,U_9193] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9189,U_9189)),hAPP(hAPP(c_Product__Type_OPair(U_9189,U_9189),U_9192),U_9193)),U_9191))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9189),U_9193),U_9190))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9189),U_9192),U_9190))
        | hAPP(c_Relation_OImage(U_9189,U_9189,U_9191),hAPP(hAPP(c_Set_Oinsert(U_9189),U_9192),c_Orderings_Obot__class_Obot(tc_fun(U_9189,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_9189,U_9189,U_9191),hAPP(hAPP(c_Set_Oinsert(U_9189),U_9193),c_Orderings_Obot__class_Obot(tc_fun(U_9189,tc_HOL_Obool))))
        | ~ sP737(U_9189,U_9190,U_9191,U_9192,U_9193) )
    & ! [U_9189,U_9190,U_9191,U_9192,U_9193] :
        ( sP736(U_9189,U_9190,U_9191,U_9192,U_9193)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9189,U_9189)),hAPP(hAPP(c_Product__Type_OPair(U_9189,U_9189),U_9192),U_9193)),U_9191))
        | ~ sP737(U_9189,U_9190,U_9191,U_9192,U_9193) )
    & ! [U_9189,U_9190,U_9191,U_9192,U_9193] :
        ( sP737(U_9189,U_9190,U_9191,U_9192,U_9193)
        | ~ c_Equiv__Relations_Oequiv(U_9189,U_9190,U_9191) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP736,sP737])],[f_2510_2]) ).

cnf(f_2510_4,plain,
    ( sP737(U_9189,U_9190,U_9191,U_9192,U_9193)
    | ~ c_Equiv__Relations_Oequiv(U_9189,U_9190,U_9191) ),
    inference(clausify,[status(thm)],[f_2510_3]) ).

cnf(f_2510_5,plain,
    ( sP736(U_9189,U_9190,U_9191,U_9192,U_9193)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9189,U_9189)),hAPP(hAPP(c_Product__Type_OPair(U_9189,U_9189),U_9192),U_9193)),U_9191))
    | ~ sP737(U_9189,U_9190,U_9191,U_9192,U_9193) ),
    inference(clausify,[status(thm)],[f_2510_3]) ).

cnf(f_2510_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9189,U_9189)),hAPP(hAPP(c_Product__Type_OPair(U_9189,U_9189),U_9192),U_9193)),U_9191))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9189),U_9193),U_9190))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9189),U_9192),U_9190))
    | hAPP(c_Relation_OImage(U_9189,U_9189,U_9191),hAPP(hAPP(c_Set_Oinsert(U_9189),U_9192),c_Orderings_Obot__class_Obot(tc_fun(U_9189,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_9189,U_9189,U_9191),hAPP(hAPP(c_Set_Oinsert(U_9189),U_9193),c_Orderings_Obot__class_Obot(tc_fun(U_9189,tc_HOL_Obool))))
    | ~ sP737(U_9189,U_9190,U_9191,U_9192,U_9193) ),
    inference(clausify,[status(thm)],[f_2510_3]) ).

cnf(f_2510_7,plain,
    ( hAPP(c_Relation_OImage(U_9189,U_9189,U_9191),hAPP(hAPP(c_Set_Oinsert(U_9189),U_9192),c_Orderings_Obot__class_Obot(tc_fun(U_9189,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_9189,U_9189,U_9191),hAPP(hAPP(c_Set_Oinsert(U_9189),U_9193),c_Orderings_Obot__class_Obot(tc_fun(U_9189,tc_HOL_Obool))))
    | ~ sP736(U_9189,U_9190,U_9191,U_9192,U_9193) ),
    inference(clausify,[status(thm)],[f_2510_3]) ).

cnf(f_2510_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9189),U_9192),U_9190))
    | ~ sP736(U_9189,U_9190,U_9191,U_9192,U_9193) ),
    inference(clausify,[status(thm)],[f_2510_3]) ).

cnf(f_2510_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9189),U_9193),U_9190))
    | ~ sP736(U_9189,U_9190,U_9191,U_9192,U_9193) ),
    inference(clausify,[status(thm)],[f_2510_3]) ).

fof(f_2511_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_2511_2,plain,
    ! [U_9198,U_9197,U_9196,U_9195,U_9194] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9194,U_9194)),hAPP(hAPP(c_Product__Type_OPair(U_9194,U_9194),U_9196),U_9197)),U_9195))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9194),U_9197),U_9198))
      | ~ c_Equiv__Relations_Oequiv(U_9194,U_9198,U_9195)
      | hAPP(c_Relation_OImage(U_9194,U_9194,U_9195),hAPP(hAPP(c_Set_Oinsert(U_9194),U_9196),c_Orderings_Obot__class_Obot(tc_fun(U_9194,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_9194,U_9194,U_9195),hAPP(hAPP(c_Set_Oinsert(U_9194),U_9197),c_Orderings_Obot__class_Obot(tc_fun(U_9194,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2511_1]) ).

fof(f_2511_3,plain,
    ! [U_9196,U_9195,U_9197,U_9194,U_9198] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9194,U_9194)),hAPP(hAPP(c_Product__Type_OPair(U_9194,U_9194),U_9196),U_9197)),U_9195))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9194),U_9197),U_9198))
      | ~ c_Equiv__Relations_Oequiv(U_9194,U_9198,U_9195)
      | hAPP(c_Relation_OImage(U_9194,U_9194,U_9195),hAPP(hAPP(c_Set_Oinsert(U_9194),U_9196),c_Orderings_Obot__class_Obot(tc_fun(U_9194,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_9194,U_9194,U_9195),hAPP(hAPP(c_Set_Oinsert(U_9194),U_9197),c_Orderings_Obot__class_Obot(tc_fun(U_9194,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2511_2]) ).

cnf(f_2511_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9194,U_9194)),hAPP(hAPP(c_Product__Type_OPair(U_9194,U_9194),U_9196),U_9197)),U_9195))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9194),U_9197),U_9198))
    | ~ c_Equiv__Relations_Oequiv(U_9194,U_9198,U_9195)
    | hAPP(c_Relation_OImage(U_9194,U_9194,U_9195),hAPP(hAPP(c_Set_Oinsert(U_9194),U_9196),c_Orderings_Obot__class_Obot(tc_fun(U_9194,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_9194,U_9194,U_9195),hAPP(hAPP(c_Set_Oinsert(U_9194),U_9197),c_Orderings_Obot__class_Obot(tc_fun(U_9194,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2511_3]) ).

fof(f_2512_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_2512_2,plain,
    ! [U_9203,U_9202,U_9201,U_9200,U_9199] :
      ( ( ( hAPP(c_Relation_OImage(U_9199,U_9199,U_9201),hAPP(hAPP(c_Set_Oinsert(U_9199),U_9202),c_Orderings_Obot__class_Obot(tc_fun(U_9199,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_9199,U_9199,U_9201),hAPP(hAPP(c_Set_Oinsert(U_9199),U_9203),c_Orderings_Obot__class_Obot(tc_fun(U_9199,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9199,U_9199)),hAPP(hAPP(c_Product__Type_OPair(U_9199,U_9199),U_9202),U_9203)),U_9201)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9199,U_9199)),hAPP(hAPP(c_Product__Type_OPair(U_9199,U_9199),U_9202),U_9203)),U_9201))
          | hAPP(c_Relation_OImage(U_9199,U_9199,U_9201),hAPP(hAPP(c_Set_Oinsert(U_9199),U_9202),c_Orderings_Obot__class_Obot(tc_fun(U_9199,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_9199,U_9199,U_9201),hAPP(hAPP(c_Set_Oinsert(U_9199),U_9203),c_Orderings_Obot__class_Obot(tc_fun(U_9199,tc_HOL_Obool)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9199),U_9203),U_9200))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9199),U_9202),U_9200))
      | ~ c_Equiv__Relations_Oequiv(U_9199,U_9200,U_9201) ),
    inference(variable_rename,[status(thm)],[f_2512_1]) ).

fof(f_2512_3,plain,
    ( ! [U_9199,U_9201,U_9202,U_9203] :
        ( hAPP(c_Relation_OImage(U_9199,U_9199,U_9201),hAPP(hAPP(c_Set_Oinsert(U_9199),U_9202),c_Orderings_Obot__class_Obot(tc_fun(U_9199,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_9199,U_9199,U_9201),hAPP(hAPP(c_Set_Oinsert(U_9199),U_9203),c_Orderings_Obot__class_Obot(tc_fun(U_9199,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9199,U_9199)),hAPP(hAPP(c_Product__Type_OPair(U_9199,U_9199),U_9202),U_9203)),U_9201))
        | ~ sP738(U_9199,U_9201,U_9202,U_9203) )
    & ! [U_9199,U_9201,U_9202,U_9203] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9199,U_9199)),hAPP(hAPP(c_Product__Type_OPair(U_9199,U_9199),U_9202),U_9203)),U_9201))
        | hAPP(c_Relation_OImage(U_9199,U_9199,U_9201),hAPP(hAPP(c_Set_Oinsert(U_9199),U_9202),c_Orderings_Obot__class_Obot(tc_fun(U_9199,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_9199,U_9199,U_9201),hAPP(hAPP(c_Set_Oinsert(U_9199),U_9203),c_Orderings_Obot__class_Obot(tc_fun(U_9199,tc_HOL_Obool))))
        | ~ sP738(U_9199,U_9201,U_9202,U_9203) )
    & ! [U_9199,U_9200,U_9201,U_9202,U_9203] :
        ( sP738(U_9199,U_9201,U_9202,U_9203)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9199),U_9203),U_9200))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9199),U_9202),U_9200))
        | ~ c_Equiv__Relations_Oequiv(U_9199,U_9200,U_9201) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP738])],[f_2512_2]) ).

cnf(f_2512_4,plain,
    ( sP738(U_9199,U_9201,U_9202,U_9203)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9199),U_9203),U_9200))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9199),U_9202),U_9200))
    | ~ c_Equiv__Relations_Oequiv(U_9199,U_9200,U_9201) ),
    inference(clausify,[status(thm)],[f_2512_3]) ).

cnf(f_2512_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9199,U_9199)),hAPP(hAPP(c_Product__Type_OPair(U_9199,U_9199),U_9202),U_9203)),U_9201))
    | hAPP(c_Relation_OImage(U_9199,U_9199,U_9201),hAPP(hAPP(c_Set_Oinsert(U_9199),U_9202),c_Orderings_Obot__class_Obot(tc_fun(U_9199,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_9199,U_9199,U_9201),hAPP(hAPP(c_Set_Oinsert(U_9199),U_9203),c_Orderings_Obot__class_Obot(tc_fun(U_9199,tc_HOL_Obool))))
    | ~ sP738(U_9199,U_9201,U_9202,U_9203) ),
    inference(clausify,[status(thm)],[f_2512_3]) ).

cnf(f_2512_6,plain,
    ( hAPP(c_Relation_OImage(U_9199,U_9199,U_9201),hAPP(hAPP(c_Set_Oinsert(U_9199),U_9202),c_Orderings_Obot__class_Obot(tc_fun(U_9199,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_9199,U_9199,U_9201),hAPP(hAPP(c_Set_Oinsert(U_9199),U_9203),c_Orderings_Obot__class_Obot(tc_fun(U_9199,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9199,U_9199)),hAPP(hAPP(c_Product__Type_OPair(U_9199,U_9199),U_9202),U_9203)),U_9201))
    | ~ sP738(U_9199,U_9201,U_9202,U_9203) ),
    inference(clausify,[status(thm)],[f_2512_3]) ).

fof(f_2513_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_2513_2,plain,
    ! [U_9208,U_9207,U_9206,U_9205,U_9204] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9204,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9204,U_9204,U_9206),hAPP(hAPP(c_Set_Oinsert(U_9204),U_9207),c_Orderings_Obot__class_Obot(tc_fun(U_9204,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_9204,U_9204,U_9206),hAPP(hAPP(c_Set_Oinsert(U_9204),U_9208),c_Orderings_Obot__class_Obot(tc_fun(U_9204,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9204,U_9204)),hAPP(hAPP(c_Product__Type_OPair(U_9204,U_9204),U_9207),U_9208)),U_9206))
      | ~ c_Equiv__Relations_Oequiv(U_9204,U_9205,U_9206) ),
    inference(variable_rename,[status(thm)],[f_2513_1]) ).

fof(f_2513_3,plain,
    ! [U_9205,U_9206,U_9207,U_9204,U_9208] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9204,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9204,U_9204,U_9206),hAPP(hAPP(c_Set_Oinsert(U_9204),U_9207),c_Orderings_Obot__class_Obot(tc_fun(U_9204,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_9204,U_9204,U_9206),hAPP(hAPP(c_Set_Oinsert(U_9204),U_9208),c_Orderings_Obot__class_Obot(tc_fun(U_9204,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9204,U_9204)),hAPP(hAPP(c_Product__Type_OPair(U_9204,U_9204),U_9207),U_9208)),U_9206))
      | ~ c_Equiv__Relations_Oequiv(U_9204,U_9205,U_9206) ),
    inference(definitional_conversion,[status(esa)],[f_2513_2]) ).

cnf(f_2513_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9204,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9204,U_9204,U_9206),hAPP(hAPP(c_Set_Oinsert(U_9204),U_9207),c_Orderings_Obot__class_Obot(tc_fun(U_9204,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_9204,U_9204,U_9206),hAPP(hAPP(c_Set_Oinsert(U_9204),U_9208),c_Orderings_Obot__class_Obot(tc_fun(U_9204,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9204,U_9204)),hAPP(hAPP(c_Product__Type_OPair(U_9204,U_9204),U_9207),U_9208)),U_9206))
    | ~ c_Equiv__Relations_Oequiv(U_9204,U_9205,U_9206) ),
    inference(clausify,[status(thm)],[f_2513_3]) ).

fof(f_2514_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_2514_2,plain,
    ! [U_9211,U_9210,U_9209] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9209,tc_HOL_Obool)),U_9210),U_9211)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9209),U_9210)) ),
    inference(variable_rename,[status(thm)],[f_2514_1]) ).

fof(f_2514_3,plain,
    ! [U_9210,U_9209,U_9211] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9209,tc_HOL_Obool)),U_9210),U_9211)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9209),U_9210)) ),
    inference(definitional_conversion,[status(esa)],[f_2514_2]) ).

cnf(f_2514_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9209,tc_HOL_Obool)),U_9210),U_9211)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9209),U_9210)) ),
    inference(clausify,[status(thm)],[f_2514_3]) ).

fof(f_2515_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_2515_2,plain,
    ! [U_9215,U_9214,U_9213,U_9212] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9214),hAPP(c_Set_Oimage(U_9212,U_9214,U_9215),U_9213)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9212),U_9213)) ),
    inference(variable_rename,[status(thm)],[f_2515_1]) ).

fof(f_2515_3,plain,
    ! [U_9212,U_9213,U_9214,U_9215] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9214),hAPP(c_Set_Oimage(U_9212,U_9214,U_9215),U_9213)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9212),U_9213)) ),
    inference(definitional_conversion,[status(esa)],[f_2515_2]) ).

cnf(f_2515_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9214),hAPP(c_Set_Oimage(U_9212,U_9214,U_9215),U_9213)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9212),U_9213)) ),
    inference(clausify,[status(thm)],[f_2515_3]) ).

fof(f_2516_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_2516_2,plain,
    ! [U_9218,U_9217,U_9216] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9216),hAPP(hAPP(c_Set_Oinsert(U_9216),U_9218),U_9217)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9216),U_9217)) ),
    inference(variable_rename,[status(thm)],[f_2516_1]) ).

fof(f_2516_3,plain,
    ! [U_9216,U_9217,U_9218] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9216),hAPP(hAPP(c_Set_Oinsert(U_9216),U_9218),U_9217)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9216),U_9217)) ),
    inference(definitional_conversion,[status(esa)],[f_2516_2]) ).

cnf(f_2516_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9216),hAPP(hAPP(c_Set_Oinsert(U_9216),U_9218),U_9217)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9216),U_9217)) ),
    inference(clausify,[status(thm)],[f_2516_3]) ).

fof(f_2517_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_2517_2,plain,
    ! [U_9219] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_9219),c_Orderings_Obot__class_Obot(tc_fun(U_9219,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2517_1]) ).

fof(f_2517_3,plain,
    ! [U_9219] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_9219),c_Orderings_Obot__class_Obot(tc_fun(U_9219,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2517_2]) ).

cnf(f_2517_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_9219),c_Orderings_Obot__class_Obot(tc_fun(U_9219,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2517_3]) ).

fof(f_2518_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_2518_2,plain,
    ! [U_9220] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9220))
        | ~ 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_9220))) )
      & ( 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_9220)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9220)) ) ),
    inference(variable_rename,[status(thm)],[f_2518_1]) ).

fof(f_2518_3,plain,
    ( ! [U_9222] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9222))
        | ~ 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_9222))) )
    & ! [U_9221] :
        ( 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_9221)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9221)) ) ),
    inference(miniscope,[status(thm)],[f_2518_2]) ).

fof(f_2518_4,plain,
    ( ! [U_9222] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9222))
        | ~ 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_9222))) )
    & ! [U_9221] :
        ( 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_9221)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9221)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2518_3]) ).

cnf(f_2518_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_9221)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9221)) ),
    inference(clausify,[status(thm)],[f_2518_4]) ).

cnf(f_2518_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9222))
    | ~ 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_9222))) ),
    inference(clausify,[status(thm)],[f_2518_4]) ).

fof(f_2519_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_2519_2,plain,
    ! [U_9223] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_9223))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9223))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9223)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_9223)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_9223) ),
    inference(variable_rename,[status(thm)],[f_2519_1]) ).

fof(f_2519_3,plain,
    ( ! [U_9223] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_9223))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9223)))
        | ~ sP739(U_9223) )
    & ! [U_9223] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9223)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_9223))
        | ~ sP739(U_9223) )
    & ! [U_9223] :
        ( sP739(U_9223)
        | ~ c_Nat__Transfer_Onat__set(U_9223) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP739])],[f_2519_2]) ).

cnf(f_2519_4,plain,
    ( sP739(U_9223)
    | ~ c_Nat__Transfer_Onat__set(U_9223) ),
    inference(clausify,[status(thm)],[f_2519_3]) ).

cnf(f_2519_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_9223)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_9223))
    | ~ sP739(U_9223) ),
    inference(clausify,[status(thm)],[f_2519_3]) ).

cnf(f_2519_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_9223))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9223)))
    | ~ sP739(U_9223) ),
    inference(clausify,[status(thm)],[f_2519_3]) ).

fof(f_2520_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_2520_2,plain,
    ! [U_9225,U_9224] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9224),U_9225))
      | ~ class_Finite__Set_Ofinite(U_9224) ),
    inference(variable_rename,[status(thm)],[f_2520_1]) ).

fof(f_2520_3,plain,
    ! [U_9224,U_9225] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9224),U_9225))
      | ~ class_Finite__Set_Ofinite(U_9224) ),
    inference(definitional_conversion,[status(esa)],[f_2520_2]) ).

cnf(f_2520_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9224),U_9225))
    | ~ class_Finite__Set_Ofinite(U_9224) ),
    inference(clausify,[status(thm)],[f_2520_3]) ).

fof(f_2521_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_2521_2,plain,
    ! [U_9227,U_9226] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9226),U_9227))
      | ~ class_Finite__Set_Ofinite(U_9226) ),
    inference(variable_rename,[status(thm)],[f_2521_1]) ).

fof(f_2521_3,plain,
    ! [U_9226,U_9227] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9226),U_9227))
      | ~ class_Finite__Set_Ofinite(U_9226) ),
    inference(definitional_conversion,[status(esa)],[f_2521_2]) ).

cnf(f_2521_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9226),U_9227))
    | ~ class_Finite__Set_Ofinite(U_9226) ),
    inference(clausify,[status(thm)],[f_2521_3]) ).

fof(f_2522_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_2522_2,plain,
    ! [U_9228] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_9228),c_Orderings_Obot__class_Obot(tc_fun(U_9228,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2522_1]) ).

fof(f_2522_3,plain,
    ! [U_9228] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_9228),c_Orderings_Obot__class_Obot(tc_fun(U_9228,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2522_2]) ).

cnf(f_2522_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_9228),c_Orderings_Obot__class_Obot(tc_fun(U_9228,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2522_3]) ).

fof(f_2523_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_2523_2,plain,
    ! [U_9231,U_9230,U_9229] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9229),hAPP(hAPP(c_Set_Oinsert(U_9229),U_9230),U_9231)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9229),U_9231)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9229),U_9231))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9229),hAPP(hAPP(c_Set_Oinsert(U_9229),U_9230),U_9231))) ) ),
    inference(variable_rename,[status(thm)],[f_2523_1]) ).

fof(f_2523_3,plain,
    ( ! [U_9237,U_9235,U_9233] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9233),hAPP(hAPP(c_Set_Oinsert(U_9233),U_9235),U_9237)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9233),U_9237)) )
    & ! [U_9236,U_9234,U_9232] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9232),U_9236))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9232),hAPP(hAPP(c_Set_Oinsert(U_9232),U_9234),U_9236))) ) ),
    inference(miniscope,[status(thm)],[f_2523_2]) ).

fof(f_2523_4,plain,
    ( ! [U_9233,U_9235,U_9237] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9233),hAPP(hAPP(c_Set_Oinsert(U_9233),U_9235),U_9237)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9233),U_9237)) )
    & ! [U_9236,U_9234,U_9232] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9232),U_9236))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9232),hAPP(hAPP(c_Set_Oinsert(U_9232),U_9234),U_9236))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2523_3]) ).

cnf(f_2523_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9232),U_9236))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9232),hAPP(hAPP(c_Set_Oinsert(U_9232),U_9234),U_9236))) ),
    inference(clausify,[status(thm)],[f_2523_4]) ).

cnf(f_2523_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9233),hAPP(hAPP(c_Set_Oinsert(U_9233),U_9235),U_9237)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9233),U_9237)) ),
    inference(clausify,[status(thm)],[f_2523_4]) ).

fof(f_2524_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_2524_2,plain,
    ! [U_9240,U_9239,U_9238] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9238),U_9240))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9238,tc_HOL_Obool)),U_9240),U_9239))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9238),U_9239)) ),
    inference(variable_rename,[status(thm)],[f_2524_1]) ).

fof(f_2524_3,plain,
    ! [U_9238,U_9239,U_9240] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9238),U_9240))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9238,tc_HOL_Obool)),U_9240),U_9239))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9238),U_9239)) ),
    inference(definitional_conversion,[status(esa)],[f_2524_2]) ).

cnf(f_2524_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9238),U_9240))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9238,tc_HOL_Obool)),U_9240),U_9239))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9238),U_9239)) ),
    inference(clausify,[status(thm)],[f_2524_3]) ).

fof(f_2525_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_2525_2,plain,
    ! [U_9243,U_9242,U_9241] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9241),U_9242))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9241),U_9243))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9241,tc_HOL_Obool)),U_9242),U_9243)) ),
    inference(variable_rename,[status(thm)],[f_2525_1]) ).

fof(f_2525_3,plain,
    ! [U_9241,U_9242,U_9243] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9241),U_9242))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9241),U_9243))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9241,tc_HOL_Obool)),U_9242),U_9243)) ),
    inference(definitional_conversion,[status(esa)],[f_2525_2]) ).

cnf(f_2525_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9241),U_9242))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9241),U_9243))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9241,tc_HOL_Obool)),U_9242),U_9243)) ),
    inference(clausify,[status(thm)],[f_2525_3]) ).

fof(f_2526_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_2526_2,plain,
    ! [U_9246,U_9245,U_9244] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9244),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9244,tc_HOL_Obool)),U_9245),U_9246)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9244),U_9246))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9244),U_9245)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9244),U_9246))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_9244),U_9245)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9244),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9244,tc_HOL_Obool)),U_9245),U_9246))) ) ),
    inference(variable_rename,[status(thm)],[f_2526_1]) ).

fof(f_2526_3,plain,
    ( ! [U_9252,U_9250,U_9248] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9248),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9248,tc_HOL_Obool)),U_9250),U_9252)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9248),U_9252))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9248),U_9250)) )
    & ! [U_9251,U_9249,U_9247] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9247),U_9251))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_9247),U_9249)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9247),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9247,tc_HOL_Obool)),U_9249),U_9251))) ) ),
    inference(miniscope,[status(thm)],[f_2526_2]) ).

fof(f_2526_4,plain,
    ( ! [U_9249,U_9247,U_9251] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9247),U_9251))
        | ~ sP740(U_9249,U_9247,U_9251) )
    & ! [U_9249,U_9247,U_9251] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9247),U_9249))
        | ~ sP740(U_9249,U_9247,U_9251) )
    & ! [U_9250,U_9252,U_9248] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9248),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9248,tc_HOL_Obool)),U_9250),U_9252)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9248),U_9252))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9248),U_9250)) )
    & ! [U_9249,U_9247,U_9251] :
        ( sP740(U_9249,U_9247,U_9251)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9247),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9247,tc_HOL_Obool)),U_9249),U_9251))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP740])],[f_2526_3]) ).

cnf(f_2526_5,plain,
    ( sP740(U_9249,U_9247,U_9251)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9247),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9247,tc_HOL_Obool)),U_9249),U_9251))) ),
    inference(clausify,[status(thm)],[f_2526_4]) ).

cnf(f_2526_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9248),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9248,tc_HOL_Obool)),U_9250),U_9252)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9248),U_9252))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9248),U_9250)) ),
    inference(clausify,[status(thm)],[f_2526_4]) ).

cnf(f_2526_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9247),U_9249))
    | ~ sP740(U_9249,U_9247,U_9251) ),
    inference(clausify,[status(thm)],[f_2526_4]) ).

cnf(f_2526_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9247),U_9251))
    | ~ sP740(U_9249,U_9247,U_9251) ),
    inference(clausify,[status(thm)],[f_2526_4]) ).

fof(f_2527_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_2527_2,plain,
    ! [U_9255,U_9254,U_9253] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9253),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9253,tc_HOL_Obool)),U_9254),U_9255)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9253),U_9255))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9253),U_9254)) ),
    inference(variable_rename,[status(thm)],[f_2527_1]) ).

fof(f_2527_3,plain,
    ! [U_9253,U_9255,U_9254] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9253),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9253,tc_HOL_Obool)),U_9254),U_9255)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9253),U_9255))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9253),U_9254)) ),
    inference(definitional_conversion,[status(esa)],[f_2527_2]) ).

cnf(f_2527_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9253),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9253,tc_HOL_Obool)),U_9254),U_9255)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9253),U_9255))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9253),U_9254)) ),
    inference(clausify,[status(thm)],[f_2527_3]) ).

fof(f_2528_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_2528_2,plain,
    ! [U_9258,U_9257,U_9256] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9256),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9256,tc_HOL_Obool)),U_9258),U_9257)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9256),U_9258)) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9256),U_9258))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9256),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9256,tc_HOL_Obool)),U_9258),U_9257))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9256),U_9257)) ),
    inference(variable_rename,[status(thm)],[f_2528_1]) ).

fof(f_2528_3,plain,
    ( ! [U_9256,U_9257,U_9258] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9256),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9256,tc_HOL_Obool)),U_9258),U_9257)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9256),U_9258))
        | ~ sP741(U_9256,U_9257,U_9258) )
    & ! [U_9256,U_9257,U_9258] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9256),U_9258))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9256),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9256,tc_HOL_Obool)),U_9258),U_9257)))
        | ~ sP741(U_9256,U_9257,U_9258) )
    & ! [U_9256,U_9257,U_9258] :
        ( sP741(U_9256,U_9257,U_9258)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9256),U_9257)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP741])],[f_2528_2]) ).

cnf(f_2528_4,plain,
    ( sP741(U_9256,U_9257,U_9258)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9256),U_9257)) ),
    inference(clausify,[status(thm)],[f_2528_3]) ).

cnf(f_2528_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9256),U_9258))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9256),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9256,tc_HOL_Obool)),U_9258),U_9257)))
    | ~ sP741(U_9256,U_9257,U_9258) ),
    inference(clausify,[status(thm)],[f_2528_3]) ).

cnf(f_2528_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9256),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9256,tc_HOL_Obool)),U_9258),U_9257)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9256),U_9258))
    | ~ sP741(U_9256,U_9257,U_9258) ),
    inference(clausify,[status(thm)],[f_2528_3]) ).

fof(f_2529_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_2529_2,plain,
    ! [U_9263,U_9262,U_9261,U_9260,U_9259] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9261),U_9262))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9261,tc_HOL_Obool)),U_9262),hAPP(c_Set_Oimage(U_9259,U_9261,U_9263),U_9260)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9259),U_9260)) ),
    inference(variable_rename,[status(thm)],[f_2529_1]) ).

fof(f_2529_3,plain,
    ! [U_9260,U_9261,U_9259,U_9262,U_9263] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9261),U_9262))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9261,tc_HOL_Obool)),U_9262),hAPP(c_Set_Oimage(U_9259,U_9261,U_9263),U_9260)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9259),U_9260)) ),
    inference(definitional_conversion,[status(esa)],[f_2529_2]) ).

cnf(f_2529_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9261),U_9262))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9261,tc_HOL_Obool)),U_9262),hAPP(c_Set_Oimage(U_9259,U_9261,U_9263),U_9260)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9259),U_9260)) ),
    inference(clausify,[status(thm)],[f_2529_3]) ).

fof(f_2530_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_2530_2,plain,
    ! [U_9267,U_9266,U_9265,U_9264] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9264),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9264,tc_HOL_Obool)),U_9265),hAPP(hAPP(c_Set_Oinsert(U_9264),U_9266),U_9267))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9264),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9264,tc_HOL_Obool)),U_9265),U_9267))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9264),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9264,tc_HOL_Obool)),U_9265),U_9267)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9264),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9264,tc_HOL_Obool)),U_9265),hAPP(hAPP(c_Set_Oinsert(U_9264),U_9266),U_9267)))) ) ),
    inference(variable_rename,[status(thm)],[f_2530_1]) ).

fof(f_2530_3,plain,
    ( ! [U_9275,U_9273,U_9271,U_9269] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9269),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9269,tc_HOL_Obool)),U_9271),hAPP(hAPP(c_Set_Oinsert(U_9269),U_9273),U_9275))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9269),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9269,tc_HOL_Obool)),U_9271),U_9275))) )
    & ! [U_9274,U_9272,U_9270,U_9268] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9268),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9268,tc_HOL_Obool)),U_9270),U_9274)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9268),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9268,tc_HOL_Obool)),U_9270),hAPP(hAPP(c_Set_Oinsert(U_9268),U_9272),U_9274)))) ) ),
    inference(miniscope,[status(thm)],[f_2530_2]) ).

fof(f_2530_4,plain,
    ( ! [U_9271,U_9269,U_9273,U_9275] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9269),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9269,tc_HOL_Obool)),U_9271),hAPP(hAPP(c_Set_Oinsert(U_9269),U_9273),U_9275))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9269),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9269,tc_HOL_Obool)),U_9271),U_9275))) )
    & ! [U_9270,U_9272,U_9274,U_9268] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9268),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9268,tc_HOL_Obool)),U_9270),U_9274)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9268),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9268,tc_HOL_Obool)),U_9270),hAPP(hAPP(c_Set_Oinsert(U_9268),U_9272),U_9274)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2530_3]) ).

cnf(f_2530_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9268),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9268,tc_HOL_Obool)),U_9270),U_9274)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9268),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9268,tc_HOL_Obool)),U_9270),hAPP(hAPP(c_Set_Oinsert(U_9268),U_9272),U_9274)))) ),
    inference(clausify,[status(thm)],[f_2530_4]) ).

cnf(f_2530_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9269),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9269,tc_HOL_Obool)),U_9271),hAPP(hAPP(c_Set_Oinsert(U_9269),U_9273),U_9275))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9269),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9269,tc_HOL_Obool)),U_9271),U_9275))) ),
    inference(clausify,[status(thm)],[f_2530_4]) ).

fof(f_2531_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_2531_2,plain,
    ! [U_9278,U_9277,U_9276] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9276,tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9276,tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool)),U_9277),U_9278)),c_Wellfounded_Ofinite__psubset(U_9276)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9276),U_9278))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9276,tc_HOL_Obool)),U_9277),U_9278)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9276),U_9278))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9276,tc_HOL_Obool)),U_9277),U_9278)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9276,tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9276,tc_HOL_Obool),tc_fun(U_9276,tc_HOL_Obool)),U_9277),U_9278)),c_Wellfounded_Ofinite__psubset(U_9276))) ) ),
    inference(variable_rename,[status(thm)],[f_2531_1]) ).

fof(f_2531_3,plain,
    ( ! [U_9284,U_9282,U_9280] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9280,tc_HOL_Obool),tc_fun(U_9280,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9280,tc_HOL_Obool),tc_fun(U_9280,tc_HOL_Obool)),U_9282),U_9284)),c_Wellfounded_Ofinite__psubset(U_9280)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9280),U_9284))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9280,tc_HOL_Obool)),U_9282),U_9284)) )
    & ! [U_9283,U_9281,U_9279] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9279),U_9283))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9279,tc_HOL_Obool)),U_9281),U_9283)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9279,tc_HOL_Obool),tc_fun(U_9279,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9279,tc_HOL_Obool),tc_fun(U_9279,tc_HOL_Obool)),U_9281),U_9283)),c_Wellfounded_Ofinite__psubset(U_9279))) ) ),
    inference(miniscope,[status(thm)],[f_2531_2]) ).

fof(f_2531_4,plain,
    ( ! [U_9281,U_9283,U_9279] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9279),U_9283))
        | ~ sP742(U_9281,U_9283,U_9279) )
    & ! [U_9281,U_9283,U_9279] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9279,tc_HOL_Obool)),U_9281),U_9283))
        | ~ sP742(U_9281,U_9283,U_9279) )
    & ! [U_9282,U_9280,U_9284] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9280,tc_HOL_Obool),tc_fun(U_9280,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9280,tc_HOL_Obool),tc_fun(U_9280,tc_HOL_Obool)),U_9282),U_9284)),c_Wellfounded_Ofinite__psubset(U_9280)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9280),U_9284))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9280,tc_HOL_Obool)),U_9282),U_9284)) )
    & ! [U_9281,U_9283,U_9279] :
        ( sP742(U_9281,U_9283,U_9279)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9279,tc_HOL_Obool),tc_fun(U_9279,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9279,tc_HOL_Obool),tc_fun(U_9279,tc_HOL_Obool)),U_9281),U_9283)),c_Wellfounded_Ofinite__psubset(U_9279))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP742])],[f_2531_3]) ).

cnf(f_2531_5,plain,
    ( sP742(U_9281,U_9283,U_9279)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9279,tc_HOL_Obool),tc_fun(U_9279,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9279,tc_HOL_Obool),tc_fun(U_9279,tc_HOL_Obool)),U_9281),U_9283)),c_Wellfounded_Ofinite__psubset(U_9279))) ),
    inference(clausify,[status(thm)],[f_2531_4]) ).

cnf(f_2531_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9280,tc_HOL_Obool),tc_fun(U_9280,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9280,tc_HOL_Obool),tc_fun(U_9280,tc_HOL_Obool)),U_9282),U_9284)),c_Wellfounded_Ofinite__psubset(U_9280)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9280),U_9284))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9280,tc_HOL_Obool)),U_9282),U_9284)) ),
    inference(clausify,[status(thm)],[f_2531_4]) ).

cnf(f_2531_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9279,tc_HOL_Obool)),U_9281),U_9283))
    | ~ sP742(U_9281,U_9283,U_9279) ),
    inference(clausify,[status(thm)],[f_2531_4]) ).

cnf(f_2531_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9279),U_9283))
    | ~ sP742(U_9281,U_9283,U_9279) ),
    inference(clausify,[status(thm)],[f_2531_4]) ).

fof(f_2532_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_2532_2,plain,
    ! [U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(c_Set_Oimage(U_9286,tc_Hoare__Mirabelle_Otriple(U_9288),hAPP(hAPP(c_COMBS(U_9286,tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(c_COMBS(U_9286,tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),hAPP(hAPP(c_COMBB(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),U_9286),c_Hoare__Mirabelle_Otriple_Otriple(U_9288)),U_9293)),U_9291)),U_9294)),U_9287))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(c_Set_Oimage(U_9286,tc_Hoare__Mirabelle_Otriple(U_9288),hAPP(hAPP(c_COMBS(U_9286,tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(c_COMBS(U_9286,tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),hAPP(hAPP(c_COMBB(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),U_9286),c_Hoare__Mirabelle_Otriple_Otriple(U_9288)),U_9290)),U_9291)),U_9292)),U_9287))
      | ? [U_9285] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9288),hAPP(U_9293,U_9285)),hAPP(U_9291,U_9285)),hAPP(U_9294,U_9285))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9288),tc_HOL_Obool))))
          & c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9288),hAPP(U_9290,U_9285)),hAPP(U_9291,U_9285)),hAPP(U_9292,U_9285))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9288),tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9286),U_9287)) ),
    inference(variable_rename,[status(thm)],[f_2532_1]) ).

fof(f_2532_3,plain,
    ! [U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(c_Set_Oimage(U_9286,tc_Hoare__Mirabelle_Otriple(U_9288),hAPP(hAPP(c_COMBS(U_9286,tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(c_COMBS(U_9286,tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),hAPP(hAPP(c_COMBB(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),U_9286),c_Hoare__Mirabelle_Otriple_Otriple(U_9288)),U_9293)),U_9291)),U_9294)),U_9287))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(c_Set_Oimage(U_9286,tc_Hoare__Mirabelle_Otriple(U_9288),hAPP(hAPP(c_COMBS(U_9286,tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(c_COMBS(U_9286,tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),hAPP(hAPP(c_COMBB(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),U_9286),c_Hoare__Mirabelle_Otriple_Otriple(U_9288)),U_9290)),U_9291)),U_9292)),U_9287))
      | ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9288),hAPP(U_9293,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286))),hAPP(U_9291,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286))),hAPP(U_9294,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9288),tc_HOL_Obool))))
        & c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9288),hAPP(U_9290,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286))),hAPP(U_9291,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286))),hAPP(U_9292,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9288),tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9286),U_9287)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_9285,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286))],[f_2532_2]) ).

fof(f_2532_4,plain,
    ( ! [U_9286,U_9287,U_9288,U_9289,U_9290,U_9291,U_9292,U_9293,U_9294] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9288),hAPP(U_9293,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286))),hAPP(U_9291,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286))),hAPP(U_9294,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9288),tc_HOL_Obool))))
        | ~ sP743(U_9286,U_9287,U_9288,U_9289,U_9290,U_9291,U_9292,U_9293,U_9294) )
    & ! [U_9286,U_9287,U_9288,U_9289,U_9290,U_9291,U_9292,U_9293,U_9294] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9288),hAPP(U_9290,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286))),hAPP(U_9291,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286))),hAPP(U_9292,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9288),tc_HOL_Obool))))
        | ~ sP743(U_9286,U_9287,U_9288,U_9289,U_9290,U_9291,U_9292,U_9293,U_9294) )
    & ! [U_9286,U_9287,U_9288,U_9289,U_9290,U_9291,U_9292,U_9293,U_9294] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(c_Set_Oimage(U_9286,tc_Hoare__Mirabelle_Otriple(U_9288),hAPP(hAPP(c_COMBS(U_9286,tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(c_COMBS(U_9286,tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),hAPP(hAPP(c_COMBB(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),U_9286),c_Hoare__Mirabelle_Otriple_Otriple(U_9288)),U_9293)),U_9291)),U_9294)),U_9287))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(c_Set_Oimage(U_9286,tc_Hoare__Mirabelle_Otriple(U_9288),hAPP(hAPP(c_COMBS(U_9286,tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(c_COMBS(U_9286,tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),hAPP(hAPP(c_COMBB(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),U_9286),c_Hoare__Mirabelle_Otriple_Otriple(U_9288)),U_9290)),U_9291)),U_9292)),U_9287))
        | sP743(U_9286,U_9287,U_9288,U_9289,U_9290,U_9291,U_9292,U_9293,U_9294)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9286),U_9287)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP743])],[f_2532_3]) ).

cnf(f_2532_5,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(c_Set_Oimage(U_9286,tc_Hoare__Mirabelle_Otriple(U_9288),hAPP(hAPP(c_COMBS(U_9286,tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(c_COMBS(U_9286,tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),hAPP(hAPP(c_COMBB(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),U_9286),c_Hoare__Mirabelle_Otriple_Otriple(U_9288)),U_9293)),U_9291)),U_9294)),U_9287))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(c_Set_Oimage(U_9286,tc_Hoare__Mirabelle_Otriple(U_9288),hAPP(hAPP(c_COMBS(U_9286,tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(c_COMBS(U_9286,tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),hAPP(hAPP(c_COMBB(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9288,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9288))),U_9286),c_Hoare__Mirabelle_Otriple_Otriple(U_9288)),U_9290)),U_9291)),U_9292)),U_9287))
    | sP743(U_9286,U_9287,U_9288,U_9289,U_9290,U_9291,U_9292,U_9293,U_9294)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9286),U_9287)) ),
    inference(clausify,[status(thm)],[f_2532_4]) ).

cnf(f_2532_6,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9288),hAPP(U_9290,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286))),hAPP(U_9291,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286))),hAPP(U_9292,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9288),tc_HOL_Obool))))
    | ~ sP743(U_9286,U_9287,U_9288,U_9289,U_9290,U_9291,U_9292,U_9293,U_9294) ),
    inference(clausify,[status(thm)],[f_2532_4]) ).

cnf(f_2532_7,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9288,U_9289,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9288)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9288),hAPP(U_9293,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286))),hAPP(U_9291,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286))),hAPP(U_9294,sK140(U_9294,U_9293,U_9292,U_9291,U_9290,U_9289,U_9288,U_9287,U_9286)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9288),tc_HOL_Obool))))
    | ~ sP743(U_9286,U_9287,U_9288,U_9289,U_9290,U_9291,U_9292,U_9293,U_9294) ),
    inference(clausify,[status(thm)],[f_2532_4]) ).

fof(f_2533_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_2533_2,plain,
    ! [U_9299,U_9298,U_9297,U_9296,U_9295] :
      ( ( ( hAPP(U_9297,U_9298) = hAPP(hAPP(U_9296,U_9299),hAPP(U_9297,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9295,tc_HOL_Obool)),U_9298),hAPP(hAPP(c_Set_Oinsert(U_9295),U_9299),c_Orderings_Obot__class_Obot(tc_fun(U_9295,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9295,tc_HOL_Obool)),U_9298),hAPP(hAPP(c_Set_Oinsert(U_9295),U_9299),c_Orderings_Obot__class_Obot(tc_fun(U_9295,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9295,tc_HOL_Obool)) )
        & ( hAPP(U_9297,U_9298) = U_9299
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9295,tc_HOL_Obool)),U_9298),hAPP(hAPP(c_Set_Oinsert(U_9295),U_9299),c_Orderings_Obot__class_Obot(tc_fun(U_9295,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9295,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9295),U_9299),U_9298))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9295),U_9298))
      | ~ c_Finite__Set_Ofolding__one(U_9295,U_9296,U_9297) ),
    inference(variable_rename,[status(thm)],[f_2533_1]) ).

fof(f_2533_3,plain,
    ( ! [U_9296,U_9298,U_9297,U_9295,U_9299] :
        ( hAPP(U_9297,U_9298) = hAPP(hAPP(U_9296,U_9299),hAPP(U_9297,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9295,tc_HOL_Obool)),U_9298),hAPP(hAPP(c_Set_Oinsert(U_9295),U_9299),c_Orderings_Obot__class_Obot(tc_fun(U_9295,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9295,tc_HOL_Obool)),U_9298),hAPP(hAPP(c_Set_Oinsert(U_9295),U_9299),c_Orderings_Obot__class_Obot(tc_fun(U_9295,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9295,tc_HOL_Obool))
        | ~ sP744(U_9296,U_9298,U_9297,U_9295,U_9299) )
    & ! [U_9296,U_9298,U_9297,U_9295,U_9299] :
        ( hAPP(U_9297,U_9298) = U_9299
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9295,tc_HOL_Obool)),U_9298),hAPP(hAPP(c_Set_Oinsert(U_9295),U_9299),c_Orderings_Obot__class_Obot(tc_fun(U_9295,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9295,tc_HOL_Obool))
        | ~ sP744(U_9296,U_9298,U_9297,U_9295,U_9299) )
    & ! [U_9296,U_9298,U_9297,U_9295,U_9299] :
        ( sP744(U_9296,U_9298,U_9297,U_9295,U_9299)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9295),U_9299),U_9298))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9295),U_9298))
        | ~ c_Finite__Set_Ofolding__one(U_9295,U_9296,U_9297) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP744])],[f_2533_2]) ).

cnf(f_2533_4,plain,
    ( sP744(U_9296,U_9298,U_9297,U_9295,U_9299)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9295),U_9299),U_9298))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9295),U_9298))
    | ~ c_Finite__Set_Ofolding__one(U_9295,U_9296,U_9297) ),
    inference(clausify,[status(thm)],[f_2533_3]) ).

cnf(f_2533_5,plain,
    ( hAPP(U_9297,U_9298) = U_9299
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9295,tc_HOL_Obool)),U_9298),hAPP(hAPP(c_Set_Oinsert(U_9295),U_9299),c_Orderings_Obot__class_Obot(tc_fun(U_9295,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9295,tc_HOL_Obool))
    | ~ sP744(U_9296,U_9298,U_9297,U_9295,U_9299) ),
    inference(clausify,[status(thm)],[f_2533_3]) ).

cnf(f_2533_6,plain,
    ( hAPP(U_9297,U_9298) = hAPP(hAPP(U_9296,U_9299),hAPP(U_9297,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9295,tc_HOL_Obool)),U_9298),hAPP(hAPP(c_Set_Oinsert(U_9295),U_9299),c_Orderings_Obot__class_Obot(tc_fun(U_9295,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9295,tc_HOL_Obool)),U_9298),hAPP(hAPP(c_Set_Oinsert(U_9295),U_9299),c_Orderings_Obot__class_Obot(tc_fun(U_9295,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9295,tc_HOL_Obool))
    | ~ sP744(U_9296,U_9298,U_9297,U_9295,U_9299) ),
    inference(clausify,[status(thm)],[f_2533_3]) ).

fof(f_2534_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_2534_2,plain,
    ! [U_9307,U_9306,U_9305,U_9304,U_9303,U_9302,U_9301,U_9300] :
      ( hAPP(U_9305,U_9306) = hAPP(hAPP(U_9302,hAPP(U_9304,U_9307)),hAPP(U_9305,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9301,tc_HOL_Obool)),U_9306),hAPP(hAPP(c_Set_Oinsert(U_9301),U_9307),c_Orderings_Obot__class_Obot(tc_fun(U_9301,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9301),U_9307),U_9306))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9301),U_9306))
      | ~ c_Finite__Set_Ofolding__image__simple(U_9300,U_9301,U_9302,U_9303,U_9304,U_9305) ),
    inference(variable_rename,[status(thm)],[f_2534_1]) ).

fof(f_2534_3,plain,
    ! [U_9307,U_9306,U_9305,U_9304,U_9303,U_9302,U_9301] :
      ( ! [U_9300] : ~ c_Finite__Set_Ofolding__image__simple(U_9300,U_9301,U_9302,U_9303,U_9304,U_9305)
      | hAPP(U_9305,U_9306) = hAPP(hAPP(U_9302,hAPP(U_9304,U_9307)),hAPP(U_9305,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9301,tc_HOL_Obool)),U_9306),hAPP(hAPP(c_Set_Oinsert(U_9301),U_9307),c_Orderings_Obot__class_Obot(tc_fun(U_9301,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9301),U_9307),U_9306))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9301),U_9306)) ),
    inference(miniscope,[status(thm)],[f_2534_2]) ).

fof(f_2534_4,plain,
    ! [U_9302,U_9306,U_9304,U_9303,U_9300,U_9301,U_9305,U_9307] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_9300,U_9301,U_9302,U_9303,U_9304,U_9305)
      | hAPP(U_9305,U_9306) = hAPP(hAPP(U_9302,hAPP(U_9304,U_9307)),hAPP(U_9305,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9301,tc_HOL_Obool)),U_9306),hAPP(hAPP(c_Set_Oinsert(U_9301),U_9307),c_Orderings_Obot__class_Obot(tc_fun(U_9301,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9301),U_9307),U_9306))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9301),U_9306)) ),
    inference(definitional_conversion,[status(esa)],[f_2534_3]) ).

cnf(f_2534_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_9300,U_9301,U_9302,U_9303,U_9304,U_9305)
    | hAPP(U_9305,U_9306) = hAPP(hAPP(U_9302,hAPP(U_9304,U_9307)),hAPP(U_9305,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9301,tc_HOL_Obool)),U_9306),hAPP(hAPP(c_Set_Oinsert(U_9301),U_9307),c_Orderings_Obot__class_Obot(tc_fun(U_9301,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9301),U_9307),U_9306))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9301),U_9306)) ),
    inference(clausify,[status(thm)],[f_2534_4]) ).

fof(f_2535_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_2535_2,plain,
    ! [U_9313,U_9312,U_9311,U_9310,U_9309,U_9308] :
      ( hAPP(U_9313,c_Orderings_Obot__class_Obot(tc_fun(U_9309,tc_HOL_Obool))) = U_9311
      | ~ c_Finite__Set_Ofolding__image__simple(U_9308,U_9309,U_9310,U_9311,U_9312,U_9313) ),
    inference(variable_rename,[status(thm)],[f_2535_1]) ).

fof(f_2535_3,plain,
    ! [U_9313,U_9312,U_9311,U_9310,U_9309] :
      ( ! [U_9308] : ~ c_Finite__Set_Ofolding__image__simple(U_9308,U_9309,U_9310,U_9311,U_9312,U_9313)
      | hAPP(U_9313,c_Orderings_Obot__class_Obot(tc_fun(U_9309,tc_HOL_Obool))) = U_9311 ),
    inference(miniscope,[status(thm)],[f_2535_2]) ).

fof(f_2535_4,plain,
    ! [U_9313,U_9308,U_9311,U_9312,U_9310,U_9309] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_9308,U_9309,U_9310,U_9311,U_9312,U_9313)
      | hAPP(U_9313,c_Orderings_Obot__class_Obot(tc_fun(U_9309,tc_HOL_Obool))) = U_9311 ),
    inference(definitional_conversion,[status(esa)],[f_2535_3]) ).

cnf(f_2535_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_9308,U_9309,U_9310,U_9311,U_9312,U_9313)
    | hAPP(U_9313,c_Orderings_Obot__class_Obot(tc_fun(U_9309,tc_HOL_Obool))) = U_9311 ),
    inference(clausify,[status(thm)],[f_2535_4]) ).

fof(f_2536_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_2536_2,plain,
    ! [U_9317,U_9316,U_9315,U_9314] :
      ( hAPP(U_9316,hAPP(hAPP(c_Set_Oinsert(U_9314),U_9317),c_Orderings_Obot__class_Obot(tc_fun(U_9314,tc_HOL_Obool)))) = U_9317
      | ~ c_Finite__Set_Ofolding__one(U_9314,U_9315,U_9316) ),
    inference(variable_rename,[status(thm)],[f_2536_1]) ).

fof(f_2536_3,plain,
    ! [U_9314,U_9315,U_9316,U_9317] :
      ( hAPP(U_9316,hAPP(hAPP(c_Set_Oinsert(U_9314),U_9317),c_Orderings_Obot__class_Obot(tc_fun(U_9314,tc_HOL_Obool)))) = U_9317
      | ~ c_Finite__Set_Ofolding__one(U_9314,U_9315,U_9316) ),
    inference(definitional_conversion,[status(esa)],[f_2536_2]) ).

cnf(f_2536_4,plain,
    ( hAPP(U_9316,hAPP(hAPP(c_Set_Oinsert(U_9314),U_9317),c_Orderings_Obot__class_Obot(tc_fun(U_9314,tc_HOL_Obool)))) = U_9317
    | ~ c_Finite__Set_Ofolding__one(U_9314,U_9315,U_9316) ),
    inference(clausify,[status(thm)],[f_2536_3]) ).

fof(f_2537_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_2537_2,plain,
    ! [U_9325,U_9324,U_9323,U_9322,U_9321,U_9320,U_9319,U_9318] :
      ( hAPP(U_9323,hAPP(hAPP(c_Set_Oinsert(U_9319),U_9325),U_9324)) = hAPP(hAPP(U_9320,hAPP(U_9322,U_9325)),hAPP(U_9323,U_9324))
      | hBOOL(hAPP(hAPP(c_member(U_9319),U_9325),U_9324))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9319),U_9324))
      | ~ c_Finite__Set_Ofolding__image__simple(U_9318,U_9319,U_9320,U_9321,U_9322,U_9323) ),
    inference(variable_rename,[status(thm)],[f_2537_1]) ).

fof(f_2537_3,plain,
    ! [U_9325,U_9324,U_9323,U_9322,U_9321,U_9320,U_9319] :
      ( ! [U_9318] : ~ c_Finite__Set_Ofolding__image__simple(U_9318,U_9319,U_9320,U_9321,U_9322,U_9323)
      | hAPP(U_9323,hAPP(hAPP(c_Set_Oinsert(U_9319),U_9325),U_9324)) = hAPP(hAPP(U_9320,hAPP(U_9322,U_9325)),hAPP(U_9323,U_9324))
      | hBOOL(hAPP(hAPP(c_member(U_9319),U_9325),U_9324))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9319),U_9324)) ),
    inference(miniscope,[status(thm)],[f_2537_2]) ).

fof(f_2537_4,plain,
    ! [U_9318,U_9319,U_9320,U_9321,U_9322,U_9323,U_9324,U_9325] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_9318,U_9319,U_9320,U_9321,U_9322,U_9323)
      | hAPP(U_9323,hAPP(hAPP(c_Set_Oinsert(U_9319),U_9325),U_9324)) = hAPP(hAPP(U_9320,hAPP(U_9322,U_9325)),hAPP(U_9323,U_9324))
      | hBOOL(hAPP(hAPP(c_member(U_9319),U_9325),U_9324))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9319),U_9324)) ),
    inference(definitional_conversion,[status(esa)],[f_2537_3]) ).

cnf(f_2537_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_9318,U_9319,U_9320,U_9321,U_9322,U_9323)
    | hAPP(U_9323,hAPP(hAPP(c_Set_Oinsert(U_9319),U_9325),U_9324)) = hAPP(hAPP(U_9320,hAPP(U_9322,U_9325)),hAPP(U_9323,U_9324))
    | hBOOL(hAPP(hAPP(c_member(U_9319),U_9325),U_9324))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9319),U_9324)) ),
    inference(clausify,[status(thm)],[f_2537_4]) ).

fof(f_2538_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_2538_2,plain,
    ! [U_9330,U_9329,U_9328,U_9327,U_9326] :
      ( hAPP(U_9328,hAPP(hAPP(c_Set_Oinsert(U_9326),U_9330),U_9329)) = hAPP(hAPP(U_9327,U_9330),hAPP(U_9328,U_9329))
      | U_9329 = c_Orderings_Obot__class_Obot(tc_fun(U_9326,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9326),U_9330),U_9329))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9326),U_9329))
      | ~ c_Finite__Set_Ofolding__one(U_9326,U_9327,U_9328) ),
    inference(variable_rename,[status(thm)],[f_2538_1]) ).

fof(f_2538_3,plain,
    ! [U_9326,U_9327,U_9328,U_9329,U_9330] :
      ( hAPP(U_9328,hAPP(hAPP(c_Set_Oinsert(U_9326),U_9330),U_9329)) = hAPP(hAPP(U_9327,U_9330),hAPP(U_9328,U_9329))
      | U_9329 = c_Orderings_Obot__class_Obot(tc_fun(U_9326,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9326),U_9330),U_9329))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9326),U_9329))
      | ~ c_Finite__Set_Ofolding__one(U_9326,U_9327,U_9328) ),
    inference(definitional_conversion,[status(esa)],[f_2538_2]) ).

cnf(f_2538_4,plain,
    ( hAPP(U_9328,hAPP(hAPP(c_Set_Oinsert(U_9326),U_9330),U_9329)) = hAPP(hAPP(U_9327,U_9330),hAPP(U_9328,U_9329))
    | U_9329 = c_Orderings_Obot__class_Obot(tc_fun(U_9326,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9326),U_9330),U_9329))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9326),U_9329))
    | ~ c_Finite__Set_Ofolding__one(U_9326,U_9327,U_9328) ),
    inference(clausify,[status(thm)],[f_2538_3]) ).

fof(f_2539_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_2539_2,plain,
    ! [U_9335,U_9334,U_9333,U_9332,U_9331] :
      ( ( ( hAPP(U_9333,hAPP(hAPP(c_Set_Oinsert(U_9331),U_9335),U_9334)) = hAPP(hAPP(U_9332,U_9335),hAPP(U_9333,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9331,tc_HOL_Obool)),U_9334),hAPP(hAPP(c_Set_Oinsert(U_9331),U_9335),c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9331,tc_HOL_Obool)),U_9334),hAPP(hAPP(c_Set_Oinsert(U_9331),U_9335),c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool)) )
        & ( hAPP(U_9333,hAPP(hAPP(c_Set_Oinsert(U_9331),U_9335),U_9334)) = U_9335
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9331,tc_HOL_Obool)),U_9334),hAPP(hAPP(c_Set_Oinsert(U_9331),U_9335),c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9331),U_9334))
      | ~ c_Finite__Set_Ofolding__one(U_9331,U_9332,U_9333) ),
    inference(variable_rename,[status(thm)],[f_2539_1]) ).

fof(f_2539_3,plain,
    ( ! [U_9331,U_9332,U_9333,U_9334,U_9335] :
        ( hAPP(U_9333,hAPP(hAPP(c_Set_Oinsert(U_9331),U_9335),U_9334)) = hAPP(hAPP(U_9332,U_9335),hAPP(U_9333,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9331,tc_HOL_Obool)),U_9334),hAPP(hAPP(c_Set_Oinsert(U_9331),U_9335),c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9331,tc_HOL_Obool)),U_9334),hAPP(hAPP(c_Set_Oinsert(U_9331),U_9335),c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool))
        | ~ sP745(U_9331,U_9332,U_9333,U_9334,U_9335) )
    & ! [U_9331,U_9332,U_9333,U_9334,U_9335] :
        ( hAPP(U_9333,hAPP(hAPP(c_Set_Oinsert(U_9331),U_9335),U_9334)) = U_9335
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9331,tc_HOL_Obool)),U_9334),hAPP(hAPP(c_Set_Oinsert(U_9331),U_9335),c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool))
        | ~ sP745(U_9331,U_9332,U_9333,U_9334,U_9335) )
    & ! [U_9331,U_9332,U_9333,U_9334,U_9335] :
        ( sP745(U_9331,U_9332,U_9333,U_9334,U_9335)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9331),U_9334))
        | ~ c_Finite__Set_Ofolding__one(U_9331,U_9332,U_9333) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP745])],[f_2539_2]) ).

cnf(f_2539_4,plain,
    ( sP745(U_9331,U_9332,U_9333,U_9334,U_9335)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9331),U_9334))
    | ~ c_Finite__Set_Ofolding__one(U_9331,U_9332,U_9333) ),
    inference(clausify,[status(thm)],[f_2539_3]) ).

cnf(f_2539_5,plain,
    ( hAPP(U_9333,hAPP(hAPP(c_Set_Oinsert(U_9331),U_9335),U_9334)) = U_9335
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9331,tc_HOL_Obool)),U_9334),hAPP(hAPP(c_Set_Oinsert(U_9331),U_9335),c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool))
    | ~ sP745(U_9331,U_9332,U_9333,U_9334,U_9335) ),
    inference(clausify,[status(thm)],[f_2539_3]) ).

cnf(f_2539_6,plain,
    ( hAPP(U_9333,hAPP(hAPP(c_Set_Oinsert(U_9331),U_9335),U_9334)) = hAPP(hAPP(U_9332,U_9335),hAPP(U_9333,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9331,tc_HOL_Obool)),U_9334),hAPP(hAPP(c_Set_Oinsert(U_9331),U_9335),c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9331,tc_HOL_Obool)),U_9334),hAPP(hAPP(c_Set_Oinsert(U_9331),U_9335),c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9331,tc_HOL_Obool))
    | ~ sP745(U_9331,U_9332,U_9333,U_9334,U_9335) ),
    inference(clausify,[status(thm)],[f_2539_3]) ).

fof(f_2540_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_2540_2,plain,
    ! [U_9343,U_9342,U_9341,U_9340,U_9339,U_9338,U_9337,U_9336] :
      ( hAPP(U_9341,hAPP(hAPP(c_Set_Oinsert(U_9337),U_9343),U_9342)) = hAPP(hAPP(U_9338,hAPP(U_9340,U_9343)),hAPP(U_9341,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9337,tc_HOL_Obool)),U_9342),hAPP(hAPP(c_Set_Oinsert(U_9337),U_9343),c_Orderings_Obot__class_Obot(tc_fun(U_9337,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9337),U_9342))
      | ~ c_Finite__Set_Ofolding__image__simple(U_9336,U_9337,U_9338,U_9339,U_9340,U_9341) ),
    inference(variable_rename,[status(thm)],[f_2540_1]) ).

fof(f_2540_3,plain,
    ! [U_9343,U_9342,U_9341,U_9340,U_9339,U_9338,U_9337] :
      ( ! [U_9336] : ~ c_Finite__Set_Ofolding__image__simple(U_9336,U_9337,U_9338,U_9339,U_9340,U_9341)
      | hAPP(U_9341,hAPP(hAPP(c_Set_Oinsert(U_9337),U_9343),U_9342)) = hAPP(hAPP(U_9338,hAPP(U_9340,U_9343)),hAPP(U_9341,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9337,tc_HOL_Obool)),U_9342),hAPP(hAPP(c_Set_Oinsert(U_9337),U_9343),c_Orderings_Obot__class_Obot(tc_fun(U_9337,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9337),U_9342)) ),
    inference(miniscope,[status(thm)],[f_2540_2]) ).

fof(f_2540_4,plain,
    ! [U_9340,U_9339,U_9343,U_9342,U_9341,U_9336,U_9337,U_9338] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_9336,U_9337,U_9338,U_9339,U_9340,U_9341)
      | hAPP(U_9341,hAPP(hAPP(c_Set_Oinsert(U_9337),U_9343),U_9342)) = hAPP(hAPP(U_9338,hAPP(U_9340,U_9343)),hAPP(U_9341,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9337,tc_HOL_Obool)),U_9342),hAPP(hAPP(c_Set_Oinsert(U_9337),U_9343),c_Orderings_Obot__class_Obot(tc_fun(U_9337,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9337),U_9342)) ),
    inference(definitional_conversion,[status(esa)],[f_2540_3]) ).

cnf(f_2540_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_9336,U_9337,U_9338,U_9339,U_9340,U_9341)
    | hAPP(U_9341,hAPP(hAPP(c_Set_Oinsert(U_9337),U_9343),U_9342)) = hAPP(hAPP(U_9338,hAPP(U_9340,U_9343)),hAPP(U_9341,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9337,tc_HOL_Obool)),U_9342),hAPP(hAPP(c_Set_Oinsert(U_9337),U_9343),c_Orderings_Obot__class_Obot(tc_fun(U_9337,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9337),U_9342)) ),
    inference(clausify,[status(thm)],[f_2540_4]) ).

fof(f_2541_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_2541_2,plain,
    ! [U_9348] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9348))
        | ! [U_9347] :
          ? [U_9346] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9346),U_9347))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9346),U_9348)) ) )
      & ( ? [U_9345] :
          ! [U_9344] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9344),U_9345))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9344),U_9348)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9348)) ) ),
    inference(variable_rename,[status(thm)],[f_2541_1]) ).

fof(f_2541_3,plain,
    ( ! [U_9350] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9350))
        | ! [U_9347] :
          ? [U_9346] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9346),U_9347))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9346),U_9350)) ) )
    & ! [U_9349] :
        ( ? [U_9345] :
          ! [U_9344] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9344),U_9345))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9344),U_9349)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9349)) ) ),
    inference(miniscope,[status(thm)],[f_2541_2]) ).

fof(f_2541_4,plain,
    ( ! [U_9350] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9350))
        | ! [U_9347] :
          ? [U_9346] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9346),U_9347))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9346),U_9350)) ) )
    & ! [U_9349] :
        ( ! [U_9344] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9344),sK141(U_9349)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9344),U_9349)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9349)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_9345,sK141(U_9349))],[f_2541_3]) ).

fof(f_2541_5,plain,
    ( ! [U_9350] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9350))
        | ! [U_9347] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK142(U_9350,U_9347)),U_9347))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK142(U_9350,U_9347)),U_9350)) ) )
    & ! [U_9349] :
        ( ! [U_9344] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9344),sK141(U_9349)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9344),U_9349)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9349)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_9346,sK142(U_9350,U_9347))],[f_2541_4]) ).

fof(f_2541_6,plain,
    ( ! [U_9347,U_9350] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK142(U_9350,U_9347)),U_9347))
        | ~ sP746(U_9347,U_9350) )
    & ! [U_9347,U_9350] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK142(U_9350,U_9347)),U_9350))
        | ~ sP746(U_9347,U_9350) )
    & ! [U_9347,U_9350] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9350))
        | sP746(U_9347,U_9350) )
    & ! [U_9344,U_9349] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9344),sK141(U_9349)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9344),U_9349))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9349)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP746])],[f_2541_5]) ).

cnf(f_2541_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9344),sK141(U_9349)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9344),U_9349))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9349)) ),
    inference(clausify,[status(thm)],[f_2541_6]) ).

cnf(f_2541_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9350))
    | sP746(U_9347,U_9350) ),
    inference(clausify,[status(thm)],[f_2541_6]) ).

cnf(f_2541_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK142(U_9350,U_9347)),U_9350))
    | ~ sP746(U_9347,U_9350) ),
    inference(clausify,[status(thm)],[f_2541_6]) ).

cnf(f_2541_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK142(U_9350,U_9347)),U_9347))
    | ~ sP746(U_9347,U_9350) ),
    inference(clausify,[status(thm)],[f_2541_6]) ).

fof(f_2542_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_2542_2,plain,
    ! [U_9355] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9355))
        | ! [U_9354] :
          ? [U_9353] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9353),U_9354))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9353),U_9355)) ) )
      & ( ? [U_9352] :
          ! [U_9351] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9351),U_9352))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9351),U_9355)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9355)) ) ),
    inference(variable_rename,[status(thm)],[f_2542_1]) ).

fof(f_2542_3,plain,
    ( ! [U_9357] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9357))
        | ! [U_9354] :
          ? [U_9353] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9353),U_9354))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9353),U_9357)) ) )
    & ! [U_9356] :
        ( ? [U_9352] :
          ! [U_9351] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9351),U_9352))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9351),U_9356)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9356)) ) ),
    inference(miniscope,[status(thm)],[f_2542_2]) ).

fof(f_2542_4,plain,
    ( ! [U_9357] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9357))
        | ! [U_9354] :
          ? [U_9353] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9353),U_9354))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9353),U_9357)) ) )
    & ! [U_9356] :
        ( ! [U_9351] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9351),sK143(U_9356)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9351),U_9356)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9356)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_9352,sK143(U_9356))],[f_2542_3]) ).

fof(f_2542_5,plain,
    ( ! [U_9357] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9357))
        | ! [U_9354] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK144(U_9357,U_9354)),U_9354))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK144(U_9357,U_9354)),U_9357)) ) )
    & ! [U_9356] :
        ( ! [U_9351] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9351),sK143(U_9356)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9351),U_9356)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9356)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_9353,sK144(U_9357,U_9354))],[f_2542_4]) ).

fof(f_2542_6,plain,
    ( ! [U_9354,U_9357] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK144(U_9357,U_9354)),U_9354))
        | ~ sP747(U_9354,U_9357) )
    & ! [U_9354,U_9357] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK144(U_9357,U_9354)),U_9357))
        | ~ sP747(U_9354,U_9357) )
    & ! [U_9354,U_9357] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9357))
        | sP747(U_9354,U_9357) )
    & ! [U_9351,U_9356] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9351),sK143(U_9356)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9351),U_9356))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9356)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP747])],[f_2542_5]) ).

cnf(f_2542_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9351),sK143(U_9356)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9351),U_9356))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9356)) ),
    inference(clausify,[status(thm)],[f_2542_6]) ).

cnf(f_2542_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9357))
    | sP747(U_9354,U_9357) ),
    inference(clausify,[status(thm)],[f_2542_6]) ).

cnf(f_2542_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK144(U_9357,U_9354)),U_9357))
    | ~ sP747(U_9354,U_9357) ),
    inference(clausify,[status(thm)],[f_2542_6]) ).

cnf(f_2542_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK144(U_9357,U_9354)),U_9354))
    | ~ sP747(U_9354,U_9357) ),
    inference(clausify,[status(thm)],[f_2542_6]) ).

fof(f_2543_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_2543_2,plain,
    ! [U_9362,U_9361,U_9360,U_9359,U_9358] :
      ( ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9358),hAPP(hAPP(c_Set_Oinsert(U_9358),U_9361),c_Orderings_Obot__class_Obot(tc_fun(U_9358,tc_HOL_Obool)))),U_9360) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9358),hAPP(hAPP(c_Set_Oinsert(U_9358),U_9362),c_Orderings_Obot__class_Obot(tc_fun(U_9358,tc_HOL_Obool)))),U_9360)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9358,U_9358)),hAPP(hAPP(c_Product__Type_OPair(U_9358,U_9358),U_9361),U_9362)),U_9360)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9358,U_9358)),hAPP(hAPP(c_Product__Type_OPair(U_9358,U_9358),U_9361),U_9362)),U_9360))
          | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9358),hAPP(hAPP(c_Set_Oinsert(U_9358),U_9361),c_Orderings_Obot__class_Obot(tc_fun(U_9358,tc_HOL_Obool)))),U_9360) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9358),hAPP(hAPP(c_Set_Oinsert(U_9358),U_9362),c_Orderings_Obot__class_Obot(tc_fun(U_9358,tc_HOL_Obool)))),U_9360) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9358),U_9362),U_9359))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9358),U_9361),U_9359))
      | ~ c_Equiv__Relations_Oequiv(U_9358,U_9359,U_9360) ),
    inference(variable_rename,[status(thm)],[f_2543_1]) ).

fof(f_2543_3,plain,
    ( ! [U_9358,U_9361,U_9360,U_9362] :
        ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9358),hAPP(hAPP(c_Set_Oinsert(U_9358),U_9361),c_Orderings_Obot__class_Obot(tc_fun(U_9358,tc_HOL_Obool)))),U_9360) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9358),hAPP(hAPP(c_Set_Oinsert(U_9358),U_9362),c_Orderings_Obot__class_Obot(tc_fun(U_9358,tc_HOL_Obool)))),U_9360)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9358,U_9358)),hAPP(hAPP(c_Product__Type_OPair(U_9358,U_9358),U_9361),U_9362)),U_9360))
        | ~ sP748(U_9358,U_9361,U_9360,U_9362) )
    & ! [U_9358,U_9361,U_9360,U_9362] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9358,U_9358)),hAPP(hAPP(c_Product__Type_OPair(U_9358,U_9358),U_9361),U_9362)),U_9360))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9358),hAPP(hAPP(c_Set_Oinsert(U_9358),U_9361),c_Orderings_Obot__class_Obot(tc_fun(U_9358,tc_HOL_Obool)))),U_9360) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9358),hAPP(hAPP(c_Set_Oinsert(U_9358),U_9362),c_Orderings_Obot__class_Obot(tc_fun(U_9358,tc_HOL_Obool)))),U_9360)
        | ~ sP748(U_9358,U_9361,U_9360,U_9362) )
    & ! [U_9358,U_9361,U_9359,U_9360,U_9362] :
        ( sP748(U_9358,U_9361,U_9360,U_9362)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9358),U_9362),U_9359))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9358),U_9361),U_9359))
        | ~ c_Equiv__Relations_Oequiv(U_9358,U_9359,U_9360) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP748])],[f_2543_2]) ).

cnf(f_2543_4,plain,
    ( sP748(U_9358,U_9361,U_9360,U_9362)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9358),U_9362),U_9359))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9358),U_9361),U_9359))
    | ~ c_Equiv__Relations_Oequiv(U_9358,U_9359,U_9360) ),
    inference(clausify,[status(thm)],[f_2543_3]) ).

cnf(f_2543_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9358,U_9358)),hAPP(hAPP(c_Product__Type_OPair(U_9358,U_9358),U_9361),U_9362)),U_9360))
    | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9358),hAPP(hAPP(c_Set_Oinsert(U_9358),U_9361),c_Orderings_Obot__class_Obot(tc_fun(U_9358,tc_HOL_Obool)))),U_9360) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9358),hAPP(hAPP(c_Set_Oinsert(U_9358),U_9362),c_Orderings_Obot__class_Obot(tc_fun(U_9358,tc_HOL_Obool)))),U_9360)
    | ~ sP748(U_9358,U_9361,U_9360,U_9362) ),
    inference(clausify,[status(thm)],[f_2543_3]) ).

cnf(f_2543_6,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9358),hAPP(hAPP(c_Set_Oinsert(U_9358),U_9361),c_Orderings_Obot__class_Obot(tc_fun(U_9358,tc_HOL_Obool)))),U_9360) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9358),hAPP(hAPP(c_Set_Oinsert(U_9358),U_9362),c_Orderings_Obot__class_Obot(tc_fun(U_9358,tc_HOL_Obool)))),U_9360)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9358,U_9358)),hAPP(hAPP(c_Product__Type_OPair(U_9358,U_9358),U_9361),U_9362)),U_9360))
    | ~ sP748(U_9358,U_9361,U_9360,U_9362) ),
    inference(clausify,[status(thm)],[f_2543_3]) ).

fof(f_2544_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_2544_2,plain,
    ! [U_9368,U_9367,U_9366,U_9365,U_9364,U_9363] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9363,U_9363)),hAPP(hAPP(c_Product__Type_OPair(U_9363,U_9363),U_9367),U_9368)),U_9365))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9363),U_9366),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9363,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9363,U_9363,U_9365),hAPP(hAPP(c_Set_Oinsert(U_9363),U_9367),c_Orderings_Obot__class_Obot(tc_fun(U_9363,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_9363,U_9363,U_9365),hAPP(hAPP(c_Set_Oinsert(U_9363),U_9368),c_Orderings_Obot__class_Obot(tc_fun(U_9363,tc_HOL_Obool)))))))
      | ~ c_Equiv__Relations_Oequiv(U_9363,U_9364,U_9365) ),
    inference(variable_rename,[status(thm)],[f_2544_1]) ).

fof(f_2544_3,plain,
    ! [U_9367,U_9363,U_9364,U_9366,U_9365,U_9368] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9363,U_9363)),hAPP(hAPP(c_Product__Type_OPair(U_9363,U_9363),U_9367),U_9368)),U_9365))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9363),U_9366),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9363,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9363,U_9363,U_9365),hAPP(hAPP(c_Set_Oinsert(U_9363),U_9367),c_Orderings_Obot__class_Obot(tc_fun(U_9363,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_9363,U_9363,U_9365),hAPP(hAPP(c_Set_Oinsert(U_9363),U_9368),c_Orderings_Obot__class_Obot(tc_fun(U_9363,tc_HOL_Obool)))))))
      | ~ c_Equiv__Relations_Oequiv(U_9363,U_9364,U_9365) ),
    inference(definitional_conversion,[status(esa)],[f_2544_2]) ).

cnf(f_2544_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9363,U_9363)),hAPP(hAPP(c_Product__Type_OPair(U_9363,U_9363),U_9367),U_9368)),U_9365))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9363),U_9366),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9363,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9363,U_9363,U_9365),hAPP(hAPP(c_Set_Oinsert(U_9363),U_9367),c_Orderings_Obot__class_Obot(tc_fun(U_9363,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_9363,U_9363,U_9365),hAPP(hAPP(c_Set_Oinsert(U_9363),U_9368),c_Orderings_Obot__class_Obot(tc_fun(U_9363,tc_HOL_Obool)))))))
    | ~ c_Equiv__Relations_Oequiv(U_9363,U_9364,U_9365) ),
    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(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_2545_2,plain,
    ! [U_9372,U_9371,U_9370,U_9369] :
      ( ( hBOOL(hAPP(U_9371,U_9372))
        & hBOOL(hAPP(U_9370,U_9372)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9369,tc_HOL_Obool)),U_9370),U_9371),U_9372)) ),
    inference(variable_rename,[status(thm)],[f_2545_1]) ).

fof(f_2545_3,plain,
    ! [U_9372,U_9371,U_9370] :
      ( ! [U_9369] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9369,tc_HOL_Obool)),U_9370),U_9371),U_9372))
      | ( hBOOL(hAPP(U_9371,U_9372))
        & hBOOL(hAPP(U_9370,U_9372)) ) ),
    inference(miniscope,[status(thm)],[f_2545_2]) ).

fof(f_2545_4,plain,
    ( ! [U_9370,U_9371,U_9372] :
        ( hBOOL(hAPP(U_9371,U_9372))
        | ~ sP749(U_9370,U_9371,U_9372) )
    & ! [U_9370,U_9371,U_9372] :
        ( hBOOL(hAPP(U_9370,U_9372))
        | ~ sP749(U_9370,U_9371,U_9372) )
    & ! [U_9369,U_9370,U_9371,U_9372] :
        ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9369,tc_HOL_Obool)),U_9370),U_9371),U_9372))
        | sP749(U_9370,U_9371,U_9372) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP749])],[f_2545_3]) ).

cnf(f_2545_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9369,tc_HOL_Obool)),U_9370),U_9371),U_9372))
    | sP749(U_9370,U_9371,U_9372) ),
    inference(clausify,[status(thm)],[f_2545_4]) ).

cnf(f_2545_6,plain,
    ( hBOOL(hAPP(U_9370,U_9372))
    | ~ sP749(U_9370,U_9371,U_9372) ),
    inference(clausify,[status(thm)],[f_2545_4]) ).

cnf(f_2545_7,plain,
    ( hBOOL(hAPP(U_9371,U_9372))
    | ~ sP749(U_9370,U_9371,U_9372) ),
    inference(clausify,[status(thm)],[f_2545_4]) ).

fof(f_2546_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_2546_2,plain,
    ! [U_9376,U_9375,U_9374,U_9373] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9376,tc_HOL_Obool)),U_9373),U_9375),U_9374))
      | ~ hBOOL(hAPP(U_9375,U_9374))
      | ~ hBOOL(hAPP(U_9373,U_9374)) ),
    inference(variable_rename,[status(thm)],[f_2546_1]) ).

fof(f_2546_3,plain,
    ! [U_9374,U_9373,U_9375,U_9376] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9376,tc_HOL_Obool)),U_9373),U_9375),U_9374))
      | ~ hBOOL(hAPP(U_9375,U_9374))
      | ~ hBOOL(hAPP(U_9373,U_9374)) ),
    inference(definitional_conversion,[status(esa)],[f_2546_2]) ).

cnf(f_2546_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9376,tc_HOL_Obool)),U_9373),U_9375),U_9374))
    | ~ hBOOL(hAPP(U_9375,U_9374))
    | ~ hBOOL(hAPP(U_9373,U_9374)) ),
    inference(clausify,[status(thm)],[f_2546_3]) ).

fof(f_2547_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_2547_2,plain,
    ! [U_9380,U_9379,U_9378,U_9377] :
      ( hBOOL(hAPP(hAPP(c_member(U_9377),U_9378),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9377,tc_HOL_Obool)),U_9379),U_9380)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9377),U_9378),U_9380))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9377),U_9378),U_9379)) ),
    inference(variable_rename,[status(thm)],[f_2547_1]) ).

fof(f_2547_3,plain,
    ! [U_9377,U_9378,U_9379,U_9380] :
      ( hBOOL(hAPP(hAPP(c_member(U_9377),U_9378),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9377,tc_HOL_Obool)),U_9379),U_9380)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9377),U_9378),U_9380))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9377),U_9378),U_9379)) ),
    inference(definitional_conversion,[status(esa)],[f_2547_2]) ).

cnf(f_2547_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9377),U_9378),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9377,tc_HOL_Obool)),U_9379),U_9380)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9377),U_9378),U_9380))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9377),U_9378),U_9379)) ),
    inference(clausify,[status(thm)],[f_2547_3]) ).

fof(f_2548_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_2548_2,plain,
    ! [U_9384,U_9383,U_9382,U_9381] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9381),U_9382),U_9384))
        & hBOOL(hAPP(hAPP(c_member(U_9381),U_9382),U_9383)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9381),U_9382),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9381,tc_HOL_Obool)),U_9383),U_9384))) ),
    inference(variable_rename,[status(thm)],[f_2548_1]) ).

fof(f_2548_3,plain,
    ( ! [U_9381,U_9382,U_9383,U_9384] :
        ( hBOOL(hAPP(hAPP(c_member(U_9381),U_9382),U_9384))
        | ~ sP750(U_9381,U_9382,U_9383,U_9384) )
    & ! [U_9381,U_9382,U_9383,U_9384] :
        ( hBOOL(hAPP(hAPP(c_member(U_9381),U_9382),U_9383))
        | ~ sP750(U_9381,U_9382,U_9383,U_9384) )
    & ! [U_9381,U_9382,U_9383,U_9384] :
        ( sP750(U_9381,U_9382,U_9383,U_9384)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9381),U_9382),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9381,tc_HOL_Obool)),U_9383),U_9384))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP750])],[f_2548_2]) ).

cnf(f_2548_4,plain,
    ( sP750(U_9381,U_9382,U_9383,U_9384)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9381),U_9382),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9381,tc_HOL_Obool)),U_9383),U_9384))) ),
    inference(clausify,[status(thm)],[f_2548_3]) ).

cnf(f_2548_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9381),U_9382),U_9383))
    | ~ sP750(U_9381,U_9382,U_9383,U_9384) ),
    inference(clausify,[status(thm)],[f_2548_3]) ).

cnf(f_2548_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9381),U_9382),U_9384))
    | ~ sP750(U_9381,U_9382,U_9383,U_9384) ),
    inference(clausify,[status(thm)],[f_2548_3]) ).

fof(f_2549_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_2549_2,plain,
    ! [U_9387,U_9386,U_9385] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9385),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9385,tc_HOL_Obool)),U_9386),U_9387)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9385),U_9387))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9385),U_9386)) ) ),
    inference(variable_rename,[status(thm)],[f_2549_1]) ).

fof(f_2549_3,plain,
    ( ! [U_9385,U_9386,U_9387] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9385),U_9387))
        | ~ sP751(U_9385,U_9386,U_9387) )
    & ! [U_9385,U_9386,U_9387] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9385),U_9386))
        | ~ sP751(U_9385,U_9386,U_9387) )
    & ! [U_9385,U_9386,U_9387] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9385),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9385,tc_HOL_Obool)),U_9386),U_9387)))
        | sP751(U_9385,U_9386,U_9387) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP751])],[f_2549_2]) ).

cnf(f_2549_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9385),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9385,tc_HOL_Obool)),U_9386),U_9387)))
    | sP751(U_9385,U_9386,U_9387) ),
    inference(clausify,[status(thm)],[f_2549_3]) ).

cnf(f_2549_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9385),U_9386))
    | ~ sP751(U_9385,U_9386,U_9387) ),
    inference(clausify,[status(thm)],[f_2549_3]) ).

cnf(f_2549_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9385),U_9387))
    | ~ sP751(U_9385,U_9386,U_9387) ),
    inference(clausify,[status(thm)],[f_2549_3]) ).

fof(f_2550_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_2550_2,plain,
    ! [U_9392,U_9391,U_9390,U_9389,U_9388] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9388,tc_HOL_Obool)),U_9391),U_9392) = c_Orderings_Obot__class_Obot(tc_fun(U_9388,tc_HOL_Obool))
      | U_9391 = U_9392
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9388,tc_HOL_Obool)),U_9392),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9388),U_9389),U_9390)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9388,tc_HOL_Obool)),U_9391),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9388),U_9389),U_9390)))
      | ~ c_Equiv__Relations_Oequiv(U_9388,U_9389,U_9390) ),
    inference(variable_rename,[status(thm)],[f_2550_1]) ).

fof(f_2550_3,plain,
    ! [U_9388,U_9389,U_9390,U_9391,U_9392] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9388,tc_HOL_Obool)),U_9391),U_9392) = c_Orderings_Obot__class_Obot(tc_fun(U_9388,tc_HOL_Obool))
      | U_9391 = U_9392
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9388,tc_HOL_Obool)),U_9392),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9388),U_9389),U_9390)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9388,tc_HOL_Obool)),U_9391),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9388),U_9389),U_9390)))
      | ~ c_Equiv__Relations_Oequiv(U_9388,U_9389,U_9390) ),
    inference(definitional_conversion,[status(esa)],[f_2550_2]) ).

cnf(f_2550_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9388,tc_HOL_Obool)),U_9391),U_9392) = c_Orderings_Obot__class_Obot(tc_fun(U_9388,tc_HOL_Obool))
    | U_9391 = U_9392
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9388,tc_HOL_Obool)),U_9392),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9388),U_9389),U_9390)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9388,tc_HOL_Obool)),U_9391),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9388),U_9389),U_9390)))
    | ~ c_Equiv__Relations_Oequiv(U_9388,U_9389,U_9390) ),
    inference(clausify,[status(thm)],[f_2550_3]) ).

fof(f_2551_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_2551_2,plain,
    ! [U_9394,U_9393] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9393),c_Orderings_Obot__class_Obot(tc_fun(U_9393,tc_HOL_Obool))),U_9394) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9393,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2551_1]) ).

fof(f_2551_3,plain,
    ! [U_9394,U_9393] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9393),c_Orderings_Obot__class_Obot(tc_fun(U_9393,tc_HOL_Obool))),U_9394) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9393,tc_HOL_Obool),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2551_2]) ).

cnf(f_2551_4,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9393),c_Orderings_Obot__class_Obot(tc_fun(U_9393,tc_HOL_Obool))),U_9394) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9393,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2551_3]) ).

fof(f_2552_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_2552_2,plain,
    ! [U_9397,U_9396,U_9395] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9395,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9395),U_9396),U_9397)
        | U_9396 != c_Orderings_Obot__class_Obot(tc_fun(U_9395,tc_HOL_Obool)) )
      & ( U_9396 = c_Orderings_Obot__class_Obot(tc_fun(U_9395,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9395,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9395),U_9396),U_9397) ) ),
    inference(variable_rename,[status(thm)],[f_2552_1]) ).

fof(f_2552_3,plain,
    ( ! [U_9403,U_9401,U_9399] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9399,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9399),U_9401),U_9403)
        | U_9401 != c_Orderings_Obot__class_Obot(tc_fun(U_9399,tc_HOL_Obool)) )
    & ! [U_9402,U_9400,U_9398] :
        ( U_9400 = c_Orderings_Obot__class_Obot(tc_fun(U_9398,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9398,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9398),U_9400),U_9402) ) ),
    inference(miniscope,[status(thm)],[f_2552_2]) ).

fof(f_2552_4,plain,
    ( ! [U_9401,U_9403,U_9399] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9399,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9399),U_9401),U_9403)
        | U_9401 != c_Orderings_Obot__class_Obot(tc_fun(U_9399,tc_HOL_Obool)) )
    & ! [U_9402,U_9400,U_9398] :
        ( U_9400 = c_Orderings_Obot__class_Obot(tc_fun(U_9398,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9398,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9398),U_9400),U_9402) ) ),
    inference(definitional_conversion,[status(esa)],[f_2552_3]) ).

cnf(f_2552_5,plain,
    ( U_9400 = c_Orderings_Obot__class_Obot(tc_fun(U_9398,tc_HOL_Obool))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9398,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9398),U_9400),U_9402) ),
    inference(clausify,[status(thm)],[f_2552_4]) ).

cnf(f_2552_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9399,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9399),U_9401),U_9403)
    | U_9401 != c_Orderings_Obot__class_Obot(tc_fun(U_9399,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2552_4]) ).

fof(f_2553_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_2553_2,plain,
    ! [U_9406,U_9405,U_9404] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9404),U_9405),U_9406) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9404,tc_HOL_Obool),tc_HOL_Obool))
        | U_9405 != c_Orderings_Obot__class_Obot(tc_fun(U_9404,tc_HOL_Obool)) )
      & ( U_9405 = c_Orderings_Obot__class_Obot(tc_fun(U_9404,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9404),U_9405),U_9406) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9404,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2553_1]) ).

fof(f_2553_3,plain,
    ( ! [U_9412,U_9410,U_9408] :
        ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9408),U_9410),U_9412) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9408,tc_HOL_Obool),tc_HOL_Obool))
        | U_9410 != c_Orderings_Obot__class_Obot(tc_fun(U_9408,tc_HOL_Obool)) )
    & ! [U_9411,U_9409,U_9407] :
        ( U_9409 = c_Orderings_Obot__class_Obot(tc_fun(U_9407,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9407),U_9409),U_9411) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9407,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2553_2]) ).

fof(f_2553_4,plain,
    ( ! [U_9408,U_9410,U_9412] :
        ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9408),U_9410),U_9412) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9408,tc_HOL_Obool),tc_HOL_Obool))
        | U_9410 != c_Orderings_Obot__class_Obot(tc_fun(U_9408,tc_HOL_Obool)) )
    & ! [U_9409,U_9411,U_9407] :
        ( U_9409 = c_Orderings_Obot__class_Obot(tc_fun(U_9407,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9407),U_9409),U_9411) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9407,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2553_3]) ).

cnf(f_2553_5,plain,
    ( U_9409 = c_Orderings_Obot__class_Obot(tc_fun(U_9407,tc_HOL_Obool))
    | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9407),U_9409),U_9411) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9407,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2553_4]) ).

cnf(f_2553_6,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9408),U_9410),U_9412) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9408,tc_HOL_Obool),tc_HOL_Obool))
    | U_9410 != c_Orderings_Obot__class_Obot(tc_fun(U_9408,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2553_4]) ).

fof(f_2554_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_2554_2,plain,
    ! [U_9416,U_9415,U_9414,U_9413] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9413,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9413,tc_fun(U_9413,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9413)),U_9414)),hAPP(hAPP(c_COMBC(U_9413,tc_fun(U_9413,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9413)),U_9415)),U_9416))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9413),U_9416),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9413,tc_HOL_Obool)),U_9414),U_9415))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_9413),U_9416),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9413,tc_HOL_Obool)),U_9414),U_9415)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9413,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9413,tc_fun(U_9413,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9413)),U_9414)),hAPP(hAPP(c_COMBC(U_9413,tc_fun(U_9413,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9413)),U_9415)),U_9416)) ) ),
    inference(variable_rename,[status(thm)],[f_2554_1]) ).

fof(f_2554_3,plain,
    ( ! [U_9424,U_9422,U_9420,U_9418] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9418,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9418,tc_fun(U_9418,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9418)),U_9420)),hAPP(hAPP(c_COMBC(U_9418,tc_fun(U_9418,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9418)),U_9422)),U_9424))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9418),U_9424),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9418,tc_HOL_Obool)),U_9420),U_9422))) )
    & ! [U_9423,U_9421,U_9419,U_9417] :
        ( hBOOL(hAPP(hAPP(c_member(U_9417),U_9423),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9417,tc_HOL_Obool)),U_9419),U_9421)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9417,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9417,tc_fun(U_9417,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9417)),U_9419)),hAPP(hAPP(c_COMBC(U_9417,tc_fun(U_9417,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9417)),U_9421)),U_9423)) ) ),
    inference(miniscope,[status(thm)],[f_2554_2]) ).

fof(f_2554_4,plain,
    ( ! [U_9420,U_9418,U_9422,U_9424] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9418,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9418,tc_fun(U_9418,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9418)),U_9420)),hAPP(hAPP(c_COMBC(U_9418,tc_fun(U_9418,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9418)),U_9422)),U_9424))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9418),U_9424),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9418,tc_HOL_Obool)),U_9420),U_9422))) )
    & ! [U_9419,U_9423,U_9421,U_9417] :
        ( hBOOL(hAPP(hAPP(c_member(U_9417),U_9423),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9417,tc_HOL_Obool)),U_9419),U_9421)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9417,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9417,tc_fun(U_9417,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9417)),U_9419)),hAPP(hAPP(c_COMBC(U_9417,tc_fun(U_9417,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9417)),U_9421)),U_9423)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2554_3]) ).

cnf(f_2554_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9417),U_9423),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9417,tc_HOL_Obool)),U_9419),U_9421)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9417,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9417,tc_fun(U_9417,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9417)),U_9419)),hAPP(hAPP(c_COMBC(U_9417,tc_fun(U_9417,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9417)),U_9421)),U_9423)) ),
    inference(clausify,[status(thm)],[f_2554_4]) ).

cnf(f_2554_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9418,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9418,tc_fun(U_9418,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9418)),U_9420)),hAPP(hAPP(c_COMBC(U_9418,tc_fun(U_9418,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9418)),U_9422)),U_9424))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9418),U_9424),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9418,tc_HOL_Obool)),U_9420),U_9422))) ),
    inference(clausify,[status(thm)],[f_2554_4]) ).

fof(f_2555_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_2555_2,plain,
    ! [U_9428,U_9427,U_9426,U_9425] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9425),U_9426),U_9428))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9425),U_9426),U_9427)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9425),U_9426),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9425),U_9427),U_9428)))
      | ~ class_Lattices_Osemilattice__inf(U_9425) ),
    inference(variable_rename,[status(thm)],[f_2555_1]) ).

fof(f_2555_3,plain,
    ( ! [U_9425,U_9426,U_9427,U_9428] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9425),U_9426),U_9428))
        | ~ sP752(U_9425,U_9426,U_9427,U_9428) )
    & ! [U_9425,U_9426,U_9427,U_9428] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9425),U_9426),U_9427))
        | ~ sP752(U_9425,U_9426,U_9427,U_9428) )
    & ! [U_9425,U_9426,U_9427,U_9428] :
        ( sP752(U_9425,U_9426,U_9427,U_9428)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9425),U_9426),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9425),U_9427),U_9428)))
        | ~ class_Lattices_Osemilattice__inf(U_9425) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP752])],[f_2555_2]) ).

cnf(f_2555_4,plain,
    ( sP752(U_9425,U_9426,U_9427,U_9428)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9425),U_9426),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9425),U_9427),U_9428)))
    | ~ class_Lattices_Osemilattice__inf(U_9425) ),
    inference(clausify,[status(thm)],[f_2555_3]) ).

cnf(f_2555_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9425),U_9426),U_9427))
    | ~ sP752(U_9425,U_9426,U_9427,U_9428) ),
    inference(clausify,[status(thm)],[f_2555_3]) ).

cnf(f_2555_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9425),U_9426),U_9428))
    | ~ sP752(U_9425,U_9426,U_9427,U_9428) ),
    inference(clausify,[status(thm)],[f_2555_3]) ).

fof(f_2556_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_2556_2,plain,
    ! [U_9433,U_9432,U_9431,U_9430,U_9429] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9429),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9429),U_9430),U_9432)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9429),U_9431),U_9433)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9429),U_9432),U_9433))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9429),U_9430),U_9431))
      | ~ class_Lattices_Osemilattice__inf(U_9429) ),
    inference(variable_rename,[status(thm)],[f_2556_1]) ).

fof(f_2556_3,plain,
    ! [U_9429,U_9430,U_9431,U_9432,U_9433] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9429),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9429),U_9430),U_9432)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9429),U_9431),U_9433)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9429),U_9432),U_9433))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9429),U_9430),U_9431))
      | ~ class_Lattices_Osemilattice__inf(U_9429) ),
    inference(definitional_conversion,[status(esa)],[f_2556_2]) ).

cnf(f_2556_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9429),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9429),U_9430),U_9432)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9429),U_9431),U_9433)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9429),U_9432),U_9433))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9429),U_9430),U_9431))
    | ~ class_Lattices_Osemilattice__inf(U_9429) ),
    inference(clausify,[status(thm)],[f_2556_3]) ).

fof(f_2557_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_2557_2,plain,
    ! [U_9437,U_9436,U_9435,U_9434] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9434),U_9435),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9434),U_9436),U_9437)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9434),U_9435),U_9437))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9434),U_9435),U_9436))
      | ~ class_Lattices_Osemilattice__inf(U_9434) ),
    inference(variable_rename,[status(thm)],[f_2557_1]) ).

fof(f_2557_3,plain,
    ! [U_9434,U_9435,U_9436,U_9437] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9434),U_9435),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9434),U_9436),U_9437)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9434),U_9435),U_9437))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9434),U_9435),U_9436))
      | ~ class_Lattices_Osemilattice__inf(U_9434) ),
    inference(definitional_conversion,[status(esa)],[f_2557_2]) ).

cnf(f_2557_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9434),U_9435),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9434),U_9436),U_9437)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9434),U_9435),U_9437))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9434),U_9435),U_9436))
    | ~ class_Lattices_Osemilattice__inf(U_9434) ),
    inference(clausify,[status(thm)],[f_2557_3]) ).

fof(f_2558_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_2558_2,plain,
    ! [U_9441,U_9440,U_9439,U_9438] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9438),U_9439),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9438),U_9440),U_9441)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9438),U_9439),U_9441))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9438),U_9439),U_9440))
      | ~ class_Lattices_Osemilattice__inf(U_9438) ),
    inference(variable_rename,[status(thm)],[f_2558_1]) ).

fof(f_2558_3,plain,
    ! [U_9438,U_9439,U_9440,U_9441] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9438),U_9439),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9438),U_9440),U_9441)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9438),U_9439),U_9441))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9438),U_9439),U_9440))
      | ~ class_Lattices_Osemilattice__inf(U_9438) ),
    inference(definitional_conversion,[status(esa)],[f_2558_2]) ).

cnf(f_2558_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9438),U_9439),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9438),U_9440),U_9441)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9438),U_9439),U_9441))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9438),U_9439),U_9440))
    | ~ class_Lattices_Osemilattice__inf(U_9438) ),
    inference(clausify,[status(thm)],[f_2558_3]) ).

fof(f_2559_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_2559_2,plain,
    ! [U_9444,U_9443,U_9442] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9442),U_9444),U_9443) = U_9443
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9442),U_9443),U_9444))
      | ~ class_Lattices_Osemilattice__inf(U_9442) ),
    inference(variable_rename,[status(thm)],[f_2559_1]) ).

fof(f_2559_3,plain,
    ! [U_9442,U_9443,U_9444] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9442),U_9444),U_9443) = U_9443
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9442),U_9443),U_9444))
      | ~ class_Lattices_Osemilattice__inf(U_9442) ),
    inference(definitional_conversion,[status(esa)],[f_2559_2]) ).

cnf(f_2559_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9442),U_9444),U_9443) = U_9443
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9442),U_9443),U_9444))
    | ~ class_Lattices_Osemilattice__inf(U_9442) ),
    inference(clausify,[status(thm)],[f_2559_3]) ).

fof(f_2560_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_2560_2,plain,
    ! [U_9447,U_9446,U_9445] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9445),U_9446),U_9447) = U_9446
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9445),U_9446),U_9447))
      | ~ class_Lattices_Osemilattice__inf(U_9445) ),
    inference(variable_rename,[status(thm)],[f_2560_1]) ).

fof(f_2560_3,plain,
    ! [U_9445,U_9446,U_9447] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9445),U_9446),U_9447) = U_9446
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9445),U_9446),U_9447))
      | ~ class_Lattices_Osemilattice__inf(U_9445) ),
    inference(definitional_conversion,[status(esa)],[f_2560_2]) ).

cnf(f_2560_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9445),U_9446),U_9447) = U_9446
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9445),U_9446),U_9447))
    | ~ class_Lattices_Osemilattice__inf(U_9445) ),
    inference(clausify,[status(thm)],[f_2560_3]) ).

fof(f_2561_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_2561_2,plain,
    ! [U_9451,U_9450,U_9449,U_9448] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9448),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9448),U_9451),U_9449)),U_9450))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9448),U_9449),U_9450))
      | ~ class_Lattices_Osemilattice__inf(U_9448) ),
    inference(variable_rename,[status(thm)],[f_2561_1]) ).

fof(f_2561_3,plain,
    ! [U_9448,U_9449,U_9450,U_9451] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9448),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9448),U_9451),U_9449)),U_9450))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9448),U_9449),U_9450))
      | ~ class_Lattices_Osemilattice__inf(U_9448) ),
    inference(definitional_conversion,[status(esa)],[f_2561_2]) ).

cnf(f_2561_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9448),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9448),U_9451),U_9449)),U_9450))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9448),U_9449),U_9450))
    | ~ class_Lattices_Osemilattice__inf(U_9448) ),
    inference(clausify,[status(thm)],[f_2561_3]) ).

fof(f_2562_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_2562_2,plain,
    ! [U_9455,U_9454,U_9453,U_9452] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9452),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9452),U_9453),U_9455)),U_9454))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9452),U_9453),U_9454))
      | ~ class_Lattices_Osemilattice__inf(U_9452) ),
    inference(variable_rename,[status(thm)],[f_2562_1]) ).

fof(f_2562_3,plain,
    ! [U_9452,U_9453,U_9454,U_9455] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9452),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9452),U_9453),U_9455)),U_9454))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9452),U_9453),U_9454))
      | ~ class_Lattices_Osemilattice__inf(U_9452) ),
    inference(definitional_conversion,[status(esa)],[f_2562_2]) ).

cnf(f_2562_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9452),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9452),U_9453),U_9455)),U_9454))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9452),U_9453),U_9454))
    | ~ class_Lattices_Osemilattice__inf(U_9452) ),
    inference(clausify,[status(thm)],[f_2562_3]) ).

fof(f_2563_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_2563_2,plain,
    ! [U_9459,U_9458,U_9457,U_9456] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9456),U_9458),U_9459)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),U_9459))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),U_9458)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),U_9459))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),U_9458)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9456),U_9458),U_9459))) ) )
      | ~ class_Lattices_Osemilattice__inf(U_9456) ),
    inference(variable_rename,[status(thm)],[f_2563_1]) ).

fof(f_2563_3,plain,
    ( ! [U_9456,U_9457,U_9458,U_9459] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),U_9459))
        | ~ sP753(U_9456,U_9457,U_9458,U_9459) )
    & ! [U_9456,U_9457,U_9458,U_9459] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),U_9458))
        | ~ sP753(U_9456,U_9457,U_9458,U_9459) )
    & ! [U_9456,U_9457,U_9458,U_9459] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9456),U_9458),U_9459)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),U_9459))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),U_9458))
        | ~ sP754(U_9456,U_9457,U_9458,U_9459) )
    & ! [U_9456,U_9457,U_9458,U_9459] :
        ( sP753(U_9456,U_9457,U_9458,U_9459)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9456),U_9458),U_9459)))
        | ~ sP754(U_9456,U_9457,U_9458,U_9459) )
    & ! [U_9456,U_9457,U_9458,U_9459] :
        ( sP754(U_9456,U_9457,U_9458,U_9459)
        | ~ class_Lattices_Osemilattice__inf(U_9456) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP753,sP754])],[f_2563_2]) ).

cnf(f_2563_4,plain,
    ( sP754(U_9456,U_9457,U_9458,U_9459)
    | ~ class_Lattices_Osemilattice__inf(U_9456) ),
    inference(clausify,[status(thm)],[f_2563_3]) ).

cnf(f_2563_5,plain,
    ( sP753(U_9456,U_9457,U_9458,U_9459)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9456),U_9458),U_9459)))
    | ~ sP754(U_9456,U_9457,U_9458,U_9459) ),
    inference(clausify,[status(thm)],[f_2563_3]) ).

cnf(f_2563_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9456),U_9458),U_9459)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),U_9459))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),U_9458))
    | ~ sP754(U_9456,U_9457,U_9458,U_9459) ),
    inference(clausify,[status(thm)],[f_2563_3]) ).

cnf(f_2563_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),U_9458))
    | ~ sP753(U_9456,U_9457,U_9458,U_9459) ),
    inference(clausify,[status(thm)],[f_2563_3]) ).

cnf(f_2563_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9456),U_9457),U_9459))
    | ~ sP753(U_9456,U_9457,U_9458,U_9459) ),
    inference(clausify,[status(thm)],[f_2563_3]) ).

fof(f_2564_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_2564_2,plain,
    ! [U_9462,U_9461,U_9460] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9460),U_9461),U_9462))
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9460),U_9461),U_9462) != U_9461 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9460),U_9461),U_9462) = U_9461
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9460),U_9461),U_9462)) ) )
      | ~ class_Lattices_Osemilattice__inf(U_9460) ),
    inference(variable_rename,[status(thm)],[f_2564_1]) ).

fof(f_2564_3,plain,
    ( ! [U_9460,U_9461,U_9462] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9460),U_9461),U_9462))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9460),U_9461),U_9462) != U_9461
        | ~ sP755(U_9460,U_9461,U_9462) )
    & ! [U_9460,U_9461,U_9462] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9460),U_9461),U_9462) = U_9461
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9460),U_9461),U_9462))
        | ~ sP755(U_9460,U_9461,U_9462) )
    & ! [U_9460,U_9461,U_9462] :
        ( sP755(U_9460,U_9461,U_9462)
        | ~ class_Lattices_Osemilattice__inf(U_9460) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP755])],[f_2564_2]) ).

cnf(f_2564_4,plain,
    ( sP755(U_9460,U_9461,U_9462)
    | ~ class_Lattices_Osemilattice__inf(U_9460) ),
    inference(clausify,[status(thm)],[f_2564_3]) ).

cnf(f_2564_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9460),U_9461),U_9462) = U_9461
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9460),U_9461),U_9462))
    | ~ sP755(U_9460,U_9461,U_9462) ),
    inference(clausify,[status(thm)],[f_2564_3]) ).

cnf(f_2564_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9460),U_9461),U_9462))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9460),U_9461),U_9462) != U_9461
    | ~ sP755(U_9460,U_9461,U_9462) ),
    inference(clausify,[status(thm)],[f_2564_3]) ).

fof(f_2565_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_2565_2,plain,
    ! [U_9465,U_9464,U_9463] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9463),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9463),U_9464),U_9465)),U_9465))
      | ~ class_Lattices_Osemilattice__inf(U_9463) ),
    inference(variable_rename,[status(thm)],[f_2565_1]) ).

fof(f_2565_3,plain,
    ! [U_9463,U_9465,U_9464] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9463),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9463),U_9464),U_9465)),U_9465))
      | ~ class_Lattices_Osemilattice__inf(U_9463) ),
    inference(definitional_conversion,[status(esa)],[f_2565_2]) ).

cnf(f_2565_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9463),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9463),U_9464),U_9465)),U_9465))
    | ~ class_Lattices_Osemilattice__inf(U_9463) ),
    inference(clausify,[status(thm)],[f_2565_3]) ).

fof(f_2566_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_2566_2,plain,
    ! [U_9468,U_9467,U_9466] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9466),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9466),U_9467),U_9468)),U_9468))
      | ~ class_Lattices_Olattice(U_9466) ),
    inference(variable_rename,[status(thm)],[f_2566_1]) ).

fof(f_2566_3,plain,
    ! [U_9466,U_9467,U_9468] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9466),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9466),U_9467),U_9468)),U_9468))
      | ~ class_Lattices_Olattice(U_9466) ),
    inference(definitional_conversion,[status(esa)],[f_2566_2]) ).

cnf(f_2566_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9466),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9466),U_9467),U_9468)),U_9468))
    | ~ class_Lattices_Olattice(U_9466) ),
    inference(clausify,[status(thm)],[f_2566_3]) ).

fof(f_2567_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_2567_2,plain,
    ! [U_9471,U_9470,U_9469] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9469),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9469),U_9470),U_9471)),U_9470))
      | ~ class_Lattices_Osemilattice__inf(U_9469) ),
    inference(variable_rename,[status(thm)],[f_2567_1]) ).

fof(f_2567_3,plain,
    ! [U_9469,U_9470,U_9471] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9469),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9469),U_9470),U_9471)),U_9470))
      | ~ class_Lattices_Osemilattice__inf(U_9469) ),
    inference(definitional_conversion,[status(esa)],[f_2567_2]) ).

cnf(f_2567_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9469),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9469),U_9470),U_9471)),U_9470))
    | ~ class_Lattices_Osemilattice__inf(U_9469) ),
    inference(clausify,[status(thm)],[f_2567_3]) ).

fof(f_2568_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_2568_2,plain,
    ! [U_9474,U_9473,U_9472] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9472),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9472),U_9473),U_9474)),U_9473))
      | ~ class_Lattices_Olattice(U_9472) ),
    inference(variable_rename,[status(thm)],[f_2568_1]) ).

fof(f_2568_3,plain,
    ! [U_9472,U_9473,U_9474] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9472),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9472),U_9473),U_9474)),U_9473))
      | ~ class_Lattices_Olattice(U_9472) ),
    inference(definitional_conversion,[status(esa)],[f_2568_2]) ).

cnf(f_2568_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9472),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9472),U_9473),U_9474)),U_9473))
    | ~ class_Lattices_Olattice(U_9472) ),
    inference(clausify,[status(thm)],[f_2568_3]) ).

fof(f_2569_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_2569_2,plain,
    ! [U_9479,U_9478,U_9477,U_9476,U_9475] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9475,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9475,tc_HOL_Obool)),U_9476),U_9478)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9475,tc_HOL_Obool)),U_9477),U_9479)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9475,tc_HOL_Obool)),U_9478),U_9479))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9475,tc_HOL_Obool)),U_9476),U_9477)) ),
    inference(variable_rename,[status(thm)],[f_2569_1]) ).

fof(f_2569_3,plain,
    ! [U_9475,U_9476,U_9477,U_9478,U_9479] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9475,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9475,tc_HOL_Obool)),U_9476),U_9478)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9475,tc_HOL_Obool)),U_9477),U_9479)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9475,tc_HOL_Obool)),U_9478),U_9479))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9475,tc_HOL_Obool)),U_9476),U_9477)) ),
    inference(definitional_conversion,[status(esa)],[f_2569_2]) ).

cnf(f_2569_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9475,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9475,tc_HOL_Obool)),U_9476),U_9478)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9475,tc_HOL_Obool)),U_9477),U_9479)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9475,tc_HOL_Obool)),U_9478),U_9479))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9475,tc_HOL_Obool)),U_9476),U_9477)) ),
    inference(clausify,[status(thm)],[f_2569_3]) ).

fof(f_2570_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_2570_2,plain,
    ! [U_9483,U_9482,U_9481,U_9480] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9480,tc_HOL_Obool)),U_9481),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9480,tc_HOL_Obool)),U_9482),U_9483)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9480,tc_HOL_Obool)),U_9481),U_9483))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9480,tc_HOL_Obool)),U_9481),U_9482)) ),
    inference(variable_rename,[status(thm)],[f_2570_1]) ).

fof(f_2570_3,plain,
    ! [U_9480,U_9481,U_9482,U_9483] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9480,tc_HOL_Obool)),U_9481),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9480,tc_HOL_Obool)),U_9482),U_9483)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9480,tc_HOL_Obool)),U_9481),U_9483))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9480,tc_HOL_Obool)),U_9481),U_9482)) ),
    inference(definitional_conversion,[status(esa)],[f_2570_2]) ).

cnf(f_2570_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9480,tc_HOL_Obool)),U_9481),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9480,tc_HOL_Obool)),U_9482),U_9483)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9480,tc_HOL_Obool)),U_9481),U_9483))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9480,tc_HOL_Obool)),U_9481),U_9482)) ),
    inference(clausify,[status(thm)],[f_2570_3]) ).

fof(f_2571_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_2571_2,plain,
    ! [U_9486,U_9485,U_9484] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9484,tc_HOL_Obool)),U_9486),U_9485) = U_9485
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9484,tc_HOL_Obool)),U_9485),U_9486)) ),
    inference(variable_rename,[status(thm)],[f_2571_1]) ).

fof(f_2571_3,plain,
    ! [U_9484,U_9485,U_9486] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9484,tc_HOL_Obool)),U_9486),U_9485) = U_9485
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9484,tc_HOL_Obool)),U_9485),U_9486)) ),
    inference(definitional_conversion,[status(esa)],[f_2571_2]) ).

cnf(f_2571_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9484,tc_HOL_Obool)),U_9486),U_9485) = U_9485
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9484,tc_HOL_Obool)),U_9485),U_9486)) ),
    inference(clausify,[status(thm)],[f_2571_3]) ).

fof(f_2572_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_2572_2,plain,
    ! [U_9489,U_9488,U_9487] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9487,tc_HOL_Obool)),U_9488),U_9489) = U_9488
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9487,tc_HOL_Obool)),U_9488),U_9489)) ),
    inference(variable_rename,[status(thm)],[f_2572_1]) ).

fof(f_2572_3,plain,
    ! [U_9487,U_9488,U_9489] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9487,tc_HOL_Obool)),U_9488),U_9489) = U_9488
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9487,tc_HOL_Obool)),U_9488),U_9489)) ),
    inference(definitional_conversion,[status(esa)],[f_2572_2]) ).

cnf(f_2572_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9487,tc_HOL_Obool)),U_9488),U_9489) = U_9488
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9487,tc_HOL_Obool)),U_9488),U_9489)) ),
    inference(clausify,[status(thm)],[f_2572_3]) ).

fof(f_2573_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_2573_2,plain,
    ! [U_9492,U_9491,U_9490] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9490,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9490,tc_HOL_Obool)),U_9491),U_9492)),U_9492)),
    inference(variable_rename,[status(thm)],[f_2573_1]) ).

fof(f_2573_3,plain,
    ! [U_9490,U_9491,U_9492] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9490,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9490,tc_HOL_Obool)),U_9491),U_9492)),U_9492)),
    inference(definitional_conversion,[status(esa)],[f_2573_2]) ).

cnf(f_2573_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9490,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9490,tc_HOL_Obool)),U_9491),U_9492)),U_9492)),
    inference(clausify,[status(thm)],[f_2573_3]) ).

fof(f_2574_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_2574_2,plain,
    ! [U_9495,U_9494,U_9493] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9493,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9493,tc_HOL_Obool)),U_9494),U_9495)),U_9494)),
    inference(variable_rename,[status(thm)],[f_2574_1]) ).

fof(f_2574_3,plain,
    ! [U_9493,U_9494,U_9495] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9493,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9493,tc_HOL_Obool)),U_9494),U_9495)),U_9494)),
    inference(definitional_conversion,[status(esa)],[f_2574_2]) ).

cnf(f_2574_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9493,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9493,tc_HOL_Obool)),U_9494),U_9495)),U_9494)),
    inference(clausify,[status(thm)],[f_2574_3]) ).

fof(f_2575_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_2575_2,plain,
    ! [U_9499,U_9498,U_9497,U_9496] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9496),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9496),U_9497),U_9499)),U_9498))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9496),U_9497),U_9498))
      | ~ class_Lattices_Osemilattice__inf(U_9496) ),
    inference(variable_rename,[status(thm)],[f_2575_1]) ).

fof(f_2575_3,plain,
    ! [U_9496,U_9497,U_9498,U_9499] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9496),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9496),U_9497),U_9499)),U_9498))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9496),U_9497),U_9498))
      | ~ class_Lattices_Osemilattice__inf(U_9496) ),
    inference(definitional_conversion,[status(esa)],[f_2575_2]) ).

cnf(f_2575_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9496),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9496),U_9497),U_9499)),U_9498))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9496),U_9497),U_9498))
    | ~ class_Lattices_Osemilattice__inf(U_9496) ),
    inference(clausify,[status(thm)],[f_2575_3]) ).

fof(f_2576_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_2576_2,plain,
    ! [U_9503,U_9502,U_9501,U_9500] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9500),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9500),U_9503),U_9501)),U_9502))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9500),U_9501),U_9502))
      | ~ class_Lattices_Osemilattice__inf(U_9500) ),
    inference(variable_rename,[status(thm)],[f_2576_1]) ).

fof(f_2576_3,plain,
    ! [U_9500,U_9501,U_9502,U_9503] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9500),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9500),U_9503),U_9501)),U_9502))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9500),U_9501),U_9502))
      | ~ class_Lattices_Osemilattice__inf(U_9500) ),
    inference(definitional_conversion,[status(esa)],[f_2576_2]) ).

cnf(f_2576_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9500),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9500),U_9503),U_9501)),U_9502))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9500),U_9501),U_9502))
    | ~ class_Lattices_Osemilattice__inf(U_9500) ),
    inference(clausify,[status(thm)],[f_2576_3]) ).

fof(f_2577_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_2577_2,plain,
    ! [U_9505,U_9504] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9504,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9504,tc_HOL_Obool))),U_9505) = c_Orderings_Obot__class_Obot(tc_fun(U_9504,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2577_1]) ).

fof(f_2577_3,plain,
    ! [U_9504,U_9505] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9504,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9504,tc_HOL_Obool))),U_9505) = c_Orderings_Obot__class_Obot(tc_fun(U_9504,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2577_2]) ).

cnf(f_2577_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9504,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9504,tc_HOL_Obool))),U_9505) = c_Orderings_Obot__class_Obot(tc_fun(U_9504,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2577_3]) ).

fof(f_2578_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_2578_2,plain,
    ! [U_9507,U_9506] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9506,tc_HOL_Obool)),U_9507),c_Orderings_Obot__class_Obot(tc_fun(U_9506,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9506,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2578_1]) ).

fof(f_2578_3,plain,
    ! [U_9506,U_9507] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9506,tc_HOL_Obool)),U_9507),c_Orderings_Obot__class_Obot(tc_fun(U_9506,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9506,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2578_2]) ).

cnf(f_2578_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9506,tc_HOL_Obool)),U_9507),c_Orderings_Obot__class_Obot(tc_fun(U_9506,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9506,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2578_3]) ).

fof(f_2579_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_2579_2,plain,
    ! [U_9514,U_9513,U_9512] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9512,tc_HOL_Obool)),U_9513),U_9514) = c_Orderings_Obot__class_Obot(tc_fun(U_9512,tc_HOL_Obool))
        | ? [U_9511] :
            ( ? [U_9510] :
                ( U_9511 = U_9510
                & hBOOL(hAPP(hAPP(c_member(U_9512),U_9510),U_9514)) )
            & hBOOL(hAPP(hAPP(c_member(U_9512),U_9511),U_9513)) ) )
      & ( ! [U_9509] :
            ( ! [U_9508] :
                ( U_9509 != U_9508
                | ~ hBOOL(hAPP(hAPP(c_member(U_9512),U_9508),U_9514)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_9512),U_9509),U_9513)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9512,tc_HOL_Obool)),U_9513),U_9514) != c_Orderings_Obot__class_Obot(tc_fun(U_9512,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2579_1]) ).

fof(f_2579_3,plain,
    ( ! [U_9520,U_9518,U_9516] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9516,tc_HOL_Obool)),U_9518),U_9520) = c_Orderings_Obot__class_Obot(tc_fun(U_9516,tc_HOL_Obool))
        | ? [U_9511] :
            ( ? [U_9510] :
                ( U_9511 = U_9510
                & hBOOL(hAPP(hAPP(c_member(U_9516),U_9510),U_9520)) )
            & hBOOL(hAPP(hAPP(c_member(U_9516),U_9511),U_9518)) ) )
    & ! [U_9519,U_9517,U_9515] :
        ( ! [U_9509] :
            ( ! [U_9508] :
                ( U_9509 != U_9508
                | ~ hBOOL(hAPP(hAPP(c_member(U_9515),U_9508),U_9519)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_9515),U_9509),U_9517)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9515,tc_HOL_Obool)),U_9517),U_9519) != c_Orderings_Obot__class_Obot(tc_fun(U_9515,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2579_2]) ).

fof(f_2579_4,plain,
    ( ! [U_9520,U_9518,U_9516] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9516,tc_HOL_Obool)),U_9518),U_9520) = c_Orderings_Obot__class_Obot(tc_fun(U_9516,tc_HOL_Obool))
        | ( ? [U_9510] :
              ( sK145(U_9520,U_9518,U_9516) = U_9510
              & hBOOL(hAPP(hAPP(c_member(U_9516),U_9510),U_9520)) )
          & hBOOL(hAPP(hAPP(c_member(U_9516),sK145(U_9520,U_9518,U_9516)),U_9518)) ) )
    & ! [U_9519,U_9517,U_9515] :
        ( ! [U_9509] :
            ( ! [U_9508] :
                ( U_9509 != U_9508
                | ~ hBOOL(hAPP(hAPP(c_member(U_9515),U_9508),U_9519)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_9515),U_9509),U_9517)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9515,tc_HOL_Obool)),U_9517),U_9519) != c_Orderings_Obot__class_Obot(tc_fun(U_9515,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_9511,sK145(U_9520,U_9518,U_9516))],[f_2579_3]) ).

fof(f_2579_5,plain,
    ( ! [U_9520,U_9518,U_9516] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9516,tc_HOL_Obool)),U_9518),U_9520) = c_Orderings_Obot__class_Obot(tc_fun(U_9516,tc_HOL_Obool))
        | ( sK145(U_9520,U_9518,U_9516) = sK146(U_9520,U_9518,U_9516)
          & hBOOL(hAPP(hAPP(c_member(U_9516),sK146(U_9520,U_9518,U_9516)),U_9520))
          & hBOOL(hAPP(hAPP(c_member(U_9516),sK145(U_9520,U_9518,U_9516)),U_9518)) ) )
    & ! [U_9519,U_9517,U_9515] :
        ( ! [U_9509] :
            ( ! [U_9508] :
                ( U_9509 != U_9508
                | ~ hBOOL(hAPP(hAPP(c_member(U_9515),U_9508),U_9519)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_9515),U_9509),U_9517)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9515,tc_HOL_Obool)),U_9517),U_9519) != c_Orderings_Obot__class_Obot(tc_fun(U_9515,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_9510,sK146(U_9520,U_9518,U_9516))],[f_2579_4]) ).

fof(f_2579_6,plain,
    ( ! [U_9516,U_9518,U_9520] :
        ( sK145(U_9520,U_9518,U_9516) = sK146(U_9520,U_9518,U_9516)
        | ~ sP756(U_9516,U_9518,U_9520) )
    & ! [U_9516,U_9518,U_9520] :
        ( hBOOL(hAPP(hAPP(c_member(U_9516),sK146(U_9520,U_9518,U_9516)),U_9520))
        | ~ sP756(U_9516,U_9518,U_9520) )
    & ! [U_9516,U_9518,U_9520] :
        ( hBOOL(hAPP(hAPP(c_member(U_9516),sK145(U_9520,U_9518,U_9516)),U_9518))
        | ~ sP756(U_9516,U_9518,U_9520) )
    & ! [U_9516,U_9518,U_9520] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9516,tc_HOL_Obool)),U_9518),U_9520) = c_Orderings_Obot__class_Obot(tc_fun(U_9516,tc_HOL_Obool))
        | sP756(U_9516,U_9518,U_9520) )
    & ! [U_9519,U_9508,U_9509,U_9515,U_9517] :
        ( U_9509 != U_9508
        | ~ hBOOL(hAPP(hAPP(c_member(U_9515),U_9508),U_9519))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9515),U_9509),U_9517))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9515,tc_HOL_Obool)),U_9517),U_9519) != c_Orderings_Obot__class_Obot(tc_fun(U_9515,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP756])],[f_2579_5]) ).

cnf(f_2579_7,plain,
    ( U_9509 != U_9508
    | ~ hBOOL(hAPP(hAPP(c_member(U_9515),U_9508),U_9519))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9515),U_9509),U_9517))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9515,tc_HOL_Obool)),U_9517),U_9519) != c_Orderings_Obot__class_Obot(tc_fun(U_9515,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2579_6]) ).

cnf(f_2579_8,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9516,tc_HOL_Obool)),U_9518),U_9520) = c_Orderings_Obot__class_Obot(tc_fun(U_9516,tc_HOL_Obool))
    | sP756(U_9516,U_9518,U_9520) ),
    inference(clausify,[status(thm)],[f_2579_6]) ).

cnf(f_2579_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9516),sK145(U_9520,U_9518,U_9516)),U_9518))
    | ~ sP756(U_9516,U_9518,U_9520) ),
    inference(clausify,[status(thm)],[f_2579_6]) ).

cnf(f_2579_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9516),sK146(U_9520,U_9518,U_9516)),U_9520))
    | ~ sP756(U_9516,U_9518,U_9520) ),
    inference(clausify,[status(thm)],[f_2579_6]) ).

cnf(f_2579_11,plain,
    ( sK145(U_9520,U_9518,U_9516) = sK146(U_9520,U_9518,U_9516)
    | ~ sP756(U_9516,U_9518,U_9520) ),
    inference(clausify,[status(thm)],[f_2579_6]) ).

fof(f_2580_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_2580_2,plain,
    ! [U_9522,U_9521] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9521),c_Orderings_Obot__class_Obot(U_9521)),U_9522) = c_Orderings_Obot__class_Obot(U_9521)
      | ~ class_Lattices_Obounded__lattice__bot(U_9521) ),
    inference(variable_rename,[status(thm)],[f_2580_1]) ).

fof(f_2580_3,plain,
    ! [U_9521,U_9522] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9521),c_Orderings_Obot__class_Obot(U_9521)),U_9522) = c_Orderings_Obot__class_Obot(U_9521)
      | ~ class_Lattices_Obounded__lattice__bot(U_9521) ),
    inference(definitional_conversion,[status(esa)],[f_2580_2]) ).

cnf(f_2580_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9521),c_Orderings_Obot__class_Obot(U_9521)),U_9522) = c_Orderings_Obot__class_Obot(U_9521)
    | ~ class_Lattices_Obounded__lattice__bot(U_9521) ),
    inference(clausify,[status(thm)],[f_2580_3]) ).

fof(f_2581_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_2581_2,plain,
    ! [U_9524,U_9523] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9523),U_9524),c_Orderings_Obot__class_Obot(U_9523)) = c_Orderings_Obot__class_Obot(U_9523)
      | ~ class_Lattices_Obounded__lattice__bot(U_9523) ),
    inference(variable_rename,[status(thm)],[f_2581_1]) ).

fof(f_2581_3,plain,
    ! [U_9523,U_9524] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9523),U_9524),c_Orderings_Obot__class_Obot(U_9523)) = c_Orderings_Obot__class_Obot(U_9523)
      | ~ class_Lattices_Obounded__lattice__bot(U_9523) ),
    inference(definitional_conversion,[status(esa)],[f_2581_2]) ).

cnf(f_2581_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9523),U_9524),c_Orderings_Obot__class_Obot(U_9523)) = c_Orderings_Obot__class_Obot(U_9523)
    | ~ class_Lattices_Obounded__lattice__bot(U_9523) ),
    inference(clausify,[status(thm)],[f_2581_3]) ).

fof(f_2582_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_2582_2,plain,
    ! [U_9528,U_9527,U_9526,U_9525] :
      ( hBOOL(hAPP(hAPP(c_member(U_9525),U_9526),U_9528))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9525),U_9526),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9525,tc_HOL_Obool)),U_9527),U_9528))) ),
    inference(variable_rename,[status(thm)],[f_2582_1]) ).

fof(f_2582_3,plain,
    ! [U_9525,U_9526,U_9527,U_9528] :
      ( hBOOL(hAPP(hAPP(c_member(U_9525),U_9526),U_9528))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9525),U_9526),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9525,tc_HOL_Obool)),U_9527),U_9528))) ),
    inference(definitional_conversion,[status(esa)],[f_2582_2]) ).

cnf(f_2582_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9525),U_9526),U_9528))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9525),U_9526),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9525,tc_HOL_Obool)),U_9527),U_9528))) ),
    inference(clausify,[status(thm)],[f_2582_3]) ).

fof(f_2583_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_2583_2,plain,
    ! [U_9532,U_9531,U_9530,U_9529] :
      ( hBOOL(hAPP(hAPP(c_member(U_9529),U_9530),U_9531))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9529),U_9530),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9529,tc_HOL_Obool)),U_9531),U_9532))) ),
    inference(variable_rename,[status(thm)],[f_2583_1]) ).

fof(f_2583_3,plain,
    ! [U_9529,U_9530,U_9531,U_9532] :
      ( hBOOL(hAPP(hAPP(c_member(U_9529),U_9530),U_9531))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9529),U_9530),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9529,tc_HOL_Obool)),U_9531),U_9532))) ),
    inference(definitional_conversion,[status(esa)],[f_2583_2]) ).

cnf(f_2583_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9529),U_9530),U_9531))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9529),U_9530),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9529,tc_HOL_Obool)),U_9531),U_9532))) ),
    inference(clausify,[status(thm)],[f_2583_3]) ).

fof(f_2584_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_2584_2,plain,
    ! [U_9536,U_9535,U_9534,U_9533] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9533),U_9534),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9533,tc_HOL_Obool)),U_9535),U_9536)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9533),U_9534),U_9536))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9533),U_9534),U_9535)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_9533),U_9534),U_9536))
          & hBOOL(hAPP(hAPP(c_member(U_9533),U_9534),U_9535)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9533),U_9534),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9533,tc_HOL_Obool)),U_9535),U_9536))) ) ),
    inference(variable_rename,[status(thm)],[f_2584_1]) ).

fof(f_2584_3,plain,
    ( ! [U_9544,U_9542,U_9540,U_9538] :
        ( hBOOL(hAPP(hAPP(c_member(U_9538),U_9540),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9538,tc_HOL_Obool)),U_9542),U_9544)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9538),U_9540),U_9544))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9538),U_9540),U_9542)) )
    & ! [U_9543,U_9541,U_9539,U_9537] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_9537),U_9539),U_9543))
          & hBOOL(hAPP(hAPP(c_member(U_9537),U_9539),U_9541)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9537),U_9539),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9537,tc_HOL_Obool)),U_9541),U_9543))) ) ),
    inference(miniscope,[status(thm)],[f_2584_2]) ).

fof(f_2584_4,plain,
    ( ! [U_9543,U_9539,U_9537,U_9541] :
        ( hBOOL(hAPP(hAPP(c_member(U_9537),U_9539),U_9543))
        | ~ sP757(U_9543,U_9539,U_9537,U_9541) )
    & ! [U_9543,U_9539,U_9537,U_9541] :
        ( hBOOL(hAPP(hAPP(c_member(U_9537),U_9539),U_9541))
        | ~ sP757(U_9543,U_9539,U_9537,U_9541) )
    & ! [U_9540,U_9538,U_9544,U_9542] :
        ( hBOOL(hAPP(hAPP(c_member(U_9538),U_9540),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9538,tc_HOL_Obool)),U_9542),U_9544)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9538),U_9540),U_9544))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9538),U_9540),U_9542)) )
    & ! [U_9543,U_9539,U_9537,U_9541] :
        ( sP757(U_9543,U_9539,U_9537,U_9541)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9537),U_9539),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9537,tc_HOL_Obool)),U_9541),U_9543))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP757])],[f_2584_3]) ).

cnf(f_2584_5,plain,
    ( sP757(U_9543,U_9539,U_9537,U_9541)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9537),U_9539),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9537,tc_HOL_Obool)),U_9541),U_9543))) ),
    inference(clausify,[status(thm)],[f_2584_4]) ).

cnf(f_2584_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9538),U_9540),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9538,tc_HOL_Obool)),U_9542),U_9544)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9538),U_9540),U_9544))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9538),U_9540),U_9542)) ),
    inference(clausify,[status(thm)],[f_2584_4]) ).

cnf(f_2584_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9537),U_9539),U_9541))
    | ~ sP757(U_9543,U_9539,U_9537,U_9541) ),
    inference(clausify,[status(thm)],[f_2584_4]) ).

cnf(f_2584_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9537),U_9539),U_9543))
    | ~ sP757(U_9543,U_9539,U_9537,U_9541) ),
    inference(clausify,[status(thm)],[f_2584_4]) ).

fof(f_2585_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_2585_2,plain,
    ! [U_9548,U_9547,U_9546,U_9545] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9545),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9545),U_9546),U_9547)),U_9548) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9545),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9545),U_9546),U_9548)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9545),U_9547),U_9548))
      | ~ class_Lattices_Odistrib__lattice(U_9545) ),
    inference(variable_rename,[status(thm)],[f_2585_1]) ).

fof(f_2585_3,plain,
    ! [U_9546,U_9545,U_9547,U_9548] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9545),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9545),U_9546),U_9547)),U_9548) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9545),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9545),U_9546),U_9548)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9545),U_9547),U_9548))
      | ~ class_Lattices_Odistrib__lattice(U_9545) ),
    inference(definitional_conversion,[status(esa)],[f_2585_2]) ).

cnf(f_2585_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9545),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9545),U_9546),U_9547)),U_9548) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9545),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9545),U_9546),U_9548)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9545),U_9547),U_9548))
    | ~ class_Lattices_Odistrib__lattice(U_9545) ),
    inference(clausify,[status(thm)],[f_2585_3]) ).

fof(f_2586_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_2586_2,plain,
    ! [U_9552,U_9551,U_9550,U_9549] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9549),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9549),U_9550),U_9551)),U_9552) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9549),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9549),U_9550),U_9552)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9549),U_9551),U_9552))
      | ~ class_Lattices_Odistrib__lattice(U_9549) ),
    inference(variable_rename,[status(thm)],[f_2586_1]) ).

fof(f_2586_3,plain,
    ! [U_9549,U_9550,U_9551,U_9552] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9549),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9549),U_9550),U_9551)),U_9552) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9549),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9549),U_9550),U_9552)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9549),U_9551),U_9552))
      | ~ class_Lattices_Odistrib__lattice(U_9549) ),
    inference(definitional_conversion,[status(esa)],[f_2586_2]) ).

cnf(f_2586_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9549),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9549),U_9550),U_9551)),U_9552) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9549),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9549),U_9550),U_9552)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9549),U_9551),U_9552))
    | ~ class_Lattices_Odistrib__lattice(U_9549) ),
    inference(clausify,[status(thm)],[f_2586_3]) ).

fof(f_2587_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_2587_2,plain,
    ! [U_9556,U_9555,U_9554,U_9553] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9553),U_9554),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9553),U_9555),U_9556)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9553),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9553),U_9554),U_9555)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9553),U_9554),U_9556))
      | ~ class_Lattices_Odistrib__lattice(U_9553) ),
    inference(variable_rename,[status(thm)],[f_2587_1]) ).

fof(f_2587_3,plain,
    ! [U_9553,U_9554,U_9555,U_9556] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9553),U_9554),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9553),U_9555),U_9556)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9553),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9553),U_9554),U_9555)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9553),U_9554),U_9556))
      | ~ class_Lattices_Odistrib__lattice(U_9553) ),
    inference(definitional_conversion,[status(esa)],[f_2587_2]) ).

cnf(f_2587_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9553),U_9554),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9553),U_9555),U_9556)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9553),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9553),U_9554),U_9555)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9553),U_9554),U_9556))
    | ~ class_Lattices_Odistrib__lattice(U_9553) ),
    inference(clausify,[status(thm)],[f_2587_3]) ).

fof(f_2588_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_2588_2,plain,
    ! [U_9560,U_9559,U_9558,U_9557] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9557),U_9558),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9557),U_9559),U_9560)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9557),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9557),U_9558),U_9559)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9557),U_9558),U_9560))
      | ~ class_Lattices_Odistrib__lattice(U_9557) ),
    inference(variable_rename,[status(thm)],[f_2588_1]) ).

fof(f_2588_3,plain,
    ! [U_9557,U_9558,U_9559,U_9560] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9557),U_9558),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9557),U_9559),U_9560)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9557),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9557),U_9558),U_9559)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9557),U_9558),U_9560))
      | ~ class_Lattices_Odistrib__lattice(U_9557) ),
    inference(definitional_conversion,[status(esa)],[f_2588_2]) ).

cnf(f_2588_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9557),U_9558),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9557),U_9559),U_9560)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9557),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9557),U_9558),U_9559)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9557),U_9558),U_9560))
    | ~ class_Lattices_Odistrib__lattice(U_9557) ),
    inference(clausify,[status(thm)],[f_2588_3]) ).

fof(f_2589_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_2589_2,plain,
    ! [U_9563,U_9562,U_9561] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9561),U_9562),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9561),U_9562),U_9563)) = U_9562
      | ~ class_Lattices_Olattice(U_9561) ),
    inference(variable_rename,[status(thm)],[f_2589_1]) ).

fof(f_2589_3,plain,
    ! [U_9561,U_9562,U_9563] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9561),U_9562),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9561),U_9562),U_9563)) = U_9562
      | ~ class_Lattices_Olattice(U_9561) ),
    inference(definitional_conversion,[status(esa)],[f_2589_2]) ).

cnf(f_2589_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9561),U_9562),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9561),U_9562),U_9563)) = U_9562
    | ~ class_Lattices_Olattice(U_9561) ),
    inference(clausify,[status(thm)],[f_2589_3]) ).

fof(f_2590_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_2590_2,plain,
    ! [U_9566,U_9565,U_9564] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9564),U_9565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9564),U_9565),U_9566)) = U_9565
      | ~ class_Lattices_Olattice(U_9564) ),
    inference(variable_rename,[status(thm)],[f_2590_1]) ).

fof(f_2590_3,plain,
    ! [U_9564,U_9565,U_9566] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9564),U_9565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9564),U_9565),U_9566)) = U_9565
      | ~ class_Lattices_Olattice(U_9564) ),
    inference(definitional_conversion,[status(esa)],[f_2590_2]) ).

cnf(f_2590_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9564),U_9565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9564),U_9565),U_9566)) = U_9565
    | ~ class_Lattices_Olattice(U_9564) ),
    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__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_2591_2,plain,
    ! [U_9570,U_9569,U_9568,U_9567] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9567,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9567,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9567,tc_HOL_Obool)),U_9568),U_9569)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9567,tc_HOL_Obool)),U_9569),U_9570))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9567,tc_HOL_Obool)),U_9570),U_9568)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9567,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9567,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9567,tc_HOL_Obool)),U_9568),U_9569)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9567,tc_HOL_Obool)),U_9569),U_9570))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9567,tc_HOL_Obool)),U_9570),U_9568)),
    inference(variable_rename,[status(thm)],[f_2591_1]) ).

fof(f_2591_3,plain,
    ! [U_9567,U_9568,U_9569,U_9570] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9567,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9567,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9567,tc_HOL_Obool)),U_9568),U_9569)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9567,tc_HOL_Obool)),U_9569),U_9570))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9567,tc_HOL_Obool)),U_9570),U_9568)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9567,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9567,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9567,tc_HOL_Obool)),U_9568),U_9569)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9567,tc_HOL_Obool)),U_9569),U_9570))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9567,tc_HOL_Obool)),U_9570),U_9568)),
    inference(definitional_conversion,[status(esa)],[f_2591_2]) ).

cnf(f_2591_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9567,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9567,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9567,tc_HOL_Obool)),U_9568),U_9569)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9567,tc_HOL_Obool)),U_9569),U_9570))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9567,tc_HOL_Obool)),U_9570),U_9568)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9567,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9567,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9567,tc_HOL_Obool)),U_9568),U_9569)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9567,tc_HOL_Obool)),U_9569),U_9570))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9567,tc_HOL_Obool)),U_9570),U_9568)),
    inference(clausify,[status(thm)],[f_2591_3]) ).

fof(f_2592_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_2592_2,plain,
    ! [U_9574,U_9573,U_9572,U_9571] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9571,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9571,tc_HOL_Obool)),U_9572),U_9573)),U_9574) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9571,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9571,tc_HOL_Obool)),U_9572),U_9574)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9571,tc_HOL_Obool)),U_9573),U_9574)),
    inference(variable_rename,[status(thm)],[f_2592_1]) ).

fof(f_2592_3,plain,
    ! [U_9571,U_9572,U_9573,U_9574] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9571,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9571,tc_HOL_Obool)),U_9572),U_9573)),U_9574) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9571,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9571,tc_HOL_Obool)),U_9572),U_9574)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9571,tc_HOL_Obool)),U_9573),U_9574)),
    inference(definitional_conversion,[status(esa)],[f_2592_2]) ).

cnf(f_2592_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9571,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9571,tc_HOL_Obool)),U_9572),U_9573)),U_9574) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9571,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9571,tc_HOL_Obool)),U_9572),U_9574)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9571,tc_HOL_Obool)),U_9573),U_9574)),
    inference(clausify,[status(thm)],[f_2592_3]) ).

fof(f_2593_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_2593_2,plain,
    ! [U_9578,U_9577,U_9576,U_9575] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9575,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9575,tc_HOL_Obool)),U_9576),U_9577)),U_9578) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9575,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9575,tc_HOL_Obool)),U_9576),U_9578)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9575,tc_HOL_Obool)),U_9577),U_9578)),
    inference(variable_rename,[status(thm)],[f_2593_1]) ).

fof(f_2593_3,plain,
    ! [U_9575,U_9576,U_9577,U_9578] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9575,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9575,tc_HOL_Obool)),U_9576),U_9577)),U_9578) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9575,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9575,tc_HOL_Obool)),U_9576),U_9578)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9575,tc_HOL_Obool)),U_9577),U_9578)),
    inference(definitional_conversion,[status(esa)],[f_2593_2]) ).

cnf(f_2593_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9575,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9575,tc_HOL_Obool)),U_9576),U_9577)),U_9578) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9575,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9575,tc_HOL_Obool)),U_9576),U_9578)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9575,tc_HOL_Obool)),U_9577),U_9578)),
    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_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_2594_2,plain,
    ! [U_9582,U_9581,U_9580,U_9579] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9579,tc_HOL_Obool)),U_9580),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9579,tc_HOL_Obool)),U_9581),U_9582)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9579,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9579,tc_HOL_Obool)),U_9580),U_9581)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9579,tc_HOL_Obool)),U_9580),U_9582)),
    inference(variable_rename,[status(thm)],[f_2594_1]) ).

fof(f_2594_3,plain,
    ! [U_9579,U_9580,U_9581,U_9582] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9579,tc_HOL_Obool)),U_9580),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9579,tc_HOL_Obool)),U_9581),U_9582)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9579,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9579,tc_HOL_Obool)),U_9580),U_9581)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9579,tc_HOL_Obool)),U_9580),U_9582)),
    inference(definitional_conversion,[status(esa)],[f_2594_2]) ).

cnf(f_2594_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9579,tc_HOL_Obool)),U_9580),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9579,tc_HOL_Obool)),U_9581),U_9582)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9579,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9579,tc_HOL_Obool)),U_9580),U_9581)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9579,tc_HOL_Obool)),U_9580),U_9582)),
    inference(clausify,[status(thm)],[f_2594_3]) ).

fof(f_2595_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_2595_2,plain,
    ! [U_9586,U_9585,U_9584,U_9583] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9583,tc_HOL_Obool)),U_9584),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9583,tc_HOL_Obool)),U_9585),U_9586)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9583,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9583,tc_HOL_Obool)),U_9584),U_9585)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9583,tc_HOL_Obool)),U_9584),U_9586)),
    inference(variable_rename,[status(thm)],[f_2595_1]) ).

fof(f_2595_3,plain,
    ! [U_9583,U_9584,U_9585,U_9586] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9583,tc_HOL_Obool)),U_9584),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9583,tc_HOL_Obool)),U_9585),U_9586)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9583,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9583,tc_HOL_Obool)),U_9584),U_9585)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9583,tc_HOL_Obool)),U_9584),U_9586)),
    inference(definitional_conversion,[status(esa)],[f_2595_2]) ).

cnf(f_2595_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9583,tc_HOL_Obool)),U_9584),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9583,tc_HOL_Obool)),U_9585),U_9586)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9583,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9583,tc_HOL_Obool)),U_9584),U_9585)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9583,tc_HOL_Obool)),U_9584),U_9586)),
    inference(clausify,[status(thm)],[f_2595_3]) ).

fof(f_2596_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_2596_2,plain,
    ! [U_9588,U_9587] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9587),U_9588),U_9588) = U_9588
      | ~ class_Lattices_Olattice(U_9587) ),
    inference(variable_rename,[status(thm)],[f_2596_1]) ).

fof(f_2596_3,plain,
    ! [U_9587,U_9588] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9587),U_9588),U_9588) = U_9588
      | ~ class_Lattices_Olattice(U_9587) ),
    inference(definitional_conversion,[status(esa)],[f_2596_2]) ).

cnf(f_2596_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9587),U_9588),U_9588) = U_9588
    | ~ class_Lattices_Olattice(U_9587) ),
    inference(clausify,[status(thm)],[f_2596_3]) ).

fof(f_2597_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_2597_2,plain,
    ! [U_9592,U_9591,U_9590,U_9589] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9589,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9589,tc_HOL_Obool)),U_9590),U_9591)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9589,tc_HOL_Obool)),U_9592),U_9591)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9589,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9589,tc_HOL_Obool)),U_9590),U_9591)),U_9592),
    inference(variable_rename,[status(thm)],[f_2597_1]) ).

fof(f_2597_3,plain,
    ! [U_9589,U_9590,U_9591,U_9592] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9589,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9589,tc_HOL_Obool)),U_9590),U_9591)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9589,tc_HOL_Obool)),U_9592),U_9591)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9589,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9589,tc_HOL_Obool)),U_9590),U_9591)),U_9592),
    inference(definitional_conversion,[status(esa)],[f_2597_2]) ).

cnf(f_2597_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9589,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9589,tc_HOL_Obool)),U_9590),U_9591)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9589,tc_HOL_Obool)),U_9592),U_9591)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9589,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9589,tc_HOL_Obool)),U_9590),U_9591)),U_9592),
    inference(clausify,[status(thm)],[f_2597_3]) ).

fof(f_2598_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_2598_2,plain,
    ! [U_9596,U_9595,U_9594,U_9593] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9593,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9593,tc_HOL_Obool)),U_9594),U_9595)),U_9596) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9593,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9593,tc_HOL_Obool)),U_9594),U_9596)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9593,tc_HOL_Obool)),U_9595),U_9596)),
    inference(variable_rename,[status(thm)],[f_2598_1]) ).

fof(f_2598_3,plain,
    ! [U_9593,U_9594,U_9595,U_9596] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9593,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9593,tc_HOL_Obool)),U_9594),U_9595)),U_9596) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9593,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9593,tc_HOL_Obool)),U_9594),U_9596)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9593,tc_HOL_Obool)),U_9595),U_9596)),
    inference(definitional_conversion,[status(esa)],[f_2598_2]) ).

cnf(f_2598_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9593,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9593,tc_HOL_Obool)),U_9594),U_9595)),U_9596) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9593,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9593,tc_HOL_Obool)),U_9594),U_9596)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9593,tc_HOL_Obool)),U_9595),U_9596)),
    inference(clausify,[status(thm)],[f_2598_3]) ).

fof(f_2599_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_2599_2,plain,
    ! [U_9600,U_9599,U_9598,U_9597] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9597,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9597,tc_HOL_Obool)),U_9598),U_9599)),U_9600) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9597,tc_HOL_Obool)),U_9598),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9597,tc_HOL_Obool)),U_9599),U_9600)),
    inference(variable_rename,[status(thm)],[f_2599_1]) ).

fof(f_2599_3,plain,
    ! [U_9597,U_9598,U_9599,U_9600] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9597,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9597,tc_HOL_Obool)),U_9598),U_9599)),U_9600) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9597,tc_HOL_Obool)),U_9598),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9597,tc_HOL_Obool)),U_9599),U_9600)),
    inference(definitional_conversion,[status(esa)],[f_2599_2]) ).

cnf(f_2599_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9597,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9597,tc_HOL_Obool)),U_9598),U_9599)),U_9600) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9597,tc_HOL_Obool)),U_9598),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9597,tc_HOL_Obool)),U_9599),U_9600)),
    inference(clausify,[status(thm)],[f_2599_3]) ).

fof(f_2600_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_2600_2,plain,
    ! [U_9604,U_9603,U_9602,U_9601] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9601,tc_HOL_Obool)),U_9602),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9601,tc_HOL_Obool)),U_9603),U_9604)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9601,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9601,tc_HOL_Obool)),U_9602),U_9603)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9601,tc_HOL_Obool)),U_9602),U_9604)),
    inference(variable_rename,[status(thm)],[f_2600_1]) ).

fof(f_2600_3,plain,
    ! [U_9601,U_9602,U_9603,U_9604] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9601,tc_HOL_Obool)),U_9602),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9601,tc_HOL_Obool)),U_9603),U_9604)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9601,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9601,tc_HOL_Obool)),U_9602),U_9603)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9601,tc_HOL_Obool)),U_9602),U_9604)),
    inference(definitional_conversion,[status(esa)],[f_2600_2]) ).

cnf(f_2600_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9601,tc_HOL_Obool)),U_9602),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9601,tc_HOL_Obool)),U_9603),U_9604)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9601,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9601,tc_HOL_Obool)),U_9602),U_9603)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9601,tc_HOL_Obool)),U_9602),U_9604)),
    inference(clausify,[status(thm)],[f_2600_3]) ).

fof(f_2601_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_2601_2,plain,
    ! [U_9605] :
      ( c_Lattices_Osemilattice__inf__class_Oinf(U_9605) = c_Orderings_Oord__class_Omin(U_9605)
      | ~ class_Orderings_Olinorder(U_9605)
      | ~ class_Lattices_Osemilattice__inf(U_9605) ),
    inference(variable_rename,[status(thm)],[f_2601_1]) ).

fof(f_2601_3,plain,
    ! [U_9605] :
      ( c_Lattices_Osemilattice__inf__class_Oinf(U_9605) = c_Orderings_Oord__class_Omin(U_9605)
      | ~ class_Orderings_Olinorder(U_9605)
      | ~ class_Lattices_Osemilattice__inf(U_9605) ),
    inference(definitional_conversion,[status(esa)],[f_2601_2]) ).

cnf(f_2601_4,plain,
    ( c_Lattices_Osemilattice__inf__class_Oinf(U_9605) = c_Orderings_Oord__class_Omin(U_9605)
    | ~ class_Orderings_Olinorder(U_9605)
    | ~ class_Lattices_Osemilattice__inf(U_9605) ),
    inference(clausify,[status(thm)],[f_2601_3]) ).

fof(f_2602_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_2602_2,plain,
    ! [U_9610,U_9609,U_9608,U_9607,U_9606] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9607,U_9606)),U_9608),U_9609),U_9610) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9606),hAPP(U_9608,U_9610)),hAPP(U_9609,U_9610))
      | ~ class_Lattices_Olattice(U_9606) ),
    inference(variable_rename,[status(thm)],[f_2602_1]) ).

fof(f_2602_3,plain,
    ! [U_9606,U_9607,U_9608,U_9609,U_9610] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9607,U_9606)),U_9608),U_9609),U_9610) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9606),hAPP(U_9608,U_9610)),hAPP(U_9609,U_9610))
      | ~ class_Lattices_Olattice(U_9606) ),
    inference(definitional_conversion,[status(esa)],[f_2602_2]) ).

cnf(f_2602_4,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9607,U_9606)),U_9608),U_9609),U_9610) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9606),hAPP(U_9608,U_9610)),hAPP(U_9609,U_9610))
    | ~ class_Lattices_Olattice(U_9606) ),
    inference(clausify,[status(thm)],[f_2602_3]) ).

fof(f_2603_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_2603_2,plain,
    ! [U_9615,U_9614,U_9613,U_9612,U_9611] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9612,U_9611)),U_9613),U_9614),U_9615) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9611),hAPP(U_9613,U_9615)),hAPP(U_9614,U_9615))
      | ~ class_Lattices_Olattice(U_9611) ),
    inference(variable_rename,[status(thm)],[f_2603_1]) ).

fof(f_2603_3,plain,
    ! [U_9611,U_9612,U_9613,U_9614,U_9615] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9612,U_9611)),U_9613),U_9614),U_9615) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9611),hAPP(U_9613,U_9615)),hAPP(U_9614,U_9615))
      | ~ class_Lattices_Olattice(U_9611) ),
    inference(definitional_conversion,[status(esa)],[f_2603_2]) ).

cnf(f_2603_4,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9612,U_9611)),U_9613),U_9614),U_9615) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9611),hAPP(U_9613,U_9615)),hAPP(U_9614,U_9615))
    | ~ class_Lattices_Olattice(U_9611) ),
    inference(clausify,[status(thm)],[f_2603_3]) ).

fof(f_2604_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_2604_2,plain,
    ! [U_9619,U_9618,U_9617,U_9616] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9616),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9616),U_9617),U_9618)),U_9619) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9616),U_9617),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9616),U_9618),U_9619))
      | ~ class_Lattices_Osemilattice__inf(U_9616) ),
    inference(variable_rename,[status(thm)],[f_2604_1]) ).

fof(f_2604_3,plain,
    ! [U_9616,U_9617,U_9618,U_9619] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9616),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9616),U_9617),U_9618)),U_9619) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9616),U_9617),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9616),U_9618),U_9619))
      | ~ class_Lattices_Osemilattice__inf(U_9616) ),
    inference(definitional_conversion,[status(esa)],[f_2604_2]) ).

cnf(f_2604_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9616),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9616),U_9617),U_9618)),U_9619) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9616),U_9617),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9616),U_9618),U_9619))
    | ~ class_Lattices_Osemilattice__inf(U_9616) ),
    inference(clausify,[status(thm)],[f_2604_3]) ).

fof(f_2605_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_2605_2,plain,
    ! [U_9623,U_9622,U_9621,U_9620] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9620),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9620),U_9621),U_9622)),U_9623) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9620),U_9621),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9620),U_9622),U_9623))
      | ~ class_Lattices_Olattice(U_9620) ),
    inference(variable_rename,[status(thm)],[f_2605_1]) ).

fof(f_2605_3,plain,
    ! [U_9620,U_9621,U_9622,U_9623] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9620),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9620),U_9621),U_9622)),U_9623) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9620),U_9621),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9620),U_9622),U_9623))
      | ~ class_Lattices_Olattice(U_9620) ),
    inference(definitional_conversion,[status(esa)],[f_2605_2]) ).

cnf(f_2605_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9620),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9620),U_9621),U_9622)),U_9623) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9620),U_9621),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9620),U_9622),U_9623))
    | ~ class_Lattices_Olattice(U_9620) ),
    inference(clausify,[status(thm)],[f_2605_3]) ).

fof(f_2606_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_2606_2,plain,
    ! [U_9627,U_9626,U_9625,U_9624] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9624),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9624),U_9625),U_9626)),U_9627) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9624),U_9625),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9624),U_9626),U_9627))
      | ~ class_Lattices_Osemilattice__inf(U_9624) ),
    inference(variable_rename,[status(thm)],[f_2606_1]) ).

fof(f_2606_3,plain,
    ! [U_9624,U_9625,U_9626,U_9627] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9624),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9624),U_9625),U_9626)),U_9627) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9624),U_9625),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9624),U_9626),U_9627))
      | ~ class_Lattices_Osemilattice__inf(U_9624) ),
    inference(definitional_conversion,[status(esa)],[f_2606_2]) ).

cnf(f_2606_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9624),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9624),U_9625),U_9626)),U_9627) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9624),U_9625),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9624),U_9626),U_9627))
    | ~ class_Lattices_Osemilattice__inf(U_9624) ),
    inference(clausify,[status(thm)],[f_2606_3]) ).

fof(f_2607_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_2607_2,plain,
    ! [U_9631,U_9630,U_9629,U_9628] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9628),U_9629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9628),U_9630),U_9631)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9628),U_9630),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9628),U_9629),U_9631))
      | ~ class_Lattices_Osemilattice__inf(U_9628) ),
    inference(variable_rename,[status(thm)],[f_2607_1]) ).

fof(f_2607_3,plain,
    ! [U_9628,U_9629,U_9630,U_9631] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9628),U_9629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9628),U_9630),U_9631)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9628),U_9630),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9628),U_9629),U_9631))
      | ~ class_Lattices_Osemilattice__inf(U_9628) ),
    inference(definitional_conversion,[status(esa)],[f_2607_2]) ).

cnf(f_2607_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9628),U_9629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9628),U_9630),U_9631)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9628),U_9630),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9628),U_9629),U_9631))
    | ~ class_Lattices_Osemilattice__inf(U_9628) ),
    inference(clausify,[status(thm)],[f_2607_3]) ).

fof(f_2608_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_2608_2,plain,
    ! [U_9635,U_9634,U_9633,U_9632] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9632),U_9633),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9632),U_9634),U_9635)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9632),U_9634),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9632),U_9633),U_9635))
      | ~ class_Lattices_Olattice(U_9632) ),
    inference(variable_rename,[status(thm)],[f_2608_1]) ).

fof(f_2608_3,plain,
    ! [U_9632,U_9633,U_9634,U_9635] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9632),U_9633),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9632),U_9634),U_9635)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9632),U_9634),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9632),U_9633),U_9635))
      | ~ class_Lattices_Olattice(U_9632) ),
    inference(definitional_conversion,[status(esa)],[f_2608_2]) ).

cnf(f_2608_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9632),U_9633),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9632),U_9634),U_9635)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9632),U_9634),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9632),U_9633),U_9635))
    | ~ class_Lattices_Olattice(U_9632) ),
    inference(clausify,[status(thm)],[f_2608_3]) ).

fof(f_2609_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_2609_2,plain,
    ! [U_9639,U_9638,U_9637,U_9636] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9636),U_9637),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9636),U_9638),U_9639)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9636),U_9638),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9636),U_9637),U_9639))
      | ~ class_Lattices_Osemilattice__inf(U_9636) ),
    inference(variable_rename,[status(thm)],[f_2609_1]) ).

fof(f_2609_3,plain,
    ! [U_9636,U_9637,U_9638,U_9639] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9636),U_9637),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9636),U_9638),U_9639)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9636),U_9638),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9636),U_9637),U_9639))
      | ~ class_Lattices_Osemilattice__inf(U_9636) ),
    inference(definitional_conversion,[status(esa)],[f_2609_2]) ).

cnf(f_2609_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9636),U_9637),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9636),U_9638),U_9639)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9636),U_9638),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9636),U_9637),U_9639))
    | ~ class_Lattices_Osemilattice__inf(U_9636) ),
    inference(clausify,[status(thm)],[f_2609_3]) ).

fof(f_2610_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_2610_2,plain,
    ! [U_9642,U_9641,U_9640] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9640),U_9641),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9640),U_9641),U_9642)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9640),U_9641),U_9642)
      | ~ class_Lattices_Osemilattice__inf(U_9640) ),
    inference(variable_rename,[status(thm)],[f_2610_1]) ).

fof(f_2610_3,plain,
    ! [U_9641,U_9640,U_9642] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9640),U_9641),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9640),U_9641),U_9642)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9640),U_9641),U_9642)
      | ~ class_Lattices_Osemilattice__inf(U_9640) ),
    inference(definitional_conversion,[status(esa)],[f_2610_2]) ).

cnf(f_2610_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9640),U_9641),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9640),U_9641),U_9642)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9640),U_9641),U_9642)
    | ~ class_Lattices_Osemilattice__inf(U_9640) ),
    inference(clausify,[status(thm)],[f_2610_3]) ).

fof(f_2611_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_2611_2,plain,
    ! [U_9645,U_9644,U_9643] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9643),U_9644),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9643),U_9644),U_9645)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9643),U_9644),U_9645)
      | ~ class_Lattices_Olattice(U_9643) ),
    inference(variable_rename,[status(thm)],[f_2611_1]) ).

fof(f_2611_3,plain,
    ! [U_9643,U_9644,U_9645] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9643),U_9644),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9643),U_9644),U_9645)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9643),U_9644),U_9645)
      | ~ class_Lattices_Olattice(U_9643) ),
    inference(definitional_conversion,[status(esa)],[f_2611_2]) ).

cnf(f_2611_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9643),U_9644),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9643),U_9644),U_9645)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9643),U_9644),U_9645)
    | ~ class_Lattices_Olattice(U_9643) ),
    inference(clausify,[status(thm)],[f_2611_3]) ).

fof(f_2612_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_2612_2,plain,
    ! [U_9648,U_9647,U_9646] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9646),U_9647),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9646),U_9647),U_9648)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9646),U_9647),U_9648)
      | ~ class_Lattices_Osemilattice__inf(U_9646) ),
    inference(variable_rename,[status(thm)],[f_2612_1]) ).

fof(f_2612_3,plain,
    ! [U_9646,U_9647,U_9648] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9646),U_9647),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9646),U_9647),U_9648)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9646),U_9647),U_9648)
      | ~ class_Lattices_Osemilattice__inf(U_9646) ),
    inference(definitional_conversion,[status(esa)],[f_2612_2]) ).

cnf(f_2612_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9646),U_9647),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9646),U_9647),U_9648)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9646),U_9647),U_9648)
    | ~ class_Lattices_Osemilattice__inf(U_9646) ),
    inference(clausify,[status(thm)],[f_2612_3]) ).

fof(f_2613_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_2613_2,plain,
    ! [U_9651,U_9650,U_9649] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9649),U_9650),U_9651) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9649),U_9651),U_9650)
      | ~ class_Lattices_Osemilattice__inf(U_9649) ),
    inference(variable_rename,[status(thm)],[f_2613_1]) ).

fof(f_2613_3,plain,
    ! [U_9649,U_9650,U_9651] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9649),U_9650),U_9651) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9649),U_9651),U_9650)
      | ~ class_Lattices_Osemilattice__inf(U_9649) ),
    inference(definitional_conversion,[status(esa)],[f_2613_2]) ).

cnf(f_2613_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9649),U_9650),U_9651) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9649),U_9651),U_9650)
    | ~ class_Lattices_Osemilattice__inf(U_9649) ),
    inference(clausify,[status(thm)],[f_2613_3]) ).

fof(f_2614_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_2614_2,plain,
    ! [U_9654,U_9653,U_9652] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9652),U_9653),U_9654) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9652),U_9654),U_9653)
      | ~ class_Lattices_Olattice(U_9652) ),
    inference(variable_rename,[status(thm)],[f_2614_1]) ).

fof(f_2614_3,plain,
    ! [U_9652,U_9653,U_9654] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9652),U_9653),U_9654) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9652),U_9654),U_9653)
      | ~ class_Lattices_Olattice(U_9652) ),
    inference(definitional_conversion,[status(esa)],[f_2614_2]) ).

cnf(f_2614_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9652),U_9653),U_9654) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9652),U_9654),U_9653)
    | ~ class_Lattices_Olattice(U_9652) ),
    inference(clausify,[status(thm)],[f_2614_3]) ).

fof(f_2615_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_2615_2,plain,
    ! [U_9657,U_9656,U_9655] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9655),U_9656),U_9657) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9655),U_9657),U_9656)
      | ~ class_Lattices_Osemilattice__inf(U_9655) ),
    inference(variable_rename,[status(thm)],[f_2615_1]) ).

fof(f_2615_3,plain,
    ! [U_9655,U_9656,U_9657] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9655),U_9656),U_9657) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9655),U_9657),U_9656)
      | ~ class_Lattices_Osemilattice__inf(U_9655) ),
    inference(definitional_conversion,[status(esa)],[f_2615_2]) ).

cnf(f_2615_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9655),U_9656),U_9657) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9655),U_9657),U_9656)
    | ~ class_Lattices_Osemilattice__inf(U_9655) ),
    inference(clausify,[status(thm)],[f_2615_3]) ).

fof(f_2616_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_2616_2,plain,
    ! [U_9659,U_9658] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9658),U_9659),U_9659) = U_9659
      | ~ class_Lattices_Osemilattice__inf(U_9658) ),
    inference(variable_rename,[status(thm)],[f_2616_1]) ).

fof(f_2616_3,plain,
    ! [U_9658,U_9659] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9658),U_9659),U_9659) = U_9659
      | ~ class_Lattices_Osemilattice__inf(U_9658) ),
    inference(definitional_conversion,[status(esa)],[f_2616_2]) ).

cnf(f_2616_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9658),U_9659),U_9659) = U_9659
    | ~ class_Lattices_Osemilattice__inf(U_9658) ),
    inference(clausify,[status(thm)],[f_2616_3]) ).

fof(f_2617_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_2617_2,plain,
    ! [U_9661,U_9660] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9660),U_9661),U_9661) = U_9661
      | ~ class_Lattices_Osemilattice__inf(U_9660) ),
    inference(variable_rename,[status(thm)],[f_2617_1]) ).

fof(f_2617_3,plain,
    ! [U_9660,U_9661] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9660),U_9661),U_9661) = U_9661
      | ~ class_Lattices_Osemilattice__inf(U_9660) ),
    inference(definitional_conversion,[status(esa)],[f_2617_2]) ).

cnf(f_2617_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9660),U_9661),U_9661) = U_9661
    | ~ class_Lattices_Osemilattice__inf(U_9660) ),
    inference(clausify,[status(thm)],[f_2617_3]) ).

fof(f_2618_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_2618_2,plain,
    ! [U_9665,U_9664,U_9663,U_9662] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9662,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9662,tc_HOL_Obool)),U_9663),U_9664)),U_9665) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9662,tc_HOL_Obool)),U_9663),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9662,tc_HOL_Obool)),U_9664),U_9665)),
    inference(variable_rename,[status(thm)],[f_2618_1]) ).

fof(f_2618_3,plain,
    ! [U_9662,U_9663,U_9664,U_9665] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9662,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9662,tc_HOL_Obool)),U_9663),U_9664)),U_9665) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9662,tc_HOL_Obool)),U_9663),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9662,tc_HOL_Obool)),U_9664),U_9665)),
    inference(definitional_conversion,[status(esa)],[f_2618_2]) ).

cnf(f_2618_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9662,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9662,tc_HOL_Obool)),U_9663),U_9664)),U_9665) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9662,tc_HOL_Obool)),U_9663),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9662,tc_HOL_Obool)),U_9664),U_9665)),
    inference(clausify,[status(thm)],[f_2618_3]) ).

fof(f_2619_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_2619_2,plain,
    ! [U_9669,U_9668,U_9667,U_9666] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9666,tc_HOL_Obool)),U_9667),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9666,tc_HOL_Obool)),U_9668),U_9669)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9666,tc_HOL_Obool)),U_9668),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9666,tc_HOL_Obool)),U_9667),U_9669)),
    inference(variable_rename,[status(thm)],[f_2619_1]) ).

fof(f_2619_3,plain,
    ! [U_9666,U_9667,U_9668,U_9669] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9666,tc_HOL_Obool)),U_9667),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9666,tc_HOL_Obool)),U_9668),U_9669)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9666,tc_HOL_Obool)),U_9668),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9666,tc_HOL_Obool)),U_9667),U_9669)),
    inference(definitional_conversion,[status(esa)],[f_2619_2]) ).

cnf(f_2619_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9666,tc_HOL_Obool)),U_9667),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9666,tc_HOL_Obool)),U_9668),U_9669)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9666,tc_HOL_Obool)),U_9668),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9666,tc_HOL_Obool)),U_9667),U_9669)),
    inference(clausify,[status(thm)],[f_2619_3]) ).

fof(f_2620_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_2620_2,plain,
    ! [U_9672,U_9671,U_9670] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9670,tc_HOL_Obool)),U_9671),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9670,tc_HOL_Obool)),U_9671),U_9672)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9670,tc_HOL_Obool)),U_9671),U_9672),
    inference(variable_rename,[status(thm)],[f_2620_1]) ).

fof(f_2620_3,plain,
    ! [U_9670,U_9671,U_9672] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9670,tc_HOL_Obool)),U_9671),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9670,tc_HOL_Obool)),U_9671),U_9672)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9670,tc_HOL_Obool)),U_9671),U_9672),
    inference(definitional_conversion,[status(esa)],[f_2620_2]) ).

cnf(f_2620_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9670,tc_HOL_Obool)),U_9671),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9670,tc_HOL_Obool)),U_9671),U_9672)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9670,tc_HOL_Obool)),U_9671),U_9672),
    inference(clausify,[status(thm)],[f_2620_3]) ).

fof(f_2621_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_2621_2,plain,
    ! [U_9675,U_9674,U_9673] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9673,tc_HOL_Obool)),U_9674),U_9675) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9673,tc_HOL_Obool)),U_9675),U_9674),
    inference(variable_rename,[status(thm)],[f_2621_1]) ).

fof(f_2621_3,plain,
    ! [U_9673,U_9674,U_9675] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9673,tc_HOL_Obool)),U_9674),U_9675) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9673,tc_HOL_Obool)),U_9675),U_9674),
    inference(definitional_conversion,[status(esa)],[f_2621_2]) ).

cnf(f_2621_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9673,tc_HOL_Obool)),U_9674),U_9675) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9673,tc_HOL_Obool)),U_9675),U_9674),
    inference(clausify,[status(thm)],[f_2621_3]) ).

fof(f_2622_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_2622_2,plain,
    ! [U_9677,U_9676] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9676,tc_HOL_Obool)),U_9677),U_9677) = U_9677,
    inference(variable_rename,[status(thm)],[f_2622_1]) ).

fof(f_2622_3,plain,
    ! [U_9676,U_9677] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9676,tc_HOL_Obool)),U_9677),U_9677) = U_9677,
    inference(definitional_conversion,[status(esa)],[f_2622_2]) ).

cnf(f_2622_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9676,tc_HOL_Obool)),U_9677),U_9677) = U_9677,
    inference(clausify,[status(thm)],[f_2622_3]) ).

fof(f_2623_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_2623_2,plain,
    ! [U_9681,U_9680,U_9679,U_9678] :
      ( hBOOL(hAPP(U_9680,U_9681))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9678,tc_HOL_Obool)),U_9679),U_9680),U_9681)) ),
    inference(variable_rename,[status(thm)],[f_2623_1]) ).

fof(f_2623_3,plain,
    ! [U_9681,U_9680] :
      ( ! [U_9679,U_9678] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9678,tc_HOL_Obool)),U_9679),U_9680),U_9681))
      | hBOOL(hAPP(U_9680,U_9681)) ),
    inference(miniscope,[status(thm)],[f_2623_2]) ).

fof(f_2623_4,plain,
    ! [U_9678,U_9679,U_9680,U_9681] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9678,tc_HOL_Obool)),U_9679),U_9680),U_9681))
      | hBOOL(hAPP(U_9680,U_9681)) ),
    inference(definitional_conversion,[status(esa)],[f_2623_3]) ).

cnf(f_2623_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9678,tc_HOL_Obool)),U_9679),U_9680),U_9681))
    | hBOOL(hAPP(U_9680,U_9681)) ),
    inference(clausify,[status(thm)],[f_2623_4]) ).

fof(f_2624_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_2624_2,plain,
    ! [U_9685,U_9684,U_9683,U_9682] :
      ( hBOOL(hAPP(U_9683,U_9685))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9682,tc_HOL_Obool)),U_9683),U_9684),U_9685)) ),
    inference(variable_rename,[status(thm)],[f_2624_1]) ).

fof(f_2624_3,plain,
    ! [U_9685,U_9684,U_9683] :
      ( ! [U_9682] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9682,tc_HOL_Obool)),U_9683),U_9684),U_9685))
      | hBOOL(hAPP(U_9683,U_9685)) ),
    inference(miniscope,[status(thm)],[f_2624_2]) ).

fof(f_2624_4,plain,
    ! [U_9682,U_9683,U_9684,U_9685] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9682,tc_HOL_Obool)),U_9683),U_9684),U_9685))
      | hBOOL(hAPP(U_9683,U_9685)) ),
    inference(definitional_conversion,[status(esa)],[f_2624_3]) ).

cnf(f_2624_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9682,tc_HOL_Obool)),U_9683),U_9684),U_9685))
    | hBOOL(hAPP(U_9683,U_9685)) ),
    inference(clausify,[status(thm)],[f_2624_4]) ).

fof(f_2625_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_2625_2,plain,
    ! [U_9689,U_9688,U_9687,U_9686] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9686,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9686),U_9687),U_9688)),hAPP(hAPP(c_Set_Oinsert(U_9686),U_9687),U_9689)) = hAPP(hAPP(c_Set_Oinsert(U_9686),U_9687),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9686,tc_HOL_Obool)),U_9688),U_9689)),
    inference(variable_rename,[status(thm)],[f_2625_1]) ).

fof(f_2625_3,plain,
    ! [U_9686,U_9687,U_9688,U_9689] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9686,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9686),U_9687),U_9688)),hAPP(hAPP(c_Set_Oinsert(U_9686),U_9687),U_9689)) = hAPP(hAPP(c_Set_Oinsert(U_9686),U_9687),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9686,tc_HOL_Obool)),U_9688),U_9689)),
    inference(definitional_conversion,[status(esa)],[f_2625_2]) ).

cnf(f_2625_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9686,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9686),U_9687),U_9688)),hAPP(hAPP(c_Set_Oinsert(U_9686),U_9687),U_9689)) = hAPP(hAPP(c_Set_Oinsert(U_9686),U_9687),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9686,tc_HOL_Obool)),U_9688),U_9689)),
    inference(clausify,[status(thm)],[f_2625_3]) ).

fof(f_2626_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_2626_2,plain,
    ! [U_9691,U_9690] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9690),U_9691))
      | ~ c_Nat__Transfer_Onat__set(U_9691)
      | ~ c_Nat__Transfer_Onat__set(U_9690) ),
    inference(variable_rename,[status(thm)],[f_2626_1]) ).

fof(f_2626_3,plain,
    ! [U_9690,U_9691] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9690),U_9691))
      | ~ c_Nat__Transfer_Onat__set(U_9691)
      | ~ c_Nat__Transfer_Onat__set(U_9690) ),
    inference(definitional_conversion,[status(esa)],[f_2626_2]) ).

cnf(f_2626_4,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9690),U_9691))
    | ~ c_Nat__Transfer_Onat__set(U_9691)
    | ~ c_Nat__Transfer_Onat__set(U_9690) ),
    inference(clausify,[status(thm)],[f_2626_3]) ).

fof(f_2627_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_2627_2,plain,
    ! [U_9695,U_9694,U_9693,U_9692] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9692),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9692),U_9693),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9692),U_9694),U_9695))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9692),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9692),U_9693),U_9694)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9692),U_9693),U_9695))))
      | ~ class_Lattices_Olattice(U_9692) ),
    inference(variable_rename,[status(thm)],[f_2627_1]) ).

fof(f_2627_3,plain,
    ! [U_9692,U_9693,U_9694,U_9695] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9692),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9692),U_9693),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9692),U_9694),U_9695))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9692),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9692),U_9693),U_9694)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9692),U_9693),U_9695))))
      | ~ class_Lattices_Olattice(U_9692) ),
    inference(definitional_conversion,[status(esa)],[f_2627_2]) ).

cnf(f_2627_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9692),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9692),U_9693),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9692),U_9694),U_9695))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9692),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9692),U_9693),U_9694)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9692),U_9693),U_9695))))
    | ~ class_Lattices_Olattice(U_9692) ),
    inference(clausify,[status(thm)],[f_2627_3]) ).

fof(f_2628_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_2628_2,plain,
    ! [U_9699,U_9698,U_9697,U_9696] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9696),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9696),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9696),U_9697),U_9698)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9696),U_9697),U_9699))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9696),U_9697),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9696),U_9698),U_9699))))
      | ~ class_Lattices_Olattice(U_9696) ),
    inference(variable_rename,[status(thm)],[f_2628_1]) ).

fof(f_2628_3,plain,
    ! [U_9696,U_9697,U_9698,U_9699] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9696),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9696),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9696),U_9697),U_9698)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9696),U_9697),U_9699))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9696),U_9697),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9696),U_9698),U_9699))))
      | ~ class_Lattices_Olattice(U_9696) ),
    inference(definitional_conversion,[status(esa)],[f_2628_2]) ).

cnf(f_2628_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9696),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9696),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9696),U_9697),U_9698)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9696),U_9697),U_9699))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9696),U_9697),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9696),U_9698),U_9699))))
    | ~ class_Lattices_Olattice(U_9696) ),
    inference(clausify,[status(thm)],[f_2628_3]) ).

fof(f_2629_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_2629_2,plain,
    ! [U_9701,U_9700] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9700),hAPP(c_Groups_Ouminus__class_Ouminus(U_9700),U_9701)),U_9701) = c_Orderings_Obot__class_Obot(U_9700)
      | ~ class_Lattices_Oboolean__algebra(U_9700) ),
    inference(variable_rename,[status(thm)],[f_2629_1]) ).

fof(f_2629_3,plain,
    ! [U_9700,U_9701] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9700),hAPP(c_Groups_Ouminus__class_Ouminus(U_9700),U_9701)),U_9701) = c_Orderings_Obot__class_Obot(U_9700)
      | ~ class_Lattices_Oboolean__algebra(U_9700) ),
    inference(definitional_conversion,[status(esa)],[f_2629_2]) ).

cnf(f_2629_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9700),hAPP(c_Groups_Ouminus__class_Ouminus(U_9700),U_9701)),U_9701) = c_Orderings_Obot__class_Obot(U_9700)
    | ~ class_Lattices_Oboolean__algebra(U_9700) ),
    inference(clausify,[status(thm)],[f_2629_3]) ).

fof(f_2630_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_2630_2,plain,
    ! [U_9703,U_9702] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9702),U_9703),hAPP(c_Groups_Ouminus__class_Ouminus(U_9702),U_9703)) = c_Orderings_Obot__class_Obot(U_9702)
      | ~ class_Lattices_Oboolean__algebra(U_9702) ),
    inference(variable_rename,[status(thm)],[f_2630_1]) ).

fof(f_2630_3,plain,
    ! [U_9702,U_9703] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9702),U_9703),hAPP(c_Groups_Ouminus__class_Ouminus(U_9702),U_9703)) = c_Orderings_Obot__class_Obot(U_9702)
      | ~ class_Lattices_Oboolean__algebra(U_9702) ),
    inference(definitional_conversion,[status(esa)],[f_2630_2]) ).

cnf(f_2630_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9702),U_9703),hAPP(c_Groups_Ouminus__class_Ouminus(U_9702),U_9703)) = c_Orderings_Obot__class_Obot(U_9702)
    | ~ class_Lattices_Oboolean__algebra(U_9702) ),
    inference(clausify,[status(thm)],[f_2630_3]) ).

fof(f_2631_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_2631_2,plain,
    ! [U_9706,U_9705,U_9704] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9704),U_9705),U_9706) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9704),U_9705),hAPP(c_Groups_Ouminus__class_Ouminus(U_9704),U_9706))
      | ~ class_Lattices_Oboolean__algebra(U_9704) ),
    inference(variable_rename,[status(thm)],[f_2631_1]) ).

fof(f_2631_3,plain,
    ! [U_9704,U_9705,U_9706] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9704),U_9705),U_9706) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9704),U_9705),hAPP(c_Groups_Ouminus__class_Ouminus(U_9704),U_9706))
      | ~ class_Lattices_Oboolean__algebra(U_9704) ),
    inference(definitional_conversion,[status(esa)],[f_2631_2]) ).

cnf(f_2631_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9704),U_9705),U_9706) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9704),U_9705),hAPP(c_Groups_Ouminus__class_Ouminus(U_9704),U_9706))
    | ~ class_Lattices_Oboolean__algebra(U_9704) ),
    inference(clausify,[status(thm)],[f_2631_3]) ).

fof(f_2632_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_2632_2,plain,
    ! [U_9709,U_9708,U_9707] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9707),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9707),U_9708),U_9709)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9707),hAPP(c_Groups_Ouminus__class_Ouminus(U_9707),U_9708)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9707),U_9709))
      | ~ class_Lattices_Oboolean__algebra(U_9707) ),
    inference(variable_rename,[status(thm)],[f_2632_1]) ).

fof(f_2632_3,plain,
    ! [U_9707,U_9708,U_9709] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9707),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9707),U_9708),U_9709)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9707),hAPP(c_Groups_Ouminus__class_Ouminus(U_9707),U_9708)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9707),U_9709))
      | ~ class_Lattices_Oboolean__algebra(U_9707) ),
    inference(definitional_conversion,[status(esa)],[f_2632_2]) ).

cnf(f_2632_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9707),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9707),U_9708),U_9709)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9707),hAPP(c_Groups_Ouminus__class_Ouminus(U_9707),U_9708)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9707),U_9709))
    | ~ class_Lattices_Oboolean__algebra(U_9707) ),
    inference(clausify,[status(thm)],[f_2632_3]) ).

fof(f_2633_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_2633_2,plain,
    ! [U_9712,U_9711,U_9710] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9710),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9710),U_9711),U_9712)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9710),hAPP(c_Groups_Ouminus__class_Ouminus(U_9710),U_9711)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9710),U_9712))
      | ~ class_Lattices_Oboolean__algebra(U_9710) ),
    inference(variable_rename,[status(thm)],[f_2633_1]) ).

fof(f_2633_3,plain,
    ! [U_9710,U_9711,U_9712] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9710),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9710),U_9711),U_9712)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9710),hAPP(c_Groups_Ouminus__class_Ouminus(U_9710),U_9711)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9710),U_9712))
      | ~ class_Lattices_Oboolean__algebra(U_9710) ),
    inference(definitional_conversion,[status(esa)],[f_2633_2]) ).

cnf(f_2633_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_9710),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9710),U_9711),U_9712)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9710),hAPP(c_Groups_Ouminus__class_Ouminus(U_9710),U_9711)),hAPP(c_Groups_Ouminus__class_Ouminus(U_9710),U_9712))
    | ~ class_Lattices_Oboolean__algebra(U_9710) ),
    inference(clausify,[status(thm)],[f_2633_3]) ).

fof(f_2634_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_2634_2,plain,
    ! [U_9716,U_9715,U_9714,U_9713] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9713,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9713),U_9714),U_9716)),U_9715) = hAPP(hAPP(c_Set_Oinsert(U_9713),U_9714),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9713,tc_HOL_Obool)),U_9716),U_9715))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9713),U_9714),U_9715)) ),
    inference(variable_rename,[status(thm)],[f_2634_1]) ).

fof(f_2634_3,plain,
    ! [U_9713,U_9714,U_9715,U_9716] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9713,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9713),U_9714),U_9716)),U_9715) = hAPP(hAPP(c_Set_Oinsert(U_9713),U_9714),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9713,tc_HOL_Obool)),U_9716),U_9715))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9713),U_9714),U_9715)) ),
    inference(definitional_conversion,[status(esa)],[f_2634_2]) ).

cnf(f_2634_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9713,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9713),U_9714),U_9716)),U_9715) = hAPP(hAPP(c_Set_Oinsert(U_9713),U_9714),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9713,tc_HOL_Obool)),U_9716),U_9715))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9713),U_9714),U_9715)) ),
    inference(clausify,[status(thm)],[f_2634_3]) ).

fof(f_2635_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_2635_2,plain,
    ! [U_9720,U_9719,U_9718,U_9717] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9717,tc_HOL_Obool)),U_9719),hAPP(hAPP(c_Set_Oinsert(U_9717),U_9718),U_9720)) = hAPP(hAPP(c_Set_Oinsert(U_9717),U_9718),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9717,tc_HOL_Obool)),U_9719),U_9720))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9717),U_9718),U_9719)) ),
    inference(variable_rename,[status(thm)],[f_2635_1]) ).

fof(f_2635_3,plain,
    ! [U_9717,U_9718,U_9719,U_9720] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9717,tc_HOL_Obool)),U_9719),hAPP(hAPP(c_Set_Oinsert(U_9717),U_9718),U_9720)) = hAPP(hAPP(c_Set_Oinsert(U_9717),U_9718),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9717,tc_HOL_Obool)),U_9719),U_9720))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9717),U_9718),U_9719)) ),
    inference(definitional_conversion,[status(esa)],[f_2635_2]) ).

cnf(f_2635_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9717,tc_HOL_Obool)),U_9719),hAPP(hAPP(c_Set_Oinsert(U_9717),U_9718),U_9720)) = hAPP(hAPP(c_Set_Oinsert(U_9717),U_9718),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9717,tc_HOL_Obool)),U_9719),U_9720))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9717),U_9718),U_9719)) ),
    inference(clausify,[status(thm)],[f_2635_3]) ).

fof(f_2636_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_2636_2,plain,
    ! [U_9724,U_9723,U_9722,U_9721] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9721,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9721),U_9722),U_9724)),U_9723) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9721,tc_HOL_Obool)),U_9724),U_9723)
      | hBOOL(hAPP(hAPP(c_member(U_9721),U_9722),U_9723)) ),
    inference(variable_rename,[status(thm)],[f_2636_1]) ).

fof(f_2636_3,plain,
    ! [U_9721,U_9722,U_9723,U_9724] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9721,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9721),U_9722),U_9724)),U_9723) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9721,tc_HOL_Obool)),U_9724),U_9723)
      | hBOOL(hAPP(hAPP(c_member(U_9721),U_9722),U_9723)) ),
    inference(definitional_conversion,[status(esa)],[f_2636_2]) ).

cnf(f_2636_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9721,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9721),U_9722),U_9724)),U_9723) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9721,tc_HOL_Obool)),U_9724),U_9723)
    | hBOOL(hAPP(hAPP(c_member(U_9721),U_9722),U_9723)) ),
    inference(clausify,[status(thm)],[f_2636_3]) ).

fof(f_2637_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_2637_2,plain,
    ! [U_9728,U_9727,U_9726,U_9725] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9725,tc_HOL_Obool)),U_9727),hAPP(hAPP(c_Set_Oinsert(U_9725),U_9726),U_9728)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9725,tc_HOL_Obool)),U_9727),U_9728)
      | hBOOL(hAPP(hAPP(c_member(U_9725),U_9726),U_9727)) ),
    inference(variable_rename,[status(thm)],[f_2637_1]) ).

fof(f_2637_3,plain,
    ! [U_9725,U_9726,U_9727,U_9728] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9725,tc_HOL_Obool)),U_9727),hAPP(hAPP(c_Set_Oinsert(U_9725),U_9726),U_9728)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9725,tc_HOL_Obool)),U_9727),U_9728)
      | hBOOL(hAPP(hAPP(c_member(U_9725),U_9726),U_9727)) ),
    inference(definitional_conversion,[status(esa)],[f_2637_2]) ).

cnf(f_2637_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9725,tc_HOL_Obool)),U_9727),hAPP(hAPP(c_Set_Oinsert(U_9725),U_9726),U_9728)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9725,tc_HOL_Obool)),U_9727),U_9728)
    | hBOOL(hAPP(hAPP(c_member(U_9725),U_9726),U_9727)) ),
    inference(clausify,[status(thm)],[f_2637_3]) ).

fof(f_2638_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_2638_2,plain,
    ! [U_9732,U_9731,U_9730,U_9729] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9729,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9729),U_9730),U_9732)),U_9731) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9729,tc_HOL_Obool)),U_9732),U_9731)
        | hBOOL(hAPP(hAPP(c_member(U_9729),U_9730),U_9731)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9729,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9729),U_9730),U_9732)),U_9731) = hAPP(hAPP(c_Set_Oinsert(U_9729),U_9730),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9729,tc_HOL_Obool)),U_9732),U_9731))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9729),U_9730),U_9731)) ) ),
    inference(variable_rename,[status(thm)],[f_2638_1]) ).

fof(f_2638_3,plain,
    ( ! [U_9740,U_9738,U_9736,U_9734] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9734,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9734),U_9736),U_9740)),U_9738) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9734,tc_HOL_Obool)),U_9740),U_9738)
        | hBOOL(hAPP(hAPP(c_member(U_9734),U_9736),U_9738)) )
    & ! [U_9739,U_9737,U_9735,U_9733] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9733,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9733),U_9735),U_9739)),U_9737) = hAPP(hAPP(c_Set_Oinsert(U_9733),U_9735),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9733,tc_HOL_Obool)),U_9739),U_9737))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9733),U_9735),U_9737)) ) ),
    inference(miniscope,[status(thm)],[f_2638_2]) ).

fof(f_2638_4,plain,
    ( ! [U_9734,U_9736,U_9738,U_9740] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9734,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9734),U_9736),U_9740)),U_9738) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9734,tc_HOL_Obool)),U_9740),U_9738)
        | hBOOL(hAPP(hAPP(c_member(U_9734),U_9736),U_9738)) )
    & ! [U_9739,U_9735,U_9733,U_9737] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9733,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9733),U_9735),U_9739)),U_9737) = hAPP(hAPP(c_Set_Oinsert(U_9733),U_9735),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9733,tc_HOL_Obool)),U_9739),U_9737))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9733),U_9735),U_9737)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2638_3]) ).

cnf(f_2638_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9733,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9733),U_9735),U_9739)),U_9737) = hAPP(hAPP(c_Set_Oinsert(U_9733),U_9735),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9733,tc_HOL_Obool)),U_9739),U_9737))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9733),U_9735),U_9737)) ),
    inference(clausify,[status(thm)],[f_2638_4]) ).

cnf(f_2638_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9734,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9734),U_9736),U_9740)),U_9738) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9734,tc_HOL_Obool)),U_9740),U_9738)
    | hBOOL(hAPP(hAPP(c_member(U_9734),U_9736),U_9738)) ),
    inference(clausify,[status(thm)],[f_2638_4]) ).

fof(f_2639_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_2639_2,plain,
    ! [U_9744,U_9743,U_9742,U_9741] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9741,tc_HOL_Obool)),U_9743),hAPP(hAPP(c_Set_Oinsert(U_9741),U_9742),U_9744)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9741,tc_HOL_Obool)),U_9743),U_9744)
        | hBOOL(hAPP(hAPP(c_member(U_9741),U_9742),U_9743)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9741,tc_HOL_Obool)),U_9743),hAPP(hAPP(c_Set_Oinsert(U_9741),U_9742),U_9744)) = hAPP(hAPP(c_Set_Oinsert(U_9741),U_9742),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9741,tc_HOL_Obool)),U_9743),U_9744))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9741),U_9742),U_9743)) ) ),
    inference(variable_rename,[status(thm)],[f_2639_1]) ).

fof(f_2639_3,plain,
    ( ! [U_9752,U_9750,U_9748,U_9746] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9746,tc_HOL_Obool)),U_9750),hAPP(hAPP(c_Set_Oinsert(U_9746),U_9748),U_9752)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9746,tc_HOL_Obool)),U_9750),U_9752)
        | hBOOL(hAPP(hAPP(c_member(U_9746),U_9748),U_9750)) )
    & ! [U_9751,U_9749,U_9747,U_9745] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9745,tc_HOL_Obool)),U_9749),hAPP(hAPP(c_Set_Oinsert(U_9745),U_9747),U_9751)) = hAPP(hAPP(c_Set_Oinsert(U_9745),U_9747),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9745,tc_HOL_Obool)),U_9749),U_9751))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9745),U_9747),U_9749)) ) ),
    inference(miniscope,[status(thm)],[f_2639_2]) ).

fof(f_2639_4,plain,
    ( ! [U_9746,U_9748,U_9750,U_9752] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9746,tc_HOL_Obool)),U_9750),hAPP(hAPP(c_Set_Oinsert(U_9746),U_9748),U_9752)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9746,tc_HOL_Obool)),U_9750),U_9752)
        | hBOOL(hAPP(hAPP(c_member(U_9746),U_9748),U_9750)) )
    & ! [U_9749,U_9751,U_9747,U_9745] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9745,tc_HOL_Obool)),U_9749),hAPP(hAPP(c_Set_Oinsert(U_9745),U_9747),U_9751)) = hAPP(hAPP(c_Set_Oinsert(U_9745),U_9747),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9745,tc_HOL_Obool)),U_9749),U_9751))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9745),U_9747),U_9749)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2639_3]) ).

cnf(f_2639_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9745,tc_HOL_Obool)),U_9749),hAPP(hAPP(c_Set_Oinsert(U_9745),U_9747),U_9751)) = hAPP(hAPP(c_Set_Oinsert(U_9745),U_9747),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9745,tc_HOL_Obool)),U_9749),U_9751))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9745),U_9747),U_9749)) ),
    inference(clausify,[status(thm)],[f_2639_4]) ).

cnf(f_2639_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9746,tc_HOL_Obool)),U_9750),hAPP(hAPP(c_Set_Oinsert(U_9746),U_9748),U_9752)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9746,tc_HOL_Obool)),U_9750),U_9752)
    | hBOOL(hAPP(hAPP(c_member(U_9746),U_9748),U_9750)) ),
    inference(clausify,[status(thm)],[f_2639_4]) ).

fof(f_2640_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_2640_2,plain,
    ! [U_9757,U_9756,U_9755,U_9754,U_9753] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9753,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9754,U_9753,U_9755),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9754,tc_HOL_Obool)),U_9756),U_9757))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9753,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9754,U_9753,U_9755),U_9756)),hAPP(c_Set_Oimage(U_9754,U_9753,U_9755),U_9757)))),
    inference(variable_rename,[status(thm)],[f_2640_1]) ).

fof(f_2640_3,plain,
    ! [U_9753,U_9754,U_9755,U_9756,U_9757] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9753,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9754,U_9753,U_9755),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9754,tc_HOL_Obool)),U_9756),U_9757))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9753,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9754,U_9753,U_9755),U_9756)),hAPP(c_Set_Oimage(U_9754,U_9753,U_9755),U_9757)))),
    inference(definitional_conversion,[status(esa)],[f_2640_2]) ).

cnf(f_2640_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9753,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9754,U_9753,U_9755),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9754,tc_HOL_Obool)),U_9756),U_9757))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9753,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9754,U_9753,U_9755),U_9756)),hAPP(c_Set_Oimage(U_9754,U_9753,U_9755),U_9757)))),
    inference(clausify,[status(thm)],[f_2640_3]) ).

fof(f_2641_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_2641_2,plain,
    ! [U_9760,U_9759,U_9758] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9758,tc_HOL_Obool)),U_9759),U_9760) = U_9759
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9758,tc_HOL_Obool)),U_9759),U_9760) != c_Orderings_Obot__class_Obot(tc_fun(U_9758,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2641_1]) ).

fof(f_2641_3,plain,
    ! [U_9758,U_9759,U_9760] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9758,tc_HOL_Obool)),U_9759),U_9760) = U_9759
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9758,tc_HOL_Obool)),U_9759),U_9760) != c_Orderings_Obot__class_Obot(tc_fun(U_9758,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_2641_2]) ).

cnf(f_2641_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9758,tc_HOL_Obool)),U_9759),U_9760) = U_9759
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9758,tc_HOL_Obool)),U_9759),U_9760) != c_Orderings_Obot__class_Obot(tc_fun(U_9758,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2641_3]) ).

fof(f_2642_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_2642_2,plain,
    ! [U_9763,U_9762,U_9761] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9761,tc_HOL_Obool)),U_9762),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9761,tc_HOL_Obool)),U_9763),U_9762)) = c_Orderings_Obot__class_Obot(tc_fun(U_9761,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2642_1]) ).

fof(f_2642_3,plain,
    ! [U_9761,U_9762,U_9763] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9761,tc_HOL_Obool)),U_9762),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9761,tc_HOL_Obool)),U_9763),U_9762)) = c_Orderings_Obot__class_Obot(tc_fun(U_9761,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2642_2]) ).

cnf(f_2642_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9761,tc_HOL_Obool)),U_9762),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9761,tc_HOL_Obool)),U_9763),U_9762)) = c_Orderings_Obot__class_Obot(tc_fun(U_9761,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2642_3]) ).

fof(f_2643_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_2643_2,plain,
    ! [U_9767,U_9766,U_9765,U_9764] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9764,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9764,tc_HOL_Obool)),U_9765),U_9766)),U_9767) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9764,tc_HOL_Obool)),U_9765),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9764,tc_HOL_Obool)),U_9766),U_9767))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9764,tc_HOL_Obool)),U_9767),U_9765)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9764,tc_HOL_Obool)),U_9767),U_9765))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9764,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9764,tc_HOL_Obool)),U_9765),U_9766)),U_9767) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9764,tc_HOL_Obool)),U_9765),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9764,tc_HOL_Obool)),U_9766),U_9767)) ) ),
    inference(variable_rename,[status(thm)],[f_2643_1]) ).

fof(f_2643_3,plain,
    ( ! [U_9775,U_9773,U_9771,U_9769] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9769,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9769,tc_HOL_Obool)),U_9771),U_9773)),U_9775) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9769,tc_HOL_Obool)),U_9771),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9769,tc_HOL_Obool)),U_9773),U_9775))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9769,tc_HOL_Obool)),U_9775),U_9771)) )
    & ! [U_9774,U_9772,U_9770,U_9768] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9768,tc_HOL_Obool)),U_9774),U_9770))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9768,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9768,tc_HOL_Obool)),U_9770),U_9772)),U_9774) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9768,tc_HOL_Obool)),U_9770),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9768,tc_HOL_Obool)),U_9772),U_9774)) ) ),
    inference(miniscope,[status(thm)],[f_2643_2]) ).

fof(f_2643_4,plain,
    ( ! [U_9769,U_9771,U_9773,U_9775] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9769,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9769,tc_HOL_Obool)),U_9771),U_9773)),U_9775) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9769,tc_HOL_Obool)),U_9771),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9769,tc_HOL_Obool)),U_9773),U_9775))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9769,tc_HOL_Obool)),U_9775),U_9771)) )
    & ! [U_9772,U_9774,U_9770,U_9768] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9768,tc_HOL_Obool)),U_9774),U_9770))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9768,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9768,tc_HOL_Obool)),U_9770),U_9772)),U_9774) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9768,tc_HOL_Obool)),U_9770),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9768,tc_HOL_Obool)),U_9772),U_9774)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2643_3]) ).

cnf(f_2643_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9768,tc_HOL_Obool)),U_9774),U_9770))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9768,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9768,tc_HOL_Obool)),U_9770),U_9772)),U_9774) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9768,tc_HOL_Obool)),U_9770),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9768,tc_HOL_Obool)),U_9772),U_9774)) ),
    inference(clausify,[status(thm)],[f_2643_4]) ).

cnf(f_2643_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9769,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9769,tc_HOL_Obool)),U_9771),U_9773)),U_9775) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9769,tc_HOL_Obool)),U_9771),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9769,tc_HOL_Obool)),U_9773),U_9775))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9769,tc_HOL_Obool)),U_9775),U_9771)) ),
    inference(clausify,[status(thm)],[f_2643_4]) ).

fof(f_2644_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_2644_2,plain,
    ! [U_9778,U_9777,U_9776] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9776,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9776,tc_HOL_Obool)),U_9777),U_9778)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9776,tc_HOL_Obool)),U_9777),U_9778)) = U_9777,
    inference(variable_rename,[status(thm)],[f_2644_1]) ).

fof(f_2644_3,plain,
    ! [U_9776,U_9777,U_9778] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9776,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9776,tc_HOL_Obool)),U_9777),U_9778)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9776,tc_HOL_Obool)),U_9777),U_9778)) = U_9777,
    inference(definitional_conversion,[status(esa)],[f_2644_2]) ).

cnf(f_2644_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9776,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9776,tc_HOL_Obool)),U_9777),U_9778)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9776,tc_HOL_Obool)),U_9777),U_9778)) = U_9777,
    inference(clausify,[status(thm)],[f_2644_3]) ).

fof(f_2645_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_2645_2,plain,
    ! [U_9782,U_9781,U_9780,U_9779] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9779,tc_HOL_Obool)),U_9780),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9779,tc_HOL_Obool)),U_9781),U_9782)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9779,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9779,tc_HOL_Obool)),U_9780),U_9781)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9779,tc_HOL_Obool)),U_9780),U_9782)),
    inference(variable_rename,[status(thm)],[f_2645_1]) ).

fof(f_2645_3,plain,
    ! [U_9779,U_9780,U_9781,U_9782] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9779,tc_HOL_Obool)),U_9780),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9779,tc_HOL_Obool)),U_9781),U_9782)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9779,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9779,tc_HOL_Obool)),U_9780),U_9781)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9779,tc_HOL_Obool)),U_9780),U_9782)),
    inference(definitional_conversion,[status(esa)],[f_2645_2]) ).

cnf(f_2645_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9779,tc_HOL_Obool)),U_9780),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9779,tc_HOL_Obool)),U_9781),U_9782)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9779,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9779,tc_HOL_Obool)),U_9780),U_9781)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9779,tc_HOL_Obool)),U_9780),U_9782)),
    inference(clausify,[status(thm)],[f_2645_3]) ).

fof(f_2646_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_2646_2,plain,
    ! [U_9786,U_9785,U_9784,U_9783] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9783,tc_HOL_Obool)),U_9784),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9783,tc_HOL_Obool)),U_9785),U_9786)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9783,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9783,tc_HOL_Obool)),U_9784),U_9785)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9783,tc_HOL_Obool)),U_9784),U_9786)),
    inference(variable_rename,[status(thm)],[f_2646_1]) ).

fof(f_2646_3,plain,
    ! [U_9783,U_9784,U_9785,U_9786] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9783,tc_HOL_Obool)),U_9784),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9783,tc_HOL_Obool)),U_9785),U_9786)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9783,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9783,tc_HOL_Obool)),U_9784),U_9785)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9783,tc_HOL_Obool)),U_9784),U_9786)),
    inference(definitional_conversion,[status(esa)],[f_2646_2]) ).

cnf(f_2646_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9783,tc_HOL_Obool)),U_9784),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9783,tc_HOL_Obool)),U_9785),U_9786)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9783,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9783,tc_HOL_Obool)),U_9784),U_9785)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9783,tc_HOL_Obool)),U_9784),U_9786)),
    inference(clausify,[status(thm)],[f_2646_3]) ).

fof(f_2647_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_2647_2,plain,
    ! [U_9788,U_9787] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9787),U_9788) = 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_9787)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9788))),
    inference(variable_rename,[status(thm)],[f_2647_1]) ).

fof(f_2647_3,plain,
    ! [U_9787,U_9788] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9787),U_9788) = 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_9787)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9788))),
    inference(definitional_conversion,[status(esa)],[f_2647_2]) ).

cnf(f_2647_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_9787),U_9788) = 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_9787)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9788))),
    inference(clausify,[status(thm)],[f_2647_3]) ).

fof(f_2648_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_2648_2,plain,
    ! [U_9790,U_9789] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9789,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9789,tc_HOL_Obool)),U_9790)),U_9790) = c_Orderings_Obot__class_Obot(tc_fun(U_9789,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2648_1]) ).

fof(f_2648_3,plain,
    ! [U_9789,U_9790] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9789,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9789,tc_HOL_Obool)),U_9790)),U_9790) = c_Orderings_Obot__class_Obot(tc_fun(U_9789,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2648_2]) ).

cnf(f_2648_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9789,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9789,tc_HOL_Obool)),U_9790)),U_9790) = c_Orderings_Obot__class_Obot(tc_fun(U_9789,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2648_3]) ).

fof(f_2649_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_2649_2,plain,
    ! [U_9792,U_9791] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9791,tc_HOL_Obool)),U_9792),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9791,tc_HOL_Obool)),U_9792)) = c_Orderings_Obot__class_Obot(tc_fun(U_9791,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2649_1]) ).

fof(f_2649_3,plain,
    ! [U_9791,U_9792] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9791,tc_HOL_Obool)),U_9792),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9791,tc_HOL_Obool)),U_9792)) = c_Orderings_Obot__class_Obot(tc_fun(U_9791,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2649_2]) ).

cnf(f_2649_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9791,tc_HOL_Obool)),U_9792),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9791,tc_HOL_Obool)),U_9792)) = c_Orderings_Obot__class_Obot(tc_fun(U_9791,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2649_3]) ).

fof(f_2650_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_2650_2,plain,
    ! [U_9797,U_9796,U_9795,U_9794,U_9793] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9793,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9794,U_9793,U_9795),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9794,tc_HOL_Obool)),U_9796),U_9797))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9793,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9794,U_9793,U_9795),U_9796)),hAPP(c_Relation_OImage(U_9794,U_9793,U_9795),U_9797)))),
    inference(variable_rename,[status(thm)],[f_2650_1]) ).

fof(f_2650_3,plain,
    ! [U_9793,U_9794,U_9795,U_9796,U_9797] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9793,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9794,U_9793,U_9795),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9794,tc_HOL_Obool)),U_9796),U_9797))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9793,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9794,U_9793,U_9795),U_9796)),hAPP(c_Relation_OImage(U_9794,U_9793,U_9795),U_9797)))),
    inference(definitional_conversion,[status(esa)],[f_2650_2]) ).

cnf(f_2650_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9793,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9794,U_9793,U_9795),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9794,tc_HOL_Obool)),U_9796),U_9797))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9793,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9794,U_9793,U_9795),U_9796)),hAPP(c_Relation_OImage(U_9794,U_9793,U_9795),U_9797)))),
    inference(clausify,[status(thm)],[f_2650_3]) ).

fof(f_2651_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_2651_2,plain,
    ! [U_9800,U_9799,U_9798] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9798,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9798,tc_HOL_Obool)),U_9799),U_9800)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9798,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9798,tc_HOL_Obool)),U_9799)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9798,tc_HOL_Obool)),U_9800)),
    inference(variable_rename,[status(thm)],[f_2651_1]) ).

fof(f_2651_3,plain,
    ! [U_9798,U_9799,U_9800] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9798,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9798,tc_HOL_Obool)),U_9799),U_9800)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9798,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9798,tc_HOL_Obool)),U_9799)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9798,tc_HOL_Obool)),U_9800)),
    inference(definitional_conversion,[status(esa)],[f_2651_2]) ).

cnf(f_2651_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9798,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9798,tc_HOL_Obool)),U_9799),U_9800)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9798,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9798,tc_HOL_Obool)),U_9799)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9798,tc_HOL_Obool)),U_9800)),
    inference(clausify,[status(thm)],[f_2651_3]) ).

fof(f_2652_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_2652_2,plain,
    ! [U_9803,U_9802,U_9801] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9801,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9801,tc_HOL_Obool)),U_9802),U_9803)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9801,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9801,tc_HOL_Obool)),U_9802)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9801,tc_HOL_Obool)),U_9803)),
    inference(variable_rename,[status(thm)],[f_2652_1]) ).

fof(f_2652_3,plain,
    ! [U_9801,U_9802,U_9803] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9801,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9801,tc_HOL_Obool)),U_9802),U_9803)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9801,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9801,tc_HOL_Obool)),U_9802)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9801,tc_HOL_Obool)),U_9803)),
    inference(definitional_conversion,[status(esa)],[f_2652_2]) ).

cnf(f_2652_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9801,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9801,tc_HOL_Obool)),U_9802),U_9803)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9801,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9801,tc_HOL_Obool)),U_9802)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9801,tc_HOL_Obool)),U_9803)),
    inference(clausify,[status(thm)],[f_2652_3]) ).

fof(f_2653_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_2653_2,plain,
    ! [U_9806,U_9805,U_9804] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9804,tc_HOL_Obool)),U_9805),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9804,tc_HOL_Obool)),U_9806)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9804,tc_HOL_Obool)),U_9805),U_9806),
    inference(variable_rename,[status(thm)],[f_2653_1]) ).

fof(f_2653_3,plain,
    ! [U_9804,U_9805,U_9806] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9804,tc_HOL_Obool)),U_9805),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9804,tc_HOL_Obool)),U_9806)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9804,tc_HOL_Obool)),U_9805),U_9806),
    inference(definitional_conversion,[status(esa)],[f_2653_2]) ).

cnf(f_2653_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9804,tc_HOL_Obool)),U_9805),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9804,tc_HOL_Obool)),U_9806)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9804,tc_HOL_Obool)),U_9805),U_9806),
    inference(clausify,[status(thm)],[f_2653_3]) ).

fof(f_2654_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_2654_2,plain,
    ! [U_9809,U_9808,U_9807] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9807,tc_HOL_Obool)),U_9808),U_9809) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9807,tc_HOL_Obool)),U_9808),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9807,tc_HOL_Obool)),U_9809)),
    inference(variable_rename,[status(thm)],[f_2654_1]) ).

fof(f_2654_3,plain,
    ! [U_9807,U_9808,U_9809] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9807,tc_HOL_Obool)),U_9808),U_9809) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9807,tc_HOL_Obool)),U_9808),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9807,tc_HOL_Obool)),U_9809)),
    inference(definitional_conversion,[status(esa)],[f_2654_2]) ).

cnf(f_2654_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9807,tc_HOL_Obool)),U_9808),U_9809) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9807,tc_HOL_Obool)),U_9808),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9807,tc_HOL_Obool)),U_9809)),
    inference(clausify,[status(thm)],[f_2654_3]) ).

fof(f_2655_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_2655_2,plain,
    ! [U_9811,U_9810] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9810),U_9811) = 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_9810)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9811)))
      | ~ c_Nat__Transfer_Onat__set(U_9811)
      | ~ c_Nat__Transfer_Onat__set(U_9810) ),
    inference(variable_rename,[status(thm)],[f_2655_1]) ).

fof(f_2655_3,plain,
    ! [U_9810,U_9811] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9810),U_9811) = 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_9810)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9811)))
      | ~ c_Nat__Transfer_Onat__set(U_9811)
      | ~ c_Nat__Transfer_Onat__set(U_9810) ),
    inference(definitional_conversion,[status(esa)],[f_2655_2]) ).

cnf(f_2655_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_9810),U_9811) = 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_9810)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9811)))
    | ~ c_Nat__Transfer_Onat__set(U_9811)
    | ~ c_Nat__Transfer_Onat__set(U_9810) ),
    inference(clausify,[status(thm)],[f_2655_3]) ).

fof(f_2656_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_2656_2,plain,
    ! [U_9814,U_9813,U_9812] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9812,tc_HOL_Obool)),U_9813),U_9814) = c_Orderings_Obot__class_Obot(tc_fun(U_9812,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9812,tc_HOL_Obool)),U_9813),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9812,tc_HOL_Obool)),U_9814))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9812,tc_HOL_Obool)),U_9813),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9812,tc_HOL_Obool)),U_9814)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9812,tc_HOL_Obool)),U_9813),U_9814) != c_Orderings_Obot__class_Obot(tc_fun(U_9812,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2656_1]) ).

fof(f_2656_3,plain,
    ( ! [U_9820,U_9818,U_9816] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9816,tc_HOL_Obool)),U_9818),U_9820) = c_Orderings_Obot__class_Obot(tc_fun(U_9816,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9816,tc_HOL_Obool)),U_9818),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9816,tc_HOL_Obool)),U_9820))) )
    & ! [U_9819,U_9817,U_9815] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9815,tc_HOL_Obool)),U_9817),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9815,tc_HOL_Obool)),U_9819)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9815,tc_HOL_Obool)),U_9817),U_9819) != c_Orderings_Obot__class_Obot(tc_fun(U_9815,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2656_2]) ).

fof(f_2656_4,plain,
    ( ! [U_9816,U_9818,U_9820] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9816,tc_HOL_Obool)),U_9818),U_9820) = c_Orderings_Obot__class_Obot(tc_fun(U_9816,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9816,tc_HOL_Obool)),U_9818),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9816,tc_HOL_Obool)),U_9820))) )
    & ! [U_9817,U_9815,U_9819] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9815,tc_HOL_Obool)),U_9817),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9815,tc_HOL_Obool)),U_9819)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9815,tc_HOL_Obool)),U_9817),U_9819) != c_Orderings_Obot__class_Obot(tc_fun(U_9815,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2656_3]) ).

cnf(f_2656_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9815,tc_HOL_Obool)),U_9817),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9815,tc_HOL_Obool)),U_9819)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9815,tc_HOL_Obool)),U_9817),U_9819) != c_Orderings_Obot__class_Obot(tc_fun(U_9815,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2656_4]) ).

cnf(f_2656_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9816,tc_HOL_Obool)),U_9818),U_9820) = c_Orderings_Obot__class_Obot(tc_fun(U_9816,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9816,tc_HOL_Obool)),U_9818),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9816,tc_HOL_Obool)),U_9820))) ),
    inference(clausify,[status(thm)],[f_2656_4]) ).

fof(f_2657_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_2657_2,plain,
    ! [U_9828,U_9827,U_9826,U_9825,U_9824,U_9823,U_9822,U_9821] :
      ( hAPP(hAPP(U_9823,hAPP(U_9826,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9822,tc_HOL_Obool)),U_9827),U_9828))),hAPP(U_9826,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9822,tc_HOL_Obool)),U_9827),U_9828))) = hAPP(hAPP(U_9823,hAPP(U_9826,U_9827)),hAPP(U_9826,U_9828))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9822),U_9828))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9822),U_9827))
      | ~ c_Finite__Set_Ofolding__image__simple(U_9821,U_9822,U_9823,U_9824,U_9825,U_9826) ),
    inference(variable_rename,[status(thm)],[f_2657_1]) ).

fof(f_2657_3,plain,
    ! [U_9828,U_9827,U_9826,U_9825,U_9824,U_9823,U_9822] :
      ( ! [U_9821] : ~ c_Finite__Set_Ofolding__image__simple(U_9821,U_9822,U_9823,U_9824,U_9825,U_9826)
      | hAPP(hAPP(U_9823,hAPP(U_9826,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9822,tc_HOL_Obool)),U_9827),U_9828))),hAPP(U_9826,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9822,tc_HOL_Obool)),U_9827),U_9828))) = hAPP(hAPP(U_9823,hAPP(U_9826,U_9827)),hAPP(U_9826,U_9828))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9822),U_9828))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9822),U_9827)) ),
    inference(miniscope,[status(thm)],[f_2657_2]) ).

fof(f_2657_4,plain,
    ! [U_9821,U_9822,U_9823,U_9824,U_9825,U_9826,U_9827,U_9828] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_9821,U_9822,U_9823,U_9824,U_9825,U_9826)
      | hAPP(hAPP(U_9823,hAPP(U_9826,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9822,tc_HOL_Obool)),U_9827),U_9828))),hAPP(U_9826,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9822,tc_HOL_Obool)),U_9827),U_9828))) = hAPP(hAPP(U_9823,hAPP(U_9826,U_9827)),hAPP(U_9826,U_9828))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9822),U_9828))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9822),U_9827)) ),
    inference(definitional_conversion,[status(esa)],[f_2657_3]) ).

cnf(f_2657_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_9821,U_9822,U_9823,U_9824,U_9825,U_9826)
    | hAPP(hAPP(U_9823,hAPP(U_9826,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9822,tc_HOL_Obool)),U_9827),U_9828))),hAPP(U_9826,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9822,tc_HOL_Obool)),U_9827),U_9828))) = hAPP(hAPP(U_9823,hAPP(U_9826,U_9827)),hAPP(U_9826,U_9828))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9822),U_9828))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9822),U_9827)) ),
    inference(clausify,[status(thm)],[f_2657_4]) ).

fof(f_2658_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_2658_2,plain,
    ! [U_9831,U_9830,U_9829] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9829),hAPP(hAPP(c_Set_Oinsert(U_9829),U_9830),c_Orderings_Obot__class_Obot(tc_fun(U_9829,tc_HOL_Obool)))),U_9831) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9829,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9829,U_9829,U_9831),hAPP(hAPP(c_Set_Oinsert(U_9829),U_9830),c_Orderings_Obot__class_Obot(tc_fun(U_9829,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9829,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2658_1]) ).

fof(f_2658_3,plain,
    ! [U_9829,U_9830,U_9831] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9829),hAPP(hAPP(c_Set_Oinsert(U_9829),U_9830),c_Orderings_Obot__class_Obot(tc_fun(U_9829,tc_HOL_Obool)))),U_9831) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9829,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9829,U_9829,U_9831),hAPP(hAPP(c_Set_Oinsert(U_9829),U_9830),c_Orderings_Obot__class_Obot(tc_fun(U_9829,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9829,tc_HOL_Obool),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2658_2]) ).

cnf(f_2658_4,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9829),hAPP(hAPP(c_Set_Oinsert(U_9829),U_9830),c_Orderings_Obot__class_Obot(tc_fun(U_9829,tc_HOL_Obool)))),U_9831) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_9829,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9829,U_9829,U_9831),hAPP(hAPP(c_Set_Oinsert(U_9829),U_9830),c_Orderings_Obot__class_Obot(tc_fun(U_9829,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_9829,tc_HOL_Obool),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2658_3]) ).

fof(f_2659_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_2659_2,plain,
    ! [U_9836,U_9835,U_9834,U_9833,U_9832] :
      ( hAPP(hAPP(U_9833,hAPP(U_9834,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9832,tc_HOL_Obool)),U_9835),U_9836))),hAPP(U_9834,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9832,tc_HOL_Obool)),U_9835),U_9836))) = hAPP(hAPP(U_9833,hAPP(U_9834,U_9835)),hAPP(U_9834,U_9836))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9832,tc_HOL_Obool)),U_9835),U_9836) = c_Orderings_Obot__class_Obot(tc_fun(U_9832,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9832),U_9836))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9832),U_9835))
      | ~ c_Finite__Set_Ofolding__one(U_9832,U_9833,U_9834) ),
    inference(variable_rename,[status(thm)],[f_2659_1]) ).

fof(f_2659_3,plain,
    ! [U_9832,U_9833,U_9834,U_9835,U_9836] :
      ( hAPP(hAPP(U_9833,hAPP(U_9834,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9832,tc_HOL_Obool)),U_9835),U_9836))),hAPP(U_9834,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9832,tc_HOL_Obool)),U_9835),U_9836))) = hAPP(hAPP(U_9833,hAPP(U_9834,U_9835)),hAPP(U_9834,U_9836))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9832,tc_HOL_Obool)),U_9835),U_9836) = c_Orderings_Obot__class_Obot(tc_fun(U_9832,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9832),U_9836))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9832),U_9835))
      | ~ c_Finite__Set_Ofolding__one(U_9832,U_9833,U_9834) ),
    inference(definitional_conversion,[status(esa)],[f_2659_2]) ).

cnf(f_2659_4,plain,
    ( hAPP(hAPP(U_9833,hAPP(U_9834,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9832,tc_HOL_Obool)),U_9835),U_9836))),hAPP(U_9834,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9832,tc_HOL_Obool)),U_9835),U_9836))) = hAPP(hAPP(U_9833,hAPP(U_9834,U_9835)),hAPP(U_9834,U_9836))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9832,tc_HOL_Obool)),U_9835),U_9836) = c_Orderings_Obot__class_Obot(tc_fun(U_9832,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9832),U_9836))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9832),U_9835))
    | ~ c_Finite__Set_Ofolding__one(U_9832,U_9833,U_9834) ),
    inference(clausify,[status(thm)],[f_2659_3]) ).

fof(f_2660_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_2660_2,plain,
    ! [U_9841,U_9840,U_9839,U_9838,U_9837] :
      ( hAPP(U_9839,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9837,tc_HOL_Obool)),U_9840),U_9841)) = hAPP(hAPP(U_9838,hAPP(U_9839,U_9840)),hAPP(U_9839,U_9841))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9837,tc_HOL_Obool)),U_9840),U_9841) != c_Orderings_Obot__class_Obot(tc_fun(U_9837,tc_HOL_Obool))
      | U_9841 = c_Orderings_Obot__class_Obot(tc_fun(U_9837,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9837),U_9841))
      | U_9840 = c_Orderings_Obot__class_Obot(tc_fun(U_9837,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9837),U_9840))
      | ~ c_Finite__Set_Ofolding__one(U_9837,U_9838,U_9839) ),
    inference(variable_rename,[status(thm)],[f_2660_1]) ).

fof(f_2660_3,plain,
    ! [U_9837,U_9839,U_9838,U_9840,U_9841] :
      ( hAPP(U_9839,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9837,tc_HOL_Obool)),U_9840),U_9841)) = hAPP(hAPP(U_9838,hAPP(U_9839,U_9840)),hAPP(U_9839,U_9841))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9837,tc_HOL_Obool)),U_9840),U_9841) != c_Orderings_Obot__class_Obot(tc_fun(U_9837,tc_HOL_Obool))
      | U_9841 = c_Orderings_Obot__class_Obot(tc_fun(U_9837,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9837),U_9841))
      | U_9840 = c_Orderings_Obot__class_Obot(tc_fun(U_9837,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9837),U_9840))
      | ~ c_Finite__Set_Ofolding__one(U_9837,U_9838,U_9839) ),
    inference(definitional_conversion,[status(esa)],[f_2660_2]) ).

cnf(f_2660_4,plain,
    ( hAPP(U_9839,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9837,tc_HOL_Obool)),U_9840),U_9841)) = hAPP(hAPP(U_9838,hAPP(U_9839,U_9840)),hAPP(U_9839,U_9841))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9837,tc_HOL_Obool)),U_9840),U_9841) != c_Orderings_Obot__class_Obot(tc_fun(U_9837,tc_HOL_Obool))
    | U_9841 = c_Orderings_Obot__class_Obot(tc_fun(U_9837,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9837),U_9841))
    | U_9840 = c_Orderings_Obot__class_Obot(tc_fun(U_9837,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9837),U_9840))
    | ~ c_Finite__Set_Ofolding__one(U_9837,U_9838,U_9839) ),
    inference(clausify,[status(thm)],[f_2660_3]) ).

fof(f_2661_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_2661_2,plain,
    ! [U_9849,U_9848,U_9847,U_9846,U_9845,U_9844,U_9843,U_9842] :
      ( hAPP(U_9847,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9843,tc_HOL_Obool)),U_9848),U_9849)) = hAPP(hAPP(U_9844,hAPP(U_9847,U_9848)),hAPP(U_9847,U_9849))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9843,tc_HOL_Obool)),U_9848),U_9849) != c_Orderings_Obot__class_Obot(tc_fun(U_9843,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9843),U_9849))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9843),U_9848))
      | ~ c_Finite__Set_Ofolding__image__simple(U_9842,U_9843,U_9844,U_9845,U_9846,U_9847) ),
    inference(variable_rename,[status(thm)],[f_2661_1]) ).

fof(f_2661_3,plain,
    ! [U_9849,U_9848,U_9847,U_9846,U_9845,U_9844,U_9843] :
      ( ! [U_9842] : ~ c_Finite__Set_Ofolding__image__simple(U_9842,U_9843,U_9844,U_9845,U_9846,U_9847)
      | hAPP(U_9847,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9843,tc_HOL_Obool)),U_9848),U_9849)) = hAPP(hAPP(U_9844,hAPP(U_9847,U_9848)),hAPP(U_9847,U_9849))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9843,tc_HOL_Obool)),U_9848),U_9849) != c_Orderings_Obot__class_Obot(tc_fun(U_9843,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9843),U_9849))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9843),U_9848)) ),
    inference(miniscope,[status(thm)],[f_2661_2]) ).

fof(f_2661_4,plain,
    ! [U_9845,U_9849,U_9843,U_9846,U_9847,U_9848,U_9844,U_9842] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_9842,U_9843,U_9844,U_9845,U_9846,U_9847)
      | hAPP(U_9847,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9843,tc_HOL_Obool)),U_9848),U_9849)) = hAPP(hAPP(U_9844,hAPP(U_9847,U_9848)),hAPP(U_9847,U_9849))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9843,tc_HOL_Obool)),U_9848),U_9849) != c_Orderings_Obot__class_Obot(tc_fun(U_9843,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9843),U_9849))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9843),U_9848)) ),
    inference(definitional_conversion,[status(esa)],[f_2661_3]) ).

cnf(f_2661_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_9842,U_9843,U_9844,U_9845,U_9846,U_9847)
    | hAPP(U_9847,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9843,tc_HOL_Obool)),U_9848),U_9849)) = hAPP(hAPP(U_9844,hAPP(U_9847,U_9848)),hAPP(U_9847,U_9849))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9843,tc_HOL_Obool)),U_9848),U_9849) != c_Orderings_Obot__class_Obot(tc_fun(U_9843,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9843),U_9849))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9843),U_9848)) ),
    inference(clausify,[status(thm)],[f_2661_4]) ).

fof(f_2662_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_2662_2,plain,
    ! [U_9853,U_9852,U_9851,U_9850] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9850,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9850,U_9850,U_9853),hAPP(hAPP(c_Set_Oinsert(U_9850),U_9851),c_Orderings_Obot__class_Obot(tc_fun(U_9850,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9850),U_9852),U_9853)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9850),U_9851),U_9852)) ),
    inference(variable_rename,[status(thm)],[f_2662_1]) ).

fof(f_2662_3,plain,
    ! [U_9852,U_9851,U_9850,U_9853] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9850,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9850,U_9850,U_9853),hAPP(hAPP(c_Set_Oinsert(U_9850),U_9851),c_Orderings_Obot__class_Obot(tc_fun(U_9850,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9850),U_9852),U_9853)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9850),U_9851),U_9852)) ),
    inference(definitional_conversion,[status(esa)],[f_2662_2]) ).

cnf(f_2662_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_9850,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_9850,U_9850,U_9853),hAPP(hAPP(c_Set_Oinsert(U_9850),U_9851),c_Orderings_Obot__class_Obot(tc_fun(U_9850,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9850),U_9852),U_9853)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9850),U_9851),U_9852)) ),
    inference(clausify,[status(thm)],[f_2662_3]) ).

fof(f_2663_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_2663_2,plain,
    ! [U_9860,U_9859,U_9858,U_9857,U_9856,U_9855,U_9854] :
      ( ( ( U_9857 = U_9858
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9854,U_9854)),hAPP(hAPP(c_Product__Type_OPair(U_9854,U_9854),U_9859),U_9860)),U_9856)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9854,U_9854)),hAPP(hAPP(c_Product__Type_OPair(U_9854,U_9854),U_9859),U_9860)),U_9856))
          | U_9857 != U_9858 ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9854),U_9860),U_9858))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9854),U_9859),U_9857))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9854,tc_HOL_Obool)),U_9858),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9854),U_9855),U_9856)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9854,tc_HOL_Obool)),U_9857),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9854),U_9855),U_9856)))
      | ~ c_Equiv__Relations_Oequiv(U_9854,U_9855,U_9856) ),
    inference(variable_rename,[status(thm)],[f_2663_1]) ).

fof(f_2663_3,plain,
    ( ! [U_9854,U_9856,U_9857,U_9858,U_9859,U_9860] :
        ( U_9857 = U_9858
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9854,U_9854)),hAPP(hAPP(c_Product__Type_OPair(U_9854,U_9854),U_9859),U_9860)),U_9856))
        | ~ sP758(U_9854,U_9856,U_9857,U_9858,U_9859,U_9860) )
    & ! [U_9854,U_9856,U_9857,U_9858,U_9859,U_9860] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9854,U_9854)),hAPP(hAPP(c_Product__Type_OPair(U_9854,U_9854),U_9859),U_9860)),U_9856))
        | U_9857 != U_9858
        | ~ sP758(U_9854,U_9856,U_9857,U_9858,U_9859,U_9860) )
    & ! [U_9854,U_9855,U_9856,U_9857,U_9858,U_9859,U_9860] :
        ( sP758(U_9854,U_9856,U_9857,U_9858,U_9859,U_9860)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9854),U_9860),U_9858))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9854),U_9859),U_9857))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9854,tc_HOL_Obool)),U_9858),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9854),U_9855),U_9856)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9854,tc_HOL_Obool)),U_9857),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9854),U_9855),U_9856)))
        | ~ c_Equiv__Relations_Oequiv(U_9854,U_9855,U_9856) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP758])],[f_2663_2]) ).

cnf(f_2663_4,plain,
    ( sP758(U_9854,U_9856,U_9857,U_9858,U_9859,U_9860)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9854),U_9860),U_9858))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9854),U_9859),U_9857))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9854,tc_HOL_Obool)),U_9858),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9854),U_9855),U_9856)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9854,tc_HOL_Obool)),U_9857),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9854),U_9855),U_9856)))
    | ~ c_Equiv__Relations_Oequiv(U_9854,U_9855,U_9856) ),
    inference(clausify,[status(thm)],[f_2663_3]) ).

cnf(f_2663_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9854,U_9854)),hAPP(hAPP(c_Product__Type_OPair(U_9854,U_9854),U_9859),U_9860)),U_9856))
    | U_9857 != U_9858
    | ~ sP758(U_9854,U_9856,U_9857,U_9858,U_9859,U_9860) ),
    inference(clausify,[status(thm)],[f_2663_3]) ).

cnf(f_2663_6,plain,
    ( U_9857 = U_9858
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9854,U_9854)),hAPP(hAPP(c_Product__Type_OPair(U_9854,U_9854),U_9859),U_9860)),U_9856))
    | ~ sP758(U_9854,U_9856,U_9857,U_9858,U_9859,U_9860) ),
    inference(clausify,[status(thm)],[f_2663_3]) ).

fof(f_2664_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_2664_2,plain,
    ! [U_9867,U_9866,U_9865,U_9864,U_9863,U_9862,U_9861] :
      ( U_9864 = U_9865
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9861,U_9861)),hAPP(hAPP(c_Product__Type_OPair(U_9861,U_9861),U_9866),U_9867)),U_9863))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9861),U_9867),U_9865))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9861),U_9866),U_9864))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9861,tc_HOL_Obool)),U_9865),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9861),U_9862),U_9863)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9861,tc_HOL_Obool)),U_9864),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9861),U_9862),U_9863)))
      | ~ c_Equiv__Relations_Oequiv(U_9861,U_9862,U_9863) ),
    inference(variable_rename,[status(thm)],[f_2664_1]) ).

fof(f_2664_3,plain,
    ! [U_9866,U_9865,U_9862,U_9863,U_9867,U_9861,U_9864] :
      ( U_9864 = U_9865
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9861,U_9861)),hAPP(hAPP(c_Product__Type_OPair(U_9861,U_9861),U_9866),U_9867)),U_9863))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9861),U_9867),U_9865))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9861),U_9866),U_9864))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9861,tc_HOL_Obool)),U_9865),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9861),U_9862),U_9863)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9861,tc_HOL_Obool)),U_9864),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9861),U_9862),U_9863)))
      | ~ c_Equiv__Relations_Oequiv(U_9861,U_9862,U_9863) ),
    inference(definitional_conversion,[status(esa)],[f_2664_2]) ).

cnf(f_2664_4,plain,
    ( U_9864 = U_9865
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9861,U_9861)),hAPP(hAPP(c_Product__Type_OPair(U_9861,U_9861),U_9866),U_9867)),U_9863))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9861),U_9867),U_9865))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9861),U_9866),U_9864))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9861,tc_HOL_Obool)),U_9865),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9861),U_9862),U_9863)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9861,tc_HOL_Obool)),U_9864),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9861),U_9862),U_9863)))
    | ~ c_Equiv__Relations_Oequiv(U_9861,U_9862,U_9863) ),
    inference(clausify,[status(thm)],[f_2664_3]) ).

fof(f_2665_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_2665_2,plain,
    ! [U_9869,U_9868] :
      ( 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_9869,U_9868) = 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_9868),U_9869)) ),
    inference(variable_rename,[status(thm)],[f_2665_1]) ).

fof(f_2665_3,plain,
    ! [U_9869,U_9868] :
      ( 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_9869,U_9868) = 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_9868),U_9869)) ),
    inference(definitional_conversion,[status(esa)],[f_2665_2]) ).

cnf(f_2665_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_9869,U_9868) = 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_9868),U_9869)) ),
    inference(clausify,[status(thm)],[f_2665_3]) ).

fof(f_2666_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_2666_2,plain,
    ! [U_9871,U_9870] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9870),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_9871)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9871),U_9870))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9870),U_9871)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9871),U_9870))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9870),U_9871)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9870),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_9871))) ) ),
    inference(variable_rename,[status(thm)],[f_2666_1]) ).

fof(f_2666_3,plain,
    ( ! [U_9875,U_9873] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9873),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_9875)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9875),U_9873))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9873),U_9875)) )
    & ! [U_9874,U_9872] :
        ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9874),U_9872))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9872),U_9874)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9872),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_9874))) ) ),
    inference(miniscope,[status(thm)],[f_2666_2]) ).

fof(f_2666_4,plain,
    ( ! [U_9874,U_9872] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9874),U_9872))
        | ~ sP759(U_9874,U_9872) )
    & ! [U_9874,U_9872] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9872),U_9874))
        | ~ sP759(U_9874,U_9872) )
    & ! [U_9875,U_9873] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9873),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_9875)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9875),U_9873))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9873),U_9875)) )
    & ! [U_9874,U_9872] :
        ( sP759(U_9874,U_9872)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9872),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_9874))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP759])],[f_2666_3]) ).

cnf(f_2666_5,plain,
    ( sP759(U_9874,U_9872)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9872),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_9874))) ),
    inference(clausify,[status(thm)],[f_2666_4]) ).

cnf(f_2666_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9873),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_9875)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9875),U_9873))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9873),U_9875)) ),
    inference(clausify,[status(thm)],[f_2666_4]) ).

cnf(f_2666_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9872),U_9874))
    | ~ sP759(U_9874,U_9872) ),
    inference(clausify,[status(thm)],[f_2666_4]) ).

cnf(f_2666_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9874),U_9872))
    | ~ sP759(U_9874,U_9872) ),
    inference(clausify,[status(thm)],[f_2666_4]) ).

fof(f_2667_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_2667_2,plain,
    ! [U_9877,U_9876] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9876),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_9877)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9876),U_9877))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9877),U_9876)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9876),U_9877))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9877),U_9876)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9876),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_9877))) ) ),
    inference(variable_rename,[status(thm)],[f_2667_1]) ).

fof(f_2667_3,plain,
    ( ! [U_9881,U_9879] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9879),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_9881)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9879),U_9881))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9881),U_9879)) )
    & ! [U_9880,U_9878] :
        ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9878),U_9880))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9880),U_9878)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9878),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_9880))) ) ),
    inference(miniscope,[status(thm)],[f_2667_2]) ).

fof(f_2667_4,plain,
    ( ! [U_9880,U_9878] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9878),U_9880))
        | ~ sP760(U_9880,U_9878) )
    & ! [U_9880,U_9878] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9880),U_9878))
        | ~ sP760(U_9880,U_9878) )
    & ! [U_9879,U_9881] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9879),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_9881)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9879),U_9881))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9881),U_9879)) )
    & ! [U_9880,U_9878] :
        ( sP760(U_9880,U_9878)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9878),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_9880))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP760])],[f_2667_3]) ).

cnf(f_2667_5,plain,
    ( sP760(U_9880,U_9878)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9878),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_9880))) ),
    inference(clausify,[status(thm)],[f_2667_4]) ).

cnf(f_2667_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9879),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_9881)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9879),U_9881))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9881),U_9879)) ),
    inference(clausify,[status(thm)],[f_2667_4]) ).

cnf(f_2667_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9880),U_9878))
    | ~ sP760(U_9880,U_9878) ),
    inference(clausify,[status(thm)],[f_2667_4]) ).

cnf(f_2667_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9878),U_9880))
    | ~ sP760(U_9880,U_9878) ),
    inference(clausify,[status(thm)],[f_2667_4]) ).

fof(f_2668_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_2668_2,plain,
    ! [U_9883,U_9882] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9882),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9883)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9882),U_9883)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9882),U_9883))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9882),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9883))) ) ),
    inference(variable_rename,[status(thm)],[f_2668_1]) ).

fof(f_2668_3,plain,
    ( ! [U_9887,U_9885] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9885),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9887)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9885),U_9887)) )
    & ! [U_9886,U_9884] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9884),U_9886))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9884),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9886))) ) ),
    inference(miniscope,[status(thm)],[f_2668_2]) ).

fof(f_2668_4,plain,
    ( ! [U_9885,U_9887] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9885),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9887)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9885),U_9887)) )
    & ! [U_9886,U_9884] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9884),U_9886))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9884),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9886))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2668_3]) ).

cnf(f_2668_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9884),U_9886))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9884),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9886))) ),
    inference(clausify,[status(thm)],[f_2668_4]) ).

cnf(f_2668_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9885),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9887)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9885),U_9887)) ),
    inference(clausify,[status(thm)],[f_2668_4]) ).

fof(f_2669_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_2669_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_2669_1]) ).

cnf(f_2669_3,plain,
    c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2669_2]) ).

fof(f_2670_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_2670_2,plain,
    ! [U_9893,U_9892,U_9891,U_9890,U_9889,U_9888] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9888,tc_fun(U_9889,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9888,tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_fun(U_9889,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9889,tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_fun(U_9889,tc_HOL_Obool)),U_9888),c_COMBC(U_9889,tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9889,tc_prod(U_9888,U_9889)),tc_fun(U_9889,tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool)),U_9888),hAPP(c_COMBB(tc_prod(U_9888,U_9889),tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool),U_9889),c_member(tc_prod(U_9888,U_9889)))),c_Product__Type_OPair(U_9888,U_9889)))),U_9890)),hAPP(hAPP(c_COMBC(U_9888,tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_fun(U_9889,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9889,tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_fun(U_9889,tc_HOL_Obool)),U_9888),c_COMBC(U_9889,tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9889,tc_prod(U_9888,U_9889)),tc_fun(U_9889,tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool)),U_9888),hAPP(c_COMBB(tc_prod(U_9888,U_9889),tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool),U_9889),c_member(tc_prod(U_9888,U_9889)))),c_Product__Type_OPair(U_9888,U_9889)))),U_9891)),U_9892),U_9893))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9888,U_9889)),hAPP(hAPP(c_Product__Type_OPair(U_9888,U_9889),U_9892),U_9893)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool)),U_9890),U_9891))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9888,U_9889)),hAPP(hAPP(c_Product__Type_OPair(U_9888,U_9889),U_9892),U_9893)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool)),U_9890),U_9891)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9888,tc_fun(U_9889,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9888,tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_fun(U_9889,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9889,tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_fun(U_9889,tc_HOL_Obool)),U_9888),c_COMBC(U_9889,tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9889,tc_prod(U_9888,U_9889)),tc_fun(U_9889,tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool)),U_9888),hAPP(c_COMBB(tc_prod(U_9888,U_9889),tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool),U_9889),c_member(tc_prod(U_9888,U_9889)))),c_Product__Type_OPair(U_9888,U_9889)))),U_9890)),hAPP(hAPP(c_COMBC(U_9888,tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_fun(U_9889,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9889,tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_fun(U_9889,tc_HOL_Obool)),U_9888),c_COMBC(U_9889,tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9889,tc_prod(U_9888,U_9889)),tc_fun(U_9889,tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool)),U_9888),hAPP(c_COMBB(tc_prod(U_9888,U_9889),tc_fun(tc_fun(tc_prod(U_9888,U_9889),tc_HOL_Obool),tc_HOL_Obool),U_9889),c_member(tc_prod(U_9888,U_9889)))),c_Product__Type_OPair(U_9888,U_9889)))),U_9891)),U_9892),U_9893)) ) ),
    inference(variable_rename,[status(thm)],[f_2670_1]) ).

fof(f_2670_3,plain,
    ( ! [U_9905,U_9903,U_9901,U_9899,U_9897,U_9895] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9895,tc_fun(U_9897,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9895,tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_fun(U_9897,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9897,tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_fun(U_9897,tc_HOL_Obool)),U_9895),c_COMBC(U_9897,tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9897,tc_prod(U_9895,U_9897)),tc_fun(U_9897,tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),U_9895),hAPP(c_COMBB(tc_prod(U_9895,U_9897),tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool),U_9897),c_member(tc_prod(U_9895,U_9897)))),c_Product__Type_OPair(U_9895,U_9897)))),U_9899)),hAPP(hAPP(c_COMBC(U_9895,tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_fun(U_9897,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9897,tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_fun(U_9897,tc_HOL_Obool)),U_9895),c_COMBC(U_9897,tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9897,tc_prod(U_9895,U_9897)),tc_fun(U_9897,tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),U_9895),hAPP(c_COMBB(tc_prod(U_9895,U_9897),tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool),U_9897),c_member(tc_prod(U_9895,U_9897)))),c_Product__Type_OPair(U_9895,U_9897)))),U_9901)),U_9903),U_9905))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9895,U_9897)),hAPP(hAPP(c_Product__Type_OPair(U_9895,U_9897),U_9903),U_9905)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool)),U_9899),U_9901))) )
    & ! [U_9904,U_9902,U_9900,U_9898,U_9896,U_9894] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9894,U_9896)),hAPP(hAPP(c_Product__Type_OPair(U_9894,U_9896),U_9902),U_9904)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool)),U_9898),U_9900)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9894,tc_fun(U_9896,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9894,tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),U_9894),c_COMBC(U_9896,tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_prod(U_9894,U_9896)),tc_fun(U_9896,tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),U_9894),hAPP(c_COMBB(tc_prod(U_9894,U_9896),tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool),U_9896),c_member(tc_prod(U_9894,U_9896)))),c_Product__Type_OPair(U_9894,U_9896)))),U_9898)),hAPP(hAPP(c_COMBC(U_9894,tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),U_9894),c_COMBC(U_9896,tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_prod(U_9894,U_9896)),tc_fun(U_9896,tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),U_9894),hAPP(c_COMBB(tc_prod(U_9894,U_9896),tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool),U_9896),c_member(tc_prod(U_9894,U_9896)))),c_Product__Type_OPair(U_9894,U_9896)))),U_9900)),U_9902),U_9904)) ) ),
    inference(miniscope,[status(thm)],[f_2670_2]) ).

fof(f_2670_4,plain,
    ( ! [U_9895,U_9897,U_9899,U_9901,U_9903,U_9905] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9895,tc_fun(U_9897,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9895,tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_fun(U_9897,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9897,tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_fun(U_9897,tc_HOL_Obool)),U_9895),c_COMBC(U_9897,tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9897,tc_prod(U_9895,U_9897)),tc_fun(U_9897,tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),U_9895),hAPP(c_COMBB(tc_prod(U_9895,U_9897),tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool),U_9897),c_member(tc_prod(U_9895,U_9897)))),c_Product__Type_OPair(U_9895,U_9897)))),U_9899)),hAPP(hAPP(c_COMBC(U_9895,tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_fun(U_9897,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9897,tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_fun(U_9897,tc_HOL_Obool)),U_9895),c_COMBC(U_9897,tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9897,tc_prod(U_9895,U_9897)),tc_fun(U_9897,tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),U_9895),hAPP(c_COMBB(tc_prod(U_9895,U_9897),tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool),U_9897),c_member(tc_prod(U_9895,U_9897)))),c_Product__Type_OPair(U_9895,U_9897)))),U_9901)),U_9903),U_9905))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9895,U_9897)),hAPP(hAPP(c_Product__Type_OPair(U_9895,U_9897),U_9903),U_9905)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool)),U_9899),U_9901))) )
    & ! [U_9900,U_9896,U_9898,U_9894,U_9902,U_9904] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9894,U_9896)),hAPP(hAPP(c_Product__Type_OPair(U_9894,U_9896),U_9902),U_9904)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool)),U_9898),U_9900)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9894,tc_fun(U_9896,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9894,tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),U_9894),c_COMBC(U_9896,tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_prod(U_9894,U_9896)),tc_fun(U_9896,tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),U_9894),hAPP(c_COMBB(tc_prod(U_9894,U_9896),tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool),U_9896),c_member(tc_prod(U_9894,U_9896)))),c_Product__Type_OPair(U_9894,U_9896)))),U_9898)),hAPP(hAPP(c_COMBC(U_9894,tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),U_9894),c_COMBC(U_9896,tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_prod(U_9894,U_9896)),tc_fun(U_9896,tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),U_9894),hAPP(c_COMBB(tc_prod(U_9894,U_9896),tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool),U_9896),c_member(tc_prod(U_9894,U_9896)))),c_Product__Type_OPair(U_9894,U_9896)))),U_9900)),U_9902),U_9904)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2670_3]) ).

cnf(f_2670_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9894,U_9896)),hAPP(hAPP(c_Product__Type_OPair(U_9894,U_9896),U_9902),U_9904)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool)),U_9898),U_9900)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9894,tc_fun(U_9896,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9894,tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),U_9894),c_COMBC(U_9896,tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_prod(U_9894,U_9896)),tc_fun(U_9896,tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),U_9894),hAPP(c_COMBB(tc_prod(U_9894,U_9896),tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool),U_9896),c_member(tc_prod(U_9894,U_9896)))),c_Product__Type_OPair(U_9894,U_9896)))),U_9898)),hAPP(hAPP(c_COMBC(U_9894,tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_fun(U_9896,tc_HOL_Obool)),U_9894),c_COMBC(U_9896,tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9896,tc_prod(U_9894,U_9896)),tc_fun(U_9896,tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool)),U_9894),hAPP(c_COMBB(tc_prod(U_9894,U_9896),tc_fun(tc_fun(tc_prod(U_9894,U_9896),tc_HOL_Obool),tc_HOL_Obool),U_9896),c_member(tc_prod(U_9894,U_9896)))),c_Product__Type_OPair(U_9894,U_9896)))),U_9900)),U_9902),U_9904)) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

cnf(f_2670_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9895,tc_fun(U_9897,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9895,tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_fun(U_9897,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9897,tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_fun(U_9897,tc_HOL_Obool)),U_9895),c_COMBC(U_9897,tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9897,tc_prod(U_9895,U_9897)),tc_fun(U_9897,tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),U_9895),hAPP(c_COMBB(tc_prod(U_9895,U_9897),tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool),U_9897),c_member(tc_prod(U_9895,U_9897)))),c_Product__Type_OPair(U_9895,U_9897)))),U_9899)),hAPP(hAPP(c_COMBC(U_9895,tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_fun(U_9897,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9897,tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_fun(U_9897,tc_HOL_Obool)),U_9895),c_COMBC(U_9897,tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9897,tc_prod(U_9895,U_9897)),tc_fun(U_9897,tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool)),U_9895),hAPP(c_COMBB(tc_prod(U_9895,U_9897),tc_fun(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool),tc_HOL_Obool),U_9897),c_member(tc_prod(U_9895,U_9897)))),c_Product__Type_OPair(U_9895,U_9897)))),U_9901)),U_9903),U_9905))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9895,U_9897)),hAPP(hAPP(c_Product__Type_OPair(U_9895,U_9897),U_9903),U_9905)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9895,U_9897),tc_HOL_Obool)),U_9899),U_9901))) ),
    inference(clausify,[status(thm)],[f_2670_4]) ).

fof(f_2671_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_2671_2,plain,
    ! [U_9910,U_9909,U_9908,U_9907,U_9906] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9906),U_9907),c_SetInterval_Oord_OgreaterThanLessThan(U_9906,U_9908,U_9909,U_9910)))
        | ~ hBOOL(hAPP(hAPP(U_9908,U_9907),U_9910))
        | ~ hBOOL(hAPP(hAPP(U_9908,U_9909),U_9907)) )
      & ( ( hBOOL(hAPP(hAPP(U_9908,U_9907),U_9910))
          & hBOOL(hAPP(hAPP(U_9908,U_9909),U_9907)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9906),U_9907),c_SetInterval_Oord_OgreaterThanLessThan(U_9906,U_9908,U_9909,U_9910))) ) ),
    inference(variable_rename,[status(thm)],[f_2671_1]) ).

fof(f_2671_3,plain,
    ( ! [U_9920,U_9918,U_9916,U_9914] :
        ( ! [U_9912] : hBOOL(hAPP(hAPP(c_member(U_9912),U_9914),c_SetInterval_Oord_OgreaterThanLessThan(U_9912,U_9916,U_9918,U_9920)))
        | ~ hBOOL(hAPP(hAPP(U_9916,U_9914),U_9920))
        | ~ hBOOL(hAPP(hAPP(U_9916,U_9918),U_9914)) )
    & ! [U_9919,U_9917,U_9915,U_9913] :
        ( ! [U_9911] : ~ hBOOL(hAPP(hAPP(c_member(U_9911),U_9913),c_SetInterval_Oord_OgreaterThanLessThan(U_9911,U_9915,U_9917,U_9919)))
        | ( hBOOL(hAPP(hAPP(U_9915,U_9913),U_9919))
          & hBOOL(hAPP(hAPP(U_9915,U_9917),U_9913)) ) ) ),
    inference(miniscope,[status(thm)],[f_2671_2]) ).

fof(f_2671_4,plain,
    ( ! [U_9913,U_9915,U_9917,U_9919] :
        ( hBOOL(hAPP(hAPP(U_9915,U_9913),U_9919))
        | ~ sP761(U_9913,U_9915,U_9917,U_9919) )
    & ! [U_9913,U_9915,U_9917,U_9919] :
        ( hBOOL(hAPP(hAPP(U_9915,U_9917),U_9913))
        | ~ sP761(U_9913,U_9915,U_9917,U_9919) )
    & ! [U_9916,U_9914,U_9912,U_9920,U_9918] :
        ( hBOOL(hAPP(hAPP(c_member(U_9912),U_9914),c_SetInterval_Oord_OgreaterThanLessThan(U_9912,U_9916,U_9918,U_9920)))
        | ~ hBOOL(hAPP(hAPP(U_9916,U_9914),U_9920))
        | ~ hBOOL(hAPP(hAPP(U_9916,U_9918),U_9914)) )
    & ! [U_9911,U_9913,U_9915,U_9917,U_9919] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9911),U_9913),c_SetInterval_Oord_OgreaterThanLessThan(U_9911,U_9915,U_9917,U_9919)))
        | sP761(U_9913,U_9915,U_9917,U_9919) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP761])],[f_2671_3]) ).

cnf(f_2671_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9911),U_9913),c_SetInterval_Oord_OgreaterThanLessThan(U_9911,U_9915,U_9917,U_9919)))
    | sP761(U_9913,U_9915,U_9917,U_9919) ),
    inference(clausify,[status(thm)],[f_2671_4]) ).

cnf(f_2671_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9912),U_9914),c_SetInterval_Oord_OgreaterThanLessThan(U_9912,U_9916,U_9918,U_9920)))
    | ~ hBOOL(hAPP(hAPP(U_9916,U_9914),U_9920))
    | ~ hBOOL(hAPP(hAPP(U_9916,U_9918),U_9914)) ),
    inference(clausify,[status(thm)],[f_2671_4]) ).

cnf(f_2671_7,plain,
    ( hBOOL(hAPP(hAPP(U_9915,U_9917),U_9913))
    | ~ sP761(U_9913,U_9915,U_9917,U_9919) ),
    inference(clausify,[status(thm)],[f_2671_4]) ).

cnf(f_2671_8,plain,
    ( hBOOL(hAPP(hAPP(U_9915,U_9913),U_9919))
    | ~ sP761(U_9913,U_9915,U_9917,U_9919) ),
    inference(clausify,[status(thm)],[f_2671_4]) ).

fof(f_2672_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_2672_2,plain,
    ! [U_9924,U_9923,U_9922,U_9921] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9921),U_9922),c_SetInterval_Oord_OgreaterThan(U_9921,U_9923,U_9924)))
        | ~ hBOOL(hAPP(hAPP(U_9923,U_9924),U_9922)) )
      & ( hBOOL(hAPP(hAPP(U_9923,U_9924),U_9922))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9921),U_9922),c_SetInterval_Oord_OgreaterThan(U_9921,U_9923,U_9924))) ) ),
    inference(variable_rename,[status(thm)],[f_2672_1]) ).

fof(f_2672_3,plain,
    ( ! [U_9932,U_9930,U_9928] :
        ( ! [U_9926] : hBOOL(hAPP(hAPP(c_member(U_9926),U_9928),c_SetInterval_Oord_OgreaterThan(U_9926,U_9930,U_9932)))
        | ~ hBOOL(hAPP(hAPP(U_9930,U_9932),U_9928)) )
    & ! [U_9931,U_9929,U_9927] :
        ( ! [U_9925] : ~ hBOOL(hAPP(hAPP(c_member(U_9925),U_9927),c_SetInterval_Oord_OgreaterThan(U_9925,U_9929,U_9931)))
        | hBOOL(hAPP(hAPP(U_9929,U_9931),U_9927)) ) ),
    inference(miniscope,[status(thm)],[f_2672_2]) ).

fof(f_2672_4,plain,
    ( ! [U_9926,U_9928,U_9930,U_9932] :
        ( hBOOL(hAPP(hAPP(c_member(U_9926),U_9928),c_SetInterval_Oord_OgreaterThan(U_9926,U_9930,U_9932)))
        | ~ hBOOL(hAPP(hAPP(U_9930,U_9932),U_9928)) )
    & ! [U_9931,U_9925,U_9927,U_9929] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9925),U_9927),c_SetInterval_Oord_OgreaterThan(U_9925,U_9929,U_9931)))
        | hBOOL(hAPP(hAPP(U_9929,U_9931),U_9927)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2672_3]) ).

cnf(f_2672_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9925),U_9927),c_SetInterval_Oord_OgreaterThan(U_9925,U_9929,U_9931)))
    | hBOOL(hAPP(hAPP(U_9929,U_9931),U_9927)) ),
    inference(clausify,[status(thm)],[f_2672_4]) ).

cnf(f_2672_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9926),U_9928),c_SetInterval_Oord_OgreaterThan(U_9926,U_9930,U_9932)))
    | ~ hBOOL(hAPP(hAPP(U_9930,U_9932),U_9928)) ),
    inference(clausify,[status(thm)],[f_2672_4]) ).

fof(f_2673_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_2673_2,plain,
    ! [U_9936,U_9935,U_9934,U_9933] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9933),U_9934),c_SetInterval_Oord_OlessThan(U_9933,U_9935,U_9936)))
        | ~ hBOOL(hAPP(hAPP(U_9935,U_9934),U_9936)) )
      & ( hBOOL(hAPP(hAPP(U_9935,U_9934),U_9936))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9933),U_9934),c_SetInterval_Oord_OlessThan(U_9933,U_9935,U_9936))) ) ),
    inference(variable_rename,[status(thm)],[f_2673_1]) ).

fof(f_2673_3,plain,
    ( ! [U_9944,U_9942,U_9940] :
        ( ! [U_9938] : hBOOL(hAPP(hAPP(c_member(U_9938),U_9940),c_SetInterval_Oord_OlessThan(U_9938,U_9942,U_9944)))
        | ~ hBOOL(hAPP(hAPP(U_9942,U_9940),U_9944)) )
    & ! [U_9943,U_9941,U_9939] :
        ( ! [U_9937] : ~ hBOOL(hAPP(hAPP(c_member(U_9937),U_9939),c_SetInterval_Oord_OlessThan(U_9937,U_9941,U_9943)))
        | hBOOL(hAPP(hAPP(U_9941,U_9939),U_9943)) ) ),
    inference(miniscope,[status(thm)],[f_2673_2]) ).

fof(f_2673_4,plain,
    ( ! [U_9942,U_9940,U_9944,U_9938] :
        ( hBOOL(hAPP(hAPP(c_member(U_9938),U_9940),c_SetInterval_Oord_OlessThan(U_9938,U_9942,U_9944)))
        | ~ hBOOL(hAPP(hAPP(U_9942,U_9940),U_9944)) )
    & ! [U_9941,U_9939,U_9937,U_9943] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9937),U_9939),c_SetInterval_Oord_OlessThan(U_9937,U_9941,U_9943)))
        | hBOOL(hAPP(hAPP(U_9941,U_9939),U_9943)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2673_3]) ).

cnf(f_2673_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9937),U_9939),c_SetInterval_Oord_OlessThan(U_9937,U_9941,U_9943)))
    | hBOOL(hAPP(hAPP(U_9941,U_9939),U_9943)) ),
    inference(clausify,[status(thm)],[f_2673_4]) ).

cnf(f_2673_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9938),U_9940),c_SetInterval_Oord_OlessThan(U_9938,U_9942,U_9944)))
    | ~ hBOOL(hAPP(hAPP(U_9942,U_9940),U_9944)) ),
    inference(clausify,[status(thm)],[f_2673_4]) ).

fof(f_2674_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_2674_2,plain,
    ! [U_9948,U_9947,U_9946,U_9945] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9945),U_9946),c_SetInterval_Oord_OatMost(U_9945,U_9947,U_9948)))
        | ~ hBOOL(hAPP(hAPP(U_9947,U_9946),U_9948)) )
      & ( hBOOL(hAPP(hAPP(U_9947,U_9946),U_9948))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9945),U_9946),c_SetInterval_Oord_OatMost(U_9945,U_9947,U_9948))) ) ),
    inference(variable_rename,[status(thm)],[f_2674_1]) ).

fof(f_2674_3,plain,
    ( ! [U_9956,U_9954,U_9952] :
        ( ! [U_9950] : hBOOL(hAPP(hAPP(c_member(U_9950),U_9952),c_SetInterval_Oord_OatMost(U_9950,U_9954,U_9956)))
        | ~ hBOOL(hAPP(hAPP(U_9954,U_9952),U_9956)) )
    & ! [U_9955,U_9953,U_9951] :
        ( ! [U_9949] : ~ hBOOL(hAPP(hAPP(c_member(U_9949),U_9951),c_SetInterval_Oord_OatMost(U_9949,U_9953,U_9955)))
        | hBOOL(hAPP(hAPP(U_9953,U_9951),U_9955)) ) ),
    inference(miniscope,[status(thm)],[f_2674_2]) ).

fof(f_2674_4,plain,
    ( ! [U_9956,U_9950,U_9952,U_9954] :
        ( hBOOL(hAPP(hAPP(c_member(U_9950),U_9952),c_SetInterval_Oord_OatMost(U_9950,U_9954,U_9956)))
        | ~ hBOOL(hAPP(hAPP(U_9954,U_9952),U_9956)) )
    & ! [U_9953,U_9951,U_9949,U_9955] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9949),U_9951),c_SetInterval_Oord_OatMost(U_9949,U_9953,U_9955)))
        | hBOOL(hAPP(hAPP(U_9953,U_9951),U_9955)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2674_3]) ).

cnf(f_2674_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9949),U_9951),c_SetInterval_Oord_OatMost(U_9949,U_9953,U_9955)))
    | hBOOL(hAPP(hAPP(U_9953,U_9951),U_9955)) ),
    inference(clausify,[status(thm)],[f_2674_4]) ).

cnf(f_2674_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9950),U_9952),c_SetInterval_Oord_OatMost(U_9950,U_9954,U_9956)))
    | ~ hBOOL(hAPP(hAPP(U_9954,U_9952),U_9956)) ),
    inference(clausify,[status(thm)],[f_2674_4]) ).

fof(f_2675_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_2675_2,plain,
    ! [U_9958,U_9957] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9957),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9958)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9958),U_9957)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9958),U_9957))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9957),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9958))) ) ),
    inference(variable_rename,[status(thm)],[f_2675_1]) ).

fof(f_2675_3,plain,
    ( ! [U_9962,U_9960] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9960),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9962)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9962),U_9960)) )
    & ! [U_9961,U_9959] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9961),U_9959))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9959),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9961))) ) ),
    inference(miniscope,[status(thm)],[f_2675_2]) ).

fof(f_2675_4,plain,
    ( ! [U_9960,U_9962] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9960),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9962)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9962),U_9960)) )
    & ! [U_9961,U_9959] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9961),U_9959))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9959),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9961))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2675_3]) ).

cnf(f_2675_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9961),U_9959))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9959),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9961))) ),
    inference(clausify,[status(thm)],[f_2675_4]) ).

cnf(f_2675_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9960),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9962)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9962),U_9960)) ),
    inference(clausify,[status(thm)],[f_2675_4]) ).

fof(f_2676_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_2676_2,plain,
    ! [U_9967,U_9966,U_9965,U_9964] :
      ( ? [U_9963] :
          ( hBOOL(hAPP(hAPP(c_member(U_9964),U_9963),U_9966))
          & U_9965 = hAPP(c_Relation_OImage(U_9964,U_9964,U_9967),hAPP(hAPP(c_Set_Oinsert(U_9964),U_9963),c_Orderings_Obot__class_Obot(tc_fun(U_9964,tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9964,tc_HOL_Obool)),U_9965),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9964),U_9966),U_9967))) ),
    inference(variable_rename,[status(thm)],[f_2676_1]) ).

fof(f_2676_3,plain,
    ! [U_9967,U_9966,U_9965,U_9964] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9964),sK147(U_9967,U_9966,U_9965,U_9964)),U_9966))
        & U_9965 = hAPP(c_Relation_OImage(U_9964,U_9964,U_9967),hAPP(hAPP(c_Set_Oinsert(U_9964),sK147(U_9967,U_9966,U_9965,U_9964)),c_Orderings_Obot__class_Obot(tc_fun(U_9964,tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9964,tc_HOL_Obool)),U_9965),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9964),U_9966),U_9967))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_9963,sK147(U_9967,U_9966,U_9965,U_9964))],[f_2676_2]) ).

fof(f_2676_4,plain,
    ( ! [U_9964,U_9965,U_9966,U_9967] :
        ( hBOOL(hAPP(hAPP(c_member(U_9964),sK147(U_9967,U_9966,U_9965,U_9964)),U_9966))
        | ~ sP762(U_9964,U_9965,U_9966,U_9967) )
    & ! [U_9964,U_9965,U_9966,U_9967] :
        ( U_9965 = hAPP(c_Relation_OImage(U_9964,U_9964,U_9967),hAPP(hAPP(c_Set_Oinsert(U_9964),sK147(U_9967,U_9966,U_9965,U_9964)),c_Orderings_Obot__class_Obot(tc_fun(U_9964,tc_HOL_Obool))))
        | ~ sP762(U_9964,U_9965,U_9966,U_9967) )
    & ! [U_9964,U_9965,U_9966,U_9967] :
        ( sP762(U_9964,U_9965,U_9966,U_9967)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9964,tc_HOL_Obool)),U_9965),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9964),U_9966),U_9967))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP762])],[f_2676_3]) ).

cnf(f_2676_5,plain,
    ( sP762(U_9964,U_9965,U_9966,U_9967)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_9964,tc_HOL_Obool)),U_9965),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_9964),U_9966),U_9967))) ),
    inference(clausify,[status(thm)],[f_2676_4]) ).

cnf(f_2676_6,plain,
    ( U_9965 = hAPP(c_Relation_OImage(U_9964,U_9964,U_9967),hAPP(hAPP(c_Set_Oinsert(U_9964),sK147(U_9967,U_9966,U_9965,U_9964)),c_Orderings_Obot__class_Obot(tc_fun(U_9964,tc_HOL_Obool))))
    | ~ sP762(U_9964,U_9965,U_9966,U_9967) ),
    inference(clausify,[status(thm)],[f_2676_4]) ).

cnf(f_2676_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9964),sK147(U_9967,U_9966,U_9965,U_9964)),U_9966))
    | ~ sP762(U_9964,U_9965,U_9966,U_9967) ),
    inference(clausify,[status(thm)],[f_2676_4]) ).

fof(f_2677_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_2677_2,plain,
    ! [U_9973,U_9972,U_9971,U_9970,U_9969,U_9968] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9968),U_9969),c_SetInterval_Oord_OgreaterThanAtMost(U_9968,U_9970,U_9971,U_9972,U_9973)))
        | ~ hBOOL(hAPP(hAPP(U_9970,U_9969),U_9973))
        | ~ hBOOL(hAPP(hAPP(U_9971,U_9972),U_9969)) )
      & ( ( hBOOL(hAPP(hAPP(U_9970,U_9969),U_9973))
          & hBOOL(hAPP(hAPP(U_9971,U_9972),U_9969)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9968),U_9969),c_SetInterval_Oord_OgreaterThanAtMost(U_9968,U_9970,U_9971,U_9972,U_9973))) ) ),
    inference(variable_rename,[status(thm)],[f_2677_1]) ).

fof(f_2677_3,plain,
    ( ! [U_9985,U_9983,U_9981,U_9979,U_9977] :
        ( ! [U_9975] : hBOOL(hAPP(hAPP(c_member(U_9975),U_9977),c_SetInterval_Oord_OgreaterThanAtMost(U_9975,U_9979,U_9981,U_9983,U_9985)))
        | ~ hBOOL(hAPP(hAPP(U_9979,U_9977),U_9985))
        | ~ hBOOL(hAPP(hAPP(U_9981,U_9983),U_9977)) )
    & ! [U_9984,U_9982,U_9980,U_9978,U_9976] :
        ( ! [U_9974] : ~ hBOOL(hAPP(hAPP(c_member(U_9974),U_9976),c_SetInterval_Oord_OgreaterThanAtMost(U_9974,U_9978,U_9980,U_9982,U_9984)))
        | ( hBOOL(hAPP(hAPP(U_9978,U_9976),U_9984))
          & hBOOL(hAPP(hAPP(U_9980,U_9982),U_9976)) ) ) ),
    inference(miniscope,[status(thm)],[f_2677_2]) ).

fof(f_2677_4,plain,
    ( ! [U_9978,U_9976,U_9980,U_9982,U_9984] :
        ( hBOOL(hAPP(hAPP(U_9978,U_9976),U_9984))
        | ~ sP763(U_9978,U_9976,U_9980,U_9982,U_9984) )
    & ! [U_9978,U_9976,U_9980,U_9982,U_9984] :
        ( hBOOL(hAPP(hAPP(U_9980,U_9982),U_9976))
        | ~ sP763(U_9978,U_9976,U_9980,U_9982,U_9984) )
    & ! [U_9977,U_9975,U_9979,U_9981,U_9985,U_9983] :
        ( hBOOL(hAPP(hAPP(c_member(U_9975),U_9977),c_SetInterval_Oord_OgreaterThanAtMost(U_9975,U_9979,U_9981,U_9983,U_9985)))
        | ~ hBOOL(hAPP(hAPP(U_9979,U_9977),U_9985))
        | ~ hBOOL(hAPP(hAPP(U_9981,U_9983),U_9977)) )
    & ! [U_9978,U_9976,U_9974,U_9980,U_9982,U_9984] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9974),U_9976),c_SetInterval_Oord_OgreaterThanAtMost(U_9974,U_9978,U_9980,U_9982,U_9984)))
        | sP763(U_9978,U_9976,U_9980,U_9982,U_9984) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP763])],[f_2677_3]) ).

cnf(f_2677_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9974),U_9976),c_SetInterval_Oord_OgreaterThanAtMost(U_9974,U_9978,U_9980,U_9982,U_9984)))
    | sP763(U_9978,U_9976,U_9980,U_9982,U_9984) ),
    inference(clausify,[status(thm)],[f_2677_4]) ).

cnf(f_2677_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9975),U_9977),c_SetInterval_Oord_OgreaterThanAtMost(U_9975,U_9979,U_9981,U_9983,U_9985)))
    | ~ hBOOL(hAPP(hAPP(U_9979,U_9977),U_9985))
    | ~ hBOOL(hAPP(hAPP(U_9981,U_9983),U_9977)) ),
    inference(clausify,[status(thm)],[f_2677_4]) ).

cnf(f_2677_7,plain,
    ( hBOOL(hAPP(hAPP(U_9980,U_9982),U_9976))
    | ~ sP763(U_9978,U_9976,U_9980,U_9982,U_9984) ),
    inference(clausify,[status(thm)],[f_2677_4]) ).

cnf(f_2677_8,plain,
    ( hBOOL(hAPP(hAPP(U_9978,U_9976),U_9984))
    | ~ sP763(U_9978,U_9976,U_9980,U_9982,U_9984) ),
    inference(clausify,[status(thm)],[f_2677_4]) ).

fof(f_2678_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_2678_2,plain,
    ! [U_9991,U_9990,U_9989,U_9988,U_9987,U_9986] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9986),U_9987),c_SetInterval_Oord_OatLeastLessThan(U_9986,U_9988,U_9989,U_9990,U_9991)))
        | ~ hBOOL(hAPP(hAPP(U_9989,U_9987),U_9991))
        | ~ hBOOL(hAPP(hAPP(U_9988,U_9990),U_9987)) )
      & ( ( hBOOL(hAPP(hAPP(U_9989,U_9987),U_9991))
          & hBOOL(hAPP(hAPP(U_9988,U_9990),U_9987)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9986),U_9987),c_SetInterval_Oord_OatLeastLessThan(U_9986,U_9988,U_9989,U_9990,U_9991))) ) ),
    inference(variable_rename,[status(thm)],[f_2678_1]) ).

fof(f_2678_3,plain,
    ( ! [U_10003,U_10001,U_9999,U_9997,U_9995] :
        ( ! [U_9993] : hBOOL(hAPP(hAPP(c_member(U_9993),U_9995),c_SetInterval_Oord_OatLeastLessThan(U_9993,U_9997,U_9999,U_10001,U_10003)))
        | ~ hBOOL(hAPP(hAPP(U_9999,U_9995),U_10003))
        | ~ hBOOL(hAPP(hAPP(U_9997,U_10001),U_9995)) )
    & ! [U_10002,U_10000,U_9998,U_9996,U_9994] :
        ( ! [U_9992] : ~ hBOOL(hAPP(hAPP(c_member(U_9992),U_9994),c_SetInterval_Oord_OatLeastLessThan(U_9992,U_9996,U_9998,U_10000,U_10002)))
        | ( hBOOL(hAPP(hAPP(U_9998,U_9994),U_10002))
          & hBOOL(hAPP(hAPP(U_9996,U_10000),U_9994)) ) ) ),
    inference(miniscope,[status(thm)],[f_2678_2]) ).

fof(f_2678_4,plain,
    ( ! [U_10000,U_9994,U_9996,U_9998,U_10002] :
        ( hBOOL(hAPP(hAPP(U_9998,U_9994),U_10002))
        | ~ sP764(U_10000,U_9994,U_9996,U_9998,U_10002) )
    & ! [U_10000,U_9994,U_9996,U_9998,U_10002] :
        ( hBOOL(hAPP(hAPP(U_9996,U_10000),U_9994))
        | ~ sP764(U_10000,U_9994,U_9996,U_9998,U_10002) )
    & ! [U_9997,U_9993,U_9995,U_10003,U_10001,U_9999] :
        ( hBOOL(hAPP(hAPP(c_member(U_9993),U_9995),c_SetInterval_Oord_OatLeastLessThan(U_9993,U_9997,U_9999,U_10001,U_10003)))
        | ~ hBOOL(hAPP(hAPP(U_9999,U_9995),U_10003))
        | ~ hBOOL(hAPP(hAPP(U_9997,U_10001),U_9995)) )
    & ! [U_10000,U_9992,U_9994,U_9996,U_9998,U_10002] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9992),U_9994),c_SetInterval_Oord_OatLeastLessThan(U_9992,U_9996,U_9998,U_10000,U_10002)))
        | sP764(U_10000,U_9994,U_9996,U_9998,U_10002) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP764])],[f_2678_3]) ).

cnf(f_2678_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9992),U_9994),c_SetInterval_Oord_OatLeastLessThan(U_9992,U_9996,U_9998,U_10000,U_10002)))
    | sP764(U_10000,U_9994,U_9996,U_9998,U_10002) ),
    inference(clausify,[status(thm)],[f_2678_4]) ).

cnf(f_2678_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9993),U_9995),c_SetInterval_Oord_OatLeastLessThan(U_9993,U_9997,U_9999,U_10001,U_10003)))
    | ~ hBOOL(hAPP(hAPP(U_9999,U_9995),U_10003))
    | ~ hBOOL(hAPP(hAPP(U_9997,U_10001),U_9995)) ),
    inference(clausify,[status(thm)],[f_2678_4]) ).

cnf(f_2678_7,plain,
    ( hBOOL(hAPP(hAPP(U_9996,U_10000),U_9994))
    | ~ sP764(U_10000,U_9994,U_9996,U_9998,U_10002) ),
    inference(clausify,[status(thm)],[f_2678_4]) ).

cnf(f_2678_8,plain,
    ( hBOOL(hAPP(hAPP(U_9998,U_9994),U_10002))
    | ~ sP764(U_10000,U_9994,U_9996,U_9998,U_10002) ),
    inference(clausify,[status(thm)],[f_2678_4]) ).

fof(f_2679_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_2679_2,plain,
    ! [U_10009,U_10008,U_10007,U_10006,U_10005,U_10004] :
      ( ( hBOOL(hAPP(hAPP(U_10007,U_10008),U_10009))
        & hBOOL(hAPP(hAPP(U_10006,U_10008),U_10009)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10004,tc_fun(U_10005,tc_HOL_Obool))),U_10006),U_10007),U_10008),U_10009)) ),
    inference(variable_rename,[status(thm)],[f_2679_1]) ).

fof(f_2679_3,plain,
    ! [U_10009,U_10008,U_10007,U_10006] :
      ( ! [U_10005,U_10004] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10004,tc_fun(U_10005,tc_HOL_Obool))),U_10006),U_10007),U_10008),U_10009))
      | ( hBOOL(hAPP(hAPP(U_10007,U_10008),U_10009))
        & hBOOL(hAPP(hAPP(U_10006,U_10008),U_10009)) ) ),
    inference(miniscope,[status(thm)],[f_2679_2]) ).

fof(f_2679_4,plain,
    ( ! [U_10006,U_10007,U_10008,U_10009] :
        ( hBOOL(hAPP(hAPP(U_10007,U_10008),U_10009))
        | ~ sP765(U_10006,U_10007,U_10008,U_10009) )
    & ! [U_10006,U_10007,U_10008,U_10009] :
        ( hBOOL(hAPP(hAPP(U_10006,U_10008),U_10009))
        | ~ sP765(U_10006,U_10007,U_10008,U_10009) )
    & ! [U_10006,U_10007,U_10004,U_10005,U_10008,U_10009] :
        ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10004,tc_fun(U_10005,tc_HOL_Obool))),U_10006),U_10007),U_10008),U_10009))
        | sP765(U_10006,U_10007,U_10008,U_10009) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP765])],[f_2679_3]) ).

cnf(f_2679_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10004,tc_fun(U_10005,tc_HOL_Obool))),U_10006),U_10007),U_10008),U_10009))
    | sP765(U_10006,U_10007,U_10008,U_10009) ),
    inference(clausify,[status(thm)],[f_2679_4]) ).

cnf(f_2679_6,plain,
    ( hBOOL(hAPP(hAPP(U_10006,U_10008),U_10009))
    | ~ sP765(U_10006,U_10007,U_10008,U_10009) ),
    inference(clausify,[status(thm)],[f_2679_4]) ).

cnf(f_2679_7,plain,
    ( hBOOL(hAPP(hAPP(U_10007,U_10008),U_10009))
    | ~ sP765(U_10006,U_10007,U_10008,U_10009) ),
    inference(clausify,[status(thm)],[f_2679_4]) ).

fof(f_2680_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_2680_2,plain,
    ! [U_10015,U_10014,U_10013,U_10012,U_10011,U_10010] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10014,tc_fun(U_10015,tc_HOL_Obool))),U_10010),U_10013),U_10011),U_10012))
      | ~ hBOOL(hAPP(hAPP(U_10013,U_10011),U_10012))
      | ~ hBOOL(hAPP(hAPP(U_10010,U_10011),U_10012)) ),
    inference(variable_rename,[status(thm)],[f_2680_1]) ).

fof(f_2680_3,plain,
    ! [U_10010,U_10011,U_10012,U_10013,U_10014,U_10015] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10014,tc_fun(U_10015,tc_HOL_Obool))),U_10010),U_10013),U_10011),U_10012))
      | ~ hBOOL(hAPP(hAPP(U_10013,U_10011),U_10012))
      | ~ hBOOL(hAPP(hAPP(U_10010,U_10011),U_10012)) ),
    inference(definitional_conversion,[status(esa)],[f_2680_2]) ).

cnf(f_2680_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10014,tc_fun(U_10015,tc_HOL_Obool))),U_10010),U_10013),U_10011),U_10012))
    | ~ hBOOL(hAPP(hAPP(U_10013,U_10011),U_10012))
    | ~ hBOOL(hAPP(hAPP(U_10010,U_10011),U_10012)) ),
    inference(clausify,[status(thm)],[f_2680_3]) ).

fof(f_2681_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_2681_2,plain,
    ! [U_10021,U_10020,U_10019,U_10018,U_10017,U_10016] :
      ( hBOOL(hAPP(hAPP(U_10019,U_10020),U_10021))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10016,tc_fun(U_10017,tc_HOL_Obool))),U_10018),U_10019),U_10020),U_10021)) ),
    inference(variable_rename,[status(thm)],[f_2681_1]) ).

fof(f_2681_3,plain,
    ! [U_10021,U_10020,U_10019] :
      ( ! [U_10018,U_10017,U_10016] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10016,tc_fun(U_10017,tc_HOL_Obool))),U_10018),U_10019),U_10020),U_10021))
      | hBOOL(hAPP(hAPP(U_10019,U_10020),U_10021)) ),
    inference(miniscope,[status(thm)],[f_2681_2]) ).

fof(f_2681_4,plain,
    ! [U_10017,U_10016,U_10018,U_10019,U_10020,U_10021] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10016,tc_fun(U_10017,tc_HOL_Obool))),U_10018),U_10019),U_10020),U_10021))
      | hBOOL(hAPP(hAPP(U_10019,U_10020),U_10021)) ),
    inference(definitional_conversion,[status(esa)],[f_2681_3]) ).

cnf(f_2681_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10016,tc_fun(U_10017,tc_HOL_Obool))),U_10018),U_10019),U_10020),U_10021))
    | hBOOL(hAPP(hAPP(U_10019,U_10020),U_10021)) ),
    inference(clausify,[status(thm)],[f_2681_4]) ).

fof(f_2682_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_2682_2,plain,
    ! [U_10027,U_10026,U_10025,U_10024,U_10023,U_10022] :
      ( hBOOL(hAPP(hAPP(U_10024,U_10026),U_10027))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10022,tc_fun(U_10023,tc_HOL_Obool))),U_10024),U_10025),U_10026),U_10027)) ),
    inference(variable_rename,[status(thm)],[f_2682_1]) ).

fof(f_2682_3,plain,
    ! [U_10027,U_10026,U_10025,U_10024] :
      ( ! [U_10023,U_10022] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10022,tc_fun(U_10023,tc_HOL_Obool))),U_10024),U_10025),U_10026),U_10027))
      | hBOOL(hAPP(hAPP(U_10024,U_10026),U_10027)) ),
    inference(miniscope,[status(thm)],[f_2682_2]) ).

fof(f_2682_4,plain,
    ! [U_10022,U_10023,U_10024,U_10025,U_10026,U_10027] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10022,tc_fun(U_10023,tc_HOL_Obool))),U_10024),U_10025),U_10026),U_10027))
      | hBOOL(hAPP(hAPP(U_10024,U_10026),U_10027)) ),
    inference(definitional_conversion,[status(esa)],[f_2682_3]) ).

cnf(f_2682_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10022,tc_fun(U_10023,tc_HOL_Obool))),U_10024),U_10025),U_10026),U_10027))
    | hBOOL(hAPP(hAPP(U_10024,U_10026),U_10027)) ),
    inference(clausify,[status(thm)],[f_2682_4]) ).

fof(f_2683_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_2683_2,plain,
    ! [U_10029,U_10028] :
      ( 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_10029,U_10028) = 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_10028),U_10029)) ),
    inference(variable_rename,[status(thm)],[f_2683_1]) ).

fof(f_2683_3,plain,
    ! [U_10029,U_10028] :
      ( 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_10029,U_10028) = 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_10028),U_10029)) ),
    inference(definitional_conversion,[status(esa)],[f_2683_2]) ).

cnf(f_2683_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_10029,U_10028) = 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_10028),U_10029)) ),
    inference(clausify,[status(thm)],[f_2683_3]) ).

fof(f_2684_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_2684_2,plain,
    ! [U_10031,U_10030] :
      ( 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_10031,U_10030) = 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_10030),U_10031)) ),
    inference(variable_rename,[status(thm)],[f_2684_1]) ).

fof(f_2684_3,plain,
    ! [U_10030,U_10031] :
      ( 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_10031,U_10030) = 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_10030),U_10031)) ),
    inference(definitional_conversion,[status(esa)],[f_2684_2]) ).

cnf(f_2684_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_10031,U_10030) = 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_10030),U_10031)) ),
    inference(clausify,[status(thm)],[f_2684_3]) ).

fof(f_2685_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_2685_2,plain,
    ! [U_10033,U_10032] :
      ( ( 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_10032,U_10033) = 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_10033),U_10032))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10032),U_10033)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10033),U_10032))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10032),U_10033))
        | 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_10032,U_10033) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2685_1]) ).

fof(f_2685_3,plain,
    ( ! [U_10037,U_10035] :
        ( 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_10035,U_10037) = 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_10037),U_10035))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10035),U_10037)) ) )
    & ! [U_10036,U_10034] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10036),U_10034))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10034),U_10036))
        | 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_10034,U_10036) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2685_2]) ).

fof(f_2685_4,plain,
    ( ! [U_10037,U_10035] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10037),U_10035))
        | ~ sP766(U_10037,U_10035) )
    & ! [U_10037,U_10035] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10035),U_10037))
        | ~ sP766(U_10037,U_10035) )
    & ! [U_10037,U_10035] :
        ( 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_10035,U_10037) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | sP766(U_10037,U_10035) )
    & ! [U_10034,U_10036] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10036),U_10034))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10034),U_10036))
        | 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_10034,U_10036) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP766])],[f_2685_3]) ).

cnf(f_2685_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10036),U_10034))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10034),U_10036))
    | 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_10034,U_10036) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2685_4]) ).

cnf(f_2685_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_10035,U_10037) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | sP766(U_10037,U_10035) ),
    inference(clausify,[status(thm)],[f_2685_4]) ).

cnf(f_2685_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10035),U_10037))
    | ~ sP766(U_10037,U_10035) ),
    inference(clausify,[status(thm)],[f_2685_4]) ).

cnf(f_2685_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10037),U_10035))
    | ~ sP766(U_10037,U_10035) ),
    inference(clausify,[status(thm)],[f_2685_4]) ).

fof(f_2686_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_2686_2,plain,
    ! [U_10039,U_10038] :
      ( ( 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_10038,U_10039) = 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_10039),U_10038))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10038),U_10039)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10039),U_10038))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10038),U_10039))
        | 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_10038,U_10039) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2686_1]) ).

fof(f_2686_3,plain,
    ( ! [U_10043,U_10041] :
        ( 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_10041,U_10043) = 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_10043),U_10041))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10041),U_10043)) ) )
    & ! [U_10042,U_10040] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10042),U_10040))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10040),U_10042))
        | 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_10040,U_10042) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2686_2]) ).

fof(f_2686_4,plain,
    ( ! [U_10043,U_10041] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10043),U_10041))
        | ~ sP767(U_10043,U_10041) )
    & ! [U_10043,U_10041] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10041),U_10043))
        | ~ sP767(U_10043,U_10041) )
    & ! [U_10043,U_10041] :
        ( 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_10041,U_10043) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | sP767(U_10043,U_10041) )
    & ! [U_10040,U_10042] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10042),U_10040))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10040),U_10042))
        | 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_10040,U_10042) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP767])],[f_2686_3]) ).

cnf(f_2686_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10042),U_10040))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10040),U_10042))
    | 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_10040,U_10042) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2686_4]) ).

cnf(f_2686_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_10041,U_10043) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | sP767(U_10043,U_10041) ),
    inference(clausify,[status(thm)],[f_2686_4]) ).

cnf(f_2686_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10041),U_10043))
    | ~ sP767(U_10043,U_10041) ),
    inference(clausify,[status(thm)],[f_2686_4]) ).

cnf(f_2686_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10043),U_10041))
    | ~ sP767(U_10043,U_10041) ),
    inference(clausify,[status(thm)],[f_2686_4]) ).

fof(f_2687_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_2687_2,plain,
    ! [U_10045,U_10044] :
      ( ( 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_10044,U_10045)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10045),U_10044))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10044),U_10045)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10045),U_10044))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10044),U_10045))
        | 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_10044,U_10045) ) ),
    inference(variable_rename,[status(thm)],[f_2687_1]) ).

fof(f_2687_3,plain,
    ( ! [U_10049,U_10047] :
        ( 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_10047,U_10049)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10049),U_10047))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10047),U_10049)) ) )
    & ! [U_10048,U_10046] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10048),U_10046))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10046),U_10048))
        | 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_10046,U_10048) ) ),
    inference(miniscope,[status(thm)],[f_2687_2]) ).

fof(f_2687_4,plain,
    ( ! [U_10049,U_10047] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10049),U_10047))
        | ~ sP768(U_10049,U_10047) )
    & ! [U_10049,U_10047] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10047),U_10049))
        | ~ sP768(U_10049,U_10047) )
    & ! [U_10049,U_10047] :
        ( 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_10047,U_10049)
        | sP768(U_10049,U_10047) )
    & ! [U_10046,U_10048] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10048),U_10046))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10046),U_10048))
        | 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_10046,U_10048) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP768])],[f_2687_3]) ).

cnf(f_2687_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10048),U_10046))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10046),U_10048))
    | 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_10046,U_10048) ),
    inference(clausify,[status(thm)],[f_2687_4]) ).

cnf(f_2687_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_10047,U_10049)
    | sP768(U_10049,U_10047) ),
    inference(clausify,[status(thm)],[f_2687_4]) ).

cnf(f_2687_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10047),U_10049))
    | ~ sP768(U_10049,U_10047) ),
    inference(clausify,[status(thm)],[f_2687_4]) ).

cnf(f_2687_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10049),U_10047))
    | ~ sP768(U_10049,U_10047) ),
    inference(clausify,[status(thm)],[f_2687_4]) ).

fof(f_2688_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_2688_2,plain,
    ! [U_10051,U_10050] :
      ( ( 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_10050,U_10051)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10051),U_10050))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10050),U_10051)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10051),U_10050))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10050),U_10051))
        | 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_10050,U_10051) ) ),
    inference(variable_rename,[status(thm)],[f_2688_1]) ).

fof(f_2688_3,plain,
    ( ! [U_10055,U_10053] :
        ( 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_10053,U_10055)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10055),U_10053))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10053),U_10055)) ) )
    & ! [U_10054,U_10052] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10054),U_10052))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10052),U_10054))
        | 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_10052,U_10054) ) ),
    inference(miniscope,[status(thm)],[f_2688_2]) ).

fof(f_2688_4,plain,
    ( ! [U_10053,U_10055] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10055),U_10053))
        | ~ sP769(U_10053,U_10055) )
    & ! [U_10053,U_10055] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10053),U_10055))
        | ~ sP769(U_10053,U_10055) )
    & ! [U_10053,U_10055] :
        ( 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_10053,U_10055)
        | sP769(U_10053,U_10055) )
    & ! [U_10052,U_10054] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10054),U_10052))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10052),U_10054))
        | 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_10052,U_10054) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP769])],[f_2688_3]) ).

cnf(f_2688_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10054),U_10052))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10052),U_10054))
    | 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_10052,U_10054) ),
    inference(clausify,[status(thm)],[f_2688_4]) ).

cnf(f_2688_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_10053,U_10055)
    | sP769(U_10053,U_10055) ),
    inference(clausify,[status(thm)],[f_2688_4]) ).

cnf(f_2688_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10053),U_10055))
    | ~ sP769(U_10053,U_10055) ),
    inference(clausify,[status(thm)],[f_2688_4]) ).

cnf(f_2688_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10055),U_10053))
    | ~ sP769(U_10053,U_10055) ),
    inference(clausify,[status(thm)],[f_2688_4]) ).

fof(f_2689_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_2689_2,plain,
    ! [U_10059,U_10058,U_10057,U_10056] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_10056),U_10057),c_SetInterval_Oord_OatLeast(U_10056,U_10058,U_10059)))
        | ~ hBOOL(hAPP(hAPP(U_10058,U_10059),U_10057)) )
      & ( hBOOL(hAPP(hAPP(U_10058,U_10059),U_10057))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10056),U_10057),c_SetInterval_Oord_OatLeast(U_10056,U_10058,U_10059))) ) ),
    inference(variable_rename,[status(thm)],[f_2689_1]) ).

fof(f_2689_3,plain,
    ( ! [U_10067,U_10065,U_10063] :
        ( ! [U_10061] : hBOOL(hAPP(hAPP(c_member(U_10061),U_10063),c_SetInterval_Oord_OatLeast(U_10061,U_10065,U_10067)))
        | ~ hBOOL(hAPP(hAPP(U_10065,U_10067),U_10063)) )
    & ! [U_10066,U_10064,U_10062] :
        ( ! [U_10060] : ~ hBOOL(hAPP(hAPP(c_member(U_10060),U_10062),c_SetInterval_Oord_OatLeast(U_10060,U_10064,U_10066)))
        | hBOOL(hAPP(hAPP(U_10064,U_10066),U_10062)) ) ),
    inference(miniscope,[status(thm)],[f_2689_2]) ).

fof(f_2689_4,plain,
    ( ! [U_10061,U_10063,U_10065,U_10067] :
        ( hBOOL(hAPP(hAPP(c_member(U_10061),U_10063),c_SetInterval_Oord_OatLeast(U_10061,U_10065,U_10067)))
        | ~ hBOOL(hAPP(hAPP(U_10065,U_10067),U_10063)) )
    & ! [U_10064,U_10066,U_10060,U_10062] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_10060),U_10062),c_SetInterval_Oord_OatLeast(U_10060,U_10064,U_10066)))
        | hBOOL(hAPP(hAPP(U_10064,U_10066),U_10062)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2689_3]) ).

cnf(f_2689_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_10060),U_10062),c_SetInterval_Oord_OatLeast(U_10060,U_10064,U_10066)))
    | hBOOL(hAPP(hAPP(U_10064,U_10066),U_10062)) ),
    inference(clausify,[status(thm)],[f_2689_4]) ).

cnf(f_2689_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10061),U_10063),c_SetInterval_Oord_OatLeast(U_10061,U_10065,U_10067)))
    | ~ hBOOL(hAPP(hAPP(U_10065,U_10067),U_10063)) ),
    inference(clausify,[status(thm)],[f_2689_4]) ).

fof(f_2690_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_2690_2,plain,
    ! [U_10072,U_10071,U_10070,U_10069,U_10068] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_10068),U_10069),c_SetInterval_Oord_OatLeastAtMost(U_10068,U_10070,U_10071,U_10072)))
        | ~ hBOOL(hAPP(hAPP(U_10070,U_10069),U_10072))
        | ~ hBOOL(hAPP(hAPP(U_10070,U_10071),U_10069)) )
      & ( ( hBOOL(hAPP(hAPP(U_10070,U_10069),U_10072))
          & hBOOL(hAPP(hAPP(U_10070,U_10071),U_10069)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_10068),U_10069),c_SetInterval_Oord_OatLeastAtMost(U_10068,U_10070,U_10071,U_10072))) ) ),
    inference(variable_rename,[status(thm)],[f_2690_1]) ).

fof(f_2690_3,plain,
    ( ! [U_10082,U_10080,U_10078,U_10076] :
        ( ! [U_10074] : hBOOL(hAPP(hAPP(c_member(U_10074),U_10076),c_SetInterval_Oord_OatLeastAtMost(U_10074,U_10078,U_10080,U_10082)))
        | ~ hBOOL(hAPP(hAPP(U_10078,U_10076),U_10082))
        | ~ hBOOL(hAPP(hAPP(U_10078,U_10080),U_10076)) )
    & ! [U_10081,U_10079,U_10077,U_10075] :
        ( ! [U_10073] : ~ hBOOL(hAPP(hAPP(c_member(U_10073),U_10075),c_SetInterval_Oord_OatLeastAtMost(U_10073,U_10077,U_10079,U_10081)))
        | ( hBOOL(hAPP(hAPP(U_10077,U_10075),U_10081))
          & hBOOL(hAPP(hAPP(U_10077,U_10079),U_10075)) ) ) ),
    inference(miniscope,[status(thm)],[f_2690_2]) ).

fof(f_2690_4,plain,
    ( ! [U_10075,U_10077,U_10079,U_10081] :
        ( hBOOL(hAPP(hAPP(U_10077,U_10075),U_10081))
        | ~ sP770(U_10075,U_10077,U_10079,U_10081) )
    & ! [U_10075,U_10077,U_10079,U_10081] :
        ( hBOOL(hAPP(hAPP(U_10077,U_10079),U_10075))
        | ~ sP770(U_10075,U_10077,U_10079,U_10081) )
    & ! [U_10078,U_10080,U_10074,U_10076,U_10082] :
        ( hBOOL(hAPP(hAPP(c_member(U_10074),U_10076),c_SetInterval_Oord_OatLeastAtMost(U_10074,U_10078,U_10080,U_10082)))
        | ~ hBOOL(hAPP(hAPP(U_10078,U_10076),U_10082))
        | ~ hBOOL(hAPP(hAPP(U_10078,U_10080),U_10076)) )
    & ! [U_10073,U_10075,U_10077,U_10079,U_10081] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_10073),U_10075),c_SetInterval_Oord_OatLeastAtMost(U_10073,U_10077,U_10079,U_10081)))
        | sP770(U_10075,U_10077,U_10079,U_10081) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP770])],[f_2690_3]) ).

cnf(f_2690_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_10073),U_10075),c_SetInterval_Oord_OatLeastAtMost(U_10073,U_10077,U_10079,U_10081)))
    | sP770(U_10075,U_10077,U_10079,U_10081) ),
    inference(clausify,[status(thm)],[f_2690_4]) ).

cnf(f_2690_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10074),U_10076),c_SetInterval_Oord_OatLeastAtMost(U_10074,U_10078,U_10080,U_10082)))
    | ~ hBOOL(hAPP(hAPP(U_10078,U_10076),U_10082))
    | ~ hBOOL(hAPP(hAPP(U_10078,U_10080),U_10076)) ),
    inference(clausify,[status(thm)],[f_2690_4]) ).

cnf(f_2690_7,plain,
    ( hBOOL(hAPP(hAPP(U_10077,U_10079),U_10075))
    | ~ sP770(U_10075,U_10077,U_10079,U_10081) ),
    inference(clausify,[status(thm)],[f_2690_4]) ).

cnf(f_2690_8,plain,
    ( hBOOL(hAPP(hAPP(U_10077,U_10075),U_10081))
    | ~ sP770(U_10075,U_10077,U_10079,U_10081) ),
    inference(clausify,[status(thm)],[f_2690_4]) ).

fof(f_2691_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_2691_2,plain,
    ! [U_10085,U_10084,U_10083] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_10083,U_10084) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10083),U_10085),c_Big__Operators_Olattice__class_OInf__fin(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(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)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10083,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(U_10083,U_10084) = U_10085
          | 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)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10083,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_10083),U_10085),U_10084))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10083),U_10084))
      | ~ class_Lattices_Olattice(U_10083) ),
    inference(variable_rename,[status(thm)],[f_2691_1]) ).

fof(f_2691_3,plain,
    ( ! [U_10083,U_10084,U_10085] :
        ( c_Big__Operators_Olattice__class_OInf__fin(U_10083,U_10084) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10083),U_10085),c_Big__Operators_Olattice__class_OInf__fin(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(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)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10083,tc_HOL_Obool))
        | ~ sP771(U_10083,U_10084,U_10085) )
    & ! [U_10083,U_10084,U_10085] :
        ( c_Big__Operators_Olattice__class_OInf__fin(U_10083,U_10084) = U_10085
        | 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)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10083,tc_HOL_Obool))
        | ~ sP771(U_10083,U_10084,U_10085) )
    & ! [U_10083,U_10084,U_10085] :
        ( sP771(U_10083,U_10084,U_10085)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10083),U_10085),U_10084))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10083),U_10084))
        | ~ class_Lattices_Olattice(U_10083) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP771])],[f_2691_2]) ).

cnf(f_2691_4,plain,
    ( sP771(U_10083,U_10084,U_10085)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10083),U_10085),U_10084))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10083),U_10084))
    | ~ class_Lattices_Olattice(U_10083) ),
    inference(clausify,[status(thm)],[f_2691_3]) ).

cnf(f_2691_5,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_10083,U_10084) = U_10085
    | 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)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10083,tc_HOL_Obool))
    | ~ sP771(U_10083,U_10084,U_10085) ),
    inference(clausify,[status(thm)],[f_2691_3]) ).

cnf(f_2691_6,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_10083,U_10084) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10083),U_10085),c_Big__Operators_Olattice__class_OInf__fin(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(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)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10083,tc_HOL_Obool))
    | ~ sP771(U_10083,U_10084,U_10085) ),
    inference(clausify,[status(thm)],[f_2691_3]) ).

fof(f_2692_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_2692_2,plain,
    ! [U_10088,U_10087,U_10086] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_10086,U_10087) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10086),U_10088),c_Big__Operators_Olattice__class_OSup__fin(U_10086,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_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)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10086,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(U_10086,U_10087) = U_10088
          | 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)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10086,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_10086),U_10088),U_10087))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10086),U_10087))
      | ~ class_Lattices_Olattice(U_10086) ),
    inference(variable_rename,[status(thm)],[f_2692_1]) ).

fof(f_2692_3,plain,
    ( ! [U_10087,U_10088,U_10086] :
        ( c_Big__Operators_Olattice__class_OSup__fin(U_10086,U_10087) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10086),U_10088),c_Big__Operators_Olattice__class_OSup__fin(U_10086,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_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)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10086,tc_HOL_Obool))
        | ~ sP772(U_10087,U_10088,U_10086) )
    & ! [U_10087,U_10088,U_10086] :
        ( c_Big__Operators_Olattice__class_OSup__fin(U_10086,U_10087) = U_10088
        | 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)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10086,tc_HOL_Obool))
        | ~ sP772(U_10087,U_10088,U_10086) )
    & ! [U_10087,U_10088,U_10086] :
        ( sP772(U_10087,U_10088,U_10086)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10086),U_10088),U_10087))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10086),U_10087))
        | ~ class_Lattices_Olattice(U_10086) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP772])],[f_2692_2]) ).

cnf(f_2692_4,plain,
    ( sP772(U_10087,U_10088,U_10086)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10086),U_10088),U_10087))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10086),U_10087))
    | ~ class_Lattices_Olattice(U_10086) ),
    inference(clausify,[status(thm)],[f_2692_3]) ).

cnf(f_2692_5,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10086,U_10087) = U_10088
    | 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)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10086,tc_HOL_Obool))
    | ~ sP772(U_10087,U_10088,U_10086) ),
    inference(clausify,[status(thm)],[f_2692_3]) ).

cnf(f_2692_6,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10086,U_10087) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10086),U_10088),c_Big__Operators_Olattice__class_OSup__fin(U_10086,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_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)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10086,tc_HOL_Obool))
    | ~ sP772(U_10087,U_10088,U_10086) ),
    inference(clausify,[status(thm)],[f_2692_3]) ).

fof(f_2693_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_2693_2,plain,
    ! [U_10091,U_10090,U_10089] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(U_10089,U_10090) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10089),U_10091),c_Big__Operators_Olinorder__class_OMax(U_10089,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10089,tc_HOL_Obool)),U_10090),hAPP(hAPP(c_Set_Oinsert(U_10089),U_10091),c_Orderings_Obot__class_Obot(tc_fun(U_10089,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10089,tc_HOL_Obool)),U_10090),hAPP(hAPP(c_Set_Oinsert(U_10089),U_10091),c_Orderings_Obot__class_Obot(tc_fun(U_10089,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10089,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(U_10089,U_10090) = U_10091
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10089,tc_HOL_Obool)),U_10090),hAPP(hAPP(c_Set_Oinsert(U_10089),U_10091),c_Orderings_Obot__class_Obot(tc_fun(U_10089,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10089,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_10089),U_10091),U_10090))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10089),U_10090))
      | ~ class_Orderings_Olinorder(U_10089) ),
    inference(variable_rename,[status(thm)],[f_2693_1]) ).

fof(f_2693_3,plain,
    ( ! [U_10090,U_10091,U_10089] :
        ( c_Big__Operators_Olinorder__class_OMax(U_10089,U_10090) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10089),U_10091),c_Big__Operators_Olinorder__class_OMax(U_10089,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10089,tc_HOL_Obool)),U_10090),hAPP(hAPP(c_Set_Oinsert(U_10089),U_10091),c_Orderings_Obot__class_Obot(tc_fun(U_10089,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10089,tc_HOL_Obool)),U_10090),hAPP(hAPP(c_Set_Oinsert(U_10089),U_10091),c_Orderings_Obot__class_Obot(tc_fun(U_10089,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10089,tc_HOL_Obool))
        | ~ sP773(U_10090,U_10091,U_10089) )
    & ! [U_10090,U_10091,U_10089] :
        ( c_Big__Operators_Olinorder__class_OMax(U_10089,U_10090) = U_10091
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10089,tc_HOL_Obool)),U_10090),hAPP(hAPP(c_Set_Oinsert(U_10089),U_10091),c_Orderings_Obot__class_Obot(tc_fun(U_10089,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10089,tc_HOL_Obool))
        | ~ sP773(U_10090,U_10091,U_10089) )
    & ! [U_10090,U_10091,U_10089] :
        ( sP773(U_10090,U_10091,U_10089)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10089),U_10091),U_10090))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10089),U_10090))
        | ~ class_Orderings_Olinorder(U_10089) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP773])],[f_2693_2]) ).

cnf(f_2693_4,plain,
    ( sP773(U_10090,U_10091,U_10089)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10089),U_10091),U_10090))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10089),U_10090))
    | ~ class_Orderings_Olinorder(U_10089) ),
    inference(clausify,[status(thm)],[f_2693_3]) ).

cnf(f_2693_5,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10089,U_10090) = U_10091
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10089,tc_HOL_Obool)),U_10090),hAPP(hAPP(c_Set_Oinsert(U_10089),U_10091),c_Orderings_Obot__class_Obot(tc_fun(U_10089,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10089,tc_HOL_Obool))
    | ~ sP773(U_10090,U_10091,U_10089) ),
    inference(clausify,[status(thm)],[f_2693_3]) ).

cnf(f_2693_6,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10089,U_10090) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10089),U_10091),c_Big__Operators_Olinorder__class_OMax(U_10089,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10089,tc_HOL_Obool)),U_10090),hAPP(hAPP(c_Set_Oinsert(U_10089),U_10091),c_Orderings_Obot__class_Obot(tc_fun(U_10089,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10089,tc_HOL_Obool)),U_10090),hAPP(hAPP(c_Set_Oinsert(U_10089),U_10091),c_Orderings_Obot__class_Obot(tc_fun(U_10089,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10089,tc_HOL_Obool))
    | ~ sP773(U_10090,U_10091,U_10089) ),
    inference(clausify,[status(thm)],[f_2693_3]) ).

fof(f_2694_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_2694_2,plain,
    ! [U_10093,U_10092] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10092),c_Big__Operators_Olattice__class_OInf__fin(U_10092,U_10093)),c_Big__Operators_Olattice__class_OSup__fin(U_10092,U_10093)))
      | U_10093 = c_Orderings_Obot__class_Obot(tc_fun(U_10092,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10092),U_10093))
      | ~ class_Lattices_Olattice(U_10092) ),
    inference(variable_rename,[status(thm)],[f_2694_1]) ).

fof(f_2694_3,plain,
    ! [U_10093,U_10092] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10092),c_Big__Operators_Olattice__class_OInf__fin(U_10092,U_10093)),c_Big__Operators_Olattice__class_OSup__fin(U_10092,U_10093)))
      | U_10093 = c_Orderings_Obot__class_Obot(tc_fun(U_10092,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10092),U_10093))
      | ~ class_Lattices_Olattice(U_10092) ),
    inference(definitional_conversion,[status(esa)],[f_2694_2]) ).

cnf(f_2694_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10092),c_Big__Operators_Olattice__class_OInf__fin(U_10092,U_10093)),c_Big__Operators_Olattice__class_OSup__fin(U_10092,U_10093)))
    | U_10093 = c_Orderings_Obot__class_Obot(tc_fun(U_10092,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10092),U_10093))
    | ~ class_Lattices_Olattice(U_10092) ),
    inference(clausify,[status(thm)],[f_2694_3]) ).

fof(f_2695_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_2695_2,plain,
    ! [U_10095,U_10094] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10094,hAPP(hAPP(c_Set_Oinsert(U_10094),U_10095),c_Orderings_Obot__class_Obot(tc_fun(U_10094,tc_HOL_Obool)))) = U_10095
      | ~ class_Orderings_Olinorder(U_10094) ),
    inference(variable_rename,[status(thm)],[f_2695_1]) ).

fof(f_2695_3,plain,
    ! [U_10095,U_10094] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10094,hAPP(hAPP(c_Set_Oinsert(U_10094),U_10095),c_Orderings_Obot__class_Obot(tc_fun(U_10094,tc_HOL_Obool)))) = U_10095
      | ~ class_Orderings_Olinorder(U_10094) ),
    inference(definitional_conversion,[status(esa)],[f_2695_2]) ).

cnf(f_2695_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10094,hAPP(hAPP(c_Set_Oinsert(U_10094),U_10095),c_Orderings_Obot__class_Obot(tc_fun(U_10094,tc_HOL_Obool)))) = U_10095
    | ~ class_Orderings_Olinorder(U_10094) ),
    inference(clausify,[status(thm)],[f_2695_3]) ).

fof(f_2696_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_2696_2,plain,
    ! [U_10097,U_10096] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_10096,hAPP(hAPP(c_Set_Oinsert(U_10096),U_10097),c_Orderings_Obot__class_Obot(tc_fun(U_10096,tc_HOL_Obool)))) = U_10097
      | ~ class_Lattices_Olattice(U_10096) ),
    inference(variable_rename,[status(thm)],[f_2696_1]) ).

fof(f_2696_3,plain,
    ! [U_10096,U_10097] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_10096,hAPP(hAPP(c_Set_Oinsert(U_10096),U_10097),c_Orderings_Obot__class_Obot(tc_fun(U_10096,tc_HOL_Obool)))) = U_10097
      | ~ class_Lattices_Olattice(U_10096) ),
    inference(definitional_conversion,[status(esa)],[f_2696_2]) ).

cnf(f_2696_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_10096,hAPP(hAPP(c_Set_Oinsert(U_10096),U_10097),c_Orderings_Obot__class_Obot(tc_fun(U_10096,tc_HOL_Obool)))) = U_10097
    | ~ class_Lattices_Olattice(U_10096) ),
    inference(clausify,[status(thm)],[f_2696_3]) ).

fof(f_2697_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_2697_2,plain,
    ! [U_10099,U_10098] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10098,hAPP(hAPP(c_Set_Oinsert(U_10098),U_10099),c_Orderings_Obot__class_Obot(tc_fun(U_10098,tc_HOL_Obool)))) = U_10099
      | ~ class_Lattices_Olattice(U_10098) ),
    inference(variable_rename,[status(thm)],[f_2697_1]) ).

fof(f_2697_3,plain,
    ! [U_10098,U_10099] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10098,hAPP(hAPP(c_Set_Oinsert(U_10098),U_10099),c_Orderings_Obot__class_Obot(tc_fun(U_10098,tc_HOL_Obool)))) = U_10099
      | ~ class_Lattices_Olattice(U_10098) ),
    inference(definitional_conversion,[status(esa)],[f_2697_2]) ).

cnf(f_2697_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10098,hAPP(hAPP(c_Set_Oinsert(U_10098),U_10099),c_Orderings_Obot__class_Obot(tc_fun(U_10098,tc_HOL_Obool)))) = U_10099
    | ~ class_Lattices_Olattice(U_10098) ),
    inference(clausify,[status(thm)],[f_2697_3]) ).

fof(f_2698_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_2698_2,plain,
    ! [U_10102,U_10101,U_10100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10100),U_10102),c_Big__Operators_Olinorder__class_OMax(U_10100,U_10101)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10100),U_10102),U_10101))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10100),U_10101))
      | ~ class_Orderings_Olinorder(U_10100) ),
    inference(variable_rename,[status(thm)],[f_2698_1]) ).

fof(f_2698_3,plain,
    ! [U_10100,U_10101,U_10102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10100),U_10102),c_Big__Operators_Olinorder__class_OMax(U_10100,U_10101)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10100),U_10102),U_10101))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10100),U_10101))
      | ~ class_Orderings_Olinorder(U_10100) ),
    inference(definitional_conversion,[status(esa)],[f_2698_2]) ).

cnf(f_2698_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10100),U_10102),c_Big__Operators_Olinorder__class_OMax(U_10100,U_10101)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10100),U_10102),U_10101))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10100),U_10101))
    | ~ class_Orderings_Olinorder(U_10100) ),
    inference(clausify,[status(thm)],[f_2698_3]) ).

fof(f_2699_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_2699_2,plain,
    ! [U_10104,U_10103] :
      ( hBOOL(hAPP(hAPP(c_member(U_10103),c_Big__Operators_Olinorder__class_OMax(U_10103,U_10104)),U_10104))
      | U_10104 = c_Orderings_Obot__class_Obot(tc_fun(U_10103,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10103),U_10104))
      | ~ class_Orderings_Olinorder(U_10103) ),
    inference(variable_rename,[status(thm)],[f_2699_1]) ).

fof(f_2699_3,plain,
    ! [U_10104,U_10103] :
      ( hBOOL(hAPP(hAPP(c_member(U_10103),c_Big__Operators_Olinorder__class_OMax(U_10103,U_10104)),U_10104))
      | U_10104 = c_Orderings_Obot__class_Obot(tc_fun(U_10103,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10103),U_10104))
      | ~ class_Orderings_Olinorder(U_10103) ),
    inference(definitional_conversion,[status(esa)],[f_2699_2]) ).

cnf(f_2699_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10103),c_Big__Operators_Olinorder__class_OMax(U_10103,U_10104)),U_10104))
    | U_10104 = c_Orderings_Obot__class_Obot(tc_fun(U_10103,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10103),U_10104))
    | ~ class_Orderings_Olinorder(U_10103) ),
    inference(clausify,[status(thm)],[f_2699_3]) ).

fof(f_2700_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_2700_2,plain,
    ! [U_10107,U_10106,U_10105] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10105),U_10107),c_Big__Operators_Olattice__class_OInf__fin(U_10105,U_10106)) = U_10107
      | ~ hBOOL(hAPP(hAPP(c_member(U_10105),U_10107),U_10106))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10105),U_10106))
      | ~ class_Lattices_Olattice(U_10105) ),
    inference(variable_rename,[status(thm)],[f_2700_1]) ).

fof(f_2700_3,plain,
    ! [U_10106,U_10105,U_10107] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10105),U_10107),c_Big__Operators_Olattice__class_OInf__fin(U_10105,U_10106)) = U_10107
      | ~ hBOOL(hAPP(hAPP(c_member(U_10105),U_10107),U_10106))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10105),U_10106))
      | ~ class_Lattices_Olattice(U_10105) ),
    inference(definitional_conversion,[status(esa)],[f_2700_2]) ).

cnf(f_2700_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10105),U_10107),c_Big__Operators_Olattice__class_OInf__fin(U_10105,U_10106)) = U_10107
    | ~ hBOOL(hAPP(hAPP(c_member(U_10105),U_10107),U_10106))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10105),U_10106))
    | ~ class_Lattices_Olattice(U_10105) ),
    inference(clausify,[status(thm)],[f_2700_3]) ).

fof(f_2701_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_2701_2,plain,
    ! [U_10110,U_10109,U_10108] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10108),U_10110),c_Big__Operators_Olattice__class_OSup__fin(U_10108,U_10109)) = c_Big__Operators_Olattice__class_OSup__fin(U_10108,U_10109)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10108),U_10110),U_10109))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10108),U_10109))
      | ~ class_Lattices_Olattice(U_10108) ),
    inference(variable_rename,[status(thm)],[f_2701_1]) ).

fof(f_2701_3,plain,
    ! [U_10109,U_10108,U_10110] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10108),U_10110),c_Big__Operators_Olattice__class_OSup__fin(U_10108,U_10109)) = c_Big__Operators_Olattice__class_OSup__fin(U_10108,U_10109)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10108),U_10110),U_10109))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10108),U_10109))
      | ~ class_Lattices_Olattice(U_10108) ),
    inference(definitional_conversion,[status(esa)],[f_2701_2]) ).

cnf(f_2701_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10108),U_10110),c_Big__Operators_Olattice__class_OSup__fin(U_10108,U_10109)) = c_Big__Operators_Olattice__class_OSup__fin(U_10108,U_10109)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10108),U_10110),U_10109))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10108),U_10109))
    | ~ class_Lattices_Olattice(U_10108) ),
    inference(clausify,[status(thm)],[f_2701_3]) ).

fof(f_2702_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_2702_2,plain,
    ! [U_10113,U_10112,U_10111] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10111),U_10113),c_Big__Operators_Olattice__class_OInf__fin(U_10111,U_10112)) = c_Big__Operators_Olattice__class_OInf__fin(U_10111,U_10112)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10111),U_10113),U_10112))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10111),U_10112))
      | ~ class_Lattices_Olattice(U_10111) ),
    inference(variable_rename,[status(thm)],[f_2702_1]) ).

fof(f_2702_3,plain,
    ! [U_10112,U_10111,U_10113] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10111),U_10113),c_Big__Operators_Olattice__class_OInf__fin(U_10111,U_10112)) = c_Big__Operators_Olattice__class_OInf__fin(U_10111,U_10112)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10111),U_10113),U_10112))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10111),U_10112))
      | ~ class_Lattices_Olattice(U_10111) ),
    inference(definitional_conversion,[status(esa)],[f_2702_2]) ).

cnf(f_2702_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10111),U_10113),c_Big__Operators_Olattice__class_OInf__fin(U_10111,U_10112)) = c_Big__Operators_Olattice__class_OInf__fin(U_10111,U_10112)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10111),U_10113),U_10112))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10111),U_10112))
    | ~ class_Lattices_Olattice(U_10111) ),
    inference(clausify,[status(thm)],[f_2702_3]) ).

fof(f_2703_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_2703_2,plain,
    ! [U_10116,U_10115,U_10114] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10114),U_10116),c_Big__Operators_Olattice__class_OSup__fin(U_10114,U_10115)) = U_10116
      | ~ hBOOL(hAPP(hAPP(c_member(U_10114),U_10116),U_10115))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10114),U_10115))
      | ~ class_Lattices_Olattice(U_10114) ),
    inference(variable_rename,[status(thm)],[f_2703_1]) ).

fof(f_2703_3,plain,
    ! [U_10115,U_10114,U_10116] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10114),U_10116),c_Big__Operators_Olattice__class_OSup__fin(U_10114,U_10115)) = U_10116
      | ~ hBOOL(hAPP(hAPP(c_member(U_10114),U_10116),U_10115))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10114),U_10115))
      | ~ class_Lattices_Olattice(U_10114) ),
    inference(definitional_conversion,[status(esa)],[f_2703_2]) ).

cnf(f_2703_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10114),U_10116),c_Big__Operators_Olattice__class_OSup__fin(U_10114,U_10115)) = U_10116
    | ~ hBOOL(hAPP(hAPP(c_member(U_10114),U_10116),U_10115))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10114),U_10115))
    | ~ class_Lattices_Olattice(U_10114) ),
    inference(clausify,[status(thm)],[f_2703_3]) ).

fof(f_2704_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_2704_2,plain,
    ! [U_10119,U_10118,U_10117] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10117),U_10119),c_Big__Operators_Olinorder__class_OMax(U_10117,U_10118)) = c_Big__Operators_Olinorder__class_OMax(U_10117,U_10118)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10117),U_10119),U_10118))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10117),U_10118))
      | ~ class_Orderings_Olinorder(U_10117) ),
    inference(variable_rename,[status(thm)],[f_2704_1]) ).

fof(f_2704_3,plain,
    ! [U_10118,U_10117,U_10119] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10117),U_10119),c_Big__Operators_Olinorder__class_OMax(U_10117,U_10118)) = c_Big__Operators_Olinorder__class_OMax(U_10117,U_10118)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10117),U_10119),U_10118))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10117),U_10118))
      | ~ class_Orderings_Olinorder(U_10117) ),
    inference(definitional_conversion,[status(esa)],[f_2704_2]) ).

cnf(f_2704_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10117),U_10119),c_Big__Operators_Olinorder__class_OMax(U_10117,U_10118)) = c_Big__Operators_Olinorder__class_OMax(U_10117,U_10118)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10117),U_10119),U_10118))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10117),U_10118))
    | ~ class_Orderings_Olinorder(U_10117) ),
    inference(clausify,[status(thm)],[f_2704_3]) ).

fof(f_2705_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_2705_2,plain,
    ! [U_10121,U_10120] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10120,U_10121) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10120),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | U_10120 != U_10121 ),
    inference(variable_rename,[status(thm)],[f_2705_1]) ).

fof(f_2705_3,plain,
    ! [U_10120,U_10121] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10120,U_10121) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10120),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | U_10120 != U_10121 ),
    inference(definitional_conversion,[status(esa)],[f_2705_2]) ).

cnf(f_2705_4,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10120,U_10121) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10120),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | U_10120 != U_10121 ),
    inference(clausify,[status(thm)],[f_2705_3]) ).

fof(f_2706_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_2706_2,plain,
    ! [U_10122] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10122,U_10122) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10122),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2706_1]) ).

fof(f_2706_3,plain,
    ! [U_10122] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10122,U_10122) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10122),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2706_2]) ).

cnf(f_2706_4,plain,
    c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10122,U_10122) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10122),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2706_3]) ).

fof(f_2707_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_2707_2,plain,
    ! [U_10125,U_10124,U_10123] :
      ( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10123,U_10124) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10125),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
        | U_10124 != U_10125
        | U_10123 != U_10124 )
      & ( ( U_10124 = U_10125
          & U_10123 = U_10124 )
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10123,U_10124) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10125),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_2707_1]) ).

fof(f_2707_3,plain,
    ( ! [U_10131,U_10129,U_10127] :
        ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10127,U_10129) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10131),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
        | U_10129 != U_10131
        | U_10127 != U_10129 )
    & ! [U_10130,U_10128,U_10126] :
        ( ( U_10128 = U_10130
          & U_10126 = U_10128 )
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10126,U_10128) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10130),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_2707_2]) ).

fof(f_2707_4,plain,
    ( ! [U_10130,U_10126,U_10128] :
        ( U_10128 = U_10130
        | ~ sP774(U_10130,U_10126,U_10128) )
    & ! [U_10130,U_10126,U_10128] :
        ( U_10126 = U_10128
        | ~ sP774(U_10130,U_10126,U_10128) )
    & ! [U_10127,U_10129,U_10131] :
        ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10127,U_10129) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10131),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
        | U_10129 != U_10131
        | U_10127 != U_10129 )
    & ! [U_10130,U_10126,U_10128] :
        ( sP774(U_10130,U_10126,U_10128)
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10126,U_10128) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10130),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP774])],[f_2707_3]) ).

cnf(f_2707_5,plain,
    ( sP774(U_10130,U_10126,U_10128)
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10126,U_10128) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10130),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_2707_4]) ).

cnf(f_2707_6,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10127,U_10129) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_10131),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | U_10129 != U_10131
    | U_10127 != U_10129 ),
    inference(clausify,[status(thm)],[f_2707_4]) ).

cnf(f_2707_7,plain,
    ( U_10126 = U_10128
    | ~ sP774(U_10130,U_10126,U_10128) ),
    inference(clausify,[status(thm)],[f_2707_4]) ).

cnf(f_2707_8,plain,
    ( U_10128 = U_10130
    | ~ sP774(U_10130,U_10126,U_10128) ),
    inference(clausify,[status(thm)],[f_2707_4]) ).

fof(f_2708_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_2708_2,plain,
    ! [U_10133,U_10132] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10133,U_10132) = 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_10133),U_10132))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10132),U_10133)) ),
    inference(variable_rename,[status(thm)],[f_2708_1]) ).

fof(f_2708_3,plain,
    ! [U_10133,U_10132] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10133,U_10132) = 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_10133),U_10132))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10132),U_10133)) ),
    inference(definitional_conversion,[status(esa)],[f_2708_2]) ).

cnf(f_2708_4,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10133,U_10132) = 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_10133),U_10132))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10132),U_10133)) ),
    inference(clausify,[status(thm)],[f_2708_3]) ).

fof(f_2709_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_2709_2,plain,
    ! [U_10135,U_10134] :
      ( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10134,U_10135) = 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_10134),U_10135)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10134),U_10135))
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10134,U_10135) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2709_1]) ).

fof(f_2709_3,plain,
    ( ! [U_10139,U_10137] :
        ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10137,U_10139) = 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_10137),U_10139)) )
    & ! [U_10138,U_10136] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10136),U_10138))
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10136,U_10138) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2709_2]) ).

fof(f_2709_4,plain,
    ( ! [U_10139,U_10137] :
        ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10137,U_10139) = 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_10137),U_10139)) )
    & ! [U_10136,U_10138] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10136),U_10138))
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10136,U_10138) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2709_3]) ).

cnf(f_2709_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10136),U_10138))
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10136,U_10138) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2709_4]) ).

cnf(f_2709_6,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10137,U_10139) = 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_10137),U_10139)) ),
    inference(clausify,[status(thm)],[f_2709_4]) ).

fof(f_2710_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_2710_2,plain,
    ! [U_10141,U_10140] :
      ( ( 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_10140,U_10141)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10140),U_10141)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10140),U_10141))
        | 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_10140,U_10141) ) ),
    inference(variable_rename,[status(thm)],[f_2710_1]) ).

fof(f_2710_3,plain,
    ( ! [U_10145,U_10143] :
        ( 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_10143,U_10145)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10143),U_10145)) )
    & ! [U_10144,U_10142] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10142),U_10144))
        | 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_10142,U_10144) ) ),
    inference(miniscope,[status(thm)],[f_2710_2]) ).

fof(f_2710_4,plain,
    ( ! [U_10145,U_10143] :
        ( 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_10143,U_10145)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10143),U_10145)) )
    & ! [U_10142,U_10144] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10142),U_10144))
        | 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_10142,U_10144) ) ),
    inference(definitional_conversion,[status(esa)],[f_2710_3]) ).

cnf(f_2710_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10142),U_10144))
    | 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_10142,U_10144) ),
    inference(clausify,[status(thm)],[f_2710_4]) ).

cnf(f_2710_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_10143,U_10145)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10143),U_10145)) ),
    inference(clausify,[status(thm)],[f_2710_4]) ).

fof(f_2711_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_2711_2,plain,
    ! [U_10148,U_10147,U_10146] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10146),c_Big__Operators_Olinorder__class_OMax(U_10146,U_10147)),c_Big__Operators_Olinorder__class_OMax(U_10146,U_10148)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10146),U_10148))
      | U_10147 = c_Orderings_Obot__class_Obot(tc_fun(U_10146,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10146,tc_HOL_Obool)),U_10147),U_10148))
      | ~ class_Orderings_Olinorder(U_10146) ),
    inference(variable_rename,[status(thm)],[f_2711_1]) ).

fof(f_2711_3,plain,
    ! [U_10146,U_10147,U_10148] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10146),c_Big__Operators_Olinorder__class_OMax(U_10146,U_10147)),c_Big__Operators_Olinorder__class_OMax(U_10146,U_10148)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10146),U_10148))
      | U_10147 = c_Orderings_Obot__class_Obot(tc_fun(U_10146,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10146,tc_HOL_Obool)),U_10147),U_10148))
      | ~ class_Orderings_Olinorder(U_10146) ),
    inference(definitional_conversion,[status(esa)],[f_2711_2]) ).

cnf(f_2711_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10146),c_Big__Operators_Olinorder__class_OMax(U_10146,U_10147)),c_Big__Operators_Olinorder__class_OMax(U_10146,U_10148)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10146),U_10148))
    | U_10147 = c_Orderings_Obot__class_Obot(tc_fun(U_10146,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10146,tc_HOL_Obool)),U_10147),U_10148))
    | ~ class_Orderings_Olinorder(U_10146) ),
    inference(clausify,[status(thm)],[f_2711_3]) ).

fof(f_2712_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_2712_2,plain,
    ! [U_10151,U_10150,U_10149] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10149,hAPP(hAPP(c_Set_Oinsert(U_10149),U_10151),U_10150)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10149),U_10151),c_Big__Operators_Olattice__class_OSup__fin(U_10149,U_10150))
      | U_10150 = c_Orderings_Obot__class_Obot(tc_fun(U_10149,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10149),U_10150))
      | ~ class_Lattices_Olattice(U_10149) ),
    inference(variable_rename,[status(thm)],[f_2712_1]) ).

fof(f_2712_3,plain,
    ! [U_10150,U_10151,U_10149] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10149,hAPP(hAPP(c_Set_Oinsert(U_10149),U_10151),U_10150)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10149),U_10151),c_Big__Operators_Olattice__class_OSup__fin(U_10149,U_10150))
      | U_10150 = c_Orderings_Obot__class_Obot(tc_fun(U_10149,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10149),U_10150))
      | ~ class_Lattices_Olattice(U_10149) ),
    inference(definitional_conversion,[status(esa)],[f_2712_2]) ).

cnf(f_2712_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10149,hAPP(hAPP(c_Set_Oinsert(U_10149),U_10151),U_10150)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10149),U_10151),c_Big__Operators_Olattice__class_OSup__fin(U_10149,U_10150))
    | U_10150 = c_Orderings_Obot__class_Obot(tc_fun(U_10149,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10149),U_10150))
    | ~ class_Lattices_Olattice(U_10149) ),
    inference(clausify,[status(thm)],[f_2712_3]) ).

fof(f_2713_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_2713_2,plain,
    ! [U_10154,U_10153,U_10152] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_10152,hAPP(hAPP(c_Set_Oinsert(U_10152),U_10154),U_10153)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10152),U_10154),c_Big__Operators_Olattice__class_OInf__fin(U_10152,U_10153))
      | U_10153 = c_Orderings_Obot__class_Obot(tc_fun(U_10152,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10152),U_10153))
      | ~ class_Lattices_Olattice(U_10152) ),
    inference(variable_rename,[status(thm)],[f_2713_1]) ).

fof(f_2713_3,plain,
    ! [U_10152,U_10153,U_10154] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_10152,hAPP(hAPP(c_Set_Oinsert(U_10152),U_10154),U_10153)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10152),U_10154),c_Big__Operators_Olattice__class_OInf__fin(U_10152,U_10153))
      | U_10153 = c_Orderings_Obot__class_Obot(tc_fun(U_10152,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10152),U_10153))
      | ~ class_Lattices_Olattice(U_10152) ),
    inference(definitional_conversion,[status(esa)],[f_2713_2]) ).

cnf(f_2713_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_10152,hAPP(hAPP(c_Set_Oinsert(U_10152),U_10154),U_10153)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10152),U_10154),c_Big__Operators_Olattice__class_OInf__fin(U_10152,U_10153))
    | U_10153 = c_Orderings_Obot__class_Obot(tc_fun(U_10152,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10152),U_10153))
    | ~ class_Lattices_Olattice(U_10152) ),
    inference(clausify,[status(thm)],[f_2713_3]) ).

fof(f_2714_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_2714_2,plain,
    ! [U_10157,U_10156,U_10155] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10155,hAPP(hAPP(c_Set_Oinsert(U_10155),U_10157),U_10156)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10155),U_10157),c_Big__Operators_Olinorder__class_OMax(U_10155,U_10156))
      | U_10156 = c_Orderings_Obot__class_Obot(tc_fun(U_10155,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10155),U_10156))
      | ~ class_Orderings_Olinorder(U_10155) ),
    inference(variable_rename,[status(thm)],[f_2714_1]) ).

fof(f_2714_3,plain,
    ! [U_10155,U_10156,U_10157] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10155,hAPP(hAPP(c_Set_Oinsert(U_10155),U_10157),U_10156)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10155),U_10157),c_Big__Operators_Olinorder__class_OMax(U_10155,U_10156))
      | U_10156 = c_Orderings_Obot__class_Obot(tc_fun(U_10155,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10155),U_10156))
      | ~ class_Orderings_Olinorder(U_10155) ),
    inference(definitional_conversion,[status(esa)],[f_2714_2]) ).

cnf(f_2714_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10155,hAPP(hAPP(c_Set_Oinsert(U_10155),U_10157),U_10156)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10155),U_10157),c_Big__Operators_Olinorder__class_OMax(U_10155,U_10156))
    | U_10156 = c_Orderings_Obot__class_Obot(tc_fun(U_10155,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10155),U_10156))
    | ~ class_Orderings_Olinorder(U_10155) ),
    inference(clausify,[status(thm)],[f_2714_3]) ).

fof(f_2715_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_2715_2,plain,
    ! [U_10160,U_10159,U_10158] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10158),c_Big__Operators_Olattice__class_OSup__fin(U_10158,U_10160)),c_Big__Operators_Olattice__class_OSup__fin(U_10158,U_10159)) = c_Big__Operators_Olattice__class_OSup__fin(U_10158,U_10159)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10158,tc_HOL_Obool)),U_10160),U_10159))
      | U_10160 = c_Orderings_Obot__class_Obot(tc_fun(U_10158,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10158),U_10159))
      | ~ class_Lattices_Olattice(U_10158) ),
    inference(variable_rename,[status(thm)],[f_2715_1]) ).

fof(f_2715_3,plain,
    ! [U_10158,U_10159,U_10160] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10158),c_Big__Operators_Olattice__class_OSup__fin(U_10158,U_10160)),c_Big__Operators_Olattice__class_OSup__fin(U_10158,U_10159)) = c_Big__Operators_Olattice__class_OSup__fin(U_10158,U_10159)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10158,tc_HOL_Obool)),U_10160),U_10159))
      | U_10160 = c_Orderings_Obot__class_Obot(tc_fun(U_10158,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10158),U_10159))
      | ~ class_Lattices_Olattice(U_10158) ),
    inference(definitional_conversion,[status(esa)],[f_2715_2]) ).

cnf(f_2715_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10158),c_Big__Operators_Olattice__class_OSup__fin(U_10158,U_10160)),c_Big__Operators_Olattice__class_OSup__fin(U_10158,U_10159)) = c_Big__Operators_Olattice__class_OSup__fin(U_10158,U_10159)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10158,tc_HOL_Obool)),U_10160),U_10159))
    | U_10160 = c_Orderings_Obot__class_Obot(tc_fun(U_10158,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10158),U_10159))
    | ~ class_Lattices_Olattice(U_10158) ),
    inference(clausify,[status(thm)],[f_2715_3]) ).

fof(f_2716_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_2716_2,plain,
    ! [U_10163,U_10162,U_10161] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10161),c_Big__Operators_Olattice__class_OInf__fin(U_10161,U_10163)),c_Big__Operators_Olattice__class_OInf__fin(U_10161,U_10162)) = c_Big__Operators_Olattice__class_OInf__fin(U_10161,U_10162)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10161,tc_HOL_Obool)),U_10163),U_10162))
      | U_10163 = c_Orderings_Obot__class_Obot(tc_fun(U_10161,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10161),U_10162))
      | ~ class_Lattices_Olattice(U_10161) ),
    inference(variable_rename,[status(thm)],[f_2716_1]) ).

fof(f_2716_3,plain,
    ! [U_10162,U_10163,U_10161] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10161),c_Big__Operators_Olattice__class_OInf__fin(U_10161,U_10163)),c_Big__Operators_Olattice__class_OInf__fin(U_10161,U_10162)) = c_Big__Operators_Olattice__class_OInf__fin(U_10161,U_10162)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10161,tc_HOL_Obool)),U_10163),U_10162))
      | U_10163 = c_Orderings_Obot__class_Obot(tc_fun(U_10161,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10161),U_10162))
      | ~ class_Lattices_Olattice(U_10161) ),
    inference(definitional_conversion,[status(esa)],[f_2716_2]) ).

cnf(f_2716_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10161),c_Big__Operators_Olattice__class_OInf__fin(U_10161,U_10163)),c_Big__Operators_Olattice__class_OInf__fin(U_10161,U_10162)) = c_Big__Operators_Olattice__class_OInf__fin(U_10161,U_10162)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10161,tc_HOL_Obool)),U_10163),U_10162))
    | U_10163 = c_Orderings_Obot__class_Obot(tc_fun(U_10161,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10161),U_10162))
    | ~ class_Lattices_Olattice(U_10161) ),
    inference(clausify,[status(thm)],[f_2716_3]) ).

fof(f_2717_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_2717_2,plain,
    ! [U_10166,U_10165,U_10164] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10164,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10164,tc_HOL_Obool)),U_10165),U_10166)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10164),c_Big__Operators_Olattice__class_OSup__fin(U_10164,U_10165)),c_Big__Operators_Olattice__class_OSup__fin(U_10164,U_10166))
      | U_10166 = c_Orderings_Obot__class_Obot(tc_fun(U_10164,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10164),U_10166))
      | U_10165 = c_Orderings_Obot__class_Obot(tc_fun(U_10164,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10164),U_10165))
      | ~ class_Lattices_Olattice(U_10164) ),
    inference(variable_rename,[status(thm)],[f_2717_1]) ).

fof(f_2717_3,plain,
    ! [U_10164,U_10165,U_10166] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10164,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10164,tc_HOL_Obool)),U_10165),U_10166)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10164),c_Big__Operators_Olattice__class_OSup__fin(U_10164,U_10165)),c_Big__Operators_Olattice__class_OSup__fin(U_10164,U_10166))
      | U_10166 = c_Orderings_Obot__class_Obot(tc_fun(U_10164,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10164),U_10166))
      | U_10165 = c_Orderings_Obot__class_Obot(tc_fun(U_10164,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10164),U_10165))
      | ~ class_Lattices_Olattice(U_10164) ),
    inference(definitional_conversion,[status(esa)],[f_2717_2]) ).

cnf(f_2717_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10164,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10164,tc_HOL_Obool)),U_10165),U_10166)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10164),c_Big__Operators_Olattice__class_OSup__fin(U_10164,U_10165)),c_Big__Operators_Olattice__class_OSup__fin(U_10164,U_10166))
    | U_10166 = c_Orderings_Obot__class_Obot(tc_fun(U_10164,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10164),U_10166))
    | U_10165 = c_Orderings_Obot__class_Obot(tc_fun(U_10164,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10164),U_10165))
    | ~ class_Lattices_Olattice(U_10164) ),
    inference(clausify,[status(thm)],[f_2717_3]) ).

fof(f_2718_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_2718_2,plain,
    ! [U_10169,U_10168,U_10167] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10167),c_Big__Operators_Olinorder__class_OMax(U_10167,U_10169)),c_Big__Operators_Olinorder__class_OMax(U_10167,U_10168)) = c_Big__Operators_Olinorder__class_OMax(U_10167,U_10168)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10167,tc_HOL_Obool)),U_10169),U_10168))
      | U_10169 = c_Orderings_Obot__class_Obot(tc_fun(U_10167,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10167),U_10168))
      | ~ class_Orderings_Olinorder(U_10167) ),
    inference(variable_rename,[status(thm)],[f_2718_1]) ).

fof(f_2718_3,plain,
    ! [U_10169,U_10168,U_10167] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10167),c_Big__Operators_Olinorder__class_OMax(U_10167,U_10169)),c_Big__Operators_Olinorder__class_OMax(U_10167,U_10168)) = c_Big__Operators_Olinorder__class_OMax(U_10167,U_10168)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10167,tc_HOL_Obool)),U_10169),U_10168))
      | U_10169 = c_Orderings_Obot__class_Obot(tc_fun(U_10167,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10167),U_10168))
      | ~ class_Orderings_Olinorder(U_10167) ),
    inference(definitional_conversion,[status(esa)],[f_2718_2]) ).

cnf(f_2718_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10167),c_Big__Operators_Olinorder__class_OMax(U_10167,U_10169)),c_Big__Operators_Olinorder__class_OMax(U_10167,U_10168)) = c_Big__Operators_Olinorder__class_OMax(U_10167,U_10168)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10167,tc_HOL_Obool)),U_10169),U_10168))
    | U_10169 = c_Orderings_Obot__class_Obot(tc_fun(U_10167,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10167),U_10168))
    | ~ class_Orderings_Olinorder(U_10167) ),
    inference(clausify,[status(thm)],[f_2718_3]) ).

fof(f_2719_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_2719_2,plain,
    ! [U_10172,U_10171,U_10170] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_10170,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10170,tc_HOL_Obool)),U_10171),U_10172)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10170),c_Big__Operators_Olattice__class_OInf__fin(U_10170,U_10171)),c_Big__Operators_Olattice__class_OInf__fin(U_10170,U_10172))
      | U_10172 = c_Orderings_Obot__class_Obot(tc_fun(U_10170,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10170),U_10172))
      | U_10171 = c_Orderings_Obot__class_Obot(tc_fun(U_10170,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10170),U_10171))
      | ~ class_Lattices_Olattice(U_10170) ),
    inference(variable_rename,[status(thm)],[f_2719_1]) ).

fof(f_2719_3,plain,
    ! [U_10170,U_10171,U_10172] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_10170,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10170,tc_HOL_Obool)),U_10171),U_10172)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10170),c_Big__Operators_Olattice__class_OInf__fin(U_10170,U_10171)),c_Big__Operators_Olattice__class_OInf__fin(U_10170,U_10172))
      | U_10172 = c_Orderings_Obot__class_Obot(tc_fun(U_10170,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10170),U_10172))
      | U_10171 = c_Orderings_Obot__class_Obot(tc_fun(U_10170,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10170),U_10171))
      | ~ class_Lattices_Olattice(U_10170) ),
    inference(definitional_conversion,[status(esa)],[f_2719_2]) ).

cnf(f_2719_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_10170,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10170,tc_HOL_Obool)),U_10171),U_10172)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10170),c_Big__Operators_Olattice__class_OInf__fin(U_10170,U_10171)),c_Big__Operators_Olattice__class_OInf__fin(U_10170,U_10172))
    | U_10172 = c_Orderings_Obot__class_Obot(tc_fun(U_10170,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10170),U_10172))
    | U_10171 = c_Orderings_Obot__class_Obot(tc_fun(U_10170,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10170),U_10171))
    | ~ class_Lattices_Olattice(U_10170) ),
    inference(clausify,[status(thm)],[f_2719_3]) ).

fof(f_2720_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_2720_2,plain,
    ! [U_10175,U_10174,U_10173] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10173,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10173,tc_HOL_Obool)),U_10174),U_10175)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10173),c_Big__Operators_Olinorder__class_OMax(U_10173,U_10174)),c_Big__Operators_Olinorder__class_OMax(U_10173,U_10175))
      | U_10175 = c_Orderings_Obot__class_Obot(tc_fun(U_10173,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10173),U_10175))
      | U_10174 = c_Orderings_Obot__class_Obot(tc_fun(U_10173,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10173),U_10174))
      | ~ class_Orderings_Olinorder(U_10173) ),
    inference(variable_rename,[status(thm)],[f_2720_1]) ).

fof(f_2720_3,plain,
    ! [U_10174,U_10175,U_10173] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10173,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10173,tc_HOL_Obool)),U_10174),U_10175)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10173),c_Big__Operators_Olinorder__class_OMax(U_10173,U_10174)),c_Big__Operators_Olinorder__class_OMax(U_10173,U_10175))
      | U_10175 = c_Orderings_Obot__class_Obot(tc_fun(U_10173,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10173),U_10175))
      | U_10174 = c_Orderings_Obot__class_Obot(tc_fun(U_10173,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10173),U_10174))
      | ~ class_Orderings_Olinorder(U_10173) ),
    inference(definitional_conversion,[status(esa)],[f_2720_2]) ).

cnf(f_2720_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10173,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10173,tc_HOL_Obool)),U_10174),U_10175)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10173),c_Big__Operators_Olinorder__class_OMax(U_10173,U_10174)),c_Big__Operators_Olinorder__class_OMax(U_10173,U_10175))
    | U_10175 = c_Orderings_Obot__class_Obot(tc_fun(U_10173,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10173),U_10175))
    | U_10174 = c_Orderings_Obot__class_Obot(tc_fun(U_10173,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10173),U_10174))
    | ~ class_Orderings_Olinorder(U_10173) ),
    inference(clausify,[status(thm)],[f_2720_3]) ).

fof(f_2721_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_2721_2,plain,
    ! [U_10179,U_10178,U_10177,U_10176] :
      ( ( 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_10176,U_10177)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10178,U_10179)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10177),U_10179))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10178),U_10176)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10176),U_10177)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10177),U_10179))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10178),U_10176)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10176),U_10177))
        | ~ 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_10176,U_10177)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10178,U_10179))) ) ),
    inference(variable_rename,[status(thm)],[f_2721_1]) ).

fof(f_2721_3,plain,
    ( ! [U_10187,U_10185,U_10183,U_10181] :
        ( 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_10181,U_10183)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10185,U_10187)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10183),U_10187))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10185),U_10181)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10181),U_10183)) ) )
    & ! [U_10186,U_10184,U_10182,U_10180] :
        ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10182),U_10186))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10184),U_10180)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10180),U_10182))
        | ~ 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_10180,U_10182)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10184,U_10186))) ) ),
    inference(miniscope,[status(thm)],[f_2721_2]) ).

fof(f_2721_4,plain,
    ( ! [U_10183,U_10181,U_10187,U_10185] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10183),U_10187))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10185),U_10181))
        | ~ sP776(U_10183,U_10181,U_10187,U_10185) )
    & ! [U_10183,U_10181,U_10187,U_10185] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10181),U_10183))
        | ~ sP776(U_10183,U_10181,U_10187,U_10185) )
    & ! [U_10180,U_10182,U_10184,U_10186] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10182),U_10186))
        | ~ sP775(U_10180,U_10182,U_10184,U_10186) )
    & ! [U_10180,U_10182,U_10184,U_10186] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10184),U_10180))
        | ~ sP775(U_10180,U_10182,U_10184,U_10186) )
    & ! [U_10183,U_10181,U_10187,U_10185] :
        ( 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_10181,U_10183)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10185,U_10187)))
        | sP776(U_10183,U_10181,U_10187,U_10185) )
    & ! [U_10180,U_10182,U_10184,U_10186] :
        ( sP775(U_10180,U_10182,U_10184,U_10186)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10180),U_10182))
        | ~ 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_10180,U_10182)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10184,U_10186))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP775,sP776])],[f_2721_3]) ).

cnf(f_2721_5,plain,
    ( sP775(U_10180,U_10182,U_10184,U_10186)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10180),U_10182))
    | ~ 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_10180,U_10182)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10184,U_10186))) ),
    inference(clausify,[status(thm)],[f_2721_4]) ).

cnf(f_2721_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_10181,U_10183)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10185,U_10187)))
    | sP776(U_10183,U_10181,U_10187,U_10185) ),
    inference(clausify,[status(thm)],[f_2721_4]) ).

cnf(f_2721_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10184),U_10180))
    | ~ sP775(U_10180,U_10182,U_10184,U_10186) ),
    inference(clausify,[status(thm)],[f_2721_4]) ).

cnf(f_2721_8,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10182),U_10186))
    | ~ sP775(U_10180,U_10182,U_10184,U_10186) ),
    inference(clausify,[status(thm)],[f_2721_4]) ).

cnf(f_2721_9,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10181),U_10183))
    | ~ sP776(U_10183,U_10181,U_10187,U_10185) ),
    inference(clausify,[status(thm)],[f_2721_4]) ).

cnf(f_2721_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10183),U_10187))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10185),U_10181))
    | ~ sP776(U_10183,U_10181,U_10187,U_10185) ),
    inference(clausify,[status(thm)],[f_2721_4]) ).

fof(f_2722_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_2722_2,plain,
    ! [U_10191,U_10190,U_10189,U_10188] :
      ( ( 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_10188,U_10189)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10190,U_10191)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10190),U_10191))
        | ( ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10191),U_10189))
                | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10189),U_10191)) )
              & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10188),U_10190))
                | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10190),U_10188)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10189),U_10191))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10190),U_10188)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10188),U_10189)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10190),U_10191))
          & ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10191),U_10189))
                  & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10189),U_10191)) )
                | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10188),U_10190))
                  & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10190),U_10188)) ) )
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10189),U_10191))
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10190),U_10188)) )
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10188),U_10189)) ) )
        | ~ 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_10188,U_10189)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10190,U_10191))) ) ),
    inference(variable_rename,[status(thm)],[f_2722_1]) ).

fof(f_2722_3,plain,
    ( ! [U_10199,U_10197,U_10195,U_10193] :
        ( 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_10193,U_10195)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10197,U_10199)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10197),U_10199))
        | ( ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10199),U_10195))
                | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10195),U_10199)) )
              & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10193),U_10197))
                | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10197),U_10193)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10195),U_10199))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10197),U_10193)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10193),U_10195)) ) )
    & ! [U_10198,U_10196,U_10194,U_10192] :
        ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10196),U_10198))
          & ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10198),U_10194))
                  & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10194),U_10198)) )
                | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10192),U_10196))
                  & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10196),U_10192)) ) )
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10194),U_10198))
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10196),U_10192)) )
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10192),U_10194)) ) )
        | ~ 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_10192,U_10194)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10196,U_10198))) ) ),
    inference(miniscope,[status(thm)],[f_2722_2]) ).

fof(f_2722_4,plain,
    ( ! [U_10193,U_10199,U_10195,U_10197] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10199),U_10195))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10195),U_10199))
        | ~ sP781(U_10193,U_10199,U_10195,U_10197) )
    & ! [U_10193,U_10199,U_10195,U_10197] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10193),U_10197))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10197),U_10193))
        | ~ sP781(U_10193,U_10199,U_10195,U_10197) )
    & ! [U_10193,U_10199,U_10195,U_10197] :
        ( sP781(U_10193,U_10199,U_10195,U_10197)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10195),U_10199))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10197),U_10193))
        | ~ sP782(U_10193,U_10199,U_10195,U_10197) )
    & ! [U_10193,U_10199,U_10195,U_10197] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10193),U_10195))
        | ~ sP782(U_10193,U_10199,U_10195,U_10197) )
    & ! [U_10194,U_10198] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10198),U_10194))
        | ~ sP778(U_10194,U_10198) )
    & ! [U_10194,U_10198] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10194),U_10198))
        | ~ sP778(U_10194,U_10198) )
    & ! [U_10192,U_10196] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10192),U_10196))
        | ~ sP777(U_10192,U_10196) )
    & ! [U_10192,U_10196] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10196),U_10192))
        | ~ sP777(U_10192,U_10196) )
    & ! [U_10192,U_10196,U_10194,U_10198] :
        ( sP778(U_10194,U_10198)
        | sP777(U_10192,U_10196)
        | ~ sP779(U_10192,U_10196,U_10194,U_10198) )
    & ! [U_10192,U_10196,U_10194,U_10198] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10194),U_10198))
        | ~ sP779(U_10192,U_10196,U_10194,U_10198) )
    & ! [U_10192,U_10196,U_10194,U_10198] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10196),U_10192))
        | ~ sP779(U_10192,U_10196,U_10194,U_10198) )
    & ! [U_10192,U_10196,U_10194,U_10198] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10196),U_10198))
        | ~ sP780(U_10192,U_10196,U_10194,U_10198) )
    & ! [U_10192,U_10196,U_10194,U_10198] :
        ( sP779(U_10192,U_10196,U_10194,U_10198)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10192),U_10194))
        | ~ sP780(U_10192,U_10196,U_10194,U_10198) )
    & ! [U_10193,U_10199,U_10195,U_10197] :
        ( 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_10193,U_10195)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10197,U_10199)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10197),U_10199))
        | sP782(U_10193,U_10199,U_10195,U_10197) )
    & ! [U_10192,U_10196,U_10194,U_10198] :
        ( sP780(U_10192,U_10196,U_10194,U_10198)
        | ~ 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_10192,U_10194)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10196,U_10198))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP777,sP778,sP779,sP780,sP781,sP782])],[f_2722_3]) ).

cnf(f_2722_5,plain,
    ( sP780(U_10192,U_10196,U_10194,U_10198)
    | ~ 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_10192,U_10194)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10196,U_10198))) ),
    inference(clausify,[status(thm)],[f_2722_4]) ).

cnf(f_2722_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_10193,U_10195)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10197,U_10199)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10197),U_10199))
    | sP782(U_10193,U_10199,U_10195,U_10197) ),
    inference(clausify,[status(thm)],[f_2722_4]) ).

cnf(f_2722_7,plain,
    ( sP779(U_10192,U_10196,U_10194,U_10198)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10192),U_10194))
    | ~ sP780(U_10192,U_10196,U_10194,U_10198) ),
    inference(clausify,[status(thm)],[f_2722_4]) ).

cnf(f_2722_8,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10196),U_10198))
    | ~ sP780(U_10192,U_10196,U_10194,U_10198) ),
    inference(clausify,[status(thm)],[f_2722_4]) ).

cnf(f_2722_9,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10196),U_10192))
    | ~ sP779(U_10192,U_10196,U_10194,U_10198) ),
    inference(clausify,[status(thm)],[f_2722_4]) ).

cnf(f_2722_10,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10194),U_10198))
    | ~ sP779(U_10192,U_10196,U_10194,U_10198) ),
    inference(clausify,[status(thm)],[f_2722_4]) ).

cnf(f_2722_11,plain,
    ( sP778(U_10194,U_10198)
    | sP777(U_10192,U_10196)
    | ~ sP779(U_10192,U_10196,U_10194,U_10198) ),
    inference(clausify,[status(thm)],[f_2722_4]) ).

cnf(f_2722_12,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10196),U_10192))
    | ~ sP777(U_10192,U_10196) ),
    inference(clausify,[status(thm)],[f_2722_4]) ).

cnf(f_2722_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10192),U_10196))
    | ~ sP777(U_10192,U_10196) ),
    inference(clausify,[status(thm)],[f_2722_4]) ).

cnf(f_2722_14,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10194),U_10198))
    | ~ sP778(U_10194,U_10198) ),
    inference(clausify,[status(thm)],[f_2722_4]) ).

cnf(f_2722_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10198),U_10194))
    | ~ sP778(U_10194,U_10198) ),
    inference(clausify,[status(thm)],[f_2722_4]) ).

cnf(f_2722_16,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10193),U_10195))
    | ~ sP782(U_10193,U_10199,U_10195,U_10197) ),
    inference(clausify,[status(thm)],[f_2722_4]) ).

cnf(f_2722_17,plain,
    ( sP781(U_10193,U_10199,U_10195,U_10197)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10195),U_10199))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10197),U_10193))
    | ~ sP782(U_10193,U_10199,U_10195,U_10197) ),
    inference(clausify,[status(thm)],[f_2722_4]) ).

cnf(f_2722_18,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10193),U_10197))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10197),U_10193))
    | ~ sP781(U_10193,U_10199,U_10195,U_10197) ),
    inference(clausify,[status(thm)],[f_2722_4]) ).

cnf(f_2722_19,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10199),U_10195))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10195),U_10199))
    | ~ sP781(U_10193,U_10199,U_10195,U_10197) ),
    inference(clausify,[status(thm)],[f_2722_4]) ).

fof(f_2723_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_2723_2,plain,
    ! [U_10202,U_10201,U_10200] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10200,hAPP(hAPP(c_Set_Oinsert(U_10200),U_10202),U_10201)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10200),U_10202),c_Big__Operators_Olattice__class_OSup__fin(U_10200,U_10201))
      | U_10201 = c_Orderings_Obot__class_Obot(tc_fun(U_10200,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10200),U_10202),U_10201))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10200),U_10201))
      | ~ class_Lattices_Olattice(U_10200) ),
    inference(variable_rename,[status(thm)],[f_2723_1]) ).

fof(f_2723_3,plain,
    ! [U_10201,U_10202,U_10200] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10200,hAPP(hAPP(c_Set_Oinsert(U_10200),U_10202),U_10201)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10200),U_10202),c_Big__Operators_Olattice__class_OSup__fin(U_10200,U_10201))
      | U_10201 = c_Orderings_Obot__class_Obot(tc_fun(U_10200,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10200),U_10202),U_10201))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10200),U_10201))
      | ~ class_Lattices_Olattice(U_10200) ),
    inference(definitional_conversion,[status(esa)],[f_2723_2]) ).

cnf(f_2723_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10200,hAPP(hAPP(c_Set_Oinsert(U_10200),U_10202),U_10201)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10200),U_10202),c_Big__Operators_Olattice__class_OSup__fin(U_10200,U_10201))
    | U_10201 = c_Orderings_Obot__class_Obot(tc_fun(U_10200,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_10200),U_10202),U_10201))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10200),U_10201))
    | ~ class_Lattices_Olattice(U_10200) ),
    inference(clausify,[status(thm)],[f_2723_3]) ).

fof(f_2724_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_2724_2,plain,
    ! [U_10205,U_10204,U_10203] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_10203,hAPP(hAPP(c_Set_Oinsert(U_10203),U_10205),U_10204)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10203),U_10205),c_Big__Operators_Olattice__class_OInf__fin(U_10203,U_10204))
      | U_10204 = c_Orderings_Obot__class_Obot(tc_fun(U_10203,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10203),U_10205),U_10204))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10203),U_10204))
      | ~ class_Lattices_Olattice(U_10203) ),
    inference(variable_rename,[status(thm)],[f_2724_1]) ).

fof(f_2724_3,plain,
    ! [U_10203,U_10205,U_10204] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_10203,hAPP(hAPP(c_Set_Oinsert(U_10203),U_10205),U_10204)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10203),U_10205),c_Big__Operators_Olattice__class_OInf__fin(U_10203,U_10204))
      | U_10204 = c_Orderings_Obot__class_Obot(tc_fun(U_10203,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10203),U_10205),U_10204))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10203),U_10204))
      | ~ class_Lattices_Olattice(U_10203) ),
    inference(definitional_conversion,[status(esa)],[f_2724_2]) ).

cnf(f_2724_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_10203,hAPP(hAPP(c_Set_Oinsert(U_10203),U_10205),U_10204)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10203),U_10205),c_Big__Operators_Olattice__class_OInf__fin(U_10203,U_10204))
    | U_10204 = c_Orderings_Obot__class_Obot(tc_fun(U_10203,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_10203),U_10205),U_10204))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10203),U_10204))
    | ~ class_Lattices_Olattice(U_10203) ),
    inference(clausify,[status(thm)],[f_2724_3]) ).

fof(f_2725_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_2725_2,plain,
    ! [U_10208,U_10207,U_10206] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10206,hAPP(hAPP(c_Set_Oinsert(U_10206),U_10208),U_10207)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10206),U_10208),c_Big__Operators_Olinorder__class_OMax(U_10206,U_10207))
      | U_10207 = c_Orderings_Obot__class_Obot(tc_fun(U_10206,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10206),U_10208),U_10207))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10206),U_10207))
      | ~ class_Orderings_Olinorder(U_10206) ),
    inference(variable_rename,[status(thm)],[f_2725_1]) ).

fof(f_2725_3,plain,
    ! [U_10206,U_10207,U_10208] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10206,hAPP(hAPP(c_Set_Oinsert(U_10206),U_10208),U_10207)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10206),U_10208),c_Big__Operators_Olinorder__class_OMax(U_10206,U_10207))
      | U_10207 = c_Orderings_Obot__class_Obot(tc_fun(U_10206,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10206),U_10208),U_10207))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10206),U_10207))
      | ~ class_Orderings_Olinorder(U_10206) ),
    inference(definitional_conversion,[status(esa)],[f_2725_2]) ).

cnf(f_2725_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10206,hAPP(hAPP(c_Set_Oinsert(U_10206),U_10208),U_10207)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10206),U_10208),c_Big__Operators_Olinorder__class_OMax(U_10206,U_10207))
    | U_10207 = c_Orderings_Obot__class_Obot(tc_fun(U_10206,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_10206),U_10208),U_10207))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10206),U_10207))
    | ~ class_Orderings_Olinorder(U_10206) ),
    inference(clausify,[status(thm)],[f_2725_3]) ).

fof(f_2726_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_2726_2,plain,
    ! [U_10211,U_10210,U_10209] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_10209,hAPP(hAPP(c_Set_Oinsert(U_10209),U_10211),U_10210)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10209),U_10211),c_Big__Operators_Olattice__class_OSup__fin(U_10209,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10209,tc_HOL_Obool)),U_10210),hAPP(hAPP(c_Set_Oinsert(U_10209),U_10211),c_Orderings_Obot__class_Obot(tc_fun(U_10209,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10209,tc_HOL_Obool)),U_10210),hAPP(hAPP(c_Set_Oinsert(U_10209),U_10211),c_Orderings_Obot__class_Obot(tc_fun(U_10209,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10209,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(U_10209,hAPP(hAPP(c_Set_Oinsert(U_10209),U_10211),U_10210)) = U_10211
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10209,tc_HOL_Obool)),U_10210),hAPP(hAPP(c_Set_Oinsert(U_10209),U_10211),c_Orderings_Obot__class_Obot(tc_fun(U_10209,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10209,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10209),U_10210))
      | ~ class_Lattices_Olattice(U_10209) ),
    inference(variable_rename,[status(thm)],[f_2726_1]) ).

fof(f_2726_3,plain,
    ( ! [U_10210,U_10211,U_10209] :
        ( c_Big__Operators_Olattice__class_OSup__fin(U_10209,hAPP(hAPP(c_Set_Oinsert(U_10209),U_10211),U_10210)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10209),U_10211),c_Big__Operators_Olattice__class_OSup__fin(U_10209,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10209,tc_HOL_Obool)),U_10210),hAPP(hAPP(c_Set_Oinsert(U_10209),U_10211),c_Orderings_Obot__class_Obot(tc_fun(U_10209,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10209,tc_HOL_Obool)),U_10210),hAPP(hAPP(c_Set_Oinsert(U_10209),U_10211),c_Orderings_Obot__class_Obot(tc_fun(U_10209,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10209,tc_HOL_Obool))
        | ~ sP783(U_10210,U_10211,U_10209) )
    & ! [U_10210,U_10211,U_10209] :
        ( c_Big__Operators_Olattice__class_OSup__fin(U_10209,hAPP(hAPP(c_Set_Oinsert(U_10209),U_10211),U_10210)) = U_10211
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10209,tc_HOL_Obool)),U_10210),hAPP(hAPP(c_Set_Oinsert(U_10209),U_10211),c_Orderings_Obot__class_Obot(tc_fun(U_10209,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10209,tc_HOL_Obool))
        | ~ sP783(U_10210,U_10211,U_10209) )
    & ! [U_10210,U_10211,U_10209] :
        ( sP783(U_10210,U_10211,U_10209)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10209),U_10210))
        | ~ class_Lattices_Olattice(U_10209) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP783])],[f_2726_2]) ).

cnf(f_2726_4,plain,
    ( sP783(U_10210,U_10211,U_10209)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10209),U_10210))
    | ~ class_Lattices_Olattice(U_10209) ),
    inference(clausify,[status(thm)],[f_2726_3]) ).

cnf(f_2726_5,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10209,hAPP(hAPP(c_Set_Oinsert(U_10209),U_10211),U_10210)) = U_10211
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10209,tc_HOL_Obool)),U_10210),hAPP(hAPP(c_Set_Oinsert(U_10209),U_10211),c_Orderings_Obot__class_Obot(tc_fun(U_10209,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10209,tc_HOL_Obool))
    | ~ sP783(U_10210,U_10211,U_10209) ),
    inference(clausify,[status(thm)],[f_2726_3]) ).

cnf(f_2726_6,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10209,hAPP(hAPP(c_Set_Oinsert(U_10209),U_10211),U_10210)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10209),U_10211),c_Big__Operators_Olattice__class_OSup__fin(U_10209,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10209,tc_HOL_Obool)),U_10210),hAPP(hAPP(c_Set_Oinsert(U_10209),U_10211),c_Orderings_Obot__class_Obot(tc_fun(U_10209,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10209,tc_HOL_Obool)),U_10210),hAPP(hAPP(c_Set_Oinsert(U_10209),U_10211),c_Orderings_Obot__class_Obot(tc_fun(U_10209,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10209,tc_HOL_Obool))
    | ~ sP783(U_10210,U_10211,U_10209) ),
    inference(clausify,[status(thm)],[f_2726_3]) ).

fof(f_2727_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_2727_2,plain,
    ! [U_10214,U_10213,U_10212] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_10212,hAPP(hAPP(c_Set_Oinsert(U_10212),U_10214),U_10213)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10212),U_10214),c_Big__Operators_Olattice__class_OInf__fin(U_10212,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10212,tc_HOL_Obool)),U_10213),hAPP(hAPP(c_Set_Oinsert(U_10212),U_10214),c_Orderings_Obot__class_Obot(tc_fun(U_10212,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10212,tc_HOL_Obool)),U_10213),hAPP(hAPP(c_Set_Oinsert(U_10212),U_10214),c_Orderings_Obot__class_Obot(tc_fun(U_10212,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10212,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(U_10212,hAPP(hAPP(c_Set_Oinsert(U_10212),U_10214),U_10213)) = U_10214
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10212,tc_HOL_Obool)),U_10213),hAPP(hAPP(c_Set_Oinsert(U_10212),U_10214),c_Orderings_Obot__class_Obot(tc_fun(U_10212,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10212,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10212),U_10213))
      | ~ class_Lattices_Olattice(U_10212) ),
    inference(variable_rename,[status(thm)],[f_2727_1]) ).

fof(f_2727_3,plain,
    ( ! [U_10212,U_10214,U_10213] :
        ( c_Big__Operators_Olattice__class_OInf__fin(U_10212,hAPP(hAPP(c_Set_Oinsert(U_10212),U_10214),U_10213)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10212),U_10214),c_Big__Operators_Olattice__class_OInf__fin(U_10212,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10212,tc_HOL_Obool)),U_10213),hAPP(hAPP(c_Set_Oinsert(U_10212),U_10214),c_Orderings_Obot__class_Obot(tc_fun(U_10212,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10212,tc_HOL_Obool)),U_10213),hAPP(hAPP(c_Set_Oinsert(U_10212),U_10214),c_Orderings_Obot__class_Obot(tc_fun(U_10212,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10212,tc_HOL_Obool))
        | ~ sP784(U_10212,U_10214,U_10213) )
    & ! [U_10212,U_10214,U_10213] :
        ( c_Big__Operators_Olattice__class_OInf__fin(U_10212,hAPP(hAPP(c_Set_Oinsert(U_10212),U_10214),U_10213)) = U_10214
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10212,tc_HOL_Obool)),U_10213),hAPP(hAPP(c_Set_Oinsert(U_10212),U_10214),c_Orderings_Obot__class_Obot(tc_fun(U_10212,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10212,tc_HOL_Obool))
        | ~ sP784(U_10212,U_10214,U_10213) )
    & ! [U_10212,U_10214,U_10213] :
        ( sP784(U_10212,U_10214,U_10213)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10212),U_10213))
        | ~ class_Lattices_Olattice(U_10212) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP784])],[f_2727_2]) ).

cnf(f_2727_4,plain,
    ( sP784(U_10212,U_10214,U_10213)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10212),U_10213))
    | ~ class_Lattices_Olattice(U_10212) ),
    inference(clausify,[status(thm)],[f_2727_3]) ).

cnf(f_2727_5,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_10212,hAPP(hAPP(c_Set_Oinsert(U_10212),U_10214),U_10213)) = U_10214
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10212,tc_HOL_Obool)),U_10213),hAPP(hAPP(c_Set_Oinsert(U_10212),U_10214),c_Orderings_Obot__class_Obot(tc_fun(U_10212,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10212,tc_HOL_Obool))
    | ~ sP784(U_10212,U_10214,U_10213) ),
    inference(clausify,[status(thm)],[f_2727_3]) ).

cnf(f_2727_6,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_10212,hAPP(hAPP(c_Set_Oinsert(U_10212),U_10214),U_10213)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10212),U_10214),c_Big__Operators_Olattice__class_OInf__fin(U_10212,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10212,tc_HOL_Obool)),U_10213),hAPP(hAPP(c_Set_Oinsert(U_10212),U_10214),c_Orderings_Obot__class_Obot(tc_fun(U_10212,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10212,tc_HOL_Obool)),U_10213),hAPP(hAPP(c_Set_Oinsert(U_10212),U_10214),c_Orderings_Obot__class_Obot(tc_fun(U_10212,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10212,tc_HOL_Obool))
    | ~ sP784(U_10212,U_10214,U_10213) ),
    inference(clausify,[status(thm)],[f_2727_3]) ).

fof(f_2728_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_2728_2,plain,
    ! [U_10217,U_10216,U_10215] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10215,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10215,tc_HOL_Obool)),U_10216),U_10217)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10215),c_Big__Operators_Olattice__class_OSup__fin(U_10215,U_10216)),c_Big__Operators_Olattice__class_OSup__fin(U_10215,U_10217))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10215,tc_HOL_Obool)),U_10216),U_10217) != c_Orderings_Obot__class_Obot(tc_fun(U_10215,tc_HOL_Obool))
      | U_10217 = c_Orderings_Obot__class_Obot(tc_fun(U_10215,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10215),U_10217))
      | U_10216 = c_Orderings_Obot__class_Obot(tc_fun(U_10215,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10215),U_10216))
      | ~ class_Lattices_Olattice(U_10215) ),
    inference(variable_rename,[status(thm)],[f_2728_1]) ).

fof(f_2728_3,plain,
    ! [U_10215,U_10216,U_10217] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10215,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10215,tc_HOL_Obool)),U_10216),U_10217)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10215),c_Big__Operators_Olattice__class_OSup__fin(U_10215,U_10216)),c_Big__Operators_Olattice__class_OSup__fin(U_10215,U_10217))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10215,tc_HOL_Obool)),U_10216),U_10217) != c_Orderings_Obot__class_Obot(tc_fun(U_10215,tc_HOL_Obool))
      | U_10217 = c_Orderings_Obot__class_Obot(tc_fun(U_10215,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10215),U_10217))
      | U_10216 = c_Orderings_Obot__class_Obot(tc_fun(U_10215,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10215),U_10216))
      | ~ class_Lattices_Olattice(U_10215) ),
    inference(definitional_conversion,[status(esa)],[f_2728_2]) ).

cnf(f_2728_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10215,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10215,tc_HOL_Obool)),U_10216),U_10217)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10215),c_Big__Operators_Olattice__class_OSup__fin(U_10215,U_10216)),c_Big__Operators_Olattice__class_OSup__fin(U_10215,U_10217))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10215,tc_HOL_Obool)),U_10216),U_10217) != c_Orderings_Obot__class_Obot(tc_fun(U_10215,tc_HOL_Obool))
    | U_10217 = c_Orderings_Obot__class_Obot(tc_fun(U_10215,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10215),U_10217))
    | U_10216 = c_Orderings_Obot__class_Obot(tc_fun(U_10215,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10215),U_10216))
    | ~ class_Lattices_Olattice(U_10215) ),
    inference(clausify,[status(thm)],[f_2728_3]) ).

fof(f_2729_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_2729_2,plain,
    ! [U_10220,U_10219,U_10218] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10218),c_Big__Operators_Olattice__class_OSup__fin(U_10218,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10218,tc_HOL_Obool)),U_10219),U_10220))),c_Big__Operators_Olattice__class_OSup__fin(U_10218,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10218,tc_HOL_Obool)),U_10219),U_10220))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10218),c_Big__Operators_Olattice__class_OSup__fin(U_10218,U_10219)),c_Big__Operators_Olattice__class_OSup__fin(U_10218,U_10220))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10218,tc_HOL_Obool)),U_10219),U_10220) = c_Orderings_Obot__class_Obot(tc_fun(U_10218,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10218),U_10220))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10218),U_10219))
      | ~ class_Lattices_Olattice(U_10218) ),
    inference(variable_rename,[status(thm)],[f_2729_1]) ).

fof(f_2729_3,plain,
    ! [U_10219,U_10218,U_10220] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10218),c_Big__Operators_Olattice__class_OSup__fin(U_10218,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10218,tc_HOL_Obool)),U_10219),U_10220))),c_Big__Operators_Olattice__class_OSup__fin(U_10218,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10218,tc_HOL_Obool)),U_10219),U_10220))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10218),c_Big__Operators_Olattice__class_OSup__fin(U_10218,U_10219)),c_Big__Operators_Olattice__class_OSup__fin(U_10218,U_10220))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10218,tc_HOL_Obool)),U_10219),U_10220) = c_Orderings_Obot__class_Obot(tc_fun(U_10218,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10218),U_10220))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10218),U_10219))
      | ~ class_Lattices_Olattice(U_10218) ),
    inference(definitional_conversion,[status(esa)],[f_2729_2]) ).

cnf(f_2729_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10218),c_Big__Operators_Olattice__class_OSup__fin(U_10218,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10218,tc_HOL_Obool)),U_10219),U_10220))),c_Big__Operators_Olattice__class_OSup__fin(U_10218,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10218,tc_HOL_Obool)),U_10219),U_10220))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10218),c_Big__Operators_Olattice__class_OSup__fin(U_10218,U_10219)),c_Big__Operators_Olattice__class_OSup__fin(U_10218,U_10220))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10218,tc_HOL_Obool)),U_10219),U_10220) = c_Orderings_Obot__class_Obot(tc_fun(U_10218,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10218),U_10220))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10218),U_10219))
    | ~ class_Lattices_Olattice(U_10218) ),
    inference(clausify,[status(thm)],[f_2729_3]) ).

fof(f_2730_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_2730_2,plain,
    ! [U_10223,U_10222,U_10221] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(U_10221,hAPP(hAPP(c_Set_Oinsert(U_10221),U_10223),U_10222)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10221),U_10223),c_Big__Operators_Olinorder__class_OMax(U_10221,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10221,tc_HOL_Obool)),U_10222),hAPP(hAPP(c_Set_Oinsert(U_10221),U_10223),c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10221,tc_HOL_Obool)),U_10222),hAPP(hAPP(c_Set_Oinsert(U_10221),U_10223),c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(U_10221,hAPP(hAPP(c_Set_Oinsert(U_10221),U_10223),U_10222)) = U_10223
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10221,tc_HOL_Obool)),U_10222),hAPP(hAPP(c_Set_Oinsert(U_10221),U_10223),c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10221),U_10222))
      | ~ class_Orderings_Olinorder(U_10221) ),
    inference(variable_rename,[status(thm)],[f_2730_1]) ).

fof(f_2730_3,plain,
    ( ! [U_10222,U_10221,U_10223] :
        ( c_Big__Operators_Olinorder__class_OMax(U_10221,hAPP(hAPP(c_Set_Oinsert(U_10221),U_10223),U_10222)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10221),U_10223),c_Big__Operators_Olinorder__class_OMax(U_10221,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10221,tc_HOL_Obool)),U_10222),hAPP(hAPP(c_Set_Oinsert(U_10221),U_10223),c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10221,tc_HOL_Obool)),U_10222),hAPP(hAPP(c_Set_Oinsert(U_10221),U_10223),c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool))
        | ~ sP785(U_10222,U_10221,U_10223) )
    & ! [U_10222,U_10221,U_10223] :
        ( c_Big__Operators_Olinorder__class_OMax(U_10221,hAPP(hAPP(c_Set_Oinsert(U_10221),U_10223),U_10222)) = U_10223
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10221,tc_HOL_Obool)),U_10222),hAPP(hAPP(c_Set_Oinsert(U_10221),U_10223),c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool))
        | ~ sP785(U_10222,U_10221,U_10223) )
    & ! [U_10222,U_10221,U_10223] :
        ( sP785(U_10222,U_10221,U_10223)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10221),U_10222))
        | ~ class_Orderings_Olinorder(U_10221) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP785])],[f_2730_2]) ).

cnf(f_2730_4,plain,
    ( sP785(U_10222,U_10221,U_10223)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10221),U_10222))
    | ~ class_Orderings_Olinorder(U_10221) ),
    inference(clausify,[status(thm)],[f_2730_3]) ).

cnf(f_2730_5,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10221,hAPP(hAPP(c_Set_Oinsert(U_10221),U_10223),U_10222)) = U_10223
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10221,tc_HOL_Obool)),U_10222),hAPP(hAPP(c_Set_Oinsert(U_10221),U_10223),c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool))
    | ~ sP785(U_10222,U_10221,U_10223) ),
    inference(clausify,[status(thm)],[f_2730_3]) ).

cnf(f_2730_6,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10221,hAPP(hAPP(c_Set_Oinsert(U_10221),U_10223),U_10222)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10221),U_10223),c_Big__Operators_Olinorder__class_OMax(U_10221,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10221,tc_HOL_Obool)),U_10222),hAPP(hAPP(c_Set_Oinsert(U_10221),U_10223),c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10221,tc_HOL_Obool)),U_10222),hAPP(hAPP(c_Set_Oinsert(U_10221),U_10223),c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10221,tc_HOL_Obool))
    | ~ sP785(U_10222,U_10221,U_10223) ),
    inference(clausify,[status(thm)],[f_2730_3]) ).

fof(f_2731_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_2731_2,plain,
    ! [U_10226,U_10225,U_10224] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10224),c_Big__Operators_Olattice__class_OInf__fin(U_10224,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10224,tc_HOL_Obool)),U_10225),U_10226))),c_Big__Operators_Olattice__class_OInf__fin(U_10224,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10224,tc_HOL_Obool)),U_10225),U_10226))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10224),c_Big__Operators_Olattice__class_OInf__fin(U_10224,U_10225)),c_Big__Operators_Olattice__class_OInf__fin(U_10224,U_10226))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10224,tc_HOL_Obool)),U_10225),U_10226) = c_Orderings_Obot__class_Obot(tc_fun(U_10224,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10224),U_10226))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10224),U_10225))
      | ~ class_Lattices_Olattice(U_10224) ),
    inference(variable_rename,[status(thm)],[f_2731_1]) ).

fof(f_2731_3,plain,
    ! [U_10226,U_10224,U_10225] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10224),c_Big__Operators_Olattice__class_OInf__fin(U_10224,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10224,tc_HOL_Obool)),U_10225),U_10226))),c_Big__Operators_Olattice__class_OInf__fin(U_10224,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10224,tc_HOL_Obool)),U_10225),U_10226))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10224),c_Big__Operators_Olattice__class_OInf__fin(U_10224,U_10225)),c_Big__Operators_Olattice__class_OInf__fin(U_10224,U_10226))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10224,tc_HOL_Obool)),U_10225),U_10226) = c_Orderings_Obot__class_Obot(tc_fun(U_10224,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10224),U_10226))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10224),U_10225))
      | ~ class_Lattices_Olattice(U_10224) ),
    inference(definitional_conversion,[status(esa)],[f_2731_2]) ).

cnf(f_2731_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10224),c_Big__Operators_Olattice__class_OInf__fin(U_10224,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10224,tc_HOL_Obool)),U_10225),U_10226))),c_Big__Operators_Olattice__class_OInf__fin(U_10224,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10224,tc_HOL_Obool)),U_10225),U_10226))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10224),c_Big__Operators_Olattice__class_OInf__fin(U_10224,U_10225)),c_Big__Operators_Olattice__class_OInf__fin(U_10224,U_10226))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10224,tc_HOL_Obool)),U_10225),U_10226) = c_Orderings_Obot__class_Obot(tc_fun(U_10224,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10224),U_10226))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10224),U_10225))
    | ~ class_Lattices_Olattice(U_10224) ),
    inference(clausify,[status(thm)],[f_2731_3]) ).

fof(f_2732_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_2732_2,plain,
    ! [U_10229,U_10228,U_10227] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_10227,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10227,tc_HOL_Obool)),U_10228),U_10229)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10227),c_Big__Operators_Olattice__class_OInf__fin(U_10227,U_10228)),c_Big__Operators_Olattice__class_OInf__fin(U_10227,U_10229))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10227,tc_HOL_Obool)),U_10228),U_10229) != c_Orderings_Obot__class_Obot(tc_fun(U_10227,tc_HOL_Obool))
      | U_10229 = c_Orderings_Obot__class_Obot(tc_fun(U_10227,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10227),U_10229))
      | U_10228 = c_Orderings_Obot__class_Obot(tc_fun(U_10227,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10227),U_10228))
      | ~ class_Lattices_Olattice(U_10227) ),
    inference(variable_rename,[status(thm)],[f_2732_1]) ).

fof(f_2732_3,plain,
    ! [U_10228,U_10227,U_10229] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_10227,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10227,tc_HOL_Obool)),U_10228),U_10229)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10227),c_Big__Operators_Olattice__class_OInf__fin(U_10227,U_10228)),c_Big__Operators_Olattice__class_OInf__fin(U_10227,U_10229))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10227,tc_HOL_Obool)),U_10228),U_10229) != c_Orderings_Obot__class_Obot(tc_fun(U_10227,tc_HOL_Obool))
      | U_10229 = c_Orderings_Obot__class_Obot(tc_fun(U_10227,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10227),U_10229))
      | U_10228 = c_Orderings_Obot__class_Obot(tc_fun(U_10227,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10227),U_10228))
      | ~ class_Lattices_Olattice(U_10227) ),
    inference(definitional_conversion,[status(esa)],[f_2732_2]) ).

cnf(f_2732_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_10227,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10227,tc_HOL_Obool)),U_10228),U_10229)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10227),c_Big__Operators_Olattice__class_OInf__fin(U_10227,U_10228)),c_Big__Operators_Olattice__class_OInf__fin(U_10227,U_10229))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10227,tc_HOL_Obool)),U_10228),U_10229) != c_Orderings_Obot__class_Obot(tc_fun(U_10227,tc_HOL_Obool))
    | U_10229 = c_Orderings_Obot__class_Obot(tc_fun(U_10227,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10227),U_10229))
    | U_10228 = c_Orderings_Obot__class_Obot(tc_fun(U_10227,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10227),U_10228))
    | ~ class_Lattices_Olattice(U_10227) ),
    inference(clausify,[status(thm)],[f_2732_3]) ).

fof(f_2733_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_2733_2,plain,
    ! [U_10232,U_10231,U_10230] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10230),c_Big__Operators_Olinorder__class_OMax(U_10230,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10230,tc_HOL_Obool)),U_10231),U_10232))),c_Big__Operators_Olinorder__class_OMax(U_10230,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10230,tc_HOL_Obool)),U_10231),U_10232))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10230),c_Big__Operators_Olinorder__class_OMax(U_10230,U_10231)),c_Big__Operators_Olinorder__class_OMax(U_10230,U_10232))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10230,tc_HOL_Obool)),U_10231),U_10232) = c_Orderings_Obot__class_Obot(tc_fun(U_10230,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10230),U_10232))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10230),U_10231))
      | ~ class_Orderings_Olinorder(U_10230) ),
    inference(variable_rename,[status(thm)],[f_2733_1]) ).

fof(f_2733_3,plain,
    ! [U_10230,U_10231,U_10232] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10230),c_Big__Operators_Olinorder__class_OMax(U_10230,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10230,tc_HOL_Obool)),U_10231),U_10232))),c_Big__Operators_Olinorder__class_OMax(U_10230,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10230,tc_HOL_Obool)),U_10231),U_10232))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10230),c_Big__Operators_Olinorder__class_OMax(U_10230,U_10231)),c_Big__Operators_Olinorder__class_OMax(U_10230,U_10232))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10230,tc_HOL_Obool)),U_10231),U_10232) = c_Orderings_Obot__class_Obot(tc_fun(U_10230,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10230),U_10232))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10230),U_10231))
      | ~ class_Orderings_Olinorder(U_10230) ),
    inference(definitional_conversion,[status(esa)],[f_2733_2]) ).

cnf(f_2733_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10230),c_Big__Operators_Olinorder__class_OMax(U_10230,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10230,tc_HOL_Obool)),U_10231),U_10232))),c_Big__Operators_Olinorder__class_OMax(U_10230,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10230,tc_HOL_Obool)),U_10231),U_10232))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10230),c_Big__Operators_Olinorder__class_OMax(U_10230,U_10231)),c_Big__Operators_Olinorder__class_OMax(U_10230,U_10232))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10230,tc_HOL_Obool)),U_10231),U_10232) = c_Orderings_Obot__class_Obot(tc_fun(U_10230,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10230),U_10232))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10230),U_10231))
    | ~ class_Orderings_Olinorder(U_10230) ),
    inference(clausify,[status(thm)],[f_2733_3]) ).

fof(f_2734_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_2734_2,plain,
    ! [U_10235,U_10234,U_10233] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10233,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10233,tc_HOL_Obool)),U_10234),U_10235)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10233),c_Big__Operators_Olinorder__class_OMax(U_10233,U_10234)),c_Big__Operators_Olinorder__class_OMax(U_10233,U_10235))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10233,tc_HOL_Obool)),U_10234),U_10235) != c_Orderings_Obot__class_Obot(tc_fun(U_10233,tc_HOL_Obool))
      | U_10235 = c_Orderings_Obot__class_Obot(tc_fun(U_10233,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10233),U_10235))
      | U_10234 = c_Orderings_Obot__class_Obot(tc_fun(U_10233,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10233),U_10234))
      | ~ class_Orderings_Olinorder(U_10233) ),
    inference(variable_rename,[status(thm)],[f_2734_1]) ).

fof(f_2734_3,plain,
    ! [U_10234,U_10233,U_10235] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10233,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10233,tc_HOL_Obool)),U_10234),U_10235)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10233),c_Big__Operators_Olinorder__class_OMax(U_10233,U_10234)),c_Big__Operators_Olinorder__class_OMax(U_10233,U_10235))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10233,tc_HOL_Obool)),U_10234),U_10235) != c_Orderings_Obot__class_Obot(tc_fun(U_10233,tc_HOL_Obool))
      | U_10235 = c_Orderings_Obot__class_Obot(tc_fun(U_10233,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10233),U_10235))
      | U_10234 = c_Orderings_Obot__class_Obot(tc_fun(U_10233,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10233),U_10234))
      | ~ class_Orderings_Olinorder(U_10233) ),
    inference(definitional_conversion,[status(esa)],[f_2734_2]) ).

cnf(f_2734_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10233,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10233,tc_HOL_Obool)),U_10234),U_10235)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10233),c_Big__Operators_Olinorder__class_OMax(U_10233,U_10234)),c_Big__Operators_Olinorder__class_OMax(U_10233,U_10235))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10233,tc_HOL_Obool)),U_10234),U_10235) != c_Orderings_Obot__class_Obot(tc_fun(U_10233,tc_HOL_Obool))
    | U_10235 = c_Orderings_Obot__class_Obot(tc_fun(U_10233,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10233),U_10235))
    | U_10234 = c_Orderings_Obot__class_Obot(tc_fun(U_10233,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10233),U_10234))
    | ~ class_Orderings_Olinorder(U_10233) ),
    inference(clausify,[status(thm)],[f_2734_3]) ).

fof(f_2735_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_2735_2,plain,
    ! [U_10239,U_10238] :
      ( hBOOL(hAPP(hAPP(c_member(U_10238),c_Big__Operators_Olinorder__class_OMax(U_10238,U_10239)),U_10239))
      | ? [U_10237,U_10236] : ~ hBOOL(hAPP(hAPP(c_member(U_10238),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10238),U_10237),U_10236)),hAPP(hAPP(c_Set_Oinsert(U_10238),U_10237),hAPP(hAPP(c_Set_Oinsert(U_10238),U_10236),c_Orderings_Obot__class_Obot(tc_fun(U_10238,tc_HOL_Obool))))))
      | U_10239 = c_Orderings_Obot__class_Obot(tc_fun(U_10238,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10238),U_10239))
      | ~ class_Orderings_Olinorder(U_10238) ),
    inference(variable_rename,[status(thm)],[f_2735_1]) ).

fof(f_2735_3,plain,
    ! [U_10239,U_10238] :
      ( hBOOL(hAPP(hAPP(c_member(U_10238),c_Big__Operators_Olinorder__class_OMax(U_10238,U_10239)),U_10239))
      | ? [U_10236] : ~ hBOOL(hAPP(hAPP(c_member(U_10238),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10238),sK148(U_10239,U_10238)),U_10236)),hAPP(hAPP(c_Set_Oinsert(U_10238),sK148(U_10239,U_10238)),hAPP(hAPP(c_Set_Oinsert(U_10238),U_10236),c_Orderings_Obot__class_Obot(tc_fun(U_10238,tc_HOL_Obool))))))
      | U_10239 = c_Orderings_Obot__class_Obot(tc_fun(U_10238,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10238),U_10239))
      | ~ class_Orderings_Olinorder(U_10238) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_10237,sK148(U_10239,U_10238))],[f_2735_2]) ).

fof(f_2735_4,plain,
    ! [U_10239,U_10238] :
      ( hBOOL(hAPP(hAPP(c_member(U_10238),c_Big__Operators_Olinorder__class_OMax(U_10238,U_10239)),U_10239))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10238),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10238),sK148(U_10239,U_10238)),sK149(U_10239,U_10238))),hAPP(hAPP(c_Set_Oinsert(U_10238),sK148(U_10239,U_10238)),hAPP(hAPP(c_Set_Oinsert(U_10238),sK149(U_10239,U_10238)),c_Orderings_Obot__class_Obot(tc_fun(U_10238,tc_HOL_Obool))))))
      | U_10239 = c_Orderings_Obot__class_Obot(tc_fun(U_10238,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10238),U_10239))
      | ~ class_Orderings_Olinorder(U_10238) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_10236,sK149(U_10239,U_10238))],[f_2735_3]) ).

fof(f_2735_5,plain,
    ! [U_10239,U_10238] :
      ( hBOOL(hAPP(hAPP(c_member(U_10238),c_Big__Operators_Olinorder__class_OMax(U_10238,U_10239)),U_10239))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10238),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10238),sK148(U_10239,U_10238)),sK149(U_10239,U_10238))),hAPP(hAPP(c_Set_Oinsert(U_10238),sK148(U_10239,U_10238)),hAPP(hAPP(c_Set_Oinsert(U_10238),sK149(U_10239,U_10238)),c_Orderings_Obot__class_Obot(tc_fun(U_10238,tc_HOL_Obool))))))
      | U_10239 = c_Orderings_Obot__class_Obot(tc_fun(U_10238,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10238),U_10239))
      | ~ class_Orderings_Olinorder(U_10238) ),
    inference(definitional_conversion,[status(esa)],[f_2735_4]) ).

cnf(f_2735_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10238),c_Big__Operators_Olinorder__class_OMax(U_10238,U_10239)),U_10239))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10238),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10238),sK148(U_10239,U_10238)),sK149(U_10239,U_10238))),hAPP(hAPP(c_Set_Oinsert(U_10238),sK148(U_10239,U_10238)),hAPP(hAPP(c_Set_Oinsert(U_10238),sK149(U_10239,U_10238)),c_Orderings_Obot__class_Obot(tc_fun(U_10238,tc_HOL_Obool))))))
    | U_10239 = c_Orderings_Obot__class_Obot(tc_fun(U_10238,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10238),U_10239))
    | ~ class_Orderings_Olinorder(U_10238) ),
    inference(clausify,[status(thm)],[f_2735_5]) ).

fof(f_2736_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_2736_2,plain,
    ! [U_10243,U_10242] :
      ( hBOOL(hAPP(hAPP(c_member(U_10242),c_Big__Operators_Olattice__class_OInf__fin(U_10242,U_10243)),U_10243))
      | ? [U_10241,U_10240] : ~ hBOOL(hAPP(hAPP(c_member(U_10242),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10242),U_10241),U_10240)),hAPP(hAPP(c_Set_Oinsert(U_10242),U_10241),hAPP(hAPP(c_Set_Oinsert(U_10242),U_10240),c_Orderings_Obot__class_Obot(tc_fun(U_10242,tc_HOL_Obool))))))
      | U_10243 = c_Orderings_Obot__class_Obot(tc_fun(U_10242,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10242),U_10243))
      | ~ class_Lattices_Olattice(U_10242) ),
    inference(variable_rename,[status(thm)],[f_2736_1]) ).

fof(f_2736_3,plain,
    ! [U_10243,U_10242] :
      ( hBOOL(hAPP(hAPP(c_member(U_10242),c_Big__Operators_Olattice__class_OInf__fin(U_10242,U_10243)),U_10243))
      | ? [U_10240] : ~ hBOOL(hAPP(hAPP(c_member(U_10242),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10242),sK150(U_10243,U_10242)),U_10240)),hAPP(hAPP(c_Set_Oinsert(U_10242),sK150(U_10243,U_10242)),hAPP(hAPP(c_Set_Oinsert(U_10242),U_10240),c_Orderings_Obot__class_Obot(tc_fun(U_10242,tc_HOL_Obool))))))
      | U_10243 = c_Orderings_Obot__class_Obot(tc_fun(U_10242,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10242),U_10243))
      | ~ class_Lattices_Olattice(U_10242) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_10241,sK150(U_10243,U_10242))],[f_2736_2]) ).

fof(f_2736_4,plain,
    ! [U_10243,U_10242] :
      ( hBOOL(hAPP(hAPP(c_member(U_10242),c_Big__Operators_Olattice__class_OInf__fin(U_10242,U_10243)),U_10243))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10242),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10242),sK150(U_10243,U_10242)),sK151(U_10243,U_10242))),hAPP(hAPP(c_Set_Oinsert(U_10242),sK150(U_10243,U_10242)),hAPP(hAPP(c_Set_Oinsert(U_10242),sK151(U_10243,U_10242)),c_Orderings_Obot__class_Obot(tc_fun(U_10242,tc_HOL_Obool))))))
      | U_10243 = c_Orderings_Obot__class_Obot(tc_fun(U_10242,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10242),U_10243))
      | ~ class_Lattices_Olattice(U_10242) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_10240,sK151(U_10243,U_10242))],[f_2736_3]) ).

fof(f_2736_5,plain,
    ! [U_10242,U_10243] :
      ( hBOOL(hAPP(hAPP(c_member(U_10242),c_Big__Operators_Olattice__class_OInf__fin(U_10242,U_10243)),U_10243))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10242),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10242),sK150(U_10243,U_10242)),sK151(U_10243,U_10242))),hAPP(hAPP(c_Set_Oinsert(U_10242),sK150(U_10243,U_10242)),hAPP(hAPP(c_Set_Oinsert(U_10242),sK151(U_10243,U_10242)),c_Orderings_Obot__class_Obot(tc_fun(U_10242,tc_HOL_Obool))))))
      | U_10243 = c_Orderings_Obot__class_Obot(tc_fun(U_10242,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10242),U_10243))
      | ~ class_Lattices_Olattice(U_10242) ),
    inference(definitional_conversion,[status(esa)],[f_2736_4]) ).

cnf(f_2736_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10242),c_Big__Operators_Olattice__class_OInf__fin(U_10242,U_10243)),U_10243))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10242),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10242),sK150(U_10243,U_10242)),sK151(U_10243,U_10242))),hAPP(hAPP(c_Set_Oinsert(U_10242),sK150(U_10243,U_10242)),hAPP(hAPP(c_Set_Oinsert(U_10242),sK151(U_10243,U_10242)),c_Orderings_Obot__class_Obot(tc_fun(U_10242,tc_HOL_Obool))))))
    | U_10243 = c_Orderings_Obot__class_Obot(tc_fun(U_10242,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10242),U_10243))
    | ~ class_Lattices_Olattice(U_10242) ),
    inference(clausify,[status(thm)],[f_2736_5]) ).

fof(f_2737_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_2737_2,plain,
    ! [U_10247,U_10246] :
      ( hBOOL(hAPP(hAPP(c_member(U_10246),c_Big__Operators_Olattice__class_OSup__fin(U_10246,U_10247)),U_10247))
      | ? [U_10245,U_10244] : ~ hBOOL(hAPP(hAPP(c_member(U_10246),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10246),U_10245),U_10244)),hAPP(hAPP(c_Set_Oinsert(U_10246),U_10245),hAPP(hAPP(c_Set_Oinsert(U_10246),U_10244),c_Orderings_Obot__class_Obot(tc_fun(U_10246,tc_HOL_Obool))))))
      | U_10247 = c_Orderings_Obot__class_Obot(tc_fun(U_10246,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10246),U_10247))
      | ~ class_Lattices_Olattice(U_10246) ),
    inference(variable_rename,[status(thm)],[f_2737_1]) ).

fof(f_2737_3,plain,
    ! [U_10247,U_10246] :
      ( hBOOL(hAPP(hAPP(c_member(U_10246),c_Big__Operators_Olattice__class_OSup__fin(U_10246,U_10247)),U_10247))
      | ? [U_10244] : ~ hBOOL(hAPP(hAPP(c_member(U_10246),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10246),sK152(U_10247,U_10246)),U_10244)),hAPP(hAPP(c_Set_Oinsert(U_10246),sK152(U_10247,U_10246)),hAPP(hAPP(c_Set_Oinsert(U_10246),U_10244),c_Orderings_Obot__class_Obot(tc_fun(U_10246,tc_HOL_Obool))))))
      | U_10247 = c_Orderings_Obot__class_Obot(tc_fun(U_10246,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10246),U_10247))
      | ~ class_Lattices_Olattice(U_10246) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_10245,sK152(U_10247,U_10246))],[f_2737_2]) ).

fof(f_2737_4,plain,
    ! [U_10247,U_10246] :
      ( hBOOL(hAPP(hAPP(c_member(U_10246),c_Big__Operators_Olattice__class_OSup__fin(U_10246,U_10247)),U_10247))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10246),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10246),sK152(U_10247,U_10246)),sK153(U_10247,U_10246))),hAPP(hAPP(c_Set_Oinsert(U_10246),sK152(U_10247,U_10246)),hAPP(hAPP(c_Set_Oinsert(U_10246),sK153(U_10247,U_10246)),c_Orderings_Obot__class_Obot(tc_fun(U_10246,tc_HOL_Obool))))))
      | U_10247 = c_Orderings_Obot__class_Obot(tc_fun(U_10246,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10246),U_10247))
      | ~ class_Lattices_Olattice(U_10246) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_10244,sK153(U_10247,U_10246))],[f_2737_3]) ).

fof(f_2737_5,plain,
    ! [U_10246,U_10247] :
      ( hBOOL(hAPP(hAPP(c_member(U_10246),c_Big__Operators_Olattice__class_OSup__fin(U_10246,U_10247)),U_10247))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10246),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10246),sK152(U_10247,U_10246)),sK153(U_10247,U_10246))),hAPP(hAPP(c_Set_Oinsert(U_10246),sK152(U_10247,U_10246)),hAPP(hAPP(c_Set_Oinsert(U_10246),sK153(U_10247,U_10246)),c_Orderings_Obot__class_Obot(tc_fun(U_10246,tc_HOL_Obool))))))
      | U_10247 = c_Orderings_Obot__class_Obot(tc_fun(U_10246,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10246),U_10247))
      | ~ class_Lattices_Olattice(U_10246) ),
    inference(definitional_conversion,[status(esa)],[f_2737_4]) ).

cnf(f_2737_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10246),c_Big__Operators_Olattice__class_OSup__fin(U_10246,U_10247)),U_10247))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10246),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10246),sK152(U_10247,U_10246)),sK153(U_10247,U_10246))),hAPP(hAPP(c_Set_Oinsert(U_10246),sK152(U_10247,U_10246)),hAPP(hAPP(c_Set_Oinsert(U_10246),sK153(U_10247,U_10246)),c_Orderings_Obot__class_Obot(tc_fun(U_10246,tc_HOL_Obool))))))
    | U_10247 = c_Orderings_Obot__class_Obot(tc_fun(U_10246,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10246),U_10247))
    | ~ class_Lattices_Olattice(U_10246) ),
    inference(clausify,[status(thm)],[f_2737_5]) ).

fof(f_2738_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_2738_2,plain,
    ! [U_10250,U_10249,U_10248] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(U_10248,U_10249) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10248),U_10250),c_Big__Operators_Olinorder__class_OMin(U_10248,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10248,tc_HOL_Obool)),U_10249),hAPP(hAPP(c_Set_Oinsert(U_10248),U_10250),c_Orderings_Obot__class_Obot(tc_fun(U_10248,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10248,tc_HOL_Obool)),U_10249),hAPP(hAPP(c_Set_Oinsert(U_10248),U_10250),c_Orderings_Obot__class_Obot(tc_fun(U_10248,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10248,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(U_10248,U_10249) = U_10250
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10248,tc_HOL_Obool)),U_10249),hAPP(hAPP(c_Set_Oinsert(U_10248),U_10250),c_Orderings_Obot__class_Obot(tc_fun(U_10248,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10248,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_10248),U_10250),U_10249))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10248),U_10249))
      | ~ class_Orderings_Olinorder(U_10248) ),
    inference(variable_rename,[status(thm)],[f_2738_1]) ).

fof(f_2738_3,plain,
    ( ! [U_10248,U_10249,U_10250] :
        ( c_Big__Operators_Olinorder__class_OMin(U_10248,U_10249) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10248),U_10250),c_Big__Operators_Olinorder__class_OMin(U_10248,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10248,tc_HOL_Obool)),U_10249),hAPP(hAPP(c_Set_Oinsert(U_10248),U_10250),c_Orderings_Obot__class_Obot(tc_fun(U_10248,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10248,tc_HOL_Obool)),U_10249),hAPP(hAPP(c_Set_Oinsert(U_10248),U_10250),c_Orderings_Obot__class_Obot(tc_fun(U_10248,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10248,tc_HOL_Obool))
        | ~ sP786(U_10248,U_10249,U_10250) )
    & ! [U_10248,U_10249,U_10250] :
        ( c_Big__Operators_Olinorder__class_OMin(U_10248,U_10249) = U_10250
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10248,tc_HOL_Obool)),U_10249),hAPP(hAPP(c_Set_Oinsert(U_10248),U_10250),c_Orderings_Obot__class_Obot(tc_fun(U_10248,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10248,tc_HOL_Obool))
        | ~ sP786(U_10248,U_10249,U_10250) )
    & ! [U_10248,U_10249,U_10250] :
        ( sP786(U_10248,U_10249,U_10250)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10248),U_10250),U_10249))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10248),U_10249))
        | ~ class_Orderings_Olinorder(U_10248) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP786])],[f_2738_2]) ).

cnf(f_2738_4,plain,
    ( sP786(U_10248,U_10249,U_10250)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10248),U_10250),U_10249))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10248),U_10249))
    | ~ class_Orderings_Olinorder(U_10248) ),
    inference(clausify,[status(thm)],[f_2738_3]) ).

cnf(f_2738_5,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10248,U_10249) = U_10250
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10248,tc_HOL_Obool)),U_10249),hAPP(hAPP(c_Set_Oinsert(U_10248),U_10250),c_Orderings_Obot__class_Obot(tc_fun(U_10248,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10248,tc_HOL_Obool))
    | ~ sP786(U_10248,U_10249,U_10250) ),
    inference(clausify,[status(thm)],[f_2738_3]) ).

cnf(f_2738_6,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10248,U_10249) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10248),U_10250),c_Big__Operators_Olinorder__class_OMin(U_10248,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10248,tc_HOL_Obool)),U_10249),hAPP(hAPP(c_Set_Oinsert(U_10248),U_10250),c_Orderings_Obot__class_Obot(tc_fun(U_10248,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10248,tc_HOL_Obool)),U_10249),hAPP(hAPP(c_Set_Oinsert(U_10248),U_10250),c_Orderings_Obot__class_Obot(tc_fun(U_10248,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10248,tc_HOL_Obool))
    | ~ sP786(U_10248,U_10249,U_10250) ),
    inference(clausify,[status(thm)],[f_2738_3]) ).

fof(f_2739_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_2739_2,plain,
    ! [U_10252,U_10251] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10251,hAPP(hAPP(c_Set_Oinsert(U_10251),U_10252),c_Orderings_Obot__class_Obot(tc_fun(U_10251,tc_HOL_Obool)))) = U_10252
      | ~ class_Orderings_Olinorder(U_10251) ),
    inference(variable_rename,[status(thm)],[f_2739_1]) ).

fof(f_2739_3,plain,
    ! [U_10252,U_10251] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10251,hAPP(hAPP(c_Set_Oinsert(U_10251),U_10252),c_Orderings_Obot__class_Obot(tc_fun(U_10251,tc_HOL_Obool)))) = U_10252
      | ~ class_Orderings_Olinorder(U_10251) ),
    inference(definitional_conversion,[status(esa)],[f_2739_2]) ).

cnf(f_2739_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10251,hAPP(hAPP(c_Set_Oinsert(U_10251),U_10252),c_Orderings_Obot__class_Obot(tc_fun(U_10251,tc_HOL_Obool)))) = U_10252
    | ~ class_Orderings_Olinorder(U_10251) ),
    inference(clausify,[status(thm)],[f_2739_3]) ).

fof(f_2740_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_2740_2,plain,
    ! [U_10255,U_10254,U_10253] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10253),c_Big__Operators_Olinorder__class_OMin(U_10253,U_10254)),U_10255))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10253),U_10255),U_10254))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10253),U_10254))
      | ~ class_Orderings_Olinorder(U_10253) ),
    inference(variable_rename,[status(thm)],[f_2740_1]) ).

fof(f_2740_3,plain,
    ! [U_10253,U_10254,U_10255] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10253),c_Big__Operators_Olinorder__class_OMin(U_10253,U_10254)),U_10255))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10253),U_10255),U_10254))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10253),U_10254))
      | ~ class_Orderings_Olinorder(U_10253) ),
    inference(definitional_conversion,[status(esa)],[f_2740_2]) ).

cnf(f_2740_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10253),c_Big__Operators_Olinorder__class_OMin(U_10253,U_10254)),U_10255))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10253),U_10255),U_10254))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10253),U_10254))
    | ~ class_Orderings_Olinorder(U_10253) ),
    inference(clausify,[status(thm)],[f_2740_3]) ).

fof(f_2741_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_2741_2,plain,
    ! [U_10257,U_10256] :
      ( hBOOL(hAPP(hAPP(c_member(U_10256),c_Big__Operators_Olinorder__class_OMin(U_10256,U_10257)),U_10257))
      | U_10257 = c_Orderings_Obot__class_Obot(tc_fun(U_10256,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10256),U_10257))
      | ~ class_Orderings_Olinorder(U_10256) ),
    inference(variable_rename,[status(thm)],[f_2741_1]) ).

fof(f_2741_3,plain,
    ! [U_10256,U_10257] :
      ( hBOOL(hAPP(hAPP(c_member(U_10256),c_Big__Operators_Olinorder__class_OMin(U_10256,U_10257)),U_10257))
      | U_10257 = c_Orderings_Obot__class_Obot(tc_fun(U_10256,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10256),U_10257))
      | ~ class_Orderings_Olinorder(U_10256) ),
    inference(definitional_conversion,[status(esa)],[f_2741_2]) ).

cnf(f_2741_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10256),c_Big__Operators_Olinorder__class_OMin(U_10256,U_10257)),U_10257))
    | U_10257 = c_Orderings_Obot__class_Obot(tc_fun(U_10256,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10256),U_10257))
    | ~ class_Orderings_Olinorder(U_10256) ),
    inference(clausify,[status(thm)],[f_2741_3]) ).

fof(f_2742_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_2742_2,plain,
    ! [U_10260,U_10259,U_10258] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10258),U_10260),c_Big__Operators_Olinorder__class_OMin(U_10258,U_10259)) = c_Big__Operators_Olinorder__class_OMin(U_10258,U_10259)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10258),U_10260),U_10259))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10258),U_10259))
      | ~ class_Orderings_Olinorder(U_10258) ),
    inference(variable_rename,[status(thm)],[f_2742_1]) ).

fof(f_2742_3,plain,
    ! [U_10258,U_10259,U_10260] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10258),U_10260),c_Big__Operators_Olinorder__class_OMin(U_10258,U_10259)) = c_Big__Operators_Olinorder__class_OMin(U_10258,U_10259)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10258),U_10260),U_10259))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10258),U_10259))
      | ~ class_Orderings_Olinorder(U_10258) ),
    inference(definitional_conversion,[status(esa)],[f_2742_2]) ).

cnf(f_2742_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10258),U_10260),c_Big__Operators_Olinorder__class_OMin(U_10258,U_10259)) = c_Big__Operators_Olinorder__class_OMin(U_10258,U_10259)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10258),U_10260),U_10259))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10258),U_10259))
    | ~ class_Orderings_Olinorder(U_10258) ),
    inference(clausify,[status(thm)],[f_2742_3]) ).

fof(f_2743_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_2743_2,plain,
    ! [U_10263,U_10262,U_10261] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10261),c_Big__Operators_Olinorder__class_OMin(U_10261,U_10263)),c_Big__Operators_Olinorder__class_OMin(U_10261,U_10262)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10261),U_10263))
      | U_10262 = c_Orderings_Obot__class_Obot(tc_fun(U_10261,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10261,tc_HOL_Obool)),U_10262),U_10263))
      | ~ class_Orderings_Olinorder(U_10261) ),
    inference(variable_rename,[status(thm)],[f_2743_1]) ).

fof(f_2743_3,plain,
    ! [U_10261,U_10262,U_10263] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10261),c_Big__Operators_Olinorder__class_OMin(U_10261,U_10263)),c_Big__Operators_Olinorder__class_OMin(U_10261,U_10262)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10261),U_10263))
      | U_10262 = c_Orderings_Obot__class_Obot(tc_fun(U_10261,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10261,tc_HOL_Obool)),U_10262),U_10263))
      | ~ class_Orderings_Olinorder(U_10261) ),
    inference(definitional_conversion,[status(esa)],[f_2743_2]) ).

cnf(f_2743_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10261),c_Big__Operators_Olinorder__class_OMin(U_10261,U_10263)),c_Big__Operators_Olinorder__class_OMin(U_10261,U_10262)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10261),U_10263))
    | U_10262 = c_Orderings_Obot__class_Obot(tc_fun(U_10261,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10261,tc_HOL_Obool)),U_10262),U_10263))
    | ~ class_Orderings_Olinorder(U_10261) ),
    inference(clausify,[status(thm)],[f_2743_3]) ).

fof(f_2744_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_2744_2,plain,
    ! [U_10266,U_10265,U_10264] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10264,hAPP(hAPP(c_Set_Oinsert(U_10264),U_10266),U_10265)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10264),U_10266),c_Big__Operators_Olinorder__class_OMin(U_10264,U_10265))
      | U_10265 = c_Orderings_Obot__class_Obot(tc_fun(U_10264,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10264),U_10265))
      | ~ class_Orderings_Olinorder(U_10264) ),
    inference(variable_rename,[status(thm)],[f_2744_1]) ).

fof(f_2744_3,plain,
    ! [U_10264,U_10265,U_10266] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10264,hAPP(hAPP(c_Set_Oinsert(U_10264),U_10266),U_10265)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10264),U_10266),c_Big__Operators_Olinorder__class_OMin(U_10264,U_10265))
      | U_10265 = c_Orderings_Obot__class_Obot(tc_fun(U_10264,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10264),U_10265))
      | ~ class_Orderings_Olinorder(U_10264) ),
    inference(definitional_conversion,[status(esa)],[f_2744_2]) ).

cnf(f_2744_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10264,hAPP(hAPP(c_Set_Oinsert(U_10264),U_10266),U_10265)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10264),U_10266),c_Big__Operators_Olinorder__class_OMin(U_10264,U_10265))
    | U_10265 = c_Orderings_Obot__class_Obot(tc_fun(U_10264,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10264),U_10265))
    | ~ class_Orderings_Olinorder(U_10264) ),
    inference(clausify,[status(thm)],[f_2744_3]) ).

fof(f_2745_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_2745_2,plain,
    ! [U_10269,U_10268,U_10267] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10267),c_Big__Operators_Olinorder__class_OMin(U_10267,U_10269)),c_Big__Operators_Olinorder__class_OMin(U_10267,U_10268)) = c_Big__Operators_Olinorder__class_OMin(U_10267,U_10268)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10267,tc_HOL_Obool)),U_10269),U_10268))
      | U_10269 = c_Orderings_Obot__class_Obot(tc_fun(U_10267,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10267),U_10268))
      | ~ class_Orderings_Olinorder(U_10267) ),
    inference(variable_rename,[status(thm)],[f_2745_1]) ).

fof(f_2745_3,plain,
    ! [U_10267,U_10268,U_10269] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10267),c_Big__Operators_Olinorder__class_OMin(U_10267,U_10269)),c_Big__Operators_Olinorder__class_OMin(U_10267,U_10268)) = c_Big__Operators_Olinorder__class_OMin(U_10267,U_10268)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10267,tc_HOL_Obool)),U_10269),U_10268))
      | U_10269 = c_Orderings_Obot__class_Obot(tc_fun(U_10267,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10267),U_10268))
      | ~ class_Orderings_Olinorder(U_10267) ),
    inference(definitional_conversion,[status(esa)],[f_2745_2]) ).

cnf(f_2745_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10267),c_Big__Operators_Olinorder__class_OMin(U_10267,U_10269)),c_Big__Operators_Olinorder__class_OMin(U_10267,U_10268)) = c_Big__Operators_Olinorder__class_OMin(U_10267,U_10268)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10267,tc_HOL_Obool)),U_10269),U_10268))
    | U_10269 = c_Orderings_Obot__class_Obot(tc_fun(U_10267,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10267),U_10268))
    | ~ class_Orderings_Olinorder(U_10267) ),
    inference(clausify,[status(thm)],[f_2745_3]) ).

fof(f_2746_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_2746_2,plain,
    ! [U_10272,U_10271,U_10270] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10270,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10270,tc_HOL_Obool)),U_10271),U_10272)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10270),c_Big__Operators_Olinorder__class_OMin(U_10270,U_10271)),c_Big__Operators_Olinorder__class_OMin(U_10270,U_10272))
      | U_10272 = c_Orderings_Obot__class_Obot(tc_fun(U_10270,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10270),U_10272))
      | U_10271 = c_Orderings_Obot__class_Obot(tc_fun(U_10270,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10270),U_10271))
      | ~ class_Orderings_Olinorder(U_10270) ),
    inference(variable_rename,[status(thm)],[f_2746_1]) ).

fof(f_2746_3,plain,
    ! [U_10271,U_10270,U_10272] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10270,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10270,tc_HOL_Obool)),U_10271),U_10272)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10270),c_Big__Operators_Olinorder__class_OMin(U_10270,U_10271)),c_Big__Operators_Olinorder__class_OMin(U_10270,U_10272))
      | U_10272 = c_Orderings_Obot__class_Obot(tc_fun(U_10270,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10270),U_10272))
      | U_10271 = c_Orderings_Obot__class_Obot(tc_fun(U_10270,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10270),U_10271))
      | ~ class_Orderings_Olinorder(U_10270) ),
    inference(definitional_conversion,[status(esa)],[f_2746_2]) ).

cnf(f_2746_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10270,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10270,tc_HOL_Obool)),U_10271),U_10272)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10270),c_Big__Operators_Olinorder__class_OMin(U_10270,U_10271)),c_Big__Operators_Olinorder__class_OMin(U_10270,U_10272))
    | U_10272 = c_Orderings_Obot__class_Obot(tc_fun(U_10270,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10270),U_10272))
    | U_10271 = c_Orderings_Obot__class_Obot(tc_fun(U_10270,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10270),U_10271))
    | ~ class_Orderings_Olinorder(U_10270) ),
    inference(clausify,[status(thm)],[f_2746_3]) ).

fof(f_2747_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_2747_2,plain,
    ! [U_10275,U_10274,U_10273] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10273,hAPP(hAPP(c_Set_Oinsert(U_10273),U_10275),U_10274)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10273),U_10275),c_Big__Operators_Olinorder__class_OMin(U_10273,U_10274))
      | U_10274 = c_Orderings_Obot__class_Obot(tc_fun(U_10273,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10273),U_10275),U_10274))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10273),U_10274))
      | ~ class_Orderings_Olinorder(U_10273) ),
    inference(variable_rename,[status(thm)],[f_2747_1]) ).

fof(f_2747_3,plain,
    ! [U_10275,U_10274,U_10273] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10273,hAPP(hAPP(c_Set_Oinsert(U_10273),U_10275),U_10274)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10273),U_10275),c_Big__Operators_Olinorder__class_OMin(U_10273,U_10274))
      | U_10274 = c_Orderings_Obot__class_Obot(tc_fun(U_10273,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10273),U_10275),U_10274))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10273),U_10274))
      | ~ class_Orderings_Olinorder(U_10273) ),
    inference(definitional_conversion,[status(esa)],[f_2747_2]) ).

cnf(f_2747_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10273,hAPP(hAPP(c_Set_Oinsert(U_10273),U_10275),U_10274)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10273),U_10275),c_Big__Operators_Olinorder__class_OMin(U_10273,U_10274))
    | U_10274 = c_Orderings_Obot__class_Obot(tc_fun(U_10273,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_10273),U_10275),U_10274))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10273),U_10274))
    | ~ class_Orderings_Olinorder(U_10273) ),
    inference(clausify,[status(thm)],[f_2747_3]) ).

fof(f_2748_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_2748_2,plain,
    ! [U_10278,U_10277,U_10276] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(U_10276,hAPP(hAPP(c_Set_Oinsert(U_10276),U_10278),U_10277)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10276),U_10278),c_Big__Operators_Olinorder__class_OMin(U_10276,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10276,tc_HOL_Obool)),U_10277),hAPP(hAPP(c_Set_Oinsert(U_10276),U_10278),c_Orderings_Obot__class_Obot(tc_fun(U_10276,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10276,tc_HOL_Obool)),U_10277),hAPP(hAPP(c_Set_Oinsert(U_10276),U_10278),c_Orderings_Obot__class_Obot(tc_fun(U_10276,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10276,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(U_10276,hAPP(hAPP(c_Set_Oinsert(U_10276),U_10278),U_10277)) = U_10278
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10276,tc_HOL_Obool)),U_10277),hAPP(hAPP(c_Set_Oinsert(U_10276),U_10278),c_Orderings_Obot__class_Obot(tc_fun(U_10276,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10276,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10276),U_10277))
      | ~ class_Orderings_Olinorder(U_10276) ),
    inference(variable_rename,[status(thm)],[f_2748_1]) ).

fof(f_2748_3,plain,
    ( ! [U_10276,U_10277,U_10278] :
        ( c_Big__Operators_Olinorder__class_OMin(U_10276,hAPP(hAPP(c_Set_Oinsert(U_10276),U_10278),U_10277)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10276),U_10278),c_Big__Operators_Olinorder__class_OMin(U_10276,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10276,tc_HOL_Obool)),U_10277),hAPP(hAPP(c_Set_Oinsert(U_10276),U_10278),c_Orderings_Obot__class_Obot(tc_fun(U_10276,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10276,tc_HOL_Obool)),U_10277),hAPP(hAPP(c_Set_Oinsert(U_10276),U_10278),c_Orderings_Obot__class_Obot(tc_fun(U_10276,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10276,tc_HOL_Obool))
        | ~ sP787(U_10276,U_10277,U_10278) )
    & ! [U_10276,U_10277,U_10278] :
        ( c_Big__Operators_Olinorder__class_OMin(U_10276,hAPP(hAPP(c_Set_Oinsert(U_10276),U_10278),U_10277)) = U_10278
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10276,tc_HOL_Obool)),U_10277),hAPP(hAPP(c_Set_Oinsert(U_10276),U_10278),c_Orderings_Obot__class_Obot(tc_fun(U_10276,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10276,tc_HOL_Obool))
        | ~ sP787(U_10276,U_10277,U_10278) )
    & ! [U_10276,U_10277,U_10278] :
        ( sP787(U_10276,U_10277,U_10278)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10276),U_10277))
        | ~ class_Orderings_Olinorder(U_10276) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP787])],[f_2748_2]) ).

cnf(f_2748_4,plain,
    ( sP787(U_10276,U_10277,U_10278)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10276),U_10277))
    | ~ class_Orderings_Olinorder(U_10276) ),
    inference(clausify,[status(thm)],[f_2748_3]) ).

cnf(f_2748_5,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10276,hAPP(hAPP(c_Set_Oinsert(U_10276),U_10278),U_10277)) = U_10278
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10276,tc_HOL_Obool)),U_10277),hAPP(hAPP(c_Set_Oinsert(U_10276),U_10278),c_Orderings_Obot__class_Obot(tc_fun(U_10276,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10276,tc_HOL_Obool))
    | ~ sP787(U_10276,U_10277,U_10278) ),
    inference(clausify,[status(thm)],[f_2748_3]) ).

cnf(f_2748_6,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10276,hAPP(hAPP(c_Set_Oinsert(U_10276),U_10278),U_10277)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10276),U_10278),c_Big__Operators_Olinorder__class_OMin(U_10276,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10276,tc_HOL_Obool)),U_10277),hAPP(hAPP(c_Set_Oinsert(U_10276),U_10278),c_Orderings_Obot__class_Obot(tc_fun(U_10276,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10276,tc_HOL_Obool)),U_10277),hAPP(hAPP(c_Set_Oinsert(U_10276),U_10278),c_Orderings_Obot__class_Obot(tc_fun(U_10276,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10276,tc_HOL_Obool))
    | ~ sP787(U_10276,U_10277,U_10278) ),
    inference(clausify,[status(thm)],[f_2748_3]) ).

fof(f_2749_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_2749_2,plain,
    ! [U_10281,U_10280,U_10279] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10279),c_Big__Operators_Olinorder__class_OMin(U_10279,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10279,tc_HOL_Obool)),U_10280),U_10281))),c_Big__Operators_Olinorder__class_OMin(U_10279,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10279,tc_HOL_Obool)),U_10280),U_10281))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10279),c_Big__Operators_Olinorder__class_OMin(U_10279,U_10280)),c_Big__Operators_Olinorder__class_OMin(U_10279,U_10281))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10279,tc_HOL_Obool)),U_10280),U_10281) = c_Orderings_Obot__class_Obot(tc_fun(U_10279,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10279),U_10281))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10279),U_10280))
      | ~ class_Orderings_Olinorder(U_10279) ),
    inference(variable_rename,[status(thm)],[f_2749_1]) ).

fof(f_2749_3,plain,
    ! [U_10279,U_10281,U_10280] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10279),c_Big__Operators_Olinorder__class_OMin(U_10279,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10279,tc_HOL_Obool)),U_10280),U_10281))),c_Big__Operators_Olinorder__class_OMin(U_10279,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10279,tc_HOL_Obool)),U_10280),U_10281))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10279),c_Big__Operators_Olinorder__class_OMin(U_10279,U_10280)),c_Big__Operators_Olinorder__class_OMin(U_10279,U_10281))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10279,tc_HOL_Obool)),U_10280),U_10281) = c_Orderings_Obot__class_Obot(tc_fun(U_10279,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10279),U_10281))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10279),U_10280))
      | ~ class_Orderings_Olinorder(U_10279) ),
    inference(definitional_conversion,[status(esa)],[f_2749_2]) ).

cnf(f_2749_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10279),c_Big__Operators_Olinorder__class_OMin(U_10279,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10279,tc_HOL_Obool)),U_10280),U_10281))),c_Big__Operators_Olinorder__class_OMin(U_10279,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10279,tc_HOL_Obool)),U_10280),U_10281))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10279),c_Big__Operators_Olinorder__class_OMin(U_10279,U_10280)),c_Big__Operators_Olinorder__class_OMin(U_10279,U_10281))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10279,tc_HOL_Obool)),U_10280),U_10281) = c_Orderings_Obot__class_Obot(tc_fun(U_10279,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10279),U_10281))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10279),U_10280))
    | ~ class_Orderings_Olinorder(U_10279) ),
    inference(clausify,[status(thm)],[f_2749_3]) ).

fof(f_2750_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_2750_2,plain,
    ! [U_10284,U_10283,U_10282] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10282,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10282,tc_HOL_Obool)),U_10283),U_10284)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10282),c_Big__Operators_Olinorder__class_OMin(U_10282,U_10283)),c_Big__Operators_Olinorder__class_OMin(U_10282,U_10284))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10282,tc_HOL_Obool)),U_10283),U_10284) != c_Orderings_Obot__class_Obot(tc_fun(U_10282,tc_HOL_Obool))
      | U_10284 = c_Orderings_Obot__class_Obot(tc_fun(U_10282,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10282),U_10284))
      | U_10283 = c_Orderings_Obot__class_Obot(tc_fun(U_10282,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10282),U_10283))
      | ~ class_Orderings_Olinorder(U_10282) ),
    inference(variable_rename,[status(thm)],[f_2750_1]) ).

fof(f_2750_3,plain,
    ! [U_10282,U_10283,U_10284] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10282,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10282,tc_HOL_Obool)),U_10283),U_10284)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10282),c_Big__Operators_Olinorder__class_OMin(U_10282,U_10283)),c_Big__Operators_Olinorder__class_OMin(U_10282,U_10284))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10282,tc_HOL_Obool)),U_10283),U_10284) != c_Orderings_Obot__class_Obot(tc_fun(U_10282,tc_HOL_Obool))
      | U_10284 = c_Orderings_Obot__class_Obot(tc_fun(U_10282,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10282),U_10284))
      | U_10283 = c_Orderings_Obot__class_Obot(tc_fun(U_10282,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10282),U_10283))
      | ~ class_Orderings_Olinorder(U_10282) ),
    inference(definitional_conversion,[status(esa)],[f_2750_2]) ).

cnf(f_2750_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10282,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10282,tc_HOL_Obool)),U_10283),U_10284)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10282),c_Big__Operators_Olinorder__class_OMin(U_10282,U_10283)),c_Big__Operators_Olinorder__class_OMin(U_10282,U_10284))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10282,tc_HOL_Obool)),U_10283),U_10284) != c_Orderings_Obot__class_Obot(tc_fun(U_10282,tc_HOL_Obool))
    | U_10284 = c_Orderings_Obot__class_Obot(tc_fun(U_10282,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10282),U_10284))
    | U_10283 = c_Orderings_Obot__class_Obot(tc_fun(U_10282,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10282),U_10283))
    | ~ class_Orderings_Olinorder(U_10282) ),
    inference(clausify,[status(thm)],[f_2750_3]) ).

fof(f_2751_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_2751_2,plain,
    ! [U_10286,U_10285] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10285),c_Big__Operators_Olinorder__class_OMax(U_10285,U_10286)) = c_Big__Operators_Olinorder__class_OMin(U_10285,hAPP(c_Set_Oimage(U_10285,U_10285,c_Groups_Ouminus__class_Ouminus(U_10285)),U_10286))
      | U_10286 = c_Orderings_Obot__class_Obot(tc_fun(U_10285,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10285),U_10286))
      | ~ class_Groups_Olinordered__ab__group__add(U_10285) ),
    inference(variable_rename,[status(thm)],[f_2751_1]) ).

fof(f_2751_3,plain,
    ! [U_10286,U_10285] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10285),c_Big__Operators_Olinorder__class_OMax(U_10285,U_10286)) = c_Big__Operators_Olinorder__class_OMin(U_10285,hAPP(c_Set_Oimage(U_10285,U_10285,c_Groups_Ouminus__class_Ouminus(U_10285)),U_10286))
      | U_10286 = c_Orderings_Obot__class_Obot(tc_fun(U_10285,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10285),U_10286))
      | ~ class_Groups_Olinordered__ab__group__add(U_10285) ),
    inference(definitional_conversion,[status(esa)],[f_2751_2]) ).

cnf(f_2751_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10285),c_Big__Operators_Olinorder__class_OMax(U_10285,U_10286)) = c_Big__Operators_Olinorder__class_OMin(U_10285,hAPP(c_Set_Oimage(U_10285,U_10285,c_Groups_Ouminus__class_Ouminus(U_10285)),U_10286))
    | U_10286 = c_Orderings_Obot__class_Obot(tc_fun(U_10285,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10285),U_10286))
    | ~ class_Groups_Olinordered__ab__group__add(U_10285) ),
    inference(clausify,[status(thm)],[f_2751_3]) ).

fof(f_2752_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_2752_2,plain,
    ! [U_10288,U_10287] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10287),c_Big__Operators_Olinorder__class_OMin(U_10287,U_10288)) = c_Big__Operators_Olinorder__class_OMax(U_10287,hAPP(c_Set_Oimage(U_10287,U_10287,c_Groups_Ouminus__class_Ouminus(U_10287)),U_10288))
      | U_10288 = c_Orderings_Obot__class_Obot(tc_fun(U_10287,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10287),U_10288))
      | ~ class_Groups_Olinordered__ab__group__add(U_10287) ),
    inference(variable_rename,[status(thm)],[f_2752_1]) ).

fof(f_2752_3,plain,
    ! [U_10287,U_10288] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10287),c_Big__Operators_Olinorder__class_OMin(U_10287,U_10288)) = c_Big__Operators_Olinorder__class_OMax(U_10287,hAPP(c_Set_Oimage(U_10287,U_10287,c_Groups_Ouminus__class_Ouminus(U_10287)),U_10288))
      | U_10288 = c_Orderings_Obot__class_Obot(tc_fun(U_10287,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10287),U_10288))
      | ~ class_Groups_Olinordered__ab__group__add(U_10287) ),
    inference(definitional_conversion,[status(esa)],[f_2752_2]) ).

cnf(f_2752_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10287),c_Big__Operators_Olinorder__class_OMin(U_10287,U_10288)) = c_Big__Operators_Olinorder__class_OMax(U_10287,hAPP(c_Set_Oimage(U_10287,U_10287,c_Groups_Ouminus__class_Ouminus(U_10287)),U_10288))
    | U_10288 = c_Orderings_Obot__class_Obot(tc_fun(U_10287,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10287),U_10288))
    | ~ class_Groups_Olinordered__ab__group__add(U_10287) ),
    inference(clausify,[status(thm)],[f_2752_3]) ).

fof(f_2753_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_2753_2,plain,
    ! [U_10292,U_10291] :
      ( hBOOL(hAPP(hAPP(c_member(U_10291),c_Big__Operators_Olinorder__class_OMin(U_10291,U_10292)),U_10292))
      | ? [U_10290,U_10289] : ~ hBOOL(hAPP(hAPP(c_member(U_10291),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),U_10290),U_10289)),hAPP(hAPP(c_Set_Oinsert(U_10291),U_10290),hAPP(hAPP(c_Set_Oinsert(U_10291),U_10289),c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))))))
      | U_10292 = c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10291),U_10292))
      | ~ class_Orderings_Olinorder(U_10291) ),
    inference(variable_rename,[status(thm)],[f_2753_1]) ).

fof(f_2753_3,plain,
    ! [U_10292,U_10291] :
      ( hBOOL(hAPP(hAPP(c_member(U_10291),c_Big__Operators_Olinorder__class_OMin(U_10291,U_10292)),U_10292))
      | ? [U_10289] : ~ hBOOL(hAPP(hAPP(c_member(U_10291),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),sK154(U_10292,U_10291)),U_10289)),hAPP(hAPP(c_Set_Oinsert(U_10291),sK154(U_10292,U_10291)),hAPP(hAPP(c_Set_Oinsert(U_10291),U_10289),c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))))))
      | U_10292 = c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10291),U_10292))
      | ~ class_Orderings_Olinorder(U_10291) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_10290,sK154(U_10292,U_10291))],[f_2753_2]) ).

fof(f_2753_4,plain,
    ! [U_10292,U_10291] :
      ( hBOOL(hAPP(hAPP(c_member(U_10291),c_Big__Operators_Olinorder__class_OMin(U_10291,U_10292)),U_10292))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10291),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),sK154(U_10292,U_10291)),sK155(U_10292,U_10291))),hAPP(hAPP(c_Set_Oinsert(U_10291),sK154(U_10292,U_10291)),hAPP(hAPP(c_Set_Oinsert(U_10291),sK155(U_10292,U_10291)),c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))))))
      | U_10292 = c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10291),U_10292))
      | ~ class_Orderings_Olinorder(U_10291) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_10289,sK155(U_10292,U_10291))],[f_2753_3]) ).

fof(f_2753_5,plain,
    ! [U_10291,U_10292] :
      ( hBOOL(hAPP(hAPP(c_member(U_10291),c_Big__Operators_Olinorder__class_OMin(U_10291,U_10292)),U_10292))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10291),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),sK154(U_10292,U_10291)),sK155(U_10292,U_10291))),hAPP(hAPP(c_Set_Oinsert(U_10291),sK154(U_10292,U_10291)),hAPP(hAPP(c_Set_Oinsert(U_10291),sK155(U_10292,U_10291)),c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))))))
      | U_10292 = c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10291),U_10292))
      | ~ class_Orderings_Olinorder(U_10291) ),
    inference(definitional_conversion,[status(esa)],[f_2753_4]) ).

cnf(f_2753_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10291),c_Big__Operators_Olinorder__class_OMin(U_10291,U_10292)),U_10292))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10291),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),sK154(U_10292,U_10291)),sK155(U_10292,U_10291))),hAPP(hAPP(c_Set_Oinsert(U_10291),sK154(U_10292,U_10291)),hAPP(hAPP(c_Set_Oinsert(U_10291),sK155(U_10292,U_10291)),c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))))))
    | U_10292 = c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10291),U_10292))
    | ~ class_Orderings_Olinorder(U_10291) ),
    inference(clausify,[status(thm)],[f_2753_5]) ).

fof(f_2754_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_2754_2,plain,
    ! [U_10295,U_10294,U_10293] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(U_10293,c_Orderings_Oord__class_Omax(U_10293),U_10294) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10293),U_10295),c_Big__Operators_Olattice_OSup__fin(U_10293,c_Orderings_Oord__class_Omax(U_10293),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10293,tc_HOL_Obool)),U_10294),hAPP(hAPP(c_Set_Oinsert(U_10293),U_10295),c_Orderings_Obot__class_Obot(tc_fun(U_10293,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10293,tc_HOL_Obool)),U_10294),hAPP(hAPP(c_Set_Oinsert(U_10293),U_10295),c_Orderings_Obot__class_Obot(tc_fun(U_10293,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10293,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(U_10293,c_Orderings_Oord__class_Omax(U_10293),U_10294) = U_10295
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10293,tc_HOL_Obool)),U_10294),hAPP(hAPP(c_Set_Oinsert(U_10293),U_10295),c_Orderings_Obot__class_Obot(tc_fun(U_10293,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10293,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_10293),U_10295),U_10294))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10293),U_10294))
      | ~ class_Orderings_Olinorder(U_10293) ),
    inference(variable_rename,[status(thm)],[f_2754_1]) ).

fof(f_2754_3,plain,
    ( ! [U_10293,U_10294,U_10295] :
        ( c_Big__Operators_Olattice_OSup__fin(U_10293,c_Orderings_Oord__class_Omax(U_10293),U_10294) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10293),U_10295),c_Big__Operators_Olattice_OSup__fin(U_10293,c_Orderings_Oord__class_Omax(U_10293),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10293,tc_HOL_Obool)),U_10294),hAPP(hAPP(c_Set_Oinsert(U_10293),U_10295),c_Orderings_Obot__class_Obot(tc_fun(U_10293,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10293,tc_HOL_Obool)),U_10294),hAPP(hAPP(c_Set_Oinsert(U_10293),U_10295),c_Orderings_Obot__class_Obot(tc_fun(U_10293,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10293,tc_HOL_Obool))
        | ~ sP788(U_10293,U_10294,U_10295) )
    & ! [U_10293,U_10294,U_10295] :
        ( c_Big__Operators_Olattice_OSup__fin(U_10293,c_Orderings_Oord__class_Omax(U_10293),U_10294) = U_10295
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10293,tc_HOL_Obool)),U_10294),hAPP(hAPP(c_Set_Oinsert(U_10293),U_10295),c_Orderings_Obot__class_Obot(tc_fun(U_10293,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10293,tc_HOL_Obool))
        | ~ sP788(U_10293,U_10294,U_10295) )
    & ! [U_10293,U_10294,U_10295] :
        ( sP788(U_10293,U_10294,U_10295)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10293),U_10295),U_10294))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10293),U_10294))
        | ~ class_Orderings_Olinorder(U_10293) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP788])],[f_2754_2]) ).

cnf(f_2754_4,plain,
    ( sP788(U_10293,U_10294,U_10295)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10293),U_10295),U_10294))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10293),U_10294))
    | ~ class_Orderings_Olinorder(U_10293) ),
    inference(clausify,[status(thm)],[f_2754_3]) ).

cnf(f_2754_5,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_10293,c_Orderings_Oord__class_Omax(U_10293),U_10294) = U_10295
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10293,tc_HOL_Obool)),U_10294),hAPP(hAPP(c_Set_Oinsert(U_10293),U_10295),c_Orderings_Obot__class_Obot(tc_fun(U_10293,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10293,tc_HOL_Obool))
    | ~ sP788(U_10293,U_10294,U_10295) ),
    inference(clausify,[status(thm)],[f_2754_3]) ).

cnf(f_2754_6,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_10293,c_Orderings_Oord__class_Omax(U_10293),U_10294) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10293),U_10295),c_Big__Operators_Olattice_OSup__fin(U_10293,c_Orderings_Oord__class_Omax(U_10293),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10293,tc_HOL_Obool)),U_10294),hAPP(hAPP(c_Set_Oinsert(U_10293),U_10295),c_Orderings_Obot__class_Obot(tc_fun(U_10293,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10293,tc_HOL_Obool)),U_10294),hAPP(hAPP(c_Set_Oinsert(U_10293),U_10295),c_Orderings_Obot__class_Obot(tc_fun(U_10293,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10293,tc_HOL_Obool))
    | ~ sP788(U_10293,U_10294,U_10295) ),
    inference(clausify,[status(thm)],[f_2754_3]) ).

fof(f_2755_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_2755_2,plain,
    ! [U_10298,U_10297,U_10296] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(U_10296,c_Orderings_Oord__class_Omin(U_10296),U_10297) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10296),U_10298),c_Big__Operators_Olattice_OInf__fin(U_10296,c_Orderings_Oord__class_Omin(U_10296),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10296,tc_HOL_Obool)),U_10297),hAPP(hAPP(c_Set_Oinsert(U_10296),U_10298),c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10296,tc_HOL_Obool)),U_10297),hAPP(hAPP(c_Set_Oinsert(U_10296),U_10298),c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(U_10296,c_Orderings_Oord__class_Omin(U_10296),U_10297) = U_10298
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10296,tc_HOL_Obool)),U_10297),hAPP(hAPP(c_Set_Oinsert(U_10296),U_10298),c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_10296),U_10298),U_10297))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10296),U_10297))
      | ~ class_Orderings_Olinorder(U_10296) ),
    inference(variable_rename,[status(thm)],[f_2755_1]) ).

fof(f_2755_3,plain,
    ( ! [U_10297,U_10298,U_10296] :
        ( c_Big__Operators_Olattice_OInf__fin(U_10296,c_Orderings_Oord__class_Omin(U_10296),U_10297) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10296),U_10298),c_Big__Operators_Olattice_OInf__fin(U_10296,c_Orderings_Oord__class_Omin(U_10296),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10296,tc_HOL_Obool)),U_10297),hAPP(hAPP(c_Set_Oinsert(U_10296),U_10298),c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10296,tc_HOL_Obool)),U_10297),hAPP(hAPP(c_Set_Oinsert(U_10296),U_10298),c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool))
        | ~ sP789(U_10297,U_10298,U_10296) )
    & ! [U_10297,U_10298,U_10296] :
        ( c_Big__Operators_Olattice_OInf__fin(U_10296,c_Orderings_Oord__class_Omin(U_10296),U_10297) = U_10298
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10296,tc_HOL_Obool)),U_10297),hAPP(hAPP(c_Set_Oinsert(U_10296),U_10298),c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool))
        | ~ sP789(U_10297,U_10298,U_10296) )
    & ! [U_10297,U_10298,U_10296] :
        ( sP789(U_10297,U_10298,U_10296)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10296),U_10298),U_10297))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10296),U_10297))
        | ~ class_Orderings_Olinorder(U_10296) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP789])],[f_2755_2]) ).

cnf(f_2755_4,plain,
    ( sP789(U_10297,U_10298,U_10296)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10296),U_10298),U_10297))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10296),U_10297))
    | ~ class_Orderings_Olinorder(U_10296) ),
    inference(clausify,[status(thm)],[f_2755_3]) ).

cnf(f_2755_5,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_10296,c_Orderings_Oord__class_Omin(U_10296),U_10297) = U_10298
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10296,tc_HOL_Obool)),U_10297),hAPP(hAPP(c_Set_Oinsert(U_10296),U_10298),c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool))
    | ~ sP789(U_10297,U_10298,U_10296) ),
    inference(clausify,[status(thm)],[f_2755_3]) ).

cnf(f_2755_6,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_10296,c_Orderings_Oord__class_Omin(U_10296),U_10297) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10296),U_10298),c_Big__Operators_Olattice_OInf__fin(U_10296,c_Orderings_Oord__class_Omin(U_10296),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10296,tc_HOL_Obool)),U_10297),hAPP(hAPP(c_Set_Oinsert(U_10296),U_10298),c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10296,tc_HOL_Obool)),U_10297),hAPP(hAPP(c_Set_Oinsert(U_10296),U_10298),c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10296,tc_HOL_Obool))
    | ~ sP789(U_10297,U_10298,U_10296) ),
    inference(clausify,[status(thm)],[f_2755_3]) ).

fof(f_2756_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_2756_2,plain,
    ! [U_10300,U_10299] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10299),c_Big__Operators_Olattice_OInf__fin(U_10299,c_Orderings_Oord__class_Omin(U_10299),U_10300)),c_Big__Operators_Olattice_OSup__fin(U_10299,c_Orderings_Oord__class_Omax(U_10299),U_10300)))
      | U_10300 = c_Orderings_Obot__class_Obot(tc_fun(U_10299,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10299),U_10300))
      | ~ class_Orderings_Olinorder(U_10299) ),
    inference(variable_rename,[status(thm)],[f_2756_1]) ).

fof(f_2756_3,plain,
    ! [U_10300,U_10299] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10299),c_Big__Operators_Olattice_OInf__fin(U_10299,c_Orderings_Oord__class_Omin(U_10299),U_10300)),c_Big__Operators_Olattice_OSup__fin(U_10299,c_Orderings_Oord__class_Omax(U_10299),U_10300)))
      | U_10300 = c_Orderings_Obot__class_Obot(tc_fun(U_10299,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10299),U_10300))
      | ~ class_Orderings_Olinorder(U_10299) ),
    inference(definitional_conversion,[status(esa)],[f_2756_2]) ).

cnf(f_2756_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10299),c_Big__Operators_Olattice_OInf__fin(U_10299,c_Orderings_Oord__class_Omin(U_10299),U_10300)),c_Big__Operators_Olattice_OSup__fin(U_10299,c_Orderings_Oord__class_Omax(U_10299),U_10300)))
    | U_10300 = c_Orderings_Obot__class_Obot(tc_fun(U_10299,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10299),U_10300))
    | ~ class_Orderings_Olinorder(U_10299) ),
    inference(clausify,[status(thm)],[f_2756_3]) ).

fof(f_2757_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_2757_2,plain,
    ! [U_10303,U_10302,U_10301] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10301),U_10303),c_Big__Operators_Olattice_OInf__fin(U_10301,c_Orderings_Oord__class_Omin(U_10301),U_10302)) = c_Big__Operators_Olattice_OInf__fin(U_10301,c_Orderings_Oord__class_Omin(U_10301),U_10302)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10301),U_10303),U_10302))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10301),U_10302))
      | ~ class_Orderings_Olinorder(U_10301) ),
    inference(variable_rename,[status(thm)],[f_2757_1]) ).

fof(f_2757_3,plain,
    ! [U_10301,U_10302,U_10303] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10301),U_10303),c_Big__Operators_Olattice_OInf__fin(U_10301,c_Orderings_Oord__class_Omin(U_10301),U_10302)) = c_Big__Operators_Olattice_OInf__fin(U_10301,c_Orderings_Oord__class_Omin(U_10301),U_10302)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10301),U_10303),U_10302))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10301),U_10302))
      | ~ class_Orderings_Olinorder(U_10301) ),
    inference(definitional_conversion,[status(esa)],[f_2757_2]) ).

cnf(f_2757_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10301),U_10303),c_Big__Operators_Olattice_OInf__fin(U_10301,c_Orderings_Oord__class_Omin(U_10301),U_10302)) = c_Big__Operators_Olattice_OInf__fin(U_10301,c_Orderings_Oord__class_Omin(U_10301),U_10302)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10301),U_10303),U_10302))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10301),U_10302))
    | ~ class_Orderings_Olinorder(U_10301) ),
    inference(clausify,[status(thm)],[f_2757_3]) ).

fof(f_2758_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_2758_2,plain,
    ! [U_10306,U_10305,U_10304] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10304),U_10306),c_Big__Operators_Olattice_OSup__fin(U_10304,c_Orderings_Oord__class_Omax(U_10304),U_10305)) = c_Big__Operators_Olattice_OSup__fin(U_10304,c_Orderings_Oord__class_Omax(U_10304),U_10305)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10304),U_10306),U_10305))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10304),U_10305))
      | ~ class_Orderings_Olinorder(U_10304) ),
    inference(variable_rename,[status(thm)],[f_2758_1]) ).

fof(f_2758_3,plain,
    ! [U_10305,U_10304,U_10306] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10304),U_10306),c_Big__Operators_Olattice_OSup__fin(U_10304,c_Orderings_Oord__class_Omax(U_10304),U_10305)) = c_Big__Operators_Olattice_OSup__fin(U_10304,c_Orderings_Oord__class_Omax(U_10304),U_10305)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10304),U_10306),U_10305))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10304),U_10305))
      | ~ class_Orderings_Olinorder(U_10304) ),
    inference(definitional_conversion,[status(esa)],[f_2758_2]) ).

cnf(f_2758_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10304),U_10306),c_Big__Operators_Olattice_OSup__fin(U_10304,c_Orderings_Oord__class_Omax(U_10304),U_10305)) = c_Big__Operators_Olattice_OSup__fin(U_10304,c_Orderings_Oord__class_Omax(U_10304),U_10305)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10304),U_10306),U_10305))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10304),U_10305))
    | ~ class_Orderings_Olinorder(U_10304) ),
    inference(clausify,[status(thm)],[f_2758_3]) ).

fof(f_2759_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_2759_2,plain,
    ! [U_10308,U_10307] :
      ( c_Big__Operators_Olattice_OInf__fin(U_10307,c_Orderings_Oord__class_Omin(U_10307),hAPP(hAPP(c_Set_Oinsert(U_10307),U_10308),c_Orderings_Obot__class_Obot(tc_fun(U_10307,tc_HOL_Obool)))) = U_10308
      | ~ class_Orderings_Olinorder(U_10307) ),
    inference(variable_rename,[status(thm)],[f_2759_1]) ).

fof(f_2759_3,plain,
    ! [U_10307,U_10308] :
      ( c_Big__Operators_Olattice_OInf__fin(U_10307,c_Orderings_Oord__class_Omin(U_10307),hAPP(hAPP(c_Set_Oinsert(U_10307),U_10308),c_Orderings_Obot__class_Obot(tc_fun(U_10307,tc_HOL_Obool)))) = U_10308
      | ~ class_Orderings_Olinorder(U_10307) ),
    inference(definitional_conversion,[status(esa)],[f_2759_2]) ).

cnf(f_2759_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_10307,c_Orderings_Oord__class_Omin(U_10307),hAPP(hAPP(c_Set_Oinsert(U_10307),U_10308),c_Orderings_Obot__class_Obot(tc_fun(U_10307,tc_HOL_Obool)))) = U_10308
    | ~ class_Orderings_Olinorder(U_10307) ),
    inference(clausify,[status(thm)],[f_2759_3]) ).

fof(f_2760_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_2760_2,plain,
    ! [U_10310,U_10309] :
      ( c_Big__Operators_Olattice_OSup__fin(U_10309,c_Orderings_Oord__class_Omax(U_10309),hAPP(hAPP(c_Set_Oinsert(U_10309),U_10310),c_Orderings_Obot__class_Obot(tc_fun(U_10309,tc_HOL_Obool)))) = U_10310
      | ~ class_Orderings_Olinorder(U_10309) ),
    inference(variable_rename,[status(thm)],[f_2760_1]) ).

fof(f_2760_3,plain,
    ! [U_10309,U_10310] :
      ( c_Big__Operators_Olattice_OSup__fin(U_10309,c_Orderings_Oord__class_Omax(U_10309),hAPP(hAPP(c_Set_Oinsert(U_10309),U_10310),c_Orderings_Obot__class_Obot(tc_fun(U_10309,tc_HOL_Obool)))) = U_10310
      | ~ class_Orderings_Olinorder(U_10309) ),
    inference(definitional_conversion,[status(esa)],[f_2760_2]) ).

cnf(f_2760_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_10309,c_Orderings_Oord__class_Omax(U_10309),hAPP(hAPP(c_Set_Oinsert(U_10309),U_10310),c_Orderings_Obot__class_Obot(tc_fun(U_10309,tc_HOL_Obool)))) = U_10310
    | ~ class_Orderings_Olinorder(U_10309) ),
    inference(clausify,[status(thm)],[f_2760_3]) ).

fof(f_2761_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_2761_2,plain,
    ! [U_10313,U_10312,U_10311] :
      ( c_Big__Operators_Olattice_OInf__fin(U_10311,c_Orderings_Oord__class_Omin(U_10311),hAPP(hAPP(c_Set_Oinsert(U_10311),U_10313),U_10312)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10311),U_10313),c_Big__Operators_Olattice_OInf__fin(U_10311,c_Orderings_Oord__class_Omin(U_10311),U_10312))
      | U_10312 = c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10311),U_10312))
      | ~ class_Orderings_Olinorder(U_10311) ),
    inference(variable_rename,[status(thm)],[f_2761_1]) ).

fof(f_2761_3,plain,
    ! [U_10311,U_10312,U_10313] :
      ( c_Big__Operators_Olattice_OInf__fin(U_10311,c_Orderings_Oord__class_Omin(U_10311),hAPP(hAPP(c_Set_Oinsert(U_10311),U_10313),U_10312)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10311),U_10313),c_Big__Operators_Olattice_OInf__fin(U_10311,c_Orderings_Oord__class_Omin(U_10311),U_10312))
      | U_10312 = c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10311),U_10312))
      | ~ class_Orderings_Olinorder(U_10311) ),
    inference(definitional_conversion,[status(esa)],[f_2761_2]) ).

cnf(f_2761_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_10311,c_Orderings_Oord__class_Omin(U_10311),hAPP(hAPP(c_Set_Oinsert(U_10311),U_10313),U_10312)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10311),U_10313),c_Big__Operators_Olattice_OInf__fin(U_10311,c_Orderings_Oord__class_Omin(U_10311),U_10312))
    | U_10312 = c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10311),U_10312))
    | ~ class_Orderings_Olinorder(U_10311) ),
    inference(clausify,[status(thm)],[f_2761_3]) ).

fof(f_2762_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_2762_2,plain,
    ! [U_10316,U_10315,U_10314] :
      ( c_Big__Operators_Olattice_OSup__fin(U_10314,c_Orderings_Oord__class_Omax(U_10314),hAPP(hAPP(c_Set_Oinsert(U_10314),U_10316),U_10315)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10314),U_10316),c_Big__Operators_Olattice_OSup__fin(U_10314,c_Orderings_Oord__class_Omax(U_10314),U_10315))
      | U_10315 = c_Orderings_Obot__class_Obot(tc_fun(U_10314,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10314),U_10315))
      | ~ class_Orderings_Olinorder(U_10314) ),
    inference(variable_rename,[status(thm)],[f_2762_1]) ).

fof(f_2762_3,plain,
    ! [U_10314,U_10315,U_10316] :
      ( c_Big__Operators_Olattice_OSup__fin(U_10314,c_Orderings_Oord__class_Omax(U_10314),hAPP(hAPP(c_Set_Oinsert(U_10314),U_10316),U_10315)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10314),U_10316),c_Big__Operators_Olattice_OSup__fin(U_10314,c_Orderings_Oord__class_Omax(U_10314),U_10315))
      | U_10315 = c_Orderings_Obot__class_Obot(tc_fun(U_10314,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10314),U_10315))
      | ~ class_Orderings_Olinorder(U_10314) ),
    inference(definitional_conversion,[status(esa)],[f_2762_2]) ).

cnf(f_2762_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_10314,c_Orderings_Oord__class_Omax(U_10314),hAPP(hAPP(c_Set_Oinsert(U_10314),U_10316),U_10315)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10314),U_10316),c_Big__Operators_Olattice_OSup__fin(U_10314,c_Orderings_Oord__class_Omax(U_10314),U_10315))
    | U_10315 = c_Orderings_Obot__class_Obot(tc_fun(U_10314,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10314),U_10315))
    | ~ class_Orderings_Olinorder(U_10314) ),
    inference(clausify,[status(thm)],[f_2762_3]) ).

fof(f_2763_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_2763_2,plain,
    ! [U_10319,U_10318,U_10317] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10317),c_Big__Operators_Olattice_OInf__fin(U_10317,c_Orderings_Oord__class_Omin(U_10317),U_10319)),c_Big__Operators_Olattice_OInf__fin(U_10317,c_Orderings_Oord__class_Omin(U_10317),U_10318)) = c_Big__Operators_Olattice_OInf__fin(U_10317,c_Orderings_Oord__class_Omin(U_10317),U_10318)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10317,tc_HOL_Obool)),U_10319),U_10318))
      | U_10319 = c_Orderings_Obot__class_Obot(tc_fun(U_10317,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10317),U_10318))
      | ~ class_Orderings_Olinorder(U_10317) ),
    inference(variable_rename,[status(thm)],[f_2763_1]) ).

fof(f_2763_3,plain,
    ! [U_10318,U_10317,U_10319] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10317),c_Big__Operators_Olattice_OInf__fin(U_10317,c_Orderings_Oord__class_Omin(U_10317),U_10319)),c_Big__Operators_Olattice_OInf__fin(U_10317,c_Orderings_Oord__class_Omin(U_10317),U_10318)) = c_Big__Operators_Olattice_OInf__fin(U_10317,c_Orderings_Oord__class_Omin(U_10317),U_10318)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10317,tc_HOL_Obool)),U_10319),U_10318))
      | U_10319 = c_Orderings_Obot__class_Obot(tc_fun(U_10317,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10317),U_10318))
      | ~ class_Orderings_Olinorder(U_10317) ),
    inference(definitional_conversion,[status(esa)],[f_2763_2]) ).

cnf(f_2763_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10317),c_Big__Operators_Olattice_OInf__fin(U_10317,c_Orderings_Oord__class_Omin(U_10317),U_10319)),c_Big__Operators_Olattice_OInf__fin(U_10317,c_Orderings_Oord__class_Omin(U_10317),U_10318)) = c_Big__Operators_Olattice_OInf__fin(U_10317,c_Orderings_Oord__class_Omin(U_10317),U_10318)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10317,tc_HOL_Obool)),U_10319),U_10318))
    | U_10319 = c_Orderings_Obot__class_Obot(tc_fun(U_10317,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10317),U_10318))
    | ~ class_Orderings_Olinorder(U_10317) ),
    inference(clausify,[status(thm)],[f_2763_3]) ).

fof(f_2764_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_2764_2,plain,
    ! [U_10322,U_10321,U_10320] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10320),c_Big__Operators_Olattice_OSup__fin(U_10320,c_Orderings_Oord__class_Omax(U_10320),U_10322)),c_Big__Operators_Olattice_OSup__fin(U_10320,c_Orderings_Oord__class_Omax(U_10320),U_10321)) = c_Big__Operators_Olattice_OSup__fin(U_10320,c_Orderings_Oord__class_Omax(U_10320),U_10321)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10320,tc_HOL_Obool)),U_10322),U_10321))
      | U_10322 = c_Orderings_Obot__class_Obot(tc_fun(U_10320,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10320),U_10321))
      | ~ class_Orderings_Olinorder(U_10320) ),
    inference(variable_rename,[status(thm)],[f_2764_1]) ).

fof(f_2764_3,plain,
    ! [U_10320,U_10321,U_10322] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10320),c_Big__Operators_Olattice_OSup__fin(U_10320,c_Orderings_Oord__class_Omax(U_10320),U_10322)),c_Big__Operators_Olattice_OSup__fin(U_10320,c_Orderings_Oord__class_Omax(U_10320),U_10321)) = c_Big__Operators_Olattice_OSup__fin(U_10320,c_Orderings_Oord__class_Omax(U_10320),U_10321)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10320,tc_HOL_Obool)),U_10322),U_10321))
      | U_10322 = c_Orderings_Obot__class_Obot(tc_fun(U_10320,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10320),U_10321))
      | ~ class_Orderings_Olinorder(U_10320) ),
    inference(definitional_conversion,[status(esa)],[f_2764_2]) ).

cnf(f_2764_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10320),c_Big__Operators_Olattice_OSup__fin(U_10320,c_Orderings_Oord__class_Omax(U_10320),U_10322)),c_Big__Operators_Olattice_OSup__fin(U_10320,c_Orderings_Oord__class_Omax(U_10320),U_10321)) = c_Big__Operators_Olattice_OSup__fin(U_10320,c_Orderings_Oord__class_Omax(U_10320),U_10321)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10320,tc_HOL_Obool)),U_10322),U_10321))
    | U_10322 = c_Orderings_Obot__class_Obot(tc_fun(U_10320,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10320),U_10321))
    | ~ class_Orderings_Olinorder(U_10320) ),
    inference(clausify,[status(thm)],[f_2764_3]) ).

fof(f_2765_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_2765_2,plain,
    ! [U_10325,U_10324,U_10323] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10323),U_10325),c_Big__Operators_Olattice_OSup__fin(U_10323,c_Orderings_Oord__class_Omax(U_10323),U_10324)) = U_10325
      | ~ hBOOL(hAPP(hAPP(c_member(U_10323),U_10325),U_10324))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10323),U_10324))
      | ~ class_Orderings_Olinorder(U_10323) ),
    inference(variable_rename,[status(thm)],[f_2765_1]) ).

fof(f_2765_3,plain,
    ! [U_10325,U_10323,U_10324] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10323),U_10325),c_Big__Operators_Olattice_OSup__fin(U_10323,c_Orderings_Oord__class_Omax(U_10323),U_10324)) = U_10325
      | ~ hBOOL(hAPP(hAPP(c_member(U_10323),U_10325),U_10324))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10323),U_10324))
      | ~ class_Orderings_Olinorder(U_10323) ),
    inference(definitional_conversion,[status(esa)],[f_2765_2]) ).

cnf(f_2765_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10323),U_10325),c_Big__Operators_Olattice_OSup__fin(U_10323,c_Orderings_Oord__class_Omax(U_10323),U_10324)) = U_10325
    | ~ hBOOL(hAPP(hAPP(c_member(U_10323),U_10325),U_10324))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10323),U_10324))
    | ~ class_Orderings_Olinorder(U_10323) ),
    inference(clausify,[status(thm)],[f_2765_3]) ).

fof(f_2766_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_2766_2,plain,
    ! [U_10328,U_10327,U_10326] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10326),U_10328),c_Big__Operators_Olattice_OInf__fin(U_10326,c_Orderings_Oord__class_Omin(U_10326),U_10327)) = U_10328
      | ~ hBOOL(hAPP(hAPP(c_member(U_10326),U_10328),U_10327))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10326),U_10327))
      | ~ class_Orderings_Olinorder(U_10326) ),
    inference(variable_rename,[status(thm)],[f_2766_1]) ).

fof(f_2766_3,plain,
    ! [U_10326,U_10327,U_10328] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10326),U_10328),c_Big__Operators_Olattice_OInf__fin(U_10326,c_Orderings_Oord__class_Omin(U_10326),U_10327)) = U_10328
      | ~ hBOOL(hAPP(hAPP(c_member(U_10326),U_10328),U_10327))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10326),U_10327))
      | ~ class_Orderings_Olinorder(U_10326) ),
    inference(definitional_conversion,[status(esa)],[f_2766_2]) ).

cnf(f_2766_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10326),U_10328),c_Big__Operators_Olattice_OInf__fin(U_10326,c_Orderings_Oord__class_Omin(U_10326),U_10327)) = U_10328
    | ~ hBOOL(hAPP(hAPP(c_member(U_10326),U_10328),U_10327))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10326),U_10327))
    | ~ class_Orderings_Olinorder(U_10326) ),
    inference(clausify,[status(thm)],[f_2766_3]) ).

fof(f_2767_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_2767_2,plain,
    ! [U_10331,U_10330,U_10329] :
      ( c_Big__Operators_Olattice_OInf__fin(U_10329,c_Orderings_Oord__class_Omin(U_10329),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10329,tc_HOL_Obool)),U_10330),U_10331)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10329),c_Big__Operators_Olattice_OInf__fin(U_10329,c_Orderings_Oord__class_Omin(U_10329),U_10330)),c_Big__Operators_Olattice_OInf__fin(U_10329,c_Orderings_Oord__class_Omin(U_10329),U_10331))
      | U_10331 = c_Orderings_Obot__class_Obot(tc_fun(U_10329,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10329),U_10331))
      | U_10330 = c_Orderings_Obot__class_Obot(tc_fun(U_10329,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10329),U_10330))
      | ~ class_Orderings_Olinorder(U_10329) ),
    inference(variable_rename,[status(thm)],[f_2767_1]) ).

fof(f_2767_3,plain,
    ! [U_10330,U_10329,U_10331] :
      ( c_Big__Operators_Olattice_OInf__fin(U_10329,c_Orderings_Oord__class_Omin(U_10329),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10329,tc_HOL_Obool)),U_10330),U_10331)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10329),c_Big__Operators_Olattice_OInf__fin(U_10329,c_Orderings_Oord__class_Omin(U_10329),U_10330)),c_Big__Operators_Olattice_OInf__fin(U_10329,c_Orderings_Oord__class_Omin(U_10329),U_10331))
      | U_10331 = c_Orderings_Obot__class_Obot(tc_fun(U_10329,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10329),U_10331))
      | U_10330 = c_Orderings_Obot__class_Obot(tc_fun(U_10329,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10329),U_10330))
      | ~ class_Orderings_Olinorder(U_10329) ),
    inference(definitional_conversion,[status(esa)],[f_2767_2]) ).

cnf(f_2767_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_10329,c_Orderings_Oord__class_Omin(U_10329),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10329,tc_HOL_Obool)),U_10330),U_10331)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10329),c_Big__Operators_Olattice_OInf__fin(U_10329,c_Orderings_Oord__class_Omin(U_10329),U_10330)),c_Big__Operators_Olattice_OInf__fin(U_10329,c_Orderings_Oord__class_Omin(U_10329),U_10331))
    | U_10331 = c_Orderings_Obot__class_Obot(tc_fun(U_10329,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10329),U_10331))
    | U_10330 = c_Orderings_Obot__class_Obot(tc_fun(U_10329,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10329),U_10330))
    | ~ class_Orderings_Olinorder(U_10329) ),
    inference(clausify,[status(thm)],[f_2767_3]) ).

fof(f_2768_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_2768_2,plain,
    ! [U_10334,U_10333,U_10332] :
      ( c_Big__Operators_Olattice_OSup__fin(U_10332,c_Orderings_Oord__class_Omax(U_10332),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10332,tc_HOL_Obool)),U_10333),U_10334)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10332),c_Big__Operators_Olattice_OSup__fin(U_10332,c_Orderings_Oord__class_Omax(U_10332),U_10333)),c_Big__Operators_Olattice_OSup__fin(U_10332,c_Orderings_Oord__class_Omax(U_10332),U_10334))
      | U_10334 = c_Orderings_Obot__class_Obot(tc_fun(U_10332,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10332),U_10334))
      | U_10333 = c_Orderings_Obot__class_Obot(tc_fun(U_10332,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10332),U_10333))
      | ~ class_Orderings_Olinorder(U_10332) ),
    inference(variable_rename,[status(thm)],[f_2768_1]) ).

fof(f_2768_3,plain,
    ! [U_10332,U_10334,U_10333] :
      ( c_Big__Operators_Olattice_OSup__fin(U_10332,c_Orderings_Oord__class_Omax(U_10332),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10332,tc_HOL_Obool)),U_10333),U_10334)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10332),c_Big__Operators_Olattice_OSup__fin(U_10332,c_Orderings_Oord__class_Omax(U_10332),U_10333)),c_Big__Operators_Olattice_OSup__fin(U_10332,c_Orderings_Oord__class_Omax(U_10332),U_10334))
      | U_10334 = c_Orderings_Obot__class_Obot(tc_fun(U_10332,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10332),U_10334))
      | U_10333 = c_Orderings_Obot__class_Obot(tc_fun(U_10332,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10332),U_10333))
      | ~ class_Orderings_Olinorder(U_10332) ),
    inference(definitional_conversion,[status(esa)],[f_2768_2]) ).

cnf(f_2768_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_10332,c_Orderings_Oord__class_Omax(U_10332),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10332,tc_HOL_Obool)),U_10333),U_10334)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10332),c_Big__Operators_Olattice_OSup__fin(U_10332,c_Orderings_Oord__class_Omax(U_10332),U_10333)),c_Big__Operators_Olattice_OSup__fin(U_10332,c_Orderings_Oord__class_Omax(U_10332),U_10334))
    | U_10334 = c_Orderings_Obot__class_Obot(tc_fun(U_10332,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10332),U_10334))
    | U_10333 = c_Orderings_Obot__class_Obot(tc_fun(U_10332,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10332),U_10333))
    | ~ class_Orderings_Olinorder(U_10332) ),
    inference(clausify,[status(thm)],[f_2768_3]) ).

fof(f_2769_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_2769_2,plain,
    ! [U_10337,U_10336,U_10335] :
      ( c_Big__Operators_Olattice_OInf__fin(U_10335,c_Orderings_Oord__class_Omin(U_10335),hAPP(hAPP(c_Set_Oinsert(U_10335),U_10337),U_10336)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10335),U_10337),c_Big__Operators_Olattice_OInf__fin(U_10335,c_Orderings_Oord__class_Omin(U_10335),U_10336))
      | U_10336 = c_Orderings_Obot__class_Obot(tc_fun(U_10335,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10335),U_10337),U_10336))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10335),U_10336))
      | ~ class_Orderings_Olinorder(U_10335) ),
    inference(variable_rename,[status(thm)],[f_2769_1]) ).

fof(f_2769_3,plain,
    ! [U_10336,U_10337,U_10335] :
      ( c_Big__Operators_Olattice_OInf__fin(U_10335,c_Orderings_Oord__class_Omin(U_10335),hAPP(hAPP(c_Set_Oinsert(U_10335),U_10337),U_10336)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10335),U_10337),c_Big__Operators_Olattice_OInf__fin(U_10335,c_Orderings_Oord__class_Omin(U_10335),U_10336))
      | U_10336 = c_Orderings_Obot__class_Obot(tc_fun(U_10335,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10335),U_10337),U_10336))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10335),U_10336))
      | ~ class_Orderings_Olinorder(U_10335) ),
    inference(definitional_conversion,[status(esa)],[f_2769_2]) ).

cnf(f_2769_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_10335,c_Orderings_Oord__class_Omin(U_10335),hAPP(hAPP(c_Set_Oinsert(U_10335),U_10337),U_10336)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10335),U_10337),c_Big__Operators_Olattice_OInf__fin(U_10335,c_Orderings_Oord__class_Omin(U_10335),U_10336))
    | U_10336 = c_Orderings_Obot__class_Obot(tc_fun(U_10335,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_10335),U_10337),U_10336))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10335),U_10336))
    | ~ class_Orderings_Olinorder(U_10335) ),
    inference(clausify,[status(thm)],[f_2769_3]) ).

fof(f_2770_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_2770_2,plain,
    ! [U_10340,U_10339,U_10338] :
      ( c_Big__Operators_Olattice_OSup__fin(U_10338,c_Orderings_Oord__class_Omax(U_10338),hAPP(hAPP(c_Set_Oinsert(U_10338),U_10340),U_10339)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10338),U_10340),c_Big__Operators_Olattice_OSup__fin(U_10338,c_Orderings_Oord__class_Omax(U_10338),U_10339))
      | U_10339 = c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10338),U_10340),U_10339))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10338),U_10339))
      | ~ class_Orderings_Olinorder(U_10338) ),
    inference(variable_rename,[status(thm)],[f_2770_1]) ).

fof(f_2770_3,plain,
    ! [U_10339,U_10338,U_10340] :
      ( c_Big__Operators_Olattice_OSup__fin(U_10338,c_Orderings_Oord__class_Omax(U_10338),hAPP(hAPP(c_Set_Oinsert(U_10338),U_10340),U_10339)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10338),U_10340),c_Big__Operators_Olattice_OSup__fin(U_10338,c_Orderings_Oord__class_Omax(U_10338),U_10339))
      | U_10339 = c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10338),U_10340),U_10339))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10338),U_10339))
      | ~ class_Orderings_Olinorder(U_10338) ),
    inference(definitional_conversion,[status(esa)],[f_2770_2]) ).

cnf(f_2770_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_10338,c_Orderings_Oord__class_Omax(U_10338),hAPP(hAPP(c_Set_Oinsert(U_10338),U_10340),U_10339)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10338),U_10340),c_Big__Operators_Olattice_OSup__fin(U_10338,c_Orderings_Oord__class_Omax(U_10338),U_10339))
    | U_10339 = c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_10338),U_10340),U_10339))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10338),U_10339))
    | ~ class_Orderings_Olinorder(U_10338) ),
    inference(clausify,[status(thm)],[f_2770_3]) ).

fof(f_2771_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_2771_2,plain,
    ! [U_10343,U_10342,U_10341] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(U_10341,c_Orderings_Oord__class_Omin(U_10341),hAPP(hAPP(c_Set_Oinsert(U_10341),U_10343),U_10342)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10341),U_10343),c_Big__Operators_Olattice_OInf__fin(U_10341,c_Orderings_Oord__class_Omin(U_10341),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10341,tc_HOL_Obool)),U_10342),hAPP(hAPP(c_Set_Oinsert(U_10341),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10341,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10341,tc_HOL_Obool)),U_10342),hAPP(hAPP(c_Set_Oinsert(U_10341),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10341,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10341,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(U_10341,c_Orderings_Oord__class_Omin(U_10341),hAPP(hAPP(c_Set_Oinsert(U_10341),U_10343),U_10342)) = U_10343
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10341,tc_HOL_Obool)),U_10342),hAPP(hAPP(c_Set_Oinsert(U_10341),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10341,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10341,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10341),U_10342))
      | ~ class_Orderings_Olinorder(U_10341) ),
    inference(variable_rename,[status(thm)],[f_2771_1]) ).

fof(f_2771_3,plain,
    ( ! [U_10341,U_10342,U_10343] :
        ( c_Big__Operators_Olattice_OInf__fin(U_10341,c_Orderings_Oord__class_Omin(U_10341),hAPP(hAPP(c_Set_Oinsert(U_10341),U_10343),U_10342)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10341),U_10343),c_Big__Operators_Olattice_OInf__fin(U_10341,c_Orderings_Oord__class_Omin(U_10341),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10341,tc_HOL_Obool)),U_10342),hAPP(hAPP(c_Set_Oinsert(U_10341),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10341,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10341,tc_HOL_Obool)),U_10342),hAPP(hAPP(c_Set_Oinsert(U_10341),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10341,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10341,tc_HOL_Obool))
        | ~ sP790(U_10341,U_10342,U_10343) )
    & ! [U_10341,U_10342,U_10343] :
        ( c_Big__Operators_Olattice_OInf__fin(U_10341,c_Orderings_Oord__class_Omin(U_10341),hAPP(hAPP(c_Set_Oinsert(U_10341),U_10343),U_10342)) = U_10343
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10341,tc_HOL_Obool)),U_10342),hAPP(hAPP(c_Set_Oinsert(U_10341),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10341,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10341,tc_HOL_Obool))
        | ~ sP790(U_10341,U_10342,U_10343) )
    & ! [U_10341,U_10342,U_10343] :
        ( sP790(U_10341,U_10342,U_10343)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10341),U_10342))
        | ~ class_Orderings_Olinorder(U_10341) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP790])],[f_2771_2]) ).

cnf(f_2771_4,plain,
    ( sP790(U_10341,U_10342,U_10343)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10341),U_10342))
    | ~ class_Orderings_Olinorder(U_10341) ),
    inference(clausify,[status(thm)],[f_2771_3]) ).

cnf(f_2771_5,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_10341,c_Orderings_Oord__class_Omin(U_10341),hAPP(hAPP(c_Set_Oinsert(U_10341),U_10343),U_10342)) = U_10343
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10341,tc_HOL_Obool)),U_10342),hAPP(hAPP(c_Set_Oinsert(U_10341),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10341,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10341,tc_HOL_Obool))
    | ~ sP790(U_10341,U_10342,U_10343) ),
    inference(clausify,[status(thm)],[f_2771_3]) ).

cnf(f_2771_6,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_10341,c_Orderings_Oord__class_Omin(U_10341),hAPP(hAPP(c_Set_Oinsert(U_10341),U_10343),U_10342)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10341),U_10343),c_Big__Operators_Olattice_OInf__fin(U_10341,c_Orderings_Oord__class_Omin(U_10341),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10341,tc_HOL_Obool)),U_10342),hAPP(hAPP(c_Set_Oinsert(U_10341),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10341,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10341,tc_HOL_Obool)),U_10342),hAPP(hAPP(c_Set_Oinsert(U_10341),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10341,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10341,tc_HOL_Obool))
    | ~ sP790(U_10341,U_10342,U_10343) ),
    inference(clausify,[status(thm)],[f_2771_3]) ).

fof(f_2772_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_2772_2,plain,
    ! [U_10346,U_10345,U_10344] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(U_10344,c_Orderings_Oord__class_Omax(U_10344),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10346),U_10345)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10344),U_10346),c_Big__Operators_Olattice_OSup__fin(U_10344,c_Orderings_Oord__class_Omax(U_10344),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10344,tc_HOL_Obool)),U_10345),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10346),c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10344,tc_HOL_Obool)),U_10345),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10346),c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(U_10344,c_Orderings_Oord__class_Omax(U_10344),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10346),U_10345)) = U_10346
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10344,tc_HOL_Obool)),U_10345),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10346),c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10344),U_10345))
      | ~ class_Orderings_Olinorder(U_10344) ),
    inference(variable_rename,[status(thm)],[f_2772_1]) ).

fof(f_2772_3,plain,
    ( ! [U_10344,U_10345,U_10346] :
        ( c_Big__Operators_Olattice_OSup__fin(U_10344,c_Orderings_Oord__class_Omax(U_10344),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10346),U_10345)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10344),U_10346),c_Big__Operators_Olattice_OSup__fin(U_10344,c_Orderings_Oord__class_Omax(U_10344),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10344,tc_HOL_Obool)),U_10345),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10346),c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10344,tc_HOL_Obool)),U_10345),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10346),c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool))
        | ~ sP791(U_10344,U_10345,U_10346) )
    & ! [U_10344,U_10345,U_10346] :
        ( c_Big__Operators_Olattice_OSup__fin(U_10344,c_Orderings_Oord__class_Omax(U_10344),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10346),U_10345)) = U_10346
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10344,tc_HOL_Obool)),U_10345),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10346),c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool))
        | ~ sP791(U_10344,U_10345,U_10346) )
    & ! [U_10344,U_10345,U_10346] :
        ( sP791(U_10344,U_10345,U_10346)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10344),U_10345))
        | ~ class_Orderings_Olinorder(U_10344) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP791])],[f_2772_2]) ).

cnf(f_2772_4,plain,
    ( sP791(U_10344,U_10345,U_10346)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10344),U_10345))
    | ~ class_Orderings_Olinorder(U_10344) ),
    inference(clausify,[status(thm)],[f_2772_3]) ).

cnf(f_2772_5,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_10344,c_Orderings_Oord__class_Omax(U_10344),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10346),U_10345)) = U_10346
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10344,tc_HOL_Obool)),U_10345),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10346),c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool))
    | ~ sP791(U_10344,U_10345,U_10346) ),
    inference(clausify,[status(thm)],[f_2772_3]) ).

cnf(f_2772_6,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_10344,c_Orderings_Oord__class_Omax(U_10344),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10346),U_10345)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10344),U_10346),c_Big__Operators_Olattice_OSup__fin(U_10344,c_Orderings_Oord__class_Omax(U_10344),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10344,tc_HOL_Obool)),U_10345),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10346),c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10344,tc_HOL_Obool)),U_10345),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10346),c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool))
    | ~ sP791(U_10344,U_10345,U_10346) ),
    inference(clausify,[status(thm)],[f_2772_3]) ).

fof(f_2773_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_2773_2,plain,
    ! [U_10349,U_10348,U_10347] :
      ( c_Big__Operators_Olattice_OInf__fin(U_10347,c_Orderings_Oord__class_Omin(U_10347),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10347,tc_HOL_Obool)),U_10348),U_10349)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10347),c_Big__Operators_Olattice_OInf__fin(U_10347,c_Orderings_Oord__class_Omin(U_10347),U_10348)),c_Big__Operators_Olattice_OInf__fin(U_10347,c_Orderings_Oord__class_Omin(U_10347),U_10349))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10347,tc_HOL_Obool)),U_10348),U_10349) != c_Orderings_Obot__class_Obot(tc_fun(U_10347,tc_HOL_Obool))
      | U_10349 = c_Orderings_Obot__class_Obot(tc_fun(U_10347,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10347),U_10349))
      | U_10348 = c_Orderings_Obot__class_Obot(tc_fun(U_10347,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10347),U_10348))
      | ~ class_Orderings_Olinorder(U_10347) ),
    inference(variable_rename,[status(thm)],[f_2773_1]) ).

fof(f_2773_3,plain,
    ! [U_10348,U_10347,U_10349] :
      ( c_Big__Operators_Olattice_OInf__fin(U_10347,c_Orderings_Oord__class_Omin(U_10347),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10347,tc_HOL_Obool)),U_10348),U_10349)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10347),c_Big__Operators_Olattice_OInf__fin(U_10347,c_Orderings_Oord__class_Omin(U_10347),U_10348)),c_Big__Operators_Olattice_OInf__fin(U_10347,c_Orderings_Oord__class_Omin(U_10347),U_10349))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10347,tc_HOL_Obool)),U_10348),U_10349) != c_Orderings_Obot__class_Obot(tc_fun(U_10347,tc_HOL_Obool))
      | U_10349 = c_Orderings_Obot__class_Obot(tc_fun(U_10347,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10347),U_10349))
      | U_10348 = c_Orderings_Obot__class_Obot(tc_fun(U_10347,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10347),U_10348))
      | ~ class_Orderings_Olinorder(U_10347) ),
    inference(definitional_conversion,[status(esa)],[f_2773_2]) ).

cnf(f_2773_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_10347,c_Orderings_Oord__class_Omin(U_10347),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10347,tc_HOL_Obool)),U_10348),U_10349)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10347),c_Big__Operators_Olattice_OInf__fin(U_10347,c_Orderings_Oord__class_Omin(U_10347),U_10348)),c_Big__Operators_Olattice_OInf__fin(U_10347,c_Orderings_Oord__class_Omin(U_10347),U_10349))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10347,tc_HOL_Obool)),U_10348),U_10349) != c_Orderings_Obot__class_Obot(tc_fun(U_10347,tc_HOL_Obool))
    | U_10349 = c_Orderings_Obot__class_Obot(tc_fun(U_10347,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10347),U_10349))
    | U_10348 = c_Orderings_Obot__class_Obot(tc_fun(U_10347,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10347),U_10348))
    | ~ class_Orderings_Olinorder(U_10347) ),
    inference(clausify,[status(thm)],[f_2773_3]) ).

fof(f_2774_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_2774_2,plain,
    ! [U_10352,U_10351,U_10350] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10350),c_Big__Operators_Olattice_OInf__fin(U_10350,c_Orderings_Oord__class_Omin(U_10350),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10350,tc_HOL_Obool)),U_10351),U_10352))),c_Big__Operators_Olattice_OInf__fin(U_10350,c_Orderings_Oord__class_Omin(U_10350),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10350,tc_HOL_Obool)),U_10351),U_10352))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10350),c_Big__Operators_Olattice_OInf__fin(U_10350,c_Orderings_Oord__class_Omin(U_10350),U_10351)),c_Big__Operators_Olattice_OInf__fin(U_10350,c_Orderings_Oord__class_Omin(U_10350),U_10352))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10350,tc_HOL_Obool)),U_10351),U_10352) = c_Orderings_Obot__class_Obot(tc_fun(U_10350,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10350),U_10352))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10350),U_10351))
      | ~ class_Orderings_Olinorder(U_10350) ),
    inference(variable_rename,[status(thm)],[f_2774_1]) ).

fof(f_2774_3,plain,
    ! [U_10350,U_10351,U_10352] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10350),c_Big__Operators_Olattice_OInf__fin(U_10350,c_Orderings_Oord__class_Omin(U_10350),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10350,tc_HOL_Obool)),U_10351),U_10352))),c_Big__Operators_Olattice_OInf__fin(U_10350,c_Orderings_Oord__class_Omin(U_10350),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10350,tc_HOL_Obool)),U_10351),U_10352))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10350),c_Big__Operators_Olattice_OInf__fin(U_10350,c_Orderings_Oord__class_Omin(U_10350),U_10351)),c_Big__Operators_Olattice_OInf__fin(U_10350,c_Orderings_Oord__class_Omin(U_10350),U_10352))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10350,tc_HOL_Obool)),U_10351),U_10352) = c_Orderings_Obot__class_Obot(tc_fun(U_10350,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10350),U_10352))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10350),U_10351))
      | ~ class_Orderings_Olinorder(U_10350) ),
    inference(definitional_conversion,[status(esa)],[f_2774_2]) ).

cnf(f_2774_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10350),c_Big__Operators_Olattice_OInf__fin(U_10350,c_Orderings_Oord__class_Omin(U_10350),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10350,tc_HOL_Obool)),U_10351),U_10352))),c_Big__Operators_Olattice_OInf__fin(U_10350,c_Orderings_Oord__class_Omin(U_10350),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10350,tc_HOL_Obool)),U_10351),U_10352))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10350),c_Big__Operators_Olattice_OInf__fin(U_10350,c_Orderings_Oord__class_Omin(U_10350),U_10351)),c_Big__Operators_Olattice_OInf__fin(U_10350,c_Orderings_Oord__class_Omin(U_10350),U_10352))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10350,tc_HOL_Obool)),U_10351),U_10352) = c_Orderings_Obot__class_Obot(tc_fun(U_10350,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10350),U_10352))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10350),U_10351))
    | ~ class_Orderings_Olinorder(U_10350) ),
    inference(clausify,[status(thm)],[f_2774_3]) ).

fof(f_2775_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_2775_2,plain,
    ! [U_10355,U_10354,U_10353] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10353),c_Big__Operators_Olattice_OSup__fin(U_10353,c_Orderings_Oord__class_Omax(U_10353),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10353,tc_HOL_Obool)),U_10354),U_10355))),c_Big__Operators_Olattice_OSup__fin(U_10353,c_Orderings_Oord__class_Omax(U_10353),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10353,tc_HOL_Obool)),U_10354),U_10355))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10353),c_Big__Operators_Olattice_OSup__fin(U_10353,c_Orderings_Oord__class_Omax(U_10353),U_10354)),c_Big__Operators_Olattice_OSup__fin(U_10353,c_Orderings_Oord__class_Omax(U_10353),U_10355))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10353,tc_HOL_Obool)),U_10354),U_10355) = c_Orderings_Obot__class_Obot(tc_fun(U_10353,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10353),U_10355))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10353),U_10354))
      | ~ class_Orderings_Olinorder(U_10353) ),
    inference(variable_rename,[status(thm)],[f_2775_1]) ).

fof(f_2775_3,plain,
    ! [U_10354,U_10353,U_10355] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10353),c_Big__Operators_Olattice_OSup__fin(U_10353,c_Orderings_Oord__class_Omax(U_10353),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10353,tc_HOL_Obool)),U_10354),U_10355))),c_Big__Operators_Olattice_OSup__fin(U_10353,c_Orderings_Oord__class_Omax(U_10353),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10353,tc_HOL_Obool)),U_10354),U_10355))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10353),c_Big__Operators_Olattice_OSup__fin(U_10353,c_Orderings_Oord__class_Omax(U_10353),U_10354)),c_Big__Operators_Olattice_OSup__fin(U_10353,c_Orderings_Oord__class_Omax(U_10353),U_10355))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10353,tc_HOL_Obool)),U_10354),U_10355) = c_Orderings_Obot__class_Obot(tc_fun(U_10353,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10353),U_10355))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10353),U_10354))
      | ~ class_Orderings_Olinorder(U_10353) ),
    inference(definitional_conversion,[status(esa)],[f_2775_2]) ).

cnf(f_2775_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10353),c_Big__Operators_Olattice_OSup__fin(U_10353,c_Orderings_Oord__class_Omax(U_10353),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10353,tc_HOL_Obool)),U_10354),U_10355))),c_Big__Operators_Olattice_OSup__fin(U_10353,c_Orderings_Oord__class_Omax(U_10353),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10353,tc_HOL_Obool)),U_10354),U_10355))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10353),c_Big__Operators_Olattice_OSup__fin(U_10353,c_Orderings_Oord__class_Omax(U_10353),U_10354)),c_Big__Operators_Olattice_OSup__fin(U_10353,c_Orderings_Oord__class_Omax(U_10353),U_10355))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10353,tc_HOL_Obool)),U_10354),U_10355) = c_Orderings_Obot__class_Obot(tc_fun(U_10353,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10353),U_10355))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10353),U_10354))
    | ~ class_Orderings_Olinorder(U_10353) ),
    inference(clausify,[status(thm)],[f_2775_3]) ).

fof(f_2776_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_2776_2,plain,
    ! [U_10358,U_10357,U_10356] :
      ( c_Big__Operators_Olattice_OSup__fin(U_10356,c_Orderings_Oord__class_Omax(U_10356),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10356,tc_HOL_Obool)),U_10357),U_10358)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10356),c_Big__Operators_Olattice_OSup__fin(U_10356,c_Orderings_Oord__class_Omax(U_10356),U_10357)),c_Big__Operators_Olattice_OSup__fin(U_10356,c_Orderings_Oord__class_Omax(U_10356),U_10358))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10356,tc_HOL_Obool)),U_10357),U_10358) != c_Orderings_Obot__class_Obot(tc_fun(U_10356,tc_HOL_Obool))
      | U_10358 = c_Orderings_Obot__class_Obot(tc_fun(U_10356,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10356),U_10358))
      | U_10357 = c_Orderings_Obot__class_Obot(tc_fun(U_10356,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10356),U_10357))
      | ~ class_Orderings_Olinorder(U_10356) ),
    inference(variable_rename,[status(thm)],[f_2776_1]) ).

fof(f_2776_3,plain,
    ! [U_10357,U_10356,U_10358] :
      ( c_Big__Operators_Olattice_OSup__fin(U_10356,c_Orderings_Oord__class_Omax(U_10356),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10356,tc_HOL_Obool)),U_10357),U_10358)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10356),c_Big__Operators_Olattice_OSup__fin(U_10356,c_Orderings_Oord__class_Omax(U_10356),U_10357)),c_Big__Operators_Olattice_OSup__fin(U_10356,c_Orderings_Oord__class_Omax(U_10356),U_10358))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10356,tc_HOL_Obool)),U_10357),U_10358) != c_Orderings_Obot__class_Obot(tc_fun(U_10356,tc_HOL_Obool))
      | U_10358 = c_Orderings_Obot__class_Obot(tc_fun(U_10356,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10356),U_10358))
      | U_10357 = c_Orderings_Obot__class_Obot(tc_fun(U_10356,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10356),U_10357))
      | ~ class_Orderings_Olinorder(U_10356) ),
    inference(definitional_conversion,[status(esa)],[f_2776_2]) ).

cnf(f_2776_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_10356,c_Orderings_Oord__class_Omax(U_10356),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10356,tc_HOL_Obool)),U_10357),U_10358)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10356),c_Big__Operators_Olattice_OSup__fin(U_10356,c_Orderings_Oord__class_Omax(U_10356),U_10357)),c_Big__Operators_Olattice_OSup__fin(U_10356,c_Orderings_Oord__class_Omax(U_10356),U_10358))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10356,tc_HOL_Obool)),U_10357),U_10358) != c_Orderings_Obot__class_Obot(tc_fun(U_10356,tc_HOL_Obool))
    | U_10358 = c_Orderings_Obot__class_Obot(tc_fun(U_10356,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10356),U_10358))
    | U_10357 = c_Orderings_Obot__class_Obot(tc_fun(U_10356,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10356),U_10357))
    | ~ class_Orderings_Olinorder(U_10356) ),
    inference(clausify,[status(thm)],[f_2776_3]) ).

fof(f_2777_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_2777_2,plain,
    ! [U_10362,U_10361] :
      ( hBOOL(hAPP(hAPP(c_member(U_10361),c_Big__Operators_Olattice_OSup__fin(U_10361,c_Orderings_Oord__class_Omax(U_10361),U_10362)),U_10362))
      | ? [U_10360,U_10359] : ~ hBOOL(hAPP(hAPP(c_member(U_10361),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10361),U_10360),U_10359)),hAPP(hAPP(c_Set_Oinsert(U_10361),U_10360),hAPP(hAPP(c_Set_Oinsert(U_10361),U_10359),c_Orderings_Obot__class_Obot(tc_fun(U_10361,tc_HOL_Obool))))))
      | U_10362 = c_Orderings_Obot__class_Obot(tc_fun(U_10361,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10361),U_10362))
      | ~ class_Orderings_Olinorder(U_10361) ),
    inference(variable_rename,[status(thm)],[f_2777_1]) ).

fof(f_2777_3,plain,
    ! [U_10362,U_10361] :
      ( hBOOL(hAPP(hAPP(c_member(U_10361),c_Big__Operators_Olattice_OSup__fin(U_10361,c_Orderings_Oord__class_Omax(U_10361),U_10362)),U_10362))
      | ? [U_10359] : ~ hBOOL(hAPP(hAPP(c_member(U_10361),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10361),sK156(U_10362,U_10361)),U_10359)),hAPP(hAPP(c_Set_Oinsert(U_10361),sK156(U_10362,U_10361)),hAPP(hAPP(c_Set_Oinsert(U_10361),U_10359),c_Orderings_Obot__class_Obot(tc_fun(U_10361,tc_HOL_Obool))))))
      | U_10362 = c_Orderings_Obot__class_Obot(tc_fun(U_10361,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10361),U_10362))
      | ~ class_Orderings_Olinorder(U_10361) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_10360,sK156(U_10362,U_10361))],[f_2777_2]) ).

fof(f_2777_4,plain,
    ! [U_10362,U_10361] :
      ( hBOOL(hAPP(hAPP(c_member(U_10361),c_Big__Operators_Olattice_OSup__fin(U_10361,c_Orderings_Oord__class_Omax(U_10361),U_10362)),U_10362))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10361),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10361),sK156(U_10362,U_10361)),sK157(U_10362,U_10361))),hAPP(hAPP(c_Set_Oinsert(U_10361),sK156(U_10362,U_10361)),hAPP(hAPP(c_Set_Oinsert(U_10361),sK157(U_10362,U_10361)),c_Orderings_Obot__class_Obot(tc_fun(U_10361,tc_HOL_Obool))))))
      | U_10362 = c_Orderings_Obot__class_Obot(tc_fun(U_10361,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10361),U_10362))
      | ~ class_Orderings_Olinorder(U_10361) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_10359,sK157(U_10362,U_10361))],[f_2777_3]) ).

fof(f_2777_5,plain,
    ! [U_10362,U_10361] :
      ( hBOOL(hAPP(hAPP(c_member(U_10361),c_Big__Operators_Olattice_OSup__fin(U_10361,c_Orderings_Oord__class_Omax(U_10361),U_10362)),U_10362))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10361),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10361),sK156(U_10362,U_10361)),sK157(U_10362,U_10361))),hAPP(hAPP(c_Set_Oinsert(U_10361),sK156(U_10362,U_10361)),hAPP(hAPP(c_Set_Oinsert(U_10361),sK157(U_10362,U_10361)),c_Orderings_Obot__class_Obot(tc_fun(U_10361,tc_HOL_Obool))))))
      | U_10362 = c_Orderings_Obot__class_Obot(tc_fun(U_10361,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10361),U_10362))
      | ~ class_Orderings_Olinorder(U_10361) ),
    inference(definitional_conversion,[status(esa)],[f_2777_4]) ).

cnf(f_2777_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10361),c_Big__Operators_Olattice_OSup__fin(U_10361,c_Orderings_Oord__class_Omax(U_10361),U_10362)),U_10362))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10361),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10361),sK156(U_10362,U_10361)),sK157(U_10362,U_10361))),hAPP(hAPP(c_Set_Oinsert(U_10361),sK156(U_10362,U_10361)),hAPP(hAPP(c_Set_Oinsert(U_10361),sK157(U_10362,U_10361)),c_Orderings_Obot__class_Obot(tc_fun(U_10361,tc_HOL_Obool))))))
    | U_10362 = c_Orderings_Obot__class_Obot(tc_fun(U_10361,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10361),U_10362))
    | ~ class_Orderings_Olinorder(U_10361) ),
    inference(clausify,[status(thm)],[f_2777_5]) ).

fof(f_2778_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_2778_2,plain,
    ! [U_10366,U_10365] :
      ( hBOOL(hAPP(hAPP(c_member(U_10365),c_Big__Operators_Olattice_OInf__fin(U_10365,c_Orderings_Oord__class_Omin(U_10365),U_10366)),U_10366))
      | ? [U_10364,U_10363] : ~ hBOOL(hAPP(hAPP(c_member(U_10365),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10365),U_10364),U_10363)),hAPP(hAPP(c_Set_Oinsert(U_10365),U_10364),hAPP(hAPP(c_Set_Oinsert(U_10365),U_10363),c_Orderings_Obot__class_Obot(tc_fun(U_10365,tc_HOL_Obool))))))
      | U_10366 = c_Orderings_Obot__class_Obot(tc_fun(U_10365,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10365),U_10366))
      | ~ class_Orderings_Olinorder(U_10365) ),
    inference(variable_rename,[status(thm)],[f_2778_1]) ).

fof(f_2778_3,plain,
    ! [U_10366,U_10365] :
      ( hBOOL(hAPP(hAPP(c_member(U_10365),c_Big__Operators_Olattice_OInf__fin(U_10365,c_Orderings_Oord__class_Omin(U_10365),U_10366)),U_10366))
      | ? [U_10363] : ~ hBOOL(hAPP(hAPP(c_member(U_10365),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10365),sK158(U_10366,U_10365)),U_10363)),hAPP(hAPP(c_Set_Oinsert(U_10365),sK158(U_10366,U_10365)),hAPP(hAPP(c_Set_Oinsert(U_10365),U_10363),c_Orderings_Obot__class_Obot(tc_fun(U_10365,tc_HOL_Obool))))))
      | U_10366 = c_Orderings_Obot__class_Obot(tc_fun(U_10365,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10365),U_10366))
      | ~ class_Orderings_Olinorder(U_10365) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_10364,sK158(U_10366,U_10365))],[f_2778_2]) ).

fof(f_2778_4,plain,
    ! [U_10366,U_10365] :
      ( hBOOL(hAPP(hAPP(c_member(U_10365),c_Big__Operators_Olattice_OInf__fin(U_10365,c_Orderings_Oord__class_Omin(U_10365),U_10366)),U_10366))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10365),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10365),sK158(U_10366,U_10365)),sK159(U_10366,U_10365))),hAPP(hAPP(c_Set_Oinsert(U_10365),sK158(U_10366,U_10365)),hAPP(hAPP(c_Set_Oinsert(U_10365),sK159(U_10366,U_10365)),c_Orderings_Obot__class_Obot(tc_fun(U_10365,tc_HOL_Obool))))))
      | U_10366 = c_Orderings_Obot__class_Obot(tc_fun(U_10365,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10365),U_10366))
      | ~ class_Orderings_Olinorder(U_10365) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_10363,sK159(U_10366,U_10365))],[f_2778_3]) ).

fof(f_2778_5,plain,
    ! [U_10365,U_10366] :
      ( hBOOL(hAPP(hAPP(c_member(U_10365),c_Big__Operators_Olattice_OInf__fin(U_10365,c_Orderings_Oord__class_Omin(U_10365),U_10366)),U_10366))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10365),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10365),sK158(U_10366,U_10365)),sK159(U_10366,U_10365))),hAPP(hAPP(c_Set_Oinsert(U_10365),sK158(U_10366,U_10365)),hAPP(hAPP(c_Set_Oinsert(U_10365),sK159(U_10366,U_10365)),c_Orderings_Obot__class_Obot(tc_fun(U_10365,tc_HOL_Obool))))))
      | U_10366 = c_Orderings_Obot__class_Obot(tc_fun(U_10365,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10365),U_10366))
      | ~ class_Orderings_Olinorder(U_10365) ),
    inference(definitional_conversion,[status(esa)],[f_2778_4]) ).

cnf(f_2778_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10365),c_Big__Operators_Olattice_OInf__fin(U_10365,c_Orderings_Oord__class_Omin(U_10365),U_10366)),U_10366))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10365),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10365),sK158(U_10366,U_10365)),sK159(U_10366,U_10365))),hAPP(hAPP(c_Set_Oinsert(U_10365),sK158(U_10366,U_10365)),hAPP(hAPP(c_Set_Oinsert(U_10365),sK159(U_10366,U_10365)),c_Orderings_Obot__class_Obot(tc_fun(U_10365,tc_HOL_Obool))))))
    | U_10366 = c_Orderings_Obot__class_Obot(tc_fun(U_10365,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10365),U_10366))
    | ~ class_Orderings_Olinorder(U_10365) ),
    inference(clausify,[status(thm)],[f_2778_5]) ).

fof(f_2779_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_2779_2,plain,
    ! [U_10372,U_10371,U_10370,U_10369] :
      ( hBOOL(hAPP(hAPP(c_member(U_10369),hAPP(U_10371,U_10372)),U_10372))
      | ? [U_10368,U_10367] : ~ hBOOL(hAPP(hAPP(c_member(U_10369),hAPP(hAPP(U_10370,U_10368),U_10367)),hAPP(hAPP(c_Set_Oinsert(U_10369),U_10368),hAPP(hAPP(c_Set_Oinsert(U_10369),U_10367),c_Orderings_Obot__class_Obot(tc_fun(U_10369,tc_HOL_Obool))))))
      | U_10372 = c_Orderings_Obot__class_Obot(tc_fun(U_10369,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10369),U_10372))
      | ~ c_Finite__Set_Ofolding__one(U_10369,U_10370,U_10371) ),
    inference(variable_rename,[status(thm)],[f_2779_1]) ).

fof(f_2779_3,plain,
    ! [U_10372,U_10371,U_10370,U_10369] :
      ( hBOOL(hAPP(hAPP(c_member(U_10369),hAPP(U_10371,U_10372)),U_10372))
      | ? [U_10367] : ~ hBOOL(hAPP(hAPP(c_member(U_10369),hAPP(hAPP(U_10370,sK160(U_10372,U_10371,U_10370,U_10369)),U_10367)),hAPP(hAPP(c_Set_Oinsert(U_10369),sK160(U_10372,U_10371,U_10370,U_10369)),hAPP(hAPP(c_Set_Oinsert(U_10369),U_10367),c_Orderings_Obot__class_Obot(tc_fun(U_10369,tc_HOL_Obool))))))
      | U_10372 = c_Orderings_Obot__class_Obot(tc_fun(U_10369,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10369),U_10372))
      | ~ c_Finite__Set_Ofolding__one(U_10369,U_10370,U_10371) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_10368,sK160(U_10372,U_10371,U_10370,U_10369))],[f_2779_2]) ).

fof(f_2779_4,plain,
    ! [U_10372,U_10371,U_10370,U_10369] :
      ( hBOOL(hAPP(hAPP(c_member(U_10369),hAPP(U_10371,U_10372)),U_10372))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10369),hAPP(hAPP(U_10370,sK160(U_10372,U_10371,U_10370,U_10369)),sK161(U_10372,U_10371,U_10370,U_10369))),hAPP(hAPP(c_Set_Oinsert(U_10369),sK160(U_10372,U_10371,U_10370,U_10369)),hAPP(hAPP(c_Set_Oinsert(U_10369),sK161(U_10372,U_10371,U_10370,U_10369)),c_Orderings_Obot__class_Obot(tc_fun(U_10369,tc_HOL_Obool))))))
      | U_10372 = c_Orderings_Obot__class_Obot(tc_fun(U_10369,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10369),U_10372))
      | ~ c_Finite__Set_Ofolding__one(U_10369,U_10370,U_10371) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_10367,sK161(U_10372,U_10371,U_10370,U_10369))],[f_2779_3]) ).

fof(f_2779_5,plain,
    ! [U_10369,U_10370,U_10371,U_10372] :
      ( hBOOL(hAPP(hAPP(c_member(U_10369),hAPP(U_10371,U_10372)),U_10372))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10369),hAPP(hAPP(U_10370,sK160(U_10372,U_10371,U_10370,U_10369)),sK161(U_10372,U_10371,U_10370,U_10369))),hAPP(hAPP(c_Set_Oinsert(U_10369),sK160(U_10372,U_10371,U_10370,U_10369)),hAPP(hAPP(c_Set_Oinsert(U_10369),sK161(U_10372,U_10371,U_10370,U_10369)),c_Orderings_Obot__class_Obot(tc_fun(U_10369,tc_HOL_Obool))))))
      | U_10372 = c_Orderings_Obot__class_Obot(tc_fun(U_10369,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10369),U_10372))
      | ~ c_Finite__Set_Ofolding__one(U_10369,U_10370,U_10371) ),
    inference(definitional_conversion,[status(esa)],[f_2779_4]) ).

cnf(f_2779_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10369),hAPP(U_10371,U_10372)),U_10372))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10369),hAPP(hAPP(U_10370,sK160(U_10372,U_10371,U_10370,U_10369)),sK161(U_10372,U_10371,U_10370,U_10369))),hAPP(hAPP(c_Set_Oinsert(U_10369),sK160(U_10372,U_10371,U_10370,U_10369)),hAPP(hAPP(c_Set_Oinsert(U_10369),sK161(U_10372,U_10371,U_10370,U_10369)),c_Orderings_Obot__class_Obot(tc_fun(U_10369,tc_HOL_Obool))))))
    | U_10372 = c_Orderings_Obot__class_Obot(tc_fun(U_10369,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10369),U_10372))
    | ~ c_Finite__Set_Ofolding__one(U_10369,U_10370,U_10371) ),
    inference(clausify,[status(thm)],[f_2779_5]) ).

fof(f_2780_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_2780_2,plain,
    ! [U_10375,U_10374,U_10373] :
      ( hAPP(c_Finite__Set_Ocard(U_10373),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10373,tc_HOL_Obool)),U_10374),hAPP(hAPP(c_Set_Oinsert(U_10373),U_10375),c_Orderings_Obot__class_Obot(tc_fun(U_10373,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10373),U_10374)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10373),U_10375),U_10374))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10373),U_10374)) ),
    inference(variable_rename,[status(thm)],[f_2780_1]) ).

fof(f_2780_3,plain,
    ! [U_10374,U_10373,U_10375] :
      ( hAPP(c_Finite__Set_Ocard(U_10373),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10373,tc_HOL_Obool)),U_10374),hAPP(hAPP(c_Set_Oinsert(U_10373),U_10375),c_Orderings_Obot__class_Obot(tc_fun(U_10373,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10373),U_10374)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10373),U_10375),U_10374))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10373),U_10374)) ),
    inference(definitional_conversion,[status(esa)],[f_2780_2]) ).

cnf(f_2780_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10373),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10373,tc_HOL_Obool)),U_10374),hAPP(hAPP(c_Set_Oinsert(U_10373),U_10375),c_Orderings_Obot__class_Obot(tc_fun(U_10373,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10373),U_10374)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10373),U_10375),U_10374))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10373),U_10374)) ),
    inference(clausify,[status(thm)],[f_2780_3]) ).

fof(f_2781_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_2781_2,plain,
    ! [U_10378,U_10377,U_10376] :
      ( ( ( hAPP(c_Finite__Set_Ocard(U_10376),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10376,tc_HOL_Obool)),U_10377),hAPP(hAPP(c_Set_Oinsert(U_10376),U_10378),c_Orderings_Obot__class_Obot(tc_fun(U_10376,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_10376),U_10377)
          | hBOOL(hAPP(hAPP(c_member(U_10376),U_10378),U_10377)) )
        & ( hAPP(c_Finite__Set_Ocard(U_10376),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10376,tc_HOL_Obool)),U_10377),hAPP(hAPP(c_Set_Oinsert(U_10376),U_10378),c_Orderings_Obot__class_Obot(tc_fun(U_10376,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10376),U_10377)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
          | ~ hBOOL(hAPP(hAPP(c_member(U_10376),U_10378),U_10377)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10376),U_10377)) ),
    inference(variable_rename,[status(thm)],[f_2781_1]) ).

fof(f_2781_3,plain,
    ( ! [U_10376,U_10377,U_10378] :
        ( hAPP(c_Finite__Set_Ocard(U_10376),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10376,tc_HOL_Obool)),U_10377),hAPP(hAPP(c_Set_Oinsert(U_10376),U_10378),c_Orderings_Obot__class_Obot(tc_fun(U_10376,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_10376),U_10377)
        | hBOOL(hAPP(hAPP(c_member(U_10376),U_10378),U_10377))
        | ~ sP792(U_10376,U_10377,U_10378) )
    & ! [U_10376,U_10377,U_10378] :
        ( hAPP(c_Finite__Set_Ocard(U_10376),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10376,tc_HOL_Obool)),U_10377),hAPP(hAPP(c_Set_Oinsert(U_10376),U_10378),c_Orderings_Obot__class_Obot(tc_fun(U_10376,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10376),U_10377)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10376),U_10378),U_10377))
        | ~ sP792(U_10376,U_10377,U_10378) )
    & ! [U_10376,U_10377,U_10378] :
        ( sP792(U_10376,U_10377,U_10378)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10376),U_10377)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP792])],[f_2781_2]) ).

cnf(f_2781_4,plain,
    ( sP792(U_10376,U_10377,U_10378)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10376),U_10377)) ),
    inference(clausify,[status(thm)],[f_2781_3]) ).

cnf(f_2781_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10376),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10376,tc_HOL_Obool)),U_10377),hAPP(hAPP(c_Set_Oinsert(U_10376),U_10378),c_Orderings_Obot__class_Obot(tc_fun(U_10376,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10376),U_10377)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10376),U_10378),U_10377))
    | ~ sP792(U_10376,U_10377,U_10378) ),
    inference(clausify,[status(thm)],[f_2781_3]) ).

cnf(f_2781_6,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10376),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10376,tc_HOL_Obool)),U_10377),hAPP(hAPP(c_Set_Oinsert(U_10376),U_10378),c_Orderings_Obot__class_Obot(tc_fun(U_10376,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_10376),U_10377)
    | hBOOL(hAPP(hAPP(c_member(U_10376),U_10378),U_10377))
    | ~ sP792(U_10376,U_10377,U_10378) ),
    inference(clausify,[status(thm)],[f_2781_3]) ).

fof(f_2782_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_2782_2,plain,
    ! [U_10381,U_10380,U_10379] :
      ( hAPP(c_Finite__Set_Ocard(U_10379),U_10380) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10379),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10379,tc_HOL_Obool)),U_10380),hAPP(hAPP(c_Set_Oinsert(U_10379),U_10381),c_Orderings_Obot__class_Obot(tc_fun(U_10379,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10379),U_10381),U_10380))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10379),U_10380)) ),
    inference(variable_rename,[status(thm)],[f_2782_1]) ).

fof(f_2782_3,plain,
    ! [U_10379,U_10380,U_10381] :
      ( hAPP(c_Finite__Set_Ocard(U_10379),U_10380) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10379),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10379,tc_HOL_Obool)),U_10380),hAPP(hAPP(c_Set_Oinsert(U_10379),U_10381),c_Orderings_Obot__class_Obot(tc_fun(U_10379,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10379),U_10381),U_10380))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10379),U_10380)) ),
    inference(definitional_conversion,[status(esa)],[f_2782_2]) ).

cnf(f_2782_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10379),U_10380) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10379),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10379,tc_HOL_Obool)),U_10380),hAPP(hAPP(c_Set_Oinsert(U_10379),U_10381),c_Orderings_Obot__class_Obot(tc_fun(U_10379,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10379),U_10381),U_10380))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10379),U_10380)) ),
    inference(clausify,[status(thm)],[f_2782_3]) ).

fof(f_2783_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_2783_2,plain,
    ! [U_10382] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_10382) = 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_10382)),
    inference(variable_rename,[status(thm)],[f_2783_1]) ).

fof(f_2783_3,plain,
    ! [U_10382] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_10382) = 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_10382)),
    inference(definitional_conversion,[status(esa)],[f_2783_2]) ).

cnf(f_2783_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_10382) = 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_10382)),
    inference(clausify,[status(thm)],[f_2783_3]) ).

fof(f_2784_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_2784_2,plain,
    ! [U_10383] :
      ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_10383) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10383))
      | ~ c_Nat__Transfer_Onat__set(U_10383) ),
    inference(variable_rename,[status(thm)],[f_2784_1]) ).

fof(f_2784_3,plain,
    ! [U_10383] :
      ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_10383) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10383))
      | ~ c_Nat__Transfer_Onat__set(U_10383) ),
    inference(definitional_conversion,[status(esa)],[f_2784_2]) ).

cnf(f_2784_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_10383) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10383))
    | ~ c_Nat__Transfer_Onat__set(U_10383) ),
    inference(clausify,[status(thm)],[f_2784_3]) ).

fof(f_2785_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_2785_2,plain,
    ! [U_10384] : hAPP(c_Finite__Set_Ocard(U_10384),c_Orderings_Obot__class_Obot(tc_fun(U_10384,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_2785_1]) ).

fof(f_2785_3,plain,
    ! [U_10384] : hAPP(c_Finite__Set_Ocard(U_10384),c_Orderings_Obot__class_Obot(tc_fun(U_10384,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_2785_2]) ).

cnf(f_2785_4,plain,
    hAPP(c_Finite__Set_Ocard(U_10384),c_Orderings_Obot__class_Obot(tc_fun(U_10384,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2785_3]) ).

fof(f_2786_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_2786_2,plain,
    ! [U_10386,U_10385] :
      ( hAPP(c_Finite__Set_Ocard(U_10385),U_10386) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10385),U_10386)) ),
    inference(variable_rename,[status(thm)],[f_2786_1]) ).

fof(f_2786_3,plain,
    ! [U_10385,U_10386] :
      ( hAPP(c_Finite__Set_Ocard(U_10385),U_10386) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10385),U_10386)) ),
    inference(definitional_conversion,[status(esa)],[f_2786_2]) ).

cnf(f_2786_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10385),U_10386) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10385),U_10386)) ),
    inference(clausify,[status(thm)],[f_2786_3]) ).

fof(f_2787_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_2787_2,plain,
    ! [U_10388,U_10387] :
      ( ( hAPP(c_Finite__Set_Ocard(U_10387),U_10388) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10387),U_10388))
          & U_10388 != c_Orderings_Obot__class_Obot(tc_fun(U_10387,tc_HOL_Obool)) ) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10387),U_10388))
        | U_10388 = c_Orderings_Obot__class_Obot(tc_fun(U_10387,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(U_10387),U_10388) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_2787_1]) ).

fof(f_2787_3,plain,
    ( ! [U_10392,U_10390] :
        ( hAPP(c_Finite__Set_Ocard(U_10390),U_10392) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10390),U_10392))
          & U_10392 != c_Orderings_Obot__class_Obot(tc_fun(U_10390,tc_HOL_Obool)) ) )
    & ! [U_10391,U_10389] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10389),U_10391))
        | U_10391 = c_Orderings_Obot__class_Obot(tc_fun(U_10389,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(U_10389),U_10391) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_2787_2]) ).

fof(f_2787_4,plain,
    ( ! [U_10392,U_10390] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10390),U_10392))
        | ~ sP793(U_10392,U_10390) )
    & ! [U_10392,U_10390] :
        ( U_10392 != c_Orderings_Obot__class_Obot(tc_fun(U_10390,tc_HOL_Obool))
        | ~ sP793(U_10392,U_10390) )
    & ! [U_10392,U_10390] :
        ( hAPP(c_Finite__Set_Ocard(U_10390),U_10392) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP793(U_10392,U_10390) )
    & ! [U_10391,U_10389] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10389),U_10391))
        | U_10391 = c_Orderings_Obot__class_Obot(tc_fun(U_10389,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(U_10389),U_10391) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP793])],[f_2787_3]) ).

cnf(f_2787_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10389),U_10391))
    | U_10391 = c_Orderings_Obot__class_Obot(tc_fun(U_10389,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_10389),U_10391) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2787_4]) ).

cnf(f_2787_6,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10390),U_10392) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP793(U_10392,U_10390) ),
    inference(clausify,[status(thm)],[f_2787_4]) ).

cnf(f_2787_7,plain,
    ( U_10392 != c_Orderings_Obot__class_Obot(tc_fun(U_10390,tc_HOL_Obool))
    | ~ sP793(U_10392,U_10390) ),
    inference(clausify,[status(thm)],[f_2787_4]) ).

cnf(f_2787_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10390),U_10392))
    | ~ sP793(U_10392,U_10390) ),
    inference(clausify,[status(thm)],[f_2787_4]) ).

fof(f_2788_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_2788_2,plain,
    ! [U_10394,U_10393] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10393),U_10394))
      | ~ 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_10393),U_10394))) ),
    inference(variable_rename,[status(thm)],[f_2788_1]) ).

fof(f_2788_3,plain,
    ! [U_10393,U_10394] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10393),U_10394))
      | ~ 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_10393),U_10394))) ),
    inference(definitional_conversion,[status(esa)],[f_2788_2]) ).

cnf(f_2788_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10393),U_10394))
    | ~ 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_10393),U_10394))) ),
    inference(clausify,[status(thm)],[f_2788_3]) ).

fof(f_2789_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_2789_2,plain,
    ! [U_10397,U_10396,U_10395] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10395),U_10396)),hAPP(c_Finite__Set_Ocard(U_10395),hAPP(hAPP(c_Set_Oinsert(U_10395),U_10397),U_10396))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10395),U_10396)) ),
    inference(variable_rename,[status(thm)],[f_2789_1]) ).

fof(f_2789_3,plain,
    ! [U_10395,U_10396,U_10397] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10395),U_10396)),hAPP(c_Finite__Set_Ocard(U_10395),hAPP(hAPP(c_Set_Oinsert(U_10395),U_10397),U_10396))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10395),U_10396)) ),
    inference(definitional_conversion,[status(esa)],[f_2789_2]) ).

cnf(f_2789_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10395),U_10396)),hAPP(c_Finite__Set_Ocard(U_10395),hAPP(hAPP(c_Set_Oinsert(U_10395),U_10397),U_10396))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10395),U_10396)) ),
    inference(clausify,[status(thm)],[f_2789_3]) ).

fof(f_2790_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_2790_2,plain,
    ! [U_10400,U_10399,U_10398] :
      ( U_10400 = U_10399
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10398),U_10399)),hAPP(c_Finite__Set_Ocard(U_10398),U_10400)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10398,tc_HOL_Obool)),U_10400),U_10399))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10398),U_10399)) ),
    inference(variable_rename,[status(thm)],[f_2790_1]) ).

fof(f_2790_3,plain,
    ! [U_10398,U_10399,U_10400] :
      ( U_10400 = U_10399
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10398),U_10399)),hAPP(c_Finite__Set_Ocard(U_10398),U_10400)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10398,tc_HOL_Obool)),U_10400),U_10399))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10398),U_10399)) ),
    inference(definitional_conversion,[status(esa)],[f_2790_2]) ).

cnf(f_2790_4,plain,
    ( U_10400 = U_10399
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10398),U_10399)),hAPP(c_Finite__Set_Ocard(U_10398),U_10400)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10398,tc_HOL_Obool)),U_10400),U_10399))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10398),U_10399)) ),
    inference(clausify,[status(thm)],[f_2790_3]) ).

fof(f_2791_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_2791_2,plain,
    ! [U_10403,U_10402,U_10401] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10401),U_10403)),hAPP(c_Finite__Set_Ocard(U_10401),U_10402)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10401,tc_HOL_Obool)),U_10403),U_10402))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10401),U_10402)) ),
    inference(variable_rename,[status(thm)],[f_2791_1]) ).

fof(f_2791_3,plain,
    ! [U_10401,U_10402,U_10403] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10401),U_10403)),hAPP(c_Finite__Set_Ocard(U_10401),U_10402)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10401,tc_HOL_Obool)),U_10403),U_10402))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10401),U_10402)) ),
    inference(definitional_conversion,[status(esa)],[f_2791_2]) ).

cnf(f_2791_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10401),U_10403)),hAPP(c_Finite__Set_Ocard(U_10401),U_10402)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10401,tc_HOL_Obool)),U_10403),U_10402))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10401),U_10402)) ),
    inference(clausify,[status(thm)],[f_2791_3]) ).

fof(f_2792_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_2792_2,plain,
    ! [U_10407,U_10406,U_10405,U_10404] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10406),hAPP(c_Set_Oimage(U_10404,U_10406,U_10407),U_10405))),hAPP(c_Finite__Set_Ocard(U_10404),U_10405)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10404),U_10405)) ),
    inference(variable_rename,[status(thm)],[f_2792_1]) ).

fof(f_2792_3,plain,
    ! [U_10404,U_10405,U_10406,U_10407] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10406),hAPP(c_Set_Oimage(U_10404,U_10406,U_10407),U_10405))),hAPP(c_Finite__Set_Ocard(U_10404),U_10405)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10404),U_10405)) ),
    inference(definitional_conversion,[status(esa)],[f_2792_2]) ).

cnf(f_2792_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10406),hAPP(c_Set_Oimage(U_10404,U_10406,U_10407),U_10405))),hAPP(c_Finite__Set_Ocard(U_10404),U_10405)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10404),U_10405)) ),
    inference(clausify,[status(thm)],[f_2792_3]) ).

fof(f_2793_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_2793_2,plain,
    ! [U_10410,U_10409,U_10408] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10408),U_10410)),hAPP(c_Finite__Set_Ocard(U_10408),U_10409)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_10408,tc_HOL_Obool)),U_10410),U_10409))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10408),U_10409)) ),
    inference(variable_rename,[status(thm)],[f_2793_1]) ).

fof(f_2793_3,plain,
    ! [U_10408,U_10409,U_10410] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10408),U_10410)),hAPP(c_Finite__Set_Ocard(U_10408),U_10409)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_10408,tc_HOL_Obool)),U_10410),U_10409))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10408),U_10409)) ),
    inference(definitional_conversion,[status(esa)],[f_2793_2]) ).

cnf(f_2793_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10408),U_10410)),hAPP(c_Finite__Set_Ocard(U_10408),U_10409)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_10408,tc_HOL_Obool)),U_10410),U_10409))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10408),U_10409)) ),
    inference(clausify,[status(thm)],[f_2793_3]) ).

fof(f_2794_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_2794_2,plain,
    ! [U_10413,U_10412,U_10411] :
      ( ( ( hAPP(c_Finite__Set_Ocard(U_10411),hAPP(hAPP(c_Set_Oinsert(U_10411),U_10413),U_10412)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10411),U_10412))
          | hBOOL(hAPP(hAPP(c_member(U_10411),U_10413),U_10412)) )
        & ( hAPP(c_Finite__Set_Ocard(U_10411),hAPP(hAPP(c_Set_Oinsert(U_10411),U_10413),U_10412)) = hAPP(c_Finite__Set_Ocard(U_10411),U_10412)
          | ~ hBOOL(hAPP(hAPP(c_member(U_10411),U_10413),U_10412)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10411),U_10412)) ),
    inference(variable_rename,[status(thm)],[f_2794_1]) ).

fof(f_2794_3,plain,
    ( ! [U_10411,U_10412,U_10413] :
        ( hAPP(c_Finite__Set_Ocard(U_10411),hAPP(hAPP(c_Set_Oinsert(U_10411),U_10413),U_10412)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10411),U_10412))
        | hBOOL(hAPP(hAPP(c_member(U_10411),U_10413),U_10412))
        | ~ sP794(U_10411,U_10412,U_10413) )
    & ! [U_10411,U_10412,U_10413] :
        ( hAPP(c_Finite__Set_Ocard(U_10411),hAPP(hAPP(c_Set_Oinsert(U_10411),U_10413),U_10412)) = hAPP(c_Finite__Set_Ocard(U_10411),U_10412)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10411),U_10413),U_10412))
        | ~ sP794(U_10411,U_10412,U_10413) )
    & ! [U_10411,U_10412,U_10413] :
        ( sP794(U_10411,U_10412,U_10413)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10411),U_10412)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP794])],[f_2794_2]) ).

cnf(f_2794_4,plain,
    ( sP794(U_10411,U_10412,U_10413)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10411),U_10412)) ),
    inference(clausify,[status(thm)],[f_2794_3]) ).

cnf(f_2794_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10411),hAPP(hAPP(c_Set_Oinsert(U_10411),U_10413),U_10412)) = hAPP(c_Finite__Set_Ocard(U_10411),U_10412)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10411),U_10413),U_10412))
    | ~ sP794(U_10411,U_10412,U_10413) ),
    inference(clausify,[status(thm)],[f_2794_3]) ).

cnf(f_2794_6,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10411),hAPP(hAPP(c_Set_Oinsert(U_10411),U_10413),U_10412)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10411),U_10412))
    | hBOOL(hAPP(hAPP(c_member(U_10411),U_10413),U_10412))
    | ~ sP794(U_10411,U_10412,U_10413) ),
    inference(clausify,[status(thm)],[f_2794_3]) ).

fof(f_2795_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_2795_2,plain,
    ! [U_10416,U_10415,U_10414] :
      ( hAPP(c_Finite__Set_Ocard(U_10414),hAPP(hAPP(c_Set_Oinsert(U_10414),U_10416),U_10415)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10414),U_10415))
      | hBOOL(hAPP(hAPP(c_member(U_10414),U_10416),U_10415))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10414),U_10415)) ),
    inference(variable_rename,[status(thm)],[f_2795_1]) ).

fof(f_2795_3,plain,
    ! [U_10414,U_10415,U_10416] :
      ( hAPP(c_Finite__Set_Ocard(U_10414),hAPP(hAPP(c_Set_Oinsert(U_10414),U_10416),U_10415)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10414),U_10415))
      | hBOOL(hAPP(hAPP(c_member(U_10414),U_10416),U_10415))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10414),U_10415)) ),
    inference(definitional_conversion,[status(esa)],[f_2795_2]) ).

cnf(f_2795_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10414),hAPP(hAPP(c_Set_Oinsert(U_10414),U_10416),U_10415)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10414),U_10415))
    | hBOOL(hAPP(hAPP(c_member(U_10414),U_10416),U_10415))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10414),U_10415)) ),
    inference(clausify,[status(thm)],[f_2795_3]) ).

fof(f_2796_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_2796_2,plain,
    ! [U_10418,U_10417] :
      ( ( 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_10417),U_10418)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10417),U_10418))
        | U_10418 = c_Orderings_Obot__class_Obot(tc_fun(U_10417,tc_HOL_Obool)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10417),U_10418))
          & U_10418 != c_Orderings_Obot__class_Obot(tc_fun(U_10417,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_10417),U_10418))) ) ),
    inference(variable_rename,[status(thm)],[f_2796_1]) ).

fof(f_2796_3,plain,
    ( ! [U_10422,U_10420] :
        ( 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_10420),U_10422)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10420),U_10422))
        | U_10422 = c_Orderings_Obot__class_Obot(tc_fun(U_10420,tc_HOL_Obool)) )
    & ! [U_10421,U_10419] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10419),U_10421))
          & U_10421 != c_Orderings_Obot__class_Obot(tc_fun(U_10419,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_10419),U_10421))) ) ),
    inference(miniscope,[status(thm)],[f_2796_2]) ).

fof(f_2796_4,plain,
    ( ! [U_10421,U_10419] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10419),U_10421))
        | ~ sP795(U_10421,U_10419) )
    & ! [U_10421,U_10419] :
        ( U_10421 != c_Orderings_Obot__class_Obot(tc_fun(U_10419,tc_HOL_Obool))
        | ~ sP795(U_10421,U_10419) )
    & ! [U_10422,U_10420] :
        ( 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_10420),U_10422)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10420),U_10422))
        | U_10422 = c_Orderings_Obot__class_Obot(tc_fun(U_10420,tc_HOL_Obool)) )
    & ! [U_10421,U_10419] :
        ( sP795(U_10421,U_10419)
        | ~ 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_10419),U_10421))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP795])],[f_2796_3]) ).

cnf(f_2796_5,plain,
    ( sP795(U_10421,U_10419)
    | ~ 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_10419),U_10421))) ),
    inference(clausify,[status(thm)],[f_2796_4]) ).

cnf(f_2796_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_10420),U_10422)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10420),U_10422))
    | U_10422 = c_Orderings_Obot__class_Obot(tc_fun(U_10420,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2796_4]) ).

cnf(f_2796_7,plain,
    ( U_10421 != c_Orderings_Obot__class_Obot(tc_fun(U_10419,tc_HOL_Obool))
    | ~ sP795(U_10421,U_10419) ),
    inference(clausify,[status(thm)],[f_2796_4]) ).

cnf(f_2796_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10419),U_10421))
    | ~ sP795(U_10421,U_10419) ),
    inference(clausify,[status(thm)],[f_2796_4]) ).

fof(f_2797_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_2797_2,plain,
    ! [U_10425,U_10424,U_10423] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10423),U_10424)),hAPP(c_Finite__Set_Ocard(U_10423),U_10425)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10423),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10423,tc_HOL_Obool)),U_10424),U_10425))),hAPP(c_Finite__Set_Ocard(U_10423),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10423,tc_HOL_Obool)),U_10424),U_10425)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10423),U_10425))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10423),U_10424)) ),
    inference(variable_rename,[status(thm)],[f_2797_1]) ).

fof(f_2797_3,plain,
    ! [U_10423,U_10424,U_10425] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10423),U_10424)),hAPP(c_Finite__Set_Ocard(U_10423),U_10425)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10423),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10423,tc_HOL_Obool)),U_10424),U_10425))),hAPP(c_Finite__Set_Ocard(U_10423),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10423,tc_HOL_Obool)),U_10424),U_10425)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10423),U_10425))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10423),U_10424)) ),
    inference(definitional_conversion,[status(esa)],[f_2797_2]) ).

cnf(f_2797_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10423),U_10424)),hAPP(c_Finite__Set_Ocard(U_10423),U_10425)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10423),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10423,tc_HOL_Obool)),U_10424),U_10425))),hAPP(c_Finite__Set_Ocard(U_10423),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10423,tc_HOL_Obool)),U_10424),U_10425)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10423),U_10425))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10423),U_10424)) ),
    inference(clausify,[status(thm)],[f_2797_3]) ).

fof(f_2798_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_2798_2,plain,
    ! [U_10428,U_10427,U_10426] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10426),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10426,tc_HOL_Obool)),U_10427),U_10428))),hAPP(c_Finite__Set_Ocard(U_10426),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10426,tc_HOL_Obool)),U_10427),U_10428))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10426),U_10427)),hAPP(c_Finite__Set_Ocard(U_10426),U_10428))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10426),U_10428))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10426),U_10427)) ),
    inference(variable_rename,[status(thm)],[f_2798_1]) ).

fof(f_2798_3,plain,
    ! [U_10426,U_10427,U_10428] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10426),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10426,tc_HOL_Obool)),U_10427),U_10428))),hAPP(c_Finite__Set_Ocard(U_10426),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10426,tc_HOL_Obool)),U_10427),U_10428))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10426),U_10427)),hAPP(c_Finite__Set_Ocard(U_10426),U_10428))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10426),U_10428))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10426),U_10427)) ),
    inference(definitional_conversion,[status(esa)],[f_2798_2]) ).

cnf(f_2798_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10426),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10426,tc_HOL_Obool)),U_10427),U_10428))),hAPP(c_Finite__Set_Ocard(U_10426),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10426,tc_HOL_Obool)),U_10427),U_10428))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10426),U_10427)),hAPP(c_Finite__Set_Ocard(U_10426),U_10428))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10426),U_10428))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10426),U_10427)) ),
    inference(clausify,[status(thm)],[f_2798_3]) ).

fof(f_2799_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_2799_2,plain,
    ! [U_10431,U_10430,U_10429] :
      ( hAPP(c_Finite__Set_Ocard(U_10429),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10429,tc_HOL_Obool)),U_10431),U_10430)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10429),U_10431)),hAPP(c_Finite__Set_Ocard(U_10429),U_10430))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10429,tc_HOL_Obool)),U_10430),U_10431))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10429),U_10430)) ),
    inference(variable_rename,[status(thm)],[f_2799_1]) ).

fof(f_2799_3,plain,
    ! [U_10429,U_10430,U_10431] :
      ( hAPP(c_Finite__Set_Ocard(U_10429),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10429,tc_HOL_Obool)),U_10431),U_10430)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10429),U_10431)),hAPP(c_Finite__Set_Ocard(U_10429),U_10430))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10429,tc_HOL_Obool)),U_10430),U_10431))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10429),U_10430)) ),
    inference(definitional_conversion,[status(esa)],[f_2799_2]) ).

cnf(f_2799_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10429),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10429,tc_HOL_Obool)),U_10431),U_10430)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10429),U_10431)),hAPP(c_Finite__Set_Ocard(U_10429),U_10430))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10429,tc_HOL_Obool)),U_10430),U_10431))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10429),U_10430)) ),
    inference(clausify,[status(thm)],[f_2799_3]) ).

fof(f_2800_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_2800_2,plain,
    ! [U_10434,U_10433,U_10432] :
      ( hAPP(c_Finite__Set_Ocard(U_10432),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10432,tc_HOL_Obool)),U_10433),U_10434)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10432),U_10433)),hAPP(c_Finite__Set_Ocard(U_10432),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10432,tc_HOL_Obool)),U_10433),U_10434)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10432),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10432,tc_HOL_Obool)),U_10433),U_10434))) ),
    inference(variable_rename,[status(thm)],[f_2800_1]) ).

fof(f_2800_3,plain,
    ! [U_10432,U_10433,U_10434] :
      ( hAPP(c_Finite__Set_Ocard(U_10432),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10432,tc_HOL_Obool)),U_10433),U_10434)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10432),U_10433)),hAPP(c_Finite__Set_Ocard(U_10432),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10432,tc_HOL_Obool)),U_10433),U_10434)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10432),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10432,tc_HOL_Obool)),U_10433),U_10434))) ),
    inference(definitional_conversion,[status(esa)],[f_2800_2]) ).

cnf(f_2800_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10432),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10432,tc_HOL_Obool)),U_10433),U_10434)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10432),U_10433)),hAPP(c_Finite__Set_Ocard(U_10432),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10432,tc_HOL_Obool)),U_10433),U_10434)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10432),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10432,tc_HOL_Obool)),U_10433),U_10434))) ),
    inference(clausify,[status(thm)],[f_2800_3]) ).

fof(f_2801_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_2801_2,plain,
    ! [U_10437,U_10436,U_10435] :
      ( 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_10435),U_10437)),hAPP(c_Finite__Set_Ocard(U_10435),U_10436))),hAPP(c_Finite__Set_Ocard(U_10435),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10435,tc_HOL_Obool)),U_10437),U_10436))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10435),U_10436)) ),
    inference(variable_rename,[status(thm)],[f_2801_1]) ).

fof(f_2801_3,plain,
    ! [U_10435,U_10436,U_10437] :
      ( 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_10435),U_10437)),hAPP(c_Finite__Set_Ocard(U_10435),U_10436))),hAPP(c_Finite__Set_Ocard(U_10435),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10435,tc_HOL_Obool)),U_10437),U_10436))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10435),U_10436)) ),
    inference(definitional_conversion,[status(esa)],[f_2801_2]) ).

cnf(f_2801_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_10435),U_10437)),hAPP(c_Finite__Set_Ocard(U_10435),U_10436))),hAPP(c_Finite__Set_Ocard(U_10435),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10435,tc_HOL_Obool)),U_10437),U_10436))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10435),U_10436)) ),
    inference(clausify,[status(thm)],[f_2801_3]) ).

fof(f_2802_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_2802_2,plain,
    ! [U_10440,U_10439,U_10438] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_10438,tc_HOL_Obool)),U_10440),U_10439))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10438),U_10440)),hAPP(c_Finite__Set_Ocard(U_10438),U_10439)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10438,tc_HOL_Obool)),U_10440),U_10439))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10438),U_10439)) ),
    inference(variable_rename,[status(thm)],[f_2802_1]) ).

fof(f_2802_3,plain,
    ! [U_10438,U_10439,U_10440] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_10438,tc_HOL_Obool)),U_10440),U_10439))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10438),U_10440)),hAPP(c_Finite__Set_Ocard(U_10438),U_10439)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10438,tc_HOL_Obool)),U_10440),U_10439))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10438),U_10439)) ),
    inference(definitional_conversion,[status(esa)],[f_2802_2]) ).

cnf(f_2802_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_10438,tc_HOL_Obool)),U_10440),U_10439))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10438),U_10440)),hAPP(c_Finite__Set_Ocard(U_10438),U_10439)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10438,tc_HOL_Obool)),U_10440),U_10439))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10438),U_10439)) ),
    inference(clausify,[status(thm)],[f_2802_3]) ).

fof(f_2803_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_2803_2,plain,
    ! [U_10443,U_10442,U_10441] :
      ( hAPP(c_Finite__Set_Ocard(U_10441),hAPP(hAPP(c_Set_Oinsert(U_10441),U_10443),U_10442)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10441,tc_HOL_Obool)),U_10442),hAPP(hAPP(c_Set_Oinsert(U_10441),U_10443),c_Orderings_Obot__class_Obot(tc_fun(U_10441,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10441),U_10442)) ),
    inference(variable_rename,[status(thm)],[f_2803_1]) ).

fof(f_2803_3,plain,
    ! [U_10441,U_10442,U_10443] :
      ( hAPP(c_Finite__Set_Ocard(U_10441),hAPP(hAPP(c_Set_Oinsert(U_10441),U_10443),U_10442)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10441,tc_HOL_Obool)),U_10442),hAPP(hAPP(c_Set_Oinsert(U_10441),U_10443),c_Orderings_Obot__class_Obot(tc_fun(U_10441,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10441),U_10442)) ),
    inference(definitional_conversion,[status(esa)],[f_2803_2]) ).

cnf(f_2803_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10441),hAPP(hAPP(c_Set_Oinsert(U_10441),U_10443),U_10442)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10441,tc_HOL_Obool)),U_10442),hAPP(hAPP(c_Set_Oinsert(U_10441),U_10443),c_Orderings_Obot__class_Obot(tc_fun(U_10441,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10441),U_10442)) ),
    inference(clausify,[status(thm)],[f_2803_3]) ).

fof(f_2804_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_2804_2,plain,
    ! [U_10446,U_10445,U_10444] :
      ( hAPP(c_Finite__Set_Ocard(U_10444),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10444,tc_HOL_Obool)),U_10445),U_10446)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10444),U_10445)),hAPP(c_Finite__Set_Ocard(U_10444),U_10446))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10444,tc_HOL_Obool)),U_10445),U_10446) != c_Orderings_Obot__class_Obot(tc_fun(U_10444,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10444),U_10446))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10444),U_10445)) ),
    inference(variable_rename,[status(thm)],[f_2804_1]) ).

fof(f_2804_3,plain,
    ! [U_10444,U_10445,U_10446] :
      ( hAPP(c_Finite__Set_Ocard(U_10444),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10444,tc_HOL_Obool)),U_10445),U_10446)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10444),U_10445)),hAPP(c_Finite__Set_Ocard(U_10444),U_10446))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10444,tc_HOL_Obool)),U_10445),U_10446) != c_Orderings_Obot__class_Obot(tc_fun(U_10444,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10444),U_10446))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10444),U_10445)) ),
    inference(definitional_conversion,[status(esa)],[f_2804_2]) ).

cnf(f_2804_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10444),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10444,tc_HOL_Obool)),U_10445),U_10446)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10444),U_10445)),hAPP(c_Finite__Set_Ocard(U_10444),U_10446))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10444,tc_HOL_Obool)),U_10445),U_10446) != c_Orderings_Obot__class_Obot(tc_fun(U_10444,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10444),U_10446))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10444),U_10445)) ),
    inference(clausify,[status(thm)],[f_2804_3]) ).

fof(f_2805_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_2805_2,plain,
    ! [U_10449,U_10448,U_10447] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10447,tc_HOL_Obool)),U_10448),hAPP(hAPP(c_Set_Oinsert(U_10447),U_10449),c_Orderings_Obot__class_Obot(tc_fun(U_10447,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10447),U_10448)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10447),U_10448)) ),
    inference(variable_rename,[status(thm)],[f_2805_1]) ).

fof(f_2805_3,plain,
    ! [U_10447,U_10448,U_10449] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10447,tc_HOL_Obool)),U_10448),hAPP(hAPP(c_Set_Oinsert(U_10447),U_10449),c_Orderings_Obot__class_Obot(tc_fun(U_10447,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10447),U_10448)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10447),U_10448)) ),
    inference(definitional_conversion,[status(esa)],[f_2805_2]) ).

cnf(f_2805_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10447,tc_HOL_Obool)),U_10448),hAPP(hAPP(c_Set_Oinsert(U_10447),U_10449),c_Orderings_Obot__class_Obot(tc_fun(U_10447,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10447),U_10448)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10447),U_10448)) ),
    inference(clausify,[status(thm)],[f_2805_3]) ).

fof(f_2806_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_2806_2,plain,
    ! [U_10452,U_10451,U_10450] :
      ( hAPP(c_Finite__Set_Ocard(U_10450),hAPP(hAPP(c_Set_Oinsert(U_10450),U_10452),U_10451)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10450),U_10451))
      | hBOOL(hAPP(hAPP(c_member(U_10450),U_10452),U_10451))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10450),U_10451)) ),
    inference(variable_rename,[status(thm)],[f_2806_1]) ).

fof(f_2806_3,plain,
    ! [U_10450,U_10451,U_10452] :
      ( hAPP(c_Finite__Set_Ocard(U_10450),hAPP(hAPP(c_Set_Oinsert(U_10450),U_10452),U_10451)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10450),U_10451))
      | hBOOL(hAPP(hAPP(c_member(U_10450),U_10452),U_10451))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10450),U_10451)) ),
    inference(definitional_conversion,[status(esa)],[f_2806_2]) ).

cnf(f_2806_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10450),hAPP(hAPP(c_Set_Oinsert(U_10450),U_10452),U_10451)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10450),U_10451))
    | hBOOL(hAPP(hAPP(c_member(U_10450),U_10452),U_10451))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10450),U_10451)) ),
    inference(clausify,[status(thm)],[f_2806_3]) ).

fof(f_2807_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_2807_2,plain,
    ! [U_10455,U_10454,U_10453] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10453),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10453,tc_HOL_Obool)),U_10454),hAPP(hAPP(c_Set_Oinsert(U_10453),U_10455),c_Orderings_Obot__class_Obot(tc_fun(U_10453,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_10453),U_10454)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10453),U_10455),U_10454))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10453),U_10454)) ),
    inference(variable_rename,[status(thm)],[f_2807_1]) ).

fof(f_2807_3,plain,
    ! [U_10453,U_10454,U_10455] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10453),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10453,tc_HOL_Obool)),U_10454),hAPP(hAPP(c_Set_Oinsert(U_10453),U_10455),c_Orderings_Obot__class_Obot(tc_fun(U_10453,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_10453),U_10454)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10453),U_10455),U_10454))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10453),U_10454)) ),
    inference(definitional_conversion,[status(esa)],[f_2807_2]) ).

cnf(f_2807_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_10453),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10453,tc_HOL_Obool)),U_10454),hAPP(hAPP(c_Set_Oinsert(U_10453),U_10455),c_Orderings_Obot__class_Obot(tc_fun(U_10453,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_10453),U_10454)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10453),U_10455),U_10454))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10453),U_10454)) ),
    inference(clausify,[status(thm)],[f_2807_3]) ).

fof(f_2808_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_2808_2,plain,
    ! [U_10459,U_10458,U_10457,U_10456] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10456),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10456,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10456,tc_HOL_Obool)),U_10457),hAPP(hAPP(c_Set_Oinsert(U_10456),U_10458),c_Orderings_Obot__class_Obot(tc_fun(U_10456,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_10456),U_10459),c_Orderings_Obot__class_Obot(tc_fun(U_10456,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10456),U_10457)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10456),U_10459),U_10457))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10456),U_10458),U_10457))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10456),U_10457)) ),
    inference(variable_rename,[status(thm)],[f_2808_1]) ).

fof(f_2808_3,plain,
    ! [U_10456,U_10457,U_10458,U_10459] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10456),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10456,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10456,tc_HOL_Obool)),U_10457),hAPP(hAPP(c_Set_Oinsert(U_10456),U_10458),c_Orderings_Obot__class_Obot(tc_fun(U_10456,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_10456),U_10459),c_Orderings_Obot__class_Obot(tc_fun(U_10456,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10456),U_10457)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10456),U_10459),U_10457))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10456),U_10458),U_10457))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10456),U_10457)) ),
    inference(definitional_conversion,[status(esa)],[f_2808_2]) ).

cnf(f_2808_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10456),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10456,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10456,tc_HOL_Obool)),U_10457),hAPP(hAPP(c_Set_Oinsert(U_10456),U_10458),c_Orderings_Obot__class_Obot(tc_fun(U_10456,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_10456),U_10459),c_Orderings_Obot__class_Obot(tc_fun(U_10456,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10456),U_10457)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10456),U_10459),U_10457))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10456),U_10458),U_10457))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10456),U_10457)) ),
    inference(clausify,[status(thm)],[f_2808_3]) ).

fof(f_2809_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_2809_2,plain,
    ! [U_10462,U_10461,U_10460] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10460),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10460,tc_HOL_Obool)),U_10461),hAPP(hAPP(c_Set_Oinsert(U_10460),U_10462),c_Orderings_Obot__class_Obot(tc_fun(U_10460,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10460),U_10461)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10460),U_10462),U_10461))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10460),U_10461)) ),
    inference(variable_rename,[status(thm)],[f_2809_1]) ).

fof(f_2809_3,plain,
    ! [U_10460,U_10461,U_10462] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10460),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10460,tc_HOL_Obool)),U_10461),hAPP(hAPP(c_Set_Oinsert(U_10460),U_10462),c_Orderings_Obot__class_Obot(tc_fun(U_10460,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10460),U_10461)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10460),U_10462),U_10461))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10460),U_10461)) ),
    inference(definitional_conversion,[status(esa)],[f_2809_2]) ).

cnf(f_2809_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10460),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10460,tc_HOL_Obool)),U_10461),hAPP(hAPP(c_Set_Oinsert(U_10460),U_10462),c_Orderings_Obot__class_Obot(tc_fun(U_10460,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_10460),U_10461)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10460),U_10462),U_10461))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10460),U_10461)) ),
    inference(clausify,[status(thm)],[f_2809_3]) ).

fof(f_2810_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_2810_2,plain,
    ! [U_10466,U_10465,U_10464,U_10463] :
      ( hAPP(c_Finite__Set_Ocard(U_10463),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10463,tc_HOL_Obool)),U_10464),hAPP(hAPP(c_Set_Oinsert(U_10463),U_10465),U_10466))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10463),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10463,tc_HOL_Obool)),U_10464),U_10466))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | hBOOL(hAPP(hAPP(c_member(U_10463),U_10465),U_10466))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10463),U_10465),U_10464))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10463),U_10464)) ),
    inference(variable_rename,[status(thm)],[f_2810_1]) ).

fof(f_2810_3,plain,
    ! [U_10463,U_10464,U_10465,U_10466] :
      ( hAPP(c_Finite__Set_Ocard(U_10463),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10463,tc_HOL_Obool)),U_10464),hAPP(hAPP(c_Set_Oinsert(U_10463),U_10465),U_10466))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10463),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10463,tc_HOL_Obool)),U_10464),U_10466))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | hBOOL(hAPP(hAPP(c_member(U_10463),U_10465),U_10466))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10463),U_10465),U_10464))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10463),U_10464)) ),
    inference(definitional_conversion,[status(esa)],[f_2810_2]) ).

cnf(f_2810_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10463),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10463,tc_HOL_Obool)),U_10464),hAPP(hAPP(c_Set_Oinsert(U_10463),U_10465),U_10466))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10463),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10463,tc_HOL_Obool)),U_10464),U_10466))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | hBOOL(hAPP(hAPP(c_member(U_10463),U_10465),U_10466))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10463),U_10465),U_10464))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10463),U_10464)) ),
    inference(clausify,[status(thm)],[f_2810_3]) ).

fof(f_2811_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_2811_2,plain,
    ! [U_10469,U_10468,U_10467] :
      ( hAPP(c_Finite__Set_Ocard(U_10467),hAPP(hAPP(c_Set_Oinsert(U_10467),U_10469),U_10468)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10467),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10467,tc_HOL_Obool)),U_10468),hAPP(hAPP(c_Set_Oinsert(U_10467),U_10469),c_Orderings_Obot__class_Obot(tc_fun(U_10467,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10467),U_10468)) ),
    inference(variable_rename,[status(thm)],[f_2811_1]) ).

fof(f_2811_3,plain,
    ! [U_10467,U_10468,U_10469] :
      ( hAPP(c_Finite__Set_Ocard(U_10467),hAPP(hAPP(c_Set_Oinsert(U_10467),U_10469),U_10468)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10467),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10467,tc_HOL_Obool)),U_10468),hAPP(hAPP(c_Set_Oinsert(U_10467),U_10469),c_Orderings_Obot__class_Obot(tc_fun(U_10467,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10467),U_10468)) ),
    inference(definitional_conversion,[status(esa)],[f_2811_2]) ).

cnf(f_2811_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10467),hAPP(hAPP(c_Set_Oinsert(U_10467),U_10469),U_10468)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_10467),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10467,tc_HOL_Obool)),U_10468),hAPP(hAPP(c_Set_Oinsert(U_10467),U_10469),c_Orderings_Obot__class_Obot(tc_fun(U_10467,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10467),U_10468)) ),
    inference(clausify,[status(thm)],[f_2811_3]) ).

fof(f_2812_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_2812_2,plain,
    ! [U_10473,U_10472,U_10471] :
      ( hAPP(c_Finite__Set_Ocard(U_10471),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10471,tc_HOL_Obool)),U_10472),U_10473)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10471),U_10472)),hAPP(c_Finite__Set_Ocard(U_10471),U_10473))
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & ? [U_10470] : hBOOL(hAPP(hAPP(c_member(U_10471),U_10470),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10471,tc_HOL_Obool)),U_10472),U_10473))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10471),U_10473))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10471),U_10472)) ),
    inference(variable_rename,[status(thm)],[f_2812_1]) ).

fof(f_2812_3,plain,
    ! [U_10473,U_10472,U_10471] :
      ( hAPP(c_Finite__Set_Ocard(U_10471),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10471,tc_HOL_Obool)),U_10472),U_10473)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10471),U_10472)),hAPP(c_Finite__Set_Ocard(U_10471),U_10473))
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & hBOOL(hAPP(hAPP(c_member(U_10471),sK162(U_10473,U_10472,U_10471)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10471,tc_HOL_Obool)),U_10472),U_10473))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10471),U_10473))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10471),U_10472)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_10470,sK162(U_10473,U_10472,U_10471))],[f_2812_2]) ).

fof(f_2812_4,plain,
    ( ! [U_10471,U_10472,U_10473] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP796(U_10471,U_10472,U_10473) )
    & ! [U_10471,U_10472,U_10473] :
        ( hBOOL(hAPP(hAPP(c_member(U_10471),sK162(U_10473,U_10472,U_10471)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10471,tc_HOL_Obool)),U_10472),U_10473)))
        | ~ sP796(U_10471,U_10472,U_10473) )
    & ! [U_10471,U_10472,U_10473] :
        ( hAPP(c_Finite__Set_Ocard(U_10471),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10471,tc_HOL_Obool)),U_10472),U_10473)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10471),U_10472)),hAPP(c_Finite__Set_Ocard(U_10471),U_10473))
        | sP796(U_10471,U_10472,U_10473)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10471),U_10473))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10471),U_10472)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP796])],[f_2812_3]) ).

cnf(f_2812_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10471),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10471,tc_HOL_Obool)),U_10472),U_10473)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10471),U_10472)),hAPP(c_Finite__Set_Ocard(U_10471),U_10473))
    | sP796(U_10471,U_10472,U_10473)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10471),U_10473))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10471),U_10472)) ),
    inference(clausify,[status(thm)],[f_2812_4]) ).

cnf(f_2812_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10471),sK162(U_10473,U_10472,U_10471)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10471,tc_HOL_Obool)),U_10472),U_10473)))
    | ~ sP796(U_10471,U_10472,U_10473) ),
    inference(clausify,[status(thm)],[f_2812_4]) ).

cnf(f_2812_7,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP796(U_10471,U_10472,U_10473) ),
    inference(clausify,[status(thm)],[f_2812_4]) ).

fof(f_2813_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_2813_2,plain,
    ! [U_10480,U_10479,U_10478] :
      ( ( hAPP(c_Finite__Set_Ocard(U_10478),U_10479) = hAPP(c_Nat_OSuc,U_10480)
        | ! [U_10477,U_10476] :
            ( ( U_10476 != c_Orderings_Obot__class_Obot(tc_fun(U_10478,tc_HOL_Obool))
              & U_10480 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_10478),U_10476) != U_10480
            | hBOOL(hAPP(hAPP(c_member(U_10478),U_10477),U_10476))
            | U_10479 != hAPP(hAPP(c_Set_Oinsert(U_10478),U_10477),U_10476) ) )
      & ( ? [U_10475,U_10474] :
            ( ( U_10474 = c_Orderings_Obot__class_Obot(tc_fun(U_10478,tc_HOL_Obool))
              | U_10480 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_10478),U_10474) = U_10480
            & ~ hBOOL(hAPP(hAPP(c_member(U_10478),U_10475),U_10474))
            & U_10479 = hAPP(hAPP(c_Set_Oinsert(U_10478),U_10475),U_10474) )
        | hAPP(c_Finite__Set_Ocard(U_10478),U_10479) != hAPP(c_Nat_OSuc,U_10480) ) ),
    inference(variable_rename,[status(thm)],[f_2813_1]) ).

fof(f_2813_3,plain,
    ( ! [U_10486,U_10484,U_10482] :
        ( hAPP(c_Finite__Set_Ocard(U_10482),U_10484) = hAPP(c_Nat_OSuc,U_10486)
        | ! [U_10477,U_10476] :
            ( ( U_10476 != c_Orderings_Obot__class_Obot(tc_fun(U_10482,tc_HOL_Obool))
              & U_10486 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_10482),U_10476) != U_10486
            | hBOOL(hAPP(hAPP(c_member(U_10482),U_10477),U_10476))
            | U_10484 != hAPP(hAPP(c_Set_Oinsert(U_10482),U_10477),U_10476) ) )
    & ! [U_10485,U_10483,U_10481] :
        ( ? [U_10475,U_10474] :
            ( ( U_10474 = c_Orderings_Obot__class_Obot(tc_fun(U_10481,tc_HOL_Obool))
              | U_10485 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_10481),U_10474) = U_10485
            & ~ hBOOL(hAPP(hAPP(c_member(U_10481),U_10475),U_10474))
            & U_10483 = hAPP(hAPP(c_Set_Oinsert(U_10481),U_10475),U_10474) )
        | hAPP(c_Finite__Set_Ocard(U_10481),U_10483) != hAPP(c_Nat_OSuc,U_10485) ) ),
    inference(miniscope,[status(thm)],[f_2813_2]) ).

fof(f_2813_4,plain,
    ( ! [U_10486,U_10484,U_10482] :
        ( hAPP(c_Finite__Set_Ocard(U_10482),U_10484) = hAPP(c_Nat_OSuc,U_10486)
        | ! [U_10477,U_10476] :
            ( ( U_10476 != c_Orderings_Obot__class_Obot(tc_fun(U_10482,tc_HOL_Obool))
              & U_10486 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_10482),U_10476) != U_10486
            | hBOOL(hAPP(hAPP(c_member(U_10482),U_10477),U_10476))
            | U_10484 != hAPP(hAPP(c_Set_Oinsert(U_10482),U_10477),U_10476) ) )
    & ! [U_10485,U_10483,U_10481] :
        ( ? [U_10474] :
            ( ( U_10474 = c_Orderings_Obot__class_Obot(tc_fun(U_10481,tc_HOL_Obool))
              | U_10485 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_10481),U_10474) = U_10485
            & ~ hBOOL(hAPP(hAPP(c_member(U_10481),sK163(U_10485,U_10483,U_10481)),U_10474))
            & U_10483 = hAPP(hAPP(c_Set_Oinsert(U_10481),sK163(U_10485,U_10483,U_10481)),U_10474) )
        | hAPP(c_Finite__Set_Ocard(U_10481),U_10483) != hAPP(c_Nat_OSuc,U_10485) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_10475,sK163(U_10485,U_10483,U_10481))],[f_2813_3]) ).

fof(f_2813_5,plain,
    ( ! [U_10486,U_10484,U_10482] :
        ( hAPP(c_Finite__Set_Ocard(U_10482),U_10484) = hAPP(c_Nat_OSuc,U_10486)
        | ! [U_10477,U_10476] :
            ( ( U_10476 != c_Orderings_Obot__class_Obot(tc_fun(U_10482,tc_HOL_Obool))
              & U_10486 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_10482),U_10476) != U_10486
            | hBOOL(hAPP(hAPP(c_member(U_10482),U_10477),U_10476))
            | U_10484 != hAPP(hAPP(c_Set_Oinsert(U_10482),U_10477),U_10476) ) )
    & ! [U_10485,U_10483,U_10481] :
        ( ( ( sK164(U_10485,U_10483,U_10481) = c_Orderings_Obot__class_Obot(tc_fun(U_10481,tc_HOL_Obool))
            | U_10485 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & hAPP(c_Finite__Set_Ocard(U_10481),sK164(U_10485,U_10483,U_10481)) = U_10485
          & ~ hBOOL(hAPP(hAPP(c_member(U_10481),sK163(U_10485,U_10483,U_10481)),sK164(U_10485,U_10483,U_10481)))
          & U_10483 = hAPP(hAPP(c_Set_Oinsert(U_10481),sK163(U_10485,U_10483,U_10481)),sK164(U_10485,U_10483,U_10481)) )
        | hAPP(c_Finite__Set_Ocard(U_10481),U_10483) != hAPP(c_Nat_OSuc,U_10485) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_10474,sK164(U_10485,U_10483,U_10481))],[f_2813_4]) ).

fof(f_2813_6,plain,
    ( ! [U_10486,U_10476,U_10482] :
        ( U_10476 != c_Orderings_Obot__class_Obot(tc_fun(U_10482,tc_HOL_Obool))
        | ~ sP798(U_10486,U_10476,U_10482) )
    & ! [U_10486,U_10476,U_10482] :
        ( U_10486 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP798(U_10486,U_10476,U_10482) )
    & ! [U_10485,U_10483,U_10481] :
        ( sK164(U_10485,U_10483,U_10481) = c_Orderings_Obot__class_Obot(tc_fun(U_10481,tc_HOL_Obool))
        | U_10485 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP797(U_10485,U_10483,U_10481) )
    & ! [U_10485,U_10483,U_10481] :
        ( hAPP(c_Finite__Set_Ocard(U_10481),sK164(U_10485,U_10483,U_10481)) = U_10485
        | ~ sP797(U_10485,U_10483,U_10481) )
    & ! [U_10485,U_10483,U_10481] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_10481),sK163(U_10485,U_10483,U_10481)),sK164(U_10485,U_10483,U_10481)))
        | ~ sP797(U_10485,U_10483,U_10481) )
    & ! [U_10485,U_10483,U_10481] :
        ( U_10483 = hAPP(hAPP(c_Set_Oinsert(U_10481),sK163(U_10485,U_10483,U_10481)),sK164(U_10485,U_10483,U_10481))
        | ~ sP797(U_10485,U_10483,U_10481) )
    & ! [U_10486,U_10476,U_10477,U_10484,U_10482] :
        ( hAPP(c_Finite__Set_Ocard(U_10482),U_10484) = hAPP(c_Nat_OSuc,U_10486)
        | sP798(U_10486,U_10476,U_10482)
        | hAPP(c_Finite__Set_Ocard(U_10482),U_10476) != U_10486
        | hBOOL(hAPP(hAPP(c_member(U_10482),U_10477),U_10476))
        | U_10484 != hAPP(hAPP(c_Set_Oinsert(U_10482),U_10477),U_10476) )
    & ! [U_10485,U_10483,U_10481] :
        ( sP797(U_10485,U_10483,U_10481)
        | hAPP(c_Finite__Set_Ocard(U_10481),U_10483) != hAPP(c_Nat_OSuc,U_10485) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP797,sP798])],[f_2813_5]) ).

cnf(f_2813_7,plain,
    ( sP797(U_10485,U_10483,U_10481)
    | hAPP(c_Finite__Set_Ocard(U_10481),U_10483) != hAPP(c_Nat_OSuc,U_10485) ),
    inference(clausify,[status(thm)],[f_2813_6]) ).

cnf(f_2813_8,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10482),U_10484) = hAPP(c_Nat_OSuc,U_10486)
    | sP798(U_10486,U_10476,U_10482)
    | hAPP(c_Finite__Set_Ocard(U_10482),U_10476) != U_10486
    | hBOOL(hAPP(hAPP(c_member(U_10482),U_10477),U_10476))
    | U_10484 != hAPP(hAPP(c_Set_Oinsert(U_10482),U_10477),U_10476) ),
    inference(clausify,[status(thm)],[f_2813_6]) ).

cnf(f_2813_9,plain,
    ( U_10483 = hAPP(hAPP(c_Set_Oinsert(U_10481),sK163(U_10485,U_10483,U_10481)),sK164(U_10485,U_10483,U_10481))
    | ~ sP797(U_10485,U_10483,U_10481) ),
    inference(clausify,[status(thm)],[f_2813_6]) ).

cnf(f_2813_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_10481),sK163(U_10485,U_10483,U_10481)),sK164(U_10485,U_10483,U_10481)))
    | ~ sP797(U_10485,U_10483,U_10481) ),
    inference(clausify,[status(thm)],[f_2813_6]) ).

cnf(f_2813_11,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10481),sK164(U_10485,U_10483,U_10481)) = U_10485
    | ~ sP797(U_10485,U_10483,U_10481) ),
    inference(clausify,[status(thm)],[f_2813_6]) ).

cnf(f_2813_12,plain,
    ( sK164(U_10485,U_10483,U_10481) = c_Orderings_Obot__class_Obot(tc_fun(U_10481,tc_HOL_Obool))
    | U_10485 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP797(U_10485,U_10483,U_10481) ),
    inference(clausify,[status(thm)],[f_2813_6]) ).

cnf(f_2813_13,plain,
    ( U_10486 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP798(U_10486,U_10476,U_10482) ),
    inference(clausify,[status(thm)],[f_2813_6]) ).

cnf(f_2813_14,plain,
    ( U_10476 != c_Orderings_Obot__class_Obot(tc_fun(U_10482,tc_HOL_Obool))
    | ~ sP798(U_10486,U_10476,U_10482) ),
    inference(clausify,[status(thm)],[f_2813_6]) ).

fof(f_2814_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_2814_2,plain,
    ! [U_10491,U_10490,U_10489,U_10488] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10491),hAPP(c_Finite__Set_Ocard(U_10488),U_10489)))
      | ? [U_10487] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10491),hAPP(c_Finite__Set_Ocard(U_10488),U_10487)))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_10488,tc_HOL_Obool)),U_10487),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10488),U_10489),U_10490))) )
      | ~ c_Equiv__Relations_Oequiv(U_10488,U_10489,U_10490)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10488),U_10489)) ),
    inference(variable_rename,[status(thm)],[f_2814_1]) ).

fof(f_2814_3,plain,
    ! [U_10491,U_10490,U_10489,U_10488] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10491),hAPP(c_Finite__Set_Ocard(U_10488),U_10489)))
      | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10491),hAPP(c_Finite__Set_Ocard(U_10488),sK165(U_10491,U_10490,U_10489,U_10488))))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_10488,tc_HOL_Obool)),sK165(U_10491,U_10490,U_10489,U_10488)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10488),U_10489),U_10490))) )
      | ~ c_Equiv__Relations_Oequiv(U_10488,U_10489,U_10490)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10488),U_10489)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_10487,sK165(U_10491,U_10490,U_10489,U_10488))],[f_2814_2]) ).

fof(f_2814_4,plain,
    ( ! [U_10490,U_10491,U_10489,U_10488] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10491),hAPP(c_Finite__Set_Ocard(U_10488),sK165(U_10491,U_10490,U_10489,U_10488))))
        | ~ sP799(U_10490,U_10491,U_10489,U_10488) )
    & ! [U_10490,U_10491,U_10489,U_10488] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10488,tc_HOL_Obool)),sK165(U_10491,U_10490,U_10489,U_10488)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10488),U_10489),U_10490)))
        | ~ sP799(U_10490,U_10491,U_10489,U_10488) )
    & ! [U_10490,U_10491,U_10489,U_10488] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10491),hAPP(c_Finite__Set_Ocard(U_10488),U_10489)))
        | sP799(U_10490,U_10491,U_10489,U_10488)
        | ~ c_Equiv__Relations_Oequiv(U_10488,U_10489,U_10490)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10488),U_10489)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP799])],[f_2814_3]) ).

cnf(f_2814_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10491),hAPP(c_Finite__Set_Ocard(U_10488),U_10489)))
    | sP799(U_10490,U_10491,U_10489,U_10488)
    | ~ c_Equiv__Relations_Oequiv(U_10488,U_10489,U_10490)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10488),U_10489)) ),
    inference(clausify,[status(thm)],[f_2814_4]) ).

cnf(f_2814_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10488,tc_HOL_Obool)),sK165(U_10491,U_10490,U_10489,U_10488)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10488),U_10489),U_10490)))
    | ~ sP799(U_10490,U_10491,U_10489,U_10488) ),
    inference(clausify,[status(thm)],[f_2814_4]) ).

cnf(f_2814_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_10491),hAPP(c_Finite__Set_Ocard(U_10488),sK165(U_10491,U_10490,U_10489,U_10488))))
    | ~ sP799(U_10490,U_10491,U_10489,U_10488) ),
    inference(clausify,[status(thm)],[f_2814_4]) ).

fof(f_2815_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_2815_2,plain,
    ! [U_10493,U_10492] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10492,U_10493)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10493),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10492),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_2815_1]) ).

fof(f_2815_3,plain,
    ! [U_10493,U_10492] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10492,U_10493)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10493),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10492),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_2815_2]) ).

cnf(f_2815_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10492,U_10493)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10493),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10492),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_2815_3]) ).

fof(f_2816_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_2816_2,plain,
    ! [U_10497,U_10496,U_10495,U_10494] :
      ( ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10494,U_10496)),c_Sum__Type_OPlus(U_10494,U_10496,U_10495,U_10497)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10496),U_10497))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_10494),U_10495)) ) )
      & ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10494,U_10496)),c_Sum__Type_OPlus(U_10494,U_10496,U_10495,U_10497)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10494),U_10495)),hAPP(c_Finite__Set_Ocard(U_10496),U_10497))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10496),U_10497))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10494),U_10495)) ) ),
    inference(variable_rename,[status(thm)],[f_2816_1]) ).

fof(f_2816_3,plain,
    ( ! [U_10505,U_10503,U_10501,U_10499] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10499,U_10503)),c_Sum__Type_OPlus(U_10499,U_10503,U_10501,U_10505)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10503),U_10505))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_10499),U_10501)) ) )
    & ! [U_10504,U_10502,U_10500,U_10498] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10498,U_10502)),c_Sum__Type_OPlus(U_10498,U_10502,U_10500,U_10504)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10498),U_10500)),hAPP(c_Finite__Set_Ocard(U_10502),U_10504))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10502),U_10504))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10498),U_10500)) ) ),
    inference(miniscope,[status(thm)],[f_2816_2]) ).

fof(f_2816_4,plain,
    ( ! [U_10499,U_10501,U_10503,U_10505] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10503),U_10505))
        | ~ sP800(U_10499,U_10501,U_10503,U_10505) )
    & ! [U_10499,U_10501,U_10503,U_10505] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10499),U_10501))
        | ~ sP800(U_10499,U_10501,U_10503,U_10505) )
    & ! [U_10499,U_10501,U_10503,U_10505] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10499,U_10503)),c_Sum__Type_OPlus(U_10499,U_10503,U_10501,U_10505)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP800(U_10499,U_10501,U_10503,U_10505) )
    & ! [U_10498,U_10500,U_10502,U_10504] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10498,U_10502)),c_Sum__Type_OPlus(U_10498,U_10502,U_10500,U_10504)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10498),U_10500)),hAPP(c_Finite__Set_Ocard(U_10502),U_10504))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10502),U_10504))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10498),U_10500)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP800])],[f_2816_3]) ).

cnf(f_2816_5,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10498,U_10502)),c_Sum__Type_OPlus(U_10498,U_10502,U_10500,U_10504)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10498),U_10500)),hAPP(c_Finite__Set_Ocard(U_10502),U_10504))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10502),U_10504))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10498),U_10500)) ),
    inference(clausify,[status(thm)],[f_2816_4]) ).

cnf(f_2816_6,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10499,U_10503)),c_Sum__Type_OPlus(U_10499,U_10503,U_10501,U_10505)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP800(U_10499,U_10501,U_10503,U_10505) ),
    inference(clausify,[status(thm)],[f_2816_4]) ).

cnf(f_2816_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10499),U_10501))
    | ~ sP800(U_10499,U_10501,U_10503,U_10505) ),
    inference(clausify,[status(thm)],[f_2816_4]) ).

cnf(f_2816_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10503),U_10505))
    | ~ sP800(U_10499,U_10501,U_10503,U_10505) ),
    inference(clausify,[status(thm)],[f_2816_4]) ).

fof(f_2817_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_2817_2,plain,
    ! [U_10511,U_10510,U_10509,U_10508,U_10507,U_10506] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10507,U_10506),hAPP(hAPP(c_COMBC(U_10507,U_10506,U_10506),hAPP(hAPP(c_COMBS(U_10507,U_10506,tc_fun(U_10506,U_10506)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10506,tc_fun(U_10506,U_10506)),U_10507),c_If(U_10506)),hAPP(hAPP(c_COMBC(U_10507,U_10507,tc_HOL_Obool),c_fequal),U_10509))),U_10510)),U_10511)),U_10508) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10506),U_10511),hAPP(c_Finite__Set_Ocard(U_10507),U_10508))
          | hBOOL(hAPP(hAPP(c_member(U_10507),U_10509),U_10508)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10507,U_10506),hAPP(hAPP(c_COMBC(U_10507,U_10506,U_10506),hAPP(hAPP(c_COMBS(U_10507,U_10506,tc_fun(U_10506,U_10506)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10506,tc_fun(U_10506,U_10506)),U_10507),c_If(U_10506)),hAPP(hAPP(c_COMBC(U_10507,U_10507,tc_HOL_Obool),c_fequal),U_10509))),U_10510)),U_10511)),U_10508) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10506),hAPP(U_10510,U_10509)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10506),U_10511),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10507),U_10508)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_member(U_10507),U_10509),U_10508)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10507),U_10508))
      | ~ class_Groups_Ocomm__monoid__mult(U_10506) ),
    inference(variable_rename,[status(thm)],[f_2817_1]) ).

fof(f_2817_3,plain,
    ( ! [U_10506,U_10507,U_10508,U_10509,U_10510,U_10511] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10507,U_10506),hAPP(hAPP(c_COMBC(U_10507,U_10506,U_10506),hAPP(hAPP(c_COMBS(U_10507,U_10506,tc_fun(U_10506,U_10506)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10506,tc_fun(U_10506,U_10506)),U_10507),c_If(U_10506)),hAPP(hAPP(c_COMBC(U_10507,U_10507,tc_HOL_Obool),c_fequal),U_10509))),U_10510)),U_10511)),U_10508) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10506),U_10511),hAPP(c_Finite__Set_Ocard(U_10507),U_10508))
        | hBOOL(hAPP(hAPP(c_member(U_10507),U_10509),U_10508))
        | ~ sP801(U_10506,U_10507,U_10508,U_10509,U_10510,U_10511) )
    & ! [U_10506,U_10507,U_10508,U_10509,U_10510,U_10511] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10507,U_10506),hAPP(hAPP(c_COMBC(U_10507,U_10506,U_10506),hAPP(hAPP(c_COMBS(U_10507,U_10506,tc_fun(U_10506,U_10506)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10506,tc_fun(U_10506,U_10506)),U_10507),c_If(U_10506)),hAPP(hAPP(c_COMBC(U_10507,U_10507,tc_HOL_Obool),c_fequal),U_10509))),U_10510)),U_10511)),U_10508) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10506),hAPP(U_10510,U_10509)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10506),U_10511),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10507),U_10508)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10507),U_10509),U_10508))
        | ~ sP801(U_10506,U_10507,U_10508,U_10509,U_10510,U_10511) )
    & ! [U_10506,U_10507,U_10508,U_10509,U_10510,U_10511] :
        ( sP801(U_10506,U_10507,U_10508,U_10509,U_10510,U_10511)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10507),U_10508))
        | ~ class_Groups_Ocomm__monoid__mult(U_10506) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP801])],[f_2817_2]) ).

cnf(f_2817_4,plain,
    ( sP801(U_10506,U_10507,U_10508,U_10509,U_10510,U_10511)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10507),U_10508))
    | ~ class_Groups_Ocomm__monoid__mult(U_10506) ),
    inference(clausify,[status(thm)],[f_2817_3]) ).

cnf(f_2817_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10507,U_10506),hAPP(hAPP(c_COMBC(U_10507,U_10506,U_10506),hAPP(hAPP(c_COMBS(U_10507,U_10506,tc_fun(U_10506,U_10506)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10506,tc_fun(U_10506,U_10506)),U_10507),c_If(U_10506)),hAPP(hAPP(c_COMBC(U_10507,U_10507,tc_HOL_Obool),c_fequal),U_10509))),U_10510)),U_10511)),U_10508) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10506),hAPP(U_10510,U_10509)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10506),U_10511),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10507),U_10508)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10507),U_10509),U_10508))
    | ~ sP801(U_10506,U_10507,U_10508,U_10509,U_10510,U_10511) ),
    inference(clausify,[status(thm)],[f_2817_3]) ).

cnf(f_2817_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10507,U_10506),hAPP(hAPP(c_COMBC(U_10507,U_10506,U_10506),hAPP(hAPP(c_COMBS(U_10507,U_10506,tc_fun(U_10506,U_10506)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10506,tc_fun(U_10506,U_10506)),U_10507),c_If(U_10506)),hAPP(hAPP(c_COMBC(U_10507,U_10507,tc_HOL_Obool),c_fequal),U_10509))),U_10510)),U_10511)),U_10508) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10506),U_10511),hAPP(c_Finite__Set_Ocard(U_10507),U_10508))
    | hBOOL(hAPP(hAPP(c_member(U_10507),U_10509),U_10508))
    | ~ sP801(U_10506,U_10507,U_10508,U_10509,U_10510,U_10511) ),
    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_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__greaterThanLessThan__int]) ).

fof(f_2818_2,plain,
    ! [U_10513,U_10512] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10512,U_10513))),
    inference(variable_rename,[status(thm)],[f_2818_1]) ).

fof(f_2818_3,plain,
    ! [U_10513,U_10512] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10512,U_10513))),
    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_OgreaterThanLessThan(tc_Int_Oint,U_10512,U_10513))),
    inference(clausify,[status(thm)],[f_2818_3]) ).

fof(f_2819_1,plain,
    ! [V_A_2,T_c,V_B_2,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_sum(T_c,T_b)),hAPP(c_Sum__Type_OInr(T_b,T_c),V_b_2)),c_Sum__Type_OPlus(T_c,T_b,V_A_2,V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_InrI]) ).

fof(f_2819_2,plain,
    ! [U_10518,U_10517,U_10516,U_10515,U_10514] :
      ( hBOOL(hAPP(hAPP(c_member(tc_sum(U_10517,U_10514)),hAPP(c_Sum__Type_OInr(U_10514,U_10517),U_10515)),c_Sum__Type_OPlus(U_10517,U_10514,U_10518,U_10516)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10514),U_10515),U_10516)) ),
    inference(variable_rename,[status(thm)],[f_2819_1]) ).

fof(f_2819_3,plain,
    ! [U_10514,U_10516,U_10517,U_10515,U_10518] :
      ( hBOOL(hAPP(hAPP(c_member(tc_sum(U_10517,U_10514)),hAPP(c_Sum__Type_OInr(U_10514,U_10517),U_10515)),c_Sum__Type_OPlus(U_10517,U_10514,U_10518,U_10516)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10514),U_10515),U_10516)) ),
    inference(definitional_conversion,[status(esa)],[f_2819_2]) ).

cnf(f_2819_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_sum(U_10517,U_10514)),hAPP(c_Sum__Type_OInr(U_10514,U_10517),U_10515)),c_Sum__Type_OPlus(U_10517,U_10514,U_10518,U_10516)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10514),U_10515),U_10516)) ),
    inference(clausify,[status(thm)],[f_2819_3]) ).

fof(f_2820_1,plain,
    ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_sum(T_b,T_c)),hAPP(c_Sum__Type_OInl(T_b,T_c),V_a_2)),c_Sum__Type_OPlus(T_b,T_c,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_InlI]) ).

fof(f_2820_2,plain,
    ! [U_10523,U_10522,U_10521,U_10520,U_10519] :
      ( hBOOL(hAPP(hAPP(c_member(tc_sum(U_10519,U_10522)),hAPP(c_Sum__Type_OInl(U_10519,U_10522),U_10520)),c_Sum__Type_OPlus(U_10519,U_10522,U_10521,U_10523)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10519),U_10520),U_10521)) ),
    inference(variable_rename,[status(thm)],[f_2820_1]) ).

fof(f_2820_3,plain,
    ! [U_10519,U_10520,U_10521,U_10522,U_10523] :
      ( hBOOL(hAPP(hAPP(c_member(tc_sum(U_10519,U_10522)),hAPP(c_Sum__Type_OInl(U_10519,U_10522),U_10520)),c_Sum__Type_OPlus(U_10519,U_10522,U_10521,U_10523)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10519),U_10520),U_10521)) ),
    inference(definitional_conversion,[status(esa)],[f_2820_2]) ).

cnf(f_2820_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_sum(U_10519,U_10522)),hAPP(c_Sum__Type_OInl(U_10519,U_10522),U_10520)),c_Sum__Type_OPlus(U_10519,U_10522,U_10521,U_10523)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10519),U_10520),U_10521)) ),
    inference(clausify,[status(thm)],[f_2820_3]) ).

fof(f_2821_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_2821_2,plain,
    ! [U_10527,U_10526,U_10525,U_10524] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_10524),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10525,U_10524),U_10526),U_10527)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10525,U_10524),hAPP(hAPP(c_COMBB(U_10524,U_10524,U_10525),c_Groups_Oabs__class_Oabs(U_10524)),U_10526)),U_10527)
      | ~ class_Fields_Olinordered__field(U_10524) ),
    inference(variable_rename,[status(thm)],[f_2821_1]) ).

fof(f_2821_3,plain,
    ! [U_10524,U_10525,U_10526,U_10527] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_10524),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10525,U_10524),U_10526),U_10527)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10525,U_10524),hAPP(hAPP(c_COMBB(U_10524,U_10524,U_10525),c_Groups_Oabs__class_Oabs(U_10524)),U_10526)),U_10527)
      | ~ class_Fields_Olinordered__field(U_10524) ),
    inference(definitional_conversion,[status(esa)],[f_2821_2]) ).

cnf(f_2821_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_10524),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10525,U_10524),U_10526),U_10527)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10525,U_10524),hAPP(hAPP(c_COMBB(U_10524,U_10524,U_10525),c_Groups_Oabs__class_Oabs(U_10524)),U_10526)),U_10527)
    | ~ class_Fields_Olinordered__field(U_10524) ),
    inference(clausify,[status(thm)],[f_2821_3]) ).

fof(f_2822_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_2822_2,plain,
    ! [U_10532,U_10531,U_10530,U_10529,U_10528] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10529,U_10528),hAPP(hAPP(c_COMBS(U_10529,U_10528,U_10528),hAPP(hAPP(c_COMBB(U_10528,tc_fun(U_10528,U_10528),U_10529),c_Groups_Otimes__class_Otimes(U_10528)),U_10530)),U_10531)),U_10532) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10528),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10529,U_10528),U_10530),U_10532)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10529,U_10528),U_10531),U_10532))
      | ~ class_Groups_Ocomm__monoid__mult(U_10528) ),
    inference(variable_rename,[status(thm)],[f_2822_1]) ).

fof(f_2822_3,plain,
    ! [U_10528,U_10529,U_10530,U_10531,U_10532] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10529,U_10528),hAPP(hAPP(c_COMBS(U_10529,U_10528,U_10528),hAPP(hAPP(c_COMBB(U_10528,tc_fun(U_10528,U_10528),U_10529),c_Groups_Otimes__class_Otimes(U_10528)),U_10530)),U_10531)),U_10532) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10528),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10529,U_10528),U_10530),U_10532)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10529,U_10528),U_10531),U_10532))
      | ~ class_Groups_Ocomm__monoid__mult(U_10528) ),
    inference(definitional_conversion,[status(esa)],[f_2822_2]) ).

cnf(f_2822_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10529,U_10528),hAPP(hAPP(c_COMBS(U_10529,U_10528,U_10528),hAPP(hAPP(c_COMBB(U_10528,tc_fun(U_10528,U_10528),U_10529),c_Groups_Otimes__class_Otimes(U_10528)),U_10530)),U_10531)),U_10532) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10528),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10529,U_10528),U_10530),U_10532)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10529,U_10528),U_10531),U_10532))
    | ~ class_Groups_Ocomm__monoid__mult(U_10528) ),
    inference(clausify,[status(thm)],[f_2822_3]) ).

fof(f_2823_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_2823_2,plain,
    ! [U_10535,U_10534,U_10533] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10534,U_10533),hAPP(c_COMBK(U_10533,U_10534),c_Groups_Oone__class_Oone(U_10533))),U_10535) = c_Groups_Oone__class_Oone(U_10533)
      | ~ class_Groups_Ocomm__monoid__mult(U_10533) ),
    inference(variable_rename,[status(thm)],[f_2823_1]) ).

fof(f_2823_3,plain,
    ! [U_10533,U_10534,U_10535] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10534,U_10533),hAPP(c_COMBK(U_10533,U_10534),c_Groups_Oone__class_Oone(U_10533))),U_10535) = c_Groups_Oone__class_Oone(U_10533)
      | ~ class_Groups_Ocomm__monoid__mult(U_10533) ),
    inference(definitional_conversion,[status(esa)],[f_2823_2]) ).

cnf(f_2823_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10534,U_10533),hAPP(c_COMBK(U_10533,U_10534),c_Groups_Oone__class_Oone(U_10533))),U_10535) = c_Groups_Oone__class_Oone(U_10533)
    | ~ class_Groups_Ocomm__monoid__mult(U_10533) ),
    inference(clausify,[status(thm)],[f_2823_3]) ).

fof(f_2824_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_2824_2,plain,
    ! [U_10538,U_10537,U_10536] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10536,tc_Nat_Onat),U_10537),U_10538) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10536,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10536),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10537)),U_10538)),
    inference(variable_rename,[status(thm)],[f_2824_1]) ).

fof(f_2824_3,plain,
    ! [U_10536,U_10537,U_10538] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10536,tc_Nat_Onat),U_10537),U_10538) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10536,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10536),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10537)),U_10538)),
    inference(definitional_conversion,[status(esa)],[f_2824_2]) ).

cnf(f_2824_4,plain,
    hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10536,tc_Nat_Onat),U_10537),U_10538) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10536,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10536),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10537)),U_10538)),
    inference(clausify,[status(thm)],[f_2824_3]) ).

fof(f_2825_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_2825_2,plain,
    ! [U_10541,U_10540,U_10539] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10539,tc_Nat_Onat),U_10540),U_10541)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10539,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10539),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10540)),U_10541),
    inference(variable_rename,[status(thm)],[f_2825_1]) ).

fof(f_2825_3,plain,
    ! [U_10539,U_10540,U_10541] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10539,tc_Nat_Onat),U_10540),U_10541)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10539,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10539),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10540)),U_10541),
    inference(definitional_conversion,[status(esa)],[f_2825_2]) ).

cnf(f_2825_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10539,tc_Nat_Onat),U_10540),U_10541)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10539,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10539),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10540)),U_10541),
    inference(clausify,[status(thm)],[f_2825_3]) ).

fof(f_2826_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_2826_2,plain,
    ! [U_10545,U_10544,U_10543,U_10542] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10542),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10543,tc_Nat_Onat),U_10544),U_10545)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10543,U_10542),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10542,U_10543),c_Nat_Osemiring__1__class_Oof__nat(U_10542)),U_10544)),U_10545)
      | ~ class_Rings_Osemiring__1(U_10542)
      | ~ class_Groups_Ocomm__monoid__mult(U_10542) ),
    inference(variable_rename,[status(thm)],[f_2826_1]) ).

fof(f_2826_3,plain,
    ! [U_10542,U_10543,U_10544,U_10545] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10542),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10543,tc_Nat_Onat),U_10544),U_10545)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10543,U_10542),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10542,U_10543),c_Nat_Osemiring__1__class_Oof__nat(U_10542)),U_10544)),U_10545)
      | ~ class_Rings_Osemiring__1(U_10542)
      | ~ class_Groups_Ocomm__monoid__mult(U_10542) ),
    inference(definitional_conversion,[status(esa)],[f_2826_2]) ).

cnf(f_2826_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10542),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10543,tc_Nat_Onat),U_10544),U_10545)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10543,U_10542),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10542,U_10543),c_Nat_Osemiring__1__class_Oof__nat(U_10542)),U_10544)),U_10545)
    | ~ class_Rings_Osemiring__1(U_10542)
    | ~ class_Groups_Ocomm__monoid__mult(U_10542) ),
    inference(clausify,[status(thm)],[f_2826_3]) ).

fof(f_2827_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_2827_2,plain,
    ! [U_10549,U_10548,U_10547,U_10546] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_10546),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10547,tc_Int_Oint),U_10548),U_10549)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10547,U_10546),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10546,U_10547),c_Int_Oring__1__class_Oof__int(U_10546)),U_10548)),U_10549)
      | ~ class_Rings_Oring__1(U_10546)
      | ~ class_Groups_Ocomm__monoid__mult(U_10546) ),
    inference(variable_rename,[status(thm)],[f_2827_1]) ).

fof(f_2827_3,plain,
    ! [U_10546,U_10547,U_10548,U_10549] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_10546),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10547,tc_Int_Oint),U_10548),U_10549)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10547,U_10546),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10546,U_10547),c_Int_Oring__1__class_Oof__int(U_10546)),U_10548)),U_10549)
      | ~ class_Rings_Oring__1(U_10546)
      | ~ class_Groups_Ocomm__monoid__mult(U_10546) ),
    inference(definitional_conversion,[status(esa)],[f_2827_2]) ).

cnf(f_2827_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_10546),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10547,tc_Int_Oint),U_10548),U_10549)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10547,U_10546),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10546,U_10547),c_Int_Oring__1__class_Oof__int(U_10546)),U_10548)),U_10549)
    | ~ class_Rings_Oring__1(U_10546)
    | ~ class_Groups_Ocomm__monoid__mult(U_10546) ),
    inference(clausify,[status(thm)],[f_2827_3]) ).

fof(f_2828_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_2828_2,plain,
    ! [U_10552,U_10551,U_10550] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10550),U_10551),U_10552) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10550),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10550,tc_Int_Oint),U_10551),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10552))
      | ~ class_Groups_Ocomm__monoid__mult(U_10550)
      | ~ class_Groups_Ocomm__monoid__add(U_10550) ),
    inference(variable_rename,[status(thm)],[f_2828_1]) ).

fof(f_2828_3,plain,
    ! [U_10550,U_10551,U_10552] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10550),U_10551),U_10552) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10550),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10550,tc_Int_Oint),U_10551),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10552))
      | ~ class_Groups_Ocomm__monoid__mult(U_10550)
      | ~ class_Groups_Ocomm__monoid__add(U_10550) ),
    inference(definitional_conversion,[status(esa)],[f_2828_2]) ).

cnf(f_2828_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10550),U_10551),U_10552) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10550),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10550,tc_Int_Oint),U_10551),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10552))
    | ~ class_Groups_Ocomm__monoid__mult(U_10550)
    | ~ class_Groups_Ocomm__monoid__add(U_10550) ),
    inference(clausify,[status(thm)],[f_2828_3]) ).

fof(f_2829_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_2829_2,plain,
    ! [U_10558,U_10557,U_10556,U_10555] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10556,U_10555),U_10558),U_10557) = c_Groups_Ozero__class_Ozero(U_10555)
          | ! [U_10554] :
              ( hAPP(U_10558,U_10554) != c_Groups_Ozero__class_Ozero(U_10555)
              | ~ hBOOL(hAPP(hAPP(c_member(U_10556),U_10554),U_10557)) ) )
        & ( ? [U_10553] :
              ( hAPP(U_10558,U_10553) = c_Groups_Ozero__class_Ozero(U_10555)
              & hBOOL(hAPP(hAPP(c_member(U_10556),U_10553),U_10557)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10556,U_10555),U_10558),U_10557) != c_Groups_Ozero__class_Ozero(U_10555) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10556),U_10557))
      | ~ class_Rings_Ono__zero__divisors(U_10555)
      | ~ class_Rings_Ocomm__semiring__1(U_10555) ),
    inference(variable_rename,[status(thm)],[f_2829_1]) ).

fof(f_2829_3,plain,
    ! [U_10558,U_10557,U_10556,U_10555] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10556,U_10555),U_10558),U_10557) = c_Groups_Ozero__class_Ozero(U_10555)
          | ! [U_10554] :
              ( hAPP(U_10558,U_10554) != c_Groups_Ozero__class_Ozero(U_10555)
              | ~ hBOOL(hAPP(hAPP(c_member(U_10556),U_10554),U_10557)) ) )
        & ( ( hAPP(U_10558,sK166(U_10558,U_10557,U_10556,U_10555)) = c_Groups_Ozero__class_Ozero(U_10555)
            & hBOOL(hAPP(hAPP(c_member(U_10556),sK166(U_10558,U_10557,U_10556,U_10555)),U_10557)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10556,U_10555),U_10558),U_10557) != c_Groups_Ozero__class_Ozero(U_10555) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10556),U_10557))
      | ~ class_Rings_Ono__zero__divisors(U_10555)
      | ~ class_Rings_Ocomm__semiring__1(U_10555) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_10553,sK166(U_10558,U_10557,U_10556,U_10555))],[f_2829_2]) ).

fof(f_2829_4,plain,
    ( ! [U_10555,U_10556,U_10557,U_10558] :
        ( hAPP(U_10558,sK166(U_10558,U_10557,U_10556,U_10555)) = c_Groups_Ozero__class_Ozero(U_10555)
        | ~ sP802(U_10555,U_10556,U_10557,U_10558) )
    & ! [U_10555,U_10556,U_10557,U_10558] :
        ( hBOOL(hAPP(hAPP(c_member(U_10556),sK166(U_10558,U_10557,U_10556,U_10555)),U_10557))
        | ~ sP802(U_10555,U_10556,U_10557,U_10558) )
    & ! [U_10554,U_10555,U_10556,U_10557,U_10558] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10556,U_10555),U_10558),U_10557) = c_Groups_Ozero__class_Ozero(U_10555)
        | hAPP(U_10558,U_10554) != c_Groups_Ozero__class_Ozero(U_10555)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10556),U_10554),U_10557))
        | ~ sP803(U_10554,U_10555,U_10556,U_10557,U_10558) )
    & ! [U_10554,U_10555,U_10556,U_10557,U_10558] :
        ( sP802(U_10555,U_10556,U_10557,U_10558)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10556,U_10555),U_10558),U_10557) != c_Groups_Ozero__class_Ozero(U_10555)
        | ~ sP803(U_10554,U_10555,U_10556,U_10557,U_10558) )
    & ! [U_10554,U_10555,U_10556,U_10557,U_10558] :
        ( sP803(U_10554,U_10555,U_10556,U_10557,U_10558)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10556),U_10557))
        | ~ class_Rings_Ono__zero__divisors(U_10555)
        | ~ class_Rings_Ocomm__semiring__1(U_10555) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP802,sP803])],[f_2829_3]) ).

cnf(f_2829_5,plain,
    ( sP803(U_10554,U_10555,U_10556,U_10557,U_10558)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10556),U_10557))
    | ~ class_Rings_Ono__zero__divisors(U_10555)
    | ~ class_Rings_Ocomm__semiring__1(U_10555) ),
    inference(clausify,[status(thm)],[f_2829_4]) ).

cnf(f_2829_6,plain,
    ( sP802(U_10555,U_10556,U_10557,U_10558)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10556,U_10555),U_10558),U_10557) != c_Groups_Ozero__class_Ozero(U_10555)
    | ~ sP803(U_10554,U_10555,U_10556,U_10557,U_10558) ),
    inference(clausify,[status(thm)],[f_2829_4]) ).

cnf(f_2829_7,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10556,U_10555),U_10558),U_10557) = c_Groups_Ozero__class_Ozero(U_10555)
    | hAPP(U_10558,U_10554) != c_Groups_Ozero__class_Ozero(U_10555)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10556),U_10554),U_10557))
    | ~ sP803(U_10554,U_10555,U_10556,U_10557,U_10558) ),
    inference(clausify,[status(thm)],[f_2829_4]) ).

cnf(f_2829_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10556),sK166(U_10558,U_10557,U_10556,U_10555)),U_10557))
    | ~ sP802(U_10555,U_10556,U_10557,U_10558) ),
    inference(clausify,[status(thm)],[f_2829_4]) ).

cnf(f_2829_9,plain,
    ( hAPP(U_10558,sK166(U_10558,U_10557,U_10556,U_10555)) = c_Groups_Ozero__class_Ozero(U_10555)
    | ~ sP802(U_10555,U_10556,U_10557,U_10558) ),
    inference(clausify,[status(thm)],[f_2829_4]) ).

fof(f_2830_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_2830_2,plain,
    ! [U_10563,U_10562,U_10561,U_10560] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10561,U_10560),U_10563),U_10562) = c_Groups_Ozero__class_Ozero(U_10560)
      | ! [U_10559] :
          ( hAPP(U_10563,U_10559) != c_Groups_Ozero__class_Ozero(U_10560)
          | ~ hBOOL(hAPP(hAPP(c_member(U_10561),U_10559),U_10562)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10561),U_10562))
      | ~ class_Rings_Ocomm__semiring__1(U_10560) ),
    inference(variable_rename,[status(thm)],[f_2830_1]) ).

fof(f_2830_3,plain,
    ! [U_10563,U_10561,U_10562,U_10559,U_10560] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10561,U_10560),U_10563),U_10562) = c_Groups_Ozero__class_Ozero(U_10560)
      | hAPP(U_10563,U_10559) != c_Groups_Ozero__class_Ozero(U_10560)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10561),U_10559),U_10562))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10561),U_10562))
      | ~ class_Rings_Ocomm__semiring__1(U_10560) ),
    inference(definitional_conversion,[status(esa)],[f_2830_2]) ).

cnf(f_2830_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10561,U_10560),U_10563),U_10562) = c_Groups_Ozero__class_Ozero(U_10560)
    | hAPP(U_10563,U_10559) != c_Groups_Ozero__class_Ozero(U_10560)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10561),U_10559),U_10562))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10561),U_10562))
    | ~ class_Rings_Ocomm__semiring__1(U_10560) ),
    inference(clausify,[status(thm)],[f_2830_3]) ).

fof(f_2831_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_2831_2,plain,
    ! [U_10566,U_10565,U_10564] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10565,U_10564),U_10566),c_Orderings_Obot__class_Obot(tc_fun(U_10565,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10564)
      | ~ class_Groups_Ocomm__monoid__mult(U_10564) ),
    inference(variable_rename,[status(thm)],[f_2831_1]) ).

fof(f_2831_3,plain,
    ! [U_10565,U_10566,U_10564] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10565,U_10564),U_10566),c_Orderings_Obot__class_Obot(tc_fun(U_10565,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10564)
      | ~ class_Groups_Ocomm__monoid__mult(U_10564) ),
    inference(definitional_conversion,[status(esa)],[f_2831_2]) ).

cnf(f_2831_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10565,U_10564),U_10566),c_Orderings_Obot__class_Obot(tc_fun(U_10565,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10564)
    | ~ class_Groups_Ocomm__monoid__mult(U_10564) ),
    inference(clausify,[status(thm)],[f_2831_3]) ).

fof(f_2832_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_2832_2,plain,
    ! [U_10569,U_10568,U_10567] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10568,U_10567),U_10569),c_Orderings_Obot__class_Obot(tc_fun(U_10568,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10567)
      | ~ class_Groups_Ocomm__monoid__mult(U_10567) ),
    inference(variable_rename,[status(thm)],[f_2832_1]) ).

fof(f_2832_3,plain,
    ! [U_10567,U_10568,U_10569] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10568,U_10567),U_10569),c_Orderings_Obot__class_Obot(tc_fun(U_10568,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10567)
      | ~ class_Groups_Ocomm__monoid__mult(U_10567) ),
    inference(definitional_conversion,[status(esa)],[f_2832_2]) ).

cnf(f_2832_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10568,U_10567),U_10569),c_Orderings_Obot__class_Obot(tc_fun(U_10568,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10567)
    | ~ class_Groups_Ocomm__monoid__mult(U_10567) ),
    inference(clausify,[status(thm)],[f_2832_3]) ).

fof(f_2833_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_2833_2,plain,
    ! [U_10573,U_10572,U_10571,U_10570] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10571,U_10570),U_10573),U_10572) = c_Groups_Oone__class_Oone(U_10570)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10571),U_10572))
      | ~ class_Groups_Ocomm__monoid__mult(U_10570) ),
    inference(variable_rename,[status(thm)],[f_2833_1]) ).

fof(f_2833_3,plain,
    ! [U_10570,U_10571,U_10572,U_10573] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10571,U_10570),U_10573),U_10572) = c_Groups_Oone__class_Oone(U_10570)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10571),U_10572))
      | ~ class_Groups_Ocomm__monoid__mult(U_10570) ),
    inference(definitional_conversion,[status(esa)],[f_2833_2]) ).

cnf(f_2833_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10571,U_10570),U_10573),U_10572) = c_Groups_Oone__class_Oone(U_10570)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10571),U_10572))
    | ~ class_Groups_Ocomm__monoid__mult(U_10570) ),
    inference(clausify,[status(thm)],[f_2833_3]) ).

fof(f_2834_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_2834_2,plain,
    ! [U_10577,U_10576,U_10575,U_10574] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10575,U_10574),U_10577),U_10576) = c_Groups_Oone__class_Oone(U_10574)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10575),U_10576))
      | ~ class_Groups_Ocomm__monoid__mult(U_10574) ),
    inference(variable_rename,[status(thm)],[f_2834_1]) ).

fof(f_2834_3,plain,
    ! [U_10575,U_10574,U_10576,U_10577] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10575,U_10574),U_10577),U_10576) = c_Groups_Oone__class_Oone(U_10574)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10575),U_10576))
      | ~ class_Groups_Ocomm__monoid__mult(U_10574) ),
    inference(definitional_conversion,[status(esa)],[f_2834_2]) ).

cnf(f_2834_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10575,U_10574),U_10577),U_10576) = c_Groups_Oone__class_Oone(U_10574)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10575),U_10576))
    | ~ class_Groups_Ocomm__monoid__mult(U_10574) ),
    inference(clausify,[status(thm)],[f_2834_3]) ).

fof(f_2835_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_2835_2,plain,
    ! [U_10582,U_10581,U_10580] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10580,tc_Nat_Onat),U_10582),U_10581) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ? [U_10579] :
              ( hAPP(U_10582,U_10579) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_10580),U_10579),U_10581)) ) )
        & ( ! [U_10578] :
              ( hAPP(U_10582,U_10578) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_10580),U_10578),U_10581)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10580,tc_Nat_Onat),U_10582),U_10581) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10580),U_10581)) ),
    inference(variable_rename,[status(thm)],[f_2835_1]) ).

fof(f_2835_3,plain,
    ! [U_10582,U_10581,U_10580] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10580,tc_Nat_Onat),U_10582),U_10581) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ( hAPP(U_10582,sK167(U_10582,U_10581,U_10580)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_10580),sK167(U_10582,U_10581,U_10580)),U_10581)) ) )
        & ( ! [U_10578] :
              ( hAPP(U_10582,U_10578) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_10580),U_10578),U_10581)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10580,tc_Nat_Onat),U_10582),U_10581) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10580),U_10581)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_10579,sK167(U_10582,U_10581,U_10580))],[f_2835_2]) ).

fof(f_2835_4,plain,
    ( ! [U_10580,U_10581,U_10582] :
        ( hAPP(U_10582,sK167(U_10582,U_10581,U_10580)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP804(U_10580,U_10581,U_10582) )
    & ! [U_10580,U_10581,U_10582] :
        ( hBOOL(hAPP(hAPP(c_member(U_10580),sK167(U_10582,U_10581,U_10580)),U_10581))
        | ~ sP804(U_10580,U_10581,U_10582) )
    & ! [U_10580,U_10578,U_10581,U_10582] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10580,tc_Nat_Onat),U_10582),U_10581) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | sP804(U_10580,U_10581,U_10582)
        | ~ sP805(U_10580,U_10578,U_10581,U_10582) )
    & ! [U_10580,U_10578,U_10581,U_10582] :
        ( hAPP(U_10582,U_10578) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10580),U_10578),U_10581))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10580,tc_Nat_Onat),U_10582),U_10581) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP805(U_10580,U_10578,U_10581,U_10582) )
    & ! [U_10580,U_10578,U_10581,U_10582] :
        ( sP805(U_10580,U_10578,U_10581,U_10582)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10580),U_10581)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP804,sP805])],[f_2835_3]) ).

cnf(f_2835_5,plain,
    ( sP805(U_10580,U_10578,U_10581,U_10582)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10580),U_10581)) ),
    inference(clausify,[status(thm)],[f_2835_4]) ).

cnf(f_2835_6,plain,
    ( hAPP(U_10582,U_10578) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10580),U_10578),U_10581))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10580,tc_Nat_Onat),U_10582),U_10581) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP805(U_10580,U_10578,U_10581,U_10582) ),
    inference(clausify,[status(thm)],[f_2835_4]) ).

cnf(f_2835_7,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10580,tc_Nat_Onat),U_10582),U_10581) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | sP804(U_10580,U_10581,U_10582)
    | ~ sP805(U_10580,U_10578,U_10581,U_10582) ),
    inference(clausify,[status(thm)],[f_2835_4]) ).

cnf(f_2835_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10580),sK167(U_10582,U_10581,U_10580)),U_10581))
    | ~ sP804(U_10580,U_10581,U_10582) ),
    inference(clausify,[status(thm)],[f_2835_4]) ).

cnf(f_2835_9,plain,
    ( hAPP(U_10582,sK167(U_10582,U_10581,U_10580)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP804(U_10580,U_10581,U_10582) ),
    inference(clausify,[status(thm)],[f_2835_4]) ).

fof(f_2836_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_2836_2,plain,
    ! [U_10586,U_10585,U_10584,U_10583] :
      ( ( c_Sum__Type_OPlus(U_10583,U_10584,U_10585,U_10586) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10583,U_10584),tc_HOL_Obool))
        | U_10586 != c_Orderings_Obot__class_Obot(tc_fun(U_10584,tc_HOL_Obool))
        | U_10585 != c_Orderings_Obot__class_Obot(tc_fun(U_10583,tc_HOL_Obool)) )
      & ( ( U_10586 = c_Orderings_Obot__class_Obot(tc_fun(U_10584,tc_HOL_Obool))
          & U_10585 = c_Orderings_Obot__class_Obot(tc_fun(U_10583,tc_HOL_Obool)) )
        | c_Sum__Type_OPlus(U_10583,U_10584,U_10585,U_10586) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10583,U_10584),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2836_1]) ).

fof(f_2836_3,plain,
    ( ! [U_10594,U_10592,U_10590,U_10588] :
        ( c_Sum__Type_OPlus(U_10588,U_10590,U_10592,U_10594) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10588,U_10590),tc_HOL_Obool))
        | U_10594 != c_Orderings_Obot__class_Obot(tc_fun(U_10590,tc_HOL_Obool))
        | U_10592 != c_Orderings_Obot__class_Obot(tc_fun(U_10588,tc_HOL_Obool)) )
    & ! [U_10593,U_10591,U_10589,U_10587] :
        ( ( U_10593 = c_Orderings_Obot__class_Obot(tc_fun(U_10589,tc_HOL_Obool))
          & U_10591 = c_Orderings_Obot__class_Obot(tc_fun(U_10587,tc_HOL_Obool)) )
        | c_Sum__Type_OPlus(U_10587,U_10589,U_10591,U_10593) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10587,U_10589),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2836_2]) ).

fof(f_2836_4,plain,
    ( ! [U_10587,U_10591,U_10589,U_10593] :
        ( U_10593 = c_Orderings_Obot__class_Obot(tc_fun(U_10589,tc_HOL_Obool))
        | ~ sP806(U_10587,U_10591,U_10589,U_10593) )
    & ! [U_10587,U_10591,U_10589,U_10593] :
        ( U_10591 = c_Orderings_Obot__class_Obot(tc_fun(U_10587,tc_HOL_Obool))
        | ~ sP806(U_10587,U_10591,U_10589,U_10593) )
    & ! [U_10592,U_10594,U_10590,U_10588] :
        ( c_Sum__Type_OPlus(U_10588,U_10590,U_10592,U_10594) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10588,U_10590),tc_HOL_Obool))
        | U_10594 != c_Orderings_Obot__class_Obot(tc_fun(U_10590,tc_HOL_Obool))
        | U_10592 != c_Orderings_Obot__class_Obot(tc_fun(U_10588,tc_HOL_Obool)) )
    & ! [U_10587,U_10591,U_10589,U_10593] :
        ( sP806(U_10587,U_10591,U_10589,U_10593)
        | c_Sum__Type_OPlus(U_10587,U_10589,U_10591,U_10593) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10587,U_10589),tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP806])],[f_2836_3]) ).

cnf(f_2836_5,plain,
    ( sP806(U_10587,U_10591,U_10589,U_10593)
    | c_Sum__Type_OPlus(U_10587,U_10589,U_10591,U_10593) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10587,U_10589),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2836_4]) ).

cnf(f_2836_6,plain,
    ( c_Sum__Type_OPlus(U_10588,U_10590,U_10592,U_10594) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10588,U_10590),tc_HOL_Obool))
    | U_10594 != c_Orderings_Obot__class_Obot(tc_fun(U_10590,tc_HOL_Obool))
    | U_10592 != c_Orderings_Obot__class_Obot(tc_fun(U_10588,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2836_4]) ).

cnf(f_2836_7,plain,
    ( U_10591 = c_Orderings_Obot__class_Obot(tc_fun(U_10587,tc_HOL_Obool))
    | ~ sP806(U_10587,U_10591,U_10589,U_10593) ),
    inference(clausify,[status(thm)],[f_2836_4]) ).

cnf(f_2836_8,plain,
    ( U_10593 = c_Orderings_Obot__class_Obot(tc_fun(U_10589,tc_HOL_Obool))
    | ~ sP806(U_10587,U_10591,U_10589,U_10593) ),
    inference(clausify,[status(thm)],[f_2836_4]) ).

fof(f_2837_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_2837_2,plain,
    ! [U_10598,U_10597,U_10596,U_10595] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10595,U_10596)),c_Sum__Type_OPlus(U_10595,U_10596,U_10597,U_10598)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10596),U_10598))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10595),U_10597)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10596),U_10598))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_10595),U_10597)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10595,U_10596)),c_Sum__Type_OPlus(U_10595,U_10596,U_10597,U_10598))) ) ),
    inference(variable_rename,[status(thm)],[f_2837_1]) ).

fof(f_2837_3,plain,
    ( ! [U_10606,U_10604,U_10602,U_10600] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10600,U_10602)),c_Sum__Type_OPlus(U_10600,U_10602,U_10604,U_10606)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10602),U_10606))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10600),U_10604)) )
    & ! [U_10605,U_10603,U_10601,U_10599] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10601),U_10605))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_10599),U_10603)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10599,U_10601)),c_Sum__Type_OPlus(U_10599,U_10601,U_10603,U_10605))) ) ),
    inference(miniscope,[status(thm)],[f_2837_2]) ).

fof(f_2837_4,plain,
    ( ! [U_10599,U_10601,U_10605,U_10603] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10601),U_10605))
        | ~ sP807(U_10599,U_10601,U_10605,U_10603) )
    & ! [U_10599,U_10601,U_10605,U_10603] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10599),U_10603))
        | ~ sP807(U_10599,U_10601,U_10605,U_10603) )
    & ! [U_10602,U_10600,U_10606,U_10604] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10600,U_10602)),c_Sum__Type_OPlus(U_10600,U_10602,U_10604,U_10606)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10602),U_10606))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10600),U_10604)) )
    & ! [U_10599,U_10601,U_10605,U_10603] :
        ( sP807(U_10599,U_10601,U_10605,U_10603)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10599,U_10601)),c_Sum__Type_OPlus(U_10599,U_10601,U_10603,U_10605))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP807])],[f_2837_3]) ).

cnf(f_2837_5,plain,
    ( sP807(U_10599,U_10601,U_10605,U_10603)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10599,U_10601)),c_Sum__Type_OPlus(U_10599,U_10601,U_10603,U_10605))) ),
    inference(clausify,[status(thm)],[f_2837_4]) ).

cnf(f_2837_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10600,U_10602)),c_Sum__Type_OPlus(U_10600,U_10602,U_10604,U_10606)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10602),U_10606))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10600),U_10604)) ),
    inference(clausify,[status(thm)],[f_2837_4]) ).

cnf(f_2837_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10599),U_10603))
    | ~ sP807(U_10599,U_10601,U_10605,U_10603) ),
    inference(clausify,[status(thm)],[f_2837_4]) ).

cnf(f_2837_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10601),U_10605))
    | ~ sP807(U_10599,U_10601,U_10605,U_10603) ),
    inference(clausify,[status(thm)],[f_2837_4]) ).

fof(f_2838_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_2838_2,plain,
    ! [U_10610,U_10609,U_10608,U_10607] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10607,U_10609)),c_Sum__Type_OPlus(U_10607,U_10609,U_10608,U_10610)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10609),U_10610))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10607),U_10608)) ),
    inference(variable_rename,[status(thm)],[f_2838_1]) ).

fof(f_2838_3,plain,
    ! [U_10609,U_10608,U_10607,U_10610] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10607,U_10609)),c_Sum__Type_OPlus(U_10607,U_10609,U_10608,U_10610)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10609),U_10610))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10607),U_10608)) ),
    inference(definitional_conversion,[status(esa)],[f_2838_2]) ).

cnf(f_2838_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10607,U_10609)),c_Sum__Type_OPlus(U_10607,U_10609,U_10608,U_10610)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10609),U_10610))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10607),U_10608)) ),
    inference(clausify,[status(thm)],[f_2838_3]) ).

fof(f_2839_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_2839_2,plain,
    ! [U_10614,U_10613,U_10612,U_10611] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10611),U_10613))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10611,U_10612)),c_Sum__Type_OPlus(U_10611,U_10612,U_10613,U_10614))) ),
    inference(variable_rename,[status(thm)],[f_2839_1]) ).

fof(f_2839_3,plain,
    ! [U_10611,U_10612,U_10613,U_10614] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10611),U_10613))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10611,U_10612)),c_Sum__Type_OPlus(U_10611,U_10612,U_10613,U_10614))) ),
    inference(definitional_conversion,[status(esa)],[f_2839_2]) ).

cnf(f_2839_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10611),U_10613))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10611,U_10612)),c_Sum__Type_OPlus(U_10611,U_10612,U_10613,U_10614))) ),
    inference(clausify,[status(thm)],[f_2839_3]) ).

fof(f_2840_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_2840_2,plain,
    ! [U_10618,U_10617,U_10616,U_10615] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10616),U_10618))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10615,U_10616)),c_Sum__Type_OPlus(U_10615,U_10616,U_10617,U_10618))) ),
    inference(variable_rename,[status(thm)],[f_2840_1]) ).

fof(f_2840_3,plain,
    ! [U_10618,U_10617,U_10616] :
      ( ! [U_10615] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10615,U_10616)),c_Sum__Type_OPlus(U_10615,U_10616,U_10617,U_10618)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10616),U_10618)) ),
    inference(miniscope,[status(thm)],[f_2840_2]) ).

fof(f_2840_4,plain,
    ! [U_10615,U_10616,U_10617,U_10618] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10615,U_10616)),c_Sum__Type_OPlus(U_10615,U_10616,U_10617,U_10618)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10616),U_10618)) ),
    inference(definitional_conversion,[status(esa)],[f_2840_3]) ).

cnf(f_2840_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10615,U_10616)),c_Sum__Type_OPlus(U_10615,U_10616,U_10617,U_10618)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10616),U_10618)) ),
    inference(clausify,[status(thm)],[f_2840_4]) ).

fof(f_2841_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_2841_2,plain,
    ! [U_10621,U_10620,U_10619] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10619),U_10621),U_10620) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10619),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10619,tc_Nat_Onat),U_10621),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10620))
      | ~ c_Nat__Transfer_Onat__set(U_10620)
      | ~ class_Groups_Ocomm__monoid__mult(U_10619)
      | ~ class_Groups_Ocomm__monoid__add(U_10619) ),
    inference(variable_rename,[status(thm)],[f_2841_1]) ).

fof(f_2841_3,plain,
    ! [U_10619,U_10620,U_10621] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10619),U_10621),U_10620) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10619),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10619,tc_Nat_Onat),U_10621),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10620))
      | ~ c_Nat__Transfer_Onat__set(U_10620)
      | ~ class_Groups_Ocomm__monoid__mult(U_10619)
      | ~ class_Groups_Ocomm__monoid__add(U_10619) ),
    inference(definitional_conversion,[status(esa)],[f_2841_2]) ).

cnf(f_2841_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10619),U_10621),U_10620) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10619),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10619,tc_Nat_Onat),U_10621),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10620))
    | ~ c_Nat__Transfer_Onat__set(U_10620)
    | ~ class_Groups_Ocomm__monoid__mult(U_10619)
    | ~ class_Groups_Ocomm__monoid__add(U_10619) ),
    inference(clausify,[status(thm)],[f_2841_3]) ).

fof(f_2842_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_2842_2,plain,
    ! [U_10626,U_10625,U_10624,U_10623,U_10622] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10623,U_10622),hAPP(hAPP(c_COMBS(U_10623,U_10622,U_10622),hAPP(hAPP(c_COMBB(U_10622,tc_fun(U_10622,U_10622),U_10623),c_Groups_Otimes__class_Otimes(U_10622)),U_10625)),U_10626)),U_10624) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10622),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10623,U_10622),U_10625),U_10624)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10623,U_10622),U_10626),U_10624))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10623),U_10624))
      | ~ class_Groups_Ocomm__monoid__mult(U_10622) ),
    inference(variable_rename,[status(thm)],[f_2842_1]) ).

fof(f_2842_3,plain,
    ! [U_10622,U_10623,U_10624,U_10625,U_10626] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10623,U_10622),hAPP(hAPP(c_COMBS(U_10623,U_10622,U_10622),hAPP(hAPP(c_COMBB(U_10622,tc_fun(U_10622,U_10622),U_10623),c_Groups_Otimes__class_Otimes(U_10622)),U_10625)),U_10626)),U_10624) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10622),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10623,U_10622),U_10625),U_10624)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10623,U_10622),U_10626),U_10624))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10623),U_10624))
      | ~ class_Groups_Ocomm__monoid__mult(U_10622) ),
    inference(definitional_conversion,[status(esa)],[f_2842_2]) ).

cnf(f_2842_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10623,U_10622),hAPP(hAPP(c_COMBS(U_10623,U_10622,U_10622),hAPP(hAPP(c_COMBB(U_10622,tc_fun(U_10622,U_10622),U_10623),c_Groups_Otimes__class_Otimes(U_10622)),U_10625)),U_10626)),U_10624) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10622),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10623,U_10622),U_10625),U_10624)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10623,U_10622),U_10626),U_10624))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10623),U_10624))
    | ~ class_Groups_Ocomm__monoid__mult(U_10622) ),
    inference(clausify,[status(thm)],[f_2842_3]) ).

fof(f_2843_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_2843_2,plain,
    ! [U_10631,U_10630,U_10629,U_10628,U_10627] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10628,U_10627),hAPP(hAPP(c_COMBS(U_10628,U_10627,U_10627),hAPP(hAPP(c_COMBB(U_10627,tc_fun(U_10627,U_10627),U_10628),c_Rings_Oinverse__class_Odivide(U_10627)),U_10630)),U_10631)),U_10629) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10627),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10628,U_10627),U_10630),U_10629)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10628,U_10627),U_10631),U_10629))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10628),U_10629))
      | ~ class_Fields_Ofield__inverse__zero(U_10627) ),
    inference(variable_rename,[status(thm)],[f_2843_1]) ).

fof(f_2843_3,plain,
    ! [U_10627,U_10628,U_10629,U_10630,U_10631] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10628,U_10627),hAPP(hAPP(c_COMBS(U_10628,U_10627,U_10627),hAPP(hAPP(c_COMBB(U_10627,tc_fun(U_10627,U_10627),U_10628),c_Rings_Oinverse__class_Odivide(U_10627)),U_10630)),U_10631)),U_10629) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10627),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10628,U_10627),U_10630),U_10629)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10628,U_10627),U_10631),U_10629))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10628),U_10629))
      | ~ class_Fields_Ofield__inverse__zero(U_10627) ),
    inference(definitional_conversion,[status(esa)],[f_2843_2]) ).

cnf(f_2843_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10628,U_10627),hAPP(hAPP(c_COMBS(U_10628,U_10627,U_10627),hAPP(hAPP(c_COMBB(U_10627,tc_fun(U_10627,U_10627),U_10628),c_Rings_Oinverse__class_Odivide(U_10627)),U_10630)),U_10631)),U_10629) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10627),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10628,U_10627),U_10630),U_10629)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10628,U_10627),U_10631),U_10629))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10628),U_10629))
    | ~ class_Fields_Ofield__inverse__zero(U_10627) ),
    inference(clausify,[status(thm)],[f_2843_3]) ).

fof(f_2844_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_2844_2,plain,
    ! [U_10636,U_10635,U_10634,U_10633,U_10632] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10632),hAPP(U_10636,U_10635)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10633,U_10632),U_10636),U_10634)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10633),U_10635),U_10634))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10633),U_10634))
      | ~ class_Rings_Ocomm__semiring__1(U_10632) ),
    inference(variable_rename,[status(thm)],[f_2844_1]) ).

fof(f_2844_3,plain,
    ! [U_10632,U_10633,U_10634,U_10635,U_10636] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10632),hAPP(U_10636,U_10635)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10633,U_10632),U_10636),U_10634)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10633),U_10635),U_10634))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10633),U_10634))
      | ~ class_Rings_Ocomm__semiring__1(U_10632) ),
    inference(definitional_conversion,[status(esa)],[f_2844_2]) ).

cnf(f_2844_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10632),hAPP(U_10636,U_10635)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10633,U_10632),U_10636),U_10634)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10633),U_10635),U_10634))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10633),U_10634))
    | ~ class_Rings_Ocomm__semiring__1(U_10632) ),
    inference(clausify,[status(thm)],[f_2844_3]) ).

fof(f_2845_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_2845_2,plain,
    ! [U_10641,U_10640,U_10639] :
      ( ( ( 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_10639,tc_Nat_Onat),U_10641),U_10640)))
          | ? [U_10638] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10641,U_10638)))
              & hBOOL(hAPP(hAPP(c_member(U_10639),U_10638),U_10640)) ) )
        & ( ! [U_10637] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10641,U_10637)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10639),U_10637),U_10640)) )
          | ~ 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_10639,tc_Nat_Onat),U_10641),U_10640))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10639),U_10640)) ),
    inference(variable_rename,[status(thm)],[f_2845_1]) ).

fof(f_2845_3,plain,
    ! [U_10641,U_10640,U_10639] :
      ( ( ( 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_10639,tc_Nat_Onat),U_10641),U_10640)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10641,sK168(U_10641,U_10640,U_10639))))
            & hBOOL(hAPP(hAPP(c_member(U_10639),sK168(U_10641,U_10640,U_10639)),U_10640)) ) )
        & ( ! [U_10637] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10641,U_10637)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10639),U_10637),U_10640)) )
          | ~ 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_10639,tc_Nat_Onat),U_10641),U_10640))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10639),U_10640)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_10638,sK168(U_10641,U_10640,U_10639))],[f_2845_2]) ).

fof(f_2845_4,plain,
    ( ! [U_10639,U_10640,U_10641] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10641,sK168(U_10641,U_10640,U_10639))))
        | ~ sP808(U_10639,U_10640,U_10641) )
    & ! [U_10639,U_10640,U_10641] :
        ( hBOOL(hAPP(hAPP(c_member(U_10639),sK168(U_10641,U_10640,U_10639)),U_10640))
        | ~ sP808(U_10639,U_10640,U_10641) )
    & ! [U_10637,U_10639,U_10640,U_10641] :
        ( 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_10639,tc_Nat_Onat),U_10641),U_10640)))
        | sP808(U_10639,U_10640,U_10641)
        | ~ sP809(U_10637,U_10639,U_10640,U_10641) )
    & ! [U_10637,U_10639,U_10640,U_10641] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10641,U_10637)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10639),U_10637),U_10640))
        | ~ 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_10639,tc_Nat_Onat),U_10641),U_10640)))
        | ~ sP809(U_10637,U_10639,U_10640,U_10641) )
    & ! [U_10637,U_10639,U_10640,U_10641] :
        ( sP809(U_10637,U_10639,U_10640,U_10641)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10639),U_10640)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP808,sP809])],[f_2845_3]) ).

cnf(f_2845_5,plain,
    ( sP809(U_10637,U_10639,U_10640,U_10641)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10639),U_10640)) ),
    inference(clausify,[status(thm)],[f_2845_4]) ).

cnf(f_2845_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10641,U_10637)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10639),U_10637),U_10640))
    | ~ 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_10639,tc_Nat_Onat),U_10641),U_10640)))
    | ~ sP809(U_10637,U_10639,U_10640,U_10641) ),
    inference(clausify,[status(thm)],[f_2845_4]) ).

cnf(f_2845_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_10639,tc_Nat_Onat),U_10641),U_10640)))
    | sP808(U_10639,U_10640,U_10641)
    | ~ sP809(U_10637,U_10639,U_10640,U_10641) ),
    inference(clausify,[status(thm)],[f_2845_4]) ).

cnf(f_2845_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10639),sK168(U_10641,U_10640,U_10639)),U_10640))
    | ~ sP808(U_10639,U_10640,U_10641) ),
    inference(clausify,[status(thm)],[f_2845_4]) ).

cnf(f_2845_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10641,sK168(U_10641,U_10640,U_10639))))
    | ~ sP808(U_10639,U_10640,U_10641) ),
    inference(clausify,[status(thm)],[f_2845_4]) ).

fof(f_2846_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_2846_2,plain,
    ! [U_10646,U_10645,U_10644,U_10643,U_10642] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10642),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10643,U_10642),U_10646),U_10645)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10643,U_10642),U_10646),U_10644)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10643,tc_HOL_Obool)),U_10645),U_10644))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10643),U_10644))
      | ~ class_Rings_Odvd(U_10642)
      | ~ class_Groups_Ocomm__monoid__mult(U_10642) ),
    inference(variable_rename,[status(thm)],[f_2846_1]) ).

fof(f_2846_3,plain,
    ! [U_10645,U_10644,U_10643,U_10642,U_10646] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10642),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10643,U_10642),U_10646),U_10645)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10643,U_10642),U_10646),U_10644)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10643,tc_HOL_Obool)),U_10645),U_10644))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10643),U_10644))
      | ~ class_Rings_Odvd(U_10642)
      | ~ class_Groups_Ocomm__monoid__mult(U_10642) ),
    inference(definitional_conversion,[status(esa)],[f_2846_2]) ).

cnf(f_2846_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10642),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10643,U_10642),U_10646),U_10645)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10643,U_10642),U_10646),U_10644)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10643,tc_HOL_Obool)),U_10645),U_10644))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10643),U_10644))
    | ~ class_Rings_Odvd(U_10642)
    | ~ class_Groups_Ocomm__monoid__mult(U_10642) ),
    inference(clausify,[status(thm)],[f_2846_3]) ).

fof(f_2847_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_2847_2,plain,
    ! [U_10649,U_10648,U_10647] :
      ( c_SetInterval_Oord__class_OgreaterThanLessThan(U_10647,U_10649,U_10648) = c_Orderings_Obot__class_Obot(tc_fun(U_10647,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10647),U_10648),U_10649))
      | ~ class_Orderings_Oorder(U_10647) ),
    inference(variable_rename,[status(thm)],[f_2847_1]) ).

fof(f_2847_3,plain,
    ! [U_10649,U_10648,U_10647] :
      ( c_SetInterval_Oord__class_OgreaterThanLessThan(U_10647,U_10649,U_10648) = c_Orderings_Obot__class_Obot(tc_fun(U_10647,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10647),U_10648),U_10649))
      | ~ class_Orderings_Oorder(U_10647) ),
    inference(definitional_conversion,[status(esa)],[f_2847_2]) ).

cnf(f_2847_4,plain,
    ( c_SetInterval_Oord__class_OgreaterThanLessThan(U_10647,U_10649,U_10648) = c_Orderings_Obot__class_Obot(tc_fun(U_10647,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10647),U_10648),U_10649))
    | ~ class_Orderings_Oorder(U_10647) ),
    inference(clausify,[status(thm)],[f_2847_3]) ).

fof(f_2848_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_2848_2,plain,
    ! [U_10652,U_10651,U_10650] :
      ( hAPP(c_Set_Oimage(U_10650,U_10650,c_Groups_Ouminus__class_Ouminus(U_10650)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10650,U_10651,U_10652)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10650,hAPP(c_Groups_Ouminus__class_Ouminus(U_10650),U_10652),hAPP(c_Groups_Ouminus__class_Ouminus(U_10650),U_10651))
      | ~ class_Groups_Oordered__ab__group__add(U_10650) ),
    inference(variable_rename,[status(thm)],[f_2848_1]) ).

fof(f_2848_3,plain,
    ! [U_10650,U_10651,U_10652] :
      ( hAPP(c_Set_Oimage(U_10650,U_10650,c_Groups_Ouminus__class_Ouminus(U_10650)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10650,U_10651,U_10652)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10650,hAPP(c_Groups_Ouminus__class_Ouminus(U_10650),U_10652),hAPP(c_Groups_Ouminus__class_Ouminus(U_10650),U_10651))
      | ~ class_Groups_Oordered__ab__group__add(U_10650) ),
    inference(definitional_conversion,[status(esa)],[f_2848_2]) ).

cnf(f_2848_4,plain,
    ( hAPP(c_Set_Oimage(U_10650,U_10650,c_Groups_Ouminus__class_Ouminus(U_10650)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10650,U_10651,U_10652)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10650,hAPP(c_Groups_Ouminus__class_Ouminus(U_10650),U_10652),hAPP(c_Groups_Ouminus__class_Ouminus(U_10650),U_10651))
    | ~ class_Groups_Oordered__ab__group__add(U_10650) ),
    inference(clausify,[status(thm)],[f_2848_3]) ).

fof(f_2849_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_2849_2,plain,
    ! [U_10657,U_10656,U_10655,U_10654,U_10653] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10654,U_10653),hAPP(hAPP(c_COMBC(U_10654,U_10653,U_10653),hAPP(hAPP(c_COMBS(U_10654,U_10653,tc_fun(U_10653,U_10653)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10653,tc_fun(U_10653,U_10653)),U_10654),c_If(U_10653)),hAPP(hAPP(c_COMBC(U_10654,U_10654,tc_HOL_Obool),c_fequal),U_10656))),U_10657)),c_Groups_Oone__class_Oone(U_10653))),U_10655) = c_Groups_Oone__class_Oone(U_10653)
          | hBOOL(hAPP(hAPP(c_member(U_10654),U_10656),U_10655)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10654,U_10653),hAPP(hAPP(c_COMBC(U_10654,U_10653,U_10653),hAPP(hAPP(c_COMBS(U_10654,U_10653,tc_fun(U_10653,U_10653)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10653,tc_fun(U_10653,U_10653)),U_10654),c_If(U_10653)),hAPP(hAPP(c_COMBC(U_10654,U_10654,tc_HOL_Obool),c_fequal),U_10656))),U_10657)),c_Groups_Oone__class_Oone(U_10653))),U_10655) = hAPP(U_10657,U_10656)
          | ~ hBOOL(hAPP(hAPP(c_member(U_10654),U_10656),U_10655)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10654),U_10655))
      | ~ class_Groups_Ocomm__monoid__mult(U_10653) ),
    inference(variable_rename,[status(thm)],[f_2849_1]) ).

fof(f_2849_3,plain,
    ( ! [U_10653,U_10654,U_10655,U_10656,U_10657] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10654,U_10653),hAPP(hAPP(c_COMBC(U_10654,U_10653,U_10653),hAPP(hAPP(c_COMBS(U_10654,U_10653,tc_fun(U_10653,U_10653)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10653,tc_fun(U_10653,U_10653)),U_10654),c_If(U_10653)),hAPP(hAPP(c_COMBC(U_10654,U_10654,tc_HOL_Obool),c_fequal),U_10656))),U_10657)),c_Groups_Oone__class_Oone(U_10653))),U_10655) = c_Groups_Oone__class_Oone(U_10653)
        | hBOOL(hAPP(hAPP(c_member(U_10654),U_10656),U_10655))
        | ~ sP810(U_10653,U_10654,U_10655,U_10656,U_10657) )
    & ! [U_10653,U_10654,U_10655,U_10656,U_10657] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10654,U_10653),hAPP(hAPP(c_COMBC(U_10654,U_10653,U_10653),hAPP(hAPP(c_COMBS(U_10654,U_10653,tc_fun(U_10653,U_10653)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10653,tc_fun(U_10653,U_10653)),U_10654),c_If(U_10653)),hAPP(hAPP(c_COMBC(U_10654,U_10654,tc_HOL_Obool),c_fequal),U_10656))),U_10657)),c_Groups_Oone__class_Oone(U_10653))),U_10655) = hAPP(U_10657,U_10656)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10654),U_10656),U_10655))
        | ~ sP810(U_10653,U_10654,U_10655,U_10656,U_10657) )
    & ! [U_10653,U_10654,U_10655,U_10656,U_10657] :
        ( sP810(U_10653,U_10654,U_10655,U_10656,U_10657)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10654),U_10655))
        | ~ class_Groups_Ocomm__monoid__mult(U_10653) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP810])],[f_2849_2]) ).

cnf(f_2849_4,plain,
    ( sP810(U_10653,U_10654,U_10655,U_10656,U_10657)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10654),U_10655))
    | ~ class_Groups_Ocomm__monoid__mult(U_10653) ),
    inference(clausify,[status(thm)],[f_2849_3]) ).

cnf(f_2849_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10654,U_10653),hAPP(hAPP(c_COMBC(U_10654,U_10653,U_10653),hAPP(hAPP(c_COMBS(U_10654,U_10653,tc_fun(U_10653,U_10653)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10653,tc_fun(U_10653,U_10653)),U_10654),c_If(U_10653)),hAPP(hAPP(c_COMBC(U_10654,U_10654,tc_HOL_Obool),c_fequal),U_10656))),U_10657)),c_Groups_Oone__class_Oone(U_10653))),U_10655) = hAPP(U_10657,U_10656)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10654),U_10656),U_10655))
    | ~ sP810(U_10653,U_10654,U_10655,U_10656,U_10657) ),
    inference(clausify,[status(thm)],[f_2849_3]) ).

cnf(f_2849_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10654,U_10653),hAPP(hAPP(c_COMBC(U_10654,U_10653,U_10653),hAPP(hAPP(c_COMBS(U_10654,U_10653,tc_fun(U_10653,U_10653)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10653,tc_fun(U_10653,U_10653)),U_10654),c_If(U_10653)),hAPP(hAPP(c_COMBC(U_10654,U_10654,tc_HOL_Obool),c_fequal),U_10656))),U_10657)),c_Groups_Oone__class_Oone(U_10653))),U_10655) = c_Groups_Oone__class_Oone(U_10653)
    | hBOOL(hAPP(hAPP(c_member(U_10654),U_10656),U_10655))
    | ~ sP810(U_10653,U_10654,U_10655,U_10656,U_10657) ),
    inference(clausify,[status(thm)],[f_2849_3]) ).

fof(f_2850_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_2850_2,plain,
    ! [U_10662,U_10661,U_10660,U_10659,U_10658] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10659,U_10658),hAPP(hAPP(c_COMBC(U_10659,U_10658,U_10658),hAPP(hAPP(c_COMBS(U_10659,U_10658,tc_fun(U_10658,U_10658)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10658,tc_fun(U_10658,U_10658)),U_10659),c_If(U_10658)),hAPP(c_fequal,U_10661))),U_10662)),c_Groups_Oone__class_Oone(U_10658))),U_10660) = c_Groups_Oone__class_Oone(U_10658)
          | hBOOL(hAPP(hAPP(c_member(U_10659),U_10661),U_10660)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10659,U_10658),hAPP(hAPP(c_COMBC(U_10659,U_10658,U_10658),hAPP(hAPP(c_COMBS(U_10659,U_10658,tc_fun(U_10658,U_10658)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10658,tc_fun(U_10658,U_10658)),U_10659),c_If(U_10658)),hAPP(c_fequal,U_10661))),U_10662)),c_Groups_Oone__class_Oone(U_10658))),U_10660) = hAPP(U_10662,U_10661)
          | ~ hBOOL(hAPP(hAPP(c_member(U_10659),U_10661),U_10660)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10659),U_10660))
      | ~ class_Groups_Ocomm__monoid__mult(U_10658) ),
    inference(variable_rename,[status(thm)],[f_2850_1]) ).

fof(f_2850_3,plain,
    ( ! [U_10660,U_10661,U_10659,U_10658,U_10662] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10659,U_10658),hAPP(hAPP(c_COMBC(U_10659,U_10658,U_10658),hAPP(hAPP(c_COMBS(U_10659,U_10658,tc_fun(U_10658,U_10658)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10658,tc_fun(U_10658,U_10658)),U_10659),c_If(U_10658)),hAPP(c_fequal,U_10661))),U_10662)),c_Groups_Oone__class_Oone(U_10658))),U_10660) = c_Groups_Oone__class_Oone(U_10658)
        | hBOOL(hAPP(hAPP(c_member(U_10659),U_10661),U_10660))
        | ~ sP811(U_10660,U_10661,U_10659,U_10658,U_10662) )
    & ! [U_10660,U_10661,U_10659,U_10658,U_10662] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10659,U_10658),hAPP(hAPP(c_COMBC(U_10659,U_10658,U_10658),hAPP(hAPP(c_COMBS(U_10659,U_10658,tc_fun(U_10658,U_10658)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10658,tc_fun(U_10658,U_10658)),U_10659),c_If(U_10658)),hAPP(c_fequal,U_10661))),U_10662)),c_Groups_Oone__class_Oone(U_10658))),U_10660) = hAPP(U_10662,U_10661)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10659),U_10661),U_10660))
        | ~ sP811(U_10660,U_10661,U_10659,U_10658,U_10662) )
    & ! [U_10660,U_10661,U_10659,U_10658,U_10662] :
        ( sP811(U_10660,U_10661,U_10659,U_10658,U_10662)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10659),U_10660))
        | ~ class_Groups_Ocomm__monoid__mult(U_10658) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP811])],[f_2850_2]) ).

cnf(f_2850_4,plain,
    ( sP811(U_10660,U_10661,U_10659,U_10658,U_10662)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10659),U_10660))
    | ~ class_Groups_Ocomm__monoid__mult(U_10658) ),
    inference(clausify,[status(thm)],[f_2850_3]) ).

cnf(f_2850_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10659,U_10658),hAPP(hAPP(c_COMBC(U_10659,U_10658,U_10658),hAPP(hAPP(c_COMBS(U_10659,U_10658,tc_fun(U_10658,U_10658)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10658,tc_fun(U_10658,U_10658)),U_10659),c_If(U_10658)),hAPP(c_fequal,U_10661))),U_10662)),c_Groups_Oone__class_Oone(U_10658))),U_10660) = hAPP(U_10662,U_10661)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10659),U_10661),U_10660))
    | ~ sP811(U_10660,U_10661,U_10659,U_10658,U_10662) ),
    inference(clausify,[status(thm)],[f_2850_3]) ).

cnf(f_2850_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10659,U_10658),hAPP(hAPP(c_COMBC(U_10659,U_10658,U_10658),hAPP(hAPP(c_COMBS(U_10659,U_10658,tc_fun(U_10658,U_10658)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10658,tc_fun(U_10658,U_10658)),U_10659),c_If(U_10658)),hAPP(c_fequal,U_10661))),U_10662)),c_Groups_Oone__class_Oone(U_10658))),U_10660) = c_Groups_Oone__class_Oone(U_10658)
    | hBOOL(hAPP(hAPP(c_member(U_10659),U_10661),U_10660))
    | ~ sP811(U_10660,U_10661,U_10659,U_10658,U_10662) ),
    inference(clausify,[status(thm)],[f_2850_3]) ).

fof(f_2851_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_2851_2,plain,
    ! [U_10666,U_10665,U_10664,U_10663] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10664,U_10663),hAPP(c_COMBK(U_10663,U_10664),U_10666)),U_10665) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10663),U_10666),hAPP(c_Finite__Set_Ocard(U_10664),U_10665))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10664),U_10665))
      | ~ class_Groups_Ocomm__monoid__mult(U_10663) ),
    inference(variable_rename,[status(thm)],[f_2851_1]) ).

fof(f_2851_3,plain,
    ! [U_10664,U_10665,U_10663,U_10666] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10664,U_10663),hAPP(c_COMBK(U_10663,U_10664),U_10666)),U_10665) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10663),U_10666),hAPP(c_Finite__Set_Ocard(U_10664),U_10665))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10664),U_10665))
      | ~ class_Groups_Ocomm__monoid__mult(U_10663) ),
    inference(definitional_conversion,[status(esa)],[f_2851_2]) ).

cnf(f_2851_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10664,U_10663),hAPP(c_COMBK(U_10663,U_10664),U_10666)),U_10665) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10663),U_10666),hAPP(c_Finite__Set_Ocard(U_10664),U_10665))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10664),U_10665))
    | ~ class_Groups_Ocomm__monoid__mult(U_10663) ),
    inference(clausify,[status(thm)],[f_2851_3]) ).

fof(f_2852_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_2852_2,plain,
    ! [U_10671,U_10670,U_10669,U_10668,U_10667] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10668,U_10667),U_10671),hAPP(hAPP(c_Set_Oinsert(U_10668),U_10670),U_10669)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10667),hAPP(U_10671,U_10670)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10668,U_10667),U_10671),U_10669))
      | hBOOL(hAPP(hAPP(c_member(U_10668),U_10670),U_10669))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10668),U_10669))
      | ~ class_Groups_Ocomm__monoid__mult(U_10667) ),
    inference(variable_rename,[status(thm)],[f_2852_1]) ).

fof(f_2852_3,plain,
    ! [U_10667,U_10668,U_10669,U_10670,U_10671] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10668,U_10667),U_10671),hAPP(hAPP(c_Set_Oinsert(U_10668),U_10670),U_10669)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10667),hAPP(U_10671,U_10670)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10668,U_10667),U_10671),U_10669))
      | hBOOL(hAPP(hAPP(c_member(U_10668),U_10670),U_10669))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10668),U_10669))
      | ~ class_Groups_Ocomm__monoid__mult(U_10667) ),
    inference(definitional_conversion,[status(esa)],[f_2852_2]) ).

cnf(f_2852_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10668,U_10667),U_10671),hAPP(hAPP(c_Set_Oinsert(U_10668),U_10670),U_10669)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10667),hAPP(U_10671,U_10670)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10668,U_10667),U_10671),U_10669))
    | hBOOL(hAPP(hAPP(c_member(U_10668),U_10670),U_10669))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10668),U_10669))
    | ~ class_Groups_Ocomm__monoid__mult(U_10667) ),
    inference(clausify,[status(thm)],[f_2852_3]) ).

fof(f_2853_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_2853_2,plain,
    ! [U_10676,U_10675,U_10674,U_10673,U_10672] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10673,U_10672),U_10676),hAPP(hAPP(c_Set_Oinsert(U_10673),U_10675),U_10674)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10672),hAPP(U_10676,U_10675)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10673,U_10672),U_10676),U_10674))
      | hBOOL(hAPP(hAPP(c_member(U_10673),U_10675),U_10674))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10673),U_10674))
      | ~ class_Groups_Ocomm__monoid__mult(U_10672) ),
    inference(variable_rename,[status(thm)],[f_2853_1]) ).

fof(f_2853_3,plain,
    ! [U_10672,U_10673,U_10674,U_10675,U_10676] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10673,U_10672),U_10676),hAPP(hAPP(c_Set_Oinsert(U_10673),U_10675),U_10674)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10672),hAPP(U_10676,U_10675)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10673,U_10672),U_10676),U_10674))
      | hBOOL(hAPP(hAPP(c_member(U_10673),U_10675),U_10674))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10673),U_10674))
      | ~ class_Groups_Ocomm__monoid__mult(U_10672) ),
    inference(definitional_conversion,[status(esa)],[f_2853_2]) ).

cnf(f_2853_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10673,U_10672),U_10676),hAPP(hAPP(c_Set_Oinsert(U_10673),U_10675),U_10674)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10672),hAPP(U_10676,U_10675)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10673,U_10672),U_10676),U_10674))
    | hBOOL(hAPP(hAPP(c_member(U_10673),U_10675),U_10674))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10673),U_10674))
    | ~ class_Groups_Ocomm__monoid__mult(U_10672) ),
    inference(clausify,[status(thm)],[f_2853_3]) ).

fof(f_2854_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_2854_2,plain,
    ! [U_10681,U_10680,U_10679,U_10678,U_10677] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10677),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10678,U_10677),U_10681),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10678,tc_HOL_Obool)),U_10679),U_10680))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10678,U_10677),U_10681),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10678,tc_HOL_Obool)),U_10679),U_10680))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10677),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10678,U_10677),U_10681),U_10679)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10678,U_10677),U_10681),U_10680))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10678),U_10680))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10678),U_10679))
      | ~ class_Groups_Ocomm__monoid__mult(U_10677) ),
    inference(variable_rename,[status(thm)],[f_2854_1]) ).

fof(f_2854_3,plain,
    ! [U_10678,U_10677,U_10679,U_10680,U_10681] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10677),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10678,U_10677),U_10681),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10678,tc_HOL_Obool)),U_10679),U_10680))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10678,U_10677),U_10681),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10678,tc_HOL_Obool)),U_10679),U_10680))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10677),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10678,U_10677),U_10681),U_10679)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10678,U_10677),U_10681),U_10680))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10678),U_10680))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10678),U_10679))
      | ~ class_Groups_Ocomm__monoid__mult(U_10677) ),
    inference(definitional_conversion,[status(esa)],[f_2854_2]) ).

cnf(f_2854_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10677),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10678,U_10677),U_10681),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10678,tc_HOL_Obool)),U_10679),U_10680))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10678,U_10677),U_10681),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10678,tc_HOL_Obool)),U_10679),U_10680))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10677),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10678,U_10677),U_10681),U_10679)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10678,U_10677),U_10681),U_10680))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10678),U_10680))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10678),U_10679))
    | ~ class_Groups_Ocomm__monoid__mult(U_10677) ),
    inference(clausify,[status(thm)],[f_2854_3]) ).

fof(f_2855_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_2855_2,plain,
    ! [U_10686,U_10685,U_10684,U_10683,U_10682] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10682),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10683,U_10682),U_10686),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10683,tc_HOL_Obool)),U_10684),U_10685))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10683,U_10682),U_10686),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10683,tc_HOL_Obool)),U_10684),U_10685))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10682),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10683,U_10682),U_10686),U_10684)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10683,U_10682),U_10686),U_10685))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10683),U_10685))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10683),U_10684))
      | ~ class_Groups_Ocomm__monoid__mult(U_10682) ),
    inference(variable_rename,[status(thm)],[f_2855_1]) ).

fof(f_2855_3,plain,
    ! [U_10683,U_10682,U_10684,U_10685,U_10686] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10682),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10683,U_10682),U_10686),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10683,tc_HOL_Obool)),U_10684),U_10685))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10683,U_10682),U_10686),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10683,tc_HOL_Obool)),U_10684),U_10685))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10682),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10683,U_10682),U_10686),U_10684)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10683,U_10682),U_10686),U_10685))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10683),U_10685))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10683),U_10684))
      | ~ class_Groups_Ocomm__monoid__mult(U_10682) ),
    inference(definitional_conversion,[status(esa)],[f_2855_2]) ).

cnf(f_2855_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10682),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10683,U_10682),U_10686),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10683,tc_HOL_Obool)),U_10684),U_10685))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10683,U_10682),U_10686),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10683,tc_HOL_Obool)),U_10684),U_10685))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10682),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10683,U_10682),U_10686),U_10684)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10683,U_10682),U_10686),U_10685))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10683),U_10685))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10683),U_10684))
    | ~ class_Groups_Ocomm__monoid__mult(U_10682) ),
    inference(clausify,[status(thm)],[f_2855_3]) ).

fof(f_2856_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) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_sum(T_b,T_c),c_Sum__Type_OInl(T_b,T_c)),V_A_2)),hAPP(c_Set_Oimage(T_c,tc_sum(T_b,T_c),c_Sum__Type_OInr(T_c,T_b)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Plus__def]) ).

fof(f_2856_2,plain,
    ! [U_10690,U_10689,U_10688,U_10687] : c_Sum__Type_OPlus(U_10687,U_10688,U_10689,U_10690) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(U_10687,U_10688),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10687,tc_sum(U_10687,U_10688),c_Sum__Type_OInl(U_10687,U_10688)),U_10689)),hAPP(c_Set_Oimage(U_10688,tc_sum(U_10687,U_10688),c_Sum__Type_OInr(U_10688,U_10687)),U_10690)),
    inference(variable_rename,[status(thm)],[f_2856_1]) ).

fof(f_2856_3,plain,
    ! [U_10687,U_10688,U_10689,U_10690] : c_Sum__Type_OPlus(U_10687,U_10688,U_10689,U_10690) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(U_10687,U_10688),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10687,tc_sum(U_10687,U_10688),c_Sum__Type_OInl(U_10687,U_10688)),U_10689)),hAPP(c_Set_Oimage(U_10688,tc_sum(U_10687,U_10688),c_Sum__Type_OInr(U_10688,U_10687)),U_10690)),
    inference(definitional_conversion,[status(esa)],[f_2856_2]) ).

cnf(f_2856_4,plain,
    c_Sum__Type_OPlus(U_10687,U_10688,U_10689,U_10690) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(U_10687,U_10688),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10687,tc_sum(U_10687,U_10688),c_Sum__Type_OInl(U_10687,U_10688)),U_10689)),hAPP(c_Set_Oimage(U_10688,tc_sum(U_10687,U_10688),c_Sum__Type_OInr(U_10688,U_10687)),U_10690)),
    inference(clausify,[status(thm)],[f_2856_3]) ).

fof(f_2857_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_2857_2,plain,
    ! [U_10695,U_10694,U_10693,U_10692,U_10691] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10691,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10691,U_10692,U_10693)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10691,U_10694,U_10695)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10691,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10691),U_10692),U_10694),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10691),U_10693),U_10695))
      | ~ class_Orderings_Olinorder(U_10691) ),
    inference(variable_rename,[status(thm)],[f_2857_1]) ).

fof(f_2857_3,plain,
    ! [U_10691,U_10692,U_10693,U_10694,U_10695] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10691,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10691,U_10692,U_10693)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10691,U_10694,U_10695)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10691,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10691),U_10692),U_10694),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10691),U_10693),U_10695))
      | ~ class_Orderings_Olinorder(U_10691) ),
    inference(definitional_conversion,[status(esa)],[f_2857_2]) ).

cnf(f_2857_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10691,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10691,U_10692,U_10693)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10691,U_10694,U_10695)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10691,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10691),U_10692),U_10694),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10691),U_10693),U_10695))
    | ~ class_Orderings_Olinorder(U_10691) ),
    inference(clausify,[status(thm)],[f_2857_3]) ).

fof(f_2858_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_2858_2,plain,
    ! [U_10700,U_10699,U_10698,U_10697,U_10696] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10697,U_10696),U_10699),hAPP(hAPP(c_Set_Oinsert(U_10697),U_10700),U_10698)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10696),hAPP(U_10699,U_10700)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10697,U_10696),U_10699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10697,tc_HOL_Obool)),U_10698),hAPP(hAPP(c_Set_Oinsert(U_10697),U_10700),c_Orderings_Obot__class_Obot(tc_fun(U_10697,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10697),U_10698))
      | ~ class_Groups_Ocomm__monoid__mult(U_10696) ),
    inference(variable_rename,[status(thm)],[f_2858_1]) ).

fof(f_2858_3,plain,
    ! [U_10696,U_10697,U_10698,U_10699,U_10700] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10697,U_10696),U_10699),hAPP(hAPP(c_Set_Oinsert(U_10697),U_10700),U_10698)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10696),hAPP(U_10699,U_10700)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10697,U_10696),U_10699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10697,tc_HOL_Obool)),U_10698),hAPP(hAPP(c_Set_Oinsert(U_10697),U_10700),c_Orderings_Obot__class_Obot(tc_fun(U_10697,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10697),U_10698))
      | ~ class_Groups_Ocomm__monoid__mult(U_10696) ),
    inference(definitional_conversion,[status(esa)],[f_2858_2]) ).

cnf(f_2858_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10697,U_10696),U_10699),hAPP(hAPP(c_Set_Oinsert(U_10697),U_10700),U_10698)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10696),hAPP(U_10699,U_10700)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10697,U_10696),U_10699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10697,tc_HOL_Obool)),U_10698),hAPP(hAPP(c_Set_Oinsert(U_10697),U_10700),c_Orderings_Obot__class_Obot(tc_fun(U_10697,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10697),U_10698))
    | ~ class_Groups_Ocomm__monoid__mult(U_10696) ),
    inference(clausify,[status(thm)],[f_2858_3]) ).

fof(f_2859_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_2859_2,plain,
    ! [U_10705,U_10704,U_10703,U_10702,U_10701] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10702,U_10701),U_10705),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10702,tc_HOL_Obool)),U_10703),U_10704)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10701),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10702,U_10701),U_10705),U_10703)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10702,U_10701),U_10705),U_10704))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10702,tc_HOL_Obool)),U_10703),U_10704) != c_Orderings_Obot__class_Obot(tc_fun(U_10702,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10702),U_10704))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10702),U_10703))
      | ~ class_Groups_Ocomm__monoid__mult(U_10701) ),
    inference(variable_rename,[status(thm)],[f_2859_1]) ).

fof(f_2859_3,plain,
    ! [U_10702,U_10701,U_10703,U_10704,U_10705] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10702,U_10701),U_10705),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10702,tc_HOL_Obool)),U_10703),U_10704)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10701),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10702,U_10701),U_10705),U_10703)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10702,U_10701),U_10705),U_10704))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10702,tc_HOL_Obool)),U_10703),U_10704) != c_Orderings_Obot__class_Obot(tc_fun(U_10702,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10702),U_10704))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10702),U_10703))
      | ~ class_Groups_Ocomm__monoid__mult(U_10701) ),
    inference(definitional_conversion,[status(esa)],[f_2859_2]) ).

cnf(f_2859_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10702,U_10701),U_10705),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10702,tc_HOL_Obool)),U_10703),U_10704)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10701),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10702,U_10701),U_10705),U_10703)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10702,U_10701),U_10705),U_10704))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10702,tc_HOL_Obool)),U_10703),U_10704) != c_Orderings_Obot__class_Obot(tc_fun(U_10702,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10702),U_10704))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10702),U_10703))
    | ~ class_Groups_Ocomm__monoid__mult(U_10701) ),
    inference(clausify,[status(thm)],[f_2859_3]) ).

fof(f_2860_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_2860_2,plain,
    ! [U_10710,U_10709,U_10708,U_10707,U_10706] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10707,U_10706),U_10710),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10707,tc_HOL_Obool)),U_10708),U_10709)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10706),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10707,U_10706),U_10710),U_10708)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10707,U_10706),U_10710),U_10709))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10707,tc_HOL_Obool)),U_10708),U_10709) != c_Orderings_Obot__class_Obot(tc_fun(U_10707,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10707),U_10709))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10707),U_10708))
      | ~ class_Groups_Ocomm__monoid__mult(U_10706) ),
    inference(variable_rename,[status(thm)],[f_2860_1]) ).

fof(f_2860_3,plain,
    ! [U_10706,U_10707,U_10708,U_10709,U_10710] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10707,U_10706),U_10710),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10707,tc_HOL_Obool)),U_10708),U_10709)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10706),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10707,U_10706),U_10710),U_10708)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10707,U_10706),U_10710),U_10709))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10707,tc_HOL_Obool)),U_10708),U_10709) != c_Orderings_Obot__class_Obot(tc_fun(U_10707,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10707),U_10709))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10707),U_10708))
      | ~ class_Groups_Ocomm__monoid__mult(U_10706) ),
    inference(definitional_conversion,[status(esa)],[f_2860_2]) ).

cnf(f_2860_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10707,U_10706),U_10710),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10707,tc_HOL_Obool)),U_10708),U_10709)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10706),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10707,U_10706),U_10710),U_10708)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10707,U_10706),U_10710),U_10709))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10707,tc_HOL_Obool)),U_10708),U_10709) != c_Orderings_Obot__class_Obot(tc_fun(U_10707,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10707),U_10709))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10707),U_10708))
    | ~ class_Groups_Ocomm__monoid__mult(U_10706) ),
    inference(clausify,[status(thm)],[f_2860_3]) ).

fof(f_2861_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_2861_2,plain,
    ! [U_10714,U_10713,U_10712,U_10711] :
      ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10711,U_10713)),c_Sum__Type_OPlus(U_10711,U_10713,U_10712,U_10714)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10711),U_10712)),hAPP(c_Finite__Set_Ocard(U_10713),U_10714))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10713),U_10714))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10711),U_10712)) ),
    inference(variable_rename,[status(thm)],[f_2861_1]) ).

fof(f_2861_3,plain,
    ! [U_10713,U_10712,U_10711,U_10714] :
      ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10711,U_10713)),c_Sum__Type_OPlus(U_10711,U_10713,U_10712,U_10714)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10711),U_10712)),hAPP(c_Finite__Set_Ocard(U_10713),U_10714))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10713),U_10714))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10711),U_10712)) ),
    inference(definitional_conversion,[status(esa)],[f_2861_2]) ).

cnf(f_2861_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10711,U_10713)),c_Sum__Type_OPlus(U_10711,U_10713,U_10712,U_10714)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10711),U_10712)),hAPP(c_Finite__Set_Ocard(U_10713),U_10714))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10713),U_10714))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10711),U_10712)) ),
    inference(clausify,[status(thm)],[f_2861_3]) ).

fof(f_2862_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_2862_2,plain,
    ! [U_10719,U_10718,U_10717,U_10716,U_10715] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10716,U_10715),U_10719),U_10717) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10715),hAPP(U_10719,U_10718)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10716,U_10715),U_10719),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10716,tc_HOL_Obool)),U_10717),hAPP(hAPP(c_Set_Oinsert(U_10716),U_10718),c_Orderings_Obot__class_Obot(tc_fun(U_10716,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10716),U_10718),U_10717))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10716),U_10717))
      | ~ class_Groups_Ocomm__monoid__mult(U_10715) ),
    inference(variable_rename,[status(thm)],[f_2862_1]) ).

fof(f_2862_3,plain,
    ! [U_10715,U_10716,U_10717,U_10718,U_10719] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10716,U_10715),U_10719),U_10717) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10715),hAPP(U_10719,U_10718)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10716,U_10715),U_10719),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10716,tc_HOL_Obool)),U_10717),hAPP(hAPP(c_Set_Oinsert(U_10716),U_10718),c_Orderings_Obot__class_Obot(tc_fun(U_10716,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10716),U_10718),U_10717))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10716),U_10717))
      | ~ class_Groups_Ocomm__monoid__mult(U_10715) ),
    inference(definitional_conversion,[status(esa)],[f_2862_2]) ).

cnf(f_2862_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10716,U_10715),U_10719),U_10717) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10715),hAPP(U_10719,U_10718)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10716,U_10715),U_10719),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10716,tc_HOL_Obool)),U_10717),hAPP(hAPP(c_Set_Oinsert(U_10716),U_10718),c_Orderings_Obot__class_Obot(tc_fun(U_10716,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10716),U_10718),U_10717))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10716),U_10717))
    | ~ class_Groups_Ocomm__monoid__mult(U_10715) ),
    inference(clausify,[status(thm)],[f_2862_3]) ).

fof(f_2863_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_2863_2,plain,
    ! [U_10724,U_10723,U_10722,U_10721,U_10720] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10721,U_10720),U_10723),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10721,tc_HOL_Obool)),U_10722),hAPP(hAPP(c_Set_Oinsert(U_10721),U_10724),c_Orderings_Obot__class_Obot(tc_fun(U_10721,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10721,U_10720),U_10723),U_10722)
          | hBOOL(hAPP(hAPP(c_member(U_10721),U_10724),U_10722)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10721,U_10720),U_10723),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10721,tc_HOL_Obool)),U_10722),hAPP(hAPP(c_Set_Oinsert(U_10721),U_10724),c_Orderings_Obot__class_Obot(tc_fun(U_10721,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10720),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10721,U_10720),U_10723),U_10722)),hAPP(U_10723,U_10724))
          | ~ hBOOL(hAPP(hAPP(c_member(U_10721),U_10724),U_10722)) ) )
      | hAPP(U_10723,U_10724) = c_Groups_Ozero__class_Ozero(U_10720)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10721),U_10722))
      | ~ class_Fields_Ofield(U_10720) ),
    inference(variable_rename,[status(thm)],[f_2863_1]) ).

fof(f_2863_3,plain,
    ( ! [U_10720,U_10721,U_10722,U_10723,U_10724] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10721,U_10720),U_10723),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10721,tc_HOL_Obool)),U_10722),hAPP(hAPP(c_Set_Oinsert(U_10721),U_10724),c_Orderings_Obot__class_Obot(tc_fun(U_10721,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10721,U_10720),U_10723),U_10722)
        | hBOOL(hAPP(hAPP(c_member(U_10721),U_10724),U_10722))
        | ~ sP812(U_10720,U_10721,U_10722,U_10723,U_10724) )
    & ! [U_10720,U_10721,U_10722,U_10723,U_10724] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10721,U_10720),U_10723),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10721,tc_HOL_Obool)),U_10722),hAPP(hAPP(c_Set_Oinsert(U_10721),U_10724),c_Orderings_Obot__class_Obot(tc_fun(U_10721,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10720),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10721,U_10720),U_10723),U_10722)),hAPP(U_10723,U_10724))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10721),U_10724),U_10722))
        | ~ sP812(U_10720,U_10721,U_10722,U_10723,U_10724) )
    & ! [U_10720,U_10721,U_10722,U_10723,U_10724] :
        ( sP812(U_10720,U_10721,U_10722,U_10723,U_10724)
        | hAPP(U_10723,U_10724) = c_Groups_Ozero__class_Ozero(U_10720)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10721),U_10722))
        | ~ class_Fields_Ofield(U_10720) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP812])],[f_2863_2]) ).

cnf(f_2863_4,plain,
    ( sP812(U_10720,U_10721,U_10722,U_10723,U_10724)
    | hAPP(U_10723,U_10724) = c_Groups_Ozero__class_Ozero(U_10720)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10721),U_10722))
    | ~ class_Fields_Ofield(U_10720) ),
    inference(clausify,[status(thm)],[f_2863_3]) ).

cnf(f_2863_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10721,U_10720),U_10723),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10721,tc_HOL_Obool)),U_10722),hAPP(hAPP(c_Set_Oinsert(U_10721),U_10724),c_Orderings_Obot__class_Obot(tc_fun(U_10721,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10720),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10721,U_10720),U_10723),U_10722)),hAPP(U_10723,U_10724))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10721),U_10724),U_10722))
    | ~ sP812(U_10720,U_10721,U_10722,U_10723,U_10724) ),
    inference(clausify,[status(thm)],[f_2863_3]) ).

cnf(f_2863_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10721,U_10720),U_10723),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10721,tc_HOL_Obool)),U_10722),hAPP(hAPP(c_Set_Oinsert(U_10721),U_10724),c_Orderings_Obot__class_Obot(tc_fun(U_10721,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10721,U_10720),U_10723),U_10722)
    | hBOOL(hAPP(hAPP(c_member(U_10721),U_10724),U_10722))
    | ~ sP812(U_10720,U_10721,U_10722,U_10723,U_10724) ),
    inference(clausify,[status(thm)],[f_2863_3]) ).

fof(f_2864_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_2864_2,plain,
    ! [U_10730,U_10729,U_10728,U_10727,U_10726] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10727,tc_HOL_Obool)),U_10728),U_10729)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10726),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),U_10728)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),U_10729))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10727,tc_HOL_Obool)),U_10728),U_10729)))
      | ? [U_10725] :
          ( hAPP(U_10730,U_10725) = c_Groups_Ozero__class_Ozero(U_10726)
          & hBOOL(hAPP(hAPP(c_member(U_10727),U_10725),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10727,tc_HOL_Obool)),U_10728),U_10729))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10727),U_10729))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10727),U_10728))
      | ~ class_Fields_Ofield(U_10726) ),
    inference(variable_rename,[status(thm)],[f_2864_1]) ).

fof(f_2864_3,plain,
    ! [U_10730,U_10729,U_10728,U_10727,U_10726] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10727,tc_HOL_Obool)),U_10728),U_10729)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10726),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),U_10728)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),U_10729))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10727,tc_HOL_Obool)),U_10728),U_10729)))
      | ( hAPP(U_10730,sK169(U_10730,U_10729,U_10728,U_10727,U_10726)) = c_Groups_Ozero__class_Ozero(U_10726)
        & hBOOL(hAPP(hAPP(c_member(U_10727),sK169(U_10730,U_10729,U_10728,U_10727,U_10726)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10727,tc_HOL_Obool)),U_10728),U_10729))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10727),U_10729))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10727),U_10728))
      | ~ class_Fields_Ofield(U_10726) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_10725,sK169(U_10730,U_10729,U_10728,U_10727,U_10726))],[f_2864_2]) ).

fof(f_2864_4,plain,
    ( ! [U_10727,U_10726,U_10728,U_10729,U_10730] :
        ( hAPP(U_10730,sK169(U_10730,U_10729,U_10728,U_10727,U_10726)) = c_Groups_Ozero__class_Ozero(U_10726)
        | ~ sP813(U_10727,U_10726,U_10728,U_10729,U_10730) )
    & ! [U_10727,U_10726,U_10728,U_10729,U_10730] :
        ( hBOOL(hAPP(hAPP(c_member(U_10727),sK169(U_10730,U_10729,U_10728,U_10727,U_10726)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10727,tc_HOL_Obool)),U_10728),U_10729)))
        | ~ sP813(U_10727,U_10726,U_10728,U_10729,U_10730) )
    & ! [U_10727,U_10726,U_10728,U_10729,U_10730] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10727,tc_HOL_Obool)),U_10728),U_10729)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10726),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),U_10728)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),U_10729))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10727,tc_HOL_Obool)),U_10728),U_10729)))
        | sP813(U_10727,U_10726,U_10728,U_10729,U_10730)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10727),U_10729))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10727),U_10728))
        | ~ class_Fields_Ofield(U_10726) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP813])],[f_2864_3]) ).

cnf(f_2864_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10727,tc_HOL_Obool)),U_10728),U_10729)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10726),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),U_10728)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),U_10729))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10727,U_10726),U_10730),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10727,tc_HOL_Obool)),U_10728),U_10729)))
    | sP813(U_10727,U_10726,U_10728,U_10729,U_10730)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10727),U_10729))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10727),U_10728))
    | ~ class_Fields_Ofield(U_10726) ),
    inference(clausify,[status(thm)],[f_2864_4]) ).

cnf(f_2864_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10727),sK169(U_10730,U_10729,U_10728,U_10727,U_10726)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10727,tc_HOL_Obool)),U_10728),U_10729)))
    | ~ sP813(U_10727,U_10726,U_10728,U_10729,U_10730) ),
    inference(clausify,[status(thm)],[f_2864_4]) ).

cnf(f_2864_7,plain,
    ( hAPP(U_10730,sK169(U_10730,U_10729,U_10728,U_10727,U_10726)) = c_Groups_Ozero__class_Ozero(U_10726)
    | ~ sP813(U_10727,U_10726,U_10728,U_10729,U_10730) ),
    inference(clausify,[status(thm)],[f_2864_4]) ).

fof(f_2865_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_2865_2,plain,
    ! [U_10736,U_10735,U_10734,U_10733,U_10732] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10733,U_10732),U_10736),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10733,tc_HOL_Obool)),U_10734),U_10735)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10732),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10733,U_10732),U_10736),U_10734)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10733,U_10732),U_10736),U_10735))
      | ? [U_10731] :
          ( hAPP(U_10736,U_10731) != c_Groups_Oone__class_Oone(U_10732)
          & hBOOL(hAPP(hAPP(c_member(U_10733),U_10731),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10733,tc_HOL_Obool)),U_10734),U_10735))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10733),U_10735))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10733),U_10734))
      | ~ class_Groups_Ocomm__monoid__mult(U_10732) ),
    inference(variable_rename,[status(thm)],[f_2865_1]) ).

fof(f_2865_3,plain,
    ! [U_10736,U_10735,U_10734,U_10733,U_10732] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10733,U_10732),U_10736),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10733,tc_HOL_Obool)),U_10734),U_10735)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10732),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10733,U_10732),U_10736),U_10734)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10733,U_10732),U_10736),U_10735))
      | ( hAPP(U_10736,sK170(U_10736,U_10735,U_10734,U_10733,U_10732)) != c_Groups_Oone__class_Oone(U_10732)
        & hBOOL(hAPP(hAPP(c_member(U_10733),sK170(U_10736,U_10735,U_10734,U_10733,U_10732)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10733,tc_HOL_Obool)),U_10734),U_10735))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10733),U_10735))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10733),U_10734))
      | ~ class_Groups_Ocomm__monoid__mult(U_10732) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_10731,sK170(U_10736,U_10735,U_10734,U_10733,U_10732))],[f_2865_2]) ).

fof(f_2865_4,plain,
    ( ! [U_10735,U_10734,U_10732,U_10733,U_10736] :
        ( hAPP(U_10736,sK170(U_10736,U_10735,U_10734,U_10733,U_10732)) != c_Groups_Oone__class_Oone(U_10732)
        | ~ sP814(U_10735,U_10734,U_10732,U_10733,U_10736) )
    & ! [U_10735,U_10734,U_10732,U_10733,U_10736] :
        ( hBOOL(hAPP(hAPP(c_member(U_10733),sK170(U_10736,U_10735,U_10734,U_10733,U_10732)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10733,tc_HOL_Obool)),U_10734),U_10735)))
        | ~ sP814(U_10735,U_10734,U_10732,U_10733,U_10736) )
    & ! [U_10735,U_10734,U_10732,U_10733,U_10736] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10733,U_10732),U_10736),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10733,tc_HOL_Obool)),U_10734),U_10735)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10732),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10733,U_10732),U_10736),U_10734)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10733,U_10732),U_10736),U_10735))
        | sP814(U_10735,U_10734,U_10732,U_10733,U_10736)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10733),U_10735))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10733),U_10734))
        | ~ class_Groups_Ocomm__monoid__mult(U_10732) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP814])],[f_2865_3]) ).

cnf(f_2865_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10733,U_10732),U_10736),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10733,tc_HOL_Obool)),U_10734),U_10735)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10732),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10733,U_10732),U_10736),U_10734)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10733,U_10732),U_10736),U_10735))
    | sP814(U_10735,U_10734,U_10732,U_10733,U_10736)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10733),U_10735))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10733),U_10734))
    | ~ class_Groups_Ocomm__monoid__mult(U_10732) ),
    inference(clausify,[status(thm)],[f_2865_4]) ).

cnf(f_2865_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10733),sK170(U_10736,U_10735,U_10734,U_10733,U_10732)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10733,tc_HOL_Obool)),U_10734),U_10735)))
    | ~ sP814(U_10735,U_10734,U_10732,U_10733,U_10736) ),
    inference(clausify,[status(thm)],[f_2865_4]) ).

cnf(f_2865_7,plain,
    ( hAPP(U_10736,sK170(U_10736,U_10735,U_10734,U_10733,U_10732)) != c_Groups_Oone__class_Oone(U_10732)
    | ~ sP814(U_10735,U_10734,U_10732,U_10733,U_10736) ),
    inference(clausify,[status(thm)],[f_2865_4]) ).

fof(f_2866_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_2866_2,plain,
    ! [U_10742,U_10741,U_10740,U_10739,U_10738] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10739,U_10738),U_10742),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10739,tc_HOL_Obool)),U_10740),U_10741)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10738),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10739,U_10738),U_10742),U_10740)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10739,U_10738),U_10742),U_10741))
      | ? [U_10737] :
          ( hAPP(U_10742,U_10737) != c_Groups_Oone__class_Oone(U_10738)
          & hBOOL(hAPP(hAPP(c_member(U_10739),U_10737),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10739,tc_HOL_Obool)),U_10740),U_10741))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10739),U_10741))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10739),U_10740))
      | ~ class_Groups_Ocomm__monoid__mult(U_10738) ),
    inference(variable_rename,[status(thm)],[f_2866_1]) ).

fof(f_2866_3,plain,
    ! [U_10742,U_10741,U_10740,U_10739,U_10738] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10739,U_10738),U_10742),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10739,tc_HOL_Obool)),U_10740),U_10741)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10738),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10739,U_10738),U_10742),U_10740)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10739,U_10738),U_10742),U_10741))
      | ( hAPP(U_10742,sK171(U_10742,U_10741,U_10740,U_10739,U_10738)) != c_Groups_Oone__class_Oone(U_10738)
        & hBOOL(hAPP(hAPP(c_member(U_10739),sK171(U_10742,U_10741,U_10740,U_10739,U_10738)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10739,tc_HOL_Obool)),U_10740),U_10741))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10739),U_10741))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10739),U_10740))
      | ~ class_Groups_Ocomm__monoid__mult(U_10738) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_10737,sK171(U_10742,U_10741,U_10740,U_10739,U_10738))],[f_2866_2]) ).

fof(f_2866_4,plain,
    ( ! [U_10738,U_10739,U_10740,U_10741,U_10742] :
        ( hAPP(U_10742,sK171(U_10742,U_10741,U_10740,U_10739,U_10738)) != c_Groups_Oone__class_Oone(U_10738)
        | ~ sP815(U_10738,U_10739,U_10740,U_10741,U_10742) )
    & ! [U_10738,U_10739,U_10740,U_10741,U_10742] :
        ( hBOOL(hAPP(hAPP(c_member(U_10739),sK171(U_10742,U_10741,U_10740,U_10739,U_10738)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10739,tc_HOL_Obool)),U_10740),U_10741)))
        | ~ sP815(U_10738,U_10739,U_10740,U_10741,U_10742) )
    & ! [U_10738,U_10739,U_10740,U_10741,U_10742] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10739,U_10738),U_10742),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10739,tc_HOL_Obool)),U_10740),U_10741)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10738),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10739,U_10738),U_10742),U_10740)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10739,U_10738),U_10742),U_10741))
        | sP815(U_10738,U_10739,U_10740,U_10741,U_10742)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10739),U_10741))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10739),U_10740))
        | ~ class_Groups_Ocomm__monoid__mult(U_10738) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP815])],[f_2866_3]) ).

cnf(f_2866_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10739,U_10738),U_10742),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10739,tc_HOL_Obool)),U_10740),U_10741)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10738),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10739,U_10738),U_10742),U_10740)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10739,U_10738),U_10742),U_10741))
    | sP815(U_10738,U_10739,U_10740,U_10741,U_10742)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10739),U_10741))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10739),U_10740))
    | ~ class_Groups_Ocomm__monoid__mult(U_10738) ),
    inference(clausify,[status(thm)],[f_2866_4]) ).

cnf(f_2866_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10739),sK171(U_10742,U_10741,U_10740,U_10739,U_10738)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10739,tc_HOL_Obool)),U_10740),U_10741)))
    | ~ sP815(U_10738,U_10739,U_10740,U_10741,U_10742) ),
    inference(clausify,[status(thm)],[f_2866_4]) ).

cnf(f_2866_7,plain,
    ( hAPP(U_10742,sK171(U_10742,U_10741,U_10740,U_10739,U_10738)) != c_Groups_Oone__class_Oone(U_10738)
    | ~ sP815(U_10738,U_10739,U_10740,U_10741,U_10742) ),
    inference(clausify,[status(thm)],[f_2866_4]) ).

fof(f_2867_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_2867_2,plain,
    ! [U_10744,U_10743] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10743,U_10744))),
    inference(variable_rename,[status(thm)],[f_2867_1]) ).

fof(f_2867_3,plain,
    ! [U_10744,U_10743] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10743,U_10744))),
    inference(definitional_conversion,[status(esa)],[f_2867_2]) ).

cnf(f_2867_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10743,U_10744))),
    inference(clausify,[status(thm)],[f_2867_3]) ).

fof(f_2868_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_2868_2,plain,
    ! [U_10746,U_10745] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10745,U_10746)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10746),hAPP(c_Nat_OSuc,U_10745)),
    inference(variable_rename,[status(thm)],[f_2868_1]) ).

fof(f_2868_3,plain,
    ! [U_10746,U_10745] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10745,U_10746)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10746),hAPP(c_Nat_OSuc,U_10745)),
    inference(definitional_conversion,[status(esa)],[f_2868_2]) ).

cnf(f_2868_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10745,U_10746)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10746),hAPP(c_Nat_OSuc,U_10745)),
    inference(clausify,[status(thm)],[f_2868_3]) ).

fof(f_2869_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_2869_2,plain,
    ! [U_10750,U_10749,U_10748] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10748,tc_Int_Oint),U_10750),U_10749) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10748,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10748),c_Int_Onat),U_10750)),U_10749))
      | ? [U_10747] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10750,U_10747))
          & hBOOL(hAPP(hAPP(c_member(U_10748),U_10747),U_10749)) ) ),
    inference(variable_rename,[status(thm)],[f_2869_1]) ).

fof(f_2869_3,plain,
    ! [U_10750,U_10749,U_10748] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10748,tc_Int_Oint),U_10750),U_10749) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10748,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10748),c_Int_Onat),U_10750)),U_10749))
      | ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10750,sK172(U_10750,U_10749,U_10748)))
        & hBOOL(hAPP(hAPP(c_member(U_10748),sK172(U_10750,U_10749,U_10748)),U_10749)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_10747,sK172(U_10750,U_10749,U_10748))],[f_2869_2]) ).

fof(f_2869_4,plain,
    ( ! [U_10748,U_10749,U_10750] :
        ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10750,sK172(U_10750,U_10749,U_10748)))
        | ~ sP816(U_10748,U_10749,U_10750) )
    & ! [U_10748,U_10749,U_10750] :
        ( hBOOL(hAPP(hAPP(c_member(U_10748),sK172(U_10750,U_10749,U_10748)),U_10749))
        | ~ sP816(U_10748,U_10749,U_10750) )
    & ! [U_10748,U_10749,U_10750] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10748,tc_Int_Oint),U_10750),U_10749) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10748,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10748),c_Int_Onat),U_10750)),U_10749))
        | sP816(U_10748,U_10749,U_10750) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP816])],[f_2869_3]) ).

cnf(f_2869_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10748,tc_Int_Oint),U_10750),U_10749) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10748,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10748),c_Int_Onat),U_10750)),U_10749))
    | sP816(U_10748,U_10749,U_10750) ),
    inference(clausify,[status(thm)],[f_2869_4]) ).

cnf(f_2869_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10748),sK172(U_10750,U_10749,U_10748)),U_10749))
    | ~ sP816(U_10748,U_10749,U_10750) ),
    inference(clausify,[status(thm)],[f_2869_4]) ).

cnf(f_2869_7,plain,
    ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10750,sK172(U_10750,U_10749,U_10748)))
    | ~ sP816(U_10748,U_10749,U_10750) ),
    inference(clausify,[status(thm)],[f_2869_4]) ).

fof(f_2870_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_2870_2,plain,
    ! [U_10753,U_10752,U_10751] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10751,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10751,U_10752,U_10753)),hAPP(hAPP(c_Set_Oinsert(U_10751),U_10753),c_Orderings_Obot__class_Obot(tc_fun(U_10751,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10751,U_10752,U_10753)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10751),U_10752),U_10753))
      | ~ class_Orderings_Olinorder(U_10751) ),
    inference(variable_rename,[status(thm)],[f_2870_1]) ).

fof(f_2870_3,plain,
    ! [U_10751,U_10752,U_10753] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10751,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10751,U_10752,U_10753)),hAPP(hAPP(c_Set_Oinsert(U_10751),U_10753),c_Orderings_Obot__class_Obot(tc_fun(U_10751,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10751,U_10752,U_10753)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10751),U_10752),U_10753))
      | ~ class_Orderings_Olinorder(U_10751) ),
    inference(definitional_conversion,[status(esa)],[f_2870_2]) ).

cnf(f_2870_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10751,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10751,U_10752,U_10753)),hAPP(hAPP(c_Set_Oinsert(U_10751),U_10753),c_Orderings_Obot__class_Obot(tc_fun(U_10751,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10751,U_10752,U_10753)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10751),U_10752),U_10753))
    | ~ class_Orderings_Olinorder(U_10751) ),
    inference(clausify,[status(thm)],[f_2870_3]) ).

fof(f_2871_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_2871_2,plain,
    ! [U_10756,U_10755,U_10754] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10754),U_10755),U_10756) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10754,tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool)),U_10755),hAPP(hAPP(c_COMBC(U_10754,tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10754,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool)),U_10754),c_Set_Oinsert(tc_fun(U_10754,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10754,tc_HOL_Obool),tc_fun(U_10754,tc_HOL_Obool),U_10754),c_Relation_OImage(U_10754,U_10754,U_10756)),hAPP(hAPP(c_COMBC(U_10754,tc_fun(U_10754,tc_HOL_Obool),tc_fun(U_10754,tc_HOL_Obool)),c_Set_Oinsert(U_10754)),c_Orderings_Obot__class_Obot(tc_fun(U_10754,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2871_1]) ).

fof(f_2871_3,plain,
    ! [U_10754,U_10755,U_10756] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10754),U_10755),U_10756) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10754,tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool)),U_10755),hAPP(hAPP(c_COMBC(U_10754,tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10754,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool)),U_10754),c_Set_Oinsert(tc_fun(U_10754,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10754,tc_HOL_Obool),tc_fun(U_10754,tc_HOL_Obool),U_10754),c_Relation_OImage(U_10754,U_10754,U_10756)),hAPP(hAPP(c_COMBC(U_10754,tc_fun(U_10754,tc_HOL_Obool),tc_fun(U_10754,tc_HOL_Obool)),c_Set_Oinsert(U_10754)),c_Orderings_Obot__class_Obot(tc_fun(U_10754,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2871_2]) ).

cnf(f_2871_4,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10754),U_10755),U_10756) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10754,tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool)),U_10755),hAPP(hAPP(c_COMBC(U_10754,tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10754,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool)),U_10754),c_Set_Oinsert(tc_fun(U_10754,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10754,tc_HOL_Obool),tc_fun(U_10754,tc_HOL_Obool),U_10754),c_Relation_OImage(U_10754,U_10754,U_10756)),hAPP(hAPP(c_COMBC(U_10754,tc_fun(U_10754,tc_HOL_Obool),tc_fun(U_10754,tc_HOL_Obool)),c_Set_Oinsert(U_10754)),c_Orderings_Obot__class_Obot(tc_fun(U_10754,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10754,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2871_3]) ).

fof(f_2872_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_2872_2,plain,
    ! [U_10758,U_10757] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10757,U_10758))),
    inference(variable_rename,[status(thm)],[f_2872_1]) ).

fof(f_2872_3,plain,
    ! [U_10757,U_10758] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10757,U_10758))),
    inference(definitional_conversion,[status(esa)],[f_2872_2]) ).

cnf(f_2872_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10757,U_10758))),
    inference(clausify,[status(thm)],[f_2872_3]) ).

fof(f_2873_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_2873_2,plain,
    ! [U_10760,U_10759] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10759,U_10760))),
    inference(variable_rename,[status(thm)],[f_2873_1]) ).

fof(f_2873_3,plain,
    ! [U_10759,U_10760] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10759,U_10760))),
    inference(definitional_conversion,[status(esa)],[f_2873_2]) ).

cnf(f_2873_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10759,U_10760))),
    inference(clausify,[status(thm)],[f_2873_3]) ).

fof(f_2874_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_2874_2,plain,
    ! [U_10766,U_10765,U_10764,U_10763,U_10762,U_10761] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10761,tc_fun(U_10766,tc_HOL_Obool)),U_10763),U_10764),U_10765))
      | ~ hBOOL(hAPP(hAPP(U_10764,U_10762),U_10765))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10761),U_10762),U_10763)) ),
    inference(variable_rename,[status(thm)],[f_2874_1]) ).

fof(f_2874_3,plain,
    ! [U_10761,U_10762,U_10763,U_10764,U_10765,U_10766] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10761,tc_fun(U_10766,tc_HOL_Obool)),U_10763),U_10764),U_10765))
      | ~ hBOOL(hAPP(hAPP(U_10764,U_10762),U_10765))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10761),U_10762),U_10763)) ),
    inference(definitional_conversion,[status(esa)],[f_2874_2]) ).

cnf(f_2874_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10761,tc_fun(U_10766,tc_HOL_Obool)),U_10763),U_10764),U_10765))
    | ~ hBOOL(hAPP(hAPP(U_10764,U_10762),U_10765))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10761),U_10762),U_10763)) ),
    inference(clausify,[status(thm)],[f_2874_3]) ).

fof(f_2875_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_2875_2,plain,
    ! [U_10772,U_10771,U_10770,U_10769] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10769,tc_fun(U_10771,tc_HOL_Obool)),U_10770),U_10772)))
          | ? [U_10768] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(U_10772,U_10768)))
              & hBOOL(hAPP(hAPP(c_member(U_10769),U_10768),U_10770)) ) )
        & ( ! [U_10767] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(U_10772,U_10767)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10769),U_10767),U_10770)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10769,tc_fun(U_10771,tc_HOL_Obool)),U_10770),U_10772))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10769),U_10770)) ),
    inference(variable_rename,[status(thm)],[f_2875_1]) ).

fof(f_2875_3,plain,
    ! [U_10772,U_10771,U_10770,U_10769] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10769,tc_fun(U_10771,tc_HOL_Obool)),U_10770),U_10772)))
          | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(U_10772,sK173(U_10772,U_10771,U_10770,U_10769))))
            & hBOOL(hAPP(hAPP(c_member(U_10769),sK173(U_10772,U_10771,U_10770,U_10769)),U_10770)) ) )
        & ( ! [U_10767] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(U_10772,U_10767)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10769),U_10767),U_10770)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10769,tc_fun(U_10771,tc_HOL_Obool)),U_10770),U_10772))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10769),U_10770)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_10768,sK173(U_10772,U_10771,U_10770,U_10769))],[f_2875_2]) ).

fof(f_2875_4,plain,
    ( ! [U_10769,U_10770,U_10771,U_10772] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(U_10772,sK173(U_10772,U_10771,U_10770,U_10769))))
        | ~ sP817(U_10769,U_10770,U_10771,U_10772) )
    & ! [U_10769,U_10770,U_10771,U_10772] :
        ( hBOOL(hAPP(hAPP(c_member(U_10769),sK173(U_10772,U_10771,U_10770,U_10769)),U_10770))
        | ~ sP817(U_10769,U_10770,U_10771,U_10772) )
    & ! [U_10767,U_10769,U_10770,U_10771,U_10772] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10769,tc_fun(U_10771,tc_HOL_Obool)),U_10770),U_10772)))
        | sP817(U_10769,U_10770,U_10771,U_10772)
        | ~ sP818(U_10767,U_10769,U_10770,U_10771,U_10772) )
    & ! [U_10767,U_10769,U_10770,U_10771,U_10772] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(U_10772,U_10767)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10769),U_10767),U_10770))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10769,tc_fun(U_10771,tc_HOL_Obool)),U_10770),U_10772)))
        | ~ sP818(U_10767,U_10769,U_10770,U_10771,U_10772) )
    & ! [U_10767,U_10769,U_10770,U_10771,U_10772] :
        ( sP818(U_10767,U_10769,U_10770,U_10771,U_10772)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10769),U_10770)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP817,sP818])],[f_2875_3]) ).

cnf(f_2875_5,plain,
    ( sP818(U_10767,U_10769,U_10770,U_10771,U_10772)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10769),U_10770)) ),
    inference(clausify,[status(thm)],[f_2875_4]) ).

cnf(f_2875_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(U_10772,U_10767)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10769),U_10767),U_10770))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10769,tc_fun(U_10771,tc_HOL_Obool)),U_10770),U_10772)))
    | ~ sP818(U_10767,U_10769,U_10770,U_10771,U_10772) ),
    inference(clausify,[status(thm)],[f_2875_4]) ).

cnf(f_2875_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10769,tc_fun(U_10771,tc_HOL_Obool)),U_10770),U_10772)))
    | sP817(U_10769,U_10770,U_10771,U_10772)
    | ~ sP818(U_10767,U_10769,U_10770,U_10771,U_10772) ),
    inference(clausify,[status(thm)],[f_2875_4]) ).

cnf(f_2875_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10769),sK173(U_10772,U_10771,U_10770,U_10769)),U_10770))
    | ~ sP817(U_10769,U_10770,U_10771,U_10772) ),
    inference(clausify,[status(thm)],[f_2875_4]) ).

cnf(f_2875_9,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10771),hAPP(U_10772,sK173(U_10772,U_10771,U_10770,U_10769))))
    | ~ sP817(U_10769,U_10770,U_10771,U_10772) ),
    inference(clausify,[status(thm)],[f_2875_4]) ).

fof(f_2876_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_2876_2,plain,
    ! [U_10779,U_10778,U_10777,U_10776,U_10775] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10775,tc_fun(U_10776,tc_HOL_Obool)),U_10777),U_10778),U_10779))
        | ! [U_10774] :
            ( ~ hBOOL(hAPP(hAPP(U_10778,U_10774),U_10779))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10775),U_10774),U_10777)) ) )
      & ( ? [U_10773] :
            ( hBOOL(hAPP(hAPP(U_10778,U_10773),U_10779))
            & hBOOL(hAPP(hAPP(c_member(U_10775),U_10773),U_10777)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10775,tc_fun(U_10776,tc_HOL_Obool)),U_10777),U_10778),U_10779)) ) ),
    inference(variable_rename,[status(thm)],[f_2876_1]) ).

fof(f_2876_3,plain,
    ( ! [U_10789,U_10787,U_10785,U_10783,U_10781] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10781,tc_fun(U_10783,tc_HOL_Obool)),U_10785),U_10787),U_10789))
        | ! [U_10774] :
            ( ~ hBOOL(hAPP(hAPP(U_10787,U_10774),U_10789))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10781),U_10774),U_10785)) ) )
    & ! [U_10788,U_10786,U_10784,U_10782,U_10780] :
        ( ? [U_10773] :
            ( hBOOL(hAPP(hAPP(U_10786,U_10773),U_10788))
            & hBOOL(hAPP(hAPP(c_member(U_10780),U_10773),U_10784)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10780,tc_fun(U_10782,tc_HOL_Obool)),U_10784),U_10786),U_10788)) ) ),
    inference(miniscope,[status(thm)],[f_2876_2]) ).

fof(f_2876_4,plain,
    ( ! [U_10789,U_10787,U_10785,U_10783,U_10781] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10781,tc_fun(U_10783,tc_HOL_Obool)),U_10785),U_10787),U_10789))
        | ! [U_10774] :
            ( ~ hBOOL(hAPP(hAPP(U_10787,U_10774),U_10789))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10781),U_10774),U_10785)) ) )
    & ! [U_10788,U_10786,U_10784,U_10782,U_10780] :
        ( ( hBOOL(hAPP(hAPP(U_10786,sK174(U_10788,U_10786,U_10784,U_10782,U_10780)),U_10788))
          & hBOOL(hAPP(hAPP(c_member(U_10780),sK174(U_10788,U_10786,U_10784,U_10782,U_10780)),U_10784)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10780,tc_fun(U_10782,tc_HOL_Obool)),U_10784),U_10786),U_10788)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_10773,sK174(U_10788,U_10786,U_10784,U_10782,U_10780))],[f_2876_3]) ).

fof(f_2876_5,plain,
    ( ! [U_10784,U_10786,U_10782,U_10780,U_10788] :
        ( hBOOL(hAPP(hAPP(U_10786,sK174(U_10788,U_10786,U_10784,U_10782,U_10780)),U_10788))
        | ~ sP819(U_10784,U_10786,U_10782,U_10780,U_10788) )
    & ! [U_10784,U_10786,U_10782,U_10780,U_10788] :
        ( hBOOL(hAPP(hAPP(c_member(U_10780),sK174(U_10788,U_10786,U_10784,U_10782,U_10780)),U_10784))
        | ~ sP819(U_10784,U_10786,U_10782,U_10780,U_10788) )
    & ! [U_10774,U_10781,U_10783,U_10787,U_10785,U_10789] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10781,tc_fun(U_10783,tc_HOL_Obool)),U_10785),U_10787),U_10789))
        | ~ hBOOL(hAPP(hAPP(U_10787,U_10774),U_10789))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10781),U_10774),U_10785)) )
    & ! [U_10784,U_10786,U_10782,U_10780,U_10788] :
        ( sP819(U_10784,U_10786,U_10782,U_10780,U_10788)
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10780,tc_fun(U_10782,tc_HOL_Obool)),U_10784),U_10786),U_10788)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP819])],[f_2876_4]) ).

cnf(f_2876_6,plain,
    ( sP819(U_10784,U_10786,U_10782,U_10780,U_10788)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10780,tc_fun(U_10782,tc_HOL_Obool)),U_10784),U_10786),U_10788)) ),
    inference(clausify,[status(thm)],[f_2876_5]) ).

cnf(f_2876_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10781,tc_fun(U_10783,tc_HOL_Obool)),U_10785),U_10787),U_10789))
    | ~ hBOOL(hAPP(hAPP(U_10787,U_10774),U_10789))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10781),U_10774),U_10785)) ),
    inference(clausify,[status(thm)],[f_2876_5]) ).

cnf(f_2876_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10780),sK174(U_10788,U_10786,U_10784,U_10782,U_10780)),U_10784))
    | ~ sP819(U_10784,U_10786,U_10782,U_10780,U_10788) ),
    inference(clausify,[status(thm)],[f_2876_5]) ).

cnf(f_2876_9,plain,
    ( hBOOL(hAPP(hAPP(U_10786,sK174(U_10788,U_10786,U_10784,U_10782,U_10780)),U_10788))
    | ~ sP819(U_10784,U_10786,U_10782,U_10780,U_10788) ),
    inference(clausify,[status(thm)],[f_2876_5]) ).

fof(f_2877_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_2877_2,plain,
    ! [U_10795,U_10794,U_10793,U_10792,U_10791,U_10790] : hAPP(c_Relation_OImage(U_10790,U_10791,U_10792),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10793,tc_fun(U_10790,tc_HOL_Obool)),U_10794),U_10795)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10793,tc_fun(U_10791,tc_HOL_Obool)),U_10794),hAPP(hAPP(c_COMBB(tc_fun(U_10790,tc_HOL_Obool),tc_fun(U_10791,tc_HOL_Obool),U_10793),c_Relation_OImage(U_10790,U_10791,U_10792)),U_10795)),
    inference(variable_rename,[status(thm)],[f_2877_1]) ).

fof(f_2877_3,plain,
    ! [U_10791,U_10790,U_10792,U_10793,U_10794,U_10795] : hAPP(c_Relation_OImage(U_10790,U_10791,U_10792),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10793,tc_fun(U_10790,tc_HOL_Obool)),U_10794),U_10795)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10793,tc_fun(U_10791,tc_HOL_Obool)),U_10794),hAPP(hAPP(c_COMBB(tc_fun(U_10790,tc_HOL_Obool),tc_fun(U_10791,tc_HOL_Obool),U_10793),c_Relation_OImage(U_10790,U_10791,U_10792)),U_10795)),
    inference(definitional_conversion,[status(esa)],[f_2877_2]) ).

cnf(f_2877_4,plain,
    hAPP(c_Relation_OImage(U_10790,U_10791,U_10792),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10793,tc_fun(U_10790,tc_HOL_Obool)),U_10794),U_10795)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10793,tc_fun(U_10791,tc_HOL_Obool)),U_10794),hAPP(hAPP(c_COMBB(tc_fun(U_10790,tc_HOL_Obool),tc_fun(U_10791,tc_HOL_Obool),U_10793),c_Relation_OImage(U_10790,U_10791,U_10792)),U_10795)),
    inference(clausify,[status(thm)],[f_2877_3]) ).

fof(f_2878_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_2878_2,plain,
    ! [U_10798,U_10797,U_10796] :
      ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10796,U_10798,U_10797) = c_Orderings_Obot__class_Obot(tc_fun(U_10796,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10796),U_10797),U_10798))
      | ~ class_Orderings_Oorder(U_10796) ),
    inference(variable_rename,[status(thm)],[f_2878_1]) ).

fof(f_2878_3,plain,
    ! [U_10796,U_10798,U_10797] :
      ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10796,U_10798,U_10797) = c_Orderings_Obot__class_Obot(tc_fun(U_10796,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10796),U_10797),U_10798))
      | ~ class_Orderings_Oorder(U_10796) ),
    inference(definitional_conversion,[status(esa)],[f_2878_2]) ).

cnf(f_2878_4,plain,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10796,U_10798,U_10797) = c_Orderings_Obot__class_Obot(tc_fun(U_10796,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10796),U_10797),U_10798))
    | ~ class_Orderings_Oorder(U_10796) ),
    inference(clausify,[status(thm)],[f_2878_3]) ).

fof(f_2879_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_2879_2,plain,
    ! [U_10801,U_10800,U_10799] :
      ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10799,U_10800,U_10801) = c_Orderings_Obot__class_Obot(tc_fun(U_10799,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10799),U_10800),U_10801)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10799),U_10800),U_10801))
          | c_SetInterval_Oord__class_OgreaterThanAtMost(U_10799,U_10800,U_10801) != c_Orderings_Obot__class_Obot(tc_fun(U_10799,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_10799) ),
    inference(variable_rename,[status(thm)],[f_2879_1]) ).

fof(f_2879_3,plain,
    ( ! [U_10799,U_10800,U_10801] :
        ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10799,U_10800,U_10801) = c_Orderings_Obot__class_Obot(tc_fun(U_10799,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10799),U_10800),U_10801))
        | ~ sP820(U_10799,U_10800,U_10801) )
    & ! [U_10799,U_10800,U_10801] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10799),U_10800),U_10801))
        | c_SetInterval_Oord__class_OgreaterThanAtMost(U_10799,U_10800,U_10801) != c_Orderings_Obot__class_Obot(tc_fun(U_10799,tc_HOL_Obool))
        | ~ sP820(U_10799,U_10800,U_10801) )
    & ! [U_10799,U_10800,U_10801] :
        ( sP820(U_10799,U_10800,U_10801)
        | ~ class_Orderings_Oorder(U_10799) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP820])],[f_2879_2]) ).

cnf(f_2879_4,plain,
    ( sP820(U_10799,U_10800,U_10801)
    | ~ class_Orderings_Oorder(U_10799) ),
    inference(clausify,[status(thm)],[f_2879_3]) ).

cnf(f_2879_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10799),U_10800),U_10801))
    | c_SetInterval_Oord__class_OgreaterThanAtMost(U_10799,U_10800,U_10801) != c_Orderings_Obot__class_Obot(tc_fun(U_10799,tc_HOL_Obool))
    | ~ sP820(U_10799,U_10800,U_10801) ),
    inference(clausify,[status(thm)],[f_2879_3]) ).

cnf(f_2879_6,plain,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10799,U_10800,U_10801) = c_Orderings_Obot__class_Obot(tc_fun(U_10799,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10799),U_10800),U_10801))
    | ~ sP820(U_10799,U_10800,U_10801) ),
    inference(clausify,[status(thm)],[f_2879_3]) ).

fof(f_2880_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_2880_2,plain,
    ! [U_10804,U_10803,U_10802] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_10802,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10802,U_10803,U_10804)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10802),U_10803),U_10804)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10802),U_10803),U_10804))
          | c_Orderings_Obot__class_Obot(tc_fun(U_10802,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_10802,U_10803,U_10804) ) )
      | ~ class_Orderings_Oorder(U_10802) ),
    inference(variable_rename,[status(thm)],[f_2880_1]) ).

fof(f_2880_3,plain,
    ( ! [U_10803,U_10804,U_10802] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_10802,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10802,U_10803,U_10804)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10802),U_10803),U_10804))
        | ~ sP821(U_10803,U_10804,U_10802) )
    & ! [U_10803,U_10804,U_10802] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10802),U_10803),U_10804))
        | c_Orderings_Obot__class_Obot(tc_fun(U_10802,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_10802,U_10803,U_10804)
        | ~ sP821(U_10803,U_10804,U_10802) )
    & ! [U_10803,U_10804,U_10802] :
        ( sP821(U_10803,U_10804,U_10802)
        | ~ class_Orderings_Oorder(U_10802) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP821])],[f_2880_2]) ).

cnf(f_2880_4,plain,
    ( sP821(U_10803,U_10804,U_10802)
    | ~ class_Orderings_Oorder(U_10802) ),
    inference(clausify,[status(thm)],[f_2880_3]) ).

cnf(f_2880_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10802),U_10803),U_10804))
    | c_Orderings_Obot__class_Obot(tc_fun(U_10802,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_10802,U_10803,U_10804)
    | ~ sP821(U_10803,U_10804,U_10802) ),
    inference(clausify,[status(thm)],[f_2880_3]) ).

cnf(f_2880_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_10802,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10802,U_10803,U_10804)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10802),U_10803),U_10804))
    | ~ sP821(U_10803,U_10804,U_10802) ),
    inference(clausify,[status(thm)],[f_2880_3]) ).

fof(f_2881_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_2881_2,plain,
    ! [U_10808,U_10807,U_10806,U_10805] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10805,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10805,U_10806,U_10807)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10805,U_10807,U_10808)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10805,U_10806,U_10808)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10805),U_10807),U_10808))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10805),U_10806),U_10807))
      | ~ class_Orderings_Olinorder(U_10805) ),
    inference(variable_rename,[status(thm)],[f_2881_1]) ).

fof(f_2881_3,plain,
    ! [U_10805,U_10806,U_10807,U_10808] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10805,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10805,U_10806,U_10807)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10805,U_10807,U_10808)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10805,U_10806,U_10808)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10805),U_10807),U_10808))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10805),U_10806),U_10807))
      | ~ class_Orderings_Olinorder(U_10805) ),
    inference(definitional_conversion,[status(esa)],[f_2881_2]) ).

cnf(f_2881_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10805,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10805,U_10806,U_10807)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10805,U_10807,U_10808)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10805,U_10806,U_10808)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10805),U_10807),U_10808))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10805),U_10806),U_10807))
    | ~ class_Orderings_Olinorder(U_10805) ),
    inference(clausify,[status(thm)],[f_2881_3]) ).

fof(f_2882_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_2882_2,plain,
    ! [U_10812,U_10811,U_10810,U_10809] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10809,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10809,U_10810,U_10811)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10809,U_10811,U_10812)) = c_Orderings_Obot__class_Obot(tc_fun(U_10809,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_10809) ),
    inference(variable_rename,[status(thm)],[f_2882_1]) ).

fof(f_2882_3,plain,
    ! [U_10810,U_10812,U_10811,U_10809] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10809,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10809,U_10810,U_10811)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10809,U_10811,U_10812)) = c_Orderings_Obot__class_Obot(tc_fun(U_10809,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_10809) ),
    inference(definitional_conversion,[status(esa)],[f_2882_2]) ).

cnf(f_2882_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10809,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10809,U_10810,U_10811)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10809,U_10811,U_10812)) = c_Orderings_Obot__class_Obot(tc_fun(U_10809,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_10809) ),
    inference(clausify,[status(thm)],[f_2882_3]) ).

fof(f_2883_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_2883_2,plain,
    ! [U_10814,U_10813] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10813,U_10814)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10814),U_10813),
    inference(variable_rename,[status(thm)],[f_2883_1]) ).

fof(f_2883_3,plain,
    ! [U_10813,U_10814] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10813,U_10814)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10814),U_10813),
    inference(definitional_conversion,[status(esa)],[f_2883_2]) ).

cnf(f_2883_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10813,U_10814)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10814),U_10813),
    inference(clausify,[status(thm)],[f_2883_3]) ).

fof(f_2884_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_2884_2,plain,
    ! [U_10818,U_10817,U_10816,U_10815] : hAPP(c_Relation_OImage(U_10815,U_10816,U_10817),U_10818) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10815,tc_fun(U_10816,tc_HOL_Obool)),U_10818),hAPP(hAPP(c_COMBB(tc_fun(U_10815,tc_HOL_Obool),tc_fun(U_10816,tc_HOL_Obool),U_10815),c_Relation_OImage(U_10815,U_10816,U_10817)),hAPP(hAPP(c_COMBC(U_10815,tc_fun(U_10815,tc_HOL_Obool),tc_fun(U_10815,tc_HOL_Obool)),c_Set_Oinsert(U_10815)),c_Orderings_Obot__class_Obot(tc_fun(U_10815,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2884_1]) ).

fof(f_2884_3,plain,
    ! [U_10815,U_10816,U_10817,U_10818] : hAPP(c_Relation_OImage(U_10815,U_10816,U_10817),U_10818) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10815,tc_fun(U_10816,tc_HOL_Obool)),U_10818),hAPP(hAPP(c_COMBB(tc_fun(U_10815,tc_HOL_Obool),tc_fun(U_10816,tc_HOL_Obool),U_10815),c_Relation_OImage(U_10815,U_10816,U_10817)),hAPP(hAPP(c_COMBC(U_10815,tc_fun(U_10815,tc_HOL_Obool),tc_fun(U_10815,tc_HOL_Obool)),c_Set_Oinsert(U_10815)),c_Orderings_Obot__class_Obot(tc_fun(U_10815,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2884_2]) ).

cnf(f_2884_4,plain,
    hAPP(c_Relation_OImage(U_10815,U_10816,U_10817),U_10818) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10815,tc_fun(U_10816,tc_HOL_Obool)),U_10818),hAPP(hAPP(c_COMBB(tc_fun(U_10815,tc_HOL_Obool),tc_fun(U_10816,tc_HOL_Obool),U_10815),c_Relation_OImage(U_10815,U_10816,U_10817)),hAPP(hAPP(c_COMBC(U_10815,tc_fun(U_10815,tc_HOL_Obool),tc_fun(U_10815,tc_HOL_Obool)),c_Set_Oinsert(U_10815)),c_Orderings_Obot__class_Obot(tc_fun(U_10815,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2884_3]) ).

fof(f_2885_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_2885_2,plain,
    ! [U_10823,U_10822,U_10821,U_10820,U_10819] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10819,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10819,U_10820,U_10821)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10819,U_10822,U_10823)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10819,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10819),U_10820),U_10822),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10819),U_10821),U_10823))
      | ~ class_Orderings_Olinorder(U_10819) ),
    inference(variable_rename,[status(thm)],[f_2885_1]) ).

fof(f_2885_3,plain,
    ! [U_10819,U_10820,U_10821,U_10822,U_10823] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10819,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10819,U_10820,U_10821)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10819,U_10822,U_10823)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10819,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10819),U_10820),U_10822),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10819),U_10821),U_10823))
      | ~ class_Orderings_Olinorder(U_10819) ),
    inference(definitional_conversion,[status(esa)],[f_2885_2]) ).

cnf(f_2885_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10819,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10819,U_10820,U_10821)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10819,U_10822,U_10823)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10819,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10819),U_10820),U_10822),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10819),U_10821),U_10823))
    | ~ class_Orderings_Olinorder(U_10819) ),
    inference(clausify,[status(thm)],[f_2885_3]) ).

fof(f_2886_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_2886_2,plain,
    ! [U_10827,U_10826,U_10825,U_10824] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10824,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10824,U_10825,U_10826)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10824,U_10826,U_10827)) = c_Orderings_Obot__class_Obot(tc_fun(U_10824,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_10824) ),
    inference(variable_rename,[status(thm)],[f_2886_1]) ).

fof(f_2886_3,plain,
    ! [U_10824,U_10825,U_10826,U_10827] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10824,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10824,U_10825,U_10826)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10824,U_10826,U_10827)) = c_Orderings_Obot__class_Obot(tc_fun(U_10824,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_10824) ),
    inference(definitional_conversion,[status(esa)],[f_2886_2]) ).

cnf(f_2886_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10824,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10824,U_10825,U_10826)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10824,U_10826,U_10827)) = c_Orderings_Obot__class_Obot(tc_fun(U_10824,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_10824) ),
    inference(clausify,[status(thm)],[f_2886_3]) ).

fof(f_2887_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_2887_2,plain,
    ! [U_10829,U_10828] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10828,U_10829)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10829),U_10828)),
    inference(variable_rename,[status(thm)],[f_2887_1]) ).

fof(f_2887_3,plain,
    ! [U_10828,U_10829] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10828,U_10829)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10829),U_10828)),
    inference(definitional_conversion,[status(esa)],[f_2887_2]) ).

cnf(f_2887_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10828,U_10829)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10829),U_10828)),
    inference(clausify,[status(thm)],[f_2887_3]) ).

fof(f_2888_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_2888_2,plain,
    ! [U_10833,U_10832,U_10831,U_10830] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10830,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10830,U_10831,U_10832)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10830,U_10832,U_10833)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10830,U_10831,U_10833)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10830),U_10832),U_10833))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10830),U_10831),U_10832))
      | ~ class_Orderings_Olinorder(U_10830) ),
    inference(variable_rename,[status(thm)],[f_2888_1]) ).

fof(f_2888_3,plain,
    ! [U_10830,U_10831,U_10832,U_10833] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10830,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10830,U_10831,U_10832)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10830,U_10832,U_10833)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10830,U_10831,U_10833)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10830),U_10832),U_10833))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10830),U_10831),U_10832))
      | ~ class_Orderings_Olinorder(U_10830) ),
    inference(definitional_conversion,[status(esa)],[f_2888_2]) ).

cnf(f_2888_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10830,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10830,U_10831,U_10832)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10830,U_10832,U_10833)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10830,U_10831,U_10833)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10830),U_10832),U_10833))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10830),U_10831),U_10832))
    | ~ class_Orderings_Olinorder(U_10830) ),
    inference(clausify,[status(thm)],[f_2888_3]) ).

fof(f_2889_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_2889_2,plain,
    ! [U_10839,U_10838,U_10837,U_10836,U_10835,U_10834] :
      ( hBOOL(hAPP(hAPP(c_member(U_10837),U_10838),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10834,tc_fun(U_10837,tc_HOL_Obool)),U_10836),U_10839)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10837),U_10838),hAPP(U_10839,U_10835)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10834),U_10835),U_10836)) ),
    inference(variable_rename,[status(thm)],[f_2889_1]) ).

fof(f_2889_3,plain,
    ! [U_10836,U_10835,U_10837,U_10834,U_10838,U_10839] :
      ( hBOOL(hAPP(hAPP(c_member(U_10837),U_10838),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10834,tc_fun(U_10837,tc_HOL_Obool)),U_10836),U_10839)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10837),U_10838),hAPP(U_10839,U_10835)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10834),U_10835),U_10836)) ),
    inference(definitional_conversion,[status(esa)],[f_2889_2]) ).

cnf(f_2889_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10837),U_10838),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10834,tc_fun(U_10837,tc_HOL_Obool)),U_10836),U_10839)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10837),U_10838),hAPP(U_10839,U_10835)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10834),U_10835),U_10836)) ),
    inference(clausify,[status(thm)],[f_2889_3]) ).

fof(f_2890_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_2890_2,plain,
    ! [U_10843,U_10842,U_10841,U_10840] : hAPP(c_Set_Oimage(U_10840,U_10841,U_10842),U_10843) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10840,tc_fun(U_10841,tc_HOL_Obool)),U_10843),hAPP(hAPP(c_COMBC(U_10840,tc_fun(U_10841,tc_HOL_Obool),tc_fun(U_10841,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10841,tc_fun(tc_fun(U_10841,tc_HOL_Obool),tc_fun(U_10841,tc_HOL_Obool)),U_10840),c_Set_Oinsert(U_10841)),U_10842)),c_Orderings_Obot__class_Obot(tc_fun(U_10841,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2890_1]) ).

fof(f_2890_3,plain,
    ! [U_10840,U_10841,U_10842,U_10843] : hAPP(c_Set_Oimage(U_10840,U_10841,U_10842),U_10843) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10840,tc_fun(U_10841,tc_HOL_Obool)),U_10843),hAPP(hAPP(c_COMBC(U_10840,tc_fun(U_10841,tc_HOL_Obool),tc_fun(U_10841,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10841,tc_fun(tc_fun(U_10841,tc_HOL_Obool),tc_fun(U_10841,tc_HOL_Obool)),U_10840),c_Set_Oinsert(U_10841)),U_10842)),c_Orderings_Obot__class_Obot(tc_fun(U_10841,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2890_2]) ).

cnf(f_2890_4,plain,
    hAPP(c_Set_Oimage(U_10840,U_10841,U_10842),U_10843) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10840,tc_fun(U_10841,tc_HOL_Obool)),U_10843),hAPP(hAPP(c_COMBC(U_10840,tc_fun(U_10841,tc_HOL_Obool),tc_fun(U_10841,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10841,tc_fun(tc_fun(U_10841,tc_HOL_Obool),tc_fun(U_10841,tc_HOL_Obool)),U_10840),c_Set_Oinsert(U_10841)),U_10842)),c_Orderings_Obot__class_Obot(tc_fun(U_10841,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2890_3]) ).

fof(f_2891_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_2891_2,plain,
    ! [U_10849,U_10848,U_10847,U_10846,U_10845,U_10844] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10844,tc_fun(U_10847,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10844,U_10844,U_10846),hAPP(hAPP(c_Set_Oinsert(U_10844),U_10849),c_Orderings_Obot__class_Obot(tc_fun(U_10844,tc_HOL_Obool))))),U_10848) = hAPP(U_10848,U_10849)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10844),U_10849),U_10845))
      | ~ c_Equiv__Relations_Ocongruent(U_10844,tc_fun(U_10847,tc_HOL_Obool),U_10846,U_10848)
      | ~ c_Equiv__Relations_Oequiv(U_10844,U_10845,U_10846) ),
    inference(variable_rename,[status(thm)],[f_2891_1]) ).

fof(f_2891_3,plain,
    ! [U_10844,U_10845,U_10846,U_10847,U_10848,U_10849] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10844,tc_fun(U_10847,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10844,U_10844,U_10846),hAPP(hAPP(c_Set_Oinsert(U_10844),U_10849),c_Orderings_Obot__class_Obot(tc_fun(U_10844,tc_HOL_Obool))))),U_10848) = hAPP(U_10848,U_10849)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10844),U_10849),U_10845))
      | ~ c_Equiv__Relations_Ocongruent(U_10844,tc_fun(U_10847,tc_HOL_Obool),U_10846,U_10848)
      | ~ c_Equiv__Relations_Oequiv(U_10844,U_10845,U_10846) ),
    inference(definitional_conversion,[status(esa)],[f_2891_2]) ).

cnf(f_2891_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10844,tc_fun(U_10847,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10844,U_10844,U_10846),hAPP(hAPP(c_Set_Oinsert(U_10844),U_10849),c_Orderings_Obot__class_Obot(tc_fun(U_10844,tc_HOL_Obool))))),U_10848) = hAPP(U_10848,U_10849)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10844),U_10849),U_10845))
    | ~ c_Equiv__Relations_Ocongruent(U_10844,tc_fun(U_10847,tc_HOL_Obool),U_10846,U_10848)
    | ~ c_Equiv__Relations_Oequiv(U_10844,U_10845,U_10846) ),
    inference(clausify,[status(thm)],[f_2891_3]) ).

fof(f_2892_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_2892_2,plain,
    ! [U_10860,U_10859,U_10858,U_10857,U_10856] :
      ( ( ! [U_10855] :
            ( hBOOL(hAPP(U_10860,U_10855))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10856),U_10855),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10857,tc_fun(U_10856,tc_HOL_Obool)),U_10858),U_10859))) )
        | ? [U_10854] :
            ( ? [U_10853] :
                ( ~ hBOOL(hAPP(U_10860,U_10853))
                & hBOOL(hAPP(hAPP(c_member(U_10856),U_10853),hAPP(U_10859,U_10854))) )
            & hBOOL(hAPP(hAPP(c_member(U_10857),U_10854),U_10858)) ) )
      & ( ! [U_10852] :
            ( ! [U_10851] :
                ( hBOOL(hAPP(U_10860,U_10851))
                | ~ hBOOL(hAPP(hAPP(c_member(U_10856),U_10851),hAPP(U_10859,U_10852))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10857),U_10852),U_10858)) )
        | ? [U_10850] :
            ( ~ hBOOL(hAPP(U_10860,U_10850))
            & hBOOL(hAPP(hAPP(c_member(U_10856),U_10850),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10857,tc_fun(U_10856,tc_HOL_Obool)),U_10858),U_10859))) ) ) ),
    inference(variable_rename,[status(thm)],[f_2892_1]) ).

fof(f_2892_3,plain,
    ( ! [U_10870,U_10868,U_10866,U_10864,U_10862] :
        ( ! [U_10855] :
            ( hBOOL(hAPP(U_10870,U_10855))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10862),U_10855),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10864,tc_fun(U_10862,tc_HOL_Obool)),U_10866),U_10868))) )
        | ? [U_10854] :
            ( ? [U_10853] :
                ( ~ hBOOL(hAPP(U_10870,U_10853))
                & hBOOL(hAPP(hAPP(c_member(U_10862),U_10853),hAPP(U_10868,U_10854))) )
            & hBOOL(hAPP(hAPP(c_member(U_10864),U_10854),U_10866)) ) )
    & ! [U_10869,U_10867,U_10865,U_10863,U_10861] :
        ( ! [U_10852] :
            ( ! [U_10851] :
                ( hBOOL(hAPP(U_10869,U_10851))
                | ~ hBOOL(hAPP(hAPP(c_member(U_10861),U_10851),hAPP(U_10867,U_10852))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10863),U_10852),U_10865)) )
        | ? [U_10850] :
            ( ~ hBOOL(hAPP(U_10869,U_10850))
            & hBOOL(hAPP(hAPP(c_member(U_10861),U_10850),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10863,tc_fun(U_10861,tc_HOL_Obool)),U_10865),U_10867))) ) ) ),
    inference(miniscope,[status(thm)],[f_2892_2]) ).

fof(f_2892_4,plain,
    ( ! [U_10870,U_10868,U_10866,U_10864,U_10862] :
        ( ! [U_10855] :
            ( hBOOL(hAPP(U_10870,U_10855))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10862),U_10855),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10864,tc_fun(U_10862,tc_HOL_Obool)),U_10866),U_10868))) )
        | ? [U_10854] :
            ( ? [U_10853] :
                ( ~ hBOOL(hAPP(U_10870,U_10853))
                & hBOOL(hAPP(hAPP(c_member(U_10862),U_10853),hAPP(U_10868,U_10854))) )
            & hBOOL(hAPP(hAPP(c_member(U_10864),U_10854),U_10866)) ) )
    & ! [U_10869,U_10867,U_10865,U_10863,U_10861] :
        ( ! [U_10852] :
            ( ! [U_10851] :
                ( hBOOL(hAPP(U_10869,U_10851))
                | ~ hBOOL(hAPP(hAPP(c_member(U_10861),U_10851),hAPP(U_10867,U_10852))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10863),U_10852),U_10865)) )
        | ( ~ hBOOL(hAPP(U_10869,sK175(U_10869,U_10867,U_10865,U_10863,U_10861)))
          & hBOOL(hAPP(hAPP(c_member(U_10861),sK175(U_10869,U_10867,U_10865,U_10863,U_10861)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10863,tc_fun(U_10861,tc_HOL_Obool)),U_10865),U_10867))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_10850,sK175(U_10869,U_10867,U_10865,U_10863,U_10861))],[f_2892_3]) ).

fof(f_2892_5,plain,
    ( ! [U_10870,U_10868,U_10866,U_10864,U_10862] :
        ( ! [U_10855] :
            ( hBOOL(hAPP(U_10870,U_10855))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10862),U_10855),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10864,tc_fun(U_10862,tc_HOL_Obool)),U_10866),U_10868))) )
        | ( ? [U_10853] :
              ( ~ hBOOL(hAPP(U_10870,U_10853))
              & hBOOL(hAPP(hAPP(c_member(U_10862),U_10853),hAPP(U_10868,sK176(U_10870,U_10868,U_10866,U_10864,U_10862)))) )
          & hBOOL(hAPP(hAPP(c_member(U_10864),sK176(U_10870,U_10868,U_10866,U_10864,U_10862)),U_10866)) ) )
    & ! [U_10869,U_10867,U_10865,U_10863,U_10861] :
        ( ! [U_10852] :
            ( ! [U_10851] :
                ( hBOOL(hAPP(U_10869,U_10851))
                | ~ hBOOL(hAPP(hAPP(c_member(U_10861),U_10851),hAPP(U_10867,U_10852))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10863),U_10852),U_10865)) )
        | ( ~ hBOOL(hAPP(U_10869,sK175(U_10869,U_10867,U_10865,U_10863,U_10861)))
          & hBOOL(hAPP(hAPP(c_member(U_10861),sK175(U_10869,U_10867,U_10865,U_10863,U_10861)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10863,tc_fun(U_10861,tc_HOL_Obool)),U_10865),U_10867))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_10854,sK176(U_10870,U_10868,U_10866,U_10864,U_10862))],[f_2892_4]) ).

fof(f_2892_6,plain,
    ( ! [U_10870,U_10868,U_10866,U_10864,U_10862] :
        ( ! [U_10855] :
            ( hBOOL(hAPP(U_10870,U_10855))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10862),U_10855),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10864,tc_fun(U_10862,tc_HOL_Obool)),U_10866),U_10868))) )
        | ( ~ hBOOL(hAPP(U_10870,sK177(U_10870,U_10868,U_10866,U_10864,U_10862)))
          & hBOOL(hAPP(hAPP(c_member(U_10862),sK177(U_10870,U_10868,U_10866,U_10864,U_10862)),hAPP(U_10868,sK176(U_10870,U_10868,U_10866,U_10864,U_10862))))
          & hBOOL(hAPP(hAPP(c_member(U_10864),sK176(U_10870,U_10868,U_10866,U_10864,U_10862)),U_10866)) ) )
    & ! [U_10869,U_10867,U_10865,U_10863,U_10861] :
        ( ! [U_10852] :
            ( ! [U_10851] :
                ( hBOOL(hAPP(U_10869,U_10851))
                | ~ hBOOL(hAPP(hAPP(c_member(U_10861),U_10851),hAPP(U_10867,U_10852))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10863),U_10852),U_10865)) )
        | ( ~ hBOOL(hAPP(U_10869,sK175(U_10869,U_10867,U_10865,U_10863,U_10861)))
          & hBOOL(hAPP(hAPP(c_member(U_10861),sK175(U_10869,U_10867,U_10865,U_10863,U_10861)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10863,tc_fun(U_10861,tc_HOL_Obool)),U_10865),U_10867))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_10853,sK177(U_10870,U_10868,U_10866,U_10864,U_10862))],[f_2892_5]) ).

fof(f_2892_7,plain,
    ( ! [U_10862,U_10866,U_10864,U_10868,U_10870] :
        ( ~ hBOOL(hAPP(U_10870,sK177(U_10870,U_10868,U_10866,U_10864,U_10862)))
        | ~ sP823(U_10862,U_10866,U_10864,U_10868,U_10870) )
    & ! [U_10862,U_10866,U_10864,U_10868,U_10870] :
        ( hBOOL(hAPP(hAPP(c_member(U_10862),sK177(U_10870,U_10868,U_10866,U_10864,U_10862)),hAPP(U_10868,sK176(U_10870,U_10868,U_10866,U_10864,U_10862))))
        | ~ sP823(U_10862,U_10866,U_10864,U_10868,U_10870) )
    & ! [U_10862,U_10866,U_10864,U_10868,U_10870] :
        ( hBOOL(hAPP(hAPP(c_member(U_10864),sK176(U_10870,U_10868,U_10866,U_10864,U_10862)),U_10866))
        | ~ sP823(U_10862,U_10866,U_10864,U_10868,U_10870) )
    & ! [U_10865,U_10861,U_10863,U_10867,U_10869] :
        ( ~ hBOOL(hAPP(U_10869,sK175(U_10869,U_10867,U_10865,U_10863,U_10861)))
        | ~ sP822(U_10865,U_10861,U_10863,U_10867,U_10869) )
    & ! [U_10865,U_10861,U_10863,U_10867,U_10869] :
        ( hBOOL(hAPP(hAPP(c_member(U_10861),sK175(U_10869,U_10867,U_10865,U_10863,U_10861)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10863,tc_fun(U_10861,tc_HOL_Obool)),U_10865),U_10867)))
        | ~ sP822(U_10865,U_10861,U_10863,U_10867,U_10869) )
    & ! [U_10862,U_10866,U_10855,U_10864,U_10868,U_10870] :
        ( hBOOL(hAPP(U_10870,U_10855))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10862),U_10855),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10864,tc_fun(U_10862,tc_HOL_Obool)),U_10866),U_10868)))
        | sP823(U_10862,U_10866,U_10864,U_10868,U_10870) )
    & ! [U_10851,U_10852,U_10865,U_10861,U_10863,U_10867,U_10869] :
        ( hBOOL(hAPP(U_10869,U_10851))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10861),U_10851),hAPP(U_10867,U_10852)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10863),U_10852),U_10865))
        | sP822(U_10865,U_10861,U_10863,U_10867,U_10869) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP822,sP823])],[f_2892_6]) ).

cnf(f_2892_8,plain,
    ( hBOOL(hAPP(U_10869,U_10851))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10861),U_10851),hAPP(U_10867,U_10852)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10863),U_10852),U_10865))
    | sP822(U_10865,U_10861,U_10863,U_10867,U_10869) ),
    inference(clausify,[status(thm)],[f_2892_7]) ).

cnf(f_2892_9,plain,
    ( hBOOL(hAPP(U_10870,U_10855))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10862),U_10855),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10864,tc_fun(U_10862,tc_HOL_Obool)),U_10866),U_10868)))
    | sP823(U_10862,U_10866,U_10864,U_10868,U_10870) ),
    inference(clausify,[status(thm)],[f_2892_7]) ).

cnf(f_2892_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10861),sK175(U_10869,U_10867,U_10865,U_10863,U_10861)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10863,tc_fun(U_10861,tc_HOL_Obool)),U_10865),U_10867)))
    | ~ sP822(U_10865,U_10861,U_10863,U_10867,U_10869) ),
    inference(clausify,[status(thm)],[f_2892_7]) ).

cnf(f_2892_11,plain,
    ( ~ hBOOL(hAPP(U_10869,sK175(U_10869,U_10867,U_10865,U_10863,U_10861)))
    | ~ sP822(U_10865,U_10861,U_10863,U_10867,U_10869) ),
    inference(clausify,[status(thm)],[f_2892_7]) ).

cnf(f_2892_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10864),sK176(U_10870,U_10868,U_10866,U_10864,U_10862)),U_10866))
    | ~ sP823(U_10862,U_10866,U_10864,U_10868,U_10870) ),
    inference(clausify,[status(thm)],[f_2892_7]) ).

cnf(f_2892_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10862),sK177(U_10870,U_10868,U_10866,U_10864,U_10862)),hAPP(U_10868,sK176(U_10870,U_10868,U_10866,U_10864,U_10862))))
    | ~ sP823(U_10862,U_10866,U_10864,U_10868,U_10870) ),
    inference(clausify,[status(thm)],[f_2892_7]) ).

cnf(f_2892_14,plain,
    ( ~ hBOOL(hAPP(U_10870,sK177(U_10870,U_10868,U_10866,U_10864,U_10862)))
    | ~ sP823(U_10862,U_10866,U_10864,U_10868,U_10870) ),
    inference(clausify,[status(thm)],[f_2892_7]) ).

fof(f_2893_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_2893_2,plain,
    ! [U_10876,U_10875,U_10874,U_10873] :
      ( ( c_Equiv__Relations_Ocongruent(U_10873,U_10874,U_10875,U_10876)
        | ? [U_10872] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10873,U_10873,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10873,tc_fun(U_10873,U_10874),tc_fun(U_10873,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10874,tc_HOL_Obool),tc_fun(tc_fun(U_10873,U_10874),tc_fun(U_10873,tc_HOL_Obool)),U_10873),c_COMBB(U_10874,tc_HOL_Obool,U_10873)),hAPP(hAPP(c_COMBB(U_10874,tc_fun(U_10874,tc_HOL_Obool),U_10873),c_fequal),U_10876))),U_10876)),U_10872))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_10873,U_10873)),U_10872),U_10875)) ) )
      & ( ! [U_10871] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10873,U_10873,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10873,tc_fun(U_10873,U_10874),tc_fun(U_10873,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10874,tc_HOL_Obool),tc_fun(tc_fun(U_10873,U_10874),tc_fun(U_10873,tc_HOL_Obool)),U_10873),c_COMBB(U_10874,tc_HOL_Obool,U_10873)),hAPP(hAPP(c_COMBB(U_10874,tc_fun(U_10874,tc_HOL_Obool),U_10873),c_fequal),U_10876))),U_10876)),U_10871))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10873,U_10873)),U_10871),U_10875)) )
        | ~ c_Equiv__Relations_Ocongruent(U_10873,U_10874,U_10875,U_10876) ) ),
    inference(variable_rename,[status(thm)],[f_2893_1]) ).

fof(f_2893_3,plain,
    ( ! [U_10884,U_10882,U_10880,U_10878] :
        ( c_Equiv__Relations_Ocongruent(U_10878,U_10880,U_10882,U_10884)
        | ? [U_10872] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10878,U_10878,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10878,tc_fun(U_10878,U_10880),tc_fun(U_10878,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10880,tc_HOL_Obool),tc_fun(tc_fun(U_10878,U_10880),tc_fun(U_10878,tc_HOL_Obool)),U_10878),c_COMBB(U_10880,tc_HOL_Obool,U_10878)),hAPP(hAPP(c_COMBB(U_10880,tc_fun(U_10880,tc_HOL_Obool),U_10878),c_fequal),U_10884))),U_10884)),U_10872))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_10878,U_10878)),U_10872),U_10882)) ) )
    & ! [U_10883,U_10881,U_10879,U_10877] :
        ( ! [U_10871] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10877,U_10877,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10877,tc_fun(U_10877,U_10879),tc_fun(U_10877,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10879,tc_HOL_Obool),tc_fun(tc_fun(U_10877,U_10879),tc_fun(U_10877,tc_HOL_Obool)),U_10877),c_COMBB(U_10879,tc_HOL_Obool,U_10877)),hAPP(hAPP(c_COMBB(U_10879,tc_fun(U_10879,tc_HOL_Obool),U_10877),c_fequal),U_10883))),U_10883)),U_10871))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10877,U_10877)),U_10871),U_10881)) )
        | ~ c_Equiv__Relations_Ocongruent(U_10877,U_10879,U_10881,U_10883) ) ),
    inference(miniscope,[status(thm)],[f_2893_2]) ).

fof(f_2893_4,plain,
    ( ! [U_10884,U_10882,U_10880,U_10878] :
        ( c_Equiv__Relations_Ocongruent(U_10878,U_10880,U_10882,U_10884)
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10878,U_10878,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10878,tc_fun(U_10878,U_10880),tc_fun(U_10878,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10880,tc_HOL_Obool),tc_fun(tc_fun(U_10878,U_10880),tc_fun(U_10878,tc_HOL_Obool)),U_10878),c_COMBB(U_10880,tc_HOL_Obool,U_10878)),hAPP(hAPP(c_COMBB(U_10880,tc_fun(U_10880,tc_HOL_Obool),U_10878),c_fequal),U_10884))),U_10884)),sK178(U_10884,U_10882,U_10880,U_10878)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_10878,U_10878)),sK178(U_10884,U_10882,U_10880,U_10878)),U_10882)) ) )
    & ! [U_10883,U_10881,U_10879,U_10877] :
        ( ! [U_10871] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10877,U_10877,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10877,tc_fun(U_10877,U_10879),tc_fun(U_10877,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10879,tc_HOL_Obool),tc_fun(tc_fun(U_10877,U_10879),tc_fun(U_10877,tc_HOL_Obool)),U_10877),c_COMBB(U_10879,tc_HOL_Obool,U_10877)),hAPP(hAPP(c_COMBB(U_10879,tc_fun(U_10879,tc_HOL_Obool),U_10877),c_fequal),U_10883))),U_10883)),U_10871))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10877,U_10877)),U_10871),U_10881)) )
        | ~ c_Equiv__Relations_Ocongruent(U_10877,U_10879,U_10881,U_10883) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_10872,sK178(U_10884,U_10882,U_10880,U_10878))],[f_2893_3]) ).

fof(f_2893_5,plain,
    ( ! [U_10878,U_10882,U_10884,U_10880] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10878,U_10878,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10878,tc_fun(U_10878,U_10880),tc_fun(U_10878,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10880,tc_HOL_Obool),tc_fun(tc_fun(U_10878,U_10880),tc_fun(U_10878,tc_HOL_Obool)),U_10878),c_COMBB(U_10880,tc_HOL_Obool,U_10878)),hAPP(hAPP(c_COMBB(U_10880,tc_fun(U_10880,tc_HOL_Obool),U_10878),c_fequal),U_10884))),U_10884)),sK178(U_10884,U_10882,U_10880,U_10878)))
        | ~ sP824(U_10878,U_10882,U_10884,U_10880) )
    & ! [U_10878,U_10882,U_10884,U_10880] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10878,U_10878)),sK178(U_10884,U_10882,U_10880,U_10878)),U_10882))
        | ~ sP824(U_10878,U_10882,U_10884,U_10880) )
    & ! [U_10878,U_10882,U_10884,U_10880] :
        ( c_Equiv__Relations_Ocongruent(U_10878,U_10880,U_10882,U_10884)
        | sP824(U_10878,U_10882,U_10884,U_10880) )
    & ! [U_10871,U_10879,U_10877,U_10883,U_10881] :
        ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10877,U_10877,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10877,tc_fun(U_10877,U_10879),tc_fun(U_10877,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10879,tc_HOL_Obool),tc_fun(tc_fun(U_10877,U_10879),tc_fun(U_10877,tc_HOL_Obool)),U_10877),c_COMBB(U_10879,tc_HOL_Obool,U_10877)),hAPP(hAPP(c_COMBB(U_10879,tc_fun(U_10879,tc_HOL_Obool),U_10877),c_fequal),U_10883))),U_10883)),U_10871))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10877,U_10877)),U_10871),U_10881))
        | ~ c_Equiv__Relations_Ocongruent(U_10877,U_10879,U_10881,U_10883) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP824])],[f_2893_4]) ).

cnf(f_2893_6,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10877,U_10877,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10877,tc_fun(U_10877,U_10879),tc_fun(U_10877,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10879,tc_HOL_Obool),tc_fun(tc_fun(U_10877,U_10879),tc_fun(U_10877,tc_HOL_Obool)),U_10877),c_COMBB(U_10879,tc_HOL_Obool,U_10877)),hAPP(hAPP(c_COMBB(U_10879,tc_fun(U_10879,tc_HOL_Obool),U_10877),c_fequal),U_10883))),U_10883)),U_10871))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10877,U_10877)),U_10871),U_10881))
    | ~ c_Equiv__Relations_Ocongruent(U_10877,U_10879,U_10881,U_10883) ),
    inference(clausify,[status(thm)],[f_2893_5]) ).

cnf(f_2893_7,plain,
    ( c_Equiv__Relations_Ocongruent(U_10878,U_10880,U_10882,U_10884)
    | sP824(U_10878,U_10882,U_10884,U_10880) ),
    inference(clausify,[status(thm)],[f_2893_5]) ).

cnf(f_2893_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10878,U_10878)),sK178(U_10884,U_10882,U_10880,U_10878)),U_10882))
    | ~ sP824(U_10878,U_10882,U_10884,U_10880) ),
    inference(clausify,[status(thm)],[f_2893_5]) ).

cnf(f_2893_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10878,U_10878,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10878,tc_fun(U_10878,U_10880),tc_fun(U_10878,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10880,tc_HOL_Obool),tc_fun(tc_fun(U_10878,U_10880),tc_fun(U_10878,tc_HOL_Obool)),U_10878),c_COMBB(U_10880,tc_HOL_Obool,U_10878)),hAPP(hAPP(c_COMBB(U_10880,tc_fun(U_10880,tc_HOL_Obool),U_10878),c_fequal),U_10884))),U_10884)),sK178(U_10884,U_10882,U_10880,U_10878)))
    | ~ sP824(U_10878,U_10882,U_10884,U_10880) ),
    inference(clausify,[status(thm)],[f_2893_5]) ).

fof(f_2894_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_2894_2,plain,
    ! [U_10890,U_10889,U_10888,U_10887,U_10886,U_10885] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10886,U_10885),U_10887),hAPP(hAPP(c_COMBB(tc_fun(U_10888,U_10885),U_10885,U_10886),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10888,U_10885),U_10889)),U_10890)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10888,U_10885),U_10889),hAPP(hAPP(c_COMBB(tc_fun(U_10886,U_10885),U_10885,U_10888),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10886,U_10885),U_10887)),hAPP(c_COMBC(U_10886,U_10888,U_10885),U_10890)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10885) ),
    inference(variable_rename,[status(thm)],[f_2894_1]) ).

fof(f_2894_3,plain,
    ! [U_10888,U_10885,U_10887,U_10886,U_10889,U_10890] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10886,U_10885),U_10887),hAPP(hAPP(c_COMBB(tc_fun(U_10888,U_10885),U_10885,U_10886),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10888,U_10885),U_10889)),U_10890)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10888,U_10885),U_10889),hAPP(hAPP(c_COMBB(tc_fun(U_10886,U_10885),U_10885,U_10888),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10886,U_10885),U_10887)),hAPP(c_COMBC(U_10886,U_10888,U_10885),U_10890)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10885) ),
    inference(definitional_conversion,[status(esa)],[f_2894_2]) ).

cnf(f_2894_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10886,U_10885),U_10887),hAPP(hAPP(c_COMBB(tc_fun(U_10888,U_10885),U_10885,U_10886),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10888,U_10885),U_10889)),U_10890)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10888,U_10885),U_10889),hAPP(hAPP(c_COMBB(tc_fun(U_10886,U_10885),U_10885,U_10888),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10886,U_10885),U_10887)),hAPP(c_COMBC(U_10886,U_10888,U_10885),U_10890)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10885) ),
    inference(clausify,[status(thm)],[f_2894_3]) ).

fof(f_2895_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_2895_2,plain,
    ! [U_10896,U_10895,U_10894,U_10893,U_10892,U_10891] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10891,tc_fun(U_10892,tc_HOL_Obool)),U_10893),hAPP(hAPP(c_COMBC(U_10891,tc_fun(U_10894,tc_fun(U_10892,tc_HOL_Obool)),tc_fun(U_10892,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10894,tc_HOL_Obool),tc_fun(tc_fun(U_10894,tc_fun(U_10892,tc_HOL_Obool)),tc_fun(U_10892,tc_HOL_Obool)),U_10891),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10894,tc_fun(U_10892,tc_HOL_Obool))),U_10895)),U_10896)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10894,tc_fun(U_10892,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10891,tc_fun(U_10894,tc_HOL_Obool)),U_10893),U_10895)),U_10896),
    inference(variable_rename,[status(thm)],[f_2895_1]) ).

fof(f_2895_3,plain,
    ! [U_10891,U_10892,U_10893,U_10894,U_10895,U_10896] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10891,tc_fun(U_10892,tc_HOL_Obool)),U_10893),hAPP(hAPP(c_COMBC(U_10891,tc_fun(U_10894,tc_fun(U_10892,tc_HOL_Obool)),tc_fun(U_10892,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10894,tc_HOL_Obool),tc_fun(tc_fun(U_10894,tc_fun(U_10892,tc_HOL_Obool)),tc_fun(U_10892,tc_HOL_Obool)),U_10891),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10894,tc_fun(U_10892,tc_HOL_Obool))),U_10895)),U_10896)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10894,tc_fun(U_10892,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10891,tc_fun(U_10894,tc_HOL_Obool)),U_10893),U_10895)),U_10896),
    inference(definitional_conversion,[status(esa)],[f_2895_2]) ).

cnf(f_2895_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10891,tc_fun(U_10892,tc_HOL_Obool)),U_10893),hAPP(hAPP(c_COMBC(U_10891,tc_fun(U_10894,tc_fun(U_10892,tc_HOL_Obool)),tc_fun(U_10892,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10894,tc_HOL_Obool),tc_fun(tc_fun(U_10894,tc_fun(U_10892,tc_HOL_Obool)),tc_fun(U_10892,tc_HOL_Obool)),U_10891),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10894,tc_fun(U_10892,tc_HOL_Obool))),U_10895)),U_10896)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10894,tc_fun(U_10892,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10891,tc_fun(U_10894,tc_HOL_Obool)),U_10893),U_10895)),U_10896),
    inference(clausify,[status(thm)],[f_2895_3]) ).

fof(f_2896_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_2896_2,plain,
    ! [U_10902,U_10901,U_10900,U_10899,U_10898,U_10897] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10897,tc_fun(U_10898,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10899,tc_fun(U_10897,tc_HOL_Obool)),U_10900),U_10901)),U_10902) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10899,tc_fun(U_10898,tc_HOL_Obool)),U_10900),hAPP(hAPP(c_COMBC(U_10899,tc_fun(U_10897,tc_fun(U_10898,tc_HOL_Obool)),tc_fun(U_10898,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10897,tc_HOL_Obool),tc_fun(tc_fun(U_10897,tc_fun(U_10898,tc_HOL_Obool)),tc_fun(U_10898,tc_HOL_Obool)),U_10899),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10897,tc_fun(U_10898,tc_HOL_Obool))),U_10901)),U_10902)),
    inference(variable_rename,[status(thm)],[f_2896_1]) ).

fof(f_2896_3,plain,
    ! [U_10897,U_10898,U_10899,U_10900,U_10901,U_10902] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10897,tc_fun(U_10898,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10899,tc_fun(U_10897,tc_HOL_Obool)),U_10900),U_10901)),U_10902) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10899,tc_fun(U_10898,tc_HOL_Obool)),U_10900),hAPP(hAPP(c_COMBC(U_10899,tc_fun(U_10897,tc_fun(U_10898,tc_HOL_Obool)),tc_fun(U_10898,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10897,tc_HOL_Obool),tc_fun(tc_fun(U_10897,tc_fun(U_10898,tc_HOL_Obool)),tc_fun(U_10898,tc_HOL_Obool)),U_10899),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10897,tc_fun(U_10898,tc_HOL_Obool))),U_10901)),U_10902)),
    inference(definitional_conversion,[status(esa)],[f_2896_2]) ).

cnf(f_2896_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10897,tc_fun(U_10898,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10899,tc_fun(U_10897,tc_HOL_Obool)),U_10900),U_10901)),U_10902) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10899,tc_fun(U_10898,tc_HOL_Obool)),U_10900),hAPP(hAPP(c_COMBC(U_10899,tc_fun(U_10897,tc_fun(U_10898,tc_HOL_Obool)),tc_fun(U_10898,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10897,tc_HOL_Obool),tc_fun(tc_fun(U_10897,tc_fun(U_10898,tc_HOL_Obool)),tc_fun(U_10898,tc_HOL_Obool)),U_10899),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10897,tc_fun(U_10898,tc_HOL_Obool))),U_10901)),U_10902)),
    inference(clausify,[status(thm)],[f_2896_3]) ).

fof(f_2897_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_2897_2,plain,
    ! [U_10908,U_10907,U_10906,U_10905,U_10904,U_10903] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10903,tc_fun(U_10904,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10905,tc_fun(U_10903,tc_HOL_Obool)),U_10906),U_10907)),U_10908) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10905,tc_fun(U_10904,tc_HOL_Obool)),U_10906),hAPP(hAPP(c_COMBC(U_10905,tc_fun(U_10903,tc_fun(U_10904,tc_HOL_Obool)),tc_fun(U_10904,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10903,tc_HOL_Obool),tc_fun(tc_fun(U_10903,tc_fun(U_10904,tc_HOL_Obool)),tc_fun(U_10904,tc_HOL_Obool)),U_10905),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10903,tc_fun(U_10904,tc_HOL_Obool))),U_10907)),U_10908)),
    inference(variable_rename,[status(thm)],[f_2897_1]) ).

fof(f_2897_3,plain,
    ! [U_10903,U_10904,U_10905,U_10906,U_10907,U_10908] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10903,tc_fun(U_10904,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10905,tc_fun(U_10903,tc_HOL_Obool)),U_10906),U_10907)),U_10908) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10905,tc_fun(U_10904,tc_HOL_Obool)),U_10906),hAPP(hAPP(c_COMBC(U_10905,tc_fun(U_10903,tc_fun(U_10904,tc_HOL_Obool)),tc_fun(U_10904,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10903,tc_HOL_Obool),tc_fun(tc_fun(U_10903,tc_fun(U_10904,tc_HOL_Obool)),tc_fun(U_10904,tc_HOL_Obool)),U_10905),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10903,tc_fun(U_10904,tc_HOL_Obool))),U_10907)),U_10908)),
    inference(definitional_conversion,[status(esa)],[f_2897_2]) ).

cnf(f_2897_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10903,tc_fun(U_10904,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10905,tc_fun(U_10903,tc_HOL_Obool)),U_10906),U_10907)),U_10908) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10905,tc_fun(U_10904,tc_HOL_Obool)),U_10906),hAPP(hAPP(c_COMBC(U_10905,tc_fun(U_10903,tc_fun(U_10904,tc_HOL_Obool)),tc_fun(U_10904,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10903,tc_HOL_Obool),tc_fun(tc_fun(U_10903,tc_fun(U_10904,tc_HOL_Obool)),tc_fun(U_10904,tc_HOL_Obool)),U_10905),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10903,tc_fun(U_10904,tc_HOL_Obool))),U_10907)),U_10908)),
    inference(clausify,[status(thm)],[f_2897_3]) ).

fof(f_2898_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_2898_2,plain,
    ! [U_10914,U_10913,U_10912,U_10911,U_10910,U_10909] :
      ( hAPP(U_10912,U_10913) = hAPP(U_10912,U_10914)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10909,U_10909)),hAPP(hAPP(c_Product__Type_OPair(U_10909,U_10909),U_10913),U_10914)),U_10911))
      | ~ c_Equiv__Relations_Ocongruent(U_10909,U_10910,U_10911,U_10912) ),
    inference(variable_rename,[status(thm)],[f_2898_1]) ).

fof(f_2898_3,plain,
    ! [U_10909,U_10910,U_10911,U_10912,U_10913,U_10914] :
      ( hAPP(U_10912,U_10913) = hAPP(U_10912,U_10914)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10909,U_10909)),hAPP(hAPP(c_Product__Type_OPair(U_10909,U_10909),U_10913),U_10914)),U_10911))
      | ~ c_Equiv__Relations_Ocongruent(U_10909,U_10910,U_10911,U_10912) ),
    inference(definitional_conversion,[status(esa)],[f_2898_2]) ).

cnf(f_2898_4,plain,
    ( hAPP(U_10912,U_10913) = hAPP(U_10912,U_10914)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10909,U_10909)),hAPP(hAPP(c_Product__Type_OPair(U_10909,U_10909),U_10913),U_10914)),U_10911))
    | ~ c_Equiv__Relations_Ocongruent(U_10909,U_10910,U_10911,U_10912) ),
    inference(clausify,[status(thm)],[f_2898_3]) ).

fof(f_2899_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_2899_2,plain,
    ! [U_10921,U_10920,U_10919,U_10918,U_10917] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10918,U_10917),U_10919),U_10920)),U_10921))
          | ? [U_10916] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(U_10920,U_10916)),U_10921))
              & hBOOL(hAPP(hAPP(c_member(U_10918),U_10916),U_10919)) ) )
        & ( ! [U_10915] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(U_10920,U_10915)),U_10921))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10918),U_10915),U_10919)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10918,U_10917),U_10919),U_10920)),U_10921)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10917) ),
    inference(variable_rename,[status(thm)],[f_2899_1]) ).

fof(f_2899_3,plain,
    ! [U_10921,U_10920,U_10919,U_10918,U_10917] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10918,U_10917),U_10919),U_10920)),U_10921))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(U_10920,sK179(U_10921,U_10920,U_10919,U_10918,U_10917))),U_10921))
            & hBOOL(hAPP(hAPP(c_member(U_10918),sK179(U_10921,U_10920,U_10919,U_10918,U_10917)),U_10919)) ) )
        & ( ! [U_10915] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(U_10920,U_10915)),U_10921))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10918),U_10915),U_10919)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10918,U_10917),U_10919),U_10920)),U_10921)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10917) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_10916,sK179(U_10921,U_10920,U_10919,U_10918,U_10917))],[f_2899_2]) ).

fof(f_2899_4,plain,
    ( ! [U_10917,U_10918,U_10919,U_10920,U_10921] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(U_10920,sK179(U_10921,U_10920,U_10919,U_10918,U_10917))),U_10921))
        | ~ sP825(U_10917,U_10918,U_10919,U_10920,U_10921) )
    & ! [U_10917,U_10918,U_10919,U_10920,U_10921] :
        ( hBOOL(hAPP(hAPP(c_member(U_10918),sK179(U_10921,U_10920,U_10919,U_10918,U_10917)),U_10919))
        | ~ sP825(U_10917,U_10918,U_10919,U_10920,U_10921) )
    & ! [U_10915,U_10917,U_10918,U_10919,U_10920,U_10921] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10918,U_10917),U_10919),U_10920)),U_10921))
        | sP825(U_10917,U_10918,U_10919,U_10920,U_10921)
        | ~ sP826(U_10915,U_10917,U_10918,U_10919,U_10920,U_10921) )
    & ! [U_10915,U_10917,U_10918,U_10919,U_10920,U_10921] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(U_10920,U_10915)),U_10921))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10918),U_10915),U_10919))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10918,U_10917),U_10919),U_10920)),U_10921))
        | ~ sP826(U_10915,U_10917,U_10918,U_10919,U_10920,U_10921) )
    & ! [U_10915,U_10917,U_10918,U_10919,U_10920,U_10921] :
        ( sP826(U_10915,U_10917,U_10918,U_10919,U_10920,U_10921)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_10917) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP825,sP826])],[f_2899_3]) ).

cnf(f_2899_5,plain,
    ( sP826(U_10915,U_10917,U_10918,U_10919,U_10920,U_10921)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10917) ),
    inference(clausify,[status(thm)],[f_2899_4]) ).

cnf(f_2899_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(U_10920,U_10915)),U_10921))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10918),U_10915),U_10919))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10918,U_10917),U_10919),U_10920)),U_10921))
    | ~ sP826(U_10915,U_10917,U_10918,U_10919,U_10920,U_10921) ),
    inference(clausify,[status(thm)],[f_2899_4]) ).

cnf(f_2899_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10918,U_10917),U_10919),U_10920)),U_10921))
    | sP825(U_10917,U_10918,U_10919,U_10920,U_10921)
    | ~ sP826(U_10915,U_10917,U_10918,U_10919,U_10920,U_10921) ),
    inference(clausify,[status(thm)],[f_2899_4]) ).

cnf(f_2899_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10918),sK179(U_10921,U_10920,U_10919,U_10918,U_10917)),U_10919))
    | ~ sP825(U_10917,U_10918,U_10919,U_10920,U_10921) ),
    inference(clausify,[status(thm)],[f_2899_4]) ).

cnf(f_2899_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10917),hAPP(U_10920,sK179(U_10921,U_10920,U_10919,U_10918,U_10917))),U_10921))
    | ~ sP825(U_10917,U_10918,U_10919,U_10920,U_10921) ),
    inference(clausify,[status(thm)],[f_2899_4]) ).

fof(f_2900_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_2900_2,plain,
    ! [U_10928,U_10927,U_10926,U_10925,U_10924] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10926,U_10924),U_10927),U_10928)))
          | ! [U_10923] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(U_10928,U_10923)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10926),U_10923),U_10927)) ) )
        & ( ? [U_10922] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(U_10928,U_10922)))
              & hBOOL(hAPP(hAPP(c_member(U_10926),U_10922),U_10927)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10926,U_10924),U_10927),U_10928))) ) )
      | ~ class_Orderings_Olinorder(U_10924)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10924) ),
    inference(variable_rename,[status(thm)],[f_2900_1]) ).

fof(f_2900_3,plain,
    ! [U_10928,U_10927,U_10926,U_10925,U_10924] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10926,U_10924),U_10927),U_10928)))
          | ! [U_10923] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(U_10928,U_10923)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10926),U_10923),U_10927)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(U_10928,sK180(U_10928,U_10927,U_10926,U_10925,U_10924))))
            & hBOOL(hAPP(hAPP(c_member(U_10926),sK180(U_10928,U_10927,U_10926,U_10925,U_10924)),U_10927)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10926,U_10924),U_10927),U_10928))) ) )
      | ~ class_Orderings_Olinorder(U_10924)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10924) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_10922,sK180(U_10928,U_10927,U_10926,U_10925,U_10924))],[f_2900_2]) ).

fof(f_2900_4,plain,
    ( ! [U_10928,U_10926,U_10927,U_10924,U_10925] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(U_10928,sK180(U_10928,U_10927,U_10926,U_10925,U_10924))))
        | ~ sP827(U_10928,U_10926,U_10927,U_10924,U_10925) )
    & ! [U_10928,U_10926,U_10927,U_10924,U_10925] :
        ( hBOOL(hAPP(hAPP(c_member(U_10926),sK180(U_10928,U_10927,U_10926,U_10925,U_10924)),U_10927))
        | ~ sP827(U_10928,U_10926,U_10927,U_10924,U_10925) )
    & ! [U_10928,U_10926,U_10923,U_10927,U_10924,U_10925] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10926,U_10924),U_10927),U_10928)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(U_10928,U_10923)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10926),U_10923),U_10927))
        | ~ sP828(U_10928,U_10926,U_10923,U_10927,U_10924,U_10925) )
    & ! [U_10928,U_10926,U_10923,U_10927,U_10924,U_10925] :
        ( sP827(U_10928,U_10926,U_10927,U_10924,U_10925)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10926,U_10924),U_10927),U_10928)))
        | ~ sP828(U_10928,U_10926,U_10923,U_10927,U_10924,U_10925) )
    & ! [U_10928,U_10926,U_10923,U_10927,U_10924,U_10925] :
        ( sP828(U_10928,U_10926,U_10923,U_10927,U_10924,U_10925)
        | ~ class_Orderings_Olinorder(U_10924)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_10924) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP827,sP828])],[f_2900_3]) ).

cnf(f_2900_5,plain,
    ( sP828(U_10928,U_10926,U_10923,U_10927,U_10924,U_10925)
    | ~ class_Orderings_Olinorder(U_10924)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10924) ),
    inference(clausify,[status(thm)],[f_2900_4]) ).

cnf(f_2900_6,plain,
    ( sP827(U_10928,U_10926,U_10927,U_10924,U_10925)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10926,U_10924),U_10927),U_10928)))
    | ~ sP828(U_10928,U_10926,U_10923,U_10927,U_10924,U_10925) ),
    inference(clausify,[status(thm)],[f_2900_4]) ).

cnf(f_2900_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10926,U_10924),U_10927),U_10928)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(U_10928,U_10923)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10926),U_10923),U_10927))
    | ~ sP828(U_10928,U_10926,U_10923,U_10927,U_10924,U_10925) ),
    inference(clausify,[status(thm)],[f_2900_4]) ).

cnf(f_2900_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10926),sK180(U_10928,U_10927,U_10926,U_10925,U_10924)),U_10927))
    | ~ sP827(U_10928,U_10926,U_10927,U_10924,U_10925) ),
    inference(clausify,[status(thm)],[f_2900_4]) ).

cnf(f_2900_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10924),U_10925),hAPP(U_10928,sK180(U_10928,U_10927,U_10926,U_10925,U_10924))))
    | ~ sP827(U_10928,U_10926,U_10927,U_10924,U_10925) ),
    inference(clausify,[status(thm)],[f_2900_4]) ).

fof(f_2901_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_2901_2,plain,
    ! [U_10935,U_10934,U_10933,U_10932,U_10931] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_10931),U_10932),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10933,tc_fun(U_10931,tc_HOL_Obool)),U_10934),U_10935)))
        | ! [U_10930] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_10931),U_10932),hAPP(U_10935,U_10930)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10933),U_10930),U_10934)) ) )
      & ( ? [U_10929] :
            ( hBOOL(hAPP(hAPP(c_member(U_10931),U_10932),hAPP(U_10935,U_10929)))
            & hBOOL(hAPP(hAPP(c_member(U_10933),U_10929),U_10934)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_10931),U_10932),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10933,tc_fun(U_10931,tc_HOL_Obool)),U_10934),U_10935))) ) ),
    inference(variable_rename,[status(thm)],[f_2901_1]) ).

fof(f_2901_3,plain,
    ( ! [U_10945,U_10943,U_10941,U_10939,U_10937] :
        ( hBOOL(hAPP(hAPP(c_member(U_10937),U_10939),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10941,tc_fun(U_10937,tc_HOL_Obool)),U_10943),U_10945)))
        | ! [U_10930] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_10937),U_10939),hAPP(U_10945,U_10930)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10941),U_10930),U_10943)) ) )
    & ! [U_10944,U_10942,U_10940,U_10938,U_10936] :
        ( ? [U_10929] :
            ( hBOOL(hAPP(hAPP(c_member(U_10936),U_10938),hAPP(U_10944,U_10929)))
            & hBOOL(hAPP(hAPP(c_member(U_10940),U_10929),U_10942)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_10936),U_10938),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10940,tc_fun(U_10936,tc_HOL_Obool)),U_10942),U_10944))) ) ),
    inference(miniscope,[status(thm)],[f_2901_2]) ).

fof(f_2901_4,plain,
    ( ! [U_10945,U_10943,U_10941,U_10939,U_10937] :
        ( hBOOL(hAPP(hAPP(c_member(U_10937),U_10939),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10941,tc_fun(U_10937,tc_HOL_Obool)),U_10943),U_10945)))
        | ! [U_10930] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_10937),U_10939),hAPP(U_10945,U_10930)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10941),U_10930),U_10943)) ) )
    & ! [U_10944,U_10942,U_10940,U_10938,U_10936] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_10936),U_10938),hAPP(U_10944,sK181(U_10944,U_10942,U_10940,U_10938,U_10936))))
          & hBOOL(hAPP(hAPP(c_member(U_10940),sK181(U_10944,U_10942,U_10940,U_10938,U_10936)),U_10942)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_10936),U_10938),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10940,tc_fun(U_10936,tc_HOL_Obool)),U_10942),U_10944))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_10929,sK181(U_10944,U_10942,U_10940,U_10938,U_10936))],[f_2901_3]) ).

fof(f_2901_5,plain,
    ( ! [U_10940,U_10938,U_10936,U_10944,U_10942] :
        ( hBOOL(hAPP(hAPP(c_member(U_10936),U_10938),hAPP(U_10944,sK181(U_10944,U_10942,U_10940,U_10938,U_10936))))
        | ~ sP829(U_10940,U_10938,U_10936,U_10944,U_10942) )
    & ! [U_10940,U_10938,U_10936,U_10944,U_10942] :
        ( hBOOL(hAPP(hAPP(c_member(U_10940),sK181(U_10944,U_10942,U_10940,U_10938,U_10936)),U_10942))
        | ~ sP829(U_10940,U_10938,U_10936,U_10944,U_10942) )
    & ! [U_10930,U_10939,U_10937,U_10943,U_10941,U_10945] :
        ( hBOOL(hAPP(hAPP(c_member(U_10937),U_10939),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10941,tc_fun(U_10937,tc_HOL_Obool)),U_10943),U_10945)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10937),U_10939),hAPP(U_10945,U_10930)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10941),U_10930),U_10943)) )
    & ! [U_10940,U_10938,U_10936,U_10944,U_10942] :
        ( sP829(U_10940,U_10938,U_10936,U_10944,U_10942)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10936),U_10938),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10940,tc_fun(U_10936,tc_HOL_Obool)),U_10942),U_10944))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP829])],[f_2901_4]) ).

cnf(f_2901_6,plain,
    ( sP829(U_10940,U_10938,U_10936,U_10944,U_10942)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10936),U_10938),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10940,tc_fun(U_10936,tc_HOL_Obool)),U_10942),U_10944))) ),
    inference(clausify,[status(thm)],[f_2901_5]) ).

cnf(f_2901_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10937),U_10939),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10941,tc_fun(U_10937,tc_HOL_Obool)),U_10943),U_10945)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10937),U_10939),hAPP(U_10945,U_10930)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10941),U_10930),U_10943)) ),
    inference(clausify,[status(thm)],[f_2901_5]) ).

cnf(f_2901_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10940),sK181(U_10944,U_10942,U_10940,U_10938,U_10936)),U_10942))
    | ~ sP829(U_10940,U_10938,U_10936,U_10944,U_10942) ),
    inference(clausify,[status(thm)],[f_2901_5]) ).

cnf(f_2901_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10936),U_10938),hAPP(U_10944,sK181(U_10944,U_10942,U_10940,U_10938,U_10936))))
    | ~ sP829(U_10940,U_10938,U_10936,U_10944,U_10942) ),
    inference(clausify,[status(thm)],[f_2901_5]) ).

fof(f_2902_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_2902_2,plain,
    ! [U_10949,U_10948,U_10947,U_10946] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10948,U_10946),U_10947),hAPP(c_COMBK(U_10946,U_10948),U_10949)) = U_10949
      | U_10947 = c_Orderings_Obot__class_Obot(tc_fun(U_10948,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10946) ),
    inference(variable_rename,[status(thm)],[f_2902_1]) ).

fof(f_2902_3,plain,
    ! [U_10947,U_10946,U_10949,U_10948] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10948,U_10946),U_10947),hAPP(c_COMBK(U_10946,U_10948),U_10949)) = U_10949
      | U_10947 = c_Orderings_Obot__class_Obot(tc_fun(U_10948,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10946) ),
    inference(definitional_conversion,[status(esa)],[f_2902_2]) ).

cnf(f_2902_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10948,U_10946),U_10947),hAPP(c_COMBK(U_10946,U_10948),U_10949)) = U_10949
    | U_10947 = c_Orderings_Obot__class_Obot(tc_fun(U_10948,tc_HOL_Obool))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10946) ),
    inference(clausify,[status(thm)],[f_2902_3]) ).

fof(f_2903_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_2903_2,plain,
    ! [U_10955,U_10954,U_10953,U_10952] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10952,tc_fun(U_10953,tc_HOL_Obool)),U_10954),U_10955) = c_Orderings_Obot__class_Obot(tc_fun(U_10953,tc_HOL_Obool))
        | ? [U_10951] :
            ( hAPP(U_10955,U_10951) != c_Orderings_Obot__class_Obot(tc_fun(U_10953,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_10952),U_10951),U_10954)) ) )
      & ( ! [U_10950] :
            ( hAPP(U_10955,U_10950) = c_Orderings_Obot__class_Obot(tc_fun(U_10953,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10952),U_10950),U_10954)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10952,tc_fun(U_10953,tc_HOL_Obool)),U_10954),U_10955) != c_Orderings_Obot__class_Obot(tc_fun(U_10953,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2903_1]) ).

fof(f_2903_3,plain,
    ( ! [U_10963,U_10961,U_10959,U_10957] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10957,tc_fun(U_10959,tc_HOL_Obool)),U_10961),U_10963) = c_Orderings_Obot__class_Obot(tc_fun(U_10959,tc_HOL_Obool))
        | ? [U_10951] :
            ( hAPP(U_10963,U_10951) != c_Orderings_Obot__class_Obot(tc_fun(U_10959,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_10957),U_10951),U_10961)) ) )
    & ! [U_10962,U_10960,U_10958,U_10956] :
        ( ! [U_10950] :
            ( hAPP(U_10962,U_10950) = c_Orderings_Obot__class_Obot(tc_fun(U_10958,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10956),U_10950),U_10960)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10956,tc_fun(U_10958,tc_HOL_Obool)),U_10960),U_10962) != c_Orderings_Obot__class_Obot(tc_fun(U_10958,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2903_2]) ).

fof(f_2903_4,plain,
    ( ! [U_10963,U_10961,U_10959,U_10957] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10957,tc_fun(U_10959,tc_HOL_Obool)),U_10961),U_10963) = c_Orderings_Obot__class_Obot(tc_fun(U_10959,tc_HOL_Obool))
        | ( hAPP(U_10963,sK182(U_10963,U_10961,U_10959,U_10957)) != c_Orderings_Obot__class_Obot(tc_fun(U_10959,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_10957),sK182(U_10963,U_10961,U_10959,U_10957)),U_10961)) ) )
    & ! [U_10962,U_10960,U_10958,U_10956] :
        ( ! [U_10950] :
            ( hAPP(U_10962,U_10950) = c_Orderings_Obot__class_Obot(tc_fun(U_10958,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10956),U_10950),U_10960)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10956,tc_fun(U_10958,tc_HOL_Obool)),U_10960),U_10962) != c_Orderings_Obot__class_Obot(tc_fun(U_10958,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_10951,sK182(U_10963,U_10961,U_10959,U_10957))],[f_2903_3]) ).

fof(f_2903_5,plain,
    ( ! [U_10963,U_10961,U_10957,U_10959] :
        ( hAPP(U_10963,sK182(U_10963,U_10961,U_10959,U_10957)) != c_Orderings_Obot__class_Obot(tc_fun(U_10959,tc_HOL_Obool))
        | ~ sP830(U_10963,U_10961,U_10957,U_10959) )
    & ! [U_10963,U_10961,U_10957,U_10959] :
        ( hBOOL(hAPP(hAPP(c_member(U_10957),sK182(U_10963,U_10961,U_10959,U_10957)),U_10961))
        | ~ sP830(U_10963,U_10961,U_10957,U_10959) )
    & ! [U_10963,U_10961,U_10957,U_10959] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10957,tc_fun(U_10959,tc_HOL_Obool)),U_10961),U_10963) = c_Orderings_Obot__class_Obot(tc_fun(U_10959,tc_HOL_Obool))
        | sP830(U_10963,U_10961,U_10957,U_10959) )
    & ! [U_10958,U_10962,U_10950,U_10956,U_10960] :
        ( hAPP(U_10962,U_10950) = c_Orderings_Obot__class_Obot(tc_fun(U_10958,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10956),U_10950),U_10960))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10956,tc_fun(U_10958,tc_HOL_Obool)),U_10960),U_10962) != c_Orderings_Obot__class_Obot(tc_fun(U_10958,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP830])],[f_2903_4]) ).

cnf(f_2903_6,plain,
    ( hAPP(U_10962,U_10950) = c_Orderings_Obot__class_Obot(tc_fun(U_10958,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10956),U_10950),U_10960))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10956,tc_fun(U_10958,tc_HOL_Obool)),U_10960),U_10962) != c_Orderings_Obot__class_Obot(tc_fun(U_10958,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2903_5]) ).

cnf(f_2903_7,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10957,tc_fun(U_10959,tc_HOL_Obool)),U_10961),U_10963) = c_Orderings_Obot__class_Obot(tc_fun(U_10959,tc_HOL_Obool))
    | sP830(U_10963,U_10961,U_10957,U_10959) ),
    inference(clausify,[status(thm)],[f_2903_5]) ).

cnf(f_2903_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10957),sK182(U_10963,U_10961,U_10959,U_10957)),U_10961))
    | ~ sP830(U_10963,U_10961,U_10957,U_10959) ),
    inference(clausify,[status(thm)],[f_2903_5]) ).

cnf(f_2903_9,plain,
    ( hAPP(U_10963,sK182(U_10963,U_10961,U_10959,U_10957)) != c_Orderings_Obot__class_Obot(tc_fun(U_10959,tc_HOL_Obool))
    | ~ sP830(U_10963,U_10961,U_10957,U_10959) ),
    inference(clausify,[status(thm)],[f_2903_5]) ).

fof(f_2904_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_2904_2,plain,
    ! [U_10967,U_10966,U_10965,U_10964] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10965,tc_fun(U_10966,tc_HOL_Obool)),U_10964),hAPP(c_COMBK(tc_fun(U_10966,tc_HOL_Obool),U_10965),U_10967)) = U_10967
        | U_10964 = c_Orderings_Obot__class_Obot(tc_fun(U_10965,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10965,tc_fun(U_10966,tc_HOL_Obool)),U_10964),hAPP(c_COMBK(tc_fun(U_10966,tc_HOL_Obool),U_10965),U_10967)) = c_Orderings_Obot__class_Obot(tc_fun(U_10966,tc_HOL_Obool))
        | U_10964 != c_Orderings_Obot__class_Obot(tc_fun(U_10965,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2904_1]) ).

fof(f_2904_3,plain,
    ( ! [U_10975,U_10973,U_10971,U_10969] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10971,tc_fun(U_10973,tc_HOL_Obool)),U_10969),hAPP(c_COMBK(tc_fun(U_10973,tc_HOL_Obool),U_10971),U_10975)) = U_10975
        | U_10969 = c_Orderings_Obot__class_Obot(tc_fun(U_10971,tc_HOL_Obool)) )
    & ! [U_10974,U_10972,U_10970,U_10968] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10970,tc_fun(U_10972,tc_HOL_Obool)),U_10968),hAPP(c_COMBK(tc_fun(U_10972,tc_HOL_Obool),U_10970),U_10974)) = c_Orderings_Obot__class_Obot(tc_fun(U_10972,tc_HOL_Obool))
        | U_10968 != c_Orderings_Obot__class_Obot(tc_fun(U_10970,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2904_2]) ).

fof(f_2904_4,plain,
    ( ! [U_10969,U_10971,U_10973,U_10975] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10971,tc_fun(U_10973,tc_HOL_Obool)),U_10969),hAPP(c_COMBK(tc_fun(U_10973,tc_HOL_Obool),U_10971),U_10975)) = U_10975
        | U_10969 = c_Orderings_Obot__class_Obot(tc_fun(U_10971,tc_HOL_Obool)) )
    & ! [U_10972,U_10968,U_10974,U_10970] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10970,tc_fun(U_10972,tc_HOL_Obool)),U_10968),hAPP(c_COMBK(tc_fun(U_10972,tc_HOL_Obool),U_10970),U_10974)) = c_Orderings_Obot__class_Obot(tc_fun(U_10972,tc_HOL_Obool))
        | U_10968 != c_Orderings_Obot__class_Obot(tc_fun(U_10970,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2904_3]) ).

cnf(f_2904_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10970,tc_fun(U_10972,tc_HOL_Obool)),U_10968),hAPP(c_COMBK(tc_fun(U_10972,tc_HOL_Obool),U_10970),U_10974)) = c_Orderings_Obot__class_Obot(tc_fun(U_10972,tc_HOL_Obool))
    | U_10968 != c_Orderings_Obot__class_Obot(tc_fun(U_10970,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2904_4]) ).

cnf(f_2904_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10971,tc_fun(U_10973,tc_HOL_Obool)),U_10969),hAPP(c_COMBK(tc_fun(U_10973,tc_HOL_Obool),U_10971),U_10975)) = U_10975
    | U_10969 = c_Orderings_Obot__class_Obot(tc_fun(U_10971,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2904_4]) ).

fof(f_2905_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_2905_2,plain,
    ! [U_10978,U_10977,U_10976] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10976,tc_fun(U_10977,tc_HOL_Obool)),U_10978),hAPP(c_COMBK(tc_fun(U_10977,tc_HOL_Obool),U_10976),c_Orderings_Obot__class_Obot(tc_fun(U_10977,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10977,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2905_1]) ).

fof(f_2905_3,plain,
    ! [U_10977,U_10976,U_10978] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10976,tc_fun(U_10977,tc_HOL_Obool)),U_10978),hAPP(c_COMBK(tc_fun(U_10977,tc_HOL_Obool),U_10976),c_Orderings_Obot__class_Obot(tc_fun(U_10977,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10977,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2905_2]) ).

cnf(f_2905_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10976,tc_fun(U_10977,tc_HOL_Obool)),U_10978),hAPP(c_COMBK(tc_fun(U_10977,tc_HOL_Obool),U_10976),c_Orderings_Obot__class_Obot(tc_fun(U_10977,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10977,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2905_3]) ).

fof(f_2906_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_2906_2,plain,
    ! [U_10984,U_10983,U_10982,U_10981] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_10981,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10982,tc_fun(U_10981,tc_HOL_Obool)),U_10983),U_10984)
        | ? [U_10980] :
            ( hAPP(U_10984,U_10980) != c_Orderings_Obot__class_Obot(tc_fun(U_10981,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_10982),U_10980),U_10983)) ) )
      & ( ! [U_10979] :
            ( hAPP(U_10984,U_10979) = c_Orderings_Obot__class_Obot(tc_fun(U_10981,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10982),U_10979),U_10983)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_10981,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10982,tc_fun(U_10981,tc_HOL_Obool)),U_10983),U_10984) ) ),
    inference(variable_rename,[status(thm)],[f_2906_1]) ).

fof(f_2906_3,plain,
    ( ! [U_10992,U_10990,U_10988,U_10986] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_10986,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10988,tc_fun(U_10986,tc_HOL_Obool)),U_10990),U_10992)
        | ? [U_10980] :
            ( hAPP(U_10992,U_10980) != c_Orderings_Obot__class_Obot(tc_fun(U_10986,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_10988),U_10980),U_10990)) ) )
    & ! [U_10991,U_10989,U_10987,U_10985] :
        ( ! [U_10979] :
            ( hAPP(U_10991,U_10979) = c_Orderings_Obot__class_Obot(tc_fun(U_10985,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10987),U_10979),U_10989)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_10985,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10987,tc_fun(U_10985,tc_HOL_Obool)),U_10989),U_10991) ) ),
    inference(miniscope,[status(thm)],[f_2906_2]) ).

fof(f_2906_4,plain,
    ( ! [U_10992,U_10990,U_10988,U_10986] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_10986,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10988,tc_fun(U_10986,tc_HOL_Obool)),U_10990),U_10992)
        | ( hAPP(U_10992,sK183(U_10992,U_10990,U_10988,U_10986)) != c_Orderings_Obot__class_Obot(tc_fun(U_10986,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_10988),sK183(U_10992,U_10990,U_10988,U_10986)),U_10990)) ) )
    & ! [U_10991,U_10989,U_10987,U_10985] :
        ( ! [U_10979] :
            ( hAPP(U_10991,U_10979) = c_Orderings_Obot__class_Obot(tc_fun(U_10985,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10987),U_10979),U_10989)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_10985,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10987,tc_fun(U_10985,tc_HOL_Obool)),U_10989),U_10991) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_10980,sK183(U_10992,U_10990,U_10988,U_10986))],[f_2906_3]) ).

fof(f_2906_5,plain,
    ( ! [U_10990,U_10986,U_10992,U_10988] :
        ( hAPP(U_10992,sK183(U_10992,U_10990,U_10988,U_10986)) != c_Orderings_Obot__class_Obot(tc_fun(U_10986,tc_HOL_Obool))
        | ~ sP831(U_10990,U_10986,U_10992,U_10988) )
    & ! [U_10990,U_10986,U_10992,U_10988] :
        ( hBOOL(hAPP(hAPP(c_member(U_10988),sK183(U_10992,U_10990,U_10988,U_10986)),U_10990))
        | ~ sP831(U_10990,U_10986,U_10992,U_10988) )
    & ! [U_10990,U_10986,U_10992,U_10988] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_10986,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10988,tc_fun(U_10986,tc_HOL_Obool)),U_10990),U_10992)
        | sP831(U_10990,U_10986,U_10992,U_10988) )
    & ! [U_10987,U_10991,U_10979,U_10985,U_10989] :
        ( hAPP(U_10991,U_10979) = c_Orderings_Obot__class_Obot(tc_fun(U_10985,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10987),U_10979),U_10989))
        | c_Orderings_Obot__class_Obot(tc_fun(U_10985,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10987,tc_fun(U_10985,tc_HOL_Obool)),U_10989),U_10991) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP831])],[f_2906_4]) ).

cnf(f_2906_6,plain,
    ( hAPP(U_10991,U_10979) = c_Orderings_Obot__class_Obot(tc_fun(U_10985,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10987),U_10979),U_10989))
    | c_Orderings_Obot__class_Obot(tc_fun(U_10985,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10987,tc_fun(U_10985,tc_HOL_Obool)),U_10989),U_10991) ),
    inference(clausify,[status(thm)],[f_2906_5]) ).

cnf(f_2906_7,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_10986,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10988,tc_fun(U_10986,tc_HOL_Obool)),U_10990),U_10992)
    | sP831(U_10990,U_10986,U_10992,U_10988) ),
    inference(clausify,[status(thm)],[f_2906_5]) ).

cnf(f_2906_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10988),sK183(U_10992,U_10990,U_10988,U_10986)),U_10990))
    | ~ sP831(U_10990,U_10986,U_10992,U_10988) ),
    inference(clausify,[status(thm)],[f_2906_5]) ).

cnf(f_2906_9,plain,
    ( hAPP(U_10992,sK183(U_10992,U_10990,U_10988,U_10986)) != c_Orderings_Obot__class_Obot(tc_fun(U_10986,tc_HOL_Obool))
    | ~ sP831(U_10990,U_10986,U_10992,U_10988) ),
    inference(clausify,[status(thm)],[f_2906_5]) ).

fof(f_2907_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_2907_2,plain,
    ! [U_10999,U_10998,U_10997,U_10996,U_10995] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10995,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10996,tc_fun(U_10995,tc_HOL_Obool)),U_10997),U_10998)),U_10999))
        | ? [U_10994] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10995,tc_HOL_Obool)),hAPP(U_10998,U_10994)),U_10999))
            & hBOOL(hAPP(hAPP(c_member(U_10996),U_10994),U_10997)) ) )
      & ( ! [U_10993] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10995,tc_HOL_Obool)),hAPP(U_10998,U_10993)),U_10999))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10996),U_10993),U_10997)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10995,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10996,tc_fun(U_10995,tc_HOL_Obool)),U_10997),U_10998)),U_10999)) ) ),
    inference(variable_rename,[status(thm)],[f_2907_1]) ).

fof(f_2907_3,plain,
    ( ! [U_11009,U_11007,U_11005,U_11003,U_11001] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11001,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11003,tc_fun(U_11001,tc_HOL_Obool)),U_11005),U_11007)),U_11009))
        | ? [U_10994] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11001,tc_HOL_Obool)),hAPP(U_11007,U_10994)),U_11009))
            & hBOOL(hAPP(hAPP(c_member(U_11003),U_10994),U_11005)) ) )
    & ! [U_11008,U_11006,U_11004,U_11002,U_11000] :
        ( ! [U_10993] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11000,tc_HOL_Obool)),hAPP(U_11006,U_10993)),U_11008))
            | ~ hBOOL(hAPP(hAPP(c_member(U_11002),U_10993),U_11004)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11000,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11002,tc_fun(U_11000,tc_HOL_Obool)),U_11004),U_11006)),U_11008)) ) ),
    inference(miniscope,[status(thm)],[f_2907_2]) ).

fof(f_2907_4,plain,
    ( ! [U_11009,U_11007,U_11005,U_11003,U_11001] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11001,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11003,tc_fun(U_11001,tc_HOL_Obool)),U_11005),U_11007)),U_11009))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11001,tc_HOL_Obool)),hAPP(U_11007,sK184(U_11009,U_11007,U_11005,U_11003,U_11001))),U_11009))
          & hBOOL(hAPP(hAPP(c_member(U_11003),sK184(U_11009,U_11007,U_11005,U_11003,U_11001)),U_11005)) ) )
    & ! [U_11008,U_11006,U_11004,U_11002,U_11000] :
        ( ! [U_10993] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11000,tc_HOL_Obool)),hAPP(U_11006,U_10993)),U_11008))
            | ~ hBOOL(hAPP(hAPP(c_member(U_11002),U_10993),U_11004)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11000,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11002,tc_fun(U_11000,tc_HOL_Obool)),U_11004),U_11006)),U_11008)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_10994,sK184(U_11009,U_11007,U_11005,U_11003,U_11001))],[f_2907_3]) ).

fof(f_2907_5,plain,
    ( ! [U_11005,U_11001,U_11003,U_11007,U_11009] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11001,tc_HOL_Obool)),hAPP(U_11007,sK184(U_11009,U_11007,U_11005,U_11003,U_11001))),U_11009))
        | ~ sP832(U_11005,U_11001,U_11003,U_11007,U_11009) )
    & ! [U_11005,U_11001,U_11003,U_11007,U_11009] :
        ( hBOOL(hAPP(hAPP(c_member(U_11003),sK184(U_11009,U_11007,U_11005,U_11003,U_11001)),U_11005))
        | ~ sP832(U_11005,U_11001,U_11003,U_11007,U_11009) )
    & ! [U_11005,U_11001,U_11003,U_11007,U_11009] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11001,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11003,tc_fun(U_11001,tc_HOL_Obool)),U_11005),U_11007)),U_11009))
        | sP832(U_11005,U_11001,U_11003,U_11007,U_11009) )
    & ! [U_10993,U_11000,U_11006,U_11002,U_11008,U_11004] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11000,tc_HOL_Obool)),hAPP(U_11006,U_10993)),U_11008))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11002),U_10993),U_11004))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11000,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11002,tc_fun(U_11000,tc_HOL_Obool)),U_11004),U_11006)),U_11008)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP832])],[f_2907_4]) ).

cnf(f_2907_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11000,tc_HOL_Obool)),hAPP(U_11006,U_10993)),U_11008))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11002),U_10993),U_11004))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11000,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11002,tc_fun(U_11000,tc_HOL_Obool)),U_11004),U_11006)),U_11008)) ),
    inference(clausify,[status(thm)],[f_2907_5]) ).

cnf(f_2907_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11001,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11003,tc_fun(U_11001,tc_HOL_Obool)),U_11005),U_11007)),U_11009))
    | sP832(U_11005,U_11001,U_11003,U_11007,U_11009) ),
    inference(clausify,[status(thm)],[f_2907_5]) ).

cnf(f_2907_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11003),sK184(U_11009,U_11007,U_11005,U_11003,U_11001)),U_11005))
    | ~ sP832(U_11005,U_11001,U_11003,U_11007,U_11009) ),
    inference(clausify,[status(thm)],[f_2907_5]) ).

cnf(f_2907_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11001,tc_HOL_Obool)),hAPP(U_11007,sK184(U_11009,U_11007,U_11005,U_11003,U_11001))),U_11009))
    | ~ sP832(U_11005,U_11001,U_11003,U_11007,U_11009) ),
    inference(clausify,[status(thm)],[f_2907_5]) ).

fof(f_2908_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_2908_2,plain,
    ! [U_11015,U_11014,U_11013,U_11012,U_11011,U_11010] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11010,tc_fun(U_11011,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11012,U_11010,U_11013),U_11014)),U_11015) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11012,tc_fun(U_11011,tc_HOL_Obool)),U_11014),hAPP(hAPP(c_COMBB(U_11010,tc_fun(U_11011,tc_HOL_Obool),U_11012),U_11015),U_11013)),
    inference(variable_rename,[status(thm)],[f_2908_1]) ).

fof(f_2908_3,plain,
    ! [U_11011,U_11010,U_11012,U_11013,U_11014,U_11015] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11010,tc_fun(U_11011,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11012,U_11010,U_11013),U_11014)),U_11015) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11012,tc_fun(U_11011,tc_HOL_Obool)),U_11014),hAPP(hAPP(c_COMBB(U_11010,tc_fun(U_11011,tc_HOL_Obool),U_11012),U_11015),U_11013)),
    inference(definitional_conversion,[status(esa)],[f_2908_2]) ).

cnf(f_2908_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11010,tc_fun(U_11011,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11012,U_11010,U_11013),U_11014)),U_11015) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11012,tc_fun(U_11011,tc_HOL_Obool)),U_11014),hAPP(hAPP(c_COMBB(U_11010,tc_fun(U_11011,tc_HOL_Obool),U_11012),U_11015),U_11013)),
    inference(clausify,[status(thm)],[f_2908_3]) ).

fof(f_2909_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_2909_2,plain,
    ! [U_11021,U_11020,U_11019,U_11018,U_11017,U_11016] : hAPP(c_Set_Oimage(U_11016,U_11017,U_11018),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11019,tc_fun(U_11016,tc_HOL_Obool)),U_11020),U_11021)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11019,tc_fun(U_11017,tc_HOL_Obool)),U_11020),hAPP(hAPP(c_COMBB(tc_fun(U_11016,tc_HOL_Obool),tc_fun(U_11017,tc_HOL_Obool),U_11019),c_Set_Oimage(U_11016,U_11017,U_11018)),U_11021)),
    inference(variable_rename,[status(thm)],[f_2909_1]) ).

fof(f_2909_3,plain,
    ! [U_11016,U_11017,U_11018,U_11019,U_11020,U_11021] : hAPP(c_Set_Oimage(U_11016,U_11017,U_11018),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11019,tc_fun(U_11016,tc_HOL_Obool)),U_11020),U_11021)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11019,tc_fun(U_11017,tc_HOL_Obool)),U_11020),hAPP(hAPP(c_COMBB(tc_fun(U_11016,tc_HOL_Obool),tc_fun(U_11017,tc_HOL_Obool),U_11019),c_Set_Oimage(U_11016,U_11017,U_11018)),U_11021)),
    inference(definitional_conversion,[status(esa)],[f_2909_2]) ).

cnf(f_2909_4,plain,
    hAPP(c_Set_Oimage(U_11016,U_11017,U_11018),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11019,tc_fun(U_11016,tc_HOL_Obool)),U_11020),U_11021)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11019,tc_fun(U_11017,tc_HOL_Obool)),U_11020),hAPP(hAPP(c_COMBB(tc_fun(U_11016,tc_HOL_Obool),tc_fun(U_11017,tc_HOL_Obool),U_11019),c_Set_Oimage(U_11016,U_11017,U_11018)),U_11021)),
    inference(clausify,[status(thm)],[f_2909_3]) ).

fof(f_2910_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_2910_2,plain,
    ! [U_11027,U_11026,U_11025,U_11024,U_11023,U_11022] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11022,tc_fun(U_11023,tc_HOL_Obool)),U_11024),hAPP(hAPP(c_COMBB(U_11025,tc_fun(U_11023,tc_HOL_Obool),U_11022),U_11026),U_11027)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11025,tc_fun(U_11023,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11022,U_11025,U_11027),U_11024)),U_11026),
    inference(variable_rename,[status(thm)],[f_2910_1]) ).

fof(f_2910_3,plain,
    ! [U_11022,U_11023,U_11024,U_11025,U_11026,U_11027] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11022,tc_fun(U_11023,tc_HOL_Obool)),U_11024),hAPP(hAPP(c_COMBB(U_11025,tc_fun(U_11023,tc_HOL_Obool),U_11022),U_11026),U_11027)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11025,tc_fun(U_11023,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11022,U_11025,U_11027),U_11024)),U_11026),
    inference(definitional_conversion,[status(esa)],[f_2910_2]) ).

cnf(f_2910_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11022,tc_fun(U_11023,tc_HOL_Obool)),U_11024),hAPP(hAPP(c_COMBB(U_11025,tc_fun(U_11023,tc_HOL_Obool),U_11022),U_11026),U_11027)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11025,tc_fun(U_11023,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11022,U_11025,U_11027),U_11024)),U_11026),
    inference(clausify,[status(thm)],[f_2910_3]) ).

fof(f_2911_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_2911_2,plain,
    ! [U_11032,U_11031,U_11030,U_11029,U_11028] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11028,tc_fun(U_11029,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11028,tc_HOL_Obool)),U_11030),U_11031)),U_11032) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11029,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11028,tc_fun(U_11029,tc_HOL_Obool)),U_11030),U_11032)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11028,tc_fun(U_11029,tc_HOL_Obool)),U_11031),U_11032)),
    inference(variable_rename,[status(thm)],[f_2911_1]) ).

fof(f_2911_3,plain,
    ! [U_11028,U_11029,U_11030,U_11031,U_11032] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11028,tc_fun(U_11029,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11028,tc_HOL_Obool)),U_11030),U_11031)),U_11032) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11029,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11028,tc_fun(U_11029,tc_HOL_Obool)),U_11030),U_11032)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11028,tc_fun(U_11029,tc_HOL_Obool)),U_11031),U_11032)),
    inference(definitional_conversion,[status(esa)],[f_2911_2]) ).

cnf(f_2911_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11028,tc_fun(U_11029,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11028,tc_HOL_Obool)),U_11030),U_11031)),U_11032) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11029,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11028,tc_fun(U_11029,tc_HOL_Obool)),U_11030),U_11032)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11028,tc_fun(U_11029,tc_HOL_Obool)),U_11031),U_11032)),
    inference(clausify,[status(thm)],[f_2911_3]) ).

fof(f_2912_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_2912_2,plain,
    ! [U_11037,U_11036,U_11035,U_11034,U_11033] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11033,tc_fun(U_11034,tc_HOL_Obool)),U_11035),hAPP(hAPP(c_COMBS(U_11033,tc_fun(U_11034,tc_HOL_Obool),tc_fun(U_11034,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11034,tc_HOL_Obool),tc_fun(tc_fun(U_11034,tc_HOL_Obool),tc_fun(U_11034,tc_HOL_Obool)),U_11033),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11034,tc_HOL_Obool))),U_11036)),U_11037)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11034,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11033,tc_fun(U_11034,tc_HOL_Obool)),U_11035),U_11036)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11033,tc_fun(U_11034,tc_HOL_Obool)),U_11035),U_11037)),
    inference(variable_rename,[status(thm)],[f_2912_1]) ).

fof(f_2912_3,plain,
    ! [U_11033,U_11034,U_11035,U_11036,U_11037] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11033,tc_fun(U_11034,tc_HOL_Obool)),U_11035),hAPP(hAPP(c_COMBS(U_11033,tc_fun(U_11034,tc_HOL_Obool),tc_fun(U_11034,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11034,tc_HOL_Obool),tc_fun(tc_fun(U_11034,tc_HOL_Obool),tc_fun(U_11034,tc_HOL_Obool)),U_11033),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11034,tc_HOL_Obool))),U_11036)),U_11037)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11034,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11033,tc_fun(U_11034,tc_HOL_Obool)),U_11035),U_11036)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11033,tc_fun(U_11034,tc_HOL_Obool)),U_11035),U_11037)),
    inference(definitional_conversion,[status(esa)],[f_2912_2]) ).

cnf(f_2912_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11033,tc_fun(U_11034,tc_HOL_Obool)),U_11035),hAPP(hAPP(c_COMBS(U_11033,tc_fun(U_11034,tc_HOL_Obool),tc_fun(U_11034,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11034,tc_HOL_Obool),tc_fun(tc_fun(U_11034,tc_HOL_Obool),tc_fun(U_11034,tc_HOL_Obool)),U_11033),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11034,tc_HOL_Obool))),U_11036)),U_11037)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11034,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11033,tc_fun(U_11034,tc_HOL_Obool)),U_11035),U_11036)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11033,tc_fun(U_11034,tc_HOL_Obool)),U_11035),U_11037)),
    inference(clausify,[status(thm)],[f_2912_3]) ).

fof(f_2913_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_2913_2,plain,
    ! [U_11044,U_11043,U_11042,U_11041,U_11040,U_11039,U_11038] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11038,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11039,tc_fun(U_11038,tc_HOL_Obool)),U_11040),U_11041)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11042,tc_fun(U_11038,tc_HOL_Obool)),U_11043),U_11044)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11039,tc_fun(U_11038,tc_HOL_Obool)),U_11040),hAPP(hAPP(c_COMBB(tc_fun(U_11042,tc_fun(U_11038,tc_HOL_Obool)),tc_fun(U_11038,tc_HOL_Obool),U_11039),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11042,tc_fun(U_11038,tc_HOL_Obool)),U_11043)),hAPP(hAPP(c_COMBC(U_11039,tc_fun(U_11042,tc_fun(U_11038,tc_HOL_Obool)),tc_fun(U_11042,tc_fun(U_11038,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11038,tc_HOL_Obool),tc_fun(U_11038,tc_HOL_Obool)),tc_fun(tc_fun(U_11042,tc_fun(U_11038,tc_HOL_Obool)),tc_fun(U_11042,tc_fun(U_11038,tc_HOL_Obool))),U_11039),c_COMBB(tc_fun(U_11038,tc_HOL_Obool),tc_fun(U_11038,tc_HOL_Obool),U_11042)),hAPP(hAPP(c_COMBB(tc_fun(U_11038,tc_HOL_Obool),tc_fun(tc_fun(U_11038,tc_HOL_Obool),tc_fun(U_11038,tc_HOL_Obool)),U_11039),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11038,tc_HOL_Obool))),U_11041))),U_11044))),
    inference(variable_rename,[status(thm)],[f_2913_1]) ).

fof(f_2913_3,plain,
    ! [U_11038,U_11039,U_11040,U_11041,U_11042,U_11043,U_11044] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11038,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11039,tc_fun(U_11038,tc_HOL_Obool)),U_11040),U_11041)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11042,tc_fun(U_11038,tc_HOL_Obool)),U_11043),U_11044)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11039,tc_fun(U_11038,tc_HOL_Obool)),U_11040),hAPP(hAPP(c_COMBB(tc_fun(U_11042,tc_fun(U_11038,tc_HOL_Obool)),tc_fun(U_11038,tc_HOL_Obool),U_11039),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11042,tc_fun(U_11038,tc_HOL_Obool)),U_11043)),hAPP(hAPP(c_COMBC(U_11039,tc_fun(U_11042,tc_fun(U_11038,tc_HOL_Obool)),tc_fun(U_11042,tc_fun(U_11038,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11038,tc_HOL_Obool),tc_fun(U_11038,tc_HOL_Obool)),tc_fun(tc_fun(U_11042,tc_fun(U_11038,tc_HOL_Obool)),tc_fun(U_11042,tc_fun(U_11038,tc_HOL_Obool))),U_11039),c_COMBB(tc_fun(U_11038,tc_HOL_Obool),tc_fun(U_11038,tc_HOL_Obool),U_11042)),hAPP(hAPP(c_COMBB(tc_fun(U_11038,tc_HOL_Obool),tc_fun(tc_fun(U_11038,tc_HOL_Obool),tc_fun(U_11038,tc_HOL_Obool)),U_11039),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11038,tc_HOL_Obool))),U_11041))),U_11044))),
    inference(definitional_conversion,[status(esa)],[f_2913_2]) ).

cnf(f_2913_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11038,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11039,tc_fun(U_11038,tc_HOL_Obool)),U_11040),U_11041)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11042,tc_fun(U_11038,tc_HOL_Obool)),U_11043),U_11044)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11039,tc_fun(U_11038,tc_HOL_Obool)),U_11040),hAPP(hAPP(c_COMBB(tc_fun(U_11042,tc_fun(U_11038,tc_HOL_Obool)),tc_fun(U_11038,tc_HOL_Obool),U_11039),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11042,tc_fun(U_11038,tc_HOL_Obool)),U_11043)),hAPP(hAPP(c_COMBC(U_11039,tc_fun(U_11042,tc_fun(U_11038,tc_HOL_Obool)),tc_fun(U_11042,tc_fun(U_11038,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11038,tc_HOL_Obool),tc_fun(U_11038,tc_HOL_Obool)),tc_fun(tc_fun(U_11042,tc_fun(U_11038,tc_HOL_Obool)),tc_fun(U_11042,tc_fun(U_11038,tc_HOL_Obool))),U_11039),c_COMBB(tc_fun(U_11038,tc_HOL_Obool),tc_fun(U_11038,tc_HOL_Obool),U_11042)),hAPP(hAPP(c_COMBB(tc_fun(U_11038,tc_HOL_Obool),tc_fun(tc_fun(U_11038,tc_HOL_Obool),tc_fun(U_11038,tc_HOL_Obool)),U_11039),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11038,tc_HOL_Obool))),U_11041))),U_11044))),
    inference(clausify,[status(thm)],[f_2913_3]) ).

fof(f_2914_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_2914_2,plain,
    ! [U_11049,U_11048,U_11047,U_11046,U_11045] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11045,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11046,tc_fun(U_11045,tc_HOL_Obool)),U_11047),U_11048)),U_11049) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11046,tc_fun(U_11045,tc_HOL_Obool)),U_11047),hAPP(hAPP(c_COMBC(U_11046,tc_fun(U_11045,tc_HOL_Obool),tc_fun(U_11045,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11045,tc_HOL_Obool),tc_fun(tc_fun(U_11045,tc_HOL_Obool),tc_fun(U_11045,tc_HOL_Obool)),U_11046),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11045,tc_HOL_Obool))),U_11048)),U_11049)),
    inference(variable_rename,[status(thm)],[f_2914_1]) ).

fof(f_2914_3,plain,
    ! [U_11045,U_11046,U_11047,U_11048,U_11049] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11045,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11046,tc_fun(U_11045,tc_HOL_Obool)),U_11047),U_11048)),U_11049) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11046,tc_fun(U_11045,tc_HOL_Obool)),U_11047),hAPP(hAPP(c_COMBC(U_11046,tc_fun(U_11045,tc_HOL_Obool),tc_fun(U_11045,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11045,tc_HOL_Obool),tc_fun(tc_fun(U_11045,tc_HOL_Obool),tc_fun(U_11045,tc_HOL_Obool)),U_11046),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11045,tc_HOL_Obool))),U_11048)),U_11049)),
    inference(definitional_conversion,[status(esa)],[f_2914_2]) ).

cnf(f_2914_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11045,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11046,tc_fun(U_11045,tc_HOL_Obool)),U_11047),U_11048)),U_11049) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11046,tc_fun(U_11045,tc_HOL_Obool)),U_11047),hAPP(hAPP(c_COMBC(U_11046,tc_fun(U_11045,tc_HOL_Obool),tc_fun(U_11045,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11045,tc_HOL_Obool),tc_fun(tc_fun(U_11045,tc_HOL_Obool),tc_fun(U_11045,tc_HOL_Obool)),U_11046),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11045,tc_HOL_Obool))),U_11048)),U_11049)),
    inference(clausify,[status(thm)],[f_2914_3]) ).

fof(f_2915_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_2915_2,plain,
    ! [U_11054,U_11053,U_11052,U_11051,U_11050] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11050,tc_HOL_Obool)),U_11051),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11052,tc_fun(U_11050,tc_HOL_Obool)),U_11053),U_11054)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11052,tc_fun(U_11050,tc_HOL_Obool)),U_11053),hAPP(hAPP(c_COMBB(tc_fun(U_11050,tc_HOL_Obool),tc_fun(U_11050,tc_HOL_Obool),U_11052),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11050,tc_HOL_Obool)),U_11051)),U_11054)),
    inference(variable_rename,[status(thm)],[f_2915_1]) ).

fof(f_2915_3,plain,
    ! [U_11050,U_11051,U_11052,U_11053,U_11054] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11050,tc_HOL_Obool)),U_11051),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11052,tc_fun(U_11050,tc_HOL_Obool)),U_11053),U_11054)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11052,tc_fun(U_11050,tc_HOL_Obool)),U_11053),hAPP(hAPP(c_COMBB(tc_fun(U_11050,tc_HOL_Obool),tc_fun(U_11050,tc_HOL_Obool),U_11052),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11050,tc_HOL_Obool)),U_11051)),U_11054)),
    inference(definitional_conversion,[status(esa)],[f_2915_2]) ).

cnf(f_2915_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11050,tc_HOL_Obool)),U_11051),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11052,tc_fun(U_11050,tc_HOL_Obool)),U_11053),U_11054)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11052,tc_fun(U_11050,tc_HOL_Obool)),U_11053),hAPP(hAPP(c_COMBB(tc_fun(U_11050,tc_HOL_Obool),tc_fun(U_11050,tc_HOL_Obool),U_11052),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11050,tc_HOL_Obool)),U_11051)),U_11054)),
    inference(clausify,[status(thm)],[f_2915_3]) ).

fof(f_2916_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_2916_2,plain,
    ! [U_11059,U_11058,U_11057,U_11056,U_11055] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11055,tc_HOL_Obool)),U_11056),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11057,tc_fun(U_11055,tc_HOL_Obool)),U_11058),U_11059)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11057,tc_fun(U_11055,tc_HOL_Obool)),U_11058),hAPP(hAPP(c_COMBB(tc_fun(U_11055,tc_HOL_Obool),tc_fun(U_11055,tc_HOL_Obool),U_11057),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11055,tc_HOL_Obool)),U_11056)),U_11059)),
    inference(variable_rename,[status(thm)],[f_2916_1]) ).

fof(f_2916_3,plain,
    ! [U_11055,U_11056,U_11057,U_11058,U_11059] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11055,tc_HOL_Obool)),U_11056),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11057,tc_fun(U_11055,tc_HOL_Obool)),U_11058),U_11059)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11057,tc_fun(U_11055,tc_HOL_Obool)),U_11058),hAPP(hAPP(c_COMBB(tc_fun(U_11055,tc_HOL_Obool),tc_fun(U_11055,tc_HOL_Obool),U_11057),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11055,tc_HOL_Obool)),U_11056)),U_11059)),
    inference(definitional_conversion,[status(esa)],[f_2916_2]) ).

cnf(f_2916_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11055,tc_HOL_Obool)),U_11056),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11057,tc_fun(U_11055,tc_HOL_Obool)),U_11058),U_11059)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11057,tc_fun(U_11055,tc_HOL_Obool)),U_11058),hAPP(hAPP(c_COMBB(tc_fun(U_11055,tc_HOL_Obool),tc_fun(U_11055,tc_HOL_Obool),U_11057),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11055,tc_HOL_Obool)),U_11056)),U_11059)),
    inference(clausify,[status(thm)],[f_2916_3]) ).

fof(f_2917_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_2917_2,plain,
    ! [U_11064,U_11063,U_11062,U_11061,U_11060] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11060,tc_fun(U_11061,tc_HOL_Obool)),U_11062),hAPP(hAPP(c_COMBC(U_11060,tc_fun(U_11061,tc_HOL_Obool),tc_fun(U_11061,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11061,tc_HOL_Obool),tc_fun(tc_fun(U_11061,tc_HOL_Obool),tc_fun(U_11061,tc_HOL_Obool)),U_11060),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11061,tc_HOL_Obool))),U_11063)),U_11064)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11061,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11060,tc_fun(U_11061,tc_HOL_Obool)),U_11062),U_11063)),U_11064),
    inference(variable_rename,[status(thm)],[f_2917_1]) ).

fof(f_2917_3,plain,
    ! [U_11060,U_11061,U_11062,U_11063,U_11064] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11060,tc_fun(U_11061,tc_HOL_Obool)),U_11062),hAPP(hAPP(c_COMBC(U_11060,tc_fun(U_11061,tc_HOL_Obool),tc_fun(U_11061,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11061,tc_HOL_Obool),tc_fun(tc_fun(U_11061,tc_HOL_Obool),tc_fun(U_11061,tc_HOL_Obool)),U_11060),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11061,tc_HOL_Obool))),U_11063)),U_11064)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11061,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11060,tc_fun(U_11061,tc_HOL_Obool)),U_11062),U_11063)),U_11064),
    inference(definitional_conversion,[status(esa)],[f_2917_2]) ).

cnf(f_2917_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11060,tc_fun(U_11061,tc_HOL_Obool)),U_11062),hAPP(hAPP(c_COMBC(U_11060,tc_fun(U_11061,tc_HOL_Obool),tc_fun(U_11061,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11061,tc_HOL_Obool),tc_fun(tc_fun(U_11061,tc_HOL_Obool),tc_fun(U_11061,tc_HOL_Obool)),U_11060),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11061,tc_HOL_Obool))),U_11063)),U_11064)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11061,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11060,tc_fun(U_11061,tc_HOL_Obool)),U_11062),U_11063)),U_11064),
    inference(clausify,[status(thm)],[f_2917_3]) ).

fof(f_2918_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_2918_2,plain,
    ! [U_11069,U_11068,U_11067,U_11066,U_11065] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11065,tc_fun(U_11066,tc_HOL_Obool)),U_11067),hAPP(hAPP(c_COMBB(tc_fun(U_11066,tc_HOL_Obool),tc_fun(U_11066,tc_HOL_Obool),U_11065),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11066,tc_HOL_Obool)),U_11068)),U_11069)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11066,tc_HOL_Obool)),U_11068),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11065,tc_fun(U_11066,tc_HOL_Obool)),U_11067),U_11069)),
    inference(variable_rename,[status(thm)],[f_2918_1]) ).

fof(f_2918_3,plain,
    ! [U_11065,U_11066,U_11067,U_11068,U_11069] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11065,tc_fun(U_11066,tc_HOL_Obool)),U_11067),hAPP(hAPP(c_COMBB(tc_fun(U_11066,tc_HOL_Obool),tc_fun(U_11066,tc_HOL_Obool),U_11065),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11066,tc_HOL_Obool)),U_11068)),U_11069)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11066,tc_HOL_Obool)),U_11068),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11065,tc_fun(U_11066,tc_HOL_Obool)),U_11067),U_11069)),
    inference(definitional_conversion,[status(esa)],[f_2918_2]) ).

cnf(f_2918_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11065,tc_fun(U_11066,tc_HOL_Obool)),U_11067),hAPP(hAPP(c_COMBB(tc_fun(U_11066,tc_HOL_Obool),tc_fun(U_11066,tc_HOL_Obool),U_11065),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11066,tc_HOL_Obool)),U_11068)),U_11069)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11066,tc_HOL_Obool)),U_11068),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11065,tc_fun(U_11066,tc_HOL_Obool)),U_11067),U_11069)),
    inference(clausify,[status(thm)],[f_2918_3]) ).

fof(f_2919_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_2919_2,plain,
    ! [U_11075,U_11074,U_11073,U_11072,U_11071,U_11070] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11071,tc_fun(U_11072,U_11070)),U_11073),U_11074),U_11075) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11071,U_11070),U_11073),hAPP(hAPP(c_COMBC(U_11071,U_11072,U_11070),U_11074),U_11075))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_11070) ),
    inference(variable_rename,[status(thm)],[f_2919_1]) ).

fof(f_2919_3,plain,
    ! [U_11070,U_11071,U_11072,U_11073,U_11074,U_11075] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11071,tc_fun(U_11072,U_11070)),U_11073),U_11074),U_11075) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11071,U_11070),U_11073),hAPP(hAPP(c_COMBC(U_11071,U_11072,U_11070),U_11074),U_11075))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_11070) ),
    inference(definitional_conversion,[status(esa)],[f_2919_2]) ).

cnf(f_2919_4,plain,
    ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11071,tc_fun(U_11072,U_11070)),U_11073),U_11074),U_11075) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11071,U_11070),U_11073),hAPP(hAPP(c_COMBC(U_11071,U_11072,U_11070),U_11074),U_11075))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_11070) ),
    inference(clausify,[status(thm)],[f_2919_3]) ).

fof(f_2920_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_2920_2,plain,
    ! [U_11080,U_11079,U_11078,U_11077,U_11076] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11076,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11077,tc_fun(U_11076,tc_HOL_Obool)),U_11078),U_11079)),U_11080) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11077,tc_fun(U_11076,tc_HOL_Obool)),U_11078),hAPP(hAPP(c_COMBC(U_11077,tc_fun(U_11076,tc_HOL_Obool),tc_fun(U_11076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11076,tc_HOL_Obool),tc_fun(tc_fun(U_11076,tc_HOL_Obool),tc_fun(U_11076,tc_HOL_Obool)),U_11077),c_Groups_Ominus__class_Ominus(tc_fun(U_11076,tc_HOL_Obool))),U_11079)),U_11080)),
    inference(variable_rename,[status(thm)],[f_2920_1]) ).

fof(f_2920_3,plain,
    ! [U_11076,U_11077,U_11078,U_11079,U_11080] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11076,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11077,tc_fun(U_11076,tc_HOL_Obool)),U_11078),U_11079)),U_11080) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11077,tc_fun(U_11076,tc_HOL_Obool)),U_11078),hAPP(hAPP(c_COMBC(U_11077,tc_fun(U_11076,tc_HOL_Obool),tc_fun(U_11076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11076,tc_HOL_Obool),tc_fun(tc_fun(U_11076,tc_HOL_Obool),tc_fun(U_11076,tc_HOL_Obool)),U_11077),c_Groups_Ominus__class_Ominus(tc_fun(U_11076,tc_HOL_Obool))),U_11079)),U_11080)),
    inference(definitional_conversion,[status(esa)],[f_2920_2]) ).

cnf(f_2920_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11076,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11077,tc_fun(U_11076,tc_HOL_Obool)),U_11078),U_11079)),U_11080) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11077,tc_fun(U_11076,tc_HOL_Obool)),U_11078),hAPP(hAPP(c_COMBC(U_11077,tc_fun(U_11076,tc_HOL_Obool),tc_fun(U_11076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11076,tc_HOL_Obool),tc_fun(tc_fun(U_11076,tc_HOL_Obool),tc_fun(U_11076,tc_HOL_Obool)),U_11077),c_Groups_Ominus__class_Ominus(tc_fun(U_11076,tc_HOL_Obool))),U_11079)),U_11080)),
    inference(clausify,[status(thm)],[f_2920_3]) ).

fof(f_2921_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_2921_2,plain,
    ! [U_11085,U_11084,U_11083,U_11082,U_11081] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11081,tc_fun(U_11082,tc_HOL_Obool)),U_11083),hAPP(hAPP(c_COMBC(U_11081,tc_fun(U_11082,tc_HOL_Obool),tc_fun(U_11082,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11082,tc_HOL_Obool),tc_fun(tc_fun(U_11082,tc_HOL_Obool),tc_fun(U_11082,tc_HOL_Obool)),U_11081),c_Groups_Ominus__class_Ominus(tc_fun(U_11082,tc_HOL_Obool))),U_11084)),U_11085)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11082,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11081,tc_fun(U_11082,tc_HOL_Obool)),U_11083),U_11084)),U_11085),
    inference(variable_rename,[status(thm)],[f_2921_1]) ).

fof(f_2921_3,plain,
    ! [U_11081,U_11082,U_11083,U_11084,U_11085] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11081,tc_fun(U_11082,tc_HOL_Obool)),U_11083),hAPP(hAPP(c_COMBC(U_11081,tc_fun(U_11082,tc_HOL_Obool),tc_fun(U_11082,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11082,tc_HOL_Obool),tc_fun(tc_fun(U_11082,tc_HOL_Obool),tc_fun(U_11082,tc_HOL_Obool)),U_11081),c_Groups_Ominus__class_Ominus(tc_fun(U_11082,tc_HOL_Obool))),U_11084)),U_11085)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11082,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11081,tc_fun(U_11082,tc_HOL_Obool)),U_11083),U_11084)),U_11085),
    inference(definitional_conversion,[status(esa)],[f_2921_2]) ).

cnf(f_2921_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11081,tc_fun(U_11082,tc_HOL_Obool)),U_11083),hAPP(hAPP(c_COMBC(U_11081,tc_fun(U_11082,tc_HOL_Obool),tc_fun(U_11082,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11082,tc_HOL_Obool),tc_fun(tc_fun(U_11082,tc_HOL_Obool),tc_fun(U_11082,tc_HOL_Obool)),U_11081),c_Groups_Ominus__class_Ominus(tc_fun(U_11082,tc_HOL_Obool))),U_11084)),U_11085)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11082,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11081,tc_fun(U_11082,tc_HOL_Obool)),U_11083),U_11084)),U_11085),
    inference(clausify,[status(thm)],[f_2921_3]) ).

fof(f_2922_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_2922_2,plain,
    ! [U_11090,U_11089,U_11088,U_11087,U_11086] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11086),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11087,U_11086),U_11088),U_11090)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11087,U_11086),U_11089),U_11090)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11087,tc_HOL_Obool)),U_11088),U_11089))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_11086) ),
    inference(variable_rename,[status(thm)],[f_2922_1]) ).

fof(f_2922_3,plain,
    ! [U_11086,U_11087,U_11088,U_11089,U_11090] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11086),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11087,U_11086),U_11088),U_11090)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11087,U_11086),U_11089),U_11090)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11087,tc_HOL_Obool)),U_11088),U_11089))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_11086) ),
    inference(definitional_conversion,[status(esa)],[f_2922_2]) ).

cnf(f_2922_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11086),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11087,U_11086),U_11088),U_11090)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11087,U_11086),U_11089),U_11090)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11087,tc_HOL_Obool)),U_11088),U_11089))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_11086) ),
    inference(clausify,[status(thm)],[f_2922_3]) ).

fof(f_2923_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_2923_2,plain,
    ! [U_11095,U_11094,U_11093,U_11092,U_11091] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11091),hAPP(U_11095,U_11093)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11092,U_11091),U_11094),U_11095)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11092),U_11093),U_11094))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_11091) ),
    inference(variable_rename,[status(thm)],[f_2923_1]) ).

fof(f_2923_3,plain,
    ! [U_11092,U_11091,U_11093,U_11094,U_11095] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11091),hAPP(U_11095,U_11093)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11092,U_11091),U_11094),U_11095)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11092),U_11093),U_11094))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_11091) ),
    inference(definitional_conversion,[status(esa)],[f_2923_2]) ).

cnf(f_2923_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11091),hAPP(U_11095,U_11093)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11092,U_11091),U_11094),U_11095)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11092),U_11093),U_11094))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_11091) ),
    inference(clausify,[status(thm)],[f_2923_3]) ).

fof(f_2924_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_2924_2,plain,
    ! [U_11101,U_11100,U_11099,U_11098,U_11097,U_11096] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11096,tc_fun(U_11099,tc_HOL_Obool)),U_11098),hAPP(hAPP(c_COMBB(tc_fun(U_11099,tc_HOL_Obool),tc_fun(U_11099,tc_HOL_Obool),U_11096),hAPP(c_Set_Oinsert(U_11099),U_11100)),U_11101)) = hAPP(hAPP(c_Set_Oinsert(U_11099),U_11100),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11096,tc_fun(U_11099,tc_HOL_Obool)),U_11098),U_11101))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11096),U_11097),U_11098)) ),
    inference(variable_rename,[status(thm)],[f_2924_1]) ).

fof(f_2924_3,plain,
    ! [U_11096,U_11097,U_11098,U_11099,U_11100,U_11101] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11096,tc_fun(U_11099,tc_HOL_Obool)),U_11098),hAPP(hAPP(c_COMBB(tc_fun(U_11099,tc_HOL_Obool),tc_fun(U_11099,tc_HOL_Obool),U_11096),hAPP(c_Set_Oinsert(U_11099),U_11100)),U_11101)) = hAPP(hAPP(c_Set_Oinsert(U_11099),U_11100),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11096,tc_fun(U_11099,tc_HOL_Obool)),U_11098),U_11101))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11096),U_11097),U_11098)) ),
    inference(definitional_conversion,[status(esa)],[f_2924_2]) ).

cnf(f_2924_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11096,tc_fun(U_11099,tc_HOL_Obool)),U_11098),hAPP(hAPP(c_COMBB(tc_fun(U_11099,tc_HOL_Obool),tc_fun(U_11099,tc_HOL_Obool),U_11096),hAPP(c_Set_Oinsert(U_11099),U_11100)),U_11101)) = hAPP(hAPP(c_Set_Oinsert(U_11099),U_11100),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11096,tc_fun(U_11099,tc_HOL_Obool)),U_11098),U_11101))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11096),U_11097),U_11098)) ),
    inference(clausify,[status(thm)],[f_2924_3]) ).

fof(f_2925_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_2925_2,plain,
    ! [U_11106,U_11105,U_11104,U_11103,U_11102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11105,tc_HOL_Obool)),hAPP(U_11106,U_11103)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11102,tc_fun(U_11105,tc_HOL_Obool)),U_11104),U_11106)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11102),U_11103),U_11104)) ),
    inference(variable_rename,[status(thm)],[f_2925_1]) ).

fof(f_2925_3,plain,
    ! [U_11103,U_11102,U_11104,U_11105,U_11106] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11105,tc_HOL_Obool)),hAPP(U_11106,U_11103)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11102,tc_fun(U_11105,tc_HOL_Obool)),U_11104),U_11106)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11102),U_11103),U_11104)) ),
    inference(definitional_conversion,[status(esa)],[f_2925_2]) ).

cnf(f_2925_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11105,tc_HOL_Obool)),hAPP(U_11106,U_11103)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11102,tc_fun(U_11105,tc_HOL_Obool)),U_11104),U_11106)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11102),U_11103),U_11104)) ),
    inference(clausify,[status(thm)],[f_2925_3]) ).

fof(f_2926_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_2926_2,plain,
    ! [U_11111,U_11110,U_11109,U_11108,U_11107] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11110,tc_HOL_Obool)),hAPP(U_11111,U_11108)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11107,tc_fun(U_11110,tc_HOL_Obool)),U_11109),U_11111)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11107,tc_fun(U_11110,tc_HOL_Obool)),U_11109),U_11111)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11107),U_11108),U_11109)) ),
    inference(variable_rename,[status(thm)],[f_2926_1]) ).

fof(f_2926_3,plain,
    ! [U_11111,U_11107,U_11108,U_11109,U_11110] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11110,tc_HOL_Obool)),hAPP(U_11111,U_11108)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11107,tc_fun(U_11110,tc_HOL_Obool)),U_11109),U_11111)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11107,tc_fun(U_11110,tc_HOL_Obool)),U_11109),U_11111)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11107),U_11108),U_11109)) ),
    inference(definitional_conversion,[status(esa)],[f_2926_2]) ).

cnf(f_2926_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11110,tc_HOL_Obool)),hAPP(U_11111,U_11108)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11107,tc_fun(U_11110,tc_HOL_Obool)),U_11109),U_11111)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11107,tc_fun(U_11110,tc_HOL_Obool)),U_11109),U_11111)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11107),U_11108),U_11109)) ),
    inference(clausify,[status(thm)],[f_2926_3]) ).

fof(f_2927_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_2927_2,plain,
    ! [U_11116,U_11115,U_11114,U_11113,U_11112] :
      ( ( hAPP(hAPP(c_Set_Oinsert(U_11114),U_11115),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11113,tc_fun(U_11114,tc_HOL_Obool)),U_11112),U_11116)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11113,tc_fun(U_11114,tc_HOL_Obool)),U_11112),hAPP(hAPP(c_COMBB(tc_fun(U_11114,tc_HOL_Obool),tc_fun(U_11114,tc_HOL_Obool),U_11113),hAPP(c_Set_Oinsert(U_11114),U_11115)),U_11116))
        | U_11112 = c_Orderings_Obot__class_Obot(tc_fun(U_11113,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Set_Oinsert(U_11114),U_11115),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11113,tc_fun(U_11114,tc_HOL_Obool)),U_11112),U_11116)) = hAPP(hAPP(c_Set_Oinsert(U_11114),U_11115),c_Orderings_Obot__class_Obot(tc_fun(U_11114,tc_HOL_Obool)))
        | U_11112 != c_Orderings_Obot__class_Obot(tc_fun(U_11113,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2927_1]) ).

fof(f_2927_3,plain,
    ( ! [U_11126,U_11124,U_11122,U_11120,U_11118] :
        ( hAPP(hAPP(c_Set_Oinsert(U_11122),U_11124),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11120,tc_fun(U_11122,tc_HOL_Obool)),U_11118),U_11126)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11120,tc_fun(U_11122,tc_HOL_Obool)),U_11118),hAPP(hAPP(c_COMBB(tc_fun(U_11122,tc_HOL_Obool),tc_fun(U_11122,tc_HOL_Obool),U_11120),hAPP(c_Set_Oinsert(U_11122),U_11124)),U_11126))
        | U_11118 = c_Orderings_Obot__class_Obot(tc_fun(U_11120,tc_HOL_Obool)) )
    & ! [U_11125,U_11123,U_11121,U_11119,U_11117] :
        ( hAPP(hAPP(c_Set_Oinsert(U_11121),U_11123),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11119,tc_fun(U_11121,tc_HOL_Obool)),U_11117),U_11125)) = hAPP(hAPP(c_Set_Oinsert(U_11121),U_11123),c_Orderings_Obot__class_Obot(tc_fun(U_11121,tc_HOL_Obool)))
        | U_11117 != c_Orderings_Obot__class_Obot(tc_fun(U_11119,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2927_2]) ).

fof(f_2927_4,plain,
    ( ! [U_11118,U_11120,U_11122,U_11124,U_11126] :
        ( hAPP(hAPP(c_Set_Oinsert(U_11122),U_11124),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11120,tc_fun(U_11122,tc_HOL_Obool)),U_11118),U_11126)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11120,tc_fun(U_11122,tc_HOL_Obool)),U_11118),hAPP(hAPP(c_COMBB(tc_fun(U_11122,tc_HOL_Obool),tc_fun(U_11122,tc_HOL_Obool),U_11120),hAPP(c_Set_Oinsert(U_11122),U_11124)),U_11126))
        | U_11118 = c_Orderings_Obot__class_Obot(tc_fun(U_11120,tc_HOL_Obool)) )
    & ! [U_11117,U_11121,U_11125,U_11119,U_11123] :
        ( hAPP(hAPP(c_Set_Oinsert(U_11121),U_11123),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11119,tc_fun(U_11121,tc_HOL_Obool)),U_11117),U_11125)) = hAPP(hAPP(c_Set_Oinsert(U_11121),U_11123),c_Orderings_Obot__class_Obot(tc_fun(U_11121,tc_HOL_Obool)))
        | U_11117 != c_Orderings_Obot__class_Obot(tc_fun(U_11119,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2927_3]) ).

cnf(f_2927_5,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_11121),U_11123),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11119,tc_fun(U_11121,tc_HOL_Obool)),U_11117),U_11125)) = hAPP(hAPP(c_Set_Oinsert(U_11121),U_11123),c_Orderings_Obot__class_Obot(tc_fun(U_11121,tc_HOL_Obool)))
    | U_11117 != c_Orderings_Obot__class_Obot(tc_fun(U_11119,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2927_4]) ).

cnf(f_2927_6,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_11122),U_11124),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11120,tc_fun(U_11122,tc_HOL_Obool)),U_11118),U_11126)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11120,tc_fun(U_11122,tc_HOL_Obool)),U_11118),hAPP(hAPP(c_COMBB(tc_fun(U_11122,tc_HOL_Obool),tc_fun(U_11122,tc_HOL_Obool),U_11120),hAPP(c_Set_Oinsert(U_11122),U_11124)),U_11126))
    | U_11118 = c_Orderings_Obot__class_Obot(tc_fun(U_11120,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2927_4]) ).

fof(f_2928_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_2928_2,plain,
    ! [U_11128,U_11127] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11127,tc_fun(U_11127,tc_HOL_Obool)),U_11128),hAPP(hAPP(c_COMBC(U_11127,tc_fun(U_11127,tc_HOL_Obool),tc_fun(U_11127,tc_HOL_Obool)),c_Set_Oinsert(U_11127)),c_Orderings_Obot__class_Obot(tc_fun(U_11127,tc_HOL_Obool)))) = U_11128,
    inference(variable_rename,[status(thm)],[f_2928_1]) ).

fof(f_2928_3,plain,
    ! [U_11127,U_11128] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11127,tc_fun(U_11127,tc_HOL_Obool)),U_11128),hAPP(hAPP(c_COMBC(U_11127,tc_fun(U_11127,tc_HOL_Obool),tc_fun(U_11127,tc_HOL_Obool)),c_Set_Oinsert(U_11127)),c_Orderings_Obot__class_Obot(tc_fun(U_11127,tc_HOL_Obool)))) = U_11128,
    inference(definitional_conversion,[status(esa)],[f_2928_2]) ).

cnf(f_2928_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11127,tc_fun(U_11127,tc_HOL_Obool)),U_11128),hAPP(hAPP(c_COMBC(U_11127,tc_fun(U_11127,tc_HOL_Obool),tc_fun(U_11127,tc_HOL_Obool)),c_Set_Oinsert(U_11127)),c_Orderings_Obot__class_Obot(tc_fun(U_11127,tc_HOL_Obool)))) = U_11128,
    inference(clausify,[status(thm)],[f_2928_3]) ).

fof(f_2929_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_2929_2,plain,
    ! [U_11133,U_11132,U_11131,U_11130,U_11129] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11130,tc_fun(U_11131,tc_HOL_Obool)),U_11129),hAPP(hAPP(c_COMBB(tc_fun(U_11131,tc_HOL_Obool),tc_fun(U_11131,tc_HOL_Obool),U_11130),hAPP(c_Set_Oinsert(U_11131),U_11132)),U_11133)) = hAPP(hAPP(c_Set_Oinsert(U_11131),U_11132),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11130,tc_fun(U_11131,tc_HOL_Obool)),U_11129),U_11133))
        | U_11129 = c_Orderings_Obot__class_Obot(tc_fun(U_11130,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11130,tc_fun(U_11131,tc_HOL_Obool)),U_11129),hAPP(hAPP(c_COMBB(tc_fun(U_11131,tc_HOL_Obool),tc_fun(U_11131,tc_HOL_Obool),U_11130),hAPP(c_Set_Oinsert(U_11131),U_11132)),U_11133)) = c_Orderings_Obot__class_Obot(tc_fun(U_11131,tc_HOL_Obool))
        | U_11129 != c_Orderings_Obot__class_Obot(tc_fun(U_11130,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2929_1]) ).

fof(f_2929_3,plain,
    ( ! [U_11143,U_11141,U_11139,U_11137,U_11135] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11137,tc_fun(U_11139,tc_HOL_Obool)),U_11135),hAPP(hAPP(c_COMBB(tc_fun(U_11139,tc_HOL_Obool),tc_fun(U_11139,tc_HOL_Obool),U_11137),hAPP(c_Set_Oinsert(U_11139),U_11141)),U_11143)) = hAPP(hAPP(c_Set_Oinsert(U_11139),U_11141),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11137,tc_fun(U_11139,tc_HOL_Obool)),U_11135),U_11143))
        | U_11135 = c_Orderings_Obot__class_Obot(tc_fun(U_11137,tc_HOL_Obool)) )
    & ! [U_11142,U_11140,U_11138,U_11136,U_11134] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11136,tc_fun(U_11138,tc_HOL_Obool)),U_11134),hAPP(hAPP(c_COMBB(tc_fun(U_11138,tc_HOL_Obool),tc_fun(U_11138,tc_HOL_Obool),U_11136),hAPP(c_Set_Oinsert(U_11138),U_11140)),U_11142)) = c_Orderings_Obot__class_Obot(tc_fun(U_11138,tc_HOL_Obool))
        | U_11134 != c_Orderings_Obot__class_Obot(tc_fun(U_11136,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2929_2]) ).

fof(f_2929_4,plain,
    ( ! [U_11135,U_11137,U_11139,U_11141,U_11143] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11137,tc_fun(U_11139,tc_HOL_Obool)),U_11135),hAPP(hAPP(c_COMBB(tc_fun(U_11139,tc_HOL_Obool),tc_fun(U_11139,tc_HOL_Obool),U_11137),hAPP(c_Set_Oinsert(U_11139),U_11141)),U_11143)) = hAPP(hAPP(c_Set_Oinsert(U_11139),U_11141),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11137,tc_fun(U_11139,tc_HOL_Obool)),U_11135),U_11143))
        | U_11135 = c_Orderings_Obot__class_Obot(tc_fun(U_11137,tc_HOL_Obool)) )
    & ! [U_11136,U_11140,U_11134,U_11138,U_11142] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11136,tc_fun(U_11138,tc_HOL_Obool)),U_11134),hAPP(hAPP(c_COMBB(tc_fun(U_11138,tc_HOL_Obool),tc_fun(U_11138,tc_HOL_Obool),U_11136),hAPP(c_Set_Oinsert(U_11138),U_11140)),U_11142)) = c_Orderings_Obot__class_Obot(tc_fun(U_11138,tc_HOL_Obool))
        | U_11134 != c_Orderings_Obot__class_Obot(tc_fun(U_11136,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2929_3]) ).

cnf(f_2929_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11136,tc_fun(U_11138,tc_HOL_Obool)),U_11134),hAPP(hAPP(c_COMBB(tc_fun(U_11138,tc_HOL_Obool),tc_fun(U_11138,tc_HOL_Obool),U_11136),hAPP(c_Set_Oinsert(U_11138),U_11140)),U_11142)) = c_Orderings_Obot__class_Obot(tc_fun(U_11138,tc_HOL_Obool))
    | U_11134 != c_Orderings_Obot__class_Obot(tc_fun(U_11136,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2929_4]) ).

cnf(f_2929_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11137,tc_fun(U_11139,tc_HOL_Obool)),U_11135),hAPP(hAPP(c_COMBB(tc_fun(U_11139,tc_HOL_Obool),tc_fun(U_11139,tc_HOL_Obool),U_11137),hAPP(c_Set_Oinsert(U_11139),U_11141)),U_11143)) = hAPP(hAPP(c_Set_Oinsert(U_11139),U_11141),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11137,tc_fun(U_11139,tc_HOL_Obool)),U_11135),U_11143))
    | U_11135 = c_Orderings_Obot__class_Obot(tc_fun(U_11137,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2929_4]) ).

fof(f_2930_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_2930_2,plain,
    ! [U_11148,U_11147,U_11146,U_11145,U_11144] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11145,tc_fun(U_11146,tc_HOL_Obool)),U_11144),hAPP(hAPP(c_COMBB(tc_fun(U_11146,tc_HOL_Obool),tc_fun(U_11146,tc_HOL_Obool),U_11145),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11146,tc_HOL_Obool)),U_11147)),U_11148)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11146,tc_HOL_Obool)),U_11147),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11145,tc_fun(U_11146,tc_HOL_Obool)),U_11144),U_11148))
        | U_11144 = c_Orderings_Obot__class_Obot(tc_fun(U_11145,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11145,tc_fun(U_11146,tc_HOL_Obool)),U_11144),hAPP(hAPP(c_COMBB(tc_fun(U_11146,tc_HOL_Obool),tc_fun(U_11146,tc_HOL_Obool),U_11145),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11146,tc_HOL_Obool)),U_11147)),U_11148)) = c_Orderings_Obot__class_Obot(tc_fun(U_11146,tc_HOL_Obool))
        | U_11144 != c_Orderings_Obot__class_Obot(tc_fun(U_11145,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2930_1]) ).

fof(f_2930_3,plain,
    ( ! [U_11158,U_11156,U_11154,U_11152,U_11150] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11152,tc_fun(U_11154,tc_HOL_Obool)),U_11150),hAPP(hAPP(c_COMBB(tc_fun(U_11154,tc_HOL_Obool),tc_fun(U_11154,tc_HOL_Obool),U_11152),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11154,tc_HOL_Obool)),U_11156)),U_11158)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11154,tc_HOL_Obool)),U_11156),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11152,tc_fun(U_11154,tc_HOL_Obool)),U_11150),U_11158))
        | U_11150 = c_Orderings_Obot__class_Obot(tc_fun(U_11152,tc_HOL_Obool)) )
    & ! [U_11157,U_11155,U_11153,U_11151,U_11149] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11151,tc_fun(U_11153,tc_HOL_Obool)),U_11149),hAPP(hAPP(c_COMBB(tc_fun(U_11153,tc_HOL_Obool),tc_fun(U_11153,tc_HOL_Obool),U_11151),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11153,tc_HOL_Obool)),U_11155)),U_11157)) = c_Orderings_Obot__class_Obot(tc_fun(U_11153,tc_HOL_Obool))
        | U_11149 != c_Orderings_Obot__class_Obot(tc_fun(U_11151,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2930_2]) ).

fof(f_2930_4,plain,
    ( ! [U_11150,U_11152,U_11154,U_11156,U_11158] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11152,tc_fun(U_11154,tc_HOL_Obool)),U_11150),hAPP(hAPP(c_COMBB(tc_fun(U_11154,tc_HOL_Obool),tc_fun(U_11154,tc_HOL_Obool),U_11152),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11154,tc_HOL_Obool)),U_11156)),U_11158)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11154,tc_HOL_Obool)),U_11156),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11152,tc_fun(U_11154,tc_HOL_Obool)),U_11150),U_11158))
        | U_11150 = c_Orderings_Obot__class_Obot(tc_fun(U_11152,tc_HOL_Obool)) )
    & ! [U_11151,U_11153,U_11155,U_11157,U_11149] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11151,tc_fun(U_11153,tc_HOL_Obool)),U_11149),hAPP(hAPP(c_COMBB(tc_fun(U_11153,tc_HOL_Obool),tc_fun(U_11153,tc_HOL_Obool),U_11151),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11153,tc_HOL_Obool)),U_11155)),U_11157)) = c_Orderings_Obot__class_Obot(tc_fun(U_11153,tc_HOL_Obool))
        | U_11149 != c_Orderings_Obot__class_Obot(tc_fun(U_11151,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2930_3]) ).

cnf(f_2930_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11151,tc_fun(U_11153,tc_HOL_Obool)),U_11149),hAPP(hAPP(c_COMBB(tc_fun(U_11153,tc_HOL_Obool),tc_fun(U_11153,tc_HOL_Obool),U_11151),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11153,tc_HOL_Obool)),U_11155)),U_11157)) = c_Orderings_Obot__class_Obot(tc_fun(U_11153,tc_HOL_Obool))
    | U_11149 != c_Orderings_Obot__class_Obot(tc_fun(U_11151,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2930_4]) ).

cnf(f_2930_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11152,tc_fun(U_11154,tc_HOL_Obool)),U_11150),hAPP(hAPP(c_COMBB(tc_fun(U_11154,tc_HOL_Obool),tc_fun(U_11154,tc_HOL_Obool),U_11152),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11154,tc_HOL_Obool)),U_11156)),U_11158)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11154,tc_HOL_Obool)),U_11156),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11152,tc_fun(U_11154,tc_HOL_Obool)),U_11150),U_11158))
    | U_11150 = c_Orderings_Obot__class_Obot(tc_fun(U_11152,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2930_4]) ).

fof(f_2931_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_2931_2,plain,
    ! [U_11163,U_11162,U_11161,U_11160,U_11159] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11160,tc_fun(U_11161,tc_HOL_Obool)),U_11159),hAPP(hAPP(c_COMBC(U_11160,tc_fun(U_11161,tc_HOL_Obool),tc_fun(U_11161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11161,tc_HOL_Obool),tc_fun(tc_fun(U_11161,tc_HOL_Obool),tc_fun(U_11161,tc_HOL_Obool)),U_11160),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11161,tc_HOL_Obool))),U_11162)),U_11163)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11161,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11160,tc_fun(U_11161,tc_HOL_Obool)),U_11159),U_11162)),U_11163)
        | U_11159 = c_Orderings_Obot__class_Obot(tc_fun(U_11160,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11160,tc_fun(U_11161,tc_HOL_Obool)),U_11159),hAPP(hAPP(c_COMBC(U_11160,tc_fun(U_11161,tc_HOL_Obool),tc_fun(U_11161,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11161,tc_HOL_Obool),tc_fun(tc_fun(U_11161,tc_HOL_Obool),tc_fun(U_11161,tc_HOL_Obool)),U_11160),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11161,tc_HOL_Obool))),U_11162)),U_11163)) = c_Orderings_Obot__class_Obot(tc_fun(U_11161,tc_HOL_Obool))
        | U_11159 != c_Orderings_Obot__class_Obot(tc_fun(U_11160,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2931_1]) ).

fof(f_2931_3,plain,
    ( ! [U_11173,U_11171,U_11169,U_11167,U_11165] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11167,tc_fun(U_11169,tc_HOL_Obool)),U_11165),hAPP(hAPP(c_COMBC(U_11167,tc_fun(U_11169,tc_HOL_Obool),tc_fun(U_11169,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11169,tc_HOL_Obool),tc_fun(tc_fun(U_11169,tc_HOL_Obool),tc_fun(U_11169,tc_HOL_Obool)),U_11167),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11169,tc_HOL_Obool))),U_11171)),U_11173)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11169,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11167,tc_fun(U_11169,tc_HOL_Obool)),U_11165),U_11171)),U_11173)
        | U_11165 = c_Orderings_Obot__class_Obot(tc_fun(U_11167,tc_HOL_Obool)) )
    & ! [U_11172,U_11170,U_11168,U_11166,U_11164] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11166,tc_fun(U_11168,tc_HOL_Obool)),U_11164),hAPP(hAPP(c_COMBC(U_11166,tc_fun(U_11168,tc_HOL_Obool),tc_fun(U_11168,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11168,tc_HOL_Obool),tc_fun(tc_fun(U_11168,tc_HOL_Obool),tc_fun(U_11168,tc_HOL_Obool)),U_11166),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11168,tc_HOL_Obool))),U_11170)),U_11172)) = c_Orderings_Obot__class_Obot(tc_fun(U_11168,tc_HOL_Obool))
        | U_11164 != c_Orderings_Obot__class_Obot(tc_fun(U_11166,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2931_2]) ).

fof(f_2931_4,plain,
    ( ! [U_11165,U_11167,U_11169,U_11171,U_11173] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11167,tc_fun(U_11169,tc_HOL_Obool)),U_11165),hAPP(hAPP(c_COMBC(U_11167,tc_fun(U_11169,tc_HOL_Obool),tc_fun(U_11169,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11169,tc_HOL_Obool),tc_fun(tc_fun(U_11169,tc_HOL_Obool),tc_fun(U_11169,tc_HOL_Obool)),U_11167),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11169,tc_HOL_Obool))),U_11171)),U_11173)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11169,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11167,tc_fun(U_11169,tc_HOL_Obool)),U_11165),U_11171)),U_11173)
        | U_11165 = c_Orderings_Obot__class_Obot(tc_fun(U_11167,tc_HOL_Obool)) )
    & ! [U_11170,U_11166,U_11164,U_11168,U_11172] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11166,tc_fun(U_11168,tc_HOL_Obool)),U_11164),hAPP(hAPP(c_COMBC(U_11166,tc_fun(U_11168,tc_HOL_Obool),tc_fun(U_11168,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11168,tc_HOL_Obool),tc_fun(tc_fun(U_11168,tc_HOL_Obool),tc_fun(U_11168,tc_HOL_Obool)),U_11166),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11168,tc_HOL_Obool))),U_11170)),U_11172)) = c_Orderings_Obot__class_Obot(tc_fun(U_11168,tc_HOL_Obool))
        | U_11164 != c_Orderings_Obot__class_Obot(tc_fun(U_11166,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2931_3]) ).

cnf(f_2931_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11166,tc_fun(U_11168,tc_HOL_Obool)),U_11164),hAPP(hAPP(c_COMBC(U_11166,tc_fun(U_11168,tc_HOL_Obool),tc_fun(U_11168,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11168,tc_HOL_Obool),tc_fun(tc_fun(U_11168,tc_HOL_Obool),tc_fun(U_11168,tc_HOL_Obool)),U_11166),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11168,tc_HOL_Obool))),U_11170)),U_11172)) = c_Orderings_Obot__class_Obot(tc_fun(U_11168,tc_HOL_Obool))
    | U_11164 != c_Orderings_Obot__class_Obot(tc_fun(U_11166,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2931_4]) ).

cnf(f_2931_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11167,tc_fun(U_11169,tc_HOL_Obool)),U_11165),hAPP(hAPP(c_COMBC(U_11167,tc_fun(U_11169,tc_HOL_Obool),tc_fun(U_11169,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11169,tc_HOL_Obool),tc_fun(tc_fun(U_11169,tc_HOL_Obool),tc_fun(U_11169,tc_HOL_Obool)),U_11167),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11169,tc_HOL_Obool))),U_11171)),U_11173)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11169,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11167,tc_fun(U_11169,tc_HOL_Obool)),U_11165),U_11171)),U_11173)
    | U_11165 = c_Orderings_Obot__class_Obot(tc_fun(U_11167,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2931_4]) ).

fof(f_2932_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_2932_2,plain,
    ! [U_11178,U_11177,U_11176,U_11175,U_11174] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11176,tc_HOL_Obool)),U_11177),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11175,tc_fun(U_11176,tc_HOL_Obool)),U_11174),U_11178)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11175,tc_fun(U_11176,tc_HOL_Obool)),U_11174),hAPP(hAPP(c_COMBB(tc_fun(U_11176,tc_HOL_Obool),tc_fun(U_11176,tc_HOL_Obool),U_11175),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11176,tc_HOL_Obool)),U_11177)),U_11178))
        | U_11174 = c_Orderings_Obot__class_Obot(tc_fun(U_11175,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11176,tc_HOL_Obool)),U_11177),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11175,tc_fun(U_11176,tc_HOL_Obool)),U_11174),U_11178)) = U_11177
        | U_11174 != c_Orderings_Obot__class_Obot(tc_fun(U_11175,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2932_1]) ).

fof(f_2932_3,plain,
    ( ! [U_11188,U_11186,U_11184,U_11182,U_11180] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11184,tc_HOL_Obool)),U_11186),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11182,tc_fun(U_11184,tc_HOL_Obool)),U_11180),U_11188)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11182,tc_fun(U_11184,tc_HOL_Obool)),U_11180),hAPP(hAPP(c_COMBB(tc_fun(U_11184,tc_HOL_Obool),tc_fun(U_11184,tc_HOL_Obool),U_11182),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11184,tc_HOL_Obool)),U_11186)),U_11188))
        | U_11180 = c_Orderings_Obot__class_Obot(tc_fun(U_11182,tc_HOL_Obool)) )
    & ! [U_11187,U_11185,U_11183,U_11181,U_11179] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11183,tc_HOL_Obool)),U_11185),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11181,tc_fun(U_11183,tc_HOL_Obool)),U_11179),U_11187)) = U_11185
        | U_11179 != c_Orderings_Obot__class_Obot(tc_fun(U_11181,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2932_2]) ).

fof(f_2932_4,plain,
    ( ! [U_11180,U_11182,U_11184,U_11186,U_11188] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11184,tc_HOL_Obool)),U_11186),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11182,tc_fun(U_11184,tc_HOL_Obool)),U_11180),U_11188)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11182,tc_fun(U_11184,tc_HOL_Obool)),U_11180),hAPP(hAPP(c_COMBB(tc_fun(U_11184,tc_HOL_Obool),tc_fun(U_11184,tc_HOL_Obool),U_11182),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11184,tc_HOL_Obool)),U_11186)),U_11188))
        | U_11180 = c_Orderings_Obot__class_Obot(tc_fun(U_11182,tc_HOL_Obool)) )
    & ! [U_11181,U_11185,U_11183,U_11179,U_11187] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11183,tc_HOL_Obool)),U_11185),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11181,tc_fun(U_11183,tc_HOL_Obool)),U_11179),U_11187)) = U_11185
        | U_11179 != c_Orderings_Obot__class_Obot(tc_fun(U_11181,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2932_3]) ).

cnf(f_2932_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11183,tc_HOL_Obool)),U_11185),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11181,tc_fun(U_11183,tc_HOL_Obool)),U_11179),U_11187)) = U_11185
    | U_11179 != c_Orderings_Obot__class_Obot(tc_fun(U_11181,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2932_4]) ).

cnf(f_2932_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11184,tc_HOL_Obool)),U_11186),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11182,tc_fun(U_11184,tc_HOL_Obool)),U_11180),U_11188)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11182,tc_fun(U_11184,tc_HOL_Obool)),U_11180),hAPP(hAPP(c_COMBB(tc_fun(U_11184,tc_HOL_Obool),tc_fun(U_11184,tc_HOL_Obool),U_11182),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11184,tc_HOL_Obool)),U_11186)),U_11188))
    | U_11180 = c_Orderings_Obot__class_Obot(tc_fun(U_11182,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2932_4]) ).

fof(f_2933_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_2933_2,plain,
    ! [U_11193,U_11192,U_11191,U_11190,U_11189] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11191,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11190,tc_fun(U_11191,tc_HOL_Obool)),U_11189),U_11192)),U_11193) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11190,tc_fun(U_11191,tc_HOL_Obool)),U_11189),hAPP(hAPP(c_COMBC(U_11190,tc_fun(U_11191,tc_HOL_Obool),tc_fun(U_11191,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11191,tc_HOL_Obool),tc_fun(tc_fun(U_11191,tc_HOL_Obool),tc_fun(U_11191,tc_HOL_Obool)),U_11190),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11191,tc_HOL_Obool))),U_11192)),U_11193))
        | U_11189 = c_Orderings_Obot__class_Obot(tc_fun(U_11190,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11191,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11190,tc_fun(U_11191,tc_HOL_Obool)),U_11189),U_11192)),U_11193) = U_11193
        | U_11189 != c_Orderings_Obot__class_Obot(tc_fun(U_11190,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2933_1]) ).

fof(f_2933_3,plain,
    ( ! [U_11203,U_11201,U_11199,U_11197,U_11195] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11199,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11197,tc_fun(U_11199,tc_HOL_Obool)),U_11195),U_11201)),U_11203) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11197,tc_fun(U_11199,tc_HOL_Obool)),U_11195),hAPP(hAPP(c_COMBC(U_11197,tc_fun(U_11199,tc_HOL_Obool),tc_fun(U_11199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11199,tc_HOL_Obool),tc_fun(tc_fun(U_11199,tc_HOL_Obool),tc_fun(U_11199,tc_HOL_Obool)),U_11197),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11199,tc_HOL_Obool))),U_11201)),U_11203))
        | U_11195 = c_Orderings_Obot__class_Obot(tc_fun(U_11197,tc_HOL_Obool)) )
    & ! [U_11202,U_11200,U_11198,U_11196,U_11194] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11198,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11196,tc_fun(U_11198,tc_HOL_Obool)),U_11194),U_11200)),U_11202) = U_11202
        | U_11194 != c_Orderings_Obot__class_Obot(tc_fun(U_11196,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2933_2]) ).

fof(f_2933_4,plain,
    ( ! [U_11195,U_11203,U_11197,U_11199,U_11201] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11199,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11197,tc_fun(U_11199,tc_HOL_Obool)),U_11195),U_11201)),U_11203) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11197,tc_fun(U_11199,tc_HOL_Obool)),U_11195),hAPP(hAPP(c_COMBC(U_11197,tc_fun(U_11199,tc_HOL_Obool),tc_fun(U_11199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11199,tc_HOL_Obool),tc_fun(tc_fun(U_11199,tc_HOL_Obool),tc_fun(U_11199,tc_HOL_Obool)),U_11197),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11199,tc_HOL_Obool))),U_11201)),U_11203))
        | U_11195 = c_Orderings_Obot__class_Obot(tc_fun(U_11197,tc_HOL_Obool)) )
    & ! [U_11198,U_11202,U_11196,U_11200,U_11194] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11198,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11196,tc_fun(U_11198,tc_HOL_Obool)),U_11194),U_11200)),U_11202) = U_11202
        | U_11194 != c_Orderings_Obot__class_Obot(tc_fun(U_11196,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2933_3]) ).

cnf(f_2933_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11198,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11196,tc_fun(U_11198,tc_HOL_Obool)),U_11194),U_11200)),U_11202) = U_11202
    | U_11194 != c_Orderings_Obot__class_Obot(tc_fun(U_11196,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2933_4]) ).

cnf(f_2933_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11199,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11197,tc_fun(U_11199,tc_HOL_Obool)),U_11195),U_11201)),U_11203) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11197,tc_fun(U_11199,tc_HOL_Obool)),U_11195),hAPP(hAPP(c_COMBC(U_11197,tc_fun(U_11199,tc_HOL_Obool),tc_fun(U_11199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11199,tc_HOL_Obool),tc_fun(tc_fun(U_11199,tc_HOL_Obool),tc_fun(U_11199,tc_HOL_Obool)),U_11197),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11199,tc_HOL_Obool))),U_11201)),U_11203))
    | U_11195 = c_Orderings_Obot__class_Obot(tc_fun(U_11197,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2933_4]) ).

fof(f_2934_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_2934_2,plain,
    ! [U_11208,U_11207,U_11206,U_11205,U_11204] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11204,tc_fun(U_11205,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11204),U_11206),U_11207)),U_11208) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11205,tc_HOL_Obool)),hAPP(U_11208,U_11206)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11204,tc_fun(U_11205,tc_HOL_Obool)),U_11207),U_11208)),
    inference(variable_rename,[status(thm)],[f_2934_1]) ).

fof(f_2934_3,plain,
    ! [U_11204,U_11206,U_11205,U_11207,U_11208] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11204,tc_fun(U_11205,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11204),U_11206),U_11207)),U_11208) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11205,tc_HOL_Obool)),hAPP(U_11208,U_11206)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11204,tc_fun(U_11205,tc_HOL_Obool)),U_11207),U_11208)),
    inference(definitional_conversion,[status(esa)],[f_2934_2]) ).

cnf(f_2934_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11204,tc_fun(U_11205,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11204),U_11206),U_11207)),U_11208) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11205,tc_HOL_Obool)),hAPP(U_11208,U_11206)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11204,tc_fun(U_11205,tc_HOL_Obool)),U_11207),U_11208)),
    inference(clausify,[status(thm)],[f_2934_3]) ).

fof(f_2935_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_2935_2,plain,
    ! [U_11217,U_11216,U_11215,U_11214,U_11213,U_11212,U_11211,U_11210,U_11209] :
      ( c_Equiv__Relations_Ocongruent(U_11209,tc_fun(U_11215,tc_HOL_Obool),U_11211,hAPP(hAPP(c_COMBB(tc_fun(U_11212,tc_fun(U_11215,tc_HOL_Obool)),tc_fun(U_11215,tc_HOL_Obool),U_11209),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11212,tc_fun(U_11215,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11212,U_11212,U_11214),hAPP(hAPP(c_Set_Oinsert(U_11212),U_11217),c_Orderings_Obot__class_Obot(tc_fun(U_11212,tc_HOL_Obool)))))),U_11216))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11212),U_11217),U_11213))
      | ~ c_Equiv__Relations_Ocongruent2(U_11209,U_11212,tc_fun(U_11215,tc_HOL_Obool),U_11211,U_11214,U_11216)
      | ~ c_Equiv__Relations_Oequiv(U_11212,U_11213,U_11214)
      | ~ c_Equiv__Relations_Oequiv(U_11209,U_11210,U_11211) ),
    inference(variable_rename,[status(thm)],[f_2935_1]) ).

fof(f_2935_3,plain,
    ! [U_11209,U_11212,U_11210,U_11211,U_11213,U_11214,U_11215,U_11216,U_11217] :
      ( c_Equiv__Relations_Ocongruent(U_11209,tc_fun(U_11215,tc_HOL_Obool),U_11211,hAPP(hAPP(c_COMBB(tc_fun(U_11212,tc_fun(U_11215,tc_HOL_Obool)),tc_fun(U_11215,tc_HOL_Obool),U_11209),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11212,tc_fun(U_11215,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11212,U_11212,U_11214),hAPP(hAPP(c_Set_Oinsert(U_11212),U_11217),c_Orderings_Obot__class_Obot(tc_fun(U_11212,tc_HOL_Obool)))))),U_11216))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11212),U_11217),U_11213))
      | ~ c_Equiv__Relations_Ocongruent2(U_11209,U_11212,tc_fun(U_11215,tc_HOL_Obool),U_11211,U_11214,U_11216)
      | ~ c_Equiv__Relations_Oequiv(U_11212,U_11213,U_11214)
      | ~ c_Equiv__Relations_Oequiv(U_11209,U_11210,U_11211) ),
    inference(definitional_conversion,[status(esa)],[f_2935_2]) ).

cnf(f_2935_4,plain,
    ( c_Equiv__Relations_Ocongruent(U_11209,tc_fun(U_11215,tc_HOL_Obool),U_11211,hAPP(hAPP(c_COMBB(tc_fun(U_11212,tc_fun(U_11215,tc_HOL_Obool)),tc_fun(U_11215,tc_HOL_Obool),U_11209),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11212,tc_fun(U_11215,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11212,U_11212,U_11214),hAPP(hAPP(c_Set_Oinsert(U_11212),U_11217),c_Orderings_Obot__class_Obot(tc_fun(U_11212,tc_HOL_Obool)))))),U_11216))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11212),U_11217),U_11213))
    | ~ c_Equiv__Relations_Ocongruent2(U_11209,U_11212,tc_fun(U_11215,tc_HOL_Obool),U_11211,U_11214,U_11216)
    | ~ c_Equiv__Relations_Oequiv(U_11212,U_11213,U_11214)
    | ~ c_Equiv__Relations_Oequiv(U_11209,U_11210,U_11211) ),
    inference(clausify,[status(thm)],[f_2935_3]) ).

fof(f_2936_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_2936_2,plain,
    ! [U_11218] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11218) = 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_11218)),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_2936_1]) ).

fof(f_2936_3,plain,
    ! [U_11218] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11218) = 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_11218)),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_2936_2]) ).

cnf(f_2936_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11218) = 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_11218)),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_2936_3]) ).

fof(f_2937_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_2937_2,plain,
    ! [U_11228,U_11227,U_11226,U_11225,U_11224,U_11223,U_11222,U_11221,U_11220,U_11219] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11219,tc_fun(U_11225,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11219,U_11219,U_11221),hAPP(hAPP(c_Set_Oinsert(U_11219),U_11227),c_Orderings_Obot__class_Obot(tc_fun(U_11219,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_11222,tc_fun(U_11225,tc_HOL_Obool)),tc_fun(U_11225,tc_HOL_Obool),U_11219),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11222,tc_fun(U_11225,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11222,U_11222,U_11224),hAPP(hAPP(c_Set_Oinsert(U_11222),U_11228),c_Orderings_Obot__class_Obot(tc_fun(U_11222,tc_HOL_Obool)))))),U_11226)) = hAPP(hAPP(U_11226,U_11227),U_11228)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11222),U_11228),U_11223))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11219),U_11227),U_11220))
      | ~ c_Equiv__Relations_Ocongruent2(U_11219,U_11222,tc_fun(U_11225,tc_HOL_Obool),U_11221,U_11224,U_11226)
      | ~ c_Equiv__Relations_Oequiv(U_11222,U_11223,U_11224)
      | ~ c_Equiv__Relations_Oequiv(U_11219,U_11220,U_11221) ),
    inference(variable_rename,[status(thm)],[f_2937_1]) ).

fof(f_2937_3,plain,
    ! [U_11220,U_11219,U_11221,U_11222,U_11223,U_11224,U_11225,U_11226,U_11227,U_11228] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11219,tc_fun(U_11225,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11219,U_11219,U_11221),hAPP(hAPP(c_Set_Oinsert(U_11219),U_11227),c_Orderings_Obot__class_Obot(tc_fun(U_11219,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_11222,tc_fun(U_11225,tc_HOL_Obool)),tc_fun(U_11225,tc_HOL_Obool),U_11219),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11222,tc_fun(U_11225,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11222,U_11222,U_11224),hAPP(hAPP(c_Set_Oinsert(U_11222),U_11228),c_Orderings_Obot__class_Obot(tc_fun(U_11222,tc_HOL_Obool)))))),U_11226)) = hAPP(hAPP(U_11226,U_11227),U_11228)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11222),U_11228),U_11223))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11219),U_11227),U_11220))
      | ~ c_Equiv__Relations_Ocongruent2(U_11219,U_11222,tc_fun(U_11225,tc_HOL_Obool),U_11221,U_11224,U_11226)
      | ~ c_Equiv__Relations_Oequiv(U_11222,U_11223,U_11224)
      | ~ c_Equiv__Relations_Oequiv(U_11219,U_11220,U_11221) ),
    inference(definitional_conversion,[status(esa)],[f_2937_2]) ).

cnf(f_2937_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11219,tc_fun(U_11225,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11219,U_11219,U_11221),hAPP(hAPP(c_Set_Oinsert(U_11219),U_11227),c_Orderings_Obot__class_Obot(tc_fun(U_11219,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_11222,tc_fun(U_11225,tc_HOL_Obool)),tc_fun(U_11225,tc_HOL_Obool),U_11219),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11222,tc_fun(U_11225,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11222,U_11222,U_11224),hAPP(hAPP(c_Set_Oinsert(U_11222),U_11228),c_Orderings_Obot__class_Obot(tc_fun(U_11222,tc_HOL_Obool)))))),U_11226)) = hAPP(hAPP(U_11226,U_11227),U_11228)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11222),U_11228),U_11223))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11219),U_11227),U_11220))
    | ~ c_Equiv__Relations_Ocongruent2(U_11219,U_11222,tc_fun(U_11225,tc_HOL_Obool),U_11221,U_11224,U_11226)
    | ~ c_Equiv__Relations_Oequiv(U_11222,U_11223,U_11224)
    | ~ c_Equiv__Relations_Oequiv(U_11219,U_11220,U_11221) ),
    inference(clausify,[status(thm)],[f_2937_3]) ).

fof(f_2938_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_2938_2,plain,
    ! [U_11236,U_11235,U_11234,U_11233,U_11232,U_11231,U_11230,U_11229] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11229,tc_fun(U_11235,tc_fun(U_11236,tc_HOL_Obool))),U_11231),U_11232),U_11233),U_11234))
      | ~ hBOOL(hAPP(hAPP(hAPP(U_11232,U_11230),U_11233),U_11234))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11229),U_11230),U_11231)) ),
    inference(variable_rename,[status(thm)],[f_2938_1]) ).

fof(f_2938_3,plain,
    ! [U_11230,U_11231,U_11233,U_11235,U_11232,U_11229,U_11234,U_11236] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11229,tc_fun(U_11235,tc_fun(U_11236,tc_HOL_Obool))),U_11231),U_11232),U_11233),U_11234))
      | ~ hBOOL(hAPP(hAPP(hAPP(U_11232,U_11230),U_11233),U_11234))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11229),U_11230),U_11231)) ),
    inference(definitional_conversion,[status(esa)],[f_2938_2]) ).

cnf(f_2938_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11229,tc_fun(U_11235,tc_fun(U_11236,tc_HOL_Obool))),U_11231),U_11232),U_11233),U_11234))
    | ~ hBOOL(hAPP(hAPP(hAPP(U_11232,U_11230),U_11233),U_11234))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11229),U_11230),U_11231)) ),
    inference(clausify,[status(thm)],[f_2938_3]) ).

fof(f_2939_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_2939_2,plain,
    ! [U_11238,U_11237] :
      ( ( hAPP(c_Int_ORep__Integ,U_11237) = hAPP(c_Int_ORep__Integ,U_11238)
        | U_11237 != U_11238 )
      & ( U_11237 = U_11238
        | hAPP(c_Int_ORep__Integ,U_11237) != hAPP(c_Int_ORep__Integ,U_11238) ) ),
    inference(variable_rename,[status(thm)],[f_2939_1]) ).

fof(f_2939_3,plain,
    ( ! [U_11242,U_11240] :
        ( hAPP(c_Int_ORep__Integ,U_11240) = hAPP(c_Int_ORep__Integ,U_11242)
        | U_11240 != U_11242 )
    & ! [U_11241,U_11239] :
        ( U_11239 = U_11241
        | hAPP(c_Int_ORep__Integ,U_11239) != hAPP(c_Int_ORep__Integ,U_11241) ) ),
    inference(miniscope,[status(thm)],[f_2939_2]) ).

fof(f_2939_4,plain,
    ( ! [U_11240,U_11242] :
        ( hAPP(c_Int_ORep__Integ,U_11240) = hAPP(c_Int_ORep__Integ,U_11242)
        | U_11240 != U_11242 )
    & ! [U_11241,U_11239] :
        ( U_11239 = U_11241
        | hAPP(c_Int_ORep__Integ,U_11239) != hAPP(c_Int_ORep__Integ,U_11241) ) ),
    inference(definitional_conversion,[status(esa)],[f_2939_3]) ).

cnf(f_2939_5,plain,
    ( U_11239 = U_11241
    | hAPP(c_Int_ORep__Integ,U_11239) != hAPP(c_Int_ORep__Integ,U_11241) ),
    inference(clausify,[status(thm)],[f_2939_4]) ).

cnf(f_2939_6,plain,
    ( hAPP(c_Int_ORep__Integ,U_11240) = hAPP(c_Int_ORep__Integ,U_11242)
    | U_11240 != U_11242 ),
    inference(clausify,[status(thm)],[f_2939_4]) ).

fof(f_2940_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_2940_2,plain,
    ! [U_11243] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_11243)) = U_11243,
    inference(variable_rename,[status(thm)],[f_2940_1]) ).

fof(f_2940_3,plain,
    ! [U_11243] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_11243)) = U_11243,
    inference(definitional_conversion,[status(esa)],[f_2940_2]) ).

cnf(f_2940_4,plain,
    hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_11243)) = U_11243,
    inference(clausify,[status(thm)],[f_2940_3]) ).

fof(f_2941_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_2941_2,plain,
    ! [U_11253,U_11252,U_11251,U_11250,U_11249,U_11248,U_11247,U_11246,U_11245,U_11244] :
      ( hAPP(hAPP(U_11249,U_11250),U_11252) = hAPP(hAPP(U_11249,U_11251),U_11253)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11245,U_11245)),hAPP(hAPP(c_Product__Type_OPair(U_11245,U_11245),U_11252),U_11253)),U_11248))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11244,U_11244)),hAPP(hAPP(c_Product__Type_OPair(U_11244,U_11244),U_11250),U_11251)),U_11247))
      | ~ c_Equiv__Relations_Ocongruent2(U_11244,U_11245,U_11246,U_11247,U_11248,U_11249) ),
    inference(variable_rename,[status(thm)],[f_2941_1]) ).

fof(f_2941_3,plain,
    ! [U_11244,U_11245,U_11246,U_11247,U_11248,U_11249,U_11250,U_11251,U_11252,U_11253] :
      ( hAPP(hAPP(U_11249,U_11250),U_11252) = hAPP(hAPP(U_11249,U_11251),U_11253)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11245,U_11245)),hAPP(hAPP(c_Product__Type_OPair(U_11245,U_11245),U_11252),U_11253)),U_11248))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11244,U_11244)),hAPP(hAPP(c_Product__Type_OPair(U_11244,U_11244),U_11250),U_11251)),U_11247))
      | ~ c_Equiv__Relations_Ocongruent2(U_11244,U_11245,U_11246,U_11247,U_11248,U_11249) ),
    inference(definitional_conversion,[status(esa)],[f_2941_2]) ).

cnf(f_2941_4,plain,
    ( hAPP(hAPP(U_11249,U_11250),U_11252) = hAPP(hAPP(U_11249,U_11251),U_11253)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11245,U_11245)),hAPP(hAPP(c_Product__Type_OPair(U_11245,U_11245),U_11252),U_11253)),U_11248))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11244,U_11244)),hAPP(hAPP(c_Product__Type_OPair(U_11244,U_11244),U_11250),U_11251)),U_11247))
    | ~ c_Equiv__Relations_Ocongruent2(U_11244,U_11245,U_11246,U_11247,U_11248,U_11249) ),
    inference(clausify,[status(thm)],[f_2941_3]) ).

fof(f_2942_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_2942_2,plain,
    ! [U_11254] : hAPP(c_Int_Onat,U_11254) = 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_11254)),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_2942_1]) ).

fof(f_2942_3,plain,
    ! [U_11254] : hAPP(c_Int_Onat,U_11254) = 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_11254)),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_2942_2]) ).

cnf(f_2942_4,plain,
    hAPP(c_Int_Onat,U_11254) = 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_11254)),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_2942_3]) ).

fof(f_2943_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_2943_2,plain,
    ! [U_11262,U_11261,U_11260,U_11259,U_11258,U_11257,U_11256,U_11255] :
      ( c_Equiv__Relations_Ocongruent(U_11258,U_11259,U_11260,hAPP(U_11261,U_11262))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11255),U_11262),U_11256))
      | ~ c_Equiv__Relations_Ocongruent2(U_11255,U_11258,U_11259,U_11257,U_11260,U_11261)
      | ~ c_Equiv__Relations_Oequiv(U_11255,U_11256,U_11257) ),
    inference(variable_rename,[status(thm)],[f_2943_1]) ).

fof(f_2943_3,plain,
    ! [U_11255,U_11257,U_11256,U_11258,U_11259,U_11260,U_11261,U_11262] :
      ( c_Equiv__Relations_Ocongruent(U_11258,U_11259,U_11260,hAPP(U_11261,U_11262))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11255),U_11262),U_11256))
      | ~ c_Equiv__Relations_Ocongruent2(U_11255,U_11258,U_11259,U_11257,U_11260,U_11261)
      | ~ c_Equiv__Relations_Oequiv(U_11255,U_11256,U_11257) ),
    inference(definitional_conversion,[status(esa)],[f_2943_2]) ).

cnf(f_2943_4,plain,
    ( c_Equiv__Relations_Ocongruent(U_11258,U_11259,U_11260,hAPP(U_11261,U_11262))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11255),U_11262),U_11256))
    | ~ c_Equiv__Relations_Ocongruent2(U_11255,U_11258,U_11259,U_11257,U_11260,U_11261)
    | ~ c_Equiv__Relations_Oequiv(U_11255,U_11256,U_11257) ),
    inference(clausify,[status(thm)],[f_2943_3]) ).

fof(f_2944_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_2944_2,plain,
    ! [U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265] :
      ( U_11270 = U_11271
      | ? [U_11264] :
          ( ? [U_11263] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11265,U_11265)),hAPP(hAPP(c_Product__Type_OPair(U_11265,U_11265),U_11264),U_11263)),U_11267))
              & hAPP(U_11269,U_11264) = hAPP(U_11269,U_11263)
              & hBOOL(hAPP(hAPP(c_member(U_11265),U_11263),U_11266)) )
          & hBOOL(hAPP(hAPP(c_member(U_11265),U_11264),U_11266)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11265,tc_HOL_Obool)),U_11271),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11265),U_11266),U_11267)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11265,tc_HOL_Obool)),U_11270),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11265),U_11266),U_11267)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11265,tc_fun(U_11268,tc_HOL_Obool)),U_11270),U_11269) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11265,tc_fun(U_11268,tc_HOL_Obool)),U_11271),U_11269)
      | ~ c_Equiv__Relations_Ocongruent(U_11265,tc_fun(U_11268,tc_HOL_Obool),U_11267,U_11269)
      | ~ c_Equiv__Relations_Oequiv(U_11265,U_11266,U_11267) ),
    inference(variable_rename,[status(thm)],[f_2944_1]) ).

fof(f_2944_3,plain,
    ! [U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265] :
      ( U_11270 = U_11271
      | ( ? [U_11263] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11265,U_11265)),hAPP(hAPP(c_Product__Type_OPair(U_11265,U_11265),sK185(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265)),U_11263)),U_11267))
            & hAPP(U_11269,sK185(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265)) = hAPP(U_11269,U_11263)
            & hBOOL(hAPP(hAPP(c_member(U_11265),U_11263),U_11266)) )
        & hBOOL(hAPP(hAPP(c_member(U_11265),sK185(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265)),U_11266)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11265,tc_HOL_Obool)),U_11271),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11265),U_11266),U_11267)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11265,tc_HOL_Obool)),U_11270),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11265),U_11266),U_11267)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11265,tc_fun(U_11268,tc_HOL_Obool)),U_11270),U_11269) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11265,tc_fun(U_11268,tc_HOL_Obool)),U_11271),U_11269)
      | ~ c_Equiv__Relations_Ocongruent(U_11265,tc_fun(U_11268,tc_HOL_Obool),U_11267,U_11269)
      | ~ c_Equiv__Relations_Oequiv(U_11265,U_11266,U_11267) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_11264,sK185(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265))],[f_2944_2]) ).

fof(f_2944_4,plain,
    ! [U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265] :
      ( U_11270 = U_11271
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11265,U_11265)),hAPP(hAPP(c_Product__Type_OPair(U_11265,U_11265),sK185(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265)),sK186(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265))),U_11267))
        & hAPP(U_11269,sK185(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265)) = hAPP(U_11269,sK186(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265))
        & hBOOL(hAPP(hAPP(c_member(U_11265),sK186(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265)),U_11266))
        & hBOOL(hAPP(hAPP(c_member(U_11265),sK185(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265)),U_11266)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11265,tc_HOL_Obool)),U_11271),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11265),U_11266),U_11267)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11265,tc_HOL_Obool)),U_11270),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11265),U_11266),U_11267)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11265,tc_fun(U_11268,tc_HOL_Obool)),U_11270),U_11269) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11265,tc_fun(U_11268,tc_HOL_Obool)),U_11271),U_11269)
      | ~ c_Equiv__Relations_Ocongruent(U_11265,tc_fun(U_11268,tc_HOL_Obool),U_11267,U_11269)
      | ~ c_Equiv__Relations_Oequiv(U_11265,U_11266,U_11267) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_11263,sK186(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265))],[f_2944_3]) ).

fof(f_2944_5,plain,
    ( ! [U_11265,U_11266,U_11267,U_11268,U_11269,U_11270,U_11271] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11265,U_11265)),hAPP(hAPP(c_Product__Type_OPair(U_11265,U_11265),sK185(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265)),sK186(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265))),U_11267))
        | ~ sP833(U_11265,U_11266,U_11267,U_11268,U_11269,U_11270,U_11271) )
    & ! [U_11265,U_11266,U_11267,U_11268,U_11269,U_11270,U_11271] :
        ( hAPP(U_11269,sK185(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265)) = hAPP(U_11269,sK186(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265))
        | ~ sP833(U_11265,U_11266,U_11267,U_11268,U_11269,U_11270,U_11271) )
    & ! [U_11265,U_11266,U_11267,U_11268,U_11269,U_11270,U_11271] :
        ( hBOOL(hAPP(hAPP(c_member(U_11265),sK186(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265)),U_11266))
        | ~ sP833(U_11265,U_11266,U_11267,U_11268,U_11269,U_11270,U_11271) )
    & ! [U_11265,U_11266,U_11267,U_11268,U_11269,U_11270,U_11271] :
        ( hBOOL(hAPP(hAPP(c_member(U_11265),sK185(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265)),U_11266))
        | ~ sP833(U_11265,U_11266,U_11267,U_11268,U_11269,U_11270,U_11271) )
    & ! [U_11265,U_11266,U_11267,U_11268,U_11269,U_11270,U_11271] :
        ( U_11270 = U_11271
        | sP833(U_11265,U_11266,U_11267,U_11268,U_11269,U_11270,U_11271)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11265,tc_HOL_Obool)),U_11271),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11265),U_11266),U_11267)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11265,tc_HOL_Obool)),U_11270),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11265),U_11266),U_11267)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11265,tc_fun(U_11268,tc_HOL_Obool)),U_11270),U_11269) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11265,tc_fun(U_11268,tc_HOL_Obool)),U_11271),U_11269)
        | ~ c_Equiv__Relations_Ocongruent(U_11265,tc_fun(U_11268,tc_HOL_Obool),U_11267,U_11269)
        | ~ c_Equiv__Relations_Oequiv(U_11265,U_11266,U_11267) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP833])],[f_2944_4]) ).

cnf(f_2944_6,plain,
    ( U_11270 = U_11271
    | sP833(U_11265,U_11266,U_11267,U_11268,U_11269,U_11270,U_11271)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11265,tc_HOL_Obool)),U_11271),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11265),U_11266),U_11267)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11265,tc_HOL_Obool)),U_11270),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11265),U_11266),U_11267)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11265,tc_fun(U_11268,tc_HOL_Obool)),U_11270),U_11269) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11265,tc_fun(U_11268,tc_HOL_Obool)),U_11271),U_11269)
    | ~ c_Equiv__Relations_Ocongruent(U_11265,tc_fun(U_11268,tc_HOL_Obool),U_11267,U_11269)
    | ~ c_Equiv__Relations_Oequiv(U_11265,U_11266,U_11267) ),
    inference(clausify,[status(thm)],[f_2944_5]) ).

cnf(f_2944_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11265),sK185(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265)),U_11266))
    | ~ sP833(U_11265,U_11266,U_11267,U_11268,U_11269,U_11270,U_11271) ),
    inference(clausify,[status(thm)],[f_2944_5]) ).

cnf(f_2944_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11265),sK186(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265)),U_11266))
    | ~ sP833(U_11265,U_11266,U_11267,U_11268,U_11269,U_11270,U_11271) ),
    inference(clausify,[status(thm)],[f_2944_5]) ).

cnf(f_2944_9,plain,
    ( hAPP(U_11269,sK185(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265)) = hAPP(U_11269,sK186(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265))
    | ~ sP833(U_11265,U_11266,U_11267,U_11268,U_11269,U_11270,U_11271) ),
    inference(clausify,[status(thm)],[f_2944_5]) ).

cnf(f_2944_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11265,U_11265)),hAPP(hAPP(c_Product__Type_OPair(U_11265,U_11265),sK185(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265)),sK186(U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265))),U_11267))
    | ~ sP833(U_11265,U_11266,U_11267,U_11268,U_11269,U_11270,U_11271) ),
    inference(clausify,[status(thm)],[f_2944_5]) ).

fof(f_2945_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_2945_2,plain,
    ! [U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11280,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11274,tc_fun(U_11280,tc_HOL_Obool)),U_11282),hAPP(hAPP(c_COMBB(tc_fun(U_11277,tc_fun(U_11280,tc_HOL_Obool)),tc_fun(U_11280,tc_HOL_Obool),U_11274),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11277,tc_fun(U_11280,tc_HOL_Obool)),U_11283)),U_11281))),U_11284))
      | ? [U_11273] :
          ( ? [U_11272] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11280,tc_HOL_Obool)),hAPP(hAPP(U_11281,U_11273),U_11272)),U_11284))
              & hBOOL(hAPP(hAPP(c_member(U_11277),U_11272),U_11278)) )
          & hBOOL(hAPP(hAPP(c_member(U_11274),U_11273),U_11275)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11277,tc_HOL_Obool)),U_11283),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11277),U_11278),U_11279)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11274,tc_HOL_Obool)),U_11282),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11274),U_11275),U_11276)))
      | ~ c_Equiv__Relations_Ocongruent2(U_11274,U_11277,tc_fun(U_11280,tc_HOL_Obool),U_11276,U_11279,U_11281)
      | ~ c_Equiv__Relations_Oequiv(U_11277,U_11278,U_11279)
      | ~ c_Equiv__Relations_Oequiv(U_11274,U_11275,U_11276) ),
    inference(variable_rename,[status(thm)],[f_2945_1]) ).

fof(f_2945_3,plain,
    ! [U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11280,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11274,tc_fun(U_11280,tc_HOL_Obool)),U_11282),hAPP(hAPP(c_COMBB(tc_fun(U_11277,tc_fun(U_11280,tc_HOL_Obool)),tc_fun(U_11280,tc_HOL_Obool),U_11274),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11277,tc_fun(U_11280,tc_HOL_Obool)),U_11283)),U_11281))),U_11284))
      | ( ? [U_11272] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11280,tc_HOL_Obool)),hAPP(hAPP(U_11281,sK187(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274)),U_11272)),U_11284))
            & hBOOL(hAPP(hAPP(c_member(U_11277),U_11272),U_11278)) )
        & hBOOL(hAPP(hAPP(c_member(U_11274),sK187(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274)),U_11275)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11277,tc_HOL_Obool)),U_11283),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11277),U_11278),U_11279)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11274,tc_HOL_Obool)),U_11282),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11274),U_11275),U_11276)))
      | ~ c_Equiv__Relations_Ocongruent2(U_11274,U_11277,tc_fun(U_11280,tc_HOL_Obool),U_11276,U_11279,U_11281)
      | ~ c_Equiv__Relations_Oequiv(U_11277,U_11278,U_11279)
      | ~ c_Equiv__Relations_Oequiv(U_11274,U_11275,U_11276) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(U_11273,sK187(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274))],[f_2945_2]) ).

fof(f_2945_4,plain,
    ! [U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11280,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11274,tc_fun(U_11280,tc_HOL_Obool)),U_11282),hAPP(hAPP(c_COMBB(tc_fun(U_11277,tc_fun(U_11280,tc_HOL_Obool)),tc_fun(U_11280,tc_HOL_Obool),U_11274),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11277,tc_fun(U_11280,tc_HOL_Obool)),U_11283)),U_11281))),U_11284))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11280,tc_HOL_Obool)),hAPP(hAPP(U_11281,sK187(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274)),sK188(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274))),U_11284))
        & hBOOL(hAPP(hAPP(c_member(U_11277),sK188(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274)),U_11278))
        & hBOOL(hAPP(hAPP(c_member(U_11274),sK187(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274)),U_11275)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11277,tc_HOL_Obool)),U_11283),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11277),U_11278),U_11279)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11274,tc_HOL_Obool)),U_11282),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11274),U_11275),U_11276)))
      | ~ c_Equiv__Relations_Ocongruent2(U_11274,U_11277,tc_fun(U_11280,tc_HOL_Obool),U_11276,U_11279,U_11281)
      | ~ c_Equiv__Relations_Oequiv(U_11277,U_11278,U_11279)
      | ~ c_Equiv__Relations_Oequiv(U_11274,U_11275,U_11276) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(U_11272,sK188(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274))],[f_2945_3]) ).

fof(f_2945_5,plain,
    ( ! [U_11274,U_11276,U_11275,U_11278,U_11277,U_11279,U_11280,U_11281,U_11282,U_11283,U_11284] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11280,tc_HOL_Obool)),hAPP(hAPP(U_11281,sK187(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274)),sK188(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274))),U_11284))
        | ~ sP834(U_11274,U_11276,U_11275,U_11278,U_11277,U_11279,U_11280,U_11281,U_11282,U_11283,U_11284) )
    & ! [U_11274,U_11276,U_11275,U_11278,U_11277,U_11279,U_11280,U_11281,U_11282,U_11283,U_11284] :
        ( hBOOL(hAPP(hAPP(c_member(U_11277),sK188(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274)),U_11278))
        | ~ sP834(U_11274,U_11276,U_11275,U_11278,U_11277,U_11279,U_11280,U_11281,U_11282,U_11283,U_11284) )
    & ! [U_11274,U_11276,U_11275,U_11278,U_11277,U_11279,U_11280,U_11281,U_11282,U_11283,U_11284] :
        ( hBOOL(hAPP(hAPP(c_member(U_11274),sK187(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274)),U_11275))
        | ~ sP834(U_11274,U_11276,U_11275,U_11278,U_11277,U_11279,U_11280,U_11281,U_11282,U_11283,U_11284) )
    & ! [U_11274,U_11276,U_11275,U_11278,U_11277,U_11279,U_11280,U_11281,U_11282,U_11283,U_11284] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11280,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11274,tc_fun(U_11280,tc_HOL_Obool)),U_11282),hAPP(hAPP(c_COMBB(tc_fun(U_11277,tc_fun(U_11280,tc_HOL_Obool)),tc_fun(U_11280,tc_HOL_Obool),U_11274),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11277,tc_fun(U_11280,tc_HOL_Obool)),U_11283)),U_11281))),U_11284))
        | sP834(U_11274,U_11276,U_11275,U_11278,U_11277,U_11279,U_11280,U_11281,U_11282,U_11283,U_11284)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11277,tc_HOL_Obool)),U_11283),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11277),U_11278),U_11279)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11274,tc_HOL_Obool)),U_11282),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11274),U_11275),U_11276)))
        | ~ c_Equiv__Relations_Ocongruent2(U_11274,U_11277,tc_fun(U_11280,tc_HOL_Obool),U_11276,U_11279,U_11281)
        | ~ c_Equiv__Relations_Oequiv(U_11277,U_11278,U_11279)
        | ~ c_Equiv__Relations_Oequiv(U_11274,U_11275,U_11276) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP834])],[f_2945_4]) ).

cnf(f_2945_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11280,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11274,tc_fun(U_11280,tc_HOL_Obool)),U_11282),hAPP(hAPP(c_COMBB(tc_fun(U_11277,tc_fun(U_11280,tc_HOL_Obool)),tc_fun(U_11280,tc_HOL_Obool),U_11274),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11277,tc_fun(U_11280,tc_HOL_Obool)),U_11283)),U_11281))),U_11284))
    | sP834(U_11274,U_11276,U_11275,U_11278,U_11277,U_11279,U_11280,U_11281,U_11282,U_11283,U_11284)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11277,tc_HOL_Obool)),U_11283),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11277),U_11278),U_11279)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11274,tc_HOL_Obool)),U_11282),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11274),U_11275),U_11276)))
    | ~ c_Equiv__Relations_Ocongruent2(U_11274,U_11277,tc_fun(U_11280,tc_HOL_Obool),U_11276,U_11279,U_11281)
    | ~ c_Equiv__Relations_Oequiv(U_11277,U_11278,U_11279)
    | ~ c_Equiv__Relations_Oequiv(U_11274,U_11275,U_11276) ),
    inference(clausify,[status(thm)],[f_2945_5]) ).

cnf(f_2945_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11274),sK187(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274)),U_11275))
    | ~ sP834(U_11274,U_11276,U_11275,U_11278,U_11277,U_11279,U_11280,U_11281,U_11282,U_11283,U_11284) ),
    inference(clausify,[status(thm)],[f_2945_5]) ).

cnf(f_2945_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11277),sK188(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274)),U_11278))
    | ~ sP834(U_11274,U_11276,U_11275,U_11278,U_11277,U_11279,U_11280,U_11281,U_11282,U_11283,U_11284) ),
    inference(clausify,[status(thm)],[f_2945_5]) ).

cnf(f_2945_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11280,tc_HOL_Obool)),hAPP(hAPP(U_11281,sK187(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274)),sK188(U_11284,U_11283,U_11282,U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275,U_11274))),U_11284))
    | ~ sP834(U_11274,U_11276,U_11275,U_11278,U_11277,U_11279,U_11280,U_11281,U_11282,U_11283,U_11284) ),
    inference(clausify,[status(thm)],[f_2945_5]) ).

fof(f_2946_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_2946_2,plain,
    ! [U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11289,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11286,tc_fun(U_11289,tc_HOL_Obool)),U_11291),U_11290)),U_11292))
      | ? [U_11285] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11289,tc_HOL_Obool)),hAPP(U_11290,U_11285)),U_11292))
          & hBOOL(hAPP(hAPP(c_member(U_11286),U_11285),U_11287)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11286,tc_HOL_Obool)),U_11291),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11286),U_11287),U_11288)))
      | ~ c_Equiv__Relations_Ocongruent(U_11286,tc_fun(U_11289,tc_HOL_Obool),U_11288,U_11290)
      | ~ c_Equiv__Relations_Oequiv(U_11286,U_11287,U_11288) ),
    inference(variable_rename,[status(thm)],[f_2946_1]) ).

fof(f_2946_3,plain,
    ! [U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11289,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11286,tc_fun(U_11289,tc_HOL_Obool)),U_11291),U_11290)),U_11292))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11289,tc_HOL_Obool)),hAPP(U_11290,sK189(U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286))),U_11292))
        & hBOOL(hAPP(hAPP(c_member(U_11286),sK189(U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286)),U_11287)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11286,tc_HOL_Obool)),U_11291),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11286),U_11287),U_11288)))
      | ~ c_Equiv__Relations_Ocongruent(U_11286,tc_fun(U_11289,tc_HOL_Obool),U_11288,U_11290)
      | ~ c_Equiv__Relations_Oequiv(U_11286,U_11287,U_11288) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK189]),skolemize(U_11285,sK189(U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286))],[f_2946_2]) ).

fof(f_2946_4,plain,
    ( ! [U_11291,U_11286,U_11287,U_11289,U_11292,U_11290,U_11288] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11289,tc_HOL_Obool)),hAPP(U_11290,sK189(U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286))),U_11292))
        | ~ sP835(U_11291,U_11286,U_11287,U_11289,U_11292,U_11290,U_11288) )
    & ! [U_11291,U_11286,U_11287,U_11289,U_11292,U_11290,U_11288] :
        ( hBOOL(hAPP(hAPP(c_member(U_11286),sK189(U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286)),U_11287))
        | ~ sP835(U_11291,U_11286,U_11287,U_11289,U_11292,U_11290,U_11288) )
    & ! [U_11291,U_11286,U_11287,U_11289,U_11292,U_11290,U_11288] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11289,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11286,tc_fun(U_11289,tc_HOL_Obool)),U_11291),U_11290)),U_11292))
        | sP835(U_11291,U_11286,U_11287,U_11289,U_11292,U_11290,U_11288)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11286,tc_HOL_Obool)),U_11291),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11286),U_11287),U_11288)))
        | ~ c_Equiv__Relations_Ocongruent(U_11286,tc_fun(U_11289,tc_HOL_Obool),U_11288,U_11290)
        | ~ c_Equiv__Relations_Oequiv(U_11286,U_11287,U_11288) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP835])],[f_2946_3]) ).

cnf(f_2946_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11289,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11286,tc_fun(U_11289,tc_HOL_Obool)),U_11291),U_11290)),U_11292))
    | sP835(U_11291,U_11286,U_11287,U_11289,U_11292,U_11290,U_11288)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11286,tc_HOL_Obool)),U_11291),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11286),U_11287),U_11288)))
    | ~ c_Equiv__Relations_Ocongruent(U_11286,tc_fun(U_11289,tc_HOL_Obool),U_11288,U_11290)
    | ~ c_Equiv__Relations_Oequiv(U_11286,U_11287,U_11288) ),
    inference(clausify,[status(thm)],[f_2946_4]) ).

cnf(f_2946_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11286),sK189(U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286)),U_11287))
    | ~ sP835(U_11291,U_11286,U_11287,U_11289,U_11292,U_11290,U_11288) ),
    inference(clausify,[status(thm)],[f_2946_4]) ).

cnf(f_2946_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11289,tc_HOL_Obool)),hAPP(U_11290,sK189(U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286))),U_11292))
    | ~ sP835(U_11291,U_11286,U_11287,U_11289,U_11292,U_11290,U_11288) ),
    inference(clausify,[status(thm)],[f_2946_4]) ).

fof(f_2947_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_2947_2,plain,
    ! [U_11301,U_11300,U_11299,U_11298,U_11297,U_11296,U_11295] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11295,tc_fun(U_11296,tc_fun(U_11297,tc_HOL_Obool))),U_11298),U_11299),U_11300),U_11301))
        | ! [U_11294] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_11299,U_11294),U_11300),U_11301))
            | ~ hBOOL(hAPP(hAPP(c_member(U_11295),U_11294),U_11298)) ) )
      & ( ? [U_11293] :
            ( hBOOL(hAPP(hAPP(hAPP(U_11299,U_11293),U_11300),U_11301))
            & hBOOL(hAPP(hAPP(c_member(U_11295),U_11293),U_11298)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11295,tc_fun(U_11296,tc_fun(U_11297,tc_HOL_Obool))),U_11298),U_11299),U_11300),U_11301)) ) ),
    inference(variable_rename,[status(thm)],[f_2947_1]) ).

fof(f_2947_3,plain,
    ( ! [U_11315,U_11313,U_11311,U_11309,U_11307,U_11305,U_11303] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11303,tc_fun(U_11305,tc_fun(U_11307,tc_HOL_Obool))),U_11309),U_11311),U_11313),U_11315))
        | ! [U_11294] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_11311,U_11294),U_11313),U_11315))
            | ~ hBOOL(hAPP(hAPP(c_member(U_11303),U_11294),U_11309)) ) )
    & ! [U_11314,U_11312,U_11310,U_11308,U_11306,U_11304,U_11302] :
        ( ? [U_11293] :
            ( hBOOL(hAPP(hAPP(hAPP(U_11310,U_11293),U_11312),U_11314))
            & hBOOL(hAPP(hAPP(c_member(U_11302),U_11293),U_11308)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11302,tc_fun(U_11304,tc_fun(U_11306,tc_HOL_Obool))),U_11308),U_11310),U_11312),U_11314)) ) ),
    inference(miniscope,[status(thm)],[f_2947_2]) ).

fof(f_2947_4,plain,
    ( ! [U_11315,U_11313,U_11311,U_11309,U_11307,U_11305,U_11303] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11303,tc_fun(U_11305,tc_fun(U_11307,tc_HOL_Obool))),U_11309),U_11311),U_11313),U_11315))
        | ! [U_11294] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_11311,U_11294),U_11313),U_11315))
            | ~ hBOOL(hAPP(hAPP(c_member(U_11303),U_11294),U_11309)) ) )
    & ! [U_11314,U_11312,U_11310,U_11308,U_11306,U_11304,U_11302] :
        ( ( hBOOL(hAPP(hAPP(hAPP(U_11310,sK190(U_11314,U_11312,U_11310,U_11308,U_11306,U_11304,U_11302)),U_11312),U_11314))
          & hBOOL(hAPP(hAPP(c_member(U_11302),sK190(U_11314,U_11312,U_11310,U_11308,U_11306,U_11304,U_11302)),U_11308)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11302,tc_fun(U_11304,tc_fun(U_11306,tc_HOL_Obool))),U_11308),U_11310),U_11312),U_11314)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK190]),skolemize(U_11293,sK190(U_11314,U_11312,U_11310,U_11308,U_11306,U_11304,U_11302))],[f_2947_3]) ).

fof(f_2947_5,plain,
    ( ! [U_11306,U_11304,U_11302,U_11310,U_11312,U_11308,U_11314] :
        ( hBOOL(hAPP(hAPP(hAPP(U_11310,sK190(U_11314,U_11312,U_11310,U_11308,U_11306,U_11304,U_11302)),U_11312),U_11314))
        | ~ sP836(U_11306,U_11304,U_11302,U_11310,U_11312,U_11308,U_11314) )
    & ! [U_11306,U_11304,U_11302,U_11310,U_11312,U_11308,U_11314] :
        ( hBOOL(hAPP(hAPP(c_member(U_11302),sK190(U_11314,U_11312,U_11310,U_11308,U_11306,U_11304,U_11302)),U_11308))
        | ~ sP836(U_11306,U_11304,U_11302,U_11310,U_11312,U_11308,U_11314) )
    & ! [U_11294,U_11309,U_11303,U_11305,U_11307,U_11313,U_11311,U_11315] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11303,tc_fun(U_11305,tc_fun(U_11307,tc_HOL_Obool))),U_11309),U_11311),U_11313),U_11315))
        | ~ hBOOL(hAPP(hAPP(hAPP(U_11311,U_11294),U_11313),U_11315))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11303),U_11294),U_11309)) )
    & ! [U_11306,U_11304,U_11302,U_11310,U_11312,U_11308,U_11314] :
        ( sP836(U_11306,U_11304,U_11302,U_11310,U_11312,U_11308,U_11314)
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11302,tc_fun(U_11304,tc_fun(U_11306,tc_HOL_Obool))),U_11308),U_11310),U_11312),U_11314)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP836])],[f_2947_4]) ).

cnf(f_2947_6,plain,
    ( sP836(U_11306,U_11304,U_11302,U_11310,U_11312,U_11308,U_11314)
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11302,tc_fun(U_11304,tc_fun(U_11306,tc_HOL_Obool))),U_11308),U_11310),U_11312),U_11314)) ),
    inference(clausify,[status(thm)],[f_2947_5]) ).

cnf(f_2947_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11303,tc_fun(U_11305,tc_fun(U_11307,tc_HOL_Obool))),U_11309),U_11311),U_11313),U_11315))
    | ~ hBOOL(hAPP(hAPP(hAPP(U_11311,U_11294),U_11313),U_11315))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11303),U_11294),U_11309)) ),
    inference(clausify,[status(thm)],[f_2947_5]) ).

cnf(f_2947_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11302),sK190(U_11314,U_11312,U_11310,U_11308,U_11306,U_11304,U_11302)),U_11308))
    | ~ sP836(U_11306,U_11304,U_11302,U_11310,U_11312,U_11308,U_11314) ),
    inference(clausify,[status(thm)],[f_2947_5]) ).

cnf(f_2947_9,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_11310,sK190(U_11314,U_11312,U_11310,U_11308,U_11306,U_11304,U_11302)),U_11312),U_11314))
    | ~ sP836(U_11306,U_11304,U_11302,U_11310,U_11312,U_11308,U_11314) ),
    inference(clausify,[status(thm)],[f_2947_5]) ).

fof(f_2948_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_2948_2,plain,
    ! [U_11317,U_11316] : c_Relation_OId__on(U_11316,U_11317) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11316,tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool)),U_11317),hAPP(hAPP(c_COMBC(U_11316,tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool),tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_11316,U_11316),tc_fun(tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool),tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool)),U_11316),c_Set_Oinsert(tc_prod(U_11316,U_11316))),hAPP(hAPP(c_COMBS(U_11316,U_11316,tc_prod(U_11316,U_11316)),c_Product__Type_OPair(U_11316,U_11316)),c_COMBI(U_11316)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2948_1]) ).

fof(f_2948_3,plain,
    ! [U_11316,U_11317] : c_Relation_OId__on(U_11316,U_11317) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11316,tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool)),U_11317),hAPP(hAPP(c_COMBC(U_11316,tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool),tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_11316,U_11316),tc_fun(tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool),tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool)),U_11316),c_Set_Oinsert(tc_prod(U_11316,U_11316))),hAPP(hAPP(c_COMBS(U_11316,U_11316,tc_prod(U_11316,U_11316)),c_Product__Type_OPair(U_11316,U_11316)),c_COMBI(U_11316)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2948_2]) ).

cnf(f_2948_4,plain,
    c_Relation_OId__on(U_11316,U_11317) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11316,tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool)),U_11317),hAPP(hAPP(c_COMBC(U_11316,tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool),tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_11316,U_11316),tc_fun(tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool),tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool)),U_11316),c_Set_Oinsert(tc_prod(U_11316,U_11316))),hAPP(hAPP(c_COMBS(U_11316,U_11316,tc_prod(U_11316,U_11316)),c_Product__Type_OPair(U_11316,U_11316)),c_COMBI(U_11316)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11316,U_11316),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2948_3]) ).

fof(f_2949_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_2949_2,plain,
    ! [U_11324,U_11323,U_11322] :
      ( ( c_Relation_Orefl__on(U_11322,U_11323,U_11324)
        | ? [U_11321] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11322,U_11322)),hAPP(hAPP(c_Product__Type_OPair(U_11322,U_11322),U_11321),U_11321)),U_11324))
            & hBOOL(hAPP(hAPP(c_member(U_11322),U_11321),U_11323)) )
        | ? [U_11320] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11322,U_11322,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11322,tc_fun(U_11322,tc_HOL_Obool),tc_fun(U_11322,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11322,tc_HOL_Obool),tc_fun(U_11322,tc_HOL_Obool)),U_11322),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11322)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11322),c_fconj),hAPP(hAPP(c_COMBC(U_11322,tc_fun(U_11322,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11322)),U_11323)))),hAPP(hAPP(c_COMBC(U_11322,tc_fun(U_11322,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11322)),U_11323))),U_11320))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_11322,U_11322)),U_11320),U_11324)) ) )
      & ( ( ! [U_11319] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11322,U_11322)),hAPP(hAPP(c_Product__Type_OPair(U_11322,U_11322),U_11319),U_11319)),U_11324))
              | ~ hBOOL(hAPP(hAPP(c_member(U_11322),U_11319),U_11323)) )
          & ! [U_11318] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11322,U_11322,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11322,tc_fun(U_11322,tc_HOL_Obool),tc_fun(U_11322,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11322,tc_HOL_Obool),tc_fun(U_11322,tc_HOL_Obool)),U_11322),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11322)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11322),c_fconj),hAPP(hAPP(c_COMBC(U_11322,tc_fun(U_11322,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11322)),U_11323)))),hAPP(hAPP(c_COMBC(U_11322,tc_fun(U_11322,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11322)),U_11323))),U_11318))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11322,U_11322)),U_11318),U_11324)) ) )
        | ~ c_Relation_Orefl__on(U_11322,U_11323,U_11324) ) ),
    inference(variable_rename,[status(thm)],[f_2949_1]) ).

fof(f_2949_3,plain,
    ( ! [U_11330,U_11328,U_11326] :
        ( c_Relation_Orefl__on(U_11326,U_11328,U_11330)
        | ? [U_11321] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11326,U_11326)),hAPP(hAPP(c_Product__Type_OPair(U_11326,U_11326),U_11321),U_11321)),U_11330))
            & hBOOL(hAPP(hAPP(c_member(U_11326),U_11321),U_11328)) )
        | ? [U_11320] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11326,U_11326,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11326,tc_fun(U_11326,tc_HOL_Obool),tc_fun(U_11326,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11326,tc_HOL_Obool),tc_fun(U_11326,tc_HOL_Obool)),U_11326),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11326)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11326),c_fconj),hAPP(hAPP(c_COMBC(U_11326,tc_fun(U_11326,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11326)),U_11328)))),hAPP(hAPP(c_COMBC(U_11326,tc_fun(U_11326,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11326)),U_11328))),U_11320))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_11326,U_11326)),U_11320),U_11330)) ) )
    & ! [U_11329,U_11327,U_11325] :
        ( ( ! [U_11319] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11325,U_11325)),hAPP(hAPP(c_Product__Type_OPair(U_11325,U_11325),U_11319),U_11319)),U_11329))
              | ~ hBOOL(hAPP(hAPP(c_member(U_11325),U_11319),U_11327)) )
          & ! [U_11318] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11325,U_11325,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11325,tc_fun(U_11325,tc_HOL_Obool),tc_fun(U_11325,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11325,tc_HOL_Obool),tc_fun(U_11325,tc_HOL_Obool)),U_11325),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11325)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11325),c_fconj),hAPP(hAPP(c_COMBC(U_11325,tc_fun(U_11325,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11325)),U_11327)))),hAPP(hAPP(c_COMBC(U_11325,tc_fun(U_11325,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11325)),U_11327))),U_11318))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11325,U_11325)),U_11318),U_11329)) ) )
        | ~ c_Relation_Orefl__on(U_11325,U_11327,U_11329) ) ),
    inference(miniscope,[status(thm)],[f_2949_2]) ).

fof(f_2949_4,plain,
    ( ! [U_11330,U_11328,U_11326] :
        ( c_Relation_Orefl__on(U_11326,U_11328,U_11330)
        | ? [U_11321] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11326,U_11326)),hAPP(hAPP(c_Product__Type_OPair(U_11326,U_11326),U_11321),U_11321)),U_11330))
            & hBOOL(hAPP(hAPP(c_member(U_11326),U_11321),U_11328)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11326,U_11326,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11326,tc_fun(U_11326,tc_HOL_Obool),tc_fun(U_11326,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11326,tc_HOL_Obool),tc_fun(U_11326,tc_HOL_Obool)),U_11326),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11326)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11326),c_fconj),hAPP(hAPP(c_COMBC(U_11326,tc_fun(U_11326,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11326)),U_11328)))),hAPP(hAPP(c_COMBC(U_11326,tc_fun(U_11326,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11326)),U_11328))),sK191(U_11330,U_11328,U_11326)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_11326,U_11326)),sK191(U_11330,U_11328,U_11326)),U_11330)) ) )
    & ! [U_11329,U_11327,U_11325] :
        ( ( ! [U_11319] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11325,U_11325)),hAPP(hAPP(c_Product__Type_OPair(U_11325,U_11325),U_11319),U_11319)),U_11329))
              | ~ hBOOL(hAPP(hAPP(c_member(U_11325),U_11319),U_11327)) )
          & ! [U_11318] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11325,U_11325,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11325,tc_fun(U_11325,tc_HOL_Obool),tc_fun(U_11325,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11325,tc_HOL_Obool),tc_fun(U_11325,tc_HOL_Obool)),U_11325),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11325)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11325),c_fconj),hAPP(hAPP(c_COMBC(U_11325,tc_fun(U_11325,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11325)),U_11327)))),hAPP(hAPP(c_COMBC(U_11325,tc_fun(U_11325,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11325)),U_11327))),U_11318))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11325,U_11325)),U_11318),U_11329)) ) )
        | ~ c_Relation_Orefl__on(U_11325,U_11327,U_11329) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK191]),skolemize(U_11320,sK191(U_11330,U_11328,U_11326))],[f_2949_3]) ).

fof(f_2949_5,plain,
    ( ! [U_11330,U_11328,U_11326] :
        ( c_Relation_Orefl__on(U_11326,U_11328,U_11330)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11326,U_11326)),hAPP(hAPP(c_Product__Type_OPair(U_11326,U_11326),sK192(U_11330,U_11328,U_11326)),sK192(U_11330,U_11328,U_11326))),U_11330))
          & hBOOL(hAPP(hAPP(c_member(U_11326),sK192(U_11330,U_11328,U_11326)),U_11328)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11326,U_11326,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11326,tc_fun(U_11326,tc_HOL_Obool),tc_fun(U_11326,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11326,tc_HOL_Obool),tc_fun(U_11326,tc_HOL_Obool)),U_11326),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11326)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11326),c_fconj),hAPP(hAPP(c_COMBC(U_11326,tc_fun(U_11326,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11326)),U_11328)))),hAPP(hAPP(c_COMBC(U_11326,tc_fun(U_11326,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11326)),U_11328))),sK191(U_11330,U_11328,U_11326)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_11326,U_11326)),sK191(U_11330,U_11328,U_11326)),U_11330)) ) )
    & ! [U_11329,U_11327,U_11325] :
        ( ( ! [U_11319] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11325,U_11325)),hAPP(hAPP(c_Product__Type_OPair(U_11325,U_11325),U_11319),U_11319)),U_11329))
              | ~ hBOOL(hAPP(hAPP(c_member(U_11325),U_11319),U_11327)) )
          & ! [U_11318] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11325,U_11325,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11325,tc_fun(U_11325,tc_HOL_Obool),tc_fun(U_11325,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11325,tc_HOL_Obool),tc_fun(U_11325,tc_HOL_Obool)),U_11325),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11325)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11325),c_fconj),hAPP(hAPP(c_COMBC(U_11325,tc_fun(U_11325,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11325)),U_11327)))),hAPP(hAPP(c_COMBC(U_11325,tc_fun(U_11325,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11325)),U_11327))),U_11318))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11325,U_11325)),U_11318),U_11329)) ) )
        | ~ c_Relation_Orefl__on(U_11325,U_11327,U_11329) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK192]),skolemize(U_11321,sK192(U_11330,U_11328,U_11326))],[f_2949_4]) ).

fof(f_2949_6,plain,
    ( ! [U_11326,U_11330,U_11328] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11326,U_11326)),hAPP(hAPP(c_Product__Type_OPair(U_11326,U_11326),sK192(U_11330,U_11328,U_11326)),sK192(U_11330,U_11328,U_11326))),U_11330))
        | ~ sP839(U_11326,U_11330,U_11328) )
    & ! [U_11326,U_11330,U_11328] :
        ( hBOOL(hAPP(hAPP(c_member(U_11326),sK192(U_11330,U_11328,U_11326)),U_11328))
        | ~ sP839(U_11326,U_11330,U_11328) )
    & ! [U_11326,U_11330,U_11328] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11326,U_11326,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11326,tc_fun(U_11326,tc_HOL_Obool),tc_fun(U_11326,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11326,tc_HOL_Obool),tc_fun(U_11326,tc_HOL_Obool)),U_11326),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11326)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11326),c_fconj),hAPP(hAPP(c_COMBC(U_11326,tc_fun(U_11326,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11326)),U_11328)))),hAPP(hAPP(c_COMBC(U_11326,tc_fun(U_11326,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11326)),U_11328))),sK191(U_11330,U_11328,U_11326)))
        | ~ sP838(U_11326,U_11330,U_11328) )
    & ! [U_11326,U_11330,U_11328] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11326,U_11326)),sK191(U_11330,U_11328,U_11326)),U_11330))
        | ~ sP838(U_11326,U_11330,U_11328) )
    & ! [U_11319,U_11318,U_11325,U_11329,U_11327] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11325,U_11325)),hAPP(hAPP(c_Product__Type_OPair(U_11325,U_11325),U_11319),U_11319)),U_11329))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11325),U_11319),U_11327))
        | ~ sP837(U_11319,U_11318,U_11325,U_11329,U_11327) )
    & ! [U_11319,U_11318,U_11325,U_11329,U_11327] :
        ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11325,U_11325,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11325,tc_fun(U_11325,tc_HOL_Obool),tc_fun(U_11325,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11325,tc_HOL_Obool),tc_fun(U_11325,tc_HOL_Obool)),U_11325),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11325)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11325),c_fconj),hAPP(hAPP(c_COMBC(U_11325,tc_fun(U_11325,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11325)),U_11327)))),hAPP(hAPP(c_COMBC(U_11325,tc_fun(U_11325,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11325)),U_11327))),U_11318))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11325,U_11325)),U_11318),U_11329))
        | ~ sP837(U_11319,U_11318,U_11325,U_11329,U_11327) )
    & ! [U_11326,U_11330,U_11328] :
        ( c_Relation_Orefl__on(U_11326,U_11328,U_11330)
        | sP839(U_11326,U_11330,U_11328)
        | sP838(U_11326,U_11330,U_11328) )
    & ! [U_11319,U_11318,U_11325,U_11329,U_11327] :
        ( sP837(U_11319,U_11318,U_11325,U_11329,U_11327)
        | ~ c_Relation_Orefl__on(U_11325,U_11327,U_11329) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP837,sP838,sP839])],[f_2949_5]) ).

cnf(f_2949_7,plain,
    ( sP837(U_11319,U_11318,U_11325,U_11329,U_11327)
    | ~ c_Relation_Orefl__on(U_11325,U_11327,U_11329) ),
    inference(clausify,[status(thm)],[f_2949_6]) ).

cnf(f_2949_8,plain,
    ( c_Relation_Orefl__on(U_11326,U_11328,U_11330)
    | sP839(U_11326,U_11330,U_11328)
    | sP838(U_11326,U_11330,U_11328) ),
    inference(clausify,[status(thm)],[f_2949_6]) ).

cnf(f_2949_9,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11325,U_11325,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11325,tc_fun(U_11325,tc_HOL_Obool),tc_fun(U_11325,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11325,tc_HOL_Obool),tc_fun(U_11325,tc_HOL_Obool)),U_11325),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11325)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11325),c_fconj),hAPP(hAPP(c_COMBC(U_11325,tc_fun(U_11325,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11325)),U_11327)))),hAPP(hAPP(c_COMBC(U_11325,tc_fun(U_11325,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11325)),U_11327))),U_11318))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11325,U_11325)),U_11318),U_11329))
    | ~ sP837(U_11319,U_11318,U_11325,U_11329,U_11327) ),
    inference(clausify,[status(thm)],[f_2949_6]) ).

cnf(f_2949_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11325,U_11325)),hAPP(hAPP(c_Product__Type_OPair(U_11325,U_11325),U_11319),U_11319)),U_11329))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11325),U_11319),U_11327))
    | ~ sP837(U_11319,U_11318,U_11325,U_11329,U_11327) ),
    inference(clausify,[status(thm)],[f_2949_6]) ).

cnf(f_2949_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11326,U_11326)),sK191(U_11330,U_11328,U_11326)),U_11330))
    | ~ sP838(U_11326,U_11330,U_11328) ),
    inference(clausify,[status(thm)],[f_2949_6]) ).

cnf(f_2949_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11326,U_11326,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11326,tc_fun(U_11326,tc_HOL_Obool),tc_fun(U_11326,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11326,tc_HOL_Obool),tc_fun(U_11326,tc_HOL_Obool)),U_11326),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11326)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11326),c_fconj),hAPP(hAPP(c_COMBC(U_11326,tc_fun(U_11326,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11326)),U_11328)))),hAPP(hAPP(c_COMBC(U_11326,tc_fun(U_11326,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11326)),U_11328))),sK191(U_11330,U_11328,U_11326)))
    | ~ sP838(U_11326,U_11330,U_11328) ),
    inference(clausify,[status(thm)],[f_2949_6]) ).

cnf(f_2949_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11326),sK192(U_11330,U_11328,U_11326)),U_11328))
    | ~ sP839(U_11326,U_11330,U_11328) ),
    inference(clausify,[status(thm)],[f_2949_6]) ).

cnf(f_2949_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11326,U_11326)),hAPP(hAPP(c_Product__Type_OPair(U_11326,U_11326),sK192(U_11330,U_11328,U_11326)),sK192(U_11330,U_11328,U_11326))),U_11330))
    | ~ sP839(U_11326,U_11330,U_11328) ),
    inference(clausify,[status(thm)],[f_2949_6]) ).

fof(f_2950_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_2950_2,plain,
    ! [U_11335,U_11334,U_11333,U_11332,U_11331] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11331,U_11332,c_Groups_Otimes__class_Otimes(U_11331)),U_11335),c_Groups_Oone__class_Oone(U_11331)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11332,tc_HOL_Obool)),U_11333),U_11334)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11331),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11331,U_11332,c_Groups_Otimes__class_Otimes(U_11331)),U_11335),c_Groups_Oone__class_Oone(U_11331)),U_11333)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11331,U_11332,c_Groups_Otimes__class_Otimes(U_11331)),U_11335),c_Groups_Oone__class_Oone(U_11331)),U_11334))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11332,tc_HOL_Obool)),U_11333),U_11334) != c_Orderings_Obot__class_Obot(tc_fun(U_11332,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11332),U_11334))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11332),U_11333))
      | ~ class_Groups_Ocomm__monoid__mult(U_11331) ),
    inference(variable_rename,[status(thm)],[f_2950_1]) ).

fof(f_2950_3,plain,
    ! [U_11333,U_11334,U_11331,U_11335,U_11332] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11331,U_11332,c_Groups_Otimes__class_Otimes(U_11331)),U_11335),c_Groups_Oone__class_Oone(U_11331)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11332,tc_HOL_Obool)),U_11333),U_11334)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11331),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11331,U_11332,c_Groups_Otimes__class_Otimes(U_11331)),U_11335),c_Groups_Oone__class_Oone(U_11331)),U_11333)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11331,U_11332,c_Groups_Otimes__class_Otimes(U_11331)),U_11335),c_Groups_Oone__class_Oone(U_11331)),U_11334))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11332,tc_HOL_Obool)),U_11333),U_11334) != c_Orderings_Obot__class_Obot(tc_fun(U_11332,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11332),U_11334))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11332),U_11333))
      | ~ class_Groups_Ocomm__monoid__mult(U_11331) ),
    inference(definitional_conversion,[status(esa)],[f_2950_2]) ).

cnf(f_2950_4,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11331,U_11332,c_Groups_Otimes__class_Otimes(U_11331)),U_11335),c_Groups_Oone__class_Oone(U_11331)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11332,tc_HOL_Obool)),U_11333),U_11334)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11331),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11331,U_11332,c_Groups_Otimes__class_Otimes(U_11331)),U_11335),c_Groups_Oone__class_Oone(U_11331)),U_11333)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11331,U_11332,c_Groups_Otimes__class_Otimes(U_11331)),U_11335),c_Groups_Oone__class_Oone(U_11331)),U_11334))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11332,tc_HOL_Obool)),U_11333),U_11334) != c_Orderings_Obot__class_Obot(tc_fun(U_11332,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11332),U_11334))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11332),U_11333))
    | ~ class_Groups_Ocomm__monoid__mult(U_11331) ),
    inference(clausify,[status(thm)],[f_2950_3]) ).

fof(f_2951_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_2951_2,plain,
    ! [U_11340,U_11339,U_11338,U_11337,U_11336] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11336,U_11337,U_11338),U_11339),U_11340),c_Orderings_Obot__class_Obot(tc_fun(U_11337,tc_HOL_Obool))) = U_11340,
    inference(variable_rename,[status(thm)],[f_2951_1]) ).

fof(f_2951_3,plain,
    ! [U_11339,U_11336,U_11340,U_11337,U_11338] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11336,U_11337,U_11338),U_11339),U_11340),c_Orderings_Obot__class_Obot(tc_fun(U_11337,tc_HOL_Obool))) = U_11340,
    inference(definitional_conversion,[status(esa)],[f_2951_2]) ).

cnf(f_2951_4,plain,
    hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11336,U_11337,U_11338),U_11339),U_11340),c_Orderings_Obot__class_Obot(tc_fun(U_11337,tc_HOL_Obool))) = U_11340,
    inference(clausify,[status(thm)],[f_2951_3]) ).

fof(f_2952_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_2952_2,plain,
    ! [U_11342,U_11341] : c_Relation_Orefl__on(U_11341,U_11342,c_Relation_OId__on(U_11341,U_11342)),
    inference(variable_rename,[status(thm)],[f_2952_1]) ).

fof(f_2952_3,plain,
    ! [U_11342,U_11341] : c_Relation_Orefl__on(U_11341,U_11342,c_Relation_OId__on(U_11341,U_11342)),
    inference(definitional_conversion,[status(esa)],[f_2952_2]) ).

cnf(f_2952_4,plain,
    c_Relation_Orefl__on(U_11341,U_11342,c_Relation_OId__on(U_11341,U_11342)),
    inference(clausify,[status(thm)],[f_2952_3]) ).

fof(f_2953_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_2953_2,plain,
    ! [U_11344,U_11343] : c_Relation_OId__on(U_11343,U_11344) = hAPP(c_Product__Type_Oprod_Oprod__case(U_11343,U_11343,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_11343,tc_HOL_Obool,tc_fun(U_11343,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11343,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_11343,tc_HOL_Obool)),U_11343),c_COMBC(U_11343,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11343,tc_HOL_Obool),tc_fun(U_11343,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11343),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11343),c_fconj)),c_fequal))),U_11344)),
    inference(variable_rename,[status(thm)],[f_2953_1]) ).

fof(f_2953_3,plain,
    ! [U_11343,U_11344] : c_Relation_OId__on(U_11343,U_11344) = hAPP(c_Product__Type_Oprod_Oprod__case(U_11343,U_11343,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_11343,tc_HOL_Obool,tc_fun(U_11343,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11343,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_11343,tc_HOL_Obool)),U_11343),c_COMBC(U_11343,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11343,tc_HOL_Obool),tc_fun(U_11343,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11343),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11343),c_fconj)),c_fequal))),U_11344)),
    inference(definitional_conversion,[status(esa)],[f_2953_2]) ).

cnf(f_2953_4,plain,
    c_Relation_OId__on(U_11343,U_11344) = hAPP(c_Product__Type_Oprod_Oprod__case(U_11343,U_11343,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_11343,tc_HOL_Obool,tc_fun(U_11343,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11343,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_11343,tc_HOL_Obool)),U_11343),c_COMBC(U_11343,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11343,tc_HOL_Obool),tc_fun(U_11343,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11343),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11343),c_fconj)),c_fequal))),U_11344)),
    inference(clausify,[status(thm)],[f_2953_3]) ).

fof(f_2954_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_2954_2,plain,
    ! [U_11351,U_11350,U_11349,U_11348,U_11347,U_11346,U_11345] :
      ( hAPP(U_11350,U_11351) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11345,U_11346,U_11347),U_11349),U_11348),U_11351)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11346),U_11351))
      | ~ c_Finite__Set_Ofolding__image__simple(U_11345,U_11346,U_11347,U_11348,U_11349,U_11350) ),
    inference(variable_rename,[status(thm)],[f_2954_1]) ).

fof(f_2954_3,plain,
    ! [U_11345,U_11346,U_11347,U_11348,U_11349,U_11350,U_11351] :
      ( hAPP(U_11350,U_11351) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11345,U_11346,U_11347),U_11349),U_11348),U_11351)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11346),U_11351))
      | ~ c_Finite__Set_Ofolding__image__simple(U_11345,U_11346,U_11347,U_11348,U_11349,U_11350) ),
    inference(definitional_conversion,[status(esa)],[f_2954_2]) ).

cnf(f_2954_4,plain,
    ( hAPP(U_11350,U_11351) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11345,U_11346,U_11347),U_11349),U_11348),U_11351)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11346),U_11351))
    | ~ c_Finite__Set_Ofolding__image__simple(U_11345,U_11346,U_11347,U_11348,U_11349,U_11350) ),
    inference(clausify,[status(thm)],[f_2954_3]) ).

fof(f_2955_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_2955_2,plain,
    ! [U_11352] : c_Relation_Orefl__on(U_11352,c_Orderings_Obot__class_Obot(tc_fun(U_11352,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11352,U_11352),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2955_1]) ).

fof(f_2955_3,plain,
    ! [U_11352] : c_Relation_Orefl__on(U_11352,c_Orderings_Obot__class_Obot(tc_fun(U_11352,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11352,U_11352),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2955_2]) ).

cnf(f_2955_4,plain,
    c_Relation_Orefl__on(U_11352,c_Orderings_Obot__class_Obot(tc_fun(U_11352,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11352,U_11352),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2955_3]) ).

fof(f_2956_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_2956_2,plain,
    ! [U_11357,U_11356,U_11355,U_11354,U_11353] :
      ( c_Relation_Orefl__on(U_11353,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11353,tc_HOL_Obool)),U_11354),U_11356),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11353,U_11353),tc_HOL_Obool)),U_11355),U_11357))
      | ~ c_Relation_Orefl__on(U_11353,U_11356,U_11357)
      | ~ c_Relation_Orefl__on(U_11353,U_11354,U_11355) ),
    inference(variable_rename,[status(thm)],[f_2956_1]) ).

fof(f_2956_3,plain,
    ! [U_11353,U_11354,U_11355,U_11356,U_11357] :
      ( c_Relation_Orefl__on(U_11353,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11353,tc_HOL_Obool)),U_11354),U_11356),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11353,U_11353),tc_HOL_Obool)),U_11355),U_11357))
      | ~ c_Relation_Orefl__on(U_11353,U_11356,U_11357)
      | ~ c_Relation_Orefl__on(U_11353,U_11354,U_11355) ),
    inference(definitional_conversion,[status(esa)],[f_2956_2]) ).

cnf(f_2956_4,plain,
    ( c_Relation_Orefl__on(U_11353,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11353,tc_HOL_Obool)),U_11354),U_11356),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11353,U_11353),tc_HOL_Obool)),U_11355),U_11357))
    | ~ c_Relation_Orefl__on(U_11353,U_11356,U_11357)
    | ~ c_Relation_Orefl__on(U_11353,U_11354,U_11355) ),
    inference(clausify,[status(thm)],[f_2956_3]) ).

fof(f_2957_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_2957_2,plain,
    ! [U_11362,U_11361,U_11360,U_11359,U_11358] :
      ( c_Relation_Orefl__on(U_11358,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11358,tc_HOL_Obool)),U_11359),U_11361),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool)),U_11360),U_11362))
      | ~ c_Relation_Orefl__on(U_11358,U_11361,U_11362)
      | ~ c_Relation_Orefl__on(U_11358,U_11359,U_11360) ),
    inference(variable_rename,[status(thm)],[f_2957_1]) ).

fof(f_2957_3,plain,
    ! [U_11358,U_11359,U_11360,U_11361,U_11362] :
      ( c_Relation_Orefl__on(U_11358,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11358,tc_HOL_Obool)),U_11359),U_11361),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool)),U_11360),U_11362))
      | ~ c_Relation_Orefl__on(U_11358,U_11361,U_11362)
      | ~ c_Relation_Orefl__on(U_11358,U_11359,U_11360) ),
    inference(definitional_conversion,[status(esa)],[f_2957_2]) ).

cnf(f_2957_4,plain,
    ( c_Relation_Orefl__on(U_11358,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11358,tc_HOL_Obool)),U_11359),U_11361),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11358,U_11358),tc_HOL_Obool)),U_11360),U_11362))
    | ~ c_Relation_Orefl__on(U_11358,U_11361,U_11362)
    | ~ c_Relation_Orefl__on(U_11358,U_11359,U_11360) ),
    inference(clausify,[status(thm)],[f_2957_3]) ).

fof(f_2958_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_2958_2,plain,
    ! [U_11363] : c_Relation_OId__on(U_11363,c_Orderings_Obot__class_Obot(tc_fun(U_11363,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11363,U_11363),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2958_1]) ).

fof(f_2958_3,plain,
    ! [U_11363] : c_Relation_OId__on(U_11363,c_Orderings_Obot__class_Obot(tc_fun(U_11363,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11363,U_11363),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2958_2]) ).

cnf(f_2958_4,plain,
    c_Relation_OId__on(U_11363,c_Orderings_Obot__class_Obot(tc_fun(U_11363,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11363,U_11363),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2958_3]) ).

fof(f_2959_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_2959_2,plain,
    ! [U_11366,U_11365,U_11364] : hAPP(c_Relation_OImage(U_11364,U_11364,c_Relation_OId__on(U_11364,U_11365)),U_11366) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11364,tc_HOL_Obool)),U_11365),U_11366),
    inference(variable_rename,[status(thm)],[f_2959_1]) ).

fof(f_2959_3,plain,
    ! [U_11364,U_11365,U_11366] : hAPP(c_Relation_OImage(U_11364,U_11364,c_Relation_OId__on(U_11364,U_11365)),U_11366) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11364,tc_HOL_Obool)),U_11365),U_11366),
    inference(definitional_conversion,[status(esa)],[f_2959_2]) ).

cnf(f_2959_4,plain,
    hAPP(c_Relation_OImage(U_11364,U_11364,c_Relation_OId__on(U_11364,U_11365)),U_11366) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11364,tc_HOL_Obool)),U_11365),U_11366),
    inference(clausify,[status(thm)],[f_2959_3]) ).

fof(f_2960_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_2960_2,plain,
    ! [U_11371,U_11370,U_11369,U_11368,U_11367] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11367,U_11368,c_Groups_Otimes__class_Otimes(U_11367)),hAPP(hAPP(c_COMBS(U_11368,U_11367,U_11367),hAPP(hAPP(c_COMBB(U_11367,tc_fun(U_11367,U_11367),U_11368),c_Groups_Otimes__class_Otimes(U_11367)),U_11370)),U_11371)),c_Groups_Oone__class_Oone(U_11367)),U_11369) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11367),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11367,U_11368,c_Groups_Otimes__class_Otimes(U_11367)),U_11370),c_Groups_Oone__class_Oone(U_11367)),U_11369)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11367,U_11368,c_Groups_Otimes__class_Otimes(U_11367)),U_11371),c_Groups_Oone__class_Oone(U_11367)),U_11369))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11368),U_11369))
      | ~ class_Groups_Ocomm__monoid__mult(U_11367) ),
    inference(variable_rename,[status(thm)],[f_2960_1]) ).

fof(f_2960_3,plain,
    ! [U_11367,U_11368,U_11369,U_11370,U_11371] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11367,U_11368,c_Groups_Otimes__class_Otimes(U_11367)),hAPP(hAPP(c_COMBS(U_11368,U_11367,U_11367),hAPP(hAPP(c_COMBB(U_11367,tc_fun(U_11367,U_11367),U_11368),c_Groups_Otimes__class_Otimes(U_11367)),U_11370)),U_11371)),c_Groups_Oone__class_Oone(U_11367)),U_11369) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11367),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11367,U_11368,c_Groups_Otimes__class_Otimes(U_11367)),U_11370),c_Groups_Oone__class_Oone(U_11367)),U_11369)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11367,U_11368,c_Groups_Otimes__class_Otimes(U_11367)),U_11371),c_Groups_Oone__class_Oone(U_11367)),U_11369))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11368),U_11369))
      | ~ class_Groups_Ocomm__monoid__mult(U_11367) ),
    inference(definitional_conversion,[status(esa)],[f_2960_2]) ).

cnf(f_2960_4,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11367,U_11368,c_Groups_Otimes__class_Otimes(U_11367)),hAPP(hAPP(c_COMBS(U_11368,U_11367,U_11367),hAPP(hAPP(c_COMBB(U_11367,tc_fun(U_11367,U_11367),U_11368),c_Groups_Otimes__class_Otimes(U_11367)),U_11370)),U_11371)),c_Groups_Oone__class_Oone(U_11367)),U_11369) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11367),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11367,U_11368,c_Groups_Otimes__class_Otimes(U_11367)),U_11370),c_Groups_Oone__class_Oone(U_11367)),U_11369)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11367,U_11368,c_Groups_Otimes__class_Otimes(U_11367)),U_11371),c_Groups_Oone__class_Oone(U_11367)),U_11369))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11368),U_11369))
    | ~ class_Groups_Ocomm__monoid__mult(U_11367) ),
    inference(clausify,[status(thm)],[f_2960_3]) ).

fof(f_2961_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_2961_2,plain,
    ! [U_11376,U_11375,U_11374,U_11373,U_11372] :
      ( hBOOL(hAPP(hAPP(c_member(U_11372),U_11376),U_11373))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11372,U_11372)),hAPP(hAPP(c_Product__Type_OPair(U_11372,U_11372),U_11375),U_11376)),U_11374))
      | ~ c_Relation_Orefl__on(U_11372,U_11373,U_11374) ),
    inference(variable_rename,[status(thm)],[f_2961_1]) ).

fof(f_2961_3,plain,
    ! [U_11373,U_11372,U_11374,U_11375,U_11376] :
      ( hBOOL(hAPP(hAPP(c_member(U_11372),U_11376),U_11373))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11372,U_11372)),hAPP(hAPP(c_Product__Type_OPair(U_11372,U_11372),U_11375),U_11376)),U_11374))
      | ~ c_Relation_Orefl__on(U_11372,U_11373,U_11374) ),
    inference(definitional_conversion,[status(esa)],[f_2961_2]) ).

cnf(f_2961_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11372),U_11376),U_11373))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11372,U_11372)),hAPP(hAPP(c_Product__Type_OPair(U_11372,U_11372),U_11375),U_11376)),U_11374))
    | ~ c_Relation_Orefl__on(U_11372,U_11373,U_11374) ),
    inference(clausify,[status(thm)],[f_2961_3]) ).

fof(f_2962_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_2962_2,plain,
    ! [U_11381,U_11380,U_11379,U_11378,U_11377] :
      ( hBOOL(hAPP(hAPP(c_member(U_11377),U_11380),U_11378))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11377,U_11377)),hAPP(hAPP(c_Product__Type_OPair(U_11377,U_11377),U_11380),U_11381)),U_11379))
      | ~ c_Relation_Orefl__on(U_11377,U_11378,U_11379) ),
    inference(variable_rename,[status(thm)],[f_2962_1]) ).

fof(f_2962_3,plain,
    ! [U_11377,U_11378,U_11379,U_11380,U_11381] :
      ( hBOOL(hAPP(hAPP(c_member(U_11377),U_11380),U_11378))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11377,U_11377)),hAPP(hAPP(c_Product__Type_OPair(U_11377,U_11377),U_11380),U_11381)),U_11379))
      | ~ c_Relation_Orefl__on(U_11377,U_11378,U_11379) ),
    inference(definitional_conversion,[status(esa)],[f_2962_2]) ).

cnf(f_2962_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11377),U_11380),U_11378))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11377,U_11377)),hAPP(hAPP(c_Product__Type_OPair(U_11377,U_11377),U_11380),U_11381)),U_11379))
    | ~ c_Relation_Orefl__on(U_11377,U_11378,U_11379) ),
    inference(clausify,[status(thm)],[f_2962_3]) ).

fof(f_2963_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_2963_2,plain,
    ! [U_11385,U_11384,U_11383,U_11382] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11382,U_11382)),hAPP(hAPP(c_Product__Type_OPair(U_11382,U_11382),U_11385),U_11385)),U_11384))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11382),U_11385),U_11383))
      | ~ c_Relation_Orefl__on(U_11382,U_11383,U_11384) ),
    inference(variable_rename,[status(thm)],[f_2963_1]) ).

fof(f_2963_3,plain,
    ! [U_11382,U_11383,U_11384,U_11385] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11382,U_11382)),hAPP(hAPP(c_Product__Type_OPair(U_11382,U_11382),U_11385),U_11385)),U_11384))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11382),U_11385),U_11383))
      | ~ c_Relation_Orefl__on(U_11382,U_11383,U_11384) ),
    inference(definitional_conversion,[status(esa)],[f_2963_2]) ).

cnf(f_2963_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11382,U_11382)),hAPP(hAPP(c_Product__Type_OPair(U_11382,U_11382),U_11385),U_11385)),U_11384))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11382),U_11385),U_11383))
    | ~ c_Relation_Orefl__on(U_11382,U_11383,U_11384) ),
    inference(clausify,[status(thm)],[f_2963_3]) ).

fof(f_2964_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_2964_2,plain,
    ! [U_11391,U_11390,U_11389,U_11388,U_11387,U_11386] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11386,U_11387,c_Groups_Otimes__class_Otimes(U_11386)),U_11390),U_11391),hAPP(hAPP(c_Set_Oinsert(U_11387),U_11389),U_11388)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11386),hAPP(U_11390,U_11389)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11386,U_11387,c_Groups_Otimes__class_Otimes(U_11386)),U_11390),U_11391),U_11388))
      | hBOOL(hAPP(hAPP(c_member(U_11387),U_11389),U_11388))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11387),U_11388))
      | ~ class_Groups_Oab__semigroup__mult(U_11386) ),
    inference(variable_rename,[status(thm)],[f_2964_1]) ).

fof(f_2964_3,plain,
    ! [U_11386,U_11387,U_11388,U_11389,U_11390,U_11391] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11386,U_11387,c_Groups_Otimes__class_Otimes(U_11386)),U_11390),U_11391),hAPP(hAPP(c_Set_Oinsert(U_11387),U_11389),U_11388)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11386),hAPP(U_11390,U_11389)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11386,U_11387,c_Groups_Otimes__class_Otimes(U_11386)),U_11390),U_11391),U_11388))
      | hBOOL(hAPP(hAPP(c_member(U_11387),U_11389),U_11388))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11387),U_11388))
      | ~ class_Groups_Oab__semigroup__mult(U_11386) ),
    inference(definitional_conversion,[status(esa)],[f_2964_2]) ).

cnf(f_2964_4,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11386,U_11387,c_Groups_Otimes__class_Otimes(U_11386)),U_11390),U_11391),hAPP(hAPP(c_Set_Oinsert(U_11387),U_11389),U_11388)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11386),hAPP(U_11390,U_11389)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11386,U_11387,c_Groups_Otimes__class_Otimes(U_11386)),U_11390),U_11391),U_11388))
    | hBOOL(hAPP(hAPP(c_member(U_11387),U_11389),U_11388))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11387),U_11388))
    | ~ class_Groups_Oab__semigroup__mult(U_11386) ),
    inference(clausify,[status(thm)],[f_2964_3]) ).

fof(f_2965_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_2965_2,plain,
    ! [U_11395,U_11394,U_11393,U_11392] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11393,U_11392),U_11395),U_11394) = c_Groups_Oone__class_Oone(U_11392)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11393),U_11394)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11393,U_11392),U_11395),U_11394) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11392,U_11393,c_Groups_Otimes__class_Otimes(U_11392)),U_11395),c_Groups_Oone__class_Oone(U_11392)),U_11394)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11393),U_11394)) ) )
      | ~ class_Groups_Ocomm__monoid__mult(U_11392) ),
    inference(variable_rename,[status(thm)],[f_2965_1]) ).

fof(f_2965_3,plain,
    ( ! [U_11392,U_11393,U_11394,U_11395] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11393,U_11392),U_11395),U_11394) = c_Groups_Oone__class_Oone(U_11392)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11393),U_11394))
        | ~ sP840(U_11392,U_11393,U_11394,U_11395) )
    & ! [U_11392,U_11393,U_11394,U_11395] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11393,U_11392),U_11395),U_11394) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11392,U_11393,c_Groups_Otimes__class_Otimes(U_11392)),U_11395),c_Groups_Oone__class_Oone(U_11392)),U_11394)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11393),U_11394))
        | ~ sP840(U_11392,U_11393,U_11394,U_11395) )
    & ! [U_11392,U_11393,U_11394,U_11395] :
        ( sP840(U_11392,U_11393,U_11394,U_11395)
        | ~ class_Groups_Ocomm__monoid__mult(U_11392) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP840])],[f_2965_2]) ).

cnf(f_2965_4,plain,
    ( sP840(U_11392,U_11393,U_11394,U_11395)
    | ~ class_Groups_Ocomm__monoid__mult(U_11392) ),
    inference(clausify,[status(thm)],[f_2965_3]) ).

cnf(f_2965_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11393,U_11392),U_11395),U_11394) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11392,U_11393,c_Groups_Otimes__class_Otimes(U_11392)),U_11395),c_Groups_Oone__class_Oone(U_11392)),U_11394)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11393),U_11394))
    | ~ sP840(U_11392,U_11393,U_11394,U_11395) ),
    inference(clausify,[status(thm)],[f_2965_3]) ).

cnf(f_2965_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11393,U_11392),U_11395),U_11394) = c_Groups_Oone__class_Oone(U_11392)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11393),U_11394))
    | ~ sP840(U_11392,U_11393,U_11394,U_11395) ),
    inference(clausify,[status(thm)],[f_2965_3]) ).

fof(f_2966_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_2966_2,plain,
    ! [U_11399,U_11398,U_11397,U_11396] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11397,U_11396),U_11399),U_11398) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11396,U_11397,c_Groups_Otimes__class_Otimes(U_11396)),U_11399),c_Groups_Oone__class_Oone(U_11396)),U_11398)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11397),U_11398))
      | ~ class_Groups_Ocomm__monoid__mult(U_11396) ),
    inference(variable_rename,[status(thm)],[f_2966_1]) ).

fof(f_2966_3,plain,
    ! [U_11399,U_11398,U_11396,U_11397] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11397,U_11396),U_11399),U_11398) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11396,U_11397,c_Groups_Otimes__class_Otimes(U_11396)),U_11399),c_Groups_Oone__class_Oone(U_11396)),U_11398)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11397),U_11398))
      | ~ class_Groups_Ocomm__monoid__mult(U_11396) ),
    inference(definitional_conversion,[status(esa)],[f_2966_2]) ).

cnf(f_2966_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11397,U_11396),U_11399),U_11398) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11396,U_11397,c_Groups_Otimes__class_Otimes(U_11396)),U_11399),c_Groups_Oone__class_Oone(U_11396)),U_11398)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11397),U_11398))
    | ~ class_Groups_Ocomm__monoid__mult(U_11396) ),
    inference(clausify,[status(thm)],[f_2966_3]) ).

fof(f_2967_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_2967_2,plain,
    ! [U_11403,U_11402,U_11401,U_11400] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11400,U_11400)),hAPP(hAPP(c_Product__Type_OPair(U_11400,U_11400),U_11401),U_11402)),c_Relation_OId__on(U_11400,U_11403)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11400),U_11401),U_11403))
        | U_11401 != U_11402 )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_11400),U_11401),U_11403))
          & U_11401 = U_11402 )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11400,U_11400)),hAPP(hAPP(c_Product__Type_OPair(U_11400,U_11400),U_11401),U_11402)),c_Relation_OId__on(U_11400,U_11403))) ) ),
    inference(variable_rename,[status(thm)],[f_2967_1]) ).

fof(f_2967_3,plain,
    ( ! [U_11411,U_11409,U_11407,U_11405] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11405,U_11405)),hAPP(hAPP(c_Product__Type_OPair(U_11405,U_11405),U_11407),U_11409)),c_Relation_OId__on(U_11405,U_11411)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11405),U_11407),U_11411))
        | U_11407 != U_11409 )
    & ! [U_11410,U_11408,U_11406,U_11404] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_11404),U_11406),U_11410))
          & U_11406 = U_11408 )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11404,U_11404)),hAPP(hAPP(c_Product__Type_OPair(U_11404,U_11404),U_11406),U_11408)),c_Relation_OId__on(U_11404,U_11410))) ) ),
    inference(miniscope,[status(thm)],[f_2967_2]) ).

fof(f_2967_4,plain,
    ( ! [U_11406,U_11410,U_11404,U_11408] :
        ( hBOOL(hAPP(hAPP(c_member(U_11404),U_11406),U_11410))
        | ~ sP841(U_11406,U_11410,U_11404,U_11408) )
    & ! [U_11406,U_11410,U_11404,U_11408] :
        ( U_11406 = U_11408
        | ~ sP841(U_11406,U_11410,U_11404,U_11408) )
    & ! [U_11409,U_11405,U_11411,U_11407] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11405,U_11405)),hAPP(hAPP(c_Product__Type_OPair(U_11405,U_11405),U_11407),U_11409)),c_Relation_OId__on(U_11405,U_11411)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11405),U_11407),U_11411))
        | U_11407 != U_11409 )
    & ! [U_11406,U_11410,U_11404,U_11408] :
        ( sP841(U_11406,U_11410,U_11404,U_11408)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11404,U_11404)),hAPP(hAPP(c_Product__Type_OPair(U_11404,U_11404),U_11406),U_11408)),c_Relation_OId__on(U_11404,U_11410))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP841])],[f_2967_3]) ).

cnf(f_2967_5,plain,
    ( sP841(U_11406,U_11410,U_11404,U_11408)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11404,U_11404)),hAPP(hAPP(c_Product__Type_OPair(U_11404,U_11404),U_11406),U_11408)),c_Relation_OId__on(U_11404,U_11410))) ),
    inference(clausify,[status(thm)],[f_2967_4]) ).

cnf(f_2967_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11405,U_11405)),hAPP(hAPP(c_Product__Type_OPair(U_11405,U_11405),U_11407),U_11409)),c_Relation_OId__on(U_11405,U_11411)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11405),U_11407),U_11411))
    | U_11407 != U_11409 ),
    inference(clausify,[status(thm)],[f_2967_4]) ).

cnf(f_2967_7,plain,
    ( U_11406 = U_11408
    | ~ sP841(U_11406,U_11410,U_11404,U_11408) ),
    inference(clausify,[status(thm)],[f_2967_4]) ).

cnf(f_2967_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11404),U_11406),U_11410))
    | ~ sP841(U_11406,U_11410,U_11404,U_11408) ),
    inference(clausify,[status(thm)],[f_2967_4]) ).

fof(f_2968_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_2968_2,plain,
    ! [U_11415,U_11414,U_11413,U_11412] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11414,U_11414)),hAPP(hAPP(c_Product__Type_OPair(U_11414,U_11414),U_11412),U_11413)),c_Relation_OId__on(U_11414,U_11415)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11414),U_11412),U_11415))
      | U_11412 != U_11413 ),
    inference(variable_rename,[status(thm)],[f_2968_1]) ).

fof(f_2968_3,plain,
    ! [U_11413,U_11412,U_11414,U_11415] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11414,U_11414)),hAPP(hAPP(c_Product__Type_OPair(U_11414,U_11414),U_11412),U_11413)),c_Relation_OId__on(U_11414,U_11415)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11414),U_11412),U_11415))
      | U_11412 != U_11413 ),
    inference(definitional_conversion,[status(esa)],[f_2968_2]) ).

cnf(f_2968_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11414,U_11414)),hAPP(hAPP(c_Product__Type_OPair(U_11414,U_11414),U_11412),U_11413)),c_Relation_OId__on(U_11414,U_11415)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11414),U_11412),U_11415))
    | U_11412 != U_11413 ),
    inference(clausify,[status(thm)],[f_2968_3]) ).

fof(f_2969_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_2969_2,plain,
    ! [U_11420,U_11419,U_11418,U_11417,U_11416] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11416),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11416,U_11417,c_Groups_Otimes__class_Otimes(U_11416)),U_11420),c_Groups_Oone__class_Oone(U_11416)),U_11418)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11416,U_11417,c_Groups_Otimes__class_Otimes(U_11416)),U_11420),c_Groups_Oone__class_Oone(U_11416)),U_11419)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11416),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11416,U_11417,c_Groups_Otimes__class_Otimes(U_11416)),U_11420),c_Groups_Oone__class_Oone(U_11416)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11417,tc_HOL_Obool)),U_11418),U_11419))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11416,U_11417,c_Groups_Otimes__class_Otimes(U_11416)),U_11420),c_Groups_Oone__class_Oone(U_11416)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11417,tc_HOL_Obool)),U_11418),U_11419)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11417),U_11419))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11417),U_11418))
      | ~ class_Groups_Ocomm__monoid__mult(U_11416) ),
    inference(variable_rename,[status(thm)],[f_2969_1]) ).

fof(f_2969_3,plain,
    ! [U_11416,U_11417,U_11418,U_11419,U_11420] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11416),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11416,U_11417,c_Groups_Otimes__class_Otimes(U_11416)),U_11420),c_Groups_Oone__class_Oone(U_11416)),U_11418)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11416,U_11417,c_Groups_Otimes__class_Otimes(U_11416)),U_11420),c_Groups_Oone__class_Oone(U_11416)),U_11419)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11416),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11416,U_11417,c_Groups_Otimes__class_Otimes(U_11416)),U_11420),c_Groups_Oone__class_Oone(U_11416)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11417,tc_HOL_Obool)),U_11418),U_11419))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11416,U_11417,c_Groups_Otimes__class_Otimes(U_11416)),U_11420),c_Groups_Oone__class_Oone(U_11416)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11417,tc_HOL_Obool)),U_11418),U_11419)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11417),U_11419))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11417),U_11418))
      | ~ class_Groups_Ocomm__monoid__mult(U_11416) ),
    inference(definitional_conversion,[status(esa)],[f_2969_2]) ).

cnf(f_2969_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11416),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11416,U_11417,c_Groups_Otimes__class_Otimes(U_11416)),U_11420),c_Groups_Oone__class_Oone(U_11416)),U_11418)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11416,U_11417,c_Groups_Otimes__class_Otimes(U_11416)),U_11420),c_Groups_Oone__class_Oone(U_11416)),U_11419)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11416),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11416,U_11417,c_Groups_Otimes__class_Otimes(U_11416)),U_11420),c_Groups_Oone__class_Oone(U_11416)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11417,tc_HOL_Obool)),U_11418),U_11419))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11416,U_11417,c_Groups_Otimes__class_Otimes(U_11416)),U_11420),c_Groups_Oone__class_Oone(U_11416)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11417,tc_HOL_Obool)),U_11418),U_11419)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11417),U_11419))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11417),U_11418))
    | ~ class_Groups_Ocomm__monoid__mult(U_11416) ),
    inference(clausify,[status(thm)],[f_2969_3]) ).

fof(f_2970_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_2970_2,plain,
    ! [U_11424,U_11423,U_11422,U_11421] :
      ( hAPP(c_Set_Oimage(U_11421,U_11423,U_11424),U_11422) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_11423,tc_HOL_Obool),U_11421,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11423,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11421,tc_fun(U_11423,tc_HOL_Obool),tc_fun(U_11423,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_11423,tc_fun(tc_fun(U_11423,tc_HOL_Obool),tc_fun(U_11423,tc_HOL_Obool)),U_11421),c_Set_Oinsert(U_11423)),U_11424)),c_Orderings_Obot__class_Obot(tc_fun(U_11423,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_11423,tc_HOL_Obool))),U_11422)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11421),U_11422)) ),
    inference(variable_rename,[status(thm)],[f_2970_1]) ).

fof(f_2970_3,plain,
    ! [U_11421,U_11424,U_11422,U_11423] :
      ( hAPP(c_Set_Oimage(U_11421,U_11423,U_11424),U_11422) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_11423,tc_HOL_Obool),U_11421,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11423,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11421,tc_fun(U_11423,tc_HOL_Obool),tc_fun(U_11423,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_11423,tc_fun(tc_fun(U_11423,tc_HOL_Obool),tc_fun(U_11423,tc_HOL_Obool)),U_11421),c_Set_Oinsert(U_11423)),U_11424)),c_Orderings_Obot__class_Obot(tc_fun(U_11423,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_11423,tc_HOL_Obool))),U_11422)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11421),U_11422)) ),
    inference(definitional_conversion,[status(esa)],[f_2970_2]) ).

cnf(f_2970_4,plain,
    ( hAPP(c_Set_Oimage(U_11421,U_11423,U_11424),U_11422) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_11423,tc_HOL_Obool),U_11421,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11423,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11421,tc_fun(U_11423,tc_HOL_Obool),tc_fun(U_11423,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_11423,tc_fun(tc_fun(U_11423,tc_HOL_Obool),tc_fun(U_11423,tc_HOL_Obool)),U_11421),c_Set_Oinsert(U_11423)),U_11424)),c_Orderings_Obot__class_Obot(tc_fun(U_11423,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_11423,tc_HOL_Obool))),U_11422)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11421),U_11422)) ),
    inference(clausify,[status(thm)],[f_2970_3]) ).

fof(f_2971_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_2971_2,plain,
    ! [U_11426,U_11425] :
      ( hAPP(c_Finite__Set_Ocard(U_11425),U_11426) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11425,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11425),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11426)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11425),U_11426)) ),
    inference(variable_rename,[status(thm)],[f_2971_1]) ).

fof(f_2971_3,plain,
    ! [U_11425,U_11426] :
      ( hAPP(c_Finite__Set_Ocard(U_11425),U_11426) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11425,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11425),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11426)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11425),U_11426)) ),
    inference(definitional_conversion,[status(esa)],[f_2971_2]) ).

cnf(f_2971_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11425),U_11426) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11425,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11425),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11426)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11425),U_11426)) ),
    inference(clausify,[status(thm)],[f_2971_3]) ).

fof(f_2972_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_2972_2,plain,
    ! [U_11428,U_11427] :
      ( ( hAPP(c_Finite__Set_Ocard(U_11427),U_11428) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11427),U_11428)) )
      & ( hAPP(c_Finite__Set_Ocard(U_11427),U_11428) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11427,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11427),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11428)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11427),U_11428)) ) ),
    inference(variable_rename,[status(thm)],[f_2972_1]) ).

fof(f_2972_3,plain,
    ( ! [U_11432,U_11430] :
        ( hAPP(c_Finite__Set_Ocard(U_11430),U_11432) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11430),U_11432)) )
    & ! [U_11431,U_11429] :
        ( hAPP(c_Finite__Set_Ocard(U_11429),U_11431) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11429,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11429),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11431)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11429),U_11431)) ) ),
    inference(miniscope,[status(thm)],[f_2972_2]) ).

fof(f_2972_4,plain,
    ( ! [U_11430,U_11432] :
        ( hAPP(c_Finite__Set_Ocard(U_11430),U_11432) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11430),U_11432)) )
    & ! [U_11431,U_11429] :
        ( hAPP(c_Finite__Set_Ocard(U_11429),U_11431) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11429,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11429),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11431)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11429),U_11431)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2972_3]) ).

cnf(f_2972_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11429),U_11431) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11429,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11429),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11431)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11429),U_11431)) ),
    inference(clausify,[status(thm)],[f_2972_4]) ).

cnf(f_2972_6,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11430),U_11432) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11430),U_11432)) ),
    inference(clausify,[status(thm)],[f_2972_4]) ).

fof(f_2973_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_2973_2,plain,
    ! [U_11439,U_11438,U_11437,U_11436,U_11435,U_11434,U_11433] :
      ( ( ( hAPP(hAPP(U_11437,U_11439),U_11438) = U_11436
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11434),U_11438)) )
        & ( hAPP(hAPP(U_11437,U_11439),U_11438) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11433,U_11434,U_11435),U_11439),U_11436),U_11438)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11434),U_11438)) ) )
      | ~ c_Big__Operators_Ocomm__monoid__big(U_11433,U_11434,U_11435,U_11436,U_11437) ),
    inference(variable_rename,[status(thm)],[f_2973_1]) ).

fof(f_2973_3,plain,
    ( ! [U_11433,U_11434,U_11435,U_11436,U_11437,U_11438,U_11439] :
        ( hAPP(hAPP(U_11437,U_11439),U_11438) = U_11436
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11434),U_11438))
        | ~ sP842(U_11433,U_11434,U_11435,U_11436,U_11437,U_11438,U_11439) )
    & ! [U_11433,U_11434,U_11435,U_11436,U_11437,U_11438,U_11439] :
        ( hAPP(hAPP(U_11437,U_11439),U_11438) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11433,U_11434,U_11435),U_11439),U_11436),U_11438)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11434),U_11438))
        | ~ sP842(U_11433,U_11434,U_11435,U_11436,U_11437,U_11438,U_11439) )
    & ! [U_11433,U_11434,U_11435,U_11436,U_11437,U_11438,U_11439] :
        ( sP842(U_11433,U_11434,U_11435,U_11436,U_11437,U_11438,U_11439)
        | ~ c_Big__Operators_Ocomm__monoid__big(U_11433,U_11434,U_11435,U_11436,U_11437) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP842])],[f_2973_2]) ).

cnf(f_2973_4,plain,
    ( sP842(U_11433,U_11434,U_11435,U_11436,U_11437,U_11438,U_11439)
    | ~ c_Big__Operators_Ocomm__monoid__big(U_11433,U_11434,U_11435,U_11436,U_11437) ),
    inference(clausify,[status(thm)],[f_2973_3]) ).

cnf(f_2973_5,plain,
    ( hAPP(hAPP(U_11437,U_11439),U_11438) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11433,U_11434,U_11435),U_11439),U_11436),U_11438)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11434),U_11438))
    | ~ sP842(U_11433,U_11434,U_11435,U_11436,U_11437,U_11438,U_11439) ),
    inference(clausify,[status(thm)],[f_2973_3]) ).

cnf(f_2973_6,plain,
    ( hAPP(hAPP(U_11437,U_11439),U_11438) = U_11436
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11434),U_11438))
    | ~ sP842(U_11433,U_11434,U_11435,U_11436,U_11437,U_11438,U_11439) ),
    inference(clausify,[status(thm)],[f_2973_3]) ).

fof(f_2974_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_2974_2,plain,
    ! [U_11445,U_11444,U_11443,U_11442,U_11441] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11441,U_11442,c_Groups_Otimes__class_Otimes(U_11441)),U_11445),c_Groups_Oone__class_Oone(U_11441)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11442,tc_HOL_Obool)),U_11443),U_11444)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11441),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11441,U_11442,c_Groups_Otimes__class_Otimes(U_11441)),U_11445),c_Groups_Oone__class_Oone(U_11441)),U_11443)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11441,U_11442,c_Groups_Otimes__class_Otimes(U_11441)),U_11445),c_Groups_Oone__class_Oone(U_11441)),U_11444))
      | ? [U_11440] :
          ( hAPP(U_11445,U_11440) != c_Groups_Oone__class_Oone(U_11441)
          & hBOOL(hAPP(hAPP(c_member(U_11442),U_11440),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11442,tc_HOL_Obool)),U_11443),U_11444))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11442),U_11444))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11442),U_11443))
      | ~ class_Groups_Ocomm__monoid__mult(U_11441) ),
    inference(variable_rename,[status(thm)],[f_2974_1]) ).

fof(f_2974_3,plain,
    ! [U_11445,U_11444,U_11443,U_11442,U_11441] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11441,U_11442,c_Groups_Otimes__class_Otimes(U_11441)),U_11445),c_Groups_Oone__class_Oone(U_11441)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11442,tc_HOL_Obool)),U_11443),U_11444)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11441),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11441,U_11442,c_Groups_Otimes__class_Otimes(U_11441)),U_11445),c_Groups_Oone__class_Oone(U_11441)),U_11443)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11441,U_11442,c_Groups_Otimes__class_Otimes(U_11441)),U_11445),c_Groups_Oone__class_Oone(U_11441)),U_11444))
      | ( hAPP(U_11445,sK193(U_11445,U_11444,U_11443,U_11442,U_11441)) != c_Groups_Oone__class_Oone(U_11441)
        & hBOOL(hAPP(hAPP(c_member(U_11442),sK193(U_11445,U_11444,U_11443,U_11442,U_11441)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11442,tc_HOL_Obool)),U_11443),U_11444))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11442),U_11444))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11442),U_11443))
      | ~ class_Groups_Ocomm__monoid__mult(U_11441) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(U_11440,sK193(U_11445,U_11444,U_11443,U_11442,U_11441))],[f_2974_2]) ).

fof(f_2974_4,plain,
    ( ! [U_11441,U_11442,U_11443,U_11444,U_11445] :
        ( hAPP(U_11445,sK193(U_11445,U_11444,U_11443,U_11442,U_11441)) != c_Groups_Oone__class_Oone(U_11441)
        | ~ sP843(U_11441,U_11442,U_11443,U_11444,U_11445) )
    & ! [U_11441,U_11442,U_11443,U_11444,U_11445] :
        ( hBOOL(hAPP(hAPP(c_member(U_11442),sK193(U_11445,U_11444,U_11443,U_11442,U_11441)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11442,tc_HOL_Obool)),U_11443),U_11444)))
        | ~ sP843(U_11441,U_11442,U_11443,U_11444,U_11445) )
    & ! [U_11441,U_11442,U_11443,U_11444,U_11445] :
        ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11441,U_11442,c_Groups_Otimes__class_Otimes(U_11441)),U_11445),c_Groups_Oone__class_Oone(U_11441)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11442,tc_HOL_Obool)),U_11443),U_11444)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11441),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11441,U_11442,c_Groups_Otimes__class_Otimes(U_11441)),U_11445),c_Groups_Oone__class_Oone(U_11441)),U_11443)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11441,U_11442,c_Groups_Otimes__class_Otimes(U_11441)),U_11445),c_Groups_Oone__class_Oone(U_11441)),U_11444))
        | sP843(U_11441,U_11442,U_11443,U_11444,U_11445)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11442),U_11444))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11442),U_11443))
        | ~ class_Groups_Ocomm__monoid__mult(U_11441) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP843])],[f_2974_3]) ).

cnf(f_2974_5,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11441,U_11442,c_Groups_Otimes__class_Otimes(U_11441)),U_11445),c_Groups_Oone__class_Oone(U_11441)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11442,tc_HOL_Obool)),U_11443),U_11444)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11441),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11441,U_11442,c_Groups_Otimes__class_Otimes(U_11441)),U_11445),c_Groups_Oone__class_Oone(U_11441)),U_11443)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11441,U_11442,c_Groups_Otimes__class_Otimes(U_11441)),U_11445),c_Groups_Oone__class_Oone(U_11441)),U_11444))
    | sP843(U_11441,U_11442,U_11443,U_11444,U_11445)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11442),U_11444))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11442),U_11443))
    | ~ class_Groups_Ocomm__monoid__mult(U_11441) ),
    inference(clausify,[status(thm)],[f_2974_4]) ).

cnf(f_2974_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11442),sK193(U_11445,U_11444,U_11443,U_11442,U_11441)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11442,tc_HOL_Obool)),U_11443),U_11444)))
    | ~ sP843(U_11441,U_11442,U_11443,U_11444,U_11445) ),
    inference(clausify,[status(thm)],[f_2974_4]) ).

cnf(f_2974_7,plain,
    ( hAPP(U_11445,sK193(U_11445,U_11444,U_11443,U_11442,U_11441)) != c_Groups_Oone__class_Oone(U_11441)
    | ~ sP843(U_11441,U_11442,U_11443,U_11444,U_11445) ),
    inference(clausify,[status(thm)],[f_2974_4]) ).

fof(f_2975_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_2975_2,plain,
    ! [U_11449,U_11448,U_11447] :
      ( ? [U_11446] :
          ( U_11448 = hAPP(hAPP(c_Product__Type_OPair(U_11447,U_11447),U_11446),U_11446)
          & hBOOL(hAPP(hAPP(c_member(U_11447),U_11446),U_11449)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11447,U_11447)),U_11448),c_Relation_OId__on(U_11447,U_11449))) ),
    inference(variable_rename,[status(thm)],[f_2975_1]) ).

fof(f_2975_3,plain,
    ! [U_11449,U_11448,U_11447] :
      ( ( U_11448 = hAPP(hAPP(c_Product__Type_OPair(U_11447,U_11447),sK194(U_11449,U_11448,U_11447)),sK194(U_11449,U_11448,U_11447))
        & hBOOL(hAPP(hAPP(c_member(U_11447),sK194(U_11449,U_11448,U_11447)),U_11449)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11447,U_11447)),U_11448),c_Relation_OId__on(U_11447,U_11449))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(U_11446,sK194(U_11449,U_11448,U_11447))],[f_2975_2]) ).

fof(f_2975_4,plain,
    ( ! [U_11449,U_11448,U_11447] :
        ( U_11448 = hAPP(hAPP(c_Product__Type_OPair(U_11447,U_11447),sK194(U_11449,U_11448,U_11447)),sK194(U_11449,U_11448,U_11447))
        | ~ sP844(U_11449,U_11448,U_11447) )
    & ! [U_11449,U_11448,U_11447] :
        ( hBOOL(hAPP(hAPP(c_member(U_11447),sK194(U_11449,U_11448,U_11447)),U_11449))
        | ~ sP844(U_11449,U_11448,U_11447) )
    & ! [U_11449,U_11448,U_11447] :
        ( sP844(U_11449,U_11448,U_11447)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11447,U_11447)),U_11448),c_Relation_OId__on(U_11447,U_11449))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP844])],[f_2975_3]) ).

cnf(f_2975_5,plain,
    ( sP844(U_11449,U_11448,U_11447)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11447,U_11447)),U_11448),c_Relation_OId__on(U_11447,U_11449))) ),
    inference(clausify,[status(thm)],[f_2975_4]) ).

cnf(f_2975_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11447),sK194(U_11449,U_11448,U_11447)),U_11449))
    | ~ sP844(U_11449,U_11448,U_11447) ),
    inference(clausify,[status(thm)],[f_2975_4]) ).

cnf(f_2975_7,plain,
    ( U_11448 = hAPP(hAPP(c_Product__Type_OPair(U_11447,U_11447),sK194(U_11449,U_11448,U_11447)),sK194(U_11449,U_11448,U_11447))
    | ~ sP844(U_11449,U_11448,U_11447) ),
    inference(clausify,[status(thm)],[f_2975_4]) ).

fof(f_2976_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_2976_2,plain,
    ! [U_11456,U_11455,U_11454,U_11453,U_11452,U_11451,U_11450] :
      ( hAPP(hAPP(U_11454,U_11456),U_11455) = U_11453
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11451),U_11455))
      | ~ c_Big__Operators_Ocomm__monoid__big(U_11450,U_11451,U_11452,U_11453,U_11454) ),
    inference(variable_rename,[status(thm)],[f_2976_1]) ).

fof(f_2976_3,plain,
    ! [U_11456,U_11455,U_11454,U_11453,U_11452,U_11451] :
      ( ! [U_11450] : ~ c_Big__Operators_Ocomm__monoid__big(U_11450,U_11451,U_11452,U_11453,U_11454)
      | hAPP(hAPP(U_11454,U_11456),U_11455) = U_11453
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11451),U_11455)) ),
    inference(miniscope,[status(thm)],[f_2976_2]) ).

fof(f_2976_4,plain,
    ! [U_11450,U_11454,U_11451,U_11452,U_11453,U_11455,U_11456] :
      ( ~ c_Big__Operators_Ocomm__monoid__big(U_11450,U_11451,U_11452,U_11453,U_11454)
      | hAPP(hAPP(U_11454,U_11456),U_11455) = U_11453
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11451),U_11455)) ),
    inference(definitional_conversion,[status(esa)],[f_2976_3]) ).

cnf(f_2976_5,plain,
    ( ~ c_Big__Operators_Ocomm__monoid__big(U_11450,U_11451,U_11452,U_11453,U_11454)
    | hAPP(hAPP(U_11454,U_11456),U_11455) = U_11453
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11451),U_11455)) ),
    inference(clausify,[status(thm)],[f_2976_4]) ).

fof(f_2977_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_2977_2,plain,
    ! [U_11461,U_11460,U_11459] :
      ( hAPP(U_11460,c_Big__Operators_Olattice_OSup__fin(U_11459,c_Orderings_Oord__class_Omax(U_11459),U_11461)) = c_Big__Operators_Olattice_OSup__fin(U_11459,c_Orderings_Oord__class_Omax(U_11459),hAPP(c_Set_Oimage(U_11459,U_11459,U_11460),U_11461))
      | U_11461 = c_Orderings_Obot__class_Obot(tc_fun(U_11459,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11459),U_11461))
      | ? [U_11458,U_11457] : hAPP(U_11460,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11459),U_11458),U_11457)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11459),hAPP(U_11460,U_11458)),hAPP(U_11460,U_11457))
      | ~ class_Orderings_Olinorder(U_11459) ),
    inference(variable_rename,[status(thm)],[f_2977_1]) ).

fof(f_2977_3,plain,
    ! [U_11461,U_11460,U_11459] :
      ( hAPP(U_11460,c_Big__Operators_Olattice_OSup__fin(U_11459,c_Orderings_Oord__class_Omax(U_11459),U_11461)) = c_Big__Operators_Olattice_OSup__fin(U_11459,c_Orderings_Oord__class_Omax(U_11459),hAPP(c_Set_Oimage(U_11459,U_11459,U_11460),U_11461))
      | U_11461 = c_Orderings_Obot__class_Obot(tc_fun(U_11459,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11459),U_11461))
      | ? [U_11457] : hAPP(U_11460,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11459),sK195(U_11461,U_11460,U_11459)),U_11457)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11459),hAPP(U_11460,sK195(U_11461,U_11460,U_11459))),hAPP(U_11460,U_11457))
      | ~ class_Orderings_Olinorder(U_11459) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK195]),skolemize(U_11458,sK195(U_11461,U_11460,U_11459))],[f_2977_2]) ).

fof(f_2977_4,plain,
    ! [U_11461,U_11460,U_11459] :
      ( hAPP(U_11460,c_Big__Operators_Olattice_OSup__fin(U_11459,c_Orderings_Oord__class_Omax(U_11459),U_11461)) = c_Big__Operators_Olattice_OSup__fin(U_11459,c_Orderings_Oord__class_Omax(U_11459),hAPP(c_Set_Oimage(U_11459,U_11459,U_11460),U_11461))
      | U_11461 = c_Orderings_Obot__class_Obot(tc_fun(U_11459,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11459),U_11461))
      | hAPP(U_11460,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11459),sK195(U_11461,U_11460,U_11459)),sK196(U_11461,U_11460,U_11459))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11459),hAPP(U_11460,sK195(U_11461,U_11460,U_11459))),hAPP(U_11460,sK196(U_11461,U_11460,U_11459)))
      | ~ class_Orderings_Olinorder(U_11459) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(U_11457,sK196(U_11461,U_11460,U_11459))],[f_2977_3]) ).

fof(f_2977_5,plain,
    ! [U_11459,U_11460,U_11461] :
      ( hAPP(U_11460,c_Big__Operators_Olattice_OSup__fin(U_11459,c_Orderings_Oord__class_Omax(U_11459),U_11461)) = c_Big__Operators_Olattice_OSup__fin(U_11459,c_Orderings_Oord__class_Omax(U_11459),hAPP(c_Set_Oimage(U_11459,U_11459,U_11460),U_11461))
      | U_11461 = c_Orderings_Obot__class_Obot(tc_fun(U_11459,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11459),U_11461))
      | hAPP(U_11460,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11459),sK195(U_11461,U_11460,U_11459)),sK196(U_11461,U_11460,U_11459))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11459),hAPP(U_11460,sK195(U_11461,U_11460,U_11459))),hAPP(U_11460,sK196(U_11461,U_11460,U_11459)))
      | ~ class_Orderings_Olinorder(U_11459) ),
    inference(definitional_conversion,[status(esa)],[f_2977_4]) ).

cnf(f_2977_6,plain,
    ( hAPP(U_11460,c_Big__Operators_Olattice_OSup__fin(U_11459,c_Orderings_Oord__class_Omax(U_11459),U_11461)) = c_Big__Operators_Olattice_OSup__fin(U_11459,c_Orderings_Oord__class_Omax(U_11459),hAPP(c_Set_Oimage(U_11459,U_11459,U_11460),U_11461))
    | U_11461 = c_Orderings_Obot__class_Obot(tc_fun(U_11459,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11459),U_11461))
    | hAPP(U_11460,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11459),sK195(U_11461,U_11460,U_11459)),sK196(U_11461,U_11460,U_11459))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11459),hAPP(U_11460,sK195(U_11461,U_11460,U_11459))),hAPP(U_11460,sK196(U_11461,U_11460,U_11459)))
    | ~ class_Orderings_Olinorder(U_11459) ),
    inference(clausify,[status(thm)],[f_2977_5]) ).

fof(f_2978_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_2978_2,plain,
    ! [U_11466,U_11465,U_11464] :
      ( hAPP(U_11465,c_Big__Operators_Olattice_OInf__fin(U_11464,c_Orderings_Oord__class_Omin(U_11464),U_11466)) = c_Big__Operators_Olattice_OInf__fin(U_11464,c_Orderings_Oord__class_Omin(U_11464),hAPP(c_Set_Oimage(U_11464,U_11464,U_11465),U_11466))
      | U_11466 = c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11464),U_11466))
      | ? [U_11463,U_11462] : hAPP(U_11465,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11464),U_11463),U_11462)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11464),hAPP(U_11465,U_11463)),hAPP(U_11465,U_11462))
      | ~ class_Orderings_Olinorder(U_11464) ),
    inference(variable_rename,[status(thm)],[f_2978_1]) ).

fof(f_2978_3,plain,
    ! [U_11466,U_11465,U_11464] :
      ( hAPP(U_11465,c_Big__Operators_Olattice_OInf__fin(U_11464,c_Orderings_Oord__class_Omin(U_11464),U_11466)) = c_Big__Operators_Olattice_OInf__fin(U_11464,c_Orderings_Oord__class_Omin(U_11464),hAPP(c_Set_Oimage(U_11464,U_11464,U_11465),U_11466))
      | U_11466 = c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11464),U_11466))
      | ? [U_11462] : hAPP(U_11465,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11464),sK197(U_11466,U_11465,U_11464)),U_11462)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11464),hAPP(U_11465,sK197(U_11466,U_11465,U_11464))),hAPP(U_11465,U_11462))
      | ~ class_Orderings_Olinorder(U_11464) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(U_11463,sK197(U_11466,U_11465,U_11464))],[f_2978_2]) ).

fof(f_2978_4,plain,
    ! [U_11466,U_11465,U_11464] :
      ( hAPP(U_11465,c_Big__Operators_Olattice_OInf__fin(U_11464,c_Orderings_Oord__class_Omin(U_11464),U_11466)) = c_Big__Operators_Olattice_OInf__fin(U_11464,c_Orderings_Oord__class_Omin(U_11464),hAPP(c_Set_Oimage(U_11464,U_11464,U_11465),U_11466))
      | U_11466 = c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11464),U_11466))
      | hAPP(U_11465,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11464),sK197(U_11466,U_11465,U_11464)),sK198(U_11466,U_11465,U_11464))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11464),hAPP(U_11465,sK197(U_11466,U_11465,U_11464))),hAPP(U_11465,sK198(U_11466,U_11465,U_11464)))
      | ~ class_Orderings_Olinorder(U_11464) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(U_11462,sK198(U_11466,U_11465,U_11464))],[f_2978_3]) ).

fof(f_2978_5,plain,
    ! [U_11464,U_11465,U_11466] :
      ( hAPP(U_11465,c_Big__Operators_Olattice_OInf__fin(U_11464,c_Orderings_Oord__class_Omin(U_11464),U_11466)) = c_Big__Operators_Olattice_OInf__fin(U_11464,c_Orderings_Oord__class_Omin(U_11464),hAPP(c_Set_Oimage(U_11464,U_11464,U_11465),U_11466))
      | U_11466 = c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11464),U_11466))
      | hAPP(U_11465,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11464),sK197(U_11466,U_11465,U_11464)),sK198(U_11466,U_11465,U_11464))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11464),hAPP(U_11465,sK197(U_11466,U_11465,U_11464))),hAPP(U_11465,sK198(U_11466,U_11465,U_11464)))
      | ~ class_Orderings_Olinorder(U_11464) ),
    inference(definitional_conversion,[status(esa)],[f_2978_4]) ).

cnf(f_2978_6,plain,
    ( hAPP(U_11465,c_Big__Operators_Olattice_OInf__fin(U_11464,c_Orderings_Oord__class_Omin(U_11464),U_11466)) = c_Big__Operators_Olattice_OInf__fin(U_11464,c_Orderings_Oord__class_Omin(U_11464),hAPP(c_Set_Oimage(U_11464,U_11464,U_11465),U_11466))
    | U_11466 = c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11464),U_11466))
    | hAPP(U_11465,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11464),sK197(U_11466,U_11465,U_11464)),sK198(U_11466,U_11465,U_11464))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11464),hAPP(U_11465,sK197(U_11466,U_11465,U_11464))),hAPP(U_11465,sK198(U_11466,U_11465,U_11464)))
    | ~ class_Orderings_Olinorder(U_11464) ),
    inference(clausify,[status(thm)],[f_2978_5]) ).

fof(f_2979_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_2979_2,plain,
    ! [U_11471,U_11470,U_11469] :
      ( hAPP(U_11470,c_Big__Operators_Olinorder__class_OMax(U_11469,U_11471)) = c_Big__Operators_Olinorder__class_OMax(U_11469,hAPP(c_Set_Oimage(U_11469,U_11469,U_11470),U_11471))
      | U_11471 = c_Orderings_Obot__class_Obot(tc_fun(U_11469,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11469),U_11471))
      | ? [U_11468,U_11467] : hAPP(U_11470,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11469),U_11468),U_11467)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11469),hAPP(U_11470,U_11468)),hAPP(U_11470,U_11467))
      | ~ class_Orderings_Olinorder(U_11469) ),
    inference(variable_rename,[status(thm)],[f_2979_1]) ).

fof(f_2979_3,plain,
    ! [U_11471,U_11470,U_11469] :
      ( hAPP(U_11470,c_Big__Operators_Olinorder__class_OMax(U_11469,U_11471)) = c_Big__Operators_Olinorder__class_OMax(U_11469,hAPP(c_Set_Oimage(U_11469,U_11469,U_11470),U_11471))
      | U_11471 = c_Orderings_Obot__class_Obot(tc_fun(U_11469,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11469),U_11471))
      | ? [U_11467] : hAPP(U_11470,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11469),sK199(U_11471,U_11470,U_11469)),U_11467)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11469),hAPP(U_11470,sK199(U_11471,U_11470,U_11469))),hAPP(U_11470,U_11467))
      | ~ class_Orderings_Olinorder(U_11469) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(U_11468,sK199(U_11471,U_11470,U_11469))],[f_2979_2]) ).

fof(f_2979_4,plain,
    ! [U_11471,U_11470,U_11469] :
      ( hAPP(U_11470,c_Big__Operators_Olinorder__class_OMax(U_11469,U_11471)) = c_Big__Operators_Olinorder__class_OMax(U_11469,hAPP(c_Set_Oimage(U_11469,U_11469,U_11470),U_11471))
      | U_11471 = c_Orderings_Obot__class_Obot(tc_fun(U_11469,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11469),U_11471))
      | hAPP(U_11470,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11469),sK199(U_11471,U_11470,U_11469)),sK200(U_11471,U_11470,U_11469))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11469),hAPP(U_11470,sK199(U_11471,U_11470,U_11469))),hAPP(U_11470,sK200(U_11471,U_11470,U_11469)))
      | ~ class_Orderings_Olinorder(U_11469) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(U_11467,sK200(U_11471,U_11470,U_11469))],[f_2979_3]) ).

fof(f_2979_5,plain,
    ! [U_11469,U_11470,U_11471] :
      ( hAPP(U_11470,c_Big__Operators_Olinorder__class_OMax(U_11469,U_11471)) = c_Big__Operators_Olinorder__class_OMax(U_11469,hAPP(c_Set_Oimage(U_11469,U_11469,U_11470),U_11471))
      | U_11471 = c_Orderings_Obot__class_Obot(tc_fun(U_11469,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11469),U_11471))
      | hAPP(U_11470,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11469),sK199(U_11471,U_11470,U_11469)),sK200(U_11471,U_11470,U_11469))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11469),hAPP(U_11470,sK199(U_11471,U_11470,U_11469))),hAPP(U_11470,sK200(U_11471,U_11470,U_11469)))
      | ~ class_Orderings_Olinorder(U_11469) ),
    inference(definitional_conversion,[status(esa)],[f_2979_4]) ).

cnf(f_2979_6,plain,
    ( hAPP(U_11470,c_Big__Operators_Olinorder__class_OMax(U_11469,U_11471)) = c_Big__Operators_Olinorder__class_OMax(U_11469,hAPP(c_Set_Oimage(U_11469,U_11469,U_11470),U_11471))
    | U_11471 = c_Orderings_Obot__class_Obot(tc_fun(U_11469,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11469),U_11471))
    | hAPP(U_11470,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11469),sK199(U_11471,U_11470,U_11469)),sK200(U_11471,U_11470,U_11469))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11469),hAPP(U_11470,sK199(U_11471,U_11470,U_11469))),hAPP(U_11470,sK200(U_11471,U_11470,U_11469)))
    | ~ class_Orderings_Olinorder(U_11469) ),
    inference(clausify,[status(thm)],[f_2979_5]) ).

fof(f_2980_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_2980_2,plain,
    ! [U_11476,U_11475,U_11474] :
      ( hAPP(U_11475,c_Big__Operators_Olinorder__class_OMin(U_11474,U_11476)) = c_Big__Operators_Olinorder__class_OMin(U_11474,hAPP(c_Set_Oimage(U_11474,U_11474,U_11475),U_11476))
      | U_11476 = c_Orderings_Obot__class_Obot(tc_fun(U_11474,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11474),U_11476))
      | ? [U_11473,U_11472] : hAPP(U_11475,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11474),U_11473),U_11472)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11474),hAPP(U_11475,U_11473)),hAPP(U_11475,U_11472))
      | ~ class_Orderings_Olinorder(U_11474) ),
    inference(variable_rename,[status(thm)],[f_2980_1]) ).

fof(f_2980_3,plain,
    ! [U_11476,U_11475,U_11474] :
      ( hAPP(U_11475,c_Big__Operators_Olinorder__class_OMin(U_11474,U_11476)) = c_Big__Operators_Olinorder__class_OMin(U_11474,hAPP(c_Set_Oimage(U_11474,U_11474,U_11475),U_11476))
      | U_11476 = c_Orderings_Obot__class_Obot(tc_fun(U_11474,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11474),U_11476))
      | ? [U_11472] : hAPP(U_11475,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11474),sK201(U_11476,U_11475,U_11474)),U_11472)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11474),hAPP(U_11475,sK201(U_11476,U_11475,U_11474))),hAPP(U_11475,U_11472))
      | ~ class_Orderings_Olinorder(U_11474) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(U_11473,sK201(U_11476,U_11475,U_11474))],[f_2980_2]) ).

fof(f_2980_4,plain,
    ! [U_11476,U_11475,U_11474] :
      ( hAPP(U_11475,c_Big__Operators_Olinorder__class_OMin(U_11474,U_11476)) = c_Big__Operators_Olinorder__class_OMin(U_11474,hAPP(c_Set_Oimage(U_11474,U_11474,U_11475),U_11476))
      | U_11476 = c_Orderings_Obot__class_Obot(tc_fun(U_11474,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11474),U_11476))
      | hAPP(U_11475,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11474),sK201(U_11476,U_11475,U_11474)),sK202(U_11476,U_11475,U_11474))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11474),hAPP(U_11475,sK201(U_11476,U_11475,U_11474))),hAPP(U_11475,sK202(U_11476,U_11475,U_11474)))
      | ~ class_Orderings_Olinorder(U_11474) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(U_11472,sK202(U_11476,U_11475,U_11474))],[f_2980_3]) ).

fof(f_2980_5,plain,
    ! [U_11474,U_11475,U_11476] :
      ( hAPP(U_11475,c_Big__Operators_Olinorder__class_OMin(U_11474,U_11476)) = c_Big__Operators_Olinorder__class_OMin(U_11474,hAPP(c_Set_Oimage(U_11474,U_11474,U_11475),U_11476))
      | U_11476 = c_Orderings_Obot__class_Obot(tc_fun(U_11474,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11474),U_11476))
      | hAPP(U_11475,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11474),sK201(U_11476,U_11475,U_11474)),sK202(U_11476,U_11475,U_11474))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11474),hAPP(U_11475,sK201(U_11476,U_11475,U_11474))),hAPP(U_11475,sK202(U_11476,U_11475,U_11474)))
      | ~ class_Orderings_Olinorder(U_11474) ),
    inference(definitional_conversion,[status(esa)],[f_2980_4]) ).

cnf(f_2980_6,plain,
    ( hAPP(U_11475,c_Big__Operators_Olinorder__class_OMin(U_11474,U_11476)) = c_Big__Operators_Olinorder__class_OMin(U_11474,hAPP(c_Set_Oimage(U_11474,U_11474,U_11475),U_11476))
    | U_11476 = c_Orderings_Obot__class_Obot(tc_fun(U_11474,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11474),U_11476))
    | hAPP(U_11475,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11474),sK201(U_11476,U_11475,U_11474)),sK202(U_11476,U_11475,U_11474))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11474),hAPP(U_11475,sK201(U_11476,U_11475,U_11474))),hAPP(U_11475,sK202(U_11476,U_11475,U_11474)))
    | ~ class_Orderings_Olinorder(U_11474) ),
    inference(clausify,[status(thm)],[f_2980_5]) ).

fof(f_2981_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_2981_2,plain,
    ! [U_11481,U_11480,U_11479] :
      ( hAPP(U_11480,c_Big__Operators_Olattice__class_OInf__fin(U_11479,U_11481)) = c_Big__Operators_Olattice__class_OInf__fin(U_11479,hAPP(c_Set_Oimage(U_11479,U_11479,U_11480),U_11481))
      | U_11481 = c_Orderings_Obot__class_Obot(tc_fun(U_11479,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11479),U_11481))
      | ? [U_11478,U_11477] : hAPP(U_11480,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11479),U_11478),U_11477)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11479),hAPP(U_11480,U_11478)),hAPP(U_11480,U_11477))
      | ~ class_Lattices_Olattice(U_11479) ),
    inference(variable_rename,[status(thm)],[f_2981_1]) ).

fof(f_2981_3,plain,
    ! [U_11481,U_11480,U_11479] :
      ( hAPP(U_11480,c_Big__Operators_Olattice__class_OInf__fin(U_11479,U_11481)) = c_Big__Operators_Olattice__class_OInf__fin(U_11479,hAPP(c_Set_Oimage(U_11479,U_11479,U_11480),U_11481))
      | U_11481 = c_Orderings_Obot__class_Obot(tc_fun(U_11479,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11479),U_11481))
      | ? [U_11477] : hAPP(U_11480,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11479),sK203(U_11481,U_11480,U_11479)),U_11477)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11479),hAPP(U_11480,sK203(U_11481,U_11480,U_11479))),hAPP(U_11480,U_11477))
      | ~ class_Lattices_Olattice(U_11479) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(U_11478,sK203(U_11481,U_11480,U_11479))],[f_2981_2]) ).

fof(f_2981_4,plain,
    ! [U_11481,U_11480,U_11479] :
      ( hAPP(U_11480,c_Big__Operators_Olattice__class_OInf__fin(U_11479,U_11481)) = c_Big__Operators_Olattice__class_OInf__fin(U_11479,hAPP(c_Set_Oimage(U_11479,U_11479,U_11480),U_11481))
      | U_11481 = c_Orderings_Obot__class_Obot(tc_fun(U_11479,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11479),U_11481))
      | hAPP(U_11480,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11479),sK203(U_11481,U_11480,U_11479)),sK204(U_11481,U_11480,U_11479))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11479),hAPP(U_11480,sK203(U_11481,U_11480,U_11479))),hAPP(U_11480,sK204(U_11481,U_11480,U_11479)))
      | ~ class_Lattices_Olattice(U_11479) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(U_11477,sK204(U_11481,U_11480,U_11479))],[f_2981_3]) ).

fof(f_2981_5,plain,
    ! [U_11479,U_11480,U_11481] :
      ( hAPP(U_11480,c_Big__Operators_Olattice__class_OInf__fin(U_11479,U_11481)) = c_Big__Operators_Olattice__class_OInf__fin(U_11479,hAPP(c_Set_Oimage(U_11479,U_11479,U_11480),U_11481))
      | U_11481 = c_Orderings_Obot__class_Obot(tc_fun(U_11479,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11479),U_11481))
      | hAPP(U_11480,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11479),sK203(U_11481,U_11480,U_11479)),sK204(U_11481,U_11480,U_11479))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11479),hAPP(U_11480,sK203(U_11481,U_11480,U_11479))),hAPP(U_11480,sK204(U_11481,U_11480,U_11479)))
      | ~ class_Lattices_Olattice(U_11479) ),
    inference(definitional_conversion,[status(esa)],[f_2981_4]) ).

cnf(f_2981_6,plain,
    ( hAPP(U_11480,c_Big__Operators_Olattice__class_OInf__fin(U_11479,U_11481)) = c_Big__Operators_Olattice__class_OInf__fin(U_11479,hAPP(c_Set_Oimage(U_11479,U_11479,U_11480),U_11481))
    | U_11481 = c_Orderings_Obot__class_Obot(tc_fun(U_11479,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11479),U_11481))
    | hAPP(U_11480,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11479),sK203(U_11481,U_11480,U_11479)),sK204(U_11481,U_11480,U_11479))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11479),hAPP(U_11480,sK203(U_11481,U_11480,U_11479))),hAPP(U_11480,sK204(U_11481,U_11480,U_11479)))
    | ~ class_Lattices_Olattice(U_11479) ),
    inference(clausify,[status(thm)],[f_2981_5]) ).

fof(f_2982_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_2982_2,plain,
    ! [U_11486,U_11485,U_11484] :
      ( hAPP(U_11485,c_Big__Operators_Olattice__class_OSup__fin(U_11484,U_11486)) = c_Big__Operators_Olattice__class_OSup__fin(U_11484,hAPP(c_Set_Oimage(U_11484,U_11484,U_11485),U_11486))
      | U_11486 = c_Orderings_Obot__class_Obot(tc_fun(U_11484,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11484),U_11486))
      | ? [U_11483,U_11482] : hAPP(U_11485,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11484),U_11483),U_11482)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11484),hAPP(U_11485,U_11483)),hAPP(U_11485,U_11482))
      | ~ class_Lattices_Olattice(U_11484) ),
    inference(variable_rename,[status(thm)],[f_2982_1]) ).

fof(f_2982_3,plain,
    ! [U_11486,U_11485,U_11484] :
      ( hAPP(U_11485,c_Big__Operators_Olattice__class_OSup__fin(U_11484,U_11486)) = c_Big__Operators_Olattice__class_OSup__fin(U_11484,hAPP(c_Set_Oimage(U_11484,U_11484,U_11485),U_11486))
      | U_11486 = c_Orderings_Obot__class_Obot(tc_fun(U_11484,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11484),U_11486))
      | ? [U_11482] : hAPP(U_11485,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11484),sK205(U_11486,U_11485,U_11484)),U_11482)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11484),hAPP(U_11485,sK205(U_11486,U_11485,U_11484))),hAPP(U_11485,U_11482))
      | ~ class_Lattices_Olattice(U_11484) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(U_11483,sK205(U_11486,U_11485,U_11484))],[f_2982_2]) ).

fof(f_2982_4,plain,
    ! [U_11486,U_11485,U_11484] :
      ( hAPP(U_11485,c_Big__Operators_Olattice__class_OSup__fin(U_11484,U_11486)) = c_Big__Operators_Olattice__class_OSup__fin(U_11484,hAPP(c_Set_Oimage(U_11484,U_11484,U_11485),U_11486))
      | U_11486 = c_Orderings_Obot__class_Obot(tc_fun(U_11484,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11484),U_11486))
      | hAPP(U_11485,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11484),sK205(U_11486,U_11485,U_11484)),sK206(U_11486,U_11485,U_11484))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11484),hAPP(U_11485,sK205(U_11486,U_11485,U_11484))),hAPP(U_11485,sK206(U_11486,U_11485,U_11484)))
      | ~ class_Lattices_Olattice(U_11484) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(U_11482,sK206(U_11486,U_11485,U_11484))],[f_2982_3]) ).

fof(f_2982_5,plain,
    ! [U_11484,U_11485,U_11486] :
      ( hAPP(U_11485,c_Big__Operators_Olattice__class_OSup__fin(U_11484,U_11486)) = c_Big__Operators_Olattice__class_OSup__fin(U_11484,hAPP(c_Set_Oimage(U_11484,U_11484,U_11485),U_11486))
      | U_11486 = c_Orderings_Obot__class_Obot(tc_fun(U_11484,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11484),U_11486))
      | hAPP(U_11485,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11484),sK205(U_11486,U_11485,U_11484)),sK206(U_11486,U_11485,U_11484))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11484),hAPP(U_11485,sK205(U_11486,U_11485,U_11484))),hAPP(U_11485,sK206(U_11486,U_11485,U_11484)))
      | ~ class_Lattices_Olattice(U_11484) ),
    inference(definitional_conversion,[status(esa)],[f_2982_4]) ).

cnf(f_2982_6,plain,
    ( hAPP(U_11485,c_Big__Operators_Olattice__class_OSup__fin(U_11484,U_11486)) = c_Big__Operators_Olattice__class_OSup__fin(U_11484,hAPP(c_Set_Oimage(U_11484,U_11484,U_11485),U_11486))
    | U_11486 = c_Orderings_Obot__class_Obot(tc_fun(U_11484,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11484),U_11486))
    | hAPP(U_11485,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11484),sK205(U_11486,U_11485,U_11484)),sK206(U_11486,U_11485,U_11484))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11484),hAPP(U_11485,sK205(U_11486,U_11485,U_11484))),hAPP(U_11485,sK206(U_11486,U_11485,U_11484)))
    | ~ class_Lattices_Olattice(U_11484) ),
    inference(clausify,[status(thm)],[f_2982_5]) ).

fof(f_2983_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_2983_2,plain,
    ! [U_11492,U_11491,U_11490,U_11489,U_11488] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11489,U_11488),U_11492),U_11490) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11489,U_11488),U_11492),U_11491)
      | ? [U_11487] :
          ( hAPP(U_11492,U_11487) != c_Groups_Oone__class_Oone(U_11488)
          & hBOOL(hAPP(hAPP(c_member(U_11489),U_11487),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11489,tc_HOL_Obool)),U_11490),U_11491))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11489,tc_HOL_Obool)),U_11491),U_11490))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11489),U_11490))
      | ~ class_Groups_Ocomm__monoid__mult(U_11488) ),
    inference(variable_rename,[status(thm)],[f_2983_1]) ).

fof(f_2983_3,plain,
    ! [U_11492,U_11491,U_11490,U_11489,U_11488] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11489,U_11488),U_11492),U_11490) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11489,U_11488),U_11492),U_11491)
      | ( hAPP(U_11492,sK207(U_11492,U_11491,U_11490,U_11489,U_11488)) != c_Groups_Oone__class_Oone(U_11488)
        & hBOOL(hAPP(hAPP(c_member(U_11489),sK207(U_11492,U_11491,U_11490,U_11489,U_11488)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11489,tc_HOL_Obool)),U_11490),U_11491))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11489,tc_HOL_Obool)),U_11491),U_11490))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11489),U_11490))
      | ~ class_Groups_Ocomm__monoid__mult(U_11488) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(U_11487,sK207(U_11492,U_11491,U_11490,U_11489,U_11488))],[f_2983_2]) ).

fof(f_2983_4,plain,
    ( ! [U_11489,U_11488,U_11490,U_11491,U_11492] :
        ( hAPP(U_11492,sK207(U_11492,U_11491,U_11490,U_11489,U_11488)) != c_Groups_Oone__class_Oone(U_11488)
        | ~ sP845(U_11489,U_11488,U_11490,U_11491,U_11492) )
    & ! [U_11489,U_11488,U_11490,U_11491,U_11492] :
        ( hBOOL(hAPP(hAPP(c_member(U_11489),sK207(U_11492,U_11491,U_11490,U_11489,U_11488)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11489,tc_HOL_Obool)),U_11490),U_11491)))
        | ~ sP845(U_11489,U_11488,U_11490,U_11491,U_11492) )
    & ! [U_11489,U_11488,U_11490,U_11491,U_11492] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11489,U_11488),U_11492),U_11490) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11489,U_11488),U_11492),U_11491)
        | sP845(U_11489,U_11488,U_11490,U_11491,U_11492)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11489,tc_HOL_Obool)),U_11491),U_11490))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11489),U_11490))
        | ~ class_Groups_Ocomm__monoid__mult(U_11488) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP845])],[f_2983_3]) ).

cnf(f_2983_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11489,U_11488),U_11492),U_11490) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11489,U_11488),U_11492),U_11491)
    | sP845(U_11489,U_11488,U_11490,U_11491,U_11492)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11489,tc_HOL_Obool)),U_11491),U_11490))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11489),U_11490))
    | ~ class_Groups_Ocomm__monoid__mult(U_11488) ),
    inference(clausify,[status(thm)],[f_2983_4]) ).

cnf(f_2983_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11489),sK207(U_11492,U_11491,U_11490,U_11489,U_11488)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11489,tc_HOL_Obool)),U_11490),U_11491)))
    | ~ sP845(U_11489,U_11488,U_11490,U_11491,U_11492) ),
    inference(clausify,[status(thm)],[f_2983_4]) ).

cnf(f_2983_7,plain,
    ( hAPP(U_11492,sK207(U_11492,U_11491,U_11490,U_11489,U_11488)) != c_Groups_Oone__class_Oone(U_11488)
    | ~ sP845(U_11489,U_11488,U_11490,U_11491,U_11492) ),
    inference(clausify,[status(thm)],[f_2983_4]) ).

fof(f_2984_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_2984_2,plain,
    ! [U_11498,U_11497,U_11496,U_11495,U_11494] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11495,U_11494),U_11498),U_11497) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11495,U_11494),U_11498),U_11496)
      | ? [U_11493] :
          ( hAPP(U_11498,U_11493) != c_Groups_Oone__class_Oone(U_11494)
          & hBOOL(hAPP(hAPP(c_member(U_11495),U_11493),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11495,tc_HOL_Obool)),U_11496),U_11497))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11495,tc_HOL_Obool)),U_11497),U_11496))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11495),U_11496))
      | ~ class_Groups_Ocomm__monoid__mult(U_11494) ),
    inference(variable_rename,[status(thm)],[f_2984_1]) ).

fof(f_2984_3,plain,
    ! [U_11498,U_11497,U_11496,U_11495,U_11494] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11495,U_11494),U_11498),U_11497) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11495,U_11494),U_11498),U_11496)
      | ( hAPP(U_11498,sK208(U_11498,U_11497,U_11496,U_11495,U_11494)) != c_Groups_Oone__class_Oone(U_11494)
        & hBOOL(hAPP(hAPP(c_member(U_11495),sK208(U_11498,U_11497,U_11496,U_11495,U_11494)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11495,tc_HOL_Obool)),U_11496),U_11497))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11495,tc_HOL_Obool)),U_11497),U_11496))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11495),U_11496))
      | ~ class_Groups_Ocomm__monoid__mult(U_11494) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(U_11493,sK208(U_11498,U_11497,U_11496,U_11495,U_11494))],[f_2984_2]) ).

fof(f_2984_4,plain,
    ( ! [U_11495,U_11496,U_11494,U_11498,U_11497] :
        ( hAPP(U_11498,sK208(U_11498,U_11497,U_11496,U_11495,U_11494)) != c_Groups_Oone__class_Oone(U_11494)
        | ~ sP846(U_11495,U_11496,U_11494,U_11498,U_11497) )
    & ! [U_11495,U_11496,U_11494,U_11498,U_11497] :
        ( hBOOL(hAPP(hAPP(c_member(U_11495),sK208(U_11498,U_11497,U_11496,U_11495,U_11494)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11495,tc_HOL_Obool)),U_11496),U_11497)))
        | ~ sP846(U_11495,U_11496,U_11494,U_11498,U_11497) )
    & ! [U_11495,U_11496,U_11494,U_11498,U_11497] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11495,U_11494),U_11498),U_11497) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11495,U_11494),U_11498),U_11496)
        | sP846(U_11495,U_11496,U_11494,U_11498,U_11497)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11495,tc_HOL_Obool)),U_11497),U_11496))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11495),U_11496))
        | ~ class_Groups_Ocomm__monoid__mult(U_11494) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP846])],[f_2984_3]) ).

cnf(f_2984_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11495,U_11494),U_11498),U_11497) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11495,U_11494),U_11498),U_11496)
    | sP846(U_11495,U_11496,U_11494,U_11498,U_11497)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11495,tc_HOL_Obool)),U_11497),U_11496))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11495),U_11496))
    | ~ class_Groups_Ocomm__monoid__mult(U_11494) ),
    inference(clausify,[status(thm)],[f_2984_4]) ).

cnf(f_2984_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11495),sK208(U_11498,U_11497,U_11496,U_11495,U_11494)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11495,tc_HOL_Obool)),U_11496),U_11497)))
    | ~ sP846(U_11495,U_11496,U_11494,U_11498,U_11497) ),
    inference(clausify,[status(thm)],[f_2984_4]) ).

cnf(f_2984_7,plain,
    ( hAPP(U_11498,sK208(U_11498,U_11497,U_11496,U_11495,U_11494)) != c_Groups_Oone__class_Oone(U_11494)
    | ~ sP846(U_11495,U_11496,U_11494,U_11498,U_11497) ),
    inference(clausify,[status(thm)],[f_2984_4]) ).

fof(f_2985_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_2985_2,plain,
    ! [U_11500,U_11499] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11499,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11499),U_11500)) = 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_11499),U_11500))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11499),U_11500)) ),
    inference(variable_rename,[status(thm)],[f_2985_1]) ).

fof(f_2985_3,plain,
    ! [U_11500,U_11499] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11499,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11499),U_11500)) = 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_11499),U_11500))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11499),U_11500)) ),
    inference(definitional_conversion,[status(esa)],[f_2985_2]) ).

cnf(f_2985_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11499,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11499),U_11500)) = 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_11499),U_11500))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11499),U_11500)) ),
    inference(clausify,[status(thm)],[f_2985_3]) ).

fof(f_2986_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_2986_2,plain,
    ! [U_11503,U_11502,U_11501] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11501,tc_HOL_Obool)),U_11502),hAPP(c_Set_OPow(U_11501),U_11503)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11501,tc_HOL_Obool)),U_11502),U_11503)) ),
    inference(variable_rename,[status(thm)],[f_2986_1]) ).

fof(f_2986_3,plain,
    ! [U_11502,U_11501,U_11503] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11501,tc_HOL_Obool)),U_11502),hAPP(c_Set_OPow(U_11501),U_11503)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11501,tc_HOL_Obool)),U_11502),U_11503)) ),
    inference(definitional_conversion,[status(esa)],[f_2986_2]) ).

cnf(f_2986_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11501,tc_HOL_Obool)),U_11502),hAPP(c_Set_OPow(U_11501),U_11503)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11501,tc_HOL_Obool)),U_11502),U_11503)) ),
    inference(clausify,[status(thm)],[f_2986_3]) ).

fof(f_2987_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_2987_2,plain,
    ! [U_11505,U_11504] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_11504,tc_HOL_Obool)),U_11505),hAPP(c_Set_OPow(U_11504),U_11505))),
    inference(variable_rename,[status(thm)],[f_2987_1]) ).

fof(f_2987_3,plain,
    ! [U_11504,U_11505] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_11504,tc_HOL_Obool)),U_11505),hAPP(c_Set_OPow(U_11504),U_11505))),
    inference(definitional_conversion,[status(esa)],[f_2987_2]) ).

cnf(f_2987_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(U_11504,tc_HOL_Obool)),U_11505),hAPP(c_Set_OPow(U_11504),U_11505))),
    inference(clausify,[status(thm)],[f_2987_3]) ).

fof(f_2988_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_2988_2,plain,
    ! [U_11507,U_11506] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11506,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11506),U_11507)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11506),U_11507)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11506),U_11507))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11506,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11506),U_11507))) ) ),
    inference(variable_rename,[status(thm)],[f_2988_1]) ).

fof(f_2988_3,plain,
    ( ! [U_11511,U_11509] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11509,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11509),U_11511)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11509),U_11511)) )
    & ! [U_11510,U_11508] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11508),U_11510))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11508,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11508),U_11510))) ) ),
    inference(miniscope,[status(thm)],[f_2988_2]) ).

fof(f_2988_4,plain,
    ( ! [U_11509,U_11511] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11509,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11509),U_11511)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11509),U_11511)) )
    & ! [U_11510,U_11508] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11508),U_11510))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11508,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11508),U_11510))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2988_3]) ).

cnf(f_2988_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11508),U_11510))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11508,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11508),U_11510))) ),
    inference(clausify,[status(thm)],[f_2988_4]) ).

cnf(f_2988_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11509,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11509),U_11511)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11509),U_11511)) ),
    inference(clausify,[status(thm)],[f_2988_4]) ).

fof(f_2989_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_2989_2,plain,
    ! [U_11516,U_11515,U_11514,U_11513,U_11512] :
      ( hAPP(c_Set_Oimage(tc_fun(U_11512,tc_HOL_Obool),tc_fun(U_11513,tc_HOL_Obool),c_Set_Oimage(U_11512,U_11513,U_11514)),hAPP(c_Set_OPow(U_11512),U_11515)) = hAPP(c_Set_OPow(U_11513),U_11516)
      | hAPP(c_Set_Oimage(U_11512,U_11513,U_11514),U_11515) != U_11516 ),
    inference(variable_rename,[status(thm)],[f_2989_1]) ).

fof(f_2989_3,plain,
    ! [U_11512,U_11513,U_11514,U_11515,U_11516] :
      ( hAPP(c_Set_Oimage(tc_fun(U_11512,tc_HOL_Obool),tc_fun(U_11513,tc_HOL_Obool),c_Set_Oimage(U_11512,U_11513,U_11514)),hAPP(c_Set_OPow(U_11512),U_11515)) = hAPP(c_Set_OPow(U_11513),U_11516)
      | hAPP(c_Set_Oimage(U_11512,U_11513,U_11514),U_11515) != U_11516 ),
    inference(definitional_conversion,[status(esa)],[f_2989_2]) ).

cnf(f_2989_4,plain,
    ( hAPP(c_Set_Oimage(tc_fun(U_11512,tc_HOL_Obool),tc_fun(U_11513,tc_HOL_Obool),c_Set_Oimage(U_11512,U_11513,U_11514)),hAPP(c_Set_OPow(U_11512),U_11515)) = hAPP(c_Set_OPow(U_11513),U_11516)
    | hAPP(c_Set_Oimage(U_11512,U_11513,U_11514),U_11515) != U_11516 ),
    inference(clausify,[status(thm)],[f_2989_3]) ).

fof(f_2990_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_2990_2,plain,
    ! [U_11519,U_11518,U_11517] : hAPP(c_Set_OPow(U_11517),hAPP(hAPP(c_Set_Oinsert(U_11517),U_11518),U_11519)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11517,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11517),U_11519)),hAPP(c_Set_Oimage(tc_fun(U_11517,tc_HOL_Obool),tc_fun(U_11517,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_11517),U_11518)),hAPP(c_Set_OPow(U_11517),U_11519))),
    inference(variable_rename,[status(thm)],[f_2990_1]) ).

fof(f_2990_3,plain,
    ! [U_11517,U_11518,U_11519] : hAPP(c_Set_OPow(U_11517),hAPP(hAPP(c_Set_Oinsert(U_11517),U_11518),U_11519)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11517,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11517),U_11519)),hAPP(c_Set_Oimage(tc_fun(U_11517,tc_HOL_Obool),tc_fun(U_11517,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_11517),U_11518)),hAPP(c_Set_OPow(U_11517),U_11519))),
    inference(definitional_conversion,[status(esa)],[f_2990_2]) ).

cnf(f_2990_4,plain,
    hAPP(c_Set_OPow(U_11517),hAPP(hAPP(c_Set_Oinsert(U_11517),U_11518),U_11519)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11517,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11517),U_11519)),hAPP(c_Set_Oimage(tc_fun(U_11517,tc_HOL_Obool),tc_fun(U_11517,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_11517),U_11518)),hAPP(c_Set_OPow(U_11517),U_11519))),
    inference(clausify,[status(thm)],[f_2990_3]) ).

fof(f_2991_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_2991_2,plain,
    ! [U_11521,U_11520] : hAPP(c_Set_OPow(U_11520),U_11521) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11520,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2991_1]) ).

fof(f_2991_3,plain,
    ! [U_11520,U_11521] : hAPP(c_Set_OPow(U_11520),U_11521) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11520,tc_HOL_Obool),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2991_2]) ).

cnf(f_2991_4,plain,
    hAPP(c_Set_OPow(U_11520),U_11521) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11520,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2991_3]) ).

fof(f_2992_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_2992_2,plain,
    ! [U_11524,U_11523,U_11522] : hAPP(c_Set_OPow(U_11522),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11522,tc_HOL_Obool)),U_11523),U_11524)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_11522,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11522),U_11523)),hAPP(c_Set_OPow(U_11522),U_11524)),
    inference(variable_rename,[status(thm)],[f_2992_1]) ).

fof(f_2992_3,plain,
    ! [U_11522,U_11523,U_11524] : hAPP(c_Set_OPow(U_11522),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11522,tc_HOL_Obool)),U_11523),U_11524)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_11522,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11522),U_11523)),hAPP(c_Set_OPow(U_11522),U_11524)),
    inference(definitional_conversion,[status(esa)],[f_2992_2]) ).

cnf(f_2992_4,plain,
    hAPP(c_Set_OPow(U_11522),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11522,tc_HOL_Obool)),U_11523),U_11524)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_11522,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11522),U_11523)),hAPP(c_Set_OPow(U_11522),U_11524)),
    inference(clausify,[status(thm)],[f_2992_3]) ).

fof(f_2993_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_2993_2,plain,
    ! [U_11526,U_11525] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_11525,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11525,tc_HOL_Obool))),hAPP(c_Set_OPow(U_11525),U_11526))),
    inference(variable_rename,[status(thm)],[f_2993_1]) ).

fof(f_2993_3,plain,
    ! [U_11525,U_11526] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_11525,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11525,tc_HOL_Obool))),hAPP(c_Set_OPow(U_11525),U_11526))),
    inference(definitional_conversion,[status(esa)],[f_2993_2]) ).

cnf(f_2993_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(U_11525,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11525,tc_HOL_Obool))),hAPP(c_Set_OPow(U_11525),U_11526))),
    inference(clausify,[status(thm)],[f_2993_3]) ).

fof(f_2994_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_2994_2,plain,
    ! [U_11529,U_11528,U_11527] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11527,tc_HOL_Obool)),U_11528),U_11529))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11527,tc_HOL_Obool)),U_11528),hAPP(c_Set_OPow(U_11527),U_11529))) ),
    inference(variable_rename,[status(thm)],[f_2994_1]) ).

fof(f_2994_3,plain,
    ! [U_11527,U_11528,U_11529] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11527,tc_HOL_Obool)),U_11528),U_11529))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11527,tc_HOL_Obool)),U_11528),hAPP(c_Set_OPow(U_11527),U_11529))) ),
    inference(definitional_conversion,[status(esa)],[f_2994_2]) ).

cnf(f_2994_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11527,tc_HOL_Obool)),U_11528),U_11529))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11527,tc_HOL_Obool)),U_11528),hAPP(c_Set_OPow(U_11527),U_11529))) ),
    inference(clausify,[status(thm)],[f_2994_3]) ).

fof(f_2995_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_2995_2,plain,
    ! [U_11532,U_11531,U_11530] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11530,tc_HOL_Obool)),U_11531),hAPP(c_Set_OPow(U_11530),U_11532)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11530,tc_HOL_Obool)),U_11531),U_11532)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11530,tc_HOL_Obool)),U_11531),U_11532))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11530,tc_HOL_Obool)),U_11531),hAPP(c_Set_OPow(U_11530),U_11532))) ) ),
    inference(variable_rename,[status(thm)],[f_2995_1]) ).

fof(f_2995_3,plain,
    ( ! [U_11538,U_11536,U_11534] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11534,tc_HOL_Obool)),U_11536),hAPP(c_Set_OPow(U_11534),U_11538)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11534,tc_HOL_Obool)),U_11536),U_11538)) )
    & ! [U_11537,U_11535,U_11533] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11533,tc_HOL_Obool)),U_11535),U_11537))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11533,tc_HOL_Obool)),U_11535),hAPP(c_Set_OPow(U_11533),U_11537))) ) ),
    inference(miniscope,[status(thm)],[f_2995_2]) ).

fof(f_2995_4,plain,
    ( ! [U_11534,U_11536,U_11538] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11534,tc_HOL_Obool)),U_11536),hAPP(c_Set_OPow(U_11534),U_11538)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11534,tc_HOL_Obool)),U_11536),U_11538)) )
    & ! [U_11535,U_11537,U_11533] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11533,tc_HOL_Obool)),U_11535),U_11537))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11533,tc_HOL_Obool)),U_11535),hAPP(c_Set_OPow(U_11533),U_11537))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2995_3]) ).

cnf(f_2995_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11533,tc_HOL_Obool)),U_11535),U_11537))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11533,tc_HOL_Obool)),U_11535),hAPP(c_Set_OPow(U_11533),U_11537))) ),
    inference(clausify,[status(thm)],[f_2995_4]) ).

cnf(f_2995_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11534,tc_HOL_Obool)),U_11536),hAPP(c_Set_OPow(U_11534),U_11538)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11534,tc_HOL_Obool)),U_11536),U_11538)) ),
    inference(clausify,[status(thm)],[f_2995_4]) ).

fof(f_2996_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_2996_2,plain,
    ! [U_11541,U_11540,U_11539] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11539,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11539),U_11540)),hAPP(c_Set_OPow(U_11539),U_11541)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11539,tc_HOL_Obool)),U_11540),U_11541)) ),
    inference(variable_rename,[status(thm)],[f_2996_1]) ).

fof(f_2996_3,plain,
    ! [U_11539,U_11540,U_11541] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11539,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11539),U_11540)),hAPP(c_Set_OPow(U_11539),U_11541)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11539,tc_HOL_Obool)),U_11540),U_11541)) ),
    inference(definitional_conversion,[status(esa)],[f_2996_2]) ).

cnf(f_2996_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11539,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11539),U_11540)),hAPP(c_Set_OPow(U_11539),U_11541)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11539,tc_HOL_Obool)),U_11540),U_11541)) ),
    inference(clausify,[status(thm)],[f_2996_3]) ).

fof(f_2997_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_2997_2,plain,
    ! [U_11544,U_11543,U_11542] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11542,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11542,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11542),U_11543)),hAPP(c_Set_OPow(U_11542),U_11544))),hAPP(c_Set_OPow(U_11542),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11542,tc_HOL_Obool)),U_11543),U_11544)))),
    inference(variable_rename,[status(thm)],[f_2997_1]) ).

fof(f_2997_3,plain,
    ! [U_11542,U_11543,U_11544] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11542,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11542,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11542),U_11543)),hAPP(c_Set_OPow(U_11542),U_11544))),hAPP(c_Set_OPow(U_11542),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11542,tc_HOL_Obool)),U_11543),U_11544)))),
    inference(definitional_conversion,[status(esa)],[f_2997_2]) ).

cnf(f_2997_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11542,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11542,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11542),U_11543)),hAPP(c_Set_OPow(U_11542),U_11544))),hAPP(c_Set_OPow(U_11542),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11542,tc_HOL_Obool)),U_11543),U_11544)))),
    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] :
      ( 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_2998_2,plain,
    ! [U_11549,U_11548,U_11547,U_11546,U_11545] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11545,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_11546,tc_HOL_Obool),tc_fun(U_11545,tc_HOL_Obool),c_Set_Oimage(U_11546,U_11545,U_11547)),hAPP(c_Set_OPow(U_11546),U_11548))),hAPP(c_Set_OPow(U_11545),U_11549)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11545,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11546,U_11545,U_11547),U_11548)),U_11549)) ),
    inference(variable_rename,[status(thm)],[f_2998_1]) ).

fof(f_2998_3,plain,
    ! [U_11545,U_11546,U_11547,U_11548,U_11549] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11545,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_11546,tc_HOL_Obool),tc_fun(U_11545,tc_HOL_Obool),c_Set_Oimage(U_11546,U_11545,U_11547)),hAPP(c_Set_OPow(U_11546),U_11548))),hAPP(c_Set_OPow(U_11545),U_11549)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11545,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11546,U_11545,U_11547),U_11548)),U_11549)) ),
    inference(definitional_conversion,[status(esa)],[f_2998_2]) ).

cnf(f_2998_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11545,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_11546,tc_HOL_Obool),tc_fun(U_11545,tc_HOL_Obool),c_Set_Oimage(U_11546,U_11545,U_11547)),hAPP(c_Set_OPow(U_11546),U_11548))),hAPP(c_Set_OPow(U_11545),U_11549)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11545,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11546,U_11545,U_11547),U_11548)),U_11549)) ),
    inference(clausify,[status(thm)],[f_2998_3]) ).

fof(f_2999_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_2999_2,plain,
    ! [U_11550] : hAPP(c_Set_OPow(U_11550),c_Orderings_Obot__class_Obot(tc_fun(U_11550,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_11550,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11550,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11550,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2999_1]) ).

fof(f_2999_3,plain,
    ! [U_11550] : hAPP(c_Set_OPow(U_11550),c_Orderings_Obot__class_Obot(tc_fun(U_11550,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_11550,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11550,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11550,tc_HOL_Obool),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2999_2]) ).

cnf(f_2999_4,plain,
    hAPP(c_Set_OPow(U_11550),c_Orderings_Obot__class_Obot(tc_fun(U_11550,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_11550,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11550,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11550,tc_HOL_Obool),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2999_3]) ).

fof(f_3000_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_3000_2,plain,
    ! [U_11553,U_11552,U_11551] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(U_11551,hAPP(hAPP(c_COMBC(U_11551,tc_fun(U_11551,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11551)),U_11552)),U_11553))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11551,tc_HOL_Obool)),U_11553),hAPP(c_Set_OPow(U_11551),U_11552))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11551,tc_HOL_Obool)),U_11553),hAPP(c_Set_OPow(U_11551),U_11552)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_11551,hAPP(hAPP(c_COMBC(U_11551,tc_fun(U_11551,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11551)),U_11552)),U_11553)) ) ),
    inference(variable_rename,[status(thm)],[f_3000_1]) ).

fof(f_3000_3,plain,
    ( ! [U_11559,U_11557,U_11555] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_11555,hAPP(hAPP(c_COMBC(U_11555,tc_fun(U_11555,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11555)),U_11557)),U_11559))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11555,tc_HOL_Obool)),U_11559),hAPP(c_Set_OPow(U_11555),U_11557))) )
    & ! [U_11558,U_11556,U_11554] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11554,tc_HOL_Obool)),U_11558),hAPP(c_Set_OPow(U_11554),U_11556)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_11554,hAPP(hAPP(c_COMBC(U_11554,tc_fun(U_11554,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11554)),U_11556)),U_11558)) ) ),
    inference(miniscope,[status(thm)],[f_3000_2]) ).

fof(f_3000_4,plain,
    ( ! [U_11555,U_11557,U_11559] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_11555,hAPP(hAPP(c_COMBC(U_11555,tc_fun(U_11555,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11555)),U_11557)),U_11559))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11555,tc_HOL_Obool)),U_11559),hAPP(c_Set_OPow(U_11555),U_11557))) )
    & ! [U_11556,U_11558,U_11554] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11554,tc_HOL_Obool)),U_11558),hAPP(c_Set_OPow(U_11554),U_11556)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_11554,hAPP(hAPP(c_COMBC(U_11554,tc_fun(U_11554,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11554)),U_11556)),U_11558)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3000_3]) ).

cnf(f_3000_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11554,tc_HOL_Obool)),U_11558),hAPP(c_Set_OPow(U_11554),U_11556)))
    | ~ hBOOL(hAPP(c_Predicate_OPowp(U_11554,hAPP(hAPP(c_COMBC(U_11554,tc_fun(U_11554,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11554)),U_11556)),U_11558)) ),
    inference(clausify,[status(thm)],[f_3000_4]) ).

cnf(f_3000_6,plain,
    ( hBOOL(hAPP(c_Predicate_OPowp(U_11555,hAPP(hAPP(c_COMBC(U_11555,tc_fun(U_11555,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11555)),U_11557)),U_11559))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11555,tc_HOL_Obool)),U_11559),hAPP(c_Set_OPow(U_11555),U_11557))) ),
    inference(clausify,[status(thm)],[f_3000_4]) ).

fof(f_3001_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_3001_2,plain,
    ! [U_11563,U_11562,U_11561,U_11560] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11560,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11561,tc_fun(tc_fun(U_11560,tc_HOL_Obool),tc_HOL_Obool)),U_11562),hAPP(hAPP(c_COMBB(tc_fun(U_11560,tc_HOL_Obool),tc_fun(tc_fun(U_11560,tc_HOL_Obool),tc_HOL_Obool),U_11561),c_Set_OPow(U_11560)),U_11563))),hAPP(c_Set_OPow(U_11560),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11561,tc_fun(U_11560,tc_HOL_Obool)),U_11562),U_11563)))),
    inference(variable_rename,[status(thm)],[f_3001_1]) ).

fof(f_3001_3,plain,
    ! [U_11560,U_11561,U_11562,U_11563] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11560,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11561,tc_fun(tc_fun(U_11560,tc_HOL_Obool),tc_HOL_Obool)),U_11562),hAPP(hAPP(c_COMBB(tc_fun(U_11560,tc_HOL_Obool),tc_fun(tc_fun(U_11560,tc_HOL_Obool),tc_HOL_Obool),U_11561),c_Set_OPow(U_11560)),U_11563))),hAPP(c_Set_OPow(U_11560),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11561,tc_fun(U_11560,tc_HOL_Obool)),U_11562),U_11563)))),
    inference(definitional_conversion,[status(esa)],[f_3001_2]) ).

cnf(f_3001_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11560,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11561,tc_fun(tc_fun(U_11560,tc_HOL_Obool),tc_HOL_Obool)),U_11562),hAPP(hAPP(c_COMBB(tc_fun(U_11560,tc_HOL_Obool),tc_fun(tc_fun(U_11560,tc_HOL_Obool),tc_HOL_Obool),U_11561),c_Set_OPow(U_11560)),U_11563))),hAPP(c_Set_OPow(U_11560),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11561,tc_fun(U_11560,tc_HOL_Obool)),U_11562),U_11563)))),
    inference(clausify,[status(thm)],[f_3001_3]) ).

fof(f_3002_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_3002_2,plain,
    ! [U_11566,U_11565,U_11564] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11564,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11564),U_11565),U_11566)) = hAPP(c_Finite__Set_Ocard(U_11564),U_11565)
      | ~ c_Fun_Oinj__on(U_11564,tc_fun(tc_fun(U_11564,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11564,tc_fun(tc_prod(U_11564,U_11564),tc_HOL_Obool),tc_fun(tc_fun(U_11564,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11564,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11564,U_11564),tc_HOL_Obool),tc_fun(tc_fun(U_11564,tc_HOL_Obool),tc_HOL_Obool)),U_11564),c_Equiv__Relations_Oquotient(U_11564)),hAPP(hAPP(c_COMBC(U_11564,tc_fun(U_11564,tc_HOL_Obool),tc_fun(U_11564,tc_HOL_Obool)),c_Set_Oinsert(U_11564)),c_Orderings_Obot__class_Obot(tc_fun(U_11564,tc_HOL_Obool))))),U_11566),U_11565)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11564),U_11565)) ),
    inference(variable_rename,[status(thm)],[f_3002_1]) ).

fof(f_3002_3,plain,
    ! [U_11564,U_11565,U_11566] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11564,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11564),U_11565),U_11566)) = hAPP(c_Finite__Set_Ocard(U_11564),U_11565)
      | ~ c_Fun_Oinj__on(U_11564,tc_fun(tc_fun(U_11564,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11564,tc_fun(tc_prod(U_11564,U_11564),tc_HOL_Obool),tc_fun(tc_fun(U_11564,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11564,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11564,U_11564),tc_HOL_Obool),tc_fun(tc_fun(U_11564,tc_HOL_Obool),tc_HOL_Obool)),U_11564),c_Equiv__Relations_Oquotient(U_11564)),hAPP(hAPP(c_COMBC(U_11564,tc_fun(U_11564,tc_HOL_Obool),tc_fun(U_11564,tc_HOL_Obool)),c_Set_Oinsert(U_11564)),c_Orderings_Obot__class_Obot(tc_fun(U_11564,tc_HOL_Obool))))),U_11566),U_11565)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11564),U_11565)) ),
    inference(definitional_conversion,[status(esa)],[f_3002_2]) ).

cnf(f_3002_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11564,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11564),U_11565),U_11566)) = hAPP(c_Finite__Set_Ocard(U_11564),U_11565)
    | ~ c_Fun_Oinj__on(U_11564,tc_fun(tc_fun(U_11564,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11564,tc_fun(tc_prod(U_11564,U_11564),tc_HOL_Obool),tc_fun(tc_fun(U_11564,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11564,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11564,U_11564),tc_HOL_Obool),tc_fun(tc_fun(U_11564,tc_HOL_Obool),tc_HOL_Obool)),U_11564),c_Equiv__Relations_Oquotient(U_11564)),hAPP(hAPP(c_COMBC(U_11564,tc_fun(U_11564,tc_HOL_Obool),tc_fun(U_11564,tc_HOL_Obool)),c_Set_Oinsert(U_11564)),c_Orderings_Obot__class_Obot(tc_fun(U_11564,tc_HOL_Obool))))),U_11566),U_11565)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11564),U_11565)) ),
    inference(clausify,[status(thm)],[f_3002_3]) ).

fof(f_3003_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_3003_2,plain,
    ! [U_11571,U_11570,U_11569] :
      ( hBOOL(hAPP(U_11571,c_Orderings_Obot__class_Obot(tc_fun(U_11569,tc_HOL_Obool))))
      | ? [U_11568,U_11567] :
          ( ~ hBOOL(hAPP(U_11571,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11569,tc_HOL_Obool)),U_11567),hAPP(hAPP(c_Set_Oinsert(U_11569),U_11568),c_Orderings_Obot__class_Obot(tc_fun(U_11569,tc_HOL_Obool))))))
          & hBOOL(hAPP(U_11571,U_11567))
          & hBOOL(hAPP(hAPP(c_member(U_11569),U_11568),U_11567))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11569),U_11567)) )
      | ~ hBOOL(hAPP(U_11571,U_11570))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11569),U_11570)) ),
    inference(variable_rename,[status(thm)],[f_3003_1]) ).

fof(f_3003_3,plain,
    ! [U_11571,U_11570,U_11569] :
      ( hBOOL(hAPP(U_11571,c_Orderings_Obot__class_Obot(tc_fun(U_11569,tc_HOL_Obool))))
      | ? [U_11567] :
          ( ~ hBOOL(hAPP(U_11571,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11569,tc_HOL_Obool)),U_11567),hAPP(hAPP(c_Set_Oinsert(U_11569),sK209(U_11571,U_11570,U_11569)),c_Orderings_Obot__class_Obot(tc_fun(U_11569,tc_HOL_Obool))))))
          & hBOOL(hAPP(U_11571,U_11567))
          & hBOOL(hAPP(hAPP(c_member(U_11569),sK209(U_11571,U_11570,U_11569)),U_11567))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11569),U_11567)) )
      | ~ hBOOL(hAPP(U_11571,U_11570))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11569),U_11570)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK209]),skolemize(U_11568,sK209(U_11571,U_11570,U_11569))],[f_3003_2]) ).

fof(f_3003_4,plain,
    ! [U_11571,U_11570,U_11569] :
      ( hBOOL(hAPP(U_11571,c_Orderings_Obot__class_Obot(tc_fun(U_11569,tc_HOL_Obool))))
      | ( ~ hBOOL(hAPP(U_11571,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11569,tc_HOL_Obool)),sK210(U_11571,U_11570,U_11569)),hAPP(hAPP(c_Set_Oinsert(U_11569),sK209(U_11571,U_11570,U_11569)),c_Orderings_Obot__class_Obot(tc_fun(U_11569,tc_HOL_Obool))))))
        & hBOOL(hAPP(U_11571,sK210(U_11571,U_11570,U_11569)))
        & hBOOL(hAPP(hAPP(c_member(U_11569),sK209(U_11571,U_11570,U_11569)),sK210(U_11571,U_11570,U_11569)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11569),sK210(U_11571,U_11570,U_11569))) )
      | ~ hBOOL(hAPP(U_11571,U_11570))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11569),U_11570)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK210]),skolemize(U_11567,sK210(U_11571,U_11570,U_11569))],[f_3003_3]) ).

fof(f_3003_5,plain,
    ( ! [U_11569,U_11570,U_11571] :
        ( ~ hBOOL(hAPP(U_11571,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11569,tc_HOL_Obool)),sK210(U_11571,U_11570,U_11569)),hAPP(hAPP(c_Set_Oinsert(U_11569),sK209(U_11571,U_11570,U_11569)),c_Orderings_Obot__class_Obot(tc_fun(U_11569,tc_HOL_Obool))))))
        | ~ sP847(U_11569,U_11570,U_11571) )
    & ! [U_11569,U_11570,U_11571] :
        ( hBOOL(hAPP(U_11571,sK210(U_11571,U_11570,U_11569)))
        | ~ sP847(U_11569,U_11570,U_11571) )
    & ! [U_11569,U_11570,U_11571] :
        ( hBOOL(hAPP(hAPP(c_member(U_11569),sK209(U_11571,U_11570,U_11569)),sK210(U_11571,U_11570,U_11569)))
        | ~ sP847(U_11569,U_11570,U_11571) )
    & ! [U_11569,U_11570,U_11571] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11569),sK210(U_11571,U_11570,U_11569)))
        | ~ sP847(U_11569,U_11570,U_11571) )
    & ! [U_11569,U_11570,U_11571] :
        ( hBOOL(hAPP(U_11571,c_Orderings_Obot__class_Obot(tc_fun(U_11569,tc_HOL_Obool))))
        | sP847(U_11569,U_11570,U_11571)
        | ~ hBOOL(hAPP(U_11571,U_11570))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11569),U_11570)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP847])],[f_3003_4]) ).

cnf(f_3003_6,plain,
    ( hBOOL(hAPP(U_11571,c_Orderings_Obot__class_Obot(tc_fun(U_11569,tc_HOL_Obool))))
    | sP847(U_11569,U_11570,U_11571)
    | ~ hBOOL(hAPP(U_11571,U_11570))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11569),U_11570)) ),
    inference(clausify,[status(thm)],[f_3003_5]) ).

cnf(f_3003_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11569),sK210(U_11571,U_11570,U_11569)))
    | ~ sP847(U_11569,U_11570,U_11571) ),
    inference(clausify,[status(thm)],[f_3003_5]) ).

cnf(f_3003_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11569),sK209(U_11571,U_11570,U_11569)),sK210(U_11571,U_11570,U_11569)))
    | ~ sP847(U_11569,U_11570,U_11571) ),
    inference(clausify,[status(thm)],[f_3003_5]) ).

cnf(f_3003_9,plain,
    ( hBOOL(hAPP(U_11571,sK210(U_11571,U_11570,U_11569)))
    | ~ sP847(U_11569,U_11570,U_11571) ),
    inference(clausify,[status(thm)],[f_3003_5]) ).

cnf(f_3003_10,plain,
    ( ~ hBOOL(hAPP(U_11571,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11569,tc_HOL_Obool)),sK210(U_11571,U_11570,U_11569)),hAPP(hAPP(c_Set_Oinsert(U_11569),sK209(U_11571,U_11570,U_11569)),c_Orderings_Obot__class_Obot(tc_fun(U_11569,tc_HOL_Obool))))))
    | ~ sP847(U_11569,U_11570,U_11571) ),
    inference(clausify,[status(thm)],[f_3003_5]) ).

fof(f_3004_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_3004_2,plain,
    ! [U_11575,U_11574,U_11573,U_11572] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11572,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11572,U_11573,U_11574)),c_SetInterval_Oord__class_OatLeastAtMost(U_11572,U_11574,U_11575)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11572,U_11573,U_11575)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11572),U_11574),U_11575))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11572),U_11573),U_11574))
      | ~ class_Orderings_Olinorder(U_11572) ),
    inference(variable_rename,[status(thm)],[f_3004_1]) ).

fof(f_3004_3,plain,
    ! [U_11574,U_11575,U_11573,U_11572] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11572,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11572,U_11573,U_11574)),c_SetInterval_Oord__class_OatLeastAtMost(U_11572,U_11574,U_11575)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11572,U_11573,U_11575)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11572),U_11574),U_11575))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11572),U_11573),U_11574))
      | ~ class_Orderings_Olinorder(U_11572) ),
    inference(definitional_conversion,[status(esa)],[f_3004_2]) ).

cnf(f_3004_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11572,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11572,U_11573,U_11574)),c_SetInterval_Oord__class_OatLeastAtMost(U_11572,U_11574,U_11575)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11572,U_11573,U_11575)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11572),U_11574),U_11575))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11572),U_11573),U_11574))
    | ~ class_Orderings_Olinorder(U_11572) ),
    inference(clausify,[status(thm)],[f_3004_3]) ).

fof(f_3005_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_3005_2,plain,
    ! [U_11577,U_11576] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11576,U_11577))),
    inference(variable_rename,[status(thm)],[f_3005_1]) ).

fof(f_3005_3,plain,
    ! [U_11577,U_11576] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11576,U_11577))),
    inference(definitional_conversion,[status(esa)],[f_3005_2]) ).

cnf(f_3005_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11576,U_11577))),
    inference(clausify,[status(thm)],[f_3005_3]) ).

fof(f_3006_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_3006_2,plain,
    ! [U_11579,U_11578] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11578,U_11579))),
    inference(variable_rename,[status(thm)],[f_3006_1]) ).

fof(f_3006_3,plain,
    ! [U_11579,U_11578] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11578,U_11579))),
    inference(definitional_conversion,[status(esa)],[f_3006_2]) ).

cnf(f_3006_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11578,U_11579))),
    inference(clausify,[status(thm)],[f_3006_3]) ).

fof(f_3007_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_3007_2,plain,
    ! [U_11582,U_11581,U_11580] : 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_11580)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11581,U_11582)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11581),U_11580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11582),U_11580)),
    inference(variable_rename,[status(thm)],[f_3007_1]) ).

fof(f_3007_3,plain,
    ! [U_11580,U_11581,U_11582] : 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_11580)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11581,U_11582)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11581),U_11580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11582),U_11580)),
    inference(definitional_conversion,[status(esa)],[f_3007_2]) ).

cnf(f_3007_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_11580)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11581,U_11582)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11581),U_11580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11582),U_11580)),
    inference(clausify,[status(thm)],[f_3007_3]) ).

fof(f_3008_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_3008_2,plain,
    ! [U_11584,U_11583] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11583,U_11584)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11583),hAPP(c_Nat_OSuc,U_11584)),
    inference(variable_rename,[status(thm)],[f_3008_1]) ).

fof(f_3008_3,plain,
    ! [U_11583,U_11584] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11583,U_11584)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11583),hAPP(c_Nat_OSuc,U_11584)),
    inference(definitional_conversion,[status(esa)],[f_3008_2]) ).

cnf(f_3008_4,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11583,U_11584)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11583),hAPP(c_Nat_OSuc,U_11584)),
    inference(clausify,[status(thm)],[f_3008_3]) ).

fof(f_3009_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_3009_2,plain,
    ! [U_11586,U_11585] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11585,U_11586) = 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_11585),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11586))),
    inference(variable_rename,[status(thm)],[f_3009_1]) ).

fof(f_3009_3,plain,
    ! [U_11585,U_11586] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11585,U_11586) = 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_11585),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11586))),
    inference(definitional_conversion,[status(esa)],[f_3009_2]) ).

cnf(f_3009_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11585,U_11586) = 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_11585),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11586))),
    inference(clausify,[status(thm)],[f_3009_3]) ).

fof(f_3010_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_3010_2,plain,
    ! [U_11590,U_11589,U_11588,U_11587] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11588),U_11590))
      | ~ c_Fun_Oinj__on(U_11588,U_11587,U_11589,U_11590)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11587),hAPP(c_Set_Oimage(U_11588,U_11587,U_11589),U_11590))) ),
    inference(variable_rename,[status(thm)],[f_3010_1]) ).

fof(f_3010_3,plain,
    ! [U_11587,U_11588,U_11589,U_11590] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11588),U_11590))
      | ~ c_Fun_Oinj__on(U_11588,U_11587,U_11589,U_11590)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11587),hAPP(c_Set_Oimage(U_11588,U_11587,U_11589),U_11590))) ),
    inference(definitional_conversion,[status(esa)],[f_3010_2]) ).

cnf(f_3010_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11588),U_11590))
    | ~ c_Fun_Oinj__on(U_11588,U_11587,U_11589,U_11590)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11587),hAPP(c_Set_Oimage(U_11588,U_11587,U_11589),U_11590))) ),
    inference(clausify,[status(thm)],[f_3010_3]) ).

fof(f_3011_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_3011_2,plain,
    ! [U_11594,U_11593,U_11592,U_11591] :
      ( hAPP(c_Finite__Set_Ocard(U_11592),hAPP(c_Set_Oimage(U_11591,U_11592,U_11593),U_11594)) = hAPP(c_Finite__Set_Ocard(U_11591),U_11594)
      | ~ c_Fun_Oinj__on(U_11591,U_11592,U_11593,U_11594) ),
    inference(variable_rename,[status(thm)],[f_3011_1]) ).

fof(f_3011_3,plain,
    ! [U_11591,U_11592,U_11593,U_11594] :
      ( hAPP(c_Finite__Set_Ocard(U_11592),hAPP(c_Set_Oimage(U_11591,U_11592,U_11593),U_11594)) = hAPP(c_Finite__Set_Ocard(U_11591),U_11594)
      | ~ c_Fun_Oinj__on(U_11591,U_11592,U_11593,U_11594) ),
    inference(definitional_conversion,[status(esa)],[f_3011_2]) ).

cnf(f_3011_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11592),hAPP(c_Set_Oimage(U_11591,U_11592,U_11593),U_11594)) = hAPP(c_Finite__Set_Ocard(U_11591),U_11594)
    | ~ c_Fun_Oinj__on(U_11591,U_11592,U_11593,U_11594) ),
    inference(clausify,[status(thm)],[f_3011_3]) ).

fof(f_3012_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_3012_2,plain,
    ! [U_11596,U_11595] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11595,U_11596) = 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_11595),hAPP(c_Int_Onat,U_11596)))
      | ~ c_Nat__Transfer_Ois__nat(U_11596)
      | ~ c_Nat__Transfer_Ois__nat(U_11595) ),
    inference(variable_rename,[status(thm)],[f_3012_1]) ).

fof(f_3012_3,plain,
    ! [U_11595,U_11596] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11595,U_11596) = 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_11595),hAPP(c_Int_Onat,U_11596)))
      | ~ c_Nat__Transfer_Ois__nat(U_11596)
      | ~ c_Nat__Transfer_Ois__nat(U_11595) ),
    inference(definitional_conversion,[status(esa)],[f_3012_2]) ).

cnf(f_3012_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11595,U_11596) = 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_11595),hAPP(c_Int_Onat,U_11596)))
    | ~ c_Nat__Transfer_Ois__nat(U_11596)
    | ~ c_Nat__Transfer_Ois__nat(U_11595) ),
    inference(clausify,[status(thm)],[f_3012_3]) ).

fof(f_3013_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_3013_2,plain,
    ! [U_11598,U_11597] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11597,U_11598))
      | ~ c_Nat__Transfer_Ois__nat(U_11597) ),
    inference(variable_rename,[status(thm)],[f_3013_1]) ).

fof(f_3013_3,plain,
    ! [U_11598,U_11597] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11597,U_11598))
      | ~ c_Nat__Transfer_Ois__nat(U_11597) ),
    inference(definitional_conversion,[status(esa)],[f_3013_2]) ).

cnf(f_3013_4,plain,
    ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11597,U_11598))
    | ~ c_Nat__Transfer_Ois__nat(U_11597) ),
    inference(clausify,[status(thm)],[f_3013_3]) ).

fof(f_3014_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_3014_2,plain,
    ! [U_11601,U_11600,U_11599] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_11599,U_11600,U_11601) = c_Orderings_Obot__class_Obot(tc_fun(U_11599,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11599),U_11600),U_11601)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11599),U_11600),U_11601))
          | c_SetInterval_Oord__class_OatLeastAtMost(U_11599,U_11600,U_11601) != c_Orderings_Obot__class_Obot(tc_fun(U_11599,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_11599) ),
    inference(variable_rename,[status(thm)],[f_3014_1]) ).

fof(f_3014_3,plain,
    ( ! [U_11599,U_11600,U_11601] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(U_11599,U_11600,U_11601) = c_Orderings_Obot__class_Obot(tc_fun(U_11599,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11599),U_11600),U_11601))
        | ~ sP848(U_11599,U_11600,U_11601) )
    & ! [U_11599,U_11600,U_11601] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11599),U_11600),U_11601))
        | c_SetInterval_Oord__class_OatLeastAtMost(U_11599,U_11600,U_11601) != c_Orderings_Obot__class_Obot(tc_fun(U_11599,tc_HOL_Obool))
        | ~ sP848(U_11599,U_11600,U_11601) )
    & ! [U_11599,U_11600,U_11601] :
        ( sP848(U_11599,U_11600,U_11601)
        | ~ class_Orderings_Oorder(U_11599) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP848])],[f_3014_2]) ).

cnf(f_3014_4,plain,
    ( sP848(U_11599,U_11600,U_11601)
    | ~ class_Orderings_Oorder(U_11599) ),
    inference(clausify,[status(thm)],[f_3014_3]) ).

cnf(f_3014_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11599),U_11600),U_11601))
    | c_SetInterval_Oord__class_OatLeastAtMost(U_11599,U_11600,U_11601) != c_Orderings_Obot__class_Obot(tc_fun(U_11599,tc_HOL_Obool))
    | ~ sP848(U_11599,U_11600,U_11601) ),
    inference(clausify,[status(thm)],[f_3014_3]) ).

cnf(f_3014_6,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_11599,U_11600,U_11601) = c_Orderings_Obot__class_Obot(tc_fun(U_11599,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11599),U_11600),U_11601))
    | ~ sP848(U_11599,U_11600,U_11601) ),
    inference(clausify,[status(thm)],[f_3014_3]) ).

fof(f_3015_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_3015_2,plain,
    ! [U_11604,U_11603,U_11602] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_11602,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11602,U_11603,U_11604)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11602),U_11603),U_11604)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11602),U_11603),U_11604))
          | c_Orderings_Obot__class_Obot(tc_fun(U_11602,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_11602,U_11603,U_11604) ) )
      | ~ class_Orderings_Oorder(U_11602) ),
    inference(variable_rename,[status(thm)],[f_3015_1]) ).

fof(f_3015_3,plain,
    ( ! [U_11603,U_11604,U_11602] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_11602,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11602,U_11603,U_11604)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11602),U_11603),U_11604))
        | ~ sP849(U_11603,U_11604,U_11602) )
    & ! [U_11603,U_11604,U_11602] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11602),U_11603),U_11604))
        | c_Orderings_Obot__class_Obot(tc_fun(U_11602,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_11602,U_11603,U_11604)
        | ~ sP849(U_11603,U_11604,U_11602) )
    & ! [U_11603,U_11604,U_11602] :
        ( sP849(U_11603,U_11604,U_11602)
        | ~ class_Orderings_Oorder(U_11602) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP849])],[f_3015_2]) ).

cnf(f_3015_4,plain,
    ( sP849(U_11603,U_11604,U_11602)
    | ~ class_Orderings_Oorder(U_11602) ),
    inference(clausify,[status(thm)],[f_3015_3]) ).

cnf(f_3015_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11602),U_11603),U_11604))
    | c_Orderings_Obot__class_Obot(tc_fun(U_11602,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_11602,U_11603,U_11604)
    | ~ sP849(U_11603,U_11604,U_11602) ),
    inference(clausify,[status(thm)],[f_3015_3]) ).

cnf(f_3015_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_11602,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11602,U_11603,U_11604)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11602),U_11603),U_11604))
    | ~ sP849(U_11603,U_11604,U_11602) ),
    inference(clausify,[status(thm)],[f_3015_3]) ).

fof(f_3016_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_3016_2,plain,
    ! [U_11607,U_11606,U_11605] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11605,U_11607,U_11606) = c_Orderings_Obot__class_Obot(tc_fun(U_11605,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11605),U_11606),U_11607))
      | ~ class_Orderings_Oorder(U_11605) ),
    inference(variable_rename,[status(thm)],[f_3016_1]) ).

fof(f_3016_3,plain,
    ! [U_11607,U_11606,U_11605] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11605,U_11607,U_11606) = c_Orderings_Obot__class_Obot(tc_fun(U_11605,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11605),U_11606),U_11607))
      | ~ class_Orderings_Oorder(U_11605) ),
    inference(definitional_conversion,[status(esa)],[f_3016_2]) ).

cnf(f_3016_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_11605,U_11607,U_11606) = c_Orderings_Obot__class_Obot(tc_fun(U_11605,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11605),U_11606),U_11607))
    | ~ class_Orderings_Oorder(U_11605) ),
    inference(clausify,[status(thm)],[f_3016_3]) ).

fof(f_3017_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_3017_2,plain,
    ! [U_11612,U_11611,U_11610,U_11609,U_11608] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11608,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11608,U_11609,U_11610)),c_SetInterval_Oord__class_OatLeastAtMost(U_11608,U_11611,U_11612)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11610),U_11612))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11611),U_11609)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11609),U_11610)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11610),U_11612))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11611),U_11609)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11609),U_11610))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11608,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11608,U_11609,U_11610)),c_SetInterval_Oord__class_OatLeastAtMost(U_11608,U_11611,U_11612))) ) )
      | ~ class_Orderings_Oorder(U_11608) ),
    inference(variable_rename,[status(thm)],[f_3017_1]) ).

fof(f_3017_3,plain,
    ( ! [U_11608,U_11609,U_11610,U_11611,U_11612] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11610),U_11612))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11611),U_11609))
        | ~ sP851(U_11608,U_11609,U_11610,U_11611,U_11612) )
    & ! [U_11608,U_11609,U_11610,U_11611,U_11612] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11609),U_11610))
        | ~ sP851(U_11608,U_11609,U_11610,U_11611,U_11612) )
    & ! [U_11608,U_11609,U_11610,U_11611,U_11612] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11610),U_11612))
        | ~ sP850(U_11608,U_11609,U_11610,U_11611,U_11612) )
    & ! [U_11608,U_11609,U_11610,U_11611,U_11612] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11611),U_11609))
        | ~ sP850(U_11608,U_11609,U_11610,U_11611,U_11612) )
    & ! [U_11608,U_11609,U_11610,U_11611,U_11612] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11608,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11608,U_11609,U_11610)),c_SetInterval_Oord__class_OatLeastAtMost(U_11608,U_11611,U_11612)))
        | sP851(U_11608,U_11609,U_11610,U_11611,U_11612)
        | ~ sP852(U_11608,U_11609,U_11610,U_11611,U_11612) )
    & ! [U_11608,U_11609,U_11610,U_11611,U_11612] :
        ( sP850(U_11608,U_11609,U_11610,U_11611,U_11612)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11609),U_11610))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11608,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11608,U_11609,U_11610)),c_SetInterval_Oord__class_OatLeastAtMost(U_11608,U_11611,U_11612)))
        | ~ sP852(U_11608,U_11609,U_11610,U_11611,U_11612) )
    & ! [U_11608,U_11609,U_11610,U_11611,U_11612] :
        ( sP852(U_11608,U_11609,U_11610,U_11611,U_11612)
        | ~ class_Orderings_Oorder(U_11608) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP850,sP851,sP852])],[f_3017_2]) ).

cnf(f_3017_4,plain,
    ( sP852(U_11608,U_11609,U_11610,U_11611,U_11612)
    | ~ class_Orderings_Oorder(U_11608) ),
    inference(clausify,[status(thm)],[f_3017_3]) ).

cnf(f_3017_5,plain,
    ( sP850(U_11608,U_11609,U_11610,U_11611,U_11612)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11609),U_11610))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11608,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11608,U_11609,U_11610)),c_SetInterval_Oord__class_OatLeastAtMost(U_11608,U_11611,U_11612)))
    | ~ sP852(U_11608,U_11609,U_11610,U_11611,U_11612) ),
    inference(clausify,[status(thm)],[f_3017_3]) ).

cnf(f_3017_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11608,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11608,U_11609,U_11610)),c_SetInterval_Oord__class_OatLeastAtMost(U_11608,U_11611,U_11612)))
    | sP851(U_11608,U_11609,U_11610,U_11611,U_11612)
    | ~ sP852(U_11608,U_11609,U_11610,U_11611,U_11612) ),
    inference(clausify,[status(thm)],[f_3017_3]) ).

cnf(f_3017_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11611),U_11609))
    | ~ sP850(U_11608,U_11609,U_11610,U_11611,U_11612) ),
    inference(clausify,[status(thm)],[f_3017_3]) ).

cnf(f_3017_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11610),U_11612))
    | ~ sP850(U_11608,U_11609,U_11610,U_11611,U_11612) ),
    inference(clausify,[status(thm)],[f_3017_3]) ).

cnf(f_3017_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11609),U_11610))
    | ~ sP851(U_11608,U_11609,U_11610,U_11611,U_11612) ),
    inference(clausify,[status(thm)],[f_3017_3]) ).

cnf(f_3017_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11610),U_11612))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11608),U_11611),U_11609))
    | ~ sP851(U_11608,U_11609,U_11610,U_11611,U_11612) ),
    inference(clausify,[status(thm)],[f_3017_3]) ).

fof(f_3018_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_3018_2,plain,
    ! [U_11615,U_11614,U_11613] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11613,U_11614,U_11615) = hAPP(hAPP(c_Set_Oinsert(U_11613),U_11614),c_Orderings_Obot__class_Obot(tc_fun(U_11613,tc_HOL_Obool)))
      | U_11614 != U_11615
      | ~ class_Orderings_Oorder(U_11613) ),
    inference(variable_rename,[status(thm)],[f_3018_1]) ).

fof(f_3018_3,plain,
    ! [U_11615,U_11613,U_11614] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11613,U_11614,U_11615) = hAPP(hAPP(c_Set_Oinsert(U_11613),U_11614),c_Orderings_Obot__class_Obot(tc_fun(U_11613,tc_HOL_Obool)))
      | U_11614 != U_11615
      | ~ class_Orderings_Oorder(U_11613) ),
    inference(definitional_conversion,[status(esa)],[f_3018_2]) ).

cnf(f_3018_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_11613,U_11614,U_11615) = hAPP(hAPP(c_Set_Oinsert(U_11613),U_11614),c_Orderings_Obot__class_Obot(tc_fun(U_11613,tc_HOL_Obool)))
    | U_11614 != U_11615
    | ~ class_Orderings_Oorder(U_11613) ),
    inference(clausify,[status(thm)],[f_3018_3]) ).

fof(f_3019_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_3019_2,plain,
    ! [U_11619,U_11618,U_11617,U_11616] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_11616,U_11617,U_11618) = hAPP(hAPP(c_Set_Oinsert(U_11616),U_11619),c_Orderings_Obot__class_Obot(tc_fun(U_11616,tc_HOL_Obool)))
          | U_11618 != U_11619
          | U_11617 != U_11618 )
        & ( ( U_11618 = U_11619
            & U_11617 = U_11618 )
          | c_SetInterval_Oord__class_OatLeastAtMost(U_11616,U_11617,U_11618) != hAPP(hAPP(c_Set_Oinsert(U_11616),U_11619),c_Orderings_Obot__class_Obot(tc_fun(U_11616,tc_HOL_Obool))) ) )
      | ~ class_Orderings_Oorder(U_11616) ),
    inference(variable_rename,[status(thm)],[f_3019_1]) ).

fof(f_3019_3,plain,
    ( ! [U_11617,U_11619,U_11618] :
        ( U_11618 = U_11619
        | ~ sP853(U_11617,U_11619,U_11618) )
    & ! [U_11617,U_11619,U_11618] :
        ( U_11617 = U_11618
        | ~ sP853(U_11617,U_11619,U_11618) )
    & ! [U_11616,U_11617,U_11619,U_11618] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(U_11616,U_11617,U_11618) = hAPP(hAPP(c_Set_Oinsert(U_11616),U_11619),c_Orderings_Obot__class_Obot(tc_fun(U_11616,tc_HOL_Obool)))
        | U_11618 != U_11619
        | U_11617 != U_11618
        | ~ sP854(U_11616,U_11617,U_11619,U_11618) )
    & ! [U_11616,U_11617,U_11619,U_11618] :
        ( sP853(U_11617,U_11619,U_11618)
        | c_SetInterval_Oord__class_OatLeastAtMost(U_11616,U_11617,U_11618) != hAPP(hAPP(c_Set_Oinsert(U_11616),U_11619),c_Orderings_Obot__class_Obot(tc_fun(U_11616,tc_HOL_Obool)))
        | ~ sP854(U_11616,U_11617,U_11619,U_11618) )
    & ! [U_11616,U_11617,U_11619,U_11618] :
        ( sP854(U_11616,U_11617,U_11619,U_11618)
        | ~ class_Orderings_Oorder(U_11616) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP853,sP854])],[f_3019_2]) ).

cnf(f_3019_4,plain,
    ( sP854(U_11616,U_11617,U_11619,U_11618)
    | ~ class_Orderings_Oorder(U_11616) ),
    inference(clausify,[status(thm)],[f_3019_3]) ).

cnf(f_3019_5,plain,
    ( sP853(U_11617,U_11619,U_11618)
    | c_SetInterval_Oord__class_OatLeastAtMost(U_11616,U_11617,U_11618) != hAPP(hAPP(c_Set_Oinsert(U_11616),U_11619),c_Orderings_Obot__class_Obot(tc_fun(U_11616,tc_HOL_Obool)))
    | ~ sP854(U_11616,U_11617,U_11619,U_11618) ),
    inference(clausify,[status(thm)],[f_3019_3]) ).

cnf(f_3019_6,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_11616,U_11617,U_11618) = hAPP(hAPP(c_Set_Oinsert(U_11616),U_11619),c_Orderings_Obot__class_Obot(tc_fun(U_11616,tc_HOL_Obool)))
    | U_11618 != U_11619
    | U_11617 != U_11618
    | ~ sP854(U_11616,U_11617,U_11619,U_11618) ),
    inference(clausify,[status(thm)],[f_3019_3]) ).

cnf(f_3019_7,plain,
    ( U_11617 = U_11618
    | ~ sP853(U_11617,U_11619,U_11618) ),
    inference(clausify,[status(thm)],[f_3019_3]) ).

cnf(f_3019_8,plain,
    ( U_11618 = U_11619
    | ~ sP853(U_11617,U_11619,U_11618) ),
    inference(clausify,[status(thm)],[f_3019_3]) ).

fof(f_3020_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_3020_2,plain,
    ! [U_11621,U_11620] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11620,U_11621,U_11621) = hAPP(hAPP(c_Set_Oinsert(U_11620),U_11621),c_Orderings_Obot__class_Obot(tc_fun(U_11620,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_11620) ),
    inference(variable_rename,[status(thm)],[f_3020_1]) ).

fof(f_3020_3,plain,
    ! [U_11620,U_11621] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11620,U_11621,U_11621) = hAPP(hAPP(c_Set_Oinsert(U_11620),U_11621),c_Orderings_Obot__class_Obot(tc_fun(U_11620,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_11620) ),
    inference(definitional_conversion,[status(esa)],[f_3020_2]) ).

cnf(f_3020_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_11620,U_11621,U_11621) = hAPP(hAPP(c_Set_Oinsert(U_11620),U_11621),c_Orderings_Obot__class_Obot(tc_fun(U_11620,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_11620) ),
    inference(clausify,[status(thm)],[f_3020_3]) ).

fof(f_3021_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_3021_2,plain,
    ! [U_11624,U_11623,U_11622] :
      ( hAPP(c_Set_Oimage(U_11622,U_11622,c_Groups_Ouminus__class_Ouminus(U_11622)),c_SetInterval_Oord__class_OatLeastAtMost(U_11622,U_11623,U_11624)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11622,hAPP(c_Groups_Ouminus__class_Ouminus(U_11622),U_11624),hAPP(c_Groups_Ouminus__class_Ouminus(U_11622),U_11623))
      | ~ class_Groups_Oordered__ab__group__add(U_11622) ),
    inference(variable_rename,[status(thm)],[f_3021_1]) ).

fof(f_3021_3,plain,
    ! [U_11623,U_11624,U_11622] :
      ( hAPP(c_Set_Oimage(U_11622,U_11622,c_Groups_Ouminus__class_Ouminus(U_11622)),c_SetInterval_Oord__class_OatLeastAtMost(U_11622,U_11623,U_11624)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11622,hAPP(c_Groups_Ouminus__class_Ouminus(U_11622),U_11624),hAPP(c_Groups_Ouminus__class_Ouminus(U_11622),U_11623))
      | ~ class_Groups_Oordered__ab__group__add(U_11622) ),
    inference(definitional_conversion,[status(esa)],[f_3021_2]) ).

cnf(f_3021_4,plain,
    ( hAPP(c_Set_Oimage(U_11622,U_11622,c_Groups_Ouminus__class_Ouminus(U_11622)),c_SetInterval_Oord__class_OatLeastAtMost(U_11622,U_11623,U_11624)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11622,hAPP(c_Groups_Ouminus__class_Ouminus(U_11622),U_11624),hAPP(c_Groups_Ouminus__class_Ouminus(U_11622),U_11623))
    | ~ class_Groups_Oordered__ab__group__add(U_11622) ),
    inference(clausify,[status(thm)],[f_3021_3]) ).

fof(f_3022_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_3022_2,plain,
    ! [U_11626,U_11625] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11625),U_11626) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_11625,U_11626),
    inference(variable_rename,[status(thm)],[f_3022_1]) ).

fof(f_3022_3,plain,
    ! [U_11626,U_11625] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11625),U_11626) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_11625,U_11626),
    inference(definitional_conversion,[status(esa)],[f_3022_2]) ).

cnf(f_3022_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11625),U_11626) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_11625,U_11626),
    inference(clausify,[status(thm)],[f_3022_3]) ).

fof(f_3023_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_3023_2,plain,
    ! [U_11629,U_11628,U_11627] :
      ( c_Fun_Oinj__on(U_11627,U_11627,U_11629,U_11628)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11627,tc_HOL_Obool)),U_11628),hAPP(c_Set_Oimage(U_11627,U_11627,U_11629),U_11628)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11627),U_11628)) ),
    inference(variable_rename,[status(thm)],[f_3023_1]) ).

fof(f_3023_3,plain,
    ! [U_11627,U_11628,U_11629] :
      ( c_Fun_Oinj__on(U_11627,U_11627,U_11629,U_11628)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11627,tc_HOL_Obool)),U_11628),hAPP(c_Set_Oimage(U_11627,U_11627,U_11629),U_11628)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11627),U_11628)) ),
    inference(definitional_conversion,[status(esa)],[f_3023_2]) ).

cnf(f_3023_4,plain,
    ( c_Fun_Oinj__on(U_11627,U_11627,U_11629,U_11628)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11627,tc_HOL_Obool)),U_11628),hAPP(c_Set_Oimage(U_11627,U_11627,U_11629),U_11628)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11627),U_11628)) ),
    inference(clausify,[status(thm)],[f_3023_3]) ).

fof(f_3024_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_3024_2,plain,
    ! [U_11632,U_11631,U_11630] :
      ( hAPP(c_Set_Oimage(U_11630,U_11630,U_11632),U_11631) = U_11631
      | ~ c_Fun_Oinj__on(U_11630,U_11630,U_11632,U_11631)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11630,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11630,U_11630,U_11632),U_11631)),U_11631))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11630),U_11631)) ),
    inference(variable_rename,[status(thm)],[f_3024_1]) ).

fof(f_3024_3,plain,
    ! [U_11630,U_11631,U_11632] :
      ( hAPP(c_Set_Oimage(U_11630,U_11630,U_11632),U_11631) = U_11631
      | ~ c_Fun_Oinj__on(U_11630,U_11630,U_11632,U_11631)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11630,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11630,U_11630,U_11632),U_11631)),U_11631))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11630),U_11631)) ),
    inference(definitional_conversion,[status(esa)],[f_3024_2]) ).

cnf(f_3024_4,plain,
    ( hAPP(c_Set_Oimage(U_11630,U_11630,U_11632),U_11631) = U_11631
    | ~ c_Fun_Oinj__on(U_11630,U_11630,U_11632,U_11631)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11630,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11630,U_11630,U_11632),U_11631)),U_11631))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11630),U_11631)) ),
    inference(clausify,[status(thm)],[f_3024_3]) ).

fof(f_3025_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_3025_2,plain,
    ! [U_11636,U_11635,U_11634,U_11633] :
      ( ( ( c_Fun_Oinj__on(U_11633,U_11635,U_11636,U_11634)
          | hAPP(c_Finite__Set_Ocard(U_11635),hAPP(c_Set_Oimage(U_11633,U_11635,U_11636),U_11634)) != hAPP(c_Finite__Set_Ocard(U_11633),U_11634) )
        & ( hAPP(c_Finite__Set_Ocard(U_11635),hAPP(c_Set_Oimage(U_11633,U_11635,U_11636),U_11634)) = hAPP(c_Finite__Set_Ocard(U_11633),U_11634)
          | ~ c_Fun_Oinj__on(U_11633,U_11635,U_11636,U_11634) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11633),U_11634)) ),
    inference(variable_rename,[status(thm)],[f_3025_1]) ).

fof(f_3025_3,plain,
    ( ! [U_11634,U_11633,U_11635,U_11636] :
        ( c_Fun_Oinj__on(U_11633,U_11635,U_11636,U_11634)
        | hAPP(c_Finite__Set_Ocard(U_11635),hAPP(c_Set_Oimage(U_11633,U_11635,U_11636),U_11634)) != hAPP(c_Finite__Set_Ocard(U_11633),U_11634)
        | ~ sP855(U_11634,U_11633,U_11635,U_11636) )
    & ! [U_11634,U_11633,U_11635,U_11636] :
        ( hAPP(c_Finite__Set_Ocard(U_11635),hAPP(c_Set_Oimage(U_11633,U_11635,U_11636),U_11634)) = hAPP(c_Finite__Set_Ocard(U_11633),U_11634)
        | ~ c_Fun_Oinj__on(U_11633,U_11635,U_11636,U_11634)
        | ~ sP855(U_11634,U_11633,U_11635,U_11636) )
    & ! [U_11634,U_11633,U_11635,U_11636] :
        ( sP855(U_11634,U_11633,U_11635,U_11636)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11633),U_11634)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP855])],[f_3025_2]) ).

cnf(f_3025_4,plain,
    ( sP855(U_11634,U_11633,U_11635,U_11636)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11633),U_11634)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11635),hAPP(c_Set_Oimage(U_11633,U_11635,U_11636),U_11634)) = hAPP(c_Finite__Set_Ocard(U_11633),U_11634)
    | ~ c_Fun_Oinj__on(U_11633,U_11635,U_11636,U_11634)
    | ~ sP855(U_11634,U_11633,U_11635,U_11636) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_6,plain,
    ( c_Fun_Oinj__on(U_11633,U_11635,U_11636,U_11634)
    | hAPP(c_Finite__Set_Ocard(U_11635),hAPP(c_Set_Oimage(U_11633,U_11635,U_11636),U_11634)) != hAPP(c_Finite__Set_Ocard(U_11633),U_11634)
    | ~ sP855(U_11634,U_11633,U_11635,U_11636) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

fof(f_3026_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_3026_2,plain,
    ! [U_11640,U_11639,U_11638,U_11637] :
      ( c_Fun_Oinj__on(U_11637,U_11639,U_11640,U_11638)
      | hAPP(c_Finite__Set_Ocard(U_11639),hAPP(c_Set_Oimage(U_11637,U_11639,U_11640),U_11638)) != hAPP(c_Finite__Set_Ocard(U_11637),U_11638)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11637),U_11638)) ),
    inference(variable_rename,[status(thm)],[f_3026_1]) ).

fof(f_3026_3,plain,
    ! [U_11639,U_11638,U_11640,U_11637] :
      ( c_Fun_Oinj__on(U_11637,U_11639,U_11640,U_11638)
      | hAPP(c_Finite__Set_Ocard(U_11639),hAPP(c_Set_Oimage(U_11637,U_11639,U_11640),U_11638)) != hAPP(c_Finite__Set_Ocard(U_11637),U_11638)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11637),U_11638)) ),
    inference(definitional_conversion,[status(esa)],[f_3026_2]) ).

cnf(f_3026_4,plain,
    ( c_Fun_Oinj__on(U_11637,U_11639,U_11640,U_11638)
    | hAPP(c_Finite__Set_Ocard(U_11639),hAPP(c_Set_Oimage(U_11637,U_11639,U_11640),U_11638)) != hAPP(c_Finite__Set_Ocard(U_11637),U_11638)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11637),U_11638)) ),
    inference(clausify,[status(thm)],[f_3026_3]) ).

fof(f_3027_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_3027_2,plain,
    ! [U_11644,U_11643,U_11642,U_11641] :
      ( ~ c_Fun_Oinj__on(U_11642,U_11641,U_11643,U_11644)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11641),hAPP(c_Set_Oimage(U_11642,U_11641,U_11643),U_11644))),hAPP(c_Finite__Set_Ocard(U_11642),U_11644))) ),
    inference(variable_rename,[status(thm)],[f_3027_1]) ).

fof(f_3027_3,plain,
    ! [U_11641,U_11642,U_11643,U_11644] :
      ( ~ c_Fun_Oinj__on(U_11642,U_11641,U_11643,U_11644)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11641),hAPP(c_Set_Oimage(U_11642,U_11641,U_11643),U_11644))),hAPP(c_Finite__Set_Ocard(U_11642),U_11644))) ),
    inference(definitional_conversion,[status(esa)],[f_3027_2]) ).

cnf(f_3027_4,plain,
    ( ~ c_Fun_Oinj__on(U_11642,U_11641,U_11643,U_11644)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11641),hAPP(c_Set_Oimage(U_11642,U_11641,U_11643),U_11644))),hAPP(c_Finite__Set_Ocard(U_11642),U_11644))) ),
    inference(clausify,[status(thm)],[f_3027_3]) ).

fof(f_3028_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_3028_2,plain,
    ! [U_11646,U_11645] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11645,U_11646))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11645)) ),
    inference(variable_rename,[status(thm)],[f_3028_1]) ).

fof(f_3028_3,plain,
    ! [U_11645,U_11646] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11645,U_11646))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11645)) ),
    inference(definitional_conversion,[status(esa)],[f_3028_2]) ).

cnf(f_3028_4,plain,
    ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11645,U_11646))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11645)) ),
    inference(clausify,[status(thm)],[f_3028_3]) ).

fof(f_3029_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_3029_2,plain,
    ! [U_11648,U_11647] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11647,U_11648)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11648)),U_11647),
    inference(variable_rename,[status(thm)],[f_3029_1]) ).

fof(f_3029_3,plain,
    ! [U_11647,U_11648] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11647,U_11648)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11648)),U_11647),
    inference(definitional_conversion,[status(esa)],[f_3029_2]) ).

cnf(f_3029_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11647,U_11648)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11648)),U_11647),
    inference(clausify,[status(thm)],[f_3029_3]) ).

fof(f_3030_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_3030_2,plain,
    ! [U_11650,U_11649] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11649,hAPP(c_Nat_OSuc,U_11650)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11650)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11649,U_11650))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11649),hAPP(c_Nat_OSuc,U_11650))) ),
    inference(variable_rename,[status(thm)],[f_3030_1]) ).

fof(f_3030_3,plain,
    ! [U_11649,U_11650] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11649,hAPP(c_Nat_OSuc,U_11650)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11650)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11649,U_11650))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11649),hAPP(c_Nat_OSuc,U_11650))) ),
    inference(definitional_conversion,[status(esa)],[f_3030_2]) ).

cnf(f_3030_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11649,hAPP(c_Nat_OSuc,U_11650)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11650)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11649,U_11650))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11649),hAPP(c_Nat_OSuc,U_11650))) ),
    inference(clausify,[status(thm)],[f_3030_3]) ).

fof(f_3031_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_3031_2,plain,
    ! [U_11652,U_11651] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11651),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11652) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_11651,U_11652),
    inference(variable_rename,[status(thm)],[f_3031_1]) ).

fof(f_3031_3,plain,
    ! [U_11651,U_11652] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11651),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11652) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_11651,U_11652),
    inference(definitional_conversion,[status(esa)],[f_3031_2]) ).

cnf(f_3031_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11651),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11652) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_11651,U_11652),
    inference(clausify,[status(thm)],[f_3031_3]) ).

fof(f_3032_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_3032_2,plain,
    ! [U_11658,U_11657,U_11656,U_11655,U_11654,U_11653] :
      ( hAPP(c_Finite__Set_Ocard(U_11653),U_11656) = hAPP(c_Finite__Set_Ocard(U_11654),U_11657)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11654),U_11657))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11653),U_11656))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11653,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11654,U_11653,U_11658),U_11657)),U_11656))
      | ~ c_Fun_Oinj__on(U_11654,U_11653,U_11658,U_11657)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11654,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11653,U_11654,U_11655),U_11656)),U_11657))
      | ~ c_Fun_Oinj__on(U_11653,U_11654,U_11655,U_11656) ),
    inference(variable_rename,[status(thm)],[f_3032_1]) ).

fof(f_3032_3,plain,
    ! [U_11653,U_11654,U_11655,U_11656,U_11657,U_11658] :
      ( hAPP(c_Finite__Set_Ocard(U_11653),U_11656) = hAPP(c_Finite__Set_Ocard(U_11654),U_11657)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11654),U_11657))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11653),U_11656))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11653,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11654,U_11653,U_11658),U_11657)),U_11656))
      | ~ c_Fun_Oinj__on(U_11654,U_11653,U_11658,U_11657)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11654,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11653,U_11654,U_11655),U_11656)),U_11657))
      | ~ c_Fun_Oinj__on(U_11653,U_11654,U_11655,U_11656) ),
    inference(definitional_conversion,[status(esa)],[f_3032_2]) ).

cnf(f_3032_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11653),U_11656) = hAPP(c_Finite__Set_Ocard(U_11654),U_11657)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11654),U_11657))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11653),U_11656))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11653,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11654,U_11653,U_11658),U_11657)),U_11656))
    | ~ c_Fun_Oinj__on(U_11654,U_11653,U_11658,U_11657)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11654,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11653,U_11654,U_11655),U_11656)),U_11657))
    | ~ c_Fun_Oinj__on(U_11653,U_11654,U_11655,U_11656) ),
    inference(clausify,[status(thm)],[f_3032_3]) ).

fof(f_3033_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_3033_2,plain,
    ! [U_11663,U_11662,U_11661,U_11660,U_11659] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11659,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11659,U_11660,U_11661)),c_SetInterval_Oord__class_OatLeastAtMost(U_11659,U_11662,U_11663)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11659,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11659),U_11660),U_11662),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11659),U_11661),U_11663))
      | ~ class_Orderings_Olinorder(U_11659) ),
    inference(variable_rename,[status(thm)],[f_3033_1]) ).

fof(f_3033_3,plain,
    ! [U_11662,U_11661,U_11659,U_11663,U_11660] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11659,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11659,U_11660,U_11661)),c_SetInterval_Oord__class_OatLeastAtMost(U_11659,U_11662,U_11663)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11659,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11659),U_11660),U_11662),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11659),U_11661),U_11663))
      | ~ class_Orderings_Olinorder(U_11659) ),
    inference(definitional_conversion,[status(esa)],[f_3033_2]) ).

cnf(f_3033_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11659,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11659,U_11660,U_11661)),c_SetInterval_Oord__class_OatLeastAtMost(U_11659,U_11662,U_11663)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11659,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11659),U_11660),U_11662),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11659),U_11661),U_11663))
    | ~ class_Orderings_Olinorder(U_11659) ),
    inference(clausify,[status(thm)],[f_3033_3]) ).

fof(f_3034_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_3034_2,plain,
    ! [U_11668,U_11667,U_11666,U_11665,U_11664] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11664,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11664,U_11665,U_11666)),c_SetInterval_Oord__class_OatLeastAtMost(U_11664,U_11667,U_11668)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11667),U_11668))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11664),U_11666),U_11668))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11664),U_11667),U_11665)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11666),U_11668))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11667),U_11665)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11665),U_11666)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11667),U_11668))
            & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11664),U_11666),U_11668))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11664),U_11667),U_11665)) )
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11666),U_11668))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11667),U_11665)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11665),U_11666)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11664,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11664,U_11665,U_11666)),c_SetInterval_Oord__class_OatLeastAtMost(U_11664,U_11667,U_11668))) ) )
      | ~ class_Orderings_Oorder(U_11664) ),
    inference(variable_rename,[status(thm)],[f_3034_1]) ).

fof(f_3034_3,plain,
    ( ! [U_11664,U_11665,U_11666,U_11667,U_11668] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11664),U_11666),U_11668))
        | ~ sP858(U_11664,U_11665,U_11666,U_11667,U_11668) )
    & ! [U_11664,U_11665,U_11666,U_11667,U_11668] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11664),U_11667),U_11665))
        | ~ sP858(U_11664,U_11665,U_11666,U_11667,U_11668) )
    & ! [U_11664,U_11665,U_11666,U_11667,U_11668] :
        ( sP858(U_11664,U_11665,U_11666,U_11667,U_11668)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11666),U_11668))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11667),U_11665))
        | ~ sP859(U_11664,U_11665,U_11666,U_11667,U_11668) )
    & ! [U_11664,U_11665,U_11666,U_11667,U_11668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11665),U_11666))
        | ~ sP859(U_11664,U_11665,U_11666,U_11667,U_11668) )
    & ! [U_11664,U_11665,U_11666,U_11667,U_11668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11664),U_11666),U_11668))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11664),U_11667),U_11665))
        | ~ sP856(U_11664,U_11665,U_11666,U_11667,U_11668) )
    & ! [U_11664,U_11665,U_11666,U_11667,U_11668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11666),U_11668))
        | ~ sP856(U_11664,U_11665,U_11666,U_11667,U_11668) )
    & ! [U_11664,U_11665,U_11666,U_11667,U_11668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11667),U_11665))
        | ~ sP856(U_11664,U_11665,U_11666,U_11667,U_11668) )
    & ! [U_11664,U_11665,U_11666,U_11667,U_11668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11667),U_11668))
        | ~ sP857(U_11664,U_11665,U_11666,U_11667,U_11668) )
    & ! [U_11664,U_11665,U_11666,U_11667,U_11668] :
        ( sP856(U_11664,U_11665,U_11666,U_11667,U_11668)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11665),U_11666))
        | ~ sP857(U_11664,U_11665,U_11666,U_11667,U_11668) )
    & ! [U_11664,U_11665,U_11666,U_11667,U_11668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11664,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11664,U_11665,U_11666)),c_SetInterval_Oord__class_OatLeastAtMost(U_11664,U_11667,U_11668)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11667),U_11668))
        | sP859(U_11664,U_11665,U_11666,U_11667,U_11668)
        | ~ sP860(U_11664,U_11665,U_11666,U_11667,U_11668) )
    & ! [U_11664,U_11665,U_11666,U_11667,U_11668] :
        ( sP857(U_11664,U_11665,U_11666,U_11667,U_11668)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11664,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11664,U_11665,U_11666)),c_SetInterval_Oord__class_OatLeastAtMost(U_11664,U_11667,U_11668)))
        | ~ sP860(U_11664,U_11665,U_11666,U_11667,U_11668) )
    & ! [U_11664,U_11665,U_11666,U_11667,U_11668] :
        ( sP860(U_11664,U_11665,U_11666,U_11667,U_11668)
        | ~ class_Orderings_Oorder(U_11664) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP856,sP857,sP858,sP859,sP860])],[f_3034_2]) ).

cnf(f_3034_4,plain,
    ( sP860(U_11664,U_11665,U_11666,U_11667,U_11668)
    | ~ class_Orderings_Oorder(U_11664) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

cnf(f_3034_5,plain,
    ( sP857(U_11664,U_11665,U_11666,U_11667,U_11668)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11664,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11664,U_11665,U_11666)),c_SetInterval_Oord__class_OatLeastAtMost(U_11664,U_11667,U_11668)))
    | ~ sP860(U_11664,U_11665,U_11666,U_11667,U_11668) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

cnf(f_3034_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11664,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11664,U_11665,U_11666)),c_SetInterval_Oord__class_OatLeastAtMost(U_11664,U_11667,U_11668)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11667),U_11668))
    | sP859(U_11664,U_11665,U_11666,U_11667,U_11668)
    | ~ sP860(U_11664,U_11665,U_11666,U_11667,U_11668) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

cnf(f_3034_7,plain,
    ( sP856(U_11664,U_11665,U_11666,U_11667,U_11668)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11665),U_11666))
    | ~ sP857(U_11664,U_11665,U_11666,U_11667,U_11668) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

cnf(f_3034_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11667),U_11668))
    | ~ sP857(U_11664,U_11665,U_11666,U_11667,U_11668) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

cnf(f_3034_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11667),U_11665))
    | ~ sP856(U_11664,U_11665,U_11666,U_11667,U_11668) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

cnf(f_3034_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11666),U_11668))
    | ~ sP856(U_11664,U_11665,U_11666,U_11667,U_11668) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

cnf(f_3034_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11664),U_11666),U_11668))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11664),U_11667),U_11665))
    | ~ sP856(U_11664,U_11665,U_11666,U_11667,U_11668) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

cnf(f_3034_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11665),U_11666))
    | ~ sP859(U_11664,U_11665,U_11666,U_11667,U_11668) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

cnf(f_3034_13,plain,
    ( sP858(U_11664,U_11665,U_11666,U_11667,U_11668)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11666),U_11668))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11664),U_11667),U_11665))
    | ~ sP859(U_11664,U_11665,U_11666,U_11667,U_11668) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

cnf(f_3034_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11664),U_11667),U_11665))
    | ~ sP858(U_11664,U_11665,U_11666,U_11667,U_11668) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

cnf(f_3034_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11664),U_11666),U_11668))
    | ~ sP858(U_11664,U_11665,U_11666,U_11667,U_11668) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

fof(f_3035_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_3035_2,plain,
    ! [U_11672,U_11671,U_11670,U_11669] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11669,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11669,U_11670,U_11671)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11669,U_11671,U_11672)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11669,U_11670,U_11672)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11669),U_11671),U_11672))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11669),U_11670),U_11671))
      | ~ class_Orderings_Olinorder(U_11669) ),
    inference(variable_rename,[status(thm)],[f_3035_1]) ).

fof(f_3035_3,plain,
    ! [U_11672,U_11670,U_11671,U_11669] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11669,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11669,U_11670,U_11671)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11669,U_11671,U_11672)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11669,U_11670,U_11672)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11669),U_11671),U_11672))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11669),U_11670),U_11671))
      | ~ class_Orderings_Olinorder(U_11669) ),
    inference(definitional_conversion,[status(esa)],[f_3035_2]) ).

cnf(f_3035_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11669,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11669,U_11670,U_11671)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11669,U_11671,U_11672)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11669,U_11670,U_11672)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11669),U_11671),U_11672))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11669),U_11670),U_11671))
    | ~ class_Orderings_Olinorder(U_11669) ),
    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__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_3036_2,plain,
    ! [U_11676,U_11675,U_11674,U_11673] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11673,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11673,U_11674,U_11675)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11673,U_11675,U_11676)) = c_Orderings_Obot__class_Obot(tc_fun(U_11673,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11673) ),
    inference(variable_rename,[status(thm)],[f_3036_1]) ).

fof(f_3036_3,plain,
    ! [U_11675,U_11674,U_11673,U_11676] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11673,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11673,U_11674,U_11675)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11673,U_11675,U_11676)) = c_Orderings_Obot__class_Obot(tc_fun(U_11673,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11673) ),
    inference(definitional_conversion,[status(esa)],[f_3036_2]) ).

cnf(f_3036_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11673,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11673,U_11674,U_11675)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11673,U_11675,U_11676)) = c_Orderings_Obot__class_Obot(tc_fun(U_11673,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11673) ),
    inference(clausify,[status(thm)],[f_3036_3]) ).

fof(f_3037_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_3037_2,plain,
    ! [U_11680,U_11679,U_11678,U_11677] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11677,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11677,U_11678,U_11679)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11677,U_11679,U_11680)) = c_Orderings_Obot__class_Obot(tc_fun(U_11677,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11677) ),
    inference(variable_rename,[status(thm)],[f_3037_1]) ).

fof(f_3037_3,plain,
    ! [U_11678,U_11679,U_11677,U_11680] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11677,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11677,U_11678,U_11679)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11677,U_11679,U_11680)) = c_Orderings_Obot__class_Obot(tc_fun(U_11677,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11677) ),
    inference(definitional_conversion,[status(esa)],[f_3037_2]) ).

cnf(f_3037_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11677,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11677,U_11678,U_11679)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11677,U_11679,U_11680)) = c_Orderings_Obot__class_Obot(tc_fun(U_11677,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11677) ),
    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)),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_3038_2,plain,
    ! [U_11684,U_11683,U_11682,U_11681] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11681,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11681,U_11682,U_11683)),c_SetInterval_Oord__class_OatLeastAtMost(U_11681,U_11683,U_11684)) = c_Orderings_Obot__class_Obot(tc_fun(U_11681,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11681) ),
    inference(variable_rename,[status(thm)],[f_3038_1]) ).

fof(f_3038_3,plain,
    ! [U_11681,U_11682,U_11683,U_11684] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11681,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11681,U_11682,U_11683)),c_SetInterval_Oord__class_OatLeastAtMost(U_11681,U_11683,U_11684)) = c_Orderings_Obot__class_Obot(tc_fun(U_11681,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11681) ),
    inference(definitional_conversion,[status(esa)],[f_3038_2]) ).

cnf(f_3038_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11681,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11681,U_11682,U_11683)),c_SetInterval_Oord__class_OatLeastAtMost(U_11681,U_11683,U_11684)) = c_Orderings_Obot__class_Obot(tc_fun(U_11681,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11681) ),
    inference(clausify,[status(thm)],[f_3038_3]) ).

fof(f_3039_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_3039_2,plain,
    ! [U_11686,U_11685] :
      ( ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11686,U_11685) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_11686),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11686),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11685))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11685),U_11686)) )
      & ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11686,U_11685) = 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_11685),U_11686)) ) ),
    inference(variable_rename,[status(thm)],[f_3039_1]) ).

fof(f_3039_3,plain,
    ( ! [U_11690,U_11688] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11690,U_11688) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_11690),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11690),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11688))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11688),U_11690)) )
    & ! [U_11689,U_11687] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11689,U_11687) = 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_11687),U_11689)) ) ),
    inference(miniscope,[status(thm)],[f_3039_2]) ).

fof(f_3039_4,plain,
    ( ! [U_11690,U_11688] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11690,U_11688) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_11690),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11690),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11688))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11688),U_11690)) )
    & ! [U_11689,U_11687] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11689,U_11687) = 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_11687),U_11689)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3039_3]) ).

cnf(f_3039_5,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11689,U_11687) = 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_11687),U_11689)) ),
    inference(clausify,[status(thm)],[f_3039_4]) ).

cnf(f_3039_6,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11690,U_11688) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_11690),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11690),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11688))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11688),U_11690)) ),
    inference(clausify,[status(thm)],[f_3039_4]) ).

fof(f_3040_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_3040_2,plain,
    ! [U_11696,U_11695,U_11694,U_11693] :
      ( ( ( ? [U_11692] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11695,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11693,U_11695,U_11692),U_11694)),U_11696))
              & c_Fun_Oinj__on(U_11693,U_11695,U_11692,U_11694) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11693),U_11694)),hAPP(c_Finite__Set_Ocard(U_11695),U_11696))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11693),U_11694)),hAPP(c_Finite__Set_Ocard(U_11695),U_11696)))
          | ! [U_11691] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11695,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11693,U_11695,U_11691),U_11694)),U_11696))
              | ~ c_Fun_Oinj__on(U_11693,U_11695,U_11691,U_11694) ) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11695),U_11696))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11693),U_11694)) ),
    inference(variable_rename,[status(thm)],[f_3040_1]) ).

fof(f_3040_3,plain,
    ! [U_11696,U_11695,U_11694,U_11693] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11695,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11693,U_11695,sK211(U_11696,U_11695,U_11694,U_11693)),U_11694)),U_11696))
            & c_Fun_Oinj__on(U_11693,U_11695,sK211(U_11696,U_11695,U_11694,U_11693),U_11694) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11693),U_11694)),hAPP(c_Finite__Set_Ocard(U_11695),U_11696))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11693),U_11694)),hAPP(c_Finite__Set_Ocard(U_11695),U_11696)))
          | ! [U_11691] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11695,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11693,U_11695,U_11691),U_11694)),U_11696))
              | ~ c_Fun_Oinj__on(U_11693,U_11695,U_11691,U_11694) ) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11695),U_11696))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11693),U_11694)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK211]),skolemize(U_11692,sK211(U_11696,U_11695,U_11694,U_11693))],[f_3040_2]) ).

fof(f_3040_4,plain,
    ( ! [U_11693,U_11694,U_11695,U_11696] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11695,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11693,U_11695,sK211(U_11696,U_11695,U_11694,U_11693)),U_11694)),U_11696))
        | ~ sP861(U_11693,U_11694,U_11695,U_11696) )
    & ! [U_11693,U_11694,U_11695,U_11696] :
        ( c_Fun_Oinj__on(U_11693,U_11695,sK211(U_11696,U_11695,U_11694,U_11693),U_11694)
        | ~ sP861(U_11693,U_11694,U_11695,U_11696) )
    & ! [U_11691,U_11693,U_11694,U_11695,U_11696] :
        ( sP861(U_11693,U_11694,U_11695,U_11696)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11693),U_11694)),hAPP(c_Finite__Set_Ocard(U_11695),U_11696)))
        | ~ sP862(U_11691,U_11693,U_11694,U_11695,U_11696) )
    & ! [U_11691,U_11693,U_11694,U_11695,U_11696] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11693),U_11694)),hAPP(c_Finite__Set_Ocard(U_11695),U_11696)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11695,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11693,U_11695,U_11691),U_11694)),U_11696))
        | ~ c_Fun_Oinj__on(U_11693,U_11695,U_11691,U_11694)
        | ~ sP862(U_11691,U_11693,U_11694,U_11695,U_11696) )
    & ! [U_11691,U_11693,U_11694,U_11695,U_11696] :
        ( sP862(U_11691,U_11693,U_11694,U_11695,U_11696)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11695),U_11696))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11693),U_11694)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP861,sP862])],[f_3040_3]) ).

cnf(f_3040_5,plain,
    ( sP862(U_11691,U_11693,U_11694,U_11695,U_11696)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11695),U_11696))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11693),U_11694)) ),
    inference(clausify,[status(thm)],[f_3040_4]) ).

cnf(f_3040_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11693),U_11694)),hAPP(c_Finite__Set_Ocard(U_11695),U_11696)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11695,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11693,U_11695,U_11691),U_11694)),U_11696))
    | ~ c_Fun_Oinj__on(U_11693,U_11695,U_11691,U_11694)
    | ~ sP862(U_11691,U_11693,U_11694,U_11695,U_11696) ),
    inference(clausify,[status(thm)],[f_3040_4]) ).

cnf(f_3040_7,plain,
    ( sP861(U_11693,U_11694,U_11695,U_11696)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11693),U_11694)),hAPP(c_Finite__Set_Ocard(U_11695),U_11696)))
    | ~ sP862(U_11691,U_11693,U_11694,U_11695,U_11696) ),
    inference(clausify,[status(thm)],[f_3040_4]) ).

cnf(f_3040_8,plain,
    ( c_Fun_Oinj__on(U_11693,U_11695,sK211(U_11696,U_11695,U_11694,U_11693),U_11694)
    | ~ sP861(U_11693,U_11694,U_11695,U_11696) ),
    inference(clausify,[status(thm)],[f_3040_4]) ).

cnf(f_3040_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11695,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11693,U_11695,sK211(U_11696,U_11695,U_11694,U_11693)),U_11694)),U_11696))
    | ~ sP861(U_11693,U_11694,U_11695,U_11696) ),
    inference(clausify,[status(thm)],[f_3040_4]) ).

fof(f_3041_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_3041_2,plain,
    ! [U_11701,U_11700,U_11699,U_11698,U_11697] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11697),U_11700)),hAPP(c_Finite__Set_Ocard(U_11698),U_11701)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11698),U_11701))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11698,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11697,U_11698,U_11699),U_11700)),U_11701))
      | ~ c_Fun_Oinj__on(U_11697,U_11698,U_11699,U_11700) ),
    inference(variable_rename,[status(thm)],[f_3041_1]) ).

fof(f_3041_3,plain,
    ! [U_11698,U_11697,U_11700,U_11701,U_11699] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11697),U_11700)),hAPP(c_Finite__Set_Ocard(U_11698),U_11701)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11698),U_11701))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11698,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11697,U_11698,U_11699),U_11700)),U_11701))
      | ~ c_Fun_Oinj__on(U_11697,U_11698,U_11699,U_11700) ),
    inference(definitional_conversion,[status(esa)],[f_3041_2]) ).

cnf(f_3041_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11697),U_11700)),hAPP(c_Finite__Set_Ocard(U_11698),U_11701)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11698),U_11701))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11698,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11697,U_11698,U_11699),U_11700)),U_11701))
    | ~ c_Fun_Oinj__on(U_11697,U_11698,U_11699,U_11700) ),
    inference(clausify,[status(thm)],[f_3041_3]) ).

fof(f_3042_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_3042_2,plain,
    ! [U_11705,U_11704,U_11703,U_11702] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11702),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11702,tc_HOL_Obool)),U_11704),hAPP(hAPP(c_Set_Oinsert(U_11702),U_11705),c_Orderings_Obot__class_Obot(tc_fun(U_11702,tc_HOL_Obool))))),U_11703) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_11702,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11702),U_11704),U_11703)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11702),hAPP(hAPP(c_Set_Oinsert(U_11702),U_11705),c_Orderings_Obot__class_Obot(tc_fun(U_11702,tc_HOL_Obool)))),U_11703))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11702),U_11705),U_11704))
      | ~ c_Fun_Oinj__on(U_11702,tc_fun(tc_fun(U_11702,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11702,tc_fun(tc_prod(U_11702,U_11702),tc_HOL_Obool),tc_fun(tc_fun(U_11702,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11702,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11702,U_11702),tc_HOL_Obool),tc_fun(tc_fun(U_11702,tc_HOL_Obool),tc_HOL_Obool)),U_11702),c_Equiv__Relations_Oquotient(U_11702)),hAPP(hAPP(c_COMBC(U_11702,tc_fun(U_11702,tc_HOL_Obool),tc_fun(U_11702,tc_HOL_Obool)),c_Set_Oinsert(U_11702)),c_Orderings_Obot__class_Obot(tc_fun(U_11702,tc_HOL_Obool))))),U_11703),U_11704) ),
    inference(variable_rename,[status(thm)],[f_3042_1]) ).

fof(f_3042_3,plain,
    ! [U_11702,U_11703,U_11704,U_11705] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11702),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11702,tc_HOL_Obool)),U_11704),hAPP(hAPP(c_Set_Oinsert(U_11702),U_11705),c_Orderings_Obot__class_Obot(tc_fun(U_11702,tc_HOL_Obool))))),U_11703) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_11702,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11702),U_11704),U_11703)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11702),hAPP(hAPP(c_Set_Oinsert(U_11702),U_11705),c_Orderings_Obot__class_Obot(tc_fun(U_11702,tc_HOL_Obool)))),U_11703))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11702),U_11705),U_11704))
      | ~ c_Fun_Oinj__on(U_11702,tc_fun(tc_fun(U_11702,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11702,tc_fun(tc_prod(U_11702,U_11702),tc_HOL_Obool),tc_fun(tc_fun(U_11702,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11702,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11702,U_11702),tc_HOL_Obool),tc_fun(tc_fun(U_11702,tc_HOL_Obool),tc_HOL_Obool)),U_11702),c_Equiv__Relations_Oquotient(U_11702)),hAPP(hAPP(c_COMBC(U_11702,tc_fun(U_11702,tc_HOL_Obool),tc_fun(U_11702,tc_HOL_Obool)),c_Set_Oinsert(U_11702)),c_Orderings_Obot__class_Obot(tc_fun(U_11702,tc_HOL_Obool))))),U_11703),U_11704) ),
    inference(definitional_conversion,[status(esa)],[f_3042_2]) ).

cnf(f_3042_4,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11702),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11702,tc_HOL_Obool)),U_11704),hAPP(hAPP(c_Set_Oinsert(U_11702),U_11705),c_Orderings_Obot__class_Obot(tc_fun(U_11702,tc_HOL_Obool))))),U_11703) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_11702,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11702),U_11704),U_11703)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11702),hAPP(hAPP(c_Set_Oinsert(U_11702),U_11705),c_Orderings_Obot__class_Obot(tc_fun(U_11702,tc_HOL_Obool)))),U_11703))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11702),U_11705),U_11704))
    | ~ c_Fun_Oinj__on(U_11702,tc_fun(tc_fun(U_11702,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11702,tc_fun(tc_prod(U_11702,U_11702),tc_HOL_Obool),tc_fun(tc_fun(U_11702,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11702,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11702,U_11702),tc_HOL_Obool),tc_fun(tc_fun(U_11702,tc_HOL_Obool),tc_HOL_Obool)),U_11702),c_Equiv__Relations_Oquotient(U_11702)),hAPP(hAPP(c_COMBC(U_11702,tc_fun(U_11702,tc_HOL_Obool),tc_fun(U_11702,tc_HOL_Obool)),c_Set_Oinsert(U_11702)),c_Orderings_Obot__class_Obot(tc_fun(U_11702,tc_HOL_Obool))))),U_11703),U_11704) ),
    inference(clausify,[status(thm)],[f_3042_3]) ).

fof(f_3043_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_3043_2,plain,
    ! [U_11707,U_11706] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11706,U_11707)) = 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_11707),U_11706)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_3043_1]) ).

fof(f_3043_3,plain,
    ! [U_11706,U_11707] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11706,U_11707)) = 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_11707),U_11706)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_3043_2]) ).

cnf(f_3043_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11706,U_11707)) = 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_11707),U_11706)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_3043_3]) ).

fof(f_3044_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_3044_2,plain,
    ! [U_11710,U_11709,U_11708] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11708,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11708),U_11709),c_Orderings_Obot__class_Obot(tc_fun(U_11708,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11708,U_11709,U_11710)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11708,U_11709,U_11710)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11708),U_11709),U_11710))
      | ~ class_Orderings_Olinorder(U_11708) ),
    inference(variable_rename,[status(thm)],[f_3044_1]) ).

fof(f_3044_3,plain,
    ! [U_11708,U_11709,U_11710] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11708,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11708),U_11709),c_Orderings_Obot__class_Obot(tc_fun(U_11708,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11708,U_11709,U_11710)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11708,U_11709,U_11710)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11708),U_11709),U_11710))
      | ~ class_Orderings_Olinorder(U_11708) ),
    inference(definitional_conversion,[status(esa)],[f_3044_2]) ).

cnf(f_3044_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11708,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11708),U_11709),c_Orderings_Obot__class_Obot(tc_fun(U_11708,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11708,U_11709,U_11710)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11708,U_11709,U_11710)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11708),U_11709),U_11710))
    | ~ class_Orderings_Olinorder(U_11708) ),
    inference(clausify,[status(thm)],[f_3044_3]) ).

fof(f_3045_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_3045_2,plain,
    ! [U_11715,U_11714,U_11713,U_11712,U_11711] :
      ( ( c_Fun_Oinj__on(U_11711,U_11712,U_11713,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11711,tc_HOL_Obool)),U_11714),U_11715))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11712,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11711,U_11712,U_11713),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11711,tc_HOL_Obool)),U_11714),U_11715))),hAPP(c_Set_Oimage(U_11711,U_11712,U_11713),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11711,tc_HOL_Obool)),U_11715),U_11714))) != c_Orderings_Obot__class_Obot(tc_fun(U_11712,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_11711,U_11712,U_11713,U_11715)
        | ~ c_Fun_Oinj__on(U_11711,U_11712,U_11713,U_11714) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11712,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11711,U_11712,U_11713),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11711,tc_HOL_Obool)),U_11714),U_11715))),hAPP(c_Set_Oimage(U_11711,U_11712,U_11713),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11711,tc_HOL_Obool)),U_11715),U_11714))) = c_Orderings_Obot__class_Obot(tc_fun(U_11712,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_11711,U_11712,U_11713,U_11715)
          & c_Fun_Oinj__on(U_11711,U_11712,U_11713,U_11714) )
        | ~ c_Fun_Oinj__on(U_11711,U_11712,U_11713,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11711,tc_HOL_Obool)),U_11714),U_11715)) ) ),
    inference(variable_rename,[status(thm)],[f_3045_1]) ).

fof(f_3045_3,plain,
    ( ! [U_11725,U_11723,U_11721,U_11719,U_11717] :
        ( c_Fun_Oinj__on(U_11717,U_11719,U_11721,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11717,tc_HOL_Obool)),U_11723),U_11725))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11719,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11717,U_11719,U_11721),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11717,tc_HOL_Obool)),U_11723),U_11725))),hAPP(c_Set_Oimage(U_11717,U_11719,U_11721),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11717,tc_HOL_Obool)),U_11725),U_11723))) != c_Orderings_Obot__class_Obot(tc_fun(U_11719,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_11717,U_11719,U_11721,U_11725)
        | ~ c_Fun_Oinj__on(U_11717,U_11719,U_11721,U_11723) )
    & ! [U_11724,U_11722,U_11720,U_11718,U_11716] :
        ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11718,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11716,U_11718,U_11720),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11716,tc_HOL_Obool)),U_11722),U_11724))),hAPP(c_Set_Oimage(U_11716,U_11718,U_11720),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11716,tc_HOL_Obool)),U_11724),U_11722))) = c_Orderings_Obot__class_Obot(tc_fun(U_11718,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_11716,U_11718,U_11720,U_11724)
          & c_Fun_Oinj__on(U_11716,U_11718,U_11720,U_11722) )
        | ~ c_Fun_Oinj__on(U_11716,U_11718,U_11720,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11716,tc_HOL_Obool)),U_11722),U_11724)) ) ),
    inference(miniscope,[status(thm)],[f_3045_2]) ).

fof(f_3045_4,plain,
    ( ! [U_11720,U_11718,U_11716,U_11722,U_11724] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11718,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11716,U_11718,U_11720),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11716,tc_HOL_Obool)),U_11722),U_11724))),hAPP(c_Set_Oimage(U_11716,U_11718,U_11720),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11716,tc_HOL_Obool)),U_11724),U_11722))) = c_Orderings_Obot__class_Obot(tc_fun(U_11718,tc_HOL_Obool))
        | ~ sP863(U_11720,U_11718,U_11716,U_11722,U_11724) )
    & ! [U_11720,U_11718,U_11716,U_11722,U_11724] :
        ( c_Fun_Oinj__on(U_11716,U_11718,U_11720,U_11724)
        | ~ sP863(U_11720,U_11718,U_11716,U_11722,U_11724) )
    & ! [U_11720,U_11718,U_11716,U_11722,U_11724] :
        ( c_Fun_Oinj__on(U_11716,U_11718,U_11720,U_11722)
        | ~ sP863(U_11720,U_11718,U_11716,U_11722,U_11724) )
    & ! [U_11719,U_11717,U_11721,U_11723,U_11725] :
        ( c_Fun_Oinj__on(U_11717,U_11719,U_11721,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11717,tc_HOL_Obool)),U_11723),U_11725))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11719,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11717,U_11719,U_11721),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11717,tc_HOL_Obool)),U_11723),U_11725))),hAPP(c_Set_Oimage(U_11717,U_11719,U_11721),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11717,tc_HOL_Obool)),U_11725),U_11723))) != c_Orderings_Obot__class_Obot(tc_fun(U_11719,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_11717,U_11719,U_11721,U_11725)
        | ~ c_Fun_Oinj__on(U_11717,U_11719,U_11721,U_11723) )
    & ! [U_11720,U_11718,U_11716,U_11722,U_11724] :
        ( sP863(U_11720,U_11718,U_11716,U_11722,U_11724)
        | ~ c_Fun_Oinj__on(U_11716,U_11718,U_11720,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11716,tc_HOL_Obool)),U_11722),U_11724)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP863])],[f_3045_3]) ).

cnf(f_3045_5,plain,
    ( sP863(U_11720,U_11718,U_11716,U_11722,U_11724)
    | ~ c_Fun_Oinj__on(U_11716,U_11718,U_11720,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11716,tc_HOL_Obool)),U_11722),U_11724)) ),
    inference(clausify,[status(thm)],[f_3045_4]) ).

cnf(f_3045_6,plain,
    ( c_Fun_Oinj__on(U_11717,U_11719,U_11721,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11717,tc_HOL_Obool)),U_11723),U_11725))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11719,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11717,U_11719,U_11721),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11717,tc_HOL_Obool)),U_11723),U_11725))),hAPP(c_Set_Oimage(U_11717,U_11719,U_11721),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11717,tc_HOL_Obool)),U_11725),U_11723))) != c_Orderings_Obot__class_Obot(tc_fun(U_11719,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_11717,U_11719,U_11721,U_11725)
    | ~ c_Fun_Oinj__on(U_11717,U_11719,U_11721,U_11723) ),
    inference(clausify,[status(thm)],[f_3045_4]) ).

cnf(f_3045_7,plain,
    ( c_Fun_Oinj__on(U_11716,U_11718,U_11720,U_11722)
    | ~ sP863(U_11720,U_11718,U_11716,U_11722,U_11724) ),
    inference(clausify,[status(thm)],[f_3045_4]) ).

cnf(f_3045_8,plain,
    ( c_Fun_Oinj__on(U_11716,U_11718,U_11720,U_11724)
    | ~ sP863(U_11720,U_11718,U_11716,U_11722,U_11724) ),
    inference(clausify,[status(thm)],[f_3045_4]) ).

cnf(f_3045_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11718,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11716,U_11718,U_11720),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11716,tc_HOL_Obool)),U_11722),U_11724))),hAPP(c_Set_Oimage(U_11716,U_11718,U_11720),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11716,tc_HOL_Obool)),U_11724),U_11722))) = c_Orderings_Obot__class_Obot(tc_fun(U_11718,tc_HOL_Obool))
    | ~ sP863(U_11720,U_11718,U_11716,U_11722,U_11724) ),
    inference(clausify,[status(thm)],[f_3045_4]) ).

fof(f_3046_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_3046_2,plain,
    ! [U_11730,U_11729,U_11728,U_11727,U_11726] :
      ( ( c_Fun_Oinj__on(U_11726,U_11727,U_11728,hAPP(hAPP(c_Set_Oinsert(U_11726),U_11729),U_11730))
        | hBOOL(hAPP(hAPP(c_member(U_11727),hAPP(U_11728,U_11729)),hAPP(c_Set_Oimage(U_11726,U_11727,U_11728),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11726,tc_HOL_Obool)),U_11730),hAPP(hAPP(c_Set_Oinsert(U_11726),U_11729),c_Orderings_Obot__class_Obot(tc_fun(U_11726,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(U_11726,U_11727,U_11728,U_11730) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(U_11727),hAPP(U_11728,U_11729)),hAPP(c_Set_Oimage(U_11726,U_11727,U_11728),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11726,tc_HOL_Obool)),U_11730),hAPP(hAPP(c_Set_Oinsert(U_11726),U_11729),c_Orderings_Obot__class_Obot(tc_fun(U_11726,tc_HOL_Obool)))))))
          & c_Fun_Oinj__on(U_11726,U_11727,U_11728,U_11730) )
        | ~ c_Fun_Oinj__on(U_11726,U_11727,U_11728,hAPP(hAPP(c_Set_Oinsert(U_11726),U_11729),U_11730)) ) ),
    inference(variable_rename,[status(thm)],[f_3046_1]) ).

fof(f_3046_3,plain,
    ( ! [U_11740,U_11738,U_11736,U_11734,U_11732] :
        ( c_Fun_Oinj__on(U_11732,U_11734,U_11736,hAPP(hAPP(c_Set_Oinsert(U_11732),U_11738),U_11740))
        | hBOOL(hAPP(hAPP(c_member(U_11734),hAPP(U_11736,U_11738)),hAPP(c_Set_Oimage(U_11732,U_11734,U_11736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11732,tc_HOL_Obool)),U_11740),hAPP(hAPP(c_Set_Oinsert(U_11732),U_11738),c_Orderings_Obot__class_Obot(tc_fun(U_11732,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(U_11732,U_11734,U_11736,U_11740) )
    & ! [U_11739,U_11737,U_11735,U_11733,U_11731] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_11733),hAPP(U_11735,U_11737)),hAPP(c_Set_Oimage(U_11731,U_11733,U_11735),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11731,tc_HOL_Obool)),U_11739),hAPP(hAPP(c_Set_Oinsert(U_11731),U_11737),c_Orderings_Obot__class_Obot(tc_fun(U_11731,tc_HOL_Obool)))))))
          & c_Fun_Oinj__on(U_11731,U_11733,U_11735,U_11739) )
        | ~ c_Fun_Oinj__on(U_11731,U_11733,U_11735,hAPP(hAPP(c_Set_Oinsert(U_11731),U_11737),U_11739)) ) ),
    inference(miniscope,[status(thm)],[f_3046_2]) ).

fof(f_3046_4,plain,
    ( ! [U_11733,U_11731,U_11735,U_11737,U_11739] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_11733),hAPP(U_11735,U_11737)),hAPP(c_Set_Oimage(U_11731,U_11733,U_11735),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11731,tc_HOL_Obool)),U_11739),hAPP(hAPP(c_Set_Oinsert(U_11731),U_11737),c_Orderings_Obot__class_Obot(tc_fun(U_11731,tc_HOL_Obool)))))))
        | ~ sP864(U_11733,U_11731,U_11735,U_11737,U_11739) )
    & ! [U_11733,U_11731,U_11735,U_11737,U_11739] :
        ( c_Fun_Oinj__on(U_11731,U_11733,U_11735,U_11739)
        | ~ sP864(U_11733,U_11731,U_11735,U_11737,U_11739) )
    & ! [U_11734,U_11732,U_11738,U_11736,U_11740] :
        ( c_Fun_Oinj__on(U_11732,U_11734,U_11736,hAPP(hAPP(c_Set_Oinsert(U_11732),U_11738),U_11740))
        | hBOOL(hAPP(hAPP(c_member(U_11734),hAPP(U_11736,U_11738)),hAPP(c_Set_Oimage(U_11732,U_11734,U_11736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11732,tc_HOL_Obool)),U_11740),hAPP(hAPP(c_Set_Oinsert(U_11732),U_11738),c_Orderings_Obot__class_Obot(tc_fun(U_11732,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(U_11732,U_11734,U_11736,U_11740) )
    & ! [U_11733,U_11731,U_11735,U_11737,U_11739] :
        ( sP864(U_11733,U_11731,U_11735,U_11737,U_11739)
        | ~ c_Fun_Oinj__on(U_11731,U_11733,U_11735,hAPP(hAPP(c_Set_Oinsert(U_11731),U_11737),U_11739)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP864])],[f_3046_3]) ).

cnf(f_3046_5,plain,
    ( sP864(U_11733,U_11731,U_11735,U_11737,U_11739)
    | ~ c_Fun_Oinj__on(U_11731,U_11733,U_11735,hAPP(hAPP(c_Set_Oinsert(U_11731),U_11737),U_11739)) ),
    inference(clausify,[status(thm)],[f_3046_4]) ).

cnf(f_3046_6,plain,
    ( c_Fun_Oinj__on(U_11732,U_11734,U_11736,hAPP(hAPP(c_Set_Oinsert(U_11732),U_11738),U_11740))
    | hBOOL(hAPP(hAPP(c_member(U_11734),hAPP(U_11736,U_11738)),hAPP(c_Set_Oimage(U_11732,U_11734,U_11736),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11732,tc_HOL_Obool)),U_11740),hAPP(hAPP(c_Set_Oinsert(U_11732),U_11738),c_Orderings_Obot__class_Obot(tc_fun(U_11732,tc_HOL_Obool)))))))
    | ~ c_Fun_Oinj__on(U_11732,U_11734,U_11736,U_11740) ),
    inference(clausify,[status(thm)],[f_3046_4]) ).

cnf(f_3046_7,plain,
    ( c_Fun_Oinj__on(U_11731,U_11733,U_11735,U_11739)
    | ~ sP864(U_11733,U_11731,U_11735,U_11737,U_11739) ),
    inference(clausify,[status(thm)],[f_3046_4]) ).

cnf(f_3046_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_11733),hAPP(U_11735,U_11737)),hAPP(c_Set_Oimage(U_11731,U_11733,U_11735),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11731,tc_HOL_Obool)),U_11739),hAPP(hAPP(c_Set_Oinsert(U_11731),U_11737),c_Orderings_Obot__class_Obot(tc_fun(U_11731,tc_HOL_Obool)))))))
    | ~ sP864(U_11733,U_11731,U_11735,U_11737,U_11739) ),
    inference(clausify,[status(thm)],[f_3046_4]) ).

fof(f_3047_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_3047_2,plain,
    ! [U_11742,U_11741] :
      ( c_Fun_Oinj__on(U_11741,U_11741,c_Groups_Ouminus__class_Ouminus(U_11741),U_11742)
      | ~ class_Groups_Oordered__ab__group__add(U_11741) ),
    inference(variable_rename,[status(thm)],[f_3047_1]) ).

fof(f_3047_3,plain,
    ! [U_11742,U_11741] :
      ( c_Fun_Oinj__on(U_11741,U_11741,c_Groups_Ouminus__class_Ouminus(U_11741),U_11742)
      | ~ class_Groups_Oordered__ab__group__add(U_11741) ),
    inference(definitional_conversion,[status(esa)],[f_3047_2]) ).

cnf(f_3047_4,plain,
    ( c_Fun_Oinj__on(U_11741,U_11741,c_Groups_Ouminus__class_Ouminus(U_11741),U_11742)
    | ~ class_Groups_Oordered__ab__group__add(U_11741) ),
    inference(clausify,[status(thm)],[f_3047_3]) ).

fof(f_3048_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_3048_2,plain,
    ! [U_11745,U_11744,U_11743] : c_Fun_Oinj__on(U_11743,U_11744,U_11745,c_Orderings_Obot__class_Obot(tc_fun(U_11743,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3048_1]) ).

fof(f_3048_3,plain,
    ! [U_11744,U_11743,U_11745] : c_Fun_Oinj__on(U_11743,U_11744,U_11745,c_Orderings_Obot__class_Obot(tc_fun(U_11743,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3048_2]) ).

cnf(f_3048_4,plain,
    c_Fun_Oinj__on(U_11743,U_11744,U_11745,c_Orderings_Obot__class_Obot(tc_fun(U_11743,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3048_3]) ).

fof(f_3049_1,plain,
    ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(T_b,tc_sum(T_b,T_c),c_Sum__Type_OInl(T_b,T_c),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_inj__Inl]) ).

fof(f_3049_2,plain,
    ! [U_11748,U_11747,U_11746] : c_Fun_Oinj__on(U_11746,tc_sum(U_11746,U_11747),c_Sum__Type_OInl(U_11746,U_11747),U_11748),
    inference(variable_rename,[status(thm)],[f_3049_1]) ).

fof(f_3049_3,plain,
    ! [U_11746,U_11748,U_11747] : c_Fun_Oinj__on(U_11746,tc_sum(U_11746,U_11747),c_Sum__Type_OInl(U_11746,U_11747),U_11748),
    inference(definitional_conversion,[status(esa)],[f_3049_2]) ).

cnf(f_3049_4,plain,
    c_Fun_Oinj__on(U_11746,tc_sum(U_11746,U_11747),c_Sum__Type_OInl(U_11746,U_11747),U_11748),
    inference(clausify,[status(thm)],[f_3049_3]) ).

fof(f_3050_1,plain,
    ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(T_b,tc_sum(T_c,T_b),c_Sum__Type_OInr(T_b,T_c),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_inj__Inr]) ).

fof(f_3050_2,plain,
    ! [U_11751,U_11750,U_11749] : c_Fun_Oinj__on(U_11749,tc_sum(U_11750,U_11749),c_Sum__Type_OInr(U_11749,U_11750),U_11751),
    inference(variable_rename,[status(thm)],[f_3050_1]) ).

fof(f_3050_3,plain,
    ! [U_11749,U_11750,U_11751] : c_Fun_Oinj__on(U_11749,tc_sum(U_11750,U_11749),c_Sum__Type_OInr(U_11749,U_11750),U_11751),
    inference(definitional_conversion,[status(esa)],[f_3050_2]) ).

cnf(f_3050_4,plain,
    c_Fun_Oinj__on(U_11749,tc_sum(U_11750,U_11749),c_Sum__Type_OInr(U_11749,U_11750),U_11751),
    inference(clausify,[status(thm)],[f_3050_3]) ).

fof(f_3051_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_3051_2,plain,
    ! [U_11752] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_11752),
    inference(variable_rename,[status(thm)],[f_3051_1]) ).

fof(f_3051_3,plain,
    ! [U_11752] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_11752),
    inference(definitional_conversion,[status(esa)],[f_3051_2]) ).

cnf(f_3051_4,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_11752),
    inference(clausify,[status(thm)],[f_3051_3]) ).

fof(f_3052_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_3052_2,plain,
    ! [U_11754,U_11753] : c_Fun_Oinj__on(U_11753,tc_Option_Ooption(U_11753),c_Option_Ooption_OSome(U_11753),U_11754),
    inference(variable_rename,[status(thm)],[f_3052_1]) ).

fof(f_3052_3,plain,
    ! [U_11753,U_11754] : c_Fun_Oinj__on(U_11753,tc_Option_Ooption(U_11753),c_Option_Ooption_OSome(U_11753),U_11754),
    inference(definitional_conversion,[status(esa)],[f_3052_2]) ).

cnf(f_3052_4,plain,
    c_Fun_Oinj__on(U_11753,tc_Option_Ooption(U_11753),c_Option_Ooption_OSome(U_11753),U_11754),
    inference(clausify,[status(thm)],[f_3052_3]) ).

fof(f_3053_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_3053_2,plain,
    ! [U_11756,U_11755] : 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_11755),U_11756),
    inference(variable_rename,[status(thm)],[f_3053_1]) ).

fof(f_3053_3,plain,
    ! [U_11755,U_11756] : 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_11755),U_11756),
    inference(definitional_conversion,[status(esa)],[f_3053_2]) ).

cnf(f_3053_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_11755),U_11756),
    inference(clausify,[status(thm)],[f_3053_3]) ).

fof(f_3054_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_3054_2,plain,
    ! [U_11759,U_11758,U_11757] : c_Fun_Oinj__on(tc_prod(U_11757,U_11758),tc_prod(U_11758,U_11757),hAPP(c_Product__Type_Oprod_Oprod__case(U_11757,U_11758,tc_prod(U_11758,U_11757)),hAPP(c_COMBC(U_11758,U_11757,tc_prod(U_11758,U_11757)),c_Product__Type_OPair(U_11758,U_11757))),U_11759),
    inference(variable_rename,[status(thm)],[f_3054_1]) ).

fof(f_3054_3,plain,
    ! [U_11757,U_11758,U_11759] : c_Fun_Oinj__on(tc_prod(U_11757,U_11758),tc_prod(U_11758,U_11757),hAPP(c_Product__Type_Oprod_Oprod__case(U_11757,U_11758,tc_prod(U_11758,U_11757)),hAPP(c_COMBC(U_11758,U_11757,tc_prod(U_11758,U_11757)),c_Product__Type_OPair(U_11758,U_11757))),U_11759),
    inference(definitional_conversion,[status(esa)],[f_3054_2]) ).

cnf(f_3054_4,plain,
    c_Fun_Oinj__on(tc_prod(U_11757,U_11758),tc_prod(U_11758,U_11757),hAPP(c_Product__Type_Oprod_Oprod__case(U_11757,U_11758,tc_prod(U_11758,U_11757)),hAPP(c_COMBC(U_11758,U_11757,tc_prod(U_11758,U_11757)),c_Product__Type_OPair(U_11758,U_11757))),U_11759),
    inference(clausify,[status(thm)],[f_3054_3]) ).

fof(f_3055_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_3055_2,plain,
    ! [U_11767,U_11766,U_11765,U_11764] :
      ( ( c_Fun_Oinj__on(U_11764,U_11765,U_11766,U_11767)
        | ? [U_11763] :
            ( ? [U_11762] :
                ( U_11763 != U_11762
                & hAPP(U_11766,U_11763) = hAPP(U_11766,U_11762)
                & hBOOL(hAPP(hAPP(c_member(U_11764),U_11762),U_11767)) )
            & hBOOL(hAPP(hAPP(c_member(U_11764),U_11763),U_11767)) ) )
      & ( ! [U_11761] :
            ( ! [U_11760] :
                ( U_11761 = U_11760
                | hAPP(U_11766,U_11761) != hAPP(U_11766,U_11760)
                | ~ hBOOL(hAPP(hAPP(c_member(U_11764),U_11760),U_11767)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_11764),U_11761),U_11767)) )
        | ~ c_Fun_Oinj__on(U_11764,U_11765,U_11766,U_11767) ) ),
    inference(variable_rename,[status(thm)],[f_3055_1]) ).

fof(f_3055_3,plain,
    ( ! [U_11775,U_11773,U_11771,U_11769] :
        ( c_Fun_Oinj__on(U_11769,U_11771,U_11773,U_11775)
        | ? [U_11763] :
            ( ? [U_11762] :
                ( U_11763 != U_11762
                & hAPP(U_11773,U_11763) = hAPP(U_11773,U_11762)
                & hBOOL(hAPP(hAPP(c_member(U_11769),U_11762),U_11775)) )
            & hBOOL(hAPP(hAPP(c_member(U_11769),U_11763),U_11775)) ) )
    & ! [U_11774,U_11772,U_11770,U_11768] :
        ( ! [U_11761] :
            ( ! [U_11760] :
                ( U_11761 = U_11760
                | hAPP(U_11772,U_11761) != hAPP(U_11772,U_11760)
                | ~ hBOOL(hAPP(hAPP(c_member(U_11768),U_11760),U_11774)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_11768),U_11761),U_11774)) )
        | ~ c_Fun_Oinj__on(U_11768,U_11770,U_11772,U_11774) ) ),
    inference(miniscope,[status(thm)],[f_3055_2]) ).

fof(f_3055_4,plain,
    ( ! [U_11775,U_11773,U_11771,U_11769] :
        ( c_Fun_Oinj__on(U_11769,U_11771,U_11773,U_11775)
        | ( ? [U_11762] :
              ( sK212(U_11775,U_11773,U_11771,U_11769) != U_11762
              & hAPP(U_11773,sK212(U_11775,U_11773,U_11771,U_11769)) = hAPP(U_11773,U_11762)
              & hBOOL(hAPP(hAPP(c_member(U_11769),U_11762),U_11775)) )
          & hBOOL(hAPP(hAPP(c_member(U_11769),sK212(U_11775,U_11773,U_11771,U_11769)),U_11775)) ) )
    & ! [U_11774,U_11772,U_11770,U_11768] :
        ( ! [U_11761] :
            ( ! [U_11760] :
                ( U_11761 = U_11760
                | hAPP(U_11772,U_11761) != hAPP(U_11772,U_11760)
                | ~ hBOOL(hAPP(hAPP(c_member(U_11768),U_11760),U_11774)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_11768),U_11761),U_11774)) )
        | ~ c_Fun_Oinj__on(U_11768,U_11770,U_11772,U_11774) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(U_11763,sK212(U_11775,U_11773,U_11771,U_11769))],[f_3055_3]) ).

fof(f_3055_5,plain,
    ( ! [U_11775,U_11773,U_11771,U_11769] :
        ( c_Fun_Oinj__on(U_11769,U_11771,U_11773,U_11775)
        | ( sK212(U_11775,U_11773,U_11771,U_11769) != sK213(U_11775,U_11773,U_11771,U_11769)
          & hAPP(U_11773,sK212(U_11775,U_11773,U_11771,U_11769)) = hAPP(U_11773,sK213(U_11775,U_11773,U_11771,U_11769))
          & hBOOL(hAPP(hAPP(c_member(U_11769),sK213(U_11775,U_11773,U_11771,U_11769)),U_11775))
          & hBOOL(hAPP(hAPP(c_member(U_11769),sK212(U_11775,U_11773,U_11771,U_11769)),U_11775)) ) )
    & ! [U_11774,U_11772,U_11770,U_11768] :
        ( ! [U_11761] :
            ( ! [U_11760] :
                ( U_11761 = U_11760
                | hAPP(U_11772,U_11761) != hAPP(U_11772,U_11760)
                | ~ hBOOL(hAPP(hAPP(c_member(U_11768),U_11760),U_11774)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_11768),U_11761),U_11774)) )
        | ~ c_Fun_Oinj__on(U_11768,U_11770,U_11772,U_11774) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK213]),skolemize(U_11762,sK213(U_11775,U_11773,U_11771,U_11769))],[f_3055_4]) ).

fof(f_3055_6,plain,
    ( ! [U_11771,U_11775,U_11773,U_11769] :
        ( sK212(U_11775,U_11773,U_11771,U_11769) != sK213(U_11775,U_11773,U_11771,U_11769)
        | ~ sP865(U_11771,U_11775,U_11773,U_11769) )
    & ! [U_11771,U_11775,U_11773,U_11769] :
        ( hAPP(U_11773,sK212(U_11775,U_11773,U_11771,U_11769)) = hAPP(U_11773,sK213(U_11775,U_11773,U_11771,U_11769))
        | ~ sP865(U_11771,U_11775,U_11773,U_11769) )
    & ! [U_11771,U_11775,U_11773,U_11769] :
        ( hBOOL(hAPP(hAPP(c_member(U_11769),sK213(U_11775,U_11773,U_11771,U_11769)),U_11775))
        | ~ sP865(U_11771,U_11775,U_11773,U_11769) )
    & ! [U_11771,U_11775,U_11773,U_11769] :
        ( hBOOL(hAPP(hAPP(c_member(U_11769),sK212(U_11775,U_11773,U_11771,U_11769)),U_11775))
        | ~ sP865(U_11771,U_11775,U_11773,U_11769) )
    & ! [U_11771,U_11775,U_11773,U_11769] :
        ( c_Fun_Oinj__on(U_11769,U_11771,U_11773,U_11775)
        | sP865(U_11771,U_11775,U_11773,U_11769) )
    & ! [U_11772,U_11760,U_11761,U_11770,U_11768,U_11774] :
        ( U_11761 = U_11760
        | hAPP(U_11772,U_11761) != hAPP(U_11772,U_11760)
        | ~ hBOOL(hAPP(hAPP(c_member(U_11768),U_11760),U_11774))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11768),U_11761),U_11774))
        | ~ c_Fun_Oinj__on(U_11768,U_11770,U_11772,U_11774) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP865])],[f_3055_5]) ).

cnf(f_3055_7,plain,
    ( U_11761 = U_11760
    | hAPP(U_11772,U_11761) != hAPP(U_11772,U_11760)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11768),U_11760),U_11774))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11768),U_11761),U_11774))
    | ~ c_Fun_Oinj__on(U_11768,U_11770,U_11772,U_11774) ),
    inference(clausify,[status(thm)],[f_3055_6]) ).

cnf(f_3055_8,plain,
    ( c_Fun_Oinj__on(U_11769,U_11771,U_11773,U_11775)
    | sP865(U_11771,U_11775,U_11773,U_11769) ),
    inference(clausify,[status(thm)],[f_3055_6]) ).

cnf(f_3055_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11769),sK212(U_11775,U_11773,U_11771,U_11769)),U_11775))
    | ~ sP865(U_11771,U_11775,U_11773,U_11769) ),
    inference(clausify,[status(thm)],[f_3055_6]) ).

cnf(f_3055_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11769),sK213(U_11775,U_11773,U_11771,U_11769)),U_11775))
    | ~ sP865(U_11771,U_11775,U_11773,U_11769) ),
    inference(clausify,[status(thm)],[f_3055_6]) ).

cnf(f_3055_11,plain,
    ( hAPP(U_11773,sK212(U_11775,U_11773,U_11771,U_11769)) = hAPP(U_11773,sK213(U_11775,U_11773,U_11771,U_11769))
    | ~ sP865(U_11771,U_11775,U_11773,U_11769) ),
    inference(clausify,[status(thm)],[f_3055_6]) ).

cnf(f_3055_12,plain,
    ( sK212(U_11775,U_11773,U_11771,U_11769) != sK213(U_11775,U_11773,U_11771,U_11769)
    | ~ sP865(U_11771,U_11775,U_11773,U_11769) ),
    inference(clausify,[status(thm)],[f_3055_6]) ).

fof(f_3056_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_3056_2,plain,
    ! [U_11777,U_11776] : hAPP(c_Set_Oimage(U_11776,U_11776,c_COMBI(U_11776)),U_11777) = U_11777,
    inference(variable_rename,[status(thm)],[f_3056_1]) ).

fof(f_3056_3,plain,
    ! [U_11777,U_11776] : hAPP(c_Set_Oimage(U_11776,U_11776,c_COMBI(U_11776)),U_11777) = U_11777,
    inference(definitional_conversion,[status(esa)],[f_3056_2]) ).

cnf(f_3056_4,plain,
    hAPP(c_Set_Oimage(U_11776,U_11776,c_COMBI(U_11776)),U_11777) = U_11777,
    inference(clausify,[status(thm)],[f_3056_3]) ).

fof(f_3057_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_3057_2,plain,
    ! [U_11779,U_11778] : c_Fun_Oinj__on(U_11778,U_11778,c_COMBI(U_11778),U_11779),
    inference(variable_rename,[status(thm)],[f_3057_1]) ).

fof(f_3057_3,plain,
    ! [U_11778,U_11779] : c_Fun_Oinj__on(U_11778,U_11778,c_COMBI(U_11778),U_11779),
    inference(definitional_conversion,[status(esa)],[f_3057_2]) ).

cnf(f_3057_4,plain,
    c_Fun_Oinj__on(U_11778,U_11778,c_COMBI(U_11778),U_11779),
    inference(clausify,[status(thm)],[f_3057_3]) ).

fof(f_3058_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_3058_2,plain,
    ! [U_11785,U_11784,U_11783,U_11782,U_11781,U_11780] :
      ( U_11784 = U_11785
      | ~ hBOOL(hAPP(hAPP(c_member(U_11780),U_11785),U_11783))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11780),U_11784),U_11783))
      | hAPP(U_11782,U_11784) != hAPP(U_11782,U_11785)
      | ~ c_Fun_Oinj__on(U_11780,U_11781,U_11782,U_11783) ),
    inference(variable_rename,[status(thm)],[f_3058_1]) ).

fof(f_3058_3,plain,
    ! [U_11780,U_11785,U_11781,U_11783,U_11784,U_11782] :
      ( U_11784 = U_11785
      | ~ hBOOL(hAPP(hAPP(c_member(U_11780),U_11785),U_11783))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11780),U_11784),U_11783))
      | hAPP(U_11782,U_11784) != hAPP(U_11782,U_11785)
      | ~ c_Fun_Oinj__on(U_11780,U_11781,U_11782,U_11783) ),
    inference(definitional_conversion,[status(esa)],[f_3058_2]) ).

cnf(f_3058_4,plain,
    ( U_11784 = U_11785
    | ~ hBOOL(hAPP(hAPP(c_member(U_11780),U_11785),U_11783))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11780),U_11784),U_11783))
    | hAPP(U_11782,U_11784) != hAPP(U_11782,U_11785)
    | ~ c_Fun_Oinj__on(U_11780,U_11781,U_11782,U_11783) ),
    inference(clausify,[status(thm)],[f_3058_3]) ).

fof(f_3059_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_3059_2,plain,
    ! [U_11791,U_11790,U_11789,U_11788,U_11787,U_11786] :
      ( ( ( hAPP(U_11788,U_11790) = hAPP(U_11788,U_11791)
          | U_11790 != U_11791 )
        & ( U_11790 = U_11791
          | hAPP(U_11788,U_11790) != hAPP(U_11788,U_11791) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_11786),U_11791),U_11789))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11786),U_11790),U_11789))
      | ~ c_Fun_Oinj__on(U_11786,U_11787,U_11788,U_11789) ),
    inference(variable_rename,[status(thm)],[f_3059_1]) ).

fof(f_3059_3,plain,
    ( ! [U_11788,U_11790,U_11791] :
        ( hAPP(U_11788,U_11790) = hAPP(U_11788,U_11791)
        | U_11790 != U_11791
        | ~ sP866(U_11788,U_11790,U_11791) )
    & ! [U_11788,U_11790,U_11791] :
        ( U_11790 = U_11791
        | hAPP(U_11788,U_11790) != hAPP(U_11788,U_11791)
        | ~ sP866(U_11788,U_11790,U_11791) )
    & ! [U_11786,U_11787,U_11788,U_11789,U_11790,U_11791] :
        ( sP866(U_11788,U_11790,U_11791)
        | ~ hBOOL(hAPP(hAPP(c_member(U_11786),U_11791),U_11789))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11786),U_11790),U_11789))
        | ~ c_Fun_Oinj__on(U_11786,U_11787,U_11788,U_11789) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP866])],[f_3059_2]) ).

cnf(f_3059_4,plain,
    ( sP866(U_11788,U_11790,U_11791)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11786),U_11791),U_11789))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11786),U_11790),U_11789))
    | ~ c_Fun_Oinj__on(U_11786,U_11787,U_11788,U_11789) ),
    inference(clausify,[status(thm)],[f_3059_3]) ).

cnf(f_3059_5,plain,
    ( U_11790 = U_11791
    | hAPP(U_11788,U_11790) != hAPP(U_11788,U_11791)
    | ~ sP866(U_11788,U_11790,U_11791) ),
    inference(clausify,[status(thm)],[f_3059_3]) ).

cnf(f_3059_6,plain,
    ( hAPP(U_11788,U_11790) = hAPP(U_11788,U_11791)
    | U_11790 != U_11791
    | ~ sP866(U_11788,U_11790,U_11791) ),
    inference(clausify,[status(thm)],[f_3059_3]) ).

fof(f_3060_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_3060_2,plain,
    ! [U_11797,U_11796,U_11795,U_11794,U_11793,U_11792] :
      ( hAPP(U_11794,U_11796) != hAPP(U_11794,U_11797)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11792),U_11797),U_11795))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11792),U_11796),U_11795))
      | U_11796 = U_11797
      | ~ c_Fun_Oinj__on(U_11792,U_11793,U_11794,U_11795) ),
    inference(variable_rename,[status(thm)],[f_3060_1]) ).

fof(f_3060_3,plain,
    ! [U_11796,U_11795,U_11797,U_11794,U_11793,U_11792] :
      ( hAPP(U_11794,U_11796) != hAPP(U_11794,U_11797)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11792),U_11797),U_11795))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11792),U_11796),U_11795))
      | U_11796 = U_11797
      | ~ c_Fun_Oinj__on(U_11792,U_11793,U_11794,U_11795) ),
    inference(definitional_conversion,[status(esa)],[f_3060_2]) ).

cnf(f_3060_4,plain,
    ( hAPP(U_11794,U_11796) != hAPP(U_11794,U_11797)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11792),U_11797),U_11795))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11792),U_11796),U_11795))
    | U_11796 = U_11797
    | ~ c_Fun_Oinj__on(U_11792,U_11793,U_11794,U_11795) ),
    inference(clausify,[status(thm)],[f_3060_3]) ).

fof(f_3061_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_3061_2,plain,
    ! [U_11802,U_11801,U_11800,U_11799,U_11798] :
      ( c_Fun_Oinj__on(U_11798,U_11799,U_11800,U_11802)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11798,tc_HOL_Obool)),U_11802),U_11801))
      | ~ c_Fun_Oinj__on(U_11798,U_11799,U_11800,U_11801) ),
    inference(variable_rename,[status(thm)],[f_3061_1]) ).

fof(f_3061_3,plain,
    ! [U_11800,U_11801,U_11798,U_11802,U_11799] :
      ( c_Fun_Oinj__on(U_11798,U_11799,U_11800,U_11802)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11798,tc_HOL_Obool)),U_11802),U_11801))
      | ~ c_Fun_Oinj__on(U_11798,U_11799,U_11800,U_11801) ),
    inference(definitional_conversion,[status(esa)],[f_3061_2]) ).

cnf(f_3061_4,plain,
    ( c_Fun_Oinj__on(U_11798,U_11799,U_11800,U_11802)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11798,tc_HOL_Obool)),U_11802),U_11801))
    | ~ c_Fun_Oinj__on(U_11798,U_11799,U_11800,U_11801) ),
    inference(clausify,[status(thm)],[f_3061_3]) ).

fof(f_3062_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_3062_2,plain,
    ! [U_11807,U_11806,U_11805,U_11804,U_11803] :
      ( c_Fun_Oinj__on(U_11803,U_11804,U_11805,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11803,tc_HOL_Obool)),U_11806),U_11807))
      | ~ c_Fun_Oinj__on(U_11803,U_11804,U_11805,U_11807)
      | ~ c_Fun_Oinj__on(U_11803,U_11804,U_11805,U_11806) ),
    inference(variable_rename,[status(thm)],[f_3062_1]) ).

fof(f_3062_3,plain,
    ! [U_11805,U_11806,U_11803,U_11804,U_11807] :
      ( c_Fun_Oinj__on(U_11803,U_11804,U_11805,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11803,tc_HOL_Obool)),U_11806),U_11807))
      | ~ c_Fun_Oinj__on(U_11803,U_11804,U_11805,U_11807)
      | ~ c_Fun_Oinj__on(U_11803,U_11804,U_11805,U_11806) ),
    inference(definitional_conversion,[status(esa)],[f_3062_2]) ).

cnf(f_3062_4,plain,
    ( c_Fun_Oinj__on(U_11803,U_11804,U_11805,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11803,tc_HOL_Obool)),U_11806),U_11807))
    | ~ c_Fun_Oinj__on(U_11803,U_11804,U_11805,U_11807)
    | ~ c_Fun_Oinj__on(U_11803,U_11804,U_11805,U_11806) ),
    inference(clausify,[status(thm)],[f_3062_3]) ).

fof(f_3063_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_3063_2,plain,
    ! [U_11812,U_11811,U_11810,U_11809,U_11808] :
      ( c_Fun_Oinj__on(U_11808,U_11809,U_11810,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11808,tc_HOL_Obool)),U_11811),U_11812))
      | ~ c_Fun_Oinj__on(U_11808,U_11809,U_11810,U_11811) ),
    inference(variable_rename,[status(thm)],[f_3063_1]) ).

fof(f_3063_3,plain,
    ! [U_11809,U_11808,U_11812,U_11811,U_11810] :
      ( c_Fun_Oinj__on(U_11808,U_11809,U_11810,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11808,tc_HOL_Obool)),U_11811),U_11812))
      | ~ c_Fun_Oinj__on(U_11808,U_11809,U_11810,U_11811) ),
    inference(definitional_conversion,[status(esa)],[f_3063_2]) ).

cnf(f_3063_4,plain,
    ( c_Fun_Oinj__on(U_11808,U_11809,U_11810,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11808,tc_HOL_Obool)),U_11811),U_11812))
    | ~ c_Fun_Oinj__on(U_11808,U_11809,U_11810,U_11811) ),
    inference(clausify,[status(thm)],[f_3063_3]) ).

fof(f_3064_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_3064_2,plain,
    ! [U_11815,U_11814,U_11813] : hAPP(c_Set_Oimage(U_11814,tc_fun(U_11814,tc_HOL_Obool),U_11813),U_11815) != hAPP(c_Set_OPow(U_11814),U_11815),
    inference(variable_rename,[status(thm)],[f_3064_1]) ).

fof(f_3064_3,plain,
    ! [U_11814,U_11813,U_11815] : hAPP(c_Set_Oimage(U_11814,tc_fun(U_11814,tc_HOL_Obool),U_11813),U_11815) != hAPP(c_Set_OPow(U_11814),U_11815),
    inference(definitional_conversion,[status(esa)],[f_3064_2]) ).

cnf(f_3064_4,plain,
    hAPP(c_Set_Oimage(U_11814,tc_fun(U_11814,tc_HOL_Obool),U_11813),U_11815) != hAPP(c_Set_OPow(U_11814),U_11815),
    inference(clausify,[status(thm)],[f_3064_3]) ).

fof(f_3065_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_3065_2,plain,
    ! [U_11820,U_11819,U_11818,U_11817,U_11816] :
      ( ( ( hAPP(c_Set_Oimage(U_11816,U_11817,U_11818),U_11819) = hAPP(c_Set_Oimage(U_11816,U_11817,U_11818),U_11820)
          | U_11819 != U_11820 )
        & ( U_11819 = U_11820
          | hAPP(c_Set_Oimage(U_11816,U_11817,U_11818),U_11819) != hAPP(c_Set_Oimage(U_11816,U_11817,U_11818),U_11820) ) )
      | ~ c_Fun_Oinj__on(U_11816,U_11817,U_11818,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11816,tc_HOL_Obool)),U_11819),U_11820)) ),
    inference(variable_rename,[status(thm)],[f_3065_1]) ).

fof(f_3065_3,plain,
    ( ! [U_11816,U_11817,U_11818,U_11819,U_11820] :
        ( hAPP(c_Set_Oimage(U_11816,U_11817,U_11818),U_11819) = hAPP(c_Set_Oimage(U_11816,U_11817,U_11818),U_11820)
        | U_11819 != U_11820
        | ~ sP867(U_11816,U_11817,U_11818,U_11819,U_11820) )
    & ! [U_11816,U_11817,U_11818,U_11819,U_11820] :
        ( U_11819 = U_11820
        | hAPP(c_Set_Oimage(U_11816,U_11817,U_11818),U_11819) != hAPP(c_Set_Oimage(U_11816,U_11817,U_11818),U_11820)
        | ~ sP867(U_11816,U_11817,U_11818,U_11819,U_11820) )
    & ! [U_11816,U_11817,U_11818,U_11819,U_11820] :
        ( sP867(U_11816,U_11817,U_11818,U_11819,U_11820)
        | ~ c_Fun_Oinj__on(U_11816,U_11817,U_11818,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11816,tc_HOL_Obool)),U_11819),U_11820)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP867])],[f_3065_2]) ).

cnf(f_3065_4,plain,
    ( sP867(U_11816,U_11817,U_11818,U_11819,U_11820)
    | ~ c_Fun_Oinj__on(U_11816,U_11817,U_11818,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11816,tc_HOL_Obool)),U_11819),U_11820)) ),
    inference(clausify,[status(thm)],[f_3065_3]) ).

cnf(f_3065_5,plain,
    ( U_11819 = U_11820
    | hAPP(c_Set_Oimage(U_11816,U_11817,U_11818),U_11819) != hAPP(c_Set_Oimage(U_11816,U_11817,U_11818),U_11820)
    | ~ sP867(U_11816,U_11817,U_11818,U_11819,U_11820) ),
    inference(clausify,[status(thm)],[f_3065_3]) ).

cnf(f_3065_6,plain,
    ( hAPP(c_Set_Oimage(U_11816,U_11817,U_11818),U_11819) = hAPP(c_Set_Oimage(U_11816,U_11817,U_11818),U_11820)
    | U_11819 != U_11820
    | ~ sP867(U_11816,U_11817,U_11818,U_11819,U_11820) ),
    inference(clausify,[status(thm)],[f_3065_3]) ).

fof(f_3066_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_3066_2,plain,
    ! [U_11825,U_11824,U_11823,U_11822,U_11821] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11822,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11821,U_11822,U_11823),U_11825)),hAPP(c_Set_Oimage(U_11821,U_11822,U_11823),U_11824)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11821,tc_HOL_Obool)),U_11825),U_11824))
      | ~ c_Fun_Oinj__on(U_11821,U_11822,U_11823,U_11824) ),
    inference(variable_rename,[status(thm)],[f_3066_1]) ).

fof(f_3066_3,plain,
    ! [U_11822,U_11821,U_11823,U_11824,U_11825] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11822,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11821,U_11822,U_11823),U_11825)),hAPP(c_Set_Oimage(U_11821,U_11822,U_11823),U_11824)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11821,tc_HOL_Obool)),U_11825),U_11824))
      | ~ c_Fun_Oinj__on(U_11821,U_11822,U_11823,U_11824) ),
    inference(definitional_conversion,[status(esa)],[f_3066_2]) ).

cnf(f_3066_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11822,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11821,U_11822,U_11823),U_11825)),hAPP(c_Set_Oimage(U_11821,U_11822,U_11823),U_11824)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11821,tc_HOL_Obool)),U_11825),U_11824))
    | ~ c_Fun_Oinj__on(U_11821,U_11822,U_11823,U_11824) ),
    inference(clausify,[status(thm)],[f_3066_3]) ).

fof(f_3067_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_3067_2,plain,
    ! [U_11831,U_11830,U_11829,U_11828,U_11827,U_11826] :
      ( hAPP(c_Set_Oimage(U_11826,U_11827,U_11828),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11826,tc_HOL_Obool)),U_11830),U_11831)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11827,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11826,U_11827,U_11828),U_11830)),hAPP(c_Set_Oimage(U_11826,U_11827,U_11828),U_11831))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11826,tc_HOL_Obool)),U_11831),U_11829))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11826,tc_HOL_Obool)),U_11830),U_11829))
      | ~ c_Fun_Oinj__on(U_11826,U_11827,U_11828,U_11829) ),
    inference(variable_rename,[status(thm)],[f_3067_1]) ).

fof(f_3067_3,plain,
    ! [U_11826,U_11827,U_11828,U_11829,U_11830,U_11831] :
      ( hAPP(c_Set_Oimage(U_11826,U_11827,U_11828),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11826,tc_HOL_Obool)),U_11830),U_11831)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11827,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11826,U_11827,U_11828),U_11830)),hAPP(c_Set_Oimage(U_11826,U_11827,U_11828),U_11831))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11826,tc_HOL_Obool)),U_11831),U_11829))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11826,tc_HOL_Obool)),U_11830),U_11829))
      | ~ c_Fun_Oinj__on(U_11826,U_11827,U_11828,U_11829) ),
    inference(definitional_conversion,[status(esa)],[f_3067_2]) ).

cnf(f_3067_4,plain,
    ( hAPP(c_Set_Oimage(U_11826,U_11827,U_11828),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11826,tc_HOL_Obool)),U_11830),U_11831)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11827,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11826,U_11827,U_11828),U_11830)),hAPP(c_Set_Oimage(U_11826,U_11827,U_11828),U_11831))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11826,tc_HOL_Obool)),U_11831),U_11829))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11826,tc_HOL_Obool)),U_11830),U_11829))
    | ~ c_Fun_Oinj__on(U_11826,U_11827,U_11828,U_11829) ),
    inference(clausify,[status(thm)],[f_3067_3]) ).

fof(f_3068_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_3068_2,plain,
    ! [U_11837,U_11836,U_11835,U_11834,U_11833,U_11832] :
      ( hAPP(c_Set_Oimage(U_11832,U_11833,U_11834),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11832,tc_HOL_Obool)),U_11836),U_11837)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11833,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11832,U_11833,U_11834),U_11836)),hAPP(c_Set_Oimage(U_11832,U_11833,U_11834),U_11837))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11832,tc_HOL_Obool)),U_11837),U_11835))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11832,tc_HOL_Obool)),U_11836),U_11835))
      | ~ c_Fun_Oinj__on(U_11832,U_11833,U_11834,U_11835) ),
    inference(variable_rename,[status(thm)],[f_3068_1]) ).

fof(f_3068_3,plain,
    ! [U_11832,U_11833,U_11834,U_11835,U_11836,U_11837] :
      ( hAPP(c_Set_Oimage(U_11832,U_11833,U_11834),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11832,tc_HOL_Obool)),U_11836),U_11837)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11833,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11832,U_11833,U_11834),U_11836)),hAPP(c_Set_Oimage(U_11832,U_11833,U_11834),U_11837))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11832,tc_HOL_Obool)),U_11837),U_11835))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11832,tc_HOL_Obool)),U_11836),U_11835))
      | ~ c_Fun_Oinj__on(U_11832,U_11833,U_11834,U_11835) ),
    inference(definitional_conversion,[status(esa)],[f_3068_2]) ).

cnf(f_3068_4,plain,
    ( hAPP(c_Set_Oimage(U_11832,U_11833,U_11834),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11832,tc_HOL_Obool)),U_11836),U_11837)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11833,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11832,U_11833,U_11834),U_11836)),hAPP(c_Set_Oimage(U_11832,U_11833,U_11834),U_11837))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11832,tc_HOL_Obool)),U_11837),U_11835))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11832,tc_HOL_Obool)),U_11836),U_11835))
    | ~ c_Fun_Oinj__on(U_11832,U_11833,U_11834,U_11835) ),
    inference(clausify,[status(thm)],[f_3068_3]) ).

fof(f_3069_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_3069_2,plain,
    ! [U_11845,U_11844,U_11843,U_11842] :
      ( ( ( ? [U_11841] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11844,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11843,U_11844,U_11841),U_11842)),U_11845))
              & c_Fun_Oinj__on(U_11843,U_11844,U_11841,U_11842) )
          | ! [U_11840] : hAPP(c_Set_Oimage(U_11844,U_11843,U_11840),U_11845) != U_11842 )
        & ( ? [U_11839] : hAPP(c_Set_Oimage(U_11844,U_11843,U_11839),U_11845) = U_11842
          | ! [U_11838] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11844,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11843,U_11844,U_11838),U_11842)),U_11845))
              | ~ c_Fun_Oinj__on(U_11843,U_11844,U_11838,U_11842) ) ) )
      | U_11842 = c_Orderings_Obot__class_Obot(tc_fun(U_11843,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3069_1]) ).

fof(f_3069_3,plain,
    ! [U_11845,U_11844,U_11843,U_11842] :
      ( ( ( ? [U_11841] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11844,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11843,U_11844,U_11841),U_11842)),U_11845))
              & c_Fun_Oinj__on(U_11843,U_11844,U_11841,U_11842) )
          | ! [U_11840] : hAPP(c_Set_Oimage(U_11844,U_11843,U_11840),U_11845) != U_11842 )
        & ( hAPP(c_Set_Oimage(U_11844,U_11843,sK214(U_11845,U_11844,U_11843,U_11842)),U_11845) = U_11842
          | ! [U_11838] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11844,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11843,U_11844,U_11838),U_11842)),U_11845))
              | ~ c_Fun_Oinj__on(U_11843,U_11844,U_11838,U_11842) ) ) )
      | U_11842 = c_Orderings_Obot__class_Obot(tc_fun(U_11843,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK214]),skolemize(U_11839,sK214(U_11845,U_11844,U_11843,U_11842))],[f_3069_2]) ).

fof(f_3069_4,plain,
    ! [U_11845,U_11844,U_11843,U_11842] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11844,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11843,U_11844,sK215(U_11845,U_11844,U_11843,U_11842)),U_11842)),U_11845))
            & c_Fun_Oinj__on(U_11843,U_11844,sK215(U_11845,U_11844,U_11843,U_11842),U_11842) )
          | ! [U_11840] : hAPP(c_Set_Oimage(U_11844,U_11843,U_11840),U_11845) != U_11842 )
        & ( hAPP(c_Set_Oimage(U_11844,U_11843,sK214(U_11845,U_11844,U_11843,U_11842)),U_11845) = U_11842
          | ! [U_11838] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11844,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11843,U_11844,U_11838),U_11842)),U_11845))
              | ~ c_Fun_Oinj__on(U_11843,U_11844,U_11838,U_11842) ) ) )
      | U_11842 = c_Orderings_Obot__class_Obot(tc_fun(U_11843,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK215]),skolemize(U_11841,sK215(U_11845,U_11844,U_11843,U_11842))],[f_3069_3]) ).

fof(f_3069_5,plain,
    ( ! [U_11842,U_11843,U_11844,U_11845] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11844,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11843,U_11844,sK215(U_11845,U_11844,U_11843,U_11842)),U_11842)),U_11845))
        | ~ sP868(U_11842,U_11843,U_11844,U_11845) )
    & ! [U_11842,U_11843,U_11844,U_11845] :
        ( c_Fun_Oinj__on(U_11843,U_11844,sK215(U_11845,U_11844,U_11843,U_11842),U_11842)
        | ~ sP868(U_11842,U_11843,U_11844,U_11845) )
    & ! [U_11838,U_11840,U_11842,U_11843,U_11844,U_11845] :
        ( sP868(U_11842,U_11843,U_11844,U_11845)
        | hAPP(c_Set_Oimage(U_11844,U_11843,U_11840),U_11845) != U_11842
        | ~ sP869(U_11838,U_11840,U_11842,U_11843,U_11844,U_11845) )
    & ! [U_11838,U_11840,U_11842,U_11843,U_11844,U_11845] :
        ( hAPP(c_Set_Oimage(U_11844,U_11843,sK214(U_11845,U_11844,U_11843,U_11842)),U_11845) = U_11842
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11844,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11843,U_11844,U_11838),U_11842)),U_11845))
        | ~ c_Fun_Oinj__on(U_11843,U_11844,U_11838,U_11842)
        | ~ sP869(U_11838,U_11840,U_11842,U_11843,U_11844,U_11845) )
    & ! [U_11838,U_11840,U_11842,U_11843,U_11844,U_11845] :
        ( sP869(U_11838,U_11840,U_11842,U_11843,U_11844,U_11845)
        | U_11842 = c_Orderings_Obot__class_Obot(tc_fun(U_11843,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP868,sP869])],[f_3069_4]) ).

cnf(f_3069_6,plain,
    ( sP869(U_11838,U_11840,U_11842,U_11843,U_11844,U_11845)
    | U_11842 = c_Orderings_Obot__class_Obot(tc_fun(U_11843,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3069_5]) ).

cnf(f_3069_7,plain,
    ( hAPP(c_Set_Oimage(U_11844,U_11843,sK214(U_11845,U_11844,U_11843,U_11842)),U_11845) = U_11842
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11844,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11843,U_11844,U_11838),U_11842)),U_11845))
    | ~ c_Fun_Oinj__on(U_11843,U_11844,U_11838,U_11842)
    | ~ sP869(U_11838,U_11840,U_11842,U_11843,U_11844,U_11845) ),
    inference(clausify,[status(thm)],[f_3069_5]) ).

cnf(f_3069_8,plain,
    ( sP868(U_11842,U_11843,U_11844,U_11845)
    | hAPP(c_Set_Oimage(U_11844,U_11843,U_11840),U_11845) != U_11842
    | ~ sP869(U_11838,U_11840,U_11842,U_11843,U_11844,U_11845) ),
    inference(clausify,[status(thm)],[f_3069_5]) ).

cnf(f_3069_9,plain,
    ( c_Fun_Oinj__on(U_11843,U_11844,sK215(U_11845,U_11844,U_11843,U_11842),U_11842)
    | ~ sP868(U_11842,U_11843,U_11844,U_11845) ),
    inference(clausify,[status(thm)],[f_3069_5]) ).

cnf(f_3069_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11844,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11843,U_11844,sK215(U_11845,U_11844,U_11843,U_11842)),U_11842)),U_11845))
    | ~ sP868(U_11842,U_11843,U_11844,U_11845) ),
    inference(clausify,[status(thm)],[f_3069_5]) ).

fof(f_3070_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_3070_2,plain,
    ! [U_11851,U_11850] :
      ( ( ? [U_11849] :
            ( hBOOL(hAPP(U_11851,U_11849))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11849),U_11850)) )
        | ! [U_11848] :
            ( ~ hBOOL(hAPP(U_11851,U_11848))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11848),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11850))) ) )
      & ( ? [U_11847] :
            ( hBOOL(hAPP(U_11851,U_11847))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11847),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11850))) )
        | ! [U_11846] :
            ( ~ hBOOL(hAPP(U_11851,U_11846))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11846),U_11850)) ) ) ),
    inference(variable_rename,[status(thm)],[f_3070_1]) ).

fof(f_3070_3,plain,
    ( ! [U_11855,U_11853] :
        ( ? [U_11849] :
            ( hBOOL(hAPP(U_11855,U_11849))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11849),U_11853)) )
        | ! [U_11848] :
            ( ~ hBOOL(hAPP(U_11855,U_11848))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11848),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11853))) ) )
    & ! [U_11854,U_11852] :
        ( ? [U_11847] :
            ( hBOOL(hAPP(U_11854,U_11847))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11847),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11852))) )
        | ! [U_11846] :
            ( ~ hBOOL(hAPP(U_11854,U_11846))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11846),U_11852)) ) ) ),
    inference(miniscope,[status(thm)],[f_3070_2]) ).

fof(f_3070_4,plain,
    ( ! [U_11855,U_11853] :
        ( ? [U_11849] :
            ( hBOOL(hAPP(U_11855,U_11849))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11849),U_11853)) )
        | ! [U_11848] :
            ( ~ hBOOL(hAPP(U_11855,U_11848))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11848),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11853))) ) )
    & ! [U_11854,U_11852] :
        ( ( hBOOL(hAPP(U_11854,sK216(U_11854,U_11852)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK216(U_11854,U_11852)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11852))) )
        | ! [U_11846] :
            ( ~ hBOOL(hAPP(U_11854,U_11846))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11846),U_11852)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK216]),skolemize(U_11847,sK216(U_11854,U_11852))],[f_3070_3]) ).

fof(f_3070_5,plain,
    ( ! [U_11855,U_11853] :
        ( ( hBOOL(hAPP(U_11855,sK217(U_11855,U_11853)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK217(U_11855,U_11853)),U_11853)) )
        | ! [U_11848] :
            ( ~ hBOOL(hAPP(U_11855,U_11848))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11848),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11853))) ) )
    & ! [U_11854,U_11852] :
        ( ( hBOOL(hAPP(U_11854,sK216(U_11854,U_11852)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK216(U_11854,U_11852)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11852))) )
        | ! [U_11846] :
            ( ~ hBOOL(hAPP(U_11854,U_11846))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11846),U_11852)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(U_11849,sK217(U_11855,U_11853))],[f_3070_4]) ).

fof(f_3070_6,plain,
    ( ! [U_11855,U_11853] :
        ( hBOOL(hAPP(U_11855,sK217(U_11855,U_11853)))
        | ~ sP871(U_11855,U_11853) )
    & ! [U_11855,U_11853] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK217(U_11855,U_11853)),U_11853))
        | ~ sP871(U_11855,U_11853) )
    & ! [U_11852,U_11854] :
        ( hBOOL(hAPP(U_11854,sK216(U_11854,U_11852)))
        | ~ sP870(U_11852,U_11854) )
    & ! [U_11852,U_11854] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK216(U_11854,U_11852)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11852)))
        | ~ sP870(U_11852,U_11854) )
    & ! [U_11855,U_11853,U_11848] :
        ( sP871(U_11855,U_11853)
        | ~ hBOOL(hAPP(U_11855,U_11848))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11848),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11853))) )
    & ! [U_11846,U_11852,U_11854] :
        ( sP870(U_11852,U_11854)
        | ~ hBOOL(hAPP(U_11854,U_11846))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11846),U_11852)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP870,sP871])],[f_3070_5]) ).

cnf(f_3070_7,plain,
    ( sP870(U_11852,U_11854)
    | ~ hBOOL(hAPP(U_11854,U_11846))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11846),U_11852)) ),
    inference(clausify,[status(thm)],[f_3070_6]) ).

cnf(f_3070_8,plain,
    ( sP871(U_11855,U_11853)
    | ~ hBOOL(hAPP(U_11855,U_11848))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11848),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11853))) ),
    inference(clausify,[status(thm)],[f_3070_6]) ).

cnf(f_3070_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK216(U_11854,U_11852)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11852)))
    | ~ sP870(U_11852,U_11854) ),
    inference(clausify,[status(thm)],[f_3070_6]) ).

cnf(f_3070_10,plain,
    ( hBOOL(hAPP(U_11854,sK216(U_11854,U_11852)))
    | ~ sP870(U_11852,U_11854) ),
    inference(clausify,[status(thm)],[f_3070_6]) ).

cnf(f_3070_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK217(U_11855,U_11853)),U_11853))
    | ~ sP871(U_11855,U_11853) ),
    inference(clausify,[status(thm)],[f_3070_6]) ).

cnf(f_3070_12,plain,
    ( hBOOL(hAPP(U_11855,sK217(U_11855,U_11853)))
    | ~ sP871(U_11855,U_11853) ),
    inference(clausify,[status(thm)],[f_3070_6]) ).

fof(f_3071_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_3071_2,plain,
    ! [U_11861,U_11860] :
      ( ( ! [U_11859] :
            ( hBOOL(hAPP(U_11861,U_11859))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11859),U_11860)) )
        | ? [U_11858] :
            ( ~ hBOOL(hAPP(U_11861,U_11858))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11858),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11860))) ) )
      & ( ! [U_11857] :
            ( hBOOL(hAPP(U_11861,U_11857))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11857),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11860))) )
        | ? [U_11856] :
            ( ~ hBOOL(hAPP(U_11861,U_11856))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11856),U_11860)) ) ) ),
    inference(variable_rename,[status(thm)],[f_3071_1]) ).

fof(f_3071_3,plain,
    ( ! [U_11865,U_11863] :
        ( ! [U_11859] :
            ( hBOOL(hAPP(U_11865,U_11859))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11859),U_11863)) )
        | ? [U_11858] :
            ( ~ hBOOL(hAPP(U_11865,U_11858))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11858),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11863))) ) )
    & ! [U_11864,U_11862] :
        ( ! [U_11857] :
            ( hBOOL(hAPP(U_11864,U_11857))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11857),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11862))) )
        | ? [U_11856] :
            ( ~ hBOOL(hAPP(U_11864,U_11856))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11856),U_11862)) ) ) ),
    inference(miniscope,[status(thm)],[f_3071_2]) ).

fof(f_3071_4,plain,
    ( ! [U_11865,U_11863] :
        ( ! [U_11859] :
            ( hBOOL(hAPP(U_11865,U_11859))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11859),U_11863)) )
        | ? [U_11858] :
            ( ~ hBOOL(hAPP(U_11865,U_11858))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11858),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11863))) ) )
    & ! [U_11864,U_11862] :
        ( ! [U_11857] :
            ( hBOOL(hAPP(U_11864,U_11857))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11857),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11862))) )
        | ( ~ hBOOL(hAPP(U_11864,sK218(U_11864,U_11862)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK218(U_11864,U_11862)),U_11862)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK218]),skolemize(U_11856,sK218(U_11864,U_11862))],[f_3071_3]) ).

fof(f_3071_5,plain,
    ( ! [U_11865,U_11863] :
        ( ! [U_11859] :
            ( hBOOL(hAPP(U_11865,U_11859))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11859),U_11863)) )
        | ( ~ hBOOL(hAPP(U_11865,sK219(U_11865,U_11863)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK219(U_11865,U_11863)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11863))) ) )
    & ! [U_11864,U_11862] :
        ( ! [U_11857] :
            ( hBOOL(hAPP(U_11864,U_11857))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11857),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11862))) )
        | ( ~ hBOOL(hAPP(U_11864,sK218(U_11864,U_11862)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK218(U_11864,U_11862)),U_11862)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK219]),skolemize(U_11858,sK219(U_11865,U_11863))],[f_3071_4]) ).

fof(f_3071_6,plain,
    ( ! [U_11865,U_11863] :
        ( ~ hBOOL(hAPP(U_11865,sK219(U_11865,U_11863)))
        | ~ sP873(U_11865,U_11863) )
    & ! [U_11865,U_11863] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK219(U_11865,U_11863)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11863)))
        | ~ sP873(U_11865,U_11863) )
    & ! [U_11862,U_11864] :
        ( ~ hBOOL(hAPP(U_11864,sK218(U_11864,U_11862)))
        | ~ sP872(U_11862,U_11864) )
    & ! [U_11862,U_11864] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK218(U_11864,U_11862)),U_11862))
        | ~ sP872(U_11862,U_11864) )
    & ! [U_11865,U_11859,U_11863] :
        ( hBOOL(hAPP(U_11865,U_11859))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11859),U_11863))
        | sP873(U_11865,U_11863) )
    & ! [U_11857,U_11862,U_11864] :
        ( hBOOL(hAPP(U_11864,U_11857))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11857),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11862)))
        | sP872(U_11862,U_11864) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP872,sP873])],[f_3071_5]) ).

cnf(f_3071_7,plain,
    ( hBOOL(hAPP(U_11864,U_11857))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11857),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11862)))
    | sP872(U_11862,U_11864) ),
    inference(clausify,[status(thm)],[f_3071_6]) ).

cnf(f_3071_8,plain,
    ( hBOOL(hAPP(U_11865,U_11859))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11859),U_11863))
    | sP873(U_11865,U_11863) ),
    inference(clausify,[status(thm)],[f_3071_6]) ).

cnf(f_3071_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK218(U_11864,U_11862)),U_11862))
    | ~ sP872(U_11862,U_11864) ),
    inference(clausify,[status(thm)],[f_3071_6]) ).

cnf(f_3071_10,plain,
    ( ~ hBOOL(hAPP(U_11864,sK218(U_11864,U_11862)))
    | ~ sP872(U_11862,U_11864) ),
    inference(clausify,[status(thm)],[f_3071_6]) ).

cnf(f_3071_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK219(U_11865,U_11863)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11863)))
    | ~ sP873(U_11865,U_11863) ),
    inference(clausify,[status(thm)],[f_3071_6]) ).

cnf(f_3071_12,plain,
    ( ~ hBOOL(hAPP(U_11865,sK219(U_11865,U_11863)))
    | ~ sP873(U_11865,U_11863) ),
    inference(clausify,[status(thm)],[f_3071_6]) ).

fof(f_3072_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_3072_2,plain,
    ! [U_11871,U_11870,U_11869] :
      ( ! [U_11868] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11870),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11868),U_11869)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11870),U_11868))
          | ? [U_11867] :
              ( ? [U_11866] :
                  ( U_11868 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11866),U_11867)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11866),U_11871)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11867),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11869))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11870),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11871))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11869)) ),
    inference(variable_rename,[status(thm)],[f_3072_1]) ).

fof(f_3072_3,plain,
    ! [U_11871,U_11870,U_11869] :
      ( ! [U_11868] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11870),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11868),U_11869)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11870),U_11868))
          | ( ? [U_11866] :
                ( U_11868 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11866),sK220(U_11871,U_11870,U_11869,U_11868))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11866),U_11871)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK220(U_11871,U_11870,U_11869,U_11868)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11869))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11870),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11871))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11869)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK220]),skolemize(U_11867,sK220(U_11871,U_11870,U_11869,U_11868))],[f_3072_2]) ).

fof(f_3072_4,plain,
    ! [U_11871,U_11870,U_11869] :
      ( ! [U_11868] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11870),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11868),U_11869)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11870),U_11868))
          | ( U_11868 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK221(U_11871,U_11870,U_11869,U_11868)),sK220(U_11871,U_11870,U_11869,U_11868))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK221(U_11871,U_11870,U_11869,U_11868)),U_11871))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK220(U_11871,U_11870,U_11869,U_11868)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11869))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11870),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11871))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11869)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK221]),skolemize(U_11866,sK221(U_11871,U_11870,U_11869,U_11868))],[f_3072_3]) ).

fof(f_3072_5,plain,
    ( ! [U_11868,U_11869,U_11870,U_11871] :
        ( U_11868 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK221(U_11871,U_11870,U_11869,U_11868)),sK220(U_11871,U_11870,U_11869,U_11868))
        | ~ sP874(U_11868,U_11869,U_11870,U_11871) )
    & ! [U_11868,U_11869,U_11870,U_11871] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK221(U_11871,U_11870,U_11869,U_11868)),U_11871))
        | ~ sP874(U_11868,U_11869,U_11870,U_11871) )
    & ! [U_11868,U_11869,U_11870,U_11871] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK220(U_11871,U_11870,U_11869,U_11868)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11869)))
        | ~ sP874(U_11868,U_11869,U_11870,U_11871) )
    & ! [U_11868,U_11869,U_11870,U_11871] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11870),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11868),U_11869)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11870),U_11868))
        | sP874(U_11868,U_11869,U_11870,U_11871)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11870),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11871))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11869)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP874])],[f_3072_4]) ).

cnf(f_3072_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11870),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11868),U_11869)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11870),U_11868))
    | sP874(U_11868,U_11869,U_11870,U_11871)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11870),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11871))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11869)) ),
    inference(clausify,[status(thm)],[f_3072_5]) ).

cnf(f_3072_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK220(U_11871,U_11870,U_11869,U_11868)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11869)))
    | ~ sP874(U_11868,U_11869,U_11870,U_11871) ),
    inference(clausify,[status(thm)],[f_3072_5]) ).

cnf(f_3072_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK221(U_11871,U_11870,U_11869,U_11868)),U_11871))
    | ~ sP874(U_11868,U_11869,U_11870,U_11871) ),
    inference(clausify,[status(thm)],[f_3072_5]) ).

cnf(f_3072_9,plain,
    ( U_11868 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK221(U_11871,U_11870,U_11869,U_11868)),sK220(U_11871,U_11870,U_11869,U_11868))
    | ~ sP874(U_11868,U_11869,U_11870,U_11871) ),
    inference(clausify,[status(thm)],[f_3072_5]) ).

fof(f_3073_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_3073_2,plain,
    ! [U_11877,U_11876,U_11875] :
      ( ! [U_11874] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11874),U_11875)),U_11876))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11874),U_11876))
          | ? [U_11873] :
              ( ? [U_11872] :
                  ( U_11874 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11872),U_11873)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11872),U_11877)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11873),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11875))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11876),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11877))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11875)) ),
    inference(variable_rename,[status(thm)],[f_3073_1]) ).

fof(f_3073_3,plain,
    ! [U_11877,U_11876,U_11875] :
      ( ! [U_11874] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11874),U_11875)),U_11876))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11874),U_11876))
          | ( ? [U_11872] :
                ( U_11874 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11872),sK222(U_11877,U_11876,U_11875,U_11874))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11872),U_11877)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK222(U_11877,U_11876,U_11875,U_11874)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11875))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11876),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11877))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11875)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK222]),skolemize(U_11873,sK222(U_11877,U_11876,U_11875,U_11874))],[f_3073_2]) ).

fof(f_3073_4,plain,
    ! [U_11877,U_11876,U_11875] :
      ( ! [U_11874] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11874),U_11875)),U_11876))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11874),U_11876))
          | ( U_11874 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK223(U_11877,U_11876,U_11875,U_11874)),sK222(U_11877,U_11876,U_11875,U_11874))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK223(U_11877,U_11876,U_11875,U_11874)),U_11877))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK222(U_11877,U_11876,U_11875,U_11874)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11875))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11876),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11877))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11875)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(U_11872,sK223(U_11877,U_11876,U_11875,U_11874))],[f_3073_3]) ).

fof(f_3073_5,plain,
    ( ! [U_11874,U_11877,U_11875,U_11876] :
        ( U_11874 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK223(U_11877,U_11876,U_11875,U_11874)),sK222(U_11877,U_11876,U_11875,U_11874))
        | ~ sP875(U_11874,U_11877,U_11875,U_11876) )
    & ! [U_11874,U_11877,U_11875,U_11876] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK223(U_11877,U_11876,U_11875,U_11874)),U_11877))
        | ~ sP875(U_11874,U_11877,U_11875,U_11876) )
    & ! [U_11874,U_11877,U_11875,U_11876] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK222(U_11877,U_11876,U_11875,U_11874)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11875)))
        | ~ sP875(U_11874,U_11877,U_11875,U_11876) )
    & ! [U_11874,U_11877,U_11875,U_11876] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11874),U_11875)),U_11876))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11874),U_11876))
        | sP875(U_11874,U_11877,U_11875,U_11876)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11876),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11877))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11875)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP875])],[f_3073_4]) ).

cnf(f_3073_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_11874),U_11875)),U_11876))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11874),U_11876))
    | sP875(U_11874,U_11877,U_11875,U_11876)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11876),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11877))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11875)) ),
    inference(clausify,[status(thm)],[f_3073_5]) ).

cnf(f_3073_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK222(U_11877,U_11876,U_11875,U_11874)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11875)))
    | ~ sP875(U_11874,U_11877,U_11875,U_11876) ),
    inference(clausify,[status(thm)],[f_3073_5]) ).

cnf(f_3073_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK223(U_11877,U_11876,U_11875,U_11874)),U_11877))
    | ~ sP875(U_11874,U_11877,U_11875,U_11876) ),
    inference(clausify,[status(thm)],[f_3073_5]) ).

cnf(f_3073_9,plain,
    ( U_11874 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK223(U_11877,U_11876,U_11875,U_11874)),sK222(U_11877,U_11876,U_11875,U_11874))
    | ~ sP875(U_11874,U_11877,U_11875,U_11876) ),
    inference(clausify,[status(thm)],[f_3073_5]) ).

fof(f_3074_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_3074_2,plain,
    ! [U_11883,U_11882,U_11881] :
      ( ! [U_11880] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11880),U_11881) != U_11882
          | U_11880 = U_11882
          | ? [U_11879] :
              ( ? [U_11878] :
                  ( U_11880 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11878),U_11879)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11878),U_11883)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11879),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11881))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11882),U_11883))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11881)) ),
    inference(variable_rename,[status(thm)],[f_3074_1]) ).

fof(f_3074_3,plain,
    ! [U_11883,U_11882,U_11881] :
      ( ! [U_11880] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11880),U_11881) != U_11882
          | U_11880 = U_11882
          | ( ? [U_11878] :
                ( U_11880 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11878),sK224(U_11883,U_11882,U_11881,U_11880))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11878),U_11883)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK224(U_11883,U_11882,U_11881,U_11880)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11881))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11882),U_11883))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11881)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK224]),skolemize(U_11879,sK224(U_11883,U_11882,U_11881,U_11880))],[f_3074_2]) ).

fof(f_3074_4,plain,
    ! [U_11883,U_11882,U_11881] :
      ( ! [U_11880] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11880),U_11881) != U_11882
          | U_11880 = U_11882
          | ( U_11880 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK225(U_11883,U_11882,U_11881,U_11880)),sK224(U_11883,U_11882,U_11881,U_11880))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK225(U_11883,U_11882,U_11881,U_11880)),U_11883))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK224(U_11883,U_11882,U_11881,U_11880)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11881))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11882),U_11883))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11881)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK225]),skolemize(U_11878,sK225(U_11883,U_11882,U_11881,U_11880))],[f_3074_3]) ).

fof(f_3074_5,plain,
    ( ! [U_11880,U_11881,U_11882,U_11883] :
        ( U_11880 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK225(U_11883,U_11882,U_11881,U_11880)),sK224(U_11883,U_11882,U_11881,U_11880))
        | ~ sP876(U_11880,U_11881,U_11882,U_11883) )
    & ! [U_11880,U_11881,U_11882,U_11883] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK225(U_11883,U_11882,U_11881,U_11880)),U_11883))
        | ~ sP876(U_11880,U_11881,U_11882,U_11883) )
    & ! [U_11880,U_11881,U_11882,U_11883] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK224(U_11883,U_11882,U_11881,U_11880)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11881)))
        | ~ sP876(U_11880,U_11881,U_11882,U_11883) )
    & ! [U_11880,U_11881,U_11882,U_11883] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11880),U_11881) != U_11882
        | U_11880 = U_11882
        | sP876(U_11880,U_11881,U_11882,U_11883)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11882),U_11883))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11881)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP876])],[f_3074_4]) ).

cnf(f_3074_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11880),U_11881) != U_11882
    | U_11880 = U_11882
    | sP876(U_11880,U_11881,U_11882,U_11883)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11882),U_11883))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11881)) ),
    inference(clausify,[status(thm)],[f_3074_5]) ).

cnf(f_3074_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK224(U_11883,U_11882,U_11881,U_11880)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11881)))
    | ~ sP876(U_11880,U_11881,U_11882,U_11883) ),
    inference(clausify,[status(thm)],[f_3074_5]) ).

cnf(f_3074_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK225(U_11883,U_11882,U_11881,U_11880)),U_11883))
    | ~ sP876(U_11880,U_11881,U_11882,U_11883) ),
    inference(clausify,[status(thm)],[f_3074_5]) ).

cnf(f_3074_9,plain,
    ( U_11880 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK225(U_11883,U_11882,U_11881,U_11880)),sK224(U_11883,U_11882,U_11881,U_11880))
    | ~ sP876(U_11880,U_11881,U_11882,U_11883) ),
    inference(clausify,[status(thm)],[f_3074_5]) ).

fof(f_3075_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_3075_2,plain,
    ! [U_11888,U_11887,U_11886] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11887),U_11886) = U_11887
      | ? [U_11885] :
          ( ? [U_11884] :
              ( U_11887 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11884),U_11885)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11884),U_11888)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11885),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11886))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11887),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11888))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11886)) ),
    inference(variable_rename,[status(thm)],[f_3075_1]) ).

fof(f_3075_3,plain,
    ! [U_11888,U_11887,U_11886] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11887),U_11886) = U_11887
      | ( ? [U_11884] :
            ( U_11887 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11884),sK226(U_11888,U_11887,U_11886))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11884),U_11888)) )
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK226(U_11888,U_11887,U_11886)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11886))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11887),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11888))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11886)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK226]),skolemize(U_11885,sK226(U_11888,U_11887,U_11886))],[f_3075_2]) ).

fof(f_3075_4,plain,
    ! [U_11888,U_11887,U_11886] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11887),U_11886) = U_11887
      | ( U_11887 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK227(U_11888,U_11887,U_11886)),sK226(U_11888,U_11887,U_11886))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK227(U_11888,U_11887,U_11886)),U_11888))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK226(U_11888,U_11887,U_11886)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11886))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11887),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11888))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11886)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK227]),skolemize(U_11884,sK227(U_11888,U_11887,U_11886))],[f_3075_3]) ).

fof(f_3075_5,plain,
    ( ! [U_11887,U_11886,U_11888] :
        ( U_11887 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK227(U_11888,U_11887,U_11886)),sK226(U_11888,U_11887,U_11886))
        | ~ sP877(U_11887,U_11886,U_11888) )
    & ! [U_11887,U_11886,U_11888] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK227(U_11888,U_11887,U_11886)),U_11888))
        | ~ sP877(U_11887,U_11886,U_11888) )
    & ! [U_11887,U_11886,U_11888] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK226(U_11888,U_11887,U_11886)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11886)))
        | ~ sP877(U_11887,U_11886,U_11888) )
    & ! [U_11887,U_11886,U_11888] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11887),U_11886) = U_11887
        | sP877(U_11887,U_11886,U_11888)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11887),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11888))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11886)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP877])],[f_3075_4]) ).

cnf(f_3075_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11887),U_11886) = U_11887
    | sP877(U_11887,U_11886,U_11888)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11887),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11888))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11886)) ),
    inference(clausify,[status(thm)],[f_3075_5]) ).

cnf(f_3075_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK226(U_11888,U_11887,U_11886)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11886)))
    | ~ sP877(U_11887,U_11886,U_11888) ),
    inference(clausify,[status(thm)],[f_3075_5]) ).

cnf(f_3075_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK227(U_11888,U_11887,U_11886)),U_11888))
    | ~ sP877(U_11887,U_11886,U_11888) ),
    inference(clausify,[status(thm)],[f_3075_5]) ).

cnf(f_3075_9,plain,
    ( U_11887 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK227(U_11888,U_11887,U_11886)),sK226(U_11888,U_11887,U_11886))
    | ~ sP877(U_11887,U_11886,U_11888) ),
    inference(clausify,[status(thm)],[f_3075_5]) ).

fof(f_3076_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_3076_2,plain,
    ! [U_11893,U_11892,U_11891] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11892),U_11891) = U_11892
      | ? [U_11890] :
          ( ? [U_11889] :
              ( U_11892 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11889),U_11890)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11889),U_11893)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11890),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11891))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11892),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11893))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11891)) ),
    inference(variable_rename,[status(thm)],[f_3076_1]) ).

fof(f_3076_3,plain,
    ! [U_11893,U_11892,U_11891] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11892),U_11891) = U_11892
      | ( ? [U_11889] :
            ( U_11892 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11889),sK228(U_11893,U_11892,U_11891))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11889),U_11893)) )
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK228(U_11893,U_11892,U_11891)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11891))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11892),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11893))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11891)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK228]),skolemize(U_11890,sK228(U_11893,U_11892,U_11891))],[f_3076_2]) ).

fof(f_3076_4,plain,
    ! [U_11893,U_11892,U_11891] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11892),U_11891) = U_11892
      | ( U_11892 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK229(U_11893,U_11892,U_11891)),sK228(U_11893,U_11892,U_11891))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK229(U_11893,U_11892,U_11891)),U_11893))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK228(U_11893,U_11892,U_11891)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11891))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11892),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11893))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11891)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK229]),skolemize(U_11889,sK229(U_11893,U_11892,U_11891))],[f_3076_3]) ).

fof(f_3076_5,plain,
    ( ! [U_11892,U_11891,U_11893] :
        ( U_11892 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK229(U_11893,U_11892,U_11891)),sK228(U_11893,U_11892,U_11891))
        | ~ sP878(U_11892,U_11891,U_11893) )
    & ! [U_11892,U_11891,U_11893] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK229(U_11893,U_11892,U_11891)),U_11893))
        | ~ sP878(U_11892,U_11891,U_11893) )
    & ! [U_11892,U_11891,U_11893] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK228(U_11893,U_11892,U_11891)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11891)))
        | ~ sP878(U_11892,U_11891,U_11893) )
    & ! [U_11892,U_11891,U_11893] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11892),U_11891) = U_11892
        | sP878(U_11892,U_11891,U_11893)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11892),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11893))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11891)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP878])],[f_3076_4]) ).

cnf(f_3076_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11892),U_11891) = U_11892
    | sP878(U_11892,U_11891,U_11893)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11892),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11893))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11891)) ),
    inference(clausify,[status(thm)],[f_3076_5]) ).

cnf(f_3076_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK228(U_11893,U_11892,U_11891)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11891)))
    | ~ sP878(U_11892,U_11891,U_11893) ),
    inference(clausify,[status(thm)],[f_3076_5]) ).

cnf(f_3076_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK229(U_11893,U_11892,U_11891)),U_11893))
    | ~ sP878(U_11892,U_11891,U_11893) ),
    inference(clausify,[status(thm)],[f_3076_5]) ).

cnf(f_3076_9,plain,
    ( U_11892 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK229(U_11893,U_11892,U_11891)),sK228(U_11893,U_11892,U_11891))
    | ~ sP878(U_11892,U_11891,U_11893) ),
    inference(clausify,[status(thm)],[f_3076_5]) ).

fof(f_3077_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_3077_2,plain,
    ! [U_11899,U_11898,U_11897] :
      ( ! [U_11896] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11896),U_11897)),U_11898))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11896),U_11898))
          | ? [U_11895] :
              ( ? [U_11894] :
                  ( U_11896 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11894),U_11895)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11894),U_11899)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11895),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11897))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11898),U_11899))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11897)) ),
    inference(variable_rename,[status(thm)],[f_3077_1]) ).

fof(f_3077_3,plain,
    ! [U_11899,U_11898,U_11897] :
      ( ! [U_11896] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11896),U_11897)),U_11898))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11896),U_11898))
          | ( ? [U_11894] :
                ( U_11896 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11894),sK230(U_11899,U_11898,U_11897,U_11896))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11894),U_11899)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK230(U_11899,U_11898,U_11897,U_11896)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11897))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11898),U_11899))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11897)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK230]),skolemize(U_11895,sK230(U_11899,U_11898,U_11897,U_11896))],[f_3077_2]) ).

fof(f_3077_4,plain,
    ! [U_11899,U_11898,U_11897] :
      ( ! [U_11896] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11896),U_11897)),U_11898))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11896),U_11898))
          | ( U_11896 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK231(U_11899,U_11898,U_11897,U_11896)),sK230(U_11899,U_11898,U_11897,U_11896))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK231(U_11899,U_11898,U_11897,U_11896)),U_11899))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK230(U_11899,U_11898,U_11897,U_11896)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11897))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11898),U_11899))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11897)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK231]),skolemize(U_11894,sK231(U_11899,U_11898,U_11897,U_11896))],[f_3077_3]) ).

fof(f_3077_5,plain,
    ( ! [U_11896,U_11897,U_11898,U_11899] :
        ( U_11896 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK231(U_11899,U_11898,U_11897,U_11896)),sK230(U_11899,U_11898,U_11897,U_11896))
        | ~ sP879(U_11896,U_11897,U_11898,U_11899) )
    & ! [U_11896,U_11897,U_11898,U_11899] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK231(U_11899,U_11898,U_11897,U_11896)),U_11899))
        | ~ sP879(U_11896,U_11897,U_11898,U_11899) )
    & ! [U_11896,U_11897,U_11898,U_11899] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK230(U_11899,U_11898,U_11897,U_11896)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11897)))
        | ~ sP879(U_11896,U_11897,U_11898,U_11899) )
    & ! [U_11896,U_11897,U_11898,U_11899] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11896),U_11897)),U_11898))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11896),U_11898))
        | sP879(U_11896,U_11897,U_11898,U_11899)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11898),U_11899))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11897)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP879])],[f_3077_4]) ).

cnf(f_3077_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11896),U_11897)),U_11898))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11896),U_11898))
    | sP879(U_11896,U_11897,U_11898,U_11899)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11898),U_11899))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11897)) ),
    inference(clausify,[status(thm)],[f_3077_5]) ).

cnf(f_3077_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK230(U_11899,U_11898,U_11897,U_11896)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11897)))
    | ~ sP879(U_11896,U_11897,U_11898,U_11899) ),
    inference(clausify,[status(thm)],[f_3077_5]) ).

cnf(f_3077_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK231(U_11899,U_11898,U_11897,U_11896)),U_11899))
    | ~ sP879(U_11896,U_11897,U_11898,U_11899) ),
    inference(clausify,[status(thm)],[f_3077_5]) ).

cnf(f_3077_9,plain,
    ( U_11896 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK231(U_11899,U_11898,U_11897,U_11896)),sK230(U_11899,U_11898,U_11897,U_11896))
    | ~ sP879(U_11896,U_11897,U_11898,U_11899) ),
    inference(clausify,[status(thm)],[f_3077_5]) ).

fof(f_3078_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_3078_2,plain,
    ! [U_11905,U_11904,U_11903] :
      ( ! [U_11902] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11902),U_11903) != U_11904
          | U_11902 = U_11904
          | ? [U_11901] :
              ( ? [U_11900] :
                  ( U_11902 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11900),U_11901)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11900),U_11905)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11901),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11903))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11904),U_11905))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11903)) ),
    inference(variable_rename,[status(thm)],[f_3078_1]) ).

fof(f_3078_3,plain,
    ! [U_11905,U_11904,U_11903] :
      ( ! [U_11902] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11902),U_11903) != U_11904
          | U_11902 = U_11904
          | ( ? [U_11900] :
                ( U_11902 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11900),sK232(U_11905,U_11904,U_11903,U_11902))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11900),U_11905)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK232(U_11905,U_11904,U_11903,U_11902)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11903))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11904),U_11905))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11903)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK232]),skolemize(U_11901,sK232(U_11905,U_11904,U_11903,U_11902))],[f_3078_2]) ).

fof(f_3078_4,plain,
    ! [U_11905,U_11904,U_11903] :
      ( ! [U_11902] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11902),U_11903) != U_11904
          | U_11902 = U_11904
          | ( U_11902 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK233(U_11905,U_11904,U_11903,U_11902)),sK232(U_11905,U_11904,U_11903,U_11902))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK233(U_11905,U_11904,U_11903,U_11902)),U_11905))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK232(U_11905,U_11904,U_11903,U_11902)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11903))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11904),U_11905))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11903)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK233]),skolemize(U_11900,sK233(U_11905,U_11904,U_11903,U_11902))],[f_3078_3]) ).

fof(f_3078_5,plain,
    ( ! [U_11903,U_11905,U_11902,U_11904] :
        ( U_11902 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK233(U_11905,U_11904,U_11903,U_11902)),sK232(U_11905,U_11904,U_11903,U_11902))
        | ~ sP880(U_11903,U_11905,U_11902,U_11904) )
    & ! [U_11903,U_11905,U_11902,U_11904] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK233(U_11905,U_11904,U_11903,U_11902)),U_11905))
        | ~ sP880(U_11903,U_11905,U_11902,U_11904) )
    & ! [U_11903,U_11905,U_11902,U_11904] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK232(U_11905,U_11904,U_11903,U_11902)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11903)))
        | ~ sP880(U_11903,U_11905,U_11902,U_11904) )
    & ! [U_11903,U_11905,U_11902,U_11904] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11902),U_11903) != U_11904
        | U_11902 = U_11904
        | sP880(U_11903,U_11905,U_11902,U_11904)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11904),U_11905))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11903)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP880])],[f_3078_4]) ).

cnf(f_3078_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11902),U_11903) != U_11904
    | U_11902 = U_11904
    | sP880(U_11903,U_11905,U_11902,U_11904)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11904),U_11905))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11903)) ),
    inference(clausify,[status(thm)],[f_3078_5]) ).

cnf(f_3078_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK232(U_11905,U_11904,U_11903,U_11902)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11903)))
    | ~ sP880(U_11903,U_11905,U_11902,U_11904) ),
    inference(clausify,[status(thm)],[f_3078_5]) ).

cnf(f_3078_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK233(U_11905,U_11904,U_11903,U_11902)),U_11905))
    | ~ sP880(U_11903,U_11905,U_11902,U_11904) ),
    inference(clausify,[status(thm)],[f_3078_5]) ).

cnf(f_3078_9,plain,
    ( U_11902 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK233(U_11905,U_11904,U_11903,U_11902)),sK232(U_11905,U_11904,U_11903,U_11902))
    | ~ sP880(U_11903,U_11905,U_11902,U_11904) ),
    inference(clausify,[status(thm)],[f_3078_5]) ).

fof(f_3079_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_3079_2,plain,
    ! [U_11911,U_11910,U_11909] :
      ( ! [U_11908] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11910),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11908),U_11909)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11910),U_11908))
          | ? [U_11907] :
              ( ? [U_11906] :
                  ( U_11908 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11906),U_11907)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11906),U_11911)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11907),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11909))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11910),U_11911))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11909)) ),
    inference(variable_rename,[status(thm)],[f_3079_1]) ).

fof(f_3079_3,plain,
    ! [U_11911,U_11910,U_11909] :
      ( ! [U_11908] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11910),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11908),U_11909)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11910),U_11908))
          | ( ? [U_11906] :
                ( U_11908 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11906),sK234(U_11911,U_11910,U_11909,U_11908))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11906),U_11911)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK234(U_11911,U_11910,U_11909,U_11908)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11909))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11910),U_11911))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11909)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK234]),skolemize(U_11907,sK234(U_11911,U_11910,U_11909,U_11908))],[f_3079_2]) ).

fof(f_3079_4,plain,
    ! [U_11911,U_11910,U_11909] :
      ( ! [U_11908] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11910),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11908),U_11909)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11910),U_11908))
          | ( U_11908 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK235(U_11911,U_11910,U_11909,U_11908)),sK234(U_11911,U_11910,U_11909,U_11908))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK235(U_11911,U_11910,U_11909,U_11908)),U_11911))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK234(U_11911,U_11910,U_11909,U_11908)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11909))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11910),U_11911))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11909)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK235]),skolemize(U_11906,sK235(U_11911,U_11910,U_11909,U_11908))],[f_3079_3]) ).

fof(f_3079_5,plain,
    ( ! [U_11909,U_11911,U_11908,U_11910] :
        ( U_11908 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK235(U_11911,U_11910,U_11909,U_11908)),sK234(U_11911,U_11910,U_11909,U_11908))
        | ~ sP881(U_11909,U_11911,U_11908,U_11910) )
    & ! [U_11909,U_11911,U_11908,U_11910] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK235(U_11911,U_11910,U_11909,U_11908)),U_11911))
        | ~ sP881(U_11909,U_11911,U_11908,U_11910) )
    & ! [U_11909,U_11911,U_11908,U_11910] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK234(U_11911,U_11910,U_11909,U_11908)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11909)))
        | ~ sP881(U_11909,U_11911,U_11908,U_11910) )
    & ! [U_11909,U_11911,U_11908,U_11910] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11910),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11908),U_11909)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11910),U_11908))
        | sP881(U_11909,U_11911,U_11908,U_11910)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11910),U_11911))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11909)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP881])],[f_3079_4]) ).

cnf(f_3079_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11910),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11908),U_11909)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11910),U_11908))
    | sP881(U_11909,U_11911,U_11908,U_11910)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11910),U_11911))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11909)) ),
    inference(clausify,[status(thm)],[f_3079_5]) ).

cnf(f_3079_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK234(U_11911,U_11910,U_11909,U_11908)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11909)))
    | ~ sP881(U_11909,U_11911,U_11908,U_11910) ),
    inference(clausify,[status(thm)],[f_3079_5]) ).

cnf(f_3079_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK235(U_11911,U_11910,U_11909,U_11908)),U_11911))
    | ~ sP881(U_11909,U_11911,U_11908,U_11910) ),
    inference(clausify,[status(thm)],[f_3079_5]) ).

cnf(f_3079_9,plain,
    ( U_11908 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK235(U_11911,U_11910,U_11909,U_11908)),sK234(U_11911,U_11910,U_11909,U_11908))
    | ~ sP881(U_11909,U_11911,U_11908,U_11910) ),
    inference(clausify,[status(thm)],[f_3079_5]) ).

fof(f_3080_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_3080_2,plain,
    ! [U_11917,U_11916,U_11915] :
      ( ! [U_11914] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11914),U_11915)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11917),U_11914))
          | ? [U_11913] :
              ( ? [U_11912] :
                  ( U_11914 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11912),U_11913)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11912),U_11916)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11913),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11915))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11915)) ),
    inference(variable_rename,[status(thm)],[f_3080_1]) ).

fof(f_3080_3,plain,
    ! [U_11917,U_11916,U_11915] :
      ( ! [U_11914] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11914),U_11915)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11917),U_11914))
          | ( ? [U_11912] :
                ( U_11914 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11912),sK236(U_11917,U_11916,U_11915,U_11914))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11912),U_11916)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK236(U_11917,U_11916,U_11915,U_11914)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11915))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11915)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK236]),skolemize(U_11913,sK236(U_11917,U_11916,U_11915,U_11914))],[f_3080_2]) ).

fof(f_3080_4,plain,
    ! [U_11917,U_11916,U_11915] :
      ( ! [U_11914] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11914),U_11915)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11917),U_11914))
          | ( U_11914 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK237(U_11917,U_11916,U_11915,U_11914)),sK236(U_11917,U_11916,U_11915,U_11914))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK237(U_11917,U_11916,U_11915,U_11914)),U_11916))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK236(U_11917,U_11916,U_11915,U_11914)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11915))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11915)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK237]),skolemize(U_11912,sK237(U_11917,U_11916,U_11915,U_11914))],[f_3080_3]) ).

fof(f_3080_5,plain,
    ( ! [U_11915,U_11914,U_11916,U_11917] :
        ( U_11914 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK237(U_11917,U_11916,U_11915,U_11914)),sK236(U_11917,U_11916,U_11915,U_11914))
        | ~ sP882(U_11915,U_11914,U_11916,U_11917) )
    & ! [U_11915,U_11914,U_11916,U_11917] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK237(U_11917,U_11916,U_11915,U_11914)),U_11916))
        | ~ sP882(U_11915,U_11914,U_11916,U_11917) )
    & ! [U_11915,U_11914,U_11916,U_11917] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK236(U_11917,U_11916,U_11915,U_11914)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11915)))
        | ~ sP882(U_11915,U_11914,U_11916,U_11917) )
    & ! [U_11915,U_11914,U_11916,U_11917] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11914),U_11915)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11917),U_11914))
        | sP882(U_11915,U_11914,U_11916,U_11917)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11915)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP882])],[f_3080_4]) ).

cnf(f_3080_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11914),U_11915)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11917),U_11914))
    | sP882(U_11915,U_11914,U_11916,U_11917)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11915)) ),
    inference(clausify,[status(thm)],[f_3080_5]) ).

cnf(f_3080_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK236(U_11917,U_11916,U_11915,U_11914)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11915)))
    | ~ sP882(U_11915,U_11914,U_11916,U_11917) ),
    inference(clausify,[status(thm)],[f_3080_5]) ).

cnf(f_3080_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK237(U_11917,U_11916,U_11915,U_11914)),U_11916))
    | ~ sP882(U_11915,U_11914,U_11916,U_11917) ),
    inference(clausify,[status(thm)],[f_3080_5]) ).

cnf(f_3080_9,plain,
    ( U_11914 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK237(U_11917,U_11916,U_11915,U_11914)),sK236(U_11917,U_11916,U_11915,U_11914))
    | ~ sP882(U_11915,U_11914,U_11916,U_11917) ),
    inference(clausify,[status(thm)],[f_3080_5]) ).

fof(f_3081_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_3081_2,plain,
    ! [U_11923,U_11922,U_11921] :
      ( ! [U_11920] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11920),U_11921)),U_11923))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11920),U_11923))
          | ? [U_11919] :
              ( ? [U_11918] :
                  ( U_11920 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11918),U_11919)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11918),U_11922)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11919),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11921))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11921)) ),
    inference(variable_rename,[status(thm)],[f_3081_1]) ).

fof(f_3081_3,plain,
    ! [U_11923,U_11922,U_11921] :
      ( ! [U_11920] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11920),U_11921)),U_11923))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11920),U_11923))
          | ( ? [U_11918] :
                ( U_11920 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11918),sK238(U_11923,U_11922,U_11921,U_11920))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11918),U_11922)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK238(U_11923,U_11922,U_11921,U_11920)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11921))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11921)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK238]),skolemize(U_11919,sK238(U_11923,U_11922,U_11921,U_11920))],[f_3081_2]) ).

fof(f_3081_4,plain,
    ! [U_11923,U_11922,U_11921] :
      ( ! [U_11920] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11920),U_11921)),U_11923))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11920),U_11923))
          | ( U_11920 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK239(U_11923,U_11922,U_11921,U_11920)),sK238(U_11923,U_11922,U_11921,U_11920))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK239(U_11923,U_11922,U_11921,U_11920)),U_11922))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK238(U_11923,U_11922,U_11921,U_11920)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11921))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11921)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK239]),skolemize(U_11918,sK239(U_11923,U_11922,U_11921,U_11920))],[f_3081_3]) ).

fof(f_3081_5,plain,
    ( ! [U_11920,U_11921,U_11922,U_11923] :
        ( U_11920 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK239(U_11923,U_11922,U_11921,U_11920)),sK238(U_11923,U_11922,U_11921,U_11920))
        | ~ sP883(U_11920,U_11921,U_11922,U_11923) )
    & ! [U_11920,U_11921,U_11922,U_11923] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK239(U_11923,U_11922,U_11921,U_11920)),U_11922))
        | ~ sP883(U_11920,U_11921,U_11922,U_11923) )
    & ! [U_11920,U_11921,U_11922,U_11923] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK238(U_11923,U_11922,U_11921,U_11920)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11921)))
        | ~ sP883(U_11920,U_11921,U_11922,U_11923) )
    & ! [U_11920,U_11921,U_11922,U_11923] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11920),U_11921)),U_11923))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11920),U_11923))
        | sP883(U_11920,U_11921,U_11922,U_11923)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11921)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP883])],[f_3081_4]) ).

cnf(f_3081_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_11920),U_11921)),U_11923))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11920),U_11923))
    | sP883(U_11920,U_11921,U_11922,U_11923)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11921)) ),
    inference(clausify,[status(thm)],[f_3081_5]) ).

cnf(f_3081_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK238(U_11923,U_11922,U_11921,U_11920)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11921)))
    | ~ sP883(U_11920,U_11921,U_11922,U_11923) ),
    inference(clausify,[status(thm)],[f_3081_5]) ).

cnf(f_3081_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK239(U_11923,U_11922,U_11921,U_11920)),U_11922))
    | ~ sP883(U_11920,U_11921,U_11922,U_11923) ),
    inference(clausify,[status(thm)],[f_3081_5]) ).

cnf(f_3081_9,plain,
    ( U_11920 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK239(U_11923,U_11922,U_11921,U_11920)),sK238(U_11923,U_11922,U_11921,U_11920))
    | ~ sP883(U_11920,U_11921,U_11922,U_11923) ),
    inference(clausify,[status(thm)],[f_3081_5]) ).

fof(f_3082_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_3082_2,plain,
    ! [U_11931,U_11930] :
      ( ( ( ? [U_11929] : hBOOL(hAPP(U_11931,U_11929))
          | ! [U_11928] :
              ( ~ hBOOL(hAPP(U_11931,U_11928))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11928),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) ) )
        & ( ? [U_11927] :
              ( hBOOL(hAPP(U_11931,U_11927))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11927),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) )
          | ! [U_11926] : ~ hBOOL(hAPP(U_11931,U_11926)) ) )
      | ? [U_11925,U_11924] :
          ( ( ~ hBOOL(hAPP(U_11931,U_11925))
            & hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11924),U_11930)))) )
          | ( ~ hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11925),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11924),U_11930))))
            & hBOOL(hAPP(U_11931,U_11925)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11930)) ),
    inference(variable_rename,[status(thm)],[f_3082_1]) ).

fof(f_3082_3,plain,
    ! [U_11931,U_11930] :
      ( ( ( ? [U_11929] : hBOOL(hAPP(U_11931,U_11929))
          | ! [U_11928] :
              ( ~ hBOOL(hAPP(U_11931,U_11928))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11928),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) ) )
        & ( ? [U_11927] :
              ( hBOOL(hAPP(U_11931,U_11927))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11927),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) )
          | ! [U_11926] : ~ hBOOL(hAPP(U_11931,U_11926)) ) )
      | ? [U_11935] :
          ( ? [U_11933] : hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11933),U_11930))))
          & ~ hBOOL(hAPP(U_11931,U_11935)) )
      | ? [U_11934] :
          ( ? [U_11932] : ~ hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11934),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11932),U_11930))))
          & hBOOL(hAPP(U_11931,U_11934)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11930)) ),
    inference(miniscope,[status(thm)],[f_3082_2]) ).

fof(f_3082_4,plain,
    ! [U_11931,U_11930] :
      ( ( ( ? [U_11929] : hBOOL(hAPP(U_11931,U_11929))
          | ! [U_11928] :
              ( ~ hBOOL(hAPP(U_11931,U_11928))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11928),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) ) )
        & ( ? [U_11927] :
              ( hBOOL(hAPP(U_11931,U_11927))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11927),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) )
          | ! [U_11926] : ~ hBOOL(hAPP(U_11931,U_11926)) ) )
      | ? [U_11935] :
          ( ? [U_11933] : hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11933),U_11930))))
          & ~ hBOOL(hAPP(U_11931,U_11935)) )
      | ( ? [U_11932] : ~ hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK240(U_11931,U_11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11932),U_11930))))
        & hBOOL(hAPP(U_11931,sK240(U_11931,U_11930))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11930)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK240]),skolemize(U_11934,sK240(U_11931,U_11930))],[f_3082_3]) ).

fof(f_3082_5,plain,
    ! [U_11931,U_11930] :
      ( ( ( ? [U_11929] : hBOOL(hAPP(U_11931,U_11929))
          | ! [U_11928] :
              ( ~ hBOOL(hAPP(U_11931,U_11928))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11928),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) ) )
        & ( ? [U_11927] :
              ( hBOOL(hAPP(U_11931,U_11927))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11927),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) )
          | ! [U_11926] : ~ hBOOL(hAPP(U_11931,U_11926)) ) )
      | ? [U_11935] :
          ( ? [U_11933] : hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11933),U_11930))))
          & ~ hBOOL(hAPP(U_11931,U_11935)) )
      | ( ~ hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK240(U_11931,U_11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK241(U_11931,U_11930)),U_11930))))
        & hBOOL(hAPP(U_11931,sK240(U_11931,U_11930))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11930)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK241]),skolemize(U_11932,sK241(U_11931,U_11930))],[f_3082_4]) ).

fof(f_3082_6,plain,
    ! [U_11931,U_11930] :
      ( ( ( ? [U_11929] : hBOOL(hAPP(U_11931,U_11929))
          | ! [U_11928] :
              ( ~ hBOOL(hAPP(U_11931,U_11928))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11928),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) ) )
        & ( ? [U_11927] :
              ( hBOOL(hAPP(U_11931,U_11927))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11927),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) )
          | ! [U_11926] : ~ hBOOL(hAPP(U_11931,U_11926)) ) )
      | ( ? [U_11933] : hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK242(U_11931,U_11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11933),U_11930))))
        & ~ hBOOL(hAPP(U_11931,sK242(U_11931,U_11930))) )
      | ( ~ hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK240(U_11931,U_11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK241(U_11931,U_11930)),U_11930))))
        & hBOOL(hAPP(U_11931,sK240(U_11931,U_11930))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11930)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK242]),skolemize(U_11935,sK242(U_11931,U_11930))],[f_3082_5]) ).

fof(f_3082_7,plain,
    ! [U_11931,U_11930] :
      ( ( ( ? [U_11929] : hBOOL(hAPP(U_11931,U_11929))
          | ! [U_11928] :
              ( ~ hBOOL(hAPP(U_11931,U_11928))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11928),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) ) )
        & ( ? [U_11927] :
              ( hBOOL(hAPP(U_11931,U_11927))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11927),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) )
          | ! [U_11926] : ~ hBOOL(hAPP(U_11931,U_11926)) ) )
      | ( hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK242(U_11931,U_11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK243(U_11931,U_11930)),U_11930))))
        & ~ hBOOL(hAPP(U_11931,sK242(U_11931,U_11930))) )
      | ( ~ hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK240(U_11931,U_11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK241(U_11931,U_11930)),U_11930))))
        & hBOOL(hAPP(U_11931,sK240(U_11931,U_11930))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11930)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK243]),skolemize(U_11933,sK243(U_11931,U_11930))],[f_3082_6]) ).

fof(f_3082_8,plain,
    ! [U_11931,U_11930] :
      ( ( ( ? [U_11929] : hBOOL(hAPP(U_11931,U_11929))
          | ! [U_11928] :
              ( ~ hBOOL(hAPP(U_11931,U_11928))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11928),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) ) )
        & ( ( hBOOL(hAPP(U_11931,sK244(U_11931,U_11930)))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK244(U_11931,U_11930)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) )
          | ! [U_11926] : ~ hBOOL(hAPP(U_11931,U_11926)) ) )
      | ( hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK242(U_11931,U_11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK243(U_11931,U_11930)),U_11930))))
        & ~ hBOOL(hAPP(U_11931,sK242(U_11931,U_11930))) )
      | ( ~ hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK240(U_11931,U_11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK241(U_11931,U_11930)),U_11930))))
        & hBOOL(hAPP(U_11931,sK240(U_11931,U_11930))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11930)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK244]),skolemize(U_11927,sK244(U_11931,U_11930))],[f_3082_7]) ).

fof(f_3082_9,plain,
    ! [U_11931,U_11930] :
      ( ( ( hBOOL(hAPP(U_11931,sK245(U_11931,U_11930)))
          | ! [U_11928] :
              ( ~ hBOOL(hAPP(U_11931,U_11928))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11928),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) ) )
        & ( ( hBOOL(hAPP(U_11931,sK244(U_11931,U_11930)))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK244(U_11931,U_11930)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930))) )
          | ! [U_11926] : ~ hBOOL(hAPP(U_11931,U_11926)) ) )
      | ( hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK242(U_11931,U_11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK243(U_11931,U_11930)),U_11930))))
        & ~ hBOOL(hAPP(U_11931,sK242(U_11931,U_11930))) )
      | ( ~ hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK240(U_11931,U_11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK241(U_11931,U_11930)),U_11930))))
        & hBOOL(hAPP(U_11931,sK240(U_11931,U_11930))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11930)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK245]),skolemize(U_11929,sK245(U_11931,U_11930))],[f_3082_8]) ).

fof(f_3082_10,plain,
    ( ! [U_11930,U_11931] :
        ( hBOOL(hAPP(U_11931,sK244(U_11931,U_11930)))
        | ~ sP886(U_11930,U_11931) )
    & ! [U_11930,U_11931] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK244(U_11931,U_11930)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930)))
        | ~ sP886(U_11930,U_11931) )
    & ! [U_11930,U_11931,U_11926,U_11928] :
        ( hBOOL(hAPP(U_11931,sK245(U_11931,U_11930)))
        | ~ hBOOL(hAPP(U_11931,U_11928))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11928),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930)))
        | ~ sP887(U_11930,U_11931,U_11926,U_11928) )
    & ! [U_11930,U_11931,U_11926,U_11928] :
        ( sP886(U_11930,U_11931)
        | ~ hBOOL(hAPP(U_11931,U_11926))
        | ~ sP887(U_11930,U_11931,U_11926,U_11928) )
    & ! [U_11930,U_11931] :
        ( hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK242(U_11931,U_11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK243(U_11931,U_11930)),U_11930))))
        | ~ sP885(U_11930,U_11931) )
    & ! [U_11930,U_11931] :
        ( ~ hBOOL(hAPP(U_11931,sK242(U_11931,U_11930)))
        | ~ sP885(U_11930,U_11931) )
    & ! [U_11930,U_11931] :
        ( ~ hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK240(U_11931,U_11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK241(U_11931,U_11930)),U_11930))))
        | ~ sP884(U_11930,U_11931) )
    & ! [U_11930,U_11931] :
        ( hBOOL(hAPP(U_11931,sK240(U_11931,U_11930)))
        | ~ sP884(U_11930,U_11931) )
    & ! [U_11930,U_11931,U_11926,U_11928] :
        ( sP887(U_11930,U_11931,U_11926,U_11928)
        | sP885(U_11930,U_11931)
        | sP884(U_11930,U_11931)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11930)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP884,sP885,sP886,sP887])],[f_3082_9]) ).

cnf(f_3082_11,plain,
    ( sP887(U_11930,U_11931,U_11926,U_11928)
    | sP885(U_11930,U_11931)
    | sP884(U_11930,U_11931)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11930)) ),
    inference(clausify,[status(thm)],[f_3082_10]) ).

cnf(f_3082_12,plain,
    ( hBOOL(hAPP(U_11931,sK240(U_11931,U_11930)))
    | ~ sP884(U_11930,U_11931) ),
    inference(clausify,[status(thm)],[f_3082_10]) ).

cnf(f_3082_13,plain,
    ( ~ hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK240(U_11931,U_11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK241(U_11931,U_11930)),U_11930))))
    | ~ sP884(U_11930,U_11931) ),
    inference(clausify,[status(thm)],[f_3082_10]) ).

cnf(f_3082_14,plain,
    ( ~ hBOOL(hAPP(U_11931,sK242(U_11931,U_11930)))
    | ~ sP885(U_11930,U_11931) ),
    inference(clausify,[status(thm)],[f_3082_10]) ).

cnf(f_3082_15,plain,
    ( hBOOL(hAPP(U_11931,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK242(U_11931,U_11930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK243(U_11931,U_11930)),U_11930))))
    | ~ sP885(U_11930,U_11931) ),
    inference(clausify,[status(thm)],[f_3082_10]) ).

cnf(f_3082_16,plain,
    ( sP886(U_11930,U_11931)
    | ~ hBOOL(hAPP(U_11931,U_11926))
    | ~ sP887(U_11930,U_11931,U_11926,U_11928) ),
    inference(clausify,[status(thm)],[f_3082_10]) ).

cnf(f_3082_17,plain,
    ( hBOOL(hAPP(U_11931,sK245(U_11931,U_11930)))
    | ~ hBOOL(hAPP(U_11931,U_11928))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11928),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930)))
    | ~ sP887(U_11930,U_11931,U_11926,U_11928) ),
    inference(clausify,[status(thm)],[f_3082_10]) ).

cnf(f_3082_18,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK244(U_11931,U_11930)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11930)))
    | ~ sP886(U_11930,U_11931) ),
    inference(clausify,[status(thm)],[f_3082_10]) ).

cnf(f_3082_19,plain,
    ( hBOOL(hAPP(U_11931,sK244(U_11931,U_11930)))
    | ~ sP886(U_11930,U_11931) ),
    inference(clausify,[status(thm)],[f_3082_10]) ).

fof(f_3083_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_3083_2,plain,
    ! [U_11941,U_11940,U_11939] :
      ( ! [U_11938] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11938),U_11939)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11941),U_11938))
          | ? [U_11937] :
              ( ? [U_11936] :
                  ( U_11938 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11936),U_11937)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11936),U_11940)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11937),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11939))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11939)) ),
    inference(variable_rename,[status(thm)],[f_3083_1]) ).

fof(f_3083_3,plain,
    ! [U_11941,U_11940,U_11939] :
      ( ! [U_11938] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11938),U_11939)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11941),U_11938))
          | ( ? [U_11936] :
                ( U_11938 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11936),sK246(U_11941,U_11940,U_11939,U_11938))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11936),U_11940)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK246(U_11941,U_11940,U_11939,U_11938)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11939))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11939)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK246]),skolemize(U_11937,sK246(U_11941,U_11940,U_11939,U_11938))],[f_3083_2]) ).

fof(f_3083_4,plain,
    ! [U_11941,U_11940,U_11939] :
      ( ! [U_11938] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11938),U_11939)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11941),U_11938))
          | ( U_11938 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK247(U_11941,U_11940,U_11939,U_11938)),sK246(U_11941,U_11940,U_11939,U_11938))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK247(U_11941,U_11940,U_11939,U_11938)),U_11940))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK246(U_11941,U_11940,U_11939,U_11938)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11939))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11939)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK247]),skolemize(U_11936,sK247(U_11941,U_11940,U_11939,U_11938))],[f_3083_3]) ).

fof(f_3083_5,plain,
    ( ! [U_11940,U_11938,U_11939,U_11941] :
        ( U_11938 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK247(U_11941,U_11940,U_11939,U_11938)),sK246(U_11941,U_11940,U_11939,U_11938))
        | ~ sP888(U_11940,U_11938,U_11939,U_11941) )
    & ! [U_11940,U_11938,U_11939,U_11941] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK247(U_11941,U_11940,U_11939,U_11938)),U_11940))
        | ~ sP888(U_11940,U_11938,U_11939,U_11941) )
    & ! [U_11940,U_11938,U_11939,U_11941] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK246(U_11941,U_11940,U_11939,U_11938)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11939)))
        | ~ sP888(U_11940,U_11938,U_11939,U_11941) )
    & ! [U_11940,U_11938,U_11939,U_11941] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11938),U_11939)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11941),U_11938))
        | sP888(U_11940,U_11938,U_11939,U_11941)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11939)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP888])],[f_3083_4]) ).

cnf(f_3083_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11938),U_11939)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11941),U_11938))
    | sP888(U_11940,U_11938,U_11939,U_11941)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11939)) ),
    inference(clausify,[status(thm)],[f_3083_5]) ).

cnf(f_3083_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK246(U_11941,U_11940,U_11939,U_11938)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11939)))
    | ~ sP888(U_11940,U_11938,U_11939,U_11941) ),
    inference(clausify,[status(thm)],[f_3083_5]) ).

cnf(f_3083_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK247(U_11941,U_11940,U_11939,U_11938)),U_11940))
    | ~ sP888(U_11940,U_11938,U_11939,U_11941) ),
    inference(clausify,[status(thm)],[f_3083_5]) ).

cnf(f_3083_9,plain,
    ( U_11938 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK247(U_11941,U_11940,U_11939,U_11938)),sK246(U_11941,U_11940,U_11939,U_11938))
    | ~ sP888(U_11940,U_11938,U_11939,U_11941) ),
    inference(clausify,[status(thm)],[f_3083_5]) ).

fof(f_3084_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_3084_2,plain,
    ! [U_11947,U_11946,U_11945] :
      ( ! [U_11944] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11944),U_11945)),U_11947))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11944),U_11947))
          | ? [U_11943] :
              ( ? [U_11942] :
                  ( U_11944 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11942),U_11943)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11942),U_11946)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11943),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11945))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11945)) ),
    inference(variable_rename,[status(thm)],[f_3084_1]) ).

fof(f_3084_3,plain,
    ! [U_11947,U_11946,U_11945] :
      ( ! [U_11944] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11944),U_11945)),U_11947))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11944),U_11947))
          | ( ? [U_11942] :
                ( U_11944 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11942),sK248(U_11947,U_11946,U_11945,U_11944))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11942),U_11946)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK248(U_11947,U_11946,U_11945,U_11944)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11945))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11945)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK248]),skolemize(U_11943,sK248(U_11947,U_11946,U_11945,U_11944))],[f_3084_2]) ).

fof(f_3084_4,plain,
    ! [U_11947,U_11946,U_11945] :
      ( ! [U_11944] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11944),U_11945)),U_11947))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11944),U_11947))
          | ( U_11944 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK249(U_11947,U_11946,U_11945,U_11944)),sK248(U_11947,U_11946,U_11945,U_11944))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK249(U_11947,U_11946,U_11945,U_11944)),U_11946))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK248(U_11947,U_11946,U_11945,U_11944)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11945))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11945)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK249]),skolemize(U_11942,sK249(U_11947,U_11946,U_11945,U_11944))],[f_3084_3]) ).

fof(f_3084_5,plain,
    ( ! [U_11944,U_11945,U_11946,U_11947] :
        ( U_11944 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK249(U_11947,U_11946,U_11945,U_11944)),sK248(U_11947,U_11946,U_11945,U_11944))
        | ~ sP889(U_11944,U_11945,U_11946,U_11947) )
    & ! [U_11944,U_11945,U_11946,U_11947] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK249(U_11947,U_11946,U_11945,U_11944)),U_11946))
        | ~ sP889(U_11944,U_11945,U_11946,U_11947) )
    & ! [U_11944,U_11945,U_11946,U_11947] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK248(U_11947,U_11946,U_11945,U_11944)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11945)))
        | ~ sP889(U_11944,U_11945,U_11946,U_11947) )
    & ! [U_11944,U_11945,U_11946,U_11947] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11944),U_11945)),U_11947))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11944),U_11947))
        | sP889(U_11944,U_11945,U_11946,U_11947)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11945)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP889])],[f_3084_4]) ).

cnf(f_3084_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11944),U_11945)),U_11947))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11944),U_11947))
    | sP889(U_11944,U_11945,U_11946,U_11947)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11945)) ),
    inference(clausify,[status(thm)],[f_3084_5]) ).

cnf(f_3084_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK248(U_11947,U_11946,U_11945,U_11944)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11945)))
    | ~ sP889(U_11944,U_11945,U_11946,U_11947) ),
    inference(clausify,[status(thm)],[f_3084_5]) ).

cnf(f_3084_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK249(U_11947,U_11946,U_11945,U_11944)),U_11946))
    | ~ sP889(U_11944,U_11945,U_11946,U_11947) ),
    inference(clausify,[status(thm)],[f_3084_5]) ).

cnf(f_3084_9,plain,
    ( U_11944 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK249(U_11947,U_11946,U_11945,U_11944)),sK248(U_11947,U_11946,U_11945,U_11944))
    | ~ sP889(U_11944,U_11945,U_11946,U_11947) ),
    inference(clausify,[status(thm)],[f_3084_5]) ).

fof(f_3085_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_3085_2,plain,
    ! [U_11950,U_11949,U_11948] :
      ( ( ( ( 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_11948)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11950),U_11949)) = 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_11950),U_11949)) )
          & ( 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_11948)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11950),U_11949)) = 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_11950),U_11949)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11948),U_11949)) )
      & ( 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_11948)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11950),U_11949)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11950),U_11948)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11949),U_11948))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11948),U_11949)) ) ),
    inference(variable_rename,[status(thm)],[f_3085_1]) ).

fof(f_3085_3,plain,
    ( ! [U_11956,U_11954,U_11952] :
        ( ( ( 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_11952)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11956),U_11954)) = 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_11956),U_11954)) )
          & ( 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_11952)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11956),U_11954)) = 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_11956),U_11954)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11952),U_11954)) )
    & ! [U_11955,U_11953,U_11951] :
        ( 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_11951)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11955),U_11953)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11955),U_11951)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11953),U_11951))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11951),U_11953)) ) ),
    inference(miniscope,[status(thm)],[f_3085_2]) ).

fof(f_3085_4,plain,
    ( ! [U_11956,U_11952,U_11954] :
        ( 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_11952)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11956),U_11954)) = 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_11956),U_11954))
        | ~ sP890(U_11956,U_11952,U_11954) )
    & ! [U_11956,U_11952,U_11954] :
        ( 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_11952)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11956),U_11954)) = 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_11956),U_11954))
        | ~ sP890(U_11956,U_11952,U_11954) )
    & ! [U_11956,U_11952,U_11954] :
        ( sP890(U_11956,U_11952,U_11954)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11952),U_11954)) )
    & ! [U_11955,U_11951,U_11953] :
        ( 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_11951)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11955),U_11953)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11955),U_11951)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11953),U_11951))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11951),U_11953)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP890])],[f_3085_3]) ).

cnf(f_3085_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_11951)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11955),U_11953)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11955),U_11951)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11953),U_11951))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11951),U_11953)) ),
    inference(clausify,[status(thm)],[f_3085_4]) ).

cnf(f_3085_6,plain,
    ( sP890(U_11956,U_11952,U_11954)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11952),U_11954)) ),
    inference(clausify,[status(thm)],[f_3085_4]) ).

cnf(f_3085_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_11952)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11956),U_11954)) = 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_11956),U_11954))
    | ~ sP890(U_11956,U_11952,U_11954) ),
    inference(clausify,[status(thm)],[f_3085_4]) ).

cnf(f_3085_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_11952)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11956),U_11954)) = 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_11956),U_11954))
    | ~ sP890(U_11956,U_11952,U_11954) ),
    inference(clausify,[status(thm)],[f_3085_4]) ).

fof(f_3086_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_3086_2,plain,
    ! [U_11963,U_11962,U_11961,U_11960] :
      ( ! [U_11959] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11960),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11959),U_11961)),U_11963)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11960),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11959),U_11963)))
          | ? [U_11958] :
              ( ? [U_11957] :
                  ( U_11959 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11957),U_11958)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11957),U_11962)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11958),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11961))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11960),U_11961)) ),
    inference(variable_rename,[status(thm)],[f_3086_1]) ).

fof(f_3086_3,plain,
    ! [U_11963,U_11962,U_11961,U_11960] :
      ( ! [U_11959] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11960),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11959),U_11961)),U_11963)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11960),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11959),U_11963)))
          | ( ? [U_11957] :
                ( U_11959 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11957),sK250(U_11963,U_11962,U_11961,U_11960,U_11959))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11957),U_11962)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK250(U_11963,U_11962,U_11961,U_11960,U_11959)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11961))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11960),U_11961)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(U_11958,sK250(U_11963,U_11962,U_11961,U_11960,U_11959))],[f_3086_2]) ).

fof(f_3086_4,plain,
    ! [U_11963,U_11962,U_11961,U_11960] :
      ( ! [U_11959] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11960),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11959),U_11961)),U_11963)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11960),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11959),U_11963)))
          | ( U_11959 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK251(U_11963,U_11962,U_11961,U_11960,U_11959)),sK250(U_11963,U_11962,U_11961,U_11960,U_11959))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK251(U_11963,U_11962,U_11961,U_11960,U_11959)),U_11962))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK250(U_11963,U_11962,U_11961,U_11960,U_11959)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11961))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11960),U_11961)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK251]),skolemize(U_11957,sK251(U_11963,U_11962,U_11961,U_11960,U_11959))],[f_3086_3]) ).

fof(f_3086_5,plain,
    ( ! [U_11961,U_11959,U_11960,U_11962,U_11963] :
        ( U_11959 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK251(U_11963,U_11962,U_11961,U_11960,U_11959)),sK250(U_11963,U_11962,U_11961,U_11960,U_11959))
        | ~ sP891(U_11961,U_11959,U_11960,U_11962,U_11963) )
    & ! [U_11961,U_11959,U_11960,U_11962,U_11963] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK251(U_11963,U_11962,U_11961,U_11960,U_11959)),U_11962))
        | ~ sP891(U_11961,U_11959,U_11960,U_11962,U_11963) )
    & ! [U_11961,U_11959,U_11960,U_11962,U_11963] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK250(U_11963,U_11962,U_11961,U_11960,U_11959)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11961)))
        | ~ sP891(U_11961,U_11959,U_11960,U_11962,U_11963) )
    & ! [U_11961,U_11959,U_11960,U_11962,U_11963] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11960),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11959),U_11961)),U_11963)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11960),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11959),U_11963)))
        | sP891(U_11961,U_11959,U_11960,U_11962,U_11963)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11960),U_11961)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP891])],[f_3086_4]) ).

cnf(f_3086_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11960),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11959),U_11961)),U_11963)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11960),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11959),U_11963)))
    | sP891(U_11961,U_11959,U_11960,U_11962,U_11963)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_11960),U_11961)) ),
    inference(clausify,[status(thm)],[f_3086_5]) ).

cnf(f_3086_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK250(U_11963,U_11962,U_11961,U_11960,U_11959)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11961)))
    | ~ sP891(U_11961,U_11959,U_11960,U_11962,U_11963) ),
    inference(clausify,[status(thm)],[f_3086_5]) ).

cnf(f_3086_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK251(U_11963,U_11962,U_11961,U_11960,U_11959)),U_11962))
    | ~ sP891(U_11961,U_11959,U_11960,U_11962,U_11963) ),
    inference(clausify,[status(thm)],[f_3086_5]) ).

cnf(f_3086_9,plain,
    ( U_11959 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK251(U_11963,U_11962,U_11961,U_11960,U_11959)),sK250(U_11963,U_11962,U_11961,U_11960,U_11959))
    | ~ sP891(U_11961,U_11959,U_11960,U_11962,U_11963) ),
    inference(clausify,[status(thm)],[f_3086_5]) ).

fof(f_3087_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_3087_2,plain,
    ! [U_11965,U_11964] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11964),U_11965))),
    inference(variable_rename,[status(thm)],[f_3087_1]) ).

fof(f_3087_3,plain,
    ! [U_11965,U_11964] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11964),U_11965))),
    inference(definitional_conversion,[status(esa)],[f_3087_2]) ).

cnf(f_3087_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11964),U_11965))),
    inference(clausify,[status(thm)],[f_3087_3]) ).

fof(f_3088_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_3088_2,plain,
    ! [U_11970,U_11969,U_11968,U_11967,U_11966] :
      ( U_11968 = U_11970
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11966),U_11969),U_11970))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11966),U_11967),U_11968))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11966,U_11967),U_11968) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11966,U_11969),U_11970)
      | ~ class_Orderings_Olinorder(U_11966) ),
    inference(variable_rename,[status(thm)],[f_3088_1]) ).

fof(f_3088_3,plain,
    ! [U_11966,U_11970,U_11967,U_11968,U_11969] :
      ( U_11968 = U_11970
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11966),U_11969),U_11970))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11966),U_11967),U_11968))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11966,U_11967),U_11968) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11966,U_11969),U_11970)
      | ~ class_Orderings_Olinorder(U_11966) ),
    inference(definitional_conversion,[status(esa)],[f_3088_2]) ).

cnf(f_3088_4,plain,
    ( U_11968 = U_11970
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11966),U_11969),U_11970))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11966),U_11967),U_11968))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11966,U_11967),U_11968) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11966,U_11969),U_11970)
    | ~ class_Orderings_Olinorder(U_11966) ),
    inference(clausify,[status(thm)],[f_3088_3]) ).

fof(f_3089_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_3089_2,plain,
    ! [U_11975,U_11974,U_11973,U_11972,U_11971] :
      ( U_11972 = U_11974
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11971),U_11974),U_11975))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11971),U_11972),U_11973))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11971,U_11972),U_11973) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11971,U_11974),U_11975)
      | ~ class_Orderings_Olinorder(U_11971) ),
    inference(variable_rename,[status(thm)],[f_3089_1]) ).

fof(f_3089_3,plain,
    ! [U_11973,U_11974,U_11975,U_11971,U_11972] :
      ( U_11972 = U_11974
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11971),U_11974),U_11975))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11971),U_11972),U_11973))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11971,U_11972),U_11973) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11971,U_11974),U_11975)
      | ~ class_Orderings_Olinorder(U_11971) ),
    inference(definitional_conversion,[status(esa)],[f_3089_2]) ).

cnf(f_3089_4,plain,
    ( U_11972 = U_11974
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11971),U_11974),U_11975))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11971),U_11972),U_11973))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11971,U_11972),U_11973) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11971,U_11974),U_11975)
    | ~ class_Orderings_Olinorder(U_11971) ),
    inference(clausify,[status(thm)],[f_3089_3]) ).

fof(f_3090_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_3090_2,plain,
    ! [U_11980,U_11979,U_11978,U_11977,U_11976] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11976,U_11977),U_11978) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11976,U_11979),U_11980)
          | U_11978 != U_11980
          | U_11977 != U_11979 )
        & ( ( U_11978 = U_11980
            & U_11977 = U_11979 )
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11976,U_11977),U_11978) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11976,U_11979),U_11980) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11976),U_11979),U_11980))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11976),U_11977),U_11978))
      | ~ class_Orderings_Olinorder(U_11976) ),
    inference(variable_rename,[status(thm)],[f_3090_1]) ).

fof(f_3090_3,plain,
    ( ! [U_11977,U_11978,U_11979,U_11980] :
        ( U_11978 = U_11980
        | ~ sP892(U_11977,U_11978,U_11979,U_11980) )
    & ! [U_11977,U_11978,U_11979,U_11980] :
        ( U_11977 = U_11979
        | ~ sP892(U_11977,U_11978,U_11979,U_11980) )
    & ! [U_11976,U_11977,U_11978,U_11979,U_11980] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11976,U_11977),U_11978) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11976,U_11979),U_11980)
        | U_11978 != U_11980
        | U_11977 != U_11979
        | ~ sP893(U_11976,U_11977,U_11978,U_11979,U_11980) )
    & ! [U_11976,U_11977,U_11978,U_11979,U_11980] :
        ( sP892(U_11977,U_11978,U_11979,U_11980)
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11976,U_11977),U_11978) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11976,U_11979),U_11980)
        | ~ sP893(U_11976,U_11977,U_11978,U_11979,U_11980) )
    & ! [U_11976,U_11977,U_11978,U_11979,U_11980] :
        ( sP893(U_11976,U_11977,U_11978,U_11979,U_11980)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11976),U_11979),U_11980))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11976),U_11977),U_11978))
        | ~ class_Orderings_Olinorder(U_11976) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP892,sP893])],[f_3090_2]) ).

cnf(f_3090_4,plain,
    ( sP893(U_11976,U_11977,U_11978,U_11979,U_11980)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11976),U_11979),U_11980))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11976),U_11977),U_11978))
    | ~ class_Orderings_Olinorder(U_11976) ),
    inference(clausify,[status(thm)],[f_3090_3]) ).

cnf(f_3090_5,plain,
    ( sP892(U_11977,U_11978,U_11979,U_11980)
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11976,U_11977),U_11978) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11976,U_11979),U_11980)
    | ~ sP893(U_11976,U_11977,U_11978,U_11979,U_11980) ),
    inference(clausify,[status(thm)],[f_3090_3]) ).

cnf(f_3090_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11976,U_11977),U_11978) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11976,U_11979),U_11980)
    | U_11978 != U_11980
    | U_11977 != U_11979
    | ~ sP893(U_11976,U_11977,U_11978,U_11979,U_11980) ),
    inference(clausify,[status(thm)],[f_3090_3]) ).

cnf(f_3090_7,plain,
    ( U_11977 = U_11979
    | ~ sP892(U_11977,U_11978,U_11979,U_11980) ),
    inference(clausify,[status(thm)],[f_3090_3]) ).

cnf(f_3090_8,plain,
    ( U_11978 = U_11980
    | ~ sP892(U_11977,U_11978,U_11979,U_11980) ),
    inference(clausify,[status(thm)],[f_3090_3]) ).

fof(f_3091_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_3091_2,plain,
    ! [U_11986,U_11985] :
      ( ( ! [U_11984] :
            ( hBOOL(hAPP(U_11986,U_11984))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11984),U_11985)) )
        | ? [U_11983] :
            ( ~ hBOOL(hAPP(U_11986,U_11983))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11983),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11985))) ) )
      & ( ! [U_11982] :
            ( hBOOL(hAPP(U_11986,U_11982))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11982),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11985))) )
        | ? [U_11981] :
            ( ~ hBOOL(hAPP(U_11986,U_11981))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11981),U_11985)) ) ) ),
    inference(variable_rename,[status(thm)],[f_3091_1]) ).

fof(f_3091_3,plain,
    ( ! [U_11990,U_11988] :
        ( ! [U_11984] :
            ( hBOOL(hAPP(U_11990,U_11984))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11984),U_11988)) )
        | ? [U_11983] :
            ( ~ hBOOL(hAPP(U_11990,U_11983))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11983),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11988))) ) )
    & ! [U_11989,U_11987] :
        ( ! [U_11982] :
            ( hBOOL(hAPP(U_11989,U_11982))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11982),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11987))) )
        | ? [U_11981] :
            ( ~ hBOOL(hAPP(U_11989,U_11981))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11981),U_11987)) ) ) ),
    inference(miniscope,[status(thm)],[f_3091_2]) ).

fof(f_3091_4,plain,
    ( ! [U_11990,U_11988] :
        ( ! [U_11984] :
            ( hBOOL(hAPP(U_11990,U_11984))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11984),U_11988)) )
        | ? [U_11983] :
            ( ~ hBOOL(hAPP(U_11990,U_11983))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11983),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11988))) ) )
    & ! [U_11989,U_11987] :
        ( ! [U_11982] :
            ( hBOOL(hAPP(U_11989,U_11982))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11982),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11987))) )
        | ( ~ hBOOL(hAPP(U_11989,sK252(U_11989,U_11987)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK252(U_11989,U_11987)),U_11987)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK252]),skolemize(U_11981,sK252(U_11989,U_11987))],[f_3091_3]) ).

fof(f_3091_5,plain,
    ( ! [U_11990,U_11988] :
        ( ! [U_11984] :
            ( hBOOL(hAPP(U_11990,U_11984))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11984),U_11988)) )
        | ( ~ hBOOL(hAPP(U_11990,sK253(U_11990,U_11988)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK253(U_11990,U_11988)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11988))) ) )
    & ! [U_11989,U_11987] :
        ( ! [U_11982] :
            ( hBOOL(hAPP(U_11989,U_11982))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11982),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11987))) )
        | ( ~ hBOOL(hAPP(U_11989,sK252(U_11989,U_11987)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK252(U_11989,U_11987)),U_11987)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK253]),skolemize(U_11983,sK253(U_11990,U_11988))],[f_3091_4]) ).

fof(f_3091_6,plain,
    ( ! [U_11988,U_11990] :
        ( ~ hBOOL(hAPP(U_11990,sK253(U_11990,U_11988)))
        | ~ sP895(U_11988,U_11990) )
    & ! [U_11988,U_11990] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK253(U_11990,U_11988)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11988)))
        | ~ sP895(U_11988,U_11990) )
    & ! [U_11987,U_11989] :
        ( ~ hBOOL(hAPP(U_11989,sK252(U_11989,U_11987)))
        | ~ sP894(U_11987,U_11989) )
    & ! [U_11987,U_11989] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK252(U_11989,U_11987)),U_11987))
        | ~ sP894(U_11987,U_11989) )
    & ! [U_11984,U_11988,U_11990] :
        ( hBOOL(hAPP(U_11990,U_11984))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11984),U_11988))
        | sP895(U_11988,U_11990) )
    & ! [U_11987,U_11989,U_11982] :
        ( hBOOL(hAPP(U_11989,U_11982))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11982),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11987)))
        | sP894(U_11987,U_11989) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP894,sP895])],[f_3091_5]) ).

cnf(f_3091_7,plain,
    ( hBOOL(hAPP(U_11989,U_11982))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11982),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11987)))
    | sP894(U_11987,U_11989) ),
    inference(clausify,[status(thm)],[f_3091_6]) ).

cnf(f_3091_8,plain,
    ( hBOOL(hAPP(U_11990,U_11984))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11984),U_11988))
    | sP895(U_11988,U_11990) ),
    inference(clausify,[status(thm)],[f_3091_6]) ).

cnf(f_3091_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK252(U_11989,U_11987)),U_11987))
    | ~ sP894(U_11987,U_11989) ),
    inference(clausify,[status(thm)],[f_3091_6]) ).

cnf(f_3091_10,plain,
    ( ~ hBOOL(hAPP(U_11989,sK252(U_11989,U_11987)))
    | ~ sP894(U_11987,U_11989) ),
    inference(clausify,[status(thm)],[f_3091_6]) ).

cnf(f_3091_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK253(U_11990,U_11988)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11988)))
    | ~ sP895(U_11988,U_11990) ),
    inference(clausify,[status(thm)],[f_3091_6]) ).

cnf(f_3091_12,plain,
    ( ~ hBOOL(hAPP(U_11990,sK253(U_11990,U_11988)))
    | ~ sP895(U_11988,U_11990) ),
    inference(clausify,[status(thm)],[f_3091_6]) ).

fof(f_3092_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_3092_2,plain,
    ! [U_11996,U_11995] :
      ( ( ? [U_11994] :
            ( hBOOL(hAPP(U_11996,U_11994))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11994),U_11995)) )
        | ! [U_11993] :
            ( ~ hBOOL(hAPP(U_11996,U_11993))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11993),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11995))) ) )
      & ( ? [U_11992] :
            ( hBOOL(hAPP(U_11996,U_11992))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11992),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11995))) )
        | ! [U_11991] :
            ( ~ hBOOL(hAPP(U_11996,U_11991))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11991),U_11995)) ) ) ),
    inference(variable_rename,[status(thm)],[f_3092_1]) ).

fof(f_3092_3,plain,
    ( ! [U_12000,U_11998] :
        ( ? [U_11994] :
            ( hBOOL(hAPP(U_12000,U_11994))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11994),U_11998)) )
        | ! [U_11993] :
            ( ~ hBOOL(hAPP(U_12000,U_11993))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11993),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11998))) ) )
    & ! [U_11999,U_11997] :
        ( ? [U_11992] :
            ( hBOOL(hAPP(U_11999,U_11992))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11992),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11997))) )
        | ! [U_11991] :
            ( ~ hBOOL(hAPP(U_11999,U_11991))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11991),U_11997)) ) ) ),
    inference(miniscope,[status(thm)],[f_3092_2]) ).

fof(f_3092_4,plain,
    ( ! [U_12000,U_11998] :
        ( ? [U_11994] :
            ( hBOOL(hAPP(U_12000,U_11994))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11994),U_11998)) )
        | ! [U_11993] :
            ( ~ hBOOL(hAPP(U_12000,U_11993))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11993),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11998))) ) )
    & ! [U_11999,U_11997] :
        ( ( hBOOL(hAPP(U_11999,sK254(U_11999,U_11997)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK254(U_11999,U_11997)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11997))) )
        | ! [U_11991] :
            ( ~ hBOOL(hAPP(U_11999,U_11991))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11991),U_11997)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK254]),skolemize(U_11992,sK254(U_11999,U_11997))],[f_3092_3]) ).

fof(f_3092_5,plain,
    ( ! [U_12000,U_11998] :
        ( ( hBOOL(hAPP(U_12000,sK255(U_12000,U_11998)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK255(U_12000,U_11998)),U_11998)) )
        | ! [U_11993] :
            ( ~ hBOOL(hAPP(U_12000,U_11993))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11993),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11998))) ) )
    & ! [U_11999,U_11997] :
        ( ( hBOOL(hAPP(U_11999,sK254(U_11999,U_11997)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK254(U_11999,U_11997)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11997))) )
        | ! [U_11991] :
            ( ~ hBOOL(hAPP(U_11999,U_11991))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11991),U_11997)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK255]),skolemize(U_11994,sK255(U_12000,U_11998))],[f_3092_4]) ).

fof(f_3092_6,plain,
    ( ! [U_12000,U_11998] :
        ( hBOOL(hAPP(U_12000,sK255(U_12000,U_11998)))
        | ~ sP897(U_12000,U_11998) )
    & ! [U_12000,U_11998] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK255(U_12000,U_11998)),U_11998))
        | ~ sP897(U_12000,U_11998) )
    & ! [U_11997,U_11999] :
        ( hBOOL(hAPP(U_11999,sK254(U_11999,U_11997)))
        | ~ sP896(U_11997,U_11999) )
    & ! [U_11997,U_11999] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK254(U_11999,U_11997)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11997)))
        | ~ sP896(U_11997,U_11999) )
    & ! [U_11993,U_12000,U_11998] :
        ( sP897(U_12000,U_11998)
        | ~ hBOOL(hAPP(U_12000,U_11993))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11993),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11998))) )
    & ! [U_11991,U_11997,U_11999] :
        ( sP896(U_11997,U_11999)
        | ~ hBOOL(hAPP(U_11999,U_11991))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11991),U_11997)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP896,sP897])],[f_3092_5]) ).

cnf(f_3092_7,plain,
    ( sP896(U_11997,U_11999)
    | ~ hBOOL(hAPP(U_11999,U_11991))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11991),U_11997)) ),
    inference(clausify,[status(thm)],[f_3092_6]) ).

cnf(f_3092_8,plain,
    ( sP897(U_12000,U_11998)
    | ~ hBOOL(hAPP(U_12000,U_11993))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11993),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11998))) ),
    inference(clausify,[status(thm)],[f_3092_6]) ).

cnf(f_3092_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK254(U_11999,U_11997)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11997)))
    | ~ sP896(U_11997,U_11999) ),
    inference(clausify,[status(thm)],[f_3092_6]) ).

cnf(f_3092_10,plain,
    ( hBOOL(hAPP(U_11999,sK254(U_11999,U_11997)))
    | ~ sP896(U_11997,U_11999) ),
    inference(clausify,[status(thm)],[f_3092_6]) ).

cnf(f_3092_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK255(U_12000,U_11998)),U_11998))
    | ~ sP897(U_12000,U_11998) ),
    inference(clausify,[status(thm)],[f_3092_6]) ).

cnf(f_3092_12,plain,
    ( hBOOL(hAPP(U_12000,sK255(U_12000,U_11998)))
    | ~ sP897(U_12000,U_11998) ),
    inference(clausify,[status(thm)],[f_3092_6]) ).

fof(f_3093_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_3093_2,plain,
    ! [U_12002,U_12001] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12001),hAPP(c_Nat_OSuc,U_12002)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12001,U_12002),
    inference(variable_rename,[status(thm)],[f_3093_1]) ).

fof(f_3093_3,plain,
    ! [U_12002,U_12001] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12001),hAPP(c_Nat_OSuc,U_12002)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12001,U_12002),
    inference(definitional_conversion,[status(esa)],[f_3093_2]) ).

cnf(f_3093_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12001),hAPP(c_Nat_OSuc,U_12002)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12001,U_12002),
    inference(clausify,[status(thm)],[f_3093_3]) ).

fof(f_3094_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_3094_2,plain,
    ! [U_12003] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12003),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_3094_1]) ).

fof(f_3094_3,plain,
    ! [U_12003] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12003),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_3094_2]) ).

cnf(f_3094_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12003),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_3094_3]) ).

fof(f_3095_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_3095_2,plain,
    ! [U_12005,U_12004] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12004),U_12005)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12005),U_12004),
    inference(variable_rename,[status(thm)],[f_3095_1]) ).

fof(f_3095_3,plain,
    ! [U_12004,U_12005] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12004),U_12005)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12005),U_12004),
    inference(definitional_conversion,[status(esa)],[f_3095_2]) ).

cnf(f_3095_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12004),U_12005)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12005),U_12004),
    inference(clausify,[status(thm)],[f_3095_3]) ).

fof(f_3096_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_3096_2,plain,
    ! [U_12007,U_12006] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12006),U_12007)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12006)),hAPP(c_Nat_OSuc,U_12007)),
    inference(variable_rename,[status(thm)],[f_3096_1]) ).

fof(f_3096_3,plain,
    ! [U_12007,U_12006] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12006),U_12007)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12006)),hAPP(c_Nat_OSuc,U_12007)),
    inference(definitional_conversion,[status(esa)],[f_3096_2]) ).

cnf(f_3096_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_12006),U_12007)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12006)),hAPP(c_Nat_OSuc,U_12007)),
    inference(clausify,[status(thm)],[f_3096_3]) ).

fof(f_3097_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_3097_2,plain,
    ! [U_12010,U_12009,U_12008] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12008,U_12010),U_12009) = c_Orderings_Obot__class_Obot(tc_fun(U_12008,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12008),U_12009),U_12010))
      | ~ class_Orderings_Oorder(U_12008) ),
    inference(variable_rename,[status(thm)],[f_3097_1]) ).

fof(f_3097_3,plain,
    ! [U_12008,U_12009,U_12010] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12008,U_12010),U_12009) = c_Orderings_Obot__class_Obot(tc_fun(U_12008,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12008),U_12009),U_12010))
      | ~ class_Orderings_Oorder(U_12008) ),
    inference(definitional_conversion,[status(esa)],[f_3097_2]) ).

cnf(f_3097_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12008,U_12010),U_12009) = c_Orderings_Obot__class_Obot(tc_fun(U_12008,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12008),U_12009),U_12010))
    | ~ class_Orderings_Oorder(U_12008) ),
    inference(clausify,[status(thm)],[f_3097_3]) ).

fof(f_3098_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_3098_2,plain,
    ! [U_12013,U_12012,U_12011] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_12011,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12011,U_12012),U_12013)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12011),U_12012),U_12013)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12011),U_12012),U_12013))
          | c_Orderings_Obot__class_Obot(tc_fun(U_12011,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12011,U_12012),U_12013) ) )
      | ~ class_Orderings_Oorder(U_12011) ),
    inference(variable_rename,[status(thm)],[f_3098_1]) ).

fof(f_3098_3,plain,
    ( ! [U_12011,U_12012,U_12013] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_12011,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12011,U_12012),U_12013)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12011),U_12012),U_12013))
        | ~ sP898(U_12011,U_12012,U_12013) )
    & ! [U_12011,U_12012,U_12013] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12011),U_12012),U_12013))
        | c_Orderings_Obot__class_Obot(tc_fun(U_12011,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12011,U_12012),U_12013)
        | ~ sP898(U_12011,U_12012,U_12013) )
    & ! [U_12011,U_12012,U_12013] :
        ( sP898(U_12011,U_12012,U_12013)
        | ~ class_Orderings_Oorder(U_12011) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP898])],[f_3098_2]) ).

cnf(f_3098_4,plain,
    ( sP898(U_12011,U_12012,U_12013)
    | ~ class_Orderings_Oorder(U_12011) ),
    inference(clausify,[status(thm)],[f_3098_3]) ).

cnf(f_3098_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12011),U_12012),U_12013))
    | c_Orderings_Obot__class_Obot(tc_fun(U_12011,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12011,U_12012),U_12013)
    | ~ sP898(U_12011,U_12012,U_12013) ),
    inference(clausify,[status(thm)],[f_3098_3]) ).

cnf(f_3098_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_12011,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12011,U_12012),U_12013)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12011),U_12012),U_12013))
    | ~ sP898(U_12011,U_12012,U_12013) ),
    inference(clausify,[status(thm)],[f_3098_3]) ).

fof(f_3099_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_3099_2,plain,
    ! [U_12016,U_12015,U_12014] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12014,U_12015),U_12016) = c_Orderings_Obot__class_Obot(tc_fun(U_12014,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12014),U_12015),U_12016)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12014),U_12015),U_12016))
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12014,U_12015),U_12016) != c_Orderings_Obot__class_Obot(tc_fun(U_12014,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_12014) ),
    inference(variable_rename,[status(thm)],[f_3099_1]) ).

fof(f_3099_3,plain,
    ( ! [U_12016,U_12014,U_12015] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12014,U_12015),U_12016) = c_Orderings_Obot__class_Obot(tc_fun(U_12014,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12014),U_12015),U_12016))
        | ~ sP899(U_12016,U_12014,U_12015) )
    & ! [U_12016,U_12014,U_12015] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12014),U_12015),U_12016))
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12014,U_12015),U_12016) != c_Orderings_Obot__class_Obot(tc_fun(U_12014,tc_HOL_Obool))
        | ~ sP899(U_12016,U_12014,U_12015) )
    & ! [U_12016,U_12014,U_12015] :
        ( sP899(U_12016,U_12014,U_12015)
        | ~ class_Orderings_Oorder(U_12014) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP899])],[f_3099_2]) ).

cnf(f_3099_4,plain,
    ( sP899(U_12016,U_12014,U_12015)
    | ~ class_Orderings_Oorder(U_12014) ),
    inference(clausify,[status(thm)],[f_3099_3]) ).

cnf(f_3099_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12014),U_12015),U_12016))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12014,U_12015),U_12016) != c_Orderings_Obot__class_Obot(tc_fun(U_12014,tc_HOL_Obool))
    | ~ sP899(U_12016,U_12014,U_12015) ),
    inference(clausify,[status(thm)],[f_3099_3]) ).

cnf(f_3099_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12014,U_12015),U_12016) = c_Orderings_Obot__class_Obot(tc_fun(U_12014,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12014),U_12015),U_12016))
    | ~ sP899(U_12016,U_12014,U_12015) ),
    inference(clausify,[status(thm)],[f_3099_3]) ).

fof(f_3100_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_3100_2,plain,
    ! [U_12021,U_12020,U_12019,U_12018,U_12017] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12017),U_12019),U_12021))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12017),U_12020),U_12018)) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12017),U_12019),U_12018))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12017,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12017,U_12018),U_12019)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12017,U_12020),U_12021)))
      | ~ class_Orderings_Olinorder(U_12017) ),
    inference(variable_rename,[status(thm)],[f_3100_1]) ).

fof(f_3100_3,plain,
    ( ! [U_12018,U_12017,U_12019,U_12020,U_12021] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12017),U_12019),U_12021))
        | ~ sP900(U_12018,U_12017,U_12019,U_12020,U_12021) )
    & ! [U_12018,U_12017,U_12019,U_12020,U_12021] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12017),U_12020),U_12018))
        | ~ sP900(U_12018,U_12017,U_12019,U_12020,U_12021) )
    & ! [U_12018,U_12017,U_12019,U_12020,U_12021] :
        ( sP900(U_12018,U_12017,U_12019,U_12020,U_12021)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12017),U_12019),U_12018))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12017,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12017,U_12018),U_12019)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12017,U_12020),U_12021)))
        | ~ class_Orderings_Olinorder(U_12017) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP900])],[f_3100_2]) ).

cnf(f_3100_4,plain,
    ( sP900(U_12018,U_12017,U_12019,U_12020,U_12021)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12017),U_12019),U_12018))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12017,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12017,U_12018),U_12019)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12017,U_12020),U_12021)))
    | ~ class_Orderings_Olinorder(U_12017) ),
    inference(clausify,[status(thm)],[f_3100_3]) ).

cnf(f_3100_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12017),U_12020),U_12018))
    | ~ sP900(U_12018,U_12017,U_12019,U_12020,U_12021) ),
    inference(clausify,[status(thm)],[f_3100_3]) ).

cnf(f_3100_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12017),U_12019),U_12021))
    | ~ sP900(U_12018,U_12017,U_12019,U_12020,U_12021) ),
    inference(clausify,[status(thm)],[f_3100_3]) ).

fof(f_3101_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_3101_2,plain,
    ! [U_12025,U_12024,U_12023,U_12022] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12022,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12022,U_12023),U_12024)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12022,U_12024),U_12025)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12022,U_12023),U_12025)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12022),U_12024),U_12025))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12022),U_12023),U_12024))
      | ~ class_Orderings_Olinorder(U_12022) ),
    inference(variable_rename,[status(thm)],[f_3101_1]) ).

fof(f_3101_3,plain,
    ! [U_12022,U_12023,U_12024,U_12025] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12022,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12022,U_12023),U_12024)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12022,U_12024),U_12025)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12022,U_12023),U_12025)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12022),U_12024),U_12025))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12022),U_12023),U_12024))
      | ~ class_Orderings_Olinorder(U_12022) ),
    inference(definitional_conversion,[status(esa)],[f_3101_2]) ).

cnf(f_3101_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12022,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12022,U_12023),U_12024)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12022,U_12024),U_12025)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12022,U_12023),U_12025)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12022),U_12024),U_12025))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12022),U_12023),U_12024))
    | ~ class_Orderings_Olinorder(U_12022) ),
    inference(clausify,[status(thm)],[f_3101_3]) ).

fof(f_3102_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_3102_2,plain,
    ! [U_12029,U_12028,U_12027,U_12026] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12026,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12026,U_12027),U_12029)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12026,U_12027),U_12028)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12026,U_12028),U_12029)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12026),U_12027),U_12028))
      | ~ class_Orderings_Olinorder(U_12026) ),
    inference(variable_rename,[status(thm)],[f_3102_1]) ).

fof(f_3102_3,plain,
    ! [U_12026,U_12027,U_12028,U_12029] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12026,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12026,U_12027),U_12029)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12026,U_12027),U_12028)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12026,U_12028),U_12029)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12026),U_12027),U_12028))
      | ~ class_Orderings_Olinorder(U_12026) ),
    inference(definitional_conversion,[status(esa)],[f_3102_2]) ).

cnf(f_3102_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12026,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12026,U_12027),U_12029)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12026,U_12027),U_12028)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12026,U_12028),U_12029)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12026),U_12027),U_12028))
    | ~ class_Orderings_Olinorder(U_12026) ),
    inference(clausify,[status(thm)],[f_3102_3]) ).

fof(f_3103_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_3103_2,plain,
    ! [U_12033,U_12032,U_12031,U_12030] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12030,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12030,U_12031),U_12032)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12030,U_12032),U_12033)) = c_Orderings_Obot__class_Obot(tc_fun(U_12030,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12030) ),
    inference(variable_rename,[status(thm)],[f_3103_1]) ).

fof(f_3103_3,plain,
    ! [U_12030,U_12031,U_12032,U_12033] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12030,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12030,U_12031),U_12032)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12030,U_12032),U_12033)) = c_Orderings_Obot__class_Obot(tc_fun(U_12030,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12030) ),
    inference(definitional_conversion,[status(esa)],[f_3103_2]) ).

cnf(f_3103_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12030,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12030,U_12031),U_12032)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12030,U_12032),U_12033)) = c_Orderings_Obot__class_Obot(tc_fun(U_12030,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12030) ),
    inference(clausify,[status(thm)],[f_3103_3]) ).

fof(f_3104_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_3104_2,plain,
    ! [U_12035,U_12034] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12034)),U_12035) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_12034,U_12035),
    inference(variable_rename,[status(thm)],[f_3104_1]) ).

fof(f_3104_3,plain,
    ! [U_12034,U_12035] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12034)),U_12035) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_12034,U_12035),
    inference(definitional_conversion,[status(esa)],[f_3104_2]) ).

cnf(f_3104_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12034)),U_12035) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_12034,U_12035),
    inference(clausify,[status(thm)],[f_3104_3]) ).

fof(f_3105_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_3105_2,plain,
    ! [U_12038,U_12037,U_12036] : 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_12036)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12037),U_12038)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12037),U_12036)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12038),U_12036)),
    inference(variable_rename,[status(thm)],[f_3105_1]) ).

fof(f_3105_3,plain,
    ! [U_12036,U_12037,U_12038] : 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_12036)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12037),U_12038)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12037),U_12036)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12038),U_12036)),
    inference(definitional_conversion,[status(esa)],[f_3105_2]) ).

cnf(f_3105_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_12036)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12037),U_12038)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12037),U_12036)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12038),U_12036)),
    inference(clausify,[status(thm)],[f_3105_3]) ).

fof(f_3106_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_3106_2,plain,
    ! [U_12039] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12039),hAPP(c_Nat_OSuc,U_12039)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12039),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3106_1]) ).

fof(f_3106_3,plain,
    ! [U_12039] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12039),hAPP(c_Nat_OSuc,U_12039)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12039),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3106_2]) ).

cnf(f_3106_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12039),hAPP(c_Nat_OSuc,U_12039)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12039),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3106_3]) ).

fof(f_3107_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_3107_2,plain,
    ! [U_12043,U_12042,U_12041,U_12040] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12040,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12040,U_12041),U_12042)),c_SetInterval_Oord__class_OatLeastAtMost(U_12040,U_12042,U_12043)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12040,U_12041,U_12043)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12040),U_12042),U_12043))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12040),U_12041),U_12042))
      | ~ class_Orderings_Olinorder(U_12040) ),
    inference(variable_rename,[status(thm)],[f_3107_1]) ).

fof(f_3107_3,plain,
    ! [U_12040,U_12041,U_12042,U_12043] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12040,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12040,U_12041),U_12042)),c_SetInterval_Oord__class_OatLeastAtMost(U_12040,U_12042,U_12043)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12040,U_12041,U_12043)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12040),U_12042),U_12043))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12040),U_12041),U_12042))
      | ~ class_Orderings_Olinorder(U_12040) ),
    inference(definitional_conversion,[status(esa)],[f_3107_2]) ).

cnf(f_3107_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12040,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12040,U_12041),U_12042)),c_SetInterval_Oord__class_OatLeastAtMost(U_12040,U_12042,U_12043)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12040,U_12041,U_12043)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12040),U_12042),U_12043))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12040),U_12041),U_12042))
    | ~ class_Orderings_Olinorder(U_12040) ),
    inference(clausify,[status(thm)],[f_3107_3]) ).

fof(f_3108_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_3108_2,plain,
    ! [U_12046,U_12045,U_12044] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12044),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12045),U_12046)) = 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_12044),U_12045)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12045),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12045),U_12046)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12044),U_12045)) ),
    inference(variable_rename,[status(thm)],[f_3108_1]) ).

fof(f_3108_3,plain,
    ! [U_12046,U_12045,U_12044] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12044),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12045),U_12046)) = 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_12044),U_12045)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12045),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12045),U_12046)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12044),U_12045)) ),
    inference(definitional_conversion,[status(esa)],[f_3108_2]) ).

cnf(f_3108_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12044),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12045),U_12046)) = 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_12044),U_12045)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12045),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12045),U_12046)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12044),U_12045)) ),
    inference(clausify,[status(thm)],[f_3108_3]) ).

fof(f_3109_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_3109_2,plain,
    ! [U_12050,U_12049,U_12048,U_12047] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12047,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12047,U_12048),U_12049)),c_SetInterval_Oord__class_OatLeastAtMost(U_12047,U_12049,U_12050)) = c_Orderings_Obot__class_Obot(tc_fun(U_12047,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12047) ),
    inference(variable_rename,[status(thm)],[f_3109_1]) ).

fof(f_3109_3,plain,
    ! [U_12047,U_12048,U_12049,U_12050] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12047,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12047,U_12048),U_12049)),c_SetInterval_Oord__class_OatLeastAtMost(U_12047,U_12049,U_12050)) = c_Orderings_Obot__class_Obot(tc_fun(U_12047,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12047) ),
    inference(definitional_conversion,[status(esa)],[f_3109_2]) ).

cnf(f_3109_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12047,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12047,U_12048),U_12049)),c_SetInterval_Oord__class_OatLeastAtMost(U_12047,U_12049,U_12050)) = c_Orderings_Obot__class_Obot(tc_fun(U_12047,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12047) ),
    inference(clausify,[status(thm)],[f_3109_3]) ).

fof(f_3110_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_3110_2,plain,
    ! [U_12055,U_12054,U_12053,U_12052,U_12051] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12051,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12051,U_12052),U_12053)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12051,U_12054),U_12055)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12051,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12051),U_12052),U_12054)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12051),U_12053),U_12055))
      | ~ class_Orderings_Olinorder(U_12051) ),
    inference(variable_rename,[status(thm)],[f_3110_1]) ).

fof(f_3110_3,plain,
    ! [U_12051,U_12052,U_12053,U_12054,U_12055] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12051,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12051,U_12052),U_12053)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12051,U_12054),U_12055)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12051,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12051),U_12052),U_12054)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12051),U_12053),U_12055))
      | ~ class_Orderings_Olinorder(U_12051) ),
    inference(definitional_conversion,[status(esa)],[f_3110_2]) ).

cnf(f_3110_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12051,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12051,U_12052),U_12053)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12051,U_12054),U_12055)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12051,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12051),U_12052),U_12054)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12051),U_12053),U_12055))
    | ~ class_Orderings_Olinorder(U_12051) ),
    inference(clausify,[status(thm)],[f_3110_3]) ).

fof(f_3111_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_3111_2,plain,
    ! [U_12057,U_12056] :
      ( U_12056 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12057),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12057),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_12056)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_12056),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12057),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12057),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_12056))))) ),
    inference(variable_rename,[status(thm)],[f_3111_1]) ).

fof(f_3111_3,plain,
    ! [U_12056,U_12057] :
      ( U_12056 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12057),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12057),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_12056)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_12056),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12057),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12057),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_12056))))) ),
    inference(definitional_conversion,[status(esa)],[f_3111_2]) ).

cnf(f_3111_4,plain,
    ( U_12056 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12057),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12057),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_12056)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_12056),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12057),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12057),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_12056))))) ),
    inference(clausify,[status(thm)],[f_3111_3]) ).

fof(f_3112_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_3112_2,plain,
    ! [U_12061,U_12060,U_12059,U_12058] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12058,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12058,U_12059,U_12060)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12058,U_12060),U_12061)) = c_Orderings_Obot__class_Obot(tc_fun(U_12058,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12058) ),
    inference(variable_rename,[status(thm)],[f_3112_1]) ).

fof(f_3112_3,plain,
    ! [U_12058,U_12059,U_12060,U_12061] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12058,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12058,U_12059,U_12060)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12058,U_12060),U_12061)) = c_Orderings_Obot__class_Obot(tc_fun(U_12058,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12058) ),
    inference(definitional_conversion,[status(esa)],[f_3112_2]) ).

cnf(f_3112_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12058,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12058,U_12059,U_12060)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12058,U_12060),U_12061)) = c_Orderings_Obot__class_Obot(tc_fun(U_12058,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12058) ),
    inference(clausify,[status(thm)],[f_3112_3]) ).

fof(f_3113_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_3113_2,plain,
    ! [U_12064,U_12063,U_12062] :
      ( hAPP(c_Set_Oimage(U_12062,U_12062,c_Groups_Ouminus__class_Ouminus(U_12062)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12062,U_12063,U_12064)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12062,hAPP(c_Groups_Ouminus__class_Ouminus(U_12062),U_12064)),hAPP(c_Groups_Ouminus__class_Ouminus(U_12062),U_12063))
      | ~ class_Groups_Oordered__ab__group__add(U_12062) ),
    inference(variable_rename,[status(thm)],[f_3113_1]) ).

fof(f_3113_3,plain,
    ! [U_12062,U_12063,U_12064] :
      ( hAPP(c_Set_Oimage(U_12062,U_12062,c_Groups_Ouminus__class_Ouminus(U_12062)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12062,U_12063,U_12064)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12062,hAPP(c_Groups_Ouminus__class_Ouminus(U_12062),U_12064)),hAPP(c_Groups_Ouminus__class_Ouminus(U_12062),U_12063))
      | ~ class_Groups_Oordered__ab__group__add(U_12062) ),
    inference(definitional_conversion,[status(esa)],[f_3113_2]) ).

cnf(f_3113_4,plain,
    ( hAPP(c_Set_Oimage(U_12062,U_12062,c_Groups_Ouminus__class_Ouminus(U_12062)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12062,U_12063,U_12064)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12062,hAPP(c_Groups_Ouminus__class_Ouminus(U_12062),U_12064)),hAPP(c_Groups_Ouminus__class_Ouminus(U_12062),U_12063))
    | ~ class_Groups_Oordered__ab__group__add(U_12062) ),
    inference(clausify,[status(thm)],[f_3113_3]) ).

fof(f_3114_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_3114_2,plain,
    ! [U_12067,U_12066,U_12065] :
      ( hAPP(c_Set_Oimage(U_12065,U_12065,c_Groups_Ouminus__class_Ouminus(U_12065)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12065,U_12066),U_12067)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_12065,hAPP(c_Groups_Ouminus__class_Ouminus(U_12065),U_12067),hAPP(c_Groups_Ouminus__class_Ouminus(U_12065),U_12066))
      | ~ class_Groups_Oordered__ab__group__add(U_12065) ),
    inference(variable_rename,[status(thm)],[f_3114_1]) ).

fof(f_3114_3,plain,
    ! [U_12065,U_12066,U_12067] :
      ( hAPP(c_Set_Oimage(U_12065,U_12065,c_Groups_Ouminus__class_Ouminus(U_12065)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12065,U_12066),U_12067)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_12065,hAPP(c_Groups_Ouminus__class_Ouminus(U_12065),U_12067),hAPP(c_Groups_Ouminus__class_Ouminus(U_12065),U_12066))
      | ~ class_Groups_Oordered__ab__group__add(U_12065) ),
    inference(definitional_conversion,[status(esa)],[f_3114_2]) ).

cnf(f_3114_4,plain,
    ( hAPP(c_Set_Oimage(U_12065,U_12065,c_Groups_Ouminus__class_Ouminus(U_12065)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12065,U_12066),U_12067)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_12065,hAPP(c_Groups_Ouminus__class_Ouminus(U_12065),U_12067),hAPP(c_Groups_Ouminus__class_Ouminus(U_12065),U_12066))
    | ~ class_Groups_Oordered__ab__group__add(U_12065) ),
    inference(clausify,[status(thm)],[f_3114_3]) ).

fof(f_3115_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_3115_2,plain,
    ! [U_12069,U_12068] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12068),hAPP(c_Nat_OSuc,U_12069)) = 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_12068),U_12069)) )
      & ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12068),hAPP(c_Nat_OSuc,U_12069)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12069),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12068),U_12069))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12068),U_12069)) ) ),
    inference(variable_rename,[status(thm)],[f_3115_1]) ).

fof(f_3115_3,plain,
    ( ! [U_12073,U_12071] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12071),hAPP(c_Nat_OSuc,U_12073)) = 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_12071),U_12073)) )
    & ! [U_12072,U_12070] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12070),hAPP(c_Nat_OSuc,U_12072)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12072),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12070),U_12072))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12070),U_12072)) ) ),
    inference(miniscope,[status(thm)],[f_3115_2]) ).

fof(f_3115_4,plain,
    ( ! [U_12071,U_12073] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12071),hAPP(c_Nat_OSuc,U_12073)) = 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_12071),U_12073)) )
    & ! [U_12072,U_12070] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12070),hAPP(c_Nat_OSuc,U_12072)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12072),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12070),U_12072))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12070),U_12072)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3115_3]) ).

cnf(f_3115_5,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12070),hAPP(c_Nat_OSuc,U_12072)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12072),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12070),U_12072))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12070),U_12072)) ),
    inference(clausify,[status(thm)],[f_3115_4]) ).

cnf(f_3115_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12071),hAPP(c_Nat_OSuc,U_12073)) = 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_12071),U_12073)) ),
    inference(clausify,[status(thm)],[f_3115_4]) ).

fof(f_3116_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_3116_2,plain,
    ! [U_12077,U_12076,U_12075,U_12074] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12074,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12074,U_12075,U_12076)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12074,U_12076),U_12077)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_12074,U_12075,U_12077)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12074),U_12076),U_12077))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12074),U_12075),U_12076))
      | ~ class_Orderings_Olinorder(U_12074) ),
    inference(variable_rename,[status(thm)],[f_3116_1]) ).

fof(f_3116_3,plain,
    ! [U_12074,U_12075,U_12076,U_12077] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12074,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12074,U_12075,U_12076)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12074,U_12076),U_12077)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_12074,U_12075,U_12077)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12074),U_12076),U_12077))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12074),U_12075),U_12076))
      | ~ class_Orderings_Olinorder(U_12074) ),
    inference(definitional_conversion,[status(esa)],[f_3116_2]) ).

cnf(f_3116_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12074,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12074,U_12075,U_12076)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12074,U_12076),U_12077)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_12074,U_12075,U_12077)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12074),U_12076),U_12077))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12074),U_12075),U_12076))
    | ~ class_Orderings_Olinorder(U_12074) ),
    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__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_3117_2,plain,
    ! [U_12080,U_12079,U_12078] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12078,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12078,U_12079),U_12080)),hAPP(hAPP(c_Set_Oinsert(U_12078),U_12080),c_Orderings_Obot__class_Obot(tc_fun(U_12078,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_12078,U_12079,U_12080)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12078),U_12079),U_12080))
      | ~ class_Orderings_Olinorder(U_12078) ),
    inference(variable_rename,[status(thm)],[f_3117_1]) ).

fof(f_3117_3,plain,
    ! [U_12078,U_12079,U_12080] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12078,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12078,U_12079),U_12080)),hAPP(hAPP(c_Set_Oinsert(U_12078),U_12080),c_Orderings_Obot__class_Obot(tc_fun(U_12078,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_12078,U_12079,U_12080)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12078),U_12079),U_12080))
      | ~ class_Orderings_Olinorder(U_12078) ),
    inference(definitional_conversion,[status(esa)],[f_3117_2]) ).

cnf(f_3117_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12078,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12078,U_12079),U_12080)),hAPP(hAPP(c_Set_Oinsert(U_12078),U_12080),c_Orderings_Obot__class_Obot(tc_fun(U_12078,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_12078,U_12079,U_12080)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12078),U_12079),U_12080))
    | ~ class_Orderings_Olinorder(U_12078) ),
    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__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_3118_2,plain,
    ! [U_12083,U_12082,U_12081] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12081,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12081),U_12082),c_Orderings_Obot__class_Obot(tc_fun(U_12081,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12081,U_12082,U_12083)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12081,U_12082),U_12083)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12081),U_12082),U_12083))
      | ~ class_Orderings_Olinorder(U_12081) ),
    inference(variable_rename,[status(thm)],[f_3118_1]) ).

fof(f_3118_3,plain,
    ! [U_12081,U_12082,U_12083] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12081,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12081),U_12082),c_Orderings_Obot__class_Obot(tc_fun(U_12081,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12081,U_12082,U_12083)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12081,U_12082),U_12083)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12081),U_12082),U_12083))
      | ~ class_Orderings_Olinorder(U_12081) ),
    inference(definitional_conversion,[status(esa)],[f_3118_2]) ).

cnf(f_3118_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12081,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12081),U_12082),c_Orderings_Obot__class_Obot(tc_fun(U_12081,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12081,U_12082,U_12083)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12081,U_12082),U_12083)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12081),U_12082),U_12083))
    | ~ class_Orderings_Olinorder(U_12081) ),
    inference(clausify,[status(thm)],[f_3118_3]) ).

fof(f_3119_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_3119_2,plain,
    ! [U_12087,U_12086,U_12085,U_12084] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12084,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12084,U_12085,U_12086)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12084,U_12086,U_12087)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12084,U_12085),U_12087)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12084),U_12086),U_12087))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12084),U_12085),U_12086))
      | ~ class_Orderings_Olinorder(U_12084) ),
    inference(variable_rename,[status(thm)],[f_3119_1]) ).

fof(f_3119_3,plain,
    ! [U_12084,U_12085,U_12086,U_12087] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12084,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12084,U_12085,U_12086)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12084,U_12086,U_12087)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12084,U_12085),U_12087)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12084),U_12086),U_12087))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12084),U_12085),U_12086))
      | ~ class_Orderings_Olinorder(U_12084) ),
    inference(definitional_conversion,[status(esa)],[f_3119_2]) ).

cnf(f_3119_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12084,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12084,U_12085,U_12086)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12084,U_12086,U_12087)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12084,U_12085),U_12087)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12084),U_12086),U_12087))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12084),U_12085),U_12086))
    | ~ class_Orderings_Olinorder(U_12084) ),
    inference(clausify,[status(thm)],[f_3119_3]) ).

fof(f_3120_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_3120_2,plain,
    ! [U_12094,U_12093,U_12092,U_12091] :
      ( ! [U_12090] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12091),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12090),U_12092)),U_12094)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12091),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12090),U_12094)))
          | ? [U_12089] :
              ( ? [U_12088] :
                  ( U_12090 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12088),U_12089)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12088),U_12093)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12089),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12092))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12091),U_12092)) ),
    inference(variable_rename,[status(thm)],[f_3120_1]) ).

fof(f_3120_3,plain,
    ! [U_12094,U_12093,U_12092,U_12091] :
      ( ! [U_12090] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12091),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12090),U_12092)),U_12094)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12091),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12090),U_12094)))
          | ( ? [U_12088] :
                ( U_12090 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12088),sK256(U_12094,U_12093,U_12092,U_12091,U_12090))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12088),U_12093)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK256(U_12094,U_12093,U_12092,U_12091,U_12090)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12092))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12091),U_12092)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK256]),skolemize(U_12089,sK256(U_12094,U_12093,U_12092,U_12091,U_12090))],[f_3120_2]) ).

fof(f_3120_4,plain,
    ! [U_12094,U_12093,U_12092,U_12091] :
      ( ! [U_12090] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12091),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12090),U_12092)),U_12094)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12091),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12090),U_12094)))
          | ( U_12090 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK257(U_12094,U_12093,U_12092,U_12091,U_12090)),sK256(U_12094,U_12093,U_12092,U_12091,U_12090))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK257(U_12094,U_12093,U_12092,U_12091,U_12090)),U_12093))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK256(U_12094,U_12093,U_12092,U_12091,U_12090)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12092))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12091),U_12092)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK257]),skolemize(U_12088,sK257(U_12094,U_12093,U_12092,U_12091,U_12090))],[f_3120_3]) ).

fof(f_3120_5,plain,
    ( ! [U_12090,U_12091,U_12092,U_12093,U_12094] :
        ( U_12090 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK257(U_12094,U_12093,U_12092,U_12091,U_12090)),sK256(U_12094,U_12093,U_12092,U_12091,U_12090))
        | ~ sP901(U_12090,U_12091,U_12092,U_12093,U_12094) )
    & ! [U_12090,U_12091,U_12092,U_12093,U_12094] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK257(U_12094,U_12093,U_12092,U_12091,U_12090)),U_12093))
        | ~ sP901(U_12090,U_12091,U_12092,U_12093,U_12094) )
    & ! [U_12090,U_12091,U_12092,U_12093,U_12094] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK256(U_12094,U_12093,U_12092,U_12091,U_12090)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12092)))
        | ~ sP901(U_12090,U_12091,U_12092,U_12093,U_12094) )
    & ! [U_12090,U_12091,U_12092,U_12093,U_12094] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12091),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12090),U_12092)),U_12094)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12091),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12090),U_12094)))
        | sP901(U_12090,U_12091,U_12092,U_12093,U_12094)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12091),U_12092)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP901])],[f_3120_4]) ).

cnf(f_3120_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12091),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12090),U_12092)),U_12094)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12091),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12090),U_12094)))
    | sP901(U_12090,U_12091,U_12092,U_12093,U_12094)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12091),U_12092)) ),
    inference(clausify,[status(thm)],[f_3120_5]) ).

cnf(f_3120_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK256(U_12094,U_12093,U_12092,U_12091,U_12090)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12092)))
    | ~ sP901(U_12090,U_12091,U_12092,U_12093,U_12094) ),
    inference(clausify,[status(thm)],[f_3120_5]) ).

cnf(f_3120_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK257(U_12094,U_12093,U_12092,U_12091,U_12090)),U_12093))
    | ~ sP901(U_12090,U_12091,U_12092,U_12093,U_12094) ),
    inference(clausify,[status(thm)],[f_3120_5]) ).

cnf(f_3120_9,plain,
    ( U_12090 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK257(U_12094,U_12093,U_12092,U_12091,U_12090)),sK256(U_12094,U_12093,U_12092,U_12091,U_12090))
    | ~ sP901(U_12090,U_12091,U_12092,U_12093,U_12094) ),
    inference(clausify,[status(thm)],[f_3120_5]) ).

fof(f_3121_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_3121_2,plain,
    ! [U_12101,U_12100,U_12099,U_12098] :
      ( ! [U_12097] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12098),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12097),U_12099)),U_12101)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12098),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12097),U_12101)))
          | ? [U_12096] :
              ( ? [U_12095] :
                  ( U_12097 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12095),U_12096)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12095),U_12100)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12096),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12099))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12098),U_12099)) ),
    inference(variable_rename,[status(thm)],[f_3121_1]) ).

fof(f_3121_3,plain,
    ! [U_12101,U_12100,U_12099,U_12098] :
      ( ! [U_12097] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12098),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12097),U_12099)),U_12101)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12098),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12097),U_12101)))
          | ( ? [U_12095] :
                ( U_12097 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12095),sK258(U_12101,U_12100,U_12099,U_12098,U_12097))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12095),U_12100)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK258(U_12101,U_12100,U_12099,U_12098,U_12097)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12099))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12098),U_12099)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK258]),skolemize(U_12096,sK258(U_12101,U_12100,U_12099,U_12098,U_12097))],[f_3121_2]) ).

fof(f_3121_4,plain,
    ! [U_12101,U_12100,U_12099,U_12098] :
      ( ! [U_12097] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12098),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12097),U_12099)),U_12101)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12098),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12097),U_12101)))
          | ( U_12097 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK259(U_12101,U_12100,U_12099,U_12098,U_12097)),sK258(U_12101,U_12100,U_12099,U_12098,U_12097))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK259(U_12101,U_12100,U_12099,U_12098,U_12097)),U_12100))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK258(U_12101,U_12100,U_12099,U_12098,U_12097)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12099))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12098),U_12099)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK259]),skolemize(U_12095,sK259(U_12101,U_12100,U_12099,U_12098,U_12097))],[f_3121_3]) ).

fof(f_3121_5,plain,
    ( ! [U_12099,U_12100,U_12101,U_12097,U_12098] :
        ( U_12097 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK259(U_12101,U_12100,U_12099,U_12098,U_12097)),sK258(U_12101,U_12100,U_12099,U_12098,U_12097))
        | ~ sP902(U_12099,U_12100,U_12101,U_12097,U_12098) )
    & ! [U_12099,U_12100,U_12101,U_12097,U_12098] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK259(U_12101,U_12100,U_12099,U_12098,U_12097)),U_12100))
        | ~ sP902(U_12099,U_12100,U_12101,U_12097,U_12098) )
    & ! [U_12099,U_12100,U_12101,U_12097,U_12098] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK258(U_12101,U_12100,U_12099,U_12098,U_12097)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12099)))
        | ~ sP902(U_12099,U_12100,U_12101,U_12097,U_12098) )
    & ! [U_12099,U_12100,U_12101,U_12097,U_12098] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12098),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12097),U_12099)),U_12101)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12098),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12097),U_12101)))
        | sP902(U_12099,U_12100,U_12101,U_12097,U_12098)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12098),U_12099)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP902])],[f_3121_4]) ).

cnf(f_3121_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12098),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12097),U_12099)),U_12101)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12098),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12097),U_12101)))
    | sP902(U_12099,U_12100,U_12101,U_12097,U_12098)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12098),U_12099)) ),
    inference(clausify,[status(thm)],[f_3121_5]) ).

cnf(f_3121_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK258(U_12101,U_12100,U_12099,U_12098,U_12097)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12099)))
    | ~ sP902(U_12099,U_12100,U_12101,U_12097,U_12098) ),
    inference(clausify,[status(thm)],[f_3121_5]) ).

cnf(f_3121_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK259(U_12101,U_12100,U_12099,U_12098,U_12097)),U_12100))
    | ~ sP902(U_12099,U_12100,U_12101,U_12097,U_12098) ),
    inference(clausify,[status(thm)],[f_3121_5]) ).

cnf(f_3121_9,plain,
    ( U_12097 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK259(U_12101,U_12100,U_12099,U_12098,U_12097)),sK258(U_12101,U_12100,U_12099,U_12098,U_12097))
    | ~ sP902(U_12099,U_12100,U_12101,U_12097,U_12098) ),
    inference(clausify,[status(thm)],[f_3121_5]) ).

fof(f_3122_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_3122_2,plain,
    ! [U_12108,U_12107,U_12106,U_12105] :
      ( ! [U_12104] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12105),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12104),U_12106)),U_12108)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12105),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12104),U_12108)))
          | ? [U_12103] :
              ( ? [U_12102] :
                  ( U_12104 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12102),U_12103)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12102),U_12107)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12103),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12106))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12105),U_12106)) ),
    inference(variable_rename,[status(thm)],[f_3122_1]) ).

fof(f_3122_3,plain,
    ! [U_12108,U_12107,U_12106,U_12105] :
      ( ! [U_12104] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12105),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12104),U_12106)),U_12108)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12105),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12104),U_12108)))
          | ( ? [U_12102] :
                ( U_12104 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12102),sK260(U_12108,U_12107,U_12106,U_12105,U_12104))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12102),U_12107)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK260(U_12108,U_12107,U_12106,U_12105,U_12104)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12106))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12105),U_12106)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK260]),skolemize(U_12103,sK260(U_12108,U_12107,U_12106,U_12105,U_12104))],[f_3122_2]) ).

fof(f_3122_4,plain,
    ! [U_12108,U_12107,U_12106,U_12105] :
      ( ! [U_12104] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12105),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12104),U_12106)),U_12108)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12105),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12104),U_12108)))
          | ( U_12104 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK261(U_12108,U_12107,U_12106,U_12105,U_12104)),sK260(U_12108,U_12107,U_12106,U_12105,U_12104))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK261(U_12108,U_12107,U_12106,U_12105,U_12104)),U_12107))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK260(U_12108,U_12107,U_12106,U_12105,U_12104)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12106))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12105),U_12106)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK261]),skolemize(U_12102,sK261(U_12108,U_12107,U_12106,U_12105,U_12104))],[f_3122_3]) ).

fof(f_3122_5,plain,
    ( ! [U_12104,U_12105,U_12106,U_12107,U_12108] :
        ( U_12104 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK261(U_12108,U_12107,U_12106,U_12105,U_12104)),sK260(U_12108,U_12107,U_12106,U_12105,U_12104))
        | ~ sP903(U_12104,U_12105,U_12106,U_12107,U_12108) )
    & ! [U_12104,U_12105,U_12106,U_12107,U_12108] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK261(U_12108,U_12107,U_12106,U_12105,U_12104)),U_12107))
        | ~ sP903(U_12104,U_12105,U_12106,U_12107,U_12108) )
    & ! [U_12104,U_12105,U_12106,U_12107,U_12108] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK260(U_12108,U_12107,U_12106,U_12105,U_12104)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12106)))
        | ~ sP903(U_12104,U_12105,U_12106,U_12107,U_12108) )
    & ! [U_12104,U_12105,U_12106,U_12107,U_12108] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12105),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12104),U_12106)),U_12108)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12105),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12104),U_12108)))
        | sP903(U_12104,U_12105,U_12106,U_12107,U_12108)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12105),U_12106)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP903])],[f_3122_4]) ).

cnf(f_3122_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12105),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12104),U_12106)),U_12108)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12105),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12104),U_12108)))
    | sP903(U_12104,U_12105,U_12106,U_12107,U_12108)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12105),U_12106)) ),
    inference(clausify,[status(thm)],[f_3122_5]) ).

cnf(f_3122_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK260(U_12108,U_12107,U_12106,U_12105,U_12104)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12106)))
    | ~ sP903(U_12104,U_12105,U_12106,U_12107,U_12108) ),
    inference(clausify,[status(thm)],[f_3122_5]) ).

cnf(f_3122_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK261(U_12108,U_12107,U_12106,U_12105,U_12104)),U_12107))
    | ~ sP903(U_12104,U_12105,U_12106,U_12107,U_12108) ),
    inference(clausify,[status(thm)],[f_3122_5]) ).

cnf(f_3122_9,plain,
    ( U_12104 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK261(U_12108,U_12107,U_12106,U_12105,U_12104)),sK260(U_12108,U_12107,U_12106,U_12105,U_12104))
    | ~ sP903(U_12104,U_12105,U_12106,U_12107,U_12108) ),
    inference(clausify,[status(thm)],[f_3122_5]) ).

fof(f_3123_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_3123_2,plain,
    ! [U_12110,U_12109] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12109),U_12110))),
    inference(variable_rename,[status(thm)],[f_3123_1]) ).

fof(f_3123_3,plain,
    ! [U_12110,U_12109] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12109),U_12110))),
    inference(definitional_conversion,[status(esa)],[f_3123_2]) ).

cnf(f_3123_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12109),U_12110))),
    inference(clausify,[status(thm)],[f_3123_3]) ).

fof(f_3124_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_3124_2,plain,
    ! [U_12111] : 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_12111))),
    inference(variable_rename,[status(thm)],[f_3124_1]) ).

fof(f_3124_3,plain,
    ! [U_12111] : 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_12111))),
    inference(definitional_conversion,[status(esa)],[f_3124_2]) ).

cnf(f_3124_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_12111))),
    inference(clausify,[status(thm)],[f_3124_3]) ).

fof(f_3125_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_3125_2,plain,
    ! [U_12113,U_12112] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12113),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_12112,U_12113),
    inference(variable_rename,[status(thm)],[f_3125_1]) ).

fof(f_3125_3,plain,
    ! [U_12112,U_12113] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12113),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_12112,U_12113),
    inference(definitional_conversion,[status(esa)],[f_3125_2]) ).

cnf(f_3125_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12112),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12113),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_12112,U_12113),
    inference(clausify,[status(thm)],[f_3125_3]) ).

fof(f_3126_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_3126_2,plain,
    ! [U_12115,U_12114] : 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_12114)),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_12115),U_12114))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12114),U_12115),
    inference(variable_rename,[status(thm)],[f_3126_1]) ).

fof(f_3126_3,plain,
    ! [U_12114,U_12115] : 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_12114)),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_12115),U_12114))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12114),U_12115),
    inference(definitional_conversion,[status(esa)],[f_3126_2]) ).

cnf(f_3126_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_12114)),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_12115),U_12114))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12114),U_12115),
    inference(clausify,[status(thm)],[f_3126_3]) ).

fof(f_3127_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_3127_2,plain,
    ! [U_12116] : 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_12116)) = hAPP(c_Int_Onat,U_12116),
    inference(variable_rename,[status(thm)],[f_3127_1]) ).

fof(f_3127_3,plain,
    ! [U_12116] : 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_12116)) = hAPP(c_Int_Onat,U_12116),
    inference(definitional_conversion,[status(esa)],[f_3127_2]) ).

cnf(f_3127_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_12116)) = hAPP(c_Int_Onat,U_12116),
    inference(clausify,[status(thm)],[f_3127_3]) ).

fof(f_3128_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_3128_2,plain,
    ! [U_12118,U_12117] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12117),U_12118)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12118),U_12117)),
    inference(variable_rename,[status(thm)],[f_3128_1]) ).

fof(f_3128_3,plain,
    ! [U_12117,U_12118] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12117),U_12118)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12118),U_12117)),
    inference(definitional_conversion,[status(esa)],[f_3128_2]) ).

cnf(f_3128_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12117),U_12118)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12118),U_12117)),
    inference(clausify,[status(thm)],[f_3128_3]) ).

fof(f_3129_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_3129_2,plain,
    ! [U_12120,U_12119] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12119),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_12120) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_12119,U_12120),
    inference(variable_rename,[status(thm)],[f_3129_1]) ).

fof(f_3129_3,plain,
    ! [U_12119,U_12120] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12119),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_12120) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_12119,U_12120),
    inference(definitional_conversion,[status(esa)],[f_3129_2]) ).

cnf(f_3129_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12119),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_12120) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_12119,U_12120),
    inference(clausify,[status(thm)],[f_3129_3]) ).

fof(f_3130_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_3130_2,plain,
    ! [U_12121] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12121) = 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_12121))),
    inference(variable_rename,[status(thm)],[f_3130_1]) ).

fof(f_3130_3,plain,
    ! [U_12121] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12121) = 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_12121))),
    inference(definitional_conversion,[status(esa)],[f_3130_2]) ).

cnf(f_3130_4,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12121) = 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_12121))),
    inference(clausify,[status(thm)],[f_3130_3]) ).

fof(f_3131_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_3131_2,plain,
    ! [U_12127,U_12126,U_12125,U_12124,U_12123,U_12122] :
      ( ( hAPP(c_Set_Oimage(U_12122,U_12125,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12122,U_12125),U_12126),U_12123),U_12127)),U_12124) = hAPP(c_Set_Oimage(U_12122,U_12125,U_12126),U_12124)
        | hBOOL(hAPP(hAPP(c_member(U_12122),U_12123),U_12124)) )
      & ( hAPP(c_Set_Oimage(U_12122,U_12125,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12122,U_12125),U_12126),U_12123),U_12127)),U_12124) = hAPP(hAPP(c_Set_Oinsert(U_12125),U_12127),hAPP(c_Set_Oimage(U_12122,U_12125,U_12126),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12122,tc_HOL_Obool)),U_12124),hAPP(hAPP(c_Set_Oinsert(U_12122),U_12123),c_Orderings_Obot__class_Obot(tc_fun(U_12122,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12122),U_12123),U_12124)) ) ),
    inference(variable_rename,[status(thm)],[f_3131_1]) ).

fof(f_3131_3,plain,
    ( ! [U_12139,U_12137,U_12135,U_12133,U_12131,U_12129] :
        ( hAPP(c_Set_Oimage(U_12129,U_12135,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12129,U_12135),U_12137),U_12131),U_12139)),U_12133) = hAPP(c_Set_Oimage(U_12129,U_12135,U_12137),U_12133)
        | hBOOL(hAPP(hAPP(c_member(U_12129),U_12131),U_12133)) )
    & ! [U_12138,U_12136,U_12134,U_12132,U_12130,U_12128] :
        ( hAPP(c_Set_Oimage(U_12128,U_12134,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12128,U_12134),U_12136),U_12130),U_12138)),U_12132) = hAPP(hAPP(c_Set_Oinsert(U_12134),U_12138),hAPP(c_Set_Oimage(U_12128,U_12134,U_12136),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12128,tc_HOL_Obool)),U_12132),hAPP(hAPP(c_Set_Oinsert(U_12128),U_12130),c_Orderings_Obot__class_Obot(tc_fun(U_12128,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12128),U_12130),U_12132)) ) ),
    inference(miniscope,[status(thm)],[f_3131_2]) ).

fof(f_3131_4,plain,
    ( ! [U_12129,U_12131,U_12133,U_12135,U_12137,U_12139] :
        ( hAPP(c_Set_Oimage(U_12129,U_12135,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12129,U_12135),U_12137),U_12131),U_12139)),U_12133) = hAPP(c_Set_Oimage(U_12129,U_12135,U_12137),U_12133)
        | hBOOL(hAPP(hAPP(c_member(U_12129),U_12131),U_12133)) )
    & ! [U_12134,U_12128,U_12130,U_12136,U_12132,U_12138] :
        ( hAPP(c_Set_Oimage(U_12128,U_12134,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12128,U_12134),U_12136),U_12130),U_12138)),U_12132) = hAPP(hAPP(c_Set_Oinsert(U_12134),U_12138),hAPP(c_Set_Oimage(U_12128,U_12134,U_12136),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12128,tc_HOL_Obool)),U_12132),hAPP(hAPP(c_Set_Oinsert(U_12128),U_12130),c_Orderings_Obot__class_Obot(tc_fun(U_12128,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12128),U_12130),U_12132)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3131_3]) ).

cnf(f_3131_5,plain,
    ( hAPP(c_Set_Oimage(U_12128,U_12134,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12128,U_12134),U_12136),U_12130),U_12138)),U_12132) = hAPP(hAPP(c_Set_Oinsert(U_12134),U_12138),hAPP(c_Set_Oimage(U_12128,U_12134,U_12136),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12128,tc_HOL_Obool)),U_12132),hAPP(hAPP(c_Set_Oinsert(U_12128),U_12130),c_Orderings_Obot__class_Obot(tc_fun(U_12128,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12128),U_12130),U_12132)) ),
    inference(clausify,[status(thm)],[f_3131_4]) ).

cnf(f_3131_6,plain,
    ( hAPP(c_Set_Oimage(U_12129,U_12135,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12129,U_12135),U_12137),U_12131),U_12139)),U_12133) = hAPP(c_Set_Oimage(U_12129,U_12135,U_12137),U_12133)
    | hBOOL(hAPP(hAPP(c_member(U_12129),U_12131),U_12133)) ),
    inference(clausify,[status(thm)],[f_3131_4]) ).

fof(f_3132_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_3132_2,plain,
    ! [U_12145,U_12144,U_12143,U_12142,U_12141,U_12140] :
      ( hBOOL(hAPP(hAPP(c_member(U_12140),hAPP(c_Fun_Othe__inv__into(U_12140,U_12141,U_12143,U_12142),U_12144)),U_12145))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12140,tc_HOL_Obool)),U_12143),U_12145))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12141),U_12144),hAPP(c_Set_Oimage(U_12140,U_12141,U_12142),U_12143)))
      | ~ c_Fun_Oinj__on(U_12140,U_12141,U_12142,U_12143) ),
    inference(variable_rename,[status(thm)],[f_3132_1]) ).

fof(f_3132_3,plain,
    ! [U_12140,U_12141,U_12142,U_12143,U_12144,U_12145] :
      ( hBOOL(hAPP(hAPP(c_member(U_12140),hAPP(c_Fun_Othe__inv__into(U_12140,U_12141,U_12143,U_12142),U_12144)),U_12145))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12140,tc_HOL_Obool)),U_12143),U_12145))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12141),U_12144),hAPP(c_Set_Oimage(U_12140,U_12141,U_12142),U_12143)))
      | ~ c_Fun_Oinj__on(U_12140,U_12141,U_12142,U_12143) ),
    inference(definitional_conversion,[status(esa)],[f_3132_2]) ).

cnf(f_3132_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12140),hAPP(c_Fun_Othe__inv__into(U_12140,U_12141,U_12143,U_12142),U_12144)),U_12145))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12140,tc_HOL_Obool)),U_12143),U_12145))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12141),U_12144),hAPP(c_Set_Oimage(U_12140,U_12141,U_12142),U_12143)))
    | ~ c_Fun_Oinj__on(U_12140,U_12141,U_12142,U_12143) ),
    inference(clausify,[status(thm)],[f_3132_3]) ).

fof(f_3133_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_3133_2,plain,
    ! [U_12149,U_12148,U_12147,U_12146] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12146,U_12147),U_12148),U_12149),hAPP(U_12148,U_12149)) = U_12148,
    inference(variable_rename,[status(thm)],[f_3133_1]) ).

fof(f_3133_3,plain,
    ! [U_12146,U_12148,U_12147,U_12149] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12146,U_12147),U_12148),U_12149),hAPP(U_12148,U_12149)) = U_12148,
    inference(definitional_conversion,[status(esa)],[f_3133_2]) ).

cnf(f_3133_4,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12146,U_12147),U_12148),U_12149),hAPP(U_12148,U_12149)) = U_12148,
    inference(clausify,[status(thm)],[f_3133_3]) ).

fof(f_3134_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_3134_2,plain,
    ! [U_12150] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12150))),
    inference(variable_rename,[status(thm)],[f_3134_1]) ).

fof(f_3134_3,plain,
    ! [U_12150] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12150))),
    inference(definitional_conversion,[status(esa)],[f_3134_2]) ).

cnf(f_3134_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12150))),
    inference(clausify,[status(thm)],[f_3134_3]) ).

fof(f_3135_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_3135_2,plain,
    ! [U_12153,U_12152,U_12151] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatMost(U_12151),U_12152) = hAPP(c_SetInterval_Oord__class_OatMost(U_12151),U_12153)
          | U_12152 != U_12153 )
        & ( U_12152 = U_12153
          | hAPP(c_SetInterval_Oord__class_OatMost(U_12151),U_12152) != hAPP(c_SetInterval_Oord__class_OatMost(U_12151),U_12153) ) )
      | ~ class_Orderings_Olinorder(U_12151) ),
    inference(variable_rename,[status(thm)],[f_3135_1]) ).

fof(f_3135_3,plain,
    ( ! [U_12151,U_12152,U_12153] :
        ( hAPP(c_SetInterval_Oord__class_OatMost(U_12151),U_12152) = hAPP(c_SetInterval_Oord__class_OatMost(U_12151),U_12153)
        | U_12152 != U_12153
        | ~ sP904(U_12151,U_12152,U_12153) )
    & ! [U_12151,U_12152,U_12153] :
        ( U_12152 = U_12153
        | hAPP(c_SetInterval_Oord__class_OatMost(U_12151),U_12152) != hAPP(c_SetInterval_Oord__class_OatMost(U_12151),U_12153)
        | ~ sP904(U_12151,U_12152,U_12153) )
    & ! [U_12151,U_12152,U_12153] :
        ( sP904(U_12151,U_12152,U_12153)
        | ~ class_Orderings_Olinorder(U_12151) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP904])],[f_3135_2]) ).

cnf(f_3135_4,plain,
    ( sP904(U_12151,U_12152,U_12153)
    | ~ class_Orderings_Olinorder(U_12151) ),
    inference(clausify,[status(thm)],[f_3135_3]) ).

cnf(f_3135_5,plain,
    ( U_12152 = U_12153
    | hAPP(c_SetInterval_Oord__class_OatMost(U_12151),U_12152) != hAPP(c_SetInterval_Oord__class_OatMost(U_12151),U_12153)
    | ~ sP904(U_12151,U_12152,U_12153) ),
    inference(clausify,[status(thm)],[f_3135_3]) ).

cnf(f_3135_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OatMost(U_12151),U_12152) = hAPP(c_SetInterval_Oord__class_OatMost(U_12151),U_12153)
    | U_12152 != U_12153
    | ~ sP904(U_12151,U_12152,U_12153) ),
    inference(clausify,[status(thm)],[f_3135_3]) ).

fof(f_3136_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_3136_2,plain,
    ! [U_12159,U_12158,U_12157,U_12156,U_12155,U_12154] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12156,U_12157),U_12158),U_12155),U_12159),U_12154) = hAPP(U_12158,U_12154)
        | U_12154 = U_12155 )
      & ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12156,U_12157),U_12158),U_12155),U_12159),U_12154) = U_12159
        | U_12154 != U_12155 ) ),
    inference(variable_rename,[status(thm)],[f_3136_1]) ).

fof(f_3136_3,plain,
    ( ! [U_12171,U_12169,U_12167,U_12165,U_12163,U_12161] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12165,U_12167),U_12169),U_12163),U_12171),U_12161) = hAPP(U_12169,U_12161)
        | U_12161 = U_12163 )
    & ! [U_12170,U_12168,U_12166,U_12164,U_12162,U_12160] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12164,U_12166),U_12168),U_12162),U_12170),U_12160) = U_12170
        | U_12160 != U_12162 ) ),
    inference(miniscope,[status(thm)],[f_3136_2]) ).

fof(f_3136_4,plain,
    ( ! [U_12161,U_12163,U_12165,U_12167,U_12169,U_12171] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12165,U_12167),U_12169),U_12163),U_12171),U_12161) = hAPP(U_12169,U_12161)
        | U_12161 = U_12163 )
    & ! [U_12164,U_12162,U_12166,U_12160,U_12168,U_12170] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12164,U_12166),U_12168),U_12162),U_12170),U_12160) = U_12170
        | U_12160 != U_12162 ) ),
    inference(definitional_conversion,[status(esa)],[f_3136_3]) ).

cnf(f_3136_5,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12164,U_12166),U_12168),U_12162),U_12170),U_12160) = U_12170
    | U_12160 != U_12162 ),
    inference(clausify,[status(thm)],[f_3136_4]) ).

cnf(f_3136_6,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12165,U_12167),U_12169),U_12163),U_12171),U_12161) = hAPP(U_12169,U_12161)
    | U_12161 = U_12163 ),
    inference(clausify,[status(thm)],[f_3136_4]) ).

fof(f_3137_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_3137_2,plain,
    ! [U_12176,U_12175,U_12174,U_12173,U_12172] :
      ( ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12172,U_12173),U_12174),U_12175),U_12176) = U_12174
        | hAPP(U_12174,U_12175) != U_12176 )
      & ( hAPP(U_12174,U_12175) = U_12176
        | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12172,U_12173),U_12174),U_12175),U_12176) != U_12174 ) ),
    inference(variable_rename,[status(thm)],[f_3137_1]) ).

fof(f_3137_3,plain,
    ( ! [U_12186,U_12184,U_12182] :
        ( ! [U_12180,U_12178] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12178,U_12180),U_12182),U_12184),U_12186) = U_12182
        | hAPP(U_12182,U_12184) != U_12186 )
    & ! [U_12185,U_12183,U_12181] :
        ( ! [U_12179,U_12177] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12177,U_12179),U_12181),U_12183),U_12185) != U_12181
        | hAPP(U_12181,U_12183) = U_12185 ) ),
    inference(miniscope,[status(thm)],[f_3137_2]) ).

fof(f_3137_4,plain,
    ( ! [U_12186,U_12178,U_12180,U_12182,U_12184] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12178,U_12180),U_12182),U_12184),U_12186) = U_12182
        | hAPP(U_12182,U_12184) != U_12186 )
    & ! [U_12185,U_12181,U_12179,U_12177,U_12183] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12177,U_12179),U_12181),U_12183),U_12185) != U_12181
        | hAPP(U_12181,U_12183) = U_12185 ) ),
    inference(definitional_conversion,[status(esa)],[f_3137_3]) ).

cnf(f_3137_5,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12177,U_12179),U_12181),U_12183),U_12185) != U_12181
    | hAPP(U_12181,U_12183) = U_12185 ),
    inference(clausify,[status(thm)],[f_3137_4]) ).

cnf(f_3137_6,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12178,U_12180),U_12182),U_12184),U_12186) = U_12182
    | hAPP(U_12182,U_12184) != U_12186 ),
    inference(clausify,[status(thm)],[f_3137_4]) ).

fof(f_3138_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_3138_2,plain,
    ! [U_12192,U_12191,U_12190,U_12189,U_12188,U_12187] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12187,U_12188),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12187,U_12188),U_12189),U_12190),U_12191)),U_12190),U_12192) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12187,U_12188),U_12189),U_12190),U_12192),
    inference(variable_rename,[status(thm)],[f_3138_1]) ).

fof(f_3138_3,plain,
    ! [U_12187,U_12188,U_12189,U_12190,U_12191,U_12192] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12187,U_12188),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12187,U_12188),U_12189),U_12190),U_12191)),U_12190),U_12192) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12187,U_12188),U_12189),U_12190),U_12192),
    inference(definitional_conversion,[status(esa)],[f_3138_2]) ).

cnf(f_3138_4,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12187,U_12188),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12187,U_12188),U_12189),U_12190),U_12191)),U_12190),U_12192) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12187,U_12188),U_12189),U_12190),U_12192),
    inference(clausify,[status(thm)],[f_3138_3]) ).

fof(f_3139_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_3139_2,plain,
    ! [U_12197,U_12196,U_12195,U_12194,U_12193] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12193,U_12194),U_12195),U_12196),U_12197),U_12196) = U_12197,
    inference(variable_rename,[status(thm)],[f_3139_1]) ).

fof(f_3139_3,plain,
    ! [U_12193,U_12194,U_12195,U_12196,U_12197] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12193,U_12194),U_12195),U_12196),U_12197),U_12196) = U_12197,
    inference(definitional_conversion,[status(esa)],[f_3139_2]) ).

cnf(f_3139_4,plain,
    hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12193,U_12194),U_12195),U_12196),U_12197),U_12196) = U_12197,
    inference(clausify,[status(thm)],[f_3139_3]) ).

fof(f_3140_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_3140_2,plain,
    ! [U_12203,U_12202,U_12201,U_12200,U_12199,U_12198] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12200,U_12201),U_12202),U_12199),U_12203),U_12198) = hAPP(U_12202,U_12198)
        | U_12198 = U_12199 )
      & ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12200,U_12201),U_12202),U_12199),U_12203),U_12198) = U_12203
        | U_12198 != U_12199 ) ),
    inference(variable_rename,[status(thm)],[f_3140_1]) ).

fof(f_3140_3,plain,
    ( ! [U_12215,U_12213,U_12211,U_12209,U_12207,U_12205] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12209,U_12211),U_12213),U_12207),U_12215),U_12205) = hAPP(U_12213,U_12205)
        | U_12205 = U_12207 )
    & ! [U_12214,U_12212,U_12210,U_12208,U_12206,U_12204] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12208,U_12210),U_12212),U_12206),U_12214),U_12204) = U_12214
        | U_12204 != U_12206 ) ),
    inference(miniscope,[status(thm)],[f_3140_2]) ).

fof(f_3140_4,plain,
    ( ! [U_12205,U_12207,U_12209,U_12211,U_12213,U_12215] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12209,U_12211),U_12213),U_12207),U_12215),U_12205) = hAPP(U_12213,U_12205)
        | U_12205 = U_12207 )
    & ! [U_12210,U_12208,U_12204,U_12206,U_12212,U_12214] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12208,U_12210),U_12212),U_12206),U_12214),U_12204) = U_12214
        | U_12204 != U_12206 ) ),
    inference(definitional_conversion,[status(esa)],[f_3140_3]) ).

cnf(f_3140_5,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12208,U_12210),U_12212),U_12206),U_12214),U_12204) = U_12214
    | U_12204 != U_12206 ),
    inference(clausify,[status(thm)],[f_3140_4]) ).

cnf(f_3140_6,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12209,U_12211),U_12213),U_12207),U_12215),U_12205) = hAPP(U_12213,U_12205)
    | U_12205 = U_12207 ),
    inference(clausify,[status(thm)],[f_3140_4]) ).

fof(f_3141_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_3141_2,plain,
    ! [U_12222,U_12221,U_12220,U_12219,U_12218,U_12217,U_12216] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12218,U_12219),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12218,U_12219),U_12220),U_12216),U_12221)),U_12217),U_12222) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12218,U_12219),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12218,U_12219),U_12220),U_12217),U_12222)),U_12216),U_12221)
      | U_12216 = U_12217 ),
    inference(variable_rename,[status(thm)],[f_3141_1]) ).

fof(f_3141_3,plain,
    ! [U_12216,U_12217,U_12218,U_12219,U_12220,U_12221,U_12222] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12218,U_12219),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12218,U_12219),U_12220),U_12216),U_12221)),U_12217),U_12222) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12218,U_12219),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12218,U_12219),U_12220),U_12217),U_12222)),U_12216),U_12221)
      | U_12216 = U_12217 ),
    inference(definitional_conversion,[status(esa)],[f_3141_2]) ).

cnf(f_3141_4,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12218,U_12219),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12218,U_12219),U_12220),U_12216),U_12221)),U_12217),U_12222) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12218,U_12219),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12218,U_12219),U_12220),U_12217),U_12222)),U_12216),U_12221)
    | U_12216 = U_12217 ),
    inference(clausify,[status(thm)],[f_3141_3]) ).

fof(f_3142_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_3142_2,plain,
    ! [U_12228,U_12227,U_12226,U_12225,U_12224,U_12223] :
      ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12225,U_12226),U_12227),U_12224),U_12228),U_12223) = hAPP(U_12227,U_12223)
      | U_12223 = U_12224 ),
    inference(variable_rename,[status(thm)],[f_3142_1]) ).

fof(f_3142_3,plain,
    ! [U_12226,U_12225,U_12223,U_12224,U_12227,U_12228] :
      ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12225,U_12226),U_12227),U_12224),U_12228),U_12223) = hAPP(U_12227,U_12223)
      | U_12223 = U_12224 ),
    inference(definitional_conversion,[status(esa)],[f_3142_2]) ).

cnf(f_3142_4,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12225,U_12226),U_12227),U_12224),U_12228),U_12223) = hAPP(U_12227,U_12223)
    | U_12223 = U_12224 ),
    inference(clausify,[status(thm)],[f_3142_3]) ).

fof(f_3143_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_3143_2,plain,
    ! [U_12233,U_12232,U_12231,U_12230,U_12229] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12232,U_12233),U_12229),U_12230),U_12231) = U_12229
      | hAPP(U_12229,U_12230) != U_12231 ),
    inference(variable_rename,[status(thm)],[f_3143_1]) ).

fof(f_3143_3,plain,
    ! [U_12230,U_12229,U_12231,U_12232,U_12233] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12232,U_12233),U_12229),U_12230),U_12231) = U_12229
      | hAPP(U_12229,U_12230) != U_12231 ),
    inference(definitional_conversion,[status(esa)],[f_3143_2]) ).

cnf(f_3143_4,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12232,U_12233),U_12229),U_12230),U_12231) = U_12229
    | hAPP(U_12229,U_12230) != U_12231 ),
    inference(clausify,[status(thm)],[f_3143_3]) ).

fof(f_3144_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_3144_2,plain,
    ! [U_12234] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_12234) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12234),
    inference(variable_rename,[status(thm)],[f_3144_1]) ).

fof(f_3144_3,plain,
    ! [U_12234] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_12234) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12234),
    inference(definitional_conversion,[status(esa)],[f_3144_2]) ).

cnf(f_3144_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_12234) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12234),
    inference(clausify,[status(thm)],[f_3144_3]) ).

fof(f_3145_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_3145_2,plain,
    ! [U_12235] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12235)) = hAPP(c_Nat_OSuc,U_12235),
    inference(variable_rename,[status(thm)],[f_3145_1]) ).

fof(f_3145_3,plain,
    ! [U_12235] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12235)) = hAPP(c_Nat_OSuc,U_12235),
    inference(definitional_conversion,[status(esa)],[f_3145_2]) ).

cnf(f_3145_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12235)) = hAPP(c_Nat_OSuc,U_12235),
    inference(clausify,[status(thm)],[f_3145_3]) ).

fof(f_3146_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_3146_2,plain,
    ! [U_12236] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12236)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12236)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12236)),
    inference(variable_rename,[status(thm)],[f_3146_1]) ).

fof(f_3146_3,plain,
    ! [U_12236] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12236)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12236)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12236)),
    inference(definitional_conversion,[status(esa)],[f_3146_2]) ).

cnf(f_3146_4,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12236)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12236)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12236)),
    inference(clausify,[status(thm)],[f_3146_3]) ).

fof(f_3147_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_3147_2,plain,
    ! [U_12239,U_12238,U_12237] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_12237),U_12238),hAPP(c_SetInterval_Oord__class_OatMost(U_12237),U_12239)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12237),U_12238),U_12239)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12237),U_12238),U_12239))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12237),U_12238),hAPP(c_SetInterval_Oord__class_OatMost(U_12237),U_12239))) ) )
      | ~ class_Orderings_Oord(U_12237) ),
    inference(variable_rename,[status(thm)],[f_3147_1]) ).

fof(f_3147_3,plain,
    ( ! [U_12237,U_12238,U_12239] :
        ( hBOOL(hAPP(hAPP(c_member(U_12237),U_12238),hAPP(c_SetInterval_Oord__class_OatMost(U_12237),U_12239)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12237),U_12238),U_12239))
        | ~ sP905(U_12237,U_12238,U_12239) )
    & ! [U_12237,U_12238,U_12239] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12237),U_12238),U_12239))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12237),U_12238),hAPP(c_SetInterval_Oord__class_OatMost(U_12237),U_12239)))
        | ~ sP905(U_12237,U_12238,U_12239) )
    & ! [U_12237,U_12238,U_12239] :
        ( sP905(U_12237,U_12238,U_12239)
        | ~ class_Orderings_Oord(U_12237) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP905])],[f_3147_2]) ).

cnf(f_3147_4,plain,
    ( sP905(U_12237,U_12238,U_12239)
    | ~ class_Orderings_Oord(U_12237) ),
    inference(clausify,[status(thm)],[f_3147_3]) ).

cnf(f_3147_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12237),U_12238),U_12239))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12237),U_12238),hAPP(c_SetInterval_Oord__class_OatMost(U_12237),U_12239)))
    | ~ sP905(U_12237,U_12238,U_12239) ),
    inference(clausify,[status(thm)],[f_3147_3]) ).

cnf(f_3147_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12237),U_12238),hAPP(c_SetInterval_Oord__class_OatMost(U_12237),U_12239)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12237),U_12238),U_12239))
    | ~ sP905(U_12237,U_12238,U_12239) ),
    inference(clausify,[status(thm)],[f_3147_3]) ).

fof(f_3148_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_3148_2,plain,
    ! [U_12242,U_12241,U_12240] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12240,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12240),U_12241)),hAPP(c_SetInterval_Oord__class_OatMost(U_12240),U_12242)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12240),U_12241),U_12242)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12240),U_12241),U_12242))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12240,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12240),U_12241)),hAPP(c_SetInterval_Oord__class_OatMost(U_12240),U_12242))) ) )
      | ~ class_Orderings_Oorder(U_12240) ),
    inference(variable_rename,[status(thm)],[f_3148_1]) ).

fof(f_3148_3,plain,
    ( ! [U_12241,U_12242,U_12240] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12240,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12240),U_12241)),hAPP(c_SetInterval_Oord__class_OatMost(U_12240),U_12242)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12240),U_12241),U_12242))
        | ~ sP906(U_12241,U_12242,U_12240) )
    & ! [U_12241,U_12242,U_12240] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12240),U_12241),U_12242))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12240,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12240),U_12241)),hAPP(c_SetInterval_Oord__class_OatMost(U_12240),U_12242)))
        | ~ sP906(U_12241,U_12242,U_12240) )
    & ! [U_12241,U_12242,U_12240] :
        ( sP906(U_12241,U_12242,U_12240)
        | ~ class_Orderings_Oorder(U_12240) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP906])],[f_3148_2]) ).

cnf(f_3148_4,plain,
    ( sP906(U_12241,U_12242,U_12240)
    | ~ class_Orderings_Oorder(U_12240) ),
    inference(clausify,[status(thm)],[f_3148_3]) ).

cnf(f_3148_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12240),U_12241),U_12242))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12240,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12240),U_12241)),hAPP(c_SetInterval_Oord__class_OatMost(U_12240),U_12242)))
    | ~ sP906(U_12241,U_12242,U_12240) ),
    inference(clausify,[status(thm)],[f_3148_3]) ).

cnf(f_3148_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12240,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12240),U_12241)),hAPP(c_SetInterval_Oord__class_OatMost(U_12240),U_12242)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12240),U_12241),U_12242))
    | ~ sP906(U_12241,U_12242,U_12240) ),
    inference(clausify,[status(thm)],[f_3148_3]) ).

fof(f_3149_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_3149_2,plain,
    ! [U_12246,U_12245,U_12244,U_12243] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12243,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12244)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_12243,tc_HOL_Obool),tc_Nat_Onat),U_12245),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12246))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12243,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12246,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12244),U_12246))),U_12245),
    inference(variable_rename,[status(thm)],[f_3149_1]) ).

fof(f_3149_3,plain,
    ! [U_12244,U_12243,U_12245,U_12246] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12243,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12244)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_12243,tc_HOL_Obool),tc_Nat_Onat),U_12245),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12246))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12243,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12246,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12244),U_12246))),U_12245),
    inference(definitional_conversion,[status(esa)],[f_3149_2]) ).

cnf(f_3149_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12243,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12244)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_12243,tc_HOL_Obool),tc_Nat_Onat),U_12245),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12246))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12243,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12246,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12244),U_12246))),U_12245),
    inference(clausify,[status(thm)],[f_3149_3]) ).

fof(f_3150_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_3150_2,plain,
    ! [U_12252,U_12251,U_12250,U_12249,U_12248,U_12247] :
      ( hAPP(c_Fun_Othe__inv__into(U_12247,U_12248,U_12250,U_12249),U_12252) = U_12251
      | ~ hBOOL(hAPP(hAPP(c_member(U_12247),U_12251),U_12250))
      | hAPP(U_12249,U_12251) != U_12252
      | ~ c_Fun_Oinj__on(U_12247,U_12248,U_12249,U_12250) ),
    inference(variable_rename,[status(thm)],[f_3150_1]) ).

fof(f_3150_3,plain,
    ! [U_12248,U_12247,U_12249,U_12250,U_12251,U_12252] :
      ( hAPP(c_Fun_Othe__inv__into(U_12247,U_12248,U_12250,U_12249),U_12252) = U_12251
      | ~ hBOOL(hAPP(hAPP(c_member(U_12247),U_12251),U_12250))
      | hAPP(U_12249,U_12251) != U_12252
      | ~ c_Fun_Oinj__on(U_12247,U_12248,U_12249,U_12250) ),
    inference(definitional_conversion,[status(esa)],[f_3150_2]) ).

cnf(f_3150_4,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_12247,U_12248,U_12250,U_12249),U_12252) = U_12251
    | ~ hBOOL(hAPP(hAPP(c_member(U_12247),U_12251),U_12250))
    | hAPP(U_12249,U_12251) != U_12252
    | ~ c_Fun_Oinj__on(U_12247,U_12248,U_12249,U_12250) ),
    inference(clausify,[status(thm)],[f_3150_3]) ).

fof(f_3151_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_3151_2,plain,
    ! [U_12257,U_12256,U_12255,U_12254,U_12253] :
      ( hAPP(c_Fun_Othe__inv__into(U_12253,U_12254,U_12256,U_12255),hAPP(U_12255,U_12257)) = U_12257
      | ~ hBOOL(hAPP(hAPP(c_member(U_12253),U_12257),U_12256))
      | ~ c_Fun_Oinj__on(U_12253,U_12254,U_12255,U_12256) ),
    inference(variable_rename,[status(thm)],[f_3151_1]) ).

fof(f_3151_3,plain,
    ! [U_12253,U_12254,U_12255,U_12256,U_12257] :
      ( hAPP(c_Fun_Othe__inv__into(U_12253,U_12254,U_12256,U_12255),hAPP(U_12255,U_12257)) = U_12257
      | ~ hBOOL(hAPP(hAPP(c_member(U_12253),U_12257),U_12256))
      | ~ c_Fun_Oinj__on(U_12253,U_12254,U_12255,U_12256) ),
    inference(definitional_conversion,[status(esa)],[f_3151_2]) ).

cnf(f_3151_4,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_12253,U_12254,U_12256,U_12255),hAPP(U_12255,U_12257)) = U_12257
    | ~ hBOOL(hAPP(hAPP(c_member(U_12253),U_12257),U_12256))
    | ~ c_Fun_Oinj__on(U_12253,U_12254,U_12255,U_12256) ),
    inference(clausify,[status(thm)],[f_3151_3]) ).

fof(f_3152_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_3152_2,plain,
    ! [U_12261,U_12260,U_12259,U_12258] :
      ( c_Fun_Oinj__on(U_12259,U_12258,c_Fun_Othe__inv__into(U_12258,U_12259,U_12261,U_12260),hAPP(c_Set_Oimage(U_12258,U_12259,U_12260),U_12261))
      | ~ c_Fun_Oinj__on(U_12258,U_12259,U_12260,U_12261) ),
    inference(variable_rename,[status(thm)],[f_3152_1]) ).

fof(f_3152_3,plain,
    ! [U_12259,U_12258,U_12260,U_12261] :
      ( c_Fun_Oinj__on(U_12259,U_12258,c_Fun_Othe__inv__into(U_12258,U_12259,U_12261,U_12260),hAPP(c_Set_Oimage(U_12258,U_12259,U_12260),U_12261))
      | ~ c_Fun_Oinj__on(U_12258,U_12259,U_12260,U_12261) ),
    inference(definitional_conversion,[status(esa)],[f_3152_2]) ).

cnf(f_3152_4,plain,
    ( c_Fun_Oinj__on(U_12259,U_12258,c_Fun_Othe__inv__into(U_12258,U_12259,U_12261,U_12260),hAPP(c_Set_Oimage(U_12258,U_12259,U_12260),U_12261))
    | ~ c_Fun_Oinj__on(U_12258,U_12259,U_12260,U_12261) ),
    inference(clausify,[status(thm)],[f_3152_3]) ).

fof(f_3153_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_3153_2,plain,
    ! [U_12265,U_12264,U_12263,U_12262] :
      ( hAPP(c_Set_Oimage(U_12263,U_12262,c_Fun_Othe__inv__into(U_12262,U_12263,U_12265,U_12264)),hAPP(c_Set_Oimage(U_12262,U_12263,U_12264),U_12265)) = U_12265
      | ~ c_Fun_Oinj__on(U_12262,U_12263,U_12264,U_12265) ),
    inference(variable_rename,[status(thm)],[f_3153_1]) ).

fof(f_3153_3,plain,
    ! [U_12262,U_12263,U_12264,U_12265] :
      ( hAPP(c_Set_Oimage(U_12263,U_12262,c_Fun_Othe__inv__into(U_12262,U_12263,U_12265,U_12264)),hAPP(c_Set_Oimage(U_12262,U_12263,U_12264),U_12265)) = U_12265
      | ~ c_Fun_Oinj__on(U_12262,U_12263,U_12264,U_12265) ),
    inference(definitional_conversion,[status(esa)],[f_3153_2]) ).

cnf(f_3153_4,plain,
    ( hAPP(c_Set_Oimage(U_12263,U_12262,c_Fun_Othe__inv__into(U_12262,U_12263,U_12265,U_12264)),hAPP(c_Set_Oimage(U_12262,U_12263,U_12264),U_12265)) = U_12265
    | ~ c_Fun_Oinj__on(U_12262,U_12263,U_12264,U_12265) ),
    inference(clausify,[status(thm)],[f_3153_3]) ).

fof(f_3154_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_3154_2,plain,
    ! [U_12271,U_12270,U_12269,U_12268,U_12267,U_12266] :
      ( c_Fun_Oinj__on(U_12266,U_12267,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12266,U_12267),U_12268),U_12271),U_12270),U_12269)
      | hBOOL(hAPP(hAPP(c_member(U_12267),U_12270),hAPP(c_Set_Oimage(U_12266,U_12267,U_12268),U_12269)))
      | ~ c_Fun_Oinj__on(U_12266,U_12267,U_12268,U_12269) ),
    inference(variable_rename,[status(thm)],[f_3154_1]) ).

fof(f_3154_3,plain,
    ! [U_12267,U_12266,U_12268,U_12269,U_12270,U_12271] :
      ( c_Fun_Oinj__on(U_12266,U_12267,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12266,U_12267),U_12268),U_12271),U_12270),U_12269)
      | hBOOL(hAPP(hAPP(c_member(U_12267),U_12270),hAPP(c_Set_Oimage(U_12266,U_12267,U_12268),U_12269)))
      | ~ c_Fun_Oinj__on(U_12266,U_12267,U_12268,U_12269) ),
    inference(definitional_conversion,[status(esa)],[f_3154_2]) ).

cnf(f_3154_4,plain,
    ( c_Fun_Oinj__on(U_12266,U_12267,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12266,U_12267),U_12268),U_12271),U_12270),U_12269)
    | hBOOL(hAPP(hAPP(c_member(U_12267),U_12270),hAPP(c_Set_Oimage(U_12266,U_12267,U_12268),U_12269)))
    | ~ c_Fun_Oinj__on(U_12266,U_12267,U_12268,U_12269) ),
    inference(clausify,[status(thm)],[f_3154_3]) ).

fof(f_3155_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_3155_2,plain,
    ! [U_12276,U_12275,U_12274,U_12273,U_12272] : hAPP(c_Fun_Othe__inv__into(U_12272,U_12273,U_12274,U_12275),U_12276) = c_HOL_OThe(U_12272,hAPP(hAPP(c_COMBS(U_12272,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12272),c_fconj),hAPP(hAPP(c_COMBC(U_12272,tc_fun(U_12272,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12272)),U_12274))),hAPP(hAPP(c_COMBC(U_12272,U_12273,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12273,tc_fun(U_12273,tc_HOL_Obool),U_12272),c_fequal),U_12275)),U_12276))),
    inference(variable_rename,[status(thm)],[f_3155_1]) ).

fof(f_3155_3,plain,
    ! [U_12272,U_12273,U_12274,U_12275,U_12276] : hAPP(c_Fun_Othe__inv__into(U_12272,U_12273,U_12274,U_12275),U_12276) = c_HOL_OThe(U_12272,hAPP(hAPP(c_COMBS(U_12272,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12272),c_fconj),hAPP(hAPP(c_COMBC(U_12272,tc_fun(U_12272,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12272)),U_12274))),hAPP(hAPP(c_COMBC(U_12272,U_12273,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12273,tc_fun(U_12273,tc_HOL_Obool),U_12272),c_fequal),U_12275)),U_12276))),
    inference(definitional_conversion,[status(esa)],[f_3155_2]) ).

cnf(f_3155_4,plain,
    hAPP(c_Fun_Othe__inv__into(U_12272,U_12273,U_12274,U_12275),U_12276) = c_HOL_OThe(U_12272,hAPP(hAPP(c_COMBS(U_12272,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12272),c_fconj),hAPP(hAPP(c_COMBC(U_12272,tc_fun(U_12272,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12272)),U_12274))),hAPP(hAPP(c_COMBC(U_12272,U_12273,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12273,tc_fun(U_12273,tc_HOL_Obool),U_12272),c_fequal),U_12275)),U_12276))),
    inference(clausify,[status(thm)],[f_3155_3]) ).

fof(f_3156_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_3156_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_3156_1]) ).

cnf(f_3156_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_3156_2]) ).

fof(f_3157_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_3157_2,plain,
    ! [U_12280,U_12279,U_12278,U_12277] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12277,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12277),U_12278)),c_SetInterval_Oord__class_OatLeastAtMost(U_12277,U_12279,U_12280)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12277,U_12279,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12277),U_12278),U_12280))
      | ~ class_Orderings_Olinorder(U_12277) ),
    inference(variable_rename,[status(thm)],[f_3157_1]) ).

fof(f_3157_3,plain,
    ! [U_12277,U_12278,U_12279,U_12280] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12277,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12277),U_12278)),c_SetInterval_Oord__class_OatLeastAtMost(U_12277,U_12279,U_12280)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12277,U_12279,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12277),U_12278),U_12280))
      | ~ class_Orderings_Olinorder(U_12277) ),
    inference(definitional_conversion,[status(esa)],[f_3157_2]) ).

cnf(f_3157_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12277,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12277),U_12278)),c_SetInterval_Oord__class_OatLeastAtMost(U_12277,U_12279,U_12280)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12277,U_12279,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12277),U_12278),U_12280))
    | ~ class_Orderings_Olinorder(U_12277) ),
    inference(clausify,[status(thm)],[f_3157_3]) ).

fof(f_3158_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_3158_2,plain,
    ! [U_12284,U_12283,U_12282,U_12281] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12281,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12281,U_12282,U_12283)),hAPP(c_SetInterval_Oord__class_OatMost(U_12281),U_12284)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12281,U_12282,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12281),U_12283),U_12284))
      | ~ class_Orderings_Olinorder(U_12281) ),
    inference(variable_rename,[status(thm)],[f_3158_1]) ).

fof(f_3158_3,plain,
    ! [U_12281,U_12282,U_12283,U_12284] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12281,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12281,U_12282,U_12283)),hAPP(c_SetInterval_Oord__class_OatMost(U_12281),U_12284)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12281,U_12282,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12281),U_12283),U_12284))
      | ~ class_Orderings_Olinorder(U_12281) ),
    inference(definitional_conversion,[status(esa)],[f_3158_2]) ).

cnf(f_3158_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12281,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12281,U_12282,U_12283)),hAPP(c_SetInterval_Oord__class_OatMost(U_12281),U_12284)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12281,U_12282,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12281),U_12283),U_12284))
    | ~ class_Orderings_Olinorder(U_12281) ),
    inference(clausify,[status(thm)],[f_3158_3]) ).

fof(f_3159_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_3159_2,plain,
    ! [U_12287,U_12286,U_12285] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12285,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12285),U_12286)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12285,U_12286,U_12287)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12285),U_12287)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12285),U_12286),U_12287))
      | ~ class_Orderings_Olinorder(U_12285) ),
    inference(variable_rename,[status(thm)],[f_3159_1]) ).

fof(f_3159_3,plain,
    ! [U_12285,U_12286,U_12287] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12285,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12285),U_12286)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12285,U_12286,U_12287)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12285),U_12287)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12285),U_12286),U_12287))
      | ~ class_Orderings_Olinorder(U_12285) ),
    inference(definitional_conversion,[status(esa)],[f_3159_2]) ).

cnf(f_3159_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12285,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12285),U_12286)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12285,U_12286,U_12287)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12285),U_12287)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12285),U_12286),U_12287))
    | ~ class_Orderings_Olinorder(U_12285) ),
    inference(clausify,[status(thm)],[f_3159_3]) ).

fof(f_3160_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_3160_2,plain,
    ! [U_12290,U_12289,U_12288] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12288,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12288),U_12289)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12288,U_12289,U_12290)) = c_Orderings_Obot__class_Obot(tc_fun(U_12288,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12288) ),
    inference(variable_rename,[status(thm)],[f_3160_1]) ).

fof(f_3160_3,plain,
    ! [U_12288,U_12289,U_12290] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12288,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12288),U_12289)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12288,U_12289,U_12290)) = c_Orderings_Obot__class_Obot(tc_fun(U_12288,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12288) ),
    inference(definitional_conversion,[status(esa)],[f_3160_2]) ).

cnf(f_3160_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12288,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12288),U_12289)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12288,U_12289,U_12290)) = c_Orderings_Obot__class_Obot(tc_fun(U_12288,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12288) ),
    inference(clausify,[status(thm)],[f_3160_3]) ).

fof(f_3161_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_3161_2,plain,
    ! [U_12293,U_12292,U_12291] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12291,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12291),U_12292)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12291,U_12292,U_12293)) = c_Orderings_Obot__class_Obot(tc_fun(U_12291,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12291) ),
    inference(variable_rename,[status(thm)],[f_3161_1]) ).

fof(f_3161_3,plain,
    ! [U_12291,U_12292,U_12293] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12291,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12291),U_12292)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12291,U_12292,U_12293)) = c_Orderings_Obot__class_Obot(tc_fun(U_12291,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12291) ),
    inference(definitional_conversion,[status(esa)],[f_3161_2]) ).

cnf(f_3161_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12291,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12291),U_12292)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12291,U_12292,U_12293)) = c_Orderings_Obot__class_Obot(tc_fun(U_12291,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12291) ),
    inference(clausify,[status(thm)],[f_3161_3]) ).

fof(f_3162_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_3162_2,plain,
    ! [U_12298,U_12297,U_12296,U_12295,U_12294] :
      ( hAPP(U_12296,hAPP(c_Fun_Othe__inv__into(U_12294,U_12295,U_12297,U_12296),U_12298)) = U_12298
      | ~ hBOOL(hAPP(hAPP(c_member(U_12295),U_12298),hAPP(c_Set_Oimage(U_12294,U_12295,U_12296),U_12297)))
      | ~ c_Fun_Oinj__on(U_12294,U_12295,U_12296,U_12297) ),
    inference(variable_rename,[status(thm)],[f_3162_1]) ).

fof(f_3162_3,plain,
    ! [U_12294,U_12295,U_12296,U_12297,U_12298] :
      ( hAPP(U_12296,hAPP(c_Fun_Othe__inv__into(U_12294,U_12295,U_12297,U_12296),U_12298)) = U_12298
      | ~ hBOOL(hAPP(hAPP(c_member(U_12295),U_12298),hAPP(c_Set_Oimage(U_12294,U_12295,U_12296),U_12297)))
      | ~ c_Fun_Oinj__on(U_12294,U_12295,U_12296,U_12297) ),
    inference(definitional_conversion,[status(esa)],[f_3162_2]) ).

cnf(f_3162_4,plain,
    ( hAPP(U_12296,hAPP(c_Fun_Othe__inv__into(U_12294,U_12295,U_12297,U_12296),U_12298)) = U_12298
    | ~ hBOOL(hAPP(hAPP(c_member(U_12295),U_12298),hAPP(c_Set_Oimage(U_12294,U_12295,U_12296),U_12297)))
    | ~ c_Fun_Oinj__on(U_12294,U_12295,U_12296,U_12297) ),
    inference(clausify,[status(thm)],[f_3162_3]) ).

fof(f_3163_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_3163_2,plain,
    ! [U_12301,U_12300,U_12299] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12299,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12300)),U_12301) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12299,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12299,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_12300)),U_12301)),hAPP(U_12301,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3163_1]) ).

fof(f_3163_3,plain,
    ! [U_12299,U_12300,U_12301] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12299,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12300)),U_12301) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12299,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12299,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_12300)),U_12301)),hAPP(U_12301,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_3163_2]) ).

cnf(f_3163_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12299,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12300)),U_12301) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12299,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12299,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_12300)),U_12301)),hAPP(U_12301,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3163_3]) ).

fof(f_3164_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_3164_2,plain,
    ! [U_12306,U_12305,U_12304,U_12303,U_12302] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12302,tc_Option_Ooption(U_12303)),U_12304),U_12305),hAPP(c_Option_Ooption_OSome(U_12303),U_12306)) != hAPP(c_COMBK(tc_Option_Ooption(U_12303),U_12302),c_Option_Ooption_ONone(U_12303)),
    inference(variable_rename,[status(thm)],[f_3164_1]) ).

fof(f_3164_3,plain,
    ! [U_12302,U_12303,U_12304,U_12305,U_12306] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12302,tc_Option_Ooption(U_12303)),U_12304),U_12305),hAPP(c_Option_Ooption_OSome(U_12303),U_12306)) != hAPP(c_COMBK(tc_Option_Ooption(U_12303),U_12302),c_Option_Ooption_ONone(U_12303)),
    inference(definitional_conversion,[status(esa)],[f_3164_2]) ).

cnf(f_3164_4,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12302,tc_Option_Ooption(U_12303)),U_12304),U_12305),hAPP(c_Option_Ooption_OSome(U_12303),U_12306)) != hAPP(c_COMBK(tc_Option_Ooption(U_12303),U_12302),c_Option_Ooption_ONone(U_12303)),
    inference(clausify,[status(thm)],[f_3164_3]) ).

fof(f_3165_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_3165_2,plain,
    ! [U_12307] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12307) = 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_12307)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12307)) ),
    inference(variable_rename,[status(thm)],[f_3165_1]) ).

fof(f_3165_3,plain,
    ! [U_12307] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12307) = 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_12307)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12307)) ),
    inference(definitional_conversion,[status(esa)],[f_3165_2]) ).

cnf(f_3165_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12307) = 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_12307)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12307)) ),
    inference(clausify,[status(thm)],[f_3165_3]) ).

fof(f_3166_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_3166_2,plain,
    ! [U_12313,U_12312,U_12311,U_12310,U_12309,U_12308] :
      ( hAPP(c_Set_Oimage(U_12308,tc_Option_Ooption(U_12311),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12308,tc_Option_Ooption(U_12311)),U_12312),U_12309),hAPP(c_Option_Ooption_OSome(U_12311),U_12313))),U_12310) = hAPP(c_Set_Oimage(U_12308,tc_Option_Ooption(U_12311),U_12312),U_12310)
      | hBOOL(hAPP(hAPP(c_member(U_12308),U_12309),U_12310)) ),
    inference(variable_rename,[status(thm)],[f_3166_1]) ).

fof(f_3166_3,plain,
    ! [U_12308,U_12309,U_12310,U_12311,U_12312,U_12313] :
      ( hAPP(c_Set_Oimage(U_12308,tc_Option_Ooption(U_12311),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12308,tc_Option_Ooption(U_12311)),U_12312),U_12309),hAPP(c_Option_Ooption_OSome(U_12311),U_12313))),U_12310) = hAPP(c_Set_Oimage(U_12308,tc_Option_Ooption(U_12311),U_12312),U_12310)
      | hBOOL(hAPP(hAPP(c_member(U_12308),U_12309),U_12310)) ),
    inference(definitional_conversion,[status(esa)],[f_3166_2]) ).

cnf(f_3166_4,plain,
    ( hAPP(c_Set_Oimage(U_12308,tc_Option_Ooption(U_12311),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12308,tc_Option_Ooption(U_12311)),U_12312),U_12309),hAPP(c_Option_Ooption_OSome(U_12311),U_12313))),U_12310) = hAPP(c_Set_Oimage(U_12308,tc_Option_Ooption(U_12311),U_12312),U_12310)
    | hBOOL(hAPP(hAPP(c_member(U_12308),U_12309),U_12310)) ),
    inference(clausify,[status(thm)],[f_3166_3]) ).

fof(f_3167_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_3167_2,plain,
    ! [U_12314] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12314))),
    inference(variable_rename,[status(thm)],[f_3167_1]) ).

fof(f_3167_3,plain,
    ! [U_12314] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12314))),
    inference(definitional_conversion,[status(esa)],[f_3167_2]) ).

cnf(f_3167_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12314))),
    inference(clausify,[status(thm)],[f_3167_3]) ).

fof(f_3168_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_3168_2,plain,
    ! [U_12315] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12315)) = U_12315,
    inference(variable_rename,[status(thm)],[f_3168_1]) ).

fof(f_3168_3,plain,
    ! [U_12315] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12315)) = U_12315,
    inference(definitional_conversion,[status(esa)],[f_3168_2]) ).

cnf(f_3168_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12315)) = U_12315,
    inference(clausify,[status(thm)],[f_3168_3]) ).

fof(f_3169_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_3169_2,plain,
    ! [U_12318,U_12317,U_12316] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(U_12316),U_12317) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12316),U_12318)
          | U_12317 != U_12318 )
        & ( U_12317 = U_12318
          | hAPP(c_SetInterval_Oord__class_OlessThan(U_12316),U_12317) != hAPP(c_SetInterval_Oord__class_OlessThan(U_12316),U_12318) ) )
      | ~ class_Orderings_Olinorder(U_12316) ),
    inference(variable_rename,[status(thm)],[f_3169_1]) ).

fof(f_3169_3,plain,
    ( ! [U_12316,U_12317,U_12318] :
        ( hAPP(c_SetInterval_Oord__class_OlessThan(U_12316),U_12317) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12316),U_12318)
        | U_12317 != U_12318
        | ~ sP907(U_12316,U_12317,U_12318) )
    & ! [U_12316,U_12317,U_12318] :
        ( U_12317 = U_12318
        | hAPP(c_SetInterval_Oord__class_OlessThan(U_12316),U_12317) != hAPP(c_SetInterval_Oord__class_OlessThan(U_12316),U_12318)
        | ~ sP907(U_12316,U_12317,U_12318) )
    & ! [U_12316,U_12317,U_12318] :
        ( sP907(U_12316,U_12317,U_12318)
        | ~ class_Orderings_Olinorder(U_12316) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP907])],[f_3169_2]) ).

cnf(f_3169_4,plain,
    ( sP907(U_12316,U_12317,U_12318)
    | ~ class_Orderings_Olinorder(U_12316) ),
    inference(clausify,[status(thm)],[f_3169_3]) ).

cnf(f_3169_5,plain,
    ( U_12317 = U_12318
    | hAPP(c_SetInterval_Oord__class_OlessThan(U_12316),U_12317) != hAPP(c_SetInterval_Oord__class_OlessThan(U_12316),U_12318)
    | ~ sP907(U_12316,U_12317,U_12318) ),
    inference(clausify,[status(thm)],[f_3169_3]) ).

cnf(f_3169_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OlessThan(U_12316),U_12317) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12316),U_12318)
    | U_12317 != U_12318
    | ~ sP907(U_12316,U_12317,U_12318) ),
    inference(clausify,[status(thm)],[f_3169_3]) ).

fof(f_3170_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_3170_2,plain,
    ! [U_12319] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12319) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12319),
    inference(variable_rename,[status(thm)],[f_3170_1]) ).

fof(f_3170_3,plain,
    ! [U_12319] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12319) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12319),
    inference(definitional_conversion,[status(esa)],[f_3170_2]) ).

cnf(f_3170_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12319) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12319),
    inference(clausify,[status(thm)],[f_3170_3]) ).

fof(f_3171_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_3171_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_3171_1]) ).

cnf(f_3171_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_3171_2]) ).

fof(f_3172_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_3172_2,plain,
    ! [U_12320] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12320)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12320),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12320)),
    inference(variable_rename,[status(thm)],[f_3172_1]) ).

fof(f_3172_3,plain,
    ! [U_12320] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12320)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12320),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12320)),
    inference(definitional_conversion,[status(esa)],[f_3172_2]) ).

cnf(f_3172_4,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12320)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12320),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12320)),
    inference(clausify,[status(thm)],[f_3172_3]) ).

fof(f_3173_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_3173_2,plain,
    ! [U_12321] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12321)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12321),
    inference(variable_rename,[status(thm)],[f_3173_1]) ).

fof(f_3173_3,plain,
    ! [U_12321] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12321)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12321),
    inference(definitional_conversion,[status(esa)],[f_3173_2]) ).

cnf(f_3173_4,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12321)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12321),
    inference(clausify,[status(thm)],[f_3173_3]) ).

fof(f_3174_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_3174_2,plain,
    ! [U_12324,U_12323,U_12322] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_12322),U_12323),hAPP(c_SetInterval_Oord__class_OlessThan(U_12322),U_12324)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12322),U_12323),U_12324)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12322),U_12323),U_12324))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12322),U_12323),hAPP(c_SetInterval_Oord__class_OlessThan(U_12322),U_12324))) ) )
      | ~ class_Orderings_Oord(U_12322) ),
    inference(variable_rename,[status(thm)],[f_3174_1]) ).

fof(f_3174_3,plain,
    ( ! [U_12322,U_12323,U_12324] :
        ( hBOOL(hAPP(hAPP(c_member(U_12322),U_12323),hAPP(c_SetInterval_Oord__class_OlessThan(U_12322),U_12324)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12322),U_12323),U_12324))
        | ~ sP908(U_12322,U_12323,U_12324) )
    & ! [U_12322,U_12323,U_12324] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12322),U_12323),U_12324))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12322),U_12323),hAPP(c_SetInterval_Oord__class_OlessThan(U_12322),U_12324)))
        | ~ sP908(U_12322,U_12323,U_12324) )
    & ! [U_12322,U_12323,U_12324] :
        ( sP908(U_12322,U_12323,U_12324)
        | ~ class_Orderings_Oord(U_12322) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP908])],[f_3174_2]) ).

cnf(f_3174_4,plain,
    ( sP908(U_12322,U_12323,U_12324)
    | ~ class_Orderings_Oord(U_12322) ),
    inference(clausify,[status(thm)],[f_3174_3]) ).

cnf(f_3174_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12322),U_12323),U_12324))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12322),U_12323),hAPP(c_SetInterval_Oord__class_OlessThan(U_12322),U_12324)))
    | ~ sP908(U_12322,U_12323,U_12324) ),
    inference(clausify,[status(thm)],[f_3174_3]) ).

cnf(f_3174_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12322),U_12323),hAPP(c_SetInterval_Oord__class_OlessThan(U_12322),U_12324)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12322),U_12323),U_12324))
    | ~ sP908(U_12322,U_12323,U_12324) ),
    inference(clausify,[status(thm)],[f_3174_3]) ).

fof(f_3175_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_3175_2,plain,
    ! [U_12327,U_12326,U_12325] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12325,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12325),U_12326)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12325),U_12327)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12325),U_12326),U_12327)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12325),U_12326),U_12327))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12325,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12325),U_12326)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12325),U_12327))) ) )
      | ~ class_Orderings_Olinorder(U_12325) ),
    inference(variable_rename,[status(thm)],[f_3175_1]) ).

fof(f_3175_3,plain,
    ( ! [U_12327,U_12326,U_12325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12325,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12325),U_12326)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12325),U_12327)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12325),U_12326),U_12327))
        | ~ sP909(U_12327,U_12326,U_12325) )
    & ! [U_12327,U_12326,U_12325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12325),U_12326),U_12327))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12325,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12325),U_12326)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12325),U_12327)))
        | ~ sP909(U_12327,U_12326,U_12325) )
    & ! [U_12327,U_12326,U_12325] :
        ( sP909(U_12327,U_12326,U_12325)
        | ~ class_Orderings_Olinorder(U_12325) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP909])],[f_3175_2]) ).

cnf(f_3175_4,plain,
    ( sP909(U_12327,U_12326,U_12325)
    | ~ class_Orderings_Olinorder(U_12325) ),
    inference(clausify,[status(thm)],[f_3175_3]) ).

cnf(f_3175_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12325),U_12326),U_12327))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12325,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12325),U_12326)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12325),U_12327)))
    | ~ sP909(U_12327,U_12326,U_12325) ),
    inference(clausify,[status(thm)],[f_3175_3]) ).

cnf(f_3175_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12325,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12325),U_12326)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12325),U_12327)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12325),U_12326),U_12327))
    | ~ sP909(U_12327,U_12326,U_12325) ),
    inference(clausify,[status(thm)],[f_3175_3]) ).

fof(f_3176_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_3176_2,plain,
    ! [U_12330,U_12329,U_12328] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12328,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12328),U_12329)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12328),U_12330)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12328),U_12329),U_12330)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12328),U_12329),U_12330))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12328,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12328),U_12329)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12328),U_12330))) ) )
      | ~ class_Orderings_Olinorder(U_12328) ),
    inference(variable_rename,[status(thm)],[f_3176_1]) ).

fof(f_3176_3,plain,
    ( ! [U_12329,U_12328,U_12330] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12328,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12328),U_12329)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12328),U_12330)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12328),U_12329),U_12330))
        | ~ sP910(U_12329,U_12328,U_12330) )
    & ! [U_12329,U_12328,U_12330] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12328),U_12329),U_12330))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12328,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12328),U_12329)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12328),U_12330)))
        | ~ sP910(U_12329,U_12328,U_12330) )
    & ! [U_12329,U_12328,U_12330] :
        ( sP910(U_12329,U_12328,U_12330)
        | ~ class_Orderings_Olinorder(U_12328) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP910])],[f_3176_2]) ).

cnf(f_3176_4,plain,
    ( sP910(U_12329,U_12328,U_12330)
    | ~ class_Orderings_Olinorder(U_12328) ),
    inference(clausify,[status(thm)],[f_3176_3]) ).

cnf(f_3176_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12328),U_12329),U_12330))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12328,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12328),U_12329)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12328),U_12330)))
    | ~ sP910(U_12329,U_12328,U_12330) ),
    inference(clausify,[status(thm)],[f_3176_3]) ).

cnf(f_3176_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12328,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12328),U_12329)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12328),U_12330)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12328),U_12329),U_12330))
    | ~ sP910(U_12329,U_12328,U_12330) ),
    inference(clausify,[status(thm)],[f_3176_3]) ).

fof(f_3177_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_3177_2,plain,
    ! [U_12337,U_12336,U_12335,U_12334,U_12333,U_12332,U_12331] :
      ( U_12335 = U_12337
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12331,tc_Option_Ooption(U_12332)),U_12333),U_12334),hAPP(c_Option_Ooption_OSome(U_12332),U_12335)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12331,tc_Option_Ooption(U_12332)),U_12336),U_12334),hAPP(c_Option_Ooption_OSome(U_12332),U_12337)) ),
    inference(variable_rename,[status(thm)],[f_3177_1]) ).

fof(f_3177_3,plain,
    ! [U_12337,U_12336,U_12335] :
      ( ! [U_12334,U_12333,U_12332,U_12331] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12331,tc_Option_Ooption(U_12332)),U_12333),U_12334),hAPP(c_Option_Ooption_OSome(U_12332),U_12335)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12331,tc_Option_Ooption(U_12332)),U_12336),U_12334),hAPP(c_Option_Ooption_OSome(U_12332),U_12337))
      | U_12335 = U_12337 ),
    inference(miniscope,[status(thm)],[f_3177_2]) ).

fof(f_3177_4,plain,
    ! [U_12332,U_12331,U_12333,U_12334,U_12335,U_12336,U_12337] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12331,tc_Option_Ooption(U_12332)),U_12333),U_12334),hAPP(c_Option_Ooption_OSome(U_12332),U_12335)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12331,tc_Option_Ooption(U_12332)),U_12336),U_12334),hAPP(c_Option_Ooption_OSome(U_12332),U_12337))
      | U_12335 = U_12337 ),
    inference(definitional_conversion,[status(esa)],[f_3177_3]) ).

cnf(f_3177_5,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12331,tc_Option_Ooption(U_12332)),U_12333),U_12334),hAPP(c_Option_Ooption_OSome(U_12332),U_12335)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12331,tc_Option_Ooption(U_12332)),U_12336),U_12334),hAPP(c_Option_Ooption_OSome(U_12332),U_12337))
    | U_12335 = U_12337 ),
    inference(clausify,[status(thm)],[f_3177_4]) ).

fof(f_3178_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_3178_2,plain,
    ! [U_12342,U_12341,U_12340,U_12339,U_12338] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12342,tc_Option_Ooption(U_12340)),U_12338),U_12339),hAPP(c_Option_Ooption_OSome(U_12340),U_12341)) = U_12338
      | hAPP(U_12338,U_12339) != hAPP(c_Option_Ooption_OSome(U_12340),U_12341) ),
    inference(variable_rename,[status(thm)],[f_3178_1]) ).

fof(f_3178_3,plain,
    ! [U_12339,U_12338,U_12340,U_12341,U_12342] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12342,tc_Option_Ooption(U_12340)),U_12338),U_12339),hAPP(c_Option_Ooption_OSome(U_12340),U_12341)) = U_12338
      | hAPP(U_12338,U_12339) != hAPP(c_Option_Ooption_OSome(U_12340),U_12341) ),
    inference(definitional_conversion,[status(esa)],[f_3178_2]) ).

cnf(f_3178_4,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12342,tc_Option_Ooption(U_12340)),U_12338),U_12339),hAPP(c_Option_Ooption_OSome(U_12340),U_12341)) = U_12338
    | hAPP(U_12338,U_12339) != hAPP(c_Option_Ooption_OSome(U_12340),U_12341) ),
    inference(clausify,[status(thm)],[f_3178_3]) ).

fof(f_3179_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_3179_2,plain,
    ! [U_12349,U_12348,U_12347,U_12346,U_12345,U_12344,U_12343] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12343,tc_Option_Ooption(U_12344)),U_12345),U_12346),hAPP(c_Option_Ooption_OSome(U_12344),U_12347)),U_12348) = hAPP(c_Option_Ooption_OSome(U_12344),U_12349)
        | ( ( hAPP(U_12345,U_12348) != hAPP(c_Option_Ooption_OSome(U_12344),U_12349)
            | U_12348 = U_12346 )
          & ( U_12347 != U_12349
            | U_12348 != U_12346 ) ) )
      & ( ( hAPP(U_12345,U_12348) = hAPP(c_Option_Ooption_OSome(U_12344),U_12349)
          & U_12348 != U_12346 )
        | ( U_12347 = U_12349
          & U_12348 = U_12346 )
        | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12343,tc_Option_Ooption(U_12344)),U_12345),U_12346),hAPP(c_Option_Ooption_OSome(U_12344),U_12347)),U_12348) != hAPP(c_Option_Ooption_OSome(U_12344),U_12349) ) ),
    inference(variable_rename,[status(thm)],[f_3179_1]) ).

fof(f_3179_3,plain,
    ( ! [U_12363,U_12361,U_12359,U_12357,U_12355,U_12353] :
        ( ! [U_12351] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12351,tc_Option_Ooption(U_12353)),U_12355),U_12357),hAPP(c_Option_Ooption_OSome(U_12353),U_12359)),U_12361) = hAPP(c_Option_Ooption_OSome(U_12353),U_12363)
        | ( ( hAPP(U_12355,U_12361) != hAPP(c_Option_Ooption_OSome(U_12353),U_12363)
            | U_12361 = U_12357 )
          & ( U_12359 != U_12363
            | U_12361 != U_12357 ) ) )
    & ! [U_12362,U_12360,U_12358,U_12356,U_12354,U_12352] :
        ( ! [U_12350] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12350,tc_Option_Ooption(U_12352)),U_12354),U_12356),hAPP(c_Option_Ooption_OSome(U_12352),U_12358)),U_12360) != hAPP(c_Option_Ooption_OSome(U_12352),U_12362)
        | ( hAPP(U_12354,U_12360) = hAPP(c_Option_Ooption_OSome(U_12352),U_12362)
          & U_12360 != U_12356 )
        | ( U_12358 = U_12362
          & U_12360 = U_12356 ) ) ),
    inference(miniscope,[status(thm)],[f_3179_2]) ).

fof(f_3179_4,plain,
    ( ! [U_12359,U_12357,U_12353,U_12355,U_12361,U_12363] :
        ( hAPP(U_12355,U_12361) != hAPP(c_Option_Ooption_OSome(U_12353),U_12363)
        | U_12361 = U_12357
        | ~ sP913(U_12359,U_12357,U_12353,U_12355,U_12361,U_12363) )
    & ! [U_12359,U_12357,U_12353,U_12355,U_12361,U_12363] :
        ( U_12359 != U_12363
        | U_12361 != U_12357
        | ~ sP913(U_12359,U_12357,U_12353,U_12355,U_12361,U_12363) )
    & ! [U_12354,U_12352,U_12356,U_12362,U_12360] :
        ( hAPP(U_12354,U_12360) = hAPP(c_Option_Ooption_OSome(U_12352),U_12362)
        | ~ sP912(U_12354,U_12352,U_12356,U_12362,U_12360) )
    & ! [U_12354,U_12352,U_12356,U_12362,U_12360] :
        ( U_12360 != U_12356
        | ~ sP912(U_12354,U_12352,U_12356,U_12362,U_12360) )
    & ! [U_12358,U_12356,U_12362,U_12360] :
        ( U_12358 = U_12362
        | ~ sP911(U_12358,U_12356,U_12362,U_12360) )
    & ! [U_12358,U_12356,U_12362,U_12360] :
        ( U_12360 = U_12356
        | ~ sP911(U_12358,U_12356,U_12362,U_12360) )
    & ! [U_12359,U_12351,U_12357,U_12353,U_12355,U_12361,U_12363] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12351,tc_Option_Ooption(U_12353)),U_12355),U_12357),hAPP(c_Option_Ooption_OSome(U_12353),U_12359)),U_12361) = hAPP(c_Option_Ooption_OSome(U_12353),U_12363)
        | sP913(U_12359,U_12357,U_12353,U_12355,U_12361,U_12363) )
    & ! [U_12350,U_12354,U_12352,U_12358,U_12356,U_12362,U_12360] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12350,tc_Option_Ooption(U_12352)),U_12354),U_12356),hAPP(c_Option_Ooption_OSome(U_12352),U_12358)),U_12360) != hAPP(c_Option_Ooption_OSome(U_12352),U_12362)
        | sP912(U_12354,U_12352,U_12356,U_12362,U_12360)
        | sP911(U_12358,U_12356,U_12362,U_12360) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP911,sP912,sP913])],[f_3179_3]) ).

cnf(f_3179_5,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12350,tc_Option_Ooption(U_12352)),U_12354),U_12356),hAPP(c_Option_Ooption_OSome(U_12352),U_12358)),U_12360) != hAPP(c_Option_Ooption_OSome(U_12352),U_12362)
    | sP912(U_12354,U_12352,U_12356,U_12362,U_12360)
    | sP911(U_12358,U_12356,U_12362,U_12360) ),
    inference(clausify,[status(thm)],[f_3179_4]) ).

cnf(f_3179_6,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12351,tc_Option_Ooption(U_12353)),U_12355),U_12357),hAPP(c_Option_Ooption_OSome(U_12353),U_12359)),U_12361) = hAPP(c_Option_Ooption_OSome(U_12353),U_12363)
    | sP913(U_12359,U_12357,U_12353,U_12355,U_12361,U_12363) ),
    inference(clausify,[status(thm)],[f_3179_4]) ).

cnf(f_3179_7,plain,
    ( U_12360 = U_12356
    | ~ sP911(U_12358,U_12356,U_12362,U_12360) ),
    inference(clausify,[status(thm)],[f_3179_4]) ).

cnf(f_3179_8,plain,
    ( U_12358 = U_12362
    | ~ sP911(U_12358,U_12356,U_12362,U_12360) ),
    inference(clausify,[status(thm)],[f_3179_4]) ).

cnf(f_3179_9,plain,
    ( U_12360 != U_12356
    | ~ sP912(U_12354,U_12352,U_12356,U_12362,U_12360) ),
    inference(clausify,[status(thm)],[f_3179_4]) ).

cnf(f_3179_10,plain,
    ( hAPP(U_12354,U_12360) = hAPP(c_Option_Ooption_OSome(U_12352),U_12362)
    | ~ sP912(U_12354,U_12352,U_12356,U_12362,U_12360) ),
    inference(clausify,[status(thm)],[f_3179_4]) ).

cnf(f_3179_11,plain,
    ( U_12359 != U_12363
    | U_12361 != U_12357
    | ~ sP913(U_12359,U_12357,U_12353,U_12355,U_12361,U_12363) ),
    inference(clausify,[status(thm)],[f_3179_4]) ).

cnf(f_3179_12,plain,
    ( hAPP(U_12355,U_12361) != hAPP(c_Option_Ooption_OSome(U_12353),U_12363)
    | U_12361 = U_12357
    | ~ sP913(U_12359,U_12357,U_12353,U_12355,U_12361,U_12363) ),
    inference(clausify,[status(thm)],[f_3179_4]) ).

fof(f_3180_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_3180_2,plain,
    ! [U_12365,U_12364] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12364,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12364),U_12365),c_Orderings_Obot__class_Obot(tc_fun(U_12364,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_12364),U_12365)) = hAPP(hAPP(c_Set_Oinsert(U_12364),U_12365),c_Orderings_Obot__class_Obot(tc_fun(U_12364,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_12364) ),
    inference(variable_rename,[status(thm)],[f_3180_1]) ).

fof(f_3180_3,plain,
    ! [U_12364,U_12365] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12364,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12364),U_12365),c_Orderings_Obot__class_Obot(tc_fun(U_12364,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_12364),U_12365)) = hAPP(hAPP(c_Set_Oinsert(U_12364),U_12365),c_Orderings_Obot__class_Obot(tc_fun(U_12364,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_12364) ),
    inference(definitional_conversion,[status(esa)],[f_3180_2]) ).

cnf(f_3180_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12364,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12364),U_12365),c_Orderings_Obot__class_Obot(tc_fun(U_12364,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_12364),U_12365)) = hAPP(hAPP(c_Set_Oinsert(U_12364),U_12365),c_Orderings_Obot__class_Obot(tc_fun(U_12364,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_12364) ),
    inference(clausify,[status(thm)],[f_3180_3]) ).

fof(f_3181_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_3181_2,plain,
    ! [U_12368,U_12367,U_12366] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12366,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12366),U_12367)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12366,U_12367),U_12368)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12366),U_12368)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12366),U_12367),U_12368))
      | ~ class_Orderings_Olinorder(U_12366) ),
    inference(variable_rename,[status(thm)],[f_3181_1]) ).

fof(f_3181_3,plain,
    ! [U_12366,U_12367,U_12368] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12366,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12366),U_12367)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12366,U_12367),U_12368)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12366),U_12368)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12366),U_12367),U_12368))
      | ~ class_Orderings_Olinorder(U_12366) ),
    inference(definitional_conversion,[status(esa)],[f_3181_2]) ).

cnf(f_3181_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12366,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12366),U_12367)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12366,U_12367),U_12368)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12366),U_12368)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12366),U_12367),U_12368))
    | ~ class_Orderings_Olinorder(U_12366) ),
    inference(clausify,[status(thm)],[f_3181_3]) ).

fof(f_3182_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_3182_2,plain,
    ! [U_12371,U_12370,U_12369] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12369,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12369),U_12370)),c_SetInterval_Oord__class_OatLeastAtMost(U_12369,U_12370,U_12371)) = c_Orderings_Obot__class_Obot(tc_fun(U_12369,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12369) ),
    inference(variable_rename,[status(thm)],[f_3182_1]) ).

fof(f_3182_3,plain,
    ! [U_12369,U_12370,U_12371] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12369,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12369),U_12370)),c_SetInterval_Oord__class_OatLeastAtMost(U_12369,U_12370,U_12371)) = c_Orderings_Obot__class_Obot(tc_fun(U_12369,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12369) ),
    inference(definitional_conversion,[status(esa)],[f_3182_2]) ).

cnf(f_3182_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12369,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12369),U_12370)),c_SetInterval_Oord__class_OatLeastAtMost(U_12369,U_12370,U_12371)) = c_Orderings_Obot__class_Obot(tc_fun(U_12369,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12369) ),
    inference(clausify,[status(thm)],[f_3182_3]) ).

fof(f_3183_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_3183_2,plain,
    ! [U_12374,U_12373,U_12372] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12372,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12372),U_12373)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12372,U_12373),U_12374)) = c_Orderings_Obot__class_Obot(tc_fun(U_12372,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12372) ),
    inference(variable_rename,[status(thm)],[f_3183_1]) ).

fof(f_3183_3,plain,
    ! [U_12372,U_12373,U_12374] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12372,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12372),U_12373)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12372,U_12373),U_12374)) = c_Orderings_Obot__class_Obot(tc_fun(U_12372,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12372) ),
    inference(definitional_conversion,[status(esa)],[f_3183_2]) ).

cnf(f_3183_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12372,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12372),U_12373)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12372,U_12373),U_12374)) = c_Orderings_Obot__class_Obot(tc_fun(U_12372,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12372) ),
    inference(clausify,[status(thm)],[f_3183_3]) ).

fof(f_3184_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_3184_2,plain,
    ! [U_12378,U_12377,U_12376,U_12375] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12375,tc_Option_Ooption(U_12376)),hAPP(c_COMBK(tc_Option_Ooption(U_12376),U_12375),c_Option_Ooption_ONone(U_12376))),U_12377),c_Option_Ooption_ONone(U_12376)),U_12378) = c_Option_Ooption_ONone(U_12376),
    inference(variable_rename,[status(thm)],[f_3184_1]) ).

fof(f_3184_3,plain,
    ! [U_12375,U_12376,U_12377,U_12378] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12375,tc_Option_Ooption(U_12376)),hAPP(c_COMBK(tc_Option_Ooption(U_12376),U_12375),c_Option_Ooption_ONone(U_12376))),U_12377),c_Option_Ooption_ONone(U_12376)),U_12378) = c_Option_Ooption_ONone(U_12376),
    inference(definitional_conversion,[status(esa)],[f_3184_2]) ).

cnf(f_3184_4,plain,
    hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12375,tc_Option_Ooption(U_12376)),hAPP(c_COMBK(tc_Option_Ooption(U_12376),U_12375),c_Option_Ooption_ONone(U_12376))),U_12377),c_Option_Ooption_ONone(U_12376)),U_12378) = c_Option_Ooption_ONone(U_12376),
    inference(clausify,[status(thm)],[f_3184_3]) ).

fof(f_3185_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_3185_2,plain,
    ! [U_12379] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12379)) = 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_12379))),
    inference(variable_rename,[status(thm)],[f_3185_1]) ).

fof(f_3185_3,plain,
    ! [U_12379] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12379)) = 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_12379))),
    inference(definitional_conversion,[status(esa)],[f_3185_2]) ).

cnf(f_3185_4,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12379)) = 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_12379))),
    inference(clausify,[status(thm)],[f_3185_3]) ).

fof(f_3186_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_3186_2,plain,
    ! [U_12381,U_12380] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12380,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12380),U_12381)),hAPP(hAPP(c_Set_Oinsert(U_12380),U_12381),c_Orderings_Obot__class_Obot(tc_fun(U_12380,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_12380),U_12381)
      | ~ class_Orderings_Olinorder(U_12380) ),
    inference(variable_rename,[status(thm)],[f_3186_1]) ).

fof(f_3186_3,plain,
    ! [U_12380,U_12381] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12380,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12380),U_12381)),hAPP(hAPP(c_Set_Oinsert(U_12380),U_12381),c_Orderings_Obot__class_Obot(tc_fun(U_12380,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_12380),U_12381)
      | ~ class_Orderings_Olinorder(U_12380) ),
    inference(definitional_conversion,[status(esa)],[f_3186_2]) ).

cnf(f_3186_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12380,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12380),U_12381)),hAPP(hAPP(c_Set_Oinsert(U_12380),U_12381),c_Orderings_Obot__class_Obot(tc_fun(U_12380,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_12380),U_12381)
    | ~ class_Orderings_Olinorder(U_12380) ),
    inference(clausify,[status(thm)],[f_3186_3]) ).

fof(f_3187_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_3187_2,plain,
    ! [U_12384,U_12383,U_12382] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12382,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12382),U_12383)),c_SetInterval_Oord__class_OatLeastAtMost(U_12382,U_12383,U_12384)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12382),U_12384)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12382),U_12383),U_12384))
      | ~ class_Orderings_Olinorder(U_12382) ),
    inference(variable_rename,[status(thm)],[f_3187_1]) ).

fof(f_3187_3,plain,
    ! [U_12382,U_12383,U_12384] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12382,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12382),U_12383)),c_SetInterval_Oord__class_OatLeastAtMost(U_12382,U_12383,U_12384)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12382),U_12384)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12382),U_12383),U_12384))
      | ~ class_Orderings_Olinorder(U_12382) ),
    inference(definitional_conversion,[status(esa)],[f_3187_2]) ).

cnf(f_3187_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12382,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12382),U_12383)),c_SetInterval_Oord__class_OatLeastAtMost(U_12382,U_12383,U_12384)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12382),U_12384)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12382),U_12383),U_12384))
    | ~ class_Orderings_Olinorder(U_12382) ),
    inference(clausify,[status(thm)],[f_3187_3]) ).

fof(f_3188_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_3188_2,plain,
    ! [U_12387,U_12386,U_12385] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12385,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12385),U_12386)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12385,U_12386,U_12387)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12385),U_12387)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12385),U_12386),U_12387))
      | ~ class_Orderings_Olinorder(U_12385) ),
    inference(variable_rename,[status(thm)],[f_3188_1]) ).

fof(f_3188_3,plain,
    ! [U_12385,U_12386,U_12387] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12385,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12385),U_12386)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12385,U_12386,U_12387)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12385),U_12387)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12385),U_12386),U_12387))
      | ~ class_Orderings_Olinorder(U_12385) ),
    inference(definitional_conversion,[status(esa)],[f_3188_2]) ).

cnf(f_3188_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12385,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12385),U_12386)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12385,U_12386,U_12387)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12385),U_12387)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12385),U_12386),U_12387))
    | ~ class_Orderings_Olinorder(U_12385) ),
    inference(clausify,[status(thm)],[f_3188_3]) ).

fof(f_3189_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_3189_2,plain,
    ! [U_12390,U_12389,U_12388] : 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_12388)),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_12389))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12390))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_12390)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12388),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12388),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_12390),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_12389)))),
    inference(variable_rename,[status(thm)],[f_3189_1]) ).

fof(f_3189_3,plain,
    ! [U_12388,U_12389,U_12390] : 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_12388)),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_12389))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12390))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_12390)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12388),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12388),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_12390),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_12389)))),
    inference(definitional_conversion,[status(esa)],[f_3189_2]) ).

cnf(f_3189_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_12388)),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_12389))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12390))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_12390)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12388),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12388),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_12390),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_12389)))),
    inference(clausify,[status(thm)],[f_3189_3]) ).

fof(f_3190_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_3190_2,plain,
    ! [U_12395,U_12394,U_12393,U_12392,U_12391] :
      ( c_Map_Oran(U_12394,U_12393,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12394,tc_Option_Ooption(U_12393)),U_12391),U_12392),hAPP(c_Option_Ooption_OSome(U_12393),U_12395))) = hAPP(hAPP(c_Set_Oinsert(U_12393),U_12395),c_Map_Oran(U_12394,U_12393,U_12391))
      | hAPP(U_12391,U_12392) != c_Option_Ooption_ONone(U_12393) ),
    inference(variable_rename,[status(thm)],[f_3190_1]) ).

fof(f_3190_3,plain,
    ! [U_12391,U_12392,U_12393,U_12394,U_12395] :
      ( c_Map_Oran(U_12394,U_12393,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12394,tc_Option_Ooption(U_12393)),U_12391),U_12392),hAPP(c_Option_Ooption_OSome(U_12393),U_12395))) = hAPP(hAPP(c_Set_Oinsert(U_12393),U_12395),c_Map_Oran(U_12394,U_12393,U_12391))
      | hAPP(U_12391,U_12392) != c_Option_Ooption_ONone(U_12393) ),
    inference(definitional_conversion,[status(esa)],[f_3190_2]) ).

cnf(f_3190_4,plain,
    ( c_Map_Oran(U_12394,U_12393,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12394,tc_Option_Ooption(U_12393)),U_12391),U_12392),hAPP(c_Option_Ooption_OSome(U_12393),U_12395))) = hAPP(hAPP(c_Set_Oinsert(U_12393),U_12395),c_Map_Oran(U_12394,U_12393,U_12391))
    | hAPP(U_12391,U_12392) != c_Option_Ooption_ONone(U_12393) ),
    inference(clausify,[status(thm)],[f_3190_3]) ).

fof(f_3191_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_3191_2,plain,
    ! [U_12400,U_12399,U_12398,U_12397,U_12396] :
      ( ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12396,tc_Option_Ooption(U_12399)),c_Map_Orestrict__map(U_12396,U_12399,U_12400,U_12398)),U_12397),c_Option_Ooption_ONone(U_12399)) = c_Map_Orestrict__map(U_12396,U_12399,U_12400,U_12398)
        | hBOOL(hAPP(hAPP(c_member(U_12396),U_12397),U_12398)) )
      & ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12396,tc_Option_Ooption(U_12399)),c_Map_Orestrict__map(U_12396,U_12399,U_12400,U_12398)),U_12397),c_Option_Ooption_ONone(U_12399)) = c_Map_Orestrict__map(U_12396,U_12399,U_12400,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12396,tc_HOL_Obool)),U_12398),hAPP(hAPP(c_Set_Oinsert(U_12396),U_12397),c_Orderings_Obot__class_Obot(tc_fun(U_12396,tc_HOL_Obool)))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12396),U_12397),U_12398)) ) ),
    inference(variable_rename,[status(thm)],[f_3191_1]) ).

fof(f_3191_3,plain,
    ( ! [U_12410,U_12408,U_12406,U_12404,U_12402] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12402,tc_Option_Ooption(U_12408)),c_Map_Orestrict__map(U_12402,U_12408,U_12410,U_12406)),U_12404),c_Option_Ooption_ONone(U_12408)) = c_Map_Orestrict__map(U_12402,U_12408,U_12410,U_12406)
        | hBOOL(hAPP(hAPP(c_member(U_12402),U_12404),U_12406)) )
    & ! [U_12409,U_12407,U_12405,U_12403,U_12401] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12401,tc_Option_Ooption(U_12407)),c_Map_Orestrict__map(U_12401,U_12407,U_12409,U_12405)),U_12403),c_Option_Ooption_ONone(U_12407)) = c_Map_Orestrict__map(U_12401,U_12407,U_12409,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12401,tc_HOL_Obool)),U_12405),hAPP(hAPP(c_Set_Oinsert(U_12401),U_12403),c_Orderings_Obot__class_Obot(tc_fun(U_12401,tc_HOL_Obool)))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12401),U_12403),U_12405)) ) ),
    inference(miniscope,[status(thm)],[f_3191_2]) ).

fof(f_3191_4,plain,
    ( ! [U_12402,U_12404,U_12406,U_12408,U_12410] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12402,tc_Option_Ooption(U_12408)),c_Map_Orestrict__map(U_12402,U_12408,U_12410,U_12406)),U_12404),c_Option_Ooption_ONone(U_12408)) = c_Map_Orestrict__map(U_12402,U_12408,U_12410,U_12406)
        | hBOOL(hAPP(hAPP(c_member(U_12402),U_12404),U_12406)) )
    & ! [U_12401,U_12403,U_12405,U_12407,U_12409] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12401,tc_Option_Ooption(U_12407)),c_Map_Orestrict__map(U_12401,U_12407,U_12409,U_12405)),U_12403),c_Option_Ooption_ONone(U_12407)) = c_Map_Orestrict__map(U_12401,U_12407,U_12409,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12401,tc_HOL_Obool)),U_12405),hAPP(hAPP(c_Set_Oinsert(U_12401),U_12403),c_Orderings_Obot__class_Obot(tc_fun(U_12401,tc_HOL_Obool)))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12401),U_12403),U_12405)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3191_3]) ).

cnf(f_3191_5,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12401,tc_Option_Ooption(U_12407)),c_Map_Orestrict__map(U_12401,U_12407,U_12409,U_12405)),U_12403),c_Option_Ooption_ONone(U_12407)) = c_Map_Orestrict__map(U_12401,U_12407,U_12409,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12401,tc_HOL_Obool)),U_12405),hAPP(hAPP(c_Set_Oinsert(U_12401),U_12403),c_Orderings_Obot__class_Obot(tc_fun(U_12401,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12401),U_12403),U_12405)) ),
    inference(clausify,[status(thm)],[f_3191_4]) ).

cnf(f_3191_6,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12402,tc_Option_Ooption(U_12408)),c_Map_Orestrict__map(U_12402,U_12408,U_12410,U_12406)),U_12404),c_Option_Ooption_ONone(U_12408)) = c_Map_Orestrict__map(U_12402,U_12408,U_12410,U_12406)
    | hBOOL(hAPP(hAPP(c_member(U_12402),U_12404),U_12406)) ),
    inference(clausify,[status(thm)],[f_3191_4]) ).

fof(f_3192_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_3192_2,plain,
    ! [U_12414,U_12413,U_12412,U_12411] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12411),hAPP(c_Groups_Oabs__class_Oabs(U_12411),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12412,U_12411),U_12413),U_12414))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12412,U_12411),hAPP(hAPP(c_COMBB(U_12411,U_12411,U_12412),c_Groups_Oabs__class_Oabs(U_12411)),U_12413)),U_12414)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_12411) ),
    inference(variable_rename,[status(thm)],[f_3192_1]) ).

fof(f_3192_3,plain,
    ! [U_12412,U_12411,U_12413,U_12414] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12411),hAPP(c_Groups_Oabs__class_Oabs(U_12411),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12412,U_12411),U_12413),U_12414))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12412,U_12411),hAPP(hAPP(c_COMBB(U_12411,U_12411,U_12412),c_Groups_Oabs__class_Oabs(U_12411)),U_12413)),U_12414)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_12411) ),
    inference(definitional_conversion,[status(esa)],[f_3192_2]) ).

cnf(f_3192_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12411),hAPP(c_Groups_Oabs__class_Oabs(U_12411),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12412,U_12411),U_12413),U_12414))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12412,U_12411),hAPP(hAPP(c_COMBB(U_12411,U_12411,U_12412),c_Groups_Oabs__class_Oabs(U_12411)),U_12413)),U_12414)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_12411) ),
    inference(clausify,[status(thm)],[f_3192_3]) ).

fof(f_3193_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_3193_2,plain,
    ! [U_12418,U_12417,U_12416,U_12415] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12415),c_Groups_Ozero__class_Ozero(U_12415)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12416,U_12415),hAPP(hAPP(c_COMBB(U_12415,U_12415,U_12416),c_Groups_Oabs__class_Oabs(U_12415)),U_12417)),U_12418)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_12415) ),
    inference(variable_rename,[status(thm)],[f_3193_1]) ).

fof(f_3193_3,plain,
    ! [U_12415,U_12416,U_12417,U_12418] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12415),c_Groups_Ozero__class_Ozero(U_12415)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12416,U_12415),hAPP(hAPP(c_COMBB(U_12415,U_12415,U_12416),c_Groups_Oabs__class_Oabs(U_12415)),U_12417)),U_12418)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_12415) ),
    inference(definitional_conversion,[status(esa)],[f_3193_2]) ).

cnf(f_3193_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12415),c_Groups_Ozero__class_Ozero(U_12415)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12416,U_12415),hAPP(hAPP(c_COMBB(U_12415,U_12415,U_12416),c_Groups_Oabs__class_Oabs(U_12415)),U_12417)),U_12418)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_12415) ),
    inference(clausify,[status(thm)],[f_3193_3]) ).

fof(f_3194_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_3194_2,plain,
    ! [U_12423,U_12422,U_12421,U_12420,U_12419] :
      ( hAPP(c_Map_Orestrict__map(U_12419,U_12422,U_12423,U_12421),U_12420) = hAPP(U_12423,U_12420)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12419),U_12420),U_12421)) ),
    inference(variable_rename,[status(thm)],[f_3194_1]) ).

fof(f_3194_3,plain,
    ! [U_12419,U_12420,U_12421,U_12422,U_12423] :
      ( hAPP(c_Map_Orestrict__map(U_12419,U_12422,U_12423,U_12421),U_12420) = hAPP(U_12423,U_12420)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12419),U_12420),U_12421)) ),
    inference(definitional_conversion,[status(esa)],[f_3194_2]) ).

cnf(f_3194_4,plain,
    ( hAPP(c_Map_Orestrict__map(U_12419,U_12422,U_12423,U_12421),U_12420) = hAPP(U_12423,U_12420)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12419),U_12420),U_12421)) ),
    inference(clausify,[status(thm)],[f_3194_3]) ).

fof(f_3195_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_3195_2,plain,
    ! [U_12428,U_12427,U_12426,U_12425,U_12424] : c_Map_Orestrict__map(U_12424,U_12425,c_Map_Orestrict__map(U_12424,U_12425,U_12426,U_12427),U_12428) = c_Map_Orestrict__map(U_12424,U_12425,U_12426,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12424,tc_HOL_Obool)),U_12427),U_12428)),
    inference(variable_rename,[status(thm)],[f_3195_1]) ).

fof(f_3195_3,plain,
    ! [U_12425,U_12424,U_12426,U_12427,U_12428] : c_Map_Orestrict__map(U_12424,U_12425,c_Map_Orestrict__map(U_12424,U_12425,U_12426,U_12427),U_12428) = c_Map_Orestrict__map(U_12424,U_12425,U_12426,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12424,tc_HOL_Obool)),U_12427),U_12428)),
    inference(definitional_conversion,[status(esa)],[f_3195_2]) ).

cnf(f_3195_4,plain,
    c_Map_Orestrict__map(U_12424,U_12425,c_Map_Orestrict__map(U_12424,U_12425,U_12426,U_12427),U_12428) = c_Map_Orestrict__map(U_12424,U_12425,U_12426,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12424,tc_HOL_Obool)),U_12427),U_12428)),
    inference(clausify,[status(thm)],[f_3195_3]) ).

fof(f_3196_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_3196_2,plain,
    ! [U_12432,U_12431,U_12430,U_12429] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_12429),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12430,U_12429),hAPP(hAPP(c_COMBB(U_12429,U_12429,U_12430),c_Groups_Oabs__class_Oabs(U_12429)),U_12431)),U_12432)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12430,U_12429),hAPP(hAPP(c_COMBB(U_12429,U_12429,U_12430),c_Groups_Oabs__class_Oabs(U_12429)),U_12431)),U_12432)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_12429) ),
    inference(variable_rename,[status(thm)],[f_3196_1]) ).

fof(f_3196_3,plain,
    ! [U_12429,U_12430,U_12431,U_12432] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_12429),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12430,U_12429),hAPP(hAPP(c_COMBB(U_12429,U_12429,U_12430),c_Groups_Oabs__class_Oabs(U_12429)),U_12431)),U_12432)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12430,U_12429),hAPP(hAPP(c_COMBB(U_12429,U_12429,U_12430),c_Groups_Oabs__class_Oabs(U_12429)),U_12431)),U_12432)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_12429) ),
    inference(definitional_conversion,[status(esa)],[f_3196_2]) ).

cnf(f_3196_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_12429),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12430,U_12429),hAPP(hAPP(c_COMBB(U_12429,U_12429,U_12430),c_Groups_Oabs__class_Oabs(U_12429)),U_12431)),U_12432)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12430,U_12429),hAPP(hAPP(c_COMBB(U_12429,U_12429,U_12430),c_Groups_Oabs__class_Oabs(U_12429)),U_12431)),U_12432)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_12429) ),
    inference(clausify,[status(thm)],[f_3196_3]) ).

fof(f_3197_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_3197_2,plain,
    ! [U_12437,U_12436,U_12435,U_12434,U_12433] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12433),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12434,U_12433),U_12435),U_12436)),U_12437) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12434,U_12433),hAPP(hAPP(c_COMBC(U_12434,U_12433,U_12433),hAPP(hAPP(c_COMBB(U_12433,tc_fun(U_12433,U_12433),U_12434),c_Rings_Oinverse__class_Odivide(U_12433)),U_12435)),U_12437)),U_12436)
      | ~ class_Fields_Ofield(U_12433) ),
    inference(variable_rename,[status(thm)],[f_3197_1]) ).

fof(f_3197_3,plain,
    ! [U_12433,U_12434,U_12435,U_12436,U_12437] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12433),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12434,U_12433),U_12435),U_12436)),U_12437) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12434,U_12433),hAPP(hAPP(c_COMBC(U_12434,U_12433,U_12433),hAPP(hAPP(c_COMBB(U_12433,tc_fun(U_12433,U_12433),U_12434),c_Rings_Oinverse__class_Odivide(U_12433)),U_12435)),U_12437)),U_12436)
      | ~ class_Fields_Ofield(U_12433) ),
    inference(definitional_conversion,[status(esa)],[f_3197_2]) ).

cnf(f_3197_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12433),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12434,U_12433),U_12435),U_12436)),U_12437) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12434,U_12433),hAPP(hAPP(c_COMBC(U_12434,U_12433,U_12433),hAPP(hAPP(c_COMBB(U_12433,tc_fun(U_12433,U_12433),U_12434),c_Rings_Oinverse__class_Odivide(U_12433)),U_12435)),U_12437)),U_12436)
    | ~ class_Fields_Ofield(U_12433) ),
    inference(clausify,[status(thm)],[f_3197_3]) ).

fof(f_3198_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_3198_2,plain,
    ! [U_12441,U_12440,U_12439,U_12438] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12439,U_12438),hAPP(hAPP(c_COMBB(U_12438,U_12438,U_12439),c_Groups_Ouminus__class_Ouminus(U_12438)),U_12440)),U_12441) = hAPP(c_Groups_Ouminus__class_Ouminus(U_12438),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12439,U_12438),U_12440),U_12441))
      | ~ class_Groups_Oab__group__add(U_12438) ),
    inference(variable_rename,[status(thm)],[f_3198_1]) ).

fof(f_3198_3,plain,
    ! [U_12438,U_12439,U_12440,U_12441] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12439,U_12438),hAPP(hAPP(c_COMBB(U_12438,U_12438,U_12439),c_Groups_Ouminus__class_Ouminus(U_12438)),U_12440)),U_12441) = hAPP(c_Groups_Ouminus__class_Ouminus(U_12438),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12439,U_12438),U_12440),U_12441))
      | ~ class_Groups_Oab__group__add(U_12438) ),
    inference(definitional_conversion,[status(esa)],[f_3198_2]) ).

cnf(f_3198_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12439,U_12438),hAPP(hAPP(c_COMBB(U_12438,U_12438,U_12439),c_Groups_Ouminus__class_Ouminus(U_12438)),U_12440)),U_12441) = hAPP(c_Groups_Ouminus__class_Ouminus(U_12438),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12439,U_12438),U_12440),U_12441))
    | ~ class_Groups_Oab__group__add(U_12438) ),
    inference(clausify,[status(thm)],[f_3198_3]) ).

fof(f_3199_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_3199_2,plain,
    ! [U_12444,U_12443,U_12442] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12443,U_12442),hAPP(c_COMBK(U_12442,U_12443),c_Groups_Ozero__class_Ozero(U_12442))),U_12444) = c_Groups_Ozero__class_Ozero(U_12442)
      | ~ class_Groups_Ocomm__monoid__add(U_12442) ),
    inference(variable_rename,[status(thm)],[f_3199_1]) ).

fof(f_3199_3,plain,
    ! [U_12442,U_12443,U_12444] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12443,U_12442),hAPP(c_COMBK(U_12442,U_12443),c_Groups_Ozero__class_Ozero(U_12442))),U_12444) = c_Groups_Ozero__class_Ozero(U_12442)
      | ~ class_Groups_Ocomm__monoid__add(U_12442) ),
    inference(definitional_conversion,[status(esa)],[f_3199_2]) ).

cnf(f_3199_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12443,U_12442),hAPP(c_COMBK(U_12442,U_12443),c_Groups_Ozero__class_Ozero(U_12442))),U_12444) = c_Groups_Ozero__class_Ozero(U_12442)
    | ~ class_Groups_Ocomm__monoid__add(U_12442) ),
    inference(clausify,[status(thm)],[f_3199_3]) ).

fof(f_3200_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_3200_2,plain,
    ! [U_12448,U_12447,U_12446,U_12445] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12445),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12446,tc_Nat_Onat),U_12447),U_12448)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12446,U_12445),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12445,U_12446),c_Nat_Osemiring__1__class_Oof__nat(U_12445)),U_12447)),U_12448)
      | ~ class_Rings_Osemiring__1(U_12445) ),
    inference(variable_rename,[status(thm)],[f_3200_1]) ).

fof(f_3200_3,plain,
    ! [U_12445,U_12446,U_12447,U_12448] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12445),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12446,tc_Nat_Onat),U_12447),U_12448)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12446,U_12445),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12445,U_12446),c_Nat_Osemiring__1__class_Oof__nat(U_12445)),U_12447)),U_12448)
      | ~ class_Rings_Osemiring__1(U_12445) ),
    inference(definitional_conversion,[status(esa)],[f_3200_2]) ).

cnf(f_3200_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12445),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12446,tc_Nat_Onat),U_12447),U_12448)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12446,U_12445),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12445,U_12446),c_Nat_Osemiring__1__class_Oof__nat(U_12445)),U_12447)),U_12448)
    | ~ class_Rings_Osemiring__1(U_12445) ),
    inference(clausify,[status(thm)],[f_3200_3]) ).

fof(f_3201_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_3201_2,plain,
    ! [U_12452,U_12451,U_12450,U_12449] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_12449),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12450,tc_Int_Oint),U_12451),U_12452)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12450,U_12449),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12449,U_12450),c_Int_Oring__1__class_Oof__int(U_12449)),U_12451)),U_12452)
      | ~ class_Rings_Oring__1(U_12449) ),
    inference(variable_rename,[status(thm)],[f_3201_1]) ).

fof(f_3201_3,plain,
    ! [U_12449,U_12450,U_12451,U_12452] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_12449),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12450,tc_Int_Oint),U_12451),U_12452)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12450,U_12449),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12449,U_12450),c_Int_Oring__1__class_Oof__int(U_12449)),U_12451)),U_12452)
      | ~ class_Rings_Oring__1(U_12449) ),
    inference(definitional_conversion,[status(esa)],[f_3201_2]) ).

cnf(f_3201_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_12449),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12450,tc_Int_Oint),U_12451),U_12452)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12450,U_12449),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12449,U_12450),c_Int_Oring__1__class_Oof__int(U_12449)),U_12451)),U_12452)
    | ~ class_Rings_Oring__1(U_12449) ),
    inference(clausify,[status(thm)],[f_3201_3]) ).

fof(f_3202_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_3202_2,plain,
    ! [U_12458,U_12457,U_12456,U_12455,U_12454,U_12453] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12454,U_12453),hAPP(hAPP(c_COMBC(U_12454,tc_fun(U_12455,tc_HOL_Obool),U_12453),hAPP(hAPP(c_COMBB(tc_fun(U_12455,U_12453),tc_fun(tc_fun(U_12455,tc_HOL_Obool),U_12453),U_12454),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12455,U_12453)),U_12456)),U_12457)),U_12458) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12455,U_12453),hAPP(hAPP(c_COMBC(U_12455,tc_fun(U_12454,tc_HOL_Obool),U_12453),hAPP(hAPP(c_COMBB(tc_fun(U_12454,U_12453),tc_fun(tc_fun(U_12454,tc_HOL_Obool),U_12453),U_12455),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12454,U_12453)),hAPP(c_COMBC(U_12454,U_12455,U_12453),U_12456))),U_12458)),U_12457)
      | ~ class_Groups_Ocomm__monoid__add(U_12453) ),
    inference(variable_rename,[status(thm)],[f_3202_1]) ).

fof(f_3202_3,plain,
    ! [U_12453,U_12454,U_12455,U_12456,U_12457,U_12458] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12454,U_12453),hAPP(hAPP(c_COMBC(U_12454,tc_fun(U_12455,tc_HOL_Obool),U_12453),hAPP(hAPP(c_COMBB(tc_fun(U_12455,U_12453),tc_fun(tc_fun(U_12455,tc_HOL_Obool),U_12453),U_12454),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12455,U_12453)),U_12456)),U_12457)),U_12458) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12455,U_12453),hAPP(hAPP(c_COMBC(U_12455,tc_fun(U_12454,tc_HOL_Obool),U_12453),hAPP(hAPP(c_COMBB(tc_fun(U_12454,U_12453),tc_fun(tc_fun(U_12454,tc_HOL_Obool),U_12453),U_12455),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12454,U_12453)),hAPP(c_COMBC(U_12454,U_12455,U_12453),U_12456))),U_12458)),U_12457)
      | ~ class_Groups_Ocomm__monoid__add(U_12453) ),
    inference(definitional_conversion,[status(esa)],[f_3202_2]) ).

cnf(f_3202_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12454,U_12453),hAPP(hAPP(c_COMBC(U_12454,tc_fun(U_12455,tc_HOL_Obool),U_12453),hAPP(hAPP(c_COMBB(tc_fun(U_12455,U_12453),tc_fun(tc_fun(U_12455,tc_HOL_Obool),U_12453),U_12454),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12455,U_12453)),U_12456)),U_12457)),U_12458) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12455,U_12453),hAPP(hAPP(c_COMBC(U_12455,tc_fun(U_12454,tc_HOL_Obool),U_12453),hAPP(hAPP(c_COMBB(tc_fun(U_12454,U_12453),tc_fun(tc_fun(U_12454,tc_HOL_Obool),U_12453),U_12455),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12454,U_12453)),hAPP(c_COMBC(U_12454,U_12455,U_12453),U_12456))),U_12458)),U_12457)
    | ~ class_Groups_Ocomm__monoid__add(U_12453) ),
    inference(clausify,[status(thm)],[f_3202_3]) ).

fof(f_3203_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_3203_2,plain,
    ! [U_12465,U_12464,U_12463,U_12462,U_12461,U_12460,U_12459] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12459),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12460,U_12459),U_12461),U_12462)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12463,U_12459),U_12464),U_12465)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12460,U_12459),hAPP(hAPP(c_COMBC(U_12460,tc_fun(U_12463,tc_HOL_Obool),U_12459),hAPP(hAPP(c_COMBB(tc_fun(U_12463,U_12459),tc_fun(tc_fun(U_12463,tc_HOL_Obool),U_12459),U_12460),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12463,U_12459)),hAPP(hAPP(c_COMBC(U_12460,tc_fun(U_12463,U_12459),tc_fun(U_12463,U_12459)),hAPP(hAPP(c_COMBB(tc_fun(U_12459,U_12459),tc_fun(tc_fun(U_12463,U_12459),tc_fun(U_12463,U_12459)),U_12460),c_COMBB(U_12459,U_12459,U_12463)),hAPP(hAPP(c_COMBB(U_12459,tc_fun(U_12459,U_12459),U_12460),c_Groups_Otimes__class_Otimes(U_12459)),U_12461))),U_12464))),U_12465)),U_12462)
      | ~ class_Rings_Osemiring__0(U_12459) ),
    inference(variable_rename,[status(thm)],[f_3203_1]) ).

fof(f_3203_3,plain,
    ! [U_12459,U_12460,U_12461,U_12462,U_12463,U_12464,U_12465] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12459),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12460,U_12459),U_12461),U_12462)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12463,U_12459),U_12464),U_12465)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12460,U_12459),hAPP(hAPP(c_COMBC(U_12460,tc_fun(U_12463,tc_HOL_Obool),U_12459),hAPP(hAPP(c_COMBB(tc_fun(U_12463,U_12459),tc_fun(tc_fun(U_12463,tc_HOL_Obool),U_12459),U_12460),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12463,U_12459)),hAPP(hAPP(c_COMBC(U_12460,tc_fun(U_12463,U_12459),tc_fun(U_12463,U_12459)),hAPP(hAPP(c_COMBB(tc_fun(U_12459,U_12459),tc_fun(tc_fun(U_12463,U_12459),tc_fun(U_12463,U_12459)),U_12460),c_COMBB(U_12459,U_12459,U_12463)),hAPP(hAPP(c_COMBB(U_12459,tc_fun(U_12459,U_12459),U_12460),c_Groups_Otimes__class_Otimes(U_12459)),U_12461))),U_12464))),U_12465)),U_12462)
      | ~ class_Rings_Osemiring__0(U_12459) ),
    inference(definitional_conversion,[status(esa)],[f_3203_2]) ).

cnf(f_3203_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12459),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12460,U_12459),U_12461),U_12462)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12463,U_12459),U_12464),U_12465)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12460,U_12459),hAPP(hAPP(c_COMBC(U_12460,tc_fun(U_12463,tc_HOL_Obool),U_12459),hAPP(hAPP(c_COMBB(tc_fun(U_12463,U_12459),tc_fun(tc_fun(U_12463,tc_HOL_Obool),U_12459),U_12460),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12463,U_12459)),hAPP(hAPP(c_COMBC(U_12460,tc_fun(U_12463,U_12459),tc_fun(U_12463,U_12459)),hAPP(hAPP(c_COMBB(tc_fun(U_12459,U_12459),tc_fun(tc_fun(U_12463,U_12459),tc_fun(U_12463,U_12459)),U_12460),c_COMBB(U_12459,U_12459,U_12463)),hAPP(hAPP(c_COMBB(U_12459,tc_fun(U_12459,U_12459),U_12460),c_Groups_Otimes__class_Otimes(U_12459)),U_12461))),U_12464))),U_12465)),U_12462)
    | ~ class_Rings_Osemiring__0(U_12459) ),
    inference(clausify,[status(thm)],[f_3203_3]) ).

fof(f_3204_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_3204_2,plain,
    ! [U_12470,U_12469,U_12468,U_12467,U_12466] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12466),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12467,U_12466),U_12468),U_12469)),U_12470) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12467,U_12466),hAPP(hAPP(c_COMBC(U_12467,U_12466,U_12466),hAPP(hAPP(c_COMBB(U_12466,tc_fun(U_12466,U_12466),U_12467),c_Groups_Otimes__class_Otimes(U_12466)),U_12468)),U_12470)),U_12469)
      | ~ class_Rings_Osemiring__0(U_12466) ),
    inference(variable_rename,[status(thm)],[f_3204_1]) ).

fof(f_3204_3,plain,
    ! [U_12466,U_12467,U_12468,U_12469,U_12470] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12466),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12467,U_12466),U_12468),U_12469)),U_12470) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12467,U_12466),hAPP(hAPP(c_COMBC(U_12467,U_12466,U_12466),hAPP(hAPP(c_COMBB(U_12466,tc_fun(U_12466,U_12466),U_12467),c_Groups_Otimes__class_Otimes(U_12466)),U_12468)),U_12470)),U_12469)
      | ~ class_Rings_Osemiring__0(U_12466) ),
    inference(definitional_conversion,[status(esa)],[f_3204_2]) ).

cnf(f_3204_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12466),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12467,U_12466),U_12468),U_12469)),U_12470) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12467,U_12466),hAPP(hAPP(c_COMBC(U_12467,U_12466,U_12466),hAPP(hAPP(c_COMBB(U_12466,tc_fun(U_12466,U_12466),U_12467),c_Groups_Otimes__class_Otimes(U_12466)),U_12468)),U_12470)),U_12469)
    | ~ class_Rings_Osemiring__0(U_12466) ),
    inference(clausify,[status(thm)],[f_3204_3]) ).

fof(f_3205_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_3205_2,plain,
    ! [U_12475,U_12474,U_12473,U_12472,U_12471] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12471),U_12472),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12473,U_12471),U_12474),U_12475)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12473,U_12471),hAPP(hAPP(c_COMBB(U_12471,U_12471,U_12473),hAPP(c_Groups_Otimes__class_Otimes(U_12471),U_12472)),U_12474)),U_12475)
      | ~ class_Rings_Osemiring__0(U_12471) ),
    inference(variable_rename,[status(thm)],[f_3205_1]) ).

fof(f_3205_3,plain,
    ! [U_12471,U_12472,U_12473,U_12474,U_12475] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12471),U_12472),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12473,U_12471),U_12474),U_12475)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12473,U_12471),hAPP(hAPP(c_COMBB(U_12471,U_12471,U_12473),hAPP(c_Groups_Otimes__class_Otimes(U_12471),U_12472)),U_12474)),U_12475)
      | ~ class_Rings_Osemiring__0(U_12471) ),
    inference(definitional_conversion,[status(esa)],[f_3205_2]) ).

cnf(f_3205_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12471),U_12472),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12473,U_12471),U_12474),U_12475)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12473,U_12471),hAPP(hAPP(c_COMBB(U_12471,U_12471,U_12473),hAPP(c_Groups_Otimes__class_Otimes(U_12471),U_12472)),U_12474)),U_12475)
    | ~ class_Rings_Osemiring__0(U_12471) ),
    inference(clausify,[status(thm)],[f_3205_3]) ).

fof(f_3206_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_3206_2,plain,
    ! [U_12480,U_12479,U_12478,U_12477,U_12476] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12477,U_12476),hAPP(hAPP(c_COMBS(U_12477,U_12476,U_12476),hAPP(hAPP(c_COMBB(U_12476,tc_fun(U_12476,U_12476),U_12477),c_Groups_Oplus__class_Oplus(U_12476)),U_12478)),U_12479)),U_12480) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12476),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12477,U_12476),U_12478),U_12480)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12477,U_12476),U_12479),U_12480))
      | ~ class_Groups_Ocomm__monoid__add(U_12476) ),
    inference(variable_rename,[status(thm)],[f_3206_1]) ).

fof(f_3206_3,plain,
    ! [U_12476,U_12477,U_12478,U_12479,U_12480] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12477,U_12476),hAPP(hAPP(c_COMBS(U_12477,U_12476,U_12476),hAPP(hAPP(c_COMBB(U_12476,tc_fun(U_12476,U_12476),U_12477),c_Groups_Oplus__class_Oplus(U_12476)),U_12478)),U_12479)),U_12480) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12476),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12477,U_12476),U_12478),U_12480)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12477,U_12476),U_12479),U_12480))
      | ~ class_Groups_Ocomm__monoid__add(U_12476) ),
    inference(definitional_conversion,[status(esa)],[f_3206_2]) ).

cnf(f_3206_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12477,U_12476),hAPP(hAPP(c_COMBS(U_12477,U_12476,U_12476),hAPP(hAPP(c_COMBB(U_12476,tc_fun(U_12476,U_12476),U_12477),c_Groups_Oplus__class_Oplus(U_12476)),U_12478)),U_12479)),U_12480) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12476),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12477,U_12476),U_12478),U_12480)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12477,U_12476),U_12479),U_12480))
    | ~ class_Groups_Ocomm__monoid__add(U_12476) ),
    inference(clausify,[status(thm)],[f_3206_3]) ).

fof(f_3207_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_3207_2,plain,
    ! [U_12484,U_12483,U_12482,U_12481] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12482,U_12481),U_12484),U_12483) = c_Groups_Ozero__class_Ozero(U_12481)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12482),U_12483))
      | ~ class_Groups_Ocomm__monoid__add(U_12481) ),
    inference(variable_rename,[status(thm)],[f_3207_1]) ).

fof(f_3207_3,plain,
    ! [U_12481,U_12482,U_12483,U_12484] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12482,U_12481),U_12484),U_12483) = c_Groups_Ozero__class_Ozero(U_12481)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12482),U_12483))
      | ~ class_Groups_Ocomm__monoid__add(U_12481) ),
    inference(definitional_conversion,[status(esa)],[f_3207_2]) ).

cnf(f_3207_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12482,U_12481),U_12484),U_12483) = c_Groups_Ozero__class_Ozero(U_12481)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12482),U_12483))
    | ~ class_Groups_Ocomm__monoid__add(U_12481) ),
    inference(clausify,[status(thm)],[f_3207_3]) ).

fof(f_3208_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_3208_2,plain,
    ! [U_12488,U_12487,U_12486,U_12485] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12486,U_12485),U_12488),U_12487) = c_Groups_Ozero__class_Ozero(U_12485)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12486),U_12487))
      | ~ class_Groups_Ocomm__monoid__add(U_12485) ),
    inference(variable_rename,[status(thm)],[f_3208_1]) ).

fof(f_3208_3,plain,
    ! [U_12486,U_12485,U_12487,U_12488] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12486,U_12485),U_12488),U_12487) = c_Groups_Ozero__class_Ozero(U_12485)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12486),U_12487))
      | ~ class_Groups_Ocomm__monoid__add(U_12485) ),
    inference(definitional_conversion,[status(esa)],[f_3208_2]) ).

cnf(f_3208_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12486,U_12485),U_12488),U_12487) = c_Groups_Ozero__class_Ozero(U_12485)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12486),U_12487))
    | ~ class_Groups_Ocomm__monoid__add(U_12485) ),
    inference(clausify,[status(thm)],[f_3208_3]) ).

fof(f_3209_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_3209_2,plain,
    ! [U_12491,U_12490,U_12489] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12490,U_12489),U_12491),c_Orderings_Obot__class_Obot(tc_fun(U_12490,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_12489)
      | ~ class_Groups_Ocomm__monoid__add(U_12489) ),
    inference(variable_rename,[status(thm)],[f_3209_1]) ).

fof(f_3209_3,plain,
    ! [U_12490,U_12489,U_12491] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12490,U_12489),U_12491),c_Orderings_Obot__class_Obot(tc_fun(U_12490,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_12489)
      | ~ class_Groups_Ocomm__monoid__add(U_12489) ),
    inference(definitional_conversion,[status(esa)],[f_3209_2]) ).

cnf(f_3209_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12490,U_12489),U_12491),c_Orderings_Obot__class_Obot(tc_fun(U_12490,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_12489)
    | ~ class_Groups_Ocomm__monoid__add(U_12489) ),
    inference(clausify,[status(thm)],[f_3209_3]) ).

fof(f_3210_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_3210_2,plain,
    ! [U_12494,U_12493,U_12492] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12493,U_12492),U_12494),c_Orderings_Obot__class_Obot(tc_fun(U_12493,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_12492)
      | ~ class_Groups_Ocomm__monoid__add(U_12492) ),
    inference(variable_rename,[status(thm)],[f_3210_1]) ).

fof(f_3210_3,plain,
    ! [U_12492,U_12493,U_12494] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12493,U_12492),U_12494),c_Orderings_Obot__class_Obot(tc_fun(U_12493,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_12492)
      | ~ class_Groups_Ocomm__monoid__add(U_12492) ),
    inference(definitional_conversion,[status(esa)],[f_3210_2]) ).

cnf(f_3210_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12493,U_12492),U_12494),c_Orderings_Obot__class_Obot(tc_fun(U_12493,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_12492)
    | ~ class_Groups_Ocomm__monoid__add(U_12492) ),
    inference(clausify,[status(thm)],[f_3210_3]) ).

fof(f_3211_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_3211_2,plain,
    ! [U_12499,U_12498,U_12497,U_12496,U_12495] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12496,U_12495),hAPP(hAPP(c_COMBS(U_12496,U_12495,U_12495),hAPP(hAPP(c_COMBB(U_12495,tc_fun(U_12495,U_12495),U_12496),c_Groups_Ominus__class_Ominus(U_12495)),U_12497)),U_12498)),U_12499) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12495),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12496,U_12495),U_12497),U_12499)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12496,U_12495),U_12498),U_12499))
      | ~ class_Groups_Oab__group__add(U_12495) ),
    inference(variable_rename,[status(thm)],[f_3211_1]) ).

fof(f_3211_3,plain,
    ! [U_12495,U_12496,U_12497,U_12498,U_12499] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12496,U_12495),hAPP(hAPP(c_COMBS(U_12496,U_12495,U_12495),hAPP(hAPP(c_COMBB(U_12495,tc_fun(U_12495,U_12495),U_12496),c_Groups_Ominus__class_Ominus(U_12495)),U_12497)),U_12498)),U_12499) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12495),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12496,U_12495),U_12497),U_12499)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12496,U_12495),U_12498),U_12499))
      | ~ class_Groups_Oab__group__add(U_12495) ),
    inference(definitional_conversion,[status(esa)],[f_3211_2]) ).

cnf(f_3211_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12496,U_12495),hAPP(hAPP(c_COMBS(U_12496,U_12495,U_12495),hAPP(hAPP(c_COMBB(U_12495,tc_fun(U_12495,U_12495),U_12496),c_Groups_Ominus__class_Ominus(U_12495)),U_12497)),U_12498)),U_12499) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12495),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12496,U_12495),U_12497),U_12499)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12496,U_12495),U_12498),U_12499))
    | ~ class_Groups_Oab__group__add(U_12495) ),
    inference(clausify,[status(thm)],[f_3211_3]) ).

fof(f_3212_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_3212_2,plain,
    ! [U_12503,U_12502,U_12501,U_12500] : hAPP(c_Map_Orestrict__map(U_12500,U_12501,hAPP(c_COMBK(tc_Option_Ooption(U_12501),U_12500),c_Option_Ooption_ONone(U_12501)),U_12502),U_12503) = c_Option_Ooption_ONone(U_12501),
    inference(variable_rename,[status(thm)],[f_3212_1]) ).

fof(f_3212_3,plain,
    ! [U_12500,U_12501,U_12502,U_12503] : hAPP(c_Map_Orestrict__map(U_12500,U_12501,hAPP(c_COMBK(tc_Option_Ooption(U_12501),U_12500),c_Option_Ooption_ONone(U_12501)),U_12502),U_12503) = c_Option_Ooption_ONone(U_12501),
    inference(definitional_conversion,[status(esa)],[f_3212_2]) ).

cnf(f_3212_4,plain,
    hAPP(c_Map_Orestrict__map(U_12500,U_12501,hAPP(c_COMBK(tc_Option_Ooption(U_12501),U_12500),c_Option_Ooption_ONone(U_12501)),U_12502),U_12503) = c_Option_Ooption_ONone(U_12501),
    inference(clausify,[status(thm)],[f_3212_3]) ).

fof(f_3213_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_3213_2,plain,
    ! [U_12508,U_12507,U_12506,U_12505,U_12504] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,U_12504),hAPP(hAPP(c_COMBS(U_12505,U_12504,U_12504),hAPP(hAPP(c_COMBB(U_12504,tc_fun(U_12504,U_12504),U_12505),c_Groups_Oplus__class_Oplus(U_12504)),U_12507)),U_12508)),U_12506) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12504),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,U_12504),U_12507),U_12506)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,U_12504),U_12508),U_12506))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12505),U_12506))
      | ~ class_Groups_Ocomm__monoid__add(U_12504) ),
    inference(variable_rename,[status(thm)],[f_3213_1]) ).

fof(f_3213_3,plain,
    ! [U_12504,U_12505,U_12506,U_12507,U_12508] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,U_12504),hAPP(hAPP(c_COMBS(U_12505,U_12504,U_12504),hAPP(hAPP(c_COMBB(U_12504,tc_fun(U_12504,U_12504),U_12505),c_Groups_Oplus__class_Oplus(U_12504)),U_12507)),U_12508)),U_12506) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12504),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,U_12504),U_12507),U_12506)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,U_12504),U_12508),U_12506))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12505),U_12506))
      | ~ class_Groups_Ocomm__monoid__add(U_12504) ),
    inference(definitional_conversion,[status(esa)],[f_3213_2]) ).

cnf(f_3213_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,U_12504),hAPP(hAPP(c_COMBS(U_12505,U_12504,U_12504),hAPP(hAPP(c_COMBB(U_12504,tc_fun(U_12504,U_12504),U_12505),c_Groups_Oplus__class_Oplus(U_12504)),U_12507)),U_12508)),U_12506) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12504),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,U_12504),U_12507),U_12506)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,U_12504),U_12508),U_12506))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12505),U_12506))
    | ~ class_Groups_Ocomm__monoid__add(U_12504) ),
    inference(clausify,[status(thm)],[f_3213_3]) ).

fof(f_3214_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_3214_2,plain,
    ! [U_12512,U_12511,U_12510,U_12509] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12509),U_12510),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12511)),hAPP(c_Nat_OSuc,U_12512))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12509),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12509,tc_Nat_Onat),U_12510),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12511),U_12512))
      | ~ class_Groups_Ocomm__monoid__add(U_12509) ),
    inference(variable_rename,[status(thm)],[f_3214_1]) ).

fof(f_3214_3,plain,
    ! [U_12510,U_12509,U_12511,U_12512] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12509),U_12510),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12511)),hAPP(c_Nat_OSuc,U_12512))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12509),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12509,tc_Nat_Onat),U_12510),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12511),U_12512))
      | ~ class_Groups_Ocomm__monoid__add(U_12509) ),
    inference(definitional_conversion,[status(esa)],[f_3214_2]) ).

cnf(f_3214_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12509),U_12510),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12511)),hAPP(c_Nat_OSuc,U_12512))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12509),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12509,tc_Nat_Onat),U_12510),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12511),U_12512))
    | ~ class_Groups_Ocomm__monoid__add(U_12509) ),
    inference(clausify,[status(thm)],[f_3214_3]) ).

fof(f_3215_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_3215_2,plain,
    ! [U_12517,U_12516,U_12515,U_12514,U_12513] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12513),U_12514),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12515),U_12516)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12517),U_12516))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12513),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12513,tc_Nat_Onat),U_12514),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12516))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12515),U_12517))
      | ~ class_Groups_Ocomm__monoid__add(U_12513) ),
    inference(variable_rename,[status(thm)],[f_3215_1]) ).

fof(f_3215_3,plain,
    ! [U_12513,U_12514,U_12515,U_12516,U_12517] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12513),U_12514),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12515),U_12516)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12517),U_12516))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12513),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12513,tc_Nat_Onat),U_12514),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12516))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12515),U_12517))
      | ~ class_Groups_Ocomm__monoid__add(U_12513) ),
    inference(definitional_conversion,[status(esa)],[f_3215_2]) ).

cnf(f_3215_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12513),U_12514),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12515),U_12516)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12517),U_12516))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12513),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12513,tc_Nat_Onat),U_12514),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12516))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12515),U_12517))
    | ~ class_Groups_Ocomm__monoid__add(U_12513) ),
    inference(clausify,[status(thm)],[f_3215_3]) ).

fof(f_3216_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_3216_2,plain,
    ! [U_12521,U_12520,U_12519,U_12518] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12518),U_12519),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12520),hAPP(c_Nat_OSuc,U_12521))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12518),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12518,tc_Nat_Onat),U_12519),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12520,U_12521))
      | ~ class_Groups_Ocomm__monoid__add(U_12518) ),
    inference(variable_rename,[status(thm)],[f_3216_1]) ).

fof(f_3216_3,plain,
    ! [U_12518,U_12519,U_12520,U_12521] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12518),U_12519),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12520),hAPP(c_Nat_OSuc,U_12521))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12518),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12518,tc_Nat_Onat),U_12519),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12520,U_12521))
      | ~ class_Groups_Ocomm__monoid__add(U_12518) ),
    inference(definitional_conversion,[status(esa)],[f_3216_2]) ).

cnf(f_3216_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12518),U_12519),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12520),hAPP(c_Nat_OSuc,U_12521))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12518),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12518,tc_Nat_Onat),U_12519),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12520,U_12521))
    | ~ class_Groups_Ocomm__monoid__add(U_12518) ),
    inference(clausify,[status(thm)],[f_3216_3]) ).

fof(f_3217_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_3217_2,plain,
    ! [U_12526,U_12525,U_12524,U_12523,U_12522] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12522),U_12523),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12524),U_12525),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12526),U_12525))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12522),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12522,tc_Nat_Onat),U_12523),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12525))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12524,U_12526))
      | ~ class_Groups_Ocomm__monoid__add(U_12522) ),
    inference(variable_rename,[status(thm)],[f_3217_1]) ).

fof(f_3217_3,plain,
    ! [U_12522,U_12523,U_12524,U_12525,U_12526] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12522),U_12523),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12524),U_12525),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12526),U_12525))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12522),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12522,tc_Nat_Onat),U_12523),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12525))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12524,U_12526))
      | ~ class_Groups_Ocomm__monoid__add(U_12522) ),
    inference(definitional_conversion,[status(esa)],[f_3217_2]) ).

cnf(f_3217_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12522),U_12523),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12524),U_12525),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12526),U_12525))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12522),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12522,tc_Nat_Onat),U_12523),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12525))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12524,U_12526))
    | ~ class_Groups_Ocomm__monoid__add(U_12522) ),
    inference(clausify,[status(thm)],[f_3217_3]) ).

fof(f_3218_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_3218_2,plain,
    ! [U_12531,U_12530,U_12529,U_12528,U_12527] :
      ( hAPP(c_Map_Orestrict__map(U_12527,U_12530,U_12531,U_12529),U_12528) = c_Option_Ooption_ONone(U_12530)
      | hBOOL(hAPP(hAPP(c_member(U_12527),U_12528),U_12529)) ),
    inference(variable_rename,[status(thm)],[f_3218_1]) ).

fof(f_3218_3,plain,
    ! [U_12527,U_12528,U_12529,U_12530,U_12531] :
      ( hAPP(c_Map_Orestrict__map(U_12527,U_12530,U_12531,U_12529),U_12528) = c_Option_Ooption_ONone(U_12530)
      | hBOOL(hAPP(hAPP(c_member(U_12527),U_12528),U_12529)) ),
    inference(definitional_conversion,[status(esa)],[f_3218_2]) ).

cnf(f_3218_4,plain,
    ( hAPP(c_Map_Orestrict__map(U_12527,U_12530,U_12531,U_12529),U_12528) = c_Option_Ooption_ONone(U_12530)
    | hBOOL(hAPP(hAPP(c_member(U_12527),U_12528),U_12529)) ),
    inference(clausify,[status(thm)],[f_3218_3]) ).

fof(f_3219_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_3219_2,plain,
    ! [U_12536,U_12535,U_12534,U_12533,U_12532] : c_Map_Orestrict__map(U_12532,U_12533,U_12534,hAPP(hAPP(c_Set_Oinsert(U_12532),U_12535),U_12536)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12532,tc_Option_Ooption(U_12533)),c_Map_Orestrict__map(U_12532,U_12533,U_12534,U_12536)),U_12535),hAPP(U_12534,U_12535)),
    inference(variable_rename,[status(thm)],[f_3219_1]) ).

fof(f_3219_3,plain,
    ! [U_12532,U_12533,U_12534,U_12535,U_12536] : c_Map_Orestrict__map(U_12532,U_12533,U_12534,hAPP(hAPP(c_Set_Oinsert(U_12532),U_12535),U_12536)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12532,tc_Option_Ooption(U_12533)),c_Map_Orestrict__map(U_12532,U_12533,U_12534,U_12536)),U_12535),hAPP(U_12534,U_12535)),
    inference(definitional_conversion,[status(esa)],[f_3219_2]) ).

cnf(f_3219_4,plain,
    c_Map_Orestrict__map(U_12532,U_12533,U_12534,hAPP(hAPP(c_Set_Oinsert(U_12532),U_12535),U_12536)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12532,tc_Option_Ooption(U_12533)),c_Map_Orestrict__map(U_12532,U_12533,U_12534,U_12536)),U_12535),hAPP(U_12534,U_12535)),
    inference(clausify,[status(thm)],[f_3219_3]) ).

fof(f_3220_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_3220_2,plain,
    ! [U_12541,U_12540,U_12539,U_12538,U_12537] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12537),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12537),U_12541),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12538),U_12539))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12537),U_12541),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12539),U_12540))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12537),U_12541),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12538),U_12540))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12539),U_12540))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12538),U_12539))
      | ~ class_Groups_Ocomm__monoid__add(U_12537) ),
    inference(variable_rename,[status(thm)],[f_3220_1]) ).

fof(f_3220_3,plain,
    ! [U_12537,U_12538,U_12539,U_12540,U_12541] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12537),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12537),U_12541),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12538),U_12539))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12537),U_12541),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12539),U_12540))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12537),U_12541),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12538),U_12540))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12539),U_12540))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12538),U_12539))
      | ~ class_Groups_Ocomm__monoid__add(U_12537) ),
    inference(definitional_conversion,[status(esa)],[f_3220_2]) ).

cnf(f_3220_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12537),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12537),U_12541),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12538),U_12539))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12537),U_12541),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12539),U_12540))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12537),U_12541),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12538),U_12540))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12539),U_12540))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12538),U_12539))
    | ~ class_Groups_Ocomm__monoid__add(U_12537) ),
    inference(clausify,[status(thm)],[f_3220_3]) ).

fof(f_3221_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_3221_2,plain,
    ! [U_12546,U_12545,U_12544,U_12543,U_12542] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12542),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12542),U_12546),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12543),U_12545))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12542),U_12546),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12543),U_12544))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12542),U_12546),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12544),U_12545))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12544),U_12545))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12543),U_12544))
      | ~ class_Groups_Oab__group__add(U_12542) ),
    inference(variable_rename,[status(thm)],[f_3221_1]) ).

fof(f_3221_3,plain,
    ! [U_12543,U_12542,U_12544,U_12545,U_12546] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12542),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12542),U_12546),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12543),U_12545))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12542),U_12546),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12543),U_12544))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12542),U_12546),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12544),U_12545))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12544),U_12545))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12543),U_12544))
      | ~ class_Groups_Oab__group__add(U_12542) ),
    inference(definitional_conversion,[status(esa)],[f_3221_2]) ).

cnf(f_3221_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12542),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12542),U_12546),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12543),U_12545))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12542),U_12546),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12543),U_12544))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12542),U_12546),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12544),U_12545))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12544),U_12545))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12543),U_12544))
    | ~ class_Groups_Oab__group__add(U_12542) ),
    inference(clausify,[status(thm)],[f_3221_3]) ).

fof(f_3222_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_3222_2,plain,
    ! [U_12551,U_12550,U_12549,U_12548,U_12547] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12548,U_12547),hAPP(hAPP(c_COMBC(U_12548,U_12547,U_12547),hAPP(hAPP(c_COMBS(U_12548,U_12547,tc_fun(U_12547,U_12547)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12547,tc_fun(U_12547,U_12547)),U_12548),c_If(U_12547)),hAPP(c_fequal,U_12550))),U_12551)),c_Groups_Ozero__class_Ozero(U_12547))),U_12549) = c_Groups_Ozero__class_Ozero(U_12547)
          | hBOOL(hAPP(hAPP(c_member(U_12548),U_12550),U_12549)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12548,U_12547),hAPP(hAPP(c_COMBC(U_12548,U_12547,U_12547),hAPP(hAPP(c_COMBS(U_12548,U_12547,tc_fun(U_12547,U_12547)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12547,tc_fun(U_12547,U_12547)),U_12548),c_If(U_12547)),hAPP(c_fequal,U_12550))),U_12551)),c_Groups_Ozero__class_Ozero(U_12547))),U_12549) = hAPP(U_12551,U_12550)
          | ~ hBOOL(hAPP(hAPP(c_member(U_12548),U_12550),U_12549)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12548),U_12549))
      | ~ class_Groups_Ocomm__monoid__add(U_12547) ),
    inference(variable_rename,[status(thm)],[f_3222_1]) ).

fof(f_3222_3,plain,
    ( ! [U_12547,U_12548,U_12549,U_12550,U_12551] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12548,U_12547),hAPP(hAPP(c_COMBC(U_12548,U_12547,U_12547),hAPP(hAPP(c_COMBS(U_12548,U_12547,tc_fun(U_12547,U_12547)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12547,tc_fun(U_12547,U_12547)),U_12548),c_If(U_12547)),hAPP(c_fequal,U_12550))),U_12551)),c_Groups_Ozero__class_Ozero(U_12547))),U_12549) = c_Groups_Ozero__class_Ozero(U_12547)
        | hBOOL(hAPP(hAPP(c_member(U_12548),U_12550),U_12549))
        | ~ sP914(U_12547,U_12548,U_12549,U_12550,U_12551) )
    & ! [U_12547,U_12548,U_12549,U_12550,U_12551] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12548,U_12547),hAPP(hAPP(c_COMBC(U_12548,U_12547,U_12547),hAPP(hAPP(c_COMBS(U_12548,U_12547,tc_fun(U_12547,U_12547)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12547,tc_fun(U_12547,U_12547)),U_12548),c_If(U_12547)),hAPP(c_fequal,U_12550))),U_12551)),c_Groups_Ozero__class_Ozero(U_12547))),U_12549) = hAPP(U_12551,U_12550)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12548),U_12550),U_12549))
        | ~ sP914(U_12547,U_12548,U_12549,U_12550,U_12551) )
    & ! [U_12547,U_12548,U_12549,U_12550,U_12551] :
        ( sP914(U_12547,U_12548,U_12549,U_12550,U_12551)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12548),U_12549))
        | ~ class_Groups_Ocomm__monoid__add(U_12547) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP914])],[f_3222_2]) ).

cnf(f_3222_4,plain,
    ( sP914(U_12547,U_12548,U_12549,U_12550,U_12551)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12548),U_12549))
    | ~ class_Groups_Ocomm__monoid__add(U_12547) ),
    inference(clausify,[status(thm)],[f_3222_3]) ).

cnf(f_3222_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12548,U_12547),hAPP(hAPP(c_COMBC(U_12548,U_12547,U_12547),hAPP(hAPP(c_COMBS(U_12548,U_12547,tc_fun(U_12547,U_12547)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12547,tc_fun(U_12547,U_12547)),U_12548),c_If(U_12547)),hAPP(c_fequal,U_12550))),U_12551)),c_Groups_Ozero__class_Ozero(U_12547))),U_12549) = hAPP(U_12551,U_12550)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12548),U_12550),U_12549))
    | ~ sP914(U_12547,U_12548,U_12549,U_12550,U_12551) ),
    inference(clausify,[status(thm)],[f_3222_3]) ).

cnf(f_3222_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12548,U_12547),hAPP(hAPP(c_COMBC(U_12548,U_12547,U_12547),hAPP(hAPP(c_COMBS(U_12548,U_12547,tc_fun(U_12547,U_12547)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12547,tc_fun(U_12547,U_12547)),U_12548),c_If(U_12547)),hAPP(c_fequal,U_12550))),U_12551)),c_Groups_Ozero__class_Ozero(U_12547))),U_12549) = c_Groups_Ozero__class_Ozero(U_12547)
    | hBOOL(hAPP(hAPP(c_member(U_12548),U_12550),U_12549))
    | ~ sP914(U_12547,U_12548,U_12549,U_12550,U_12551) ),
    inference(clausify,[status(thm)],[f_3222_3]) ).

fof(f_3223_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_3223_2,plain,
    ! [U_12556,U_12555,U_12554,U_12553,U_12552] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12553,U_12552),hAPP(hAPP(c_COMBC(U_12553,U_12552,U_12552),hAPP(hAPP(c_COMBS(U_12553,U_12552,tc_fun(U_12552,U_12552)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12552,tc_fun(U_12552,U_12552)),U_12553),c_If(U_12552)),hAPP(hAPP(c_COMBC(U_12553,U_12553,tc_HOL_Obool),c_fequal),U_12555))),U_12556)),c_Groups_Ozero__class_Ozero(U_12552))),U_12554) = c_Groups_Ozero__class_Ozero(U_12552)
          | hBOOL(hAPP(hAPP(c_member(U_12553),U_12555),U_12554)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12553,U_12552),hAPP(hAPP(c_COMBC(U_12553,U_12552,U_12552),hAPP(hAPP(c_COMBS(U_12553,U_12552,tc_fun(U_12552,U_12552)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12552,tc_fun(U_12552,U_12552)),U_12553),c_If(U_12552)),hAPP(hAPP(c_COMBC(U_12553,U_12553,tc_HOL_Obool),c_fequal),U_12555))),U_12556)),c_Groups_Ozero__class_Ozero(U_12552))),U_12554) = hAPP(U_12556,U_12555)
          | ~ hBOOL(hAPP(hAPP(c_member(U_12553),U_12555),U_12554)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12553),U_12554))
      | ~ class_Groups_Ocomm__monoid__add(U_12552) ),
    inference(variable_rename,[status(thm)],[f_3223_1]) ).

fof(f_3223_3,plain,
    ( ! [U_12553,U_12552,U_12554,U_12555,U_12556] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12553,U_12552),hAPP(hAPP(c_COMBC(U_12553,U_12552,U_12552),hAPP(hAPP(c_COMBS(U_12553,U_12552,tc_fun(U_12552,U_12552)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12552,tc_fun(U_12552,U_12552)),U_12553),c_If(U_12552)),hAPP(hAPP(c_COMBC(U_12553,U_12553,tc_HOL_Obool),c_fequal),U_12555))),U_12556)),c_Groups_Ozero__class_Ozero(U_12552))),U_12554) = c_Groups_Ozero__class_Ozero(U_12552)
        | hBOOL(hAPP(hAPP(c_member(U_12553),U_12555),U_12554))
        | ~ sP915(U_12553,U_12552,U_12554,U_12555,U_12556) )
    & ! [U_12553,U_12552,U_12554,U_12555,U_12556] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12553,U_12552),hAPP(hAPP(c_COMBC(U_12553,U_12552,U_12552),hAPP(hAPP(c_COMBS(U_12553,U_12552,tc_fun(U_12552,U_12552)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12552,tc_fun(U_12552,U_12552)),U_12553),c_If(U_12552)),hAPP(hAPP(c_COMBC(U_12553,U_12553,tc_HOL_Obool),c_fequal),U_12555))),U_12556)),c_Groups_Ozero__class_Ozero(U_12552))),U_12554) = hAPP(U_12556,U_12555)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12553),U_12555),U_12554))
        | ~ sP915(U_12553,U_12552,U_12554,U_12555,U_12556) )
    & ! [U_12553,U_12552,U_12554,U_12555,U_12556] :
        ( sP915(U_12553,U_12552,U_12554,U_12555,U_12556)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12553),U_12554))
        | ~ class_Groups_Ocomm__monoid__add(U_12552) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP915])],[f_3223_2]) ).

cnf(f_3223_4,plain,
    ( sP915(U_12553,U_12552,U_12554,U_12555,U_12556)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12553),U_12554))
    | ~ class_Groups_Ocomm__monoid__add(U_12552) ),
    inference(clausify,[status(thm)],[f_3223_3]) ).

cnf(f_3223_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12553,U_12552),hAPP(hAPP(c_COMBC(U_12553,U_12552,U_12552),hAPP(hAPP(c_COMBS(U_12553,U_12552,tc_fun(U_12552,U_12552)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12552,tc_fun(U_12552,U_12552)),U_12553),c_If(U_12552)),hAPP(hAPP(c_COMBC(U_12553,U_12553,tc_HOL_Obool),c_fequal),U_12555))),U_12556)),c_Groups_Ozero__class_Ozero(U_12552))),U_12554) = hAPP(U_12556,U_12555)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12553),U_12555),U_12554))
    | ~ sP915(U_12553,U_12552,U_12554,U_12555,U_12556) ),
    inference(clausify,[status(thm)],[f_3223_3]) ).

cnf(f_3223_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12553,U_12552),hAPP(hAPP(c_COMBC(U_12553,U_12552,U_12552),hAPP(hAPP(c_COMBS(U_12553,U_12552,tc_fun(U_12552,U_12552)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12552,tc_fun(U_12552,U_12552)),U_12553),c_If(U_12552)),hAPP(hAPP(c_COMBC(U_12553,U_12553,tc_HOL_Obool),c_fequal),U_12555))),U_12556)),c_Groups_Ozero__class_Ozero(U_12552))),U_12554) = c_Groups_Ozero__class_Ozero(U_12552)
    | hBOOL(hAPP(hAPP(c_member(U_12553),U_12555),U_12554))
    | ~ sP915(U_12553,U_12552,U_12554,U_12555,U_12556) ),
    inference(clausify,[status(thm)],[f_3223_3]) ).

fof(f_3224_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_3224_2,plain,
    ! [U_12561,U_12560,U_12559,U_12558,U_12557] :
      ( ( hAPP(c_Map_Orestrict__map(U_12557,U_12560,U_12561,U_12559),U_12558) = c_Option_Ooption_ONone(U_12560)
        | hBOOL(hAPP(hAPP(c_member(U_12557),U_12558),U_12559)) )
      & ( hAPP(c_Map_Orestrict__map(U_12557,U_12560,U_12561,U_12559),U_12558) = hAPP(U_12561,U_12558)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12557),U_12558),U_12559)) ) ),
    inference(variable_rename,[status(thm)],[f_3224_1]) ).

fof(f_3224_3,plain,
    ( ! [U_12571,U_12569,U_12567,U_12565,U_12563] :
        ( hAPP(c_Map_Orestrict__map(U_12563,U_12569,U_12571,U_12567),U_12565) = c_Option_Ooption_ONone(U_12569)
        | hBOOL(hAPP(hAPP(c_member(U_12563),U_12565),U_12567)) )
    & ! [U_12570,U_12568,U_12566,U_12564,U_12562] :
        ( hAPP(c_Map_Orestrict__map(U_12562,U_12568,U_12570,U_12566),U_12564) = hAPP(U_12570,U_12564)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12562),U_12564),U_12566)) ) ),
    inference(miniscope,[status(thm)],[f_3224_2]) ).

fof(f_3224_4,plain,
    ( ! [U_12563,U_12567,U_12569,U_12565,U_12571] :
        ( hAPP(c_Map_Orestrict__map(U_12563,U_12569,U_12571,U_12567),U_12565) = c_Option_Ooption_ONone(U_12569)
        | hBOOL(hAPP(hAPP(c_member(U_12563),U_12565),U_12567)) )
    & ! [U_12562,U_12564,U_12570,U_12566,U_12568] :
        ( hAPP(c_Map_Orestrict__map(U_12562,U_12568,U_12570,U_12566),U_12564) = hAPP(U_12570,U_12564)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12562),U_12564),U_12566)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3224_3]) ).

cnf(f_3224_5,plain,
    ( hAPP(c_Map_Orestrict__map(U_12562,U_12568,U_12570,U_12566),U_12564) = hAPP(U_12570,U_12564)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12562),U_12564),U_12566)) ),
    inference(clausify,[status(thm)],[f_3224_4]) ).

cnf(f_3224_6,plain,
    ( hAPP(c_Map_Orestrict__map(U_12563,U_12569,U_12571,U_12567),U_12565) = c_Option_Ooption_ONone(U_12569)
    | hBOOL(hAPP(hAPP(c_member(U_12563),U_12565),U_12567)) ),
    inference(clausify,[status(thm)],[f_3224_4]) ).

fof(f_3225_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_3225_2,plain,
    ! [U_12575,U_12574,U_12573,U_12572] : hAPP(c_Map_Orestrict__map(U_12572,U_12573,U_12574,c_Orderings_Obot__class_Obot(tc_fun(U_12572,tc_HOL_Obool))),U_12575) = c_Option_Ooption_ONone(U_12573),
    inference(variable_rename,[status(thm)],[f_3225_1]) ).

fof(f_3225_3,plain,
    ! [U_12573,U_12572,U_12574,U_12575] : hAPP(c_Map_Orestrict__map(U_12572,U_12573,U_12574,c_Orderings_Obot__class_Obot(tc_fun(U_12572,tc_HOL_Obool))),U_12575) = c_Option_Ooption_ONone(U_12573),
    inference(definitional_conversion,[status(esa)],[f_3225_2]) ).

cnf(f_3225_4,plain,
    hAPP(c_Map_Orestrict__map(U_12572,U_12573,U_12574,c_Orderings_Obot__class_Obot(tc_fun(U_12572,tc_HOL_Obool))),U_12575) = c_Option_Ooption_ONone(U_12573),
    inference(clausify,[status(thm)],[f_3225_3]) ).

fof(f_3226_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_3226_2,plain,
    ! [U_12579,U_12578,U_12577,U_12576] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12577,U_12576),hAPP(c_COMBK(U_12576,U_12577),U_12578)),U_12579) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12576),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12576),hAPP(c_Finite__Set_Ocard(U_12577),U_12579))),U_12578)
      | ~ class_Rings_Osemiring__1(U_12576) ),
    inference(variable_rename,[status(thm)],[f_3226_1]) ).

fof(f_3226_3,plain,
    ! [U_12576,U_12577,U_12578,U_12579] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12577,U_12576),hAPP(c_COMBK(U_12576,U_12577),U_12578)),U_12579) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12576),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12576),hAPP(c_Finite__Set_Ocard(U_12577),U_12579))),U_12578)
      | ~ class_Rings_Osemiring__1(U_12576) ),
    inference(definitional_conversion,[status(esa)],[f_3226_2]) ).

cnf(f_3226_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12577,U_12576),hAPP(c_COMBK(U_12576,U_12577),U_12578)),U_12579) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12576),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12576),hAPP(c_Finite__Set_Ocard(U_12577),U_12579))),U_12578)
    | ~ class_Rings_Osemiring__1(U_12576) ),
    inference(clausify,[status(thm)],[f_3226_3]) ).

fof(f_3227_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_3227_2,plain,
    ! [U_12582,U_12581,U_12580] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12580),U_12581),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12582))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12580),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12580),U_12581),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12582))),hAPP(U_12581,U_12582))
      | ~ class_Groups_Ocomm__monoid__add(U_12580) ),
    inference(variable_rename,[status(thm)],[f_3227_1]) ).

fof(f_3227_3,plain,
    ! [U_12580,U_12581,U_12582] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12580),U_12581),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12582))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12580),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12580),U_12581),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12582))),hAPP(U_12581,U_12582))
      | ~ class_Groups_Ocomm__monoid__add(U_12580) ),
    inference(definitional_conversion,[status(esa)],[f_3227_2]) ).

cnf(f_3227_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12580),U_12581),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12582))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12580),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12580),U_12581),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12582))),hAPP(U_12581,U_12582))
    | ~ class_Groups_Ocomm__monoid__add(U_12580) ),
    inference(clausify,[status(thm)],[f_3227_3]) ).

fof(f_3228_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_3228_2,plain,
    ! [U_12585,U_12584,U_12583] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12583),U_12584),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12585))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12583),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12583),U_12584),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12585))),hAPP(U_12584,hAPP(c_Nat_OSuc,U_12585)))
      | ~ class_Groups_Ocomm__monoid__add(U_12583) ),
    inference(variable_rename,[status(thm)],[f_3228_1]) ).

fof(f_3228_3,plain,
    ! [U_12583,U_12584,U_12585] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12583),U_12584),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12585))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12583),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12583),U_12584),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12585))),hAPP(U_12584,hAPP(c_Nat_OSuc,U_12585)))
      | ~ class_Groups_Ocomm__monoid__add(U_12583) ),
    inference(definitional_conversion,[status(esa)],[f_3228_2]) ).

cnf(f_3228_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12583),U_12584),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12585))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12583),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12583),U_12584),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12585))),hAPP(U_12584,hAPP(c_Nat_OSuc,U_12585)))
    | ~ class_Groups_Ocomm__monoid__add(U_12583) ),
    inference(clausify,[status(thm)],[f_3228_3]) ).

fof(f_3229_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_3229_2,plain,
    ! [U_12590,U_12589,U_12588,U_12587,U_12586] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12587,U_12586),U_12590),hAPP(hAPP(c_Set_Oinsert(U_12587),U_12589),U_12588)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12586),hAPP(U_12590,U_12589)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12587,U_12586),U_12590),U_12588))
      | hBOOL(hAPP(hAPP(c_member(U_12587),U_12589),U_12588))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12587),U_12588))
      | ~ class_Groups_Ocomm__monoid__add(U_12586) ),
    inference(variable_rename,[status(thm)],[f_3229_1]) ).

fof(f_3229_3,plain,
    ! [U_12586,U_12587,U_12588,U_12589,U_12590] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12587,U_12586),U_12590),hAPP(hAPP(c_Set_Oinsert(U_12587),U_12589),U_12588)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12586),hAPP(U_12590,U_12589)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12587,U_12586),U_12590),U_12588))
      | hBOOL(hAPP(hAPP(c_member(U_12587),U_12589),U_12588))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12587),U_12588))
      | ~ class_Groups_Ocomm__monoid__add(U_12586) ),
    inference(definitional_conversion,[status(esa)],[f_3229_2]) ).

cnf(f_3229_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12587,U_12586),U_12590),hAPP(hAPP(c_Set_Oinsert(U_12587),U_12589),U_12588)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12586),hAPP(U_12590,U_12589)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12587,U_12586),U_12590),U_12588))
    | hBOOL(hAPP(hAPP(c_member(U_12587),U_12589),U_12588))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12587),U_12588))
    | ~ class_Groups_Ocomm__monoid__add(U_12586) ),
    inference(clausify,[status(thm)],[f_3229_3]) ).

fof(f_3230_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_3230_2,plain,
    ! [U_12595,U_12594,U_12593,U_12592,U_12591] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12592,U_12591),U_12595),hAPP(hAPP(c_Set_Oinsert(U_12592),U_12594),U_12593)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12591),hAPP(U_12595,U_12594)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12592,U_12591),U_12595),U_12593))
      | hBOOL(hAPP(hAPP(c_member(U_12592),U_12594),U_12593))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12592),U_12593))
      | ~ class_Groups_Ocomm__monoid__add(U_12591) ),
    inference(variable_rename,[status(thm)],[f_3230_1]) ).

fof(f_3230_3,plain,
    ! [U_12592,U_12591,U_12593,U_12594,U_12595] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12592,U_12591),U_12595),hAPP(hAPP(c_Set_Oinsert(U_12592),U_12594),U_12593)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12591),hAPP(U_12595,U_12594)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12592,U_12591),U_12595),U_12593))
      | hBOOL(hAPP(hAPP(c_member(U_12592),U_12594),U_12593))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12592),U_12593))
      | ~ class_Groups_Ocomm__monoid__add(U_12591) ),
    inference(definitional_conversion,[status(esa)],[f_3230_2]) ).

cnf(f_3230_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12592,U_12591),U_12595),hAPP(hAPP(c_Set_Oinsert(U_12592),U_12594),U_12593)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12591),hAPP(U_12595,U_12594)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12592,U_12591),U_12595),U_12593))
    | hBOOL(hAPP(hAPP(c_member(U_12592),U_12594),U_12593))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12592),U_12593))
    | ~ class_Groups_Ocomm__monoid__add(U_12591) ),
    inference(clausify,[status(thm)],[f_3230_3]) ).

fof(f_3231_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_3231_2,plain,
    ! [U_12600,U_12599,U_12598,U_12597,U_12596] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12596),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12597,U_12596),U_12600),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12597,tc_HOL_Obool)),U_12598),U_12599))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12597,U_12596),U_12600),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12597,tc_HOL_Obool)),U_12598),U_12599))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12596),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12597,U_12596),U_12600),U_12598)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12597,U_12596),U_12600),U_12599))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12597),U_12599))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12597),U_12598))
      | ~ class_Groups_Ocomm__monoid__add(U_12596) ),
    inference(variable_rename,[status(thm)],[f_3231_1]) ).

fof(f_3231_3,plain,
    ! [U_12596,U_12597,U_12598,U_12599,U_12600] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12596),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12597,U_12596),U_12600),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12597,tc_HOL_Obool)),U_12598),U_12599))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12597,U_12596),U_12600),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12597,tc_HOL_Obool)),U_12598),U_12599))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12596),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12597,U_12596),U_12600),U_12598)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12597,U_12596),U_12600),U_12599))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12597),U_12599))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12597),U_12598))
      | ~ class_Groups_Ocomm__monoid__add(U_12596) ),
    inference(definitional_conversion,[status(esa)],[f_3231_2]) ).

cnf(f_3231_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12596),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12597,U_12596),U_12600),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12597,tc_HOL_Obool)),U_12598),U_12599))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12597,U_12596),U_12600),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12597,tc_HOL_Obool)),U_12598),U_12599))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12596),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12597,U_12596),U_12600),U_12598)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12597,U_12596),U_12600),U_12599))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12597),U_12599))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12597),U_12598))
    | ~ class_Groups_Ocomm__monoid__add(U_12596) ),
    inference(clausify,[status(thm)],[f_3231_3]) ).

fof(f_3232_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_3232_2,plain,
    ! [U_12605,U_12604,U_12603,U_12602,U_12601] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12602,U_12601),U_12605),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12602,tc_HOL_Obool)),U_12603),U_12604)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12601),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12602,U_12601),U_12605),U_12603)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12602,U_12601),U_12605),U_12604))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12602,tc_HOL_Obool)),U_12604),U_12603))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12602),U_12603))
      | ~ class_Groups_Oab__group__add(U_12601) ),
    inference(variable_rename,[status(thm)],[f_3232_1]) ).

fof(f_3232_3,plain,
    ! [U_12601,U_12602,U_12603,U_12604,U_12605] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12602,U_12601),U_12605),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12602,tc_HOL_Obool)),U_12603),U_12604)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12601),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12602,U_12601),U_12605),U_12603)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12602,U_12601),U_12605),U_12604))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12602,tc_HOL_Obool)),U_12604),U_12603))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12602),U_12603))
      | ~ class_Groups_Oab__group__add(U_12601) ),
    inference(definitional_conversion,[status(esa)],[f_3232_2]) ).

cnf(f_3232_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12602,U_12601),U_12605),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12602,tc_HOL_Obool)),U_12603),U_12604)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12601),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12602,U_12601),U_12605),U_12603)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12602,U_12601),U_12605),U_12604))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12602,tc_HOL_Obool)),U_12604),U_12603))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12602),U_12603))
    | ~ class_Groups_Oab__group__add(U_12601) ),
    inference(clausify,[status(thm)],[f_3232_3]) ).

fof(f_3233_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_3233_2,plain,
    ! [U_12609,U_12608,U_12607,U_12606] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12607,U_12606),U_12609),U_12608) = c_Groups_Ozero__class_Ozero(U_12606)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12607),U_12608)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12607,U_12606),U_12609),U_12608) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12606,U_12607,c_Groups_Oplus__class_Oplus(U_12606)),U_12609),c_Groups_Ozero__class_Ozero(U_12606)),U_12608)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12607),U_12608)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_12606) ),
    inference(variable_rename,[status(thm)],[f_3233_1]) ).

fof(f_3233_3,plain,
    ( ! [U_12606,U_12607,U_12608,U_12609] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12607,U_12606),U_12609),U_12608) = c_Groups_Ozero__class_Ozero(U_12606)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12607),U_12608))
        | ~ sP916(U_12606,U_12607,U_12608,U_12609) )
    & ! [U_12606,U_12607,U_12608,U_12609] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12607,U_12606),U_12609),U_12608) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12606,U_12607,c_Groups_Oplus__class_Oplus(U_12606)),U_12609),c_Groups_Ozero__class_Ozero(U_12606)),U_12608)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12607),U_12608))
        | ~ sP916(U_12606,U_12607,U_12608,U_12609) )
    & ! [U_12606,U_12607,U_12608,U_12609] :
        ( sP916(U_12606,U_12607,U_12608,U_12609)
        | ~ class_Groups_Ocomm__monoid__add(U_12606) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP916])],[f_3233_2]) ).

cnf(f_3233_4,plain,
    ( sP916(U_12606,U_12607,U_12608,U_12609)
    | ~ class_Groups_Ocomm__monoid__add(U_12606) ),
    inference(clausify,[status(thm)],[f_3233_3]) ).

cnf(f_3233_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12607,U_12606),U_12609),U_12608) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12606,U_12607,c_Groups_Oplus__class_Oplus(U_12606)),U_12609),c_Groups_Ozero__class_Ozero(U_12606)),U_12608)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12607),U_12608))
    | ~ sP916(U_12606,U_12607,U_12608,U_12609) ),
    inference(clausify,[status(thm)],[f_3233_3]) ).

cnf(f_3233_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12607,U_12606),U_12609),U_12608) = c_Groups_Ozero__class_Ozero(U_12606)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12607),U_12608))
    | ~ sP916(U_12606,U_12607,U_12608,U_12609) ),
    inference(clausify,[status(thm)],[f_3233_3]) ).

fof(f_3234_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_3234_2,plain,
    ! [U_12613,U_12612,U_12611,U_12610] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12611,U_12610),U_12613),U_12612) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12610,U_12611,c_Groups_Oplus__class_Oplus(U_12610)),U_12613),c_Groups_Ozero__class_Ozero(U_12610)),U_12612)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12611),U_12612))
      | ~ class_Groups_Ocomm__monoid__add(U_12610) ),
    inference(variable_rename,[status(thm)],[f_3234_1]) ).

fof(f_3234_3,plain,
    ! [U_12611,U_12610,U_12612,U_12613] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12611,U_12610),U_12613),U_12612) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12610,U_12611,c_Groups_Oplus__class_Oplus(U_12610)),U_12613),c_Groups_Ozero__class_Ozero(U_12610)),U_12612)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12611),U_12612))
      | ~ class_Groups_Ocomm__monoid__add(U_12610) ),
    inference(definitional_conversion,[status(esa)],[f_3234_2]) ).

cnf(f_3234_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12611,U_12610),U_12613),U_12612) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12610,U_12611,c_Groups_Oplus__class_Oplus(U_12610)),U_12613),c_Groups_Ozero__class_Ozero(U_12610)),U_12612)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12611),U_12612))
    | ~ class_Groups_Ocomm__monoid__add(U_12610) ),
    inference(clausify,[status(thm)],[f_3234_3]) ).

fof(f_3235_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_3235_2,plain,
    ! [U_12616,U_12615,U_12614] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12614),U_12615),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_12616)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12614),U_12615),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12616))
      | hAPP(U_12615,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_12614)
      | ~ class_Groups_Ocomm__monoid__add(U_12614) ),
    inference(variable_rename,[status(thm)],[f_3235_1]) ).

fof(f_3235_3,plain,
    ! [U_12615,U_12616,U_12614] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12614),U_12615),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_12616)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12614),U_12615),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12616))
      | hAPP(U_12615,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_12614)
      | ~ class_Groups_Ocomm__monoid__add(U_12614) ),
    inference(definitional_conversion,[status(esa)],[f_3235_2]) ).

cnf(f_3235_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12614),U_12615),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_12616)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12614),U_12615),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12616))
    | hAPP(U_12615,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_12614)
    | ~ class_Groups_Ocomm__monoid__add(U_12614) ),
    inference(clausify,[status(thm)],[f_3235_3]) ).

fof(f_3236_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_3236_2,plain,
    ! [U_12620,U_12619,U_12618,U_12617] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12617),U_12620),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12618),U_12619)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12617),hAPP(U_12620,U_12618)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12617),U_12620),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12618)),U_12619)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12618),U_12619))
      | ~ class_Groups_Ocomm__monoid__add(U_12617) ),
    inference(variable_rename,[status(thm)],[f_3236_1]) ).

fof(f_3236_3,plain,
    ! [U_12618,U_12617,U_12619,U_12620] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12617),U_12620),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12618),U_12619)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12617),hAPP(U_12620,U_12618)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12617),U_12620),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12618)),U_12619)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12618),U_12619))
      | ~ class_Groups_Ocomm__monoid__add(U_12617) ),
    inference(definitional_conversion,[status(esa)],[f_3236_2]) ).

cnf(f_3236_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12617),U_12620),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12618),U_12619)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12617),hAPP(U_12620,U_12618)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12617),U_12620),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12618)),U_12619)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12618),U_12619))
    | ~ class_Groups_Ocomm__monoid__add(U_12617) ),
    inference(clausify,[status(thm)],[f_3236_3]) ).

fof(f_3237_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_3237_2,plain,
    ! [U_12624,U_12623,U_12622,U_12621] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12621),U_12624),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12622,U_12623)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12621),hAPP(U_12624,U_12622)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12621),U_12624),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12622),U_12623)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12622),U_12623))
      | ~ class_Groups_Ocomm__monoid__add(U_12621) ),
    inference(variable_rename,[status(thm)],[f_3237_1]) ).

fof(f_3237_3,plain,
    ! [U_12622,U_12621,U_12623,U_12624] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12621),U_12624),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12622,U_12623)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12621),hAPP(U_12624,U_12622)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12621),U_12624),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12622),U_12623)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12622),U_12623))
      | ~ class_Groups_Ocomm__monoid__add(U_12621) ),
    inference(definitional_conversion,[status(esa)],[f_3237_2]) ).

cnf(f_3237_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12621),U_12624),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12622,U_12623)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12621),hAPP(U_12624,U_12622)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12621),U_12624),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12622),U_12623)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12622),U_12623))
    | ~ class_Groups_Ocomm__monoid__add(U_12621) ),
    inference(clausify,[status(thm)],[f_3237_3]) ).

fof(f_3238_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_3238_2,plain,
    ! [U_12629,U_12628,U_12627,U_12626,U_12625] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12626,U_12625),U_12628),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12626,tc_HOL_Obool)),U_12627),U_12629)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12626,U_12625),hAPP(hAPP(c_COMBC(U_12626,U_12625,U_12625),hAPP(hAPP(c_COMBS(U_12626,U_12625,tc_fun(U_12625,U_12625)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12625,tc_fun(U_12625,U_12625)),U_12626),c_If(U_12625)),hAPP(hAPP(c_COMBC(U_12626,tc_fun(U_12626,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12626)),U_12629))),U_12628)),c_Groups_Ozero__class_Ozero(U_12625))),U_12627)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12626),U_12627))
      | ~ class_Groups_Ocomm__monoid__add(U_12625) ),
    inference(variable_rename,[status(thm)],[f_3238_1]) ).

fof(f_3238_3,plain,
    ! [U_12625,U_12626,U_12627,U_12628,U_12629] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12626,U_12625),U_12628),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12626,tc_HOL_Obool)),U_12627),U_12629)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12626,U_12625),hAPP(hAPP(c_COMBC(U_12626,U_12625,U_12625),hAPP(hAPP(c_COMBS(U_12626,U_12625,tc_fun(U_12625,U_12625)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12625,tc_fun(U_12625,U_12625)),U_12626),c_If(U_12625)),hAPP(hAPP(c_COMBC(U_12626,tc_fun(U_12626,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12626)),U_12629))),U_12628)),c_Groups_Ozero__class_Ozero(U_12625))),U_12627)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12626),U_12627))
      | ~ class_Groups_Ocomm__monoid__add(U_12625) ),
    inference(definitional_conversion,[status(esa)],[f_3238_2]) ).

cnf(f_3238_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12626,U_12625),U_12628),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12626,tc_HOL_Obool)),U_12627),U_12629)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12626,U_12625),hAPP(hAPP(c_COMBC(U_12626,U_12625,U_12625),hAPP(hAPP(c_COMBS(U_12626,U_12625,tc_fun(U_12625,U_12625)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12625,tc_fun(U_12625,U_12625)),U_12626),c_If(U_12625)),hAPP(hAPP(c_COMBC(U_12626,tc_fun(U_12626,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12626)),U_12629))),U_12628)),c_Groups_Ozero__class_Ozero(U_12625))),U_12627)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12626),U_12627))
    | ~ class_Groups_Ocomm__monoid__add(U_12625) ),
    inference(clausify,[status(thm)],[f_3238_3]) ).

fof(f_3239_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_3239_2,plain,
    ! [U_12634,U_12633,U_12632,U_12631,U_12630] :
      ( hBOOL(hAPP(hAPP(c_member(U_12632),U_12633),c_Map_Oran(U_12634,U_12632,U_12630)))
      | hAPP(U_12630,U_12631) != hAPP(c_Option_Ooption_OSome(U_12632),U_12633) ),
    inference(variable_rename,[status(thm)],[f_3239_1]) ).

fof(f_3239_3,plain,
    ! [U_12632,U_12631,U_12630,U_12633,U_12634] :
      ( hBOOL(hAPP(hAPP(c_member(U_12632),U_12633),c_Map_Oran(U_12634,U_12632,U_12630)))
      | hAPP(U_12630,U_12631) != hAPP(c_Option_Ooption_OSome(U_12632),U_12633) ),
    inference(definitional_conversion,[status(esa)],[f_3239_2]) ).

cnf(f_3239_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12632),U_12633),c_Map_Oran(U_12634,U_12632,U_12630)))
    | hAPP(U_12630,U_12631) != hAPP(c_Option_Ooption_OSome(U_12632),U_12633) ),
    inference(clausify,[status(thm)],[f_3239_3]) ).

fof(f_3240_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_3240_2,plain,
    ! [U_12639,U_12638,U_12637,U_12636,U_12635] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12636,U_12635),U_12638),hAPP(hAPP(c_Set_Oinsert(U_12636),U_12639),U_12637)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12635),hAPP(U_12638,U_12639)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12636,U_12635),U_12638),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12636,tc_HOL_Obool)),U_12637),hAPP(hAPP(c_Set_Oinsert(U_12636),U_12639),c_Orderings_Obot__class_Obot(tc_fun(U_12636,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12636),U_12637))
      | ~ class_Groups_Ocomm__monoid__add(U_12635) ),
    inference(variable_rename,[status(thm)],[f_3240_1]) ).

fof(f_3240_3,plain,
    ! [U_12635,U_12636,U_12637,U_12638,U_12639] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12636,U_12635),U_12638),hAPP(hAPP(c_Set_Oinsert(U_12636),U_12639),U_12637)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12635),hAPP(U_12638,U_12639)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12636,U_12635),U_12638),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12636,tc_HOL_Obool)),U_12637),hAPP(hAPP(c_Set_Oinsert(U_12636),U_12639),c_Orderings_Obot__class_Obot(tc_fun(U_12636,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12636),U_12637))
      | ~ class_Groups_Ocomm__monoid__add(U_12635) ),
    inference(definitional_conversion,[status(esa)],[f_3240_2]) ).

cnf(f_3240_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12636,U_12635),U_12638),hAPP(hAPP(c_Set_Oinsert(U_12636),U_12639),U_12637)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12635),hAPP(U_12638,U_12639)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12636,U_12635),U_12638),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12636,tc_HOL_Obool)),U_12637),hAPP(hAPP(c_Set_Oinsert(U_12636),U_12639),c_Orderings_Obot__class_Obot(tc_fun(U_12636,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12636),U_12637))
    | ~ class_Groups_Ocomm__monoid__add(U_12635) ),
    inference(clausify,[status(thm)],[f_3240_3]) ).

fof(f_3241_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_3241_2,plain,
    ! [U_12644,U_12643,U_12642,U_12641,U_12640] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12641,U_12640),U_12644),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12641,tc_HOL_Obool)),U_12642),U_12643)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12640),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12641,U_12640),U_12644),U_12642)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12641,U_12640),U_12644),U_12643))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12641,tc_HOL_Obool)),U_12642),U_12643) != c_Orderings_Obot__class_Obot(tc_fun(U_12641,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12641),U_12643))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12641),U_12642))
      | ~ class_Groups_Ocomm__monoid__add(U_12640) ),
    inference(variable_rename,[status(thm)],[f_3241_1]) ).

fof(f_3241_3,plain,
    ! [U_12640,U_12641,U_12642,U_12643,U_12644] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12641,U_12640),U_12644),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12641,tc_HOL_Obool)),U_12642),U_12643)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12640),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12641,U_12640),U_12644),U_12642)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12641,U_12640),U_12644),U_12643))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12641,tc_HOL_Obool)),U_12642),U_12643) != c_Orderings_Obot__class_Obot(tc_fun(U_12641,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12641),U_12643))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12641),U_12642))
      | ~ class_Groups_Ocomm__monoid__add(U_12640) ),
    inference(definitional_conversion,[status(esa)],[f_3241_2]) ).

cnf(f_3241_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12641,U_12640),U_12644),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12641,tc_HOL_Obool)),U_12642),U_12643)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12640),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12641,U_12640),U_12644),U_12642)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12641,U_12640),U_12644),U_12643))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12641,tc_HOL_Obool)),U_12642),U_12643) != c_Orderings_Obot__class_Obot(tc_fun(U_12641,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12641),U_12643))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12641),U_12642))
    | ~ class_Groups_Ocomm__monoid__add(U_12640) ),
    inference(clausify,[status(thm)],[f_3241_3]) ).

fof(f_3242_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_3242_2,plain,
    ! [U_12649,U_12648,U_12647,U_12646,U_12645] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12646,U_12645),U_12649),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12646,tc_HOL_Obool)),U_12647),U_12648)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12645),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12645),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12646,U_12645),U_12649),U_12647)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12646,U_12645),U_12649),U_12648))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12646,U_12645),U_12649),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12646,tc_HOL_Obool)),U_12647),U_12648)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12646),U_12648))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12646),U_12647))
      | ~ class_Groups_Oab__group__add(U_12645) ),
    inference(variable_rename,[status(thm)],[f_3242_1]) ).

fof(f_3242_3,plain,
    ! [U_12646,U_12645,U_12647,U_12648,U_12649] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12646,U_12645),U_12649),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12646,tc_HOL_Obool)),U_12647),U_12648)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12645),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12645),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12646,U_12645),U_12649),U_12647)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12646,U_12645),U_12649),U_12648))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12646,U_12645),U_12649),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12646,tc_HOL_Obool)),U_12647),U_12648)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12646),U_12648))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12646),U_12647))
      | ~ class_Groups_Oab__group__add(U_12645) ),
    inference(definitional_conversion,[status(esa)],[f_3242_2]) ).

cnf(f_3242_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12646,U_12645),U_12649),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12646,tc_HOL_Obool)),U_12647),U_12648)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12645),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12645),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12646,U_12645),U_12649),U_12647)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12646,U_12645),U_12649),U_12648))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12646,U_12645),U_12649),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12646,tc_HOL_Obool)),U_12647),U_12648)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12646),U_12648))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12646),U_12647))
    | ~ class_Groups_Oab__group__add(U_12645) ),
    inference(clausify,[status(thm)],[f_3242_3]) ).

fof(f_3243_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_3243_2,plain,
    ! [U_12653,U_12652,U_12651,U_12650] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12650),U_12653),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12652),hAPP(c_Nat_OSuc,U_12651))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12650),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12650),U_12653),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12652),U_12651))),hAPP(U_12653,U_12651))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12651),U_12652)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12650),U_12653),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12652),hAPP(c_Nat_OSuc,U_12651))) = c_Groups_Ozero__class_Ozero(U_12650)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12651),U_12652)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_12650) ),
    inference(variable_rename,[status(thm)],[f_3243_1]) ).

fof(f_3243_3,plain,
    ( ! [U_12650,U_12651,U_12652,U_12653] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12650),U_12653),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12652),hAPP(c_Nat_OSuc,U_12651))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12650),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12650),U_12653),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12652),U_12651))),hAPP(U_12653,U_12651))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12651),U_12652))
        | ~ sP917(U_12650,U_12651,U_12652,U_12653) )
    & ! [U_12650,U_12651,U_12652,U_12653] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12650),U_12653),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12652),hAPP(c_Nat_OSuc,U_12651))) = c_Groups_Ozero__class_Ozero(U_12650)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12651),U_12652))
        | ~ sP917(U_12650,U_12651,U_12652,U_12653) )
    & ! [U_12650,U_12651,U_12652,U_12653] :
        ( sP917(U_12650,U_12651,U_12652,U_12653)
        | ~ class_Groups_Ocomm__monoid__add(U_12650) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP917])],[f_3243_2]) ).

cnf(f_3243_4,plain,
    ( sP917(U_12650,U_12651,U_12652,U_12653)
    | ~ class_Groups_Ocomm__monoid__add(U_12650) ),
    inference(clausify,[status(thm)],[f_3243_3]) ).

cnf(f_3243_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12650),U_12653),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12652),hAPP(c_Nat_OSuc,U_12651))) = c_Groups_Ozero__class_Ozero(U_12650)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12651),U_12652))
    | ~ sP917(U_12650,U_12651,U_12652,U_12653) ),
    inference(clausify,[status(thm)],[f_3243_3]) ).

cnf(f_3243_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12650),U_12653),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12652),hAPP(c_Nat_OSuc,U_12651))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12650),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12650),U_12653),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12652),U_12651))),hAPP(U_12653,U_12651))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12651),U_12652))
    | ~ sP917(U_12650,U_12651,U_12652,U_12653) ),
    inference(clausify,[status(thm)],[f_3243_3]) ).

fof(f_3244_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_3244_2,plain,
    ! [U_12657,U_12656,U_12655,U_12654] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12654),U_12657),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12656,hAPP(c_Nat_OSuc,U_12655))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12654),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12654),U_12657),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12656,U_12655))),hAPP(U_12657,hAPP(c_Nat_OSuc,U_12655)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12655)),U_12656)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12654),U_12657),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12656,hAPP(c_Nat_OSuc,U_12655))) = c_Groups_Ozero__class_Ozero(U_12654)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12655)),U_12656)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_12654) ),
    inference(variable_rename,[status(thm)],[f_3244_1]) ).

fof(f_3244_3,plain,
    ( ! [U_12657,U_12656,U_12654,U_12655] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12654),U_12657),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12656,hAPP(c_Nat_OSuc,U_12655))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12654),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12654),U_12657),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12656,U_12655))),hAPP(U_12657,hAPP(c_Nat_OSuc,U_12655)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12655)),U_12656))
        | ~ sP918(U_12657,U_12656,U_12654,U_12655) )
    & ! [U_12657,U_12656,U_12654,U_12655] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12654),U_12657),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12656,hAPP(c_Nat_OSuc,U_12655))) = c_Groups_Ozero__class_Ozero(U_12654)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12655)),U_12656))
        | ~ sP918(U_12657,U_12656,U_12654,U_12655) )
    & ! [U_12657,U_12656,U_12654,U_12655] :
        ( sP918(U_12657,U_12656,U_12654,U_12655)
        | ~ class_Groups_Ocomm__monoid__add(U_12654) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP918])],[f_3244_2]) ).

cnf(f_3244_4,plain,
    ( sP918(U_12657,U_12656,U_12654,U_12655)
    | ~ class_Groups_Ocomm__monoid__add(U_12654) ),
    inference(clausify,[status(thm)],[f_3244_3]) ).

cnf(f_3244_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12654),U_12657),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12656,hAPP(c_Nat_OSuc,U_12655))) = c_Groups_Ozero__class_Ozero(U_12654)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12655)),U_12656))
    | ~ sP918(U_12657,U_12656,U_12654,U_12655) ),
    inference(clausify,[status(thm)],[f_3244_3]) ).

cnf(f_3244_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12654),U_12657),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12656,hAPP(c_Nat_OSuc,U_12655))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12654),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12654),U_12657),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12656,U_12655))),hAPP(U_12657,hAPP(c_Nat_OSuc,U_12655)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12655)),U_12656))
    | ~ sP918(U_12657,U_12656,U_12654,U_12655) ),
    inference(clausify,[status(thm)],[f_3244_3]) ).

fof(f_3245_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_3245_2,plain,
    ! [U_12661,U_12660,U_12659,U_12658] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12658),U_12661),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12659,U_12660)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12658),hAPP(U_12661,U_12659)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12658),U_12661),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_12659,U_12660)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12659),U_12660))
      | ~ class_Groups_Ocomm__monoid__add(U_12658) ),
    inference(variable_rename,[status(thm)],[f_3245_1]) ).

fof(f_3245_3,plain,
    ! [U_12659,U_12660,U_12658,U_12661] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12658),U_12661),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12659,U_12660)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12658),hAPP(U_12661,U_12659)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12658),U_12661),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_12659,U_12660)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12659),U_12660))
      | ~ class_Groups_Ocomm__monoid__add(U_12658) ),
    inference(definitional_conversion,[status(esa)],[f_3245_2]) ).

cnf(f_3245_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12658),U_12661),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12659,U_12660)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12658),hAPP(U_12661,U_12659)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12658),U_12661),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_12659,U_12660)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12659),U_12660))
    | ~ class_Groups_Ocomm__monoid__add(U_12658) ),
    inference(clausify,[status(thm)],[f_3245_3]) ).

fof(f_3246_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_3246_2,plain,
    ! [U_12666,U_12665,U_12664,U_12663,U_12662] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12662),U_12665),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12663,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12664),U_12666))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12662),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12662),U_12665),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12663,U_12664))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12662),U_12665),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12664),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12664),U_12666))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12664),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | ~ class_Groups_Ocomm__monoid__add(U_12662) ),
    inference(variable_rename,[status(thm)],[f_3246_1]) ).

fof(f_3246_3,plain,
    ! [U_12663,U_12662,U_12664,U_12665,U_12666] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12662),U_12665),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12663,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12664),U_12666))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12662),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12662),U_12665),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12663,U_12664))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12662),U_12665),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12664),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12664),U_12666))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12664),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | ~ class_Groups_Ocomm__monoid__add(U_12662) ),
    inference(definitional_conversion,[status(esa)],[f_3246_2]) ).

cnf(f_3246_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12662),U_12665),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12663,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12664),U_12666))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12662),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12662),U_12665),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12663,U_12664))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12662),U_12665),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12664),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12664),U_12666))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12664),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ class_Groups_Ocomm__monoid__add(U_12662) ),
    inference(clausify,[status(thm)],[f_3246_3]) ).

fof(f_3247_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_3247_2,plain,
    ! [U_12672,U_12671,U_12670,U_12669,U_12668,U_12667] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12667,tc_Option_Ooption(U_12668)),c_Map_Orestrict__map(U_12667,U_12668,U_12669,U_12670)),U_12671),U_12672) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12667,tc_Option_Ooption(U_12668)),c_Map_Orestrict__map(U_12667,U_12668,U_12669,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12667,tc_HOL_Obool)),U_12670),hAPP(hAPP(c_Set_Oinsert(U_12667),U_12671),c_Orderings_Obot__class_Obot(tc_fun(U_12667,tc_HOL_Obool)))))),U_12671),U_12672),
    inference(variable_rename,[status(thm)],[f_3247_1]) ).

fof(f_3247_3,plain,
    ! [U_12668,U_12667,U_12669,U_12670,U_12671,U_12672] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12667,tc_Option_Ooption(U_12668)),c_Map_Orestrict__map(U_12667,U_12668,U_12669,U_12670)),U_12671),U_12672) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12667,tc_Option_Ooption(U_12668)),c_Map_Orestrict__map(U_12667,U_12668,U_12669,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12667,tc_HOL_Obool)),U_12670),hAPP(hAPP(c_Set_Oinsert(U_12667),U_12671),c_Orderings_Obot__class_Obot(tc_fun(U_12667,tc_HOL_Obool)))))),U_12671),U_12672),
    inference(definitional_conversion,[status(esa)],[f_3247_2]) ).

cnf(f_3247_4,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12667,tc_Option_Ooption(U_12668)),c_Map_Orestrict__map(U_12667,U_12668,U_12669,U_12670)),U_12671),U_12672) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12667,tc_Option_Ooption(U_12668)),c_Map_Orestrict__map(U_12667,U_12668,U_12669,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12667,tc_HOL_Obool)),U_12670),hAPP(hAPP(c_Set_Oinsert(U_12667),U_12671),c_Orderings_Obot__class_Obot(tc_fun(U_12667,tc_HOL_Obool)))))),U_12671),U_12672),
    inference(clausify,[status(thm)],[f_3247_3]) ).

fof(f_3248_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_3248_2,plain,
    ! [U_12674,U_12673] : c_Map_Oran(U_12673,U_12674,hAPP(c_COMBK(tc_Option_Ooption(U_12674),U_12673),c_Option_Ooption_ONone(U_12674))) = c_Orderings_Obot__class_Obot(tc_fun(U_12674,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3248_1]) ).

fof(f_3248_3,plain,
    ! [U_12674,U_12673] : c_Map_Oran(U_12673,U_12674,hAPP(c_COMBK(tc_Option_Ooption(U_12674),U_12673),c_Option_Ooption_ONone(U_12674))) = c_Orderings_Obot__class_Obot(tc_fun(U_12674,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3248_2]) ).

cnf(f_3248_4,plain,
    c_Map_Oran(U_12673,U_12674,hAPP(c_COMBK(tc_Option_Ooption(U_12674),U_12673),c_Option_Ooption_ONone(U_12674))) = c_Orderings_Obot__class_Obot(tc_fun(U_12674,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3248_3]) ).

fof(f_3249_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_3249_2,plain,
    ! [U_12679,U_12678,U_12677,U_12676,U_12675] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12676,U_12675),U_12679),U_12677) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12675),hAPP(U_12679,U_12678)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12676,U_12675),U_12679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12676,tc_HOL_Obool)),U_12677),hAPP(hAPP(c_Set_Oinsert(U_12676),U_12678),c_Orderings_Obot__class_Obot(tc_fun(U_12676,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12676),U_12678),U_12677))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12676),U_12677))
      | ~ class_Groups_Ocomm__monoid__add(U_12675) ),
    inference(variable_rename,[status(thm)],[f_3249_1]) ).

fof(f_3249_3,plain,
    ! [U_12675,U_12676,U_12677,U_12678,U_12679] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12676,U_12675),U_12679),U_12677) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12675),hAPP(U_12679,U_12678)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12676,U_12675),U_12679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12676,tc_HOL_Obool)),U_12677),hAPP(hAPP(c_Set_Oinsert(U_12676),U_12678),c_Orderings_Obot__class_Obot(tc_fun(U_12676,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12676),U_12678),U_12677))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12676),U_12677))
      | ~ class_Groups_Ocomm__monoid__add(U_12675) ),
    inference(definitional_conversion,[status(esa)],[f_3249_2]) ).

cnf(f_3249_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12676,U_12675),U_12679),U_12677) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12675),hAPP(U_12679,U_12678)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12676,U_12675),U_12679),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12676,tc_HOL_Obool)),U_12677),hAPP(hAPP(c_Set_Oinsert(U_12676),U_12678),c_Orderings_Obot__class_Obot(tc_fun(U_12676,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12676),U_12678),U_12677))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12676),U_12677))
    | ~ class_Groups_Ocomm__monoid__add(U_12675) ),
    inference(clausify,[status(thm)],[f_3249_3]) ).

fof(f_3250_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_3250_2,plain,
    ! [U_12684,U_12683,U_12682,U_12681,U_12680] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12681,U_12680),U_12684),U_12682) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12680),hAPP(U_12684,U_12683)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12681,U_12680),U_12684),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12681,tc_HOL_Obool)),U_12682),hAPP(hAPP(c_Set_Oinsert(U_12681),U_12683),c_Orderings_Obot__class_Obot(tc_fun(U_12681,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12681),U_12683),U_12682))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12681),U_12682))
      | ~ class_Groups_Ocomm__monoid__add(U_12680) ),
    inference(variable_rename,[status(thm)],[f_3250_1]) ).

fof(f_3250_3,plain,
    ! [U_12680,U_12681,U_12682,U_12683,U_12684] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12681,U_12680),U_12684),U_12682) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12680),hAPP(U_12684,U_12683)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12681,U_12680),U_12684),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12681,tc_HOL_Obool)),U_12682),hAPP(hAPP(c_Set_Oinsert(U_12681),U_12683),c_Orderings_Obot__class_Obot(tc_fun(U_12681,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12681),U_12683),U_12682))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12681),U_12682))
      | ~ class_Groups_Ocomm__monoid__add(U_12680) ),
    inference(definitional_conversion,[status(esa)],[f_3250_2]) ).

cnf(f_3250_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12681,U_12680),U_12684),U_12682) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12680),hAPP(U_12684,U_12683)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12681,U_12680),U_12684),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12681,tc_HOL_Obool)),U_12682),hAPP(hAPP(c_Set_Oinsert(U_12681),U_12683),c_Orderings_Obot__class_Obot(tc_fun(U_12681,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12681),U_12683),U_12682))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12681),U_12682))
    | ~ class_Groups_Ocomm__monoid__add(U_12680) ),
    inference(clausify,[status(thm)],[f_3250_3]) ).

fof(f_3251_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_3251_2,plain,
    ! [U_12689,U_12688,U_12687,U_12686,U_12685] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12686,U_12685),U_12689),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12686,tc_HOL_Obool)),U_12687),hAPP(hAPP(c_Set_Oinsert(U_12686),U_12688),c_Orderings_Obot__class_Obot(tc_fun(U_12686,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12686,U_12685),U_12689),U_12687)
          | hBOOL(hAPP(hAPP(c_member(U_12686),U_12688),U_12687)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12686,U_12685),U_12689),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12686,tc_HOL_Obool)),U_12687),hAPP(hAPP(c_Set_Oinsert(U_12686),U_12688),c_Orderings_Obot__class_Obot(tc_fun(U_12686,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12685),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12686,U_12685),U_12689),U_12687)),hAPP(U_12689,U_12688))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12686),U_12688),U_12687)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12686),U_12687))
      | ~ class_Groups_Oab__group__add(U_12685) ),
    inference(variable_rename,[status(thm)],[f_3251_1]) ).

fof(f_3251_3,plain,
    ( ! [U_12685,U_12686,U_12687,U_12688,U_12689] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12686,U_12685),U_12689),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12686,tc_HOL_Obool)),U_12687),hAPP(hAPP(c_Set_Oinsert(U_12686),U_12688),c_Orderings_Obot__class_Obot(tc_fun(U_12686,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12686,U_12685),U_12689),U_12687)
        | hBOOL(hAPP(hAPP(c_member(U_12686),U_12688),U_12687))
        | ~ sP919(U_12685,U_12686,U_12687,U_12688,U_12689) )
    & ! [U_12685,U_12686,U_12687,U_12688,U_12689] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12686,U_12685),U_12689),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12686,tc_HOL_Obool)),U_12687),hAPP(hAPP(c_Set_Oinsert(U_12686),U_12688),c_Orderings_Obot__class_Obot(tc_fun(U_12686,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12685),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12686,U_12685),U_12689),U_12687)),hAPP(U_12689,U_12688))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12686),U_12688),U_12687))
        | ~ sP919(U_12685,U_12686,U_12687,U_12688,U_12689) )
    & ! [U_12685,U_12686,U_12687,U_12688,U_12689] :
        ( sP919(U_12685,U_12686,U_12687,U_12688,U_12689)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12686),U_12687))
        | ~ class_Groups_Oab__group__add(U_12685) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP919])],[f_3251_2]) ).

cnf(f_3251_4,plain,
    ( sP919(U_12685,U_12686,U_12687,U_12688,U_12689)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12686),U_12687))
    | ~ class_Groups_Oab__group__add(U_12685) ),
    inference(clausify,[status(thm)],[f_3251_3]) ).

cnf(f_3251_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12686,U_12685),U_12689),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12686,tc_HOL_Obool)),U_12687),hAPP(hAPP(c_Set_Oinsert(U_12686),U_12688),c_Orderings_Obot__class_Obot(tc_fun(U_12686,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12685),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12686,U_12685),U_12689),U_12687)),hAPP(U_12689,U_12688))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12686),U_12688),U_12687))
    | ~ sP919(U_12685,U_12686,U_12687,U_12688,U_12689) ),
    inference(clausify,[status(thm)],[f_3251_3]) ).

cnf(f_3251_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12686,U_12685),U_12689),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12686,tc_HOL_Obool)),U_12687),hAPP(hAPP(c_Set_Oinsert(U_12686),U_12688),c_Orderings_Obot__class_Obot(tc_fun(U_12686,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12686,U_12685),U_12689),U_12687)
    | hBOOL(hAPP(hAPP(c_member(U_12686),U_12688),U_12687))
    | ~ sP919(U_12685,U_12686,U_12687,U_12688,U_12689) ),
    inference(clausify,[status(thm)],[f_3251_3]) ).

fof(f_3252_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_3252_2,plain,
    ! [U_12694,U_12693,U_12692,U_12691,U_12690] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12691,U_12690),U_12694),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12691,tc_HOL_Obool)),U_12692),hAPP(hAPP(c_Set_Oinsert(U_12691),U_12693),c_Orderings_Obot__class_Obot(tc_fun(U_12691,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12690),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12691,U_12690),U_12694),U_12692)),hAPP(U_12694,U_12693))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12691),U_12693),U_12692))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12691),U_12692))
      | ~ class_Rings_Oring(U_12690) ),
    inference(variable_rename,[status(thm)],[f_3252_1]) ).

fof(f_3252_3,plain,
    ! [U_12691,U_12690,U_12692,U_12693,U_12694] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12691,U_12690),U_12694),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12691,tc_HOL_Obool)),U_12692),hAPP(hAPP(c_Set_Oinsert(U_12691),U_12693),c_Orderings_Obot__class_Obot(tc_fun(U_12691,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12690),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12691,U_12690),U_12694),U_12692)),hAPP(U_12694,U_12693))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12691),U_12693),U_12692))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12691),U_12692))
      | ~ class_Rings_Oring(U_12690) ),
    inference(definitional_conversion,[status(esa)],[f_3252_2]) ).

cnf(f_3252_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12691,U_12690),U_12694),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12691,tc_HOL_Obool)),U_12692),hAPP(hAPP(c_Set_Oinsert(U_12691),U_12693),c_Orderings_Obot__class_Obot(tc_fun(U_12691,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12690),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12691,U_12690),U_12694),U_12692)),hAPP(U_12694,U_12693))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12691),U_12693),U_12692))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12691),U_12692))
    | ~ class_Rings_Oring(U_12690) ),
    inference(clausify,[status(thm)],[f_3252_3]) ).

fof(f_3253_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_3253_2,plain,
    ! [U_12697,U_12696,U_12695] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12695),hAPP(c_Power_Opower__class_Opower(U_12695),U_12696)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12697)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12695),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12695),hAPP(hAPP(c_Power_Opower__class_Opower(U_12695),U_12696),U_12697)),c_Groups_Oone__class_Oone(U_12695))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12695),U_12696),c_Groups_Oone__class_Oone(U_12695)))
      | U_12696 = c_Groups_Oone__class_Oone(U_12695)
      | ~ class_Fields_Ofield(U_12695) ),
    inference(variable_rename,[status(thm)],[f_3253_1]) ).

fof(f_3253_3,plain,
    ! [U_12696,U_12695,U_12697] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12695),hAPP(c_Power_Opower__class_Opower(U_12695),U_12696)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12697)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12695),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12695),hAPP(hAPP(c_Power_Opower__class_Opower(U_12695),U_12696),U_12697)),c_Groups_Oone__class_Oone(U_12695))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12695),U_12696),c_Groups_Oone__class_Oone(U_12695)))
      | U_12696 = c_Groups_Oone__class_Oone(U_12695)
      | ~ class_Fields_Ofield(U_12695) ),
    inference(definitional_conversion,[status(esa)],[f_3253_2]) ).

cnf(f_3253_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12695),hAPP(c_Power_Opower__class_Opower(U_12695),U_12696)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12697)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12695),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12695),hAPP(hAPP(c_Power_Opower__class_Opower(U_12695),U_12696),U_12697)),c_Groups_Oone__class_Oone(U_12695))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12695),U_12696),c_Groups_Oone__class_Oone(U_12695)))
    | U_12696 = c_Groups_Oone__class_Oone(U_12695)
    | ~ class_Fields_Ofield(U_12695) ),
    inference(clausify,[status(thm)],[f_3253_3]) ).

fof(f_3254_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_3254_2,plain,
    ! [U_12699,U_12698] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12698),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12698),c_Groups_Oone__class_Oone(U_12698)),c_Groups_Oone__class_Oone(U_12698))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12698),c_Nat_Osemiring__1__class_Oof__nat(U_12698)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_12699))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12698),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12698),U_12699)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12698),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12698),U_12699)),c_Groups_Oone__class_Oone(U_12698)))
      | ~ class_Rings_Ocomm__semiring__1(U_12698) ),
    inference(variable_rename,[status(thm)],[f_3254_1]) ).

fof(f_3254_3,plain,
    ! [U_12698,U_12699] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12698),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12698),c_Groups_Oone__class_Oone(U_12698)),c_Groups_Oone__class_Oone(U_12698))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12698),c_Nat_Osemiring__1__class_Oof__nat(U_12698)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_12699))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12698),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12698),U_12699)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12698),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12698),U_12699)),c_Groups_Oone__class_Oone(U_12698)))
      | ~ class_Rings_Ocomm__semiring__1(U_12698) ),
    inference(definitional_conversion,[status(esa)],[f_3254_2]) ).

cnf(f_3254_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12698),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12698),c_Groups_Oone__class_Oone(U_12698)),c_Groups_Oone__class_Oone(U_12698))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12698),c_Nat_Osemiring__1__class_Oof__nat(U_12698)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_12699))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12698),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12698),U_12699)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12698),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12698),U_12699)),c_Groups_Oone__class_Oone(U_12698)))
    | ~ class_Rings_Ocomm__semiring__1(U_12698) ),
    inference(clausify,[status(thm)],[f_3254_3]) ).

fof(f_3255_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_3255_2,plain,
    ! [U_12703,U_12702,U_12701,U_12700] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12700),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12700,U_12700),hAPP(hAPP(c_COMBB(U_12700,tc_fun(U_12700,U_12700),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12700)),U_12703)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12700,tc_Nat_Onat),U_12703),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_12701,U_12702)) = c_Groups_Ozero__class_Ozero(U_12700)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12701),U_12702)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12700),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12700,U_12700),hAPP(hAPP(c_COMBB(U_12700,tc_fun(U_12700,U_12700),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12700)),U_12703)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12700,tc_Nat_Onat),U_12703),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_12701,U_12702)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12700),hAPP(U_12703,U_12701)),hAPP(U_12703,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12702),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12701),U_12702)) ) )
      | ~ class_Groups_Oab__group__add(U_12700) ),
    inference(variable_rename,[status(thm)],[f_3255_1]) ).

fof(f_3255_3,plain,
    ( ! [U_12700,U_12701,U_12702,U_12703] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12700),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12700,U_12700),hAPP(hAPP(c_COMBB(U_12700,tc_fun(U_12700,U_12700),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12700)),U_12703)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12700,tc_Nat_Onat),U_12703),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_12701,U_12702)) = c_Groups_Ozero__class_Ozero(U_12700)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12701),U_12702))
        | ~ sP920(U_12700,U_12701,U_12702,U_12703) )
    & ! [U_12700,U_12701,U_12702,U_12703] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12700),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12700,U_12700),hAPP(hAPP(c_COMBB(U_12700,tc_fun(U_12700,U_12700),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12700)),U_12703)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12700,tc_Nat_Onat),U_12703),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_12701,U_12702)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12700),hAPP(U_12703,U_12701)),hAPP(U_12703,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12702),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12701),U_12702))
        | ~ sP920(U_12700,U_12701,U_12702,U_12703) )
    & ! [U_12700,U_12701,U_12702,U_12703] :
        ( sP920(U_12700,U_12701,U_12702,U_12703)
        | ~ class_Groups_Oab__group__add(U_12700) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP920])],[f_3255_2]) ).

cnf(f_3255_4,plain,
    ( sP920(U_12700,U_12701,U_12702,U_12703)
    | ~ class_Groups_Oab__group__add(U_12700) ),
    inference(clausify,[status(thm)],[f_3255_3]) ).

cnf(f_3255_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12700),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12700,U_12700),hAPP(hAPP(c_COMBB(U_12700,tc_fun(U_12700,U_12700),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12700)),U_12703)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12700,tc_Nat_Onat),U_12703),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_12701,U_12702)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12700),hAPP(U_12703,U_12701)),hAPP(U_12703,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12702),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12701),U_12702))
    | ~ sP920(U_12700,U_12701,U_12702,U_12703) ),
    inference(clausify,[status(thm)],[f_3255_3]) ).

cnf(f_3255_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12700),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12700,U_12700),hAPP(hAPP(c_COMBB(U_12700,tc_fun(U_12700,U_12700),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12700)),U_12703)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12700,tc_Nat_Onat),U_12703),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_12701,U_12702)) = c_Groups_Ozero__class_Ozero(U_12700)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12701),U_12702))
    | ~ sP920(U_12700,U_12701,U_12702,U_12703) ),
    inference(clausify,[status(thm)],[f_3255_3]) ).

fof(f_3256_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_3256_2,plain,
    ! [U_12709,U_12708,U_12707,U_12706,U_12705,U_12704] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12704,tc_Option_Ooption(U_12707)),c_Map_Orestrict__map(U_12704,U_12707,U_12708,U_12706)),U_12705),U_12709) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12704,tc_Option_Ooption(U_12707)),c_Map_Orestrict__map(U_12704,U_12707,U_12708,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12704,tc_HOL_Obool)),U_12706),hAPP(hAPP(c_Set_Oinsert(U_12704),U_12705),c_Orderings_Obot__class_Obot(tc_fun(U_12704,tc_HOL_Obool)))))),U_12705),U_12709)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12704),U_12705),U_12706)) ),
    inference(variable_rename,[status(thm)],[f_3256_1]) ).

fof(f_3256_3,plain,
    ! [U_12705,U_12706,U_12704,U_12707,U_12708,U_12709] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12704,tc_Option_Ooption(U_12707)),c_Map_Orestrict__map(U_12704,U_12707,U_12708,U_12706)),U_12705),U_12709) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12704,tc_Option_Ooption(U_12707)),c_Map_Orestrict__map(U_12704,U_12707,U_12708,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12704,tc_HOL_Obool)),U_12706),hAPP(hAPP(c_Set_Oinsert(U_12704),U_12705),c_Orderings_Obot__class_Obot(tc_fun(U_12704,tc_HOL_Obool)))))),U_12705),U_12709)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12704),U_12705),U_12706)) ),
    inference(definitional_conversion,[status(esa)],[f_3256_2]) ).

cnf(f_3256_4,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12704,tc_Option_Ooption(U_12707)),c_Map_Orestrict__map(U_12704,U_12707,U_12708,U_12706)),U_12705),U_12709) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12704,tc_Option_Ooption(U_12707)),c_Map_Orestrict__map(U_12704,U_12707,U_12708,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12704,tc_HOL_Obool)),U_12706),hAPP(hAPP(c_Set_Oinsert(U_12704),U_12705),c_Orderings_Obot__class_Obot(tc_fun(U_12704,tc_HOL_Obool)))))),U_12705),U_12709)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12704),U_12705),U_12706)) ),
    inference(clausify,[status(thm)],[f_3256_3]) ).

fof(f_3257_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_3257_2,plain,
    ! [U_12715,U_12714,U_12713,U_12712,U_12711,U_12710] :
      ( ( c_Map_Orestrict__map(U_12710,U_12713,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12710,tc_Option_Ooption(U_12713)),U_12714),U_12711),U_12715),U_12712) = c_Map_Orestrict__map(U_12710,U_12713,U_12714,U_12712)
        | hBOOL(hAPP(hAPP(c_member(U_12710),U_12711),U_12712)) )
      & ( c_Map_Orestrict__map(U_12710,U_12713,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12710,tc_Option_Ooption(U_12713)),U_12714),U_12711),U_12715),U_12712) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12710,tc_Option_Ooption(U_12713)),c_Map_Orestrict__map(U_12710,U_12713,U_12714,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12710,tc_HOL_Obool)),U_12712),hAPP(hAPP(c_Set_Oinsert(U_12710),U_12711),c_Orderings_Obot__class_Obot(tc_fun(U_12710,tc_HOL_Obool)))))),U_12711),U_12715)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12710),U_12711),U_12712)) ) ),
    inference(variable_rename,[status(thm)],[f_3257_1]) ).

fof(f_3257_3,plain,
    ( ! [U_12727,U_12725,U_12723,U_12721,U_12719,U_12717] :
        ( c_Map_Orestrict__map(U_12717,U_12723,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12717,tc_Option_Ooption(U_12723)),U_12725),U_12719),U_12727),U_12721) = c_Map_Orestrict__map(U_12717,U_12723,U_12725,U_12721)
        | hBOOL(hAPP(hAPP(c_member(U_12717),U_12719),U_12721)) )
    & ! [U_12726,U_12724,U_12722,U_12720,U_12718,U_12716] :
        ( c_Map_Orestrict__map(U_12716,U_12722,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12716,tc_Option_Ooption(U_12722)),U_12724),U_12718),U_12726),U_12720) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12716,tc_Option_Ooption(U_12722)),c_Map_Orestrict__map(U_12716,U_12722,U_12724,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12716,tc_HOL_Obool)),U_12720),hAPP(hAPP(c_Set_Oinsert(U_12716),U_12718),c_Orderings_Obot__class_Obot(tc_fun(U_12716,tc_HOL_Obool)))))),U_12718),U_12726)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12716),U_12718),U_12720)) ) ),
    inference(miniscope,[status(thm)],[f_3257_2]) ).

fof(f_3257_4,plain,
    ( ! [U_12717,U_12719,U_12727,U_12721,U_12723,U_12725] :
        ( c_Map_Orestrict__map(U_12717,U_12723,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12717,tc_Option_Ooption(U_12723)),U_12725),U_12719),U_12727),U_12721) = c_Map_Orestrict__map(U_12717,U_12723,U_12725,U_12721)
        | hBOOL(hAPP(hAPP(c_member(U_12717),U_12719),U_12721)) )
    & ! [U_12716,U_12718,U_12720,U_12722,U_12724,U_12726] :
        ( c_Map_Orestrict__map(U_12716,U_12722,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12716,tc_Option_Ooption(U_12722)),U_12724),U_12718),U_12726),U_12720) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12716,tc_Option_Ooption(U_12722)),c_Map_Orestrict__map(U_12716,U_12722,U_12724,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12716,tc_HOL_Obool)),U_12720),hAPP(hAPP(c_Set_Oinsert(U_12716),U_12718),c_Orderings_Obot__class_Obot(tc_fun(U_12716,tc_HOL_Obool)))))),U_12718),U_12726)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12716),U_12718),U_12720)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3257_3]) ).

cnf(f_3257_5,plain,
    ( c_Map_Orestrict__map(U_12716,U_12722,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12716,tc_Option_Ooption(U_12722)),U_12724),U_12718),U_12726),U_12720) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12716,tc_Option_Ooption(U_12722)),c_Map_Orestrict__map(U_12716,U_12722,U_12724,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12716,tc_HOL_Obool)),U_12720),hAPP(hAPP(c_Set_Oinsert(U_12716),U_12718),c_Orderings_Obot__class_Obot(tc_fun(U_12716,tc_HOL_Obool)))))),U_12718),U_12726)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12716),U_12718),U_12720)) ),
    inference(clausify,[status(thm)],[f_3257_4]) ).

cnf(f_3257_6,plain,
    ( c_Map_Orestrict__map(U_12717,U_12723,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12717,tc_Option_Ooption(U_12723)),U_12725),U_12719),U_12727),U_12721) = c_Map_Orestrict__map(U_12717,U_12723,U_12725,U_12721)
    | hBOOL(hAPP(hAPP(c_member(U_12717),U_12719),U_12721)) ),
    inference(clausify,[status(thm)],[f_3257_4]) ).

fof(f_3258_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_3258_2,plain,
    ! [U_12731,U_12730,U_12729,U_12728] : c_Map_Orestrict__map(U_12728,U_12729,U_12730,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12728,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12728),U_12731),c_Orderings_Obot__class_Obot(tc_fun(U_12728,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12728,tc_Option_Ooption(U_12729)),U_12730),U_12731),c_Option_Ooption_ONone(U_12729)),
    inference(variable_rename,[status(thm)],[f_3258_1]) ).

fof(f_3258_3,plain,
    ! [U_12728,U_12729,U_12730,U_12731] : c_Map_Orestrict__map(U_12728,U_12729,U_12730,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12728,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12728),U_12731),c_Orderings_Obot__class_Obot(tc_fun(U_12728,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12728,tc_Option_Ooption(U_12729)),U_12730),U_12731),c_Option_Ooption_ONone(U_12729)),
    inference(definitional_conversion,[status(esa)],[f_3258_2]) ).

cnf(f_3258_4,plain,
    c_Map_Orestrict__map(U_12728,U_12729,U_12730,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12728,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12728),U_12731),c_Orderings_Obot__class_Obot(tc_fun(U_12728,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12728,tc_Option_Ooption(U_12729)),U_12730),U_12731),c_Option_Ooption_ONone(U_12729)),
    inference(clausify,[status(thm)],[f_3258_3]) ).

fof(f_3259_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_3259_2,plain,
    ! [U_12736,U_12735,U_12734,U_12733,U_12732] : c_Map_Orestrict__map(U_12732,U_12733,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12732,tc_Option_Ooption(U_12733)),U_12734),U_12735),hAPP(c_Option_Ooption_OSome(U_12733),U_12736)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12732,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12732),U_12735),c_Orderings_Obot__class_Obot(tc_fun(U_12732,tc_HOL_Obool))))) = c_Map_Orestrict__map(U_12732,U_12733,U_12734,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12732,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12732),U_12735),c_Orderings_Obot__class_Obot(tc_fun(U_12732,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3259_1]) ).

fof(f_3259_3,plain,
    ! [U_12733,U_12732,U_12734,U_12735,U_12736] : c_Map_Orestrict__map(U_12732,U_12733,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12732,tc_Option_Ooption(U_12733)),U_12734),U_12735),hAPP(c_Option_Ooption_OSome(U_12733),U_12736)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12732,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12732),U_12735),c_Orderings_Obot__class_Obot(tc_fun(U_12732,tc_HOL_Obool))))) = c_Map_Orestrict__map(U_12732,U_12733,U_12734,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12732,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12732),U_12735),c_Orderings_Obot__class_Obot(tc_fun(U_12732,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3259_2]) ).

cnf(f_3259_4,plain,
    c_Map_Orestrict__map(U_12732,U_12733,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12732,tc_Option_Ooption(U_12733)),U_12734),U_12735),hAPP(c_Option_Ooption_OSome(U_12733),U_12736)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12732,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12732),U_12735),c_Orderings_Obot__class_Obot(tc_fun(U_12732,tc_HOL_Obool))))) = c_Map_Orestrict__map(U_12732,U_12733,U_12734,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12732,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12732),U_12735),c_Orderings_Obot__class_Obot(tc_fun(U_12732,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3259_3]) ).

fof(f_3260_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_3260_2,plain,
    ! [U_12740,U_12739,U_12738,U_12737] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12737),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12737),c_Groups_Oone__class_Oone(U_12737)),c_Groups_Oone__class_Oone(U_12737))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12737),hAPP(hAPP(c_COMBB(U_12737,U_12737,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_12737),U_12738)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_12737,U_12737),hAPP(hAPP(c_COMBB(U_12737,tc_fun(U_12737,U_12737),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_12737)),c_Nat_Osemiring__1__class_Oof__nat(U_12737))),U_12739))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12740))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12737),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12737),U_12740)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12737),U_12738),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12737),U_12738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12737),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12737),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12740),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_12739))))
      | ~ class_Rings_Ocomm__semiring__1(U_12737) ),
    inference(variable_rename,[status(thm)],[f_3260_1]) ).

fof(f_3260_3,plain,
    ! [U_12737,U_12738,U_12739,U_12740] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12737),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12737),c_Groups_Oone__class_Oone(U_12737)),c_Groups_Oone__class_Oone(U_12737))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12737),hAPP(hAPP(c_COMBB(U_12737,U_12737,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_12737),U_12738)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_12737,U_12737),hAPP(hAPP(c_COMBB(U_12737,tc_fun(U_12737,U_12737),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_12737)),c_Nat_Osemiring__1__class_Oof__nat(U_12737))),U_12739))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12740))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12737),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12737),U_12740)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12737),U_12738),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12737),U_12738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12737),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12737),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12740),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_12739))))
      | ~ class_Rings_Ocomm__semiring__1(U_12737) ),
    inference(definitional_conversion,[status(esa)],[f_3260_2]) ).

cnf(f_3260_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12737),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12737),c_Groups_Oone__class_Oone(U_12737)),c_Groups_Oone__class_Oone(U_12737))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12737),hAPP(hAPP(c_COMBB(U_12737,U_12737,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_12737),U_12738)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_12737,U_12737),hAPP(hAPP(c_COMBB(U_12737,tc_fun(U_12737,U_12737),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_12737)),c_Nat_Osemiring__1__class_Oof__nat(U_12737))),U_12739))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12740))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12737),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12737),U_12740)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12737),U_12738),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12737),U_12738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12737),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12737),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12740),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_12739))))
    | ~ class_Rings_Ocomm__semiring__1(U_12737) ),
    inference(clausify,[status(thm)],[f_3260_3]) ).

fof(f_3261_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_3261_2,plain,
    ! [U_12746,U_12745,U_12744,U_12743,U_12742] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12742),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12743,U_12742),U_12746),U_12745)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12743,U_12742),U_12746),U_12744)))
      | ? [U_12741] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12742),c_Groups_Ozero__class_Ozero(U_12742)),hAPP(U_12746,U_12741)))
          & hBOOL(hAPP(hAPP(c_member(U_12743),U_12741),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12743,tc_HOL_Obool)),U_12744),U_12745))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12743,tc_HOL_Obool)),U_12745),U_12744))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12743),U_12744))
      | ~ class_Groups_Oordered__comm__monoid__add(U_12742) ),
    inference(variable_rename,[status(thm)],[f_3261_1]) ).

fof(f_3261_3,plain,
    ! [U_12746,U_12745,U_12744,U_12743,U_12742] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12742),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12743,U_12742),U_12746),U_12745)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12743,U_12742),U_12746),U_12744)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12742),c_Groups_Ozero__class_Ozero(U_12742)),hAPP(U_12746,sK262(U_12746,U_12745,U_12744,U_12743,U_12742))))
        & hBOOL(hAPP(hAPP(c_member(U_12743),sK262(U_12746,U_12745,U_12744,U_12743,U_12742)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12743,tc_HOL_Obool)),U_12744),U_12745))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12743,tc_HOL_Obool)),U_12745),U_12744))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12743),U_12744))
      | ~ class_Groups_Oordered__comm__monoid__add(U_12742) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK262]),skolemize(U_12741,sK262(U_12746,U_12745,U_12744,U_12743,U_12742))],[f_3261_2]) ).

fof(f_3261_4,plain,
    ( ! [U_12742,U_12743,U_12744,U_12745,U_12746] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12742),c_Groups_Ozero__class_Ozero(U_12742)),hAPP(U_12746,sK262(U_12746,U_12745,U_12744,U_12743,U_12742))))
        | ~ sP921(U_12742,U_12743,U_12744,U_12745,U_12746) )
    & ! [U_12742,U_12743,U_12744,U_12745,U_12746] :
        ( hBOOL(hAPP(hAPP(c_member(U_12743),sK262(U_12746,U_12745,U_12744,U_12743,U_12742)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12743,tc_HOL_Obool)),U_12744),U_12745)))
        | ~ sP921(U_12742,U_12743,U_12744,U_12745,U_12746) )
    & ! [U_12742,U_12743,U_12744,U_12745,U_12746] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12742),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12743,U_12742),U_12746),U_12745)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12743,U_12742),U_12746),U_12744)))
        | sP921(U_12742,U_12743,U_12744,U_12745,U_12746)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12743,tc_HOL_Obool)),U_12745),U_12744))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12743),U_12744))
        | ~ class_Groups_Oordered__comm__monoid__add(U_12742) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP921])],[f_3261_3]) ).

cnf(f_3261_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12742),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12743,U_12742),U_12746),U_12745)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12743,U_12742),U_12746),U_12744)))
    | sP921(U_12742,U_12743,U_12744,U_12745,U_12746)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12743,tc_HOL_Obool)),U_12745),U_12744))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12743),U_12744))
    | ~ class_Groups_Oordered__comm__monoid__add(U_12742) ),
    inference(clausify,[status(thm)],[f_3261_4]) ).

cnf(f_3261_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12743),sK262(U_12746,U_12745,U_12744,U_12743,U_12742)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12743,tc_HOL_Obool)),U_12744),U_12745)))
    | ~ sP921(U_12742,U_12743,U_12744,U_12745,U_12746) ),
    inference(clausify,[status(thm)],[f_3261_4]) ).

cnf(f_3261_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12742),c_Groups_Ozero__class_Ozero(U_12742)),hAPP(U_12746,sK262(U_12746,U_12745,U_12744,U_12743,U_12742))))
    | ~ sP921(U_12742,U_12743,U_12744,U_12745,U_12746) ),
    inference(clausify,[status(thm)],[f_3261_4]) ).

fof(f_3262_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_3262_2,plain,
    ! [U_12752,U_12751,U_12750,U_12749,U_12748] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12748),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12749,U_12748),U_12751),U_12750)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12748),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12748),hAPP(c_Finite__Set_Ocard(U_12749),U_12750))),U_12752)))
      | ? [U_12747] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12748),hAPP(U_12751,U_12747)),U_12752))
          & hBOOL(hAPP(hAPP(c_member(U_12749),U_12747),U_12750)) )
      | ~ class_Rings_Osemiring__1(U_12748)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_12748) ),
    inference(variable_rename,[status(thm)],[f_3262_1]) ).

fof(f_3262_3,plain,
    ! [U_12752,U_12751,U_12750,U_12749,U_12748] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12748),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12749,U_12748),U_12751),U_12750)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12748),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12748),hAPP(c_Finite__Set_Ocard(U_12749),U_12750))),U_12752)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12748),hAPP(U_12751,sK263(U_12752,U_12751,U_12750,U_12749,U_12748))),U_12752))
        & hBOOL(hAPP(hAPP(c_member(U_12749),sK263(U_12752,U_12751,U_12750,U_12749,U_12748)),U_12750)) )
      | ~ class_Rings_Osemiring__1(U_12748)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_12748) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK263]),skolemize(U_12747,sK263(U_12752,U_12751,U_12750,U_12749,U_12748))],[f_3262_2]) ).

fof(f_3262_4,plain,
    ( ! [U_12749,U_12750,U_12748,U_12751,U_12752] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12748),hAPP(U_12751,sK263(U_12752,U_12751,U_12750,U_12749,U_12748))),U_12752))
        | ~ sP922(U_12749,U_12750,U_12748,U_12751,U_12752) )
    & ! [U_12749,U_12750,U_12748,U_12751,U_12752] :
        ( hBOOL(hAPP(hAPP(c_member(U_12749),sK263(U_12752,U_12751,U_12750,U_12749,U_12748)),U_12750))
        | ~ sP922(U_12749,U_12750,U_12748,U_12751,U_12752) )
    & ! [U_12749,U_12750,U_12748,U_12751,U_12752] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12748),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12749,U_12748),U_12751),U_12750)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12748),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12748),hAPP(c_Finite__Set_Ocard(U_12749),U_12750))),U_12752)))
        | sP922(U_12749,U_12750,U_12748,U_12751,U_12752)
        | ~ class_Rings_Osemiring__1(U_12748)
        | ~ class_Groups_Oordered__ab__semigroup__add(U_12748) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP922])],[f_3262_3]) ).

cnf(f_3262_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12748),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12749,U_12748),U_12751),U_12750)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12748),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12748),hAPP(c_Finite__Set_Ocard(U_12749),U_12750))),U_12752)))
    | sP922(U_12749,U_12750,U_12748,U_12751,U_12752)
    | ~ class_Rings_Osemiring__1(U_12748)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_12748) ),
    inference(clausify,[status(thm)],[f_3262_4]) ).

cnf(f_3262_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12749),sK263(U_12752,U_12751,U_12750,U_12749,U_12748)),U_12750))
    | ~ sP922(U_12749,U_12750,U_12748,U_12751,U_12752) ),
    inference(clausify,[status(thm)],[f_3262_4]) ).

cnf(f_3262_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12748),hAPP(U_12751,sK263(U_12752,U_12751,U_12750,U_12749,U_12748))),U_12752))
    | ~ sP922(U_12749,U_12750,U_12748,U_12751,U_12752) ),
    inference(clausify,[status(thm)],[f_3262_4]) ).

fof(f_3263_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_3263_2,plain,
    ! [U_12758,U_12757,U_12756,U_12755,U_12754] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12755,U_12754),U_12758),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12755,tc_HOL_Obool)),U_12756),U_12757)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12754),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12755,U_12754),U_12758),U_12756)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12755,U_12754),U_12758),U_12757))
      | ? [U_12753] :
          ( hAPP(U_12758,U_12753) != c_Groups_Ozero__class_Ozero(U_12754)
          & hBOOL(hAPP(hAPP(c_member(U_12755),U_12753),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12755,tc_HOL_Obool)),U_12756),U_12757))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12755),U_12757))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12755),U_12756))
      | ~ class_Groups_Ocomm__monoid__add(U_12754) ),
    inference(variable_rename,[status(thm)],[f_3263_1]) ).

fof(f_3263_3,plain,
    ! [U_12758,U_12757,U_12756,U_12755,U_12754] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12755,U_12754),U_12758),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12755,tc_HOL_Obool)),U_12756),U_12757)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12754),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12755,U_12754),U_12758),U_12756)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12755,U_12754),U_12758),U_12757))
      | ( hAPP(U_12758,sK264(U_12758,U_12757,U_12756,U_12755,U_12754)) != c_Groups_Ozero__class_Ozero(U_12754)
        & hBOOL(hAPP(hAPP(c_member(U_12755),sK264(U_12758,U_12757,U_12756,U_12755,U_12754)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12755,tc_HOL_Obool)),U_12756),U_12757))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12755),U_12757))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12755),U_12756))
      | ~ class_Groups_Ocomm__monoid__add(U_12754) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK264]),skolemize(U_12753,sK264(U_12758,U_12757,U_12756,U_12755,U_12754))],[f_3263_2]) ).

fof(f_3263_4,plain,
    ( ! [U_12754,U_12755,U_12756,U_12757,U_12758] :
        ( hAPP(U_12758,sK264(U_12758,U_12757,U_12756,U_12755,U_12754)) != c_Groups_Ozero__class_Ozero(U_12754)
        | ~ sP923(U_12754,U_12755,U_12756,U_12757,U_12758) )
    & ! [U_12754,U_12755,U_12756,U_12757,U_12758] :
        ( hBOOL(hAPP(hAPP(c_member(U_12755),sK264(U_12758,U_12757,U_12756,U_12755,U_12754)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12755,tc_HOL_Obool)),U_12756),U_12757)))
        | ~ sP923(U_12754,U_12755,U_12756,U_12757,U_12758) )
    & ! [U_12754,U_12755,U_12756,U_12757,U_12758] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12755,U_12754),U_12758),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12755,tc_HOL_Obool)),U_12756),U_12757)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12754),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12755,U_12754),U_12758),U_12756)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12755,U_12754),U_12758),U_12757))
        | sP923(U_12754,U_12755,U_12756,U_12757,U_12758)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12755),U_12757))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12755),U_12756))
        | ~ class_Groups_Ocomm__monoid__add(U_12754) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP923])],[f_3263_3]) ).

cnf(f_3263_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12755,U_12754),U_12758),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12755,tc_HOL_Obool)),U_12756),U_12757)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12754),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12755,U_12754),U_12758),U_12756)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12755,U_12754),U_12758),U_12757))
    | sP923(U_12754,U_12755,U_12756,U_12757,U_12758)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12755),U_12757))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12755),U_12756))
    | ~ class_Groups_Ocomm__monoid__add(U_12754) ),
    inference(clausify,[status(thm)],[f_3263_4]) ).

cnf(f_3263_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12755),sK264(U_12758,U_12757,U_12756,U_12755,U_12754)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12755,tc_HOL_Obool)),U_12756),U_12757)))
    | ~ sP923(U_12754,U_12755,U_12756,U_12757,U_12758) ),
    inference(clausify,[status(thm)],[f_3263_4]) ).

cnf(f_3263_7,plain,
    ( hAPP(U_12758,sK264(U_12758,U_12757,U_12756,U_12755,U_12754)) != c_Groups_Ozero__class_Ozero(U_12754)
    | ~ sP923(U_12754,U_12755,U_12756,U_12757,U_12758) ),
    inference(clausify,[status(thm)],[f_3263_4]) ).

fof(f_3264_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_3264_2,plain,
    ! [U_12763,U_12762,U_12761] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12761,tc_Nat_Onat),U_12763),U_12762) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ? [U_12760] :
              ( hAPP(U_12763,U_12760) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_12761),U_12760),U_12762)) ) )
        & ( ! [U_12759] :
              ( hAPP(U_12763,U_12759) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_12761),U_12759),U_12762)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12761,tc_Nat_Onat),U_12763),U_12762) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12761),U_12762)) ),
    inference(variable_rename,[status(thm)],[f_3264_1]) ).

fof(f_3264_3,plain,
    ! [U_12763,U_12762,U_12761] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12761,tc_Nat_Onat),U_12763),U_12762) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ( hAPP(U_12763,sK265(U_12763,U_12762,U_12761)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_12761),sK265(U_12763,U_12762,U_12761)),U_12762)) ) )
        & ( ! [U_12759] :
              ( hAPP(U_12763,U_12759) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_12761),U_12759),U_12762)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12761,tc_Nat_Onat),U_12763),U_12762) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12761),U_12762)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK265]),skolemize(U_12760,sK265(U_12763,U_12762,U_12761))],[f_3264_2]) ).

fof(f_3264_4,plain,
    ( ! [U_12763,U_12762,U_12761] :
        ( hAPP(U_12763,sK265(U_12763,U_12762,U_12761)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP924(U_12763,U_12762,U_12761) )
    & ! [U_12763,U_12762,U_12761] :
        ( hBOOL(hAPP(hAPP(c_member(U_12761),sK265(U_12763,U_12762,U_12761)),U_12762))
        | ~ sP924(U_12763,U_12762,U_12761) )
    & ! [U_12763,U_12762,U_12761,U_12759] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12761,tc_Nat_Onat),U_12763),U_12762) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP924(U_12763,U_12762,U_12761)
        | ~ sP925(U_12763,U_12762,U_12761,U_12759) )
    & ! [U_12763,U_12762,U_12761,U_12759] :
        ( hAPP(U_12763,U_12759) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12761),U_12759),U_12762))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12761,tc_Nat_Onat),U_12763),U_12762) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP925(U_12763,U_12762,U_12761,U_12759) )
    & ! [U_12763,U_12762,U_12761,U_12759] :
        ( sP925(U_12763,U_12762,U_12761,U_12759)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12761),U_12762)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP924,sP925])],[f_3264_3]) ).

cnf(f_3264_5,plain,
    ( sP925(U_12763,U_12762,U_12761,U_12759)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12761),U_12762)) ),
    inference(clausify,[status(thm)],[f_3264_4]) ).

cnf(f_3264_6,plain,
    ( hAPP(U_12763,U_12759) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12761),U_12759),U_12762))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12761,tc_Nat_Onat),U_12763),U_12762) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP925(U_12763,U_12762,U_12761,U_12759) ),
    inference(clausify,[status(thm)],[f_3264_4]) ).

cnf(f_3264_7,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12761,tc_Nat_Onat),U_12763),U_12762) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP924(U_12763,U_12762,U_12761)
    | ~ sP925(U_12763,U_12762,U_12761,U_12759) ),
    inference(clausify,[status(thm)],[f_3264_4]) ).

cnf(f_3264_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12761),sK265(U_12763,U_12762,U_12761)),U_12762))
    | ~ sP924(U_12763,U_12762,U_12761) ),
    inference(clausify,[status(thm)],[f_3264_4]) ).

cnf(f_3264_9,plain,
    ( hAPP(U_12763,sK265(U_12763,U_12762,U_12761)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP924(U_12763,U_12762,U_12761) ),
    inference(clausify,[status(thm)],[f_3264_4]) ).

fof(f_3265_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_3265_2,plain,
    ! [U_12765,U_12764] : hAPP(c_Finite__Set_Ocard(U_12764),U_12765) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12764,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_12764),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12765),
    inference(variable_rename,[status(thm)],[f_3265_1]) ).

fof(f_3265_3,plain,
    ! [U_12765,U_12764] : hAPP(c_Finite__Set_Ocard(U_12764),U_12765) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12764,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_12764),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12765),
    inference(definitional_conversion,[status(esa)],[f_3265_2]) ).

cnf(f_3265_4,plain,
    hAPP(c_Finite__Set_Ocard(U_12764),U_12765) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12764,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_12764),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12765),
    inference(clausify,[status(thm)],[f_3265_3]) ).

fof(f_3266_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_3266_2,plain,
    ! [U_12768,U_12767,U_12766] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12766,tc_Nat_Onat),U_12767),U_12768)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12766,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12766),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12767)),U_12768),
    inference(variable_rename,[status(thm)],[f_3266_1]) ).

fof(f_3266_3,plain,
    ! [U_12766,U_12767,U_12768] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12766,tc_Nat_Onat),U_12767),U_12768)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12766,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12766),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12767)),U_12768),
    inference(definitional_conversion,[status(esa)],[f_3266_2]) ).

cnf(f_3266_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12766,tc_Nat_Onat),U_12767),U_12768)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12766,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12766),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12767)),U_12768),
    inference(clausify,[status(thm)],[f_3266_3]) ).

fof(f_3267_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_3267_2,plain,
    ! [U_12775,U_12774,U_12773] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12773,tc_Nat_Onat),U_12775),U_12774) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_12772] :
              ( ? [U_12771] :
                  ( hAPP(U_12775,U_12771) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_12772 != U_12771
                  & hBOOL(hAPP(hAPP(c_member(U_12773),U_12771),U_12774)) )
              | hAPP(U_12775,U_12772) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12773),U_12772),U_12774)) ) )
        & ( ? [U_12770] :
              ( ! [U_12769] :
                  ( hAPP(U_12775,U_12769) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | U_12770 = U_12769
                  | ~ hBOOL(hAPP(hAPP(c_member(U_12773),U_12769),U_12774)) )
              & hAPP(U_12775,U_12770) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              & hBOOL(hAPP(hAPP(c_member(U_12773),U_12770),U_12774)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12773,tc_Nat_Onat),U_12775),U_12774) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12773),U_12774)) ),
    inference(variable_rename,[status(thm)],[f_3267_1]) ).

fof(f_3267_3,plain,
    ! [U_12775,U_12774,U_12773] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12773,tc_Nat_Onat),U_12775),U_12774) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_12772] :
              ( ? [U_12771] :
                  ( hAPP(U_12775,U_12771) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_12772 != U_12771
                  & hBOOL(hAPP(hAPP(c_member(U_12773),U_12771),U_12774)) )
              | hAPP(U_12775,U_12772) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12773),U_12772),U_12774)) ) )
        & ( ( ! [U_12769] :
                ( hAPP(U_12775,U_12769) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK266(U_12775,U_12774,U_12773) = U_12769
                | ~ hBOOL(hAPP(hAPP(c_member(U_12773),U_12769),U_12774)) )
            & hAPP(U_12775,sK266(U_12775,U_12774,U_12773)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & hBOOL(hAPP(hAPP(c_member(U_12773),sK266(U_12775,U_12774,U_12773)),U_12774)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12773,tc_Nat_Onat),U_12775),U_12774) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12773),U_12774)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK266]),skolemize(U_12770,sK266(U_12775,U_12774,U_12773))],[f_3267_2]) ).

fof(f_3267_4,plain,
    ! [U_12775,U_12774,U_12773] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12773,tc_Nat_Onat),U_12775),U_12774) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_12772] :
              ( ( hAPP(U_12775,sK267(U_12775,U_12774,U_12773,U_12772)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                & U_12772 != sK267(U_12775,U_12774,U_12773,U_12772)
                & hBOOL(hAPP(hAPP(c_member(U_12773),sK267(U_12775,U_12774,U_12773,U_12772)),U_12774)) )
              | hAPP(U_12775,U_12772) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12773),U_12772),U_12774)) ) )
        & ( ( ! [U_12769] :
                ( hAPP(U_12775,U_12769) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK266(U_12775,U_12774,U_12773) = U_12769
                | ~ hBOOL(hAPP(hAPP(c_member(U_12773),U_12769),U_12774)) )
            & hAPP(U_12775,sK266(U_12775,U_12774,U_12773)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & hBOOL(hAPP(hAPP(c_member(U_12773),sK266(U_12775,U_12774,U_12773)),U_12774)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12773,tc_Nat_Onat),U_12775),U_12774) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12773),U_12774)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK267]),skolemize(U_12771,sK267(U_12775,U_12774,U_12773,U_12772))],[f_3267_3]) ).

fof(f_3267_5,plain,
    ( ! [U_12772,U_12773,U_12774,U_12775] :
        ( hAPP(U_12775,sK267(U_12775,U_12774,U_12773,U_12772)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP927(U_12772,U_12773,U_12774,U_12775) )
    & ! [U_12772,U_12773,U_12774,U_12775] :
        ( U_12772 != sK267(U_12775,U_12774,U_12773,U_12772)
        | ~ sP927(U_12772,U_12773,U_12774,U_12775) )
    & ! [U_12772,U_12773,U_12774,U_12775] :
        ( hBOOL(hAPP(hAPP(c_member(U_12773),sK267(U_12775,U_12774,U_12773,U_12772)),U_12774))
        | ~ sP927(U_12772,U_12773,U_12774,U_12775) )
    & ! [U_12769,U_12773,U_12774,U_12775] :
        ( hAPP(U_12775,U_12769) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sK266(U_12775,U_12774,U_12773) = U_12769
        | ~ hBOOL(hAPP(hAPP(c_member(U_12773),U_12769),U_12774))
        | ~ sP926(U_12769,U_12773,U_12774,U_12775) )
    & ! [U_12769,U_12773,U_12774,U_12775] :
        ( hAPP(U_12775,sK266(U_12775,U_12774,U_12773)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP926(U_12769,U_12773,U_12774,U_12775) )
    & ! [U_12769,U_12773,U_12774,U_12775] :
        ( hBOOL(hAPP(hAPP(c_member(U_12773),sK266(U_12775,U_12774,U_12773)),U_12774))
        | ~ sP926(U_12769,U_12773,U_12774,U_12775) )
    & ! [U_12769,U_12772,U_12773,U_12774,U_12775] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12773,tc_Nat_Onat),U_12775),U_12774) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | sP927(U_12772,U_12773,U_12774,U_12775)
        | hAPP(U_12775,U_12772) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12773),U_12772),U_12774))
        | ~ sP928(U_12769,U_12772,U_12773,U_12774,U_12775) )
    & ! [U_12769,U_12772,U_12773,U_12774,U_12775] :
        ( sP926(U_12769,U_12773,U_12774,U_12775)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12773,tc_Nat_Onat),U_12775),U_12774) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP928(U_12769,U_12772,U_12773,U_12774,U_12775) )
    & ! [U_12769,U_12772,U_12773,U_12774,U_12775] :
        ( sP928(U_12769,U_12772,U_12773,U_12774,U_12775)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12773),U_12774)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP926,sP927,sP928])],[f_3267_4]) ).

cnf(f_3267_6,plain,
    ( sP928(U_12769,U_12772,U_12773,U_12774,U_12775)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12773),U_12774)) ),
    inference(clausify,[status(thm)],[f_3267_5]) ).

cnf(f_3267_7,plain,
    ( sP926(U_12769,U_12773,U_12774,U_12775)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12773,tc_Nat_Onat),U_12775),U_12774) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP928(U_12769,U_12772,U_12773,U_12774,U_12775) ),
    inference(clausify,[status(thm)],[f_3267_5]) ).

cnf(f_3267_8,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12773,tc_Nat_Onat),U_12775),U_12774) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | sP927(U_12772,U_12773,U_12774,U_12775)
    | hAPP(U_12775,U_12772) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12773),U_12772),U_12774))
    | ~ sP928(U_12769,U_12772,U_12773,U_12774,U_12775) ),
    inference(clausify,[status(thm)],[f_3267_5]) ).

cnf(f_3267_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12773),sK266(U_12775,U_12774,U_12773)),U_12774))
    | ~ sP926(U_12769,U_12773,U_12774,U_12775) ),
    inference(clausify,[status(thm)],[f_3267_5]) ).

cnf(f_3267_10,plain,
    ( hAPP(U_12775,sK266(U_12775,U_12774,U_12773)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP926(U_12769,U_12773,U_12774,U_12775) ),
    inference(clausify,[status(thm)],[f_3267_5]) ).

cnf(f_3267_11,plain,
    ( hAPP(U_12775,U_12769) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sK266(U_12775,U_12774,U_12773) = U_12769
    | ~ hBOOL(hAPP(hAPP(c_member(U_12773),U_12769),U_12774))
    | ~ sP926(U_12769,U_12773,U_12774,U_12775) ),
    inference(clausify,[status(thm)],[f_3267_5]) ).

cnf(f_3267_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12773),sK267(U_12775,U_12774,U_12773,U_12772)),U_12774))
    | ~ sP927(U_12772,U_12773,U_12774,U_12775) ),
    inference(clausify,[status(thm)],[f_3267_5]) ).

cnf(f_3267_13,plain,
    ( U_12772 != sK267(U_12775,U_12774,U_12773,U_12772)
    | ~ sP927(U_12772,U_12773,U_12774,U_12775) ),
    inference(clausify,[status(thm)],[f_3267_5]) ).

cnf(f_3267_14,plain,
    ( hAPP(U_12775,sK267(U_12775,U_12774,U_12773,U_12772)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP927(U_12772,U_12773,U_12774,U_12775) ),
    inference(clausify,[status(thm)],[f_3267_5]) ).

fof(f_3268_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_3268_2,plain,
    ! [U_12782,U_12781,U_12780] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12780,tc_Nat_Onat),U_12782),U_12781) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_12779] :
              ( ? [U_12778] :
                  ( hAPP(U_12782,U_12778) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_12779 != U_12778
                  & hBOOL(hAPP(hAPP(c_member(U_12780),U_12778),U_12781)) )
              | hAPP(U_12782,U_12779) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_12780),U_12779),U_12781)) ) )
        & ( ? [U_12777] :
              ( ! [U_12776] :
                  ( hAPP(U_12782,U_12776) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | U_12777 = U_12776
                  | ~ hBOOL(hAPP(hAPP(c_member(U_12780),U_12776),U_12781)) )
              & hAPP(U_12782,U_12777) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_12780),U_12777),U_12781)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12780,tc_Nat_Onat),U_12782),U_12781) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12780),U_12781)) ),
    inference(variable_rename,[status(thm)],[f_3268_1]) ).

fof(f_3268_3,plain,
    ! [U_12782,U_12781,U_12780] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12780,tc_Nat_Onat),U_12782),U_12781) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_12779] :
              ( ? [U_12778] :
                  ( hAPP(U_12782,U_12778) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_12779 != U_12778
                  & hBOOL(hAPP(hAPP(c_member(U_12780),U_12778),U_12781)) )
              | hAPP(U_12782,U_12779) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_12780),U_12779),U_12781)) ) )
        & ( ( ! [U_12776] :
                ( hAPP(U_12782,U_12776) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK268(U_12782,U_12781,U_12780) = U_12776
                | ~ hBOOL(hAPP(hAPP(c_member(U_12780),U_12776),U_12781)) )
            & hAPP(U_12782,sK268(U_12782,U_12781,U_12780)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_12780),sK268(U_12782,U_12781,U_12780)),U_12781)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12780,tc_Nat_Onat),U_12782),U_12781) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12780),U_12781)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK268]),skolemize(U_12777,sK268(U_12782,U_12781,U_12780))],[f_3268_2]) ).

fof(f_3268_4,plain,
    ! [U_12782,U_12781,U_12780] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12780,tc_Nat_Onat),U_12782),U_12781) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_12779] :
              ( ( hAPP(U_12782,sK269(U_12782,U_12781,U_12780,U_12779)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                & U_12779 != sK269(U_12782,U_12781,U_12780,U_12779)
                & hBOOL(hAPP(hAPP(c_member(U_12780),sK269(U_12782,U_12781,U_12780,U_12779)),U_12781)) )
              | hAPP(U_12782,U_12779) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_12780),U_12779),U_12781)) ) )
        & ( ( ! [U_12776] :
                ( hAPP(U_12782,U_12776) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK268(U_12782,U_12781,U_12780) = U_12776
                | ~ hBOOL(hAPP(hAPP(c_member(U_12780),U_12776),U_12781)) )
            & hAPP(U_12782,sK268(U_12782,U_12781,U_12780)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_12780),sK268(U_12782,U_12781,U_12780)),U_12781)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12780,tc_Nat_Onat),U_12782),U_12781) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12780),U_12781)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(U_12778,sK269(U_12782,U_12781,U_12780,U_12779))],[f_3268_3]) ).

fof(f_3268_5,plain,
    ( ! [U_12782,U_12779,U_12780,U_12781] :
        ( hAPP(U_12782,sK269(U_12782,U_12781,U_12780,U_12779)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP930(U_12782,U_12779,U_12780,U_12781) )
    & ! [U_12782,U_12779,U_12780,U_12781] :
        ( U_12779 != sK269(U_12782,U_12781,U_12780,U_12779)
        | ~ sP930(U_12782,U_12779,U_12780,U_12781) )
    & ! [U_12782,U_12779,U_12780,U_12781] :
        ( hBOOL(hAPP(hAPP(c_member(U_12780),sK269(U_12782,U_12781,U_12780,U_12779)),U_12781))
        | ~ sP930(U_12782,U_12779,U_12780,U_12781) )
    & ! [U_12782,U_12776,U_12780,U_12781] :
        ( hAPP(U_12782,U_12776) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sK268(U_12782,U_12781,U_12780) = U_12776
        | ~ hBOOL(hAPP(hAPP(c_member(U_12780),U_12776),U_12781))
        | ~ sP929(U_12782,U_12776,U_12780,U_12781) )
    & ! [U_12782,U_12776,U_12780,U_12781] :
        ( hAPP(U_12782,sK268(U_12782,U_12781,U_12780)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP929(U_12782,U_12776,U_12780,U_12781) )
    & ! [U_12782,U_12776,U_12780,U_12781] :
        ( hBOOL(hAPP(hAPP(c_member(U_12780),sK268(U_12782,U_12781,U_12780)),U_12781))
        | ~ sP929(U_12782,U_12776,U_12780,U_12781) )
    & ! [U_12782,U_12779,U_12776,U_12780,U_12781] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12780,tc_Nat_Onat),U_12782),U_12781) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | sP930(U_12782,U_12779,U_12780,U_12781)
        | hAPP(U_12782,U_12779) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12780),U_12779),U_12781))
        | ~ sP931(U_12782,U_12779,U_12776,U_12780,U_12781) )
    & ! [U_12782,U_12779,U_12776,U_12780,U_12781] :
        ( sP929(U_12782,U_12776,U_12780,U_12781)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12780,tc_Nat_Onat),U_12782),U_12781) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP931(U_12782,U_12779,U_12776,U_12780,U_12781) )
    & ! [U_12782,U_12779,U_12776,U_12780,U_12781] :
        ( sP931(U_12782,U_12779,U_12776,U_12780,U_12781)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12780),U_12781)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP929,sP930,sP931])],[f_3268_4]) ).

cnf(f_3268_6,plain,
    ( sP931(U_12782,U_12779,U_12776,U_12780,U_12781)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12780),U_12781)) ),
    inference(clausify,[status(thm)],[f_3268_5]) ).

cnf(f_3268_7,plain,
    ( sP929(U_12782,U_12776,U_12780,U_12781)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12780,tc_Nat_Onat),U_12782),U_12781) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP931(U_12782,U_12779,U_12776,U_12780,U_12781) ),
    inference(clausify,[status(thm)],[f_3268_5]) ).

cnf(f_3268_8,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12780,tc_Nat_Onat),U_12782),U_12781) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | sP930(U_12782,U_12779,U_12780,U_12781)
    | hAPP(U_12782,U_12779) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12780),U_12779),U_12781))
    | ~ sP931(U_12782,U_12779,U_12776,U_12780,U_12781) ),
    inference(clausify,[status(thm)],[f_3268_5]) ).

cnf(f_3268_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12780),sK268(U_12782,U_12781,U_12780)),U_12781))
    | ~ sP929(U_12782,U_12776,U_12780,U_12781) ),
    inference(clausify,[status(thm)],[f_3268_5]) ).

cnf(f_3268_10,plain,
    ( hAPP(U_12782,sK268(U_12782,U_12781,U_12780)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP929(U_12782,U_12776,U_12780,U_12781) ),
    inference(clausify,[status(thm)],[f_3268_5]) ).

cnf(f_3268_11,plain,
    ( hAPP(U_12782,U_12776) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sK268(U_12782,U_12781,U_12780) = U_12776
    | ~ hBOOL(hAPP(hAPP(c_member(U_12780),U_12776),U_12781))
    | ~ sP929(U_12782,U_12776,U_12780,U_12781) ),
    inference(clausify,[status(thm)],[f_3268_5]) ).

cnf(f_3268_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12780),sK269(U_12782,U_12781,U_12780,U_12779)),U_12781))
    | ~ sP930(U_12782,U_12779,U_12780,U_12781) ),
    inference(clausify,[status(thm)],[f_3268_5]) ).

cnf(f_3268_13,plain,
    ( U_12779 != sK269(U_12782,U_12781,U_12780,U_12779)
    | ~ sP930(U_12782,U_12779,U_12780,U_12781) ),
    inference(clausify,[status(thm)],[f_3268_5]) ).

cnf(f_3268_14,plain,
    ( hAPP(U_12782,sK269(U_12782,U_12781,U_12780,U_12779)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP930(U_12782,U_12779,U_12780,U_12781) ),
    inference(clausify,[status(thm)],[f_3268_5]) ).

fof(f_3269_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_3269_2,plain,
    ! [U_12784,U_12783] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12783),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12784)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12783),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_12784))
      | hAPP(U_12783,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_3269_1]) ).

fof(f_3269_3,plain,
    ! [U_12783,U_12784] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12783),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12784)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12783),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_12784))
      | hAPP(U_12783,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_3269_2]) ).

cnf(f_3269_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12783),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12784)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12783),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_12784))
    | hAPP(U_12783,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3269_3]) ).

fof(f_3270_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_3270_2,plain,
    ! [U_12787,U_12786,U_12785] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12785,tc_Nat_Onat),U_12786),U_12787) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12785,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12785),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12786)),U_12787)),
    inference(variable_rename,[status(thm)],[f_3270_1]) ).

fof(f_3270_3,plain,
    ! [U_12787,U_12785,U_12786] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12785,tc_Nat_Onat),U_12786),U_12787) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12785,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12785),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12786)),U_12787)),
    inference(definitional_conversion,[status(esa)],[f_3270_2]) ).

cnf(f_3270_4,plain,
    hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12785,tc_Nat_Onat),U_12786),U_12787) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12785,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12785),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12786)),U_12787)),
    inference(clausify,[status(thm)],[f_3270_3]) ).

fof(f_3271_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_3271_2,plain,
    ! [U_12791,U_12790,U_12789,U_12788] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12788,tc_Nat_Onat),U_12791),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12788,tc_HOL_Obool)),U_12790),U_12789)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12788,tc_Nat_Onat),U_12791),U_12790)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12788,tc_Nat_Onat),U_12791),U_12789))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12788,tc_HOL_Obool)),U_12789),U_12790))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12788),U_12789)) ),
    inference(variable_rename,[status(thm)],[f_3271_1]) ).

fof(f_3271_3,plain,
    ! [U_12789,U_12788,U_12790,U_12791] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12788,tc_Nat_Onat),U_12791),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12788,tc_HOL_Obool)),U_12790),U_12789)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12788,tc_Nat_Onat),U_12791),U_12790)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12788,tc_Nat_Onat),U_12791),U_12789))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12788,tc_HOL_Obool)),U_12789),U_12790))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12788),U_12789)) ),
    inference(definitional_conversion,[status(esa)],[f_3271_2]) ).

cnf(f_3271_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12788,tc_Nat_Onat),U_12791),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12788,tc_HOL_Obool)),U_12790),U_12789)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12788,tc_Nat_Onat),U_12791),U_12790)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12788,tc_Nat_Onat),U_12791),U_12789))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12788,tc_HOL_Obool)),U_12789),U_12790))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12788),U_12789)) ),
    inference(clausify,[status(thm)],[f_3271_3]) ).

fof(f_3272_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_3272_2,plain,
    ! [U_12794,U_12793,U_12792] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12792),U_12793),U_12794) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12792),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12792,tc_Int_Oint),U_12793),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12794))
      | ~ class_Groups_Ocomm__monoid__mult(U_12792)
      | ~ class_Groups_Ocomm__monoid__add(U_12792) ),
    inference(variable_rename,[status(thm)],[f_3272_1]) ).

fof(f_3272_3,plain,
    ! [U_12792,U_12793,U_12794] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12792),U_12793),U_12794) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12792),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12792,tc_Int_Oint),U_12793),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12794))
      | ~ class_Groups_Ocomm__monoid__mult(U_12792)
      | ~ class_Groups_Ocomm__monoid__add(U_12792) ),
    inference(definitional_conversion,[status(esa)],[f_3272_2]) ).

cnf(f_3272_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12792),U_12793),U_12794) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12792),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12792,tc_Int_Oint),U_12793),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12794))
    | ~ class_Groups_Ocomm__monoid__mult(U_12792)
    | ~ class_Groups_Ocomm__monoid__add(U_12792) ),
    inference(clausify,[status(thm)],[f_3272_3]) ).

fof(f_3273_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_3273_2,plain,
    ! [U_12798,U_12797,U_12796,U_12795] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12795,tc_Nat_Onat),U_12798),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12795,tc_HOL_Obool)),U_12797),hAPP(hAPP(c_Set_Oinsert(U_12795),U_12796),c_Orderings_Obot__class_Obot(tc_fun(U_12795,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12795,tc_Nat_Onat),U_12798),U_12797)
        | hBOOL(hAPP(hAPP(c_member(U_12795),U_12796),U_12797)) )
      & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12795,tc_Nat_Onat),U_12798),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12795,tc_HOL_Obool)),U_12797),hAPP(hAPP(c_Set_Oinsert(U_12795),U_12796),c_Orderings_Obot__class_Obot(tc_fun(U_12795,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12795,tc_Nat_Onat),U_12798),U_12797)),hAPP(U_12798,U_12796))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12795),U_12796),U_12797)) ) ),
    inference(variable_rename,[status(thm)],[f_3273_1]) ).

fof(f_3273_3,plain,
    ( ! [U_12806,U_12804,U_12802,U_12800] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12800,tc_Nat_Onat),U_12806),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12800,tc_HOL_Obool)),U_12804),hAPP(hAPP(c_Set_Oinsert(U_12800),U_12802),c_Orderings_Obot__class_Obot(tc_fun(U_12800,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12800,tc_Nat_Onat),U_12806),U_12804)
        | hBOOL(hAPP(hAPP(c_member(U_12800),U_12802),U_12804)) )
    & ! [U_12805,U_12803,U_12801,U_12799] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12799,tc_Nat_Onat),U_12805),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12799,tc_HOL_Obool)),U_12803),hAPP(hAPP(c_Set_Oinsert(U_12799),U_12801),c_Orderings_Obot__class_Obot(tc_fun(U_12799,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12799,tc_Nat_Onat),U_12805),U_12803)),hAPP(U_12805,U_12801))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12799),U_12801),U_12803)) ) ),
    inference(miniscope,[status(thm)],[f_3273_2]) ).

fof(f_3273_4,plain,
    ( ! [U_12800,U_12802,U_12804,U_12806] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12800,tc_Nat_Onat),U_12806),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12800,tc_HOL_Obool)),U_12804),hAPP(hAPP(c_Set_Oinsert(U_12800),U_12802),c_Orderings_Obot__class_Obot(tc_fun(U_12800,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12800,tc_Nat_Onat),U_12806),U_12804)
        | hBOOL(hAPP(hAPP(c_member(U_12800),U_12802),U_12804)) )
    & ! [U_12803,U_12801,U_12805,U_12799] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12799,tc_Nat_Onat),U_12805),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12799,tc_HOL_Obool)),U_12803),hAPP(hAPP(c_Set_Oinsert(U_12799),U_12801),c_Orderings_Obot__class_Obot(tc_fun(U_12799,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12799,tc_Nat_Onat),U_12805),U_12803)),hAPP(U_12805,U_12801))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12799),U_12801),U_12803)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3273_3]) ).

cnf(f_3273_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12799,tc_Nat_Onat),U_12805),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12799,tc_HOL_Obool)),U_12803),hAPP(hAPP(c_Set_Oinsert(U_12799),U_12801),c_Orderings_Obot__class_Obot(tc_fun(U_12799,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12799,tc_Nat_Onat),U_12805),U_12803)),hAPP(U_12805,U_12801))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12799),U_12801),U_12803)) ),
    inference(clausify,[status(thm)],[f_3273_4]) ).

cnf(f_3273_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12800,tc_Nat_Onat),U_12806),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12800,tc_HOL_Obool)),U_12804),hAPP(hAPP(c_Set_Oinsert(U_12800),U_12802),c_Orderings_Obot__class_Obot(tc_fun(U_12800,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12800,tc_Nat_Onat),U_12806),U_12804)
    | hBOOL(hAPP(hAPP(c_member(U_12800),U_12802),U_12804)) ),
    inference(clausify,[status(thm)],[f_3273_4]) ).

fof(f_3274_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_3274_2,plain,
    ! [U_12810,U_12809,U_12808,U_12807] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12807,tc_Nat_Onat),U_12810),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12807,tc_HOL_Obool)),U_12808),U_12809)) = 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_12807,tc_Nat_Onat),U_12810),U_12808)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12807,tc_Nat_Onat),U_12810),U_12809))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12807,tc_Nat_Onat),U_12810),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12807,tc_HOL_Obool)),U_12808),U_12809)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12807),U_12809))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12807),U_12808)) ),
    inference(variable_rename,[status(thm)],[f_3274_1]) ).

fof(f_3274_3,plain,
    ! [U_12807,U_12808,U_12809,U_12810] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12807,tc_Nat_Onat),U_12810),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12807,tc_HOL_Obool)),U_12808),U_12809)) = 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_12807,tc_Nat_Onat),U_12810),U_12808)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12807,tc_Nat_Onat),U_12810),U_12809))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12807,tc_Nat_Onat),U_12810),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12807,tc_HOL_Obool)),U_12808),U_12809)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12807),U_12809))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12807),U_12808)) ),
    inference(definitional_conversion,[status(esa)],[f_3274_2]) ).

cnf(f_3274_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12807,tc_Nat_Onat),U_12810),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12807,tc_HOL_Obool)),U_12808),U_12809)) = 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_12807,tc_Nat_Onat),U_12810),U_12808)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12807,tc_Nat_Onat),U_12810),U_12809))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12807,tc_Nat_Onat),U_12810),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12807,tc_HOL_Obool)),U_12808),U_12809)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12807),U_12809))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12807),U_12808)) ),
    inference(clausify,[status(thm)],[f_3274_3]) ).

fof(f_3275_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_3275_2,plain,
    ! [U_12813,U_12812,U_12811] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12811),U_12813),U_12812) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12811),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12811,tc_Nat_Onat),U_12813),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_12812))
      | ~ c_Nat__Transfer_Onat__set(U_12812)
      | ~ class_Groups_Ocomm__monoid__mult(U_12811)
      | ~ class_Groups_Ocomm__monoid__add(U_12811) ),
    inference(variable_rename,[status(thm)],[f_3275_1]) ).

fof(f_3275_3,plain,
    ! [U_12812,U_12811,U_12813] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12811),U_12813),U_12812) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12811),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12811,tc_Nat_Onat),U_12813),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_12812))
      | ~ c_Nat__Transfer_Onat__set(U_12812)
      | ~ class_Groups_Ocomm__monoid__mult(U_12811)
      | ~ class_Groups_Ocomm__monoid__add(U_12811) ),
    inference(definitional_conversion,[status(esa)],[f_3275_2]) ).

cnf(f_3275_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12811),U_12813),U_12812) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12811),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12811,tc_Nat_Onat),U_12813),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_12812))
    | ~ c_Nat__Transfer_Onat__set(U_12812)
    | ~ class_Groups_Ocomm__monoid__mult(U_12811)
    | ~ class_Groups_Ocomm__monoid__add(U_12811) ),
    inference(clausify,[status(thm)],[f_3275_3]) ).

fof(f_3276_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_3276_2,plain,
    ! [U_12816,U_12815,U_12814] : 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_12814)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_12815))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12816))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12816),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12814),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12814),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12816),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12815)))),
    inference(variable_rename,[status(thm)],[f_3276_1]) ).

fof(f_3276_3,plain,
    ! [U_12814,U_12815,U_12816] : 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_12814)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_12815))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12816))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12816),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12814),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12814),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12816),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12815)))),
    inference(definitional_conversion,[status(esa)],[f_3276_2]) ).

cnf(f_3276_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_12814)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_12815))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12816))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12816),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12814),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12814),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12816),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12815)))),
    inference(clausify,[status(thm)],[f_3276_3]) ).

fof(f_3277_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_3277_2,plain,
    ! [U_12820,U_12819,U_12818] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12818,tc_Int_Oint),U_12820),U_12819) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12818,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_12818),c_Int_Onat),U_12820)),U_12819))
      | ? [U_12817] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_12820,U_12817))
          & hBOOL(hAPP(hAPP(c_member(U_12818),U_12817),U_12819)) ) ),
    inference(variable_rename,[status(thm)],[f_3277_1]) ).

fof(f_3277_3,plain,
    ! [U_12820,U_12819,U_12818] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12818,tc_Int_Oint),U_12820),U_12819) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12818,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_12818),c_Int_Onat),U_12820)),U_12819))
      | ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_12820,sK270(U_12820,U_12819,U_12818)))
        & hBOOL(hAPP(hAPP(c_member(U_12818),sK270(U_12820,U_12819,U_12818)),U_12819)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK270]),skolemize(U_12817,sK270(U_12820,U_12819,U_12818))],[f_3277_2]) ).

fof(f_3277_4,plain,
    ( ! [U_12818,U_12819,U_12820] :
        ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_12820,sK270(U_12820,U_12819,U_12818)))
        | ~ sP932(U_12818,U_12819,U_12820) )
    & ! [U_12818,U_12819,U_12820] :
        ( hBOOL(hAPP(hAPP(c_member(U_12818),sK270(U_12820,U_12819,U_12818)),U_12819))
        | ~ sP932(U_12818,U_12819,U_12820) )
    & ! [U_12818,U_12819,U_12820] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12818,tc_Int_Oint),U_12820),U_12819) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12818,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_12818),c_Int_Onat),U_12820)),U_12819))
        | sP932(U_12818,U_12819,U_12820) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP932])],[f_3277_3]) ).

cnf(f_3277_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12818,tc_Int_Oint),U_12820),U_12819) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12818,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_12818),c_Int_Onat),U_12820)),U_12819))
    | sP932(U_12818,U_12819,U_12820) ),
    inference(clausify,[status(thm)],[f_3277_4]) ).

cnf(f_3277_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12818),sK270(U_12820,U_12819,U_12818)),U_12819))
    | ~ sP932(U_12818,U_12819,U_12820) ),
    inference(clausify,[status(thm)],[f_3277_4]) ).

cnf(f_3277_7,plain,
    ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_12820,sK270(U_12820,U_12819,U_12818)))
    | ~ sP932(U_12818,U_12819,U_12820) ),
    inference(clausify,[status(thm)],[f_3277_4]) ).

fof(f_3278_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_3278_2,plain,
    ! [U_12826,U_12825,U_12824,U_12823,U_12822] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12823,U_12822),U_12826),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12823,tc_HOL_Obool)),U_12824),U_12825)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12822),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12823,U_12822),U_12826),U_12824)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12823,U_12822),U_12826),U_12825))
      | ? [U_12821] :
          ( hAPP(U_12826,U_12821) != c_Groups_Ozero__class_Ozero(U_12822)
          & hBOOL(hAPP(hAPP(c_member(U_12823),U_12821),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12823,tc_HOL_Obool)),U_12824),U_12825))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),U_12825))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),U_12824))
      | ~ class_Groups_Ocomm__monoid__add(U_12822) ),
    inference(variable_rename,[status(thm)],[f_3278_1]) ).

fof(f_3278_3,plain,
    ! [U_12826,U_12825,U_12824,U_12823,U_12822] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12823,U_12822),U_12826),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12823,tc_HOL_Obool)),U_12824),U_12825)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12822),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12823,U_12822),U_12826),U_12824)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12823,U_12822),U_12826),U_12825))
      | ( hAPP(U_12826,sK271(U_12826,U_12825,U_12824,U_12823,U_12822)) != c_Groups_Ozero__class_Ozero(U_12822)
        & hBOOL(hAPP(hAPP(c_member(U_12823),sK271(U_12826,U_12825,U_12824,U_12823,U_12822)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12823,tc_HOL_Obool)),U_12824),U_12825))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),U_12825))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),U_12824))
      | ~ class_Groups_Ocomm__monoid__add(U_12822) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK271]),skolemize(U_12821,sK271(U_12826,U_12825,U_12824,U_12823,U_12822))],[f_3278_2]) ).

fof(f_3278_4,plain,
    ( ! [U_12822,U_12823,U_12824,U_12825,U_12826] :
        ( hAPP(U_12826,sK271(U_12826,U_12825,U_12824,U_12823,U_12822)) != c_Groups_Ozero__class_Ozero(U_12822)
        | ~ sP933(U_12822,U_12823,U_12824,U_12825,U_12826) )
    & ! [U_12822,U_12823,U_12824,U_12825,U_12826] :
        ( hBOOL(hAPP(hAPP(c_member(U_12823),sK271(U_12826,U_12825,U_12824,U_12823,U_12822)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12823,tc_HOL_Obool)),U_12824),U_12825)))
        | ~ sP933(U_12822,U_12823,U_12824,U_12825,U_12826) )
    & ! [U_12822,U_12823,U_12824,U_12825,U_12826] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12823,U_12822),U_12826),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12823,tc_HOL_Obool)),U_12824),U_12825)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12822),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12823,U_12822),U_12826),U_12824)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12823,U_12822),U_12826),U_12825))
        | sP933(U_12822,U_12823,U_12824,U_12825,U_12826)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),U_12825))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),U_12824))
        | ~ class_Groups_Ocomm__monoid__add(U_12822) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP933])],[f_3278_3]) ).

cnf(f_3278_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12823,U_12822),U_12826),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12823,tc_HOL_Obool)),U_12824),U_12825)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12822),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12823,U_12822),U_12826),U_12824)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12823,U_12822),U_12826),U_12825))
    | sP933(U_12822,U_12823,U_12824,U_12825,U_12826)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),U_12825))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12823),U_12824))
    | ~ class_Groups_Ocomm__monoid__add(U_12822) ),
    inference(clausify,[status(thm)],[f_3278_4]) ).

cnf(f_3278_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12823),sK271(U_12826,U_12825,U_12824,U_12823,U_12822)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12823,tc_HOL_Obool)),U_12824),U_12825)))
    | ~ sP933(U_12822,U_12823,U_12824,U_12825,U_12826) ),
    inference(clausify,[status(thm)],[f_3278_4]) ).

cnf(f_3278_7,plain,
    ( hAPP(U_12826,sK271(U_12826,U_12825,U_12824,U_12823,U_12822)) != c_Groups_Ozero__class_Ozero(U_12822)
    | ~ sP933(U_12822,U_12823,U_12824,U_12825,U_12826) ),
    inference(clausify,[status(thm)],[f_3278_4]) ).

fof(f_3279_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_3279_2,plain,
    ! [U_12832,U_12831,U_12830,U_12829,U_12828] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12828),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12829,U_12828),U_12832),U_12831)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12829,U_12828),U_12832),U_12830)))
      | ? [U_12827] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12828),c_Groups_Ozero__class_Ozero(U_12828)),hAPP(U_12832,U_12827)))
          & hBOOL(hAPP(hAPP(c_member(U_12829),U_12827),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12829,tc_HOL_Obool)),U_12830),U_12831))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12829,tc_HOL_Obool)),U_12831),U_12830))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12829),U_12830))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_12828)
      | ~ class_Groups_Ocomm__monoid__add(U_12828) ),
    inference(variable_rename,[status(thm)],[f_3279_1]) ).

fof(f_3279_3,plain,
    ! [U_12832,U_12831,U_12830,U_12829,U_12828] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12828),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12829,U_12828),U_12832),U_12831)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12829,U_12828),U_12832),U_12830)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12828),c_Groups_Ozero__class_Ozero(U_12828)),hAPP(U_12832,sK272(U_12832,U_12831,U_12830,U_12829,U_12828))))
        & hBOOL(hAPP(hAPP(c_member(U_12829),sK272(U_12832,U_12831,U_12830,U_12829,U_12828)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12829,tc_HOL_Obool)),U_12830),U_12831))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12829,tc_HOL_Obool)),U_12831),U_12830))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12829),U_12830))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_12828)
      | ~ class_Groups_Ocomm__monoid__add(U_12828) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK272]),skolemize(U_12827,sK272(U_12832,U_12831,U_12830,U_12829,U_12828))],[f_3279_2]) ).

fof(f_3279_4,plain,
    ( ! [U_12830,U_12829,U_12828,U_12831,U_12832] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12828),c_Groups_Ozero__class_Ozero(U_12828)),hAPP(U_12832,sK272(U_12832,U_12831,U_12830,U_12829,U_12828))))
        | ~ sP934(U_12830,U_12829,U_12828,U_12831,U_12832) )
    & ! [U_12830,U_12829,U_12828,U_12831,U_12832] :
        ( hBOOL(hAPP(hAPP(c_member(U_12829),sK272(U_12832,U_12831,U_12830,U_12829,U_12828)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12829,tc_HOL_Obool)),U_12830),U_12831)))
        | ~ sP934(U_12830,U_12829,U_12828,U_12831,U_12832) )
    & ! [U_12830,U_12829,U_12828,U_12831,U_12832] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12828),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12829,U_12828),U_12832),U_12831)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12829,U_12828),U_12832),U_12830)))
        | sP934(U_12830,U_12829,U_12828,U_12831,U_12832)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12829,tc_HOL_Obool)),U_12831),U_12830))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12829),U_12830))
        | ~ class_Groups_Oordered__ab__semigroup__add(U_12828)
        | ~ class_Groups_Ocomm__monoid__add(U_12828) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP934])],[f_3279_3]) ).

cnf(f_3279_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12828),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12829,U_12828),U_12832),U_12831)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12829,U_12828),U_12832),U_12830)))
    | sP934(U_12830,U_12829,U_12828,U_12831,U_12832)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12829,tc_HOL_Obool)),U_12831),U_12830))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12829),U_12830))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_12828)
    | ~ class_Groups_Ocomm__monoid__add(U_12828) ),
    inference(clausify,[status(thm)],[f_3279_4]) ).

cnf(f_3279_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12829),sK272(U_12832,U_12831,U_12830,U_12829,U_12828)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12829,tc_HOL_Obool)),U_12830),U_12831)))
    | ~ sP934(U_12830,U_12829,U_12828,U_12831,U_12832) ),
    inference(clausify,[status(thm)],[f_3279_4]) ).

cnf(f_3279_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12828),c_Groups_Ozero__class_Ozero(U_12828)),hAPP(U_12832,sK272(U_12832,U_12831,U_12830,U_12829,U_12828))))
    | ~ sP934(U_12830,U_12829,U_12828,U_12831,U_12832) ),
    inference(clausify,[status(thm)],[f_3279_4]) ).

fof(f_3280_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_3280_2,plain,
    ! [U_12838,U_12837,U_12836,U_12835,U_12834] :
      ( hAPP(U_12837,U_12838) = c_Groups_Ozero__class_Ozero(U_12834)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12835),U_12838),U_12836))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12835,U_12834),U_12837),U_12836) != c_Groups_Ozero__class_Ozero(U_12834)
      | ? [U_12833] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),c_Groups_Ozero__class_Ozero(U_12834)),hAPP(U_12837,U_12833)))
          & hBOOL(hAPP(hAPP(c_member(U_12835),U_12833),U_12836)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12835),U_12836))
      | ~ class_Groups_Oordered__ab__group__add(U_12834) ),
    inference(variable_rename,[status(thm)],[f_3280_1]) ).

fof(f_3280_3,plain,
    ! [U_12838,U_12837,U_12836,U_12835,U_12834] :
      ( hAPP(U_12837,U_12838) = c_Groups_Ozero__class_Ozero(U_12834)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12835),U_12838),U_12836))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12835,U_12834),U_12837),U_12836) != c_Groups_Ozero__class_Ozero(U_12834)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),c_Groups_Ozero__class_Ozero(U_12834)),hAPP(U_12837,sK273(U_12838,U_12837,U_12836,U_12835,U_12834))))
        & hBOOL(hAPP(hAPP(c_member(U_12835),sK273(U_12838,U_12837,U_12836,U_12835,U_12834)),U_12836)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12835),U_12836))
      | ~ class_Groups_Oordered__ab__group__add(U_12834) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK273]),skolemize(U_12833,sK273(U_12838,U_12837,U_12836,U_12835,U_12834))],[f_3280_2]) ).

fof(f_3280_4,plain,
    ( ! [U_12837,U_12834,U_12838,U_12835,U_12836] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),c_Groups_Ozero__class_Ozero(U_12834)),hAPP(U_12837,sK273(U_12838,U_12837,U_12836,U_12835,U_12834))))
        | ~ sP935(U_12837,U_12834,U_12838,U_12835,U_12836) )
    & ! [U_12837,U_12834,U_12838,U_12835,U_12836] :
        ( hBOOL(hAPP(hAPP(c_member(U_12835),sK273(U_12838,U_12837,U_12836,U_12835,U_12834)),U_12836))
        | ~ sP935(U_12837,U_12834,U_12838,U_12835,U_12836) )
    & ! [U_12837,U_12834,U_12838,U_12835,U_12836] :
        ( hAPP(U_12837,U_12838) = c_Groups_Ozero__class_Ozero(U_12834)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12835),U_12838),U_12836))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12835,U_12834),U_12837),U_12836) != c_Groups_Ozero__class_Ozero(U_12834)
        | sP935(U_12837,U_12834,U_12838,U_12835,U_12836)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12835),U_12836))
        | ~ class_Groups_Oordered__ab__group__add(U_12834) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP935])],[f_3280_3]) ).

cnf(f_3280_5,plain,
    ( hAPP(U_12837,U_12838) = c_Groups_Ozero__class_Ozero(U_12834)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12835),U_12838),U_12836))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12835,U_12834),U_12837),U_12836) != c_Groups_Ozero__class_Ozero(U_12834)
    | sP935(U_12837,U_12834,U_12838,U_12835,U_12836)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12835),U_12836))
    | ~ class_Groups_Oordered__ab__group__add(U_12834) ),
    inference(clausify,[status(thm)],[f_3280_4]) ).

cnf(f_3280_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12835),sK273(U_12838,U_12837,U_12836,U_12835,U_12834)),U_12836))
    | ~ sP935(U_12837,U_12834,U_12838,U_12835,U_12836) ),
    inference(clausify,[status(thm)],[f_3280_4]) ).

cnf(f_3280_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),c_Groups_Ozero__class_Ozero(U_12834)),hAPP(U_12837,sK273(U_12838,U_12837,U_12836,U_12835,U_12834))))
    | ~ sP935(U_12837,U_12834,U_12838,U_12835,U_12836) ),
    inference(clausify,[status(thm)],[f_3280_4]) ).

fof(f_3281_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_3281_2,plain,
    ! [U_12845,U_12844,U_12843,U_12842,U_12841,U_12840] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12840),hAPP(U_12843,U_12845)),U_12844))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12841),U_12845),U_12842))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12841,U_12840),U_12843),U_12842) != U_12844
      | ? [U_12839] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12840),c_Groups_Ozero__class_Ozero(U_12840)),hAPP(U_12843,U_12839)))
          & hBOOL(hAPP(hAPP(c_member(U_12841),U_12839),U_12842)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12841),U_12842))
      | ~ class_Groups_Oordered__ab__group__add(U_12840) ),
    inference(variable_rename,[status(thm)],[f_3281_1]) ).

fof(f_3281_3,plain,
    ! [U_12845,U_12844,U_12843,U_12842,U_12841,U_12840] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12840),hAPP(U_12843,U_12845)),U_12844))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12841),U_12845),U_12842))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12841,U_12840),U_12843),U_12842) != U_12844
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12840),c_Groups_Ozero__class_Ozero(U_12840)),hAPP(U_12843,sK274(U_12845,U_12844,U_12843,U_12842,U_12841,U_12840))))
        & hBOOL(hAPP(hAPP(c_member(U_12841),sK274(U_12845,U_12844,U_12843,U_12842,U_12841,U_12840)),U_12842)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12841),U_12842))
      | ~ class_Groups_Oordered__ab__group__add(U_12840) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK274]),skolemize(U_12839,sK274(U_12845,U_12844,U_12843,U_12842,U_12841,U_12840))],[f_3281_2]) ).

fof(f_3281_4,plain,
    ( ! [U_12843,U_12842,U_12844,U_12845,U_12840,U_12841] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12840),c_Groups_Ozero__class_Ozero(U_12840)),hAPP(U_12843,sK274(U_12845,U_12844,U_12843,U_12842,U_12841,U_12840))))
        | ~ sP936(U_12843,U_12842,U_12844,U_12845,U_12840,U_12841) )
    & ! [U_12843,U_12842,U_12844,U_12845,U_12840,U_12841] :
        ( hBOOL(hAPP(hAPP(c_member(U_12841),sK274(U_12845,U_12844,U_12843,U_12842,U_12841,U_12840)),U_12842))
        | ~ sP936(U_12843,U_12842,U_12844,U_12845,U_12840,U_12841) )
    & ! [U_12843,U_12842,U_12844,U_12845,U_12840,U_12841] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12840),hAPP(U_12843,U_12845)),U_12844))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12841),U_12845),U_12842))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12841,U_12840),U_12843),U_12842) != U_12844
        | sP936(U_12843,U_12842,U_12844,U_12845,U_12840,U_12841)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12841),U_12842))
        | ~ class_Groups_Oordered__ab__group__add(U_12840) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP936])],[f_3281_3]) ).

cnf(f_3281_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12840),hAPP(U_12843,U_12845)),U_12844))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12841),U_12845),U_12842))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12841,U_12840),U_12843),U_12842) != U_12844
    | sP936(U_12843,U_12842,U_12844,U_12845,U_12840,U_12841)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12841),U_12842))
    | ~ class_Groups_Oordered__ab__group__add(U_12840) ),
    inference(clausify,[status(thm)],[f_3281_4]) ).

cnf(f_3281_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12841),sK274(U_12845,U_12844,U_12843,U_12842,U_12841,U_12840)),U_12842))
    | ~ sP936(U_12843,U_12842,U_12844,U_12845,U_12840,U_12841) ),
    inference(clausify,[status(thm)],[f_3281_4]) ).

cnf(f_3281_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12840),c_Groups_Ozero__class_Ozero(U_12840)),hAPP(U_12843,sK274(U_12845,U_12844,U_12843,U_12842,U_12841,U_12840))))
    | ~ sP936(U_12843,U_12842,U_12844,U_12845,U_12840,U_12841) ),
    inference(clausify,[status(thm)],[f_3281_4]) ).

fof(f_3282_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_3282_2,plain,
    ! [U_12849,U_12848,U_12847] :
      ( 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_12848),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12849))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12847),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12849))) = 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_12848)),U_12847)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12849))
      | ? [U_12846] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_12847,U_12846)),hAPP(U_12848,U_12846))) ),
    inference(variable_rename,[status(thm)],[f_3282_1]) ).

fof(f_3282_3,plain,
    ! [U_12849,U_12848,U_12847] :
      ( 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_12848),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12849))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12847),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12849))) = 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_12848)),U_12847)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12849))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_12847,sK275(U_12849,U_12848,U_12847))),hAPP(U_12848,sK275(U_12849,U_12848,U_12847)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK275]),skolemize(U_12846,sK275(U_12849,U_12848,U_12847))],[f_3282_2]) ).

fof(f_3282_4,plain,
    ! [U_12849,U_12848,U_12847] :
      ( 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_12848),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12849))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12847),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12849))) = 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_12848)),U_12847)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12849))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_12847,sK275(U_12849,U_12848,U_12847))),hAPP(U_12848,sK275(U_12849,U_12848,U_12847)))) ),
    inference(definitional_conversion,[status(esa)],[f_3282_3]) ).

cnf(f_3282_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_12848),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12849))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12847),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12849))) = 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_12848)),U_12847)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12849))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_12847,sK275(U_12849,U_12848,U_12847))),hAPP(U_12848,sK275(U_12849,U_12848,U_12847)))) ),
    inference(clausify,[status(thm)],[f_3282_4]) ).

fof(f_3283_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_3283_2,plain,
    ! [U_12855,U_12854,U_12853,U_12852,U_12851] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12852,U_12851),U_12855),U_12854) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12852,U_12851),U_12855),U_12853)
      | ? [U_12850] :
          ( hAPP(U_12855,U_12850) != c_Groups_Ozero__class_Ozero(U_12851)
          & hBOOL(hAPP(hAPP(c_member(U_12852),U_12850),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12852,tc_HOL_Obool)),U_12853),U_12854))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12852,tc_HOL_Obool)),U_12854),U_12853))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12852),U_12853))
      | ~ class_Groups_Ocomm__monoid__add(U_12851) ),
    inference(variable_rename,[status(thm)],[f_3283_1]) ).

fof(f_3283_3,plain,
    ! [U_12855,U_12854,U_12853,U_12852,U_12851] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12852,U_12851),U_12855),U_12854) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12852,U_12851),U_12855),U_12853)
      | ( hAPP(U_12855,sK276(U_12855,U_12854,U_12853,U_12852,U_12851)) != c_Groups_Ozero__class_Ozero(U_12851)
        & hBOOL(hAPP(hAPP(c_member(U_12852),sK276(U_12855,U_12854,U_12853,U_12852,U_12851)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12852,tc_HOL_Obool)),U_12853),U_12854))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12852,tc_HOL_Obool)),U_12854),U_12853))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12852),U_12853))
      | ~ class_Groups_Ocomm__monoid__add(U_12851) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK276]),skolemize(U_12850,sK276(U_12855,U_12854,U_12853,U_12852,U_12851))],[f_3283_2]) ).

fof(f_3283_4,plain,
    ( ! [U_12852,U_12851,U_12853,U_12854,U_12855] :
        ( hAPP(U_12855,sK276(U_12855,U_12854,U_12853,U_12852,U_12851)) != c_Groups_Ozero__class_Ozero(U_12851)
        | ~ sP937(U_12852,U_12851,U_12853,U_12854,U_12855) )
    & ! [U_12852,U_12851,U_12853,U_12854,U_12855] :
        ( hBOOL(hAPP(hAPP(c_member(U_12852),sK276(U_12855,U_12854,U_12853,U_12852,U_12851)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12852,tc_HOL_Obool)),U_12853),U_12854)))
        | ~ sP937(U_12852,U_12851,U_12853,U_12854,U_12855) )
    & ! [U_12852,U_12851,U_12853,U_12854,U_12855] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12852,U_12851),U_12855),U_12854) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12852,U_12851),U_12855),U_12853)
        | sP937(U_12852,U_12851,U_12853,U_12854,U_12855)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12852,tc_HOL_Obool)),U_12854),U_12853))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12852),U_12853))
        | ~ class_Groups_Ocomm__monoid__add(U_12851) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP937])],[f_3283_3]) ).

cnf(f_3283_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12852,U_12851),U_12855),U_12854) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12852,U_12851),U_12855),U_12853)
    | sP937(U_12852,U_12851,U_12853,U_12854,U_12855)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12852,tc_HOL_Obool)),U_12854),U_12853))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12852),U_12853))
    | ~ class_Groups_Ocomm__monoid__add(U_12851) ),
    inference(clausify,[status(thm)],[f_3283_4]) ).

cnf(f_3283_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12852),sK276(U_12855,U_12854,U_12853,U_12852,U_12851)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12852,tc_HOL_Obool)),U_12853),U_12854)))
    | ~ sP937(U_12852,U_12851,U_12853,U_12854,U_12855) ),
    inference(clausify,[status(thm)],[f_3283_4]) ).

cnf(f_3283_7,plain,
    ( hAPP(U_12855,sK276(U_12855,U_12854,U_12853,U_12852,U_12851)) != c_Groups_Ozero__class_Ozero(U_12851)
    | ~ sP937(U_12852,U_12851,U_12853,U_12854,U_12855) ),
    inference(clausify,[status(thm)],[f_3283_4]) ).

fof(f_3284_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_3284_2,plain,
    ! [U_12861,U_12860,U_12859,U_12858,U_12857] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12858,U_12857),U_12861),U_12859) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12858,U_12857),U_12861),U_12860)
      | ? [U_12856] :
          ( hAPP(U_12861,U_12856) != c_Groups_Ozero__class_Ozero(U_12857)
          & hBOOL(hAPP(hAPP(c_member(U_12858),U_12856),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12858,tc_HOL_Obool)),U_12859),U_12860))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12858,tc_HOL_Obool)),U_12860),U_12859))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12858),U_12859))
      | ~ class_Groups_Ocomm__monoid__add(U_12857) ),
    inference(variable_rename,[status(thm)],[f_3284_1]) ).

fof(f_3284_3,plain,
    ! [U_12861,U_12860,U_12859,U_12858,U_12857] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12858,U_12857),U_12861),U_12859) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12858,U_12857),U_12861),U_12860)
      | ( hAPP(U_12861,sK277(U_12861,U_12860,U_12859,U_12858,U_12857)) != c_Groups_Ozero__class_Ozero(U_12857)
        & hBOOL(hAPP(hAPP(c_member(U_12858),sK277(U_12861,U_12860,U_12859,U_12858,U_12857)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12858,tc_HOL_Obool)),U_12859),U_12860))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12858,tc_HOL_Obool)),U_12860),U_12859))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12858),U_12859))
      | ~ class_Groups_Ocomm__monoid__add(U_12857) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK277]),skolemize(U_12856,sK277(U_12861,U_12860,U_12859,U_12858,U_12857))],[f_3284_2]) ).

fof(f_3284_4,plain,
    ( ! [U_12858,U_12857,U_12860,U_12859,U_12861] :
        ( hAPP(U_12861,sK277(U_12861,U_12860,U_12859,U_12858,U_12857)) != c_Groups_Ozero__class_Ozero(U_12857)
        | ~ sP938(U_12858,U_12857,U_12860,U_12859,U_12861) )
    & ! [U_12858,U_12857,U_12860,U_12859,U_12861] :
        ( hBOOL(hAPP(hAPP(c_member(U_12858),sK277(U_12861,U_12860,U_12859,U_12858,U_12857)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12858,tc_HOL_Obool)),U_12859),U_12860)))
        | ~ sP938(U_12858,U_12857,U_12860,U_12859,U_12861) )
    & ! [U_12858,U_12857,U_12860,U_12859,U_12861] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12858,U_12857),U_12861),U_12859) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12858,U_12857),U_12861),U_12860)
        | sP938(U_12858,U_12857,U_12860,U_12859,U_12861)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12858,tc_HOL_Obool)),U_12860),U_12859))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12858),U_12859))
        | ~ class_Groups_Ocomm__monoid__add(U_12857) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP938])],[f_3284_3]) ).

cnf(f_3284_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12858,U_12857),U_12861),U_12859) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12858,U_12857),U_12861),U_12860)
    | sP938(U_12858,U_12857,U_12860,U_12859,U_12861)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12858,tc_HOL_Obool)),U_12860),U_12859))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12858),U_12859))
    | ~ class_Groups_Ocomm__monoid__add(U_12857) ),
    inference(clausify,[status(thm)],[f_3284_4]) ).

cnf(f_3284_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12858),sK277(U_12861,U_12860,U_12859,U_12858,U_12857)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12858,tc_HOL_Obool)),U_12859),U_12860)))
    | ~ sP938(U_12858,U_12857,U_12860,U_12859,U_12861) ),
    inference(clausify,[status(thm)],[f_3284_4]) ).

cnf(f_3284_7,plain,
    ( hAPP(U_12861,sK277(U_12861,U_12860,U_12859,U_12858,U_12857)) != c_Groups_Ozero__class_Ozero(U_12857)
    | ~ sP938(U_12858,U_12857,U_12860,U_12859,U_12861) ),
    inference(clausify,[status(thm)],[f_3284_4]) ).

fof(f_3285_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_3285_2,plain,
    ! [U_12866,U_12865,U_12864,U_12863,U_12862] :
      ( hAPP(U_12864,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12862,tc_HOL_Obool)),U_12865),U_12866)) = hAPP(hAPP(U_12863,hAPP(U_12864,U_12865)),hAPP(U_12864,U_12866))
      | U_12866 = c_Orderings_Obot__class_Obot(tc_fun(U_12862,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12862),U_12866))
      | U_12865 = c_Orderings_Obot__class_Obot(tc_fun(U_12862,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12862),U_12865))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12862,U_12863,U_12864) ),
    inference(variable_rename,[status(thm)],[f_3285_1]) ).

fof(f_3285_3,plain,
    ! [U_12863,U_12866,U_12864,U_12865,U_12862] :
      ( hAPP(U_12864,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12862,tc_HOL_Obool)),U_12865),U_12866)) = hAPP(hAPP(U_12863,hAPP(U_12864,U_12865)),hAPP(U_12864,U_12866))
      | U_12866 = c_Orderings_Obot__class_Obot(tc_fun(U_12862,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12862),U_12866))
      | U_12865 = c_Orderings_Obot__class_Obot(tc_fun(U_12862,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12862),U_12865))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12862,U_12863,U_12864) ),
    inference(definitional_conversion,[status(esa)],[f_3285_2]) ).

cnf(f_3285_4,plain,
    ( hAPP(U_12864,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12862,tc_HOL_Obool)),U_12865),U_12866)) = hAPP(hAPP(U_12863,hAPP(U_12864,U_12865)),hAPP(U_12864,U_12866))
    | U_12866 = c_Orderings_Obot__class_Obot(tc_fun(U_12862,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12862),U_12866))
    | U_12865 = c_Orderings_Obot__class_Obot(tc_fun(U_12862,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12862),U_12865))
    | ~ c_Finite__Set_Ofolding__one__idem(U_12862,U_12863,U_12864) ),
    inference(clausify,[status(thm)],[f_3285_3]) ).

fof(f_3286_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_3286_2,plain,
    ! [U_12870,U_12869,U_12868,U_12867] :
      ( hAPP(hAPP(U_12868,U_12870),U_12870) = U_12870
      | ~ c_Finite__Set_Ofolding__one__idem(U_12867,U_12868,U_12869) ),
    inference(variable_rename,[status(thm)],[f_3286_1]) ).

fof(f_3286_3,plain,
    ! [U_12870,U_12869,U_12868] :
      ( ! [U_12867] : ~ c_Finite__Set_Ofolding__one__idem(U_12867,U_12868,U_12869)
      | hAPP(hAPP(U_12868,U_12870),U_12870) = U_12870 ),
    inference(miniscope,[status(thm)],[f_3286_2]) ).

fof(f_3286_4,plain,
    ! [U_12869,U_12870,U_12867,U_12868] :
      ( ~ c_Finite__Set_Ofolding__one__idem(U_12867,U_12868,U_12869)
      | hAPP(hAPP(U_12868,U_12870),U_12870) = U_12870 ),
    inference(definitional_conversion,[status(esa)],[f_3286_3]) ).

cnf(f_3286_5,plain,
    ( ~ c_Finite__Set_Ofolding__one__idem(U_12867,U_12868,U_12869)
    | hAPP(hAPP(U_12868,U_12870),U_12870) = U_12870 ),
    inference(clausify,[status(thm)],[f_3286_4]) ).

fof(f_3287_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_3287_2,plain,
    ! [U_12875,U_12874,U_12873,U_12872,U_12871] :
      ( hAPP(hAPP(U_12872,U_12875),hAPP(U_12873,U_12874)) = hAPP(U_12873,U_12874)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12871),U_12875),U_12874))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12871),U_12874))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12871,U_12872,U_12873) ),
    inference(variable_rename,[status(thm)],[f_3287_1]) ).

fof(f_3287_3,plain,
    ! [U_12871,U_12872,U_12874,U_12875,U_12873] :
      ( hAPP(hAPP(U_12872,U_12875),hAPP(U_12873,U_12874)) = hAPP(U_12873,U_12874)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12871),U_12875),U_12874))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12871),U_12874))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12871,U_12872,U_12873) ),
    inference(definitional_conversion,[status(esa)],[f_3287_2]) ).

cnf(f_3287_4,plain,
    ( hAPP(hAPP(U_12872,U_12875),hAPP(U_12873,U_12874)) = hAPP(U_12873,U_12874)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12871),U_12875),U_12874))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12871),U_12874))
    | ~ c_Finite__Set_Ofolding__one__idem(U_12871,U_12872,U_12873) ),
    inference(clausify,[status(thm)],[f_3287_3]) ).

fof(f_3288_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_3288_2,plain,
    ! [U_12880,U_12879,U_12878,U_12877,U_12876] :
      ( hAPP(U_12878,hAPP(hAPP(c_Set_Oinsert(U_12876),U_12880),U_12879)) = hAPP(hAPP(U_12877,U_12880),hAPP(U_12878,U_12879))
      | U_12879 = c_Orderings_Obot__class_Obot(tc_fun(U_12876,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12876),U_12879))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12876,U_12877,U_12878) ),
    inference(variable_rename,[status(thm)],[f_3288_1]) ).

fof(f_3288_3,plain,
    ! [U_12877,U_12876,U_12878,U_12879,U_12880] :
      ( hAPP(U_12878,hAPP(hAPP(c_Set_Oinsert(U_12876),U_12880),U_12879)) = hAPP(hAPP(U_12877,U_12880),hAPP(U_12878,U_12879))
      | U_12879 = c_Orderings_Obot__class_Obot(tc_fun(U_12876,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12876),U_12879))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12876,U_12877,U_12878) ),
    inference(definitional_conversion,[status(esa)],[f_3288_2]) ).

cnf(f_3288_4,plain,
    ( hAPP(U_12878,hAPP(hAPP(c_Set_Oinsert(U_12876),U_12880),U_12879)) = hAPP(hAPP(U_12877,U_12880),hAPP(U_12878,U_12879))
    | U_12879 = c_Orderings_Obot__class_Obot(tc_fun(U_12876,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12876),U_12879))
    | ~ c_Finite__Set_Ofolding__one__idem(U_12876,U_12877,U_12878) ),
    inference(clausify,[status(thm)],[f_3288_3]) ).

fof(f_3289_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_3289_2,plain,
    ! [U_12885,U_12884,U_12883,U_12882,U_12881] :
      ( hAPP(hAPP(U_12882,hAPP(U_12883,U_12885)),hAPP(U_12883,U_12884)) = hAPP(U_12883,U_12884)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12881,tc_HOL_Obool)),U_12885),U_12884))
      | U_12885 = c_Orderings_Obot__class_Obot(tc_fun(U_12881,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12881),U_12884))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12881,U_12882,U_12883) ),
    inference(variable_rename,[status(thm)],[f_3289_1]) ).

fof(f_3289_3,plain,
    ! [U_12881,U_12882,U_12883,U_12884,U_12885] :
      ( hAPP(hAPP(U_12882,hAPP(U_12883,U_12885)),hAPP(U_12883,U_12884)) = hAPP(U_12883,U_12884)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12881,tc_HOL_Obool)),U_12885),U_12884))
      | U_12885 = c_Orderings_Obot__class_Obot(tc_fun(U_12881,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12881),U_12884))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12881,U_12882,U_12883) ),
    inference(definitional_conversion,[status(esa)],[f_3289_2]) ).

cnf(f_3289_4,plain,
    ( hAPP(hAPP(U_12882,hAPP(U_12883,U_12885)),hAPP(U_12883,U_12884)) = hAPP(U_12883,U_12884)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12881,tc_HOL_Obool)),U_12885),U_12884))
    | U_12885 = c_Orderings_Obot__class_Obot(tc_fun(U_12881,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12881),U_12884))
    | ~ c_Finite__Set_Ofolding__one__idem(U_12881,U_12882,U_12883) ),
    inference(clausify,[status(thm)],[f_3289_3]) ).

fof(f_3290_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_3290_2,plain,
    ! [U_12891,U_12890,U_12889,U_12888] :
      ( hBOOL(hAPP(U_12891,U_12889))
      | ? [U_12887,U_12886] :
          ( ~ hBOOL(hAPP(U_12891,hAPP(hAPP(c_Set_Oinsert(U_12888),U_12887),U_12886)))
          & hBOOL(hAPP(U_12891,U_12886))
          & ~ hBOOL(hAPP(hAPP(c_member(U_12888),U_12887),U_12886))
          & hBOOL(hAPP(hAPP(c_member(U_12888),U_12887),U_12890))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12888),U_12886)) )
      | ~ hBOOL(hAPP(U_12891,c_Orderings_Obot__class_Obot(tc_fun(U_12888,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12888,tc_HOL_Obool)),U_12889),U_12890))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12888),U_12889)) ),
    inference(variable_rename,[status(thm)],[f_3290_1]) ).

fof(f_3290_3,plain,
    ! [U_12891,U_12890,U_12889,U_12888] :
      ( hBOOL(hAPP(U_12891,U_12889))
      | ? [U_12886] :
          ( ~ hBOOL(hAPP(U_12891,hAPP(hAPP(c_Set_Oinsert(U_12888),sK278(U_12891,U_12890,U_12889,U_12888)),U_12886)))
          & hBOOL(hAPP(U_12891,U_12886))
          & ~ hBOOL(hAPP(hAPP(c_member(U_12888),sK278(U_12891,U_12890,U_12889,U_12888)),U_12886))
          & hBOOL(hAPP(hAPP(c_member(U_12888),sK278(U_12891,U_12890,U_12889,U_12888)),U_12890))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12888),U_12886)) )
      | ~ hBOOL(hAPP(U_12891,c_Orderings_Obot__class_Obot(tc_fun(U_12888,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12888,tc_HOL_Obool)),U_12889),U_12890))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12888),U_12889)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK278]),skolemize(U_12887,sK278(U_12891,U_12890,U_12889,U_12888))],[f_3290_2]) ).

fof(f_3290_4,plain,
    ! [U_12891,U_12890,U_12889,U_12888] :
      ( hBOOL(hAPP(U_12891,U_12889))
      | ( ~ hBOOL(hAPP(U_12891,hAPP(hAPP(c_Set_Oinsert(U_12888),sK278(U_12891,U_12890,U_12889,U_12888)),sK279(U_12891,U_12890,U_12889,U_12888))))
        & hBOOL(hAPP(U_12891,sK279(U_12891,U_12890,U_12889,U_12888)))
        & ~ hBOOL(hAPP(hAPP(c_member(U_12888),sK278(U_12891,U_12890,U_12889,U_12888)),sK279(U_12891,U_12890,U_12889,U_12888)))
        & hBOOL(hAPP(hAPP(c_member(U_12888),sK278(U_12891,U_12890,U_12889,U_12888)),U_12890))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12888),sK279(U_12891,U_12890,U_12889,U_12888))) )
      | ~ hBOOL(hAPP(U_12891,c_Orderings_Obot__class_Obot(tc_fun(U_12888,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12888,tc_HOL_Obool)),U_12889),U_12890))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12888),U_12889)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK279]),skolemize(U_12886,sK279(U_12891,U_12890,U_12889,U_12888))],[f_3290_3]) ).

fof(f_3290_5,plain,
    ( ! [U_12888,U_12889,U_12890,U_12891] :
        ( ~ hBOOL(hAPP(U_12891,hAPP(hAPP(c_Set_Oinsert(U_12888),sK278(U_12891,U_12890,U_12889,U_12888)),sK279(U_12891,U_12890,U_12889,U_12888))))
        | ~ sP939(U_12888,U_12889,U_12890,U_12891) )
    & ! [U_12888,U_12889,U_12890,U_12891] :
        ( hBOOL(hAPP(U_12891,sK279(U_12891,U_12890,U_12889,U_12888)))
        | ~ sP939(U_12888,U_12889,U_12890,U_12891) )
    & ! [U_12888,U_12889,U_12890,U_12891] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_12888),sK278(U_12891,U_12890,U_12889,U_12888)),sK279(U_12891,U_12890,U_12889,U_12888)))
        | ~ sP939(U_12888,U_12889,U_12890,U_12891) )
    & ! [U_12888,U_12889,U_12890,U_12891] :
        ( hBOOL(hAPP(hAPP(c_member(U_12888),sK278(U_12891,U_12890,U_12889,U_12888)),U_12890))
        | ~ sP939(U_12888,U_12889,U_12890,U_12891) )
    & ! [U_12888,U_12889,U_12890,U_12891] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12888),sK279(U_12891,U_12890,U_12889,U_12888)))
        | ~ sP939(U_12888,U_12889,U_12890,U_12891) )
    & ! [U_12888,U_12889,U_12890,U_12891] :
        ( hBOOL(hAPP(U_12891,U_12889))
        | sP939(U_12888,U_12889,U_12890,U_12891)
        | ~ hBOOL(hAPP(U_12891,c_Orderings_Obot__class_Obot(tc_fun(U_12888,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12888,tc_HOL_Obool)),U_12889),U_12890))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12888),U_12889)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP939])],[f_3290_4]) ).

cnf(f_3290_6,plain,
    ( hBOOL(hAPP(U_12891,U_12889))
    | sP939(U_12888,U_12889,U_12890,U_12891)
    | ~ hBOOL(hAPP(U_12891,c_Orderings_Obot__class_Obot(tc_fun(U_12888,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12888,tc_HOL_Obool)),U_12889),U_12890))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12888),U_12889)) ),
    inference(clausify,[status(thm)],[f_3290_5]) ).

cnf(f_3290_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12888),sK279(U_12891,U_12890,U_12889,U_12888)))
    | ~ sP939(U_12888,U_12889,U_12890,U_12891) ),
    inference(clausify,[status(thm)],[f_3290_5]) ).

cnf(f_3290_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12888),sK278(U_12891,U_12890,U_12889,U_12888)),U_12890))
    | ~ sP939(U_12888,U_12889,U_12890,U_12891) ),
    inference(clausify,[status(thm)],[f_3290_5]) ).

cnf(f_3290_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12888),sK278(U_12891,U_12890,U_12889,U_12888)),sK279(U_12891,U_12890,U_12889,U_12888)))
    | ~ sP939(U_12888,U_12889,U_12890,U_12891) ),
    inference(clausify,[status(thm)],[f_3290_5]) ).

cnf(f_3290_10,plain,
    ( hBOOL(hAPP(U_12891,sK279(U_12891,U_12890,U_12889,U_12888)))
    | ~ sP939(U_12888,U_12889,U_12890,U_12891) ),
    inference(clausify,[status(thm)],[f_3290_5]) ).

cnf(f_3290_11,plain,
    ( ~ hBOOL(hAPP(U_12891,hAPP(hAPP(c_Set_Oinsert(U_12888),sK278(U_12891,U_12890,U_12889,U_12888)),sK279(U_12891,U_12890,U_12889,U_12888))))
    | ~ sP939(U_12888,U_12889,U_12890,U_12891) ),
    inference(clausify,[status(thm)],[f_3290_5]) ).

fof(f_3291_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_3291_2,plain,
    ! [U_12897,U_12896,U_12895,U_12894,U_12893] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12893),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12894,U_12893),U_12896),U_12895)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12894,U_12893),U_12897),U_12895)))
      | ? [U_12892] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12893),hAPP(U_12896,U_12892)),hAPP(U_12897,U_12892)))
          & hBOOL(hAPP(hAPP(c_member(U_12894),U_12892),U_12895)) )
      | U_12895 = c_Orderings_Obot__class_Obot(tc_fun(U_12894,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12894),U_12895))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_12893)
      | ~ class_Groups_Ocomm__monoid__add(U_12893) ),
    inference(variable_rename,[status(thm)],[f_3291_1]) ).

fof(f_3291_3,plain,
    ! [U_12897,U_12896,U_12895,U_12894,U_12893] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12893),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12894,U_12893),U_12896),U_12895)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12894,U_12893),U_12897),U_12895)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12893),hAPP(U_12896,sK280(U_12897,U_12896,U_12895,U_12894,U_12893))),hAPP(U_12897,sK280(U_12897,U_12896,U_12895,U_12894,U_12893))))
        & hBOOL(hAPP(hAPP(c_member(U_12894),sK280(U_12897,U_12896,U_12895,U_12894,U_12893)),U_12895)) )
      | U_12895 = c_Orderings_Obot__class_Obot(tc_fun(U_12894,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12894),U_12895))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_12893)
      | ~ class_Groups_Ocomm__monoid__add(U_12893) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK280]),skolemize(U_12892,sK280(U_12897,U_12896,U_12895,U_12894,U_12893))],[f_3291_2]) ).

fof(f_3291_4,plain,
    ( ! [U_12893,U_12894,U_12897,U_12896,U_12895] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12893),hAPP(U_12896,sK280(U_12897,U_12896,U_12895,U_12894,U_12893))),hAPP(U_12897,sK280(U_12897,U_12896,U_12895,U_12894,U_12893))))
        | ~ sP940(U_12893,U_12894,U_12897,U_12896,U_12895) )
    & ! [U_12893,U_12894,U_12897,U_12896,U_12895] :
        ( hBOOL(hAPP(hAPP(c_member(U_12894),sK280(U_12897,U_12896,U_12895,U_12894,U_12893)),U_12895))
        | ~ sP940(U_12893,U_12894,U_12897,U_12896,U_12895) )
    & ! [U_12893,U_12894,U_12897,U_12896,U_12895] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12893),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12894,U_12893),U_12896),U_12895)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12894,U_12893),U_12897),U_12895)))
        | sP940(U_12893,U_12894,U_12897,U_12896,U_12895)
        | U_12895 = c_Orderings_Obot__class_Obot(tc_fun(U_12894,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12894),U_12895))
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_12893)
        | ~ class_Groups_Ocomm__monoid__add(U_12893) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP940])],[f_3291_3]) ).

cnf(f_3291_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12893),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12894,U_12893),U_12896),U_12895)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12894,U_12893),U_12897),U_12895)))
    | sP940(U_12893,U_12894,U_12897,U_12896,U_12895)
    | U_12895 = c_Orderings_Obot__class_Obot(tc_fun(U_12894,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12894),U_12895))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_12893)
    | ~ class_Groups_Ocomm__monoid__add(U_12893) ),
    inference(clausify,[status(thm)],[f_3291_4]) ).

cnf(f_3291_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12894),sK280(U_12897,U_12896,U_12895,U_12894,U_12893)),U_12895))
    | ~ sP940(U_12893,U_12894,U_12897,U_12896,U_12895) ),
    inference(clausify,[status(thm)],[f_3291_4]) ).

cnf(f_3291_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12893),hAPP(U_12896,sK280(U_12897,U_12896,U_12895,U_12894,U_12893))),hAPP(U_12897,sK280(U_12897,U_12896,U_12895,U_12894,U_12893))))
    | ~ sP940(U_12893,U_12894,U_12897,U_12896,U_12895) ),
    inference(clausify,[status(thm)],[f_3291_4]) ).

fof(f_3292_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_3292_2,plain,
    ! [U_12899,U_12898] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12898,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12898),U_12899)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12898),U_12899)) = hAPP(hAPP(c_Set_Oinsert(U_12898),U_12899),c_Orderings_Obot__class_Obot(tc_fun(U_12898,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_12898) ),
    inference(variable_rename,[status(thm)],[f_3292_1]) ).

fof(f_3292_3,plain,
    ! [U_12899,U_12898] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12898,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12898),U_12899)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12898),U_12899)) = hAPP(hAPP(c_Set_Oinsert(U_12898),U_12899),c_Orderings_Obot__class_Obot(tc_fun(U_12898,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_12898) ),
    inference(definitional_conversion,[status(esa)],[f_3292_2]) ).

cnf(f_3292_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12898,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12898),U_12899)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12898),U_12899)) = hAPP(hAPP(c_Set_Oinsert(U_12898),U_12899),c_Orderings_Obot__class_Obot(tc_fun(U_12898,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_12898) ),
    inference(clausify,[status(thm)],[f_3292_3]) ).

fof(f_3293_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_3293_2,plain,
    ! [U_12902,U_12901,U_12900] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(U_12900),U_12901) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12900),U_12902)
          | U_12901 != U_12902 )
        & ( U_12901 = U_12902
          | hAPP(c_SetInterval_Oord__class_OatLeast(U_12900),U_12901) != hAPP(c_SetInterval_Oord__class_OatLeast(U_12900),U_12902) ) )
      | ~ class_Orderings_Olinorder(U_12900) ),
    inference(variable_rename,[status(thm)],[f_3293_1]) ).

fof(f_3293_3,plain,
    ( ! [U_12900,U_12901,U_12902] :
        ( hAPP(c_SetInterval_Oord__class_OatLeast(U_12900),U_12901) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12900),U_12902)
        | U_12901 != U_12902
        | ~ sP941(U_12900,U_12901,U_12902) )
    & ! [U_12900,U_12901,U_12902] :
        ( U_12901 = U_12902
        | hAPP(c_SetInterval_Oord__class_OatLeast(U_12900),U_12901) != hAPP(c_SetInterval_Oord__class_OatLeast(U_12900),U_12902)
        | ~ sP941(U_12900,U_12901,U_12902) )
    & ! [U_12900,U_12901,U_12902] :
        ( sP941(U_12900,U_12901,U_12902)
        | ~ class_Orderings_Olinorder(U_12900) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP941])],[f_3293_2]) ).

cnf(f_3293_4,plain,
    ( sP941(U_12900,U_12901,U_12902)
    | ~ class_Orderings_Olinorder(U_12900) ),
    inference(clausify,[status(thm)],[f_3293_3]) ).

cnf(f_3293_5,plain,
    ( U_12901 = U_12902
    | hAPP(c_SetInterval_Oord__class_OatLeast(U_12900),U_12901) != hAPP(c_SetInterval_Oord__class_OatLeast(U_12900),U_12902)
    | ~ sP941(U_12900,U_12901,U_12902) ),
    inference(clausify,[status(thm)],[f_3293_3]) ).

cnf(f_3293_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeast(U_12900),U_12901) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12900),U_12902)
    | U_12901 != U_12902
    | ~ sP941(U_12900,U_12901,U_12902) ),
    inference(clausify,[status(thm)],[f_3293_3]) ).

fof(f_3294_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_3294_2,plain,
    ! [U_12905,U_12904,U_12903] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_12903),U_12904),hAPP(c_SetInterval_Oord__class_OatLeast(U_12903),U_12905)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12903),U_12905),U_12904)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12903),U_12905),U_12904))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12903),U_12904),hAPP(c_SetInterval_Oord__class_OatLeast(U_12903),U_12905))) ) )
      | ~ class_Orderings_Oord(U_12903) ),
    inference(variable_rename,[status(thm)],[f_3294_1]) ).

fof(f_3294_3,plain,
    ( ! [U_12904,U_12905,U_12903] :
        ( hBOOL(hAPP(hAPP(c_member(U_12903),U_12904),hAPP(c_SetInterval_Oord__class_OatLeast(U_12903),U_12905)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12903),U_12905),U_12904))
        | ~ sP942(U_12904,U_12905,U_12903) )
    & ! [U_12904,U_12905,U_12903] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12903),U_12905),U_12904))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12903),U_12904),hAPP(c_SetInterval_Oord__class_OatLeast(U_12903),U_12905)))
        | ~ sP942(U_12904,U_12905,U_12903) )
    & ! [U_12904,U_12905,U_12903] :
        ( sP942(U_12904,U_12905,U_12903)
        | ~ class_Orderings_Oord(U_12903) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP942])],[f_3294_2]) ).

cnf(f_3294_4,plain,
    ( sP942(U_12904,U_12905,U_12903)
    | ~ class_Orderings_Oord(U_12903) ),
    inference(clausify,[status(thm)],[f_3294_3]) ).

cnf(f_3294_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12903),U_12905),U_12904))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12903),U_12904),hAPP(c_SetInterval_Oord__class_OatLeast(U_12903),U_12905)))
    | ~ sP942(U_12904,U_12905,U_12903) ),
    inference(clausify,[status(thm)],[f_3294_3]) ).

cnf(f_3294_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12903),U_12904),hAPP(c_SetInterval_Oord__class_OatLeast(U_12903),U_12905)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12903),U_12905),U_12904))
    | ~ sP942(U_12904,U_12905,U_12903) ),
    inference(clausify,[status(thm)],[f_3294_3]) ).

fof(f_3295_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_3295_2,plain,
    ! [U_12908,U_12907,U_12906] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12906,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12906),U_12907)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12906),U_12908)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12906),U_12908),U_12907)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12906),U_12908),U_12907))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12906,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12906),U_12907)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12906),U_12908))) ) )
      | ~ class_Orderings_Oorder(U_12906) ),
    inference(variable_rename,[status(thm)],[f_3295_1]) ).

fof(f_3295_3,plain,
    ( ! [U_12908,U_12906,U_12907] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12906,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12906),U_12907)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12906),U_12908)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12906),U_12908),U_12907))
        | ~ sP943(U_12908,U_12906,U_12907) )
    & ! [U_12908,U_12906,U_12907] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12906),U_12908),U_12907))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12906,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12906),U_12907)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12906),U_12908)))
        | ~ sP943(U_12908,U_12906,U_12907) )
    & ! [U_12908,U_12906,U_12907] :
        ( sP943(U_12908,U_12906,U_12907)
        | ~ class_Orderings_Oorder(U_12906) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP943])],[f_3295_2]) ).

cnf(f_3295_4,plain,
    ( sP943(U_12908,U_12906,U_12907)
    | ~ class_Orderings_Oorder(U_12906) ),
    inference(clausify,[status(thm)],[f_3295_3]) ).

cnf(f_3295_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12906),U_12908),U_12907))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12906,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12906),U_12907)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12906),U_12908)))
    | ~ sP943(U_12908,U_12906,U_12907) ),
    inference(clausify,[status(thm)],[f_3295_3]) ).

cnf(f_3295_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12906,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12906),U_12907)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12906),U_12908)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12906),U_12908),U_12907))
    | ~ sP943(U_12908,U_12906,U_12907) ),
    inference(clausify,[status(thm)],[f_3295_3]) ).

fof(f_3296_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_3296_2,plain,
    ! [U_12910,U_12909] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12909,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12909),U_12910)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12909),U_12910)
      | ~ class_Orderings_Olinorder(U_12909) ),
    inference(variable_rename,[status(thm)],[f_3296_1]) ).

fof(f_3296_3,plain,
    ! [U_12909,U_12910] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12909,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12909),U_12910)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12909),U_12910)
      | ~ class_Orderings_Olinorder(U_12909) ),
    inference(definitional_conversion,[status(esa)],[f_3296_2]) ).

cnf(f_3296_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12909,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12909),U_12910)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12909),U_12910)
    | ~ class_Orderings_Olinorder(U_12909) ),
    inference(clausify,[status(thm)],[f_3296_3]) ).

fof(f_3297_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_3297_2,plain,
    ! [U_12912,U_12911] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12911,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12911),U_12912)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12911),U_12912)
      | ~ class_Orderings_Olinorder(U_12911) ),
    inference(variable_rename,[status(thm)],[f_3297_1]) ).

fof(f_3297_3,plain,
    ! [U_12911,U_12912] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12911,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12911),U_12912)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12911),U_12912)
      | ~ class_Orderings_Olinorder(U_12911) ),
    inference(definitional_conversion,[status(esa)],[f_3297_2]) ).

cnf(f_3297_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12911,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12911),U_12912)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12911),U_12912)
    | ~ class_Orderings_Olinorder(U_12911) ),
    inference(clausify,[status(thm)],[f_3297_3]) ).

fof(f_3298_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_3298_2,plain,
    ! [U_12915,U_12914,U_12913] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12913,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12913,U_12914),U_12915)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12913),U_12915)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12913),U_12914)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12913),U_12914),U_12915))
      | ~ class_Orderings_Olinorder(U_12913) ),
    inference(variable_rename,[status(thm)],[f_3298_1]) ).

fof(f_3298_3,plain,
    ! [U_12913,U_12914,U_12915] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12913,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12913,U_12914),U_12915)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12913),U_12915)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12913),U_12914)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12913),U_12914),U_12915))
      | ~ class_Orderings_Olinorder(U_12913) ),
    inference(definitional_conversion,[status(esa)],[f_3298_2]) ).

cnf(f_3298_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12913,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12913,U_12914),U_12915)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12913),U_12915)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12913),U_12914)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12913),U_12914),U_12915))
    | ~ class_Orderings_Olinorder(U_12913) ),
    inference(clausify,[status(thm)],[f_3298_3]) ).

fof(f_3299_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_3299_2,plain,
    ! [U_12918,U_12917,U_12916] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12916,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12916,U_12917),U_12918)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12916),U_12918)) = c_Orderings_Obot__class_Obot(tc_fun(U_12916,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12916) ),
    inference(variable_rename,[status(thm)],[f_3299_1]) ).

fof(f_3299_3,plain,
    ! [U_12916,U_12917,U_12918] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12916,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12916,U_12917),U_12918)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12916),U_12918)) = c_Orderings_Obot__class_Obot(tc_fun(U_12916,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12916) ),
    inference(definitional_conversion,[status(esa)],[f_3299_2]) ).

cnf(f_3299_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12916,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12916,U_12917),U_12918)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12916),U_12918)) = c_Orderings_Obot__class_Obot(tc_fun(U_12916,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12916) ),
    inference(clausify,[status(thm)],[f_3299_3]) ).

fof(f_3300_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_3300_2,plain,
    ! [U_12922,U_12921,U_12920,U_12919] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12919,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12919,U_12920,U_12921)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12919),U_12922)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12919,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12919),U_12920),U_12922),U_12921)
      | ~ class_Orderings_Olinorder(U_12919) ),
    inference(variable_rename,[status(thm)],[f_3300_1]) ).

fof(f_3300_3,plain,
    ! [U_12919,U_12920,U_12921,U_12922] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12919,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12919,U_12920,U_12921)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12919),U_12922)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12919,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12919),U_12920),U_12922),U_12921)
      | ~ class_Orderings_Olinorder(U_12919) ),
    inference(definitional_conversion,[status(esa)],[f_3300_2]) ).

cnf(f_3300_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12919,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12919,U_12920,U_12921)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12919),U_12922)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12919,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12919),U_12920),U_12922),U_12921)
    | ~ class_Orderings_Olinorder(U_12919) ),
    inference(clausify,[status(thm)],[f_3300_3]) ).

fof(f_3301_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_3301_2,plain,
    ! [U_12926,U_12925,U_12924,U_12923] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12923,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12923),U_12924)),c_SetInterval_Oord__class_OatLeastAtMost(U_12923,U_12925,U_12926)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12923,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12923),U_12924),U_12925),U_12926)
      | ~ class_Orderings_Olinorder(U_12923) ),
    inference(variable_rename,[status(thm)],[f_3301_1]) ).

fof(f_3301_3,plain,
    ! [U_12923,U_12924,U_12925,U_12926] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12923,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12923),U_12924)),c_SetInterval_Oord__class_OatLeastAtMost(U_12923,U_12925,U_12926)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12923,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12923),U_12924),U_12925),U_12926)
      | ~ class_Orderings_Olinorder(U_12923) ),
    inference(definitional_conversion,[status(esa)],[f_3301_2]) ).

cnf(f_3301_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12923,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12923),U_12924)),c_SetInterval_Oord__class_OatLeastAtMost(U_12923,U_12925,U_12926)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12923,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12923),U_12924),U_12925),U_12926)
    | ~ class_Orderings_Olinorder(U_12923) ),
    inference(clausify,[status(thm)],[f_3301_3]) ).

fof(f_3302_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_3302_2,plain,
    ! [U_12929,U_12928,U_12927] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12927,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12927,U_12928,U_12929)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12927),U_12929)) = c_Orderings_Obot__class_Obot(tc_fun(U_12927,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12927) ),
    inference(variable_rename,[status(thm)],[f_3302_1]) ).

fof(f_3302_3,plain,
    ! [U_12927,U_12928,U_12929] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12927,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12927,U_12928,U_12929)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12927),U_12929)) = c_Orderings_Obot__class_Obot(tc_fun(U_12927,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12927) ),
    inference(definitional_conversion,[status(esa)],[f_3302_2]) ).

cnf(f_3302_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12927,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12927,U_12928,U_12929)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12927),U_12929)) = c_Orderings_Obot__class_Obot(tc_fun(U_12927,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12927) ),
    inference(clausify,[status(thm)],[f_3302_3]) ).

fof(f_3303_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_3303_2,plain,
    ! [U_12931,U_12930] :
      ( hAPP(c_Set_Oimage(U_12930,U_12930,c_Groups_Ouminus__class_Ouminus(U_12930)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12930),U_12931)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12930),hAPP(c_Groups_Ouminus__class_Ouminus(U_12930),U_12931))
      | ~ class_Groups_Oordered__ab__group__add(U_12930) ),
    inference(variable_rename,[status(thm)],[f_3303_1]) ).

fof(f_3303_3,plain,
    ! [U_12930,U_12931] :
      ( hAPP(c_Set_Oimage(U_12930,U_12930,c_Groups_Ouminus__class_Ouminus(U_12930)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12930),U_12931)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12930),hAPP(c_Groups_Ouminus__class_Ouminus(U_12930),U_12931))
      | ~ class_Groups_Oordered__ab__group__add(U_12930) ),
    inference(definitional_conversion,[status(esa)],[f_3303_2]) ).

cnf(f_3303_4,plain,
    ( hAPP(c_Set_Oimage(U_12930,U_12930,c_Groups_Ouminus__class_Ouminus(U_12930)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12930),U_12931)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12930),hAPP(c_Groups_Ouminus__class_Ouminus(U_12930),U_12931))
    | ~ class_Groups_Oordered__ab__group__add(U_12930) ),
    inference(clausify,[status(thm)],[f_3303_3]) ).

fof(f_3304_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_3304_2,plain,
    ! [U_12933,U_12932] :
      ( hAPP(c_Set_Oimage(U_12932,U_12932,c_Groups_Ouminus__class_Ouminus(U_12932)),hAPP(c_SetInterval_Oord__class_OatMost(U_12932),U_12933)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12932),hAPP(c_Groups_Ouminus__class_Ouminus(U_12932),U_12933))
      | ~ class_Groups_Oordered__ab__group__add(U_12932) ),
    inference(variable_rename,[status(thm)],[f_3304_1]) ).

fof(f_3304_3,plain,
    ! [U_12932,U_12933] :
      ( hAPP(c_Set_Oimage(U_12932,U_12932,c_Groups_Ouminus__class_Ouminus(U_12932)),hAPP(c_SetInterval_Oord__class_OatMost(U_12932),U_12933)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12932),hAPP(c_Groups_Ouminus__class_Ouminus(U_12932),U_12933))
      | ~ class_Groups_Oordered__ab__group__add(U_12932) ),
    inference(definitional_conversion,[status(esa)],[f_3304_2]) ).

cnf(f_3304_4,plain,
    ( hAPP(c_Set_Oimage(U_12932,U_12932,c_Groups_Ouminus__class_Ouminus(U_12932)),hAPP(c_SetInterval_Oord__class_OatMost(U_12932),U_12933)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12932),hAPP(c_Groups_Ouminus__class_Ouminus(U_12932),U_12933))
    | ~ class_Groups_Oordered__ab__group__add(U_12932) ),
    inference(clausify,[status(thm)],[f_3304_3]) ).

fof(f_3305_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_3305_2,plain,
    ! [U_12934] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12934)) = 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_12934)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12934),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3305_1]) ).

fof(f_3305_3,plain,
    ! [U_12934] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12934)) = 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_12934)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12934),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3305_2]) ).

cnf(f_3305_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12934)) = 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_12934)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12934),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3305_3]) ).

fof(f_3306_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_3306_2,plain,
    ! [U_12937,U_12936,U_12935] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12935,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12935,U_12936,U_12937)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12935),U_12937)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12935),U_12936)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12935),U_12936),U_12937))
      | ~ class_Orderings_Olinorder(U_12935) ),
    inference(variable_rename,[status(thm)],[f_3306_1]) ).

fof(f_3306_3,plain,
    ! [U_12935,U_12936,U_12937] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12935,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12935,U_12936,U_12937)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12935),U_12937)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12935),U_12936)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12935),U_12936),U_12937))
      | ~ class_Orderings_Olinorder(U_12935) ),
    inference(definitional_conversion,[status(esa)],[f_3306_2]) ).

cnf(f_3306_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12935,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12935,U_12936,U_12937)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12935),U_12937)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12935),U_12936)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12935),U_12936),U_12937))
    | ~ class_Orderings_Olinorder(U_12935) ),
    inference(clausify,[status(thm)],[f_3306_3]) ).

fof(f_3307_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_3307_2,plain,
    ! [U_12940,U_12939,U_12938] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12938,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12938,U_12939,U_12940)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12938),U_12940)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12938),U_12939)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12938),U_12939),U_12940))
      | ~ class_Orderings_Olinorder(U_12938) ),
    inference(variable_rename,[status(thm)],[f_3307_1]) ).

fof(f_3307_3,plain,
    ! [U_12938,U_12939,U_12940] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12938,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12938,U_12939,U_12940)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12938),U_12940)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12938),U_12939)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12938),U_12939),U_12940))
      | ~ class_Orderings_Olinorder(U_12938) ),
    inference(definitional_conversion,[status(esa)],[f_3307_2]) ).

cnf(f_3307_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12938,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12938,U_12939,U_12940)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12938),U_12940)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12938),U_12939)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12938),U_12939),U_12940))
    | ~ class_Orderings_Olinorder(U_12938) ),
    inference(clausify,[status(thm)],[f_3307_3]) ).

fof(f_3308_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_3308_2,plain,
    ! [U_12942,U_12941] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12941,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12941),U_12942),c_Orderings_Obot__class_Obot(tc_fun(U_12941,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12941),U_12942)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12941),U_12942)
      | ~ class_Orderings_Olinorder(U_12941) ),
    inference(variable_rename,[status(thm)],[f_3308_1]) ).

fof(f_3308_3,plain,
    ! [U_12941,U_12942] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12941,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12941),U_12942),c_Orderings_Obot__class_Obot(tc_fun(U_12941,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12941),U_12942)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12941),U_12942)
      | ~ class_Orderings_Olinorder(U_12941) ),
    inference(definitional_conversion,[status(esa)],[f_3308_2]) ).

cnf(f_3308_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12941,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12941),U_12942),c_Orderings_Obot__class_Obot(tc_fun(U_12941,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12941),U_12942)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12941),U_12942)
    | ~ class_Orderings_Olinorder(U_12941) ),
    inference(clausify,[status(thm)],[f_3308_3]) ).

fof(f_3309_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_3309_2,plain,
    ! [U_12943] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12943)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_12943),
    inference(variable_rename,[status(thm)],[f_3309_1]) ).

fof(f_3309_3,plain,
    ! [U_12943] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12943)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_12943),
    inference(definitional_conversion,[status(esa)],[f_3309_2]) ).

cnf(f_3309_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12943)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_12943),
    inference(clausify,[status(thm)],[f_3309_3]) ).

fof(f_3310_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_3310_2,plain,
    ! [U_12946,U_12945,U_12944] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12944),U_12945) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12944),U_12946)
          | U_12945 != U_12946 )
        & ( U_12945 = U_12946
          | hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12944),U_12945) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12944),U_12946) ) )
      | ~ class_Orderings_Olinorder(U_12944) ),
    inference(variable_rename,[status(thm)],[f_3310_1]) ).

fof(f_3310_3,plain,
    ( ! [U_12944,U_12945,U_12946] :
        ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12944),U_12945) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12944),U_12946)
        | U_12945 != U_12946
        | ~ sP944(U_12944,U_12945,U_12946) )
    & ! [U_12944,U_12945,U_12946] :
        ( U_12945 = U_12946
        | hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12944),U_12945) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12944),U_12946)
        | ~ sP944(U_12944,U_12945,U_12946) )
    & ! [U_12944,U_12945,U_12946] :
        ( sP944(U_12944,U_12945,U_12946)
        | ~ class_Orderings_Olinorder(U_12944) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP944])],[f_3310_2]) ).

cnf(f_3310_4,plain,
    ( sP944(U_12944,U_12945,U_12946)
    | ~ class_Orderings_Olinorder(U_12944) ),
    inference(clausify,[status(thm)],[f_3310_3]) ).

cnf(f_3310_5,plain,
    ( U_12945 = U_12946
    | hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12944),U_12945) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12944),U_12946)
    | ~ sP944(U_12944,U_12945,U_12946) ),
    inference(clausify,[status(thm)],[f_3310_3]) ).

cnf(f_3310_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12944),U_12945) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12944),U_12946)
    | U_12945 != U_12946
    | ~ sP944(U_12944,U_12945,U_12946) ),
    inference(clausify,[status(thm)],[f_3310_3]) ).

fof(f_3311_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_3311_2,plain,
    ! [U_12949,U_12948,U_12947] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_12947),U_12948),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12947),U_12949)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12947),U_12949),U_12948)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12947),U_12949),U_12948))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12947),U_12948),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12947),U_12949))) ) )
      | ~ class_Orderings_Oord(U_12947) ),
    inference(variable_rename,[status(thm)],[f_3311_1]) ).

fof(f_3311_3,plain,
    ( ! [U_12948,U_12947,U_12949] :
        ( hBOOL(hAPP(hAPP(c_member(U_12947),U_12948),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12947),U_12949)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12947),U_12949),U_12948))
        | ~ sP945(U_12948,U_12947,U_12949) )
    & ! [U_12948,U_12947,U_12949] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12947),U_12949),U_12948))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12947),U_12948),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12947),U_12949)))
        | ~ sP945(U_12948,U_12947,U_12949) )
    & ! [U_12948,U_12947,U_12949] :
        ( sP945(U_12948,U_12947,U_12949)
        | ~ class_Orderings_Oord(U_12947) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP945])],[f_3311_2]) ).

cnf(f_3311_4,plain,
    ( sP945(U_12948,U_12947,U_12949)
    | ~ class_Orderings_Oord(U_12947) ),
    inference(clausify,[status(thm)],[f_3311_3]) ).

cnf(f_3311_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12947),U_12949),U_12948))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12947),U_12948),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12947),U_12949)))
    | ~ sP945(U_12948,U_12947,U_12949) ),
    inference(clausify,[status(thm)],[f_3311_3]) ).

cnf(f_3311_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12947),U_12948),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12947),U_12949)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12947),U_12949),U_12948))
    | ~ sP945(U_12948,U_12947,U_12949) ),
    inference(clausify,[status(thm)],[f_3311_3]) ).

fof(f_3312_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_3312_2,plain,
    ! [U_12952,U_12951,U_12950] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12950,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12950),U_12951)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12950),U_12952)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12950),U_12952),U_12951)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12950),U_12952),U_12951))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12950,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12950),U_12951)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12950),U_12952))) ) )
      | ~ class_Orderings_Olinorder(U_12950) ),
    inference(variable_rename,[status(thm)],[f_3312_1]) ).

fof(f_3312_3,plain,
    ( ! [U_12951,U_12952,U_12950] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12950,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12950),U_12951)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12950),U_12952)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12950),U_12952),U_12951))
        | ~ sP946(U_12951,U_12952,U_12950) )
    & ! [U_12951,U_12952,U_12950] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12950),U_12952),U_12951))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12950,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12950),U_12951)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12950),U_12952)))
        | ~ sP946(U_12951,U_12952,U_12950) )
    & ! [U_12951,U_12952,U_12950] :
        ( sP946(U_12951,U_12952,U_12950)
        | ~ class_Orderings_Olinorder(U_12950) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP946])],[f_3312_2]) ).

cnf(f_3312_4,plain,
    ( sP946(U_12951,U_12952,U_12950)
    | ~ class_Orderings_Olinorder(U_12950) ),
    inference(clausify,[status(thm)],[f_3312_3]) ).

cnf(f_3312_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12950),U_12952),U_12951))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12950,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12950),U_12951)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12950),U_12952)))
    | ~ sP946(U_12951,U_12952,U_12950) ),
    inference(clausify,[status(thm)],[f_3312_3]) ).

cnf(f_3312_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12950,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12950),U_12951)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12950),U_12952)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12950),U_12952),U_12951))
    | ~ sP946(U_12951,U_12952,U_12950) ),
    inference(clausify,[status(thm)],[f_3312_3]) ).

fof(f_3313_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_3313_2,plain,
    ! [U_12954,U_12953] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12953,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12953),U_12954)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12953),U_12954)
      | ~ class_Orderings_Olinorder(U_12953) ),
    inference(variable_rename,[status(thm)],[f_3313_1]) ).

fof(f_3313_3,plain,
    ! [U_12954,U_12953] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12953,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12953),U_12954)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12953),U_12954)
      | ~ class_Orderings_Olinorder(U_12953) ),
    inference(definitional_conversion,[status(esa)],[f_3313_2]) ).

cnf(f_3313_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12953,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12953),U_12954)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12953),U_12954)
    | ~ class_Orderings_Olinorder(U_12953) ),
    inference(clausify,[status(thm)],[f_3313_3]) ).

fof(f_3314_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_3314_2,plain,
    ! [U_12956,U_12955] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12955,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12955),U_12956)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12955),U_12956)
      | ~ class_Orderings_Olinorder(U_12955) ),
    inference(variable_rename,[status(thm)],[f_3314_1]) ).

fof(f_3314_3,plain,
    ! [U_12955,U_12956] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12955,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12955),U_12956)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12955),U_12956)
      | ~ class_Orderings_Olinorder(U_12955) ),
    inference(definitional_conversion,[status(esa)],[f_3314_2]) ).

cnf(f_3314_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12955,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12955),U_12956)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12955),U_12956)
    | ~ class_Orderings_Olinorder(U_12955) ),
    inference(clausify,[status(thm)],[f_3314_3]) ).

fof(f_3315_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_3315_2,plain,
    ! [U_12959,U_12958,U_12957] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12957,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12957,U_12958,U_12959)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12957),U_12959)) = c_Orderings_Obot__class_Obot(tc_fun(U_12957,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12957) ),
    inference(variable_rename,[status(thm)],[f_3315_1]) ).

fof(f_3315_3,plain,
    ! [U_12957,U_12958,U_12959] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12957,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12957,U_12958,U_12959)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12957),U_12959)) = c_Orderings_Obot__class_Obot(tc_fun(U_12957,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12957) ),
    inference(definitional_conversion,[status(esa)],[f_3315_2]) ).

cnf(f_3315_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12957,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12957,U_12958,U_12959)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12957),U_12959)) = c_Orderings_Obot__class_Obot(tc_fun(U_12957,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12957) ),
    inference(clausify,[status(thm)],[f_3315_3]) ).

fof(f_3316_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_3316_2,plain,
    ! [U_12962,U_12961,U_12960] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12960,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12960,U_12961,U_12962)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12960),U_12962)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12960),U_12961)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12960),U_12961),U_12962))
      | ~ class_Orderings_Olinorder(U_12960) ),
    inference(variable_rename,[status(thm)],[f_3316_1]) ).

fof(f_3316_3,plain,
    ! [U_12960,U_12961,U_12962] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12960,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12960,U_12961,U_12962)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12960),U_12962)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12960),U_12961)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12960),U_12961),U_12962))
      | ~ class_Orderings_Olinorder(U_12960) ),
    inference(definitional_conversion,[status(esa)],[f_3316_2]) ).

cnf(f_3316_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12960,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12960,U_12961,U_12962)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12960),U_12962)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12960),U_12961)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12960),U_12961),U_12962))
    | ~ class_Orderings_Olinorder(U_12960) ),
    inference(clausify,[status(thm)],[f_3316_3]) ).

fof(f_3317_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_3317_2,plain,
    ! [U_12964,U_12963] :
      ( hAPP(c_Set_Oimage(U_12963,U_12963,c_Groups_Ouminus__class_Ouminus(U_12963)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12963),U_12964)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12963),hAPP(c_Groups_Ouminus__class_Ouminus(U_12963),U_12964))
      | ~ class_Groups_Oordered__ab__group__add(U_12963) ),
    inference(variable_rename,[status(thm)],[f_3317_1]) ).

fof(f_3317_3,plain,
    ! [U_12963,U_12964] :
      ( hAPP(c_Set_Oimage(U_12963,U_12963,c_Groups_Ouminus__class_Ouminus(U_12963)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12963),U_12964)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12963),hAPP(c_Groups_Ouminus__class_Ouminus(U_12963),U_12964))
      | ~ class_Groups_Oordered__ab__group__add(U_12963) ),
    inference(definitional_conversion,[status(esa)],[f_3317_2]) ).

cnf(f_3317_4,plain,
    ( hAPP(c_Set_Oimage(U_12963,U_12963,c_Groups_Ouminus__class_Ouminus(U_12963)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12963),U_12964)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12963),hAPP(c_Groups_Ouminus__class_Ouminus(U_12963),U_12964))
    | ~ class_Groups_Oordered__ab__group__add(U_12963) ),
    inference(clausify,[status(thm)],[f_3317_3]) ).

fof(f_3318_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_3318_2,plain,
    ! [U_12966,U_12965] :
      ( hAPP(c_Set_Oimage(U_12965,U_12965,c_Groups_Ouminus__class_Ouminus(U_12965)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12965),U_12966)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12965),hAPP(c_Groups_Ouminus__class_Ouminus(U_12965),U_12966))
      | ~ class_Groups_Oordered__ab__group__add(U_12965) ),
    inference(variable_rename,[status(thm)],[f_3318_1]) ).

fof(f_3318_3,plain,
    ! [U_12965,U_12966] :
      ( hAPP(c_Set_Oimage(U_12965,U_12965,c_Groups_Ouminus__class_Ouminus(U_12965)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12965),U_12966)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12965),hAPP(c_Groups_Ouminus__class_Ouminus(U_12965),U_12966))
      | ~ class_Groups_Oordered__ab__group__add(U_12965) ),
    inference(definitional_conversion,[status(esa)],[f_3318_2]) ).

cnf(f_3318_4,plain,
    ( hAPP(c_Set_Oimage(U_12965,U_12965,c_Groups_Ouminus__class_Ouminus(U_12965)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12965),U_12966)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12965),hAPP(c_Groups_Ouminus__class_Ouminus(U_12965),U_12966))
    | ~ class_Groups_Oordered__ab__group__add(U_12965) ),
    inference(clausify,[status(thm)],[f_3318_3]) ).

fof(f_3319_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_3319_2,plain,
    ! [U_12969,U_12968,U_12967] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12967,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12967,U_12968,U_12969)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12967),U_12969)) = c_Orderings_Obot__class_Obot(tc_fun(U_12967,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12967) ),
    inference(variable_rename,[status(thm)],[f_3319_1]) ).

fof(f_3319_3,plain,
    ! [U_12967,U_12968,U_12969] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12967,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12967,U_12968,U_12969)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12967),U_12969)) = c_Orderings_Obot__class_Obot(tc_fun(U_12967,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12967) ),
    inference(definitional_conversion,[status(esa)],[f_3319_2]) ).

cnf(f_3319_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12967,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12967,U_12968,U_12969)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12967),U_12969)) = c_Orderings_Obot__class_Obot(tc_fun(U_12967,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12967) ),
    inference(clausify,[status(thm)],[f_3319_3]) ).

fof(f_3320_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_3320_2,plain,
    ! [U_12970] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12970)) = 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_12970)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12970)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3320_1]) ).

fof(f_3320_3,plain,
    ! [U_12970] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12970)) = 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_12970)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12970)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3320_2]) ).

cnf(f_3320_4,plain,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12970)) = 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_12970)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12970)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3320_3]) ).

fof(f_3321_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(tc_sum(T_b,T_c),T_d),V_f_2),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(tc_sum(T_b,T_c),T_d,T_b,V_f_2),c_Sum__Type_OInl(T_b,T_c))),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(c_Fun_Ocomp(tc_sum(T_b,T_c),T_d,T_c,V_f_2),c_Sum__Type_OInr(T_c,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))
      | ~ class_Groups_Ocomm__monoid__add(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Plus]) ).

fof(f_3321_2,plain,
    ! [U_12976,U_12975,U_12974,U_12973,U_12972,U_12971] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(U_12972,U_12974),U_12971),U_12976),c_Sum__Type_OPlus(U_12972,U_12974,U_12973,U_12975)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12971),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12972,U_12971),hAPP(c_Fun_Ocomp(tc_sum(U_12972,U_12974),U_12971,U_12972,U_12976),c_Sum__Type_OInl(U_12972,U_12974))),U_12973)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12974,U_12971),hAPP(c_Fun_Ocomp(tc_sum(U_12972,U_12974),U_12971,U_12974,U_12976),c_Sum__Type_OInr(U_12974,U_12972))),U_12975))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12974),U_12975))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12972),U_12973))
      | ~ class_Groups_Ocomm__monoid__add(U_12971) ),
    inference(variable_rename,[status(thm)],[f_3321_1]) ).

fof(f_3321_3,plain,
    ! [U_12971,U_12972,U_12973,U_12974,U_12975,U_12976] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(U_12972,U_12974),U_12971),U_12976),c_Sum__Type_OPlus(U_12972,U_12974,U_12973,U_12975)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12971),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12972,U_12971),hAPP(c_Fun_Ocomp(tc_sum(U_12972,U_12974),U_12971,U_12972,U_12976),c_Sum__Type_OInl(U_12972,U_12974))),U_12973)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12974,U_12971),hAPP(c_Fun_Ocomp(tc_sum(U_12972,U_12974),U_12971,U_12974,U_12976),c_Sum__Type_OInr(U_12974,U_12972))),U_12975))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12974),U_12975))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12972),U_12973))
      | ~ class_Groups_Ocomm__monoid__add(U_12971) ),
    inference(definitional_conversion,[status(esa)],[f_3321_2]) ).

cnf(f_3321_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(U_12972,U_12974),U_12971),U_12976),c_Sum__Type_OPlus(U_12972,U_12974,U_12973,U_12975)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12971),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12972,U_12971),hAPP(c_Fun_Ocomp(tc_sum(U_12972,U_12974),U_12971,U_12972,U_12976),c_Sum__Type_OInl(U_12972,U_12974))),U_12973)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12974,U_12971),hAPP(c_Fun_Ocomp(tc_sum(U_12972,U_12974),U_12971,U_12974,U_12976),c_Sum__Type_OInr(U_12974,U_12972))),U_12975))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12974),U_12975))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12972),U_12973))
    | ~ class_Groups_Ocomm__monoid__add(U_12971) ),
    inference(clausify,[status(thm)],[f_3321_3]) ).

fof(f_3322_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_3322_2,plain,
    ! [U_12982,U_12981,U_12980,U_12979,U_12978] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12978),U_12981),U_12979) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12978),U_12982),U_12980)
      | ? [U_12977] :
          ( hAPP(U_12981,U_12977) != hAPP(U_12982,U_12977)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12977)) )
      | ~ c_Nat__Transfer_Onat__set(U_12980)
      | U_12979 != U_12980
      | ~ class_Groups_Ocomm__monoid__mult(U_12978)
      | ~ class_Groups_Ocomm__monoid__add(U_12978) ),
    inference(variable_rename,[status(thm)],[f_3322_1]) ).

fof(f_3322_3,plain,
    ! [U_12982,U_12981,U_12980,U_12979,U_12978] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12978),U_12981),U_12979) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12978),U_12982),U_12980)
      | ( hAPP(U_12981,sK281(U_12982,U_12981,U_12980,U_12979,U_12978)) != hAPP(U_12982,sK281(U_12982,U_12981,U_12980,U_12979,U_12978))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK281(U_12982,U_12981,U_12980,U_12979,U_12978))) )
      | ~ c_Nat__Transfer_Onat__set(U_12980)
      | U_12979 != U_12980
      | ~ class_Groups_Ocomm__monoid__mult(U_12978)
      | ~ class_Groups_Ocomm__monoid__add(U_12978) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK281]),skolemize(U_12977,sK281(U_12982,U_12981,U_12980,U_12979,U_12978))],[f_3322_2]) ).

fof(f_3322_4,plain,
    ( ! [U_12978,U_12980,U_12979,U_12981,U_12982] :
        ( hAPP(U_12981,sK281(U_12982,U_12981,U_12980,U_12979,U_12978)) != hAPP(U_12982,sK281(U_12982,U_12981,U_12980,U_12979,U_12978))
        | ~ sP947(U_12978,U_12980,U_12979,U_12981,U_12982) )
    & ! [U_12978,U_12980,U_12979,U_12981,U_12982] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK281(U_12982,U_12981,U_12980,U_12979,U_12978)))
        | ~ sP947(U_12978,U_12980,U_12979,U_12981,U_12982) )
    & ! [U_12978,U_12980,U_12979,U_12981,U_12982] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12978),U_12981),U_12979) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12978),U_12982),U_12980)
        | sP947(U_12978,U_12980,U_12979,U_12981,U_12982)
        | ~ c_Nat__Transfer_Onat__set(U_12980)
        | U_12979 != U_12980
        | ~ class_Groups_Ocomm__monoid__mult(U_12978)
        | ~ class_Groups_Ocomm__monoid__add(U_12978) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP947])],[f_3322_3]) ).

cnf(f_3322_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12978),U_12981),U_12979) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12978),U_12982),U_12980)
    | sP947(U_12978,U_12980,U_12979,U_12981,U_12982)
    | ~ c_Nat__Transfer_Onat__set(U_12980)
    | U_12979 != U_12980
    | ~ class_Groups_Ocomm__monoid__mult(U_12978)
    | ~ class_Groups_Ocomm__monoid__add(U_12978) ),
    inference(clausify,[status(thm)],[f_3322_4]) ).

cnf(f_3322_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK281(U_12982,U_12981,U_12980,U_12979,U_12978)))
    | ~ sP947(U_12978,U_12980,U_12979,U_12981,U_12982) ),
    inference(clausify,[status(thm)],[f_3322_4]) ).

cnf(f_3322_7,plain,
    ( hAPP(U_12981,sK281(U_12982,U_12981,U_12980,U_12979,U_12978)) != hAPP(U_12982,sK281(U_12982,U_12981,U_12980,U_12979,U_12978))
    | ~ sP947(U_12978,U_12980,U_12979,U_12981,U_12982) ),
    inference(clausify,[status(thm)],[f_3322_4]) ).

fof(f_3323_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_3323_2,plain,
    ! [U_12988,U_12987,U_12986,U_12985] :
      ( ( c_Map_Odom(U_12985,U_12986,U_12987) = hAPP(hAPP(c_Set_Oinsert(U_12985),U_12988),c_Orderings_Obot__class_Obot(tc_fun(U_12985,tc_HOL_Obool)))
        | ! [U_12984] : U_12987 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12985,tc_Option_Ooption(U_12986)),hAPP(c_COMBK(tc_Option_Ooption(U_12986),U_12985),c_Option_Ooption_ONone(U_12986))),U_12988),hAPP(c_Option_Ooption_OSome(U_12986),U_12984)) )
      & ( ? [U_12983] : U_12987 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12985,tc_Option_Ooption(U_12986)),hAPP(c_COMBK(tc_Option_Ooption(U_12986),U_12985),c_Option_Ooption_ONone(U_12986))),U_12988),hAPP(c_Option_Ooption_OSome(U_12986),U_12983))
        | c_Map_Odom(U_12985,U_12986,U_12987) != hAPP(hAPP(c_Set_Oinsert(U_12985),U_12988),c_Orderings_Obot__class_Obot(tc_fun(U_12985,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_3323_1]) ).

fof(f_3323_3,plain,
    ( ! [U_12996,U_12994,U_12992,U_12990] :
        ( c_Map_Odom(U_12990,U_12992,U_12994) = hAPP(hAPP(c_Set_Oinsert(U_12990),U_12996),c_Orderings_Obot__class_Obot(tc_fun(U_12990,tc_HOL_Obool)))
        | ! [U_12984] : U_12994 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12990,tc_Option_Ooption(U_12992)),hAPP(c_COMBK(tc_Option_Ooption(U_12992),U_12990),c_Option_Ooption_ONone(U_12992))),U_12996),hAPP(c_Option_Ooption_OSome(U_12992),U_12984)) )
    & ! [U_12995,U_12993,U_12991,U_12989] :
        ( ? [U_12983] : U_12993 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12989,tc_Option_Ooption(U_12991)),hAPP(c_COMBK(tc_Option_Ooption(U_12991),U_12989),c_Option_Ooption_ONone(U_12991))),U_12995),hAPP(c_Option_Ooption_OSome(U_12991),U_12983))
        | c_Map_Odom(U_12989,U_12991,U_12993) != hAPP(hAPP(c_Set_Oinsert(U_12989),U_12995),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_3323_2]) ).

fof(f_3323_4,plain,
    ( ! [U_12996,U_12994,U_12992,U_12990] :
        ( c_Map_Odom(U_12990,U_12992,U_12994) = hAPP(hAPP(c_Set_Oinsert(U_12990),U_12996),c_Orderings_Obot__class_Obot(tc_fun(U_12990,tc_HOL_Obool)))
        | ! [U_12984] : U_12994 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12990,tc_Option_Ooption(U_12992)),hAPP(c_COMBK(tc_Option_Ooption(U_12992),U_12990),c_Option_Ooption_ONone(U_12992))),U_12996),hAPP(c_Option_Ooption_OSome(U_12992),U_12984)) )
    & ! [U_12995,U_12993,U_12991,U_12989] :
        ( U_12993 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12989,tc_Option_Ooption(U_12991)),hAPP(c_COMBK(tc_Option_Ooption(U_12991),U_12989),c_Option_Ooption_ONone(U_12991))),U_12995),hAPP(c_Option_Ooption_OSome(U_12991),sK282(U_12995,U_12993,U_12991,U_12989)))
        | c_Map_Odom(U_12989,U_12991,U_12993) != hAPP(hAPP(c_Set_Oinsert(U_12989),U_12995),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK282]),skolemize(U_12983,sK282(U_12995,U_12993,U_12991,U_12989))],[f_3323_3]) ).

fof(f_3323_5,plain,
    ( ! [U_12984,U_12994,U_12990,U_12992,U_12996] :
        ( c_Map_Odom(U_12990,U_12992,U_12994) = hAPP(hAPP(c_Set_Oinsert(U_12990),U_12996),c_Orderings_Obot__class_Obot(tc_fun(U_12990,tc_HOL_Obool)))
        | U_12994 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12990,tc_Option_Ooption(U_12992)),hAPP(c_COMBK(tc_Option_Ooption(U_12992),U_12990),c_Option_Ooption_ONone(U_12992))),U_12996),hAPP(c_Option_Ooption_OSome(U_12992),U_12984)) )
    & ! [U_12991,U_12989,U_12995,U_12993] :
        ( U_12993 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12989,tc_Option_Ooption(U_12991)),hAPP(c_COMBK(tc_Option_Ooption(U_12991),U_12989),c_Option_Ooption_ONone(U_12991))),U_12995),hAPP(c_Option_Ooption_OSome(U_12991),sK282(U_12995,U_12993,U_12991,U_12989)))
        | c_Map_Odom(U_12989,U_12991,U_12993) != hAPP(hAPP(c_Set_Oinsert(U_12989),U_12995),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3323_4]) ).

cnf(f_3323_6,plain,
    ( U_12993 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12989,tc_Option_Ooption(U_12991)),hAPP(c_COMBK(tc_Option_Ooption(U_12991),U_12989),c_Option_Ooption_ONone(U_12991))),U_12995),hAPP(c_Option_Ooption_OSome(U_12991),sK282(U_12995,U_12993,U_12991,U_12989)))
    | c_Map_Odom(U_12989,U_12991,U_12993) != hAPP(hAPP(c_Set_Oinsert(U_12989),U_12995),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3323_5]) ).

cnf(f_3323_7,plain,
    ( c_Map_Odom(U_12990,U_12992,U_12994) = hAPP(hAPP(c_Set_Oinsert(U_12990),U_12996),c_Orderings_Obot__class_Obot(tc_fun(U_12990,tc_HOL_Obool)))
    | U_12994 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12990,tc_Option_Ooption(U_12992)),hAPP(c_COMBK(tc_Option_Ooption(U_12992),U_12990),c_Option_Ooption_ONone(U_12992))),U_12996),hAPP(c_Option_Ooption_OSome(U_12992),U_12984)) ),
    inference(clausify,[status(thm)],[f_3323_5]) ).

fof(f_3324_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_3324_2,plain,
    ! [U_13002,U_13001,U_13000,U_12999,U_12998,U_12997] :
      ( c_Fun_Oinj__on(U_12999,U_12998,U_13000,hAPP(c_Set_Oimage(U_12997,U_12999,U_13001),U_13002))
      | ~ c_Fun_Oinj__on(U_12997,U_12998,hAPP(c_Fun_Ocomp(U_12999,U_12998,U_12997,U_13000),U_13001),U_13002) ),
    inference(variable_rename,[status(thm)],[f_3324_1]) ).

fof(f_3324_3,plain,
    ! [U_12998,U_12997,U_12999,U_13000,U_13001,U_13002] :
      ( c_Fun_Oinj__on(U_12999,U_12998,U_13000,hAPP(c_Set_Oimage(U_12997,U_12999,U_13001),U_13002))
      | ~ c_Fun_Oinj__on(U_12997,U_12998,hAPP(c_Fun_Ocomp(U_12999,U_12998,U_12997,U_13000),U_13001),U_13002) ),
    inference(definitional_conversion,[status(esa)],[f_3324_2]) ).

cnf(f_3324_4,plain,
    ( c_Fun_Oinj__on(U_12999,U_12998,U_13000,hAPP(c_Set_Oimage(U_12997,U_12999,U_13001),U_13002))
    | ~ c_Fun_Oinj__on(U_12997,U_12998,hAPP(c_Fun_Ocomp(U_12999,U_12998,U_12997,U_13000),U_13001),U_13002) ),
    inference(clausify,[status(thm)],[f_3324_3]) ).

fof(f_3325_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_3325_2,plain,
    ! [U_13008,U_13007,U_13006,U_13005,U_13004,U_13003] :
      ( c_Fun_Oinj__on(U_13003,U_13007,hAPP(c_Fun_Ocomp(U_13004,U_13007,U_13003,U_13008),U_13005),U_13006)
      | ~ c_Fun_Oinj__on(U_13004,U_13007,U_13008,hAPP(c_Set_Oimage(U_13003,U_13004,U_13005),U_13006))
      | ~ c_Fun_Oinj__on(U_13003,U_13004,U_13005,U_13006) ),
    inference(variable_rename,[status(thm)],[f_3325_1]) ).

fof(f_3325_3,plain,
    ! [U_13003,U_13004,U_13005,U_13006,U_13007,U_13008] :
      ( c_Fun_Oinj__on(U_13003,U_13007,hAPP(c_Fun_Ocomp(U_13004,U_13007,U_13003,U_13008),U_13005),U_13006)
      | ~ c_Fun_Oinj__on(U_13004,U_13007,U_13008,hAPP(c_Set_Oimage(U_13003,U_13004,U_13005),U_13006))
      | ~ c_Fun_Oinj__on(U_13003,U_13004,U_13005,U_13006) ),
    inference(definitional_conversion,[status(esa)],[f_3325_2]) ).

cnf(f_3325_4,plain,
    ( c_Fun_Oinj__on(U_13003,U_13007,hAPP(c_Fun_Ocomp(U_13004,U_13007,U_13003,U_13008),U_13005),U_13006)
    | ~ c_Fun_Oinj__on(U_13004,U_13007,U_13008,hAPP(c_Set_Oimage(U_13003,U_13004,U_13005),U_13006))
    | ~ c_Fun_Oinj__on(U_13003,U_13004,U_13005,U_13006) ),
    inference(clausify,[status(thm)],[f_3325_3]) ).

fof(f_3326_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_3326_2,plain,
    ! [U_13014,U_13013,U_13012,U_13011,U_13010,U_13009] :
      ( ( ( c_Fun_Oinj__on(U_13010,U_13013,U_13014,hAPP(c_Set_Oimage(U_13009,U_13010,U_13011),U_13012))
          | ~ c_Fun_Oinj__on(U_13009,U_13013,hAPP(c_Fun_Ocomp(U_13010,U_13013,U_13009,U_13014),U_13011),U_13012) )
        & ( c_Fun_Oinj__on(U_13009,U_13013,hAPP(c_Fun_Ocomp(U_13010,U_13013,U_13009,U_13014),U_13011),U_13012)
          | ~ c_Fun_Oinj__on(U_13010,U_13013,U_13014,hAPP(c_Set_Oimage(U_13009,U_13010,U_13011),U_13012)) ) )
      | ~ c_Fun_Oinj__on(U_13009,U_13010,U_13011,U_13012) ),
    inference(variable_rename,[status(thm)],[f_3326_1]) ).

fof(f_3326_3,plain,
    ( ! [U_13009,U_13010,U_13011,U_13012,U_13013,U_13014] :
        ( c_Fun_Oinj__on(U_13010,U_13013,U_13014,hAPP(c_Set_Oimage(U_13009,U_13010,U_13011),U_13012))
        | ~ c_Fun_Oinj__on(U_13009,U_13013,hAPP(c_Fun_Ocomp(U_13010,U_13013,U_13009,U_13014),U_13011),U_13012)
        | ~ sP948(U_13009,U_13010,U_13011,U_13012,U_13013,U_13014) )
    & ! [U_13009,U_13010,U_13011,U_13012,U_13013,U_13014] :
        ( c_Fun_Oinj__on(U_13009,U_13013,hAPP(c_Fun_Ocomp(U_13010,U_13013,U_13009,U_13014),U_13011),U_13012)
        | ~ c_Fun_Oinj__on(U_13010,U_13013,U_13014,hAPP(c_Set_Oimage(U_13009,U_13010,U_13011),U_13012))
        | ~ sP948(U_13009,U_13010,U_13011,U_13012,U_13013,U_13014) )
    & ! [U_13009,U_13010,U_13011,U_13012,U_13013,U_13014] :
        ( sP948(U_13009,U_13010,U_13011,U_13012,U_13013,U_13014)
        | ~ c_Fun_Oinj__on(U_13009,U_13010,U_13011,U_13012) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP948])],[f_3326_2]) ).

cnf(f_3326_4,plain,
    ( sP948(U_13009,U_13010,U_13011,U_13012,U_13013,U_13014)
    | ~ c_Fun_Oinj__on(U_13009,U_13010,U_13011,U_13012) ),
    inference(clausify,[status(thm)],[f_3326_3]) ).

cnf(f_3326_5,plain,
    ( c_Fun_Oinj__on(U_13009,U_13013,hAPP(c_Fun_Ocomp(U_13010,U_13013,U_13009,U_13014),U_13011),U_13012)
    | ~ c_Fun_Oinj__on(U_13010,U_13013,U_13014,hAPP(c_Set_Oimage(U_13009,U_13010,U_13011),U_13012))
    | ~ sP948(U_13009,U_13010,U_13011,U_13012,U_13013,U_13014) ),
    inference(clausify,[status(thm)],[f_3326_3]) ).

cnf(f_3326_6,plain,
    ( c_Fun_Oinj__on(U_13010,U_13013,U_13014,hAPP(c_Set_Oimage(U_13009,U_13010,U_13011),U_13012))
    | ~ c_Fun_Oinj__on(U_13009,U_13013,hAPP(c_Fun_Ocomp(U_13010,U_13013,U_13009,U_13014),U_13011),U_13012)
    | ~ sP948(U_13009,U_13010,U_13011,U_13012,U_13013,U_13014) ),
    inference(clausify,[status(thm)],[f_3326_3]) ).

fof(f_3327_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_3327_2,plain,
    ! [U_13023,U_13022,U_13021,U_13020,U_13019,U_13018,U_13017,U_13016] :
      ( ! [U_13015] : hAPP(U_13019,hAPP(U_13020,U_13015)) = hAPP(U_13022,hAPP(U_13023,U_13015))
      | hAPP(c_Fun_Ocomp(U_13016,U_13017,U_13018,U_13019),U_13020) != hAPP(c_Fun_Ocomp(U_13021,U_13017,U_13018,U_13022),U_13023) ),
    inference(variable_rename,[status(thm)],[f_3327_1]) ).

fof(f_3327_3,plain,
    ! [U_13023,U_13022,U_13021,U_13020,U_13019] :
      ( ! [U_13018,U_13017,U_13016] : hAPP(c_Fun_Ocomp(U_13016,U_13017,U_13018,U_13019),U_13020) != hAPP(c_Fun_Ocomp(U_13021,U_13017,U_13018,U_13022),U_13023)
      | ! [U_13015] : hAPP(U_13019,hAPP(U_13020,U_13015)) = hAPP(U_13022,hAPP(U_13023,U_13015)) ),
    inference(miniscope,[status(thm)],[f_3327_2]) ).

fof(f_3327_4,plain,
    ! [U_13016,U_13017,U_13015,U_13018,U_13019,U_13020,U_13021,U_13022,U_13023] :
      ( hAPP(c_Fun_Ocomp(U_13016,U_13017,U_13018,U_13019),U_13020) != hAPP(c_Fun_Ocomp(U_13021,U_13017,U_13018,U_13022),U_13023)
      | hAPP(U_13019,hAPP(U_13020,U_13015)) = hAPP(U_13022,hAPP(U_13023,U_13015)) ),
    inference(definitional_conversion,[status(esa)],[f_3327_3]) ).

cnf(f_3327_5,plain,
    ( hAPP(c_Fun_Ocomp(U_13016,U_13017,U_13018,U_13019),U_13020) != hAPP(c_Fun_Ocomp(U_13021,U_13017,U_13018,U_13022),U_13023)
    | hAPP(U_13019,hAPP(U_13020,U_13015)) = hAPP(U_13022,hAPP(U_13023,U_13015)) ),
    inference(clausify,[status(thm)],[f_3327_4]) ).

fof(f_3328_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_3328_2,plain,
    ! [U_13032,U_13031,U_13030,U_13029,U_13028,U_13027,U_13026,U_13025,U_13024] :
      ( hAPP(U_13027,hAPP(U_13028,U_13032)) = hAPP(U_13030,hAPP(U_13031,U_13032))
      | hAPP(c_Fun_Ocomp(U_13024,U_13025,U_13026,U_13027),U_13028) != hAPP(c_Fun_Ocomp(U_13029,U_13025,U_13026,U_13030),U_13031) ),
    inference(variable_rename,[status(thm)],[f_3328_1]) ).

fof(f_3328_3,plain,
    ! [U_13032,U_13031,U_13030,U_13029,U_13028,U_13027] :
      ( ! [U_13026,U_13025,U_13024] : hAPP(c_Fun_Ocomp(U_13024,U_13025,U_13026,U_13027),U_13028) != hAPP(c_Fun_Ocomp(U_13029,U_13025,U_13026,U_13030),U_13031)
      | hAPP(U_13027,hAPP(U_13028,U_13032)) = hAPP(U_13030,hAPP(U_13031,U_13032)) ),
    inference(miniscope,[status(thm)],[f_3328_2]) ).

fof(f_3328_4,plain,
    ! [U_13025,U_13024,U_13026,U_13027,U_13028,U_13029,U_13030,U_13031,U_13032] :
      ( hAPP(c_Fun_Ocomp(U_13024,U_13025,U_13026,U_13027),U_13028) != hAPP(c_Fun_Ocomp(U_13029,U_13025,U_13026,U_13030),U_13031)
      | hAPP(U_13027,hAPP(U_13028,U_13032)) = hAPP(U_13030,hAPP(U_13031,U_13032)) ),
    inference(definitional_conversion,[status(esa)],[f_3328_3]) ).

cnf(f_3328_5,plain,
    ( hAPP(c_Fun_Ocomp(U_13024,U_13025,U_13026,U_13027),U_13028) != hAPP(c_Fun_Ocomp(U_13029,U_13025,U_13026,U_13030),U_13031)
    | hAPP(U_13027,hAPP(U_13028,U_13032)) = hAPP(U_13030,hAPP(U_13031,U_13032)) ),
    inference(clausify,[status(thm)],[f_3328_4]) ).

fof(f_3329_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_3329_2,plain,
    ! [U_13038,U_13037,U_13036,U_13035,U_13034,U_13033] : hAPP(hAPP(c_Fun_Ocomp(U_13033,U_13034,U_13035,U_13036),U_13037),U_13038) = hAPP(U_13036,hAPP(U_13037,U_13038)),
    inference(variable_rename,[status(thm)],[f_3329_1]) ).

fof(f_3329_3,plain,
    ! [U_13034,U_13033,U_13035,U_13036,U_13037,U_13038] : hAPP(hAPP(c_Fun_Ocomp(U_13033,U_13034,U_13035,U_13036),U_13037),U_13038) = hAPP(U_13036,hAPP(U_13037,U_13038)),
    inference(definitional_conversion,[status(esa)],[f_3329_2]) ).

cnf(f_3329_4,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_13033,U_13034,U_13035,U_13036),U_13037),U_13038) = hAPP(U_13036,hAPP(U_13037,U_13038)),
    inference(clausify,[status(thm)],[f_3329_3]) ).

fof(f_3330_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_3330_2,plain,
    ! [U_13045,U_13044,U_13043,U_13042,U_13041,U_13040,U_13039] : hAPP(c_Fun_Ocomp(U_13039,U_13040,U_13041,U_13042),hAPP(c_Fun_Ocomp(U_13043,U_13039,U_13041,U_13044),U_13045)) = hAPP(c_Fun_Ocomp(U_13043,U_13040,U_13041,hAPP(c_Fun_Ocomp(U_13039,U_13040,U_13043,U_13042),U_13044)),U_13045),
    inference(variable_rename,[status(thm)],[f_3330_1]) ).

fof(f_3330_3,plain,
    ! [U_13039,U_13040,U_13041,U_13042,U_13043,U_13044,U_13045] : hAPP(c_Fun_Ocomp(U_13039,U_13040,U_13041,U_13042),hAPP(c_Fun_Ocomp(U_13043,U_13039,U_13041,U_13044),U_13045)) = hAPP(c_Fun_Ocomp(U_13043,U_13040,U_13041,hAPP(c_Fun_Ocomp(U_13039,U_13040,U_13043,U_13042),U_13044)),U_13045),
    inference(definitional_conversion,[status(esa)],[f_3330_2]) ).

cnf(f_3330_4,plain,
    hAPP(c_Fun_Ocomp(U_13039,U_13040,U_13041,U_13042),hAPP(c_Fun_Ocomp(U_13043,U_13039,U_13041,U_13044),U_13045)) = hAPP(c_Fun_Ocomp(U_13043,U_13040,U_13041,hAPP(c_Fun_Ocomp(U_13039,U_13040,U_13043,U_13042),U_13044)),U_13045),
    inference(clausify,[status(thm)],[f_3330_3]) ).

fof(f_3331_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_3331_2,plain,
    ! [U_13051,U_13050,U_13049,U_13048,U_13047,U_13046] : hAPP(hAPP(c_Fun_Ocomp(U_13046,U_13047,U_13048,U_13049),U_13050),U_13051) = hAPP(U_13049,hAPP(U_13050,U_13051)),
    inference(variable_rename,[status(thm)],[f_3331_1]) ).

fof(f_3331_3,plain,
    ! [U_13046,U_13047,U_13048,U_13049,U_13050,U_13051] : hAPP(hAPP(c_Fun_Ocomp(U_13046,U_13047,U_13048,U_13049),U_13050),U_13051) = hAPP(U_13049,hAPP(U_13050,U_13051)),
    inference(definitional_conversion,[status(esa)],[f_3331_2]) ).

cnf(f_3331_4,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_13046,U_13047,U_13048,U_13049),U_13050),U_13051) = hAPP(U_13049,hAPP(U_13050,U_13051)),
    inference(clausify,[status(thm)],[f_3331_3]) ).

fof(f_3332_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_3332_2,plain,
    ! [U_13062,U_13061,U_13060,U_13059,U_13058,U_13057,U_13056,U_13055,U_13054,U_13053,U_13052] :
      ( hAPP(hAPP(c_Fun_Ocomp(U_13058,U_13059,U_13060,U_13052),U_13053),U_13054) = hAPP(hAPP(c_Fun_Ocomp(U_13061,U_13059,U_13062,U_13055),U_13056),U_13057)
      | hAPP(U_13052,hAPP(U_13053,U_13054)) != hAPP(U_13055,hAPP(U_13056,U_13057)) ),
    inference(variable_rename,[status(thm)],[f_3332_1]) ).

fof(f_3332_3,plain,
    ! [U_13052,U_13053,U_13054,U_13055,U_13056,U_13057,U_13058,U_13059,U_13060,U_13061,U_13062] :
      ( hAPP(hAPP(c_Fun_Ocomp(U_13058,U_13059,U_13060,U_13052),U_13053),U_13054) = hAPP(hAPP(c_Fun_Ocomp(U_13061,U_13059,U_13062,U_13055),U_13056),U_13057)
      | hAPP(U_13052,hAPP(U_13053,U_13054)) != hAPP(U_13055,hAPP(U_13056,U_13057)) ),
    inference(definitional_conversion,[status(esa)],[f_3332_2]) ).

cnf(f_3332_4,plain,
    ( hAPP(hAPP(c_Fun_Ocomp(U_13058,U_13059,U_13060,U_13052),U_13053),U_13054) = hAPP(hAPP(c_Fun_Ocomp(U_13061,U_13059,U_13062,U_13055),U_13056),U_13057)
    | hAPP(U_13052,hAPP(U_13053,U_13054)) != hAPP(U_13055,hAPP(U_13056,U_13057)) ),
    inference(clausify,[status(thm)],[f_3332_3]) ).

fof(f_3333_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_3333_2,plain,
    ! [U_13069,U_13068,U_13067,U_13066,U_13065,U_13064,U_13063] : hAPP(c_Product__Type_Oapsnd(U_13063,U_13064,U_13065,U_13066),hAPP(c_Product__Type_Oapsnd(U_13067,U_13063,U_13065,U_13068),U_13069)) = hAPP(c_Product__Type_Oapsnd(U_13067,U_13064,U_13065,hAPP(c_Fun_Ocomp(U_13063,U_13064,U_13067,U_13066),U_13068)),U_13069),
    inference(variable_rename,[status(thm)],[f_3333_1]) ).

fof(f_3333_3,plain,
    ! [U_13063,U_13064,U_13065,U_13066,U_13067,U_13068,U_13069] : hAPP(c_Product__Type_Oapsnd(U_13063,U_13064,U_13065,U_13066),hAPP(c_Product__Type_Oapsnd(U_13067,U_13063,U_13065,U_13068),U_13069)) = hAPP(c_Product__Type_Oapsnd(U_13067,U_13064,U_13065,hAPP(c_Fun_Ocomp(U_13063,U_13064,U_13067,U_13066),U_13068)),U_13069),
    inference(definitional_conversion,[status(esa)],[f_3333_2]) ).

cnf(f_3333_4,plain,
    hAPP(c_Product__Type_Oapsnd(U_13063,U_13064,U_13065,U_13066),hAPP(c_Product__Type_Oapsnd(U_13067,U_13063,U_13065,U_13068),U_13069)) = hAPP(c_Product__Type_Oapsnd(U_13067,U_13064,U_13065,hAPP(c_Fun_Ocomp(U_13063,U_13064,U_13067,U_13066),U_13068)),U_13069),
    inference(clausify,[status(thm)],[f_3333_3]) ).

fof(f_3334_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_3334_2,plain,
    ! [U_13076,U_13075,U_13074,U_13073,U_13072,U_13071,U_13070] : hAPP(c_Product__Type_Oapfst(U_13070,U_13071,U_13072,U_13073),hAPP(c_Product__Type_Oapfst(U_13074,U_13070,U_13072,U_13075),U_13076)) = hAPP(c_Product__Type_Oapfst(U_13074,U_13071,U_13072,hAPP(c_Fun_Ocomp(U_13070,U_13071,U_13074,U_13073),U_13075)),U_13076),
    inference(variable_rename,[status(thm)],[f_3334_1]) ).

fof(f_3334_3,plain,
    ! [U_13073,U_13071,U_13070,U_13072,U_13074,U_13075,U_13076] : hAPP(c_Product__Type_Oapfst(U_13070,U_13071,U_13072,U_13073),hAPP(c_Product__Type_Oapfst(U_13074,U_13070,U_13072,U_13075),U_13076)) = hAPP(c_Product__Type_Oapfst(U_13074,U_13071,U_13072,hAPP(c_Fun_Ocomp(U_13070,U_13071,U_13074,U_13073),U_13075)),U_13076),
    inference(definitional_conversion,[status(esa)],[f_3334_2]) ).

cnf(f_3334_4,plain,
    hAPP(c_Product__Type_Oapfst(U_13070,U_13071,U_13072,U_13073),hAPP(c_Product__Type_Oapfst(U_13074,U_13070,U_13072,U_13075),U_13076)) = hAPP(c_Product__Type_Oapfst(U_13074,U_13071,U_13072,hAPP(c_Fun_Ocomp(U_13070,U_13071,U_13074,U_13073),U_13075)),U_13076),
    inference(clausify,[status(thm)],[f_3334_3]) ).

fof(f_3335_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_3335_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_3335_1]) ).

cnf(f_3335_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_3335_2]) ).

fof(f_3336_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_3336_2,plain,
    ! [U_13082,U_13081,U_13080,U_13079,U_13078,U_13077] :
      ( c_Fun_Oinj__on(U_13077,U_13079,U_13081,U_13082)
      | ~ c_Fun_Oinj__on(U_13077,U_13078,hAPP(c_Fun_Ocomp(U_13079,U_13078,U_13077,U_13080),U_13081),U_13082) ),
    inference(variable_rename,[status(thm)],[f_3336_1]) ).

fof(f_3336_3,plain,
    ! [U_13078,U_13077,U_13079,U_13080,U_13081,U_13082] :
      ( c_Fun_Oinj__on(U_13077,U_13079,U_13081,U_13082)
      | ~ c_Fun_Oinj__on(U_13077,U_13078,hAPP(c_Fun_Ocomp(U_13079,U_13078,U_13077,U_13080),U_13081),U_13082) ),
    inference(definitional_conversion,[status(esa)],[f_3336_2]) ).

cnf(f_3336_4,plain,
    ( c_Fun_Oinj__on(U_13077,U_13079,U_13081,U_13082)
    | ~ c_Fun_Oinj__on(U_13077,U_13078,hAPP(c_Fun_Ocomp(U_13079,U_13078,U_13077,U_13080),U_13081),U_13082) ),
    inference(clausify,[status(thm)],[f_3336_3]) ).

fof(f_3337_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_3337_2,plain,
    ! [U_13089,U_13088,U_13087,U_13086,U_13085,U_13084,U_13083] : hAPP(c_Fun_Ocomp(U_13083,U_13084,U_13085,U_13086),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13085,U_13083),U_13087),U_13088),U_13089)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13085,U_13084),hAPP(c_Fun_Ocomp(U_13083,U_13084,U_13085,U_13086),U_13087)),U_13088),hAPP(U_13086,U_13089)),
    inference(variable_rename,[status(thm)],[f_3337_1]) ).

fof(f_3337_3,plain,
    ! [U_13083,U_13084,U_13085,U_13086,U_13087,U_13088,U_13089] : hAPP(c_Fun_Ocomp(U_13083,U_13084,U_13085,U_13086),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13085,U_13083),U_13087),U_13088),U_13089)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13085,U_13084),hAPP(c_Fun_Ocomp(U_13083,U_13084,U_13085,U_13086),U_13087)),U_13088),hAPP(U_13086,U_13089)),
    inference(definitional_conversion,[status(esa)],[f_3337_2]) ).

cnf(f_3337_4,plain,
    hAPP(c_Fun_Ocomp(U_13083,U_13084,U_13085,U_13086),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13085,U_13083),U_13087),U_13088),U_13089)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13085,U_13084),hAPP(c_Fun_Ocomp(U_13083,U_13084,U_13085,U_13086),U_13087)),U_13088),hAPP(U_13086,U_13089)),
    inference(clausify,[status(thm)],[f_3337_3]) ).

fof(f_3338_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_3338_2,plain,
    ! [U_13095,U_13094,U_13093,U_13092,U_13091,U_13090] : hAPP(c_Set_Oimage(U_13090,U_13091,hAPP(c_Fun_Ocomp(U_13092,U_13091,U_13090,U_13093),U_13094)),U_13095) = hAPP(c_Set_Oimage(U_13092,U_13091,U_13093),hAPP(c_Set_Oimage(U_13090,U_13092,U_13094),U_13095)),
    inference(variable_rename,[status(thm)],[f_3338_1]) ).

fof(f_3338_3,plain,
    ! [U_13090,U_13091,U_13092,U_13093,U_13094,U_13095] : hAPP(c_Set_Oimage(U_13090,U_13091,hAPP(c_Fun_Ocomp(U_13092,U_13091,U_13090,U_13093),U_13094)),U_13095) = hAPP(c_Set_Oimage(U_13092,U_13091,U_13093),hAPP(c_Set_Oimage(U_13090,U_13092,U_13094),U_13095)),
    inference(definitional_conversion,[status(esa)],[f_3338_2]) ).

cnf(f_3338_4,plain,
    hAPP(c_Set_Oimage(U_13090,U_13091,hAPP(c_Fun_Ocomp(U_13092,U_13091,U_13090,U_13093),U_13094)),U_13095) = hAPP(c_Set_Oimage(U_13092,U_13091,U_13093),hAPP(c_Set_Oimage(U_13090,U_13092,U_13094),U_13095)),
    inference(clausify,[status(thm)],[f_3338_3]) ).

fof(f_3339_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_3339_2,plain,
    ! [U_13099,U_13098,U_13097,U_13096] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13096),U_13097),c_Map_Odom(U_13096,U_13098,U_13099)))
        | hAPP(U_13099,U_13097) = c_Option_Ooption_ONone(U_13098) )
      & ( hAPP(U_13099,U_13097) != c_Option_Ooption_ONone(U_13098)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13096),U_13097),c_Map_Odom(U_13096,U_13098,U_13099))) ) ),
    inference(variable_rename,[status(thm)],[f_3339_1]) ).

fof(f_3339_3,plain,
    ( ! [U_13107,U_13105,U_13103] :
        ( ! [U_13101] : hBOOL(hAPP(hAPP(c_member(U_13101),U_13103),c_Map_Odom(U_13101,U_13105,U_13107)))
        | hAPP(U_13107,U_13103) = c_Option_Ooption_ONone(U_13105) )
    & ! [U_13106,U_13104,U_13102] :
        ( ! [U_13100] : ~ hBOOL(hAPP(hAPP(c_member(U_13100),U_13102),c_Map_Odom(U_13100,U_13104,U_13106)))
        | hAPP(U_13106,U_13102) != c_Option_Ooption_ONone(U_13104) ) ),
    inference(miniscope,[status(thm)],[f_3339_2]) ).

fof(f_3339_4,plain,
    ( ! [U_13101,U_13105,U_13107,U_13103] :
        ( hBOOL(hAPP(hAPP(c_member(U_13101),U_13103),c_Map_Odom(U_13101,U_13105,U_13107)))
        | hAPP(U_13107,U_13103) = c_Option_Ooption_ONone(U_13105) )
    & ! [U_13102,U_13100,U_13106,U_13104] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_13100),U_13102),c_Map_Odom(U_13100,U_13104,U_13106)))
        | hAPP(U_13106,U_13102) != c_Option_Ooption_ONone(U_13104) ) ),
    inference(definitional_conversion,[status(esa)],[f_3339_3]) ).

cnf(f_3339_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13100),U_13102),c_Map_Odom(U_13100,U_13104,U_13106)))
    | hAPP(U_13106,U_13102) != c_Option_Ooption_ONone(U_13104) ),
    inference(clausify,[status(thm)],[f_3339_4]) ).

cnf(f_3339_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13101),U_13103),c_Map_Odom(U_13101,U_13105,U_13107)))
    | hAPP(U_13107,U_13103) = c_Option_Ooption_ONone(U_13105) ),
    inference(clausify,[status(thm)],[f_3339_4]) ).

fof(f_3340_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_3340_2,plain,
    ! [U_13112,U_13111,U_13110,U_13109,U_13108] :
      ( hBOOL(hAPP(hAPP(c_member(U_13112),U_13109),c_Map_Odom(U_13112,U_13110,U_13108)))
      | hAPP(U_13108,U_13109) != hAPP(c_Option_Ooption_OSome(U_13110),U_13111) ),
    inference(variable_rename,[status(thm)],[f_3340_1]) ).

fof(f_3340_3,plain,
    ! [U_13108,U_13109,U_13110,U_13111,U_13112] :
      ( hBOOL(hAPP(hAPP(c_member(U_13112),U_13109),c_Map_Odom(U_13112,U_13110,U_13108)))
      | hAPP(U_13108,U_13109) != hAPP(c_Option_Ooption_OSome(U_13110),U_13111) ),
    inference(definitional_conversion,[status(esa)],[f_3340_2]) ).

cnf(f_3340_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13112),U_13109),c_Map_Odom(U_13112,U_13110,U_13108)))
    | hAPP(U_13108,U_13109) != hAPP(c_Option_Ooption_OSome(U_13110),U_13111) ),
    inference(clausify,[status(thm)],[f_3340_3]) ).

fof(f_3341_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_3341_2,plain,
    ! [U_13117,U_13116,U_13115,U_13114,U_13113] :
      ( hAPP(hAPP(c_Set_Oinsert(U_13117),U_13114),c_Map_Odom(U_13117,U_13115,U_13113)) = c_Map_Odom(U_13117,U_13115,U_13113)
      | hAPP(U_13113,U_13114) != hAPP(c_Option_Ooption_OSome(U_13115),U_13116) ),
    inference(variable_rename,[status(thm)],[f_3341_1]) ).

fof(f_3341_3,plain,
    ! [U_13114,U_13113,U_13115,U_13116,U_13117] :
      ( hAPP(hAPP(c_Set_Oinsert(U_13117),U_13114),c_Map_Odom(U_13117,U_13115,U_13113)) = c_Map_Odom(U_13117,U_13115,U_13113)
      | hAPP(U_13113,U_13114) != hAPP(c_Option_Ooption_OSome(U_13115),U_13116) ),
    inference(definitional_conversion,[status(esa)],[f_3341_2]) ).

cnf(f_3341_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_13117),U_13114),c_Map_Odom(U_13117,U_13115,U_13113)) = c_Map_Odom(U_13117,U_13115,U_13113)
    | hAPP(U_13113,U_13114) != hAPP(c_Option_Ooption_OSome(U_13115),U_13116) ),
    inference(clausify,[status(thm)],[f_3341_3]) ).

fof(f_3342_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_3342_2,plain,
    ! [U_13121,U_13120,U_13119,U_13118] : c_Map_Odom(U_13118,U_13119,c_Map_Orestrict__map(U_13118,U_13119,U_13120,U_13121)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13118,tc_HOL_Obool)),c_Map_Odom(U_13118,U_13119,U_13120)),U_13121),
    inference(variable_rename,[status(thm)],[f_3342_1]) ).

fof(f_3342_3,plain,
    ! [U_13118,U_13119,U_13120,U_13121] : c_Map_Odom(U_13118,U_13119,c_Map_Orestrict__map(U_13118,U_13119,U_13120,U_13121)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13118,tc_HOL_Obool)),c_Map_Odom(U_13118,U_13119,U_13120)),U_13121),
    inference(definitional_conversion,[status(esa)],[f_3342_2]) ).

cnf(f_3342_4,plain,
    c_Map_Odom(U_13118,U_13119,c_Map_Orestrict__map(U_13118,U_13119,U_13120,U_13121)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13118,tc_HOL_Obool)),c_Map_Odom(U_13118,U_13119,U_13120)),U_13121),
    inference(clausify,[status(thm)],[f_3342_3]) ).

fof(f_3343_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_3343_2,plain,
    ! [U_13124,U_13123,U_13122] :
      ( ( c_Map_Odom(U_13122,U_13123,U_13124) = c_Orderings_Obot__class_Obot(tc_fun(U_13122,tc_HOL_Obool))
        | U_13124 != hAPP(c_COMBK(tc_Option_Ooption(U_13123),U_13122),c_Option_Ooption_ONone(U_13123)) )
      & ( U_13124 = hAPP(c_COMBK(tc_Option_Ooption(U_13123),U_13122),c_Option_Ooption_ONone(U_13123))
        | c_Map_Odom(U_13122,U_13123,U_13124) != c_Orderings_Obot__class_Obot(tc_fun(U_13122,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3343_1]) ).

fof(f_3343_3,plain,
    ( ! [U_13130,U_13128,U_13126] :
        ( c_Map_Odom(U_13126,U_13128,U_13130) = c_Orderings_Obot__class_Obot(tc_fun(U_13126,tc_HOL_Obool))
        | U_13130 != hAPP(c_COMBK(tc_Option_Ooption(U_13128),U_13126),c_Option_Ooption_ONone(U_13128)) )
    & ! [U_13129,U_13127,U_13125] :
        ( U_13129 = hAPP(c_COMBK(tc_Option_Ooption(U_13127),U_13125),c_Option_Ooption_ONone(U_13127))
        | c_Map_Odom(U_13125,U_13127,U_13129) != c_Orderings_Obot__class_Obot(tc_fun(U_13125,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3343_2]) ).

fof(f_3343_4,plain,
    ( ! [U_13130,U_13126,U_13128] :
        ( c_Map_Odom(U_13126,U_13128,U_13130) = c_Orderings_Obot__class_Obot(tc_fun(U_13126,tc_HOL_Obool))
        | U_13130 != hAPP(c_COMBK(tc_Option_Ooption(U_13128),U_13126),c_Option_Ooption_ONone(U_13128)) )
    & ! [U_13127,U_13125,U_13129] :
        ( U_13129 = hAPP(c_COMBK(tc_Option_Ooption(U_13127),U_13125),c_Option_Ooption_ONone(U_13127))
        | c_Map_Odom(U_13125,U_13127,U_13129) != c_Orderings_Obot__class_Obot(tc_fun(U_13125,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3343_3]) ).

cnf(f_3343_5,plain,
    ( U_13129 = hAPP(c_COMBK(tc_Option_Ooption(U_13127),U_13125),c_Option_Ooption_ONone(U_13127))
    | c_Map_Odom(U_13125,U_13127,U_13129) != c_Orderings_Obot__class_Obot(tc_fun(U_13125,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3343_4]) ).

cnf(f_3343_6,plain,
    ( c_Map_Odom(U_13126,U_13128,U_13130) = c_Orderings_Obot__class_Obot(tc_fun(U_13126,tc_HOL_Obool))
    | U_13130 != hAPP(c_COMBK(tc_Option_Ooption(U_13128),U_13126),c_Option_Ooption_ONone(U_13128)) ),
    inference(clausify,[status(thm)],[f_3343_4]) ).

fof(f_3344_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_3344_2,plain,
    ! [U_13132,U_13131] : c_Map_Odom(U_13131,U_13132,hAPP(c_COMBK(tc_Option_Ooption(U_13132),U_13131),c_Option_Ooption_ONone(U_13132))) = c_Orderings_Obot__class_Obot(tc_fun(U_13131,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3344_1]) ).

fof(f_3344_3,plain,
    ! [U_13131,U_13132] : c_Map_Odom(U_13131,U_13132,hAPP(c_COMBK(tc_Option_Ooption(U_13132),U_13131),c_Option_Ooption_ONone(U_13132))) = c_Orderings_Obot__class_Obot(tc_fun(U_13131,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3344_2]) ).

cnf(f_3344_4,plain,
    c_Map_Odom(U_13131,U_13132,hAPP(c_COMBK(tc_Option_Ooption(U_13132),U_13131),c_Option_Ooption_ONone(U_13132))) = c_Orderings_Obot__class_Obot(tc_fun(U_13131,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3344_3]) ).

fof(f_3345_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_3345_2,plain,
    ! [U_13138,U_13137,U_13136,U_13135,U_13134,U_13133] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13135,U_13133),U_13138),hAPP(c_Set_Oimage(U_13134,U_13135,U_13136),U_13137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13134,U_13133),hAPP(c_Fun_Ocomp(U_13135,U_13133,U_13134,U_13138),U_13136)),U_13137)
      | ~ c_Fun_Oinj__on(U_13134,U_13135,U_13136,U_13137)
      | ~ class_Groups_Ocomm__monoid__add(U_13133) ),
    inference(variable_rename,[status(thm)],[f_3345_1]) ).

fof(f_3345_3,plain,
    ! [U_13133,U_13134,U_13135,U_13136,U_13137,U_13138] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13135,U_13133),U_13138),hAPP(c_Set_Oimage(U_13134,U_13135,U_13136),U_13137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13134,U_13133),hAPP(c_Fun_Ocomp(U_13135,U_13133,U_13134,U_13138),U_13136)),U_13137)
      | ~ c_Fun_Oinj__on(U_13134,U_13135,U_13136,U_13137)
      | ~ class_Groups_Ocomm__monoid__add(U_13133) ),
    inference(definitional_conversion,[status(esa)],[f_3345_2]) ).

cnf(f_3345_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13135,U_13133),U_13138),hAPP(c_Set_Oimage(U_13134,U_13135,U_13136),U_13137)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13134,U_13133),hAPP(c_Fun_Ocomp(U_13135,U_13133,U_13134,U_13138),U_13136)),U_13137)
    | ~ c_Fun_Oinj__on(U_13134,U_13135,U_13136,U_13137)
    | ~ class_Groups_Ocomm__monoid__add(U_13133) ),
    inference(clausify,[status(thm)],[f_3345_3]) ).

fof(f_3346_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_3346_2,plain,
    ! [U_13146,U_13145,U_13144,U_13143,U_13142,U_13141,U_13140,U_13139] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13141,U_13139),U_13146),U_13144) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13140,U_13139),U_13145),U_13143)
      | U_13145 != hAPP(c_Fun_Ocomp(U_13141,U_13139,U_13140,U_13146),U_13142)
      | U_13144 != hAPP(c_Set_Oimage(U_13140,U_13141,U_13142),U_13143)
      | ~ c_Fun_Oinj__on(U_13140,U_13141,U_13142,U_13143)
      | ~ class_Groups_Ocomm__monoid__mult(U_13139) ),
    inference(variable_rename,[status(thm)],[f_3346_1]) ).

fof(f_3346_3,plain,
    ! [U_13139,U_13140,U_13141,U_13142,U_13143,U_13144,U_13145,U_13146] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13141,U_13139),U_13146),U_13144) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13140,U_13139),U_13145),U_13143)
      | U_13145 != hAPP(c_Fun_Ocomp(U_13141,U_13139,U_13140,U_13146),U_13142)
      | U_13144 != hAPP(c_Set_Oimage(U_13140,U_13141,U_13142),U_13143)
      | ~ c_Fun_Oinj__on(U_13140,U_13141,U_13142,U_13143)
      | ~ class_Groups_Ocomm__monoid__mult(U_13139) ),
    inference(definitional_conversion,[status(esa)],[f_3346_2]) ).

cnf(f_3346_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13141,U_13139),U_13146),U_13144) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13140,U_13139),U_13145),U_13143)
    | U_13145 != hAPP(c_Fun_Ocomp(U_13141,U_13139,U_13140,U_13146),U_13142)
    | U_13144 != hAPP(c_Set_Oimage(U_13140,U_13141,U_13142),U_13143)
    | ~ c_Fun_Oinj__on(U_13140,U_13141,U_13142,U_13143)
    | ~ class_Groups_Ocomm__monoid__mult(U_13139) ),
    inference(clausify,[status(thm)],[f_3346_3]) ).

fof(f_3347_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_3347_2,plain,
    ! [U_13152,U_13151,U_13150,U_13149,U_13148,U_13147] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13149,U_13147),U_13152),hAPP(c_Set_Oimage(U_13148,U_13149,U_13150),U_13151)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13148,U_13147),hAPP(c_Fun_Ocomp(U_13149,U_13147,U_13148,U_13152),U_13150)),U_13151)
      | ~ c_Fun_Oinj__on(U_13148,U_13149,U_13150,U_13151)
      | ~ class_Groups_Ocomm__monoid__mult(U_13147) ),
    inference(variable_rename,[status(thm)],[f_3347_1]) ).

fof(f_3347_3,plain,
    ! [U_13148,U_13149,U_13150,U_13147,U_13151,U_13152] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13149,U_13147),U_13152),hAPP(c_Set_Oimage(U_13148,U_13149,U_13150),U_13151)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13148,U_13147),hAPP(c_Fun_Ocomp(U_13149,U_13147,U_13148,U_13152),U_13150)),U_13151)
      | ~ c_Fun_Oinj__on(U_13148,U_13149,U_13150,U_13151)
      | ~ class_Groups_Ocomm__monoid__mult(U_13147) ),
    inference(definitional_conversion,[status(esa)],[f_3347_2]) ).

cnf(f_3347_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13149,U_13147),U_13152),hAPP(c_Set_Oimage(U_13148,U_13149,U_13150),U_13151)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13148,U_13147),hAPP(c_Fun_Ocomp(U_13149,U_13147,U_13148,U_13152),U_13150)),U_13151)
    | ~ c_Fun_Oinj__on(U_13148,U_13149,U_13150,U_13151)
    | ~ class_Groups_Ocomm__monoid__mult(U_13147) ),
    inference(clausify,[status(thm)],[f_3347_3]) ).

fof(f_3348_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_3348_2,plain,
    ! [U_13157,U_13156,U_13155,U_13154,U_13153] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13156,tc_HOL_Obool)),c_Map_Odom(U_13156,U_13155,U_13153)),hAPP(hAPP(c_Set_Oinsert(U_13156),U_13154),U_13157)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13156,tc_HOL_Obool)),c_Map_Odom(U_13156,U_13155,U_13153)),U_13157)
      | hAPP(U_13153,U_13154) != c_Option_Ooption_ONone(U_13155) ),
    inference(variable_rename,[status(thm)],[f_3348_1]) ).

fof(f_3348_3,plain,
    ! [U_13153,U_13155,U_13154,U_13156,U_13157] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13156,tc_HOL_Obool)),c_Map_Odom(U_13156,U_13155,U_13153)),hAPP(hAPP(c_Set_Oinsert(U_13156),U_13154),U_13157)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13156,tc_HOL_Obool)),c_Map_Odom(U_13156,U_13155,U_13153)),U_13157)
      | hAPP(U_13153,U_13154) != c_Option_Ooption_ONone(U_13155) ),
    inference(definitional_conversion,[status(esa)],[f_3348_2]) ).

cnf(f_3348_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13156,tc_HOL_Obool)),c_Map_Odom(U_13156,U_13155,U_13153)),hAPP(hAPP(c_Set_Oinsert(U_13156),U_13154),U_13157)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13156,tc_HOL_Obool)),c_Map_Odom(U_13156,U_13155,U_13153)),U_13157)
    | hAPP(U_13153,U_13154) != c_Option_Ooption_ONone(U_13155) ),
    inference(clausify,[status(thm)],[f_3348_3]) ).

fof(f_3349_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_3349_2,plain,
    ! [U_13162,U_13161,U_13160,U_13159,U_13158] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13159,U_13158),U_13162),hAPP(c_Set_Oimage(U_13159,U_13159,U_13161),U_13160)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13159,U_13158),hAPP(c_Fun_Ocomp(U_13159,U_13158,U_13159,U_13162),U_13161)),U_13160)
      | ~ c_Fun_Oinj__on(U_13159,U_13159,U_13161,U_13160)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13159),U_13160))
      | ~ class_Groups_Ocomm__monoid__add(U_13158) ),
    inference(variable_rename,[status(thm)],[f_3349_1]) ).

fof(f_3349_3,plain,
    ! [U_13158,U_13159,U_13160,U_13161,U_13162] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13159,U_13158),U_13162),hAPP(c_Set_Oimage(U_13159,U_13159,U_13161),U_13160)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13159,U_13158),hAPP(c_Fun_Ocomp(U_13159,U_13158,U_13159,U_13162),U_13161)),U_13160)
      | ~ c_Fun_Oinj__on(U_13159,U_13159,U_13161,U_13160)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13159),U_13160))
      | ~ class_Groups_Ocomm__monoid__add(U_13158) ),
    inference(definitional_conversion,[status(esa)],[f_3349_2]) ).

cnf(f_3349_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13159,U_13158),U_13162),hAPP(c_Set_Oimage(U_13159,U_13159,U_13161),U_13160)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13159,U_13158),hAPP(c_Fun_Ocomp(U_13159,U_13158,U_13159,U_13162),U_13161)),U_13160)
    | ~ c_Fun_Oinj__on(U_13159,U_13159,U_13161,U_13160)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13159),U_13160))
    | ~ class_Groups_Ocomm__monoid__add(U_13158) ),
    inference(clausify,[status(thm)],[f_3349_3]) ).

fof(f_3350_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_3350_2,plain,
    ! [U_13167,U_13166,U_13165,U_13164,U_13163] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13164,U_13163),U_13167),hAPP(c_Set_Oimage(U_13164,U_13164,U_13166),U_13165)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13164,U_13163),hAPP(c_Fun_Ocomp(U_13164,U_13163,U_13164,U_13167),U_13166)),U_13165)
      | ~ c_Fun_Oinj__on(U_13164,U_13164,U_13166,U_13165)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13164),U_13165))
      | ~ class_Groups_Ocomm__monoid__mult(U_13163) ),
    inference(variable_rename,[status(thm)],[f_3350_1]) ).

fof(f_3350_3,plain,
    ! [U_13163,U_13164,U_13165,U_13166,U_13167] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13164,U_13163),U_13167),hAPP(c_Set_Oimage(U_13164,U_13164,U_13166),U_13165)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13164,U_13163),hAPP(c_Fun_Ocomp(U_13164,U_13163,U_13164,U_13167),U_13166)),U_13165)
      | ~ c_Fun_Oinj__on(U_13164,U_13164,U_13166,U_13165)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13164),U_13165))
      | ~ class_Groups_Ocomm__monoid__mult(U_13163) ),
    inference(definitional_conversion,[status(esa)],[f_3350_2]) ).

cnf(f_3350_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13164,U_13163),U_13167),hAPP(c_Set_Oimage(U_13164,U_13164,U_13166),U_13165)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13164,U_13163),hAPP(c_Fun_Ocomp(U_13164,U_13163,U_13164,U_13167),U_13166)),U_13165)
    | ~ c_Fun_Oinj__on(U_13164,U_13164,U_13166,U_13165)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13164),U_13165))
    | ~ class_Groups_Ocomm__monoid__mult(U_13163) ),
    inference(clausify,[status(thm)],[f_3350_3]) ).

fof(f_3351_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_3351_2,plain,
    ! [U_13174,U_13173,U_13172,U_13171,U_13170,U_13169,U_13168] :
      ( hAPP(c_Fun_Othe__inv__into(U_13171,U_13169,U_13173,hAPP(c_Fun_Ocomp(U_13168,U_13169,U_13171,U_13170),U_13172)),U_13174) = hAPP(hAPP(c_Fun_Ocomp(U_13168,U_13171,U_13169,c_Fun_Othe__inv__into(U_13171,U_13168,U_13173,U_13172)),c_Fun_Othe__inv__into(U_13168,U_13169,hAPP(c_Set_Oimage(U_13171,U_13168,U_13172),U_13173),U_13170)),U_13174)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13169),U_13174),hAPP(c_Set_Oimage(U_13168,U_13169,U_13170),hAPP(c_Set_Oimage(U_13171,U_13168,U_13172),U_13173))))
      | ~ c_Fun_Oinj__on(U_13171,U_13168,U_13172,U_13173)
      | ~ c_Fun_Oinj__on(U_13168,U_13169,U_13170,hAPP(c_Set_Oimage(U_13171,U_13168,U_13172),U_13173)) ),
    inference(variable_rename,[status(thm)],[f_3351_1]) ).

fof(f_3351_3,plain,
    ! [U_13168,U_13169,U_13170,U_13171,U_13172,U_13173,U_13174] :
      ( hAPP(c_Fun_Othe__inv__into(U_13171,U_13169,U_13173,hAPP(c_Fun_Ocomp(U_13168,U_13169,U_13171,U_13170),U_13172)),U_13174) = hAPP(hAPP(c_Fun_Ocomp(U_13168,U_13171,U_13169,c_Fun_Othe__inv__into(U_13171,U_13168,U_13173,U_13172)),c_Fun_Othe__inv__into(U_13168,U_13169,hAPP(c_Set_Oimage(U_13171,U_13168,U_13172),U_13173),U_13170)),U_13174)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13169),U_13174),hAPP(c_Set_Oimage(U_13168,U_13169,U_13170),hAPP(c_Set_Oimage(U_13171,U_13168,U_13172),U_13173))))
      | ~ c_Fun_Oinj__on(U_13171,U_13168,U_13172,U_13173)
      | ~ c_Fun_Oinj__on(U_13168,U_13169,U_13170,hAPP(c_Set_Oimage(U_13171,U_13168,U_13172),U_13173)) ),
    inference(definitional_conversion,[status(esa)],[f_3351_2]) ).

cnf(f_3351_4,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_13171,U_13169,U_13173,hAPP(c_Fun_Ocomp(U_13168,U_13169,U_13171,U_13170),U_13172)),U_13174) = hAPP(hAPP(c_Fun_Ocomp(U_13168,U_13171,U_13169,c_Fun_Othe__inv__into(U_13171,U_13168,U_13173,U_13172)),c_Fun_Othe__inv__into(U_13168,U_13169,hAPP(c_Set_Oimage(U_13171,U_13168,U_13172),U_13173),U_13170)),U_13174)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13169),U_13174),hAPP(c_Set_Oimage(U_13168,U_13169,U_13170),hAPP(c_Set_Oimage(U_13171,U_13168,U_13172),U_13173))))
    | ~ c_Fun_Oinj__on(U_13171,U_13168,U_13172,U_13173)
    | ~ c_Fun_Oinj__on(U_13168,U_13169,U_13170,hAPP(c_Set_Oimage(U_13171,U_13168,U_13172),U_13173)) ),
    inference(clausify,[status(thm)],[f_3351_3]) ).

fof(f_3352_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_3352_2,plain,
    ! [U_13181,U_13180,U_13179,U_13178,U_13177,U_13176,U_13175] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13175,U_13178,c_Groups_Otimes__class_Otimes(U_13175)),U_13180),U_13181),hAPP(c_Set_Oimage(U_13176,U_13178,U_13179),U_13177)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13175,U_13176,c_Groups_Otimes__class_Otimes(U_13175)),hAPP(c_Fun_Ocomp(U_13178,U_13175,U_13176,U_13180),U_13179)),U_13181),U_13177)
      | ~ c_Fun_Oinj__on(U_13176,U_13178,U_13179,U_13177)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13176),U_13177))
      | ~ class_Groups_Oab__semigroup__mult(U_13175) ),
    inference(variable_rename,[status(thm)],[f_3352_1]) ).

fof(f_3352_3,plain,
    ! [U_13175,U_13176,U_13177,U_13178,U_13179,U_13180,U_13181] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13175,U_13178,c_Groups_Otimes__class_Otimes(U_13175)),U_13180),U_13181),hAPP(c_Set_Oimage(U_13176,U_13178,U_13179),U_13177)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13175,U_13176,c_Groups_Otimes__class_Otimes(U_13175)),hAPP(c_Fun_Ocomp(U_13178,U_13175,U_13176,U_13180),U_13179)),U_13181),U_13177)
      | ~ c_Fun_Oinj__on(U_13176,U_13178,U_13179,U_13177)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13176),U_13177))
      | ~ class_Groups_Oab__semigroup__mult(U_13175) ),
    inference(definitional_conversion,[status(esa)],[f_3352_2]) ).

cnf(f_3352_4,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13175,U_13178,c_Groups_Otimes__class_Otimes(U_13175)),U_13180),U_13181),hAPP(c_Set_Oimage(U_13176,U_13178,U_13179),U_13177)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13175,U_13176,c_Groups_Otimes__class_Otimes(U_13175)),hAPP(c_Fun_Ocomp(U_13178,U_13175,U_13176,U_13180),U_13179)),U_13181),U_13177)
    | ~ c_Fun_Oinj__on(U_13176,U_13178,U_13179,U_13177)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13176),U_13177))
    | ~ class_Groups_Oab__semigroup__mult(U_13175) ),
    inference(clausify,[status(thm)],[f_3352_3]) ).

fof(f_3353_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_3353_2,plain,
    ! [U_13186,U_13185,U_13184,U_13183,U_13182] :
      ( ( c_Map_Odom(U_13184,U_13183,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13184,tc_Option_Ooption(U_13183)),U_13185),U_13186),U_13182)) = hAPP(hAPP(c_Set_Oinsert(U_13184),U_13186),c_Map_Odom(U_13184,U_13183,U_13185))
        | U_13182 = c_Option_Ooption_ONone(U_13183) )
      & ( c_Map_Odom(U_13184,U_13183,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13184,tc_Option_Ooption(U_13183)),U_13185),U_13186),U_13182)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13184,tc_HOL_Obool)),c_Map_Odom(U_13184,U_13183,U_13185)),hAPP(hAPP(c_Set_Oinsert(U_13184),U_13186),c_Orderings_Obot__class_Obot(tc_fun(U_13184,tc_HOL_Obool))))
        | U_13182 != c_Option_Ooption_ONone(U_13183) ) ),
    inference(variable_rename,[status(thm)],[f_3353_1]) ).

fof(f_3353_3,plain,
    ( ! [U_13196,U_13194,U_13192,U_13190,U_13188] :
        ( c_Map_Odom(U_13192,U_13190,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13192,tc_Option_Ooption(U_13190)),U_13194),U_13196),U_13188)) = hAPP(hAPP(c_Set_Oinsert(U_13192),U_13196),c_Map_Odom(U_13192,U_13190,U_13194))
        | U_13188 = c_Option_Ooption_ONone(U_13190) )
    & ! [U_13195,U_13193,U_13191,U_13189,U_13187] :
        ( c_Map_Odom(U_13191,U_13189,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13191,tc_Option_Ooption(U_13189)),U_13193),U_13195),U_13187)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13191,tc_HOL_Obool)),c_Map_Odom(U_13191,U_13189,U_13193)),hAPP(hAPP(c_Set_Oinsert(U_13191),U_13195),c_Orderings_Obot__class_Obot(tc_fun(U_13191,tc_HOL_Obool))))
        | U_13187 != c_Option_Ooption_ONone(U_13189) ) ),
    inference(miniscope,[status(thm)],[f_3353_2]) ).

fof(f_3353_4,plain,
    ( ! [U_13188,U_13190,U_13192,U_13194,U_13196] :
        ( c_Map_Odom(U_13192,U_13190,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13192,tc_Option_Ooption(U_13190)),U_13194),U_13196),U_13188)) = hAPP(hAPP(c_Set_Oinsert(U_13192),U_13196),c_Map_Odom(U_13192,U_13190,U_13194))
        | U_13188 = c_Option_Ooption_ONone(U_13190) )
    & ! [U_13191,U_13193,U_13187,U_13189,U_13195] :
        ( c_Map_Odom(U_13191,U_13189,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13191,tc_Option_Ooption(U_13189)),U_13193),U_13195),U_13187)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13191,tc_HOL_Obool)),c_Map_Odom(U_13191,U_13189,U_13193)),hAPP(hAPP(c_Set_Oinsert(U_13191),U_13195),c_Orderings_Obot__class_Obot(tc_fun(U_13191,tc_HOL_Obool))))
        | U_13187 != c_Option_Ooption_ONone(U_13189) ) ),
    inference(definitional_conversion,[status(esa)],[f_3353_3]) ).

cnf(f_3353_5,plain,
    ( c_Map_Odom(U_13191,U_13189,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13191,tc_Option_Ooption(U_13189)),U_13193),U_13195),U_13187)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13191,tc_HOL_Obool)),c_Map_Odom(U_13191,U_13189,U_13193)),hAPP(hAPP(c_Set_Oinsert(U_13191),U_13195),c_Orderings_Obot__class_Obot(tc_fun(U_13191,tc_HOL_Obool))))
    | U_13187 != c_Option_Ooption_ONone(U_13189) ),
    inference(clausify,[status(thm)],[f_3353_4]) ).

cnf(f_3353_6,plain,
    ( c_Map_Odom(U_13192,U_13190,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13192,tc_Option_Ooption(U_13190)),U_13194),U_13196),U_13188)) = hAPP(hAPP(c_Set_Oinsert(U_13192),U_13196),c_Map_Odom(U_13192,U_13190,U_13194))
    | U_13188 = c_Option_Ooption_ONone(U_13190) ),
    inference(clausify,[status(thm)],[f_3353_4]) ).

fof(f_3354_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_3354_2,plain,
    ! [U_13202,U_13201,U_13200,U_13199,U_13198,U_13197] :
      ( hAPP(U_13200,U_13201) = hAPP(c_Fun_Ocomp(U_13198,U_13198,U_13198,hAPP(U_13200,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13197,tc_HOL_Obool)),U_13201),hAPP(hAPP(c_Set_Oinsert(U_13197),U_13202),c_Orderings_Obot__class_Obot(tc_fun(U_13197,tc_HOL_Obool)))))),hAPP(U_13199,U_13202))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13197),U_13202),U_13201))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13197),U_13201))
      | ~ c_Finite__Set_Ofolding(U_13197,U_13198,U_13199,U_13200) ),
    inference(variable_rename,[status(thm)],[f_3354_1]) ).

fof(f_3354_3,plain,
    ! [U_13197,U_13198,U_13199,U_13200,U_13201,U_13202] :
      ( hAPP(U_13200,U_13201) = hAPP(c_Fun_Ocomp(U_13198,U_13198,U_13198,hAPP(U_13200,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13197,tc_HOL_Obool)),U_13201),hAPP(hAPP(c_Set_Oinsert(U_13197),U_13202),c_Orderings_Obot__class_Obot(tc_fun(U_13197,tc_HOL_Obool)))))),hAPP(U_13199,U_13202))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13197),U_13202),U_13201))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13197),U_13201))
      | ~ c_Finite__Set_Ofolding(U_13197,U_13198,U_13199,U_13200) ),
    inference(definitional_conversion,[status(esa)],[f_3354_2]) ).

cnf(f_3354_4,plain,
    ( hAPP(U_13200,U_13201) = hAPP(c_Fun_Ocomp(U_13198,U_13198,U_13198,hAPP(U_13200,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13197,tc_HOL_Obool)),U_13201),hAPP(hAPP(c_Set_Oinsert(U_13197),U_13202),c_Orderings_Obot__class_Obot(tc_fun(U_13197,tc_HOL_Obool)))))),hAPP(U_13199,U_13202))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13197),U_13202),U_13201))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13197),U_13201))
    | ~ c_Finite__Set_Ofolding(U_13197,U_13198,U_13199,U_13200) ),
    inference(clausify,[status(thm)],[f_3354_3]) ).

fof(f_3355_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_3355_2,plain,
    ! [U_13210,U_13209,U_13208,U_13207,U_13206,U_13205,U_13204,U_13203] :
      ( hAPP(hAPP(U_13207,U_13210),hAPP(c_Set_Oimage(U_13204,U_13204,U_13209),U_13208)) = hAPP(hAPP(U_13207,hAPP(c_Fun_Ocomp(U_13204,U_13203,U_13204,U_13210),U_13209)),U_13208)
      | ~ c_Fun_Oinj__on(U_13204,U_13204,U_13209,U_13208)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13204),U_13208))
      | ~ c_Finite__Set_Ofolding__image(U_13203,U_13204,U_13205,U_13206,U_13207) ),
    inference(variable_rename,[status(thm)],[f_3355_1]) ).

fof(f_3355_3,plain,
    ! [U_13208,U_13204,U_13206,U_13207,U_13205,U_13203,U_13209,U_13210] :
      ( hAPP(hAPP(U_13207,U_13210),hAPP(c_Set_Oimage(U_13204,U_13204,U_13209),U_13208)) = hAPP(hAPP(U_13207,hAPP(c_Fun_Ocomp(U_13204,U_13203,U_13204,U_13210),U_13209)),U_13208)
      | ~ c_Fun_Oinj__on(U_13204,U_13204,U_13209,U_13208)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13204),U_13208))
      | ~ c_Finite__Set_Ofolding__image(U_13203,U_13204,U_13205,U_13206,U_13207) ),
    inference(definitional_conversion,[status(esa)],[f_3355_2]) ).

cnf(f_3355_4,plain,
    ( hAPP(hAPP(U_13207,U_13210),hAPP(c_Set_Oimage(U_13204,U_13204,U_13209),U_13208)) = hAPP(hAPP(U_13207,hAPP(c_Fun_Ocomp(U_13204,U_13203,U_13204,U_13210),U_13209)),U_13208)
    | ~ c_Fun_Oinj__on(U_13204,U_13204,U_13209,U_13208)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13204),U_13208))
    | ~ c_Finite__Set_Ofolding__image(U_13203,U_13204,U_13205,U_13206,U_13207) ),
    inference(clausify,[status(thm)],[f_3355_3]) ).

fof(f_3356_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_3356_2,plain,
    ! [U_13216,U_13215,U_13214,U_13213,U_13212,U_13211] :
      ( hAPP(U_13214,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13211,tc_HOL_Obool)),U_13215),U_13216)) = hAPP(c_Fun_Ocomp(U_13212,U_13212,U_13212,hAPP(U_13214,U_13215)),hAPP(U_13214,U_13216))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13211,tc_HOL_Obool)),U_13215),U_13216) != c_Orderings_Obot__class_Obot(tc_fun(U_13211,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13211),U_13216))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13211),U_13215))
      | ~ c_Finite__Set_Ofolding(U_13211,U_13212,U_13213,U_13214) ),
    inference(variable_rename,[status(thm)],[f_3356_1]) ).

fof(f_3356_3,plain,
    ! [U_13211,U_13214,U_13213,U_13212,U_13215,U_13216] :
      ( hAPP(U_13214,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13211,tc_HOL_Obool)),U_13215),U_13216)) = hAPP(c_Fun_Ocomp(U_13212,U_13212,U_13212,hAPP(U_13214,U_13215)),hAPP(U_13214,U_13216))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13211,tc_HOL_Obool)),U_13215),U_13216) != c_Orderings_Obot__class_Obot(tc_fun(U_13211,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13211),U_13216))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13211),U_13215))
      | ~ c_Finite__Set_Ofolding(U_13211,U_13212,U_13213,U_13214) ),
    inference(definitional_conversion,[status(esa)],[f_3356_2]) ).

cnf(f_3356_4,plain,
    ( hAPP(U_13214,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13211,tc_HOL_Obool)),U_13215),U_13216)) = hAPP(c_Fun_Ocomp(U_13212,U_13212,U_13212,hAPP(U_13214,U_13215)),hAPP(U_13214,U_13216))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13211,tc_HOL_Obool)),U_13215),U_13216) != c_Orderings_Obot__class_Obot(tc_fun(U_13211,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13211),U_13216))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13211),U_13215))
    | ~ c_Finite__Set_Ofolding(U_13211,U_13212,U_13213,U_13214) ),
    inference(clausify,[status(thm)],[f_3356_3]) ).

fof(f_3357_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_3357_2,plain,
    ! [U_13222,U_13221,U_13220,U_13219,U_13218,U_13217] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13217,tc_fun(U_13218,tc_HOL_Obool)),U_13219),hAPP(c_Fun_Ocomp(U_13220,tc_fun(U_13218,tc_HOL_Obool),U_13217,U_13221),U_13222)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13220,tc_fun(U_13218,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13217,U_13220,U_13222),U_13219)),U_13221),
    inference(variable_rename,[status(thm)],[f_3357_1]) ).

fof(f_3357_3,plain,
    ! [U_13218,U_13217,U_13219,U_13220,U_13221,U_13222] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13217,tc_fun(U_13218,tc_HOL_Obool)),U_13219),hAPP(c_Fun_Ocomp(U_13220,tc_fun(U_13218,tc_HOL_Obool),U_13217,U_13221),U_13222)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13220,tc_fun(U_13218,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13217,U_13220,U_13222),U_13219)),U_13221),
    inference(definitional_conversion,[status(esa)],[f_3357_2]) ).

cnf(f_3357_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13217,tc_fun(U_13218,tc_HOL_Obool)),U_13219),hAPP(c_Fun_Ocomp(U_13220,tc_fun(U_13218,tc_HOL_Obool),U_13217,U_13221),U_13222)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13220,tc_fun(U_13218,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13217,U_13220,U_13222),U_13219)),U_13221),
    inference(clausify,[status(thm)],[f_3357_3]) ).

fof(f_3358_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_3358_2,plain,
    ! [U_13230,U_13229,U_13228,U_13227,U_13226,U_13225,U_13224,U_13223] :
      ( hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13228)),hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13229)),U_13230)) = hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13229)),hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13228)),U_13230))
      | ~ c_Finite__Set_Ofolding(U_13223,U_13224,U_13225,U_13226) ),
    inference(variable_rename,[status(thm)],[f_3358_1]) ).

fof(f_3358_3,plain,
    ! [U_13230,U_13229,U_13228,U_13227,U_13226,U_13225,U_13224] :
      ( ! [U_13223] : ~ c_Finite__Set_Ofolding(U_13223,U_13224,U_13225,U_13226)
      | hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13228)),hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13229)),U_13230)) = hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13229)),hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13228)),U_13230)) ),
    inference(miniscope,[status(thm)],[f_3358_2]) ).

fof(f_3358_4,plain,
    ! [U_13223,U_13224,U_13225,U_13226,U_13227,U_13228,U_13229,U_13230] :
      ( ~ c_Finite__Set_Ofolding(U_13223,U_13224,U_13225,U_13226)
      | hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13228)),hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13229)),U_13230)) = hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13229)),hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13228)),U_13230)) ),
    inference(definitional_conversion,[status(esa)],[f_3358_3]) ).

cnf(f_3358_5,plain,
    ( ~ c_Finite__Set_Ofolding(U_13223,U_13224,U_13225,U_13226)
    | hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13228)),hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13229)),U_13230)) = hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13229)),hAPP(c_Fun_Ocomp(U_13224,U_13224,U_13227,hAPP(U_13225,U_13228)),U_13230)) ),
    inference(clausify,[status(thm)],[f_3358_4]) ).

fof(f_3359_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_3359_2,plain,
    ! [U_13236,U_13235,U_13234,U_13233,U_13232,U_13231] :
      ( hAPP(c_Fun_Ocomp(U_13232,U_13232,U_13232,hAPP(U_13233,U_13235)),hAPP(U_13233,U_13236)) = hAPP(c_Fun_Ocomp(U_13232,U_13232,U_13232,hAPP(U_13233,U_13236)),hAPP(U_13233,U_13235))
      | ~ c_Finite__Set_Ofolding(U_13231,U_13232,U_13233,U_13234) ),
    inference(variable_rename,[status(thm)],[f_3359_1]) ).

fof(f_3359_3,plain,
    ! [U_13236,U_13235,U_13234,U_13233,U_13232] :
      ( ! [U_13231] : ~ c_Finite__Set_Ofolding(U_13231,U_13232,U_13233,U_13234)
      | hAPP(c_Fun_Ocomp(U_13232,U_13232,U_13232,hAPP(U_13233,U_13235)),hAPP(U_13233,U_13236)) = hAPP(c_Fun_Ocomp(U_13232,U_13232,U_13232,hAPP(U_13233,U_13236)),hAPP(U_13233,U_13235)) ),
    inference(miniscope,[status(thm)],[f_3359_2]) ).

fof(f_3359_4,plain,
    ! [U_13231,U_13233,U_13232,U_13234,U_13235,U_13236] :
      ( ~ c_Finite__Set_Ofolding(U_13231,U_13232,U_13233,U_13234)
      | hAPP(c_Fun_Ocomp(U_13232,U_13232,U_13232,hAPP(U_13233,U_13235)),hAPP(U_13233,U_13236)) = hAPP(c_Fun_Ocomp(U_13232,U_13232,U_13232,hAPP(U_13233,U_13236)),hAPP(U_13233,U_13235)) ),
    inference(definitional_conversion,[status(esa)],[f_3359_3]) ).

cnf(f_3359_5,plain,
    ( ~ c_Finite__Set_Ofolding(U_13231,U_13232,U_13233,U_13234)
    | hAPP(c_Fun_Ocomp(U_13232,U_13232,U_13232,hAPP(U_13233,U_13235)),hAPP(U_13233,U_13236)) = hAPP(c_Fun_Ocomp(U_13232,U_13232,U_13232,hAPP(U_13233,U_13236)),hAPP(U_13233,U_13235)) ),
    inference(clausify,[status(thm)],[f_3359_4]) ).

fof(f_3360_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_3360_2,plain,
    ! [U_13247,U_13246,U_13245,U_13244,U_13243,U_13242,U_13241,U_13240,U_13239,U_13238,U_13237] :
      ( hAPP(c_Fun_Ocomp(U_13241,U_13242,U_13243,U_13244),hAPP(c_Fun_Ocomp(U_13245,U_13241,U_13243,U_13246),U_13247)) = hAPP(c_Fun_Ocomp(U_13245,U_13242,U_13243,hAPP(c_Fun_Ocomp(U_13241,U_13242,U_13245,U_13244),U_13246)),U_13247)
      | ~ c_Finite__Set_Ofolding(U_13237,U_13238,U_13239,U_13240) ),
    inference(variable_rename,[status(thm)],[f_3360_1]) ).

fof(f_3360_3,plain,
    ( ! [U_13247,U_13246,U_13245,U_13244,U_13243,U_13242,U_13241] : hAPP(c_Fun_Ocomp(U_13241,U_13242,U_13243,U_13244),hAPP(c_Fun_Ocomp(U_13245,U_13241,U_13243,U_13246),U_13247)) = hAPP(c_Fun_Ocomp(U_13245,U_13242,U_13243,hAPP(c_Fun_Ocomp(U_13241,U_13242,U_13245,U_13244),U_13246)),U_13247)
    | ! [U_13240,U_13239,U_13238,U_13237] : ~ c_Finite__Set_Ofolding(U_13237,U_13238,U_13239,U_13240) ),
    inference(miniscope,[status(thm)],[f_3360_2]) ).

fof(f_3360_4,plain,
    ! [U_13237,U_13239,U_13238,U_13240,U_13241,U_13242,U_13243,U_13244,U_13245,U_13246,U_13247] :
      ( hAPP(c_Fun_Ocomp(U_13241,U_13242,U_13243,U_13244),hAPP(c_Fun_Ocomp(U_13245,U_13241,U_13243,U_13246),U_13247)) = hAPP(c_Fun_Ocomp(U_13245,U_13242,U_13243,hAPP(c_Fun_Ocomp(U_13241,U_13242,U_13245,U_13244),U_13246)),U_13247)
      | ~ c_Finite__Set_Ofolding(U_13237,U_13238,U_13239,U_13240) ),
    inference(definitional_conversion,[status(esa)],[f_3360_3]) ).

cnf(f_3360_5,plain,
    ( hAPP(c_Fun_Ocomp(U_13241,U_13242,U_13243,U_13244),hAPP(c_Fun_Ocomp(U_13245,U_13241,U_13243,U_13246),U_13247)) = hAPP(c_Fun_Ocomp(U_13245,U_13242,U_13243,hAPP(c_Fun_Ocomp(U_13241,U_13242,U_13245,U_13244),U_13246)),U_13247)
    | ~ c_Finite__Set_Ofolding(U_13237,U_13238,U_13239,U_13240) ),
    inference(clausify,[status(thm)],[f_3360_4]) ).

fof(f_3361_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_3361_2,plain,
    ! [U_13255,U_13254,U_13253,U_13252,U_13251,U_13250,U_13249,U_13248] :
      ( hAPP(hAPP(U_13252,hAPP(hAPP(c_COMBS(U_13249,U_13248,U_13248),hAPP(hAPP(c_COMBB(U_13248,tc_fun(U_13248,U_13248),U_13249),U_13250),U_13254)),U_13255)),U_13253) = hAPP(hAPP(U_13250,hAPP(hAPP(U_13252,U_13254),U_13253)),hAPP(hAPP(U_13252,U_13255),U_13253))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13249),U_13253))
      | ~ c_Finite__Set_Ofolding__image(U_13248,U_13249,U_13250,U_13251,U_13252) ),
    inference(variable_rename,[status(thm)],[f_3361_1]) ).

fof(f_3361_3,plain,
    ! [U_13248,U_13249,U_13250,U_13251,U_13252,U_13253,U_13254,U_13255] :
      ( hAPP(hAPP(U_13252,hAPP(hAPP(c_COMBS(U_13249,U_13248,U_13248),hAPP(hAPP(c_COMBB(U_13248,tc_fun(U_13248,U_13248),U_13249),U_13250),U_13254)),U_13255)),U_13253) = hAPP(hAPP(U_13250,hAPP(hAPP(U_13252,U_13254),U_13253)),hAPP(hAPP(U_13252,U_13255),U_13253))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13249),U_13253))
      | ~ c_Finite__Set_Ofolding__image(U_13248,U_13249,U_13250,U_13251,U_13252) ),
    inference(definitional_conversion,[status(esa)],[f_3361_2]) ).

cnf(f_3361_4,plain,
    ( hAPP(hAPP(U_13252,hAPP(hAPP(c_COMBS(U_13249,U_13248,U_13248),hAPP(hAPP(c_COMBB(U_13248,tc_fun(U_13248,U_13248),U_13249),U_13250),U_13254)),U_13255)),U_13253) = hAPP(hAPP(U_13250,hAPP(hAPP(U_13252,U_13254),U_13253)),hAPP(hAPP(U_13252,U_13255),U_13253))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13249),U_13253))
    | ~ c_Finite__Set_Ofolding__image(U_13248,U_13249,U_13250,U_13251,U_13252) ),
    inference(clausify,[status(thm)],[f_3361_3]) ).

fof(f_3362_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_3362_2,plain,
    ! [U_13262,U_13261,U_13260,U_13259,U_13258,U_13257,U_13256] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13256,U_13257,U_13258),hAPP(c_Fun_Ocomp(U_13259,tc_fun(U_13257,U_13258),U_13256,U_13260),U_13261)),U_13262) = hAPP(hAPP(U_13260,hAPP(U_13261,hAPP(c_Product__Type_Ofst(U_13256,U_13257),U_13262))),hAPP(c_Product__Type_Osnd(U_13256,U_13257),U_13262)),
    inference(variable_rename,[status(thm)],[f_3362_1]) ).

fof(f_3362_3,plain,
    ! [U_13256,U_13257,U_13258,U_13259,U_13260,U_13261,U_13262] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13256,U_13257,U_13258),hAPP(c_Fun_Ocomp(U_13259,tc_fun(U_13257,U_13258),U_13256,U_13260),U_13261)),U_13262) = hAPP(hAPP(U_13260,hAPP(U_13261,hAPP(c_Product__Type_Ofst(U_13256,U_13257),U_13262))),hAPP(c_Product__Type_Osnd(U_13256,U_13257),U_13262)),
    inference(definitional_conversion,[status(esa)],[f_3362_2]) ).

cnf(f_3362_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13256,U_13257,U_13258),hAPP(c_Fun_Ocomp(U_13259,tc_fun(U_13257,U_13258),U_13256,U_13260),U_13261)),U_13262) = hAPP(hAPP(U_13260,hAPP(U_13261,hAPP(c_Product__Type_Ofst(U_13256,U_13257),U_13262))),hAPP(c_Product__Type_Osnd(U_13256,U_13257),U_13262)),
    inference(clausify,[status(thm)],[f_3362_3]) ).

fof(f_3363_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_3363_2,plain,
    ! [U_13268,U_13267,U_13266,U_13265,U_13264,U_13263] :
      ( hAPP(c_Fun_Ocomp(U_13264,U_13264,U_13264,hAPP(U_13265,U_13268)),hAPP(U_13266,U_13267)) = hAPP(c_Fun_Ocomp(U_13264,U_13264,U_13264,hAPP(U_13266,U_13267)),hAPP(U_13265,U_13268))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13263),U_13267))
      | ~ c_Finite__Set_Ofolding(U_13263,U_13264,U_13265,U_13266) ),
    inference(variable_rename,[status(thm)],[f_3363_1]) ).

fof(f_3363_3,plain,
    ! [U_13264,U_13263,U_13265,U_13266,U_13267,U_13268] :
      ( hAPP(c_Fun_Ocomp(U_13264,U_13264,U_13264,hAPP(U_13265,U_13268)),hAPP(U_13266,U_13267)) = hAPP(c_Fun_Ocomp(U_13264,U_13264,U_13264,hAPP(U_13266,U_13267)),hAPP(U_13265,U_13268))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13263),U_13267))
      | ~ c_Finite__Set_Ofolding(U_13263,U_13264,U_13265,U_13266) ),
    inference(definitional_conversion,[status(esa)],[f_3363_2]) ).

cnf(f_3363_4,plain,
    ( hAPP(c_Fun_Ocomp(U_13264,U_13264,U_13264,hAPP(U_13265,U_13268)),hAPP(U_13266,U_13267)) = hAPP(c_Fun_Ocomp(U_13264,U_13264,U_13264,hAPP(U_13266,U_13267)),hAPP(U_13265,U_13268))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13263),U_13267))
    | ~ c_Finite__Set_Ofolding(U_13263,U_13264,U_13265,U_13266) ),
    inference(clausify,[status(thm)],[f_3363_3]) ).

fof(f_3364_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_3364_2,plain,
    ! [U_13276,U_13275,U_13274,U_13273,U_13272,U_13271,U_13270,U_13269] :
      ( hAPP(c_Fun_Ocomp(U_13270,U_13270,U_13274,hAPP(U_13271,U_13275)),hAPP(c_Fun_Ocomp(U_13270,U_13270,U_13274,hAPP(U_13272,U_13273)),U_13276)) = hAPP(c_Fun_Ocomp(U_13270,U_13270,U_13274,hAPP(U_13272,U_13273)),hAPP(c_Fun_Ocomp(U_13270,U_13270,U_13274,hAPP(U_13271,U_13275)),U_13276))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13269),U_13273))
      | ~ c_Finite__Set_Ofolding(U_13269,U_13270,U_13271,U_13272) ),
    inference(variable_rename,[status(thm)],[f_3364_1]) ).

fof(f_3364_3,plain,
    ! [U_13270,U_13269,U_13271,U_13272,U_13273,U_13274,U_13275,U_13276] :
      ( hAPP(c_Fun_Ocomp(U_13270,U_13270,U_13274,hAPP(U_13271,U_13275)),hAPP(c_Fun_Ocomp(U_13270,U_13270,U_13274,hAPP(U_13272,U_13273)),U_13276)) = hAPP(c_Fun_Ocomp(U_13270,U_13270,U_13274,hAPP(U_13272,U_13273)),hAPP(c_Fun_Ocomp(U_13270,U_13270,U_13274,hAPP(U_13271,U_13275)),U_13276))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13269),U_13273))
      | ~ c_Finite__Set_Ofolding(U_13269,U_13270,U_13271,U_13272) ),
    inference(definitional_conversion,[status(esa)],[f_3364_2]) ).

cnf(f_3364_4,plain,
    ( hAPP(c_Fun_Ocomp(U_13270,U_13270,U_13274,hAPP(U_13271,U_13275)),hAPP(c_Fun_Ocomp(U_13270,U_13270,U_13274,hAPP(U_13272,U_13273)),U_13276)) = hAPP(c_Fun_Ocomp(U_13270,U_13270,U_13274,hAPP(U_13272,U_13273)),hAPP(c_Fun_Ocomp(U_13270,U_13270,U_13274,hAPP(U_13271,U_13275)),U_13276))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13269),U_13273))
    | ~ c_Finite__Set_Ofolding(U_13269,U_13270,U_13271,U_13272) ),
    inference(clausify,[status(thm)],[f_3364_3]) ).

fof(f_3365_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_3365_2,plain,
    ! [U_13282,U_13281,U_13280,U_13279,U_13278,U_13277] :
      ( hAPP(c_Fun_Ocomp(U_13278,U_13278,U_13278,hAPP(U_13280,U_13282)),hAPP(U_13280,U_13281)) = hAPP(c_Fun_Ocomp(U_13278,U_13278,U_13278,hAPP(U_13280,U_13281)),hAPP(U_13280,U_13282))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13277),U_13282))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13277),U_13281))
      | ~ c_Finite__Set_Ofolding(U_13277,U_13278,U_13279,U_13280) ),
    inference(variable_rename,[status(thm)],[f_3365_1]) ).

fof(f_3365_3,plain,
    ! [U_13278,U_13279,U_13277,U_13280,U_13281,U_13282] :
      ( hAPP(c_Fun_Ocomp(U_13278,U_13278,U_13278,hAPP(U_13280,U_13282)),hAPP(U_13280,U_13281)) = hAPP(c_Fun_Ocomp(U_13278,U_13278,U_13278,hAPP(U_13280,U_13281)),hAPP(U_13280,U_13282))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13277),U_13282))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13277),U_13281))
      | ~ c_Finite__Set_Ofolding(U_13277,U_13278,U_13279,U_13280) ),
    inference(definitional_conversion,[status(esa)],[f_3365_2]) ).

cnf(f_3365_4,plain,
    ( hAPP(c_Fun_Ocomp(U_13278,U_13278,U_13278,hAPP(U_13280,U_13282)),hAPP(U_13280,U_13281)) = hAPP(c_Fun_Ocomp(U_13278,U_13278,U_13278,hAPP(U_13280,U_13281)),hAPP(U_13280,U_13282))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13277),U_13282))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13277),U_13281))
    | ~ c_Finite__Set_Ofolding(U_13277,U_13278,U_13279,U_13280) ),
    inference(clausify,[status(thm)],[f_3365_3]) ).

fof(f_3366_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_3366_2,plain,
    ! [U_13290,U_13289,U_13288,U_13287,U_13286,U_13285,U_13284,U_13283] :
      ( hAPP(c_Fun_Ocomp(U_13284,U_13284,U_13289,hAPP(U_13286,U_13288)),hAPP(c_Fun_Ocomp(U_13284,U_13284,U_13289,hAPP(U_13286,U_13287)),U_13290)) = hAPP(c_Fun_Ocomp(U_13284,U_13284,U_13289,hAPP(U_13286,U_13287)),hAPP(c_Fun_Ocomp(U_13284,U_13284,U_13289,hAPP(U_13286,U_13288)),U_13290))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13283),U_13288))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13283),U_13287))
      | ~ c_Finite__Set_Ofolding(U_13283,U_13284,U_13285,U_13286) ),
    inference(variable_rename,[status(thm)],[f_3366_1]) ).

fof(f_3366_3,plain,
    ! [U_13283,U_13285,U_13284,U_13286,U_13287,U_13288,U_13289,U_13290] :
      ( hAPP(c_Fun_Ocomp(U_13284,U_13284,U_13289,hAPP(U_13286,U_13288)),hAPP(c_Fun_Ocomp(U_13284,U_13284,U_13289,hAPP(U_13286,U_13287)),U_13290)) = hAPP(c_Fun_Ocomp(U_13284,U_13284,U_13289,hAPP(U_13286,U_13287)),hAPP(c_Fun_Ocomp(U_13284,U_13284,U_13289,hAPP(U_13286,U_13288)),U_13290))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13283),U_13288))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13283),U_13287))
      | ~ c_Finite__Set_Ofolding(U_13283,U_13284,U_13285,U_13286) ),
    inference(definitional_conversion,[status(esa)],[f_3366_2]) ).

cnf(f_3366_4,plain,
    ( hAPP(c_Fun_Ocomp(U_13284,U_13284,U_13289,hAPP(U_13286,U_13288)),hAPP(c_Fun_Ocomp(U_13284,U_13284,U_13289,hAPP(U_13286,U_13287)),U_13290)) = hAPP(c_Fun_Ocomp(U_13284,U_13284,U_13289,hAPP(U_13286,U_13287)),hAPP(c_Fun_Ocomp(U_13284,U_13284,U_13289,hAPP(U_13286,U_13288)),U_13290))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13283),U_13288))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13283),U_13287))
    | ~ c_Finite__Set_Ofolding(U_13283,U_13284,U_13285,U_13286) ),
    inference(clausify,[status(thm)],[f_3366_3]) ).

fof(f_3367_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_3367_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_3367_1]) ).

cnf(f_3367_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_3367_2]) ).

fof(f_3368_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_3368_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_3368_1]) ).

cnf(f_3368_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_3368_2]) ).

fof(f_3369_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_3369_2,plain,
    ! [U_13297,U_13296,U_13295,U_13294,U_13293,U_13292,U_13291] :
      ( hAPP(hAPP(U_13295,U_13297),U_13296) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13291,U_13292,U_13293),U_13297),U_13294),U_13296)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13292),U_13296))
      | ~ c_Finite__Set_Ofolding__image(U_13291,U_13292,U_13293,U_13294,U_13295) ),
    inference(variable_rename,[status(thm)],[f_3369_1]) ).

fof(f_3369_3,plain,
    ! [U_13292,U_13291,U_13293,U_13294,U_13295,U_13296,U_13297] :
      ( hAPP(hAPP(U_13295,U_13297),U_13296) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13291,U_13292,U_13293),U_13297),U_13294),U_13296)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13292),U_13296))
      | ~ c_Finite__Set_Ofolding__image(U_13291,U_13292,U_13293,U_13294,U_13295) ),
    inference(definitional_conversion,[status(esa)],[f_3369_2]) ).

cnf(f_3369_4,plain,
    ( hAPP(hAPP(U_13295,U_13297),U_13296) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_13291,U_13292,U_13293),U_13297),U_13294),U_13296)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13292),U_13296))
    | ~ c_Finite__Set_Ofolding__image(U_13291,U_13292,U_13293,U_13294,U_13295) ),
    inference(clausify,[status(thm)],[f_3369_3]) ).

fof(f_3370_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_3370_2,plain,
    ! [U_13303,U_13302,U_13301,U_13300,U_13299,U_13298] :
      ( hAPP(U_13301,hAPP(hAPP(c_Set_Oinsert(U_13298),U_13303),U_13302)) = hAPP(c_Fun_Ocomp(U_13299,U_13299,U_13299,hAPP(U_13301,U_13302)),hAPP(U_13300,U_13303))
      | hBOOL(hAPP(hAPP(c_member(U_13298),U_13303),U_13302))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13298),U_13302))
      | ~ c_Finite__Set_Ofolding(U_13298,U_13299,U_13300,U_13301) ),
    inference(variable_rename,[status(thm)],[f_3370_1]) ).

fof(f_3370_3,plain,
    ! [U_13299,U_13300,U_13298,U_13301,U_13302,U_13303] :
      ( hAPP(U_13301,hAPP(hAPP(c_Set_Oinsert(U_13298),U_13303),U_13302)) = hAPP(c_Fun_Ocomp(U_13299,U_13299,U_13299,hAPP(U_13301,U_13302)),hAPP(U_13300,U_13303))
      | hBOOL(hAPP(hAPP(c_member(U_13298),U_13303),U_13302))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13298),U_13302))
      | ~ c_Finite__Set_Ofolding(U_13298,U_13299,U_13300,U_13301) ),
    inference(definitional_conversion,[status(esa)],[f_3370_2]) ).

cnf(f_3370_4,plain,
    ( hAPP(U_13301,hAPP(hAPP(c_Set_Oinsert(U_13298),U_13303),U_13302)) = hAPP(c_Fun_Ocomp(U_13299,U_13299,U_13299,hAPP(U_13301,U_13302)),hAPP(U_13300,U_13303))
    | hBOOL(hAPP(hAPP(c_member(U_13298),U_13303),U_13302))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13298),U_13302))
    | ~ c_Finite__Set_Ofolding(U_13298,U_13299,U_13300,U_13301) ),
    inference(clausify,[status(thm)],[f_3370_3]) ).

fof(f_3371_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_3371_2,plain,
    ! [U_13309,U_13308,U_13307,U_13306,U_13305,U_13304] :
      ( hAPP(c_Fun_Ocomp(U_13305,U_13305,U_13305,hAPP(U_13307,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13304,tc_HOL_Obool)),U_13308),U_13309))),hAPP(U_13307,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13304,tc_HOL_Obool)),U_13308),U_13309))) = hAPP(c_Fun_Ocomp(U_13305,U_13305,U_13305,hAPP(U_13307,U_13308)),hAPP(U_13307,U_13309))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13304),U_13309))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13304),U_13308))
      | ~ c_Finite__Set_Ofolding(U_13304,U_13305,U_13306,U_13307) ),
    inference(variable_rename,[status(thm)],[f_3371_1]) ).

fof(f_3371_3,plain,
    ! [U_13304,U_13305,U_13306,U_13307,U_13308,U_13309] :
      ( hAPP(c_Fun_Ocomp(U_13305,U_13305,U_13305,hAPP(U_13307,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13304,tc_HOL_Obool)),U_13308),U_13309))),hAPP(U_13307,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13304,tc_HOL_Obool)),U_13308),U_13309))) = hAPP(c_Fun_Ocomp(U_13305,U_13305,U_13305,hAPP(U_13307,U_13308)),hAPP(U_13307,U_13309))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13304),U_13309))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13304),U_13308))
      | ~ c_Finite__Set_Ofolding(U_13304,U_13305,U_13306,U_13307) ),
    inference(definitional_conversion,[status(esa)],[f_3371_2]) ).

cnf(f_3371_4,plain,
    ( hAPP(c_Fun_Ocomp(U_13305,U_13305,U_13305,hAPP(U_13307,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13304,tc_HOL_Obool)),U_13308),U_13309))),hAPP(U_13307,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13304,tc_HOL_Obool)),U_13308),U_13309))) = hAPP(c_Fun_Ocomp(U_13305,U_13305,U_13305,hAPP(U_13307,U_13308)),hAPP(U_13307,U_13309))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13304),U_13309))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13304),U_13308))
    | ~ c_Finite__Set_Ofolding(U_13304,U_13305,U_13306,U_13307) ),
    inference(clausify,[status(thm)],[f_3371_3]) ).

fof(f_3372_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_3372_2,plain,
    ! [U_13315,U_13314,U_13313,U_13312,U_13311,U_13310] :
      ( hAPP(U_13313,hAPP(hAPP(c_Set_Oinsert(U_13310),U_13315),U_13314)) = hAPP(c_Fun_Ocomp(U_13311,U_13311,U_13311,hAPP(U_13313,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13310,tc_HOL_Obool)),U_13314),hAPP(hAPP(c_Set_Oinsert(U_13310),U_13315),c_Orderings_Obot__class_Obot(tc_fun(U_13310,tc_HOL_Obool)))))),hAPP(U_13312,U_13315))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13310),U_13314))
      | ~ c_Finite__Set_Ofolding(U_13310,U_13311,U_13312,U_13313) ),
    inference(variable_rename,[status(thm)],[f_3372_1]) ).

fof(f_3372_3,plain,
    ! [U_13310,U_13312,U_13313,U_13311,U_13314,U_13315] :
      ( hAPP(U_13313,hAPP(hAPP(c_Set_Oinsert(U_13310),U_13315),U_13314)) = hAPP(c_Fun_Ocomp(U_13311,U_13311,U_13311,hAPP(U_13313,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13310,tc_HOL_Obool)),U_13314),hAPP(hAPP(c_Set_Oinsert(U_13310),U_13315),c_Orderings_Obot__class_Obot(tc_fun(U_13310,tc_HOL_Obool)))))),hAPP(U_13312,U_13315))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13310),U_13314))
      | ~ c_Finite__Set_Ofolding(U_13310,U_13311,U_13312,U_13313) ),
    inference(definitional_conversion,[status(esa)],[f_3372_2]) ).

cnf(f_3372_4,plain,
    ( hAPP(U_13313,hAPP(hAPP(c_Set_Oinsert(U_13310),U_13315),U_13314)) = hAPP(c_Fun_Ocomp(U_13311,U_13311,U_13311,hAPP(U_13313,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13310,tc_HOL_Obool)),U_13314),hAPP(hAPP(c_Set_Oinsert(U_13310),U_13315),c_Orderings_Obot__class_Obot(tc_fun(U_13310,tc_HOL_Obool)))))),hAPP(U_13312,U_13315))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13310),U_13314))
    | ~ c_Finite__Set_Ofolding(U_13310,U_13311,U_13312,U_13313) ),
    inference(clausify,[status(thm)],[f_3372_3]) ).

fof(f_3373_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_3373_2,plain,
    ! [U_13320,U_13319,U_13318,U_13317,U_13316] :
      ( c_Hoare__Mirabelle_Ohoare__valids(U_13316,U_13317,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13316)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13316),U_13318),c_Com_Ocom_OWhile(U_13319,U_13320)),c_Hoare__Mirabelle_Opeek__and(U_13316,U_13318,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_13319)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13316),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(U_13316,U_13317,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13316)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13316),c_Hoare__Mirabelle_Opeek__and(U_13316,U_13318,U_13319)),U_13320),U_13318)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13316),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3373_1]) ).

fof(f_3373_3,plain,
    ! [U_13316,U_13317,U_13318,U_13319,U_13320] :
      ( c_Hoare__Mirabelle_Ohoare__valids(U_13316,U_13317,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13316)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13316),U_13318),c_Com_Ocom_OWhile(U_13319,U_13320)),c_Hoare__Mirabelle_Opeek__and(U_13316,U_13318,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_13319)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13316),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(U_13316,U_13317,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13316)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13316),c_Hoare__Mirabelle_Opeek__and(U_13316,U_13318,U_13319)),U_13320),U_13318)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13316),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3373_2]) ).

cnf(f_3373_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__valids(U_13316,U_13317,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13316)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13316),U_13318),c_Com_Ocom_OWhile(U_13319,U_13320)),c_Hoare__Mirabelle_Opeek__and(U_13316,U_13318,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_13319)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13316),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__valids(U_13316,U_13317,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13316)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13316),c_Hoare__Mirabelle_Opeek__and(U_13316,U_13318,U_13319)),U_13320),U_13318)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13316),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3373_3]) ).

fof(f_3374_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_3374_2,plain,
    ! [U_13321] : c_Nitpick_Onum(U_13321) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_13321,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_13321)),
    inference(variable_rename,[status(thm)],[f_3374_1]) ).

fof(f_3374_3,plain,
    ! [U_13321] : c_Nitpick_Onum(U_13321) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_13321,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_13321)),
    inference(definitional_conversion,[status(esa)],[f_3374_2]) ).

cnf(f_3374_4,plain,
    c_Nitpick_Onum(U_13321) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_13321,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_13321)),
    inference(clausify,[status(thm)],[f_3374_3]) ).

fof(f_3375_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_3375_2,plain,
    ! [U_13322] : c_Nitpick_Odenom(U_13322) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_13322,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_13322)),
    inference(variable_rename,[status(thm)],[f_3375_1]) ).

fof(f_3375_3,plain,
    ! [U_13322] : c_Nitpick_Odenom(U_13322) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_13322,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_13322)),
    inference(definitional_conversion,[status(esa)],[f_3375_2]) ).

cnf(f_3375_4,plain,
    c_Nitpick_Odenom(U_13322) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_13322,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_13322)),
    inference(clausify,[status(thm)],[f_3375_3]) ).

fof(f_3376_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_3376_2,plain,
    ! [U_13327,U_13326,U_13325,U_13324,U_13323] :
      ( ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_13323,U_13324,U_13325),U_13326),U_13327))
        | ~ hBOOL(hAPP(U_13325,U_13327))
        | ~ hBOOL(hAPP(hAPP(U_13324,U_13326),U_13327)) )
      & ( ( hBOOL(hAPP(U_13325,U_13327))
          & hBOOL(hAPP(hAPP(U_13324,U_13326),U_13327)) )
        | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_13323,U_13324,U_13325),U_13326),U_13327)) ) ),
    inference(variable_rename,[status(thm)],[f_3376_1]) ).

fof(f_3376_3,plain,
    ( ! [U_13337,U_13335,U_13333,U_13331] :
        ( ! [U_13329] : hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_13329,U_13331,U_13333),U_13335),U_13337))
        | ~ hBOOL(hAPP(U_13333,U_13337))
        | ~ hBOOL(hAPP(hAPP(U_13331,U_13335),U_13337)) )
    & ! [U_13336,U_13334,U_13332,U_13330] :
        ( ! [U_13328] : ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_13328,U_13330,U_13332),U_13334),U_13336))
        | ( hBOOL(hAPP(U_13332,U_13336))
          & hBOOL(hAPP(hAPP(U_13330,U_13334),U_13336)) ) ) ),
    inference(miniscope,[status(thm)],[f_3376_2]) ).

fof(f_3376_4,plain,
    ( ! [U_13334,U_13332,U_13330,U_13336] :
        ( hBOOL(hAPP(U_13332,U_13336))
        | ~ sP949(U_13334,U_13332,U_13330,U_13336) )
    & ! [U_13334,U_13332,U_13330,U_13336] :
        ( hBOOL(hAPP(hAPP(U_13330,U_13334),U_13336))
        | ~ sP949(U_13334,U_13332,U_13330,U_13336) )
    & ! [U_13333,U_13331,U_13329,U_13335,U_13337] :
        ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_13329,U_13331,U_13333),U_13335),U_13337))
        | ~ hBOOL(hAPP(U_13333,U_13337))
        | ~ hBOOL(hAPP(hAPP(U_13331,U_13335),U_13337)) )
    & ! [U_13334,U_13332,U_13330,U_13328,U_13336] :
        ( ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_13328,U_13330,U_13332),U_13334),U_13336))
        | sP949(U_13334,U_13332,U_13330,U_13336) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP949])],[f_3376_3]) ).

cnf(f_3376_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_13328,U_13330,U_13332),U_13334),U_13336))
    | sP949(U_13334,U_13332,U_13330,U_13336) ),
    inference(clausify,[status(thm)],[f_3376_4]) ).

cnf(f_3376_6,plain,
    ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_13329,U_13331,U_13333),U_13335),U_13337))
    | ~ hBOOL(hAPP(U_13333,U_13337))
    | ~ hBOOL(hAPP(hAPP(U_13331,U_13335),U_13337)) ),
    inference(clausify,[status(thm)],[f_3376_4]) ).

cnf(f_3376_7,plain,
    ( hBOOL(hAPP(hAPP(U_13330,U_13334),U_13336))
    | ~ sP949(U_13334,U_13332,U_13330,U_13336) ),
    inference(clausify,[status(thm)],[f_3376_4]) ).

cnf(f_3376_8,plain,
    ( hBOOL(hAPP(U_13332,U_13336))
    | ~ sP949(U_13334,U_13332,U_13330,U_13336) ),
    inference(clausify,[status(thm)],[f_3376_4]) ).

fof(f_3377_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_3377_2,plain,
    ! [U_13342,U_13341,U_13340,U_13339,U_13338] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_13338,U_13339,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13338)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13338),U_13340),c_Com_Ocom_OWhile(U_13341,U_13342)),c_Hoare__Mirabelle_Opeek__and(U_13338,U_13340,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_13341)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13338),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_13338,U_13339,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13338)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13338),c_Hoare__Mirabelle_Opeek__and(U_13338,U_13340,U_13341)),U_13342),U_13340)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13338),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3377_1]) ).

fof(f_3377_3,plain,
    ! [U_13339,U_13338,U_13340,U_13341,U_13342] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_13338,U_13339,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13338)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13338),U_13340),c_Com_Ocom_OWhile(U_13341,U_13342)),c_Hoare__Mirabelle_Opeek__and(U_13338,U_13340,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_13341)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13338),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_13338,U_13339,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13338)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13338),c_Hoare__Mirabelle_Opeek__and(U_13338,U_13340,U_13341)),U_13342),U_13340)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13338),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3377_2]) ).

cnf(f_3377_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_13338,U_13339,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13338)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13338),U_13340),c_Com_Ocom_OWhile(U_13341,U_13342)),c_Hoare__Mirabelle_Opeek__and(U_13338,U_13340,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_13341)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13338),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_13338,U_13339,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13338)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13338),c_Hoare__Mirabelle_Opeek__and(U_13338,U_13340,U_13341)),U_13342),U_13340)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13338),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3377_3]) ).

fof(f_3378_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_3378_2,plain,
    ! [U_13349,U_13348,U_13347,U_13346,U_13345,U_13344,U_13343] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_13343,U_13344,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13343)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13343),U_13345),c_Com_Ocom_OCond(U_13346,U_13347,U_13349)),U_13348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13343),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_13343,U_13344,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13343)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13343),c_Hoare__Mirabelle_Opeek__and(U_13343,U_13345,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_13346))),U_13349),U_13348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13343),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_13343,U_13344,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13343)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13343),c_Hoare__Mirabelle_Opeek__and(U_13343,U_13345,U_13346)),U_13347),U_13348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13343),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3378_1]) ).

fof(f_3378_3,plain,
    ! [U_13343,U_13344,U_13345,U_13346,U_13347,U_13348,U_13349] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_13343,U_13344,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13343)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13343),U_13345),c_Com_Ocom_OCond(U_13346,U_13347,U_13349)),U_13348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13343),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_13343,U_13344,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13343)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13343),c_Hoare__Mirabelle_Opeek__and(U_13343,U_13345,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_13346))),U_13349),U_13348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13343),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_13343,U_13344,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13343)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13343),c_Hoare__Mirabelle_Opeek__and(U_13343,U_13345,U_13346)),U_13347),U_13348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13343),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3378_2]) ).

cnf(f_3378_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_13343,U_13344,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13343)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13343),U_13345),c_Com_Ocom_OCond(U_13346,U_13347,U_13349)),U_13348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13343),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_13343,U_13344,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13343)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13343),c_Hoare__Mirabelle_Opeek__and(U_13343,U_13345,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_13346))),U_13349),U_13348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13343),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_13343,U_13344,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_13343)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_13343),c_Hoare__Mirabelle_Opeek__and(U_13343,U_13345,U_13346)),U_13347),U_13348)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_13343),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3378_3]) ).

fof(f_3379_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_3379_2,plain,
    ! [U_13357,U_13356,U_13355,U_13354,U_13353,U_13352] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13357,U_13352),U_13356),hAPP(c_Set_Oimage(U_13353,U_13357,U_13355),U_13354)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13353,U_13352),hAPP(c_Fun_Ocomp(U_13357,U_13352,U_13353,U_13356),U_13355)),U_13354)
      | ? [U_13351] :
          ( ? [U_13350] :
              ( hAPP(U_13356,hAPP(U_13355,U_13351)) != c_Groups_Ozero__class_Ozero(U_13352)
              & hAPP(U_13355,U_13351) = hAPP(U_13355,U_13350)
              & U_13351 != U_13350
              & hBOOL(hAPP(hAPP(c_member(U_13353),U_13350),U_13354)) )
          & hBOOL(hAPP(hAPP(c_member(U_13353),U_13351),U_13354)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13353),U_13354))
      | ~ class_Groups_Ocomm__monoid__add(U_13352) ),
    inference(variable_rename,[status(thm)],[f_3379_1]) ).

fof(f_3379_3,plain,
    ! [U_13357,U_13356,U_13355,U_13354,U_13353,U_13352] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13357,U_13352),U_13356),hAPP(c_Set_Oimage(U_13353,U_13357,U_13355),U_13354)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13353,U_13352),hAPP(c_Fun_Ocomp(U_13357,U_13352,U_13353,U_13356),U_13355)),U_13354)
      | ( ? [U_13350] :
            ( hAPP(U_13356,hAPP(U_13355,sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352))) != c_Groups_Ozero__class_Ozero(U_13352)
            & hAPP(U_13355,sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352)) = hAPP(U_13355,U_13350)
            & sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352) != U_13350
            & hBOOL(hAPP(hAPP(c_member(U_13353),U_13350),U_13354)) )
        & hBOOL(hAPP(hAPP(c_member(U_13353),sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352)),U_13354)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13353),U_13354))
      | ~ class_Groups_Ocomm__monoid__add(U_13352) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK283]),skolemize(U_13351,sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352))],[f_3379_2]) ).

fof(f_3379_4,plain,
    ! [U_13357,U_13356,U_13355,U_13354,U_13353,U_13352] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13357,U_13352),U_13356),hAPP(c_Set_Oimage(U_13353,U_13357,U_13355),U_13354)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13353,U_13352),hAPP(c_Fun_Ocomp(U_13357,U_13352,U_13353,U_13356),U_13355)),U_13354)
      | ( hAPP(U_13356,hAPP(U_13355,sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352))) != c_Groups_Ozero__class_Ozero(U_13352)
        & hAPP(U_13355,sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352)) = hAPP(U_13355,sK284(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352))
        & sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352) != sK284(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352)
        & hBOOL(hAPP(hAPP(c_member(U_13353),sK284(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352)),U_13354))
        & hBOOL(hAPP(hAPP(c_member(U_13353),sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352)),U_13354)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13353),U_13354))
      | ~ class_Groups_Ocomm__monoid__add(U_13352) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK284]),skolemize(U_13350,sK284(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352))],[f_3379_3]) ).

fof(f_3379_5,plain,
    ( ! [U_13353,U_13352,U_13354,U_13355,U_13356,U_13357] :
        ( hAPP(U_13356,hAPP(U_13355,sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352))) != c_Groups_Ozero__class_Ozero(U_13352)
        | ~ sP950(U_13353,U_13352,U_13354,U_13355,U_13356,U_13357) )
    & ! [U_13353,U_13352,U_13354,U_13355,U_13356,U_13357] :
        ( hAPP(U_13355,sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352)) = hAPP(U_13355,sK284(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352))
        | ~ sP950(U_13353,U_13352,U_13354,U_13355,U_13356,U_13357) )
    & ! [U_13353,U_13352,U_13354,U_13355,U_13356,U_13357] :
        ( sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352) != sK284(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352)
        | ~ sP950(U_13353,U_13352,U_13354,U_13355,U_13356,U_13357) )
    & ! [U_13353,U_13352,U_13354,U_13355,U_13356,U_13357] :
        ( hBOOL(hAPP(hAPP(c_member(U_13353),sK284(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352)),U_13354))
        | ~ sP950(U_13353,U_13352,U_13354,U_13355,U_13356,U_13357) )
    & ! [U_13353,U_13352,U_13354,U_13355,U_13356,U_13357] :
        ( hBOOL(hAPP(hAPP(c_member(U_13353),sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352)),U_13354))
        | ~ sP950(U_13353,U_13352,U_13354,U_13355,U_13356,U_13357) )
    & ! [U_13353,U_13352,U_13354,U_13355,U_13356,U_13357] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13357,U_13352),U_13356),hAPP(c_Set_Oimage(U_13353,U_13357,U_13355),U_13354)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13353,U_13352),hAPP(c_Fun_Ocomp(U_13357,U_13352,U_13353,U_13356),U_13355)),U_13354)
        | sP950(U_13353,U_13352,U_13354,U_13355,U_13356,U_13357)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13353),U_13354))
        | ~ class_Groups_Ocomm__monoid__add(U_13352) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP950])],[f_3379_4]) ).

cnf(f_3379_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13357,U_13352),U_13356),hAPP(c_Set_Oimage(U_13353,U_13357,U_13355),U_13354)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13353,U_13352),hAPP(c_Fun_Ocomp(U_13357,U_13352,U_13353,U_13356),U_13355)),U_13354)
    | sP950(U_13353,U_13352,U_13354,U_13355,U_13356,U_13357)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13353),U_13354))
    | ~ class_Groups_Ocomm__monoid__add(U_13352) ),
    inference(clausify,[status(thm)],[f_3379_5]) ).

cnf(f_3379_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13353),sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352)),U_13354))
    | ~ sP950(U_13353,U_13352,U_13354,U_13355,U_13356,U_13357) ),
    inference(clausify,[status(thm)],[f_3379_5]) ).

cnf(f_3379_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13353),sK284(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352)),U_13354))
    | ~ sP950(U_13353,U_13352,U_13354,U_13355,U_13356,U_13357) ),
    inference(clausify,[status(thm)],[f_3379_5]) ).

cnf(f_3379_9,plain,
    ( sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352) != sK284(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352)
    | ~ sP950(U_13353,U_13352,U_13354,U_13355,U_13356,U_13357) ),
    inference(clausify,[status(thm)],[f_3379_5]) ).

cnf(f_3379_10,plain,
    ( hAPP(U_13355,sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352)) = hAPP(U_13355,sK284(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352))
    | ~ sP950(U_13353,U_13352,U_13354,U_13355,U_13356,U_13357) ),
    inference(clausify,[status(thm)],[f_3379_5]) ).

cnf(f_3379_11,plain,
    ( hAPP(U_13356,hAPP(U_13355,sK283(U_13357,U_13356,U_13355,U_13354,U_13353,U_13352))) != c_Groups_Ozero__class_Ozero(U_13352)
    | ~ sP950(U_13353,U_13352,U_13354,U_13355,U_13356,U_13357) ),
    inference(clausify,[status(thm)],[f_3379_5]) ).

fof(f_3380_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_3380_2,plain,
    ! [U_13361,U_13360,U_13359,U_13358] : c_Random__Sequence_Omap(U_13358,U_13359,U_13360,U_13361) = c_Random__Sequence_Obind(U_13358,U_13359,U_13361,hAPP(c_Fun_Ocomp(U_13359,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_13359)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),U_13358,c_Random__Sequence_Osingle(U_13359)),U_13360)),
    inference(variable_rename,[status(thm)],[f_3380_1]) ).

fof(f_3380_3,plain,
    ! [U_13358,U_13361,U_13360,U_13359] : c_Random__Sequence_Omap(U_13358,U_13359,U_13360,U_13361) = c_Random__Sequence_Obind(U_13358,U_13359,U_13361,hAPP(c_Fun_Ocomp(U_13359,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_13359)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),U_13358,c_Random__Sequence_Osingle(U_13359)),U_13360)),
    inference(definitional_conversion,[status(esa)],[f_3380_2]) ).

cnf(f_3380_4,plain,
    c_Random__Sequence_Omap(U_13358,U_13359,U_13360,U_13361) = c_Random__Sequence_Obind(U_13358,U_13359,U_13361,hAPP(c_Fun_Ocomp(U_13359,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_13359)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),U_13358,c_Random__Sequence_Osingle(U_13359)),U_13360)),
    inference(clausify,[status(thm)],[f_3380_3]) ).

fof(f_3381_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_3381_2,plain,
    ! [U_13367,U_13366,U_13365,U_13364,U_13363,U_13362] :
      ( hAPP(U_13365,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13362,tc_HOL_Obool)),U_13366),U_13367)) = hAPP(c_Fun_Ocomp(U_13363,U_13363,U_13363,hAPP(U_13365,U_13366)),hAPP(U_13365,U_13367))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13362),U_13367))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13362),U_13366))
      | ~ c_Finite__Set_Ofolding__idem(U_13362,U_13363,U_13364,U_13365) ),
    inference(variable_rename,[status(thm)],[f_3381_1]) ).

fof(f_3381_3,plain,
    ! [U_13363,U_13364,U_13365,U_13362,U_13366,U_13367] :
      ( hAPP(U_13365,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13362,tc_HOL_Obool)),U_13366),U_13367)) = hAPP(c_Fun_Ocomp(U_13363,U_13363,U_13363,hAPP(U_13365,U_13366)),hAPP(U_13365,U_13367))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13362),U_13367))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13362),U_13366))
      | ~ c_Finite__Set_Ofolding__idem(U_13362,U_13363,U_13364,U_13365) ),
    inference(definitional_conversion,[status(esa)],[f_3381_2]) ).

cnf(f_3381_4,plain,
    ( hAPP(U_13365,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13362,tc_HOL_Obool)),U_13366),U_13367)) = hAPP(c_Fun_Ocomp(U_13363,U_13363,U_13363,hAPP(U_13365,U_13366)),hAPP(U_13365,U_13367))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13362),U_13367))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13362),U_13366))
    | ~ c_Finite__Set_Ofolding__idem(U_13362,U_13363,U_13364,U_13365) ),
    inference(clausify,[status(thm)],[f_3381_3]) ).

fof(f_3382_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_3382_2,plain,
    ! [U_13372,U_13371,U_13370,U_13369,U_13368] :
      ( hAPP(c_Fun_Ocomp(U_13369,U_13369,U_13369,hAPP(U_13370,U_13372)),hAPP(U_13370,U_13372)) = hAPP(U_13370,U_13372)
      | ~ c_Finite__Set_Ofolding__idem(U_13368,U_13369,U_13370,U_13371) ),
    inference(variable_rename,[status(thm)],[f_3382_1]) ).

fof(f_3382_3,plain,
    ! [U_13372,U_13371,U_13370,U_13369] :
      ( ! [U_13368] : ~ c_Finite__Set_Ofolding__idem(U_13368,U_13369,U_13370,U_13371)
      | hAPP(c_Fun_Ocomp(U_13369,U_13369,U_13369,hAPP(U_13370,U_13372)),hAPP(U_13370,U_13372)) = hAPP(U_13370,U_13372) ),
    inference(miniscope,[status(thm)],[f_3382_2]) ).

fof(f_3382_4,plain,
    ! [U_13371,U_13372,U_13370,U_13368,U_13369] :
      ( ~ c_Finite__Set_Ofolding__idem(U_13368,U_13369,U_13370,U_13371)
      | hAPP(c_Fun_Ocomp(U_13369,U_13369,U_13369,hAPP(U_13370,U_13372)),hAPP(U_13370,U_13372)) = hAPP(U_13370,U_13372) ),
    inference(definitional_conversion,[status(esa)],[f_3382_3]) ).

cnf(f_3382_5,plain,
    ( ~ c_Finite__Set_Ofolding__idem(U_13368,U_13369,U_13370,U_13371)
    | hAPP(c_Fun_Ocomp(U_13369,U_13369,U_13369,hAPP(U_13370,U_13372)),hAPP(U_13370,U_13372)) = hAPP(U_13370,U_13372) ),
    inference(clausify,[status(thm)],[f_3382_4]) ).

fof(f_3383_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_3383_2,plain,
    ! [U_13379,U_13378,U_13377,U_13376,U_13375,U_13374,U_13373] :
      ( hAPP(c_Fun_Ocomp(U_13374,U_13374,U_13377,hAPP(U_13375,U_13378)),hAPP(c_Fun_Ocomp(U_13374,U_13374,U_13377,hAPP(U_13375,U_13378)),U_13379)) = hAPP(c_Fun_Ocomp(U_13374,U_13374,U_13377,hAPP(U_13375,U_13378)),U_13379)
      | ~ c_Finite__Set_Ofolding__idem(U_13373,U_13374,U_13375,U_13376) ),
    inference(variable_rename,[status(thm)],[f_3383_1]) ).

fof(f_3383_3,plain,
    ! [U_13379,U_13378,U_13377,U_13376,U_13375,U_13374] :
      ( ! [U_13373] : ~ c_Finite__Set_Ofolding__idem(U_13373,U_13374,U_13375,U_13376)
      | hAPP(c_Fun_Ocomp(U_13374,U_13374,U_13377,hAPP(U_13375,U_13378)),hAPP(c_Fun_Ocomp(U_13374,U_13374,U_13377,hAPP(U_13375,U_13378)),U_13379)) = hAPP(c_Fun_Ocomp(U_13374,U_13374,U_13377,hAPP(U_13375,U_13378)),U_13379) ),
    inference(miniscope,[status(thm)],[f_3383_2]) ).

fof(f_3383_4,plain,
    ! [U_13373,U_13374,U_13375,U_13376,U_13377,U_13378,U_13379] :
      ( ~ c_Finite__Set_Ofolding__idem(U_13373,U_13374,U_13375,U_13376)
      | hAPP(c_Fun_Ocomp(U_13374,U_13374,U_13377,hAPP(U_13375,U_13378)),hAPP(c_Fun_Ocomp(U_13374,U_13374,U_13377,hAPP(U_13375,U_13378)),U_13379)) = hAPP(c_Fun_Ocomp(U_13374,U_13374,U_13377,hAPP(U_13375,U_13378)),U_13379) ),
    inference(definitional_conversion,[status(esa)],[f_3383_3]) ).

cnf(f_3383_5,plain,
    ( ~ c_Finite__Set_Ofolding__idem(U_13373,U_13374,U_13375,U_13376)
    | hAPP(c_Fun_Ocomp(U_13374,U_13374,U_13377,hAPP(U_13375,U_13378)),hAPP(c_Fun_Ocomp(U_13374,U_13374,U_13377,hAPP(U_13375,U_13378)),U_13379)) = hAPP(c_Fun_Ocomp(U_13374,U_13374,U_13377,hAPP(U_13375,U_13378)),U_13379) ),
    inference(clausify,[status(thm)],[f_3383_4]) ).

fof(f_3384_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_3384_2,plain,
    ! [U_13385,U_13384,U_13383,U_13382,U_13381,U_13380] :
      ( hAPP(c_Fun_Ocomp(U_13381,U_13381,U_13381,hAPP(U_13383,U_13384)),hAPP(U_13382,U_13385)) = hAPP(U_13383,U_13384)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13380),U_13385),U_13384))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13380),U_13384))
      | ~ c_Finite__Set_Ofolding__idem(U_13380,U_13381,U_13382,U_13383) ),
    inference(variable_rename,[status(thm)],[f_3384_1]) ).

fof(f_3384_3,plain,
    ! [U_13381,U_13380,U_13382,U_13383,U_13384,U_13385] :
      ( hAPP(c_Fun_Ocomp(U_13381,U_13381,U_13381,hAPP(U_13383,U_13384)),hAPP(U_13382,U_13385)) = hAPP(U_13383,U_13384)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13380),U_13385),U_13384))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13380),U_13384))
      | ~ c_Finite__Set_Ofolding__idem(U_13380,U_13381,U_13382,U_13383) ),
    inference(definitional_conversion,[status(esa)],[f_3384_2]) ).

cnf(f_3384_4,plain,
    ( hAPP(c_Fun_Ocomp(U_13381,U_13381,U_13381,hAPP(U_13383,U_13384)),hAPP(U_13382,U_13385)) = hAPP(U_13383,U_13384)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13380),U_13385),U_13384))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13380),U_13384))
    | ~ c_Finite__Set_Ofolding__idem(U_13380,U_13381,U_13382,U_13383) ),
    inference(clausify,[status(thm)],[f_3384_3]) ).

fof(f_3385_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_3385_2,plain,
    ! [U_13391,U_13390,U_13389,U_13388,U_13387,U_13386] :
      ( hAPP(U_13389,hAPP(hAPP(c_Set_Oinsert(U_13386),U_13391),U_13390)) = hAPP(c_Fun_Ocomp(U_13387,U_13387,U_13387,hAPP(U_13389,U_13390)),hAPP(U_13388,U_13391))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13386),U_13390))
      | ~ c_Finite__Set_Ofolding__idem(U_13386,U_13387,U_13388,U_13389) ),
    inference(variable_rename,[status(thm)],[f_3385_1]) ).

fof(f_3385_3,plain,
    ! [U_13388,U_13386,U_13387,U_13389,U_13390,U_13391] :
      ( hAPP(U_13389,hAPP(hAPP(c_Set_Oinsert(U_13386),U_13391),U_13390)) = hAPP(c_Fun_Ocomp(U_13387,U_13387,U_13387,hAPP(U_13389,U_13390)),hAPP(U_13388,U_13391))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13386),U_13390))
      | ~ c_Finite__Set_Ofolding__idem(U_13386,U_13387,U_13388,U_13389) ),
    inference(definitional_conversion,[status(esa)],[f_3385_2]) ).

cnf(f_3385_4,plain,
    ( hAPP(U_13389,hAPP(hAPP(c_Set_Oinsert(U_13386),U_13391),U_13390)) = hAPP(c_Fun_Ocomp(U_13387,U_13387,U_13387,hAPP(U_13389,U_13390)),hAPP(U_13388,U_13391))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13386),U_13390))
    | ~ c_Finite__Set_Ofolding__idem(U_13386,U_13387,U_13388,U_13389) ),
    inference(clausify,[status(thm)],[f_3385_3]) ).

fof(f_3386_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_3386_2,plain,
    ! [U_13397,U_13396,U_13395,U_13394,U_13393,U_13392] :
      ( hAPP(c_Fun_Ocomp(U_13393,U_13393,U_13393,hAPP(U_13395,U_13396)),hAPP(U_13395,U_13397)) = hAPP(U_13395,U_13396)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13392,tc_HOL_Obool)),U_13397),U_13396))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13392),U_13396))
      | ~ c_Finite__Set_Ofolding__idem(U_13392,U_13393,U_13394,U_13395) ),
    inference(variable_rename,[status(thm)],[f_3386_1]) ).

fof(f_3386_3,plain,
    ! [U_13394,U_13393,U_13392,U_13395,U_13396,U_13397] :
      ( hAPP(c_Fun_Ocomp(U_13393,U_13393,U_13393,hAPP(U_13395,U_13396)),hAPP(U_13395,U_13397)) = hAPP(U_13395,U_13396)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13392,tc_HOL_Obool)),U_13397),U_13396))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13392),U_13396))
      | ~ c_Finite__Set_Ofolding__idem(U_13392,U_13393,U_13394,U_13395) ),
    inference(definitional_conversion,[status(esa)],[f_3386_2]) ).

cnf(f_3386_4,plain,
    ( hAPP(c_Fun_Ocomp(U_13393,U_13393,U_13393,hAPP(U_13395,U_13396)),hAPP(U_13395,U_13397)) = hAPP(U_13395,U_13396)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13392,tc_HOL_Obool)),U_13397),U_13396))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13392),U_13396))
    | ~ c_Finite__Set_Ofolding__idem(U_13392,U_13393,U_13394,U_13395) ),
    inference(clausify,[status(thm)],[f_3386_3]) ).

fof(f_3387_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_3387_2,plain,
    ! [U_13406,U_13405,U_13404,U_13403,U_13402,U_13401,U_13400,U_13399] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13401,U_13399),U_13406),U_13404) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13400,U_13399),U_13405),U_13403)
      | ? [U_13398] :
          ( hAPP(U_13405,U_13398) != hAPP(hAPP(c_Fun_Ocomp(U_13401,U_13399,U_13400,U_13406),U_13402),U_13398)
          & hBOOL(hAPP(hAPP(c_member(U_13400),U_13398),U_13403)) )
      | U_13404 != hAPP(c_Set_Oimage(U_13400,U_13401,U_13402),U_13403)
      | ~ c_Fun_Oinj__on(U_13400,U_13401,U_13402,U_13403)
      | ~ class_Groups_Ocomm__monoid__mult(U_13399) ),
    inference(variable_rename,[status(thm)],[f_3387_1]) ).

fof(f_3387_3,plain,
    ! [U_13406,U_13405,U_13404,U_13403,U_13402,U_13401,U_13400,U_13399] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13401,U_13399),U_13406),U_13404) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13400,U_13399),U_13405),U_13403)
      | ( hAPP(U_13405,sK285(U_13406,U_13405,U_13404,U_13403,U_13402,U_13401,U_13400,U_13399)) != hAPP(hAPP(c_Fun_Ocomp(U_13401,U_13399,U_13400,U_13406),U_13402),sK285(U_13406,U_13405,U_13404,U_13403,U_13402,U_13401,U_13400,U_13399))
        & hBOOL(hAPP(hAPP(c_member(U_13400),sK285(U_13406,U_13405,U_13404,U_13403,U_13402,U_13401,U_13400,U_13399)),U_13403)) )
      | U_13404 != hAPP(c_Set_Oimage(U_13400,U_13401,U_13402),U_13403)
      | ~ c_Fun_Oinj__on(U_13400,U_13401,U_13402,U_13403)
      | ~ class_Groups_Ocomm__monoid__mult(U_13399) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK285]),skolemize(U_13398,sK285(U_13406,U_13405,U_13404,U_13403,U_13402,U_13401,U_13400,U_13399))],[f_3387_2]) ).

fof(f_3387_4,plain,
    ( ! [U_13399,U_13400,U_13401,U_13402,U_13403,U_13404,U_13405,U_13406] :
        ( hAPP(U_13405,sK285(U_13406,U_13405,U_13404,U_13403,U_13402,U_13401,U_13400,U_13399)) != hAPP(hAPP(c_Fun_Ocomp(U_13401,U_13399,U_13400,U_13406),U_13402),sK285(U_13406,U_13405,U_13404,U_13403,U_13402,U_13401,U_13400,U_13399))
        | ~ sP951(U_13399,U_13400,U_13401,U_13402,U_13403,U_13404,U_13405,U_13406) )
    & ! [U_13399,U_13400,U_13401,U_13402,U_13403,U_13404,U_13405,U_13406] :
        ( hBOOL(hAPP(hAPP(c_member(U_13400),sK285(U_13406,U_13405,U_13404,U_13403,U_13402,U_13401,U_13400,U_13399)),U_13403))
        | ~ sP951(U_13399,U_13400,U_13401,U_13402,U_13403,U_13404,U_13405,U_13406) )
    & ! [U_13399,U_13400,U_13401,U_13402,U_13403,U_13404,U_13405,U_13406] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13401,U_13399),U_13406),U_13404) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13400,U_13399),U_13405),U_13403)
        | sP951(U_13399,U_13400,U_13401,U_13402,U_13403,U_13404,U_13405,U_13406)
        | U_13404 != hAPP(c_Set_Oimage(U_13400,U_13401,U_13402),U_13403)
        | ~ c_Fun_Oinj__on(U_13400,U_13401,U_13402,U_13403)
        | ~ class_Groups_Ocomm__monoid__mult(U_13399) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP951])],[f_3387_3]) ).

cnf(f_3387_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13401,U_13399),U_13406),U_13404) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13400,U_13399),U_13405),U_13403)
    | sP951(U_13399,U_13400,U_13401,U_13402,U_13403,U_13404,U_13405,U_13406)
    | U_13404 != hAPP(c_Set_Oimage(U_13400,U_13401,U_13402),U_13403)
    | ~ c_Fun_Oinj__on(U_13400,U_13401,U_13402,U_13403)
    | ~ class_Groups_Ocomm__monoid__mult(U_13399) ),
    inference(clausify,[status(thm)],[f_3387_4]) ).

cnf(f_3387_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13400),sK285(U_13406,U_13405,U_13404,U_13403,U_13402,U_13401,U_13400,U_13399)),U_13403))
    | ~ sP951(U_13399,U_13400,U_13401,U_13402,U_13403,U_13404,U_13405,U_13406) ),
    inference(clausify,[status(thm)],[f_3387_4]) ).

cnf(f_3387_7,plain,
    ( hAPP(U_13405,sK285(U_13406,U_13405,U_13404,U_13403,U_13402,U_13401,U_13400,U_13399)) != hAPP(hAPP(c_Fun_Ocomp(U_13401,U_13399,U_13400,U_13406),U_13402),sK285(U_13406,U_13405,U_13404,U_13403,U_13402,U_13401,U_13400,U_13399))
    | ~ sP951(U_13399,U_13400,U_13401,U_13402,U_13403,U_13404,U_13405,U_13406) ),
    inference(clausify,[status(thm)],[f_3387_4]) ).

fof(f_3388_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_3388_2,plain,
    ! [U_13411,U_13410,U_13409,U_13408,U_13407] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13407,U_13407,c_Groups_Otimes__class_Otimes(U_13407),U_13411,hAPP(hAPP(c_Set_Oinsert(U_13407),U_13408),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13407,tc_HOL_Obool)),U_13409),hAPP(hAPP(c_Set_Oinsert(U_13407),U_13411),c_Orderings_Obot__class_Obot(tc_fun(U_13407,tc_HOL_Obool)))))),U_13410))
      | hBOOL(hAPP(hAPP(c_member(U_13407),U_13408),U_13409))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13407),U_13411),U_13409))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13407,U_13407,c_Groups_Otimes__class_Otimes(U_13407),U_13408,U_13409),U_13410))
      | ~ class_Groups_Oab__semigroup__mult(U_13407) ),
    inference(variable_rename,[status(thm)],[f_3388_1]) ).

fof(f_3388_3,plain,
    ! [U_13408,U_13409,U_13410,U_13411,U_13407] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13407,U_13407,c_Groups_Otimes__class_Otimes(U_13407),U_13411,hAPP(hAPP(c_Set_Oinsert(U_13407),U_13408),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13407,tc_HOL_Obool)),U_13409),hAPP(hAPP(c_Set_Oinsert(U_13407),U_13411),c_Orderings_Obot__class_Obot(tc_fun(U_13407,tc_HOL_Obool)))))),U_13410))
      | hBOOL(hAPP(hAPP(c_member(U_13407),U_13408),U_13409))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13407),U_13411),U_13409))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13407,U_13407,c_Groups_Otimes__class_Otimes(U_13407),U_13408,U_13409),U_13410))
      | ~ class_Groups_Oab__semigroup__mult(U_13407) ),
    inference(definitional_conversion,[status(esa)],[f_3388_2]) ).

cnf(f_3388_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13407,U_13407,c_Groups_Otimes__class_Otimes(U_13407),U_13411,hAPP(hAPP(c_Set_Oinsert(U_13407),U_13408),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13407,tc_HOL_Obool)),U_13409),hAPP(hAPP(c_Set_Oinsert(U_13407),U_13411),c_Orderings_Obot__class_Obot(tc_fun(U_13407,tc_HOL_Obool)))))),U_13410))
    | hBOOL(hAPP(hAPP(c_member(U_13407),U_13408),U_13409))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13407),U_13411),U_13409))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13407,U_13407,c_Groups_Otimes__class_Otimes(U_13407),U_13408,U_13409),U_13410))
    | ~ class_Groups_Oab__semigroup__mult(U_13407) ),
    inference(clausify,[status(thm)],[f_3388_3]) ).

fof(f_3389_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_3389_2,plain,
    ! [U_13417,U_13416,U_13415,U_13414,U_13413] :
      ( ? [U_13412] :
          ( hAPP(U_13416,U_13412) = hAPP(c_Option_Ooption_OSome(U_13413),U_13414)
          & hBOOL(hAPP(hAPP(c_member(U_13415),U_13412),U_13417)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13413),U_13414),c_Map_Oran(U_13415,U_13413,c_Map_Orestrict__map(U_13415,U_13413,U_13416,U_13417)))) ),
    inference(variable_rename,[status(thm)],[f_3389_1]) ).

fof(f_3389_3,plain,
    ! [U_13417,U_13416,U_13415,U_13414,U_13413] :
      ( ( hAPP(U_13416,sK286(U_13417,U_13416,U_13415,U_13414,U_13413)) = hAPP(c_Option_Ooption_OSome(U_13413),U_13414)
        & hBOOL(hAPP(hAPP(c_member(U_13415),sK286(U_13417,U_13416,U_13415,U_13414,U_13413)),U_13417)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13413),U_13414),c_Map_Oran(U_13415,U_13413,c_Map_Orestrict__map(U_13415,U_13413,U_13416,U_13417)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK286]),skolemize(U_13412,sK286(U_13417,U_13416,U_13415,U_13414,U_13413))],[f_3389_2]) ).

fof(f_3389_4,plain,
    ( ! [U_13415,U_13413,U_13414,U_13416,U_13417] :
        ( hAPP(U_13416,sK286(U_13417,U_13416,U_13415,U_13414,U_13413)) = hAPP(c_Option_Ooption_OSome(U_13413),U_13414)
        | ~ sP952(U_13415,U_13413,U_13414,U_13416,U_13417) )
    & ! [U_13415,U_13413,U_13414,U_13416,U_13417] :
        ( hBOOL(hAPP(hAPP(c_member(U_13415),sK286(U_13417,U_13416,U_13415,U_13414,U_13413)),U_13417))
        | ~ sP952(U_13415,U_13413,U_13414,U_13416,U_13417) )
    & ! [U_13415,U_13413,U_13414,U_13416,U_13417] :
        ( sP952(U_13415,U_13413,U_13414,U_13416,U_13417)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13413),U_13414),c_Map_Oran(U_13415,U_13413,c_Map_Orestrict__map(U_13415,U_13413,U_13416,U_13417)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP952])],[f_3389_3]) ).

cnf(f_3389_5,plain,
    ( sP952(U_13415,U_13413,U_13414,U_13416,U_13417)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13413),U_13414),c_Map_Oran(U_13415,U_13413,c_Map_Orestrict__map(U_13415,U_13413,U_13416,U_13417)))) ),
    inference(clausify,[status(thm)],[f_3389_4]) ).

cnf(f_3389_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13415),sK286(U_13417,U_13416,U_13415,U_13414,U_13413)),U_13417))
    | ~ sP952(U_13415,U_13413,U_13414,U_13416,U_13417) ),
    inference(clausify,[status(thm)],[f_3389_4]) ).

cnf(f_3389_7,plain,
    ( hAPP(U_13416,sK286(U_13417,U_13416,U_13415,U_13414,U_13413)) = hAPP(c_Option_Ooption_OSome(U_13413),U_13414)
    | ~ sP952(U_13415,U_13413,U_13414,U_13416,U_13417) ),
    inference(clausify,[status(thm)],[f_3389_4]) ).

fof(f_3390_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_3390_2,plain,
    ! [U_13423,U_13422,U_13421,U_13420,U_13419,U_13418] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13418),U_13422))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13418,U_13419,U_13420,U_13421,U_13422),U_13423)) ),
    inference(variable_rename,[status(thm)],[f_3390_1]) ).

fof(f_3390_3,plain,
    ! [U_13418,U_13420,U_13419,U_13421,U_13422,U_13423] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13418),U_13422))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13418,U_13419,U_13420,U_13421,U_13422),U_13423)) ),
    inference(definitional_conversion,[status(esa)],[f_3390_2]) ).

cnf(f_3390_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13418),U_13422))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13418,U_13419,U_13420,U_13421,U_13422),U_13423)) ),
    inference(clausify,[status(thm)],[f_3390_3]) ).

fof(f_3391_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_3391_2,plain,
    ! [U_13427,U_13426,U_13425,U_13424] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13424,U_13425,U_13426,U_13427,c_Orderings_Obot__class_Obot(tc_fun(U_13424,tc_HOL_Obool))),U_13427)),
    inference(variable_rename,[status(thm)],[f_3391_1]) ).

fof(f_3391_3,plain,
    ! [U_13424,U_13425,U_13426,U_13427] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13424,U_13425,U_13426,U_13427,c_Orderings_Obot__class_Obot(tc_fun(U_13424,tc_HOL_Obool))),U_13427)),
    inference(definitional_conversion,[status(esa)],[f_3391_2]) ).

cnf(f_3391_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13424,U_13425,U_13426,U_13427,c_Orderings_Obot__class_Obot(tc_fun(U_13424,tc_HOL_Obool))),U_13427)),
    inference(clausify,[status(thm)],[f_3391_3]) ).

fof(f_3392_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_3392_2,plain,
    ! [U_13431,U_13430,U_13429,U_13428] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13428,U_13429,U_13430,U_13431,c_Orderings_Obot__class_Obot(tc_fun(U_13428,tc_HOL_Obool))),U_13431)),
    inference(variable_rename,[status(thm)],[f_3392_1]) ).

fof(f_3392_3,plain,
    ! [U_13428,U_13429,U_13430,U_13431] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13428,U_13429,U_13430,U_13431,c_Orderings_Obot__class_Obot(tc_fun(U_13428,tc_HOL_Obool))),U_13431)),
    inference(definitional_conversion,[status(esa)],[f_3392_2]) ).

cnf(f_3392_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13428,U_13429,U_13430,U_13431,c_Orderings_Obot__class_Obot(tc_fun(U_13428,tc_HOL_Obool))),U_13431)),
    inference(clausify,[status(thm)],[f_3392_3]) ).

fof(f_3393_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_3393_2,plain,
    ! [U_13436,U_13435,U_13434,U_13433,U_13432] :
      ( U_13436 = U_13435
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13432,U_13433,U_13434,U_13435,c_Orderings_Obot__class_Obot(tc_fun(U_13432,tc_HOL_Obool))),U_13436)) ),
    inference(variable_rename,[status(thm)],[f_3393_1]) ).

fof(f_3393_3,plain,
    ! [U_13436,U_13435] :
      ( ! [U_13434,U_13433,U_13432] : ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13432,U_13433,U_13434,U_13435,c_Orderings_Obot__class_Obot(tc_fun(U_13432,tc_HOL_Obool))),U_13436))
      | U_13436 = U_13435 ),
    inference(miniscope,[status(thm)],[f_3393_2]) ).

fof(f_3393_4,plain,
    ! [U_13432,U_13433,U_13434,U_13435,U_13436] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13432,U_13433,U_13434,U_13435,c_Orderings_Obot__class_Obot(tc_fun(U_13432,tc_HOL_Obool))),U_13436))
      | U_13436 = U_13435 ),
    inference(definitional_conversion,[status(esa)],[f_3393_3]) ).

cnf(f_3393_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13432,U_13433,U_13434,U_13435,c_Orderings_Obot__class_Obot(tc_fun(U_13432,tc_HOL_Obool))),U_13436))
    | U_13436 = U_13435 ),
    inference(clausify,[status(thm)],[f_3393_4]) ).

fof(f_3394_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_3394_2,plain,
    ! [U_13443,U_13442,U_13441,U_13440,U_13439,U_13438,U_13437] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13437,U_13440,U_13441,U_13442,hAPP(hAPP(c_Set_Oinsert(U_13437),U_13438),U_13439)),hAPP(hAPP(U_13441,U_13438),U_13443)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13437,U_13440,U_13441,U_13442,U_13439),U_13443))
      | hBOOL(hAPP(hAPP(c_member(U_13437),U_13438),U_13439)) ),
    inference(variable_rename,[status(thm)],[f_3394_1]) ).

fof(f_3394_3,plain,
    ! [U_13437,U_13438,U_13439,U_13440,U_13441,U_13442,U_13443] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13437,U_13440,U_13441,U_13442,hAPP(hAPP(c_Set_Oinsert(U_13437),U_13438),U_13439)),hAPP(hAPP(U_13441,U_13438),U_13443)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13437,U_13440,U_13441,U_13442,U_13439),U_13443))
      | hBOOL(hAPP(hAPP(c_member(U_13437),U_13438),U_13439)) ),
    inference(definitional_conversion,[status(esa)],[f_3394_2]) ).

cnf(f_3394_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13437,U_13440,U_13441,U_13442,hAPP(hAPP(c_Set_Oinsert(U_13437),U_13438),U_13439)),hAPP(hAPP(U_13441,U_13438),U_13443)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13437,U_13440,U_13441,U_13442,U_13439),U_13443))
    | hBOOL(hAPP(hAPP(c_member(U_13437),U_13438),U_13439)) ),
    inference(clausify,[status(thm)],[f_3394_3]) ).

fof(f_3395_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_3395_2,plain,
    ! [U_13448,U_13447,U_13446,U_13445,U_13444] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13444,U_13444,c_Groups_Otimes__class_Otimes(U_13444),U_13448,hAPP(hAPP(c_Set_Oinsert(U_13444),U_13445),U_13446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13444),U_13448),U_13447)))
      | hBOOL(hAPP(hAPP(c_member(U_13444),U_13445),U_13446))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13444,U_13444,c_Groups_Otimes__class_Otimes(U_13444),U_13445,U_13446),U_13447))
      | ~ class_Groups_Oab__semigroup__mult(U_13444) ),
    inference(variable_rename,[status(thm)],[f_3395_1]) ).

fof(f_3395_3,plain,
    ! [U_13444,U_13445,U_13446,U_13447,U_13448] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13444,U_13444,c_Groups_Otimes__class_Otimes(U_13444),U_13448,hAPP(hAPP(c_Set_Oinsert(U_13444),U_13445),U_13446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13444),U_13448),U_13447)))
      | hBOOL(hAPP(hAPP(c_member(U_13444),U_13445),U_13446))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13444,U_13444,c_Groups_Otimes__class_Otimes(U_13444),U_13445,U_13446),U_13447))
      | ~ class_Groups_Oab__semigroup__mult(U_13444) ),
    inference(definitional_conversion,[status(esa)],[f_3395_2]) ).

cnf(f_3395_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13444,U_13444,c_Groups_Otimes__class_Otimes(U_13444),U_13448,hAPP(hAPP(c_Set_Oinsert(U_13444),U_13445),U_13446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13444),U_13448),U_13447)))
    | hBOOL(hAPP(hAPP(c_member(U_13444),U_13445),U_13446))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13444,U_13444,c_Groups_Otimes__class_Otimes(U_13444),U_13445,U_13446),U_13447))
    | ~ class_Groups_Oab__semigroup__mult(U_13444) ),
    inference(clausify,[status(thm)],[f_3395_3]) ).

fof(f_3396_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_3396_2,plain,
    ! [U_13455,U_13454,U_13453,U_13452,U_13451,U_13450,U_13449] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13449,U_13450,U_13451,U_13452,U_13453),hAPP(hAPP(U_13451,U_13454),U_13455)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13449),U_13454),U_13453))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13449,U_13450,U_13451,U_13452,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13449,tc_HOL_Obool)),U_13453),hAPP(hAPP(c_Set_Oinsert(U_13449),U_13454),c_Orderings_Obot__class_Obot(tc_fun(U_13449,tc_HOL_Obool))))),U_13455)) ),
    inference(variable_rename,[status(thm)],[f_3396_1]) ).

fof(f_3396_3,plain,
    ! [U_13449,U_13450,U_13451,U_13452,U_13453,U_13454,U_13455] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13449,U_13450,U_13451,U_13452,U_13453),hAPP(hAPP(U_13451,U_13454),U_13455)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13449),U_13454),U_13453))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13449,U_13450,U_13451,U_13452,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13449,tc_HOL_Obool)),U_13453),hAPP(hAPP(c_Set_Oinsert(U_13449),U_13454),c_Orderings_Obot__class_Obot(tc_fun(U_13449,tc_HOL_Obool))))),U_13455)) ),
    inference(definitional_conversion,[status(esa)],[f_3396_2]) ).

cnf(f_3396_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13449,U_13450,U_13451,U_13452,U_13453),hAPP(hAPP(U_13451,U_13454),U_13455)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13449),U_13454),U_13453))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13449,U_13450,U_13451,U_13452,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13449,tc_HOL_Obool)),U_13453),hAPP(hAPP(c_Set_Oinsert(U_13449),U_13454),c_Orderings_Obot__class_Obot(tc_fun(U_13449,tc_HOL_Obool))))),U_13455)) ),
    inference(clausify,[status(thm)],[f_3396_3]) ).

fof(f_3397_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_3397_2,plain,
    ! [U_13460,U_13459,U_13458,U_13457,U_13456] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13456,U_13457,hAPP(hAPP(c_Set_Oinsert(U_13456),U_13458),U_13459)),U_13460))
      | hBOOL(hAPP(hAPP(c_member(U_13456),U_13458),U_13459))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13456,U_13456,U_13457,U_13458,U_13459),U_13460)) ),
    inference(variable_rename,[status(thm)],[f_3397_1]) ).

fof(f_3397_3,plain,
    ! [U_13457,U_13456,U_13458,U_13459,U_13460] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13456,U_13457,hAPP(hAPP(c_Set_Oinsert(U_13456),U_13458),U_13459)),U_13460))
      | hBOOL(hAPP(hAPP(c_member(U_13456),U_13458),U_13459))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13456,U_13456,U_13457,U_13458,U_13459),U_13460)) ),
    inference(definitional_conversion,[status(esa)],[f_3397_2]) ).

cnf(f_3397_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13456,U_13457,hAPP(hAPP(c_Set_Oinsert(U_13456),U_13458),U_13459)),U_13460))
    | hBOOL(hAPP(hAPP(c_member(U_13456),U_13458),U_13459))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13456,U_13456,U_13457,U_13458,U_13459),U_13460)) ),
    inference(clausify,[status(thm)],[f_3397_3]) ).

fof(f_3398_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_3398_2,plain,
    ! [U_13463,U_13462,U_13461] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_13461),U_13462) = U_13463
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13461),U_13462),U_13463) != c_Orderings_Otop__class_Otop(U_13461)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13461),U_13462),U_13463) != c_Orderings_Obot__class_Obot(U_13461)
      | ~ class_Lattices_Oboolean__algebra(U_13461) ),
    inference(variable_rename,[status(thm)],[f_3398_1]) ).

fof(f_3398_3,plain,
    ! [U_13461,U_13462,U_13463] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_13461),U_13462) = U_13463
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13461),U_13462),U_13463) != c_Orderings_Otop__class_Otop(U_13461)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13461),U_13462),U_13463) != c_Orderings_Obot__class_Obot(U_13461)
      | ~ class_Lattices_Oboolean__algebra(U_13461) ),
    inference(definitional_conversion,[status(esa)],[f_3398_2]) ).

cnf(f_3398_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_13461),U_13462) = U_13463
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13461),U_13462),U_13463) != c_Orderings_Otop__class_Otop(U_13461)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13461),U_13462),U_13463) != c_Orderings_Obot__class_Obot(U_13461)
    | ~ class_Lattices_Oboolean__algebra(U_13461) ),
    inference(clausify,[status(thm)],[f_3398_3]) ).

fof(f_3399_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_3399_2,plain,
    ! [U_13469,U_13468,U_13467,U_13466,U_13465] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_13465),U_13468),U_13466) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_13465),U_13469),U_13467)
      | ? [U_13464] :
          ( hAPP(U_13468,U_13464) != hAPP(U_13469,U_13464)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_13464)) )
      | ~ c_Nat__Transfer_Onat__set(U_13467)
      | U_13466 != U_13467
      | ~ class_Groups_Ocomm__monoid__mult(U_13465)
      | ~ class_Groups_Ocomm__monoid__add(U_13465) ),
    inference(variable_rename,[status(thm)],[f_3399_1]) ).

fof(f_3399_3,plain,
    ! [U_13469,U_13468,U_13467,U_13466,U_13465] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_13465),U_13468),U_13466) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_13465),U_13469),U_13467)
      | ( hAPP(U_13468,sK287(U_13469,U_13468,U_13467,U_13466,U_13465)) != hAPP(U_13469,sK287(U_13469,U_13468,U_13467,U_13466,U_13465))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK287(U_13469,U_13468,U_13467,U_13466,U_13465))) )
      | ~ c_Nat__Transfer_Onat__set(U_13467)
      | U_13466 != U_13467
      | ~ class_Groups_Ocomm__monoid__mult(U_13465)
      | ~ class_Groups_Ocomm__monoid__add(U_13465) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK287]),skolemize(U_13464,sK287(U_13469,U_13468,U_13467,U_13466,U_13465))],[f_3399_2]) ).

fof(f_3399_4,plain,
    ( ! [U_13465,U_13466,U_13467,U_13468,U_13469] :
        ( hAPP(U_13468,sK287(U_13469,U_13468,U_13467,U_13466,U_13465)) != hAPP(U_13469,sK287(U_13469,U_13468,U_13467,U_13466,U_13465))
        | ~ sP953(U_13465,U_13466,U_13467,U_13468,U_13469) )
    & ! [U_13465,U_13466,U_13467,U_13468,U_13469] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK287(U_13469,U_13468,U_13467,U_13466,U_13465)))
        | ~ sP953(U_13465,U_13466,U_13467,U_13468,U_13469) )
    & ! [U_13465,U_13466,U_13467,U_13468,U_13469] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_13465),U_13468),U_13466) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_13465),U_13469),U_13467)
        | sP953(U_13465,U_13466,U_13467,U_13468,U_13469)
        | ~ c_Nat__Transfer_Onat__set(U_13467)
        | U_13466 != U_13467
        | ~ class_Groups_Ocomm__monoid__mult(U_13465)
        | ~ class_Groups_Ocomm__monoid__add(U_13465) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP953])],[f_3399_3]) ).

cnf(f_3399_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_13465),U_13468),U_13466) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_13465),U_13469),U_13467)
    | sP953(U_13465,U_13466,U_13467,U_13468,U_13469)
    | ~ c_Nat__Transfer_Onat__set(U_13467)
    | U_13466 != U_13467
    | ~ class_Groups_Ocomm__monoid__mult(U_13465)
    | ~ class_Groups_Ocomm__monoid__add(U_13465) ),
    inference(clausify,[status(thm)],[f_3399_4]) ).

cnf(f_3399_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK287(U_13469,U_13468,U_13467,U_13466,U_13465)))
    | ~ sP953(U_13465,U_13466,U_13467,U_13468,U_13469) ),
    inference(clausify,[status(thm)],[f_3399_4]) ).

cnf(f_3399_7,plain,
    ( hAPP(U_13468,sK287(U_13469,U_13468,U_13467,U_13466,U_13465)) != hAPP(U_13469,sK287(U_13469,U_13468,U_13467,U_13466,U_13465))
    | ~ sP953(U_13465,U_13466,U_13467,U_13468,U_13469) ),
    inference(clausify,[status(thm)],[f_3399_4]) ).

fof(f_3400_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_3400_2,plain,
    ! [U_13471,U_13470] : hBOOL(hAPP(hAPP(c_member(U_13470),U_13471),c_Orderings_Otop__class_Otop(tc_fun(U_13470,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3400_1]) ).

fof(f_3400_3,plain,
    ! [U_13470,U_13471] : hBOOL(hAPP(hAPP(c_member(U_13470),U_13471),c_Orderings_Otop__class_Otop(tc_fun(U_13470,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3400_2]) ).

cnf(f_3400_4,plain,
    hBOOL(hAPP(hAPP(c_member(U_13470),U_13471),c_Orderings_Otop__class_Otop(tc_fun(U_13470,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3400_3]) ).

fof(f_3401_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_3401_2,plain,
    ! [U_13472] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13472),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(U_13472)),c_Option_Ooption_ONone(U_13472)),hAPP(c_Set_Oimage(U_13472,tc_Option_Ooption(U_13472),c_Option_Ooption_OSome(U_13472)),c_Orderings_Otop__class_Otop(tc_fun(U_13472,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3401_1]) ).

fof(f_3401_3,plain,
    ! [U_13472] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13472),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(U_13472)),c_Option_Ooption_ONone(U_13472)),hAPP(c_Set_Oimage(U_13472,tc_Option_Ooption(U_13472),c_Option_Ooption_OSome(U_13472)),c_Orderings_Otop__class_Otop(tc_fun(U_13472,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3401_2]) ).

cnf(f_3401_4,plain,
    c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13472),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(U_13472)),c_Option_Ooption_ONone(U_13472)),hAPP(c_Set_Oimage(U_13472,tc_Option_Ooption(U_13472),c_Option_Ooption_OSome(U_13472)),c_Orderings_Otop__class_Otop(tc_fun(U_13472,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3401_3]) ).

fof(f_3402_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_3402_2,plain,
    ! [U_13477,U_13476,U_13475,U_13474,U_13473] : hAPP(c_Set_Oimage(U_13473,U_13474,hAPP(hAPP(c_COMBB(U_13475,U_13474,U_13473),U_13476),U_13477)),c_Orderings_Otop__class_Otop(tc_fun(U_13473,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_13475,U_13474,U_13476),hAPP(c_Set_Oimage(U_13473,U_13475,U_13477),c_Orderings_Otop__class_Otop(tc_fun(U_13473,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3402_1]) ).

fof(f_3402_3,plain,
    ! [U_13473,U_13474,U_13475,U_13476,U_13477] : hAPP(c_Set_Oimage(U_13473,U_13474,hAPP(hAPP(c_COMBB(U_13475,U_13474,U_13473),U_13476),U_13477)),c_Orderings_Otop__class_Otop(tc_fun(U_13473,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_13475,U_13474,U_13476),hAPP(c_Set_Oimage(U_13473,U_13475,U_13477),c_Orderings_Otop__class_Otop(tc_fun(U_13473,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3402_2]) ).

cnf(f_3402_4,plain,
    hAPP(c_Set_Oimage(U_13473,U_13474,hAPP(hAPP(c_COMBB(U_13475,U_13474,U_13473),U_13476),U_13477)),c_Orderings_Otop__class_Otop(tc_fun(U_13473,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_13475,U_13474,U_13476),hAPP(c_Set_Oimage(U_13473,U_13475,U_13477),c_Orderings_Otop__class_Otop(tc_fun(U_13473,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3402_3]) ).

fof(f_3403_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_3403_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_3403_1]) ).

cnf(f_3403_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_3403_2]) ).

fof(f_3404_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_3404_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_3404_1]) ).

cnf(f_3404_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_3404_2]) ).

fof(f_3405_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_3405_2,plain,
    ! [U_13482,U_13481,U_13480,U_13479,U_13478] :
      ( ( ( hAPP(U_13480,U_13481) = hAPP(U_13480,U_13482)
          | U_13481 != U_13482 )
        & ( U_13481 = U_13482
          | hAPP(U_13480,U_13481) != hAPP(U_13480,U_13482) ) )
      | ~ c_Fun_Oinj__on(U_13478,U_13479,U_13480,c_Orderings_Otop__class_Otop(tc_fun(U_13478,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3405_1]) ).

fof(f_3405_3,plain,
    ! [U_13482,U_13481,U_13480] :
      ( ! [U_13479,U_13478] : ~ c_Fun_Oinj__on(U_13478,U_13479,U_13480,c_Orderings_Otop__class_Otop(tc_fun(U_13478,tc_HOL_Obool)))
      | ( ( hAPP(U_13480,U_13481) = hAPP(U_13480,U_13482)
          | U_13481 != U_13482 )
        & ( U_13481 = U_13482
          | hAPP(U_13480,U_13481) != hAPP(U_13480,U_13482) ) ) ),
    inference(miniscope,[status(thm)],[f_3405_2]) ).

fof(f_3405_4,plain,
    ( ! [U_13480,U_13481,U_13482] :
        ( hAPP(U_13480,U_13481) = hAPP(U_13480,U_13482)
        | U_13481 != U_13482
        | ~ sP954(U_13480,U_13481,U_13482) )
    & ! [U_13480,U_13481,U_13482] :
        ( U_13481 = U_13482
        | hAPP(U_13480,U_13481) != hAPP(U_13480,U_13482)
        | ~ sP954(U_13480,U_13481,U_13482) )
    & ! [U_13478,U_13479,U_13480,U_13481,U_13482] :
        ( ~ c_Fun_Oinj__on(U_13478,U_13479,U_13480,c_Orderings_Otop__class_Otop(tc_fun(U_13478,tc_HOL_Obool)))
        | sP954(U_13480,U_13481,U_13482) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP954])],[f_3405_3]) ).

cnf(f_3405_5,plain,
    ( ~ c_Fun_Oinj__on(U_13478,U_13479,U_13480,c_Orderings_Otop__class_Otop(tc_fun(U_13478,tc_HOL_Obool)))
    | sP954(U_13480,U_13481,U_13482) ),
    inference(clausify,[status(thm)],[f_3405_4]) ).

cnf(f_3405_6,plain,
    ( U_13481 = U_13482
    | hAPP(U_13480,U_13481) != hAPP(U_13480,U_13482)
    | ~ sP954(U_13480,U_13481,U_13482) ),
    inference(clausify,[status(thm)],[f_3405_4]) ).

cnf(f_3405_7,plain,
    ( hAPP(U_13480,U_13481) = hAPP(U_13480,U_13482)
    | U_13481 != U_13482
    | ~ sP954(U_13480,U_13481,U_13482) ),
    inference(clausify,[status(thm)],[f_3405_4]) ).

fof(f_3406_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_3406_2,plain,
    ! [U_13487,U_13486,U_13485,U_13484,U_13483] :
      ( U_13486 = U_13487
      | hAPP(U_13485,U_13486) != hAPP(U_13485,U_13487)
      | ~ c_Fun_Oinj__on(U_13483,U_13484,U_13485,c_Orderings_Otop__class_Otop(tc_fun(U_13483,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3406_1]) ).

fof(f_3406_3,plain,
    ! [U_13487,U_13486,U_13485] :
      ( ! [U_13484,U_13483] : ~ c_Fun_Oinj__on(U_13483,U_13484,U_13485,c_Orderings_Otop__class_Otop(tc_fun(U_13483,tc_HOL_Obool)))
      | U_13486 = U_13487
      | hAPP(U_13485,U_13486) != hAPP(U_13485,U_13487) ),
    inference(miniscope,[status(thm)],[f_3406_2]) ).

fof(f_3406_4,plain,
    ! [U_13486,U_13487,U_13485,U_13483,U_13484] :
      ( ~ c_Fun_Oinj__on(U_13483,U_13484,U_13485,c_Orderings_Otop__class_Otop(tc_fun(U_13483,tc_HOL_Obool)))
      | U_13486 = U_13487
      | hAPP(U_13485,U_13486) != hAPP(U_13485,U_13487) ),
    inference(definitional_conversion,[status(esa)],[f_3406_3]) ).

cnf(f_3406_5,plain,
    ( ~ c_Fun_Oinj__on(U_13483,U_13484,U_13485,c_Orderings_Otop__class_Otop(tc_fun(U_13483,tc_HOL_Obool)))
    | U_13486 = U_13487
    | hAPP(U_13485,U_13486) != hAPP(U_13485,U_13487) ),
    inference(clausify,[status(thm)],[f_3406_4]) ).

fof(f_3407_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_3407_2,plain,
    ! [U_13489,U_13488] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13488,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13488,tc_HOL_Obool))),U_13489) = U_13489,
    inference(variable_rename,[status(thm)],[f_3407_1]) ).

fof(f_3407_3,plain,
    ! [U_13489,U_13488] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13488,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13488,tc_HOL_Obool))),U_13489) = U_13489,
    inference(definitional_conversion,[status(esa)],[f_3407_2]) ).

cnf(f_3407_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13488,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13488,tc_HOL_Obool))),U_13489) = U_13489,
    inference(clausify,[status(thm)],[f_3407_3]) ).

fof(f_3408_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_3408_2,plain,
    ! [U_13491,U_13490] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13490,tc_HOL_Obool)),U_13491),c_Orderings_Otop__class_Otop(tc_fun(U_13490,tc_HOL_Obool))) = U_13491,
    inference(variable_rename,[status(thm)],[f_3408_1]) ).

fof(f_3408_3,plain,
    ! [U_13490,U_13491] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13490,tc_HOL_Obool)),U_13491),c_Orderings_Otop__class_Otop(tc_fun(U_13490,tc_HOL_Obool))) = U_13491,
    inference(definitional_conversion,[status(esa)],[f_3408_2]) ).

cnf(f_3408_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13490,tc_HOL_Obool)),U_13491),c_Orderings_Otop__class_Otop(tc_fun(U_13490,tc_HOL_Obool))) = U_13491,
    inference(clausify,[status(thm)],[f_3408_3]) ).

fof(f_3409_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_3409_2,plain,
    ! [U_13493,U_13492] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13492),c_Orderings_Otop__class_Otop(U_13492)),U_13493) = U_13493
      | ~ class_Lattices_Obounded__lattice__top(U_13492) ),
    inference(variable_rename,[status(thm)],[f_3409_1]) ).

fof(f_3409_3,plain,
    ! [U_13492,U_13493] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13492),c_Orderings_Otop__class_Otop(U_13492)),U_13493) = U_13493
      | ~ class_Lattices_Obounded__lattice__top(U_13492) ),
    inference(definitional_conversion,[status(esa)],[f_3409_2]) ).

cnf(f_3409_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13492),c_Orderings_Otop__class_Otop(U_13492)),U_13493) = U_13493
    | ~ class_Lattices_Obounded__lattice__top(U_13492) ),
    inference(clausify,[status(thm)],[f_3409_3]) ).

fof(f_3410_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_3410_2,plain,
    ! [U_13495,U_13494] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13494),U_13495),c_Orderings_Otop__class_Otop(U_13494)) = U_13495
      | ~ class_Lattices_Obounded__lattice__top(U_13494) ),
    inference(variable_rename,[status(thm)],[f_3410_1]) ).

fof(f_3410_3,plain,
    ! [U_13494,U_13495] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13494),U_13495),c_Orderings_Otop__class_Otop(U_13494)) = U_13495
      | ~ class_Lattices_Obounded__lattice__top(U_13494) ),
    inference(definitional_conversion,[status(esa)],[f_3410_2]) ).

cnf(f_3410_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13494),U_13495),c_Orderings_Otop__class_Otop(U_13494)) = U_13495
    | ~ class_Lattices_Obounded__lattice__top(U_13494) ),
    inference(clausify,[status(thm)],[f_3410_3]) ).

fof(f_3411_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_3411_2,plain,
    ! [U_13498,U_13497,U_13496] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13496),U_13497),U_13498) = c_Orderings_Otop__class_Otop(U_13496)
          | U_13498 != c_Orderings_Otop__class_Otop(U_13496)
          | U_13497 != c_Orderings_Otop__class_Otop(U_13496) )
        & ( ( U_13498 = c_Orderings_Otop__class_Otop(U_13496)
            & U_13497 = c_Orderings_Otop__class_Otop(U_13496) )
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13496),U_13497),U_13498) != c_Orderings_Otop__class_Otop(U_13496) ) )
      | ~ class_Lattices_Obounded__lattice__top(U_13496) ),
    inference(variable_rename,[status(thm)],[f_3411_1]) ).

fof(f_3411_3,plain,
    ( ! [U_13496,U_13497,U_13498] :
        ( U_13498 = c_Orderings_Otop__class_Otop(U_13496)
        | ~ sP955(U_13496,U_13497,U_13498) )
    & ! [U_13496,U_13497,U_13498] :
        ( U_13497 = c_Orderings_Otop__class_Otop(U_13496)
        | ~ sP955(U_13496,U_13497,U_13498) )
    & ! [U_13496,U_13497,U_13498] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13496),U_13497),U_13498) = c_Orderings_Otop__class_Otop(U_13496)
        | U_13498 != c_Orderings_Otop__class_Otop(U_13496)
        | U_13497 != c_Orderings_Otop__class_Otop(U_13496)
        | ~ sP956(U_13496,U_13497,U_13498) )
    & ! [U_13496,U_13497,U_13498] :
        ( sP955(U_13496,U_13497,U_13498)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13496),U_13497),U_13498) != c_Orderings_Otop__class_Otop(U_13496)
        | ~ sP956(U_13496,U_13497,U_13498) )
    & ! [U_13496,U_13497,U_13498] :
        ( sP956(U_13496,U_13497,U_13498)
        | ~ class_Lattices_Obounded__lattice__top(U_13496) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP955,sP956])],[f_3411_2]) ).

cnf(f_3411_4,plain,
    ( sP956(U_13496,U_13497,U_13498)
    | ~ class_Lattices_Obounded__lattice__top(U_13496) ),
    inference(clausify,[status(thm)],[f_3411_3]) ).

cnf(f_3411_5,plain,
    ( sP955(U_13496,U_13497,U_13498)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13496),U_13497),U_13498) != c_Orderings_Otop__class_Otop(U_13496)
    | ~ sP956(U_13496,U_13497,U_13498) ),
    inference(clausify,[status(thm)],[f_3411_3]) ).

cnf(f_3411_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13496),U_13497),U_13498) = c_Orderings_Otop__class_Otop(U_13496)
    | U_13498 != c_Orderings_Otop__class_Otop(U_13496)
    | U_13497 != c_Orderings_Otop__class_Otop(U_13496)
    | ~ sP956(U_13496,U_13497,U_13498) ),
    inference(clausify,[status(thm)],[f_3411_3]) ).

cnf(f_3411_7,plain,
    ( U_13497 = c_Orderings_Otop__class_Otop(U_13496)
    | ~ sP955(U_13496,U_13497,U_13498) ),
    inference(clausify,[status(thm)],[f_3411_3]) ).

cnf(f_3411_8,plain,
    ( U_13498 = c_Orderings_Otop__class_Otop(U_13496)
    | ~ sP955(U_13496,U_13497,U_13498) ),
    inference(clausify,[status(thm)],[f_3411_3]) ).

fof(f_3412_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_3412_2,plain,
    ! [U_13500,U_13499] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13499),c_Orderings_Otop__class_Otop(U_13499)),U_13500) = c_Orderings_Otop__class_Otop(U_13499)
      | ~ class_Lattices_Obounded__lattice__top(U_13499) ),
    inference(variable_rename,[status(thm)],[f_3412_1]) ).

fof(f_3412_3,plain,
    ! [U_13499,U_13500] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13499),c_Orderings_Otop__class_Otop(U_13499)),U_13500) = c_Orderings_Otop__class_Otop(U_13499)
      | ~ class_Lattices_Obounded__lattice__top(U_13499) ),
    inference(definitional_conversion,[status(esa)],[f_3412_2]) ).

cnf(f_3412_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13499),c_Orderings_Otop__class_Otop(U_13499)),U_13500) = c_Orderings_Otop__class_Otop(U_13499)
    | ~ class_Lattices_Obounded__lattice__top(U_13499) ),
    inference(clausify,[status(thm)],[f_3412_3]) ).

fof(f_3413_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_3413_2,plain,
    ! [U_13502,U_13501] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13501),U_13502),c_Orderings_Otop__class_Otop(U_13501)) = c_Orderings_Otop__class_Otop(U_13501)
      | ~ class_Lattices_Obounded__lattice__top(U_13501) ),
    inference(variable_rename,[status(thm)],[f_3413_1]) ).

fof(f_3413_3,plain,
    ! [U_13501,U_13502] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13501),U_13502),c_Orderings_Otop__class_Otop(U_13501)) = c_Orderings_Otop__class_Otop(U_13501)
      | ~ class_Lattices_Obounded__lattice__top(U_13501) ),
    inference(definitional_conversion,[status(esa)],[f_3413_2]) ).

cnf(f_3413_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13501),U_13502),c_Orderings_Otop__class_Otop(U_13501)) = c_Orderings_Otop__class_Otop(U_13501)
    | ~ class_Lattices_Obounded__lattice__top(U_13501) ),
    inference(clausify,[status(thm)],[f_3413_3]) ).

fof(f_3414_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_3414_2,plain,
    ! [U_13504,U_13503] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13503,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13503,tc_HOL_Obool))),U_13504) = c_Orderings_Otop__class_Otop(tc_fun(U_13503,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3414_1]) ).

fof(f_3414_3,plain,
    ! [U_13503,U_13504] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13503,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13503,tc_HOL_Obool))),U_13504) = c_Orderings_Otop__class_Otop(tc_fun(U_13503,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3414_2]) ).

cnf(f_3414_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13503,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13503,tc_HOL_Obool))),U_13504) = c_Orderings_Otop__class_Otop(tc_fun(U_13503,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3414_3]) ).

fof(f_3415_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_3415_2,plain,
    ! [U_13506,U_13505] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13505,tc_HOL_Obool)),U_13506),c_Orderings_Otop__class_Otop(tc_fun(U_13505,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13505,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3415_1]) ).

fof(f_3415_3,plain,
    ! [U_13505,U_13506] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13505,tc_HOL_Obool)),U_13506),c_Orderings_Otop__class_Otop(tc_fun(U_13505,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13505,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3415_2]) ).

cnf(f_3415_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13505,tc_HOL_Obool)),U_13506),c_Orderings_Otop__class_Otop(tc_fun(U_13505,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13505,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3415_3]) ).

fof(f_3416_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_3416_2,plain,
    ! [U_13507] : c_Orderings_Otop__class_Otop(tc_fun(U_13507,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_13507,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3416_1]) ).

fof(f_3416_3,plain,
    ! [U_13507] : c_Orderings_Otop__class_Otop(tc_fun(U_13507,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_13507,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3416_2]) ).

cnf(f_3416_4,plain,
    c_Orderings_Otop__class_Otop(tc_fun(U_13507,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_13507,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3416_3]) ).

fof(f_3417_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_3417_2,plain,
    ! [U_13510,U_13509,U_13508] :
      ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_13509,U_13508)),U_13510) = c_Orderings_Otop__class_Otop(U_13508)
      | ~ class_Orderings_Otop(U_13508) ),
    inference(variable_rename,[status(thm)],[f_3417_1]) ).

fof(f_3417_3,plain,
    ! [U_13508,U_13509,U_13510] :
      ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_13509,U_13508)),U_13510) = c_Orderings_Otop__class_Otop(U_13508)
      | ~ class_Orderings_Otop(U_13508) ),
    inference(definitional_conversion,[status(esa)],[f_3417_2]) ).

cnf(f_3417_4,plain,
    ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_13509,U_13508)),U_13510) = c_Orderings_Otop__class_Otop(U_13508)
    | ~ class_Orderings_Otop(U_13508) ),
    inference(clausify,[status(thm)],[f_3417_3]) ).

fof(f_3418_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_3418_2,plain,
    ! [U_13512,U_13511] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13511,tc_HOL_Obool)),U_13512),c_Orderings_Otop__class_Otop(tc_fun(U_13511,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3418_1]) ).

fof(f_3418_3,plain,
    ! [U_13511,U_13512] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13511,tc_HOL_Obool)),U_13512),c_Orderings_Otop__class_Otop(tc_fun(U_13511,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3418_2]) ).

cnf(f_3418_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13511,tc_HOL_Obool)),U_13512),c_Orderings_Otop__class_Otop(tc_fun(U_13511,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3418_3]) ).

fof(f_3419_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_3419_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_3419_1]) ).

cnf(f_3419_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_3419_2]) ).

fof(f_3420_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_3420_2,plain,
    ! [U_13514,U_13513] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13513),U_13514),c_Orderings_Otop__class_Otop(U_13513)))
      | ~ class_Orderings_Otop(U_13513) ),
    inference(variable_rename,[status(thm)],[f_3420_1]) ).

fof(f_3420_3,plain,
    ! [U_13513,U_13514] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13513),U_13514),c_Orderings_Otop__class_Otop(U_13513)))
      | ~ class_Orderings_Otop(U_13513) ),
    inference(definitional_conversion,[status(esa)],[f_3420_2]) ).

cnf(f_3420_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13513),U_13514),c_Orderings_Otop__class_Otop(U_13513)))
    | ~ class_Orderings_Otop(U_13513) ),
    inference(clausify,[status(thm)],[f_3420_3]) ).

fof(f_3421_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_3421_2,plain,
    ! [U_13516,U_13515] : c_Sum__Type_OPlus(U_13515,U_13516,c_Orderings_Otop__class_Otop(tc_fun(U_13515,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13516,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13515,U_13516),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3421_1]) ).

fof(f_3421_3,plain,
    ! [U_13515,U_13516] : c_Sum__Type_OPlus(U_13515,U_13516,c_Orderings_Otop__class_Otop(tc_fun(U_13515,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13516,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13515,U_13516),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3421_2]) ).

cnf(f_3421_4,plain,
    c_Sum__Type_OPlus(U_13515,U_13516,c_Orderings_Otop__class_Otop(tc_fun(U_13515,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13516,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13515,U_13516),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3421_3]) ).

fof(f_3422_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_3422_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_3422_1]) ).

cnf(f_3422_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_3422_2]) ).

fof(f_3423_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_3423_2,plain,
    ! [U_13517] : hAPP(c_Set_OPow(U_13517),c_Orderings_Otop__class_Otop(tc_fun(U_13517,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13517,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3423_1]) ).

fof(f_3423_3,plain,
    ! [U_13517] : hAPP(c_Set_OPow(U_13517),c_Orderings_Otop__class_Otop(tc_fun(U_13517,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13517,tc_HOL_Obool),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3423_2]) ).

cnf(f_3423_4,plain,
    hAPP(c_Set_OPow(U_13517),c_Orderings_Otop__class_Otop(tc_fun(U_13517,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13517,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3423_3]) ).

fof(f_3424_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_3424_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_3424_1]) ).

cnf(f_3424_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_3424_2]) ).

fof(f_3425_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_3425_2,plain,
    ! [U_13519,U_13518] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13518,U_13519)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13518,U_13519),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13519),c_Orderings_Otop__class_Otop(tc_fun(U_13519,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13518),c_Orderings_Otop__class_Otop(tc_fun(U_13518,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3425_1]) ).

fof(f_3425_3,plain,
    ! [U_13518,U_13519] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13518,U_13519)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13518,U_13519),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13519),c_Orderings_Otop__class_Otop(tc_fun(U_13519,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13518),c_Orderings_Otop__class_Otop(tc_fun(U_13518,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3425_2]) ).

cnf(f_3425_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13518,U_13519)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13518,U_13519),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13519),c_Orderings_Otop__class_Otop(tc_fun(U_13519,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13518),c_Orderings_Otop__class_Otop(tc_fun(U_13518,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3425_3]) ).

fof(f_3426_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_3426_2,plain,
    ! [U_13521,U_13520] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13521),c_Orderings_Otop__class_Otop(tc_fun(U_13521,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13520,U_13521)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13520,U_13521),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3426_1]) ).

fof(f_3426_3,plain,
    ! [U_13521] :
      ( ! [U_13520] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13520,U_13521)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13520,U_13521),tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13521),c_Orderings_Otop__class_Otop(tc_fun(U_13521,tc_HOL_Obool)))) ),
    inference(miniscope,[status(thm)],[f_3426_2]) ).

fof(f_3426_4,plain,
    ! [U_13520,U_13521] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13520,U_13521)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13520,U_13521),tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13521),c_Orderings_Otop__class_Otop(tc_fun(U_13521,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3426_3]) ).

cnf(f_3426_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13520,U_13521)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13520,U_13521),tc_HOL_Obool))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13521),c_Orderings_Otop__class_Otop(tc_fun(U_13521,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3426_4]) ).

fof(f_3427_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_3427_2,plain,
    ! [U_13523,U_13522] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13522,U_13523)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13522,U_13523),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13523),c_Orderings_Otop__class_Otop(tc_fun(U_13523,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13522),c_Orderings_Otop__class_Otop(tc_fun(U_13522,tc_HOL_Obool)))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13523),c_Orderings_Otop__class_Otop(tc_fun(U_13523,tc_HOL_Obool))))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13522),c_Orderings_Otop__class_Otop(tc_fun(U_13522,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13522,U_13523)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13522,U_13523),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_3427_1]) ).

fof(f_3427_3,plain,
    ( ! [U_13527,U_13525] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13525,U_13527)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13525,U_13527),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13527),c_Orderings_Otop__class_Otop(tc_fun(U_13527,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13525),c_Orderings_Otop__class_Otop(tc_fun(U_13525,tc_HOL_Obool)))) )
    & ! [U_13526,U_13524] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13526),c_Orderings_Otop__class_Otop(tc_fun(U_13526,tc_HOL_Obool))))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13524),c_Orderings_Otop__class_Otop(tc_fun(U_13524,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13524,U_13526)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13524,U_13526),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_3427_2]) ).

fof(f_3427_4,plain,
    ( ! [U_13526,U_13524] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13526),c_Orderings_Otop__class_Otop(tc_fun(U_13526,tc_HOL_Obool))))
        | ~ sP957(U_13526,U_13524) )
    & ! [U_13526,U_13524] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13524),c_Orderings_Otop__class_Otop(tc_fun(U_13524,tc_HOL_Obool))))
        | ~ sP957(U_13526,U_13524) )
    & ! [U_13525,U_13527] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13525,U_13527)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13525,U_13527),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13527),c_Orderings_Otop__class_Otop(tc_fun(U_13527,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13525),c_Orderings_Otop__class_Otop(tc_fun(U_13525,tc_HOL_Obool)))) )
    & ! [U_13526,U_13524] :
        ( sP957(U_13526,U_13524)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13524,U_13526)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13524,U_13526),tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP957])],[f_3427_3]) ).

cnf(f_3427_5,plain,
    ( sP957(U_13526,U_13524)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13524,U_13526)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13524,U_13526),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3427_4]) ).

cnf(f_3427_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13525,U_13527)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13525,U_13527),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13527),c_Orderings_Otop__class_Otop(tc_fun(U_13527,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13525),c_Orderings_Otop__class_Otop(tc_fun(U_13525,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3427_4]) ).

cnf(f_3427_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13524),c_Orderings_Otop__class_Otop(tc_fun(U_13524,tc_HOL_Obool))))
    | ~ sP957(U_13526,U_13524) ),
    inference(clausify,[status(thm)],[f_3427_4]) ).

cnf(f_3427_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13526),c_Orderings_Otop__class_Otop(tc_fun(U_13526,tc_HOL_Obool))))
    | ~ sP957(U_13526,U_13524) ),
    inference(clausify,[status(thm)],[f_3427_4]) ).

fof(f_3428_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_3428_2,plain,
    ! [U_13528] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13528)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13528),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13528),c_Orderings_Otop__class_Otop(tc_fun(U_13528,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13528),c_Orderings_Otop__class_Otop(tc_fun(U_13528,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13528)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13528),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_3428_1]) ).

fof(f_3428_3,plain,
    ( ! [U_13530] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13530)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13530),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13530),c_Orderings_Otop__class_Otop(tc_fun(U_13530,tc_HOL_Obool)))) )
    & ! [U_13529] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13529),c_Orderings_Otop__class_Otop(tc_fun(U_13529,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13529)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13529),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_3428_2]) ).

fof(f_3428_4,plain,
    ( ! [U_13530] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13530)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13530),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13530),c_Orderings_Otop__class_Otop(tc_fun(U_13530,tc_HOL_Obool)))) )
    & ! [U_13529] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13529),c_Orderings_Otop__class_Otop(tc_fun(U_13529,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13529)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13529),tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3428_3]) ).

cnf(f_3428_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13529),c_Orderings_Otop__class_Otop(tc_fun(U_13529,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13529)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13529),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3428_4]) ).

cnf(f_3428_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13530)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13530),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13530),c_Orderings_Otop__class_Otop(tc_fun(U_13530,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3428_4]) ).

fof(f_3429_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_3429_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_3429_1]) ).

cnf(f_3429_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_3429_2]) ).

fof(f_3430_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_3430_2,plain,
    ! [U_13531] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13531),c_Orderings_Otop__class_Otop(tc_fun(U_13531,tc_HOL_Obool))))
      | ~ class_Finite__Set_Ofinite(U_13531) ),
    inference(variable_rename,[status(thm)],[f_3430_1]) ).

fof(f_3430_3,plain,
    ! [U_13531] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13531),c_Orderings_Otop__class_Otop(tc_fun(U_13531,tc_HOL_Obool))))
      | ~ class_Finite__Set_Ofinite(U_13531) ),
    inference(definitional_conversion,[status(esa)],[f_3430_2]) ).

cnf(f_3430_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13531),c_Orderings_Otop__class_Otop(tc_fun(U_13531,tc_HOL_Obool))))
    | ~ class_Finite__Set_Ofinite(U_13531) ),
    inference(clausify,[status(thm)],[f_3430_3]) ).

fof(f_3431_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_3431_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_3431_1]) ).

cnf(f_3431_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_3431_2]) ).

fof(f_3432_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_3432_2,plain,
    ! [U_13534,U_13533,U_13532] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13532,U_13533,c_Orderings_Obot__class_Obot(tc_fun(U_13532,tc_HOL_Obool))),U_13534)),
    inference(variable_rename,[status(thm)],[f_3432_1]) ).

fof(f_3432_3,plain,
    ! [U_13532,U_13533,U_13534] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13532,U_13533,c_Orderings_Obot__class_Obot(tc_fun(U_13532,tc_HOL_Obool))),U_13534)),
    inference(definitional_conversion,[status(esa)],[f_3432_2]) ).

cnf(f_3432_4,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13532,U_13533,c_Orderings_Obot__class_Obot(tc_fun(U_13532,tc_HOL_Obool))),U_13534)),
    inference(clausify,[status(thm)],[f_3432_3]) ).

fof(f_3433_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_3433_2,plain,
    ! [U_13538,U_13537,U_13536,U_13535] :
      ( U_13537 != c_Orderings_Obot__class_Obot(tc_fun(U_13535,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13535,U_13536,U_13537),U_13538)) ),
    inference(variable_rename,[status(thm)],[f_3433_1]) ).

fof(f_3433_3,plain,
    ! [U_13535,U_13536,U_13537,U_13538] :
      ( U_13537 != c_Orderings_Obot__class_Obot(tc_fun(U_13535,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13535,U_13536,U_13537),U_13538)) ),
    inference(definitional_conversion,[status(esa)],[f_3433_2]) ).

cnf(f_3433_4,plain,
    ( U_13537 != c_Orderings_Obot__class_Obot(tc_fun(U_13535,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13535,U_13536,U_13537),U_13538)) ),
    inference(clausify,[status(thm)],[f_3433_3]) ).

fof(f_3434_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_3434_2,plain,
    ! [U_13542,U_13541,U_13540,U_13539] : hBOOL(hAPP(hAPP(c_member(U_13539),hAPP(U_13540,U_13541)),hAPP(c_Set_Oimage(U_13542,U_13539,U_13540),c_Orderings_Otop__class_Otop(tc_fun(U_13542,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3434_1]) ).

fof(f_3434_3,plain,
    ! [U_13539,U_13540,U_13541,U_13542] : hBOOL(hAPP(hAPP(c_member(U_13539),hAPP(U_13540,U_13541)),hAPP(c_Set_Oimage(U_13542,U_13539,U_13540),c_Orderings_Otop__class_Otop(tc_fun(U_13542,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3434_2]) ).

cnf(f_3434_4,plain,
    hBOOL(hAPP(hAPP(c_member(U_13539),hAPP(U_13540,U_13541)),hAPP(c_Set_Oimage(U_13542,U_13539,U_13540),c_Orderings_Otop__class_Otop(tc_fun(U_13542,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3434_3]) ).

fof(f_3435_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_3435_2,plain,
    ! [U_13547,U_13546,U_13545,U_13544,U_13543] :
      ( hBOOL(hAPP(hAPP(c_member(U_13546),U_13543),hAPP(c_Set_Oimage(U_13547,U_13546,U_13544),c_Orderings_Otop__class_Otop(tc_fun(U_13547,tc_HOL_Obool)))))
      | U_13543 != hAPP(U_13544,U_13545) ),
    inference(variable_rename,[status(thm)],[f_3435_1]) ).

fof(f_3435_3,plain,
    ! [U_13543,U_13544,U_13545,U_13546,U_13547] :
      ( hBOOL(hAPP(hAPP(c_member(U_13546),U_13543),hAPP(c_Set_Oimage(U_13547,U_13546,U_13544),c_Orderings_Otop__class_Otop(tc_fun(U_13547,tc_HOL_Obool)))))
      | U_13543 != hAPP(U_13544,U_13545) ),
    inference(definitional_conversion,[status(esa)],[f_3435_2]) ).

cnf(f_3435_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13546),U_13543),hAPP(c_Set_Oimage(U_13547,U_13546,U_13544),c_Orderings_Otop__class_Otop(tc_fun(U_13547,tc_HOL_Obool)))))
    | U_13543 != hAPP(U_13544,U_13545) ),
    inference(clausify,[status(thm)],[f_3435_3]) ).

fof(f_3436_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_3436_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_3436_1]) ).

cnf(f_3436_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_3436_2]) ).

fof(f_3437_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_3437_2,plain,
    ! [U_13549,U_13548] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13548,tc_HOL_Obool)),U_13549),c_Orderings_Otop__class_Otop(tc_fun(U_13548,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13548,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3437_1]) ).

fof(f_3437_3,plain,
    ! [U_13548,U_13549] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13548,tc_HOL_Obool)),U_13549),c_Orderings_Otop__class_Otop(tc_fun(U_13548,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13548,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3437_2]) ).

cnf(f_3437_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13548,tc_HOL_Obool)),U_13549),c_Orderings_Otop__class_Otop(tc_fun(U_13548,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13548,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3437_3]) ).

fof(f_3438_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_3438_2,plain,
    ! [U_13554,U_13553,U_13552,U_13551,U_13550] :
      ( hAPP(c_Set_Oimage(U_13550,U_13553,hAPP(c_Fun_Ocomp(U_13551,U_13553,U_13550,U_13554),U_13552)),c_Orderings_Otop__class_Otop(tc_fun(U_13550,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13553,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_13551,U_13553,U_13554),c_Orderings_Otop__class_Otop(tc_fun(U_13551,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13553,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_13550,U_13551,U_13552),c_Orderings_Otop__class_Otop(tc_fun(U_13550,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13551,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3438_1]) ).

fof(f_3438_3,plain,
    ! [U_13550,U_13551,U_13552,U_13553,U_13554] :
      ( hAPP(c_Set_Oimage(U_13550,U_13553,hAPP(c_Fun_Ocomp(U_13551,U_13553,U_13550,U_13554),U_13552)),c_Orderings_Otop__class_Otop(tc_fun(U_13550,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13553,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_13551,U_13553,U_13554),c_Orderings_Otop__class_Otop(tc_fun(U_13551,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13553,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_13550,U_13551,U_13552),c_Orderings_Otop__class_Otop(tc_fun(U_13550,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13551,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3438_2]) ).

cnf(f_3438_4,plain,
    ( hAPP(c_Set_Oimage(U_13550,U_13553,hAPP(c_Fun_Ocomp(U_13551,U_13553,U_13550,U_13554),U_13552)),c_Orderings_Otop__class_Otop(tc_fun(U_13550,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13553,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_13551,U_13553,U_13554),c_Orderings_Otop__class_Otop(tc_fun(U_13551,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13553,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_13550,U_13551,U_13552),c_Orderings_Otop__class_Otop(tc_fun(U_13550,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13551,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3438_3]) ).

fof(f_3439_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_3439_2,plain,
    ! [U_13556,U_13555] :
      ( U_13556 = c_Orderings_Otop__class_Otop(tc_fun(U_13555,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ocard(U_13555),U_13556) != hAPP(c_Finite__Set_Ocard(U_13555),c_Orderings_Otop__class_Otop(tc_fun(U_13555,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13555),c_Orderings_Otop__class_Otop(tc_fun(U_13555,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3439_1]) ).

fof(f_3439_3,plain,
    ! [U_13556,U_13555] :
      ( U_13556 = c_Orderings_Otop__class_Otop(tc_fun(U_13555,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ocard(U_13555),U_13556) != hAPP(c_Finite__Set_Ocard(U_13555),c_Orderings_Otop__class_Otop(tc_fun(U_13555,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13555),c_Orderings_Otop__class_Otop(tc_fun(U_13555,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3439_2]) ).

cnf(f_3439_4,plain,
    ( U_13556 = c_Orderings_Otop__class_Otop(tc_fun(U_13555,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_13555),U_13556) != hAPP(c_Finite__Set_Ocard(U_13555),c_Orderings_Otop__class_Otop(tc_fun(U_13555,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13555),c_Orderings_Otop__class_Otop(tc_fun(U_13555,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3439_3]) ).

fof(f_3440_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_3440_2,plain,
    ! [U_13561,U_13560,U_13559,U_13558,U_13557] :
      ( ( ( hAPP(c_Set_Oimage(U_13557,U_13558,U_13559),U_13560) = hAPP(c_Set_Oimage(U_13557,U_13558,U_13559),U_13561)
          | U_13560 != U_13561 )
        & ( U_13560 = U_13561
          | hAPP(c_Set_Oimage(U_13557,U_13558,U_13559),U_13560) != hAPP(c_Set_Oimage(U_13557,U_13558,U_13559),U_13561) ) )
      | ~ c_Fun_Oinj__on(U_13557,U_13558,U_13559,c_Orderings_Otop__class_Otop(tc_fun(U_13557,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3440_1]) ).

fof(f_3440_3,plain,
    ( ! [U_13557,U_13558,U_13559,U_13560,U_13561] :
        ( hAPP(c_Set_Oimage(U_13557,U_13558,U_13559),U_13560) = hAPP(c_Set_Oimage(U_13557,U_13558,U_13559),U_13561)
        | U_13560 != U_13561
        | ~ sP958(U_13557,U_13558,U_13559,U_13560,U_13561) )
    & ! [U_13557,U_13558,U_13559,U_13560,U_13561] :
        ( U_13560 = U_13561
        | hAPP(c_Set_Oimage(U_13557,U_13558,U_13559),U_13560) != hAPP(c_Set_Oimage(U_13557,U_13558,U_13559),U_13561)
        | ~ sP958(U_13557,U_13558,U_13559,U_13560,U_13561) )
    & ! [U_13557,U_13558,U_13559,U_13560,U_13561] :
        ( sP958(U_13557,U_13558,U_13559,U_13560,U_13561)
        | ~ c_Fun_Oinj__on(U_13557,U_13558,U_13559,c_Orderings_Otop__class_Otop(tc_fun(U_13557,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP958])],[f_3440_2]) ).

cnf(f_3440_4,plain,
    ( sP958(U_13557,U_13558,U_13559,U_13560,U_13561)
    | ~ c_Fun_Oinj__on(U_13557,U_13558,U_13559,c_Orderings_Otop__class_Otop(tc_fun(U_13557,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3440_3]) ).

cnf(f_3440_5,plain,
    ( U_13560 = U_13561
    | hAPP(c_Set_Oimage(U_13557,U_13558,U_13559),U_13560) != hAPP(c_Set_Oimage(U_13557,U_13558,U_13559),U_13561)
    | ~ sP958(U_13557,U_13558,U_13559,U_13560,U_13561) ),
    inference(clausify,[status(thm)],[f_3440_3]) ).

cnf(f_3440_6,plain,
    ( hAPP(c_Set_Oimage(U_13557,U_13558,U_13559),U_13560) = hAPP(c_Set_Oimage(U_13557,U_13558,U_13559),U_13561)
    | U_13560 != U_13561
    | ~ sP958(U_13557,U_13558,U_13559,U_13560,U_13561) ),
    inference(clausify,[status(thm)],[f_3440_3]) ).

fof(f_3441_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_3441_2,plain,
    ! [U_13566,U_13565,U_13564,U_13563,U_13562] :
      ( c_Fun_Oinj__on(U_13565,U_13563,hAPP(c_Fun_Ocomp(U_13562,U_13563,U_13565,U_13564),U_13566),c_Orderings_Otop__class_Otop(tc_fun(U_13565,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_13565,U_13562,U_13566,c_Orderings_Otop__class_Otop(tc_fun(U_13565,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_13562,U_13563,U_13564,c_Orderings_Otop__class_Otop(tc_fun(U_13562,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3441_1]) ).

fof(f_3441_3,plain,
    ! [U_13564,U_13563,U_13562,U_13565,U_13566] :
      ( c_Fun_Oinj__on(U_13565,U_13563,hAPP(c_Fun_Ocomp(U_13562,U_13563,U_13565,U_13564),U_13566),c_Orderings_Otop__class_Otop(tc_fun(U_13565,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_13565,U_13562,U_13566,c_Orderings_Otop__class_Otop(tc_fun(U_13565,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_13562,U_13563,U_13564,c_Orderings_Otop__class_Otop(tc_fun(U_13562,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3441_2]) ).

cnf(f_3441_4,plain,
    ( c_Fun_Oinj__on(U_13565,U_13563,hAPP(c_Fun_Ocomp(U_13562,U_13563,U_13565,U_13564),U_13566),c_Orderings_Otop__class_Otop(tc_fun(U_13565,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_13565,U_13562,U_13566,c_Orderings_Otop__class_Otop(tc_fun(U_13565,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_13562,U_13563,U_13564,c_Orderings_Otop__class_Otop(tc_fun(U_13562,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3441_3]) ).

fof(f_3442_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_3442_2,plain,
    ! [U_13567] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13567,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13567,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13567,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3442_1]) ).

fof(f_3442_3,plain,
    ! [U_13567] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13567,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13567,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13567,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3442_2]) ).

cnf(f_3442_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13567,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13567,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13567,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3442_3]) ).

fof(f_3443_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_3443_2,plain,
    ! [U_13568] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13568,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13568,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13568,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3443_1]) ).

fof(f_3443_3,plain,
    ! [U_13568] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13568,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13568,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13568,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3443_2]) ).

cnf(f_3443_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13568,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13568,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13568,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3443_3]) ).

fof(f_3444_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_3444_2,plain,
    ! [U_13570,U_13569] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13569),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13569,tc_HOL_Obool)),U_13570)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13569),c_Orderings_Otop__class_Otop(tc_fun(U_13569,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13569),c_Orderings_Otop__class_Otop(tc_fun(U_13569,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13569),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13569,tc_HOL_Obool)),U_13570))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13569),U_13570)) ),
    inference(variable_rename,[status(thm)],[f_3444_1]) ).

fof(f_3444_3,plain,
    ( ! [U_13569,U_13570] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13569),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13569,tc_HOL_Obool)),U_13570)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13569),c_Orderings_Otop__class_Otop(tc_fun(U_13569,tc_HOL_Obool))))
        | ~ sP959(U_13569,U_13570) )
    & ! [U_13569,U_13570] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13569),c_Orderings_Otop__class_Otop(tc_fun(U_13569,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13569),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13569,tc_HOL_Obool)),U_13570)))
        | ~ sP959(U_13569,U_13570) )
    & ! [U_13569,U_13570] :
        ( sP959(U_13569,U_13570)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13569),U_13570)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP959])],[f_3444_2]) ).

cnf(f_3444_4,plain,
    ( sP959(U_13569,U_13570)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13569),U_13570)) ),
    inference(clausify,[status(thm)],[f_3444_3]) ).

cnf(f_3444_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13569),c_Orderings_Otop__class_Otop(tc_fun(U_13569,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13569),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13569,tc_HOL_Obool)),U_13570)))
    | ~ sP959(U_13569,U_13570) ),
    inference(clausify,[status(thm)],[f_3444_3]) ).

cnf(f_3444_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13569),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13569,tc_HOL_Obool)),U_13570)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13569),c_Orderings_Otop__class_Otop(tc_fun(U_13569,tc_HOL_Obool))))
    | ~ sP959(U_13569,U_13570) ),
    inference(clausify,[status(thm)],[f_3444_3]) ).

fof(f_3445_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_3445_2,plain,
    ! [U_13572,U_13571] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13571,tc_HOL_Obool)),U_13572),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13571,tc_HOL_Obool)),U_13572)) = c_Orderings_Otop__class_Otop(tc_fun(U_13571,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3445_1]) ).

fof(f_3445_3,plain,
    ! [U_13572,U_13571] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13571,tc_HOL_Obool)),U_13572),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13571,tc_HOL_Obool)),U_13572)) = c_Orderings_Otop__class_Otop(tc_fun(U_13571,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3445_2]) ).

cnf(f_3445_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13571,tc_HOL_Obool)),U_13572),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13571,tc_HOL_Obool)),U_13572)) = c_Orderings_Otop__class_Otop(tc_fun(U_13571,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3445_3]) ).

fof(f_3446_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_3446_2,plain,
    ! [U_13574,U_13573] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13573,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13573,tc_HOL_Obool)),U_13574)),U_13574) = c_Orderings_Otop__class_Otop(tc_fun(U_13573,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3446_1]) ).

fof(f_3446_3,plain,
    ! [U_13573,U_13574] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13573,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13573,tc_HOL_Obool)),U_13574)),U_13574) = c_Orderings_Otop__class_Otop(tc_fun(U_13573,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3446_2]) ).

cnf(f_3446_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13573,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13573,tc_HOL_Obool)),U_13574)),U_13574) = c_Orderings_Otop__class_Otop(tc_fun(U_13573,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3446_3]) ).

fof(f_3447_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_3447_2,plain,
    ! [U_13576,U_13575] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13575,tc_HOL_Obool)),U_13576) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13575,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13575,tc_HOL_Obool))),U_13576),
    inference(variable_rename,[status(thm)],[f_3447_1]) ).

fof(f_3447_3,plain,
    ! [U_13575,U_13576] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13575,tc_HOL_Obool)),U_13576) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13575,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13575,tc_HOL_Obool))),U_13576),
    inference(definitional_conversion,[status(esa)],[f_3447_2]) ).

cnf(f_3447_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13575,tc_HOL_Obool)),U_13576) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13575,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13575,tc_HOL_Obool))),U_13576),
    inference(clausify,[status(thm)],[f_3447_3]) ).

fof(f_3448_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_3448_2,plain,
    ! [U_13578,U_13577] :
      ( ( ( hAPP(c_Code__Numeral_Oof__nat,U_13577) = hAPP(c_Code__Numeral_Oof__nat,U_13578)
          | U_13577 != U_13578 )
        & ( U_13577 = U_13578
          | hAPP(c_Code__Numeral_Oof__nat,U_13577) != hAPP(c_Code__Numeral_Oof__nat,U_13578) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13578),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13577),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3448_1]) ).

fof(f_3448_3,plain,
    ( ! [U_13577,U_13578] :
        ( hAPP(c_Code__Numeral_Oof__nat,U_13577) = hAPP(c_Code__Numeral_Oof__nat,U_13578)
        | U_13577 != U_13578
        | ~ sP960(U_13577,U_13578) )
    & ! [U_13577,U_13578] :
        ( U_13577 = U_13578
        | hAPP(c_Code__Numeral_Oof__nat,U_13577) != hAPP(c_Code__Numeral_Oof__nat,U_13578)
        | ~ sP960(U_13577,U_13578) )
    & ! [U_13577,U_13578] :
        ( sP960(U_13577,U_13578)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13578),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13577),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP960])],[f_3448_2]) ).

cnf(f_3448_4,plain,
    ( sP960(U_13577,U_13578)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13578),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13577),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3448_3]) ).

cnf(f_3448_5,plain,
    ( U_13577 = U_13578
    | hAPP(c_Code__Numeral_Oof__nat,U_13577) != hAPP(c_Code__Numeral_Oof__nat,U_13578)
    | ~ sP960(U_13577,U_13578) ),
    inference(clausify,[status(thm)],[f_3448_3]) ).

cnf(f_3448_6,plain,
    ( hAPP(c_Code__Numeral_Oof__nat,U_13577) = hAPP(c_Code__Numeral_Oof__nat,U_13578)
    | U_13577 != U_13578
    | ~ sP960(U_13577,U_13578) ),
    inference(clausify,[status(thm)],[f_3448_3]) ).

fof(f_3449_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_3449_2,plain,
    ! [U_13582,U_13581,U_13580,U_13579] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13579,tc_fun(U_13580,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13579,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13580,tc_HOL_Obool),tc_fun(U_13580,tc_HOL_Obool),U_13579),hAPP(c_COMBC(U_13580,tc_fun(U_13580,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13580))),U_13581)),U_13582))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13580),U_13582),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13579,tc_fun(U_13580,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13579,tc_HOL_Obool))),U_13581))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_13580),U_13582),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13579,tc_fun(U_13580,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13579,tc_HOL_Obool))),U_13581)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13579,tc_fun(U_13580,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13579,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13580,tc_HOL_Obool),tc_fun(U_13580,tc_HOL_Obool),U_13579),hAPP(c_COMBC(U_13580,tc_fun(U_13580,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13580))),U_13581)),U_13582)) ) ),
    inference(variable_rename,[status(thm)],[f_3449_1]) ).

fof(f_3449_3,plain,
    ( ! [U_13590,U_13588,U_13586,U_13584] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13584,tc_fun(U_13586,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13584,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13586,tc_HOL_Obool),tc_fun(U_13586,tc_HOL_Obool),U_13584),hAPP(c_COMBC(U_13586,tc_fun(U_13586,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13586))),U_13588)),U_13590))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13586),U_13590),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13584,tc_fun(U_13586,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13584,tc_HOL_Obool))),U_13588))) )
    & ! [U_13589,U_13587,U_13585,U_13583] :
        ( hBOOL(hAPP(hAPP(c_member(U_13585),U_13589),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13583,tc_fun(U_13585,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13583,tc_HOL_Obool))),U_13587)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13583,tc_fun(U_13585,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13583,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13585,tc_HOL_Obool),tc_fun(U_13585,tc_HOL_Obool),U_13583),hAPP(c_COMBC(U_13585,tc_fun(U_13585,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13585))),U_13587)),U_13589)) ) ),
    inference(miniscope,[status(thm)],[f_3449_2]) ).

fof(f_3449_4,plain,
    ( ! [U_13584,U_13586,U_13588,U_13590] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13584,tc_fun(U_13586,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13584,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13586,tc_HOL_Obool),tc_fun(U_13586,tc_HOL_Obool),U_13584),hAPP(c_COMBC(U_13586,tc_fun(U_13586,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13586))),U_13588)),U_13590))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13586),U_13590),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13584,tc_fun(U_13586,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13584,tc_HOL_Obool))),U_13588))) )
    & ! [U_13589,U_13587,U_13585,U_13583] :
        ( hBOOL(hAPP(hAPP(c_member(U_13585),U_13589),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13583,tc_fun(U_13585,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13583,tc_HOL_Obool))),U_13587)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13583,tc_fun(U_13585,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13583,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13585,tc_HOL_Obool),tc_fun(U_13585,tc_HOL_Obool),U_13583),hAPP(c_COMBC(U_13585,tc_fun(U_13585,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13585))),U_13587)),U_13589)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3449_3]) ).

cnf(f_3449_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13585),U_13589),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13583,tc_fun(U_13585,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13583,tc_HOL_Obool))),U_13587)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13583,tc_fun(U_13585,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13583,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13585,tc_HOL_Obool),tc_fun(U_13585,tc_HOL_Obool),U_13583),hAPP(c_COMBC(U_13585,tc_fun(U_13585,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13585))),U_13587)),U_13589)) ),
    inference(clausify,[status(thm)],[f_3449_4]) ).

cnf(f_3449_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13584,tc_fun(U_13586,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13584,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13586,tc_HOL_Obool),tc_fun(U_13586,tc_HOL_Obool),U_13584),hAPP(c_COMBC(U_13586,tc_fun(U_13586,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13586))),U_13588)),U_13590))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13586),U_13590),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13584,tc_fun(U_13586,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13584,tc_HOL_Obool))),U_13588))) ),
    inference(clausify,[status(thm)],[f_3449_4]) ).

fof(f_3450_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_3450_2,plain,
    ! [U_13595,U_13594,U_13593,U_13592,U_13591] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13594),hAPP(c_Set_Oimage(U_13592,U_13594,hAPP(hAPP(c_COMBB(U_13591,U_13594,U_13592),U_13595),U_13593)),c_Orderings_Otop__class_Otop(tc_fun(U_13592,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13591),hAPP(c_Set_Oimage(U_13592,U_13591,U_13593),c_Orderings_Otop__class_Otop(tc_fun(U_13592,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_3450_1]) ).

fof(f_3450_3,plain,
    ! [U_13591,U_13592,U_13593,U_13594,U_13595] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13594),hAPP(c_Set_Oimage(U_13592,U_13594,hAPP(hAPP(c_COMBB(U_13591,U_13594,U_13592),U_13595),U_13593)),c_Orderings_Otop__class_Otop(tc_fun(U_13592,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13591),hAPP(c_Set_Oimage(U_13592,U_13591,U_13593),c_Orderings_Otop__class_Otop(tc_fun(U_13592,tc_HOL_Obool))))) ),
    inference(definitional_conversion,[status(esa)],[f_3450_2]) ).

cnf(f_3450_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13594),hAPP(c_Set_Oimage(U_13592,U_13594,hAPP(hAPP(c_COMBB(U_13591,U_13594,U_13592),U_13595),U_13593)),c_Orderings_Otop__class_Otop(tc_fun(U_13592,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13591),hAPP(c_Set_Oimage(U_13592,U_13591,U_13593),c_Orderings_Otop__class_Otop(tc_fun(U_13592,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_3450_3]) ).

fof(f_3451_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_3451_2,plain,
    ! [U_13596] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_13596)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3451_1]) ).

fof(f_3451_3,plain,
    ! [U_13596] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_13596)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3451_2]) ).

cnf(f_3451_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_13596)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3451_3]) ).

fof(f_3452_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_3452_2,plain,
    ! [U_13600,U_13599,U_13598,U_13597] :
      ( hAPP(c_Fun_Othe__inv__into(U_13597,U_13598,c_Orderings_Otop__class_Otop(tc_fun(U_13597,tc_HOL_Obool)),U_13599),hAPP(U_13599,U_13600)) = U_13600
      | ~ c_Fun_Oinj__on(U_13597,U_13598,U_13599,c_Orderings_Otop__class_Otop(tc_fun(U_13597,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3452_1]) ).

fof(f_3452_3,plain,
    ! [U_13597,U_13598,U_13599,U_13600] :
      ( hAPP(c_Fun_Othe__inv__into(U_13597,U_13598,c_Orderings_Otop__class_Otop(tc_fun(U_13597,tc_HOL_Obool)),U_13599),hAPP(U_13599,U_13600)) = U_13600
      | ~ c_Fun_Oinj__on(U_13597,U_13598,U_13599,c_Orderings_Otop__class_Otop(tc_fun(U_13597,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3452_2]) ).

cnf(f_3452_4,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_13597,U_13598,c_Orderings_Otop__class_Otop(tc_fun(U_13597,tc_HOL_Obool)),U_13599),hAPP(U_13599,U_13600)) = U_13600
    | ~ c_Fun_Oinj__on(U_13597,U_13598,U_13599,c_Orderings_Otop__class_Otop(tc_fun(U_13597,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3452_3]) ).

fof(f_3453_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_3453_2,plain,
    ! [U_13602,U_13601] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13601),c_Orderings_Otop__class_Otop(tc_fun(U_13601,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(U_13602),c_Orderings_Otop__class_Otop(tc_fun(U_13602,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13601,U_13602)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13601,U_13602),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3453_1]) ).

fof(f_3453_3,plain,
    ! [U_13601,U_13602] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13601),c_Orderings_Otop__class_Otop(tc_fun(U_13601,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(U_13602),c_Orderings_Otop__class_Otop(tc_fun(U_13602,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13601,U_13602)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13601,U_13602),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3453_2]) ).

cnf(f_3453_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13601),c_Orderings_Otop__class_Otop(tc_fun(U_13601,tc_HOL_Obool))))
    | hAPP(c_Finite__Set_Ocard(U_13602),c_Orderings_Otop__class_Otop(tc_fun(U_13602,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13601,U_13602)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13601,U_13602),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3453_3]) ).

fof(f_3454_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_3454_2,plain,
    ! [U_13603] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,U_13603,c_Nat_Osemiring__1__class_Oof__nat(U_13603),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | ~ class_Nat_Osemiring__char__0(U_13603) ),
    inference(variable_rename,[status(thm)],[f_3454_1]) ).

fof(f_3454_3,plain,
    ! [U_13603] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,U_13603,c_Nat_Osemiring__1__class_Oof__nat(U_13603),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | ~ class_Nat_Osemiring__char__0(U_13603) ),
    inference(definitional_conversion,[status(esa)],[f_3454_2]) ).

cnf(f_3454_4,plain,
    ( c_Fun_Oinj__on(tc_Nat_Onat,U_13603,c_Nat_Osemiring__1__class_Oof__nat(U_13603),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | ~ class_Nat_Osemiring__char__0(U_13603) ),
    inference(clausify,[status(thm)],[f_3454_3]) ).

fof(f_3455_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_3455_2,plain,
    ! [U_13606,U_13605,U_13604] : c_Map_Odom(U_13604,U_13605,hAPP(hAPP(c_COMBB(U_13605,tc_Option_Ooption(U_13605),U_13604),c_Option_Ooption_OSome(U_13605)),U_13606)) = c_Orderings_Otop__class_Otop(tc_fun(U_13604,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3455_1]) ).

fof(f_3455_3,plain,
    ! [U_13604,U_13605,U_13606] : c_Map_Odom(U_13604,U_13605,hAPP(hAPP(c_COMBB(U_13605,tc_Option_Ooption(U_13605),U_13604),c_Option_Ooption_OSome(U_13605)),U_13606)) = c_Orderings_Otop__class_Otop(tc_fun(U_13604,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3455_2]) ).

cnf(f_3455_4,plain,
    c_Map_Odom(U_13604,U_13605,hAPP(hAPP(c_COMBB(U_13605,tc_Option_Ooption(U_13605),U_13604),c_Option_Ooption_OSome(U_13605)),U_13606)) = c_Orderings_Otop__class_Otop(tc_fun(U_13604,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3455_3]) ).

fof(f_3456_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_3456_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_3456_1]) ).

cnf(f_3456_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_3456_2]) ).

fof(f_3457_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_3457_2,plain,
    ! [U_13610,U_13609,U_13608,U_13607] :
      ( c_Fun_Oinj__on(U_13607,tc_fun(U_13610,U_13608),hAPP(hAPP(c_COMBB(U_13608,tc_fun(U_13610,U_13608),U_13607),c_COMBK(U_13608,U_13610)),U_13609),c_Orderings_Otop__class_Otop(tc_fun(U_13607,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_13607,U_13608,U_13609,c_Orderings_Otop__class_Otop(tc_fun(U_13607,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3457_1]) ).

fof(f_3457_3,plain,
    ! [U_13607,U_13608,U_13609,U_13610] :
      ( c_Fun_Oinj__on(U_13607,tc_fun(U_13610,U_13608),hAPP(hAPP(c_COMBB(U_13608,tc_fun(U_13610,U_13608),U_13607),c_COMBK(U_13608,U_13610)),U_13609),c_Orderings_Otop__class_Otop(tc_fun(U_13607,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_13607,U_13608,U_13609,c_Orderings_Otop__class_Otop(tc_fun(U_13607,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3457_2]) ).

cnf(f_3457_4,plain,
    ( c_Fun_Oinj__on(U_13607,tc_fun(U_13610,U_13608),hAPP(hAPP(c_COMBB(U_13608,tc_fun(U_13610,U_13608),U_13607),c_COMBK(U_13608,U_13610)),U_13609),c_Orderings_Otop__class_Otop(tc_fun(U_13607,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_13607,U_13608,U_13609,c_Orderings_Otop__class_Otop(tc_fun(U_13607,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3457_3]) ).

fof(f_3458_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_3458_2,plain,
    ! [U_13611] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_13611),c_Orderings_Otop__class_Otop(U_13611)) = c_Orderings_Obot__class_Obot(U_13611)
      | ~ class_Lattices_Oboolean__algebra(U_13611) ),
    inference(variable_rename,[status(thm)],[f_3458_1]) ).

fof(f_3458_3,plain,
    ! [U_13611] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_13611),c_Orderings_Otop__class_Otop(U_13611)) = c_Orderings_Obot__class_Obot(U_13611)
      | ~ class_Lattices_Oboolean__algebra(U_13611) ),
    inference(definitional_conversion,[status(esa)],[f_3458_2]) ).

cnf(f_3458_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_13611),c_Orderings_Otop__class_Otop(U_13611)) = c_Orderings_Obot__class_Obot(U_13611)
    | ~ class_Lattices_Oboolean__algebra(U_13611) ),
    inference(clausify,[status(thm)],[f_3458_3]) ).

fof(f_3459_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_3459_2,plain,
    ! [U_13612] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_13612),c_Orderings_Obot__class_Obot(U_13612)) = c_Orderings_Otop__class_Otop(U_13612)
      | ~ class_Lattices_Oboolean__algebra(U_13612) ),
    inference(variable_rename,[status(thm)],[f_3459_1]) ).

fof(f_3459_3,plain,
    ! [U_13612] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_13612),c_Orderings_Obot__class_Obot(U_13612)) = c_Orderings_Otop__class_Otop(U_13612)
      | ~ class_Lattices_Oboolean__algebra(U_13612) ),
    inference(definitional_conversion,[status(esa)],[f_3459_2]) ).

cnf(f_3459_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_13612),c_Orderings_Obot__class_Obot(U_13612)) = c_Orderings_Otop__class_Otop(U_13612)
    | ~ class_Lattices_Oboolean__algebra(U_13612) ),
    inference(clausify,[status(thm)],[f_3459_3]) ).

fof(f_3460_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_3460_2,plain,
    ! [U_13614,U_13613] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13613),U_13614),hAPP(c_Groups_Ouminus__class_Ouminus(U_13613),U_13614)) = c_Orderings_Otop__class_Otop(U_13613)
      | ~ class_Lattices_Oboolean__algebra(U_13613) ),
    inference(variable_rename,[status(thm)],[f_3460_1]) ).

fof(f_3460_3,plain,
    ! [U_13613,U_13614] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13613),U_13614),hAPP(c_Groups_Ouminus__class_Ouminus(U_13613),U_13614)) = c_Orderings_Otop__class_Otop(U_13613)
      | ~ class_Lattices_Oboolean__algebra(U_13613) ),
    inference(definitional_conversion,[status(esa)],[f_3460_2]) ).

cnf(f_3460_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13613),U_13614),hAPP(c_Groups_Ouminus__class_Ouminus(U_13613),U_13614)) = c_Orderings_Otop__class_Otop(U_13613)
    | ~ class_Lattices_Oboolean__algebra(U_13613) ),
    inference(clausify,[status(thm)],[f_3460_3]) ).

fof(f_3461_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_3461_2,plain,
    ! [U_13616,U_13615] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13615),hAPP(c_Groups_Ouminus__class_Ouminus(U_13615),U_13616)),U_13616) = c_Orderings_Otop__class_Otop(U_13615)
      | ~ class_Lattices_Oboolean__algebra(U_13615) ),
    inference(variable_rename,[status(thm)],[f_3461_1]) ).

fof(f_3461_3,plain,
    ! [U_13615,U_13616] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13615),hAPP(c_Groups_Ouminus__class_Ouminus(U_13615),U_13616)),U_13616) = c_Orderings_Otop__class_Otop(U_13615)
      | ~ class_Lattices_Oboolean__algebra(U_13615) ),
    inference(definitional_conversion,[status(esa)],[f_3461_2]) ).

cnf(f_3461_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13615),hAPP(c_Groups_Ouminus__class_Ouminus(U_13615),U_13616)),U_13616) = c_Orderings_Otop__class_Otop(U_13615)
    | ~ class_Lattices_Oboolean__algebra(U_13615) ),
    inference(clausify,[status(thm)],[f_3461_3]) ).

fof(f_3462_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_3462_2,plain,
    ! [U_13621,U_13620,U_13619,U_13618,U_13617] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_13618),hAPP(U_13619,U_13620)),hAPP(c_Set_Oimage(U_13617,U_13618,U_13619),U_13621)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_13617),U_13620),U_13621)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_13617),U_13620),U_13621))
          | ~ hBOOL(hAPP(hAPP(c_member(U_13618),hAPP(U_13619,U_13620)),hAPP(c_Set_Oimage(U_13617,U_13618,U_13619),U_13621))) ) )
      | ~ c_Fun_Oinj__on(U_13617,U_13618,U_13619,c_Orderings_Otop__class_Otop(tc_fun(U_13617,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3462_1]) ).

fof(f_3462_3,plain,
    ( ! [U_13617,U_13618,U_13619,U_13620,U_13621] :
        ( hBOOL(hAPP(hAPP(c_member(U_13618),hAPP(U_13619,U_13620)),hAPP(c_Set_Oimage(U_13617,U_13618,U_13619),U_13621)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13617),U_13620),U_13621))
        | ~ sP961(U_13617,U_13618,U_13619,U_13620,U_13621) )
    & ! [U_13617,U_13618,U_13619,U_13620,U_13621] :
        ( hBOOL(hAPP(hAPP(c_member(U_13617),U_13620),U_13621))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13618),hAPP(U_13619,U_13620)),hAPP(c_Set_Oimage(U_13617,U_13618,U_13619),U_13621)))
        | ~ sP961(U_13617,U_13618,U_13619,U_13620,U_13621) )
    & ! [U_13617,U_13618,U_13619,U_13620,U_13621] :
        ( sP961(U_13617,U_13618,U_13619,U_13620,U_13621)
        | ~ c_Fun_Oinj__on(U_13617,U_13618,U_13619,c_Orderings_Otop__class_Otop(tc_fun(U_13617,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP961])],[f_3462_2]) ).

cnf(f_3462_4,plain,
    ( sP961(U_13617,U_13618,U_13619,U_13620,U_13621)
    | ~ c_Fun_Oinj__on(U_13617,U_13618,U_13619,c_Orderings_Otop__class_Otop(tc_fun(U_13617,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3462_3]) ).

cnf(f_3462_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13617),U_13620),U_13621))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13618),hAPP(U_13619,U_13620)),hAPP(c_Set_Oimage(U_13617,U_13618,U_13619),U_13621)))
    | ~ sP961(U_13617,U_13618,U_13619,U_13620,U_13621) ),
    inference(clausify,[status(thm)],[f_3462_3]) ).

cnf(f_3462_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13618),hAPP(U_13619,U_13620)),hAPP(c_Set_Oimage(U_13617,U_13618,U_13619),U_13621)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13617),U_13620),U_13621))
    | ~ sP961(U_13617,U_13618,U_13619,U_13620,U_13621) ),
    inference(clausify,[status(thm)],[f_3462_3]) ).

fof(f_3463_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_3463_2,plain,
    ! [U_13629,U_13628,U_13627,U_13626] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_13627),U_13629),hAPP(c_Set_Oimage(U_13626,U_13627,U_13628),c_Orderings_Otop__class_Otop(tc_fun(U_13626,tc_HOL_Obool)))))
          | ! [U_13625] :
              ( ? [U_13624] :
                  ( U_13624 != U_13625
                  & U_13629 = hAPP(U_13628,U_13624) )
              | U_13629 != hAPP(U_13628,U_13625) ) )
        & ( ? [U_13623] :
              ( ! [U_13622] :
                  ( U_13622 = U_13623
                  | U_13629 != hAPP(U_13628,U_13622) )
              & U_13629 = hAPP(U_13628,U_13623) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_13627),U_13629),hAPP(c_Set_Oimage(U_13626,U_13627,U_13628),c_Orderings_Otop__class_Otop(tc_fun(U_13626,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_13626,U_13627,U_13628,c_Orderings_Otop__class_Otop(tc_fun(U_13626,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3463_1]) ).

fof(f_3463_3,plain,
    ! [U_13629,U_13628,U_13627,U_13626] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_13627),U_13629),hAPP(c_Set_Oimage(U_13626,U_13627,U_13628),c_Orderings_Otop__class_Otop(tc_fun(U_13626,tc_HOL_Obool)))))
          | ! [U_13625] :
              ( ? [U_13624] :
                  ( U_13624 != U_13625
                  & U_13629 = hAPP(U_13628,U_13624) )
              | U_13629 != hAPP(U_13628,U_13625) ) )
        & ( ( ! [U_13622] :
                ( U_13622 = sK288(U_13629,U_13628,U_13627,U_13626)
                | U_13629 != hAPP(U_13628,U_13622) )
            & U_13629 = hAPP(U_13628,sK288(U_13629,U_13628,U_13627,U_13626)) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_13627),U_13629),hAPP(c_Set_Oimage(U_13626,U_13627,U_13628),c_Orderings_Otop__class_Otop(tc_fun(U_13626,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_13626,U_13627,U_13628,c_Orderings_Otop__class_Otop(tc_fun(U_13626,tc_HOL_Obool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK288]),skolemize(U_13623,sK288(U_13629,U_13628,U_13627,U_13626))],[f_3463_2]) ).

fof(f_3463_4,plain,
    ! [U_13629,U_13628,U_13627,U_13626] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_13627),U_13629),hAPP(c_Set_Oimage(U_13626,U_13627,U_13628),c_Orderings_Otop__class_Otop(tc_fun(U_13626,tc_HOL_Obool)))))
          | ! [U_13625] :
              ( ( sK289(U_13629,U_13628,U_13627,U_13626,U_13625) != U_13625
                & U_13629 = hAPP(U_13628,sK289(U_13629,U_13628,U_13627,U_13626,U_13625)) )
              | U_13629 != hAPP(U_13628,U_13625) ) )
        & ( ( ! [U_13622] :
                ( U_13622 = sK288(U_13629,U_13628,U_13627,U_13626)
                | U_13629 != hAPP(U_13628,U_13622) )
            & U_13629 = hAPP(U_13628,sK288(U_13629,U_13628,U_13627,U_13626)) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_13627),U_13629),hAPP(c_Set_Oimage(U_13626,U_13627,U_13628),c_Orderings_Otop__class_Otop(tc_fun(U_13626,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_13626,U_13627,U_13628,c_Orderings_Otop__class_Otop(tc_fun(U_13626,tc_HOL_Obool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK289]),skolemize(U_13624,sK289(U_13629,U_13628,U_13627,U_13626,U_13625))],[f_3463_3]) ).

fof(f_3463_5,plain,
    ( ! [U_13625,U_13626,U_13627,U_13628,U_13629] :
        ( sK289(U_13629,U_13628,U_13627,U_13626,U_13625) != U_13625
        | ~ sP963(U_13625,U_13626,U_13627,U_13628,U_13629) )
    & ! [U_13625,U_13626,U_13627,U_13628,U_13629] :
        ( U_13629 = hAPP(U_13628,sK289(U_13629,U_13628,U_13627,U_13626,U_13625))
        | ~ sP963(U_13625,U_13626,U_13627,U_13628,U_13629) )
    & ! [U_13626,U_13622,U_13627,U_13628,U_13629] :
        ( U_13622 = sK288(U_13629,U_13628,U_13627,U_13626)
        | U_13629 != hAPP(U_13628,U_13622)
        | ~ sP962(U_13626,U_13622,U_13627,U_13628,U_13629) )
    & ! [U_13626,U_13622,U_13627,U_13628,U_13629] :
        ( U_13629 = hAPP(U_13628,sK288(U_13629,U_13628,U_13627,U_13626))
        | ~ sP962(U_13626,U_13622,U_13627,U_13628,U_13629) )
    & ! [U_13625,U_13626,U_13622,U_13627,U_13628,U_13629] :
        ( hBOOL(hAPP(hAPP(c_member(U_13627),U_13629),hAPP(c_Set_Oimage(U_13626,U_13627,U_13628),c_Orderings_Otop__class_Otop(tc_fun(U_13626,tc_HOL_Obool)))))
        | sP963(U_13625,U_13626,U_13627,U_13628,U_13629)
        | U_13629 != hAPP(U_13628,U_13625)
        | ~ sP964(U_13625,U_13626,U_13622,U_13627,U_13628,U_13629) )
    & ! [U_13625,U_13626,U_13622,U_13627,U_13628,U_13629] :
        ( sP962(U_13626,U_13622,U_13627,U_13628,U_13629)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13627),U_13629),hAPP(c_Set_Oimage(U_13626,U_13627,U_13628),c_Orderings_Otop__class_Otop(tc_fun(U_13626,tc_HOL_Obool)))))
        | ~ sP964(U_13625,U_13626,U_13622,U_13627,U_13628,U_13629) )
    & ! [U_13625,U_13626,U_13622,U_13627,U_13628,U_13629] :
        ( sP964(U_13625,U_13626,U_13622,U_13627,U_13628,U_13629)
        | ~ c_Fun_Oinj__on(U_13626,U_13627,U_13628,c_Orderings_Otop__class_Otop(tc_fun(U_13626,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP962,sP963,sP964])],[f_3463_4]) ).

cnf(f_3463_6,plain,
    ( sP964(U_13625,U_13626,U_13622,U_13627,U_13628,U_13629)
    | ~ c_Fun_Oinj__on(U_13626,U_13627,U_13628,c_Orderings_Otop__class_Otop(tc_fun(U_13626,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3463_5]) ).

cnf(f_3463_7,plain,
    ( sP962(U_13626,U_13622,U_13627,U_13628,U_13629)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13627),U_13629),hAPP(c_Set_Oimage(U_13626,U_13627,U_13628),c_Orderings_Otop__class_Otop(tc_fun(U_13626,tc_HOL_Obool)))))
    | ~ sP964(U_13625,U_13626,U_13622,U_13627,U_13628,U_13629) ),
    inference(clausify,[status(thm)],[f_3463_5]) ).

cnf(f_3463_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13627),U_13629),hAPP(c_Set_Oimage(U_13626,U_13627,U_13628),c_Orderings_Otop__class_Otop(tc_fun(U_13626,tc_HOL_Obool)))))
    | sP963(U_13625,U_13626,U_13627,U_13628,U_13629)
    | U_13629 != hAPP(U_13628,U_13625)
    | ~ sP964(U_13625,U_13626,U_13622,U_13627,U_13628,U_13629) ),
    inference(clausify,[status(thm)],[f_3463_5]) ).

cnf(f_3463_9,plain,
    ( U_13629 = hAPP(U_13628,sK288(U_13629,U_13628,U_13627,U_13626))
    | ~ sP962(U_13626,U_13622,U_13627,U_13628,U_13629) ),
    inference(clausify,[status(thm)],[f_3463_5]) ).

cnf(f_3463_10,plain,
    ( U_13622 = sK288(U_13629,U_13628,U_13627,U_13626)
    | U_13629 != hAPP(U_13628,U_13622)
    | ~ sP962(U_13626,U_13622,U_13627,U_13628,U_13629) ),
    inference(clausify,[status(thm)],[f_3463_5]) ).

cnf(f_3463_11,plain,
    ( U_13629 = hAPP(U_13628,sK289(U_13629,U_13628,U_13627,U_13626,U_13625))
    | ~ sP963(U_13625,U_13626,U_13627,U_13628,U_13629) ),
    inference(clausify,[status(thm)],[f_3463_5]) ).

cnf(f_3463_12,plain,
    ( sK289(U_13629,U_13628,U_13627,U_13626,U_13625) != U_13625
    | ~ sP963(U_13625,U_13626,U_13627,U_13628,U_13629) ),
    inference(clausify,[status(thm)],[f_3463_5]) ).

fof(f_3464_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_3464_2,plain,
    ! [U_13631,U_13630] :
      ( hAPP(c_Set_Oimage(U_13630,U_13630,U_13631),c_Orderings_Otop__class_Otop(tc_fun(U_13630,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13630,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(U_13630,U_13630,U_13631,c_Orderings_Otop__class_Otop(tc_fun(U_13630,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13630),c_Orderings_Otop__class_Otop(tc_fun(U_13630,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3464_1]) ).

fof(f_3464_3,plain,
    ! [U_13631,U_13630] :
      ( hAPP(c_Set_Oimage(U_13630,U_13630,U_13631),c_Orderings_Otop__class_Otop(tc_fun(U_13630,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13630,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(U_13630,U_13630,U_13631,c_Orderings_Otop__class_Otop(tc_fun(U_13630,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13630),c_Orderings_Otop__class_Otop(tc_fun(U_13630,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3464_2]) ).

cnf(f_3464_4,plain,
    ( hAPP(c_Set_Oimage(U_13630,U_13630,U_13631),c_Orderings_Otop__class_Otop(tc_fun(U_13630,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13630,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_13630,U_13630,U_13631,c_Orderings_Otop__class_Otop(tc_fun(U_13630,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13630),c_Orderings_Otop__class_Otop(tc_fun(U_13630,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3464_3]) ).

fof(f_3465_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_3465_2,plain,
    ! [U_13633,U_13632] :
      ( c_Fun_Oinj__on(U_13632,U_13632,U_13633,c_Orderings_Otop__class_Otop(tc_fun(U_13632,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(U_13632,U_13632,U_13633),c_Orderings_Otop__class_Otop(tc_fun(U_13632,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13632,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13632),c_Orderings_Otop__class_Otop(tc_fun(U_13632,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3465_1]) ).

fof(f_3465_3,plain,
    ! [U_13632,U_13633] :
      ( c_Fun_Oinj__on(U_13632,U_13632,U_13633,c_Orderings_Otop__class_Otop(tc_fun(U_13632,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(U_13632,U_13632,U_13633),c_Orderings_Otop__class_Otop(tc_fun(U_13632,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13632,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13632),c_Orderings_Otop__class_Otop(tc_fun(U_13632,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3465_2]) ).

cnf(f_3465_4,plain,
    ( c_Fun_Oinj__on(U_13632,U_13632,U_13633,c_Orderings_Otop__class_Otop(tc_fun(U_13632,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(U_13632,U_13632,U_13633),c_Orderings_Otop__class_Otop(tc_fun(U_13632,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13632,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13632),c_Orderings_Otop__class_Otop(tc_fun(U_13632,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3465_3]) ).

fof(f_3466_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_3466_2,plain,
    ! [U_13638,U_13637,U_13636,U_13635,U_13634] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13635,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13634,U_13635,U_13636),U_13637)),hAPP(c_Set_Oimage(U_13634,U_13635,U_13636),U_13638)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13634,tc_HOL_Obool)),U_13637),U_13638)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13634,tc_HOL_Obool)),U_13637),U_13638))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13635,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13634,U_13635,U_13636),U_13637)),hAPP(c_Set_Oimage(U_13634,U_13635,U_13636),U_13638))) ) )
      | ~ c_Fun_Oinj__on(U_13634,U_13635,U_13636,c_Orderings_Otop__class_Otop(tc_fun(U_13634,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3466_1]) ).

fof(f_3466_3,plain,
    ( ! [U_13636,U_13638,U_13637,U_13634,U_13635] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13635,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13634,U_13635,U_13636),U_13637)),hAPP(c_Set_Oimage(U_13634,U_13635,U_13636),U_13638)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13634,tc_HOL_Obool)),U_13637),U_13638))
        | ~ sP965(U_13636,U_13638,U_13637,U_13634,U_13635) )
    & ! [U_13636,U_13638,U_13637,U_13634,U_13635] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13634,tc_HOL_Obool)),U_13637),U_13638))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13635,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13634,U_13635,U_13636),U_13637)),hAPP(c_Set_Oimage(U_13634,U_13635,U_13636),U_13638)))
        | ~ sP965(U_13636,U_13638,U_13637,U_13634,U_13635) )
    & ! [U_13636,U_13638,U_13637,U_13634,U_13635] :
        ( sP965(U_13636,U_13638,U_13637,U_13634,U_13635)
        | ~ c_Fun_Oinj__on(U_13634,U_13635,U_13636,c_Orderings_Otop__class_Otop(tc_fun(U_13634,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP965])],[f_3466_2]) ).

cnf(f_3466_4,plain,
    ( sP965(U_13636,U_13638,U_13637,U_13634,U_13635)
    | ~ c_Fun_Oinj__on(U_13634,U_13635,U_13636,c_Orderings_Otop__class_Otop(tc_fun(U_13634,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3466_3]) ).

cnf(f_3466_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13634,tc_HOL_Obool)),U_13637),U_13638))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13635,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13634,U_13635,U_13636),U_13637)),hAPP(c_Set_Oimage(U_13634,U_13635,U_13636),U_13638)))
    | ~ sP965(U_13636,U_13638,U_13637,U_13634,U_13635) ),
    inference(clausify,[status(thm)],[f_3466_3]) ).

cnf(f_3466_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13635,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13634,U_13635,U_13636),U_13637)),hAPP(c_Set_Oimage(U_13634,U_13635,U_13636),U_13638)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13634,tc_HOL_Obool)),U_13637),U_13638))
    | ~ sP965(U_13636,U_13638,U_13637,U_13634,U_13635) ),
    inference(clausify,[status(thm)],[f_3466_3]) ).

fof(f_3467_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_3467_2,plain,
    ! [U_13643,U_13642,U_13641,U_13640,U_13639] :
      ( hAPP(c_Set_Oimage(U_13639,U_13640,U_13641),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13639,tc_HOL_Obool)),U_13642),U_13643)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13640,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13639,U_13640,U_13641),U_13642)),hAPP(c_Set_Oimage(U_13639,U_13640,U_13641),U_13643))
      | ~ c_Fun_Oinj__on(U_13639,U_13640,U_13641,c_Orderings_Otop__class_Otop(tc_fun(U_13639,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3467_1]) ).

fof(f_3467_3,plain,
    ! [U_13641,U_13639,U_13640,U_13642,U_13643] :
      ( hAPP(c_Set_Oimage(U_13639,U_13640,U_13641),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13639,tc_HOL_Obool)),U_13642),U_13643)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13640,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13639,U_13640,U_13641),U_13642)),hAPP(c_Set_Oimage(U_13639,U_13640,U_13641),U_13643))
      | ~ c_Fun_Oinj__on(U_13639,U_13640,U_13641,c_Orderings_Otop__class_Otop(tc_fun(U_13639,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3467_2]) ).

cnf(f_3467_4,plain,
    ( hAPP(c_Set_Oimage(U_13639,U_13640,U_13641),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13639,tc_HOL_Obool)),U_13642),U_13643)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13640,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13639,U_13640,U_13641),U_13642)),hAPP(c_Set_Oimage(U_13639,U_13640,U_13641),U_13643))
    | ~ c_Fun_Oinj__on(U_13639,U_13640,U_13641,c_Orderings_Otop__class_Otop(tc_fun(U_13639,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3467_3]) ).

fof(f_3468_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_3468_2,plain,
    ! [U_13648,U_13647,U_13646,U_13645,U_13644] :
      ( hAPP(c_Set_Oimage(U_13644,U_13645,U_13646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13644,tc_HOL_Obool)),U_13647),U_13648)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13645,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13644,U_13645,U_13646),U_13647)),hAPP(c_Set_Oimage(U_13644,U_13645,U_13646),U_13648))
      | ~ c_Fun_Oinj__on(U_13644,U_13645,U_13646,c_Orderings_Otop__class_Otop(tc_fun(U_13644,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3468_1]) ).

fof(f_3468_3,plain,
    ! [U_13644,U_13645,U_13646,U_13647,U_13648] :
      ( hAPP(c_Set_Oimage(U_13644,U_13645,U_13646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13644,tc_HOL_Obool)),U_13647),U_13648)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13645,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13644,U_13645,U_13646),U_13647)),hAPP(c_Set_Oimage(U_13644,U_13645,U_13646),U_13648))
      | ~ c_Fun_Oinj__on(U_13644,U_13645,U_13646,c_Orderings_Otop__class_Otop(tc_fun(U_13644,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3468_2]) ).

cnf(f_3468_4,plain,
    ( hAPP(c_Set_Oimage(U_13644,U_13645,U_13646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13644,tc_HOL_Obool)),U_13647),U_13648)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13645,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13644,U_13645,U_13646),U_13647)),hAPP(c_Set_Oimage(U_13644,U_13645,U_13646),U_13648))
    | ~ c_Fun_Oinj__on(U_13644,U_13645,U_13646,c_Orderings_Otop__class_Otop(tc_fun(U_13644,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3468_3]) ).

fof(f_3469_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_3469_2,plain,
    ! [U_13652,U_13651,U_13650,U_13649] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13650,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13650,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13649,U_13650,U_13651),U_13652))),hAPP(c_Set_Oimage(U_13649,U_13650,U_13651),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13649,tc_HOL_Obool)),U_13652))))
      | hAPP(c_Set_Oimage(U_13649,U_13650,U_13651),c_Orderings_Otop__class_Otop(tc_fun(U_13649,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13650,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3469_1]) ).

fof(f_3469_3,plain,
    ! [U_13649,U_13650,U_13651,U_13652] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13650,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13650,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13649,U_13650,U_13651),U_13652))),hAPP(c_Set_Oimage(U_13649,U_13650,U_13651),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13649,tc_HOL_Obool)),U_13652))))
      | hAPP(c_Set_Oimage(U_13649,U_13650,U_13651),c_Orderings_Otop__class_Otop(tc_fun(U_13649,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13650,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3469_2]) ).

cnf(f_3469_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13650,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13650,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13649,U_13650,U_13651),U_13652))),hAPP(c_Set_Oimage(U_13649,U_13650,U_13651),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13649,tc_HOL_Obool)),U_13652))))
    | hAPP(c_Set_Oimage(U_13649,U_13650,U_13651),c_Orderings_Otop__class_Otop(tc_fun(U_13649,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13650,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3469_3]) ).

fof(f_3470_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_3470_2,plain,
    ! [U_13653] :
      ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_13653)) = U_13653
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13653),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3470_1]) ).

fof(f_3470_3,plain,
    ! [U_13653] :
      ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_13653)) = U_13653
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13653),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3470_2]) ).

cnf(f_3470_4,plain,
    ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_13653)) = U_13653
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13653),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3470_3]) ).

fof(f_3471_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_3471_2,plain,
    ! [U_13657,U_13656,U_13655,U_13654] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13654,U_13655,hAPP(hAPP(c_Set_Oinsert(U_13654),U_13656),c_Orderings_Obot__class_Obot(tc_fun(U_13654,tc_HOL_Obool)))),U_13657))
        | U_13656 != U_13657 )
      & ( U_13656 = U_13657
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13654,U_13655,hAPP(hAPP(c_Set_Oinsert(U_13654),U_13656),c_Orderings_Obot__class_Obot(tc_fun(U_13654,tc_HOL_Obool)))),U_13657)) ) ),
    inference(variable_rename,[status(thm)],[f_3471_1]) ).

fof(f_3471_3,plain,
    ( ! [U_13665,U_13663] :
        ( ! [U_13661,U_13659] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13659,U_13661,hAPP(hAPP(c_Set_Oinsert(U_13659),U_13663),c_Orderings_Obot__class_Obot(tc_fun(U_13659,tc_HOL_Obool)))),U_13665))
        | U_13663 != U_13665 )
    & ! [U_13664,U_13662] :
        ( ! [U_13660,U_13658] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13658,U_13660,hAPP(hAPP(c_Set_Oinsert(U_13658),U_13662),c_Orderings_Obot__class_Obot(tc_fun(U_13658,tc_HOL_Obool)))),U_13664))
        | U_13662 = U_13664 ) ),
    inference(miniscope,[status(thm)],[f_3471_2]) ).

fof(f_3471_4,plain,
    ( ! [U_13659,U_13665,U_13661,U_13663] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13659,U_13661,hAPP(hAPP(c_Set_Oinsert(U_13659),U_13663),c_Orderings_Obot__class_Obot(tc_fun(U_13659,tc_HOL_Obool)))),U_13665))
        | U_13663 != U_13665 )
    & ! [U_13660,U_13662,U_13658,U_13664] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13658,U_13660,hAPP(hAPP(c_Set_Oinsert(U_13658),U_13662),c_Orderings_Obot__class_Obot(tc_fun(U_13658,tc_HOL_Obool)))),U_13664))
        | U_13662 = U_13664 ) ),
    inference(definitional_conversion,[status(esa)],[f_3471_3]) ).

cnf(f_3471_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13658,U_13660,hAPP(hAPP(c_Set_Oinsert(U_13658),U_13662),c_Orderings_Obot__class_Obot(tc_fun(U_13658,tc_HOL_Obool)))),U_13664))
    | U_13662 = U_13664 ),
    inference(clausify,[status(thm)],[f_3471_4]) ).

cnf(f_3471_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13659,U_13661,hAPP(hAPP(c_Set_Oinsert(U_13659),U_13663),c_Orderings_Obot__class_Obot(tc_fun(U_13659,tc_HOL_Obool)))),U_13665))
    | U_13663 != U_13665 ),
    inference(clausify,[status(thm)],[f_3471_4]) ).

fof(f_3472_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_3472_2,plain,
    ! [U_13670,U_13669,U_13668,U_13667,U_13666] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13666)),hAPP(c_Set_Oimage(U_13667,tc_Option_Ooption(U_13666),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13667,tc_Option_Ooption(U_13666)),U_13668),U_13669),hAPP(c_Option_Ooption_OSome(U_13666),U_13670))),c_Orderings_Otop__class_Otop(tc_fun(U_13667,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13666)),hAPP(c_Set_Oimage(U_13667,tc_Option_Ooption(U_13666),U_13668),c_Orderings_Otop__class_Otop(tc_fun(U_13667,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_3472_1]) ).

fof(f_3472_3,plain,
    ! [U_13666,U_13667,U_13668,U_13669,U_13670] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13666)),hAPP(c_Set_Oimage(U_13667,tc_Option_Ooption(U_13666),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13667,tc_Option_Ooption(U_13666)),U_13668),U_13669),hAPP(c_Option_Ooption_OSome(U_13666),U_13670))),c_Orderings_Otop__class_Otop(tc_fun(U_13667,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13666)),hAPP(c_Set_Oimage(U_13667,tc_Option_Ooption(U_13666),U_13668),c_Orderings_Otop__class_Otop(tc_fun(U_13667,tc_HOL_Obool))))) ),
    inference(definitional_conversion,[status(esa)],[f_3472_2]) ).

cnf(f_3472_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13666)),hAPP(c_Set_Oimage(U_13667,tc_Option_Ooption(U_13666),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13667,tc_Option_Ooption(U_13666)),U_13668),U_13669),hAPP(c_Option_Ooption_OSome(U_13666),U_13670))),c_Orderings_Otop__class_Otop(tc_fun(U_13667,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13666)),hAPP(c_Set_Oimage(U_13667,tc_Option_Ooption(U_13666),U_13668),c_Orderings_Otop__class_Otop(tc_fun(U_13667,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_3472_3]) ).

fof(f_3473_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_3473_2,plain,
    ! [U_13672,U_13671] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13671,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_13671,tc_HOL_Obool)),tc_fun(U_13671,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_13671,tc_HOL_Obool)),tc_fun(U_13671,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13671,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_13672)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13671,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13672),
    inference(variable_rename,[status(thm)],[f_3473_1]) ).

fof(f_3473_3,plain,
    ! [U_13672,U_13671] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13671,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_13671,tc_HOL_Obool)),tc_fun(U_13671,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_13671,tc_HOL_Obool)),tc_fun(U_13671,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13671,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_13672)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13671,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13672),
    inference(definitional_conversion,[status(esa)],[f_3473_2]) ).

cnf(f_3473_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13671,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_13671,tc_HOL_Obool)),tc_fun(U_13671,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_13671,tc_HOL_Obool)),tc_fun(U_13671,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13671,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_13672)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13671,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13672),
    inference(clausify,[status(thm)],[f_3473_3]) ).

fof(f_3474_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_3474_2,plain,
    ! [U_13673] : c_Fun_Oinj__on(U_13673,tc_fun(U_13673,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13673,tc_fun(U_13673,tc_HOL_Obool),tc_fun(U_13673,tc_HOL_Obool)),c_Set_Oinsert(U_13673)),c_Orderings_Obot__class_Obot(tc_fun(U_13673,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13673,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3474_1]) ).

fof(f_3474_3,plain,
    ! [U_13673] : c_Fun_Oinj__on(U_13673,tc_fun(U_13673,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13673,tc_fun(U_13673,tc_HOL_Obool),tc_fun(U_13673,tc_HOL_Obool)),c_Set_Oinsert(U_13673)),c_Orderings_Obot__class_Obot(tc_fun(U_13673,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13673,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3474_2]) ).

cnf(f_3474_4,plain,
    c_Fun_Oinj__on(U_13673,tc_fun(U_13673,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13673,tc_fun(U_13673,tc_HOL_Obool),tc_fun(U_13673,tc_HOL_Obool)),c_Set_Oinsert(U_13673)),c_Orderings_Obot__class_Obot(tc_fun(U_13673,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13673,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3474_3]) ).

fof(f_3475_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_3475_2,plain,
    ! [U_13674] :
      ( 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_13674),c_Orderings_Otop__class_Otop(tc_fun(U_13674,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13674),c_Orderings_Otop__class_Otop(tc_fun(U_13674,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3475_1]) ).

fof(f_3475_3,plain,
    ! [U_13674] :
      ( 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_13674),c_Orderings_Otop__class_Otop(tc_fun(U_13674,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13674),c_Orderings_Otop__class_Otop(tc_fun(U_13674,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3475_2]) ).

cnf(f_3475_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_13674),c_Orderings_Otop__class_Otop(tc_fun(U_13674,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13674),c_Orderings_Otop__class_Otop(tc_fun(U_13674,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3475_3]) ).

fof(f_3476_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_3476_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_3476_1]) ).

cnf(f_3476_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_3476_2]) ).

fof(f_3477_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_3477_2,plain,
    ! [U_13678,U_13677,U_13676,U_13675] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13676,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13675,U_13676,U_13677),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13675,tc_HOL_Obool)),U_13678))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13676,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13675,U_13676,U_13677),U_13678))))
      | ~ c_Fun_Oinj__on(U_13675,U_13676,U_13677,c_Orderings_Otop__class_Otop(tc_fun(U_13675,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3477_1]) ).

fof(f_3477_3,plain,
    ! [U_13675,U_13676,U_13677,U_13678] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13676,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13675,U_13676,U_13677),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13675,tc_HOL_Obool)),U_13678))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13676,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13675,U_13676,U_13677),U_13678))))
      | ~ c_Fun_Oinj__on(U_13675,U_13676,U_13677,c_Orderings_Otop__class_Otop(tc_fun(U_13675,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3477_2]) ).

cnf(f_3477_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13676,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13675,U_13676,U_13677),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13675,tc_HOL_Obool)),U_13678))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13676,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13675,U_13676,U_13677),U_13678))))
    | ~ c_Fun_Oinj__on(U_13675,U_13676,U_13677,c_Orderings_Otop__class_Otop(tc_fun(U_13675,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3477_3]) ).

fof(f_3478_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_3478_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_3478_1]) ).

cnf(f_3478_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_3478_2]) ).

fof(f_3479_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_3479_2,plain,
    ! [U_13684,U_13683,U_13682,U_13681,U_13680,U_13679] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13679,tc_fun(U_13680,tc_fun(U_13681,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13679,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool),tc_fun(U_13680,tc_fun(U_13681,tc_HOL_Obool)),U_13679),hAPP(c_COMBC(U_13680,tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool),tc_fun(U_13681,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13681,tc_fun(tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool),tc_fun(U_13681,tc_HOL_Obool)),U_13680),c_COMBC(U_13681,tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13681,tc_prod(U_13680,U_13681)),tc_fun(U_13681,tc_fun(tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool),tc_HOL_Obool)),U_13680),hAPP(c_COMBB(tc_prod(U_13680,U_13681),tc_fun(tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool),tc_HOL_Obool),U_13681),c_member(tc_prod(U_13680,U_13681)))),c_Product__Type_OPair(U_13680,U_13681))))),U_13682)),U_13683),U_13684))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13680,U_13681)),hAPP(hAPP(c_Product__Type_OPair(U_13680,U_13681),U_13683),U_13684)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13679,tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13679,tc_HOL_Obool))),U_13682))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13680,U_13681)),hAPP(hAPP(c_Product__Type_OPair(U_13680,U_13681),U_13683),U_13684)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13679,tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13679,tc_HOL_Obool))),U_13682)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13679,tc_fun(U_13680,tc_fun(U_13681,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13679,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool),tc_fun(U_13680,tc_fun(U_13681,tc_HOL_Obool)),U_13679),hAPP(c_COMBC(U_13680,tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool),tc_fun(U_13681,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13681,tc_fun(tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool),tc_fun(U_13681,tc_HOL_Obool)),U_13680),c_COMBC(U_13681,tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13681,tc_prod(U_13680,U_13681)),tc_fun(U_13681,tc_fun(tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool),tc_HOL_Obool)),U_13680),hAPP(c_COMBB(tc_prod(U_13680,U_13681),tc_fun(tc_fun(tc_prod(U_13680,U_13681),tc_HOL_Obool),tc_HOL_Obool),U_13681),c_member(tc_prod(U_13680,U_13681)))),c_Product__Type_OPair(U_13680,U_13681))))),U_13682)),U_13683),U_13684)) ) ),
    inference(variable_rename,[status(thm)],[f_3479_1]) ).

fof(f_3479_3,plain,
    ( ! [U_13696,U_13694,U_13692,U_13690,U_13688,U_13686] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13686,tc_fun(U_13688,tc_fun(U_13690,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13686,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_fun(U_13688,tc_fun(U_13690,tc_HOL_Obool)),U_13686),hAPP(c_COMBC(U_13688,tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_fun(U_13690,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13690,tc_fun(tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_fun(U_13690,tc_HOL_Obool)),U_13688),c_COMBC(U_13690,tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13690,tc_prod(U_13688,U_13690)),tc_fun(U_13690,tc_fun(tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_HOL_Obool)),U_13688),hAPP(c_COMBB(tc_prod(U_13688,U_13690),tc_fun(tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_HOL_Obool),U_13690),c_member(tc_prod(U_13688,U_13690)))),c_Product__Type_OPair(U_13688,U_13690))))),U_13692)),U_13694),U_13696))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13688,U_13690)),hAPP(hAPP(c_Product__Type_OPair(U_13688,U_13690),U_13694),U_13696)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13686,tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13686,tc_HOL_Obool))),U_13692))) )
    & ! [U_13695,U_13693,U_13691,U_13689,U_13687,U_13685] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13687,U_13689)),hAPP(hAPP(c_Product__Type_OPair(U_13687,U_13689),U_13693),U_13695)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13685,tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13685,tc_HOL_Obool))),U_13691)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13685,tc_fun(U_13687,tc_fun(U_13689,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13685,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_fun(U_13687,tc_fun(U_13689,tc_HOL_Obool)),U_13685),hAPP(c_COMBC(U_13687,tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_fun(U_13689,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13689,tc_fun(tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_fun(U_13689,tc_HOL_Obool)),U_13687),c_COMBC(U_13689,tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13689,tc_prod(U_13687,U_13689)),tc_fun(U_13689,tc_fun(tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_HOL_Obool)),U_13687),hAPP(c_COMBB(tc_prod(U_13687,U_13689),tc_fun(tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_HOL_Obool),U_13689),c_member(tc_prod(U_13687,U_13689)))),c_Product__Type_OPair(U_13687,U_13689))))),U_13691)),U_13693),U_13695)) ) ),
    inference(miniscope,[status(thm)],[f_3479_2]) ).

fof(f_3479_4,plain,
    ( ! [U_13686,U_13688,U_13690,U_13692,U_13694,U_13696] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13686,tc_fun(U_13688,tc_fun(U_13690,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13686,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_fun(U_13688,tc_fun(U_13690,tc_HOL_Obool)),U_13686),hAPP(c_COMBC(U_13688,tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_fun(U_13690,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13690,tc_fun(tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_fun(U_13690,tc_HOL_Obool)),U_13688),c_COMBC(U_13690,tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13690,tc_prod(U_13688,U_13690)),tc_fun(U_13690,tc_fun(tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_HOL_Obool)),U_13688),hAPP(c_COMBB(tc_prod(U_13688,U_13690),tc_fun(tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_HOL_Obool),U_13690),c_member(tc_prod(U_13688,U_13690)))),c_Product__Type_OPair(U_13688,U_13690))))),U_13692)),U_13694),U_13696))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13688,U_13690)),hAPP(hAPP(c_Product__Type_OPair(U_13688,U_13690),U_13694),U_13696)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13686,tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13686,tc_HOL_Obool))),U_13692))) )
    & ! [U_13687,U_13685,U_13691,U_13693,U_13689,U_13695] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13687,U_13689)),hAPP(hAPP(c_Product__Type_OPair(U_13687,U_13689),U_13693),U_13695)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13685,tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13685,tc_HOL_Obool))),U_13691)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13685,tc_fun(U_13687,tc_fun(U_13689,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13685,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_fun(U_13687,tc_fun(U_13689,tc_HOL_Obool)),U_13685),hAPP(c_COMBC(U_13687,tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_fun(U_13689,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13689,tc_fun(tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_fun(U_13689,tc_HOL_Obool)),U_13687),c_COMBC(U_13689,tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13689,tc_prod(U_13687,U_13689)),tc_fun(U_13689,tc_fun(tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_HOL_Obool)),U_13687),hAPP(c_COMBB(tc_prod(U_13687,U_13689),tc_fun(tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_HOL_Obool),U_13689),c_member(tc_prod(U_13687,U_13689)))),c_Product__Type_OPair(U_13687,U_13689))))),U_13691)),U_13693),U_13695)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3479_3]) ).

cnf(f_3479_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13687,U_13689)),hAPP(hAPP(c_Product__Type_OPair(U_13687,U_13689),U_13693),U_13695)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13685,tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13685,tc_HOL_Obool))),U_13691)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13685,tc_fun(U_13687,tc_fun(U_13689,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13685,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_fun(U_13687,tc_fun(U_13689,tc_HOL_Obool)),U_13685),hAPP(c_COMBC(U_13687,tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_fun(U_13689,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13689,tc_fun(tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_fun(U_13689,tc_HOL_Obool)),U_13687),c_COMBC(U_13689,tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13689,tc_prod(U_13687,U_13689)),tc_fun(U_13689,tc_fun(tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_HOL_Obool)),U_13687),hAPP(c_COMBB(tc_prod(U_13687,U_13689),tc_fun(tc_fun(tc_prod(U_13687,U_13689),tc_HOL_Obool),tc_HOL_Obool),U_13689),c_member(tc_prod(U_13687,U_13689)))),c_Product__Type_OPair(U_13687,U_13689))))),U_13691)),U_13693),U_13695)) ),
    inference(clausify,[status(thm)],[f_3479_4]) ).

cnf(f_3479_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13686,tc_fun(U_13688,tc_fun(U_13690,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13686,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_fun(U_13688,tc_fun(U_13690,tc_HOL_Obool)),U_13686),hAPP(c_COMBC(U_13688,tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_fun(U_13690,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13690,tc_fun(tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_fun(U_13690,tc_HOL_Obool)),U_13688),c_COMBC(U_13690,tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13690,tc_prod(U_13688,U_13690)),tc_fun(U_13690,tc_fun(tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_HOL_Obool)),U_13688),hAPP(c_COMBB(tc_prod(U_13688,U_13690),tc_fun(tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool),tc_HOL_Obool),U_13690),c_member(tc_prod(U_13688,U_13690)))),c_Product__Type_OPair(U_13688,U_13690))))),U_13692)),U_13694),U_13696))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13688,U_13690)),hAPP(hAPP(c_Product__Type_OPair(U_13688,U_13690),U_13694),U_13696)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13686,tc_fun(tc_prod(U_13688,U_13690),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13686,tc_HOL_Obool))),U_13692))) ),
    inference(clausify,[status(thm)],[f_3479_4]) ).

fof(f_3480_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_3480_2,plain,
    ! [U_13701,U_13700,U_13699,U_13698] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13698,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13699)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13701)))
      | ? [U_13697] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13698,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13697)),U_13699)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,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_13697),U_13700))),U_13701))) ),
    inference(variable_rename,[status(thm)],[f_3480_1]) ).

fof(f_3480_3,plain,
    ! [U_13701,U_13700,U_13699,U_13698] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13698,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13699)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13701)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13698,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK290(U_13701,U_13700,U_13699,U_13698))),U_13699)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,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),sK290(U_13701,U_13700,U_13699,U_13698)),U_13700))),U_13701))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK290]),skolemize(U_13697,sK290(U_13701,U_13700,U_13699,U_13698))],[f_3480_2]) ).

fof(f_3480_4,plain,
    ! [U_13698,U_13699,U_13700,U_13701] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13698,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13699)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13701)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13698,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK290(U_13701,U_13700,U_13699,U_13698))),U_13699)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,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),sK290(U_13701,U_13700,U_13699,U_13698)),U_13700))),U_13701))) ),
    inference(definitional_conversion,[status(esa)],[f_3480_3]) ).

cnf(f_3480_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13698,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13699)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13701)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13698,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK290(U_13701,U_13700,U_13699,U_13698))),U_13699)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13698,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),sK290(U_13701,U_13700,U_13699,U_13698)),U_13700))),U_13701))) ),
    inference(clausify,[status(thm)],[f_3480_4]) ).

fof(f_3481_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_3481_2,plain,
    ! [U_13706,U_13705,U_13704,U_13703] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13704) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13706)
      | ? [U_13702] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13702)),U_13704) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,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_13702),U_13705))),U_13706) ),
    inference(variable_rename,[status(thm)],[f_3481_1]) ).

fof(f_3481_3,plain,
    ! [U_13706,U_13705,U_13704,U_13703] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13704) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13706)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK291(U_13706,U_13705,U_13704,U_13703))),U_13704) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,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),sK291(U_13706,U_13705,U_13704,U_13703)),U_13705))),U_13706) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK291]),skolemize(U_13702,sK291(U_13706,U_13705,U_13704,U_13703))],[f_3481_2]) ).

fof(f_3481_4,plain,
    ! [U_13703,U_13704,U_13705,U_13706] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13704) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13706)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK291(U_13706,U_13705,U_13704,U_13703))),U_13704) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,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),sK291(U_13706,U_13705,U_13704,U_13703)),U_13705))),U_13706) ),
    inference(definitional_conversion,[status(esa)],[f_3481_3]) ).

cnf(f_3481_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13704) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13706)
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK291(U_13706,U_13705,U_13704,U_13703))),U_13704) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13703,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),sK291(U_13706,U_13705,U_13704,U_13703)),U_13705))),U_13706) ),
    inference(clausify,[status(thm)],[f_3481_4]) ).

fof(f_3482_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_3482_2,plain,
    ! [U_13710,U_13709,U_13708] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13708,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13708,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13709)),U_13710))
      | ? [U_13707] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13708,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13708,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13707)),U_13709)),U_13710)) ),
    inference(variable_rename,[status(thm)],[f_3482_1]) ).

fof(f_3482_3,plain,
    ! [U_13710,U_13709,U_13708] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13708,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13708,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13709)),U_13710))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13708,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13708,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK292(U_13710,U_13709,U_13708))),U_13709)),U_13710)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK292]),skolemize(U_13707,sK292(U_13710,U_13709,U_13708))],[f_3482_2]) ).

fof(f_3482_4,plain,
    ! [U_13708,U_13709,U_13710] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13708,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13708,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13709)),U_13710))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13708,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13708,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK292(U_13710,U_13709,U_13708))),U_13709)),U_13710)) ),
    inference(definitional_conversion,[status(esa)],[f_3482_3]) ).

cnf(f_3482_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13708,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13708,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_13709)),U_13710))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13708,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13708,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK292(U_13710,U_13709,U_13708))),U_13709)),U_13710)) ),
    inference(clausify,[status(thm)],[f_3482_4]) ).

fof(f_3483_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_3483_2,plain,
    ! [U_13712,U_13711] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_13711,tc_HOL_Obool)),U_13712)),
    inference(variable_rename,[status(thm)],[f_3483_1]) ).

fof(f_3483_3,plain,
    ! [U_13712,U_13711] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_13711,tc_HOL_Obool)),U_13712)),
    inference(definitional_conversion,[status(esa)],[f_3483_2]) ).

cnf(f_3483_4,plain,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_13711,tc_HOL_Obool)),U_13712)),
    inference(clausify,[status(thm)],[f_3483_3]) ).

fof(f_3484_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_3484_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_3484_1]) ).

cnf(f_3484_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_3484_2]) ).

fof(f_3485_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_3485_2,plain,
    ! [U_13714,U_13713] : hBOOL(hAPP(hAPP(c_member(U_13713),U_13714),c_Orderings_Otop__class_Otop(tc_fun(U_13713,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3485_1]) ).

fof(f_3485_3,plain,
    ! [U_13713,U_13714] : hBOOL(hAPP(hAPP(c_member(U_13713),U_13714),c_Orderings_Otop__class_Otop(tc_fun(U_13713,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3485_2]) ).

cnf(f_3485_4,plain,
    hBOOL(hAPP(hAPP(c_member(U_13713),U_13714),c_Orderings_Otop__class_Otop(tc_fun(U_13713,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3485_3]) ).

fof(f_3486_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_3486_2,plain,
    ! [U_13716,U_13715] :
      ( ( c_Equiv__Relations_Oequiv(U_13715,c_Orderings_Otop__class_Otop(tc_fun(U_13715,tc_HOL_Obool)),U_13716)
        | ~ c_Equiv__Relations_Oequivp(U_13715,hAPP(hAPP(c_COMBC(U_13715,tc_fun(tc_prod(U_13715,U_13715),tc_HOL_Obool),tc_fun(U_13715,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13715,tc_fun(tc_fun(tc_prod(U_13715,U_13715),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13715,U_13715),tc_HOL_Obool),tc_fun(U_13715,tc_HOL_Obool)),U_13715),c_COMBC(U_13715,tc_fun(tc_prod(U_13715,U_13715),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13715,tc_prod(U_13715,U_13715)),tc_fun(U_13715,tc_fun(tc_fun(tc_prod(U_13715,U_13715),tc_HOL_Obool),tc_HOL_Obool)),U_13715),hAPP(c_COMBB(tc_prod(U_13715,U_13715),tc_fun(tc_fun(tc_prod(U_13715,U_13715),tc_HOL_Obool),tc_HOL_Obool),U_13715),c_member(tc_prod(U_13715,U_13715)))),c_Product__Type_OPair(U_13715,U_13715)))),U_13716)) )
      & ( c_Equiv__Relations_Oequivp(U_13715,hAPP(hAPP(c_COMBC(U_13715,tc_fun(tc_prod(U_13715,U_13715),tc_HOL_Obool),tc_fun(U_13715,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13715,tc_fun(tc_fun(tc_prod(U_13715,U_13715),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13715,U_13715),tc_HOL_Obool),tc_fun(U_13715,tc_HOL_Obool)),U_13715),c_COMBC(U_13715,tc_fun(tc_prod(U_13715,U_13715),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13715,tc_prod(U_13715,U_13715)),tc_fun(U_13715,tc_fun(tc_fun(tc_prod(U_13715,U_13715),tc_HOL_Obool),tc_HOL_Obool)),U_13715),hAPP(c_COMBB(tc_prod(U_13715,U_13715),tc_fun(tc_fun(tc_prod(U_13715,U_13715),tc_HOL_Obool),tc_HOL_Obool),U_13715),c_member(tc_prod(U_13715,U_13715)))),c_Product__Type_OPair(U_13715,U_13715)))),U_13716))
        | ~ c_Equiv__Relations_Oequiv(U_13715,c_Orderings_Otop__class_Otop(tc_fun(U_13715,tc_HOL_Obool)),U_13716) ) ),
    inference(variable_rename,[status(thm)],[f_3486_1]) ).

fof(f_3486_3,plain,
    ( ! [U_13720,U_13718] :
        ( c_Equiv__Relations_Oequiv(U_13718,c_Orderings_Otop__class_Otop(tc_fun(U_13718,tc_HOL_Obool)),U_13720)
        | ~ c_Equiv__Relations_Oequivp(U_13718,hAPP(hAPP(c_COMBC(U_13718,tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_fun(U_13718,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13718,tc_fun(tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_fun(U_13718,tc_HOL_Obool)),U_13718),c_COMBC(U_13718,tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13718,tc_prod(U_13718,U_13718)),tc_fun(U_13718,tc_fun(tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_HOL_Obool)),U_13718),hAPP(c_COMBB(tc_prod(U_13718,U_13718),tc_fun(tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_HOL_Obool),U_13718),c_member(tc_prod(U_13718,U_13718)))),c_Product__Type_OPair(U_13718,U_13718)))),U_13720)) )
    & ! [U_13719,U_13717] :
        ( c_Equiv__Relations_Oequivp(U_13717,hAPP(hAPP(c_COMBC(U_13717,tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_fun(U_13717,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13717,tc_fun(tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_fun(U_13717,tc_HOL_Obool)),U_13717),c_COMBC(U_13717,tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13717,tc_prod(U_13717,U_13717)),tc_fun(U_13717,tc_fun(tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_HOL_Obool)),U_13717),hAPP(c_COMBB(tc_prod(U_13717,U_13717),tc_fun(tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_HOL_Obool),U_13717),c_member(tc_prod(U_13717,U_13717)))),c_Product__Type_OPair(U_13717,U_13717)))),U_13719))
        | ~ c_Equiv__Relations_Oequiv(U_13717,c_Orderings_Otop__class_Otop(tc_fun(U_13717,tc_HOL_Obool)),U_13719) ) ),
    inference(miniscope,[status(thm)],[f_3486_2]) ).

fof(f_3486_4,plain,
    ( ! [U_13720,U_13718] :
        ( c_Equiv__Relations_Oequiv(U_13718,c_Orderings_Otop__class_Otop(tc_fun(U_13718,tc_HOL_Obool)),U_13720)
        | ~ c_Equiv__Relations_Oequivp(U_13718,hAPP(hAPP(c_COMBC(U_13718,tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_fun(U_13718,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13718,tc_fun(tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_fun(U_13718,tc_HOL_Obool)),U_13718),c_COMBC(U_13718,tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13718,tc_prod(U_13718,U_13718)),tc_fun(U_13718,tc_fun(tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_HOL_Obool)),U_13718),hAPP(c_COMBB(tc_prod(U_13718,U_13718),tc_fun(tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_HOL_Obool),U_13718),c_member(tc_prod(U_13718,U_13718)))),c_Product__Type_OPair(U_13718,U_13718)))),U_13720)) )
    & ! [U_13719,U_13717] :
        ( c_Equiv__Relations_Oequivp(U_13717,hAPP(hAPP(c_COMBC(U_13717,tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_fun(U_13717,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13717,tc_fun(tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_fun(U_13717,tc_HOL_Obool)),U_13717),c_COMBC(U_13717,tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13717,tc_prod(U_13717,U_13717)),tc_fun(U_13717,tc_fun(tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_HOL_Obool)),U_13717),hAPP(c_COMBB(tc_prod(U_13717,U_13717),tc_fun(tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_HOL_Obool),U_13717),c_member(tc_prod(U_13717,U_13717)))),c_Product__Type_OPair(U_13717,U_13717)))),U_13719))
        | ~ c_Equiv__Relations_Oequiv(U_13717,c_Orderings_Otop__class_Otop(tc_fun(U_13717,tc_HOL_Obool)),U_13719) ) ),
    inference(definitional_conversion,[status(esa)],[f_3486_3]) ).

cnf(f_3486_5,plain,
    ( c_Equiv__Relations_Oequivp(U_13717,hAPP(hAPP(c_COMBC(U_13717,tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_fun(U_13717,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13717,tc_fun(tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_fun(U_13717,tc_HOL_Obool)),U_13717),c_COMBC(U_13717,tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13717,tc_prod(U_13717,U_13717)),tc_fun(U_13717,tc_fun(tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_HOL_Obool)),U_13717),hAPP(c_COMBB(tc_prod(U_13717,U_13717),tc_fun(tc_fun(tc_prod(U_13717,U_13717),tc_HOL_Obool),tc_HOL_Obool),U_13717),c_member(tc_prod(U_13717,U_13717)))),c_Product__Type_OPair(U_13717,U_13717)))),U_13719))
    | ~ c_Equiv__Relations_Oequiv(U_13717,c_Orderings_Otop__class_Otop(tc_fun(U_13717,tc_HOL_Obool)),U_13719) ),
    inference(clausify,[status(thm)],[f_3486_4]) ).

cnf(f_3486_6,plain,
    ( c_Equiv__Relations_Oequiv(U_13718,c_Orderings_Otop__class_Otop(tc_fun(U_13718,tc_HOL_Obool)),U_13720)
    | ~ c_Equiv__Relations_Oequivp(U_13718,hAPP(hAPP(c_COMBC(U_13718,tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_fun(U_13718,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13718,tc_fun(tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_fun(U_13718,tc_HOL_Obool)),U_13718),c_COMBC(U_13718,tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13718,tc_prod(U_13718,U_13718)),tc_fun(U_13718,tc_fun(tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_HOL_Obool)),U_13718),hAPP(c_COMBB(tc_prod(U_13718,U_13718),tc_fun(tc_fun(tc_prod(U_13718,U_13718),tc_HOL_Obool),tc_HOL_Obool),U_13718),c_member(tc_prod(U_13718,U_13718)))),c_Product__Type_OPair(U_13718,U_13718)))),U_13720)) ),
    inference(clausify,[status(thm)],[f_3486_4]) ).

fof(f_3487_1,plain,
    ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal),
    inference(fof_nnf,[status(thm)],[fact_identity__equivp]) ).

fof(f_3487_2,plain,
    ! [U_13721] : c_Equiv__Relations_Oequivp(U_13721,c_fequal),
    inference(variable_rename,[status(thm)],[f_3487_1]) ).

fof(f_3487_3,plain,
    ! [U_13721] : c_Equiv__Relations_Oequivp(U_13721,c_fequal),
    inference(definitional_conversion,[status(esa)],[f_3487_2]) ).

cnf(f_3487_4,plain,
    c_Equiv__Relations_Oequivp(U_13721,c_fequal),
    inference(clausify,[status(thm)],[f_3487_3]) ).

fof(f_3488_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_3488_2,plain,
    ! [U_13727,U_13726] :
      ( ( c_Equiv__Relations_Oequivp(U_13726,U_13727)
        | ? [U_13725,U_13724] :
            ( ( ~ hBOOL(hAPP(hAPP(U_13727,U_13725),U_13724))
              & hAPP(U_13727,U_13725) = hAPP(U_13727,U_13724) )
            | ( hAPP(U_13727,U_13725) != hAPP(U_13727,U_13724)
              & hBOOL(hAPP(hAPP(U_13727,U_13725),U_13724)) ) ) )
      & ( ! [U_13723,U_13722] :
            ( ( hBOOL(hAPP(hAPP(U_13727,U_13723),U_13722))
              | hAPP(U_13727,U_13723) != hAPP(U_13727,U_13722) )
            & ( hAPP(U_13727,U_13723) = hAPP(U_13727,U_13722)
              | ~ hBOOL(hAPP(hAPP(U_13727,U_13723),U_13722)) ) )
        | ~ c_Equiv__Relations_Oequivp(U_13726,U_13727) ) ),
    inference(variable_rename,[status(thm)],[f_3488_1]) ).

fof(f_3488_3,plain,
    ( ! [U_13739] :
        ( ! [U_13737] : c_Equiv__Relations_Oequivp(U_13737,U_13739)
        | ? [U_13735,U_13733] :
            ( ~ hBOOL(hAPP(hAPP(U_13739,U_13735),U_13733))
            & hAPP(U_13739,U_13735) = hAPP(U_13739,U_13733) )
        | ? [U_13734,U_13732] :
            ( hAPP(U_13739,U_13734) != hAPP(U_13739,U_13732)
            & hBOOL(hAPP(hAPP(U_13739,U_13734),U_13732)) ) )
    & ! [U_13738] :
        ( ! [U_13736] : ~ c_Equiv__Relations_Oequivp(U_13736,U_13738)
        | ( ! [U_13731,U_13729] :
              ( hBOOL(hAPP(hAPP(U_13738,U_13731),U_13729))
              | hAPP(U_13738,U_13731) != hAPP(U_13738,U_13729) )
          & ! [U_13730,U_13728] :
              ( hAPP(U_13738,U_13730) = hAPP(U_13738,U_13728)
              | ~ hBOOL(hAPP(hAPP(U_13738,U_13730),U_13728)) ) ) ) ),
    inference(miniscope,[status(thm)],[f_3488_2]) ).

fof(f_3488_4,plain,
    ( ! [U_13739] :
        ( ! [U_13737] : c_Equiv__Relations_Oequivp(U_13737,U_13739)
        | ? [U_13735,U_13733] :
            ( ~ hBOOL(hAPP(hAPP(U_13739,U_13735),U_13733))
            & hAPP(U_13739,U_13735) = hAPP(U_13739,U_13733) )
        | ? [U_13732] :
            ( hAPP(U_13739,sK293(U_13739)) != hAPP(U_13739,U_13732)
            & hBOOL(hAPP(hAPP(U_13739,sK293(U_13739)),U_13732)) ) )
    & ! [U_13738] :
        ( ! [U_13736] : ~ c_Equiv__Relations_Oequivp(U_13736,U_13738)
        | ( ! [U_13731,U_13729] :
              ( hBOOL(hAPP(hAPP(U_13738,U_13731),U_13729))
              | hAPP(U_13738,U_13731) != hAPP(U_13738,U_13729) )
          & ! [U_13730,U_13728] :
              ( hAPP(U_13738,U_13730) = hAPP(U_13738,U_13728)
              | ~ hBOOL(hAPP(hAPP(U_13738,U_13730),U_13728)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK293]),skolemize(U_13734,sK293(U_13739))],[f_3488_3]) ).

fof(f_3488_5,plain,
    ( ! [U_13739] :
        ( ! [U_13737] : c_Equiv__Relations_Oequivp(U_13737,U_13739)
        | ? [U_13735,U_13733] :
            ( ~ hBOOL(hAPP(hAPP(U_13739,U_13735),U_13733))
            & hAPP(U_13739,U_13735) = hAPP(U_13739,U_13733) )
        | ( hAPP(U_13739,sK293(U_13739)) != hAPP(U_13739,sK294(U_13739))
          & hBOOL(hAPP(hAPP(U_13739,sK293(U_13739)),sK294(U_13739))) ) )
    & ! [U_13738] :
        ( ! [U_13736] : ~ c_Equiv__Relations_Oequivp(U_13736,U_13738)
        | ( ! [U_13731,U_13729] :
              ( hBOOL(hAPP(hAPP(U_13738,U_13731),U_13729))
              | hAPP(U_13738,U_13731) != hAPP(U_13738,U_13729) )
          & ! [U_13730,U_13728] :
              ( hAPP(U_13738,U_13730) = hAPP(U_13738,U_13728)
              | ~ hBOOL(hAPP(hAPP(U_13738,U_13730),U_13728)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK294]),skolemize(U_13732,sK294(U_13739))],[f_3488_4]) ).

fof(f_3488_6,plain,
    ( ! [U_13739] :
        ( ! [U_13737] : c_Equiv__Relations_Oequivp(U_13737,U_13739)
        | ? [U_13733] :
            ( ~ hBOOL(hAPP(hAPP(U_13739,sK295(U_13739)),U_13733))
            & hAPP(U_13739,sK295(U_13739)) = hAPP(U_13739,U_13733) )
        | ( hAPP(U_13739,sK293(U_13739)) != hAPP(U_13739,sK294(U_13739))
          & hBOOL(hAPP(hAPP(U_13739,sK293(U_13739)),sK294(U_13739))) ) )
    & ! [U_13738] :
        ( ! [U_13736] : ~ c_Equiv__Relations_Oequivp(U_13736,U_13738)
        | ( ! [U_13731,U_13729] :
              ( hBOOL(hAPP(hAPP(U_13738,U_13731),U_13729))
              | hAPP(U_13738,U_13731) != hAPP(U_13738,U_13729) )
          & ! [U_13730,U_13728] :
              ( hAPP(U_13738,U_13730) = hAPP(U_13738,U_13728)
              | ~ hBOOL(hAPP(hAPP(U_13738,U_13730),U_13728)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK295]),skolemize(U_13735,sK295(U_13739))],[f_3488_5]) ).

fof(f_3488_7,plain,
    ( ! [U_13739] :
        ( ! [U_13737] : c_Equiv__Relations_Oequivp(U_13737,U_13739)
        | ( ~ hBOOL(hAPP(hAPP(U_13739,sK295(U_13739)),sK296(U_13739)))
          & hAPP(U_13739,sK295(U_13739)) = hAPP(U_13739,sK296(U_13739)) )
        | ( hAPP(U_13739,sK293(U_13739)) != hAPP(U_13739,sK294(U_13739))
          & hBOOL(hAPP(hAPP(U_13739,sK293(U_13739)),sK294(U_13739))) ) )
    & ! [U_13738] :
        ( ! [U_13736] : ~ c_Equiv__Relations_Oequivp(U_13736,U_13738)
        | ( ! [U_13731,U_13729] :
              ( hBOOL(hAPP(hAPP(U_13738,U_13731),U_13729))
              | hAPP(U_13738,U_13731) != hAPP(U_13738,U_13729) )
          & ! [U_13730,U_13728] :
              ( hAPP(U_13738,U_13730) = hAPP(U_13738,U_13728)
              | ~ hBOOL(hAPP(hAPP(U_13738,U_13730),U_13728)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK296]),skolemize(U_13733,sK296(U_13739))],[f_3488_6]) ).

fof(f_3488_8,plain,
    ( ! [U_13739] :
        ( ~ hBOOL(hAPP(hAPP(U_13739,sK295(U_13739)),sK296(U_13739)))
        | ~ sP968(U_13739) )
    & ! [U_13739] :
        ( hAPP(U_13739,sK295(U_13739)) = hAPP(U_13739,sK296(U_13739))
        | ~ sP968(U_13739) )
    & ! [U_13739] :
        ( hAPP(U_13739,sK293(U_13739)) != hAPP(U_13739,sK294(U_13739))
        | ~ sP967(U_13739) )
    & ! [U_13739] :
        ( hBOOL(hAPP(hAPP(U_13739,sK293(U_13739)),sK294(U_13739)))
        | ~ sP967(U_13739) )
    & ! [U_13730,U_13728,U_13729,U_13731,U_13738] :
        ( hBOOL(hAPP(hAPP(U_13738,U_13731),U_13729))
        | hAPP(U_13738,U_13731) != hAPP(U_13738,U_13729)
        | ~ sP966(U_13730,U_13728,U_13729,U_13731,U_13738) )
    & ! [U_13730,U_13728,U_13729,U_13731,U_13738] :
        ( hAPP(U_13738,U_13730) = hAPP(U_13738,U_13728)
        | ~ hBOOL(hAPP(hAPP(U_13738,U_13730),U_13728))
        | ~ sP966(U_13730,U_13728,U_13729,U_13731,U_13738) )
    & ! [U_13737,U_13739] :
        ( c_Equiv__Relations_Oequivp(U_13737,U_13739)
        | sP968(U_13739)
        | sP967(U_13739) )
    & ! [U_13730,U_13728,U_13729,U_13731,U_13736,U_13738] :
        ( ~ c_Equiv__Relations_Oequivp(U_13736,U_13738)
        | sP966(U_13730,U_13728,U_13729,U_13731,U_13738) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP966,sP967,sP968])],[f_3488_7]) ).

cnf(f_3488_9,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_13736,U_13738)
    | sP966(U_13730,U_13728,U_13729,U_13731,U_13738) ),
    inference(clausify,[status(thm)],[f_3488_8]) ).

cnf(f_3488_10,plain,
    ( c_Equiv__Relations_Oequivp(U_13737,U_13739)
    | sP968(U_13739)
    | sP967(U_13739) ),
    inference(clausify,[status(thm)],[f_3488_8]) ).

cnf(f_3488_11,plain,
    ( hAPP(U_13738,U_13730) = hAPP(U_13738,U_13728)
    | ~ hBOOL(hAPP(hAPP(U_13738,U_13730),U_13728))
    | ~ sP966(U_13730,U_13728,U_13729,U_13731,U_13738) ),
    inference(clausify,[status(thm)],[f_3488_8]) ).

cnf(f_3488_12,plain,
    ( hBOOL(hAPP(hAPP(U_13738,U_13731),U_13729))
    | hAPP(U_13738,U_13731) != hAPP(U_13738,U_13729)
    | ~ sP966(U_13730,U_13728,U_13729,U_13731,U_13738) ),
    inference(clausify,[status(thm)],[f_3488_8]) ).

cnf(f_3488_13,plain,
    ( hBOOL(hAPP(hAPP(U_13739,sK293(U_13739)),sK294(U_13739)))
    | ~ sP967(U_13739) ),
    inference(clausify,[status(thm)],[f_3488_8]) ).

cnf(f_3488_14,plain,
    ( hAPP(U_13739,sK293(U_13739)) != hAPP(U_13739,sK294(U_13739))
    | ~ sP967(U_13739) ),
    inference(clausify,[status(thm)],[f_3488_8]) ).

cnf(f_3488_15,plain,
    ( hAPP(U_13739,sK295(U_13739)) = hAPP(U_13739,sK296(U_13739))
    | ~ sP968(U_13739) ),
    inference(clausify,[status(thm)],[f_3488_8]) ).

cnf(f_3488_16,plain,
    ( ~ hBOOL(hAPP(hAPP(U_13739,sK295(U_13739)),sK296(U_13739)))
    | ~ sP968(U_13739) ),
    inference(clausify,[status(thm)],[f_3488_8]) ).

fof(f_3489_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_3489_2,plain,
    ! [U_13742,U_13741,U_13740] :
      ( hBOOL(hAPP(hAPP(U_13741,U_13742),U_13742))
      | ~ c_Equiv__Relations_Oequivp(U_13740,U_13741) ),
    inference(variable_rename,[status(thm)],[f_3489_1]) ).

fof(f_3489_3,plain,
    ! [U_13742,U_13741] :
      ( ! [U_13740] : ~ c_Equiv__Relations_Oequivp(U_13740,U_13741)
      | hBOOL(hAPP(hAPP(U_13741,U_13742),U_13742)) ),
    inference(miniscope,[status(thm)],[f_3489_2]) ).

fof(f_3489_4,plain,
    ! [U_13740,U_13742,U_13741] :
      ( ~ c_Equiv__Relations_Oequivp(U_13740,U_13741)
      | hBOOL(hAPP(hAPP(U_13741,U_13742),U_13742)) ),
    inference(definitional_conversion,[status(esa)],[f_3489_3]) ).

cnf(f_3489_5,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_13740,U_13741)
    | hBOOL(hAPP(hAPP(U_13741,U_13742),U_13742)) ),
    inference(clausify,[status(thm)],[f_3489_4]) ).

fof(f_3490_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_3490_2,plain,
    ! [U_13746,U_13745,U_13744,U_13743] :
      ( hBOOL(hAPP(hAPP(U_13744,U_13746),U_13745))
      | ~ hBOOL(hAPP(hAPP(U_13744,U_13745),U_13746))
      | ~ c_Equiv__Relations_Oequivp(U_13743,U_13744) ),
    inference(variable_rename,[status(thm)],[f_3490_1]) ).

fof(f_3490_3,plain,
    ! [U_13746,U_13745,U_13744] :
      ( ! [U_13743] : ~ c_Equiv__Relations_Oequivp(U_13743,U_13744)
      | hBOOL(hAPP(hAPP(U_13744,U_13746),U_13745))
      | ~ hBOOL(hAPP(hAPP(U_13744,U_13745),U_13746)) ),
    inference(miniscope,[status(thm)],[f_3490_2]) ).

fof(f_3490_4,plain,
    ! [U_13744,U_13743,U_13746,U_13745] :
      ( ~ c_Equiv__Relations_Oequivp(U_13743,U_13744)
      | hBOOL(hAPP(hAPP(U_13744,U_13746),U_13745))
      | ~ hBOOL(hAPP(hAPP(U_13744,U_13745),U_13746)) ),
    inference(definitional_conversion,[status(esa)],[f_3490_3]) ).

cnf(f_3490_5,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_13743,U_13744)
    | hBOOL(hAPP(hAPP(U_13744,U_13746),U_13745))
    | ~ hBOOL(hAPP(hAPP(U_13744,U_13745),U_13746)) ),
    inference(clausify,[status(thm)],[f_3490_4]) ).

fof(f_3491_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_3491_2,plain,
    ! [U_13751,U_13750,U_13749,U_13748,U_13747] :
      ( hBOOL(hAPP(hAPP(U_13748,U_13749),U_13751))
      | ~ hBOOL(hAPP(hAPP(U_13748,U_13750),U_13751))
      | ~ hBOOL(hAPP(hAPP(U_13748,U_13749),U_13750))
      | ~ c_Equiv__Relations_Oequivp(U_13747,U_13748) ),
    inference(variable_rename,[status(thm)],[f_3491_1]) ).

fof(f_3491_3,plain,
    ! [U_13751,U_13750,U_13749,U_13748] :
      ( ! [U_13747] : ~ c_Equiv__Relations_Oequivp(U_13747,U_13748)
      | hBOOL(hAPP(hAPP(U_13748,U_13749),U_13751))
      | ~ hBOOL(hAPP(hAPP(U_13748,U_13750),U_13751))
      | ~ hBOOL(hAPP(hAPP(U_13748,U_13749),U_13750)) ),
    inference(miniscope,[status(thm)],[f_3491_2]) ).

fof(f_3491_4,plain,
    ! [U_13751,U_13748,U_13747,U_13749,U_13750] :
      ( ~ c_Equiv__Relations_Oequivp(U_13747,U_13748)
      | hBOOL(hAPP(hAPP(U_13748,U_13749),U_13751))
      | ~ hBOOL(hAPP(hAPP(U_13748,U_13750),U_13751))
      | ~ hBOOL(hAPP(hAPP(U_13748,U_13749),U_13750)) ),
    inference(definitional_conversion,[status(esa)],[f_3491_3]) ).

cnf(f_3491_5,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_13747,U_13748)
    | hBOOL(hAPP(hAPP(U_13748,U_13749),U_13751))
    | ~ hBOOL(hAPP(hAPP(U_13748,U_13750),U_13751))
    | ~ hBOOL(hAPP(hAPP(U_13748,U_13749),U_13750)) ),
    inference(clausify,[status(thm)],[f_3491_4]) ).

fof(f_3492_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_3492_2,plain,
    ! [U_13752] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_13752)),c_Int_OInteg)),
    inference(variable_rename,[status(thm)],[f_3492_1]) ).

fof(f_3492_3,plain,
    ! [U_13752] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_13752)),c_Int_OInteg)),
    inference(definitional_conversion,[status(esa)],[f_3492_2]) ).

cnf(f_3492_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_13752)),c_Int_OInteg)),
    inference(clausify,[status(thm)],[f_3492_3]) ).

fof(f_3493_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_3493_2,plain,
    ! [U_13759,U_13758,U_13757,U_13756,U_13755,U_13754,U_13753] :
      ( hAPP(U_13756,hAPP(U_13757,U_13759)) = hAPP(U_13758,U_13759)
      | hAPP(c_Fun_Ocomp(U_13753,U_13754,U_13755,U_13756),U_13757) != U_13758 ),
    inference(variable_rename,[status(thm)],[f_3493_1]) ).

fof(f_3493_3,plain,
    ! [U_13759,U_13758,U_13757,U_13756] :
      ( ! [U_13755,U_13754,U_13753] : hAPP(c_Fun_Ocomp(U_13753,U_13754,U_13755,U_13756),U_13757) != U_13758
      | hAPP(U_13756,hAPP(U_13757,U_13759)) = hAPP(U_13758,U_13759) ),
    inference(miniscope,[status(thm)],[f_3493_2]) ).

fof(f_3493_4,plain,
    ! [U_13753,U_13754,U_13755,U_13756,U_13757,U_13758,U_13759] :
      ( hAPP(c_Fun_Ocomp(U_13753,U_13754,U_13755,U_13756),U_13757) != U_13758
      | hAPP(U_13756,hAPP(U_13757,U_13759)) = hAPP(U_13758,U_13759) ),
    inference(definitional_conversion,[status(esa)],[f_3493_3]) ).

cnf(f_3493_5,plain,
    ( hAPP(c_Fun_Ocomp(U_13753,U_13754,U_13755,U_13756),U_13757) != U_13758
    | hAPP(U_13756,hAPP(U_13757,U_13759)) = hAPP(U_13758,U_13759) ),
    inference(clausify,[status(thm)],[f_3493_4]) ).

fof(f_3494_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_3494_2,plain,
    ! [U_13765,U_13764,U_13763,U_13762,U_13761,U_13760] : hAPP(hAPP(c_Fun_Ocomp(U_13760,U_13761,U_13762,hAPP(c_COMBK(U_13761,U_13760),U_13763)),U_13764),U_13765) = U_13763,
    inference(variable_rename,[status(thm)],[f_3494_1]) ).

fof(f_3494_3,plain,
    ! [U_13761,U_13760,U_13762,U_13763,U_13764,U_13765] : hAPP(hAPP(c_Fun_Ocomp(U_13760,U_13761,U_13762,hAPP(c_COMBK(U_13761,U_13760),U_13763)),U_13764),U_13765) = U_13763,
    inference(definitional_conversion,[status(esa)],[f_3494_2]) ).

cnf(f_3494_4,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_13760,U_13761,U_13762,hAPP(c_COMBK(U_13761,U_13760),U_13763)),U_13764),U_13765) = U_13763,
    inference(clausify,[status(thm)],[f_3494_3]) ).

fof(f_3495_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_3495_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_3495_1]) ).

cnf(f_3495_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_3495_2]) ).

fof(f_3496_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_3496_2,plain,
    ! [U_13769,U_13768,U_13767,U_13766] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13766,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13766,U_13767,U_13768),hAPP(hAPP(c_Set_Oinsert(U_13767),U_13769),c_Orderings_Obot__class_Obot(tc_fun(U_13767,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_13766),c_HOL_OThe(U_13766,hAPP(hAPP(c_COMBC(U_13766,U_13767,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13767,tc_fun(U_13767,tc_HOL_Obool),U_13766),c_fequal),U_13768)),U_13769))),c_Orderings_Obot__class_Obot(tc_fun(U_13766,tc_HOL_Obool)))))
      | ~ c_Fun_Oinj__on(U_13766,U_13767,U_13768,c_Orderings_Otop__class_Otop(tc_fun(U_13766,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3496_1]) ).

fof(f_3496_3,plain,
    ! [U_13766,U_13767,U_13768,U_13769] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13766,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13766,U_13767,U_13768),hAPP(hAPP(c_Set_Oinsert(U_13767),U_13769),c_Orderings_Obot__class_Obot(tc_fun(U_13767,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_13766),c_HOL_OThe(U_13766,hAPP(hAPP(c_COMBC(U_13766,U_13767,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13767,tc_fun(U_13767,tc_HOL_Obool),U_13766),c_fequal),U_13768)),U_13769))),c_Orderings_Obot__class_Obot(tc_fun(U_13766,tc_HOL_Obool)))))
      | ~ c_Fun_Oinj__on(U_13766,U_13767,U_13768,c_Orderings_Otop__class_Otop(tc_fun(U_13766,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3496_2]) ).

cnf(f_3496_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13766,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13766,U_13767,U_13768),hAPP(hAPP(c_Set_Oinsert(U_13767),U_13769),c_Orderings_Obot__class_Obot(tc_fun(U_13767,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_13766),c_HOL_OThe(U_13766,hAPP(hAPP(c_COMBC(U_13766,U_13767,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13767,tc_fun(U_13767,tc_HOL_Obool),U_13766),c_fequal),U_13768)),U_13769))),c_Orderings_Obot__class_Obot(tc_fun(U_13766,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_13766,U_13767,U_13768,c_Orderings_Otop__class_Otop(tc_fun(U_13766,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3496_3]) ).

fof(f_3497_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_3497_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_3497_1]) ).

cnf(f_3497_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_3497_2]) ).

fof(f_3498_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_3498_2,plain,
    ! [U_13775,U_13774,U_13773,U_13772,U_13771,U_13770] :
      ( hBOOL(hAPP(hAPP(c_member(U_13775),U_13771),hAPP(c_Set_Ovimage(U_13775,U_13773,U_13770),U_13774)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13773),U_13772),U_13774))
      | hAPP(U_13770,U_13771) != U_13772 ),
    inference(variable_rename,[status(thm)],[f_3498_1]) ).

fof(f_3498_3,plain,
    ! [U_13770,U_13771,U_13772,U_13773,U_13774,U_13775] :
      ( hBOOL(hAPP(hAPP(c_member(U_13775),U_13771),hAPP(c_Set_Ovimage(U_13775,U_13773,U_13770),U_13774)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13773),U_13772),U_13774))
      | hAPP(U_13770,U_13771) != U_13772 ),
    inference(definitional_conversion,[status(esa)],[f_3498_2]) ).

cnf(f_3498_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13775),U_13771),hAPP(c_Set_Ovimage(U_13775,U_13773,U_13770),U_13774)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13773),U_13772),U_13774))
    | hAPP(U_13770,U_13771) != U_13772 ),
    inference(clausify,[status(thm)],[f_3498_3]) ).

fof(f_3499_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_3499_2,plain,
    ! [U_13781,U_13780,U_13779,U_13778,U_13777,U_13776] : hAPP(c_Set_Ovimage(U_13776,U_13777,hAPP(c_Fun_Ocomp(U_13778,U_13777,U_13776,U_13779),U_13780)),U_13781) = hAPP(c_Set_Ovimage(U_13776,U_13778,U_13780),hAPP(c_Set_Ovimage(U_13778,U_13777,U_13779),U_13781)),
    inference(variable_rename,[status(thm)],[f_3499_1]) ).

fof(f_3499_3,plain,
    ! [U_13777,U_13776,U_13778,U_13779,U_13780,U_13781] : hAPP(c_Set_Ovimage(U_13776,U_13777,hAPP(c_Fun_Ocomp(U_13778,U_13777,U_13776,U_13779),U_13780)),U_13781) = hAPP(c_Set_Ovimage(U_13776,U_13778,U_13780),hAPP(c_Set_Ovimage(U_13778,U_13777,U_13779),U_13781)),
    inference(definitional_conversion,[status(esa)],[f_3499_2]) ).

cnf(f_3499_4,plain,
    hAPP(c_Set_Ovimage(U_13776,U_13777,hAPP(c_Fun_Ocomp(U_13778,U_13777,U_13776,U_13779),U_13780)),U_13781) = hAPP(c_Set_Ovimage(U_13776,U_13778,U_13780),hAPP(c_Set_Ovimage(U_13778,U_13777,U_13779),U_13781)),
    inference(clausify,[status(thm)],[f_3499_3]) ).

fof(f_3500_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_3500_2,plain,
    ! [U_13786,U_13785,U_13784,U_13783,U_13782] : hAPP(c_Set_Ovimage(U_13782,U_13783,U_13784),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13783,tc_HOL_Obool)),U_13785),U_13786)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13782,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13782,U_13783,U_13784),U_13785)),hAPP(c_Set_Ovimage(U_13782,U_13783,U_13784),U_13786)),
    inference(variable_rename,[status(thm)],[f_3500_1]) ).

fof(f_3500_3,plain,
    ! [U_13782,U_13783,U_13784,U_13785,U_13786] : hAPP(c_Set_Ovimage(U_13782,U_13783,U_13784),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13783,tc_HOL_Obool)),U_13785),U_13786)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13782,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13782,U_13783,U_13784),U_13785)),hAPP(c_Set_Ovimage(U_13782,U_13783,U_13784),U_13786)),
    inference(definitional_conversion,[status(esa)],[f_3500_2]) ).

cnf(f_3500_4,plain,
    hAPP(c_Set_Ovimage(U_13782,U_13783,U_13784),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13783,tc_HOL_Obool)),U_13785),U_13786)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13782,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13782,U_13783,U_13784),U_13785)),hAPP(c_Set_Ovimage(U_13782,U_13783,U_13784),U_13786)),
    inference(clausify,[status(thm)],[f_3500_3]) ).

fof(f_3501_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_3501_2,plain,
    ! [U_13788,U_13787] : hAPP(c_Set_Ovimage(U_13787,U_13787,c_COMBI(U_13787)),U_13788) = U_13788,
    inference(variable_rename,[status(thm)],[f_3501_1]) ).

fof(f_3501_3,plain,
    ! [U_13787,U_13788] : hAPP(c_Set_Ovimage(U_13787,U_13787,c_COMBI(U_13787)),U_13788) = U_13788,
    inference(definitional_conversion,[status(esa)],[f_3501_2]) ).

cnf(f_3501_4,plain,
    hAPP(c_Set_Ovimage(U_13787,U_13787,c_COMBI(U_13787)),U_13788) = U_13788,
    inference(clausify,[status(thm)],[f_3501_3]) ).

fof(f_3502_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_3502_2,plain,
    ! [U_13793,U_13792,U_13791,U_13790,U_13789] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13792,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13792,U_13789,U_13793),U_13790)),hAPP(c_Set_Ovimage(U_13792,U_13789,U_13793),U_13791)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13789,tc_HOL_Obool)),U_13790),U_13791)) ),
    inference(variable_rename,[status(thm)],[f_3502_1]) ).

fof(f_3502_3,plain,
    ! [U_13789,U_13790,U_13791,U_13792,U_13793] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13792,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13792,U_13789,U_13793),U_13790)),hAPP(c_Set_Ovimage(U_13792,U_13789,U_13793),U_13791)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13789,tc_HOL_Obool)),U_13790),U_13791)) ),
    inference(definitional_conversion,[status(esa)],[f_3502_2]) ).

cnf(f_3502_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13792,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13792,U_13789,U_13793),U_13790)),hAPP(c_Set_Ovimage(U_13792,U_13789,U_13793),U_13791)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13789,tc_HOL_Obool)),U_13790),U_13791)) ),
    inference(clausify,[status(thm)],[f_3502_3]) ).

fof(f_3503_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_3503_2,plain,
    ! [U_13798,U_13797,U_13796,U_13795,U_13794] :
      ( ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_13794,U_13795,U_13796),U_13797),U_13798))
        | ~ hBOOL(hAPP(U_13797,hAPP(U_13796,U_13798))) )
      & ( hBOOL(hAPP(U_13797,hAPP(U_13796,U_13798)))
        | ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_13794,U_13795,U_13796),U_13797),U_13798)) ) ),
    inference(variable_rename,[status(thm)],[f_3503_1]) ).

fof(f_3503_3,plain,
    ( ! [U_13808,U_13806,U_13804] :
        ( ! [U_13802,U_13800] : hBOOL(hAPP(hAPP(c_Set_Ovimage(U_13800,U_13802,U_13804),U_13806),U_13808))
        | ~ hBOOL(hAPP(U_13806,hAPP(U_13804,U_13808))) )
    & ! [U_13807,U_13805,U_13803] :
        ( ! [U_13801,U_13799] : ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_13799,U_13801,U_13803),U_13805),U_13807))
        | hBOOL(hAPP(U_13805,hAPP(U_13803,U_13807))) ) ),
    inference(miniscope,[status(thm)],[f_3503_2]) ).

fof(f_3503_4,plain,
    ( ! [U_13806,U_13800,U_13802,U_13804,U_13808] :
        ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_13800,U_13802,U_13804),U_13806),U_13808))
        | ~ hBOOL(hAPP(U_13806,hAPP(U_13804,U_13808))) )
    & ! [U_13803,U_13801,U_13807,U_13799,U_13805] :
        ( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_13799,U_13801,U_13803),U_13805),U_13807))
        | hBOOL(hAPP(U_13805,hAPP(U_13803,U_13807))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3503_3]) ).

cnf(f_3503_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_13799,U_13801,U_13803),U_13805),U_13807))
    | hBOOL(hAPP(U_13805,hAPP(U_13803,U_13807))) ),
    inference(clausify,[status(thm)],[f_3503_4]) ).

cnf(f_3503_6,plain,
    ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_13800,U_13802,U_13804),U_13806),U_13808))
    | ~ hBOOL(hAPP(U_13806,hAPP(U_13804,U_13808))) ),
    inference(clausify,[status(thm)],[f_3503_4]) ).

fof(f_3504_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_3504_2,plain,
    ! [U_13812,U_13811,U_13810,U_13809] : hAPP(c_Set_Ovimage(U_13809,U_13810,U_13811),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13810,tc_HOL_Obool)),U_13812)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13809,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13809,U_13810,U_13811),U_13812)),
    inference(variable_rename,[status(thm)],[f_3504_1]) ).

fof(f_3504_3,plain,
    ! [U_13809,U_13810,U_13811,U_13812] : hAPP(c_Set_Ovimage(U_13809,U_13810,U_13811),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13810,tc_HOL_Obool)),U_13812)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13809,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13809,U_13810,U_13811),U_13812)),
    inference(definitional_conversion,[status(esa)],[f_3504_2]) ).

cnf(f_3504_4,plain,
    hAPP(c_Set_Ovimage(U_13809,U_13810,U_13811),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13810,tc_HOL_Obool)),U_13812)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13809,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13809,U_13810,U_13811),U_13812)),
    inference(clausify,[status(thm)],[f_3504_3]) ).

fof(f_3505_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_3505_2,plain,
    ! [U_13815,U_13814,U_13813] : hAPP(c_Set_Ovimage(U_13813,U_13814,U_13815),c_Orderings_Obot__class_Obot(tc_fun(U_13814,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13813,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3505_1]) ).

fof(f_3505_3,plain,
    ! [U_13813,U_13814,U_13815] : hAPP(c_Set_Ovimage(U_13813,U_13814,U_13815),c_Orderings_Obot__class_Obot(tc_fun(U_13814,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13813,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3505_2]) ).

cnf(f_3505_4,plain,
    hAPP(c_Set_Ovimage(U_13813,U_13814,U_13815),c_Orderings_Obot__class_Obot(tc_fun(U_13814,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13813,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3505_3]) ).

fof(f_3506_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_3506_2,plain,
    ! [U_13820,U_13819,U_13818,U_13817,U_13816] :
      ( hBOOL(hAPP(hAPP(c_member(U_13820),U_13818),hAPP(c_Set_Ovimage(U_13820,U_13816,U_13817),U_13819)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13816),hAPP(U_13817,U_13818)),U_13819)) ),
    inference(variable_rename,[status(thm)],[f_3506_1]) ).

fof(f_3506_3,plain,
    ! [U_13816,U_13817,U_13818,U_13819,U_13820] :
      ( hBOOL(hAPP(hAPP(c_member(U_13820),U_13818),hAPP(c_Set_Ovimage(U_13820,U_13816,U_13817),U_13819)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13816),hAPP(U_13817,U_13818)),U_13819)) ),
    inference(definitional_conversion,[status(esa)],[f_3506_2]) ).

cnf(f_3506_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13820),U_13818),hAPP(c_Set_Ovimage(U_13820,U_13816,U_13817),U_13819)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13816),hAPP(U_13817,U_13818)),U_13819)) ),
    inference(clausify,[status(thm)],[f_3506_3]) ).

fof(f_3507_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_3507_2,plain,
    ! [U_13825,U_13824,U_13823,U_13822,U_13821] :
      ( hBOOL(hAPP(hAPP(c_member(U_13823),hAPP(U_13824,U_13822)),U_13825))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13821),U_13822),hAPP(c_Set_Ovimage(U_13821,U_13823,U_13824),U_13825))) ),
    inference(variable_rename,[status(thm)],[f_3507_1]) ).

fof(f_3507_3,plain,
    ! [U_13825,U_13824,U_13823,U_13822] :
      ( ! [U_13821] : ~ hBOOL(hAPP(hAPP(c_member(U_13821),U_13822),hAPP(c_Set_Ovimage(U_13821,U_13823,U_13824),U_13825)))
      | hBOOL(hAPP(hAPP(c_member(U_13823),hAPP(U_13824,U_13822)),U_13825)) ),
    inference(miniscope,[status(thm)],[f_3507_2]) ).

fof(f_3507_4,plain,
    ! [U_13821,U_13822,U_13823,U_13824,U_13825] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_13821),U_13822),hAPP(c_Set_Ovimage(U_13821,U_13823,U_13824),U_13825)))
      | hBOOL(hAPP(hAPP(c_member(U_13823),hAPP(U_13824,U_13822)),U_13825)) ),
    inference(definitional_conversion,[status(esa)],[f_3507_3]) ).

cnf(f_3507_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13821),U_13822),hAPP(c_Set_Ovimage(U_13821,U_13823,U_13824),U_13825)))
    | hBOOL(hAPP(hAPP(c_member(U_13823),hAPP(U_13824,U_13822)),U_13825)) ),
    inference(clausify,[status(thm)],[f_3507_4]) ).

fof(f_3508_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_3508_2,plain,
    ! [U_13830,U_13829,U_13828,U_13827,U_13826] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13826),U_13827),hAPP(c_Set_Ovimage(U_13826,U_13828,U_13829),U_13830)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13828),hAPP(U_13829,U_13827)),U_13830)) )
      & ( hBOOL(hAPP(hAPP(c_member(U_13828),hAPP(U_13829,U_13827)),U_13830))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13826),U_13827),hAPP(c_Set_Ovimage(U_13826,U_13828,U_13829),U_13830))) ) ),
    inference(variable_rename,[status(thm)],[f_3508_1]) ).

fof(f_3508_3,plain,
    ( ! [U_13840,U_13838,U_13836,U_13834] :
        ( ! [U_13832] : hBOOL(hAPP(hAPP(c_member(U_13832),U_13834),hAPP(c_Set_Ovimage(U_13832,U_13836,U_13838),U_13840)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13836),hAPP(U_13838,U_13834)),U_13840)) )
    & ! [U_13839,U_13837,U_13835,U_13833] :
        ( ! [U_13831] : ~ hBOOL(hAPP(hAPP(c_member(U_13831),U_13833),hAPP(c_Set_Ovimage(U_13831,U_13835,U_13837),U_13839)))
        | hBOOL(hAPP(hAPP(c_member(U_13835),hAPP(U_13837,U_13833)),U_13839)) ) ),
    inference(miniscope,[status(thm)],[f_3508_2]) ).

fof(f_3508_4,plain,
    ( ! [U_13832,U_13834,U_13836,U_13838,U_13840] :
        ( hBOOL(hAPP(hAPP(c_member(U_13832),U_13834),hAPP(c_Set_Ovimage(U_13832,U_13836,U_13838),U_13840)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13836),hAPP(U_13838,U_13834)),U_13840)) )
    & ! [U_13835,U_13833,U_13831,U_13837,U_13839] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_13831),U_13833),hAPP(c_Set_Ovimage(U_13831,U_13835,U_13837),U_13839)))
        | hBOOL(hAPP(hAPP(c_member(U_13835),hAPP(U_13837,U_13833)),U_13839)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3508_3]) ).

cnf(f_3508_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13831),U_13833),hAPP(c_Set_Ovimage(U_13831,U_13835,U_13837),U_13839)))
    | hBOOL(hAPP(hAPP(c_member(U_13835),hAPP(U_13837,U_13833)),U_13839)) ),
    inference(clausify,[status(thm)],[f_3508_4]) ).

cnf(f_3508_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13832),U_13834),hAPP(c_Set_Ovimage(U_13832,U_13836,U_13838),U_13840)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13836),hAPP(U_13838,U_13834)),U_13840)) ),
    inference(clausify,[status(thm)],[f_3508_4]) ).

fof(f_3509_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_3509_2,plain,
    ! [U_13845,U_13844,U_13843,U_13842,U_13841] : hAPP(c_Set_Ovimage(U_13841,U_13842,U_13843),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13842,tc_HOL_Obool)),U_13844),U_13845)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13841,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13841,U_13842,U_13843),U_13844)),hAPP(c_Set_Ovimage(U_13841,U_13842,U_13843),U_13845)),
    inference(variable_rename,[status(thm)],[f_3509_1]) ).

fof(f_3509_3,plain,
    ! [U_13841,U_13842,U_13843,U_13844,U_13845] : hAPP(c_Set_Ovimage(U_13841,U_13842,U_13843),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13842,tc_HOL_Obool)),U_13844),U_13845)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13841,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13841,U_13842,U_13843),U_13844)),hAPP(c_Set_Ovimage(U_13841,U_13842,U_13843),U_13845)),
    inference(definitional_conversion,[status(esa)],[f_3509_2]) ).

cnf(f_3509_4,plain,
    hAPP(c_Set_Ovimage(U_13841,U_13842,U_13843),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13842,tc_HOL_Obool)),U_13844),U_13845)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13841,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13841,U_13842,U_13843),U_13844)),hAPP(c_Set_Ovimage(U_13841,U_13842,U_13843),U_13845)),
    inference(clausify,[status(thm)],[f_3509_3]) ).

fof(f_3510_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_3510_2,plain,
    ! [U_13850,U_13849,U_13848,U_13847,U_13846] : hAPP(c_Set_Ovimage(U_13846,U_13847,U_13848),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13847,tc_HOL_Obool)),U_13849),U_13850)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13846,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13846,U_13847,U_13848),U_13849)),hAPP(c_Set_Ovimage(U_13846,U_13847,U_13848),U_13850)),
    inference(variable_rename,[status(thm)],[f_3510_1]) ).

fof(f_3510_3,plain,
    ! [U_13847,U_13846,U_13848,U_13849,U_13850] : hAPP(c_Set_Ovimage(U_13846,U_13847,U_13848),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13847,tc_HOL_Obool)),U_13849),U_13850)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13846,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13846,U_13847,U_13848),U_13849)),hAPP(c_Set_Ovimage(U_13846,U_13847,U_13848),U_13850)),
    inference(definitional_conversion,[status(esa)],[f_3510_2]) ).

cnf(f_3510_4,plain,
    hAPP(c_Set_Ovimage(U_13846,U_13847,U_13848),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13847,tc_HOL_Obool)),U_13849),U_13850)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13846,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13846,U_13847,U_13848),U_13849)),hAPP(c_Set_Ovimage(U_13846,U_13847,U_13848),U_13850)),
    inference(clausify,[status(thm)],[f_3510_3]) ).

fof(f_3511_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_3511_2,plain,
    ! [U_13854,U_13853,U_13852,U_13851] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13851,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13852,U_13851,U_13853),hAPP(c_Set_Ovimage(U_13852,U_13851,U_13853),U_13854))),U_13854)),
    inference(variable_rename,[status(thm)],[f_3511_1]) ).

fof(f_3511_3,plain,
    ! [U_13851,U_13852,U_13853,U_13854] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13851,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13852,U_13851,U_13853),hAPP(c_Set_Ovimage(U_13852,U_13851,U_13853),U_13854))),U_13854)),
    inference(definitional_conversion,[status(esa)],[f_3511_2]) ).

cnf(f_3511_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13851,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13852,U_13851,U_13853),hAPP(c_Set_Ovimage(U_13852,U_13851,U_13853),U_13854))),U_13854)),
    inference(clausify,[status(thm)],[f_3511_3]) ).

fof(f_3512_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_3512_2,plain,
    ! [U_13860,U_13859,U_13858,U_13857,U_13856,U_13855] : hAPP(c_Set_Ovimage(U_13855,U_13856,U_13857),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13858,tc_fun(U_13856,tc_HOL_Obool)),U_13859),U_13860)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13858,tc_fun(U_13855,tc_HOL_Obool)),U_13859),hAPP(hAPP(c_COMBB(tc_fun(U_13856,tc_HOL_Obool),tc_fun(U_13855,tc_HOL_Obool),U_13858),c_Set_Ovimage(U_13855,U_13856,U_13857)),U_13860)),
    inference(variable_rename,[status(thm)],[f_3512_1]) ).

fof(f_3512_3,plain,
    ! [U_13855,U_13856,U_13857,U_13858,U_13859,U_13860] : hAPP(c_Set_Ovimage(U_13855,U_13856,U_13857),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13858,tc_fun(U_13856,tc_HOL_Obool)),U_13859),U_13860)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13858,tc_fun(U_13855,tc_HOL_Obool)),U_13859),hAPP(hAPP(c_COMBB(tc_fun(U_13856,tc_HOL_Obool),tc_fun(U_13855,tc_HOL_Obool),U_13858),c_Set_Ovimage(U_13855,U_13856,U_13857)),U_13860)),
    inference(definitional_conversion,[status(esa)],[f_3512_2]) ).

cnf(f_3512_4,plain,
    hAPP(c_Set_Ovimage(U_13855,U_13856,U_13857),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13858,tc_fun(U_13856,tc_HOL_Obool)),U_13859),U_13860)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13858,tc_fun(U_13855,tc_HOL_Obool)),U_13859),hAPP(hAPP(c_COMBB(tc_fun(U_13856,tc_HOL_Obool),tc_fun(U_13855,tc_HOL_Obool),U_13858),c_Set_Ovimage(U_13855,U_13856,U_13857)),U_13860)),
    inference(clausify,[status(thm)],[f_3512_3]) ).

fof(f_3513_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_3513_2,plain,
    ! [U_13863,U_13862,U_13861] : hAPP(c_Set_Ovimage(U_13861,U_13862,U_13863),c_Orderings_Otop__class_Otop(tc_fun(U_13862,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13861,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3513_1]) ).

fof(f_3513_3,plain,
    ! [U_13861,U_13863,U_13862] : hAPP(c_Set_Ovimage(U_13861,U_13862,U_13863),c_Orderings_Otop__class_Otop(tc_fun(U_13862,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13861,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3513_2]) ).

cnf(f_3513_4,plain,
    hAPP(c_Set_Ovimage(U_13861,U_13862,U_13863),c_Orderings_Otop__class_Otop(tc_fun(U_13862,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13861,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3513_3]) ).

fof(f_3514_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_3514_2,plain,
    ! [U_13867,U_13866,U_13865,U_13864] :
      ( hAPP(c_Set_Oimage(U_13864,U_13865,U_13866),hAPP(c_Set_Ovimage(U_13864,U_13865,U_13866),U_13867)) = U_13867
      | hAPP(c_Set_Oimage(U_13864,U_13865,U_13866),c_Orderings_Otop__class_Otop(tc_fun(U_13864,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13865,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3514_1]) ).

fof(f_3514_3,plain,
    ! [U_13864,U_13865,U_13866,U_13867] :
      ( hAPP(c_Set_Oimage(U_13864,U_13865,U_13866),hAPP(c_Set_Ovimage(U_13864,U_13865,U_13866),U_13867)) = U_13867
      | hAPP(c_Set_Oimage(U_13864,U_13865,U_13866),c_Orderings_Otop__class_Otop(tc_fun(U_13864,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13865,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3514_2]) ).

cnf(f_3514_4,plain,
    ( hAPP(c_Set_Oimage(U_13864,U_13865,U_13866),hAPP(c_Set_Ovimage(U_13864,U_13865,U_13866),U_13867)) = U_13867
    | hAPP(c_Set_Oimage(U_13864,U_13865,U_13866),c_Orderings_Otop__class_Otop(tc_fun(U_13864,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13865,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3514_3]) ).

fof(f_3515_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_3515_2,plain,
    ! [U_13872,U_13871,U_13870,U_13869,U_13868] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13868),U_13869),hAPP(c_Set_Ovimage(U_13868,U_13870,U_13871),hAPP(hAPP(c_Set_Oinsert(U_13870),U_13872),c_Orderings_Obot__class_Obot(tc_fun(U_13870,tc_HOL_Obool))))))
        | hAPP(U_13871,U_13869) != U_13872 )
      & ( hAPP(U_13871,U_13869) = U_13872
        | ~ hBOOL(hAPP(hAPP(c_member(U_13868),U_13869),hAPP(c_Set_Ovimage(U_13868,U_13870,U_13871),hAPP(hAPP(c_Set_Oinsert(U_13870),U_13872),c_Orderings_Obot__class_Obot(tc_fun(U_13870,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[f_3515_1]) ).

fof(f_3515_3,plain,
    ( ! [U_13882,U_13880,U_13878,U_13876] :
        ( ! [U_13874] : hBOOL(hAPP(hAPP(c_member(U_13874),U_13876),hAPP(c_Set_Ovimage(U_13874,U_13878,U_13880),hAPP(hAPP(c_Set_Oinsert(U_13878),U_13882),c_Orderings_Obot__class_Obot(tc_fun(U_13878,tc_HOL_Obool))))))
        | hAPP(U_13880,U_13876) != U_13882 )
    & ! [U_13881,U_13879,U_13877,U_13875] :
        ( ! [U_13873] : ~ hBOOL(hAPP(hAPP(c_member(U_13873),U_13875),hAPP(c_Set_Ovimage(U_13873,U_13877,U_13879),hAPP(hAPP(c_Set_Oinsert(U_13877),U_13881),c_Orderings_Obot__class_Obot(tc_fun(U_13877,tc_HOL_Obool))))))
        | hAPP(U_13879,U_13875) = U_13881 ) ),
    inference(miniscope,[status(thm)],[f_3515_2]) ).

fof(f_3515_4,plain,
    ( ! [U_13874,U_13876,U_13878,U_13880,U_13882] :
        ( hBOOL(hAPP(hAPP(c_member(U_13874),U_13876),hAPP(c_Set_Ovimage(U_13874,U_13878,U_13880),hAPP(hAPP(c_Set_Oinsert(U_13878),U_13882),c_Orderings_Obot__class_Obot(tc_fun(U_13878,tc_HOL_Obool))))))
        | hAPP(U_13880,U_13876) != U_13882 )
    & ! [U_13875,U_13873,U_13877,U_13879,U_13881] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_13873),U_13875),hAPP(c_Set_Ovimage(U_13873,U_13877,U_13879),hAPP(hAPP(c_Set_Oinsert(U_13877),U_13881),c_Orderings_Obot__class_Obot(tc_fun(U_13877,tc_HOL_Obool))))))
        | hAPP(U_13879,U_13875) = U_13881 ) ),
    inference(definitional_conversion,[status(esa)],[f_3515_3]) ).

cnf(f_3515_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13873),U_13875),hAPP(c_Set_Ovimage(U_13873,U_13877,U_13879),hAPP(hAPP(c_Set_Oinsert(U_13877),U_13881),c_Orderings_Obot__class_Obot(tc_fun(U_13877,tc_HOL_Obool))))))
    | hAPP(U_13879,U_13875) = U_13881 ),
    inference(clausify,[status(thm)],[f_3515_4]) ).

cnf(f_3515_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13874),U_13876),hAPP(c_Set_Ovimage(U_13874,U_13878,U_13880),hAPP(hAPP(c_Set_Oinsert(U_13878),U_13882),c_Orderings_Obot__class_Obot(tc_fun(U_13878,tc_HOL_Obool))))))
    | hAPP(U_13880,U_13876) != U_13882 ),
    inference(clausify,[status(thm)],[f_3515_4]) ).

fof(f_3516_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_3516_2,plain,
    ! [U_13887,U_13886,U_13885,U_13884,U_13883] : hAPP(c_Set_Ovimage(U_13883,U_13884,U_13885),hAPP(hAPP(c_Set_Oinsert(U_13884),U_13886),U_13887)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13883,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13883,U_13884,U_13885),hAPP(hAPP(c_Set_Oinsert(U_13884),U_13886),c_Orderings_Obot__class_Obot(tc_fun(U_13884,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_13883,U_13884,U_13885),U_13887)),
    inference(variable_rename,[status(thm)],[f_3516_1]) ).

fof(f_3516_3,plain,
    ! [U_13884,U_13883,U_13885,U_13886,U_13887] : hAPP(c_Set_Ovimage(U_13883,U_13884,U_13885),hAPP(hAPP(c_Set_Oinsert(U_13884),U_13886),U_13887)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13883,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13883,U_13884,U_13885),hAPP(hAPP(c_Set_Oinsert(U_13884),U_13886),c_Orderings_Obot__class_Obot(tc_fun(U_13884,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_13883,U_13884,U_13885),U_13887)),
    inference(definitional_conversion,[status(esa)],[f_3516_2]) ).

cnf(f_3516_4,plain,
    hAPP(c_Set_Ovimage(U_13883,U_13884,U_13885),hAPP(hAPP(c_Set_Oinsert(U_13884),U_13886),U_13887)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13883,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13883,U_13884,U_13885),hAPP(hAPP(c_Set_Oinsert(U_13884),U_13886),c_Orderings_Obot__class_Obot(tc_fun(U_13884,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_13883,U_13884,U_13885),U_13887)),
    inference(clausify,[status(thm)],[f_3516_3]) ).

fof(f_3517_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_3517_2,plain,
    ! [U_13891,U_13890,U_13889,U_13888] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13889),U_13891))
      | hAPP(c_Set_Oimage(U_13888,U_13889,U_13890),c_Orderings_Otop__class_Otop(tc_fun(U_13888,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13889,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),hAPP(c_Set_Ovimage(U_13888,U_13889,U_13890),U_13891))) ),
    inference(variable_rename,[status(thm)],[f_3517_1]) ).

fof(f_3517_3,plain,
    ! [U_13889,U_13888,U_13890,U_13891] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13889),U_13891))
      | hAPP(c_Set_Oimage(U_13888,U_13889,U_13890),c_Orderings_Otop__class_Otop(tc_fun(U_13888,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13889,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),hAPP(c_Set_Ovimage(U_13888,U_13889,U_13890),U_13891))) ),
    inference(definitional_conversion,[status(esa)],[f_3517_2]) ).

cnf(f_3517_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13889),U_13891))
    | hAPP(c_Set_Oimage(U_13888,U_13889,U_13890),c_Orderings_Otop__class_Otop(tc_fun(U_13888,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13889,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),hAPP(c_Set_Ovimage(U_13888,U_13889,U_13890),U_13891))) ),
    inference(clausify,[status(thm)],[f_3517_3]) ).

fof(f_3518_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_3518_2,plain,
    ! [U_13896,U_13895,U_13894,U_13893,U_13892] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13893,tc_HOL_Obool)),U_13895),hAPP(c_Set_Oimage(U_13892,U_13893,U_13894),U_13896)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13892,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13892,U_13893,U_13894),U_13895)),U_13896))
      | hAPP(c_Set_Oimage(U_13892,U_13893,U_13894),c_Orderings_Otop__class_Otop(tc_fun(U_13892,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13893,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3518_1]) ).

fof(f_3518_3,plain,
    ! [U_13892,U_13893,U_13894,U_13895,U_13896] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13893,tc_HOL_Obool)),U_13895),hAPP(c_Set_Oimage(U_13892,U_13893,U_13894),U_13896)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13892,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13892,U_13893,U_13894),U_13895)),U_13896))
      | hAPP(c_Set_Oimage(U_13892,U_13893,U_13894),c_Orderings_Otop__class_Otop(tc_fun(U_13892,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13893,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3518_2]) ).

cnf(f_3518_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13893,tc_HOL_Obool)),U_13895),hAPP(c_Set_Oimage(U_13892,U_13893,U_13894),U_13896)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13892,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13892,U_13893,U_13894),U_13895)),U_13896))
    | hAPP(c_Set_Oimage(U_13892,U_13893,U_13894),c_Orderings_Otop__class_Otop(tc_fun(U_13892,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_13893,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3518_3]) ).

fof(f_3519_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_3519_2,plain,
    ! [U_13900,U_13899,U_13898,U_13897] : hAPP(c_Set_Oimage(U_13897,U_13898,U_13899),hAPP(c_Set_Ovimage(U_13897,U_13898,U_13899),U_13900)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13898,tc_HOL_Obool)),U_13900),hAPP(c_Set_Oimage(U_13897,U_13898,U_13899),c_Orderings_Otop__class_Otop(tc_fun(U_13897,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3519_1]) ).

fof(f_3519_3,plain,
    ! [U_13898,U_13897,U_13899,U_13900] : hAPP(c_Set_Oimage(U_13897,U_13898,U_13899),hAPP(c_Set_Ovimage(U_13897,U_13898,U_13899),U_13900)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13898,tc_HOL_Obool)),U_13900),hAPP(c_Set_Oimage(U_13897,U_13898,U_13899),c_Orderings_Otop__class_Otop(tc_fun(U_13897,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3519_2]) ).

cnf(f_3519_4,plain,
    hAPP(c_Set_Oimage(U_13897,U_13898,U_13899),hAPP(c_Set_Ovimage(U_13897,U_13898,U_13899),U_13900)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13898,tc_HOL_Obool)),U_13900),hAPP(c_Set_Oimage(U_13897,U_13898,U_13899),c_Orderings_Otop__class_Otop(tc_fun(U_13897,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3519_3]) ).

fof(f_3520_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_3520_2,plain,
    ! [U_13904,U_13903,U_13902,U_13901] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13903),hAPP(c_Set_Ovimage(U_13903,U_13901,U_13904),U_13902)))
      | ~ c_Fun_Oinj__on(U_13903,U_13901,U_13904,c_Orderings_Otop__class_Otop(tc_fun(U_13903,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13901),U_13902)) ),
    inference(variable_rename,[status(thm)],[f_3520_1]) ).

fof(f_3520_3,plain,
    ! [U_13901,U_13902,U_13903,U_13904] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13903),hAPP(c_Set_Ovimage(U_13903,U_13901,U_13904),U_13902)))
      | ~ c_Fun_Oinj__on(U_13903,U_13901,U_13904,c_Orderings_Otop__class_Otop(tc_fun(U_13903,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13901),U_13902)) ),
    inference(definitional_conversion,[status(esa)],[f_3520_2]) ).

cnf(f_3520_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13903),hAPP(c_Set_Ovimage(U_13903,U_13901,U_13904),U_13902)))
    | ~ c_Fun_Oinj__on(U_13903,U_13901,U_13904,c_Orderings_Otop__class_Otop(tc_fun(U_13903,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13901),U_13902)) ),
    inference(clausify,[status(thm)],[f_3520_3]) ).

fof(f_3521_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_3521_2,plain,
    ! [U_13908,U_13907,U_13906,U_13905] :
      ( hAPP(c_Set_Ovimage(U_13905,U_13906,U_13907),hAPP(c_Set_Oimage(U_13905,U_13906,U_13907),U_13908)) = U_13908
      | ~ c_Fun_Oinj__on(U_13905,U_13906,U_13907,c_Orderings_Otop__class_Otop(tc_fun(U_13905,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3521_1]) ).

fof(f_3521_3,plain,
    ! [U_13905,U_13906,U_13907,U_13908] :
      ( hAPP(c_Set_Ovimage(U_13905,U_13906,U_13907),hAPP(c_Set_Oimage(U_13905,U_13906,U_13907),U_13908)) = U_13908
      | ~ c_Fun_Oinj__on(U_13905,U_13906,U_13907,c_Orderings_Otop__class_Otop(tc_fun(U_13905,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3521_2]) ).

cnf(f_3521_4,plain,
    ( hAPP(c_Set_Ovimage(U_13905,U_13906,U_13907),hAPP(c_Set_Oimage(U_13905,U_13906,U_13907),U_13908)) = U_13908
    | ~ c_Fun_Oinj__on(U_13905,U_13906,U_13907,c_Orderings_Otop__class_Otop(tc_fun(U_13905,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3521_3]) ).

fof(f_3522_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_3522_2,plain,
    ! [U_13912,U_13911,U_13910,U_13909] :
      ( ( hAPP(c_Set_Ovimage(U_13912,U_13909,hAPP(c_COMBK(U_13909,U_13912),U_13910)),U_13911) = c_Orderings_Obot__class_Obot(tc_fun(U_13912,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_13909),U_13910),U_13911)) )
      & ( hAPP(c_Set_Ovimage(U_13912,U_13909,hAPP(c_COMBK(U_13909,U_13912),U_13910)),U_13911) = c_Orderings_Otop__class_Otop(tc_fun(U_13912,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13909),U_13910),U_13911)) ) ),
    inference(variable_rename,[status(thm)],[f_3522_1]) ).

fof(f_3522_3,plain,
    ( ! [U_13920,U_13918,U_13916,U_13914] :
        ( hAPP(c_Set_Ovimage(U_13920,U_13914,hAPP(c_COMBK(U_13914,U_13920),U_13916)),U_13918) = c_Orderings_Obot__class_Obot(tc_fun(U_13920,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_13914),U_13916),U_13918)) )
    & ! [U_13919,U_13917,U_13915,U_13913] :
        ( hAPP(c_Set_Ovimage(U_13919,U_13913,hAPP(c_COMBK(U_13913,U_13919),U_13915)),U_13917) = c_Orderings_Otop__class_Otop(tc_fun(U_13919,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13913),U_13915),U_13917)) ) ),
    inference(miniscope,[status(thm)],[f_3522_2]) ).

fof(f_3522_4,plain,
    ( ! [U_13914,U_13916,U_13918,U_13920] :
        ( hAPP(c_Set_Ovimage(U_13920,U_13914,hAPP(c_COMBK(U_13914,U_13920),U_13916)),U_13918) = c_Orderings_Obot__class_Obot(tc_fun(U_13920,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_13914),U_13916),U_13918)) )
    & ! [U_13917,U_13915,U_13919,U_13913] :
        ( hAPP(c_Set_Ovimage(U_13919,U_13913,hAPP(c_COMBK(U_13913,U_13919),U_13915)),U_13917) = c_Orderings_Otop__class_Otop(tc_fun(U_13919,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13913),U_13915),U_13917)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3522_3]) ).

cnf(f_3522_5,plain,
    ( hAPP(c_Set_Ovimage(U_13919,U_13913,hAPP(c_COMBK(U_13913,U_13919),U_13915)),U_13917) = c_Orderings_Otop__class_Otop(tc_fun(U_13919,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13913),U_13915),U_13917)) ),
    inference(clausify,[status(thm)],[f_3522_4]) ).

cnf(f_3522_6,plain,
    ( hAPP(c_Set_Ovimage(U_13920,U_13914,hAPP(c_COMBK(U_13914,U_13920),U_13916)),U_13918) = c_Orderings_Obot__class_Obot(tc_fun(U_13920,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_13914),U_13916),U_13918)) ),
    inference(clausify,[status(thm)],[f_3522_4]) ).

fof(f_3523_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_3523_2,plain,
    ! [U_13924,U_13923,U_13922,U_13921] : hAPP(c_Set_Ovimage(U_13921,U_13922,U_13923),U_13924) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13922,tc_fun(U_13921,tc_HOL_Obool)),U_13924),hAPP(hAPP(c_COMBB(tc_fun(U_13922,tc_HOL_Obool),tc_fun(U_13921,tc_HOL_Obool),U_13922),c_Set_Ovimage(U_13921,U_13922,U_13923)),hAPP(hAPP(c_COMBC(U_13922,tc_fun(U_13922,tc_HOL_Obool),tc_fun(U_13922,tc_HOL_Obool)),c_Set_Oinsert(U_13922)),c_Orderings_Obot__class_Obot(tc_fun(U_13922,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3523_1]) ).

fof(f_3523_3,plain,
    ! [U_13921,U_13922,U_13923,U_13924] : hAPP(c_Set_Ovimage(U_13921,U_13922,U_13923),U_13924) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13922,tc_fun(U_13921,tc_HOL_Obool)),U_13924),hAPP(hAPP(c_COMBB(tc_fun(U_13922,tc_HOL_Obool),tc_fun(U_13921,tc_HOL_Obool),U_13922),c_Set_Ovimage(U_13921,U_13922,U_13923)),hAPP(hAPP(c_COMBC(U_13922,tc_fun(U_13922,tc_HOL_Obool),tc_fun(U_13922,tc_HOL_Obool)),c_Set_Oinsert(U_13922)),c_Orderings_Obot__class_Obot(tc_fun(U_13922,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3523_2]) ).

cnf(f_3523_4,plain,
    hAPP(c_Set_Ovimage(U_13921,U_13922,U_13923),U_13924) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13922,tc_fun(U_13921,tc_HOL_Obool)),U_13924),hAPP(hAPP(c_COMBB(tc_fun(U_13922,tc_HOL_Obool),tc_fun(U_13921,tc_HOL_Obool),U_13922),c_Set_Ovimage(U_13921,U_13922,U_13923)),hAPP(hAPP(c_COMBC(U_13922,tc_fun(U_13922,tc_HOL_Obool),tc_fun(U_13922,tc_HOL_Obool)),c_Set_Oinsert(U_13922)),c_Orderings_Obot__class_Obot(tc_fun(U_13922,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3523_3]) ).

fof(f_3524_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_3524_2,plain,
    ! [U_13929,U_13928,U_13927,U_13926,U_13925] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13925,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13925,U_13926,U_13927),U_13928)),U_13929))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13926,tc_HOL_Obool)),U_13928),hAPP(c_Set_Oimage(U_13925,U_13926,U_13927),U_13929)))
      | ~ c_Fun_Oinj__on(U_13925,U_13926,U_13927,c_Orderings_Otop__class_Otop(tc_fun(U_13925,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3524_1]) ).

fof(f_3524_3,plain,
    ! [U_13925,U_13926,U_13927,U_13928,U_13929] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13925,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13925,U_13926,U_13927),U_13928)),U_13929))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13926,tc_HOL_Obool)),U_13928),hAPP(c_Set_Oimage(U_13925,U_13926,U_13927),U_13929)))
      | ~ c_Fun_Oinj__on(U_13925,U_13926,U_13927,c_Orderings_Otop__class_Otop(tc_fun(U_13925,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3524_2]) ).

cnf(f_3524_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13925,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13925,U_13926,U_13927),U_13928)),U_13929))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13926,tc_HOL_Obool)),U_13928),hAPP(c_Set_Oimage(U_13925,U_13926,U_13927),U_13929)))
    | ~ c_Fun_Oinj__on(U_13925,U_13926,U_13927,c_Orderings_Otop__class_Otop(tc_fun(U_13925,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3524_3]) ).

fof(f_3525_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_3525_2,plain,
    ! [U_13935,U_13934,U_13933,U_13932,U_13931,U_13930] :
      ( ( ( ( hAPP(c_Set_Ovimage(U_13934,U_13930,hAPP(hAPP(c_COMBC(U_13934,U_13930,U_13930),hAPP(hAPP(c_COMBC(U_13934,U_13930,tc_fun(U_13930,U_13930)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13930,tc_fun(U_13930,U_13930)),U_13934),c_If(U_13930)),hAPP(hAPP(c_COMBC(U_13934,tc_fun(U_13934,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13934)),U_13935))),U_13931)),U_13933)),U_13932) = c_Orderings_Obot__class_Obot(tc_fun(U_13934,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_member(U_13930),U_13933),U_13932)) )
          & ( hAPP(c_Set_Ovimage(U_13934,U_13930,hAPP(hAPP(c_COMBC(U_13934,U_13930,U_13930),hAPP(hAPP(c_COMBC(U_13934,U_13930,tc_fun(U_13930,U_13930)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13930,tc_fun(U_13930,U_13930)),U_13934),c_If(U_13930)),hAPP(hAPP(c_COMBC(U_13934,tc_fun(U_13934,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13934)),U_13935))),U_13931)),U_13933)),U_13932) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13934,tc_HOL_Obool)),U_13935)
            | ~ hBOOL(hAPP(hAPP(c_member(U_13930),U_13933),U_13932)) ) )
        | hBOOL(hAPP(hAPP(c_member(U_13930),U_13931),U_13932)) )
      & ( ( ( hAPP(c_Set_Ovimage(U_13934,U_13930,hAPP(hAPP(c_COMBC(U_13934,U_13930,U_13930),hAPP(hAPP(c_COMBC(U_13934,U_13930,tc_fun(U_13930,U_13930)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13930,tc_fun(U_13930,U_13930)),U_13934),c_If(U_13930)),hAPP(hAPP(c_COMBC(U_13934,tc_fun(U_13934,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13934)),U_13935))),U_13931)),U_13933)),U_13932) = U_13935
            | hBOOL(hAPP(hAPP(c_member(U_13930),U_13933),U_13932)) )
          & ( hAPP(c_Set_Ovimage(U_13934,U_13930,hAPP(hAPP(c_COMBC(U_13934,U_13930,U_13930),hAPP(hAPP(c_COMBC(U_13934,U_13930,tc_fun(U_13930,U_13930)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13930,tc_fun(U_13930,U_13930)),U_13934),c_If(U_13930)),hAPP(hAPP(c_COMBC(U_13934,tc_fun(U_13934,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13934)),U_13935))),U_13931)),U_13933)),U_13932) = c_Orderings_Otop__class_Otop(tc_fun(U_13934,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13930),U_13933),U_13932)) ) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_13930),U_13931),U_13932)) ) ),
    inference(variable_rename,[status(thm)],[f_3525_1]) ).

fof(f_3525_3,plain,
    ( ! [U_13947,U_13945,U_13943,U_13941,U_13939,U_13937] :
        ( ( ( hAPP(c_Set_Ovimage(U_13945,U_13937,hAPP(hAPP(c_COMBC(U_13945,U_13937,U_13937),hAPP(hAPP(c_COMBC(U_13945,U_13937,tc_fun(U_13937,U_13937)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13937,tc_fun(U_13937,U_13937)),U_13945),c_If(U_13937)),hAPP(hAPP(c_COMBC(U_13945,tc_fun(U_13945,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13945)),U_13947))),U_13939)),U_13943)),U_13941) = c_Orderings_Obot__class_Obot(tc_fun(U_13945,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_member(U_13937),U_13943),U_13941)) )
          & ( hAPP(c_Set_Ovimage(U_13945,U_13937,hAPP(hAPP(c_COMBC(U_13945,U_13937,U_13937),hAPP(hAPP(c_COMBC(U_13945,U_13937,tc_fun(U_13937,U_13937)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13937,tc_fun(U_13937,U_13937)),U_13945),c_If(U_13937)),hAPP(hAPP(c_COMBC(U_13945,tc_fun(U_13945,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13945)),U_13947))),U_13939)),U_13943)),U_13941) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13945,tc_HOL_Obool)),U_13947)
            | ~ hBOOL(hAPP(hAPP(c_member(U_13937),U_13943),U_13941)) ) )
        | hBOOL(hAPP(hAPP(c_member(U_13937),U_13939),U_13941)) )
    & ! [U_13946,U_13944,U_13942,U_13940,U_13938,U_13936] :
        ( ( ( hAPP(c_Set_Ovimage(U_13944,U_13936,hAPP(hAPP(c_COMBC(U_13944,U_13936,U_13936),hAPP(hAPP(c_COMBC(U_13944,U_13936,tc_fun(U_13936,U_13936)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13936,tc_fun(U_13936,U_13936)),U_13944),c_If(U_13936)),hAPP(hAPP(c_COMBC(U_13944,tc_fun(U_13944,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13944)),U_13946))),U_13938)),U_13942)),U_13940) = U_13946
            | hBOOL(hAPP(hAPP(c_member(U_13936),U_13942),U_13940)) )
          & ( hAPP(c_Set_Ovimage(U_13944,U_13936,hAPP(hAPP(c_COMBC(U_13944,U_13936,U_13936),hAPP(hAPP(c_COMBC(U_13944,U_13936,tc_fun(U_13936,U_13936)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13936,tc_fun(U_13936,U_13936)),U_13944),c_If(U_13936)),hAPP(hAPP(c_COMBC(U_13944,tc_fun(U_13944,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13944)),U_13946))),U_13938)),U_13942)),U_13940) = c_Orderings_Otop__class_Otop(tc_fun(U_13944,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13936),U_13942),U_13940)) ) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_13936),U_13938),U_13940)) ) ),
    inference(miniscope,[status(thm)],[f_3525_2]) ).

fof(f_3525_4,plain,
    ( ! [U_13943,U_13939,U_13941,U_13937,U_13947,U_13945] :
        ( hAPP(c_Set_Ovimage(U_13945,U_13937,hAPP(hAPP(c_COMBC(U_13945,U_13937,U_13937),hAPP(hAPP(c_COMBC(U_13945,U_13937,tc_fun(U_13937,U_13937)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13937,tc_fun(U_13937,U_13937)),U_13945),c_If(U_13937)),hAPP(hAPP(c_COMBC(U_13945,tc_fun(U_13945,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13945)),U_13947))),U_13939)),U_13943)),U_13941) = c_Orderings_Obot__class_Obot(tc_fun(U_13945,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_13937),U_13943),U_13941))
        | ~ sP970(U_13943,U_13939,U_13941,U_13937,U_13947,U_13945) )
    & ! [U_13943,U_13939,U_13941,U_13937,U_13947,U_13945] :
        ( hAPP(c_Set_Ovimage(U_13945,U_13937,hAPP(hAPP(c_COMBC(U_13945,U_13937,U_13937),hAPP(hAPP(c_COMBC(U_13945,U_13937,tc_fun(U_13937,U_13937)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13937,tc_fun(U_13937,U_13937)),U_13945),c_If(U_13937)),hAPP(hAPP(c_COMBC(U_13945,tc_fun(U_13945,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13945)),U_13947))),U_13939)),U_13943)),U_13941) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13945,tc_HOL_Obool)),U_13947)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13937),U_13943),U_13941))
        | ~ sP970(U_13943,U_13939,U_13941,U_13937,U_13947,U_13945) )
    & ! [U_13936,U_13938,U_13940,U_13942,U_13946,U_13944] :
        ( hAPP(c_Set_Ovimage(U_13944,U_13936,hAPP(hAPP(c_COMBC(U_13944,U_13936,U_13936),hAPP(hAPP(c_COMBC(U_13944,U_13936,tc_fun(U_13936,U_13936)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13936,tc_fun(U_13936,U_13936)),U_13944),c_If(U_13936)),hAPP(hAPP(c_COMBC(U_13944,tc_fun(U_13944,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13944)),U_13946))),U_13938)),U_13942)),U_13940) = U_13946
        | hBOOL(hAPP(hAPP(c_member(U_13936),U_13942),U_13940))
        | ~ sP969(U_13936,U_13938,U_13940,U_13942,U_13946,U_13944) )
    & ! [U_13936,U_13938,U_13940,U_13942,U_13946,U_13944] :
        ( hAPP(c_Set_Ovimage(U_13944,U_13936,hAPP(hAPP(c_COMBC(U_13944,U_13936,U_13936),hAPP(hAPP(c_COMBC(U_13944,U_13936,tc_fun(U_13936,U_13936)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13936,tc_fun(U_13936,U_13936)),U_13944),c_If(U_13936)),hAPP(hAPP(c_COMBC(U_13944,tc_fun(U_13944,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13944)),U_13946))),U_13938)),U_13942)),U_13940) = c_Orderings_Otop__class_Otop(tc_fun(U_13944,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13936),U_13942),U_13940))
        | ~ sP969(U_13936,U_13938,U_13940,U_13942,U_13946,U_13944) )
    & ! [U_13943,U_13939,U_13941,U_13937,U_13947,U_13945] :
        ( sP970(U_13943,U_13939,U_13941,U_13937,U_13947,U_13945)
        | hBOOL(hAPP(hAPP(c_member(U_13937),U_13939),U_13941)) )
    & ! [U_13936,U_13938,U_13940,U_13942,U_13946,U_13944] :
        ( sP969(U_13936,U_13938,U_13940,U_13942,U_13946,U_13944)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13936),U_13938),U_13940)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP969,sP970])],[f_3525_3]) ).

cnf(f_3525_5,plain,
    ( sP969(U_13936,U_13938,U_13940,U_13942,U_13946,U_13944)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13936),U_13938),U_13940)) ),
    inference(clausify,[status(thm)],[f_3525_4]) ).

cnf(f_3525_6,plain,
    ( sP970(U_13943,U_13939,U_13941,U_13937,U_13947,U_13945)
    | hBOOL(hAPP(hAPP(c_member(U_13937),U_13939),U_13941)) ),
    inference(clausify,[status(thm)],[f_3525_4]) ).

cnf(f_3525_7,plain,
    ( hAPP(c_Set_Ovimage(U_13944,U_13936,hAPP(hAPP(c_COMBC(U_13944,U_13936,U_13936),hAPP(hAPP(c_COMBC(U_13944,U_13936,tc_fun(U_13936,U_13936)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13936,tc_fun(U_13936,U_13936)),U_13944),c_If(U_13936)),hAPP(hAPP(c_COMBC(U_13944,tc_fun(U_13944,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13944)),U_13946))),U_13938)),U_13942)),U_13940) = c_Orderings_Otop__class_Otop(tc_fun(U_13944,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13936),U_13942),U_13940))
    | ~ sP969(U_13936,U_13938,U_13940,U_13942,U_13946,U_13944) ),
    inference(clausify,[status(thm)],[f_3525_4]) ).

cnf(f_3525_8,plain,
    ( hAPP(c_Set_Ovimage(U_13944,U_13936,hAPP(hAPP(c_COMBC(U_13944,U_13936,U_13936),hAPP(hAPP(c_COMBC(U_13944,U_13936,tc_fun(U_13936,U_13936)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13936,tc_fun(U_13936,U_13936)),U_13944),c_If(U_13936)),hAPP(hAPP(c_COMBC(U_13944,tc_fun(U_13944,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13944)),U_13946))),U_13938)),U_13942)),U_13940) = U_13946
    | hBOOL(hAPP(hAPP(c_member(U_13936),U_13942),U_13940))
    | ~ sP969(U_13936,U_13938,U_13940,U_13942,U_13946,U_13944) ),
    inference(clausify,[status(thm)],[f_3525_4]) ).

cnf(f_3525_9,plain,
    ( hAPP(c_Set_Ovimage(U_13945,U_13937,hAPP(hAPP(c_COMBC(U_13945,U_13937,U_13937),hAPP(hAPP(c_COMBC(U_13945,U_13937,tc_fun(U_13937,U_13937)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13937,tc_fun(U_13937,U_13937)),U_13945),c_If(U_13937)),hAPP(hAPP(c_COMBC(U_13945,tc_fun(U_13945,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13945)),U_13947))),U_13939)),U_13943)),U_13941) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13945,tc_HOL_Obool)),U_13947)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13937),U_13943),U_13941))
    | ~ sP970(U_13943,U_13939,U_13941,U_13937,U_13947,U_13945) ),
    inference(clausify,[status(thm)],[f_3525_4]) ).

cnf(f_3525_10,plain,
    ( hAPP(c_Set_Ovimage(U_13945,U_13937,hAPP(hAPP(c_COMBC(U_13945,U_13937,U_13937),hAPP(hAPP(c_COMBC(U_13945,U_13937,tc_fun(U_13937,U_13937)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13937,tc_fun(U_13937,U_13937)),U_13945),c_If(U_13937)),hAPP(hAPP(c_COMBC(U_13945,tc_fun(U_13945,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13945)),U_13947))),U_13939)),U_13943)),U_13941) = c_Orderings_Obot__class_Obot(tc_fun(U_13945,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_13937),U_13943),U_13941))
    | ~ sP970(U_13943,U_13939,U_13941,U_13937,U_13947,U_13945) ),
    inference(clausify,[status(thm)],[f_3525_4]) ).

fof(f_3526_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_3526_2,plain,
    ! [U_13952,U_13951,U_13950,U_13949,U_13948] :
      ( hAPP(c_Set_Oimage(U_13948,U_13949,U_13950),c_Orderings_Otop__class_Otop(tc_fun(U_13948,tc_HOL_Obool))) = U_13952
      | ~ c_Typedef_Otype__definition(U_13948,U_13949,U_13950,U_13951,U_13952) ),
    inference(variable_rename,[status(thm)],[f_3526_1]) ).

fof(f_3526_3,plain,
    ! [U_13949,U_13948,U_13952,U_13950,U_13951] :
      ( hAPP(c_Set_Oimage(U_13948,U_13949,U_13950),c_Orderings_Otop__class_Otop(tc_fun(U_13948,tc_HOL_Obool))) = U_13952
      | ~ c_Typedef_Otype__definition(U_13948,U_13949,U_13950,U_13951,U_13952) ),
    inference(definitional_conversion,[status(esa)],[f_3526_2]) ).

cnf(f_3526_4,plain,
    ( hAPP(c_Set_Oimage(U_13948,U_13949,U_13950),c_Orderings_Otop__class_Otop(tc_fun(U_13948,tc_HOL_Obool))) = U_13952
    | ~ c_Typedef_Otype__definition(U_13948,U_13949,U_13950,U_13951,U_13952) ),
    inference(clausify,[status(thm)],[f_3526_3]) ).

fof(f_3527_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_3527_2,plain,
    ! [U_13957,U_13956,U_13955,U_13954,U_13953] :
      ( hAPP(c_Set_Oimage(U_13954,U_13953,U_13956),U_13957) = c_Orderings_Otop__class_Otop(tc_fun(U_13953,tc_HOL_Obool))
      | ~ c_Typedef_Otype__definition(U_13953,U_13954,U_13955,U_13956,U_13957) ),
    inference(variable_rename,[status(thm)],[f_3527_1]) ).

fof(f_3527_3,plain,
    ! [U_13954,U_13957,U_13955,U_13956,U_13953] :
      ( hAPP(c_Set_Oimage(U_13954,U_13953,U_13956),U_13957) = c_Orderings_Otop__class_Otop(tc_fun(U_13953,tc_HOL_Obool))
      | ~ c_Typedef_Otype__definition(U_13953,U_13954,U_13955,U_13956,U_13957) ),
    inference(definitional_conversion,[status(esa)],[f_3527_2]) ).

cnf(f_3527_4,plain,
    ( hAPP(c_Set_Oimage(U_13954,U_13953,U_13956),U_13957) = c_Orderings_Otop__class_Otop(tc_fun(U_13953,tc_HOL_Obool))
    | ~ c_Typedef_Otype__definition(U_13953,U_13954,U_13955,U_13956,U_13957) ),
    inference(clausify,[status(thm)],[f_3527_3]) ).

fof(f_3528_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_3528_2,plain,
    ! [U_13963,U_13962,U_13961,U_13960,U_13959,U_13958] :
      ( hBOOL(hAPP(hAPP(c_member(U_13959),hAPP(U_13960,U_13963)),U_13962))
      | ~ c_Typedef_Otype__definition(U_13958,U_13959,U_13960,U_13961,U_13962) ),
    inference(variable_rename,[status(thm)],[f_3528_1]) ).

fof(f_3528_3,plain,
    ! [U_13963,U_13962,U_13961,U_13960,U_13959] :
      ( ! [U_13958] : ~ c_Typedef_Otype__definition(U_13958,U_13959,U_13960,U_13961,U_13962)
      | hBOOL(hAPP(hAPP(c_member(U_13959),hAPP(U_13960,U_13963)),U_13962)) ),
    inference(miniscope,[status(thm)],[f_3528_2]) ).

fof(f_3528_4,plain,
    ! [U_13958,U_13959,U_13960,U_13961,U_13962,U_13963] :
      ( ~ c_Typedef_Otype__definition(U_13958,U_13959,U_13960,U_13961,U_13962)
      | hBOOL(hAPP(hAPP(c_member(U_13959),hAPP(U_13960,U_13963)),U_13962)) ),
    inference(definitional_conversion,[status(esa)],[f_3528_3]) ).

cnf(f_3528_5,plain,
    ( ~ c_Typedef_Otype__definition(U_13958,U_13959,U_13960,U_13961,U_13962)
    | hBOOL(hAPP(hAPP(c_member(U_13959),hAPP(U_13960,U_13963)),U_13962)) ),
    inference(clausify,[status(thm)],[f_3528_4]) ).

fof(f_3529_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_3529_2,plain,
    ! [U_13970,U_13969,U_13968,U_13967,U_13966,U_13965,U_13964] :
      ( ( ( hAPP(U_13966,U_13969) = hAPP(U_13966,U_13970)
          | U_13969 != U_13970 )
        & ( U_13969 = U_13970
          | hAPP(U_13966,U_13969) != hAPP(U_13966,U_13970) ) )
      | ~ c_Typedef_Otype__definition(U_13964,U_13965,U_13966,U_13967,U_13968) ),
    inference(variable_rename,[status(thm)],[f_3529_1]) ).

fof(f_3529_3,plain,
    ! [U_13970,U_13969,U_13968,U_13967,U_13966] :
      ( ! [U_13965,U_13964] : ~ c_Typedef_Otype__definition(U_13964,U_13965,U_13966,U_13967,U_13968)
      | ( ( hAPP(U_13966,U_13969) = hAPP(U_13966,U_13970)
          | U_13969 != U_13970 )
        & ( U_13969 = U_13970
          | hAPP(U_13966,U_13969) != hAPP(U_13966,U_13970) ) ) ),
    inference(miniscope,[status(thm)],[f_3529_2]) ).

fof(f_3529_4,plain,
    ( ! [U_13966,U_13969,U_13970] :
        ( hAPP(U_13966,U_13969) = hAPP(U_13966,U_13970)
        | U_13969 != U_13970
        | ~ sP971(U_13966,U_13969,U_13970) )
    & ! [U_13966,U_13969,U_13970] :
        ( U_13969 = U_13970
        | hAPP(U_13966,U_13969) != hAPP(U_13966,U_13970)
        | ~ sP971(U_13966,U_13969,U_13970) )
    & ! [U_13965,U_13964,U_13966,U_13967,U_13968,U_13969,U_13970] :
        ( ~ c_Typedef_Otype__definition(U_13964,U_13965,U_13966,U_13967,U_13968)
        | sP971(U_13966,U_13969,U_13970) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP971])],[f_3529_3]) ).

cnf(f_3529_5,plain,
    ( ~ c_Typedef_Otype__definition(U_13964,U_13965,U_13966,U_13967,U_13968)
    | sP971(U_13966,U_13969,U_13970) ),
    inference(clausify,[status(thm)],[f_3529_4]) ).

cnf(f_3529_6,plain,
    ( U_13969 = U_13970
    | hAPP(U_13966,U_13969) != hAPP(U_13966,U_13970)
    | ~ sP971(U_13966,U_13969,U_13970) ),
    inference(clausify,[status(thm)],[f_3529_4]) ).

cnf(f_3529_7,plain,
    ( hAPP(U_13966,U_13969) = hAPP(U_13966,U_13970)
    | U_13969 != U_13970
    | ~ sP971(U_13966,U_13969,U_13970) ),
    inference(clausify,[status(thm)],[f_3529_4]) ).

fof(f_3530_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_3530_2,plain,
    ! [U_13976,U_13975,U_13974,U_13973,U_13972,U_13971] :
      ( hAPP(U_13974,hAPP(U_13973,U_13976)) = U_13976
      | ~ c_Typedef_Otype__definition(U_13971,U_13972,U_13973,U_13974,U_13975) ),
    inference(variable_rename,[status(thm)],[f_3530_1]) ).

fof(f_3530_3,plain,
    ! [U_13976,U_13975,U_13974,U_13973] :
      ( ! [U_13972,U_13971] : ~ c_Typedef_Otype__definition(U_13971,U_13972,U_13973,U_13974,U_13975)
      | hAPP(U_13974,hAPP(U_13973,U_13976)) = U_13976 ),
    inference(miniscope,[status(thm)],[f_3530_2]) ).

fof(f_3530_4,plain,
    ! [U_13972,U_13971,U_13976,U_13975,U_13973,U_13974] :
      ( ~ c_Typedef_Otype__definition(U_13971,U_13972,U_13973,U_13974,U_13975)
      | hAPP(U_13974,hAPP(U_13973,U_13976)) = U_13976 ),
    inference(definitional_conversion,[status(esa)],[f_3530_3]) ).

cnf(f_3530_5,plain,
    ( ~ c_Typedef_Otype__definition(U_13971,U_13972,U_13973,U_13974,U_13975)
    | hAPP(U_13974,hAPP(U_13973,U_13976)) = U_13976 ),
    inference(clausify,[status(thm)],[f_3530_4]) ).

fof(f_3531_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_3531_2,plain,
    ! [U_13983,U_13982,U_13981,U_13980,U_13979,U_13978,U_13977] :
      ( ( ( hAPP(U_13980,U_13982) = hAPP(U_13980,U_13983)
          | U_13982 != U_13983 )
        & ( U_13982 = U_13983
          | hAPP(U_13980,U_13982) != hAPP(U_13980,U_13983) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13978),U_13983),U_13981))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13978),U_13982),U_13981))
      | ~ c_Typedef_Otype__definition(U_13977,U_13978,U_13979,U_13980,U_13981) ),
    inference(variable_rename,[status(thm)],[f_3531_1]) ).

fof(f_3531_3,plain,
    ! [U_13983,U_13982,U_13981,U_13980,U_13979,U_13978] :
      ( ! [U_13977] : ~ c_Typedef_Otype__definition(U_13977,U_13978,U_13979,U_13980,U_13981)
      | ( ( hAPP(U_13980,U_13982) = hAPP(U_13980,U_13983)
          | U_13982 != U_13983 )
        & ( U_13982 = U_13983
          | hAPP(U_13980,U_13982) != hAPP(U_13980,U_13983) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13978),U_13983),U_13981))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13978),U_13982),U_13981)) ),
    inference(miniscope,[status(thm)],[f_3531_2]) ).

fof(f_3531_4,plain,
    ( ! [U_13980,U_13982,U_13983] :
        ( hAPP(U_13980,U_13982) = hAPP(U_13980,U_13983)
        | U_13982 != U_13983
        | ~ sP972(U_13980,U_13982,U_13983) )
    & ! [U_13980,U_13982,U_13983] :
        ( U_13982 = U_13983
        | hAPP(U_13980,U_13982) != hAPP(U_13980,U_13983)
        | ~ sP972(U_13980,U_13982,U_13983) )
    & ! [U_13977,U_13978,U_13979,U_13980,U_13981,U_13982,U_13983] :
        ( ~ c_Typedef_Otype__definition(U_13977,U_13978,U_13979,U_13980,U_13981)
        | sP972(U_13980,U_13982,U_13983)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13978),U_13983),U_13981))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13978),U_13982),U_13981)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP972])],[f_3531_3]) ).

cnf(f_3531_5,plain,
    ( ~ c_Typedef_Otype__definition(U_13977,U_13978,U_13979,U_13980,U_13981)
    | sP972(U_13980,U_13982,U_13983)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13978),U_13983),U_13981))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13978),U_13982),U_13981)) ),
    inference(clausify,[status(thm)],[f_3531_4]) ).

cnf(f_3531_6,plain,
    ( U_13982 = U_13983
    | hAPP(U_13980,U_13982) != hAPP(U_13980,U_13983)
    | ~ sP972(U_13980,U_13982,U_13983) ),
    inference(clausify,[status(thm)],[f_3531_4]) ).

cnf(f_3531_7,plain,
    ( hAPP(U_13980,U_13982) = hAPP(U_13980,U_13983)
    | U_13982 != U_13983
    | ~ sP972(U_13980,U_13982,U_13983) ),
    inference(clausify,[status(thm)],[f_3531_4]) ).

fof(f_3532_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_3532_2,plain,
    ! [U_13989,U_13988,U_13987,U_13986,U_13985,U_13984] :
      ( hAPP(U_13986,hAPP(U_13987,U_13989)) = U_13989
      | ~ hBOOL(hAPP(hAPP(c_member(U_13985),U_13989),U_13988))
      | ~ c_Typedef_Otype__definition(U_13984,U_13985,U_13986,U_13987,U_13988) ),
    inference(variable_rename,[status(thm)],[f_3532_1]) ).

fof(f_3532_3,plain,
    ! [U_13989,U_13988,U_13987,U_13986,U_13985] :
      ( ! [U_13984] : ~ c_Typedef_Otype__definition(U_13984,U_13985,U_13986,U_13987,U_13988)
      | hAPP(U_13986,hAPP(U_13987,U_13989)) = U_13989
      | ~ hBOOL(hAPP(hAPP(c_member(U_13985),U_13989),U_13988)) ),
    inference(miniscope,[status(thm)],[f_3532_2]) ).

fof(f_3532_4,plain,
    ! [U_13986,U_13985,U_13988,U_13984,U_13989,U_13987] :
      ( ~ c_Typedef_Otype__definition(U_13984,U_13985,U_13986,U_13987,U_13988)
      | hAPP(U_13986,hAPP(U_13987,U_13989)) = U_13989
      | ~ hBOOL(hAPP(hAPP(c_member(U_13985),U_13989),U_13988)) ),
    inference(definitional_conversion,[status(esa)],[f_3532_3]) ).

cnf(f_3532_5,plain,
    ( ~ c_Typedef_Otype__definition(U_13984,U_13985,U_13986,U_13987,U_13988)
    | hAPP(U_13986,hAPP(U_13987,U_13989)) = U_13989
    | ~ hBOOL(hAPP(hAPP(c_member(U_13985),U_13989),U_13988)) ),
    inference(clausify,[status(thm)],[f_3532_4]) ).

fof(f_3533_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_3533_2,plain,
    ! [U_13997,U_13996,U_13995,U_13994] :
      ( ( c_Wellfounded_Omax__extp(U_13994,U_13995,U_13996,U_13997)
        | ? [U_13993] :
            ( ! [U_13992] :
                ( ~ hBOOL(hAPP(hAPP(U_13995,U_13993),U_13992))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13994),U_13992),U_13997)) )
            & hBOOL(hAPP(hAPP(c_member(U_13994),U_13993),U_13996)) )
        | U_13997 = c_Orderings_Obot__class_Obot(tc_fun(U_13994,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13994),U_13997))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13994),U_13996)) )
      & ( ( ! [U_13991] :
              ( ? [U_13990] :
                  ( hBOOL(hAPP(hAPP(U_13995,U_13991),U_13990))
                  & hBOOL(hAPP(hAPP(c_member(U_13994),U_13990),U_13997)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13994),U_13991),U_13996)) )
          & U_13997 != c_Orderings_Obot__class_Obot(tc_fun(U_13994,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13994),U_13997))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13994),U_13996)) )
        | ~ c_Wellfounded_Omax__extp(U_13994,U_13995,U_13996,U_13997) ) ),
    inference(variable_rename,[status(thm)],[f_3533_1]) ).

fof(f_3533_3,plain,
    ( ! [U_14005,U_14003,U_14001,U_13999] :
        ( c_Wellfounded_Omax__extp(U_13999,U_14001,U_14003,U_14005)
        | ? [U_13993] :
            ( ! [U_13992] :
                ( ~ hBOOL(hAPP(hAPP(U_14001,U_13993),U_13992))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13999),U_13992),U_14005)) )
            & hBOOL(hAPP(hAPP(c_member(U_13999),U_13993),U_14003)) )
        | U_14005 = c_Orderings_Obot__class_Obot(tc_fun(U_13999,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13999),U_14005))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13999),U_14003)) )
    & ! [U_14004,U_14002,U_14000,U_13998] :
        ( ( ! [U_13991] :
              ( ? [U_13990] :
                  ( hBOOL(hAPP(hAPP(U_14000,U_13991),U_13990))
                  & hBOOL(hAPP(hAPP(c_member(U_13998),U_13990),U_14004)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13998),U_13991),U_14002)) )
          & U_14004 != c_Orderings_Obot__class_Obot(tc_fun(U_13998,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13998),U_14004))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13998),U_14002)) )
        | ~ c_Wellfounded_Omax__extp(U_13998,U_14000,U_14002,U_14004) ) ),
    inference(miniscope,[status(thm)],[f_3533_2]) ).

fof(f_3533_4,plain,
    ( ! [U_14005,U_14003,U_14001,U_13999] :
        ( c_Wellfounded_Omax__extp(U_13999,U_14001,U_14003,U_14005)
        | ? [U_13993] :
            ( ! [U_13992] :
                ( ~ hBOOL(hAPP(hAPP(U_14001,U_13993),U_13992))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13999),U_13992),U_14005)) )
            & hBOOL(hAPP(hAPP(c_member(U_13999),U_13993),U_14003)) )
        | U_14005 = c_Orderings_Obot__class_Obot(tc_fun(U_13999,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13999),U_14005))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13999),U_14003)) )
    & ! [U_14004,U_14002,U_14000,U_13998] :
        ( ( ! [U_13991] :
              ( ( hBOOL(hAPP(hAPP(U_14000,U_13991),sK297(U_14004,U_14002,U_14000,U_13998,U_13991)))
                & hBOOL(hAPP(hAPP(c_member(U_13998),sK297(U_14004,U_14002,U_14000,U_13998,U_13991)),U_14004)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13998),U_13991),U_14002)) )
          & U_14004 != c_Orderings_Obot__class_Obot(tc_fun(U_13998,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13998),U_14004))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13998),U_14002)) )
        | ~ c_Wellfounded_Omax__extp(U_13998,U_14000,U_14002,U_14004) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK297]),skolemize(U_13990,sK297(U_14004,U_14002,U_14000,U_13998,U_13991))],[f_3533_3]) ).

fof(f_3533_5,plain,
    ( ! [U_14005,U_14003,U_14001,U_13999] :
        ( c_Wellfounded_Omax__extp(U_13999,U_14001,U_14003,U_14005)
        | ( ! [U_13992] :
              ( ~ hBOOL(hAPP(hAPP(U_14001,sK298(U_14005,U_14003,U_14001,U_13999)),U_13992))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13999),U_13992),U_14005)) )
          & hBOOL(hAPP(hAPP(c_member(U_13999),sK298(U_14005,U_14003,U_14001,U_13999)),U_14003)) )
        | U_14005 = c_Orderings_Obot__class_Obot(tc_fun(U_13999,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13999),U_14005))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13999),U_14003)) )
    & ! [U_14004,U_14002,U_14000,U_13998] :
        ( ( ! [U_13991] :
              ( ( hBOOL(hAPP(hAPP(U_14000,U_13991),sK297(U_14004,U_14002,U_14000,U_13998,U_13991)))
                & hBOOL(hAPP(hAPP(c_member(U_13998),sK297(U_14004,U_14002,U_14000,U_13998,U_13991)),U_14004)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13998),U_13991),U_14002)) )
          & U_14004 != c_Orderings_Obot__class_Obot(tc_fun(U_13998,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13998),U_14004))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13998),U_14002)) )
        | ~ c_Wellfounded_Omax__extp(U_13998,U_14000,U_14002,U_14004) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK298]),skolemize(U_13993,sK298(U_14005,U_14003,U_14001,U_13999))],[f_3533_4]) ).

fof(f_3533_6,plain,
    ( ! [U_13992,U_14003,U_14005,U_14001,U_13999] :
        ( ~ hBOOL(hAPP(hAPP(U_14001,sK298(U_14005,U_14003,U_14001,U_13999)),U_13992))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13999),U_13992),U_14005))
        | ~ sP975(U_13992,U_14003,U_14005,U_14001,U_13999) )
    & ! [U_13992,U_14003,U_14005,U_14001,U_13999] :
        ( hBOOL(hAPP(hAPP(c_member(U_13999),sK298(U_14005,U_14003,U_14001,U_13999)),U_14003))
        | ~ sP975(U_13992,U_14003,U_14005,U_14001,U_13999) )
    & ! [U_13991,U_14002,U_14000,U_13998,U_14004] :
        ( hBOOL(hAPP(hAPP(U_14000,U_13991),sK297(U_14004,U_14002,U_14000,U_13998,U_13991)))
        | ~ sP973(U_13991,U_14002,U_14000,U_13998,U_14004) )
    & ! [U_13991,U_14002,U_14000,U_13998,U_14004] :
        ( hBOOL(hAPP(hAPP(c_member(U_13998),sK297(U_14004,U_14002,U_14000,U_13998,U_13991)),U_14004))
        | ~ sP973(U_13991,U_14002,U_14000,U_13998,U_14004) )
    & ! [U_13991,U_14002,U_14000,U_13998,U_14004] :
        ( sP973(U_13991,U_14002,U_14000,U_13998,U_14004)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13998),U_13991),U_14002))
        | ~ sP974(U_13991,U_14002,U_14000,U_13998,U_14004) )
    & ! [U_13991,U_14002,U_14000,U_13998,U_14004] :
        ( U_14004 != c_Orderings_Obot__class_Obot(tc_fun(U_13998,tc_HOL_Obool))
        | ~ sP974(U_13991,U_14002,U_14000,U_13998,U_14004) )
    & ! [U_13991,U_14002,U_14000,U_13998,U_14004] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13998),U_14004))
        | ~ sP974(U_13991,U_14002,U_14000,U_13998,U_14004) )
    & ! [U_13991,U_14002,U_14000,U_13998,U_14004] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13998),U_14002))
        | ~ sP974(U_13991,U_14002,U_14000,U_13998,U_14004) )
    & ! [U_13992,U_14003,U_14005,U_14001,U_13999] :
        ( c_Wellfounded_Omax__extp(U_13999,U_14001,U_14003,U_14005)
        | sP975(U_13992,U_14003,U_14005,U_14001,U_13999)
        | U_14005 = c_Orderings_Obot__class_Obot(tc_fun(U_13999,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13999),U_14005))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13999),U_14003)) )
    & ! [U_13991,U_14002,U_14000,U_13998,U_14004] :
        ( sP974(U_13991,U_14002,U_14000,U_13998,U_14004)
        | ~ c_Wellfounded_Omax__extp(U_13998,U_14000,U_14002,U_14004) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP973,sP974,sP975])],[f_3533_5]) ).

cnf(f_3533_7,plain,
    ( sP974(U_13991,U_14002,U_14000,U_13998,U_14004)
    | ~ c_Wellfounded_Omax__extp(U_13998,U_14000,U_14002,U_14004) ),
    inference(clausify,[status(thm)],[f_3533_6]) ).

cnf(f_3533_8,plain,
    ( c_Wellfounded_Omax__extp(U_13999,U_14001,U_14003,U_14005)
    | sP975(U_13992,U_14003,U_14005,U_14001,U_13999)
    | U_14005 = c_Orderings_Obot__class_Obot(tc_fun(U_13999,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13999),U_14005))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13999),U_14003)) ),
    inference(clausify,[status(thm)],[f_3533_6]) ).

cnf(f_3533_9,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13998),U_14002))
    | ~ sP974(U_13991,U_14002,U_14000,U_13998,U_14004) ),
    inference(clausify,[status(thm)],[f_3533_6]) ).

cnf(f_3533_10,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13998),U_14004))
    | ~ sP974(U_13991,U_14002,U_14000,U_13998,U_14004) ),
    inference(clausify,[status(thm)],[f_3533_6]) ).

cnf(f_3533_11,plain,
    ( U_14004 != c_Orderings_Obot__class_Obot(tc_fun(U_13998,tc_HOL_Obool))
    | ~ sP974(U_13991,U_14002,U_14000,U_13998,U_14004) ),
    inference(clausify,[status(thm)],[f_3533_6]) ).

cnf(f_3533_12,plain,
    ( sP973(U_13991,U_14002,U_14000,U_13998,U_14004)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13998),U_13991),U_14002))
    | ~ sP974(U_13991,U_14002,U_14000,U_13998,U_14004) ),
    inference(clausify,[status(thm)],[f_3533_6]) ).

cnf(f_3533_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13998),sK297(U_14004,U_14002,U_14000,U_13998,U_13991)),U_14004))
    | ~ sP973(U_13991,U_14002,U_14000,U_13998,U_14004) ),
    inference(clausify,[status(thm)],[f_3533_6]) ).

cnf(f_3533_14,plain,
    ( hBOOL(hAPP(hAPP(U_14000,U_13991),sK297(U_14004,U_14002,U_14000,U_13998,U_13991)))
    | ~ sP973(U_13991,U_14002,U_14000,U_13998,U_14004) ),
    inference(clausify,[status(thm)],[f_3533_6]) ).

cnf(f_3533_15,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13999),sK298(U_14005,U_14003,U_14001,U_13999)),U_14003))
    | ~ sP975(U_13992,U_14003,U_14005,U_14001,U_13999) ),
    inference(clausify,[status(thm)],[f_3533_6]) ).

cnf(f_3533_16,plain,
    ( ~ hBOOL(hAPP(hAPP(U_14001,sK298(U_14005,U_14003,U_14001,U_13999)),U_13992))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13999),U_13992),U_14005))
    | ~ sP975(U_13992,U_14003,U_14005,U_14001,U_13999) ),
    inference(clausify,[status(thm)],[f_3533_6]) ).

fof(f_3534_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_3534_2,plain,
    ! [U_14011,U_14010,U_14009,U_14008] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14008,tc_HOL_Obool),tc_fun(U_14008,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14008,tc_HOL_Obool),tc_fun(U_14008,tc_HOL_Obool)),U_14009),U_14010)),c_Wellfounded_Omax__ext(U_14008,U_14011)))
      | ? [U_14007] :
          ( ! [U_14006] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14008,U_14008)),hAPP(hAPP(c_Product__Type_OPair(U_14008,U_14008),U_14007),U_14006)),U_14011))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14008),U_14006),U_14010)) )
          & hBOOL(hAPP(hAPP(c_member(U_14008),U_14007),U_14009)) )
      | U_14010 = c_Orderings_Obot__class_Obot(tc_fun(U_14008,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14008),U_14010))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14008),U_14009)) ),
    inference(variable_rename,[status(thm)],[f_3534_1]) ).

fof(f_3534_3,plain,
    ! [U_14011,U_14010,U_14009,U_14008] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14008,tc_HOL_Obool),tc_fun(U_14008,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14008,tc_HOL_Obool),tc_fun(U_14008,tc_HOL_Obool)),U_14009),U_14010)),c_Wellfounded_Omax__ext(U_14008,U_14011)))
      | ( ! [U_14006] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14008,U_14008)),hAPP(hAPP(c_Product__Type_OPair(U_14008,U_14008),sK299(U_14011,U_14010,U_14009,U_14008)),U_14006)),U_14011))
            | ~ hBOOL(hAPP(hAPP(c_member(U_14008),U_14006),U_14010)) )
        & hBOOL(hAPP(hAPP(c_member(U_14008),sK299(U_14011,U_14010,U_14009,U_14008)),U_14009)) )
      | U_14010 = c_Orderings_Obot__class_Obot(tc_fun(U_14008,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14008),U_14010))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14008),U_14009)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK299]),skolemize(U_14007,sK299(U_14011,U_14010,U_14009,U_14008))],[f_3534_2]) ).

fof(f_3534_4,plain,
    ( ! [U_14008,U_14010,U_14011,U_14006,U_14009] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14008,U_14008)),hAPP(hAPP(c_Product__Type_OPair(U_14008,U_14008),sK299(U_14011,U_14010,U_14009,U_14008)),U_14006)),U_14011))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14008),U_14006),U_14010))
        | ~ sP976(U_14008,U_14010,U_14011,U_14006,U_14009) )
    & ! [U_14008,U_14010,U_14011,U_14006,U_14009] :
        ( hBOOL(hAPP(hAPP(c_member(U_14008),sK299(U_14011,U_14010,U_14009,U_14008)),U_14009))
        | ~ sP976(U_14008,U_14010,U_14011,U_14006,U_14009) )
    & ! [U_14008,U_14010,U_14011,U_14006,U_14009] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14008,tc_HOL_Obool),tc_fun(U_14008,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14008,tc_HOL_Obool),tc_fun(U_14008,tc_HOL_Obool)),U_14009),U_14010)),c_Wellfounded_Omax__ext(U_14008,U_14011)))
        | sP976(U_14008,U_14010,U_14011,U_14006,U_14009)
        | U_14010 = c_Orderings_Obot__class_Obot(tc_fun(U_14008,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14008),U_14010))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14008),U_14009)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP976])],[f_3534_3]) ).

cnf(f_3534_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14008,tc_HOL_Obool),tc_fun(U_14008,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14008,tc_HOL_Obool),tc_fun(U_14008,tc_HOL_Obool)),U_14009),U_14010)),c_Wellfounded_Omax__ext(U_14008,U_14011)))
    | sP976(U_14008,U_14010,U_14011,U_14006,U_14009)
    | U_14010 = c_Orderings_Obot__class_Obot(tc_fun(U_14008,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14008),U_14010))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14008),U_14009)) ),
    inference(clausify,[status(thm)],[f_3534_4]) ).

cnf(f_3534_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14008),sK299(U_14011,U_14010,U_14009,U_14008)),U_14009))
    | ~ sP976(U_14008,U_14010,U_14011,U_14006,U_14009) ),
    inference(clausify,[status(thm)],[f_3534_4]) ).

cnf(f_3534_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14008,U_14008)),hAPP(hAPP(c_Product__Type_OPair(U_14008,U_14008),sK299(U_14011,U_14010,U_14009,U_14008)),U_14006)),U_14011))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14008),U_14006),U_14010))
    | ~ sP976(U_14008,U_14010,U_14011,U_14006,U_14009) ),
    inference(clausify,[status(thm)],[f_3534_4]) ).

fof(f_3535_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_3535_2,plain,
    ! [U_14020,U_14019,U_14018,U_14017,U_14016] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14016,U_14017,hAPP(hAPP(c_Set_Oinsert(U_14016),U_14018),U_14019)),U_14020))
        | ! [U_14015,U_14014] :
            ( hBOOL(hAPP(hAPP(c_member(U_14016),U_14015),U_14014))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14016,U_14016,U_14017,U_14015,U_14014),U_14020))
            | hAPP(hAPP(c_Set_Oinsert(U_14016),U_14018),U_14019) != hAPP(hAPP(c_Set_Oinsert(U_14016),U_14015),U_14014) ) )
      & ( ? [U_14013,U_14012] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_14016),U_14013),U_14012))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14016,U_14016,U_14017,U_14013,U_14012),U_14020))
            & hAPP(hAPP(c_Set_Oinsert(U_14016),U_14018),U_14019) = hAPP(hAPP(c_Set_Oinsert(U_14016),U_14013),U_14012) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14016,U_14017,hAPP(hAPP(c_Set_Oinsert(U_14016),U_14018),U_14019)),U_14020)) ) ),
    inference(variable_rename,[status(thm)],[f_3535_1]) ).

fof(f_3535_3,plain,
    ( ! [U_14030,U_14028,U_14026,U_14024,U_14022] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14022,U_14024,hAPP(hAPP(c_Set_Oinsert(U_14022),U_14026),U_14028)),U_14030))
        | ! [U_14015,U_14014] :
            ( hBOOL(hAPP(hAPP(c_member(U_14022),U_14015),U_14014))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14022,U_14022,U_14024,U_14015,U_14014),U_14030))
            | hAPP(hAPP(c_Set_Oinsert(U_14022),U_14026),U_14028) != hAPP(hAPP(c_Set_Oinsert(U_14022),U_14015),U_14014) ) )
    & ! [U_14029,U_14027,U_14025,U_14023,U_14021] :
        ( ? [U_14013,U_14012] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_14021),U_14013),U_14012))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14021,U_14021,U_14023,U_14013,U_14012),U_14029))
            & hAPP(hAPP(c_Set_Oinsert(U_14021),U_14025),U_14027) = hAPP(hAPP(c_Set_Oinsert(U_14021),U_14013),U_14012) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14021,U_14023,hAPP(hAPP(c_Set_Oinsert(U_14021),U_14025),U_14027)),U_14029)) ) ),
    inference(miniscope,[status(thm)],[f_3535_2]) ).

fof(f_3535_4,plain,
    ( ! [U_14030,U_14028,U_14026,U_14024,U_14022] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14022,U_14024,hAPP(hAPP(c_Set_Oinsert(U_14022),U_14026),U_14028)),U_14030))
        | ! [U_14015,U_14014] :
            ( hBOOL(hAPP(hAPP(c_member(U_14022),U_14015),U_14014))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14022,U_14022,U_14024,U_14015,U_14014),U_14030))
            | hAPP(hAPP(c_Set_Oinsert(U_14022),U_14026),U_14028) != hAPP(hAPP(c_Set_Oinsert(U_14022),U_14015),U_14014) ) )
    & ! [U_14029,U_14027,U_14025,U_14023,U_14021] :
        ( ? [U_14012] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_14021),sK300(U_14029,U_14027,U_14025,U_14023,U_14021)),U_14012))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14021,U_14021,U_14023,sK300(U_14029,U_14027,U_14025,U_14023,U_14021),U_14012),U_14029))
            & hAPP(hAPP(c_Set_Oinsert(U_14021),U_14025),U_14027) = hAPP(hAPP(c_Set_Oinsert(U_14021),sK300(U_14029,U_14027,U_14025,U_14023,U_14021)),U_14012) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14021,U_14023,hAPP(hAPP(c_Set_Oinsert(U_14021),U_14025),U_14027)),U_14029)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK300]),skolemize(U_14013,sK300(U_14029,U_14027,U_14025,U_14023,U_14021))],[f_3535_3]) ).

fof(f_3535_5,plain,
    ( ! [U_14030,U_14028,U_14026,U_14024,U_14022] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14022,U_14024,hAPP(hAPP(c_Set_Oinsert(U_14022),U_14026),U_14028)),U_14030))
        | ! [U_14015,U_14014] :
            ( hBOOL(hAPP(hAPP(c_member(U_14022),U_14015),U_14014))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14022,U_14022,U_14024,U_14015,U_14014),U_14030))
            | hAPP(hAPP(c_Set_Oinsert(U_14022),U_14026),U_14028) != hAPP(hAPP(c_Set_Oinsert(U_14022),U_14015),U_14014) ) )
    & ! [U_14029,U_14027,U_14025,U_14023,U_14021] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_14021),sK300(U_14029,U_14027,U_14025,U_14023,U_14021)),sK301(U_14029,U_14027,U_14025,U_14023,U_14021)))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14021,U_14021,U_14023,sK300(U_14029,U_14027,U_14025,U_14023,U_14021),sK301(U_14029,U_14027,U_14025,U_14023,U_14021)),U_14029))
          & hAPP(hAPP(c_Set_Oinsert(U_14021),U_14025),U_14027) = hAPP(hAPP(c_Set_Oinsert(U_14021),sK300(U_14029,U_14027,U_14025,U_14023,U_14021)),sK301(U_14029,U_14027,U_14025,U_14023,U_14021)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14021,U_14023,hAPP(hAPP(c_Set_Oinsert(U_14021),U_14025),U_14027)),U_14029)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK301]),skolemize(U_14012,sK301(U_14029,U_14027,U_14025,U_14023,U_14021))],[f_3535_4]) ).

fof(f_3535_6,plain,
    ( ! [U_14023,U_14021,U_14025,U_14027,U_14029] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_14021),sK300(U_14029,U_14027,U_14025,U_14023,U_14021)),sK301(U_14029,U_14027,U_14025,U_14023,U_14021)))
        | ~ sP977(U_14023,U_14021,U_14025,U_14027,U_14029) )
    & ! [U_14023,U_14021,U_14025,U_14027,U_14029] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14021,U_14021,U_14023,sK300(U_14029,U_14027,U_14025,U_14023,U_14021),sK301(U_14029,U_14027,U_14025,U_14023,U_14021)),U_14029))
        | ~ sP977(U_14023,U_14021,U_14025,U_14027,U_14029) )
    & ! [U_14023,U_14021,U_14025,U_14027,U_14029] :
        ( hAPP(hAPP(c_Set_Oinsert(U_14021),U_14025),U_14027) = hAPP(hAPP(c_Set_Oinsert(U_14021),sK300(U_14029,U_14027,U_14025,U_14023,U_14021)),sK301(U_14029,U_14027,U_14025,U_14023,U_14021))
        | ~ sP977(U_14023,U_14021,U_14025,U_14027,U_14029) )
    & ! [U_14015,U_14014,U_14028,U_14022,U_14024,U_14026,U_14030] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14022,U_14024,hAPP(hAPP(c_Set_Oinsert(U_14022),U_14026),U_14028)),U_14030))
        | hBOOL(hAPP(hAPP(c_member(U_14022),U_14015),U_14014))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14022,U_14022,U_14024,U_14015,U_14014),U_14030))
        | hAPP(hAPP(c_Set_Oinsert(U_14022),U_14026),U_14028) != hAPP(hAPP(c_Set_Oinsert(U_14022),U_14015),U_14014) )
    & ! [U_14023,U_14021,U_14025,U_14027,U_14029] :
        ( sP977(U_14023,U_14021,U_14025,U_14027,U_14029)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14021,U_14023,hAPP(hAPP(c_Set_Oinsert(U_14021),U_14025),U_14027)),U_14029)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP977])],[f_3535_5]) ).

cnf(f_3535_7,plain,
    ( sP977(U_14023,U_14021,U_14025,U_14027,U_14029)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14021,U_14023,hAPP(hAPP(c_Set_Oinsert(U_14021),U_14025),U_14027)),U_14029)) ),
    inference(clausify,[status(thm)],[f_3535_6]) ).

cnf(f_3535_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14022,U_14024,hAPP(hAPP(c_Set_Oinsert(U_14022),U_14026),U_14028)),U_14030))
    | hBOOL(hAPP(hAPP(c_member(U_14022),U_14015),U_14014))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14022,U_14022,U_14024,U_14015,U_14014),U_14030))
    | hAPP(hAPP(c_Set_Oinsert(U_14022),U_14026),U_14028) != hAPP(hAPP(c_Set_Oinsert(U_14022),U_14015),U_14014) ),
    inference(clausify,[status(thm)],[f_3535_6]) ).

cnf(f_3535_9,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_14021),U_14025),U_14027) = hAPP(hAPP(c_Set_Oinsert(U_14021),sK300(U_14029,U_14027,U_14025,U_14023,U_14021)),sK301(U_14029,U_14027,U_14025,U_14023,U_14021))
    | ~ sP977(U_14023,U_14021,U_14025,U_14027,U_14029) ),
    inference(clausify,[status(thm)],[f_3535_6]) ).

cnf(f_3535_10,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14021,U_14021,U_14023,sK300(U_14029,U_14027,U_14025,U_14023,U_14021),sK301(U_14029,U_14027,U_14025,U_14023,U_14021)),U_14029))
    | ~ sP977(U_14023,U_14021,U_14025,U_14027,U_14029) ),
    inference(clausify,[status(thm)],[f_3535_6]) ).

cnf(f_3535_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14021),sK300(U_14029,U_14027,U_14025,U_14023,U_14021)),sK301(U_14029,U_14027,U_14025,U_14023,U_14021)))
    | ~ sP977(U_14023,U_14021,U_14025,U_14027,U_14029) ),
    inference(clausify,[status(thm)],[f_3535_6]) ).

fof(f_3536_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_3536_2,plain,
    ! [U_14037,U_14036,U_14035,U_14034,U_14033] :
      ( ? [U_14032,U_14031] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_14033),U_14032),U_14031))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14033,U_14033,U_14034,U_14032,U_14031),U_14037))
          & hAPP(hAPP(c_Set_Oinsert(U_14033),U_14035),U_14036) = hAPP(hAPP(c_Set_Oinsert(U_14033),U_14032),U_14031) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14033,U_14034,hAPP(hAPP(c_Set_Oinsert(U_14033),U_14035),U_14036)),U_14037)) ),
    inference(variable_rename,[status(thm)],[f_3536_1]) ).

fof(f_3536_3,plain,
    ! [U_14037,U_14036,U_14035,U_14034,U_14033] :
      ( ? [U_14031] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_14033),sK302(U_14037,U_14036,U_14035,U_14034,U_14033)),U_14031))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14033,U_14033,U_14034,sK302(U_14037,U_14036,U_14035,U_14034,U_14033),U_14031),U_14037))
          & hAPP(hAPP(c_Set_Oinsert(U_14033),U_14035),U_14036) = hAPP(hAPP(c_Set_Oinsert(U_14033),sK302(U_14037,U_14036,U_14035,U_14034,U_14033)),U_14031) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14033,U_14034,hAPP(hAPP(c_Set_Oinsert(U_14033),U_14035),U_14036)),U_14037)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK302]),skolemize(U_14032,sK302(U_14037,U_14036,U_14035,U_14034,U_14033))],[f_3536_2]) ).

fof(f_3536_4,plain,
    ! [U_14037,U_14036,U_14035,U_14034,U_14033] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_14033),sK302(U_14037,U_14036,U_14035,U_14034,U_14033)),sK303(U_14037,U_14036,U_14035,U_14034,U_14033)))
        & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14033,U_14033,U_14034,sK302(U_14037,U_14036,U_14035,U_14034,U_14033),sK303(U_14037,U_14036,U_14035,U_14034,U_14033)),U_14037))
        & hAPP(hAPP(c_Set_Oinsert(U_14033),U_14035),U_14036) = hAPP(hAPP(c_Set_Oinsert(U_14033),sK302(U_14037,U_14036,U_14035,U_14034,U_14033)),sK303(U_14037,U_14036,U_14035,U_14034,U_14033)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14033,U_14034,hAPP(hAPP(c_Set_Oinsert(U_14033),U_14035),U_14036)),U_14037)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK303]),skolemize(U_14031,sK303(U_14037,U_14036,U_14035,U_14034,U_14033))],[f_3536_3]) ).

fof(f_3536_5,plain,
    ( ! [U_14034,U_14033,U_14035,U_14036,U_14037] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_14033),sK302(U_14037,U_14036,U_14035,U_14034,U_14033)),sK303(U_14037,U_14036,U_14035,U_14034,U_14033)))
        | ~ sP978(U_14034,U_14033,U_14035,U_14036,U_14037) )
    & ! [U_14034,U_14033,U_14035,U_14036,U_14037] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14033,U_14033,U_14034,sK302(U_14037,U_14036,U_14035,U_14034,U_14033),sK303(U_14037,U_14036,U_14035,U_14034,U_14033)),U_14037))
        | ~ sP978(U_14034,U_14033,U_14035,U_14036,U_14037) )
    & ! [U_14034,U_14033,U_14035,U_14036,U_14037] :
        ( hAPP(hAPP(c_Set_Oinsert(U_14033),U_14035),U_14036) = hAPP(hAPP(c_Set_Oinsert(U_14033),sK302(U_14037,U_14036,U_14035,U_14034,U_14033)),sK303(U_14037,U_14036,U_14035,U_14034,U_14033))
        | ~ sP978(U_14034,U_14033,U_14035,U_14036,U_14037) )
    & ! [U_14034,U_14033,U_14035,U_14036,U_14037] :
        ( sP978(U_14034,U_14033,U_14035,U_14036,U_14037)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14033,U_14034,hAPP(hAPP(c_Set_Oinsert(U_14033),U_14035),U_14036)),U_14037)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP978])],[f_3536_4]) ).

cnf(f_3536_6,plain,
    ( sP978(U_14034,U_14033,U_14035,U_14036,U_14037)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14033,U_14034,hAPP(hAPP(c_Set_Oinsert(U_14033),U_14035),U_14036)),U_14037)) ),
    inference(clausify,[status(thm)],[f_3536_5]) ).

cnf(f_3536_7,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_14033),U_14035),U_14036) = hAPP(hAPP(c_Set_Oinsert(U_14033),sK302(U_14037,U_14036,U_14035,U_14034,U_14033)),sK303(U_14037,U_14036,U_14035,U_14034,U_14033))
    | ~ sP978(U_14034,U_14033,U_14035,U_14036,U_14037) ),
    inference(clausify,[status(thm)],[f_3536_5]) ).

cnf(f_3536_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14033,U_14033,U_14034,sK302(U_14037,U_14036,U_14035,U_14034,U_14033),sK303(U_14037,U_14036,U_14035,U_14034,U_14033)),U_14037))
    | ~ sP978(U_14034,U_14033,U_14035,U_14036,U_14037) ),
    inference(clausify,[status(thm)],[f_3536_5]) ).

cnf(f_3536_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14033),sK302(U_14037,U_14036,U_14035,U_14034,U_14033)),sK303(U_14037,U_14036,U_14035,U_14034,U_14033)))
    | ~ sP978(U_14034,U_14033,U_14035,U_14036,U_14037) ),
    inference(clausify,[status(thm)],[f_3536_5]) ).

fof(f_3537_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_3537_2,plain,
    ! [U_14043,U_14042,U_14041,U_14040,U_14039,U_14038] : hAPP(c_Set_Oimage(U_14038,tc_prod(U_14039,U_14040),hAPP(hAPP(c_COMBS(U_14038,U_14040,tc_prod(U_14039,U_14040)),hAPP(hAPP(c_COMBB(U_14039,tc_fun(U_14040,tc_prod(U_14039,U_14040)),U_14038),c_Product__Type_OPair(U_14039,U_14040)),U_14041)),U_14042)),U_14043) = hAPP(hAPP(c_Product__Type_OSigma(U_14039,U_14040),hAPP(c_Set_Oimage(U_14038,U_14039,U_14041),U_14043)),hAPP(hAPP(c_COMBB(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool),U_14039),c_Set_Oimage(U_14038,U_14040,U_14042)),hAPP(hAPP(c_COMBC(U_14039,tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14038,tc_HOL_Obool),tc_fun(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool)),U_14039),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14038,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14039,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool),U_14039),c_Set_Ovimage(U_14038,U_14039,U_14041)),hAPP(hAPP(c_COMBC(U_14039,tc_fun(U_14039,tc_HOL_Obool),tc_fun(U_14039,tc_HOL_Obool)),c_Set_Oinsert(U_14039)),c_Orderings_Obot__class_Obot(tc_fun(U_14039,tc_HOL_Obool)))))),U_14043))),
    inference(variable_rename,[status(thm)],[f_3537_1]) ).

fof(f_3537_3,plain,
    ! [U_14038,U_14039,U_14040,U_14041,U_14042,U_14043] : hAPP(c_Set_Oimage(U_14038,tc_prod(U_14039,U_14040),hAPP(hAPP(c_COMBS(U_14038,U_14040,tc_prod(U_14039,U_14040)),hAPP(hAPP(c_COMBB(U_14039,tc_fun(U_14040,tc_prod(U_14039,U_14040)),U_14038),c_Product__Type_OPair(U_14039,U_14040)),U_14041)),U_14042)),U_14043) = hAPP(hAPP(c_Product__Type_OSigma(U_14039,U_14040),hAPP(c_Set_Oimage(U_14038,U_14039,U_14041),U_14043)),hAPP(hAPP(c_COMBB(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool),U_14039),c_Set_Oimage(U_14038,U_14040,U_14042)),hAPP(hAPP(c_COMBC(U_14039,tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14038,tc_HOL_Obool),tc_fun(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool)),U_14039),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14038,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14039,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool),U_14039),c_Set_Ovimage(U_14038,U_14039,U_14041)),hAPP(hAPP(c_COMBC(U_14039,tc_fun(U_14039,tc_HOL_Obool),tc_fun(U_14039,tc_HOL_Obool)),c_Set_Oinsert(U_14039)),c_Orderings_Obot__class_Obot(tc_fun(U_14039,tc_HOL_Obool)))))),U_14043))),
    inference(definitional_conversion,[status(esa)],[f_3537_2]) ).

cnf(f_3537_4,plain,
    hAPP(c_Set_Oimage(U_14038,tc_prod(U_14039,U_14040),hAPP(hAPP(c_COMBS(U_14038,U_14040,tc_prod(U_14039,U_14040)),hAPP(hAPP(c_COMBB(U_14039,tc_fun(U_14040,tc_prod(U_14039,U_14040)),U_14038),c_Product__Type_OPair(U_14039,U_14040)),U_14041)),U_14042)),U_14043) = hAPP(hAPP(c_Product__Type_OSigma(U_14039,U_14040),hAPP(c_Set_Oimage(U_14038,U_14039,U_14041),U_14043)),hAPP(hAPP(c_COMBB(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool),U_14039),c_Set_Oimage(U_14038,U_14040,U_14042)),hAPP(hAPP(c_COMBC(U_14039,tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14038,tc_HOL_Obool),tc_fun(tc_fun(U_14038,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool)),U_14039),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14038,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14039,tc_HOL_Obool),tc_fun(U_14038,tc_HOL_Obool),U_14039),c_Set_Ovimage(U_14038,U_14039,U_14041)),hAPP(hAPP(c_COMBC(U_14039,tc_fun(U_14039,tc_HOL_Obool),tc_fun(U_14039,tc_HOL_Obool)),c_Set_Oinsert(U_14039)),c_Orderings_Obot__class_Obot(tc_fun(U_14039,tc_HOL_Obool)))))),U_14043))),
    inference(clausify,[status(thm)],[f_3537_3]) ).

fof(f_3538_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_3538_2,plain,
    ! [U_14046,U_14045,U_14044] :
      ( hAPP(c_Finite__Set_Ofold1(U_14044,c_Groups_Otimes__class_Otimes(U_14044)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14044,tc_HOL_Obool)),U_14045),U_14046)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14044),hAPP(c_Finite__Set_Ofold1(U_14044,c_Groups_Otimes__class_Otimes(U_14044)),U_14045)),hAPP(c_Finite__Set_Ofold1(U_14044,c_Groups_Otimes__class_Otimes(U_14044)),U_14046))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14044,tc_HOL_Obool)),U_14045),U_14046) != c_Orderings_Obot__class_Obot(tc_fun(U_14044,tc_HOL_Obool))
      | U_14046 = c_Orderings_Obot__class_Obot(tc_fun(U_14044,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14044),U_14046))
      | U_14045 = c_Orderings_Obot__class_Obot(tc_fun(U_14044,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14044),U_14045))
      | ~ class_Groups_Oab__semigroup__mult(U_14044) ),
    inference(variable_rename,[status(thm)],[f_3538_1]) ).

fof(f_3538_3,plain,
    ! [U_14044,U_14045,U_14046] :
      ( hAPP(c_Finite__Set_Ofold1(U_14044,c_Groups_Otimes__class_Otimes(U_14044)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14044,tc_HOL_Obool)),U_14045),U_14046)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14044),hAPP(c_Finite__Set_Ofold1(U_14044,c_Groups_Otimes__class_Otimes(U_14044)),U_14045)),hAPP(c_Finite__Set_Ofold1(U_14044,c_Groups_Otimes__class_Otimes(U_14044)),U_14046))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14044,tc_HOL_Obool)),U_14045),U_14046) != c_Orderings_Obot__class_Obot(tc_fun(U_14044,tc_HOL_Obool))
      | U_14046 = c_Orderings_Obot__class_Obot(tc_fun(U_14044,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14044),U_14046))
      | U_14045 = c_Orderings_Obot__class_Obot(tc_fun(U_14044,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14044),U_14045))
      | ~ class_Groups_Oab__semigroup__mult(U_14044) ),
    inference(definitional_conversion,[status(esa)],[f_3538_2]) ).

cnf(f_3538_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_14044,c_Groups_Otimes__class_Otimes(U_14044)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14044,tc_HOL_Obool)),U_14045),U_14046)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14044),hAPP(c_Finite__Set_Ofold1(U_14044,c_Groups_Otimes__class_Otimes(U_14044)),U_14045)),hAPP(c_Finite__Set_Ofold1(U_14044,c_Groups_Otimes__class_Otimes(U_14044)),U_14046))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14044,tc_HOL_Obool)),U_14045),U_14046) != c_Orderings_Obot__class_Obot(tc_fun(U_14044,tc_HOL_Obool))
    | U_14046 = c_Orderings_Obot__class_Obot(tc_fun(U_14044,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14044),U_14046))
    | U_14045 = c_Orderings_Obot__class_Obot(tc_fun(U_14044,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14044),U_14045))
    | ~ class_Groups_Oab__semigroup__mult(U_14044) ),
    inference(clausify,[status(thm)],[f_3538_3]) ).

fof(f_3539_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_3539_2,plain,
    ! [U_14052,U_14051,U_14050,U_14049,U_14048,U_14047] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14047,U_14050)),hAPP(hAPP(c_Product__Type_OPair(U_14047,U_14050),U_14048),U_14051)),hAPP(hAPP(c_Product__Type_OSigma(U_14047,U_14050),U_14049),U_14052)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14050),U_14051),hAPP(U_14052,U_14048)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14047),U_14048),U_14049)) ),
    inference(variable_rename,[status(thm)],[f_3539_1]) ).

fof(f_3539_3,plain,
    ! [U_14047,U_14048,U_14049,U_14050,U_14051,U_14052] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14047,U_14050)),hAPP(hAPP(c_Product__Type_OPair(U_14047,U_14050),U_14048),U_14051)),hAPP(hAPP(c_Product__Type_OSigma(U_14047,U_14050),U_14049),U_14052)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14050),U_14051),hAPP(U_14052,U_14048)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14047),U_14048),U_14049)) ),
    inference(definitional_conversion,[status(esa)],[f_3539_2]) ).

cnf(f_3539_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14047,U_14050)),hAPP(hAPP(c_Product__Type_OPair(U_14047,U_14050),U_14048),U_14051)),hAPP(hAPP(c_Product__Type_OSigma(U_14047,U_14050),U_14049),U_14052)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14050),U_14051),hAPP(U_14052,U_14048)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14047),U_14048),U_14049)) ),
    inference(clausify,[status(thm)],[f_3539_3]) ).

fof(f_3540_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_3540_2,plain,
    ! [U_14058,U_14057,U_14056,U_14055,U_14054,U_14053] :
      ( ( ( hAPP(hAPP(c_Product__Type_OSigma(U_14056,U_14053),U_14057),hAPP(c_COMBK(tc_fun(U_14053,tc_HOL_Obool),U_14056),U_14055)) = hAPP(hAPP(c_Product__Type_OSigma(U_14056,U_14053),U_14058),hAPP(c_COMBK(tc_fun(U_14053,tc_HOL_Obool),U_14056),U_14055))
          | U_14057 != U_14058 )
        & ( U_14057 = U_14058
          | hAPP(hAPP(c_Product__Type_OSigma(U_14056,U_14053),U_14057),hAPP(c_COMBK(tc_fun(U_14053,tc_HOL_Obool),U_14056),U_14055)) != hAPP(hAPP(c_Product__Type_OSigma(U_14056,U_14053),U_14058),hAPP(c_COMBK(tc_fun(U_14053,tc_HOL_Obool),U_14056),U_14055)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14053),U_14054),U_14055)) ),
    inference(variable_rename,[status(thm)],[f_3540_1]) ).

fof(f_3540_3,plain,
    ( ! [U_14053,U_14055,U_14056,U_14057,U_14058] :
        ( hAPP(hAPP(c_Product__Type_OSigma(U_14056,U_14053),U_14057),hAPP(c_COMBK(tc_fun(U_14053,tc_HOL_Obool),U_14056),U_14055)) = hAPP(hAPP(c_Product__Type_OSigma(U_14056,U_14053),U_14058),hAPP(c_COMBK(tc_fun(U_14053,tc_HOL_Obool),U_14056),U_14055))
        | U_14057 != U_14058
        | ~ sP979(U_14053,U_14055,U_14056,U_14057,U_14058) )
    & ! [U_14053,U_14055,U_14056,U_14057,U_14058] :
        ( U_14057 = U_14058
        | hAPP(hAPP(c_Product__Type_OSigma(U_14056,U_14053),U_14057),hAPP(c_COMBK(tc_fun(U_14053,tc_HOL_Obool),U_14056),U_14055)) != hAPP(hAPP(c_Product__Type_OSigma(U_14056,U_14053),U_14058),hAPP(c_COMBK(tc_fun(U_14053,tc_HOL_Obool),U_14056),U_14055))
        | ~ sP979(U_14053,U_14055,U_14056,U_14057,U_14058) )
    & ! [U_14053,U_14054,U_14055,U_14056,U_14057,U_14058] :
        ( sP979(U_14053,U_14055,U_14056,U_14057,U_14058)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14053),U_14054),U_14055)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP979])],[f_3540_2]) ).

cnf(f_3540_4,plain,
    ( sP979(U_14053,U_14055,U_14056,U_14057,U_14058)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14053),U_14054),U_14055)) ),
    inference(clausify,[status(thm)],[f_3540_3]) ).

cnf(f_3540_5,plain,
    ( U_14057 = U_14058
    | hAPP(hAPP(c_Product__Type_OSigma(U_14056,U_14053),U_14057),hAPP(c_COMBK(tc_fun(U_14053,tc_HOL_Obool),U_14056),U_14055)) != hAPP(hAPP(c_Product__Type_OSigma(U_14056,U_14053),U_14058),hAPP(c_COMBK(tc_fun(U_14053,tc_HOL_Obool),U_14056),U_14055))
    | ~ sP979(U_14053,U_14055,U_14056,U_14057,U_14058) ),
    inference(clausify,[status(thm)],[f_3540_3]) ).

cnf(f_3540_6,plain,
    ( hAPP(hAPP(c_Product__Type_OSigma(U_14056,U_14053),U_14057),hAPP(c_COMBK(tc_fun(U_14053,tc_HOL_Obool),U_14056),U_14055)) = hAPP(hAPP(c_Product__Type_OSigma(U_14056,U_14053),U_14058),hAPP(c_COMBK(tc_fun(U_14053,tc_HOL_Obool),U_14056),U_14055))
    | U_14057 != U_14058
    | ~ sP979(U_14053,U_14055,U_14056,U_14057,U_14058) ),
    inference(clausify,[status(thm)],[f_3540_3]) ).

fof(f_3541_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_3541_2,plain,
    ! [U_14061,U_14060,U_14059] : hAPP(hAPP(c_Product__Type_OSigma(U_14059,U_14060),c_Orderings_Obot__class_Obot(tc_fun(U_14059,tc_HOL_Obool))),U_14061) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14059,U_14060),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3541_1]) ).

fof(f_3541_3,plain,
    ! [U_14060,U_14061,U_14059] : hAPP(hAPP(c_Product__Type_OSigma(U_14059,U_14060),c_Orderings_Obot__class_Obot(tc_fun(U_14059,tc_HOL_Obool))),U_14061) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14059,U_14060),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3541_2]) ).

cnf(f_3541_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14059,U_14060),c_Orderings_Obot__class_Obot(tc_fun(U_14059,tc_HOL_Obool))),U_14061) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14059,U_14060),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3541_3]) ).

fof(f_3542_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_3542_2,plain,
    ! [U_14066,U_14065,U_14064,U_14063,U_14062] : hAPP(hAPP(c_Product__Type_OSigma(U_14062,U_14063),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14062,tc_HOL_Obool)),U_14064),U_14065)),U_14066) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14062,U_14063),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14062,U_14063),U_14064),U_14066)),hAPP(hAPP(c_Product__Type_OSigma(U_14062,U_14063),U_14065),U_14066)),
    inference(variable_rename,[status(thm)],[f_3542_1]) ).

fof(f_3542_3,plain,
    ! [U_14062,U_14063,U_14064,U_14065,U_14066] : hAPP(hAPP(c_Product__Type_OSigma(U_14062,U_14063),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14062,tc_HOL_Obool)),U_14064),U_14065)),U_14066) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14062,U_14063),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14062,U_14063),U_14064),U_14066)),hAPP(hAPP(c_Product__Type_OSigma(U_14062,U_14063),U_14065),U_14066)),
    inference(definitional_conversion,[status(esa)],[f_3542_2]) ).

cnf(f_3542_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14062,U_14063),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14062,tc_HOL_Obool)),U_14064),U_14065)),U_14066) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14062,U_14063),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14062,U_14063),U_14064),U_14066)),hAPP(hAPP(c_Product__Type_OSigma(U_14062,U_14063),U_14065),U_14066)),
    inference(clausify,[status(thm)],[f_3542_3]) ).

fof(f_3543_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_3543_2,plain,
    ! [U_14071,U_14070,U_14069,U_14068,U_14067] : hAPP(hAPP(c_Product__Type_OSigma(U_14067,U_14068),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14067,tc_HOL_Obool)),U_14069),U_14070)),hAPP(c_COMBK(tc_fun(U_14068,tc_HOL_Obool),U_14067),U_14071)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14067,U_14068),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14067,U_14068),U_14069),hAPP(c_COMBK(tc_fun(U_14068,tc_HOL_Obool),U_14067),U_14071))),hAPP(hAPP(c_Product__Type_OSigma(U_14067,U_14068),U_14070),hAPP(c_COMBK(tc_fun(U_14068,tc_HOL_Obool),U_14067),U_14071))),
    inference(variable_rename,[status(thm)],[f_3543_1]) ).

fof(f_3543_3,plain,
    ! [U_14067,U_14068,U_14069,U_14070,U_14071] : hAPP(hAPP(c_Product__Type_OSigma(U_14067,U_14068),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14067,tc_HOL_Obool)),U_14069),U_14070)),hAPP(c_COMBK(tc_fun(U_14068,tc_HOL_Obool),U_14067),U_14071)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14067,U_14068),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14067,U_14068),U_14069),hAPP(c_COMBK(tc_fun(U_14068,tc_HOL_Obool),U_14067),U_14071))),hAPP(hAPP(c_Product__Type_OSigma(U_14067,U_14068),U_14070),hAPP(c_COMBK(tc_fun(U_14068,tc_HOL_Obool),U_14067),U_14071))),
    inference(definitional_conversion,[status(esa)],[f_3543_2]) ).

cnf(f_3543_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14067,U_14068),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14067,tc_HOL_Obool)),U_14069),U_14070)),hAPP(c_COMBK(tc_fun(U_14068,tc_HOL_Obool),U_14067),U_14071)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14067,U_14068),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14067,U_14068),U_14069),hAPP(c_COMBK(tc_fun(U_14068,tc_HOL_Obool),U_14067),U_14071))),hAPP(hAPP(c_Product__Type_OSigma(U_14067,U_14068),U_14070),hAPP(c_COMBK(tc_fun(U_14068,tc_HOL_Obool),U_14067),U_14071))),
    inference(clausify,[status(thm)],[f_3543_3]) ).

fof(f_3544_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_3544_2,plain,
    ! [U_14076,U_14075,U_14074,U_14073,U_14072] : hAPP(hAPP(c_Product__Type_OSigma(U_14072,U_14073),U_14074),hAPP(hAPP(c_COMBS(U_14072,tc_fun(U_14073,tc_HOL_Obool),tc_fun(U_14073,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14073,tc_HOL_Obool),tc_fun(tc_fun(U_14073,tc_HOL_Obool),tc_fun(U_14073,tc_HOL_Obool)),U_14072),c_Groups_Ominus__class_Ominus(tc_fun(U_14073,tc_HOL_Obool))),U_14075)),U_14076)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14072,U_14073),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14072,U_14073),U_14074),U_14075)),hAPP(hAPP(c_Product__Type_OSigma(U_14072,U_14073),U_14074),U_14076)),
    inference(variable_rename,[status(thm)],[f_3544_1]) ).

fof(f_3544_3,plain,
    ! [U_14072,U_14073,U_14074,U_14075,U_14076] : hAPP(hAPP(c_Product__Type_OSigma(U_14072,U_14073),U_14074),hAPP(hAPP(c_COMBS(U_14072,tc_fun(U_14073,tc_HOL_Obool),tc_fun(U_14073,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14073,tc_HOL_Obool),tc_fun(tc_fun(U_14073,tc_HOL_Obool),tc_fun(U_14073,tc_HOL_Obool)),U_14072),c_Groups_Ominus__class_Ominus(tc_fun(U_14073,tc_HOL_Obool))),U_14075)),U_14076)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14072,U_14073),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14072,U_14073),U_14074),U_14075)),hAPP(hAPP(c_Product__Type_OSigma(U_14072,U_14073),U_14074),U_14076)),
    inference(definitional_conversion,[status(esa)],[f_3544_2]) ).

cnf(f_3544_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14072,U_14073),U_14074),hAPP(hAPP(c_COMBS(U_14072,tc_fun(U_14073,tc_HOL_Obool),tc_fun(U_14073,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14073,tc_HOL_Obool),tc_fun(tc_fun(U_14073,tc_HOL_Obool),tc_fun(U_14073,tc_HOL_Obool)),U_14072),c_Groups_Ominus__class_Ominus(tc_fun(U_14073,tc_HOL_Obool))),U_14075)),U_14076)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14072,U_14073),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14072,U_14073),U_14074),U_14075)),hAPP(hAPP(c_Product__Type_OSigma(U_14072,U_14073),U_14074),U_14076)),
    inference(clausify,[status(thm)],[f_3544_3]) ).

fof(f_3545_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_3545_2,plain,
    ! [U_14080,U_14079,U_14078,U_14077] : hAPP(c_Finite__Set_Ocard(tc_prod(U_14077,U_14078)),hAPP(hAPP(c_Product__Type_OSigma(U_14077,U_14078),U_14079),hAPP(c_COMBK(tc_fun(U_14078,tc_HOL_Obool),U_14077),U_14080))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_14077),U_14079)),hAPP(c_Finite__Set_Ocard(U_14078),U_14080)),
    inference(variable_rename,[status(thm)],[f_3545_1]) ).

fof(f_3545_3,plain,
    ! [U_14077,U_14078,U_14079,U_14080] : hAPP(c_Finite__Set_Ocard(tc_prod(U_14077,U_14078)),hAPP(hAPP(c_Product__Type_OSigma(U_14077,U_14078),U_14079),hAPP(c_COMBK(tc_fun(U_14078,tc_HOL_Obool),U_14077),U_14080))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_14077),U_14079)),hAPP(c_Finite__Set_Ocard(U_14078),U_14080)),
    inference(definitional_conversion,[status(esa)],[f_3545_2]) ).

cnf(f_3545_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_prod(U_14077,U_14078)),hAPP(hAPP(c_Product__Type_OSigma(U_14077,U_14078),U_14079),hAPP(c_COMBK(tc_fun(U_14078,tc_HOL_Obool),U_14077),U_14080))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_14077),U_14079)),hAPP(c_Finite__Set_Ocard(U_14078),U_14080)),
    inference(clausify,[status(thm)],[f_3545_3]) ).

fof(f_3546_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_3546_2,plain,
    ! [U_14086,U_14085,U_14084,U_14083,U_14082,U_14081] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14082,U_14081),hAPP(hAPP(c_COMBC(U_14082,tc_fun(U_14083,tc_HOL_Obool),U_14081),hAPP(hAPP(c_COMBB(tc_fun(U_14083,U_14081),tc_fun(tc_fun(U_14083,tc_HOL_Obool),U_14081),U_14082),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14083,U_14081)),U_14084)),U_14085)),U_14086) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_14082,U_14083),U_14081),hAPP(c_Product__Type_Oprod_Oprod__case(U_14082,U_14083,U_14081),U_14084)),hAPP(hAPP(c_Product__Type_OSigma(U_14082,U_14083),U_14086),hAPP(c_COMBK(tc_fun(U_14083,tc_HOL_Obool),U_14082),U_14085)))
      | ~ class_Groups_Ocomm__monoid__add(U_14081) ),
    inference(variable_rename,[status(thm)],[f_3546_1]) ).

fof(f_3546_3,plain,
    ! [U_14081,U_14082,U_14083,U_14084,U_14085,U_14086] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14082,U_14081),hAPP(hAPP(c_COMBC(U_14082,tc_fun(U_14083,tc_HOL_Obool),U_14081),hAPP(hAPP(c_COMBB(tc_fun(U_14083,U_14081),tc_fun(tc_fun(U_14083,tc_HOL_Obool),U_14081),U_14082),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14083,U_14081)),U_14084)),U_14085)),U_14086) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_14082,U_14083),U_14081),hAPP(c_Product__Type_Oprod_Oprod__case(U_14082,U_14083,U_14081),U_14084)),hAPP(hAPP(c_Product__Type_OSigma(U_14082,U_14083),U_14086),hAPP(c_COMBK(tc_fun(U_14083,tc_HOL_Obool),U_14082),U_14085)))
      | ~ class_Groups_Ocomm__monoid__add(U_14081) ),
    inference(definitional_conversion,[status(esa)],[f_3546_2]) ).

cnf(f_3546_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14082,U_14081),hAPP(hAPP(c_COMBC(U_14082,tc_fun(U_14083,tc_HOL_Obool),U_14081),hAPP(hAPP(c_COMBB(tc_fun(U_14083,U_14081),tc_fun(tc_fun(U_14083,tc_HOL_Obool),U_14081),U_14082),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14083,U_14081)),U_14084)),U_14085)),U_14086) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_14082,U_14083),U_14081),hAPP(c_Product__Type_Oprod_Oprod__case(U_14082,U_14083,U_14081),U_14084)),hAPP(hAPP(c_Product__Type_OSigma(U_14082,U_14083),U_14086),hAPP(c_COMBK(tc_fun(U_14083,tc_HOL_Obool),U_14082),U_14085)))
    | ~ class_Groups_Ocomm__monoid__add(U_14081) ),
    inference(clausify,[status(thm)],[f_3546_3]) ).

fof(f_3547_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_3547_2,plain,
    ! [U_14089,U_14088,U_14087] : hAPP(hAPP(c_Product__Type_OSigma(U_14087,U_14088),U_14089),hAPP(c_COMBK(tc_fun(U_14088,tc_HOL_Obool),U_14087),c_Orderings_Obot__class_Obot(tc_fun(U_14088,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3547_1]) ).

fof(f_3547_3,plain,
    ! [U_14087,U_14088,U_14089] : hAPP(hAPP(c_Product__Type_OSigma(U_14087,U_14088),U_14089),hAPP(c_COMBK(tc_fun(U_14088,tc_HOL_Obool),U_14087),c_Orderings_Obot__class_Obot(tc_fun(U_14088,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3547_2]) ).

cnf(f_3547_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14087,U_14088),U_14089),hAPP(c_COMBK(tc_fun(U_14088,tc_HOL_Obool),U_14087),c_Orderings_Obot__class_Obot(tc_fun(U_14088,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3547_3]) ).

fof(f_3548_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_3548_2,plain,
    ! [U_14093,U_14092,U_14091,U_14090] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(U_14090,U_14091),U_14092),hAPP(c_COMBK(tc_fun(U_14091,tc_HOL_Obool),U_14090),U_14093)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14090,U_14091),tc_HOL_Obool))
        | ( U_14093 != c_Orderings_Obot__class_Obot(tc_fun(U_14091,tc_HOL_Obool))
          & U_14092 != c_Orderings_Obot__class_Obot(tc_fun(U_14090,tc_HOL_Obool)) ) )
      & ( U_14093 = c_Orderings_Obot__class_Obot(tc_fun(U_14091,tc_HOL_Obool))
        | U_14092 = c_Orderings_Obot__class_Obot(tc_fun(U_14090,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(U_14090,U_14091),U_14092),hAPP(c_COMBK(tc_fun(U_14091,tc_HOL_Obool),U_14090),U_14093)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14090,U_14091),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3548_1]) ).

fof(f_3548_3,plain,
    ( ! [U_14101,U_14099,U_14097,U_14095] :
        ( hAPP(hAPP(c_Product__Type_OSigma(U_14095,U_14097),U_14099),hAPP(c_COMBK(tc_fun(U_14097,tc_HOL_Obool),U_14095),U_14101)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool))
        | ( U_14101 != c_Orderings_Obot__class_Obot(tc_fun(U_14097,tc_HOL_Obool))
          & U_14099 != c_Orderings_Obot__class_Obot(tc_fun(U_14095,tc_HOL_Obool)) ) )
    & ! [U_14100,U_14098,U_14096,U_14094] :
        ( U_14100 = c_Orderings_Obot__class_Obot(tc_fun(U_14096,tc_HOL_Obool))
        | U_14098 = c_Orderings_Obot__class_Obot(tc_fun(U_14094,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(U_14094,U_14096),U_14098),hAPP(c_COMBK(tc_fun(U_14096,tc_HOL_Obool),U_14094),U_14100)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3548_2]) ).

fof(f_3548_4,plain,
    ( ! [U_14095,U_14101,U_14099,U_14097] :
        ( U_14101 != c_Orderings_Obot__class_Obot(tc_fun(U_14097,tc_HOL_Obool))
        | ~ sP980(U_14095,U_14101,U_14099,U_14097) )
    & ! [U_14095,U_14101,U_14099,U_14097] :
        ( U_14099 != c_Orderings_Obot__class_Obot(tc_fun(U_14095,tc_HOL_Obool))
        | ~ sP980(U_14095,U_14101,U_14099,U_14097) )
    & ! [U_14095,U_14101,U_14099,U_14097] :
        ( hAPP(hAPP(c_Product__Type_OSigma(U_14095,U_14097),U_14099),hAPP(c_COMBK(tc_fun(U_14097,tc_HOL_Obool),U_14095),U_14101)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool))
        | sP980(U_14095,U_14101,U_14099,U_14097) )
    & ! [U_14096,U_14098,U_14094,U_14100] :
        ( U_14100 = c_Orderings_Obot__class_Obot(tc_fun(U_14096,tc_HOL_Obool))
        | U_14098 = c_Orderings_Obot__class_Obot(tc_fun(U_14094,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(U_14094,U_14096),U_14098),hAPP(c_COMBK(tc_fun(U_14096,tc_HOL_Obool),U_14094),U_14100)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP980])],[f_3548_3]) ).

cnf(f_3548_5,plain,
    ( U_14100 = c_Orderings_Obot__class_Obot(tc_fun(U_14096,tc_HOL_Obool))
    | U_14098 = c_Orderings_Obot__class_Obot(tc_fun(U_14094,tc_HOL_Obool))
    | hAPP(hAPP(c_Product__Type_OSigma(U_14094,U_14096),U_14098),hAPP(c_COMBK(tc_fun(U_14096,tc_HOL_Obool),U_14094),U_14100)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3548_4]) ).

cnf(f_3548_6,plain,
    ( hAPP(hAPP(c_Product__Type_OSigma(U_14095,U_14097),U_14099),hAPP(c_COMBK(tc_fun(U_14097,tc_HOL_Obool),U_14095),U_14101)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool))
    | sP980(U_14095,U_14101,U_14099,U_14097) ),
    inference(clausify,[status(thm)],[f_3548_4]) ).

cnf(f_3548_7,plain,
    ( U_14099 != c_Orderings_Obot__class_Obot(tc_fun(U_14095,tc_HOL_Obool))
    | ~ sP980(U_14095,U_14101,U_14099,U_14097) ),
    inference(clausify,[status(thm)],[f_3548_4]) ).

cnf(f_3548_8,plain,
    ( U_14101 != c_Orderings_Obot__class_Obot(tc_fun(U_14097,tc_HOL_Obool))
    | ~ sP980(U_14095,U_14101,U_14099,U_14097) ),
    inference(clausify,[status(thm)],[f_3548_4]) ).

fof(f_3549_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_3549_2,plain,
    ! [U_14104,U_14103,U_14102] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_14102,U_14103),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14102,U_14103),c_Orderings_Otop__class_Otop(tc_fun(U_14102,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14103,tc_HOL_Obool),U_14102),U_14104))) = hAPP(hAPP(c_Product__Type_OSigma(U_14102,U_14103),c_Orderings_Otop__class_Otop(tc_fun(U_14102,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14103,tc_HOL_Obool),U_14102),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14103,tc_HOL_Obool)),U_14104))),
    inference(variable_rename,[status(thm)],[f_3549_1]) ).

fof(f_3549_3,plain,
    ! [U_14102,U_14103,U_14104] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_14102,U_14103),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14102,U_14103),c_Orderings_Otop__class_Otop(tc_fun(U_14102,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14103,tc_HOL_Obool),U_14102),U_14104))) = hAPP(hAPP(c_Product__Type_OSigma(U_14102,U_14103),c_Orderings_Otop__class_Otop(tc_fun(U_14102,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14103,tc_HOL_Obool),U_14102),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14103,tc_HOL_Obool)),U_14104))),
    inference(definitional_conversion,[status(esa)],[f_3549_2]) ).

cnf(f_3549_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_14102,U_14103),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14102,U_14103),c_Orderings_Otop__class_Otop(tc_fun(U_14102,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14103,tc_HOL_Obool),U_14102),U_14104))) = hAPP(hAPP(c_Product__Type_OSigma(U_14102,U_14103),c_Orderings_Otop__class_Otop(tc_fun(U_14102,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14103,tc_HOL_Obool),U_14102),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14103,tc_HOL_Obool)),U_14104))),
    inference(clausify,[status(thm)],[f_3549_3]) ).

fof(f_3550_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_3550_2,plain,
    ! [U_14107,U_14106,U_14105] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_14105,U_14106),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14105,U_14106),U_14107),hAPP(c_COMBK(tc_fun(U_14106,tc_HOL_Obool),U_14105),c_Orderings_Otop__class_Otop(tc_fun(U_14106,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_14105,U_14106),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14105,tc_HOL_Obool)),U_14107)),hAPP(c_COMBK(tc_fun(U_14106,tc_HOL_Obool),U_14105),c_Orderings_Otop__class_Otop(tc_fun(U_14106,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3550_1]) ).

fof(f_3550_3,plain,
    ! [U_14105,U_14106,U_14107] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_14105,U_14106),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14105,U_14106),U_14107),hAPP(c_COMBK(tc_fun(U_14106,tc_HOL_Obool),U_14105),c_Orderings_Otop__class_Otop(tc_fun(U_14106,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_14105,U_14106),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14105,tc_HOL_Obool)),U_14107)),hAPP(c_COMBK(tc_fun(U_14106,tc_HOL_Obool),U_14105),c_Orderings_Otop__class_Otop(tc_fun(U_14106,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3550_2]) ).

cnf(f_3550_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_14105,U_14106),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14105,U_14106),U_14107),hAPP(c_COMBK(tc_fun(U_14106,tc_HOL_Obool),U_14105),c_Orderings_Otop__class_Otop(tc_fun(U_14106,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_14105,U_14106),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14105,tc_HOL_Obool)),U_14107)),hAPP(c_COMBK(tc_fun(U_14106,tc_HOL_Obool),U_14105),c_Orderings_Otop__class_Otop(tc_fun(U_14106,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3550_3]) ).

fof(f_3551_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_3551_2,plain,
    ! [U_14113,U_14112,U_14111,U_14110,U_14109,U_14108] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14109,U_14108),hAPP(hAPP(c_COMBC(U_14109,tc_fun(U_14110,tc_HOL_Obool),U_14108),hAPP(hAPP(c_COMBB(tc_fun(U_14110,U_14108),tc_fun(tc_fun(U_14110,tc_HOL_Obool),U_14108),U_14109),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14110,U_14108)),U_14111)),U_14112)),U_14113) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_14109,U_14110),U_14108),hAPP(c_Product__Type_Oprod_Oprod__case(U_14109,U_14110,U_14108),U_14111)),hAPP(hAPP(c_Product__Type_OSigma(U_14109,U_14110),U_14113),hAPP(c_COMBK(tc_fun(U_14110,tc_HOL_Obool),U_14109),U_14112)))
      | ~ class_Groups_Ocomm__monoid__mult(U_14108) ),
    inference(variable_rename,[status(thm)],[f_3551_1]) ).

fof(f_3551_3,plain,
    ! [U_14108,U_14109,U_14110,U_14111,U_14112,U_14113] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14109,U_14108),hAPP(hAPP(c_COMBC(U_14109,tc_fun(U_14110,tc_HOL_Obool),U_14108),hAPP(hAPP(c_COMBB(tc_fun(U_14110,U_14108),tc_fun(tc_fun(U_14110,tc_HOL_Obool),U_14108),U_14109),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14110,U_14108)),U_14111)),U_14112)),U_14113) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_14109,U_14110),U_14108),hAPP(c_Product__Type_Oprod_Oprod__case(U_14109,U_14110,U_14108),U_14111)),hAPP(hAPP(c_Product__Type_OSigma(U_14109,U_14110),U_14113),hAPP(c_COMBK(tc_fun(U_14110,tc_HOL_Obool),U_14109),U_14112)))
      | ~ class_Groups_Ocomm__monoid__mult(U_14108) ),
    inference(definitional_conversion,[status(esa)],[f_3551_2]) ).

cnf(f_3551_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14109,U_14108),hAPP(hAPP(c_COMBC(U_14109,tc_fun(U_14110,tc_HOL_Obool),U_14108),hAPP(hAPP(c_COMBB(tc_fun(U_14110,U_14108),tc_fun(tc_fun(U_14110,tc_HOL_Obool),U_14108),U_14109),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14110,U_14108)),U_14111)),U_14112)),U_14113) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_14109,U_14110),U_14108),hAPP(c_Product__Type_Oprod_Oprod__case(U_14109,U_14110,U_14108),U_14111)),hAPP(hAPP(c_Product__Type_OSigma(U_14109,U_14110),U_14113),hAPP(c_COMBK(tc_fun(U_14110,tc_HOL_Obool),U_14109),U_14112)))
    | ~ class_Groups_Ocomm__monoid__mult(U_14108) ),
    inference(clausify,[status(thm)],[f_3551_3]) ).

fof(f_3552_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_3552_2,plain,
    ! [U_14118,U_14117,U_14116,U_14115,U_14114] : hAPP(hAPP(c_Product__Type_OSigma(U_14114,U_14115),U_14116),hAPP(hAPP(c_COMBS(U_14114,tc_fun(U_14115,tc_HOL_Obool),tc_fun(U_14115,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14115,tc_HOL_Obool),tc_fun(tc_fun(U_14115,tc_HOL_Obool),tc_fun(U_14115,tc_HOL_Obool)),U_14114),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14115,tc_HOL_Obool))),U_14117)),U_14118)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14114,U_14115),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14114,U_14115),U_14116),U_14117)),hAPP(hAPP(c_Product__Type_OSigma(U_14114,U_14115),U_14116),U_14118)),
    inference(variable_rename,[status(thm)],[f_3552_1]) ).

fof(f_3552_3,plain,
    ! [U_14114,U_14115,U_14116,U_14117,U_14118] : hAPP(hAPP(c_Product__Type_OSigma(U_14114,U_14115),U_14116),hAPP(hAPP(c_COMBS(U_14114,tc_fun(U_14115,tc_HOL_Obool),tc_fun(U_14115,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14115,tc_HOL_Obool),tc_fun(tc_fun(U_14115,tc_HOL_Obool),tc_fun(U_14115,tc_HOL_Obool)),U_14114),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14115,tc_HOL_Obool))),U_14117)),U_14118)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14114,U_14115),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14114,U_14115),U_14116),U_14117)),hAPP(hAPP(c_Product__Type_OSigma(U_14114,U_14115),U_14116),U_14118)),
    inference(definitional_conversion,[status(esa)],[f_3552_2]) ).

cnf(f_3552_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14114,U_14115),U_14116),hAPP(hAPP(c_COMBS(U_14114,tc_fun(U_14115,tc_HOL_Obool),tc_fun(U_14115,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14115,tc_HOL_Obool),tc_fun(tc_fun(U_14115,tc_HOL_Obool),tc_fun(U_14115,tc_HOL_Obool)),U_14114),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14115,tc_HOL_Obool))),U_14117)),U_14118)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14114,U_14115),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14114,U_14115),U_14116),U_14117)),hAPP(hAPP(c_Product__Type_OSigma(U_14114,U_14115),U_14116),U_14118)),
    inference(clausify,[status(thm)],[f_3552_3]) ).

fof(f_3553_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_3553_2,plain,
    ! [U_14123,U_14122,U_14121,U_14120,U_14119] : hAPP(hAPP(c_Product__Type_OSigma(U_14119,U_14120),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14119,tc_HOL_Obool)),U_14121),U_14122)),hAPP(c_COMBK(tc_fun(U_14120,tc_HOL_Obool),U_14119),U_14123)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14119,U_14120),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14119,U_14120),U_14121),hAPP(c_COMBK(tc_fun(U_14120,tc_HOL_Obool),U_14119),U_14123))),hAPP(hAPP(c_Product__Type_OSigma(U_14119,U_14120),U_14122),hAPP(c_COMBK(tc_fun(U_14120,tc_HOL_Obool),U_14119),U_14123))),
    inference(variable_rename,[status(thm)],[f_3553_1]) ).

fof(f_3553_3,plain,
    ! [U_14119,U_14120,U_14121,U_14122,U_14123] : hAPP(hAPP(c_Product__Type_OSigma(U_14119,U_14120),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14119,tc_HOL_Obool)),U_14121),U_14122)),hAPP(c_COMBK(tc_fun(U_14120,tc_HOL_Obool),U_14119),U_14123)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14119,U_14120),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14119,U_14120),U_14121),hAPP(c_COMBK(tc_fun(U_14120,tc_HOL_Obool),U_14119),U_14123))),hAPP(hAPP(c_Product__Type_OSigma(U_14119,U_14120),U_14122),hAPP(c_COMBK(tc_fun(U_14120,tc_HOL_Obool),U_14119),U_14123))),
    inference(definitional_conversion,[status(esa)],[f_3553_2]) ).

cnf(f_3553_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14119,U_14120),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14119,tc_HOL_Obool)),U_14121),U_14122)),hAPP(c_COMBK(tc_fun(U_14120,tc_HOL_Obool),U_14119),U_14123)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14119,U_14120),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14119,U_14120),U_14121),hAPP(c_COMBK(tc_fun(U_14120,tc_HOL_Obool),U_14119),U_14123))),hAPP(hAPP(c_Product__Type_OSigma(U_14119,U_14120),U_14122),hAPP(c_COMBK(tc_fun(U_14120,tc_HOL_Obool),U_14119),U_14123))),
    inference(clausify,[status(thm)],[f_3553_3]) ).

fof(f_3554_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_3554_2,plain,
    ! [U_14128,U_14127,U_14126,U_14125,U_14124] : hAPP(hAPP(c_Product__Type_OSigma(U_14124,U_14125),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14124,tc_HOL_Obool)),U_14126),U_14127)),U_14128) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14124,U_14125),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14124,U_14125),U_14126),U_14128)),hAPP(hAPP(c_Product__Type_OSigma(U_14124,U_14125),U_14127),U_14128)),
    inference(variable_rename,[status(thm)],[f_3554_1]) ).

fof(f_3554_3,plain,
    ! [U_14124,U_14125,U_14126,U_14127,U_14128] : hAPP(hAPP(c_Product__Type_OSigma(U_14124,U_14125),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14124,tc_HOL_Obool)),U_14126),U_14127)),U_14128) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14124,U_14125),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14124,U_14125),U_14126),U_14128)),hAPP(hAPP(c_Product__Type_OSigma(U_14124,U_14125),U_14127),U_14128)),
    inference(definitional_conversion,[status(esa)],[f_3554_2]) ).

cnf(f_3554_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14124,U_14125),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14124,tc_HOL_Obool)),U_14126),U_14127)),U_14128) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14124,U_14125),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14124,U_14125),U_14126),U_14128)),hAPP(hAPP(c_Product__Type_OSigma(U_14124,U_14125),U_14127),U_14128)),
    inference(clausify,[status(thm)],[f_3554_3]) ).

fof(f_3555_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_3555_2,plain,
    ! [U_14132,U_14131,U_14130,U_14129] : hAPP(c_Set_Oimage(tc_prod(U_14129,U_14130),tc_prod(U_14130,U_14129),hAPP(c_Product__Type_Oprod_Oprod__case(U_14129,U_14130,tc_prod(U_14130,U_14129)),hAPP(c_COMBC(U_14130,U_14129,tc_prod(U_14130,U_14129)),c_Product__Type_OPair(U_14130,U_14129)))),hAPP(hAPP(c_Product__Type_OSigma(U_14129,U_14130),U_14131),hAPP(c_COMBK(tc_fun(U_14130,tc_HOL_Obool),U_14129),U_14132))) = hAPP(hAPP(c_Product__Type_OSigma(U_14130,U_14129),U_14132),hAPP(c_COMBK(tc_fun(U_14129,tc_HOL_Obool),U_14130),U_14131)),
    inference(variable_rename,[status(thm)],[f_3555_1]) ).

fof(f_3555_3,plain,
    ! [U_14129,U_14130,U_14131,U_14132] : hAPP(c_Set_Oimage(tc_prod(U_14129,U_14130),tc_prod(U_14130,U_14129),hAPP(c_Product__Type_Oprod_Oprod__case(U_14129,U_14130,tc_prod(U_14130,U_14129)),hAPP(c_COMBC(U_14130,U_14129,tc_prod(U_14130,U_14129)),c_Product__Type_OPair(U_14130,U_14129)))),hAPP(hAPP(c_Product__Type_OSigma(U_14129,U_14130),U_14131),hAPP(c_COMBK(tc_fun(U_14130,tc_HOL_Obool),U_14129),U_14132))) = hAPP(hAPP(c_Product__Type_OSigma(U_14130,U_14129),U_14132),hAPP(c_COMBK(tc_fun(U_14129,tc_HOL_Obool),U_14130),U_14131)),
    inference(definitional_conversion,[status(esa)],[f_3555_2]) ).

cnf(f_3555_4,plain,
    hAPP(c_Set_Oimage(tc_prod(U_14129,U_14130),tc_prod(U_14130,U_14129),hAPP(c_Product__Type_Oprod_Oprod__case(U_14129,U_14130,tc_prod(U_14130,U_14129)),hAPP(c_COMBC(U_14130,U_14129,tc_prod(U_14130,U_14129)),c_Product__Type_OPair(U_14130,U_14129)))),hAPP(hAPP(c_Product__Type_OSigma(U_14129,U_14130),U_14131),hAPP(c_COMBK(tc_fun(U_14130,tc_HOL_Obool),U_14129),U_14132))) = hAPP(hAPP(c_Product__Type_OSigma(U_14130,U_14129),U_14132),hAPP(c_COMBK(tc_fun(U_14129,tc_HOL_Obool),U_14130),U_14131)),
    inference(clausify,[status(thm)],[f_3555_3]) ).

fof(f_3556_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_3556_2,plain,
    ! [U_14136,U_14135,U_14134,U_14133] :
      ( hAPP(U_14133,hAPP(hAPP(c_Set_Oinsert(U_14134),U_14136),c_Orderings_Obot__class_Obot(tc_fun(U_14134,tc_HOL_Obool)))) = U_14136
      | U_14133 != c_Finite__Set_Ofold1(U_14134,U_14135) ),
    inference(variable_rename,[status(thm)],[f_3556_1]) ).

fof(f_3556_3,plain,
    ! [U_14134,U_14133,U_14135,U_14136] :
      ( hAPP(U_14133,hAPP(hAPP(c_Set_Oinsert(U_14134),U_14136),c_Orderings_Obot__class_Obot(tc_fun(U_14134,tc_HOL_Obool)))) = U_14136
      | U_14133 != c_Finite__Set_Ofold1(U_14134,U_14135) ),
    inference(definitional_conversion,[status(esa)],[f_3556_2]) ).

cnf(f_3556_4,plain,
    ( hAPP(U_14133,hAPP(hAPP(c_Set_Oinsert(U_14134),U_14136),c_Orderings_Obot__class_Obot(tc_fun(U_14134,tc_HOL_Obool)))) = U_14136
    | U_14133 != c_Finite__Set_Ofold1(U_14134,U_14135) ),
    inference(clausify,[status(thm)],[f_3556_3]) ).

fof(f_3557_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_3557_2,plain,
    ! [U_14139,U_14138,U_14137] : hAPP(c_Finite__Set_Ofold1(U_14137,U_14138),hAPP(hAPP(c_Set_Oinsert(U_14137),U_14139),c_Orderings_Obot__class_Obot(tc_fun(U_14137,tc_HOL_Obool)))) = U_14139,
    inference(variable_rename,[status(thm)],[f_3557_1]) ).

fof(f_3557_3,plain,
    ! [U_14137,U_14138,U_14139] : hAPP(c_Finite__Set_Ofold1(U_14137,U_14138),hAPP(hAPP(c_Set_Oinsert(U_14137),U_14139),c_Orderings_Obot__class_Obot(tc_fun(U_14137,tc_HOL_Obool)))) = U_14139,
    inference(definitional_conversion,[status(esa)],[f_3557_2]) ).

cnf(f_3557_4,plain,
    hAPP(c_Finite__Set_Ofold1(U_14137,U_14138),hAPP(hAPP(c_Set_Oinsert(U_14137),U_14139),c_Orderings_Obot__class_Obot(tc_fun(U_14137,tc_HOL_Obool)))) = U_14139,
    inference(clausify,[status(thm)],[f_3557_3]) ).

fof(f_3558_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_3558_2,plain,
    ! [U_14143,U_14142,U_14141,U_14140] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14140,U_14142)),hAPP(hAPP(c_Product__Type_OSigma(U_14140,U_14142),U_14141),hAPP(c_COMBK(tc_fun(U_14142,tc_HOL_Obool),U_14140),U_14143))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14142),U_14143))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14140),U_14141)) ),
    inference(variable_rename,[status(thm)],[f_3558_1]) ).

fof(f_3558_3,plain,
    ! [U_14140,U_14141,U_14142,U_14143] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14140,U_14142)),hAPP(hAPP(c_Product__Type_OSigma(U_14140,U_14142),U_14141),hAPP(c_COMBK(tc_fun(U_14142,tc_HOL_Obool),U_14140),U_14143))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14142),U_14143))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14140),U_14141)) ),
    inference(definitional_conversion,[status(esa)],[f_3558_2]) ).

cnf(f_3558_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14140,U_14142)),hAPP(hAPP(c_Product__Type_OSigma(U_14140,U_14142),U_14141),hAPP(c_COMBK(tc_fun(U_14142,tc_HOL_Obool),U_14140),U_14143))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14142),U_14143))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14140),U_14141)) ),
    inference(clausify,[status(thm)],[f_3558_3]) ).

fof(f_3559_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_3559_2,plain,
    ! [U_14146,U_14145,U_14144] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14144,U_14144),tc_HOL_Obool)),U_14146),hAPP(hAPP(c_Product__Type_OSigma(U_14144,U_14144),U_14145),hAPP(c_COMBK(tc_fun(U_14144,tc_HOL_Obool),U_14144),U_14145))))
      | ~ c_Equiv__Relations_Oequiv(U_14144,U_14145,U_14146) ),
    inference(variable_rename,[status(thm)],[f_3559_1]) ).

fof(f_3559_3,plain,
    ! [U_14144,U_14145,U_14146] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14144,U_14144),tc_HOL_Obool)),U_14146),hAPP(hAPP(c_Product__Type_OSigma(U_14144,U_14144),U_14145),hAPP(c_COMBK(tc_fun(U_14144,tc_HOL_Obool),U_14144),U_14145))))
      | ~ c_Equiv__Relations_Oequiv(U_14144,U_14145,U_14146) ),
    inference(definitional_conversion,[status(esa)],[f_3559_2]) ).

cnf(f_3559_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14144,U_14144),tc_HOL_Obool)),U_14146),hAPP(hAPP(c_Product__Type_OSigma(U_14144,U_14144),U_14145),hAPP(c_COMBK(tc_fun(U_14144,tc_HOL_Obool),U_14144),U_14145))))
    | ~ c_Equiv__Relations_Oequiv(U_14144,U_14145,U_14146) ),
    inference(clausify,[status(thm)],[f_3559_3]) ).

fof(f_3560_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_3560_2,plain,
    ! [U_14151,U_14150,U_14149,U_14148,U_14147] : hAPP(hAPP(c_Product__Type_OSigma(U_14147,U_14148),U_14149),hAPP(hAPP(c_COMBS(U_14147,tc_fun(U_14148,tc_HOL_Obool),tc_fun(U_14148,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14148,tc_HOL_Obool),tc_fun(tc_fun(U_14148,tc_HOL_Obool),tc_fun(U_14148,tc_HOL_Obool)),U_14147),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14148,tc_HOL_Obool))),U_14150)),U_14151)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14147,U_14148),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14147,U_14148),U_14149),U_14150)),hAPP(hAPP(c_Product__Type_OSigma(U_14147,U_14148),U_14149),U_14151)),
    inference(variable_rename,[status(thm)],[f_3560_1]) ).

fof(f_3560_3,plain,
    ! [U_14147,U_14148,U_14149,U_14150,U_14151] : hAPP(hAPP(c_Product__Type_OSigma(U_14147,U_14148),U_14149),hAPP(hAPP(c_COMBS(U_14147,tc_fun(U_14148,tc_HOL_Obool),tc_fun(U_14148,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14148,tc_HOL_Obool),tc_fun(tc_fun(U_14148,tc_HOL_Obool),tc_fun(U_14148,tc_HOL_Obool)),U_14147),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14148,tc_HOL_Obool))),U_14150)),U_14151)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14147,U_14148),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14147,U_14148),U_14149),U_14150)),hAPP(hAPP(c_Product__Type_OSigma(U_14147,U_14148),U_14149),U_14151)),
    inference(definitional_conversion,[status(esa)],[f_3560_2]) ).

cnf(f_3560_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14147,U_14148),U_14149),hAPP(hAPP(c_COMBS(U_14147,tc_fun(U_14148,tc_HOL_Obool),tc_fun(U_14148,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14148,tc_HOL_Obool),tc_fun(tc_fun(U_14148,tc_HOL_Obool),tc_fun(U_14148,tc_HOL_Obool)),U_14147),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14148,tc_HOL_Obool))),U_14150)),U_14151)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14147,U_14148),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14147,U_14148),U_14149),U_14150)),hAPP(hAPP(c_Product__Type_OSigma(U_14147,U_14148),U_14149),U_14151)),
    inference(clausify,[status(thm)],[f_3560_3]) ).

fof(f_3561_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_3561_2,plain,
    ! [U_14156,U_14155,U_14154,U_14153,U_14152] : hAPP(hAPP(c_Product__Type_OSigma(U_14152,U_14153),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14152,tc_HOL_Obool)),U_14154),U_14155)),hAPP(c_COMBK(tc_fun(U_14153,tc_HOL_Obool),U_14152),U_14156)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14152,U_14153),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14152,U_14153),U_14154),hAPP(c_COMBK(tc_fun(U_14153,tc_HOL_Obool),U_14152),U_14156))),hAPP(hAPP(c_Product__Type_OSigma(U_14152,U_14153),U_14155),hAPP(c_COMBK(tc_fun(U_14153,tc_HOL_Obool),U_14152),U_14156))),
    inference(variable_rename,[status(thm)],[f_3561_1]) ).

fof(f_3561_3,plain,
    ! [U_14152,U_14153,U_14154,U_14155,U_14156] : hAPP(hAPP(c_Product__Type_OSigma(U_14152,U_14153),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14152,tc_HOL_Obool)),U_14154),U_14155)),hAPP(c_COMBK(tc_fun(U_14153,tc_HOL_Obool),U_14152),U_14156)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14152,U_14153),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14152,U_14153),U_14154),hAPP(c_COMBK(tc_fun(U_14153,tc_HOL_Obool),U_14152),U_14156))),hAPP(hAPP(c_Product__Type_OSigma(U_14152,U_14153),U_14155),hAPP(c_COMBK(tc_fun(U_14153,tc_HOL_Obool),U_14152),U_14156))),
    inference(definitional_conversion,[status(esa)],[f_3561_2]) ).

cnf(f_3561_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14152,U_14153),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14152,tc_HOL_Obool)),U_14154),U_14155)),hAPP(c_COMBK(tc_fun(U_14153,tc_HOL_Obool),U_14152),U_14156)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14152,U_14153),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14152,U_14153),U_14154),hAPP(c_COMBK(tc_fun(U_14153,tc_HOL_Obool),U_14152),U_14156))),hAPP(hAPP(c_Product__Type_OSigma(U_14152,U_14153),U_14155),hAPP(c_COMBK(tc_fun(U_14153,tc_HOL_Obool),U_14152),U_14156))),
    inference(clausify,[status(thm)],[f_3561_3]) ).

fof(f_3562_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_3562_2,plain,
    ! [U_14161,U_14160,U_14159,U_14158,U_14157] : hAPP(hAPP(c_Product__Type_OSigma(U_14157,U_14158),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14157,tc_HOL_Obool)),U_14159),U_14160)),U_14161) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14157,U_14158),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14157,U_14158),U_14159),U_14161)),hAPP(hAPP(c_Product__Type_OSigma(U_14157,U_14158),U_14160),U_14161)),
    inference(variable_rename,[status(thm)],[f_3562_1]) ).

fof(f_3562_3,plain,
    ! [U_14157,U_14158,U_14159,U_14160,U_14161] : hAPP(hAPP(c_Product__Type_OSigma(U_14157,U_14158),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14157,tc_HOL_Obool)),U_14159),U_14160)),U_14161) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14157,U_14158),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14157,U_14158),U_14159),U_14161)),hAPP(hAPP(c_Product__Type_OSigma(U_14157,U_14158),U_14160),U_14161)),
    inference(definitional_conversion,[status(esa)],[f_3562_2]) ).

cnf(f_3562_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14157,U_14158),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14157,tc_HOL_Obool)),U_14159),U_14160)),U_14161) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14157,U_14158),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14157,U_14158),U_14159),U_14161)),hAPP(hAPP(c_Product__Type_OSigma(U_14157,U_14158),U_14160),U_14161)),
    inference(clausify,[status(thm)],[f_3562_3]) ).

fof(f_3563_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_3563_2,plain,
    ! [U_14163,U_14162] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14162,U_14162),tc_HOL_Obool)),c_Relation_OId__on(U_14162,U_14163)),hAPP(hAPP(c_Product__Type_OSigma(U_14162,U_14162),U_14163),hAPP(c_COMBK(tc_fun(U_14162,tc_HOL_Obool),U_14162),U_14163)))),
    inference(variable_rename,[status(thm)],[f_3563_1]) ).

fof(f_3563_3,plain,
    ! [U_14162,U_14163] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14162,U_14162),tc_HOL_Obool)),c_Relation_OId__on(U_14162,U_14163)),hAPP(hAPP(c_Product__Type_OSigma(U_14162,U_14162),U_14163),hAPP(c_COMBK(tc_fun(U_14162,tc_HOL_Obool),U_14162),U_14163)))),
    inference(definitional_conversion,[status(esa)],[f_3563_2]) ).

cnf(f_3563_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14162,U_14162),tc_HOL_Obool)),c_Relation_OId__on(U_14162,U_14163)),hAPP(hAPP(c_Product__Type_OSigma(U_14162,U_14162),U_14163),hAPP(c_COMBK(tc_fun(U_14162,tc_HOL_Obool),U_14162),U_14163)))),
    inference(clausify,[status(thm)],[f_3563_3]) ).

fof(f_3564_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_3564_2,plain,
    ! [U_14165,U_14164] : hAPP(hAPP(c_Product__Type_OSigma(U_14164,U_14165),c_Orderings_Otop__class_Otop(tc_fun(U_14164,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14165,tc_HOL_Obool),U_14164),c_Orderings_Otop__class_Otop(tc_fun(U_14165,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14164,U_14165),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3564_1]) ).

fof(f_3564_3,plain,
    ! [U_14164,U_14165] : hAPP(hAPP(c_Product__Type_OSigma(U_14164,U_14165),c_Orderings_Otop__class_Otop(tc_fun(U_14164,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14165,tc_HOL_Obool),U_14164),c_Orderings_Otop__class_Otop(tc_fun(U_14165,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14164,U_14165),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3564_2]) ).

cnf(f_3564_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14164,U_14165),c_Orderings_Otop__class_Otop(tc_fun(U_14164,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14165,tc_HOL_Obool),U_14164),c_Orderings_Otop__class_Otop(tc_fun(U_14165,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14164,U_14165),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3564_3]) ).

fof(f_3565_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_3565_2,plain,
    ! [U_14171,U_14170,U_14169,U_14168,U_14167,U_14166] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_14167),U_14169),hAPP(U_14171,U_14168)))
        & hBOOL(hAPP(hAPP(c_member(U_14166),U_14168),U_14170)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14166,U_14167)),hAPP(hAPP(c_Product__Type_OPair(U_14166,U_14167),U_14168),U_14169)),hAPP(hAPP(c_Product__Type_OSigma(U_14166,U_14167),U_14170),U_14171))) ),
    inference(variable_rename,[status(thm)],[f_3565_1]) ).

fof(f_3565_3,plain,
    ( ! [U_14166,U_14167,U_14168,U_14169,U_14170,U_14171] :
        ( hBOOL(hAPP(hAPP(c_member(U_14167),U_14169),hAPP(U_14171,U_14168)))
        | ~ sP981(U_14166,U_14167,U_14168,U_14169,U_14170,U_14171) )
    & ! [U_14166,U_14167,U_14168,U_14169,U_14170,U_14171] :
        ( hBOOL(hAPP(hAPP(c_member(U_14166),U_14168),U_14170))
        | ~ sP981(U_14166,U_14167,U_14168,U_14169,U_14170,U_14171) )
    & ! [U_14166,U_14167,U_14168,U_14169,U_14170,U_14171] :
        ( sP981(U_14166,U_14167,U_14168,U_14169,U_14170,U_14171)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14166,U_14167)),hAPP(hAPP(c_Product__Type_OPair(U_14166,U_14167),U_14168),U_14169)),hAPP(hAPP(c_Product__Type_OSigma(U_14166,U_14167),U_14170),U_14171))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP981])],[f_3565_2]) ).

cnf(f_3565_4,plain,
    ( sP981(U_14166,U_14167,U_14168,U_14169,U_14170,U_14171)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14166,U_14167)),hAPP(hAPP(c_Product__Type_OPair(U_14166,U_14167),U_14168),U_14169)),hAPP(hAPP(c_Product__Type_OSigma(U_14166,U_14167),U_14170),U_14171))) ),
    inference(clausify,[status(thm)],[f_3565_3]) ).

cnf(f_3565_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14166),U_14168),U_14170))
    | ~ sP981(U_14166,U_14167,U_14168,U_14169,U_14170,U_14171) ),
    inference(clausify,[status(thm)],[f_3565_3]) ).

cnf(f_3565_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14167),U_14169),hAPP(U_14171,U_14168)))
    | ~ sP981(U_14166,U_14167,U_14168,U_14169,U_14170,U_14171) ),
    inference(clausify,[status(thm)],[f_3565_3]) ).

fof(f_3566_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_3566_2,plain,
    ! [U_14177,U_14176,U_14175,U_14174,U_14173,U_14172] :
      ( hBOOL(hAPP(hAPP(c_member(U_14173),U_14175),hAPP(U_14177,U_14174)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14172,U_14173)),hAPP(hAPP(c_Product__Type_OPair(U_14172,U_14173),U_14174),U_14175)),hAPP(hAPP(c_Product__Type_OSigma(U_14172,U_14173),U_14176),U_14177))) ),
    inference(variable_rename,[status(thm)],[f_3566_1]) ).

fof(f_3566_3,plain,
    ! [U_14177,U_14176,U_14175,U_14174,U_14173] :
      ( ! [U_14172] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14172,U_14173)),hAPP(hAPP(c_Product__Type_OPair(U_14172,U_14173),U_14174),U_14175)),hAPP(hAPP(c_Product__Type_OSigma(U_14172,U_14173),U_14176),U_14177)))
      | hBOOL(hAPP(hAPP(c_member(U_14173),U_14175),hAPP(U_14177,U_14174))) ),
    inference(miniscope,[status(thm)],[f_3566_2]) ).

fof(f_3566_4,plain,
    ! [U_14172,U_14173,U_14174,U_14175,U_14176,U_14177] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14172,U_14173)),hAPP(hAPP(c_Product__Type_OPair(U_14172,U_14173),U_14174),U_14175)),hAPP(hAPP(c_Product__Type_OSigma(U_14172,U_14173),U_14176),U_14177)))
      | hBOOL(hAPP(hAPP(c_member(U_14173),U_14175),hAPP(U_14177,U_14174))) ),
    inference(definitional_conversion,[status(esa)],[f_3566_3]) ).

cnf(f_3566_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14172,U_14173)),hAPP(hAPP(c_Product__Type_OPair(U_14172,U_14173),U_14174),U_14175)),hAPP(hAPP(c_Product__Type_OSigma(U_14172,U_14173),U_14176),U_14177)))
    | hBOOL(hAPP(hAPP(c_member(U_14173),U_14175),hAPP(U_14177,U_14174))) ),
    inference(clausify,[status(thm)],[f_3566_4]) ).

fof(f_3567_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_3567_2,plain,
    ! [U_14183,U_14182,U_14181,U_14180,U_14179,U_14178] :
      ( hBOOL(hAPP(hAPP(c_member(U_14178),U_14180),U_14182))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14178,U_14179)),hAPP(hAPP(c_Product__Type_OPair(U_14178,U_14179),U_14180),U_14181)),hAPP(hAPP(c_Product__Type_OSigma(U_14178,U_14179),U_14182),U_14183))) ),
    inference(variable_rename,[status(thm)],[f_3567_1]) ).

fof(f_3567_3,plain,
    ! [U_14178,U_14179,U_14180,U_14181,U_14182,U_14183] :
      ( hBOOL(hAPP(hAPP(c_member(U_14178),U_14180),U_14182))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14178,U_14179)),hAPP(hAPP(c_Product__Type_OPair(U_14178,U_14179),U_14180),U_14181)),hAPP(hAPP(c_Product__Type_OSigma(U_14178,U_14179),U_14182),U_14183))) ),
    inference(definitional_conversion,[status(esa)],[f_3567_2]) ).

cnf(f_3567_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14178),U_14180),U_14182))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14178,U_14179)),hAPP(hAPP(c_Product__Type_OPair(U_14178,U_14179),U_14180),U_14181)),hAPP(hAPP(c_Product__Type_OSigma(U_14178,U_14179),U_14182),U_14183))) ),
    inference(clausify,[status(thm)],[f_3567_3]) ).

fof(f_3568_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_3568_2,plain,
    ! [U_14189,U_14188,U_14187,U_14186,U_14185,U_14184] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14184,U_14185)),hAPP(hAPP(c_Product__Type_OPair(U_14184,U_14185),U_14186),U_14187)),hAPP(hAPP(c_Product__Type_OSigma(U_14184,U_14185),U_14188),U_14189)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14185),U_14187),hAPP(U_14189,U_14186)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14184),U_14186),U_14188)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_14185),U_14187),hAPP(U_14189,U_14186)))
          & hBOOL(hAPP(hAPP(c_member(U_14184),U_14186),U_14188)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14184,U_14185)),hAPP(hAPP(c_Product__Type_OPair(U_14184,U_14185),U_14186),U_14187)),hAPP(hAPP(c_Product__Type_OSigma(U_14184,U_14185),U_14188),U_14189))) ) ),
    inference(variable_rename,[status(thm)],[f_3568_1]) ).

fof(f_3568_3,plain,
    ( ! [U_14201,U_14199,U_14197,U_14195,U_14193,U_14191] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14191,U_14193)),hAPP(hAPP(c_Product__Type_OPair(U_14191,U_14193),U_14195),U_14197)),hAPP(hAPP(c_Product__Type_OSigma(U_14191,U_14193),U_14199),U_14201)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14193),U_14197),hAPP(U_14201,U_14195)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14191),U_14195),U_14199)) )
    & ! [U_14200,U_14198,U_14196,U_14194,U_14192,U_14190] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_14192),U_14196),hAPP(U_14200,U_14194)))
          & hBOOL(hAPP(hAPP(c_member(U_14190),U_14194),U_14198)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14190,U_14192)),hAPP(hAPP(c_Product__Type_OPair(U_14190,U_14192),U_14194),U_14196)),hAPP(hAPP(c_Product__Type_OSigma(U_14190,U_14192),U_14198),U_14200))) ) ),
    inference(miniscope,[status(thm)],[f_3568_2]) ).

fof(f_3568_4,plain,
    ( ! [U_14192,U_14190,U_14198,U_14194,U_14196,U_14200] :
        ( hBOOL(hAPP(hAPP(c_member(U_14192),U_14196),hAPP(U_14200,U_14194)))
        | ~ sP982(U_14192,U_14190,U_14198,U_14194,U_14196,U_14200) )
    & ! [U_14192,U_14190,U_14198,U_14194,U_14196,U_14200] :
        ( hBOOL(hAPP(hAPP(c_member(U_14190),U_14194),U_14198))
        | ~ sP982(U_14192,U_14190,U_14198,U_14194,U_14196,U_14200) )
    & ! [U_14191,U_14197,U_14193,U_14199,U_14195,U_14201] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14191,U_14193)),hAPP(hAPP(c_Product__Type_OPair(U_14191,U_14193),U_14195),U_14197)),hAPP(hAPP(c_Product__Type_OSigma(U_14191,U_14193),U_14199),U_14201)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14193),U_14197),hAPP(U_14201,U_14195)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14191),U_14195),U_14199)) )
    & ! [U_14192,U_14190,U_14198,U_14194,U_14196,U_14200] :
        ( sP982(U_14192,U_14190,U_14198,U_14194,U_14196,U_14200)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14190,U_14192)),hAPP(hAPP(c_Product__Type_OPair(U_14190,U_14192),U_14194),U_14196)),hAPP(hAPP(c_Product__Type_OSigma(U_14190,U_14192),U_14198),U_14200))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP982])],[f_3568_3]) ).

cnf(f_3568_5,plain,
    ( sP982(U_14192,U_14190,U_14198,U_14194,U_14196,U_14200)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14190,U_14192)),hAPP(hAPP(c_Product__Type_OPair(U_14190,U_14192),U_14194),U_14196)),hAPP(hAPP(c_Product__Type_OSigma(U_14190,U_14192),U_14198),U_14200))) ),
    inference(clausify,[status(thm)],[f_3568_4]) ).

cnf(f_3568_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14191,U_14193)),hAPP(hAPP(c_Product__Type_OPair(U_14191,U_14193),U_14195),U_14197)),hAPP(hAPP(c_Product__Type_OSigma(U_14191,U_14193),U_14199),U_14201)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14193),U_14197),hAPP(U_14201,U_14195)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14191),U_14195),U_14199)) ),
    inference(clausify,[status(thm)],[f_3568_4]) ).

cnf(f_3568_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14190),U_14194),U_14198))
    | ~ sP982(U_14192,U_14190,U_14198,U_14194,U_14196,U_14200) ),
    inference(clausify,[status(thm)],[f_3568_4]) ).

cnf(f_3568_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14192),U_14196),hAPP(U_14200,U_14194)))
    | ~ sP982(U_14192,U_14190,U_14198,U_14194,U_14196,U_14200) ),
    inference(clausify,[status(thm)],[f_3568_4]) ).

fof(f_3569_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_3569_2,plain,
    ! [U_14205,U_14204,U_14203,U_14202] :
      ( hAPP(U_14204,U_14205) = hAPP(c_Finite__Set_Ofold1(U_14202,U_14203),U_14205)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14202),U_14205))
      | ~ c_Finite__Set_Ofolding__one(U_14202,U_14203,U_14204) ),
    inference(variable_rename,[status(thm)],[f_3569_1]) ).

fof(f_3569_3,plain,
    ! [U_14202,U_14204,U_14205,U_14203] :
      ( hAPP(U_14204,U_14205) = hAPP(c_Finite__Set_Ofold1(U_14202,U_14203),U_14205)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14202),U_14205))
      | ~ c_Finite__Set_Ofolding__one(U_14202,U_14203,U_14204) ),
    inference(definitional_conversion,[status(esa)],[f_3569_2]) ).

cnf(f_3569_4,plain,
    ( hAPP(U_14204,U_14205) = hAPP(c_Finite__Set_Ofold1(U_14202,U_14203),U_14205)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14202),U_14205))
    | ~ c_Finite__Set_Ofolding__one(U_14202,U_14203,U_14204) ),
    inference(clausify,[status(thm)],[f_3569_3]) ).

fof(f_3570_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_3570_2,plain,
    ! [U_14209,U_14208,U_14207,U_14206] : hAPP(c_Finite__Set_Ocard(tc_prod(U_14206,U_14207)),hAPP(hAPP(c_Product__Type_OSigma(U_14206,U_14207),hAPP(hAPP(c_Set_Oinsert(U_14206),U_14208),c_Orderings_Obot__class_Obot(tc_fun(U_14206,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_14207,tc_HOL_Obool),U_14206),U_14209))) = hAPP(c_Finite__Set_Ocard(U_14207),U_14209),
    inference(variable_rename,[status(thm)],[f_3570_1]) ).

fof(f_3570_3,plain,
    ! [U_14206,U_14207,U_14208,U_14209] : hAPP(c_Finite__Set_Ocard(tc_prod(U_14206,U_14207)),hAPP(hAPP(c_Product__Type_OSigma(U_14206,U_14207),hAPP(hAPP(c_Set_Oinsert(U_14206),U_14208),c_Orderings_Obot__class_Obot(tc_fun(U_14206,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_14207,tc_HOL_Obool),U_14206),U_14209))) = hAPP(c_Finite__Set_Ocard(U_14207),U_14209),
    inference(definitional_conversion,[status(esa)],[f_3570_2]) ).

cnf(f_3570_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_prod(U_14206,U_14207)),hAPP(hAPP(c_Product__Type_OSigma(U_14206,U_14207),hAPP(hAPP(c_Set_Oinsert(U_14206),U_14208),c_Orderings_Obot__class_Obot(tc_fun(U_14206,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_14207,tc_HOL_Obool),U_14206),U_14209))) = hAPP(c_Finite__Set_Ocard(U_14207),U_14209),
    inference(clausify,[status(thm)],[f_3570_3]) ).

fof(f_3571_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_3571_2,plain,
    ! [U_14215,U_14214,U_14213,U_14212,U_14211,U_14210] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14213,U_14210),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14213,U_14210),U_14214),hAPP(c_COMBK(tc_fun(U_14210,tc_HOL_Obool),U_14213),U_14212))),hAPP(hAPP(c_Product__Type_OSigma(U_14213,U_14210),U_14215),hAPP(c_COMBK(tc_fun(U_14210,tc_HOL_Obool),U_14213),U_14212))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14213,tc_HOL_Obool)),U_14214),U_14215)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14213,tc_HOL_Obool)),U_14214),U_14215))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14213,U_14210),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14213,U_14210),U_14214),hAPP(c_COMBK(tc_fun(U_14210,tc_HOL_Obool),U_14213),U_14212))),hAPP(hAPP(c_Product__Type_OSigma(U_14213,U_14210),U_14215),hAPP(c_COMBK(tc_fun(U_14210,tc_HOL_Obool),U_14213),U_14212)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14210),U_14211),U_14212)) ),
    inference(variable_rename,[status(thm)],[f_3571_1]) ).

fof(f_3571_3,plain,
    ( ! [U_14210,U_14212,U_14213,U_14214,U_14215] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14213,U_14210),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14213,U_14210),U_14214),hAPP(c_COMBK(tc_fun(U_14210,tc_HOL_Obool),U_14213),U_14212))),hAPP(hAPP(c_Product__Type_OSigma(U_14213,U_14210),U_14215),hAPP(c_COMBK(tc_fun(U_14210,tc_HOL_Obool),U_14213),U_14212))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14213,tc_HOL_Obool)),U_14214),U_14215))
        | ~ sP983(U_14210,U_14212,U_14213,U_14214,U_14215) )
    & ! [U_14210,U_14212,U_14213,U_14214,U_14215] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14213,tc_HOL_Obool)),U_14214),U_14215))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14213,U_14210),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14213,U_14210),U_14214),hAPP(c_COMBK(tc_fun(U_14210,tc_HOL_Obool),U_14213),U_14212))),hAPP(hAPP(c_Product__Type_OSigma(U_14213,U_14210),U_14215),hAPP(c_COMBK(tc_fun(U_14210,tc_HOL_Obool),U_14213),U_14212))))
        | ~ sP983(U_14210,U_14212,U_14213,U_14214,U_14215) )
    & ! [U_14210,U_14211,U_14212,U_14213,U_14214,U_14215] :
        ( sP983(U_14210,U_14212,U_14213,U_14214,U_14215)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14210),U_14211),U_14212)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP983])],[f_3571_2]) ).

cnf(f_3571_4,plain,
    ( sP983(U_14210,U_14212,U_14213,U_14214,U_14215)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14210),U_14211),U_14212)) ),
    inference(clausify,[status(thm)],[f_3571_3]) ).

cnf(f_3571_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14213,tc_HOL_Obool)),U_14214),U_14215))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14213,U_14210),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14213,U_14210),U_14214),hAPP(c_COMBK(tc_fun(U_14210,tc_HOL_Obool),U_14213),U_14212))),hAPP(hAPP(c_Product__Type_OSigma(U_14213,U_14210),U_14215),hAPP(c_COMBK(tc_fun(U_14210,tc_HOL_Obool),U_14213),U_14212))))
    | ~ sP983(U_14210,U_14212,U_14213,U_14214,U_14215) ),
    inference(clausify,[status(thm)],[f_3571_3]) ).

cnf(f_3571_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14213,U_14210),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14213,U_14210),U_14214),hAPP(c_COMBK(tc_fun(U_14210,tc_HOL_Obool),U_14213),U_14212))),hAPP(hAPP(c_Product__Type_OSigma(U_14213,U_14210),U_14215),hAPP(c_COMBK(tc_fun(U_14210,tc_HOL_Obool),U_14213),U_14212))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14213,tc_HOL_Obool)),U_14214),U_14215))
    | ~ sP983(U_14210,U_14212,U_14213,U_14214,U_14215) ),
    inference(clausify,[status(thm)],[f_3571_3]) ).

fof(f_3572_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_3572_2,plain,
    ! [U_14221,U_14220,U_14219,U_14218,U_14217,U_14216] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14217,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14216,U_14217,U_14218),U_14221)),U_14220))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14216,U_14217),tc_HOL_Obool)),U_14218),hAPP(hAPP(c_Product__Type_OSigma(U_14216,U_14217),U_14219),hAPP(c_COMBK(tc_fun(U_14217,tc_HOL_Obool),U_14216),U_14220)))) ),
    inference(variable_rename,[status(thm)],[f_3572_1]) ).

fof(f_3572_3,plain,
    ! [U_14217,U_14216,U_14218,U_14219,U_14220,U_14221] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14217,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14216,U_14217,U_14218),U_14221)),U_14220))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14216,U_14217),tc_HOL_Obool)),U_14218),hAPP(hAPP(c_Product__Type_OSigma(U_14216,U_14217),U_14219),hAPP(c_COMBK(tc_fun(U_14217,tc_HOL_Obool),U_14216),U_14220)))) ),
    inference(definitional_conversion,[status(esa)],[f_3572_2]) ).

cnf(f_3572_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14217,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14216,U_14217,U_14218),U_14221)),U_14220))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14216,U_14217),tc_HOL_Obool)),U_14218),hAPP(hAPP(c_Product__Type_OSigma(U_14216,U_14217),U_14219),hAPP(c_COMBK(tc_fun(U_14217,tc_HOL_Obool),U_14216),U_14220)))) ),
    inference(clausify,[status(thm)],[f_3572_3]) ).

fof(f_3573_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_3573_2,plain,
    ! [U_14225,U_14224,U_14223,U_14222] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14223),U_14225))
      | U_14224 = c_Orderings_Obot__class_Obot(tc_fun(U_14222,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14222,U_14223)),hAPP(hAPP(c_Product__Type_OSigma(U_14222,U_14223),U_14224),hAPP(c_COMBK(tc_fun(U_14223,tc_HOL_Obool),U_14222),U_14225)))) ),
    inference(variable_rename,[status(thm)],[f_3573_1]) ).

fof(f_3573_3,plain,
    ! [U_14222,U_14223,U_14224,U_14225] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14223),U_14225))
      | U_14224 = c_Orderings_Obot__class_Obot(tc_fun(U_14222,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14222,U_14223)),hAPP(hAPP(c_Product__Type_OSigma(U_14222,U_14223),U_14224),hAPP(c_COMBK(tc_fun(U_14223,tc_HOL_Obool),U_14222),U_14225)))) ),
    inference(definitional_conversion,[status(esa)],[f_3573_2]) ).

cnf(f_3573_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14223),U_14225))
    | U_14224 = c_Orderings_Obot__class_Obot(tc_fun(U_14222,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14222,U_14223)),hAPP(hAPP(c_Product__Type_OSigma(U_14222,U_14223),U_14224),hAPP(c_COMBK(tc_fun(U_14223,tc_HOL_Obool),U_14222),U_14225)))) ),
    inference(clausify,[status(thm)],[f_3573_3]) ).

fof(f_3574_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_3574_2,plain,
    ! [U_14229,U_14228,U_14227,U_14226] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14226),U_14228))
      | U_14229 = c_Orderings_Obot__class_Obot(tc_fun(U_14227,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14226,U_14227)),hAPP(hAPP(c_Product__Type_OSigma(U_14226,U_14227),U_14228),hAPP(c_COMBK(tc_fun(U_14227,tc_HOL_Obool),U_14226),U_14229)))) ),
    inference(variable_rename,[status(thm)],[f_3574_1]) ).

fof(f_3574_3,plain,
    ! [U_14226,U_14227,U_14228,U_14229] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14226),U_14228))
      | U_14229 = c_Orderings_Obot__class_Obot(tc_fun(U_14227,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14226,U_14227)),hAPP(hAPP(c_Product__Type_OSigma(U_14226,U_14227),U_14228),hAPP(c_COMBK(tc_fun(U_14227,tc_HOL_Obool),U_14226),U_14229)))) ),
    inference(definitional_conversion,[status(esa)],[f_3574_2]) ).

cnf(f_3574_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14226),U_14228))
    | U_14229 = c_Orderings_Obot__class_Obot(tc_fun(U_14227,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14226,U_14227)),hAPP(hAPP(c_Product__Type_OSigma(U_14226,U_14227),U_14228),hAPP(c_COMBK(tc_fun(U_14227,tc_HOL_Obool),U_14226),U_14229)))) ),
    inference(clausify,[status(thm)],[f_3574_3]) ).

fof(f_3575_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_3575_2,plain,
    ! [U_14233,U_14232,U_14231,U_14230] :
      ( ( hAPP(c_Set_Oimage(tc_prod(U_14232,U_14231),U_14232,c_Product__Type_Ofst(U_14232,U_14231)),hAPP(hAPP(c_Product__Type_OSigma(U_14232,U_14231),U_14233),hAPP(c_COMBK(tc_fun(U_14231,tc_HOL_Obool),U_14232),U_14230))) = U_14233
        | U_14230 = c_Orderings_Obot__class_Obot(tc_fun(U_14231,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(U_14232,U_14231),U_14232,c_Product__Type_Ofst(U_14232,U_14231)),hAPP(hAPP(c_Product__Type_OSigma(U_14232,U_14231),U_14233),hAPP(c_COMBK(tc_fun(U_14231,tc_HOL_Obool),U_14232),U_14230))) = c_Orderings_Obot__class_Obot(tc_fun(U_14232,tc_HOL_Obool))
        | U_14230 != c_Orderings_Obot__class_Obot(tc_fun(U_14231,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3575_1]) ).

fof(f_3575_3,plain,
    ( ! [U_14241,U_14239,U_14237,U_14235] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14239,U_14237),U_14239,c_Product__Type_Ofst(U_14239,U_14237)),hAPP(hAPP(c_Product__Type_OSigma(U_14239,U_14237),U_14241),hAPP(c_COMBK(tc_fun(U_14237,tc_HOL_Obool),U_14239),U_14235))) = U_14241
        | U_14235 = c_Orderings_Obot__class_Obot(tc_fun(U_14237,tc_HOL_Obool)) )
    & ! [U_14240,U_14238,U_14236,U_14234] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14238,U_14236),U_14238,c_Product__Type_Ofst(U_14238,U_14236)),hAPP(hAPP(c_Product__Type_OSigma(U_14238,U_14236),U_14240),hAPP(c_COMBK(tc_fun(U_14236,tc_HOL_Obool),U_14238),U_14234))) = c_Orderings_Obot__class_Obot(tc_fun(U_14238,tc_HOL_Obool))
        | U_14234 != c_Orderings_Obot__class_Obot(tc_fun(U_14236,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3575_2]) ).

fof(f_3575_4,plain,
    ( ! [U_14235,U_14237,U_14239,U_14241] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14239,U_14237),U_14239,c_Product__Type_Ofst(U_14239,U_14237)),hAPP(hAPP(c_Product__Type_OSigma(U_14239,U_14237),U_14241),hAPP(c_COMBK(tc_fun(U_14237,tc_HOL_Obool),U_14239),U_14235))) = U_14241
        | U_14235 = c_Orderings_Obot__class_Obot(tc_fun(U_14237,tc_HOL_Obool)) )
    & ! [U_14238,U_14236,U_14240,U_14234] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14238,U_14236),U_14238,c_Product__Type_Ofst(U_14238,U_14236)),hAPP(hAPP(c_Product__Type_OSigma(U_14238,U_14236),U_14240),hAPP(c_COMBK(tc_fun(U_14236,tc_HOL_Obool),U_14238),U_14234))) = c_Orderings_Obot__class_Obot(tc_fun(U_14238,tc_HOL_Obool))
        | U_14234 != c_Orderings_Obot__class_Obot(tc_fun(U_14236,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3575_3]) ).

cnf(f_3575_5,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_14238,U_14236),U_14238,c_Product__Type_Ofst(U_14238,U_14236)),hAPP(hAPP(c_Product__Type_OSigma(U_14238,U_14236),U_14240),hAPP(c_COMBK(tc_fun(U_14236,tc_HOL_Obool),U_14238),U_14234))) = c_Orderings_Obot__class_Obot(tc_fun(U_14238,tc_HOL_Obool))
    | U_14234 != c_Orderings_Obot__class_Obot(tc_fun(U_14236,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3575_4]) ).

cnf(f_3575_6,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_14239,U_14237),U_14239,c_Product__Type_Ofst(U_14239,U_14237)),hAPP(hAPP(c_Product__Type_OSigma(U_14239,U_14237),U_14241),hAPP(c_COMBK(tc_fun(U_14237,tc_HOL_Obool),U_14239),U_14235))) = U_14241
    | U_14235 = c_Orderings_Obot__class_Obot(tc_fun(U_14237,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3575_4]) ).

fof(f_3576_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_3576_2,plain,
    ! [U_14245,U_14244,U_14243,U_14242] :
      ( ( hAPP(c_Set_Oimage(tc_prod(U_14243,U_14244),U_14244,c_Product__Type_Osnd(U_14243,U_14244)),hAPP(hAPP(c_Product__Type_OSigma(U_14243,U_14244),U_14242),hAPP(c_COMBK(tc_fun(U_14244,tc_HOL_Obool),U_14243),U_14245))) = U_14245
        | U_14242 = c_Orderings_Obot__class_Obot(tc_fun(U_14243,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(U_14243,U_14244),U_14244,c_Product__Type_Osnd(U_14243,U_14244)),hAPP(hAPP(c_Product__Type_OSigma(U_14243,U_14244),U_14242),hAPP(c_COMBK(tc_fun(U_14244,tc_HOL_Obool),U_14243),U_14245))) = c_Orderings_Obot__class_Obot(tc_fun(U_14244,tc_HOL_Obool))
        | U_14242 != c_Orderings_Obot__class_Obot(tc_fun(U_14243,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3576_1]) ).

fof(f_3576_3,plain,
    ( ! [U_14253,U_14251,U_14249,U_14247] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14249,U_14251),U_14251,c_Product__Type_Osnd(U_14249,U_14251)),hAPP(hAPP(c_Product__Type_OSigma(U_14249,U_14251),U_14247),hAPP(c_COMBK(tc_fun(U_14251,tc_HOL_Obool),U_14249),U_14253))) = U_14253
        | U_14247 = c_Orderings_Obot__class_Obot(tc_fun(U_14249,tc_HOL_Obool)) )
    & ! [U_14252,U_14250,U_14248,U_14246] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14248,U_14250),U_14250,c_Product__Type_Osnd(U_14248,U_14250)),hAPP(hAPP(c_Product__Type_OSigma(U_14248,U_14250),U_14246),hAPP(c_COMBK(tc_fun(U_14250,tc_HOL_Obool),U_14248),U_14252))) = c_Orderings_Obot__class_Obot(tc_fun(U_14250,tc_HOL_Obool))
        | U_14246 != c_Orderings_Obot__class_Obot(tc_fun(U_14248,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3576_2]) ).

fof(f_3576_4,plain,
    ( ! [U_14247,U_14249,U_14251,U_14253] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14249,U_14251),U_14251,c_Product__Type_Osnd(U_14249,U_14251)),hAPP(hAPP(c_Product__Type_OSigma(U_14249,U_14251),U_14247),hAPP(c_COMBK(tc_fun(U_14251,tc_HOL_Obool),U_14249),U_14253))) = U_14253
        | U_14247 = c_Orderings_Obot__class_Obot(tc_fun(U_14249,tc_HOL_Obool)) )
    & ! [U_14250,U_14252,U_14248,U_14246] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14248,U_14250),U_14250,c_Product__Type_Osnd(U_14248,U_14250)),hAPP(hAPP(c_Product__Type_OSigma(U_14248,U_14250),U_14246),hAPP(c_COMBK(tc_fun(U_14250,tc_HOL_Obool),U_14248),U_14252))) = c_Orderings_Obot__class_Obot(tc_fun(U_14250,tc_HOL_Obool))
        | U_14246 != c_Orderings_Obot__class_Obot(tc_fun(U_14248,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3576_3]) ).

cnf(f_3576_5,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_14248,U_14250),U_14250,c_Product__Type_Osnd(U_14248,U_14250)),hAPP(hAPP(c_Product__Type_OSigma(U_14248,U_14250),U_14246),hAPP(c_COMBK(tc_fun(U_14250,tc_HOL_Obool),U_14248),U_14252))) = c_Orderings_Obot__class_Obot(tc_fun(U_14250,tc_HOL_Obool))
    | U_14246 != c_Orderings_Obot__class_Obot(tc_fun(U_14248,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3576_4]) ).

cnf(f_3576_6,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_14249,U_14251),U_14251,c_Product__Type_Osnd(U_14249,U_14251)),hAPP(hAPP(c_Product__Type_OSigma(U_14249,U_14251),U_14247),hAPP(c_COMBK(tc_fun(U_14251,tc_HOL_Obool),U_14249),U_14253))) = U_14253
    | U_14247 = c_Orderings_Obot__class_Obot(tc_fun(U_14249,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3576_4]) ).

fof(f_3577_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_3577_2,plain,
    ! [U_14256,U_14255,U_14254] : hAPP(c_Finite__Set_Ofold1(U_14254,U_14255),U_14256) = c_HOL_OThe(U_14254,c_Finite__Set_Ofold1Set(U_14254,U_14255,U_14256)),
    inference(variable_rename,[status(thm)],[f_3577_1]) ).

fof(f_3577_3,plain,
    ! [U_14255,U_14254,U_14256] : hAPP(c_Finite__Set_Ofold1(U_14254,U_14255),U_14256) = c_HOL_OThe(U_14254,c_Finite__Set_Ofold1Set(U_14254,U_14255,U_14256)),
    inference(definitional_conversion,[status(esa)],[f_3577_2]) ).

cnf(f_3577_4,plain,
    hAPP(c_Finite__Set_Ofold1(U_14254,U_14255),U_14256) = c_HOL_OThe(U_14254,c_Finite__Set_Ofold1Set(U_14254,U_14255,U_14256)),
    inference(clausify,[status(thm)],[f_3577_3]) ).

fof(f_3578_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_3578_2,plain,
    ! [U_14258,U_14257] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_14257,U_14258) = hAPP(c_Finite__Set_Ofold1(U_14257,c_Lattices_Osemilattice__sup__class_Osup(U_14257)),U_14258)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14257),U_14258))
      | ~ class_Lattices_Olattice(U_14257) ),
    inference(variable_rename,[status(thm)],[f_3578_1]) ).

fof(f_3578_3,plain,
    ! [U_14257,U_14258] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_14257,U_14258) = hAPP(c_Finite__Set_Ofold1(U_14257,c_Lattices_Osemilattice__sup__class_Osup(U_14257)),U_14258)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14257),U_14258))
      | ~ class_Lattices_Olattice(U_14257) ),
    inference(definitional_conversion,[status(esa)],[f_3578_2]) ).

cnf(f_3578_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_14257,U_14258) = hAPP(c_Finite__Set_Ofold1(U_14257,c_Lattices_Osemilattice__sup__class_Osup(U_14257)),U_14258)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14257),U_14258))
    | ~ class_Lattices_Olattice(U_14257) ),
    inference(clausify,[status(thm)],[f_3578_3]) ).

fof(f_3579_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_3579_2,plain,
    ! [U_14260,U_14259] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_14259,U_14260) = hAPP(c_Finite__Set_Ofold1(U_14259,c_Lattices_Osemilattice__inf__class_Oinf(U_14259)),U_14260)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14259),U_14260))
      | ~ class_Lattices_Olattice(U_14259) ),
    inference(variable_rename,[status(thm)],[f_3579_1]) ).

fof(f_3579_3,plain,
    ! [U_14259,U_14260] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_14259,U_14260) = hAPP(c_Finite__Set_Ofold1(U_14259,c_Lattices_Osemilattice__inf__class_Oinf(U_14259)),U_14260)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14259),U_14260))
      | ~ class_Lattices_Olattice(U_14259) ),
    inference(definitional_conversion,[status(esa)],[f_3579_2]) ).

cnf(f_3579_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_14259,U_14260) = hAPP(c_Finite__Set_Ofold1(U_14259,c_Lattices_Osemilattice__inf__class_Oinf(U_14259)),U_14260)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14259),U_14260))
    | ~ class_Lattices_Olattice(U_14259) ),
    inference(clausify,[status(thm)],[f_3579_3]) ).

fof(f_3580_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_3580_2,plain,
    ! [U_14262,U_14261] :
      ( c_Big__Operators_Olinorder__class_OMin(U_14261,U_14262) = hAPP(c_Finite__Set_Ofold1(U_14261,c_Orderings_Oord__class_Omin(U_14261)),U_14262)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14261),U_14262))
      | ~ class_Orderings_Olinorder(U_14261) ),
    inference(variable_rename,[status(thm)],[f_3580_1]) ).

fof(f_3580_3,plain,
    ! [U_14261,U_14262] :
      ( c_Big__Operators_Olinorder__class_OMin(U_14261,U_14262) = hAPP(c_Finite__Set_Ofold1(U_14261,c_Orderings_Oord__class_Omin(U_14261)),U_14262)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14261),U_14262))
      | ~ class_Orderings_Olinorder(U_14261) ),
    inference(definitional_conversion,[status(esa)],[f_3580_2]) ).

cnf(f_3580_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_14261,U_14262) = hAPP(c_Finite__Set_Ofold1(U_14261,c_Orderings_Oord__class_Omin(U_14261)),U_14262)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14261),U_14262))
    | ~ class_Orderings_Olinorder(U_14261) ),
    inference(clausify,[status(thm)],[f_3580_3]) ).

fof(f_3581_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_3581_2,plain,
    ! [U_14264,U_14263] :
      ( c_Big__Operators_Olinorder__class_OMax(U_14263,U_14264) = hAPP(c_Finite__Set_Ofold1(U_14263,c_Orderings_Oord__class_Omax(U_14263)),U_14264)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14263),U_14264))
      | ~ class_Orderings_Olinorder(U_14263) ),
    inference(variable_rename,[status(thm)],[f_3581_1]) ).

fof(f_3581_3,plain,
    ! [U_14263,U_14264] :
      ( c_Big__Operators_Olinorder__class_OMax(U_14263,U_14264) = hAPP(c_Finite__Set_Ofold1(U_14263,c_Orderings_Oord__class_Omax(U_14263)),U_14264)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14263),U_14264))
      | ~ class_Orderings_Olinorder(U_14263) ),
    inference(definitional_conversion,[status(esa)],[f_3581_2]) ).

cnf(f_3581_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_14263,U_14264) = hAPP(c_Finite__Set_Ofold1(U_14263,c_Orderings_Oord__class_Omax(U_14263)),U_14264)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14263),U_14264))
    | ~ class_Orderings_Olinorder(U_14263) ),
    inference(clausify,[status(thm)],[f_3581_3]) ).

fof(f_3582_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_3582_2,plain,
    ! [U_14266,U_14265] :
      ( c_Big__Operators_Olattice_OInf__fin(U_14265,c_Orderings_Oord__class_Omin(U_14265),U_14266) = hAPP(c_Finite__Set_Ofold1(U_14265,c_Orderings_Oord__class_Omin(U_14265)),U_14266)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14265),U_14266))
      | ~ class_Orderings_Olinorder(U_14265) ),
    inference(variable_rename,[status(thm)],[f_3582_1]) ).

fof(f_3582_3,plain,
    ! [U_14265,U_14266] :
      ( c_Big__Operators_Olattice_OInf__fin(U_14265,c_Orderings_Oord__class_Omin(U_14265),U_14266) = hAPP(c_Finite__Set_Ofold1(U_14265,c_Orderings_Oord__class_Omin(U_14265)),U_14266)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14265),U_14266))
      | ~ class_Orderings_Olinorder(U_14265) ),
    inference(definitional_conversion,[status(esa)],[f_3582_2]) ).

cnf(f_3582_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_14265,c_Orderings_Oord__class_Omin(U_14265),U_14266) = hAPP(c_Finite__Set_Ofold1(U_14265,c_Orderings_Oord__class_Omin(U_14265)),U_14266)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14265),U_14266))
    | ~ class_Orderings_Olinorder(U_14265) ),
    inference(clausify,[status(thm)],[f_3582_3]) ).

fof(f_3583_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_3583_2,plain,
    ! [U_14268,U_14267] :
      ( c_Big__Operators_Olattice_OSup__fin(U_14267,c_Orderings_Oord__class_Omax(U_14267),U_14268) = hAPP(c_Finite__Set_Ofold1(U_14267,c_Orderings_Oord__class_Omax(U_14267)),U_14268)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14267),U_14268))
      | ~ class_Orderings_Olinorder(U_14267) ),
    inference(variable_rename,[status(thm)],[f_3583_1]) ).

fof(f_3583_3,plain,
    ! [U_14267,U_14268] :
      ( c_Big__Operators_Olattice_OSup__fin(U_14267,c_Orderings_Oord__class_Omax(U_14267),U_14268) = hAPP(c_Finite__Set_Ofold1(U_14267,c_Orderings_Oord__class_Omax(U_14267)),U_14268)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14267),U_14268))
      | ~ class_Orderings_Olinorder(U_14267) ),
    inference(definitional_conversion,[status(esa)],[f_3583_2]) ).

cnf(f_3583_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_14267,c_Orderings_Oord__class_Omax(U_14267),U_14268) = hAPP(c_Finite__Set_Ofold1(U_14267,c_Orderings_Oord__class_Omax(U_14267)),U_14268)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14267),U_14268))
    | ~ class_Orderings_Olinorder(U_14267) ),
    inference(clausify,[status(thm)],[f_3583_3]) ).

fof(f_3584_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_3584_2,plain,
    ! [U_14273,U_14272,U_14271] :
      ( ( c_Relation_Orefl__on(U_14271,U_14272,U_14273)
        | ? [U_14270] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14271,U_14271)),hAPP(hAPP(c_Product__Type_OPair(U_14271,U_14271),U_14270),U_14270)),U_14273))
            & hBOOL(hAPP(hAPP(c_member(U_14271),U_14270),U_14272)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14271,U_14271),tc_HOL_Obool)),U_14273),hAPP(hAPP(c_Product__Type_OSigma(U_14271,U_14271),U_14272),hAPP(c_COMBK(tc_fun(U_14271,tc_HOL_Obool),U_14271),U_14272)))) )
      & ( ( ! [U_14269] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14271,U_14271)),hAPP(hAPP(c_Product__Type_OPair(U_14271,U_14271),U_14269),U_14269)),U_14273))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14271),U_14269),U_14272)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14271,U_14271),tc_HOL_Obool)),U_14273),hAPP(hAPP(c_Product__Type_OSigma(U_14271,U_14271),U_14272),hAPP(c_COMBK(tc_fun(U_14271,tc_HOL_Obool),U_14271),U_14272)))) )
        | ~ c_Relation_Orefl__on(U_14271,U_14272,U_14273) ) ),
    inference(variable_rename,[status(thm)],[f_3584_1]) ).

fof(f_3584_3,plain,
    ( ! [U_14279,U_14277,U_14275] :
        ( c_Relation_Orefl__on(U_14275,U_14277,U_14279)
        | ? [U_14270] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14275,U_14275)),hAPP(hAPP(c_Product__Type_OPair(U_14275,U_14275),U_14270),U_14270)),U_14279))
            & hBOOL(hAPP(hAPP(c_member(U_14275),U_14270),U_14277)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14275,U_14275),tc_HOL_Obool)),U_14279),hAPP(hAPP(c_Product__Type_OSigma(U_14275,U_14275),U_14277),hAPP(c_COMBK(tc_fun(U_14275,tc_HOL_Obool),U_14275),U_14277)))) )
    & ! [U_14278,U_14276,U_14274] :
        ( ( ! [U_14269] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14274,U_14274)),hAPP(hAPP(c_Product__Type_OPair(U_14274,U_14274),U_14269),U_14269)),U_14278))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14274),U_14269),U_14276)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14274,U_14274),tc_HOL_Obool)),U_14278),hAPP(hAPP(c_Product__Type_OSigma(U_14274,U_14274),U_14276),hAPP(c_COMBK(tc_fun(U_14274,tc_HOL_Obool),U_14274),U_14276)))) )
        | ~ c_Relation_Orefl__on(U_14274,U_14276,U_14278) ) ),
    inference(miniscope,[status(thm)],[f_3584_2]) ).

fof(f_3584_4,plain,
    ( ! [U_14279,U_14277,U_14275] :
        ( c_Relation_Orefl__on(U_14275,U_14277,U_14279)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14275,U_14275)),hAPP(hAPP(c_Product__Type_OPair(U_14275,U_14275),sK304(U_14279,U_14277,U_14275)),sK304(U_14279,U_14277,U_14275))),U_14279))
          & hBOOL(hAPP(hAPP(c_member(U_14275),sK304(U_14279,U_14277,U_14275)),U_14277)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14275,U_14275),tc_HOL_Obool)),U_14279),hAPP(hAPP(c_Product__Type_OSigma(U_14275,U_14275),U_14277),hAPP(c_COMBK(tc_fun(U_14275,tc_HOL_Obool),U_14275),U_14277)))) )
    & ! [U_14278,U_14276,U_14274] :
        ( ( ! [U_14269] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14274,U_14274)),hAPP(hAPP(c_Product__Type_OPair(U_14274,U_14274),U_14269),U_14269)),U_14278))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14274),U_14269),U_14276)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14274,U_14274),tc_HOL_Obool)),U_14278),hAPP(hAPP(c_Product__Type_OSigma(U_14274,U_14274),U_14276),hAPP(c_COMBK(tc_fun(U_14274,tc_HOL_Obool),U_14274),U_14276)))) )
        | ~ c_Relation_Orefl__on(U_14274,U_14276,U_14278) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK304]),skolemize(U_14270,sK304(U_14279,U_14277,U_14275))],[f_3584_3]) ).

fof(f_3584_5,plain,
    ( ! [U_14277,U_14279,U_14275] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14275,U_14275)),hAPP(hAPP(c_Product__Type_OPair(U_14275,U_14275),sK304(U_14279,U_14277,U_14275)),sK304(U_14279,U_14277,U_14275))),U_14279))
        | ~ sP985(U_14277,U_14279,U_14275) )
    & ! [U_14277,U_14279,U_14275] :
        ( hBOOL(hAPP(hAPP(c_member(U_14275),sK304(U_14279,U_14277,U_14275)),U_14277))
        | ~ sP985(U_14277,U_14279,U_14275) )
    & ! [U_14269,U_14274,U_14276,U_14278] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14274,U_14274)),hAPP(hAPP(c_Product__Type_OPair(U_14274,U_14274),U_14269),U_14269)),U_14278))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14274),U_14269),U_14276))
        | ~ sP984(U_14269,U_14274,U_14276,U_14278) )
    & ! [U_14269,U_14274,U_14276,U_14278] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14274,U_14274),tc_HOL_Obool)),U_14278),hAPP(hAPP(c_Product__Type_OSigma(U_14274,U_14274),U_14276),hAPP(c_COMBK(tc_fun(U_14274,tc_HOL_Obool),U_14274),U_14276))))
        | ~ sP984(U_14269,U_14274,U_14276,U_14278) )
    & ! [U_14277,U_14279,U_14275] :
        ( c_Relation_Orefl__on(U_14275,U_14277,U_14279)
        | sP985(U_14277,U_14279,U_14275)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14275,U_14275),tc_HOL_Obool)),U_14279),hAPP(hAPP(c_Product__Type_OSigma(U_14275,U_14275),U_14277),hAPP(c_COMBK(tc_fun(U_14275,tc_HOL_Obool),U_14275),U_14277)))) )
    & ! [U_14269,U_14274,U_14276,U_14278] :
        ( sP984(U_14269,U_14274,U_14276,U_14278)
        | ~ c_Relation_Orefl__on(U_14274,U_14276,U_14278) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP984,sP985])],[f_3584_4]) ).

cnf(f_3584_6,plain,
    ( sP984(U_14269,U_14274,U_14276,U_14278)
    | ~ c_Relation_Orefl__on(U_14274,U_14276,U_14278) ),
    inference(clausify,[status(thm)],[f_3584_5]) ).

cnf(f_3584_7,plain,
    ( c_Relation_Orefl__on(U_14275,U_14277,U_14279)
    | sP985(U_14277,U_14279,U_14275)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14275,U_14275),tc_HOL_Obool)),U_14279),hAPP(hAPP(c_Product__Type_OSigma(U_14275,U_14275),U_14277),hAPP(c_COMBK(tc_fun(U_14275,tc_HOL_Obool),U_14275),U_14277)))) ),
    inference(clausify,[status(thm)],[f_3584_5]) ).

cnf(f_3584_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14274,U_14274),tc_HOL_Obool)),U_14278),hAPP(hAPP(c_Product__Type_OSigma(U_14274,U_14274),U_14276),hAPP(c_COMBK(tc_fun(U_14274,tc_HOL_Obool),U_14274),U_14276))))
    | ~ sP984(U_14269,U_14274,U_14276,U_14278) ),
    inference(clausify,[status(thm)],[f_3584_5]) ).

cnf(f_3584_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14274,U_14274)),hAPP(hAPP(c_Product__Type_OPair(U_14274,U_14274),U_14269),U_14269)),U_14278))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14274),U_14269),U_14276))
    | ~ sP984(U_14269,U_14274,U_14276,U_14278) ),
    inference(clausify,[status(thm)],[f_3584_5]) ).

cnf(f_3584_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14275),sK304(U_14279,U_14277,U_14275)),U_14277))
    | ~ sP985(U_14277,U_14279,U_14275) ),
    inference(clausify,[status(thm)],[f_3584_5]) ).

cnf(f_3584_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14275,U_14275)),hAPP(hAPP(c_Product__Type_OPair(U_14275,U_14275),sK304(U_14279,U_14277,U_14275)),sK304(U_14279,U_14277,U_14275))),U_14279))
    | ~ sP985(U_14277,U_14279,U_14275) ),
    inference(clausify,[status(thm)],[f_3584_5]) ).

fof(f_3585_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_3585_2,plain,
    ! [U_14285,U_14284,U_14283,U_14282,U_14281,U_14280] : hAPP(hAPP(c_Product__Type_OSigma(U_14280,U_14281),hAPP(hAPP(c_Set_Oinsert(U_14280),U_14282),U_14283)),hAPP(c_COMBK(tc_fun(U_14281,tc_HOL_Obool),U_14280),hAPP(hAPP(c_Set_Oinsert(U_14281),U_14284),U_14285))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14280,U_14281)),hAPP(hAPP(c_Product__Type_OPair(U_14280,U_14281),U_14282),U_14284)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14280,U_14281),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14280,U_14281),U_14283),hAPP(c_COMBK(tc_fun(U_14281,tc_HOL_Obool),U_14280),hAPP(hAPP(c_Set_Oinsert(U_14281),U_14284),U_14285)))),hAPP(hAPP(c_Product__Type_OSigma(U_14280,U_14281),hAPP(hAPP(c_Set_Oinsert(U_14280),U_14282),U_14283)),hAPP(c_COMBK(tc_fun(U_14281,tc_HOL_Obool),U_14280),U_14285)))),
    inference(variable_rename,[status(thm)],[f_3585_1]) ).

fof(f_3585_3,plain,
    ! [U_14280,U_14281,U_14282,U_14283,U_14284,U_14285] : hAPP(hAPP(c_Product__Type_OSigma(U_14280,U_14281),hAPP(hAPP(c_Set_Oinsert(U_14280),U_14282),U_14283)),hAPP(c_COMBK(tc_fun(U_14281,tc_HOL_Obool),U_14280),hAPP(hAPP(c_Set_Oinsert(U_14281),U_14284),U_14285))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14280,U_14281)),hAPP(hAPP(c_Product__Type_OPair(U_14280,U_14281),U_14282),U_14284)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14280,U_14281),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14280,U_14281),U_14283),hAPP(c_COMBK(tc_fun(U_14281,tc_HOL_Obool),U_14280),hAPP(hAPP(c_Set_Oinsert(U_14281),U_14284),U_14285)))),hAPP(hAPP(c_Product__Type_OSigma(U_14280,U_14281),hAPP(hAPP(c_Set_Oinsert(U_14280),U_14282),U_14283)),hAPP(c_COMBK(tc_fun(U_14281,tc_HOL_Obool),U_14280),U_14285)))),
    inference(definitional_conversion,[status(esa)],[f_3585_2]) ).

cnf(f_3585_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14280,U_14281),hAPP(hAPP(c_Set_Oinsert(U_14280),U_14282),U_14283)),hAPP(c_COMBK(tc_fun(U_14281,tc_HOL_Obool),U_14280),hAPP(hAPP(c_Set_Oinsert(U_14281),U_14284),U_14285))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14280,U_14281)),hAPP(hAPP(c_Product__Type_OPair(U_14280,U_14281),U_14282),U_14284)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14280,U_14281),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14280,U_14281),U_14283),hAPP(c_COMBK(tc_fun(U_14281,tc_HOL_Obool),U_14280),hAPP(hAPP(c_Set_Oinsert(U_14281),U_14284),U_14285)))),hAPP(hAPP(c_Product__Type_OSigma(U_14280,U_14281),hAPP(hAPP(c_Set_Oinsert(U_14280),U_14282),U_14283)),hAPP(c_COMBK(tc_fun(U_14281,tc_HOL_Obool),U_14280),U_14285)))),
    inference(clausify,[status(thm)],[f_3585_3]) ).

fof(f_3586_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_3586_2,plain,
    ! [U_14289,U_14288,U_14287,U_14286] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14286),U_14289))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_14286,tc_HOL_Obool)),U_14289),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_14286),U_14287),U_14288)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14286,U_14286),tc_HOL_Obool)),U_14288),hAPP(hAPP(c_Product__Type_OSigma(U_14286,U_14286),U_14287),hAPP(c_COMBK(tc_fun(U_14286,tc_HOL_Obool),U_14286),U_14287))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14286),U_14287)) ),
    inference(variable_rename,[status(thm)],[f_3586_1]) ).

fof(f_3586_3,plain,
    ! [U_14286,U_14287,U_14288,U_14289] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14286),U_14289))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_14286,tc_HOL_Obool)),U_14289),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_14286),U_14287),U_14288)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14286,U_14286),tc_HOL_Obool)),U_14288),hAPP(hAPP(c_Product__Type_OSigma(U_14286,U_14286),U_14287),hAPP(c_COMBK(tc_fun(U_14286,tc_HOL_Obool),U_14286),U_14287))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14286),U_14287)) ),
    inference(definitional_conversion,[status(esa)],[f_3586_2]) ).

cnf(f_3586_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14286),U_14289))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_14286,tc_HOL_Obool)),U_14289),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_14286),U_14287),U_14288)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14286,U_14286),tc_HOL_Obool)),U_14288),hAPP(hAPP(c_Product__Type_OSigma(U_14286,U_14286),U_14287),hAPP(c_COMBK(tc_fun(U_14286,tc_HOL_Obool),U_14286),U_14287))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14286),U_14287)) ),
    inference(clausify,[status(thm)],[f_3586_3]) ).

fof(f_3587_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_3587_2,plain,
    ! [U_14297,U_14296,U_14295,U_14294,U_14293,U_14292,U_14291,U_14290] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_14290,U_14291),tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14290,U_14291),U_14294),hAPP(c_COMBK(tc_fun(U_14291,tc_HOL_Obool),U_14290),U_14295))),hAPP(c_Product__Type_Oprod_Oprod__case(U_14290,U_14291,tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_14290,tc_fun(U_14291,tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool))),tc_fun(U_14291,tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool)),tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool)),tc_fun(tc_fun(U_14291,tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool))),tc_fun(U_14291,tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool))),U_14290),c_COMBB(tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool)),tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool),U_14291)),hAPP(hAPP(c_COMBB(tc_fun(U_14292,tc_HOL_Obool),tc_fun(tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool)),tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool)),U_14290),c_Product__Type_OSigma(U_14292,U_14293)),U_14296))),hAPP(hAPP(c_COMBB(tc_fun(U_14293,tc_HOL_Obool),tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool)),U_14291),c_COMBK(tc_fun(U_14293,tc_HOL_Obool),U_14292)),U_14297)))) = hAPP(hAPP(c_Product__Type_OSigma(U_14292,U_14293),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14290,tc_fun(U_14292,tc_HOL_Obool)),U_14294),U_14296)),hAPP(c_COMBK(tc_fun(U_14293,tc_HOL_Obool),U_14292),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14291,tc_fun(U_14293,tc_HOL_Obool)),U_14295),U_14297))),
    inference(variable_rename,[status(thm)],[f_3587_1]) ).

fof(f_3587_3,plain,
    ! [U_14290,U_14291,U_14292,U_14293,U_14294,U_14295,U_14296,U_14297] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_14290,U_14291),tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14290,U_14291),U_14294),hAPP(c_COMBK(tc_fun(U_14291,tc_HOL_Obool),U_14290),U_14295))),hAPP(c_Product__Type_Oprod_Oprod__case(U_14290,U_14291,tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_14290,tc_fun(U_14291,tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool))),tc_fun(U_14291,tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool)),tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool)),tc_fun(tc_fun(U_14291,tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool))),tc_fun(U_14291,tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool))),U_14290),c_COMBB(tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool)),tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool),U_14291)),hAPP(hAPP(c_COMBB(tc_fun(U_14292,tc_HOL_Obool),tc_fun(tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool)),tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool)),U_14290),c_Product__Type_OSigma(U_14292,U_14293)),U_14296))),hAPP(hAPP(c_COMBB(tc_fun(U_14293,tc_HOL_Obool),tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool)),U_14291),c_COMBK(tc_fun(U_14293,tc_HOL_Obool),U_14292)),U_14297)))) = hAPP(hAPP(c_Product__Type_OSigma(U_14292,U_14293),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14290,tc_fun(U_14292,tc_HOL_Obool)),U_14294),U_14296)),hAPP(c_COMBK(tc_fun(U_14293,tc_HOL_Obool),U_14292),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14291,tc_fun(U_14293,tc_HOL_Obool)),U_14295),U_14297))),
    inference(definitional_conversion,[status(esa)],[f_3587_2]) ).

cnf(f_3587_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_14290,U_14291),tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14290,U_14291),U_14294),hAPP(c_COMBK(tc_fun(U_14291,tc_HOL_Obool),U_14290),U_14295))),hAPP(c_Product__Type_Oprod_Oprod__case(U_14290,U_14291,tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_14290,tc_fun(U_14291,tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool))),tc_fun(U_14291,tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool)),tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool)),tc_fun(tc_fun(U_14291,tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool))),tc_fun(U_14291,tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool))),U_14290),c_COMBB(tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool)),tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool),U_14291)),hAPP(hAPP(c_COMBB(tc_fun(U_14292,tc_HOL_Obool),tc_fun(tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool)),tc_fun(tc_prod(U_14292,U_14293),tc_HOL_Obool)),U_14290),c_Product__Type_OSigma(U_14292,U_14293)),U_14296))),hAPP(hAPP(c_COMBB(tc_fun(U_14293,tc_HOL_Obool),tc_fun(U_14292,tc_fun(U_14293,tc_HOL_Obool)),U_14291),c_COMBK(tc_fun(U_14293,tc_HOL_Obool),U_14292)),U_14297)))) = hAPP(hAPP(c_Product__Type_OSigma(U_14292,U_14293),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14290,tc_fun(U_14292,tc_HOL_Obool)),U_14294),U_14296)),hAPP(c_COMBK(tc_fun(U_14293,tc_HOL_Obool),U_14292),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14291,tc_fun(U_14293,tc_HOL_Obool)),U_14295),U_14297))),
    inference(clausify,[status(thm)],[f_3587_3]) ).

fof(f_3588_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_3588_2,plain,
    ! [U_14301,U_14300,U_14299,U_14298] : hAPP(hAPP(c_Product__Type_OSigma(U_14298,U_14299),U_14300),U_14301) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14298,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),U_14300),hAPP(hAPP(c_COMBS(U_14298,tc_fun(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14299,tc_HOL_Obool),tc_fun(tc_fun(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),U_14298),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),U_14301)),hAPP(hAPP(c_COMBC(U_14298,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14299,tc_fun(tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),U_14298),c_COMBC(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14299,tc_prod(U_14298,U_14299)),tc_fun(U_14299,tc_fun(tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),U_14298),hAPP(c_COMBB(tc_prod(U_14298,U_14299),tc_fun(tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),U_14299),c_Set_Oinsert(tc_prod(U_14298,U_14299)))),c_Product__Type_OPair(U_14298,U_14299)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3588_1]) ).

fof(f_3588_3,plain,
    ! [U_14298,U_14299,U_14300,U_14301] : hAPP(hAPP(c_Product__Type_OSigma(U_14298,U_14299),U_14300),U_14301) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14298,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),U_14300),hAPP(hAPP(c_COMBS(U_14298,tc_fun(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14299,tc_HOL_Obool),tc_fun(tc_fun(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),U_14298),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),U_14301)),hAPP(hAPP(c_COMBC(U_14298,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14299,tc_fun(tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),U_14298),c_COMBC(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14299,tc_prod(U_14298,U_14299)),tc_fun(U_14299,tc_fun(tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),U_14298),hAPP(c_COMBB(tc_prod(U_14298,U_14299),tc_fun(tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),U_14299),c_Set_Oinsert(tc_prod(U_14298,U_14299)))),c_Product__Type_OPair(U_14298,U_14299)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3588_2]) ).

cnf(f_3588_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14298,U_14299),U_14300),U_14301) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14298,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),U_14300),hAPP(hAPP(c_COMBS(U_14298,tc_fun(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14299,tc_HOL_Obool),tc_fun(tc_fun(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),U_14298),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),U_14301)),hAPP(hAPP(c_COMBC(U_14298,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14299,tc_fun(tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),U_14298),c_COMBC(U_14299,tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14299,tc_prod(U_14298,U_14299)),tc_fun(U_14299,tc_fun(tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))),U_14298),hAPP(c_COMBB(tc_prod(U_14298,U_14299),tc_fun(tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool),tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool)),U_14299),c_Set_Oinsert(tc_prod(U_14298,U_14299)))),c_Product__Type_OPair(U_14298,U_14299)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14298,U_14299),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3588_3]) ).

fof(f_3589_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_3589_2,plain,
    ! [U_14304,U_14303,U_14302] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14302),hAPP(c_Finite__Set_Ofold1(U_14302,c_Lattices_Osemilattice__inf__class_Oinf(U_14302)),U_14303)),U_14304))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14302),U_14304),U_14303))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14302),U_14303))
      | ~ class_Lattices_Osemilattice__inf(U_14302) ),
    inference(variable_rename,[status(thm)],[f_3589_1]) ).

fof(f_3589_3,plain,
    ! [U_14302,U_14303,U_14304] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14302),hAPP(c_Finite__Set_Ofold1(U_14302,c_Lattices_Osemilattice__inf__class_Oinf(U_14302)),U_14303)),U_14304))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14302),U_14304),U_14303))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14302),U_14303))
      | ~ class_Lattices_Osemilattice__inf(U_14302) ),
    inference(definitional_conversion,[status(esa)],[f_3589_2]) ).

cnf(f_3589_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14302),hAPP(c_Finite__Set_Ofold1(U_14302,c_Lattices_Osemilattice__inf__class_Oinf(U_14302)),U_14303)),U_14304))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14302),U_14304),U_14303))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14302),U_14303))
    | ~ class_Lattices_Osemilattice__inf(U_14302) ),
    inference(clausify,[status(thm)],[f_3589_3]) ).

fof(f_3590_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_3590_2,plain,
    ! [U_14307,U_14306,U_14305] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_14305,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_14305),U_14306),U_14307)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14305,U_14305),tc_HOL_Obool)),U_14307),hAPP(hAPP(c_Product__Type_OSigma(U_14305,U_14305),U_14306),hAPP(c_COMBK(tc_fun(U_14305,tc_HOL_Obool),U_14305),U_14306))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14305),U_14306)) ),
    inference(variable_rename,[status(thm)],[f_3590_1]) ).

fof(f_3590_3,plain,
    ! [U_14305,U_14306,U_14307] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_14305,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_14305),U_14306),U_14307)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14305,U_14305),tc_HOL_Obool)),U_14307),hAPP(hAPP(c_Product__Type_OSigma(U_14305,U_14305),U_14306),hAPP(c_COMBK(tc_fun(U_14305,tc_HOL_Obool),U_14305),U_14306))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14305),U_14306)) ),
    inference(definitional_conversion,[status(esa)],[f_3590_2]) ).

cnf(f_3590_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_14305,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_14305),U_14306),U_14307)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14305,U_14305),tc_HOL_Obool)),U_14307),hAPP(hAPP(c_Product__Type_OSigma(U_14305,U_14305),U_14306),hAPP(c_COMBK(tc_fun(U_14305,tc_HOL_Obool),U_14305),U_14306))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14305),U_14306)) ),
    inference(clausify,[status(thm)],[f_3590_3]) ).

fof(f_3591_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_3591_2,plain,
    ! [U_14312,U_14311,U_14310] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),hAPP(c_Finite__Set_Ofold1(U_14310,c_Lattices_Osemilattice__inf__class_Oinf(U_14310)),U_14311)))
          | ? [U_14309] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),U_14309))
              & hBOOL(hAPP(hAPP(c_member(U_14310),U_14309),U_14311)) ) )
        & ( ! [U_14308] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),U_14308))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14310),U_14308),U_14311)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),hAPP(c_Finite__Set_Ofold1(U_14310,c_Lattices_Osemilattice__inf__class_Oinf(U_14310)),U_14311))) ) )
      | U_14311 = c_Orderings_Obot__class_Obot(tc_fun(U_14310,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14310),U_14311))
      | ~ class_Lattices_Osemilattice__inf(U_14310) ),
    inference(variable_rename,[status(thm)],[f_3591_1]) ).

fof(f_3591_3,plain,
    ! [U_14312,U_14311,U_14310] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),hAPP(c_Finite__Set_Ofold1(U_14310,c_Lattices_Osemilattice__inf__class_Oinf(U_14310)),U_14311)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),sK305(U_14312,U_14311,U_14310)))
            & hBOOL(hAPP(hAPP(c_member(U_14310),sK305(U_14312,U_14311,U_14310)),U_14311)) ) )
        & ( ! [U_14308] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),U_14308))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14310),U_14308),U_14311)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),hAPP(c_Finite__Set_Ofold1(U_14310,c_Lattices_Osemilattice__inf__class_Oinf(U_14310)),U_14311))) ) )
      | U_14311 = c_Orderings_Obot__class_Obot(tc_fun(U_14310,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14310),U_14311))
      | ~ class_Lattices_Osemilattice__inf(U_14310) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK305]),skolemize(U_14309,sK305(U_14312,U_14311,U_14310))],[f_3591_2]) ).

fof(f_3591_4,plain,
    ( ! [U_14310,U_14311,U_14312] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),sK305(U_14312,U_14311,U_14310)))
        | ~ sP986(U_14310,U_14311,U_14312) )
    & ! [U_14310,U_14311,U_14312] :
        ( hBOOL(hAPP(hAPP(c_member(U_14310),sK305(U_14312,U_14311,U_14310)),U_14311))
        | ~ sP986(U_14310,U_14311,U_14312) )
    & ! [U_14308,U_14310,U_14311,U_14312] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),hAPP(c_Finite__Set_Ofold1(U_14310,c_Lattices_Osemilattice__inf__class_Oinf(U_14310)),U_14311)))
        | sP986(U_14310,U_14311,U_14312)
        | ~ sP987(U_14308,U_14310,U_14311,U_14312) )
    & ! [U_14308,U_14310,U_14311,U_14312] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),U_14308))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14310),U_14308),U_14311))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),hAPP(c_Finite__Set_Ofold1(U_14310,c_Lattices_Osemilattice__inf__class_Oinf(U_14310)),U_14311)))
        | ~ sP987(U_14308,U_14310,U_14311,U_14312) )
    & ! [U_14308,U_14310,U_14311,U_14312] :
        ( sP987(U_14308,U_14310,U_14311,U_14312)
        | U_14311 = c_Orderings_Obot__class_Obot(tc_fun(U_14310,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14310),U_14311))
        | ~ class_Lattices_Osemilattice__inf(U_14310) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP986,sP987])],[f_3591_3]) ).

cnf(f_3591_5,plain,
    ( sP987(U_14308,U_14310,U_14311,U_14312)
    | U_14311 = c_Orderings_Obot__class_Obot(tc_fun(U_14310,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14310),U_14311))
    | ~ class_Lattices_Osemilattice__inf(U_14310) ),
    inference(clausify,[status(thm)],[f_3591_4]) ).

cnf(f_3591_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),U_14308))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14310),U_14308),U_14311))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),hAPP(c_Finite__Set_Ofold1(U_14310,c_Lattices_Osemilattice__inf__class_Oinf(U_14310)),U_14311)))
    | ~ sP987(U_14308,U_14310,U_14311,U_14312) ),
    inference(clausify,[status(thm)],[f_3591_4]) ).

cnf(f_3591_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),hAPP(c_Finite__Set_Ofold1(U_14310,c_Lattices_Osemilattice__inf__class_Oinf(U_14310)),U_14311)))
    | sP986(U_14310,U_14311,U_14312)
    | ~ sP987(U_14308,U_14310,U_14311,U_14312) ),
    inference(clausify,[status(thm)],[f_3591_4]) ).

cnf(f_3591_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14310),sK305(U_14312,U_14311,U_14310)),U_14311))
    | ~ sP986(U_14310,U_14311,U_14312) ),
    inference(clausify,[status(thm)],[f_3591_4]) ).

cnf(f_3591_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14310),U_14312),sK305(U_14312,U_14311,U_14310)))
    | ~ sP986(U_14310,U_14311,U_14312) ),
    inference(clausify,[status(thm)],[f_3591_4]) ).

fof(f_3592_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_3592_2,plain,
    ! [U_14315,U_14314,U_14313] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14313),hAPP(c_Finite__Set_Ofold1(U_14313,c_Orderings_Oord__class_Omin(U_14313)),U_14314)),U_14315))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14313),U_14315),U_14314))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14313),U_14314))
      | ~ class_Orderings_Olinorder(U_14313) ),
    inference(variable_rename,[status(thm)],[f_3592_1]) ).

fof(f_3592_3,plain,
    ! [U_14314,U_14315,U_14313] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14313),hAPP(c_Finite__Set_Ofold1(U_14313,c_Orderings_Oord__class_Omin(U_14313)),U_14314)),U_14315))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14313),U_14315),U_14314))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14313),U_14314))
      | ~ class_Orderings_Olinorder(U_14313) ),
    inference(definitional_conversion,[status(esa)],[f_3592_2]) ).

cnf(f_3592_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14313),hAPP(c_Finite__Set_Ofold1(U_14313,c_Orderings_Oord__class_Omin(U_14313)),U_14314)),U_14315))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14313),U_14315),U_14314))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14313),U_14314))
    | ~ class_Orderings_Olinorder(U_14313) ),
    inference(clausify,[status(thm)],[f_3592_3]) ).

fof(f_3593_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_3593_2,plain,
    ! [U_14318,U_14317,U_14316] :
      ( hAPP(c_Finite__Set_Ofold1(U_14316,c_Groups_Otimes__class_Otimes(U_14316)),hAPP(hAPP(c_Set_Oinsert(U_14316),U_14318),U_14317)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14316),U_14318),hAPP(c_Finite__Set_Ofold1(U_14316,c_Groups_Otimes__class_Otimes(U_14316)),U_14317))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14316),U_14317))
      | U_14317 = c_Orderings_Obot__class_Obot(tc_fun(U_14316,tc_HOL_Obool))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14316) ),
    inference(variable_rename,[status(thm)],[f_3593_1]) ).

fof(f_3593_3,plain,
    ! [U_14316,U_14318,U_14317] :
      ( hAPP(c_Finite__Set_Ofold1(U_14316,c_Groups_Otimes__class_Otimes(U_14316)),hAPP(hAPP(c_Set_Oinsert(U_14316),U_14318),U_14317)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14316),U_14318),hAPP(c_Finite__Set_Ofold1(U_14316,c_Groups_Otimes__class_Otimes(U_14316)),U_14317))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14316),U_14317))
      | U_14317 = c_Orderings_Obot__class_Obot(tc_fun(U_14316,tc_HOL_Obool))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14316) ),
    inference(definitional_conversion,[status(esa)],[f_3593_2]) ).

cnf(f_3593_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_14316,c_Groups_Otimes__class_Otimes(U_14316)),hAPP(hAPP(c_Set_Oinsert(U_14316),U_14318),U_14317)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14316),U_14318),hAPP(c_Finite__Set_Ofold1(U_14316,c_Groups_Otimes__class_Otimes(U_14316)),U_14317))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14316),U_14317))
    | U_14317 = c_Orderings_Obot__class_Obot(tc_fun(U_14316,tc_HOL_Obool))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_14316) ),
    inference(clausify,[status(thm)],[f_3593_3]) ).

fof(f_3594_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_3594_2,plain,
    ! [U_14323,U_14322,U_14321] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),hAPP(c_Finite__Set_Ofold1(U_14321,c_Orderings_Oord__class_Omin(U_14321)),U_14322)),U_14323))
          | ! [U_14320] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),U_14320),U_14323))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14321),U_14320),U_14322)) ) )
        & ( ? [U_14319] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),U_14319),U_14323))
              & hBOOL(hAPP(hAPP(c_member(U_14321),U_14319),U_14322)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),hAPP(c_Finite__Set_Ofold1(U_14321,c_Orderings_Oord__class_Omin(U_14321)),U_14322)),U_14323)) ) )
      | U_14322 = c_Orderings_Obot__class_Obot(tc_fun(U_14321,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14321),U_14322))
      | ~ class_Orderings_Olinorder(U_14321) ),
    inference(variable_rename,[status(thm)],[f_3594_1]) ).

fof(f_3594_3,plain,
    ! [U_14323,U_14322,U_14321] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),hAPP(c_Finite__Set_Ofold1(U_14321,c_Orderings_Oord__class_Omin(U_14321)),U_14322)),U_14323))
          | ! [U_14320] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),U_14320),U_14323))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14321),U_14320),U_14322)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),sK306(U_14323,U_14322,U_14321)),U_14323))
            & hBOOL(hAPP(hAPP(c_member(U_14321),sK306(U_14323,U_14322,U_14321)),U_14322)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),hAPP(c_Finite__Set_Ofold1(U_14321,c_Orderings_Oord__class_Omin(U_14321)),U_14322)),U_14323)) ) )
      | U_14322 = c_Orderings_Obot__class_Obot(tc_fun(U_14321,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14321),U_14322))
      | ~ class_Orderings_Olinorder(U_14321) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK306]),skolemize(U_14319,sK306(U_14323,U_14322,U_14321))],[f_3594_2]) ).

fof(f_3594_4,plain,
    ( ! [U_14321,U_14322,U_14323] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),sK306(U_14323,U_14322,U_14321)),U_14323))
        | ~ sP988(U_14321,U_14322,U_14323) )
    & ! [U_14321,U_14322,U_14323] :
        ( hBOOL(hAPP(hAPP(c_member(U_14321),sK306(U_14323,U_14322,U_14321)),U_14322))
        | ~ sP988(U_14321,U_14322,U_14323) )
    & ! [U_14320,U_14321,U_14322,U_14323] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),hAPP(c_Finite__Set_Ofold1(U_14321,c_Orderings_Oord__class_Omin(U_14321)),U_14322)),U_14323))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),U_14320),U_14323))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14321),U_14320),U_14322))
        | ~ sP989(U_14320,U_14321,U_14322,U_14323) )
    & ! [U_14320,U_14321,U_14322,U_14323] :
        ( sP988(U_14321,U_14322,U_14323)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),hAPP(c_Finite__Set_Ofold1(U_14321,c_Orderings_Oord__class_Omin(U_14321)),U_14322)),U_14323))
        | ~ sP989(U_14320,U_14321,U_14322,U_14323) )
    & ! [U_14320,U_14321,U_14322,U_14323] :
        ( sP989(U_14320,U_14321,U_14322,U_14323)
        | U_14322 = c_Orderings_Obot__class_Obot(tc_fun(U_14321,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14321),U_14322))
        | ~ class_Orderings_Olinorder(U_14321) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP988,sP989])],[f_3594_3]) ).

cnf(f_3594_5,plain,
    ( sP989(U_14320,U_14321,U_14322,U_14323)
    | U_14322 = c_Orderings_Obot__class_Obot(tc_fun(U_14321,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14321),U_14322))
    | ~ class_Orderings_Olinorder(U_14321) ),
    inference(clausify,[status(thm)],[f_3594_4]) ).

cnf(f_3594_6,plain,
    ( sP988(U_14321,U_14322,U_14323)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),hAPP(c_Finite__Set_Ofold1(U_14321,c_Orderings_Oord__class_Omin(U_14321)),U_14322)),U_14323))
    | ~ sP989(U_14320,U_14321,U_14322,U_14323) ),
    inference(clausify,[status(thm)],[f_3594_4]) ).

cnf(f_3594_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),hAPP(c_Finite__Set_Ofold1(U_14321,c_Orderings_Oord__class_Omin(U_14321)),U_14322)),U_14323))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),U_14320),U_14323))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14321),U_14320),U_14322))
    | ~ sP989(U_14320,U_14321,U_14322,U_14323) ),
    inference(clausify,[status(thm)],[f_3594_4]) ).

cnf(f_3594_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14321),sK306(U_14323,U_14322,U_14321)),U_14322))
    | ~ sP988(U_14321,U_14322,U_14323) ),
    inference(clausify,[status(thm)],[f_3594_4]) ).

cnf(f_3594_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14321),sK306(U_14323,U_14322,U_14321)),U_14323))
    | ~ sP988(U_14321,U_14322,U_14323) ),
    inference(clausify,[status(thm)],[f_3594_4]) ).

fof(f_3595_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_3595_2,plain,
    ! [U_14328,U_14327,U_14326] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),hAPP(c_Finite__Set_Ofold1(U_14326,c_Orderings_Oord__class_Omin(U_14326)),U_14327)))
          | ? [U_14325] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),U_14325))
              & hBOOL(hAPP(hAPP(c_member(U_14326),U_14325),U_14327)) ) )
        & ( ! [U_14324] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),U_14324))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14326),U_14324),U_14327)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),hAPP(c_Finite__Set_Ofold1(U_14326,c_Orderings_Oord__class_Omin(U_14326)),U_14327))) ) )
      | U_14327 = c_Orderings_Obot__class_Obot(tc_fun(U_14326,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14326),U_14327))
      | ~ class_Orderings_Olinorder(U_14326) ),
    inference(variable_rename,[status(thm)],[f_3595_1]) ).

fof(f_3595_3,plain,
    ! [U_14328,U_14327,U_14326] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),hAPP(c_Finite__Set_Ofold1(U_14326,c_Orderings_Oord__class_Omin(U_14326)),U_14327)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),sK307(U_14328,U_14327,U_14326)))
            & hBOOL(hAPP(hAPP(c_member(U_14326),sK307(U_14328,U_14327,U_14326)),U_14327)) ) )
        & ( ! [U_14324] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),U_14324))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14326),U_14324),U_14327)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),hAPP(c_Finite__Set_Ofold1(U_14326,c_Orderings_Oord__class_Omin(U_14326)),U_14327))) ) )
      | U_14327 = c_Orderings_Obot__class_Obot(tc_fun(U_14326,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14326),U_14327))
      | ~ class_Orderings_Olinorder(U_14326) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK307]),skolemize(U_14325,sK307(U_14328,U_14327,U_14326))],[f_3595_2]) ).

fof(f_3595_4,plain,
    ( ! [U_14326,U_14328,U_14327] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),sK307(U_14328,U_14327,U_14326)))
        | ~ sP990(U_14326,U_14328,U_14327) )
    & ! [U_14326,U_14328,U_14327] :
        ( hBOOL(hAPP(hAPP(c_member(U_14326),sK307(U_14328,U_14327,U_14326)),U_14327))
        | ~ sP990(U_14326,U_14328,U_14327) )
    & ! [U_14324,U_14326,U_14328,U_14327] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),hAPP(c_Finite__Set_Ofold1(U_14326,c_Orderings_Oord__class_Omin(U_14326)),U_14327)))
        | sP990(U_14326,U_14328,U_14327)
        | ~ sP991(U_14324,U_14326,U_14328,U_14327) )
    & ! [U_14324,U_14326,U_14328,U_14327] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),U_14324))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14326),U_14324),U_14327))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),hAPP(c_Finite__Set_Ofold1(U_14326,c_Orderings_Oord__class_Omin(U_14326)),U_14327)))
        | ~ sP991(U_14324,U_14326,U_14328,U_14327) )
    & ! [U_14324,U_14326,U_14328,U_14327] :
        ( sP991(U_14324,U_14326,U_14328,U_14327)
        | U_14327 = c_Orderings_Obot__class_Obot(tc_fun(U_14326,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14326),U_14327))
        | ~ class_Orderings_Olinorder(U_14326) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP990,sP991])],[f_3595_3]) ).

cnf(f_3595_5,plain,
    ( sP991(U_14324,U_14326,U_14328,U_14327)
    | U_14327 = c_Orderings_Obot__class_Obot(tc_fun(U_14326,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14326),U_14327))
    | ~ class_Orderings_Olinorder(U_14326) ),
    inference(clausify,[status(thm)],[f_3595_4]) ).

cnf(f_3595_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),U_14324))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14326),U_14324),U_14327))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),hAPP(c_Finite__Set_Ofold1(U_14326,c_Orderings_Oord__class_Omin(U_14326)),U_14327)))
    | ~ sP991(U_14324,U_14326,U_14328,U_14327) ),
    inference(clausify,[status(thm)],[f_3595_4]) ).

cnf(f_3595_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),hAPP(c_Finite__Set_Ofold1(U_14326,c_Orderings_Oord__class_Omin(U_14326)),U_14327)))
    | sP990(U_14326,U_14328,U_14327)
    | ~ sP991(U_14324,U_14326,U_14328,U_14327) ),
    inference(clausify,[status(thm)],[f_3595_4]) ).

cnf(f_3595_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14326),sK307(U_14328,U_14327,U_14326)),U_14327))
    | ~ sP990(U_14326,U_14328,U_14327) ),
    inference(clausify,[status(thm)],[f_3595_4]) ).

cnf(f_3595_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14326),U_14328),sK307(U_14328,U_14327,U_14326)))
    | ~ sP990(U_14326,U_14328,U_14327) ),
    inference(clausify,[status(thm)],[f_3595_4]) ).

fof(f_3596_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_3596_2,plain,
    ! [U_14331,U_14330,U_14329] :
      ( hAPP(c_Finite__Set_Ofold1(U_14329,c_Groups_Otimes__class_Otimes(U_14329)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14329,tc_HOL_Obool)),U_14330),U_14331)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14329),hAPP(c_Finite__Set_Ofold1(U_14329,c_Groups_Otimes__class_Otimes(U_14329)),U_14330)),hAPP(c_Finite__Set_Ofold1(U_14329,c_Groups_Otimes__class_Otimes(U_14329)),U_14331))
      | U_14331 = c_Orderings_Obot__class_Obot(tc_fun(U_14329,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14329),U_14331))
      | U_14330 = c_Orderings_Obot__class_Obot(tc_fun(U_14329,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14329),U_14330))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14329) ),
    inference(variable_rename,[status(thm)],[f_3596_1]) ).

fof(f_3596_3,plain,
    ! [U_14330,U_14329,U_14331] :
      ( hAPP(c_Finite__Set_Ofold1(U_14329,c_Groups_Otimes__class_Otimes(U_14329)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14329,tc_HOL_Obool)),U_14330),U_14331)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14329),hAPP(c_Finite__Set_Ofold1(U_14329,c_Groups_Otimes__class_Otimes(U_14329)),U_14330)),hAPP(c_Finite__Set_Ofold1(U_14329,c_Groups_Otimes__class_Otimes(U_14329)),U_14331))
      | U_14331 = c_Orderings_Obot__class_Obot(tc_fun(U_14329,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14329),U_14331))
      | U_14330 = c_Orderings_Obot__class_Obot(tc_fun(U_14329,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14329),U_14330))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14329) ),
    inference(definitional_conversion,[status(esa)],[f_3596_2]) ).

cnf(f_3596_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_14329,c_Groups_Otimes__class_Otimes(U_14329)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14329,tc_HOL_Obool)),U_14330),U_14331)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14329),hAPP(c_Finite__Set_Ofold1(U_14329,c_Groups_Otimes__class_Otimes(U_14329)),U_14330)),hAPP(c_Finite__Set_Ofold1(U_14329,c_Groups_Otimes__class_Otimes(U_14329)),U_14331))
    | U_14331 = c_Orderings_Obot__class_Obot(tc_fun(U_14329,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14329),U_14331))
    | U_14330 = c_Orderings_Obot__class_Obot(tc_fun(U_14329,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14329),U_14330))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_14329) ),
    inference(clausify,[status(thm)],[f_3596_3]) ).

fof(f_3597_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_3597_2,plain,
    ! [U_14336,U_14335,U_14334] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),hAPP(c_Finite__Set_Ofold1(U_14334,c_Orderings_Oord__class_Omin(U_14334)),U_14335)),U_14336))
          | ! [U_14333] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),U_14333),U_14336))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14334),U_14333),U_14335)) ) )
        & ( ? [U_14332] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),U_14332),U_14336))
              & hBOOL(hAPP(hAPP(c_member(U_14334),U_14332),U_14335)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),hAPP(c_Finite__Set_Ofold1(U_14334,c_Orderings_Oord__class_Omin(U_14334)),U_14335)),U_14336)) ) )
      | U_14335 = c_Orderings_Obot__class_Obot(tc_fun(U_14334,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14334),U_14335))
      | ~ class_Orderings_Olinorder(U_14334) ),
    inference(variable_rename,[status(thm)],[f_3597_1]) ).

fof(f_3597_3,plain,
    ! [U_14336,U_14335,U_14334] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),hAPP(c_Finite__Set_Ofold1(U_14334,c_Orderings_Oord__class_Omin(U_14334)),U_14335)),U_14336))
          | ! [U_14333] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),U_14333),U_14336))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14334),U_14333),U_14335)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),sK308(U_14336,U_14335,U_14334)),U_14336))
            & hBOOL(hAPP(hAPP(c_member(U_14334),sK308(U_14336,U_14335,U_14334)),U_14335)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),hAPP(c_Finite__Set_Ofold1(U_14334,c_Orderings_Oord__class_Omin(U_14334)),U_14335)),U_14336)) ) )
      | U_14335 = c_Orderings_Obot__class_Obot(tc_fun(U_14334,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14334),U_14335))
      | ~ class_Orderings_Olinorder(U_14334) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK308]),skolemize(U_14332,sK308(U_14336,U_14335,U_14334))],[f_3597_2]) ).

fof(f_3597_4,plain,
    ( ! [U_14334,U_14335,U_14336] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),sK308(U_14336,U_14335,U_14334)),U_14336))
        | ~ sP992(U_14334,U_14335,U_14336) )
    & ! [U_14334,U_14335,U_14336] :
        ( hBOOL(hAPP(hAPP(c_member(U_14334),sK308(U_14336,U_14335,U_14334)),U_14335))
        | ~ sP992(U_14334,U_14335,U_14336) )
    & ! [U_14333,U_14334,U_14335,U_14336] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),hAPP(c_Finite__Set_Ofold1(U_14334,c_Orderings_Oord__class_Omin(U_14334)),U_14335)),U_14336))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),U_14333),U_14336))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14334),U_14333),U_14335))
        | ~ sP993(U_14333,U_14334,U_14335,U_14336) )
    & ! [U_14333,U_14334,U_14335,U_14336] :
        ( sP992(U_14334,U_14335,U_14336)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),hAPP(c_Finite__Set_Ofold1(U_14334,c_Orderings_Oord__class_Omin(U_14334)),U_14335)),U_14336))
        | ~ sP993(U_14333,U_14334,U_14335,U_14336) )
    & ! [U_14333,U_14334,U_14335,U_14336] :
        ( sP993(U_14333,U_14334,U_14335,U_14336)
        | U_14335 = c_Orderings_Obot__class_Obot(tc_fun(U_14334,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14334),U_14335))
        | ~ class_Orderings_Olinorder(U_14334) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP992,sP993])],[f_3597_3]) ).

cnf(f_3597_5,plain,
    ( sP993(U_14333,U_14334,U_14335,U_14336)
    | U_14335 = c_Orderings_Obot__class_Obot(tc_fun(U_14334,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14334),U_14335))
    | ~ class_Orderings_Olinorder(U_14334) ),
    inference(clausify,[status(thm)],[f_3597_4]) ).

cnf(f_3597_6,plain,
    ( sP992(U_14334,U_14335,U_14336)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),hAPP(c_Finite__Set_Ofold1(U_14334,c_Orderings_Oord__class_Omin(U_14334)),U_14335)),U_14336))
    | ~ sP993(U_14333,U_14334,U_14335,U_14336) ),
    inference(clausify,[status(thm)],[f_3597_4]) ).

cnf(f_3597_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),hAPP(c_Finite__Set_Ofold1(U_14334,c_Orderings_Oord__class_Omin(U_14334)),U_14335)),U_14336))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),U_14333),U_14336))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14334),U_14333),U_14335))
    | ~ sP993(U_14333,U_14334,U_14335,U_14336) ),
    inference(clausify,[status(thm)],[f_3597_4]) ).

cnf(f_3597_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14334),sK308(U_14336,U_14335,U_14334)),U_14335))
    | ~ sP992(U_14334,U_14335,U_14336) ),
    inference(clausify,[status(thm)],[f_3597_4]) ).

cnf(f_3597_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14334),sK308(U_14336,U_14335,U_14334)),U_14336))
    | ~ sP992(U_14334,U_14335,U_14336) ),
    inference(clausify,[status(thm)],[f_3597_4]) ).

fof(f_3598_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_3598_2,plain,
    ! [U_14341,U_14340,U_14339] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),hAPP(c_Finite__Set_Ofold1(U_14339,c_Orderings_Oord__class_Omin(U_14339)),U_14340)))
          | ? [U_14338] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),U_14338))
              & hBOOL(hAPP(hAPP(c_member(U_14339),U_14338),U_14340)) ) )
        & ( ! [U_14337] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),U_14337))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14339),U_14337),U_14340)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),hAPP(c_Finite__Set_Ofold1(U_14339,c_Orderings_Oord__class_Omin(U_14339)),U_14340))) ) )
      | U_14340 = c_Orderings_Obot__class_Obot(tc_fun(U_14339,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14339),U_14340))
      | ~ class_Orderings_Olinorder(U_14339) ),
    inference(variable_rename,[status(thm)],[f_3598_1]) ).

fof(f_3598_3,plain,
    ! [U_14341,U_14340,U_14339] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),hAPP(c_Finite__Set_Ofold1(U_14339,c_Orderings_Oord__class_Omin(U_14339)),U_14340)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),sK309(U_14341,U_14340,U_14339)))
            & hBOOL(hAPP(hAPP(c_member(U_14339),sK309(U_14341,U_14340,U_14339)),U_14340)) ) )
        & ( ! [U_14337] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),U_14337))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14339),U_14337),U_14340)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),hAPP(c_Finite__Set_Ofold1(U_14339,c_Orderings_Oord__class_Omin(U_14339)),U_14340))) ) )
      | U_14340 = c_Orderings_Obot__class_Obot(tc_fun(U_14339,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14339),U_14340))
      | ~ class_Orderings_Olinorder(U_14339) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK309]),skolemize(U_14338,sK309(U_14341,U_14340,U_14339))],[f_3598_2]) ).

fof(f_3598_4,plain,
    ( ! [U_14339,U_14341,U_14340] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),sK309(U_14341,U_14340,U_14339)))
        | ~ sP994(U_14339,U_14341,U_14340) )
    & ! [U_14339,U_14341,U_14340] :
        ( hBOOL(hAPP(hAPP(c_member(U_14339),sK309(U_14341,U_14340,U_14339)),U_14340))
        | ~ sP994(U_14339,U_14341,U_14340) )
    & ! [U_14337,U_14339,U_14341,U_14340] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),hAPP(c_Finite__Set_Ofold1(U_14339,c_Orderings_Oord__class_Omin(U_14339)),U_14340)))
        | sP994(U_14339,U_14341,U_14340)
        | ~ sP995(U_14337,U_14339,U_14341,U_14340) )
    & ! [U_14337,U_14339,U_14341,U_14340] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),U_14337))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14339),U_14337),U_14340))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),hAPP(c_Finite__Set_Ofold1(U_14339,c_Orderings_Oord__class_Omin(U_14339)),U_14340)))
        | ~ sP995(U_14337,U_14339,U_14341,U_14340) )
    & ! [U_14337,U_14339,U_14341,U_14340] :
        ( sP995(U_14337,U_14339,U_14341,U_14340)
        | U_14340 = c_Orderings_Obot__class_Obot(tc_fun(U_14339,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14339),U_14340))
        | ~ class_Orderings_Olinorder(U_14339) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP994,sP995])],[f_3598_3]) ).

cnf(f_3598_5,plain,
    ( sP995(U_14337,U_14339,U_14341,U_14340)
    | U_14340 = c_Orderings_Obot__class_Obot(tc_fun(U_14339,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14339),U_14340))
    | ~ class_Orderings_Olinorder(U_14339) ),
    inference(clausify,[status(thm)],[f_3598_4]) ).

cnf(f_3598_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),U_14337))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14339),U_14337),U_14340))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),hAPP(c_Finite__Set_Ofold1(U_14339,c_Orderings_Oord__class_Omin(U_14339)),U_14340)))
    | ~ sP995(U_14337,U_14339,U_14341,U_14340) ),
    inference(clausify,[status(thm)],[f_3598_4]) ).

cnf(f_3598_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),hAPP(c_Finite__Set_Ofold1(U_14339,c_Orderings_Oord__class_Omin(U_14339)),U_14340)))
    | sP994(U_14339,U_14341,U_14340)
    | ~ sP995(U_14337,U_14339,U_14341,U_14340) ),
    inference(clausify,[status(thm)],[f_3598_4]) ).

cnf(f_3598_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14339),sK309(U_14341,U_14340,U_14339)),U_14340))
    | ~ sP994(U_14339,U_14341,U_14340) ),
    inference(clausify,[status(thm)],[f_3598_4]) ).

cnf(f_3598_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14339),U_14341),sK309(U_14341,U_14340,U_14339)))
    | ~ sP994(U_14339,U_14341,U_14340) ),
    inference(clausify,[status(thm)],[f_3598_4]) ).

fof(f_3599_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_3599_2,plain,
    ! [U_14347,U_14346,U_14345,U_14344,U_14343,U_14342] : hAPP(c_Set_Ovimage(U_14342,tc_prod(U_14343,U_14344),U_14345),hAPP(hAPP(c_Product__Type_OSigma(U_14343,U_14344),U_14346),hAPP(c_COMBK(tc_fun(U_14344,tc_HOL_Obool),U_14343),U_14347))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14342,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14342,U_14343,hAPP(c_Fun_Ocomp(tc_prod(U_14343,U_14344),U_14343,U_14342,c_Product__Type_Ofst(U_14343,U_14344)),U_14345)),U_14346)),hAPP(c_Set_Ovimage(U_14342,U_14344,hAPP(c_Fun_Ocomp(tc_prod(U_14343,U_14344),U_14344,U_14342,c_Product__Type_Osnd(U_14343,U_14344)),U_14345)),U_14347)),
    inference(variable_rename,[status(thm)],[f_3599_1]) ).

fof(f_3599_3,plain,
    ! [U_14343,U_14345,U_14347,U_14342,U_14344,U_14346] : hAPP(c_Set_Ovimage(U_14342,tc_prod(U_14343,U_14344),U_14345),hAPP(hAPP(c_Product__Type_OSigma(U_14343,U_14344),U_14346),hAPP(c_COMBK(tc_fun(U_14344,tc_HOL_Obool),U_14343),U_14347))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14342,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14342,U_14343,hAPP(c_Fun_Ocomp(tc_prod(U_14343,U_14344),U_14343,U_14342,c_Product__Type_Ofst(U_14343,U_14344)),U_14345)),U_14346)),hAPP(c_Set_Ovimage(U_14342,U_14344,hAPP(c_Fun_Ocomp(tc_prod(U_14343,U_14344),U_14344,U_14342,c_Product__Type_Osnd(U_14343,U_14344)),U_14345)),U_14347)),
    inference(definitional_conversion,[status(esa)],[f_3599_2]) ).

cnf(f_3599_4,plain,
    hAPP(c_Set_Ovimage(U_14342,tc_prod(U_14343,U_14344),U_14345),hAPP(hAPP(c_Product__Type_OSigma(U_14343,U_14344),U_14346),hAPP(c_COMBK(tc_fun(U_14344,tc_HOL_Obool),U_14343),U_14347))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14342,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14342,U_14343,hAPP(c_Fun_Ocomp(tc_prod(U_14343,U_14344),U_14343,U_14342,c_Product__Type_Ofst(U_14343,U_14344)),U_14345)),U_14346)),hAPP(c_Set_Ovimage(U_14342,U_14344,hAPP(c_Fun_Ocomp(tc_prod(U_14343,U_14344),U_14344,U_14342,c_Product__Type_Osnd(U_14343,U_14344)),U_14345)),U_14347)),
    inference(clausify,[status(thm)],[f_3599_3]) ).

fof(f_3600_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_3600_2,plain,
    ! [U_14350,U_14349,U_14348] :
      ( hAPP(c_Finite__Set_Ofold1(U_14348,c_Groups_Otimes__class_Otimes(U_14348)),hAPP(hAPP(c_Set_Oinsert(U_14348),U_14350),U_14349)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14348),U_14350),hAPP(c_Finite__Set_Ofold1(U_14348,c_Groups_Otimes__class_Otimes(U_14348)),U_14349))
      | hBOOL(hAPP(hAPP(c_member(U_14348),U_14350),U_14349))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14348),U_14349))
      | U_14349 = c_Orderings_Obot__class_Obot(tc_fun(U_14348,tc_HOL_Obool))
      | ~ class_Groups_Oab__semigroup__mult(U_14348) ),
    inference(variable_rename,[status(thm)],[f_3600_1]) ).

fof(f_3600_3,plain,
    ! [U_14348,U_14349,U_14350] :
      ( hAPP(c_Finite__Set_Ofold1(U_14348,c_Groups_Otimes__class_Otimes(U_14348)),hAPP(hAPP(c_Set_Oinsert(U_14348),U_14350),U_14349)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14348),U_14350),hAPP(c_Finite__Set_Ofold1(U_14348,c_Groups_Otimes__class_Otimes(U_14348)),U_14349))
      | hBOOL(hAPP(hAPP(c_member(U_14348),U_14350),U_14349))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14348),U_14349))
      | U_14349 = c_Orderings_Obot__class_Obot(tc_fun(U_14348,tc_HOL_Obool))
      | ~ class_Groups_Oab__semigroup__mult(U_14348) ),
    inference(definitional_conversion,[status(esa)],[f_3600_2]) ).

cnf(f_3600_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_14348,c_Groups_Otimes__class_Otimes(U_14348)),hAPP(hAPP(c_Set_Oinsert(U_14348),U_14350),U_14349)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14348),U_14350),hAPP(c_Finite__Set_Ofold1(U_14348,c_Groups_Otimes__class_Otimes(U_14348)),U_14349))
    | hBOOL(hAPP(hAPP(c_member(U_14348),U_14350),U_14349))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14348),U_14349))
    | U_14349 = c_Orderings_Obot__class_Obot(tc_fun(U_14348,tc_HOL_Obool))
    | ~ class_Groups_Oab__semigroup__mult(U_14348) ),
    inference(clausify,[status(thm)],[f_3600_3]) ).

fof(f_3601_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_3601_2,plain,
    ! [U_14353,U_14352,U_14351] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14351),hAPP(c_Finite__Set_Ofold1(U_14351,c_Orderings_Oord__class_Omin(U_14351)),U_14353)),hAPP(c_Finite__Set_Ofold1(U_14351,c_Orderings_Oord__class_Omin(U_14351)),U_14352)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14351),U_14353))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14351,tc_HOL_Obool)),U_14352),U_14353))
      | U_14352 = c_Orderings_Obot__class_Obot(tc_fun(U_14351,tc_HOL_Obool))
      | ~ class_Orderings_Olinorder(U_14351) ),
    inference(variable_rename,[status(thm)],[f_3601_1]) ).

fof(f_3601_3,plain,
    ! [U_14352,U_14351,U_14353] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14351),hAPP(c_Finite__Set_Ofold1(U_14351,c_Orderings_Oord__class_Omin(U_14351)),U_14353)),hAPP(c_Finite__Set_Ofold1(U_14351,c_Orderings_Oord__class_Omin(U_14351)),U_14352)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14351),U_14353))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14351,tc_HOL_Obool)),U_14352),U_14353))
      | U_14352 = c_Orderings_Obot__class_Obot(tc_fun(U_14351,tc_HOL_Obool))
      | ~ class_Orderings_Olinorder(U_14351) ),
    inference(definitional_conversion,[status(esa)],[f_3601_2]) ).

cnf(f_3601_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14351),hAPP(c_Finite__Set_Ofold1(U_14351,c_Orderings_Oord__class_Omin(U_14351)),U_14353)),hAPP(c_Finite__Set_Ofold1(U_14351,c_Orderings_Oord__class_Omin(U_14351)),U_14352)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14351),U_14353))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14351,tc_HOL_Obool)),U_14352),U_14353))
    | U_14352 = c_Orderings_Obot__class_Obot(tc_fun(U_14351,tc_HOL_Obool))
    | ~ class_Orderings_Olinorder(U_14351) ),
    inference(clausify,[status(thm)],[f_3601_3]) ).

fof(f_3602_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_3602_2,plain,
    ! [U_14357,U_14356,U_14355,U_14354] :
      ( hAPP(U_14356,U_14357) = hAPP(c_Finite__Set_Ofold1(U_14354,U_14355),U_14357)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14354),U_14357))
      | ~ c_Big__Operators_Osemilattice__big(U_14354,U_14355,U_14356) ),
    inference(variable_rename,[status(thm)],[f_3602_1]) ).

fof(f_3602_3,plain,
    ! [U_14356,U_14357,U_14354,U_14355] :
      ( hAPP(U_14356,U_14357) = hAPP(c_Finite__Set_Ofold1(U_14354,U_14355),U_14357)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14354),U_14357))
      | ~ c_Big__Operators_Osemilattice__big(U_14354,U_14355,U_14356) ),
    inference(definitional_conversion,[status(esa)],[f_3602_2]) ).

cnf(f_3602_4,plain,
    ( hAPP(U_14356,U_14357) = hAPP(c_Finite__Set_Ofold1(U_14354,U_14355),U_14357)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14354),U_14357))
    | ~ c_Big__Operators_Osemilattice__big(U_14354,U_14355,U_14356) ),
    inference(clausify,[status(thm)],[f_3602_3]) ).

fof(f_3603_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_3603_2,plain,
    ! [U_14362,U_14361,U_14360,U_14359] :
    ? [U_14358] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14360,U_14359),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14359,tc_prod(U_14360,U_14359),U_14358),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14360,tc_fun(U_14359,tc_HOL_Obool)),U_14361),U_14362))),hAPP(hAPP(c_Product__Type_OSigma(U_14360,U_14359),U_14361),U_14362)))
      & c_Fun_Oinj__on(U_14359,tc_prod(U_14360,U_14359),U_14358,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14360,tc_fun(U_14359,tc_HOL_Obool)),U_14361),U_14362)) ),
    inference(variable_rename,[status(thm)],[f_3603_1]) ).

fof(f_3603_3,plain,
    ! [U_14362,U_14361,U_14360,U_14359] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14360,U_14359),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14359,tc_prod(U_14360,U_14359),sK310(U_14362,U_14361,U_14360,U_14359)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14360,tc_fun(U_14359,tc_HOL_Obool)),U_14361),U_14362))),hAPP(hAPP(c_Product__Type_OSigma(U_14360,U_14359),U_14361),U_14362)))
      & c_Fun_Oinj__on(U_14359,tc_prod(U_14360,U_14359),sK310(U_14362,U_14361,U_14360,U_14359),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14360,tc_fun(U_14359,tc_HOL_Obool)),U_14361),U_14362)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK310]),skolemize(U_14358,sK310(U_14362,U_14361,U_14360,U_14359))],[f_3603_2]) ).

fof(f_3603_4,plain,
    ( ! [U_14359,U_14360,U_14361,U_14362] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14360,U_14359),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14359,tc_prod(U_14360,U_14359),sK310(U_14362,U_14361,U_14360,U_14359)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14360,tc_fun(U_14359,tc_HOL_Obool)),U_14361),U_14362))),hAPP(hAPP(c_Product__Type_OSigma(U_14360,U_14359),U_14361),U_14362)))
    & ! [U_14359,U_14360,U_14361,U_14362] : c_Fun_Oinj__on(U_14359,tc_prod(U_14360,U_14359),sK310(U_14362,U_14361,U_14360,U_14359),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14360,tc_fun(U_14359,tc_HOL_Obool)),U_14361),U_14362)) ),
    inference(definitional_conversion,[status(esa)],[f_3603_3]) ).

cnf(f_3603_5,plain,
    c_Fun_Oinj__on(U_14359,tc_prod(U_14360,U_14359),sK310(U_14362,U_14361,U_14360,U_14359),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14360,tc_fun(U_14359,tc_HOL_Obool)),U_14361),U_14362)),
    inference(clausify,[status(thm)],[f_3603_4]) ).

cnf(f_3603_6,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14360,U_14359),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14359,tc_prod(U_14360,U_14359),sK310(U_14362,U_14361,U_14360,U_14359)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14360,tc_fun(U_14359,tc_HOL_Obool)),U_14361),U_14362))),hAPP(hAPP(c_Product__Type_OSigma(U_14360,U_14359),U_14361),U_14362))),
    inference(clausify,[status(thm)],[f_3603_4]) ).

fof(f_3604_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_3604_2,plain,
    ! [U_14366,U_14365,U_14364] :
      ( c_Relation_Orefl__on(U_14364,U_14366,U_14365)
      | ? [U_14363] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14364,U_14364)),hAPP(hAPP(c_Product__Type_OPair(U_14364,U_14364),U_14363),U_14363)),U_14365))
          & hBOOL(hAPP(hAPP(c_member(U_14364),U_14363),U_14366)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14364,U_14364),tc_HOL_Obool)),U_14365),hAPP(hAPP(c_Product__Type_OSigma(U_14364,U_14364),U_14366),hAPP(c_COMBK(tc_fun(U_14364,tc_HOL_Obool),U_14364),U_14366)))) ),
    inference(variable_rename,[status(thm)],[f_3604_1]) ).

fof(f_3604_3,plain,
    ! [U_14366,U_14365,U_14364] :
      ( c_Relation_Orefl__on(U_14364,U_14366,U_14365)
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14364,U_14364)),hAPP(hAPP(c_Product__Type_OPair(U_14364,U_14364),sK311(U_14366,U_14365,U_14364)),sK311(U_14366,U_14365,U_14364))),U_14365))
        & hBOOL(hAPP(hAPP(c_member(U_14364),sK311(U_14366,U_14365,U_14364)),U_14366)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14364,U_14364),tc_HOL_Obool)),U_14365),hAPP(hAPP(c_Product__Type_OSigma(U_14364,U_14364),U_14366),hAPP(c_COMBK(tc_fun(U_14364,tc_HOL_Obool),U_14364),U_14366)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK311]),skolemize(U_14363,sK311(U_14366,U_14365,U_14364))],[f_3604_2]) ).

fof(f_3604_4,plain,
    ( ! [U_14364,U_14365,U_14366] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14364,U_14364)),hAPP(hAPP(c_Product__Type_OPair(U_14364,U_14364),sK311(U_14366,U_14365,U_14364)),sK311(U_14366,U_14365,U_14364))),U_14365))
        | ~ sP996(U_14364,U_14365,U_14366) )
    & ! [U_14364,U_14365,U_14366] :
        ( hBOOL(hAPP(hAPP(c_member(U_14364),sK311(U_14366,U_14365,U_14364)),U_14366))
        | ~ sP996(U_14364,U_14365,U_14366) )
    & ! [U_14364,U_14365,U_14366] :
        ( c_Relation_Orefl__on(U_14364,U_14366,U_14365)
        | sP996(U_14364,U_14365,U_14366)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14364,U_14364),tc_HOL_Obool)),U_14365),hAPP(hAPP(c_Product__Type_OSigma(U_14364,U_14364),U_14366),hAPP(c_COMBK(tc_fun(U_14364,tc_HOL_Obool),U_14364),U_14366)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP996])],[f_3604_3]) ).

cnf(f_3604_5,plain,
    ( c_Relation_Orefl__on(U_14364,U_14366,U_14365)
    | sP996(U_14364,U_14365,U_14366)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14364,U_14364),tc_HOL_Obool)),U_14365),hAPP(hAPP(c_Product__Type_OSigma(U_14364,U_14364),U_14366),hAPP(c_COMBK(tc_fun(U_14364,tc_HOL_Obool),U_14364),U_14366)))) ),
    inference(clausify,[status(thm)],[f_3604_4]) ).

cnf(f_3604_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14364),sK311(U_14366,U_14365,U_14364)),U_14366))
    | ~ sP996(U_14364,U_14365,U_14366) ),
    inference(clausify,[status(thm)],[f_3604_4]) ).

cnf(f_3604_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14364,U_14364)),hAPP(hAPP(c_Product__Type_OPair(U_14364,U_14364),sK311(U_14366,U_14365,U_14364)),sK311(U_14366,U_14365,U_14364))),U_14365))
    | ~ sP996(U_14364,U_14365,U_14366) ),
    inference(clausify,[status(thm)],[f_3604_4]) ).

fof(f_3605_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_3605_2,plain,
    ! [U_14373,U_14372,U_14371,U_14370,U_14369,U_14368] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14369,U_14368),hAPP(hAPP(c_COMBS(U_14369,tc_fun(U_14371,tc_HOL_Obool),U_14368),hAPP(hAPP(c_COMBB(tc_fun(U_14371,U_14368),tc_fun(tc_fun(U_14371,tc_HOL_Obool),U_14368),U_14369),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14371,U_14368)),U_14373)),U_14372)),U_14370) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_14369,U_14371),U_14368),hAPP(c_Product__Type_Oprod_Oprod__case(U_14369,U_14371,U_14368),U_14373)),hAPP(hAPP(c_Product__Type_OSigma(U_14369,U_14371),U_14370),U_14372))
      | ? [U_14367] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14371),hAPP(U_14372,U_14367)))
          & hBOOL(hAPP(hAPP(c_member(U_14369),U_14367),U_14370)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14369),U_14370))
      | ~ class_Groups_Ocomm__monoid__mult(U_14368) ),
    inference(variable_rename,[status(thm)],[f_3605_1]) ).

fof(f_3605_3,plain,
    ! [U_14373,U_14372,U_14371,U_14370,U_14369,U_14368] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14369,U_14368),hAPP(hAPP(c_COMBS(U_14369,tc_fun(U_14371,tc_HOL_Obool),U_14368),hAPP(hAPP(c_COMBB(tc_fun(U_14371,U_14368),tc_fun(tc_fun(U_14371,tc_HOL_Obool),U_14368),U_14369),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14371,U_14368)),U_14373)),U_14372)),U_14370) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_14369,U_14371),U_14368),hAPP(c_Product__Type_Oprod_Oprod__case(U_14369,U_14371,U_14368),U_14373)),hAPP(hAPP(c_Product__Type_OSigma(U_14369,U_14371),U_14370),U_14372))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14371),hAPP(U_14372,sK312(U_14373,U_14372,U_14371,U_14370,U_14369,U_14368))))
        & hBOOL(hAPP(hAPP(c_member(U_14369),sK312(U_14373,U_14372,U_14371,U_14370,U_14369,U_14368)),U_14370)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14369),U_14370))
      | ~ class_Groups_Ocomm__monoid__mult(U_14368) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK312]),skolemize(U_14367,sK312(U_14373,U_14372,U_14371,U_14370,U_14369,U_14368))],[f_3605_2]) ).

fof(f_3605_4,plain,
    ( ! [U_14368,U_14369,U_14370,U_14371,U_14372,U_14373] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14371),hAPP(U_14372,sK312(U_14373,U_14372,U_14371,U_14370,U_14369,U_14368))))
        | ~ sP997(U_14368,U_14369,U_14370,U_14371,U_14372,U_14373) )
    & ! [U_14368,U_14369,U_14370,U_14371,U_14372,U_14373] :
        ( hBOOL(hAPP(hAPP(c_member(U_14369),sK312(U_14373,U_14372,U_14371,U_14370,U_14369,U_14368)),U_14370))
        | ~ sP997(U_14368,U_14369,U_14370,U_14371,U_14372,U_14373) )
    & ! [U_14368,U_14369,U_14370,U_14371,U_14372,U_14373] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14369,U_14368),hAPP(hAPP(c_COMBS(U_14369,tc_fun(U_14371,tc_HOL_Obool),U_14368),hAPP(hAPP(c_COMBB(tc_fun(U_14371,U_14368),tc_fun(tc_fun(U_14371,tc_HOL_Obool),U_14368),U_14369),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14371,U_14368)),U_14373)),U_14372)),U_14370) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_14369,U_14371),U_14368),hAPP(c_Product__Type_Oprod_Oprod__case(U_14369,U_14371,U_14368),U_14373)),hAPP(hAPP(c_Product__Type_OSigma(U_14369,U_14371),U_14370),U_14372))
        | sP997(U_14368,U_14369,U_14370,U_14371,U_14372,U_14373)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14369),U_14370))
        | ~ class_Groups_Ocomm__monoid__mult(U_14368) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP997])],[f_3605_3]) ).

cnf(f_3605_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14369,U_14368),hAPP(hAPP(c_COMBS(U_14369,tc_fun(U_14371,tc_HOL_Obool),U_14368),hAPP(hAPP(c_COMBB(tc_fun(U_14371,U_14368),tc_fun(tc_fun(U_14371,tc_HOL_Obool),U_14368),U_14369),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14371,U_14368)),U_14373)),U_14372)),U_14370) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_14369,U_14371),U_14368),hAPP(c_Product__Type_Oprod_Oprod__case(U_14369,U_14371,U_14368),U_14373)),hAPP(hAPP(c_Product__Type_OSigma(U_14369,U_14371),U_14370),U_14372))
    | sP997(U_14368,U_14369,U_14370,U_14371,U_14372,U_14373)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14369),U_14370))
    | ~ class_Groups_Ocomm__monoid__mult(U_14368) ),
    inference(clausify,[status(thm)],[f_3605_4]) ).

cnf(f_3605_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14369),sK312(U_14373,U_14372,U_14371,U_14370,U_14369,U_14368)),U_14370))
    | ~ sP997(U_14368,U_14369,U_14370,U_14371,U_14372,U_14373) ),
    inference(clausify,[status(thm)],[f_3605_4]) ).

cnf(f_3605_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14371),hAPP(U_14372,sK312(U_14373,U_14372,U_14371,U_14370,U_14369,U_14368))))
    | ~ sP997(U_14368,U_14369,U_14370,U_14371,U_14372,U_14373) ),
    inference(clausify,[status(thm)],[f_3605_4]) ).

fof(f_3606_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_3606_2,plain,
    ! [U_14380,U_14379,U_14378,U_14377,U_14376,U_14375] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14376,U_14375),hAPP(hAPP(c_COMBS(U_14376,tc_fun(U_14378,tc_HOL_Obool),U_14375),hAPP(hAPP(c_COMBB(tc_fun(U_14378,U_14375),tc_fun(tc_fun(U_14378,tc_HOL_Obool),U_14375),U_14376),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14378,U_14375)),U_14380)),U_14379)),U_14377) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_14376,U_14378),U_14375),hAPP(c_Product__Type_Oprod_Oprod__case(U_14376,U_14378,U_14375),U_14380)),hAPP(hAPP(c_Product__Type_OSigma(U_14376,U_14378),U_14377),U_14379))
      | ? [U_14374] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14378),hAPP(U_14379,U_14374)))
          & hBOOL(hAPP(hAPP(c_member(U_14376),U_14374),U_14377)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14376),U_14377))
      | ~ class_Groups_Ocomm__monoid__add(U_14375) ),
    inference(variable_rename,[status(thm)],[f_3606_1]) ).

fof(f_3606_3,plain,
    ! [U_14380,U_14379,U_14378,U_14377,U_14376,U_14375] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14376,U_14375),hAPP(hAPP(c_COMBS(U_14376,tc_fun(U_14378,tc_HOL_Obool),U_14375),hAPP(hAPP(c_COMBB(tc_fun(U_14378,U_14375),tc_fun(tc_fun(U_14378,tc_HOL_Obool),U_14375),U_14376),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14378,U_14375)),U_14380)),U_14379)),U_14377) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_14376,U_14378),U_14375),hAPP(c_Product__Type_Oprod_Oprod__case(U_14376,U_14378,U_14375),U_14380)),hAPP(hAPP(c_Product__Type_OSigma(U_14376,U_14378),U_14377),U_14379))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14378),hAPP(U_14379,sK313(U_14380,U_14379,U_14378,U_14377,U_14376,U_14375))))
        & hBOOL(hAPP(hAPP(c_member(U_14376),sK313(U_14380,U_14379,U_14378,U_14377,U_14376,U_14375)),U_14377)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14376),U_14377))
      | ~ class_Groups_Ocomm__monoid__add(U_14375) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK313]),skolemize(U_14374,sK313(U_14380,U_14379,U_14378,U_14377,U_14376,U_14375))],[f_3606_2]) ).

fof(f_3606_4,plain,
    ( ! [U_14375,U_14376,U_14377,U_14378,U_14379,U_14380] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14378),hAPP(U_14379,sK313(U_14380,U_14379,U_14378,U_14377,U_14376,U_14375))))
        | ~ sP998(U_14375,U_14376,U_14377,U_14378,U_14379,U_14380) )
    & ! [U_14375,U_14376,U_14377,U_14378,U_14379,U_14380] :
        ( hBOOL(hAPP(hAPP(c_member(U_14376),sK313(U_14380,U_14379,U_14378,U_14377,U_14376,U_14375)),U_14377))
        | ~ sP998(U_14375,U_14376,U_14377,U_14378,U_14379,U_14380) )
    & ! [U_14375,U_14376,U_14377,U_14378,U_14379,U_14380] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14376,U_14375),hAPP(hAPP(c_COMBS(U_14376,tc_fun(U_14378,tc_HOL_Obool),U_14375),hAPP(hAPP(c_COMBB(tc_fun(U_14378,U_14375),tc_fun(tc_fun(U_14378,tc_HOL_Obool),U_14375),U_14376),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14378,U_14375)),U_14380)),U_14379)),U_14377) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_14376,U_14378),U_14375),hAPP(c_Product__Type_Oprod_Oprod__case(U_14376,U_14378,U_14375),U_14380)),hAPP(hAPP(c_Product__Type_OSigma(U_14376,U_14378),U_14377),U_14379))
        | sP998(U_14375,U_14376,U_14377,U_14378,U_14379,U_14380)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14376),U_14377))
        | ~ class_Groups_Ocomm__monoid__add(U_14375) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP998])],[f_3606_3]) ).

cnf(f_3606_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14376,U_14375),hAPP(hAPP(c_COMBS(U_14376,tc_fun(U_14378,tc_HOL_Obool),U_14375),hAPP(hAPP(c_COMBB(tc_fun(U_14378,U_14375),tc_fun(tc_fun(U_14378,tc_HOL_Obool),U_14375),U_14376),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14378,U_14375)),U_14380)),U_14379)),U_14377) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_14376,U_14378),U_14375),hAPP(c_Product__Type_Oprod_Oprod__case(U_14376,U_14378,U_14375),U_14380)),hAPP(hAPP(c_Product__Type_OSigma(U_14376,U_14378),U_14377),U_14379))
    | sP998(U_14375,U_14376,U_14377,U_14378,U_14379,U_14380)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14376),U_14377))
    | ~ class_Groups_Ocomm__monoid__add(U_14375) ),
    inference(clausify,[status(thm)],[f_3606_4]) ).

cnf(f_3606_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14376),sK313(U_14380,U_14379,U_14378,U_14377,U_14376,U_14375)),U_14377))
    | ~ sP998(U_14375,U_14376,U_14377,U_14378,U_14379,U_14380) ),
    inference(clausify,[status(thm)],[f_3606_4]) ).

cnf(f_3606_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14378),hAPP(U_14379,sK313(U_14380,U_14379,U_14378,U_14377,U_14376,U_14375))))
    | ~ sP998(U_14375,U_14376,U_14377,U_14378,U_14379,U_14380) ),
    inference(clausify,[status(thm)],[f_3606_4]) ).

fof(f_3607_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_3607_2,plain,
    ! [U_14387,U_14386,U_14385,U_14384,U_14383,U_14382] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14382,U_14383,c_Groups_Otimes__class_Otimes(U_14382)),hAPP(hAPP(c_COMBS(U_14383,tc_fun(U_14385,tc_HOL_Obool),U_14382),hAPP(hAPP(c_COMBC(U_14383,U_14382,tc_fun(tc_fun(U_14385,tc_HOL_Obool),U_14382)),hAPP(hAPP(c_COMBB(tc_fun(U_14385,U_14382),tc_fun(U_14382,tc_fun(tc_fun(U_14385,tc_HOL_Obool),U_14382)),U_14383),c_Finite__Set_Ofold__image(U_14382,U_14385,c_Groups_Otimes__class_Otimes(U_14382))),U_14387)),c_Groups_Oone__class_Oone(U_14382))),U_14386)),c_Groups_Oone__class_Oone(U_14382)),U_14384) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14382,tc_prod(U_14383,U_14385),c_Groups_Otimes__class_Otimes(U_14382)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14383,U_14385,U_14382),U_14387)),c_Groups_Oone__class_Oone(U_14382)),hAPP(hAPP(c_Product__Type_OSigma(U_14383,U_14385),U_14384),U_14386))
      | ? [U_14381] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14385),hAPP(U_14386,U_14381)))
          & hBOOL(hAPP(hAPP(c_member(U_14383),U_14381),U_14384)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14383),U_14384))
      | ~ class_Groups_Ocomm__monoid__mult(U_14382) ),
    inference(variable_rename,[status(thm)],[f_3607_1]) ).

fof(f_3607_3,plain,
    ! [U_14387,U_14386,U_14385,U_14384,U_14383,U_14382] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14382,U_14383,c_Groups_Otimes__class_Otimes(U_14382)),hAPP(hAPP(c_COMBS(U_14383,tc_fun(U_14385,tc_HOL_Obool),U_14382),hAPP(hAPP(c_COMBC(U_14383,U_14382,tc_fun(tc_fun(U_14385,tc_HOL_Obool),U_14382)),hAPP(hAPP(c_COMBB(tc_fun(U_14385,U_14382),tc_fun(U_14382,tc_fun(tc_fun(U_14385,tc_HOL_Obool),U_14382)),U_14383),c_Finite__Set_Ofold__image(U_14382,U_14385,c_Groups_Otimes__class_Otimes(U_14382))),U_14387)),c_Groups_Oone__class_Oone(U_14382))),U_14386)),c_Groups_Oone__class_Oone(U_14382)),U_14384) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14382,tc_prod(U_14383,U_14385),c_Groups_Otimes__class_Otimes(U_14382)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14383,U_14385,U_14382),U_14387)),c_Groups_Oone__class_Oone(U_14382)),hAPP(hAPP(c_Product__Type_OSigma(U_14383,U_14385),U_14384),U_14386))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14385),hAPP(U_14386,sK314(U_14387,U_14386,U_14385,U_14384,U_14383,U_14382))))
        & hBOOL(hAPP(hAPP(c_member(U_14383),sK314(U_14387,U_14386,U_14385,U_14384,U_14383,U_14382)),U_14384)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14383),U_14384))
      | ~ class_Groups_Ocomm__monoid__mult(U_14382) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK314]),skolemize(U_14381,sK314(U_14387,U_14386,U_14385,U_14384,U_14383,U_14382))],[f_3607_2]) ).

fof(f_3607_4,plain,
    ( ! [U_14382,U_14383,U_14384,U_14385,U_14386,U_14387] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14385),hAPP(U_14386,sK314(U_14387,U_14386,U_14385,U_14384,U_14383,U_14382))))
        | ~ sP999(U_14382,U_14383,U_14384,U_14385,U_14386,U_14387) )
    & ! [U_14382,U_14383,U_14384,U_14385,U_14386,U_14387] :
        ( hBOOL(hAPP(hAPP(c_member(U_14383),sK314(U_14387,U_14386,U_14385,U_14384,U_14383,U_14382)),U_14384))
        | ~ sP999(U_14382,U_14383,U_14384,U_14385,U_14386,U_14387) )
    & ! [U_14382,U_14383,U_14384,U_14385,U_14386,U_14387] :
        ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14382,U_14383,c_Groups_Otimes__class_Otimes(U_14382)),hAPP(hAPP(c_COMBS(U_14383,tc_fun(U_14385,tc_HOL_Obool),U_14382),hAPP(hAPP(c_COMBC(U_14383,U_14382,tc_fun(tc_fun(U_14385,tc_HOL_Obool),U_14382)),hAPP(hAPP(c_COMBB(tc_fun(U_14385,U_14382),tc_fun(U_14382,tc_fun(tc_fun(U_14385,tc_HOL_Obool),U_14382)),U_14383),c_Finite__Set_Ofold__image(U_14382,U_14385,c_Groups_Otimes__class_Otimes(U_14382))),U_14387)),c_Groups_Oone__class_Oone(U_14382))),U_14386)),c_Groups_Oone__class_Oone(U_14382)),U_14384) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14382,tc_prod(U_14383,U_14385),c_Groups_Otimes__class_Otimes(U_14382)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14383,U_14385,U_14382),U_14387)),c_Groups_Oone__class_Oone(U_14382)),hAPP(hAPP(c_Product__Type_OSigma(U_14383,U_14385),U_14384),U_14386))
        | sP999(U_14382,U_14383,U_14384,U_14385,U_14386,U_14387)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14383),U_14384))
        | ~ class_Groups_Ocomm__monoid__mult(U_14382) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP999])],[f_3607_3]) ).

cnf(f_3607_5,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14382,U_14383,c_Groups_Otimes__class_Otimes(U_14382)),hAPP(hAPP(c_COMBS(U_14383,tc_fun(U_14385,tc_HOL_Obool),U_14382),hAPP(hAPP(c_COMBC(U_14383,U_14382,tc_fun(tc_fun(U_14385,tc_HOL_Obool),U_14382)),hAPP(hAPP(c_COMBB(tc_fun(U_14385,U_14382),tc_fun(U_14382,tc_fun(tc_fun(U_14385,tc_HOL_Obool),U_14382)),U_14383),c_Finite__Set_Ofold__image(U_14382,U_14385,c_Groups_Otimes__class_Otimes(U_14382))),U_14387)),c_Groups_Oone__class_Oone(U_14382))),U_14386)),c_Groups_Oone__class_Oone(U_14382)),U_14384) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14382,tc_prod(U_14383,U_14385),c_Groups_Otimes__class_Otimes(U_14382)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14383,U_14385,U_14382),U_14387)),c_Groups_Oone__class_Oone(U_14382)),hAPP(hAPP(c_Product__Type_OSigma(U_14383,U_14385),U_14384),U_14386))
    | sP999(U_14382,U_14383,U_14384,U_14385,U_14386,U_14387)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14383),U_14384))
    | ~ class_Groups_Ocomm__monoid__mult(U_14382) ),
    inference(clausify,[status(thm)],[f_3607_4]) ).

cnf(f_3607_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14383),sK314(U_14387,U_14386,U_14385,U_14384,U_14383,U_14382)),U_14384))
    | ~ sP999(U_14382,U_14383,U_14384,U_14385,U_14386,U_14387) ),
    inference(clausify,[status(thm)],[f_3607_4]) ).

cnf(f_3607_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14385),hAPP(U_14386,sK314(U_14387,U_14386,U_14385,U_14384,U_14383,U_14382))))
    | ~ sP999(U_14382,U_14383,U_14384,U_14385,U_14386,U_14387) ),
    inference(clausify,[status(thm)],[f_3607_4]) ).

fof(f_3608_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_3608_2,plain,
    ! [U_14392,U_14391,U_14390,U_14389] :
      ( hAPP(c_Finite__Set_Ocard(tc_prod(U_14389,U_14391)),hAPP(hAPP(c_Product__Type_OSigma(U_14389,U_14391),U_14390),U_14392)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14389,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14391,tc_HOL_Obool),tc_Nat_Onat,U_14389),c_Finite__Set_Ocard(U_14391)),U_14392)),U_14390)
      | ? [U_14388] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14391),hAPP(U_14392,U_14388)))
          & hBOOL(hAPP(hAPP(c_member(U_14389),U_14388),U_14390)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14389),U_14390)) ),
    inference(variable_rename,[status(thm)],[f_3608_1]) ).

fof(f_3608_3,plain,
    ! [U_14392,U_14391,U_14390,U_14389] :
      ( hAPP(c_Finite__Set_Ocard(tc_prod(U_14389,U_14391)),hAPP(hAPP(c_Product__Type_OSigma(U_14389,U_14391),U_14390),U_14392)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14389,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14391,tc_HOL_Obool),tc_Nat_Onat,U_14389),c_Finite__Set_Ocard(U_14391)),U_14392)),U_14390)
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14391),hAPP(U_14392,sK315(U_14392,U_14391,U_14390,U_14389))))
        & hBOOL(hAPP(hAPP(c_member(U_14389),sK315(U_14392,U_14391,U_14390,U_14389)),U_14390)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14389),U_14390)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK315]),skolemize(U_14388,sK315(U_14392,U_14391,U_14390,U_14389))],[f_3608_2]) ).

fof(f_3608_4,plain,
    ( ! [U_14389,U_14391,U_14390,U_14392] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14391),hAPP(U_14392,sK315(U_14392,U_14391,U_14390,U_14389))))
        | ~ sP1000(U_14389,U_14391,U_14390,U_14392) )
    & ! [U_14389,U_14391,U_14390,U_14392] :
        ( hBOOL(hAPP(hAPP(c_member(U_14389),sK315(U_14392,U_14391,U_14390,U_14389)),U_14390))
        | ~ sP1000(U_14389,U_14391,U_14390,U_14392) )
    & ! [U_14389,U_14391,U_14390,U_14392] :
        ( hAPP(c_Finite__Set_Ocard(tc_prod(U_14389,U_14391)),hAPP(hAPP(c_Product__Type_OSigma(U_14389,U_14391),U_14390),U_14392)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14389,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14391,tc_HOL_Obool),tc_Nat_Onat,U_14389),c_Finite__Set_Ocard(U_14391)),U_14392)),U_14390)
        | sP1000(U_14389,U_14391,U_14390,U_14392)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14389),U_14390)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1000])],[f_3608_3]) ).

cnf(f_3608_5,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_prod(U_14389,U_14391)),hAPP(hAPP(c_Product__Type_OSigma(U_14389,U_14391),U_14390),U_14392)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14389,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14391,tc_HOL_Obool),tc_Nat_Onat,U_14389),c_Finite__Set_Ocard(U_14391)),U_14392)),U_14390)
    | sP1000(U_14389,U_14391,U_14390,U_14392)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14389),U_14390)) ),
    inference(clausify,[status(thm)],[f_3608_4]) ).

cnf(f_3608_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14389),sK315(U_14392,U_14391,U_14390,U_14389)),U_14390))
    | ~ sP1000(U_14389,U_14391,U_14390,U_14392) ),
    inference(clausify,[status(thm)],[f_3608_4]) ).

cnf(f_3608_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14391),hAPP(U_14392,sK315(U_14392,U_14391,U_14390,U_14389))))
    | ~ sP1000(U_14389,U_14391,U_14390,U_14392) ),
    inference(clausify,[status(thm)],[f_3608_4]) ).

fof(f_3609_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_3609_2,plain,
    ! [U_14396,U_14395] :
      ( hBOOL(hAPP(hAPP(c_member(U_14395),hAPP(c_Finite__Set_Ofold1(U_14395,c_Groups_Otimes__class_Otimes(U_14395)),U_14396)),U_14396))
      | ? [U_14394,U_14393] : ~ hBOOL(hAPP(hAPP(c_member(U_14395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14395),U_14394),U_14393)),hAPP(hAPP(c_Set_Oinsert(U_14395),U_14394),hAPP(hAPP(c_Set_Oinsert(U_14395),U_14393),c_Orderings_Obot__class_Obot(tc_fun(U_14395,tc_HOL_Obool))))))
      | U_14396 = c_Orderings_Obot__class_Obot(tc_fun(U_14395,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14395),U_14396))
      | ~ class_Groups_Oab__semigroup__mult(U_14395) ),
    inference(variable_rename,[status(thm)],[f_3609_1]) ).

fof(f_3609_3,plain,
    ! [U_14396,U_14395] :
      ( hBOOL(hAPP(hAPP(c_member(U_14395),hAPP(c_Finite__Set_Ofold1(U_14395,c_Groups_Otimes__class_Otimes(U_14395)),U_14396)),U_14396))
      | ? [U_14393] : ~ hBOOL(hAPP(hAPP(c_member(U_14395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14395),sK316(U_14396,U_14395)),U_14393)),hAPP(hAPP(c_Set_Oinsert(U_14395),sK316(U_14396,U_14395)),hAPP(hAPP(c_Set_Oinsert(U_14395),U_14393),c_Orderings_Obot__class_Obot(tc_fun(U_14395,tc_HOL_Obool))))))
      | U_14396 = c_Orderings_Obot__class_Obot(tc_fun(U_14395,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14395),U_14396))
      | ~ class_Groups_Oab__semigroup__mult(U_14395) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK316]),skolemize(U_14394,sK316(U_14396,U_14395))],[f_3609_2]) ).

fof(f_3609_4,plain,
    ! [U_14396,U_14395] :
      ( hBOOL(hAPP(hAPP(c_member(U_14395),hAPP(c_Finite__Set_Ofold1(U_14395,c_Groups_Otimes__class_Otimes(U_14395)),U_14396)),U_14396))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14395),sK316(U_14396,U_14395)),sK317(U_14396,U_14395))),hAPP(hAPP(c_Set_Oinsert(U_14395),sK316(U_14396,U_14395)),hAPP(hAPP(c_Set_Oinsert(U_14395),sK317(U_14396,U_14395)),c_Orderings_Obot__class_Obot(tc_fun(U_14395,tc_HOL_Obool))))))
      | U_14396 = c_Orderings_Obot__class_Obot(tc_fun(U_14395,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14395),U_14396))
      | ~ class_Groups_Oab__semigroup__mult(U_14395) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK317]),skolemize(U_14393,sK317(U_14396,U_14395))],[f_3609_3]) ).

fof(f_3609_5,plain,
    ! [U_14395,U_14396] :
      ( hBOOL(hAPP(hAPP(c_member(U_14395),hAPP(c_Finite__Set_Ofold1(U_14395,c_Groups_Otimes__class_Otimes(U_14395)),U_14396)),U_14396))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14395),sK316(U_14396,U_14395)),sK317(U_14396,U_14395))),hAPP(hAPP(c_Set_Oinsert(U_14395),sK316(U_14396,U_14395)),hAPP(hAPP(c_Set_Oinsert(U_14395),sK317(U_14396,U_14395)),c_Orderings_Obot__class_Obot(tc_fun(U_14395,tc_HOL_Obool))))))
      | U_14396 = c_Orderings_Obot__class_Obot(tc_fun(U_14395,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14395),U_14396))
      | ~ class_Groups_Oab__semigroup__mult(U_14395) ),
    inference(definitional_conversion,[status(esa)],[f_3609_4]) ).

cnf(f_3609_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14395),hAPP(c_Finite__Set_Ofold1(U_14395,c_Groups_Otimes__class_Otimes(U_14395)),U_14396)),U_14396))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14395),sK316(U_14396,U_14395)),sK317(U_14396,U_14395))),hAPP(hAPP(c_Set_Oinsert(U_14395),sK316(U_14396,U_14395)),hAPP(hAPP(c_Set_Oinsert(U_14395),sK317(U_14396,U_14395)),c_Orderings_Obot__class_Obot(tc_fun(U_14395,tc_HOL_Obool))))))
    | U_14396 = c_Orderings_Obot__class_Obot(tc_fun(U_14395,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14395),U_14396))
    | ~ class_Groups_Oab__semigroup__mult(U_14395) ),
    inference(clausify,[status(thm)],[f_3609_5]) ).

fof(f_3610_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_3610_2,plain,
    ! [U_14401,U_14400,U_14399,U_14398] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14398,U_14400)),hAPP(hAPP(c_Product__Type_OSigma(U_14398,U_14400),U_14399),U_14401)))
      | ? [U_14397] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14400),hAPP(U_14401,U_14397)))
          & hBOOL(hAPP(hAPP(c_member(U_14398),U_14397),U_14399)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14398),U_14399)) ),
    inference(variable_rename,[status(thm)],[f_3610_1]) ).

fof(f_3610_3,plain,
    ! [U_14401,U_14400,U_14399,U_14398] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14398,U_14400)),hAPP(hAPP(c_Product__Type_OSigma(U_14398,U_14400),U_14399),U_14401)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14400),hAPP(U_14401,sK318(U_14401,U_14400,U_14399,U_14398))))
        & hBOOL(hAPP(hAPP(c_member(U_14398),sK318(U_14401,U_14400,U_14399,U_14398)),U_14399)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14398),U_14399)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK318]),skolemize(U_14397,sK318(U_14401,U_14400,U_14399,U_14398))],[f_3610_2]) ).

fof(f_3610_4,plain,
    ( ! [U_14399,U_14398,U_14400,U_14401] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14400),hAPP(U_14401,sK318(U_14401,U_14400,U_14399,U_14398))))
        | ~ sP1001(U_14399,U_14398,U_14400,U_14401) )
    & ! [U_14399,U_14398,U_14400,U_14401] :
        ( hBOOL(hAPP(hAPP(c_member(U_14398),sK318(U_14401,U_14400,U_14399,U_14398)),U_14399))
        | ~ sP1001(U_14399,U_14398,U_14400,U_14401) )
    & ! [U_14399,U_14398,U_14400,U_14401] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14398,U_14400)),hAPP(hAPP(c_Product__Type_OSigma(U_14398,U_14400),U_14399),U_14401)))
        | sP1001(U_14399,U_14398,U_14400,U_14401)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14398),U_14399)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1001])],[f_3610_3]) ).

cnf(f_3610_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14398,U_14400)),hAPP(hAPP(c_Product__Type_OSigma(U_14398,U_14400),U_14399),U_14401)))
    | sP1001(U_14399,U_14398,U_14400,U_14401)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14398),U_14399)) ),
    inference(clausify,[status(thm)],[f_3610_4]) ).

cnf(f_3610_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14398),sK318(U_14401,U_14400,U_14399,U_14398)),U_14399))
    | ~ sP1001(U_14399,U_14398,U_14400,U_14401) ),
    inference(clausify,[status(thm)],[f_3610_4]) ).

cnf(f_3610_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14400),hAPP(U_14401,sK318(U_14401,U_14400,U_14399,U_14398))))
    | ~ sP1001(U_14399,U_14398,U_14400,U_14401) ),
    inference(clausify,[status(thm)],[f_3610_4]) ).

fof(f_3611_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_3611_2,plain,
    ! [U_14406,U_14405,U_14404] :
      ( hAPP(U_14405,hAPP(c_Finite__Set_Ofold1(U_14404,c_Groups_Otimes__class_Otimes(U_14404)),U_14406)) = hAPP(c_Finite__Set_Ofold1(U_14404,c_Groups_Otimes__class_Otimes(U_14404)),hAPP(c_Set_Oimage(U_14404,U_14404,U_14405),U_14406))
      | U_14406 = c_Orderings_Obot__class_Obot(tc_fun(U_14404,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14404),U_14406))
      | ? [U_14403,U_14402] : hAPP(U_14405,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14404),U_14403),U_14402)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14404),hAPP(U_14405,U_14403)),hAPP(U_14405,U_14402))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14404) ),
    inference(variable_rename,[status(thm)],[f_3611_1]) ).

fof(f_3611_3,plain,
    ! [U_14406,U_14405,U_14404] :
      ( hAPP(U_14405,hAPP(c_Finite__Set_Ofold1(U_14404,c_Groups_Otimes__class_Otimes(U_14404)),U_14406)) = hAPP(c_Finite__Set_Ofold1(U_14404,c_Groups_Otimes__class_Otimes(U_14404)),hAPP(c_Set_Oimage(U_14404,U_14404,U_14405),U_14406))
      | U_14406 = c_Orderings_Obot__class_Obot(tc_fun(U_14404,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14404),U_14406))
      | ? [U_14402] : hAPP(U_14405,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14404),sK319(U_14406,U_14405,U_14404)),U_14402)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14404),hAPP(U_14405,sK319(U_14406,U_14405,U_14404))),hAPP(U_14405,U_14402))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14404) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK319]),skolemize(U_14403,sK319(U_14406,U_14405,U_14404))],[f_3611_2]) ).

fof(f_3611_4,plain,
    ! [U_14406,U_14405,U_14404] :
      ( hAPP(U_14405,hAPP(c_Finite__Set_Ofold1(U_14404,c_Groups_Otimes__class_Otimes(U_14404)),U_14406)) = hAPP(c_Finite__Set_Ofold1(U_14404,c_Groups_Otimes__class_Otimes(U_14404)),hAPP(c_Set_Oimage(U_14404,U_14404,U_14405),U_14406))
      | U_14406 = c_Orderings_Obot__class_Obot(tc_fun(U_14404,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14404),U_14406))
      | hAPP(U_14405,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14404),sK319(U_14406,U_14405,U_14404)),sK320(U_14406,U_14405,U_14404))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14404),hAPP(U_14405,sK319(U_14406,U_14405,U_14404))),hAPP(U_14405,sK320(U_14406,U_14405,U_14404)))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14404) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK320]),skolemize(U_14402,sK320(U_14406,U_14405,U_14404))],[f_3611_3]) ).

fof(f_3611_5,plain,
    ! [U_14404,U_14405,U_14406] :
      ( hAPP(U_14405,hAPP(c_Finite__Set_Ofold1(U_14404,c_Groups_Otimes__class_Otimes(U_14404)),U_14406)) = hAPP(c_Finite__Set_Ofold1(U_14404,c_Groups_Otimes__class_Otimes(U_14404)),hAPP(c_Set_Oimage(U_14404,U_14404,U_14405),U_14406))
      | U_14406 = c_Orderings_Obot__class_Obot(tc_fun(U_14404,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14404),U_14406))
      | hAPP(U_14405,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14404),sK319(U_14406,U_14405,U_14404)),sK320(U_14406,U_14405,U_14404))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14404),hAPP(U_14405,sK319(U_14406,U_14405,U_14404))),hAPP(U_14405,sK320(U_14406,U_14405,U_14404)))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14404) ),
    inference(definitional_conversion,[status(esa)],[f_3611_4]) ).

cnf(f_3611_6,plain,
    ( hAPP(U_14405,hAPP(c_Finite__Set_Ofold1(U_14404,c_Groups_Otimes__class_Otimes(U_14404)),U_14406)) = hAPP(c_Finite__Set_Ofold1(U_14404,c_Groups_Otimes__class_Otimes(U_14404)),hAPP(c_Set_Oimage(U_14404,U_14404,U_14405),U_14406))
    | U_14406 = c_Orderings_Obot__class_Obot(tc_fun(U_14404,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14404),U_14406))
    | hAPP(U_14405,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14404),sK319(U_14406,U_14405,U_14404)),sK320(U_14406,U_14405,U_14404))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14404),hAPP(U_14405,sK319(U_14406,U_14405,U_14404))),hAPP(U_14405,sK320(U_14406,U_14405,U_14404)))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_14404) ),
    inference(clausify,[status(thm)],[f_3611_5]) ).

fof(f_3612_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_3612_2,plain,
    ! [U_14413,U_14412,U_14411,U_14410,U_14409] :
      ( ? [U_14408] :
          ( ? [U_14407] :
              ( U_14411 = hAPP(hAPP(c_Product__Type_OPair(U_14409,U_14410),U_14408),U_14407)
              & hBOOL(hAPP(hAPP(c_member(U_14410),U_14407),hAPP(U_14413,U_14408))) )
          & hBOOL(hAPP(hAPP(c_member(U_14409),U_14408),U_14412)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14409,U_14410)),U_14411),hAPP(hAPP(c_Product__Type_OSigma(U_14409,U_14410),U_14412),U_14413))) ),
    inference(variable_rename,[status(thm)],[f_3612_1]) ).

fof(f_3612_3,plain,
    ! [U_14413,U_14412,U_14411,U_14410,U_14409] :
      ( ( ? [U_14407] :
            ( U_14411 = hAPP(hAPP(c_Product__Type_OPair(U_14409,U_14410),sK321(U_14413,U_14412,U_14411,U_14410,U_14409)),U_14407)
            & hBOOL(hAPP(hAPP(c_member(U_14410),U_14407),hAPP(U_14413,sK321(U_14413,U_14412,U_14411,U_14410,U_14409)))) )
        & hBOOL(hAPP(hAPP(c_member(U_14409),sK321(U_14413,U_14412,U_14411,U_14410,U_14409)),U_14412)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14409,U_14410)),U_14411),hAPP(hAPP(c_Product__Type_OSigma(U_14409,U_14410),U_14412),U_14413))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK321]),skolemize(U_14408,sK321(U_14413,U_14412,U_14411,U_14410,U_14409))],[f_3612_2]) ).

fof(f_3612_4,plain,
    ! [U_14413,U_14412,U_14411,U_14410,U_14409] :
      ( ( U_14411 = hAPP(hAPP(c_Product__Type_OPair(U_14409,U_14410),sK321(U_14413,U_14412,U_14411,U_14410,U_14409)),sK322(U_14413,U_14412,U_14411,U_14410,U_14409))
        & hBOOL(hAPP(hAPP(c_member(U_14410),sK322(U_14413,U_14412,U_14411,U_14410,U_14409)),hAPP(U_14413,sK321(U_14413,U_14412,U_14411,U_14410,U_14409))))
        & hBOOL(hAPP(hAPP(c_member(U_14409),sK321(U_14413,U_14412,U_14411,U_14410,U_14409)),U_14412)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14409,U_14410)),U_14411),hAPP(hAPP(c_Product__Type_OSigma(U_14409,U_14410),U_14412),U_14413))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK322]),skolemize(U_14407,sK322(U_14413,U_14412,U_14411,U_14410,U_14409))],[f_3612_3]) ).

fof(f_3612_5,plain,
    ( ! [U_14409,U_14410,U_14411,U_14412,U_14413] :
        ( U_14411 = hAPP(hAPP(c_Product__Type_OPair(U_14409,U_14410),sK321(U_14413,U_14412,U_14411,U_14410,U_14409)),sK322(U_14413,U_14412,U_14411,U_14410,U_14409))
        | ~ sP1002(U_14409,U_14410,U_14411,U_14412,U_14413) )
    & ! [U_14409,U_14410,U_14411,U_14412,U_14413] :
        ( hBOOL(hAPP(hAPP(c_member(U_14410),sK322(U_14413,U_14412,U_14411,U_14410,U_14409)),hAPP(U_14413,sK321(U_14413,U_14412,U_14411,U_14410,U_14409))))
        | ~ sP1002(U_14409,U_14410,U_14411,U_14412,U_14413) )
    & ! [U_14409,U_14410,U_14411,U_14412,U_14413] :
        ( hBOOL(hAPP(hAPP(c_member(U_14409),sK321(U_14413,U_14412,U_14411,U_14410,U_14409)),U_14412))
        | ~ sP1002(U_14409,U_14410,U_14411,U_14412,U_14413) )
    & ! [U_14409,U_14410,U_14411,U_14412,U_14413] :
        ( sP1002(U_14409,U_14410,U_14411,U_14412,U_14413)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14409,U_14410)),U_14411),hAPP(hAPP(c_Product__Type_OSigma(U_14409,U_14410),U_14412),U_14413))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1002])],[f_3612_4]) ).

cnf(f_3612_6,plain,
    ( sP1002(U_14409,U_14410,U_14411,U_14412,U_14413)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14409,U_14410)),U_14411),hAPP(hAPP(c_Product__Type_OSigma(U_14409,U_14410),U_14412),U_14413))) ),
    inference(clausify,[status(thm)],[f_3612_5]) ).

cnf(f_3612_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14409),sK321(U_14413,U_14412,U_14411,U_14410,U_14409)),U_14412))
    | ~ sP1002(U_14409,U_14410,U_14411,U_14412,U_14413) ),
    inference(clausify,[status(thm)],[f_3612_5]) ).

cnf(f_3612_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14410),sK322(U_14413,U_14412,U_14411,U_14410,U_14409)),hAPP(U_14413,sK321(U_14413,U_14412,U_14411,U_14410,U_14409))))
    | ~ sP1002(U_14409,U_14410,U_14411,U_14412,U_14413) ),
    inference(clausify,[status(thm)],[f_3612_5]) ).

cnf(f_3612_9,plain,
    ( U_14411 = hAPP(hAPP(c_Product__Type_OPair(U_14409,U_14410),sK321(U_14413,U_14412,U_14411,U_14410,U_14409)),sK322(U_14413,U_14412,U_14411,U_14410,U_14409))
    | ~ sP1002(U_14409,U_14410,U_14411,U_14412,U_14413) ),
    inference(clausify,[status(thm)],[f_3612_5]) ).

fof(f_3613_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_3613_2,plain,
    ! [U_14419,U_14418,U_14417,U_14416,U_14415,U_14414] :
      ( hAPP(c_Set_Oimage(tc_prod(U_14414,U_14417),tc_prod(U_14415,U_14418),c_Product__Type_Omap__pair(U_14414,U_14415,U_14417,U_14418,U_14416,U_14419)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14414,U_14417),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14415,U_14418),tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_14417,U_14418,U_14419),c_Orderings_Otop__class_Otop(tc_fun(U_14417,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14418,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_14414,U_14415,U_14416),c_Orderings_Otop__class_Otop(tc_fun(U_14414,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14415,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3613_1]) ).

fof(f_3613_3,plain,
    ! [U_14416,U_14414,U_14415,U_14417,U_14418,U_14419] :
      ( hAPP(c_Set_Oimage(tc_prod(U_14414,U_14417),tc_prod(U_14415,U_14418),c_Product__Type_Omap__pair(U_14414,U_14415,U_14417,U_14418,U_14416,U_14419)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14414,U_14417),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14415,U_14418),tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_14417,U_14418,U_14419),c_Orderings_Otop__class_Otop(tc_fun(U_14417,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14418,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_14414,U_14415,U_14416),c_Orderings_Otop__class_Otop(tc_fun(U_14414,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14415,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3613_2]) ).

cnf(f_3613_4,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_14414,U_14417),tc_prod(U_14415,U_14418),c_Product__Type_Omap__pair(U_14414,U_14415,U_14417,U_14418,U_14416,U_14419)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14414,U_14417),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14415,U_14418),tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_14417,U_14418,U_14419),c_Orderings_Otop__class_Otop(tc_fun(U_14417,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14418,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_14414,U_14415,U_14416),c_Orderings_Otop__class_Otop(tc_fun(U_14414,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14415,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3613_3]) ).

fof(f_3614_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_3614_2,plain,
    ! [U_14427,U_14426,U_14425,U_14424,U_14423,U_14422,U_14421,U_14420] :
      ( c_Fun_Oinj__on(tc_prod(U_14420,U_14424),tc_prod(U_14421,U_14425),c_Product__Type_Omap__pair(U_14420,U_14421,U_14424,U_14425,U_14422,U_14426),hAPP(hAPP(c_Product__Type_OSigma(U_14420,U_14424),U_14423),hAPP(c_COMBK(tc_fun(U_14424,tc_HOL_Obool),U_14420),U_14427)))
      | ~ c_Fun_Oinj__on(U_14424,U_14425,U_14426,U_14427)
      | ~ c_Fun_Oinj__on(U_14420,U_14421,U_14422,U_14423) ),
    inference(variable_rename,[status(thm)],[f_3614_1]) ).

fof(f_3614_3,plain,
    ! [U_14420,U_14421,U_14422,U_14423,U_14424,U_14425,U_14426,U_14427] :
      ( c_Fun_Oinj__on(tc_prod(U_14420,U_14424),tc_prod(U_14421,U_14425),c_Product__Type_Omap__pair(U_14420,U_14421,U_14424,U_14425,U_14422,U_14426),hAPP(hAPP(c_Product__Type_OSigma(U_14420,U_14424),U_14423),hAPP(c_COMBK(tc_fun(U_14424,tc_HOL_Obool),U_14420),U_14427)))
      | ~ c_Fun_Oinj__on(U_14424,U_14425,U_14426,U_14427)
      | ~ c_Fun_Oinj__on(U_14420,U_14421,U_14422,U_14423) ),
    inference(definitional_conversion,[status(esa)],[f_3614_2]) ).

cnf(f_3614_4,plain,
    ( c_Fun_Oinj__on(tc_prod(U_14420,U_14424),tc_prod(U_14421,U_14425),c_Product__Type_Omap__pair(U_14420,U_14421,U_14424,U_14425,U_14422,U_14426),hAPP(hAPP(c_Product__Type_OSigma(U_14420,U_14424),U_14423),hAPP(c_COMBK(tc_fun(U_14424,tc_HOL_Obool),U_14420),U_14427)))
    | ~ c_Fun_Oinj__on(U_14424,U_14425,U_14426,U_14427)
    | ~ c_Fun_Oinj__on(U_14420,U_14421,U_14422,U_14423) ),
    inference(clausify,[status(thm)],[f_3614_3]) ).

fof(f_3615_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_3615_2,plain,
    ! [U_14436,U_14435,U_14434,U_14433,U_14432,U_14431,U_14430,U_14429,U_14428] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14433,U_14434)),hAPP(hAPP(c_Product__Type_OPair(U_14433,U_14434),hAPP(U_14435,U_14430)),hAPP(U_14436,U_14431))),hAPP(c_Set_Oimage(tc_prod(U_14428,U_14429),tc_prod(U_14433,U_14434),c_Product__Type_Omap__pair(U_14428,U_14433,U_14429,U_14434,U_14435,U_14436)),U_14432)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14428,U_14429)),hAPP(hAPP(c_Product__Type_OPair(U_14428,U_14429),U_14430),U_14431)),U_14432)) ),
    inference(variable_rename,[status(thm)],[f_3615_1]) ).

fof(f_3615_3,plain,
    ! [U_14428,U_14429,U_14430,U_14431,U_14432,U_14433,U_14434,U_14435,U_14436] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14433,U_14434)),hAPP(hAPP(c_Product__Type_OPair(U_14433,U_14434),hAPP(U_14435,U_14430)),hAPP(U_14436,U_14431))),hAPP(c_Set_Oimage(tc_prod(U_14428,U_14429),tc_prod(U_14433,U_14434),c_Product__Type_Omap__pair(U_14428,U_14433,U_14429,U_14434,U_14435,U_14436)),U_14432)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14428,U_14429)),hAPP(hAPP(c_Product__Type_OPair(U_14428,U_14429),U_14430),U_14431)),U_14432)) ),
    inference(definitional_conversion,[status(esa)],[f_3615_2]) ).

cnf(f_3615_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14433,U_14434)),hAPP(hAPP(c_Product__Type_OPair(U_14433,U_14434),hAPP(U_14435,U_14430)),hAPP(U_14436,U_14431))),hAPP(c_Set_Oimage(tc_prod(U_14428,U_14429),tc_prod(U_14433,U_14434),c_Product__Type_Omap__pair(U_14428,U_14433,U_14429,U_14434,U_14435,U_14436)),U_14432)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14428,U_14429)),hAPP(hAPP(c_Product__Type_OPair(U_14428,U_14429),U_14430),U_14431)),U_14432)) ),
    inference(clausify,[status(thm)],[f_3615_3]) ).

fof(f_3616_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_3616_2,plain,
    ! [U_14442,U_14441,U_14440,U_14439,U_14438,U_14437] : hAPP(c_Fun_Ocomp(tc_prod(U_14437,U_14438),U_14437,tc_prod(U_14439,U_14440),c_Product__Type_Ofst(U_14437,U_14438)),c_Product__Type_Omap__pair(U_14439,U_14437,U_14440,U_14438,U_14441,U_14442)) = hAPP(c_Fun_Ocomp(U_14439,U_14437,tc_prod(U_14439,U_14440),U_14441),c_Product__Type_Ofst(U_14439,U_14440)),
    inference(variable_rename,[status(thm)],[f_3616_1]) ).

fof(f_3616_3,plain,
    ! [U_14438,U_14437,U_14439,U_14440,U_14441,U_14442] : hAPP(c_Fun_Ocomp(tc_prod(U_14437,U_14438),U_14437,tc_prod(U_14439,U_14440),c_Product__Type_Ofst(U_14437,U_14438)),c_Product__Type_Omap__pair(U_14439,U_14437,U_14440,U_14438,U_14441,U_14442)) = hAPP(c_Fun_Ocomp(U_14439,U_14437,tc_prod(U_14439,U_14440),U_14441),c_Product__Type_Ofst(U_14439,U_14440)),
    inference(definitional_conversion,[status(esa)],[f_3616_2]) ).

cnf(f_3616_4,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_14437,U_14438),U_14437,tc_prod(U_14439,U_14440),c_Product__Type_Ofst(U_14437,U_14438)),c_Product__Type_Omap__pair(U_14439,U_14437,U_14440,U_14438,U_14441,U_14442)) = hAPP(c_Fun_Ocomp(U_14439,U_14437,tc_prod(U_14439,U_14440),U_14441),c_Product__Type_Ofst(U_14439,U_14440)),
    inference(clausify,[status(thm)],[f_3616_3]) ).

fof(f_3617_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_3617_2,plain,
    ! [U_14448,U_14447,U_14446,U_14445,U_14444,U_14443] : hAPP(c_Fun_Ocomp(tc_prod(U_14443,U_14444),U_14444,tc_prod(U_14445,U_14446),c_Product__Type_Osnd(U_14443,U_14444)),c_Product__Type_Omap__pair(U_14445,U_14443,U_14446,U_14444,U_14447,U_14448)) = hAPP(c_Fun_Ocomp(U_14446,U_14444,tc_prod(U_14445,U_14446),U_14448),c_Product__Type_Osnd(U_14445,U_14446)),
    inference(variable_rename,[status(thm)],[f_3617_1]) ).

fof(f_3617_3,plain,
    ! [U_14443,U_14444,U_14445,U_14446,U_14447,U_14448] : hAPP(c_Fun_Ocomp(tc_prod(U_14443,U_14444),U_14444,tc_prod(U_14445,U_14446),c_Product__Type_Osnd(U_14443,U_14444)),c_Product__Type_Omap__pair(U_14445,U_14443,U_14446,U_14444,U_14447,U_14448)) = hAPP(c_Fun_Ocomp(U_14446,U_14444,tc_prod(U_14445,U_14446),U_14448),c_Product__Type_Osnd(U_14445,U_14446)),
    inference(definitional_conversion,[status(esa)],[f_3617_2]) ).

cnf(f_3617_4,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_14443,U_14444),U_14444,tc_prod(U_14445,U_14446),c_Product__Type_Osnd(U_14443,U_14444)),c_Product__Type_Omap__pair(U_14445,U_14443,U_14446,U_14444,U_14447,U_14448)) = hAPP(c_Fun_Ocomp(U_14446,U_14444,tc_prod(U_14445,U_14446),U_14448),c_Product__Type_Osnd(U_14445,U_14446)),
    inference(clausify,[status(thm)],[f_3617_3]) ).

fof(f_3618_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_3618_2,plain,
    ! [U_14459,U_14458,U_14457,U_14456,U_14455,U_14454,U_14453,U_14452,U_14451,U_14450,U_14449] : hAPP(c_Product__Type_Omap__pair(U_14449,U_14450,U_14451,U_14452,U_14453,U_14454),hAPP(c_Product__Type_Omap__pair(U_14455,U_14449,U_14456,U_14451,U_14457,U_14458),U_14459)) = hAPP(c_Product__Type_Omap__pair(U_14455,U_14450,U_14456,U_14452,hAPP(c_Fun_Ocomp(U_14449,U_14450,U_14455,U_14453),U_14457),hAPP(c_Fun_Ocomp(U_14451,U_14452,U_14456,U_14454),U_14458)),U_14459),
    inference(variable_rename,[status(thm)],[f_3618_1]) ).

fof(f_3618_3,plain,
    ! [U_14449,U_14450,U_14451,U_14452,U_14453,U_14454,U_14455,U_14456,U_14457,U_14458,U_14459] : hAPP(c_Product__Type_Omap__pair(U_14449,U_14450,U_14451,U_14452,U_14453,U_14454),hAPP(c_Product__Type_Omap__pair(U_14455,U_14449,U_14456,U_14451,U_14457,U_14458),U_14459)) = hAPP(c_Product__Type_Omap__pair(U_14455,U_14450,U_14456,U_14452,hAPP(c_Fun_Ocomp(U_14449,U_14450,U_14455,U_14453),U_14457),hAPP(c_Fun_Ocomp(U_14451,U_14452,U_14456,U_14454),U_14458)),U_14459),
    inference(definitional_conversion,[status(esa)],[f_3618_2]) ).

cnf(f_3618_4,plain,
    hAPP(c_Product__Type_Omap__pair(U_14449,U_14450,U_14451,U_14452,U_14453,U_14454),hAPP(c_Product__Type_Omap__pair(U_14455,U_14449,U_14456,U_14451,U_14457,U_14458),U_14459)) = hAPP(c_Product__Type_Omap__pair(U_14455,U_14450,U_14456,U_14452,hAPP(c_Fun_Ocomp(U_14449,U_14450,U_14455,U_14453),U_14457),hAPP(c_Fun_Ocomp(U_14451,U_14452,U_14456,U_14454),U_14458)),U_14459),
    inference(clausify,[status(thm)],[f_3618_3]) ).

fof(f_3619_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_3619_2,plain,
    ! [U_14469,U_14468,U_14467,U_14466,U_14465,U_14464,U_14463,U_14462,U_14461,U_14460] : c_Product__Type_Omap__pair(U_14460,U_14461,U_14462,U_14463,hAPP(c_Fun_Ocomp(U_14464,U_14461,U_14460,U_14465),U_14466),hAPP(c_Fun_Ocomp(U_14467,U_14463,U_14462,U_14468),U_14469)) = hAPP(c_Fun_Ocomp(tc_prod(U_14464,U_14467),tc_prod(U_14461,U_14463),tc_prod(U_14460,U_14462),c_Product__Type_Omap__pair(U_14464,U_14461,U_14467,U_14463,U_14465,U_14468)),c_Product__Type_Omap__pair(U_14460,U_14464,U_14462,U_14467,U_14466,U_14469)),
    inference(variable_rename,[status(thm)],[f_3619_1]) ).

fof(f_3619_3,plain,
    ! [U_14460,U_14461,U_14462,U_14463,U_14464,U_14465,U_14466,U_14467,U_14468,U_14469] : c_Product__Type_Omap__pair(U_14460,U_14461,U_14462,U_14463,hAPP(c_Fun_Ocomp(U_14464,U_14461,U_14460,U_14465),U_14466),hAPP(c_Fun_Ocomp(U_14467,U_14463,U_14462,U_14468),U_14469)) = hAPP(c_Fun_Ocomp(tc_prod(U_14464,U_14467),tc_prod(U_14461,U_14463),tc_prod(U_14460,U_14462),c_Product__Type_Omap__pair(U_14464,U_14461,U_14467,U_14463,U_14465,U_14468)),c_Product__Type_Omap__pair(U_14460,U_14464,U_14462,U_14467,U_14466,U_14469)),
    inference(definitional_conversion,[status(esa)],[f_3619_2]) ).

cnf(f_3619_4,plain,
    c_Product__Type_Omap__pair(U_14460,U_14461,U_14462,U_14463,hAPP(c_Fun_Ocomp(U_14464,U_14461,U_14460,U_14465),U_14466),hAPP(c_Fun_Ocomp(U_14467,U_14463,U_14462,U_14468),U_14469)) = hAPP(c_Fun_Ocomp(tc_prod(U_14464,U_14467),tc_prod(U_14461,U_14463),tc_prod(U_14460,U_14462),c_Product__Type_Omap__pair(U_14464,U_14461,U_14467,U_14463,U_14465,U_14468)),c_Product__Type_Omap__pair(U_14460,U_14464,U_14462,U_14467,U_14466,U_14469)),
    inference(clausify,[status(thm)],[f_3619_3]) ).

fof(f_3620_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_3620_2,plain,
    ! [U_14479,U_14478,U_14477,U_14476,U_14475,U_14474,U_14473,U_14472,U_14471,U_14470] : hAPP(c_Fun_Ocomp(tc_prod(U_14470,U_14471),tc_prod(U_14472,U_14473),tc_prod(U_14474,U_14475),c_Product__Type_Omap__pair(U_14470,U_14472,U_14471,U_14473,U_14476,U_14477)),c_Product__Type_Omap__pair(U_14474,U_14470,U_14475,U_14471,U_14478,U_14479)) = c_Product__Type_Omap__pair(U_14474,U_14472,U_14475,U_14473,hAPP(c_Fun_Ocomp(U_14470,U_14472,U_14474,U_14476),U_14478),hAPP(c_Fun_Ocomp(U_14471,U_14473,U_14475,U_14477),U_14479)),
    inference(variable_rename,[status(thm)],[f_3620_1]) ).

fof(f_3620_3,plain,
    ! [U_14470,U_14471,U_14472,U_14473,U_14474,U_14475,U_14476,U_14477,U_14478,U_14479] : hAPP(c_Fun_Ocomp(tc_prod(U_14470,U_14471),tc_prod(U_14472,U_14473),tc_prod(U_14474,U_14475),c_Product__Type_Omap__pair(U_14470,U_14472,U_14471,U_14473,U_14476,U_14477)),c_Product__Type_Omap__pair(U_14474,U_14470,U_14475,U_14471,U_14478,U_14479)) = c_Product__Type_Omap__pair(U_14474,U_14472,U_14475,U_14473,hAPP(c_Fun_Ocomp(U_14470,U_14472,U_14474,U_14476),U_14478),hAPP(c_Fun_Ocomp(U_14471,U_14473,U_14475,U_14477),U_14479)),
    inference(definitional_conversion,[status(esa)],[f_3620_2]) ).

cnf(f_3620_4,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_14470,U_14471),tc_prod(U_14472,U_14473),tc_prod(U_14474,U_14475),c_Product__Type_Omap__pair(U_14470,U_14472,U_14471,U_14473,U_14476,U_14477)),c_Product__Type_Omap__pair(U_14474,U_14470,U_14475,U_14471,U_14478,U_14479)) = c_Product__Type_Omap__pair(U_14474,U_14472,U_14475,U_14473,hAPP(c_Fun_Ocomp(U_14470,U_14472,U_14474,U_14476),U_14478),hAPP(c_Fun_Ocomp(U_14471,U_14473,U_14475,U_14477),U_14479)),
    inference(clausify,[status(thm)],[f_3620_3]) ).

fof(f_3621_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_3621_2,plain,
    ! [U_14482,U_14481,U_14480] : hAPP(c_Product__Type_Omap__pair(U_14480,U_14480,U_14481,U_14481,c_COMBI(U_14480),c_COMBI(U_14481)),U_14482) = U_14482,
    inference(variable_rename,[status(thm)],[f_3621_1]) ).

fof(f_3621_3,plain,
    ! [U_14480,U_14481,U_14482] : hAPP(c_Product__Type_Omap__pair(U_14480,U_14480,U_14481,U_14481,c_COMBI(U_14480),c_COMBI(U_14481)),U_14482) = U_14482,
    inference(definitional_conversion,[status(esa)],[f_3621_2]) ).

cnf(f_3621_4,plain,
    hAPP(c_Product__Type_Omap__pair(U_14480,U_14480,U_14481,U_14481,c_COMBI(U_14480),c_COMBI(U_14481)),U_14482) = U_14482,
    inference(clausify,[status(thm)],[f_3621_3]) ).

fof(f_3622_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_3622_2,plain,
    ! [U_14490,U_14489,U_14488,U_14487,U_14486,U_14485,U_14484,U_14483] : hAPP(c_Product__Type_Omap__pair(U_14483,U_14484,U_14485,U_14486,U_14487,U_14488),hAPP(hAPP(c_Product__Type_OPair(U_14483,U_14485),U_14489),U_14490)) = hAPP(hAPP(c_Product__Type_OPair(U_14484,U_14486),hAPP(U_14487,U_14489)),hAPP(U_14488,U_14490)),
    inference(variable_rename,[status(thm)],[f_3622_1]) ).

fof(f_3622_3,plain,
    ! [U_14483,U_14484,U_14485,U_14486,U_14487,U_14488,U_14489,U_14490] : hAPP(c_Product__Type_Omap__pair(U_14483,U_14484,U_14485,U_14486,U_14487,U_14488),hAPP(hAPP(c_Product__Type_OPair(U_14483,U_14485),U_14489),U_14490)) = hAPP(hAPP(c_Product__Type_OPair(U_14484,U_14486),hAPP(U_14487,U_14489)),hAPP(U_14488,U_14490)),
    inference(definitional_conversion,[status(esa)],[f_3622_2]) ).

cnf(f_3622_4,plain,
    hAPP(c_Product__Type_Omap__pair(U_14483,U_14484,U_14485,U_14486,U_14487,U_14488),hAPP(hAPP(c_Product__Type_OPair(U_14483,U_14485),U_14489),U_14490)) = hAPP(hAPP(c_Product__Type_OPair(U_14484,U_14486),hAPP(U_14487,U_14489)),hAPP(U_14488,U_14490)),
    inference(clausify,[status(thm)],[f_3622_3]) ).

fof(f_3623_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_3623_2,plain,
    ! [U_14497,U_14496,U_14495,U_14494,U_14493,U_14492,U_14491] : hAPP(c_Product__Type_Osnd(U_14491,U_14492),hAPP(c_Product__Type_Omap__pair(U_14493,U_14491,U_14494,U_14492,U_14495,U_14496),U_14497)) = hAPP(U_14496,hAPP(c_Product__Type_Osnd(U_14493,U_14494),U_14497)),
    inference(variable_rename,[status(thm)],[f_3623_1]) ).

fof(f_3623_3,plain,
    ! [U_14491,U_14493,U_14492,U_14494,U_14495,U_14496,U_14497] : hAPP(c_Product__Type_Osnd(U_14491,U_14492),hAPP(c_Product__Type_Omap__pair(U_14493,U_14491,U_14494,U_14492,U_14495,U_14496),U_14497)) = hAPP(U_14496,hAPP(c_Product__Type_Osnd(U_14493,U_14494),U_14497)),
    inference(definitional_conversion,[status(esa)],[f_3623_2]) ).

cnf(f_3623_4,plain,
    hAPP(c_Product__Type_Osnd(U_14491,U_14492),hAPP(c_Product__Type_Omap__pair(U_14493,U_14491,U_14494,U_14492,U_14495,U_14496),U_14497)) = hAPP(U_14496,hAPP(c_Product__Type_Osnd(U_14493,U_14494),U_14497)),
    inference(clausify,[status(thm)],[f_3623_3]) ).

fof(f_3624_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_3624_2,plain,
    ! [U_14504,U_14503,U_14502,U_14501,U_14500,U_14499,U_14498] : hAPP(c_Product__Type_Ofst(U_14498,U_14499),hAPP(c_Product__Type_Omap__pair(U_14500,U_14498,U_14501,U_14499,U_14502,U_14503),U_14504)) = hAPP(U_14502,hAPP(c_Product__Type_Ofst(U_14500,U_14501),U_14504)),
    inference(variable_rename,[status(thm)],[f_3624_1]) ).

fof(f_3624_3,plain,
    ! [U_14498,U_14499,U_14500,U_14501,U_14502,U_14503,U_14504] : hAPP(c_Product__Type_Ofst(U_14498,U_14499),hAPP(c_Product__Type_Omap__pair(U_14500,U_14498,U_14501,U_14499,U_14502,U_14503),U_14504)) = hAPP(U_14502,hAPP(c_Product__Type_Ofst(U_14500,U_14501),U_14504)),
    inference(definitional_conversion,[status(esa)],[f_3624_2]) ).

cnf(f_3624_4,plain,
    hAPP(c_Product__Type_Ofst(U_14498,U_14499),hAPP(c_Product__Type_Omap__pair(U_14500,U_14498,U_14501,U_14499,U_14502,U_14503),U_14504)) = hAPP(U_14502,hAPP(c_Product__Type_Ofst(U_14500,U_14501),U_14504)),
    inference(clausify,[status(thm)],[f_3624_3]) ).

fof(f_3625_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_3625_2,plain,
    ! [U_14510,U_14509,U_14508,U_14507,U_14506,U_14505] : c_Product__Type_Omap__pair(U_14505,U_14506,U_14507,U_14508,U_14509,U_14510) = hAPP(c_Product__Type_Oprod_Oprod__case(U_14505,U_14507,tc_prod(U_14506,U_14508)),hAPP(hAPP(c_COMBC(U_14505,tc_fun(U_14507,U_14508),tc_fun(U_14507,tc_prod(U_14506,U_14508))),hAPP(hAPP(c_COMBB(tc_fun(U_14508,tc_prod(U_14506,U_14508)),tc_fun(tc_fun(U_14507,U_14508),tc_fun(U_14507,tc_prod(U_14506,U_14508))),U_14505),c_COMBB(U_14508,tc_prod(U_14506,U_14508),U_14507)),hAPP(hAPP(c_COMBB(U_14506,tc_fun(U_14508,tc_prod(U_14506,U_14508)),U_14505),c_Product__Type_OPair(U_14506,U_14508)),U_14509))),U_14510)),
    inference(variable_rename,[status(thm)],[f_3625_1]) ).

fof(f_3625_3,plain,
    ! [U_14505,U_14506,U_14507,U_14508,U_14509,U_14510] : c_Product__Type_Omap__pair(U_14505,U_14506,U_14507,U_14508,U_14509,U_14510) = hAPP(c_Product__Type_Oprod_Oprod__case(U_14505,U_14507,tc_prod(U_14506,U_14508)),hAPP(hAPP(c_COMBC(U_14505,tc_fun(U_14507,U_14508),tc_fun(U_14507,tc_prod(U_14506,U_14508))),hAPP(hAPP(c_COMBB(tc_fun(U_14508,tc_prod(U_14506,U_14508)),tc_fun(tc_fun(U_14507,U_14508),tc_fun(U_14507,tc_prod(U_14506,U_14508))),U_14505),c_COMBB(U_14508,tc_prod(U_14506,U_14508),U_14507)),hAPP(hAPP(c_COMBB(U_14506,tc_fun(U_14508,tc_prod(U_14506,U_14508)),U_14505),c_Product__Type_OPair(U_14506,U_14508)),U_14509))),U_14510)),
    inference(definitional_conversion,[status(esa)],[f_3625_2]) ).

cnf(f_3625_4,plain,
    c_Product__Type_Omap__pair(U_14505,U_14506,U_14507,U_14508,U_14509,U_14510) = hAPP(c_Product__Type_Oprod_Oprod__case(U_14505,U_14507,tc_prod(U_14506,U_14508)),hAPP(hAPP(c_COMBC(U_14505,tc_fun(U_14507,U_14508),tc_fun(U_14507,tc_prod(U_14506,U_14508))),hAPP(hAPP(c_COMBB(tc_fun(U_14508,tc_prod(U_14506,U_14508)),tc_fun(tc_fun(U_14507,U_14508),tc_fun(U_14507,tc_prod(U_14506,U_14508))),U_14505),c_COMBB(U_14508,tc_prod(U_14506,U_14508),U_14507)),hAPP(hAPP(c_COMBB(U_14506,tc_fun(U_14508,tc_prod(U_14506,U_14508)),U_14505),c_Product__Type_OPair(U_14506,U_14508)),U_14509))),U_14510)),
    inference(clausify,[status(thm)],[f_3625_3]) ).

fof(f_3626_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_3626_2,plain,
    ! [U_14520,U_14519,U_14518,U_14517,U_14516,U_14515,U_14514,U_14513,U_14512,U_14511] :
      ( hAPP(c_Set_Oimage(tc_prod(U_14511,U_14516),tc_prod(U_14512,U_14517),c_Product__Type_Omap__pair(U_14511,U_14512,U_14516,U_14517,U_14513,U_14518)),hAPP(hAPP(c_Product__Type_OSigma(U_14511,U_14516),U_14514),hAPP(c_COMBK(tc_fun(U_14516,tc_HOL_Obool),U_14511),U_14519))) = hAPP(hAPP(c_Product__Type_OSigma(U_14512,U_14517),U_14515),hAPP(c_COMBK(tc_fun(U_14517,tc_HOL_Obool),U_14512),U_14520))
      | hAPP(c_Set_Oimage(U_14516,U_14517,U_14518),U_14519) != U_14520
      | hAPP(c_Set_Oimage(U_14511,U_14512,U_14513),U_14514) != U_14515 ),
    inference(variable_rename,[status(thm)],[f_3626_1]) ).

fof(f_3626_3,plain,
    ! [U_14511,U_14512,U_14513,U_14514,U_14515,U_14516,U_14517,U_14518,U_14519,U_14520] :
      ( hAPP(c_Set_Oimage(tc_prod(U_14511,U_14516),tc_prod(U_14512,U_14517),c_Product__Type_Omap__pair(U_14511,U_14512,U_14516,U_14517,U_14513,U_14518)),hAPP(hAPP(c_Product__Type_OSigma(U_14511,U_14516),U_14514),hAPP(c_COMBK(tc_fun(U_14516,tc_HOL_Obool),U_14511),U_14519))) = hAPP(hAPP(c_Product__Type_OSigma(U_14512,U_14517),U_14515),hAPP(c_COMBK(tc_fun(U_14517,tc_HOL_Obool),U_14512),U_14520))
      | hAPP(c_Set_Oimage(U_14516,U_14517,U_14518),U_14519) != U_14520
      | hAPP(c_Set_Oimage(U_14511,U_14512,U_14513),U_14514) != U_14515 ),
    inference(definitional_conversion,[status(esa)],[f_3626_2]) ).

cnf(f_3626_4,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_14511,U_14516),tc_prod(U_14512,U_14517),c_Product__Type_Omap__pair(U_14511,U_14512,U_14516,U_14517,U_14513,U_14518)),hAPP(hAPP(c_Product__Type_OSigma(U_14511,U_14516),U_14514),hAPP(c_COMBK(tc_fun(U_14516,tc_HOL_Obool),U_14511),U_14519))) = hAPP(hAPP(c_Product__Type_OSigma(U_14512,U_14517),U_14515),hAPP(c_COMBK(tc_fun(U_14517,tc_HOL_Obool),U_14512),U_14520))
    | hAPP(c_Set_Oimage(U_14516,U_14517,U_14518),U_14519) != U_14520
    | hAPP(c_Set_Oimage(U_14511,U_14512,U_14513),U_14514) != U_14515 ),
    inference(clausify,[status(thm)],[f_3626_3]) ).

fof(f_3627_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_3627_2,plain,
    ! [U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523] :
      ( ? [U_14522,U_14521] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14526,U_14527)),hAPP(hAPP(c_Product__Type_OPair(U_14526,U_14527),U_14522),U_14521)),U_14530))
          & U_14525 = hAPP(hAPP(c_Product__Type_OPair(U_14523,U_14524),hAPP(U_14528,U_14522)),hAPP(U_14529,U_14521)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14523,U_14524)),U_14525),hAPP(c_Set_Oimage(tc_prod(U_14526,U_14527),tc_prod(U_14523,U_14524),c_Product__Type_Omap__pair(U_14526,U_14523,U_14527,U_14524,U_14528,U_14529)),U_14530))) ),
    inference(variable_rename,[status(thm)],[f_3627_1]) ).

fof(f_3627_3,plain,
    ! [U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523] :
      ( ? [U_14521] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14526,U_14527)),hAPP(hAPP(c_Product__Type_OPair(U_14526,U_14527),sK323(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523)),U_14521)),U_14530))
          & U_14525 = hAPP(hAPP(c_Product__Type_OPair(U_14523,U_14524),hAPP(U_14528,sK323(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523))),hAPP(U_14529,U_14521)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14523,U_14524)),U_14525),hAPP(c_Set_Oimage(tc_prod(U_14526,U_14527),tc_prod(U_14523,U_14524),c_Product__Type_Omap__pair(U_14526,U_14523,U_14527,U_14524,U_14528,U_14529)),U_14530))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK323]),skolemize(U_14522,sK323(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523))],[f_3627_2]) ).

fof(f_3627_4,plain,
    ! [U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14526,U_14527)),hAPP(hAPP(c_Product__Type_OPair(U_14526,U_14527),sK323(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523)),sK324(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523))),U_14530))
        & U_14525 = hAPP(hAPP(c_Product__Type_OPair(U_14523,U_14524),hAPP(U_14528,sK323(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523))),hAPP(U_14529,sK324(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14523,U_14524)),U_14525),hAPP(c_Set_Oimage(tc_prod(U_14526,U_14527),tc_prod(U_14523,U_14524),c_Product__Type_Omap__pair(U_14526,U_14523,U_14527,U_14524,U_14528,U_14529)),U_14530))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK324]),skolemize(U_14521,sK324(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523))],[f_3627_3]) ).

fof(f_3627_5,plain,
    ( ! [U_14523,U_14524,U_14525,U_14526,U_14527,U_14528,U_14529,U_14530] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14526,U_14527)),hAPP(hAPP(c_Product__Type_OPair(U_14526,U_14527),sK323(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523)),sK324(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523))),U_14530))
        | ~ sP1003(U_14523,U_14524,U_14525,U_14526,U_14527,U_14528,U_14529,U_14530) )
    & ! [U_14523,U_14524,U_14525,U_14526,U_14527,U_14528,U_14529,U_14530] :
        ( U_14525 = hAPP(hAPP(c_Product__Type_OPair(U_14523,U_14524),hAPP(U_14528,sK323(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523))),hAPP(U_14529,sK324(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523)))
        | ~ sP1003(U_14523,U_14524,U_14525,U_14526,U_14527,U_14528,U_14529,U_14530) )
    & ! [U_14523,U_14524,U_14525,U_14526,U_14527,U_14528,U_14529,U_14530] :
        ( sP1003(U_14523,U_14524,U_14525,U_14526,U_14527,U_14528,U_14529,U_14530)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14523,U_14524)),U_14525),hAPP(c_Set_Oimage(tc_prod(U_14526,U_14527),tc_prod(U_14523,U_14524),c_Product__Type_Omap__pair(U_14526,U_14523,U_14527,U_14524,U_14528,U_14529)),U_14530))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1003])],[f_3627_4]) ).

cnf(f_3627_6,plain,
    ( sP1003(U_14523,U_14524,U_14525,U_14526,U_14527,U_14528,U_14529,U_14530)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14523,U_14524)),U_14525),hAPP(c_Set_Oimage(tc_prod(U_14526,U_14527),tc_prod(U_14523,U_14524),c_Product__Type_Omap__pair(U_14526,U_14523,U_14527,U_14524,U_14528,U_14529)),U_14530))) ),
    inference(clausify,[status(thm)],[f_3627_5]) ).

cnf(f_3627_7,plain,
    ( U_14525 = hAPP(hAPP(c_Product__Type_OPair(U_14523,U_14524),hAPP(U_14528,sK323(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523))),hAPP(U_14529,sK324(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523)))
    | ~ sP1003(U_14523,U_14524,U_14525,U_14526,U_14527,U_14528,U_14529,U_14530) ),
    inference(clausify,[status(thm)],[f_3627_5]) ).

cnf(f_3627_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14526,U_14527)),hAPP(hAPP(c_Product__Type_OPair(U_14526,U_14527),sK323(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523)),sK324(U_14530,U_14529,U_14528,U_14527,U_14526,U_14525,U_14524,U_14523))),U_14530))
    | ~ sP1003(U_14523,U_14524,U_14525,U_14526,U_14527,U_14528,U_14529,U_14530) ),
    inference(clausify,[status(thm)],[f_3627_5]) ).

fof(f_3628_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_3628_2,plain,
    ! [U_14534,U_14533,U_14532] :
      ( 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_14532,tc_Nat_Onat),U_14534),U_14533)))
      | ? [U_14531] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_14534,U_14531)))
          & hBOOL(hAPP(hAPP(c_member(U_14532),U_14531),U_14533)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14532),U_14533)) ),
    inference(variable_rename,[status(thm)],[f_3628_1]) ).

fof(f_3628_3,plain,
    ! [U_14534,U_14533,U_14532] :
      ( 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_14532,tc_Nat_Onat),U_14534),U_14533)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_14534,sK325(U_14534,U_14533,U_14532))))
        & hBOOL(hAPP(hAPP(c_member(U_14532),sK325(U_14534,U_14533,U_14532)),U_14533)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14532),U_14533)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK325]),skolemize(U_14531,sK325(U_14534,U_14533,U_14532))],[f_3628_2]) ).

fof(f_3628_4,plain,
    ( ! [U_14532,U_14533,U_14534] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_14534,sK325(U_14534,U_14533,U_14532))))
        | ~ sP1004(U_14532,U_14533,U_14534) )
    & ! [U_14532,U_14533,U_14534] :
        ( hBOOL(hAPP(hAPP(c_member(U_14532),sK325(U_14534,U_14533,U_14532)),U_14533))
        | ~ sP1004(U_14532,U_14533,U_14534) )
    & ! [U_14532,U_14533,U_14534] :
        ( 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_14532,tc_Nat_Onat),U_14534),U_14533)))
        | sP1004(U_14532,U_14533,U_14534)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14532),U_14533)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1004])],[f_3628_3]) ).

cnf(f_3628_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_14532,tc_Nat_Onat),U_14534),U_14533)))
    | sP1004(U_14532,U_14533,U_14534)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14532),U_14533)) ),
    inference(clausify,[status(thm)],[f_3628_4]) ).

cnf(f_3628_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14532),sK325(U_14534,U_14533,U_14532)),U_14533))
    | ~ sP1004(U_14532,U_14533,U_14534) ),
    inference(clausify,[status(thm)],[f_3628_4]) ).

cnf(f_3628_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_14534,sK325(U_14534,U_14533,U_14532))))
    | ~ sP1004(U_14532,U_14533,U_14534) ),
    inference(clausify,[status(thm)],[f_3628_4]) ).

fof(f_3629_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_3629_2,plain,
    ! [U_14541,U_14540,U_14539,U_14538,U_14537] :
      ( hAPP(U_14540,hAPP(U_14539,U_14541)) = hAPP(U_14539,hAPP(c_Set_Oimage(U_14537,U_14537,U_14540),U_14541))
      | U_14541 = c_Orderings_Obot__class_Obot(tc_fun(U_14537,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14537),U_14541))
      | ? [U_14536,U_14535] : hAPP(U_14540,hAPP(hAPP(U_14538,U_14536),U_14535)) != hAPP(hAPP(U_14538,hAPP(U_14540,U_14536)),hAPP(U_14540,U_14535))
      | ~ c_Finite__Set_Ofolding__one__idem(U_14537,U_14538,U_14539) ),
    inference(variable_rename,[status(thm)],[f_3629_1]) ).

fof(f_3629_3,plain,
    ! [U_14541,U_14540,U_14539,U_14538,U_14537] :
      ( hAPP(U_14540,hAPP(U_14539,U_14541)) = hAPP(U_14539,hAPP(c_Set_Oimage(U_14537,U_14537,U_14540),U_14541))
      | U_14541 = c_Orderings_Obot__class_Obot(tc_fun(U_14537,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14537),U_14541))
      | ? [U_14535] : hAPP(U_14540,hAPP(hAPP(U_14538,sK326(U_14541,U_14540,U_14539,U_14538,U_14537)),U_14535)) != hAPP(hAPP(U_14538,hAPP(U_14540,sK326(U_14541,U_14540,U_14539,U_14538,U_14537))),hAPP(U_14540,U_14535))
      | ~ c_Finite__Set_Ofolding__one__idem(U_14537,U_14538,U_14539) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK326]),skolemize(U_14536,sK326(U_14541,U_14540,U_14539,U_14538,U_14537))],[f_3629_2]) ).

fof(f_3629_4,plain,
    ! [U_14541,U_14540,U_14539,U_14538,U_14537] :
      ( hAPP(U_14540,hAPP(U_14539,U_14541)) = hAPP(U_14539,hAPP(c_Set_Oimage(U_14537,U_14537,U_14540),U_14541))
      | U_14541 = c_Orderings_Obot__class_Obot(tc_fun(U_14537,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14537),U_14541))
      | hAPP(U_14540,hAPP(hAPP(U_14538,sK326(U_14541,U_14540,U_14539,U_14538,U_14537)),sK327(U_14541,U_14540,U_14539,U_14538,U_14537))) != hAPP(hAPP(U_14538,hAPP(U_14540,sK326(U_14541,U_14540,U_14539,U_14538,U_14537))),hAPP(U_14540,sK327(U_14541,U_14540,U_14539,U_14538,U_14537)))
      | ~ c_Finite__Set_Ofolding__one__idem(U_14537,U_14538,U_14539) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK327]),skolemize(U_14535,sK327(U_14541,U_14540,U_14539,U_14538,U_14537))],[f_3629_3]) ).

fof(f_3629_5,plain,
    ! [U_14537,U_14538,U_14539,U_14540,U_14541] :
      ( hAPP(U_14540,hAPP(U_14539,U_14541)) = hAPP(U_14539,hAPP(c_Set_Oimage(U_14537,U_14537,U_14540),U_14541))
      | U_14541 = c_Orderings_Obot__class_Obot(tc_fun(U_14537,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14537),U_14541))
      | hAPP(U_14540,hAPP(hAPP(U_14538,sK326(U_14541,U_14540,U_14539,U_14538,U_14537)),sK327(U_14541,U_14540,U_14539,U_14538,U_14537))) != hAPP(hAPP(U_14538,hAPP(U_14540,sK326(U_14541,U_14540,U_14539,U_14538,U_14537))),hAPP(U_14540,sK327(U_14541,U_14540,U_14539,U_14538,U_14537)))
      | ~ c_Finite__Set_Ofolding__one__idem(U_14537,U_14538,U_14539) ),
    inference(definitional_conversion,[status(esa)],[f_3629_4]) ).

cnf(f_3629_6,plain,
    ( hAPP(U_14540,hAPP(U_14539,U_14541)) = hAPP(U_14539,hAPP(c_Set_Oimage(U_14537,U_14537,U_14540),U_14541))
    | U_14541 = c_Orderings_Obot__class_Obot(tc_fun(U_14537,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14537),U_14541))
    | hAPP(U_14540,hAPP(hAPP(U_14538,sK326(U_14541,U_14540,U_14539,U_14538,U_14537)),sK327(U_14541,U_14540,U_14539,U_14538,U_14537))) != hAPP(hAPP(U_14538,hAPP(U_14540,sK326(U_14541,U_14540,U_14539,U_14538,U_14537))),hAPP(U_14540,sK327(U_14541,U_14540,U_14539,U_14538,U_14537)))
    | ~ c_Finite__Set_Ofolding__one__idem(U_14537,U_14538,U_14539) ),
    inference(clausify,[status(thm)],[f_3629_5]) ).

fof(f_3630_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_3630_2,plain,
    ! [U_14544,U_14543] :
      ( hBOOL(hAPP(U_14544,U_14543))
      | ? [U_14542] : ~ hBOOL(hAPP(U_14544,hAPP(c_Int_ORep__Integ,U_14542)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14543),c_Int_OInteg)) ),
    inference(variable_rename,[status(thm)],[f_3630_1]) ).

fof(f_3630_3,plain,
    ! [U_14544,U_14543] :
      ( hBOOL(hAPP(U_14544,U_14543))
      | ~ hBOOL(hAPP(U_14544,hAPP(c_Int_ORep__Integ,sK328(U_14544,U_14543))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14543),c_Int_OInteg)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK328]),skolemize(U_14542,sK328(U_14544,U_14543))],[f_3630_2]) ).

fof(f_3630_4,plain,
    ! [U_14544,U_14543] :
      ( hBOOL(hAPP(U_14544,U_14543))
      | ~ hBOOL(hAPP(U_14544,hAPP(c_Int_ORep__Integ,sK328(U_14544,U_14543))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14543),c_Int_OInteg)) ),
    inference(definitional_conversion,[status(esa)],[f_3630_3]) ).

cnf(f_3630_5,plain,
    ( hBOOL(hAPP(U_14544,U_14543))
    | ~ hBOOL(hAPP(U_14544,hAPP(c_Int_ORep__Integ,sK328(U_14544,U_14543))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14543),c_Int_OInteg)) ),
    inference(clausify,[status(thm)],[f_3630_4]) ).

fof(f_3631_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_3631_2,plain,
    ! [U_14546] :
      ( ? [U_14545] : U_14546 = hAPP(c_Int_ORep__Integ,U_14545)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14546),c_Int_OInteg)) ),
    inference(variable_rename,[status(thm)],[f_3631_1]) ).

fof(f_3631_3,plain,
    ! [U_14546] :
      ( U_14546 = hAPP(c_Int_ORep__Integ,sK329(U_14546))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14546),c_Int_OInteg)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK329]),skolemize(U_14545,sK329(U_14546))],[f_3631_2]) ).

fof(f_3631_4,plain,
    ! [U_14546] :
      ( U_14546 = hAPP(c_Int_ORep__Integ,sK329(U_14546))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14546),c_Int_OInteg)) ),
    inference(definitional_conversion,[status(esa)],[f_3631_3]) ).

cnf(f_3631_5,plain,
    ( U_14546 = hAPP(c_Int_ORep__Integ,sK329(U_14546))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_14546),c_Int_OInteg)) ),
    inference(clausify,[status(thm)],[f_3631_4]) ).

fof(f_3632_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_3632_2,plain,
    ! [U_14555,U_14554,U_14553,U_14552,U_14551,U_14550,U_14549,U_14548] :
      ( hAPP(U_14553,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14549,tc_HOL_Obool)),U_14554),U_14555)) = hAPP(hAPP(U_14550,hAPP(U_14553,U_14554)),hAPP(U_14553,U_14555))
      | ? [U_14547] :
          ( hAPP(U_14552,U_14547) != U_14551
          & hBOOL(hAPP(hAPP(c_member(U_14549),U_14547),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14549,tc_HOL_Obool)),U_14554),U_14555))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14549),U_14555))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14549),U_14554))
      | ~ c_Finite__Set_Ofolding__image__simple(U_14548,U_14549,U_14550,U_14551,U_14552,U_14553) ),
    inference(variable_rename,[status(thm)],[f_3632_1]) ).

fof(f_3632_3,plain,
    ! [U_14555,U_14554,U_14553,U_14552,U_14551,U_14550,U_14549] :
      ( ! [U_14548] : ~ c_Finite__Set_Ofolding__image__simple(U_14548,U_14549,U_14550,U_14551,U_14552,U_14553)
      | hAPP(U_14553,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14549,tc_HOL_Obool)),U_14554),U_14555)) = hAPP(hAPP(U_14550,hAPP(U_14553,U_14554)),hAPP(U_14553,U_14555))
      | ? [U_14547] :
          ( hAPP(U_14552,U_14547) != U_14551
          & hBOOL(hAPP(hAPP(c_member(U_14549),U_14547),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14549,tc_HOL_Obool)),U_14554),U_14555))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14549),U_14555))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14549),U_14554)) ),
    inference(miniscope,[status(thm)],[f_3632_2]) ).

fof(f_3632_4,plain,
    ! [U_14555,U_14554,U_14553,U_14552,U_14551,U_14550,U_14549] :
      ( ! [U_14548] : ~ c_Finite__Set_Ofolding__image__simple(U_14548,U_14549,U_14550,U_14551,U_14552,U_14553)
      | hAPP(U_14553,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14549,tc_HOL_Obool)),U_14554),U_14555)) = hAPP(hAPP(U_14550,hAPP(U_14553,U_14554)),hAPP(U_14553,U_14555))
      | ( hAPP(U_14552,sK330(U_14555,U_14554,U_14553,U_14552,U_14551,U_14550,U_14549)) != U_14551
        & hBOOL(hAPP(hAPP(c_member(U_14549),sK330(U_14555,U_14554,U_14553,U_14552,U_14551,U_14550,U_14549)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14549,tc_HOL_Obool)),U_14554),U_14555))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14549),U_14555))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14549),U_14554)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK330]),skolemize(U_14547,sK330(U_14555,U_14554,U_14553,U_14552,U_14551,U_14550,U_14549))],[f_3632_3]) ).

fof(f_3632_5,plain,
    ( ! [U_14549,U_14550,U_14551,U_14552,U_14553,U_14554,U_14555] :
        ( hAPP(U_14552,sK330(U_14555,U_14554,U_14553,U_14552,U_14551,U_14550,U_14549)) != U_14551
        | ~ sP1005(U_14549,U_14550,U_14551,U_14552,U_14553,U_14554,U_14555) )
    & ! [U_14549,U_14550,U_14551,U_14552,U_14553,U_14554,U_14555] :
        ( hBOOL(hAPP(hAPP(c_member(U_14549),sK330(U_14555,U_14554,U_14553,U_14552,U_14551,U_14550,U_14549)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14549,tc_HOL_Obool)),U_14554),U_14555)))
        | ~ sP1005(U_14549,U_14550,U_14551,U_14552,U_14553,U_14554,U_14555) )
    & ! [U_14548,U_14549,U_14550,U_14551,U_14552,U_14553,U_14554,U_14555] :
        ( ~ c_Finite__Set_Ofolding__image__simple(U_14548,U_14549,U_14550,U_14551,U_14552,U_14553)
        | hAPP(U_14553,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14549,tc_HOL_Obool)),U_14554),U_14555)) = hAPP(hAPP(U_14550,hAPP(U_14553,U_14554)),hAPP(U_14553,U_14555))
        | sP1005(U_14549,U_14550,U_14551,U_14552,U_14553,U_14554,U_14555)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14549),U_14555))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14549),U_14554)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1005])],[f_3632_4]) ).

cnf(f_3632_6,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_14548,U_14549,U_14550,U_14551,U_14552,U_14553)
    | hAPP(U_14553,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14549,tc_HOL_Obool)),U_14554),U_14555)) = hAPP(hAPP(U_14550,hAPP(U_14553,U_14554)),hAPP(U_14553,U_14555))
    | sP1005(U_14549,U_14550,U_14551,U_14552,U_14553,U_14554,U_14555)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14549),U_14555))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14549),U_14554)) ),
    inference(clausify,[status(thm)],[f_3632_5]) ).

cnf(f_3632_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14549),sK330(U_14555,U_14554,U_14553,U_14552,U_14551,U_14550,U_14549)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14549,tc_HOL_Obool)),U_14554),U_14555)))
    | ~ sP1005(U_14549,U_14550,U_14551,U_14552,U_14553,U_14554,U_14555) ),
    inference(clausify,[status(thm)],[f_3632_5]) ).

cnf(f_3632_8,plain,
    ( hAPP(U_14552,sK330(U_14555,U_14554,U_14553,U_14552,U_14551,U_14550,U_14549)) != U_14551
    | ~ sP1005(U_14549,U_14550,U_14551,U_14552,U_14553,U_14554,U_14555) ),
    inference(clausify,[status(thm)],[f_3632_5]) ).

fof(f_3633_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_3633_2,plain,
    ! [U_14556] : c_Finite__Set_Ofun__left__comm__idem(U_14556,tc_fun(U_14556,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14556,tc_HOL_Obool),tc_fun(tc_fun(U_14556,tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool)),U_14556),hAPP(c_COMBC(tc_fun(U_14556,tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_14556,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_14556,tc_fun(U_14556,tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool)),c_Set_Oinsert(U_14556)),c_Orderings_Obot__class_Obot(tc_fun(U_14556,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3633_1]) ).

fof(f_3633_3,plain,
    ! [U_14556] : c_Finite__Set_Ofun__left__comm__idem(U_14556,tc_fun(U_14556,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14556,tc_HOL_Obool),tc_fun(tc_fun(U_14556,tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool)),U_14556),hAPP(c_COMBC(tc_fun(U_14556,tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_14556,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_14556,tc_fun(U_14556,tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool)),c_Set_Oinsert(U_14556)),c_Orderings_Obot__class_Obot(tc_fun(U_14556,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3633_2]) ).

cnf(f_3633_4,plain,
    c_Finite__Set_Ofun__left__comm__idem(U_14556,tc_fun(U_14556,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14556,tc_HOL_Obool),tc_fun(tc_fun(U_14556,tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool)),U_14556),hAPP(c_COMBC(tc_fun(U_14556,tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_14556,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_14556,tc_fun(U_14556,tc_HOL_Obool),tc_fun(U_14556,tc_HOL_Obool)),c_Set_Oinsert(U_14556)),c_Orderings_Obot__class_Obot(tc_fun(U_14556,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3633_3]) ).

fof(f_3634_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_3634_2,plain,
    ! [U_14558,U_14557] :
      ( 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_14557))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14558)))) = 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_14557))),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_14558)))))
      | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14557)) ),
    inference(variable_rename,[status(thm)],[f_3634_1]) ).

fof(f_3634_3,plain,
    ! [U_14557,U_14558] :
      ( 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_14557))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14558)))) = 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_14557))),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_14558)))))
      | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14557)) ),
    inference(definitional_conversion,[status(esa)],[f_3634_2]) ).

cnf(f_3634_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_14557))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14558)))) = 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_14557))),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_14558)))))
    | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14557)) ),
    inference(clausify,[status(thm)],[f_3634_3]) ).

fof(f_3635_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_3635_2,plain,
    ! [U_14561,U_14560,U_14559] :
      ( hBOOL(hAPP(hAPP(c_member(U_14561),U_14560),hAPP(c_Set_OCollect(U_14561),U_14559)))
      | ~ hBOOL(hAPP(U_14559,U_14560)) ),
    inference(variable_rename,[status(thm)],[f_3635_1]) ).

fof(f_3635_3,plain,
    ! [U_14561,U_14559,U_14560] :
      ( hBOOL(hAPP(hAPP(c_member(U_14561),U_14560),hAPP(c_Set_OCollect(U_14561),U_14559)))
      | ~ hBOOL(hAPP(U_14559,U_14560)) ),
    inference(definitional_conversion,[status(esa)],[f_3635_2]) ).

cnf(f_3635_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14561),U_14560),hAPP(c_Set_OCollect(U_14561),U_14559)))
    | ~ hBOOL(hAPP(U_14559,U_14560)) ),
    inference(clausify,[status(thm)],[f_3635_3]) ).

fof(f_3636_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_3636_2,plain,
    ! [U_14564,U_14563,U_14562] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14562),hAPP(c_Set_OCollect(U_14562),hAPP(hAPP(c_COMBS(U_14562,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14562),c_fconj),U_14563)),U_14564))))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14562),hAPP(c_Set_OCollect(U_14562),U_14564)))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14562),hAPP(c_Set_OCollect(U_14562),U_14563))) ) ),
    inference(variable_rename,[status(thm)],[f_3636_1]) ).

fof(f_3636_3,plain,
    ( ! [U_14562,U_14563,U_14564] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14562),hAPP(c_Set_OCollect(U_14562),U_14564)))
        | ~ sP1006(U_14562,U_14563,U_14564) )
    & ! [U_14562,U_14563,U_14564] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14562),hAPP(c_Set_OCollect(U_14562),U_14563)))
        | ~ sP1006(U_14562,U_14563,U_14564) )
    & ! [U_14562,U_14563,U_14564] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14562),hAPP(c_Set_OCollect(U_14562),hAPP(hAPP(c_COMBS(U_14562,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14562),c_fconj),U_14563)),U_14564))))
        | sP1006(U_14562,U_14563,U_14564) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1006])],[f_3636_2]) ).

cnf(f_3636_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14562),hAPP(c_Set_OCollect(U_14562),hAPP(hAPP(c_COMBS(U_14562,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14562),c_fconj),U_14563)),U_14564))))
    | sP1006(U_14562,U_14563,U_14564) ),
    inference(clausify,[status(thm)],[f_3636_3]) ).

cnf(f_3636_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14562),hAPP(c_Set_OCollect(U_14562),U_14563)))
    | ~ sP1006(U_14562,U_14563,U_14564) ),
    inference(clausify,[status(thm)],[f_3636_3]) ).

cnf(f_3636_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14562),hAPP(c_Set_OCollect(U_14562),U_14564)))
    | ~ sP1006(U_14562,U_14563,U_14564) ),
    inference(clausify,[status(thm)],[f_3636_3]) ).

fof(f_3637_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_3637_2,plain,
    ! [U_14565] : 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_14565)))),
    inference(variable_rename,[status(thm)],[f_3637_1]) ).

fof(f_3637_3,plain,
    ! [U_14565] : 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_14565)))),
    inference(definitional_conversion,[status(esa)],[f_3637_2]) ).

cnf(f_3637_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_14565)))),
    inference(clausify,[status(thm)],[f_3637_3]) ).

fof(f_3638_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_3638_2,plain,
    ! [U_14566] : 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_14566)))),
    inference(variable_rename,[status(thm)],[f_3638_1]) ).

fof(f_3638_3,plain,
    ! [U_14566] : 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_14566)))),
    inference(definitional_conversion,[status(esa)],[f_3638_2]) ).

cnf(f_3638_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_14566)))),
    inference(clausify,[status(thm)],[f_3638_3]) ).

fof(f_3639_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_3639_2,plain,
    ! [U_14570,U_14569,U_14568,U_14567] :
      ( hAPP(c_Fun_Ocomp(U_14568,U_14568,U_14568,hAPP(U_14569,U_14570)),hAPP(U_14569,U_14570)) = hAPP(U_14569,U_14570)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_14567,U_14568,U_14569) ),
    inference(variable_rename,[status(thm)],[f_3639_1]) ).

fof(f_3639_3,plain,
    ! [U_14570,U_14569,U_14568] :
      ( ! [U_14567] : ~ c_Finite__Set_Ofun__left__comm__idem(U_14567,U_14568,U_14569)
      | hAPP(c_Fun_Ocomp(U_14568,U_14568,U_14568,hAPP(U_14569,U_14570)),hAPP(U_14569,U_14570)) = hAPP(U_14569,U_14570) ),
    inference(miniscope,[status(thm)],[f_3639_2]) ).

fof(f_3639_4,plain,
    ! [U_14567,U_14568,U_14569,U_14570] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(U_14567,U_14568,U_14569)
      | hAPP(c_Fun_Ocomp(U_14568,U_14568,U_14568,hAPP(U_14569,U_14570)),hAPP(U_14569,U_14570)) = hAPP(U_14569,U_14570) ),
    inference(definitional_conversion,[status(esa)],[f_3639_3]) ).

cnf(f_3639_5,plain,
    ( ~ c_Finite__Set_Ofun__left__comm__idem(U_14567,U_14568,U_14569)
    | hAPP(c_Fun_Ocomp(U_14568,U_14568,U_14568,hAPP(U_14569,U_14570)),hAPP(U_14569,U_14570)) = hAPP(U_14569,U_14570) ),
    inference(clausify,[status(thm)],[f_3639_4]) ).

fof(f_3640_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_3640_2,plain,
    ! [U_14573,U_14572,U_14571] :
      ( ( hAPP(c_Set_OCollect(U_14573),hAPP(hAPP(c_COMBS(U_14573,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14573),c_fconj),hAPP(hAPP(c_COMBC(U_14573,U_14573,tc_HOL_Obool),c_fequal),U_14572))),U_14571)) = c_Orderings_Obot__class_Obot(tc_fun(U_14573,tc_HOL_Obool))
        | hBOOL(hAPP(U_14571,U_14572)) )
      & ( hAPP(c_Set_OCollect(U_14573),hAPP(hAPP(c_COMBS(U_14573,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14573),c_fconj),hAPP(hAPP(c_COMBC(U_14573,U_14573,tc_HOL_Obool),c_fequal),U_14572))),U_14571)) = hAPP(hAPP(c_Set_Oinsert(U_14573),U_14572),c_Orderings_Obot__class_Obot(tc_fun(U_14573,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_14571,U_14572)) ) ),
    inference(variable_rename,[status(thm)],[f_3640_1]) ).

fof(f_3640_3,plain,
    ( ! [U_14579,U_14577,U_14575] :
        ( hAPP(c_Set_OCollect(U_14579),hAPP(hAPP(c_COMBS(U_14579,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14579),c_fconj),hAPP(hAPP(c_COMBC(U_14579,U_14579,tc_HOL_Obool),c_fequal),U_14577))),U_14575)) = c_Orderings_Obot__class_Obot(tc_fun(U_14579,tc_HOL_Obool))
        | hBOOL(hAPP(U_14575,U_14577)) )
    & ! [U_14578,U_14576,U_14574] :
        ( hAPP(c_Set_OCollect(U_14578),hAPP(hAPP(c_COMBS(U_14578,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14578),c_fconj),hAPP(hAPP(c_COMBC(U_14578,U_14578,tc_HOL_Obool),c_fequal),U_14576))),U_14574)) = hAPP(hAPP(c_Set_Oinsert(U_14578),U_14576),c_Orderings_Obot__class_Obot(tc_fun(U_14578,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_14574,U_14576)) ) ),
    inference(miniscope,[status(thm)],[f_3640_2]) ).

fof(f_3640_4,plain,
    ( ! [U_14575,U_14577,U_14579] :
        ( hAPP(c_Set_OCollect(U_14579),hAPP(hAPP(c_COMBS(U_14579,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14579),c_fconj),hAPP(hAPP(c_COMBC(U_14579,U_14579,tc_HOL_Obool),c_fequal),U_14577))),U_14575)) = c_Orderings_Obot__class_Obot(tc_fun(U_14579,tc_HOL_Obool))
        | hBOOL(hAPP(U_14575,U_14577)) )
    & ! [U_14578,U_14576,U_14574] :
        ( hAPP(c_Set_OCollect(U_14578),hAPP(hAPP(c_COMBS(U_14578,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14578),c_fconj),hAPP(hAPP(c_COMBC(U_14578,U_14578,tc_HOL_Obool),c_fequal),U_14576))),U_14574)) = hAPP(hAPP(c_Set_Oinsert(U_14578),U_14576),c_Orderings_Obot__class_Obot(tc_fun(U_14578,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_14574,U_14576)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3640_3]) ).

cnf(f_3640_5,plain,
    ( hAPP(c_Set_OCollect(U_14578),hAPP(hAPP(c_COMBS(U_14578,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14578),c_fconj),hAPP(hAPP(c_COMBC(U_14578,U_14578,tc_HOL_Obool),c_fequal),U_14576))),U_14574)) = hAPP(hAPP(c_Set_Oinsert(U_14578),U_14576),c_Orderings_Obot__class_Obot(tc_fun(U_14578,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(U_14574,U_14576)) ),
    inference(clausify,[status(thm)],[f_3640_4]) ).

cnf(f_3640_6,plain,
    ( hAPP(c_Set_OCollect(U_14579),hAPP(hAPP(c_COMBS(U_14579,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14579),c_fconj),hAPP(hAPP(c_COMBC(U_14579,U_14579,tc_HOL_Obool),c_fequal),U_14577))),U_14575)) = c_Orderings_Obot__class_Obot(tc_fun(U_14579,tc_HOL_Obool))
    | hBOOL(hAPP(U_14575,U_14577)) ),
    inference(clausify,[status(thm)],[f_3640_4]) ).

fof(f_3641_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_3641_2,plain,
    ! [U_14582,U_14581,U_14580] :
      ( ( hAPP(c_Set_OCollect(U_14582),hAPP(hAPP(c_COMBS(U_14582,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14582),c_fconj),hAPP(c_fequal,U_14581))),U_14580)) = c_Orderings_Obot__class_Obot(tc_fun(U_14582,tc_HOL_Obool))
        | hBOOL(hAPP(U_14580,U_14581)) )
      & ( hAPP(c_Set_OCollect(U_14582),hAPP(hAPP(c_COMBS(U_14582,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14582),c_fconj),hAPP(c_fequal,U_14581))),U_14580)) = hAPP(hAPP(c_Set_Oinsert(U_14582),U_14581),c_Orderings_Obot__class_Obot(tc_fun(U_14582,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_14580,U_14581)) ) ),
    inference(variable_rename,[status(thm)],[f_3641_1]) ).

fof(f_3641_3,plain,
    ( ! [U_14588,U_14586,U_14584] :
        ( 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(c_fequal,U_14586))),U_14584)) = c_Orderings_Obot__class_Obot(tc_fun(U_14588,tc_HOL_Obool))
        | hBOOL(hAPP(U_14584,U_14586)) )
    & ! [U_14587,U_14585,U_14583] :
        ( hAPP(c_Set_OCollect(U_14587),hAPP(hAPP(c_COMBS(U_14587,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14587),c_fconj),hAPP(c_fequal,U_14585))),U_14583)) = hAPP(hAPP(c_Set_Oinsert(U_14587),U_14585),c_Orderings_Obot__class_Obot(tc_fun(U_14587,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_14583,U_14585)) ) ),
    inference(miniscope,[status(thm)],[f_3641_2]) ).

fof(f_3641_4,plain,
    ( ! [U_14586,U_14584,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(c_fequal,U_14586))),U_14584)) = c_Orderings_Obot__class_Obot(tc_fun(U_14588,tc_HOL_Obool))
        | hBOOL(hAPP(U_14584,U_14586)) )
    & ! [U_14587,U_14585,U_14583] :
        ( hAPP(c_Set_OCollect(U_14587),hAPP(hAPP(c_COMBS(U_14587,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14587),c_fconj),hAPP(c_fequal,U_14585))),U_14583)) = hAPP(hAPP(c_Set_Oinsert(U_14587),U_14585),c_Orderings_Obot__class_Obot(tc_fun(U_14587,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_14583,U_14585)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3641_3]) ).

cnf(f_3641_5,plain,
    ( hAPP(c_Set_OCollect(U_14587),hAPP(hAPP(c_COMBS(U_14587,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14587),c_fconj),hAPP(c_fequal,U_14585))),U_14583)) = hAPP(hAPP(c_Set_Oinsert(U_14587),U_14585),c_Orderings_Obot__class_Obot(tc_fun(U_14587,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(U_14583,U_14585)) ),
    inference(clausify,[status(thm)],[f_3641_4]) ).

cnf(f_3641_6,plain,
    ( 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(c_fequal,U_14586))),U_14584)) = c_Orderings_Obot__class_Obot(tc_fun(U_14588,tc_HOL_Obool))
    | hBOOL(hAPP(U_14584,U_14586)) ),
    inference(clausify,[status(thm)],[f_3641_4]) ).

fof(f_3642_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_3642_2,plain,
    ! [U_14590,U_14589] : hAPP(c_Set_OCollect(U_14589),hAPP(hAPP(c_COMBC(U_14589,U_14589,tc_HOL_Obool),c_fequal),U_14590)) = hAPP(hAPP(c_Set_Oinsert(U_14589),U_14590),c_Orderings_Obot__class_Obot(tc_fun(U_14589,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3642_1]) ).

fof(f_3642_3,plain,
    ! [U_14589,U_14590] : hAPP(c_Set_OCollect(U_14589),hAPP(hAPP(c_COMBC(U_14589,U_14589,tc_HOL_Obool),c_fequal),U_14590)) = hAPP(hAPP(c_Set_Oinsert(U_14589),U_14590),c_Orderings_Obot__class_Obot(tc_fun(U_14589,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3642_2]) ).

cnf(f_3642_4,plain,
    hAPP(c_Set_OCollect(U_14589),hAPP(hAPP(c_COMBC(U_14589,U_14589,tc_HOL_Obool),c_fequal),U_14590)) = hAPP(hAPP(c_Set_Oinsert(U_14589),U_14590),c_Orderings_Obot__class_Obot(tc_fun(U_14589,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3642_3]) ).

fof(f_3643_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_3643_2,plain,
    ! [U_14592,U_14591] : hAPP(c_Set_OCollect(U_14591),hAPP(c_fequal,U_14592)) = hAPP(hAPP(c_Set_Oinsert(U_14591),U_14592),c_Orderings_Obot__class_Obot(tc_fun(U_14591,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3643_1]) ).

fof(f_3643_3,plain,
    ! [U_14591,U_14592] : hAPP(c_Set_OCollect(U_14591),hAPP(c_fequal,U_14592)) = hAPP(hAPP(c_Set_Oinsert(U_14591),U_14592),c_Orderings_Obot__class_Obot(tc_fun(U_14591,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3643_2]) ).

cnf(f_3643_4,plain,
    hAPP(c_Set_OCollect(U_14591),hAPP(c_fequal,U_14592)) = hAPP(hAPP(c_Set_Oinsert(U_14591),U_14592),c_Orderings_Obot__class_Obot(tc_fun(U_14591,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3643_3]) ).

fof(f_3644_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_3644_2,plain,
    ! [U_14596,U_14595,U_14594,U_14593] : hAPP(c_Set_OCollect(tc_prod(U_14593,U_14594)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14593,U_14594,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14593,tc_fun(U_14594,tc_HOL_Obool),tc_fun(U_14594,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14594,tc_HOL_Obool),tc_fun(U_14594,tc_HOL_Obool)),U_14593),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14594)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14593),c_fconj),U_14595))),U_14596))) = hAPP(hAPP(c_Product__Type_OSigma(U_14593,U_14594),hAPP(c_Set_OCollect(U_14593),U_14595)),hAPP(c_COMBK(tc_fun(U_14594,tc_HOL_Obool),U_14593),hAPP(c_Set_OCollect(U_14594),U_14596))),
    inference(variable_rename,[status(thm)],[f_3644_1]) ).

fof(f_3644_3,plain,
    ! [U_14593,U_14594,U_14595,U_14596] : hAPP(c_Set_OCollect(tc_prod(U_14593,U_14594)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14593,U_14594,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14593,tc_fun(U_14594,tc_HOL_Obool),tc_fun(U_14594,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14594,tc_HOL_Obool),tc_fun(U_14594,tc_HOL_Obool)),U_14593),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14594)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14593),c_fconj),U_14595))),U_14596))) = hAPP(hAPP(c_Product__Type_OSigma(U_14593,U_14594),hAPP(c_Set_OCollect(U_14593),U_14595)),hAPP(c_COMBK(tc_fun(U_14594,tc_HOL_Obool),U_14593),hAPP(c_Set_OCollect(U_14594),U_14596))),
    inference(definitional_conversion,[status(esa)],[f_3644_2]) ).

cnf(f_3644_4,plain,
    hAPP(c_Set_OCollect(tc_prod(U_14593,U_14594)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14593,U_14594,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14593,tc_fun(U_14594,tc_HOL_Obool),tc_fun(U_14594,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14594,tc_HOL_Obool),tc_fun(U_14594,tc_HOL_Obool)),U_14593),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14594)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14593),c_fconj),U_14595))),U_14596))) = hAPP(hAPP(c_Product__Type_OSigma(U_14593,U_14594),hAPP(c_Set_OCollect(U_14593),U_14595)),hAPP(c_COMBK(tc_fun(U_14594,tc_HOL_Obool),U_14593),hAPP(c_Set_OCollect(U_14594),U_14596))),
    inference(clausify,[status(thm)],[f_3644_3]) ).

fof(f_3645_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_3645_2,plain,
    ! [U_14600,U_14599,U_14598,U_14597] : hAPP(c_Set_OCollect(tc_prod(U_14597,U_14598)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14597,U_14598,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_14597,tc_fun(U_14598,tc_HOL_Obool),tc_fun(U_14598,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14598,tc_HOL_Obool),tc_fun(U_14598,tc_HOL_Obool)),U_14597),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14598)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14597),c_fconj),U_14599))),U_14600))) = hAPP(hAPP(c_Product__Type_OSigma(U_14597,U_14598),hAPP(c_Set_OCollect(U_14597),U_14599)),hAPP(hAPP(c_COMBB(tc_fun(U_14598,tc_HOL_Obool),tc_fun(U_14598,tc_HOL_Obool),U_14597),c_Set_OCollect(U_14598)),U_14600)),
    inference(variable_rename,[status(thm)],[f_3645_1]) ).

fof(f_3645_3,plain,
    ! [U_14597,U_14598,U_14599,U_14600] : hAPP(c_Set_OCollect(tc_prod(U_14597,U_14598)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14597,U_14598,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_14597,tc_fun(U_14598,tc_HOL_Obool),tc_fun(U_14598,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14598,tc_HOL_Obool),tc_fun(U_14598,tc_HOL_Obool)),U_14597),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14598)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14597),c_fconj),U_14599))),U_14600))) = hAPP(hAPP(c_Product__Type_OSigma(U_14597,U_14598),hAPP(c_Set_OCollect(U_14597),U_14599)),hAPP(hAPP(c_COMBB(tc_fun(U_14598,tc_HOL_Obool),tc_fun(U_14598,tc_HOL_Obool),U_14597),c_Set_OCollect(U_14598)),U_14600)),
    inference(definitional_conversion,[status(esa)],[f_3645_2]) ).

cnf(f_3645_4,plain,
    hAPP(c_Set_OCollect(tc_prod(U_14597,U_14598)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14597,U_14598,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_14597,tc_fun(U_14598,tc_HOL_Obool),tc_fun(U_14598,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14598,tc_HOL_Obool),tc_fun(U_14598,tc_HOL_Obool)),U_14597),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14598)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14597),c_fconj),U_14599))),U_14600))) = hAPP(hAPP(c_Product__Type_OSigma(U_14597,U_14598),hAPP(c_Set_OCollect(U_14597),U_14599)),hAPP(hAPP(c_COMBB(tc_fun(U_14598,tc_HOL_Obool),tc_fun(U_14598,tc_HOL_Obool),U_14597),c_Set_OCollect(U_14598)),U_14600)),
    inference(clausify,[status(thm)],[f_3645_3]) ).

fof(f_3646_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_3646_2,plain,
    ! [U_14602,U_14601] : hAPP(c_Set_OCollect(U_14601),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14601),c_fNot),U_14602)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14601,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14601),U_14602)),
    inference(variable_rename,[status(thm)],[f_3646_1]) ).

fof(f_3646_3,plain,
    ! [U_14601,U_14602] : hAPP(c_Set_OCollect(U_14601),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14601),c_fNot),U_14602)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14601,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14601),U_14602)),
    inference(definitional_conversion,[status(esa)],[f_3646_2]) ).

cnf(f_3646_4,plain,
    hAPP(c_Set_OCollect(U_14601),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14601),c_fNot),U_14602)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14601,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14601),U_14602)),
    inference(clausify,[status(thm)],[f_3646_3]) ).

fof(f_3647_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_3647_2,plain,
    ! [U_14606,U_14605,U_14604,U_14603] : hAPP(c_Set_Ovimage(U_14603,U_14604,U_14605),hAPP(c_Set_OCollect(U_14604),U_14606)) = hAPP(c_Set_OCollect(U_14603),hAPP(hAPP(c_COMBB(U_14604,tc_HOL_Obool,U_14603),U_14606),U_14605)),
    inference(variable_rename,[status(thm)],[f_3647_1]) ).

fof(f_3647_3,plain,
    ! [U_14603,U_14604,U_14605,U_14606] : hAPP(c_Set_Ovimage(U_14603,U_14604,U_14605),hAPP(c_Set_OCollect(U_14604),U_14606)) = hAPP(c_Set_OCollect(U_14603),hAPP(hAPP(c_COMBB(U_14604,tc_HOL_Obool,U_14603),U_14606),U_14605)),
    inference(definitional_conversion,[status(esa)],[f_3647_2]) ).

cnf(f_3647_4,plain,
    hAPP(c_Set_Ovimage(U_14603,U_14604,U_14605),hAPP(c_Set_OCollect(U_14604),U_14606)) = hAPP(c_Set_OCollect(U_14603),hAPP(hAPP(c_COMBB(U_14604,tc_HOL_Obool,U_14603),U_14606),U_14605)),
    inference(clausify,[status(thm)],[f_3647_3]) ).

fof(f_3648_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_3648_2,plain,
    ! [U_14609,U_14608,U_14607] : hAPP(hAPP(c_Set_Oinsert(U_14607),U_14608),U_14609) = hAPP(c_Set_OCollect(U_14607),hAPP(hAPP(c_COMBS(U_14607,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14607),c_fdisj),hAPP(hAPP(c_COMBC(U_14607,U_14607,tc_HOL_Obool),c_fequal),U_14608))),hAPP(hAPP(c_COMBC(U_14607,tc_fun(U_14607,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14607)),U_14609))),
    inference(variable_rename,[status(thm)],[f_3648_1]) ).

fof(f_3648_3,plain,
    ! [U_14607,U_14608,U_14609] : hAPP(hAPP(c_Set_Oinsert(U_14607),U_14608),U_14609) = hAPP(c_Set_OCollect(U_14607),hAPP(hAPP(c_COMBS(U_14607,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14607),c_fdisj),hAPP(hAPP(c_COMBC(U_14607,U_14607,tc_HOL_Obool),c_fequal),U_14608))),hAPP(hAPP(c_COMBC(U_14607,tc_fun(U_14607,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14607)),U_14609))),
    inference(definitional_conversion,[status(esa)],[f_3648_2]) ).

cnf(f_3648_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_14607),U_14608),U_14609) = hAPP(c_Set_OCollect(U_14607),hAPP(hAPP(c_COMBS(U_14607,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14607),c_fdisj),hAPP(hAPP(c_COMBC(U_14607,U_14607,tc_HOL_Obool),c_fequal),U_14608))),hAPP(hAPP(c_COMBC(U_14607,tc_fun(U_14607,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14607)),U_14609))),
    inference(clausify,[status(thm)],[f_3648_3]) ).

fof(f_3649_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_3649_2,plain,
    ! [U_14612,U_14611,U_14610] : hAPP(hAPP(c_Set_Oinsert(U_14610),U_14611),U_14612) = hAPP(c_Set_OCollect(U_14610),hAPP(hAPP(c_COMBS(U_14610,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14610),c_fdisj),hAPP(hAPP(c_COMBC(U_14610,U_14610,tc_HOL_Obool),c_fequal),U_14611))),hAPP(hAPP(c_COMBC(U_14610,tc_fun(U_14610,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14610)),U_14612))),
    inference(variable_rename,[status(thm)],[f_3649_1]) ).

fof(f_3649_3,plain,
    ! [U_14610,U_14611,U_14612] : hAPP(hAPP(c_Set_Oinsert(U_14610),U_14611),U_14612) = hAPP(c_Set_OCollect(U_14610),hAPP(hAPP(c_COMBS(U_14610,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14610),c_fdisj),hAPP(hAPP(c_COMBC(U_14610,U_14610,tc_HOL_Obool),c_fequal),U_14611))),hAPP(hAPP(c_COMBC(U_14610,tc_fun(U_14610,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14610)),U_14612))),
    inference(definitional_conversion,[status(esa)],[f_3649_2]) ).

cnf(f_3649_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_14610),U_14611),U_14612) = hAPP(c_Set_OCollect(U_14610),hAPP(hAPP(c_COMBS(U_14610,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14610),c_fdisj),hAPP(hAPP(c_COMBC(U_14610,U_14610,tc_HOL_Obool),c_fequal),U_14611))),hAPP(hAPP(c_COMBC(U_14610,tc_fun(U_14610,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14610)),U_14612))),
    inference(clausify,[status(thm)],[f_3649_3]) ).

fof(f_3650_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_3650_2,plain,
    ! [U_14614,U_14613] : hAPP(c_Set_OCollect(U_14613),hAPP(hAPP(c_COMBC(U_14613,tc_fun(U_14613,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14613)),U_14614)) = U_14614,
    inference(variable_rename,[status(thm)],[f_3650_1]) ).

fof(f_3650_3,plain,
    ! [U_14613,U_14614] : hAPP(c_Set_OCollect(U_14613),hAPP(hAPP(c_COMBC(U_14613,tc_fun(U_14613,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14613)),U_14614)) = U_14614,
    inference(definitional_conversion,[status(esa)],[f_3650_2]) ).

cnf(f_3650_4,plain,
    hAPP(c_Set_OCollect(U_14613),hAPP(hAPP(c_COMBC(U_14613,tc_fun(U_14613,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14613)),U_14614)) = U_14614,
    inference(clausify,[status(thm)],[f_3650_3]) ).

fof(f_3651_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_3651_2,plain,
    ! [U_14617,U_14616,U_14615] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_14615),U_14616),hAPP(c_Set_OCollect(U_14615),U_14617)))
        | ~ hBOOL(hAPP(U_14617,U_14616)) )
      & ( hBOOL(hAPP(U_14617,U_14616))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14615),U_14616),hAPP(c_Set_OCollect(U_14615),U_14617))) ) ),
    inference(variable_rename,[status(thm)],[f_3651_1]) ).

fof(f_3651_3,plain,
    ( ! [U_14623,U_14621] :
        ( ! [U_14619] : hBOOL(hAPP(hAPP(c_member(U_14619),U_14621),hAPP(c_Set_OCollect(U_14619),U_14623)))
        | ~ hBOOL(hAPP(U_14623,U_14621)) )
    & ! [U_14622,U_14620] :
        ( ! [U_14618] : ~ hBOOL(hAPP(hAPP(c_member(U_14618),U_14620),hAPP(c_Set_OCollect(U_14618),U_14622)))
        | hBOOL(hAPP(U_14622,U_14620)) ) ),
    inference(miniscope,[status(thm)],[f_3651_2]) ).

fof(f_3651_4,plain,
    ( ! [U_14619,U_14621,U_14623] :
        ( hBOOL(hAPP(hAPP(c_member(U_14619),U_14621),hAPP(c_Set_OCollect(U_14619),U_14623)))
        | ~ hBOOL(hAPP(U_14623,U_14621)) )
    & ! [U_14618,U_14620,U_14622] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_14618),U_14620),hAPP(c_Set_OCollect(U_14618),U_14622)))
        | hBOOL(hAPP(U_14622,U_14620)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3651_3]) ).

cnf(f_3651_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14618),U_14620),hAPP(c_Set_OCollect(U_14618),U_14622)))
    | hBOOL(hAPP(U_14622,U_14620)) ),
    inference(clausify,[status(thm)],[f_3651_4]) ).

cnf(f_3651_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14619),U_14621),hAPP(c_Set_OCollect(U_14619),U_14623)))
    | ~ hBOOL(hAPP(U_14623,U_14621)) ),
    inference(clausify,[status(thm)],[f_3651_4]) ).

fof(f_3652_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_3652_2,plain,
    ! [U_14626,U_14625,U_14624] :
      ( hBOOL(hAPP(U_14626,U_14625))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14624),U_14625),hAPP(c_Set_OCollect(U_14624),U_14626))) ),
    inference(variable_rename,[status(thm)],[f_3652_1]) ).

fof(f_3652_3,plain,
    ! [U_14626,U_14625] :
      ( ! [U_14624] : ~ hBOOL(hAPP(hAPP(c_member(U_14624),U_14625),hAPP(c_Set_OCollect(U_14624),U_14626)))
      | hBOOL(hAPP(U_14626,U_14625)) ),
    inference(miniscope,[status(thm)],[f_3652_2]) ).

fof(f_3652_4,plain,
    ! [U_14624,U_14625,U_14626] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_14624),U_14625),hAPP(c_Set_OCollect(U_14624),U_14626)))
      | hBOOL(hAPP(U_14626,U_14625)) ),
    inference(definitional_conversion,[status(esa)],[f_3652_3]) ).

cnf(f_3652_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14624),U_14625),hAPP(c_Set_OCollect(U_14624),U_14626)))
    | hBOOL(hAPP(U_14626,U_14625)) ),
    inference(clausify,[status(thm)],[f_3652_4]) ).

fof(f_3653_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_3653_2,plain,
    ! [U_14629,U_14628,U_14627] :
      ( hBOOL(hAPP(U_14629,U_14628))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14627),U_14628),hAPP(c_Set_OCollect(U_14627),U_14629))) ),
    inference(variable_rename,[status(thm)],[f_3653_1]) ).

fof(f_3653_3,plain,
    ! [U_14629,U_14628] :
      ( ! [U_14627] : ~ hBOOL(hAPP(hAPP(c_member(U_14627),U_14628),hAPP(c_Set_OCollect(U_14627),U_14629)))
      | hBOOL(hAPP(U_14629,U_14628)) ),
    inference(miniscope,[status(thm)],[f_3653_2]) ).

fof(f_3653_4,plain,
    ! [U_14627,U_14628,U_14629] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_14627),U_14628),hAPP(c_Set_OCollect(U_14627),U_14629)))
      | hBOOL(hAPP(U_14629,U_14628)) ),
    inference(definitional_conversion,[status(esa)],[f_3653_3]) ).

cnf(f_3653_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14627),U_14628),hAPP(c_Set_OCollect(U_14627),U_14629)))
    | hBOOL(hAPP(U_14629,U_14628)) ),
    inference(clausify,[status(thm)],[f_3653_4]) ).

fof(f_3654_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_3654_2,plain,
    ! [U_14630] : c_Orderings_Otop__class_Otop(tc_fun(U_14630,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_14630),hAPP(c_COMBK(tc_HOL_Obool,U_14630),c_fTrue)),
    inference(variable_rename,[status(thm)],[f_3654_1]) ).

fof(f_3654_3,plain,
    ! [U_14630] : c_Orderings_Otop__class_Otop(tc_fun(U_14630,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_14630),hAPP(c_COMBK(tc_HOL_Obool,U_14630),c_fTrue)),
    inference(definitional_conversion,[status(esa)],[f_3654_2]) ).

cnf(f_3654_4,plain,
    c_Orderings_Otop__class_Otop(tc_fun(U_14630,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_14630),hAPP(c_COMBK(tc_HOL_Obool,U_14630),c_fTrue)),
    inference(clausify,[status(thm)],[f_3654_3]) ).

fof(f_3655_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_3655_2,plain,
    ! [U_14633,U_14632,U_14631] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14631),hAPP(c_Set_OCollect(U_14631),hAPP(hAPP(c_COMBS(U_14631,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14631),c_fdisj),U_14632)),U_14633))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14631),hAPP(c_Set_OCollect(U_14631),U_14633)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14631),hAPP(c_Set_OCollect(U_14631),U_14632))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14631),hAPP(c_Set_OCollect(U_14631),U_14633)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14631),hAPP(c_Set_OCollect(U_14631),U_14632))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14631),hAPP(c_Set_OCollect(U_14631),hAPP(hAPP(c_COMBS(U_14631,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14631),c_fdisj),U_14632)),U_14633)))) ) ),
    inference(variable_rename,[status(thm)],[f_3655_1]) ).

fof(f_3655_3,plain,
    ( ! [U_14639,U_14637,U_14635] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14635),hAPP(c_Set_OCollect(U_14635),hAPP(hAPP(c_COMBS(U_14635,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14635),c_fdisj),U_14637)),U_14639))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14635),hAPP(c_Set_OCollect(U_14635),U_14639)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14635),hAPP(c_Set_OCollect(U_14635),U_14637))) )
    & ! [U_14638,U_14636,U_14634] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14634),hAPP(c_Set_OCollect(U_14634),U_14638)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14634),hAPP(c_Set_OCollect(U_14634),U_14636))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14634),hAPP(c_Set_OCollect(U_14634),hAPP(hAPP(c_COMBS(U_14634,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14634),c_fdisj),U_14636)),U_14638)))) ) ),
    inference(miniscope,[status(thm)],[f_3655_2]) ).

fof(f_3655_4,plain,
    ( ! [U_14636,U_14634,U_14638] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14634),hAPP(c_Set_OCollect(U_14634),U_14638)))
        | ~ sP1007(U_14636,U_14634,U_14638) )
    & ! [U_14636,U_14634,U_14638] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14634),hAPP(c_Set_OCollect(U_14634),U_14636)))
        | ~ sP1007(U_14636,U_14634,U_14638) )
    & ! [U_14639,U_14635,U_14637] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14635),hAPP(c_Set_OCollect(U_14635),hAPP(hAPP(c_COMBS(U_14635,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14635),c_fdisj),U_14637)),U_14639))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14635),hAPP(c_Set_OCollect(U_14635),U_14639)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14635),hAPP(c_Set_OCollect(U_14635),U_14637))) )
    & ! [U_14636,U_14634,U_14638] :
        ( sP1007(U_14636,U_14634,U_14638)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14634),hAPP(c_Set_OCollect(U_14634),hAPP(hAPP(c_COMBS(U_14634,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14634),c_fdisj),U_14636)),U_14638)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1007])],[f_3655_3]) ).

cnf(f_3655_5,plain,
    ( sP1007(U_14636,U_14634,U_14638)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14634),hAPP(c_Set_OCollect(U_14634),hAPP(hAPP(c_COMBS(U_14634,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14634),c_fdisj),U_14636)),U_14638)))) ),
    inference(clausify,[status(thm)],[f_3655_4]) ).

cnf(f_3655_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14635),hAPP(c_Set_OCollect(U_14635),hAPP(hAPP(c_COMBS(U_14635,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14635),c_fdisj),U_14637)),U_14639))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14635),hAPP(c_Set_OCollect(U_14635),U_14639)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14635),hAPP(c_Set_OCollect(U_14635),U_14637))) ),
    inference(clausify,[status(thm)],[f_3655_4]) ).

cnf(f_3655_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14634),hAPP(c_Set_OCollect(U_14634),U_14636)))
    | ~ sP1007(U_14636,U_14634,U_14638) ),
    inference(clausify,[status(thm)],[f_3655_4]) ).

cnf(f_3655_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14634),hAPP(c_Set_OCollect(U_14634),U_14638)))
    | ~ sP1007(U_14636,U_14634,U_14638) ),
    inference(clausify,[status(thm)],[f_3655_4]) ).

fof(f_3656_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_3656_2,plain,
    ! [U_14642,U_14641,U_14640] : hAPP(hAPP(c_Set_Oinsert(U_14640),U_14641),hAPP(c_Set_OCollect(U_14640),U_14642)) = hAPP(c_Set_OCollect(U_14640),hAPP(hAPP(c_COMBS(U_14640,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14640),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14640),c_fNot),hAPP(hAPP(c_COMBC(U_14640,U_14640,tc_HOL_Obool),c_fequal),U_14641)))),U_14642)),
    inference(variable_rename,[status(thm)],[f_3656_1]) ).

fof(f_3656_3,plain,
    ! [U_14642,U_14640,U_14641] : hAPP(hAPP(c_Set_Oinsert(U_14640),U_14641),hAPP(c_Set_OCollect(U_14640),U_14642)) = hAPP(c_Set_OCollect(U_14640),hAPP(hAPP(c_COMBS(U_14640,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14640),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14640),c_fNot),hAPP(hAPP(c_COMBC(U_14640,U_14640,tc_HOL_Obool),c_fequal),U_14641)))),U_14642)),
    inference(definitional_conversion,[status(esa)],[f_3656_2]) ).

cnf(f_3656_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_14640),U_14641),hAPP(c_Set_OCollect(U_14640),U_14642)) = hAPP(c_Set_OCollect(U_14640),hAPP(hAPP(c_COMBS(U_14640,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14640),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14640),c_fNot),hAPP(hAPP(c_COMBC(U_14640,U_14640,tc_HOL_Obool),c_fequal),U_14641)))),U_14642)),
    inference(clausify,[status(thm)],[f_3656_3]) ).

fof(f_3657_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_3657_2,plain,
    ! [U_14643] : c_Finite__Set_Ofun__left__comm__idem(U_14643,tc_fun(U_14643,tc_HOL_Obool),c_Set_Oinsert(U_14643)),
    inference(variable_rename,[status(thm)],[f_3657_1]) ).

fof(f_3657_3,plain,
    ! [U_14643] : c_Finite__Set_Ofun__left__comm__idem(U_14643,tc_fun(U_14643,tc_HOL_Obool),c_Set_Oinsert(U_14643)),
    inference(definitional_conversion,[status(esa)],[f_3657_2]) ).

cnf(f_3657_4,plain,
    c_Finite__Set_Ofun__left__comm__idem(U_14643,tc_fun(U_14643,tc_HOL_Obool),c_Set_Oinsert(U_14643)),
    inference(clausify,[status(thm)],[f_3657_3]) ).

fof(f_3658_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_3658_2,plain,
    ! [U_14644] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_14644,U_14644,c_Orderings_Oord__class_Omax(U_14644))
      | ~ class_Orderings_Olinorder(U_14644) ),
    inference(variable_rename,[status(thm)],[f_3658_1]) ).

fof(f_3658_3,plain,
    ! [U_14644] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_14644,U_14644,c_Orderings_Oord__class_Omax(U_14644))
      | ~ class_Orderings_Olinorder(U_14644) ),
    inference(definitional_conversion,[status(esa)],[f_3658_2]) ).

cnf(f_3658_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_14644,U_14644,c_Orderings_Oord__class_Omax(U_14644))
    | ~ class_Orderings_Olinorder(U_14644) ),
    inference(clausify,[status(thm)],[f_3658_3]) ).

fof(f_3659_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_3659_2,plain,
    ! [U_14645] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_14645,U_14645,c_Groups_Otimes__class_Otimes(U_14645))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14645) ),
    inference(variable_rename,[status(thm)],[f_3659_1]) ).

fof(f_3659_3,plain,
    ! [U_14645] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_14645,U_14645,c_Groups_Otimes__class_Otimes(U_14645))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14645) ),
    inference(definitional_conversion,[status(esa)],[f_3659_2]) ).

cnf(f_3659_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_14645,U_14645,c_Groups_Otimes__class_Otimes(U_14645))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_14645) ),
    inference(clausify,[status(thm)],[f_3659_3]) ).

fof(f_3660_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_3660_2,plain,
    ! [U_14648,U_14647,U_14646] : hAPP(c_Set_OCollect(U_14646),hAPP(hAPP(c_COMBS(U_14646,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14646),c_fconj),U_14647)),U_14648)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14646,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14646),U_14647)),hAPP(c_Set_OCollect(U_14646),U_14648)),
    inference(variable_rename,[status(thm)],[f_3660_1]) ).

fof(f_3660_3,plain,
    ! [U_14646,U_14647,U_14648] : hAPP(c_Set_OCollect(U_14646),hAPP(hAPP(c_COMBS(U_14646,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14646),c_fconj),U_14647)),U_14648)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14646,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14646),U_14647)),hAPP(c_Set_OCollect(U_14646),U_14648)),
    inference(definitional_conversion,[status(esa)],[f_3660_2]) ).

cnf(f_3660_4,plain,
    hAPP(c_Set_OCollect(U_14646),hAPP(hAPP(c_COMBS(U_14646,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14646),c_fconj),U_14647)),U_14648)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14646,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14646),U_14647)),hAPP(c_Set_OCollect(U_14646),U_14648)),
    inference(clausify,[status(thm)],[f_3660_3]) ).

fof(f_3661_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_3661_2,plain,
    ! [U_14651,U_14650,U_14649] : hAPP(c_Set_OCollect(U_14649),hAPP(hAPP(c_COMBS(U_14649,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14649),c_fdisj),U_14650)),U_14651)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14649,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14649),U_14650)),hAPP(c_Set_OCollect(U_14649),U_14651)),
    inference(variable_rename,[status(thm)],[f_3661_1]) ).

fof(f_3661_3,plain,
    ! [U_14649,U_14650,U_14651] : hAPP(c_Set_OCollect(U_14649),hAPP(hAPP(c_COMBS(U_14649,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14649),c_fdisj),U_14650)),U_14651)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14649,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14649),U_14650)),hAPP(c_Set_OCollect(U_14649),U_14651)),
    inference(definitional_conversion,[status(esa)],[f_3661_2]) ).

cnf(f_3661_4,plain,
    hAPP(c_Set_OCollect(U_14649),hAPP(hAPP(c_COMBS(U_14649,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14649),c_fdisj),U_14650)),U_14651)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14649,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14649),U_14650)),hAPP(c_Set_OCollect(U_14649),U_14651)),
    inference(clausify,[status(thm)],[f_3661_3]) ).

fof(f_3662_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_3662_2,plain,
    ! [U_14652] : c_Orderings_Obot__class_Obot(tc_fun(U_14652,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_14652),hAPP(c_COMBK(tc_HOL_Obool,U_14652),c_fFalse)),
    inference(variable_rename,[status(thm)],[f_3662_1]) ).

fof(f_3662_3,plain,
    ! [U_14652] : c_Orderings_Obot__class_Obot(tc_fun(U_14652,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_14652),hAPP(c_COMBK(tc_HOL_Obool,U_14652),c_fFalse)),
    inference(definitional_conversion,[status(esa)],[f_3662_2]) ).

cnf(f_3662_4,plain,
    c_Orderings_Obot__class_Obot(tc_fun(U_14652,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_14652),hAPP(c_COMBK(tc_HOL_Obool,U_14652),c_fFalse)),
    inference(clausify,[status(thm)],[f_3662_3]) ).

fof(f_3663_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_3663_2,plain,
    ! [U_14656,U_14655] :
      ( ( hAPP(c_Set_OCollect(U_14655),U_14656) = c_Orderings_Obot__class_Obot(tc_fun(U_14655,tc_HOL_Obool))
        | ? [U_14654] : hBOOL(hAPP(U_14656,U_14654)) )
      & ( ! [U_14653] : ~ hBOOL(hAPP(U_14656,U_14653))
        | hAPP(c_Set_OCollect(U_14655),U_14656) != c_Orderings_Obot__class_Obot(tc_fun(U_14655,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3663_1]) ).

fof(f_3663_3,plain,
    ( ! [U_14660] :
        ( ! [U_14658] : hAPP(c_Set_OCollect(U_14658),U_14660) = c_Orderings_Obot__class_Obot(tc_fun(U_14658,tc_HOL_Obool))
        | ? [U_14654] : hBOOL(hAPP(U_14660,U_14654)) )
    & ! [U_14659] :
        ( ! [U_14657] : hAPP(c_Set_OCollect(U_14657),U_14659) != c_Orderings_Obot__class_Obot(tc_fun(U_14657,tc_HOL_Obool))
        | ! [U_14653] : ~ hBOOL(hAPP(U_14659,U_14653)) ) ),
    inference(miniscope,[status(thm)],[f_3663_2]) ).

fof(f_3663_4,plain,
    ( ! [U_14660] :
        ( ! [U_14658] : hAPP(c_Set_OCollect(U_14658),U_14660) = c_Orderings_Obot__class_Obot(tc_fun(U_14658,tc_HOL_Obool))
        | hBOOL(hAPP(U_14660,sK331(U_14660))) )
    & ! [U_14659] :
        ( ! [U_14657] : hAPP(c_Set_OCollect(U_14657),U_14659) != c_Orderings_Obot__class_Obot(tc_fun(U_14657,tc_HOL_Obool))
        | ! [U_14653] : ~ hBOOL(hAPP(U_14659,U_14653)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK331]),skolemize(U_14654,sK331(U_14660))],[f_3663_3]) ).

fof(f_3663_5,plain,
    ( ! [U_14658,U_14660] :
        ( hAPP(c_Set_OCollect(U_14658),U_14660) = c_Orderings_Obot__class_Obot(tc_fun(U_14658,tc_HOL_Obool))
        | hBOOL(hAPP(U_14660,sK331(U_14660))) )
    & ! [U_14653,U_14657,U_14659] :
        ( hAPP(c_Set_OCollect(U_14657),U_14659) != c_Orderings_Obot__class_Obot(tc_fun(U_14657,tc_HOL_Obool))
        | ~ hBOOL(hAPP(U_14659,U_14653)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3663_4]) ).

cnf(f_3663_6,plain,
    ( hAPP(c_Set_OCollect(U_14657),U_14659) != c_Orderings_Obot__class_Obot(tc_fun(U_14657,tc_HOL_Obool))
    | ~ hBOOL(hAPP(U_14659,U_14653)) ),
    inference(clausify,[status(thm)],[f_3663_5]) ).

cnf(f_3663_7,plain,
    ( hAPP(c_Set_OCollect(U_14658),U_14660) = c_Orderings_Obot__class_Obot(tc_fun(U_14658,tc_HOL_Obool))
    | hBOOL(hAPP(U_14660,sK331(U_14660))) ),
    inference(clausify,[status(thm)],[f_3663_5]) ).

fof(f_3664_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_3664_2,plain,
    ! [U_14664,U_14663] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_14663,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_14663),U_14664)
        | ? [U_14662] : hBOOL(hAPP(U_14664,U_14662)) )
      & ( ! [U_14661] : ~ hBOOL(hAPP(U_14664,U_14661))
        | c_Orderings_Obot__class_Obot(tc_fun(U_14663,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_14663),U_14664) ) ),
    inference(variable_rename,[status(thm)],[f_3664_1]) ).

fof(f_3664_3,plain,
    ( ! [U_14668] :
        ( ! [U_14666] : c_Orderings_Obot__class_Obot(tc_fun(U_14666,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_14666),U_14668)
        | ? [U_14662] : hBOOL(hAPP(U_14668,U_14662)) )
    & ! [U_14667] :
        ( ! [U_14665] : c_Orderings_Obot__class_Obot(tc_fun(U_14665,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_14665),U_14667)
        | ! [U_14661] : ~ hBOOL(hAPP(U_14667,U_14661)) ) ),
    inference(miniscope,[status(thm)],[f_3664_2]) ).

fof(f_3664_4,plain,
    ( ! [U_14668] :
        ( ! [U_14666] : c_Orderings_Obot__class_Obot(tc_fun(U_14666,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_14666),U_14668)
        | hBOOL(hAPP(U_14668,sK332(U_14668))) )
    & ! [U_14667] :
        ( ! [U_14665] : c_Orderings_Obot__class_Obot(tc_fun(U_14665,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_14665),U_14667)
        | ! [U_14661] : ~ hBOOL(hAPP(U_14667,U_14661)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK332]),skolemize(U_14662,sK332(U_14668))],[f_3664_3]) ).

fof(f_3664_5,plain,
    ( ! [U_14666,U_14668] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_14666,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_14666),U_14668)
        | hBOOL(hAPP(U_14668,sK332(U_14668))) )
    & ! [U_14661,U_14667,U_14665] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_14665,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_14665),U_14667)
        | ~ hBOOL(hAPP(U_14667,U_14661)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3664_4]) ).

cnf(f_3664_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_14665,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_14665),U_14667)
    | ~ hBOOL(hAPP(U_14667,U_14661)) ),
    inference(clausify,[status(thm)],[f_3664_5]) ).

cnf(f_3664_7,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_14666,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_14666),U_14668)
    | hBOOL(hAPP(U_14668,sK332(U_14668))) ),
    inference(clausify,[status(thm)],[f_3664_5]) ).

fof(f_3665_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_3665_2,plain,
    ! [U_14673,U_14672,U_14671,U_14670,U_14669] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_14672,U_14670,hAPP(hAPP(c_COMBB(U_14669,tc_fun(U_14670,U_14670),U_14672),U_14671),U_14673))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_14669,U_14670,U_14671) ),
    inference(variable_rename,[status(thm)],[f_3665_1]) ).

fof(f_3665_3,plain,
    ! [U_14669,U_14670,U_14671,U_14672,U_14673] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_14672,U_14670,hAPP(hAPP(c_COMBB(U_14669,tc_fun(U_14670,U_14670),U_14672),U_14671),U_14673))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_14669,U_14670,U_14671) ),
    inference(definitional_conversion,[status(esa)],[f_3665_2]) ).

cnf(f_3665_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_14672,U_14670,hAPP(hAPP(c_COMBB(U_14669,tc_fun(U_14670,U_14670),U_14672),U_14671),U_14673))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_14669,U_14670,U_14671) ),
    inference(clausify,[status(thm)],[f_3665_3]) ).

fof(f_3666_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_3666_2,plain,
    ! [U_14678,U_14677,U_14676,U_14675,U_14674] :
      ( hAPP(hAPP(U_14676,U_14677),hAPP(hAPP(U_14676,U_14677),U_14678)) = hAPP(hAPP(U_14676,U_14677),U_14678)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_14674,U_14675,U_14676) ),
    inference(variable_rename,[status(thm)],[f_3666_1]) ).

fof(f_3666_3,plain,
    ! [U_14678,U_14677,U_14676] :
      ( ! [U_14675,U_14674] : ~ c_Finite__Set_Ofun__left__comm__idem(U_14674,U_14675,U_14676)
      | hAPP(hAPP(U_14676,U_14677),hAPP(hAPP(U_14676,U_14677),U_14678)) = hAPP(hAPP(U_14676,U_14677),U_14678) ),
    inference(miniscope,[status(thm)],[f_3666_2]) ).

fof(f_3666_4,plain,
    ! [U_14677,U_14674,U_14676,U_14675,U_14678] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(U_14674,U_14675,U_14676)
      | hAPP(hAPP(U_14676,U_14677),hAPP(hAPP(U_14676,U_14677),U_14678)) = hAPP(hAPP(U_14676,U_14677),U_14678) ),
    inference(definitional_conversion,[status(esa)],[f_3666_3]) ).

cnf(f_3666_5,plain,
    ( ~ c_Finite__Set_Ofun__left__comm__idem(U_14674,U_14675,U_14676)
    | hAPP(hAPP(U_14676,U_14677),hAPP(hAPP(U_14676,U_14677),U_14678)) = hAPP(hAPP(U_14676,U_14677),U_14678) ),
    inference(clausify,[status(thm)],[f_3666_4]) ).

fof(f_3667_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_3667_2,plain,
    ! [U_14680,U_14679] : hAPP(c_Set_OCollect(U_14679),U_14680) = U_14680,
    inference(variable_rename,[status(thm)],[f_3667_1]) ).

fof(f_3667_3,plain,
    ! [U_14679,U_14680] : hAPP(c_Set_OCollect(U_14679),U_14680) = U_14680,
    inference(definitional_conversion,[status(esa)],[f_3667_2]) ).

cnf(f_3667_4,plain,
    hAPP(c_Set_OCollect(U_14679),U_14680) = U_14680,
    inference(clausify,[status(thm)],[f_3667_3]) ).

fof(f_3668_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_3668_2,plain,
    ! [U_14681] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_14681,U_14681,c_Lattices_Osemilattice__inf__class_Oinf(U_14681))
      | ~ class_Lattices_Osemilattice__inf(U_14681) ),
    inference(variable_rename,[status(thm)],[f_3668_1]) ).

fof(f_3668_3,plain,
    ! [U_14681] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_14681,U_14681,c_Lattices_Osemilattice__inf__class_Oinf(U_14681))
      | ~ class_Lattices_Osemilattice__inf(U_14681) ),
    inference(definitional_conversion,[status(esa)],[f_3668_2]) ).

cnf(f_3668_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_14681,U_14681,c_Lattices_Osemilattice__inf__class_Oinf(U_14681))
    | ~ class_Lattices_Osemilattice__inf(U_14681) ),
    inference(clausify,[status(thm)],[f_3668_3]) ).

fof(f_3669_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_3669_2,plain,
    ! [U_14682] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_14682,U_14682,c_Lattices_Osemilattice__sup__class_Osup(U_14682))
      | ~ class_Lattices_Osemilattice__sup(U_14682) ),
    inference(variable_rename,[status(thm)],[f_3669_1]) ).

fof(f_3669_3,plain,
    ! [U_14682] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_14682,U_14682,c_Lattices_Osemilattice__sup__class_Osup(U_14682))
      | ~ class_Lattices_Osemilattice__sup(U_14682) ),
    inference(definitional_conversion,[status(esa)],[f_3669_2]) ).

cnf(f_3669_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_14682,U_14682,c_Lattices_Osemilattice__sup__class_Osup(U_14682))
    | ~ class_Lattices_Osemilattice__sup(U_14682) ),
    inference(clausify,[status(thm)],[f_3669_3]) ).

fof(f_3670_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_3670_2,plain,
    ! [U_14683] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_14683,U_14683,c_Orderings_Oord__class_Omin(U_14683))
      | ~ class_Orderings_Olinorder(U_14683) ),
    inference(variable_rename,[status(thm)],[f_3670_1]) ).

fof(f_3670_3,plain,
    ! [U_14683] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_14683,U_14683,c_Orderings_Oord__class_Omin(U_14683))
      | ~ class_Orderings_Olinorder(U_14683) ),
    inference(definitional_conversion,[status(esa)],[f_3670_2]) ).

cnf(f_3670_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_14683,U_14683,c_Orderings_Oord__class_Omin(U_14683))
    | ~ class_Orderings_Olinorder(U_14683) ),
    inference(clausify,[status(thm)],[f_3670_3]) ).

fof(f_3671_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_3671_2,plain,
    ! [U_14687,U_14686,U_14685,U_14684] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_14684),U_14685),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14684,tc_HOL_Obool)),U_14686),hAPP(c_Set_OCollect(U_14684),U_14687))))
        | ~ hBOOL(hAPP(U_14687,U_14685))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14684),U_14685),U_14686)) )
      & ( ( hBOOL(hAPP(U_14687,U_14685))
          & hBOOL(hAPP(hAPP(c_member(U_14684),U_14685),U_14686)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_14684),U_14685),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14684,tc_HOL_Obool)),U_14686),hAPP(c_Set_OCollect(U_14684),U_14687)))) ) ),
    inference(variable_rename,[status(thm)],[f_3671_1]) ).

fof(f_3671_3,plain,
    ( ! [U_14695,U_14693,U_14691,U_14689] :
        ( hBOOL(hAPP(hAPP(c_member(U_14689),U_14691),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14689,tc_HOL_Obool)),U_14693),hAPP(c_Set_OCollect(U_14689),U_14695))))
        | ~ hBOOL(hAPP(U_14695,U_14691))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14689),U_14691),U_14693)) )
    & ! [U_14694,U_14692,U_14690,U_14688] :
        ( ( hBOOL(hAPP(U_14694,U_14690))
          & hBOOL(hAPP(hAPP(c_member(U_14688),U_14690),U_14692)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_14688),U_14690),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14688,tc_HOL_Obool)),U_14692),hAPP(c_Set_OCollect(U_14688),U_14694)))) ) ),
    inference(miniscope,[status(thm)],[f_3671_2]) ).

fof(f_3671_4,plain,
    ( ! [U_14690,U_14694,U_14688,U_14692] :
        ( hBOOL(hAPP(U_14694,U_14690))
        | ~ sP1008(U_14690,U_14694,U_14688,U_14692) )
    & ! [U_14690,U_14694,U_14688,U_14692] :
        ( hBOOL(hAPP(hAPP(c_member(U_14688),U_14690),U_14692))
        | ~ sP1008(U_14690,U_14694,U_14688,U_14692) )
    & ! [U_14691,U_14689,U_14695,U_14693] :
        ( hBOOL(hAPP(hAPP(c_member(U_14689),U_14691),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14689,tc_HOL_Obool)),U_14693),hAPP(c_Set_OCollect(U_14689),U_14695))))
        | ~ hBOOL(hAPP(U_14695,U_14691))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14689),U_14691),U_14693)) )
    & ! [U_14690,U_14694,U_14688,U_14692] :
        ( sP1008(U_14690,U_14694,U_14688,U_14692)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14688),U_14690),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14688,tc_HOL_Obool)),U_14692),hAPP(c_Set_OCollect(U_14688),U_14694)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1008])],[f_3671_3]) ).

cnf(f_3671_5,plain,
    ( sP1008(U_14690,U_14694,U_14688,U_14692)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14688),U_14690),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14688,tc_HOL_Obool)),U_14692),hAPP(c_Set_OCollect(U_14688),U_14694)))) ),
    inference(clausify,[status(thm)],[f_3671_4]) ).

cnf(f_3671_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14689),U_14691),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14689,tc_HOL_Obool)),U_14693),hAPP(c_Set_OCollect(U_14689),U_14695))))
    | ~ hBOOL(hAPP(U_14695,U_14691))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14689),U_14691),U_14693)) ),
    inference(clausify,[status(thm)],[f_3671_4]) ).

cnf(f_3671_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14688),U_14690),U_14692))
    | ~ sP1008(U_14690,U_14694,U_14688,U_14692) ),
    inference(clausify,[status(thm)],[f_3671_4]) ).

cnf(f_3671_8,plain,
    ( hBOOL(hAPP(U_14694,U_14690))
    | ~ sP1008(U_14690,U_14694,U_14688,U_14692) ),
    inference(clausify,[status(thm)],[f_3671_4]) ).

fof(f_3672_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_3672_2,plain,
    ! [U_14698,U_14697,U_14696] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14696,tc_HOL_Obool)),U_14697),U_14698) = hAPP(c_Set_OCollect(U_14696),hAPP(hAPP(c_COMBS(U_14696,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14696),c_fconj),hAPP(hAPP(c_COMBC(U_14696,tc_fun(U_14696,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14696)),U_14697))),hAPP(hAPP(c_COMBC(U_14696,tc_fun(U_14696,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14696)),U_14698))),
    inference(variable_rename,[status(thm)],[f_3672_1]) ).

fof(f_3672_3,plain,
    ! [U_14696,U_14697,U_14698] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14696,tc_HOL_Obool)),U_14697),U_14698) = hAPP(c_Set_OCollect(U_14696),hAPP(hAPP(c_COMBS(U_14696,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14696),c_fconj),hAPP(hAPP(c_COMBC(U_14696,tc_fun(U_14696,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14696)),U_14697))),hAPP(hAPP(c_COMBC(U_14696,tc_fun(U_14696,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14696)),U_14698))),
    inference(definitional_conversion,[status(esa)],[f_3672_2]) ).

cnf(f_3672_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14696,tc_HOL_Obool)),U_14697),U_14698) = hAPP(c_Set_OCollect(U_14696),hAPP(hAPP(c_COMBS(U_14696,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14696),c_fconj),hAPP(hAPP(c_COMBC(U_14696,tc_fun(U_14696,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14696)),U_14697))),hAPP(hAPP(c_COMBC(U_14696,tc_fun(U_14696,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14696)),U_14698))),
    inference(clausify,[status(thm)],[f_3672_3]) ).

fof(f_3673_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_3673_2,plain,
    ! [U_14701,U_14700,U_14699] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14699,tc_HOL_Obool)),U_14700),U_14701) = hAPP(c_Set_OCollect(U_14699),hAPP(hAPP(c_COMBS(U_14699,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14699),c_fdisj),hAPP(hAPP(c_COMBC(U_14699,tc_fun(U_14699,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14699)),U_14700))),hAPP(hAPP(c_COMBC(U_14699,tc_fun(U_14699,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14699)),U_14701))),
    inference(variable_rename,[status(thm)],[f_3673_1]) ).

fof(f_3673_3,plain,
    ! [U_14699,U_14700,U_14701] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14699,tc_HOL_Obool)),U_14700),U_14701) = hAPP(c_Set_OCollect(U_14699),hAPP(hAPP(c_COMBS(U_14699,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14699),c_fdisj),hAPP(hAPP(c_COMBC(U_14699,tc_fun(U_14699,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14699)),U_14700))),hAPP(hAPP(c_COMBC(U_14699,tc_fun(U_14699,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14699)),U_14701))),
    inference(definitional_conversion,[status(esa)],[f_3673_2]) ).

cnf(f_3673_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14699,tc_HOL_Obool)),U_14700),U_14701) = hAPP(c_Set_OCollect(U_14699),hAPP(hAPP(c_COMBS(U_14699,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14699),c_fdisj),hAPP(hAPP(c_COMBC(U_14699,tc_fun(U_14699,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14699)),U_14700))),hAPP(hAPP(c_COMBC(U_14699,tc_fun(U_14699,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14699)),U_14701))),
    inference(clausify,[status(thm)],[f_3673_3]) ).

fof(f_3674_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_3674_2,plain,
    ! [U_14704,U_14703,U_14702] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14702,tc_HOL_Obool)),U_14703),U_14704) = hAPP(c_Set_OCollect(U_14702),hAPP(hAPP(c_COMBS(U_14702,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14702),c_fconj),hAPP(hAPP(c_COMBC(U_14702,tc_fun(U_14702,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14702)),U_14703))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14702),c_fNot),hAPP(hAPP(c_COMBC(U_14702,tc_fun(U_14702,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14702)),U_14704)))),
    inference(variable_rename,[status(thm)],[f_3674_1]) ).

fof(f_3674_3,plain,
    ! [U_14702,U_14703,U_14704] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14702,tc_HOL_Obool)),U_14703),U_14704) = hAPP(c_Set_OCollect(U_14702),hAPP(hAPP(c_COMBS(U_14702,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14702),c_fconj),hAPP(hAPP(c_COMBC(U_14702,tc_fun(U_14702,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14702)),U_14703))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14702),c_fNot),hAPP(hAPP(c_COMBC(U_14702,tc_fun(U_14702,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14702)),U_14704)))),
    inference(definitional_conversion,[status(esa)],[f_3674_2]) ).

cnf(f_3674_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14702,tc_HOL_Obool)),U_14703),U_14704) = hAPP(c_Set_OCollect(U_14702),hAPP(hAPP(c_COMBS(U_14702,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14702),c_fconj),hAPP(hAPP(c_COMBC(U_14702,tc_fun(U_14702,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14702)),U_14703))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14702),c_fNot),hAPP(hAPP(c_COMBC(U_14702,tc_fun(U_14702,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14702)),U_14704)))),
    inference(clausify,[status(thm)],[f_3674_3]) ).

fof(f_3675_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_3675_2,plain,
    ! [U_14706,U_14705] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14705),hAPP(c_Set_OCollect(U_14705),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14705),c_fNot),U_14706))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14705),c_Orderings_Otop__class_Otop(tc_fun(U_14705,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14705),c_Orderings_Otop__class_Otop(tc_fun(U_14705,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14705),hAPP(c_Set_OCollect(U_14705),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14705),c_fNot),U_14706)))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14705),hAPP(c_Set_OCollect(U_14705),U_14706))) ),
    inference(variable_rename,[status(thm)],[f_3675_1]) ).

fof(f_3675_3,plain,
    ( ! [U_14705,U_14706] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14705),hAPP(c_Set_OCollect(U_14705),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14705),c_fNot),U_14706))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14705),c_Orderings_Otop__class_Otop(tc_fun(U_14705,tc_HOL_Obool))))
        | ~ sP1009(U_14705,U_14706) )
    & ! [U_14705,U_14706] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14705),c_Orderings_Otop__class_Otop(tc_fun(U_14705,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14705),hAPP(c_Set_OCollect(U_14705),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14705),c_fNot),U_14706))))
        | ~ sP1009(U_14705,U_14706) )
    & ! [U_14705,U_14706] :
        ( sP1009(U_14705,U_14706)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14705),hAPP(c_Set_OCollect(U_14705),U_14706))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1009])],[f_3675_2]) ).

cnf(f_3675_4,plain,
    ( sP1009(U_14705,U_14706)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14705),hAPP(c_Set_OCollect(U_14705),U_14706))) ),
    inference(clausify,[status(thm)],[f_3675_3]) ).

cnf(f_3675_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14705),c_Orderings_Otop__class_Otop(tc_fun(U_14705,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14705),hAPP(c_Set_OCollect(U_14705),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14705),c_fNot),U_14706))))
    | ~ sP1009(U_14705,U_14706) ),
    inference(clausify,[status(thm)],[f_3675_3]) ).

cnf(f_3675_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14705),hAPP(c_Set_OCollect(U_14705),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14705),c_fNot),U_14706))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14705),c_Orderings_Otop__class_Otop(tc_fun(U_14705,tc_HOL_Obool))))
    | ~ sP1009(U_14705,U_14706) ),
    inference(clausify,[status(thm)],[f_3675_3]) ).

fof(f_3676_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_3676_2,plain,
    ! [U_14709,U_14708,U_14707] : hAPP(hAPP(c_Set_Oinsert(U_14707),U_14708),U_14709) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14707,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14707),hAPP(hAPP(c_COMBC(U_14707,U_14707,tc_HOL_Obool),c_fequal),U_14708))),U_14709),
    inference(variable_rename,[status(thm)],[f_3676_1]) ).

fof(f_3676_3,plain,
    ! [U_14708,U_14707,U_14709] : hAPP(hAPP(c_Set_Oinsert(U_14707),U_14708),U_14709) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14707,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14707),hAPP(hAPP(c_COMBC(U_14707,U_14707,tc_HOL_Obool),c_fequal),U_14708))),U_14709),
    inference(definitional_conversion,[status(esa)],[f_3676_2]) ).

cnf(f_3676_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_14707),U_14708),U_14709) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14707,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14707),hAPP(hAPP(c_COMBC(U_14707,U_14707,tc_HOL_Obool),c_fequal),U_14708))),U_14709),
    inference(clausify,[status(thm)],[f_3676_3]) ).

fof(f_3677_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_3677_2,plain,
    ! [U_14711,U_14710] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14710,tc_HOL_Obool)),U_14711) = hAPP(c_Set_OCollect(U_14710),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14710),c_fNot),hAPP(hAPP(c_COMBC(U_14710,tc_fun(U_14710,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14710)),U_14711))),
    inference(variable_rename,[status(thm)],[f_3677_1]) ).

fof(f_3677_3,plain,
    ! [U_14710,U_14711] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14710,tc_HOL_Obool)),U_14711) = hAPP(c_Set_OCollect(U_14710),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14710),c_fNot),hAPP(hAPP(c_COMBC(U_14710,tc_fun(U_14710,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14710)),U_14711))),
    inference(definitional_conversion,[status(esa)],[f_3677_2]) ).

cnf(f_3677_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14710,tc_HOL_Obool)),U_14711) = hAPP(c_Set_OCollect(U_14710),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14710),c_fNot),hAPP(hAPP(c_COMBC(U_14710,tc_fun(U_14710,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14710)),U_14711))),
    inference(clausify,[status(thm)],[f_3677_3]) ).

fof(f_3678_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_3678_2,plain,
    ! [U_14715,U_14714,U_14713,U_14712] : hAPP(c_Set_Ovimage(U_14712,U_14713,U_14714),U_14715) = hAPP(c_Set_OCollect(U_14712),hAPP(hAPP(c_COMBC(U_14712,tc_fun(U_14713,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14713,tc_fun(tc_fun(U_14713,tc_HOL_Obool),tc_HOL_Obool),U_14712),c_member(U_14713)),U_14714)),U_14715)),
    inference(variable_rename,[status(thm)],[f_3678_1]) ).

fof(f_3678_3,plain,
    ! [U_14712,U_14713,U_14714,U_14715] : hAPP(c_Set_Ovimage(U_14712,U_14713,U_14714),U_14715) = hAPP(c_Set_OCollect(U_14712),hAPP(hAPP(c_COMBC(U_14712,tc_fun(U_14713,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14713,tc_fun(tc_fun(U_14713,tc_HOL_Obool),tc_HOL_Obool),U_14712),c_member(U_14713)),U_14714)),U_14715)),
    inference(definitional_conversion,[status(esa)],[f_3678_2]) ).

cnf(f_3678_4,plain,
    hAPP(c_Set_Ovimage(U_14712,U_14713,U_14714),U_14715) = hAPP(c_Set_OCollect(U_14712),hAPP(hAPP(c_COMBC(U_14712,tc_fun(U_14713,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14713,tc_fun(tc_fun(U_14713,tc_HOL_Obool),tc_HOL_Obool),U_14712),c_member(U_14713)),U_14714)),U_14715)),
    inference(clausify,[status(thm)],[f_3678_3]) ).

fof(f_3679_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_3679_2,plain,
    ! [U_14718,U_14717,U_14716] : hAPP(c_Set_OCollect(U_14716),hAPP(hAPP(c_COMBS(U_14716,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14716),c_fimplies),U_14717)),U_14718)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14716,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14716,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14716),U_14717))),hAPP(c_Set_OCollect(U_14716),U_14718)),
    inference(variable_rename,[status(thm)],[f_3679_1]) ).

fof(f_3679_3,plain,
    ! [U_14716,U_14717,U_14718] : hAPP(c_Set_OCollect(U_14716),hAPP(hAPP(c_COMBS(U_14716,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14716),c_fimplies),U_14717)),U_14718)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14716,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14716,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14716),U_14717))),hAPP(c_Set_OCollect(U_14716),U_14718)),
    inference(definitional_conversion,[status(esa)],[f_3679_2]) ).

cnf(f_3679_4,plain,
    hAPP(c_Set_OCollect(U_14716),hAPP(hAPP(c_COMBS(U_14716,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14716),c_fimplies),U_14717)),U_14718)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14716,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14716,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14716),U_14717))),hAPP(c_Set_OCollect(U_14716),U_14718)),
    inference(clausify,[status(thm)],[f_3679_3]) ).

fof(f_3680_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_3680_2,plain,
    ! [U_14721,U_14720,U_14719] : c_Map_Odom(U_14719,U_14720,U_14721) = hAPP(c_Set_OCollect(U_14719),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14719),c_fNot),hAPP(hAPP(c_COMBC(U_14719,tc_Option_Ooption(U_14720),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_14720),tc_fun(tc_Option_Ooption(U_14720),tc_HOL_Obool),U_14719),c_fequal),U_14721)),c_Option_Ooption_ONone(U_14720)))),
    inference(variable_rename,[status(thm)],[f_3680_1]) ).

fof(f_3680_3,plain,
    ! [U_14719,U_14720,U_14721] : c_Map_Odom(U_14719,U_14720,U_14721) = hAPP(c_Set_OCollect(U_14719),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14719),c_fNot),hAPP(hAPP(c_COMBC(U_14719,tc_Option_Ooption(U_14720),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_14720),tc_fun(tc_Option_Ooption(U_14720),tc_HOL_Obool),U_14719),c_fequal),U_14721)),c_Option_Ooption_ONone(U_14720)))),
    inference(definitional_conversion,[status(esa)],[f_3680_2]) ).

cnf(f_3680_4,plain,
    c_Map_Odom(U_14719,U_14720,U_14721) = hAPP(c_Set_OCollect(U_14719),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14719),c_fNot),hAPP(hAPP(c_COMBC(U_14719,tc_Option_Ooption(U_14720),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_14720),tc_fun(tc_Option_Ooption(U_14720),tc_HOL_Obool),U_14719),c_fequal),U_14721)),c_Option_Ooption_ONone(U_14720)))),
    inference(clausify,[status(thm)],[f_3680_3]) ).

fof(f_3681_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_3681_2,plain,
    ! [U_14723,U_14722] : 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_14722)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14723))))),
    inference(variable_rename,[status(thm)],[f_3681_1]) ).

fof(f_3681_3,plain,
    ! [U_14722,U_14723] : 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_14722)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14723))))),
    inference(definitional_conversion,[status(esa)],[f_3681_2]) ).

cnf(f_3681_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_14722)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14723))))),
    inference(clausify,[status(thm)],[f_3681_3]) ).

fof(f_3682_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_3682_2,plain,
    ! [U_14730,U_14729,U_14728,U_14727,U_14726,U_14725,U_14724] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14725,U_14724),hAPP(hAPP(c_COMBS(U_14725,tc_fun(U_14727,tc_HOL_Obool),U_14724),hAPP(hAPP(c_COMBB(tc_fun(U_14727,U_14724),tc_fun(tc_fun(U_14727,tc_HOL_Obool),U_14724),U_14725),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14727,U_14724)),U_14729)),hAPP(hAPP(c_COMBB(tc_fun(U_14727,tc_HOL_Obool),tc_fun(U_14727,tc_HOL_Obool),U_14725),c_Set_OCollect(U_14727)),hAPP(hAPP(c_COMBB(tc_fun(U_14727,tc_HOL_Obool),tc_fun(U_14727,tc_HOL_Obool),U_14725),hAPP(c_COMBS(U_14727,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14727),c_fconj),hAPP(hAPP(c_COMBC(U_14727,tc_fun(U_14727,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14727)),U_14728)))),U_14730)))),U_14726) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14727,U_14724),hAPP(hAPP(c_COMBS(U_14727,tc_fun(U_14725,tc_HOL_Obool),U_14724),hAPP(hAPP(c_COMBB(tc_fun(U_14725,U_14724),tc_fun(tc_fun(U_14725,tc_HOL_Obool),U_14724),U_14727),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14725,U_14724)),hAPP(c_COMBC(U_14725,U_14727,U_14724),U_14729))),hAPP(hAPP(c_COMBB(tc_fun(U_14725,tc_HOL_Obool),tc_fun(U_14725,tc_HOL_Obool),U_14727),c_Set_OCollect(U_14725)),hAPP(hAPP(c_COMBB(tc_fun(U_14725,tc_HOL_Obool),tc_fun(U_14725,tc_HOL_Obool),U_14727),hAPP(c_COMBS(U_14725,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14725),c_fconj),hAPP(hAPP(c_COMBC(U_14725,tc_fun(U_14725,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14725)),U_14726)))),hAPP(c_COMBC(U_14725,U_14727,tc_HOL_Obool),U_14730))))),U_14728)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14727),U_14728))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14725),U_14726))
      | ~ class_Groups_Ocomm__monoid__add(U_14724) ),
    inference(variable_rename,[status(thm)],[f_3682_1]) ).

fof(f_3682_3,plain,
    ! [U_14724,U_14725,U_14726,U_14727,U_14728,U_14729,U_14730] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14725,U_14724),hAPP(hAPP(c_COMBS(U_14725,tc_fun(U_14727,tc_HOL_Obool),U_14724),hAPP(hAPP(c_COMBB(tc_fun(U_14727,U_14724),tc_fun(tc_fun(U_14727,tc_HOL_Obool),U_14724),U_14725),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14727,U_14724)),U_14729)),hAPP(hAPP(c_COMBB(tc_fun(U_14727,tc_HOL_Obool),tc_fun(U_14727,tc_HOL_Obool),U_14725),c_Set_OCollect(U_14727)),hAPP(hAPP(c_COMBB(tc_fun(U_14727,tc_HOL_Obool),tc_fun(U_14727,tc_HOL_Obool),U_14725),hAPP(c_COMBS(U_14727,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14727),c_fconj),hAPP(hAPP(c_COMBC(U_14727,tc_fun(U_14727,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14727)),U_14728)))),U_14730)))),U_14726) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14727,U_14724),hAPP(hAPP(c_COMBS(U_14727,tc_fun(U_14725,tc_HOL_Obool),U_14724),hAPP(hAPP(c_COMBB(tc_fun(U_14725,U_14724),tc_fun(tc_fun(U_14725,tc_HOL_Obool),U_14724),U_14727),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14725,U_14724)),hAPP(c_COMBC(U_14725,U_14727,U_14724),U_14729))),hAPP(hAPP(c_COMBB(tc_fun(U_14725,tc_HOL_Obool),tc_fun(U_14725,tc_HOL_Obool),U_14727),c_Set_OCollect(U_14725)),hAPP(hAPP(c_COMBB(tc_fun(U_14725,tc_HOL_Obool),tc_fun(U_14725,tc_HOL_Obool),U_14727),hAPP(c_COMBS(U_14725,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14725),c_fconj),hAPP(hAPP(c_COMBC(U_14725,tc_fun(U_14725,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14725)),U_14726)))),hAPP(c_COMBC(U_14725,U_14727,tc_HOL_Obool),U_14730))))),U_14728)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14727),U_14728))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14725),U_14726))
      | ~ class_Groups_Ocomm__monoid__add(U_14724) ),
    inference(definitional_conversion,[status(esa)],[f_3682_2]) ).

cnf(f_3682_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14725,U_14724),hAPP(hAPP(c_COMBS(U_14725,tc_fun(U_14727,tc_HOL_Obool),U_14724),hAPP(hAPP(c_COMBB(tc_fun(U_14727,U_14724),tc_fun(tc_fun(U_14727,tc_HOL_Obool),U_14724),U_14725),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14727,U_14724)),U_14729)),hAPP(hAPP(c_COMBB(tc_fun(U_14727,tc_HOL_Obool),tc_fun(U_14727,tc_HOL_Obool),U_14725),c_Set_OCollect(U_14727)),hAPP(hAPP(c_COMBB(tc_fun(U_14727,tc_HOL_Obool),tc_fun(U_14727,tc_HOL_Obool),U_14725),hAPP(c_COMBS(U_14727,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14727),c_fconj),hAPP(hAPP(c_COMBC(U_14727,tc_fun(U_14727,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14727)),U_14728)))),U_14730)))),U_14726) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14727,U_14724),hAPP(hAPP(c_COMBS(U_14727,tc_fun(U_14725,tc_HOL_Obool),U_14724),hAPP(hAPP(c_COMBB(tc_fun(U_14725,U_14724),tc_fun(tc_fun(U_14725,tc_HOL_Obool),U_14724),U_14727),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14725,U_14724)),hAPP(c_COMBC(U_14725,U_14727,U_14724),U_14729))),hAPP(hAPP(c_COMBB(tc_fun(U_14725,tc_HOL_Obool),tc_fun(U_14725,tc_HOL_Obool),U_14727),c_Set_OCollect(U_14725)),hAPP(hAPP(c_COMBB(tc_fun(U_14725,tc_HOL_Obool),tc_fun(U_14725,tc_HOL_Obool),U_14727),hAPP(c_COMBS(U_14725,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14725),c_fconj),hAPP(hAPP(c_COMBC(U_14725,tc_fun(U_14725,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14725)),U_14726)))),hAPP(c_COMBC(U_14725,U_14727,tc_HOL_Obool),U_14730))))),U_14728)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14727),U_14728))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14725),U_14726))
    | ~ class_Groups_Ocomm__monoid__add(U_14724) ),
    inference(clausify,[status(thm)],[f_3682_3]) ).

fof(f_3683_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_3683_2,plain,
    ! [U_14736,U_14735,U_14734,U_14733,U_14732,U_14731] : hAPP(c_Set_Oimage(U_14731,U_14732,hAPP(hAPP(c_COMBS(U_14731,U_14732,U_14732),hAPP(hAPP(c_COMBS(U_14731,U_14732,tc_fun(U_14732,U_14732)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14732,tc_fun(U_14732,U_14732)),U_14731),c_If(U_14732)),U_14733)),U_14734)),U_14735)),U_14736) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14732,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14731,U_14732,U_14734),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14731,tc_HOL_Obool)),U_14736),hAPP(c_Set_OCollect(U_14731),U_14733)))),hAPP(c_Set_Oimage(U_14731,U_14732,U_14735),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14731,tc_HOL_Obool)),U_14736),hAPP(c_Set_OCollect(U_14731),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14731),c_fNot),U_14733))))),
    inference(variable_rename,[status(thm)],[f_3683_1]) ).

fof(f_3683_3,plain,
    ! [U_14731,U_14732,U_14733,U_14734,U_14735,U_14736] : hAPP(c_Set_Oimage(U_14731,U_14732,hAPP(hAPP(c_COMBS(U_14731,U_14732,U_14732),hAPP(hAPP(c_COMBS(U_14731,U_14732,tc_fun(U_14732,U_14732)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14732,tc_fun(U_14732,U_14732)),U_14731),c_If(U_14732)),U_14733)),U_14734)),U_14735)),U_14736) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14732,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14731,U_14732,U_14734),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14731,tc_HOL_Obool)),U_14736),hAPP(c_Set_OCollect(U_14731),U_14733)))),hAPP(c_Set_Oimage(U_14731,U_14732,U_14735),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14731,tc_HOL_Obool)),U_14736),hAPP(c_Set_OCollect(U_14731),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14731),c_fNot),U_14733))))),
    inference(definitional_conversion,[status(esa)],[f_3683_2]) ).

cnf(f_3683_4,plain,
    hAPP(c_Set_Oimage(U_14731,U_14732,hAPP(hAPP(c_COMBS(U_14731,U_14732,U_14732),hAPP(hAPP(c_COMBS(U_14731,U_14732,tc_fun(U_14732,U_14732)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14732,tc_fun(U_14732,U_14732)),U_14731),c_If(U_14732)),U_14733)),U_14734)),U_14735)),U_14736) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14732,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14731,U_14732,U_14734),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14731,tc_HOL_Obool)),U_14736),hAPP(c_Set_OCollect(U_14731),U_14733)))),hAPP(c_Set_Oimage(U_14731,U_14732,U_14735),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14731,tc_HOL_Obool)),U_14736),hAPP(c_Set_OCollect(U_14731),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14731),c_fNot),U_14733))))),
    inference(clausify,[status(thm)],[f_3683_3]) ).

fof(f_3684_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_3684_2,plain,
    ! [U_14741,U_14740,U_14739,U_14738,U_14737] : c_Map_Odom(U_14737,U_14738,hAPP(hAPP(c_COMBS(U_14737,tc_Option_Ooption(U_14738),tc_Option_Ooption(U_14738)),hAPP(hAPP(c_COMBS(U_14737,tc_Option_Ooption(U_14738),tc_fun(tc_Option_Ooption(U_14738),tc_Option_Ooption(U_14738))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_14738),tc_fun(tc_Option_Ooption(U_14738),tc_Option_Ooption(U_14738))),U_14737),c_If(tc_Option_Ooption(U_14738))),U_14739)),U_14740)),U_14741)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14737,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14737,tc_HOL_Obool)),c_Map_Odom(U_14737,U_14738,U_14740)),hAPP(c_Set_OCollect(U_14737),U_14739))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14737,tc_HOL_Obool)),c_Map_Odom(U_14737,U_14738,U_14741)),hAPP(c_Set_OCollect(U_14737),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14737),c_fNot),U_14739)))),
    inference(variable_rename,[status(thm)],[f_3684_1]) ).

fof(f_3684_3,plain,
    ! [U_14737,U_14738,U_14739,U_14740,U_14741] : c_Map_Odom(U_14737,U_14738,hAPP(hAPP(c_COMBS(U_14737,tc_Option_Ooption(U_14738),tc_Option_Ooption(U_14738)),hAPP(hAPP(c_COMBS(U_14737,tc_Option_Ooption(U_14738),tc_fun(tc_Option_Ooption(U_14738),tc_Option_Ooption(U_14738))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_14738),tc_fun(tc_Option_Ooption(U_14738),tc_Option_Ooption(U_14738))),U_14737),c_If(tc_Option_Ooption(U_14738))),U_14739)),U_14740)),U_14741)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14737,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14737,tc_HOL_Obool)),c_Map_Odom(U_14737,U_14738,U_14740)),hAPP(c_Set_OCollect(U_14737),U_14739))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14737,tc_HOL_Obool)),c_Map_Odom(U_14737,U_14738,U_14741)),hAPP(c_Set_OCollect(U_14737),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14737),c_fNot),U_14739)))),
    inference(definitional_conversion,[status(esa)],[f_3684_2]) ).

cnf(f_3684_4,plain,
    c_Map_Odom(U_14737,U_14738,hAPP(hAPP(c_COMBS(U_14737,tc_Option_Ooption(U_14738),tc_Option_Ooption(U_14738)),hAPP(hAPP(c_COMBS(U_14737,tc_Option_Ooption(U_14738),tc_fun(tc_Option_Ooption(U_14738),tc_Option_Ooption(U_14738))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_14738),tc_fun(tc_Option_Ooption(U_14738),tc_Option_Ooption(U_14738))),U_14737),c_If(tc_Option_Ooption(U_14738))),U_14739)),U_14740)),U_14741)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14737,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14737,tc_HOL_Obool)),c_Map_Odom(U_14737,U_14738,U_14740)),hAPP(c_Set_OCollect(U_14737),U_14739))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14737,tc_HOL_Obool)),c_Map_Odom(U_14737,U_14738,U_14741)),hAPP(c_Set_OCollect(U_14737),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14737),c_fNot),U_14739)))),
    inference(clausify,[status(thm)],[f_3684_3]) ).

fof(f_3685_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_3685_2,plain,
    ! [U_14745,U_14744,U_14743,U_14742] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14743),U_14742))
      | U_14742 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_14743,U_14744),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_14745))) ),
    inference(variable_rename,[status(thm)],[f_3685_1]) ).

fof(f_3685_3,plain,
    ! [U_14742,U_14743,U_14744,U_14745] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14743),U_14742))
      | U_14742 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_14743,U_14744),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_14745))) ),
    inference(definitional_conversion,[status(esa)],[f_3685_2]) ).

cnf(f_3685_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14743),U_14742))
    | U_14742 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_14743,U_14744),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_14745))) ),
    inference(clausify,[status(thm)],[f_3685_3]) ).

fof(f_3686_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_3686_2,plain,
    ! [U_14750,U_14749,U_14748,U_14747,U_14746] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14747,U_14746),U_14749),hAPP(c_Set_OCollect(U_14747),hAPP(hAPP(c_COMBS(U_14747,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14747),c_fconj),hAPP(hAPP(c_COMBC(U_14747,tc_fun(U_14747,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14747)),U_14748))),hAPP(hAPP(c_COMBC(U_14747,tc_fun(U_14747,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14747)),U_14750)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14747,U_14746),hAPP(hAPP(c_COMBC(U_14747,U_14746,U_14746),hAPP(hAPP(c_COMBS(U_14747,U_14746,tc_fun(U_14746,U_14746)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14746,tc_fun(U_14746,U_14746)),U_14747),c_If(U_14746)),hAPP(hAPP(c_COMBC(U_14747,tc_fun(U_14747,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14747)),U_14750))),U_14749)),c_Groups_Ozero__class_Ozero(U_14746))),U_14748)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14747),U_14748))
      | ~ class_Groups_Ocomm__monoid__add(U_14746) ),
    inference(variable_rename,[status(thm)],[f_3686_1]) ).

fof(f_3686_3,plain,
    ! [U_14746,U_14747,U_14748,U_14749,U_14750] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14747,U_14746),U_14749),hAPP(c_Set_OCollect(U_14747),hAPP(hAPP(c_COMBS(U_14747,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14747),c_fconj),hAPP(hAPP(c_COMBC(U_14747,tc_fun(U_14747,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14747)),U_14748))),hAPP(hAPP(c_COMBC(U_14747,tc_fun(U_14747,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14747)),U_14750)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14747,U_14746),hAPP(hAPP(c_COMBC(U_14747,U_14746,U_14746),hAPP(hAPP(c_COMBS(U_14747,U_14746,tc_fun(U_14746,U_14746)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14746,tc_fun(U_14746,U_14746)),U_14747),c_If(U_14746)),hAPP(hAPP(c_COMBC(U_14747,tc_fun(U_14747,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14747)),U_14750))),U_14749)),c_Groups_Ozero__class_Ozero(U_14746))),U_14748)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14747),U_14748))
      | ~ class_Groups_Ocomm__monoid__add(U_14746) ),
    inference(definitional_conversion,[status(esa)],[f_3686_2]) ).

cnf(f_3686_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14747,U_14746),U_14749),hAPP(c_Set_OCollect(U_14747),hAPP(hAPP(c_COMBS(U_14747,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14747),c_fconj),hAPP(hAPP(c_COMBC(U_14747,tc_fun(U_14747,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14747)),U_14748))),hAPP(hAPP(c_COMBC(U_14747,tc_fun(U_14747,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14747)),U_14750)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14747,U_14746),hAPP(hAPP(c_COMBC(U_14747,U_14746,U_14746),hAPP(hAPP(c_COMBS(U_14747,U_14746,tc_fun(U_14746,U_14746)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14746,tc_fun(U_14746,U_14746)),U_14747),c_If(U_14746)),hAPP(hAPP(c_COMBC(U_14747,tc_fun(U_14747,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14747)),U_14750))),U_14749)),c_Groups_Ozero__class_Ozero(U_14746))),U_14748)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14747),U_14748))
    | ~ class_Groups_Ocomm__monoid__add(U_14746) ),
    inference(clausify,[status(thm)],[f_3686_3]) ).

fof(f_3687_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_3687_2,plain,
    ! [U_14756,U_14755,U_14754,U_14753,U_14752,U_14751] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14752,U_14751),U_14754),U_14753) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14755,U_14751),hAPP(hAPP(c_COMBB(tc_fun(U_14752,tc_HOL_Obool),U_14751,U_14755),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14752,U_14751),U_14754)),hAPP(hAPP(c_COMBB(tc_fun(U_14752,tc_HOL_Obool),tc_fun(U_14752,tc_HOL_Obool),U_14755),c_Set_OCollect(U_14752)),hAPP(hAPP(c_COMBB(tc_fun(U_14752,tc_HOL_Obool),tc_fun(U_14752,tc_HOL_Obool),U_14755),hAPP(c_COMBS(U_14752,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14752),c_fconj),hAPP(hAPP(c_COMBC(U_14752,tc_fun(U_14752,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14752)),U_14753)))),hAPP(c_COMBC(U_14752,U_14755,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14755,tc_fun(U_14755,tc_HOL_Obool),U_14752),c_fequal),U_14756)))))),hAPP(c_Set_Oimage(U_14752,U_14755,U_14756),U_14753))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14752),U_14753))
      | ~ class_Groups_Ocomm__monoid__add(U_14751) ),
    inference(variable_rename,[status(thm)],[f_3687_1]) ).

fof(f_3687_3,plain,
    ! [U_14751,U_14752,U_14753,U_14754,U_14755,U_14756] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14752,U_14751),U_14754),U_14753) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14755,U_14751),hAPP(hAPP(c_COMBB(tc_fun(U_14752,tc_HOL_Obool),U_14751,U_14755),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14752,U_14751),U_14754)),hAPP(hAPP(c_COMBB(tc_fun(U_14752,tc_HOL_Obool),tc_fun(U_14752,tc_HOL_Obool),U_14755),c_Set_OCollect(U_14752)),hAPP(hAPP(c_COMBB(tc_fun(U_14752,tc_HOL_Obool),tc_fun(U_14752,tc_HOL_Obool),U_14755),hAPP(c_COMBS(U_14752,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14752),c_fconj),hAPP(hAPP(c_COMBC(U_14752,tc_fun(U_14752,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14752)),U_14753)))),hAPP(c_COMBC(U_14752,U_14755,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14755,tc_fun(U_14755,tc_HOL_Obool),U_14752),c_fequal),U_14756)))))),hAPP(c_Set_Oimage(U_14752,U_14755,U_14756),U_14753))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14752),U_14753))
      | ~ class_Groups_Ocomm__monoid__add(U_14751) ),
    inference(definitional_conversion,[status(esa)],[f_3687_2]) ).

cnf(f_3687_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14752,U_14751),U_14754),U_14753) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14755,U_14751),hAPP(hAPP(c_COMBB(tc_fun(U_14752,tc_HOL_Obool),U_14751,U_14755),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14752,U_14751),U_14754)),hAPP(hAPP(c_COMBB(tc_fun(U_14752,tc_HOL_Obool),tc_fun(U_14752,tc_HOL_Obool),U_14755),c_Set_OCollect(U_14752)),hAPP(hAPP(c_COMBB(tc_fun(U_14752,tc_HOL_Obool),tc_fun(U_14752,tc_HOL_Obool),U_14755),hAPP(c_COMBS(U_14752,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14752),c_fconj),hAPP(hAPP(c_COMBC(U_14752,tc_fun(U_14752,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14752)),U_14753)))),hAPP(c_COMBC(U_14752,U_14755,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14755,tc_fun(U_14755,tc_HOL_Obool),U_14752),c_fequal),U_14756)))))),hAPP(c_Set_Oimage(U_14752,U_14755,U_14756),U_14753))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14752),U_14753))
    | ~ class_Groups_Ocomm__monoid__add(U_14751) ),
    inference(clausify,[status(thm)],[f_3687_3]) ).

fof(f_3688_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_3688_2,plain,
    ! [U_14760,U_14759,U_14758,U_14757] : hAPP(c_Relation_OImage(U_14757,U_14758,U_14759),hAPP(hAPP(c_Set_Oinsert(U_14757),U_14760),c_Orderings_Obot__class_Obot(tc_fun(U_14757,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_14758),hAPP(hAPP(c_COMBC(U_14758,tc_fun(tc_prod(U_14757,U_14758),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14757,U_14758),tc_fun(tc_fun(tc_prod(U_14757,U_14758),tc_HOL_Obool),tc_HOL_Obool),U_14758),c_member(tc_prod(U_14757,U_14758))),hAPP(c_Product__Type_OPair(U_14757,U_14758),U_14760))),U_14759)),
    inference(variable_rename,[status(thm)],[f_3688_1]) ).

fof(f_3688_3,plain,
    ! [U_14757,U_14758,U_14759,U_14760] : hAPP(c_Relation_OImage(U_14757,U_14758,U_14759),hAPP(hAPP(c_Set_Oinsert(U_14757),U_14760),c_Orderings_Obot__class_Obot(tc_fun(U_14757,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_14758),hAPP(hAPP(c_COMBC(U_14758,tc_fun(tc_prod(U_14757,U_14758),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14757,U_14758),tc_fun(tc_fun(tc_prod(U_14757,U_14758),tc_HOL_Obool),tc_HOL_Obool),U_14758),c_member(tc_prod(U_14757,U_14758))),hAPP(c_Product__Type_OPair(U_14757,U_14758),U_14760))),U_14759)),
    inference(definitional_conversion,[status(esa)],[f_3688_2]) ).

cnf(f_3688_4,plain,
    hAPP(c_Relation_OImage(U_14757,U_14758,U_14759),hAPP(hAPP(c_Set_Oinsert(U_14757),U_14760),c_Orderings_Obot__class_Obot(tc_fun(U_14757,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_14758),hAPP(hAPP(c_COMBC(U_14758,tc_fun(tc_prod(U_14757,U_14758),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14757,U_14758),tc_fun(tc_fun(tc_prod(U_14757,U_14758),tc_HOL_Obool),tc_HOL_Obool),U_14758),c_member(tc_prod(U_14757,U_14758))),hAPP(c_Product__Type_OPair(U_14757,U_14758),U_14760))),U_14759)),
    inference(clausify,[status(thm)],[f_3688_3]) ).

fof(f_3689_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_3689_2,plain,
    ! [U_14766,U_14765,U_14764,U_14763,U_14762,U_14761] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14762,U_14761),hAPP(hAPP(c_COMBS(U_14762,U_14761,U_14761),hAPP(hAPP(c_COMBS(U_14762,U_14761,tc_fun(U_14761,U_14761)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14761,tc_fun(U_14761,U_14761)),U_14762),c_If(U_14761)),U_14764)),U_14765)),U_14766)),U_14763) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_14761),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14762,U_14761),U_14765),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14762,tc_HOL_Obool)),U_14763),hAPP(c_Set_OCollect(U_14762),U_14764)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14762,U_14761),U_14766),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14762,tc_HOL_Obool)),U_14763),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14762,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14762),U_14764)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14762),U_14763))
      | ~ class_Groups_Ocomm__monoid__add(U_14761) ),
    inference(variable_rename,[status(thm)],[f_3689_1]) ).

fof(f_3689_3,plain,
    ! [U_14761,U_14762,U_14763,U_14764,U_14765,U_14766] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14762,U_14761),hAPP(hAPP(c_COMBS(U_14762,U_14761,U_14761),hAPP(hAPP(c_COMBS(U_14762,U_14761,tc_fun(U_14761,U_14761)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14761,tc_fun(U_14761,U_14761)),U_14762),c_If(U_14761)),U_14764)),U_14765)),U_14766)),U_14763) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_14761),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14762,U_14761),U_14765),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14762,tc_HOL_Obool)),U_14763),hAPP(c_Set_OCollect(U_14762),U_14764)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14762,U_14761),U_14766),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14762,tc_HOL_Obool)),U_14763),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14762,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14762),U_14764)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14762),U_14763))
      | ~ class_Groups_Ocomm__monoid__add(U_14761) ),
    inference(definitional_conversion,[status(esa)],[f_3689_2]) ).

cnf(f_3689_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14762,U_14761),hAPP(hAPP(c_COMBS(U_14762,U_14761,U_14761),hAPP(hAPP(c_COMBS(U_14762,U_14761,tc_fun(U_14761,U_14761)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14761,tc_fun(U_14761,U_14761)),U_14762),c_If(U_14761)),U_14764)),U_14765)),U_14766)),U_14763) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_14761),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14762,U_14761),U_14765),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14762,tc_HOL_Obool)),U_14763),hAPP(c_Set_OCollect(U_14762),U_14764)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14762,U_14761),U_14766),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14762,tc_HOL_Obool)),U_14763),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14762,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_14762),U_14764)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14762),U_14763))
    | ~ class_Groups_Ocomm__monoid__add(U_14761) ),
    inference(clausify,[status(thm)],[f_3689_3]) ).

fof(f_3690_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_3690_2,plain,
    ! [U_14768,U_14767] :
      ( 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_14767))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14768))))) = 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_14767))),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_14768)))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14767)) ),
    inference(variable_rename,[status(thm)],[f_3690_1]) ).

fof(f_3690_3,plain,
    ! [U_14767,U_14768] :
      ( 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_14767))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14768))))) = 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_14767))),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_14768)))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14767)) ),
    inference(definitional_conversion,[status(esa)],[f_3690_2]) ).

cnf(f_3690_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_14767))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_14768))))) = 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_14767))),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_14768)))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14767)) ),
    inference(clausify,[status(thm)],[f_3690_3]) ).

fof(f_3691_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_3691_2,plain,
    ! [U_14770,U_14769] :
      ( 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_14769))),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_14770))))) != 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_14769)) ),
    inference(variable_rename,[status(thm)],[f_3691_1]) ).

fof(f_3691_3,plain,
    ! [U_14769,U_14770] :
      ( 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_14769))),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_14770))))) != 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_14769)) ),
    inference(definitional_conversion,[status(esa)],[f_3691_2]) ).

cnf(f_3691_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_14769))),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_14770))))) != 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_14769)) ),
    inference(clausify,[status(thm)],[f_3691_3]) ).

fof(f_3692_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_3692_2,plain,
    ! [U_14775,U_14774,U_14773,U_14772,U_14771] : c_Map_Odom(U_14771,U_14772,c_Fun_Ooverride__on(U_14771,tc_Option_Ooption(U_14772),U_14773,U_14774,U_14775)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14771,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14771,tc_HOL_Obool)),c_Map_Odom(U_14771,U_14772,U_14773)),hAPP(c_Set_OCollect(U_14771),hAPP(hAPP(c_COMBC(U_14771,tc_fun(U_14771,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14771)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14771,tc_HOL_Obool)),U_14775),c_Map_Odom(U_14771,U_14772,U_14774)))))),hAPP(c_Set_OCollect(U_14771),hAPP(hAPP(c_COMBC(U_14771,tc_fun(U_14771,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14771)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14771,tc_HOL_Obool)),U_14775),c_Map_Odom(U_14771,U_14772,U_14774))))),
    inference(variable_rename,[status(thm)],[f_3692_1]) ).

fof(f_3692_3,plain,
    ! [U_14771,U_14772,U_14773,U_14774,U_14775] : c_Map_Odom(U_14771,U_14772,c_Fun_Ooverride__on(U_14771,tc_Option_Ooption(U_14772),U_14773,U_14774,U_14775)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14771,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14771,tc_HOL_Obool)),c_Map_Odom(U_14771,U_14772,U_14773)),hAPP(c_Set_OCollect(U_14771),hAPP(hAPP(c_COMBC(U_14771,tc_fun(U_14771,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14771)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14771,tc_HOL_Obool)),U_14775),c_Map_Odom(U_14771,U_14772,U_14774)))))),hAPP(c_Set_OCollect(U_14771),hAPP(hAPP(c_COMBC(U_14771,tc_fun(U_14771,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14771)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14771,tc_HOL_Obool)),U_14775),c_Map_Odom(U_14771,U_14772,U_14774))))),
    inference(definitional_conversion,[status(esa)],[f_3692_2]) ).

cnf(f_3692_4,plain,
    c_Map_Odom(U_14771,U_14772,c_Fun_Ooverride__on(U_14771,tc_Option_Ooption(U_14772),U_14773,U_14774,U_14775)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14771,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14771,tc_HOL_Obool)),c_Map_Odom(U_14771,U_14772,U_14773)),hAPP(c_Set_OCollect(U_14771),hAPP(hAPP(c_COMBC(U_14771,tc_fun(U_14771,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14771)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14771,tc_HOL_Obool)),U_14775),c_Map_Odom(U_14771,U_14772,U_14774)))))),hAPP(c_Set_OCollect(U_14771),hAPP(hAPP(c_COMBC(U_14771,tc_fun(U_14771,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14771)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14771,tc_HOL_Obool)),U_14775),c_Map_Odom(U_14771,U_14772,U_14774))))),
    inference(clausify,[status(thm)],[f_3692_3]) ).

fof(f_3693_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_3693_2,plain,
    ! [U_14782,U_14781,U_14780,U_14779,U_14778,U_14777] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14777,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14779,tc_HOL_Obool),tc_Nat_Onat,U_14777),c_Finite__Set_Ocard(U_14779)),hAPP(hAPP(c_COMBB(tc_fun(U_14779,tc_HOL_Obool),tc_fun(U_14779,tc_HOL_Obool),U_14777),c_Set_OCollect(U_14779)),hAPP(hAPP(c_COMBB(tc_fun(U_14779,tc_HOL_Obool),tc_fun(U_14779,tc_HOL_Obool),U_14777),hAPP(c_COMBS(U_14779,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14779),c_fconj),hAPP(hAPP(c_COMBC(U_14779,tc_fun(U_14779,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14779)),U_14780)))),U_14781)))),U_14778) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_14782),hAPP(c_Finite__Set_Ocard(U_14779),U_14780))
      | ? [U_14776] :
          ( hAPP(c_Finite__Set_Ocard(U_14777),hAPP(c_Set_OCollect(U_14777),hAPP(hAPP(c_COMBS(U_14777,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14777),c_fconj),hAPP(hAPP(c_COMBC(U_14777,tc_fun(U_14777,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14777)),U_14778))),hAPP(hAPP(c_COMBC(U_14777,U_14779,tc_HOL_Obool),U_14781),U_14776)))) != U_14782
          & hBOOL(hAPP(hAPP(c_member(U_14779),U_14776),U_14780)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14779),U_14780))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14777),U_14778)) ),
    inference(variable_rename,[status(thm)],[f_3693_1]) ).

fof(f_3693_3,plain,
    ! [U_14782,U_14781,U_14780,U_14779,U_14778,U_14777] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14777,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14779,tc_HOL_Obool),tc_Nat_Onat,U_14777),c_Finite__Set_Ocard(U_14779)),hAPP(hAPP(c_COMBB(tc_fun(U_14779,tc_HOL_Obool),tc_fun(U_14779,tc_HOL_Obool),U_14777),c_Set_OCollect(U_14779)),hAPP(hAPP(c_COMBB(tc_fun(U_14779,tc_HOL_Obool),tc_fun(U_14779,tc_HOL_Obool),U_14777),hAPP(c_COMBS(U_14779,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14779),c_fconj),hAPP(hAPP(c_COMBC(U_14779,tc_fun(U_14779,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14779)),U_14780)))),U_14781)))),U_14778) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_14782),hAPP(c_Finite__Set_Ocard(U_14779),U_14780))
      | ( hAPP(c_Finite__Set_Ocard(U_14777),hAPP(c_Set_OCollect(U_14777),hAPP(hAPP(c_COMBS(U_14777,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14777),c_fconj),hAPP(hAPP(c_COMBC(U_14777,tc_fun(U_14777,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14777)),U_14778))),hAPP(hAPP(c_COMBC(U_14777,U_14779,tc_HOL_Obool),U_14781),sK333(U_14782,U_14781,U_14780,U_14779,U_14778,U_14777))))) != U_14782
        & hBOOL(hAPP(hAPP(c_member(U_14779),sK333(U_14782,U_14781,U_14780,U_14779,U_14778,U_14777)),U_14780)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14779),U_14780))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14777),U_14778)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK333]),skolemize(U_14776,sK333(U_14782,U_14781,U_14780,U_14779,U_14778,U_14777))],[f_3693_2]) ).

fof(f_3693_4,plain,
    ( ! [U_14777,U_14778,U_14779,U_14780,U_14781,U_14782] :
        ( hAPP(c_Finite__Set_Ocard(U_14777),hAPP(c_Set_OCollect(U_14777),hAPP(hAPP(c_COMBS(U_14777,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14777),c_fconj),hAPP(hAPP(c_COMBC(U_14777,tc_fun(U_14777,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14777)),U_14778))),hAPP(hAPP(c_COMBC(U_14777,U_14779,tc_HOL_Obool),U_14781),sK333(U_14782,U_14781,U_14780,U_14779,U_14778,U_14777))))) != U_14782
        | ~ sP1010(U_14777,U_14778,U_14779,U_14780,U_14781,U_14782) )
    & ! [U_14777,U_14778,U_14779,U_14780,U_14781,U_14782] :
        ( hBOOL(hAPP(hAPP(c_member(U_14779),sK333(U_14782,U_14781,U_14780,U_14779,U_14778,U_14777)),U_14780))
        | ~ sP1010(U_14777,U_14778,U_14779,U_14780,U_14781,U_14782) )
    & ! [U_14777,U_14778,U_14779,U_14780,U_14781,U_14782] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14777,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14779,tc_HOL_Obool),tc_Nat_Onat,U_14777),c_Finite__Set_Ocard(U_14779)),hAPP(hAPP(c_COMBB(tc_fun(U_14779,tc_HOL_Obool),tc_fun(U_14779,tc_HOL_Obool),U_14777),c_Set_OCollect(U_14779)),hAPP(hAPP(c_COMBB(tc_fun(U_14779,tc_HOL_Obool),tc_fun(U_14779,tc_HOL_Obool),U_14777),hAPP(c_COMBS(U_14779,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14779),c_fconj),hAPP(hAPP(c_COMBC(U_14779,tc_fun(U_14779,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14779)),U_14780)))),U_14781)))),U_14778) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_14782),hAPP(c_Finite__Set_Ocard(U_14779),U_14780))
        | sP1010(U_14777,U_14778,U_14779,U_14780,U_14781,U_14782)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14779),U_14780))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14777),U_14778)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1010])],[f_3693_3]) ).

cnf(f_3693_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14777,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14779,tc_HOL_Obool),tc_Nat_Onat,U_14777),c_Finite__Set_Ocard(U_14779)),hAPP(hAPP(c_COMBB(tc_fun(U_14779,tc_HOL_Obool),tc_fun(U_14779,tc_HOL_Obool),U_14777),c_Set_OCollect(U_14779)),hAPP(hAPP(c_COMBB(tc_fun(U_14779,tc_HOL_Obool),tc_fun(U_14779,tc_HOL_Obool),U_14777),hAPP(c_COMBS(U_14779,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14779),c_fconj),hAPP(hAPP(c_COMBC(U_14779,tc_fun(U_14779,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14779)),U_14780)))),U_14781)))),U_14778) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_14782),hAPP(c_Finite__Set_Ocard(U_14779),U_14780))
    | sP1010(U_14777,U_14778,U_14779,U_14780,U_14781,U_14782)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14779),U_14780))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14777),U_14778)) ),
    inference(clausify,[status(thm)],[f_3693_4]) ).

cnf(f_3693_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14779),sK333(U_14782,U_14781,U_14780,U_14779,U_14778,U_14777)),U_14780))
    | ~ sP1010(U_14777,U_14778,U_14779,U_14780,U_14781,U_14782) ),
    inference(clausify,[status(thm)],[f_3693_4]) ).

cnf(f_3693_7,plain,
    ( hAPP(c_Finite__Set_Ocard(U_14777),hAPP(c_Set_OCollect(U_14777),hAPP(hAPP(c_COMBS(U_14777,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14777),c_fconj),hAPP(hAPP(c_COMBC(U_14777,tc_fun(U_14777,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14777)),U_14778))),hAPP(hAPP(c_COMBC(U_14777,U_14779,tc_HOL_Obool),U_14781),sK333(U_14782,U_14781,U_14780,U_14779,U_14778,U_14777))))) != U_14782
    | ~ sP1010(U_14777,U_14778,U_14779,U_14780,U_14781,U_14782) ),
    inference(clausify,[status(thm)],[f_3693_4]) ).

fof(f_3694_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_3694_2,plain,
    ! [U_14784,U_14783] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_14783,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_14783,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_14783,tc_HOL_Obool),tc_fun(U_14783,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_14783,tc_HOL_Obool))),U_14784))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14783),U_14784)) ),
    inference(variable_rename,[status(thm)],[f_3694_1]) ).

fof(f_3694_3,plain,
    ! [U_14783,U_14784] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_14783,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_14783,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_14783,tc_HOL_Obool),tc_fun(U_14783,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_14783,tc_HOL_Obool))),U_14784))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14783),U_14784)) ),
    inference(definitional_conversion,[status(esa)],[f_3694_2]) ).

cnf(f_3694_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_14783,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_14783,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_14783,tc_HOL_Obool),tc_fun(U_14783,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_14783,tc_HOL_Obool))),U_14784))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14783),U_14784)) ),
    inference(clausify,[status(thm)],[f_3694_3]) ).

fof(f_3695_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_3695_2,plain,
    ! [U_14786,U_14785] : hAPP(c_Set_OPow(U_14785),U_14786) = hAPP(c_Set_OCollect(tc_fun(U_14785,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_14785,tc_HOL_Obool),tc_fun(U_14785,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_14785,tc_HOL_Obool))),U_14786)),
    inference(variable_rename,[status(thm)],[f_3695_1]) ).

fof(f_3695_3,plain,
    ! [U_14785,U_14786] : hAPP(c_Set_OPow(U_14785),U_14786) = hAPP(c_Set_OCollect(tc_fun(U_14785,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_14785,tc_HOL_Obool),tc_fun(U_14785,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_14785,tc_HOL_Obool))),U_14786)),
    inference(definitional_conversion,[status(esa)],[f_3695_2]) ).

cnf(f_3695_4,plain,
    hAPP(c_Set_OPow(U_14785),U_14786) = hAPP(c_Set_OCollect(tc_fun(U_14785,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_14785,tc_HOL_Obool),tc_fun(U_14785,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_14785,tc_HOL_Obool))),U_14786)),
    inference(clausify,[status(thm)],[f_3695_3]) ).

fof(f_3696_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_3696_2,plain,
    ! [U_14792,U_14791,U_14790,U_14789,U_14788,U_14787] :
      ( hAPP(c_Fun_Ooverride__on(U_14787,U_14790,U_14791,U_14792,U_14789),U_14788) = hAPP(U_14791,U_14788)
      | hBOOL(hAPP(hAPP(c_member(U_14787),U_14788),U_14789)) ),
    inference(variable_rename,[status(thm)],[f_3696_1]) ).

fof(f_3696_3,plain,
    ! [U_14787,U_14788,U_14789,U_14790,U_14791,U_14792] :
      ( hAPP(c_Fun_Ooverride__on(U_14787,U_14790,U_14791,U_14792,U_14789),U_14788) = hAPP(U_14791,U_14788)
      | hBOOL(hAPP(hAPP(c_member(U_14787),U_14788),U_14789)) ),
    inference(definitional_conversion,[status(esa)],[f_3696_2]) ).

cnf(f_3696_4,plain,
    ( hAPP(c_Fun_Ooverride__on(U_14787,U_14790,U_14791,U_14792,U_14789),U_14788) = hAPP(U_14791,U_14788)
    | hBOOL(hAPP(hAPP(c_member(U_14787),U_14788),U_14789)) ),
    inference(clausify,[status(thm)],[f_3696_3]) ).

fof(f_3697_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_3697_2,plain,
    ! [U_14798,U_14797,U_14796,U_14795,U_14794,U_14793] :
      ( hAPP(c_Fun_Ooverride__on(U_14793,U_14796,U_14797,U_14798,U_14795),U_14794) = hAPP(U_14798,U_14794)
      | ~ hBOOL(hAPP(hAPP(c_member(U_14793),U_14794),U_14795)) ),
    inference(variable_rename,[status(thm)],[f_3697_1]) ).

fof(f_3697_3,plain,
    ! [U_14793,U_14794,U_14795,U_14796,U_14797,U_14798] :
      ( hAPP(c_Fun_Ooverride__on(U_14793,U_14796,U_14797,U_14798,U_14795),U_14794) = hAPP(U_14798,U_14794)
      | ~ hBOOL(hAPP(hAPP(c_member(U_14793),U_14794),U_14795)) ),
    inference(definitional_conversion,[status(esa)],[f_3697_2]) ).

cnf(f_3697_4,plain,
    ( hAPP(c_Fun_Ooverride__on(U_14793,U_14796,U_14797,U_14798,U_14795),U_14794) = hAPP(U_14798,U_14794)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14793),U_14794),U_14795)) ),
    inference(clausify,[status(thm)],[f_3697_3]) ).

fof(f_3698_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_3698_2,plain,
    ! [U_14802,U_14801,U_14800,U_14799] : c_Fun_Ooverride__on(U_14799,U_14800,U_14801,U_14802,c_Orderings_Obot__class_Obot(tc_fun(U_14799,tc_HOL_Obool))) = U_14801,
    inference(variable_rename,[status(thm)],[f_3698_1]) ).

fof(f_3698_3,plain,
    ! [U_14800,U_14799,U_14801,U_14802] : c_Fun_Ooverride__on(U_14799,U_14800,U_14801,U_14802,c_Orderings_Obot__class_Obot(tc_fun(U_14799,tc_HOL_Obool))) = U_14801,
    inference(definitional_conversion,[status(esa)],[f_3698_2]) ).

cnf(f_3698_4,plain,
    c_Fun_Ooverride__on(U_14799,U_14800,U_14801,U_14802,c_Orderings_Obot__class_Obot(tc_fun(U_14799,tc_HOL_Obool))) = U_14801,
    inference(clausify,[status(thm)],[f_3698_3]) ).

fof(f_3699_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_3699_2,plain,
    ! [U_14804,U_14803] : c_Fun_Oinj__on(tc_fun(U_14803,U_14804),tc_fun(tc_prod(U_14803,U_14804),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14803,U_14804),tc_HOL_Obool),tc_fun(tc_prod(U_14803,U_14804),tc_HOL_Obool),tc_fun(U_14803,U_14804)),c_Set_OCollect(tc_prod(U_14803,U_14804))),hAPP(hAPP(c_COMBB(tc_fun(U_14803,tc_fun(U_14804,tc_HOL_Obool)),tc_fun(tc_prod(U_14803,U_14804),tc_HOL_Obool),tc_fun(U_14803,U_14804)),c_Product__Type_Oprod_Oprod__case(U_14803,U_14804,tc_HOL_Obool)),hAPP(c_COMBB(U_14804,tc_fun(U_14804,tc_HOL_Obool),U_14803),hAPP(c_COMBC(U_14804,U_14804,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_14803,U_14804),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3699_1]) ).

fof(f_3699_3,plain,
    ! [U_14803,U_14804] : c_Fun_Oinj__on(tc_fun(U_14803,U_14804),tc_fun(tc_prod(U_14803,U_14804),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14803,U_14804),tc_HOL_Obool),tc_fun(tc_prod(U_14803,U_14804),tc_HOL_Obool),tc_fun(U_14803,U_14804)),c_Set_OCollect(tc_prod(U_14803,U_14804))),hAPP(hAPP(c_COMBB(tc_fun(U_14803,tc_fun(U_14804,tc_HOL_Obool)),tc_fun(tc_prod(U_14803,U_14804),tc_HOL_Obool),tc_fun(U_14803,U_14804)),c_Product__Type_Oprod_Oprod__case(U_14803,U_14804,tc_HOL_Obool)),hAPP(c_COMBB(U_14804,tc_fun(U_14804,tc_HOL_Obool),U_14803),hAPP(c_COMBC(U_14804,U_14804,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_14803,U_14804),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3699_2]) ).

cnf(f_3699_4,plain,
    c_Fun_Oinj__on(tc_fun(U_14803,U_14804),tc_fun(tc_prod(U_14803,U_14804),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14803,U_14804),tc_HOL_Obool),tc_fun(tc_prod(U_14803,U_14804),tc_HOL_Obool),tc_fun(U_14803,U_14804)),c_Set_OCollect(tc_prod(U_14803,U_14804))),hAPP(hAPP(c_COMBB(tc_fun(U_14803,tc_fun(U_14804,tc_HOL_Obool)),tc_fun(tc_prod(U_14803,U_14804),tc_HOL_Obool),tc_fun(U_14803,U_14804)),c_Product__Type_Oprod_Oprod__case(U_14803,U_14804,tc_HOL_Obool)),hAPP(c_COMBB(U_14804,tc_fun(U_14804,tc_HOL_Obool),U_14803),hAPP(c_COMBC(U_14804,U_14804,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_14803,U_14804),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3699_3]) ).

fof(f_3700_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_3700_2,plain,
    ! [U_14805] : 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_14805))),
    inference(variable_rename,[status(thm)],[f_3700_1]) ).

fof(f_3700_3,plain,
    ! [U_14805] : 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_14805))),
    inference(definitional_conversion,[status(esa)],[f_3700_2]) ).

cnf(f_3700_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_14805))),
    inference(clausify,[status(thm)],[f_3700_3]) ).

fof(f_3701_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_3701_2,plain,
    ! [U_14811,U_14810,U_14809,U_14808,U_14807,U_14806] :
      ( ( hAPP(c_Fun_Ooverride__on(U_14806,U_14809,U_14810,U_14811,U_14808),U_14807) = hAPP(U_14810,U_14807)
        | hBOOL(hAPP(hAPP(c_member(U_14806),U_14807),U_14808)) )
      & ( hAPP(c_Fun_Ooverride__on(U_14806,U_14809,U_14810,U_14811,U_14808),U_14807) = hAPP(U_14811,U_14807)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14806),U_14807),U_14808)) ) ),
    inference(variable_rename,[status(thm)],[f_3701_1]) ).

fof(f_3701_3,plain,
    ( ! [U_14823,U_14821,U_14819,U_14817,U_14815,U_14813] :
        ( hAPP(c_Fun_Ooverride__on(U_14813,U_14819,U_14821,U_14823,U_14817),U_14815) = hAPP(U_14821,U_14815)
        | hBOOL(hAPP(hAPP(c_member(U_14813),U_14815),U_14817)) )
    & ! [U_14822,U_14820,U_14818,U_14816,U_14814,U_14812] :
        ( hAPP(c_Fun_Ooverride__on(U_14812,U_14818,U_14820,U_14822,U_14816),U_14814) = hAPP(U_14822,U_14814)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14812),U_14814),U_14816)) ) ),
    inference(miniscope,[status(thm)],[f_3701_2]) ).

fof(f_3701_4,plain,
    ( ! [U_14813,U_14815,U_14817,U_14819,U_14821,U_14823] :
        ( hAPP(c_Fun_Ooverride__on(U_14813,U_14819,U_14821,U_14823,U_14817),U_14815) = hAPP(U_14821,U_14815)
        | hBOOL(hAPP(hAPP(c_member(U_14813),U_14815),U_14817)) )
    & ! [U_14818,U_14812,U_14814,U_14816,U_14820,U_14822] :
        ( hAPP(c_Fun_Ooverride__on(U_14812,U_14818,U_14820,U_14822,U_14816),U_14814) = hAPP(U_14822,U_14814)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14812),U_14814),U_14816)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3701_3]) ).

cnf(f_3701_5,plain,
    ( hAPP(c_Fun_Ooverride__on(U_14812,U_14818,U_14820,U_14822,U_14816),U_14814) = hAPP(U_14822,U_14814)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14812),U_14814),U_14816)) ),
    inference(clausify,[status(thm)],[f_3701_4]) ).

cnf(f_3701_6,plain,
    ( hAPP(c_Fun_Ooverride__on(U_14813,U_14819,U_14821,U_14823,U_14817),U_14815) = hAPP(U_14821,U_14815)
    | hBOOL(hAPP(hAPP(c_member(U_14813),U_14815),U_14817)) ),
    inference(clausify,[status(thm)],[f_3701_4]) ).

fof(f_3702_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_3702_2,plain,
    ! [U_14824] : c_Wellfounded_Ofinite__psubset(U_14824) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_14824,tc_HOL_Obool),tc_fun(U_14824,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_14824,tc_HOL_Obool),tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14824,tc_HOL_Obool),tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_14824,tc_HOL_Obool)),c_COMBS(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_14824,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_14824,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_14824,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_14824)))),
    inference(variable_rename,[status(thm)],[f_3702_1]) ).

fof(f_3702_3,plain,
    ! [U_14824] : c_Wellfounded_Ofinite__psubset(U_14824) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_14824,tc_HOL_Obool),tc_fun(U_14824,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_14824,tc_HOL_Obool),tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14824,tc_HOL_Obool),tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_14824,tc_HOL_Obool)),c_COMBS(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_14824,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_14824,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_14824,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_14824)))),
    inference(definitional_conversion,[status(esa)],[f_3702_2]) ).

cnf(f_3702_4,plain,
    c_Wellfounded_Ofinite__psubset(U_14824) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_14824,tc_HOL_Obool),tc_fun(U_14824,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_14824,tc_HOL_Obool),tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14824,tc_HOL_Obool),tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_14824,tc_HOL_Obool)),c_COMBS(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14824,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_14824,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_14824,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_14824,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_14824)))),
    inference(clausify,[status(thm)],[f_3702_3]) ).

fof(f_3703_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_3703_2,plain,
    ! [U_14828,U_14827,U_14826,U_14825] : hAPP(hAPP(c_Relation_Oinv__image(U_14825,U_14826),U_14827),U_14828) = hAPP(c_Set_OCollect(tc_prod(U_14826,U_14826)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14826,U_14826,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14826,tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_fun(U_14826,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14826,tc_fun(tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_fun(U_14826,tc_HOL_Obool)),U_14826),c_COMBC(U_14826,tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14826,tc_prod(U_14825,U_14825)),tc_fun(U_14826,tc_fun(tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_HOL_Obool)),U_14826),hAPP(c_COMBB(tc_prod(U_14825,U_14825),tc_fun(tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_HOL_Obool),U_14826),c_member(tc_prod(U_14825,U_14825)))),hAPP(hAPP(c_COMBC(U_14826,tc_fun(U_14826,U_14825),tc_fun(U_14826,tc_prod(U_14825,U_14825))),hAPP(hAPP(c_COMBB(tc_fun(U_14825,tc_prod(U_14825,U_14825)),tc_fun(tc_fun(U_14826,U_14825),tc_fun(U_14826,tc_prod(U_14825,U_14825))),U_14826),c_COMBB(U_14825,tc_prod(U_14825,U_14825),U_14826)),hAPP(hAPP(c_COMBB(U_14825,tc_fun(U_14825,tc_prod(U_14825,U_14825)),U_14826),c_Product__Type_OPair(U_14825,U_14825)),U_14828))),U_14828)))),U_14827))),
    inference(variable_rename,[status(thm)],[f_3703_1]) ).

fof(f_3703_3,plain,
    ! [U_14825,U_14826,U_14827,U_14828] : hAPP(hAPP(c_Relation_Oinv__image(U_14825,U_14826),U_14827),U_14828) = hAPP(c_Set_OCollect(tc_prod(U_14826,U_14826)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14826,U_14826,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14826,tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_fun(U_14826,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14826,tc_fun(tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_fun(U_14826,tc_HOL_Obool)),U_14826),c_COMBC(U_14826,tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14826,tc_prod(U_14825,U_14825)),tc_fun(U_14826,tc_fun(tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_HOL_Obool)),U_14826),hAPP(c_COMBB(tc_prod(U_14825,U_14825),tc_fun(tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_HOL_Obool),U_14826),c_member(tc_prod(U_14825,U_14825)))),hAPP(hAPP(c_COMBC(U_14826,tc_fun(U_14826,U_14825),tc_fun(U_14826,tc_prod(U_14825,U_14825))),hAPP(hAPP(c_COMBB(tc_fun(U_14825,tc_prod(U_14825,U_14825)),tc_fun(tc_fun(U_14826,U_14825),tc_fun(U_14826,tc_prod(U_14825,U_14825))),U_14826),c_COMBB(U_14825,tc_prod(U_14825,U_14825),U_14826)),hAPP(hAPP(c_COMBB(U_14825,tc_fun(U_14825,tc_prod(U_14825,U_14825)),U_14826),c_Product__Type_OPair(U_14825,U_14825)),U_14828))),U_14828)))),U_14827))),
    inference(definitional_conversion,[status(esa)],[f_3703_2]) ).

cnf(f_3703_4,plain,
    hAPP(hAPP(c_Relation_Oinv__image(U_14825,U_14826),U_14827),U_14828) = hAPP(c_Set_OCollect(tc_prod(U_14826,U_14826)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14826,U_14826,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14826,tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_fun(U_14826,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14826,tc_fun(tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_fun(U_14826,tc_HOL_Obool)),U_14826),c_COMBC(U_14826,tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14826,tc_prod(U_14825,U_14825)),tc_fun(U_14826,tc_fun(tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_HOL_Obool)),U_14826),hAPP(c_COMBB(tc_prod(U_14825,U_14825),tc_fun(tc_fun(tc_prod(U_14825,U_14825),tc_HOL_Obool),tc_HOL_Obool),U_14826),c_member(tc_prod(U_14825,U_14825)))),hAPP(hAPP(c_COMBC(U_14826,tc_fun(U_14826,U_14825),tc_fun(U_14826,tc_prod(U_14825,U_14825))),hAPP(hAPP(c_COMBB(tc_fun(U_14825,tc_prod(U_14825,U_14825)),tc_fun(tc_fun(U_14826,U_14825),tc_fun(U_14826,tc_prod(U_14825,U_14825))),U_14826),c_COMBB(U_14825,tc_prod(U_14825,U_14825),U_14826)),hAPP(hAPP(c_COMBB(U_14825,tc_fun(U_14825,tc_prod(U_14825,U_14825)),U_14826),c_Product__Type_OPair(U_14825,U_14825)),U_14828))),U_14828)))),U_14827))),
    inference(clausify,[status(thm)],[f_3703_3]) ).

fof(f_3704_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_3704_2,plain,
    ! [U_14829] : 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_14829)) = 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_14829),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3704_1]) ).

fof(f_3704_3,plain,
    ! [U_14829] : 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_14829)) = 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_14829),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_3704_2]) ).

cnf(f_3704_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_14829)) = 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_14829),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3704_3]) ).

fof(f_3705_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_3705_2,plain,
    ! [U_14830] : hAPP(c_Set_OCollect(tc_Nat_Onat),U_14830) = 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_14830),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_3705_1]) ).

fof(f_3705_3,plain,
    ! [U_14830] : hAPP(c_Set_OCollect(tc_Nat_Onat),U_14830) = 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_14830),c_Int_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_3705_2]) ).

cnf(f_3705_4,plain,
    hAPP(c_Set_OCollect(tc_Nat_Onat),U_14830) = 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_14830),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_3705_3]) ).

fof(f_3706_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_3706_2,plain,
    ! [U_14834,U_14833,U_14832,U_14831] : c_Nitpick_Oprod(U_14831,U_14832,U_14833,U_14834) = hAPP(c_Set_OCollect(tc_prod(U_14831,U_14832)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14831,U_14832,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14831,tc_fun(U_14832,tc_HOL_Obool),tc_fun(U_14832,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14832,tc_HOL_Obool),tc_fun(U_14832,tc_HOL_Obool)),U_14831),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14832)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14831),c_fconj),hAPP(hAPP(c_COMBC(U_14831,tc_fun(U_14831,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14831)),U_14833)))),hAPP(hAPP(c_COMBC(U_14832,tc_fun(U_14832,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14832)),U_14834)))),
    inference(variable_rename,[status(thm)],[f_3706_1]) ).

fof(f_3706_3,plain,
    ! [U_14831,U_14832,U_14833,U_14834] : c_Nitpick_Oprod(U_14831,U_14832,U_14833,U_14834) = hAPP(c_Set_OCollect(tc_prod(U_14831,U_14832)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14831,U_14832,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14831,tc_fun(U_14832,tc_HOL_Obool),tc_fun(U_14832,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14832,tc_HOL_Obool),tc_fun(U_14832,tc_HOL_Obool)),U_14831),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14832)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14831),c_fconj),hAPP(hAPP(c_COMBC(U_14831,tc_fun(U_14831,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14831)),U_14833)))),hAPP(hAPP(c_COMBC(U_14832,tc_fun(U_14832,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14832)),U_14834)))),
    inference(definitional_conversion,[status(esa)],[f_3706_2]) ).

cnf(f_3706_4,plain,
    c_Nitpick_Oprod(U_14831,U_14832,U_14833,U_14834) = hAPP(c_Set_OCollect(tc_prod(U_14831,U_14832)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14831,U_14832,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14831,tc_fun(U_14832,tc_HOL_Obool),tc_fun(U_14832,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14832,tc_HOL_Obool),tc_fun(U_14832,tc_HOL_Obool)),U_14831),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14832)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14831),c_fconj),hAPP(hAPP(c_COMBC(U_14831,tc_fun(U_14831,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14831)),U_14833)))),hAPP(hAPP(c_COMBC(U_14832,tc_fun(U_14832,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14832)),U_14834)))),
    inference(clausify,[status(thm)],[f_3706_3]) ).

fof(f_3707_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_3707_2,plain,
    ! [U_14835] : c_Int_Oint__ge__less__than2(U_14835) = 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_14835)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3707_1]) ).

fof(f_3707_3,plain,
    ! [U_14835] : c_Int_Oint__ge__less__than2(U_14835) = 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_14835)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_3707_2]) ).

cnf(f_3707_4,plain,
    c_Int_Oint__ge__less__than2(U_14835) = 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_14835)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3707_3]) ).

fof(f_3708_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_3708_2,plain,
    ! [U_14836] : c_Int_Oint__ge__less__than(U_14836) = 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_14836)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3708_1]) ).

fof(f_3708_3,plain,
    ! [U_14836] : c_Int_Oint__ge__less__than(U_14836) = 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_14836)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_3708_2]) ).

cnf(f_3708_4,plain,
    c_Int_Oint__ge__less__than(U_14836) = 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_14836)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3708_3]) ).

fof(f_3709_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_3709_2,plain,
    ! [U_14838,U_14837] :
      ( ( c_Predicate_Oreflp(U_14837,U_14838)
        | ~ c_Relation_Orefl__on(U_14837,c_Orderings_Otop__class_Otop(tc_fun(U_14837,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14837,U_14837)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14837,U_14837,tc_HOL_Obool),U_14838))) )
      & ( c_Relation_Orefl__on(U_14837,c_Orderings_Otop__class_Otop(tc_fun(U_14837,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14837,U_14837)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14837,U_14837,tc_HOL_Obool),U_14838)))
        | ~ c_Predicate_Oreflp(U_14837,U_14838) ) ),
    inference(variable_rename,[status(thm)],[f_3709_1]) ).

fof(f_3709_3,plain,
    ( ! [U_14842,U_14840] :
        ( c_Predicate_Oreflp(U_14840,U_14842)
        | ~ c_Relation_Orefl__on(U_14840,c_Orderings_Otop__class_Otop(tc_fun(U_14840,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14840,U_14840)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14840,U_14840,tc_HOL_Obool),U_14842))) )
    & ! [U_14841,U_14839] :
        ( c_Relation_Orefl__on(U_14839,c_Orderings_Otop__class_Otop(tc_fun(U_14839,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14839,U_14839)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14839,U_14839,tc_HOL_Obool),U_14841)))
        | ~ c_Predicate_Oreflp(U_14839,U_14841) ) ),
    inference(miniscope,[status(thm)],[f_3709_2]) ).

fof(f_3709_4,plain,
    ( ! [U_14840,U_14842] :
        ( c_Predicate_Oreflp(U_14840,U_14842)
        | ~ c_Relation_Orefl__on(U_14840,c_Orderings_Otop__class_Otop(tc_fun(U_14840,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14840,U_14840)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14840,U_14840,tc_HOL_Obool),U_14842))) )
    & ! [U_14841,U_14839] :
        ( c_Relation_Orefl__on(U_14839,c_Orderings_Otop__class_Otop(tc_fun(U_14839,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14839,U_14839)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14839,U_14839,tc_HOL_Obool),U_14841)))
        | ~ c_Predicate_Oreflp(U_14839,U_14841) ) ),
    inference(definitional_conversion,[status(esa)],[f_3709_3]) ).

cnf(f_3709_5,plain,
    ( c_Relation_Orefl__on(U_14839,c_Orderings_Otop__class_Otop(tc_fun(U_14839,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14839,U_14839)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14839,U_14839,tc_HOL_Obool),U_14841)))
    | ~ c_Predicate_Oreflp(U_14839,U_14841) ),
    inference(clausify,[status(thm)],[f_3709_4]) ).

cnf(f_3709_6,plain,
    ( c_Predicate_Oreflp(U_14840,U_14842)
    | ~ c_Relation_Orefl__on(U_14840,c_Orderings_Otop__class_Otop(tc_fun(U_14840,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_14840,U_14840)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14840,U_14840,tc_HOL_Obool),U_14842))) ),
    inference(clausify,[status(thm)],[f_3709_4]) ).

fof(f_3710_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_3710_2,plain,
    ! [U_14845,U_14844,U_14843] :
      ( hBOOL(hAPP(hAPP(U_14844,U_14845),U_14845))
      | ~ c_Predicate_Oreflp(U_14843,U_14844) ),
    inference(variable_rename,[status(thm)],[f_3710_1]) ).

fof(f_3710_3,plain,
    ! [U_14845,U_14844] :
      ( ! [U_14843] : ~ c_Predicate_Oreflp(U_14843,U_14844)
      | hBOOL(hAPP(hAPP(U_14844,U_14845),U_14845)) ),
    inference(miniscope,[status(thm)],[f_3710_2]) ).

fof(f_3710_4,plain,
    ! [U_14845,U_14843,U_14844] :
      ( ~ c_Predicate_Oreflp(U_14843,U_14844)
      | hBOOL(hAPP(hAPP(U_14844,U_14845),U_14845)) ),
    inference(definitional_conversion,[status(esa)],[f_3710_3]) ).

cnf(f_3710_5,plain,
    ( ~ c_Predicate_Oreflp(U_14843,U_14844)
    | hBOOL(hAPP(hAPP(U_14844,U_14845),U_14845)) ),
    inference(clausify,[status(thm)],[f_3710_4]) ).

fof(f_3711_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_3711_2,plain,
    ! [U_14848,U_14847,U_14846] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_14846),c_Big__Operators_Olattice_OSup__fin(U_14846,c_Orderings_Oord__class_Omax(U_14846),U_14847)),c_Big__Operators_Olattice_OSup__fin(U_14846,c_Orderings_Oord__class_Omax(U_14846),U_14848)) = c_Big__Operators_Olattice_OSup__fin(U_14846,c_Orderings_Oord__class_Omax(U_14846),hAPP(c_Set_OCollect(U_14846),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_HOL_Obool),tc_HOL_Obool,U_14846),c_HOL_OEx(U_14846)),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool)),tc_fun(U_14846,tc_HOL_Obool),U_14846),hAPP(c_COMBB(tc_fun(U_14846,tc_HOL_Obool),tc_HOL_Obool,U_14846),c_HOL_OEx(U_14846))),hAPP(hAPP(c_COMBC(U_14846,tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool)),tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_fun(tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool))),tc_fun(tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool)),tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool))),U_14846),c_COMBS(U_14846,tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_fun(U_14846,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14846,tc_fun(tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool))),U_14846),hAPP(c_COMBB(tc_fun(U_14846,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool)),U_14846),c_COMBS(U_14846,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool)),tc_fun(U_14846,tc_fun(U_14846,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14846),hAPP(c_COMBB(tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14846),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14846),c_fconj))),hAPP(hAPP(c_COMBC(U_14846,tc_fun(U_14846,tc_fun(U_14846,U_14846)),tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14846,U_14846),tc_fun(U_14846,tc_HOL_Obool)),tc_fun(tc_fun(U_14846,tc_fun(U_14846,U_14846)),tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool))),U_14846),c_COMBB(tc_fun(U_14846,U_14846),tc_fun(U_14846,tc_HOL_Obool),U_14846)),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_HOL_Obool),tc_fun(tc_fun(U_14846,U_14846),tc_fun(U_14846,tc_HOL_Obool)),U_14846),c_COMBB(U_14846,tc_HOL_Obool,U_14846)),c_fequal))),c_Orderings_Oord__class_Omin(U_14846)))))),hAPP(hAPP(c_COMBC(U_14846,tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool)),U_14846),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14846)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14846),c_fconj),hAPP(hAPP(c_COMBC(U_14846,tc_fun(U_14846,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14846)),U_14847)))),hAPP(hAPP(c_COMBC(U_14846,tc_fun(U_14846,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14846)),U_14848)))))))
      | U_14848 = c_Orderings_Obot__class_Obot(tc_fun(U_14846,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14846),U_14848))
      | U_14847 = c_Orderings_Obot__class_Obot(tc_fun(U_14846,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14846),U_14847))
      | ~ class_Orderings_Olinorder(U_14846) ),
    inference(variable_rename,[status(thm)],[f_3711_1]) ).

fof(f_3711_3,plain,
    ! [U_14846,U_14847,U_14848] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_14846),c_Big__Operators_Olattice_OSup__fin(U_14846,c_Orderings_Oord__class_Omax(U_14846),U_14847)),c_Big__Operators_Olattice_OSup__fin(U_14846,c_Orderings_Oord__class_Omax(U_14846),U_14848)) = c_Big__Operators_Olattice_OSup__fin(U_14846,c_Orderings_Oord__class_Omax(U_14846),hAPP(c_Set_OCollect(U_14846),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_HOL_Obool),tc_HOL_Obool,U_14846),c_HOL_OEx(U_14846)),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool)),tc_fun(U_14846,tc_HOL_Obool),U_14846),hAPP(c_COMBB(tc_fun(U_14846,tc_HOL_Obool),tc_HOL_Obool,U_14846),c_HOL_OEx(U_14846))),hAPP(hAPP(c_COMBC(U_14846,tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool)),tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_fun(tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool))),tc_fun(tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool)),tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool))),U_14846),c_COMBS(U_14846,tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_fun(U_14846,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14846,tc_fun(tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool))),U_14846),hAPP(c_COMBB(tc_fun(U_14846,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool)),U_14846),c_COMBS(U_14846,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool)),tc_fun(U_14846,tc_fun(U_14846,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14846),hAPP(c_COMBB(tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14846),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14846),c_fconj))),hAPP(hAPP(c_COMBC(U_14846,tc_fun(U_14846,tc_fun(U_14846,U_14846)),tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14846,U_14846),tc_fun(U_14846,tc_HOL_Obool)),tc_fun(tc_fun(U_14846,tc_fun(U_14846,U_14846)),tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool))),U_14846),c_COMBB(tc_fun(U_14846,U_14846),tc_fun(U_14846,tc_HOL_Obool),U_14846)),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_HOL_Obool),tc_fun(tc_fun(U_14846,U_14846),tc_fun(U_14846,tc_HOL_Obool)),U_14846),c_COMBB(U_14846,tc_HOL_Obool,U_14846)),c_fequal))),c_Orderings_Oord__class_Omin(U_14846)))))),hAPP(hAPP(c_COMBC(U_14846,tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool)),U_14846),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14846)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14846),c_fconj),hAPP(hAPP(c_COMBC(U_14846,tc_fun(U_14846,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14846)),U_14847)))),hAPP(hAPP(c_COMBC(U_14846,tc_fun(U_14846,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14846)),U_14848)))))))
      | U_14848 = c_Orderings_Obot__class_Obot(tc_fun(U_14846,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14846),U_14848))
      | U_14847 = c_Orderings_Obot__class_Obot(tc_fun(U_14846,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14846),U_14847))
      | ~ class_Orderings_Olinorder(U_14846) ),
    inference(definitional_conversion,[status(esa)],[f_3711_2]) ).

cnf(f_3711_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_14846),c_Big__Operators_Olattice_OSup__fin(U_14846,c_Orderings_Oord__class_Omax(U_14846),U_14847)),c_Big__Operators_Olattice_OSup__fin(U_14846,c_Orderings_Oord__class_Omax(U_14846),U_14848)) = c_Big__Operators_Olattice_OSup__fin(U_14846,c_Orderings_Oord__class_Omax(U_14846),hAPP(c_Set_OCollect(U_14846),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_HOL_Obool),tc_HOL_Obool,U_14846),c_HOL_OEx(U_14846)),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool)),tc_fun(U_14846,tc_HOL_Obool),U_14846),hAPP(c_COMBB(tc_fun(U_14846,tc_HOL_Obool),tc_HOL_Obool,U_14846),c_HOL_OEx(U_14846))),hAPP(hAPP(c_COMBC(U_14846,tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool)),tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_fun(tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool))),tc_fun(tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool)),tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool))),U_14846),c_COMBS(U_14846,tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_fun(U_14846,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14846,tc_fun(tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool))),U_14846),hAPP(c_COMBB(tc_fun(U_14846,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool)),U_14846),c_COMBS(U_14846,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool)),tc_fun(U_14846,tc_fun(U_14846,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14846),hAPP(c_COMBB(tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14846),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14846),c_fconj))),hAPP(hAPP(c_COMBC(U_14846,tc_fun(U_14846,tc_fun(U_14846,U_14846)),tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14846,U_14846),tc_fun(U_14846,tc_HOL_Obool)),tc_fun(tc_fun(U_14846,tc_fun(U_14846,U_14846)),tc_fun(U_14846,tc_fun(U_14846,tc_HOL_Obool))),U_14846),c_COMBB(tc_fun(U_14846,U_14846),tc_fun(U_14846,tc_HOL_Obool),U_14846)),hAPP(hAPP(c_COMBB(tc_fun(U_14846,tc_HOL_Obool),tc_fun(tc_fun(U_14846,U_14846),tc_fun(U_14846,tc_HOL_Obool)),U_14846),c_COMBB(U_14846,tc_HOL_Obool,U_14846)),c_fequal))),c_Orderings_Oord__class_Omin(U_14846)))))),hAPP(hAPP(c_COMBC(U_14846,tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14846,tc_HOL_Obool),tc_fun(U_14846,tc_HOL_Obool)),U_14846),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14846)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14846),c_fconj),hAPP(hAPP(c_COMBC(U_14846,tc_fun(U_14846,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14846)),U_14847)))),hAPP(hAPP(c_COMBC(U_14846,tc_fun(U_14846,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14846)),U_14848)))))))
    | U_14848 = c_Orderings_Obot__class_Obot(tc_fun(U_14846,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14846),U_14848))
    | U_14847 = c_Orderings_Obot__class_Obot(tc_fun(U_14846,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14846),U_14847))
    | ~ class_Orderings_Olinorder(U_14846) ),
    inference(clausify,[status(thm)],[f_3711_3]) ).

fof(f_3712_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_3712_2,plain,
    ! [U_14851,U_14850,U_14849] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14849),c_Big__Operators_Olattice_OInf__fin(U_14849,c_Orderings_Oord__class_Omin(U_14849),U_14850)),c_Big__Operators_Olattice_OInf__fin(U_14849,c_Orderings_Oord__class_Omin(U_14849),U_14851)) = c_Big__Operators_Olattice_OInf__fin(U_14849,c_Orderings_Oord__class_Omin(U_14849),hAPP(c_Set_OCollect(U_14849),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_HOL_Obool),tc_HOL_Obool,U_14849),c_HOL_OEx(U_14849)),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool)),tc_fun(U_14849,tc_HOL_Obool),U_14849),hAPP(c_COMBB(tc_fun(U_14849,tc_HOL_Obool),tc_HOL_Obool,U_14849),c_HOL_OEx(U_14849))),hAPP(hAPP(c_COMBC(U_14849,tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool)),tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_fun(tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool))),tc_fun(tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool)),tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool))),U_14849),c_COMBS(U_14849,tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_fun(U_14849,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14849,tc_fun(tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool))),U_14849),hAPP(c_COMBB(tc_fun(U_14849,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool)),U_14849),c_COMBS(U_14849,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool)),tc_fun(U_14849,tc_fun(U_14849,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14849),hAPP(c_COMBB(tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14849),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14849),c_fconj))),hAPP(hAPP(c_COMBC(U_14849,tc_fun(U_14849,tc_fun(U_14849,U_14849)),tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14849,U_14849),tc_fun(U_14849,tc_HOL_Obool)),tc_fun(tc_fun(U_14849,tc_fun(U_14849,U_14849)),tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool))),U_14849),c_COMBB(tc_fun(U_14849,U_14849),tc_fun(U_14849,tc_HOL_Obool),U_14849)),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_HOL_Obool),tc_fun(tc_fun(U_14849,U_14849),tc_fun(U_14849,tc_HOL_Obool)),U_14849),c_COMBB(U_14849,tc_HOL_Obool,U_14849)),c_fequal))),c_Orderings_Oord__class_Omax(U_14849)))))),hAPP(hAPP(c_COMBC(U_14849,tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool)),U_14849),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14849)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14849),c_fconj),hAPP(hAPP(c_COMBC(U_14849,tc_fun(U_14849,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14849)),U_14850)))),hAPP(hAPP(c_COMBC(U_14849,tc_fun(U_14849,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14849)),U_14851)))))))
      | U_14851 = c_Orderings_Obot__class_Obot(tc_fun(U_14849,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14849),U_14851))
      | U_14850 = c_Orderings_Obot__class_Obot(tc_fun(U_14849,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14849),U_14850))
      | ~ class_Orderings_Olinorder(U_14849) ),
    inference(variable_rename,[status(thm)],[f_3712_1]) ).

fof(f_3712_3,plain,
    ! [U_14849,U_14850,U_14851] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14849),c_Big__Operators_Olattice_OInf__fin(U_14849,c_Orderings_Oord__class_Omin(U_14849),U_14850)),c_Big__Operators_Olattice_OInf__fin(U_14849,c_Orderings_Oord__class_Omin(U_14849),U_14851)) = c_Big__Operators_Olattice_OInf__fin(U_14849,c_Orderings_Oord__class_Omin(U_14849),hAPP(c_Set_OCollect(U_14849),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_HOL_Obool),tc_HOL_Obool,U_14849),c_HOL_OEx(U_14849)),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool)),tc_fun(U_14849,tc_HOL_Obool),U_14849),hAPP(c_COMBB(tc_fun(U_14849,tc_HOL_Obool),tc_HOL_Obool,U_14849),c_HOL_OEx(U_14849))),hAPP(hAPP(c_COMBC(U_14849,tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool)),tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_fun(tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool))),tc_fun(tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool)),tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool))),U_14849),c_COMBS(U_14849,tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_fun(U_14849,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14849,tc_fun(tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool))),U_14849),hAPP(c_COMBB(tc_fun(U_14849,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool)),U_14849),c_COMBS(U_14849,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool)),tc_fun(U_14849,tc_fun(U_14849,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14849),hAPP(c_COMBB(tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14849),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14849),c_fconj))),hAPP(hAPP(c_COMBC(U_14849,tc_fun(U_14849,tc_fun(U_14849,U_14849)),tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14849,U_14849),tc_fun(U_14849,tc_HOL_Obool)),tc_fun(tc_fun(U_14849,tc_fun(U_14849,U_14849)),tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool))),U_14849),c_COMBB(tc_fun(U_14849,U_14849),tc_fun(U_14849,tc_HOL_Obool),U_14849)),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_HOL_Obool),tc_fun(tc_fun(U_14849,U_14849),tc_fun(U_14849,tc_HOL_Obool)),U_14849),c_COMBB(U_14849,tc_HOL_Obool,U_14849)),c_fequal))),c_Orderings_Oord__class_Omax(U_14849)))))),hAPP(hAPP(c_COMBC(U_14849,tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool)),U_14849),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14849)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14849),c_fconj),hAPP(hAPP(c_COMBC(U_14849,tc_fun(U_14849,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14849)),U_14850)))),hAPP(hAPP(c_COMBC(U_14849,tc_fun(U_14849,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14849)),U_14851)))))))
      | U_14851 = c_Orderings_Obot__class_Obot(tc_fun(U_14849,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14849),U_14851))
      | U_14850 = c_Orderings_Obot__class_Obot(tc_fun(U_14849,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14849),U_14850))
      | ~ class_Orderings_Olinorder(U_14849) ),
    inference(definitional_conversion,[status(esa)],[f_3712_2]) ).

cnf(f_3712_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14849),c_Big__Operators_Olattice_OInf__fin(U_14849,c_Orderings_Oord__class_Omin(U_14849),U_14850)),c_Big__Operators_Olattice_OInf__fin(U_14849,c_Orderings_Oord__class_Omin(U_14849),U_14851)) = c_Big__Operators_Olattice_OInf__fin(U_14849,c_Orderings_Oord__class_Omin(U_14849),hAPP(c_Set_OCollect(U_14849),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_HOL_Obool),tc_HOL_Obool,U_14849),c_HOL_OEx(U_14849)),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool)),tc_fun(U_14849,tc_HOL_Obool),U_14849),hAPP(c_COMBB(tc_fun(U_14849,tc_HOL_Obool),tc_HOL_Obool,U_14849),c_HOL_OEx(U_14849))),hAPP(hAPP(c_COMBC(U_14849,tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool)),tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_fun(tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool))),tc_fun(tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool)),tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool))),U_14849),c_COMBS(U_14849,tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_fun(U_14849,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14849,tc_fun(tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool))),U_14849),hAPP(c_COMBB(tc_fun(U_14849,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool)),U_14849),c_COMBS(U_14849,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool)),tc_fun(U_14849,tc_fun(U_14849,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14849),hAPP(c_COMBB(tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14849),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14849),c_fconj))),hAPP(hAPP(c_COMBC(U_14849,tc_fun(U_14849,tc_fun(U_14849,U_14849)),tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14849,U_14849),tc_fun(U_14849,tc_HOL_Obool)),tc_fun(tc_fun(U_14849,tc_fun(U_14849,U_14849)),tc_fun(U_14849,tc_fun(U_14849,tc_HOL_Obool))),U_14849),c_COMBB(tc_fun(U_14849,U_14849),tc_fun(U_14849,tc_HOL_Obool),U_14849)),hAPP(hAPP(c_COMBB(tc_fun(U_14849,tc_HOL_Obool),tc_fun(tc_fun(U_14849,U_14849),tc_fun(U_14849,tc_HOL_Obool)),U_14849),c_COMBB(U_14849,tc_HOL_Obool,U_14849)),c_fequal))),c_Orderings_Oord__class_Omax(U_14849)))))),hAPP(hAPP(c_COMBC(U_14849,tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14849,tc_HOL_Obool),tc_fun(U_14849,tc_HOL_Obool)),U_14849),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14849)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14849),c_fconj),hAPP(hAPP(c_COMBC(U_14849,tc_fun(U_14849,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14849)),U_14850)))),hAPP(hAPP(c_COMBC(U_14849,tc_fun(U_14849,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14849)),U_14851)))))))
    | U_14851 = c_Orderings_Obot__class_Obot(tc_fun(U_14849,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14849),U_14851))
    | U_14850 = c_Orderings_Obot__class_Obot(tc_fun(U_14849,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14849),U_14850))
    | ~ class_Orderings_Olinorder(U_14849) ),
    inference(clausify,[status(thm)],[f_3712_3]) ).

fof(f_3713_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_3713_2,plain,
    ! [U_14855,U_14854,U_14853,U_14852] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14854),hAPP(c_Set_OCollect(U_14854),hAPP(hAPP(c_COMBB(tc_fun(U_14852,tc_HOL_Obool),tc_HOL_Obool,U_14854),c_HOL_OEx(U_14852)),hAPP(hAPP(c_COMBC(U_14854,tc_fun(U_14852,tc_HOL_Obool),tc_fun(U_14852,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14852,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14852,tc_HOL_Obool),tc_fun(U_14852,tc_HOL_Obool)),U_14854),c_COMBS(U_14852,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14852,tc_HOL_Obool),tc_fun(U_14852,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14854),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14852),c_fconj)),hAPP(hAPP(c_COMBC(U_14854,tc_fun(U_14852,U_14854),tc_fun(U_14852,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14854,tc_HOL_Obool),tc_fun(tc_fun(U_14852,U_14854),tc_fun(U_14852,tc_HOL_Obool)),U_14854),c_COMBB(U_14854,tc_HOL_Obool,U_14852)),c_fequal)),U_14855)))),U_14853)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14852),hAPP(c_Set_OCollect(U_14852),U_14853))) ),
    inference(variable_rename,[status(thm)],[f_3713_1]) ).

fof(f_3713_3,plain,
    ! [U_14854,U_14853,U_14852,U_14855] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14854),hAPP(c_Set_OCollect(U_14854),hAPP(hAPP(c_COMBB(tc_fun(U_14852,tc_HOL_Obool),tc_HOL_Obool,U_14854),c_HOL_OEx(U_14852)),hAPP(hAPP(c_COMBC(U_14854,tc_fun(U_14852,tc_HOL_Obool),tc_fun(U_14852,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14852,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14852,tc_HOL_Obool),tc_fun(U_14852,tc_HOL_Obool)),U_14854),c_COMBS(U_14852,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14852,tc_HOL_Obool),tc_fun(U_14852,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14854),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14852),c_fconj)),hAPP(hAPP(c_COMBC(U_14854,tc_fun(U_14852,U_14854),tc_fun(U_14852,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14854,tc_HOL_Obool),tc_fun(tc_fun(U_14852,U_14854),tc_fun(U_14852,tc_HOL_Obool)),U_14854),c_COMBB(U_14854,tc_HOL_Obool,U_14852)),c_fequal)),U_14855)))),U_14853)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14852),hAPP(c_Set_OCollect(U_14852),U_14853))) ),
    inference(definitional_conversion,[status(esa)],[f_3713_2]) ).

cnf(f_3713_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14854),hAPP(c_Set_OCollect(U_14854),hAPP(hAPP(c_COMBB(tc_fun(U_14852,tc_HOL_Obool),tc_HOL_Obool,U_14854),c_HOL_OEx(U_14852)),hAPP(hAPP(c_COMBC(U_14854,tc_fun(U_14852,tc_HOL_Obool),tc_fun(U_14852,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14852,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14852,tc_HOL_Obool),tc_fun(U_14852,tc_HOL_Obool)),U_14854),c_COMBS(U_14852,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14852,tc_HOL_Obool),tc_fun(U_14852,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14854),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14852),c_fconj)),hAPP(hAPP(c_COMBC(U_14854,tc_fun(U_14852,U_14854),tc_fun(U_14852,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14854,tc_HOL_Obool),tc_fun(tc_fun(U_14852,U_14854),tc_fun(U_14852,tc_HOL_Obool)),U_14854),c_COMBB(U_14854,tc_HOL_Obool,U_14852)),c_fequal)),U_14855)))),U_14853)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14852),hAPP(c_Set_OCollect(U_14852),U_14853))) ),
    inference(clausify,[status(thm)],[f_3713_3]) ).

fof(f_3714_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_3714_2,plain,
    ! [U_14861,U_14860,U_14859,U_14858] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_HOL_Obool,U_14860),c_HOL_OEx(U_14858)),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_fun(U_14858,tc_HOL_Obool),U_14860),hAPP(c_COMBS(U_14858,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14858),c_fconj),U_14859))),U_14861)))))
          | ? [U_14857] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBC(U_14860,U_14858,tc_HOL_Obool),U_14861),U_14857))))
              & hBOOL(hAPP(U_14859,U_14857)) ) )
        & ( ! [U_14856] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBC(U_14860,U_14858,tc_HOL_Obool),U_14861),U_14856))))
              | ~ hBOOL(hAPP(U_14859,U_14856)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_HOL_Obool,U_14860),c_HOL_OEx(U_14858)),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_fun(U_14858,tc_HOL_Obool),U_14860),hAPP(c_COMBS(U_14858,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14858),c_fconj),U_14859))),U_14861))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14858),hAPP(c_Set_OCollect(U_14858),U_14859))) ),
    inference(variable_rename,[status(thm)],[f_3714_1]) ).

fof(f_3714_3,plain,
    ! [U_14861,U_14860,U_14859,U_14858] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_HOL_Obool,U_14860),c_HOL_OEx(U_14858)),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_fun(U_14858,tc_HOL_Obool),U_14860),hAPP(c_COMBS(U_14858,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14858),c_fconj),U_14859))),U_14861)))))
          | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBC(U_14860,U_14858,tc_HOL_Obool),U_14861),sK334(U_14861,U_14860,U_14859,U_14858)))))
            & hBOOL(hAPP(U_14859,sK334(U_14861,U_14860,U_14859,U_14858))) ) )
        & ( ! [U_14856] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBC(U_14860,U_14858,tc_HOL_Obool),U_14861),U_14856))))
              | ~ hBOOL(hAPP(U_14859,U_14856)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_HOL_Obool,U_14860),c_HOL_OEx(U_14858)),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_fun(U_14858,tc_HOL_Obool),U_14860),hAPP(c_COMBS(U_14858,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14858),c_fconj),U_14859))),U_14861))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14858),hAPP(c_Set_OCollect(U_14858),U_14859))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK334]),skolemize(U_14857,sK334(U_14861,U_14860,U_14859,U_14858))],[f_3714_2]) ).

fof(f_3714_4,plain,
    ( ! [U_14858,U_14859,U_14860,U_14861] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBC(U_14860,U_14858,tc_HOL_Obool),U_14861),sK334(U_14861,U_14860,U_14859,U_14858)))))
        | ~ sP1011(U_14858,U_14859,U_14860,U_14861) )
    & ! [U_14858,U_14859,U_14860,U_14861] :
        ( hBOOL(hAPP(U_14859,sK334(U_14861,U_14860,U_14859,U_14858)))
        | ~ sP1011(U_14858,U_14859,U_14860,U_14861) )
    & ! [U_14856,U_14858,U_14859,U_14860,U_14861] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_HOL_Obool,U_14860),c_HOL_OEx(U_14858)),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_fun(U_14858,tc_HOL_Obool),U_14860),hAPP(c_COMBS(U_14858,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14858),c_fconj),U_14859))),U_14861)))))
        | sP1011(U_14858,U_14859,U_14860,U_14861)
        | ~ sP1012(U_14856,U_14858,U_14859,U_14860,U_14861) )
    & ! [U_14856,U_14858,U_14859,U_14860,U_14861] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBC(U_14860,U_14858,tc_HOL_Obool),U_14861),U_14856))))
        | ~ hBOOL(hAPP(U_14859,U_14856))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_HOL_Obool,U_14860),c_HOL_OEx(U_14858)),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_fun(U_14858,tc_HOL_Obool),U_14860),hAPP(c_COMBS(U_14858,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14858),c_fconj),U_14859))),U_14861)))))
        | ~ sP1012(U_14856,U_14858,U_14859,U_14860,U_14861) )
    & ! [U_14856,U_14858,U_14859,U_14860,U_14861] :
        ( sP1012(U_14856,U_14858,U_14859,U_14860,U_14861)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14858),hAPP(c_Set_OCollect(U_14858),U_14859))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1011,sP1012])],[f_3714_3]) ).

cnf(f_3714_5,plain,
    ( sP1012(U_14856,U_14858,U_14859,U_14860,U_14861)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14858),hAPP(c_Set_OCollect(U_14858),U_14859))) ),
    inference(clausify,[status(thm)],[f_3714_4]) ).

cnf(f_3714_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBC(U_14860,U_14858,tc_HOL_Obool),U_14861),U_14856))))
    | ~ hBOOL(hAPP(U_14859,U_14856))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_HOL_Obool,U_14860),c_HOL_OEx(U_14858)),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_fun(U_14858,tc_HOL_Obool),U_14860),hAPP(c_COMBS(U_14858,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14858),c_fconj),U_14859))),U_14861)))))
    | ~ sP1012(U_14856,U_14858,U_14859,U_14860,U_14861) ),
    inference(clausify,[status(thm)],[f_3714_4]) ).

cnf(f_3714_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_HOL_Obool,U_14860),c_HOL_OEx(U_14858)),hAPP(hAPP(c_COMBB(tc_fun(U_14858,tc_HOL_Obool),tc_fun(U_14858,tc_HOL_Obool),U_14860),hAPP(c_COMBS(U_14858,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14858),c_fconj),U_14859))),U_14861)))))
    | sP1011(U_14858,U_14859,U_14860,U_14861)
    | ~ sP1012(U_14856,U_14858,U_14859,U_14860,U_14861) ),
    inference(clausify,[status(thm)],[f_3714_4]) ).

cnf(f_3714_8,plain,
    ( hBOOL(hAPP(U_14859,sK334(U_14861,U_14860,U_14859,U_14858)))
    | ~ sP1011(U_14858,U_14859,U_14860,U_14861) ),
    inference(clausify,[status(thm)],[f_3714_4]) ).

cnf(f_3714_9,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14860),hAPP(c_Set_OCollect(U_14860),hAPP(hAPP(c_COMBC(U_14860,U_14858,tc_HOL_Obool),U_14861),sK334(U_14861,U_14860,U_14859,U_14858)))))
    | ~ sP1011(U_14858,U_14859,U_14860,U_14861) ),
    inference(clausify,[status(thm)],[f_3714_4]) ).

fof(f_3715_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_3715_2,plain,
    ! [U_14864,U_14863,U_14862] : c_Map_Oran(U_14862,U_14863,U_14864) = hAPP(c_Set_OCollect(U_14863),hAPP(hAPP(c_COMBB(tc_fun(U_14862,tc_HOL_Obool),tc_HOL_Obool,U_14863),c_HOL_OEx(U_14862)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_14863),tc_fun(U_14862,tc_HOL_Obool),U_14863),hAPP(c_COMBC(U_14862,tc_Option_Ooption(U_14863),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_14863),tc_fun(tc_Option_Ooption(U_14863),tc_HOL_Obool),U_14862),c_fequal),U_14864))),c_Option_Ooption_OSome(U_14863)))),
    inference(variable_rename,[status(thm)],[f_3715_1]) ).

fof(f_3715_3,plain,
    ! [U_14863,U_14862,U_14864] : c_Map_Oran(U_14862,U_14863,U_14864) = hAPP(c_Set_OCollect(U_14863),hAPP(hAPP(c_COMBB(tc_fun(U_14862,tc_HOL_Obool),tc_HOL_Obool,U_14863),c_HOL_OEx(U_14862)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_14863),tc_fun(U_14862,tc_HOL_Obool),U_14863),hAPP(c_COMBC(U_14862,tc_Option_Ooption(U_14863),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_14863),tc_fun(tc_Option_Ooption(U_14863),tc_HOL_Obool),U_14862),c_fequal),U_14864))),c_Option_Ooption_OSome(U_14863)))),
    inference(definitional_conversion,[status(esa)],[f_3715_2]) ).

cnf(f_3715_4,plain,
    c_Map_Oran(U_14862,U_14863,U_14864) = hAPP(c_Set_OCollect(U_14863),hAPP(hAPP(c_COMBB(tc_fun(U_14862,tc_HOL_Obool),tc_HOL_Obool,U_14863),c_HOL_OEx(U_14862)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_14863),tc_fun(U_14862,tc_HOL_Obool),U_14863),hAPP(c_COMBC(U_14862,tc_Option_Ooption(U_14863),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_14863),tc_fun(tc_Option_Ooption(U_14863),tc_HOL_Obool),U_14862),c_fequal),U_14864))),c_Option_Ooption_OSome(U_14863)))),
    inference(clausify,[status(thm)],[f_3715_3]) ).

fof(f_3716_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_3716_2,plain,
    ! [U_14866,U_14865] : hAPP(c_Set_OPow(U_14865),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14865,tc_HOL_Obool)),U_14866)) = hAPP(c_Set_OCollect(tc_fun(U_14865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_14865,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_14865,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14865,tc_HOL_Obool),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_14865,tc_HOL_Obool)),c_COMBS(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_14865,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_14865,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_14865,tc_HOL_Obool),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_fun(U_14865,tc_HOL_Obool)),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_fun(U_14865,tc_HOL_Obool)),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_14865,tc_HOL_Obool)),c_COMBB(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_14865,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_14865,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_14865,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_14865,tc_HOL_Obool)),U_14866)),c_Set_OPow(U_14865))))),
    inference(variable_rename,[status(thm)],[f_3716_1]) ).

fof(f_3716_3,plain,
    ! [U_14865,U_14866] : hAPP(c_Set_OPow(U_14865),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14865,tc_HOL_Obool)),U_14866)) = hAPP(c_Set_OCollect(tc_fun(U_14865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_14865,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_14865,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14865,tc_HOL_Obool),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_14865,tc_HOL_Obool)),c_COMBS(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_14865,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_14865,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_14865,tc_HOL_Obool),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_fun(U_14865,tc_HOL_Obool)),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_fun(U_14865,tc_HOL_Obool)),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_14865,tc_HOL_Obool)),c_COMBB(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_14865,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_14865,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_14865,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_14865,tc_HOL_Obool)),U_14866)),c_Set_OPow(U_14865))))),
    inference(definitional_conversion,[status(esa)],[f_3716_2]) ).

cnf(f_3716_4,plain,
    hAPP(c_Set_OPow(U_14865),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14865,tc_HOL_Obool)),U_14866)) = hAPP(c_Set_OCollect(tc_fun(U_14865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_14865,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_14865,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14865,tc_HOL_Obool),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_14865,tc_HOL_Obool)),c_COMBS(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_14865,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_14865,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_14865,tc_HOL_Obool),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_fun(U_14865,tc_HOL_Obool)),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_fun(U_14865,tc_HOL_Obool)),tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_14865,tc_HOL_Obool)),c_COMBB(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_14865,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_14865,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14865,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_14865,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_14865,tc_HOL_Obool)),U_14866)),c_Set_OPow(U_14865))))),
    inference(clausify,[status(thm)],[f_3716_3]) ).

fof(f_3717_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_3717_2,plain,
    ! [U_14869,U_14868,U_14867] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_14867),U_14869),c_Big__Operators_Olinorder__class_OMax(U_14867,U_14868)) = c_Big__Operators_Olinorder__class_OMax(U_14867,hAPP(c_Set_OCollect(U_14867),hAPP(hAPP(c_COMBB(tc_fun(U_14867,tc_HOL_Obool),tc_HOL_Obool,U_14867),c_HOL_OEx(U_14867)),hAPP(hAPP(c_COMBC(U_14867,tc_fun(U_14867,tc_HOL_Obool),tc_fun(U_14867,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14867,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14867,tc_HOL_Obool),tc_fun(U_14867,tc_HOL_Obool)),U_14867),c_COMBS(U_14867,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14867,tc_HOL_Obool),tc_fun(U_14867,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14867),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14867),c_fconj)),hAPP(hAPP(c_COMBC(U_14867,tc_fun(U_14867,U_14867),tc_fun(U_14867,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14867,tc_HOL_Obool),tc_fun(tc_fun(U_14867,U_14867),tc_fun(U_14867,tc_HOL_Obool)),U_14867),c_COMBB(U_14867,tc_HOL_Obool,U_14867)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_14867),U_14869))))),hAPP(hAPP(c_COMBC(U_14867,tc_fun(U_14867,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14867)),U_14868)))))
      | U_14868 = c_Orderings_Obot__class_Obot(tc_fun(U_14867,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14867),U_14868))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_14867) ),
    inference(variable_rename,[status(thm)],[f_3717_1]) ).

fof(f_3717_3,plain,
    ! [U_14867,U_14868,U_14869] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_14867),U_14869),c_Big__Operators_Olinorder__class_OMax(U_14867,U_14868)) = c_Big__Operators_Olinorder__class_OMax(U_14867,hAPP(c_Set_OCollect(U_14867),hAPP(hAPP(c_COMBB(tc_fun(U_14867,tc_HOL_Obool),tc_HOL_Obool,U_14867),c_HOL_OEx(U_14867)),hAPP(hAPP(c_COMBC(U_14867,tc_fun(U_14867,tc_HOL_Obool),tc_fun(U_14867,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14867,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14867,tc_HOL_Obool),tc_fun(U_14867,tc_HOL_Obool)),U_14867),c_COMBS(U_14867,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14867,tc_HOL_Obool),tc_fun(U_14867,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14867),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14867),c_fconj)),hAPP(hAPP(c_COMBC(U_14867,tc_fun(U_14867,U_14867),tc_fun(U_14867,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14867,tc_HOL_Obool),tc_fun(tc_fun(U_14867,U_14867),tc_fun(U_14867,tc_HOL_Obool)),U_14867),c_COMBB(U_14867,tc_HOL_Obool,U_14867)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_14867),U_14869))))),hAPP(hAPP(c_COMBC(U_14867,tc_fun(U_14867,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14867)),U_14868)))))
      | U_14868 = c_Orderings_Obot__class_Obot(tc_fun(U_14867,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14867),U_14868))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_14867) ),
    inference(definitional_conversion,[status(esa)],[f_3717_2]) ).

cnf(f_3717_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_14867),U_14869),c_Big__Operators_Olinorder__class_OMax(U_14867,U_14868)) = c_Big__Operators_Olinorder__class_OMax(U_14867,hAPP(c_Set_OCollect(U_14867),hAPP(hAPP(c_COMBB(tc_fun(U_14867,tc_HOL_Obool),tc_HOL_Obool,U_14867),c_HOL_OEx(U_14867)),hAPP(hAPP(c_COMBC(U_14867,tc_fun(U_14867,tc_HOL_Obool),tc_fun(U_14867,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14867,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14867,tc_HOL_Obool),tc_fun(U_14867,tc_HOL_Obool)),U_14867),c_COMBS(U_14867,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14867,tc_HOL_Obool),tc_fun(U_14867,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14867),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14867),c_fconj)),hAPP(hAPP(c_COMBC(U_14867,tc_fun(U_14867,U_14867),tc_fun(U_14867,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14867,tc_HOL_Obool),tc_fun(tc_fun(U_14867,U_14867),tc_fun(U_14867,tc_HOL_Obool)),U_14867),c_COMBB(U_14867,tc_HOL_Obool,U_14867)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_14867),U_14869))))),hAPP(hAPP(c_COMBC(U_14867,tc_fun(U_14867,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14867)),U_14868)))))
    | U_14868 = c_Orderings_Obot__class_Obot(tc_fun(U_14867,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14867),U_14868))
    | ~ class_Groups_Olinordered__ab__semigroup__add(U_14867) ),
    inference(clausify,[status(thm)],[f_3717_3]) ).

fof(f_3718_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_3718_2,plain,
    ! [U_14872,U_14871,U_14870] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_14870),U_14872),c_Big__Operators_Olinorder__class_OMin(U_14870,U_14871)) = c_Big__Operators_Olinorder__class_OMin(U_14870,hAPP(c_Set_OCollect(U_14870),hAPP(hAPP(c_COMBB(tc_fun(U_14870,tc_HOL_Obool),tc_HOL_Obool,U_14870),c_HOL_OEx(U_14870)),hAPP(hAPP(c_COMBC(U_14870,tc_fun(U_14870,tc_HOL_Obool),tc_fun(U_14870,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14870,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14870,tc_HOL_Obool),tc_fun(U_14870,tc_HOL_Obool)),U_14870),c_COMBS(U_14870,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14870,tc_HOL_Obool),tc_fun(U_14870,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14870),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14870),c_fconj)),hAPP(hAPP(c_COMBC(U_14870,tc_fun(U_14870,U_14870),tc_fun(U_14870,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14870,tc_HOL_Obool),tc_fun(tc_fun(U_14870,U_14870),tc_fun(U_14870,tc_HOL_Obool)),U_14870),c_COMBB(U_14870,tc_HOL_Obool,U_14870)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_14870),U_14872))))),hAPP(hAPP(c_COMBC(U_14870,tc_fun(U_14870,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14870)),U_14871)))))
      | U_14871 = c_Orderings_Obot__class_Obot(tc_fun(U_14870,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14870),U_14871))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_14870) ),
    inference(variable_rename,[status(thm)],[f_3718_1]) ).

fof(f_3718_3,plain,
    ! [U_14870,U_14871,U_14872] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_14870),U_14872),c_Big__Operators_Olinorder__class_OMin(U_14870,U_14871)) = c_Big__Operators_Olinorder__class_OMin(U_14870,hAPP(c_Set_OCollect(U_14870),hAPP(hAPP(c_COMBB(tc_fun(U_14870,tc_HOL_Obool),tc_HOL_Obool,U_14870),c_HOL_OEx(U_14870)),hAPP(hAPP(c_COMBC(U_14870,tc_fun(U_14870,tc_HOL_Obool),tc_fun(U_14870,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14870,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14870,tc_HOL_Obool),tc_fun(U_14870,tc_HOL_Obool)),U_14870),c_COMBS(U_14870,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14870,tc_HOL_Obool),tc_fun(U_14870,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14870),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14870),c_fconj)),hAPP(hAPP(c_COMBC(U_14870,tc_fun(U_14870,U_14870),tc_fun(U_14870,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14870,tc_HOL_Obool),tc_fun(tc_fun(U_14870,U_14870),tc_fun(U_14870,tc_HOL_Obool)),U_14870),c_COMBB(U_14870,tc_HOL_Obool,U_14870)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_14870),U_14872))))),hAPP(hAPP(c_COMBC(U_14870,tc_fun(U_14870,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14870)),U_14871)))))
      | U_14871 = c_Orderings_Obot__class_Obot(tc_fun(U_14870,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14870),U_14871))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_14870) ),
    inference(definitional_conversion,[status(esa)],[f_3718_2]) ).

cnf(f_3718_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_14870),U_14872),c_Big__Operators_Olinorder__class_OMin(U_14870,U_14871)) = c_Big__Operators_Olinorder__class_OMin(U_14870,hAPP(c_Set_OCollect(U_14870),hAPP(hAPP(c_COMBB(tc_fun(U_14870,tc_HOL_Obool),tc_HOL_Obool,U_14870),c_HOL_OEx(U_14870)),hAPP(hAPP(c_COMBC(U_14870,tc_fun(U_14870,tc_HOL_Obool),tc_fun(U_14870,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14870,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14870,tc_HOL_Obool),tc_fun(U_14870,tc_HOL_Obool)),U_14870),c_COMBS(U_14870,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14870,tc_HOL_Obool),tc_fun(U_14870,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14870),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14870),c_fconj)),hAPP(hAPP(c_COMBC(U_14870,tc_fun(U_14870,U_14870),tc_fun(U_14870,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14870,tc_HOL_Obool),tc_fun(tc_fun(U_14870,U_14870),tc_fun(U_14870,tc_HOL_Obool)),U_14870),c_COMBB(U_14870,tc_HOL_Obool,U_14870)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_14870),U_14872))))),hAPP(hAPP(c_COMBC(U_14870,tc_fun(U_14870,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14870)),U_14871)))))
    | U_14871 = c_Orderings_Obot__class_Obot(tc_fun(U_14870,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14870),U_14871))
    | ~ class_Groups_Olinordered__ab__semigroup__add(U_14870) ),
    inference(clausify,[status(thm)],[f_3718_3]) ).

fof(f_3719_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_3719_2,plain,
    ! [U_14875,U_14874,U_14873] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14873),c_Big__Operators_Olattice__class_OInf__fin(U_14873,U_14874)),c_Big__Operators_Olattice__class_OInf__fin(U_14873,U_14875)) = c_Big__Operators_Olattice__class_OInf__fin(U_14873,hAPP(c_Set_OCollect(U_14873),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_HOL_Obool),tc_HOL_Obool,U_14873),c_HOL_OEx(U_14873)),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool)),tc_fun(U_14873,tc_HOL_Obool),U_14873),hAPP(c_COMBB(tc_fun(U_14873,tc_HOL_Obool),tc_HOL_Obool,U_14873),c_HOL_OEx(U_14873))),hAPP(hAPP(c_COMBC(U_14873,tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool)),tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_fun(tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool))),tc_fun(tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool)),tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool))),U_14873),c_COMBS(U_14873,tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_fun(U_14873,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14873,tc_fun(tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool))),U_14873),hAPP(c_COMBB(tc_fun(U_14873,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool)),U_14873),c_COMBS(U_14873,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool)),tc_fun(U_14873,tc_fun(U_14873,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14873),hAPP(c_COMBB(tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14873),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14873),c_fconj))),hAPP(hAPP(c_COMBC(U_14873,tc_fun(U_14873,tc_fun(U_14873,U_14873)),tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14873,U_14873),tc_fun(U_14873,tc_HOL_Obool)),tc_fun(tc_fun(U_14873,tc_fun(U_14873,U_14873)),tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool))),U_14873),c_COMBB(tc_fun(U_14873,U_14873),tc_fun(U_14873,tc_HOL_Obool),U_14873)),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_HOL_Obool),tc_fun(tc_fun(U_14873,U_14873),tc_fun(U_14873,tc_HOL_Obool)),U_14873),c_COMBB(U_14873,tc_HOL_Obool,U_14873)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_14873)))))),hAPP(hAPP(c_COMBC(U_14873,tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool)),U_14873),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14873)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14873),c_fconj),hAPP(hAPP(c_COMBC(U_14873,tc_fun(U_14873,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14873)),U_14874)))),hAPP(hAPP(c_COMBC(U_14873,tc_fun(U_14873,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14873)),U_14875)))))))
      | U_14875 = c_Orderings_Obot__class_Obot(tc_fun(U_14873,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14873),U_14875))
      | U_14874 = c_Orderings_Obot__class_Obot(tc_fun(U_14873,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14873),U_14874))
      | ~ class_Lattices_Odistrib__lattice(U_14873) ),
    inference(variable_rename,[status(thm)],[f_3719_1]) ).

fof(f_3719_3,plain,
    ! [U_14873,U_14874,U_14875] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14873),c_Big__Operators_Olattice__class_OInf__fin(U_14873,U_14874)),c_Big__Operators_Olattice__class_OInf__fin(U_14873,U_14875)) = c_Big__Operators_Olattice__class_OInf__fin(U_14873,hAPP(c_Set_OCollect(U_14873),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_HOL_Obool),tc_HOL_Obool,U_14873),c_HOL_OEx(U_14873)),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool)),tc_fun(U_14873,tc_HOL_Obool),U_14873),hAPP(c_COMBB(tc_fun(U_14873,tc_HOL_Obool),tc_HOL_Obool,U_14873),c_HOL_OEx(U_14873))),hAPP(hAPP(c_COMBC(U_14873,tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool)),tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_fun(tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool))),tc_fun(tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool)),tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool))),U_14873),c_COMBS(U_14873,tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_fun(U_14873,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14873,tc_fun(tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool))),U_14873),hAPP(c_COMBB(tc_fun(U_14873,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool)),U_14873),c_COMBS(U_14873,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool)),tc_fun(U_14873,tc_fun(U_14873,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14873),hAPP(c_COMBB(tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14873),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14873),c_fconj))),hAPP(hAPP(c_COMBC(U_14873,tc_fun(U_14873,tc_fun(U_14873,U_14873)),tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14873,U_14873),tc_fun(U_14873,tc_HOL_Obool)),tc_fun(tc_fun(U_14873,tc_fun(U_14873,U_14873)),tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool))),U_14873),c_COMBB(tc_fun(U_14873,U_14873),tc_fun(U_14873,tc_HOL_Obool),U_14873)),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_HOL_Obool),tc_fun(tc_fun(U_14873,U_14873),tc_fun(U_14873,tc_HOL_Obool)),U_14873),c_COMBB(U_14873,tc_HOL_Obool,U_14873)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_14873)))))),hAPP(hAPP(c_COMBC(U_14873,tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool)),U_14873),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14873)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14873),c_fconj),hAPP(hAPP(c_COMBC(U_14873,tc_fun(U_14873,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14873)),U_14874)))),hAPP(hAPP(c_COMBC(U_14873,tc_fun(U_14873,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14873)),U_14875)))))))
      | U_14875 = c_Orderings_Obot__class_Obot(tc_fun(U_14873,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14873),U_14875))
      | U_14874 = c_Orderings_Obot__class_Obot(tc_fun(U_14873,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14873),U_14874))
      | ~ class_Lattices_Odistrib__lattice(U_14873) ),
    inference(definitional_conversion,[status(esa)],[f_3719_2]) ).

cnf(f_3719_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14873),c_Big__Operators_Olattice__class_OInf__fin(U_14873,U_14874)),c_Big__Operators_Olattice__class_OInf__fin(U_14873,U_14875)) = c_Big__Operators_Olattice__class_OInf__fin(U_14873,hAPP(c_Set_OCollect(U_14873),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_HOL_Obool),tc_HOL_Obool,U_14873),c_HOL_OEx(U_14873)),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool)),tc_fun(U_14873,tc_HOL_Obool),U_14873),hAPP(c_COMBB(tc_fun(U_14873,tc_HOL_Obool),tc_HOL_Obool,U_14873),c_HOL_OEx(U_14873))),hAPP(hAPP(c_COMBC(U_14873,tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool)),tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_fun(tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool))),tc_fun(tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool)),tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool))),U_14873),c_COMBS(U_14873,tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_fun(U_14873,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14873,tc_fun(tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool))),U_14873),hAPP(c_COMBB(tc_fun(U_14873,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool)),U_14873),c_COMBS(U_14873,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool)),tc_fun(U_14873,tc_fun(U_14873,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14873),hAPP(c_COMBB(tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14873),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14873),c_fconj))),hAPP(hAPP(c_COMBC(U_14873,tc_fun(U_14873,tc_fun(U_14873,U_14873)),tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14873,U_14873),tc_fun(U_14873,tc_HOL_Obool)),tc_fun(tc_fun(U_14873,tc_fun(U_14873,U_14873)),tc_fun(U_14873,tc_fun(U_14873,tc_HOL_Obool))),U_14873),c_COMBB(tc_fun(U_14873,U_14873),tc_fun(U_14873,tc_HOL_Obool),U_14873)),hAPP(hAPP(c_COMBB(tc_fun(U_14873,tc_HOL_Obool),tc_fun(tc_fun(U_14873,U_14873),tc_fun(U_14873,tc_HOL_Obool)),U_14873),c_COMBB(U_14873,tc_HOL_Obool,U_14873)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_14873)))))),hAPP(hAPP(c_COMBC(U_14873,tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14873,tc_HOL_Obool),tc_fun(U_14873,tc_HOL_Obool)),U_14873),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14873)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14873),c_fconj),hAPP(hAPP(c_COMBC(U_14873,tc_fun(U_14873,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14873)),U_14874)))),hAPP(hAPP(c_COMBC(U_14873,tc_fun(U_14873,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14873)),U_14875)))))))
    | U_14875 = c_Orderings_Obot__class_Obot(tc_fun(U_14873,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14873),U_14875))
    | U_14874 = c_Orderings_Obot__class_Obot(tc_fun(U_14873,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14873),U_14874))
    | ~ class_Lattices_Odistrib__lattice(U_14873) ),
    inference(clausify,[status(thm)],[f_3719_3]) ).

fof(f_3720_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_3720_2,plain,
    ! [U_14878,U_14877,U_14876] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14876),U_14878),c_Big__Operators_Olattice__class_OInf__fin(U_14876,U_14877)) = c_Big__Operators_Olattice__class_OInf__fin(U_14876,hAPP(c_Set_OCollect(U_14876),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_HOL_Obool),tc_HOL_Obool,U_14876),c_HOL_OEx(U_14876)),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14876,tc_HOL_Obool),tc_fun(U_14876,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14876,tc_HOL_Obool),tc_fun(U_14876,tc_HOL_Obool)),U_14876),c_COMBS(U_14876,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_HOL_Obool),tc_fun(U_14876,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14876),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14876),c_fconj)),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14876,U_14876),tc_fun(U_14876,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_HOL_Obool),tc_fun(tc_fun(U_14876,U_14876),tc_fun(U_14876,tc_HOL_Obool)),U_14876),c_COMBB(U_14876,tc_HOL_Obool,U_14876)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14876),U_14878))))),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14876,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14876)),U_14877)))))
      | U_14877 = c_Orderings_Obot__class_Obot(tc_fun(U_14876,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14876),U_14877))
      | ~ class_Lattices_Odistrib__lattice(U_14876) ),
    inference(variable_rename,[status(thm)],[f_3720_1]) ).

fof(f_3720_3,plain,
    ! [U_14876,U_14878,U_14877] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14876),U_14878),c_Big__Operators_Olattice__class_OInf__fin(U_14876,U_14877)) = c_Big__Operators_Olattice__class_OInf__fin(U_14876,hAPP(c_Set_OCollect(U_14876),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_HOL_Obool),tc_HOL_Obool,U_14876),c_HOL_OEx(U_14876)),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14876,tc_HOL_Obool),tc_fun(U_14876,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14876,tc_HOL_Obool),tc_fun(U_14876,tc_HOL_Obool)),U_14876),c_COMBS(U_14876,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_HOL_Obool),tc_fun(U_14876,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14876),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14876),c_fconj)),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14876,U_14876),tc_fun(U_14876,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_HOL_Obool),tc_fun(tc_fun(U_14876,U_14876),tc_fun(U_14876,tc_HOL_Obool)),U_14876),c_COMBB(U_14876,tc_HOL_Obool,U_14876)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14876),U_14878))))),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14876,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14876)),U_14877)))))
      | U_14877 = c_Orderings_Obot__class_Obot(tc_fun(U_14876,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14876),U_14877))
      | ~ class_Lattices_Odistrib__lattice(U_14876) ),
    inference(definitional_conversion,[status(esa)],[f_3720_2]) ).

cnf(f_3720_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14876),U_14878),c_Big__Operators_Olattice__class_OInf__fin(U_14876,U_14877)) = c_Big__Operators_Olattice__class_OInf__fin(U_14876,hAPP(c_Set_OCollect(U_14876),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_HOL_Obool),tc_HOL_Obool,U_14876),c_HOL_OEx(U_14876)),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14876,tc_HOL_Obool),tc_fun(U_14876,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14876,tc_HOL_Obool),tc_fun(U_14876,tc_HOL_Obool)),U_14876),c_COMBS(U_14876,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_HOL_Obool),tc_fun(U_14876,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14876),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14876),c_fconj)),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14876,U_14876),tc_fun(U_14876,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_HOL_Obool),tc_fun(tc_fun(U_14876,U_14876),tc_fun(U_14876,tc_HOL_Obool)),U_14876),c_COMBB(U_14876,tc_HOL_Obool,U_14876)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14876),U_14878))))),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14876,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14876)),U_14877)))))
    | U_14877 = c_Orderings_Obot__class_Obot(tc_fun(U_14876,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14876),U_14877))
    | ~ class_Lattices_Odistrib__lattice(U_14876) ),
    inference(clausify,[status(thm)],[f_3720_3]) ).

fof(f_3721_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_3721_2,plain,
    ! [U_14881,U_14880,U_14879] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14879),U_14881),c_Big__Operators_Olattice__class_OSup__fin(U_14879,U_14880)) = c_Big__Operators_Olattice__class_OSup__fin(U_14879,hAPP(c_Set_OCollect(U_14879),hAPP(hAPP(c_COMBB(tc_fun(U_14879,tc_HOL_Obool),tc_HOL_Obool,U_14879),c_HOL_OEx(U_14879)),hAPP(hAPP(c_COMBC(U_14879,tc_fun(U_14879,tc_HOL_Obool),tc_fun(U_14879,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14879,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14879,tc_HOL_Obool),tc_fun(U_14879,tc_HOL_Obool)),U_14879),c_COMBS(U_14879,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14879,tc_HOL_Obool),tc_fun(U_14879,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14879),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14879),c_fconj)),hAPP(hAPP(c_COMBC(U_14879,tc_fun(U_14879,U_14879),tc_fun(U_14879,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14879,tc_HOL_Obool),tc_fun(tc_fun(U_14879,U_14879),tc_fun(U_14879,tc_HOL_Obool)),U_14879),c_COMBB(U_14879,tc_HOL_Obool,U_14879)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14879),U_14881))))),hAPP(hAPP(c_COMBC(U_14879,tc_fun(U_14879,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14879)),U_14880)))))
      | U_14880 = c_Orderings_Obot__class_Obot(tc_fun(U_14879,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14879),U_14880))
      | ~ class_Lattices_Odistrib__lattice(U_14879) ),
    inference(variable_rename,[status(thm)],[f_3721_1]) ).

fof(f_3721_3,plain,
    ! [U_14879,U_14880,U_14881] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14879),U_14881),c_Big__Operators_Olattice__class_OSup__fin(U_14879,U_14880)) = c_Big__Operators_Olattice__class_OSup__fin(U_14879,hAPP(c_Set_OCollect(U_14879),hAPP(hAPP(c_COMBB(tc_fun(U_14879,tc_HOL_Obool),tc_HOL_Obool,U_14879),c_HOL_OEx(U_14879)),hAPP(hAPP(c_COMBC(U_14879,tc_fun(U_14879,tc_HOL_Obool),tc_fun(U_14879,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14879,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14879,tc_HOL_Obool),tc_fun(U_14879,tc_HOL_Obool)),U_14879),c_COMBS(U_14879,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14879,tc_HOL_Obool),tc_fun(U_14879,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14879),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14879),c_fconj)),hAPP(hAPP(c_COMBC(U_14879,tc_fun(U_14879,U_14879),tc_fun(U_14879,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14879,tc_HOL_Obool),tc_fun(tc_fun(U_14879,U_14879),tc_fun(U_14879,tc_HOL_Obool)),U_14879),c_COMBB(U_14879,tc_HOL_Obool,U_14879)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14879),U_14881))))),hAPP(hAPP(c_COMBC(U_14879,tc_fun(U_14879,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14879)),U_14880)))))
      | U_14880 = c_Orderings_Obot__class_Obot(tc_fun(U_14879,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14879),U_14880))
      | ~ class_Lattices_Odistrib__lattice(U_14879) ),
    inference(definitional_conversion,[status(esa)],[f_3721_2]) ).

cnf(f_3721_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14879),U_14881),c_Big__Operators_Olattice__class_OSup__fin(U_14879,U_14880)) = c_Big__Operators_Olattice__class_OSup__fin(U_14879,hAPP(c_Set_OCollect(U_14879),hAPP(hAPP(c_COMBB(tc_fun(U_14879,tc_HOL_Obool),tc_HOL_Obool,U_14879),c_HOL_OEx(U_14879)),hAPP(hAPP(c_COMBC(U_14879,tc_fun(U_14879,tc_HOL_Obool),tc_fun(U_14879,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14879,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14879,tc_HOL_Obool),tc_fun(U_14879,tc_HOL_Obool)),U_14879),c_COMBS(U_14879,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14879,tc_HOL_Obool),tc_fun(U_14879,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14879),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14879),c_fconj)),hAPP(hAPP(c_COMBC(U_14879,tc_fun(U_14879,U_14879),tc_fun(U_14879,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14879,tc_HOL_Obool),tc_fun(tc_fun(U_14879,U_14879),tc_fun(U_14879,tc_HOL_Obool)),U_14879),c_COMBB(U_14879,tc_HOL_Obool,U_14879)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14879),U_14881))))),hAPP(hAPP(c_COMBC(U_14879,tc_fun(U_14879,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14879)),U_14880)))))
    | U_14880 = c_Orderings_Obot__class_Obot(tc_fun(U_14879,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14879),U_14880))
    | ~ class_Lattices_Odistrib__lattice(U_14879) ),
    inference(clausify,[status(thm)],[f_3721_3]) ).

fof(f_3722_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_3722_2,plain,
    ! [U_14884,U_14883,U_14882] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14882),c_Big__Operators_Olattice__class_OSup__fin(U_14882,U_14883)),c_Big__Operators_Olattice__class_OSup__fin(U_14882,U_14884)) = c_Big__Operators_Olattice__class_OSup__fin(U_14882,hAPP(c_Set_OCollect(U_14882),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_HOL_Obool),tc_HOL_Obool,U_14882),c_HOL_OEx(U_14882)),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool)),tc_fun(U_14882,tc_HOL_Obool),U_14882),hAPP(c_COMBB(tc_fun(U_14882,tc_HOL_Obool),tc_HOL_Obool,U_14882),c_HOL_OEx(U_14882))),hAPP(hAPP(c_COMBC(U_14882,tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool)),tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_fun(tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool))),tc_fun(tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool)),tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool))),U_14882),c_COMBS(U_14882,tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_fun(U_14882,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14882,tc_fun(tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool))),U_14882),hAPP(c_COMBB(tc_fun(U_14882,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool)),U_14882),c_COMBS(U_14882,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool)),tc_fun(U_14882,tc_fun(U_14882,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14882),hAPP(c_COMBB(tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14882),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14882),c_fconj))),hAPP(hAPP(c_COMBC(U_14882,tc_fun(U_14882,tc_fun(U_14882,U_14882)),tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14882,U_14882),tc_fun(U_14882,tc_HOL_Obool)),tc_fun(tc_fun(U_14882,tc_fun(U_14882,U_14882)),tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool))),U_14882),c_COMBB(tc_fun(U_14882,U_14882),tc_fun(U_14882,tc_HOL_Obool),U_14882)),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_HOL_Obool),tc_fun(tc_fun(U_14882,U_14882),tc_fun(U_14882,tc_HOL_Obool)),U_14882),c_COMBB(U_14882,tc_HOL_Obool,U_14882)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_14882)))))),hAPP(hAPP(c_COMBC(U_14882,tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool)),U_14882),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14882)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14882),c_fconj),hAPP(hAPP(c_COMBC(U_14882,tc_fun(U_14882,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14882)),U_14883)))),hAPP(hAPP(c_COMBC(U_14882,tc_fun(U_14882,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14882)),U_14884)))))))
      | U_14884 = c_Orderings_Obot__class_Obot(tc_fun(U_14882,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14882),U_14884))
      | U_14883 = c_Orderings_Obot__class_Obot(tc_fun(U_14882,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14882),U_14883))
      | ~ class_Lattices_Odistrib__lattice(U_14882) ),
    inference(variable_rename,[status(thm)],[f_3722_1]) ).

fof(f_3722_3,plain,
    ! [U_14882,U_14883,U_14884] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14882),c_Big__Operators_Olattice__class_OSup__fin(U_14882,U_14883)),c_Big__Operators_Olattice__class_OSup__fin(U_14882,U_14884)) = c_Big__Operators_Olattice__class_OSup__fin(U_14882,hAPP(c_Set_OCollect(U_14882),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_HOL_Obool),tc_HOL_Obool,U_14882),c_HOL_OEx(U_14882)),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool)),tc_fun(U_14882,tc_HOL_Obool),U_14882),hAPP(c_COMBB(tc_fun(U_14882,tc_HOL_Obool),tc_HOL_Obool,U_14882),c_HOL_OEx(U_14882))),hAPP(hAPP(c_COMBC(U_14882,tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool)),tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_fun(tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool))),tc_fun(tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool)),tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool))),U_14882),c_COMBS(U_14882,tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_fun(U_14882,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14882,tc_fun(tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool))),U_14882),hAPP(c_COMBB(tc_fun(U_14882,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool)),U_14882),c_COMBS(U_14882,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool)),tc_fun(U_14882,tc_fun(U_14882,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14882),hAPP(c_COMBB(tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14882),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14882),c_fconj))),hAPP(hAPP(c_COMBC(U_14882,tc_fun(U_14882,tc_fun(U_14882,U_14882)),tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14882,U_14882),tc_fun(U_14882,tc_HOL_Obool)),tc_fun(tc_fun(U_14882,tc_fun(U_14882,U_14882)),tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool))),U_14882),c_COMBB(tc_fun(U_14882,U_14882),tc_fun(U_14882,tc_HOL_Obool),U_14882)),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_HOL_Obool),tc_fun(tc_fun(U_14882,U_14882),tc_fun(U_14882,tc_HOL_Obool)),U_14882),c_COMBB(U_14882,tc_HOL_Obool,U_14882)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_14882)))))),hAPP(hAPP(c_COMBC(U_14882,tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool)),U_14882),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14882)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14882),c_fconj),hAPP(hAPP(c_COMBC(U_14882,tc_fun(U_14882,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14882)),U_14883)))),hAPP(hAPP(c_COMBC(U_14882,tc_fun(U_14882,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14882)),U_14884)))))))
      | U_14884 = c_Orderings_Obot__class_Obot(tc_fun(U_14882,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14882),U_14884))
      | U_14883 = c_Orderings_Obot__class_Obot(tc_fun(U_14882,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14882),U_14883))
      | ~ class_Lattices_Odistrib__lattice(U_14882) ),
    inference(definitional_conversion,[status(esa)],[f_3722_2]) ).

cnf(f_3722_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14882),c_Big__Operators_Olattice__class_OSup__fin(U_14882,U_14883)),c_Big__Operators_Olattice__class_OSup__fin(U_14882,U_14884)) = c_Big__Operators_Olattice__class_OSup__fin(U_14882,hAPP(c_Set_OCollect(U_14882),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_HOL_Obool),tc_HOL_Obool,U_14882),c_HOL_OEx(U_14882)),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool)),tc_fun(U_14882,tc_HOL_Obool),U_14882),hAPP(c_COMBB(tc_fun(U_14882,tc_HOL_Obool),tc_HOL_Obool,U_14882),c_HOL_OEx(U_14882))),hAPP(hAPP(c_COMBC(U_14882,tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool)),tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_fun(tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool))),tc_fun(tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool)),tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool))),U_14882),c_COMBS(U_14882,tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_fun(U_14882,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14882,tc_fun(tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool))),U_14882),hAPP(c_COMBB(tc_fun(U_14882,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool)),U_14882),c_COMBS(U_14882,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool)),tc_fun(U_14882,tc_fun(U_14882,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14882),hAPP(c_COMBB(tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14882),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14882),c_fconj))),hAPP(hAPP(c_COMBC(U_14882,tc_fun(U_14882,tc_fun(U_14882,U_14882)),tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14882,U_14882),tc_fun(U_14882,tc_HOL_Obool)),tc_fun(tc_fun(U_14882,tc_fun(U_14882,U_14882)),tc_fun(U_14882,tc_fun(U_14882,tc_HOL_Obool))),U_14882),c_COMBB(tc_fun(U_14882,U_14882),tc_fun(U_14882,tc_HOL_Obool),U_14882)),hAPP(hAPP(c_COMBB(tc_fun(U_14882,tc_HOL_Obool),tc_fun(tc_fun(U_14882,U_14882),tc_fun(U_14882,tc_HOL_Obool)),U_14882),c_COMBB(U_14882,tc_HOL_Obool,U_14882)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_14882)))))),hAPP(hAPP(c_COMBC(U_14882,tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14882,tc_HOL_Obool),tc_fun(U_14882,tc_HOL_Obool)),U_14882),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14882)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14882),c_fconj),hAPP(hAPP(c_COMBC(U_14882,tc_fun(U_14882,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14882)),U_14883)))),hAPP(hAPP(c_COMBC(U_14882,tc_fun(U_14882,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14882)),U_14884)))))))
    | U_14884 = c_Orderings_Obot__class_Obot(tc_fun(U_14882,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14882),U_14884))
    | U_14883 = c_Orderings_Obot__class_Obot(tc_fun(U_14882,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14882),U_14883))
    | ~ class_Lattices_Odistrib__lattice(U_14882) ),
    inference(clausify,[status(thm)],[f_3722_3]) ).

fof(f_3723_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_3723_2,plain,
    ! [U_14887,U_14886,U_14885] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14885),U_14887),c_Big__Operators_Olattice_OInf__fin(U_14885,c_Orderings_Oord__class_Omin(U_14885),U_14886)) = c_Big__Operators_Olattice_OInf__fin(U_14885,c_Orderings_Oord__class_Omin(U_14885),hAPP(c_Set_OCollect(U_14885),hAPP(hAPP(c_COMBB(tc_fun(U_14885,tc_HOL_Obool),tc_HOL_Obool,U_14885),c_HOL_OEx(U_14885)),hAPP(hAPP(c_COMBC(U_14885,tc_fun(U_14885,tc_HOL_Obool),tc_fun(U_14885,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14885,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14885,tc_HOL_Obool),tc_fun(U_14885,tc_HOL_Obool)),U_14885),c_COMBS(U_14885,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14885,tc_HOL_Obool),tc_fun(U_14885,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14885),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14885),c_fconj)),hAPP(hAPP(c_COMBC(U_14885,tc_fun(U_14885,U_14885),tc_fun(U_14885,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14885,tc_HOL_Obool),tc_fun(tc_fun(U_14885,U_14885),tc_fun(U_14885,tc_HOL_Obool)),U_14885),c_COMBB(U_14885,tc_HOL_Obool,U_14885)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_14885),U_14887))))),hAPP(hAPP(c_COMBC(U_14885,tc_fun(U_14885,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14885)),U_14886)))))
      | U_14886 = c_Orderings_Obot__class_Obot(tc_fun(U_14885,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14885),U_14886))
      | ~ class_Orderings_Olinorder(U_14885) ),
    inference(variable_rename,[status(thm)],[f_3723_1]) ).

fof(f_3723_3,plain,
    ! [U_14885,U_14887,U_14886] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14885),U_14887),c_Big__Operators_Olattice_OInf__fin(U_14885,c_Orderings_Oord__class_Omin(U_14885),U_14886)) = c_Big__Operators_Olattice_OInf__fin(U_14885,c_Orderings_Oord__class_Omin(U_14885),hAPP(c_Set_OCollect(U_14885),hAPP(hAPP(c_COMBB(tc_fun(U_14885,tc_HOL_Obool),tc_HOL_Obool,U_14885),c_HOL_OEx(U_14885)),hAPP(hAPP(c_COMBC(U_14885,tc_fun(U_14885,tc_HOL_Obool),tc_fun(U_14885,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14885,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14885,tc_HOL_Obool),tc_fun(U_14885,tc_HOL_Obool)),U_14885),c_COMBS(U_14885,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14885,tc_HOL_Obool),tc_fun(U_14885,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14885),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14885),c_fconj)),hAPP(hAPP(c_COMBC(U_14885,tc_fun(U_14885,U_14885),tc_fun(U_14885,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14885,tc_HOL_Obool),tc_fun(tc_fun(U_14885,U_14885),tc_fun(U_14885,tc_HOL_Obool)),U_14885),c_COMBB(U_14885,tc_HOL_Obool,U_14885)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_14885),U_14887))))),hAPP(hAPP(c_COMBC(U_14885,tc_fun(U_14885,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14885)),U_14886)))))
      | U_14886 = c_Orderings_Obot__class_Obot(tc_fun(U_14885,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14885),U_14886))
      | ~ class_Orderings_Olinorder(U_14885) ),
    inference(definitional_conversion,[status(esa)],[f_3723_2]) ).

cnf(f_3723_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_14885),U_14887),c_Big__Operators_Olattice_OInf__fin(U_14885,c_Orderings_Oord__class_Omin(U_14885),U_14886)) = c_Big__Operators_Olattice_OInf__fin(U_14885,c_Orderings_Oord__class_Omin(U_14885),hAPP(c_Set_OCollect(U_14885),hAPP(hAPP(c_COMBB(tc_fun(U_14885,tc_HOL_Obool),tc_HOL_Obool,U_14885),c_HOL_OEx(U_14885)),hAPP(hAPP(c_COMBC(U_14885,tc_fun(U_14885,tc_HOL_Obool),tc_fun(U_14885,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14885,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14885,tc_HOL_Obool),tc_fun(U_14885,tc_HOL_Obool)),U_14885),c_COMBS(U_14885,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14885,tc_HOL_Obool),tc_fun(U_14885,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14885),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14885),c_fconj)),hAPP(hAPP(c_COMBC(U_14885,tc_fun(U_14885,U_14885),tc_fun(U_14885,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14885,tc_HOL_Obool),tc_fun(tc_fun(U_14885,U_14885),tc_fun(U_14885,tc_HOL_Obool)),U_14885),c_COMBB(U_14885,tc_HOL_Obool,U_14885)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_14885),U_14887))))),hAPP(hAPP(c_COMBC(U_14885,tc_fun(U_14885,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14885)),U_14886)))))
    | U_14886 = c_Orderings_Obot__class_Obot(tc_fun(U_14885,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14885),U_14886))
    | ~ class_Orderings_Olinorder(U_14885) ),
    inference(clausify,[status(thm)],[f_3723_3]) ).

fof(f_3724_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_3724_2,plain,
    ! [U_14890,U_14889,U_14888] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_14888),U_14890),c_Big__Operators_Olattice_OSup__fin(U_14888,c_Orderings_Oord__class_Omax(U_14888),U_14889)) = c_Big__Operators_Olattice_OSup__fin(U_14888,c_Orderings_Oord__class_Omax(U_14888),hAPP(c_Set_OCollect(U_14888),hAPP(hAPP(c_COMBB(tc_fun(U_14888,tc_HOL_Obool),tc_HOL_Obool,U_14888),c_HOL_OEx(U_14888)),hAPP(hAPP(c_COMBC(U_14888,tc_fun(U_14888,tc_HOL_Obool),tc_fun(U_14888,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14888,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14888,tc_HOL_Obool),tc_fun(U_14888,tc_HOL_Obool)),U_14888),c_COMBS(U_14888,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14888,tc_HOL_Obool),tc_fun(U_14888,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14888),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14888),c_fconj)),hAPP(hAPP(c_COMBC(U_14888,tc_fun(U_14888,U_14888),tc_fun(U_14888,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14888,tc_HOL_Obool),tc_fun(tc_fun(U_14888,U_14888),tc_fun(U_14888,tc_HOL_Obool)),U_14888),c_COMBB(U_14888,tc_HOL_Obool,U_14888)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_14888),U_14890))))),hAPP(hAPP(c_COMBC(U_14888,tc_fun(U_14888,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14888)),U_14889)))))
      | U_14889 = c_Orderings_Obot__class_Obot(tc_fun(U_14888,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14888),U_14889))
      | ~ class_Orderings_Olinorder(U_14888) ),
    inference(variable_rename,[status(thm)],[f_3724_1]) ).

fof(f_3724_3,plain,
    ! [U_14888,U_14889,U_14890] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_14888),U_14890),c_Big__Operators_Olattice_OSup__fin(U_14888,c_Orderings_Oord__class_Omax(U_14888),U_14889)) = c_Big__Operators_Olattice_OSup__fin(U_14888,c_Orderings_Oord__class_Omax(U_14888),hAPP(c_Set_OCollect(U_14888),hAPP(hAPP(c_COMBB(tc_fun(U_14888,tc_HOL_Obool),tc_HOL_Obool,U_14888),c_HOL_OEx(U_14888)),hAPP(hAPP(c_COMBC(U_14888,tc_fun(U_14888,tc_HOL_Obool),tc_fun(U_14888,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14888,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14888,tc_HOL_Obool),tc_fun(U_14888,tc_HOL_Obool)),U_14888),c_COMBS(U_14888,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14888,tc_HOL_Obool),tc_fun(U_14888,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14888),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14888),c_fconj)),hAPP(hAPP(c_COMBC(U_14888,tc_fun(U_14888,U_14888),tc_fun(U_14888,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14888,tc_HOL_Obool),tc_fun(tc_fun(U_14888,U_14888),tc_fun(U_14888,tc_HOL_Obool)),U_14888),c_COMBB(U_14888,tc_HOL_Obool,U_14888)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_14888),U_14890))))),hAPP(hAPP(c_COMBC(U_14888,tc_fun(U_14888,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14888)),U_14889)))))
      | U_14889 = c_Orderings_Obot__class_Obot(tc_fun(U_14888,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14888),U_14889))
      | ~ class_Orderings_Olinorder(U_14888) ),
    inference(definitional_conversion,[status(esa)],[f_3724_2]) ).

cnf(f_3724_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_14888),U_14890),c_Big__Operators_Olattice_OSup__fin(U_14888,c_Orderings_Oord__class_Omax(U_14888),U_14889)) = c_Big__Operators_Olattice_OSup__fin(U_14888,c_Orderings_Oord__class_Omax(U_14888),hAPP(c_Set_OCollect(U_14888),hAPP(hAPP(c_COMBB(tc_fun(U_14888,tc_HOL_Obool),tc_HOL_Obool,U_14888),c_HOL_OEx(U_14888)),hAPP(hAPP(c_COMBC(U_14888,tc_fun(U_14888,tc_HOL_Obool),tc_fun(U_14888,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14888,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14888,tc_HOL_Obool),tc_fun(U_14888,tc_HOL_Obool)),U_14888),c_COMBS(U_14888,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14888,tc_HOL_Obool),tc_fun(U_14888,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14888),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14888),c_fconj)),hAPP(hAPP(c_COMBC(U_14888,tc_fun(U_14888,U_14888),tc_fun(U_14888,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14888,tc_HOL_Obool),tc_fun(tc_fun(U_14888,U_14888),tc_fun(U_14888,tc_HOL_Obool)),U_14888),c_COMBB(U_14888,tc_HOL_Obool,U_14888)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_14888),U_14890))))),hAPP(hAPP(c_COMBC(U_14888,tc_fun(U_14888,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14888)),U_14889)))))
    | U_14889 = c_Orderings_Obot__class_Obot(tc_fun(U_14888,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14888),U_14889))
    | ~ class_Orderings_Olinorder(U_14888) ),
    inference(clausify,[status(thm)],[f_3724_3]) ).

fof(f_3725_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_3725_2,plain,
    ! [U_14897,U_14896,U_14895,U_14894,U_14893,U_14892,U_14891] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14891),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14892,U_14891),U_14894),U_14896)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14893,U_14891),U_14895),U_14897)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14891,U_14891),c_Fun_Oid(U_14891)),hAPP(c_Set_OCollect(U_14891),hAPP(hAPP(c_COMBB(tc_fun(U_14892,tc_HOL_Obool),tc_HOL_Obool,U_14891),c_HOL_OEx(U_14892)),hAPP(hAPP(c_COMBB(tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool)),tc_fun(U_14892,tc_HOL_Obool),U_14891),hAPP(c_COMBB(tc_fun(U_14893,tc_HOL_Obool),tc_HOL_Obool,U_14892),c_HOL_OEx(U_14893))),hAPP(hAPP(c_COMBC(U_14891,tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool)),tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14892,tc_fun(tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool))),tc_fun(tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool)),tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool))),U_14891),c_COMBS(U_14892,tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14892,tc_fun(U_14893,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14892,tc_fun(tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool))),U_14891),hAPP(c_COMBB(tc_fun(U_14893,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool)),U_14892),c_COMBS(U_14893,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool)),tc_fun(U_14892,tc_fun(U_14893,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14891),hAPP(c_COMBB(tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14892),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14893),c_fconj))),hAPP(hAPP(c_COMBC(U_14891,tc_fun(U_14892,tc_fun(U_14893,U_14891)),tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14893,U_14891),tc_fun(U_14893,tc_HOL_Obool)),tc_fun(tc_fun(U_14892,tc_fun(U_14893,U_14891)),tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool))),U_14891),c_COMBB(tc_fun(U_14893,U_14891),tc_fun(U_14893,tc_HOL_Obool),U_14892)),hAPP(hAPP(c_COMBB(tc_fun(U_14891,tc_HOL_Obool),tc_fun(tc_fun(U_14893,U_14891),tc_fun(U_14893,tc_HOL_Obool)),U_14891),c_COMBB(U_14891,tc_HOL_Obool,U_14893)),c_fequal))),hAPP(hAPP(c_COMBC(U_14892,tc_fun(U_14893,U_14891),tc_fun(U_14893,U_14891)),hAPP(hAPP(c_COMBB(tc_fun(U_14891,U_14891),tc_fun(tc_fun(U_14893,U_14891),tc_fun(U_14893,U_14891)),U_14892),c_COMBB(U_14891,U_14891,U_14893)),hAPP(hAPP(c_COMBB(U_14891,tc_fun(U_14891,U_14891),U_14892),c_Groups_Otimes__class_Otimes(U_14891)),U_14894))),U_14895)))))),hAPP(hAPP(c_COMBC(U_14892,tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool)),U_14892),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14893)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14892),c_fconj),hAPP(hAPP(c_COMBC(U_14892,tc_fun(U_14892,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14892)),U_14896)))),hAPP(hAPP(c_COMBC(U_14893,tc_fun(U_14893,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14893)),U_14897)))))))
      | ~ c_Fun_Oinj__on(tc_prod(U_14892,U_14893),U_14891,hAPP(c_Product__Type_Oprod_Oprod__case(U_14892,U_14893,U_14891),hAPP(hAPP(c_COMBC(U_14892,tc_fun(U_14893,U_14891),tc_fun(U_14893,U_14891)),hAPP(hAPP(c_COMBB(tc_fun(U_14891,U_14891),tc_fun(tc_fun(U_14893,U_14891),tc_fun(U_14893,U_14891)),U_14892),c_COMBB(U_14891,U_14891,U_14893)),hAPP(hAPP(c_COMBB(U_14891,tc_fun(U_14891,U_14891),U_14892),c_Groups_Otimes__class_Otimes(U_14891)),U_14894))),U_14895)),hAPP(hAPP(c_Product__Type_OSigma(U_14892,U_14893),U_14896),hAPP(c_COMBK(tc_fun(U_14893,tc_HOL_Obool),U_14892),U_14897)))
      | ~ class_Rings_Osemiring__0(U_14891) ),
    inference(variable_rename,[status(thm)],[f_3725_1]) ).

fof(f_3725_3,plain,
    ! [U_14891,U_14892,U_14893,U_14894,U_14895,U_14896,U_14897] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14891),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14892,U_14891),U_14894),U_14896)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14893,U_14891),U_14895),U_14897)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14891,U_14891),c_Fun_Oid(U_14891)),hAPP(c_Set_OCollect(U_14891),hAPP(hAPP(c_COMBB(tc_fun(U_14892,tc_HOL_Obool),tc_HOL_Obool,U_14891),c_HOL_OEx(U_14892)),hAPP(hAPP(c_COMBB(tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool)),tc_fun(U_14892,tc_HOL_Obool),U_14891),hAPP(c_COMBB(tc_fun(U_14893,tc_HOL_Obool),tc_HOL_Obool,U_14892),c_HOL_OEx(U_14893))),hAPP(hAPP(c_COMBC(U_14891,tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool)),tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14892,tc_fun(tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool))),tc_fun(tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool)),tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool))),U_14891),c_COMBS(U_14892,tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14892,tc_fun(U_14893,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14892,tc_fun(tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool))),U_14891),hAPP(c_COMBB(tc_fun(U_14893,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool)),U_14892),c_COMBS(U_14893,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool)),tc_fun(U_14892,tc_fun(U_14893,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14891),hAPP(c_COMBB(tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14892),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14893),c_fconj))),hAPP(hAPP(c_COMBC(U_14891,tc_fun(U_14892,tc_fun(U_14893,U_14891)),tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14893,U_14891),tc_fun(U_14893,tc_HOL_Obool)),tc_fun(tc_fun(U_14892,tc_fun(U_14893,U_14891)),tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool))),U_14891),c_COMBB(tc_fun(U_14893,U_14891),tc_fun(U_14893,tc_HOL_Obool),U_14892)),hAPP(hAPP(c_COMBB(tc_fun(U_14891,tc_HOL_Obool),tc_fun(tc_fun(U_14893,U_14891),tc_fun(U_14893,tc_HOL_Obool)),U_14891),c_COMBB(U_14891,tc_HOL_Obool,U_14893)),c_fequal))),hAPP(hAPP(c_COMBC(U_14892,tc_fun(U_14893,U_14891),tc_fun(U_14893,U_14891)),hAPP(hAPP(c_COMBB(tc_fun(U_14891,U_14891),tc_fun(tc_fun(U_14893,U_14891),tc_fun(U_14893,U_14891)),U_14892),c_COMBB(U_14891,U_14891,U_14893)),hAPP(hAPP(c_COMBB(U_14891,tc_fun(U_14891,U_14891),U_14892),c_Groups_Otimes__class_Otimes(U_14891)),U_14894))),U_14895)))))),hAPP(hAPP(c_COMBC(U_14892,tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool)),U_14892),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14893)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14892),c_fconj),hAPP(hAPP(c_COMBC(U_14892,tc_fun(U_14892,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14892)),U_14896)))),hAPP(hAPP(c_COMBC(U_14893,tc_fun(U_14893,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14893)),U_14897)))))))
      | ~ c_Fun_Oinj__on(tc_prod(U_14892,U_14893),U_14891,hAPP(c_Product__Type_Oprod_Oprod__case(U_14892,U_14893,U_14891),hAPP(hAPP(c_COMBC(U_14892,tc_fun(U_14893,U_14891),tc_fun(U_14893,U_14891)),hAPP(hAPP(c_COMBB(tc_fun(U_14891,U_14891),tc_fun(tc_fun(U_14893,U_14891),tc_fun(U_14893,U_14891)),U_14892),c_COMBB(U_14891,U_14891,U_14893)),hAPP(hAPP(c_COMBB(U_14891,tc_fun(U_14891,U_14891),U_14892),c_Groups_Otimes__class_Otimes(U_14891)),U_14894))),U_14895)),hAPP(hAPP(c_Product__Type_OSigma(U_14892,U_14893),U_14896),hAPP(c_COMBK(tc_fun(U_14893,tc_HOL_Obool),U_14892),U_14897)))
      | ~ class_Rings_Osemiring__0(U_14891) ),
    inference(definitional_conversion,[status(esa)],[f_3725_2]) ).

cnf(f_3725_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14891),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14892,U_14891),U_14894),U_14896)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14893,U_14891),U_14895),U_14897)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14891,U_14891),c_Fun_Oid(U_14891)),hAPP(c_Set_OCollect(U_14891),hAPP(hAPP(c_COMBB(tc_fun(U_14892,tc_HOL_Obool),tc_HOL_Obool,U_14891),c_HOL_OEx(U_14892)),hAPP(hAPP(c_COMBB(tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool)),tc_fun(U_14892,tc_HOL_Obool),U_14891),hAPP(c_COMBB(tc_fun(U_14893,tc_HOL_Obool),tc_HOL_Obool,U_14892),c_HOL_OEx(U_14893))),hAPP(hAPP(c_COMBC(U_14891,tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool)),tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14892,tc_fun(tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool))),tc_fun(tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool)),tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool))),U_14891),c_COMBS(U_14892,tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14892,tc_fun(U_14893,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14892,tc_fun(tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool))),U_14891),hAPP(c_COMBB(tc_fun(U_14893,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool)),U_14892),c_COMBS(U_14893,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool)),tc_fun(U_14892,tc_fun(U_14893,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14891),hAPP(c_COMBB(tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14892),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14893),c_fconj))),hAPP(hAPP(c_COMBC(U_14891,tc_fun(U_14892,tc_fun(U_14893,U_14891)),tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14893,U_14891),tc_fun(U_14893,tc_HOL_Obool)),tc_fun(tc_fun(U_14892,tc_fun(U_14893,U_14891)),tc_fun(U_14892,tc_fun(U_14893,tc_HOL_Obool))),U_14891),c_COMBB(tc_fun(U_14893,U_14891),tc_fun(U_14893,tc_HOL_Obool),U_14892)),hAPP(hAPP(c_COMBB(tc_fun(U_14891,tc_HOL_Obool),tc_fun(tc_fun(U_14893,U_14891),tc_fun(U_14893,tc_HOL_Obool)),U_14891),c_COMBB(U_14891,tc_HOL_Obool,U_14893)),c_fequal))),hAPP(hAPP(c_COMBC(U_14892,tc_fun(U_14893,U_14891),tc_fun(U_14893,U_14891)),hAPP(hAPP(c_COMBB(tc_fun(U_14891,U_14891),tc_fun(tc_fun(U_14893,U_14891),tc_fun(U_14893,U_14891)),U_14892),c_COMBB(U_14891,U_14891,U_14893)),hAPP(hAPP(c_COMBB(U_14891,tc_fun(U_14891,U_14891),U_14892),c_Groups_Otimes__class_Otimes(U_14891)),U_14894))),U_14895)))))),hAPP(hAPP(c_COMBC(U_14892,tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14893,tc_HOL_Obool),tc_fun(U_14893,tc_HOL_Obool)),U_14892),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14893)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14892),c_fconj),hAPP(hAPP(c_COMBC(U_14892,tc_fun(U_14892,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14892)),U_14896)))),hAPP(hAPP(c_COMBC(U_14893,tc_fun(U_14893,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14893)),U_14897)))))))
    | ~ c_Fun_Oinj__on(tc_prod(U_14892,U_14893),U_14891,hAPP(c_Product__Type_Oprod_Oprod__case(U_14892,U_14893,U_14891),hAPP(hAPP(c_COMBC(U_14892,tc_fun(U_14893,U_14891),tc_fun(U_14893,U_14891)),hAPP(hAPP(c_COMBB(tc_fun(U_14891,U_14891),tc_fun(tc_fun(U_14893,U_14891),tc_fun(U_14893,U_14891)),U_14892),c_COMBB(U_14891,U_14891,U_14893)),hAPP(hAPP(c_COMBB(U_14891,tc_fun(U_14891,U_14891),U_14892),c_Groups_Otimes__class_Otimes(U_14891)),U_14894))),U_14895)),hAPP(hAPP(c_Product__Type_OSigma(U_14892,U_14893),U_14896),hAPP(c_COMBK(tc_fun(U_14893,tc_HOL_Obool),U_14892),U_14897)))
    | ~ class_Rings_Osemiring__0(U_14891) ),
    inference(clausify,[status(thm)],[f_3725_3]) ).

fof(f_3726_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_3726_2,plain,
    ! [U_14904,U_14903,U_14902,U_14901,U_14900,U_14899] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14899,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14901,tc_HOL_Obool),tc_Nat_Onat,U_14899),c_Finite__Set_Ocard(U_14901)),hAPP(hAPP(c_COMBB(tc_fun(U_14901,tc_HOL_Obool),tc_fun(U_14901,tc_HOL_Obool),U_14899),c_Set_OCollect(U_14901)),hAPP(hAPP(c_COMBB(tc_fun(U_14901,tc_HOL_Obool),tc_fun(U_14901,tc_HOL_Obool),U_14899),hAPP(c_COMBS(U_14901,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14901),c_fconj),hAPP(hAPP(c_COMBC(U_14901,tc_fun(U_14901,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14901)),U_14902)))),U_14903)))),U_14900) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14901,tc_Nat_Onat),U_14904),U_14902)
      | ? [U_14898] :
          ( hAPP(c_Finite__Set_Ocard(U_14899),hAPP(c_Set_OCollect(U_14899),hAPP(hAPP(c_COMBS(U_14899,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14899),c_fconj),hAPP(hAPP(c_COMBC(U_14899,tc_fun(U_14899,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14899)),U_14900))),hAPP(hAPP(c_COMBC(U_14899,U_14901,tc_HOL_Obool),U_14903),U_14898)))) != hAPP(U_14904,U_14898)
          & hBOOL(hAPP(hAPP(c_member(U_14901),U_14898),U_14902)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14901),U_14902))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14899),U_14900)) ),
    inference(variable_rename,[status(thm)],[f_3726_1]) ).

fof(f_3726_3,plain,
    ! [U_14904,U_14903,U_14902,U_14901,U_14900,U_14899] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14899,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14901,tc_HOL_Obool),tc_Nat_Onat,U_14899),c_Finite__Set_Ocard(U_14901)),hAPP(hAPP(c_COMBB(tc_fun(U_14901,tc_HOL_Obool),tc_fun(U_14901,tc_HOL_Obool),U_14899),c_Set_OCollect(U_14901)),hAPP(hAPP(c_COMBB(tc_fun(U_14901,tc_HOL_Obool),tc_fun(U_14901,tc_HOL_Obool),U_14899),hAPP(c_COMBS(U_14901,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14901),c_fconj),hAPP(hAPP(c_COMBC(U_14901,tc_fun(U_14901,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14901)),U_14902)))),U_14903)))),U_14900) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14901,tc_Nat_Onat),U_14904),U_14902)
      | ( hAPP(c_Finite__Set_Ocard(U_14899),hAPP(c_Set_OCollect(U_14899),hAPP(hAPP(c_COMBS(U_14899,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14899),c_fconj),hAPP(hAPP(c_COMBC(U_14899,tc_fun(U_14899,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14899)),U_14900))),hAPP(hAPP(c_COMBC(U_14899,U_14901,tc_HOL_Obool),U_14903),sK335(U_14904,U_14903,U_14902,U_14901,U_14900,U_14899))))) != hAPP(U_14904,sK335(U_14904,U_14903,U_14902,U_14901,U_14900,U_14899))
        & hBOOL(hAPP(hAPP(c_member(U_14901),sK335(U_14904,U_14903,U_14902,U_14901,U_14900,U_14899)),U_14902)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14901),U_14902))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14899),U_14900)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK335]),skolemize(U_14898,sK335(U_14904,U_14903,U_14902,U_14901,U_14900,U_14899))],[f_3726_2]) ).

fof(f_3726_4,plain,
    ( ! [U_14899,U_14900,U_14901,U_14902,U_14903,U_14904] :
        ( hAPP(c_Finite__Set_Ocard(U_14899),hAPP(c_Set_OCollect(U_14899),hAPP(hAPP(c_COMBS(U_14899,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14899),c_fconj),hAPP(hAPP(c_COMBC(U_14899,tc_fun(U_14899,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14899)),U_14900))),hAPP(hAPP(c_COMBC(U_14899,U_14901,tc_HOL_Obool),U_14903),sK335(U_14904,U_14903,U_14902,U_14901,U_14900,U_14899))))) != hAPP(U_14904,sK335(U_14904,U_14903,U_14902,U_14901,U_14900,U_14899))
        | ~ sP1013(U_14899,U_14900,U_14901,U_14902,U_14903,U_14904) )
    & ! [U_14899,U_14900,U_14901,U_14902,U_14903,U_14904] :
        ( hBOOL(hAPP(hAPP(c_member(U_14901),sK335(U_14904,U_14903,U_14902,U_14901,U_14900,U_14899)),U_14902))
        | ~ sP1013(U_14899,U_14900,U_14901,U_14902,U_14903,U_14904) )
    & ! [U_14899,U_14900,U_14901,U_14902,U_14903,U_14904] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14899,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14901,tc_HOL_Obool),tc_Nat_Onat,U_14899),c_Finite__Set_Ocard(U_14901)),hAPP(hAPP(c_COMBB(tc_fun(U_14901,tc_HOL_Obool),tc_fun(U_14901,tc_HOL_Obool),U_14899),c_Set_OCollect(U_14901)),hAPP(hAPP(c_COMBB(tc_fun(U_14901,tc_HOL_Obool),tc_fun(U_14901,tc_HOL_Obool),U_14899),hAPP(c_COMBS(U_14901,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14901),c_fconj),hAPP(hAPP(c_COMBC(U_14901,tc_fun(U_14901,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14901)),U_14902)))),U_14903)))),U_14900) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14901,tc_Nat_Onat),U_14904),U_14902)
        | sP1013(U_14899,U_14900,U_14901,U_14902,U_14903,U_14904)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14901),U_14902))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14899),U_14900)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1013])],[f_3726_3]) ).

cnf(f_3726_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14899,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14901,tc_HOL_Obool),tc_Nat_Onat,U_14899),c_Finite__Set_Ocard(U_14901)),hAPP(hAPP(c_COMBB(tc_fun(U_14901,tc_HOL_Obool),tc_fun(U_14901,tc_HOL_Obool),U_14899),c_Set_OCollect(U_14901)),hAPP(hAPP(c_COMBB(tc_fun(U_14901,tc_HOL_Obool),tc_fun(U_14901,tc_HOL_Obool),U_14899),hAPP(c_COMBS(U_14901,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14901),c_fconj),hAPP(hAPP(c_COMBC(U_14901,tc_fun(U_14901,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14901)),U_14902)))),U_14903)))),U_14900) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14901,tc_Nat_Onat),U_14904),U_14902)
    | sP1013(U_14899,U_14900,U_14901,U_14902,U_14903,U_14904)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14901),U_14902))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14899),U_14900)) ),
    inference(clausify,[status(thm)],[f_3726_4]) ).

cnf(f_3726_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14901),sK335(U_14904,U_14903,U_14902,U_14901,U_14900,U_14899)),U_14902))
    | ~ sP1013(U_14899,U_14900,U_14901,U_14902,U_14903,U_14904) ),
    inference(clausify,[status(thm)],[f_3726_4]) ).

cnf(f_3726_7,plain,
    ( hAPP(c_Finite__Set_Ocard(U_14899),hAPP(c_Set_OCollect(U_14899),hAPP(hAPP(c_COMBS(U_14899,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14899),c_fconj),hAPP(hAPP(c_COMBC(U_14899,tc_fun(U_14899,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14899)),U_14900))),hAPP(hAPP(c_COMBC(U_14899,U_14901,tc_HOL_Obool),U_14903),sK335(U_14904,U_14903,U_14902,U_14901,U_14900,U_14899))))) != hAPP(U_14904,sK335(U_14904,U_14903,U_14902,U_14901,U_14900,U_14899))
    | ~ sP1013(U_14899,U_14900,U_14901,U_14902,U_14903,U_14904) ),
    inference(clausify,[status(thm)],[f_3726_4]) ).

fof(f_3727_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_3727_2,plain,
    ! [U_14906,U_14905] : c_Fun_Oinj__on(U_14905,U_14905,c_Fun_Oid(U_14905),U_14906),
    inference(variable_rename,[status(thm)],[f_3727_1]) ).

fof(f_3727_3,plain,
    ! [U_14905,U_14906] : c_Fun_Oinj__on(U_14905,U_14905,c_Fun_Oid(U_14905),U_14906),
    inference(definitional_conversion,[status(esa)],[f_3727_2]) ).

cnf(f_3727_4,plain,
    c_Fun_Oinj__on(U_14905,U_14905,c_Fun_Oid(U_14905),U_14906),
    inference(clausify,[status(thm)],[f_3727_3]) ).

fof(f_3728_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_3728_2,plain,
    ! [U_14908,U_14907] : c_Product__Type_Omap__pair(U_14907,U_14907,U_14908,U_14908,c_Fun_Oid(U_14907),c_Fun_Oid(U_14908)) = c_Fun_Oid(tc_prod(U_14907,U_14908)),
    inference(variable_rename,[status(thm)],[f_3728_1]) ).

fof(f_3728_3,plain,
    ! [U_14907,U_14908] : c_Product__Type_Omap__pair(U_14907,U_14907,U_14908,U_14908,c_Fun_Oid(U_14907),c_Fun_Oid(U_14908)) = c_Fun_Oid(tc_prod(U_14907,U_14908)),
    inference(definitional_conversion,[status(esa)],[f_3728_2]) ).

cnf(f_3728_4,plain,
    c_Product__Type_Omap__pair(U_14907,U_14907,U_14908,U_14908,c_Fun_Oid(U_14907),c_Fun_Oid(U_14908)) = c_Fun_Oid(tc_prod(U_14907,U_14908)),
    inference(clausify,[status(thm)],[f_3728_3]) ).

fof(f_3729_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_3729_2,plain,
    ! [U_14910,U_14909] : c_Product__Type_Omap__pair(U_14909,U_14909,U_14910,U_14910,c_COMBI(U_14909),c_COMBI(U_14910)) = c_Fun_Oid(tc_prod(U_14909,U_14910)),
    inference(variable_rename,[status(thm)],[f_3729_1]) ).

fof(f_3729_3,plain,
    ! [U_14909,U_14910] : c_Product__Type_Omap__pair(U_14909,U_14909,U_14910,U_14910,c_COMBI(U_14909),c_COMBI(U_14910)) = c_Fun_Oid(tc_prod(U_14909,U_14910)),
    inference(definitional_conversion,[status(esa)],[f_3729_2]) ).

cnf(f_3729_4,plain,
    c_Product__Type_Omap__pair(U_14909,U_14909,U_14910,U_14910,c_COMBI(U_14909),c_COMBI(U_14910)) = c_Fun_Oid(tc_prod(U_14909,U_14910)),
    inference(clausify,[status(thm)],[f_3729_3]) ).

fof(f_3730_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_3730_2,plain,
    ! [U_14912,U_14911] : hAPP(c_Fun_Oid(U_14911),U_14912) = U_14912,
    inference(variable_rename,[status(thm)],[f_3730_1]) ).

fof(f_3730_3,plain,
    ! [U_14911,U_14912] : hAPP(c_Fun_Oid(U_14911),U_14912) = U_14912,
    inference(definitional_conversion,[status(esa)],[f_3730_2]) ).

cnf(f_3730_4,plain,
    hAPP(c_Fun_Oid(U_14911),U_14912) = U_14912,
    inference(clausify,[status(thm)],[f_3730_3]) ).

fof(f_3731_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_3731_2,plain,
    ! [U_14914,U_14913] : hAPP(c_Fun_Oid(U_14913),U_14914) = U_14914,
    inference(variable_rename,[status(thm)],[f_3731_1]) ).

fof(f_3731_3,plain,
    ! [U_14913,U_14914] : hAPP(c_Fun_Oid(U_14913),U_14914) = U_14914,
    inference(definitional_conversion,[status(esa)],[f_3731_2]) ).

cnf(f_3731_4,plain,
    hAPP(c_Fun_Oid(U_14913),U_14914) = U_14914,
    inference(clausify,[status(thm)],[f_3731_3]) ).

fof(f_3732_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_3732_2,plain,
    ! [U_14916,U_14915] : c_Product__Type_Oapsnd(U_14915,U_14915,U_14916,c_Fun_Oid(U_14915)) = c_Fun_Oid(tc_prod(U_14916,U_14915)),
    inference(variable_rename,[status(thm)],[f_3732_1]) ).

fof(f_3732_3,plain,
    ! [U_14915,U_14916] : c_Product__Type_Oapsnd(U_14915,U_14915,U_14916,c_Fun_Oid(U_14915)) = c_Fun_Oid(tc_prod(U_14916,U_14915)),
    inference(definitional_conversion,[status(esa)],[f_3732_2]) ).

cnf(f_3732_4,plain,
    c_Product__Type_Oapsnd(U_14915,U_14915,U_14916,c_Fun_Oid(U_14915)) = c_Fun_Oid(tc_prod(U_14916,U_14915)),
    inference(clausify,[status(thm)],[f_3732_3]) ).

fof(f_3733_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_3733_2,plain,
    ! [U_14918,U_14917] : c_Product__Type_Oapfst(U_14917,U_14917,U_14918,c_Fun_Oid(U_14917)) = c_Fun_Oid(tc_prod(U_14917,U_14918)),
    inference(variable_rename,[status(thm)],[f_3733_1]) ).

fof(f_3733_3,plain,
    ! [U_14917,U_14918] : c_Product__Type_Oapfst(U_14917,U_14917,U_14918,c_Fun_Oid(U_14917)) = c_Fun_Oid(tc_prod(U_14917,U_14918)),
    inference(definitional_conversion,[status(esa)],[f_3733_2]) ).

cnf(f_3733_4,plain,
    c_Product__Type_Oapfst(U_14917,U_14917,U_14918,c_Fun_Oid(U_14917)) = c_Fun_Oid(tc_prod(U_14917,U_14918)),
    inference(clausify,[status(thm)],[f_3733_3]) ).

fof(f_3734_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_3734_2,plain,
    c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_3734_1]) ).

cnf(f_3734_3,plain,
    c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_3734_2]) ).

fof(f_3735_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_3735_2,plain,
    ! [U_14920,U_14919] : hAPP(c_Set_Ovimage(U_14919,U_14919,c_Fun_Oid(U_14919)),U_14920) = U_14920,
    inference(variable_rename,[status(thm)],[f_3735_1]) ).

fof(f_3735_3,plain,
    ! [U_14919,U_14920] : hAPP(c_Set_Ovimage(U_14919,U_14919,c_Fun_Oid(U_14919)),U_14920) = U_14920,
    inference(definitional_conversion,[status(esa)],[f_3735_2]) ).

cnf(f_3735_4,plain,
    hAPP(c_Set_Ovimage(U_14919,U_14919,c_Fun_Oid(U_14919)),U_14920) = U_14920,
    inference(clausify,[status(thm)],[f_3735_3]) ).

fof(f_3736_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_3736_2,plain,
    ! [U_14927,U_14926,U_14925,U_14924,U_14923,U_14922,U_14921] :
      ( hAPP(U_14924,hAPP(U_14925,U_14927)) = hAPP(U_14926,U_14927)
      | hAPP(c_Fun_Ocomp(U_14921,U_14922,U_14923,U_14924),U_14925) != hAPP(c_Fun_Ocomp(U_14922,U_14922,U_14923,c_Fun_Oid(U_14922)),U_14926) ),
    inference(variable_rename,[status(thm)],[f_3736_1]) ).

fof(f_3736_3,plain,
    ! [U_14927,U_14926,U_14925,U_14924] :
      ( ! [U_14923,U_14922,U_14921] : hAPP(c_Fun_Ocomp(U_14921,U_14922,U_14923,U_14924),U_14925) != hAPP(c_Fun_Ocomp(U_14922,U_14922,U_14923,c_Fun_Oid(U_14922)),U_14926)
      | hAPP(U_14924,hAPP(U_14925,U_14927)) = hAPP(U_14926,U_14927) ),
    inference(miniscope,[status(thm)],[f_3736_2]) ).

fof(f_3736_4,plain,
    ! [U_14921,U_14922,U_14923,U_14924,U_14925,U_14926,U_14927] :
      ( hAPP(c_Fun_Ocomp(U_14921,U_14922,U_14923,U_14924),U_14925) != hAPP(c_Fun_Ocomp(U_14922,U_14922,U_14923,c_Fun_Oid(U_14922)),U_14926)
      | hAPP(U_14924,hAPP(U_14925,U_14927)) = hAPP(U_14926,U_14927) ),
    inference(definitional_conversion,[status(esa)],[f_3736_3]) ).

cnf(f_3736_5,plain,
    ( hAPP(c_Fun_Ocomp(U_14921,U_14922,U_14923,U_14924),U_14925) != hAPP(c_Fun_Ocomp(U_14922,U_14922,U_14923,c_Fun_Oid(U_14922)),U_14926)
    | hAPP(U_14924,hAPP(U_14925,U_14927)) = hAPP(U_14926,U_14927) ),
    inference(clausify,[status(thm)],[f_3736_4]) ).

fof(f_3737_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_3737_2,plain,
    ! [U_14930,U_14929,U_14928] : hAPP(c_Fun_Ocomp(U_14928,U_14929,U_14928,U_14930),c_Fun_Oid(U_14928)) = U_14930,
    inference(variable_rename,[status(thm)],[f_3737_1]) ).

fof(f_3737_3,plain,
    ! [U_14929,U_14928,U_14930] : hAPP(c_Fun_Ocomp(U_14928,U_14929,U_14928,U_14930),c_Fun_Oid(U_14928)) = U_14930,
    inference(definitional_conversion,[status(esa)],[f_3737_2]) ).

cnf(f_3737_4,plain,
    hAPP(c_Fun_Ocomp(U_14928,U_14929,U_14928,U_14930),c_Fun_Oid(U_14928)) = U_14930,
    inference(clausify,[status(thm)],[f_3737_3]) ).

fof(f_3738_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_3738_2,plain,
    ! [U_14933,U_14932,U_14931] : hAPP(c_Fun_Ocomp(U_14931,U_14931,U_14932,c_Fun_Oid(U_14931)),U_14933) = U_14933,
    inference(variable_rename,[status(thm)],[f_3738_1]) ).

fof(f_3738_3,plain,
    ! [U_14931,U_14932,U_14933] : hAPP(c_Fun_Ocomp(U_14931,U_14931,U_14932,c_Fun_Oid(U_14931)),U_14933) = U_14933,
    inference(definitional_conversion,[status(esa)],[f_3738_2]) ).

cnf(f_3738_4,plain,
    hAPP(c_Fun_Ocomp(U_14931,U_14931,U_14932,c_Fun_Oid(U_14931)),U_14933) = U_14933,
    inference(clausify,[status(thm)],[f_3738_3]) ).

fof(f_3739_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_3739_2,plain,
    ! [U_14935,U_14934] : hAPP(c_Set_Oimage(U_14934,U_14934,c_Fun_Oid(U_14934)),U_14935) = U_14935,
    inference(variable_rename,[status(thm)],[f_3739_1]) ).

fof(f_3739_3,plain,
    ! [U_14934,U_14935] : hAPP(c_Set_Oimage(U_14934,U_14934,c_Fun_Oid(U_14934)),U_14935) = U_14935,
    inference(definitional_conversion,[status(esa)],[f_3739_2]) ).

cnf(f_3739_4,plain,
    hAPP(c_Set_Oimage(U_14934,U_14934,c_Fun_Oid(U_14934)),U_14935) = U_14935,
    inference(clausify,[status(thm)],[f_3739_3]) ).

fof(f_3740_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_3740_2,plain,
    ! [U_14936] : hAPP(c_Set_Oimage(U_14936,U_14936,c_Fun_Oid(U_14936)),c_Orderings_Otop__class_Otop(tc_fun(U_14936,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14936,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3740_1]) ).

fof(f_3740_3,plain,
    ! [U_14936] : hAPP(c_Set_Oimage(U_14936,U_14936,c_Fun_Oid(U_14936)),c_Orderings_Otop__class_Otop(tc_fun(U_14936,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14936,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3740_2]) ).

cnf(f_3740_4,plain,
    hAPP(c_Set_Oimage(U_14936,U_14936,c_Fun_Oid(U_14936)),c_Orderings_Otop__class_Otop(tc_fun(U_14936,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14936,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3740_3]) ).

fof(f_3741_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_3741_2,plain,
    ! [U_14940,U_14939,U_14938,U_14937] :
      ( hAPP(U_14940,c_Orderings_Obot__class_Obot(tc_fun(U_14937,tc_HOL_Obool))) = c_Fun_Oid(U_14938)
      | ~ c_Finite__Set_Ofolding(U_14937,U_14938,U_14939,U_14940) ),
    inference(variable_rename,[status(thm)],[f_3741_1]) ).

fof(f_3741_3,plain,
    ! [U_14937,U_14938,U_14939,U_14940] :
      ( hAPP(U_14940,c_Orderings_Obot__class_Obot(tc_fun(U_14937,tc_HOL_Obool))) = c_Fun_Oid(U_14938)
      | ~ c_Finite__Set_Ofolding(U_14937,U_14938,U_14939,U_14940) ),
    inference(definitional_conversion,[status(esa)],[f_3741_2]) ).

cnf(f_3741_4,plain,
    ( hAPP(U_14940,c_Orderings_Obot__class_Obot(tc_fun(U_14937,tc_HOL_Obool))) = c_Fun_Oid(U_14938)
    | ~ c_Finite__Set_Ofolding(U_14937,U_14938,U_14939,U_14940) ),
    inference(clausify,[status(thm)],[f_3741_3]) ).

fof(f_3742_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_3742_2,plain,
    ! [U_14944,U_14943,U_14942,U_14941] : c_Product__Type_Oapsnd(U_14941,U_14942,U_14943,U_14944) = c_Product__Type_Omap__pair(U_14943,U_14943,U_14941,U_14942,c_Fun_Oid(U_14943),U_14944),
    inference(variable_rename,[status(thm)],[f_3742_1]) ).

fof(f_3742_3,plain,
    ! [U_14941,U_14942,U_14943,U_14944] : c_Product__Type_Oapsnd(U_14941,U_14942,U_14943,U_14944) = c_Product__Type_Omap__pair(U_14943,U_14943,U_14941,U_14942,c_Fun_Oid(U_14943),U_14944),
    inference(definitional_conversion,[status(esa)],[f_3742_2]) ).

cnf(f_3742_4,plain,
    c_Product__Type_Oapsnd(U_14941,U_14942,U_14943,U_14944) = c_Product__Type_Omap__pair(U_14943,U_14943,U_14941,U_14942,c_Fun_Oid(U_14943),U_14944),
    inference(clausify,[status(thm)],[f_3742_3]) ).

fof(f_3743_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_3743_2,plain,
    ! [U_14948,U_14947,U_14946,U_14945] : c_Product__Type_Oapfst(U_14945,U_14946,U_14947,U_14948) = c_Product__Type_Omap__pair(U_14945,U_14946,U_14947,U_14947,U_14948,c_Fun_Oid(U_14947)),
    inference(variable_rename,[status(thm)],[f_3743_1]) ).

fof(f_3743_3,plain,
    ! [U_14946,U_14945,U_14947,U_14948] : c_Product__Type_Oapfst(U_14945,U_14946,U_14947,U_14948) = c_Product__Type_Omap__pair(U_14945,U_14946,U_14947,U_14947,U_14948,c_Fun_Oid(U_14947)),
    inference(definitional_conversion,[status(esa)],[f_3743_2]) ).

cnf(f_3743_4,plain,
    c_Product__Type_Oapfst(U_14945,U_14946,U_14947,U_14948) = c_Product__Type_Omap__pair(U_14945,U_14946,U_14947,U_14947,U_14948,c_Fun_Oid(U_14947)),
    inference(clausify,[status(thm)],[f_3743_3]) ).

fof(f_3744_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_3744_2,plain,
    ! [U_14950,U_14949] : hAPP(c_Product__Type_Oprod_Oprod__case(U_14949,U_14950,tc_prod(U_14949,U_14950)),c_Product__Type_OPair(U_14949,U_14950)) = c_Fun_Oid(tc_prod(U_14949,U_14950)),
    inference(variable_rename,[status(thm)],[f_3744_1]) ).

fof(f_3744_3,plain,
    ! [U_14949,U_14950] : hAPP(c_Product__Type_Oprod_Oprod__case(U_14949,U_14950,tc_prod(U_14949,U_14950)),c_Product__Type_OPair(U_14949,U_14950)) = c_Fun_Oid(tc_prod(U_14949,U_14950)),
    inference(definitional_conversion,[status(esa)],[f_3744_2]) ).

cnf(f_3744_4,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_14949,U_14950,tc_prod(U_14949,U_14950)),c_Product__Type_OPair(U_14949,U_14950)) = c_Fun_Oid(tc_prod(U_14949,U_14950)),
    inference(clausify,[status(thm)],[f_3744_3]) ).

fof(f_3745_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_3745_2,plain,
    ! [U_14954,U_14953,U_14952,U_14951] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14952,U_14951),U_14953),U_14954) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14951,U_14951),c_Fun_Oid(U_14951)),hAPP(c_Set_Oimage(U_14952,U_14951,U_14953),U_14954))
      | ~ c_Fun_Oinj__on(U_14952,U_14951,U_14953,U_14954)
      | ~ class_Groups_Ocomm__monoid__add(U_14951) ),
    inference(variable_rename,[status(thm)],[f_3745_1]) ).

fof(f_3745_3,plain,
    ! [U_14951,U_14952,U_14953,U_14954] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14952,U_14951),U_14953),U_14954) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14951,U_14951),c_Fun_Oid(U_14951)),hAPP(c_Set_Oimage(U_14952,U_14951,U_14953),U_14954))
      | ~ c_Fun_Oinj__on(U_14952,U_14951,U_14953,U_14954)
      | ~ class_Groups_Ocomm__monoid__add(U_14951) ),
    inference(definitional_conversion,[status(esa)],[f_3745_2]) ).

cnf(f_3745_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14952,U_14951),U_14953),U_14954) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14951,U_14951),c_Fun_Oid(U_14951)),hAPP(c_Set_Oimage(U_14952,U_14951,U_14953),U_14954))
    | ~ c_Fun_Oinj__on(U_14952,U_14951,U_14953,U_14954)
    | ~ class_Groups_Ocomm__monoid__add(U_14951) ),
    inference(clausify,[status(thm)],[f_3745_3]) ).

fof(f_3746_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_3746_2,plain,
    ! [U_14958,U_14957,U_14956,U_14955] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14956,U_14955),U_14957),U_14958) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14955,U_14955),c_Fun_Oid(U_14955)),hAPP(c_Set_Oimage(U_14956,U_14955,U_14957),U_14958))
      | ~ c_Fun_Oinj__on(U_14956,U_14955,U_14957,U_14958)
      | ~ class_Groups_Ocomm__monoid__mult(U_14955) ),
    inference(variable_rename,[status(thm)],[f_3746_1]) ).

fof(f_3746_3,plain,
    ! [U_14955,U_14956,U_14957,U_14958] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14956,U_14955),U_14957),U_14958) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14955,U_14955),c_Fun_Oid(U_14955)),hAPP(c_Set_Oimage(U_14956,U_14955,U_14957),U_14958))
      | ~ c_Fun_Oinj__on(U_14956,U_14955,U_14957,U_14958)
      | ~ class_Groups_Ocomm__monoid__mult(U_14955) ),
    inference(definitional_conversion,[status(esa)],[f_3746_2]) ).

cnf(f_3746_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14956,U_14955),U_14957),U_14958) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14955,U_14955),c_Fun_Oid(U_14955)),hAPP(c_Set_Oimage(U_14956,U_14955,U_14957),U_14958))
    | ~ c_Fun_Oinj__on(U_14956,U_14955,U_14957,U_14958)
    | ~ class_Groups_Ocomm__monoid__mult(U_14955) ),
    inference(clausify,[status(thm)],[f_3746_3]) ).

fof(f_3747_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_3747_2,plain,
    ! [U_14964,U_14963] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14963),U_14964))
        | ! [U_14962,U_14961] : U_14964 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_14963,U_14961),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_14962))) )
      & ( ? [U_14960,U_14959] : U_14964 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_14963,U_14959),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_14960)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14963),U_14964)) ) ),
    inference(variable_rename,[status(thm)],[f_3747_1]) ).

fof(f_3747_3,plain,
    ( ! [U_14968,U_14966] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14966),U_14968))
        | ! [U_14962,U_14961] : U_14968 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_14966,U_14961),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_14962))) )
    & ! [U_14967,U_14965] :
        ( ? [U_14960,U_14959] : U_14967 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_14965,U_14959),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_14960)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14965),U_14967)) ) ),
    inference(miniscope,[status(thm)],[f_3747_2]) ).

fof(f_3747_4,plain,
    ( ! [U_14968,U_14966] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14966),U_14968))
        | ! [U_14962,U_14961] : U_14968 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_14966,U_14961),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_14962))) )
    & ! [U_14967,U_14965] :
        ( ? [U_14959] : U_14967 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_14965,U_14959),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)),sK336(U_14967,U_14965))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14965),U_14967)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK336]),skolemize(U_14960,sK336(U_14967,U_14965))],[f_3747_3]) ).

fof(f_3747_5,plain,
    ( ! [U_14968,U_14966] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14966),U_14968))
        | ! [U_14962,U_14961] : U_14968 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_14966,U_14961),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_14962))) )
    & ! [U_14967,U_14965] :
        ( U_14967 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_14965,sK337(U_14967,U_14965)),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)),sK336(U_14967,U_14965))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14965),U_14967)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK337]),skolemize(U_14959,sK337(U_14967,U_14965))],[f_3747_4]) ).

fof(f_3747_6,plain,
    ( ! [U_14961,U_14968,U_14962,U_14966] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14966),U_14968))
        | U_14968 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_14966,U_14961),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_14962))) )
    & ! [U_14967,U_14965] :
        ( U_14967 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_14965,sK337(U_14967,U_14965)),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)),sK336(U_14967,U_14965))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14965),U_14967)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3747_5]) ).

cnf(f_3747_7,plain,
    ( U_14967 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_14965,sK337(U_14967,U_14965)),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)),sK336(U_14967,U_14965))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14965),U_14967)) ),
    inference(clausify,[status(thm)],[f_3747_6]) ).

cnf(f_3747_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14966),U_14968))
    | U_14968 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_14966,U_14961),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_14962))) ),
    inference(clausify,[status(thm)],[f_3747_6]) ).

fof(f_3748_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_3748_2,plain,
    ! [U_14973,U_14972,U_14971,U_14970,U_14969] : hAPP(hAPP(c_Relation_Orel__comp(U_14969,U_14970,U_14971),U_14972),U_14973) = hAPP(c_Set_OCollect(tc_prod(U_14969,U_14971)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14969,U_14971,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14971,tc_fun(U_14970,tc_HOL_Obool)),tc_fun(U_14971,tc_HOL_Obool),U_14969),hAPP(c_COMBB(tc_fun(U_14970,tc_HOL_Obool),tc_HOL_Obool,U_14971),c_HOL_OEx(U_14970))),hAPP(hAPP(c_COMBC(U_14969,tc_fun(U_14971,tc_fun(U_14970,tc_HOL_Obool)),tc_fun(U_14971,tc_fun(U_14970,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14970,tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),tc_fun(tc_fun(U_14971,tc_fun(U_14970,tc_HOL_Obool)),tc_fun(U_14971,tc_fun(U_14970,tc_HOL_Obool))),U_14969),c_COMBB(tc_fun(U_14970,tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool),U_14971)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14970,tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),U_14969),c_COMBS(U_14970,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_HOL_Obool),tc_fun(U_14970,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14969),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14970),c_fconj)),hAPP(hAPP(c_COMBC(U_14969,tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_fun(tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),U_14969),c_COMBC(U_14970,tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_prod(U_14969,U_14970)),tc_fun(U_14970,tc_fun(tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_HOL_Obool)),U_14969),hAPP(c_COMBB(tc_prod(U_14969,U_14970),tc_fun(tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_HOL_Obool),U_14970),c_member(tc_prod(U_14969,U_14970)))),c_Product__Type_OPair(U_14969,U_14970)))),U_14972))))),hAPP(hAPP(c_COMBC(U_14971,tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_fun(tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),U_14971),c_COMBC(U_14970,tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_prod(U_14970,U_14971)),tc_fun(U_14970,tc_fun(tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_HOL_Obool)),U_14971),hAPP(c_COMBB(tc_prod(U_14970,U_14971),tc_fun(tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_HOL_Obool),U_14970),c_member(tc_prod(U_14970,U_14971)))),hAPP(c_COMBC(U_14970,U_14971,tc_prod(U_14970,U_14971)),c_Product__Type_OPair(U_14970,U_14971))))),U_14973))))),
    inference(variable_rename,[status(thm)],[f_3748_1]) ).

fof(f_3748_3,plain,
    ! [U_14969,U_14970,U_14971,U_14972,U_14973] : hAPP(hAPP(c_Relation_Orel__comp(U_14969,U_14970,U_14971),U_14972),U_14973) = hAPP(c_Set_OCollect(tc_prod(U_14969,U_14971)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14969,U_14971,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14971,tc_fun(U_14970,tc_HOL_Obool)),tc_fun(U_14971,tc_HOL_Obool),U_14969),hAPP(c_COMBB(tc_fun(U_14970,tc_HOL_Obool),tc_HOL_Obool,U_14971),c_HOL_OEx(U_14970))),hAPP(hAPP(c_COMBC(U_14969,tc_fun(U_14971,tc_fun(U_14970,tc_HOL_Obool)),tc_fun(U_14971,tc_fun(U_14970,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14970,tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),tc_fun(tc_fun(U_14971,tc_fun(U_14970,tc_HOL_Obool)),tc_fun(U_14971,tc_fun(U_14970,tc_HOL_Obool))),U_14969),c_COMBB(tc_fun(U_14970,tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool),U_14971)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14970,tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),U_14969),c_COMBS(U_14970,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_HOL_Obool),tc_fun(U_14970,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14969),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14970),c_fconj)),hAPP(hAPP(c_COMBC(U_14969,tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_fun(tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),U_14969),c_COMBC(U_14970,tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_prod(U_14969,U_14970)),tc_fun(U_14970,tc_fun(tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_HOL_Obool)),U_14969),hAPP(c_COMBB(tc_prod(U_14969,U_14970),tc_fun(tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_HOL_Obool),U_14970),c_member(tc_prod(U_14969,U_14970)))),c_Product__Type_OPair(U_14969,U_14970)))),U_14972))))),hAPP(hAPP(c_COMBC(U_14971,tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_fun(tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),U_14971),c_COMBC(U_14970,tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_prod(U_14970,U_14971)),tc_fun(U_14970,tc_fun(tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_HOL_Obool)),U_14971),hAPP(c_COMBB(tc_prod(U_14970,U_14971),tc_fun(tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_HOL_Obool),U_14970),c_member(tc_prod(U_14970,U_14971)))),hAPP(c_COMBC(U_14970,U_14971,tc_prod(U_14970,U_14971)),c_Product__Type_OPair(U_14970,U_14971))))),U_14973))))),
    inference(definitional_conversion,[status(esa)],[f_3748_2]) ).

cnf(f_3748_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14969,U_14970,U_14971),U_14972),U_14973) = hAPP(c_Set_OCollect(tc_prod(U_14969,U_14971)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14969,U_14971,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14971,tc_fun(U_14970,tc_HOL_Obool)),tc_fun(U_14971,tc_HOL_Obool),U_14969),hAPP(c_COMBB(tc_fun(U_14970,tc_HOL_Obool),tc_HOL_Obool,U_14971),c_HOL_OEx(U_14970))),hAPP(hAPP(c_COMBC(U_14969,tc_fun(U_14971,tc_fun(U_14970,tc_HOL_Obool)),tc_fun(U_14971,tc_fun(U_14970,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14970,tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),tc_fun(tc_fun(U_14971,tc_fun(U_14970,tc_HOL_Obool)),tc_fun(U_14971,tc_fun(U_14970,tc_HOL_Obool))),U_14969),c_COMBB(tc_fun(U_14970,tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool),U_14971)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14970,tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),U_14969),c_COMBS(U_14970,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_HOL_Obool),tc_fun(U_14970,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14969),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14970),c_fconj)),hAPP(hAPP(c_COMBC(U_14969,tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_fun(tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),U_14969),c_COMBC(U_14970,tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_prod(U_14969,U_14970)),tc_fun(U_14970,tc_fun(tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_HOL_Obool)),U_14969),hAPP(c_COMBB(tc_prod(U_14969,U_14970),tc_fun(tc_fun(tc_prod(U_14969,U_14970),tc_HOL_Obool),tc_HOL_Obool),U_14970),c_member(tc_prod(U_14969,U_14970)))),c_Product__Type_OPair(U_14969,U_14970)))),U_14972))))),hAPP(hAPP(c_COMBC(U_14971,tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_fun(tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_fun(U_14970,tc_HOL_Obool)),U_14971),c_COMBC(U_14970,tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14970,tc_prod(U_14970,U_14971)),tc_fun(U_14970,tc_fun(tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_HOL_Obool)),U_14971),hAPP(c_COMBB(tc_prod(U_14970,U_14971),tc_fun(tc_fun(tc_prod(U_14970,U_14971),tc_HOL_Obool),tc_HOL_Obool),U_14970),c_member(tc_prod(U_14970,U_14971)))),hAPP(c_COMBC(U_14970,U_14971,tc_prod(U_14970,U_14971)),c_Product__Type_OPair(U_14970,U_14971))))),U_14973))))),
    inference(clausify,[status(thm)],[f_3748_3]) ).

fof(f_3749_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_3749_2,plain,
    ! [U_14981,U_14980,U_14979,U_14978,U_14977,U_14976,U_14975,U_14974] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14974,U_14979)),hAPP(hAPP(c_Product__Type_OPair(U_14974,U_14979),U_14976),U_14980)),hAPP(hAPP(c_Relation_Orel__comp(U_14974,U_14975,U_14979),U_14978),U_14981)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14975,U_14979)),hAPP(hAPP(c_Product__Type_OPair(U_14975,U_14979),U_14977),U_14980)),U_14981))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14974,U_14975)),hAPP(hAPP(c_Product__Type_OPair(U_14974,U_14975),U_14976),U_14977)),U_14978)) ),
    inference(variable_rename,[status(thm)],[f_3749_1]) ).

fof(f_3749_3,plain,
    ! [U_14974,U_14975,U_14976,U_14977,U_14978,U_14979,U_14980,U_14981] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14974,U_14979)),hAPP(hAPP(c_Product__Type_OPair(U_14974,U_14979),U_14976),U_14980)),hAPP(hAPP(c_Relation_Orel__comp(U_14974,U_14975,U_14979),U_14978),U_14981)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14975,U_14979)),hAPP(hAPP(c_Product__Type_OPair(U_14975,U_14979),U_14977),U_14980)),U_14981))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14974,U_14975)),hAPP(hAPP(c_Product__Type_OPair(U_14974,U_14975),U_14976),U_14977)),U_14978)) ),
    inference(definitional_conversion,[status(esa)],[f_3749_2]) ).

cnf(f_3749_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14974,U_14979)),hAPP(hAPP(c_Product__Type_OPair(U_14974,U_14979),U_14976),U_14980)),hAPP(hAPP(c_Relation_Orel__comp(U_14974,U_14975,U_14979),U_14978),U_14981)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14975,U_14979)),hAPP(hAPP(c_Product__Type_OPair(U_14975,U_14979),U_14977),U_14980)),U_14981))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14974,U_14975)),hAPP(hAPP(c_Product__Type_OPair(U_14974,U_14975),U_14976),U_14977)),U_14978)) ),
    inference(clausify,[status(thm)],[f_3749_3]) ).

fof(f_3750_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_3750_2,plain,
    ! [U_14988,U_14987,U_14986,U_14985,U_14984,U_14983,U_14982] : hAPP(hAPP(c_Relation_Orel__comp(U_14982,U_14983,U_14984),U_14985),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14986,tc_fun(tc_prod(U_14983,U_14984),tc_HOL_Obool)),U_14987),U_14988)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14986,tc_fun(tc_prod(U_14982,U_14984),tc_HOL_Obool)),U_14987),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14983,U_14984),tc_HOL_Obool),tc_fun(tc_prod(U_14982,U_14984),tc_HOL_Obool),U_14986),hAPP(c_Relation_Orel__comp(U_14982,U_14983,U_14984),U_14985)),U_14988)),
    inference(variable_rename,[status(thm)],[f_3750_1]) ).

fof(f_3750_3,plain,
    ! [U_14983,U_14982,U_14984,U_14985,U_14986,U_14987,U_14988] : hAPP(hAPP(c_Relation_Orel__comp(U_14982,U_14983,U_14984),U_14985),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14986,tc_fun(tc_prod(U_14983,U_14984),tc_HOL_Obool)),U_14987),U_14988)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14986,tc_fun(tc_prod(U_14982,U_14984),tc_HOL_Obool)),U_14987),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14983,U_14984),tc_HOL_Obool),tc_fun(tc_prod(U_14982,U_14984),tc_HOL_Obool),U_14986),hAPP(c_Relation_Orel__comp(U_14982,U_14983,U_14984),U_14985)),U_14988)),
    inference(definitional_conversion,[status(esa)],[f_3750_2]) ).

cnf(f_3750_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14982,U_14983,U_14984),U_14985),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14986,tc_fun(tc_prod(U_14983,U_14984),tc_HOL_Obool)),U_14987),U_14988)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14986,tc_fun(tc_prod(U_14982,U_14984),tc_HOL_Obool)),U_14987),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14983,U_14984),tc_HOL_Obool),tc_fun(tc_prod(U_14982,U_14984),tc_HOL_Obool),U_14986),hAPP(c_Relation_Orel__comp(U_14982,U_14983,U_14984),U_14985)),U_14988)),
    inference(clausify,[status(thm)],[f_3750_3]) ).

fof(f_3751_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_3751_2,plain,
    ! [U_14995,U_14994,U_14993,U_14992,U_14991,U_14990,U_14989] : hAPP(hAPP(c_Relation_Orel__comp(U_14989,U_14990,U_14991),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14992,tc_fun(tc_prod(U_14989,U_14990),tc_HOL_Obool)),U_14993),U_14994)),U_14995) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14992,tc_fun(tc_prod(U_14989,U_14991),tc_HOL_Obool)),U_14993),hAPP(hAPP(c_COMBC(U_14992,tc_fun(tc_prod(U_14990,U_14991),tc_HOL_Obool),tc_fun(tc_prod(U_14989,U_14991),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14989,U_14990),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_14990,U_14991),tc_HOL_Obool),tc_fun(tc_prod(U_14989,U_14991),tc_HOL_Obool)),U_14992),c_Relation_Orel__comp(U_14989,U_14990,U_14991)),U_14994)),U_14995)),
    inference(variable_rename,[status(thm)],[f_3751_1]) ).

fof(f_3751_3,plain,
    ! [U_14989,U_14990,U_14991,U_14992,U_14993,U_14994,U_14995] : hAPP(hAPP(c_Relation_Orel__comp(U_14989,U_14990,U_14991),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14992,tc_fun(tc_prod(U_14989,U_14990),tc_HOL_Obool)),U_14993),U_14994)),U_14995) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14992,tc_fun(tc_prod(U_14989,U_14991),tc_HOL_Obool)),U_14993),hAPP(hAPP(c_COMBC(U_14992,tc_fun(tc_prod(U_14990,U_14991),tc_HOL_Obool),tc_fun(tc_prod(U_14989,U_14991),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14989,U_14990),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_14990,U_14991),tc_HOL_Obool),tc_fun(tc_prod(U_14989,U_14991),tc_HOL_Obool)),U_14992),c_Relation_Orel__comp(U_14989,U_14990,U_14991)),U_14994)),U_14995)),
    inference(definitional_conversion,[status(esa)],[f_3751_2]) ).

cnf(f_3751_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14989,U_14990,U_14991),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14992,tc_fun(tc_prod(U_14989,U_14990),tc_HOL_Obool)),U_14993),U_14994)),U_14995) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14992,tc_fun(tc_prod(U_14989,U_14991),tc_HOL_Obool)),U_14993),hAPP(hAPP(c_COMBC(U_14992,tc_fun(tc_prod(U_14990,U_14991),tc_HOL_Obool),tc_fun(tc_prod(U_14989,U_14991),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14989,U_14990),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_14990,U_14991),tc_HOL_Obool),tc_fun(tc_prod(U_14989,U_14991),tc_HOL_Obool)),U_14992),c_Relation_Orel__comp(U_14989,U_14990,U_14991)),U_14994)),U_14995)),
    inference(clausify,[status(thm)],[f_3751_3]) ).

fof(f_3752_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_3752_2,plain,
    ! [U_15001,U_15000,U_14999,U_14998,U_14997,U_14996] : hAPP(hAPP(c_Relation_Orel__comp(U_14996,U_14997,U_14998),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14996,U_14997),tc_HOL_Obool)),U_14999),U_15000)),U_15001) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14996,U_14998),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14996,U_14997,U_14998),U_14999),U_15001)),hAPP(hAPP(c_Relation_Orel__comp(U_14996,U_14997,U_14998),U_15000),U_15001)),
    inference(variable_rename,[status(thm)],[f_3752_1]) ).

fof(f_3752_3,plain,
    ! [U_14996,U_14997,U_14998,U_14999,U_15000,U_15001] : hAPP(hAPP(c_Relation_Orel__comp(U_14996,U_14997,U_14998),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14996,U_14997),tc_HOL_Obool)),U_14999),U_15000)),U_15001) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14996,U_14998),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14996,U_14997,U_14998),U_14999),U_15001)),hAPP(hAPP(c_Relation_Orel__comp(U_14996,U_14997,U_14998),U_15000),U_15001)),
    inference(definitional_conversion,[status(esa)],[f_3752_2]) ).

cnf(f_3752_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14996,U_14997,U_14998),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14996,U_14997),tc_HOL_Obool)),U_14999),U_15000)),U_15001) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14996,U_14998),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14996,U_14997,U_14998),U_14999),U_15001)),hAPP(hAPP(c_Relation_Orel__comp(U_14996,U_14997,U_14998),U_15000),U_15001)),
    inference(clausify,[status(thm)],[f_3752_3]) ).

fof(f_3753_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_3753_2,plain,
    ! [U_15007,U_15006,U_15005,U_15004,U_15003,U_15002] : hAPP(hAPP(c_Relation_Orel__comp(U_15002,U_15003,U_15004),U_15005),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15003,U_15004),tc_HOL_Obool)),U_15006),U_15007)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15002,U_15004),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15002,U_15003,U_15004),U_15005),U_15006)),hAPP(hAPP(c_Relation_Orel__comp(U_15002,U_15003,U_15004),U_15005),U_15007)),
    inference(variable_rename,[status(thm)],[f_3753_1]) ).

fof(f_3753_3,plain,
    ! [U_15002,U_15003,U_15004,U_15005,U_15006,U_15007] : hAPP(hAPP(c_Relation_Orel__comp(U_15002,U_15003,U_15004),U_15005),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15003,U_15004),tc_HOL_Obool)),U_15006),U_15007)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15002,U_15004),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15002,U_15003,U_15004),U_15005),U_15006)),hAPP(hAPP(c_Relation_Orel__comp(U_15002,U_15003,U_15004),U_15005),U_15007)),
    inference(definitional_conversion,[status(esa)],[f_3753_2]) ).

cnf(f_3753_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_15002,U_15003,U_15004),U_15005),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15003,U_15004),tc_HOL_Obool)),U_15006),U_15007)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15002,U_15004),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15002,U_15003,U_15004),U_15005),U_15006)),hAPP(hAPP(c_Relation_Orel__comp(U_15002,U_15003,U_15004),U_15005),U_15007)),
    inference(clausify,[status(thm)],[f_3753_3]) ).

fof(f_3754_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_3754_2,plain,
    ! [U_15011,U_15010,U_15009,U_15008] : hAPP(hAPP(c_Relation_Orel__comp(U_15008,U_15009,U_15010),U_15011),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15009,U_15010),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15008,U_15010),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3754_1]) ).

fof(f_3754_3,plain,
    ! [U_15008,U_15009,U_15010,U_15011] : hAPP(hAPP(c_Relation_Orel__comp(U_15008,U_15009,U_15010),U_15011),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15009,U_15010),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15008,U_15010),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3754_2]) ).

cnf(f_3754_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_15008,U_15009,U_15010),U_15011),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15009,U_15010),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15008,U_15010),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3754_3]) ).

fof(f_3755_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_3755_2,plain,
    ! [U_15015,U_15014,U_15013,U_15012] : hAPP(hAPP(c_Relation_Orel__comp(U_15012,U_15013,U_15014),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15012,U_15013),tc_HOL_Obool))),U_15015) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15012,U_15014),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3755_1]) ).

fof(f_3755_3,plain,
    ! [U_15012,U_15013,U_15014,U_15015] : hAPP(hAPP(c_Relation_Orel__comp(U_15012,U_15013,U_15014),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15012,U_15013),tc_HOL_Obool))),U_15015) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15012,U_15014),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3755_2]) ).

cnf(f_3755_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_15012,U_15013,U_15014),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15012,U_15013),tc_HOL_Obool))),U_15015) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15012,U_15014),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3755_3]) ).

fof(f_3756_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_3756_2,plain,
    ! [U_15022,U_15021,U_15020,U_15019,U_15018,U_15017,U_15016] : hAPP(hAPP(c_Relation_Orel__comp(U_15016,U_15017,U_15018),hAPP(hAPP(c_Relation_Orel__comp(U_15016,U_15019,U_15017),U_15020),U_15021)),U_15022) = hAPP(hAPP(c_Relation_Orel__comp(U_15016,U_15019,U_15018),U_15020),hAPP(hAPP(c_Relation_Orel__comp(U_15019,U_15017,U_15018),U_15021),U_15022)),
    inference(variable_rename,[status(thm)],[f_3756_1]) ).

fof(f_3756_3,plain,
    ! [U_15016,U_15017,U_15018,U_15019,U_15020,U_15021,U_15022] : hAPP(hAPP(c_Relation_Orel__comp(U_15016,U_15017,U_15018),hAPP(hAPP(c_Relation_Orel__comp(U_15016,U_15019,U_15017),U_15020),U_15021)),U_15022) = hAPP(hAPP(c_Relation_Orel__comp(U_15016,U_15019,U_15018),U_15020),hAPP(hAPP(c_Relation_Orel__comp(U_15019,U_15017,U_15018),U_15021),U_15022)),
    inference(definitional_conversion,[status(esa)],[f_3756_2]) ).

cnf(f_3756_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_15016,U_15017,U_15018),hAPP(hAPP(c_Relation_Orel__comp(U_15016,U_15019,U_15017),U_15020),U_15021)),U_15022) = hAPP(hAPP(c_Relation_Orel__comp(U_15016,U_15019,U_15018),U_15020),hAPP(hAPP(c_Relation_Orel__comp(U_15019,U_15017,U_15018),U_15021),U_15022)),
    inference(clausify,[status(thm)],[f_3756_3]) ).

fof(f_3757_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_3757_2,plain,
    ! [U_15029,U_15028,U_15027,U_15026,U_15025,U_15024,U_15023] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15023,U_15027),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15023,U_15024,U_15027),U_15025),U_15028)),hAPP(hAPP(c_Relation_Orel__comp(U_15023,U_15024,U_15027),U_15026),U_15029)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15024,U_15027),tc_HOL_Obool)),U_15028),U_15029))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15023,U_15024),tc_HOL_Obool)),U_15025),U_15026)) ),
    inference(variable_rename,[status(thm)],[f_3757_1]) ).

fof(f_3757_3,plain,
    ! [U_15023,U_15024,U_15025,U_15026,U_15027,U_15028,U_15029] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15023,U_15027),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15023,U_15024,U_15027),U_15025),U_15028)),hAPP(hAPP(c_Relation_Orel__comp(U_15023,U_15024,U_15027),U_15026),U_15029)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15024,U_15027),tc_HOL_Obool)),U_15028),U_15029))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15023,U_15024),tc_HOL_Obool)),U_15025),U_15026)) ),
    inference(definitional_conversion,[status(esa)],[f_3757_2]) ).

cnf(f_3757_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15023,U_15027),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15023,U_15024,U_15027),U_15025),U_15028)),hAPP(hAPP(c_Relation_Orel__comp(U_15023,U_15024,U_15027),U_15026),U_15029)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15024,U_15027),tc_HOL_Obool)),U_15028),U_15029))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15023,U_15024),tc_HOL_Obool)),U_15025),U_15026)) ),
    inference(clausify,[status(thm)],[f_3757_3]) ).

fof(f_3758_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_3758_2,plain,
    ! [U_15033,U_15032,U_15031,U_15030] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_15030,U_15030,U_15030),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15030,U_15030),tc_HOL_Obool)),U_15031),U_15033)),U_15032) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15030,U_15030),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_15030,U_15030,U_15030),U_15033),U_15032) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15030,U_15030),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_15030,U_15030,U_15030),U_15031),U_15032) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15030,U_15030),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3758_1]) ).

fof(f_3758_3,plain,
    ! [U_15030,U_15031,U_15032,U_15033] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_15030,U_15030,U_15030),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15030,U_15030),tc_HOL_Obool)),U_15031),U_15033)),U_15032) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15030,U_15030),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_15030,U_15030,U_15030),U_15033),U_15032) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15030,U_15030),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_15030,U_15030,U_15030),U_15031),U_15032) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15030,U_15030),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3758_2]) ).

cnf(f_3758_4,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_15030,U_15030,U_15030),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15030,U_15030),tc_HOL_Obool)),U_15031),U_15033)),U_15032) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15030,U_15030),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_15030,U_15030,U_15030),U_15033),U_15032) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15030,U_15030),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_15030,U_15030,U_15030),U_15031),U_15032) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15030,U_15030),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3758_3]) ).

fof(f_3759_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_3759_2,plain,
    ! [U_15037,U_15036,U_15035,U_15034] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_15034,U_15034,U_15034),U_15035),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15034,U_15034),tc_HOL_Obool)),U_15036),U_15037)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15034,U_15034),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_15034,U_15034,U_15034),U_15035),U_15037) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15034,U_15034),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_15034,U_15034,U_15034),U_15035),U_15036) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15034,U_15034),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3759_1]) ).

fof(f_3759_3,plain,
    ! [U_15034,U_15035,U_15036,U_15037] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_15034,U_15034,U_15034),U_15035),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15034,U_15034),tc_HOL_Obool)),U_15036),U_15037)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15034,U_15034),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_15034,U_15034,U_15034),U_15035),U_15037) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15034,U_15034),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_15034,U_15034,U_15034),U_15035),U_15036) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15034,U_15034),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3759_2]) ).

cnf(f_3759_4,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_15034,U_15034,U_15034),U_15035),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15034,U_15034),tc_HOL_Obool)),U_15036),U_15037)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15034,U_15034),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_15034,U_15034,U_15034),U_15035),U_15037) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15034,U_15034),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_15034,U_15034,U_15034),U_15035),U_15036) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15034,U_15034),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3759_3]) ).

fof(f_3760_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_3760_2,plain,
    ! [U_15045,U_15044,U_15043,U_15042,U_15041,U_15040,U_15039,U_15038] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15038,U_15043),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15038,U_15039,U_15043),U_15040),U_15044)),hAPP(hAPP(c_Product__Type_OSigma(U_15038,U_15043),U_15041),hAPP(c_COMBK(tc_fun(U_15043,tc_HOL_Obool),U_15038),U_15045))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15039,U_15043),tc_HOL_Obool)),U_15044),hAPP(hAPP(c_Product__Type_OSigma(U_15039,U_15043),U_15042),hAPP(c_COMBK(tc_fun(U_15043,tc_HOL_Obool),U_15039),U_15045))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15038,U_15039),tc_HOL_Obool)),U_15040),hAPP(hAPP(c_Product__Type_OSigma(U_15038,U_15039),U_15041),hAPP(c_COMBK(tc_fun(U_15039,tc_HOL_Obool),U_15038),U_15042)))) ),
    inference(variable_rename,[status(thm)],[f_3760_1]) ).

fof(f_3760_3,plain,
    ! [U_15038,U_15039,U_15040,U_15041,U_15042,U_15043,U_15044,U_15045] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15038,U_15043),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15038,U_15039,U_15043),U_15040),U_15044)),hAPP(hAPP(c_Product__Type_OSigma(U_15038,U_15043),U_15041),hAPP(c_COMBK(tc_fun(U_15043,tc_HOL_Obool),U_15038),U_15045))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15039,U_15043),tc_HOL_Obool)),U_15044),hAPP(hAPP(c_Product__Type_OSigma(U_15039,U_15043),U_15042),hAPP(c_COMBK(tc_fun(U_15043,tc_HOL_Obool),U_15039),U_15045))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15038,U_15039),tc_HOL_Obool)),U_15040),hAPP(hAPP(c_Product__Type_OSigma(U_15038,U_15039),U_15041),hAPP(c_COMBK(tc_fun(U_15039,tc_HOL_Obool),U_15038),U_15042)))) ),
    inference(definitional_conversion,[status(esa)],[f_3760_2]) ).

cnf(f_3760_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15038,U_15043),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15038,U_15039,U_15043),U_15040),U_15044)),hAPP(hAPP(c_Product__Type_OSigma(U_15038,U_15043),U_15041),hAPP(c_COMBK(tc_fun(U_15043,tc_HOL_Obool),U_15038),U_15045))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15039,U_15043),tc_HOL_Obool)),U_15044),hAPP(hAPP(c_Product__Type_OSigma(U_15039,U_15043),U_15042),hAPP(c_COMBK(tc_fun(U_15043,tc_HOL_Obool),U_15039),U_15045))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15038,U_15039),tc_HOL_Obool)),U_15040),hAPP(hAPP(c_Product__Type_OSigma(U_15038,U_15039),U_15041),hAPP(c_COMBK(tc_fun(U_15039,tc_HOL_Obool),U_15038),U_15042)))) ),
    inference(clausify,[status(thm)],[f_3760_3]) ).

fof(f_3761_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_3761_2,plain,
    ! [U_15048,U_15047,U_15046] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_15046,U_15047)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_15046,U_15048)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_15046,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_15046,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_15046,U_15047)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15046,U_15046),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15046,U_15046,U_15046),U_15047),U_15048)),U_15047)) ),
    inference(variable_rename,[status(thm)],[f_3761_1]) ).

fof(f_3761_3,plain,
    ! [U_15046,U_15047,U_15048] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_15046,U_15047)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_15046,U_15048)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_15046,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_15046,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_15046,U_15047)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15046,U_15046),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15046,U_15046,U_15046),U_15047),U_15048)),U_15047)) ),
    inference(definitional_conversion,[status(esa)],[f_3761_2]) ).

cnf(f_3761_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_15046,U_15047)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_15046,U_15048)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_15046,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_15046,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_15046,tc_HOL_Obool),tc_fun(U_15046,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_15046,U_15047)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15046,U_15046),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15046,U_15046,U_15046),U_15047),U_15048)),U_15047)) ),
    inference(clausify,[status(thm)],[f_3761_3]) ).

fof(f_3762_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_3762_2,plain,
    ! [U_15051,U_15050,U_15049] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_15049,U_15050)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_15049,U_15051)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_15049,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_15049,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_15049,U_15050)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15049,U_15049),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15049,U_15049,U_15049),U_15050),U_15051)),U_15050)) ),
    inference(variable_rename,[status(thm)],[f_3762_1]) ).

fof(f_3762_3,plain,
    ! [U_15049,U_15050,U_15051] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_15049,U_15050)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_15049,U_15051)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_15049,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_15049,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_15049,U_15050)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15049,U_15049),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15049,U_15049,U_15049),U_15050),U_15051)),U_15050)) ),
    inference(definitional_conversion,[status(esa)],[f_3762_2]) ).

cnf(f_3762_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_15049,U_15050)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_15049,U_15051)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_15049,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_15049,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_15049,tc_HOL_Obool),tc_fun(U_15049,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_15049,U_15050)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15049,U_15049),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15049,U_15049,U_15049),U_15050),U_15051)),U_15050)) ),
    inference(clausify,[status(thm)],[f_3762_3]) ).

fof(f_3763_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_3763_2,plain,
    ! [U_15058,U_15057,U_15056,U_15055,U_15054,U_15053,U_15052] :
      ( ( c_Predicate_Opred__comp(U_15052,U_15053,U_15054,hAPP(hAPP(c_COMBC(U_15052,tc_fun(tc_prod(U_15052,U_15053),tc_HOL_Obool),tc_fun(U_15053,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15053,tc_fun(tc_fun(tc_prod(U_15052,U_15053),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15052,U_15053),tc_HOL_Obool),tc_fun(U_15053,tc_HOL_Obool)),U_15052),c_COMBC(U_15053,tc_fun(tc_prod(U_15052,U_15053),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15053,tc_prod(U_15052,U_15053)),tc_fun(U_15053,tc_fun(tc_fun(tc_prod(U_15052,U_15053),tc_HOL_Obool),tc_HOL_Obool)),U_15052),hAPP(c_COMBB(tc_prod(U_15052,U_15053),tc_fun(tc_fun(tc_prod(U_15052,U_15053),tc_HOL_Obool),tc_HOL_Obool),U_15053),c_member(tc_prod(U_15052,U_15053)))),c_Product__Type_OPair(U_15052,U_15053)))),U_15055),hAPP(hAPP(c_COMBC(U_15053,tc_fun(tc_prod(U_15053,U_15054),tc_HOL_Obool),tc_fun(U_15054,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15054,tc_fun(tc_fun(tc_prod(U_15053,U_15054),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15053,U_15054),tc_HOL_Obool),tc_fun(U_15054,tc_HOL_Obool)),U_15053),c_COMBC(U_15054,tc_fun(tc_prod(U_15053,U_15054),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15054,tc_prod(U_15053,U_15054)),tc_fun(U_15054,tc_fun(tc_fun(tc_prod(U_15053,U_15054),tc_HOL_Obool),tc_HOL_Obool)),U_15053),hAPP(c_COMBB(tc_prod(U_15053,U_15054),tc_fun(tc_fun(tc_prod(U_15053,U_15054),tc_HOL_Obool),tc_HOL_Obool),U_15054),c_member(tc_prod(U_15053,U_15054)))),c_Product__Type_OPair(U_15053,U_15054)))),U_15056),U_15057,U_15058)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15052,U_15054)),hAPP(hAPP(c_Product__Type_OPair(U_15052,U_15054),U_15057),U_15058)),hAPP(hAPP(c_Relation_Orel__comp(U_15052,U_15053,U_15054),U_15055),U_15056))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15052,U_15054)),hAPP(hAPP(c_Product__Type_OPair(U_15052,U_15054),U_15057),U_15058)),hAPP(hAPP(c_Relation_Orel__comp(U_15052,U_15053,U_15054),U_15055),U_15056)))
        | ~ c_Predicate_Opred__comp(U_15052,U_15053,U_15054,hAPP(hAPP(c_COMBC(U_15052,tc_fun(tc_prod(U_15052,U_15053),tc_HOL_Obool),tc_fun(U_15053,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15053,tc_fun(tc_fun(tc_prod(U_15052,U_15053),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15052,U_15053),tc_HOL_Obool),tc_fun(U_15053,tc_HOL_Obool)),U_15052),c_COMBC(U_15053,tc_fun(tc_prod(U_15052,U_15053),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15053,tc_prod(U_15052,U_15053)),tc_fun(U_15053,tc_fun(tc_fun(tc_prod(U_15052,U_15053),tc_HOL_Obool),tc_HOL_Obool)),U_15052),hAPP(c_COMBB(tc_prod(U_15052,U_15053),tc_fun(tc_fun(tc_prod(U_15052,U_15053),tc_HOL_Obool),tc_HOL_Obool),U_15053),c_member(tc_prod(U_15052,U_15053)))),c_Product__Type_OPair(U_15052,U_15053)))),U_15055),hAPP(hAPP(c_COMBC(U_15053,tc_fun(tc_prod(U_15053,U_15054),tc_HOL_Obool),tc_fun(U_15054,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15054,tc_fun(tc_fun(tc_prod(U_15053,U_15054),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15053,U_15054),tc_HOL_Obool),tc_fun(U_15054,tc_HOL_Obool)),U_15053),c_COMBC(U_15054,tc_fun(tc_prod(U_15053,U_15054),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15054,tc_prod(U_15053,U_15054)),tc_fun(U_15054,tc_fun(tc_fun(tc_prod(U_15053,U_15054),tc_HOL_Obool),tc_HOL_Obool)),U_15053),hAPP(c_COMBB(tc_prod(U_15053,U_15054),tc_fun(tc_fun(tc_prod(U_15053,U_15054),tc_HOL_Obool),tc_HOL_Obool),U_15054),c_member(tc_prod(U_15053,U_15054)))),c_Product__Type_OPair(U_15053,U_15054)))),U_15056),U_15057,U_15058) ) ),
    inference(variable_rename,[status(thm)],[f_3763_1]) ).

fof(f_3763_3,plain,
    ( ! [U_15072,U_15070,U_15068,U_15066,U_15064,U_15062,U_15060] :
        ( c_Predicate_Opred__comp(U_15060,U_15062,U_15064,hAPP(hAPP(c_COMBC(U_15060,tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_fun(U_15062,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15062,tc_fun(tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_fun(U_15062,tc_HOL_Obool)),U_15060),c_COMBC(U_15062,tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15062,tc_prod(U_15060,U_15062)),tc_fun(U_15062,tc_fun(tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_HOL_Obool)),U_15060),hAPP(c_COMBB(tc_prod(U_15060,U_15062),tc_fun(tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_HOL_Obool),U_15062),c_member(tc_prod(U_15060,U_15062)))),c_Product__Type_OPair(U_15060,U_15062)))),U_15066),hAPP(hAPP(c_COMBC(U_15062,tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_fun(U_15064,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15064,tc_fun(tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_fun(U_15064,tc_HOL_Obool)),U_15062),c_COMBC(U_15064,tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15064,tc_prod(U_15062,U_15064)),tc_fun(U_15064,tc_fun(tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_HOL_Obool)),U_15062),hAPP(c_COMBB(tc_prod(U_15062,U_15064),tc_fun(tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_HOL_Obool),U_15064),c_member(tc_prod(U_15062,U_15064)))),c_Product__Type_OPair(U_15062,U_15064)))),U_15068),U_15070,U_15072)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15060,U_15064)),hAPP(hAPP(c_Product__Type_OPair(U_15060,U_15064),U_15070),U_15072)),hAPP(hAPP(c_Relation_Orel__comp(U_15060,U_15062,U_15064),U_15066),U_15068))) )
    & ! [U_15071,U_15069,U_15067,U_15065,U_15063,U_15061,U_15059] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15059,U_15063)),hAPP(hAPP(c_Product__Type_OPair(U_15059,U_15063),U_15069),U_15071)),hAPP(hAPP(c_Relation_Orel__comp(U_15059,U_15061,U_15063),U_15065),U_15067)))
        | ~ c_Predicate_Opred__comp(U_15059,U_15061,U_15063,hAPP(hAPP(c_COMBC(U_15059,tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_fun(U_15061,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15061,tc_fun(tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_fun(U_15061,tc_HOL_Obool)),U_15059),c_COMBC(U_15061,tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15061,tc_prod(U_15059,U_15061)),tc_fun(U_15061,tc_fun(tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_HOL_Obool)),U_15059),hAPP(c_COMBB(tc_prod(U_15059,U_15061),tc_fun(tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_HOL_Obool),U_15061),c_member(tc_prod(U_15059,U_15061)))),c_Product__Type_OPair(U_15059,U_15061)))),U_15065),hAPP(hAPP(c_COMBC(U_15061,tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_fun(U_15063,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15063,tc_fun(tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_fun(U_15063,tc_HOL_Obool)),U_15061),c_COMBC(U_15063,tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15063,tc_prod(U_15061,U_15063)),tc_fun(U_15063,tc_fun(tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_HOL_Obool)),U_15061),hAPP(c_COMBB(tc_prod(U_15061,U_15063),tc_fun(tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_HOL_Obool),U_15063),c_member(tc_prod(U_15061,U_15063)))),c_Product__Type_OPair(U_15061,U_15063)))),U_15067),U_15069,U_15071) ) ),
    inference(miniscope,[status(thm)],[f_3763_2]) ).

fof(f_3763_4,plain,
    ( ! [U_15060,U_15062,U_15064,U_15066,U_15068,U_15070,U_15072] :
        ( c_Predicate_Opred__comp(U_15060,U_15062,U_15064,hAPP(hAPP(c_COMBC(U_15060,tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_fun(U_15062,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15062,tc_fun(tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_fun(U_15062,tc_HOL_Obool)),U_15060),c_COMBC(U_15062,tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15062,tc_prod(U_15060,U_15062)),tc_fun(U_15062,tc_fun(tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_HOL_Obool)),U_15060),hAPP(c_COMBB(tc_prod(U_15060,U_15062),tc_fun(tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_HOL_Obool),U_15062),c_member(tc_prod(U_15060,U_15062)))),c_Product__Type_OPair(U_15060,U_15062)))),U_15066),hAPP(hAPP(c_COMBC(U_15062,tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_fun(U_15064,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15064,tc_fun(tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_fun(U_15064,tc_HOL_Obool)),U_15062),c_COMBC(U_15064,tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15064,tc_prod(U_15062,U_15064)),tc_fun(U_15064,tc_fun(tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_HOL_Obool)),U_15062),hAPP(c_COMBB(tc_prod(U_15062,U_15064),tc_fun(tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_HOL_Obool),U_15064),c_member(tc_prod(U_15062,U_15064)))),c_Product__Type_OPair(U_15062,U_15064)))),U_15068),U_15070,U_15072)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15060,U_15064)),hAPP(hAPP(c_Product__Type_OPair(U_15060,U_15064),U_15070),U_15072)),hAPP(hAPP(c_Relation_Orel__comp(U_15060,U_15062,U_15064),U_15066),U_15068))) )
    & ! [U_15065,U_15059,U_15063,U_15061,U_15069,U_15067,U_15071] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15059,U_15063)),hAPP(hAPP(c_Product__Type_OPair(U_15059,U_15063),U_15069),U_15071)),hAPP(hAPP(c_Relation_Orel__comp(U_15059,U_15061,U_15063),U_15065),U_15067)))
        | ~ c_Predicate_Opred__comp(U_15059,U_15061,U_15063,hAPP(hAPP(c_COMBC(U_15059,tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_fun(U_15061,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15061,tc_fun(tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_fun(U_15061,tc_HOL_Obool)),U_15059),c_COMBC(U_15061,tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15061,tc_prod(U_15059,U_15061)),tc_fun(U_15061,tc_fun(tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_HOL_Obool)),U_15059),hAPP(c_COMBB(tc_prod(U_15059,U_15061),tc_fun(tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_HOL_Obool),U_15061),c_member(tc_prod(U_15059,U_15061)))),c_Product__Type_OPair(U_15059,U_15061)))),U_15065),hAPP(hAPP(c_COMBC(U_15061,tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_fun(U_15063,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15063,tc_fun(tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_fun(U_15063,tc_HOL_Obool)),U_15061),c_COMBC(U_15063,tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15063,tc_prod(U_15061,U_15063)),tc_fun(U_15063,tc_fun(tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_HOL_Obool)),U_15061),hAPP(c_COMBB(tc_prod(U_15061,U_15063),tc_fun(tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_HOL_Obool),U_15063),c_member(tc_prod(U_15061,U_15063)))),c_Product__Type_OPair(U_15061,U_15063)))),U_15067),U_15069,U_15071) ) ),
    inference(definitional_conversion,[status(esa)],[f_3763_3]) ).

cnf(f_3763_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15059,U_15063)),hAPP(hAPP(c_Product__Type_OPair(U_15059,U_15063),U_15069),U_15071)),hAPP(hAPP(c_Relation_Orel__comp(U_15059,U_15061,U_15063),U_15065),U_15067)))
    | ~ c_Predicate_Opred__comp(U_15059,U_15061,U_15063,hAPP(hAPP(c_COMBC(U_15059,tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_fun(U_15061,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15061,tc_fun(tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_fun(U_15061,tc_HOL_Obool)),U_15059),c_COMBC(U_15061,tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15061,tc_prod(U_15059,U_15061)),tc_fun(U_15061,tc_fun(tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_HOL_Obool)),U_15059),hAPP(c_COMBB(tc_prod(U_15059,U_15061),tc_fun(tc_fun(tc_prod(U_15059,U_15061),tc_HOL_Obool),tc_HOL_Obool),U_15061),c_member(tc_prod(U_15059,U_15061)))),c_Product__Type_OPair(U_15059,U_15061)))),U_15065),hAPP(hAPP(c_COMBC(U_15061,tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_fun(U_15063,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15063,tc_fun(tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_fun(U_15063,tc_HOL_Obool)),U_15061),c_COMBC(U_15063,tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15063,tc_prod(U_15061,U_15063)),tc_fun(U_15063,tc_fun(tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_HOL_Obool)),U_15061),hAPP(c_COMBB(tc_prod(U_15061,U_15063),tc_fun(tc_fun(tc_prod(U_15061,U_15063),tc_HOL_Obool),tc_HOL_Obool),U_15063),c_member(tc_prod(U_15061,U_15063)))),c_Product__Type_OPair(U_15061,U_15063)))),U_15067),U_15069,U_15071) ),
    inference(clausify,[status(thm)],[f_3763_4]) ).

cnf(f_3763_6,plain,
    ( c_Predicate_Opred__comp(U_15060,U_15062,U_15064,hAPP(hAPP(c_COMBC(U_15060,tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_fun(U_15062,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15062,tc_fun(tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_fun(U_15062,tc_HOL_Obool)),U_15060),c_COMBC(U_15062,tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15062,tc_prod(U_15060,U_15062)),tc_fun(U_15062,tc_fun(tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_HOL_Obool)),U_15060),hAPP(c_COMBB(tc_prod(U_15060,U_15062),tc_fun(tc_fun(tc_prod(U_15060,U_15062),tc_HOL_Obool),tc_HOL_Obool),U_15062),c_member(tc_prod(U_15060,U_15062)))),c_Product__Type_OPair(U_15060,U_15062)))),U_15066),hAPP(hAPP(c_COMBC(U_15062,tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_fun(U_15064,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15064,tc_fun(tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_fun(U_15064,tc_HOL_Obool)),U_15062),c_COMBC(U_15064,tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15064,tc_prod(U_15062,U_15064)),tc_fun(U_15064,tc_fun(tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_HOL_Obool)),U_15062),hAPP(c_COMBB(tc_prod(U_15062,U_15064),tc_fun(tc_fun(tc_prod(U_15062,U_15064),tc_HOL_Obool),tc_HOL_Obool),U_15064),c_member(tc_prod(U_15062,U_15064)))),c_Product__Type_OPair(U_15062,U_15064)))),U_15068),U_15070,U_15072)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15060,U_15064)),hAPP(hAPP(c_Product__Type_OPair(U_15060,U_15064),U_15070),U_15072)),hAPP(hAPP(c_Relation_Orel__comp(U_15060,U_15062,U_15064),U_15066),U_15068))) ),
    inference(clausify,[status(thm)],[f_3763_4]) ).

fof(f_3764_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_3764_2,plain,
    ! [U_15075,U_15074,U_15073] :
      ( c_FunDef_Oreduction__pair(U_15073,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_15073,U_15073),tc_HOL_Obool),tc_fun(tc_prod(U_15073,U_15073),tc_HOL_Obool)),U_15074),U_15075))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15073,U_15073),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15073,U_15073,U_15073),U_15074),U_15075)),U_15074))
      | ~ c_Wellfounded_Owf(U_15073,U_15074) ),
    inference(variable_rename,[status(thm)],[f_3764_1]) ).

fof(f_3764_3,plain,
    ! [U_15073,U_15074,U_15075] :
      ( c_FunDef_Oreduction__pair(U_15073,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_15073,U_15073),tc_HOL_Obool),tc_fun(tc_prod(U_15073,U_15073),tc_HOL_Obool)),U_15074),U_15075))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15073,U_15073),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15073,U_15073,U_15073),U_15074),U_15075)),U_15074))
      | ~ c_Wellfounded_Owf(U_15073,U_15074) ),
    inference(definitional_conversion,[status(esa)],[f_3764_2]) ).

cnf(f_3764_4,plain,
    ( c_FunDef_Oreduction__pair(U_15073,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_15073,U_15073),tc_HOL_Obool),tc_fun(tc_prod(U_15073,U_15073),tc_HOL_Obool)),U_15074),U_15075))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15073,U_15073),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15073,U_15073,U_15073),U_15074),U_15075)),U_15074))
    | ~ c_Wellfounded_Owf(U_15073,U_15074) ),
    inference(clausify,[status(thm)],[f_3764_3]) ).

fof(f_3765_1,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(fof_nnf,[status(thm)],[fact_wf__less__than]) ).

fof(f_3765_2,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(definitional_conversion,[status(esa)],[f_3765_1]) ).

cnf(f_3765_3,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_3765_2]) ).

fof(f_3766_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_3766_2,plain,
    ! [U_15083,U_15082,U_15081,U_15080,U_15079,U_15078,U_15077,U_15076] :
      ( c_Predicate_Opred__comp(U_15081,U_15082,U_15083,U_15076,U_15079,U_15077,U_15080)
      | ~ hBOOL(hAPP(hAPP(U_15079,U_15078),U_15080))
      | ~ hBOOL(hAPP(hAPP(U_15076,U_15077),U_15078)) ),
    inference(variable_rename,[status(thm)],[f_3766_1]) ).

fof(f_3766_3,plain,
    ! [U_15082,U_15083,U_15076,U_15077,U_15078,U_15079,U_15080,U_15081] :
      ( c_Predicate_Opred__comp(U_15081,U_15082,U_15083,U_15076,U_15079,U_15077,U_15080)
      | ~ hBOOL(hAPP(hAPP(U_15079,U_15078),U_15080))
      | ~ hBOOL(hAPP(hAPP(U_15076,U_15077),U_15078)) ),
    inference(definitional_conversion,[status(esa)],[f_3766_2]) ).

cnf(f_3766_4,plain,
    ( c_Predicate_Opred__comp(U_15081,U_15082,U_15083,U_15076,U_15079,U_15077,U_15080)
    | ~ hBOOL(hAPP(hAPP(U_15079,U_15078),U_15080))
    | ~ hBOOL(hAPP(hAPP(U_15076,U_15077),U_15078)) ),
    inference(clausify,[status(thm)],[f_3766_3]) ).

fof(f_3767_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_3767_2,plain,
    ! [U_15084] : c_Wellfounded_Owf(U_15084,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15084,U_15084),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3767_1]) ).

fof(f_3767_3,plain,
    ! [U_15084] : c_Wellfounded_Owf(U_15084,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15084,U_15084),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3767_2]) ).

cnf(f_3767_4,plain,
    c_Wellfounded_Owf(U_15084,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15084,U_15084),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3767_3]) ).

fof(f_3768_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_3768_2,plain,
    ! [U_15088,U_15087,U_15086,U_15085] :
      ( c_Wellfounded_Owf(U_15087,hAPP(hAPP(c_Relation_Oinv__image(U_15085,U_15087),U_15086),U_15088))
      | ~ c_Wellfounded_Owf(U_15085,U_15086) ),
    inference(variable_rename,[status(thm)],[f_3768_1]) ).

fof(f_3768_3,plain,
    ! [U_15085,U_15086,U_15087,U_15088] :
      ( c_Wellfounded_Owf(U_15087,hAPP(hAPP(c_Relation_Oinv__image(U_15085,U_15087),U_15086),U_15088))
      | ~ c_Wellfounded_Owf(U_15085,U_15086) ),
    inference(definitional_conversion,[status(esa)],[f_3768_2]) ).

cnf(f_3768_4,plain,
    ( c_Wellfounded_Owf(U_15087,hAPP(hAPP(c_Relation_Oinv__image(U_15085,U_15087),U_15086),U_15088))
    | ~ c_Wellfounded_Owf(U_15085,U_15086) ),
    inference(clausify,[status(thm)],[f_3768_3]) ).

fof(f_3769_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_3769_2,plain,
    ! [U_15092,U_15091,U_15090,U_15089] :
      ( c_Wellfounded_Owf(tc_prod(U_15089,U_15091),c_Wellfounded_Olex__prod(U_15089,U_15091,U_15090,U_15092))
      | ~ c_Wellfounded_Owf(U_15091,U_15092)
      | ~ c_Wellfounded_Owf(U_15089,U_15090) ),
    inference(variable_rename,[status(thm)],[f_3769_1]) ).

fof(f_3769_3,plain,
    ! [U_15091,U_15090,U_15089,U_15092] :
      ( c_Wellfounded_Owf(tc_prod(U_15089,U_15091),c_Wellfounded_Olex__prod(U_15089,U_15091,U_15090,U_15092))
      | ~ c_Wellfounded_Owf(U_15091,U_15092)
      | ~ c_Wellfounded_Owf(U_15089,U_15090) ),
    inference(definitional_conversion,[status(esa)],[f_3769_2]) ).

cnf(f_3769_4,plain,
    ( c_Wellfounded_Owf(tc_prod(U_15089,U_15091),c_Wellfounded_Olex__prod(U_15089,U_15091,U_15090,U_15092))
    | ~ c_Wellfounded_Owf(U_15091,U_15092)
    | ~ c_Wellfounded_Owf(U_15089,U_15090) ),
    inference(clausify,[status(thm)],[f_3769_3]) ).

fof(f_3770_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_3770_2,plain,
    ! [U_15094,U_15093] : c_Wellfounded_Owf(U_15093,hAPP(c_Wellfounded_Omeasure(U_15093),U_15094)),
    inference(variable_rename,[status(thm)],[f_3770_1]) ).

fof(f_3770_3,plain,
    ! [U_15094,U_15093] : c_Wellfounded_Owf(U_15093,hAPP(c_Wellfounded_Omeasure(U_15093),U_15094)),
    inference(definitional_conversion,[status(esa)],[f_3770_2]) ).

cnf(f_3770_4,plain,
    c_Wellfounded_Owf(U_15093,hAPP(c_Wellfounded_Omeasure(U_15093),U_15094)),
    inference(clausify,[status(thm)],[f_3770_3]) ).

fof(f_3771_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_3771_2,plain,
    ! [U_15097,U_15096,U_15095] :
      ( ( c_Wellfounded_Owf(U_15095,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15095,U_15095),tc_HOL_Obool)),U_15096),U_15097))
        | ~ c_Wellfounded_Owf(U_15095,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15095,U_15095),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15095,U_15095),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15095,U_15095,U_15095),U_15096),U_15096)),hAPP(hAPP(c_Relation_Orel__comp(U_15095,U_15095,U_15095),U_15097),U_15096))),U_15097)) )
      & ( c_Wellfounded_Owf(U_15095,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15095,U_15095),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15095,U_15095),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15095,U_15095,U_15095),U_15096),U_15096)),hAPP(hAPP(c_Relation_Orel__comp(U_15095,U_15095,U_15095),U_15097),U_15096))),U_15097))
        | ~ c_Wellfounded_Owf(U_15095,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15095,U_15095),tc_HOL_Obool)),U_15096),U_15097)) ) ),
    inference(variable_rename,[status(thm)],[f_3771_1]) ).

fof(f_3771_3,plain,
    ( ! [U_15103,U_15101,U_15099] :
        ( c_Wellfounded_Owf(U_15099,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15099,U_15099),tc_HOL_Obool)),U_15101),U_15103))
        | ~ c_Wellfounded_Owf(U_15099,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15099,U_15099),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15099,U_15099),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15099,U_15099,U_15099),U_15101),U_15101)),hAPP(hAPP(c_Relation_Orel__comp(U_15099,U_15099,U_15099),U_15103),U_15101))),U_15103)) )
    & ! [U_15102,U_15100,U_15098] :
        ( c_Wellfounded_Owf(U_15098,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15098,U_15098),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15098,U_15098),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15098,U_15098,U_15098),U_15100),U_15100)),hAPP(hAPP(c_Relation_Orel__comp(U_15098,U_15098,U_15098),U_15102),U_15100))),U_15102))
        | ~ c_Wellfounded_Owf(U_15098,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15098,U_15098),tc_HOL_Obool)),U_15100),U_15102)) ) ),
    inference(miniscope,[status(thm)],[f_3771_2]) ).

fof(f_3771_4,plain,
    ( ! [U_15099,U_15101,U_15103] :
        ( c_Wellfounded_Owf(U_15099,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15099,U_15099),tc_HOL_Obool)),U_15101),U_15103))
        | ~ c_Wellfounded_Owf(U_15099,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15099,U_15099),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15099,U_15099),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15099,U_15099,U_15099),U_15101),U_15101)),hAPP(hAPP(c_Relation_Orel__comp(U_15099,U_15099,U_15099),U_15103),U_15101))),U_15103)) )
    & ! [U_15102,U_15100,U_15098] :
        ( c_Wellfounded_Owf(U_15098,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15098,U_15098),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15098,U_15098),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15098,U_15098,U_15098),U_15100),U_15100)),hAPP(hAPP(c_Relation_Orel__comp(U_15098,U_15098,U_15098),U_15102),U_15100))),U_15102))
        | ~ c_Wellfounded_Owf(U_15098,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15098,U_15098),tc_HOL_Obool)),U_15100),U_15102)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3771_3]) ).

cnf(f_3771_5,plain,
    ( c_Wellfounded_Owf(U_15098,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15098,U_15098),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15098,U_15098),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15098,U_15098,U_15098),U_15100),U_15100)),hAPP(hAPP(c_Relation_Orel__comp(U_15098,U_15098,U_15098),U_15102),U_15100))),U_15102))
    | ~ c_Wellfounded_Owf(U_15098,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15098,U_15098),tc_HOL_Obool)),U_15100),U_15102)) ),
    inference(clausify,[status(thm)],[f_3771_4]) ).

cnf(f_3771_6,plain,
    ( c_Wellfounded_Owf(U_15099,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15099,U_15099),tc_HOL_Obool)),U_15101),U_15103))
    | ~ c_Wellfounded_Owf(U_15099,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15099,U_15099),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15099,U_15099),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15099,U_15099,U_15099),U_15101),U_15101)),hAPP(hAPP(c_Relation_Orel__comp(U_15099,U_15099,U_15099),U_15103),U_15101))),U_15103)) ),
    inference(clausify,[status(thm)],[f_3771_4]) ).

fof(f_3772_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_3772_2,plain,
    ! [U_15105,U_15104] :
      ( c_Wellfounded_Owf(U_15104,U_15105)
      | hAPP(hAPP(c_Relation_Orel__comp(U_15104,U_15104,U_15104),U_15105),U_15105) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15104,U_15104),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3772_1]) ).

fof(f_3772_3,plain,
    ! [U_15104,U_15105] :
      ( c_Wellfounded_Owf(U_15104,U_15105)
      | hAPP(hAPP(c_Relation_Orel__comp(U_15104,U_15104,U_15104),U_15105),U_15105) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15104,U_15104),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3772_2]) ).

cnf(f_3772_4,plain,
    ( c_Wellfounded_Owf(U_15104,U_15105)
    | hAPP(hAPP(c_Relation_Orel__comp(U_15104,U_15104,U_15104),U_15105),U_15105) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15104,U_15104),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3772_3]) ).

fof(f_3773_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_3773_2,plain,
    ! [U_15107,U_15106] :
      ( ( c_Wellfounded_Owf(U_15106,U_15107)
        | ~ c_Wellfounded_Owf(U_15106,hAPP(hAPP(c_Relation_Orel__comp(U_15106,U_15106,U_15106),U_15107),U_15107)) )
      & ( c_Wellfounded_Owf(U_15106,hAPP(hAPP(c_Relation_Orel__comp(U_15106,U_15106,U_15106),U_15107),U_15107))
        | ~ c_Wellfounded_Owf(U_15106,U_15107) ) ),
    inference(variable_rename,[status(thm)],[f_3773_1]) ).

fof(f_3773_3,plain,
    ( ! [U_15111,U_15109] :
        ( c_Wellfounded_Owf(U_15109,U_15111)
        | ~ c_Wellfounded_Owf(U_15109,hAPP(hAPP(c_Relation_Orel__comp(U_15109,U_15109,U_15109),U_15111),U_15111)) )
    & ! [U_15110,U_15108] :
        ( c_Wellfounded_Owf(U_15108,hAPP(hAPP(c_Relation_Orel__comp(U_15108,U_15108,U_15108),U_15110),U_15110))
        | ~ c_Wellfounded_Owf(U_15108,U_15110) ) ),
    inference(miniscope,[status(thm)],[f_3773_2]) ).

fof(f_3773_4,plain,
    ( ! [U_15109,U_15111] :
        ( c_Wellfounded_Owf(U_15109,U_15111)
        | ~ c_Wellfounded_Owf(U_15109,hAPP(hAPP(c_Relation_Orel__comp(U_15109,U_15109,U_15109),U_15111),U_15111)) )
    & ! [U_15110,U_15108] :
        ( c_Wellfounded_Owf(U_15108,hAPP(hAPP(c_Relation_Orel__comp(U_15108,U_15108,U_15108),U_15110),U_15110))
        | ~ c_Wellfounded_Owf(U_15108,U_15110) ) ),
    inference(definitional_conversion,[status(esa)],[f_3773_3]) ).

cnf(f_3773_5,plain,
    ( c_Wellfounded_Owf(U_15108,hAPP(hAPP(c_Relation_Orel__comp(U_15108,U_15108,U_15108),U_15110),U_15110))
    | ~ c_Wellfounded_Owf(U_15108,U_15110) ),
    inference(clausify,[status(thm)],[f_3773_4]) ).

cnf(f_3773_6,plain,
    ( c_Wellfounded_Owf(U_15109,U_15111)
    | ~ c_Wellfounded_Owf(U_15109,hAPP(hAPP(c_Relation_Orel__comp(U_15109,U_15109,U_15109),U_15111),U_15111)) ),
    inference(clausify,[status(thm)],[f_3773_4]) ).

fof(f_3774_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_3774_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_3774_1]) ).

cnf(f_3774_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_3774_2]) ).

fof(f_3775_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_3775_2,plain,
    ! [U_15112] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_15112)),
    inference(variable_rename,[status(thm)],[f_3775_1]) ).

fof(f_3775_3,plain,
    ! [U_15112] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_15112)),
    inference(definitional_conversion,[status(esa)],[f_3775_2]) ).

cnf(f_3775_4,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_15112)),
    inference(clausify,[status(thm)],[f_3775_3]) ).

fof(f_3776_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_3776_2,plain,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(definitional_conversion,[status(esa)],[f_3776_1]) ).

cnf(f_3776_3,plain,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(clausify,[status(thm)],[f_3776_2]) ).

fof(f_3777_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_3777_2,plain,
    ! [U_15115,U_15114,U_15113] :
      ( c_Wellfounded_Owf(U_15113,U_15115)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15113,U_15113),tc_HOL_Obool)),U_15115),U_15114))
      | ~ c_Wellfounded_Owf(U_15113,U_15114) ),
    inference(variable_rename,[status(thm)],[f_3777_1]) ).

fof(f_3777_3,plain,
    ! [U_15113,U_15114,U_15115] :
      ( c_Wellfounded_Owf(U_15113,U_15115)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15113,U_15113),tc_HOL_Obool)),U_15115),U_15114))
      | ~ c_Wellfounded_Owf(U_15113,U_15114) ),
    inference(definitional_conversion,[status(esa)],[f_3777_2]) ).

cnf(f_3777_4,plain,
    ( c_Wellfounded_Owf(U_15113,U_15115)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15113,U_15113),tc_HOL_Obool)),U_15115),U_15114))
    | ~ c_Wellfounded_Owf(U_15113,U_15114) ),
    inference(clausify,[status(thm)],[f_3777_3]) ).

fof(f_3778_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_3778_2,plain,
    ! [U_15117,U_15116] :
      ( c_Wellfounded_Owf(tc_fun(U_15116,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_15116,U_15117))
      | ~ c_Wellfounded_Owf(U_15116,U_15117) ),
    inference(variable_rename,[status(thm)],[f_3778_1]) ).

fof(f_3778_3,plain,
    ! [U_15116,U_15117] :
      ( c_Wellfounded_Owf(tc_fun(U_15116,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_15116,U_15117))
      | ~ c_Wellfounded_Owf(U_15116,U_15117) ),
    inference(definitional_conversion,[status(esa)],[f_3778_2]) ).

cnf(f_3778_4,plain,
    ( c_Wellfounded_Owf(tc_fun(U_15116,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_15116,U_15117))
    | ~ c_Wellfounded_Owf(U_15116,U_15117) ),
    inference(clausify,[status(thm)],[f_3778_3]) ).

fof(f_3779_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_3779_2,plain,
    ! [U_15126,U_15125,U_15124,U_15123,U_15122,U_15121,U_15120] :
      ( ( c_Predicate_Opred__comp(U_15120,U_15121,U_15122,U_15123,U_15124,U_15125,U_15126)
        | ! [U_15119] :
            ( ~ hBOOL(hAPP(hAPP(U_15124,U_15119),U_15126))
            | ~ hBOOL(hAPP(hAPP(U_15123,U_15125),U_15119)) ) )
      & ( ? [U_15118] :
            ( hBOOL(hAPP(hAPP(U_15124,U_15118),U_15126))
            & hBOOL(hAPP(hAPP(U_15123,U_15125),U_15118)) )
        | ~ c_Predicate_Opred__comp(U_15120,U_15121,U_15122,U_15123,U_15124,U_15125,U_15126) ) ),
    inference(variable_rename,[status(thm)],[f_3779_1]) ).

fof(f_3779_3,plain,
    ( ! [U_15140,U_15138,U_15136,U_15134] :
        ( ! [U_15132,U_15130,U_15128] : c_Predicate_Opred__comp(U_15128,U_15130,U_15132,U_15134,U_15136,U_15138,U_15140)
        | ! [U_15119] :
            ( ~ hBOOL(hAPP(hAPP(U_15136,U_15119),U_15140))
            | ~ hBOOL(hAPP(hAPP(U_15134,U_15138),U_15119)) ) )
    & ! [U_15139,U_15137,U_15135,U_15133] :
        ( ! [U_15131,U_15129,U_15127] : ~ c_Predicate_Opred__comp(U_15127,U_15129,U_15131,U_15133,U_15135,U_15137,U_15139)
        | ? [U_15118] :
            ( hBOOL(hAPP(hAPP(U_15135,U_15118),U_15139))
            & hBOOL(hAPP(hAPP(U_15133,U_15137),U_15118)) ) ) ),
    inference(miniscope,[status(thm)],[f_3779_2]) ).

fof(f_3779_4,plain,
    ( ! [U_15140,U_15138,U_15136,U_15134] :
        ( ! [U_15132,U_15130,U_15128] : c_Predicate_Opred__comp(U_15128,U_15130,U_15132,U_15134,U_15136,U_15138,U_15140)
        | ! [U_15119] :
            ( ~ hBOOL(hAPP(hAPP(U_15136,U_15119),U_15140))
            | ~ hBOOL(hAPP(hAPP(U_15134,U_15138),U_15119)) ) )
    & ! [U_15139,U_15137,U_15135,U_15133] :
        ( ! [U_15131,U_15129,U_15127] : ~ c_Predicate_Opred__comp(U_15127,U_15129,U_15131,U_15133,U_15135,U_15137,U_15139)
        | ( hBOOL(hAPP(hAPP(U_15135,sK338(U_15139,U_15137,U_15135,U_15133)),U_15139))
          & hBOOL(hAPP(hAPP(U_15133,U_15137),sK338(U_15139,U_15137,U_15135,U_15133))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK338]),skolemize(U_15118,sK338(U_15139,U_15137,U_15135,U_15133))],[f_3779_3]) ).

fof(f_3779_5,plain,
    ( ! [U_15133,U_15137,U_15139,U_15135] :
        ( hBOOL(hAPP(hAPP(U_15135,sK338(U_15139,U_15137,U_15135,U_15133)),U_15139))
        | ~ sP1014(U_15133,U_15137,U_15139,U_15135) )
    & ! [U_15133,U_15137,U_15139,U_15135] :
        ( hBOOL(hAPP(hAPP(U_15133,U_15137),sK338(U_15139,U_15137,U_15135,U_15133)))
        | ~ sP1014(U_15133,U_15137,U_15139,U_15135) )
    & ! [U_15136,U_15134,U_15119,U_15128,U_15130,U_15132,U_15138,U_15140] :
        ( c_Predicate_Opred__comp(U_15128,U_15130,U_15132,U_15134,U_15136,U_15138,U_15140)
        | ~ hBOOL(hAPP(hAPP(U_15136,U_15119),U_15140))
        | ~ hBOOL(hAPP(hAPP(U_15134,U_15138),U_15119)) )
    & ! [U_15133,U_15137,U_15139,U_15127,U_15129,U_15131,U_15135] :
        ( ~ c_Predicate_Opred__comp(U_15127,U_15129,U_15131,U_15133,U_15135,U_15137,U_15139)
        | sP1014(U_15133,U_15137,U_15139,U_15135) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1014])],[f_3779_4]) ).

cnf(f_3779_6,plain,
    ( ~ c_Predicate_Opred__comp(U_15127,U_15129,U_15131,U_15133,U_15135,U_15137,U_15139)
    | sP1014(U_15133,U_15137,U_15139,U_15135) ),
    inference(clausify,[status(thm)],[f_3779_5]) ).

cnf(f_3779_7,plain,
    ( c_Predicate_Opred__comp(U_15128,U_15130,U_15132,U_15134,U_15136,U_15138,U_15140)
    | ~ hBOOL(hAPP(hAPP(U_15136,U_15119),U_15140))
    | ~ hBOOL(hAPP(hAPP(U_15134,U_15138),U_15119)) ),
    inference(clausify,[status(thm)],[f_3779_5]) ).

cnf(f_3779_8,plain,
    ( hBOOL(hAPP(hAPP(U_15133,U_15137),sK338(U_15139,U_15137,U_15135,U_15133)))
    | ~ sP1014(U_15133,U_15137,U_15139,U_15135) ),
    inference(clausify,[status(thm)],[f_3779_5]) ).

cnf(f_3779_9,plain,
    ( hBOOL(hAPP(hAPP(U_15135,sK338(U_15139,U_15137,U_15135,U_15133)),U_15139))
    | ~ sP1014(U_15133,U_15137,U_15139,U_15135) ),
    inference(clausify,[status(thm)],[f_3779_5]) ).

fof(f_3780_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_3780_2,plain,
    ! [U_15142,U_15141] :
      ( c_Wellfounded_Owf(tc_fun(U_15141,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_15141,U_15142))
      | ~ c_Wellfounded_Owf(U_15141,U_15142) ),
    inference(variable_rename,[status(thm)],[f_3780_1]) ).

fof(f_3780_3,plain,
    ! [U_15142,U_15141] :
      ( c_Wellfounded_Owf(tc_fun(U_15141,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_15141,U_15142))
      | ~ c_Wellfounded_Owf(U_15141,U_15142) ),
    inference(definitional_conversion,[status(esa)],[f_3780_2]) ).

cnf(f_3780_4,plain,
    ( c_Wellfounded_Owf(tc_fun(U_15141,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_15141,U_15142))
    | ~ c_Wellfounded_Owf(U_15141,U_15142) ),
    inference(clausify,[status(thm)],[f_3780_3]) ).

fof(f_3781_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_3781_2,plain,
    ! [U_15143] : c_Wellfounded_Owf(tc_fun(U_15143,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_15143)),
    inference(variable_rename,[status(thm)],[f_3781_1]) ).

fof(f_3781_3,plain,
    ! [U_15143] : c_Wellfounded_Owf(tc_fun(U_15143,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_15143)),
    inference(definitional_conversion,[status(esa)],[f_3781_2]) ).

cnf(f_3781_4,plain,
    c_Wellfounded_Owf(tc_fun(U_15143,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_15143)),
    inference(clausify,[status(thm)],[f_3781_3]) ).

fof(f_3782_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_3782_2,plain,
    ! [U_15146,U_15145,U_15144] :
      ( c_Wellfounded_Owf(U_15144,c_Wellfounded_Omlex__prod(U_15144,U_15146,U_15145))
      | ~ c_Wellfounded_Owf(U_15144,U_15145) ),
    inference(variable_rename,[status(thm)],[f_3782_1]) ).

fof(f_3782_3,plain,
    ! [U_15145,U_15144,U_15146] :
      ( c_Wellfounded_Owf(U_15144,c_Wellfounded_Omlex__prod(U_15144,U_15146,U_15145))
      | ~ c_Wellfounded_Owf(U_15144,U_15145) ),
    inference(definitional_conversion,[status(esa)],[f_3782_2]) ).

cnf(f_3782_4,plain,
    ( c_Wellfounded_Owf(U_15144,c_Wellfounded_Omlex__prod(U_15144,U_15146,U_15145))
    | ~ c_Wellfounded_Owf(U_15144,U_15145) ),
    inference(clausify,[status(thm)],[f_3782_3]) ).

fof(f_3783_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_3783_2,plain,
    ! [U_15149,U_15148,U_15147] :
      ( c_Wellfounded_Owf(U_15147,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15147,U_15147),tc_HOL_Obool)),U_15149),U_15148))
      | ~ c_Wellfounded_Owf(U_15147,U_15148) ),
    inference(variable_rename,[status(thm)],[f_3783_1]) ).

fof(f_3783_3,plain,
    ! [U_15147,U_15148,U_15149] :
      ( c_Wellfounded_Owf(U_15147,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15147,U_15147),tc_HOL_Obool)),U_15149),U_15148))
      | ~ c_Wellfounded_Owf(U_15147,U_15148) ),
    inference(definitional_conversion,[status(esa)],[f_3783_2]) ).

cnf(f_3783_4,plain,
    ( c_Wellfounded_Owf(U_15147,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15147,U_15147),tc_HOL_Obool)),U_15149),U_15148))
    | ~ c_Wellfounded_Owf(U_15147,U_15148) ),
    inference(clausify,[status(thm)],[f_3783_3]) ).

fof(f_3784_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_3784_2,plain,
    ! [U_15152,U_15151,U_15150] :
      ( c_Wellfounded_Owf(U_15150,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15150,U_15150),tc_HOL_Obool)),U_15151),U_15152))
      | ~ c_Wellfounded_Owf(U_15150,U_15151) ),
    inference(variable_rename,[status(thm)],[f_3784_1]) ).

fof(f_3784_3,plain,
    ! [U_15150,U_15151,U_15152] :
      ( c_Wellfounded_Owf(U_15150,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15150,U_15150),tc_HOL_Obool)),U_15151),U_15152))
      | ~ c_Wellfounded_Owf(U_15150,U_15151) ),
    inference(definitional_conversion,[status(esa)],[f_3784_2]) ).

cnf(f_3784_4,plain,
    ( c_Wellfounded_Owf(U_15150,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15150,U_15150),tc_HOL_Obool)),U_15151),U_15152))
    | ~ c_Wellfounded_Owf(U_15150,U_15151) ),
    inference(clausify,[status(thm)],[f_3784_3]) ).

fof(f_3785_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_3785_2,plain,
    ! [U_15155,U_15154,U_15153] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15153,U_15153)),hAPP(hAPP(c_Product__Type_OPair(U_15153,U_15153),U_15155),U_15155)),U_15154))
      | ~ c_Wellfounded_Owf(U_15153,U_15154) ),
    inference(variable_rename,[status(thm)],[f_3785_1]) ).

fof(f_3785_3,plain,
    ! [U_15153,U_15154,U_15155] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15153,U_15153)),hAPP(hAPP(c_Product__Type_OPair(U_15153,U_15153),U_15155),U_15155)),U_15154))
      | ~ c_Wellfounded_Owf(U_15153,U_15154) ),
    inference(definitional_conversion,[status(esa)],[f_3785_2]) ).

cnf(f_3785_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15153,U_15153)),hAPP(hAPP(c_Product__Type_OPair(U_15153,U_15153),U_15155),U_15155)),U_15154))
    | ~ c_Wellfounded_Owf(U_15153,U_15154) ),
    inference(clausify,[status(thm)],[f_3785_3]) ).

fof(f_3786_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_3786_2,plain,
    ! [U_15159,U_15158,U_15157,U_15156] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15156,U_15156)),hAPP(hAPP(c_Product__Type_OPair(U_15156,U_15156),U_15159),U_15158)),U_15157))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15156,U_15156)),hAPP(hAPP(c_Product__Type_OPair(U_15156,U_15156),U_15158),U_15159)),U_15157))
      | ~ c_Wellfounded_Owf(U_15156,U_15157) ),
    inference(variable_rename,[status(thm)],[f_3786_1]) ).

fof(f_3786_3,plain,
    ! [U_15156,U_15157,U_15158,U_15159] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15156,U_15156)),hAPP(hAPP(c_Product__Type_OPair(U_15156,U_15156),U_15159),U_15158)),U_15157))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15156,U_15156)),hAPP(hAPP(c_Product__Type_OPair(U_15156,U_15156),U_15158),U_15159)),U_15157))
      | ~ c_Wellfounded_Owf(U_15156,U_15157) ),
    inference(definitional_conversion,[status(esa)],[f_3786_2]) ).

cnf(f_3786_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15156,U_15156)),hAPP(hAPP(c_Product__Type_OPair(U_15156,U_15156),U_15159),U_15158)),U_15157))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15156,U_15156)),hAPP(hAPP(c_Product__Type_OPair(U_15156,U_15156),U_15158),U_15159)),U_15157))
    | ~ c_Wellfounded_Owf(U_15156,U_15157) ),
    inference(clausify,[status(thm)],[f_3786_3]) ).

fof(f_3787_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_3787_2,plain,
    ! [U_15163,U_15162,U_15161,U_15160] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15160,U_15160)),hAPP(hAPP(c_Product__Type_OPair(U_15160,U_15160),U_15163),U_15162)),U_15161))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15160,U_15160)),hAPP(hAPP(c_Product__Type_OPair(U_15160,U_15160),U_15162),U_15163)),U_15161))
      | ~ c_Wellfounded_Owf(U_15160,U_15161) ),
    inference(variable_rename,[status(thm)],[f_3787_1]) ).

fof(f_3787_3,plain,
    ! [U_15160,U_15161,U_15162,U_15163] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15160,U_15160)),hAPP(hAPP(c_Product__Type_OPair(U_15160,U_15160),U_15163),U_15162)),U_15161))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15160,U_15160)),hAPP(hAPP(c_Product__Type_OPair(U_15160,U_15160),U_15162),U_15163)),U_15161))
      | ~ c_Wellfounded_Owf(U_15160,U_15161) ),
    inference(definitional_conversion,[status(esa)],[f_3787_2]) ).

cnf(f_3787_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15160,U_15160)),hAPP(hAPP(c_Product__Type_OPair(U_15160,U_15160),U_15163),U_15162)),U_15161))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15160,U_15160)),hAPP(hAPP(c_Product__Type_OPair(U_15160,U_15160),U_15162),U_15163)),U_15161))
    | ~ c_Wellfounded_Owf(U_15160,U_15161) ),
    inference(clausify,[status(thm)],[f_3787_3]) ).

fof(f_3788_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_3788_2,plain,
    ! [U_15166,U_15165,U_15164] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15164,U_15164)),hAPP(hAPP(c_Product__Type_OPair(U_15164,U_15164),U_15166),U_15166)),U_15165))
      | ~ c_Wellfounded_Owf(U_15164,U_15165) ),
    inference(variable_rename,[status(thm)],[f_3788_1]) ).

fof(f_3788_3,plain,
    ! [U_15164,U_15165,U_15166] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15164,U_15164)),hAPP(hAPP(c_Product__Type_OPair(U_15164,U_15164),U_15166),U_15166)),U_15165))
      | ~ c_Wellfounded_Owf(U_15164,U_15165) ),
    inference(definitional_conversion,[status(esa)],[f_3788_2]) ).

cnf(f_3788_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15164,U_15164)),hAPP(hAPP(c_Product__Type_OPair(U_15164,U_15164),U_15166),U_15166)),U_15165))
    | ~ c_Wellfounded_Owf(U_15164,U_15165) ),
    inference(clausify,[status(thm)],[f_3788_3]) ).

fof(f_3789_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_3789_2,plain,
    ! [U_15169,U_15168,U_15167] :
      ( hBOOL(hAPP(hAPP(c_member(U_15167),U_15169),c_Wellfounded_Oacc(U_15167,U_15168)))
      | ~ c_Wellfounded_Owf(U_15167,U_15168) ),
    inference(variable_rename,[status(thm)],[f_3789_1]) ).

fof(f_3789_3,plain,
    ! [U_15167,U_15168,U_15169] :
      ( hBOOL(hAPP(hAPP(c_member(U_15167),U_15169),c_Wellfounded_Oacc(U_15167,U_15168)))
      | ~ c_Wellfounded_Owf(U_15167,U_15168) ),
    inference(definitional_conversion,[status(esa)],[f_3789_2]) ).

cnf(f_3789_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15167),U_15169),c_Wellfounded_Oacc(U_15167,U_15168)))
    | ~ c_Wellfounded_Owf(U_15167,U_15168) ),
    inference(clausify,[status(thm)],[f_3789_3]) ).

fof(f_3790_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_3790_2,plain,
    ! [U_15173,U_15172] :
      ( ( c_Wellfounded_Owf(U_15172,U_15173)
        | ? [U_15171] : ~ hBOOL(hAPP(hAPP(c_member(U_15172),U_15171),c_Wellfounded_Oacc(U_15172,U_15173))) )
      & ( ! [U_15170] : hBOOL(hAPP(hAPP(c_member(U_15172),U_15170),c_Wellfounded_Oacc(U_15172,U_15173)))
        | ~ c_Wellfounded_Owf(U_15172,U_15173) ) ),
    inference(variable_rename,[status(thm)],[f_3790_1]) ).

fof(f_3790_3,plain,
    ( ! [U_15177,U_15175] :
        ( c_Wellfounded_Owf(U_15175,U_15177)
        | ? [U_15171] : ~ hBOOL(hAPP(hAPP(c_member(U_15175),U_15171),c_Wellfounded_Oacc(U_15175,U_15177))) )
    & ! [U_15176,U_15174] :
        ( ! [U_15170] : hBOOL(hAPP(hAPP(c_member(U_15174),U_15170),c_Wellfounded_Oacc(U_15174,U_15176)))
        | ~ c_Wellfounded_Owf(U_15174,U_15176) ) ),
    inference(miniscope,[status(thm)],[f_3790_2]) ).

fof(f_3790_4,plain,
    ( ! [U_15177,U_15175] :
        ( c_Wellfounded_Owf(U_15175,U_15177)
        | ~ hBOOL(hAPP(hAPP(c_member(U_15175),sK339(U_15177,U_15175)),c_Wellfounded_Oacc(U_15175,U_15177))) )
    & ! [U_15176,U_15174] :
        ( ! [U_15170] : hBOOL(hAPP(hAPP(c_member(U_15174),U_15170),c_Wellfounded_Oacc(U_15174,U_15176)))
        | ~ c_Wellfounded_Owf(U_15174,U_15176) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK339]),skolemize(U_15171,sK339(U_15177,U_15175))],[f_3790_3]) ).

fof(f_3790_5,plain,
    ( ! [U_15175,U_15177] :
        ( c_Wellfounded_Owf(U_15175,U_15177)
        | ~ hBOOL(hAPP(hAPP(c_member(U_15175),sK339(U_15177,U_15175)),c_Wellfounded_Oacc(U_15175,U_15177))) )
    & ! [U_15176,U_15170,U_15174] :
        ( hBOOL(hAPP(hAPP(c_member(U_15174),U_15170),c_Wellfounded_Oacc(U_15174,U_15176)))
        | ~ c_Wellfounded_Owf(U_15174,U_15176) ) ),
    inference(definitional_conversion,[status(esa)],[f_3790_4]) ).

cnf(f_3790_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15174),U_15170),c_Wellfounded_Oacc(U_15174,U_15176)))
    | ~ c_Wellfounded_Owf(U_15174,U_15176) ),
    inference(clausify,[status(thm)],[f_3790_5]) ).

cnf(f_3790_7,plain,
    ( c_Wellfounded_Owf(U_15175,U_15177)
    | ~ hBOOL(hAPP(hAPP(c_member(U_15175),sK339(U_15177,U_15175)),c_Wellfounded_Oacc(U_15175,U_15177))) ),
    inference(clausify,[status(thm)],[f_3790_5]) ).

fof(f_3791_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_3791_2,plain,
    ! [U_15178] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_15178)),
    inference(variable_rename,[status(thm)],[f_3791_1]) ).

fof(f_3791_3,plain,
    ! [U_15178] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_15178)),
    inference(definitional_conversion,[status(esa)],[f_3791_2]) ).

cnf(f_3791_4,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_15178)),
    inference(clausify,[status(thm)],[f_3791_3]) ).

fof(f_3792_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_3792_2,plain,
    ! [U_15184,U_15183] :
      ( ( c_Wellfounded_Owf(U_15183,U_15184)
        | ? [U_15182] :
          ! [U_15181] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15183,U_15183)),hAPP(hAPP(c_Product__Type_OPair(U_15183,U_15183),hAPP(U_15182,hAPP(c_Nat_OSuc,U_15181))),hAPP(U_15182,U_15181))),U_15184)) )
      & ( ! [U_15180] :
          ? [U_15179] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15183,U_15183)),hAPP(hAPP(c_Product__Type_OPair(U_15183,U_15183),hAPP(U_15180,hAPP(c_Nat_OSuc,U_15179))),hAPP(U_15180,U_15179))),U_15184))
        | ~ c_Wellfounded_Owf(U_15183,U_15184) ) ),
    inference(variable_rename,[status(thm)],[f_3792_1]) ).

fof(f_3792_3,plain,
    ( ! [U_15188,U_15186] :
        ( c_Wellfounded_Owf(U_15186,U_15188)
        | ? [U_15182] :
          ! [U_15181] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15186,U_15186)),hAPP(hAPP(c_Product__Type_OPair(U_15186,U_15186),hAPP(U_15182,hAPP(c_Nat_OSuc,U_15181))),hAPP(U_15182,U_15181))),U_15188)) )
    & ! [U_15187,U_15185] :
        ( ! [U_15180] :
          ? [U_15179] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15185,U_15185)),hAPP(hAPP(c_Product__Type_OPair(U_15185,U_15185),hAPP(U_15180,hAPP(c_Nat_OSuc,U_15179))),hAPP(U_15180,U_15179))),U_15187))
        | ~ c_Wellfounded_Owf(U_15185,U_15187) ) ),
    inference(miniscope,[status(thm)],[f_3792_2]) ).

fof(f_3792_4,plain,
    ( ! [U_15188,U_15186] :
        ( c_Wellfounded_Owf(U_15186,U_15188)
        | ? [U_15182] :
          ! [U_15181] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15186,U_15186)),hAPP(hAPP(c_Product__Type_OPair(U_15186,U_15186),hAPP(U_15182,hAPP(c_Nat_OSuc,U_15181))),hAPP(U_15182,U_15181))),U_15188)) )
    & ! [U_15187,U_15185] :
        ( ! [U_15180] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15185,U_15185)),hAPP(hAPP(c_Product__Type_OPair(U_15185,U_15185),hAPP(U_15180,hAPP(c_Nat_OSuc,sK340(U_15187,U_15185,U_15180)))),hAPP(U_15180,sK340(U_15187,U_15185,U_15180)))),U_15187))
        | ~ c_Wellfounded_Owf(U_15185,U_15187) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK340]),skolemize(U_15179,sK340(U_15187,U_15185,U_15180))],[f_3792_3]) ).

fof(f_3792_5,plain,
    ( ! [U_15188,U_15186] :
        ( c_Wellfounded_Owf(U_15186,U_15188)
        | ! [U_15181] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15186,U_15186)),hAPP(hAPP(c_Product__Type_OPair(U_15186,U_15186),hAPP(sK341(U_15188,U_15186),hAPP(c_Nat_OSuc,U_15181))),hAPP(sK341(U_15188,U_15186),U_15181))),U_15188)) )
    & ! [U_15187,U_15185] :
        ( ! [U_15180] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15185,U_15185)),hAPP(hAPP(c_Product__Type_OPair(U_15185,U_15185),hAPP(U_15180,hAPP(c_Nat_OSuc,sK340(U_15187,U_15185,U_15180)))),hAPP(U_15180,sK340(U_15187,U_15185,U_15180)))),U_15187))
        | ~ c_Wellfounded_Owf(U_15185,U_15187) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK341]),skolemize(U_15182,sK341(U_15188,U_15186))],[f_3792_4]) ).

fof(f_3792_6,plain,
    ( ! [U_15181,U_15186,U_15188] :
        ( c_Wellfounded_Owf(U_15186,U_15188)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15186,U_15186)),hAPP(hAPP(c_Product__Type_OPair(U_15186,U_15186),hAPP(sK341(U_15188,U_15186),hAPP(c_Nat_OSuc,U_15181))),hAPP(sK341(U_15188,U_15186),U_15181))),U_15188)) )
    & ! [U_15187,U_15180,U_15185] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15185,U_15185)),hAPP(hAPP(c_Product__Type_OPair(U_15185,U_15185),hAPP(U_15180,hAPP(c_Nat_OSuc,sK340(U_15187,U_15185,U_15180)))),hAPP(U_15180,sK340(U_15187,U_15185,U_15180)))),U_15187))
        | ~ c_Wellfounded_Owf(U_15185,U_15187) ) ),
    inference(definitional_conversion,[status(esa)],[f_3792_5]) ).

cnf(f_3792_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15185,U_15185)),hAPP(hAPP(c_Product__Type_OPair(U_15185,U_15185),hAPP(U_15180,hAPP(c_Nat_OSuc,sK340(U_15187,U_15185,U_15180)))),hAPP(U_15180,sK340(U_15187,U_15185,U_15180)))),U_15187))
    | ~ c_Wellfounded_Owf(U_15185,U_15187) ),
    inference(clausify,[status(thm)],[f_3792_6]) ).

cnf(f_3792_8,plain,
    ( c_Wellfounded_Owf(U_15186,U_15188)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15186,U_15186)),hAPP(hAPP(c_Product__Type_OPair(U_15186,U_15186),hAPP(sK341(U_15188,U_15186),hAPP(c_Nat_OSuc,U_15181))),hAPP(sK341(U_15188,U_15186),U_15181))),U_15188)) ),
    inference(clausify,[status(thm)],[f_3792_6]) ).

fof(f_3793_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_3793_2,plain,
    ! [U_15191,U_15190,U_15189] :
      ( U_15191 = c_Orderings_Obot__class_Obot(tc_fun(U_15189,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15189,tc_HOL_Obool)),U_15191),hAPP(c_Relation_OImage(U_15189,U_15189,U_15190),U_15191)))
      | ~ c_Wellfounded_Owf(U_15189,U_15190) ),
    inference(variable_rename,[status(thm)],[f_3793_1]) ).

fof(f_3793_3,plain,
    ! [U_15189,U_15190,U_15191] :
      ( U_15191 = c_Orderings_Obot__class_Obot(tc_fun(U_15189,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15189,tc_HOL_Obool)),U_15191),hAPP(c_Relation_OImage(U_15189,U_15189,U_15190),U_15191)))
      | ~ c_Wellfounded_Owf(U_15189,U_15190) ),
    inference(definitional_conversion,[status(esa)],[f_3793_2]) ).

cnf(f_3793_4,plain,
    ( U_15191 = c_Orderings_Obot__class_Obot(tc_fun(U_15189,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15189,tc_HOL_Obool)),U_15191),hAPP(c_Relation_OImage(U_15189,U_15189,U_15190),U_15191)))
    | ~ c_Wellfounded_Owf(U_15189,U_15190) ),
    inference(clausify,[status(thm)],[f_3793_3]) ).

fof(f_3794_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_3794_2,plain,
    ! [U_15194,U_15193,U_15192] :
      ( c_Wellfounded_Owf(U_15192,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15192,U_15192),tc_HOL_Obool)),U_15193),U_15194))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15192,U_15192),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15192,U_15192,U_15192),U_15193),U_15194)),U_15193))
      | ~ c_Wellfounded_Owf(U_15192,U_15194)
      | ~ c_Wellfounded_Owf(U_15192,U_15193) ),
    inference(variable_rename,[status(thm)],[f_3794_1]) ).

fof(f_3794_3,plain,
    ! [U_15192,U_15193,U_15194] :
      ( c_Wellfounded_Owf(U_15192,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15192,U_15192),tc_HOL_Obool)),U_15193),U_15194))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15192,U_15192),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15192,U_15192,U_15192),U_15193),U_15194)),U_15193))
      | ~ c_Wellfounded_Owf(U_15192,U_15194)
      | ~ c_Wellfounded_Owf(U_15192,U_15193) ),
    inference(definitional_conversion,[status(esa)],[f_3794_2]) ).

cnf(f_3794_4,plain,
    ( c_Wellfounded_Owf(U_15192,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15192,U_15192),tc_HOL_Obool)),U_15193),U_15194))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15192,U_15192),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15192,U_15192,U_15192),U_15193),U_15194)),U_15193))
    | ~ c_Wellfounded_Owf(U_15192,U_15194)
    | ~ c_Wellfounded_Owf(U_15192,U_15193) ),
    inference(clausify,[status(thm)],[f_3794_3]) ).

fof(f_3795_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_3795_2,plain,
    ! [U_15195] :
      ( c_Wellfounded_Owf(U_15195,hAPP(c_Set_OCollect(tc_prod(U_15195,U_15195)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15195,U_15195,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_15195))))
      | ~ class_Orderings_Owellorder(U_15195) ),
    inference(variable_rename,[status(thm)],[f_3795_1]) ).

fof(f_3795_3,plain,
    ! [U_15195] :
      ( c_Wellfounded_Owf(U_15195,hAPP(c_Set_OCollect(tc_prod(U_15195,U_15195)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15195,U_15195,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_15195))))
      | ~ class_Orderings_Owellorder(U_15195) ),
    inference(definitional_conversion,[status(esa)],[f_3795_2]) ).

cnf(f_3795_4,plain,
    ( c_Wellfounded_Owf(U_15195,hAPP(c_Set_OCollect(tc_prod(U_15195,U_15195)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15195,U_15195,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_15195))))
    | ~ class_Orderings_Owellorder(U_15195) ),
    inference(clausify,[status(thm)],[f_3795_3]) ).

fof(f_3796_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_3796_2,plain,
    ! [U_15197,U_15196] :
      ( ( c_FunDef_Oreduction__pair(U_15196,U_15197)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15196,U_15196,U_15196),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool),tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool)),U_15197)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool),tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool)),U_15197))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool),tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool)),U_15197)))
        | ~ c_Wellfounded_Owf(U_15196,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool),tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool)),U_15197)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15196,U_15196,U_15196),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool),tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool)),U_15197)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool),tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool)),U_15197))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool),tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool)),U_15197)))
          & c_Wellfounded_Owf(U_15196,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool),tc_fun(tc_prod(U_15196,U_15196),tc_HOL_Obool)),U_15197)) )
        | ~ c_FunDef_Oreduction__pair(U_15196,U_15197) ) ),
    inference(variable_rename,[status(thm)],[f_3796_1]) ).

fof(f_3796_3,plain,
    ( ! [U_15201,U_15199] :
        ( c_FunDef_Oreduction__pair(U_15199,U_15201)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15199,U_15199,U_15199),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool),tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool)),U_15201)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool),tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool)),U_15201))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool),tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool)),U_15201)))
        | ~ c_Wellfounded_Owf(U_15199,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool),tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool)),U_15201)) )
    & ! [U_15200,U_15198] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15198,U_15198,U_15198),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool),tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool)),U_15200)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool),tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool)),U_15200))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool),tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool)),U_15200)))
          & c_Wellfounded_Owf(U_15198,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool),tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool)),U_15200)) )
        | ~ c_FunDef_Oreduction__pair(U_15198,U_15200) ) ),
    inference(miniscope,[status(thm)],[f_3796_2]) ).

fof(f_3796_4,plain,
    ( ! [U_15200,U_15198] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15198,U_15198,U_15198),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool),tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool)),U_15200)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool),tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool)),U_15200))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool),tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool)),U_15200)))
        | ~ sP1015(U_15200,U_15198) )
    & ! [U_15200,U_15198] :
        ( c_Wellfounded_Owf(U_15198,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool),tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool)),U_15200))
        | ~ sP1015(U_15200,U_15198) )
    & ! [U_15199,U_15201] :
        ( c_FunDef_Oreduction__pair(U_15199,U_15201)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15199,U_15199,U_15199),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool),tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool)),U_15201)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool),tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool)),U_15201))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool),tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool)),U_15201)))
        | ~ c_Wellfounded_Owf(U_15199,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool),tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool)),U_15201)) )
    & ! [U_15200,U_15198] :
        ( sP1015(U_15200,U_15198)
        | ~ c_FunDef_Oreduction__pair(U_15198,U_15200) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1015])],[f_3796_3]) ).

cnf(f_3796_5,plain,
    ( sP1015(U_15200,U_15198)
    | ~ c_FunDef_Oreduction__pair(U_15198,U_15200) ),
    inference(clausify,[status(thm)],[f_3796_4]) ).

cnf(f_3796_6,plain,
    ( c_FunDef_Oreduction__pair(U_15199,U_15201)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15199,U_15199,U_15199),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool),tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool)),U_15201)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool),tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool)),U_15201))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool),tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool)),U_15201)))
    | ~ c_Wellfounded_Owf(U_15199,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool),tc_fun(tc_prod(U_15199,U_15199),tc_HOL_Obool)),U_15201)) ),
    inference(clausify,[status(thm)],[f_3796_4]) ).

cnf(f_3796_7,plain,
    ( c_Wellfounded_Owf(U_15198,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool),tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool)),U_15200))
    | ~ sP1015(U_15200,U_15198) ),
    inference(clausify,[status(thm)],[f_3796_4]) ).

cnf(f_3796_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15198,U_15198,U_15198),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool),tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool)),U_15200)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool),tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool)),U_15200))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool),tc_fun(tc_prod(U_15198,U_15198),tc_HOL_Obool)),U_15200)))
    | ~ sP1015(U_15200,U_15198) ),
    inference(clausify,[status(thm)],[f_3796_4]) ).

fof(f_3797_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_3797_2,plain,
    ! [U_15205,U_15204,U_15203,U_15202] :
      ( c_Wellfounded_Owf(U_15202,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool)),U_15204),U_15205))
      | ~ c_Wellfounded_Owf(U_15202,U_15205)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool)),U_15205),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool),tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool)),U_15203)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool)),U_15204),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool),tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool)),U_15203)))
      | ~ c_FunDef_Oreduction__pair(U_15202,U_15203) ),
    inference(variable_rename,[status(thm)],[f_3797_1]) ).

fof(f_3797_3,plain,
    ! [U_15203,U_15202,U_15204,U_15205] :
      ( c_Wellfounded_Owf(U_15202,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool)),U_15204),U_15205))
      | ~ c_Wellfounded_Owf(U_15202,U_15205)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool)),U_15205),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool),tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool)),U_15203)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool)),U_15204),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool),tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool)),U_15203)))
      | ~ c_FunDef_Oreduction__pair(U_15202,U_15203) ),
    inference(definitional_conversion,[status(esa)],[f_3797_2]) ).

cnf(f_3797_4,plain,
    ( c_Wellfounded_Owf(U_15202,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool)),U_15204),U_15205))
    | ~ c_Wellfounded_Owf(U_15202,U_15205)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool)),U_15205),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool),tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool)),U_15203)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool)),U_15204),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool),tc_fun(tc_prod(U_15202,U_15202),tc_HOL_Obool)),U_15203)))
    | ~ c_FunDef_Oreduction__pair(U_15202,U_15203) ),
    inference(clausify,[status(thm)],[f_3797_3]) ).

fof(f_3798_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_3798_2,plain,
    ! [U_15209,U_15208,U_15207,U_15206] :
      ( c_Wellfounded_Owf(U_15208,hAPP(c_Set_Oimage(tc_prod(U_15206,U_15206),tc_prod(U_15208,U_15208),c_Product__Type_Omap__pair(U_15206,U_15208,U_15206,U_15208,U_15209,U_15209)),U_15207))
      | ~ c_Fun_Oinj__on(U_15206,U_15208,U_15209,c_Orderings_Otop__class_Otop(tc_fun(U_15206,tc_HOL_Obool)))
      | ~ c_Wellfounded_Owf(U_15206,U_15207) ),
    inference(variable_rename,[status(thm)],[f_3798_1]) ).

fof(f_3798_3,plain,
    ! [U_15208,U_15207,U_15209,U_15206] :
      ( c_Wellfounded_Owf(U_15208,hAPP(c_Set_Oimage(tc_prod(U_15206,U_15206),tc_prod(U_15208,U_15208),c_Product__Type_Omap__pair(U_15206,U_15208,U_15206,U_15208,U_15209,U_15209)),U_15207))
      | ~ c_Fun_Oinj__on(U_15206,U_15208,U_15209,c_Orderings_Otop__class_Otop(tc_fun(U_15206,tc_HOL_Obool)))
      | ~ c_Wellfounded_Owf(U_15206,U_15207) ),
    inference(definitional_conversion,[status(esa)],[f_3798_2]) ).

cnf(f_3798_4,plain,
    ( c_Wellfounded_Owf(U_15208,hAPP(c_Set_Oimage(tc_prod(U_15206,U_15206),tc_prod(U_15208,U_15208),c_Product__Type_Omap__pair(U_15206,U_15208,U_15206,U_15208,U_15209,U_15209)),U_15207))
    | ~ c_Fun_Oinj__on(U_15206,U_15208,U_15209,c_Orderings_Otop__class_Otop(tc_fun(U_15206,tc_HOL_Obool)))
    | ~ c_Wellfounded_Owf(U_15206,U_15207) ),
    inference(clausify,[status(thm)],[f_3798_3]) ).

fof(f_3799_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_3799_2,plain,
    ! [U_15211,U_15210] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_15210),c_List_Olenlex(U_15210,U_15211))
      | ~ c_Wellfounded_Owf(U_15210,U_15211) ),
    inference(variable_rename,[status(thm)],[f_3799_1]) ).

fof(f_3799_3,plain,
    ! [U_15210,U_15211] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_15210),c_List_Olenlex(U_15210,U_15211))
      | ~ c_Wellfounded_Owf(U_15210,U_15211) ),
    inference(definitional_conversion,[status(esa)],[f_3799_2]) ).

cnf(f_3799_4,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_15210),c_List_Olenlex(U_15210,U_15211))
    | ~ c_Wellfounded_Owf(U_15210,U_15211) ),
    inference(clausify,[status(thm)],[f_3799_3]) ).

fof(f_3800_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_3800_2,plain,
    ! [U_15216,U_15215,U_15214,U_15213] :
      ( c_Wellfounded_Owf(U_15216,hAPP(c_Set_OCollect(tc_prod(U_15216,U_15216)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15216,U_15216,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15216,tc_HOL_Obool),tc_fun(U_15216,tc_HOL_Obool),U_15216),hAPP(c_COMBS(U_15216,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15216),c_fconj),U_15213))),hAPP(hAPP(c_COMBC(U_15216,tc_fun(U_15216,U_15216),tc_fun(U_15216,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15216,tc_HOL_Obool),tc_fun(tc_fun(U_15216,U_15216),tc_fun(U_15216,tc_HOL_Obool)),U_15216),c_COMBB(U_15216,tc_HOL_Obool,U_15216)),c_fequal)),U_15215)))))
      | ? [U_15212] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_15214,hAPP(U_15215,U_15212))),hAPP(U_15214,U_15212)))
          & hBOOL(hAPP(U_15213,U_15212)) ) ),
    inference(variable_rename,[status(thm)],[f_3800_1]) ).

fof(f_3800_3,plain,
    ! [U_15216,U_15215,U_15214,U_15213] :
      ( c_Wellfounded_Owf(U_15216,hAPP(c_Set_OCollect(tc_prod(U_15216,U_15216)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15216,U_15216,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15216,tc_HOL_Obool),tc_fun(U_15216,tc_HOL_Obool),U_15216),hAPP(c_COMBS(U_15216,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15216),c_fconj),U_15213))),hAPP(hAPP(c_COMBC(U_15216,tc_fun(U_15216,U_15216),tc_fun(U_15216,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15216,tc_HOL_Obool),tc_fun(tc_fun(U_15216,U_15216),tc_fun(U_15216,tc_HOL_Obool)),U_15216),c_COMBB(U_15216,tc_HOL_Obool,U_15216)),c_fequal)),U_15215)))))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_15214,hAPP(U_15215,sK342(U_15216,U_15215,U_15214,U_15213)))),hAPP(U_15214,sK342(U_15216,U_15215,U_15214,U_15213))))
        & hBOOL(hAPP(U_15213,sK342(U_15216,U_15215,U_15214,U_15213))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK342]),skolemize(U_15212,sK342(U_15216,U_15215,U_15214,U_15213))],[f_3800_2]) ).

fof(f_3800_4,plain,
    ( ! [U_15213,U_15214,U_15215,U_15216] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_15214,hAPP(U_15215,sK342(U_15216,U_15215,U_15214,U_15213)))),hAPP(U_15214,sK342(U_15216,U_15215,U_15214,U_15213))))
        | ~ sP1016(U_15213,U_15214,U_15215,U_15216) )
    & ! [U_15213,U_15214,U_15215,U_15216] :
        ( hBOOL(hAPP(U_15213,sK342(U_15216,U_15215,U_15214,U_15213)))
        | ~ sP1016(U_15213,U_15214,U_15215,U_15216) )
    & ! [U_15213,U_15214,U_15215,U_15216] :
        ( c_Wellfounded_Owf(U_15216,hAPP(c_Set_OCollect(tc_prod(U_15216,U_15216)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15216,U_15216,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15216,tc_HOL_Obool),tc_fun(U_15216,tc_HOL_Obool),U_15216),hAPP(c_COMBS(U_15216,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15216),c_fconj),U_15213))),hAPP(hAPP(c_COMBC(U_15216,tc_fun(U_15216,U_15216),tc_fun(U_15216,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15216,tc_HOL_Obool),tc_fun(tc_fun(U_15216,U_15216),tc_fun(U_15216,tc_HOL_Obool)),U_15216),c_COMBB(U_15216,tc_HOL_Obool,U_15216)),c_fequal)),U_15215)))))
        | sP1016(U_15213,U_15214,U_15215,U_15216) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1016])],[f_3800_3]) ).

cnf(f_3800_5,plain,
    ( c_Wellfounded_Owf(U_15216,hAPP(c_Set_OCollect(tc_prod(U_15216,U_15216)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15216,U_15216,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15216,tc_HOL_Obool),tc_fun(U_15216,tc_HOL_Obool),U_15216),hAPP(c_COMBS(U_15216,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15216),c_fconj),U_15213))),hAPP(hAPP(c_COMBC(U_15216,tc_fun(U_15216,U_15216),tc_fun(U_15216,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15216,tc_HOL_Obool),tc_fun(tc_fun(U_15216,U_15216),tc_fun(U_15216,tc_HOL_Obool)),U_15216),c_COMBB(U_15216,tc_HOL_Obool,U_15216)),c_fequal)),U_15215)))))
    | sP1016(U_15213,U_15214,U_15215,U_15216) ),
    inference(clausify,[status(thm)],[f_3800_4]) ).

cnf(f_3800_6,plain,
    ( hBOOL(hAPP(U_15213,sK342(U_15216,U_15215,U_15214,U_15213)))
    | ~ sP1016(U_15213,U_15214,U_15215,U_15216) ),
    inference(clausify,[status(thm)],[f_3800_4]) ).

cnf(f_3800_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_15214,hAPP(U_15215,sK342(U_15216,U_15215,U_15214,U_15213)))),hAPP(U_15214,sK342(U_15216,U_15215,U_15214,U_15213))))
    | ~ sP1016(U_15213,U_15214,U_15215,U_15216) ),
    inference(clausify,[status(thm)],[f_3800_4]) ).

fof(f_3801_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_3801_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_3801_1]) ).

cnf(f_3801_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_3801_2]) ).

fof(f_3802_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_3802_2,plain,
    ! [U_15218,U_15217] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_15217),c_List_Olex(U_15217,U_15218))
      | ~ c_Wellfounded_Owf(U_15217,U_15218) ),
    inference(variable_rename,[status(thm)],[f_3802_1]) ).

fof(f_3802_3,plain,
    ! [U_15217,U_15218] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_15217),c_List_Olex(U_15217,U_15218))
      | ~ c_Wellfounded_Owf(U_15217,U_15218) ),
    inference(definitional_conversion,[status(esa)],[f_3802_2]) ).

cnf(f_3802_4,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_15217),c_List_Olex(U_15217,U_15218))
    | ~ c_Wellfounded_Owf(U_15217,U_15218) ),
    inference(clausify,[status(thm)],[f_3802_3]) ).

fof(f_3803_1,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(fof_nnf,[status(thm)],[fact_wf__pred__nat]) ).

fof(f_3803_2,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(definitional_conversion,[status(esa)],[f_3803_1]) ).

cnf(f_3803_3,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(clausify,[status(thm)],[f_3803_2]) ).

fof(f_3804_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_3804_2,plain,
    ! [U_15220,U_15219] : c_List_Olex(U_15219,U_15220) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_15219),tc_List_Olist(U_15219)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_15219,U_15220)),
    inference(variable_rename,[status(thm)],[f_3804_1]) ).

fof(f_3804_3,plain,
    ! [U_15219,U_15220] : c_List_Olex(U_15219,U_15220) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_15219),tc_List_Olist(U_15219)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_15219,U_15220)),
    inference(definitional_conversion,[status(esa)],[f_3804_2]) ).

cnf(f_3804_4,plain,
    c_List_Olex(U_15219,U_15220) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_15219),tc_List_Olist(U_15219)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_15219,U_15220)),
    inference(clausify,[status(thm)],[f_3804_3]) ).

fof(f_3805_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_3805_2,plain,
    ! [U_15223,U_15222,U_15221] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_15221),hAPP(c_List_Olexn(U_15221,U_15222),U_15223))
      | ~ c_Wellfounded_Owf(U_15221,U_15222) ),
    inference(variable_rename,[status(thm)],[f_3805_1]) ).

fof(f_3805_3,plain,
    ! [U_15221,U_15222,U_15223] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_15221),hAPP(c_List_Olexn(U_15221,U_15222),U_15223))
      | ~ c_Wellfounded_Owf(U_15221,U_15222) ),
    inference(definitional_conversion,[status(esa)],[f_3805_2]) ).

cnf(f_3805_4,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_15221),hAPP(c_List_Olexn(U_15221,U_15222),U_15223))
    | ~ c_Wellfounded_Owf(U_15221,U_15222) ),
    inference(clausify,[status(thm)],[f_3805_3]) ).

fof(f_3806_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_3806_2,plain,
    ! [U_15225,U_15224] : hAPP(c_List_Olexn(U_15224,U_15225),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_15224),tc_List_Olist(U_15224)),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3806_1]) ).

fof(f_3806_3,plain,
    ! [U_15224,U_15225] : hAPP(c_List_Olexn(U_15224,U_15225),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_15224),tc_List_Olist(U_15224)),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3806_2]) ).

cnf(f_3806_4,plain,
    hAPP(c_List_Olexn(U_15224,U_15225),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_15224),tc_List_Olist(U_15224)),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3806_3]) ).

fof(f_3807_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_3807_2,plain,
    ! [U_15230,U_15229,U_15228,U_15227] :
      ( c_Wellfounded_Owf(tc_prod(U_15230,U_15228),c_Recdef_Osame__fst(U_15230,U_15228,U_15227,U_15229))
      | ? [U_15226] :
          ( ~ c_Wellfounded_Owf(U_15228,hAPP(U_15229,U_15226))
          & hBOOL(hAPP(U_15227,U_15226)) ) ),
    inference(variable_rename,[status(thm)],[f_3807_1]) ).

fof(f_3807_3,plain,
    ! [U_15230,U_15229,U_15228,U_15227] :
      ( c_Wellfounded_Owf(tc_prod(U_15230,U_15228),c_Recdef_Osame__fst(U_15230,U_15228,U_15227,U_15229))
      | ( ~ c_Wellfounded_Owf(U_15228,hAPP(U_15229,sK343(U_15230,U_15229,U_15228,U_15227)))
        & hBOOL(hAPP(U_15227,sK343(U_15230,U_15229,U_15228,U_15227))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK343]),skolemize(U_15226,sK343(U_15230,U_15229,U_15228,U_15227))],[f_3807_2]) ).

fof(f_3807_4,plain,
    ( ! [U_15227,U_15228,U_15229,U_15230] :
        ( ~ c_Wellfounded_Owf(U_15228,hAPP(U_15229,sK343(U_15230,U_15229,U_15228,U_15227)))
        | ~ sP1017(U_15227,U_15228,U_15229,U_15230) )
    & ! [U_15227,U_15228,U_15229,U_15230] :
        ( hBOOL(hAPP(U_15227,sK343(U_15230,U_15229,U_15228,U_15227)))
        | ~ sP1017(U_15227,U_15228,U_15229,U_15230) )
    & ! [U_15227,U_15228,U_15229,U_15230] :
        ( c_Wellfounded_Owf(tc_prod(U_15230,U_15228),c_Recdef_Osame__fst(U_15230,U_15228,U_15227,U_15229))
        | sP1017(U_15227,U_15228,U_15229,U_15230) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1017])],[f_3807_3]) ).

cnf(f_3807_5,plain,
    ( c_Wellfounded_Owf(tc_prod(U_15230,U_15228),c_Recdef_Osame__fst(U_15230,U_15228,U_15227,U_15229))
    | sP1017(U_15227,U_15228,U_15229,U_15230) ),
    inference(clausify,[status(thm)],[f_3807_4]) ).

cnf(f_3807_6,plain,
    ( hBOOL(hAPP(U_15227,sK343(U_15230,U_15229,U_15228,U_15227)))
    | ~ sP1017(U_15227,U_15228,U_15229,U_15230) ),
    inference(clausify,[status(thm)],[f_3807_4]) ).

cnf(f_3807_7,plain,
    ( ~ c_Wellfounded_Owf(U_15228,hAPP(U_15229,sK343(U_15230,U_15229,U_15228,U_15227)))
    | ~ sP1017(U_15227,U_15228,U_15229,U_15230) ),
    inference(clausify,[status(thm)],[f_3807_4]) ).

fof(f_3808_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_3808_2,plain,
    ! [U_15233,U_15232,U_15231] : hAPP(c_Relation_ORange(U_15231,U_15232),hAPP(c_Set_OCollect(tc_prod(U_15231,U_15232)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15231,U_15232,tc_HOL_Obool),U_15233))) = hAPP(c_Set_OCollect(U_15232),hAPP(hAPP(c_COMBB(tc_fun(U_15231,tc_HOL_Obool),tc_HOL_Obool,U_15232),c_HOL_OEx(U_15231)),hAPP(c_COMBC(U_15231,U_15232,tc_HOL_Obool),U_15233))),
    inference(variable_rename,[status(thm)],[f_3808_1]) ).

fof(f_3808_3,plain,
    ! [U_15231,U_15232,U_15233] : hAPP(c_Relation_ORange(U_15231,U_15232),hAPP(c_Set_OCollect(tc_prod(U_15231,U_15232)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15231,U_15232,tc_HOL_Obool),U_15233))) = hAPP(c_Set_OCollect(U_15232),hAPP(hAPP(c_COMBB(tc_fun(U_15231,tc_HOL_Obool),tc_HOL_Obool,U_15232),c_HOL_OEx(U_15231)),hAPP(c_COMBC(U_15231,U_15232,tc_HOL_Obool),U_15233))),
    inference(definitional_conversion,[status(esa)],[f_3808_2]) ).

cnf(f_3808_4,plain,
    hAPP(c_Relation_ORange(U_15231,U_15232),hAPP(c_Set_OCollect(tc_prod(U_15231,U_15232)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15231,U_15232,tc_HOL_Obool),U_15233))) = hAPP(c_Set_OCollect(U_15232),hAPP(hAPP(c_COMBB(tc_fun(U_15231,tc_HOL_Obool),tc_HOL_Obool,U_15232),c_HOL_OEx(U_15231)),hAPP(c_COMBC(U_15231,U_15232,tc_HOL_Obool),U_15233))),
    inference(clausify,[status(thm)],[f_3808_3]) ).

fof(f_3809_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_3809_2,plain,
    ! [U_15238,U_15237,U_15236,U_15235,U_15234] :
      ( hBOOL(hAPP(hAPP(c_member(U_15235),U_15237),hAPP(c_Relation_ORange(U_15234,U_15235),U_15238)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15234,U_15235)),hAPP(hAPP(c_Product__Type_OPair(U_15234,U_15235),U_15236),U_15237)),U_15238)) ),
    inference(variable_rename,[status(thm)],[f_3809_1]) ).

fof(f_3809_3,plain,
    ! [U_15234,U_15235,U_15236,U_15237,U_15238] :
      ( hBOOL(hAPP(hAPP(c_member(U_15235),U_15237),hAPP(c_Relation_ORange(U_15234,U_15235),U_15238)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15234,U_15235)),hAPP(hAPP(c_Product__Type_OPair(U_15234,U_15235),U_15236),U_15237)),U_15238)) ),
    inference(definitional_conversion,[status(esa)],[f_3809_2]) ).

cnf(f_3809_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15235),U_15237),hAPP(c_Relation_ORange(U_15234,U_15235),U_15238)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15234,U_15235)),hAPP(hAPP(c_Product__Type_OPair(U_15234,U_15235),U_15236),U_15237)),U_15238)) ),
    inference(clausify,[status(thm)],[f_3809_3]) ).

fof(f_3810_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_3810_2,plain,
    ! [U_15240,U_15239] : hAPP(c_Relation_ORange(U_15239,U_15239),c_Relation_OId__on(U_15239,U_15240)) = U_15240,
    inference(variable_rename,[status(thm)],[f_3810_1]) ).

fof(f_3810_3,plain,
    ! [U_15239,U_15240] : hAPP(c_Relation_ORange(U_15239,U_15239),c_Relation_OId__on(U_15239,U_15240)) = U_15240,
    inference(definitional_conversion,[status(esa)],[f_3810_2]) ).

cnf(f_3810_4,plain,
    hAPP(c_Relation_ORange(U_15239,U_15239),c_Relation_OId__on(U_15239,U_15240)) = U_15240,
    inference(clausify,[status(thm)],[f_3810_3]) ).

fof(f_3811_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_3811_2,plain,
    ! [U_15243,U_15242,U_15241] :
      ( ( hAPP(c_Relation_ORange(U_15241,U_15242),U_15243) = c_Orderings_Obot__class_Obot(tc_fun(U_15242,tc_HOL_Obool))
        | U_15243 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15241,U_15242),tc_HOL_Obool)) )
      & ( U_15243 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15241,U_15242),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(U_15241,U_15242),U_15243) != c_Orderings_Obot__class_Obot(tc_fun(U_15242,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3811_1]) ).

fof(f_3811_3,plain,
    ( ! [U_15249,U_15247,U_15245] :
        ( hAPP(c_Relation_ORange(U_15245,U_15247),U_15249) = c_Orderings_Obot__class_Obot(tc_fun(U_15247,tc_HOL_Obool))
        | U_15249 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15245,U_15247),tc_HOL_Obool)) )
    & ! [U_15248,U_15246,U_15244] :
        ( U_15248 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15244,U_15246),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(U_15244,U_15246),U_15248) != c_Orderings_Obot__class_Obot(tc_fun(U_15246,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3811_2]) ).

fof(f_3811_4,plain,
    ( ! [U_15245,U_15247,U_15249] :
        ( hAPP(c_Relation_ORange(U_15245,U_15247),U_15249) = c_Orderings_Obot__class_Obot(tc_fun(U_15247,tc_HOL_Obool))
        | U_15249 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15245,U_15247),tc_HOL_Obool)) )
    & ! [U_15246,U_15248,U_15244] :
        ( U_15248 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15244,U_15246),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(U_15244,U_15246),U_15248) != c_Orderings_Obot__class_Obot(tc_fun(U_15246,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3811_3]) ).

cnf(f_3811_5,plain,
    ( U_15248 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15244,U_15246),tc_HOL_Obool))
    | hAPP(c_Relation_ORange(U_15244,U_15246),U_15248) != c_Orderings_Obot__class_Obot(tc_fun(U_15246,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3811_4]) ).

cnf(f_3811_6,plain,
    ( hAPP(c_Relation_ORange(U_15245,U_15247),U_15249) = c_Orderings_Obot__class_Obot(tc_fun(U_15247,tc_HOL_Obool))
    | U_15249 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15245,U_15247),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3811_4]) ).

fof(f_3812_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_3812_2,plain,
    ! [U_15251,U_15250] : hAPP(c_Relation_ORange(U_15250,U_15251),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15250,U_15251),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_15251,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3812_1]) ).

fof(f_3812_3,plain,
    ! [U_15250,U_15251] : hAPP(c_Relation_ORange(U_15250,U_15251),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15250,U_15251),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_15251,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3812_2]) ).

cnf(f_3812_4,plain,
    hAPP(c_Relation_ORange(U_15250,U_15251),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15250,U_15251),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_15251,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3812_3]) ).

fof(f_3813_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_3813_2,plain,
    ! [U_15255,U_15254,U_15253,U_15252] : hAPP(c_Relation_ORange(U_15252,U_15253),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15252,U_15253),tc_HOL_Obool)),U_15254),U_15255)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15253,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_15252,U_15253),U_15254)),hAPP(c_Relation_ORange(U_15252,U_15253),U_15255)),
    inference(variable_rename,[status(thm)],[f_3813_1]) ).

fof(f_3813_3,plain,
    ! [U_15252,U_15253,U_15254,U_15255] : hAPP(c_Relation_ORange(U_15252,U_15253),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15252,U_15253),tc_HOL_Obool)),U_15254),U_15255)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15253,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_15252,U_15253),U_15254)),hAPP(c_Relation_ORange(U_15252,U_15253),U_15255)),
    inference(definitional_conversion,[status(esa)],[f_3813_2]) ).

cnf(f_3813_4,plain,
    hAPP(c_Relation_ORange(U_15252,U_15253),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15252,U_15253),tc_HOL_Obool)),U_15254),U_15255)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15253,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_15252,U_15253),U_15254)),hAPP(c_Relation_ORange(U_15252,U_15253),U_15255)),
    inference(clausify,[status(thm)],[f_3813_3]) ).

fof(f_3814_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_3814_2,plain,
    ! [U_15258,U_15257,U_15256] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15257),hAPP(c_Relation_ORange(U_15256,U_15257),U_15258)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15256,U_15257)),U_15258)) ),
    inference(variable_rename,[status(thm)],[f_3814_1]) ).

fof(f_3814_3,plain,
    ! [U_15256,U_15257,U_15258] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15257),hAPP(c_Relation_ORange(U_15256,U_15257),U_15258)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15256,U_15257)),U_15258)) ),
    inference(definitional_conversion,[status(esa)],[f_3814_2]) ).

cnf(f_3814_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15257),hAPP(c_Relation_ORange(U_15256,U_15257),U_15258)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15256,U_15257)),U_15258)) ),
    inference(clausify,[status(thm)],[f_3814_3]) ).

fof(f_3815_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_3815_2,plain,
    ! [U_15261,U_15260,U_15259] : hAPP(c_Set_Oimage(tc_prod(U_15259,U_15260),U_15260,c_Product__Type_Osnd(U_15259,U_15260)),U_15261) = hAPP(c_Relation_ORange(U_15259,U_15260),U_15261),
    inference(variable_rename,[status(thm)],[f_3815_1]) ).

fof(f_3815_3,plain,
    ! [U_15259,U_15260,U_15261] : hAPP(c_Set_Oimage(tc_prod(U_15259,U_15260),U_15260,c_Product__Type_Osnd(U_15259,U_15260)),U_15261) = hAPP(c_Relation_ORange(U_15259,U_15260),U_15261),
    inference(definitional_conversion,[status(esa)],[f_3815_2]) ).

cnf(f_3815_4,plain,
    hAPP(c_Set_Oimage(tc_prod(U_15259,U_15260),U_15260,c_Product__Type_Osnd(U_15259,U_15260)),U_15261) = hAPP(c_Relation_ORange(U_15259,U_15260),U_15261),
    inference(clausify,[status(thm)],[f_3815_3]) ).

fof(f_3816_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_3816_2,plain,
    ! [U_15267,U_15266,U_15265,U_15264] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_15264),U_15265),hAPP(c_Relation_ORange(U_15266,U_15264),U_15267)))
        | ! [U_15263] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15266,U_15264)),hAPP(hAPP(c_Product__Type_OPair(U_15266,U_15264),U_15263),U_15265)),U_15267)) )
      & ( ? [U_15262] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15266,U_15264)),hAPP(hAPP(c_Product__Type_OPair(U_15266,U_15264),U_15262),U_15265)),U_15267))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15264),U_15265),hAPP(c_Relation_ORange(U_15266,U_15264),U_15267))) ) ),
    inference(variable_rename,[status(thm)],[f_3816_1]) ).

fof(f_3816_3,plain,
    ( ! [U_15275,U_15273,U_15271,U_15269] :
        ( hBOOL(hAPP(hAPP(c_member(U_15269),U_15271),hAPP(c_Relation_ORange(U_15273,U_15269),U_15275)))
        | ! [U_15263] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15273,U_15269)),hAPP(hAPP(c_Product__Type_OPair(U_15273,U_15269),U_15263),U_15271)),U_15275)) )
    & ! [U_15274,U_15272,U_15270,U_15268] :
        ( ? [U_15262] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15272,U_15268)),hAPP(hAPP(c_Product__Type_OPair(U_15272,U_15268),U_15262),U_15270)),U_15274))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15268),U_15270),hAPP(c_Relation_ORange(U_15272,U_15268),U_15274))) ) ),
    inference(miniscope,[status(thm)],[f_3816_2]) ).

fof(f_3816_4,plain,
    ( ! [U_15275,U_15273,U_15271,U_15269] :
        ( hBOOL(hAPP(hAPP(c_member(U_15269),U_15271),hAPP(c_Relation_ORange(U_15273,U_15269),U_15275)))
        | ! [U_15263] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15273,U_15269)),hAPP(hAPP(c_Product__Type_OPair(U_15273,U_15269),U_15263),U_15271)),U_15275)) )
    & ! [U_15274,U_15272,U_15270,U_15268] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15272,U_15268)),hAPP(hAPP(c_Product__Type_OPair(U_15272,U_15268),sK344(U_15274,U_15272,U_15270,U_15268)),U_15270)),U_15274))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15268),U_15270),hAPP(c_Relation_ORange(U_15272,U_15268),U_15274))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK344]),skolemize(U_15262,sK344(U_15274,U_15272,U_15270,U_15268))],[f_3816_3]) ).

fof(f_3816_5,plain,
    ( ! [U_15263,U_15269,U_15271,U_15273,U_15275] :
        ( hBOOL(hAPP(hAPP(c_member(U_15269),U_15271),hAPP(c_Relation_ORange(U_15273,U_15269),U_15275)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15273,U_15269)),hAPP(hAPP(c_Product__Type_OPair(U_15273,U_15269),U_15263),U_15271)),U_15275)) )
    & ! [U_15270,U_15272,U_15274,U_15268] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15272,U_15268)),hAPP(hAPP(c_Product__Type_OPair(U_15272,U_15268),sK344(U_15274,U_15272,U_15270,U_15268)),U_15270)),U_15274))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15268),U_15270),hAPP(c_Relation_ORange(U_15272,U_15268),U_15274))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3816_4]) ).

cnf(f_3816_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15272,U_15268)),hAPP(hAPP(c_Product__Type_OPair(U_15272,U_15268),sK344(U_15274,U_15272,U_15270,U_15268)),U_15270)),U_15274))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15268),U_15270),hAPP(c_Relation_ORange(U_15272,U_15268),U_15274))) ),
    inference(clausify,[status(thm)],[f_3816_5]) ).

cnf(f_3816_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15269),U_15271),hAPP(c_Relation_ORange(U_15273,U_15269),U_15275)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15273,U_15269)),hAPP(hAPP(c_Product__Type_OPair(U_15273,U_15269),U_15263),U_15271)),U_15275)) ),
    inference(clausify,[status(thm)],[f_3816_5]) ).

fof(f_3817_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_3817_2,plain,
    ! [U_15280,U_15279,U_15278,U_15277,U_15276] : hAPP(c_Relation_ORange(U_15276,U_15277),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15276,U_15277)),hAPP(hAPP(c_Product__Type_OPair(U_15276,U_15277),U_15278),U_15279)),U_15280)) = hAPP(hAPP(c_Set_Oinsert(U_15277),U_15279),hAPP(c_Relation_ORange(U_15276,U_15277),U_15280)),
    inference(variable_rename,[status(thm)],[f_3817_1]) ).

fof(f_3817_3,plain,
    ! [U_15276,U_15277,U_15278,U_15279,U_15280] : hAPP(c_Relation_ORange(U_15276,U_15277),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15276,U_15277)),hAPP(hAPP(c_Product__Type_OPair(U_15276,U_15277),U_15278),U_15279)),U_15280)) = hAPP(hAPP(c_Set_Oinsert(U_15277),U_15279),hAPP(c_Relation_ORange(U_15276,U_15277),U_15280)),
    inference(definitional_conversion,[status(esa)],[f_3817_2]) ).

cnf(f_3817_4,plain,
    hAPP(c_Relation_ORange(U_15276,U_15277),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15276,U_15277)),hAPP(hAPP(c_Product__Type_OPair(U_15276,U_15277),U_15278),U_15279)),U_15280)) = hAPP(hAPP(c_Set_Oinsert(U_15277),U_15279),hAPP(c_Relation_ORange(U_15276,U_15277),U_15280)),
    inference(clausify,[status(thm)],[f_3817_3]) ).

fof(f_3818_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_3818_2,plain,
    ! [U_15284,U_15283,U_15282,U_15281] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15281,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_15282,U_15281),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15282,U_15281),tc_HOL_Obool)),U_15283),U_15284))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15281,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_15282,U_15281),U_15283)),hAPP(c_Relation_ORange(U_15282,U_15281),U_15284)))),
    inference(variable_rename,[status(thm)],[f_3818_1]) ).

fof(f_3818_3,plain,
    ! [U_15281,U_15282,U_15283,U_15284] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15281,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_15282,U_15281),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15282,U_15281),tc_HOL_Obool)),U_15283),U_15284))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15281,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_15282,U_15281),U_15283)),hAPP(c_Relation_ORange(U_15282,U_15281),U_15284)))),
    inference(definitional_conversion,[status(esa)],[f_3818_2]) ).

cnf(f_3818_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15281,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_15282,U_15281),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15282,U_15281),tc_HOL_Obool)),U_15283),U_15284))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15281,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_15282,U_15281),U_15283)),hAPP(c_Relation_ORange(U_15282,U_15281),U_15284)))),
    inference(clausify,[status(thm)],[f_3818_3]) ).

fof(f_3819_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_3819_2,plain,
    ! [U_15288,U_15287,U_15286,U_15285] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15285,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15285,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_15286,U_15285),U_15287)),hAPP(c_Relation_ORange(U_15286,U_15285),U_15288))),hAPP(c_Relation_ORange(U_15286,U_15285),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_15286,U_15285),tc_HOL_Obool)),U_15287),U_15288)))),
    inference(variable_rename,[status(thm)],[f_3819_1]) ).

fof(f_3819_3,plain,
    ! [U_15285,U_15286,U_15287,U_15288] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15285,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15285,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_15286,U_15285),U_15287)),hAPP(c_Relation_ORange(U_15286,U_15285),U_15288))),hAPP(c_Relation_ORange(U_15286,U_15285),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_15286,U_15285),tc_HOL_Obool)),U_15287),U_15288)))),
    inference(definitional_conversion,[status(esa)],[f_3819_2]) ).

cnf(f_3819_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15285,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15285,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_15286,U_15285),U_15287)),hAPP(c_Relation_ORange(U_15286,U_15285),U_15288))),hAPP(c_Relation_ORange(U_15286,U_15285),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_15286,U_15285),tc_HOL_Obool)),U_15287),U_15288)))),
    inference(clausify,[status(thm)],[f_3819_3]) ).

fof(f_3820_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_3820_2,plain,
    ! [U_15292,U_15291,U_15290,U_15289] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(U_15289,U_15290,hAPP(hAPP(c_COMBC(U_15289,tc_fun(tc_prod(U_15289,U_15290),tc_HOL_Obool),tc_fun(U_15290,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15290,tc_fun(tc_fun(tc_prod(U_15289,U_15290),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15289,U_15290),tc_HOL_Obool),tc_fun(U_15290,tc_HOL_Obool)),U_15289),c_COMBC(U_15290,tc_fun(tc_prod(U_15289,U_15290),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15290,tc_prod(U_15289,U_15290)),tc_fun(U_15290,tc_fun(tc_fun(tc_prod(U_15289,U_15290),tc_HOL_Obool),tc_HOL_Obool)),U_15289),hAPP(c_COMBB(tc_prod(U_15289,U_15290),tc_fun(tc_fun(tc_prod(U_15289,U_15290),tc_HOL_Obool),tc_HOL_Obool),U_15290),c_member(tc_prod(U_15289,U_15290)))),c_Product__Type_OPair(U_15289,U_15290)))),U_15291)),U_15292))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15290),U_15292),hAPP(c_Relation_ORange(U_15289,U_15290),U_15291))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_15290),U_15292),hAPP(c_Relation_ORange(U_15289,U_15290),U_15291)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_15289,U_15290,hAPP(hAPP(c_COMBC(U_15289,tc_fun(tc_prod(U_15289,U_15290),tc_HOL_Obool),tc_fun(U_15290,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15290,tc_fun(tc_fun(tc_prod(U_15289,U_15290),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15289,U_15290),tc_HOL_Obool),tc_fun(U_15290,tc_HOL_Obool)),U_15289),c_COMBC(U_15290,tc_fun(tc_prod(U_15289,U_15290),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15290,tc_prod(U_15289,U_15290)),tc_fun(U_15290,tc_fun(tc_fun(tc_prod(U_15289,U_15290),tc_HOL_Obool),tc_HOL_Obool)),U_15289),hAPP(c_COMBB(tc_prod(U_15289,U_15290),tc_fun(tc_fun(tc_prod(U_15289,U_15290),tc_HOL_Obool),tc_HOL_Obool),U_15290),c_member(tc_prod(U_15289,U_15290)))),c_Product__Type_OPair(U_15289,U_15290)))),U_15291)),U_15292)) ) ),
    inference(variable_rename,[status(thm)],[f_3820_1]) ).

fof(f_3820_3,plain,
    ( ! [U_15300,U_15298,U_15296,U_15294] :
        ( hBOOL(hAPP(c_Predicate_ORangeP(U_15294,U_15296,hAPP(hAPP(c_COMBC(U_15294,tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_fun(U_15296,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15296,tc_fun(tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_fun(U_15296,tc_HOL_Obool)),U_15294),c_COMBC(U_15296,tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15296,tc_prod(U_15294,U_15296)),tc_fun(U_15296,tc_fun(tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_HOL_Obool)),U_15294),hAPP(c_COMBB(tc_prod(U_15294,U_15296),tc_fun(tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_HOL_Obool),U_15296),c_member(tc_prod(U_15294,U_15296)))),c_Product__Type_OPair(U_15294,U_15296)))),U_15298)),U_15300))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15296),U_15300),hAPP(c_Relation_ORange(U_15294,U_15296),U_15298))) )
    & ! [U_15299,U_15297,U_15295,U_15293] :
        ( hBOOL(hAPP(hAPP(c_member(U_15295),U_15299),hAPP(c_Relation_ORange(U_15293,U_15295),U_15297)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_15293,U_15295,hAPP(hAPP(c_COMBC(U_15293,tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_fun(U_15295,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15295,tc_fun(tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_fun(U_15295,tc_HOL_Obool)),U_15293),c_COMBC(U_15295,tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15295,tc_prod(U_15293,U_15295)),tc_fun(U_15295,tc_fun(tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_HOL_Obool)),U_15293),hAPP(c_COMBB(tc_prod(U_15293,U_15295),tc_fun(tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_HOL_Obool),U_15295),c_member(tc_prod(U_15293,U_15295)))),c_Product__Type_OPair(U_15293,U_15295)))),U_15297)),U_15299)) ) ),
    inference(miniscope,[status(thm)],[f_3820_2]) ).

fof(f_3820_4,plain,
    ( ! [U_15294,U_15296,U_15298,U_15300] :
        ( hBOOL(hAPP(c_Predicate_ORangeP(U_15294,U_15296,hAPP(hAPP(c_COMBC(U_15294,tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_fun(U_15296,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15296,tc_fun(tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_fun(U_15296,tc_HOL_Obool)),U_15294),c_COMBC(U_15296,tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15296,tc_prod(U_15294,U_15296)),tc_fun(U_15296,tc_fun(tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_HOL_Obool)),U_15294),hAPP(c_COMBB(tc_prod(U_15294,U_15296),tc_fun(tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_HOL_Obool),U_15296),c_member(tc_prod(U_15294,U_15296)))),c_Product__Type_OPair(U_15294,U_15296)))),U_15298)),U_15300))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15296),U_15300),hAPP(c_Relation_ORange(U_15294,U_15296),U_15298))) )
    & ! [U_15299,U_15295,U_15297,U_15293] :
        ( hBOOL(hAPP(hAPP(c_member(U_15295),U_15299),hAPP(c_Relation_ORange(U_15293,U_15295),U_15297)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_15293,U_15295,hAPP(hAPP(c_COMBC(U_15293,tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_fun(U_15295,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15295,tc_fun(tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_fun(U_15295,tc_HOL_Obool)),U_15293),c_COMBC(U_15295,tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15295,tc_prod(U_15293,U_15295)),tc_fun(U_15295,tc_fun(tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_HOL_Obool)),U_15293),hAPP(c_COMBB(tc_prod(U_15293,U_15295),tc_fun(tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_HOL_Obool),U_15295),c_member(tc_prod(U_15293,U_15295)))),c_Product__Type_OPair(U_15293,U_15295)))),U_15297)),U_15299)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3820_3]) ).

cnf(f_3820_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15295),U_15299),hAPP(c_Relation_ORange(U_15293,U_15295),U_15297)))
    | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_15293,U_15295,hAPP(hAPP(c_COMBC(U_15293,tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_fun(U_15295,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15295,tc_fun(tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_fun(U_15295,tc_HOL_Obool)),U_15293),c_COMBC(U_15295,tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15295,tc_prod(U_15293,U_15295)),tc_fun(U_15295,tc_fun(tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_HOL_Obool)),U_15293),hAPP(c_COMBB(tc_prod(U_15293,U_15295),tc_fun(tc_fun(tc_prod(U_15293,U_15295),tc_HOL_Obool),tc_HOL_Obool),U_15295),c_member(tc_prod(U_15293,U_15295)))),c_Product__Type_OPair(U_15293,U_15295)))),U_15297)),U_15299)) ),
    inference(clausify,[status(thm)],[f_3820_4]) ).

cnf(f_3820_6,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_15294,U_15296,hAPP(hAPP(c_COMBC(U_15294,tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_fun(U_15296,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15296,tc_fun(tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_fun(U_15296,tc_HOL_Obool)),U_15294),c_COMBC(U_15296,tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15296,tc_prod(U_15294,U_15296)),tc_fun(U_15296,tc_fun(tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_HOL_Obool)),U_15294),hAPP(c_COMBB(tc_prod(U_15294,U_15296),tc_fun(tc_fun(tc_prod(U_15294,U_15296),tc_HOL_Obool),tc_HOL_Obool),U_15296),c_member(tc_prod(U_15294,U_15296)))),c_Product__Type_OPair(U_15294,U_15296)))),U_15298)),U_15300))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15296),U_15300),hAPP(c_Relation_ORange(U_15294,U_15296),U_15298))) ),
    inference(clausify,[status(thm)],[f_3820_4]) ).

fof(f_3821_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_3821_2,plain,
    ! [U_15305,U_15304,U_15303,U_15302] :
      ( ? [U_15301] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15304,U_15302)),hAPP(hAPP(c_Product__Type_OPair(U_15304,U_15302),U_15301),U_15303)),U_15305))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15302),U_15303),hAPP(c_Relation_ORange(U_15304,U_15302),U_15305))) ),
    inference(variable_rename,[status(thm)],[f_3821_1]) ).

fof(f_3821_3,plain,
    ! [U_15305,U_15304,U_15303,U_15302] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15304,U_15302)),hAPP(hAPP(c_Product__Type_OPair(U_15304,U_15302),sK345(U_15305,U_15304,U_15303,U_15302)),U_15303)),U_15305))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15302),U_15303),hAPP(c_Relation_ORange(U_15304,U_15302),U_15305))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK345]),skolemize(U_15301,sK345(U_15305,U_15304,U_15303,U_15302))],[f_3821_2]) ).

fof(f_3821_4,plain,
    ! [U_15302,U_15303,U_15304,U_15305] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15304,U_15302)),hAPP(hAPP(c_Product__Type_OPair(U_15304,U_15302),sK345(U_15305,U_15304,U_15303,U_15302)),U_15303)),U_15305))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15302),U_15303),hAPP(c_Relation_ORange(U_15304,U_15302),U_15305))) ),
    inference(definitional_conversion,[status(esa)],[f_3821_3]) ).

cnf(f_3821_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15304,U_15302)),hAPP(hAPP(c_Product__Type_OPair(U_15304,U_15302),sK345(U_15305,U_15304,U_15303,U_15302)),U_15303)),U_15305))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15302),U_15303),hAPP(c_Relation_ORange(U_15304,U_15302),U_15305))) ),
    inference(clausify,[status(thm)],[f_3821_4]) ).

fof(f_3822_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_3822_2,plain,
    ! [U_15310,U_15309,U_15308,U_15307,U_15306] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(U_15309,U_15310,U_15306),U_15308))
      | ~ hBOOL(hAPP(hAPP(U_15306,U_15307),U_15308)) ),
    inference(variable_rename,[status(thm)],[f_3822_1]) ).

fof(f_3822_3,plain,
    ! [U_15306,U_15308,U_15307,U_15309,U_15310] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(U_15309,U_15310,U_15306),U_15308))
      | ~ hBOOL(hAPP(hAPP(U_15306,U_15307),U_15308)) ),
    inference(definitional_conversion,[status(esa)],[f_3822_2]) ).

cnf(f_3822_4,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_15309,U_15310,U_15306),U_15308))
    | ~ hBOOL(hAPP(hAPP(U_15306,U_15307),U_15308)) ),
    inference(clausify,[status(thm)],[f_3822_3]) ).

fof(f_3823_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_3823_2,plain,
    ! [U_15316,U_15315,U_15314,U_15313] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(U_15313,U_15314,U_15315),U_15316))
        | ! [U_15312] : ~ hBOOL(hAPP(hAPP(U_15315,U_15312),U_15316)) )
      & ( ? [U_15311] : hBOOL(hAPP(hAPP(U_15315,U_15311),U_15316))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_15313,U_15314,U_15315),U_15316)) ) ),
    inference(variable_rename,[status(thm)],[f_3823_1]) ).

fof(f_3823_3,plain,
    ( ! [U_15324,U_15322] :
        ( ! [U_15320,U_15318] : hBOOL(hAPP(c_Predicate_ORangeP(U_15318,U_15320,U_15322),U_15324))
        | ! [U_15312] : ~ hBOOL(hAPP(hAPP(U_15322,U_15312),U_15324)) )
    & ! [U_15323,U_15321] :
        ( ! [U_15319,U_15317] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_15317,U_15319,U_15321),U_15323))
        | ? [U_15311] : hBOOL(hAPP(hAPP(U_15321,U_15311),U_15323)) ) ),
    inference(miniscope,[status(thm)],[f_3823_2]) ).

fof(f_3823_4,plain,
    ( ! [U_15324,U_15322] :
        ( ! [U_15320,U_15318] : hBOOL(hAPP(c_Predicate_ORangeP(U_15318,U_15320,U_15322),U_15324))
        | ! [U_15312] : ~ hBOOL(hAPP(hAPP(U_15322,U_15312),U_15324)) )
    & ! [U_15323,U_15321] :
        ( ! [U_15319,U_15317] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_15317,U_15319,U_15321),U_15323))
        | hBOOL(hAPP(hAPP(U_15321,sK346(U_15323,U_15321)),U_15323)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK346]),skolemize(U_15311,sK346(U_15323,U_15321))],[f_3823_3]) ).

fof(f_3823_5,plain,
    ( ! [U_15324,U_15312,U_15318,U_15320,U_15322] :
        ( hBOOL(hAPP(c_Predicate_ORangeP(U_15318,U_15320,U_15322),U_15324))
        | ~ hBOOL(hAPP(hAPP(U_15322,U_15312),U_15324)) )
    & ! [U_15321,U_15319,U_15317,U_15323] :
        ( ~ hBOOL(hAPP(c_Predicate_ORangeP(U_15317,U_15319,U_15321),U_15323))
        | hBOOL(hAPP(hAPP(U_15321,sK346(U_15323,U_15321)),U_15323)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3823_4]) ).

cnf(f_3823_6,plain,
    ( ~ hBOOL(hAPP(c_Predicate_ORangeP(U_15317,U_15319,U_15321),U_15323))
    | hBOOL(hAPP(hAPP(U_15321,sK346(U_15323,U_15321)),U_15323)) ),
    inference(clausify,[status(thm)],[f_3823_5]) ).

cnf(f_3823_7,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_15318,U_15320,U_15322),U_15324))
    | ~ hBOOL(hAPP(hAPP(U_15322,U_15312),U_15324)) ),
    inference(clausify,[status(thm)],[f_3823_5]) ).

fof(f_3824_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_3824_2,plain,
    ! [U_15327,U_15326,U_15325] :
      ( c_Wellfounded_Owf(U_15325,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15325,U_15325),tc_HOL_Obool)),U_15326),U_15327))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15325,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15325,U_15325),U_15326)),hAPP(c_Relation_ORange(U_15325,U_15325),U_15327)) != c_Orderings_Obot__class_Obot(tc_fun(U_15325,tc_HOL_Obool))
      | ~ c_Wellfounded_Owf(U_15325,U_15327)
      | ~ c_Wellfounded_Owf(U_15325,U_15326) ),
    inference(variable_rename,[status(thm)],[f_3824_1]) ).

fof(f_3824_3,plain,
    ! [U_15325,U_15326,U_15327] :
      ( c_Wellfounded_Owf(U_15325,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15325,U_15325),tc_HOL_Obool)),U_15326),U_15327))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15325,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15325,U_15325),U_15326)),hAPP(c_Relation_ORange(U_15325,U_15325),U_15327)) != c_Orderings_Obot__class_Obot(tc_fun(U_15325,tc_HOL_Obool))
      | ~ c_Wellfounded_Owf(U_15325,U_15327)
      | ~ c_Wellfounded_Owf(U_15325,U_15326) ),
    inference(definitional_conversion,[status(esa)],[f_3824_2]) ).

cnf(f_3824_4,plain,
    ( c_Wellfounded_Owf(U_15325,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15325,U_15325),tc_HOL_Obool)),U_15326),U_15327))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15325,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15325,U_15325),U_15326)),hAPP(c_Relation_ORange(U_15325,U_15325),U_15327)) != c_Orderings_Obot__class_Obot(tc_fun(U_15325,tc_HOL_Obool))
    | ~ c_Wellfounded_Owf(U_15325,U_15327)
    | ~ c_Wellfounded_Owf(U_15325,U_15326) ),
    inference(clausify,[status(thm)],[f_3824_3]) ).

fof(f_3825_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_3825_2,plain,
    ! [U_15329,U_15328] :
      ( ( c_Wellfounded_OwfP(U_15328,U_15329)
        | ~ c_Wellfounded_Owf(U_15328,hAPP(c_Set_OCollect(tc_prod(U_15328,U_15328)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15328,U_15328,tc_HOL_Obool),U_15329))) )
      & ( c_Wellfounded_Owf(U_15328,hAPP(c_Set_OCollect(tc_prod(U_15328,U_15328)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15328,U_15328,tc_HOL_Obool),U_15329)))
        | ~ c_Wellfounded_OwfP(U_15328,U_15329) ) ),
    inference(variable_rename,[status(thm)],[f_3825_1]) ).

fof(f_3825_3,plain,
    ( ! [U_15333,U_15331] :
        ( c_Wellfounded_OwfP(U_15331,U_15333)
        | ~ c_Wellfounded_Owf(U_15331,hAPP(c_Set_OCollect(tc_prod(U_15331,U_15331)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15331,U_15331,tc_HOL_Obool),U_15333))) )
    & ! [U_15332,U_15330] :
        ( c_Wellfounded_Owf(U_15330,hAPP(c_Set_OCollect(tc_prod(U_15330,U_15330)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15330,U_15330,tc_HOL_Obool),U_15332)))
        | ~ c_Wellfounded_OwfP(U_15330,U_15332) ) ),
    inference(miniscope,[status(thm)],[f_3825_2]) ).

fof(f_3825_4,plain,
    ( ! [U_15331,U_15333] :
        ( c_Wellfounded_OwfP(U_15331,U_15333)
        | ~ c_Wellfounded_Owf(U_15331,hAPP(c_Set_OCollect(tc_prod(U_15331,U_15331)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15331,U_15331,tc_HOL_Obool),U_15333))) )
    & ! [U_15330,U_15332] :
        ( c_Wellfounded_Owf(U_15330,hAPP(c_Set_OCollect(tc_prod(U_15330,U_15330)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15330,U_15330,tc_HOL_Obool),U_15332)))
        | ~ c_Wellfounded_OwfP(U_15330,U_15332) ) ),
    inference(definitional_conversion,[status(esa)],[f_3825_3]) ).

cnf(f_3825_5,plain,
    ( c_Wellfounded_Owf(U_15330,hAPP(c_Set_OCollect(tc_prod(U_15330,U_15330)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15330,U_15330,tc_HOL_Obool),U_15332)))
    | ~ c_Wellfounded_OwfP(U_15330,U_15332) ),
    inference(clausify,[status(thm)],[f_3825_4]) ).

cnf(f_3825_6,plain,
    ( c_Wellfounded_OwfP(U_15331,U_15333)
    | ~ c_Wellfounded_Owf(U_15331,hAPP(c_Set_OCollect(tc_prod(U_15331,U_15331)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15331,U_15331,tc_HOL_Obool),U_15333))) ),
    inference(clausify,[status(thm)],[f_3825_4]) ).

fof(f_3826_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_3826_2,plain,
    ! [U_15334] : c_Wellfounded_OwfP(U_15334,hAPP(c_COMBK(tc_fun(U_15334,tc_HOL_Obool),U_15334),hAPP(c_COMBK(tc_HOL_Obool,U_15334),c_fFalse))),
    inference(variable_rename,[status(thm)],[f_3826_1]) ).

fof(f_3826_3,plain,
    ! [U_15334] : c_Wellfounded_OwfP(U_15334,hAPP(c_COMBK(tc_fun(U_15334,tc_HOL_Obool),U_15334),hAPP(c_COMBK(tc_HOL_Obool,U_15334),c_fFalse))),
    inference(definitional_conversion,[status(esa)],[f_3826_2]) ).

cnf(f_3826_4,plain,
    c_Wellfounded_OwfP(U_15334,hAPP(c_COMBK(tc_fun(U_15334,tc_HOL_Obool),U_15334),hAPP(c_COMBK(tc_HOL_Obool,U_15334),c_fFalse))),
    inference(clausify,[status(thm)],[f_3826_3]) ).

fof(f_3827_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_3827_2,plain,
    ! [U_15339,U_15338,U_15337,U_15336,U_15335] :
      ( hBOOL(hAPP(hAPP(c_member(U_15335),U_15337),hAPP(c_Relation_ODomain(U_15335,U_15336),U_15339)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15335,U_15336)),hAPP(hAPP(c_Product__Type_OPair(U_15335,U_15336),U_15337),U_15338)),U_15339)) ),
    inference(variable_rename,[status(thm)],[f_3827_1]) ).

fof(f_3827_3,plain,
    ! [U_15335,U_15336,U_15337,U_15338,U_15339] :
      ( hBOOL(hAPP(hAPP(c_member(U_15335),U_15337),hAPP(c_Relation_ODomain(U_15335,U_15336),U_15339)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15335,U_15336)),hAPP(hAPP(c_Product__Type_OPair(U_15335,U_15336),U_15337),U_15338)),U_15339)) ),
    inference(definitional_conversion,[status(esa)],[f_3827_2]) ).

cnf(f_3827_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15335),U_15337),hAPP(c_Relation_ODomain(U_15335,U_15336),U_15339)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15335,U_15336)),hAPP(hAPP(c_Product__Type_OPair(U_15335,U_15336),U_15337),U_15338)),U_15339)) ),
    inference(clausify,[status(thm)],[f_3827_3]) ).

fof(f_3828_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_3828_2,plain,
    ! [U_15341,U_15340] : hAPP(c_Relation_ODomain(U_15340,U_15340),c_Relation_OId__on(U_15340,U_15341)) = U_15341,
    inference(variable_rename,[status(thm)],[f_3828_1]) ).

fof(f_3828_3,plain,
    ! [U_15340,U_15341] : hAPP(c_Relation_ODomain(U_15340,U_15340),c_Relation_OId__on(U_15340,U_15341)) = U_15341,
    inference(definitional_conversion,[status(esa)],[f_3828_2]) ).

cnf(f_3828_4,plain,
    hAPP(c_Relation_ODomain(U_15340,U_15340),c_Relation_OId__on(U_15340,U_15341)) = U_15341,
    inference(clausify,[status(thm)],[f_3828_3]) ).

fof(f_3829_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_3829_2,plain,
    ! [U_15345,U_15344] :
      ( ( c_Wellfounded_OwfP(U_15344,U_15345)
        | ? [U_15343] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_15344,U_15345),U_15343)) )
      & ( ! [U_15342] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_15344,U_15345),U_15342))
        | ~ c_Wellfounded_OwfP(U_15344,U_15345) ) ),
    inference(variable_rename,[status(thm)],[f_3829_1]) ).

fof(f_3829_3,plain,
    ( ! [U_15349,U_15347] :
        ( c_Wellfounded_OwfP(U_15347,U_15349)
        | ? [U_15343] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_15347,U_15349),U_15343)) )
    & ! [U_15348,U_15346] :
        ( ! [U_15342] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_15346,U_15348),U_15342))
        | ~ c_Wellfounded_OwfP(U_15346,U_15348) ) ),
    inference(miniscope,[status(thm)],[f_3829_2]) ).

fof(f_3829_4,plain,
    ( ! [U_15349,U_15347] :
        ( c_Wellfounded_OwfP(U_15347,U_15349)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_15347,U_15349),sK347(U_15349,U_15347))) )
    & ! [U_15348,U_15346] :
        ( ! [U_15342] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_15346,U_15348),U_15342))
        | ~ c_Wellfounded_OwfP(U_15346,U_15348) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK347]),skolemize(U_15343,sK347(U_15349,U_15347))],[f_3829_3]) ).

fof(f_3829_5,plain,
    ( ! [U_15347,U_15349] :
        ( c_Wellfounded_OwfP(U_15347,U_15349)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_15347,U_15349),sK347(U_15349,U_15347))) )
    & ! [U_15348,U_15342,U_15346] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_15346,U_15348),U_15342))
        | ~ c_Wellfounded_OwfP(U_15346,U_15348) ) ),
    inference(definitional_conversion,[status(esa)],[f_3829_4]) ).

cnf(f_3829_6,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_15346,U_15348),U_15342))
    | ~ c_Wellfounded_OwfP(U_15346,U_15348) ),
    inference(clausify,[status(thm)],[f_3829_5]) ).

cnf(f_3829_7,plain,
    ( c_Wellfounded_OwfP(U_15347,U_15349)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_15347,U_15349),sK347(U_15349,U_15347))) ),
    inference(clausify,[status(thm)],[f_3829_5]) ).

fof(f_3830_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_3830_2,plain,
    ! [U_15352,U_15351,U_15350] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_15350,U_15351),U_15352))
      | ~ c_Wellfounded_OwfP(U_15350,U_15351) ),
    inference(variable_rename,[status(thm)],[f_3830_1]) ).

fof(f_3830_3,plain,
    ! [U_15350,U_15351,U_15352] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_15350,U_15351),U_15352))
      | ~ c_Wellfounded_OwfP(U_15350,U_15351) ),
    inference(definitional_conversion,[status(esa)],[f_3830_2]) ).

cnf(f_3830_4,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_15350,U_15351),U_15352))
    | ~ c_Wellfounded_OwfP(U_15350,U_15351) ),
    inference(clausify,[status(thm)],[f_3830_3]) ).

fof(f_3831_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_3831_2,plain,
    ! [U_15355,U_15354,U_15353] :
      ( c_Wellfounded_OwfP(U_15353,U_15355)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15353,tc_fun(U_15353,tc_HOL_Obool))),U_15355),U_15354))
      | ~ c_Wellfounded_OwfP(U_15353,U_15354) ),
    inference(variable_rename,[status(thm)],[f_3831_1]) ).

fof(f_3831_3,plain,
    ! [U_15353,U_15354,U_15355] :
      ( c_Wellfounded_OwfP(U_15353,U_15355)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15353,tc_fun(U_15353,tc_HOL_Obool))),U_15355),U_15354))
      | ~ c_Wellfounded_OwfP(U_15353,U_15354) ),
    inference(definitional_conversion,[status(esa)],[f_3831_2]) ).

cnf(f_3831_4,plain,
    ( c_Wellfounded_OwfP(U_15353,U_15355)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15353,tc_fun(U_15353,tc_HOL_Obool))),U_15355),U_15354))
    | ~ c_Wellfounded_OwfP(U_15353,U_15354) ),
    inference(clausify,[status(thm)],[f_3831_3]) ).

fof(f_3832_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_3832_2,plain,
    ! [U_15358,U_15357,U_15356] :
      ( ( hAPP(c_Relation_ODomain(U_15356,U_15357),U_15358) = c_Orderings_Obot__class_Obot(tc_fun(U_15356,tc_HOL_Obool))
        | U_15358 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15356,U_15357),tc_HOL_Obool)) )
      & ( U_15358 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15356,U_15357),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(U_15356,U_15357),U_15358) != c_Orderings_Obot__class_Obot(tc_fun(U_15356,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3832_1]) ).

fof(f_3832_3,plain,
    ( ! [U_15364,U_15362,U_15360] :
        ( hAPP(c_Relation_ODomain(U_15360,U_15362),U_15364) = c_Orderings_Obot__class_Obot(tc_fun(U_15360,tc_HOL_Obool))
        | U_15364 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15360,U_15362),tc_HOL_Obool)) )
    & ! [U_15363,U_15361,U_15359] :
        ( U_15363 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15359,U_15361),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(U_15359,U_15361),U_15363) != c_Orderings_Obot__class_Obot(tc_fun(U_15359,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3832_2]) ).

fof(f_3832_4,plain,
    ( ! [U_15360,U_15362,U_15364] :
        ( hAPP(c_Relation_ODomain(U_15360,U_15362),U_15364) = c_Orderings_Obot__class_Obot(tc_fun(U_15360,tc_HOL_Obool))
        | U_15364 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15360,U_15362),tc_HOL_Obool)) )
    & ! [U_15363,U_15361,U_15359] :
        ( U_15363 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15359,U_15361),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(U_15359,U_15361),U_15363) != c_Orderings_Obot__class_Obot(tc_fun(U_15359,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3832_3]) ).

cnf(f_3832_5,plain,
    ( U_15363 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15359,U_15361),tc_HOL_Obool))
    | hAPP(c_Relation_ODomain(U_15359,U_15361),U_15363) != c_Orderings_Obot__class_Obot(tc_fun(U_15359,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3832_4]) ).

cnf(f_3832_6,plain,
    ( hAPP(c_Relation_ODomain(U_15360,U_15362),U_15364) = c_Orderings_Obot__class_Obot(tc_fun(U_15360,tc_HOL_Obool))
    | U_15364 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15360,U_15362),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3832_4]) ).

fof(f_3833_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_3833_2,plain,
    ! [U_15366,U_15365] : hAPP(c_Relation_ODomain(U_15365,U_15366),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15365,U_15366),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_15365,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3833_1]) ).

fof(f_3833_3,plain,
    ! [U_15365,U_15366] : hAPP(c_Relation_ODomain(U_15365,U_15366),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15365,U_15366),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_15365,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3833_2]) ).

cnf(f_3833_4,plain,
    hAPP(c_Relation_ODomain(U_15365,U_15366),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15365,U_15366),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_15365,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3833_3]) ).

fof(f_3834_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_3834_2,plain,
    ! [U_15370,U_15369,U_15368,U_15367] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15367,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15367,U_15368),U_15369)),hAPP(c_Relation_ODomain(U_15367,U_15368),U_15370)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15367,U_15368),tc_HOL_Obool)),U_15369),U_15370)) ),
    inference(variable_rename,[status(thm)],[f_3834_1]) ).

fof(f_3834_3,plain,
    ! [U_15367,U_15368,U_15369,U_15370] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15367,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15367,U_15368),U_15369)),hAPP(c_Relation_ODomain(U_15367,U_15368),U_15370)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15367,U_15368),tc_HOL_Obool)),U_15369),U_15370)) ),
    inference(definitional_conversion,[status(esa)],[f_3834_2]) ).

cnf(f_3834_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15367,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15367,U_15368),U_15369)),hAPP(c_Relation_ODomain(U_15367,U_15368),U_15370)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15367,U_15368),tc_HOL_Obool)),U_15369),U_15370)) ),
    inference(clausify,[status(thm)],[f_3834_3]) ).

fof(f_3835_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_3835_2,plain,
    ! [U_15374,U_15373,U_15372,U_15371] : hAPP(c_Relation_ODomain(U_15371,U_15372),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15371,U_15372),tc_HOL_Obool)),U_15373),U_15374)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15371,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15371,U_15372),U_15373)),hAPP(c_Relation_ODomain(U_15371,U_15372),U_15374)),
    inference(variable_rename,[status(thm)],[f_3835_1]) ).

fof(f_3835_3,plain,
    ! [U_15371,U_15372,U_15373,U_15374] : hAPP(c_Relation_ODomain(U_15371,U_15372),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15371,U_15372),tc_HOL_Obool)),U_15373),U_15374)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15371,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15371,U_15372),U_15373)),hAPP(c_Relation_ODomain(U_15371,U_15372),U_15374)),
    inference(definitional_conversion,[status(esa)],[f_3835_2]) ).

cnf(f_3835_4,plain,
    hAPP(c_Relation_ODomain(U_15371,U_15372),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15371,U_15372),tc_HOL_Obool)),U_15373),U_15374)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15371,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15371,U_15372),U_15373)),hAPP(c_Relation_ODomain(U_15371,U_15372),U_15374)),
    inference(clausify,[status(thm)],[f_3835_3]) ).

fof(f_3836_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_3836_2,plain,
    ! [U_15377,U_15376,U_15375] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15375),hAPP(c_Relation_ODomain(U_15375,U_15376),U_15377)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15375,U_15376)),U_15377)) ),
    inference(variable_rename,[status(thm)],[f_3836_1]) ).

fof(f_3836_3,plain,
    ! [U_15375,U_15376,U_15377] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15375),hAPP(c_Relation_ODomain(U_15375,U_15376),U_15377)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15375,U_15376)),U_15377)) ),
    inference(definitional_conversion,[status(esa)],[f_3836_2]) ).

cnf(f_3836_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15375),hAPP(c_Relation_ODomain(U_15375,U_15376),U_15377)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15375,U_15376)),U_15377)) ),
    inference(clausify,[status(thm)],[f_3836_3]) ).

fof(f_3837_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_3837_2,plain,
    ! [U_15380,U_15379,U_15378] : hAPP(c_Set_Oimage(tc_prod(U_15378,U_15379),U_15378,c_Product__Type_Ofst(U_15378,U_15379)),U_15380) = hAPP(c_Relation_ODomain(U_15378,U_15379),U_15380),
    inference(variable_rename,[status(thm)],[f_3837_1]) ).

fof(f_3837_3,plain,
    ! [U_15378,U_15379,U_15380] : hAPP(c_Set_Oimage(tc_prod(U_15378,U_15379),U_15378,c_Product__Type_Ofst(U_15378,U_15379)),U_15380) = hAPP(c_Relation_ODomain(U_15378,U_15379),U_15380),
    inference(definitional_conversion,[status(esa)],[f_3837_2]) ).

cnf(f_3837_4,plain,
    hAPP(c_Set_Oimage(tc_prod(U_15378,U_15379),U_15378,c_Product__Type_Ofst(U_15378,U_15379)),U_15380) = hAPP(c_Relation_ODomain(U_15378,U_15379),U_15380),
    inference(clausify,[status(thm)],[f_3837_3]) ).

fof(f_3838_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_3838_2,plain,
    ! [U_15386,U_15385,U_15384,U_15383] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_15383),U_15384),hAPP(c_Relation_ODomain(U_15383,U_15385),U_15386)))
        | ! [U_15382] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15383,U_15385)),hAPP(hAPP(c_Product__Type_OPair(U_15383,U_15385),U_15384),U_15382)),U_15386)) )
      & ( ? [U_15381] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15383,U_15385)),hAPP(hAPP(c_Product__Type_OPair(U_15383,U_15385),U_15384),U_15381)),U_15386))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15383),U_15384),hAPP(c_Relation_ODomain(U_15383,U_15385),U_15386))) ) ),
    inference(variable_rename,[status(thm)],[f_3838_1]) ).

fof(f_3838_3,plain,
    ( ! [U_15394,U_15392,U_15390,U_15388] :
        ( hBOOL(hAPP(hAPP(c_member(U_15388),U_15390),hAPP(c_Relation_ODomain(U_15388,U_15392),U_15394)))
        | ! [U_15382] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15388,U_15392)),hAPP(hAPP(c_Product__Type_OPair(U_15388,U_15392),U_15390),U_15382)),U_15394)) )
    & ! [U_15393,U_15391,U_15389,U_15387] :
        ( ? [U_15381] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15387,U_15391)),hAPP(hAPP(c_Product__Type_OPair(U_15387,U_15391),U_15389),U_15381)),U_15393))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15387),U_15389),hAPP(c_Relation_ODomain(U_15387,U_15391),U_15393))) ) ),
    inference(miniscope,[status(thm)],[f_3838_2]) ).

fof(f_3838_4,plain,
    ( ! [U_15394,U_15392,U_15390,U_15388] :
        ( hBOOL(hAPP(hAPP(c_member(U_15388),U_15390),hAPP(c_Relation_ODomain(U_15388,U_15392),U_15394)))
        | ! [U_15382] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15388,U_15392)),hAPP(hAPP(c_Product__Type_OPair(U_15388,U_15392),U_15390),U_15382)),U_15394)) )
    & ! [U_15393,U_15391,U_15389,U_15387] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15387,U_15391)),hAPP(hAPP(c_Product__Type_OPair(U_15387,U_15391),U_15389),sK348(U_15393,U_15391,U_15389,U_15387))),U_15393))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15387),U_15389),hAPP(c_Relation_ODomain(U_15387,U_15391),U_15393))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK348]),skolemize(U_15381,sK348(U_15393,U_15391,U_15389,U_15387))],[f_3838_3]) ).

fof(f_3838_5,plain,
    ( ! [U_15382,U_15388,U_15390,U_15392,U_15394] :
        ( hBOOL(hAPP(hAPP(c_member(U_15388),U_15390),hAPP(c_Relation_ODomain(U_15388,U_15392),U_15394)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15388,U_15392)),hAPP(hAPP(c_Product__Type_OPair(U_15388,U_15392),U_15390),U_15382)),U_15394)) )
    & ! [U_15393,U_15391,U_15389,U_15387] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15387,U_15391)),hAPP(hAPP(c_Product__Type_OPair(U_15387,U_15391),U_15389),sK348(U_15393,U_15391,U_15389,U_15387))),U_15393))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15387),U_15389),hAPP(c_Relation_ODomain(U_15387,U_15391),U_15393))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3838_4]) ).

cnf(f_3838_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15387,U_15391)),hAPP(hAPP(c_Product__Type_OPair(U_15387,U_15391),U_15389),sK348(U_15393,U_15391,U_15389,U_15387))),U_15393))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15387),U_15389),hAPP(c_Relation_ODomain(U_15387,U_15391),U_15393))) ),
    inference(clausify,[status(thm)],[f_3838_5]) ).

cnf(f_3838_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15388),U_15390),hAPP(c_Relation_ODomain(U_15388,U_15392),U_15394)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15388,U_15392)),hAPP(hAPP(c_Product__Type_OPair(U_15388,U_15392),U_15390),U_15382)),U_15394)) ),
    inference(clausify,[status(thm)],[f_3838_5]) ).

fof(f_3839_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_3839_2,plain,
    ! [U_15399,U_15398,U_15397,U_15396,U_15395] : hAPP(c_Relation_ODomain(U_15395,U_15396),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15395,U_15396)),hAPP(hAPP(c_Product__Type_OPair(U_15395,U_15396),U_15397),U_15398)),U_15399)) = hAPP(hAPP(c_Set_Oinsert(U_15395),U_15397),hAPP(c_Relation_ODomain(U_15395,U_15396),U_15399)),
    inference(variable_rename,[status(thm)],[f_3839_1]) ).

fof(f_3839_3,plain,
    ! [U_15395,U_15396,U_15397,U_15398,U_15399] : hAPP(c_Relation_ODomain(U_15395,U_15396),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15395,U_15396)),hAPP(hAPP(c_Product__Type_OPair(U_15395,U_15396),U_15397),U_15398)),U_15399)) = hAPP(hAPP(c_Set_Oinsert(U_15395),U_15397),hAPP(c_Relation_ODomain(U_15395,U_15396),U_15399)),
    inference(definitional_conversion,[status(esa)],[f_3839_2]) ).

cnf(f_3839_4,plain,
    hAPP(c_Relation_ODomain(U_15395,U_15396),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15395,U_15396)),hAPP(hAPP(c_Product__Type_OPair(U_15395,U_15396),U_15397),U_15398)),U_15399)) = hAPP(hAPP(c_Set_Oinsert(U_15395),U_15397),hAPP(c_Relation_ODomain(U_15395,U_15396),U_15399)),
    inference(clausify,[status(thm)],[f_3839_3]) ).

fof(f_3840_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_3840_2,plain,
    ! [U_15403,U_15402,U_15401,U_15400] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15400,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15400,U_15401),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15400,U_15401),tc_HOL_Obool)),U_15402),U_15403))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15400,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15400,U_15401),U_15402)),hAPP(c_Relation_ODomain(U_15400,U_15401),U_15403)))),
    inference(variable_rename,[status(thm)],[f_3840_1]) ).

fof(f_3840_3,plain,
    ! [U_15400,U_15401,U_15402,U_15403] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15400,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15400,U_15401),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15400,U_15401),tc_HOL_Obool)),U_15402),U_15403))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15400,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15400,U_15401),U_15402)),hAPP(c_Relation_ODomain(U_15400,U_15401),U_15403)))),
    inference(definitional_conversion,[status(esa)],[f_3840_2]) ).

cnf(f_3840_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15400,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15400,U_15401),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15400,U_15401),tc_HOL_Obool)),U_15402),U_15403))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15400,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15400,U_15401),U_15402)),hAPP(c_Relation_ODomain(U_15400,U_15401),U_15403)))),
    inference(clausify,[status(thm)],[f_3840_3]) ).

fof(f_3841_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_3841_2,plain,
    ! [U_15407,U_15406,U_15405,U_15404] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15404,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15404,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15404,U_15405),U_15406)),hAPP(c_Relation_ODomain(U_15404,U_15405),U_15407))),hAPP(c_Relation_ODomain(U_15404,U_15405),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_15404,U_15405),tc_HOL_Obool)),U_15406),U_15407)))),
    inference(variable_rename,[status(thm)],[f_3841_1]) ).

fof(f_3841_3,plain,
    ! [U_15404,U_15405,U_15406,U_15407] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15404,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15404,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15404,U_15405),U_15406)),hAPP(c_Relation_ODomain(U_15404,U_15405),U_15407))),hAPP(c_Relation_ODomain(U_15404,U_15405),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_15404,U_15405),tc_HOL_Obool)),U_15406),U_15407)))),
    inference(definitional_conversion,[status(esa)],[f_3841_2]) ).

cnf(f_3841_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15404,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15404,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15404,U_15405),U_15406)),hAPP(c_Relation_ODomain(U_15404,U_15405),U_15407))),hAPP(c_Relation_ODomain(U_15404,U_15405),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_15404,U_15405),tc_HOL_Obool)),U_15406),U_15407)))),
    inference(clausify,[status(thm)],[f_3841_3]) ).

fof(f_3842_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_3842_2,plain,
    ! [U_15409,U_15408] : hAPP(c_Relation_OField(U_15408),U_15409) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15408,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15408,U_15408),U_15409)),hAPP(c_Relation_ORange(U_15408,U_15408),U_15409)),
    inference(variable_rename,[status(thm)],[f_3842_1]) ).

fof(f_3842_3,plain,
    ! [U_15408,U_15409] : hAPP(c_Relation_OField(U_15408),U_15409) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15408,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15408,U_15408),U_15409)),hAPP(c_Relation_ORange(U_15408,U_15408),U_15409)),
    inference(definitional_conversion,[status(esa)],[f_3842_2]) ).

cnf(f_3842_4,plain,
    hAPP(c_Relation_OField(U_15408),U_15409) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15408,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_15408,U_15408),U_15409)),hAPP(c_Relation_ORange(U_15408,U_15408),U_15409)),
    inference(clausify,[status(thm)],[f_3842_3]) ).

fof(f_3843_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_3843_2,plain,
    ! [U_15411,U_15410] :
      ( c_Wellfounded_OwfP(U_15410,c_FunDef_Oin__rel(U_15410,U_15410,U_15411))
      | ~ c_Wellfounded_Owf(U_15410,U_15411) ),
    inference(variable_rename,[status(thm)],[f_3843_1]) ).

fof(f_3843_3,plain,
    ! [U_15411,U_15410] :
      ( c_Wellfounded_OwfP(U_15410,c_FunDef_Oin__rel(U_15410,U_15410,U_15411))
      | ~ c_Wellfounded_Owf(U_15410,U_15411) ),
    inference(definitional_conversion,[status(esa)],[f_3843_2]) ).

cnf(f_3843_4,plain,
    ( c_Wellfounded_OwfP(U_15410,c_FunDef_Oin__rel(U_15410,U_15410,U_15411))
    | ~ c_Wellfounded_Owf(U_15410,U_15411) ),
    inference(clausify,[status(thm)],[f_3843_3]) ).

fof(f_3844_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_3844_2,plain,
    ! [U_15413,U_15412] :
      ( ( c_Wellfounded_OwfP(U_15412,hAPP(hAPP(c_COMBC(U_15412,tc_fun(tc_prod(U_15412,U_15412),tc_HOL_Obool),tc_fun(U_15412,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15412,tc_fun(tc_fun(tc_prod(U_15412,U_15412),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15412,U_15412),tc_HOL_Obool),tc_fun(U_15412,tc_HOL_Obool)),U_15412),c_COMBC(U_15412,tc_fun(tc_prod(U_15412,U_15412),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15412,tc_prod(U_15412,U_15412)),tc_fun(U_15412,tc_fun(tc_fun(tc_prod(U_15412,U_15412),tc_HOL_Obool),tc_HOL_Obool)),U_15412),hAPP(c_COMBB(tc_prod(U_15412,U_15412),tc_fun(tc_fun(tc_prod(U_15412,U_15412),tc_HOL_Obool),tc_HOL_Obool),U_15412),c_member(tc_prod(U_15412,U_15412)))),c_Product__Type_OPair(U_15412,U_15412)))),U_15413))
        | ~ c_Wellfounded_Owf(U_15412,U_15413) )
      & ( c_Wellfounded_Owf(U_15412,U_15413)
        | ~ c_Wellfounded_OwfP(U_15412,hAPP(hAPP(c_COMBC(U_15412,tc_fun(tc_prod(U_15412,U_15412),tc_HOL_Obool),tc_fun(U_15412,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15412,tc_fun(tc_fun(tc_prod(U_15412,U_15412),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15412,U_15412),tc_HOL_Obool),tc_fun(U_15412,tc_HOL_Obool)),U_15412),c_COMBC(U_15412,tc_fun(tc_prod(U_15412,U_15412),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15412,tc_prod(U_15412,U_15412)),tc_fun(U_15412,tc_fun(tc_fun(tc_prod(U_15412,U_15412),tc_HOL_Obool),tc_HOL_Obool)),U_15412),hAPP(c_COMBB(tc_prod(U_15412,U_15412),tc_fun(tc_fun(tc_prod(U_15412,U_15412),tc_HOL_Obool),tc_HOL_Obool),U_15412),c_member(tc_prod(U_15412,U_15412)))),c_Product__Type_OPair(U_15412,U_15412)))),U_15413)) ) ),
    inference(variable_rename,[status(thm)],[f_3844_1]) ).

fof(f_3844_3,plain,
    ( ! [U_15417,U_15415] :
        ( c_Wellfounded_OwfP(U_15415,hAPP(hAPP(c_COMBC(U_15415,tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_fun(U_15415,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15415,tc_fun(tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_fun(U_15415,tc_HOL_Obool)),U_15415),c_COMBC(U_15415,tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15415,tc_prod(U_15415,U_15415)),tc_fun(U_15415,tc_fun(tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_HOL_Obool)),U_15415),hAPP(c_COMBB(tc_prod(U_15415,U_15415),tc_fun(tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_HOL_Obool),U_15415),c_member(tc_prod(U_15415,U_15415)))),c_Product__Type_OPair(U_15415,U_15415)))),U_15417))
        | ~ c_Wellfounded_Owf(U_15415,U_15417) )
    & ! [U_15416,U_15414] :
        ( c_Wellfounded_Owf(U_15414,U_15416)
        | ~ c_Wellfounded_OwfP(U_15414,hAPP(hAPP(c_COMBC(U_15414,tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_fun(U_15414,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15414,tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_fun(U_15414,tc_HOL_Obool)),U_15414),c_COMBC(U_15414,tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15414,tc_prod(U_15414,U_15414)),tc_fun(U_15414,tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),U_15414),hAPP(c_COMBB(tc_prod(U_15414,U_15414),tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool),U_15414),c_member(tc_prod(U_15414,U_15414)))),c_Product__Type_OPair(U_15414,U_15414)))),U_15416)) ) ),
    inference(miniscope,[status(thm)],[f_3844_2]) ).

fof(f_3844_4,plain,
    ( ! [U_15417,U_15415] :
        ( c_Wellfounded_OwfP(U_15415,hAPP(hAPP(c_COMBC(U_15415,tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_fun(U_15415,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15415,tc_fun(tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_fun(U_15415,tc_HOL_Obool)),U_15415),c_COMBC(U_15415,tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15415,tc_prod(U_15415,U_15415)),tc_fun(U_15415,tc_fun(tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_HOL_Obool)),U_15415),hAPP(c_COMBB(tc_prod(U_15415,U_15415),tc_fun(tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_HOL_Obool),U_15415),c_member(tc_prod(U_15415,U_15415)))),c_Product__Type_OPair(U_15415,U_15415)))),U_15417))
        | ~ c_Wellfounded_Owf(U_15415,U_15417) )
    & ! [U_15416,U_15414] :
        ( c_Wellfounded_Owf(U_15414,U_15416)
        | ~ c_Wellfounded_OwfP(U_15414,hAPP(hAPP(c_COMBC(U_15414,tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_fun(U_15414,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15414,tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_fun(U_15414,tc_HOL_Obool)),U_15414),c_COMBC(U_15414,tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15414,tc_prod(U_15414,U_15414)),tc_fun(U_15414,tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),U_15414),hAPP(c_COMBB(tc_prod(U_15414,U_15414),tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool),U_15414),c_member(tc_prod(U_15414,U_15414)))),c_Product__Type_OPair(U_15414,U_15414)))),U_15416)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3844_3]) ).

cnf(f_3844_5,plain,
    ( c_Wellfounded_Owf(U_15414,U_15416)
    | ~ c_Wellfounded_OwfP(U_15414,hAPP(hAPP(c_COMBC(U_15414,tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_fun(U_15414,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15414,tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_fun(U_15414,tc_HOL_Obool)),U_15414),c_COMBC(U_15414,tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15414,tc_prod(U_15414,U_15414)),tc_fun(U_15414,tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),U_15414),hAPP(c_COMBB(tc_prod(U_15414,U_15414),tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool),U_15414),c_member(tc_prod(U_15414,U_15414)))),c_Product__Type_OPair(U_15414,U_15414)))),U_15416)) ),
    inference(clausify,[status(thm)],[f_3844_4]) ).

cnf(f_3844_6,plain,
    ( c_Wellfounded_OwfP(U_15415,hAPP(hAPP(c_COMBC(U_15415,tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_fun(U_15415,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15415,tc_fun(tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_fun(U_15415,tc_HOL_Obool)),U_15415),c_COMBC(U_15415,tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15415,tc_prod(U_15415,U_15415)),tc_fun(U_15415,tc_fun(tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_HOL_Obool)),U_15415),hAPP(c_COMBB(tc_prod(U_15415,U_15415),tc_fun(tc_fun(tc_prod(U_15415,U_15415),tc_HOL_Obool),tc_HOL_Obool),U_15415),c_member(tc_prod(U_15415,U_15415)))),c_Product__Type_OPair(U_15415,U_15415)))),U_15417))
    | ~ c_Wellfounded_Owf(U_15415,U_15417) ),
    inference(clausify,[status(thm)],[f_3844_4]) ).

fof(f_3845_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_3845_2,plain,
    ! [U_15420,U_15419,U_15418] : hAPP(c_Relation_ODomain(U_15418,U_15419),hAPP(c_Set_OCollect(tc_prod(U_15418,U_15419)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15418,U_15419,tc_HOL_Obool),U_15420))) = hAPP(c_Set_OCollect(U_15418),hAPP(hAPP(c_COMBB(tc_fun(U_15419,tc_HOL_Obool),tc_HOL_Obool,U_15418),c_HOL_OEx(U_15419)),U_15420)),
    inference(variable_rename,[status(thm)],[f_3845_1]) ).

fof(f_3845_3,plain,
    ! [U_15418,U_15419,U_15420] : hAPP(c_Relation_ODomain(U_15418,U_15419),hAPP(c_Set_OCollect(tc_prod(U_15418,U_15419)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15418,U_15419,tc_HOL_Obool),U_15420))) = hAPP(c_Set_OCollect(U_15418),hAPP(hAPP(c_COMBB(tc_fun(U_15419,tc_HOL_Obool),tc_HOL_Obool,U_15418),c_HOL_OEx(U_15419)),U_15420)),
    inference(definitional_conversion,[status(esa)],[f_3845_2]) ).

cnf(f_3845_4,plain,
    hAPP(c_Relation_ODomain(U_15418,U_15419),hAPP(c_Set_OCollect(tc_prod(U_15418,U_15419)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15418,U_15419,tc_HOL_Obool),U_15420))) = hAPP(c_Set_OCollect(U_15418),hAPP(hAPP(c_COMBB(tc_fun(U_15419,tc_HOL_Obool),tc_HOL_Obool,U_15418),c_HOL_OEx(U_15419)),U_15420)),
    inference(clausify,[status(thm)],[f_3845_3]) ).

fof(f_3846_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_3846_2,plain,
    ! [U_15424,U_15423,U_15422,U_15421] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(U_15421,U_15422,hAPP(hAPP(c_COMBC(U_15421,tc_fun(tc_prod(U_15421,U_15422),tc_HOL_Obool),tc_fun(U_15422,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15422,tc_fun(tc_fun(tc_prod(U_15421,U_15422),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15421,U_15422),tc_HOL_Obool),tc_fun(U_15422,tc_HOL_Obool)),U_15421),c_COMBC(U_15422,tc_fun(tc_prod(U_15421,U_15422),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15422,tc_prod(U_15421,U_15422)),tc_fun(U_15422,tc_fun(tc_fun(tc_prod(U_15421,U_15422),tc_HOL_Obool),tc_HOL_Obool)),U_15421),hAPP(c_COMBB(tc_prod(U_15421,U_15422),tc_fun(tc_fun(tc_prod(U_15421,U_15422),tc_HOL_Obool),tc_HOL_Obool),U_15422),c_member(tc_prod(U_15421,U_15422)))),c_Product__Type_OPair(U_15421,U_15422)))),U_15423)),U_15424))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15421),U_15424),hAPP(c_Relation_ODomain(U_15421,U_15422),U_15423))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_15421),U_15424),hAPP(c_Relation_ODomain(U_15421,U_15422),U_15423)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_15421,U_15422,hAPP(hAPP(c_COMBC(U_15421,tc_fun(tc_prod(U_15421,U_15422),tc_HOL_Obool),tc_fun(U_15422,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15422,tc_fun(tc_fun(tc_prod(U_15421,U_15422),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15421,U_15422),tc_HOL_Obool),tc_fun(U_15422,tc_HOL_Obool)),U_15421),c_COMBC(U_15422,tc_fun(tc_prod(U_15421,U_15422),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15422,tc_prod(U_15421,U_15422)),tc_fun(U_15422,tc_fun(tc_fun(tc_prod(U_15421,U_15422),tc_HOL_Obool),tc_HOL_Obool)),U_15421),hAPP(c_COMBB(tc_prod(U_15421,U_15422),tc_fun(tc_fun(tc_prod(U_15421,U_15422),tc_HOL_Obool),tc_HOL_Obool),U_15422),c_member(tc_prod(U_15421,U_15422)))),c_Product__Type_OPair(U_15421,U_15422)))),U_15423)),U_15424)) ) ),
    inference(variable_rename,[status(thm)],[f_3846_1]) ).

fof(f_3846_3,plain,
    ( ! [U_15432,U_15430,U_15428,U_15426] :
        ( hBOOL(hAPP(c_Predicate_ODomainP(U_15426,U_15428,hAPP(hAPP(c_COMBC(U_15426,tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_fun(U_15428,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15428,tc_fun(tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_fun(U_15428,tc_HOL_Obool)),U_15426),c_COMBC(U_15428,tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15428,tc_prod(U_15426,U_15428)),tc_fun(U_15428,tc_fun(tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_HOL_Obool)),U_15426),hAPP(c_COMBB(tc_prod(U_15426,U_15428),tc_fun(tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_HOL_Obool),U_15428),c_member(tc_prod(U_15426,U_15428)))),c_Product__Type_OPair(U_15426,U_15428)))),U_15430)),U_15432))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15426),U_15432),hAPP(c_Relation_ODomain(U_15426,U_15428),U_15430))) )
    & ! [U_15431,U_15429,U_15427,U_15425] :
        ( hBOOL(hAPP(hAPP(c_member(U_15425),U_15431),hAPP(c_Relation_ODomain(U_15425,U_15427),U_15429)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_15425,U_15427,hAPP(hAPP(c_COMBC(U_15425,tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_fun(U_15427,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15427,tc_fun(tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_fun(U_15427,tc_HOL_Obool)),U_15425),c_COMBC(U_15427,tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15427,tc_prod(U_15425,U_15427)),tc_fun(U_15427,tc_fun(tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_HOL_Obool)),U_15425),hAPP(c_COMBB(tc_prod(U_15425,U_15427),tc_fun(tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_HOL_Obool),U_15427),c_member(tc_prod(U_15425,U_15427)))),c_Product__Type_OPair(U_15425,U_15427)))),U_15429)),U_15431)) ) ),
    inference(miniscope,[status(thm)],[f_3846_2]) ).

fof(f_3846_4,plain,
    ( ! [U_15426,U_15428,U_15430,U_15432] :
        ( hBOOL(hAPP(c_Predicate_ODomainP(U_15426,U_15428,hAPP(hAPP(c_COMBC(U_15426,tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_fun(U_15428,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15428,tc_fun(tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_fun(U_15428,tc_HOL_Obool)),U_15426),c_COMBC(U_15428,tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15428,tc_prod(U_15426,U_15428)),tc_fun(U_15428,tc_fun(tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_HOL_Obool)),U_15426),hAPP(c_COMBB(tc_prod(U_15426,U_15428),tc_fun(tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_HOL_Obool),U_15428),c_member(tc_prod(U_15426,U_15428)))),c_Product__Type_OPair(U_15426,U_15428)))),U_15430)),U_15432))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15426),U_15432),hAPP(c_Relation_ODomain(U_15426,U_15428),U_15430))) )
    & ! [U_15427,U_15431,U_15425,U_15429] :
        ( hBOOL(hAPP(hAPP(c_member(U_15425),U_15431),hAPP(c_Relation_ODomain(U_15425,U_15427),U_15429)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_15425,U_15427,hAPP(hAPP(c_COMBC(U_15425,tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_fun(U_15427,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15427,tc_fun(tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_fun(U_15427,tc_HOL_Obool)),U_15425),c_COMBC(U_15427,tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15427,tc_prod(U_15425,U_15427)),tc_fun(U_15427,tc_fun(tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_HOL_Obool)),U_15425),hAPP(c_COMBB(tc_prod(U_15425,U_15427),tc_fun(tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_HOL_Obool),U_15427),c_member(tc_prod(U_15425,U_15427)))),c_Product__Type_OPair(U_15425,U_15427)))),U_15429)),U_15431)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3846_3]) ).

cnf(f_3846_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15425),U_15431),hAPP(c_Relation_ODomain(U_15425,U_15427),U_15429)))
    | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_15425,U_15427,hAPP(hAPP(c_COMBC(U_15425,tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_fun(U_15427,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15427,tc_fun(tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_fun(U_15427,tc_HOL_Obool)),U_15425),c_COMBC(U_15427,tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15427,tc_prod(U_15425,U_15427)),tc_fun(U_15427,tc_fun(tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_HOL_Obool)),U_15425),hAPP(c_COMBB(tc_prod(U_15425,U_15427),tc_fun(tc_fun(tc_prod(U_15425,U_15427),tc_HOL_Obool),tc_HOL_Obool),U_15427),c_member(tc_prod(U_15425,U_15427)))),c_Product__Type_OPair(U_15425,U_15427)))),U_15429)),U_15431)) ),
    inference(clausify,[status(thm)],[f_3846_4]) ).

cnf(f_3846_6,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_15426,U_15428,hAPP(hAPP(c_COMBC(U_15426,tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_fun(U_15428,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15428,tc_fun(tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_fun(U_15428,tc_HOL_Obool)),U_15426),c_COMBC(U_15428,tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15428,tc_prod(U_15426,U_15428)),tc_fun(U_15428,tc_fun(tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_HOL_Obool)),U_15426),hAPP(c_COMBB(tc_prod(U_15426,U_15428),tc_fun(tc_fun(tc_prod(U_15426,U_15428),tc_HOL_Obool),tc_HOL_Obool),U_15428),c_member(tc_prod(U_15426,U_15428)))),c_Product__Type_OPair(U_15426,U_15428)))),U_15430)),U_15432))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15426),U_15432),hAPP(c_Relation_ODomain(U_15426,U_15428),U_15430))) ),
    inference(clausify,[status(thm)],[f_3846_4]) ).

fof(f_3847_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_3847_2,plain,
    ! [U_15437,U_15436,U_15435,U_15434] :
      ( ? [U_15433] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15434,U_15436)),hAPP(hAPP(c_Product__Type_OPair(U_15434,U_15436),U_15435),U_15433)),U_15437))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15434),U_15435),hAPP(c_Relation_ODomain(U_15434,U_15436),U_15437))) ),
    inference(variable_rename,[status(thm)],[f_3847_1]) ).

fof(f_3847_3,plain,
    ! [U_15437,U_15436,U_15435,U_15434] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15434,U_15436)),hAPP(hAPP(c_Product__Type_OPair(U_15434,U_15436),U_15435),sK349(U_15437,U_15436,U_15435,U_15434))),U_15437))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15434),U_15435),hAPP(c_Relation_ODomain(U_15434,U_15436),U_15437))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK349]),skolemize(U_15433,sK349(U_15437,U_15436,U_15435,U_15434))],[f_3847_2]) ).

fof(f_3847_4,plain,
    ! [U_15434,U_15435,U_15436,U_15437] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15434,U_15436)),hAPP(hAPP(c_Product__Type_OPair(U_15434,U_15436),U_15435),sK349(U_15437,U_15436,U_15435,U_15434))),U_15437))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15434),U_15435),hAPP(c_Relation_ODomain(U_15434,U_15436),U_15437))) ),
    inference(definitional_conversion,[status(esa)],[f_3847_3]) ).

cnf(f_3847_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15434,U_15436)),hAPP(hAPP(c_Product__Type_OPair(U_15434,U_15436),U_15435),sK349(U_15437,U_15436,U_15435,U_15434))),U_15437))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15434),U_15435),hAPP(c_Relation_ODomain(U_15434,U_15436),U_15437))) ),
    inference(clausify,[status(thm)],[f_3847_4]) ).

fof(f_3848_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_3848_2,plain,
    ! [U_15442,U_15441,U_15440,U_15439,U_15438] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(U_15441,U_15442,U_15438),U_15439))
      | ~ hBOOL(hAPP(hAPP(U_15438,U_15439),U_15440)) ),
    inference(variable_rename,[status(thm)],[f_3848_1]) ).

fof(f_3848_3,plain,
    ! [U_15438,U_15439,U_15440,U_15441,U_15442] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(U_15441,U_15442,U_15438),U_15439))
      | ~ hBOOL(hAPP(hAPP(U_15438,U_15439),U_15440)) ),
    inference(definitional_conversion,[status(esa)],[f_3848_2]) ).

cnf(f_3848_4,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_15441,U_15442,U_15438),U_15439))
    | ~ hBOOL(hAPP(hAPP(U_15438,U_15439),U_15440)) ),
    inference(clausify,[status(thm)],[f_3848_3]) ).

fof(f_3849_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_3849_2,plain,
    ! [U_15448,U_15447,U_15446,U_15445] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(U_15445,U_15446,U_15447),U_15448))
        | ! [U_15444] : ~ hBOOL(hAPP(hAPP(U_15447,U_15448),U_15444)) )
      & ( ? [U_15443] : hBOOL(hAPP(hAPP(U_15447,U_15448),U_15443))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_15445,U_15446,U_15447),U_15448)) ) ),
    inference(variable_rename,[status(thm)],[f_3849_1]) ).

fof(f_3849_3,plain,
    ( ! [U_15456,U_15454] :
        ( ! [U_15452,U_15450] : hBOOL(hAPP(c_Predicate_ODomainP(U_15450,U_15452,U_15454),U_15456))
        | ! [U_15444] : ~ hBOOL(hAPP(hAPP(U_15454,U_15456),U_15444)) )
    & ! [U_15455,U_15453] :
        ( ! [U_15451,U_15449] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_15449,U_15451,U_15453),U_15455))
        | ? [U_15443] : hBOOL(hAPP(hAPP(U_15453,U_15455),U_15443)) ) ),
    inference(miniscope,[status(thm)],[f_3849_2]) ).

fof(f_3849_4,plain,
    ( ! [U_15456,U_15454] :
        ( ! [U_15452,U_15450] : hBOOL(hAPP(c_Predicate_ODomainP(U_15450,U_15452,U_15454),U_15456))
        | ! [U_15444] : ~ hBOOL(hAPP(hAPP(U_15454,U_15456),U_15444)) )
    & ! [U_15455,U_15453] :
        ( ! [U_15451,U_15449] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_15449,U_15451,U_15453),U_15455))
        | hBOOL(hAPP(hAPP(U_15453,U_15455),sK350(U_15455,U_15453))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK350]),skolemize(U_15443,sK350(U_15455,U_15453))],[f_3849_3]) ).

fof(f_3849_5,plain,
    ( ! [U_15456,U_15444,U_15450,U_15452,U_15454] :
        ( hBOOL(hAPP(c_Predicate_ODomainP(U_15450,U_15452,U_15454),U_15456))
        | ~ hBOOL(hAPP(hAPP(U_15454,U_15456),U_15444)) )
    & ! [U_15453,U_15451,U_15449,U_15455] :
        ( ~ hBOOL(hAPP(c_Predicate_ODomainP(U_15449,U_15451,U_15453),U_15455))
        | hBOOL(hAPP(hAPP(U_15453,U_15455),sK350(U_15455,U_15453))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3849_4]) ).

cnf(f_3849_6,plain,
    ( ~ hBOOL(hAPP(c_Predicate_ODomainP(U_15449,U_15451,U_15453),U_15455))
    | hBOOL(hAPP(hAPP(U_15453,U_15455),sK350(U_15455,U_15453))) ),
    inference(clausify,[status(thm)],[f_3849_5]) ).

cnf(f_3849_7,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_15450,U_15452,U_15454),U_15456))
    | ~ hBOOL(hAPP(hAPP(U_15454,U_15456),U_15444)) ),
    inference(clausify,[status(thm)],[f_3849_5]) ).

fof(f_3850_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_3850_2,plain,
    ! [U_15458,U_15457] :
      ( c_Wellfounded_Oacyclic(U_15457,hAPP(c_Set_OCollect(tc_prod(U_15457,U_15457)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15457,U_15457,tc_HOL_Obool),U_15458)))
      | ~ c_Wellfounded_OwfP(U_15457,U_15458) ),
    inference(variable_rename,[status(thm)],[f_3850_1]) ).

fof(f_3850_3,plain,
    ! [U_15457,U_15458] :
      ( c_Wellfounded_Oacyclic(U_15457,hAPP(c_Set_OCollect(tc_prod(U_15457,U_15457)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15457,U_15457,tc_HOL_Obool),U_15458)))
      | ~ c_Wellfounded_OwfP(U_15457,U_15458) ),
    inference(definitional_conversion,[status(esa)],[f_3850_2]) ).

cnf(f_3850_4,plain,
    ( c_Wellfounded_Oacyclic(U_15457,hAPP(c_Set_OCollect(tc_prod(U_15457,U_15457)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15457,U_15457,tc_HOL_Obool),U_15458)))
    | ~ c_Wellfounded_OwfP(U_15457,U_15458) ),
    inference(clausify,[status(thm)],[f_3850_3]) ).

fof(f_3851_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_3851_2,plain,
    ! [U_15462,U_15461,U_15460,U_15459] : c_New__Random__Sequence_Opos__map(U_15459,U_15460,U_15461,U_15462) = c_New__Random__Sequence_Opos__bind(U_15459,U_15460,U_15462,hAPP(c_Fun_Ocomp(U_15460,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_15460))))),U_15459,c_New__Random__Sequence_Opos__single(U_15460)),U_15461)),
    inference(variable_rename,[status(thm)],[f_3851_1]) ).

fof(f_3851_3,plain,
    ! [U_15462,U_15459,U_15460,U_15461] : c_New__Random__Sequence_Opos__map(U_15459,U_15460,U_15461,U_15462) = c_New__Random__Sequence_Opos__bind(U_15459,U_15460,U_15462,hAPP(c_Fun_Ocomp(U_15460,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_15460))))),U_15459,c_New__Random__Sequence_Opos__single(U_15460)),U_15461)),
    inference(definitional_conversion,[status(esa)],[f_3851_2]) ).

cnf(f_3851_4,plain,
    c_New__Random__Sequence_Opos__map(U_15459,U_15460,U_15461,U_15462) = c_New__Random__Sequence_Opos__bind(U_15459,U_15460,U_15462,hAPP(c_Fun_Ocomp(U_15460,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_15460))))),U_15459,c_New__Random__Sequence_Opos__single(U_15460)),U_15461)),
    inference(clausify,[status(thm)],[f_3851_3]) ).

fof(f_3852_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_3852_2,plain,
    ! [U_15464,U_15463] :
      ( c_Wellfounded_Oacyclic(U_15463,U_15464)
      | ~ c_Wellfounded_Owf(U_15463,U_15464) ),
    inference(variable_rename,[status(thm)],[f_3852_1]) ).

fof(f_3852_3,plain,
    ! [U_15464,U_15463] :
      ( c_Wellfounded_Oacyclic(U_15463,U_15464)
      | ~ c_Wellfounded_Owf(U_15463,U_15464) ),
    inference(definitional_conversion,[status(esa)],[f_3852_2]) ).

cnf(f_3852_4,plain,
    ( c_Wellfounded_Oacyclic(U_15463,U_15464)
    | ~ c_Wellfounded_Owf(U_15463,U_15464) ),
    inference(clausify,[status(thm)],[f_3852_3]) ).

fof(f_3853_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_3853_2,plain,
    ! [U_15467,U_15466,U_15465] :
      ( c_Wellfounded_Oacyclic(U_15465,U_15467)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15465,U_15465),tc_HOL_Obool)),U_15467),U_15466))
      | ~ c_Wellfounded_Oacyclic(U_15465,U_15466) ),
    inference(variable_rename,[status(thm)],[f_3853_1]) ).

fof(f_3853_3,plain,
    ! [U_15465,U_15466,U_15467] :
      ( c_Wellfounded_Oacyclic(U_15465,U_15467)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15465,U_15465),tc_HOL_Obool)),U_15467),U_15466))
      | ~ c_Wellfounded_Oacyclic(U_15465,U_15466) ),
    inference(definitional_conversion,[status(esa)],[f_3853_2]) ).

cnf(f_3853_4,plain,
    ( c_Wellfounded_Oacyclic(U_15465,U_15467)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15465,U_15465),tc_HOL_Obool)),U_15467),U_15466))
    | ~ c_Wellfounded_Oacyclic(U_15465,U_15466) ),
    inference(clausify,[status(thm)],[f_3853_3]) ).

fof(f_3854_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_3854_2,plain,
    ! [U_15469,U_15468] :
      ( ( ( c_Wellfounded_Owf(U_15468,U_15469)
          | ~ c_Wellfounded_Oacyclic(U_15468,U_15469) )
        & ( c_Wellfounded_Oacyclic(U_15468,U_15469)
          | ~ c_Wellfounded_Owf(U_15468,U_15469) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15468,U_15468)),U_15469)) ),
    inference(variable_rename,[status(thm)],[f_3854_1]) ).

fof(f_3854_3,plain,
    ( ! [U_15468,U_15469] :
        ( c_Wellfounded_Owf(U_15468,U_15469)
        | ~ c_Wellfounded_Oacyclic(U_15468,U_15469)
        | ~ sP1018(U_15468,U_15469) )
    & ! [U_15468,U_15469] :
        ( c_Wellfounded_Oacyclic(U_15468,U_15469)
        | ~ c_Wellfounded_Owf(U_15468,U_15469)
        | ~ sP1018(U_15468,U_15469) )
    & ! [U_15468,U_15469] :
        ( sP1018(U_15468,U_15469)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15468,U_15468)),U_15469)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1018])],[f_3854_2]) ).

cnf(f_3854_4,plain,
    ( sP1018(U_15468,U_15469)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15468,U_15468)),U_15469)) ),
    inference(clausify,[status(thm)],[f_3854_3]) ).

cnf(f_3854_5,plain,
    ( c_Wellfounded_Oacyclic(U_15468,U_15469)
    | ~ c_Wellfounded_Owf(U_15468,U_15469)
    | ~ sP1018(U_15468,U_15469) ),
    inference(clausify,[status(thm)],[f_3854_3]) ).

cnf(f_3854_6,plain,
    ( c_Wellfounded_Owf(U_15468,U_15469)
    | ~ c_Wellfounded_Oacyclic(U_15468,U_15469)
    | ~ sP1018(U_15468,U_15469) ),
    inference(clausify,[status(thm)],[f_3854_3]) ).

fof(f_3855_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_3855_2,plain,
    ! [U_15471,U_15470] :
      ( c_Wellfounded_Owf(U_15470,U_15471)
      | ~ c_Wellfounded_Oacyclic(U_15470,U_15471)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15470,U_15470)),U_15471)) ),
    inference(variable_rename,[status(thm)],[f_3855_1]) ).

fof(f_3855_3,plain,
    ! [U_15470,U_15471] :
      ( c_Wellfounded_Owf(U_15470,U_15471)
      | ~ c_Wellfounded_Oacyclic(U_15470,U_15471)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15470,U_15470)),U_15471)) ),
    inference(definitional_conversion,[status(esa)],[f_3855_2]) ).

cnf(f_3855_4,plain,
    ( c_Wellfounded_Owf(U_15470,U_15471)
    | ~ c_Wellfounded_Oacyclic(U_15470,U_15471)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15470,U_15470)),U_15471)) ),
    inference(clausify,[status(thm)],[f_3855_3]) ).

fof(f_3856_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_3856_2,plain,
    ! [U_15476,U_15475,U_15474,U_15473,U_15472] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_15472),U_15473),U_15474),U_15475),U_15476) = c_New__DSequence_Opos__single(U_15472,U_15473),
    inference(variable_rename,[status(thm)],[f_3856_1]) ).

fof(f_3856_3,plain,
    ! [U_15472,U_15473,U_15474,U_15475,U_15476] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_15472),U_15473),U_15474),U_15475),U_15476) = c_New__DSequence_Opos__single(U_15472,U_15473),
    inference(definitional_conversion,[status(esa)],[f_3856_2]) ).

cnf(f_3856_4,plain,
    hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_15472),U_15473),U_15474),U_15475),U_15476) = c_New__DSequence_Opos__single(U_15472,U_15473),
    inference(clausify,[status(thm)],[f_3856_3]) ).

fof(f_3857_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_3857_2,plain,
    ! [U_15478,U_15477] :
      ( ( c_Nitpick_Owf_H(U_15477,U_15478)
        | ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
          & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15477,U_15477)),U_15478)) )
        | ~ c_Wellfounded_Oacyclic(U_15477,U_15478) )
      & ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
            | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15477,U_15477)),U_15478)) )
          & c_Wellfounded_Oacyclic(U_15477,U_15478) )
        | ~ c_Nitpick_Owf_H(U_15477,U_15478) ) ),
    inference(variable_rename,[status(thm)],[f_3857_1]) ).

fof(f_3857_3,plain,
    ( ! [U_15482,U_15480] :
        ( c_Nitpick_Owf_H(U_15480,U_15482)
        | ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
          & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15480,U_15480)),U_15482)) )
        | ~ c_Wellfounded_Oacyclic(U_15480,U_15482) )
    & ! [U_15481,U_15479] :
        ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
            | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15479,U_15479)),U_15481)) )
          & c_Wellfounded_Oacyclic(U_15479,U_15481) )
        | ~ c_Nitpick_Owf_H(U_15479,U_15481) ) ),
    inference(miniscope,[status(thm)],[f_3857_2]) ).

fof(f_3857_4,plain,
    ( ! [U_15482,U_15480] :
        ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
        | ~ sP1020(U_15482,U_15480) )
    & ! [U_15482,U_15480] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15480,U_15480)),U_15482))
        | ~ sP1020(U_15482,U_15480) )
    & ! [U_15481,U_15479] :
        ( c_Nitpick_Ounknown(tc_HOL_Obool)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15479,U_15479)),U_15481))
        | ~ sP1019(U_15481,U_15479) )
    & ! [U_15481,U_15479] :
        ( c_Wellfounded_Oacyclic(U_15479,U_15481)
        | ~ sP1019(U_15481,U_15479) )
    & ! [U_15482,U_15480] :
        ( c_Nitpick_Owf_H(U_15480,U_15482)
        | sP1020(U_15482,U_15480)
        | ~ c_Wellfounded_Oacyclic(U_15480,U_15482) )
    & ! [U_15481,U_15479] :
        ( sP1019(U_15481,U_15479)
        | ~ c_Nitpick_Owf_H(U_15479,U_15481) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1019,sP1020])],[f_3857_3]) ).

cnf(f_3857_5,plain,
    ( sP1019(U_15481,U_15479)
    | ~ c_Nitpick_Owf_H(U_15479,U_15481) ),
    inference(clausify,[status(thm)],[f_3857_4]) ).

cnf(f_3857_6,plain,
    ( c_Nitpick_Owf_H(U_15480,U_15482)
    | sP1020(U_15482,U_15480)
    | ~ c_Wellfounded_Oacyclic(U_15480,U_15482) ),
    inference(clausify,[status(thm)],[f_3857_4]) ).

cnf(f_3857_7,plain,
    ( c_Wellfounded_Oacyclic(U_15479,U_15481)
    | ~ sP1019(U_15481,U_15479) ),
    inference(clausify,[status(thm)],[f_3857_4]) ).

cnf(f_3857_8,plain,
    ( c_Nitpick_Ounknown(tc_HOL_Obool)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15479,U_15479)),U_15481))
    | ~ sP1019(U_15481,U_15479) ),
    inference(clausify,[status(thm)],[f_3857_4]) ).

cnf(f_3857_9,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15480,U_15480)),U_15482))
    | ~ sP1020(U_15482,U_15480) ),
    inference(clausify,[status(thm)],[f_3857_4]) ).

cnf(f_3857_10,plain,
    ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
    | ~ sP1020(U_15482,U_15480) ),
    inference(clausify,[status(thm)],[f_3857_4]) ).

fof(f_3858_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_3858_2,plain,
    ! [U_15485,U_15484,U_15483] : hAPP(c_New__DSequence_Opos__single(U_15483,U_15484),U_15485) = c_Lazy__Sequence_Osingle(U_15483,U_15484),
    inference(variable_rename,[status(thm)],[f_3858_1]) ).

fof(f_3858_3,plain,
    ! [U_15483,U_15484,U_15485] : hAPP(c_New__DSequence_Opos__single(U_15483,U_15484),U_15485) = c_Lazy__Sequence_Osingle(U_15483,U_15484),
    inference(definitional_conversion,[status(esa)],[f_3858_2]) ).

cnf(f_3858_4,plain,
    hAPP(c_New__DSequence_Opos__single(U_15483,U_15484),U_15485) = c_Lazy__Sequence_Osingle(U_15483,U_15484),
    inference(clausify,[status(thm)],[f_3858_3]) ).

fof(f_3859_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_3859_2,plain,
    ! [U_15489,U_15488,U_15487,U_15486] : c_New__Random__Sequence_Oneg__map(U_15486,U_15487,U_15488,U_15489) = c_New__Random__Sequence_Oneg__bind(U_15486,U_15487,U_15489,hAPP(c_Fun_Ocomp(U_15487,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_15487)))))),U_15486,c_New__Random__Sequence_Oneg__single(U_15487)),U_15488)),
    inference(variable_rename,[status(thm)],[f_3859_1]) ).

fof(f_3859_3,plain,
    ! [U_15487,U_15486,U_15488,U_15489] : c_New__Random__Sequence_Oneg__map(U_15486,U_15487,U_15488,U_15489) = c_New__Random__Sequence_Oneg__bind(U_15486,U_15487,U_15489,hAPP(c_Fun_Ocomp(U_15487,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_15487)))))),U_15486,c_New__Random__Sequence_Oneg__single(U_15487)),U_15488)),
    inference(definitional_conversion,[status(esa)],[f_3859_2]) ).

cnf(f_3859_4,plain,
    c_New__Random__Sequence_Oneg__map(U_15486,U_15487,U_15488,U_15489) = c_New__Random__Sequence_Oneg__bind(U_15486,U_15487,U_15489,hAPP(c_Fun_Ocomp(U_15487,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_15487)))))),U_15486,c_New__Random__Sequence_Oneg__single(U_15487)),U_15488)),
    inference(clausify,[status(thm)],[f_3859_3]) ).

fof(f_3860_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_3860_2,plain,
    ! [U_15494,U_15493,U_15492,U_15491,U_15490] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_15490),U_15491),U_15492),U_15493),U_15494) = c_New__DSequence_Oneg__single(U_15490,U_15491),
    inference(variable_rename,[status(thm)],[f_3860_1]) ).

fof(f_3860_3,plain,
    ! [U_15492,U_15491,U_15493,U_15490,U_15494] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_15490),U_15491),U_15492),U_15493),U_15494) = c_New__DSequence_Oneg__single(U_15490,U_15491),
    inference(definitional_conversion,[status(esa)],[f_3860_2]) ).

cnf(f_3860_4,plain,
    hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_15490),U_15491),U_15492),U_15493),U_15494) = c_New__DSequence_Oneg__single(U_15490,U_15491),
    inference(clausify,[status(thm)],[f_3860_3]) ).

fof(f_3861_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_3861_2,plain,
    ! [U_15499,U_15498,U_15497,U_15496] :
      ( ? [U_15495] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15496),hAPP(c_Set_OCollect(U_15496),hAPP(hAPP(c_COMBS(U_15496,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15496),c_fconj),hAPP(hAPP(c_COMBC(U_15496,tc_fun(U_15496,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15496)),U_15497))),hAPP(hAPP(c_COMBC(U_15496,U_15498,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_15498,tc_fun(U_15498,tc_HOL_Obool),U_15496),c_fequal),U_15499)),hAPP(U_15499,U_15495))))))
          & hBOOL(hAPP(hAPP(c_member(U_15496),U_15495),U_15497)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15498),hAPP(c_Set_Oimage(U_15496,U_15498,U_15499),U_15497)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15496),U_15497)) ),
    inference(variable_rename,[status(thm)],[f_3861_1]) ).

fof(f_3861_3,plain,
    ! [U_15499,U_15498,U_15497,U_15496] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15496),hAPP(c_Set_OCollect(U_15496),hAPP(hAPP(c_COMBS(U_15496,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15496),c_fconj),hAPP(hAPP(c_COMBC(U_15496,tc_fun(U_15496,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15496)),U_15497))),hAPP(hAPP(c_COMBC(U_15496,U_15498,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_15498,tc_fun(U_15498,tc_HOL_Obool),U_15496),c_fequal),U_15499)),hAPP(U_15499,sK351(U_15499,U_15498,U_15497,U_15496)))))))
        & hBOOL(hAPP(hAPP(c_member(U_15496),sK351(U_15499,U_15498,U_15497,U_15496)),U_15497)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15498),hAPP(c_Set_Oimage(U_15496,U_15498,U_15499),U_15497)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15496),U_15497)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK351]),skolemize(U_15495,sK351(U_15499,U_15498,U_15497,U_15496))],[f_3861_2]) ).

fof(f_3861_4,plain,
    ( ! [U_15496,U_15497,U_15498,U_15499] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15496),hAPP(c_Set_OCollect(U_15496),hAPP(hAPP(c_COMBS(U_15496,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15496),c_fconj),hAPP(hAPP(c_COMBC(U_15496,tc_fun(U_15496,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15496)),U_15497))),hAPP(hAPP(c_COMBC(U_15496,U_15498,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_15498,tc_fun(U_15498,tc_HOL_Obool),U_15496),c_fequal),U_15499)),hAPP(U_15499,sK351(U_15499,U_15498,U_15497,U_15496)))))))
        | ~ sP1021(U_15496,U_15497,U_15498,U_15499) )
    & ! [U_15496,U_15497,U_15498,U_15499] :
        ( hBOOL(hAPP(hAPP(c_member(U_15496),sK351(U_15499,U_15498,U_15497,U_15496)),U_15497))
        | ~ sP1021(U_15496,U_15497,U_15498,U_15499) )
    & ! [U_15496,U_15497,U_15498,U_15499] :
        ( sP1021(U_15496,U_15497,U_15498,U_15499)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15498),hAPP(c_Set_Oimage(U_15496,U_15498,U_15499),U_15497)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15496),U_15497)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1021])],[f_3861_3]) ).

cnf(f_3861_5,plain,
    ( sP1021(U_15496,U_15497,U_15498,U_15499)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15498),hAPP(c_Set_Oimage(U_15496,U_15498,U_15499),U_15497)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15496),U_15497)) ),
    inference(clausify,[status(thm)],[f_3861_4]) ).

cnf(f_3861_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15496),sK351(U_15499,U_15498,U_15497,U_15496)),U_15497))
    | ~ sP1021(U_15496,U_15497,U_15498,U_15499) ),
    inference(clausify,[status(thm)],[f_3861_4]) ).

cnf(f_3861_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15496),hAPP(c_Set_OCollect(U_15496),hAPP(hAPP(c_COMBS(U_15496,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15496),c_fconj),hAPP(hAPP(c_COMBC(U_15496,tc_fun(U_15496,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15496)),U_15497))),hAPP(hAPP(c_COMBC(U_15496,U_15498,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_15498,tc_fun(U_15498,tc_HOL_Obool),U_15496),c_fequal),U_15499)),hAPP(U_15499,sK351(U_15499,U_15498,U_15497,U_15496)))))))
    | ~ sP1021(U_15496,U_15497,U_15498,U_15499) ),
    inference(clausify,[status(thm)],[f_3861_4]) ).

fof(f_3862_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_3862_2,plain,
    ! [U_15502,U_15501,U_15500] : hAPP(c_New__DSequence_Oneg__single(U_15500,U_15501),U_15502) = c_Lazy__Sequence_Ohb__single(U_15500,U_15501),
    inference(variable_rename,[status(thm)],[f_3862_1]) ).

fof(f_3862_3,plain,
    ! [U_15501,U_15502,U_15500] : hAPP(c_New__DSequence_Oneg__single(U_15500,U_15501),U_15502) = c_Lazy__Sequence_Ohb__single(U_15500,U_15501),
    inference(definitional_conversion,[status(esa)],[f_3862_2]) ).

cnf(f_3862_4,plain,
    hAPP(c_New__DSequence_Oneg__single(U_15500,U_15501),U_15502) = c_Lazy__Sequence_Ohb__single(U_15500,U_15501),
    inference(clausify,[status(thm)],[f_3862_3]) ).

fof(f_3863_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_3863_2,plain,
    ! [U_15504] :
    ? [U_15503] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_15503),c_Int_OInteg))
      & U_15504 = hAPP(c_Int_OAbs__Integ,U_15503) ),
    inference(variable_rename,[status(thm)],[f_3863_1]) ).

fof(f_3863_3,plain,
    ! [U_15504] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK352(U_15504)),c_Int_OInteg))
      & U_15504 = hAPP(c_Int_OAbs__Integ,sK352(U_15504)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK352]),skolemize(U_15503,sK352(U_15504))],[f_3863_2]) ).

fof(f_3863_4,plain,
    ( ! [U_15504] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK352(U_15504)),c_Int_OInteg))
    & ! [U_15504] : U_15504 = hAPP(c_Int_OAbs__Integ,sK352(U_15504)) ),
    inference(definitional_conversion,[status(esa)],[f_3863_3]) ).

cnf(f_3863_5,plain,
    U_15504 = hAPP(c_Int_OAbs__Integ,sK352(U_15504)),
    inference(clausify,[status(thm)],[f_3863_4]) ).

cnf(f_3863_6,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK352(U_15504)),c_Int_OInteg)),
    inference(clausify,[status(thm)],[f_3863_4]) ).

fof(f_3864_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_3864_2,plain,
    ! [U_15507,U_15506] :
      ( hBOOL(hAPP(U_15506,U_15507))
      | ? [U_15505] :
          ( ~ hBOOL(hAPP(U_15506,hAPP(c_Int_OAbs__Integ,U_15505)))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_15505),c_Int_OInteg)) ) ),
    inference(variable_rename,[status(thm)],[f_3864_1]) ).

fof(f_3864_3,plain,
    ! [U_15507,U_15506] :
      ( hBOOL(hAPP(U_15506,U_15507))
      | ( ~ hBOOL(hAPP(U_15506,hAPP(c_Int_OAbs__Integ,sK353(U_15507,U_15506))))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK353(U_15507,U_15506)),c_Int_OInteg)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK353]),skolemize(U_15505,sK353(U_15507,U_15506))],[f_3864_2]) ).

fof(f_3864_4,plain,
    ( ! [U_15506,U_15507] :
        ( ~ hBOOL(hAPP(U_15506,hAPP(c_Int_OAbs__Integ,sK353(U_15507,U_15506))))
        | ~ sP1022(U_15506,U_15507) )
    & ! [U_15506,U_15507] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK353(U_15507,U_15506)),c_Int_OInteg))
        | ~ sP1022(U_15506,U_15507) )
    & ! [U_15506,U_15507] :
        ( hBOOL(hAPP(U_15506,U_15507))
        | sP1022(U_15506,U_15507) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1022])],[f_3864_3]) ).

cnf(f_3864_5,plain,
    ( hBOOL(hAPP(U_15506,U_15507))
    | sP1022(U_15506,U_15507) ),
    inference(clausify,[status(thm)],[f_3864_4]) ).

cnf(f_3864_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK353(U_15507,U_15506)),c_Int_OInteg))
    | ~ sP1022(U_15506,U_15507) ),
    inference(clausify,[status(thm)],[f_3864_4]) ).

cnf(f_3864_7,plain,
    ( ~ hBOOL(hAPP(U_15506,hAPP(c_Int_OAbs__Integ,sK353(U_15507,U_15506))))
    | ~ sP1022(U_15506,U_15507) ),
    inference(clausify,[status(thm)],[f_3864_4]) ).

fof(f_3865_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_3865_2,plain,
    ! [U_15512,U_15511,U_15510,U_15509] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15511),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15509,tc_fun(U_15511,tc_HOL_Obool)),U_15510),U_15512)))
      | ? [U_15508] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15511),hAPP(U_15512,U_15508)))
          & hBOOL(hAPP(hAPP(c_member(U_15509),U_15508),U_15510)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15509),U_15510)) ),
    inference(variable_rename,[status(thm)],[f_3865_1]) ).

fof(f_3865_3,plain,
    ! [U_15512,U_15511,U_15510,U_15509] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15511),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15509,tc_fun(U_15511,tc_HOL_Obool)),U_15510),U_15512)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15511),hAPP(U_15512,sK354(U_15512,U_15511,U_15510,U_15509))))
        & hBOOL(hAPP(hAPP(c_member(U_15509),sK354(U_15512,U_15511,U_15510,U_15509)),U_15510)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15509),U_15510)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK354]),skolemize(U_15508,sK354(U_15512,U_15511,U_15510,U_15509))],[f_3865_2]) ).

fof(f_3865_4,plain,
    ( ! [U_15509,U_15510,U_15511,U_15512] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15511),hAPP(U_15512,sK354(U_15512,U_15511,U_15510,U_15509))))
        | ~ sP1023(U_15509,U_15510,U_15511,U_15512) )
    & ! [U_15509,U_15510,U_15511,U_15512] :
        ( hBOOL(hAPP(hAPP(c_member(U_15509),sK354(U_15512,U_15511,U_15510,U_15509)),U_15510))
        | ~ sP1023(U_15509,U_15510,U_15511,U_15512) )
    & ! [U_15509,U_15510,U_15511,U_15512] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15511),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15509,tc_fun(U_15511,tc_HOL_Obool)),U_15510),U_15512)))
        | sP1023(U_15509,U_15510,U_15511,U_15512)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15509),U_15510)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1023])],[f_3865_3]) ).

cnf(f_3865_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15511),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15509,tc_fun(U_15511,tc_HOL_Obool)),U_15510),U_15512)))
    | sP1023(U_15509,U_15510,U_15511,U_15512)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15509),U_15510)) ),
    inference(clausify,[status(thm)],[f_3865_4]) ).

cnf(f_3865_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15509),sK354(U_15512,U_15511,U_15510,U_15509)),U_15510))
    | ~ sP1023(U_15509,U_15510,U_15511,U_15512) ),
    inference(clausify,[status(thm)],[f_3865_4]) ).

cnf(f_3865_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15511),hAPP(U_15512,sK354(U_15512,U_15511,U_15510,U_15509))))
    | ~ sP1023(U_15509,U_15510,U_15511,U_15512) ),
    inference(clausify,[status(thm)],[f_3865_4]) ).

fof(f_3866_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_3866_2,plain,
    ! [U_15515,U_15514] :
      ( 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_15515),U_15514)
      | ? [U_15513] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15515),U_15513))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15513),U_15514)) ) ),
    inference(variable_rename,[status(thm)],[f_3866_1]) ).

fof(f_3866_3,plain,
    ! [U_15515,U_15514] :
      ( 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_15515),U_15514)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15515),sK355(U_15515,U_15514)))
        & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK355(U_15515,U_15514)),U_15514)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK355]),skolemize(U_15513,sK355(U_15515,U_15514))],[f_3866_2]) ).

fof(f_3866_4,plain,
    ( ! [U_15515,U_15514] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15515),sK355(U_15515,U_15514)))
        | ~ sP1024(U_15515,U_15514) )
    & ! [U_15515,U_15514] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK355(U_15515,U_15514)),U_15514))
        | ~ sP1024(U_15515,U_15514) )
    & ! [U_15515,U_15514] :
        ( 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_15515),U_15514)
        | sP1024(U_15515,U_15514) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1024])],[f_3866_3]) ).

cnf(f_3866_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_15515),U_15514)
    | sP1024(U_15515,U_15514) ),
    inference(clausify,[status(thm)],[f_3866_4]) ).

cnf(f_3866_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK355(U_15515,U_15514)),U_15514))
    | ~ sP1024(U_15515,U_15514) ),
    inference(clausify,[status(thm)],[f_3866_4]) ).

cnf(f_3866_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15515),sK355(U_15515,U_15514)))
    | ~ sP1024(U_15515,U_15514) ),
    inference(clausify,[status(thm)],[f_3866_4]) ).

fof(f_3867_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_3867_2,plain,
    ! [U_15521,U_15520,U_15519] :
      ( c_Wellfounded_OwfP(U_15519,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15521,tc_fun(U_15519,tc_fun(U_15519,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_15521,tc_HOL_Obool))),U_15520))
      | ? [U_15518,U_15517] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15519,tc_HOL_Obool)),c_Predicate_ODomainP(U_15519,U_15519,hAPP(U_15520,U_15518))),c_Predicate_ORangeP(U_15519,U_15519,hAPP(U_15520,U_15517))) != c_Orderings_Obot__class_Obot(tc_fun(U_15519,tc_HOL_Obool))
          & hAPP(U_15520,U_15518) != hAPP(U_15520,U_15517) )
      | ? [U_15516] : ~ c_Wellfounded_OwfP(U_15519,hAPP(U_15520,U_15516)) ),
    inference(variable_rename,[status(thm)],[f_3867_1]) ).

fof(f_3867_3,plain,
    ! [U_15521,U_15520,U_15519] :
      ( c_Wellfounded_OwfP(U_15519,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15521,tc_fun(U_15519,tc_fun(U_15519,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_15521,tc_HOL_Obool))),U_15520))
      | ? [U_15518,U_15517] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15519,tc_HOL_Obool)),c_Predicate_ODomainP(U_15519,U_15519,hAPP(U_15520,U_15518))),c_Predicate_ORangeP(U_15519,U_15519,hAPP(U_15520,U_15517))) != c_Orderings_Obot__class_Obot(tc_fun(U_15519,tc_HOL_Obool))
          & hAPP(U_15520,U_15518) != hAPP(U_15520,U_15517) )
      | ~ c_Wellfounded_OwfP(U_15519,hAPP(U_15520,sK356(U_15521,U_15520,U_15519))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK356]),skolemize(U_15516,sK356(U_15521,U_15520,U_15519))],[f_3867_2]) ).

fof(f_3867_4,plain,
    ! [U_15521,U_15520,U_15519] :
      ( c_Wellfounded_OwfP(U_15519,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15521,tc_fun(U_15519,tc_fun(U_15519,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_15521,tc_HOL_Obool))),U_15520))
      | ? [U_15517] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15519,tc_HOL_Obool)),c_Predicate_ODomainP(U_15519,U_15519,hAPP(U_15520,sK357(U_15521,U_15520,U_15519)))),c_Predicate_ORangeP(U_15519,U_15519,hAPP(U_15520,U_15517))) != c_Orderings_Obot__class_Obot(tc_fun(U_15519,tc_HOL_Obool))
          & hAPP(U_15520,sK357(U_15521,U_15520,U_15519)) != hAPP(U_15520,U_15517) )
      | ~ c_Wellfounded_OwfP(U_15519,hAPP(U_15520,sK356(U_15521,U_15520,U_15519))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK357]),skolemize(U_15518,sK357(U_15521,U_15520,U_15519))],[f_3867_3]) ).

fof(f_3867_5,plain,
    ! [U_15521,U_15520,U_15519] :
      ( c_Wellfounded_OwfP(U_15519,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15521,tc_fun(U_15519,tc_fun(U_15519,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_15521,tc_HOL_Obool))),U_15520))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15519,tc_HOL_Obool)),c_Predicate_ODomainP(U_15519,U_15519,hAPP(U_15520,sK357(U_15521,U_15520,U_15519)))),c_Predicate_ORangeP(U_15519,U_15519,hAPP(U_15520,sK358(U_15521,U_15520,U_15519)))) != c_Orderings_Obot__class_Obot(tc_fun(U_15519,tc_HOL_Obool))
        & hAPP(U_15520,sK357(U_15521,U_15520,U_15519)) != hAPP(U_15520,sK358(U_15521,U_15520,U_15519)) )
      | ~ c_Wellfounded_OwfP(U_15519,hAPP(U_15520,sK356(U_15521,U_15520,U_15519))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK358]),skolemize(U_15517,sK358(U_15521,U_15520,U_15519))],[f_3867_4]) ).

fof(f_3867_6,plain,
    ( ! [U_15519,U_15520,U_15521] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15519,tc_HOL_Obool)),c_Predicate_ODomainP(U_15519,U_15519,hAPP(U_15520,sK357(U_15521,U_15520,U_15519)))),c_Predicate_ORangeP(U_15519,U_15519,hAPP(U_15520,sK358(U_15521,U_15520,U_15519)))) != c_Orderings_Obot__class_Obot(tc_fun(U_15519,tc_HOL_Obool))
        | ~ sP1025(U_15519,U_15520,U_15521) )
    & ! [U_15519,U_15520,U_15521] :
        ( hAPP(U_15520,sK357(U_15521,U_15520,U_15519)) != hAPP(U_15520,sK358(U_15521,U_15520,U_15519))
        | ~ sP1025(U_15519,U_15520,U_15521) )
    & ! [U_15519,U_15520,U_15521] :
        ( c_Wellfounded_OwfP(U_15519,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15521,tc_fun(U_15519,tc_fun(U_15519,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_15521,tc_HOL_Obool))),U_15520))
        | sP1025(U_15519,U_15520,U_15521)
        | ~ c_Wellfounded_OwfP(U_15519,hAPP(U_15520,sK356(U_15521,U_15520,U_15519))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1025])],[f_3867_5]) ).

cnf(f_3867_7,plain,
    ( c_Wellfounded_OwfP(U_15519,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15521,tc_fun(U_15519,tc_fun(U_15519,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_15521,tc_HOL_Obool))),U_15520))
    | sP1025(U_15519,U_15520,U_15521)
    | ~ c_Wellfounded_OwfP(U_15519,hAPP(U_15520,sK356(U_15521,U_15520,U_15519))) ),
    inference(clausify,[status(thm)],[f_3867_6]) ).

cnf(f_3867_8,plain,
    ( hAPP(U_15520,sK357(U_15521,U_15520,U_15519)) != hAPP(U_15520,sK358(U_15521,U_15520,U_15519))
    | ~ sP1025(U_15519,U_15520,U_15521) ),
    inference(clausify,[status(thm)],[f_3867_6]) ).

cnf(f_3867_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15519,tc_HOL_Obool)),c_Predicate_ODomainP(U_15519,U_15519,hAPP(U_15520,sK357(U_15521,U_15520,U_15519)))),c_Predicate_ORangeP(U_15519,U_15519,hAPP(U_15520,sK358(U_15521,U_15520,U_15519)))) != c_Orderings_Obot__class_Obot(tc_fun(U_15519,tc_HOL_Obool))
    | ~ sP1025(U_15519,U_15520,U_15521) ),
    inference(clausify,[status(thm)],[f_3867_6]) ).

fof(f_3868_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_3868_2,plain,
    ! [U_15525,U_15524] :
      ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_15524,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_15525)
      | ? [U_15523,U_15522] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15524),hAPP(U_15525,U_15523)),hAPP(U_15525,U_15522)))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_15522),U_15523))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_15523),U_15522)) )
      | ~ class_Orderings_Oorder(U_15524) ),
    inference(variable_rename,[status(thm)],[f_3868_1]) ).

fof(f_3868_3,plain,
    ! [U_15525,U_15524] :
      ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_15524,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_15525)
      | ? [U_15522] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15524),hAPP(U_15525,sK359(U_15525,U_15524))),hAPP(U_15525,U_15522)))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_15522),sK359(U_15525,U_15524)))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK359(U_15525,U_15524)),U_15522)) )
      | ~ class_Orderings_Oorder(U_15524) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK359]),skolemize(U_15523,sK359(U_15525,U_15524))],[f_3868_2]) ).

fof(f_3868_4,plain,
    ! [U_15525,U_15524] :
      ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_15524,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_15525)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15524),hAPP(U_15525,sK359(U_15525,U_15524))),hAPP(U_15525,sK360(U_15525,U_15524))))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK360(U_15525,U_15524)),sK359(U_15525,U_15524)))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK359(U_15525,U_15524)),sK360(U_15525,U_15524))) )
      | ~ class_Orderings_Oorder(U_15524) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK360]),skolemize(U_15522,sK360(U_15525,U_15524))],[f_3868_3]) ).

fof(f_3868_5,plain,
    ( ! [U_15524,U_15525] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15524),hAPP(U_15525,sK359(U_15525,U_15524))),hAPP(U_15525,sK360(U_15525,U_15524))))
        | ~ sP1026(U_15524,U_15525) )
    & ! [U_15524,U_15525] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK360(U_15525,U_15524)),sK359(U_15525,U_15524)))
        | ~ sP1026(U_15524,U_15525) )
    & ! [U_15524,U_15525] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK359(U_15525,U_15524)),sK360(U_15525,U_15524)))
        | ~ sP1026(U_15524,U_15525) )
    & ! [U_15524,U_15525] :
        ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_15524,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_15525)
        | sP1026(U_15524,U_15525)
        | ~ class_Orderings_Oorder(U_15524) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1026])],[f_3868_4]) ).

cnf(f_3868_6,plain,
    ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_15524,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_15525)
    | sP1026(U_15524,U_15525)
    | ~ class_Orderings_Oorder(U_15524) ),
    inference(clausify,[status(thm)],[f_3868_5]) ).

cnf(f_3868_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK359(U_15525,U_15524)),sK360(U_15525,U_15524)))
    | ~ sP1026(U_15524,U_15525) ),
    inference(clausify,[status(thm)],[f_3868_5]) ).

cnf(f_3868_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK360(U_15525,U_15524)),sK359(U_15525,U_15524)))
    | ~ sP1026(U_15524,U_15525) ),
    inference(clausify,[status(thm)],[f_3868_5]) ).

cnf(f_3868_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15524),hAPP(U_15525,sK359(U_15525,U_15524))),hAPP(U_15525,sK360(U_15525,U_15524))))
    | ~ sP1026(U_15524,U_15525) ),
    inference(clausify,[status(thm)],[f_3868_5]) ).

fof(f_3869_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_3869_2,plain,
    ! [U_15529,U_15528,U_15527] :
      ( ? [U_15526] : hAPP(U_15529,U_15526) = c_Option_Ooption_ONone(U_15528)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15527),c_Orderings_Otop__class_Otop(tc_fun(U_15527,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15527),c_Map_Odom(U_15527,U_15528,U_15529))) ),
    inference(variable_rename,[status(thm)],[f_3869_1]) ).

fof(f_3869_3,plain,
    ! [U_15529,U_15528,U_15527] :
      ( hAPP(U_15529,sK361(U_15529,U_15528,U_15527)) = c_Option_Ooption_ONone(U_15528)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15527),c_Orderings_Otop__class_Otop(tc_fun(U_15527,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15527),c_Map_Odom(U_15527,U_15528,U_15529))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK361]),skolemize(U_15526,sK361(U_15529,U_15528,U_15527))],[f_3869_2]) ).

fof(f_3869_4,plain,
    ! [U_15527,U_15529,U_15528] :
      ( hAPP(U_15529,sK361(U_15529,U_15528,U_15527)) = c_Option_Ooption_ONone(U_15528)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15527),c_Orderings_Otop__class_Otop(tc_fun(U_15527,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15527),c_Map_Odom(U_15527,U_15528,U_15529))) ),
    inference(definitional_conversion,[status(esa)],[f_3869_3]) ).

cnf(f_3869_5,plain,
    ( hAPP(U_15529,sK361(U_15529,U_15528,U_15527)) = c_Option_Ooption_ONone(U_15528)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15527),c_Orderings_Otop__class_Otop(tc_fun(U_15527,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15527),c_Map_Odom(U_15527,U_15528,U_15529))) ),
    inference(clausify,[status(thm)],[f_3869_4]) ).

fof(f_3870_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_3870_2,plain,
    ! [U_15537,U_15536,U_15535,U_15534,U_15533,U_15532] :
      ( ? [U_15531,U_15530] :
          ( hBOOL(hAPP(hAPP(c_member(U_15532),U_15533),hAPP(hAPP(U_15536,U_15531),U_15530)))
          & U_15537 = hAPP(hAPP(c_Product__Type_OPair(U_15534,U_15535),U_15531),U_15530) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_15532),U_15533),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15534,U_15535,tc_fun(U_15532,tc_HOL_Obool)),U_15536),U_15537))) ),
    inference(variable_rename,[status(thm)],[f_3870_1]) ).

fof(f_3870_3,plain,
    ! [U_15537,U_15536,U_15535,U_15534,U_15533,U_15532] :
      ( ? [U_15530] :
          ( hBOOL(hAPP(hAPP(c_member(U_15532),U_15533),hAPP(hAPP(U_15536,sK362(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532)),U_15530)))
          & U_15537 = hAPP(hAPP(c_Product__Type_OPair(U_15534,U_15535),sK362(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532)),U_15530) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_15532),U_15533),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15534,U_15535,tc_fun(U_15532,tc_HOL_Obool)),U_15536),U_15537))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK362]),skolemize(U_15531,sK362(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532))],[f_3870_2]) ).

fof(f_3870_4,plain,
    ! [U_15537,U_15536,U_15535,U_15534,U_15533,U_15532] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_15532),U_15533),hAPP(hAPP(U_15536,sK362(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532)),sK363(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532))))
        & U_15537 = hAPP(hAPP(c_Product__Type_OPair(U_15534,U_15535),sK362(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532)),sK363(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_15532),U_15533),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15534,U_15535,tc_fun(U_15532,tc_HOL_Obool)),U_15536),U_15537))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK363]),skolemize(U_15530,sK363(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532))],[f_3870_3]) ).

fof(f_3870_5,plain,
    ( ! [U_15532,U_15533,U_15534,U_15535,U_15536,U_15537] :
        ( hBOOL(hAPP(hAPP(c_member(U_15532),U_15533),hAPP(hAPP(U_15536,sK362(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532)),sK363(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532))))
        | ~ sP1027(U_15532,U_15533,U_15534,U_15535,U_15536,U_15537) )
    & ! [U_15532,U_15533,U_15534,U_15535,U_15536,U_15537] :
        ( U_15537 = hAPP(hAPP(c_Product__Type_OPair(U_15534,U_15535),sK362(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532)),sK363(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532))
        | ~ sP1027(U_15532,U_15533,U_15534,U_15535,U_15536,U_15537) )
    & ! [U_15532,U_15533,U_15534,U_15535,U_15536,U_15537] :
        ( sP1027(U_15532,U_15533,U_15534,U_15535,U_15536,U_15537)
        | ~ hBOOL(hAPP(hAPP(c_member(U_15532),U_15533),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15534,U_15535,tc_fun(U_15532,tc_HOL_Obool)),U_15536),U_15537))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1027])],[f_3870_4]) ).

cnf(f_3870_6,plain,
    ( sP1027(U_15532,U_15533,U_15534,U_15535,U_15536,U_15537)
    | ~ hBOOL(hAPP(hAPP(c_member(U_15532),U_15533),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15534,U_15535,tc_fun(U_15532,tc_HOL_Obool)),U_15536),U_15537))) ),
    inference(clausify,[status(thm)],[f_3870_5]) ).

cnf(f_3870_7,plain,
    ( U_15537 = hAPP(hAPP(c_Product__Type_OPair(U_15534,U_15535),sK362(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532)),sK363(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532))
    | ~ sP1027(U_15532,U_15533,U_15534,U_15535,U_15536,U_15537) ),
    inference(clausify,[status(thm)],[f_3870_5]) ).

cnf(f_3870_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15532),U_15533),hAPP(hAPP(U_15536,sK362(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532)),sK363(U_15537,U_15536,U_15535,U_15534,U_15533,U_15532))))
    | ~ sP1027(U_15532,U_15533,U_15534,U_15535,U_15536,U_15537) ),
    inference(clausify,[status(thm)],[f_3870_5]) ).

fof(f_3871_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_3871_2,plain,
    ! [U_15545,U_15544,U_15543,U_15542,U_15541,U_15540] :
      ( hBOOL(hAPP(hAPP(c_member(U_15543),U_15544),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15541,U_15542,tc_fun(U_15543,tc_HOL_Obool)),U_15545),U_15540)))
      | ? [U_15539,U_15538] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_15543),U_15544),hAPP(hAPP(U_15545,U_15539),U_15538)))
          & U_15540 = hAPP(hAPP(c_Product__Type_OPair(U_15541,U_15542),U_15539),U_15538) ) ),
    inference(variable_rename,[status(thm)],[f_3871_1]) ).

fof(f_3871_3,plain,
    ! [U_15545,U_15544,U_15543,U_15542,U_15541,U_15540] :
      ( hBOOL(hAPP(hAPP(c_member(U_15543),U_15544),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15541,U_15542,tc_fun(U_15543,tc_HOL_Obool)),U_15545),U_15540)))
      | ? [U_15538] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_15543),U_15544),hAPP(hAPP(U_15545,sK364(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540)),U_15538)))
          & U_15540 = hAPP(hAPP(c_Product__Type_OPair(U_15541,U_15542),sK364(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540)),U_15538) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK364]),skolemize(U_15539,sK364(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540))],[f_3871_2]) ).

fof(f_3871_4,plain,
    ! [U_15545,U_15544,U_15543,U_15542,U_15541,U_15540] :
      ( hBOOL(hAPP(hAPP(c_member(U_15543),U_15544),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15541,U_15542,tc_fun(U_15543,tc_HOL_Obool)),U_15545),U_15540)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_15543),U_15544),hAPP(hAPP(U_15545,sK364(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540)),sK365(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540))))
        & U_15540 = hAPP(hAPP(c_Product__Type_OPair(U_15541,U_15542),sK364(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540)),sK365(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK365]),skolemize(U_15538,sK365(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540))],[f_3871_3]) ).

fof(f_3871_5,plain,
    ( ! [U_15541,U_15540,U_15542,U_15543,U_15544,U_15545] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_15543),U_15544),hAPP(hAPP(U_15545,sK364(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540)),sK365(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540))))
        | ~ sP1028(U_15541,U_15540,U_15542,U_15543,U_15544,U_15545) )
    & ! [U_15541,U_15540,U_15542,U_15543,U_15544,U_15545] :
        ( U_15540 = hAPP(hAPP(c_Product__Type_OPair(U_15541,U_15542),sK364(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540)),sK365(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540))
        | ~ sP1028(U_15541,U_15540,U_15542,U_15543,U_15544,U_15545) )
    & ! [U_15541,U_15540,U_15542,U_15543,U_15544,U_15545] :
        ( hBOOL(hAPP(hAPP(c_member(U_15543),U_15544),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15541,U_15542,tc_fun(U_15543,tc_HOL_Obool)),U_15545),U_15540)))
        | sP1028(U_15541,U_15540,U_15542,U_15543,U_15544,U_15545) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1028])],[f_3871_4]) ).

cnf(f_3871_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15543),U_15544),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15541,U_15542,tc_fun(U_15543,tc_HOL_Obool)),U_15545),U_15540)))
    | sP1028(U_15541,U_15540,U_15542,U_15543,U_15544,U_15545) ),
    inference(clausify,[status(thm)],[f_3871_5]) ).

cnf(f_3871_7,plain,
    ( U_15540 = hAPP(hAPP(c_Product__Type_OPair(U_15541,U_15542),sK364(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540)),sK365(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540))
    | ~ sP1028(U_15541,U_15540,U_15542,U_15543,U_15544,U_15545) ),
    inference(clausify,[status(thm)],[f_3871_5]) ).

cnf(f_3871_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15543),U_15544),hAPP(hAPP(U_15545,sK364(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540)),sK365(U_15545,U_15544,U_15543,U_15542,U_15541,U_15540))))
    | ~ sP1028(U_15541,U_15540,U_15542,U_15543,U_15544,U_15545) ),
    inference(clausify,[status(thm)],[f_3871_5]) ).

fof(f_3872_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_3872_2,plain,
    ! [U_15550,U_15549,U_15548,U_15547] :
      ( ? [U_15546] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_15548,U_15546)))
          & hBOOL(hAPP(hAPP(c_member(U_15547),U_15546),U_15549)) )
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15547,tc_Nat_Onat),U_15548),U_15549) != hAPP(c_Nat_OSuc,U_15550) ),
    inference(variable_rename,[status(thm)],[f_3872_1]) ).

fof(f_3872_3,plain,
    ! [U_15550,U_15549,U_15548,U_15547] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_15548,sK366(U_15550,U_15549,U_15548,U_15547))))
        & hBOOL(hAPP(hAPP(c_member(U_15547),sK366(U_15550,U_15549,U_15548,U_15547)),U_15549)) )
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15547,tc_Nat_Onat),U_15548),U_15549) != hAPP(c_Nat_OSuc,U_15550) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK366]),skolemize(U_15546,sK366(U_15550,U_15549,U_15548,U_15547))],[f_3872_2]) ).

fof(f_3872_4,plain,
    ( ! [U_15548,U_15547,U_15549,U_15550] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_15548,sK366(U_15550,U_15549,U_15548,U_15547))))
        | ~ sP1029(U_15548,U_15547,U_15549,U_15550) )
    & ! [U_15548,U_15547,U_15549,U_15550] :
        ( hBOOL(hAPP(hAPP(c_member(U_15547),sK366(U_15550,U_15549,U_15548,U_15547)),U_15549))
        | ~ sP1029(U_15548,U_15547,U_15549,U_15550) )
    & ! [U_15548,U_15547,U_15549,U_15550] :
        ( sP1029(U_15548,U_15547,U_15549,U_15550)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15547,tc_Nat_Onat),U_15548),U_15549) != hAPP(c_Nat_OSuc,U_15550) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1029])],[f_3872_3]) ).

cnf(f_3872_5,plain,
    ( sP1029(U_15548,U_15547,U_15549,U_15550)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15547,tc_Nat_Onat),U_15548),U_15549) != hAPP(c_Nat_OSuc,U_15550) ),
    inference(clausify,[status(thm)],[f_3872_4]) ).

cnf(f_3872_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15547),sK366(U_15550,U_15549,U_15548,U_15547)),U_15549))
    | ~ sP1029(U_15548,U_15547,U_15549,U_15550) ),
    inference(clausify,[status(thm)],[f_3872_4]) ).

cnf(f_3872_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_15548,sK366(U_15550,U_15549,U_15548,U_15547))))
    | ~ sP1029(U_15548,U_15547,U_15549,U_15550) ),
    inference(clausify,[status(thm)],[f_3872_4]) ).

fof(f_3873_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_3873_2,plain,
    ! [U_15553,U_15552,U_15551] : c_Hilbert__Choice_OEps(tc_prod(U_15551,U_15552),hAPP(c_Product__Type_Oprod_Oprod__case(U_15551,U_15552,tc_HOL_Obool),U_15553)) = c_Hilbert__Choice_OEps(tc_prod(U_15551,U_15552),hAPP(hAPP(c_COMBS(tc_prod(U_15551,U_15552),U_15552,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_15551,tc_fun(U_15552,tc_HOL_Obool),tc_prod(U_15551,U_15552)),U_15553),c_Product__Type_Ofst(U_15551,U_15552))),c_Product__Type_Osnd(U_15551,U_15552))),
    inference(variable_rename,[status(thm)],[f_3873_1]) ).

fof(f_3873_3,plain,
    ! [U_15551,U_15552,U_15553] : c_Hilbert__Choice_OEps(tc_prod(U_15551,U_15552),hAPP(c_Product__Type_Oprod_Oprod__case(U_15551,U_15552,tc_HOL_Obool),U_15553)) = c_Hilbert__Choice_OEps(tc_prod(U_15551,U_15552),hAPP(hAPP(c_COMBS(tc_prod(U_15551,U_15552),U_15552,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_15551,tc_fun(U_15552,tc_HOL_Obool),tc_prod(U_15551,U_15552)),U_15553),c_Product__Type_Ofst(U_15551,U_15552))),c_Product__Type_Osnd(U_15551,U_15552))),
    inference(definitional_conversion,[status(esa)],[f_3873_2]) ).

cnf(f_3873_4,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_15551,U_15552),hAPP(c_Product__Type_Oprod_Oprod__case(U_15551,U_15552,tc_HOL_Obool),U_15553)) = c_Hilbert__Choice_OEps(tc_prod(U_15551,U_15552),hAPP(hAPP(c_COMBS(tc_prod(U_15551,U_15552),U_15552,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_15551,tc_fun(U_15552,tc_HOL_Obool),tc_prod(U_15551,U_15552)),U_15553),c_Product__Type_Ofst(U_15551,U_15552))),c_Product__Type_Osnd(U_15551,U_15552))),
    inference(clausify,[status(thm)],[f_3873_3]) ).

fof(f_3874_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_3874_2,plain,
    ! [U_15557,U_15556,U_15555] :
      ( hBOOL(hAPP(U_15555,U_15556))
      | U_15556 != c_Hilbert__Choice_OEps(U_15557,U_15555)
      | ! [U_15554] : ~ hBOOL(hAPP(U_15555,U_15554)) ),
    inference(variable_rename,[status(thm)],[f_3874_1]) ).

fof(f_3874_3,plain,
    ! [U_15555,U_15554,U_15556,U_15557] :
      ( hBOOL(hAPP(U_15555,U_15556))
      | U_15556 != c_Hilbert__Choice_OEps(U_15557,U_15555)
      | ~ hBOOL(hAPP(U_15555,U_15554)) ),
    inference(definitional_conversion,[status(esa)],[f_3874_2]) ).

cnf(f_3874_4,plain,
    ( hBOOL(hAPP(U_15555,U_15556))
    | U_15556 != c_Hilbert__Choice_OEps(U_15557,U_15555)
    | ~ hBOOL(hAPP(U_15555,U_15554)) ),
    inference(clausify,[status(thm)],[f_3874_3]) ).

fof(f_3875_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_3875_2,plain,
    ! [U_15559,U_15558] : c_Hilbert__Choice_OEps(U_15558,hAPP(c_fequal,U_15559)) = U_15559,
    inference(variable_rename,[status(thm)],[f_3875_1]) ).

fof(f_3875_3,plain,
    ! [U_15558,U_15559] : c_Hilbert__Choice_OEps(U_15558,hAPP(c_fequal,U_15559)) = U_15559,
    inference(definitional_conversion,[status(esa)],[f_3875_2]) ).

cnf(f_3875_4,plain,
    c_Hilbert__Choice_OEps(U_15558,hAPP(c_fequal,U_15559)) = U_15559,
    inference(clausify,[status(thm)],[f_3875_3]) ).

fof(f_3876_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_3876_2,plain,
    ! [U_15561,U_15560] : c_Hilbert__Choice_OEps(U_15560,hAPP(hAPP(c_COMBC(U_15560,U_15560,tc_HOL_Obool),c_fequal),U_15561)) = U_15561,
    inference(variable_rename,[status(thm)],[f_3876_1]) ).

fof(f_3876_3,plain,
    ! [U_15560,U_15561] : c_Hilbert__Choice_OEps(U_15560,hAPP(hAPP(c_COMBC(U_15560,U_15560,tc_HOL_Obool),c_fequal),U_15561)) = U_15561,
    inference(definitional_conversion,[status(esa)],[f_3876_2]) ).

cnf(f_3876_4,plain,
    c_Hilbert__Choice_OEps(U_15560,hAPP(hAPP(c_COMBC(U_15560,U_15560,tc_HOL_Obool),c_fequal),U_15561)) = U_15561,
    inference(clausify,[status(thm)],[f_3876_3]) ).

fof(f_3877_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_3877_2,plain,
    ! [U_15565,U_15564] :
      ( ( hBOOL(hAPP(U_15564,c_Hilbert__Choice_OEps(U_15565,U_15564)))
        | ! [U_15563] : ~ hBOOL(hAPP(U_15564,U_15563)) )
      & ( ? [U_15562] : hBOOL(hAPP(U_15564,U_15562))
        | ~ hBOOL(hAPP(U_15564,c_Hilbert__Choice_OEps(U_15565,U_15564))) ) ),
    inference(variable_rename,[status(thm)],[f_3877_1]) ).

fof(f_3877_3,plain,
    ( ! [U_15569,U_15567] :
        ( hBOOL(hAPP(U_15567,c_Hilbert__Choice_OEps(U_15569,U_15567)))
        | ! [U_15563] : ~ hBOOL(hAPP(U_15567,U_15563)) )
    & ! [U_15568,U_15566] :
        ( ? [U_15562] : hBOOL(hAPP(U_15566,U_15562))
        | ~ hBOOL(hAPP(U_15566,c_Hilbert__Choice_OEps(U_15568,U_15566))) ) ),
    inference(miniscope,[status(thm)],[f_3877_2]) ).

fof(f_3877_4,plain,
    ( ! [U_15569,U_15567] :
        ( hBOOL(hAPP(U_15567,c_Hilbert__Choice_OEps(U_15569,U_15567)))
        | ! [U_15563] : ~ hBOOL(hAPP(U_15567,U_15563)) )
    & ! [U_15568,U_15566] :
        ( hBOOL(hAPP(U_15566,sK367(U_15568,U_15566)))
        | ~ hBOOL(hAPP(U_15566,c_Hilbert__Choice_OEps(U_15568,U_15566))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK367]),skolemize(U_15562,sK367(U_15568,U_15566))],[f_3877_3]) ).

fof(f_3877_5,plain,
    ( ! [U_15563,U_15567,U_15569] :
        ( hBOOL(hAPP(U_15567,c_Hilbert__Choice_OEps(U_15569,U_15567)))
        | ~ hBOOL(hAPP(U_15567,U_15563)) )
    & ! [U_15568,U_15566] :
        ( hBOOL(hAPP(U_15566,sK367(U_15568,U_15566)))
        | ~ hBOOL(hAPP(U_15566,c_Hilbert__Choice_OEps(U_15568,U_15566))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3877_4]) ).

cnf(f_3877_6,plain,
    ( hBOOL(hAPP(U_15566,sK367(U_15568,U_15566)))
    | ~ hBOOL(hAPP(U_15566,c_Hilbert__Choice_OEps(U_15568,U_15566))) ),
    inference(clausify,[status(thm)],[f_3877_5]) ).

cnf(f_3877_7,plain,
    ( hBOOL(hAPP(U_15567,c_Hilbert__Choice_OEps(U_15569,U_15567)))
    | ~ hBOOL(hAPP(U_15567,U_15563)) ),
    inference(clausify,[status(thm)],[f_3877_5]) ).

fof(f_3878_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_3878_2,plain,
    ! [U_15572,U_15571] :
      ( hBOOL(hAPP(U_15571,c_Hilbert__Choice_OEps(U_15572,U_15571)))
      | ! [U_15570] : ~ hBOOL(hAPP(U_15571,U_15570)) ),
    inference(variable_rename,[status(thm)],[f_3878_1]) ).

fof(f_3878_3,plain,
    ! [U_15570,U_15571,U_15572] :
      ( hBOOL(hAPP(U_15571,c_Hilbert__Choice_OEps(U_15572,U_15571)))
      | ~ hBOOL(hAPP(U_15571,U_15570)) ),
    inference(definitional_conversion,[status(esa)],[f_3878_2]) ).

cnf(f_3878_4,plain,
    ( hBOOL(hAPP(U_15571,c_Hilbert__Choice_OEps(U_15572,U_15571)))
    | ~ hBOOL(hAPP(U_15571,U_15570)) ),
    inference(clausify,[status(thm)],[f_3878_3]) ).

fof(f_3879_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_3879_2,plain,
    ! [U_15575,U_15574] :
      ( hBOOL(hAPP(U_15574,c_Hilbert__Choice_OEps(U_15575,U_15574)))
      | ! [U_15573] : ~ hBOOL(hAPP(U_15574,U_15573)) ),
    inference(variable_rename,[status(thm)],[f_3879_1]) ).

fof(f_3879_3,plain,
    ! [U_15573,U_15574,U_15575] :
      ( hBOOL(hAPP(U_15574,c_Hilbert__Choice_OEps(U_15575,U_15574)))
      | ~ hBOOL(hAPP(U_15574,U_15573)) ),
    inference(definitional_conversion,[status(esa)],[f_3879_2]) ).

cnf(f_3879_4,plain,
    ( hBOOL(hAPP(U_15574,c_Hilbert__Choice_OEps(U_15575,U_15574)))
    | ~ hBOOL(hAPP(U_15574,U_15573)) ),
    inference(clausify,[status(thm)],[f_3879_3]) ).

fof(f_3880_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_3880_2,plain,
    ! [U_15578,U_15577,U_15576] :
      ( hBOOL(hAPP(U_15576,c_Hilbert__Choice_OEps(U_15578,U_15576)))
      | ~ hBOOL(hAPP(U_15576,U_15577)) ),
    inference(variable_rename,[status(thm)],[f_3880_1]) ).

fof(f_3880_3,plain,
    ! [U_15576,U_15577,U_15578] :
      ( hBOOL(hAPP(U_15576,c_Hilbert__Choice_OEps(U_15578,U_15576)))
      | ~ hBOOL(hAPP(U_15576,U_15577)) ),
    inference(definitional_conversion,[status(esa)],[f_3880_2]) ).

cnf(f_3880_4,plain,
    ( hBOOL(hAPP(U_15576,c_Hilbert__Choice_OEps(U_15578,U_15576)))
    | ~ hBOOL(hAPP(U_15576,U_15577)) ),
    inference(clausify,[status(thm)],[f_3880_3]) ).

fof(f_3881_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_3881_2,plain,
    ! [U_15581,U_15580,U_15579] : c_Hilbert__Choice_OEps(tc_prod(U_15579,U_15580),U_15581) = c_Hilbert__Choice_OEps(tc_prod(U_15579,U_15580),hAPP(c_Product__Type_Oprod_Oprod__case(U_15579,U_15580,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15580,tc_prod(U_15579,U_15580)),tc_fun(U_15580,tc_HOL_Obool),U_15579),hAPP(c_COMBB(tc_prod(U_15579,U_15580),tc_HOL_Obool,U_15580),U_15581)),c_Product__Type_OPair(U_15579,U_15580)))),
    inference(variable_rename,[status(thm)],[f_3881_1]) ).

fof(f_3881_3,plain,
    ! [U_15579,U_15580,U_15581] : c_Hilbert__Choice_OEps(tc_prod(U_15579,U_15580),U_15581) = c_Hilbert__Choice_OEps(tc_prod(U_15579,U_15580),hAPP(c_Product__Type_Oprod_Oprod__case(U_15579,U_15580,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15580,tc_prod(U_15579,U_15580)),tc_fun(U_15580,tc_HOL_Obool),U_15579),hAPP(c_COMBB(tc_prod(U_15579,U_15580),tc_HOL_Obool,U_15580),U_15581)),c_Product__Type_OPair(U_15579,U_15580)))),
    inference(definitional_conversion,[status(esa)],[f_3881_2]) ).

cnf(f_3881_4,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_15579,U_15580),U_15581) = c_Hilbert__Choice_OEps(tc_prod(U_15579,U_15580),hAPP(c_Product__Type_Oprod_Oprod__case(U_15579,U_15580,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15580,tc_prod(U_15579,U_15580)),tc_fun(U_15580,tc_HOL_Obool),U_15579),hAPP(c_COMBB(tc_prod(U_15579,U_15580),tc_HOL_Obool,U_15580),U_15581)),c_Product__Type_OPair(U_15579,U_15580)))),
    inference(clausify,[status(thm)],[f_3881_3]) ).

fof(f_3882_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_3882_2,plain,
    ! [U_15585,U_15584,U_15583,U_15582] : c_Hilbert__Choice_OEps(tc_prod(U_15582,U_15583),hAPP(c_Product__Type_Oprod_Oprod__case(U_15582,U_15583,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15582,tc_fun(U_15583,tc_HOL_Obool),tc_fun(U_15583,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15583,tc_HOL_Obool),tc_fun(U_15583,tc_HOL_Obool)),U_15582),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15583)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15582),c_fconj),hAPP(c_fequal,U_15584)))),hAPP(c_fequal,U_15585)))) = hAPP(hAPP(c_Product__Type_OPair(U_15582,U_15583),U_15584),U_15585),
    inference(variable_rename,[status(thm)],[f_3882_1]) ).

fof(f_3882_3,plain,
    ! [U_15582,U_15583,U_15584,U_15585] : c_Hilbert__Choice_OEps(tc_prod(U_15582,U_15583),hAPP(c_Product__Type_Oprod_Oprod__case(U_15582,U_15583,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15582,tc_fun(U_15583,tc_HOL_Obool),tc_fun(U_15583,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15583,tc_HOL_Obool),tc_fun(U_15583,tc_HOL_Obool)),U_15582),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15583)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15582),c_fconj),hAPP(c_fequal,U_15584)))),hAPP(c_fequal,U_15585)))) = hAPP(hAPP(c_Product__Type_OPair(U_15582,U_15583),U_15584),U_15585),
    inference(definitional_conversion,[status(esa)],[f_3882_2]) ).

cnf(f_3882_4,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_15582,U_15583),hAPP(c_Product__Type_Oprod_Oprod__case(U_15582,U_15583,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15582,tc_fun(U_15583,tc_HOL_Obool),tc_fun(U_15583,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15583,tc_HOL_Obool),tc_fun(U_15583,tc_HOL_Obool)),U_15582),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15583)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15582),c_fconj),hAPP(c_fequal,U_15584)))),hAPP(c_fequal,U_15585)))) = hAPP(hAPP(c_Product__Type_OPair(U_15582,U_15583),U_15584),U_15585),
    inference(clausify,[status(thm)],[f_3882_3]) ).

fof(f_3883_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_3883_2,plain,
    ! [U_15588,U_15587] :
      ( c_Wellfounded_Owf(U_15587,U_15588)
      | ? [U_15586] :
          ( U_15586 != c_Orderings_Obot__class_Obot(tc_fun(U_15587,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15587,tc_HOL_Obool)),U_15586),hAPP(c_Relation_OImage(U_15587,U_15587,U_15588),U_15586))) ) ),
    inference(variable_rename,[status(thm)],[f_3883_1]) ).

fof(f_3883_3,plain,
    ! [U_15588,U_15587] :
      ( c_Wellfounded_Owf(U_15587,U_15588)
      | ( sK368(U_15588,U_15587) != c_Orderings_Obot__class_Obot(tc_fun(U_15587,tc_HOL_Obool))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15587,tc_HOL_Obool)),sK368(U_15588,U_15587)),hAPP(c_Relation_OImage(U_15587,U_15587,U_15588),sK368(U_15588,U_15587)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK368]),skolemize(U_15586,sK368(U_15588,U_15587))],[f_3883_2]) ).

fof(f_3883_4,plain,
    ( ! [U_15587,U_15588] :
        ( sK368(U_15588,U_15587) != c_Orderings_Obot__class_Obot(tc_fun(U_15587,tc_HOL_Obool))
        | ~ sP1030(U_15587,U_15588) )
    & ! [U_15587,U_15588] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15587,tc_HOL_Obool)),sK368(U_15588,U_15587)),hAPP(c_Relation_OImage(U_15587,U_15587,U_15588),sK368(U_15588,U_15587))))
        | ~ sP1030(U_15587,U_15588) )
    & ! [U_15587,U_15588] :
        ( c_Wellfounded_Owf(U_15587,U_15588)
        | sP1030(U_15587,U_15588) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1030])],[f_3883_3]) ).

cnf(f_3883_5,plain,
    ( c_Wellfounded_Owf(U_15587,U_15588)
    | sP1030(U_15587,U_15588) ),
    inference(clausify,[status(thm)],[f_3883_4]) ).

cnf(f_3883_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15587,tc_HOL_Obool)),sK368(U_15588,U_15587)),hAPP(c_Relation_OImage(U_15587,U_15587,U_15588),sK368(U_15588,U_15587))))
    | ~ sP1030(U_15587,U_15588) ),
    inference(clausify,[status(thm)],[f_3883_4]) ).

cnf(f_3883_7,plain,
    ( sK368(U_15588,U_15587) != c_Orderings_Obot__class_Obot(tc_fun(U_15587,tc_HOL_Obool))
    | ~ sP1030(U_15587,U_15588) ),
    inference(clausify,[status(thm)],[f_3883_4]) ).

fof(f_3884_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_3884_2,plain,
    ! [U_15595,U_15594,U_15593,U_15592,U_15591,U_15590] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15590,U_15593),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_15590,U_15593),U_15591),U_15594)),hAPP(hAPP(c_Product__Type_OSigma(U_15590,U_15593),U_15592),U_15595)))
      | ? [U_15589] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15593,tc_HOL_Obool)),hAPP(U_15594,U_15589)),hAPP(U_15595,U_15589)))
          & hBOOL(hAPP(hAPP(c_member(U_15590),U_15589),U_15591)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15590,tc_HOL_Obool)),U_15591),U_15592)) ),
    inference(variable_rename,[status(thm)],[f_3884_1]) ).

fof(f_3884_3,plain,
    ! [U_15595,U_15594,U_15593,U_15592,U_15591,U_15590] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15590,U_15593),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_15590,U_15593),U_15591),U_15594)),hAPP(hAPP(c_Product__Type_OSigma(U_15590,U_15593),U_15592),U_15595)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15593,tc_HOL_Obool)),hAPP(U_15594,sK369(U_15595,U_15594,U_15593,U_15592,U_15591,U_15590))),hAPP(U_15595,sK369(U_15595,U_15594,U_15593,U_15592,U_15591,U_15590))))
        & hBOOL(hAPP(hAPP(c_member(U_15590),sK369(U_15595,U_15594,U_15593,U_15592,U_15591,U_15590)),U_15591)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15590,tc_HOL_Obool)),U_15591),U_15592)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK369]),skolemize(U_15589,sK369(U_15595,U_15594,U_15593,U_15592,U_15591,U_15590))],[f_3884_2]) ).

fof(f_3884_4,plain,
    ( ! [U_15590,U_15591,U_15592,U_15593,U_15594,U_15595] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15593,tc_HOL_Obool)),hAPP(U_15594,sK369(U_15595,U_15594,U_15593,U_15592,U_15591,U_15590))),hAPP(U_15595,sK369(U_15595,U_15594,U_15593,U_15592,U_15591,U_15590))))
        | ~ sP1031(U_15590,U_15591,U_15592,U_15593,U_15594,U_15595) )
    & ! [U_15590,U_15591,U_15592,U_15593,U_15594,U_15595] :
        ( hBOOL(hAPP(hAPP(c_member(U_15590),sK369(U_15595,U_15594,U_15593,U_15592,U_15591,U_15590)),U_15591))
        | ~ sP1031(U_15590,U_15591,U_15592,U_15593,U_15594,U_15595) )
    & ! [U_15590,U_15591,U_15592,U_15593,U_15594,U_15595] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15590,U_15593),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_15590,U_15593),U_15591),U_15594)),hAPP(hAPP(c_Product__Type_OSigma(U_15590,U_15593),U_15592),U_15595)))
        | sP1031(U_15590,U_15591,U_15592,U_15593,U_15594,U_15595)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15590,tc_HOL_Obool)),U_15591),U_15592)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1031])],[f_3884_3]) ).

cnf(f_3884_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15590,U_15593),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_15590,U_15593),U_15591),U_15594)),hAPP(hAPP(c_Product__Type_OSigma(U_15590,U_15593),U_15592),U_15595)))
    | sP1031(U_15590,U_15591,U_15592,U_15593,U_15594,U_15595)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15590,tc_HOL_Obool)),U_15591),U_15592)) ),
    inference(clausify,[status(thm)],[f_3884_4]) ).

cnf(f_3884_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15590),sK369(U_15595,U_15594,U_15593,U_15592,U_15591,U_15590)),U_15591))
    | ~ sP1031(U_15590,U_15591,U_15592,U_15593,U_15594,U_15595) ),
    inference(clausify,[status(thm)],[f_3884_4]) ).

cnf(f_3884_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15593,tc_HOL_Obool)),hAPP(U_15594,sK369(U_15595,U_15594,U_15593,U_15592,U_15591,U_15590))),hAPP(U_15595,sK369(U_15595,U_15594,U_15593,U_15592,U_15591,U_15590))))
    | ~ sP1031(U_15590,U_15591,U_15592,U_15593,U_15594,U_15595) ),
    inference(clausify,[status(thm)],[f_3884_4]) ).

fof(f_3885_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_3885_2,plain,
    ! [U_15599,U_15598,U_15597] :
      ( hBOOL(hAPP(hAPP(c_member(U_15597),U_15598),c_Wellfounded_Oacc(U_15597,U_15599)))
      | ? [U_15596] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_15597),U_15596),c_Wellfounded_Oacc(U_15597,U_15599)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15597,U_15597)),hAPP(hAPP(c_Product__Type_OPair(U_15597,U_15597),U_15596),U_15598)),U_15599)) ) ),
    inference(variable_rename,[status(thm)],[f_3885_1]) ).

fof(f_3885_3,plain,
    ! [U_15599,U_15598,U_15597] :
      ( hBOOL(hAPP(hAPP(c_member(U_15597),U_15598),c_Wellfounded_Oacc(U_15597,U_15599)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_15597),sK370(U_15599,U_15598,U_15597)),c_Wellfounded_Oacc(U_15597,U_15599)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15597,U_15597)),hAPP(hAPP(c_Product__Type_OPair(U_15597,U_15597),sK370(U_15599,U_15598,U_15597)),U_15598)),U_15599)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK370]),skolemize(U_15596,sK370(U_15599,U_15598,U_15597))],[f_3885_2]) ).

fof(f_3885_4,plain,
    ( ! [U_15597,U_15598,U_15599] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_15597),sK370(U_15599,U_15598,U_15597)),c_Wellfounded_Oacc(U_15597,U_15599)))
        | ~ sP1032(U_15597,U_15598,U_15599) )
    & ! [U_15597,U_15598,U_15599] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15597,U_15597)),hAPP(hAPP(c_Product__Type_OPair(U_15597,U_15597),sK370(U_15599,U_15598,U_15597)),U_15598)),U_15599))
        | ~ sP1032(U_15597,U_15598,U_15599) )
    & ! [U_15597,U_15598,U_15599] :
        ( hBOOL(hAPP(hAPP(c_member(U_15597),U_15598),c_Wellfounded_Oacc(U_15597,U_15599)))
        | sP1032(U_15597,U_15598,U_15599) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1032])],[f_3885_3]) ).

cnf(f_3885_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15597),U_15598),c_Wellfounded_Oacc(U_15597,U_15599)))
    | sP1032(U_15597,U_15598,U_15599) ),
    inference(clausify,[status(thm)],[f_3885_4]) ).

cnf(f_3885_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15597,U_15597)),hAPP(hAPP(c_Product__Type_OPair(U_15597,U_15597),sK370(U_15599,U_15598,U_15597)),U_15598)),U_15599))
    | ~ sP1032(U_15597,U_15598,U_15599) ),
    inference(clausify,[status(thm)],[f_3885_4]) ).

cnf(f_3885_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15597),sK370(U_15599,U_15598,U_15597)),c_Wellfounded_Oacc(U_15597,U_15599)))
    | ~ sP1032(U_15597,U_15598,U_15599) ),
    inference(clausify,[status(thm)],[f_3885_4]) ).

fof(f_3886_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_3886_2,plain,
    ! [U_15603,U_15602,U_15601] :
      ( ? [U_15600] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_15601),U_15600),c_Wellfounded_Oacc(U_15601,U_15603)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15601,U_15601)),hAPP(hAPP(c_Product__Type_OPair(U_15601,U_15601),U_15600),U_15602)),U_15603)) )
      | hBOOL(hAPP(hAPP(c_member(U_15601),U_15602),c_Wellfounded_Oacc(U_15601,U_15603))) ),
    inference(variable_rename,[status(thm)],[f_3886_1]) ).

fof(f_3886_3,plain,
    ! [U_15603,U_15602,U_15601] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_15601),sK371(U_15603,U_15602,U_15601)),c_Wellfounded_Oacc(U_15601,U_15603)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15601,U_15601)),hAPP(hAPP(c_Product__Type_OPair(U_15601,U_15601),sK371(U_15603,U_15602,U_15601)),U_15602)),U_15603)) )
      | hBOOL(hAPP(hAPP(c_member(U_15601),U_15602),c_Wellfounded_Oacc(U_15601,U_15603))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK371]),skolemize(U_15600,sK371(U_15603,U_15602,U_15601))],[f_3886_2]) ).

fof(f_3886_4,plain,
    ( ! [U_15601,U_15602,U_15603] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_15601),sK371(U_15603,U_15602,U_15601)),c_Wellfounded_Oacc(U_15601,U_15603)))
        | ~ sP1033(U_15601,U_15602,U_15603) )
    & ! [U_15601,U_15602,U_15603] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15601,U_15601)),hAPP(hAPP(c_Product__Type_OPair(U_15601,U_15601),sK371(U_15603,U_15602,U_15601)),U_15602)),U_15603))
        | ~ sP1033(U_15601,U_15602,U_15603) )
    & ! [U_15601,U_15602,U_15603] :
        ( sP1033(U_15601,U_15602,U_15603)
        | hBOOL(hAPP(hAPP(c_member(U_15601),U_15602),c_Wellfounded_Oacc(U_15601,U_15603))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1033])],[f_3886_3]) ).

cnf(f_3886_5,plain,
    ( sP1033(U_15601,U_15602,U_15603)
    | hBOOL(hAPP(hAPP(c_member(U_15601),U_15602),c_Wellfounded_Oacc(U_15601,U_15603))) ),
    inference(clausify,[status(thm)],[f_3886_4]) ).

cnf(f_3886_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15601,U_15601)),hAPP(hAPP(c_Product__Type_OPair(U_15601,U_15601),sK371(U_15603,U_15602,U_15601)),U_15602)),U_15603))
    | ~ sP1033(U_15601,U_15602,U_15603) ),
    inference(clausify,[status(thm)],[f_3886_4]) ).

cnf(f_3886_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15601),sK371(U_15603,U_15602,U_15601)),c_Wellfounded_Oacc(U_15601,U_15603)))
    | ~ sP1033(U_15601,U_15602,U_15603) ),
    inference(clausify,[status(thm)],[f_3886_4]) ).

fof(f_3887_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_3887_2,plain,
    ! [U_15608,U_15607,U_15606,U_15605] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15605,U_15606,c_Groups_Otimes__class_Otimes(U_15605)),U_15608),c_Groups_Oone__class_Oone(U_15605)),U_15607) = c_Groups_Oone__class_Oone(U_15605)
      | ? [U_15604] :
          ( hAPP(U_15608,U_15604) != c_Groups_Oone__class_Oone(U_15605)
          & hBOOL(hAPP(hAPP(c_member(U_15606),U_15604),U_15607)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15606),U_15607))
      | ~ class_Groups_Ocomm__monoid__mult(U_15605) ),
    inference(variable_rename,[status(thm)],[f_3887_1]) ).

fof(f_3887_3,plain,
    ! [U_15608,U_15607,U_15606,U_15605] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15605,U_15606,c_Groups_Otimes__class_Otimes(U_15605)),U_15608),c_Groups_Oone__class_Oone(U_15605)),U_15607) = c_Groups_Oone__class_Oone(U_15605)
      | ( hAPP(U_15608,sK372(U_15608,U_15607,U_15606,U_15605)) != c_Groups_Oone__class_Oone(U_15605)
        & hBOOL(hAPP(hAPP(c_member(U_15606),sK372(U_15608,U_15607,U_15606,U_15605)),U_15607)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15606),U_15607))
      | ~ class_Groups_Ocomm__monoid__mult(U_15605) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK372]),skolemize(U_15604,sK372(U_15608,U_15607,U_15606,U_15605))],[f_3887_2]) ).

fof(f_3887_4,plain,
    ( ! [U_15605,U_15606,U_15607,U_15608] :
        ( hAPP(U_15608,sK372(U_15608,U_15607,U_15606,U_15605)) != c_Groups_Oone__class_Oone(U_15605)
        | ~ sP1034(U_15605,U_15606,U_15607,U_15608) )
    & ! [U_15605,U_15606,U_15607,U_15608] :
        ( hBOOL(hAPP(hAPP(c_member(U_15606),sK372(U_15608,U_15607,U_15606,U_15605)),U_15607))
        | ~ sP1034(U_15605,U_15606,U_15607,U_15608) )
    & ! [U_15605,U_15606,U_15607,U_15608] :
        ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15605,U_15606,c_Groups_Otimes__class_Otimes(U_15605)),U_15608),c_Groups_Oone__class_Oone(U_15605)),U_15607) = c_Groups_Oone__class_Oone(U_15605)
        | sP1034(U_15605,U_15606,U_15607,U_15608)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15606),U_15607))
        | ~ class_Groups_Ocomm__monoid__mult(U_15605) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1034])],[f_3887_3]) ).

cnf(f_3887_5,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15605,U_15606,c_Groups_Otimes__class_Otimes(U_15605)),U_15608),c_Groups_Oone__class_Oone(U_15605)),U_15607) = c_Groups_Oone__class_Oone(U_15605)
    | sP1034(U_15605,U_15606,U_15607,U_15608)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15606),U_15607))
    | ~ class_Groups_Ocomm__monoid__mult(U_15605) ),
    inference(clausify,[status(thm)],[f_3887_4]) ).

cnf(f_3887_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15606),sK372(U_15608,U_15607,U_15606,U_15605)),U_15607))
    | ~ sP1034(U_15605,U_15606,U_15607,U_15608) ),
    inference(clausify,[status(thm)],[f_3887_4]) ).

cnf(f_3887_7,plain,
    ( hAPP(U_15608,sK372(U_15608,U_15607,U_15606,U_15605)) != c_Groups_Oone__class_Oone(U_15605)
    | ~ sP1034(U_15605,U_15606,U_15607,U_15608) ),
    inference(clausify,[status(thm)],[f_3887_4]) ).

fof(f_3888_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_3888_2,plain,
    ! [U_15611,U_15610] :
      ( hAPP(c_Finite__Set_Ocard(U_15610),U_15611) = 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_15609] : hBOOL(hAPP(hAPP(c_member(U_15610),U_15609),U_15611)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15610),U_15611)) ),
    inference(variable_rename,[status(thm)],[f_3888_1]) ).

fof(f_3888_3,plain,
    ! [U_15611,U_15610] :
      ( hAPP(c_Finite__Set_Ocard(U_15610),U_15611) = 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_15610),sK373(U_15611,U_15610)),U_15611)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15610),U_15611)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK373]),skolemize(U_15609,sK373(U_15611,U_15610))],[f_3888_2]) ).

fof(f_3888_4,plain,
    ( ! [U_15611,U_15610] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1035(U_15611,U_15610) )
    & ! [U_15611,U_15610] :
        ( hBOOL(hAPP(hAPP(c_member(U_15610),sK373(U_15611,U_15610)),U_15611))
        | ~ sP1035(U_15611,U_15610) )
    & ! [U_15611,U_15610] :
        ( hAPP(c_Finite__Set_Ocard(U_15610),U_15611) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP1035(U_15611,U_15610)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15610),U_15611)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1035])],[f_3888_3]) ).

cnf(f_3888_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_15610),U_15611) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP1035(U_15611,U_15610)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15610),U_15611)) ),
    inference(clausify,[status(thm)],[f_3888_4]) ).

cnf(f_3888_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15610),sK373(U_15611,U_15610)),U_15611))
    | ~ sP1035(U_15611,U_15610) ),
    inference(clausify,[status(thm)],[f_3888_4]) ).

cnf(f_3888_7,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1035(U_15611,U_15610) ),
    inference(clausify,[status(thm)],[f_3888_4]) ).

fof(f_3889_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_3889_2,plain,
    ! [U_15619,U_15618,U_15617,U_15616] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15616,tc_HOL_Obool),tc_fun(U_15616,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15616,tc_HOL_Obool),tc_fun(U_15616,tc_HOL_Obool)),U_15617),U_15618)),c_Wellfounded_Omax__ext(U_15616,U_15619)))
        | ? [U_15615] :
            ( ! [U_15614] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15616,U_15616)),hAPP(hAPP(c_Product__Type_OPair(U_15616,U_15616),U_15615),U_15614)),U_15619))
                | ~ hBOOL(hAPP(hAPP(c_member(U_15616),U_15614),U_15618)) )
            & hBOOL(hAPP(hAPP(c_member(U_15616),U_15615),U_15617)) )
        | U_15618 = c_Orderings_Obot__class_Obot(tc_fun(U_15616,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15616),U_15618))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15616),U_15617)) )
      & ( ( ! [U_15613] :
              ( ? [U_15612] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15616,U_15616)),hAPP(hAPP(c_Product__Type_OPair(U_15616,U_15616),U_15613),U_15612)),U_15619))
                  & hBOOL(hAPP(hAPP(c_member(U_15616),U_15612),U_15618)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_15616),U_15613),U_15617)) )
          & U_15618 != c_Orderings_Obot__class_Obot(tc_fun(U_15616,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15616),U_15618))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15616),U_15617)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15616,tc_HOL_Obool),tc_fun(U_15616,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15616,tc_HOL_Obool),tc_fun(U_15616,tc_HOL_Obool)),U_15617),U_15618)),c_Wellfounded_Omax__ext(U_15616,U_15619))) ) ),
    inference(variable_rename,[status(thm)],[f_3889_1]) ).

fof(f_3889_3,plain,
    ( ! [U_15627,U_15625,U_15623,U_15621] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15621,tc_HOL_Obool),tc_fun(U_15621,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15621,tc_HOL_Obool),tc_fun(U_15621,tc_HOL_Obool)),U_15623),U_15625)),c_Wellfounded_Omax__ext(U_15621,U_15627)))
        | ? [U_15615] :
            ( ! [U_15614] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15621,U_15621)),hAPP(hAPP(c_Product__Type_OPair(U_15621,U_15621),U_15615),U_15614)),U_15627))
                | ~ hBOOL(hAPP(hAPP(c_member(U_15621),U_15614),U_15625)) )
            & hBOOL(hAPP(hAPP(c_member(U_15621),U_15615),U_15623)) )
        | U_15625 = c_Orderings_Obot__class_Obot(tc_fun(U_15621,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15621),U_15625))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15621),U_15623)) )
    & ! [U_15626,U_15624,U_15622,U_15620] :
        ( ( ! [U_15613] :
              ( ? [U_15612] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15620,U_15620)),hAPP(hAPP(c_Product__Type_OPair(U_15620,U_15620),U_15613),U_15612)),U_15626))
                  & hBOOL(hAPP(hAPP(c_member(U_15620),U_15612),U_15624)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_15620),U_15613),U_15622)) )
          & U_15624 != c_Orderings_Obot__class_Obot(tc_fun(U_15620,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15620),U_15624))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15620),U_15622)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15620,tc_HOL_Obool),tc_fun(U_15620,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15620,tc_HOL_Obool),tc_fun(U_15620,tc_HOL_Obool)),U_15622),U_15624)),c_Wellfounded_Omax__ext(U_15620,U_15626))) ) ),
    inference(miniscope,[status(thm)],[f_3889_2]) ).

fof(f_3889_4,plain,
    ( ! [U_15627,U_15625,U_15623,U_15621] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15621,tc_HOL_Obool),tc_fun(U_15621,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15621,tc_HOL_Obool),tc_fun(U_15621,tc_HOL_Obool)),U_15623),U_15625)),c_Wellfounded_Omax__ext(U_15621,U_15627)))
        | ? [U_15615] :
            ( ! [U_15614] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15621,U_15621)),hAPP(hAPP(c_Product__Type_OPair(U_15621,U_15621),U_15615),U_15614)),U_15627))
                | ~ hBOOL(hAPP(hAPP(c_member(U_15621),U_15614),U_15625)) )
            & hBOOL(hAPP(hAPP(c_member(U_15621),U_15615),U_15623)) )
        | U_15625 = c_Orderings_Obot__class_Obot(tc_fun(U_15621,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15621),U_15625))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15621),U_15623)) )
    & ! [U_15626,U_15624,U_15622,U_15620] :
        ( ( ! [U_15613] :
              ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15620,U_15620)),hAPP(hAPP(c_Product__Type_OPair(U_15620,U_15620),U_15613),sK374(U_15626,U_15624,U_15622,U_15620,U_15613))),U_15626))
                & hBOOL(hAPP(hAPP(c_member(U_15620),sK374(U_15626,U_15624,U_15622,U_15620,U_15613)),U_15624)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_15620),U_15613),U_15622)) )
          & U_15624 != c_Orderings_Obot__class_Obot(tc_fun(U_15620,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15620),U_15624))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15620),U_15622)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15620,tc_HOL_Obool),tc_fun(U_15620,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15620,tc_HOL_Obool),tc_fun(U_15620,tc_HOL_Obool)),U_15622),U_15624)),c_Wellfounded_Omax__ext(U_15620,U_15626))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK374]),skolemize(U_15612,sK374(U_15626,U_15624,U_15622,U_15620,U_15613))],[f_3889_3]) ).

fof(f_3889_5,plain,
    ( ! [U_15627,U_15625,U_15623,U_15621] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15621,tc_HOL_Obool),tc_fun(U_15621,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15621,tc_HOL_Obool),tc_fun(U_15621,tc_HOL_Obool)),U_15623),U_15625)),c_Wellfounded_Omax__ext(U_15621,U_15627)))
        | ( ! [U_15614] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15621,U_15621)),hAPP(hAPP(c_Product__Type_OPair(U_15621,U_15621),sK375(U_15627,U_15625,U_15623,U_15621)),U_15614)),U_15627))
              | ~ hBOOL(hAPP(hAPP(c_member(U_15621),U_15614),U_15625)) )
          & hBOOL(hAPP(hAPP(c_member(U_15621),sK375(U_15627,U_15625,U_15623,U_15621)),U_15623)) )
        | U_15625 = c_Orderings_Obot__class_Obot(tc_fun(U_15621,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15621),U_15625))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15621),U_15623)) )
    & ! [U_15626,U_15624,U_15622,U_15620] :
        ( ( ! [U_15613] :
              ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15620,U_15620)),hAPP(hAPP(c_Product__Type_OPair(U_15620,U_15620),U_15613),sK374(U_15626,U_15624,U_15622,U_15620,U_15613))),U_15626))
                & hBOOL(hAPP(hAPP(c_member(U_15620),sK374(U_15626,U_15624,U_15622,U_15620,U_15613)),U_15624)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_15620),U_15613),U_15622)) )
          & U_15624 != c_Orderings_Obot__class_Obot(tc_fun(U_15620,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15620),U_15624))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15620),U_15622)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15620,tc_HOL_Obool),tc_fun(U_15620,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15620,tc_HOL_Obool),tc_fun(U_15620,tc_HOL_Obool)),U_15622),U_15624)),c_Wellfounded_Omax__ext(U_15620,U_15626))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK375]),skolemize(U_15615,sK375(U_15627,U_15625,U_15623,U_15621))],[f_3889_4]) ).

fof(f_3889_6,plain,
    ( ! [U_15627,U_15623,U_15625,U_15614,U_15621] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15621,U_15621)),hAPP(hAPP(c_Product__Type_OPair(U_15621,U_15621),sK375(U_15627,U_15625,U_15623,U_15621)),U_15614)),U_15627))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15621),U_15614),U_15625))
        | ~ sP1038(U_15627,U_15623,U_15625,U_15614,U_15621) )
    & ! [U_15627,U_15623,U_15625,U_15614,U_15621] :
        ( hBOOL(hAPP(hAPP(c_member(U_15621),sK375(U_15627,U_15625,U_15623,U_15621)),U_15623))
        | ~ sP1038(U_15627,U_15623,U_15625,U_15614,U_15621) )
    & ! [U_15613,U_15620,U_15622,U_15626,U_15624] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15620,U_15620)),hAPP(hAPP(c_Product__Type_OPair(U_15620,U_15620),U_15613),sK374(U_15626,U_15624,U_15622,U_15620,U_15613))),U_15626))
        | ~ sP1036(U_15613,U_15620,U_15622,U_15626,U_15624) )
    & ! [U_15613,U_15620,U_15622,U_15626,U_15624] :
        ( hBOOL(hAPP(hAPP(c_member(U_15620),sK374(U_15626,U_15624,U_15622,U_15620,U_15613)),U_15624))
        | ~ sP1036(U_15613,U_15620,U_15622,U_15626,U_15624) )
    & ! [U_15613,U_15620,U_15622,U_15626,U_15624] :
        ( sP1036(U_15613,U_15620,U_15622,U_15626,U_15624)
        | ~ hBOOL(hAPP(hAPP(c_member(U_15620),U_15613),U_15622))
        | ~ sP1037(U_15613,U_15620,U_15622,U_15626,U_15624) )
    & ! [U_15613,U_15620,U_15622,U_15626,U_15624] :
        ( U_15624 != c_Orderings_Obot__class_Obot(tc_fun(U_15620,tc_HOL_Obool))
        | ~ sP1037(U_15613,U_15620,U_15622,U_15626,U_15624) )
    & ! [U_15613,U_15620,U_15622,U_15626,U_15624] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15620),U_15624))
        | ~ sP1037(U_15613,U_15620,U_15622,U_15626,U_15624) )
    & ! [U_15613,U_15620,U_15622,U_15626,U_15624] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15620),U_15622))
        | ~ sP1037(U_15613,U_15620,U_15622,U_15626,U_15624) )
    & ! [U_15627,U_15623,U_15625,U_15614,U_15621] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15621,tc_HOL_Obool),tc_fun(U_15621,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15621,tc_HOL_Obool),tc_fun(U_15621,tc_HOL_Obool)),U_15623),U_15625)),c_Wellfounded_Omax__ext(U_15621,U_15627)))
        | sP1038(U_15627,U_15623,U_15625,U_15614,U_15621)
        | U_15625 = c_Orderings_Obot__class_Obot(tc_fun(U_15621,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15621),U_15625))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15621),U_15623)) )
    & ! [U_15613,U_15620,U_15622,U_15626,U_15624] :
        ( sP1037(U_15613,U_15620,U_15622,U_15626,U_15624)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15620,tc_HOL_Obool),tc_fun(U_15620,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15620,tc_HOL_Obool),tc_fun(U_15620,tc_HOL_Obool)),U_15622),U_15624)),c_Wellfounded_Omax__ext(U_15620,U_15626))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1036,sP1037,sP1038])],[f_3889_5]) ).

cnf(f_3889_7,plain,
    ( sP1037(U_15613,U_15620,U_15622,U_15626,U_15624)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15620,tc_HOL_Obool),tc_fun(U_15620,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15620,tc_HOL_Obool),tc_fun(U_15620,tc_HOL_Obool)),U_15622),U_15624)),c_Wellfounded_Omax__ext(U_15620,U_15626))) ),
    inference(clausify,[status(thm)],[f_3889_6]) ).

cnf(f_3889_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15621,tc_HOL_Obool),tc_fun(U_15621,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15621,tc_HOL_Obool),tc_fun(U_15621,tc_HOL_Obool)),U_15623),U_15625)),c_Wellfounded_Omax__ext(U_15621,U_15627)))
    | sP1038(U_15627,U_15623,U_15625,U_15614,U_15621)
    | U_15625 = c_Orderings_Obot__class_Obot(tc_fun(U_15621,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15621),U_15625))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15621),U_15623)) ),
    inference(clausify,[status(thm)],[f_3889_6]) ).

cnf(f_3889_9,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15620),U_15622))
    | ~ sP1037(U_15613,U_15620,U_15622,U_15626,U_15624) ),
    inference(clausify,[status(thm)],[f_3889_6]) ).

cnf(f_3889_10,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15620),U_15624))
    | ~ sP1037(U_15613,U_15620,U_15622,U_15626,U_15624) ),
    inference(clausify,[status(thm)],[f_3889_6]) ).

cnf(f_3889_11,plain,
    ( U_15624 != c_Orderings_Obot__class_Obot(tc_fun(U_15620,tc_HOL_Obool))
    | ~ sP1037(U_15613,U_15620,U_15622,U_15626,U_15624) ),
    inference(clausify,[status(thm)],[f_3889_6]) ).

cnf(f_3889_12,plain,
    ( sP1036(U_15613,U_15620,U_15622,U_15626,U_15624)
    | ~ hBOOL(hAPP(hAPP(c_member(U_15620),U_15613),U_15622))
    | ~ sP1037(U_15613,U_15620,U_15622,U_15626,U_15624) ),
    inference(clausify,[status(thm)],[f_3889_6]) ).

cnf(f_3889_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15620),sK374(U_15626,U_15624,U_15622,U_15620,U_15613)),U_15624))
    | ~ sP1036(U_15613,U_15620,U_15622,U_15626,U_15624) ),
    inference(clausify,[status(thm)],[f_3889_6]) ).

cnf(f_3889_14,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15620,U_15620)),hAPP(hAPP(c_Product__Type_OPair(U_15620,U_15620),U_15613),sK374(U_15626,U_15624,U_15622,U_15620,U_15613))),U_15626))
    | ~ sP1036(U_15613,U_15620,U_15622,U_15626,U_15624) ),
    inference(clausify,[status(thm)],[f_3889_6]) ).

cnf(f_3889_15,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15621),sK375(U_15627,U_15625,U_15623,U_15621)),U_15623))
    | ~ sP1038(U_15627,U_15623,U_15625,U_15614,U_15621) ),
    inference(clausify,[status(thm)],[f_3889_6]) ).

cnf(f_3889_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15621,U_15621)),hAPP(hAPP(c_Product__Type_OPair(U_15621,U_15621),sK375(U_15627,U_15625,U_15623,U_15621)),U_15614)),U_15627))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15621),U_15614),U_15625))
    | ~ sP1038(U_15627,U_15623,U_15625,U_15614,U_15621) ),
    inference(clausify,[status(thm)],[f_3889_6]) ).

fof(f_3890_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_3890_2,plain,
    ! [U_15634,U_15633,U_15632,U_15631,U_15630,U_15629] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15629,U_15630,c_Groups_Otimes__class_Otimes(U_15629)),U_15632),U_15634),U_15631) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15629,U_15630,c_Groups_Otimes__class_Otimes(U_15629)),U_15633),U_15634),U_15631)
      | ? [U_15628] :
          ( hAPP(U_15632,U_15628) != hAPP(U_15633,U_15628)
          & hBOOL(hAPP(hAPP(c_member(U_15630),U_15628),U_15631)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15630),U_15631))
      | ~ class_Groups_Oab__semigroup__mult(U_15629) ),
    inference(variable_rename,[status(thm)],[f_3890_1]) ).

fof(f_3890_3,plain,
    ! [U_15634,U_15633,U_15632,U_15631,U_15630,U_15629] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15629,U_15630,c_Groups_Otimes__class_Otimes(U_15629)),U_15632),U_15634),U_15631) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15629,U_15630,c_Groups_Otimes__class_Otimes(U_15629)),U_15633),U_15634),U_15631)
      | ( hAPP(U_15632,sK376(U_15634,U_15633,U_15632,U_15631,U_15630,U_15629)) != hAPP(U_15633,sK376(U_15634,U_15633,U_15632,U_15631,U_15630,U_15629))
        & hBOOL(hAPP(hAPP(c_member(U_15630),sK376(U_15634,U_15633,U_15632,U_15631,U_15630,U_15629)),U_15631)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15630),U_15631))
      | ~ class_Groups_Oab__semigroup__mult(U_15629) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK376]),skolemize(U_15628,sK376(U_15634,U_15633,U_15632,U_15631,U_15630,U_15629))],[f_3890_2]) ).

fof(f_3890_4,plain,
    ( ! [U_15634,U_15632,U_15630,U_15633,U_15631,U_15629] :
        ( hAPP(U_15632,sK376(U_15634,U_15633,U_15632,U_15631,U_15630,U_15629)) != hAPP(U_15633,sK376(U_15634,U_15633,U_15632,U_15631,U_15630,U_15629))
        | ~ sP1039(U_15634,U_15632,U_15630,U_15633,U_15631,U_15629) )
    & ! [U_15634,U_15632,U_15630,U_15633,U_15631,U_15629] :
        ( hBOOL(hAPP(hAPP(c_member(U_15630),sK376(U_15634,U_15633,U_15632,U_15631,U_15630,U_15629)),U_15631))
        | ~ sP1039(U_15634,U_15632,U_15630,U_15633,U_15631,U_15629) )
    & ! [U_15634,U_15632,U_15630,U_15633,U_15631,U_15629] :
        ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15629,U_15630,c_Groups_Otimes__class_Otimes(U_15629)),U_15632),U_15634),U_15631) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15629,U_15630,c_Groups_Otimes__class_Otimes(U_15629)),U_15633),U_15634),U_15631)
        | sP1039(U_15634,U_15632,U_15630,U_15633,U_15631,U_15629)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15630),U_15631))
        | ~ class_Groups_Oab__semigroup__mult(U_15629) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1039])],[f_3890_3]) ).

cnf(f_3890_5,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15629,U_15630,c_Groups_Otimes__class_Otimes(U_15629)),U_15632),U_15634),U_15631) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15629,U_15630,c_Groups_Otimes__class_Otimes(U_15629)),U_15633),U_15634),U_15631)
    | sP1039(U_15634,U_15632,U_15630,U_15633,U_15631,U_15629)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15630),U_15631))
    | ~ class_Groups_Oab__semigroup__mult(U_15629) ),
    inference(clausify,[status(thm)],[f_3890_4]) ).

cnf(f_3890_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15630),sK376(U_15634,U_15633,U_15632,U_15631,U_15630,U_15629)),U_15631))
    | ~ sP1039(U_15634,U_15632,U_15630,U_15633,U_15631,U_15629) ),
    inference(clausify,[status(thm)],[f_3890_4]) ).

cnf(f_3890_7,plain,
    ( hAPP(U_15632,sK376(U_15634,U_15633,U_15632,U_15631,U_15630,U_15629)) != hAPP(U_15633,sK376(U_15634,U_15633,U_15632,U_15631,U_15630,U_15629))
    | ~ sP1039(U_15634,U_15632,U_15630,U_15633,U_15631,U_15629) ),
    inference(clausify,[status(thm)],[f_3890_4]) ).

fof(f_3891_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_3891_2,plain,
    ! [U_15641,U_15640,U_15639,U_15638,U_15637,U_15636] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15636),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15637,U_15636),U_15640),U_15639)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15637,U_15636),U_15641),U_15638)))
      | ? [U_15635] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15636),hAPP(U_15640,U_15635)),hAPP(U_15641,U_15635)))
          & hBOOL(hAPP(hAPP(c_member(U_15637),U_15635),U_15639)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15637,tc_HOL_Obool)),U_15639),U_15638))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15637),U_15638))
      | ~ class_Rings_Ocomm__semiring__1(U_15636) ),
    inference(variable_rename,[status(thm)],[f_3891_1]) ).

fof(f_3891_3,plain,
    ! [U_15641,U_15640,U_15639,U_15638,U_15637,U_15636] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15636),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15637,U_15636),U_15640),U_15639)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15637,U_15636),U_15641),U_15638)))
      | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15636),hAPP(U_15640,sK377(U_15641,U_15640,U_15639,U_15638,U_15637,U_15636))),hAPP(U_15641,sK377(U_15641,U_15640,U_15639,U_15638,U_15637,U_15636))))
        & hBOOL(hAPP(hAPP(c_member(U_15637),sK377(U_15641,U_15640,U_15639,U_15638,U_15637,U_15636)),U_15639)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15637,tc_HOL_Obool)),U_15639),U_15638))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15637),U_15638))
      | ~ class_Rings_Ocomm__semiring__1(U_15636) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK377]),skolemize(U_15635,sK377(U_15641,U_15640,U_15639,U_15638,U_15637,U_15636))],[f_3891_2]) ).

fof(f_3891_4,plain,
    ( ! [U_15636,U_15637,U_15638,U_15639,U_15640,U_15641] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15636),hAPP(U_15640,sK377(U_15641,U_15640,U_15639,U_15638,U_15637,U_15636))),hAPP(U_15641,sK377(U_15641,U_15640,U_15639,U_15638,U_15637,U_15636))))
        | ~ sP1040(U_15636,U_15637,U_15638,U_15639,U_15640,U_15641) )
    & ! [U_15636,U_15637,U_15638,U_15639,U_15640,U_15641] :
        ( hBOOL(hAPP(hAPP(c_member(U_15637),sK377(U_15641,U_15640,U_15639,U_15638,U_15637,U_15636)),U_15639))
        | ~ sP1040(U_15636,U_15637,U_15638,U_15639,U_15640,U_15641) )
    & ! [U_15636,U_15637,U_15638,U_15639,U_15640,U_15641] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15636),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15637,U_15636),U_15640),U_15639)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15637,U_15636),U_15641),U_15638)))
        | sP1040(U_15636,U_15637,U_15638,U_15639,U_15640,U_15641)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15637,tc_HOL_Obool)),U_15639),U_15638))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15637),U_15638))
        | ~ class_Rings_Ocomm__semiring__1(U_15636) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1040])],[f_3891_3]) ).

cnf(f_3891_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15636),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15637,U_15636),U_15640),U_15639)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15637,U_15636),U_15641),U_15638)))
    | sP1040(U_15636,U_15637,U_15638,U_15639,U_15640,U_15641)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15637,tc_HOL_Obool)),U_15639),U_15638))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15637),U_15638))
    | ~ class_Rings_Ocomm__semiring__1(U_15636) ),
    inference(clausify,[status(thm)],[f_3891_4]) ).

cnf(f_3891_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15637),sK377(U_15641,U_15640,U_15639,U_15638,U_15637,U_15636)),U_15639))
    | ~ sP1040(U_15636,U_15637,U_15638,U_15639,U_15640,U_15641) ),
    inference(clausify,[status(thm)],[f_3891_4]) ).

cnf(f_3891_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15636),hAPP(U_15640,sK377(U_15641,U_15640,U_15639,U_15638,U_15637,U_15636))),hAPP(U_15641,sK377(U_15641,U_15640,U_15639,U_15638,U_15637,U_15636))))
    | ~ sP1040(U_15636,U_15637,U_15638,U_15639,U_15640,U_15641) ),
    inference(clausify,[status(thm)],[f_3891_4]) ).

fof(f_3892_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_3892_2,plain,
    ! [U_15645,U_15644,U_15643] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15643,U_15644) = U_15645
      | ~ hBOOL(hAPP(hAPP(c_member(U_15643),U_15645),U_15644))
      | ? [U_15642] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15643),U_15642),U_15645))
          & hBOOL(hAPP(hAPP(c_member(U_15643),U_15642),U_15644)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15643),U_15644))
      | ~ class_Orderings_Olinorder(U_15643) ),
    inference(variable_rename,[status(thm)],[f_3892_1]) ).

fof(f_3892_3,plain,
    ! [U_15645,U_15644,U_15643] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15643,U_15644) = U_15645
      | ~ hBOOL(hAPP(hAPP(c_member(U_15643),U_15645),U_15644))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15643),sK378(U_15645,U_15644,U_15643)),U_15645))
        & hBOOL(hAPP(hAPP(c_member(U_15643),sK378(U_15645,U_15644,U_15643)),U_15644)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15643),U_15644))
      | ~ class_Orderings_Olinorder(U_15643) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK378]),skolemize(U_15642,sK378(U_15645,U_15644,U_15643))],[f_3892_2]) ).

fof(f_3892_4,plain,
    ( ! [U_15643,U_15645,U_15644] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15643),sK378(U_15645,U_15644,U_15643)),U_15645))
        | ~ sP1041(U_15643,U_15645,U_15644) )
    & ! [U_15643,U_15645,U_15644] :
        ( hBOOL(hAPP(hAPP(c_member(U_15643),sK378(U_15645,U_15644,U_15643)),U_15644))
        | ~ sP1041(U_15643,U_15645,U_15644) )
    & ! [U_15643,U_15645,U_15644] :
        ( c_Big__Operators_Olinorder__class_OMax(U_15643,U_15644) = U_15645
        | ~ hBOOL(hAPP(hAPP(c_member(U_15643),U_15645),U_15644))
        | sP1041(U_15643,U_15645,U_15644)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15643),U_15644))
        | ~ class_Orderings_Olinorder(U_15643) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1041])],[f_3892_3]) ).

cnf(f_3892_5,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_15643,U_15644) = U_15645
    | ~ hBOOL(hAPP(hAPP(c_member(U_15643),U_15645),U_15644))
    | sP1041(U_15643,U_15645,U_15644)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15643),U_15644))
    | ~ class_Orderings_Olinorder(U_15643) ),
    inference(clausify,[status(thm)],[f_3892_4]) ).

cnf(f_3892_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15643),sK378(U_15645,U_15644,U_15643)),U_15644))
    | ~ sP1041(U_15643,U_15645,U_15644) ),
    inference(clausify,[status(thm)],[f_3892_4]) ).

cnf(f_3892_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15643),sK378(U_15645,U_15644,U_15643)),U_15645))
    | ~ sP1041(U_15643,U_15645,U_15644) ),
    inference(clausify,[status(thm)],[f_3892_4]) ).

fof(f_3893_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_3893_2,plain,
    ! [U_15649,U_15648,U_15647] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15647,U_15648) = U_15649
      | ~ hBOOL(hAPP(hAPP(c_member(U_15647),U_15649),U_15648))
      | ? [U_15646] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15647),U_15649),U_15646))
          & hBOOL(hAPP(hAPP(c_member(U_15647),U_15646),U_15648)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15647),U_15648))
      | ~ class_Orderings_Olinorder(U_15647) ),
    inference(variable_rename,[status(thm)],[f_3893_1]) ).

fof(f_3893_3,plain,
    ! [U_15649,U_15648,U_15647] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15647,U_15648) = U_15649
      | ~ hBOOL(hAPP(hAPP(c_member(U_15647),U_15649),U_15648))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15647),U_15649),sK379(U_15649,U_15648,U_15647)))
        & hBOOL(hAPP(hAPP(c_member(U_15647),sK379(U_15649,U_15648,U_15647)),U_15648)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15647),U_15648))
      | ~ class_Orderings_Olinorder(U_15647) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK379]),skolemize(U_15646,sK379(U_15649,U_15648,U_15647))],[f_3893_2]) ).

fof(f_3893_4,plain,
    ( ! [U_15648,U_15649,U_15647] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15647),U_15649),sK379(U_15649,U_15648,U_15647)))
        | ~ sP1042(U_15648,U_15649,U_15647) )
    & ! [U_15648,U_15649,U_15647] :
        ( hBOOL(hAPP(hAPP(c_member(U_15647),sK379(U_15649,U_15648,U_15647)),U_15648))
        | ~ sP1042(U_15648,U_15649,U_15647) )
    & ! [U_15648,U_15649,U_15647] :
        ( c_Big__Operators_Olinorder__class_OMin(U_15647,U_15648) = U_15649
        | ~ hBOOL(hAPP(hAPP(c_member(U_15647),U_15649),U_15648))
        | sP1042(U_15648,U_15649,U_15647)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15647),U_15648))
        | ~ class_Orderings_Olinorder(U_15647) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1042])],[f_3893_3]) ).

cnf(f_3893_5,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_15647,U_15648) = U_15649
    | ~ hBOOL(hAPP(hAPP(c_member(U_15647),U_15649),U_15648))
    | sP1042(U_15648,U_15649,U_15647)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15647),U_15648))
    | ~ class_Orderings_Olinorder(U_15647) ),
    inference(clausify,[status(thm)],[f_3893_4]) ).

cnf(f_3893_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15647),sK379(U_15649,U_15648,U_15647)),U_15648))
    | ~ sP1042(U_15648,U_15649,U_15647) ),
    inference(clausify,[status(thm)],[f_3893_4]) ).

cnf(f_3893_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15647),U_15649),sK379(U_15649,U_15648,U_15647)))
    | ~ sP1042(U_15648,U_15649,U_15647) ),
    inference(clausify,[status(thm)],[f_3893_4]) ).

fof(f_3894_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_3894_2,plain,
    ! [U_15653,U_15652,U_15651] :
      ( ? [U_15650] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15651,U_15651)),hAPP(hAPP(c_Product__Type_OPair(U_15651,U_15651),hAPP(U_15653,hAPP(c_Nat_OSuc,U_15650))),hAPP(U_15653,U_15650))),U_15652))
      | ~ c_Wellfounded_Owf(U_15651,U_15652) ),
    inference(variable_rename,[status(thm)],[f_3894_1]) ).

fof(f_3894_3,plain,
    ! [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),hAPP(U_15653,hAPP(c_Nat_OSuc,sK380(U_15653,U_15652,U_15651)))),hAPP(U_15653,sK380(U_15653,U_15652,U_15651)))),U_15652))
      | ~ c_Wellfounded_Owf(U_15651,U_15652) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK380]),skolemize(U_15650,sK380(U_15653,U_15652,U_15651))],[f_3894_2]) ).

fof(f_3894_4,plain,
    ! [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),hAPP(U_15653,hAPP(c_Nat_OSuc,sK380(U_15653,U_15652,U_15651)))),hAPP(U_15653,sK380(U_15653,U_15652,U_15651)))),U_15652))
      | ~ c_Wellfounded_Owf(U_15651,U_15652) ),
    inference(definitional_conversion,[status(esa)],[f_3894_3]) ).

cnf(f_3894_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15651,U_15651)),hAPP(hAPP(c_Product__Type_OPair(U_15651,U_15651),hAPP(U_15653,hAPP(c_Nat_OSuc,sK380(U_15653,U_15652,U_15651)))),hAPP(U_15653,sK380(U_15653,U_15652,U_15651)))),U_15652))
    | ~ c_Wellfounded_Owf(U_15651,U_15652) ),
    inference(clausify,[status(thm)],[f_3894_4]) ).

fof(f_3895_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_3895_2,plain,
    ! [U_15662,U_15661,U_15660,U_15659,U_15658,U_15657,U_15656,U_15655] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15657,U_15655),U_15662),U_15660) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15656,U_15655),U_15661),U_15659)
      | ? [U_15654] :
          ( hAPP(U_15661,U_15654) != hAPP(U_15662,hAPP(U_15658,U_15654))
          & hBOOL(hAPP(hAPP(c_member(U_15656),U_15654),U_15659)) )
      | U_15660 != hAPP(c_Set_Oimage(U_15656,U_15657,U_15658),U_15659)
      | ~ c_Fun_Oinj__on(U_15656,U_15657,U_15658,U_15659)
      | ~ class_Groups_Ocomm__monoid__add(U_15655) ),
    inference(variable_rename,[status(thm)],[f_3895_1]) ).

fof(f_3895_3,plain,
    ! [U_15662,U_15661,U_15660,U_15659,U_15658,U_15657,U_15656,U_15655] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15657,U_15655),U_15662),U_15660) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15656,U_15655),U_15661),U_15659)
      | ( hAPP(U_15661,sK381(U_15662,U_15661,U_15660,U_15659,U_15658,U_15657,U_15656,U_15655)) != hAPP(U_15662,hAPP(U_15658,sK381(U_15662,U_15661,U_15660,U_15659,U_15658,U_15657,U_15656,U_15655)))
        & hBOOL(hAPP(hAPP(c_member(U_15656),sK381(U_15662,U_15661,U_15660,U_15659,U_15658,U_15657,U_15656,U_15655)),U_15659)) )
      | U_15660 != hAPP(c_Set_Oimage(U_15656,U_15657,U_15658),U_15659)
      | ~ c_Fun_Oinj__on(U_15656,U_15657,U_15658,U_15659)
      | ~ class_Groups_Ocomm__monoid__add(U_15655) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK381]),skolemize(U_15654,sK381(U_15662,U_15661,U_15660,U_15659,U_15658,U_15657,U_15656,U_15655))],[f_3895_2]) ).

fof(f_3895_4,plain,
    ( ! [U_15655,U_15656,U_15657,U_15658,U_15659,U_15660,U_15661,U_15662] :
        ( hAPP(U_15661,sK381(U_15662,U_15661,U_15660,U_15659,U_15658,U_15657,U_15656,U_15655)) != hAPP(U_15662,hAPP(U_15658,sK381(U_15662,U_15661,U_15660,U_15659,U_15658,U_15657,U_15656,U_15655)))
        | ~ sP1043(U_15655,U_15656,U_15657,U_15658,U_15659,U_15660,U_15661,U_15662) )
    & ! [U_15655,U_15656,U_15657,U_15658,U_15659,U_15660,U_15661,U_15662] :
        ( hBOOL(hAPP(hAPP(c_member(U_15656),sK381(U_15662,U_15661,U_15660,U_15659,U_15658,U_15657,U_15656,U_15655)),U_15659))
        | ~ sP1043(U_15655,U_15656,U_15657,U_15658,U_15659,U_15660,U_15661,U_15662) )
    & ! [U_15655,U_15656,U_15657,U_15658,U_15659,U_15660,U_15661,U_15662] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15657,U_15655),U_15662),U_15660) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15656,U_15655),U_15661),U_15659)
        | sP1043(U_15655,U_15656,U_15657,U_15658,U_15659,U_15660,U_15661,U_15662)
        | U_15660 != hAPP(c_Set_Oimage(U_15656,U_15657,U_15658),U_15659)
        | ~ c_Fun_Oinj__on(U_15656,U_15657,U_15658,U_15659)
        | ~ class_Groups_Ocomm__monoid__add(U_15655) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1043])],[f_3895_3]) ).

cnf(f_3895_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15657,U_15655),U_15662),U_15660) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15656,U_15655),U_15661),U_15659)
    | sP1043(U_15655,U_15656,U_15657,U_15658,U_15659,U_15660,U_15661,U_15662)
    | U_15660 != hAPP(c_Set_Oimage(U_15656,U_15657,U_15658),U_15659)
    | ~ c_Fun_Oinj__on(U_15656,U_15657,U_15658,U_15659)
    | ~ class_Groups_Ocomm__monoid__add(U_15655) ),
    inference(clausify,[status(thm)],[f_3895_4]) ).

cnf(f_3895_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15656),sK381(U_15662,U_15661,U_15660,U_15659,U_15658,U_15657,U_15656,U_15655)),U_15659))
    | ~ sP1043(U_15655,U_15656,U_15657,U_15658,U_15659,U_15660,U_15661,U_15662) ),
    inference(clausify,[status(thm)],[f_3895_4]) ).

cnf(f_3895_7,plain,
    ( hAPP(U_15661,sK381(U_15662,U_15661,U_15660,U_15659,U_15658,U_15657,U_15656,U_15655)) != hAPP(U_15662,hAPP(U_15658,sK381(U_15662,U_15661,U_15660,U_15659,U_15658,U_15657,U_15656,U_15655)))
    | ~ sP1043(U_15655,U_15656,U_15657,U_15658,U_15659,U_15660,U_15661,U_15662) ),
    inference(clausify,[status(thm)],[f_3895_4]) ).

fof(f_3896_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_3896_2,plain,
    ! [U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15665,U_15664),U_15670),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15665,U_15666),U_15668)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15665,U_15664),U_15671),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15665,U_15667),U_15669))
      | ? [U_15663] :
          ( hAPP(U_15670,U_15663) != hAPP(U_15671,U_15663)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15665),U_15663),U_15669))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15665),U_15667),U_15663)) )
      | U_15668 != U_15669
      | U_15666 != U_15667
      | ~ class_Orderings_Oord(U_15665)
      | ~ class_Groups_Ocomm__monoid__add(U_15664) ),
    inference(variable_rename,[status(thm)],[f_3896_1]) ).

fof(f_3896_3,plain,
    ! [U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15665,U_15664),U_15670),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15665,U_15666),U_15668)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15665,U_15664),U_15671),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15665,U_15667),U_15669))
      | ( hAPP(U_15670,sK382(U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664)) != hAPP(U_15671,sK382(U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15665),sK382(U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664)),U_15669))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15665),U_15667),sK382(U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664))) )
      | U_15668 != U_15669
      | U_15666 != U_15667
      | ~ class_Orderings_Oord(U_15665)
      | ~ class_Groups_Ocomm__monoid__add(U_15664) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK382]),skolemize(U_15663,sK382(U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664))],[f_3896_2]) ).

fof(f_3896_4,plain,
    ( ! [U_15664,U_15665,U_15666,U_15667,U_15668,U_15669,U_15670,U_15671] :
        ( hAPP(U_15670,sK382(U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664)) != hAPP(U_15671,sK382(U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664))
        | ~ sP1044(U_15664,U_15665,U_15666,U_15667,U_15668,U_15669,U_15670,U_15671) )
    & ! [U_15664,U_15665,U_15666,U_15667,U_15668,U_15669,U_15670,U_15671] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15665),sK382(U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664)),U_15669))
        | ~ sP1044(U_15664,U_15665,U_15666,U_15667,U_15668,U_15669,U_15670,U_15671) )
    & ! [U_15664,U_15665,U_15666,U_15667,U_15668,U_15669,U_15670,U_15671] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15665),U_15667),sK382(U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664)))
        | ~ sP1044(U_15664,U_15665,U_15666,U_15667,U_15668,U_15669,U_15670,U_15671) )
    & ! [U_15664,U_15665,U_15666,U_15667,U_15668,U_15669,U_15670,U_15671] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15665,U_15664),U_15670),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15665,U_15666),U_15668)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15665,U_15664),U_15671),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15665,U_15667),U_15669))
        | sP1044(U_15664,U_15665,U_15666,U_15667,U_15668,U_15669,U_15670,U_15671)
        | U_15668 != U_15669
        | U_15666 != U_15667
        | ~ class_Orderings_Oord(U_15665)
        | ~ class_Groups_Ocomm__monoid__add(U_15664) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1044])],[f_3896_3]) ).

cnf(f_3896_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15665,U_15664),U_15670),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15665,U_15666),U_15668)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15665,U_15664),U_15671),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15665,U_15667),U_15669))
    | sP1044(U_15664,U_15665,U_15666,U_15667,U_15668,U_15669,U_15670,U_15671)
    | U_15668 != U_15669
    | U_15666 != U_15667
    | ~ class_Orderings_Oord(U_15665)
    | ~ class_Groups_Ocomm__monoid__add(U_15664) ),
    inference(clausify,[status(thm)],[f_3896_4]) ).

cnf(f_3896_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15665),U_15667),sK382(U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664)))
    | ~ sP1044(U_15664,U_15665,U_15666,U_15667,U_15668,U_15669,U_15670,U_15671) ),
    inference(clausify,[status(thm)],[f_3896_4]) ).

cnf(f_3896_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15665),sK382(U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664)),U_15669))
    | ~ sP1044(U_15664,U_15665,U_15666,U_15667,U_15668,U_15669,U_15670,U_15671) ),
    inference(clausify,[status(thm)],[f_3896_4]) ).

cnf(f_3896_8,plain,
    ( hAPP(U_15670,sK382(U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664)) != hAPP(U_15671,sK382(U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664))
    | ~ sP1044(U_15664,U_15665,U_15666,U_15667,U_15668,U_15669,U_15670,U_15671) ),
    inference(clausify,[status(thm)],[f_3896_4]) ).

fof(f_3897_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_3897_2,plain,
    ! [U_15673,U_15672] :
      ( ( 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_15672),U_15673)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15672),U_15673)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15672),U_15673))
        | ~ 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_15672),U_15673)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(variable_rename,[status(thm)],[f_3897_1]) ).

fof(f_3897_3,plain,
    ( ! [U_15677,U_15675] :
        ( 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_15675),U_15677)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15675),U_15677)) )
    & ! [U_15676,U_15674] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15674),U_15676))
        | ~ 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_15674),U_15676)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(miniscope,[status(thm)],[f_3897_2]) ).

fof(f_3897_4,plain,
    ( ! [U_15677,U_15675] :
        ( 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_15675),U_15677)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15675),U_15677)) )
    & ! [U_15676,U_15674] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15674),U_15676))
        | ~ 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_15674),U_15676)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3897_3]) ).

cnf(f_3897_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15674),U_15676))
    | ~ 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_15674),U_15676)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
    inference(clausify,[status(thm)],[f_3897_4]) ).

cnf(f_3897_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_15675),U_15677)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15675),U_15677)) ),
    inference(clausify,[status(thm)],[f_3897_4]) ).

fof(f_3898_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_3898_2,plain,
    ! [U_15680,U_15679,U_15678] :
      ( c_Big__Operators_Olattice_OSup__fin(U_15678,c_Orderings_Oord__class_Omax(U_15678),hAPP(hAPP(c_Set_Oinsert(U_15678),U_15680),U_15679)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15678,U_15678,c_Orderings_Oord__class_Omax(U_15678)),U_15680),U_15679)
      | hBOOL(hAPP(hAPP(c_member(U_15678),U_15680),U_15679))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15678),U_15679))
      | ~ class_Orderings_Olinorder(U_15678) ),
    inference(variable_rename,[status(thm)],[f_3898_1]) ).

fof(f_3898_3,plain,
    ! [U_15678,U_15679,U_15680] :
      ( c_Big__Operators_Olattice_OSup__fin(U_15678,c_Orderings_Oord__class_Omax(U_15678),hAPP(hAPP(c_Set_Oinsert(U_15678),U_15680),U_15679)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15678,U_15678,c_Orderings_Oord__class_Omax(U_15678)),U_15680),U_15679)
      | hBOOL(hAPP(hAPP(c_member(U_15678),U_15680),U_15679))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15678),U_15679))
      | ~ class_Orderings_Olinorder(U_15678) ),
    inference(definitional_conversion,[status(esa)],[f_3898_2]) ).

cnf(f_3898_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_15678,c_Orderings_Oord__class_Omax(U_15678),hAPP(hAPP(c_Set_Oinsert(U_15678),U_15680),U_15679)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15678,U_15678,c_Orderings_Oord__class_Omax(U_15678)),U_15680),U_15679)
    | hBOOL(hAPP(hAPP(c_member(U_15678),U_15680),U_15679))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15678),U_15679))
    | ~ class_Orderings_Olinorder(U_15678) ),
    inference(clausify,[status(thm)],[f_3898_3]) ).

fof(f_3899_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_3899_2,plain,
    ! [U_15684,U_15683,U_15682,U_15681] : hAPP(hAPP(c_Finite__Set_Ofold(U_15681,U_15682,U_15683),U_15684),c_Orderings_Obot__class_Obot(tc_fun(U_15681,tc_HOL_Obool))) = U_15684,
    inference(variable_rename,[status(thm)],[f_3899_1]) ).

fof(f_3899_3,plain,
    ! [U_15682,U_15681,U_15683,U_15684] : hAPP(hAPP(c_Finite__Set_Ofold(U_15681,U_15682,U_15683),U_15684),c_Orderings_Obot__class_Obot(tc_fun(U_15681,tc_HOL_Obool))) = U_15684,
    inference(definitional_conversion,[status(esa)],[f_3899_2]) ).

cnf(f_3899_4,plain,
    hAPP(hAPP(c_Finite__Set_Ofold(U_15681,U_15682,U_15683),U_15684),c_Orderings_Obot__class_Obot(tc_fun(U_15681,tc_HOL_Obool))) = U_15684,
    inference(clausify,[status(thm)],[f_3899_3]) ).

fof(f_3900_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_3900_2,plain,
    ! [U_15690,U_15689,U_15688,U_15687,U_15686,U_15685] :
      ( hAPP(hAPP(U_15688,U_15689),U_15690) = hAPP(hAPP(c_Finite__Set_Ofold(U_15685,U_15686,U_15687),U_15690),U_15689)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15685),U_15689))
      | ~ c_Finite__Set_Ofolding(U_15685,U_15686,U_15687,U_15688) ),
    inference(variable_rename,[status(thm)],[f_3900_1]) ).

fof(f_3900_3,plain,
    ! [U_15685,U_15686,U_15687,U_15688,U_15689,U_15690] :
      ( hAPP(hAPP(U_15688,U_15689),U_15690) = hAPP(hAPP(c_Finite__Set_Ofold(U_15685,U_15686,U_15687),U_15690),U_15689)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15685),U_15689))
      | ~ c_Finite__Set_Ofolding(U_15685,U_15686,U_15687,U_15688) ),
    inference(definitional_conversion,[status(esa)],[f_3900_2]) ).

cnf(f_3900_4,plain,
    ( hAPP(hAPP(U_15688,U_15689),U_15690) = hAPP(hAPP(c_Finite__Set_Ofold(U_15685,U_15686,U_15687),U_15690),U_15689)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15685),U_15689))
    | ~ c_Finite__Set_Ofolding(U_15685,U_15686,U_15687,U_15688) ),
    inference(clausify,[status(thm)],[f_3900_3]) ).

fof(f_3901_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_3901_2,plain,
    ! [U_15694,U_15693,U_15692,U_15691] : hAPP(c_Finite__Set_Ofold__image(U_15691,U_15692,U_15693),U_15694) = c_Finite__Set_Ofold(U_15692,U_15691,hAPP(hAPP(c_COMBB(U_15691,tc_fun(U_15691,U_15691),U_15692),U_15693),U_15694)),
    inference(variable_rename,[status(thm)],[f_3901_1]) ).

fof(f_3901_3,plain,
    ! [U_15692,U_15691,U_15693,U_15694] : hAPP(c_Finite__Set_Ofold__image(U_15691,U_15692,U_15693),U_15694) = c_Finite__Set_Ofold(U_15692,U_15691,hAPP(hAPP(c_COMBB(U_15691,tc_fun(U_15691,U_15691),U_15692),U_15693),U_15694)),
    inference(definitional_conversion,[status(esa)],[f_3901_2]) ).

cnf(f_3901_4,plain,
    hAPP(c_Finite__Set_Ofold__image(U_15691,U_15692,U_15693),U_15694) = c_Finite__Set_Ofold(U_15692,U_15691,hAPP(hAPP(c_COMBB(U_15691,tc_fun(U_15691,U_15691),U_15692),U_15693),U_15694)),
    inference(clausify,[status(thm)],[f_3901_3]) ).

fof(f_3902_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_3902_2,plain,
    ! [U_15696,U_15695] :
      ( c_Wellfounded_Owf(U_15695,c_Transitive__Closure_Otrancl(U_15695,U_15696))
      | ~ c_Wellfounded_Owf(U_15695,U_15696) ),
    inference(variable_rename,[status(thm)],[f_3902_1]) ).

fof(f_3902_3,plain,
    ! [U_15696,U_15695] :
      ( c_Wellfounded_Owf(U_15695,c_Transitive__Closure_Otrancl(U_15695,U_15696))
      | ~ c_Wellfounded_Owf(U_15695,U_15696) ),
    inference(definitional_conversion,[status(esa)],[f_3902_2]) ).

cnf(f_3902_4,plain,
    ( c_Wellfounded_Owf(U_15695,c_Transitive__Closure_Otrancl(U_15695,U_15696))
    | ~ c_Wellfounded_Owf(U_15695,U_15696) ),
    inference(clausify,[status(thm)],[f_3902_3]) ).

fof(f_3903_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_3903_2,plain,
    ! [U_15701,U_15700,U_15699,U_15698,U_15697] : hAPP(hAPP(c_Finite__Set_Ofold(U_15697,U_15698,U_15699),U_15700),U_15701) = c_HOL_OThe(U_15698,c_Finite__Set_Ofold__graph(U_15697,U_15698,U_15699,U_15700,U_15701)),
    inference(variable_rename,[status(thm)],[f_3903_1]) ).

fof(f_3903_3,plain,
    ! [U_15697,U_15698,U_15699,U_15700,U_15701] : hAPP(hAPP(c_Finite__Set_Ofold(U_15697,U_15698,U_15699),U_15700),U_15701) = c_HOL_OThe(U_15698,c_Finite__Set_Ofold__graph(U_15697,U_15698,U_15699,U_15700,U_15701)),
    inference(definitional_conversion,[status(esa)],[f_3903_2]) ).

cnf(f_3903_4,plain,
    hAPP(hAPP(c_Finite__Set_Ofold(U_15697,U_15698,U_15699),U_15700),U_15701) = c_HOL_OThe(U_15698,c_Finite__Set_Ofold__graph(U_15697,U_15698,U_15699,U_15700,U_15701)),
    inference(clausify,[status(thm)],[f_3903_3]) ).

fof(f_3904_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_3904_2,plain,
    ! [U_15704,U_15703,U_15702] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15702,tc_HOL_Obool)),U_15703),U_15704) = hAPP(hAPP(c_Finite__Set_Ofold(U_15702,tc_fun(U_15702,tc_HOL_Obool),c_Set_Oinsert(U_15702)),U_15704),U_15703)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15702),U_15703)) ),
    inference(variable_rename,[status(thm)],[f_3904_1]) ).

fof(f_3904_3,plain,
    ! [U_15702,U_15703,U_15704] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15702,tc_HOL_Obool)),U_15703),U_15704) = hAPP(hAPP(c_Finite__Set_Ofold(U_15702,tc_fun(U_15702,tc_HOL_Obool),c_Set_Oinsert(U_15702)),U_15704),U_15703)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15702),U_15703)) ),
    inference(definitional_conversion,[status(esa)],[f_3904_2]) ).

cnf(f_3904_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15702,tc_HOL_Obool)),U_15703),U_15704) = hAPP(hAPP(c_Finite__Set_Ofold(U_15702,tc_fun(U_15702,tc_HOL_Obool),c_Set_Oinsert(U_15702)),U_15704),U_15703)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15702),U_15703)) ),
    inference(clausify,[status(thm)],[f_3904_3]) ).

fof(f_3905_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_3905_2,plain,
    ! [U_15708,U_15707,U_15706,U_15705] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15705,U_15705,c_Lattices_Osemilattice__sup__class_Osup(U_15705)),U_15707),hAPP(hAPP(c_Set_Oinsert(U_15705),U_15708),U_15706)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15705),U_15708),hAPP(hAPP(c_Finite__Set_Ofold(U_15705,U_15705,c_Lattices_Osemilattice__sup__class_Osup(U_15705)),U_15707),U_15706))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15705),U_15706))
      | ~ class_Lattices_Osemilattice__sup(U_15705) ),
    inference(variable_rename,[status(thm)],[f_3905_1]) ).

fof(f_3905_3,plain,
    ! [U_15705,U_15706,U_15707,U_15708] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15705,U_15705,c_Lattices_Osemilattice__sup__class_Osup(U_15705)),U_15707),hAPP(hAPP(c_Set_Oinsert(U_15705),U_15708),U_15706)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15705),U_15708),hAPP(hAPP(c_Finite__Set_Ofold(U_15705,U_15705,c_Lattices_Osemilattice__sup__class_Osup(U_15705)),U_15707),U_15706))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15705),U_15706))
      | ~ class_Lattices_Osemilattice__sup(U_15705) ),
    inference(definitional_conversion,[status(esa)],[f_3905_2]) ).

cnf(f_3905_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15705,U_15705,c_Lattices_Osemilattice__sup__class_Osup(U_15705)),U_15707),hAPP(hAPP(c_Set_Oinsert(U_15705),U_15708),U_15706)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15705),U_15708),hAPP(hAPP(c_Finite__Set_Ofold(U_15705,U_15705,c_Lattices_Osemilattice__sup__class_Osup(U_15705)),U_15707),U_15706))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15705),U_15706))
    | ~ class_Lattices_Osemilattice__sup(U_15705) ),
    inference(clausify,[status(thm)],[f_3905_3]) ).

fof(f_3906_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_3906_2,plain,
    ! [U_15712,U_15711,U_15710,U_15709] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15709,U_15709,c_Lattices_Osemilattice__inf__class_Oinf(U_15709)),U_15711),hAPP(hAPP(c_Set_Oinsert(U_15709),U_15712),U_15710)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15709),U_15712),hAPP(hAPP(c_Finite__Set_Ofold(U_15709,U_15709,c_Lattices_Osemilattice__inf__class_Oinf(U_15709)),U_15711),U_15710))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15709),U_15710))
      | ~ class_Lattices_Osemilattice__inf(U_15709) ),
    inference(variable_rename,[status(thm)],[f_3906_1]) ).

fof(f_3906_3,plain,
    ! [U_15709,U_15710,U_15711,U_15712] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15709,U_15709,c_Lattices_Osemilattice__inf__class_Oinf(U_15709)),U_15711),hAPP(hAPP(c_Set_Oinsert(U_15709),U_15712),U_15710)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15709),U_15712),hAPP(hAPP(c_Finite__Set_Ofold(U_15709,U_15709,c_Lattices_Osemilattice__inf__class_Oinf(U_15709)),U_15711),U_15710))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15709),U_15710))
      | ~ class_Lattices_Osemilattice__inf(U_15709) ),
    inference(definitional_conversion,[status(esa)],[f_3906_2]) ).

cnf(f_3906_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15709,U_15709,c_Lattices_Osemilattice__inf__class_Oinf(U_15709)),U_15711),hAPP(hAPP(c_Set_Oinsert(U_15709),U_15712),U_15710)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15709),U_15712),hAPP(hAPP(c_Finite__Set_Ofold(U_15709,U_15709,c_Lattices_Osemilattice__inf__class_Oinf(U_15709)),U_15711),U_15710))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15709),U_15710))
    | ~ class_Lattices_Osemilattice__inf(U_15709) ),
    inference(clausify,[status(thm)],[f_3906_3]) ).

fof(f_3907_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_3907_2,plain,
    c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(definitional_conversion,[status(esa)],[f_3907_1]) ).

cnf(f_3907_3,plain,
    c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(clausify,[status(thm)],[f_3907_2]) ).

fof(f_3908_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_3908_2,plain,
    ! [U_15716,U_15715,U_15714,U_15713] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15713,U_15713,c_Orderings_Oord__class_Omin(U_15713)),U_15715),hAPP(hAPP(c_Set_Oinsert(U_15713),U_15716),U_15714)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15713),U_15716),hAPP(hAPP(c_Finite__Set_Ofold(U_15713,U_15713,c_Orderings_Oord__class_Omin(U_15713)),U_15715),U_15714))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15713),U_15714))
      | ~ class_Orderings_Olinorder(U_15713) ),
    inference(variable_rename,[status(thm)],[f_3908_1]) ).

fof(f_3908_3,plain,
    ! [U_15713,U_15714,U_15715,U_15716] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15713,U_15713,c_Orderings_Oord__class_Omin(U_15713)),U_15715),hAPP(hAPP(c_Set_Oinsert(U_15713),U_15716),U_15714)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15713),U_15716),hAPP(hAPP(c_Finite__Set_Ofold(U_15713,U_15713,c_Orderings_Oord__class_Omin(U_15713)),U_15715),U_15714))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15713),U_15714))
      | ~ class_Orderings_Olinorder(U_15713) ),
    inference(definitional_conversion,[status(esa)],[f_3908_2]) ).

cnf(f_3908_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15713,U_15713,c_Orderings_Oord__class_Omin(U_15713)),U_15715),hAPP(hAPP(c_Set_Oinsert(U_15713),U_15716),U_15714)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15713),U_15716),hAPP(hAPP(c_Finite__Set_Ofold(U_15713,U_15713,c_Orderings_Oord__class_Omin(U_15713)),U_15715),U_15714))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15713),U_15714))
    | ~ class_Orderings_Olinorder(U_15713) ),
    inference(clausify,[status(thm)],[f_3908_3]) ).

fof(f_3909_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_3909_2,plain,
    ! [U_15720,U_15719,U_15718,U_15717] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15717,U_15717,c_Orderings_Oord__class_Omax(U_15717)),U_15719),hAPP(hAPP(c_Set_Oinsert(U_15717),U_15720),U_15718)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15717),U_15720),hAPP(hAPP(c_Finite__Set_Ofold(U_15717,U_15717,c_Orderings_Oord__class_Omax(U_15717)),U_15719),U_15718))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15717),U_15718))
      | ~ class_Orderings_Olinorder(U_15717) ),
    inference(variable_rename,[status(thm)],[f_3909_1]) ).

fof(f_3909_3,plain,
    ! [U_15717,U_15718,U_15719,U_15720] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15717,U_15717,c_Orderings_Oord__class_Omax(U_15717)),U_15719),hAPP(hAPP(c_Set_Oinsert(U_15717),U_15720),U_15718)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15717),U_15720),hAPP(hAPP(c_Finite__Set_Ofold(U_15717,U_15717,c_Orderings_Oord__class_Omax(U_15717)),U_15719),U_15718))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15717),U_15718))
      | ~ class_Orderings_Olinorder(U_15717) ),
    inference(definitional_conversion,[status(esa)],[f_3909_2]) ).

cnf(f_3909_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15717,U_15717,c_Orderings_Oord__class_Omax(U_15717)),U_15719),hAPP(hAPP(c_Set_Oinsert(U_15717),U_15720),U_15718)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15717),U_15720),hAPP(hAPP(c_Finite__Set_Ofold(U_15717,U_15717,c_Orderings_Oord__class_Omax(U_15717)),U_15719),U_15718))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15717),U_15718))
    | ~ class_Orderings_Olinorder(U_15717) ),
    inference(clausify,[status(thm)],[f_3909_3]) ).

fof(f_3910_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_3910_2,plain,
    ! [U_15724,U_15723] :
      ( ( c_Wellfounded_Oacyclic(U_15723,U_15724)
        | ? [U_15722] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15723,U_15723)),hAPP(hAPP(c_Product__Type_OPair(U_15723,U_15723),U_15722),U_15722)),c_Transitive__Closure_Otrancl(U_15723,U_15724))) )
      & ( ! [U_15721] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15723,U_15723)),hAPP(hAPP(c_Product__Type_OPair(U_15723,U_15723),U_15721),U_15721)),c_Transitive__Closure_Otrancl(U_15723,U_15724)))
        | ~ c_Wellfounded_Oacyclic(U_15723,U_15724) ) ),
    inference(variable_rename,[status(thm)],[f_3910_1]) ).

fof(f_3910_3,plain,
    ( ! [U_15728,U_15726] :
        ( c_Wellfounded_Oacyclic(U_15726,U_15728)
        | ? [U_15722] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15726,U_15726)),hAPP(hAPP(c_Product__Type_OPair(U_15726,U_15726),U_15722),U_15722)),c_Transitive__Closure_Otrancl(U_15726,U_15728))) )
    & ! [U_15727,U_15725] :
        ( ! [U_15721] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15725,U_15725)),hAPP(hAPP(c_Product__Type_OPair(U_15725,U_15725),U_15721),U_15721)),c_Transitive__Closure_Otrancl(U_15725,U_15727)))
        | ~ c_Wellfounded_Oacyclic(U_15725,U_15727) ) ),
    inference(miniscope,[status(thm)],[f_3910_2]) ).

fof(f_3910_4,plain,
    ( ! [U_15728,U_15726] :
        ( c_Wellfounded_Oacyclic(U_15726,U_15728)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15726,U_15726)),hAPP(hAPP(c_Product__Type_OPair(U_15726,U_15726),sK383(U_15728,U_15726)),sK383(U_15728,U_15726))),c_Transitive__Closure_Otrancl(U_15726,U_15728))) )
    & ! [U_15727,U_15725] :
        ( ! [U_15721] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15725,U_15725)),hAPP(hAPP(c_Product__Type_OPair(U_15725,U_15725),U_15721),U_15721)),c_Transitive__Closure_Otrancl(U_15725,U_15727)))
        | ~ c_Wellfounded_Oacyclic(U_15725,U_15727) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK383]),skolemize(U_15722,sK383(U_15728,U_15726))],[f_3910_3]) ).

fof(f_3910_5,plain,
    ( ! [U_15726,U_15728] :
        ( c_Wellfounded_Oacyclic(U_15726,U_15728)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15726,U_15726)),hAPP(hAPP(c_Product__Type_OPair(U_15726,U_15726),sK383(U_15728,U_15726)),sK383(U_15728,U_15726))),c_Transitive__Closure_Otrancl(U_15726,U_15728))) )
    & ! [U_15727,U_15721,U_15725] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15725,U_15725)),hAPP(hAPP(c_Product__Type_OPair(U_15725,U_15725),U_15721),U_15721)),c_Transitive__Closure_Otrancl(U_15725,U_15727)))
        | ~ c_Wellfounded_Oacyclic(U_15725,U_15727) ) ),
    inference(definitional_conversion,[status(esa)],[f_3910_4]) ).

cnf(f_3910_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15725,U_15725)),hAPP(hAPP(c_Product__Type_OPair(U_15725,U_15725),U_15721),U_15721)),c_Transitive__Closure_Otrancl(U_15725,U_15727)))
    | ~ c_Wellfounded_Oacyclic(U_15725,U_15727) ),
    inference(clausify,[status(thm)],[f_3910_5]) ).

cnf(f_3910_7,plain,
    ( c_Wellfounded_Oacyclic(U_15726,U_15728)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15726,U_15726)),hAPP(hAPP(c_Product__Type_OPair(U_15726,U_15726),sK383(U_15728,U_15726)),sK383(U_15728,U_15726))),c_Transitive__Closure_Otrancl(U_15726,U_15728))) ),
    inference(clausify,[status(thm)],[f_3910_5]) ).

fof(f_3911_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_3911_2,plain,
    ! [U_15734,U_15733,U_15732,U_15731,U_15730,U_15729] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15729,U_15730,U_15731),U_15733),hAPP(hAPP(c_Set_Oinsert(U_15729),U_15734),U_15732)) = hAPP(hAPP(U_15731,U_15734),hAPP(hAPP(c_Finite__Set_Ofold(U_15729,U_15730,U_15731),U_15733),U_15732))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15729),U_15732))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15729,U_15730,U_15731) ),
    inference(variable_rename,[status(thm)],[f_3911_1]) ).

fof(f_3911_3,plain,
    ! [U_15729,U_15730,U_15731,U_15732,U_15733,U_15734] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15729,U_15730,U_15731),U_15733),hAPP(hAPP(c_Set_Oinsert(U_15729),U_15734),U_15732)) = hAPP(hAPP(U_15731,U_15734),hAPP(hAPP(c_Finite__Set_Ofold(U_15729,U_15730,U_15731),U_15733),U_15732))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15729),U_15732))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15729,U_15730,U_15731) ),
    inference(definitional_conversion,[status(esa)],[f_3911_2]) ).

cnf(f_3911_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15729,U_15730,U_15731),U_15733),hAPP(hAPP(c_Set_Oinsert(U_15729),U_15734),U_15732)) = hAPP(hAPP(U_15731,U_15734),hAPP(hAPP(c_Finite__Set_Ofold(U_15729,U_15730,U_15731),U_15733),U_15732))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15729),U_15732))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_15729,U_15730,U_15731) ),
    inference(clausify,[status(thm)],[f_3911_3]) ).

fof(f_3912_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_3912_2,plain,
    ! [U_15740,U_15739,U_15738,U_15737,U_15736,U_15735] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15735,U_15736,U_15737),U_15739),hAPP(hAPP(c_Set_Oinsert(U_15735),U_15740),U_15738)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15735,U_15736,U_15737),hAPP(hAPP(U_15737,U_15740),U_15739)),U_15738)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15735),U_15738))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15735,U_15736,U_15737) ),
    inference(variable_rename,[status(thm)],[f_3912_1]) ).

fof(f_3912_3,plain,
    ! [U_15735,U_15736,U_15737,U_15738,U_15739,U_15740] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15735,U_15736,U_15737),U_15739),hAPP(hAPP(c_Set_Oinsert(U_15735),U_15740),U_15738)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15735,U_15736,U_15737),hAPP(hAPP(U_15737,U_15740),U_15739)),U_15738)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15735),U_15738))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15735,U_15736,U_15737) ),
    inference(definitional_conversion,[status(esa)],[f_3912_2]) ).

cnf(f_3912_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15735,U_15736,U_15737),U_15739),hAPP(hAPP(c_Set_Oinsert(U_15735),U_15740),U_15738)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15735,U_15736,U_15737),hAPP(hAPP(U_15737,U_15740),U_15739)),U_15738)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15735),U_15738))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_15735,U_15736,U_15737) ),
    inference(clausify,[status(thm)],[f_3912_3]) ).

fof(f_3913_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_3913_2,plain,
    ! [U_15745,U_15744,U_15743,U_15742,U_15741] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15741),U_15744),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15742,U_15741),U_15743),U_15745)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15742,U_15741,hAPP(hAPP(c_COMBB(U_15741,tc_fun(U_15741,U_15741),U_15742),c_Lattices_Osemilattice__sup__class_Osup(U_15741)),U_15745)),U_15744),U_15743)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15742),U_15743))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15741) ),
    inference(variable_rename,[status(thm)],[f_3913_1]) ).

fof(f_3913_3,plain,
    ! [U_15741,U_15742,U_15743,U_15744,U_15745] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15741),U_15744),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15742,U_15741),U_15743),U_15745)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15742,U_15741,hAPP(hAPP(c_COMBB(U_15741,tc_fun(U_15741,U_15741),U_15742),c_Lattices_Osemilattice__sup__class_Osup(U_15741)),U_15745)),U_15744),U_15743)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15742),U_15743))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15741) ),
    inference(definitional_conversion,[status(esa)],[f_3913_2]) ).

cnf(f_3913_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15741),U_15744),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15742,U_15741),U_15743),U_15745)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15742,U_15741,hAPP(hAPP(c_COMBB(U_15741,tc_fun(U_15741,U_15741),U_15742),c_Lattices_Osemilattice__sup__class_Osup(U_15741)),U_15745)),U_15744),U_15743)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15742),U_15743))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_15741) ),
    inference(clausify,[status(thm)],[f_3913_3]) ).

fof(f_3914_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_3914_2,plain,
    ! [U_15750,U_15749,U_15748,U_15747,U_15746] :
      ( hAPP(U_15748,hAPP(hAPP(c_Set_Oinsert(U_15746),U_15750),U_15749)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15746,U_15746,U_15747),U_15750),U_15749)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15746),U_15749))
      | ~ c_Finite__Set_Ofolding__one__idem(U_15746,U_15747,U_15748) ),
    inference(variable_rename,[status(thm)],[f_3914_1]) ).

fof(f_3914_3,plain,
    ! [U_15746,U_15747,U_15748,U_15749,U_15750] :
      ( hAPP(U_15748,hAPP(hAPP(c_Set_Oinsert(U_15746),U_15750),U_15749)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15746,U_15746,U_15747),U_15750),U_15749)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15746),U_15749))
      | ~ c_Finite__Set_Ofolding__one__idem(U_15746,U_15747,U_15748) ),
    inference(definitional_conversion,[status(esa)],[f_3914_2]) ).

cnf(f_3914_4,plain,
    ( hAPP(U_15748,hAPP(hAPP(c_Set_Oinsert(U_15746),U_15750),U_15749)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15746,U_15746,U_15747),U_15750),U_15749)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15746),U_15749))
    | ~ c_Finite__Set_Ofolding__one__idem(U_15746,U_15747,U_15748) ),
    inference(clausify,[status(thm)],[f_3914_3]) ).

fof(f_3915_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_3915_2,plain,
    ! [U_15754,U_15753,U_15752,U_15751] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15751),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15751),U_15753),U_15754)),hAPP(hAPP(c_Finite__Set_Ofold(U_15751,U_15751,c_Lattices_Osemilattice__sup__class_Osup(U_15751)),U_15754),U_15752)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15751),U_15753),U_15752))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15751),U_15752))
      | ~ class_Lattices_Osemilattice__sup(U_15751) ),
    inference(variable_rename,[status(thm)],[f_3915_1]) ).

fof(f_3915_3,plain,
    ! [U_15751,U_15752,U_15753,U_15754] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15751),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15751),U_15753),U_15754)),hAPP(hAPP(c_Finite__Set_Ofold(U_15751,U_15751,c_Lattices_Osemilattice__sup__class_Osup(U_15751)),U_15754),U_15752)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15751),U_15753),U_15752))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15751),U_15752))
      | ~ class_Lattices_Osemilattice__sup(U_15751) ),
    inference(definitional_conversion,[status(esa)],[f_3915_2]) ).

cnf(f_3915_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15751),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15751),U_15753),U_15754)),hAPP(hAPP(c_Finite__Set_Ofold(U_15751,U_15751,c_Lattices_Osemilattice__sup__class_Osup(U_15751)),U_15754),U_15752)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15751),U_15753),U_15752))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15751),U_15752))
    | ~ class_Lattices_Osemilattice__sup(U_15751) ),
    inference(clausify,[status(thm)],[f_3915_3]) ).

fof(f_3916_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_3916_2,plain,
    ! [U_15758,U_15757,U_15756,U_15755] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15755),hAPP(hAPP(c_Finite__Set_Ofold(U_15755,U_15755,c_Lattices_Osemilattice__inf__class_Oinf(U_15755)),U_15758),U_15756)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15755),U_15757),U_15758)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15755),U_15757),U_15756))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15755),U_15756))
      | ~ class_Lattices_Osemilattice__inf(U_15755) ),
    inference(variable_rename,[status(thm)],[f_3916_1]) ).

fof(f_3916_3,plain,
    ! [U_15755,U_15756,U_15757,U_15758] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15755),hAPP(hAPP(c_Finite__Set_Ofold(U_15755,U_15755,c_Lattices_Osemilattice__inf__class_Oinf(U_15755)),U_15758),U_15756)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15755),U_15757),U_15758)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15755),U_15757),U_15756))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15755),U_15756))
      | ~ class_Lattices_Osemilattice__inf(U_15755) ),
    inference(definitional_conversion,[status(esa)],[f_3916_2]) ).

cnf(f_3916_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15755),hAPP(hAPP(c_Finite__Set_Ofold(U_15755,U_15755,c_Lattices_Osemilattice__inf__class_Oinf(U_15755)),U_15758),U_15756)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15755),U_15757),U_15758)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15755),U_15757),U_15756))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15755),U_15756))
    | ~ class_Lattices_Osemilattice__inf(U_15755) ),
    inference(clausify,[status(thm)],[f_3916_3]) ).

fof(f_3917_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_3917_2,plain,
    ! [U_15762,U_15761,U_15760,U_15759] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15759),hAPP(hAPP(c_Finite__Set_Ofold(U_15759,U_15759,c_Orderings_Oord__class_Omin(U_15759)),U_15762),U_15760)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15759),U_15761),U_15762)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15759),U_15761),U_15760))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15759),U_15760))
      | ~ class_Orderings_Olinorder(U_15759) ),
    inference(variable_rename,[status(thm)],[f_3917_1]) ).

fof(f_3917_3,plain,
    ! [U_15759,U_15760,U_15761,U_15762] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15759),hAPP(hAPP(c_Finite__Set_Ofold(U_15759,U_15759,c_Orderings_Oord__class_Omin(U_15759)),U_15762),U_15760)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15759),U_15761),U_15762)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15759),U_15761),U_15760))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15759),U_15760))
      | ~ class_Orderings_Olinorder(U_15759) ),
    inference(definitional_conversion,[status(esa)],[f_3917_2]) ).

cnf(f_3917_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15759),hAPP(hAPP(c_Finite__Set_Ofold(U_15759,U_15759,c_Orderings_Oord__class_Omin(U_15759)),U_15762),U_15760)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15759),U_15761),U_15762)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15759),U_15761),U_15760))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15759),U_15760))
    | ~ class_Orderings_Olinorder(U_15759) ),
    inference(clausify,[status(thm)],[f_3917_3]) ).

fof(f_3918_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_3918_2,plain,
    ! [U_15766,U_15765,U_15764,U_15763] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15763),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15763),U_15765),U_15766)),hAPP(hAPP(c_Finite__Set_Ofold(U_15763,U_15763,c_Orderings_Oord__class_Omax(U_15763)),U_15766),U_15764)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15763),U_15765),U_15764))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15763),U_15764))
      | ~ class_Orderings_Olinorder(U_15763) ),
    inference(variable_rename,[status(thm)],[f_3918_1]) ).

fof(f_3918_3,plain,
    ! [U_15763,U_15764,U_15765,U_15766] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15763),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15763),U_15765),U_15766)),hAPP(hAPP(c_Finite__Set_Ofold(U_15763,U_15763,c_Orderings_Oord__class_Omax(U_15763)),U_15766),U_15764)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15763),U_15765),U_15764))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15763),U_15764))
      | ~ class_Orderings_Olinorder(U_15763) ),
    inference(definitional_conversion,[status(esa)],[f_3918_2]) ).

cnf(f_3918_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15763),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15763),U_15765),U_15766)),hAPP(hAPP(c_Finite__Set_Ofold(U_15763,U_15763,c_Orderings_Oord__class_Omax(U_15763)),U_15766),U_15764)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15763),U_15765),U_15764))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15763),U_15764))
    | ~ class_Orderings_Olinorder(U_15763) ),
    inference(clausify,[status(thm)],[f_3918_3]) ).

fof(f_3919_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_3919_2,plain,
    ! [U_15769,U_15768,U_15767] :
      ( hAPP(c_Finite__Set_Ofold1(U_15767,c_Groups_Otimes__class_Otimes(U_15767)),hAPP(hAPP(c_Set_Oinsert(U_15767),U_15769),U_15768)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15767,U_15767,c_Groups_Otimes__class_Otimes(U_15767)),U_15769),U_15768)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15767),U_15768))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_15767) ),
    inference(variable_rename,[status(thm)],[f_3919_1]) ).

fof(f_3919_3,plain,
    ! [U_15767,U_15768,U_15769] :
      ( hAPP(c_Finite__Set_Ofold1(U_15767,c_Groups_Otimes__class_Otimes(U_15767)),hAPP(hAPP(c_Set_Oinsert(U_15767),U_15769),U_15768)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15767,U_15767,c_Groups_Otimes__class_Otimes(U_15767)),U_15769),U_15768)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15767),U_15768))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_15767) ),
    inference(definitional_conversion,[status(esa)],[f_3919_2]) ).

cnf(f_3919_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_15767,c_Groups_Otimes__class_Otimes(U_15767)),hAPP(hAPP(c_Set_Oinsert(U_15767),U_15769),U_15768)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15767,U_15767,c_Groups_Otimes__class_Otimes(U_15767)),U_15769),U_15768)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15767),U_15768))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_15767) ),
    inference(clausify,[status(thm)],[f_3919_3]) ).

fof(f_3920_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_3920_2,plain,
    ! [U_15772,U_15771,U_15770] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_15770,hAPP(hAPP(c_Set_Oinsert(U_15770),U_15772),U_15771)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15770,U_15770,c_Lattices_Osemilattice__sup__class_Osup(U_15770)),U_15772),U_15771)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15770),U_15771))
      | ~ class_Lattices_Olattice(U_15770) ),
    inference(variable_rename,[status(thm)],[f_3920_1]) ).

fof(f_3920_3,plain,
    ! [U_15772,U_15770,U_15771] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_15770,hAPP(hAPP(c_Set_Oinsert(U_15770),U_15772),U_15771)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15770,U_15770,c_Lattices_Osemilattice__sup__class_Osup(U_15770)),U_15772),U_15771)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15770),U_15771))
      | ~ class_Lattices_Olattice(U_15770) ),
    inference(definitional_conversion,[status(esa)],[f_3920_2]) ).

cnf(f_3920_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_15770,hAPP(hAPP(c_Set_Oinsert(U_15770),U_15772),U_15771)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15770,U_15770,c_Lattices_Osemilattice__sup__class_Osup(U_15770)),U_15772),U_15771)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15770),U_15771))
    | ~ class_Lattices_Olattice(U_15770) ),
    inference(clausify,[status(thm)],[f_3920_3]) ).

fof(f_3921_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_3921_2,plain,
    ! [U_15775,U_15774,U_15773] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_15773,hAPP(hAPP(c_Set_Oinsert(U_15773),U_15775),U_15774)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15773,U_15773,c_Lattices_Osemilattice__inf__class_Oinf(U_15773)),U_15775),U_15774)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15773),U_15774))
      | ~ class_Lattices_Olattice(U_15773) ),
    inference(variable_rename,[status(thm)],[f_3921_1]) ).

fof(f_3921_3,plain,
    ! [U_15773,U_15774,U_15775] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_15773,hAPP(hAPP(c_Set_Oinsert(U_15773),U_15775),U_15774)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15773,U_15773,c_Lattices_Osemilattice__inf__class_Oinf(U_15773)),U_15775),U_15774)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15773),U_15774))
      | ~ class_Lattices_Olattice(U_15773) ),
    inference(definitional_conversion,[status(esa)],[f_3921_2]) ).

cnf(f_3921_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_15773,hAPP(hAPP(c_Set_Oinsert(U_15773),U_15775),U_15774)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15773,U_15773,c_Lattices_Osemilattice__inf__class_Oinf(U_15773)),U_15775),U_15774)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15773),U_15774))
    | ~ class_Lattices_Olattice(U_15773) ),
    inference(clausify,[status(thm)],[f_3921_3]) ).

fof(f_3922_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_3922_2,plain,
    ! [U_15778,U_15777,U_15776] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15776,hAPP(hAPP(c_Set_Oinsert(U_15776),U_15778),U_15777)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15776,U_15776,c_Orderings_Oord__class_Omin(U_15776)),U_15778),U_15777)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15776),U_15777))
      | ~ class_Orderings_Olinorder(U_15776) ),
    inference(variable_rename,[status(thm)],[f_3922_1]) ).

fof(f_3922_3,plain,
    ! [U_15776,U_15777,U_15778] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15776,hAPP(hAPP(c_Set_Oinsert(U_15776),U_15778),U_15777)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15776,U_15776,c_Orderings_Oord__class_Omin(U_15776)),U_15778),U_15777)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15776),U_15777))
      | ~ class_Orderings_Olinorder(U_15776) ),
    inference(definitional_conversion,[status(esa)],[f_3922_2]) ).

cnf(f_3922_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_15776,hAPP(hAPP(c_Set_Oinsert(U_15776),U_15778),U_15777)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15776,U_15776,c_Orderings_Oord__class_Omin(U_15776)),U_15778),U_15777)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15776),U_15777))
    | ~ class_Orderings_Olinorder(U_15776) ),
    inference(clausify,[status(thm)],[f_3922_3]) ).

fof(f_3923_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_3923_2,plain,
    ! [U_15781,U_15780,U_15779] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15779,hAPP(hAPP(c_Set_Oinsert(U_15779),U_15781),U_15780)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15779,U_15779,c_Orderings_Oord__class_Omax(U_15779)),U_15781),U_15780)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15779),U_15780))
      | ~ class_Orderings_Olinorder(U_15779) ),
    inference(variable_rename,[status(thm)],[f_3923_1]) ).

fof(f_3923_3,plain,
    ! [U_15779,U_15780,U_15781] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15779,hAPP(hAPP(c_Set_Oinsert(U_15779),U_15781),U_15780)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15779,U_15779,c_Orderings_Oord__class_Omax(U_15779)),U_15781),U_15780)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15779),U_15780))
      | ~ class_Orderings_Olinorder(U_15779) ),
    inference(definitional_conversion,[status(esa)],[f_3923_2]) ).

cnf(f_3923_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_15779,hAPP(hAPP(c_Set_Oinsert(U_15779),U_15781),U_15780)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15779,U_15779,c_Orderings_Oord__class_Omax(U_15779)),U_15781),U_15780)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15779),U_15780))
    | ~ class_Orderings_Olinorder(U_15779) ),
    inference(clausify,[status(thm)],[f_3923_3]) ).

fof(f_3924_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_3924_2,plain,
    ! [U_15784,U_15783,U_15782] :
      ( c_Big__Operators_Olattice_OInf__fin(U_15782,c_Orderings_Oord__class_Omin(U_15782),hAPP(hAPP(c_Set_Oinsert(U_15782),U_15784),U_15783)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15782,U_15782,c_Orderings_Oord__class_Omin(U_15782)),U_15784),U_15783)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15782),U_15783))
      | ~ class_Orderings_Olinorder(U_15782) ),
    inference(variable_rename,[status(thm)],[f_3924_1]) ).

fof(f_3924_3,plain,
    ! [U_15782,U_15783,U_15784] :
      ( c_Big__Operators_Olattice_OInf__fin(U_15782,c_Orderings_Oord__class_Omin(U_15782),hAPP(hAPP(c_Set_Oinsert(U_15782),U_15784),U_15783)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15782,U_15782,c_Orderings_Oord__class_Omin(U_15782)),U_15784),U_15783)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15782),U_15783))
      | ~ class_Orderings_Olinorder(U_15782) ),
    inference(definitional_conversion,[status(esa)],[f_3924_2]) ).

cnf(f_3924_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_15782,c_Orderings_Oord__class_Omin(U_15782),hAPP(hAPP(c_Set_Oinsert(U_15782),U_15784),U_15783)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15782,U_15782,c_Orderings_Oord__class_Omin(U_15782)),U_15784),U_15783)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15782),U_15783))
    | ~ class_Orderings_Olinorder(U_15782) ),
    inference(clausify,[status(thm)],[f_3924_3]) ).

fof(f_3925_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_3925_2,plain,
    ! [U_15787,U_15786,U_15785] :
      ( c_Big__Operators_Olattice_OSup__fin(U_15785,c_Orderings_Oord__class_Omax(U_15785),hAPP(hAPP(c_Set_Oinsert(U_15785),U_15787),U_15786)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15785,U_15785,c_Orderings_Oord__class_Omax(U_15785)),U_15787),U_15786)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15785),U_15786))
      | ~ class_Orderings_Olinorder(U_15785) ),
    inference(variable_rename,[status(thm)],[f_3925_1]) ).

fof(f_3925_3,plain,
    ! [U_15785,U_15786,U_15787] :
      ( c_Big__Operators_Olattice_OSup__fin(U_15785,c_Orderings_Oord__class_Omax(U_15785),hAPP(hAPP(c_Set_Oinsert(U_15785),U_15787),U_15786)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15785,U_15785,c_Orderings_Oord__class_Omax(U_15785)),U_15787),U_15786)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15785),U_15786))
      | ~ class_Orderings_Olinorder(U_15785) ),
    inference(definitional_conversion,[status(esa)],[f_3925_2]) ).

cnf(f_3925_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_15785,c_Orderings_Oord__class_Omax(U_15785),hAPP(hAPP(c_Set_Oinsert(U_15785),U_15787),U_15786)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15785,U_15785,c_Orderings_Oord__class_Omax(U_15785)),U_15787),U_15786)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15785),U_15786))
    | ~ class_Orderings_Olinorder(U_15785) ),
    inference(clausify,[status(thm)],[f_3925_3]) ).

fof(f_3926_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_3926_2,plain,
    ! [U_15790,U_15789,U_15788] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15788,tc_HOL_Obool)),U_15790),U_15789) = hAPP(hAPP(c_Finite__Set_Ofold(U_15788,tc_fun(U_15788,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15788,tc_HOL_Obool),tc_fun(tc_fun(U_15788,tc_HOL_Obool),tc_fun(U_15788,tc_HOL_Obool)),U_15788),hAPP(c_COMBC(tc_fun(U_15788,tc_HOL_Obool),tc_fun(U_15788,tc_HOL_Obool),tc_fun(U_15788,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_15788,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_15788,tc_fun(U_15788,tc_HOL_Obool),tc_fun(U_15788,tc_HOL_Obool)),c_Set_Oinsert(U_15788)),c_Orderings_Obot__class_Obot(tc_fun(U_15788,tc_HOL_Obool))))),U_15790),U_15789)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15788),U_15789)) ),
    inference(variable_rename,[status(thm)],[f_3926_1]) ).

fof(f_3926_3,plain,
    ! [U_15788,U_15789,U_15790] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15788,tc_HOL_Obool)),U_15790),U_15789) = hAPP(hAPP(c_Finite__Set_Ofold(U_15788,tc_fun(U_15788,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15788,tc_HOL_Obool),tc_fun(tc_fun(U_15788,tc_HOL_Obool),tc_fun(U_15788,tc_HOL_Obool)),U_15788),hAPP(c_COMBC(tc_fun(U_15788,tc_HOL_Obool),tc_fun(U_15788,tc_HOL_Obool),tc_fun(U_15788,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_15788,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_15788,tc_fun(U_15788,tc_HOL_Obool),tc_fun(U_15788,tc_HOL_Obool)),c_Set_Oinsert(U_15788)),c_Orderings_Obot__class_Obot(tc_fun(U_15788,tc_HOL_Obool))))),U_15790),U_15789)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15788),U_15789)) ),
    inference(definitional_conversion,[status(esa)],[f_3926_2]) ).

cnf(f_3926_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15788,tc_HOL_Obool)),U_15790),U_15789) = hAPP(hAPP(c_Finite__Set_Ofold(U_15788,tc_fun(U_15788,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15788,tc_HOL_Obool),tc_fun(tc_fun(U_15788,tc_HOL_Obool),tc_fun(U_15788,tc_HOL_Obool)),U_15788),hAPP(c_COMBC(tc_fun(U_15788,tc_HOL_Obool),tc_fun(U_15788,tc_HOL_Obool),tc_fun(U_15788,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_15788,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_15788,tc_fun(U_15788,tc_HOL_Obool),tc_fun(U_15788,tc_HOL_Obool)),c_Set_Oinsert(U_15788)),c_Orderings_Obot__class_Obot(tc_fun(U_15788,tc_HOL_Obool))))),U_15790),U_15789)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15788),U_15789)) ),
    inference(clausify,[status(thm)],[f_3926_3]) ).

fof(f_3927_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_3927_2,plain,
    ! [U_15795,U_15794,U_15793,U_15792,U_15791] :
      ( hAPP(U_15793,hAPP(hAPP(c_Set_Oinsert(U_15791),U_15795),U_15794)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15791,U_15791,U_15792),U_15795),U_15794)
      | hBOOL(hAPP(hAPP(c_member(U_15791),U_15795),U_15794))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15791),U_15794))
      | ~ c_Finite__Set_Ofolding__one(U_15791,U_15792,U_15793) ),
    inference(variable_rename,[status(thm)],[f_3927_1]) ).

fof(f_3927_3,plain,
    ! [U_15791,U_15792,U_15793,U_15794,U_15795] :
      ( hAPP(U_15793,hAPP(hAPP(c_Set_Oinsert(U_15791),U_15795),U_15794)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15791,U_15791,U_15792),U_15795),U_15794)
      | hBOOL(hAPP(hAPP(c_member(U_15791),U_15795),U_15794))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15791),U_15794))
      | ~ c_Finite__Set_Ofolding__one(U_15791,U_15792,U_15793) ),
    inference(definitional_conversion,[status(esa)],[f_3927_2]) ).

cnf(f_3927_4,plain,
    ( hAPP(U_15793,hAPP(hAPP(c_Set_Oinsert(U_15791),U_15795),U_15794)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15791,U_15791,U_15792),U_15795),U_15794)
    | hBOOL(hAPP(hAPP(c_member(U_15791),U_15795),U_15794))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15791),U_15794))
    | ~ c_Finite__Set_Ofolding__one(U_15791,U_15792,U_15793) ),
    inference(clausify,[status(thm)],[f_3927_3]) ).

fof(f_3928_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_3928_2,plain,
    ! [U_15799,U_15798,U_15797,U_15796] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15797,U_15796),U_15798),U_15799) = hAPP(hAPP(c_Finite__Set_Ofold(U_15797,U_15796,hAPP(hAPP(c_COMBB(U_15796,tc_fun(U_15796,U_15796),U_15797),c_Lattices_Osemilattice__sup__class_Osup(U_15796)),U_15799)),c_Orderings_Obot__class_Obot(U_15796)),U_15798)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15797),U_15798))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15796) ),
    inference(variable_rename,[status(thm)],[f_3928_1]) ).

fof(f_3928_3,plain,
    ! [U_15796,U_15797,U_15798,U_15799] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15797,U_15796),U_15798),U_15799) = hAPP(hAPP(c_Finite__Set_Ofold(U_15797,U_15796,hAPP(hAPP(c_COMBB(U_15796,tc_fun(U_15796,U_15796),U_15797),c_Lattices_Osemilattice__sup__class_Osup(U_15796)),U_15799)),c_Orderings_Obot__class_Obot(U_15796)),U_15798)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15797),U_15798))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15796) ),
    inference(definitional_conversion,[status(esa)],[f_3928_2]) ).

cnf(f_3928_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15797,U_15796),U_15798),U_15799) = hAPP(hAPP(c_Finite__Set_Ofold(U_15797,U_15796,hAPP(hAPP(c_COMBB(U_15796,tc_fun(U_15796,U_15796),U_15797),c_Lattices_Osemilattice__sup__class_Osup(U_15796)),U_15799)),c_Orderings_Obot__class_Obot(U_15796)),U_15798)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15797),U_15798))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_15796) ),
    inference(clausify,[status(thm)],[f_3928_3]) ).

fof(f_3929_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_3929_2,plain,
    ! [U_15802,U_15801,U_15800] :
      ( hAPP(c_Finite__Set_Ofold1(U_15800,c_Groups_Otimes__class_Otimes(U_15800)),hAPP(hAPP(c_Set_Oinsert(U_15800),U_15802),U_15801)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15800,U_15800,c_Groups_Otimes__class_Otimes(U_15800)),U_15802),U_15801)
      | hBOOL(hAPP(hAPP(c_member(U_15800),U_15802),U_15801))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15800),U_15801))
      | ~ class_Groups_Oab__semigroup__mult(U_15800) ),
    inference(variable_rename,[status(thm)],[f_3929_1]) ).

fof(f_3929_3,plain,
    ! [U_15800,U_15801,U_15802] :
      ( hAPP(c_Finite__Set_Ofold1(U_15800,c_Groups_Otimes__class_Otimes(U_15800)),hAPP(hAPP(c_Set_Oinsert(U_15800),U_15802),U_15801)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15800,U_15800,c_Groups_Otimes__class_Otimes(U_15800)),U_15802),U_15801)
      | hBOOL(hAPP(hAPP(c_member(U_15800),U_15802),U_15801))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15800),U_15801))
      | ~ class_Groups_Oab__semigroup__mult(U_15800) ),
    inference(definitional_conversion,[status(esa)],[f_3929_2]) ).

cnf(f_3929_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_15800,c_Groups_Otimes__class_Otimes(U_15800)),hAPP(hAPP(c_Set_Oinsert(U_15800),U_15802),U_15801)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15800,U_15800,c_Groups_Otimes__class_Otimes(U_15800)),U_15802),U_15801)
    | hBOOL(hAPP(hAPP(c_member(U_15800),U_15802),U_15801))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15800),U_15801))
    | ~ class_Groups_Oab__semigroup__mult(U_15800) ),
    inference(clausify,[status(thm)],[f_3929_3]) ).

fof(f_3930_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_3930_2,plain,
    ! [U_15805,U_15804,U_15803] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_15803,hAPP(hAPP(c_Set_Oinsert(U_15803),U_15805),U_15804)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15803,U_15803,c_Lattices_Osemilattice__sup__class_Osup(U_15803)),U_15805),U_15804)
      | hBOOL(hAPP(hAPP(c_member(U_15803),U_15805),U_15804))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15803),U_15804))
      | ~ class_Lattices_Olattice(U_15803) ),
    inference(variable_rename,[status(thm)],[f_3930_1]) ).

fof(f_3930_3,plain,
    ! [U_15803,U_15804,U_15805] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_15803,hAPP(hAPP(c_Set_Oinsert(U_15803),U_15805),U_15804)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15803,U_15803,c_Lattices_Osemilattice__sup__class_Osup(U_15803)),U_15805),U_15804)
      | hBOOL(hAPP(hAPP(c_member(U_15803),U_15805),U_15804))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15803),U_15804))
      | ~ class_Lattices_Olattice(U_15803) ),
    inference(definitional_conversion,[status(esa)],[f_3930_2]) ).

cnf(f_3930_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_15803,hAPP(hAPP(c_Set_Oinsert(U_15803),U_15805),U_15804)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15803,U_15803,c_Lattices_Osemilattice__sup__class_Osup(U_15803)),U_15805),U_15804)
    | hBOOL(hAPP(hAPP(c_member(U_15803),U_15805),U_15804))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15803),U_15804))
    | ~ class_Lattices_Olattice(U_15803) ),
    inference(clausify,[status(thm)],[f_3930_3]) ).

fof(f_3931_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_3931_2,plain,
    ! [U_15808,U_15807,U_15806] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_15806,hAPP(hAPP(c_Set_Oinsert(U_15806),U_15808),U_15807)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15806,U_15806,c_Lattices_Osemilattice__inf__class_Oinf(U_15806)),U_15808),U_15807)
      | hBOOL(hAPP(hAPP(c_member(U_15806),U_15808),U_15807))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15806),U_15807))
      | ~ class_Lattices_Olattice(U_15806) ),
    inference(variable_rename,[status(thm)],[f_3931_1]) ).

fof(f_3931_3,plain,
    ! [U_15806,U_15807,U_15808] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_15806,hAPP(hAPP(c_Set_Oinsert(U_15806),U_15808),U_15807)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15806,U_15806,c_Lattices_Osemilattice__inf__class_Oinf(U_15806)),U_15808),U_15807)
      | hBOOL(hAPP(hAPP(c_member(U_15806),U_15808),U_15807))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15806),U_15807))
      | ~ class_Lattices_Olattice(U_15806) ),
    inference(definitional_conversion,[status(esa)],[f_3931_2]) ).

cnf(f_3931_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_15806,hAPP(hAPP(c_Set_Oinsert(U_15806),U_15808),U_15807)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15806,U_15806,c_Lattices_Osemilattice__inf__class_Oinf(U_15806)),U_15808),U_15807)
    | hBOOL(hAPP(hAPP(c_member(U_15806),U_15808),U_15807))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15806),U_15807))
    | ~ class_Lattices_Olattice(U_15806) ),
    inference(clausify,[status(thm)],[f_3931_3]) ).

fof(f_3932_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_3932_2,plain,
    ! [U_15811,U_15810,U_15809] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15809,hAPP(hAPP(c_Set_Oinsert(U_15809),U_15811),U_15810)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15809,U_15809,c_Orderings_Oord__class_Omin(U_15809)),U_15811),U_15810)
      | hBOOL(hAPP(hAPP(c_member(U_15809),U_15811),U_15810))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15809),U_15810))
      | ~ class_Orderings_Olinorder(U_15809) ),
    inference(variable_rename,[status(thm)],[f_3932_1]) ).

fof(f_3932_3,plain,
    ! [U_15809,U_15810,U_15811] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15809,hAPP(hAPP(c_Set_Oinsert(U_15809),U_15811),U_15810)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15809,U_15809,c_Orderings_Oord__class_Omin(U_15809)),U_15811),U_15810)
      | hBOOL(hAPP(hAPP(c_member(U_15809),U_15811),U_15810))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15809),U_15810))
      | ~ class_Orderings_Olinorder(U_15809) ),
    inference(definitional_conversion,[status(esa)],[f_3932_2]) ).

cnf(f_3932_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_15809,hAPP(hAPP(c_Set_Oinsert(U_15809),U_15811),U_15810)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15809,U_15809,c_Orderings_Oord__class_Omin(U_15809)),U_15811),U_15810)
    | hBOOL(hAPP(hAPP(c_member(U_15809),U_15811),U_15810))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15809),U_15810))
    | ~ class_Orderings_Olinorder(U_15809) ),
    inference(clausify,[status(thm)],[f_3932_3]) ).

fof(f_3933_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_3933_2,plain,
    ! [U_15814,U_15813,U_15812] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15812,hAPP(hAPP(c_Set_Oinsert(U_15812),U_15814),U_15813)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15812,U_15812,c_Orderings_Oord__class_Omax(U_15812)),U_15814),U_15813)
      | hBOOL(hAPP(hAPP(c_member(U_15812),U_15814),U_15813))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15812),U_15813))
      | ~ class_Orderings_Olinorder(U_15812) ),
    inference(variable_rename,[status(thm)],[f_3933_1]) ).

fof(f_3933_3,plain,
    ! [U_15812,U_15813,U_15814] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15812,hAPP(hAPP(c_Set_Oinsert(U_15812),U_15814),U_15813)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15812,U_15812,c_Orderings_Oord__class_Omax(U_15812)),U_15814),U_15813)
      | hBOOL(hAPP(hAPP(c_member(U_15812),U_15814),U_15813))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15812),U_15813))
      | ~ class_Orderings_Olinorder(U_15812) ),
    inference(definitional_conversion,[status(esa)],[f_3933_2]) ).

cnf(f_3933_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_15812,hAPP(hAPP(c_Set_Oinsert(U_15812),U_15814),U_15813)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15812,U_15812,c_Orderings_Oord__class_Omax(U_15812)),U_15814),U_15813)
    | hBOOL(hAPP(hAPP(c_member(U_15812),U_15814),U_15813))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15812),U_15813))
    | ~ class_Orderings_Olinorder(U_15812) ),
    inference(clausify,[status(thm)],[f_3933_3]) ).

fof(f_3934_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_3934_2,plain,
    ! [U_15817,U_15816,U_15815] :
      ( c_Big__Operators_Olattice_OInf__fin(U_15815,c_Orderings_Oord__class_Omin(U_15815),hAPP(hAPP(c_Set_Oinsert(U_15815),U_15817),U_15816)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15815,U_15815,c_Orderings_Oord__class_Omin(U_15815)),U_15817),U_15816)
      | hBOOL(hAPP(hAPP(c_member(U_15815),U_15817),U_15816))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15815),U_15816))
      | ~ class_Orderings_Olinorder(U_15815) ),
    inference(variable_rename,[status(thm)],[f_3934_1]) ).

fof(f_3934_3,plain,
    ! [U_15815,U_15816,U_15817] :
      ( c_Big__Operators_Olattice_OInf__fin(U_15815,c_Orderings_Oord__class_Omin(U_15815),hAPP(hAPP(c_Set_Oinsert(U_15815),U_15817),U_15816)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15815,U_15815,c_Orderings_Oord__class_Omin(U_15815)),U_15817),U_15816)
      | hBOOL(hAPP(hAPP(c_member(U_15815),U_15817),U_15816))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15815),U_15816))
      | ~ class_Orderings_Olinorder(U_15815) ),
    inference(definitional_conversion,[status(esa)],[f_3934_2]) ).

cnf(f_3934_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_15815,c_Orderings_Oord__class_Omin(U_15815),hAPP(hAPP(c_Set_Oinsert(U_15815),U_15817),U_15816)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15815,U_15815,c_Orderings_Oord__class_Omin(U_15815)),U_15817),U_15816)
    | hBOOL(hAPP(hAPP(c_member(U_15815),U_15817),U_15816))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15815),U_15816))
    | ~ class_Orderings_Olinorder(U_15815) ),
    inference(clausify,[status(thm)],[f_3934_3]) ).

fof(f_3935_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_3935_2,plain,
    ! [U_15821,U_15820,U_15819,U_15818] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15818,U_15818)),hAPP(hAPP(c_Product__Type_OPair(U_15818,U_15818),U_15819),U_15820)),c_Transitive__Closure_Otrancl(U_15818,U_15821)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15818,U_15818)),hAPP(hAPP(c_Product__Type_OPair(U_15818,U_15818),U_15819),U_15820)),U_15821)) ),
    inference(variable_rename,[status(thm)],[f_3935_1]) ).

fof(f_3935_3,plain,
    ! [U_15819,U_15818,U_15820,U_15821] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15818,U_15818)),hAPP(hAPP(c_Product__Type_OPair(U_15818,U_15818),U_15819),U_15820)),c_Transitive__Closure_Otrancl(U_15818,U_15821)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15818,U_15818)),hAPP(hAPP(c_Product__Type_OPair(U_15818,U_15818),U_15819),U_15820)),U_15821)) ),
    inference(definitional_conversion,[status(esa)],[f_3935_2]) ).

cnf(f_3935_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15818,U_15818)),hAPP(hAPP(c_Product__Type_OPair(U_15818,U_15818),U_15819),U_15820)),c_Transitive__Closure_Otrancl(U_15818,U_15821)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15818,U_15818)),hAPP(hAPP(c_Product__Type_OPair(U_15818,U_15818),U_15819),U_15820)),U_15821)) ),
    inference(clausify,[status(thm)],[f_3935_3]) ).

fof(f_3936_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_3936_2,plain,
    ! [U_15823,U_15822] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15822,U_15822),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15822,U_15823)),hAPP(hAPP(c_Product__Type_OSigma(U_15822,U_15822),hAPP(c_Relation_OField(U_15822),U_15823)),hAPP(c_COMBK(tc_fun(U_15822,tc_HOL_Obool),U_15822),hAPP(c_Relation_OField(U_15822),U_15823))))),
    inference(variable_rename,[status(thm)],[f_3936_1]) ).

fof(f_3936_3,plain,
    ! [U_15822,U_15823] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15822,U_15822),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15822,U_15823)),hAPP(hAPP(c_Product__Type_OSigma(U_15822,U_15822),hAPP(c_Relation_OField(U_15822),U_15823)),hAPP(c_COMBK(tc_fun(U_15822,tc_HOL_Obool),U_15822),hAPP(c_Relation_OField(U_15822),U_15823))))),
    inference(definitional_conversion,[status(esa)],[f_3936_2]) ).

cnf(f_3936_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15822,U_15822),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15822,U_15823)),hAPP(hAPP(c_Product__Type_OSigma(U_15822,U_15822),hAPP(c_Relation_OField(U_15822),U_15823)),hAPP(c_COMBK(tc_fun(U_15822,tc_HOL_Obool),U_15822),hAPP(c_Relation_OField(U_15822),U_15823))))),
    inference(clausify,[status(thm)],[f_3936_3]) ).

fof(f_3937_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_3937_2,plain,
    ! [U_15826,U_15825,U_15824] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15824,U_15824)),U_15825),c_Transitive__Closure_Otrancl(U_15824,U_15826)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15824,U_15824)),U_15825),U_15826)) ),
    inference(variable_rename,[status(thm)],[f_3937_1]) ).

fof(f_3937_3,plain,
    ! [U_15824,U_15825,U_15826] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15824,U_15824)),U_15825),c_Transitive__Closure_Otrancl(U_15824,U_15826)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15824,U_15824)),U_15825),U_15826)) ),
    inference(definitional_conversion,[status(esa)],[f_3937_2]) ).

cnf(f_3937_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15824,U_15824)),U_15825),c_Transitive__Closure_Otrancl(U_15824,U_15826)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15824,U_15824)),U_15825),U_15826)) ),
    inference(clausify,[status(thm)],[f_3937_3]) ).

fof(f_3938_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_3938_2,plain,
    ! [U_15827] : c_Transitive__Closure_Otrancl(U_15827,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15827,U_15827),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15827,U_15827),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3938_1]) ).

fof(f_3938_3,plain,
    ! [U_15827] : c_Transitive__Closure_Otrancl(U_15827,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15827,U_15827),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15827,U_15827),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3938_2]) ).

cnf(f_3938_4,plain,
    c_Transitive__Closure_Otrancl(U_15827,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15827,U_15827),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15827,U_15827),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3938_3]) ).

fof(f_3939_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_3939_2,plain,
    ! [U_15829,U_15828] : hAPP(c_Relation_ODomain(U_15828,U_15828),c_Transitive__Closure_Otrancl(U_15828,U_15829)) = hAPP(c_Relation_ODomain(U_15828,U_15828),U_15829),
    inference(variable_rename,[status(thm)],[f_3939_1]) ).

fof(f_3939_3,plain,
    ! [U_15828,U_15829] : hAPP(c_Relation_ODomain(U_15828,U_15828),c_Transitive__Closure_Otrancl(U_15828,U_15829)) = hAPP(c_Relation_ODomain(U_15828,U_15828),U_15829),
    inference(definitional_conversion,[status(esa)],[f_3939_2]) ).

cnf(f_3939_4,plain,
    hAPP(c_Relation_ODomain(U_15828,U_15828),c_Transitive__Closure_Otrancl(U_15828,U_15829)) = hAPP(c_Relation_ODomain(U_15828,U_15828),U_15829),
    inference(clausify,[status(thm)],[f_3939_3]) ).

fof(f_3940_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_3940_2,plain,
    ! [U_15831,U_15830] : hAPP(c_Relation_ORange(U_15830,U_15830),c_Transitive__Closure_Otrancl(U_15830,U_15831)) = hAPP(c_Relation_ORange(U_15830,U_15830),U_15831),
    inference(variable_rename,[status(thm)],[f_3940_1]) ).

fof(f_3940_3,plain,
    ! [U_15830,U_15831] : hAPP(c_Relation_ORange(U_15830,U_15830),c_Transitive__Closure_Otrancl(U_15830,U_15831)) = hAPP(c_Relation_ORange(U_15830,U_15830),U_15831),
    inference(definitional_conversion,[status(esa)],[f_3940_2]) ).

cnf(f_3940_4,plain,
    hAPP(c_Relation_ORange(U_15830,U_15830),c_Transitive__Closure_Otrancl(U_15830,U_15831)) = hAPP(c_Relation_ORange(U_15830,U_15830),U_15831),
    inference(clausify,[status(thm)],[f_3940_3]) ).

fof(f_3941_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_3941_2,plain,
    ! [U_15833,U_15832] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15832,U_15832)),c_Transitive__Closure_Otrancl(U_15832,U_15833)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15832,U_15832)),U_15833)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15832,U_15832)),U_15833))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15832,U_15832)),c_Transitive__Closure_Otrancl(U_15832,U_15833))) ) ),
    inference(variable_rename,[status(thm)],[f_3941_1]) ).

fof(f_3941_3,plain,
    ( ! [U_15837,U_15835] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15835,U_15835)),c_Transitive__Closure_Otrancl(U_15835,U_15837)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15835,U_15835)),U_15837)) )
    & ! [U_15836,U_15834] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15834,U_15834)),U_15836))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15834,U_15834)),c_Transitive__Closure_Otrancl(U_15834,U_15836))) ) ),
    inference(miniscope,[status(thm)],[f_3941_2]) ).

fof(f_3941_4,plain,
    ( ! [U_15835,U_15837] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15835,U_15835)),c_Transitive__Closure_Otrancl(U_15835,U_15837)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15835,U_15835)),U_15837)) )
    & ! [U_15836,U_15834] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15834,U_15834)),U_15836))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15834,U_15834)),c_Transitive__Closure_Otrancl(U_15834,U_15836))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3941_3]) ).

cnf(f_3941_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15834,U_15834)),U_15836))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15834,U_15834)),c_Transitive__Closure_Otrancl(U_15834,U_15836))) ),
    inference(clausify,[status(thm)],[f_3941_4]) ).

cnf(f_3941_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15835,U_15835)),c_Transitive__Closure_Otrancl(U_15835,U_15837)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_15835,U_15835)),U_15837)) ),
    inference(clausify,[status(thm)],[f_3941_4]) ).

fof(f_3942_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_3942_2,plain,
    ! [U_15842,U_15841,U_15840,U_15839,U_15838] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15838,U_15838)),hAPP(hAPP(c_Product__Type_OPair(U_15838,U_15838),U_15839),U_15842)),c_Transitive__Closure_Otrancl(U_15838,U_15841)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15838,U_15838)),hAPP(hAPP(c_Product__Type_OPair(U_15838,U_15838),U_15840),U_15842)),c_Transitive__Closure_Otrancl(U_15838,U_15841)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15838,U_15838)),hAPP(hAPP(c_Product__Type_OPair(U_15838,U_15838),U_15839),U_15840)),c_Transitive__Closure_Otrancl(U_15838,U_15841))) ),
    inference(variable_rename,[status(thm)],[f_3942_1]) ).

fof(f_3942_3,plain,
    ! [U_15838,U_15839,U_15840,U_15841,U_15842] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15838,U_15838)),hAPP(hAPP(c_Product__Type_OPair(U_15838,U_15838),U_15839),U_15842)),c_Transitive__Closure_Otrancl(U_15838,U_15841)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15838,U_15838)),hAPP(hAPP(c_Product__Type_OPair(U_15838,U_15838),U_15840),U_15842)),c_Transitive__Closure_Otrancl(U_15838,U_15841)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15838,U_15838)),hAPP(hAPP(c_Product__Type_OPair(U_15838,U_15838),U_15839),U_15840)),c_Transitive__Closure_Otrancl(U_15838,U_15841))) ),
    inference(definitional_conversion,[status(esa)],[f_3942_2]) ).

cnf(f_3942_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15838,U_15838)),hAPP(hAPP(c_Product__Type_OPair(U_15838,U_15838),U_15839),U_15842)),c_Transitive__Closure_Otrancl(U_15838,U_15841)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15838,U_15838)),hAPP(hAPP(c_Product__Type_OPair(U_15838,U_15838),U_15840),U_15842)),c_Transitive__Closure_Otrancl(U_15838,U_15841)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15838,U_15838)),hAPP(hAPP(c_Product__Type_OPair(U_15838,U_15838),U_15839),U_15840)),c_Transitive__Closure_Otrancl(U_15838,U_15841))) ),
    inference(clausify,[status(thm)],[f_3942_3]) ).

fof(f_3943_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_3943_2,plain,
    ! [U_15847,U_15846,U_15845,U_15844,U_15843] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15843,U_15843)),hAPP(hAPP(c_Product__Type_OPair(U_15843,U_15843),U_15844),U_15847)),c_Transitive__Closure_Otrancl(U_15843,U_15846)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15843,U_15843)),hAPP(hAPP(c_Product__Type_OPair(U_15843,U_15843),U_15845),U_15847)),U_15846))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15843,U_15843)),hAPP(hAPP(c_Product__Type_OPair(U_15843,U_15843),U_15844),U_15845)),c_Transitive__Closure_Otrancl(U_15843,U_15846))) ),
    inference(variable_rename,[status(thm)],[f_3943_1]) ).

fof(f_3943_3,plain,
    ! [U_15843,U_15844,U_15845,U_15846,U_15847] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15843,U_15843)),hAPP(hAPP(c_Product__Type_OPair(U_15843,U_15843),U_15844),U_15847)),c_Transitive__Closure_Otrancl(U_15843,U_15846)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15843,U_15843)),hAPP(hAPP(c_Product__Type_OPair(U_15843,U_15843),U_15845),U_15847)),U_15846))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15843,U_15843)),hAPP(hAPP(c_Product__Type_OPair(U_15843,U_15843),U_15844),U_15845)),c_Transitive__Closure_Otrancl(U_15843,U_15846))) ),
    inference(definitional_conversion,[status(esa)],[f_3943_2]) ).

cnf(f_3943_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15843,U_15843)),hAPP(hAPP(c_Product__Type_OPair(U_15843,U_15843),U_15844),U_15847)),c_Transitive__Closure_Otrancl(U_15843,U_15846)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15843,U_15843)),hAPP(hAPP(c_Product__Type_OPair(U_15843,U_15843),U_15845),U_15847)),U_15846))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15843,U_15843)),hAPP(hAPP(c_Product__Type_OPair(U_15843,U_15843),U_15844),U_15845)),c_Transitive__Closure_Otrancl(U_15843,U_15846))) ),
    inference(clausify,[status(thm)],[f_3943_3]) ).

fof(f_3944_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_3944_2,plain,
    ! [U_15852,U_15851,U_15850,U_15849,U_15848] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15848,U_15848)),hAPP(hAPP(c_Product__Type_OPair(U_15848,U_15848),U_15849),U_15852)),c_Transitive__Closure_Otrancl(U_15848,U_15851)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15848,U_15848)),hAPP(hAPP(c_Product__Type_OPair(U_15848,U_15848),U_15850),U_15852)),c_Transitive__Closure_Otrancl(U_15848,U_15851)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15848,U_15848)),hAPP(hAPP(c_Product__Type_OPair(U_15848,U_15848),U_15849),U_15850)),U_15851)) ),
    inference(variable_rename,[status(thm)],[f_3944_1]) ).

fof(f_3944_3,plain,
    ! [U_15848,U_15849,U_15850,U_15851,U_15852] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15848,U_15848)),hAPP(hAPP(c_Product__Type_OPair(U_15848,U_15848),U_15849),U_15852)),c_Transitive__Closure_Otrancl(U_15848,U_15851)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15848,U_15848)),hAPP(hAPP(c_Product__Type_OPair(U_15848,U_15848),U_15850),U_15852)),c_Transitive__Closure_Otrancl(U_15848,U_15851)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15848,U_15848)),hAPP(hAPP(c_Product__Type_OPair(U_15848,U_15848),U_15849),U_15850)),U_15851)) ),
    inference(definitional_conversion,[status(esa)],[f_3944_2]) ).

cnf(f_3944_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15848,U_15848)),hAPP(hAPP(c_Product__Type_OPair(U_15848,U_15848),U_15849),U_15852)),c_Transitive__Closure_Otrancl(U_15848,U_15851)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15848,U_15848)),hAPP(hAPP(c_Product__Type_OPair(U_15848,U_15848),U_15850),U_15852)),c_Transitive__Closure_Otrancl(U_15848,U_15851)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15848,U_15848)),hAPP(hAPP(c_Product__Type_OPair(U_15848,U_15848),U_15849),U_15850)),U_15851)) ),
    inference(clausify,[status(thm)],[f_3944_3]) ).

fof(f_3945_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_3945_2,plain,
    ! [U_15857,U_15856,U_15855,U_15854,U_15853] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15853,U_15853)),hAPP(hAPP(c_Product__Type_OPair(U_15853,U_15853),U_15854),U_15857)),c_Transitive__Closure_Otrancl(U_15853,U_15856)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15853,U_15853)),hAPP(hAPP(c_Product__Type_OPair(U_15853,U_15853),U_15855),U_15857)),U_15856))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15853,U_15853)),hAPP(hAPP(c_Product__Type_OPair(U_15853,U_15853),U_15854),U_15855)),U_15856)) ),
    inference(variable_rename,[status(thm)],[f_3945_1]) ).

fof(f_3945_3,plain,
    ! [U_15853,U_15854,U_15855,U_15856,U_15857] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15853,U_15853)),hAPP(hAPP(c_Product__Type_OPair(U_15853,U_15853),U_15854),U_15857)),c_Transitive__Closure_Otrancl(U_15853,U_15856)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15853,U_15853)),hAPP(hAPP(c_Product__Type_OPair(U_15853,U_15853),U_15855),U_15857)),U_15856))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15853,U_15853)),hAPP(hAPP(c_Product__Type_OPair(U_15853,U_15853),U_15854),U_15855)),U_15856)) ),
    inference(definitional_conversion,[status(esa)],[f_3945_2]) ).

cnf(f_3945_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15853,U_15853)),hAPP(hAPP(c_Product__Type_OPair(U_15853,U_15853),U_15854),U_15857)),c_Transitive__Closure_Otrancl(U_15853,U_15856)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15853,U_15853)),hAPP(hAPP(c_Product__Type_OPair(U_15853,U_15853),U_15855),U_15857)),U_15856))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15853,U_15853)),hAPP(hAPP(c_Product__Type_OPair(U_15853,U_15853),U_15854),U_15855)),U_15856)) ),
    inference(clausify,[status(thm)],[f_3945_3]) ).

fof(f_3946_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_3946_2,plain,
    ! [U_15861,U_15860,U_15859,U_15858] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15858,U_15858)),U_15859),c_Transitive__Closure_Otrancl(U_15858,U_15861)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15858,U_15858),tc_HOL_Obool)),U_15860),U_15861))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15858,U_15858)),U_15859),c_Transitive__Closure_Otrancl(U_15858,U_15860))) ),
    inference(variable_rename,[status(thm)],[f_3946_1]) ).

fof(f_3946_3,plain,
    ! [U_15858,U_15859,U_15860,U_15861] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15858,U_15858)),U_15859),c_Transitive__Closure_Otrancl(U_15858,U_15861)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15858,U_15858),tc_HOL_Obool)),U_15860),U_15861))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15858,U_15858)),U_15859),c_Transitive__Closure_Otrancl(U_15858,U_15860))) ),
    inference(definitional_conversion,[status(esa)],[f_3946_2]) ).

cnf(f_3946_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15858,U_15858)),U_15859),c_Transitive__Closure_Otrancl(U_15858,U_15861)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15858,U_15858),tc_HOL_Obool)),U_15860),U_15861))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15858,U_15858)),U_15859),c_Transitive__Closure_Otrancl(U_15858,U_15860))) ),
    inference(clausify,[status(thm)],[f_3946_3]) ).

fof(f_3947_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_3947_2,plain,
    ! [U_15863,U_15862] : c_Transitive__Closure_Otrancl(U_15862,U_15863) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15862,U_15862),tc_HOL_Obool)),U_15863),hAPP(hAPP(c_Relation_Orel__comp(U_15862,U_15862,U_15862),c_Transitive__Closure_Otrancl(U_15862,U_15863)),U_15863)),
    inference(variable_rename,[status(thm)],[f_3947_1]) ).

fof(f_3947_3,plain,
    ! [U_15862,U_15863] : c_Transitive__Closure_Otrancl(U_15862,U_15863) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15862,U_15862),tc_HOL_Obool)),U_15863),hAPP(hAPP(c_Relation_Orel__comp(U_15862,U_15862,U_15862),c_Transitive__Closure_Otrancl(U_15862,U_15863)),U_15863)),
    inference(definitional_conversion,[status(esa)],[f_3947_2]) ).

cnf(f_3947_4,plain,
    c_Transitive__Closure_Otrancl(U_15862,U_15863) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15862,U_15862),tc_HOL_Obool)),U_15863),hAPP(hAPP(c_Relation_Orel__comp(U_15862,U_15862,U_15862),c_Transitive__Closure_Otrancl(U_15862,U_15863)),U_15863)),
    inference(clausify,[status(thm)],[f_3947_3]) ).

fof(f_3948_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_3948_2,plain,
    ! [U_15866,U_15865,U_15864] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15864,U_15864),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15864,U_15865)),hAPP(hAPP(c_Product__Type_OSigma(U_15864,U_15864),U_15866),hAPP(c_COMBK(tc_fun(U_15864,tc_HOL_Obool),U_15864),U_15866))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15864,U_15864),tc_HOL_Obool)),U_15865),hAPP(hAPP(c_Product__Type_OSigma(U_15864,U_15864),U_15866),hAPP(c_COMBK(tc_fun(U_15864,tc_HOL_Obool),U_15864),U_15866)))) ),
    inference(variable_rename,[status(thm)],[f_3948_1]) ).

fof(f_3948_3,plain,
    ! [U_15864,U_15865,U_15866] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15864,U_15864),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15864,U_15865)),hAPP(hAPP(c_Product__Type_OSigma(U_15864,U_15864),U_15866),hAPP(c_COMBK(tc_fun(U_15864,tc_HOL_Obool),U_15864),U_15866))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15864,U_15864),tc_HOL_Obool)),U_15865),hAPP(hAPP(c_Product__Type_OSigma(U_15864,U_15864),U_15866),hAPP(c_COMBK(tc_fun(U_15864,tc_HOL_Obool),U_15864),U_15866)))) ),
    inference(definitional_conversion,[status(esa)],[f_3948_2]) ).

cnf(f_3948_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15864,U_15864),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15864,U_15865)),hAPP(hAPP(c_Product__Type_OSigma(U_15864,U_15864),U_15866),hAPP(c_COMBK(tc_fun(U_15864,tc_HOL_Obool),U_15864),U_15866))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15864,U_15864),tc_HOL_Obool)),U_15865),hAPP(hAPP(c_Product__Type_OSigma(U_15864,U_15864),U_15866),hAPP(c_COMBK(tc_fun(U_15864,tc_HOL_Obool),U_15864),U_15866)))) ),
    inference(clausify,[status(thm)],[f_3948_3]) ).

fof(f_3949_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_3949_2,plain,
    ! [U_15869,U_15868,U_15867] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15867,U_15867),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15867,U_15868)),U_15869))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15867,U_15867),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15867,U_15867,U_15867),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15867,U_15867),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15867,U_15868)),U_15869)),U_15868)),U_15869))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15867,U_15867),tc_HOL_Obool)),U_15868),U_15869)) ),
    inference(variable_rename,[status(thm)],[f_3949_1]) ).

fof(f_3949_3,plain,
    ! [U_15867,U_15868,U_15869] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15867,U_15867),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15867,U_15868)),U_15869))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15867,U_15867),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15867,U_15867,U_15867),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15867,U_15867),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15867,U_15868)),U_15869)),U_15868)),U_15869))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15867,U_15867),tc_HOL_Obool)),U_15868),U_15869)) ),
    inference(definitional_conversion,[status(esa)],[f_3949_2]) ).

cnf(f_3949_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15867,U_15867),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15867,U_15868)),U_15869))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15867,U_15867),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_15867,U_15867,U_15867),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15867,U_15867),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15867,U_15868)),U_15869)),U_15868)),U_15869))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15867,U_15867),tc_HOL_Obool)),U_15868),U_15869)) ),
    inference(clausify,[status(thm)],[f_3949_3]) ).

fof(f_3950_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_3950_2,plain,
    ! [U_15875,U_15874,U_15873,U_15872,U_15871,U_15870] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15870,U_15871,U_15872),U_15875),U_15873) = hAPP(hAPP(U_15872,U_15874),hAPP(hAPP(c_Finite__Set_Ofold(U_15870,U_15871,U_15872),U_15875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15870,tc_HOL_Obool)),U_15873),hAPP(hAPP(c_Set_Oinsert(U_15870),U_15874),c_Orderings_Obot__class_Obot(tc_fun(U_15870,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15870),U_15874),U_15873))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15870),U_15873))
      | ~ c_Finite__Set_Ofun__left__comm(U_15870,U_15871,U_15872) ),
    inference(variable_rename,[status(thm)],[f_3950_1]) ).

fof(f_3950_3,plain,
    ! [U_15870,U_15871,U_15872,U_15873,U_15874,U_15875] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15870,U_15871,U_15872),U_15875),U_15873) = hAPP(hAPP(U_15872,U_15874),hAPP(hAPP(c_Finite__Set_Ofold(U_15870,U_15871,U_15872),U_15875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15870,tc_HOL_Obool)),U_15873),hAPP(hAPP(c_Set_Oinsert(U_15870),U_15874),c_Orderings_Obot__class_Obot(tc_fun(U_15870,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15870),U_15874),U_15873))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15870),U_15873))
      | ~ c_Finite__Set_Ofun__left__comm(U_15870,U_15871,U_15872) ),
    inference(definitional_conversion,[status(esa)],[f_3950_2]) ).

cnf(f_3950_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15870,U_15871,U_15872),U_15875),U_15873) = hAPP(hAPP(U_15872,U_15874),hAPP(hAPP(c_Finite__Set_Ofold(U_15870,U_15871,U_15872),U_15875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15870,tc_HOL_Obool)),U_15873),hAPP(hAPP(c_Set_Oinsert(U_15870),U_15874),c_Orderings_Obot__class_Obot(tc_fun(U_15870,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15870),U_15874),U_15873))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15870),U_15873))
    | ~ c_Finite__Set_Ofun__left__comm(U_15870,U_15871,U_15872) ),
    inference(clausify,[status(thm)],[f_3950_3]) ).

fof(f_3951_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_3951_2,plain,
    ! [U_15881,U_15880,U_15879,U_15878,U_15877,U_15876] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15876,U_15877,U_15878),U_15880),hAPP(hAPP(c_Set_Oinsert(U_15876),U_15881),U_15879)) = hAPP(hAPP(U_15878,U_15881),hAPP(hAPP(c_Finite__Set_Ofold(U_15876,U_15877,U_15878),U_15880),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15876,tc_HOL_Obool)),U_15879),hAPP(hAPP(c_Set_Oinsert(U_15876),U_15881),c_Orderings_Obot__class_Obot(tc_fun(U_15876,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15876),U_15879))
      | ~ c_Finite__Set_Ofun__left__comm(U_15876,U_15877,U_15878) ),
    inference(variable_rename,[status(thm)],[f_3951_1]) ).

fof(f_3951_3,plain,
    ! [U_15876,U_15877,U_15878,U_15879,U_15880,U_15881] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15876,U_15877,U_15878),U_15880),hAPP(hAPP(c_Set_Oinsert(U_15876),U_15881),U_15879)) = hAPP(hAPP(U_15878,U_15881),hAPP(hAPP(c_Finite__Set_Ofold(U_15876,U_15877,U_15878),U_15880),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15876,tc_HOL_Obool)),U_15879),hAPP(hAPP(c_Set_Oinsert(U_15876),U_15881),c_Orderings_Obot__class_Obot(tc_fun(U_15876,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15876),U_15879))
      | ~ c_Finite__Set_Ofun__left__comm(U_15876,U_15877,U_15878) ),
    inference(definitional_conversion,[status(esa)],[f_3951_2]) ).

cnf(f_3951_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15876,U_15877,U_15878),U_15880),hAPP(hAPP(c_Set_Oinsert(U_15876),U_15881),U_15879)) = hAPP(hAPP(U_15878,U_15881),hAPP(hAPP(c_Finite__Set_Ofold(U_15876,U_15877,U_15878),U_15880),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15876,tc_HOL_Obool)),U_15879),hAPP(hAPP(c_Set_Oinsert(U_15876),U_15881),c_Orderings_Obot__class_Obot(tc_fun(U_15876,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15876),U_15879))
    | ~ c_Finite__Set_Ofun__left__comm(U_15876,U_15877,U_15878) ),
    inference(clausify,[status(thm)],[f_3951_3]) ).

fof(f_3952_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_3952_2,plain,
    ! [U_15886,U_15885,U_15884,U_15883,U_15882] :
      ( hAPP(c_Fun_Ocomp(U_15883,U_15883,U_15883,hAPP(U_15884,U_15885)),hAPP(U_15884,U_15886)) = hAPP(c_Fun_Ocomp(U_15883,U_15883,U_15883,hAPP(U_15884,U_15886)),hAPP(U_15884,U_15885))
      | ~ c_Finite__Set_Ofun__left__comm(U_15882,U_15883,U_15884) ),
    inference(variable_rename,[status(thm)],[f_3952_1]) ).

fof(f_3952_3,plain,
    ! [U_15886,U_15885,U_15884,U_15883] :
      ( ! [U_15882] : ~ c_Finite__Set_Ofun__left__comm(U_15882,U_15883,U_15884)
      | hAPP(c_Fun_Ocomp(U_15883,U_15883,U_15883,hAPP(U_15884,U_15885)),hAPP(U_15884,U_15886)) = hAPP(c_Fun_Ocomp(U_15883,U_15883,U_15883,hAPP(U_15884,U_15886)),hAPP(U_15884,U_15885)) ),
    inference(miniscope,[status(thm)],[f_3952_2]) ).

fof(f_3952_4,plain,
    ! [U_15884,U_15882,U_15883,U_15885,U_15886] :
      ( ~ c_Finite__Set_Ofun__left__comm(U_15882,U_15883,U_15884)
      | hAPP(c_Fun_Ocomp(U_15883,U_15883,U_15883,hAPP(U_15884,U_15885)),hAPP(U_15884,U_15886)) = hAPP(c_Fun_Ocomp(U_15883,U_15883,U_15883,hAPP(U_15884,U_15886)),hAPP(U_15884,U_15885)) ),
    inference(definitional_conversion,[status(esa)],[f_3952_3]) ).

cnf(f_3952_5,plain,
    ( ~ c_Finite__Set_Ofun__left__comm(U_15882,U_15883,U_15884)
    | hAPP(c_Fun_Ocomp(U_15883,U_15883,U_15883,hAPP(U_15884,U_15885)),hAPP(U_15884,U_15886)) = hAPP(c_Fun_Ocomp(U_15883,U_15883,U_15883,hAPP(U_15884,U_15886)),hAPP(U_15884,U_15885)) ),
    inference(clausify,[status(thm)],[f_3952_4]) ).

fof(f_3953_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_3953_2,plain,
    ! [U_15893,U_15892,U_15891,U_15890,U_15889,U_15888,U_15887] :
      ( U_15893 = U_15892
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15887,U_15888,U_15889,U_15890,U_15891),U_15893))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15887,U_15888,U_15889,U_15890,U_15891),U_15892))
      | ~ c_Finite__Set_Ofun__left__comm(U_15887,U_15888,U_15889) ),
    inference(variable_rename,[status(thm)],[f_3953_1]) ).

fof(f_3953_3,plain,
    ! [U_15887,U_15888,U_15889,U_15890,U_15891,U_15892,U_15893] :
      ( U_15893 = U_15892
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15887,U_15888,U_15889,U_15890,U_15891),U_15893))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15887,U_15888,U_15889,U_15890,U_15891),U_15892))
      | ~ c_Finite__Set_Ofun__left__comm(U_15887,U_15888,U_15889) ),
    inference(definitional_conversion,[status(esa)],[f_3953_2]) ).

cnf(f_3953_4,plain,
    ( U_15893 = U_15892
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15887,U_15888,U_15889,U_15890,U_15891),U_15893))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15887,U_15888,U_15889,U_15890,U_15891),U_15892))
    | ~ c_Finite__Set_Ofun__left__comm(U_15887,U_15888,U_15889) ),
    inference(clausify,[status(thm)],[f_3953_3]) ).

fof(f_3954_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_3954_2,plain,
    ! [U_15898,U_15897,U_15896,U_15895,U_15894] :
      ( c_Finite__Set_Ofun__left__comm(U_15897,U_15895,hAPP(hAPP(c_COMBB(U_15894,tc_fun(U_15895,U_15895),U_15897),U_15896),U_15898))
      | ~ c_Finite__Set_Ofun__left__comm(U_15894,U_15895,U_15896) ),
    inference(variable_rename,[status(thm)],[f_3954_1]) ).

fof(f_3954_3,plain,
    ! [U_15897,U_15898,U_15896,U_15895,U_15894] :
      ( c_Finite__Set_Ofun__left__comm(U_15897,U_15895,hAPP(hAPP(c_COMBB(U_15894,tc_fun(U_15895,U_15895),U_15897),U_15896),U_15898))
      | ~ c_Finite__Set_Ofun__left__comm(U_15894,U_15895,U_15896) ),
    inference(definitional_conversion,[status(esa)],[f_3954_2]) ).

cnf(f_3954_4,plain,
    ( c_Finite__Set_Ofun__left__comm(U_15897,U_15895,hAPP(hAPP(c_COMBB(U_15894,tc_fun(U_15895,U_15895),U_15897),U_15896),U_15898))
    | ~ c_Finite__Set_Ofun__left__comm(U_15894,U_15895,U_15896) ),
    inference(clausify,[status(thm)],[f_3954_3]) ).

fof(f_3955_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_3955_2,plain,
    ! [U_15904,U_15903,U_15902,U_15901,U_15900,U_15899] :
      ( hAPP(hAPP(U_15901,U_15902),hAPP(hAPP(U_15901,U_15903),U_15904)) = hAPP(hAPP(U_15901,U_15903),hAPP(hAPP(U_15901,U_15902),U_15904))
      | ~ c_Finite__Set_Ofun__left__comm(U_15899,U_15900,U_15901) ),
    inference(variable_rename,[status(thm)],[f_3955_1]) ).

fof(f_3955_3,plain,
    ! [U_15904,U_15903,U_15902,U_15901] :
      ( ! [U_15900,U_15899] : ~ c_Finite__Set_Ofun__left__comm(U_15899,U_15900,U_15901)
      | hAPP(hAPP(U_15901,U_15902),hAPP(hAPP(U_15901,U_15903),U_15904)) = hAPP(hAPP(U_15901,U_15903),hAPP(hAPP(U_15901,U_15902),U_15904)) ),
    inference(miniscope,[status(thm)],[f_3955_2]) ).

fof(f_3955_4,plain,
    ! [U_15900,U_15901,U_15899,U_15902,U_15903,U_15904] :
      ( ~ c_Finite__Set_Ofun__left__comm(U_15899,U_15900,U_15901)
      | hAPP(hAPP(U_15901,U_15902),hAPP(hAPP(U_15901,U_15903),U_15904)) = hAPP(hAPP(U_15901,U_15903),hAPP(hAPP(U_15901,U_15902),U_15904)) ),
    inference(definitional_conversion,[status(esa)],[f_3955_3]) ).

cnf(f_3955_5,plain,
    ( ~ c_Finite__Set_Ofun__left__comm(U_15899,U_15900,U_15901)
    | hAPP(hAPP(U_15901,U_15902),hAPP(hAPP(U_15901,U_15903),U_15904)) = hAPP(hAPP(U_15901,U_15903),hAPP(hAPP(U_15901,U_15902),U_15904)) ),
    inference(clausify,[status(thm)],[f_3955_4]) ).

fof(f_3956_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_3956_2,plain,
    ! [U_15905] :
      ( c_Finite__Set_Ofun__left__comm(U_15905,U_15905,c_Groups_Otimes__class_Otimes(U_15905))
      | ~ class_Groups_Oab__semigroup__mult(U_15905) ),
    inference(variable_rename,[status(thm)],[f_3956_1]) ).

fof(f_3956_3,plain,
    ! [U_15905] :
      ( c_Finite__Set_Ofun__left__comm(U_15905,U_15905,c_Groups_Otimes__class_Otimes(U_15905))
      | ~ class_Groups_Oab__semigroup__mult(U_15905) ),
    inference(definitional_conversion,[status(esa)],[f_3956_2]) ).

cnf(f_3956_4,plain,
    ( c_Finite__Set_Ofun__left__comm(U_15905,U_15905,c_Groups_Otimes__class_Otimes(U_15905))
    | ~ class_Groups_Oab__semigroup__mult(U_15905) ),
    inference(clausify,[status(thm)],[f_3956_3]) ).

fof(f_3957_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_3957_2,plain,
    ! [U_15911,U_15910,U_15909,U_15908,U_15907,U_15906] :
      ( hAPP(hAPP(U_15908,U_15910),hAPP(hAPP(c_Finite__Set_Ofold(U_15906,U_15907,U_15908),U_15911),U_15909)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15906,U_15907,U_15908),hAPP(hAPP(U_15908,U_15910),U_15911)),U_15909)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15906),U_15909))
      | ~ c_Finite__Set_Ofun__left__comm(U_15906,U_15907,U_15908) ),
    inference(variable_rename,[status(thm)],[f_3957_1]) ).

fof(f_3957_3,plain,
    ! [U_15906,U_15907,U_15908,U_15909,U_15910,U_15911] :
      ( hAPP(hAPP(U_15908,U_15910),hAPP(hAPP(c_Finite__Set_Ofold(U_15906,U_15907,U_15908),U_15911),U_15909)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15906,U_15907,U_15908),hAPP(hAPP(U_15908,U_15910),U_15911)),U_15909)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15906),U_15909))
      | ~ c_Finite__Set_Ofun__left__comm(U_15906,U_15907,U_15908) ),
    inference(definitional_conversion,[status(esa)],[f_3957_2]) ).

cnf(f_3957_4,plain,
    ( hAPP(hAPP(U_15908,U_15910),hAPP(hAPP(c_Finite__Set_Ofold(U_15906,U_15907,U_15908),U_15911),U_15909)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15906,U_15907,U_15908),hAPP(hAPP(U_15908,U_15910),U_15911)),U_15909)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15906),U_15909))
    | ~ c_Finite__Set_Ofun__left__comm(U_15906,U_15907,U_15908) ),
    inference(clausify,[status(thm)],[f_3957_3]) ).

fof(f_3958_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_3958_2,plain,
    ! [U_15917,U_15916,U_15915,U_15914,U_15913,U_15912] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15912,U_15913,U_15914),U_15915),U_15916) = U_15917
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15912,U_15913,U_15914,U_15915,U_15916),U_15917))
      | ~ c_Finite__Set_Ofun__left__comm(U_15912,U_15913,U_15914) ),
    inference(variable_rename,[status(thm)],[f_3958_1]) ).

fof(f_3958_3,plain,
    ! [U_15912,U_15913,U_15914,U_15915,U_15916,U_15917] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15912,U_15913,U_15914),U_15915),U_15916) = U_15917
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15912,U_15913,U_15914,U_15915,U_15916),U_15917))
      | ~ c_Finite__Set_Ofun__left__comm(U_15912,U_15913,U_15914) ),
    inference(definitional_conversion,[status(esa)],[f_3958_2]) ).

cnf(f_3958_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15912,U_15913,U_15914),U_15915),U_15916) = U_15917
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15912,U_15913,U_15914,U_15915,U_15916),U_15917))
    | ~ c_Finite__Set_Ofun__left__comm(U_15912,U_15913,U_15914) ),
    inference(clausify,[status(thm)],[f_3958_3]) ).

fof(f_3959_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_3959_2,plain,
    ! [U_15922,U_15921,U_15920,U_15919,U_15918] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15918,U_15919,U_15920,U_15922,U_15921),hAPP(hAPP(c_Finite__Set_Ofold(U_15918,U_15919,U_15920),U_15922),U_15921)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15918),U_15921))
      | ~ c_Finite__Set_Ofun__left__comm(U_15918,U_15919,U_15920) ),
    inference(variable_rename,[status(thm)],[f_3959_1]) ).

fof(f_3959_3,plain,
    ! [U_15918,U_15919,U_15920,U_15921,U_15922] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15918,U_15919,U_15920,U_15922,U_15921),hAPP(hAPP(c_Finite__Set_Ofold(U_15918,U_15919,U_15920),U_15922),U_15921)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15918),U_15921))
      | ~ c_Finite__Set_Ofun__left__comm(U_15918,U_15919,U_15920) ),
    inference(definitional_conversion,[status(esa)],[f_3959_2]) ).

cnf(f_3959_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15918,U_15919,U_15920,U_15922,U_15921),hAPP(hAPP(c_Finite__Set_Ofold(U_15918,U_15919,U_15920),U_15922),U_15921)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15918),U_15921))
    | ~ c_Finite__Set_Ofun__left__comm(U_15918,U_15919,U_15920) ),
    inference(clausify,[status(thm)],[f_3959_3]) ).

fof(f_3960_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_3960_2,plain,
    ! [U_15928,U_15927,U_15926,U_15925,U_15924,U_15923] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15923,U_15924,U_15925),U_15928),hAPP(hAPP(c_Set_Oinsert(U_15923),U_15927),U_15926)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15923,U_15924,U_15925),hAPP(hAPP(U_15925,U_15927),U_15928)),U_15926)
      | hBOOL(hAPP(hAPP(c_member(U_15923),U_15927),U_15926))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15923),U_15926))
      | ~ c_Finite__Set_Ofun__left__comm(U_15923,U_15924,U_15925) ),
    inference(variable_rename,[status(thm)],[f_3960_1]) ).

fof(f_3960_3,plain,
    ! [U_15923,U_15924,U_15925,U_15926,U_15927,U_15928] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15923,U_15924,U_15925),U_15928),hAPP(hAPP(c_Set_Oinsert(U_15923),U_15927),U_15926)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15923,U_15924,U_15925),hAPP(hAPP(U_15925,U_15927),U_15928)),U_15926)
      | hBOOL(hAPP(hAPP(c_member(U_15923),U_15927),U_15926))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15923),U_15926))
      | ~ c_Finite__Set_Ofun__left__comm(U_15923,U_15924,U_15925) ),
    inference(definitional_conversion,[status(esa)],[f_3960_2]) ).

cnf(f_3960_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15923,U_15924,U_15925),U_15928),hAPP(hAPP(c_Set_Oinsert(U_15923),U_15927),U_15926)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15923,U_15924,U_15925),hAPP(hAPP(U_15925,U_15927),U_15928)),U_15926)
    | hBOOL(hAPP(hAPP(c_member(U_15923),U_15927),U_15926))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15923),U_15926))
    | ~ c_Finite__Set_Ofun__left__comm(U_15923,U_15924,U_15925) ),
    inference(clausify,[status(thm)],[f_3960_3]) ).

fof(f_3961_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_3961_2,plain,
    ! [U_15934,U_15933,U_15932,U_15931,U_15930,U_15929] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15929,U_15930,U_15931),U_15934),hAPP(hAPP(c_Set_Oinsert(U_15929),U_15933),U_15932)) = hAPP(hAPP(U_15931,U_15933),hAPP(hAPP(c_Finite__Set_Ofold(U_15929,U_15930,U_15931),U_15934),U_15932))
      | hBOOL(hAPP(hAPP(c_member(U_15929),U_15933),U_15932))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15929),U_15932))
      | ~ c_Finite__Set_Ofun__left__comm(U_15929,U_15930,U_15931) ),
    inference(variable_rename,[status(thm)],[f_3961_1]) ).

fof(f_3961_3,plain,
    ! [U_15929,U_15930,U_15931,U_15932,U_15933,U_15934] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15929,U_15930,U_15931),U_15934),hAPP(hAPP(c_Set_Oinsert(U_15929),U_15933),U_15932)) = hAPP(hAPP(U_15931,U_15933),hAPP(hAPP(c_Finite__Set_Ofold(U_15929,U_15930,U_15931),U_15934),U_15932))
      | hBOOL(hAPP(hAPP(c_member(U_15929),U_15933),U_15932))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15929),U_15932))
      | ~ c_Finite__Set_Ofun__left__comm(U_15929,U_15930,U_15931) ),
    inference(definitional_conversion,[status(esa)],[f_3961_2]) ).

cnf(f_3961_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15929,U_15930,U_15931),U_15934),hAPP(hAPP(c_Set_Oinsert(U_15929),U_15933),U_15932)) = hAPP(hAPP(U_15931,U_15933),hAPP(hAPP(c_Finite__Set_Ofold(U_15929,U_15930,U_15931),U_15934),U_15932))
    | hBOOL(hAPP(hAPP(c_member(U_15929),U_15933),U_15932))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15929),U_15932))
    | ~ c_Finite__Set_Ofun__left__comm(U_15929,U_15930,U_15931) ),
    inference(clausify,[status(thm)],[f_3961_3]) ).

fof(f_3962_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_3962_2,plain,
    ! [U_15942,U_15941,U_15940,U_15939,U_15938,U_15937,U_15936] :
      ( ? [U_15935] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15936,U_15937,U_15938,U_15939,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15936,tc_HOL_Obool)),U_15940),hAPP(hAPP(c_Set_Oinsert(U_15936),U_15942),c_Orderings_Obot__class_Obot(tc_fun(U_15936,tc_HOL_Obool))))),U_15935))
          & U_15941 = hAPP(hAPP(U_15938,U_15942),U_15935) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_15936),U_15942),U_15940))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15936,U_15937,U_15938,U_15939,U_15940),U_15941))
      | ~ c_Finite__Set_Ofun__left__comm(U_15936,U_15937,U_15938) ),
    inference(variable_rename,[status(thm)],[f_3962_1]) ).

fof(f_3962_3,plain,
    ! [U_15942,U_15941,U_15940,U_15939,U_15938,U_15937,U_15936] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15936,U_15937,U_15938,U_15939,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15936,tc_HOL_Obool)),U_15940),hAPP(hAPP(c_Set_Oinsert(U_15936),U_15942),c_Orderings_Obot__class_Obot(tc_fun(U_15936,tc_HOL_Obool))))),sK384(U_15942,U_15941,U_15940,U_15939,U_15938,U_15937,U_15936)))
        & U_15941 = hAPP(hAPP(U_15938,U_15942),sK384(U_15942,U_15941,U_15940,U_15939,U_15938,U_15937,U_15936)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_15936),U_15942),U_15940))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15936,U_15937,U_15938,U_15939,U_15940),U_15941))
      | ~ c_Finite__Set_Ofun__left__comm(U_15936,U_15937,U_15938) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK384]),skolemize(U_15935,sK384(U_15942,U_15941,U_15940,U_15939,U_15938,U_15937,U_15936))],[f_3962_2]) ).

fof(f_3962_4,plain,
    ( ! [U_15936,U_15937,U_15938,U_15939,U_15940,U_15941,U_15942] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15936,U_15937,U_15938,U_15939,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15936,tc_HOL_Obool)),U_15940),hAPP(hAPP(c_Set_Oinsert(U_15936),U_15942),c_Orderings_Obot__class_Obot(tc_fun(U_15936,tc_HOL_Obool))))),sK384(U_15942,U_15941,U_15940,U_15939,U_15938,U_15937,U_15936)))
        | ~ sP1045(U_15936,U_15937,U_15938,U_15939,U_15940,U_15941,U_15942) )
    & ! [U_15936,U_15937,U_15938,U_15939,U_15940,U_15941,U_15942] :
        ( U_15941 = hAPP(hAPP(U_15938,U_15942),sK384(U_15942,U_15941,U_15940,U_15939,U_15938,U_15937,U_15936))
        | ~ sP1045(U_15936,U_15937,U_15938,U_15939,U_15940,U_15941,U_15942) )
    & ! [U_15936,U_15937,U_15938,U_15939,U_15940,U_15941,U_15942] :
        ( sP1045(U_15936,U_15937,U_15938,U_15939,U_15940,U_15941,U_15942)
        | ~ hBOOL(hAPP(hAPP(c_member(U_15936),U_15942),U_15940))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15936,U_15937,U_15938,U_15939,U_15940),U_15941))
        | ~ c_Finite__Set_Ofun__left__comm(U_15936,U_15937,U_15938) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1045])],[f_3962_3]) ).

cnf(f_3962_5,plain,
    ( sP1045(U_15936,U_15937,U_15938,U_15939,U_15940,U_15941,U_15942)
    | ~ hBOOL(hAPP(hAPP(c_member(U_15936),U_15942),U_15940))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15936,U_15937,U_15938,U_15939,U_15940),U_15941))
    | ~ c_Finite__Set_Ofun__left__comm(U_15936,U_15937,U_15938) ),
    inference(clausify,[status(thm)],[f_3962_4]) ).

cnf(f_3962_6,plain,
    ( U_15941 = hAPP(hAPP(U_15938,U_15942),sK384(U_15942,U_15941,U_15940,U_15939,U_15938,U_15937,U_15936))
    | ~ sP1045(U_15936,U_15937,U_15938,U_15939,U_15940,U_15941,U_15942) ),
    inference(clausify,[status(thm)],[f_3962_4]) ).

cnf(f_3962_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15936,U_15937,U_15938,U_15939,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15936,tc_HOL_Obool)),U_15940),hAPP(hAPP(c_Set_Oinsert(U_15936),U_15942),c_Orderings_Obot__class_Obot(tc_fun(U_15936,tc_HOL_Obool))))),sK384(U_15942,U_15941,U_15940,U_15939,U_15938,U_15937,U_15936)))
    | ~ sP1045(U_15936,U_15937,U_15938,U_15939,U_15940,U_15941,U_15942) ),
    inference(clausify,[status(thm)],[f_3962_4]) ).

fof(f_3963_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_3963_2,plain,
    ! [U_15946,U_15945,U_15944,U_15943] : c_Transitive__Closure_Otrancl(U_15943,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15943,U_15943)),hAPP(hAPP(c_Product__Type_OPair(U_15943,U_15943),U_15944),U_15945)),U_15946)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15943,U_15943),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15943,U_15946)),hAPP(c_Set_OCollect(tc_prod(U_15943,U_15943)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15943,U_15943,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15943,tc_fun(U_15943,tc_HOL_Obool),tc_fun(U_15943,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15943,tc_HOL_Obool),tc_fun(U_15943,tc_HOL_Obool)),U_15943),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15943)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15943),c_fconj),hAPP(hAPP(c_COMBC(U_15943,tc_fun(tc_prod(U_15943,U_15943),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_15943,U_15943),tc_fun(tc_fun(tc_prod(U_15943,U_15943),tc_HOL_Obool),tc_HOL_Obool),U_15943),c_member(tc_prod(U_15943,U_15943))),hAPP(hAPP(c_COMBC(U_15943,U_15943,tc_prod(U_15943,U_15943)),c_Product__Type_OPair(U_15943,U_15943)),U_15944))),c_Transitive__Closure_Ortrancl(U_15943,U_15946))))),hAPP(hAPP(c_COMBC(U_15943,tc_fun(tc_prod(U_15943,U_15943),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_15943,U_15943),tc_fun(tc_fun(tc_prod(U_15943,U_15943),tc_HOL_Obool),tc_HOL_Obool),U_15943),c_member(tc_prod(U_15943,U_15943))),hAPP(c_Product__Type_OPair(U_15943,U_15943),U_15945))),c_Transitive__Closure_Ortrancl(U_15943,U_15946)))))),
    inference(variable_rename,[status(thm)],[f_3963_1]) ).

fof(f_3963_3,plain,
    ! [U_15943,U_15944,U_15945,U_15946] : c_Transitive__Closure_Otrancl(U_15943,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15943,U_15943)),hAPP(hAPP(c_Product__Type_OPair(U_15943,U_15943),U_15944),U_15945)),U_15946)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15943,U_15943),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15943,U_15946)),hAPP(c_Set_OCollect(tc_prod(U_15943,U_15943)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15943,U_15943,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15943,tc_fun(U_15943,tc_HOL_Obool),tc_fun(U_15943,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15943,tc_HOL_Obool),tc_fun(U_15943,tc_HOL_Obool)),U_15943),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15943)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15943),c_fconj),hAPP(hAPP(c_COMBC(U_15943,tc_fun(tc_prod(U_15943,U_15943),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_15943,U_15943),tc_fun(tc_fun(tc_prod(U_15943,U_15943),tc_HOL_Obool),tc_HOL_Obool),U_15943),c_member(tc_prod(U_15943,U_15943))),hAPP(hAPP(c_COMBC(U_15943,U_15943,tc_prod(U_15943,U_15943)),c_Product__Type_OPair(U_15943,U_15943)),U_15944))),c_Transitive__Closure_Ortrancl(U_15943,U_15946))))),hAPP(hAPP(c_COMBC(U_15943,tc_fun(tc_prod(U_15943,U_15943),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_15943,U_15943),tc_fun(tc_fun(tc_prod(U_15943,U_15943),tc_HOL_Obool),tc_HOL_Obool),U_15943),c_member(tc_prod(U_15943,U_15943))),hAPP(c_Product__Type_OPair(U_15943,U_15943),U_15945))),c_Transitive__Closure_Ortrancl(U_15943,U_15946)))))),
    inference(definitional_conversion,[status(esa)],[f_3963_2]) ).

cnf(f_3963_4,plain,
    c_Transitive__Closure_Otrancl(U_15943,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_15943,U_15943)),hAPP(hAPP(c_Product__Type_OPair(U_15943,U_15943),U_15944),U_15945)),U_15946)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15943,U_15943),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_15943,U_15946)),hAPP(c_Set_OCollect(tc_prod(U_15943,U_15943)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15943,U_15943,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15943,tc_fun(U_15943,tc_HOL_Obool),tc_fun(U_15943,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15943,tc_HOL_Obool),tc_fun(U_15943,tc_HOL_Obool)),U_15943),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15943)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15943),c_fconj),hAPP(hAPP(c_COMBC(U_15943,tc_fun(tc_prod(U_15943,U_15943),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_15943,U_15943),tc_fun(tc_fun(tc_prod(U_15943,U_15943),tc_HOL_Obool),tc_HOL_Obool),U_15943),c_member(tc_prod(U_15943,U_15943))),hAPP(hAPP(c_COMBC(U_15943,U_15943,tc_prod(U_15943,U_15943)),c_Product__Type_OPair(U_15943,U_15943)),U_15944))),c_Transitive__Closure_Ortrancl(U_15943,U_15946))))),hAPP(hAPP(c_COMBC(U_15943,tc_fun(tc_prod(U_15943,U_15943),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_15943,U_15943),tc_fun(tc_fun(tc_prod(U_15943,U_15943),tc_HOL_Obool),tc_HOL_Obool),U_15943),c_member(tc_prod(U_15943,U_15943))),hAPP(c_Product__Type_OPair(U_15943,U_15943),U_15945))),c_Transitive__Closure_Ortrancl(U_15943,U_15946)))))),
    inference(clausify,[status(thm)],[f_3963_3]) ).

fof(f_3964_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_3964_2,plain,
    ! [U_15949,U_15948,U_15947] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15947,U_15947)),U_15948),c_Transitive__Closure_Ortrancl(U_15947,U_15949)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15947,U_15947)),U_15948),U_15949)) ),
    inference(variable_rename,[status(thm)],[f_3964_1]) ).

fof(f_3964_3,plain,
    ! [U_15947,U_15948,U_15949] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15947,U_15947)),U_15948),c_Transitive__Closure_Ortrancl(U_15947,U_15949)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15947,U_15947)),U_15948),U_15949)) ),
    inference(definitional_conversion,[status(esa)],[f_3964_2]) ).

cnf(f_3964_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15947,U_15947)),U_15948),c_Transitive__Closure_Ortrancl(U_15947,U_15949)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15947,U_15947)),U_15948),U_15949)) ),
    inference(clausify,[status(thm)],[f_3964_3]) ).

fof(f_3965_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_3965_2,plain,
    ! [U_15952,U_15951,U_15950] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15950,U_15950)),hAPP(hAPP(c_Product__Type_OPair(U_15950,U_15950),U_15951),U_15951)),c_Transitive__Closure_Ortrancl(U_15950,U_15952))),
    inference(variable_rename,[status(thm)],[f_3965_1]) ).

fof(f_3965_3,plain,
    ! [U_15950,U_15951,U_15952] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15950,U_15950)),hAPP(hAPP(c_Product__Type_OPair(U_15950,U_15950),U_15951),U_15951)),c_Transitive__Closure_Ortrancl(U_15950,U_15952))),
    inference(definitional_conversion,[status(esa)],[f_3965_2]) ).

cnf(f_3965_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_15950,U_15950)),hAPP(hAPP(c_Product__Type_OPair(U_15950,U_15950),U_15951),U_15951)),c_Transitive__Closure_Ortrancl(U_15950,U_15952))),
    inference(clausify,[status(thm)],[f_3965_3]) ).

fof(f_3966_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_3966_2,plain,
    ! [U_15956,U_15955,U_15954,U_15953] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15953,U_15953)),hAPP(hAPP(c_Product__Type_OPair(U_15953,U_15953),U_15954),U_15955)),c_Transitive__Closure_Ortrancl(U_15953,U_15956)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15953,U_15953)),hAPP(hAPP(c_Product__Type_OPair(U_15953,U_15953),U_15954),U_15955)),c_Transitive__Closure_Otrancl(U_15953,U_15956))) ),
    inference(variable_rename,[status(thm)],[f_3966_1]) ).

fof(f_3966_3,plain,
    ! [U_15953,U_15954,U_15955,U_15956] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15953,U_15953)),hAPP(hAPP(c_Product__Type_OPair(U_15953,U_15953),U_15954),U_15955)),c_Transitive__Closure_Ortrancl(U_15953,U_15956)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15953,U_15953)),hAPP(hAPP(c_Product__Type_OPair(U_15953,U_15953),U_15954),U_15955)),c_Transitive__Closure_Otrancl(U_15953,U_15956))) ),
    inference(definitional_conversion,[status(esa)],[f_3966_2]) ).

cnf(f_3966_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15953,U_15953)),hAPP(hAPP(c_Product__Type_OPair(U_15953,U_15953),U_15954),U_15955)),c_Transitive__Closure_Ortrancl(U_15953,U_15956)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15953,U_15953)),hAPP(hAPP(c_Product__Type_OPair(U_15953,U_15953),U_15954),U_15955)),c_Transitive__Closure_Otrancl(U_15953,U_15956))) ),
    inference(clausify,[status(thm)],[f_3966_3]) ).

fof(f_3967_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_3967_2,plain,
    ! [U_15958,U_15957] : hAPP(c_Relation_ODomain(U_15957,U_15957),c_Transitive__Closure_Ortrancl(U_15957,U_15958)) = c_Orderings_Otop__class_Otop(tc_fun(U_15957,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3967_1]) ).

fof(f_3967_3,plain,
    ! [U_15957,U_15958] : hAPP(c_Relation_ODomain(U_15957,U_15957),c_Transitive__Closure_Ortrancl(U_15957,U_15958)) = c_Orderings_Otop__class_Otop(tc_fun(U_15957,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3967_2]) ).

cnf(f_3967_4,plain,
    hAPP(c_Relation_ODomain(U_15957,U_15957),c_Transitive__Closure_Ortrancl(U_15957,U_15958)) = c_Orderings_Otop__class_Otop(tc_fun(U_15957,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3967_3]) ).

fof(f_3968_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_3968_2,plain,
    ! [U_15960,U_15959] : hAPP(c_Relation_ORange(U_15959,U_15959),c_Transitive__Closure_Ortrancl(U_15959,U_15960)) = c_Orderings_Otop__class_Otop(tc_fun(U_15959,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3968_1]) ).

fof(f_3968_3,plain,
    ! [U_15959,U_15960] : hAPP(c_Relation_ORange(U_15959,U_15959),c_Transitive__Closure_Ortrancl(U_15959,U_15960)) = c_Orderings_Otop__class_Otop(tc_fun(U_15959,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3968_2]) ).

cnf(f_3968_4,plain,
    hAPP(c_Relation_ORange(U_15959,U_15959),c_Transitive__Closure_Ortrancl(U_15959,U_15960)) = c_Orderings_Otop__class_Otop(tc_fun(U_15959,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3968_3]) ).

fof(f_3969_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_3969_2,plain,
    ! [U_15962,U_15961] : hAPP(hAPP(c_Relation_Orel__comp(U_15961,U_15961,U_15961),c_Transitive__Closure_Ortrancl(U_15961,U_15962)),c_Transitive__Closure_Ortrancl(U_15961,U_15962)) = c_Transitive__Closure_Ortrancl(U_15961,U_15962),
    inference(variable_rename,[status(thm)],[f_3969_1]) ).

fof(f_3969_3,plain,
    ! [U_15961,U_15962] : hAPP(hAPP(c_Relation_Orel__comp(U_15961,U_15961,U_15961),c_Transitive__Closure_Ortrancl(U_15961,U_15962)),c_Transitive__Closure_Ortrancl(U_15961,U_15962)) = c_Transitive__Closure_Ortrancl(U_15961,U_15962),
    inference(definitional_conversion,[status(esa)],[f_3969_2]) ).

cnf(f_3969_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_15961,U_15961,U_15961),c_Transitive__Closure_Ortrancl(U_15961,U_15962)),c_Transitive__Closure_Ortrancl(U_15961,U_15962)) = c_Transitive__Closure_Ortrancl(U_15961,U_15962),
    inference(clausify,[status(thm)],[f_3969_3]) ).

fof(f_3970_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_3970_2,plain,
    ! [U_15964,U_15963] : hAPP(hAPP(c_Relation_Orel__comp(U_15963,U_15963,U_15963),U_15964),c_Transitive__Closure_Ortrancl(U_15963,U_15964)) = hAPP(hAPP(c_Relation_Orel__comp(U_15963,U_15963,U_15963),c_Transitive__Closure_Ortrancl(U_15963,U_15964)),U_15964),
    inference(variable_rename,[status(thm)],[f_3970_1]) ).

fof(f_3970_3,plain,
    ! [U_15963,U_15964] : hAPP(hAPP(c_Relation_Orel__comp(U_15963,U_15963,U_15963),U_15964),c_Transitive__Closure_Ortrancl(U_15963,U_15964)) = hAPP(hAPP(c_Relation_Orel__comp(U_15963,U_15963,U_15963),c_Transitive__Closure_Ortrancl(U_15963,U_15964)),U_15964),
    inference(definitional_conversion,[status(esa)],[f_3970_2]) ).

cnf(f_3970_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_15963,U_15963,U_15963),U_15964),c_Transitive__Closure_Ortrancl(U_15963,U_15964)) = hAPP(hAPP(c_Relation_Orel__comp(U_15963,U_15963,U_15963),c_Transitive__Closure_Ortrancl(U_15963,U_15964)),U_15964),
    inference(clausify,[status(thm)],[f_3970_3]) ).

fof(f_3971_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_3971_2,plain,
    ! [U_15967,U_15966,U_15965] :
      ( hAPP(c_Relation_OImage(U_15965,U_15965,c_Transitive__Closure_Ortrancl(U_15965,U_15966)),U_15967) = U_15967
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15965,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15965,U_15965,U_15966),U_15967)),U_15967)) ),
    inference(variable_rename,[status(thm)],[f_3971_1]) ).

fof(f_3971_3,plain,
    ! [U_15965,U_15966,U_15967] :
      ( hAPP(c_Relation_OImage(U_15965,U_15965,c_Transitive__Closure_Ortrancl(U_15965,U_15966)),U_15967) = U_15967
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15965,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15965,U_15965,U_15966),U_15967)),U_15967)) ),
    inference(definitional_conversion,[status(esa)],[f_3971_2]) ).

cnf(f_3971_4,plain,
    ( hAPP(c_Relation_OImage(U_15965,U_15965,c_Transitive__Closure_Ortrancl(U_15965,U_15966)),U_15967) = U_15967
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15965,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15965,U_15965,U_15966),U_15967)),U_15967)) ),
    inference(clausify,[status(thm)],[f_3971_3]) ).

fof(f_3972_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_3972_2,plain,
    ! [U_15970,U_15969,U_15968] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15968,U_15968),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15968,U_15969)),c_Transitive__Closure_Ortrancl(U_15968,U_15970)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15968,U_15968),tc_HOL_Obool)),U_15969),U_15970)) ),
    inference(variable_rename,[status(thm)],[f_3972_1]) ).

fof(f_3972_3,plain,
    ! [U_15968,U_15969,U_15970] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15968,U_15968),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15968,U_15969)),c_Transitive__Closure_Ortrancl(U_15968,U_15970)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15968,U_15968),tc_HOL_Obool)),U_15969),U_15970)) ),
    inference(definitional_conversion,[status(esa)],[f_3972_2]) ).

cnf(f_3972_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15968,U_15968),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15968,U_15969)),c_Transitive__Closure_Ortrancl(U_15968,U_15970)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15968,U_15968),tc_HOL_Obool)),U_15969),U_15970)) ),
    inference(clausify,[status(thm)],[f_3972_3]) ).

fof(f_3973_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_3973_2,plain,
    ! [U_15973,U_15972,U_15971] :
      ( c_Transitive__Closure_Ortrancl(U_15971,U_15973) = c_Transitive__Closure_Ortrancl(U_15971,U_15972)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15971,U_15971),tc_HOL_Obool)),U_15973),c_Transitive__Closure_Ortrancl(U_15971,U_15972)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15971,U_15971),tc_HOL_Obool)),U_15972),U_15973)) ),
    inference(variable_rename,[status(thm)],[f_3973_1]) ).

fof(f_3973_3,plain,
    ! [U_15971,U_15972,U_15973] :
      ( c_Transitive__Closure_Ortrancl(U_15971,U_15973) = c_Transitive__Closure_Ortrancl(U_15971,U_15972)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15971,U_15971),tc_HOL_Obool)),U_15973),c_Transitive__Closure_Ortrancl(U_15971,U_15972)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15971,U_15971),tc_HOL_Obool)),U_15972),U_15973)) ),
    inference(definitional_conversion,[status(esa)],[f_3973_2]) ).

cnf(f_3973_4,plain,
    ( c_Transitive__Closure_Ortrancl(U_15971,U_15973) = c_Transitive__Closure_Ortrancl(U_15971,U_15972)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15971,U_15971),tc_HOL_Obool)),U_15973),c_Transitive__Closure_Ortrancl(U_15971,U_15972)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15971,U_15971),tc_HOL_Obool)),U_15972),U_15973)) ),
    inference(clausify,[status(thm)],[f_3973_3]) ).

fof(f_3974_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_3974_2,plain,
    ! [U_15976,U_15975,U_15974] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15974,U_15974),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15974,U_15975)),c_Transitive__Closure_Ortrancl(U_15974,U_15976)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15974,U_15974),tc_HOL_Obool)),U_15975),c_Transitive__Closure_Ortrancl(U_15974,U_15976))) ),
    inference(variable_rename,[status(thm)],[f_3974_1]) ).

fof(f_3974_3,plain,
    ! [U_15974,U_15975,U_15976] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15974,U_15974),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15974,U_15975)),c_Transitive__Closure_Ortrancl(U_15974,U_15976)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15974,U_15974),tc_HOL_Obool)),U_15975),c_Transitive__Closure_Ortrancl(U_15974,U_15976))) ),
    inference(definitional_conversion,[status(esa)],[f_3974_2]) ).

cnf(f_3974_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15974,U_15974),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15974,U_15975)),c_Transitive__Closure_Ortrancl(U_15974,U_15976)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15974,U_15974),tc_HOL_Obool)),U_15975),c_Transitive__Closure_Ortrancl(U_15974,U_15976))) ),
    inference(clausify,[status(thm)],[f_3974_3]) ).

fof(f_3975_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_3975_2,plain,
    ! [U_15979,U_15978,U_15977] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15977,U_15977),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15977,U_15977),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15977,U_15978)),c_Transitive__Closure_Ortrancl(U_15977,U_15979))),c_Transitive__Closure_Ortrancl(U_15977,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15977,U_15977),tc_HOL_Obool)),U_15978),U_15979)))),
    inference(variable_rename,[status(thm)],[f_3975_1]) ).

fof(f_3975_3,plain,
    ! [U_15977,U_15978,U_15979] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15977,U_15977),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15977,U_15977),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15977,U_15978)),c_Transitive__Closure_Ortrancl(U_15977,U_15979))),c_Transitive__Closure_Ortrancl(U_15977,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15977,U_15977),tc_HOL_Obool)),U_15978),U_15979)))),
    inference(definitional_conversion,[status(esa)],[f_3975_2]) ).

cnf(f_3975_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15977,U_15977),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15977,U_15977),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15977,U_15978)),c_Transitive__Closure_Ortrancl(U_15977,U_15979))),c_Transitive__Closure_Ortrancl(U_15977,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15977,U_15977),tc_HOL_Obool)),U_15978),U_15979)))),
    inference(clausify,[status(thm)],[f_3975_3]) ).

fof(f_3976_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_3976_2,plain,
    ! [U_15982,U_15981,U_15980] : c_Transitive__Closure_Ortrancl(U_15980,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15980,U_15980),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15980,U_15981)),c_Transitive__Closure_Ortrancl(U_15980,U_15982))) = c_Transitive__Closure_Ortrancl(U_15980,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15980,U_15980),tc_HOL_Obool)),U_15981),U_15982)),
    inference(variable_rename,[status(thm)],[f_3976_1]) ).

fof(f_3976_3,plain,
    ! [U_15980,U_15981,U_15982] : c_Transitive__Closure_Ortrancl(U_15980,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15980,U_15980),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15980,U_15981)),c_Transitive__Closure_Ortrancl(U_15980,U_15982))) = c_Transitive__Closure_Ortrancl(U_15980,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15980,U_15980),tc_HOL_Obool)),U_15981),U_15982)),
    inference(definitional_conversion,[status(esa)],[f_3976_2]) ).

cnf(f_3976_4,plain,
    c_Transitive__Closure_Ortrancl(U_15980,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15980,U_15980),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15980,U_15981)),c_Transitive__Closure_Ortrancl(U_15980,U_15982))) = c_Transitive__Closure_Ortrancl(U_15980,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15980,U_15980),tc_HOL_Obool)),U_15981),U_15982)),
    inference(clausify,[status(thm)],[f_3976_3]) ).

fof(f_3977_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_3977_2,plain,
    ! [U_15986,U_15985,U_15984,U_15983] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15983,U_15983)),U_15984),c_Transitive__Closure_Ortrancl(U_15983,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15983,U_15983),tc_HOL_Obool)),U_15985),U_15986))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15983,U_15983)),U_15984),c_Transitive__Closure_Ortrancl(U_15983,U_15986)))
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15983,U_15983)),U_15984),c_Transitive__Closure_Ortrancl(U_15983,U_15985))) ) ),
    inference(variable_rename,[status(thm)],[f_3977_1]) ).

fof(f_3977_3,plain,
    ( ! [U_15983,U_15984,U_15985,U_15986] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15983,U_15983)),U_15984),c_Transitive__Closure_Ortrancl(U_15983,U_15986)))
        | ~ sP1046(U_15983,U_15984,U_15985,U_15986) )
    & ! [U_15983,U_15984,U_15985,U_15986] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15983,U_15983)),U_15984),c_Transitive__Closure_Ortrancl(U_15983,U_15985)))
        | ~ sP1046(U_15983,U_15984,U_15985,U_15986) )
    & ! [U_15983,U_15984,U_15985,U_15986] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15983,U_15983)),U_15984),c_Transitive__Closure_Ortrancl(U_15983,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15983,U_15983),tc_HOL_Obool)),U_15985),U_15986))))
        | sP1046(U_15983,U_15984,U_15985,U_15986) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1046])],[f_3977_2]) ).

cnf(f_3977_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15983,U_15983)),U_15984),c_Transitive__Closure_Ortrancl(U_15983,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15983,U_15983),tc_HOL_Obool)),U_15985),U_15986))))
    | sP1046(U_15983,U_15984,U_15985,U_15986) ),
    inference(clausify,[status(thm)],[f_3977_3]) ).

cnf(f_3977_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15983,U_15983)),U_15984),c_Transitive__Closure_Ortrancl(U_15983,U_15985)))
    | ~ sP1046(U_15983,U_15984,U_15985,U_15986) ),
    inference(clausify,[status(thm)],[f_3977_3]) ).

cnf(f_3977_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15983,U_15983)),U_15984),c_Transitive__Closure_Ortrancl(U_15983,U_15986)))
    | ~ sP1046(U_15983,U_15984,U_15985,U_15986) ),
    inference(clausify,[status(thm)],[f_3977_3]) ).

fof(f_3978_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_3978_2,plain,
    ! [U_15991,U_15990,U_15989,U_15988,U_15987] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15987,U_15987)),hAPP(hAPP(c_Product__Type_OPair(U_15987,U_15987),U_15988),U_15991)),c_Transitive__Closure_Ortrancl(U_15987,U_15990)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15987,U_15987)),hAPP(hAPP(c_Product__Type_OPair(U_15987,U_15987),U_15989),U_15991)),c_Transitive__Closure_Ortrancl(U_15987,U_15990)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15987,U_15987)),hAPP(hAPP(c_Product__Type_OPair(U_15987,U_15987),U_15988),U_15989)),U_15990)) ),
    inference(variable_rename,[status(thm)],[f_3978_1]) ).

fof(f_3978_3,plain,
    ! [U_15987,U_15988,U_15989,U_15990,U_15991] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15987,U_15987)),hAPP(hAPP(c_Product__Type_OPair(U_15987,U_15987),U_15988),U_15991)),c_Transitive__Closure_Ortrancl(U_15987,U_15990)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15987,U_15987)),hAPP(hAPP(c_Product__Type_OPair(U_15987,U_15987),U_15989),U_15991)),c_Transitive__Closure_Ortrancl(U_15987,U_15990)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15987,U_15987)),hAPP(hAPP(c_Product__Type_OPair(U_15987,U_15987),U_15988),U_15989)),U_15990)) ),
    inference(definitional_conversion,[status(esa)],[f_3978_2]) ).

cnf(f_3978_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15987,U_15987)),hAPP(hAPP(c_Product__Type_OPair(U_15987,U_15987),U_15988),U_15991)),c_Transitive__Closure_Ortrancl(U_15987,U_15990)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15987,U_15987)),hAPP(hAPP(c_Product__Type_OPair(U_15987,U_15987),U_15989),U_15991)),c_Transitive__Closure_Ortrancl(U_15987,U_15990)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15987,U_15987)),hAPP(hAPP(c_Product__Type_OPair(U_15987,U_15987),U_15988),U_15989)),U_15990)) ),
    inference(clausify,[status(thm)],[f_3978_3]) ).

fof(f_3979_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_3979_2,plain,
    ! [U_15996,U_15995,U_15994,U_15993,U_15992] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15992,U_15992)),hAPP(hAPP(c_Product__Type_OPair(U_15992,U_15992),U_15993),U_15996)),c_Transitive__Closure_Ortrancl(U_15992,U_15995)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15992,U_15992)),hAPP(hAPP(c_Product__Type_OPair(U_15992,U_15992),U_15994),U_15996)),U_15995))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15992,U_15992)),hAPP(hAPP(c_Product__Type_OPair(U_15992,U_15992),U_15993),U_15994)),c_Transitive__Closure_Ortrancl(U_15992,U_15995))) ),
    inference(variable_rename,[status(thm)],[f_3979_1]) ).

fof(f_3979_3,plain,
    ! [U_15992,U_15993,U_15994,U_15995,U_15996] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15992,U_15992)),hAPP(hAPP(c_Product__Type_OPair(U_15992,U_15992),U_15993),U_15996)),c_Transitive__Closure_Ortrancl(U_15992,U_15995)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15992,U_15992)),hAPP(hAPP(c_Product__Type_OPair(U_15992,U_15992),U_15994),U_15996)),U_15995))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15992,U_15992)),hAPP(hAPP(c_Product__Type_OPair(U_15992,U_15992),U_15993),U_15994)),c_Transitive__Closure_Ortrancl(U_15992,U_15995))) ),
    inference(definitional_conversion,[status(esa)],[f_3979_2]) ).

cnf(f_3979_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15992,U_15992)),hAPP(hAPP(c_Product__Type_OPair(U_15992,U_15992),U_15993),U_15996)),c_Transitive__Closure_Ortrancl(U_15992,U_15995)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15992,U_15992)),hAPP(hAPP(c_Product__Type_OPair(U_15992,U_15992),U_15994),U_15996)),U_15995))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15992,U_15992)),hAPP(hAPP(c_Product__Type_OPair(U_15992,U_15992),U_15993),U_15994)),c_Transitive__Closure_Ortrancl(U_15992,U_15995))) ),
    inference(clausify,[status(thm)],[f_3979_3]) ).

fof(f_3980_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_3980_2,plain,
    ! [U_16001,U_16000,U_15999,U_15998,U_15997] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15997,U_15997)),hAPP(hAPP(c_Product__Type_OPair(U_15997,U_15997),U_15998),U_16001)),c_Transitive__Closure_Ortrancl(U_15997,U_16000)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15997,U_15997)),hAPP(hAPP(c_Product__Type_OPair(U_15997,U_15997),U_15999),U_16001)),c_Transitive__Closure_Ortrancl(U_15997,U_16000)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15997,U_15997)),hAPP(hAPP(c_Product__Type_OPair(U_15997,U_15997),U_15998),U_15999)),c_Transitive__Closure_Ortrancl(U_15997,U_16000))) ),
    inference(variable_rename,[status(thm)],[f_3980_1]) ).

fof(f_3980_3,plain,
    ! [U_15997,U_15998,U_15999,U_16000,U_16001] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15997,U_15997)),hAPP(hAPP(c_Product__Type_OPair(U_15997,U_15997),U_15998),U_16001)),c_Transitive__Closure_Ortrancl(U_15997,U_16000)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15997,U_15997)),hAPP(hAPP(c_Product__Type_OPair(U_15997,U_15997),U_15999),U_16001)),c_Transitive__Closure_Ortrancl(U_15997,U_16000)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15997,U_15997)),hAPP(hAPP(c_Product__Type_OPair(U_15997,U_15997),U_15998),U_15999)),c_Transitive__Closure_Ortrancl(U_15997,U_16000))) ),
    inference(definitional_conversion,[status(esa)],[f_3980_2]) ).

cnf(f_3980_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15997,U_15997)),hAPP(hAPP(c_Product__Type_OPair(U_15997,U_15997),U_15998),U_16001)),c_Transitive__Closure_Ortrancl(U_15997,U_16000)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15997,U_15997)),hAPP(hAPP(c_Product__Type_OPair(U_15997,U_15997),U_15999),U_16001)),c_Transitive__Closure_Ortrancl(U_15997,U_16000)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15997,U_15997)),hAPP(hAPP(c_Product__Type_OPair(U_15997,U_15997),U_15998),U_15999)),c_Transitive__Closure_Ortrancl(U_15997,U_16000))) ),
    inference(clausify,[status(thm)],[f_3980_3]) ).

fof(f_3981_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_3981_2,plain,
    ! [U_16003,U_16002] : c_Relation_Orefl__on(U_16002,c_Orderings_Otop__class_Otop(tc_fun(U_16002,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16002,U_16003)),
    inference(variable_rename,[status(thm)],[f_3981_1]) ).

fof(f_3981_3,plain,
    ! [U_16002,U_16003] : c_Relation_Orefl__on(U_16002,c_Orderings_Otop__class_Otop(tc_fun(U_16002,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16002,U_16003)),
    inference(definitional_conversion,[status(esa)],[f_3981_2]) ).

cnf(f_3981_4,plain,
    c_Relation_Orefl__on(U_16002,c_Orderings_Otop__class_Otop(tc_fun(U_16002,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16002,U_16003)),
    inference(clausify,[status(thm)],[f_3981_3]) ).

fof(f_3982_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_3982_2,plain,
    ! [U_16005,U_16004] : c_Transitive__Closure_Ortrancl(U_16004,c_Transitive__Closure_Ortrancl(U_16004,U_16005)) = c_Transitive__Closure_Ortrancl(U_16004,U_16005),
    inference(variable_rename,[status(thm)],[f_3982_1]) ).

fof(f_3982_3,plain,
    ! [U_16004,U_16005] : c_Transitive__Closure_Ortrancl(U_16004,c_Transitive__Closure_Ortrancl(U_16004,U_16005)) = c_Transitive__Closure_Ortrancl(U_16004,U_16005),
    inference(definitional_conversion,[status(esa)],[f_3982_2]) ).

cnf(f_3982_4,plain,
    c_Transitive__Closure_Ortrancl(U_16004,c_Transitive__Closure_Ortrancl(U_16004,U_16005)) = c_Transitive__Closure_Ortrancl(U_16004,U_16005),
    inference(clausify,[status(thm)],[f_3982_3]) ).

fof(f_3983_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_3983_2,plain,
    ! [U_16007,U_16006] : c_Transitive__Closure_Otrancl(U_16006,c_Transitive__Closure_Ortrancl(U_16006,U_16007)) = c_Transitive__Closure_Ortrancl(U_16006,U_16007),
    inference(variable_rename,[status(thm)],[f_3983_1]) ).

fof(f_3983_3,plain,
    ! [U_16006,U_16007] : c_Transitive__Closure_Otrancl(U_16006,c_Transitive__Closure_Ortrancl(U_16006,U_16007)) = c_Transitive__Closure_Ortrancl(U_16006,U_16007),
    inference(definitional_conversion,[status(esa)],[f_3983_2]) ).

cnf(f_3983_4,plain,
    c_Transitive__Closure_Otrancl(U_16006,c_Transitive__Closure_Ortrancl(U_16006,U_16007)) = c_Transitive__Closure_Ortrancl(U_16006,U_16007),
    inference(clausify,[status(thm)],[f_3983_3]) ).

fof(f_3984_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_3984_2,plain,
    ! [U_16009,U_16008] : c_Transitive__Closure_Ortrancl(U_16008,c_Transitive__Closure_Otrancl(U_16008,U_16009)) = c_Transitive__Closure_Ortrancl(U_16008,U_16009),
    inference(variable_rename,[status(thm)],[f_3984_1]) ).

fof(f_3984_3,plain,
    ! [U_16008,U_16009] : c_Transitive__Closure_Ortrancl(U_16008,c_Transitive__Closure_Otrancl(U_16008,U_16009)) = c_Transitive__Closure_Ortrancl(U_16008,U_16009),
    inference(definitional_conversion,[status(esa)],[f_3984_2]) ).

cnf(f_3984_4,plain,
    c_Transitive__Closure_Ortrancl(U_16008,c_Transitive__Closure_Otrancl(U_16008,U_16009)) = c_Transitive__Closure_Ortrancl(U_16008,U_16009),
    inference(clausify,[status(thm)],[f_3984_3]) ).

fof(f_3985_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_3985_2,plain,
    ! [U_16011,U_16010] : c_Transitive__Closure_Otrancl(U_16010,U_16011) = hAPP(hAPP(c_Relation_Orel__comp(U_16010,U_16010,U_16010),U_16011),c_Transitive__Closure_Ortrancl(U_16010,U_16011)),
    inference(variable_rename,[status(thm)],[f_3985_1]) ).

fof(f_3985_3,plain,
    ! [U_16010,U_16011] : c_Transitive__Closure_Otrancl(U_16010,U_16011) = hAPP(hAPP(c_Relation_Orel__comp(U_16010,U_16010,U_16010),U_16011),c_Transitive__Closure_Ortrancl(U_16010,U_16011)),
    inference(definitional_conversion,[status(esa)],[f_3985_2]) ).

cnf(f_3985_4,plain,
    c_Transitive__Closure_Otrancl(U_16010,U_16011) = hAPP(hAPP(c_Relation_Orel__comp(U_16010,U_16010,U_16010),U_16011),c_Transitive__Closure_Ortrancl(U_16010,U_16011)),
    inference(clausify,[status(thm)],[f_3985_3]) ).

fof(f_3986_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_3986_2,plain,
    ! [U_16013,U_16012] : c_Transitive__Closure_Otrancl(U_16012,U_16013) = hAPP(hAPP(c_Relation_Orel__comp(U_16012,U_16012,U_16012),c_Transitive__Closure_Ortrancl(U_16012,U_16013)),U_16013),
    inference(variable_rename,[status(thm)],[f_3986_1]) ).

fof(f_3986_3,plain,
    ! [U_16012,U_16013] : c_Transitive__Closure_Otrancl(U_16012,U_16013) = hAPP(hAPP(c_Relation_Orel__comp(U_16012,U_16012,U_16012),c_Transitive__Closure_Ortrancl(U_16012,U_16013)),U_16013),
    inference(definitional_conversion,[status(esa)],[f_3986_2]) ).

cnf(f_3986_4,plain,
    c_Transitive__Closure_Otrancl(U_16012,U_16013) = hAPP(hAPP(c_Relation_Orel__comp(U_16012,U_16012,U_16012),c_Transitive__Closure_Ortrancl(U_16012,U_16013)),U_16013),
    inference(clausify,[status(thm)],[f_3986_3]) ).

fof(f_3987_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_3987_2,plain,
    ! [U_16017,U_16016,U_16015,U_16014] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16014,U_16014)),hAPP(hAPP(c_Product__Type_OPair(U_16014,U_16014),U_16015),U_16016)),c_Transitive__Closure_Ortrancl(U_16014,U_16017)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16014,U_16014)),hAPP(hAPP(c_Product__Type_OPair(U_16014,U_16014),U_16015),U_16016)),c_Transitive__Closure_Otrancl(U_16014,U_16017)))
            | U_16015 = U_16016 )
          & U_16015 != U_16016 ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16014,U_16014)),hAPP(hAPP(c_Product__Type_OPair(U_16014,U_16014),U_16015),U_16016)),c_Transitive__Closure_Otrancl(U_16014,U_16017)))
          & U_16015 != U_16016 )
        | U_16015 = U_16016
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16014,U_16014)),hAPP(hAPP(c_Product__Type_OPair(U_16014,U_16014),U_16015),U_16016)),c_Transitive__Closure_Ortrancl(U_16014,U_16017))) ) ),
    inference(variable_rename,[status(thm)],[f_3987_1]) ).

fof(f_3987_3,plain,
    ( ! [U_16025,U_16023,U_16021,U_16019] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16019,U_16019)),hAPP(hAPP(c_Product__Type_OPair(U_16019,U_16019),U_16021),U_16023)),c_Transitive__Closure_Ortrancl(U_16019,U_16025)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16019,U_16019)),hAPP(hAPP(c_Product__Type_OPair(U_16019,U_16019),U_16021),U_16023)),c_Transitive__Closure_Otrancl(U_16019,U_16025)))
            | U_16021 = U_16023 )
          & U_16021 != U_16023 ) )
    & ! [U_16024,U_16022,U_16020,U_16018] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16018,U_16018)),hAPP(hAPP(c_Product__Type_OPair(U_16018,U_16018),U_16020),U_16022)),c_Transitive__Closure_Otrancl(U_16018,U_16024)))
          & U_16020 != U_16022 )
        | U_16020 = U_16022
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16018,U_16018)),hAPP(hAPP(c_Product__Type_OPair(U_16018,U_16018),U_16020),U_16022)),c_Transitive__Closure_Ortrancl(U_16018,U_16024))) ) ),
    inference(miniscope,[status(thm)],[f_3987_2]) ).

fof(f_3987_4,plain,
    ( ! [U_16019,U_16021,U_16023,U_16025] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16019,U_16019)),hAPP(hAPP(c_Product__Type_OPair(U_16019,U_16019),U_16021),U_16023)),c_Transitive__Closure_Otrancl(U_16019,U_16025)))
        | U_16021 = U_16023
        | ~ sP1048(U_16019,U_16021,U_16023,U_16025) )
    & ! [U_16019,U_16021,U_16023,U_16025] :
        ( U_16021 != U_16023
        | ~ sP1048(U_16019,U_16021,U_16023,U_16025) )
    & ! [U_16022,U_16020,U_16018,U_16024] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16018,U_16018)),hAPP(hAPP(c_Product__Type_OPair(U_16018,U_16018),U_16020),U_16022)),c_Transitive__Closure_Otrancl(U_16018,U_16024)))
        | ~ sP1047(U_16022,U_16020,U_16018,U_16024) )
    & ! [U_16022,U_16020,U_16018,U_16024] :
        ( U_16020 != U_16022
        | ~ sP1047(U_16022,U_16020,U_16018,U_16024) )
    & ! [U_16019,U_16021,U_16023,U_16025] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16019,U_16019)),hAPP(hAPP(c_Product__Type_OPair(U_16019,U_16019),U_16021),U_16023)),c_Transitive__Closure_Ortrancl(U_16019,U_16025)))
        | sP1048(U_16019,U_16021,U_16023,U_16025) )
    & ! [U_16022,U_16020,U_16018,U_16024] :
        ( sP1047(U_16022,U_16020,U_16018,U_16024)
        | U_16020 = U_16022
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16018,U_16018)),hAPP(hAPP(c_Product__Type_OPair(U_16018,U_16018),U_16020),U_16022)),c_Transitive__Closure_Ortrancl(U_16018,U_16024))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1047,sP1048])],[f_3987_3]) ).

cnf(f_3987_5,plain,
    ( sP1047(U_16022,U_16020,U_16018,U_16024)
    | U_16020 = U_16022
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16018,U_16018)),hAPP(hAPP(c_Product__Type_OPair(U_16018,U_16018),U_16020),U_16022)),c_Transitive__Closure_Ortrancl(U_16018,U_16024))) ),
    inference(clausify,[status(thm)],[f_3987_4]) ).

cnf(f_3987_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16019,U_16019)),hAPP(hAPP(c_Product__Type_OPair(U_16019,U_16019),U_16021),U_16023)),c_Transitive__Closure_Ortrancl(U_16019,U_16025)))
    | sP1048(U_16019,U_16021,U_16023,U_16025) ),
    inference(clausify,[status(thm)],[f_3987_4]) ).

cnf(f_3987_7,plain,
    ( U_16020 != U_16022
    | ~ sP1047(U_16022,U_16020,U_16018,U_16024) ),
    inference(clausify,[status(thm)],[f_3987_4]) ).

cnf(f_3987_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16018,U_16018)),hAPP(hAPP(c_Product__Type_OPair(U_16018,U_16018),U_16020),U_16022)),c_Transitive__Closure_Otrancl(U_16018,U_16024)))
    | ~ sP1047(U_16022,U_16020,U_16018,U_16024) ),
    inference(clausify,[status(thm)],[f_3987_4]) ).

cnf(f_3987_9,plain,
    ( U_16021 != U_16023
    | ~ sP1048(U_16019,U_16021,U_16023,U_16025) ),
    inference(clausify,[status(thm)],[f_3987_4]) ).

cnf(f_3987_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16019,U_16019)),hAPP(hAPP(c_Product__Type_OPair(U_16019,U_16019),U_16021),U_16023)),c_Transitive__Closure_Otrancl(U_16019,U_16025)))
    | U_16021 = U_16023
    | ~ sP1048(U_16019,U_16021,U_16023,U_16025) ),
    inference(clausify,[status(thm)],[f_3987_4]) ).

fof(f_3988_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_3988_2,plain,
    ! [U_16030,U_16029,U_16028,U_16027,U_16026] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16026,U_16026)),hAPP(hAPP(c_Product__Type_OPair(U_16026,U_16026),U_16027),U_16030)),c_Transitive__Closure_Otrancl(U_16026,U_16029)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16026,U_16026)),hAPP(hAPP(c_Product__Type_OPair(U_16026,U_16026),U_16028),U_16030)),c_Transitive__Closure_Ortrancl(U_16026,U_16029)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16026,U_16026)),hAPP(hAPP(c_Product__Type_OPair(U_16026,U_16026),U_16027),U_16028)),U_16029)) ),
    inference(variable_rename,[status(thm)],[f_3988_1]) ).

fof(f_3988_3,plain,
    ! [U_16027,U_16028,U_16026,U_16029,U_16030] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16026,U_16026)),hAPP(hAPP(c_Product__Type_OPair(U_16026,U_16026),U_16027),U_16030)),c_Transitive__Closure_Otrancl(U_16026,U_16029)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16026,U_16026)),hAPP(hAPP(c_Product__Type_OPair(U_16026,U_16026),U_16028),U_16030)),c_Transitive__Closure_Ortrancl(U_16026,U_16029)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16026,U_16026)),hAPP(hAPP(c_Product__Type_OPair(U_16026,U_16026),U_16027),U_16028)),U_16029)) ),
    inference(definitional_conversion,[status(esa)],[f_3988_2]) ).

cnf(f_3988_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16026,U_16026)),hAPP(hAPP(c_Product__Type_OPair(U_16026,U_16026),U_16027),U_16030)),c_Transitive__Closure_Otrancl(U_16026,U_16029)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16026,U_16026)),hAPP(hAPP(c_Product__Type_OPair(U_16026,U_16026),U_16028),U_16030)),c_Transitive__Closure_Ortrancl(U_16026,U_16029)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16026,U_16026)),hAPP(hAPP(c_Product__Type_OPair(U_16026,U_16026),U_16027),U_16028)),U_16029)) ),
    inference(clausify,[status(thm)],[f_3988_3]) ).

fof(f_3989_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_3989_2,plain,
    ! [U_16034,U_16033,U_16032,U_16031] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16031,U_16031)),hAPP(hAPP(c_Product__Type_OPair(U_16031,U_16031),U_16032),U_16033)),c_Transitive__Closure_Otrancl(U_16031,U_16034)))
        & U_16032 != U_16033 )
      | U_16032 = U_16033
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16031,U_16031)),hAPP(hAPP(c_Product__Type_OPair(U_16031,U_16031),U_16032),U_16033)),c_Transitive__Closure_Ortrancl(U_16031,U_16034))) ),
    inference(variable_rename,[status(thm)],[f_3989_1]) ).

fof(f_3989_3,plain,
    ( ! [U_16031,U_16032,U_16033,U_16034] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16031,U_16031)),hAPP(hAPP(c_Product__Type_OPair(U_16031,U_16031),U_16032),U_16033)),c_Transitive__Closure_Otrancl(U_16031,U_16034)))
        | ~ sP1049(U_16031,U_16032,U_16033,U_16034) )
    & ! [U_16031,U_16032,U_16033,U_16034] :
        ( U_16032 != U_16033
        | ~ sP1049(U_16031,U_16032,U_16033,U_16034) )
    & ! [U_16031,U_16032,U_16033,U_16034] :
        ( sP1049(U_16031,U_16032,U_16033,U_16034)
        | U_16032 = U_16033
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16031,U_16031)),hAPP(hAPP(c_Product__Type_OPair(U_16031,U_16031),U_16032),U_16033)),c_Transitive__Closure_Ortrancl(U_16031,U_16034))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1049])],[f_3989_2]) ).

cnf(f_3989_4,plain,
    ( sP1049(U_16031,U_16032,U_16033,U_16034)
    | U_16032 = U_16033
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16031,U_16031)),hAPP(hAPP(c_Product__Type_OPair(U_16031,U_16031),U_16032),U_16033)),c_Transitive__Closure_Ortrancl(U_16031,U_16034))) ),
    inference(clausify,[status(thm)],[f_3989_3]) ).

cnf(f_3989_5,plain,
    ( U_16032 != U_16033
    | ~ sP1049(U_16031,U_16032,U_16033,U_16034) ),
    inference(clausify,[status(thm)],[f_3989_3]) ).

cnf(f_3989_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16031,U_16031)),hAPP(hAPP(c_Product__Type_OPair(U_16031,U_16031),U_16032),U_16033)),c_Transitive__Closure_Otrancl(U_16031,U_16034)))
    | ~ sP1049(U_16031,U_16032,U_16033,U_16034) ),
    inference(clausify,[status(thm)],[f_3989_3]) ).

fof(f_3990_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_3990_2,plain,
    ! [U_16039,U_16038,U_16037,U_16036,U_16035] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16035,U_16035)),hAPP(hAPP(c_Product__Type_OPair(U_16035,U_16035),U_16036),U_16039)),c_Transitive__Closure_Otrancl(U_16035,U_16038)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16035,U_16035)),hAPP(hAPP(c_Product__Type_OPair(U_16035,U_16035),U_16037),U_16039)),U_16038))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16035,U_16035)),hAPP(hAPP(c_Product__Type_OPair(U_16035,U_16035),U_16036),U_16037)),c_Transitive__Closure_Ortrancl(U_16035,U_16038))) ),
    inference(variable_rename,[status(thm)],[f_3990_1]) ).

fof(f_3990_3,plain,
    ! [U_16036,U_16035,U_16037,U_16038,U_16039] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16035,U_16035)),hAPP(hAPP(c_Product__Type_OPair(U_16035,U_16035),U_16036),U_16039)),c_Transitive__Closure_Otrancl(U_16035,U_16038)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16035,U_16035)),hAPP(hAPP(c_Product__Type_OPair(U_16035,U_16035),U_16037),U_16039)),U_16038))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16035,U_16035)),hAPP(hAPP(c_Product__Type_OPair(U_16035,U_16035),U_16036),U_16037)),c_Transitive__Closure_Ortrancl(U_16035,U_16038))) ),
    inference(definitional_conversion,[status(esa)],[f_3990_2]) ).

cnf(f_3990_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16035,U_16035)),hAPP(hAPP(c_Product__Type_OPair(U_16035,U_16035),U_16036),U_16039)),c_Transitive__Closure_Otrancl(U_16035,U_16038)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16035,U_16035)),hAPP(hAPP(c_Product__Type_OPair(U_16035,U_16035),U_16037),U_16039)),U_16038))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16035,U_16035)),hAPP(hAPP(c_Product__Type_OPair(U_16035,U_16035),U_16036),U_16037)),c_Transitive__Closure_Ortrancl(U_16035,U_16038))) ),
    inference(clausify,[status(thm)],[f_3990_3]) ).

fof(f_3991_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_3991_2,plain,
    ! [U_16044,U_16043,U_16042,U_16041,U_16040] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16040,U_16040)),hAPP(hAPP(c_Product__Type_OPair(U_16040,U_16040),U_16041),U_16044)),c_Transitive__Closure_Otrancl(U_16040,U_16043)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16040,U_16040)),hAPP(hAPP(c_Product__Type_OPair(U_16040,U_16040),U_16042),U_16044)),c_Transitive__Closure_Ortrancl(U_16040,U_16043)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16040,U_16040)),hAPP(hAPP(c_Product__Type_OPair(U_16040,U_16040),U_16041),U_16042)),c_Transitive__Closure_Otrancl(U_16040,U_16043))) ),
    inference(variable_rename,[status(thm)],[f_3991_1]) ).

fof(f_3991_3,plain,
    ! [U_16040,U_16041,U_16042,U_16043,U_16044] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16040,U_16040)),hAPP(hAPP(c_Product__Type_OPair(U_16040,U_16040),U_16041),U_16044)),c_Transitive__Closure_Otrancl(U_16040,U_16043)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16040,U_16040)),hAPP(hAPP(c_Product__Type_OPair(U_16040,U_16040),U_16042),U_16044)),c_Transitive__Closure_Ortrancl(U_16040,U_16043)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16040,U_16040)),hAPP(hAPP(c_Product__Type_OPair(U_16040,U_16040),U_16041),U_16042)),c_Transitive__Closure_Otrancl(U_16040,U_16043))) ),
    inference(definitional_conversion,[status(esa)],[f_3991_2]) ).

cnf(f_3991_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16040,U_16040)),hAPP(hAPP(c_Product__Type_OPair(U_16040,U_16040),U_16041),U_16044)),c_Transitive__Closure_Otrancl(U_16040,U_16043)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16040,U_16040)),hAPP(hAPP(c_Product__Type_OPair(U_16040,U_16040),U_16042),U_16044)),c_Transitive__Closure_Ortrancl(U_16040,U_16043)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16040,U_16040)),hAPP(hAPP(c_Product__Type_OPair(U_16040,U_16040),U_16041),U_16042)),c_Transitive__Closure_Otrancl(U_16040,U_16043))) ),
    inference(clausify,[status(thm)],[f_3991_3]) ).

fof(f_3992_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_3992_2,plain,
    ! [U_16049,U_16048,U_16047,U_16046,U_16045] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16045,U_16045)),hAPP(hAPP(c_Product__Type_OPair(U_16045,U_16045),U_16046),U_16049)),c_Transitive__Closure_Otrancl(U_16045,U_16048)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16045,U_16045)),hAPP(hAPP(c_Product__Type_OPair(U_16045,U_16045),U_16047),U_16049)),c_Transitive__Closure_Otrancl(U_16045,U_16048)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16045,U_16045)),hAPP(hAPP(c_Product__Type_OPair(U_16045,U_16045),U_16046),U_16047)),c_Transitive__Closure_Ortrancl(U_16045,U_16048))) ),
    inference(variable_rename,[status(thm)],[f_3992_1]) ).

fof(f_3992_3,plain,
    ! [U_16045,U_16046,U_16047,U_16048,U_16049] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16045,U_16045)),hAPP(hAPP(c_Product__Type_OPair(U_16045,U_16045),U_16046),U_16049)),c_Transitive__Closure_Otrancl(U_16045,U_16048)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16045,U_16045)),hAPP(hAPP(c_Product__Type_OPair(U_16045,U_16045),U_16047),U_16049)),c_Transitive__Closure_Otrancl(U_16045,U_16048)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16045,U_16045)),hAPP(hAPP(c_Product__Type_OPair(U_16045,U_16045),U_16046),U_16047)),c_Transitive__Closure_Ortrancl(U_16045,U_16048))) ),
    inference(definitional_conversion,[status(esa)],[f_3992_2]) ).

cnf(f_3992_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16045,U_16045)),hAPP(hAPP(c_Product__Type_OPair(U_16045,U_16045),U_16046),U_16049)),c_Transitive__Closure_Otrancl(U_16045,U_16048)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16045,U_16045)),hAPP(hAPP(c_Product__Type_OPair(U_16045,U_16045),U_16047),U_16049)),c_Transitive__Closure_Otrancl(U_16045,U_16048)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16045,U_16045)),hAPP(hAPP(c_Product__Type_OPair(U_16045,U_16045),U_16046),U_16047)),c_Transitive__Closure_Ortrancl(U_16045,U_16048))) ),
    inference(clausify,[status(thm)],[f_3992_3]) ).

fof(f_3993_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_3993_2,plain,
    ! [U_16053,U_16052,U_16051,U_16050] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16050,U_16050)),hAPP(hAPP(c_Product__Type_OPair(U_16050,U_16050),U_16051),U_16053)),c_Transitive__Closure_Ortrancl(U_16050,U_16052)))
          | U_16051 != U_16053 )
        & ( U_16051 = U_16053
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16050,U_16050)),hAPP(hAPP(c_Product__Type_OPair(U_16050,U_16050),U_16051),U_16053)),c_Transitive__Closure_Ortrancl(U_16050,U_16052))) ) )
      | hBOOL(hAPP(hAPP(c_member(U_16050),U_16051),hAPP(c_Relation_ODomain(U_16050,U_16050),U_16052))) ),
    inference(variable_rename,[status(thm)],[f_3993_1]) ).

fof(f_3993_3,plain,
    ( ! [U_16051,U_16052,U_16053,U_16050] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16050,U_16050)),hAPP(hAPP(c_Product__Type_OPair(U_16050,U_16050),U_16051),U_16053)),c_Transitive__Closure_Ortrancl(U_16050,U_16052)))
        | U_16051 != U_16053
        | ~ sP1050(U_16051,U_16052,U_16053,U_16050) )
    & ! [U_16051,U_16052,U_16053,U_16050] :
        ( U_16051 = U_16053
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16050,U_16050)),hAPP(hAPP(c_Product__Type_OPair(U_16050,U_16050),U_16051),U_16053)),c_Transitive__Closure_Ortrancl(U_16050,U_16052)))
        | ~ sP1050(U_16051,U_16052,U_16053,U_16050) )
    & ! [U_16051,U_16052,U_16053,U_16050] :
        ( sP1050(U_16051,U_16052,U_16053,U_16050)
        | hBOOL(hAPP(hAPP(c_member(U_16050),U_16051),hAPP(c_Relation_ODomain(U_16050,U_16050),U_16052))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1050])],[f_3993_2]) ).

cnf(f_3993_4,plain,
    ( sP1050(U_16051,U_16052,U_16053,U_16050)
    | hBOOL(hAPP(hAPP(c_member(U_16050),U_16051),hAPP(c_Relation_ODomain(U_16050,U_16050),U_16052))) ),
    inference(clausify,[status(thm)],[f_3993_3]) ).

cnf(f_3993_5,plain,
    ( U_16051 = U_16053
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16050,U_16050)),hAPP(hAPP(c_Product__Type_OPair(U_16050,U_16050),U_16051),U_16053)),c_Transitive__Closure_Ortrancl(U_16050,U_16052)))
    | ~ sP1050(U_16051,U_16052,U_16053,U_16050) ),
    inference(clausify,[status(thm)],[f_3993_3]) ).

cnf(f_3993_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16050,U_16050)),hAPP(hAPP(c_Product__Type_OPair(U_16050,U_16050),U_16051),U_16053)),c_Transitive__Closure_Ortrancl(U_16050,U_16052)))
    | U_16051 != U_16053
    | ~ sP1050(U_16051,U_16052,U_16053,U_16050) ),
    inference(clausify,[status(thm)],[f_3993_3]) ).

fof(f_3994_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_3994_2,plain,
    ! [U_16057,U_16056,U_16055,U_16054] :
      ( hBOOL(hAPP(hAPP(c_member(U_16054),U_16057),c_Wellfounded_Oacc(U_16054,U_16056)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16054,U_16054)),hAPP(hAPP(c_Product__Type_OPair(U_16054,U_16054),U_16057),U_16055)),c_Transitive__Closure_Ortrancl(U_16054,U_16056)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16054),U_16055),c_Wellfounded_Oacc(U_16054,U_16056))) ),
    inference(variable_rename,[status(thm)],[f_3994_1]) ).

fof(f_3994_3,plain,
    ! [U_16054,U_16055,U_16056,U_16057] :
      ( hBOOL(hAPP(hAPP(c_member(U_16054),U_16057),c_Wellfounded_Oacc(U_16054,U_16056)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16054,U_16054)),hAPP(hAPP(c_Product__Type_OPair(U_16054,U_16054),U_16057),U_16055)),c_Transitive__Closure_Ortrancl(U_16054,U_16056)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16054),U_16055),c_Wellfounded_Oacc(U_16054,U_16056))) ),
    inference(definitional_conversion,[status(esa)],[f_3994_2]) ).

cnf(f_3994_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16054),U_16057),c_Wellfounded_Oacc(U_16054,U_16056)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16054,U_16054)),hAPP(hAPP(c_Product__Type_OPair(U_16054,U_16054),U_16057),U_16055)),c_Transitive__Closure_Ortrancl(U_16054,U_16056)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16054),U_16055),c_Wellfounded_Oacc(U_16054,U_16056))) ),
    inference(clausify,[status(thm)],[f_3994_3]) ).

fof(f_3995_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_3995_2,plain,
    ! [U_16061,U_16060,U_16059,U_16058] :
      ( hBOOL(hAPP(hAPP(c_member(U_16058),U_16059),c_Wellfounded_Oacc(U_16058,U_16061)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16058),U_16060),c_Wellfounded_Oacc(U_16058,U_16061)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16058,U_16058)),hAPP(hAPP(c_Product__Type_OPair(U_16058,U_16058),U_16059),U_16060)),c_Transitive__Closure_Ortrancl(U_16058,U_16061))) ),
    inference(variable_rename,[status(thm)],[f_3995_1]) ).

fof(f_3995_3,plain,
    ! [U_16058,U_16059,U_16060,U_16061] :
      ( hBOOL(hAPP(hAPP(c_member(U_16058),U_16059),c_Wellfounded_Oacc(U_16058,U_16061)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16058),U_16060),c_Wellfounded_Oacc(U_16058,U_16061)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16058,U_16058)),hAPP(hAPP(c_Product__Type_OPair(U_16058,U_16058),U_16059),U_16060)),c_Transitive__Closure_Ortrancl(U_16058,U_16061))) ),
    inference(definitional_conversion,[status(esa)],[f_3995_2]) ).

cnf(f_3995_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16058),U_16059),c_Wellfounded_Oacc(U_16058,U_16061)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16058),U_16060),c_Wellfounded_Oacc(U_16058,U_16061)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16058,U_16058)),hAPP(hAPP(c_Product__Type_OPair(U_16058,U_16058),U_16059),U_16060)),c_Transitive__Closure_Ortrancl(U_16058,U_16061))) ),
    inference(clausify,[status(thm)],[f_3995_3]) ).

fof(f_3996_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_3996_2,plain,
    ! [U_16065,U_16064,U_16063,U_16062] :
      ( ( c_Wellfounded_Owf(U_16062,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16062,U_16062)),hAPP(hAPP(c_Product__Type_OPair(U_16062,U_16062),U_16063),U_16064)),U_16065))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16062,U_16062)),hAPP(hAPP(c_Product__Type_OPair(U_16062,U_16062),U_16064),U_16063)),c_Transitive__Closure_Ortrancl(U_16062,U_16065)))
        | ~ c_Wellfounded_Owf(U_16062,U_16065) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16062,U_16062)),hAPP(hAPP(c_Product__Type_OPair(U_16062,U_16062),U_16064),U_16063)),c_Transitive__Closure_Ortrancl(U_16062,U_16065)))
          & c_Wellfounded_Owf(U_16062,U_16065) )
        | ~ c_Wellfounded_Owf(U_16062,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16062,U_16062)),hAPP(hAPP(c_Product__Type_OPair(U_16062,U_16062),U_16063),U_16064)),U_16065)) ) ),
    inference(variable_rename,[status(thm)],[f_3996_1]) ).

fof(f_3996_3,plain,
    ( ! [U_16073,U_16071,U_16069,U_16067] :
        ( c_Wellfounded_Owf(U_16067,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16067,U_16067)),hAPP(hAPP(c_Product__Type_OPair(U_16067,U_16067),U_16069),U_16071)),U_16073))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16067,U_16067)),hAPP(hAPP(c_Product__Type_OPair(U_16067,U_16067),U_16071),U_16069)),c_Transitive__Closure_Ortrancl(U_16067,U_16073)))
        | ~ c_Wellfounded_Owf(U_16067,U_16073) )
    & ! [U_16072,U_16070,U_16068,U_16066] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16066,U_16066)),hAPP(hAPP(c_Product__Type_OPair(U_16066,U_16066),U_16070),U_16068)),c_Transitive__Closure_Ortrancl(U_16066,U_16072)))
          & c_Wellfounded_Owf(U_16066,U_16072) )
        | ~ c_Wellfounded_Owf(U_16066,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16066,U_16066)),hAPP(hAPP(c_Product__Type_OPair(U_16066,U_16066),U_16068),U_16070)),U_16072)) ) ),
    inference(miniscope,[status(thm)],[f_3996_2]) ).

fof(f_3996_4,plain,
    ( ! [U_16068,U_16066,U_16070,U_16072] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16066,U_16066)),hAPP(hAPP(c_Product__Type_OPair(U_16066,U_16066),U_16070),U_16068)),c_Transitive__Closure_Ortrancl(U_16066,U_16072)))
        | ~ sP1051(U_16068,U_16066,U_16070,U_16072) )
    & ! [U_16068,U_16066,U_16070,U_16072] :
        ( c_Wellfounded_Owf(U_16066,U_16072)
        | ~ sP1051(U_16068,U_16066,U_16070,U_16072) )
    & ! [U_16069,U_16067,U_16071,U_16073] :
        ( c_Wellfounded_Owf(U_16067,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16067,U_16067)),hAPP(hAPP(c_Product__Type_OPair(U_16067,U_16067),U_16069),U_16071)),U_16073))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16067,U_16067)),hAPP(hAPP(c_Product__Type_OPair(U_16067,U_16067),U_16071),U_16069)),c_Transitive__Closure_Ortrancl(U_16067,U_16073)))
        | ~ c_Wellfounded_Owf(U_16067,U_16073) )
    & ! [U_16068,U_16066,U_16070,U_16072] :
        ( sP1051(U_16068,U_16066,U_16070,U_16072)
        | ~ c_Wellfounded_Owf(U_16066,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16066,U_16066)),hAPP(hAPP(c_Product__Type_OPair(U_16066,U_16066),U_16068),U_16070)),U_16072)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1051])],[f_3996_3]) ).

cnf(f_3996_5,plain,
    ( sP1051(U_16068,U_16066,U_16070,U_16072)
    | ~ c_Wellfounded_Owf(U_16066,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16066,U_16066)),hAPP(hAPP(c_Product__Type_OPair(U_16066,U_16066),U_16068),U_16070)),U_16072)) ),
    inference(clausify,[status(thm)],[f_3996_4]) ).

cnf(f_3996_6,plain,
    ( c_Wellfounded_Owf(U_16067,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16067,U_16067)),hAPP(hAPP(c_Product__Type_OPair(U_16067,U_16067),U_16069),U_16071)),U_16073))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16067,U_16067)),hAPP(hAPP(c_Product__Type_OPair(U_16067,U_16067),U_16071),U_16069)),c_Transitive__Closure_Ortrancl(U_16067,U_16073)))
    | ~ c_Wellfounded_Owf(U_16067,U_16073) ),
    inference(clausify,[status(thm)],[f_3996_4]) ).

cnf(f_3996_7,plain,
    ( c_Wellfounded_Owf(U_16066,U_16072)
    | ~ sP1051(U_16068,U_16066,U_16070,U_16072) ),
    inference(clausify,[status(thm)],[f_3996_4]) ).

cnf(f_3996_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16066,U_16066)),hAPP(hAPP(c_Product__Type_OPair(U_16066,U_16066),U_16070),U_16068)),c_Transitive__Closure_Ortrancl(U_16066,U_16072)))
    | ~ sP1051(U_16068,U_16066,U_16070,U_16072) ),
    inference(clausify,[status(thm)],[f_3996_4]) ).

fof(f_3997_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_3997_2,plain,
    ! [U_16077,U_16076,U_16075,U_16074] :
      ( ( c_Wellfounded_Oacyclic(U_16074,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16074,U_16074)),hAPP(hAPP(c_Product__Type_OPair(U_16074,U_16074),U_16075),U_16076)),U_16077))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16074,U_16074)),hAPP(hAPP(c_Product__Type_OPair(U_16074,U_16074),U_16076),U_16075)),c_Transitive__Closure_Ortrancl(U_16074,U_16077)))
        | ~ c_Wellfounded_Oacyclic(U_16074,U_16077) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16074,U_16074)),hAPP(hAPP(c_Product__Type_OPair(U_16074,U_16074),U_16076),U_16075)),c_Transitive__Closure_Ortrancl(U_16074,U_16077)))
          & c_Wellfounded_Oacyclic(U_16074,U_16077) )
        | ~ c_Wellfounded_Oacyclic(U_16074,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16074,U_16074)),hAPP(hAPP(c_Product__Type_OPair(U_16074,U_16074),U_16075),U_16076)),U_16077)) ) ),
    inference(variable_rename,[status(thm)],[f_3997_1]) ).

fof(f_3997_3,plain,
    ( ! [U_16085,U_16083,U_16081,U_16079] :
        ( c_Wellfounded_Oacyclic(U_16079,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16079,U_16079)),hAPP(hAPP(c_Product__Type_OPair(U_16079,U_16079),U_16081),U_16083)),U_16085))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16079,U_16079)),hAPP(hAPP(c_Product__Type_OPair(U_16079,U_16079),U_16083),U_16081)),c_Transitive__Closure_Ortrancl(U_16079,U_16085)))
        | ~ c_Wellfounded_Oacyclic(U_16079,U_16085) )
    & ! [U_16084,U_16082,U_16080,U_16078] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16078,U_16078)),hAPP(hAPP(c_Product__Type_OPair(U_16078,U_16078),U_16082),U_16080)),c_Transitive__Closure_Ortrancl(U_16078,U_16084)))
          & c_Wellfounded_Oacyclic(U_16078,U_16084) )
        | ~ c_Wellfounded_Oacyclic(U_16078,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16078,U_16078)),hAPP(hAPP(c_Product__Type_OPair(U_16078,U_16078),U_16080),U_16082)),U_16084)) ) ),
    inference(miniscope,[status(thm)],[f_3997_2]) ).

fof(f_3997_4,plain,
    ( ! [U_16078,U_16082,U_16080,U_16084] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16078,U_16078)),hAPP(hAPP(c_Product__Type_OPair(U_16078,U_16078),U_16082),U_16080)),c_Transitive__Closure_Ortrancl(U_16078,U_16084)))
        | ~ sP1052(U_16078,U_16082,U_16080,U_16084) )
    & ! [U_16078,U_16082,U_16080,U_16084] :
        ( c_Wellfounded_Oacyclic(U_16078,U_16084)
        | ~ sP1052(U_16078,U_16082,U_16080,U_16084) )
    & ! [U_16081,U_16079,U_16085,U_16083] :
        ( c_Wellfounded_Oacyclic(U_16079,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16079,U_16079)),hAPP(hAPP(c_Product__Type_OPair(U_16079,U_16079),U_16081),U_16083)),U_16085))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16079,U_16079)),hAPP(hAPP(c_Product__Type_OPair(U_16079,U_16079),U_16083),U_16081)),c_Transitive__Closure_Ortrancl(U_16079,U_16085)))
        | ~ c_Wellfounded_Oacyclic(U_16079,U_16085) )
    & ! [U_16078,U_16082,U_16080,U_16084] :
        ( sP1052(U_16078,U_16082,U_16080,U_16084)
        | ~ c_Wellfounded_Oacyclic(U_16078,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16078,U_16078)),hAPP(hAPP(c_Product__Type_OPair(U_16078,U_16078),U_16080),U_16082)),U_16084)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1052])],[f_3997_3]) ).

cnf(f_3997_5,plain,
    ( sP1052(U_16078,U_16082,U_16080,U_16084)
    | ~ c_Wellfounded_Oacyclic(U_16078,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16078,U_16078)),hAPP(hAPP(c_Product__Type_OPair(U_16078,U_16078),U_16080),U_16082)),U_16084)) ),
    inference(clausify,[status(thm)],[f_3997_4]) ).

cnf(f_3997_6,plain,
    ( c_Wellfounded_Oacyclic(U_16079,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_16079,U_16079)),hAPP(hAPP(c_Product__Type_OPair(U_16079,U_16079),U_16081),U_16083)),U_16085))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16079,U_16079)),hAPP(hAPP(c_Product__Type_OPair(U_16079,U_16079),U_16083),U_16081)),c_Transitive__Closure_Ortrancl(U_16079,U_16085)))
    | ~ c_Wellfounded_Oacyclic(U_16079,U_16085) ),
    inference(clausify,[status(thm)],[f_3997_4]) ).

cnf(f_3997_7,plain,
    ( c_Wellfounded_Oacyclic(U_16078,U_16084)
    | ~ sP1052(U_16078,U_16082,U_16080,U_16084) ),
    inference(clausify,[status(thm)],[f_3997_4]) ).

cnf(f_3997_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16078,U_16078)),hAPP(hAPP(c_Product__Type_OPair(U_16078,U_16078),U_16082),U_16080)),c_Transitive__Closure_Ortrancl(U_16078,U_16084)))
    | ~ sP1052(U_16078,U_16082,U_16080,U_16084) ),
    inference(clausify,[status(thm)],[f_3997_4]) ).

fof(f_3998_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_3998_2,plain,
    ! [U_16087,U_16086] :
      ( ( 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_16086),U_16087)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16086),U_16087)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16086),U_16087))
        | ~ 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_16086),U_16087)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(variable_rename,[status(thm)],[f_3998_1]) ).

fof(f_3998_3,plain,
    ( ! [U_16091,U_16089] :
        ( 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_16089),U_16091)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16089),U_16091)) )
    & ! [U_16090,U_16088] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16088),U_16090))
        | ~ 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_16088),U_16090)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(miniscope,[status(thm)],[f_3998_2]) ).

fof(f_3998_4,plain,
    ( ! [U_16089,U_16091] :
        ( 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_16089),U_16091)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16089),U_16091)) )
    & ! [U_16088,U_16090] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16088),U_16090))
        | ~ 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_16088),U_16090)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3998_3]) ).

cnf(f_3998_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16088),U_16090))
    | ~ 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_16088),U_16090)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
    inference(clausify,[status(thm)],[f_3998_4]) ).

cnf(f_3998_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_16089),U_16091)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16089),U_16091)) ),
    inference(clausify,[status(thm)],[f_3998_4]) ).

fof(f_3999_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_3999_2,plain,
    ! [U_16096,U_16095,U_16094,U_16093,U_16092] :
      ( hBOOL(hAPP(hAPP(c_member(U_16092),U_16093),U_16096))
      | U_16093 = U_16094
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16092,U_16092),tc_HOL_Obool)),U_16095),hAPP(hAPP(c_Product__Type_OSigma(U_16092,U_16092),U_16096),hAPP(c_COMBK(tc_fun(U_16092,tc_HOL_Obool),U_16092),U_16096))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16092,U_16092)),hAPP(hAPP(c_Product__Type_OPair(U_16092,U_16092),U_16093),U_16094)),c_Transitive__Closure_Ortrancl(U_16092,U_16095))) ),
    inference(variable_rename,[status(thm)],[f_3999_1]) ).

fof(f_3999_3,plain,
    ! [U_16092,U_16093,U_16094,U_16095,U_16096] :
      ( hBOOL(hAPP(hAPP(c_member(U_16092),U_16093),U_16096))
      | U_16093 = U_16094
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16092,U_16092),tc_HOL_Obool)),U_16095),hAPP(hAPP(c_Product__Type_OSigma(U_16092,U_16092),U_16096),hAPP(c_COMBK(tc_fun(U_16092,tc_HOL_Obool),U_16092),U_16096))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16092,U_16092)),hAPP(hAPP(c_Product__Type_OPair(U_16092,U_16092),U_16093),U_16094)),c_Transitive__Closure_Ortrancl(U_16092,U_16095))) ),
    inference(definitional_conversion,[status(esa)],[f_3999_2]) ).

cnf(f_3999_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16092),U_16093),U_16096))
    | U_16093 = U_16094
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16092,U_16092),tc_HOL_Obool)),U_16095),hAPP(hAPP(c_Product__Type_OSigma(U_16092,U_16092),U_16096),hAPP(c_COMBK(tc_fun(U_16092,tc_HOL_Obool),U_16092),U_16096))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16092,U_16092)),hAPP(hAPP(c_Product__Type_OPair(U_16092,U_16092),U_16093),U_16094)),c_Transitive__Closure_Ortrancl(U_16092,U_16095))) ),
    inference(clausify,[status(thm)],[f_3999_3]) ).

fof(f_4000_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_4000_2,plain,
    ! [U_16099,U_16098,U_16097] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16097,U_16097)),hAPP(hAPP(c_Product__Type_OPair(U_16097,U_16097),U_16099),U_16099)),c_Transitive__Closure_Otrancl(U_16097,U_16098)))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16097,U_16097),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_16097,U_16097),U_16098)),c_Transitive__Closure_Ortrancl(U_16097,U_16098)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_16097,U_16097),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4000_1]) ).

fof(f_4000_3,plain,
    ! [U_16097,U_16098,U_16099] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16097,U_16097)),hAPP(hAPP(c_Product__Type_OPair(U_16097,U_16097),U_16099),U_16099)),c_Transitive__Closure_Otrancl(U_16097,U_16098)))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16097,U_16097),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_16097,U_16097),U_16098)),c_Transitive__Closure_Ortrancl(U_16097,U_16098)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_16097,U_16097),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_4000_2]) ).

cnf(f_4000_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16097,U_16097)),hAPP(hAPP(c_Product__Type_OPair(U_16097,U_16097),U_16099),U_16099)),c_Transitive__Closure_Otrancl(U_16097,U_16098)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16097,U_16097),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_16097,U_16097),U_16098)),c_Transitive__Closure_Ortrancl(U_16097,U_16098)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_16097,U_16097),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4000_3]) ).

fof(f_4001_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_4001_2,plain,
    ! [U_16103,U_16102,U_16101,U_16100] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16101,U_16100),U_16102),U_16103) = hAPP(hAPP(c_Finite__Set_Ofold(U_16101,U_16100,hAPP(hAPP(c_COMBB(U_16100,tc_fun(U_16100,U_16100),U_16101),c_Lattices_Osemilattice__inf__class_Oinf(U_16100)),U_16103)),c_Orderings_Otop__class_Otop(U_16100)),U_16102)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16101),U_16102))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16100) ),
    inference(variable_rename,[status(thm)],[f_4001_1]) ).

fof(f_4001_3,plain,
    ! [U_16100,U_16101,U_16102,U_16103] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16101,U_16100),U_16102),U_16103) = hAPP(hAPP(c_Finite__Set_Ofold(U_16101,U_16100,hAPP(hAPP(c_COMBB(U_16100,tc_fun(U_16100,U_16100),U_16101),c_Lattices_Osemilattice__inf__class_Oinf(U_16100)),U_16103)),c_Orderings_Otop__class_Otop(U_16100)),U_16102)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16101),U_16102))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16100) ),
    inference(definitional_conversion,[status(esa)],[f_4001_2]) ).

cnf(f_4001_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16101,U_16100),U_16102),U_16103) = hAPP(hAPP(c_Finite__Set_Ofold(U_16101,U_16100,hAPP(hAPP(c_COMBB(U_16100,tc_fun(U_16100,U_16100),U_16101),c_Lattices_Osemilattice__inf__class_Oinf(U_16100)),U_16103)),c_Orderings_Otop__class_Otop(U_16100)),U_16102)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16101),U_16102))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16100) ),
    inference(clausify,[status(thm)],[f_4001_3]) ).

fof(f_4002_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_4002_2,plain,
    ! [U_16109,U_16108,U_16107,U_16106,U_16105,U_16104] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_16104),U_16109),U_16106))
      | hBOOL(hAPP(hAPP(U_16107,U_16109),U_16108))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16104,tc_fun(U_16105,tc_HOL_Obool)),U_16106),U_16107),U_16108)) ),
    inference(variable_rename,[status(thm)],[f_4002_1]) ).

fof(f_4002_3,plain,
    ! [U_16104,U_16105,U_16106,U_16107,U_16108,U_16109] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_16104),U_16109),U_16106))
      | hBOOL(hAPP(hAPP(U_16107,U_16109),U_16108))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16104,tc_fun(U_16105,tc_HOL_Obool)),U_16106),U_16107),U_16108)) ),
    inference(definitional_conversion,[status(esa)],[f_4002_2]) ).

cnf(f_4002_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16104),U_16109),U_16106))
    | hBOOL(hAPP(hAPP(U_16107,U_16109),U_16108))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16104,tc_fun(U_16105,tc_HOL_Obool)),U_16106),U_16107),U_16108)) ),
    inference(clausify,[status(thm)],[f_4002_3]) ).

fof(f_4003_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_4003_2,plain,
    ! [U_16115,U_16114,U_16113,U_16112,U_16111,U_16110] :
      ( hBOOL(hAPP(hAPP(U_16113,U_16115),U_16114))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16110),U_16115),U_16112))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16110,tc_fun(U_16111,tc_HOL_Obool)),U_16112),U_16113),U_16114)) ),
    inference(variable_rename,[status(thm)],[f_4003_1]) ).

fof(f_4003_3,plain,
    ! [U_16110,U_16111,U_16112,U_16113,U_16114,U_16115] :
      ( hBOOL(hAPP(hAPP(U_16113,U_16115),U_16114))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16110),U_16115),U_16112))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16110,tc_fun(U_16111,tc_HOL_Obool)),U_16112),U_16113),U_16114)) ),
    inference(definitional_conversion,[status(esa)],[f_4003_2]) ).

cnf(f_4003_4,plain,
    ( hBOOL(hAPP(hAPP(U_16113,U_16115),U_16114))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16110),U_16115),U_16112))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16110,tc_fun(U_16111,tc_HOL_Obool)),U_16112),U_16113),U_16114)) ),
    inference(clausify,[status(thm)],[f_4003_3]) ).

fof(f_4004_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_4004_2,plain,
    ! [U_16121,U_16120,U_16119,U_16118,U_16117,U_16116] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_16118),U_16121),U_16119))
      | hBOOL(hAPP(hAPP(c_member(U_16116),U_16117),hAPP(U_16120,U_16121)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16116),U_16117),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16118,tc_fun(U_16116,tc_HOL_Obool)),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,U_16121] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_16118),U_16121),U_16119))
      | hBOOL(hAPP(hAPP(c_member(U_16116),U_16117),hAPP(U_16120,U_16121)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16116),U_16117),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16118,tc_fun(U_16116,tc_HOL_Obool)),U_16119),U_16120))) ),
    inference(definitional_conversion,[status(esa)],[f_4004_2]) ).

cnf(f_4004_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16118),U_16121),U_16119))
    | hBOOL(hAPP(hAPP(c_member(U_16116),U_16117),hAPP(U_16120,U_16121)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16116),U_16117),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16118,tc_fun(U_16116,tc_HOL_Obool)),U_16119),U_16120))) ),
    inference(clausify,[status(thm)],[f_4004_3]) ).

fof(f_4005_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_4005_2,plain,
    ! [U_16127,U_16126,U_16125,U_16124,U_16123,U_16122] :
      ( hBOOL(hAPP(hAPP(c_member(U_16122),U_16123),hAPP(U_16126,U_16127)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16124),U_16127),U_16125))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16122),U_16123),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16124,tc_fun(U_16122,tc_HOL_Obool)),U_16125),U_16126))) ),
    inference(variable_rename,[status(thm)],[f_4005_1]) ).

fof(f_4005_3,plain,
    ! [U_16122,U_16123,U_16124,U_16125,U_16126,U_16127] :
      ( hBOOL(hAPP(hAPP(c_member(U_16122),U_16123),hAPP(U_16126,U_16127)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16124),U_16127),U_16125))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16122),U_16123),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16124,tc_fun(U_16122,tc_HOL_Obool)),U_16125),U_16126))) ),
    inference(definitional_conversion,[status(esa)],[f_4005_2]) ).

cnf(f_4005_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16122),U_16123),hAPP(U_16126,U_16127)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16124),U_16127),U_16125))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16122),U_16123),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16124,tc_fun(U_16122,tc_HOL_Obool)),U_16125),U_16126))) ),
    inference(clausify,[status(thm)],[f_4005_3]) ).

fof(f_4006_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_4006_2,plain,
    ! [U_16135,U_16134,U_16133,U_16132,U_16131,U_16130,U_16129,U_16128] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_16128),U_16135),U_16131))
      | hBOOL(hAPP(hAPP(hAPP(U_16132,U_16135),U_16133),U_16134))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16128,tc_fun(U_16129,tc_fun(U_16130,tc_HOL_Obool))),U_16131),U_16132),U_16133),U_16134)) ),
    inference(variable_rename,[status(thm)],[f_4006_1]) ).

fof(f_4006_3,plain,
    ! [U_16128,U_16129,U_16130,U_16131,U_16132,U_16133,U_16134,U_16135] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_16128),U_16135),U_16131))
      | hBOOL(hAPP(hAPP(hAPP(U_16132,U_16135),U_16133),U_16134))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16128,tc_fun(U_16129,tc_fun(U_16130,tc_HOL_Obool))),U_16131),U_16132),U_16133),U_16134)) ),
    inference(definitional_conversion,[status(esa)],[f_4006_2]) ).

cnf(f_4006_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16128),U_16135),U_16131))
    | hBOOL(hAPP(hAPP(hAPP(U_16132,U_16135),U_16133),U_16134))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16128,tc_fun(U_16129,tc_fun(U_16130,tc_HOL_Obool))),U_16131),U_16132),U_16133),U_16134)) ),
    inference(clausify,[status(thm)],[f_4006_3]) ).

fof(f_4007_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_4007_2,plain,
    ! [U_16143,U_16142,U_16141,U_16140,U_16139,U_16138,U_16137,U_16136] :
      ( hBOOL(hAPP(hAPP(hAPP(U_16140,U_16143),U_16141),U_16142))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16136),U_16143),U_16139))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16136,tc_fun(U_16137,tc_fun(U_16138,tc_HOL_Obool))),U_16139),U_16140),U_16141),U_16142)) ),
    inference(variable_rename,[status(thm)],[f_4007_1]) ).

fof(f_4007_3,plain,
    ! [U_16136,U_16137,U_16138,U_16139,U_16140,U_16141,U_16142,U_16143] :
      ( hBOOL(hAPP(hAPP(hAPP(U_16140,U_16143),U_16141),U_16142))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16136),U_16143),U_16139))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16136,tc_fun(U_16137,tc_fun(U_16138,tc_HOL_Obool))),U_16139),U_16140),U_16141),U_16142)) ),
    inference(definitional_conversion,[status(esa)],[f_4007_2]) ).

cnf(f_4007_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_16140,U_16143),U_16141),U_16142))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16136),U_16143),U_16139))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16136,tc_fun(U_16137,tc_fun(U_16138,tc_HOL_Obool))),U_16139),U_16140),U_16141),U_16142)) ),
    inference(clausify,[status(thm)],[f_4007_3]) ).

fof(f_4008_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_4008_2,plain,
    ! [U_16148,U_16147,U_16146,U_16145] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16147),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16145,tc_fun(U_16147,tc_HOL_Obool)),U_16146),U_16148)))
      | ! [U_16144] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16147),hAPP(U_16148,U_16144)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_16145),U_16144),U_16146)) ) ),
    inference(variable_rename,[status(thm)],[f_4008_1]) ).

fof(f_4008_3,plain,
    ! [U_16145,U_16144,U_16146,U_16147,U_16148] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16147),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16145,tc_fun(U_16147,tc_HOL_Obool)),U_16146),U_16148)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16147),hAPP(U_16148,U_16144)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16145),U_16144),U_16146)) ),
    inference(definitional_conversion,[status(esa)],[f_4008_2]) ).

cnf(f_4008_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16147),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16145,tc_fun(U_16147,tc_HOL_Obool)),U_16146),U_16148)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16147),hAPP(U_16148,U_16144)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16145),U_16144),U_16146)) ),
    inference(clausify,[status(thm)],[f_4008_3]) ).

fof(f_4009_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_4009_2,plain,
    ! [U_16150,U_16149] : c_Transitive__Closure_Ortrancl(U_16149,hAPP(c_Relation_Oconverse(U_16149,U_16149),U_16150)) = hAPP(c_Relation_Oconverse(U_16149,U_16149),c_Transitive__Closure_Ortrancl(U_16149,U_16150)),
    inference(variable_rename,[status(thm)],[f_4009_1]) ).

fof(f_4009_3,plain,
    ! [U_16150,U_16149] : c_Transitive__Closure_Ortrancl(U_16149,hAPP(c_Relation_Oconverse(U_16149,U_16149),U_16150)) = hAPP(c_Relation_Oconverse(U_16149,U_16149),c_Transitive__Closure_Ortrancl(U_16149,U_16150)),
    inference(definitional_conversion,[status(esa)],[f_4009_2]) ).

cnf(f_4009_4,plain,
    c_Transitive__Closure_Ortrancl(U_16149,hAPP(c_Relation_Oconverse(U_16149,U_16149),U_16150)) = hAPP(c_Relation_Oconverse(U_16149,U_16149),c_Transitive__Closure_Ortrancl(U_16149,U_16150)),
    inference(clausify,[status(thm)],[f_4009_3]) ).

fof(f_4010_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_4010_2,plain,
    ! [U_16152,U_16151] : c_Transitive__Closure_Otrancl(U_16151,hAPP(c_Relation_Oconverse(U_16151,U_16151),U_16152)) = hAPP(c_Relation_Oconverse(U_16151,U_16151),c_Transitive__Closure_Otrancl(U_16151,U_16152)),
    inference(variable_rename,[status(thm)],[f_4010_1]) ).

fof(f_4010_3,plain,
    ! [U_16151,U_16152] : c_Transitive__Closure_Otrancl(U_16151,hAPP(c_Relation_Oconverse(U_16151,U_16151),U_16152)) = hAPP(c_Relation_Oconverse(U_16151,U_16151),c_Transitive__Closure_Otrancl(U_16151,U_16152)),
    inference(definitional_conversion,[status(esa)],[f_4010_2]) ).

cnf(f_4010_4,plain,
    c_Transitive__Closure_Otrancl(U_16151,hAPP(c_Relation_Oconverse(U_16151,U_16151),U_16152)) = hAPP(c_Relation_Oconverse(U_16151,U_16151),c_Transitive__Closure_Otrancl(U_16151,U_16152)),
    inference(clausify,[status(thm)],[f_4010_3]) ).

fof(f_4011_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_4011_2,plain,
    ! [U_16154,U_16153] :
      ( c_Wellfounded_Owf(U_16153,hAPP(c_Relation_Oconverse(U_16153,U_16153),c_Transitive__Closure_Otrancl(U_16153,U_16154)))
      | ~ c_Wellfounded_Owf(U_16153,hAPP(c_Relation_Oconverse(U_16153,U_16153),U_16154)) ),
    inference(variable_rename,[status(thm)],[f_4011_1]) ).

fof(f_4011_3,plain,
    ! [U_16153,U_16154] :
      ( c_Wellfounded_Owf(U_16153,hAPP(c_Relation_Oconverse(U_16153,U_16153),c_Transitive__Closure_Otrancl(U_16153,U_16154)))
      | ~ c_Wellfounded_Owf(U_16153,hAPP(c_Relation_Oconverse(U_16153,U_16153),U_16154)) ),
    inference(definitional_conversion,[status(esa)],[f_4011_2]) ).

cnf(f_4011_4,plain,
    ( c_Wellfounded_Owf(U_16153,hAPP(c_Relation_Oconverse(U_16153,U_16153),c_Transitive__Closure_Otrancl(U_16153,U_16154)))
    | ~ c_Wellfounded_Owf(U_16153,hAPP(c_Relation_Oconverse(U_16153,U_16153),U_16154)) ),
    inference(clausify,[status(thm)],[f_4011_3]) ).

fof(f_4012_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_4012_2,plain,
    ! [U_16156,U_16155] :
      ( ( c_Wellfounded_Oacyclic(U_16155,hAPP(c_Relation_Oconverse(U_16155,U_16155),U_16156))
        | ~ c_Wellfounded_Oacyclic(U_16155,U_16156) )
      & ( c_Wellfounded_Oacyclic(U_16155,U_16156)
        | ~ c_Wellfounded_Oacyclic(U_16155,hAPP(c_Relation_Oconverse(U_16155,U_16155),U_16156)) ) ),
    inference(variable_rename,[status(thm)],[f_4012_1]) ).

fof(f_4012_3,plain,
    ( ! [U_16160,U_16158] :
        ( c_Wellfounded_Oacyclic(U_16158,hAPP(c_Relation_Oconverse(U_16158,U_16158),U_16160))
        | ~ c_Wellfounded_Oacyclic(U_16158,U_16160) )
    & ! [U_16159,U_16157] :
        ( c_Wellfounded_Oacyclic(U_16157,U_16159)
        | ~ c_Wellfounded_Oacyclic(U_16157,hAPP(c_Relation_Oconverse(U_16157,U_16157),U_16159)) ) ),
    inference(miniscope,[status(thm)],[f_4012_2]) ).

fof(f_4012_4,plain,
    ( ! [U_16158,U_16160] :
        ( c_Wellfounded_Oacyclic(U_16158,hAPP(c_Relation_Oconverse(U_16158,U_16158),U_16160))
        | ~ c_Wellfounded_Oacyclic(U_16158,U_16160) )
    & ! [U_16159,U_16157] :
        ( c_Wellfounded_Oacyclic(U_16157,U_16159)
        | ~ c_Wellfounded_Oacyclic(U_16157,hAPP(c_Relation_Oconverse(U_16157,U_16157),U_16159)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4012_3]) ).

cnf(f_4012_5,plain,
    ( c_Wellfounded_Oacyclic(U_16157,U_16159)
    | ~ c_Wellfounded_Oacyclic(U_16157,hAPP(c_Relation_Oconverse(U_16157,U_16157),U_16159)) ),
    inference(clausify,[status(thm)],[f_4012_4]) ).

cnf(f_4012_6,plain,
    ( c_Wellfounded_Oacyclic(U_16158,hAPP(c_Relation_Oconverse(U_16158,U_16158),U_16160))
    | ~ c_Wellfounded_Oacyclic(U_16158,U_16160) ),
    inference(clausify,[status(thm)],[f_4012_4]) ).

fof(f_4013_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_4013_2,plain,
    ! [U_16165,U_16164,U_16163,U_16162,U_16161] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16163,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16162,tc_fun(U_16163,tc_HOL_Obool)),U_16161),U_16164)),U_16165) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16162,tc_fun(U_16163,tc_HOL_Obool)),U_16161),hAPP(hAPP(c_COMBC(U_16162,tc_fun(U_16163,tc_HOL_Obool),tc_fun(U_16163,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16163,tc_HOL_Obool),tc_fun(tc_fun(U_16163,tc_HOL_Obool),tc_fun(U_16163,tc_HOL_Obool)),U_16162),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16163,tc_HOL_Obool))),U_16164)),U_16165))
        | U_16161 = c_Orderings_Obot__class_Obot(tc_fun(U_16162,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16163,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16162,tc_fun(U_16163,tc_HOL_Obool)),U_16161),U_16164)),U_16165) = U_16165
        | U_16161 != c_Orderings_Obot__class_Obot(tc_fun(U_16162,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4013_1]) ).

fof(f_4013_3,plain,
    ( ! [U_16175,U_16173,U_16171,U_16169,U_16167] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16171,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16169,tc_fun(U_16171,tc_HOL_Obool)),U_16167),U_16173)),U_16175) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16169,tc_fun(U_16171,tc_HOL_Obool)),U_16167),hAPP(hAPP(c_COMBC(U_16169,tc_fun(U_16171,tc_HOL_Obool),tc_fun(U_16171,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16171,tc_HOL_Obool),tc_fun(tc_fun(U_16171,tc_HOL_Obool),tc_fun(U_16171,tc_HOL_Obool)),U_16169),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16171,tc_HOL_Obool))),U_16173)),U_16175))
        | U_16167 = c_Orderings_Obot__class_Obot(tc_fun(U_16169,tc_HOL_Obool)) )
    & ! [U_16174,U_16172,U_16170,U_16168,U_16166] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16170,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16168,tc_fun(U_16170,tc_HOL_Obool)),U_16166),U_16172)),U_16174) = U_16174
        | U_16166 != c_Orderings_Obot__class_Obot(tc_fun(U_16168,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4013_2]) ).

fof(f_4013_4,plain,
    ( ! [U_16175,U_16167,U_16169,U_16171,U_16173] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16171,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16169,tc_fun(U_16171,tc_HOL_Obool)),U_16167),U_16173)),U_16175) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16169,tc_fun(U_16171,tc_HOL_Obool)),U_16167),hAPP(hAPP(c_COMBC(U_16169,tc_fun(U_16171,tc_HOL_Obool),tc_fun(U_16171,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16171,tc_HOL_Obool),tc_fun(tc_fun(U_16171,tc_HOL_Obool),tc_fun(U_16171,tc_HOL_Obool)),U_16169),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16171,tc_HOL_Obool))),U_16173)),U_16175))
        | U_16167 = c_Orderings_Obot__class_Obot(tc_fun(U_16169,tc_HOL_Obool)) )
    & ! [U_16172,U_16168,U_16166,U_16174,U_16170] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16170,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16168,tc_fun(U_16170,tc_HOL_Obool)),U_16166),U_16172)),U_16174) = U_16174
        | U_16166 != c_Orderings_Obot__class_Obot(tc_fun(U_16168,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4013_3]) ).

cnf(f_4013_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16170,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16168,tc_fun(U_16170,tc_HOL_Obool)),U_16166),U_16172)),U_16174) = U_16174
    | U_16166 != c_Orderings_Obot__class_Obot(tc_fun(U_16168,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4013_4]) ).

cnf(f_4013_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16171,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16169,tc_fun(U_16171,tc_HOL_Obool)),U_16167),U_16173)),U_16175) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16169,tc_fun(U_16171,tc_HOL_Obool)),U_16167),hAPP(hAPP(c_COMBC(U_16169,tc_fun(U_16171,tc_HOL_Obool),tc_fun(U_16171,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16171,tc_HOL_Obool),tc_fun(tc_fun(U_16171,tc_HOL_Obool),tc_fun(U_16171,tc_HOL_Obool)),U_16169),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16171,tc_HOL_Obool))),U_16173)),U_16175))
    | U_16167 = c_Orderings_Obot__class_Obot(tc_fun(U_16169,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4013_4]) ).

fof(f_4014_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_4014_2,plain,
    ! [U_16180,U_16179,U_16178,U_16177,U_16176] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16178,tc_HOL_Obool)),U_16179),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16177,tc_fun(U_16178,tc_HOL_Obool)),U_16176),U_16180)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16177,tc_fun(U_16178,tc_HOL_Obool)),U_16176),hAPP(hAPP(c_COMBB(tc_fun(U_16178,tc_HOL_Obool),tc_fun(U_16178,tc_HOL_Obool),U_16177),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16178,tc_HOL_Obool)),U_16179)),U_16180))
        | U_16176 = c_Orderings_Obot__class_Obot(tc_fun(U_16177,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16178,tc_HOL_Obool)),U_16179),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16177,tc_fun(U_16178,tc_HOL_Obool)),U_16176),U_16180)) = U_16179
        | U_16176 != c_Orderings_Obot__class_Obot(tc_fun(U_16177,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4014_1]) ).

fof(f_4014_3,plain,
    ( ! [U_16190,U_16188,U_16186,U_16184,U_16182] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16186,tc_HOL_Obool)),U_16188),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16184,tc_fun(U_16186,tc_HOL_Obool)),U_16182),U_16190)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16184,tc_fun(U_16186,tc_HOL_Obool)),U_16182),hAPP(hAPP(c_COMBB(tc_fun(U_16186,tc_HOL_Obool),tc_fun(U_16186,tc_HOL_Obool),U_16184),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16186,tc_HOL_Obool)),U_16188)),U_16190))
        | U_16182 = c_Orderings_Obot__class_Obot(tc_fun(U_16184,tc_HOL_Obool)) )
    & ! [U_16189,U_16187,U_16185,U_16183,U_16181] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16185,tc_HOL_Obool)),U_16187),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16183,tc_fun(U_16185,tc_HOL_Obool)),U_16181),U_16189)) = U_16187
        | U_16181 != c_Orderings_Obot__class_Obot(tc_fun(U_16183,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4014_2]) ).

fof(f_4014_4,plain,
    ( ! [U_16182,U_16184,U_16186,U_16188,U_16190] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16186,tc_HOL_Obool)),U_16188),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16184,tc_fun(U_16186,tc_HOL_Obool)),U_16182),U_16190)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16184,tc_fun(U_16186,tc_HOL_Obool)),U_16182),hAPP(hAPP(c_COMBB(tc_fun(U_16186,tc_HOL_Obool),tc_fun(U_16186,tc_HOL_Obool),U_16184),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16186,tc_HOL_Obool)),U_16188)),U_16190))
        | U_16182 = c_Orderings_Obot__class_Obot(tc_fun(U_16184,tc_HOL_Obool)) )
    & ! [U_16185,U_16183,U_16187,U_16181,U_16189] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16185,tc_HOL_Obool)),U_16187),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16183,tc_fun(U_16185,tc_HOL_Obool)),U_16181),U_16189)) = U_16187
        | U_16181 != c_Orderings_Obot__class_Obot(tc_fun(U_16183,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4014_3]) ).

cnf(f_4014_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16185,tc_HOL_Obool)),U_16187),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16183,tc_fun(U_16185,tc_HOL_Obool)),U_16181),U_16189)) = U_16187
    | U_16181 != c_Orderings_Obot__class_Obot(tc_fun(U_16183,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4014_4]) ).

cnf(f_4014_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16186,tc_HOL_Obool)),U_16188),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16184,tc_fun(U_16186,tc_HOL_Obool)),U_16182),U_16190)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16184,tc_fun(U_16186,tc_HOL_Obool)),U_16182),hAPP(hAPP(c_COMBB(tc_fun(U_16186,tc_HOL_Obool),tc_fun(U_16186,tc_HOL_Obool),U_16184),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16186,tc_HOL_Obool)),U_16188)),U_16190))
    | U_16182 = c_Orderings_Obot__class_Obot(tc_fun(U_16184,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4014_4]) ).

fof(f_4015_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_4015_2,plain,
    ! [U_16194,U_16193,U_16192,U_16191] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16193,U_16191),U_16192),hAPP(c_COMBK(U_16191,U_16193),U_16194)) = U_16194
      | U_16192 = c_Orderings_Obot__class_Obot(tc_fun(U_16193,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16191) ),
    inference(variable_rename,[status(thm)],[f_4015_1]) ).

fof(f_4015_3,plain,
    ! [U_16191,U_16193,U_16192,U_16194] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16193,U_16191),U_16192),hAPP(c_COMBK(U_16191,U_16193),U_16194)) = U_16194
      | U_16192 = c_Orderings_Obot__class_Obot(tc_fun(U_16193,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16191) ),
    inference(definitional_conversion,[status(esa)],[f_4015_2]) ).

cnf(f_4015_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16193,U_16191),U_16192),hAPP(c_COMBK(U_16191,U_16193),U_16194)) = U_16194
    | U_16192 = c_Orderings_Obot__class_Obot(tc_fun(U_16193,tc_HOL_Obool))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16191) ),
    inference(clausify,[status(thm)],[f_4015_3]) ).

fof(f_4016_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_4016_2,plain,
    ! [U_16198,U_16197,U_16196,U_16195] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16196,tc_fun(U_16197,tc_HOL_Obool)),U_16195),hAPP(c_COMBK(tc_fun(U_16197,tc_HOL_Obool),U_16196),U_16198)) = U_16198
        | U_16195 = c_Orderings_Obot__class_Obot(tc_fun(U_16196,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16196,tc_fun(U_16197,tc_HOL_Obool)),U_16195),hAPP(c_COMBK(tc_fun(U_16197,tc_HOL_Obool),U_16196),U_16198)) = c_Orderings_Otop__class_Otop(tc_fun(U_16197,tc_HOL_Obool))
        | U_16195 != c_Orderings_Obot__class_Obot(tc_fun(U_16196,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4016_1]) ).

fof(f_4016_3,plain,
    ( ! [U_16206,U_16204,U_16202,U_16200] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16202,tc_fun(U_16204,tc_HOL_Obool)),U_16200),hAPP(c_COMBK(tc_fun(U_16204,tc_HOL_Obool),U_16202),U_16206)) = U_16206
        | U_16200 = c_Orderings_Obot__class_Obot(tc_fun(U_16202,tc_HOL_Obool)) )
    & ! [U_16205,U_16203,U_16201,U_16199] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16201,tc_fun(U_16203,tc_HOL_Obool)),U_16199),hAPP(c_COMBK(tc_fun(U_16203,tc_HOL_Obool),U_16201),U_16205)) = c_Orderings_Otop__class_Otop(tc_fun(U_16203,tc_HOL_Obool))
        | U_16199 != c_Orderings_Obot__class_Obot(tc_fun(U_16201,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4016_2]) ).

fof(f_4016_4,plain,
    ( ! [U_16200,U_16202,U_16204,U_16206] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16202,tc_fun(U_16204,tc_HOL_Obool)),U_16200),hAPP(c_COMBK(tc_fun(U_16204,tc_HOL_Obool),U_16202),U_16206)) = U_16206
        | U_16200 = c_Orderings_Obot__class_Obot(tc_fun(U_16202,tc_HOL_Obool)) )
    & ! [U_16201,U_16205,U_16199,U_16203] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16201,tc_fun(U_16203,tc_HOL_Obool)),U_16199),hAPP(c_COMBK(tc_fun(U_16203,tc_HOL_Obool),U_16201),U_16205)) = c_Orderings_Otop__class_Otop(tc_fun(U_16203,tc_HOL_Obool))
        | U_16199 != c_Orderings_Obot__class_Obot(tc_fun(U_16201,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4016_3]) ).

cnf(f_4016_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16201,tc_fun(U_16203,tc_HOL_Obool)),U_16199),hAPP(c_COMBK(tc_fun(U_16203,tc_HOL_Obool),U_16201),U_16205)) = c_Orderings_Otop__class_Otop(tc_fun(U_16203,tc_HOL_Obool))
    | U_16199 != c_Orderings_Obot__class_Obot(tc_fun(U_16201,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4016_4]) ).

cnf(f_4016_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16202,tc_fun(U_16204,tc_HOL_Obool)),U_16200),hAPP(c_COMBK(tc_fun(U_16204,tc_HOL_Obool),U_16202),U_16206)) = U_16206
    | U_16200 = c_Orderings_Obot__class_Obot(tc_fun(U_16202,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4016_4]) ).

fof(f_4017_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_4017_2,plain,
    ! [U_16209,U_16208,U_16207] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16207,tc_fun(U_16208,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_16207,tc_HOL_Obool))),U_16209) = c_Orderings_Otop__class_Otop(tc_fun(U_16208,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4017_1]) ).

fof(f_4017_3,plain,
    ! [U_16207,U_16208,U_16209] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16207,tc_fun(U_16208,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_16207,tc_HOL_Obool))),U_16209) = c_Orderings_Otop__class_Otop(tc_fun(U_16208,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4017_2]) ).

cnf(f_4017_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16207,tc_fun(U_16208,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_16207,tc_HOL_Obool))),U_16209) = c_Orderings_Otop__class_Otop(tc_fun(U_16208,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4017_3]) ).

fof(f_4018_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_4018_2,plain,
    ! [U_16214,U_16213,U_16212,U_16211,U_16210] : hAPP(c_Relation_Oconverse(U_16210,U_16211),hAPP(hAPP(c_Relation_Orel__comp(U_16210,U_16212,U_16211),U_16213),U_16214)) = hAPP(hAPP(c_Relation_Orel__comp(U_16211,U_16212,U_16210),hAPP(c_Relation_Oconverse(U_16212,U_16211),U_16214)),hAPP(c_Relation_Oconverse(U_16210,U_16212),U_16213)),
    inference(variable_rename,[status(thm)],[f_4018_1]) ).

fof(f_4018_3,plain,
    ! [U_16210,U_16211,U_16212,U_16213,U_16214] : hAPP(c_Relation_Oconverse(U_16210,U_16211),hAPP(hAPP(c_Relation_Orel__comp(U_16210,U_16212,U_16211),U_16213),U_16214)) = hAPP(hAPP(c_Relation_Orel__comp(U_16211,U_16212,U_16210),hAPP(c_Relation_Oconverse(U_16212,U_16211),U_16214)),hAPP(c_Relation_Oconverse(U_16210,U_16212),U_16213)),
    inference(definitional_conversion,[status(esa)],[f_4018_2]) ).

cnf(f_4018_4,plain,
    hAPP(c_Relation_Oconverse(U_16210,U_16211),hAPP(hAPP(c_Relation_Orel__comp(U_16210,U_16212,U_16211),U_16213),U_16214)) = hAPP(hAPP(c_Relation_Orel__comp(U_16211,U_16212,U_16210),hAPP(c_Relation_Oconverse(U_16212,U_16211),U_16214)),hAPP(c_Relation_Oconverse(U_16210,U_16212),U_16213)),
    inference(clausify,[status(thm)],[f_4018_3]) ).

fof(f_4019_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_4019_2,plain,
    ! [U_16219,U_16218,U_16217,U_16216,U_16215] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16215,tc_fun(U_16216,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_16215),U_16217),U_16218)),U_16219) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16216,tc_HOL_Obool)),hAPP(U_16219,U_16217)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16215,tc_fun(U_16216,tc_HOL_Obool)),U_16218),U_16219)),
    inference(variable_rename,[status(thm)],[f_4019_1]) ).

fof(f_4019_3,plain,
    ! [U_16215,U_16216,U_16217,U_16218,U_16219] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16215,tc_fun(U_16216,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_16215),U_16217),U_16218)),U_16219) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16216,tc_HOL_Obool)),hAPP(U_16219,U_16217)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16215,tc_fun(U_16216,tc_HOL_Obool)),U_16218),U_16219)),
    inference(definitional_conversion,[status(esa)],[f_4019_2]) ).

cnf(f_4019_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16215,tc_fun(U_16216,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_16215),U_16217),U_16218)),U_16219) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16216,tc_HOL_Obool)),hAPP(U_16219,U_16217)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16215,tc_fun(U_16216,tc_HOL_Obool)),U_16218),U_16219)),
    inference(clausify,[status(thm)],[f_4019_3]) ).

fof(f_4020_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_4020_2,plain,
    ! [U_16224,U_16223,U_16222,U_16221,U_16220] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16220,tc_fun(U_16221,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16220,tc_HOL_Obool)),U_16222),U_16223)),U_16224) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16221,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16220,tc_fun(U_16221,tc_HOL_Obool)),U_16222),U_16224)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16220,tc_fun(U_16221,tc_HOL_Obool)),U_16223),U_16224)),
    inference(variable_rename,[status(thm)],[f_4020_1]) ).

fof(f_4020_3,plain,
    ! [U_16220,U_16221,U_16222,U_16223,U_16224] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16220,tc_fun(U_16221,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16220,tc_HOL_Obool)),U_16222),U_16223)),U_16224) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16221,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16220,tc_fun(U_16221,tc_HOL_Obool)),U_16222),U_16224)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16220,tc_fun(U_16221,tc_HOL_Obool)),U_16223),U_16224)),
    inference(definitional_conversion,[status(esa)],[f_4020_2]) ).

cnf(f_4020_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16220,tc_fun(U_16221,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16220,tc_HOL_Obool)),U_16222),U_16223)),U_16224) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16221,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16220,tc_fun(U_16221,tc_HOL_Obool)),U_16222),U_16224)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16220,tc_fun(U_16221,tc_HOL_Obool)),U_16223),U_16224)),
    inference(clausify,[status(thm)],[f_4020_3]) ).

fof(f_4021_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_4021_2,plain,
    ! [U_16231,U_16230,U_16229,U_16228,U_16227] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16227,tc_HOL_Obool)),U_16228),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16229,tc_fun(U_16227,tc_HOL_Obool)),U_16230),U_16231)))
        | ? [U_16226] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16227,tc_HOL_Obool)),U_16228),hAPP(U_16231,U_16226)))
            & hBOOL(hAPP(hAPP(c_member(U_16229),U_16226),U_16230)) ) )
      & ( ! [U_16225] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16227,tc_HOL_Obool)),U_16228),hAPP(U_16231,U_16225)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16229),U_16225),U_16230)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16227,tc_HOL_Obool)),U_16228),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16229,tc_fun(U_16227,tc_HOL_Obool)),U_16230),U_16231))) ) ),
    inference(variable_rename,[status(thm)],[f_4021_1]) ).

fof(f_4021_3,plain,
    ( ! [U_16241,U_16239,U_16237,U_16235,U_16233] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16233,tc_HOL_Obool)),U_16235),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16237,tc_fun(U_16233,tc_HOL_Obool)),U_16239),U_16241)))
        | ? [U_16226] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16233,tc_HOL_Obool)),U_16235),hAPP(U_16241,U_16226)))
            & hBOOL(hAPP(hAPP(c_member(U_16237),U_16226),U_16239)) ) )
    & ! [U_16240,U_16238,U_16236,U_16234,U_16232] :
        ( ! [U_16225] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16232,tc_HOL_Obool)),U_16234),hAPP(U_16240,U_16225)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16236),U_16225),U_16238)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16232,tc_HOL_Obool)),U_16234),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16236,tc_fun(U_16232,tc_HOL_Obool)),U_16238),U_16240))) ) ),
    inference(miniscope,[status(thm)],[f_4021_2]) ).

fof(f_4021_4,plain,
    ( ! [U_16241,U_16239,U_16237,U_16235,U_16233] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16233,tc_HOL_Obool)),U_16235),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16237,tc_fun(U_16233,tc_HOL_Obool)),U_16239),U_16241)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16233,tc_HOL_Obool)),U_16235),hAPP(U_16241,sK385(U_16241,U_16239,U_16237,U_16235,U_16233))))
          & hBOOL(hAPP(hAPP(c_member(U_16237),sK385(U_16241,U_16239,U_16237,U_16235,U_16233)),U_16239)) ) )
    & ! [U_16240,U_16238,U_16236,U_16234,U_16232] :
        ( ! [U_16225] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16232,tc_HOL_Obool)),U_16234),hAPP(U_16240,U_16225)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16236),U_16225),U_16238)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16232,tc_HOL_Obool)),U_16234),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16236,tc_fun(U_16232,tc_HOL_Obool)),U_16238),U_16240))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK385]),skolemize(U_16226,sK385(U_16241,U_16239,U_16237,U_16235,U_16233))],[f_4021_3]) ).

fof(f_4021_5,plain,
    ( ! [U_16237,U_16233,U_16235,U_16239,U_16241] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16233,tc_HOL_Obool)),U_16235),hAPP(U_16241,sK385(U_16241,U_16239,U_16237,U_16235,U_16233))))
        | ~ sP1053(U_16237,U_16233,U_16235,U_16239,U_16241) )
    & ! [U_16237,U_16233,U_16235,U_16239,U_16241] :
        ( hBOOL(hAPP(hAPP(c_member(U_16237),sK385(U_16241,U_16239,U_16237,U_16235,U_16233)),U_16239))
        | ~ sP1053(U_16237,U_16233,U_16235,U_16239,U_16241) )
    & ! [U_16237,U_16233,U_16235,U_16239,U_16241] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16233,tc_HOL_Obool)),U_16235),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16237,tc_fun(U_16233,tc_HOL_Obool)),U_16239),U_16241)))
        | sP1053(U_16237,U_16233,U_16235,U_16239,U_16241) )
    & ! [U_16225,U_16232,U_16234,U_16240,U_16236,U_16238] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16232,tc_HOL_Obool)),U_16234),hAPP(U_16240,U_16225)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16236),U_16225),U_16238))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16232,tc_HOL_Obool)),U_16234),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16236,tc_fun(U_16232,tc_HOL_Obool)),U_16238),U_16240))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1053])],[f_4021_4]) ).

cnf(f_4021_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16232,tc_HOL_Obool)),U_16234),hAPP(U_16240,U_16225)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16236),U_16225),U_16238))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16232,tc_HOL_Obool)),U_16234),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16236,tc_fun(U_16232,tc_HOL_Obool)),U_16238),U_16240))) ),
    inference(clausify,[status(thm)],[f_4021_5]) ).

cnf(f_4021_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16233,tc_HOL_Obool)),U_16235),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16237,tc_fun(U_16233,tc_HOL_Obool)),U_16239),U_16241)))
    | sP1053(U_16237,U_16233,U_16235,U_16239,U_16241) ),
    inference(clausify,[status(thm)],[f_4021_5]) ).

cnf(f_4021_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16237),sK385(U_16241,U_16239,U_16237,U_16235,U_16233)),U_16239))
    | ~ sP1053(U_16237,U_16233,U_16235,U_16239,U_16241) ),
    inference(clausify,[status(thm)],[f_4021_5]) ).

cnf(f_4021_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16233,tc_HOL_Obool)),U_16235),hAPP(U_16241,sK385(U_16241,U_16239,U_16237,U_16235,U_16233))))
    | ~ sP1053(U_16237,U_16233,U_16235,U_16239,U_16241) ),
    inference(clausify,[status(thm)],[f_4021_5]) ).

fof(f_4022_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_4022_2,plain,
    ! [U_16248,U_16247,U_16246,U_16245,U_16244,U_16243,U_16242] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16242,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16243,tc_fun(U_16242,tc_HOL_Obool)),U_16244),U_16245)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16246,tc_fun(U_16242,tc_HOL_Obool)),U_16247),U_16248)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16243,tc_fun(U_16242,tc_HOL_Obool)),U_16244),hAPP(hAPP(c_COMBB(tc_fun(U_16246,tc_fun(U_16242,tc_HOL_Obool)),tc_fun(U_16242,tc_HOL_Obool),U_16243),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16246,tc_fun(U_16242,tc_HOL_Obool)),U_16247)),hAPP(hAPP(c_COMBC(U_16243,tc_fun(U_16246,tc_fun(U_16242,tc_HOL_Obool)),tc_fun(U_16246,tc_fun(U_16242,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16242,tc_HOL_Obool),tc_fun(U_16242,tc_HOL_Obool)),tc_fun(tc_fun(U_16246,tc_fun(U_16242,tc_HOL_Obool)),tc_fun(U_16246,tc_fun(U_16242,tc_HOL_Obool))),U_16243),c_COMBB(tc_fun(U_16242,tc_HOL_Obool),tc_fun(U_16242,tc_HOL_Obool),U_16246)),hAPP(hAPP(c_COMBB(tc_fun(U_16242,tc_HOL_Obool),tc_fun(tc_fun(U_16242,tc_HOL_Obool),tc_fun(U_16242,tc_HOL_Obool)),U_16243),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16242,tc_HOL_Obool))),U_16245))),U_16248))),
    inference(variable_rename,[status(thm)],[f_4022_1]) ).

fof(f_4022_3,plain,
    ! [U_16242,U_16243,U_16244,U_16245,U_16246,U_16247,U_16248] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16242,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16243,tc_fun(U_16242,tc_HOL_Obool)),U_16244),U_16245)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16246,tc_fun(U_16242,tc_HOL_Obool)),U_16247),U_16248)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16243,tc_fun(U_16242,tc_HOL_Obool)),U_16244),hAPP(hAPP(c_COMBB(tc_fun(U_16246,tc_fun(U_16242,tc_HOL_Obool)),tc_fun(U_16242,tc_HOL_Obool),U_16243),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16246,tc_fun(U_16242,tc_HOL_Obool)),U_16247)),hAPP(hAPP(c_COMBC(U_16243,tc_fun(U_16246,tc_fun(U_16242,tc_HOL_Obool)),tc_fun(U_16246,tc_fun(U_16242,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16242,tc_HOL_Obool),tc_fun(U_16242,tc_HOL_Obool)),tc_fun(tc_fun(U_16246,tc_fun(U_16242,tc_HOL_Obool)),tc_fun(U_16246,tc_fun(U_16242,tc_HOL_Obool))),U_16243),c_COMBB(tc_fun(U_16242,tc_HOL_Obool),tc_fun(U_16242,tc_HOL_Obool),U_16246)),hAPP(hAPP(c_COMBB(tc_fun(U_16242,tc_HOL_Obool),tc_fun(tc_fun(U_16242,tc_HOL_Obool),tc_fun(U_16242,tc_HOL_Obool)),U_16243),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16242,tc_HOL_Obool))),U_16245))),U_16248))),
    inference(definitional_conversion,[status(esa)],[f_4022_2]) ).

cnf(f_4022_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16242,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16243,tc_fun(U_16242,tc_HOL_Obool)),U_16244),U_16245)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16246,tc_fun(U_16242,tc_HOL_Obool)),U_16247),U_16248)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16243,tc_fun(U_16242,tc_HOL_Obool)),U_16244),hAPP(hAPP(c_COMBB(tc_fun(U_16246,tc_fun(U_16242,tc_HOL_Obool)),tc_fun(U_16242,tc_HOL_Obool),U_16243),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16246,tc_fun(U_16242,tc_HOL_Obool)),U_16247)),hAPP(hAPP(c_COMBC(U_16243,tc_fun(U_16246,tc_fun(U_16242,tc_HOL_Obool)),tc_fun(U_16246,tc_fun(U_16242,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16242,tc_HOL_Obool),tc_fun(U_16242,tc_HOL_Obool)),tc_fun(tc_fun(U_16246,tc_fun(U_16242,tc_HOL_Obool)),tc_fun(U_16246,tc_fun(U_16242,tc_HOL_Obool))),U_16243),c_COMBB(tc_fun(U_16242,tc_HOL_Obool),tc_fun(U_16242,tc_HOL_Obool),U_16246)),hAPP(hAPP(c_COMBB(tc_fun(U_16242,tc_HOL_Obool),tc_fun(tc_fun(U_16242,tc_HOL_Obool),tc_fun(U_16242,tc_HOL_Obool)),U_16243),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16242,tc_HOL_Obool))),U_16245))),U_16248))),
    inference(clausify,[status(thm)],[f_4022_3]) ).

fof(f_4023_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_4023_2,plain,
    ! [U_16253,U_16252,U_16251,U_16250,U_16249] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16249,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16250,tc_fun(U_16249,tc_HOL_Obool)),U_16251),U_16252)),U_16253) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16250,tc_fun(U_16249,tc_HOL_Obool)),U_16251),hAPP(hAPP(c_COMBC(U_16250,tc_fun(U_16249,tc_HOL_Obool),tc_fun(U_16249,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16249,tc_HOL_Obool),tc_fun(tc_fun(U_16249,tc_HOL_Obool),tc_fun(U_16249,tc_HOL_Obool)),U_16250),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16249,tc_HOL_Obool))),U_16252)),U_16253)),
    inference(variable_rename,[status(thm)],[f_4023_1]) ).

fof(f_4023_3,plain,
    ! [U_16249,U_16250,U_16251,U_16252,U_16253] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16249,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16250,tc_fun(U_16249,tc_HOL_Obool)),U_16251),U_16252)),U_16253) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16250,tc_fun(U_16249,tc_HOL_Obool)),U_16251),hAPP(hAPP(c_COMBC(U_16250,tc_fun(U_16249,tc_HOL_Obool),tc_fun(U_16249,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16249,tc_HOL_Obool),tc_fun(tc_fun(U_16249,tc_HOL_Obool),tc_fun(U_16249,tc_HOL_Obool)),U_16250),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16249,tc_HOL_Obool))),U_16252)),U_16253)),
    inference(definitional_conversion,[status(esa)],[f_4023_2]) ).

cnf(f_4023_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16249,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16250,tc_fun(U_16249,tc_HOL_Obool)),U_16251),U_16252)),U_16253) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16250,tc_fun(U_16249,tc_HOL_Obool)),U_16251),hAPP(hAPP(c_COMBC(U_16250,tc_fun(U_16249,tc_HOL_Obool),tc_fun(U_16249,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16249,tc_HOL_Obool),tc_fun(tc_fun(U_16249,tc_HOL_Obool),tc_fun(U_16249,tc_HOL_Obool)),U_16250),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16249,tc_HOL_Obool))),U_16252)),U_16253)),
    inference(clausify,[status(thm)],[f_4023_3]) ).

fof(f_4024_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_4024_2,plain,
    ! [U_16258,U_16257,U_16256,U_16255,U_16254] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16254,tc_HOL_Obool)),U_16255),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16256,tc_fun(U_16254,tc_HOL_Obool)),U_16257),U_16258)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16256,tc_fun(U_16254,tc_HOL_Obool)),U_16257),hAPP(hAPP(c_COMBB(tc_fun(U_16254,tc_HOL_Obool),tc_fun(U_16254,tc_HOL_Obool),U_16256),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16254,tc_HOL_Obool)),U_16255)),U_16258)),
    inference(variable_rename,[status(thm)],[f_4024_1]) ).

fof(f_4024_3,plain,
    ! [U_16254,U_16255,U_16256,U_16257,U_16258] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16254,tc_HOL_Obool)),U_16255),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16256,tc_fun(U_16254,tc_HOL_Obool)),U_16257),U_16258)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16256,tc_fun(U_16254,tc_HOL_Obool)),U_16257),hAPP(hAPP(c_COMBB(tc_fun(U_16254,tc_HOL_Obool),tc_fun(U_16254,tc_HOL_Obool),U_16256),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16254,tc_HOL_Obool)),U_16255)),U_16258)),
    inference(definitional_conversion,[status(esa)],[f_4024_2]) ).

cnf(f_4024_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16254,tc_HOL_Obool)),U_16255),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16256,tc_fun(U_16254,tc_HOL_Obool)),U_16257),U_16258)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16256,tc_fun(U_16254,tc_HOL_Obool)),U_16257),hAPP(hAPP(c_COMBB(tc_fun(U_16254,tc_HOL_Obool),tc_fun(U_16254,tc_HOL_Obool),U_16256),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16254,tc_HOL_Obool)),U_16255)),U_16258)),
    inference(clausify,[status(thm)],[f_4024_3]) ).

fof(f_4025_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_4025_2,plain,
    ! [U_16263,U_16262,U_16261,U_16260,U_16259] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16259,tc_HOL_Obool)),U_16260),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16261,tc_fun(U_16259,tc_HOL_Obool)),U_16262),U_16263)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16261,tc_fun(U_16259,tc_HOL_Obool)),U_16262),hAPP(hAPP(c_COMBB(tc_fun(U_16259,tc_HOL_Obool),tc_fun(U_16259,tc_HOL_Obool),U_16261),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16259,tc_HOL_Obool)),U_16260)),U_16263)),
    inference(variable_rename,[status(thm)],[f_4025_1]) ).

fof(f_4025_3,plain,
    ! [U_16259,U_16260,U_16261,U_16262,U_16263] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16259,tc_HOL_Obool)),U_16260),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16261,tc_fun(U_16259,tc_HOL_Obool)),U_16262),U_16263)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16261,tc_fun(U_16259,tc_HOL_Obool)),U_16262),hAPP(hAPP(c_COMBB(tc_fun(U_16259,tc_HOL_Obool),tc_fun(U_16259,tc_HOL_Obool),U_16261),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16259,tc_HOL_Obool)),U_16260)),U_16263)),
    inference(definitional_conversion,[status(esa)],[f_4025_2]) ).

cnf(f_4025_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16259,tc_HOL_Obool)),U_16260),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16261,tc_fun(U_16259,tc_HOL_Obool)),U_16262),U_16263)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16261,tc_fun(U_16259,tc_HOL_Obool)),U_16262),hAPP(hAPP(c_COMBB(tc_fun(U_16259,tc_HOL_Obool),tc_fun(U_16259,tc_HOL_Obool),U_16261),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16259,tc_HOL_Obool)),U_16260)),U_16263)),
    inference(clausify,[status(thm)],[f_4025_3]) ).

fof(f_4026_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_4026_2,plain,
    ! [U_16268,U_16267,U_16266,U_16265,U_16264] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16264,tc_fun(U_16265,tc_HOL_Obool)),U_16266),hAPP(hAPP(c_COMBC(U_16264,tc_fun(U_16265,tc_HOL_Obool),tc_fun(U_16265,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16265,tc_HOL_Obool),tc_fun(tc_fun(U_16265,tc_HOL_Obool),tc_fun(U_16265,tc_HOL_Obool)),U_16264),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16265,tc_HOL_Obool))),U_16267)),U_16268)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16265,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16264,tc_fun(U_16265,tc_HOL_Obool)),U_16266),U_16267)),U_16268),
    inference(variable_rename,[status(thm)],[f_4026_1]) ).

fof(f_4026_3,plain,
    ! [U_16264,U_16265,U_16266,U_16267,U_16268] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16264,tc_fun(U_16265,tc_HOL_Obool)),U_16266),hAPP(hAPP(c_COMBC(U_16264,tc_fun(U_16265,tc_HOL_Obool),tc_fun(U_16265,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16265,tc_HOL_Obool),tc_fun(tc_fun(U_16265,tc_HOL_Obool),tc_fun(U_16265,tc_HOL_Obool)),U_16264),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16265,tc_HOL_Obool))),U_16267)),U_16268)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16265,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16264,tc_fun(U_16265,tc_HOL_Obool)),U_16266),U_16267)),U_16268),
    inference(definitional_conversion,[status(esa)],[f_4026_2]) ).

cnf(f_4026_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16264,tc_fun(U_16265,tc_HOL_Obool)),U_16266),hAPP(hAPP(c_COMBC(U_16264,tc_fun(U_16265,tc_HOL_Obool),tc_fun(U_16265,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16265,tc_HOL_Obool),tc_fun(tc_fun(U_16265,tc_HOL_Obool),tc_fun(U_16265,tc_HOL_Obool)),U_16264),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16265,tc_HOL_Obool))),U_16267)),U_16268)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16265,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16264,tc_fun(U_16265,tc_HOL_Obool)),U_16266),U_16267)),U_16268),
    inference(clausify,[status(thm)],[f_4026_3]) ).

fof(f_4027_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_4027_2,plain,
    ! [U_16273,U_16272,U_16271,U_16270,U_16269] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16269,tc_fun(U_16270,tc_HOL_Obool)),U_16271),hAPP(hAPP(c_COMBB(tc_fun(U_16270,tc_HOL_Obool),tc_fun(U_16270,tc_HOL_Obool),U_16269),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16270,tc_HOL_Obool)),U_16272)),U_16273)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16270,tc_HOL_Obool)),U_16272),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16269,tc_fun(U_16270,tc_HOL_Obool)),U_16271),U_16273)),
    inference(variable_rename,[status(thm)],[f_4027_1]) ).

fof(f_4027_3,plain,
    ! [U_16269,U_16270,U_16271,U_16272,U_16273] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16269,tc_fun(U_16270,tc_HOL_Obool)),U_16271),hAPP(hAPP(c_COMBB(tc_fun(U_16270,tc_HOL_Obool),tc_fun(U_16270,tc_HOL_Obool),U_16269),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16270,tc_HOL_Obool)),U_16272)),U_16273)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16270,tc_HOL_Obool)),U_16272),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16269,tc_fun(U_16270,tc_HOL_Obool)),U_16271),U_16273)),
    inference(definitional_conversion,[status(esa)],[f_4027_2]) ).

cnf(f_4027_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16269,tc_fun(U_16270,tc_HOL_Obool)),U_16271),hAPP(hAPP(c_COMBB(tc_fun(U_16270,tc_HOL_Obool),tc_fun(U_16270,tc_HOL_Obool),U_16269),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16270,tc_HOL_Obool)),U_16272)),U_16273)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16270,tc_HOL_Obool)),U_16272),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16269,tc_fun(U_16270,tc_HOL_Obool)),U_16271),U_16273)),
    inference(clausify,[status(thm)],[f_4027_3]) ).

fof(f_4028_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_4028_2,plain,
    ! [U_16277,U_16276,U_16275,U_16274] : hAPP(c_Relation_Oconverse(U_16274,U_16275),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16274,U_16275),tc_HOL_Obool)),U_16276),U_16277)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16275,U_16274),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_16274,U_16275),U_16276)),hAPP(c_Relation_Oconverse(U_16274,U_16275),U_16277)),
    inference(variable_rename,[status(thm)],[f_4028_1]) ).

fof(f_4028_3,plain,
    ! [U_16274,U_16275,U_16276,U_16277] : hAPP(c_Relation_Oconverse(U_16274,U_16275),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16274,U_16275),tc_HOL_Obool)),U_16276),U_16277)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16275,U_16274),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_16274,U_16275),U_16276)),hAPP(c_Relation_Oconverse(U_16274,U_16275),U_16277)),
    inference(definitional_conversion,[status(esa)],[f_4028_2]) ).

cnf(f_4028_4,plain,
    hAPP(c_Relation_Oconverse(U_16274,U_16275),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16274,U_16275),tc_HOL_Obool)),U_16276),U_16277)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16275,U_16274),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_16274,U_16275),U_16276)),hAPP(c_Relation_Oconverse(U_16274,U_16275),U_16277)),
    inference(clausify,[status(thm)],[f_4028_3]) ).

fof(f_4029_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_4029_2,plain,
    ! [U_16284,U_16283,U_16282,U_16281,U_16280] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16282,U_16280),U_16283),U_16284)))
          | ? [U_16279] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(U_16284,U_16279)))
              & hBOOL(hAPP(hAPP(c_member(U_16282),U_16279),U_16283)) ) )
        & ( ! [U_16278] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(U_16284,U_16278)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16282),U_16278),U_16283)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16282,U_16280),U_16283),U_16284))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16280) ),
    inference(variable_rename,[status(thm)],[f_4029_1]) ).

fof(f_4029_3,plain,
    ! [U_16284,U_16283,U_16282,U_16281,U_16280] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16282,U_16280),U_16283),U_16284)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(U_16284,sK386(U_16284,U_16283,U_16282,U_16281,U_16280))))
            & hBOOL(hAPP(hAPP(c_member(U_16282),sK386(U_16284,U_16283,U_16282,U_16281,U_16280)),U_16283)) ) )
        & ( ! [U_16278] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(U_16284,U_16278)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16282),U_16278),U_16283)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16282,U_16280),U_16283),U_16284))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16280) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK386]),skolemize(U_16279,sK386(U_16284,U_16283,U_16282,U_16281,U_16280))],[f_4029_2]) ).

fof(f_4029_4,plain,
    ( ! [U_16280,U_16281,U_16282,U_16283,U_16284] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(U_16284,sK386(U_16284,U_16283,U_16282,U_16281,U_16280))))
        | ~ sP1054(U_16280,U_16281,U_16282,U_16283,U_16284) )
    & ! [U_16280,U_16281,U_16282,U_16283,U_16284] :
        ( hBOOL(hAPP(hAPP(c_member(U_16282),sK386(U_16284,U_16283,U_16282,U_16281,U_16280)),U_16283))
        | ~ sP1054(U_16280,U_16281,U_16282,U_16283,U_16284) )
    & ! [U_16278,U_16280,U_16281,U_16282,U_16283,U_16284] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16282,U_16280),U_16283),U_16284)))
        | sP1054(U_16280,U_16281,U_16282,U_16283,U_16284)
        | ~ sP1055(U_16278,U_16280,U_16281,U_16282,U_16283,U_16284) )
    & ! [U_16278,U_16280,U_16281,U_16282,U_16283,U_16284] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(U_16284,U_16278)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16282),U_16278),U_16283))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16282,U_16280),U_16283),U_16284)))
        | ~ sP1055(U_16278,U_16280,U_16281,U_16282,U_16283,U_16284) )
    & ! [U_16278,U_16280,U_16281,U_16282,U_16283,U_16284] :
        ( sP1055(U_16278,U_16280,U_16281,U_16282,U_16283,U_16284)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_16280) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1054,sP1055])],[f_4029_3]) ).

cnf(f_4029_5,plain,
    ( sP1055(U_16278,U_16280,U_16281,U_16282,U_16283,U_16284)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16280) ),
    inference(clausify,[status(thm)],[f_4029_4]) ).

cnf(f_4029_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(U_16284,U_16278)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16282),U_16278),U_16283))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16282,U_16280),U_16283),U_16284)))
    | ~ sP1055(U_16278,U_16280,U_16281,U_16282,U_16283,U_16284) ),
    inference(clausify,[status(thm)],[f_4029_4]) ).

cnf(f_4029_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16282,U_16280),U_16283),U_16284)))
    | sP1054(U_16280,U_16281,U_16282,U_16283,U_16284)
    | ~ sP1055(U_16278,U_16280,U_16281,U_16282,U_16283,U_16284) ),
    inference(clausify,[status(thm)],[f_4029_4]) ).

cnf(f_4029_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16282),sK386(U_16284,U_16283,U_16282,U_16281,U_16280)),U_16283))
    | ~ sP1054(U_16280,U_16281,U_16282,U_16283,U_16284) ),
    inference(clausify,[status(thm)],[f_4029_4]) ).

cnf(f_4029_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16280),U_16281),hAPP(U_16284,sK386(U_16284,U_16283,U_16282,U_16281,U_16280))))
    | ~ sP1054(U_16280,U_16281,U_16282,U_16283,U_16284) ),
    inference(clausify,[status(thm)],[f_4029_4]) ).

fof(f_4030_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_4030_2,plain,
    ! [U_16289,U_16288,U_16287,U_16286,U_16285] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16285,tc_fun(U_16286,tc_HOL_Obool)),U_16287),hAPP(hAPP(c_COMBB(tc_fun(U_16286,tc_HOL_Obool),tc_fun(U_16286,tc_HOL_Obool),U_16285),hAPP(c_Set_Oinsert(U_16286),U_16288)),U_16289)) = hAPP(hAPP(c_Set_Oinsert(U_16286),U_16288),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16285,tc_fun(U_16286,tc_HOL_Obool)),U_16287),U_16289)),
    inference(variable_rename,[status(thm)],[f_4030_1]) ).

fof(f_4030_3,plain,
    ! [U_16289,U_16285,U_16286,U_16287,U_16288] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16285,tc_fun(U_16286,tc_HOL_Obool)),U_16287),hAPP(hAPP(c_COMBB(tc_fun(U_16286,tc_HOL_Obool),tc_fun(U_16286,tc_HOL_Obool),U_16285),hAPP(c_Set_Oinsert(U_16286),U_16288)),U_16289)) = hAPP(hAPP(c_Set_Oinsert(U_16286),U_16288),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16285,tc_fun(U_16286,tc_HOL_Obool)),U_16287),U_16289)),
    inference(definitional_conversion,[status(esa)],[f_4030_2]) ).

cnf(f_4030_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16285,tc_fun(U_16286,tc_HOL_Obool)),U_16287),hAPP(hAPP(c_COMBB(tc_fun(U_16286,tc_HOL_Obool),tc_fun(U_16286,tc_HOL_Obool),U_16285),hAPP(c_Set_Oinsert(U_16286),U_16288)),U_16289)) = hAPP(hAPP(c_Set_Oinsert(U_16286),U_16288),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16285,tc_fun(U_16286,tc_HOL_Obool)),U_16287),U_16289)),
    inference(clausify,[status(thm)],[f_4030_3]) ).

fof(f_4031_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_4031_2,plain,
    ! [U_16294,U_16293,U_16292,U_16291,U_16290] : hAPP(hAPP(c_Set_Oinsert(U_16290),U_16291),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16292,tc_fun(U_16290,tc_HOL_Obool)),U_16293),U_16294)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16292,tc_fun(U_16290,tc_HOL_Obool)),U_16293),hAPP(hAPP(c_COMBB(tc_fun(U_16290,tc_HOL_Obool),tc_fun(U_16290,tc_HOL_Obool),U_16292),hAPP(c_Set_Oinsert(U_16290),U_16291)),U_16294)),
    inference(variable_rename,[status(thm)],[f_4031_1]) ).

fof(f_4031_3,plain,
    ! [U_16290,U_16292,U_16291,U_16293,U_16294] : hAPP(hAPP(c_Set_Oinsert(U_16290),U_16291),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16292,tc_fun(U_16290,tc_HOL_Obool)),U_16293),U_16294)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16292,tc_fun(U_16290,tc_HOL_Obool)),U_16293),hAPP(hAPP(c_COMBB(tc_fun(U_16290,tc_HOL_Obool),tc_fun(U_16290,tc_HOL_Obool),U_16292),hAPP(c_Set_Oinsert(U_16290),U_16291)),U_16294)),
    inference(definitional_conversion,[status(esa)],[f_4031_2]) ).

cnf(f_4031_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_16290),U_16291),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16292,tc_fun(U_16290,tc_HOL_Obool)),U_16293),U_16294)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16292,tc_fun(U_16290,tc_HOL_Obool)),U_16293),hAPP(hAPP(c_COMBB(tc_fun(U_16290,tc_HOL_Obool),tc_fun(U_16290,tc_HOL_Obool),U_16292),hAPP(c_Set_Oinsert(U_16290),U_16291)),U_16294)),
    inference(clausify,[status(thm)],[f_4031_3]) ).

fof(f_4032_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_4032_2,plain,
    ! [U_16300,U_16299,U_16298,U_16297,U_16296,U_16295] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16295,tc_fun(U_16298,tc_HOL_Obool)),U_16297),hAPP(hAPP(c_COMBB(tc_fun(U_16298,tc_HOL_Obool),tc_fun(U_16298,tc_HOL_Obool),U_16295),hAPP(c_Set_Oinsert(U_16298),U_16299)),U_16300)) = hAPP(hAPP(c_Set_Oinsert(U_16298),U_16299),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16295,tc_fun(U_16298,tc_HOL_Obool)),U_16297),U_16300))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16295),U_16296),U_16297)) ),
    inference(variable_rename,[status(thm)],[f_4032_1]) ).

fof(f_4032_3,plain,
    ! [U_16295,U_16296,U_16297,U_16298,U_16299,U_16300] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16295,tc_fun(U_16298,tc_HOL_Obool)),U_16297),hAPP(hAPP(c_COMBB(tc_fun(U_16298,tc_HOL_Obool),tc_fun(U_16298,tc_HOL_Obool),U_16295),hAPP(c_Set_Oinsert(U_16298),U_16299)),U_16300)) = hAPP(hAPP(c_Set_Oinsert(U_16298),U_16299),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16295,tc_fun(U_16298,tc_HOL_Obool)),U_16297),U_16300))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16295),U_16296),U_16297)) ),
    inference(definitional_conversion,[status(esa)],[f_4032_2]) ).

cnf(f_4032_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16295,tc_fun(U_16298,tc_HOL_Obool)),U_16297),hAPP(hAPP(c_COMBB(tc_fun(U_16298,tc_HOL_Obool),tc_fun(U_16298,tc_HOL_Obool),U_16295),hAPP(c_Set_Oinsert(U_16298),U_16299)),U_16300)) = hAPP(hAPP(c_Set_Oinsert(U_16298),U_16299),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16295,tc_fun(U_16298,tc_HOL_Obool)),U_16297),U_16300))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16295),U_16296),U_16297)) ),
    inference(clausify,[status(thm)],[f_4032_3]) ).

fof(f_4033_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_4033_2,plain,
    ! [U_16305,U_16304,U_16303,U_16302,U_16301] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16304,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16301,tc_fun(U_16304,tc_HOL_Obool)),U_16303),U_16305)),hAPP(U_16305,U_16302)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16301),U_16302),U_16303)) ),
    inference(variable_rename,[status(thm)],[f_4033_1]) ).

fof(f_4033_3,plain,
    ! [U_16302,U_16301,U_16303,U_16304,U_16305] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16304,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16301,tc_fun(U_16304,tc_HOL_Obool)),U_16303),U_16305)),hAPP(U_16305,U_16302)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16301),U_16302),U_16303)) ),
    inference(definitional_conversion,[status(esa)],[f_4033_2]) ).

cnf(f_4033_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16304,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16301,tc_fun(U_16304,tc_HOL_Obool)),U_16303),U_16305)),hAPP(U_16305,U_16302)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16301),U_16302),U_16303)) ),
    inference(clausify,[status(thm)],[f_4033_3]) ).

fof(f_4034_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_4034_2,plain,
    ! [U_16311,U_16310,U_16309,U_16308,U_16307,U_16306] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16306,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16307,U_16306,U_16308),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16309,tc_fun(U_16307,tc_HOL_Obool)),U_16310),U_16311))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16309,tc_fun(U_16306,tc_HOL_Obool)),U_16310),hAPP(hAPP(c_COMBB(tc_fun(U_16307,tc_HOL_Obool),tc_fun(U_16306,tc_HOL_Obool),U_16309),c_Relation_OImage(U_16307,U_16306,U_16308)),U_16311)))),
    inference(variable_rename,[status(thm)],[f_4034_1]) ).

fof(f_4034_3,plain,
    ! [U_16306,U_16307,U_16308,U_16309,U_16310,U_16311] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16306,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16307,U_16306,U_16308),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16309,tc_fun(U_16307,tc_HOL_Obool)),U_16310),U_16311))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16309,tc_fun(U_16306,tc_HOL_Obool)),U_16310),hAPP(hAPP(c_COMBB(tc_fun(U_16307,tc_HOL_Obool),tc_fun(U_16306,tc_HOL_Obool),U_16309),c_Relation_OImage(U_16307,U_16306,U_16308)),U_16311)))),
    inference(definitional_conversion,[status(esa)],[f_4034_2]) ).

cnf(f_4034_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16306,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16307,U_16306,U_16308),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16309,tc_fun(U_16307,tc_HOL_Obool)),U_16310),U_16311))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16309,tc_fun(U_16306,tc_HOL_Obool)),U_16310),hAPP(hAPP(c_COMBB(tc_fun(U_16307,tc_HOL_Obool),tc_fun(U_16306,tc_HOL_Obool),U_16309),c_Relation_OImage(U_16307,U_16306,U_16308)),U_16311)))),
    inference(clausify,[status(thm)],[f_4034_3]) ).

fof(f_4035_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_4035_2,plain,
    ! [U_16317,U_16316,U_16315,U_16314,U_16313,U_16312] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16312,tc_fun(U_16313,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16314,U_16312,U_16315),U_16316)),U_16317) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16314,tc_fun(U_16313,tc_HOL_Obool)),U_16316),hAPP(hAPP(c_COMBB(U_16312,tc_fun(U_16313,tc_HOL_Obool),U_16314),U_16317),U_16315)),
    inference(variable_rename,[status(thm)],[f_4035_1]) ).

fof(f_4035_3,plain,
    ! [U_16312,U_16313,U_16314,U_16315,U_16316,U_16317] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16312,tc_fun(U_16313,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16314,U_16312,U_16315),U_16316)),U_16317) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16314,tc_fun(U_16313,tc_HOL_Obool)),U_16316),hAPP(hAPP(c_COMBB(U_16312,tc_fun(U_16313,tc_HOL_Obool),U_16314),U_16317),U_16315)),
    inference(definitional_conversion,[status(esa)],[f_4035_2]) ).

cnf(f_4035_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16312,tc_fun(U_16313,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16314,U_16312,U_16315),U_16316)),U_16317) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16314,tc_fun(U_16313,tc_HOL_Obool)),U_16316),hAPP(hAPP(c_COMBB(U_16312,tc_fun(U_16313,tc_HOL_Obool),U_16314),U_16317),U_16315)),
    inference(clausify,[status(thm)],[f_4035_3]) ).

fof(f_4036_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_4036_2,plain,
    ! [U_16323,U_16322,U_16321,U_16320,U_16319,U_16318] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16318,tc_fun(U_16319,tc_HOL_Obool)),U_16320),hAPP(hAPP(c_COMBB(U_16321,tc_fun(U_16319,tc_HOL_Obool),U_16318),U_16322),U_16323)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16321,tc_fun(U_16319,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16318,U_16321,U_16323),U_16320)),U_16322),
    inference(variable_rename,[status(thm)],[f_4036_1]) ).

fof(f_4036_3,plain,
    ! [U_16318,U_16319,U_16320,U_16321,U_16322,U_16323] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16318,tc_fun(U_16319,tc_HOL_Obool)),U_16320),hAPP(hAPP(c_COMBB(U_16321,tc_fun(U_16319,tc_HOL_Obool),U_16318),U_16322),U_16323)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16321,tc_fun(U_16319,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16318,U_16321,U_16323),U_16320)),U_16322),
    inference(definitional_conversion,[status(esa)],[f_4036_2]) ).

cnf(f_4036_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16318,tc_fun(U_16319,tc_HOL_Obool)),U_16320),hAPP(hAPP(c_COMBB(U_16321,tc_fun(U_16319,tc_HOL_Obool),U_16318),U_16322),U_16323)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16321,tc_fun(U_16319,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16318,U_16321,U_16323),U_16320)),U_16322),
    inference(clausify,[status(thm)],[f_4036_3]) ).

fof(f_4037_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_4037_2,plain,
    ! [U_16329,U_16328,U_16327,U_16326,U_16325,U_16324] : hAPP(c_Set_Ovimage(U_16324,U_16325,U_16326),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16327,tc_fun(U_16325,tc_HOL_Obool)),U_16328),U_16329)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16327,tc_fun(U_16324,tc_HOL_Obool)),U_16328),hAPP(hAPP(c_COMBB(tc_fun(U_16325,tc_HOL_Obool),tc_fun(U_16324,tc_HOL_Obool),U_16327),c_Set_Ovimage(U_16324,U_16325,U_16326)),U_16329)),
    inference(variable_rename,[status(thm)],[f_4037_1]) ).

fof(f_4037_3,plain,
    ! [U_16324,U_16325,U_16326,U_16327,U_16328,U_16329] : hAPP(c_Set_Ovimage(U_16324,U_16325,U_16326),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16327,tc_fun(U_16325,tc_HOL_Obool)),U_16328),U_16329)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16327,tc_fun(U_16324,tc_HOL_Obool)),U_16328),hAPP(hAPP(c_COMBB(tc_fun(U_16325,tc_HOL_Obool),tc_fun(U_16324,tc_HOL_Obool),U_16327),c_Set_Ovimage(U_16324,U_16325,U_16326)),U_16329)),
    inference(definitional_conversion,[status(esa)],[f_4037_2]) ).

cnf(f_4037_4,plain,
    hAPP(c_Set_Ovimage(U_16324,U_16325,U_16326),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16327,tc_fun(U_16325,tc_HOL_Obool)),U_16328),U_16329)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16327,tc_fun(U_16324,tc_HOL_Obool)),U_16328),hAPP(hAPP(c_COMBB(tc_fun(U_16325,tc_HOL_Obool),tc_fun(U_16324,tc_HOL_Obool),U_16327),c_Set_Ovimage(U_16324,U_16325,U_16326)),U_16329)),
    inference(clausify,[status(thm)],[f_4037_3]) ).

fof(f_4038_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_4038_2,plain,
    ! [U_16336,U_16335,U_16334,U_16333,U_16332] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_16332),U_16333),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16334,tc_fun(U_16332,tc_HOL_Obool)),U_16335),U_16336)))
        | ? [U_16331] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_16332),U_16333),hAPP(U_16336,U_16331)))
            & hBOOL(hAPP(hAPP(c_member(U_16334),U_16331),U_16335)) ) )
      & ( ! [U_16330] :
            ( hBOOL(hAPP(hAPP(c_member(U_16332),U_16333),hAPP(U_16336,U_16330)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16334),U_16330),U_16335)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_16332),U_16333),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16334,tc_fun(U_16332,tc_HOL_Obool)),U_16335),U_16336))) ) ),
    inference(variable_rename,[status(thm)],[f_4038_1]) ).

fof(f_4038_3,plain,
    ( ! [U_16346,U_16344,U_16342,U_16340,U_16338] :
        ( hBOOL(hAPP(hAPP(c_member(U_16338),U_16340),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16342,tc_fun(U_16338,tc_HOL_Obool)),U_16344),U_16346)))
        | ? [U_16331] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_16338),U_16340),hAPP(U_16346,U_16331)))
            & hBOOL(hAPP(hAPP(c_member(U_16342),U_16331),U_16344)) ) )
    & ! [U_16345,U_16343,U_16341,U_16339,U_16337] :
        ( ! [U_16330] :
            ( hBOOL(hAPP(hAPP(c_member(U_16337),U_16339),hAPP(U_16345,U_16330)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16341),U_16330),U_16343)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_16337),U_16339),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16341,tc_fun(U_16337,tc_HOL_Obool)),U_16343),U_16345))) ) ),
    inference(miniscope,[status(thm)],[f_4038_2]) ).

fof(f_4038_4,plain,
    ( ! [U_16346,U_16344,U_16342,U_16340,U_16338] :
        ( hBOOL(hAPP(hAPP(c_member(U_16338),U_16340),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16342,tc_fun(U_16338,tc_HOL_Obool)),U_16344),U_16346)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_16338),U_16340),hAPP(U_16346,sK387(U_16346,U_16344,U_16342,U_16340,U_16338))))
          & hBOOL(hAPP(hAPP(c_member(U_16342),sK387(U_16346,U_16344,U_16342,U_16340,U_16338)),U_16344)) ) )
    & ! [U_16345,U_16343,U_16341,U_16339,U_16337] :
        ( ! [U_16330] :
            ( hBOOL(hAPP(hAPP(c_member(U_16337),U_16339),hAPP(U_16345,U_16330)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16341),U_16330),U_16343)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_16337),U_16339),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16341,tc_fun(U_16337,tc_HOL_Obool)),U_16343),U_16345))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK387]),skolemize(U_16331,sK387(U_16346,U_16344,U_16342,U_16340,U_16338))],[f_4038_3]) ).

fof(f_4038_5,plain,
    ( ! [U_16340,U_16338,U_16344,U_16346,U_16342] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_16338),U_16340),hAPP(U_16346,sK387(U_16346,U_16344,U_16342,U_16340,U_16338))))
        | ~ sP1056(U_16340,U_16338,U_16344,U_16346,U_16342) )
    & ! [U_16340,U_16338,U_16344,U_16346,U_16342] :
        ( hBOOL(hAPP(hAPP(c_member(U_16342),sK387(U_16346,U_16344,U_16342,U_16340,U_16338)),U_16344))
        | ~ sP1056(U_16340,U_16338,U_16344,U_16346,U_16342) )
    & ! [U_16340,U_16338,U_16344,U_16346,U_16342] :
        ( hBOOL(hAPP(hAPP(c_member(U_16338),U_16340),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16342,tc_fun(U_16338,tc_HOL_Obool)),U_16344),U_16346)))
        | sP1056(U_16340,U_16338,U_16344,U_16346,U_16342) )
    & ! [U_16341,U_16339,U_16330,U_16337,U_16345,U_16343] :
        ( hBOOL(hAPP(hAPP(c_member(U_16337),U_16339),hAPP(U_16345,U_16330)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16341),U_16330),U_16343))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16337),U_16339),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16341,tc_fun(U_16337,tc_HOL_Obool)),U_16343),U_16345))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1056])],[f_4038_4]) ).

cnf(f_4038_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16337),U_16339),hAPP(U_16345,U_16330)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16341),U_16330),U_16343))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16337),U_16339),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16341,tc_fun(U_16337,tc_HOL_Obool)),U_16343),U_16345))) ),
    inference(clausify,[status(thm)],[f_4038_5]) ).

cnf(f_4038_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16338),U_16340),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16342,tc_fun(U_16338,tc_HOL_Obool)),U_16344),U_16346)))
    | sP1056(U_16340,U_16338,U_16344,U_16346,U_16342) ),
    inference(clausify,[status(thm)],[f_4038_5]) ).

cnf(f_4038_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16342),sK387(U_16346,U_16344,U_16342,U_16340,U_16338)),U_16344))
    | ~ sP1056(U_16340,U_16338,U_16344,U_16346,U_16342) ),
    inference(clausify,[status(thm)],[f_4038_5]) ).

cnf(f_4038_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16338),U_16340),hAPP(U_16346,sK387(U_16346,U_16344,U_16342,U_16340,U_16338))))
    | ~ sP1056(U_16340,U_16338,U_16344,U_16346,U_16342) ),
    inference(clausify,[status(thm)],[f_4038_5]) ).

fof(f_4039_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_4039_2,plain,
    ! [U_16351,U_16350,U_16349,U_16348,U_16347] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16350,tc_HOL_Obool)),hAPP(U_16351,U_16348)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16347,tc_fun(U_16350,tc_HOL_Obool)),U_16349),U_16351)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16347,tc_fun(U_16350,tc_HOL_Obool)),U_16349),U_16351)
      | ~ hBOOL(hAPP(hAPP(c_member(U_16347),U_16348),U_16349)) ),
    inference(variable_rename,[status(thm)],[f_4039_1]) ).

fof(f_4039_3,plain,
    ! [U_16347,U_16348,U_16349,U_16350,U_16351] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16350,tc_HOL_Obool)),hAPP(U_16351,U_16348)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16347,tc_fun(U_16350,tc_HOL_Obool)),U_16349),U_16351)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16347,tc_fun(U_16350,tc_HOL_Obool)),U_16349),U_16351)
      | ~ hBOOL(hAPP(hAPP(c_member(U_16347),U_16348),U_16349)) ),
    inference(definitional_conversion,[status(esa)],[f_4039_2]) ).

cnf(f_4039_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16350,tc_HOL_Obool)),hAPP(U_16351,U_16348)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16347,tc_fun(U_16350,tc_HOL_Obool)),U_16349),U_16351)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16347,tc_fun(U_16350,tc_HOL_Obool)),U_16349),U_16351)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16347),U_16348),U_16349)) ),
    inference(clausify,[status(thm)],[f_4039_3]) ).

fof(f_4040_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_4040_2,plain,
    ! [U_16356,U_16355,U_16354,U_16353,U_16352] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16353,U_16352)),hAPP(hAPP(c_Product__Type_OPair(U_16353,U_16352),U_16355),U_16354)),U_16356))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16352,U_16353)),hAPP(hAPP(c_Product__Type_OPair(U_16352,U_16353),U_16354),U_16355)),hAPP(c_Relation_Oconverse(U_16353,U_16352),U_16356))) ),
    inference(variable_rename,[status(thm)],[f_4040_1]) ).

fof(f_4040_3,plain,
    ! [U_16352,U_16353,U_16354,U_16355,U_16356] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16353,U_16352)),hAPP(hAPP(c_Product__Type_OPair(U_16353,U_16352),U_16355),U_16354)),U_16356))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16352,U_16353)),hAPP(hAPP(c_Product__Type_OPair(U_16352,U_16353),U_16354),U_16355)),hAPP(c_Relation_Oconverse(U_16353,U_16352),U_16356))) ),
    inference(definitional_conversion,[status(esa)],[f_4040_2]) ).

cnf(f_4040_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16353,U_16352)),hAPP(hAPP(c_Product__Type_OPair(U_16353,U_16352),U_16355),U_16354)),U_16356))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16352,U_16353)),hAPP(hAPP(c_Product__Type_OPair(U_16352,U_16353),U_16354),U_16355)),hAPP(c_Relation_Oconverse(U_16353,U_16352),U_16356))) ),
    inference(clausify,[status(thm)],[f_4040_3]) ).

fof(f_4041_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_4041_2,plain,
    ! [U_16361,U_16360,U_16359,U_16358,U_16357] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16358,U_16357)),hAPP(hAPP(c_Product__Type_OPair(U_16358,U_16357),U_16360),U_16359)),hAPP(c_Relation_Oconverse(U_16357,U_16358),U_16361)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16357,U_16358)),hAPP(hAPP(c_Product__Type_OPair(U_16357,U_16358),U_16359),U_16360)),U_16361)) ),
    inference(variable_rename,[status(thm)],[f_4041_1]) ).

fof(f_4041_3,plain,
    ! [U_16357,U_16358,U_16359,U_16360,U_16361] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16358,U_16357)),hAPP(hAPP(c_Product__Type_OPair(U_16358,U_16357),U_16360),U_16359)),hAPP(c_Relation_Oconverse(U_16357,U_16358),U_16361)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16357,U_16358)),hAPP(hAPP(c_Product__Type_OPair(U_16357,U_16358),U_16359),U_16360)),U_16361)) ),
    inference(definitional_conversion,[status(esa)],[f_4041_2]) ).

cnf(f_4041_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16358,U_16357)),hAPP(hAPP(c_Product__Type_OPair(U_16358,U_16357),U_16360),U_16359)),hAPP(c_Relation_Oconverse(U_16357,U_16358),U_16361)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16357,U_16358)),hAPP(hAPP(c_Product__Type_OPair(U_16357,U_16358),U_16359),U_16360)),U_16361)) ),
    inference(clausify,[status(thm)],[f_4041_3]) ).

fof(f_4042_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_4042_2,plain,
    ! [U_16366,U_16365,U_16364,U_16363,U_16362] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16362,U_16363)),hAPP(hAPP(c_Product__Type_OPair(U_16362,U_16363),U_16364),U_16365)),hAPP(c_Relation_Oconverse(U_16363,U_16362),U_16366)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16363,U_16362)),hAPP(hAPP(c_Product__Type_OPair(U_16363,U_16362),U_16365),U_16364)),U_16366)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16363,U_16362)),hAPP(hAPP(c_Product__Type_OPair(U_16363,U_16362),U_16365),U_16364)),U_16366))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16362,U_16363)),hAPP(hAPP(c_Product__Type_OPair(U_16362,U_16363),U_16364),U_16365)),hAPP(c_Relation_Oconverse(U_16363,U_16362),U_16366))) ) ),
    inference(variable_rename,[status(thm)],[f_4042_1]) ).

fof(f_4042_3,plain,
    ( ! [U_16376,U_16374,U_16372,U_16370,U_16368] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16368,U_16370)),hAPP(hAPP(c_Product__Type_OPair(U_16368,U_16370),U_16372),U_16374)),hAPP(c_Relation_Oconverse(U_16370,U_16368),U_16376)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16370,U_16368)),hAPP(hAPP(c_Product__Type_OPair(U_16370,U_16368),U_16374),U_16372)),U_16376)) )
    & ! [U_16375,U_16373,U_16371,U_16369,U_16367] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16369,U_16367)),hAPP(hAPP(c_Product__Type_OPair(U_16369,U_16367),U_16373),U_16371)),U_16375))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16367,U_16369)),hAPP(hAPP(c_Product__Type_OPair(U_16367,U_16369),U_16371),U_16373)),hAPP(c_Relation_Oconverse(U_16369,U_16367),U_16375))) ) ),
    inference(miniscope,[status(thm)],[f_4042_2]) ).

fof(f_4042_4,plain,
    ( ! [U_16368,U_16370,U_16372,U_16374,U_16376] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16368,U_16370)),hAPP(hAPP(c_Product__Type_OPair(U_16368,U_16370),U_16372),U_16374)),hAPP(c_Relation_Oconverse(U_16370,U_16368),U_16376)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16370,U_16368)),hAPP(hAPP(c_Product__Type_OPair(U_16370,U_16368),U_16374),U_16372)),U_16376)) )
    & ! [U_16373,U_16371,U_16369,U_16367,U_16375] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16369,U_16367)),hAPP(hAPP(c_Product__Type_OPair(U_16369,U_16367),U_16373),U_16371)),U_16375))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16367,U_16369)),hAPP(hAPP(c_Product__Type_OPair(U_16367,U_16369),U_16371),U_16373)),hAPP(c_Relation_Oconverse(U_16369,U_16367),U_16375))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4042_3]) ).

cnf(f_4042_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16369,U_16367)),hAPP(hAPP(c_Product__Type_OPair(U_16369,U_16367),U_16373),U_16371)),U_16375))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16367,U_16369)),hAPP(hAPP(c_Product__Type_OPair(U_16367,U_16369),U_16371),U_16373)),hAPP(c_Relation_Oconverse(U_16369,U_16367),U_16375))) ),
    inference(clausify,[status(thm)],[f_4042_4]) ).

cnf(f_4042_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16368,U_16370)),hAPP(hAPP(c_Product__Type_OPair(U_16368,U_16370),U_16372),U_16374)),hAPP(c_Relation_Oconverse(U_16370,U_16368),U_16376)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16370,U_16368)),hAPP(hAPP(c_Product__Type_OPair(U_16370,U_16368),U_16374),U_16372)),U_16376)) ),
    inference(clausify,[status(thm)],[f_4042_4]) ).

fof(f_4043_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_4043_2,plain,
    ! [U_16380,U_16379,U_16378,U_16377] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16377,tc_fun(U_16378,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16377,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16378,tc_HOL_Obool),tc_fun(U_16378,tc_HOL_Obool),U_16377),hAPP(c_COMBC(U_16378,tc_fun(U_16378,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16378))),U_16379)),U_16380))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16378),U_16380),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16377,tc_fun(U_16378,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16377,tc_HOL_Obool))),U_16379))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_16378),U_16380),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16377,tc_fun(U_16378,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16377,tc_HOL_Obool))),U_16379)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16377,tc_fun(U_16378,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16377,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16378,tc_HOL_Obool),tc_fun(U_16378,tc_HOL_Obool),U_16377),hAPP(c_COMBC(U_16378,tc_fun(U_16378,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16378))),U_16379)),U_16380)) ) ),
    inference(variable_rename,[status(thm)],[f_4043_1]) ).

fof(f_4043_3,plain,
    ( ! [U_16388,U_16386,U_16384,U_16382] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16382,tc_fun(U_16384,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16382,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16384,tc_HOL_Obool),tc_fun(U_16384,tc_HOL_Obool),U_16382),hAPP(c_COMBC(U_16384,tc_fun(U_16384,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16384))),U_16386)),U_16388))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16384),U_16388),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16382,tc_fun(U_16384,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16382,tc_HOL_Obool))),U_16386))) )
    & ! [U_16387,U_16385,U_16383,U_16381] :
        ( hBOOL(hAPP(hAPP(c_member(U_16383),U_16387),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16381,tc_fun(U_16383,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16381,tc_HOL_Obool))),U_16385)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16381,tc_fun(U_16383,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16381,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16383,tc_HOL_Obool),tc_fun(U_16383,tc_HOL_Obool),U_16381),hAPP(c_COMBC(U_16383,tc_fun(U_16383,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16383))),U_16385)),U_16387)) ) ),
    inference(miniscope,[status(thm)],[f_4043_2]) ).

fof(f_4043_4,plain,
    ( ! [U_16382,U_16384,U_16386,U_16388] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16382,tc_fun(U_16384,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16382,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16384,tc_HOL_Obool),tc_fun(U_16384,tc_HOL_Obool),U_16382),hAPP(c_COMBC(U_16384,tc_fun(U_16384,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16384))),U_16386)),U_16388))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16384),U_16388),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16382,tc_fun(U_16384,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16382,tc_HOL_Obool))),U_16386))) )
    & ! [U_16387,U_16383,U_16381,U_16385] :
        ( hBOOL(hAPP(hAPP(c_member(U_16383),U_16387),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16381,tc_fun(U_16383,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16381,tc_HOL_Obool))),U_16385)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16381,tc_fun(U_16383,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16381,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16383,tc_HOL_Obool),tc_fun(U_16383,tc_HOL_Obool),U_16381),hAPP(c_COMBC(U_16383,tc_fun(U_16383,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16383))),U_16385)),U_16387)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4043_3]) ).

cnf(f_4043_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16383),U_16387),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16381,tc_fun(U_16383,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16381,tc_HOL_Obool))),U_16385)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16381,tc_fun(U_16383,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16381,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16383,tc_HOL_Obool),tc_fun(U_16383,tc_HOL_Obool),U_16381),hAPP(c_COMBC(U_16383,tc_fun(U_16383,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16383))),U_16385)),U_16387)) ),
    inference(clausify,[status(thm)],[f_4043_4]) ).

cnf(f_4043_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16382,tc_fun(U_16384,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16382,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16384,tc_HOL_Obool),tc_fun(U_16384,tc_HOL_Obool),U_16382),hAPP(c_COMBC(U_16384,tc_fun(U_16384,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16384))),U_16386)),U_16388))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16384),U_16388),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16382,tc_fun(U_16384,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16382,tc_HOL_Obool))),U_16386))) ),
    inference(clausify,[status(thm)],[f_4043_4]) ).

fof(f_4044_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_4044_2,plain,
    ! [U_16394,U_16393,U_16392,U_16391,U_16390,U_16389] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16389,tc_fun(U_16390,tc_fun(U_16391,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16389,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool),tc_fun(U_16390,tc_fun(U_16391,tc_HOL_Obool)),U_16389),hAPP(c_COMBC(U_16390,tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool),tc_fun(U_16391,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16391,tc_fun(tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool),tc_fun(U_16391,tc_HOL_Obool)),U_16390),c_COMBC(U_16391,tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16391,tc_prod(U_16390,U_16391)),tc_fun(U_16391,tc_fun(tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool),tc_HOL_Obool)),U_16390),hAPP(c_COMBB(tc_prod(U_16390,U_16391),tc_fun(tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool),tc_HOL_Obool),U_16391),c_member(tc_prod(U_16390,U_16391)))),c_Product__Type_OPair(U_16390,U_16391))))),U_16392)),U_16393),U_16394))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16390,U_16391)),hAPP(hAPP(c_Product__Type_OPair(U_16390,U_16391),U_16393),U_16394)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16389,tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16389,tc_HOL_Obool))),U_16392))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16390,U_16391)),hAPP(hAPP(c_Product__Type_OPair(U_16390,U_16391),U_16393),U_16394)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16389,tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16389,tc_HOL_Obool))),U_16392)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16389,tc_fun(U_16390,tc_fun(U_16391,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16389,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool),tc_fun(U_16390,tc_fun(U_16391,tc_HOL_Obool)),U_16389),hAPP(c_COMBC(U_16390,tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool),tc_fun(U_16391,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16391,tc_fun(tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool),tc_fun(U_16391,tc_HOL_Obool)),U_16390),c_COMBC(U_16391,tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16391,tc_prod(U_16390,U_16391)),tc_fun(U_16391,tc_fun(tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool),tc_HOL_Obool)),U_16390),hAPP(c_COMBB(tc_prod(U_16390,U_16391),tc_fun(tc_fun(tc_prod(U_16390,U_16391),tc_HOL_Obool),tc_HOL_Obool),U_16391),c_member(tc_prod(U_16390,U_16391)))),c_Product__Type_OPair(U_16390,U_16391))))),U_16392)),U_16393),U_16394)) ) ),
    inference(variable_rename,[status(thm)],[f_4044_1]) ).

fof(f_4044_3,plain,
    ( ! [U_16406,U_16404,U_16402,U_16400,U_16398,U_16396] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16396,tc_fun(U_16398,tc_fun(U_16400,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16396,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_fun(U_16398,tc_fun(U_16400,tc_HOL_Obool)),U_16396),hAPP(c_COMBC(U_16398,tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_fun(U_16400,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16400,tc_fun(tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_fun(U_16400,tc_HOL_Obool)),U_16398),c_COMBC(U_16400,tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16400,tc_prod(U_16398,U_16400)),tc_fun(U_16400,tc_fun(tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_HOL_Obool)),U_16398),hAPP(c_COMBB(tc_prod(U_16398,U_16400),tc_fun(tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_HOL_Obool),U_16400),c_member(tc_prod(U_16398,U_16400)))),c_Product__Type_OPair(U_16398,U_16400))))),U_16402)),U_16404),U_16406))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16398,U_16400)),hAPP(hAPP(c_Product__Type_OPair(U_16398,U_16400),U_16404),U_16406)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16396,tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16396,tc_HOL_Obool))),U_16402))) )
    & ! [U_16405,U_16403,U_16401,U_16399,U_16397,U_16395] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16397,U_16399)),hAPP(hAPP(c_Product__Type_OPair(U_16397,U_16399),U_16403),U_16405)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16395,tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16395,tc_HOL_Obool))),U_16401)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16395,tc_fun(U_16397,tc_fun(U_16399,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16395,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_fun(U_16397,tc_fun(U_16399,tc_HOL_Obool)),U_16395),hAPP(c_COMBC(U_16397,tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_fun(U_16399,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16399,tc_fun(tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_fun(U_16399,tc_HOL_Obool)),U_16397),c_COMBC(U_16399,tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16399,tc_prod(U_16397,U_16399)),tc_fun(U_16399,tc_fun(tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_HOL_Obool)),U_16397),hAPP(c_COMBB(tc_prod(U_16397,U_16399),tc_fun(tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_HOL_Obool),U_16399),c_member(tc_prod(U_16397,U_16399)))),c_Product__Type_OPair(U_16397,U_16399))))),U_16401)),U_16403),U_16405)) ) ),
    inference(miniscope,[status(thm)],[f_4044_2]) ).

fof(f_4044_4,plain,
    ( ! [U_16396,U_16398,U_16400,U_16402,U_16404,U_16406] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16396,tc_fun(U_16398,tc_fun(U_16400,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16396,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_fun(U_16398,tc_fun(U_16400,tc_HOL_Obool)),U_16396),hAPP(c_COMBC(U_16398,tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_fun(U_16400,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16400,tc_fun(tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_fun(U_16400,tc_HOL_Obool)),U_16398),c_COMBC(U_16400,tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16400,tc_prod(U_16398,U_16400)),tc_fun(U_16400,tc_fun(tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_HOL_Obool)),U_16398),hAPP(c_COMBB(tc_prod(U_16398,U_16400),tc_fun(tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_HOL_Obool),U_16400),c_member(tc_prod(U_16398,U_16400)))),c_Product__Type_OPair(U_16398,U_16400))))),U_16402)),U_16404),U_16406))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16398,U_16400)),hAPP(hAPP(c_Product__Type_OPair(U_16398,U_16400),U_16404),U_16406)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16396,tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16396,tc_HOL_Obool))),U_16402))) )
    & ! [U_16401,U_16397,U_16399,U_16395,U_16403,U_16405] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16397,U_16399)),hAPP(hAPP(c_Product__Type_OPair(U_16397,U_16399),U_16403),U_16405)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16395,tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16395,tc_HOL_Obool))),U_16401)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16395,tc_fun(U_16397,tc_fun(U_16399,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16395,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_fun(U_16397,tc_fun(U_16399,tc_HOL_Obool)),U_16395),hAPP(c_COMBC(U_16397,tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_fun(U_16399,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16399,tc_fun(tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_fun(U_16399,tc_HOL_Obool)),U_16397),c_COMBC(U_16399,tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16399,tc_prod(U_16397,U_16399)),tc_fun(U_16399,tc_fun(tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_HOL_Obool)),U_16397),hAPP(c_COMBB(tc_prod(U_16397,U_16399),tc_fun(tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_HOL_Obool),U_16399),c_member(tc_prod(U_16397,U_16399)))),c_Product__Type_OPair(U_16397,U_16399))))),U_16401)),U_16403),U_16405)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4044_3]) ).

cnf(f_4044_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16397,U_16399)),hAPP(hAPP(c_Product__Type_OPair(U_16397,U_16399),U_16403),U_16405)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16395,tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16395,tc_HOL_Obool))),U_16401)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16395,tc_fun(U_16397,tc_fun(U_16399,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16395,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_fun(U_16397,tc_fun(U_16399,tc_HOL_Obool)),U_16395),hAPP(c_COMBC(U_16397,tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_fun(U_16399,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16399,tc_fun(tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_fun(U_16399,tc_HOL_Obool)),U_16397),c_COMBC(U_16399,tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16399,tc_prod(U_16397,U_16399)),tc_fun(U_16399,tc_fun(tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_HOL_Obool)),U_16397),hAPP(c_COMBB(tc_prod(U_16397,U_16399),tc_fun(tc_fun(tc_prod(U_16397,U_16399),tc_HOL_Obool),tc_HOL_Obool),U_16399),c_member(tc_prod(U_16397,U_16399)))),c_Product__Type_OPair(U_16397,U_16399))))),U_16401)),U_16403),U_16405)) ),
    inference(clausify,[status(thm)],[f_4044_4]) ).

cnf(f_4044_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16396,tc_fun(U_16398,tc_fun(U_16400,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16396,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_fun(U_16398,tc_fun(U_16400,tc_HOL_Obool)),U_16396),hAPP(c_COMBC(U_16398,tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_fun(U_16400,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16400,tc_fun(tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_fun(U_16400,tc_HOL_Obool)),U_16398),c_COMBC(U_16400,tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16400,tc_prod(U_16398,U_16400)),tc_fun(U_16400,tc_fun(tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_HOL_Obool)),U_16398),hAPP(c_COMBB(tc_prod(U_16398,U_16400),tc_fun(tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool),tc_HOL_Obool),U_16400),c_member(tc_prod(U_16398,U_16400)))),c_Product__Type_OPair(U_16398,U_16400))))),U_16402)),U_16404),U_16406))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16398,U_16400)),hAPP(hAPP(c_Product__Type_OPair(U_16398,U_16400),U_16404),U_16406)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16396,tc_fun(tc_prod(U_16398,U_16400),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16396,tc_HOL_Obool))),U_16402))) ),
    inference(clausify,[status(thm)],[f_4044_4]) ).

fof(f_4045_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_4045_2,plain,
    ! [U_16412,U_16411,U_16410,U_16409] :
      ( ( c_Orderings_Otop__class_Otop(tc_fun(U_16409,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16410,tc_fun(U_16409,tc_HOL_Obool)),U_16411),U_16412)
        | ? [U_16408] :
            ( hAPP(U_16412,U_16408) != c_Orderings_Otop__class_Otop(tc_fun(U_16409,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_16410),U_16408),U_16411)) ) )
      & ( ! [U_16407] :
            ( hAPP(U_16412,U_16407) = c_Orderings_Otop__class_Otop(tc_fun(U_16409,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16410),U_16407),U_16411)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_16409,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16410,tc_fun(U_16409,tc_HOL_Obool)),U_16411),U_16412) ) ),
    inference(variable_rename,[status(thm)],[f_4045_1]) ).

fof(f_4045_3,plain,
    ( ! [U_16420,U_16418,U_16416,U_16414] :
        ( c_Orderings_Otop__class_Otop(tc_fun(U_16414,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16416,tc_fun(U_16414,tc_HOL_Obool)),U_16418),U_16420)
        | ? [U_16408] :
            ( hAPP(U_16420,U_16408) != c_Orderings_Otop__class_Otop(tc_fun(U_16414,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_16416),U_16408),U_16418)) ) )
    & ! [U_16419,U_16417,U_16415,U_16413] :
        ( ! [U_16407] :
            ( hAPP(U_16419,U_16407) = c_Orderings_Otop__class_Otop(tc_fun(U_16413,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16415),U_16407),U_16417)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_16413,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16415,tc_fun(U_16413,tc_HOL_Obool)),U_16417),U_16419) ) ),
    inference(miniscope,[status(thm)],[f_4045_2]) ).

fof(f_4045_4,plain,
    ( ! [U_16420,U_16418,U_16416,U_16414] :
        ( c_Orderings_Otop__class_Otop(tc_fun(U_16414,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16416,tc_fun(U_16414,tc_HOL_Obool)),U_16418),U_16420)
        | ( hAPP(U_16420,sK388(U_16420,U_16418,U_16416,U_16414)) != c_Orderings_Otop__class_Otop(tc_fun(U_16414,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_16416),sK388(U_16420,U_16418,U_16416,U_16414)),U_16418)) ) )
    & ! [U_16419,U_16417,U_16415,U_16413] :
        ( ! [U_16407] :
            ( hAPP(U_16419,U_16407) = c_Orderings_Otop__class_Otop(tc_fun(U_16413,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16415),U_16407),U_16417)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_16413,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16415,tc_fun(U_16413,tc_HOL_Obool)),U_16417),U_16419) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK388]),skolemize(U_16408,sK388(U_16420,U_16418,U_16416,U_16414))],[f_4045_3]) ).

fof(f_4045_5,plain,
    ( ! [U_16418,U_16420,U_16414,U_16416] :
        ( hAPP(U_16420,sK388(U_16420,U_16418,U_16416,U_16414)) != c_Orderings_Otop__class_Otop(tc_fun(U_16414,tc_HOL_Obool))
        | ~ sP1057(U_16418,U_16420,U_16414,U_16416) )
    & ! [U_16418,U_16420,U_16414,U_16416] :
        ( hBOOL(hAPP(hAPP(c_member(U_16416),sK388(U_16420,U_16418,U_16416,U_16414)),U_16418))
        | ~ sP1057(U_16418,U_16420,U_16414,U_16416) )
    & ! [U_16418,U_16420,U_16414,U_16416] :
        ( c_Orderings_Otop__class_Otop(tc_fun(U_16414,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16416,tc_fun(U_16414,tc_HOL_Obool)),U_16418),U_16420)
        | sP1057(U_16418,U_16420,U_16414,U_16416) )
    & ! [U_16407,U_16419,U_16415,U_16413,U_16417] :
        ( hAPP(U_16419,U_16407) = c_Orderings_Otop__class_Otop(tc_fun(U_16413,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16415),U_16407),U_16417))
        | c_Orderings_Otop__class_Otop(tc_fun(U_16413,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16415,tc_fun(U_16413,tc_HOL_Obool)),U_16417),U_16419) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1057])],[f_4045_4]) ).

cnf(f_4045_6,plain,
    ( hAPP(U_16419,U_16407) = c_Orderings_Otop__class_Otop(tc_fun(U_16413,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16415),U_16407),U_16417))
    | c_Orderings_Otop__class_Otop(tc_fun(U_16413,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16415,tc_fun(U_16413,tc_HOL_Obool)),U_16417),U_16419) ),
    inference(clausify,[status(thm)],[f_4045_5]) ).

cnf(f_4045_7,plain,
    ( c_Orderings_Otop__class_Otop(tc_fun(U_16414,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16416,tc_fun(U_16414,tc_HOL_Obool)),U_16418),U_16420)
    | sP1057(U_16418,U_16420,U_16414,U_16416) ),
    inference(clausify,[status(thm)],[f_4045_5]) ).

cnf(f_4045_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16416),sK388(U_16420,U_16418,U_16416,U_16414)),U_16418))
    | ~ sP1057(U_16418,U_16420,U_16414,U_16416) ),
    inference(clausify,[status(thm)],[f_4045_5]) ).

cnf(f_4045_9,plain,
    ( hAPP(U_16420,sK388(U_16420,U_16418,U_16416,U_16414)) != c_Orderings_Otop__class_Otop(tc_fun(U_16414,tc_HOL_Obool))
    | ~ sP1057(U_16418,U_16420,U_16414,U_16416) ),
    inference(clausify,[status(thm)],[f_4045_5]) ).

fof(f_4046_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_4046_2,plain,
    ! [U_16426,U_16425,U_16424,U_16423] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16423,tc_fun(U_16424,tc_HOL_Obool)),U_16425),U_16426) = c_Orderings_Otop__class_Otop(tc_fun(U_16424,tc_HOL_Obool))
        | ? [U_16422] :
            ( hAPP(U_16426,U_16422) != c_Orderings_Otop__class_Otop(tc_fun(U_16424,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_16423),U_16422),U_16425)) ) )
      & ( ! [U_16421] :
            ( hAPP(U_16426,U_16421) = c_Orderings_Otop__class_Otop(tc_fun(U_16424,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16423),U_16421),U_16425)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16423,tc_fun(U_16424,tc_HOL_Obool)),U_16425),U_16426) != c_Orderings_Otop__class_Otop(tc_fun(U_16424,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4046_1]) ).

fof(f_4046_3,plain,
    ( ! [U_16434,U_16432,U_16430,U_16428] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16428,tc_fun(U_16430,tc_HOL_Obool)),U_16432),U_16434) = c_Orderings_Otop__class_Otop(tc_fun(U_16430,tc_HOL_Obool))
        | ? [U_16422] :
            ( hAPP(U_16434,U_16422) != c_Orderings_Otop__class_Otop(tc_fun(U_16430,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_16428),U_16422),U_16432)) ) )
    & ! [U_16433,U_16431,U_16429,U_16427] :
        ( ! [U_16421] :
            ( hAPP(U_16433,U_16421) = c_Orderings_Otop__class_Otop(tc_fun(U_16429,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16427),U_16421),U_16431)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16427,tc_fun(U_16429,tc_HOL_Obool)),U_16431),U_16433) != c_Orderings_Otop__class_Otop(tc_fun(U_16429,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4046_2]) ).

fof(f_4046_4,plain,
    ( ! [U_16434,U_16432,U_16430,U_16428] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16428,tc_fun(U_16430,tc_HOL_Obool)),U_16432),U_16434) = c_Orderings_Otop__class_Otop(tc_fun(U_16430,tc_HOL_Obool))
        | ( hAPP(U_16434,sK389(U_16434,U_16432,U_16430,U_16428)) != c_Orderings_Otop__class_Otop(tc_fun(U_16430,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_16428),sK389(U_16434,U_16432,U_16430,U_16428)),U_16432)) ) )
    & ! [U_16433,U_16431,U_16429,U_16427] :
        ( ! [U_16421] :
            ( hAPP(U_16433,U_16421) = c_Orderings_Otop__class_Otop(tc_fun(U_16429,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16427),U_16421),U_16431)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16427,tc_fun(U_16429,tc_HOL_Obool)),U_16431),U_16433) != c_Orderings_Otop__class_Otop(tc_fun(U_16429,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK389]),skolemize(U_16422,sK389(U_16434,U_16432,U_16430,U_16428))],[f_4046_3]) ).

fof(f_4046_5,plain,
    ( ! [U_16430,U_16432,U_16428,U_16434] :
        ( hAPP(U_16434,sK389(U_16434,U_16432,U_16430,U_16428)) != c_Orderings_Otop__class_Otop(tc_fun(U_16430,tc_HOL_Obool))
        | ~ sP1058(U_16430,U_16432,U_16428,U_16434) )
    & ! [U_16430,U_16432,U_16428,U_16434] :
        ( hBOOL(hAPP(hAPP(c_member(U_16428),sK389(U_16434,U_16432,U_16430,U_16428)),U_16432))
        | ~ sP1058(U_16430,U_16432,U_16428,U_16434) )
    & ! [U_16430,U_16432,U_16428,U_16434] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16428,tc_fun(U_16430,tc_HOL_Obool)),U_16432),U_16434) = c_Orderings_Otop__class_Otop(tc_fun(U_16430,tc_HOL_Obool))
        | sP1058(U_16430,U_16432,U_16428,U_16434) )
    & ! [U_16421,U_16429,U_16433,U_16427,U_16431] :
        ( hAPP(U_16433,U_16421) = c_Orderings_Otop__class_Otop(tc_fun(U_16429,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16427),U_16421),U_16431))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16427,tc_fun(U_16429,tc_HOL_Obool)),U_16431),U_16433) != c_Orderings_Otop__class_Otop(tc_fun(U_16429,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1058])],[f_4046_4]) ).

cnf(f_4046_6,plain,
    ( hAPP(U_16433,U_16421) = c_Orderings_Otop__class_Otop(tc_fun(U_16429,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16427),U_16421),U_16431))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16427,tc_fun(U_16429,tc_HOL_Obool)),U_16431),U_16433) != c_Orderings_Otop__class_Otop(tc_fun(U_16429,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4046_5]) ).

cnf(f_4046_7,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16428,tc_fun(U_16430,tc_HOL_Obool)),U_16432),U_16434) = c_Orderings_Otop__class_Otop(tc_fun(U_16430,tc_HOL_Obool))
    | sP1058(U_16430,U_16432,U_16428,U_16434) ),
    inference(clausify,[status(thm)],[f_4046_5]) ).

cnf(f_4046_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16428),sK389(U_16434,U_16432,U_16430,U_16428)),U_16432))
    | ~ sP1058(U_16430,U_16432,U_16428,U_16434) ),
    inference(clausify,[status(thm)],[f_4046_5]) ).

cnf(f_4046_9,plain,
    ( hAPP(U_16434,sK389(U_16434,U_16432,U_16430,U_16428)) != c_Orderings_Otop__class_Otop(tc_fun(U_16430,tc_HOL_Obool))
    | ~ sP1058(U_16430,U_16432,U_16428,U_16434) ),
    inference(clausify,[status(thm)],[f_4046_5]) ).

fof(f_4047_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_4047_2,plain,
    ! [U_16437,U_16436,U_16435] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16435,U_16436)),hAPP(c_Relation_Oconverse(U_16436,U_16435),U_16437)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16436,U_16435)),U_16437)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16436,U_16435)),U_16437))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16435,U_16436)),hAPP(c_Relation_Oconverse(U_16436,U_16435),U_16437))) ) ),
    inference(variable_rename,[status(thm)],[f_4047_1]) ).

fof(f_4047_3,plain,
    ( ! [U_16443,U_16441,U_16439] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16439,U_16441)),hAPP(c_Relation_Oconverse(U_16441,U_16439),U_16443)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16441,U_16439)),U_16443)) )
    & ! [U_16442,U_16440,U_16438] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16440,U_16438)),U_16442))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16438,U_16440)),hAPP(c_Relation_Oconverse(U_16440,U_16438),U_16442))) ) ),
    inference(miniscope,[status(thm)],[f_4047_2]) ).

fof(f_4047_4,plain,
    ( ! [U_16439,U_16441,U_16443] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16439,U_16441)),hAPP(c_Relation_Oconverse(U_16441,U_16439),U_16443)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16441,U_16439)),U_16443)) )
    & ! [U_16440,U_16442,U_16438] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16440,U_16438)),U_16442))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16438,U_16440)),hAPP(c_Relation_Oconverse(U_16440,U_16438),U_16442))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4047_3]) ).

cnf(f_4047_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16440,U_16438)),U_16442))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16438,U_16440)),hAPP(c_Relation_Oconverse(U_16440,U_16438),U_16442))) ),
    inference(clausify,[status(thm)],[f_4047_4]) ).

cnf(f_4047_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16439,U_16441)),hAPP(c_Relation_Oconverse(U_16441,U_16439),U_16443)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16441,U_16439)),U_16443)) ),
    inference(clausify,[status(thm)],[f_4047_4]) ).

fof(f_4048_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_4048_2,plain,
    ! [U_16450,U_16449,U_16448,U_16447,U_16446] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,U_16446),U_16448),U_16449)),U_16450))
          | ! [U_16445] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(U_16449,U_16445)),U_16450))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16447),U_16445),U_16448)) ) )
        & ( ? [U_16444] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(U_16449,U_16444)),U_16450))
              & hBOOL(hAPP(hAPP(c_member(U_16447),U_16444),U_16448)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,U_16446),U_16448),U_16449)),U_16450)) ) )
      | ~ class_Orderings_Olinorder(U_16446)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16446) ),
    inference(variable_rename,[status(thm)],[f_4048_1]) ).

fof(f_4048_3,plain,
    ! [U_16450,U_16449,U_16448,U_16447,U_16446] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,U_16446),U_16448),U_16449)),U_16450))
          | ! [U_16445] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(U_16449,U_16445)),U_16450))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16447),U_16445),U_16448)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(U_16449,sK390(U_16450,U_16449,U_16448,U_16447,U_16446))),U_16450))
            & hBOOL(hAPP(hAPP(c_member(U_16447),sK390(U_16450,U_16449,U_16448,U_16447,U_16446)),U_16448)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,U_16446),U_16448),U_16449)),U_16450)) ) )
      | ~ class_Orderings_Olinorder(U_16446)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16446) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK390]),skolemize(U_16444,sK390(U_16450,U_16449,U_16448,U_16447,U_16446))],[f_4048_2]) ).

fof(f_4048_4,plain,
    ( ! [U_16446,U_16447,U_16448,U_16449,U_16450] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(U_16449,sK390(U_16450,U_16449,U_16448,U_16447,U_16446))),U_16450))
        | ~ sP1059(U_16446,U_16447,U_16448,U_16449,U_16450) )
    & ! [U_16446,U_16447,U_16448,U_16449,U_16450] :
        ( hBOOL(hAPP(hAPP(c_member(U_16447),sK390(U_16450,U_16449,U_16448,U_16447,U_16446)),U_16448))
        | ~ sP1059(U_16446,U_16447,U_16448,U_16449,U_16450) )
    & ! [U_16445,U_16446,U_16447,U_16448,U_16449,U_16450] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,U_16446),U_16448),U_16449)),U_16450))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(U_16449,U_16445)),U_16450))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16447),U_16445),U_16448))
        | ~ sP1060(U_16445,U_16446,U_16447,U_16448,U_16449,U_16450) )
    & ! [U_16445,U_16446,U_16447,U_16448,U_16449,U_16450] :
        ( sP1059(U_16446,U_16447,U_16448,U_16449,U_16450)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,U_16446),U_16448),U_16449)),U_16450))
        | ~ sP1060(U_16445,U_16446,U_16447,U_16448,U_16449,U_16450) )
    & ! [U_16445,U_16446,U_16447,U_16448,U_16449,U_16450] :
        ( sP1060(U_16445,U_16446,U_16447,U_16448,U_16449,U_16450)
        | ~ class_Orderings_Olinorder(U_16446)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_16446) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1059,sP1060])],[f_4048_3]) ).

cnf(f_4048_5,plain,
    ( sP1060(U_16445,U_16446,U_16447,U_16448,U_16449,U_16450)
    | ~ class_Orderings_Olinorder(U_16446)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16446) ),
    inference(clausify,[status(thm)],[f_4048_4]) ).

cnf(f_4048_6,plain,
    ( sP1059(U_16446,U_16447,U_16448,U_16449,U_16450)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,U_16446),U_16448),U_16449)),U_16450))
    | ~ sP1060(U_16445,U_16446,U_16447,U_16448,U_16449,U_16450) ),
    inference(clausify,[status(thm)],[f_4048_4]) ).

cnf(f_4048_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,U_16446),U_16448),U_16449)),U_16450))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(U_16449,U_16445)),U_16450))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16447),U_16445),U_16448))
    | ~ sP1060(U_16445,U_16446,U_16447,U_16448,U_16449,U_16450) ),
    inference(clausify,[status(thm)],[f_4048_4]) ).

cnf(f_4048_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16447),sK390(U_16450,U_16449,U_16448,U_16447,U_16446)),U_16448))
    | ~ sP1059(U_16446,U_16447,U_16448,U_16449,U_16450) ),
    inference(clausify,[status(thm)],[f_4048_4]) ).

cnf(f_4048_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16446),hAPP(U_16449,sK390(U_16450,U_16449,U_16448,U_16447,U_16446))),U_16450))
    | ~ sP1059(U_16446,U_16447,U_16448,U_16449,U_16450) ),
    inference(clausify,[status(thm)],[f_4048_4]) ).

fof(f_4049_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_4049_2,plain,
    ! [U_16454,U_16453,U_16452,U_16451] : hAPP(c_Relation_Oconverse(U_16451,U_16452),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16451,U_16452),tc_HOL_Obool)),U_16453),U_16454)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16452,U_16451),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_16451,U_16452),U_16453)),hAPP(c_Relation_Oconverse(U_16451,U_16452),U_16454)),
    inference(variable_rename,[status(thm)],[f_4049_1]) ).

fof(f_4049_3,plain,
    ! [U_16451,U_16452,U_16454,U_16453] : hAPP(c_Relation_Oconverse(U_16451,U_16452),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16451,U_16452),tc_HOL_Obool)),U_16453),U_16454)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16452,U_16451),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_16451,U_16452),U_16453)),hAPP(c_Relation_Oconverse(U_16451,U_16452),U_16454)),
    inference(definitional_conversion,[status(esa)],[f_4049_2]) ).

cnf(f_4049_4,plain,
    hAPP(c_Relation_Oconverse(U_16451,U_16452),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16451,U_16452),tc_HOL_Obool)),U_16453),U_16454)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16452,U_16451),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_16451,U_16452),U_16453)),hAPP(c_Relation_Oconverse(U_16451,U_16452),U_16454)),
    inference(clausify,[status(thm)],[f_4049_3]) ).

fof(f_4050_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_4050_2,plain,
    ! [U_16459,U_16458,U_16457,U_16456,U_16455] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16455,tc_fun(U_16456,tc_HOL_Obool)),U_16457),hAPP(hAPP(c_COMBS(U_16455,tc_fun(U_16456,tc_HOL_Obool),tc_fun(U_16456,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16456,tc_HOL_Obool),tc_fun(tc_fun(U_16456,tc_HOL_Obool),tc_fun(U_16456,tc_HOL_Obool)),U_16455),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16456,tc_HOL_Obool))),U_16458)),U_16459)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16456,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16455,tc_fun(U_16456,tc_HOL_Obool)),U_16457),U_16458)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16455,tc_fun(U_16456,tc_HOL_Obool)),U_16457),U_16459)),
    inference(variable_rename,[status(thm)],[f_4050_1]) ).

fof(f_4050_3,plain,
    ! [U_16455,U_16456,U_16457,U_16458,U_16459] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16455,tc_fun(U_16456,tc_HOL_Obool)),U_16457),hAPP(hAPP(c_COMBS(U_16455,tc_fun(U_16456,tc_HOL_Obool),tc_fun(U_16456,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16456,tc_HOL_Obool),tc_fun(tc_fun(U_16456,tc_HOL_Obool),tc_fun(U_16456,tc_HOL_Obool)),U_16455),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16456,tc_HOL_Obool))),U_16458)),U_16459)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16456,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16455,tc_fun(U_16456,tc_HOL_Obool)),U_16457),U_16458)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16455,tc_fun(U_16456,tc_HOL_Obool)),U_16457),U_16459)),
    inference(definitional_conversion,[status(esa)],[f_4050_2]) ).

cnf(f_4050_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16455,tc_fun(U_16456,tc_HOL_Obool)),U_16457),hAPP(hAPP(c_COMBS(U_16455,tc_fun(U_16456,tc_HOL_Obool),tc_fun(U_16456,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16456,tc_HOL_Obool),tc_fun(tc_fun(U_16456,tc_HOL_Obool),tc_fun(U_16456,tc_HOL_Obool)),U_16455),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16456,tc_HOL_Obool))),U_16458)),U_16459)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16456,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16455,tc_fun(U_16456,tc_HOL_Obool)),U_16457),U_16458)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16455,tc_fun(U_16456,tc_HOL_Obool)),U_16457),U_16459)),
    inference(clausify,[status(thm)],[f_4050_3]) ).

fof(f_4051_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_4051_2,plain,
    ! [U_16465,U_16464,U_16463,U_16462,U_16461,U_16460] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16461,U_16460),U_16462),hAPP(hAPP(c_COMBB(tc_fun(U_16463,U_16460),U_16460,U_16461),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16463,U_16460),U_16464)),U_16465)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16463,U_16460),U_16464),hAPP(hAPP(c_COMBB(tc_fun(U_16461,U_16460),U_16460,U_16463),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16461,U_16460),U_16462)),hAPP(c_COMBC(U_16461,U_16463,U_16460),U_16465)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16460) ),
    inference(variable_rename,[status(thm)],[f_4051_1]) ).

fof(f_4051_3,plain,
    ! [U_16460,U_16461,U_16462,U_16463,U_16464,U_16465] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16461,U_16460),U_16462),hAPP(hAPP(c_COMBB(tc_fun(U_16463,U_16460),U_16460,U_16461),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16463,U_16460),U_16464)),U_16465)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16463,U_16460),U_16464),hAPP(hAPP(c_COMBB(tc_fun(U_16461,U_16460),U_16460,U_16463),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16461,U_16460),U_16462)),hAPP(c_COMBC(U_16461,U_16463,U_16460),U_16465)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16460) ),
    inference(definitional_conversion,[status(esa)],[f_4051_2]) ).

cnf(f_4051_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16461,U_16460),U_16462),hAPP(hAPP(c_COMBB(tc_fun(U_16463,U_16460),U_16460,U_16461),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16463,U_16460),U_16464)),U_16465)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16463,U_16460),U_16464),hAPP(hAPP(c_COMBB(tc_fun(U_16461,U_16460),U_16460,U_16463),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16461,U_16460),U_16462)),hAPP(c_COMBC(U_16461,U_16463,U_16460),U_16465)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16460) ),
    inference(clausify,[status(thm)],[f_4051_3]) ).

fof(f_4052_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_4052_2,plain,
    ! [U_16471,U_16470,U_16469,U_16468,U_16467,U_16466] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16467,tc_fun(U_16468,U_16466)),U_16469),U_16470),U_16471) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16467,U_16466),U_16469),hAPP(hAPP(c_COMBC(U_16467,U_16468,U_16466),U_16470),U_16471))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16466) ),
    inference(variable_rename,[status(thm)],[f_4052_1]) ).

fof(f_4052_3,plain,
    ! [U_16466,U_16467,U_16468,U_16469,U_16470,U_16471] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16467,tc_fun(U_16468,U_16466)),U_16469),U_16470),U_16471) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16467,U_16466),U_16469),hAPP(hAPP(c_COMBC(U_16467,U_16468,U_16466),U_16470),U_16471))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16466) ),
    inference(definitional_conversion,[status(esa)],[f_4052_2]) ).

cnf(f_4052_4,plain,
    ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16467,tc_fun(U_16468,U_16466)),U_16469),U_16470),U_16471) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16467,U_16466),U_16469),hAPP(hAPP(c_COMBC(U_16467,U_16468,U_16466),U_16470),U_16471))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16466) ),
    inference(clausify,[status(thm)],[f_4052_3]) ).

fof(f_4053_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_4053_2,plain,
    ! [U_16475,U_16474,U_16473,U_16472] : hAPP(c_Relation_Oconverse(U_16472,U_16472),hAPP(hAPP(c_Relation_Oinv__image(U_16473,U_16472),U_16474),U_16475)) = hAPP(hAPP(c_Relation_Oinv__image(U_16473,U_16472),hAPP(c_Relation_Oconverse(U_16473,U_16473),U_16474)),U_16475),
    inference(variable_rename,[status(thm)],[f_4053_1]) ).

fof(f_4053_3,plain,
    ! [U_16473,U_16472,U_16474,U_16475] : hAPP(c_Relation_Oconverse(U_16472,U_16472),hAPP(hAPP(c_Relation_Oinv__image(U_16473,U_16472),U_16474),U_16475)) = hAPP(hAPP(c_Relation_Oinv__image(U_16473,U_16472),hAPP(c_Relation_Oconverse(U_16473,U_16473),U_16474)),U_16475),
    inference(definitional_conversion,[status(esa)],[f_4053_2]) ).

cnf(f_4053_4,plain,
    hAPP(c_Relation_Oconverse(U_16472,U_16472),hAPP(hAPP(c_Relation_Oinv__image(U_16473,U_16472),U_16474),U_16475)) = hAPP(hAPP(c_Relation_Oinv__image(U_16473,U_16472),hAPP(c_Relation_Oconverse(U_16473,U_16473),U_16474)),U_16475),
    inference(clausify,[status(thm)],[f_4053_3]) ).

fof(f_4054_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_4054_2,plain,
    ! [U_16477,U_16476] : hAPP(c_Relation_OField(U_16476),hAPP(c_Relation_Oconverse(U_16476,U_16476),U_16477)) = hAPP(c_Relation_OField(U_16476),U_16477),
    inference(variable_rename,[status(thm)],[f_4054_1]) ).

fof(f_4054_3,plain,
    ! [U_16476,U_16477] : hAPP(c_Relation_OField(U_16476),hAPP(c_Relation_Oconverse(U_16476,U_16476),U_16477)) = hAPP(c_Relation_OField(U_16476),U_16477),
    inference(definitional_conversion,[status(esa)],[f_4054_2]) ).

cnf(f_4054_4,plain,
    hAPP(c_Relation_OField(U_16476),hAPP(c_Relation_Oconverse(U_16476,U_16476),U_16477)) = hAPP(c_Relation_OField(U_16476),U_16477),
    inference(clausify,[status(thm)],[f_4054_3]) ).

fof(f_4055_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_4055_2,plain,
    ! [U_16482,U_16481,U_16480,U_16479,U_16478] : hAPP(c_Relation_Oconverse(U_16478,U_16479),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16480,tc_fun(tc_prod(U_16478,U_16479),tc_HOL_Obool)),U_16481),U_16482)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16480,tc_fun(tc_prod(U_16479,U_16478),tc_HOL_Obool)),U_16481),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16478,U_16479),tc_HOL_Obool),tc_fun(tc_prod(U_16479,U_16478),tc_HOL_Obool),U_16480),c_Relation_Oconverse(U_16478,U_16479)),U_16482)),
    inference(variable_rename,[status(thm)],[f_4055_1]) ).

fof(f_4055_3,plain,
    ! [U_16478,U_16479,U_16480,U_16481,U_16482] : hAPP(c_Relation_Oconverse(U_16478,U_16479),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16480,tc_fun(tc_prod(U_16478,U_16479),tc_HOL_Obool)),U_16481),U_16482)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16480,tc_fun(tc_prod(U_16479,U_16478),tc_HOL_Obool)),U_16481),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16478,U_16479),tc_HOL_Obool),tc_fun(tc_prod(U_16479,U_16478),tc_HOL_Obool),U_16480),c_Relation_Oconverse(U_16478,U_16479)),U_16482)),
    inference(definitional_conversion,[status(esa)],[f_4055_2]) ).

cnf(f_4055_4,plain,
    hAPP(c_Relation_Oconverse(U_16478,U_16479),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16480,tc_fun(tc_prod(U_16478,U_16479),tc_HOL_Obool)),U_16481),U_16482)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16480,tc_fun(tc_prod(U_16479,U_16478),tc_HOL_Obool)),U_16481),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16478,U_16479),tc_HOL_Obool),tc_fun(tc_prod(U_16479,U_16478),tc_HOL_Obool),U_16480),c_Relation_Oconverse(U_16478,U_16479)),U_16482)),
    inference(clausify,[status(thm)],[f_4055_3]) ).

fof(f_4056_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_4056_2,plain,
    ! [U_16485,U_16484,U_16483] : hAPP(c_Relation_Oconverse(U_16483,U_16484),hAPP(c_Relation_Oconverse(U_16484,U_16483),U_16485)) = U_16485,
    inference(variable_rename,[status(thm)],[f_4056_1]) ).

fof(f_4056_3,plain,
    ! [U_16483,U_16484,U_16485] : hAPP(c_Relation_Oconverse(U_16483,U_16484),hAPP(c_Relation_Oconverse(U_16484,U_16483),U_16485)) = U_16485,
    inference(definitional_conversion,[status(esa)],[f_4056_2]) ).

cnf(f_4056_4,plain,
    hAPP(c_Relation_Oconverse(U_16483,U_16484),hAPP(c_Relation_Oconverse(U_16484,U_16483),U_16485)) = U_16485,
    inference(clausify,[status(thm)],[f_4056_3]) ).

fof(f_4057_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_4057_2,plain,
    ! [U_16486] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16486,tc_HOL_Obool) = c_Set_OBall(U_16486),
    inference(variable_rename,[status(thm)],[f_4057_1]) ).

fof(f_4057_3,plain,
    ! [U_16486] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16486,tc_HOL_Obool) = c_Set_OBall(U_16486),
    inference(definitional_conversion,[status(esa)],[f_4057_2]) ).

cnf(f_4057_4,plain,
    c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16486,tc_HOL_Obool) = c_Set_OBall(U_16486),
    inference(clausify,[status(thm)],[f_4057_3]) ).

fof(f_4058_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_4058_2,plain,
    ! [U_16489,U_16488,U_16487] :
      ( ( c_Relation_Orefl__on(U_16487,U_16488,hAPP(c_Relation_Oconverse(U_16487,U_16487),U_16489))
        | ~ c_Relation_Orefl__on(U_16487,U_16488,U_16489) )
      & ( c_Relation_Orefl__on(U_16487,U_16488,U_16489)
        | ~ c_Relation_Orefl__on(U_16487,U_16488,hAPP(c_Relation_Oconverse(U_16487,U_16487),U_16489)) ) ),
    inference(variable_rename,[status(thm)],[f_4058_1]) ).

fof(f_4058_3,plain,
    ( ! [U_16495,U_16493,U_16491] :
        ( c_Relation_Orefl__on(U_16491,U_16493,hAPP(c_Relation_Oconverse(U_16491,U_16491),U_16495))
        | ~ c_Relation_Orefl__on(U_16491,U_16493,U_16495) )
    & ! [U_16494,U_16492,U_16490] :
        ( c_Relation_Orefl__on(U_16490,U_16492,U_16494)
        | ~ c_Relation_Orefl__on(U_16490,U_16492,hAPP(c_Relation_Oconverse(U_16490,U_16490),U_16494)) ) ),
    inference(miniscope,[status(thm)],[f_4058_2]) ).

fof(f_4058_4,plain,
    ( ! [U_16495,U_16493,U_16491] :
        ( c_Relation_Orefl__on(U_16491,U_16493,hAPP(c_Relation_Oconverse(U_16491,U_16491),U_16495))
        | ~ c_Relation_Orefl__on(U_16491,U_16493,U_16495) )
    & ! [U_16492,U_16490,U_16494] :
        ( c_Relation_Orefl__on(U_16490,U_16492,U_16494)
        | ~ c_Relation_Orefl__on(U_16490,U_16492,hAPP(c_Relation_Oconverse(U_16490,U_16490),U_16494)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4058_3]) ).

cnf(f_4058_5,plain,
    ( c_Relation_Orefl__on(U_16490,U_16492,U_16494)
    | ~ c_Relation_Orefl__on(U_16490,U_16492,hAPP(c_Relation_Oconverse(U_16490,U_16490),U_16494)) ),
    inference(clausify,[status(thm)],[f_4058_4]) ).

cnf(f_4058_6,plain,
    ( c_Relation_Orefl__on(U_16491,U_16493,hAPP(c_Relation_Oconverse(U_16491,U_16491),U_16495))
    | ~ c_Relation_Orefl__on(U_16491,U_16493,U_16495) ),
    inference(clausify,[status(thm)],[f_4058_4]) ).

fof(f_4059_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_4059_2,plain,
    ! [U_16497,U_16496] : hAPP(c_Relation_Oconverse(U_16496,U_16496),c_Relation_OId__on(U_16496,U_16497)) = c_Relation_OId__on(U_16496,U_16497),
    inference(variable_rename,[status(thm)],[f_4059_1]) ).

fof(f_4059_3,plain,
    ! [U_16496,U_16497] : hAPP(c_Relation_Oconverse(U_16496,U_16496),c_Relation_OId__on(U_16496,U_16497)) = c_Relation_OId__on(U_16496,U_16497),
    inference(definitional_conversion,[status(esa)],[f_4059_2]) ).

cnf(f_4059_4,plain,
    hAPP(c_Relation_Oconverse(U_16496,U_16496),c_Relation_OId__on(U_16496,U_16497)) = c_Relation_OId__on(U_16496,U_16497),
    inference(clausify,[status(thm)],[f_4059_3]) ).

fof(f_4060_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_4060_2,plain,
    ! [U_16501,U_16500,U_16499,U_16498] : hAPP(c_Set_OPow(U_16498),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16499,tc_fun(U_16498,tc_HOL_Obool)),U_16500),U_16501)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16499,tc_fun(tc_fun(U_16498,tc_HOL_Obool),tc_HOL_Obool)),U_16500),hAPP(hAPP(c_COMBB(tc_fun(U_16498,tc_HOL_Obool),tc_fun(tc_fun(U_16498,tc_HOL_Obool),tc_HOL_Obool),U_16499),c_Set_OPow(U_16498)),U_16501)),
    inference(variable_rename,[status(thm)],[f_4060_1]) ).

fof(f_4060_3,plain,
    ! [U_16498,U_16499,U_16500,U_16501] : hAPP(c_Set_OPow(U_16498),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16499,tc_fun(U_16498,tc_HOL_Obool)),U_16500),U_16501)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16499,tc_fun(tc_fun(U_16498,tc_HOL_Obool),tc_HOL_Obool)),U_16500),hAPP(hAPP(c_COMBB(tc_fun(U_16498,tc_HOL_Obool),tc_fun(tc_fun(U_16498,tc_HOL_Obool),tc_HOL_Obool),U_16499),c_Set_OPow(U_16498)),U_16501)),
    inference(definitional_conversion,[status(esa)],[f_4060_2]) ).

cnf(f_4060_4,plain,
    hAPP(c_Set_OPow(U_16498),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16499,tc_fun(U_16498,tc_HOL_Obool)),U_16500),U_16501)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16499,tc_fun(tc_fun(U_16498,tc_HOL_Obool),tc_HOL_Obool)),U_16500),hAPP(hAPP(c_COMBB(tc_fun(U_16498,tc_HOL_Obool),tc_fun(tc_fun(U_16498,tc_HOL_Obool),tc_HOL_Obool),U_16499),c_Set_OPow(U_16498)),U_16501)),
    inference(clausify,[status(thm)],[f_4060_3]) ).

fof(f_4061_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_4061_2,plain,
    ! [U_16505,U_16504,U_16503,U_16502] : hAPP(c_Set_OCollect(U_16502),hAPP(hAPP(c_COMBB(tc_fun(U_16503,tc_HOL_Obool),tc_HOL_Obool,U_16502),c_HOL_OAll(U_16503)),hAPP(hAPP(c_COMBB(tc_fun(U_16503,tc_HOL_Obool),tc_fun(U_16503,tc_HOL_Obool),U_16502),hAPP(c_COMBS(U_16503,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16503),c_fimplies),hAPP(hAPP(c_COMBC(U_16503,tc_fun(U_16503,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16503)),U_16504)))),U_16505))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16503,tc_fun(U_16502,tc_HOL_Obool)),U_16504),hAPP(hAPP(c_COMBB(tc_fun(U_16502,tc_HOL_Obool),tc_fun(U_16502,tc_HOL_Obool),U_16503),c_Set_OCollect(U_16502)),hAPP(c_COMBC(U_16502,U_16503,tc_HOL_Obool),U_16505))),
    inference(variable_rename,[status(thm)],[f_4061_1]) ).

fof(f_4061_3,plain,
    ! [U_16502,U_16503,U_16504,U_16505] : hAPP(c_Set_OCollect(U_16502),hAPP(hAPP(c_COMBB(tc_fun(U_16503,tc_HOL_Obool),tc_HOL_Obool,U_16502),c_HOL_OAll(U_16503)),hAPP(hAPP(c_COMBB(tc_fun(U_16503,tc_HOL_Obool),tc_fun(U_16503,tc_HOL_Obool),U_16502),hAPP(c_COMBS(U_16503,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16503),c_fimplies),hAPP(hAPP(c_COMBC(U_16503,tc_fun(U_16503,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16503)),U_16504)))),U_16505))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16503,tc_fun(U_16502,tc_HOL_Obool)),U_16504),hAPP(hAPP(c_COMBB(tc_fun(U_16502,tc_HOL_Obool),tc_fun(U_16502,tc_HOL_Obool),U_16503),c_Set_OCollect(U_16502)),hAPP(c_COMBC(U_16502,U_16503,tc_HOL_Obool),U_16505))),
    inference(definitional_conversion,[status(esa)],[f_4061_2]) ).

cnf(f_4061_4,plain,
    hAPP(c_Set_OCollect(U_16502),hAPP(hAPP(c_COMBB(tc_fun(U_16503,tc_HOL_Obool),tc_HOL_Obool,U_16502),c_HOL_OAll(U_16503)),hAPP(hAPP(c_COMBB(tc_fun(U_16503,tc_HOL_Obool),tc_fun(U_16503,tc_HOL_Obool),U_16502),hAPP(c_COMBS(U_16503,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16503),c_fimplies),hAPP(hAPP(c_COMBC(U_16503,tc_fun(U_16503,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16503)),U_16504)))),U_16505))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16503,tc_fun(U_16502,tc_HOL_Obool)),U_16504),hAPP(hAPP(c_COMBB(tc_fun(U_16502,tc_HOL_Obool),tc_fun(U_16502,tc_HOL_Obool),U_16503),c_Set_OCollect(U_16502)),hAPP(c_COMBC(U_16502,U_16503,tc_HOL_Obool),U_16505))),
    inference(clausify,[status(thm)],[f_4061_3]) ).

fof(f_4062_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_4062_2,plain,
    ! [U_16510,U_16509,U_16508,U_16507,U_16506] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16506,tc_HOL_Obool)),U_16507),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16508,tc_fun(U_16506,tc_HOL_Obool)),U_16509),U_16510)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16508,tc_fun(U_16506,tc_HOL_Obool)),U_16509),hAPP(hAPP(c_COMBB(tc_fun(U_16506,tc_HOL_Obool),tc_fun(U_16506,tc_HOL_Obool),U_16508),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16506,tc_HOL_Obool)),U_16507)),U_16510)),
    inference(variable_rename,[status(thm)],[f_4062_1]) ).

fof(f_4062_3,plain,
    ! [U_16507,U_16506,U_16508,U_16509,U_16510] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16506,tc_HOL_Obool)),U_16507),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16508,tc_fun(U_16506,tc_HOL_Obool)),U_16509),U_16510)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16508,tc_fun(U_16506,tc_HOL_Obool)),U_16509),hAPP(hAPP(c_COMBB(tc_fun(U_16506,tc_HOL_Obool),tc_fun(U_16506,tc_HOL_Obool),U_16508),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16506,tc_HOL_Obool)),U_16507)),U_16510)),
    inference(definitional_conversion,[status(esa)],[f_4062_2]) ).

cnf(f_4062_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16506,tc_HOL_Obool)),U_16507),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16508,tc_fun(U_16506,tc_HOL_Obool)),U_16509),U_16510)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16508,tc_fun(U_16506,tc_HOL_Obool)),U_16509),hAPP(hAPP(c_COMBB(tc_fun(U_16506,tc_HOL_Obool),tc_fun(U_16506,tc_HOL_Obool),U_16508),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16506,tc_HOL_Obool)),U_16507)),U_16510)),
    inference(clausify,[status(thm)],[f_4062_3]) ).

fof(f_4063_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_4063_2,plain,
    ! [U_16515,U_16514,U_16513,U_16512,U_16511] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16511,tc_fun(U_16512,tc_HOL_Obool)),U_16513),hAPP(hAPP(c_COMBB(tc_fun(U_16512,tc_HOL_Obool),tc_fun(U_16512,tc_HOL_Obool),U_16511),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16512,tc_HOL_Obool)),U_16514)),U_16515)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16512,tc_HOL_Obool)),U_16514),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16511,tc_fun(U_16512,tc_HOL_Obool)),U_16513),U_16515)),
    inference(variable_rename,[status(thm)],[f_4063_1]) ).

fof(f_4063_3,plain,
    ! [U_16511,U_16512,U_16513,U_16514,U_16515] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16511,tc_fun(U_16512,tc_HOL_Obool)),U_16513),hAPP(hAPP(c_COMBB(tc_fun(U_16512,tc_HOL_Obool),tc_fun(U_16512,tc_HOL_Obool),U_16511),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16512,tc_HOL_Obool)),U_16514)),U_16515)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16512,tc_HOL_Obool)),U_16514),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16511,tc_fun(U_16512,tc_HOL_Obool)),U_16513),U_16515)),
    inference(definitional_conversion,[status(esa)],[f_4063_2]) ).

cnf(f_4063_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16511,tc_fun(U_16512,tc_HOL_Obool)),U_16513),hAPP(hAPP(c_COMBB(tc_fun(U_16512,tc_HOL_Obool),tc_fun(U_16512,tc_HOL_Obool),U_16511),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16512,tc_HOL_Obool)),U_16514)),U_16515)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16512,tc_HOL_Obool)),U_16514),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16511,tc_fun(U_16512,tc_HOL_Obool)),U_16513),U_16515)),
    inference(clausify,[status(thm)],[f_4063_3]) ).

fof(f_4064_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_4064_2,plain,
    ! [U_16520,U_16519,U_16518,U_16517,U_16516] : hAPP(c_Relation_Oconverse(U_16516,U_16517),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16518,tc_fun(tc_prod(U_16516,U_16517),tc_HOL_Obool)),U_16519),U_16520)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16518,tc_fun(tc_prod(U_16517,U_16516),tc_HOL_Obool)),U_16519),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16516,U_16517),tc_HOL_Obool),tc_fun(tc_prod(U_16517,U_16516),tc_HOL_Obool),U_16518),c_Relation_Oconverse(U_16516,U_16517)),U_16520)),
    inference(variable_rename,[status(thm)],[f_4064_1]) ).

fof(f_4064_3,plain,
    ! [U_16516,U_16517,U_16518,U_16519,U_16520] : hAPP(c_Relation_Oconverse(U_16516,U_16517),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16518,tc_fun(tc_prod(U_16516,U_16517),tc_HOL_Obool)),U_16519),U_16520)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16518,tc_fun(tc_prod(U_16517,U_16516),tc_HOL_Obool)),U_16519),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16516,U_16517),tc_HOL_Obool),tc_fun(tc_prod(U_16517,U_16516),tc_HOL_Obool),U_16518),c_Relation_Oconverse(U_16516,U_16517)),U_16520)),
    inference(definitional_conversion,[status(esa)],[f_4064_2]) ).

cnf(f_4064_4,plain,
    hAPP(c_Relation_Oconverse(U_16516,U_16517),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16518,tc_fun(tc_prod(U_16516,U_16517),tc_HOL_Obool)),U_16519),U_16520)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16518,tc_fun(tc_prod(U_16517,U_16516),tc_HOL_Obool)),U_16519),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16516,U_16517),tc_HOL_Obool),tc_fun(tc_prod(U_16517,U_16516),tc_HOL_Obool),U_16518),c_Relation_Oconverse(U_16516,U_16517)),U_16520)),
    inference(clausify,[status(thm)],[f_4064_3]) ).

fof(f_4065_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_4065_2,plain,
    ! [U_16526,U_16525,U_16524,U_16523,U_16522,U_16521] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16521,tc_fun(U_16522,tc_HOL_Obool)),U_16523),hAPP(hAPP(c_COMBC(U_16521,tc_fun(U_16524,tc_fun(U_16522,tc_HOL_Obool)),tc_fun(U_16522,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16524,tc_HOL_Obool),tc_fun(tc_fun(U_16524,tc_fun(U_16522,tc_HOL_Obool)),tc_fun(U_16522,tc_HOL_Obool)),U_16521),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16524,tc_fun(U_16522,tc_HOL_Obool))),U_16525)),U_16526)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16524,tc_fun(U_16522,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16521,tc_fun(U_16524,tc_HOL_Obool)),U_16523),U_16525)),U_16526),
    inference(variable_rename,[status(thm)],[f_4065_1]) ).

fof(f_4065_3,plain,
    ! [U_16521,U_16522,U_16523,U_16524,U_16525,U_16526] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16521,tc_fun(U_16522,tc_HOL_Obool)),U_16523),hAPP(hAPP(c_COMBC(U_16521,tc_fun(U_16524,tc_fun(U_16522,tc_HOL_Obool)),tc_fun(U_16522,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16524,tc_HOL_Obool),tc_fun(tc_fun(U_16524,tc_fun(U_16522,tc_HOL_Obool)),tc_fun(U_16522,tc_HOL_Obool)),U_16521),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16524,tc_fun(U_16522,tc_HOL_Obool))),U_16525)),U_16526)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16524,tc_fun(U_16522,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16521,tc_fun(U_16524,tc_HOL_Obool)),U_16523),U_16525)),U_16526),
    inference(definitional_conversion,[status(esa)],[f_4065_2]) ).

cnf(f_4065_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16521,tc_fun(U_16522,tc_HOL_Obool)),U_16523),hAPP(hAPP(c_COMBC(U_16521,tc_fun(U_16524,tc_fun(U_16522,tc_HOL_Obool)),tc_fun(U_16522,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16524,tc_HOL_Obool),tc_fun(tc_fun(U_16524,tc_fun(U_16522,tc_HOL_Obool)),tc_fun(U_16522,tc_HOL_Obool)),U_16521),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16524,tc_fun(U_16522,tc_HOL_Obool))),U_16525)),U_16526)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16524,tc_fun(U_16522,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16521,tc_fun(U_16524,tc_HOL_Obool)),U_16523),U_16525)),U_16526),
    inference(clausify,[status(thm)],[f_4065_3]) ).

fof(f_4066_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_4066_2,plain,
    ! [U_16532,U_16531,U_16530,U_16529,U_16528,U_16527] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16527,tc_fun(U_16528,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16529,tc_fun(U_16527,tc_HOL_Obool)),U_16530),U_16531)),U_16532) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16529,tc_fun(U_16528,tc_HOL_Obool)),U_16530),hAPP(hAPP(c_COMBC(U_16529,tc_fun(U_16527,tc_fun(U_16528,tc_HOL_Obool)),tc_fun(U_16528,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16527,tc_HOL_Obool),tc_fun(tc_fun(U_16527,tc_fun(U_16528,tc_HOL_Obool)),tc_fun(U_16528,tc_HOL_Obool)),U_16529),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16527,tc_fun(U_16528,tc_HOL_Obool))),U_16531)),U_16532)),
    inference(variable_rename,[status(thm)],[f_4066_1]) ).

fof(f_4066_3,plain,
    ! [U_16527,U_16528,U_16529,U_16530,U_16531,U_16532] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16527,tc_fun(U_16528,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16529,tc_fun(U_16527,tc_HOL_Obool)),U_16530),U_16531)),U_16532) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16529,tc_fun(U_16528,tc_HOL_Obool)),U_16530),hAPP(hAPP(c_COMBC(U_16529,tc_fun(U_16527,tc_fun(U_16528,tc_HOL_Obool)),tc_fun(U_16528,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16527,tc_HOL_Obool),tc_fun(tc_fun(U_16527,tc_fun(U_16528,tc_HOL_Obool)),tc_fun(U_16528,tc_HOL_Obool)),U_16529),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16527,tc_fun(U_16528,tc_HOL_Obool))),U_16531)),U_16532)),
    inference(definitional_conversion,[status(esa)],[f_4066_2]) ).

cnf(f_4066_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16527,tc_fun(U_16528,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16529,tc_fun(U_16527,tc_HOL_Obool)),U_16530),U_16531)),U_16532) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16529,tc_fun(U_16528,tc_HOL_Obool)),U_16530),hAPP(hAPP(c_COMBC(U_16529,tc_fun(U_16527,tc_fun(U_16528,tc_HOL_Obool)),tc_fun(U_16528,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16527,tc_HOL_Obool),tc_fun(tc_fun(U_16527,tc_fun(U_16528,tc_HOL_Obool)),tc_fun(U_16528,tc_HOL_Obool)),U_16529),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16527,tc_fun(U_16528,tc_HOL_Obool))),U_16531)),U_16532)),
    inference(clausify,[status(thm)],[f_4066_3]) ).

fof(f_4067_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_4067_2,plain,
    ! [U_16536,U_16535,U_16534,U_16533] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16533,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16534,tc_fun(U_16533,tc_HOL_Obool)),U_16535),U_16536)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16534,tc_fun(U_16533,tc_HOL_Obool)),U_16535),hAPP(hAPP(c_COMBB(tc_fun(U_16533,tc_HOL_Obool),tc_fun(U_16533,tc_HOL_Obool),U_16534),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16533,tc_HOL_Obool))),U_16536)),
    inference(variable_rename,[status(thm)],[f_4067_1]) ).

fof(f_4067_3,plain,
    ! [U_16533,U_16534,U_16535,U_16536] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16533,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16534,tc_fun(U_16533,tc_HOL_Obool)),U_16535),U_16536)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16534,tc_fun(U_16533,tc_HOL_Obool)),U_16535),hAPP(hAPP(c_COMBB(tc_fun(U_16533,tc_HOL_Obool),tc_fun(U_16533,tc_HOL_Obool),U_16534),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16533,tc_HOL_Obool))),U_16536)),
    inference(definitional_conversion,[status(esa)],[f_4067_2]) ).

cnf(f_4067_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16533,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16534,tc_fun(U_16533,tc_HOL_Obool)),U_16535),U_16536)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16534,tc_fun(U_16533,tc_HOL_Obool)),U_16535),hAPP(hAPP(c_COMBB(tc_fun(U_16533,tc_HOL_Obool),tc_fun(U_16533,tc_HOL_Obool),U_16534),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16533,tc_HOL_Obool))),U_16536)),
    inference(clausify,[status(thm)],[f_4067_3]) ).

fof(f_4068_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_4068_2,plain,
    ! [U_16540,U_16539,U_16538,U_16537] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16537,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16538,tc_fun(U_16537,tc_HOL_Obool)),U_16539),U_16540)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16538,tc_fun(U_16537,tc_HOL_Obool)),U_16539),hAPP(hAPP(c_COMBB(tc_fun(U_16537,tc_HOL_Obool),tc_fun(U_16537,tc_HOL_Obool),U_16538),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16537,tc_HOL_Obool))),U_16540)),
    inference(variable_rename,[status(thm)],[f_4068_1]) ).

fof(f_4068_3,plain,
    ! [U_16537,U_16538,U_16539,U_16540] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16537,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16538,tc_fun(U_16537,tc_HOL_Obool)),U_16539),U_16540)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16538,tc_fun(U_16537,tc_HOL_Obool)),U_16539),hAPP(hAPP(c_COMBB(tc_fun(U_16537,tc_HOL_Obool),tc_fun(U_16537,tc_HOL_Obool),U_16538),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16537,tc_HOL_Obool))),U_16540)),
    inference(definitional_conversion,[status(esa)],[f_4068_2]) ).

cnf(f_4068_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16537,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16538,tc_fun(U_16537,tc_HOL_Obool)),U_16539),U_16540)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16538,tc_fun(U_16537,tc_HOL_Obool)),U_16539),hAPP(hAPP(c_COMBB(tc_fun(U_16537,tc_HOL_Obool),tc_fun(U_16537,tc_HOL_Obool),U_16538),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16537,tc_HOL_Obool))),U_16540)),
    inference(clausify,[status(thm)],[f_4068_3]) ).

fof(f_4069_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_4069_2,plain,
    ! [U_16543,U_16542,U_16541] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_16541,U_16541,U_16541),hAPP(c_Relation_Oconverse(U_16541,U_16541),U_16543)),U_16543) = U_16543
      | ~ c_Equiv__Relations_Oequiv(U_16541,U_16542,U_16543) ),
    inference(variable_rename,[status(thm)],[f_4069_1]) ).

fof(f_4069_3,plain,
    ! [U_16541,U_16542,U_16543] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_16541,U_16541,U_16541),hAPP(c_Relation_Oconverse(U_16541,U_16541),U_16543)),U_16543) = U_16543
      | ~ c_Equiv__Relations_Oequiv(U_16541,U_16542,U_16543) ),
    inference(definitional_conversion,[status(esa)],[f_4069_2]) ).

cnf(f_4069_4,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_16541,U_16541,U_16541),hAPP(c_Relation_Oconverse(U_16541,U_16541),U_16543)),U_16543) = U_16543
    | ~ c_Equiv__Relations_Oequiv(U_16541,U_16542,U_16543) ),
    inference(clausify,[status(thm)],[f_4069_3]) ).

fof(f_4070_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_4070_2,plain,
    ! [U_16546,U_16545,U_16544] : hAPP(c_Relation_ORange(U_16544,U_16545),hAPP(c_Relation_Oconverse(U_16545,U_16544),U_16546)) = hAPP(c_Relation_ODomain(U_16545,U_16544),U_16546),
    inference(variable_rename,[status(thm)],[f_4070_1]) ).

fof(f_4070_3,plain,
    ! [U_16544,U_16545,U_16546] : hAPP(c_Relation_ORange(U_16544,U_16545),hAPP(c_Relation_Oconverse(U_16545,U_16544),U_16546)) = hAPP(c_Relation_ODomain(U_16545,U_16544),U_16546),
    inference(definitional_conversion,[status(esa)],[f_4070_2]) ).

cnf(f_4070_4,plain,
    hAPP(c_Relation_ORange(U_16544,U_16545),hAPP(c_Relation_Oconverse(U_16545,U_16544),U_16546)) = hAPP(c_Relation_ODomain(U_16545,U_16544),U_16546),
    inference(clausify,[status(thm)],[f_4070_3]) ).

fof(f_4071_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_4071_2,plain,
    ! [U_16549,U_16548,U_16547] : hAPP(c_Relation_ODomain(U_16547,U_16548),hAPP(c_Relation_Oconverse(U_16548,U_16547),U_16549)) = hAPP(c_Relation_ORange(U_16548,U_16547),U_16549),
    inference(variable_rename,[status(thm)],[f_4071_1]) ).

fof(f_4071_3,plain,
    ! [U_16547,U_16548,U_16549] : hAPP(c_Relation_ODomain(U_16547,U_16548),hAPP(c_Relation_Oconverse(U_16548,U_16547),U_16549)) = hAPP(c_Relation_ORange(U_16548,U_16547),U_16549),
    inference(definitional_conversion,[status(esa)],[f_4071_2]) ).

cnf(f_4071_4,plain,
    hAPP(c_Relation_ODomain(U_16547,U_16548),hAPP(c_Relation_Oconverse(U_16548,U_16547),U_16549)) = hAPP(c_Relation_ORange(U_16548,U_16547),U_16549),
    inference(clausify,[status(thm)],[f_4071_3]) ).

fof(f_4072_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_4072_2,plain,
    ! [U_16552,U_16551,U_16550] : hAPP(c_Relation_ORange(U_16550,U_16551),U_16552) = hAPP(c_Relation_ODomain(U_16551,U_16550),hAPP(c_Relation_Oconverse(U_16550,U_16551),U_16552)),
    inference(variable_rename,[status(thm)],[f_4072_1]) ).

fof(f_4072_3,plain,
    ! [U_16550,U_16551,U_16552] : hAPP(c_Relation_ORange(U_16550,U_16551),U_16552) = hAPP(c_Relation_ODomain(U_16551,U_16550),hAPP(c_Relation_Oconverse(U_16550,U_16551),U_16552)),
    inference(definitional_conversion,[status(esa)],[f_4072_2]) ).

cnf(f_4072_4,plain,
    hAPP(c_Relation_ORange(U_16550,U_16551),U_16552) = hAPP(c_Relation_ODomain(U_16551,U_16550),hAPP(c_Relation_Oconverse(U_16550,U_16551),U_16552)),
    inference(clausify,[status(thm)],[f_4072_3]) ).

fof(f_4073_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_4073_2,plain,
    ! [U_16557,U_16556,U_16555,U_16554,U_16553] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16553),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16554,U_16553),U_16556),U_16557)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16554,U_16553),U_16555),U_16557)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16554,tc_HOL_Obool)),U_16555),U_16556))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16553) ),
    inference(variable_rename,[status(thm)],[f_4073_1]) ).

fof(f_4073_3,plain,
    ! [U_16553,U_16554,U_16555,U_16556,U_16557] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16553),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16554,U_16553),U_16556),U_16557)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16554,U_16553),U_16555),U_16557)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16554,tc_HOL_Obool)),U_16555),U_16556))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16553) ),
    inference(definitional_conversion,[status(esa)],[f_4073_2]) ).

cnf(f_4073_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16553),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16554,U_16553),U_16556),U_16557)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16554,U_16553),U_16555),U_16557)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16554,tc_HOL_Obool)),U_16555),U_16556))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16553) ),
    inference(clausify,[status(thm)],[f_4073_3]) ).

fof(f_4074_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_4074_2,plain,
    ! [U_16561,U_16560,U_16559,U_16558] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16558,tc_fun(U_16559,tc_HOL_Obool)),U_16560),U_16561) = hAPP(c_Set_OCollect(U_16559),hAPP(hAPP(c_COMBB(tc_fun(U_16558,tc_HOL_Obool),tc_HOL_Obool,U_16559),c_HOL_OAll(U_16558)),hAPP(hAPP(c_COMBB(tc_fun(U_16558,tc_HOL_Obool),tc_fun(U_16558,tc_HOL_Obool),U_16559),hAPP(c_COMBS(U_16558,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16558),c_fimplies),hAPP(hAPP(c_COMBC(U_16558,tc_fun(U_16558,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16558)),U_16560)))),hAPP(hAPP(c_COMBC(U_16559,tc_fun(U_16558,tc_fun(U_16559,tc_HOL_Obool)),tc_fun(U_16558,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16559,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_16558,tc_fun(U_16559,tc_HOL_Obool)),tc_fun(U_16558,tc_HOL_Obool)),U_16559),c_COMBB(tc_fun(U_16559,tc_HOL_Obool),tc_HOL_Obool,U_16558)),c_member(U_16559))),U_16561)))),
    inference(variable_rename,[status(thm)],[f_4074_1]) ).

fof(f_4074_3,plain,
    ! [U_16558,U_16559,U_16560,U_16561] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16558,tc_fun(U_16559,tc_HOL_Obool)),U_16560),U_16561) = hAPP(c_Set_OCollect(U_16559),hAPP(hAPP(c_COMBB(tc_fun(U_16558,tc_HOL_Obool),tc_HOL_Obool,U_16559),c_HOL_OAll(U_16558)),hAPP(hAPP(c_COMBB(tc_fun(U_16558,tc_HOL_Obool),tc_fun(U_16558,tc_HOL_Obool),U_16559),hAPP(c_COMBS(U_16558,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16558),c_fimplies),hAPP(hAPP(c_COMBC(U_16558,tc_fun(U_16558,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16558)),U_16560)))),hAPP(hAPP(c_COMBC(U_16559,tc_fun(U_16558,tc_fun(U_16559,tc_HOL_Obool)),tc_fun(U_16558,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16559,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_16558,tc_fun(U_16559,tc_HOL_Obool)),tc_fun(U_16558,tc_HOL_Obool)),U_16559),c_COMBB(tc_fun(U_16559,tc_HOL_Obool),tc_HOL_Obool,U_16558)),c_member(U_16559))),U_16561)))),
    inference(definitional_conversion,[status(esa)],[f_4074_2]) ).

cnf(f_4074_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16558,tc_fun(U_16559,tc_HOL_Obool)),U_16560),U_16561) = hAPP(c_Set_OCollect(U_16559),hAPP(hAPP(c_COMBB(tc_fun(U_16558,tc_HOL_Obool),tc_HOL_Obool,U_16559),c_HOL_OAll(U_16558)),hAPP(hAPP(c_COMBB(tc_fun(U_16558,tc_HOL_Obool),tc_fun(U_16558,tc_HOL_Obool),U_16559),hAPP(c_COMBS(U_16558,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16558),c_fimplies),hAPP(hAPP(c_COMBC(U_16558,tc_fun(U_16558,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16558)),U_16560)))),hAPP(hAPP(c_COMBC(U_16559,tc_fun(U_16558,tc_fun(U_16559,tc_HOL_Obool)),tc_fun(U_16558,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16559,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_16558,tc_fun(U_16559,tc_HOL_Obool)),tc_fun(U_16558,tc_HOL_Obool)),U_16559),c_COMBB(tc_fun(U_16559,tc_HOL_Obool),tc_HOL_Obool,U_16558)),c_member(U_16559))),U_16561)))),
    inference(clausify,[status(thm)],[f_4074_3]) ).

fof(f_4075_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_4075_2,plain,
    ! [U_16566,U_16565,U_16564,U_16563,U_16562] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16563,tc_fun(U_16564,tc_HOL_Obool)),U_16562),hAPP(hAPP(c_COMBB(tc_fun(U_16564,tc_HOL_Obool),tc_fun(U_16564,tc_HOL_Obool),U_16563),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16564,tc_HOL_Obool)),U_16565)),U_16566)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16564,tc_HOL_Obool)),U_16565),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16563,tc_fun(U_16564,tc_HOL_Obool)),U_16562),U_16566))
        | U_16562 = c_Orderings_Obot__class_Obot(tc_fun(U_16563,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16563,tc_fun(U_16564,tc_HOL_Obool)),U_16562),hAPP(hAPP(c_COMBB(tc_fun(U_16564,tc_HOL_Obool),tc_fun(U_16564,tc_HOL_Obool),U_16563),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16564,tc_HOL_Obool)),U_16565)),U_16566)) = c_Orderings_Otop__class_Otop(tc_fun(U_16564,tc_HOL_Obool))
        | U_16562 != c_Orderings_Obot__class_Obot(tc_fun(U_16563,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4075_1]) ).

fof(f_4075_3,plain,
    ( ! [U_16576,U_16574,U_16572,U_16570,U_16568] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16570,tc_fun(U_16572,tc_HOL_Obool)),U_16568),hAPP(hAPP(c_COMBB(tc_fun(U_16572,tc_HOL_Obool),tc_fun(U_16572,tc_HOL_Obool),U_16570),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16572,tc_HOL_Obool)),U_16574)),U_16576)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16572,tc_HOL_Obool)),U_16574),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16570,tc_fun(U_16572,tc_HOL_Obool)),U_16568),U_16576))
        | U_16568 = c_Orderings_Obot__class_Obot(tc_fun(U_16570,tc_HOL_Obool)) )
    & ! [U_16575,U_16573,U_16571,U_16569,U_16567] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16569,tc_fun(U_16571,tc_HOL_Obool)),U_16567),hAPP(hAPP(c_COMBB(tc_fun(U_16571,tc_HOL_Obool),tc_fun(U_16571,tc_HOL_Obool),U_16569),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16571,tc_HOL_Obool)),U_16573)),U_16575)) = c_Orderings_Otop__class_Otop(tc_fun(U_16571,tc_HOL_Obool))
        | U_16567 != c_Orderings_Obot__class_Obot(tc_fun(U_16569,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4075_2]) ).

fof(f_4075_4,plain,
    ( ! [U_16568,U_16570,U_16572,U_16574,U_16576] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16570,tc_fun(U_16572,tc_HOL_Obool)),U_16568),hAPP(hAPP(c_COMBB(tc_fun(U_16572,tc_HOL_Obool),tc_fun(U_16572,tc_HOL_Obool),U_16570),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16572,tc_HOL_Obool)),U_16574)),U_16576)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16572,tc_HOL_Obool)),U_16574),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16570,tc_fun(U_16572,tc_HOL_Obool)),U_16568),U_16576))
        | U_16568 = c_Orderings_Obot__class_Obot(tc_fun(U_16570,tc_HOL_Obool)) )
    & ! [U_16573,U_16569,U_16567,U_16571,U_16575] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16569,tc_fun(U_16571,tc_HOL_Obool)),U_16567),hAPP(hAPP(c_COMBB(tc_fun(U_16571,tc_HOL_Obool),tc_fun(U_16571,tc_HOL_Obool),U_16569),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16571,tc_HOL_Obool)),U_16573)),U_16575)) = c_Orderings_Otop__class_Otop(tc_fun(U_16571,tc_HOL_Obool))
        | U_16567 != c_Orderings_Obot__class_Obot(tc_fun(U_16569,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4075_3]) ).

cnf(f_4075_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16569,tc_fun(U_16571,tc_HOL_Obool)),U_16567),hAPP(hAPP(c_COMBB(tc_fun(U_16571,tc_HOL_Obool),tc_fun(U_16571,tc_HOL_Obool),U_16569),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16571,tc_HOL_Obool)),U_16573)),U_16575)) = c_Orderings_Otop__class_Otop(tc_fun(U_16571,tc_HOL_Obool))
    | U_16567 != c_Orderings_Obot__class_Obot(tc_fun(U_16569,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4075_4]) ).

cnf(f_4075_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16570,tc_fun(U_16572,tc_HOL_Obool)),U_16568),hAPP(hAPP(c_COMBB(tc_fun(U_16572,tc_HOL_Obool),tc_fun(U_16572,tc_HOL_Obool),U_16570),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16572,tc_HOL_Obool)),U_16574)),U_16576)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16572,tc_HOL_Obool)),U_16574),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16570,tc_fun(U_16572,tc_HOL_Obool)),U_16568),U_16576))
    | U_16568 = c_Orderings_Obot__class_Obot(tc_fun(U_16570,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4075_4]) ).

fof(f_4076_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_4076_2,plain,
    ! [U_16581,U_16580,U_16579,U_16578,U_16577] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16578,tc_fun(U_16579,tc_HOL_Obool)),U_16577),hAPP(hAPP(c_COMBC(U_16578,tc_fun(U_16579,tc_HOL_Obool),tc_fun(U_16579,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16579,tc_HOL_Obool),tc_fun(tc_fun(U_16579,tc_HOL_Obool),tc_fun(U_16579,tc_HOL_Obool)),U_16578),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16579,tc_HOL_Obool))),U_16580)),U_16581)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16579,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16578,tc_fun(U_16579,tc_HOL_Obool)),U_16577),U_16580)),U_16581)
        | U_16577 = c_Orderings_Obot__class_Obot(tc_fun(U_16578,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16578,tc_fun(U_16579,tc_HOL_Obool)),U_16577),hAPP(hAPP(c_COMBC(U_16578,tc_fun(U_16579,tc_HOL_Obool),tc_fun(U_16579,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16579,tc_HOL_Obool),tc_fun(tc_fun(U_16579,tc_HOL_Obool),tc_fun(U_16579,tc_HOL_Obool)),U_16578),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16579,tc_HOL_Obool))),U_16580)),U_16581)) = c_Orderings_Otop__class_Otop(tc_fun(U_16579,tc_HOL_Obool))
        | U_16577 != c_Orderings_Obot__class_Obot(tc_fun(U_16578,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4076_1]) ).

fof(f_4076_3,plain,
    ( ! [U_16591,U_16589,U_16587,U_16585,U_16583] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16585,tc_fun(U_16587,tc_HOL_Obool)),U_16583),hAPP(hAPP(c_COMBC(U_16585,tc_fun(U_16587,tc_HOL_Obool),tc_fun(U_16587,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16587,tc_HOL_Obool),tc_fun(tc_fun(U_16587,tc_HOL_Obool),tc_fun(U_16587,tc_HOL_Obool)),U_16585),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16587,tc_HOL_Obool))),U_16589)),U_16591)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16587,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16585,tc_fun(U_16587,tc_HOL_Obool)),U_16583),U_16589)),U_16591)
        | U_16583 = c_Orderings_Obot__class_Obot(tc_fun(U_16585,tc_HOL_Obool)) )
    & ! [U_16590,U_16588,U_16586,U_16584,U_16582] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16584,tc_fun(U_16586,tc_HOL_Obool)),U_16582),hAPP(hAPP(c_COMBC(U_16584,tc_fun(U_16586,tc_HOL_Obool),tc_fun(U_16586,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16586,tc_HOL_Obool),tc_fun(tc_fun(U_16586,tc_HOL_Obool),tc_fun(U_16586,tc_HOL_Obool)),U_16584),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16586,tc_HOL_Obool))),U_16588)),U_16590)) = c_Orderings_Otop__class_Otop(tc_fun(U_16586,tc_HOL_Obool))
        | U_16582 != c_Orderings_Obot__class_Obot(tc_fun(U_16584,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4076_2]) ).

fof(f_4076_4,plain,
    ( ! [U_16583,U_16585,U_16587,U_16589,U_16591] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16585,tc_fun(U_16587,tc_HOL_Obool)),U_16583),hAPP(hAPP(c_COMBC(U_16585,tc_fun(U_16587,tc_HOL_Obool),tc_fun(U_16587,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16587,tc_HOL_Obool),tc_fun(tc_fun(U_16587,tc_HOL_Obool),tc_fun(U_16587,tc_HOL_Obool)),U_16585),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16587,tc_HOL_Obool))),U_16589)),U_16591)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16587,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16585,tc_fun(U_16587,tc_HOL_Obool)),U_16583),U_16589)),U_16591)
        | U_16583 = c_Orderings_Obot__class_Obot(tc_fun(U_16585,tc_HOL_Obool)) )
    & ! [U_16588,U_16584,U_16582,U_16586,U_16590] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16584,tc_fun(U_16586,tc_HOL_Obool)),U_16582),hAPP(hAPP(c_COMBC(U_16584,tc_fun(U_16586,tc_HOL_Obool),tc_fun(U_16586,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16586,tc_HOL_Obool),tc_fun(tc_fun(U_16586,tc_HOL_Obool),tc_fun(U_16586,tc_HOL_Obool)),U_16584),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16586,tc_HOL_Obool))),U_16588)),U_16590)) = c_Orderings_Otop__class_Otop(tc_fun(U_16586,tc_HOL_Obool))
        | U_16582 != c_Orderings_Obot__class_Obot(tc_fun(U_16584,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4076_3]) ).

cnf(f_4076_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16584,tc_fun(U_16586,tc_HOL_Obool)),U_16582),hAPP(hAPP(c_COMBC(U_16584,tc_fun(U_16586,tc_HOL_Obool),tc_fun(U_16586,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16586,tc_HOL_Obool),tc_fun(tc_fun(U_16586,tc_HOL_Obool),tc_fun(U_16586,tc_HOL_Obool)),U_16584),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16586,tc_HOL_Obool))),U_16588)),U_16590)) = c_Orderings_Otop__class_Otop(tc_fun(U_16586,tc_HOL_Obool))
    | U_16582 != c_Orderings_Obot__class_Obot(tc_fun(U_16584,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4076_4]) ).

cnf(f_4076_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16585,tc_fun(U_16587,tc_HOL_Obool)),U_16583),hAPP(hAPP(c_COMBC(U_16585,tc_fun(U_16587,tc_HOL_Obool),tc_fun(U_16587,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16587,tc_HOL_Obool),tc_fun(tc_fun(U_16587,tc_HOL_Obool),tc_fun(U_16587,tc_HOL_Obool)),U_16585),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16587,tc_HOL_Obool))),U_16589)),U_16591)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16587,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16585,tc_fun(U_16587,tc_HOL_Obool)),U_16583),U_16589)),U_16591)
    | U_16583 = c_Orderings_Obot__class_Obot(tc_fun(U_16585,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4076_4]) ).

fof(f_4077_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_4077_2,plain,
    ! [U_16596,U_16595,U_16594,U_16593,U_16592] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16593,tc_fun(U_16594,tc_HOL_Obool)),U_16592),hAPP(hAPP(c_COMBC(U_16593,tc_fun(U_16594,tc_HOL_Obool),tc_fun(U_16594,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16594,tc_HOL_Obool),tc_fun(tc_fun(U_16594,tc_HOL_Obool),tc_fun(U_16594,tc_HOL_Obool)),U_16593),c_Groups_Ominus__class_Ominus(tc_fun(U_16594,tc_HOL_Obool))),U_16595)),U_16596)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16594,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16593,tc_fun(U_16594,tc_HOL_Obool)),U_16592),U_16595)),U_16596)
        | U_16592 = c_Orderings_Obot__class_Obot(tc_fun(U_16593,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16593,tc_fun(U_16594,tc_HOL_Obool)),U_16592),hAPP(hAPP(c_COMBC(U_16593,tc_fun(U_16594,tc_HOL_Obool),tc_fun(U_16594,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16594,tc_HOL_Obool),tc_fun(tc_fun(U_16594,tc_HOL_Obool),tc_fun(U_16594,tc_HOL_Obool)),U_16593),c_Groups_Ominus__class_Ominus(tc_fun(U_16594,tc_HOL_Obool))),U_16595)),U_16596)) = c_Orderings_Otop__class_Otop(tc_fun(U_16594,tc_HOL_Obool))
        | U_16592 != c_Orderings_Obot__class_Obot(tc_fun(U_16593,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4077_1]) ).

fof(f_4077_3,plain,
    ( ! [U_16606,U_16604,U_16602,U_16600,U_16598] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16600,tc_fun(U_16602,tc_HOL_Obool)),U_16598),hAPP(hAPP(c_COMBC(U_16600,tc_fun(U_16602,tc_HOL_Obool),tc_fun(U_16602,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16602,tc_HOL_Obool),tc_fun(tc_fun(U_16602,tc_HOL_Obool),tc_fun(U_16602,tc_HOL_Obool)),U_16600),c_Groups_Ominus__class_Ominus(tc_fun(U_16602,tc_HOL_Obool))),U_16604)),U_16606)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16602,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16600,tc_fun(U_16602,tc_HOL_Obool)),U_16598),U_16604)),U_16606)
        | U_16598 = c_Orderings_Obot__class_Obot(tc_fun(U_16600,tc_HOL_Obool)) )
    & ! [U_16605,U_16603,U_16601,U_16599,U_16597] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16599,tc_fun(U_16601,tc_HOL_Obool)),U_16597),hAPP(hAPP(c_COMBC(U_16599,tc_fun(U_16601,tc_HOL_Obool),tc_fun(U_16601,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16601,tc_HOL_Obool),tc_fun(tc_fun(U_16601,tc_HOL_Obool),tc_fun(U_16601,tc_HOL_Obool)),U_16599),c_Groups_Ominus__class_Ominus(tc_fun(U_16601,tc_HOL_Obool))),U_16603)),U_16605)) = c_Orderings_Otop__class_Otop(tc_fun(U_16601,tc_HOL_Obool))
        | U_16597 != c_Orderings_Obot__class_Obot(tc_fun(U_16599,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4077_2]) ).

fof(f_4077_4,plain,
    ( ! [U_16598,U_16600,U_16602,U_16604,U_16606] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16600,tc_fun(U_16602,tc_HOL_Obool)),U_16598),hAPP(hAPP(c_COMBC(U_16600,tc_fun(U_16602,tc_HOL_Obool),tc_fun(U_16602,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16602,tc_HOL_Obool),tc_fun(tc_fun(U_16602,tc_HOL_Obool),tc_fun(U_16602,tc_HOL_Obool)),U_16600),c_Groups_Ominus__class_Ominus(tc_fun(U_16602,tc_HOL_Obool))),U_16604)),U_16606)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16602,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16600,tc_fun(U_16602,tc_HOL_Obool)),U_16598),U_16604)),U_16606)
        | U_16598 = c_Orderings_Obot__class_Obot(tc_fun(U_16600,tc_HOL_Obool)) )
    & ! [U_16603,U_16599,U_16597,U_16601,U_16605] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16599,tc_fun(U_16601,tc_HOL_Obool)),U_16597),hAPP(hAPP(c_COMBC(U_16599,tc_fun(U_16601,tc_HOL_Obool),tc_fun(U_16601,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16601,tc_HOL_Obool),tc_fun(tc_fun(U_16601,tc_HOL_Obool),tc_fun(U_16601,tc_HOL_Obool)),U_16599),c_Groups_Ominus__class_Ominus(tc_fun(U_16601,tc_HOL_Obool))),U_16603)),U_16605)) = c_Orderings_Otop__class_Otop(tc_fun(U_16601,tc_HOL_Obool))
        | U_16597 != c_Orderings_Obot__class_Obot(tc_fun(U_16599,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4077_3]) ).

cnf(f_4077_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16599,tc_fun(U_16601,tc_HOL_Obool)),U_16597),hAPP(hAPP(c_COMBC(U_16599,tc_fun(U_16601,tc_HOL_Obool),tc_fun(U_16601,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16601,tc_HOL_Obool),tc_fun(tc_fun(U_16601,tc_HOL_Obool),tc_fun(U_16601,tc_HOL_Obool)),U_16599),c_Groups_Ominus__class_Ominus(tc_fun(U_16601,tc_HOL_Obool))),U_16603)),U_16605)) = c_Orderings_Otop__class_Otop(tc_fun(U_16601,tc_HOL_Obool))
    | U_16597 != c_Orderings_Obot__class_Obot(tc_fun(U_16599,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4077_4]) ).

cnf(f_4077_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16600,tc_fun(U_16602,tc_HOL_Obool)),U_16598),hAPP(hAPP(c_COMBC(U_16600,tc_fun(U_16602,tc_HOL_Obool),tc_fun(U_16602,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16602,tc_HOL_Obool),tc_fun(tc_fun(U_16602,tc_HOL_Obool),tc_fun(U_16602,tc_HOL_Obool)),U_16600),c_Groups_Ominus__class_Ominus(tc_fun(U_16602,tc_HOL_Obool))),U_16604)),U_16606)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16602,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16600,tc_fun(U_16602,tc_HOL_Obool)),U_16598),U_16604)),U_16606)
    | U_16598 = c_Orderings_Obot__class_Obot(tc_fun(U_16600,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4077_4]) ).

fof(f_4078_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_4078_2,plain,
    ! [U_16611,U_16610,U_16609,U_16608,U_16607] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16609,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16608,tc_fun(U_16609,tc_HOL_Obool)),U_16607),U_16610)),U_16611) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16608,tc_fun(U_16609,tc_HOL_Obool)),U_16607),hAPP(hAPP(c_COMBC(U_16608,tc_fun(U_16609,tc_HOL_Obool),tc_fun(U_16609,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16609,tc_HOL_Obool),tc_fun(tc_fun(U_16609,tc_HOL_Obool),tc_fun(U_16609,tc_HOL_Obool)),U_16608),c_Groups_Ominus__class_Ominus(tc_fun(U_16609,tc_HOL_Obool))),U_16610)),U_16611))
        | U_16607 = c_Orderings_Obot__class_Obot(tc_fun(U_16608,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16609,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16608,tc_fun(U_16609,tc_HOL_Obool)),U_16607),U_16610)),U_16611) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16609,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16609,tc_HOL_Obool))),U_16611)
        | U_16607 != c_Orderings_Obot__class_Obot(tc_fun(U_16608,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4078_1]) ).

fof(f_4078_3,plain,
    ( ! [U_16621,U_16619,U_16617,U_16615,U_16613] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16617,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16615,tc_fun(U_16617,tc_HOL_Obool)),U_16613),U_16619)),U_16621) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16615,tc_fun(U_16617,tc_HOL_Obool)),U_16613),hAPP(hAPP(c_COMBC(U_16615,tc_fun(U_16617,tc_HOL_Obool),tc_fun(U_16617,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16617,tc_HOL_Obool),tc_fun(tc_fun(U_16617,tc_HOL_Obool),tc_fun(U_16617,tc_HOL_Obool)),U_16615),c_Groups_Ominus__class_Ominus(tc_fun(U_16617,tc_HOL_Obool))),U_16619)),U_16621))
        | U_16613 = c_Orderings_Obot__class_Obot(tc_fun(U_16615,tc_HOL_Obool)) )
    & ! [U_16620,U_16618,U_16616,U_16614,U_16612] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16616,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16614,tc_fun(U_16616,tc_HOL_Obool)),U_16612),U_16618)),U_16620) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16616,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16616,tc_HOL_Obool))),U_16620)
        | U_16612 != c_Orderings_Obot__class_Obot(tc_fun(U_16614,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4078_2]) ).

fof(f_4078_4,plain,
    ( ! [U_16613,U_16615,U_16617,U_16619,U_16621] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16617,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16615,tc_fun(U_16617,tc_HOL_Obool)),U_16613),U_16619)),U_16621) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16615,tc_fun(U_16617,tc_HOL_Obool)),U_16613),hAPP(hAPP(c_COMBC(U_16615,tc_fun(U_16617,tc_HOL_Obool),tc_fun(U_16617,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16617,tc_HOL_Obool),tc_fun(tc_fun(U_16617,tc_HOL_Obool),tc_fun(U_16617,tc_HOL_Obool)),U_16615),c_Groups_Ominus__class_Ominus(tc_fun(U_16617,tc_HOL_Obool))),U_16619)),U_16621))
        | U_16613 = c_Orderings_Obot__class_Obot(tc_fun(U_16615,tc_HOL_Obool)) )
    & ! [U_16616,U_16618,U_16614,U_16612,U_16620] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16616,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16614,tc_fun(U_16616,tc_HOL_Obool)),U_16612),U_16618)),U_16620) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16616,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16616,tc_HOL_Obool))),U_16620)
        | U_16612 != c_Orderings_Obot__class_Obot(tc_fun(U_16614,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4078_3]) ).

cnf(f_4078_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16616,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16614,tc_fun(U_16616,tc_HOL_Obool)),U_16612),U_16618)),U_16620) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16616,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16616,tc_HOL_Obool))),U_16620)
    | U_16612 != c_Orderings_Obot__class_Obot(tc_fun(U_16614,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4078_4]) ).

cnf(f_4078_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16617,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16615,tc_fun(U_16617,tc_HOL_Obool)),U_16613),U_16619)),U_16621) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16615,tc_fun(U_16617,tc_HOL_Obool)),U_16613),hAPP(hAPP(c_COMBC(U_16615,tc_fun(U_16617,tc_HOL_Obool),tc_fun(U_16617,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16617,tc_HOL_Obool),tc_fun(tc_fun(U_16617,tc_HOL_Obool),tc_fun(U_16617,tc_HOL_Obool)),U_16615),c_Groups_Ominus__class_Ominus(tc_fun(U_16617,tc_HOL_Obool))),U_16619)),U_16621))
    | U_16613 = c_Orderings_Obot__class_Obot(tc_fun(U_16615,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4078_4]) ).

fof(f_4079_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_4079_2,plain,
    ! [U_16626,U_16625,U_16624,U_16623,U_16622] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16624,tc_HOL_Obool)),U_16625),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16623,tc_fun(U_16624,tc_HOL_Obool)),U_16622),U_16626)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16623,tc_fun(U_16624,tc_HOL_Obool)),U_16622),hAPP(hAPP(c_COMBB(tc_fun(U_16624,tc_HOL_Obool),tc_fun(U_16624,tc_HOL_Obool),U_16623),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16624,tc_HOL_Obool)),U_16625)),U_16626))
        | U_16622 = c_Orderings_Obot__class_Obot(tc_fun(U_16623,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16624,tc_HOL_Obool)),U_16625),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16623,tc_fun(U_16624,tc_HOL_Obool)),U_16622),U_16626)) = U_16625
        | U_16622 != c_Orderings_Obot__class_Obot(tc_fun(U_16623,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4079_1]) ).

fof(f_4079_3,plain,
    ( ! [U_16636,U_16634,U_16632,U_16630,U_16628] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16632,tc_HOL_Obool)),U_16634),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16630,tc_fun(U_16632,tc_HOL_Obool)),U_16628),U_16636)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16630,tc_fun(U_16632,tc_HOL_Obool)),U_16628),hAPP(hAPP(c_COMBB(tc_fun(U_16632,tc_HOL_Obool),tc_fun(U_16632,tc_HOL_Obool),U_16630),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16632,tc_HOL_Obool)),U_16634)),U_16636))
        | U_16628 = c_Orderings_Obot__class_Obot(tc_fun(U_16630,tc_HOL_Obool)) )
    & ! [U_16635,U_16633,U_16631,U_16629,U_16627] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16631,tc_HOL_Obool)),U_16633),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16629,tc_fun(U_16631,tc_HOL_Obool)),U_16627),U_16635)) = U_16633
        | U_16627 != c_Orderings_Obot__class_Obot(tc_fun(U_16629,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4079_2]) ).

fof(f_4079_4,plain,
    ( ! [U_16628,U_16630,U_16632,U_16634,U_16636] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16632,tc_HOL_Obool)),U_16634),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16630,tc_fun(U_16632,tc_HOL_Obool)),U_16628),U_16636)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16630,tc_fun(U_16632,tc_HOL_Obool)),U_16628),hAPP(hAPP(c_COMBB(tc_fun(U_16632,tc_HOL_Obool),tc_fun(U_16632,tc_HOL_Obool),U_16630),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16632,tc_HOL_Obool)),U_16634)),U_16636))
        | U_16628 = c_Orderings_Obot__class_Obot(tc_fun(U_16630,tc_HOL_Obool)) )
    & ! [U_16629,U_16633,U_16627,U_16631,U_16635] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16631,tc_HOL_Obool)),U_16633),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16629,tc_fun(U_16631,tc_HOL_Obool)),U_16627),U_16635)) = U_16633
        | U_16627 != c_Orderings_Obot__class_Obot(tc_fun(U_16629,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4079_3]) ).

cnf(f_4079_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16631,tc_HOL_Obool)),U_16633),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16629,tc_fun(U_16631,tc_HOL_Obool)),U_16627),U_16635)) = U_16633
    | U_16627 != c_Orderings_Obot__class_Obot(tc_fun(U_16629,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4079_4]) ).

cnf(f_4079_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16632,tc_HOL_Obool)),U_16634),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16630,tc_fun(U_16632,tc_HOL_Obool)),U_16628),U_16636)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16630,tc_fun(U_16632,tc_HOL_Obool)),U_16628),hAPP(hAPP(c_COMBB(tc_fun(U_16632,tc_HOL_Obool),tc_fun(U_16632,tc_HOL_Obool),U_16630),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16632,tc_HOL_Obool)),U_16634)),U_16636))
    | U_16628 = c_Orderings_Obot__class_Obot(tc_fun(U_16630,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4079_4]) ).

fof(f_4080_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_4080_2,plain,
    ! [U_16640,U_16639,U_16638,U_16637] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16637,U_16637)),hAPP(hAPP(c_Product__Type_OPair(U_16637,U_16637),U_16639),U_16638)),c_Transitive__Closure_Ortrancl(U_16637,U_16640)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16637,U_16637)),hAPP(hAPP(c_Product__Type_OPair(U_16637,U_16637),U_16638),U_16639)),c_Transitive__Closure_Ortrancl(U_16637,hAPP(c_Relation_Oconverse(U_16637,U_16637),U_16640)))) ),
    inference(variable_rename,[status(thm)],[f_4080_1]) ).

fof(f_4080_3,plain,
    ! [U_16637,U_16638,U_16639,U_16640] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16637,U_16637)),hAPP(hAPP(c_Product__Type_OPair(U_16637,U_16637),U_16639),U_16638)),c_Transitive__Closure_Ortrancl(U_16637,U_16640)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16637,U_16637)),hAPP(hAPP(c_Product__Type_OPair(U_16637,U_16637),U_16638),U_16639)),c_Transitive__Closure_Ortrancl(U_16637,hAPP(c_Relation_Oconverse(U_16637,U_16637),U_16640)))) ),
    inference(definitional_conversion,[status(esa)],[f_4080_2]) ).

cnf(f_4080_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16637,U_16637)),hAPP(hAPP(c_Product__Type_OPair(U_16637,U_16637),U_16639),U_16638)),c_Transitive__Closure_Ortrancl(U_16637,U_16640)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16637,U_16637)),hAPP(hAPP(c_Product__Type_OPair(U_16637,U_16637),U_16638),U_16639)),c_Transitive__Closure_Ortrancl(U_16637,hAPP(c_Relation_Oconverse(U_16637,U_16637),U_16640)))) ),
    inference(clausify,[status(thm)],[f_4080_3]) ).

fof(f_4081_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_4081_2,plain,
    ! [U_16644,U_16643,U_16642,U_16641] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16641,U_16641)),hAPP(hAPP(c_Product__Type_OPair(U_16641,U_16641),U_16643),U_16642)),c_Transitive__Closure_Ortrancl(U_16641,hAPP(c_Relation_Oconverse(U_16641,U_16641),U_16644))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16641,U_16641)),hAPP(hAPP(c_Product__Type_OPair(U_16641,U_16641),U_16642),U_16643)),c_Transitive__Closure_Ortrancl(U_16641,U_16644))) ),
    inference(variable_rename,[status(thm)],[f_4081_1]) ).

fof(f_4081_3,plain,
    ! [U_16641,U_16642,U_16643,U_16644] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16641,U_16641)),hAPP(hAPP(c_Product__Type_OPair(U_16641,U_16641),U_16643),U_16642)),c_Transitive__Closure_Ortrancl(U_16641,hAPP(c_Relation_Oconverse(U_16641,U_16641),U_16644))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16641,U_16641)),hAPP(hAPP(c_Product__Type_OPair(U_16641,U_16641),U_16642),U_16643)),c_Transitive__Closure_Ortrancl(U_16641,U_16644))) ),
    inference(definitional_conversion,[status(esa)],[f_4081_2]) ).

cnf(f_4081_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16641,U_16641)),hAPP(hAPP(c_Product__Type_OPair(U_16641,U_16641),U_16643),U_16642)),c_Transitive__Closure_Ortrancl(U_16641,hAPP(c_Relation_Oconverse(U_16641,U_16641),U_16644))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16641,U_16641)),hAPP(hAPP(c_Product__Type_OPair(U_16641,U_16641),U_16642),U_16643)),c_Transitive__Closure_Ortrancl(U_16641,U_16644))) ),
    inference(clausify,[status(thm)],[f_4081_3]) ).

fof(f_4082_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_4082_2,plain,
    ! [U_16648,U_16647,U_16646,U_16645] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16645,U_16645)),hAPP(hAPP(c_Product__Type_OPair(U_16645,U_16645),U_16646),U_16647)),hAPP(c_Relation_Oconverse(U_16645,U_16645),c_Transitive__Closure_Otrancl(U_16645,U_16648))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16645,U_16645)),hAPP(hAPP(c_Product__Type_OPair(U_16645,U_16645),U_16646),U_16647)),c_Transitive__Closure_Otrancl(U_16645,hAPP(c_Relation_Oconverse(U_16645,U_16645),U_16648)))) ),
    inference(variable_rename,[status(thm)],[f_4082_1]) ).

fof(f_4082_3,plain,
    ! [U_16645,U_16646,U_16647,U_16648] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16645,U_16645)),hAPP(hAPP(c_Product__Type_OPair(U_16645,U_16645),U_16646),U_16647)),hAPP(c_Relation_Oconverse(U_16645,U_16645),c_Transitive__Closure_Otrancl(U_16645,U_16648))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16645,U_16645)),hAPP(hAPP(c_Product__Type_OPair(U_16645,U_16645),U_16646),U_16647)),c_Transitive__Closure_Otrancl(U_16645,hAPP(c_Relation_Oconverse(U_16645,U_16645),U_16648)))) ),
    inference(definitional_conversion,[status(esa)],[f_4082_2]) ).

cnf(f_4082_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16645,U_16645)),hAPP(hAPP(c_Product__Type_OPair(U_16645,U_16645),U_16646),U_16647)),hAPP(c_Relation_Oconverse(U_16645,U_16645),c_Transitive__Closure_Otrancl(U_16645,U_16648))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16645,U_16645)),hAPP(hAPP(c_Product__Type_OPair(U_16645,U_16645),U_16646),U_16647)),c_Transitive__Closure_Otrancl(U_16645,hAPP(c_Relation_Oconverse(U_16645,U_16645),U_16648)))) ),
    inference(clausify,[status(thm)],[f_4082_3]) ).

fof(f_4083_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_4083_2,plain,
    ! [U_16652,U_16651,U_16650,U_16649] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16649,U_16649)),hAPP(hAPP(c_Product__Type_OPair(U_16649,U_16649),U_16650),U_16651)),c_Transitive__Closure_Otrancl(U_16649,hAPP(c_Relation_Oconverse(U_16649,U_16649),U_16652))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16649,U_16649)),hAPP(hAPP(c_Product__Type_OPair(U_16649,U_16649),U_16650),U_16651)),hAPP(c_Relation_Oconverse(U_16649,U_16649),c_Transitive__Closure_Otrancl(U_16649,U_16652)))) ),
    inference(variable_rename,[status(thm)],[f_4083_1]) ).

fof(f_4083_3,plain,
    ! [U_16649,U_16650,U_16651,U_16652] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16649,U_16649)),hAPP(hAPP(c_Product__Type_OPair(U_16649,U_16649),U_16650),U_16651)),c_Transitive__Closure_Otrancl(U_16649,hAPP(c_Relation_Oconverse(U_16649,U_16649),U_16652))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16649,U_16649)),hAPP(hAPP(c_Product__Type_OPair(U_16649,U_16649),U_16650),U_16651)),hAPP(c_Relation_Oconverse(U_16649,U_16649),c_Transitive__Closure_Otrancl(U_16649,U_16652)))) ),
    inference(definitional_conversion,[status(esa)],[f_4083_2]) ).

cnf(f_4083_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16649,U_16649)),hAPP(hAPP(c_Product__Type_OPair(U_16649,U_16649),U_16650),U_16651)),c_Transitive__Closure_Otrancl(U_16649,hAPP(c_Relation_Oconverse(U_16649,U_16649),U_16652))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16649,U_16649)),hAPP(hAPP(c_Product__Type_OPair(U_16649,U_16649),U_16650),U_16651)),hAPP(c_Relation_Oconverse(U_16649,U_16649),c_Transitive__Closure_Otrancl(U_16649,U_16652)))) ),
    inference(clausify,[status(thm)],[f_4083_3]) ).

fof(f_4084_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_4084_2,plain,
    ! [U_16657,U_16656,U_16655,U_16654,U_16653] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16653,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16654,U_16653,U_16655),U_16656)),U_16657))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16654,tc_HOL_Obool)),U_16656),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16654,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16653,U_16654,hAPP(c_Relation_Oconverse(U_16654,U_16653),U_16655)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16653,tc_HOL_Obool)),U_16657))))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16654,tc_HOL_Obool)),U_16656),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16654,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16653,U_16654,hAPP(c_Relation_Oconverse(U_16654,U_16653),U_16655)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16653,tc_HOL_Obool)),U_16657)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16653,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16654,U_16653,U_16655),U_16656)),U_16657)) ) ),
    inference(variable_rename,[status(thm)],[f_4084_1]) ).

fof(f_4084_3,plain,
    ( ! [U_16667,U_16665,U_16663,U_16661,U_16659] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16659,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16661,U_16659,U_16663),U_16665)),U_16667))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16661,tc_HOL_Obool)),U_16665),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16661,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16659,U_16661,hAPP(c_Relation_Oconverse(U_16661,U_16659),U_16663)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16659,tc_HOL_Obool)),U_16667))))) )
    & ! [U_16666,U_16664,U_16662,U_16660,U_16658] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16660,tc_HOL_Obool)),U_16664),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16660,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16658,U_16660,hAPP(c_Relation_Oconverse(U_16660,U_16658),U_16662)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16658,tc_HOL_Obool)),U_16666)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16658,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16660,U_16658,U_16662),U_16664)),U_16666)) ) ),
    inference(miniscope,[status(thm)],[f_4084_2]) ).

fof(f_4084_4,plain,
    ( ! [U_16659,U_16661,U_16663,U_16665,U_16667] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16659,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16661,U_16659,U_16663),U_16665)),U_16667))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16661,tc_HOL_Obool)),U_16665),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16661,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16659,U_16661,hAPP(c_Relation_Oconverse(U_16661,U_16659),U_16663)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16659,tc_HOL_Obool)),U_16667))))) )
    & ! [U_16664,U_16660,U_16658,U_16662,U_16666] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16660,tc_HOL_Obool)),U_16664),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16660,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16658,U_16660,hAPP(c_Relation_Oconverse(U_16660,U_16658),U_16662)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16658,tc_HOL_Obool)),U_16666)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16658,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16660,U_16658,U_16662),U_16664)),U_16666)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4084_3]) ).

cnf(f_4084_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16660,tc_HOL_Obool)),U_16664),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16660,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16658,U_16660,hAPP(c_Relation_Oconverse(U_16660,U_16658),U_16662)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16658,tc_HOL_Obool)),U_16666)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16658,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16660,U_16658,U_16662),U_16664)),U_16666)) ),
    inference(clausify,[status(thm)],[f_4084_4]) ).

cnf(f_4084_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16659,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16661,U_16659,U_16663),U_16665)),U_16667))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16661,tc_HOL_Obool)),U_16665),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16661,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16659,U_16661,hAPP(c_Relation_Oconverse(U_16661,U_16659),U_16663)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16659,tc_HOL_Obool)),U_16667))))) ),
    inference(clausify,[status(thm)],[f_4084_4]) ).

fof(f_4085_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_4085_2,plain,
    ! [U_16672,U_16671,U_16670,U_16669,U_16668] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16668),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16669,U_16668),U_16671),U_16672)),hAPP(U_16672,U_16670)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16669),U_16670),U_16671))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16668) ),
    inference(variable_rename,[status(thm)],[f_4085_1]) ).

fof(f_4085_3,plain,
    ! [U_16668,U_16670,U_16669,U_16671,U_16672] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16668),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16669,U_16668),U_16671),U_16672)),hAPP(U_16672,U_16670)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16669),U_16670),U_16671))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16668) ),
    inference(definitional_conversion,[status(esa)],[f_4085_2]) ).

cnf(f_4085_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16668),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16669,U_16668),U_16671),U_16672)),hAPP(U_16672,U_16670)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16669),U_16670),U_16671))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16668) ),
    inference(clausify,[status(thm)],[f_4085_3]) ).

fof(f_4086_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_4086_2,plain,
    ! [U_16675,U_16674,U_16673] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16673,U_16673),tc_HOL_Obool)),U_16675),hAPP(hAPP(c_Relation_Orel__comp(U_16673,U_16673,U_16673),hAPP(c_Relation_Oconverse(U_16673,U_16673),U_16675)),U_16675)))
      | ~ c_Relation_Orefl__on(U_16673,U_16674,U_16675) ),
    inference(variable_rename,[status(thm)],[f_4086_1]) ).

fof(f_4086_3,plain,
    ! [U_16673,U_16674,U_16675] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16673,U_16673),tc_HOL_Obool)),U_16675),hAPP(hAPP(c_Relation_Orel__comp(U_16673,U_16673,U_16673),hAPP(c_Relation_Oconverse(U_16673,U_16673),U_16675)),U_16675)))
      | ~ c_Relation_Orefl__on(U_16673,U_16674,U_16675) ),
    inference(definitional_conversion,[status(esa)],[f_4086_2]) ).

cnf(f_4086_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16673,U_16673),tc_HOL_Obool)),U_16675),hAPP(hAPP(c_Relation_Orel__comp(U_16673,U_16673,U_16673),hAPP(c_Relation_Oconverse(U_16673,U_16673),U_16675)),U_16675)))
    | ~ c_Relation_Orefl__on(U_16673,U_16674,U_16675) ),
    inference(clausify,[status(thm)],[f_4086_3]) ).

fof(f_4087_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_4087_2,plain,
    ! [U_16678,U_16677,U_16676] :
      ( c_Equiv__Relations_Oequiv(U_16676,U_16678,U_16677)
      | hAPP(c_Relation_ODomain(U_16676,U_16676),U_16677) != U_16678
      | hAPP(hAPP(c_Relation_Orel__comp(U_16676,U_16676,U_16676),hAPP(c_Relation_Oconverse(U_16676,U_16676),U_16677)),U_16677) != U_16677 ),
    inference(variable_rename,[status(thm)],[f_4087_1]) ).

fof(f_4087_3,plain,
    ! [U_16676,U_16677,U_16678] :
      ( c_Equiv__Relations_Oequiv(U_16676,U_16678,U_16677)
      | hAPP(c_Relation_ODomain(U_16676,U_16676),U_16677) != U_16678
      | hAPP(hAPP(c_Relation_Orel__comp(U_16676,U_16676,U_16676),hAPP(c_Relation_Oconverse(U_16676,U_16676),U_16677)),U_16677) != U_16677 ),
    inference(definitional_conversion,[status(esa)],[f_4087_2]) ).

cnf(f_4087_4,plain,
    ( c_Equiv__Relations_Oequiv(U_16676,U_16678,U_16677)
    | hAPP(c_Relation_ODomain(U_16676,U_16676),U_16677) != U_16678
    | hAPP(hAPP(c_Relation_Orel__comp(U_16676,U_16676,U_16676),hAPP(c_Relation_Oconverse(U_16676,U_16676),U_16677)),U_16677) != U_16677 ),
    inference(clausify,[status(thm)],[f_4087_3]) ).

fof(f_4088_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_4088_2,plain,
    ! [U_16680,U_16679] :
      ( c_Wellfounded_Owf(U_16679,hAPP(c_Relation_Oconverse(U_16679,U_16679),U_16680))
      | ~ c_Wellfounded_Oacyclic(U_16679,U_16680)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16679,U_16679)),U_16680)) ),
    inference(variable_rename,[status(thm)],[f_4088_1]) ).

fof(f_4088_3,plain,
    ! [U_16679,U_16680] :
      ( c_Wellfounded_Owf(U_16679,hAPP(c_Relation_Oconverse(U_16679,U_16679),U_16680))
      | ~ c_Wellfounded_Oacyclic(U_16679,U_16680)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16679,U_16679)),U_16680)) ),
    inference(definitional_conversion,[status(esa)],[f_4088_2]) ).

cnf(f_4088_4,plain,
    ( c_Wellfounded_Owf(U_16679,hAPP(c_Relation_Oconverse(U_16679,U_16679),U_16680))
    | ~ c_Wellfounded_Oacyclic(U_16679,U_16680)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_16679,U_16679)),U_16680)) ),
    inference(clausify,[status(thm)],[f_4088_3]) ).

fof(f_4089_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_4089_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_4089_1]) ).

cnf(f_4089_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_4089_2]) ).

fof(f_4090_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_4090_2,plain,
    ! [U_16685,U_16684,U_16683,U_16682,U_16681] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16682,tc_fun(U_16683,tc_HOL_Obool)),U_16681),hAPP(hAPP(c_COMBB(tc_fun(U_16683,tc_HOL_Obool),tc_fun(U_16683,tc_HOL_Obool),U_16682),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16683,tc_HOL_Obool)),U_16684)),U_16685)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16683,tc_HOL_Obool)),U_16684),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16682,tc_fun(U_16683,tc_HOL_Obool)),U_16681),U_16685))
        | U_16681 = c_Orderings_Obot__class_Obot(tc_fun(U_16682,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16682,tc_fun(U_16683,tc_HOL_Obool)),U_16681),hAPP(hAPP(c_COMBB(tc_fun(U_16683,tc_HOL_Obool),tc_fun(U_16683,tc_HOL_Obool),U_16682),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16683,tc_HOL_Obool)),U_16684)),U_16685)) = c_Orderings_Otop__class_Otop(tc_fun(U_16683,tc_HOL_Obool))
        | U_16681 != c_Orderings_Obot__class_Obot(tc_fun(U_16682,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4090_1]) ).

fof(f_4090_3,plain,
    ( ! [U_16695,U_16693,U_16691,U_16689,U_16687] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16689,tc_fun(U_16691,tc_HOL_Obool)),U_16687),hAPP(hAPP(c_COMBB(tc_fun(U_16691,tc_HOL_Obool),tc_fun(U_16691,tc_HOL_Obool),U_16689),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16691,tc_HOL_Obool)),U_16693)),U_16695)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16691,tc_HOL_Obool)),U_16693),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16689,tc_fun(U_16691,tc_HOL_Obool)),U_16687),U_16695))
        | U_16687 = c_Orderings_Obot__class_Obot(tc_fun(U_16689,tc_HOL_Obool)) )
    & ! [U_16694,U_16692,U_16690,U_16688,U_16686] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16688,tc_fun(U_16690,tc_HOL_Obool)),U_16686),hAPP(hAPP(c_COMBB(tc_fun(U_16690,tc_HOL_Obool),tc_fun(U_16690,tc_HOL_Obool),U_16688),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16690,tc_HOL_Obool)),U_16692)),U_16694)) = c_Orderings_Otop__class_Otop(tc_fun(U_16690,tc_HOL_Obool))
        | U_16686 != c_Orderings_Obot__class_Obot(tc_fun(U_16688,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4090_2]) ).

fof(f_4090_4,plain,
    ( ! [U_16687,U_16689,U_16691,U_16693,U_16695] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16689,tc_fun(U_16691,tc_HOL_Obool)),U_16687),hAPP(hAPP(c_COMBB(tc_fun(U_16691,tc_HOL_Obool),tc_fun(U_16691,tc_HOL_Obool),U_16689),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16691,tc_HOL_Obool)),U_16693)),U_16695)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16691,tc_HOL_Obool)),U_16693),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16689,tc_fun(U_16691,tc_HOL_Obool)),U_16687),U_16695))
        | U_16687 = c_Orderings_Obot__class_Obot(tc_fun(U_16689,tc_HOL_Obool)) )
    & ! [U_16688,U_16692,U_16686,U_16690,U_16694] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16688,tc_fun(U_16690,tc_HOL_Obool)),U_16686),hAPP(hAPP(c_COMBB(tc_fun(U_16690,tc_HOL_Obool),tc_fun(U_16690,tc_HOL_Obool),U_16688),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16690,tc_HOL_Obool)),U_16692)),U_16694)) = c_Orderings_Otop__class_Otop(tc_fun(U_16690,tc_HOL_Obool))
        | U_16686 != c_Orderings_Obot__class_Obot(tc_fun(U_16688,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4090_3]) ).

cnf(f_4090_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16688,tc_fun(U_16690,tc_HOL_Obool)),U_16686),hAPP(hAPP(c_COMBB(tc_fun(U_16690,tc_HOL_Obool),tc_fun(U_16690,tc_HOL_Obool),U_16688),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16690,tc_HOL_Obool)),U_16692)),U_16694)) = c_Orderings_Otop__class_Otop(tc_fun(U_16690,tc_HOL_Obool))
    | U_16686 != c_Orderings_Obot__class_Obot(tc_fun(U_16688,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4090_4]) ).

cnf(f_4090_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16689,tc_fun(U_16691,tc_HOL_Obool)),U_16687),hAPP(hAPP(c_COMBB(tc_fun(U_16691,tc_HOL_Obool),tc_fun(U_16691,tc_HOL_Obool),U_16689),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16691,tc_HOL_Obool)),U_16693)),U_16695)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16691,tc_HOL_Obool)),U_16693),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16689,tc_fun(U_16691,tc_HOL_Obool)),U_16687),U_16695))
    | U_16687 = c_Orderings_Obot__class_Obot(tc_fun(U_16689,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4090_4]) ).

fof(f_4091_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_4091_2,plain,
    ! [U_16698,U_16697,U_16696] : hAPP(c_Relation_Oconverse(U_16696,U_16697),U_16698) = hAPP(c_Set_OCollect(tc_prod(U_16697,U_16696)),hAPP(c_Product__Type_Oprod_Oprod__case(U_16697,U_16696,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_16697,tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_fun(U_16696,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16696,tc_fun(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_fun(U_16696,tc_HOL_Obool)),U_16697),c_COMBC(U_16696,tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16696,tc_prod(U_16696,U_16697)),tc_fun(U_16696,tc_fun(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_HOL_Obool)),U_16697),hAPP(c_COMBB(tc_prod(U_16696,U_16697),tc_fun(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_HOL_Obool),U_16696),c_member(tc_prod(U_16696,U_16697)))),hAPP(c_COMBC(U_16696,U_16697,tc_prod(U_16696,U_16697)),c_Product__Type_OPair(U_16696,U_16697))))),U_16698))),
    inference(variable_rename,[status(thm)],[f_4091_1]) ).

fof(f_4091_3,plain,
    ! [U_16696,U_16697,U_16698] : hAPP(c_Relation_Oconverse(U_16696,U_16697),U_16698) = hAPP(c_Set_OCollect(tc_prod(U_16697,U_16696)),hAPP(c_Product__Type_Oprod_Oprod__case(U_16697,U_16696,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_16697,tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_fun(U_16696,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16696,tc_fun(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_fun(U_16696,tc_HOL_Obool)),U_16697),c_COMBC(U_16696,tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16696,tc_prod(U_16696,U_16697)),tc_fun(U_16696,tc_fun(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_HOL_Obool)),U_16697),hAPP(c_COMBB(tc_prod(U_16696,U_16697),tc_fun(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_HOL_Obool),U_16696),c_member(tc_prod(U_16696,U_16697)))),hAPP(c_COMBC(U_16696,U_16697,tc_prod(U_16696,U_16697)),c_Product__Type_OPair(U_16696,U_16697))))),U_16698))),
    inference(definitional_conversion,[status(esa)],[f_4091_2]) ).

cnf(f_4091_4,plain,
    hAPP(c_Relation_Oconverse(U_16696,U_16697),U_16698) = hAPP(c_Set_OCollect(tc_prod(U_16697,U_16696)),hAPP(c_Product__Type_Oprod_Oprod__case(U_16697,U_16696,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_16697,tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_fun(U_16696,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16696,tc_fun(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_fun(U_16696,tc_HOL_Obool)),U_16697),c_COMBC(U_16696,tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16696,tc_prod(U_16696,U_16697)),tc_fun(U_16696,tc_fun(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_HOL_Obool)),U_16697),hAPP(c_COMBB(tc_prod(U_16696,U_16697),tc_fun(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_HOL_Obool),U_16696),c_member(tc_prod(U_16696,U_16697)))),hAPP(c_COMBC(U_16696,U_16697,tc_prod(U_16696,U_16697)),c_Product__Type_OPair(U_16696,U_16697))))),U_16698))),
    inference(clausify,[status(thm)],[f_4091_3]) ).

fof(f_4092_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_4092_2,plain,
    ! [U_16703,U_16702,U_16701,U_16700,U_16699] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16699),U_16702),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16700,U_16699),U_16701),U_16703)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16700,U_16699,hAPP(hAPP(c_COMBB(U_16699,tc_fun(U_16699,U_16699),U_16700),c_Lattices_Osemilattice__inf__class_Oinf(U_16699)),U_16703)),U_16702),U_16701)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16700),U_16701))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16699) ),
    inference(variable_rename,[status(thm)],[f_4092_1]) ).

fof(f_4092_3,plain,
    ! [U_16699,U_16700,U_16701,U_16702,U_16703] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16699),U_16702),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16700,U_16699),U_16701),U_16703)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16700,U_16699,hAPP(hAPP(c_COMBB(U_16699,tc_fun(U_16699,U_16699),U_16700),c_Lattices_Osemilattice__inf__class_Oinf(U_16699)),U_16703)),U_16702),U_16701)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16700),U_16701))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16699) ),
    inference(definitional_conversion,[status(esa)],[f_4092_2]) ).

cnf(f_4092_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16699),U_16702),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16700,U_16699),U_16701),U_16703)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16700,U_16699,hAPP(hAPP(c_COMBB(U_16699,tc_fun(U_16699,U_16699),U_16700),c_Lattices_Osemilattice__inf__class_Oinf(U_16699)),U_16703)),U_16702),U_16701)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16700),U_16701))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16699) ),
    inference(clausify,[status(thm)],[f_4092_3]) ).

fof(f_4093_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_4093_2,plain,
    ! [U_16709,U_16708,U_16707,U_16706,U_16705] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16705,U_16705)),hAPP(hAPP(c_Product__Type_OPair(U_16705,U_16705),hAPP(U_16706,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16708),U_16709))),hAPP(U_16706,U_16708))),c_Transitive__Closure_Ortrancl(U_16705,U_16707)))
      | ? [U_16704] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16705,U_16705)),hAPP(hAPP(c_Product__Type_OPair(U_16705,U_16705),hAPP(U_16706,hAPP(c_Nat_OSuc,U_16704))),hAPP(U_16706,U_16704))),c_Transitive__Closure_Ortrancl(U_16705,U_16707))) ),
    inference(variable_rename,[status(thm)],[f_4093_1]) ).

fof(f_4093_3,plain,
    ! [U_16709,U_16708,U_16707,U_16706,U_16705] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16705,U_16705)),hAPP(hAPP(c_Product__Type_OPair(U_16705,U_16705),hAPP(U_16706,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16708),U_16709))),hAPP(U_16706,U_16708))),c_Transitive__Closure_Ortrancl(U_16705,U_16707)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16705,U_16705)),hAPP(hAPP(c_Product__Type_OPair(U_16705,U_16705),hAPP(U_16706,hAPP(c_Nat_OSuc,sK391(U_16709,U_16708,U_16707,U_16706,U_16705)))),hAPP(U_16706,sK391(U_16709,U_16708,U_16707,U_16706,U_16705)))),c_Transitive__Closure_Ortrancl(U_16705,U_16707))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK391]),skolemize(U_16704,sK391(U_16709,U_16708,U_16707,U_16706,U_16705))],[f_4093_2]) ).

fof(f_4093_4,plain,
    ! [U_16705,U_16706,U_16707,U_16708,U_16709] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16705,U_16705)),hAPP(hAPP(c_Product__Type_OPair(U_16705,U_16705),hAPP(U_16706,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16708),U_16709))),hAPP(U_16706,U_16708))),c_Transitive__Closure_Ortrancl(U_16705,U_16707)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16705,U_16705)),hAPP(hAPP(c_Product__Type_OPair(U_16705,U_16705),hAPP(U_16706,hAPP(c_Nat_OSuc,sK391(U_16709,U_16708,U_16707,U_16706,U_16705)))),hAPP(U_16706,sK391(U_16709,U_16708,U_16707,U_16706,U_16705)))),c_Transitive__Closure_Ortrancl(U_16705,U_16707))) ),
    inference(definitional_conversion,[status(esa)],[f_4093_3]) ).

cnf(f_4093_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16705,U_16705)),hAPP(hAPP(c_Product__Type_OPair(U_16705,U_16705),hAPP(U_16706,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16708),U_16709))),hAPP(U_16706,U_16708))),c_Transitive__Closure_Ortrancl(U_16705,U_16707)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16705,U_16705)),hAPP(hAPP(c_Product__Type_OPair(U_16705,U_16705),hAPP(U_16706,hAPP(c_Nat_OSuc,sK391(U_16709,U_16708,U_16707,U_16706,U_16705)))),hAPP(U_16706,sK391(U_16709,U_16708,U_16707,U_16706,U_16705)))),c_Transitive__Closure_Ortrancl(U_16705,U_16707))) ),
    inference(clausify,[status(thm)],[f_4093_4]) ).

fof(f_4094_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_4094_2,plain,
    ! [U_16713,U_16712,U_16711,U_16710] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16710,tc_fun(U_16710,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16710,tc_fun(tc_prod(U_16710,U_16710),tc_HOL_Obool),tc_fun(U_16710,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16710,tc_fun(tc_fun(tc_prod(U_16710,U_16710),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16710,U_16710),tc_HOL_Obool),tc_fun(U_16710,tc_HOL_Obool)),U_16710),c_COMBC(U_16710,tc_fun(tc_prod(U_16710,U_16710),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16710,tc_prod(U_16710,U_16710)),tc_fun(U_16710,tc_fun(tc_fun(tc_prod(U_16710,U_16710),tc_HOL_Obool),tc_HOL_Obool)),U_16710),hAPP(c_COMBB(tc_prod(U_16710,U_16710),tc_fun(tc_fun(tc_prod(U_16710,U_16710),tc_HOL_Obool),tc_HOL_Obool),U_16710),c_member(tc_prod(U_16710,U_16710)))),c_Product__Type_OPair(U_16710,U_16710)))),U_16711)),c_fequal),U_16712),U_16713))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16710,U_16710)),hAPP(hAPP(c_Product__Type_OPair(U_16710,U_16710),U_16712),U_16713)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16710,U_16710),tc_HOL_Obool)),U_16711),c_Relation_OId(U_16710)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16710,U_16710)),hAPP(hAPP(c_Product__Type_OPair(U_16710,U_16710),U_16712),U_16713)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16710,U_16710),tc_HOL_Obool)),U_16711),c_Relation_OId(U_16710))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16710,tc_fun(U_16710,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16710,tc_fun(tc_prod(U_16710,U_16710),tc_HOL_Obool),tc_fun(U_16710,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16710,tc_fun(tc_fun(tc_prod(U_16710,U_16710),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16710,U_16710),tc_HOL_Obool),tc_fun(U_16710,tc_HOL_Obool)),U_16710),c_COMBC(U_16710,tc_fun(tc_prod(U_16710,U_16710),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16710,tc_prod(U_16710,U_16710)),tc_fun(U_16710,tc_fun(tc_fun(tc_prod(U_16710,U_16710),tc_HOL_Obool),tc_HOL_Obool)),U_16710),hAPP(c_COMBB(tc_prod(U_16710,U_16710),tc_fun(tc_fun(tc_prod(U_16710,U_16710),tc_HOL_Obool),tc_HOL_Obool),U_16710),c_member(tc_prod(U_16710,U_16710)))),c_Product__Type_OPair(U_16710,U_16710)))),U_16711)),c_fequal),U_16712),U_16713)) ) ),
    inference(variable_rename,[status(thm)],[f_4094_1]) ).

fof(f_4094_3,plain,
    ( ! [U_16721,U_16719,U_16717,U_16715] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16715,tc_fun(U_16715,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16715,tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_fun(U_16715,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16715,tc_fun(tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_fun(U_16715,tc_HOL_Obool)),U_16715),c_COMBC(U_16715,tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16715,tc_prod(U_16715,U_16715)),tc_fun(U_16715,tc_fun(tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_HOL_Obool)),U_16715),hAPP(c_COMBB(tc_prod(U_16715,U_16715),tc_fun(tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_HOL_Obool),U_16715),c_member(tc_prod(U_16715,U_16715)))),c_Product__Type_OPair(U_16715,U_16715)))),U_16717)),c_fequal),U_16719),U_16721))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16715,U_16715)),hAPP(hAPP(c_Product__Type_OPair(U_16715,U_16715),U_16719),U_16721)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool)),U_16717),c_Relation_OId(U_16715)))) )
    & ! [U_16720,U_16718,U_16716,U_16714] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16714,U_16714)),hAPP(hAPP(c_Product__Type_OPair(U_16714,U_16714),U_16718),U_16720)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool)),U_16716),c_Relation_OId(U_16714))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16714,tc_fun(U_16714,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16714,tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_fun(U_16714,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16714,tc_fun(tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_fun(U_16714,tc_HOL_Obool)),U_16714),c_COMBC(U_16714,tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16714,tc_prod(U_16714,U_16714)),tc_fun(U_16714,tc_fun(tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_HOL_Obool)),U_16714),hAPP(c_COMBB(tc_prod(U_16714,U_16714),tc_fun(tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_HOL_Obool),U_16714),c_member(tc_prod(U_16714,U_16714)))),c_Product__Type_OPair(U_16714,U_16714)))),U_16716)),c_fequal),U_16718),U_16720)) ) ),
    inference(miniscope,[status(thm)],[f_4094_2]) ).

fof(f_4094_4,plain,
    ( ! [U_16715,U_16717,U_16719,U_16721] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16715,tc_fun(U_16715,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16715,tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_fun(U_16715,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16715,tc_fun(tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_fun(U_16715,tc_HOL_Obool)),U_16715),c_COMBC(U_16715,tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16715,tc_prod(U_16715,U_16715)),tc_fun(U_16715,tc_fun(tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_HOL_Obool)),U_16715),hAPP(c_COMBB(tc_prod(U_16715,U_16715),tc_fun(tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_HOL_Obool),U_16715),c_member(tc_prod(U_16715,U_16715)))),c_Product__Type_OPair(U_16715,U_16715)))),U_16717)),c_fequal),U_16719),U_16721))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16715,U_16715)),hAPP(hAPP(c_Product__Type_OPair(U_16715,U_16715),U_16719),U_16721)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool)),U_16717),c_Relation_OId(U_16715)))) )
    & ! [U_16716,U_16720,U_16714,U_16718] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16714,U_16714)),hAPP(hAPP(c_Product__Type_OPair(U_16714,U_16714),U_16718),U_16720)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool)),U_16716),c_Relation_OId(U_16714))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16714,tc_fun(U_16714,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16714,tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_fun(U_16714,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16714,tc_fun(tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_fun(U_16714,tc_HOL_Obool)),U_16714),c_COMBC(U_16714,tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16714,tc_prod(U_16714,U_16714)),tc_fun(U_16714,tc_fun(tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_HOL_Obool)),U_16714),hAPP(c_COMBB(tc_prod(U_16714,U_16714),tc_fun(tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_HOL_Obool),U_16714),c_member(tc_prod(U_16714,U_16714)))),c_Product__Type_OPair(U_16714,U_16714)))),U_16716)),c_fequal),U_16718),U_16720)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4094_3]) ).

cnf(f_4094_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16714,U_16714)),hAPP(hAPP(c_Product__Type_OPair(U_16714,U_16714),U_16718),U_16720)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool)),U_16716),c_Relation_OId(U_16714))))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16714,tc_fun(U_16714,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16714,tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_fun(U_16714,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16714,tc_fun(tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_fun(U_16714,tc_HOL_Obool)),U_16714),c_COMBC(U_16714,tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16714,tc_prod(U_16714,U_16714)),tc_fun(U_16714,tc_fun(tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_HOL_Obool)),U_16714),hAPP(c_COMBB(tc_prod(U_16714,U_16714),tc_fun(tc_fun(tc_prod(U_16714,U_16714),tc_HOL_Obool),tc_HOL_Obool),U_16714),c_member(tc_prod(U_16714,U_16714)))),c_Product__Type_OPair(U_16714,U_16714)))),U_16716)),c_fequal),U_16718),U_16720)) ),
    inference(clausify,[status(thm)],[f_4094_4]) ).

cnf(f_4094_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16715,tc_fun(U_16715,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_16715,tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_fun(U_16715,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16715,tc_fun(tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_fun(U_16715,tc_HOL_Obool)),U_16715),c_COMBC(U_16715,tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16715,tc_prod(U_16715,U_16715)),tc_fun(U_16715,tc_fun(tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_HOL_Obool)),U_16715),hAPP(c_COMBB(tc_prod(U_16715,U_16715),tc_fun(tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool),tc_HOL_Obool),U_16715),c_member(tc_prod(U_16715,U_16715)))),c_Product__Type_OPair(U_16715,U_16715)))),U_16717)),c_fequal),U_16719),U_16721))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16715,U_16715)),hAPP(hAPP(c_Product__Type_OPair(U_16715,U_16715),U_16719),U_16721)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16715,U_16715),tc_HOL_Obool)),U_16717),c_Relation_OId(U_16715)))) ),
    inference(clausify,[status(thm)],[f_4094_4]) ).

fof(f_4095_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_4095_2,plain,
    ! [U_16723,U_16722] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16722,U_16722)),hAPP(hAPP(c_Product__Type_OPair(U_16722,U_16722),U_16723),U_16723)),c_Relation_OId(U_16722))),
    inference(variable_rename,[status(thm)],[f_4095_1]) ).

fof(f_4095_3,plain,
    ! [U_16722,U_16723] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16722,U_16722)),hAPP(hAPP(c_Product__Type_OPair(U_16722,U_16722),U_16723),U_16723)),c_Relation_OId(U_16722))),
    inference(definitional_conversion,[status(esa)],[f_4095_2]) ).

cnf(f_4095_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_16722,U_16722)),hAPP(hAPP(c_Product__Type_OPair(U_16722,U_16722),U_16723),U_16723)),c_Relation_OId(U_16722))),
    inference(clausify,[status(thm)],[f_4095_3]) ).

fof(f_4096_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_4096_2,plain,
    ! [U_16730,U_16729,U_16728,U_16727,U_16726] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16726,tc_fun(U_16727,tc_HOL_Obool)),U_16728),U_16729),U_16730))
        | ? [U_16725] :
            ( ~ hBOOL(hAPP(hAPP(U_16729,U_16725),U_16730))
            & hBOOL(hAPP(hAPP(c_member(U_16726),U_16725),U_16728)) ) )
      & ( ! [U_16724] :
            ( hBOOL(hAPP(hAPP(U_16729,U_16724),U_16730))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16726),U_16724),U_16728)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16726,tc_fun(U_16727,tc_HOL_Obool)),U_16728),U_16729),U_16730)) ) ),
    inference(variable_rename,[status(thm)],[f_4096_1]) ).

fof(f_4096_3,plain,
    ( ! [U_16740,U_16738,U_16736,U_16734,U_16732] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16732,tc_fun(U_16734,tc_HOL_Obool)),U_16736),U_16738),U_16740))
        | ? [U_16725] :
            ( ~ hBOOL(hAPP(hAPP(U_16738,U_16725),U_16740))
            & hBOOL(hAPP(hAPP(c_member(U_16732),U_16725),U_16736)) ) )
    & ! [U_16739,U_16737,U_16735,U_16733,U_16731] :
        ( ! [U_16724] :
            ( hBOOL(hAPP(hAPP(U_16737,U_16724),U_16739))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16731),U_16724),U_16735)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16731,tc_fun(U_16733,tc_HOL_Obool)),U_16735),U_16737),U_16739)) ) ),
    inference(miniscope,[status(thm)],[f_4096_2]) ).

fof(f_4096_4,plain,
    ( ! [U_16740,U_16738,U_16736,U_16734,U_16732] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16732,tc_fun(U_16734,tc_HOL_Obool)),U_16736),U_16738),U_16740))
        | ( ~ hBOOL(hAPP(hAPP(U_16738,sK392(U_16740,U_16738,U_16736,U_16734,U_16732)),U_16740))
          & hBOOL(hAPP(hAPP(c_member(U_16732),sK392(U_16740,U_16738,U_16736,U_16734,U_16732)),U_16736)) ) )
    & ! [U_16739,U_16737,U_16735,U_16733,U_16731] :
        ( ! [U_16724] :
            ( hBOOL(hAPP(hAPP(U_16737,U_16724),U_16739))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16731),U_16724),U_16735)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16731,tc_fun(U_16733,tc_HOL_Obool)),U_16735),U_16737),U_16739)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK392]),skolemize(U_16725,sK392(U_16740,U_16738,U_16736,U_16734,U_16732))],[f_4096_3]) ).

fof(f_4096_5,plain,
    ( ! [U_16736,U_16732,U_16734,U_16738,U_16740] :
        ( ~ hBOOL(hAPP(hAPP(U_16738,sK392(U_16740,U_16738,U_16736,U_16734,U_16732)),U_16740))
        | ~ sP1061(U_16736,U_16732,U_16734,U_16738,U_16740) )
    & ! [U_16736,U_16732,U_16734,U_16738,U_16740] :
        ( hBOOL(hAPP(hAPP(c_member(U_16732),sK392(U_16740,U_16738,U_16736,U_16734,U_16732)),U_16736))
        | ~ sP1061(U_16736,U_16732,U_16734,U_16738,U_16740) )
    & ! [U_16736,U_16732,U_16734,U_16738,U_16740] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16732,tc_fun(U_16734,tc_HOL_Obool)),U_16736),U_16738),U_16740))
        | sP1061(U_16736,U_16732,U_16734,U_16738,U_16740) )
    & ! [U_16724,U_16735,U_16737,U_16731,U_16733,U_16739] :
        ( hBOOL(hAPP(hAPP(U_16737,U_16724),U_16739))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16731),U_16724),U_16735))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16731,tc_fun(U_16733,tc_HOL_Obool)),U_16735),U_16737),U_16739)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1061])],[f_4096_4]) ).

cnf(f_4096_6,plain,
    ( hBOOL(hAPP(hAPP(U_16737,U_16724),U_16739))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16731),U_16724),U_16735))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16731,tc_fun(U_16733,tc_HOL_Obool)),U_16735),U_16737),U_16739)) ),
    inference(clausify,[status(thm)],[f_4096_5]) ).

cnf(f_4096_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16732,tc_fun(U_16734,tc_HOL_Obool)),U_16736),U_16738),U_16740))
    | sP1061(U_16736,U_16732,U_16734,U_16738,U_16740) ),
    inference(clausify,[status(thm)],[f_4096_5]) ).

cnf(f_4096_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16732),sK392(U_16740,U_16738,U_16736,U_16734,U_16732)),U_16736))
    | ~ sP1061(U_16736,U_16732,U_16734,U_16738,U_16740) ),
    inference(clausify,[status(thm)],[f_4096_5]) ).

cnf(f_4096_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_16738,sK392(U_16740,U_16738,U_16736,U_16734,U_16732)),U_16740))
    | ~ sP1061(U_16736,U_16732,U_16734,U_16738,U_16740) ),
    inference(clausify,[status(thm)],[f_4096_5]) ).

fof(f_4097_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_4097_2,plain,
    ! [U_16749,U_16748,U_16747,U_16746,U_16745,U_16744,U_16743] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16743,tc_fun(U_16744,tc_fun(U_16745,tc_HOL_Obool))),U_16746),U_16747),U_16748),U_16749))
        | ? [U_16742] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_16747,U_16742),U_16748),U_16749))
            & hBOOL(hAPP(hAPP(c_member(U_16743),U_16742),U_16746)) ) )
      & ( ! [U_16741] :
            ( hBOOL(hAPP(hAPP(hAPP(U_16747,U_16741),U_16748),U_16749))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16743),U_16741),U_16746)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16743,tc_fun(U_16744,tc_fun(U_16745,tc_HOL_Obool))),U_16746),U_16747),U_16748),U_16749)) ) ),
    inference(variable_rename,[status(thm)],[f_4097_1]) ).

fof(f_4097_3,plain,
    ( ! [U_16763,U_16761,U_16759,U_16757,U_16755,U_16753,U_16751] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16751,tc_fun(U_16753,tc_fun(U_16755,tc_HOL_Obool))),U_16757),U_16759),U_16761),U_16763))
        | ? [U_16742] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_16759,U_16742),U_16761),U_16763))
            & hBOOL(hAPP(hAPP(c_member(U_16751),U_16742),U_16757)) ) )
    & ! [U_16762,U_16760,U_16758,U_16756,U_16754,U_16752,U_16750] :
        ( ! [U_16741] :
            ( hBOOL(hAPP(hAPP(hAPP(U_16758,U_16741),U_16760),U_16762))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16750),U_16741),U_16756)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16750,tc_fun(U_16752,tc_fun(U_16754,tc_HOL_Obool))),U_16756),U_16758),U_16760),U_16762)) ) ),
    inference(miniscope,[status(thm)],[f_4097_2]) ).

fof(f_4097_4,plain,
    ( ! [U_16763,U_16761,U_16759,U_16757,U_16755,U_16753,U_16751] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16751,tc_fun(U_16753,tc_fun(U_16755,tc_HOL_Obool))),U_16757),U_16759),U_16761),U_16763))
        | ( ~ hBOOL(hAPP(hAPP(hAPP(U_16759,sK393(U_16763,U_16761,U_16759,U_16757,U_16755,U_16753,U_16751)),U_16761),U_16763))
          & hBOOL(hAPP(hAPP(c_member(U_16751),sK393(U_16763,U_16761,U_16759,U_16757,U_16755,U_16753,U_16751)),U_16757)) ) )
    & ! [U_16762,U_16760,U_16758,U_16756,U_16754,U_16752,U_16750] :
        ( ! [U_16741] :
            ( hBOOL(hAPP(hAPP(hAPP(U_16758,U_16741),U_16760),U_16762))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16750),U_16741),U_16756)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16750,tc_fun(U_16752,tc_fun(U_16754,tc_HOL_Obool))),U_16756),U_16758),U_16760),U_16762)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK393]),skolemize(U_16742,sK393(U_16763,U_16761,U_16759,U_16757,U_16755,U_16753,U_16751))],[f_4097_3]) ).

fof(f_4097_5,plain,
    ( ! [U_16751,U_16753,U_16755,U_16757,U_16761,U_16759,U_16763] :
        ( ~ hBOOL(hAPP(hAPP(hAPP(U_16759,sK393(U_16763,U_16761,U_16759,U_16757,U_16755,U_16753,U_16751)),U_16761),U_16763))
        | ~ sP1062(U_16751,U_16753,U_16755,U_16757,U_16761,U_16759,U_16763) )
    & ! [U_16751,U_16753,U_16755,U_16757,U_16761,U_16759,U_16763] :
        ( hBOOL(hAPP(hAPP(c_member(U_16751),sK393(U_16763,U_16761,U_16759,U_16757,U_16755,U_16753,U_16751)),U_16757))
        | ~ sP1062(U_16751,U_16753,U_16755,U_16757,U_16761,U_16759,U_16763) )
    & ! [U_16751,U_16753,U_16755,U_16757,U_16761,U_16759,U_16763] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16751,tc_fun(U_16753,tc_fun(U_16755,tc_HOL_Obool))),U_16757),U_16759),U_16761),U_16763))
        | sP1062(U_16751,U_16753,U_16755,U_16757,U_16761,U_16759,U_16763) )
    & ! [U_16741,U_16754,U_16752,U_16750,U_16758,U_16762,U_16756,U_16760] :
        ( hBOOL(hAPP(hAPP(hAPP(U_16758,U_16741),U_16760),U_16762))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16750),U_16741),U_16756))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16750,tc_fun(U_16752,tc_fun(U_16754,tc_HOL_Obool))),U_16756),U_16758),U_16760),U_16762)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1062])],[f_4097_4]) ).

cnf(f_4097_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_16758,U_16741),U_16760),U_16762))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16750),U_16741),U_16756))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16750,tc_fun(U_16752,tc_fun(U_16754,tc_HOL_Obool))),U_16756),U_16758),U_16760),U_16762)) ),
    inference(clausify,[status(thm)],[f_4097_5]) ).

cnf(f_4097_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16751,tc_fun(U_16753,tc_fun(U_16755,tc_HOL_Obool))),U_16757),U_16759),U_16761),U_16763))
    | sP1062(U_16751,U_16753,U_16755,U_16757,U_16761,U_16759,U_16763) ),
    inference(clausify,[status(thm)],[f_4097_5]) ).

cnf(f_4097_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16751),sK393(U_16763,U_16761,U_16759,U_16757,U_16755,U_16753,U_16751)),U_16757))
    | ~ sP1062(U_16751,U_16753,U_16755,U_16757,U_16761,U_16759,U_16763) ),
    inference(clausify,[status(thm)],[f_4097_5]) ).

cnf(f_4097_9,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(U_16759,sK393(U_16763,U_16761,U_16759,U_16757,U_16755,U_16753,U_16751)),U_16761),U_16763))
    | ~ sP1062(U_16751,U_16753,U_16755,U_16757,U_16761,U_16759,U_16763) ),
    inference(clausify,[status(thm)],[f_4097_5]) ).

fof(f_4098_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_4098_2,plain,
    ! [U_16764] : hAPP(c_Relation_Oconverse(U_16764,U_16764),c_Relation_OId(U_16764)) = c_Relation_OId(U_16764),
    inference(variable_rename,[status(thm)],[f_4098_1]) ).

fof(f_4098_3,plain,
    ! [U_16764] : hAPP(c_Relation_Oconverse(U_16764,U_16764),c_Relation_OId(U_16764)) = c_Relation_OId(U_16764),
    inference(definitional_conversion,[status(esa)],[f_4098_2]) ).

cnf(f_4098_4,plain,
    hAPP(c_Relation_Oconverse(U_16764,U_16764),c_Relation_OId(U_16764)) = c_Relation_OId(U_16764),
    inference(clausify,[status(thm)],[f_4098_3]) ).

fof(f_4099_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_4099_2,plain,
    ! [U_16766,U_16765] : hAPP(c_Relation_OImage(U_16765,U_16765,c_Relation_OId(U_16765)),U_16766) = U_16766,
    inference(variable_rename,[status(thm)],[f_4099_1]) ).

fof(f_4099_3,plain,
    ! [U_16766,U_16765] : hAPP(c_Relation_OImage(U_16765,U_16765,c_Relation_OId(U_16765)),U_16766) = U_16766,
    inference(definitional_conversion,[status(esa)],[f_4099_2]) ).

cnf(f_4099_4,plain,
    hAPP(c_Relation_OImage(U_16765,U_16765,c_Relation_OId(U_16765)),U_16766) = U_16766,
    inference(clausify,[status(thm)],[f_4099_3]) ).

fof(f_4100_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_4100_2,plain,
    ! [U_16769,U_16768,U_16767] : hAPP(hAPP(c_Relation_Orel__comp(U_16767,U_16768,U_16768),U_16769),c_Relation_OId(U_16768)) = U_16769,
    inference(variable_rename,[status(thm)],[f_4100_1]) ).

fof(f_4100_3,plain,
    ! [U_16767,U_16768,U_16769] : hAPP(hAPP(c_Relation_Orel__comp(U_16767,U_16768,U_16768),U_16769),c_Relation_OId(U_16768)) = U_16769,
    inference(definitional_conversion,[status(esa)],[f_4100_2]) ).

cnf(f_4100_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_16767,U_16768,U_16768),U_16769),c_Relation_OId(U_16768)) = U_16769,
    inference(clausify,[status(thm)],[f_4100_3]) ).

fof(f_4101_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_4101_2,plain,
    ! [U_16772,U_16771,U_16770] : hAPP(hAPP(c_Relation_Orel__comp(U_16770,U_16770,U_16771),c_Relation_OId(U_16770)),U_16772) = U_16772,
    inference(variable_rename,[status(thm)],[f_4101_1]) ).

fof(f_4101_3,plain,
    ! [U_16770,U_16771,U_16772] : hAPP(hAPP(c_Relation_Orel__comp(U_16770,U_16770,U_16771),c_Relation_OId(U_16770)),U_16772) = U_16772,
    inference(definitional_conversion,[status(esa)],[f_4101_2]) ).

cnf(f_4101_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_16770,U_16770,U_16771),c_Relation_OId(U_16770)),U_16772) = U_16772,
    inference(clausify,[status(thm)],[f_4101_3]) ).

fof(f_4102_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_4102_2,plain,
    ! [U_16775,U_16774,U_16773] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16773,U_16773)),hAPP(hAPP(c_Product__Type_OPair(U_16773,U_16773),U_16774),U_16775)),c_Relation_OId(U_16773)))
        | U_16774 != U_16775 )
      & ( U_16774 = U_16775
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16773,U_16773)),hAPP(hAPP(c_Product__Type_OPair(U_16773,U_16773),U_16774),U_16775)),c_Relation_OId(U_16773))) ) ),
    inference(variable_rename,[status(thm)],[f_4102_1]) ).

fof(f_4102_3,plain,
    ( ! [U_16781,U_16779] :
        ( ! [U_16777] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16777,U_16777)),hAPP(hAPP(c_Product__Type_OPair(U_16777,U_16777),U_16779),U_16781)),c_Relation_OId(U_16777)))
        | U_16779 != U_16781 )
    & ! [U_16780,U_16778] :
        ( ! [U_16776] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16776,U_16776)),hAPP(hAPP(c_Product__Type_OPair(U_16776,U_16776),U_16778),U_16780)),c_Relation_OId(U_16776)))
        | U_16778 = U_16780 ) ),
    inference(miniscope,[status(thm)],[f_4102_2]) ).

fof(f_4102_4,plain,
    ( ! [U_16777,U_16779,U_16781] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16777,U_16777)),hAPP(hAPP(c_Product__Type_OPair(U_16777,U_16777),U_16779),U_16781)),c_Relation_OId(U_16777)))
        | U_16779 != U_16781 )
    & ! [U_16776,U_16780,U_16778] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16776,U_16776)),hAPP(hAPP(c_Product__Type_OPair(U_16776,U_16776),U_16778),U_16780)),c_Relation_OId(U_16776)))
        | U_16778 = U_16780 ) ),
    inference(definitional_conversion,[status(esa)],[f_4102_3]) ).

cnf(f_4102_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16776,U_16776)),hAPP(hAPP(c_Product__Type_OPair(U_16776,U_16776),U_16778),U_16780)),c_Relation_OId(U_16776)))
    | U_16778 = U_16780 ),
    inference(clausify,[status(thm)],[f_4102_4]) ).

cnf(f_4102_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16777,U_16777)),hAPP(hAPP(c_Product__Type_OPair(U_16777,U_16777),U_16779),U_16781)),c_Relation_OId(U_16777)))
    | U_16779 != U_16781 ),
    inference(clausify,[status(thm)],[f_4102_4]) ).

fof(f_4103_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_4103_2,plain,
    ! [U_16782] : hAPP(c_Relation_ODomain(U_16782,U_16782),c_Relation_OId(U_16782)) = c_Orderings_Otop__class_Otop(tc_fun(U_16782,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4103_1]) ).

fof(f_4103_3,plain,
    ! [U_16782] : hAPP(c_Relation_ODomain(U_16782,U_16782),c_Relation_OId(U_16782)) = c_Orderings_Otop__class_Otop(tc_fun(U_16782,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4103_2]) ).

cnf(f_4103_4,plain,
    hAPP(c_Relation_ODomain(U_16782,U_16782),c_Relation_OId(U_16782)) = c_Orderings_Otop__class_Otop(tc_fun(U_16782,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4103_3]) ).

fof(f_4104_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_4104_2,plain,
    ! [U_16783] : c_Transitive__Closure_Ortrancl(U_16783,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_16783,U_16783),tc_HOL_Obool))) = c_Relation_OId(U_16783),
    inference(variable_rename,[status(thm)],[f_4104_1]) ).

fof(f_4104_3,plain,
    ! [U_16783] : c_Transitive__Closure_Ortrancl(U_16783,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_16783,U_16783),tc_HOL_Obool))) = c_Relation_OId(U_16783),
    inference(definitional_conversion,[status(esa)],[f_4104_2]) ).

cnf(f_4104_4,plain,
    c_Transitive__Closure_Ortrancl(U_16783,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_16783,U_16783),tc_HOL_Obool))) = c_Relation_OId(U_16783),
    inference(clausify,[status(thm)],[f_4104_3]) ).

fof(f_4105_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_4105_2,plain,
    ! [U_16784] : hAPP(c_Relation_ORange(U_16784,U_16784),c_Relation_OId(U_16784)) = c_Orderings_Otop__class_Otop(tc_fun(U_16784,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4105_1]) ).

fof(f_4105_3,plain,
    ! [U_16784] : hAPP(c_Relation_ORange(U_16784,U_16784),c_Relation_OId(U_16784)) = c_Orderings_Otop__class_Otop(tc_fun(U_16784,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4105_2]) ).

cnf(f_4105_4,plain,
    hAPP(c_Relation_ORange(U_16784,U_16784),c_Relation_OId(U_16784)) = c_Orderings_Otop__class_Otop(tc_fun(U_16784,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4105_3]) ).

fof(f_4106_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_4106_2,plain,
    ! [U_16786,U_16785] : c_Transitive__Closure_Ortrancl(U_16785,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16785,U_16785),tc_HOL_Obool)),U_16786),c_Relation_OId(U_16785))) = c_Transitive__Closure_Ortrancl(U_16785,U_16786),
    inference(variable_rename,[status(thm)],[f_4106_1]) ).

fof(f_4106_3,plain,
    ! [U_16785,U_16786] : c_Transitive__Closure_Ortrancl(U_16785,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16785,U_16785),tc_HOL_Obool)),U_16786),c_Relation_OId(U_16785))) = c_Transitive__Closure_Ortrancl(U_16785,U_16786),
    inference(definitional_conversion,[status(esa)],[f_4106_2]) ).

cnf(f_4106_4,plain,
    c_Transitive__Closure_Ortrancl(U_16785,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16785,U_16785),tc_HOL_Obool)),U_16786),c_Relation_OId(U_16785))) = c_Transitive__Closure_Ortrancl(U_16785,U_16786),
    inference(clausify,[status(thm)],[f_4106_3]) ).

fof(f_4107_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_4107_2,plain,
    ! [U_16788,U_16787] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16787,U_16787),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16787,U_16788)),c_Relation_OId(U_16787)) = c_Transitive__Closure_Ortrancl(U_16787,U_16788),
    inference(variable_rename,[status(thm)],[f_4107_1]) ).

fof(f_4107_3,plain,
    ! [U_16787,U_16788] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16787,U_16787),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16787,U_16788)),c_Relation_OId(U_16787)) = c_Transitive__Closure_Ortrancl(U_16787,U_16788),
    inference(definitional_conversion,[status(esa)],[f_4107_2]) ).

cnf(f_4107_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16787,U_16787),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16787,U_16788)),c_Relation_OId(U_16787)) = c_Transitive__Closure_Ortrancl(U_16787,U_16788),
    inference(clausify,[status(thm)],[f_4107_3]) ).

fof(f_4108_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_4108_2,plain,
    ! [U_16789] : c_Relation_Orefl__on(U_16789,c_Orderings_Otop__class_Otop(tc_fun(U_16789,tc_HOL_Obool)),c_Relation_OId(U_16789)),
    inference(variable_rename,[status(thm)],[f_4108_1]) ).

fof(f_4108_3,plain,
    ! [U_16789] : c_Relation_Orefl__on(U_16789,c_Orderings_Otop__class_Otop(tc_fun(U_16789,tc_HOL_Obool)),c_Relation_OId(U_16789)),
    inference(definitional_conversion,[status(esa)],[f_4108_2]) ).

cnf(f_4108_4,plain,
    c_Relation_Orefl__on(U_16789,c_Orderings_Otop__class_Otop(tc_fun(U_16789,tc_HOL_Obool)),c_Relation_OId(U_16789)),
    inference(clausify,[status(thm)],[f_4108_3]) ).

fof(f_4109_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_4109_2,plain,
    ! [U_16791,U_16790] : c_Transitive__Closure_Ortrancl(U_16790,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16790,U_16790),tc_HOL_Obool)),U_16791),c_Relation_OId(U_16790))) = c_Transitive__Closure_Ortrancl(U_16790,U_16791),
    inference(variable_rename,[status(thm)],[f_4109_1]) ).

fof(f_4109_3,plain,
    ! [U_16790,U_16791] : c_Transitive__Closure_Ortrancl(U_16790,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16790,U_16790),tc_HOL_Obool)),U_16791),c_Relation_OId(U_16790))) = c_Transitive__Closure_Ortrancl(U_16790,U_16791),
    inference(definitional_conversion,[status(esa)],[f_4109_2]) ).

cnf(f_4109_4,plain,
    c_Transitive__Closure_Ortrancl(U_16790,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16790,U_16790),tc_HOL_Obool)),U_16791),c_Relation_OId(U_16790))) = c_Transitive__Closure_Ortrancl(U_16790,U_16791),
    inference(clausify,[status(thm)],[f_4109_3]) ).

fof(f_4110_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_4110_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_4110_1]) ).

cnf(f_4110_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_4110_2]) ).

fof(f_4111_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_4111_2,plain,
    ! [U_16793,U_16792] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16792,U_16792),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_16792,U_16793)),c_Relation_OId(U_16792)) = c_Transitive__Closure_Ortrancl(U_16792,U_16793),
    inference(variable_rename,[status(thm)],[f_4111_1]) ).

fof(f_4111_3,plain,
    ! [U_16792,U_16793] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16792,U_16792),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_16792,U_16793)),c_Relation_OId(U_16792)) = c_Transitive__Closure_Ortrancl(U_16792,U_16793),
    inference(definitional_conversion,[status(esa)],[f_4111_2]) ).

cnf(f_4111_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16792,U_16792),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_16792,U_16793)),c_Relation_OId(U_16792)) = c_Transitive__Closure_Ortrancl(U_16792,U_16793),
    inference(clausify,[status(thm)],[f_4111_3]) ).

fof(f_4112_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_4112_2,plain,
    ! [U_16795,U_16794] : c_Transitive__Closure_Otrancl(U_16794,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16794,U_16794),tc_HOL_Obool)),U_16795),c_Relation_OId(U_16794))) = c_Transitive__Closure_Ortrancl(U_16794,U_16795),
    inference(variable_rename,[status(thm)],[f_4112_1]) ).

fof(f_4112_3,plain,
    ! [U_16794,U_16795] : c_Transitive__Closure_Otrancl(U_16794,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16794,U_16794),tc_HOL_Obool)),U_16795),c_Relation_OId(U_16794))) = c_Transitive__Closure_Ortrancl(U_16794,U_16795),
    inference(definitional_conversion,[status(esa)],[f_4112_2]) ).

cnf(f_4112_4,plain,
    c_Transitive__Closure_Otrancl(U_16794,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16794,U_16794),tc_HOL_Obool)),U_16795),c_Relation_OId(U_16794))) = c_Transitive__Closure_Ortrancl(U_16794,U_16795),
    inference(clausify,[status(thm)],[f_4112_3]) ).

fof(f_4113_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_4113_2,plain,
    ! [U_16797,U_16796] : c_Transitive__Closure_Ortrancl(U_16796,U_16797) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16796,U_16796),tc_HOL_Obool)),c_Relation_OId(U_16796)),hAPP(hAPP(c_Relation_Orel__comp(U_16796,U_16796,U_16796),c_Transitive__Closure_Ortrancl(U_16796,U_16797)),U_16797)),
    inference(variable_rename,[status(thm)],[f_4113_1]) ).

fof(f_4113_3,plain,
    ! [U_16796,U_16797] : c_Transitive__Closure_Ortrancl(U_16796,U_16797) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16796,U_16796),tc_HOL_Obool)),c_Relation_OId(U_16796)),hAPP(hAPP(c_Relation_Orel__comp(U_16796,U_16796,U_16796),c_Transitive__Closure_Ortrancl(U_16796,U_16797)),U_16797)),
    inference(definitional_conversion,[status(esa)],[f_4113_2]) ).

cnf(f_4113_4,plain,
    c_Transitive__Closure_Ortrancl(U_16796,U_16797) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16796,U_16796),tc_HOL_Obool)),c_Relation_OId(U_16796)),hAPP(hAPP(c_Relation_Orel__comp(U_16796,U_16796,U_16796),c_Transitive__Closure_Ortrancl(U_16796,U_16797)),U_16797)),
    inference(clausify,[status(thm)],[f_4113_3]) ).

fof(f_4114_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_4114_2,plain,
    ! [U_16799,U_16798] : c_Relation_Orefl__on(U_16798,c_Orderings_Otop__class_Otop(tc_fun(U_16798,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16798,U_16798),tc_HOL_Obool)),U_16799),c_Relation_OId(U_16798))),
    inference(variable_rename,[status(thm)],[f_4114_1]) ).

fof(f_4114_3,plain,
    ! [U_16798,U_16799] : c_Relation_Orefl__on(U_16798,c_Orderings_Otop__class_Otop(tc_fun(U_16798,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16798,U_16798),tc_HOL_Obool)),U_16799),c_Relation_OId(U_16798))),
    inference(definitional_conversion,[status(esa)],[f_4114_2]) ).

cnf(f_4114_4,plain,
    c_Relation_Orefl__on(U_16798,c_Orderings_Otop__class_Otop(tc_fun(U_16798,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_16798,U_16798),tc_HOL_Obool)),U_16799),c_Relation_OId(U_16798))),
    inference(clausify,[status(thm)],[f_4114_3]) ).

fof(f_4115_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_4115_2,plain,
    ! [U_16800] : c_Relation_OId(U_16800) = hAPP(c_Set_OCollect(tc_prod(U_16800,U_16800)),hAPP(hAPP(c_COMBB(tc_fun(U_16800,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_16800,U_16800)),c_HOL_OEx(U_16800)),hAPP(hAPP(c_COMBC(tc_prod(U_16800,U_16800),tc_fun(U_16800,tc_prod(U_16800,U_16800)),tc_fun(U_16800,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16800,U_16800),tc_HOL_Obool),tc_fun(tc_fun(U_16800,tc_prod(U_16800,U_16800)),tc_fun(U_16800,tc_HOL_Obool)),tc_prod(U_16800,U_16800)),c_COMBB(tc_prod(U_16800,U_16800),tc_HOL_Obool,U_16800)),c_fequal)),hAPP(hAPP(c_COMBS(U_16800,U_16800,tc_prod(U_16800,U_16800)),c_Product__Type_OPair(U_16800,U_16800)),c_COMBI(U_16800))))),
    inference(variable_rename,[status(thm)],[f_4115_1]) ).

fof(f_4115_3,plain,
    ! [U_16800] : c_Relation_OId(U_16800) = hAPP(c_Set_OCollect(tc_prod(U_16800,U_16800)),hAPP(hAPP(c_COMBB(tc_fun(U_16800,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_16800,U_16800)),c_HOL_OEx(U_16800)),hAPP(hAPP(c_COMBC(tc_prod(U_16800,U_16800),tc_fun(U_16800,tc_prod(U_16800,U_16800)),tc_fun(U_16800,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16800,U_16800),tc_HOL_Obool),tc_fun(tc_fun(U_16800,tc_prod(U_16800,U_16800)),tc_fun(U_16800,tc_HOL_Obool)),tc_prod(U_16800,U_16800)),c_COMBB(tc_prod(U_16800,U_16800),tc_HOL_Obool,U_16800)),c_fequal)),hAPP(hAPP(c_COMBS(U_16800,U_16800,tc_prod(U_16800,U_16800)),c_Product__Type_OPair(U_16800,U_16800)),c_COMBI(U_16800))))),
    inference(definitional_conversion,[status(esa)],[f_4115_2]) ).

cnf(f_4115_4,plain,
    c_Relation_OId(U_16800) = hAPP(c_Set_OCollect(tc_prod(U_16800,U_16800)),hAPP(hAPP(c_COMBB(tc_fun(U_16800,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_16800,U_16800)),c_HOL_OEx(U_16800)),hAPP(hAPP(c_COMBC(tc_prod(U_16800,U_16800),tc_fun(U_16800,tc_prod(U_16800,U_16800)),tc_fun(U_16800,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16800,U_16800),tc_HOL_Obool),tc_fun(tc_fun(U_16800,tc_prod(U_16800,U_16800)),tc_fun(U_16800,tc_HOL_Obool)),tc_prod(U_16800,U_16800)),c_COMBB(tc_prod(U_16800,U_16800),tc_HOL_Obool,U_16800)),c_fequal)),hAPP(hAPP(c_COMBS(U_16800,U_16800,tc_prod(U_16800,U_16800)),c_Product__Type_OPair(U_16800,U_16800)),c_COMBI(U_16800))))),
    inference(clausify,[status(thm)],[f_4115_3]) ).

fof(f_4116_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_4116_2,plain,
    ! [U_16802,U_16801] : c_Relation_Oirrefl(U_16801,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16801,U_16801),tc_HOL_Obool)),U_16802),c_Relation_OId(U_16801))),
    inference(variable_rename,[status(thm)],[f_4116_1]) ).

fof(f_4116_3,plain,
    ! [U_16801,U_16802] : c_Relation_Oirrefl(U_16801,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16801,U_16801),tc_HOL_Obool)),U_16802),c_Relation_OId(U_16801))),
    inference(definitional_conversion,[status(esa)],[f_4116_2]) ).

cnf(f_4116_4,plain,
    c_Relation_Oirrefl(U_16801,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16801,U_16801),tc_HOL_Obool)),U_16802),c_Relation_OId(U_16801))),
    inference(clausify,[status(thm)],[f_4116_3]) ).

fof(f_4117_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_4117_2,plain,
    ! [U_16805,U_16804,U_16803] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16803,U_16803),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16803,U_16805)),U_16804))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16803,U_16803),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_16803,U_16803,U_16803),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16803,U_16803),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16803,U_16805)),U_16804)),U_16805)),U_16804))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16803,U_16803),tc_HOL_Obool)),c_Relation_OId(U_16803)),U_16804)) ),
    inference(variable_rename,[status(thm)],[f_4117_1]) ).

fof(f_4117_3,plain,
    ! [U_16803,U_16804,U_16805] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16803,U_16803),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16803,U_16805)),U_16804))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16803,U_16803),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_16803,U_16803,U_16803),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16803,U_16803),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16803,U_16805)),U_16804)),U_16805)),U_16804))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16803,U_16803),tc_HOL_Obool)),c_Relation_OId(U_16803)),U_16804)) ),
    inference(definitional_conversion,[status(esa)],[f_4117_2]) ).

cnf(f_4117_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16803,U_16803),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16803,U_16805)),U_16804))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16803,U_16803),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_16803,U_16803,U_16803),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_16803,U_16803),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_16803,U_16805)),U_16804)),U_16805)),U_16804))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16803,U_16803),tc_HOL_Obool)),c_Relation_OId(U_16803)),U_16804)) ),
    inference(clausify,[status(thm)],[f_4117_3]) ).

fof(f_4118_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_4118_2,plain,
    ! [U_16811,U_16810,U_16809,U_16808,U_16807,U_16806] :
      ( hAPP(c_Relation_OImage(U_16807,U_16806,U_16808),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16810,tc_fun(U_16807,tc_HOL_Obool)),U_16809),U_16811)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16810,tc_fun(U_16806,tc_HOL_Obool)),U_16809),hAPP(hAPP(c_COMBB(tc_fun(U_16807,tc_HOL_Obool),tc_fun(U_16806,tc_HOL_Obool),U_16810),c_Relation_OImage(U_16807,U_16806,U_16808)),U_16811))
      | U_16809 = c_Orderings_Obot__class_Obot(tc_fun(U_16810,tc_HOL_Obool))
      | ~ c_Relation_Osingle__valued(U_16806,U_16807,hAPP(c_Relation_Oconverse(U_16807,U_16806),U_16808)) ),
    inference(variable_rename,[status(thm)],[f_4118_1]) ).

fof(f_4118_3,plain,
    ! [U_16806,U_16807,U_16808,U_16809,U_16810,U_16811] :
      ( hAPP(c_Relation_OImage(U_16807,U_16806,U_16808),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16810,tc_fun(U_16807,tc_HOL_Obool)),U_16809),U_16811)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16810,tc_fun(U_16806,tc_HOL_Obool)),U_16809),hAPP(hAPP(c_COMBB(tc_fun(U_16807,tc_HOL_Obool),tc_fun(U_16806,tc_HOL_Obool),U_16810),c_Relation_OImage(U_16807,U_16806,U_16808)),U_16811))
      | U_16809 = c_Orderings_Obot__class_Obot(tc_fun(U_16810,tc_HOL_Obool))
      | ~ c_Relation_Osingle__valued(U_16806,U_16807,hAPP(c_Relation_Oconverse(U_16807,U_16806),U_16808)) ),
    inference(definitional_conversion,[status(esa)],[f_4118_2]) ).

cnf(f_4118_4,plain,
    ( hAPP(c_Relation_OImage(U_16807,U_16806,U_16808),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16810,tc_fun(U_16807,tc_HOL_Obool)),U_16809),U_16811)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16810,tc_fun(U_16806,tc_HOL_Obool)),U_16809),hAPP(hAPP(c_COMBB(tc_fun(U_16807,tc_HOL_Obool),tc_fun(U_16806,tc_HOL_Obool),U_16810),c_Relation_OImage(U_16807,U_16806,U_16808)),U_16811))
    | U_16809 = c_Orderings_Obot__class_Obot(tc_fun(U_16810,tc_HOL_Obool))
    | ~ c_Relation_Osingle__valued(U_16806,U_16807,hAPP(c_Relation_Oconverse(U_16807,U_16806),U_16808)) ),
    inference(clausify,[status(thm)],[f_4118_3]) ).

fof(f_4119_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_4119_2,plain,
    ! [U_16820,U_16819,U_16818,U_16817,U_16816,U_16815,U_16814,U_16813] :
      ( hAPP(c_Set_Oimage(U_16813,U_16814,U_16815),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16817,tc_fun(U_16813,tc_HOL_Obool)),U_16818),U_16819)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16817,tc_fun(U_16814,tc_HOL_Obool)),U_16818),hAPP(hAPP(c_COMBB(tc_fun(U_16813,tc_HOL_Obool),tc_fun(U_16814,tc_HOL_Obool),U_16817),c_Set_Oimage(U_16813,U_16814,U_16815)),U_16819))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16817),U_16820),U_16818))
      | ? [U_16812] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16813,tc_HOL_Obool)),hAPP(U_16819,U_16812)),U_16816))
          & hBOOL(hAPP(hAPP(c_member(U_16817),U_16812),U_16818)) )
      | ~ c_Fun_Oinj__on(U_16813,U_16814,U_16815,U_16816) ),
    inference(variable_rename,[status(thm)],[f_4119_1]) ).

fof(f_4119_3,plain,
    ! [U_16820,U_16819,U_16818,U_16817,U_16816,U_16815,U_16814,U_16813] :
      ( hAPP(c_Set_Oimage(U_16813,U_16814,U_16815),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16817,tc_fun(U_16813,tc_HOL_Obool)),U_16818),U_16819)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16817,tc_fun(U_16814,tc_HOL_Obool)),U_16818),hAPP(hAPP(c_COMBB(tc_fun(U_16813,tc_HOL_Obool),tc_fun(U_16814,tc_HOL_Obool),U_16817),c_Set_Oimage(U_16813,U_16814,U_16815)),U_16819))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16817),U_16820),U_16818))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16813,tc_HOL_Obool)),hAPP(U_16819,sK394(U_16820,U_16819,U_16818,U_16817,U_16816,U_16815,U_16814,U_16813))),U_16816))
        & hBOOL(hAPP(hAPP(c_member(U_16817),sK394(U_16820,U_16819,U_16818,U_16817,U_16816,U_16815,U_16814,U_16813)),U_16818)) )
      | ~ c_Fun_Oinj__on(U_16813,U_16814,U_16815,U_16816) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK394]),skolemize(U_16812,sK394(U_16820,U_16819,U_16818,U_16817,U_16816,U_16815,U_16814,U_16813))],[f_4119_2]) ).

fof(f_4119_4,plain,
    ( ! [U_16813,U_16815,U_16814,U_16816,U_16817,U_16818,U_16819,U_16820] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16813,tc_HOL_Obool)),hAPP(U_16819,sK394(U_16820,U_16819,U_16818,U_16817,U_16816,U_16815,U_16814,U_16813))),U_16816))
        | ~ sP1063(U_16813,U_16815,U_16814,U_16816,U_16817,U_16818,U_16819,U_16820) )
    & ! [U_16813,U_16815,U_16814,U_16816,U_16817,U_16818,U_16819,U_16820] :
        ( hBOOL(hAPP(hAPP(c_member(U_16817),sK394(U_16820,U_16819,U_16818,U_16817,U_16816,U_16815,U_16814,U_16813)),U_16818))
        | ~ sP1063(U_16813,U_16815,U_16814,U_16816,U_16817,U_16818,U_16819,U_16820) )
    & ! [U_16813,U_16815,U_16814,U_16816,U_16817,U_16818,U_16819,U_16820] :
        ( hAPP(c_Set_Oimage(U_16813,U_16814,U_16815),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16817,tc_fun(U_16813,tc_HOL_Obool)),U_16818),U_16819)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16817,tc_fun(U_16814,tc_HOL_Obool)),U_16818),hAPP(hAPP(c_COMBB(tc_fun(U_16813,tc_HOL_Obool),tc_fun(U_16814,tc_HOL_Obool),U_16817),c_Set_Oimage(U_16813,U_16814,U_16815)),U_16819))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16817),U_16820),U_16818))
        | sP1063(U_16813,U_16815,U_16814,U_16816,U_16817,U_16818,U_16819,U_16820)
        | ~ c_Fun_Oinj__on(U_16813,U_16814,U_16815,U_16816) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1063])],[f_4119_3]) ).

cnf(f_4119_5,plain,
    ( hAPP(c_Set_Oimage(U_16813,U_16814,U_16815),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16817,tc_fun(U_16813,tc_HOL_Obool)),U_16818),U_16819)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16817,tc_fun(U_16814,tc_HOL_Obool)),U_16818),hAPP(hAPP(c_COMBB(tc_fun(U_16813,tc_HOL_Obool),tc_fun(U_16814,tc_HOL_Obool),U_16817),c_Set_Oimage(U_16813,U_16814,U_16815)),U_16819))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16817),U_16820),U_16818))
    | sP1063(U_16813,U_16815,U_16814,U_16816,U_16817,U_16818,U_16819,U_16820)
    | ~ c_Fun_Oinj__on(U_16813,U_16814,U_16815,U_16816) ),
    inference(clausify,[status(thm)],[f_4119_4]) ).

cnf(f_4119_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16817),sK394(U_16820,U_16819,U_16818,U_16817,U_16816,U_16815,U_16814,U_16813)),U_16818))
    | ~ sP1063(U_16813,U_16815,U_16814,U_16816,U_16817,U_16818,U_16819,U_16820) ),
    inference(clausify,[status(thm)],[f_4119_4]) ).

cnf(f_4119_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16813,tc_HOL_Obool)),hAPP(U_16819,sK394(U_16820,U_16819,U_16818,U_16817,U_16816,U_16815,U_16814,U_16813))),U_16816))
    | ~ sP1063(U_16813,U_16815,U_16814,U_16816,U_16817,U_16818,U_16819,U_16820) ),
    inference(clausify,[status(thm)],[f_4119_4]) ).

fof(f_4120_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_4120_2,plain,
    ! [U_16821] : c_Relation_Osingle__valued(U_16821,U_16821,c_Relation_OId(U_16821)),
    inference(variable_rename,[status(thm)],[f_4120_1]) ).

fof(f_4120_3,plain,
    ! [U_16821] : c_Relation_Osingle__valued(U_16821,U_16821,c_Relation_OId(U_16821)),
    inference(definitional_conversion,[status(esa)],[f_4120_2]) ).

cnf(f_4120_4,plain,
    c_Relation_Osingle__valued(U_16821,U_16821,c_Relation_OId(U_16821)),
    inference(clausify,[status(thm)],[f_4120_3]) ).

fof(f_4121_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_4121_2,plain,
    ! [U_16826,U_16825,U_16824,U_16823,U_16822] :
      ( c_Relation_Osingle__valued(U_16822,U_16825,hAPP(hAPP(c_Relation_Orel__comp(U_16822,U_16823,U_16825),U_16824),U_16826))
      | ~ c_Relation_Osingle__valued(U_16823,U_16825,U_16826)
      | ~ c_Relation_Osingle__valued(U_16822,U_16823,U_16824) ),
    inference(variable_rename,[status(thm)],[f_4121_1]) ).

fof(f_4121_3,plain,
    ! [U_16824,U_16822,U_16825,U_16826,U_16823] :
      ( c_Relation_Osingle__valued(U_16822,U_16825,hAPP(hAPP(c_Relation_Orel__comp(U_16822,U_16823,U_16825),U_16824),U_16826))
      | ~ c_Relation_Osingle__valued(U_16823,U_16825,U_16826)
      | ~ c_Relation_Osingle__valued(U_16822,U_16823,U_16824) ),
    inference(definitional_conversion,[status(esa)],[f_4121_2]) ).

cnf(f_4121_4,plain,
    ( c_Relation_Osingle__valued(U_16822,U_16825,hAPP(hAPP(c_Relation_Orel__comp(U_16822,U_16823,U_16825),U_16824),U_16826))
    | ~ c_Relation_Osingle__valued(U_16823,U_16825,U_16826)
    | ~ c_Relation_Osingle__valued(U_16822,U_16823,U_16824) ),
    inference(clausify,[status(thm)],[f_4121_3]) ).

fof(f_4122_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_4122_2,plain,
    ! [U_16830,U_16829,U_16828,U_16827] :
      ( c_Relation_Osingle__valued(U_16827,U_16828,U_16829)
      | ~ c_Relation_Osingle__valued(U_16827,U_16828,U_16830)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16827,U_16828),tc_HOL_Obool)),U_16829),U_16830)) ),
    inference(variable_rename,[status(thm)],[f_4122_1]) ).

fof(f_4122_3,plain,
    ! [U_16828,U_16827,U_16829,U_16830] :
      ( c_Relation_Osingle__valued(U_16827,U_16828,U_16829)
      | ~ c_Relation_Osingle__valued(U_16827,U_16828,U_16830)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16827,U_16828),tc_HOL_Obool)),U_16829),U_16830)) ),
    inference(definitional_conversion,[status(esa)],[f_4122_2]) ).

cnf(f_4122_4,plain,
    ( c_Relation_Osingle__valued(U_16827,U_16828,U_16829)
    | ~ c_Relation_Osingle__valued(U_16827,U_16828,U_16830)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_16827,U_16828),tc_HOL_Obool)),U_16829),U_16830)) ),
    inference(clausify,[status(thm)],[f_4122_3]) ).

fof(f_4123_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_4123_2,plain,
    ! [U_16832,U_16831] : c_Relation_Osingle__valued(U_16831,U_16831,c_Relation_OId__on(U_16831,U_16832)),
    inference(variable_rename,[status(thm)],[f_4123_1]) ).

fof(f_4123_3,plain,
    ! [U_16831,U_16832] : c_Relation_Osingle__valued(U_16831,U_16831,c_Relation_OId__on(U_16831,U_16832)),
    inference(definitional_conversion,[status(esa)],[f_4123_2]) ).

cnf(f_4123_4,plain,
    c_Relation_Osingle__valued(U_16831,U_16831,c_Relation_OId__on(U_16831,U_16832)),
    inference(clausify,[status(thm)],[f_4123_3]) ).

fof(f_4124_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_4124_2,plain,
    ! [U_16841,U_16840,U_16839] :
      ( ( c_Relation_Osingle__valued(U_16839,U_16840,U_16841)
        | ? [U_16838,U_16837] :
            ( ? [U_16836] :
                ( U_16837 != U_16836
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16839,U_16840)),hAPP(hAPP(c_Product__Type_OPair(U_16839,U_16840),U_16838),U_16836)),U_16841)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16839,U_16840)),hAPP(hAPP(c_Product__Type_OPair(U_16839,U_16840),U_16838),U_16837)),U_16841)) ) )
      & ( ! [U_16835,U_16834] :
            ( ! [U_16833] :
                ( U_16834 = U_16833
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16839,U_16840)),hAPP(hAPP(c_Product__Type_OPair(U_16839,U_16840),U_16835),U_16833)),U_16841)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16839,U_16840)),hAPP(hAPP(c_Product__Type_OPair(U_16839,U_16840),U_16835),U_16834)),U_16841)) )
        | ~ c_Relation_Osingle__valued(U_16839,U_16840,U_16841) ) ),
    inference(variable_rename,[status(thm)],[f_4124_1]) ).

fof(f_4124_3,plain,
    ( ! [U_16847,U_16845,U_16843] :
        ( c_Relation_Osingle__valued(U_16843,U_16845,U_16847)
        | ? [U_16838,U_16837] :
            ( ? [U_16836] :
                ( U_16837 != U_16836
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16843,U_16845)),hAPP(hAPP(c_Product__Type_OPair(U_16843,U_16845),U_16838),U_16836)),U_16847)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16843,U_16845)),hAPP(hAPP(c_Product__Type_OPair(U_16843,U_16845),U_16838),U_16837)),U_16847)) ) )
    & ! [U_16846,U_16844,U_16842] :
        ( ! [U_16835,U_16834] :
            ( ! [U_16833] :
                ( U_16834 = U_16833
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16842,U_16844)),hAPP(hAPP(c_Product__Type_OPair(U_16842,U_16844),U_16835),U_16833)),U_16846)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16842,U_16844)),hAPP(hAPP(c_Product__Type_OPair(U_16842,U_16844),U_16835),U_16834)),U_16846)) )
        | ~ c_Relation_Osingle__valued(U_16842,U_16844,U_16846) ) ),
    inference(miniscope,[status(thm)],[f_4124_2]) ).

fof(f_4124_4,plain,
    ( ! [U_16847,U_16845,U_16843] :
        ( c_Relation_Osingle__valued(U_16843,U_16845,U_16847)
        | ? [U_16837] :
            ( ? [U_16836] :
                ( U_16837 != U_16836
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16843,U_16845)),hAPP(hAPP(c_Product__Type_OPair(U_16843,U_16845),sK395(U_16847,U_16845,U_16843)),U_16836)),U_16847)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16843,U_16845)),hAPP(hAPP(c_Product__Type_OPair(U_16843,U_16845),sK395(U_16847,U_16845,U_16843)),U_16837)),U_16847)) ) )
    & ! [U_16846,U_16844,U_16842] :
        ( ! [U_16835,U_16834] :
            ( ! [U_16833] :
                ( U_16834 = U_16833
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16842,U_16844)),hAPP(hAPP(c_Product__Type_OPair(U_16842,U_16844),U_16835),U_16833)),U_16846)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16842,U_16844)),hAPP(hAPP(c_Product__Type_OPair(U_16842,U_16844),U_16835),U_16834)),U_16846)) )
        | ~ c_Relation_Osingle__valued(U_16842,U_16844,U_16846) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK395]),skolemize(U_16838,sK395(U_16847,U_16845,U_16843))],[f_4124_3]) ).

fof(f_4124_5,plain,
    ( ! [U_16847,U_16845,U_16843] :
        ( c_Relation_Osingle__valued(U_16843,U_16845,U_16847)
        | ( ? [U_16836] :
              ( sK396(U_16847,U_16845,U_16843) != U_16836
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16843,U_16845)),hAPP(hAPP(c_Product__Type_OPair(U_16843,U_16845),sK395(U_16847,U_16845,U_16843)),U_16836)),U_16847)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16843,U_16845)),hAPP(hAPP(c_Product__Type_OPair(U_16843,U_16845),sK395(U_16847,U_16845,U_16843)),sK396(U_16847,U_16845,U_16843))),U_16847)) ) )
    & ! [U_16846,U_16844,U_16842] :
        ( ! [U_16835,U_16834] :
            ( ! [U_16833] :
                ( U_16834 = U_16833
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16842,U_16844)),hAPP(hAPP(c_Product__Type_OPair(U_16842,U_16844),U_16835),U_16833)),U_16846)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16842,U_16844)),hAPP(hAPP(c_Product__Type_OPair(U_16842,U_16844),U_16835),U_16834)),U_16846)) )
        | ~ c_Relation_Osingle__valued(U_16842,U_16844,U_16846) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK396]),skolemize(U_16837,sK396(U_16847,U_16845,U_16843))],[f_4124_4]) ).

fof(f_4124_6,plain,
    ( ! [U_16847,U_16845,U_16843] :
        ( c_Relation_Osingle__valued(U_16843,U_16845,U_16847)
        | ( sK396(U_16847,U_16845,U_16843) != sK397(U_16847,U_16845,U_16843)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16843,U_16845)),hAPP(hAPP(c_Product__Type_OPair(U_16843,U_16845),sK395(U_16847,U_16845,U_16843)),sK397(U_16847,U_16845,U_16843))),U_16847))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16843,U_16845)),hAPP(hAPP(c_Product__Type_OPair(U_16843,U_16845),sK395(U_16847,U_16845,U_16843)),sK396(U_16847,U_16845,U_16843))),U_16847)) ) )
    & ! [U_16846,U_16844,U_16842] :
        ( ! [U_16835,U_16834] :
            ( ! [U_16833] :
                ( U_16834 = U_16833
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16842,U_16844)),hAPP(hAPP(c_Product__Type_OPair(U_16842,U_16844),U_16835),U_16833)),U_16846)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16842,U_16844)),hAPP(hAPP(c_Product__Type_OPair(U_16842,U_16844),U_16835),U_16834)),U_16846)) )
        | ~ c_Relation_Osingle__valued(U_16842,U_16844,U_16846) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK397]),skolemize(U_16836,sK397(U_16847,U_16845,U_16843))],[f_4124_5]) ).

fof(f_4124_7,plain,
    ( ! [U_16843,U_16845,U_16847] :
        ( sK396(U_16847,U_16845,U_16843) != sK397(U_16847,U_16845,U_16843)
        | ~ sP1064(U_16843,U_16845,U_16847) )
    & ! [U_16843,U_16845,U_16847] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16843,U_16845)),hAPP(hAPP(c_Product__Type_OPair(U_16843,U_16845),sK395(U_16847,U_16845,U_16843)),sK397(U_16847,U_16845,U_16843))),U_16847))
        | ~ sP1064(U_16843,U_16845,U_16847) )
    & ! [U_16843,U_16845,U_16847] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16843,U_16845)),hAPP(hAPP(c_Product__Type_OPair(U_16843,U_16845),sK395(U_16847,U_16845,U_16843)),sK396(U_16847,U_16845,U_16843))),U_16847))
        | ~ sP1064(U_16843,U_16845,U_16847) )
    & ! [U_16843,U_16845,U_16847] :
        ( c_Relation_Osingle__valued(U_16843,U_16845,U_16847)
        | sP1064(U_16843,U_16845,U_16847) )
    & ! [U_16846,U_16833,U_16844,U_16834,U_16835,U_16842] :
        ( U_16834 = U_16833
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16842,U_16844)),hAPP(hAPP(c_Product__Type_OPair(U_16842,U_16844),U_16835),U_16833)),U_16846))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16842,U_16844)),hAPP(hAPP(c_Product__Type_OPair(U_16842,U_16844),U_16835),U_16834)),U_16846))
        | ~ c_Relation_Osingle__valued(U_16842,U_16844,U_16846) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1064])],[f_4124_6]) ).

cnf(f_4124_8,plain,
    ( U_16834 = U_16833
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16842,U_16844)),hAPP(hAPP(c_Product__Type_OPair(U_16842,U_16844),U_16835),U_16833)),U_16846))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16842,U_16844)),hAPP(hAPP(c_Product__Type_OPair(U_16842,U_16844),U_16835),U_16834)),U_16846))
    | ~ c_Relation_Osingle__valued(U_16842,U_16844,U_16846) ),
    inference(clausify,[status(thm)],[f_4124_7]) ).

cnf(f_4124_9,plain,
    ( c_Relation_Osingle__valued(U_16843,U_16845,U_16847)
    | sP1064(U_16843,U_16845,U_16847) ),
    inference(clausify,[status(thm)],[f_4124_7]) ).

cnf(f_4124_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16843,U_16845)),hAPP(hAPP(c_Product__Type_OPair(U_16843,U_16845),sK395(U_16847,U_16845,U_16843)),sK396(U_16847,U_16845,U_16843))),U_16847))
    | ~ sP1064(U_16843,U_16845,U_16847) ),
    inference(clausify,[status(thm)],[f_4124_7]) ).

cnf(f_4124_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16843,U_16845)),hAPP(hAPP(c_Product__Type_OPair(U_16843,U_16845),sK395(U_16847,U_16845,U_16843)),sK397(U_16847,U_16845,U_16843))),U_16847))
    | ~ sP1064(U_16843,U_16845,U_16847) ),
    inference(clausify,[status(thm)],[f_4124_7]) ).

cnf(f_4124_12,plain,
    ( sK396(U_16847,U_16845,U_16843) != sK397(U_16847,U_16845,U_16843)
    | ~ sP1064(U_16843,U_16845,U_16847) ),
    inference(clausify,[status(thm)],[f_4124_7]) ).

fof(f_4125_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_4125_2,plain,
    ! [U_16853,U_16852,U_16851,U_16850,U_16849,U_16848] :
      ( U_16852 = U_16853
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16848,U_16849)),hAPP(hAPP(c_Product__Type_OPair(U_16848,U_16849),U_16851),U_16853)),U_16850))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16848,U_16849)),hAPP(hAPP(c_Product__Type_OPair(U_16848,U_16849),U_16851),U_16852)),U_16850))
      | ~ c_Relation_Osingle__valued(U_16848,U_16849,U_16850) ),
    inference(variable_rename,[status(thm)],[f_4125_1]) ).

fof(f_4125_3,plain,
    ! [U_16850,U_16849,U_16848,U_16851,U_16852,U_16853] :
      ( U_16852 = U_16853
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16848,U_16849)),hAPP(hAPP(c_Product__Type_OPair(U_16848,U_16849),U_16851),U_16853)),U_16850))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16848,U_16849)),hAPP(hAPP(c_Product__Type_OPair(U_16848,U_16849),U_16851),U_16852)),U_16850))
      | ~ c_Relation_Osingle__valued(U_16848,U_16849,U_16850) ),
    inference(definitional_conversion,[status(esa)],[f_4125_2]) ).

cnf(f_4125_4,plain,
    ( U_16852 = U_16853
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16848,U_16849)),hAPP(hAPP(c_Product__Type_OPair(U_16848,U_16849),U_16851),U_16853)),U_16850))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16848,U_16849)),hAPP(hAPP(c_Product__Type_OPair(U_16848,U_16849),U_16851),U_16852)),U_16850))
    | ~ c_Relation_Osingle__valued(U_16848,U_16849,U_16850) ),
    inference(clausify,[status(thm)],[f_4125_3]) ).

fof(f_4126_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_4126_2,plain,
    ! [U_16858,U_16857,U_16856,U_16855,U_16854] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16854,U_16854)),hAPP(hAPP(c_Product__Type_OPair(U_16854,U_16854),U_16858),U_16857)),c_Transitive__Closure_Ortrancl(U_16854,U_16855)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16854,U_16854)),hAPP(hAPP(c_Product__Type_OPair(U_16854,U_16854),U_16857),U_16858)),c_Transitive__Closure_Ortrancl(U_16854,U_16855)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16854,U_16854)),hAPP(hAPP(c_Product__Type_OPair(U_16854,U_16854),U_16856),U_16858)),c_Transitive__Closure_Ortrancl(U_16854,U_16855)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16854,U_16854)),hAPP(hAPP(c_Product__Type_OPair(U_16854,U_16854),U_16856),U_16857)),c_Transitive__Closure_Ortrancl(U_16854,U_16855)))
      | ~ c_Relation_Osingle__valued(U_16854,U_16854,U_16855) ),
    inference(variable_rename,[status(thm)],[f_4126_1]) ).

fof(f_4126_3,plain,
    ! [U_16854,U_16855,U_16856,U_16857,U_16858] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16854,U_16854)),hAPP(hAPP(c_Product__Type_OPair(U_16854,U_16854),U_16858),U_16857)),c_Transitive__Closure_Ortrancl(U_16854,U_16855)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16854,U_16854)),hAPP(hAPP(c_Product__Type_OPair(U_16854,U_16854),U_16857),U_16858)),c_Transitive__Closure_Ortrancl(U_16854,U_16855)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16854,U_16854)),hAPP(hAPP(c_Product__Type_OPair(U_16854,U_16854),U_16856),U_16858)),c_Transitive__Closure_Ortrancl(U_16854,U_16855)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16854,U_16854)),hAPP(hAPP(c_Product__Type_OPair(U_16854,U_16854),U_16856),U_16857)),c_Transitive__Closure_Ortrancl(U_16854,U_16855)))
      | ~ c_Relation_Osingle__valued(U_16854,U_16854,U_16855) ),
    inference(definitional_conversion,[status(esa)],[f_4126_2]) ).

cnf(f_4126_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16854,U_16854)),hAPP(hAPP(c_Product__Type_OPair(U_16854,U_16854),U_16858),U_16857)),c_Transitive__Closure_Ortrancl(U_16854,U_16855)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16854,U_16854)),hAPP(hAPP(c_Product__Type_OPair(U_16854,U_16854),U_16857),U_16858)),c_Transitive__Closure_Ortrancl(U_16854,U_16855)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16854,U_16854)),hAPP(hAPP(c_Product__Type_OPair(U_16854,U_16854),U_16856),U_16858)),c_Transitive__Closure_Ortrancl(U_16854,U_16855)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16854,U_16854)),hAPP(hAPP(c_Product__Type_OPair(U_16854,U_16854),U_16856),U_16857)),c_Transitive__Closure_Ortrancl(U_16854,U_16855)))
    | ~ c_Relation_Osingle__valued(U_16854,U_16854,U_16855) ),
    inference(clausify,[status(thm)],[f_4126_3]) ).

fof(f_4127_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_4127_2,plain,
    ! [U_16863,U_16862,U_16861,U_16860,U_16859] :
      ( hAPP(c_Relation_OImage(U_16860,U_16859,U_16861),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16860,tc_HOL_Obool)),U_16862),U_16863)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16859,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16860,U_16859,U_16861),U_16862)),hAPP(c_Relation_OImage(U_16860,U_16859,U_16861),U_16863))
      | ~ c_Relation_Osingle__valued(U_16859,U_16860,hAPP(c_Relation_Oconverse(U_16860,U_16859),U_16861)) ),
    inference(variable_rename,[status(thm)],[f_4127_1]) ).

fof(f_4127_3,plain,
    ! [U_16859,U_16860,U_16861,U_16862,U_16863] :
      ( hAPP(c_Relation_OImage(U_16860,U_16859,U_16861),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16860,tc_HOL_Obool)),U_16862),U_16863)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16859,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16860,U_16859,U_16861),U_16862)),hAPP(c_Relation_OImage(U_16860,U_16859,U_16861),U_16863))
      | ~ c_Relation_Osingle__valued(U_16859,U_16860,hAPP(c_Relation_Oconverse(U_16860,U_16859),U_16861)) ),
    inference(definitional_conversion,[status(esa)],[f_4127_2]) ).

cnf(f_4127_4,plain,
    ( hAPP(c_Relation_OImage(U_16860,U_16859,U_16861),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16860,tc_HOL_Obool)),U_16862),U_16863)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16859,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16860,U_16859,U_16861),U_16862)),hAPP(c_Relation_OImage(U_16860,U_16859,U_16861),U_16863))
    | ~ c_Relation_Osingle__valued(U_16859,U_16860,hAPP(c_Relation_Oconverse(U_16860,U_16859),U_16861)) ),
    inference(clausify,[status(thm)],[f_4127_3]) ).

fof(f_4128_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_4128_2,plain,
    ! [U_16866,U_16865,U_16864] :
      ( ( c_Relation_Ototal__on(U_16864,U_16865,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16864,U_16864),tc_HOL_Obool)),U_16866),c_Relation_OId(U_16864)))
        | ~ c_Relation_Ototal__on(U_16864,U_16865,U_16866) )
      & ( c_Relation_Ototal__on(U_16864,U_16865,U_16866)
        | ~ c_Relation_Ototal__on(U_16864,U_16865,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16864,U_16864),tc_HOL_Obool)),U_16866),c_Relation_OId(U_16864))) ) ),
    inference(variable_rename,[status(thm)],[f_4128_1]) ).

fof(f_4128_3,plain,
    ( ! [U_16872,U_16870,U_16868] :
        ( c_Relation_Ototal__on(U_16868,U_16870,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16868,U_16868),tc_HOL_Obool)),U_16872),c_Relation_OId(U_16868)))
        | ~ c_Relation_Ototal__on(U_16868,U_16870,U_16872) )
    & ! [U_16871,U_16869,U_16867] :
        ( c_Relation_Ototal__on(U_16867,U_16869,U_16871)
        | ~ c_Relation_Ototal__on(U_16867,U_16869,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16867,U_16867),tc_HOL_Obool)),U_16871),c_Relation_OId(U_16867))) ) ),
    inference(miniscope,[status(thm)],[f_4128_2]) ).

fof(f_4128_4,plain,
    ( ! [U_16870,U_16868,U_16872] :
        ( c_Relation_Ototal__on(U_16868,U_16870,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16868,U_16868),tc_HOL_Obool)),U_16872),c_Relation_OId(U_16868)))
        | ~ c_Relation_Ototal__on(U_16868,U_16870,U_16872) )
    & ! [U_16869,U_16867,U_16871] :
        ( c_Relation_Ototal__on(U_16867,U_16869,U_16871)
        | ~ c_Relation_Ototal__on(U_16867,U_16869,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16867,U_16867),tc_HOL_Obool)),U_16871),c_Relation_OId(U_16867))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4128_3]) ).

cnf(f_4128_5,plain,
    ( c_Relation_Ototal__on(U_16867,U_16869,U_16871)
    | ~ c_Relation_Ototal__on(U_16867,U_16869,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16867,U_16867),tc_HOL_Obool)),U_16871),c_Relation_OId(U_16867))) ),
    inference(clausify,[status(thm)],[f_4128_4]) ).

cnf(f_4128_6,plain,
    ( c_Relation_Ototal__on(U_16868,U_16870,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_16868,U_16868),tc_HOL_Obool)),U_16872),c_Relation_OId(U_16868)))
    | ~ c_Relation_Ototal__on(U_16868,U_16870,U_16872) ),
    inference(clausify,[status(thm)],[f_4128_4]) ).

fof(f_4129_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_4129_2,plain,
    ! [U_16875,U_16874,U_16873] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16873,U_16873)),U_16874),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_16873,U_16873),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_16873,U_16873),tc_HOL_Obool),tc_fun(tc_prod(U_16873,U_16873),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_16873,U_16873),tc_HOL_Obool)),U_16875))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16873,U_16873)),U_16874),c_Transitive__Closure_Ortrancl(U_16873,U_16875))) ),
    inference(variable_rename,[status(thm)],[f_4129_1]) ).

fof(f_4129_3,plain,
    ! [U_16873,U_16874,U_16875] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16873,U_16873)),U_16874),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_16873,U_16873),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_16873,U_16873),tc_HOL_Obool),tc_fun(tc_prod(U_16873,U_16873),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_16873,U_16873),tc_HOL_Obool)),U_16875))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16873,U_16873)),U_16874),c_Transitive__Closure_Ortrancl(U_16873,U_16875))) ),
    inference(definitional_conversion,[status(esa)],[f_4129_2]) ).

cnf(f_4129_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16873,U_16873)),U_16874),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_16873,U_16873),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_16873,U_16873),tc_HOL_Obool),tc_fun(tc_prod(U_16873,U_16873),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_16873,U_16873),tc_HOL_Obool)),U_16875))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16873,U_16873)),U_16874),c_Transitive__Closure_Ortrancl(U_16873,U_16875))) ),
    inference(clausify,[status(thm)],[f_4129_3]) ).

fof(f_4130_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_4130_2,plain,
    ! [U_16877,U_16876] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16876,U_16876),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16877) = c_Relation_OId(U_16876),
    inference(variable_rename,[status(thm)],[f_4130_1]) ).

fof(f_4130_3,plain,
    ! [U_16876,U_16877] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16876,U_16876),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16877) = c_Relation_OId(U_16876),
    inference(definitional_conversion,[status(esa)],[f_4130_2]) ).

cnf(f_4130_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16876,U_16876),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16877) = c_Relation_OId(U_16876),
    inference(clausify,[status(thm)],[f_4130_3]) ).

fof(f_4131_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_4131_2,plain,
    ! [U_16880,U_16879,U_16878] :
      ( c_Relation_Osingle__valued(U_16878,U_16878,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16878,U_16878),tc_HOL_Obool),U_16880),U_16879))
      | ~ c_Relation_Osingle__valued(U_16878,U_16878,U_16879) ),
    inference(variable_rename,[status(thm)],[f_4131_1]) ).

fof(f_4131_3,plain,
    ! [U_16878,U_16879,U_16880] :
      ( c_Relation_Osingle__valued(U_16878,U_16878,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16878,U_16878),tc_HOL_Obool),U_16880),U_16879))
      | ~ c_Relation_Osingle__valued(U_16878,U_16878,U_16879) ),
    inference(definitional_conversion,[status(esa)],[f_4131_2]) ).

cnf(f_4131_4,plain,
    ( c_Relation_Osingle__valued(U_16878,U_16878,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16878,U_16878),tc_HOL_Obool),U_16880),U_16879))
    | ~ c_Relation_Osingle__valued(U_16878,U_16878,U_16879) ),
    inference(clausify,[status(thm)],[f_4131_3]) ).

fof(f_4132_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_4132_2,plain,
    ! [U_16885,U_16884,U_16883] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16883,U_16883)),U_16884),c_Transitive__Closure_Ortrancl(U_16883,U_16885)))
        | ! [U_16882] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16883,U_16883)),U_16884),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16883,U_16883),tc_HOL_Obool),U_16882),U_16885))) )
      & ( ? [U_16881] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16883,U_16883)),U_16884),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16883,U_16883),tc_HOL_Obool),U_16881),U_16885)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16883,U_16883)),U_16884),c_Transitive__Closure_Ortrancl(U_16883,U_16885))) ) ),
    inference(variable_rename,[status(thm)],[f_4132_1]) ).

fof(f_4132_3,plain,
    ( ! [U_16891,U_16889,U_16887] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16887,U_16887)),U_16889),c_Transitive__Closure_Ortrancl(U_16887,U_16891)))
        | ! [U_16882] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16887,U_16887)),U_16889),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16887,U_16887),tc_HOL_Obool),U_16882),U_16891))) )
    & ! [U_16890,U_16888,U_16886] :
        ( ? [U_16881] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16886,U_16886)),U_16888),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16886,U_16886),tc_HOL_Obool),U_16881),U_16890)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16886,U_16886)),U_16888),c_Transitive__Closure_Ortrancl(U_16886,U_16890))) ) ),
    inference(miniscope,[status(thm)],[f_4132_2]) ).

fof(f_4132_4,plain,
    ( ! [U_16891,U_16889,U_16887] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16887,U_16887)),U_16889),c_Transitive__Closure_Ortrancl(U_16887,U_16891)))
        | ! [U_16882] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16887,U_16887)),U_16889),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16887,U_16887),tc_HOL_Obool),U_16882),U_16891))) )
    & ! [U_16890,U_16888,U_16886] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16886,U_16886)),U_16888),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16886,U_16886),tc_HOL_Obool),sK398(U_16890,U_16888,U_16886)),U_16890)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16886,U_16886)),U_16888),c_Transitive__Closure_Ortrancl(U_16886,U_16890))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK398]),skolemize(U_16881,sK398(U_16890,U_16888,U_16886))],[f_4132_3]) ).

fof(f_4132_5,plain,
    ( ! [U_16882,U_16887,U_16889,U_16891] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16887,U_16887)),U_16889),c_Transitive__Closure_Ortrancl(U_16887,U_16891)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16887,U_16887)),U_16889),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16887,U_16887),tc_HOL_Obool),U_16882),U_16891))) )
    & ! [U_16888,U_16886,U_16890] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16886,U_16886)),U_16888),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16886,U_16886),tc_HOL_Obool),sK398(U_16890,U_16888,U_16886)),U_16890)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16886,U_16886)),U_16888),c_Transitive__Closure_Ortrancl(U_16886,U_16890))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4132_4]) ).

cnf(f_4132_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16886,U_16886)),U_16888),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16886,U_16886),tc_HOL_Obool),sK398(U_16890,U_16888,U_16886)),U_16890)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16886,U_16886)),U_16888),c_Transitive__Closure_Ortrancl(U_16886,U_16890))) ),
    inference(clausify,[status(thm)],[f_4132_5]) ).

cnf(f_4132_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16887,U_16887)),U_16889),c_Transitive__Closure_Ortrancl(U_16887,U_16891)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16887,U_16887)),U_16889),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16887,U_16887),tc_HOL_Obool),U_16882),U_16891))) ),
    inference(clausify,[status(thm)],[f_4132_5]) ).

fof(f_4133_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_4133_2,plain,
    ! [U_16895,U_16894,U_16893,U_16892] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16892,U_16892)),U_16893),c_Transitive__Closure_Ortrancl(U_16892,U_16895)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16892,U_16892)),U_16893),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16892,U_16892),tc_HOL_Obool),U_16894),U_16895))) ),
    inference(variable_rename,[status(thm)],[f_4133_1]) ).

fof(f_4133_3,plain,
    ! [U_16892,U_16893,U_16894,U_16895] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16892,U_16892)),U_16893),c_Transitive__Closure_Ortrancl(U_16892,U_16895)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16892,U_16892)),U_16893),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16892,U_16892),tc_HOL_Obool),U_16894),U_16895))) ),
    inference(definitional_conversion,[status(esa)],[f_4133_2]) ).

cnf(f_4133_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16892,U_16892)),U_16893),c_Transitive__Closure_Ortrancl(U_16892,U_16895)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16892,U_16892)),U_16893),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16892,U_16892),tc_HOL_Obool),U_16894),U_16895))) ),
    inference(clausify,[status(thm)],[f_4133_3]) ).

fof(f_4134_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_4134_2,plain,
    ! [U_16898,U_16897,U_16896] :
      ( c_Wellfounded_Owf(U_16896,U_16898)
      | ~ c_Wellfounded_Owf(U_16896,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16896,U_16896),tc_HOL_Obool),U_16897),U_16898)) ),
    inference(variable_rename,[status(thm)],[f_4134_1]) ).

fof(f_4134_3,plain,
    ! [U_16896,U_16897,U_16898] :
      ( c_Wellfounded_Owf(U_16896,U_16898)
      | ~ c_Wellfounded_Owf(U_16896,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16896,U_16896),tc_HOL_Obool),U_16897),U_16898)) ),
    inference(definitional_conversion,[status(esa)],[f_4134_2]) ).

cnf(f_4134_4,plain,
    ( c_Wellfounded_Owf(U_16896,U_16898)
    | ~ c_Wellfounded_Owf(U_16896,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16896,U_16896),tc_HOL_Obool),U_16897),U_16898)) ),
    inference(clausify,[status(thm)],[f_4134_3]) ).

fof(f_4135_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_4135_2,plain,
    ! [U_16902,U_16901,U_16900,U_16899] : hAPP(hAPP(c_Nat_Ocompow(U_16899,U_16899),U_16900),hAPP(hAPP(c_Nat_Ocompow(U_16899,U_16899),U_16901),U_16902)) = hAPP(hAPP(c_Nat_Ocompow(U_16899,U_16899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16901),U_16900)),U_16902),
    inference(variable_rename,[status(thm)],[f_4135_1]) ).

fof(f_4135_3,plain,
    ! [U_16899,U_16900,U_16901,U_16902] : hAPP(hAPP(c_Nat_Ocompow(U_16899,U_16899),U_16900),hAPP(hAPP(c_Nat_Ocompow(U_16899,U_16899),U_16901),U_16902)) = hAPP(hAPP(c_Nat_Ocompow(U_16899,U_16899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16901),U_16900)),U_16902),
    inference(definitional_conversion,[status(esa)],[f_4135_2]) ).

cnf(f_4135_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_16899,U_16899),U_16900),hAPP(hAPP(c_Nat_Ocompow(U_16899,U_16899),U_16901),U_16902)) = hAPP(hAPP(c_Nat_Ocompow(U_16899,U_16899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16901),U_16900)),U_16902),
    inference(clausify,[status(thm)],[f_4135_3]) ).

fof(f_4136_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_4136_2,plain,
    ! [U_16906,U_16905,U_16904,U_16903] : hAPP(U_16903,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_16904,U_16904),U_16905),U_16903),U_16906)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_16904,U_16904),U_16905),U_16903),hAPP(U_16903,U_16906)),
    inference(variable_rename,[status(thm)],[f_4136_1]) ).

fof(f_4136_3,plain,
    ! [U_16903,U_16904,U_16905,U_16906] : hAPP(U_16903,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_16904,U_16904),U_16905),U_16903),U_16906)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_16904,U_16904),U_16905),U_16903),hAPP(U_16903,U_16906)),
    inference(definitional_conversion,[status(esa)],[f_4136_2]) ).

cnf(f_4136_4,plain,
    hAPP(U_16903,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_16904,U_16904),U_16905),U_16903),U_16906)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_16904,U_16904),U_16905),U_16903),hAPP(U_16903,U_16906)),
    inference(clausify,[status(thm)],[f_4136_3]) ).

fof(f_4137_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_4137_2,plain,
    ! [U_16910,U_16909,U_16908,U_16907] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_16907,U_16908),tc_fun(U_16907,U_16908)),U_16909),c_Fun_Ocomp(U_16908,U_16908,U_16907,U_16910)) = c_Fun_Ocomp(U_16908,U_16908,U_16907,hAPP(hAPP(c_Nat_Ocompow(U_16908,U_16908),U_16909),U_16910)),
    inference(variable_rename,[status(thm)],[f_4137_1]) ).

fof(f_4137_3,plain,
    ! [U_16907,U_16908,U_16909,U_16910] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_16907,U_16908),tc_fun(U_16907,U_16908)),U_16909),c_Fun_Ocomp(U_16908,U_16908,U_16907,U_16910)) = c_Fun_Ocomp(U_16908,U_16908,U_16907,hAPP(hAPP(c_Nat_Ocompow(U_16908,U_16908),U_16909),U_16910)),
    inference(definitional_conversion,[status(esa)],[f_4137_2]) ).

cnf(f_4137_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_16907,U_16908),tc_fun(U_16907,U_16908)),U_16909),c_Fun_Ocomp(U_16908,U_16908,U_16907,U_16910)) = c_Fun_Ocomp(U_16908,U_16908,U_16907,hAPP(hAPP(c_Nat_Ocompow(U_16908,U_16908),U_16909),U_16910)),
    inference(clausify,[status(thm)],[f_4137_3]) ).

fof(f_4138_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_4138_2,plain,
    ! [U_16914,U_16913,U_16912,U_16911] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16911,U_16911),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16912),U_16913)),U_16914) = hAPP(hAPP(c_Relation_Orel__comp(U_16911,U_16911,U_16911),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16911,U_16911),tc_HOL_Obool),U_16912),U_16914)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16911,U_16911),tc_HOL_Obool),U_16913),U_16914)),
    inference(variable_rename,[status(thm)],[f_4138_1]) ).

fof(f_4138_3,plain,
    ! [U_16911,U_16912,U_16913,U_16914] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16911,U_16911),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16912),U_16913)),U_16914) = hAPP(hAPP(c_Relation_Orel__comp(U_16911,U_16911,U_16911),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16911,U_16911),tc_HOL_Obool),U_16912),U_16914)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16911,U_16911),tc_HOL_Obool),U_16913),U_16914)),
    inference(definitional_conversion,[status(esa)],[f_4138_2]) ).

cnf(f_4138_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16911,U_16911),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16912),U_16913)),U_16914) = hAPP(hAPP(c_Relation_Orel__comp(U_16911,U_16911,U_16911),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16911,U_16911),tc_HOL_Obool),U_16912),U_16914)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16911,U_16911),tc_HOL_Obool),U_16913),U_16914)),
    inference(clausify,[status(thm)],[f_4138_3]) ).

fof(f_4139_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_4139_2,plain,
    ! [U_16917,U_16916,U_16915] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16915,U_16915),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16916)),U_16917) = hAPP(hAPP(c_Relation_Orel__comp(U_16915,U_16915,U_16915),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16915,U_16915),tc_HOL_Obool),U_16916),U_16917)),U_16917),
    inference(variable_rename,[status(thm)],[f_4139_1]) ).

fof(f_4139_3,plain,
    ! [U_16915,U_16916,U_16917] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16915,U_16915),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16916)),U_16917) = hAPP(hAPP(c_Relation_Orel__comp(U_16915,U_16915,U_16915),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16915,U_16915),tc_HOL_Obool),U_16916),U_16917)),U_16917),
    inference(definitional_conversion,[status(esa)],[f_4139_2]) ).

cnf(f_4139_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16915,U_16915),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16916)),U_16917) = hAPP(hAPP(c_Relation_Orel__comp(U_16915,U_16915,U_16915),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16915,U_16915),tc_HOL_Obool),U_16916),U_16917)),U_16917),
    inference(clausify,[status(thm)],[f_4139_3]) ).

fof(f_4140_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_4140_2,plain,
    ! [U_16920,U_16919,U_16918] : hAPP(hAPP(c_Relation_Orel__comp(U_16918,U_16918,U_16918),U_16919),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16918,U_16918),tc_HOL_Obool),U_16920),U_16919)) = hAPP(hAPP(c_Relation_Orel__comp(U_16918,U_16918,U_16918),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16918,U_16918),tc_HOL_Obool),U_16920),U_16919)),U_16919),
    inference(variable_rename,[status(thm)],[f_4140_1]) ).

fof(f_4140_3,plain,
    ! [U_16918,U_16919,U_16920] : hAPP(hAPP(c_Relation_Orel__comp(U_16918,U_16918,U_16918),U_16919),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16918,U_16918),tc_HOL_Obool),U_16920),U_16919)) = hAPP(hAPP(c_Relation_Orel__comp(U_16918,U_16918,U_16918),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16918,U_16918),tc_HOL_Obool),U_16920),U_16919)),U_16919),
    inference(definitional_conversion,[status(esa)],[f_4140_2]) ).

cnf(f_4140_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_16918,U_16918,U_16918),U_16919),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16918,U_16918),tc_HOL_Obool),U_16920),U_16919)) = hAPP(hAPP(c_Relation_Orel__comp(U_16918,U_16918,U_16918),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16918,U_16918),tc_HOL_Obool),U_16920),U_16919)),U_16919),
    inference(clausify,[status(thm)],[f_4140_3]) ).

fof(f_4141_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_4141_2,plain,
    ! [U_16922,U_16921] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16921,U_16921),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_16922) = U_16922,
    inference(variable_rename,[status(thm)],[f_4141_1]) ).

fof(f_4141_3,plain,
    ! [U_16921,U_16922] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16921,U_16921),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_16922) = U_16922,
    inference(definitional_conversion,[status(esa)],[f_4141_2]) ).

cnf(f_4141_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16921,U_16921),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_16922) = U_16922,
    inference(clausify,[status(thm)],[f_4141_3]) ).

fof(f_4142_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_4142_2,plain,
    ! [U_16924,U_16923] : c_Relation_Ototal__on(U_16923,c_Orderings_Obot__class_Obot(tc_fun(U_16923,tc_HOL_Obool)),U_16924),
    inference(variable_rename,[status(thm)],[f_4142_1]) ).

fof(f_4142_3,plain,
    ! [U_16923,U_16924] : c_Relation_Ototal__on(U_16923,c_Orderings_Obot__class_Obot(tc_fun(U_16923,tc_HOL_Obool)),U_16924),
    inference(definitional_conversion,[status(esa)],[f_4142_2]) ).

cnf(f_4142_4,plain,
    c_Relation_Ototal__on(U_16923,c_Orderings_Obot__class_Obot(tc_fun(U_16923,tc_HOL_Obool)),U_16924),
    inference(clausify,[status(thm)],[f_4142_3]) ).

fof(f_4143_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_4143_2,plain,
    ! [U_16927,U_16926,U_16925] :
      ( ( c_Relation_Ototal__on(U_16925,U_16926,hAPP(c_Relation_Oconverse(U_16925,U_16925),U_16927))
        | ~ c_Relation_Ototal__on(U_16925,U_16926,U_16927) )
      & ( c_Relation_Ototal__on(U_16925,U_16926,U_16927)
        | ~ c_Relation_Ototal__on(U_16925,U_16926,hAPP(c_Relation_Oconverse(U_16925,U_16925),U_16927)) ) ),
    inference(variable_rename,[status(thm)],[f_4143_1]) ).

fof(f_4143_3,plain,
    ( ! [U_16933,U_16931,U_16929] :
        ( c_Relation_Ototal__on(U_16929,U_16931,hAPP(c_Relation_Oconverse(U_16929,U_16929),U_16933))
        | ~ c_Relation_Ototal__on(U_16929,U_16931,U_16933) )
    & ! [U_16932,U_16930,U_16928] :
        ( c_Relation_Ototal__on(U_16928,U_16930,U_16932)
        | ~ c_Relation_Ototal__on(U_16928,U_16930,hAPP(c_Relation_Oconverse(U_16928,U_16928),U_16932)) ) ),
    inference(miniscope,[status(thm)],[f_4143_2]) ).

fof(f_4143_4,plain,
    ( ! [U_16931,U_16929,U_16933] :
        ( c_Relation_Ototal__on(U_16929,U_16931,hAPP(c_Relation_Oconverse(U_16929,U_16929),U_16933))
        | ~ c_Relation_Ototal__on(U_16929,U_16931,U_16933) )
    & ! [U_16930,U_16932,U_16928] :
        ( c_Relation_Ototal__on(U_16928,U_16930,U_16932)
        | ~ c_Relation_Ototal__on(U_16928,U_16930,hAPP(c_Relation_Oconverse(U_16928,U_16928),U_16932)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4143_3]) ).

cnf(f_4143_5,plain,
    ( c_Relation_Ototal__on(U_16928,U_16930,U_16932)
    | ~ c_Relation_Ototal__on(U_16928,U_16930,hAPP(c_Relation_Oconverse(U_16928,U_16928),U_16932)) ),
    inference(clausify,[status(thm)],[f_4143_4]) ).

cnf(f_4143_6,plain,
    ( c_Relation_Ototal__on(U_16929,U_16931,hAPP(c_Relation_Oconverse(U_16929,U_16929),U_16933))
    | ~ c_Relation_Ototal__on(U_16929,U_16931,U_16933) ),
    inference(clausify,[status(thm)],[f_4143_4]) ).

fof(f_4144_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_4144_2,plain,
    ! [U_16937,U_16936,U_16935,U_16934] :
      ( U_16935 = U_16936
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16934,U_16934)),hAPP(hAPP(c_Product__Type_OPair(U_16934,U_16934),U_16935),U_16936)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16934,U_16934),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16937))) ),
    inference(variable_rename,[status(thm)],[f_4144_1]) ).

fof(f_4144_3,plain,
    ! [U_16937,U_16936,U_16935] :
      ( ! [U_16934] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16934,U_16934)),hAPP(hAPP(c_Product__Type_OPair(U_16934,U_16934),U_16935),U_16936)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16934,U_16934),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16937)))
      | U_16935 = U_16936 ),
    inference(miniscope,[status(thm)],[f_4144_2]) ).

fof(f_4144_4,plain,
    ! [U_16934,U_16935,U_16936,U_16937] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16934,U_16934)),hAPP(hAPP(c_Product__Type_OPair(U_16934,U_16934),U_16935),U_16936)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16934,U_16934),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16937)))
      | U_16935 = U_16936 ),
    inference(definitional_conversion,[status(esa)],[f_4144_3]) ).

cnf(f_4144_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16934,U_16934)),hAPP(hAPP(c_Product__Type_OPair(U_16934,U_16934),U_16935),U_16936)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16934,U_16934),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16937)))
    | U_16935 = U_16936 ),
    inference(clausify,[status(thm)],[f_4144_4]) ).

fof(f_4145_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_4145_2,plain,
    ! [U_16940,U_16939,U_16938] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16938,U_16938)),hAPP(hAPP(c_Product__Type_OPair(U_16938,U_16938),U_16939),U_16939)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16938,U_16938),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16940))),
    inference(variable_rename,[status(thm)],[f_4145_1]) ).

fof(f_4145_3,plain,
    ! [U_16938,U_16939,U_16940] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16938,U_16938)),hAPP(hAPP(c_Product__Type_OPair(U_16938,U_16938),U_16939),U_16939)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16938,U_16938),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16940))),
    inference(definitional_conversion,[status(esa)],[f_4145_2]) ).

cnf(f_4145_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_16938,U_16938)),hAPP(hAPP(c_Product__Type_OPair(U_16938,U_16938),U_16939),U_16939)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16938,U_16938),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16940))),
    inference(clausify,[status(thm)],[f_4145_3]) ).

fof(f_4146_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_4146_2,plain,
    ! [U_16946,U_16945,U_16944,U_16943,U_16942,U_16941] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16941,U_16941)),hAPP(hAPP(c_Product__Type_OPair(U_16941,U_16941),U_16942),U_16945)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16941,U_16941),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16946)),U_16944)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16941,U_16941)),hAPP(hAPP(c_Product__Type_OPair(U_16941,U_16941),U_16943),U_16945)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16941,U_16941),tc_HOL_Obool),U_16946),U_16944)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16941,U_16941)),hAPP(hAPP(c_Product__Type_OPair(U_16941,U_16941),U_16942),U_16943)),U_16944)) ),
    inference(variable_rename,[status(thm)],[f_4146_1]) ).

fof(f_4146_3,plain,
    ! [U_16941,U_16942,U_16943,U_16944,U_16945,U_16946] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16941,U_16941)),hAPP(hAPP(c_Product__Type_OPair(U_16941,U_16941),U_16942),U_16945)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16941,U_16941),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16946)),U_16944)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16941,U_16941)),hAPP(hAPP(c_Product__Type_OPair(U_16941,U_16941),U_16943),U_16945)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16941,U_16941),tc_HOL_Obool),U_16946),U_16944)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16941,U_16941)),hAPP(hAPP(c_Product__Type_OPair(U_16941,U_16941),U_16942),U_16943)),U_16944)) ),
    inference(definitional_conversion,[status(esa)],[f_4146_2]) ).

cnf(f_4146_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16941,U_16941)),hAPP(hAPP(c_Product__Type_OPair(U_16941,U_16941),U_16942),U_16945)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16941,U_16941),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16946)),U_16944)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16941,U_16941)),hAPP(hAPP(c_Product__Type_OPair(U_16941,U_16941),U_16943),U_16945)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16941,U_16941),tc_HOL_Obool),U_16946),U_16944)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16941,U_16941)),hAPP(hAPP(c_Product__Type_OPair(U_16941,U_16941),U_16942),U_16943)),U_16944)) ),
    inference(clausify,[status(thm)],[f_4146_3]) ).

fof(f_4147_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_4147_2,plain,
    ! [U_16952,U_16951,U_16950,U_16949,U_16948,U_16947] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16947,U_16947)),hAPP(hAPP(c_Product__Type_OPair(U_16947,U_16947),U_16948),U_16952)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16947,U_16947),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16950)),U_16951)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16947,U_16947)),hAPP(hAPP(c_Product__Type_OPair(U_16947,U_16947),U_16949),U_16952)),U_16951))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16947,U_16947)),hAPP(hAPP(c_Product__Type_OPair(U_16947,U_16947),U_16948),U_16949)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16947,U_16947),tc_HOL_Obool),U_16950),U_16951))) ),
    inference(variable_rename,[status(thm)],[f_4147_1]) ).

fof(f_4147_3,plain,
    ! [U_16947,U_16948,U_16949,U_16950,U_16951,U_16952] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16947,U_16947)),hAPP(hAPP(c_Product__Type_OPair(U_16947,U_16947),U_16948),U_16952)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16947,U_16947),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16950)),U_16951)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16947,U_16947)),hAPP(hAPP(c_Product__Type_OPair(U_16947,U_16947),U_16949),U_16952)),U_16951))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16947,U_16947)),hAPP(hAPP(c_Product__Type_OPair(U_16947,U_16947),U_16948),U_16949)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16947,U_16947),tc_HOL_Obool),U_16950),U_16951))) ),
    inference(definitional_conversion,[status(esa)],[f_4147_2]) ).

cnf(f_4147_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16947,U_16947)),hAPP(hAPP(c_Product__Type_OPair(U_16947,U_16947),U_16948),U_16952)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16947,U_16947),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_16950)),U_16951)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16947,U_16947)),hAPP(hAPP(c_Product__Type_OPair(U_16947,U_16947),U_16949),U_16952)),U_16951))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16947,U_16947)),hAPP(hAPP(c_Product__Type_OPair(U_16947,U_16947),U_16948),U_16949)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16947,U_16947),tc_HOL_Obool),U_16950),U_16951))) ),
    inference(clausify,[status(thm)],[f_4147_3]) ).

fof(f_4148_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_4148_2,plain,
    ! [U_16955,U_16954,U_16953] : hAPP(hAPP(c_Nat_Ocompow(U_16953,U_16953),hAPP(c_Nat_OSuc,U_16954)),U_16955) = hAPP(c_Fun_Ocomp(U_16953,U_16953,U_16953,U_16955),hAPP(hAPP(c_Nat_Ocompow(U_16953,U_16953),U_16954),U_16955)),
    inference(variable_rename,[status(thm)],[f_4148_1]) ).

fof(f_4148_3,plain,
    ! [U_16954,U_16953,U_16955] : hAPP(hAPP(c_Nat_Ocompow(U_16953,U_16953),hAPP(c_Nat_OSuc,U_16954)),U_16955) = hAPP(c_Fun_Ocomp(U_16953,U_16953,U_16953,U_16955),hAPP(hAPP(c_Nat_Ocompow(U_16953,U_16953),U_16954),U_16955)),
    inference(definitional_conversion,[status(esa)],[f_4148_2]) ).

cnf(f_4148_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_16953,U_16953),hAPP(c_Nat_OSuc,U_16954)),U_16955) = hAPP(c_Fun_Ocomp(U_16953,U_16953,U_16953,U_16955),hAPP(hAPP(c_Nat_Ocompow(U_16953,U_16953),U_16954),U_16955)),
    inference(clausify,[status(thm)],[f_4148_3]) ).

fof(f_4149_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_4149_2,plain,
    ! [U_16959,U_16958,U_16957,U_16956] : hAPP(hAPP(c_Nat_Ocompow(U_16956,U_16956),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16957),U_16958)),U_16959) = hAPP(c_Fun_Ocomp(U_16956,U_16956,U_16956,hAPP(hAPP(c_Nat_Ocompow(U_16956,U_16956),U_16957),U_16959)),hAPP(hAPP(c_Nat_Ocompow(U_16956,U_16956),U_16958),U_16959)),
    inference(variable_rename,[status(thm)],[f_4149_1]) ).

fof(f_4149_3,plain,
    ! [U_16956,U_16957,U_16958,U_16959] : hAPP(hAPP(c_Nat_Ocompow(U_16956,U_16956),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16957),U_16958)),U_16959) = hAPP(c_Fun_Ocomp(U_16956,U_16956,U_16956,hAPP(hAPP(c_Nat_Ocompow(U_16956,U_16956),U_16957),U_16959)),hAPP(hAPP(c_Nat_Ocompow(U_16956,U_16956),U_16958),U_16959)),
    inference(definitional_conversion,[status(esa)],[f_4149_2]) ).

cnf(f_4149_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_16956,U_16956),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16957),U_16958)),U_16959) = hAPP(c_Fun_Ocomp(U_16956,U_16956,U_16956,hAPP(hAPP(c_Nat_Ocompow(U_16956,U_16956),U_16957),U_16959)),hAPP(hAPP(c_Nat_Ocompow(U_16956,U_16956),U_16958),U_16959)),
    inference(clausify,[status(thm)],[f_4149_3]) ).

fof(f_4150_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_4150_2,plain,
    ! [U_16961,U_16960] : hAPP(hAPP(c_Nat_Ocompow(U_16960,U_16960),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16961) = c_Fun_Oid(U_16960),
    inference(variable_rename,[status(thm)],[f_4150_1]) ).

fof(f_4150_3,plain,
    ! [U_16961,U_16960] : hAPP(hAPP(c_Nat_Ocompow(U_16960,U_16960),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16961) = c_Fun_Oid(U_16960),
    inference(definitional_conversion,[status(esa)],[f_4150_2]) ).

cnf(f_4150_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_16960,U_16960),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16961) = c_Fun_Oid(U_16960),
    inference(clausify,[status(thm)],[f_4150_3]) ).

fof(f_4151_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_4151_2,plain,
    ! [U_16966,U_16965,U_16964] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16964,U_16964)),U_16965),c_Transitive__Closure_Otrancl(U_16964,U_16966)))
        | ! [U_16963] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16964,U_16964)),U_16965),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16964,U_16964),tc_HOL_Obool),U_16963),U_16966)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16963)) ) )
      & ( ? [U_16962] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16964,U_16964)),U_16965),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16964,U_16964),tc_HOL_Obool),U_16962),U_16966)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16962)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16964,U_16964)),U_16965),c_Transitive__Closure_Otrancl(U_16964,U_16966))) ) ),
    inference(variable_rename,[status(thm)],[f_4151_1]) ).

fof(f_4151_3,plain,
    ( ! [U_16972,U_16970,U_16968] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16968,U_16968)),U_16970),c_Transitive__Closure_Otrancl(U_16968,U_16972)))
        | ! [U_16963] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16968,U_16968)),U_16970),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16968,U_16968),tc_HOL_Obool),U_16963),U_16972)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16963)) ) )
    & ! [U_16971,U_16969,U_16967] :
        ( ? [U_16962] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16967,U_16967)),U_16969),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16967,U_16967),tc_HOL_Obool),U_16962),U_16971)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16962)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16967,U_16967)),U_16969),c_Transitive__Closure_Otrancl(U_16967,U_16971))) ) ),
    inference(miniscope,[status(thm)],[f_4151_2]) ).

fof(f_4151_4,plain,
    ( ! [U_16972,U_16970,U_16968] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16968,U_16968)),U_16970),c_Transitive__Closure_Otrancl(U_16968,U_16972)))
        | ! [U_16963] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16968,U_16968)),U_16970),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16968,U_16968),tc_HOL_Obool),U_16963),U_16972)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16963)) ) )
    & ! [U_16971,U_16969,U_16967] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16967,U_16967)),U_16969),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16967,U_16967),tc_HOL_Obool),sK399(U_16971,U_16969,U_16967)),U_16971)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK399(U_16971,U_16969,U_16967))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16967,U_16967)),U_16969),c_Transitive__Closure_Otrancl(U_16967,U_16971))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK399]),skolemize(U_16962,sK399(U_16971,U_16969,U_16967))],[f_4151_3]) ).

fof(f_4151_5,plain,
    ( ! [U_16969,U_16967,U_16971] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16967,U_16967)),U_16969),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16967,U_16967),tc_HOL_Obool),sK399(U_16971,U_16969,U_16967)),U_16971)))
        | ~ sP1065(U_16969,U_16967,U_16971) )
    & ! [U_16969,U_16967,U_16971] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK399(U_16971,U_16969,U_16967)))
        | ~ sP1065(U_16969,U_16967,U_16971) )
    & ! [U_16972,U_16963,U_16970,U_16968] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16968,U_16968)),U_16970),c_Transitive__Closure_Otrancl(U_16968,U_16972)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16968,U_16968)),U_16970),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16968,U_16968),tc_HOL_Obool),U_16963),U_16972)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16963)) )
    & ! [U_16969,U_16967,U_16971] :
        ( sP1065(U_16969,U_16967,U_16971)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16967,U_16967)),U_16969),c_Transitive__Closure_Otrancl(U_16967,U_16971))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1065])],[f_4151_4]) ).

cnf(f_4151_6,plain,
    ( sP1065(U_16969,U_16967,U_16971)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16967,U_16967)),U_16969),c_Transitive__Closure_Otrancl(U_16967,U_16971))) ),
    inference(clausify,[status(thm)],[f_4151_5]) ).

cnf(f_4151_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16968,U_16968)),U_16970),c_Transitive__Closure_Otrancl(U_16968,U_16972)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16968,U_16968)),U_16970),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16968,U_16968),tc_HOL_Obool),U_16963),U_16972)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16963)) ),
    inference(clausify,[status(thm)],[f_4151_5]) ).

cnf(f_4151_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK399(U_16971,U_16969,U_16967)))
    | ~ sP1065(U_16969,U_16967,U_16971) ),
    inference(clausify,[status(thm)],[f_4151_5]) ).

cnf(f_4151_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16967,U_16967)),U_16969),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16967,U_16967),tc_HOL_Obool),sK399(U_16971,U_16969,U_16967)),U_16971)))
    | ~ sP1065(U_16969,U_16967,U_16971) ),
    inference(clausify,[status(thm)],[f_4151_5]) ).

fof(f_4152_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_4152_2,plain,
    ! [U_16979,U_16978,U_16977] :
      ( ( c_Relation_Ototal__on(U_16977,U_16978,U_16979)
        | ? [U_16976] :
            ( ? [U_16975] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16977,U_16977)),hAPP(hAPP(c_Product__Type_OPair(U_16977,U_16977),U_16975),U_16976)),U_16979))
                & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16977,U_16977)),hAPP(hAPP(c_Product__Type_OPair(U_16977,U_16977),U_16976),U_16975)),U_16979))
                & U_16976 != U_16975
                & hBOOL(hAPP(hAPP(c_member(U_16977),U_16975),U_16978)) )
            & hBOOL(hAPP(hAPP(c_member(U_16977),U_16976),U_16978)) ) )
      & ( ! [U_16974] :
            ( ! [U_16973] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16977,U_16977)),hAPP(hAPP(c_Product__Type_OPair(U_16977,U_16977),U_16973),U_16974)),U_16979))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16977,U_16977)),hAPP(hAPP(c_Product__Type_OPair(U_16977,U_16977),U_16974),U_16973)),U_16979))
                | U_16974 = U_16973
                | ~ hBOOL(hAPP(hAPP(c_member(U_16977),U_16973),U_16978)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_16977),U_16974),U_16978)) )
        | ~ c_Relation_Ototal__on(U_16977,U_16978,U_16979) ) ),
    inference(variable_rename,[status(thm)],[f_4152_1]) ).

fof(f_4152_3,plain,
    ( ! [U_16985,U_16983,U_16981] :
        ( c_Relation_Ototal__on(U_16981,U_16983,U_16985)
        | ? [U_16976] :
            ( ? [U_16975] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16981,U_16981)),hAPP(hAPP(c_Product__Type_OPair(U_16981,U_16981),U_16975),U_16976)),U_16985))
                & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16981,U_16981)),hAPP(hAPP(c_Product__Type_OPair(U_16981,U_16981),U_16976),U_16975)),U_16985))
                & U_16976 != U_16975
                & hBOOL(hAPP(hAPP(c_member(U_16981),U_16975),U_16983)) )
            & hBOOL(hAPP(hAPP(c_member(U_16981),U_16976),U_16983)) ) )
    & ! [U_16984,U_16982,U_16980] :
        ( ! [U_16974] :
            ( ! [U_16973] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16980,U_16980)),hAPP(hAPP(c_Product__Type_OPair(U_16980,U_16980),U_16973),U_16974)),U_16984))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16980,U_16980)),hAPP(hAPP(c_Product__Type_OPair(U_16980,U_16980),U_16974),U_16973)),U_16984))
                | U_16974 = U_16973
                | ~ hBOOL(hAPP(hAPP(c_member(U_16980),U_16973),U_16982)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_16980),U_16974),U_16982)) )
        | ~ c_Relation_Ototal__on(U_16980,U_16982,U_16984) ) ),
    inference(miniscope,[status(thm)],[f_4152_2]) ).

fof(f_4152_4,plain,
    ( ! [U_16985,U_16983,U_16981] :
        ( c_Relation_Ototal__on(U_16981,U_16983,U_16985)
        | ( ? [U_16975] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16981,U_16981)),hAPP(hAPP(c_Product__Type_OPair(U_16981,U_16981),U_16975),sK400(U_16985,U_16983,U_16981))),U_16985))
              & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16981,U_16981)),hAPP(hAPP(c_Product__Type_OPair(U_16981,U_16981),sK400(U_16985,U_16983,U_16981)),U_16975)),U_16985))
              & sK400(U_16985,U_16983,U_16981) != U_16975
              & hBOOL(hAPP(hAPP(c_member(U_16981),U_16975),U_16983)) )
          & hBOOL(hAPP(hAPP(c_member(U_16981),sK400(U_16985,U_16983,U_16981)),U_16983)) ) )
    & ! [U_16984,U_16982,U_16980] :
        ( ! [U_16974] :
            ( ! [U_16973] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16980,U_16980)),hAPP(hAPP(c_Product__Type_OPair(U_16980,U_16980),U_16973),U_16974)),U_16984))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16980,U_16980)),hAPP(hAPP(c_Product__Type_OPair(U_16980,U_16980),U_16974),U_16973)),U_16984))
                | U_16974 = U_16973
                | ~ hBOOL(hAPP(hAPP(c_member(U_16980),U_16973),U_16982)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_16980),U_16974),U_16982)) )
        | ~ c_Relation_Ototal__on(U_16980,U_16982,U_16984) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK400]),skolemize(U_16976,sK400(U_16985,U_16983,U_16981))],[f_4152_3]) ).

fof(f_4152_5,plain,
    ( ! [U_16985,U_16983,U_16981] :
        ( c_Relation_Ototal__on(U_16981,U_16983,U_16985)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16981,U_16981)),hAPP(hAPP(c_Product__Type_OPair(U_16981,U_16981),sK401(U_16985,U_16983,U_16981)),sK400(U_16985,U_16983,U_16981))),U_16985))
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16981,U_16981)),hAPP(hAPP(c_Product__Type_OPair(U_16981,U_16981),sK400(U_16985,U_16983,U_16981)),sK401(U_16985,U_16983,U_16981))),U_16985))
          & sK400(U_16985,U_16983,U_16981) != sK401(U_16985,U_16983,U_16981)
          & hBOOL(hAPP(hAPP(c_member(U_16981),sK401(U_16985,U_16983,U_16981)),U_16983))
          & hBOOL(hAPP(hAPP(c_member(U_16981),sK400(U_16985,U_16983,U_16981)),U_16983)) ) )
    & ! [U_16984,U_16982,U_16980] :
        ( ! [U_16974] :
            ( ! [U_16973] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16980,U_16980)),hAPP(hAPP(c_Product__Type_OPair(U_16980,U_16980),U_16973),U_16974)),U_16984))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16980,U_16980)),hAPP(hAPP(c_Product__Type_OPair(U_16980,U_16980),U_16974),U_16973)),U_16984))
                | U_16974 = U_16973
                | ~ hBOOL(hAPP(hAPP(c_member(U_16980),U_16973),U_16982)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_16980),U_16974),U_16982)) )
        | ~ c_Relation_Ototal__on(U_16980,U_16982,U_16984) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK401]),skolemize(U_16975,sK401(U_16985,U_16983,U_16981))],[f_4152_4]) ).

fof(f_4152_6,plain,
    ( ! [U_16981,U_16983,U_16985] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16981,U_16981)),hAPP(hAPP(c_Product__Type_OPair(U_16981,U_16981),sK401(U_16985,U_16983,U_16981)),sK400(U_16985,U_16983,U_16981))),U_16985))
        | ~ sP1066(U_16981,U_16983,U_16985) )
    & ! [U_16981,U_16983,U_16985] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16981,U_16981)),hAPP(hAPP(c_Product__Type_OPair(U_16981,U_16981),sK400(U_16985,U_16983,U_16981)),sK401(U_16985,U_16983,U_16981))),U_16985))
        | ~ sP1066(U_16981,U_16983,U_16985) )
    & ! [U_16981,U_16983,U_16985] :
        ( sK400(U_16985,U_16983,U_16981) != sK401(U_16985,U_16983,U_16981)
        | ~ sP1066(U_16981,U_16983,U_16985) )
    & ! [U_16981,U_16983,U_16985] :
        ( hBOOL(hAPP(hAPP(c_member(U_16981),sK401(U_16985,U_16983,U_16981)),U_16983))
        | ~ sP1066(U_16981,U_16983,U_16985) )
    & ! [U_16981,U_16983,U_16985] :
        ( hBOOL(hAPP(hAPP(c_member(U_16981),sK400(U_16985,U_16983,U_16981)),U_16983))
        | ~ sP1066(U_16981,U_16983,U_16985) )
    & ! [U_16981,U_16983,U_16985] :
        ( c_Relation_Ototal__on(U_16981,U_16983,U_16985)
        | sP1066(U_16981,U_16983,U_16985) )
    & ! [U_16974,U_16973,U_16980,U_16984,U_16982] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16980,U_16980)),hAPP(hAPP(c_Product__Type_OPair(U_16980,U_16980),U_16973),U_16974)),U_16984))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16980,U_16980)),hAPP(hAPP(c_Product__Type_OPair(U_16980,U_16980),U_16974),U_16973)),U_16984))
        | U_16974 = U_16973
        | ~ hBOOL(hAPP(hAPP(c_member(U_16980),U_16973),U_16982))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16980),U_16974),U_16982))
        | ~ c_Relation_Ototal__on(U_16980,U_16982,U_16984) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1066])],[f_4152_5]) ).

cnf(f_4152_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16980,U_16980)),hAPP(hAPP(c_Product__Type_OPair(U_16980,U_16980),U_16973),U_16974)),U_16984))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16980,U_16980)),hAPP(hAPP(c_Product__Type_OPair(U_16980,U_16980),U_16974),U_16973)),U_16984))
    | U_16974 = U_16973
    | ~ hBOOL(hAPP(hAPP(c_member(U_16980),U_16973),U_16982))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16980),U_16974),U_16982))
    | ~ c_Relation_Ototal__on(U_16980,U_16982,U_16984) ),
    inference(clausify,[status(thm)],[f_4152_6]) ).

cnf(f_4152_8,plain,
    ( c_Relation_Ototal__on(U_16981,U_16983,U_16985)
    | sP1066(U_16981,U_16983,U_16985) ),
    inference(clausify,[status(thm)],[f_4152_6]) ).

cnf(f_4152_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16981),sK400(U_16985,U_16983,U_16981)),U_16983))
    | ~ sP1066(U_16981,U_16983,U_16985) ),
    inference(clausify,[status(thm)],[f_4152_6]) ).

cnf(f_4152_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16981),sK401(U_16985,U_16983,U_16981)),U_16983))
    | ~ sP1066(U_16981,U_16983,U_16985) ),
    inference(clausify,[status(thm)],[f_4152_6]) ).

cnf(f_4152_11,plain,
    ( sK400(U_16985,U_16983,U_16981) != sK401(U_16985,U_16983,U_16981)
    | ~ sP1066(U_16981,U_16983,U_16985) ),
    inference(clausify,[status(thm)],[f_4152_6]) ).

cnf(f_4152_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16981,U_16981)),hAPP(hAPP(c_Product__Type_OPair(U_16981,U_16981),sK400(U_16985,U_16983,U_16981)),sK401(U_16985,U_16983,U_16981))),U_16985))
    | ~ sP1066(U_16981,U_16983,U_16985) ),
    inference(clausify,[status(thm)],[f_4152_6]) ).

cnf(f_4152_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16981,U_16981)),hAPP(hAPP(c_Product__Type_OPair(U_16981,U_16981),sK401(U_16985,U_16983,U_16981)),sK400(U_16985,U_16983,U_16981))),U_16985))
    | ~ sP1066(U_16981,U_16983,U_16985) ),
    inference(clausify,[status(thm)],[f_4152_6]) ).

fof(f_4153_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_4153_2,plain,
    ! [U_16987,U_16986] : c_Transitive__Closure_Ortrancl(U_16986,U_16987) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_16986,U_16986),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_16986,U_16986),tc_HOL_Obool),tc_fun(tc_prod(U_16986,U_16986),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_16986,U_16986),tc_HOL_Obool)),U_16987)),
    inference(variable_rename,[status(thm)],[f_4153_1]) ).

fof(f_4153_3,plain,
    ! [U_16987,U_16986] : c_Transitive__Closure_Ortrancl(U_16986,U_16987) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_16986,U_16986),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_16986,U_16986),tc_HOL_Obool),tc_fun(tc_prod(U_16986,U_16986),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_16986,U_16986),tc_HOL_Obool)),U_16987)),
    inference(definitional_conversion,[status(esa)],[f_4153_2]) ).

cnf(f_4153_4,plain,
    c_Transitive__Closure_Ortrancl(U_16986,U_16987) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_16986,U_16986),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_16986,U_16986),tc_HOL_Obool),tc_fun(tc_prod(U_16986,U_16986),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_16986,U_16986),tc_HOL_Obool)),U_16987)),
    inference(clausify,[status(thm)],[f_4153_3]) ).

fof(f_4154_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_4154_2,plain,
    ! [U_16988] : c_Nat_Ofunpow(U_16988) = c_Nat_Ocompow(U_16988,U_16988),
    inference(variable_rename,[status(thm)],[f_4154_1]) ).

fof(f_4154_3,plain,
    ! [U_16988] : c_Nat_Ofunpow(U_16988) = c_Nat_Ocompow(U_16988,U_16988),
    inference(definitional_conversion,[status(esa)],[f_4154_2]) ).

cnf(f_4154_4,plain,
    c_Nat_Ofunpow(U_16988) = c_Nat_Ocompow(U_16988,U_16988),
    inference(clausify,[status(thm)],[f_4154_3]) ).

fof(f_4155_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_4155_2,plain,
    ! [U_16995,U_16994,U_16993,U_16992,U_16991] :
      ( ? [U_16990,U_16989] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16991,U_16991)),hAPP(hAPP(c_Product__Type_OPair(U_16991,U_16991),U_16990),U_16993)),U_16995))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16991,U_16991)),hAPP(hAPP(c_Product__Type_OPair(U_16991,U_16991),U_16992),U_16990)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16991,U_16991),tc_HOL_Obool),U_16989),U_16995)))
          & U_16994 = hAPP(c_Nat_OSuc,U_16989) )
      | ( U_16992 = U_16993
        & U_16994 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16991,U_16991)),hAPP(hAPP(c_Product__Type_OPair(U_16991,U_16991),U_16992),U_16993)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16991,U_16991),tc_HOL_Obool),U_16994),U_16995))) ),
    inference(variable_rename,[status(thm)],[f_4155_1]) ).

fof(f_4155_3,plain,
    ! [U_16995,U_16994,U_16993,U_16992,U_16991] :
      ( ? [U_16989] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16991,U_16991)),hAPP(hAPP(c_Product__Type_OPair(U_16991,U_16991),sK402(U_16995,U_16994,U_16993,U_16992,U_16991)),U_16993)),U_16995))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16991,U_16991)),hAPP(hAPP(c_Product__Type_OPair(U_16991,U_16991),U_16992),sK402(U_16995,U_16994,U_16993,U_16992,U_16991))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16991,U_16991),tc_HOL_Obool),U_16989),U_16995)))
          & U_16994 = hAPP(c_Nat_OSuc,U_16989) )
      | ( U_16992 = U_16993
        & U_16994 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16991,U_16991)),hAPP(hAPP(c_Product__Type_OPair(U_16991,U_16991),U_16992),U_16993)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16991,U_16991),tc_HOL_Obool),U_16994),U_16995))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK402]),skolemize(U_16990,sK402(U_16995,U_16994,U_16993,U_16992,U_16991))],[f_4155_2]) ).

fof(f_4155_4,plain,
    ! [U_16995,U_16994,U_16993,U_16992,U_16991] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16991,U_16991)),hAPP(hAPP(c_Product__Type_OPair(U_16991,U_16991),sK402(U_16995,U_16994,U_16993,U_16992,U_16991)),U_16993)),U_16995))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16991,U_16991)),hAPP(hAPP(c_Product__Type_OPair(U_16991,U_16991),U_16992),sK402(U_16995,U_16994,U_16993,U_16992,U_16991))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16991,U_16991),tc_HOL_Obool),sK403(U_16995,U_16994,U_16993,U_16992,U_16991)),U_16995)))
        & U_16994 = hAPP(c_Nat_OSuc,sK403(U_16995,U_16994,U_16993,U_16992,U_16991)) )
      | ( U_16992 = U_16993
        & U_16994 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16991,U_16991)),hAPP(hAPP(c_Product__Type_OPair(U_16991,U_16991),U_16992),U_16993)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16991,U_16991),tc_HOL_Obool),U_16994),U_16995))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK403]),skolemize(U_16989,sK403(U_16995,U_16994,U_16993,U_16992,U_16991))],[f_4155_3]) ).

fof(f_4155_5,plain,
    ( ! [U_16991,U_16992,U_16993,U_16994,U_16995] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16991,U_16991)),hAPP(hAPP(c_Product__Type_OPair(U_16991,U_16991),sK402(U_16995,U_16994,U_16993,U_16992,U_16991)),U_16993)),U_16995))
        | ~ sP1068(U_16991,U_16992,U_16993,U_16994,U_16995) )
    & ! [U_16991,U_16992,U_16993,U_16994,U_16995] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16991,U_16991)),hAPP(hAPP(c_Product__Type_OPair(U_16991,U_16991),U_16992),sK402(U_16995,U_16994,U_16993,U_16992,U_16991))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16991,U_16991),tc_HOL_Obool),sK403(U_16995,U_16994,U_16993,U_16992,U_16991)),U_16995)))
        | ~ sP1068(U_16991,U_16992,U_16993,U_16994,U_16995) )
    & ! [U_16991,U_16992,U_16993,U_16994,U_16995] :
        ( U_16994 = hAPP(c_Nat_OSuc,sK403(U_16995,U_16994,U_16993,U_16992,U_16991))
        | ~ sP1068(U_16991,U_16992,U_16993,U_16994,U_16995) )
    & ! [U_16992,U_16993,U_16994] :
        ( U_16992 = U_16993
        | ~ sP1067(U_16992,U_16993,U_16994) )
    & ! [U_16992,U_16993,U_16994] :
        ( U_16994 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1067(U_16992,U_16993,U_16994) )
    & ! [U_16991,U_16992,U_16993,U_16994,U_16995] :
        ( sP1068(U_16991,U_16992,U_16993,U_16994,U_16995)
        | sP1067(U_16992,U_16993,U_16994)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16991,U_16991)),hAPP(hAPP(c_Product__Type_OPair(U_16991,U_16991),U_16992),U_16993)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16991,U_16991),tc_HOL_Obool),U_16994),U_16995))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1067,sP1068])],[f_4155_4]) ).

cnf(f_4155_6,plain,
    ( sP1068(U_16991,U_16992,U_16993,U_16994,U_16995)
    | sP1067(U_16992,U_16993,U_16994)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16991,U_16991)),hAPP(hAPP(c_Product__Type_OPair(U_16991,U_16991),U_16992),U_16993)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16991,U_16991),tc_HOL_Obool),U_16994),U_16995))) ),
    inference(clausify,[status(thm)],[f_4155_5]) ).

cnf(f_4155_7,plain,
    ( U_16994 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1067(U_16992,U_16993,U_16994) ),
    inference(clausify,[status(thm)],[f_4155_5]) ).

cnf(f_4155_8,plain,
    ( U_16992 = U_16993
    | ~ sP1067(U_16992,U_16993,U_16994) ),
    inference(clausify,[status(thm)],[f_4155_5]) ).

cnf(f_4155_9,plain,
    ( U_16994 = hAPP(c_Nat_OSuc,sK403(U_16995,U_16994,U_16993,U_16992,U_16991))
    | ~ sP1068(U_16991,U_16992,U_16993,U_16994,U_16995) ),
    inference(clausify,[status(thm)],[f_4155_5]) ).

cnf(f_4155_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16991,U_16991)),hAPP(hAPP(c_Product__Type_OPair(U_16991,U_16991),U_16992),sK402(U_16995,U_16994,U_16993,U_16992,U_16991))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16991,U_16991),tc_HOL_Obool),sK403(U_16995,U_16994,U_16993,U_16992,U_16991)),U_16995)))
    | ~ sP1068(U_16991,U_16992,U_16993,U_16994,U_16995) ),
    inference(clausify,[status(thm)],[f_4155_5]) ).

cnf(f_4155_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16991,U_16991)),hAPP(hAPP(c_Product__Type_OPair(U_16991,U_16991),sK402(U_16995,U_16994,U_16993,U_16992,U_16991)),U_16993)),U_16995))
    | ~ sP1068(U_16991,U_16992,U_16993,U_16994,U_16995) ),
    inference(clausify,[status(thm)],[f_4155_5]) ).

fof(f_4156_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_4156_2,plain,
    ! [U_17002,U_17001,U_17000,U_16999,U_16998] :
      ( ? [U_16997,U_16996] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16998,U_16998)),hAPP(hAPP(c_Product__Type_OPair(U_16998,U_16998),U_16997),U_17000)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16998,U_16998),tc_HOL_Obool),U_16996),U_17002)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16998,U_16998)),hAPP(hAPP(c_Product__Type_OPair(U_16998,U_16998),U_16999),U_16997)),U_17002))
          & U_17001 = hAPP(c_Nat_OSuc,U_16996) )
      | ( U_16999 = U_17000
        & U_17001 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16998,U_16998)),hAPP(hAPP(c_Product__Type_OPair(U_16998,U_16998),U_16999),U_17000)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16998,U_16998),tc_HOL_Obool),U_17001),U_17002))) ),
    inference(variable_rename,[status(thm)],[f_4156_1]) ).

fof(f_4156_3,plain,
    ! [U_17002,U_17001,U_17000,U_16999,U_16998] :
      ( ? [U_16996] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16998,U_16998)),hAPP(hAPP(c_Product__Type_OPair(U_16998,U_16998),sK404(U_17002,U_17001,U_17000,U_16999,U_16998)),U_17000)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16998,U_16998),tc_HOL_Obool),U_16996),U_17002)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16998,U_16998)),hAPP(hAPP(c_Product__Type_OPair(U_16998,U_16998),U_16999),sK404(U_17002,U_17001,U_17000,U_16999,U_16998))),U_17002))
          & U_17001 = hAPP(c_Nat_OSuc,U_16996) )
      | ( U_16999 = U_17000
        & U_17001 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16998,U_16998)),hAPP(hAPP(c_Product__Type_OPair(U_16998,U_16998),U_16999),U_17000)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16998,U_16998),tc_HOL_Obool),U_17001),U_17002))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK404]),skolemize(U_16997,sK404(U_17002,U_17001,U_17000,U_16999,U_16998))],[f_4156_2]) ).

fof(f_4156_4,plain,
    ! [U_17002,U_17001,U_17000,U_16999,U_16998] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16998,U_16998)),hAPP(hAPP(c_Product__Type_OPair(U_16998,U_16998),sK404(U_17002,U_17001,U_17000,U_16999,U_16998)),U_17000)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16998,U_16998),tc_HOL_Obool),sK405(U_17002,U_17001,U_17000,U_16999,U_16998)),U_17002)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16998,U_16998)),hAPP(hAPP(c_Product__Type_OPair(U_16998,U_16998),U_16999),sK404(U_17002,U_17001,U_17000,U_16999,U_16998))),U_17002))
        & U_17001 = hAPP(c_Nat_OSuc,sK405(U_17002,U_17001,U_17000,U_16999,U_16998)) )
      | ( U_16999 = U_17000
        & U_17001 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16998,U_16998)),hAPP(hAPP(c_Product__Type_OPair(U_16998,U_16998),U_16999),U_17000)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16998,U_16998),tc_HOL_Obool),U_17001),U_17002))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK405]),skolemize(U_16996,sK405(U_17002,U_17001,U_17000,U_16999,U_16998))],[f_4156_3]) ).

fof(f_4156_5,plain,
    ( ! [U_17000,U_16998,U_16999,U_17001,U_17002] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16998,U_16998)),hAPP(hAPP(c_Product__Type_OPair(U_16998,U_16998),sK404(U_17002,U_17001,U_17000,U_16999,U_16998)),U_17000)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16998,U_16998),tc_HOL_Obool),sK405(U_17002,U_17001,U_17000,U_16999,U_16998)),U_17002)))
        | ~ sP1070(U_17000,U_16998,U_16999,U_17001,U_17002) )
    & ! [U_17000,U_16998,U_16999,U_17001,U_17002] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16998,U_16998)),hAPP(hAPP(c_Product__Type_OPair(U_16998,U_16998),U_16999),sK404(U_17002,U_17001,U_17000,U_16999,U_16998))),U_17002))
        | ~ sP1070(U_17000,U_16998,U_16999,U_17001,U_17002) )
    & ! [U_17000,U_16998,U_16999,U_17001,U_17002] :
        ( U_17001 = hAPP(c_Nat_OSuc,sK405(U_17002,U_17001,U_17000,U_16999,U_16998))
        | ~ sP1070(U_17000,U_16998,U_16999,U_17001,U_17002) )
    & ! [U_17000,U_16999,U_17001] :
        ( U_16999 = U_17000
        | ~ sP1069(U_17000,U_16999,U_17001) )
    & ! [U_17000,U_16999,U_17001] :
        ( U_17001 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1069(U_17000,U_16999,U_17001) )
    & ! [U_17000,U_16998,U_16999,U_17001,U_17002] :
        ( sP1070(U_17000,U_16998,U_16999,U_17001,U_17002)
        | sP1069(U_17000,U_16999,U_17001)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16998,U_16998)),hAPP(hAPP(c_Product__Type_OPair(U_16998,U_16998),U_16999),U_17000)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16998,U_16998),tc_HOL_Obool),U_17001),U_17002))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1069,sP1070])],[f_4156_4]) ).

cnf(f_4156_6,plain,
    ( sP1070(U_17000,U_16998,U_16999,U_17001,U_17002)
    | sP1069(U_17000,U_16999,U_17001)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16998,U_16998)),hAPP(hAPP(c_Product__Type_OPair(U_16998,U_16998),U_16999),U_17000)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16998,U_16998),tc_HOL_Obool),U_17001),U_17002))) ),
    inference(clausify,[status(thm)],[f_4156_5]) ).

cnf(f_4156_7,plain,
    ( U_17001 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1069(U_17000,U_16999,U_17001) ),
    inference(clausify,[status(thm)],[f_4156_5]) ).

cnf(f_4156_8,plain,
    ( U_16999 = U_17000
    | ~ sP1069(U_17000,U_16999,U_17001) ),
    inference(clausify,[status(thm)],[f_4156_5]) ).

cnf(f_4156_9,plain,
    ( U_17001 = hAPP(c_Nat_OSuc,sK405(U_17002,U_17001,U_17000,U_16999,U_16998))
    | ~ sP1070(U_17000,U_16998,U_16999,U_17001,U_17002) ),
    inference(clausify,[status(thm)],[f_4156_5]) ).

cnf(f_4156_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16998,U_16998)),hAPP(hAPP(c_Product__Type_OPair(U_16998,U_16998),U_16999),sK404(U_17002,U_17001,U_17000,U_16999,U_16998))),U_17002))
    | ~ sP1070(U_17000,U_16998,U_16999,U_17001,U_17002) ),
    inference(clausify,[status(thm)],[f_4156_5]) ).

cnf(f_4156_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16998,U_16998)),hAPP(hAPP(c_Product__Type_OPair(U_16998,U_16998),sK404(U_17002,U_17001,U_17000,U_16999,U_16998)),U_17000)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_16998,U_16998),tc_HOL_Obool),sK405(U_17002,U_17001,U_17000,U_16999,U_16998)),U_17002)))
    | ~ sP1070(U_17000,U_16998,U_16999,U_17001,U_17002) ),
    inference(clausify,[status(thm)],[f_4156_5]) ).

fof(f_4157_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_4157_2,plain,
    ! [U_17004,U_17003] :
      ( c_Complete__Lattice_OInf__class_OInf(U_17003,U_17004) = hAPP(hAPP(c_Finite__Set_Ofold(U_17003,U_17003,c_Lattices_Osemilattice__inf__class_Oinf(U_17003)),c_Orderings_Otop__class_Otop(U_17003)),U_17004)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17003),U_17004))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17003) ),
    inference(variable_rename,[status(thm)],[f_4157_1]) ).

fof(f_4157_3,plain,
    ! [U_17003,U_17004] :
      ( c_Complete__Lattice_OInf__class_OInf(U_17003,U_17004) = hAPP(hAPP(c_Finite__Set_Ofold(U_17003,U_17003,c_Lattices_Osemilattice__inf__class_Oinf(U_17003)),c_Orderings_Otop__class_Otop(U_17003)),U_17004)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17003),U_17004))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17003) ),
    inference(definitional_conversion,[status(esa)],[f_4157_2]) ).

cnf(f_4157_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_17003,U_17004) = hAPP(hAPP(c_Finite__Set_Ofold(U_17003,U_17003,c_Lattices_Osemilattice__inf__class_Oinf(U_17003)),c_Orderings_Otop__class_Otop(U_17003)),U_17004)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17003),U_17004))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17003) ),
    inference(clausify,[status(thm)],[f_4157_3]) ).

fof(f_4158_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_4158_2,plain,
    ! [U_17007,U_17006] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_17006),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17006,tc_HOL_Obool),U_17007)))
      | ! [U_17005] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17006),U_17005))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17006,tc_HOL_Obool)),U_17005),U_17007)) ) ),
    inference(variable_rename,[status(thm)],[f_4158_1]) ).

fof(f_4158_3,plain,
    ! [U_17005,U_17006,U_17007] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_17006),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17006,tc_HOL_Obool),U_17007)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17006),U_17005))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17006,tc_HOL_Obool)),U_17005),U_17007)) ),
    inference(definitional_conversion,[status(esa)],[f_4158_2]) ).

cnf(f_4158_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_17006),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17006,tc_HOL_Obool),U_17007)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17006),U_17005))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17006,tc_HOL_Obool)),U_17005),U_17007)) ),
    inference(clausify,[status(thm)],[f_4158_3]) ).

fof(f_4159_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_4159_2,plain,
    ! [U_17011,U_17010,U_17009,U_17008] :
      ( hBOOL(hAPP(hAPP(c_member(U_17008),U_17009),U_17011))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17008,tc_HOL_Obool)),U_17011),U_17010))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17008),U_17009),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17008,tc_HOL_Obool),U_17010))) ),
    inference(variable_rename,[status(thm)],[f_4159_1]) ).

fof(f_4159_3,plain,
    ! [U_17009,U_17008,U_17010,U_17011] :
      ( hBOOL(hAPP(hAPP(c_member(U_17008),U_17009),U_17011))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17008,tc_HOL_Obool)),U_17011),U_17010))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17008),U_17009),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17008,tc_HOL_Obool),U_17010))) ),
    inference(definitional_conversion,[status(esa)],[f_4159_2]) ).

cnf(f_4159_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17008),U_17009),U_17011))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17008,tc_HOL_Obool)),U_17011),U_17010))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17008),U_17009),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17008,tc_HOL_Obool),U_17010))) ),
    inference(clausify,[status(thm)],[f_4159_3]) ).

fof(f_4160_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_4160_2,plain,
    ! [U_17015,U_17014,U_17013,U_17012] :
      ( hBOOL(hAPP(hAPP(c_member(U_17012),U_17013),U_17015))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17012,tc_HOL_Obool)),U_17015),U_17014))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17012),U_17013),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17012,tc_HOL_Obool),U_17014))) ),
    inference(variable_rename,[status(thm)],[f_4160_1]) ).

fof(f_4160_3,plain,
    ! [U_17012,U_17013,U_17014,U_17015] :
      ( hBOOL(hAPP(hAPP(c_member(U_17012),U_17013),U_17015))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17012,tc_HOL_Obool)),U_17015),U_17014))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17012),U_17013),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17012,tc_HOL_Obool),U_17014))) ),
    inference(definitional_conversion,[status(esa)],[f_4160_2]) ).

cnf(f_4160_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17012),U_17013),U_17015))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17012,tc_HOL_Obool)),U_17015),U_17014))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17012),U_17013),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17012,tc_HOL_Obool),U_17014))) ),
    inference(clausify,[status(thm)],[f_4160_3]) ).

fof(f_4161_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_4161_2,plain,
    ! [U_17018,U_17017,U_17016] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17016,tc_HOL_Obool)),U_17017),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17016,tc_HOL_Obool),U_17018)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_17016,tc_HOL_Obool),tc_fun(U_17016,tc_HOL_Obool)),U_17018),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17016,tc_HOL_Obool)),U_17017)),
    inference(variable_rename,[status(thm)],[f_4161_1]) ).

fof(f_4161_3,plain,
    ! [U_17016,U_17017,U_17018] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17016,tc_HOL_Obool)),U_17017),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17016,tc_HOL_Obool),U_17018)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_17016,tc_HOL_Obool),tc_fun(U_17016,tc_HOL_Obool)),U_17018),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17016,tc_HOL_Obool)),U_17017)),
    inference(definitional_conversion,[status(esa)],[f_4161_2]) ).

cnf(f_4161_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17016,tc_HOL_Obool)),U_17017),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17016,tc_HOL_Obool),U_17018)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_17016,tc_HOL_Obool),tc_fun(U_17016,tc_HOL_Obool)),U_17018),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17016,tc_HOL_Obool)),U_17017)),
    inference(clausify,[status(thm)],[f_4161_3]) ).

fof(f_4162_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_4162_2,plain,
    ! [U_17023,U_17022,U_17021] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),c_Complete__Lattice_OInf__class_OInf(U_17021,U_17022)),U_17023))
          | ! [U_17020] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),U_17020),U_17023))
              | ~ hBOOL(hAPP(hAPP(c_member(U_17021),U_17020),U_17022)) ) )
        & ( ? [U_17019] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),U_17019),U_17023))
              & hBOOL(hAPP(hAPP(c_member(U_17021),U_17019),U_17022)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),c_Complete__Lattice_OInf__class_OInf(U_17021,U_17022)),U_17023)) ) )
      | ~ class_Orderings_Olinorder(U_17021)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17021) ),
    inference(variable_rename,[status(thm)],[f_4162_1]) ).

fof(f_4162_3,plain,
    ! [U_17023,U_17022,U_17021] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),c_Complete__Lattice_OInf__class_OInf(U_17021,U_17022)),U_17023))
          | ! [U_17020] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),U_17020),U_17023))
              | ~ hBOOL(hAPP(hAPP(c_member(U_17021),U_17020),U_17022)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),sK406(U_17023,U_17022,U_17021)),U_17023))
            & hBOOL(hAPP(hAPP(c_member(U_17021),sK406(U_17023,U_17022,U_17021)),U_17022)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),c_Complete__Lattice_OInf__class_OInf(U_17021,U_17022)),U_17023)) ) )
      | ~ class_Orderings_Olinorder(U_17021)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17021) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK406]),skolemize(U_17019,sK406(U_17023,U_17022,U_17021))],[f_4162_2]) ).

fof(f_4162_4,plain,
    ( ! [U_17021,U_17022,U_17023] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),sK406(U_17023,U_17022,U_17021)),U_17023))
        | ~ sP1071(U_17021,U_17022,U_17023) )
    & ! [U_17021,U_17022,U_17023] :
        ( hBOOL(hAPP(hAPP(c_member(U_17021),sK406(U_17023,U_17022,U_17021)),U_17022))
        | ~ sP1071(U_17021,U_17022,U_17023) )
    & ! [U_17020,U_17021,U_17022,U_17023] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),c_Complete__Lattice_OInf__class_OInf(U_17021,U_17022)),U_17023))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),U_17020),U_17023))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17021),U_17020),U_17022))
        | ~ sP1072(U_17020,U_17021,U_17022,U_17023) )
    & ! [U_17020,U_17021,U_17022,U_17023] :
        ( sP1071(U_17021,U_17022,U_17023)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),c_Complete__Lattice_OInf__class_OInf(U_17021,U_17022)),U_17023))
        | ~ sP1072(U_17020,U_17021,U_17022,U_17023) )
    & ! [U_17020,U_17021,U_17022,U_17023] :
        ( sP1072(U_17020,U_17021,U_17022,U_17023)
        | ~ class_Orderings_Olinorder(U_17021)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_17021) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1071,sP1072])],[f_4162_3]) ).

cnf(f_4162_5,plain,
    ( sP1072(U_17020,U_17021,U_17022,U_17023)
    | ~ class_Orderings_Olinorder(U_17021)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17021) ),
    inference(clausify,[status(thm)],[f_4162_4]) ).

cnf(f_4162_6,plain,
    ( sP1071(U_17021,U_17022,U_17023)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),c_Complete__Lattice_OInf__class_OInf(U_17021,U_17022)),U_17023))
    | ~ sP1072(U_17020,U_17021,U_17022,U_17023) ),
    inference(clausify,[status(thm)],[f_4162_4]) ).

cnf(f_4162_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),c_Complete__Lattice_OInf__class_OInf(U_17021,U_17022)),U_17023))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),U_17020),U_17023))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17021),U_17020),U_17022))
    | ~ sP1072(U_17020,U_17021,U_17022,U_17023) ),
    inference(clausify,[status(thm)],[f_4162_4]) ).

cnf(f_4162_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17021),sK406(U_17023,U_17022,U_17021)),U_17022))
    | ~ sP1071(U_17021,U_17022,U_17023) ),
    inference(clausify,[status(thm)],[f_4162_4]) ).

cnf(f_4162_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17021),sK406(U_17023,U_17022,U_17021)),U_17023))
    | ~ sP1071(U_17021,U_17022,U_17023) ),
    inference(clausify,[status(thm)],[f_4162_4]) ).

fof(f_4163_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_4163_2,plain,
    ! [U_17026,U_17025,U_17024] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17024,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17024,tc_HOL_Obool),U_17026)),U_17025))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17024,tc_HOL_Obool)),U_17025),U_17026)) ),
    inference(variable_rename,[status(thm)],[f_4163_1]) ).

fof(f_4163_3,plain,
    ! [U_17026,U_17024,U_17025] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17024,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17024,tc_HOL_Obool),U_17026)),U_17025))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17024,tc_HOL_Obool)),U_17025),U_17026)) ),
    inference(definitional_conversion,[status(esa)],[f_4163_2]) ).

cnf(f_4163_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17024,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17024,tc_HOL_Obool),U_17026)),U_17025))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17024,tc_HOL_Obool)),U_17025),U_17026)) ),
    inference(clausify,[status(thm)],[f_4163_3]) ).

fof(f_4164_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_4164_2,plain,
    ! [U_17031,U_17030,U_17029] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),c_Complete__Lattice_OInf__class_OInf(U_17029,U_17031)))
          | ? [U_17028] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),U_17028))
              & hBOOL(hAPP(hAPP(c_member(U_17029),U_17028),U_17031)) ) )
        & ( ! [U_17027] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),U_17027))
              | ~ hBOOL(hAPP(hAPP(c_member(U_17029),U_17027),U_17031)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),c_Complete__Lattice_OInf__class_OInf(U_17029,U_17031))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17029) ),
    inference(variable_rename,[status(thm)],[f_4164_1]) ).

fof(f_4164_3,plain,
    ! [U_17031,U_17030,U_17029] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),c_Complete__Lattice_OInf__class_OInf(U_17029,U_17031)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),sK407(U_17031,U_17030,U_17029)))
            & hBOOL(hAPP(hAPP(c_member(U_17029),sK407(U_17031,U_17030,U_17029)),U_17031)) ) )
        & ( ! [U_17027] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),U_17027))
              | ~ hBOOL(hAPP(hAPP(c_member(U_17029),U_17027),U_17031)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),c_Complete__Lattice_OInf__class_OInf(U_17029,U_17031))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17029) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK407]),skolemize(U_17028,sK407(U_17031,U_17030,U_17029))],[f_4164_2]) ).

fof(f_4164_4,plain,
    ( ! [U_17029,U_17030,U_17031] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),sK407(U_17031,U_17030,U_17029)))
        | ~ sP1073(U_17029,U_17030,U_17031) )
    & ! [U_17029,U_17030,U_17031] :
        ( hBOOL(hAPP(hAPP(c_member(U_17029),sK407(U_17031,U_17030,U_17029)),U_17031))
        | ~ sP1073(U_17029,U_17030,U_17031) )
    & ! [U_17027,U_17029,U_17030,U_17031] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),c_Complete__Lattice_OInf__class_OInf(U_17029,U_17031)))
        | sP1073(U_17029,U_17030,U_17031)
        | ~ sP1074(U_17027,U_17029,U_17030,U_17031) )
    & ! [U_17027,U_17029,U_17030,U_17031] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),U_17027))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17029),U_17027),U_17031))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),c_Complete__Lattice_OInf__class_OInf(U_17029,U_17031)))
        | ~ sP1074(U_17027,U_17029,U_17030,U_17031) )
    & ! [U_17027,U_17029,U_17030,U_17031] :
        ( sP1074(U_17027,U_17029,U_17030,U_17031)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_17029) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1073,sP1074])],[f_4164_3]) ).

cnf(f_4164_5,plain,
    ( sP1074(U_17027,U_17029,U_17030,U_17031)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17029) ),
    inference(clausify,[status(thm)],[f_4164_4]) ).

cnf(f_4164_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),U_17027))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17029),U_17027),U_17031))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),c_Complete__Lattice_OInf__class_OInf(U_17029,U_17031)))
    | ~ sP1074(U_17027,U_17029,U_17030,U_17031) ),
    inference(clausify,[status(thm)],[f_4164_4]) ).

cnf(f_4164_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),c_Complete__Lattice_OInf__class_OInf(U_17029,U_17031)))
    | sP1073(U_17029,U_17030,U_17031)
    | ~ sP1074(U_17027,U_17029,U_17030,U_17031) ),
    inference(clausify,[status(thm)],[f_4164_4]) ).

cnf(f_4164_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17029),sK407(U_17031,U_17030,U_17029)),U_17031))
    | ~ sP1073(U_17029,U_17030,U_17031) ),
    inference(clausify,[status(thm)],[f_4164_4]) ).

cnf(f_4164_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17029),U_17030),sK407(U_17031,U_17030,U_17029)))
    | ~ sP1073(U_17029,U_17030,U_17031) ),
    inference(clausify,[status(thm)],[f_4164_4]) ).

fof(f_4165_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_4165_2,plain,
    ! [U_17034,U_17033,U_17032] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17032,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17032,tc_HOL_Obool)),U_17033),U_17034)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17032,tc_HOL_Obool)),U_17033),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17032,tc_HOL_Obool),U_17034)),
    inference(variable_rename,[status(thm)],[f_4165_1]) ).

fof(f_4165_3,plain,
    ! [U_17033,U_17034,U_17032] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17032,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17032,tc_HOL_Obool)),U_17033),U_17034)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17032,tc_HOL_Obool)),U_17033),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17032,tc_HOL_Obool),U_17034)),
    inference(definitional_conversion,[status(esa)],[f_4165_2]) ).

cnf(f_4165_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17032,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17032,tc_HOL_Obool)),U_17033),U_17034)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17032,tc_HOL_Obool)),U_17033),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17032,tc_HOL_Obool),U_17034)),
    inference(clausify,[status(thm)],[f_4165_3]) ).

fof(f_4166_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_4166_2,plain,
    ! [U_17036,U_17035] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17035,tc_HOL_Obool),U_17036) = hAPP(c_Set_OCollect(U_17035),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_17035,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_17035),c_HOL_OAll(tc_fun(U_17035,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_17035,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_17035,tc_HOL_Obool),tc_HOL_Obool),U_17035),hAPP(c_COMBS(tc_fun(U_17035,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_17035,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_17035,tc_HOL_Obool),tc_fun(tc_fun(U_17035,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_17035,tc_HOL_Obool))),U_17036)))),c_member(U_17035)))),
    inference(variable_rename,[status(thm)],[f_4166_1]) ).

fof(f_4166_3,plain,
    ! [U_17035,U_17036] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17035,tc_HOL_Obool),U_17036) = hAPP(c_Set_OCollect(U_17035),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_17035,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_17035),c_HOL_OAll(tc_fun(U_17035,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_17035,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_17035,tc_HOL_Obool),tc_HOL_Obool),U_17035),hAPP(c_COMBS(tc_fun(U_17035,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_17035,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_17035,tc_HOL_Obool),tc_fun(tc_fun(U_17035,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_17035,tc_HOL_Obool))),U_17036)))),c_member(U_17035)))),
    inference(definitional_conversion,[status(esa)],[f_4166_2]) ).

cnf(f_4166_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17035,tc_HOL_Obool),U_17036) = hAPP(c_Set_OCollect(U_17035),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_17035,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_17035),c_HOL_OAll(tc_fun(U_17035,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_17035,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_17035,tc_HOL_Obool),tc_HOL_Obool),U_17035),hAPP(c_COMBS(tc_fun(U_17035,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_17035,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_17035,tc_HOL_Obool),tc_fun(tc_fun(U_17035,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_17035,tc_HOL_Obool))),U_17036)))),c_member(U_17035)))),
    inference(clausify,[status(thm)],[f_4166_3]) ).

fof(f_4167_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_4167_2,plain,
    ! [U_17037] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17037,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17037,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_17037,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4167_1]) ).

fof(f_4167_3,plain,
    ! [U_17037] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17037,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17037,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_17037,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4167_2]) ).

cnf(f_4167_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17037,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17037,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_17037,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4167_3]) ).

fof(f_4168_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_4168_2,plain,
    ! [U_17040,U_17039,U_17038] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17038,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17038,tc_HOL_Obool),U_17040)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17038,tc_HOL_Obool),U_17039)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_17038,tc_HOL_Obool),tc_HOL_Obool)),U_17039),U_17040)) ),
    inference(variable_rename,[status(thm)],[f_4168_1]) ).

fof(f_4168_3,plain,
    ! [U_17038,U_17039,U_17040] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17038,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17038,tc_HOL_Obool),U_17040)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17038,tc_HOL_Obool),U_17039)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_17038,tc_HOL_Obool),tc_HOL_Obool)),U_17039),U_17040)) ),
    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_17038,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17038,tc_HOL_Obool),U_17040)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17038,tc_HOL_Obool),U_17039)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_17038,tc_HOL_Obool),tc_HOL_Obool)),U_17039),U_17040)) ),
    inference(clausify,[status(thm)],[f_4168_3]) ).

fof(f_4169_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_4169_2,plain,
    ! [U_17041] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17041,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_17041,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_17041,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4169_1]) ).

fof(f_4169_3,plain,
    ! [U_17041] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17041,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_17041,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_17041,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4169_2]) ).

cnf(f_4169_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17041,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_17041,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_17041,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4169_3]) ).

fof(f_4170_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_4170_2,plain,
    ! [U_17044,U_17043,U_17042] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17042),c_Complete__Lattice_OInf__class_OInf(U_17042,U_17044)),U_17043))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17042),U_17043),U_17044))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17042) ),
    inference(variable_rename,[status(thm)],[f_4170_1]) ).

fof(f_4170_3,plain,
    ! [U_17042,U_17043,U_17044] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17042),c_Complete__Lattice_OInf__class_OInf(U_17042,U_17044)),U_17043))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17042),U_17043),U_17044))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17042) ),
    inference(definitional_conversion,[status(esa)],[f_4170_2]) ).

cnf(f_4170_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17042),c_Complete__Lattice_OInf__class_OInf(U_17042,U_17044)),U_17043))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17042),U_17043),U_17044))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17042) ),
    inference(clausify,[status(thm)],[f_4170_3]) ).

fof(f_4171_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_4171_2,plain,
    ! [U_17047,U_17046,U_17045] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17045,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_17045,tc_HOL_Obool),tc_HOL_Obool)),U_17046),U_17047)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17045,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17045,tc_HOL_Obool),U_17046)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17045,tc_HOL_Obool),U_17047)),
    inference(variable_rename,[status(thm)],[f_4171_1]) ).

fof(f_4171_3,plain,
    ! [U_17045,U_17046,U_17047] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17045,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_17045,tc_HOL_Obool),tc_HOL_Obool)),U_17046),U_17047)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17045,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17045,tc_HOL_Obool),U_17046)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17045,tc_HOL_Obool),U_17047)),
    inference(definitional_conversion,[status(esa)],[f_4171_2]) ).

cnf(f_4171_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17045,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_17045,tc_HOL_Obool),tc_HOL_Obool)),U_17046),U_17047)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17045,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17045,tc_HOL_Obool),U_17046)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17045,tc_HOL_Obool),U_17047)),
    inference(clausify,[status(thm)],[f_4171_3]) ).

fof(f_4172_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_4172_2,plain,
    ! [U_17049,U_17048] :
      ( c_Complete__Lattice_OInf__class_OInf(U_17048,hAPP(hAPP(c_Set_Oinsert(U_17048),U_17049),c_Orderings_Obot__class_Obot(tc_fun(U_17048,tc_HOL_Obool)))) = U_17049
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17048) ),
    inference(variable_rename,[status(thm)],[f_4172_1]) ).

fof(f_4172_3,plain,
    ! [U_17048,U_17049] :
      ( c_Complete__Lattice_OInf__class_OInf(U_17048,hAPP(hAPP(c_Set_Oinsert(U_17048),U_17049),c_Orderings_Obot__class_Obot(tc_fun(U_17048,tc_HOL_Obool)))) = U_17049
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17048) ),
    inference(definitional_conversion,[status(esa)],[f_4172_2]) ).

cnf(f_4172_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_17048,hAPP(hAPP(c_Set_Oinsert(U_17048),U_17049),c_Orderings_Obot__class_Obot(tc_fun(U_17048,tc_HOL_Obool)))) = U_17049
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17048) ),
    inference(clausify,[status(thm)],[f_4172_3]) ).

fof(f_4173_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_4173_2,plain,
    ! [U_17050] :
      ( c_Complete__Lattice_OInf__class_OInf(U_17050,c_Orderings_Obot__class_Obot(tc_fun(U_17050,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_17050)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17050) ),
    inference(variable_rename,[status(thm)],[f_4173_1]) ).

fof(f_4173_3,plain,
    ! [U_17050] :
      ( c_Complete__Lattice_OInf__class_OInf(U_17050,c_Orderings_Obot__class_Obot(tc_fun(U_17050,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_17050)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17050) ),
    inference(definitional_conversion,[status(esa)],[f_4173_2]) ).

cnf(f_4173_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_17050,c_Orderings_Obot__class_Obot(tc_fun(U_17050,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_17050)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17050) ),
    inference(clausify,[status(thm)],[f_4173_3]) ).

fof(f_4174_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_4174_2,plain,
    ! [U_17051] :
      ( c_Complete__Lattice_OInf__class_OInf(U_17051,c_Orderings_Otop__class_Otop(tc_fun(U_17051,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_17051)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17051) ),
    inference(variable_rename,[status(thm)],[f_4174_1]) ).

fof(f_4174_3,plain,
    ! [U_17051] :
      ( c_Complete__Lattice_OInf__class_OInf(U_17051,c_Orderings_Otop__class_Otop(tc_fun(U_17051,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_17051)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17051) ),
    inference(definitional_conversion,[status(esa)],[f_4174_2]) ).

cnf(f_4174_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_17051,c_Orderings_Otop__class_Otop(tc_fun(U_17051,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_17051)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17051) ),
    inference(clausify,[status(thm)],[f_4174_3]) ).

fof(f_4175_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_4175_2,plain,
    ! [U_17054,U_17053,U_17052] :
      ( c_Complete__Lattice_OInf__class_OInf(U_17052,hAPP(hAPP(c_Set_Oinsert(U_17052),U_17053),U_17054)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_17052),U_17053),c_Complete__Lattice_OInf__class_OInf(U_17052,U_17054))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17052) ),
    inference(variable_rename,[status(thm)],[f_4175_1]) ).

fof(f_4175_3,plain,
    ! [U_17052,U_17053,U_17054] :
      ( c_Complete__Lattice_OInf__class_OInf(U_17052,hAPP(hAPP(c_Set_Oinsert(U_17052),U_17053),U_17054)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_17052),U_17053),c_Complete__Lattice_OInf__class_OInf(U_17052,U_17054))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17052) ),
    inference(definitional_conversion,[status(esa)],[f_4175_2]) ).

cnf(f_4175_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_17052,hAPP(hAPP(c_Set_Oinsert(U_17052),U_17053),U_17054)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_17052),U_17053),c_Complete__Lattice_OInf__class_OInf(U_17052,U_17054))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17052) ),
    inference(clausify,[status(thm)],[f_4175_3]) ).

fof(f_4176_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_4176_2,plain,
    ! [U_17058,U_17057,U_17056,U_17055] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17055,tc_fun(U_17056,tc_HOL_Obool)),U_17057),U_17058) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17056,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17055,tc_fun(U_17056,tc_HOL_Obool),U_17058),U_17057)),
    inference(variable_rename,[status(thm)],[f_4176_1]) ).

fof(f_4176_3,plain,
    ! [U_17055,U_17056,U_17057,U_17058] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17055,tc_fun(U_17056,tc_HOL_Obool)),U_17057),U_17058) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17056,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17055,tc_fun(U_17056,tc_HOL_Obool),U_17058),U_17057)),
    inference(definitional_conversion,[status(esa)],[f_4176_2]) ).

cnf(f_4176_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17055,tc_fun(U_17056,tc_HOL_Obool)),U_17057),U_17058) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17056,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17055,tc_fun(U_17056,tc_HOL_Obool),U_17058),U_17057)),
    inference(clausify,[status(thm)],[f_4176_3]) ).

fof(f_4177_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_4177_2,plain,
    ! [U_17062,U_17061,U_17060,U_17059] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17059,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17060,tc_fun(U_17059,tc_HOL_Obool),U_17061),U_17062)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17060,tc_fun(U_17059,tc_HOL_Obool)),U_17062),U_17061),
    inference(variable_rename,[status(thm)],[f_4177_1]) ).

fof(f_4177_3,plain,
    ! [U_17059,U_17060,U_17061,U_17062] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17059,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17060,tc_fun(U_17059,tc_HOL_Obool),U_17061),U_17062)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17060,tc_fun(U_17059,tc_HOL_Obool)),U_17062),U_17061),
    inference(definitional_conversion,[status(esa)],[f_4177_2]) ).

cnf(f_4177_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17059,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17060,tc_fun(U_17059,tc_HOL_Obool),U_17061),U_17062)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17060,tc_fun(U_17059,tc_HOL_Obool)),U_17062),U_17061),
    inference(clausify,[status(thm)],[f_4177_3]) ).

fof(f_4178_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_4178_2,plain,
    ! [U_17065,U_17064,U_17063] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17063,tc_HOL_Obool)),U_17064),U_17065) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17063,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17063,tc_HOL_Obool)),U_17064),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17063,tc_HOL_Obool)),U_17065),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17063,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_4178_1]) ).

fof(f_4178_3,plain,
    ! [U_17063,U_17064,U_17065] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17063,tc_HOL_Obool)),U_17064),U_17065) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17063,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17063,tc_HOL_Obool)),U_17064),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17063,tc_HOL_Obool)),U_17065),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17063,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_4178_2]) ).

cnf(f_4178_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17063,tc_HOL_Obool)),U_17064),U_17065) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17063,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17063,tc_HOL_Obool)),U_17064),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17063,tc_HOL_Obool)),U_17065),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17063,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_4178_3]) ).

fof(f_4179_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_4179_2,plain,
    ! [U_17070,U_17069,U_17068,U_17067,U_17066] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17066,tc_fun(U_17067,tc_HOL_Obool)),U_17068),hAPP(hAPP(c_COMBS(U_17066,tc_fun(U_17067,tc_HOL_Obool),tc_fun(U_17067,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17067,tc_HOL_Obool),tc_fun(tc_fun(U_17067,tc_HOL_Obool),tc_fun(U_17067,tc_HOL_Obool)),U_17066),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17067,tc_HOL_Obool))),U_17069)),U_17070)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17067,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17067,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17066,tc_fun(U_17067,tc_HOL_Obool),U_17069),U_17068))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17067,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17066,tc_fun(U_17067,tc_HOL_Obool),U_17070),U_17068))),
    inference(variable_rename,[status(thm)],[f_4179_1]) ).

fof(f_4179_3,plain,
    ! [U_17067,U_17068,U_17069,U_17070,U_17066] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17066,tc_fun(U_17067,tc_HOL_Obool)),U_17068),hAPP(hAPP(c_COMBS(U_17066,tc_fun(U_17067,tc_HOL_Obool),tc_fun(U_17067,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17067,tc_HOL_Obool),tc_fun(tc_fun(U_17067,tc_HOL_Obool),tc_fun(U_17067,tc_HOL_Obool)),U_17066),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17067,tc_HOL_Obool))),U_17069)),U_17070)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17067,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17067,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17066,tc_fun(U_17067,tc_HOL_Obool),U_17069),U_17068))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17067,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17066,tc_fun(U_17067,tc_HOL_Obool),U_17070),U_17068))),
    inference(definitional_conversion,[status(esa)],[f_4179_2]) ).

cnf(f_4179_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17066,tc_fun(U_17067,tc_HOL_Obool)),U_17068),hAPP(hAPP(c_COMBS(U_17066,tc_fun(U_17067,tc_HOL_Obool),tc_fun(U_17067,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17067,tc_HOL_Obool),tc_fun(tc_fun(U_17067,tc_HOL_Obool),tc_fun(U_17067,tc_HOL_Obool)),U_17066),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17067,tc_HOL_Obool))),U_17069)),U_17070)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17067,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17067,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17066,tc_fun(U_17067,tc_HOL_Obool),U_17069),U_17068))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17067,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17066,tc_fun(U_17067,tc_HOL_Obool),U_17070),U_17068))),
    inference(clausify,[status(thm)],[f_4179_3]) ).

fof(f_4180_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_4180_2,plain,
    ! [U_17073,U_17072,U_17071] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17071,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17071,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17071,tc_HOL_Obool),U_17072)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17071,tc_HOL_Obool),U_17073))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17071,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_17071,tc_HOL_Obool),tc_HOL_Obool)),U_17072),U_17073)))),
    inference(variable_rename,[status(thm)],[f_4180_1]) ).

fof(f_4180_3,plain,
    ! [U_17071,U_17072,U_17073] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17071,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17071,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17071,tc_HOL_Obool),U_17072)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17071,tc_HOL_Obool),U_17073))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17071,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_17071,tc_HOL_Obool),tc_HOL_Obool)),U_17072),U_17073)))),
    inference(definitional_conversion,[status(esa)],[f_4180_2]) ).

cnf(f_4180_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17071,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17071,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17071,tc_HOL_Obool),U_17072)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17071,tc_HOL_Obool),U_17073))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17071,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_17071,tc_HOL_Obool),tc_HOL_Obool)),U_17072),U_17073)))),
    inference(clausify,[status(thm)],[f_4180_3]) ).

fof(f_4181_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_4181_2,plain,
    ! [U_17076,U_17075,U_17074] :
      ( c_Complete__Lattice_OInf__class_OInf(U_17074,hAPP(hAPP(c_Set_Oinsert(U_17074),U_17075),hAPP(hAPP(c_Set_Oinsert(U_17074),U_17076),c_Orderings_Obot__class_Obot(tc_fun(U_17074,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_17074),U_17075),U_17076)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17074) ),
    inference(variable_rename,[status(thm)],[f_4181_1]) ).

fof(f_4181_3,plain,
    ! [U_17074,U_17075,U_17076] :
      ( c_Complete__Lattice_OInf__class_OInf(U_17074,hAPP(hAPP(c_Set_Oinsert(U_17074),U_17075),hAPP(hAPP(c_Set_Oinsert(U_17074),U_17076),c_Orderings_Obot__class_Obot(tc_fun(U_17074,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_17074),U_17075),U_17076)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17074) ),
    inference(definitional_conversion,[status(esa)],[f_4181_2]) ).

cnf(f_4181_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_17074,hAPP(hAPP(c_Set_Oinsert(U_17074),U_17075),hAPP(hAPP(c_Set_Oinsert(U_17074),U_17076),c_Orderings_Obot__class_Obot(tc_fun(U_17074,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_17074),U_17075),U_17076)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17074) ),
    inference(clausify,[status(thm)],[f_4181_3]) ).

fof(f_4182_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_4182_2,plain,
    ! [U_17079,U_17078,U_17077] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_17077),U_17079),c_Complete__Lattice_OInf__class_OInf(U_17077,U_17078)) = hAPP(hAPP(c_Finite__Set_Ofold(U_17077,U_17077,c_Lattices_Osemilattice__inf__class_Oinf(U_17077)),U_17079),U_17078)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17077),U_17078))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17077) ),
    inference(variable_rename,[status(thm)],[f_4182_1]) ).

fof(f_4182_3,plain,
    ! [U_17077,U_17078,U_17079] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_17077),U_17079),c_Complete__Lattice_OInf__class_OInf(U_17077,U_17078)) = hAPP(hAPP(c_Finite__Set_Ofold(U_17077,U_17077,c_Lattices_Osemilattice__inf__class_Oinf(U_17077)),U_17079),U_17078)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17077),U_17078))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17077) ),
    inference(definitional_conversion,[status(esa)],[f_4182_2]) ).

cnf(f_4182_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_17077),U_17079),c_Complete__Lattice_OInf__class_OInf(U_17077,U_17078)) = hAPP(hAPP(c_Finite__Set_Ofold(U_17077,U_17077,c_Lattices_Osemilattice__inf__class_Oinf(U_17077)),U_17079),U_17078)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17077),U_17078))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17077) ),
    inference(clausify,[status(thm)],[f_4182_3]) ).

fof(f_4183_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_4183_2,plain,
    ! [U_17081,U_17080] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_17080,U_17081) = c_Complete__Lattice_OInf__class_OInf(U_17080,U_17081)
      | U_17081 = c_Orderings_Obot__class_Obot(tc_fun(U_17080,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17080),U_17081))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17080) ),
    inference(variable_rename,[status(thm)],[f_4183_1]) ).

fof(f_4183_3,plain,
    ! [U_17080,U_17081] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_17080,U_17081) = c_Complete__Lattice_OInf__class_OInf(U_17080,U_17081)
      | U_17081 = c_Orderings_Obot__class_Obot(tc_fun(U_17080,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17080),U_17081))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17080) ),
    inference(definitional_conversion,[status(esa)],[f_4183_2]) ).

cnf(f_4183_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_17080,U_17081) = c_Complete__Lattice_OInf__class_OInf(U_17080,U_17081)
    | U_17081 = c_Orderings_Obot__class_Obot(tc_fun(U_17080,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17080),U_17081))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17080) ),
    inference(clausify,[status(thm)],[f_4183_3]) ).

fof(f_4184_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_4184_2,plain,
    ! [U_17083,U_17082] :
      ( c_Complete__Lattice_OInf__class_OInf(U_17082,U_17083) = c_Complete__Lattice_OSup__class_OSup(U_17082,hAPP(c_Set_OCollect(U_17082),hAPP(hAPP(c_COMBB(tc_fun(U_17082,tc_HOL_Obool),tc_HOL_Obool,U_17082),c_HOL_OAll(U_17082)),hAPP(hAPP(c_COMBB(tc_fun(U_17082,tc_HOL_Obool),tc_fun(U_17082,tc_HOL_Obool),U_17082),hAPP(c_COMBS(U_17082,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17082),c_fimplies),hAPP(hAPP(c_COMBC(U_17082,tc_fun(U_17082,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17082)),U_17083)))),c_Orderings_Oord__class_Oless__eq(U_17082)))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17082) ),
    inference(variable_rename,[status(thm)],[f_4184_1]) ).

fof(f_4184_3,plain,
    ! [U_17082,U_17083] :
      ( c_Complete__Lattice_OInf__class_OInf(U_17082,U_17083) = c_Complete__Lattice_OSup__class_OSup(U_17082,hAPP(c_Set_OCollect(U_17082),hAPP(hAPP(c_COMBB(tc_fun(U_17082,tc_HOL_Obool),tc_HOL_Obool,U_17082),c_HOL_OAll(U_17082)),hAPP(hAPP(c_COMBB(tc_fun(U_17082,tc_HOL_Obool),tc_fun(U_17082,tc_HOL_Obool),U_17082),hAPP(c_COMBS(U_17082,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17082),c_fimplies),hAPP(hAPP(c_COMBC(U_17082,tc_fun(U_17082,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17082)),U_17083)))),c_Orderings_Oord__class_Oless__eq(U_17082)))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17082) ),
    inference(definitional_conversion,[status(esa)],[f_4184_2]) ).

cnf(f_4184_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_17082,U_17083) = c_Complete__Lattice_OSup__class_OSup(U_17082,hAPP(c_Set_OCollect(U_17082),hAPP(hAPP(c_COMBB(tc_fun(U_17082,tc_HOL_Obool),tc_HOL_Obool,U_17082),c_HOL_OAll(U_17082)),hAPP(hAPP(c_COMBB(tc_fun(U_17082,tc_HOL_Obool),tc_fun(U_17082,tc_HOL_Obool),U_17082),hAPP(c_COMBS(U_17082,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17082),c_fimplies),hAPP(hAPP(c_COMBC(U_17082,tc_fun(U_17082,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17082)),U_17083)))),c_Orderings_Oord__class_Oless__eq(U_17082)))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17082) ),
    inference(clausify,[status(thm)],[f_4184_3]) ).

fof(f_4185_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_4185_2,plain,
    ! [U_17085,U_17084] :
      ( c_Complete__Lattice_OSup__class_OSup(U_17084,U_17085) = c_Complete__Lattice_OInf__class_OInf(U_17084,hAPP(c_Set_OCollect(U_17084),hAPP(hAPP(c_COMBB(tc_fun(U_17084,tc_HOL_Obool),tc_HOL_Obool,U_17084),c_HOL_OAll(U_17084)),hAPP(hAPP(c_COMBB(tc_fun(U_17084,tc_HOL_Obool),tc_fun(U_17084,tc_HOL_Obool),U_17084),hAPP(c_COMBS(U_17084,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17084),c_fimplies),hAPP(hAPP(c_COMBC(U_17084,tc_fun(U_17084,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17084)),U_17085)))),hAPP(c_COMBC(U_17084,U_17084,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_17084))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17084) ),
    inference(variable_rename,[status(thm)],[f_4185_1]) ).

fof(f_4185_3,plain,
    ! [U_17084,U_17085] :
      ( c_Complete__Lattice_OSup__class_OSup(U_17084,U_17085) = c_Complete__Lattice_OInf__class_OInf(U_17084,hAPP(c_Set_OCollect(U_17084),hAPP(hAPP(c_COMBB(tc_fun(U_17084,tc_HOL_Obool),tc_HOL_Obool,U_17084),c_HOL_OAll(U_17084)),hAPP(hAPP(c_COMBB(tc_fun(U_17084,tc_HOL_Obool),tc_fun(U_17084,tc_HOL_Obool),U_17084),hAPP(c_COMBS(U_17084,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17084),c_fimplies),hAPP(hAPP(c_COMBC(U_17084,tc_fun(U_17084,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17084)),U_17085)))),hAPP(c_COMBC(U_17084,U_17084,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_17084))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17084) ),
    inference(definitional_conversion,[status(esa)],[f_4185_2]) ).

cnf(f_4185_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_17084,U_17085) = c_Complete__Lattice_OInf__class_OInf(U_17084,hAPP(c_Set_OCollect(U_17084),hAPP(hAPP(c_COMBB(tc_fun(U_17084,tc_HOL_Obool),tc_HOL_Obool,U_17084),c_HOL_OAll(U_17084)),hAPP(hAPP(c_COMBB(tc_fun(U_17084,tc_HOL_Obool),tc_fun(U_17084,tc_HOL_Obool),U_17084),hAPP(c_COMBS(U_17084,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17084),c_fimplies),hAPP(hAPP(c_COMBC(U_17084,tc_fun(U_17084,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17084)),U_17085)))),hAPP(c_COMBC(U_17084,U_17084,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_17084))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17084) ),
    inference(clausify,[status(thm)],[f_4185_3]) ).

fof(f_4186_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_4186_2,plain,
    ! [U_17089,U_17088,U_17087,U_17086] :
      ( hBOOL(hAPP(hAPP(c_member(U_17086),U_17089),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17086,tc_HOL_Obool),U_17088)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17086),U_17089),U_17087))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17086,tc_HOL_Obool)),U_17087),U_17088)) ),
    inference(variable_rename,[status(thm)],[f_4186_1]) ).

fof(f_4186_3,plain,
    ! [U_17086,U_17087,U_17088,U_17089] :
      ( hBOOL(hAPP(hAPP(c_member(U_17086),U_17089),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17086,tc_HOL_Obool),U_17088)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17086),U_17089),U_17087))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17086,tc_HOL_Obool)),U_17087),U_17088)) ),
    inference(definitional_conversion,[status(esa)],[f_4186_2]) ).

cnf(f_4186_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17086),U_17089),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17086,tc_HOL_Obool),U_17088)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17086),U_17089),U_17087))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17086,tc_HOL_Obool)),U_17087),U_17088)) ),
    inference(clausify,[status(thm)],[f_4186_3]) ).

fof(f_4187_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_4187_2,plain,
    ! [U_17091,U_17090] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17090,tc_HOL_Obool),U_17091) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_17090,tc_HOL_Obool),tc_fun(U_17090,tc_HOL_Obool)),U_17091),c_COMBI(tc_fun(U_17090,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4187_1]) ).

fof(f_4187_3,plain,
    ! [U_17091,U_17090] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17090,tc_HOL_Obool),U_17091) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_17090,tc_HOL_Obool),tc_fun(U_17090,tc_HOL_Obool)),U_17091),c_COMBI(tc_fun(U_17090,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_4187_2]) ).

cnf(f_4187_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17090,tc_HOL_Obool),U_17091) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_17090,tc_HOL_Obool),tc_fun(U_17090,tc_HOL_Obool)),U_17091),c_COMBI(tc_fun(U_17090,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4187_3]) ).

fof(f_4188_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_4188_2,plain,
    ! [U_17095,U_17094,U_17093,U_17092] : hAPP(c_Set_Oimage(U_17092,U_17093,U_17094),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17092,tc_HOL_Obool),U_17095)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17092,tc_HOL_Obool),tc_fun(U_17093,tc_HOL_Obool)),U_17095),c_Set_Oimage(U_17092,U_17093,U_17094)),
    inference(variable_rename,[status(thm)],[f_4188_1]) ).

fof(f_4188_3,plain,
    ! [U_17092,U_17093,U_17094,U_17095] : hAPP(c_Set_Oimage(U_17092,U_17093,U_17094),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17092,tc_HOL_Obool),U_17095)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17092,tc_HOL_Obool),tc_fun(U_17093,tc_HOL_Obool)),U_17095),c_Set_Oimage(U_17092,U_17093,U_17094)),
    inference(definitional_conversion,[status(esa)],[f_4188_2]) ).

cnf(f_4188_4,plain,
    hAPP(c_Set_Oimage(U_17092,U_17093,U_17094),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17092,tc_HOL_Obool),U_17095)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17092,tc_HOL_Obool),tc_fun(U_17093,tc_HOL_Obool)),U_17095),c_Set_Oimage(U_17092,U_17093,U_17094)),
    inference(clausify,[status(thm)],[f_4188_3]) ).

fof(f_4189_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_4189_2,plain,
    ! [U_17099,U_17098,U_17097,U_17096] : hAPP(hAPP(c_Product__Type_OSigma(U_17096,U_17097),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17096,tc_HOL_Obool),U_17098)),U_17099) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17096,tc_HOL_Obool),tc_fun(tc_prod(U_17096,U_17097),tc_HOL_Obool)),U_17098),hAPP(hAPP(c_COMBC(tc_fun(U_17096,tc_HOL_Obool),tc_fun(U_17096,tc_fun(U_17097,tc_HOL_Obool)),tc_fun(tc_prod(U_17096,U_17097),tc_HOL_Obool)),c_Product__Type_OSigma(U_17096,U_17097)),U_17099)),
    inference(variable_rename,[status(thm)],[f_4189_1]) ).

fof(f_4189_3,plain,
    ! [U_17096,U_17097,U_17098,U_17099] : hAPP(hAPP(c_Product__Type_OSigma(U_17096,U_17097),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17096,tc_HOL_Obool),U_17098)),U_17099) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17096,tc_HOL_Obool),tc_fun(tc_prod(U_17096,U_17097),tc_HOL_Obool)),U_17098),hAPP(hAPP(c_COMBC(tc_fun(U_17096,tc_HOL_Obool),tc_fun(U_17096,tc_fun(U_17097,tc_HOL_Obool)),tc_fun(tc_prod(U_17096,U_17097),tc_HOL_Obool)),c_Product__Type_OSigma(U_17096,U_17097)),U_17099)),
    inference(definitional_conversion,[status(esa)],[f_4189_2]) ).

cnf(f_4189_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_17096,U_17097),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17096,tc_HOL_Obool),U_17098)),U_17099) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17096,tc_HOL_Obool),tc_fun(tc_prod(U_17096,U_17097),tc_HOL_Obool)),U_17098),hAPP(hAPP(c_COMBC(tc_fun(U_17096,tc_HOL_Obool),tc_fun(U_17096,tc_fun(U_17097,tc_HOL_Obool)),tc_fun(tc_prod(U_17096,U_17097),tc_HOL_Obool)),c_Product__Type_OSigma(U_17096,U_17097)),U_17099)),
    inference(clausify,[status(thm)],[f_4189_3]) ).

fof(f_4190_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_4190_2,plain,
    ! [U_17103,U_17102,U_17101,U_17100] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17100,tc_fun(U_17101,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17100,tc_HOL_Obool),U_17102)),U_17103) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17100,tc_HOL_Obool),tc_fun(U_17101,tc_HOL_Obool)),U_17102),hAPP(hAPP(c_COMBC(tc_fun(U_17100,tc_HOL_Obool),tc_fun(U_17100,tc_fun(U_17101,tc_HOL_Obool)),tc_fun(U_17101,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17100,tc_fun(U_17101,tc_HOL_Obool))),U_17103)),
    inference(variable_rename,[status(thm)],[f_4190_1]) ).

fof(f_4190_3,plain,
    ! [U_17100,U_17101,U_17102,U_17103] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17100,tc_fun(U_17101,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17100,tc_HOL_Obool),U_17102)),U_17103) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17100,tc_HOL_Obool),tc_fun(U_17101,tc_HOL_Obool)),U_17102),hAPP(hAPP(c_COMBC(tc_fun(U_17100,tc_HOL_Obool),tc_fun(U_17100,tc_fun(U_17101,tc_HOL_Obool)),tc_fun(U_17101,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17100,tc_fun(U_17101,tc_HOL_Obool))),U_17103)),
    inference(definitional_conversion,[status(esa)],[f_4190_2]) ).

cnf(f_4190_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17100,tc_fun(U_17101,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17100,tc_HOL_Obool),U_17102)),U_17103) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17100,tc_HOL_Obool),tc_fun(U_17101,tc_HOL_Obool)),U_17102),hAPP(hAPP(c_COMBC(tc_fun(U_17100,tc_HOL_Obool),tc_fun(U_17100,tc_fun(U_17101,tc_HOL_Obool)),tc_fun(U_17101,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17100,tc_fun(U_17101,tc_HOL_Obool))),U_17103)),
    inference(clausify,[status(thm)],[f_4190_3]) ).

fof(f_4191_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_4191_2,plain,
    ! [U_17107,U_17106,U_17105,U_17104] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17104,tc_HOL_Obool),tc_fun(U_17105,tc_HOL_Obool)),U_17106),hAPP(hAPP(c_COMBC(tc_fun(U_17104,tc_HOL_Obool),tc_fun(U_17104,tc_fun(U_17105,tc_HOL_Obool)),tc_fun(U_17105,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17104,tc_fun(U_17105,tc_HOL_Obool))),U_17107)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17104,tc_fun(U_17105,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17104,tc_HOL_Obool),U_17106)),U_17107),
    inference(variable_rename,[status(thm)],[f_4191_1]) ).

fof(f_4191_3,plain,
    ! [U_17104,U_17105,U_17106,U_17107] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17104,tc_HOL_Obool),tc_fun(U_17105,tc_HOL_Obool)),U_17106),hAPP(hAPP(c_COMBC(tc_fun(U_17104,tc_HOL_Obool),tc_fun(U_17104,tc_fun(U_17105,tc_HOL_Obool)),tc_fun(U_17105,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17104,tc_fun(U_17105,tc_HOL_Obool))),U_17107)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17104,tc_fun(U_17105,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17104,tc_HOL_Obool),U_17106)),U_17107),
    inference(definitional_conversion,[status(esa)],[f_4191_2]) ).

cnf(f_4191_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17104,tc_HOL_Obool),tc_fun(U_17105,tc_HOL_Obool)),U_17106),hAPP(hAPP(c_COMBC(tc_fun(U_17104,tc_HOL_Obool),tc_fun(U_17104,tc_fun(U_17105,tc_HOL_Obool)),tc_fun(U_17105,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17104,tc_fun(U_17105,tc_HOL_Obool))),U_17107)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17104,tc_fun(U_17105,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17104,tc_HOL_Obool),U_17106)),U_17107),
    inference(clausify,[status(thm)],[f_4191_3]) ).

fof(f_4192_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_4192_2,plain,
    ! [U_17110,U_17109,U_17108] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17108,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17108,tc_HOL_Obool),U_17109)),U_17110) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17108,tc_HOL_Obool),tc_fun(U_17108,tc_HOL_Obool)),U_17109),hAPP(hAPP(c_COMBC(tc_fun(U_17108,tc_HOL_Obool),tc_fun(U_17108,tc_HOL_Obool),tc_fun(U_17108,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17108,tc_HOL_Obool))),U_17110)),
    inference(variable_rename,[status(thm)],[f_4192_1]) ).

fof(f_4192_3,plain,
    ! [U_17108,U_17109,U_17110] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17108,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17108,tc_HOL_Obool),U_17109)),U_17110) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17108,tc_HOL_Obool),tc_fun(U_17108,tc_HOL_Obool)),U_17109),hAPP(hAPP(c_COMBC(tc_fun(U_17108,tc_HOL_Obool),tc_fun(U_17108,tc_HOL_Obool),tc_fun(U_17108,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17108,tc_HOL_Obool))),U_17110)),
    inference(definitional_conversion,[status(esa)],[f_4192_2]) ).

cnf(f_4192_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17108,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17108,tc_HOL_Obool),U_17109)),U_17110) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17108,tc_HOL_Obool),tc_fun(U_17108,tc_HOL_Obool)),U_17109),hAPP(hAPP(c_COMBC(tc_fun(U_17108,tc_HOL_Obool),tc_fun(U_17108,tc_HOL_Obool),tc_fun(U_17108,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17108,tc_HOL_Obool))),U_17110)),
    inference(clausify,[status(thm)],[f_4192_3]) ).

fof(f_4193_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_4193_2,plain,
    ! [U_17113,U_17112,U_17111] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17111,tc_HOL_Obool)),U_17112),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17111,tc_HOL_Obool),U_17113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17111,tc_HOL_Obool),tc_fun(U_17111,tc_HOL_Obool)),U_17113),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17111,tc_HOL_Obool)),U_17112)),
    inference(variable_rename,[status(thm)],[f_4193_1]) ).

fof(f_4193_3,plain,
    ! [U_17111,U_17112,U_17113] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17111,tc_HOL_Obool)),U_17112),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17111,tc_HOL_Obool),U_17113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17111,tc_HOL_Obool),tc_fun(U_17111,tc_HOL_Obool)),U_17113),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17111,tc_HOL_Obool)),U_17112)),
    inference(definitional_conversion,[status(esa)],[f_4193_2]) ).

cnf(f_4193_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17111,tc_HOL_Obool)),U_17112),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17111,tc_HOL_Obool),U_17113)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17111,tc_HOL_Obool),tc_fun(U_17111,tc_HOL_Obool)),U_17113),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17111,tc_HOL_Obool)),U_17112)),
    inference(clausify,[status(thm)],[f_4193_3]) ).

fof(f_4194_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_4194_2,plain,
    ! [U_17117,U_17116,U_17115,U_17114] : hAPP(c_Set_Ovimage(U_17114,U_17115,U_17116),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17115,tc_HOL_Obool),U_17117)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17115,tc_HOL_Obool),tc_fun(U_17114,tc_HOL_Obool)),U_17117),c_Set_Ovimage(U_17114,U_17115,U_17116)),
    inference(variable_rename,[status(thm)],[f_4194_1]) ).

fof(f_4194_3,plain,
    ! [U_17114,U_17115,U_17116,U_17117] : hAPP(c_Set_Ovimage(U_17114,U_17115,U_17116),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17115,tc_HOL_Obool),U_17117)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17115,tc_HOL_Obool),tc_fun(U_17114,tc_HOL_Obool)),U_17117),c_Set_Ovimage(U_17114,U_17115,U_17116)),
    inference(definitional_conversion,[status(esa)],[f_4194_2]) ).

cnf(f_4194_4,plain,
    hAPP(c_Set_Ovimage(U_17114,U_17115,U_17116),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17115,tc_HOL_Obool),U_17117)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17115,tc_HOL_Obool),tc_fun(U_17114,tc_HOL_Obool)),U_17117),c_Set_Ovimage(U_17114,U_17115,U_17116)),
    inference(clausify,[status(thm)],[f_4194_3]) ).

fof(f_4195_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_4195_2,plain,
    ! [U_17120,U_17119,U_17118] : hAPP(c_Relation_ORange(U_17118,U_17119),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_17118,U_17119),tc_HOL_Obool),U_17120)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_17118,U_17119),tc_HOL_Obool),tc_fun(U_17119,tc_HOL_Obool)),U_17120),c_Relation_ORange(U_17118,U_17119)),
    inference(variable_rename,[status(thm)],[f_4195_1]) ).

fof(f_4195_3,plain,
    ! [U_17118,U_17119,U_17120] : hAPP(c_Relation_ORange(U_17118,U_17119),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_17118,U_17119),tc_HOL_Obool),U_17120)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_17118,U_17119),tc_HOL_Obool),tc_fun(U_17119,tc_HOL_Obool)),U_17120),c_Relation_ORange(U_17118,U_17119)),
    inference(definitional_conversion,[status(esa)],[f_4195_2]) ).

cnf(f_4195_4,plain,
    hAPP(c_Relation_ORange(U_17118,U_17119),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_17118,U_17119),tc_HOL_Obool),U_17120)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_17118,U_17119),tc_HOL_Obool),tc_fun(U_17119,tc_HOL_Obool)),U_17120),c_Relation_ORange(U_17118,U_17119)),
    inference(clausify,[status(thm)],[f_4195_3]) ).

fof(f_4196_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_4196_2,plain,
    ! [U_17123,U_17122,U_17121] : hAPP(c_Relation_ODomain(U_17121,U_17122),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_17121,U_17122),tc_HOL_Obool),U_17123)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_17121,U_17122),tc_HOL_Obool),tc_fun(U_17121,tc_HOL_Obool)),U_17123),c_Relation_ODomain(U_17121,U_17122)),
    inference(variable_rename,[status(thm)],[f_4196_1]) ).

fof(f_4196_3,plain,
    ! [U_17121,U_17122,U_17123] : hAPP(c_Relation_ODomain(U_17121,U_17122),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_17121,U_17122),tc_HOL_Obool),U_17123)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_17121,U_17122),tc_HOL_Obool),tc_fun(U_17121,tc_HOL_Obool)),U_17123),c_Relation_ODomain(U_17121,U_17122)),
    inference(definitional_conversion,[status(esa)],[f_4196_2]) ).

cnf(f_4196_4,plain,
    hAPP(c_Relation_ODomain(U_17121,U_17122),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_17121,U_17122),tc_HOL_Obool),U_17123)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_17121,U_17122),tc_HOL_Obool),tc_fun(U_17121,tc_HOL_Obool)),U_17123),c_Relation_ODomain(U_17121,U_17122)),
    inference(clausify,[status(thm)],[f_4196_3]) ).

fof(f_4197_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_4197_2,plain,
    ! [U_17127,U_17126,U_17125,U_17124] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_17124,tc_HOL_Obool),tc_fun(U_17125,tc_HOL_Obool)),U_17126),hAPP(hAPP(c_COMBC(tc_fun(U_17124,tc_HOL_Obool),tc_fun(U_17124,tc_fun(U_17125,tc_HOL_Obool)),tc_fun(U_17125,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17124,tc_fun(U_17125,tc_HOL_Obool))),U_17127)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17124,tc_fun(U_17125,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17124,tc_HOL_Obool),U_17126)),U_17127),
    inference(variable_rename,[status(thm)],[f_4197_1]) ).

fof(f_4197_3,plain,
    ! [U_17124,U_17125,U_17126,U_17127] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_17124,tc_HOL_Obool),tc_fun(U_17125,tc_HOL_Obool)),U_17126),hAPP(hAPP(c_COMBC(tc_fun(U_17124,tc_HOL_Obool),tc_fun(U_17124,tc_fun(U_17125,tc_HOL_Obool)),tc_fun(U_17125,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17124,tc_fun(U_17125,tc_HOL_Obool))),U_17127)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17124,tc_fun(U_17125,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17124,tc_HOL_Obool),U_17126)),U_17127),
    inference(definitional_conversion,[status(esa)],[f_4197_2]) ).

cnf(f_4197_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_17124,tc_HOL_Obool),tc_fun(U_17125,tc_HOL_Obool)),U_17126),hAPP(hAPP(c_COMBC(tc_fun(U_17124,tc_HOL_Obool),tc_fun(U_17124,tc_fun(U_17125,tc_HOL_Obool)),tc_fun(U_17125,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17124,tc_fun(U_17125,tc_HOL_Obool))),U_17127)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17124,tc_fun(U_17125,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17124,tc_HOL_Obool),U_17126)),U_17127),
    inference(clausify,[status(thm)],[f_4197_3]) ).

fof(f_4198_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_4198_2,plain,
    ! [U_17131,U_17130,U_17129,U_17128] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17128,tc_fun(U_17129,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17128,tc_HOL_Obool),U_17130)),U_17131) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_17128,tc_HOL_Obool),tc_fun(U_17129,tc_HOL_Obool)),U_17130),hAPP(hAPP(c_COMBC(tc_fun(U_17128,tc_HOL_Obool),tc_fun(U_17128,tc_fun(U_17129,tc_HOL_Obool)),tc_fun(U_17129,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17128,tc_fun(U_17129,tc_HOL_Obool))),U_17131)),
    inference(variable_rename,[status(thm)],[f_4198_1]) ).

fof(f_4198_3,plain,
    ! [U_17128,U_17129,U_17130,U_17131] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17128,tc_fun(U_17129,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17128,tc_HOL_Obool),U_17130)),U_17131) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_17128,tc_HOL_Obool),tc_fun(U_17129,tc_HOL_Obool)),U_17130),hAPP(hAPP(c_COMBC(tc_fun(U_17128,tc_HOL_Obool),tc_fun(U_17128,tc_fun(U_17129,tc_HOL_Obool)),tc_fun(U_17129,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17128,tc_fun(U_17129,tc_HOL_Obool))),U_17131)),
    inference(definitional_conversion,[status(esa)],[f_4198_2]) ).

cnf(f_4198_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17128,tc_fun(U_17129,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17128,tc_HOL_Obool),U_17130)),U_17131) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_17128,tc_HOL_Obool),tc_fun(U_17129,tc_HOL_Obool)),U_17130),hAPP(hAPP(c_COMBC(tc_fun(U_17128,tc_HOL_Obool),tc_fun(U_17128,tc_fun(U_17129,tc_HOL_Obool)),tc_fun(U_17129,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17128,tc_fun(U_17129,tc_HOL_Obool))),U_17131)),
    inference(clausify,[status(thm)],[f_4198_3]) ).

fof(f_4199_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_4199_2,plain,
    ! [U_17132] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17132,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_17132,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_17132,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4199_1]) ).

fof(f_4199_3,plain,
    ! [U_17132] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17132,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_17132,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_17132,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4199_2]) ).

cnf(f_4199_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17132,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_17132,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_17132,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4199_3]) ).

fof(f_4200_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_4200_2,plain,
    ! [U_17134,U_17133] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_17133,tc_HOL_Obool),tc_HOL_Obool)),U_17134),hAPP(c_Set_OPow(U_17133),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17133,tc_HOL_Obool),U_17134)))),
    inference(variable_rename,[status(thm)],[f_4200_1]) ).

fof(f_4200_3,plain,
    ! [U_17133,U_17134] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_17133,tc_HOL_Obool),tc_HOL_Obool)),U_17134),hAPP(c_Set_OPow(U_17133),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17133,tc_HOL_Obool),U_17134)))),
    inference(definitional_conversion,[status(esa)],[f_4200_2]) ).

cnf(f_4200_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_17133,tc_HOL_Obool),tc_HOL_Obool)),U_17134),hAPP(c_Set_OPow(U_17133),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17133,tc_HOL_Obool),U_17134)))),
    inference(clausify,[status(thm)],[f_4200_3]) ).

fof(f_4201_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_4201_2,plain,
    ! [U_17136,U_17135] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_17135,tc_HOL_Obool)),U_17136))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17135),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17135,tc_HOL_Obool),U_17136))) ),
    inference(variable_rename,[status(thm)],[f_4201_1]) ).

fof(f_4201_3,plain,
    ! [U_17135,U_17136] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_17135,tc_HOL_Obool)),U_17136))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17135),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17135,tc_HOL_Obool),U_17136))) ),
    inference(definitional_conversion,[status(esa)],[f_4201_2]) ).

cnf(f_4201_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_17135,tc_HOL_Obool)),U_17136))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17135),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17135,tc_HOL_Obool),U_17136))) ),
    inference(clausify,[status(thm)],[f_4201_3]) ).

fof(f_4202_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_4202_2,plain,
    ! [U_17141,U_17140,U_17139] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17139,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17139,tc_HOL_Obool),U_17140)),U_17141) = c_Orderings_Obot__class_Obot(tc_fun(U_17139,tc_HOL_Obool))
        | ? [U_17138] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17139,tc_HOL_Obool)),U_17138),U_17141) != c_Orderings_Obot__class_Obot(tc_fun(U_17139,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17139,tc_HOL_Obool)),U_17138),U_17140)) ) )
      & ( ! [U_17137] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17139,tc_HOL_Obool)),U_17137),U_17141) = c_Orderings_Obot__class_Obot(tc_fun(U_17139,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17139,tc_HOL_Obool)),U_17137),U_17140)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17139,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17139,tc_HOL_Obool),U_17140)),U_17141) != c_Orderings_Obot__class_Obot(tc_fun(U_17139,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4202_1]) ).

fof(f_4202_3,plain,
    ( ! [U_17147,U_17145,U_17143] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17143,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17143,tc_HOL_Obool),U_17145)),U_17147) = c_Orderings_Obot__class_Obot(tc_fun(U_17143,tc_HOL_Obool))
        | ? [U_17138] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17143,tc_HOL_Obool)),U_17138),U_17147) != c_Orderings_Obot__class_Obot(tc_fun(U_17143,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17143,tc_HOL_Obool)),U_17138),U_17145)) ) )
    & ! [U_17146,U_17144,U_17142] :
        ( ! [U_17137] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17142,tc_HOL_Obool)),U_17137),U_17146) = c_Orderings_Obot__class_Obot(tc_fun(U_17142,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17142,tc_HOL_Obool)),U_17137),U_17144)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17142,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17142,tc_HOL_Obool),U_17144)),U_17146) != c_Orderings_Obot__class_Obot(tc_fun(U_17142,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4202_2]) ).

fof(f_4202_4,plain,
    ( ! [U_17147,U_17145,U_17143] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17143,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17143,tc_HOL_Obool),U_17145)),U_17147) = c_Orderings_Obot__class_Obot(tc_fun(U_17143,tc_HOL_Obool))
        | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17143,tc_HOL_Obool)),sK408(U_17147,U_17145,U_17143)),U_17147) != c_Orderings_Obot__class_Obot(tc_fun(U_17143,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17143,tc_HOL_Obool)),sK408(U_17147,U_17145,U_17143)),U_17145)) ) )
    & ! [U_17146,U_17144,U_17142] :
        ( ! [U_17137] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17142,tc_HOL_Obool)),U_17137),U_17146) = c_Orderings_Obot__class_Obot(tc_fun(U_17142,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17142,tc_HOL_Obool)),U_17137),U_17144)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17142,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17142,tc_HOL_Obool),U_17144)),U_17146) != c_Orderings_Obot__class_Obot(tc_fun(U_17142,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK408]),skolemize(U_17138,sK408(U_17147,U_17145,U_17143))],[f_4202_3]) ).

fof(f_4202_5,plain,
    ( ! [U_17147,U_17145,U_17143] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17143,tc_HOL_Obool)),sK408(U_17147,U_17145,U_17143)),U_17147) != c_Orderings_Obot__class_Obot(tc_fun(U_17143,tc_HOL_Obool))
        | ~ sP1075(U_17147,U_17145,U_17143) )
    & ! [U_17147,U_17145,U_17143] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17143,tc_HOL_Obool)),sK408(U_17147,U_17145,U_17143)),U_17145))
        | ~ sP1075(U_17147,U_17145,U_17143) )
    & ! [U_17147,U_17145,U_17143] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17143,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17143,tc_HOL_Obool),U_17145)),U_17147) = c_Orderings_Obot__class_Obot(tc_fun(U_17143,tc_HOL_Obool))
        | sP1075(U_17147,U_17145,U_17143) )
    & ! [U_17146,U_17137,U_17142,U_17144] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17142,tc_HOL_Obool)),U_17137),U_17146) = c_Orderings_Obot__class_Obot(tc_fun(U_17142,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17142,tc_HOL_Obool)),U_17137),U_17144))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17142,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17142,tc_HOL_Obool),U_17144)),U_17146) != c_Orderings_Obot__class_Obot(tc_fun(U_17142,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1075])],[f_4202_4]) ).

cnf(f_4202_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17142,tc_HOL_Obool)),U_17137),U_17146) = c_Orderings_Obot__class_Obot(tc_fun(U_17142,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17142,tc_HOL_Obool)),U_17137),U_17144))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17142,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17142,tc_HOL_Obool),U_17144)),U_17146) != c_Orderings_Obot__class_Obot(tc_fun(U_17142,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4202_5]) ).

cnf(f_4202_7,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17143,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17143,tc_HOL_Obool),U_17145)),U_17147) = c_Orderings_Obot__class_Obot(tc_fun(U_17143,tc_HOL_Obool))
    | sP1075(U_17147,U_17145,U_17143) ),
    inference(clausify,[status(thm)],[f_4202_5]) ).

cnf(f_4202_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17143,tc_HOL_Obool)),sK408(U_17147,U_17145,U_17143)),U_17145))
    | ~ sP1075(U_17147,U_17145,U_17143) ),
    inference(clausify,[status(thm)],[f_4202_5]) ).

cnf(f_4202_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17143,tc_HOL_Obool)),sK408(U_17147,U_17145,U_17143)),U_17147) != c_Orderings_Obot__class_Obot(tc_fun(U_17143,tc_HOL_Obool))
    | ~ sP1075(U_17147,U_17145,U_17143) ),
    inference(clausify,[status(thm)],[f_4202_5]) ).

fof(f_4203_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_4203_2,plain,
    ! [U_17148] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17148,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17148,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_17148,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4203_1]) ).

fof(f_4203_3,plain,
    ! [U_17148] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17148,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17148,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_17148,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4203_2]) ).

cnf(f_4203_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17148,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17148,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_17148,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4203_3]) ).

fof(f_4204_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_4204_2,plain,
    ! [U_17151,U_17150,U_17149] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17149,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17149,tc_HOL_Obool),U_17150)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17149,tc_HOL_Obool),U_17151)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_17149,tc_HOL_Obool),tc_HOL_Obool)),U_17150),U_17151)) ),
    inference(variable_rename,[status(thm)],[f_4204_1]) ).

fof(f_4204_3,plain,
    ! [U_17149,U_17150,U_17151] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17149,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17149,tc_HOL_Obool),U_17150)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17149,tc_HOL_Obool),U_17151)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_17149,tc_HOL_Obool),tc_HOL_Obool)),U_17150),U_17151)) ),
    inference(definitional_conversion,[status(esa)],[f_4204_2]) ).

cnf(f_4204_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17149,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17149,tc_HOL_Obool),U_17150)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17149,tc_HOL_Obool),U_17151)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_17149,tc_HOL_Obool),tc_HOL_Obool)),U_17150),U_17151)) ),
    inference(clausify,[status(thm)],[f_4204_3]) ).

fof(f_4205_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_4205_2,plain,
    ! [U_17156,U_17155,U_17154] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),c_Complete__Lattice_OSup__class_OSup(U_17154,U_17155)),U_17156))
          | ? [U_17153] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),U_17153),U_17156))
              & hBOOL(hAPP(hAPP(c_member(U_17154),U_17153),U_17155)) ) )
        & ( ! [U_17152] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),U_17152),U_17156))
              | ~ hBOOL(hAPP(hAPP(c_member(U_17154),U_17152),U_17155)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),c_Complete__Lattice_OSup__class_OSup(U_17154,U_17155)),U_17156)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17154) ),
    inference(variable_rename,[status(thm)],[f_4205_1]) ).

fof(f_4205_3,plain,
    ! [U_17156,U_17155,U_17154] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),c_Complete__Lattice_OSup__class_OSup(U_17154,U_17155)),U_17156))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),sK409(U_17156,U_17155,U_17154)),U_17156))
            & hBOOL(hAPP(hAPP(c_member(U_17154),sK409(U_17156,U_17155,U_17154)),U_17155)) ) )
        & ( ! [U_17152] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),U_17152),U_17156))
              | ~ hBOOL(hAPP(hAPP(c_member(U_17154),U_17152),U_17155)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),c_Complete__Lattice_OSup__class_OSup(U_17154,U_17155)),U_17156)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17154) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK409]),skolemize(U_17153,sK409(U_17156,U_17155,U_17154))],[f_4205_2]) ).

fof(f_4205_4,plain,
    ( ! [U_17154,U_17155,U_17156] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),sK409(U_17156,U_17155,U_17154)),U_17156))
        | ~ sP1076(U_17154,U_17155,U_17156) )
    & ! [U_17154,U_17155,U_17156] :
        ( hBOOL(hAPP(hAPP(c_member(U_17154),sK409(U_17156,U_17155,U_17154)),U_17155))
        | ~ sP1076(U_17154,U_17155,U_17156) )
    & ! [U_17152,U_17154,U_17155,U_17156] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),c_Complete__Lattice_OSup__class_OSup(U_17154,U_17155)),U_17156))
        | sP1076(U_17154,U_17155,U_17156)
        | ~ sP1077(U_17152,U_17154,U_17155,U_17156) )
    & ! [U_17152,U_17154,U_17155,U_17156] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),U_17152),U_17156))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17154),U_17152),U_17155))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),c_Complete__Lattice_OSup__class_OSup(U_17154,U_17155)),U_17156))
        | ~ sP1077(U_17152,U_17154,U_17155,U_17156) )
    & ! [U_17152,U_17154,U_17155,U_17156] :
        ( sP1077(U_17152,U_17154,U_17155,U_17156)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_17154) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1076,sP1077])],[f_4205_3]) ).

cnf(f_4205_5,plain,
    ( sP1077(U_17152,U_17154,U_17155,U_17156)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17154) ),
    inference(clausify,[status(thm)],[f_4205_4]) ).

cnf(f_4205_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),U_17152),U_17156))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17154),U_17152),U_17155))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),c_Complete__Lattice_OSup__class_OSup(U_17154,U_17155)),U_17156))
    | ~ sP1077(U_17152,U_17154,U_17155,U_17156) ),
    inference(clausify,[status(thm)],[f_4205_4]) ).

cnf(f_4205_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),c_Complete__Lattice_OSup__class_OSup(U_17154,U_17155)),U_17156))
    | sP1076(U_17154,U_17155,U_17156)
    | ~ sP1077(U_17152,U_17154,U_17155,U_17156) ),
    inference(clausify,[status(thm)],[f_4205_4]) ).

cnf(f_4205_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17154),sK409(U_17156,U_17155,U_17154)),U_17155))
    | ~ sP1076(U_17154,U_17155,U_17156) ),
    inference(clausify,[status(thm)],[f_4205_4]) ).

cnf(f_4205_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17154),sK409(U_17156,U_17155,U_17154)),U_17156))
    | ~ sP1076(U_17154,U_17155,U_17156) ),
    inference(clausify,[status(thm)],[f_4205_4]) ).

fof(f_4206_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_4206_2,plain,
    ! [U_17159,U_17158,U_17157] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17157,tc_HOL_Obool)),U_17158),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17157,tc_HOL_Obool),U_17159)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17157,tc_HOL_Obool)),U_17158),U_17159)) ),
    inference(variable_rename,[status(thm)],[f_4206_1]) ).

fof(f_4206_3,plain,
    ! [U_17158,U_17159,U_17157] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17157,tc_HOL_Obool)),U_17158),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17157,tc_HOL_Obool),U_17159)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17157,tc_HOL_Obool)),U_17158),U_17159)) ),
    inference(definitional_conversion,[status(esa)],[f_4206_2]) ).

cnf(f_4206_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17157,tc_HOL_Obool)),U_17158),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17157,tc_HOL_Obool),U_17159)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_17157,tc_HOL_Obool)),U_17158),U_17159)) ),
    inference(clausify,[status(thm)],[f_4206_3]) ).

fof(f_4207_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_4207_2,plain,
    ! [U_17161,U_17160] : hAPP(c_Relation_OField(U_17160),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_17160,U_17160),tc_HOL_Obool),U_17161)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17160,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_17160,U_17160),tc_HOL_Obool),tc_fun(U_17160,tc_HOL_Obool),c_Relation_OField(U_17160)),U_17161)),
    inference(variable_rename,[status(thm)],[f_4207_1]) ).

fof(f_4207_3,plain,
    ! [U_17160,U_17161] : hAPP(c_Relation_OField(U_17160),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_17160,U_17160),tc_HOL_Obool),U_17161)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17160,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_17160,U_17160),tc_HOL_Obool),tc_fun(U_17160,tc_HOL_Obool),c_Relation_OField(U_17160)),U_17161)),
    inference(definitional_conversion,[status(esa)],[f_4207_2]) ).

cnf(f_4207_4,plain,
    hAPP(c_Relation_OField(U_17160),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_17160,U_17160),tc_HOL_Obool),U_17161)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17160,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_17160,U_17160),tc_HOL_Obool),tc_fun(U_17160,tc_HOL_Obool),c_Relation_OField(U_17160)),U_17161)),
    inference(clausify,[status(thm)],[f_4207_3]) ).

fof(f_4208_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_4208_2,plain,
    ! [U_17166,U_17165,U_17164] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),c_Complete__Lattice_OSup__class_OSup(U_17164,U_17166)))
          | ! [U_17163] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),U_17163))
              | ~ hBOOL(hAPP(hAPP(c_member(U_17164),U_17163),U_17166)) ) )
        & ( ? [U_17162] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),U_17162))
              & hBOOL(hAPP(hAPP(c_member(U_17164),U_17162),U_17166)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),c_Complete__Lattice_OSup__class_OSup(U_17164,U_17166))) ) )
      | ~ class_Orderings_Olinorder(U_17164)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17164) ),
    inference(variable_rename,[status(thm)],[f_4208_1]) ).

fof(f_4208_3,plain,
    ! [U_17166,U_17165,U_17164] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),c_Complete__Lattice_OSup__class_OSup(U_17164,U_17166)))
          | ! [U_17163] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),U_17163))
              | ~ hBOOL(hAPP(hAPP(c_member(U_17164),U_17163),U_17166)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),sK410(U_17166,U_17165,U_17164)))
            & hBOOL(hAPP(hAPP(c_member(U_17164),sK410(U_17166,U_17165,U_17164)),U_17166)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),c_Complete__Lattice_OSup__class_OSup(U_17164,U_17166))) ) )
      | ~ class_Orderings_Olinorder(U_17164)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17164) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK410]),skolemize(U_17162,sK410(U_17166,U_17165,U_17164))],[f_4208_2]) ).

fof(f_4208_4,plain,
    ( ! [U_17164,U_17165,U_17166] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),sK410(U_17166,U_17165,U_17164)))
        | ~ sP1078(U_17164,U_17165,U_17166) )
    & ! [U_17164,U_17165,U_17166] :
        ( hBOOL(hAPP(hAPP(c_member(U_17164),sK410(U_17166,U_17165,U_17164)),U_17166))
        | ~ sP1078(U_17164,U_17165,U_17166) )
    & ! [U_17163,U_17164,U_17165,U_17166] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),c_Complete__Lattice_OSup__class_OSup(U_17164,U_17166)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),U_17163))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17164),U_17163),U_17166))
        | ~ sP1079(U_17163,U_17164,U_17165,U_17166) )
    & ! [U_17163,U_17164,U_17165,U_17166] :
        ( sP1078(U_17164,U_17165,U_17166)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),c_Complete__Lattice_OSup__class_OSup(U_17164,U_17166)))
        | ~ sP1079(U_17163,U_17164,U_17165,U_17166) )
    & ! [U_17163,U_17164,U_17165,U_17166] :
        ( sP1079(U_17163,U_17164,U_17165,U_17166)
        | ~ class_Orderings_Olinorder(U_17164)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_17164) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1078,sP1079])],[f_4208_3]) ).

cnf(f_4208_5,plain,
    ( sP1079(U_17163,U_17164,U_17165,U_17166)
    | ~ class_Orderings_Olinorder(U_17164)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17164) ),
    inference(clausify,[status(thm)],[f_4208_4]) ).

cnf(f_4208_6,plain,
    ( sP1078(U_17164,U_17165,U_17166)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),c_Complete__Lattice_OSup__class_OSup(U_17164,U_17166)))
    | ~ sP1079(U_17163,U_17164,U_17165,U_17166) ),
    inference(clausify,[status(thm)],[f_4208_4]) ).

cnf(f_4208_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),c_Complete__Lattice_OSup__class_OSup(U_17164,U_17166)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),U_17163))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17164),U_17163),U_17166))
    | ~ sP1079(U_17163,U_17164,U_17165,U_17166) ),
    inference(clausify,[status(thm)],[f_4208_4]) ).

cnf(f_4208_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17164),sK410(U_17166,U_17165,U_17164)),U_17166))
    | ~ sP1078(U_17164,U_17165,U_17166) ),
    inference(clausify,[status(thm)],[f_4208_4]) ).

cnf(f_4208_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_17164),U_17165),sK410(U_17166,U_17165,U_17164)))
    | ~ sP1078(U_17164,U_17165,U_17166) ),
    inference(clausify,[status(thm)],[f_4208_4]) ).

fof(f_4209_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_4209_2,plain,
    ! [U_17168,U_17167] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17167,tc_HOL_Obool),hAPP(c_Set_OPow(U_17167),U_17168)) = U_17168,
    inference(variable_rename,[status(thm)],[f_4209_1]) ).

fof(f_4209_3,plain,
    ! [U_17168,U_17167] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17167,tc_HOL_Obool),hAPP(c_Set_OPow(U_17167),U_17168)) = U_17168,
    inference(definitional_conversion,[status(esa)],[f_4209_2]) ).

cnf(f_4209_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17167,tc_HOL_Obool),hAPP(c_Set_OPow(U_17167),U_17168)) = U_17168,
    inference(clausify,[status(thm)],[f_4209_3]) ).

fof(f_4210_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_4210_2,plain,
    ! [U_17171,U_17170,U_17169] :
      ( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17169,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_17169),U_17170),U_17171)) = U_17170
      | ~ c_Equiv__Relations_Oequiv(U_17169,U_17170,U_17171) ),
    inference(variable_rename,[status(thm)],[f_4210_1]) ).

fof(f_4210_3,plain,
    ! [U_17169,U_17170,U_17171] :
      ( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17169,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_17169),U_17170),U_17171)) = U_17170
      | ~ c_Equiv__Relations_Oequiv(U_17169,U_17170,U_17171) ),
    inference(definitional_conversion,[status(esa)],[f_4210_2]) ).

cnf(f_4210_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17169,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_17169),U_17170),U_17171)) = U_17170
    | ~ c_Equiv__Relations_Oequiv(U_17169,U_17170,U_17171) ),
    inference(clausify,[status(thm)],[f_4210_3]) ).

fof(f_4211_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_4211_2,plain,
    ! [U_17174,U_17173,U_17172] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17172,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17172,tc_HOL_Obool)),U_17173),U_17174)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17172,tc_HOL_Obool)),U_17173),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17172,tc_HOL_Obool),U_17174)),
    inference(variable_rename,[status(thm)],[f_4211_1]) ).

fof(f_4211_3,plain,
    ! [U_17172,U_17173,U_17174] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17172,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17172,tc_HOL_Obool)),U_17173),U_17174)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17172,tc_HOL_Obool)),U_17173),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17172,tc_HOL_Obool),U_17174)),
    inference(definitional_conversion,[status(esa)],[f_4211_2]) ).

cnf(f_4211_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17172,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17172,tc_HOL_Obool)),U_17173),U_17174)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17172,tc_HOL_Obool)),U_17173),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17172,tc_HOL_Obool),U_17174)),
    inference(clausify,[status(thm)],[f_4211_3]) ).

fof(f_4212_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_4212_2,plain,
    ! [U_17177,U_17176,U_17175] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17175,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_17175,tc_HOL_Obool),tc_HOL_Obool)),U_17176),U_17177)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17175,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17175,tc_HOL_Obool),U_17176)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17175,tc_HOL_Obool),U_17177)),
    inference(variable_rename,[status(thm)],[f_4212_1]) ).

fof(f_4212_3,plain,
    ! [U_17175,U_17176,U_17177] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17175,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_17175,tc_HOL_Obool),tc_HOL_Obool)),U_17176),U_17177)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17175,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17175,tc_HOL_Obool),U_17176)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17175,tc_HOL_Obool),U_17177)),
    inference(definitional_conversion,[status(esa)],[f_4212_2]) ).

cnf(f_4212_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17175,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_17175,tc_HOL_Obool),tc_HOL_Obool)),U_17176),U_17177)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17175,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17175,tc_HOL_Obool),U_17176)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17175,tc_HOL_Obool),U_17177)),
    inference(clausify,[status(thm)],[f_4212_3]) ).

fof(f_4213_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_4213_2,plain,
    ! [U_17181,U_17180,U_17179,U_17178] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17178,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17179,tc_fun(U_17178,tc_HOL_Obool),U_17180),U_17181)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17179,tc_fun(U_17178,tc_HOL_Obool)),U_17181),U_17180),
    inference(variable_rename,[status(thm)],[f_4213_1]) ).

fof(f_4213_3,plain,
    ! [U_17178,U_17179,U_17180,U_17181] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17178,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17179,tc_fun(U_17178,tc_HOL_Obool),U_17180),U_17181)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17179,tc_fun(U_17178,tc_HOL_Obool)),U_17181),U_17180),
    inference(definitional_conversion,[status(esa)],[f_4213_2]) ).

cnf(f_4213_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17178,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17179,tc_fun(U_17178,tc_HOL_Obool),U_17180),U_17181)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17179,tc_fun(U_17178,tc_HOL_Obool)),U_17181),U_17180),
    inference(clausify,[status(thm)],[f_4213_3]) ).

fof(f_4214_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_4214_2,plain,
    ! [U_17185,U_17184,U_17183,U_17182] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17182,tc_fun(U_17183,tc_HOL_Obool)),U_17184),U_17185) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17183,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17182,tc_fun(U_17183,tc_HOL_Obool),U_17185),U_17184)),
    inference(variable_rename,[status(thm)],[f_4214_1]) ).

fof(f_4214_3,plain,
    ! [U_17182,U_17183,U_17184,U_17185] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17182,tc_fun(U_17183,tc_HOL_Obool)),U_17184),U_17185) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17183,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17182,tc_fun(U_17183,tc_HOL_Obool),U_17185),U_17184)),
    inference(definitional_conversion,[status(esa)],[f_4214_2]) ).

cnf(f_4214_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17182,tc_fun(U_17183,tc_HOL_Obool)),U_17184),U_17185) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17183,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17182,tc_fun(U_17183,tc_HOL_Obool),U_17185),U_17184)),
    inference(clausify,[status(thm)],[f_4214_3]) ).

fof(f_4215_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_4215_2,plain,
    ! [U_17188,U_17187,U_17186] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17186),U_17187),c_Complete__Lattice_OSup__class_OSup(U_17186,U_17188)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17186),U_17187),U_17188))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17186) ),
    inference(variable_rename,[status(thm)],[f_4215_1]) ).

fof(f_4215_3,plain,
    ! [U_17186,U_17187,U_17188] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17186),U_17187),c_Complete__Lattice_OSup__class_OSup(U_17186,U_17188)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17186),U_17187),U_17188))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17186) ),
    inference(definitional_conversion,[status(esa)],[f_4215_2]) ).

cnf(f_4215_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17186),U_17187),c_Complete__Lattice_OSup__class_OSup(U_17186,U_17188)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17186),U_17187),U_17188))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17186) ),
    inference(clausify,[status(thm)],[f_4215_3]) ).

fof(f_4216_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_4216_2,plain,
    ! [U_17189] :
      ( c_Complete__Lattice_OSup__class_OSup(U_17189,c_Orderings_Obot__class_Obot(tc_fun(U_17189,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_17189)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17189) ),
    inference(variable_rename,[status(thm)],[f_4216_1]) ).

fof(f_4216_3,plain,
    ! [U_17189] :
      ( c_Complete__Lattice_OSup__class_OSup(U_17189,c_Orderings_Obot__class_Obot(tc_fun(U_17189,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_17189)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17189) ),
    inference(definitional_conversion,[status(esa)],[f_4216_2]) ).

cnf(f_4216_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_17189,c_Orderings_Obot__class_Obot(tc_fun(U_17189,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_17189)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17189) ),
    inference(clausify,[status(thm)],[f_4216_3]) ).

fof(f_4217_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_4217_2,plain,
    ! [U_17191,U_17190] :
      ( c_Complete__Lattice_OSup__class_OSup(U_17190,hAPP(hAPP(c_Set_Oinsert(U_17190),U_17191),c_Orderings_Obot__class_Obot(tc_fun(U_17190,tc_HOL_Obool)))) = U_17191
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17190) ),
    inference(variable_rename,[status(thm)],[f_4217_1]) ).

fof(f_4217_3,plain,
    ! [U_17190,U_17191] :
      ( c_Complete__Lattice_OSup__class_OSup(U_17190,hAPP(hAPP(c_Set_Oinsert(U_17190),U_17191),c_Orderings_Obot__class_Obot(tc_fun(U_17190,tc_HOL_Obool)))) = U_17191
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17190) ),
    inference(definitional_conversion,[status(esa)],[f_4217_2]) ).

cnf(f_4217_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_17190,hAPP(hAPP(c_Set_Oinsert(U_17190),U_17191),c_Orderings_Obot__class_Obot(tc_fun(U_17190,tc_HOL_Obool)))) = U_17191
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17190) ),
    inference(clausify,[status(thm)],[f_4217_3]) ).

fof(f_4218_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_4218_2,plain,
    ! [U_17194,U_17193,U_17192] :
      ( c_Complete__Lattice_OSup__class_OSup(U_17192,hAPP(hAPP(c_Set_Oinsert(U_17192),U_17193),U_17194)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_17192),U_17193),c_Complete__Lattice_OSup__class_OSup(U_17192,U_17194))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17192) ),
    inference(variable_rename,[status(thm)],[f_4218_1]) ).

fof(f_4218_3,plain,
    ! [U_17192,U_17193,U_17194] :
      ( c_Complete__Lattice_OSup__class_OSup(U_17192,hAPP(hAPP(c_Set_Oinsert(U_17192),U_17193),U_17194)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_17192),U_17193),c_Complete__Lattice_OSup__class_OSup(U_17192,U_17194))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17192) ),
    inference(definitional_conversion,[status(esa)],[f_4218_2]) ).

cnf(f_4218_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_17192,hAPP(hAPP(c_Set_Oinsert(U_17192),U_17193),U_17194)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_17192),U_17193),c_Complete__Lattice_OSup__class_OSup(U_17192,U_17194))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17192) ),
    inference(clausify,[status(thm)],[f_4218_3]) ).

fof(f_4219_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_4219_2,plain,
    ! [U_17195] :
      ( c_Complete__Lattice_OSup__class_OSup(U_17195,c_Orderings_Otop__class_Otop(tc_fun(U_17195,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_17195)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17195) ),
    inference(variable_rename,[status(thm)],[f_4219_1]) ).

fof(f_4219_3,plain,
    ! [U_17195] :
      ( c_Complete__Lattice_OSup__class_OSup(U_17195,c_Orderings_Otop__class_Otop(tc_fun(U_17195,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_17195)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17195) ),
    inference(definitional_conversion,[status(esa)],[f_4219_2]) ).

cnf(f_4219_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_17195,c_Orderings_Otop__class_Otop(tc_fun(U_17195,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_17195)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17195) ),
    inference(clausify,[status(thm)],[f_4219_3]) ).

fof(f_4220_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_4220_2,plain,
    ! [U_17198,U_17197,U_17196] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17196,tc_HOL_Obool)),U_17197),U_17198) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17196,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17196,tc_HOL_Obool)),U_17197),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17196,tc_HOL_Obool)),U_17198),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17196,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_4220_1]) ).

fof(f_4220_3,plain,
    ! [U_17196,U_17197,U_17198] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17196,tc_HOL_Obool)),U_17197),U_17198) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17196,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17196,tc_HOL_Obool)),U_17197),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17196,tc_HOL_Obool)),U_17198),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17196,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_4220_2]) ).

cnf(f_4220_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17196,tc_HOL_Obool)),U_17197),U_17198) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17196,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17196,tc_HOL_Obool)),U_17197),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17196,tc_HOL_Obool)),U_17198),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17196,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_4220_3]) ).

fof(f_4221_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_4221_2,plain,
    ! [U_17203,U_17202,U_17201,U_17200,U_17199] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17199,tc_fun(U_17200,tc_HOL_Obool)),U_17201),hAPP(hAPP(c_COMBS(U_17199,tc_fun(U_17200,tc_HOL_Obool),tc_fun(U_17200,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17200,tc_HOL_Obool),tc_fun(tc_fun(U_17200,tc_HOL_Obool),tc_fun(U_17200,tc_HOL_Obool)),U_17199),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17200,tc_HOL_Obool))),U_17202)),U_17203)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17200,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17200,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17199,tc_fun(U_17200,tc_HOL_Obool),U_17202),U_17201))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17200,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17199,tc_fun(U_17200,tc_HOL_Obool),U_17203),U_17201))),
    inference(variable_rename,[status(thm)],[f_4221_1]) ).

fof(f_4221_3,plain,
    ! [U_17199,U_17200,U_17201,U_17202,U_17203] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17199,tc_fun(U_17200,tc_HOL_Obool)),U_17201),hAPP(hAPP(c_COMBS(U_17199,tc_fun(U_17200,tc_HOL_Obool),tc_fun(U_17200,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17200,tc_HOL_Obool),tc_fun(tc_fun(U_17200,tc_HOL_Obool),tc_fun(U_17200,tc_HOL_Obool)),U_17199),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17200,tc_HOL_Obool))),U_17202)),U_17203)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17200,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17200,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17199,tc_fun(U_17200,tc_HOL_Obool),U_17202),U_17201))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17200,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17199,tc_fun(U_17200,tc_HOL_Obool),U_17203),U_17201))),
    inference(definitional_conversion,[status(esa)],[f_4221_2]) ).

cnf(f_4221_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_17199,tc_fun(U_17200,tc_HOL_Obool)),U_17201),hAPP(hAPP(c_COMBS(U_17199,tc_fun(U_17200,tc_HOL_Obool),tc_fun(U_17200,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17200,tc_HOL_Obool),tc_fun(tc_fun(U_17200,tc_HOL_Obool),tc_fun(U_17200,tc_HOL_Obool)),U_17199),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17200,tc_HOL_Obool))),U_17202)),U_17203)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17200,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17200,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17199,tc_fun(U_17200,tc_HOL_Obool),U_17202),U_17201))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17200,tc_HOL_Obool),hAPP(c_Set_Oimage(U_17199,tc_fun(U_17200,tc_HOL_Obool),U_17203),U_17201))),
    inference(clausify,[status(thm)],[f_4221_3]) ).

fof(f_4222_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_4222_2,plain,
    ! [U_17206,U_17205,U_17204] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17204,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17204,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_17204,tc_HOL_Obool),tc_HOL_Obool)),U_17205),U_17206))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17204,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17204,tc_HOL_Obool),U_17205)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17204,tc_HOL_Obool),U_17206)))),
    inference(variable_rename,[status(thm)],[f_4222_1]) ).

fof(f_4222_3,plain,
    ! [U_17204,U_17205,U_17206] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17204,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17204,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_17204,tc_HOL_Obool),tc_HOL_Obool)),U_17205),U_17206))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17204,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17204,tc_HOL_Obool),U_17205)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17204,tc_HOL_Obool),U_17206)))),
    inference(definitional_conversion,[status(esa)],[f_4222_2]) ).

cnf(f_4222_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17204,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17204,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_17204,tc_HOL_Obool),tc_HOL_Obool)),U_17205),U_17206))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17204,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17204,tc_HOL_Obool),U_17205)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17204,tc_HOL_Obool),U_17206)))),
    inference(clausify,[status(thm)],[f_4222_3]) ).

fof(f_4223_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_4223_2,plain,
    ! [U_17209,U_17208,U_17207] :
      ( c_Complete__Lattice_OSup__class_OSup(U_17207,hAPP(hAPP(c_Set_Oinsert(U_17207),U_17208),hAPP(hAPP(c_Set_Oinsert(U_17207),U_17209),c_Orderings_Obot__class_Obot(tc_fun(U_17207,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_17207),U_17208),U_17209)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17207) ),
    inference(variable_rename,[status(thm)],[f_4223_1]) ).

fof(f_4223_3,plain,
    ! [U_17207,U_17208,U_17209] :
      ( c_Complete__Lattice_OSup__class_OSup(U_17207,hAPP(hAPP(c_Set_Oinsert(U_17207),U_17208),hAPP(hAPP(c_Set_Oinsert(U_17207),U_17209),c_Orderings_Obot__class_Obot(tc_fun(U_17207,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_17207),U_17208),U_17209)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17207) ),
    inference(definitional_conversion,[status(esa)],[f_4223_2]) ).

cnf(f_4223_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_17207,hAPP(hAPP(c_Set_Oinsert(U_17207),U_17208),hAPP(hAPP(c_Set_Oinsert(U_17207),U_17209),c_Orderings_Obot__class_Obot(tc_fun(U_17207,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_17207),U_17208),U_17209)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17207) ),
    inference(clausify,[status(thm)],[f_4223_3]) ).

fof(f_4224_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_4224_2,plain,
    ! [U_17212,U_17211,U_17210] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_17210),U_17212),c_Complete__Lattice_OSup__class_OSup(U_17210,U_17211)) = hAPP(hAPP(c_Finite__Set_Ofold(U_17210,U_17210,c_Lattices_Osemilattice__sup__class_Osup(U_17210)),U_17212),U_17211)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17210),U_17211))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17210) ),
    inference(variable_rename,[status(thm)],[f_4224_1]) ).

fof(f_4224_3,plain,
    ! [U_17210,U_17211,U_17212] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_17210),U_17212),c_Complete__Lattice_OSup__class_OSup(U_17210,U_17211)) = hAPP(hAPP(c_Finite__Set_Ofold(U_17210,U_17210,c_Lattices_Osemilattice__sup__class_Osup(U_17210)),U_17212),U_17211)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17210),U_17211))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17210) ),
    inference(definitional_conversion,[status(esa)],[f_4224_2]) ).

cnf(f_4224_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_17210),U_17212),c_Complete__Lattice_OSup__class_OSup(U_17210,U_17211)) = hAPP(hAPP(c_Finite__Set_Ofold(U_17210,U_17210,c_Lattices_Osemilattice__sup__class_Osup(U_17210)),U_17212),U_17211)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17210),U_17211))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17210) ),
    inference(clausify,[status(thm)],[f_4224_3]) ).

fof(f_4225_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_4225_2,plain,
    ! [U_17214,U_17213] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_17213,U_17214) = c_Complete__Lattice_OSup__class_OSup(U_17213,U_17214)
      | U_17214 = c_Orderings_Obot__class_Obot(tc_fun(U_17213,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17213),U_17214))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17213) ),
    inference(variable_rename,[status(thm)],[f_4225_1]) ).

fof(f_4225_3,plain,
    ! [U_17213,U_17214] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_17213,U_17214) = c_Complete__Lattice_OSup__class_OSup(U_17213,U_17214)
      | U_17214 = c_Orderings_Obot__class_Obot(tc_fun(U_17213,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17213),U_17214))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17213) ),
    inference(definitional_conversion,[status(esa)],[f_4225_2]) ).

cnf(f_4225_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_17213,U_17214) = c_Complete__Lattice_OSup__class_OSup(U_17213,U_17214)
    | U_17214 = c_Orderings_Obot__class_Obot(tc_fun(U_17213,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17213),U_17214))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17213) ),
    inference(clausify,[status(thm)],[f_4225_3]) ).

fof(f_4226_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_4226_2,plain,
    ! [U_17216,U_17215] :
      ( c_Complete__Lattice_OSup__class_OSup(U_17215,U_17216) = hAPP(hAPP(c_Finite__Set_Ofold(U_17215,U_17215,c_Lattices_Osemilattice__sup__class_Osup(U_17215)),c_Orderings_Obot__class_Obot(U_17215)),U_17216)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17215),U_17216))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17215) ),
    inference(variable_rename,[status(thm)],[f_4226_1]) ).

fof(f_4226_3,plain,
    ! [U_17215,U_17216] :
      ( c_Complete__Lattice_OSup__class_OSup(U_17215,U_17216) = hAPP(hAPP(c_Finite__Set_Ofold(U_17215,U_17215,c_Lattices_Osemilattice__sup__class_Osup(U_17215)),c_Orderings_Obot__class_Obot(U_17215)),U_17216)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17215),U_17216))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_17215) ),
    inference(definitional_conversion,[status(esa)],[f_4226_2]) ).

cnf(f_4226_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_17215,U_17216) = hAPP(hAPP(c_Finite__Set_Ofold(U_17215,U_17215,c_Lattices_Osemilattice__sup__class_Osup(U_17215)),c_Orderings_Obot__class_Obot(U_17215)),U_17216)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17215),U_17216))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_17215) ),
    inference(clausify,[status(thm)],[f_4226_3]) ).

fof(f_4227_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_4227_2,plain,
    ! [U_17221,U_17220,U_17219,U_17218] :
      ( c_Fun_Oinj__on(U_17219,U_17220,U_17221,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17219,tc_HOL_Obool),U_17218))
      | ? [U_17217] :
          ( ~ c_Fun_Oinj__on(U_17219,U_17220,U_17221,U_17217)
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17219,tc_HOL_Obool)),U_17217),U_17218)) )
      | U_17218 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17219,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4227_1]) ).

fof(f_4227_3,plain,
    ! [U_17221,U_17220,U_17219,U_17218] :
      ( c_Fun_Oinj__on(U_17219,U_17220,U_17221,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17219,tc_HOL_Obool),U_17218))
      | ( ~ c_Fun_Oinj__on(U_17219,U_17220,U_17221,sK411(U_17221,U_17220,U_17219,U_17218))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17219,tc_HOL_Obool)),sK411(U_17221,U_17220,U_17219,U_17218)),U_17218)) )
      | U_17218 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17219,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK411]),skolemize(U_17217,sK411(U_17221,U_17220,U_17219,U_17218))],[f_4227_2]) ).

fof(f_4227_4,plain,
    ( ! [U_17218,U_17219,U_17220,U_17221] :
        ( ~ c_Fun_Oinj__on(U_17219,U_17220,U_17221,sK411(U_17221,U_17220,U_17219,U_17218))
        | ~ sP1080(U_17218,U_17219,U_17220,U_17221) )
    & ! [U_17218,U_17219,U_17220,U_17221] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17219,tc_HOL_Obool)),sK411(U_17221,U_17220,U_17219,U_17218)),U_17218))
        | ~ sP1080(U_17218,U_17219,U_17220,U_17221) )
    & ! [U_17218,U_17219,U_17220,U_17221] :
        ( c_Fun_Oinj__on(U_17219,U_17220,U_17221,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17219,tc_HOL_Obool),U_17218))
        | sP1080(U_17218,U_17219,U_17220,U_17221)
        | U_17218 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17219,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1080])],[f_4227_3]) ).

cnf(f_4227_5,plain,
    ( c_Fun_Oinj__on(U_17219,U_17220,U_17221,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17219,tc_HOL_Obool),U_17218))
    | sP1080(U_17218,U_17219,U_17220,U_17221)
    | U_17218 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17219,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4227_4]) ).

cnf(f_4227_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17219,tc_HOL_Obool)),sK411(U_17221,U_17220,U_17219,U_17218)),U_17218))
    | ~ sP1080(U_17218,U_17219,U_17220,U_17221) ),
    inference(clausify,[status(thm)],[f_4227_4]) ).

cnf(f_4227_7,plain,
    ( ~ c_Fun_Oinj__on(U_17219,U_17220,U_17221,sK411(U_17221,U_17220,U_17219,U_17218))
    | ~ sP1080(U_17218,U_17219,U_17220,U_17221) ),
    inference(clausify,[status(thm)],[f_4227_4]) ).

fof(f_4228_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_4228_2,plain,
    ! [U_17225,U_17224,U_17223] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17223,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17223,tc_HOL_Obool),U_17224)),U_17225))
      | U_17224 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17223,tc_HOL_Obool),tc_HOL_Obool))
      | ? [U_17222] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17223,tc_HOL_Obool)),U_17222),U_17225))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17223,tc_HOL_Obool)),U_17222),U_17224)) ) ),
    inference(variable_rename,[status(thm)],[f_4228_1]) ).

fof(f_4228_3,plain,
    ! [U_17225,U_17224,U_17223] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17223,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17223,tc_HOL_Obool),U_17224)),U_17225))
      | U_17224 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17223,tc_HOL_Obool),tc_HOL_Obool))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17223,tc_HOL_Obool)),sK412(U_17225,U_17224,U_17223)),U_17225))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17223,tc_HOL_Obool)),sK412(U_17225,U_17224,U_17223)),U_17224)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK412]),skolemize(U_17222,sK412(U_17225,U_17224,U_17223))],[f_4228_2]) ).

fof(f_4228_4,plain,
    ( ! [U_17224,U_17223,U_17225] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17223,tc_HOL_Obool)),sK412(U_17225,U_17224,U_17223)),U_17225))
        | ~ sP1081(U_17224,U_17223,U_17225) )
    & ! [U_17224,U_17223,U_17225] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17223,tc_HOL_Obool)),sK412(U_17225,U_17224,U_17223)),U_17224))
        | ~ sP1081(U_17224,U_17223,U_17225) )
    & ! [U_17224,U_17223,U_17225] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17223,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17223,tc_HOL_Obool),U_17224)),U_17225))
        | U_17224 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17223,tc_HOL_Obool),tc_HOL_Obool))
        | sP1081(U_17224,U_17223,U_17225) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1081])],[f_4228_3]) ).

cnf(f_4228_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17223,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17223,tc_HOL_Obool),U_17224)),U_17225))
    | U_17224 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_17223,tc_HOL_Obool),tc_HOL_Obool))
    | sP1081(U_17224,U_17223,U_17225) ),
    inference(clausify,[status(thm)],[f_4228_4]) ).

cnf(f_4228_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17223,tc_HOL_Obool)),sK412(U_17225,U_17224,U_17223)),U_17224))
    | ~ sP1081(U_17224,U_17223,U_17225) ),
    inference(clausify,[status(thm)],[f_4228_4]) ).

cnf(f_4228_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17223,tc_HOL_Obool)),sK412(U_17225,U_17224,U_17223)),U_17225))
    | ~ sP1081(U_17224,U_17223,U_17225) ),
    inference(clausify,[status(thm)],[f_4228_4]) ).

fof(f_4229_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_4229_2,plain,
    ! [U_17227,U_17226] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17226,tc_HOL_Obool),U_17227) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17226,tc_HOL_Obool),tc_fun(U_17226,tc_HOL_Obool)),U_17227),c_COMBI(tc_fun(U_17226,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4229_1]) ).

fof(f_4229_3,plain,
    ! [U_17227,U_17226] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17226,tc_HOL_Obool),U_17227) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17226,tc_HOL_Obool),tc_fun(U_17226,tc_HOL_Obool)),U_17227),c_COMBI(tc_fun(U_17226,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_4229_2]) ).

cnf(f_4229_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17226,tc_HOL_Obool),U_17227) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_17226,tc_HOL_Obool),tc_fun(U_17226,tc_HOL_Obool)),U_17227),c_COMBI(tc_fun(U_17226,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4229_3]) ).

fof(f_4230_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_4230_2,plain,
    ! [U_17230,U_17229] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_17229),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17229,tc_HOL_Obool),U_17230)))
      | ? [U_17228] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17229),U_17228))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17229,tc_HOL_Obool)),U_17228),U_17230)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_17229,tc_HOL_Obool)),U_17230)) ),
    inference(variable_rename,[status(thm)],[f_4230_1]) ).

fof(f_4230_3,plain,
    ! [U_17230,U_17229] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_17229),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17229,tc_HOL_Obool),U_17230)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17229),sK413(U_17230,U_17229)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17229,tc_HOL_Obool)),sK413(U_17230,U_17229)),U_17230)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_17229,tc_HOL_Obool)),U_17230)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK413]),skolemize(U_17228,sK413(U_17230,U_17229))],[f_4230_2]) ).

fof(f_4230_4,plain,
    ( ! [U_17229,U_17230] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17229),sK413(U_17230,U_17229)))
        | ~ sP1082(U_17229,U_17230) )
    & ! [U_17229,U_17230] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17229,tc_HOL_Obool)),sK413(U_17230,U_17229)),U_17230))
        | ~ sP1082(U_17229,U_17230) )
    & ! [U_17229,U_17230] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_17229),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17229,tc_HOL_Obool),U_17230)))
        | sP1082(U_17229,U_17230)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_17229,tc_HOL_Obool)),U_17230)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1082])],[f_4230_3]) ).

cnf(f_4230_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_17229),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17229,tc_HOL_Obool),U_17230)))
    | sP1082(U_17229,U_17230)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_17229,tc_HOL_Obool)),U_17230)) ),
    inference(clausify,[status(thm)],[f_4230_4]) ).

cnf(f_4230_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17229,tc_HOL_Obool)),sK413(U_17230,U_17229)),U_17230))
    | ~ sP1082(U_17229,U_17230) ),
    inference(clausify,[status(thm)],[f_4230_4]) ).

cnf(f_4230_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17229),sK413(U_17230,U_17229)))
    | ~ sP1082(U_17229,U_17230) ),
    inference(clausify,[status(thm)],[f_4230_4]) ).

fof(f_4231_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_4231_2,plain,
    ! [U_17235,U_17234,U_17233] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17233,tc_HOL_Obool)),U_17234),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17233,tc_HOL_Obool),U_17235)) = c_Orderings_Obot__class_Obot(tc_fun(U_17233,tc_HOL_Obool))
      | ? [U_17232] :
          ( ? [U_17231] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17233,tc_HOL_Obool)),U_17232),U_17231) != c_Orderings_Obot__class_Obot(tc_fun(U_17233,tc_HOL_Obool))
              & U_17232 != U_17231
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17233,tc_HOL_Obool)),U_17231),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17233,tc_HOL_Obool)),U_17234),U_17235))) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17233,tc_HOL_Obool)),U_17232),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17233,tc_HOL_Obool)),U_17234),U_17235))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_17233,tc_HOL_Obool)),U_17234),U_17235)) ),
    inference(variable_rename,[status(thm)],[f_4231_1]) ).

fof(f_4231_3,plain,
    ! [U_17235,U_17234,U_17233] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17233,tc_HOL_Obool)),U_17234),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17233,tc_HOL_Obool),U_17235)) = c_Orderings_Obot__class_Obot(tc_fun(U_17233,tc_HOL_Obool))
      | ( ? [U_17231] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17233,tc_HOL_Obool)),sK414(U_17235,U_17234,U_17233)),U_17231) != c_Orderings_Obot__class_Obot(tc_fun(U_17233,tc_HOL_Obool))
            & sK414(U_17235,U_17234,U_17233) != U_17231
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17233,tc_HOL_Obool)),U_17231),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17233,tc_HOL_Obool)),U_17234),U_17235))) )
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17233,tc_HOL_Obool)),sK414(U_17235,U_17234,U_17233)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17233,tc_HOL_Obool)),U_17234),U_17235))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_17233,tc_HOL_Obool)),U_17234),U_17235)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK414]),skolemize(U_17232,sK414(U_17235,U_17234,U_17233))],[f_4231_2]) ).

fof(f_4231_4,plain,
    ! [U_17235,U_17234,U_17233] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17233,tc_HOL_Obool)),U_17234),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17233,tc_HOL_Obool),U_17235)) = c_Orderings_Obot__class_Obot(tc_fun(U_17233,tc_HOL_Obool))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17233,tc_HOL_Obool)),sK414(U_17235,U_17234,U_17233)),sK415(U_17235,U_17234,U_17233)) != c_Orderings_Obot__class_Obot(tc_fun(U_17233,tc_HOL_Obool))
        & sK414(U_17235,U_17234,U_17233) != sK415(U_17235,U_17234,U_17233)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17233,tc_HOL_Obool)),sK415(U_17235,U_17234,U_17233)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17233,tc_HOL_Obool)),U_17234),U_17235)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17233,tc_HOL_Obool)),sK414(U_17235,U_17234,U_17233)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17233,tc_HOL_Obool)),U_17234),U_17235))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_17233,tc_HOL_Obool)),U_17234),U_17235)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK415]),skolemize(U_17231,sK415(U_17235,U_17234,U_17233))],[f_4231_3]) ).

fof(f_4231_5,plain,
    ( ! [U_17233,U_17234,U_17235] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17233,tc_HOL_Obool)),sK414(U_17235,U_17234,U_17233)),sK415(U_17235,U_17234,U_17233)) != c_Orderings_Obot__class_Obot(tc_fun(U_17233,tc_HOL_Obool))
        | ~ sP1083(U_17233,U_17234,U_17235) )
    & ! [U_17233,U_17234,U_17235] :
        ( sK414(U_17235,U_17234,U_17233) != sK415(U_17235,U_17234,U_17233)
        | ~ sP1083(U_17233,U_17234,U_17235) )
    & ! [U_17233,U_17234,U_17235] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17233,tc_HOL_Obool)),sK415(U_17235,U_17234,U_17233)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17233,tc_HOL_Obool)),U_17234),U_17235)))
        | ~ sP1083(U_17233,U_17234,U_17235) )
    & ! [U_17233,U_17234,U_17235] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17233,tc_HOL_Obool)),sK414(U_17235,U_17234,U_17233)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17233,tc_HOL_Obool)),U_17234),U_17235)))
        | ~ sP1083(U_17233,U_17234,U_17235) )
    & ! [U_17233,U_17234,U_17235] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17233,tc_HOL_Obool)),U_17234),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17233,tc_HOL_Obool),U_17235)) = c_Orderings_Obot__class_Obot(tc_fun(U_17233,tc_HOL_Obool))
        | sP1083(U_17233,U_17234,U_17235)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(U_17233,tc_HOL_Obool)),U_17234),U_17235)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1083])],[f_4231_4]) ).

cnf(f_4231_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17233,tc_HOL_Obool)),U_17234),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17233,tc_HOL_Obool),U_17235)) = c_Orderings_Obot__class_Obot(tc_fun(U_17233,tc_HOL_Obool))
    | sP1083(U_17233,U_17234,U_17235)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_17233,tc_HOL_Obool)),U_17234),U_17235)) ),
    inference(clausify,[status(thm)],[f_4231_5]) ).

cnf(f_4231_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17233,tc_HOL_Obool)),sK414(U_17235,U_17234,U_17233)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17233,tc_HOL_Obool)),U_17234),U_17235)))
    | ~ sP1083(U_17233,U_17234,U_17235) ),
    inference(clausify,[status(thm)],[f_4231_5]) ).

cnf(f_4231_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17233,tc_HOL_Obool)),sK415(U_17235,U_17234,U_17233)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_17233,tc_HOL_Obool)),U_17234),U_17235)))
    | ~ sP1083(U_17233,U_17234,U_17235) ),
    inference(clausify,[status(thm)],[f_4231_5]) ).

cnf(f_4231_9,plain,
    ( sK414(U_17235,U_17234,U_17233) != sK415(U_17235,U_17234,U_17233)
    | ~ sP1083(U_17233,U_17234,U_17235) ),
    inference(clausify,[status(thm)],[f_4231_5]) ).

cnf(f_4231_10,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17233,tc_HOL_Obool)),sK414(U_17235,U_17234,U_17233)),sK415(U_17235,U_17234,U_17233)) != c_Orderings_Obot__class_Obot(tc_fun(U_17233,tc_HOL_Obool))
    | ~ sP1083(U_17233,U_17234,U_17235) ),
    inference(clausify,[status(thm)],[f_4231_5]) ).

fof(f_4232_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_4232_2,plain,
    ! [U_17241,U_17240,U_17239] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_17241),hAPP(c_Finite__Set_Ocard(tc_fun(U_17239,tc_HOL_Obool)),U_17240)) = hAPP(c_Finite__Set_Ocard(U_17239),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17239,tc_HOL_Obool),U_17240))
      | ? [U_17238] :
          ( ? [U_17237] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17239,tc_HOL_Obool)),U_17238),U_17237) != c_Orderings_Obot__class_Obot(tc_fun(U_17239,tc_HOL_Obool))
              & U_17238 != U_17237
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),U_17237),U_17240)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),U_17238),U_17240)) )
      | ? [U_17236] :
          ( hAPP(c_Finite__Set_Ocard(U_17239),U_17236) != U_17241
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),U_17236),U_17240)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17239),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17239,tc_HOL_Obool),U_17240)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_17239,tc_HOL_Obool)),U_17240)) ),
    inference(variable_rename,[status(thm)],[f_4232_1]) ).

fof(f_4232_3,plain,
    ! [U_17241,U_17240,U_17239] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_17241),hAPP(c_Finite__Set_Ocard(tc_fun(U_17239,tc_HOL_Obool)),U_17240)) = hAPP(c_Finite__Set_Ocard(U_17239),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17239,tc_HOL_Obool),U_17240))
      | ? [U_17238] :
          ( ? [U_17237] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17239,tc_HOL_Obool)),U_17238),U_17237) != c_Orderings_Obot__class_Obot(tc_fun(U_17239,tc_HOL_Obool))
              & U_17238 != U_17237
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),U_17237),U_17240)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),U_17238),U_17240)) )
      | ( hAPP(c_Finite__Set_Ocard(U_17239),sK416(U_17241,U_17240,U_17239)) != U_17241
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),sK416(U_17241,U_17240,U_17239)),U_17240)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17239),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17239,tc_HOL_Obool),U_17240)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_17239,tc_HOL_Obool)),U_17240)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK416]),skolemize(U_17236,sK416(U_17241,U_17240,U_17239))],[f_4232_2]) ).

fof(f_4232_4,plain,
    ! [U_17241,U_17240,U_17239] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_17241),hAPP(c_Finite__Set_Ocard(tc_fun(U_17239,tc_HOL_Obool)),U_17240)) = hAPP(c_Finite__Set_Ocard(U_17239),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17239,tc_HOL_Obool),U_17240))
      | ( ? [U_17237] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17239,tc_HOL_Obool)),sK417(U_17241,U_17240,U_17239)),U_17237) != c_Orderings_Obot__class_Obot(tc_fun(U_17239,tc_HOL_Obool))
            & sK417(U_17241,U_17240,U_17239) != U_17237
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),U_17237),U_17240)) )
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),sK417(U_17241,U_17240,U_17239)),U_17240)) )
      | ( hAPP(c_Finite__Set_Ocard(U_17239),sK416(U_17241,U_17240,U_17239)) != U_17241
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),sK416(U_17241,U_17240,U_17239)),U_17240)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17239),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17239,tc_HOL_Obool),U_17240)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_17239,tc_HOL_Obool)),U_17240)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK417]),skolemize(U_17238,sK417(U_17241,U_17240,U_17239))],[f_4232_3]) ).

fof(f_4232_5,plain,
    ! [U_17241,U_17240,U_17239] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_17241),hAPP(c_Finite__Set_Ocard(tc_fun(U_17239,tc_HOL_Obool)),U_17240)) = hAPP(c_Finite__Set_Ocard(U_17239),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17239,tc_HOL_Obool),U_17240))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17239,tc_HOL_Obool)),sK417(U_17241,U_17240,U_17239)),sK418(U_17241,U_17240,U_17239)) != c_Orderings_Obot__class_Obot(tc_fun(U_17239,tc_HOL_Obool))
        & sK417(U_17241,U_17240,U_17239) != sK418(U_17241,U_17240,U_17239)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),sK418(U_17241,U_17240,U_17239)),U_17240))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),sK417(U_17241,U_17240,U_17239)),U_17240)) )
      | ( hAPP(c_Finite__Set_Ocard(U_17239),sK416(U_17241,U_17240,U_17239)) != U_17241
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),sK416(U_17241,U_17240,U_17239)),U_17240)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17239),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17239,tc_HOL_Obool),U_17240)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_17239,tc_HOL_Obool)),U_17240)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK418]),skolemize(U_17237,sK418(U_17241,U_17240,U_17239))],[f_4232_4]) ).

fof(f_4232_6,plain,
    ( ! [U_17239,U_17240,U_17241] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17239,tc_HOL_Obool)),sK417(U_17241,U_17240,U_17239)),sK418(U_17241,U_17240,U_17239)) != c_Orderings_Obot__class_Obot(tc_fun(U_17239,tc_HOL_Obool))
        | ~ sP1085(U_17239,U_17240,U_17241) )
    & ! [U_17239,U_17240,U_17241] :
        ( sK417(U_17241,U_17240,U_17239) != sK418(U_17241,U_17240,U_17239)
        | ~ sP1085(U_17239,U_17240,U_17241) )
    & ! [U_17239,U_17240,U_17241] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),sK418(U_17241,U_17240,U_17239)),U_17240))
        | ~ sP1085(U_17239,U_17240,U_17241) )
    & ! [U_17239,U_17240,U_17241] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),sK417(U_17241,U_17240,U_17239)),U_17240))
        | ~ sP1085(U_17239,U_17240,U_17241) )
    & ! [U_17239,U_17240,U_17241] :
        ( hAPP(c_Finite__Set_Ocard(U_17239),sK416(U_17241,U_17240,U_17239)) != U_17241
        | ~ sP1084(U_17239,U_17240,U_17241) )
    & ! [U_17239,U_17240,U_17241] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),sK416(U_17241,U_17240,U_17239)),U_17240))
        | ~ sP1084(U_17239,U_17240,U_17241) )
    & ! [U_17239,U_17240,U_17241] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_17241),hAPP(c_Finite__Set_Ocard(tc_fun(U_17239,tc_HOL_Obool)),U_17240)) = hAPP(c_Finite__Set_Ocard(U_17239),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17239,tc_HOL_Obool),U_17240))
        | sP1085(U_17239,U_17240,U_17241)
        | sP1084(U_17239,U_17240,U_17241)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17239),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17239,tc_HOL_Obool),U_17240)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_17239,tc_HOL_Obool)),U_17240)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1084,sP1085])],[f_4232_5]) ).

cnf(f_4232_7,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_17241),hAPP(c_Finite__Set_Ocard(tc_fun(U_17239,tc_HOL_Obool)),U_17240)) = hAPP(c_Finite__Set_Ocard(U_17239),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17239,tc_HOL_Obool),U_17240))
    | sP1085(U_17239,U_17240,U_17241)
    | sP1084(U_17239,U_17240,U_17241)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17239),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17239,tc_HOL_Obool),U_17240)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_17239,tc_HOL_Obool)),U_17240)) ),
    inference(clausify,[status(thm)],[f_4232_6]) ).

cnf(f_4232_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),sK416(U_17241,U_17240,U_17239)),U_17240))
    | ~ sP1084(U_17239,U_17240,U_17241) ),
    inference(clausify,[status(thm)],[f_4232_6]) ).

cnf(f_4232_9,plain,
    ( hAPP(c_Finite__Set_Ocard(U_17239),sK416(U_17241,U_17240,U_17239)) != U_17241
    | ~ sP1084(U_17239,U_17240,U_17241) ),
    inference(clausify,[status(thm)],[f_4232_6]) ).

cnf(f_4232_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),sK417(U_17241,U_17240,U_17239)),U_17240))
    | ~ sP1085(U_17239,U_17240,U_17241) ),
    inference(clausify,[status(thm)],[f_4232_6]) ).

cnf(f_4232_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17239,tc_HOL_Obool)),sK418(U_17241,U_17240,U_17239)),U_17240))
    | ~ sP1085(U_17239,U_17240,U_17241) ),
    inference(clausify,[status(thm)],[f_4232_6]) ).

cnf(f_4232_12,plain,
    ( sK417(U_17241,U_17240,U_17239) != sK418(U_17241,U_17240,U_17239)
    | ~ sP1085(U_17239,U_17240,U_17241) ),
    inference(clausify,[status(thm)],[f_4232_6]) ).

cnf(f_4232_13,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17239,tc_HOL_Obool)),sK417(U_17241,U_17240,U_17239)),sK418(U_17241,U_17240,U_17239)) != c_Orderings_Obot__class_Obot(tc_fun(U_17239,tc_HOL_Obool))
    | ~ sP1085(U_17239,U_17240,U_17241) ),
    inference(clausify,[status(thm)],[f_4232_6]) ).

fof(f_4233_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_4233_2,plain,
    ! [U_17248,U_17247,U_17246,U_17245,U_17244,U_17243] :
      ( c_Fun_Oinj__on(U_17245,U_17246,U_17247,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17244,tc_fun(U_17245,tc_HOL_Obool)),U_17243),U_17248))
      | ? [U_17242] :
          ( ~ c_Fun_Oinj__on(U_17245,U_17246,U_17247,hAPP(U_17248,U_17242))
          & hBOOL(hAPP(hAPP(c_member(U_17244),U_17242),U_17243)) )
      | U_17243 = c_Orderings_Obot__class_Obot(tc_fun(U_17244,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4233_1]) ).

fof(f_4233_3,plain,
    ! [U_17248,U_17247,U_17246,U_17245,U_17244,U_17243] :
      ( c_Fun_Oinj__on(U_17245,U_17246,U_17247,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17244,tc_fun(U_17245,tc_HOL_Obool)),U_17243),U_17248))
      | ( ~ c_Fun_Oinj__on(U_17245,U_17246,U_17247,hAPP(U_17248,sK419(U_17248,U_17247,U_17246,U_17245,U_17244,U_17243)))
        & hBOOL(hAPP(hAPP(c_member(U_17244),sK419(U_17248,U_17247,U_17246,U_17245,U_17244,U_17243)),U_17243)) )
      | U_17243 = c_Orderings_Obot__class_Obot(tc_fun(U_17244,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK419]),skolemize(U_17242,sK419(U_17248,U_17247,U_17246,U_17245,U_17244,U_17243))],[f_4233_2]) ).

fof(f_4233_4,plain,
    ( ! [U_17244,U_17245,U_17243,U_17248,U_17246,U_17247] :
        ( ~ c_Fun_Oinj__on(U_17245,U_17246,U_17247,hAPP(U_17248,sK419(U_17248,U_17247,U_17246,U_17245,U_17244,U_17243)))
        | ~ sP1086(U_17244,U_17245,U_17243,U_17248,U_17246,U_17247) )
    & ! [U_17244,U_17245,U_17243,U_17248,U_17246,U_17247] :
        ( hBOOL(hAPP(hAPP(c_member(U_17244),sK419(U_17248,U_17247,U_17246,U_17245,U_17244,U_17243)),U_17243))
        | ~ sP1086(U_17244,U_17245,U_17243,U_17248,U_17246,U_17247) )
    & ! [U_17244,U_17245,U_17243,U_17248,U_17246,U_17247] :
        ( c_Fun_Oinj__on(U_17245,U_17246,U_17247,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17244,tc_fun(U_17245,tc_HOL_Obool)),U_17243),U_17248))
        | sP1086(U_17244,U_17245,U_17243,U_17248,U_17246,U_17247)
        | U_17243 = c_Orderings_Obot__class_Obot(tc_fun(U_17244,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1086])],[f_4233_3]) ).

cnf(f_4233_5,plain,
    ( c_Fun_Oinj__on(U_17245,U_17246,U_17247,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_17244,tc_fun(U_17245,tc_HOL_Obool)),U_17243),U_17248))
    | sP1086(U_17244,U_17245,U_17243,U_17248,U_17246,U_17247)
    | U_17243 = c_Orderings_Obot__class_Obot(tc_fun(U_17244,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4233_4]) ).

cnf(f_4233_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17244),sK419(U_17248,U_17247,U_17246,U_17245,U_17244,U_17243)),U_17243))
    | ~ sP1086(U_17244,U_17245,U_17243,U_17248,U_17246,U_17247) ),
    inference(clausify,[status(thm)],[f_4233_4]) ).

cnf(f_4233_7,plain,
    ( ~ c_Fun_Oinj__on(U_17245,U_17246,U_17247,hAPP(U_17248,sK419(U_17248,U_17247,U_17246,U_17245,U_17244,U_17243)))
    | ~ sP1086(U_17244,U_17245,U_17243,U_17248,U_17246,U_17247) ),
    inference(clausify,[status(thm)],[f_4233_4]) ).

fof(f_4234_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_4234_2,plain,
    ! [U_17256,U_17255,U_17254,U_17253,U_17252,U_17251,U_17250] :
      ( ? [U_17249] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_17250,U_17251,U_17252,U_17253,U_17255),U_17249))
          & U_17256 = hAPP(hAPP(U_17252,U_17254),U_17249) )
      | hBOOL(hAPP(hAPP(c_member(U_17250),U_17254),U_17255))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_17250,U_17251,U_17252,U_17253,hAPP(hAPP(c_Set_Oinsert(U_17250),U_17254),U_17255)),U_17256))
      | ~ c_Finite__Set_Ofun__left__comm(U_17250,U_17251,U_17252) ),
    inference(variable_rename,[status(thm)],[f_4234_1]) ).

fof(f_4234_3,plain,
    ! [U_17256,U_17255,U_17254,U_17253,U_17252,U_17251,U_17250] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_17250,U_17251,U_17252,U_17253,U_17255),sK420(U_17256,U_17255,U_17254,U_17253,U_17252,U_17251,U_17250)))
        & U_17256 = hAPP(hAPP(U_17252,U_17254),sK420(U_17256,U_17255,U_17254,U_17253,U_17252,U_17251,U_17250)) )
      | hBOOL(hAPP(hAPP(c_member(U_17250),U_17254),U_17255))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_17250,U_17251,U_17252,U_17253,hAPP(hAPP(c_Set_Oinsert(U_17250),U_17254),U_17255)),U_17256))
      | ~ c_Finite__Set_Ofun__left__comm(U_17250,U_17251,U_17252) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK420]),skolemize(U_17249,sK420(U_17256,U_17255,U_17254,U_17253,U_17252,U_17251,U_17250))],[f_4234_2]) ).

fof(f_4234_4,plain,
    ( ! [U_17251,U_17252,U_17250,U_17253,U_17254,U_17255,U_17256] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_17250,U_17251,U_17252,U_17253,U_17255),sK420(U_17256,U_17255,U_17254,U_17253,U_17252,U_17251,U_17250)))
        | ~ sP1087(U_17251,U_17252,U_17250,U_17253,U_17254,U_17255,U_17256) )
    & ! [U_17251,U_17252,U_17250,U_17253,U_17254,U_17255,U_17256] :
        ( U_17256 = hAPP(hAPP(U_17252,U_17254),sK420(U_17256,U_17255,U_17254,U_17253,U_17252,U_17251,U_17250))
        | ~ sP1087(U_17251,U_17252,U_17250,U_17253,U_17254,U_17255,U_17256) )
    & ! [U_17251,U_17252,U_17250,U_17253,U_17254,U_17255,U_17256] :
        ( sP1087(U_17251,U_17252,U_17250,U_17253,U_17254,U_17255,U_17256)
        | hBOOL(hAPP(hAPP(c_member(U_17250),U_17254),U_17255))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_17250,U_17251,U_17252,U_17253,hAPP(hAPP(c_Set_Oinsert(U_17250),U_17254),U_17255)),U_17256))
        | ~ c_Finite__Set_Ofun__left__comm(U_17250,U_17251,U_17252) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1087])],[f_4234_3]) ).

cnf(f_4234_5,plain,
    ( sP1087(U_17251,U_17252,U_17250,U_17253,U_17254,U_17255,U_17256)
    | hBOOL(hAPP(hAPP(c_member(U_17250),U_17254),U_17255))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_17250,U_17251,U_17252,U_17253,hAPP(hAPP(c_Set_Oinsert(U_17250),U_17254),U_17255)),U_17256))
    | ~ c_Finite__Set_Ofun__left__comm(U_17250,U_17251,U_17252) ),
    inference(clausify,[status(thm)],[f_4234_4]) ).

cnf(f_4234_6,plain,
    ( U_17256 = hAPP(hAPP(U_17252,U_17254),sK420(U_17256,U_17255,U_17254,U_17253,U_17252,U_17251,U_17250))
    | ~ sP1087(U_17251,U_17252,U_17250,U_17253,U_17254,U_17255,U_17256) ),
    inference(clausify,[status(thm)],[f_4234_4]) ).

cnf(f_4234_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_17250,U_17251,U_17252,U_17253,U_17255),sK420(U_17256,U_17255,U_17254,U_17253,U_17252,U_17251,U_17250)))
    | ~ sP1087(U_17251,U_17252,U_17250,U_17253,U_17254,U_17255,U_17256) ),
    inference(clausify,[status(thm)],[f_4234_4]) ).

fof(f_4235_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_4235_2,plain,
    ! [U_17259,U_17258] :
      ( c_Wellfounded_Oacyclic(U_17258,U_17259)
      | ? [U_17257] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_17258,U_17258)),hAPP(hAPP(c_Product__Type_OPair(U_17258,U_17258),U_17257),U_17257)),c_Transitive__Closure_Otrancl(U_17258,U_17259))) ),
    inference(variable_rename,[status(thm)],[f_4235_1]) ).

fof(f_4235_3,plain,
    ! [U_17259,U_17258] :
      ( c_Wellfounded_Oacyclic(U_17258,U_17259)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_17258,U_17258)),hAPP(hAPP(c_Product__Type_OPair(U_17258,U_17258),sK421(U_17259,U_17258)),sK421(U_17259,U_17258))),c_Transitive__Closure_Otrancl(U_17258,U_17259))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK421]),skolemize(U_17257,sK421(U_17259,U_17258))],[f_4235_2]) ).

fof(f_4235_4,plain,
    ! [U_17258,U_17259] :
      ( c_Wellfounded_Oacyclic(U_17258,U_17259)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_17258,U_17258)),hAPP(hAPP(c_Product__Type_OPair(U_17258,U_17258),sK421(U_17259,U_17258)),sK421(U_17259,U_17258))),c_Transitive__Closure_Otrancl(U_17258,U_17259))) ),
    inference(definitional_conversion,[status(esa)],[f_4235_3]) ).

cnf(f_4235_5,plain,
    ( c_Wellfounded_Oacyclic(U_17258,U_17259)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_17258,U_17258)),hAPP(hAPP(c_Product__Type_OPair(U_17258,U_17258),sK421(U_17259,U_17258)),sK421(U_17259,U_17258))),c_Transitive__Closure_Otrancl(U_17258,U_17259))) ),
    inference(clausify,[status(thm)],[f_4235_4]) ).

fof(f_4236_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_4236_2,plain,
    ! [U_17266,U_17265,U_17264,U_17263,U_17262] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),U_17263),U_17264)),c_Transitive__Closure_Ortrancl(U_17262,U_17265)))
      | ? [U_17261] :
          ( ? [U_17260] :
              ( U_17260 != U_17261
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),U_17260),U_17261)),U_17266)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),U_17261),U_17264)),c_Transitive__Closure_Ortrancl(U_17262,U_17265))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),U_17263),U_17264)),c_Transitive__Closure_Ortrancl(U_17262,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_17262,U_17262),tc_HOL_Obool)),U_17265),U_17266)))) ),
    inference(variable_rename,[status(thm)],[f_4236_1]) ).

fof(f_4236_3,plain,
    ! [U_17266,U_17265,U_17264,U_17263,U_17262] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),U_17263),U_17264)),c_Transitive__Closure_Ortrancl(U_17262,U_17265)))
      | ( ? [U_17260] :
            ( U_17260 != sK422(U_17266,U_17265,U_17264,U_17263,U_17262)
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),U_17260),sK422(U_17266,U_17265,U_17264,U_17263,U_17262))),U_17266)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),sK422(U_17266,U_17265,U_17264,U_17263,U_17262)),U_17264)),c_Transitive__Closure_Ortrancl(U_17262,U_17265))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),U_17263),U_17264)),c_Transitive__Closure_Ortrancl(U_17262,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_17262,U_17262),tc_HOL_Obool)),U_17265),U_17266)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK422]),skolemize(U_17261,sK422(U_17266,U_17265,U_17264,U_17263,U_17262))],[f_4236_2]) ).

fof(f_4236_4,plain,
    ! [U_17266,U_17265,U_17264,U_17263,U_17262] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),U_17263),U_17264)),c_Transitive__Closure_Ortrancl(U_17262,U_17265)))
      | ( sK423(U_17266,U_17265,U_17264,U_17263,U_17262) != sK422(U_17266,U_17265,U_17264,U_17263,U_17262)
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),sK423(U_17266,U_17265,U_17264,U_17263,U_17262)),sK422(U_17266,U_17265,U_17264,U_17263,U_17262))),U_17266))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),sK422(U_17266,U_17265,U_17264,U_17263,U_17262)),U_17264)),c_Transitive__Closure_Ortrancl(U_17262,U_17265))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),U_17263),U_17264)),c_Transitive__Closure_Ortrancl(U_17262,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_17262,U_17262),tc_HOL_Obool)),U_17265),U_17266)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK423]),skolemize(U_17260,sK423(U_17266,U_17265,U_17264,U_17263,U_17262))],[f_4236_3]) ).

fof(f_4236_5,plain,
    ( ! [U_17262,U_17263,U_17264,U_17265,U_17266] :
        ( sK423(U_17266,U_17265,U_17264,U_17263,U_17262) != sK422(U_17266,U_17265,U_17264,U_17263,U_17262)
        | ~ sP1088(U_17262,U_17263,U_17264,U_17265,U_17266) )
    & ! [U_17262,U_17263,U_17264,U_17265,U_17266] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),sK423(U_17266,U_17265,U_17264,U_17263,U_17262)),sK422(U_17266,U_17265,U_17264,U_17263,U_17262))),U_17266))
        | ~ sP1088(U_17262,U_17263,U_17264,U_17265,U_17266) )
    & ! [U_17262,U_17263,U_17264,U_17265,U_17266] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),sK422(U_17266,U_17265,U_17264,U_17263,U_17262)),U_17264)),c_Transitive__Closure_Ortrancl(U_17262,U_17265)))
        | ~ sP1088(U_17262,U_17263,U_17264,U_17265,U_17266) )
    & ! [U_17262,U_17263,U_17264,U_17265,U_17266] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),U_17263),U_17264)),c_Transitive__Closure_Ortrancl(U_17262,U_17265)))
        | sP1088(U_17262,U_17263,U_17264,U_17265,U_17266)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),U_17263),U_17264)),c_Transitive__Closure_Ortrancl(U_17262,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_17262,U_17262),tc_HOL_Obool)),U_17265),U_17266)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1088])],[f_4236_4]) ).

cnf(f_4236_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),U_17263),U_17264)),c_Transitive__Closure_Ortrancl(U_17262,U_17265)))
    | sP1088(U_17262,U_17263,U_17264,U_17265,U_17266)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),U_17263),U_17264)),c_Transitive__Closure_Ortrancl(U_17262,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_17262,U_17262),tc_HOL_Obool)),U_17265),U_17266)))) ),
    inference(clausify,[status(thm)],[f_4236_5]) ).

cnf(f_4236_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),sK422(U_17266,U_17265,U_17264,U_17263,U_17262)),U_17264)),c_Transitive__Closure_Ortrancl(U_17262,U_17265)))
    | ~ sP1088(U_17262,U_17263,U_17264,U_17265,U_17266) ),
    inference(clausify,[status(thm)],[f_4236_5]) ).

cnf(f_4236_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17262,U_17262)),hAPP(hAPP(c_Product__Type_OPair(U_17262,U_17262),sK423(U_17266,U_17265,U_17264,U_17263,U_17262)),sK422(U_17266,U_17265,U_17264,U_17263,U_17262))),U_17266))
    | ~ sP1088(U_17262,U_17263,U_17264,U_17265,U_17266) ),
    inference(clausify,[status(thm)],[f_4236_5]) ).

cnf(f_4236_9,plain,
    ( sK423(U_17266,U_17265,U_17264,U_17263,U_17262) != sK422(U_17266,U_17265,U_17264,U_17263,U_17262)
    | ~ sP1088(U_17262,U_17263,U_17264,U_17265,U_17266) ),
    inference(clausify,[status(thm)],[f_4236_5]) ).

fof(f_4237_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_4237_2,plain,
    ! [U_17273,U_17272,U_17271,U_17270,U_17269] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17270),U_17271)),c_Transitive__Closure_Ortrancl(U_17269,U_17272)))
      | ? [U_17268] :
          ( ? [U_17267] :
              ( U_17268 != U_17267
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17268),U_17267)),U_17273)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17270),U_17268)),c_Transitive__Closure_Ortrancl(U_17269,U_17272))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17270),U_17271)),c_Transitive__Closure_Ortrancl(U_17269,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_17269,U_17269),tc_HOL_Obool)),U_17272),U_17273)))) ),
    inference(variable_rename,[status(thm)],[f_4237_1]) ).

fof(f_4237_3,plain,
    ! [U_17273,U_17272,U_17271,U_17270,U_17269] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17270),U_17271)),c_Transitive__Closure_Ortrancl(U_17269,U_17272)))
      | ( ? [U_17267] :
            ( sK424(U_17273,U_17272,U_17271,U_17270,U_17269) != U_17267
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),sK424(U_17273,U_17272,U_17271,U_17270,U_17269)),U_17267)),U_17273)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17270),sK424(U_17273,U_17272,U_17271,U_17270,U_17269))),c_Transitive__Closure_Ortrancl(U_17269,U_17272))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17270),U_17271)),c_Transitive__Closure_Ortrancl(U_17269,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_17269,U_17269),tc_HOL_Obool)),U_17272),U_17273)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK424]),skolemize(U_17268,sK424(U_17273,U_17272,U_17271,U_17270,U_17269))],[f_4237_2]) ).

fof(f_4237_4,plain,
    ! [U_17273,U_17272,U_17271,U_17270,U_17269] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17270),U_17271)),c_Transitive__Closure_Ortrancl(U_17269,U_17272)))
      | ( sK424(U_17273,U_17272,U_17271,U_17270,U_17269) != sK425(U_17273,U_17272,U_17271,U_17270,U_17269)
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),sK424(U_17273,U_17272,U_17271,U_17270,U_17269)),sK425(U_17273,U_17272,U_17271,U_17270,U_17269))),U_17273))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17270),sK424(U_17273,U_17272,U_17271,U_17270,U_17269))),c_Transitive__Closure_Ortrancl(U_17269,U_17272))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17270),U_17271)),c_Transitive__Closure_Ortrancl(U_17269,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_17269,U_17269),tc_HOL_Obool)),U_17272),U_17273)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK425]),skolemize(U_17267,sK425(U_17273,U_17272,U_17271,U_17270,U_17269))],[f_4237_3]) ).

fof(f_4237_5,plain,
    ( ! [U_17271,U_17270,U_17269,U_17272,U_17273] :
        ( sK424(U_17273,U_17272,U_17271,U_17270,U_17269) != sK425(U_17273,U_17272,U_17271,U_17270,U_17269)
        | ~ sP1089(U_17271,U_17270,U_17269,U_17272,U_17273) )
    & ! [U_17271,U_17270,U_17269,U_17272,U_17273] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),sK424(U_17273,U_17272,U_17271,U_17270,U_17269)),sK425(U_17273,U_17272,U_17271,U_17270,U_17269))),U_17273))
        | ~ sP1089(U_17271,U_17270,U_17269,U_17272,U_17273) )
    & ! [U_17271,U_17270,U_17269,U_17272,U_17273] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17270),sK424(U_17273,U_17272,U_17271,U_17270,U_17269))),c_Transitive__Closure_Ortrancl(U_17269,U_17272)))
        | ~ sP1089(U_17271,U_17270,U_17269,U_17272,U_17273) )
    & ! [U_17271,U_17270,U_17269,U_17272,U_17273] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17270),U_17271)),c_Transitive__Closure_Ortrancl(U_17269,U_17272)))
        | sP1089(U_17271,U_17270,U_17269,U_17272,U_17273)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17270),U_17271)),c_Transitive__Closure_Ortrancl(U_17269,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_17269,U_17269),tc_HOL_Obool)),U_17272),U_17273)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1089])],[f_4237_4]) ).

cnf(f_4237_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17270),U_17271)),c_Transitive__Closure_Ortrancl(U_17269,U_17272)))
    | sP1089(U_17271,U_17270,U_17269,U_17272,U_17273)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17270),U_17271)),c_Transitive__Closure_Ortrancl(U_17269,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_17269,U_17269),tc_HOL_Obool)),U_17272),U_17273)))) ),
    inference(clausify,[status(thm)],[f_4237_5]) ).

cnf(f_4237_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),U_17270),sK424(U_17273,U_17272,U_17271,U_17270,U_17269))),c_Transitive__Closure_Ortrancl(U_17269,U_17272)))
    | ~ sP1089(U_17271,U_17270,U_17269,U_17272,U_17273) ),
    inference(clausify,[status(thm)],[f_4237_5]) ).

cnf(f_4237_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17269,U_17269)),hAPP(hAPP(c_Product__Type_OPair(U_17269,U_17269),sK424(U_17273,U_17272,U_17271,U_17270,U_17269)),sK425(U_17273,U_17272,U_17271,U_17270,U_17269))),U_17273))
    | ~ sP1089(U_17271,U_17270,U_17269,U_17272,U_17273) ),
    inference(clausify,[status(thm)],[f_4237_5]) ).

cnf(f_4237_9,plain,
    ( sK424(U_17273,U_17272,U_17271,U_17270,U_17269) != sK425(U_17273,U_17272,U_17271,U_17270,U_17269)
    | ~ sP1089(U_17271,U_17270,U_17269,U_17272,U_17273) ),
    inference(clausify,[status(thm)],[f_4237_5]) ).

fof(f_4238_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_4238_2,plain,
    ! [U_17279,U_17278,U_17277,U_17276,U_17275] :
      ( ? [U_17274] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17275,U_17275)),hAPP(hAPP(c_Product__Type_OPair(U_17275,U_17275),U_17274),U_17277)),U_17279))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17275,U_17275)),hAPP(hAPP(c_Product__Type_OPair(U_17275,U_17275),U_17276),U_17274)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17275,U_17275),tc_HOL_Obool),U_17278),U_17279))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17275,U_17275)),hAPP(hAPP(c_Product__Type_OPair(U_17275,U_17275),U_17276),U_17277)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17275,U_17275),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_17278)),U_17279))) ),
    inference(variable_rename,[status(thm)],[f_4238_1]) ).

fof(f_4238_3,plain,
    ! [U_17279,U_17278,U_17277,U_17276,U_17275] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17275,U_17275)),hAPP(hAPP(c_Product__Type_OPair(U_17275,U_17275),sK426(U_17279,U_17278,U_17277,U_17276,U_17275)),U_17277)),U_17279))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17275,U_17275)),hAPP(hAPP(c_Product__Type_OPair(U_17275,U_17275),U_17276),sK426(U_17279,U_17278,U_17277,U_17276,U_17275))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17275,U_17275),tc_HOL_Obool),U_17278),U_17279))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17275,U_17275)),hAPP(hAPP(c_Product__Type_OPair(U_17275,U_17275),U_17276),U_17277)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17275,U_17275),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_17278)),U_17279))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK426]),skolemize(U_17274,sK426(U_17279,U_17278,U_17277,U_17276,U_17275))],[f_4238_2]) ).

fof(f_4238_4,plain,
    ( ! [U_17276,U_17275,U_17277,U_17278,U_17279] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17275,U_17275)),hAPP(hAPP(c_Product__Type_OPair(U_17275,U_17275),sK426(U_17279,U_17278,U_17277,U_17276,U_17275)),U_17277)),U_17279))
        | ~ sP1090(U_17276,U_17275,U_17277,U_17278,U_17279) )
    & ! [U_17276,U_17275,U_17277,U_17278,U_17279] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17275,U_17275)),hAPP(hAPP(c_Product__Type_OPair(U_17275,U_17275),U_17276),sK426(U_17279,U_17278,U_17277,U_17276,U_17275))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17275,U_17275),tc_HOL_Obool),U_17278),U_17279)))
        | ~ sP1090(U_17276,U_17275,U_17277,U_17278,U_17279) )
    & ! [U_17276,U_17275,U_17277,U_17278,U_17279] :
        ( sP1090(U_17276,U_17275,U_17277,U_17278,U_17279)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17275,U_17275)),hAPP(hAPP(c_Product__Type_OPair(U_17275,U_17275),U_17276),U_17277)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17275,U_17275),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_17278)),U_17279))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1090])],[f_4238_3]) ).

cnf(f_4238_5,plain,
    ( sP1090(U_17276,U_17275,U_17277,U_17278,U_17279)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17275,U_17275)),hAPP(hAPP(c_Product__Type_OPair(U_17275,U_17275),U_17276),U_17277)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17275,U_17275),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_17278)),U_17279))) ),
    inference(clausify,[status(thm)],[f_4238_4]) ).

cnf(f_4238_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17275,U_17275)),hAPP(hAPP(c_Product__Type_OPair(U_17275,U_17275),U_17276),sK426(U_17279,U_17278,U_17277,U_17276,U_17275))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17275,U_17275),tc_HOL_Obool),U_17278),U_17279)))
    | ~ sP1090(U_17276,U_17275,U_17277,U_17278,U_17279) ),
    inference(clausify,[status(thm)],[f_4238_4]) ).

cnf(f_4238_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17275,U_17275)),hAPP(hAPP(c_Product__Type_OPair(U_17275,U_17275),sK426(U_17279,U_17278,U_17277,U_17276,U_17275)),U_17277)),U_17279))
    | ~ sP1090(U_17276,U_17275,U_17277,U_17278,U_17279) ),
    inference(clausify,[status(thm)],[f_4238_4]) ).

fof(f_4239_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_4239_2,plain,
    ! [U_17285,U_17284,U_17283,U_17282,U_17281] :
      ( ? [U_17280] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17281,U_17281)),hAPP(hAPP(c_Product__Type_OPair(U_17281,U_17281),U_17280),U_17283)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17281,U_17281),tc_HOL_Obool),U_17284),U_17285)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17281,U_17281)),hAPP(hAPP(c_Product__Type_OPair(U_17281,U_17281),U_17282),U_17280)),U_17285)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17281,U_17281)),hAPP(hAPP(c_Product__Type_OPair(U_17281,U_17281),U_17282),U_17283)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17281,U_17281),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_17284)),U_17285))) ),
    inference(variable_rename,[status(thm)],[f_4239_1]) ).

fof(f_4239_3,plain,
    ! [U_17285,U_17284,U_17283,U_17282,U_17281] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17281,U_17281)),hAPP(hAPP(c_Product__Type_OPair(U_17281,U_17281),sK427(U_17285,U_17284,U_17283,U_17282,U_17281)),U_17283)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17281,U_17281),tc_HOL_Obool),U_17284),U_17285)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17281,U_17281)),hAPP(hAPP(c_Product__Type_OPair(U_17281,U_17281),U_17282),sK427(U_17285,U_17284,U_17283,U_17282,U_17281))),U_17285)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17281,U_17281)),hAPP(hAPP(c_Product__Type_OPair(U_17281,U_17281),U_17282),U_17283)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17281,U_17281),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_17284)),U_17285))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK427]),skolemize(U_17280,sK427(U_17285,U_17284,U_17283,U_17282,U_17281))],[f_4239_2]) ).

fof(f_4239_4,plain,
    ( ! [U_17281,U_17282,U_17283,U_17284,U_17285] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17281,U_17281)),hAPP(hAPP(c_Product__Type_OPair(U_17281,U_17281),sK427(U_17285,U_17284,U_17283,U_17282,U_17281)),U_17283)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17281,U_17281),tc_HOL_Obool),U_17284),U_17285)))
        | ~ sP1091(U_17281,U_17282,U_17283,U_17284,U_17285) )
    & ! [U_17281,U_17282,U_17283,U_17284,U_17285] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17281,U_17281)),hAPP(hAPP(c_Product__Type_OPair(U_17281,U_17281),U_17282),sK427(U_17285,U_17284,U_17283,U_17282,U_17281))),U_17285))
        | ~ sP1091(U_17281,U_17282,U_17283,U_17284,U_17285) )
    & ! [U_17281,U_17282,U_17283,U_17284,U_17285] :
        ( sP1091(U_17281,U_17282,U_17283,U_17284,U_17285)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17281,U_17281)),hAPP(hAPP(c_Product__Type_OPair(U_17281,U_17281),U_17282),U_17283)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17281,U_17281),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_17284)),U_17285))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1091])],[f_4239_3]) ).

cnf(f_4239_5,plain,
    ( sP1091(U_17281,U_17282,U_17283,U_17284,U_17285)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17281,U_17281)),hAPP(hAPP(c_Product__Type_OPair(U_17281,U_17281),U_17282),U_17283)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17281,U_17281),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_17284)),U_17285))) ),
    inference(clausify,[status(thm)],[f_4239_4]) ).

cnf(f_4239_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17281,U_17281)),hAPP(hAPP(c_Product__Type_OPair(U_17281,U_17281),U_17282),sK427(U_17285,U_17284,U_17283,U_17282,U_17281))),U_17285))
    | ~ sP1091(U_17281,U_17282,U_17283,U_17284,U_17285) ),
    inference(clausify,[status(thm)],[f_4239_4]) ).

cnf(f_4239_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17281,U_17281)),hAPP(hAPP(c_Product__Type_OPair(U_17281,U_17281),sK427(U_17285,U_17284,U_17283,U_17282,U_17281)),U_17283)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17281,U_17281),tc_HOL_Obool),U_17284),U_17285)))
    | ~ sP1091(U_17281,U_17282,U_17283,U_17284,U_17285) ),
    inference(clausify,[status(thm)],[f_4239_4]) ).

fof(f_4240_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_4240_2,plain,
    ! [U_17291,U_17290,U_17289,U_17288,U_17287] :
      ( ? [U_17286] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17287,U_17287)),hAPP(hAPP(c_Product__Type_OPair(U_17287,U_17287),U_17286),U_17289)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17287,U_17287),tc_HOL_Obool),U_17290),U_17291)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17287,U_17287)),hAPP(hAPP(c_Product__Type_OPair(U_17287,U_17287),U_17288),U_17286)),U_17291)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17287,U_17287)),hAPP(hAPP(c_Product__Type_OPair(U_17287,U_17287),U_17288),U_17289)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17287,U_17287),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_17290)),U_17291))) ),
    inference(variable_rename,[status(thm)],[f_4240_1]) ).

fof(f_4240_3,plain,
    ! [U_17291,U_17290,U_17289,U_17288,U_17287] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17287,U_17287)),hAPP(hAPP(c_Product__Type_OPair(U_17287,U_17287),sK428(U_17291,U_17290,U_17289,U_17288,U_17287)),U_17289)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17287,U_17287),tc_HOL_Obool),U_17290),U_17291)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17287,U_17287)),hAPP(hAPP(c_Product__Type_OPair(U_17287,U_17287),U_17288),sK428(U_17291,U_17290,U_17289,U_17288,U_17287))),U_17291)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17287,U_17287)),hAPP(hAPP(c_Product__Type_OPair(U_17287,U_17287),U_17288),U_17289)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17287,U_17287),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_17290)),U_17291))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK428]),skolemize(U_17286,sK428(U_17291,U_17290,U_17289,U_17288,U_17287))],[f_4240_2]) ).

fof(f_4240_4,plain,
    ( ! [U_17287,U_17288,U_17289,U_17290,U_17291] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17287,U_17287)),hAPP(hAPP(c_Product__Type_OPair(U_17287,U_17287),sK428(U_17291,U_17290,U_17289,U_17288,U_17287)),U_17289)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17287,U_17287),tc_HOL_Obool),U_17290),U_17291)))
        | ~ sP1092(U_17287,U_17288,U_17289,U_17290,U_17291) )
    & ! [U_17287,U_17288,U_17289,U_17290,U_17291] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17287,U_17287)),hAPP(hAPP(c_Product__Type_OPair(U_17287,U_17287),U_17288),sK428(U_17291,U_17290,U_17289,U_17288,U_17287))),U_17291))
        | ~ sP1092(U_17287,U_17288,U_17289,U_17290,U_17291) )
    & ! [U_17287,U_17288,U_17289,U_17290,U_17291] :
        ( sP1092(U_17287,U_17288,U_17289,U_17290,U_17291)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17287,U_17287)),hAPP(hAPP(c_Product__Type_OPair(U_17287,U_17287),U_17288),U_17289)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17287,U_17287),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_17290)),U_17291))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1092])],[f_4240_3]) ).

cnf(f_4240_5,plain,
    ( sP1092(U_17287,U_17288,U_17289,U_17290,U_17291)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17287,U_17287)),hAPP(hAPP(c_Product__Type_OPair(U_17287,U_17287),U_17288),U_17289)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17287,U_17287),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_17290)),U_17291))) ),
    inference(clausify,[status(thm)],[f_4240_4]) ).

cnf(f_4240_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17287,U_17287)),hAPP(hAPP(c_Product__Type_OPair(U_17287,U_17287),U_17288),sK428(U_17291,U_17290,U_17289,U_17288,U_17287))),U_17291))
    | ~ sP1092(U_17287,U_17288,U_17289,U_17290,U_17291) ),
    inference(clausify,[status(thm)],[f_4240_4]) ).

cnf(f_4240_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17287,U_17287)),hAPP(hAPP(c_Product__Type_OPair(U_17287,U_17287),sK428(U_17291,U_17290,U_17289,U_17288,U_17287)),U_17289)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_17287,U_17287),tc_HOL_Obool),U_17290),U_17291)))
    | ~ sP1092(U_17287,U_17288,U_17289,U_17290,U_17291) ),
    inference(clausify,[status(thm)],[f_4240_4]) ).

fof(f_4241_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_4241_2,plain,
    ! [U_17296,U_17295,U_17294,U_17293] :
      ( ? [U_17292] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17293,U_17293)),hAPP(hAPP(c_Product__Type_OPair(U_17293,U_17293),U_17292),U_17295)),c_Transitive__Closure_Ortrancl(U_17293,U_17296)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17293,U_17293)),hAPP(hAPP(c_Product__Type_OPair(U_17293,U_17293),U_17294),U_17292)),U_17296)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17293,U_17293)),hAPP(hAPP(c_Product__Type_OPair(U_17293,U_17293),U_17294),U_17295)),c_Transitive__Closure_Otrancl(U_17293,U_17296))) ),
    inference(variable_rename,[status(thm)],[f_4241_1]) ).

fof(f_4241_3,plain,
    ! [U_17296,U_17295,U_17294,U_17293] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17293,U_17293)),hAPP(hAPP(c_Product__Type_OPair(U_17293,U_17293),sK429(U_17296,U_17295,U_17294,U_17293)),U_17295)),c_Transitive__Closure_Ortrancl(U_17293,U_17296)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17293,U_17293)),hAPP(hAPP(c_Product__Type_OPair(U_17293,U_17293),U_17294),sK429(U_17296,U_17295,U_17294,U_17293))),U_17296)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17293,U_17293)),hAPP(hAPP(c_Product__Type_OPair(U_17293,U_17293),U_17294),U_17295)),c_Transitive__Closure_Otrancl(U_17293,U_17296))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK429]),skolemize(U_17292,sK429(U_17296,U_17295,U_17294,U_17293))],[f_4241_2]) ).

fof(f_4241_4,plain,
    ( ! [U_17293,U_17294,U_17295,U_17296] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17293,U_17293)),hAPP(hAPP(c_Product__Type_OPair(U_17293,U_17293),sK429(U_17296,U_17295,U_17294,U_17293)),U_17295)),c_Transitive__Closure_Ortrancl(U_17293,U_17296)))
        | ~ sP1093(U_17293,U_17294,U_17295,U_17296) )
    & ! [U_17293,U_17294,U_17295,U_17296] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17293,U_17293)),hAPP(hAPP(c_Product__Type_OPair(U_17293,U_17293),U_17294),sK429(U_17296,U_17295,U_17294,U_17293))),U_17296))
        | ~ sP1093(U_17293,U_17294,U_17295,U_17296) )
    & ! [U_17293,U_17294,U_17295,U_17296] :
        ( sP1093(U_17293,U_17294,U_17295,U_17296)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17293,U_17293)),hAPP(hAPP(c_Product__Type_OPair(U_17293,U_17293),U_17294),U_17295)),c_Transitive__Closure_Otrancl(U_17293,U_17296))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1093])],[f_4241_3]) ).

cnf(f_4241_5,plain,
    ( sP1093(U_17293,U_17294,U_17295,U_17296)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17293,U_17293)),hAPP(hAPP(c_Product__Type_OPair(U_17293,U_17293),U_17294),U_17295)),c_Transitive__Closure_Otrancl(U_17293,U_17296))) ),
    inference(clausify,[status(thm)],[f_4241_4]) ).

cnf(f_4241_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17293,U_17293)),hAPP(hAPP(c_Product__Type_OPair(U_17293,U_17293),U_17294),sK429(U_17296,U_17295,U_17294,U_17293))),U_17296))
    | ~ sP1093(U_17293,U_17294,U_17295,U_17296) ),
    inference(clausify,[status(thm)],[f_4241_4]) ).

cnf(f_4241_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17293,U_17293)),hAPP(hAPP(c_Product__Type_OPair(U_17293,U_17293),sK429(U_17296,U_17295,U_17294,U_17293)),U_17295)),c_Transitive__Closure_Ortrancl(U_17293,U_17296)))
    | ~ sP1093(U_17293,U_17294,U_17295,U_17296) ),
    inference(clausify,[status(thm)],[f_4241_4]) ).

fof(f_4242_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_4242_2,plain,
    ! [U_17301,U_17300,U_17299,U_17298] :
      ( ? [U_17297] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17298,U_17298)),hAPP(hAPP(c_Product__Type_OPair(U_17298,U_17298),U_17297),U_17300)),U_17301))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17298,U_17298)),hAPP(hAPP(c_Product__Type_OPair(U_17298,U_17298),U_17299),U_17297)),c_Transitive__Closure_Ortrancl(U_17298,U_17301))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17298,U_17298)),hAPP(hAPP(c_Product__Type_OPair(U_17298,U_17298),U_17299),U_17300)),c_Transitive__Closure_Otrancl(U_17298,U_17301))) ),
    inference(variable_rename,[status(thm)],[f_4242_1]) ).

fof(f_4242_3,plain,
    ! [U_17301,U_17300,U_17299,U_17298] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17298,U_17298)),hAPP(hAPP(c_Product__Type_OPair(U_17298,U_17298),sK430(U_17301,U_17300,U_17299,U_17298)),U_17300)),U_17301))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17298,U_17298)),hAPP(hAPP(c_Product__Type_OPair(U_17298,U_17298),U_17299),sK430(U_17301,U_17300,U_17299,U_17298))),c_Transitive__Closure_Ortrancl(U_17298,U_17301))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17298,U_17298)),hAPP(hAPP(c_Product__Type_OPair(U_17298,U_17298),U_17299),U_17300)),c_Transitive__Closure_Otrancl(U_17298,U_17301))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK430]),skolemize(U_17297,sK430(U_17301,U_17300,U_17299,U_17298))],[f_4242_2]) ).

fof(f_4242_4,plain,
    ( ! [U_17298,U_17299,U_17300,U_17301] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17298,U_17298)),hAPP(hAPP(c_Product__Type_OPair(U_17298,U_17298),sK430(U_17301,U_17300,U_17299,U_17298)),U_17300)),U_17301))
        | ~ sP1094(U_17298,U_17299,U_17300,U_17301) )
    & ! [U_17298,U_17299,U_17300,U_17301] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17298,U_17298)),hAPP(hAPP(c_Product__Type_OPair(U_17298,U_17298),U_17299),sK430(U_17301,U_17300,U_17299,U_17298))),c_Transitive__Closure_Ortrancl(U_17298,U_17301)))
        | ~ sP1094(U_17298,U_17299,U_17300,U_17301) )
    & ! [U_17298,U_17299,U_17300,U_17301] :
        ( sP1094(U_17298,U_17299,U_17300,U_17301)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17298,U_17298)),hAPP(hAPP(c_Product__Type_OPair(U_17298,U_17298),U_17299),U_17300)),c_Transitive__Closure_Otrancl(U_17298,U_17301))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1094])],[f_4242_3]) ).

cnf(f_4242_5,plain,
    ( sP1094(U_17298,U_17299,U_17300,U_17301)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17298,U_17298)),hAPP(hAPP(c_Product__Type_OPair(U_17298,U_17298),U_17299),U_17300)),c_Transitive__Closure_Otrancl(U_17298,U_17301))) ),
    inference(clausify,[status(thm)],[f_4242_4]) ).

cnf(f_4242_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17298,U_17298)),hAPP(hAPP(c_Product__Type_OPair(U_17298,U_17298),U_17299),sK430(U_17301,U_17300,U_17299,U_17298))),c_Transitive__Closure_Ortrancl(U_17298,U_17301)))
    | ~ sP1094(U_17298,U_17299,U_17300,U_17301) ),
    inference(clausify,[status(thm)],[f_4242_4]) ).

cnf(f_4242_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17298,U_17298)),hAPP(hAPP(c_Product__Type_OPair(U_17298,U_17298),sK430(U_17301,U_17300,U_17299,U_17298)),U_17300)),U_17301))
    | ~ sP1094(U_17298,U_17299,U_17300,U_17301) ),
    inference(clausify,[status(thm)],[f_4242_4]) ).

fof(f_4243_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_4243_2,plain,
    ! [U_17306,U_17305,U_17304,U_17303] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17303),hAPP(hAPP(c_Finite__Set_Ofold(U_17303,U_17303,c_Orderings_Oord__class_Omax(U_17303)),U_17306),U_17304)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_17303),U_17305),U_17306)))
      | ? [U_17302] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17303),U_17302),U_17305))
          & hBOOL(hAPP(hAPP(c_member(U_17303),U_17302),U_17304)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17303),U_17304))
      | ~ class_Orderings_Olinorder(U_17303) ),
    inference(variable_rename,[status(thm)],[f_4243_1]) ).

fof(f_4243_3,plain,
    ! [U_17306,U_17305,U_17304,U_17303] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17303),hAPP(hAPP(c_Finite__Set_Ofold(U_17303,U_17303,c_Orderings_Oord__class_Omax(U_17303)),U_17306),U_17304)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_17303),U_17305),U_17306)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17303),sK431(U_17306,U_17305,U_17304,U_17303)),U_17305))
        & hBOOL(hAPP(hAPP(c_member(U_17303),sK431(U_17306,U_17305,U_17304,U_17303)),U_17304)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17303),U_17304))
      | ~ class_Orderings_Olinorder(U_17303) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK431]),skolemize(U_17302,sK431(U_17306,U_17305,U_17304,U_17303))],[f_4243_2]) ).

fof(f_4243_4,plain,
    ( ! [U_17303,U_17304,U_17305,U_17306] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17303),sK431(U_17306,U_17305,U_17304,U_17303)),U_17305))
        | ~ sP1095(U_17303,U_17304,U_17305,U_17306) )
    & ! [U_17303,U_17304,U_17305,U_17306] :
        ( hBOOL(hAPP(hAPP(c_member(U_17303),sK431(U_17306,U_17305,U_17304,U_17303)),U_17304))
        | ~ sP1095(U_17303,U_17304,U_17305,U_17306) )
    & ! [U_17303,U_17304,U_17305,U_17306] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17303),hAPP(hAPP(c_Finite__Set_Ofold(U_17303,U_17303,c_Orderings_Oord__class_Omax(U_17303)),U_17306),U_17304)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_17303),U_17305),U_17306)))
        | sP1095(U_17303,U_17304,U_17305,U_17306)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17303),U_17304))
        | ~ class_Orderings_Olinorder(U_17303) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1095])],[f_4243_3]) ).

cnf(f_4243_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17303),hAPP(hAPP(c_Finite__Set_Ofold(U_17303,U_17303,c_Orderings_Oord__class_Omax(U_17303)),U_17306),U_17304)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_17303),U_17305),U_17306)))
    | sP1095(U_17303,U_17304,U_17305,U_17306)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17303),U_17304))
    | ~ class_Orderings_Olinorder(U_17303) ),
    inference(clausify,[status(thm)],[f_4243_4]) ).

cnf(f_4243_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17303),sK431(U_17306,U_17305,U_17304,U_17303)),U_17304))
    | ~ sP1095(U_17303,U_17304,U_17305,U_17306) ),
    inference(clausify,[status(thm)],[f_4243_4]) ).

cnf(f_4243_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17303),sK431(U_17306,U_17305,U_17304,U_17303)),U_17305))
    | ~ sP1095(U_17303,U_17304,U_17305,U_17306) ),
    inference(clausify,[status(thm)],[f_4243_4]) ).

fof(f_4244_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_4244_2,plain,
    ! [U_17311,U_17310,U_17309,U_17308] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17308),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_17308),U_17310),U_17311)),hAPP(hAPP(c_Finite__Set_Ofold(U_17308,U_17308,c_Orderings_Oord__class_Omin(U_17308)),U_17311),U_17309)))
      | ? [U_17307] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17308),U_17310),U_17307))
          & hBOOL(hAPP(hAPP(c_member(U_17308),U_17307),U_17309)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17308),U_17309))
      | ~ class_Orderings_Olinorder(U_17308) ),
    inference(variable_rename,[status(thm)],[f_4244_1]) ).

fof(f_4244_3,plain,
    ! [U_17311,U_17310,U_17309,U_17308] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17308),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_17308),U_17310),U_17311)),hAPP(hAPP(c_Finite__Set_Ofold(U_17308,U_17308,c_Orderings_Oord__class_Omin(U_17308)),U_17311),U_17309)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17308),U_17310),sK432(U_17311,U_17310,U_17309,U_17308)))
        & hBOOL(hAPP(hAPP(c_member(U_17308),sK432(U_17311,U_17310,U_17309,U_17308)),U_17309)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17308),U_17309))
      | ~ class_Orderings_Olinorder(U_17308) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK432]),skolemize(U_17307,sK432(U_17311,U_17310,U_17309,U_17308))],[f_4244_2]) ).

fof(f_4244_4,plain,
    ( ! [U_17308,U_17309,U_17310,U_17311] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17308),U_17310),sK432(U_17311,U_17310,U_17309,U_17308)))
        | ~ sP1096(U_17308,U_17309,U_17310,U_17311) )
    & ! [U_17308,U_17309,U_17310,U_17311] :
        ( hBOOL(hAPP(hAPP(c_member(U_17308),sK432(U_17311,U_17310,U_17309,U_17308)),U_17309))
        | ~ sP1096(U_17308,U_17309,U_17310,U_17311) )
    & ! [U_17308,U_17309,U_17310,U_17311] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17308),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_17308),U_17310),U_17311)),hAPP(hAPP(c_Finite__Set_Ofold(U_17308,U_17308,c_Orderings_Oord__class_Omin(U_17308)),U_17311),U_17309)))
        | sP1096(U_17308,U_17309,U_17310,U_17311)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17308),U_17309))
        | ~ class_Orderings_Olinorder(U_17308) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1096])],[f_4244_3]) ).

cnf(f_4244_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17308),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_17308),U_17310),U_17311)),hAPP(hAPP(c_Finite__Set_Ofold(U_17308,U_17308,c_Orderings_Oord__class_Omin(U_17308)),U_17311),U_17309)))
    | sP1096(U_17308,U_17309,U_17310,U_17311)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17308),U_17309))
    | ~ class_Orderings_Olinorder(U_17308) ),
    inference(clausify,[status(thm)],[f_4244_4]) ).

cnf(f_4244_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17308),sK432(U_17311,U_17310,U_17309,U_17308)),U_17309))
    | ~ sP1096(U_17308,U_17309,U_17310,U_17311) ),
    inference(clausify,[status(thm)],[f_4244_4]) ).

cnf(f_4244_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17308),U_17310),sK432(U_17311,U_17310,U_17309,U_17308)))
    | ~ sP1096(U_17308,U_17309,U_17310,U_17311) ),
    inference(clausify,[status(thm)],[f_4244_4]) ).

fof(f_4245_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_4245_2,plain,
    ! [U_17315,U_17314,U_17313] :
      ( hBOOL(hAPP(hAPP(c_member(U_17313),U_17315),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17313,tc_HOL_Obool),U_17314)))
      | ? [U_17312] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_17313),U_17315),U_17312))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17313,tc_HOL_Obool)),U_17312),U_17314)) ) ),
    inference(variable_rename,[status(thm)],[f_4245_1]) ).

fof(f_4245_3,plain,
    ! [U_17315,U_17314,U_17313] :
      ( hBOOL(hAPP(hAPP(c_member(U_17313),U_17315),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17313,tc_HOL_Obool),U_17314)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_17313),U_17315),sK433(U_17315,U_17314,U_17313)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_17313,tc_HOL_Obool)),sK433(U_17315,U_17314,U_17313)),U_17314)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK433]),skolemize(U_17312,sK433(U_17315,U_17314,U_17313))],[f_4245_2]) ).

fof(f_4245_4,plain,
    ( ! [U_17314,U_17315,U_17313] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_17313),U_17315),sK433(U_17315,U_17314,U_17313)))
        | ~ sP1097(U_17314,U_17315,U_17313) )
    & ! [U_17314,U_17315,U_17313] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17313,tc_HOL_Obool)),sK433(U_17315,U_17314,U_17313)),U_17314))
        | ~ sP1097(U_17314,U_17315,U_17313) )
    & ! [U_17314,U_17315,U_17313] :
        ( hBOOL(hAPP(hAPP(c_member(U_17313),U_17315),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17313,tc_HOL_Obool),U_17314)))
        | sP1097(U_17314,U_17315,U_17313) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1097])],[f_4245_3]) ).

cnf(f_4245_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17313),U_17315),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_17313,tc_HOL_Obool),U_17314)))
    | sP1097(U_17314,U_17315,U_17313) ),
    inference(clausify,[status(thm)],[f_4245_4]) ).

cnf(f_4245_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17313,tc_HOL_Obool)),sK433(U_17315,U_17314,U_17313)),U_17314))
    | ~ sP1097(U_17314,U_17315,U_17313) ),
    inference(clausify,[status(thm)],[f_4245_4]) ).

cnf(f_4245_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17313),U_17315),sK433(U_17315,U_17314,U_17313)))
    | ~ sP1097(U_17314,U_17315,U_17313) ),
    inference(clausify,[status(thm)],[f_4245_4]) ).

fof(f_4246_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_4246_2,plain,
    ! [U_17320,U_17319,U_17318,U_17317] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17317),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_17317),U_17319),U_17320)),hAPP(hAPP(c_Finite__Set_Ofold(U_17317,U_17317,c_Lattices_Osemilattice__inf__class_Oinf(U_17317)),U_17320),U_17318)))
      | ? [U_17316] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17317),U_17319),U_17316))
          & hBOOL(hAPP(hAPP(c_member(U_17317),U_17316),U_17318)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17317),U_17318))
      | ~ class_Lattices_Osemilattice__inf(U_17317) ),
    inference(variable_rename,[status(thm)],[f_4246_1]) ).

fof(f_4246_3,plain,
    ! [U_17320,U_17319,U_17318,U_17317] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17317),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_17317),U_17319),U_17320)),hAPP(hAPP(c_Finite__Set_Ofold(U_17317,U_17317,c_Lattices_Osemilattice__inf__class_Oinf(U_17317)),U_17320),U_17318)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17317),U_17319),sK434(U_17320,U_17319,U_17318,U_17317)))
        & hBOOL(hAPP(hAPP(c_member(U_17317),sK434(U_17320,U_17319,U_17318,U_17317)),U_17318)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17317),U_17318))
      | ~ class_Lattices_Osemilattice__inf(U_17317) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK434]),skolemize(U_17316,sK434(U_17320,U_17319,U_17318,U_17317))],[f_4246_2]) ).

fof(f_4246_4,plain,
    ( ! [U_17317,U_17318,U_17319,U_17320] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17317),U_17319),sK434(U_17320,U_17319,U_17318,U_17317)))
        | ~ sP1098(U_17317,U_17318,U_17319,U_17320) )
    & ! [U_17317,U_17318,U_17319,U_17320] :
        ( hBOOL(hAPP(hAPP(c_member(U_17317),sK434(U_17320,U_17319,U_17318,U_17317)),U_17318))
        | ~ sP1098(U_17317,U_17318,U_17319,U_17320) )
    & ! [U_17317,U_17318,U_17319,U_17320] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17317),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_17317),U_17319),U_17320)),hAPP(hAPP(c_Finite__Set_Ofold(U_17317,U_17317,c_Lattices_Osemilattice__inf__class_Oinf(U_17317)),U_17320),U_17318)))
        | sP1098(U_17317,U_17318,U_17319,U_17320)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17317),U_17318))
        | ~ class_Lattices_Osemilattice__inf(U_17317) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1098])],[f_4246_3]) ).

cnf(f_4246_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17317),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_17317),U_17319),U_17320)),hAPP(hAPP(c_Finite__Set_Ofold(U_17317,U_17317,c_Lattices_Osemilattice__inf__class_Oinf(U_17317)),U_17320),U_17318)))
    | sP1098(U_17317,U_17318,U_17319,U_17320)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17317),U_17318))
    | ~ class_Lattices_Osemilattice__inf(U_17317) ),
    inference(clausify,[status(thm)],[f_4246_4]) ).

cnf(f_4246_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17317),sK434(U_17320,U_17319,U_17318,U_17317)),U_17318))
    | ~ sP1098(U_17317,U_17318,U_17319,U_17320) ),
    inference(clausify,[status(thm)],[f_4246_4]) ).

cnf(f_4246_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17317),U_17319),sK434(U_17320,U_17319,U_17318,U_17317)))
    | ~ sP1098(U_17317,U_17318,U_17319,U_17320) ),
    inference(clausify,[status(thm)],[f_4246_4]) ).

fof(f_4247_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_4247_2,plain,
    ! [U_17325,U_17324,U_17323,U_17322] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17322),hAPP(hAPP(c_Finite__Set_Ofold(U_17322,U_17322,c_Lattices_Osemilattice__sup__class_Osup(U_17322)),U_17325),U_17323)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_17322),U_17324),U_17325)))
      | ? [U_17321] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17322),U_17321),U_17324))
          & hBOOL(hAPP(hAPP(c_member(U_17322),U_17321),U_17323)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17322),U_17323))
      | ~ class_Lattices_Osemilattice__sup(U_17322) ),
    inference(variable_rename,[status(thm)],[f_4247_1]) ).

fof(f_4247_3,plain,
    ! [U_17325,U_17324,U_17323,U_17322] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17322),hAPP(hAPP(c_Finite__Set_Ofold(U_17322,U_17322,c_Lattices_Osemilattice__sup__class_Osup(U_17322)),U_17325),U_17323)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_17322),U_17324),U_17325)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17322),sK435(U_17325,U_17324,U_17323,U_17322)),U_17324))
        & hBOOL(hAPP(hAPP(c_member(U_17322),sK435(U_17325,U_17324,U_17323,U_17322)),U_17323)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17322),U_17323))
      | ~ class_Lattices_Osemilattice__sup(U_17322) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK435]),skolemize(U_17321,sK435(U_17325,U_17324,U_17323,U_17322))],[f_4247_2]) ).

fof(f_4247_4,plain,
    ( ! [U_17322,U_17323,U_17324,U_17325] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17322),sK435(U_17325,U_17324,U_17323,U_17322)),U_17324))
        | ~ sP1099(U_17322,U_17323,U_17324,U_17325) )
    & ! [U_17322,U_17323,U_17324,U_17325] :
        ( hBOOL(hAPP(hAPP(c_member(U_17322),sK435(U_17325,U_17324,U_17323,U_17322)),U_17323))
        | ~ sP1099(U_17322,U_17323,U_17324,U_17325) )
    & ! [U_17322,U_17323,U_17324,U_17325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17322),hAPP(hAPP(c_Finite__Set_Ofold(U_17322,U_17322,c_Lattices_Osemilattice__sup__class_Osup(U_17322)),U_17325),U_17323)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_17322),U_17324),U_17325)))
        | sP1099(U_17322,U_17323,U_17324,U_17325)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17322),U_17323))
        | ~ class_Lattices_Osemilattice__sup(U_17322) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1099])],[f_4247_3]) ).

cnf(f_4247_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17322),hAPP(hAPP(c_Finite__Set_Ofold(U_17322,U_17322,c_Lattices_Osemilattice__sup__class_Osup(U_17322)),U_17325),U_17323)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_17322),U_17324),U_17325)))
    | sP1099(U_17322,U_17323,U_17324,U_17325)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17322),U_17323))
    | ~ class_Lattices_Osemilattice__sup(U_17322) ),
    inference(clausify,[status(thm)],[f_4247_4]) ).

cnf(f_4247_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17322),sK435(U_17325,U_17324,U_17323,U_17322)),U_17323))
    | ~ sP1099(U_17322,U_17323,U_17324,U_17325) ),
    inference(clausify,[status(thm)],[f_4247_4]) ).

cnf(f_4247_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17322),sK435(U_17325,U_17324,U_17323,U_17322)),U_17324))
    | ~ sP1099(U_17322,U_17323,U_17324,U_17325) ),
    inference(clausify,[status(thm)],[f_4247_4]) ).

fof(f_4248_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_4248_2,plain,
    ! [U_17328,U_17327] :
      ( ? [U_17326] : U_17328 = hAPP(hAPP(c_Product__Type_OPair(U_17327,U_17327),U_17326),U_17326)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17327,U_17327)),U_17328),c_Relation_OId(U_17327))) ),
    inference(variable_rename,[status(thm)],[f_4248_1]) ).

fof(f_4248_3,plain,
    ! [U_17328,U_17327] :
      ( U_17328 = hAPP(hAPP(c_Product__Type_OPair(U_17327,U_17327),sK436(U_17328,U_17327)),sK436(U_17328,U_17327))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17327,U_17327)),U_17328),c_Relation_OId(U_17327))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK436]),skolemize(U_17326,sK436(U_17328,U_17327))],[f_4248_2]) ).

fof(f_4248_4,plain,
    ! [U_17328,U_17327] :
      ( U_17328 = hAPP(hAPP(c_Product__Type_OPair(U_17327,U_17327),sK436(U_17328,U_17327)),sK436(U_17328,U_17327))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17327,U_17327)),U_17328),c_Relation_OId(U_17327))) ),
    inference(definitional_conversion,[status(esa)],[f_4248_3]) ).

cnf(f_4248_5,plain,
    ( U_17328 = hAPP(hAPP(c_Product__Type_OPair(U_17327,U_17327),sK436(U_17328,U_17327)),sK436(U_17328,U_17327))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17327,U_17327)),U_17328),c_Relation_OId(U_17327))) ),
    inference(clausify,[status(thm)],[f_4248_4]) ).

fof(f_4249_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_4249_2,plain,
    ! [U_17338,U_17337] :
      ( ( c_Wellfounded_Owf(U_17337,U_17338)
        | ? [U_17336] :
            ( ! [U_17335] :
                ( ? [U_17334] :
                    ( hBOOL(hAPP(hAPP(c_member(U_17337),U_17334),U_17336))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17337,U_17337)),hAPP(hAPP(c_Product__Type_OPair(U_17337,U_17337),U_17334),U_17335)),U_17338)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_17337),U_17335),U_17336)) )
            & ? [U_17333] : hBOOL(hAPP(hAPP(c_member(U_17337),U_17333),U_17336)) ) )
      & ( ! [U_17332] :
            ( ? [U_17331] :
                ( ! [U_17330] :
                    ( ~ hBOOL(hAPP(hAPP(c_member(U_17337),U_17330),U_17332))
                    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17337,U_17337)),hAPP(hAPP(c_Product__Type_OPair(U_17337,U_17337),U_17330),U_17331)),U_17338)) )
                & hBOOL(hAPP(hAPP(c_member(U_17337),U_17331),U_17332)) )
            | ! [U_17329] : ~ hBOOL(hAPP(hAPP(c_member(U_17337),U_17329),U_17332)) )
        | ~ c_Wellfounded_Owf(U_17337,U_17338) ) ),
    inference(variable_rename,[status(thm)],[f_4249_1]) ).

fof(f_4249_3,plain,
    ( ! [U_17342,U_17340] :
        ( c_Wellfounded_Owf(U_17340,U_17342)
        | ? [U_17336] :
            ( ! [U_17335] :
                ( ? [U_17334] :
                    ( hBOOL(hAPP(hAPP(c_member(U_17340),U_17334),U_17336))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17340,U_17340)),hAPP(hAPP(c_Product__Type_OPair(U_17340,U_17340),U_17334),U_17335)),U_17342)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_17340),U_17335),U_17336)) )
            & ? [U_17333] : hBOOL(hAPP(hAPP(c_member(U_17340),U_17333),U_17336)) ) )
    & ! [U_17341,U_17339] :
        ( ! [U_17332] :
            ( ? [U_17331] :
                ( ! [U_17330] :
                    ( ~ hBOOL(hAPP(hAPP(c_member(U_17339),U_17330),U_17332))
                    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17339,U_17339)),hAPP(hAPP(c_Product__Type_OPair(U_17339,U_17339),U_17330),U_17331)),U_17341)) )
                & hBOOL(hAPP(hAPP(c_member(U_17339),U_17331),U_17332)) )
            | ! [U_17329] : ~ hBOOL(hAPP(hAPP(c_member(U_17339),U_17329),U_17332)) )
        | ~ c_Wellfounded_Owf(U_17339,U_17341) ) ),
    inference(miniscope,[status(thm)],[f_4249_2]) ).

fof(f_4249_4,plain,
    ( ! [U_17342,U_17340] :
        ( c_Wellfounded_Owf(U_17340,U_17342)
        | ? [U_17336] :
            ( ! [U_17335] :
                ( ? [U_17334] :
                    ( hBOOL(hAPP(hAPP(c_member(U_17340),U_17334),U_17336))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17340,U_17340)),hAPP(hAPP(c_Product__Type_OPair(U_17340,U_17340),U_17334),U_17335)),U_17342)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_17340),U_17335),U_17336)) )
            & ? [U_17333] : hBOOL(hAPP(hAPP(c_member(U_17340),U_17333),U_17336)) ) )
    & ! [U_17341,U_17339] :
        ( ! [U_17332] :
            ( ( ! [U_17330] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_17339),U_17330),U_17332))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17339,U_17339)),hAPP(hAPP(c_Product__Type_OPair(U_17339,U_17339),U_17330),sK437(U_17341,U_17339,U_17332))),U_17341)) )
              & hBOOL(hAPP(hAPP(c_member(U_17339),sK437(U_17341,U_17339,U_17332)),U_17332)) )
            | ! [U_17329] : ~ hBOOL(hAPP(hAPP(c_member(U_17339),U_17329),U_17332)) )
        | ~ c_Wellfounded_Owf(U_17339,U_17341) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK437]),skolemize(U_17331,sK437(U_17341,U_17339,U_17332))],[f_4249_3]) ).

fof(f_4249_5,plain,
    ( ! [U_17342,U_17340] :
        ( c_Wellfounded_Owf(U_17340,U_17342)
        | ( ! [U_17335] :
              ( ? [U_17334] :
                  ( hBOOL(hAPP(hAPP(c_member(U_17340),U_17334),sK438(U_17342,U_17340)))
                  & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17340,U_17340)),hAPP(hAPP(c_Product__Type_OPair(U_17340,U_17340),U_17334),U_17335)),U_17342)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_17340),U_17335),sK438(U_17342,U_17340))) )
          & ? [U_17333] : hBOOL(hAPP(hAPP(c_member(U_17340),U_17333),sK438(U_17342,U_17340))) ) )
    & ! [U_17341,U_17339] :
        ( ! [U_17332] :
            ( ( ! [U_17330] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_17339),U_17330),U_17332))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17339,U_17339)),hAPP(hAPP(c_Product__Type_OPair(U_17339,U_17339),U_17330),sK437(U_17341,U_17339,U_17332))),U_17341)) )
              & hBOOL(hAPP(hAPP(c_member(U_17339),sK437(U_17341,U_17339,U_17332)),U_17332)) )
            | ! [U_17329] : ~ hBOOL(hAPP(hAPP(c_member(U_17339),U_17329),U_17332)) )
        | ~ c_Wellfounded_Owf(U_17339,U_17341) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK438]),skolemize(U_17336,sK438(U_17342,U_17340))],[f_4249_4]) ).

fof(f_4249_6,plain,
    ( ! [U_17342,U_17340] :
        ( c_Wellfounded_Owf(U_17340,U_17342)
        | ( ! [U_17335] :
              ( ? [U_17334] :
                  ( hBOOL(hAPP(hAPP(c_member(U_17340),U_17334),sK438(U_17342,U_17340)))
                  & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17340,U_17340)),hAPP(hAPP(c_Product__Type_OPair(U_17340,U_17340),U_17334),U_17335)),U_17342)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_17340),U_17335),sK438(U_17342,U_17340))) )
          & hBOOL(hAPP(hAPP(c_member(U_17340),sK439(U_17342,U_17340)),sK438(U_17342,U_17340))) ) )
    & ! [U_17341,U_17339] :
        ( ! [U_17332] :
            ( ( ! [U_17330] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_17339),U_17330),U_17332))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17339,U_17339)),hAPP(hAPP(c_Product__Type_OPair(U_17339,U_17339),U_17330),sK437(U_17341,U_17339,U_17332))),U_17341)) )
              & hBOOL(hAPP(hAPP(c_member(U_17339),sK437(U_17341,U_17339,U_17332)),U_17332)) )
            | ! [U_17329] : ~ hBOOL(hAPP(hAPP(c_member(U_17339),U_17329),U_17332)) )
        | ~ c_Wellfounded_Owf(U_17339,U_17341) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK439]),skolemize(U_17333,sK439(U_17342,U_17340))],[f_4249_5]) ).

fof(f_4249_7,plain,
    ( ! [U_17342,U_17340] :
        ( c_Wellfounded_Owf(U_17340,U_17342)
        | ( ! [U_17335] :
              ( ( hBOOL(hAPP(hAPP(c_member(U_17340),sK440(U_17342,U_17340,U_17335)),sK438(U_17342,U_17340)))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17340,U_17340)),hAPP(hAPP(c_Product__Type_OPair(U_17340,U_17340),sK440(U_17342,U_17340,U_17335)),U_17335)),U_17342)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_17340),U_17335),sK438(U_17342,U_17340))) )
          & hBOOL(hAPP(hAPP(c_member(U_17340),sK439(U_17342,U_17340)),sK438(U_17342,U_17340))) ) )
    & ! [U_17341,U_17339] :
        ( ! [U_17332] :
            ( ( ! [U_17330] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_17339),U_17330),U_17332))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17339,U_17339)),hAPP(hAPP(c_Product__Type_OPair(U_17339,U_17339),U_17330),sK437(U_17341,U_17339,U_17332))),U_17341)) )
              & hBOOL(hAPP(hAPP(c_member(U_17339),sK437(U_17341,U_17339,U_17332)),U_17332)) )
            | ! [U_17329] : ~ hBOOL(hAPP(hAPP(c_member(U_17339),U_17329),U_17332)) )
        | ~ c_Wellfounded_Owf(U_17339,U_17341) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK440]),skolemize(U_17334,sK440(U_17342,U_17340,U_17335))],[f_4249_6]) ).

fof(f_4249_8,plain,
    ( ! [U_17340,U_17335,U_17342] :
        ( hBOOL(hAPP(hAPP(c_member(U_17340),sK440(U_17342,U_17340,U_17335)),sK438(U_17342,U_17340)))
        | ~ sP1101(U_17340,U_17335,U_17342) )
    & ! [U_17340,U_17335,U_17342] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17340,U_17340)),hAPP(hAPP(c_Product__Type_OPair(U_17340,U_17340),sK440(U_17342,U_17340,U_17335)),U_17335)),U_17342))
        | ~ sP1101(U_17340,U_17335,U_17342) )
    & ! [U_17340,U_17335,U_17342] :
        ( sP1101(U_17340,U_17335,U_17342)
        | ~ hBOOL(hAPP(hAPP(c_member(U_17340),U_17335),sK438(U_17342,U_17340)))
        | ~ sP1102(U_17340,U_17335,U_17342) )
    & ! [U_17340,U_17335,U_17342] :
        ( hBOOL(hAPP(hAPP(c_member(U_17340),sK439(U_17342,U_17340)),sK438(U_17342,U_17340)))
        | ~ sP1102(U_17340,U_17335,U_17342) )
    & ! [U_17330,U_17332,U_17339,U_17341] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_17339),U_17330),U_17332))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17339,U_17339)),hAPP(hAPP(c_Product__Type_OPair(U_17339,U_17339),U_17330),sK437(U_17341,U_17339,U_17332))),U_17341))
        | ~ sP1100(U_17330,U_17332,U_17339,U_17341) )
    & ! [U_17330,U_17332,U_17339,U_17341] :
        ( hBOOL(hAPP(hAPP(c_member(U_17339),sK437(U_17341,U_17339,U_17332)),U_17332))
        | ~ sP1100(U_17330,U_17332,U_17339,U_17341) )
    & ! [U_17340,U_17335,U_17342] :
        ( c_Wellfounded_Owf(U_17340,U_17342)
        | sP1102(U_17340,U_17335,U_17342) )
    & ! [U_17329,U_17330,U_17332,U_17339,U_17341] :
        ( sP1100(U_17330,U_17332,U_17339,U_17341)
        | ~ hBOOL(hAPP(hAPP(c_member(U_17339),U_17329),U_17332))
        | ~ c_Wellfounded_Owf(U_17339,U_17341) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1100,sP1101,sP1102])],[f_4249_7]) ).

cnf(f_4249_9,plain,
    ( sP1100(U_17330,U_17332,U_17339,U_17341)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17339),U_17329),U_17332))
    | ~ c_Wellfounded_Owf(U_17339,U_17341) ),
    inference(clausify,[status(thm)],[f_4249_8]) ).

cnf(f_4249_10,plain,
    ( c_Wellfounded_Owf(U_17340,U_17342)
    | sP1102(U_17340,U_17335,U_17342) ),
    inference(clausify,[status(thm)],[f_4249_8]) ).

cnf(f_4249_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17339),sK437(U_17341,U_17339,U_17332)),U_17332))
    | ~ sP1100(U_17330,U_17332,U_17339,U_17341) ),
    inference(clausify,[status(thm)],[f_4249_8]) ).

cnf(f_4249_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17339),U_17330),U_17332))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17339,U_17339)),hAPP(hAPP(c_Product__Type_OPair(U_17339,U_17339),U_17330),sK437(U_17341,U_17339,U_17332))),U_17341))
    | ~ sP1100(U_17330,U_17332,U_17339,U_17341) ),
    inference(clausify,[status(thm)],[f_4249_8]) ).

cnf(f_4249_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17340),sK439(U_17342,U_17340)),sK438(U_17342,U_17340)))
    | ~ sP1102(U_17340,U_17335,U_17342) ),
    inference(clausify,[status(thm)],[f_4249_8]) ).

cnf(f_4249_14,plain,
    ( sP1101(U_17340,U_17335,U_17342)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17340),U_17335),sK438(U_17342,U_17340)))
    | ~ sP1102(U_17340,U_17335,U_17342) ),
    inference(clausify,[status(thm)],[f_4249_8]) ).

cnf(f_4249_15,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17340,U_17340)),hAPP(hAPP(c_Product__Type_OPair(U_17340,U_17340),sK440(U_17342,U_17340,U_17335)),U_17335)),U_17342))
    | ~ sP1101(U_17340,U_17335,U_17342) ),
    inference(clausify,[status(thm)],[f_4249_8]) ).

cnf(f_4249_16,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17340),sK440(U_17342,U_17340,U_17335)),sK438(U_17342,U_17340)))
    | ~ sP1101(U_17340,U_17335,U_17342) ),
    inference(clausify,[status(thm)],[f_4249_8]) ).

fof(f_4250_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_4250_2,plain,
    ! [U_17350,U_17349,U_17348,U_17347,U_17346,U_17345,U_17344,U_17343] :
      ( hAPP(U_17348,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17344,tc_HOL_Obool)),U_17349),U_17350)) = hAPP(hAPP(U_17345,hAPP(U_17348,U_17349)),hAPP(U_17348,U_17350))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17344),U_17350))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17344),U_17349))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_17343,U_17344,U_17345,U_17346,U_17347,U_17348) ),
    inference(variable_rename,[status(thm)],[f_4250_1]) ).

fof(f_4250_3,plain,
    ! [U_17350,U_17349,U_17348,U_17347,U_17346,U_17345,U_17344] :
      ( ! [U_17343] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_17343,U_17344,U_17345,U_17346,U_17347,U_17348)
      | hAPP(U_17348,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17344,tc_HOL_Obool)),U_17349),U_17350)) = hAPP(hAPP(U_17345,hAPP(U_17348,U_17349)),hAPP(U_17348,U_17350))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17344),U_17350))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17344),U_17349)) ),
    inference(miniscope,[status(thm)],[f_4250_2]) ).

fof(f_4250_4,plain,
    ! [U_17346,U_17347,U_17349,U_17348,U_17345,U_17343,U_17344,U_17350] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_17343,U_17344,U_17345,U_17346,U_17347,U_17348)
      | hAPP(U_17348,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17344,tc_HOL_Obool)),U_17349),U_17350)) = hAPP(hAPP(U_17345,hAPP(U_17348,U_17349)),hAPP(U_17348,U_17350))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17344),U_17350))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17344),U_17349)) ),
    inference(definitional_conversion,[status(esa)],[f_4250_3]) ).

cnf(f_4250_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_17343,U_17344,U_17345,U_17346,U_17347,U_17348)
    | hAPP(U_17348,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17344,tc_HOL_Obool)),U_17349),U_17350)) = hAPP(hAPP(U_17345,hAPP(U_17348,U_17349)),hAPP(U_17348,U_17350))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17344),U_17350))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17344),U_17349)) ),
    inference(clausify,[status(thm)],[f_4250_4]) ).

fof(f_4251_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_4251_2,plain,
    ! [U_17353,U_17352] :
      ( 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_17352)) = 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_17353))
      | ? [U_17351] :
          ( ( ( ~ hBOOL(hAPP(U_17352,U_17351))
              & hBOOL(hAPP(U_17353,U_17351)) )
            | ( ~ hBOOL(hAPP(U_17353,U_17351))
              & hBOOL(hAPP(U_17352,U_17351)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_17351)) ) ),
    inference(variable_rename,[status(thm)],[f_4251_1]) ).

fof(f_4251_3,plain,
    ! [U_17353,U_17352] :
      ( 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_17352)) = 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_17353))
      | ( ( ( ~ hBOOL(hAPP(U_17352,sK441(U_17353,U_17352)))
            & hBOOL(hAPP(U_17353,sK441(U_17353,U_17352))) )
          | ( ~ hBOOL(hAPP(U_17353,sK441(U_17353,U_17352)))
            & hBOOL(hAPP(U_17352,sK441(U_17353,U_17352))) ) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK441(U_17353,U_17352))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK441]),skolemize(U_17351,sK441(U_17353,U_17352))],[f_4251_2]) ).

fof(f_4251_4,plain,
    ( ! [U_17353,U_17352] :
        ( ~ hBOOL(hAPP(U_17352,sK441(U_17353,U_17352)))
        | ~ sP1104(U_17353,U_17352) )
    & ! [U_17353,U_17352] :
        ( hBOOL(hAPP(U_17353,sK441(U_17353,U_17352)))
        | ~ sP1104(U_17353,U_17352) )
    & ! [U_17353,U_17352] :
        ( ~ hBOOL(hAPP(U_17353,sK441(U_17353,U_17352)))
        | ~ sP1103(U_17353,U_17352) )
    & ! [U_17353,U_17352] :
        ( hBOOL(hAPP(U_17352,sK441(U_17353,U_17352)))
        | ~ sP1103(U_17353,U_17352) )
    & ! [U_17353,U_17352] :
        ( sP1104(U_17353,U_17352)
        | sP1103(U_17353,U_17352)
        | ~ sP1105(U_17353,U_17352) )
    & ! [U_17353,U_17352] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK441(U_17353,U_17352)))
        | ~ sP1105(U_17353,U_17352) )
    & ! [U_17353,U_17352] :
        ( 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_17352)) = 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_17353))
        | sP1105(U_17353,U_17352) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1103,sP1104,sP1105])],[f_4251_3]) ).

cnf(f_4251_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_17352)) = 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_17353))
    | sP1105(U_17353,U_17352) ),
    inference(clausify,[status(thm)],[f_4251_4]) ).

cnf(f_4251_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK441(U_17353,U_17352)))
    | ~ sP1105(U_17353,U_17352) ),
    inference(clausify,[status(thm)],[f_4251_4]) ).

cnf(f_4251_7,plain,
    ( sP1104(U_17353,U_17352)
    | sP1103(U_17353,U_17352)
    | ~ sP1105(U_17353,U_17352) ),
    inference(clausify,[status(thm)],[f_4251_4]) ).

cnf(f_4251_8,plain,
    ( hBOOL(hAPP(U_17352,sK441(U_17353,U_17352)))
    | ~ sP1103(U_17353,U_17352) ),
    inference(clausify,[status(thm)],[f_4251_4]) ).

cnf(f_4251_9,plain,
    ( ~ hBOOL(hAPP(U_17353,sK441(U_17353,U_17352)))
    | ~ sP1103(U_17353,U_17352) ),
    inference(clausify,[status(thm)],[f_4251_4]) ).

cnf(f_4251_10,plain,
    ( hBOOL(hAPP(U_17353,sK441(U_17353,U_17352)))
    | ~ sP1104(U_17353,U_17352) ),
    inference(clausify,[status(thm)],[f_4251_4]) ).

cnf(f_4251_11,plain,
    ( ~ hBOOL(hAPP(U_17352,sK441(U_17353,U_17352)))
    | ~ sP1104(U_17353,U_17352) ),
    inference(clausify,[status(thm)],[f_4251_4]) ).

fof(f_4252_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_4252_2,plain,
    ! [U_17360,U_17359,U_17358,U_17357,U_17356,U_17355,U_17354] :
      ( hAPP(hAPP(U_17356,U_17360),U_17360) = U_17360
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_17354,U_17355,U_17356,U_17357,U_17358,U_17359) ),
    inference(variable_rename,[status(thm)],[f_4252_1]) ).

fof(f_4252_3,plain,
    ! [U_17360,U_17359,U_17358,U_17357,U_17356] :
      ( ! [U_17355,U_17354] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_17354,U_17355,U_17356,U_17357,U_17358,U_17359)
      | hAPP(hAPP(U_17356,U_17360),U_17360) = U_17360 ),
    inference(miniscope,[status(thm)],[f_4252_2]) ).

fof(f_4252_4,plain,
    ! [U_17356,U_17357,U_17359,U_17355,U_17354,U_17358,U_17360] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_17354,U_17355,U_17356,U_17357,U_17358,U_17359)
      | hAPP(hAPP(U_17356,U_17360),U_17360) = U_17360 ),
    inference(definitional_conversion,[status(esa)],[f_4252_3]) ).

cnf(f_4252_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_17354,U_17355,U_17356,U_17357,U_17358,U_17359)
    | hAPP(hAPP(U_17356,U_17360),U_17360) = U_17360 ),
    inference(clausify,[status(thm)],[f_4252_4]) ).

fof(f_4253_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_4253_2,plain,
    ! [U_17368,U_17367,U_17366,U_17365,U_17364,U_17363,U_17362,U_17361] :
      ( hAPP(hAPP(U_17363,hAPP(U_17365,U_17368)),hAPP(U_17366,U_17367)) = hAPP(U_17366,U_17367)
      | ~ hBOOL(hAPP(hAPP(c_member(U_17362),U_17368),U_17367))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17362),U_17367))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_17361,U_17362,U_17363,U_17364,U_17365,U_17366) ),
    inference(variable_rename,[status(thm)],[f_4253_1]) ).

fof(f_4253_3,plain,
    ! [U_17368,U_17367,U_17366,U_17365,U_17364,U_17363,U_17362] :
      ( ! [U_17361] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_17361,U_17362,U_17363,U_17364,U_17365,U_17366)
      | hAPP(hAPP(U_17363,hAPP(U_17365,U_17368)),hAPP(U_17366,U_17367)) = hAPP(U_17366,U_17367)
      | ~ hBOOL(hAPP(hAPP(c_member(U_17362),U_17368),U_17367))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17362),U_17367)) ),
    inference(miniscope,[status(thm)],[f_4253_2]) ).

fof(f_4253_4,plain,
    ! [U_17361,U_17362,U_17363,U_17364,U_17365,U_17366,U_17367,U_17368] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_17361,U_17362,U_17363,U_17364,U_17365,U_17366)
      | hAPP(hAPP(U_17363,hAPP(U_17365,U_17368)),hAPP(U_17366,U_17367)) = hAPP(U_17366,U_17367)
      | ~ hBOOL(hAPP(hAPP(c_member(U_17362),U_17368),U_17367))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17362),U_17367)) ),
    inference(definitional_conversion,[status(esa)],[f_4253_3]) ).

cnf(f_4253_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_17361,U_17362,U_17363,U_17364,U_17365,U_17366)
    | hAPP(hAPP(U_17363,hAPP(U_17365,U_17368)),hAPP(U_17366,U_17367)) = hAPP(U_17366,U_17367)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17362),U_17368),U_17367))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17362),U_17367)) ),
    inference(clausify,[status(thm)],[f_4253_4]) ).

fof(f_4254_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_4254_2,plain,
    ! [U_17376,U_17375,U_17374,U_17373,U_17372,U_17371,U_17370,U_17369] :
      ( hAPP(U_17374,hAPP(hAPP(c_Set_Oinsert(U_17370),U_17376),U_17375)) = hAPP(hAPP(U_17371,hAPP(U_17373,U_17376)),hAPP(U_17374,U_17375))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17370),U_17375))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_17369,U_17370,U_17371,U_17372,U_17373,U_17374) ),
    inference(variable_rename,[status(thm)],[f_4254_1]) ).

fof(f_4254_3,plain,
    ! [U_17376,U_17375,U_17374,U_17373,U_17372,U_17371,U_17370] :
      ( ! [U_17369] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_17369,U_17370,U_17371,U_17372,U_17373,U_17374)
      | hAPP(U_17374,hAPP(hAPP(c_Set_Oinsert(U_17370),U_17376),U_17375)) = hAPP(hAPP(U_17371,hAPP(U_17373,U_17376)),hAPP(U_17374,U_17375))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17370),U_17375)) ),
    inference(miniscope,[status(thm)],[f_4254_2]) ).

fof(f_4254_4,plain,
    ! [U_17370,U_17369,U_17371,U_17372,U_17373,U_17374,U_17375,U_17376] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_17369,U_17370,U_17371,U_17372,U_17373,U_17374)
      | hAPP(U_17374,hAPP(hAPP(c_Set_Oinsert(U_17370),U_17376),U_17375)) = hAPP(hAPP(U_17371,hAPP(U_17373,U_17376)),hAPP(U_17374,U_17375))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17370),U_17375)) ),
    inference(definitional_conversion,[status(esa)],[f_4254_3]) ).

cnf(f_4254_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_17369,U_17370,U_17371,U_17372,U_17373,U_17374)
    | hAPP(U_17374,hAPP(hAPP(c_Set_Oinsert(U_17370),U_17376),U_17375)) = hAPP(hAPP(U_17371,hAPP(U_17373,U_17376)),hAPP(U_17374,U_17375))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17370),U_17375)) ),
    inference(clausify,[status(thm)],[f_4254_4]) ).

fof(f_4255_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_4255_2,plain,
    ! [U_17384,U_17383,U_17382,U_17381,U_17380,U_17379,U_17378,U_17377] :
      ( hAPP(hAPP(U_17379,hAPP(U_17382,U_17384)),hAPP(U_17382,U_17383)) = hAPP(U_17382,U_17383)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17378,tc_HOL_Obool)),U_17384),U_17383))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17378),U_17383))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_17377,U_17378,U_17379,U_17380,U_17381,U_17382) ),
    inference(variable_rename,[status(thm)],[f_4255_1]) ).

fof(f_4255_3,plain,
    ! [U_17384,U_17383,U_17382,U_17381,U_17380,U_17379,U_17378] :
      ( ! [U_17377] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_17377,U_17378,U_17379,U_17380,U_17381,U_17382)
      | hAPP(hAPP(U_17379,hAPP(U_17382,U_17384)),hAPP(U_17382,U_17383)) = hAPP(U_17382,U_17383)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17378,tc_HOL_Obool)),U_17384),U_17383))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17378),U_17383)) ),
    inference(miniscope,[status(thm)],[f_4255_2]) ).

fof(f_4255_4,plain,
    ! [U_17377,U_17378,U_17379,U_17380,U_17381,U_17382,U_17383,U_17384] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_17377,U_17378,U_17379,U_17380,U_17381,U_17382)
      | hAPP(hAPP(U_17379,hAPP(U_17382,U_17384)),hAPP(U_17382,U_17383)) = hAPP(U_17382,U_17383)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17378,tc_HOL_Obool)),U_17384),U_17383))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17378),U_17383)) ),
    inference(definitional_conversion,[status(esa)],[f_4255_3]) ).

cnf(f_4255_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_17377,U_17378,U_17379,U_17380,U_17381,U_17382)
    | hAPP(hAPP(U_17379,hAPP(U_17382,U_17384)),hAPP(U_17382,U_17383)) = hAPP(U_17382,U_17383)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17378,tc_HOL_Obool)),U_17384),U_17383))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17378),U_17383)) ),
    inference(clausify,[status(thm)],[f_4255_4]) ).

fof(f_4256_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_4256_2,plain,
    ! [U_17390,U_17389,U_17388,U_17387,U_17386] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17386,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17386,tc_HOL_Obool)),U_17387),hAPP(c_Set_OCollect(U_17386),U_17389))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17386,tc_HOL_Obool)),U_17388),hAPP(c_Set_OCollect(U_17386),U_17390))))
      | ? [U_17385] :
          ( ~ hBOOL(hAPP(U_17390,U_17385))
          & hBOOL(hAPP(U_17389,U_17385))
          & hBOOL(hAPP(hAPP(c_member(U_17386),U_17385),U_17387)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17386,tc_HOL_Obool)),U_17387),U_17388)) ),
    inference(variable_rename,[status(thm)],[f_4256_1]) ).

fof(f_4256_3,plain,
    ! [U_17390,U_17389,U_17388,U_17387,U_17386] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17386,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17386,tc_HOL_Obool)),U_17387),hAPP(c_Set_OCollect(U_17386),U_17389))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17386,tc_HOL_Obool)),U_17388),hAPP(c_Set_OCollect(U_17386),U_17390))))
      | ( ~ hBOOL(hAPP(U_17390,sK442(U_17390,U_17389,U_17388,U_17387,U_17386)))
        & hBOOL(hAPP(U_17389,sK442(U_17390,U_17389,U_17388,U_17387,U_17386)))
        & hBOOL(hAPP(hAPP(c_member(U_17386),sK442(U_17390,U_17389,U_17388,U_17387,U_17386)),U_17387)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17386,tc_HOL_Obool)),U_17387),U_17388)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK442]),skolemize(U_17385,sK442(U_17390,U_17389,U_17388,U_17387,U_17386))],[f_4256_2]) ).

fof(f_4256_4,plain,
    ( ! [U_17386,U_17387,U_17388,U_17389,U_17390] :
        ( ~ hBOOL(hAPP(U_17390,sK442(U_17390,U_17389,U_17388,U_17387,U_17386)))
        | ~ sP1106(U_17386,U_17387,U_17388,U_17389,U_17390) )
    & ! [U_17386,U_17387,U_17388,U_17389,U_17390] :
        ( hBOOL(hAPP(U_17389,sK442(U_17390,U_17389,U_17388,U_17387,U_17386)))
        | ~ sP1106(U_17386,U_17387,U_17388,U_17389,U_17390) )
    & ! [U_17386,U_17387,U_17388,U_17389,U_17390] :
        ( hBOOL(hAPP(hAPP(c_member(U_17386),sK442(U_17390,U_17389,U_17388,U_17387,U_17386)),U_17387))
        | ~ sP1106(U_17386,U_17387,U_17388,U_17389,U_17390) )
    & ! [U_17386,U_17387,U_17388,U_17389,U_17390] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17386,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17386,tc_HOL_Obool)),U_17387),hAPP(c_Set_OCollect(U_17386),U_17389))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17386,tc_HOL_Obool)),U_17388),hAPP(c_Set_OCollect(U_17386),U_17390))))
        | sP1106(U_17386,U_17387,U_17388,U_17389,U_17390)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17386,tc_HOL_Obool)),U_17387),U_17388)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1106])],[f_4256_3]) ).

cnf(f_4256_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17386,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17386,tc_HOL_Obool)),U_17387),hAPP(c_Set_OCollect(U_17386),U_17389))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17386,tc_HOL_Obool)),U_17388),hAPP(c_Set_OCollect(U_17386),U_17390))))
    | sP1106(U_17386,U_17387,U_17388,U_17389,U_17390)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17386,tc_HOL_Obool)),U_17387),U_17388)) ),
    inference(clausify,[status(thm)],[f_4256_4]) ).

cnf(f_4256_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17386),sK442(U_17390,U_17389,U_17388,U_17387,U_17386)),U_17387))
    | ~ sP1106(U_17386,U_17387,U_17388,U_17389,U_17390) ),
    inference(clausify,[status(thm)],[f_4256_4]) ).

cnf(f_4256_7,plain,
    ( hBOOL(hAPP(U_17389,sK442(U_17390,U_17389,U_17388,U_17387,U_17386)))
    | ~ sP1106(U_17386,U_17387,U_17388,U_17389,U_17390) ),
    inference(clausify,[status(thm)],[f_4256_4]) ).

cnf(f_4256_8,plain,
    ( ~ hBOOL(hAPP(U_17390,sK442(U_17390,U_17389,U_17388,U_17387,U_17386)))
    | ~ sP1106(U_17386,U_17387,U_17388,U_17389,U_17390) ),
    inference(clausify,[status(thm)],[f_4256_4]) ).

fof(f_4257_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_4257_2,plain,
    ! [U_17394,U_17393,U_17392] :
      ( ? [U_17391] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17392,tc_HOL_Obool)),U_17391),U_17394))
          & hBOOL(hAPP(hAPP(c_member(U_17392),U_17393),U_17391)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_17392),U_17393),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17392,tc_HOL_Obool),U_17394))) ),
    inference(variable_rename,[status(thm)],[f_4257_1]) ).

fof(f_4257_3,plain,
    ! [U_17394,U_17393,U_17392] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17392,tc_HOL_Obool)),sK443(U_17394,U_17393,U_17392)),U_17394))
        & hBOOL(hAPP(hAPP(c_member(U_17392),U_17393),sK443(U_17394,U_17393,U_17392))) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_17392),U_17393),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17392,tc_HOL_Obool),U_17394))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK443]),skolemize(U_17391,sK443(U_17394,U_17393,U_17392))],[f_4257_2]) ).

fof(f_4257_4,plain,
    ( ! [U_17393,U_17392,U_17394] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17392,tc_HOL_Obool)),sK443(U_17394,U_17393,U_17392)),U_17394))
        | ~ sP1107(U_17393,U_17392,U_17394) )
    & ! [U_17393,U_17392,U_17394] :
        ( hBOOL(hAPP(hAPP(c_member(U_17392),U_17393),sK443(U_17394,U_17393,U_17392)))
        | ~ sP1107(U_17393,U_17392,U_17394) )
    & ! [U_17393,U_17392,U_17394] :
        ( sP1107(U_17393,U_17392,U_17394)
        | ~ hBOOL(hAPP(hAPP(c_member(U_17392),U_17393),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17392,tc_HOL_Obool),U_17394))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1107])],[f_4257_3]) ).

cnf(f_4257_5,plain,
    ( sP1107(U_17393,U_17392,U_17394)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17392),U_17393),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17392,tc_HOL_Obool),U_17394))) ),
    inference(clausify,[status(thm)],[f_4257_4]) ).

cnf(f_4257_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17392),U_17393),sK443(U_17394,U_17393,U_17392)))
    | ~ sP1107(U_17393,U_17392,U_17394) ),
    inference(clausify,[status(thm)],[f_4257_4]) ).

cnf(f_4257_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_17392,tc_HOL_Obool)),sK443(U_17394,U_17393,U_17392)),U_17394))
    | ~ sP1107(U_17393,U_17392,U_17394) ),
    inference(clausify,[status(thm)],[f_4257_4]) ).

fof(f_4258_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_4258_2,plain,
    ! [U_17400,U_17399,U_17398,U_17397,U_17396,U_17395] :
      ( c_Map_Omap__add(U_17395,U_17397,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17395,tc_Option_Ooption(U_17397)),U_17399),U_17396),hAPP(c_Option_Ooption_OSome(U_17397),U_17400)),U_17398) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17395,tc_Option_Ooption(U_17397)),c_Map_Omap__add(U_17395,U_17397,U_17399,U_17398)),U_17396),hAPP(c_Option_Ooption_OSome(U_17397),U_17400))
      | hBOOL(hAPP(hAPP(c_member(U_17395),U_17396),c_Map_Odom(U_17395,U_17397,U_17398))) ),
    inference(variable_rename,[status(thm)],[f_4258_1]) ).

fof(f_4258_3,plain,
    ! [U_17395,U_17396,U_17397,U_17398,U_17399,U_17400] :
      ( c_Map_Omap__add(U_17395,U_17397,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17395,tc_Option_Ooption(U_17397)),U_17399),U_17396),hAPP(c_Option_Ooption_OSome(U_17397),U_17400)),U_17398) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17395,tc_Option_Ooption(U_17397)),c_Map_Omap__add(U_17395,U_17397,U_17399,U_17398)),U_17396),hAPP(c_Option_Ooption_OSome(U_17397),U_17400))
      | hBOOL(hAPP(hAPP(c_member(U_17395),U_17396),c_Map_Odom(U_17395,U_17397,U_17398))) ),
    inference(definitional_conversion,[status(esa)],[f_4258_2]) ).

cnf(f_4258_4,plain,
    ( c_Map_Omap__add(U_17395,U_17397,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17395,tc_Option_Ooption(U_17397)),U_17399),U_17396),hAPP(c_Option_Ooption_OSome(U_17397),U_17400)),U_17398) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17395,tc_Option_Ooption(U_17397)),c_Map_Omap__add(U_17395,U_17397,U_17399,U_17398)),U_17396),hAPP(c_Option_Ooption_OSome(U_17397),U_17400))
    | hBOOL(hAPP(hAPP(c_member(U_17395),U_17396),c_Map_Odom(U_17395,U_17397,U_17398))) ),
    inference(clausify,[status(thm)],[f_4258_3]) ).

fof(f_4259_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_4259_2,plain,
    ! [U_17409,U_17408,U_17407,U_17406,U_17405,U_17404] :
      ( ? [U_17403,U_17402,U_17401] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17407,U_17405)),hAPP(hAPP(c_Product__Type_OPair(U_17407,U_17405),U_17402),U_17401)),U_17409))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17404,U_17407)),hAPP(hAPP(c_Product__Type_OPair(U_17404,U_17407),U_17403),U_17402)),U_17408))
          & U_17406 = hAPP(hAPP(c_Product__Type_OPair(U_17404,U_17405),U_17403),U_17401) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17404,U_17405)),U_17406),hAPP(hAPP(c_Relation_Orel__comp(U_17404,U_17407,U_17405),U_17408),U_17409))) ),
    inference(variable_rename,[status(thm)],[f_4259_1]) ).

fof(f_4259_3,plain,
    ! [U_17409,U_17408,U_17407,U_17406,U_17405,U_17404] :
      ( ? [U_17402,U_17401] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17407,U_17405)),hAPP(hAPP(c_Product__Type_OPair(U_17407,U_17405),U_17402),U_17401)),U_17409))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17404,U_17407)),hAPP(hAPP(c_Product__Type_OPair(U_17404,U_17407),sK444(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404)),U_17402)),U_17408))
          & U_17406 = hAPP(hAPP(c_Product__Type_OPair(U_17404,U_17405),sK444(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404)),U_17401) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17404,U_17405)),U_17406),hAPP(hAPP(c_Relation_Orel__comp(U_17404,U_17407,U_17405),U_17408),U_17409))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK444]),skolemize(U_17403,sK444(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404))],[f_4259_2]) ).

fof(f_4259_4,plain,
    ! [U_17409,U_17408,U_17407,U_17406,U_17405,U_17404] :
      ( ? [U_17401] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17407,U_17405)),hAPP(hAPP(c_Product__Type_OPair(U_17407,U_17405),sK445(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404)),U_17401)),U_17409))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17404,U_17407)),hAPP(hAPP(c_Product__Type_OPair(U_17404,U_17407),sK444(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404)),sK445(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404))),U_17408))
          & U_17406 = hAPP(hAPP(c_Product__Type_OPair(U_17404,U_17405),sK444(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404)),U_17401) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17404,U_17405)),U_17406),hAPP(hAPP(c_Relation_Orel__comp(U_17404,U_17407,U_17405),U_17408),U_17409))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK445]),skolemize(U_17402,sK445(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404))],[f_4259_3]) ).

fof(f_4259_5,plain,
    ! [U_17409,U_17408,U_17407,U_17406,U_17405,U_17404] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17407,U_17405)),hAPP(hAPP(c_Product__Type_OPair(U_17407,U_17405),sK445(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404)),sK446(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404))),U_17409))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17404,U_17407)),hAPP(hAPP(c_Product__Type_OPair(U_17404,U_17407),sK444(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404)),sK445(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404))),U_17408))
        & U_17406 = hAPP(hAPP(c_Product__Type_OPair(U_17404,U_17405),sK444(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404)),sK446(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17404,U_17405)),U_17406),hAPP(hAPP(c_Relation_Orel__comp(U_17404,U_17407,U_17405),U_17408),U_17409))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK446]),skolemize(U_17401,sK446(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404))],[f_4259_4]) ).

fof(f_4259_6,plain,
    ( ! [U_17404,U_17405,U_17406,U_17407,U_17408,U_17409] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17407,U_17405)),hAPP(hAPP(c_Product__Type_OPair(U_17407,U_17405),sK445(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404)),sK446(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404))),U_17409))
        | ~ sP1108(U_17404,U_17405,U_17406,U_17407,U_17408,U_17409) )
    & ! [U_17404,U_17405,U_17406,U_17407,U_17408,U_17409] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17404,U_17407)),hAPP(hAPP(c_Product__Type_OPair(U_17404,U_17407),sK444(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404)),sK445(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404))),U_17408))
        | ~ sP1108(U_17404,U_17405,U_17406,U_17407,U_17408,U_17409) )
    & ! [U_17404,U_17405,U_17406,U_17407,U_17408,U_17409] :
        ( U_17406 = hAPP(hAPP(c_Product__Type_OPair(U_17404,U_17405),sK444(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404)),sK446(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404))
        | ~ sP1108(U_17404,U_17405,U_17406,U_17407,U_17408,U_17409) )
    & ! [U_17404,U_17405,U_17406,U_17407,U_17408,U_17409] :
        ( sP1108(U_17404,U_17405,U_17406,U_17407,U_17408,U_17409)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17404,U_17405)),U_17406),hAPP(hAPP(c_Relation_Orel__comp(U_17404,U_17407,U_17405),U_17408),U_17409))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1108])],[f_4259_5]) ).

cnf(f_4259_7,plain,
    ( sP1108(U_17404,U_17405,U_17406,U_17407,U_17408,U_17409)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17404,U_17405)),U_17406),hAPP(hAPP(c_Relation_Orel__comp(U_17404,U_17407,U_17405),U_17408),U_17409))) ),
    inference(clausify,[status(thm)],[f_4259_6]) ).

cnf(f_4259_8,plain,
    ( U_17406 = hAPP(hAPP(c_Product__Type_OPair(U_17404,U_17405),sK444(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404)),sK446(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404))
    | ~ sP1108(U_17404,U_17405,U_17406,U_17407,U_17408,U_17409) ),
    inference(clausify,[status(thm)],[f_4259_6]) ).

cnf(f_4259_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17404,U_17407)),hAPP(hAPP(c_Product__Type_OPair(U_17404,U_17407),sK444(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404)),sK445(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404))),U_17408))
    | ~ sP1108(U_17404,U_17405,U_17406,U_17407,U_17408,U_17409) ),
    inference(clausify,[status(thm)],[f_4259_6]) ).

cnf(f_4259_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17407,U_17405)),hAPP(hAPP(c_Product__Type_OPair(U_17407,U_17405),sK445(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404)),sK446(U_17409,U_17408,U_17407,U_17406,U_17405,U_17404))),U_17409))
    | ~ sP1108(U_17404,U_17405,U_17406,U_17407,U_17408,U_17409) ),
    inference(clausify,[status(thm)],[f_4259_6]) ).

fof(f_4260_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_4260_2,plain,
    ! [U_17415,U_17414,U_17413,U_17412,U_17411,U_17410] : c_Map_Omap__add(U_17410,U_17411,U_17412,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17410,tc_Option_Ooption(U_17411)),U_17413),U_17414),hAPP(c_Option_Ooption_OSome(U_17411),U_17415))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17410,tc_Option_Ooption(U_17411)),c_Map_Omap__add(U_17410,U_17411,U_17412,U_17413)),U_17414),hAPP(c_Option_Ooption_OSome(U_17411),U_17415)),
    inference(variable_rename,[status(thm)],[f_4260_1]) ).

fof(f_4260_3,plain,
    ! [U_17410,U_17411,U_17412,U_17413,U_17414,U_17415] : c_Map_Omap__add(U_17410,U_17411,U_17412,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17410,tc_Option_Ooption(U_17411)),U_17413),U_17414),hAPP(c_Option_Ooption_OSome(U_17411),U_17415))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17410,tc_Option_Ooption(U_17411)),c_Map_Omap__add(U_17410,U_17411,U_17412,U_17413)),U_17414),hAPP(c_Option_Ooption_OSome(U_17411),U_17415)),
    inference(definitional_conversion,[status(esa)],[f_4260_2]) ).

cnf(f_4260_4,plain,
    c_Map_Omap__add(U_17410,U_17411,U_17412,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17410,tc_Option_Ooption(U_17411)),U_17413),U_17414),hAPP(c_Option_Ooption_OSome(U_17411),U_17415))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17410,tc_Option_Ooption(U_17411)),c_Map_Omap__add(U_17410,U_17411,U_17412,U_17413)),U_17414),hAPP(c_Option_Ooption_OSome(U_17411),U_17415)),
    inference(clausify,[status(thm)],[f_4260_3]) ).

fof(f_4261_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_4261_2,plain,
    ! [U_17421,U_17420,U_17419,U_17418,U_17417,U_17416] :
      ( ( hAPP(U_17418,U_17420) = hAPP(c_Option_Ooption_OSome(U_17417),U_17421)
        & hAPP(U_17419,U_17420) = c_Option_Ooption_ONone(U_17417) )
      | hAPP(U_17419,U_17420) = hAPP(c_Option_Ooption_OSome(U_17417),U_17421)
      | hAPP(c_Map_Omap__add(U_17416,U_17417,U_17418,U_17419),U_17420) != hAPP(c_Option_Ooption_OSome(U_17417),U_17421) ),
    inference(variable_rename,[status(thm)],[f_4261_1]) ).

fof(f_4261_3,plain,
    ! [U_17421,U_17420,U_17419,U_17418,U_17417] :
      ( ! [U_17416] : hAPP(c_Map_Omap__add(U_17416,U_17417,U_17418,U_17419),U_17420) != hAPP(c_Option_Ooption_OSome(U_17417),U_17421)
      | ( hAPP(U_17418,U_17420) = hAPP(c_Option_Ooption_OSome(U_17417),U_17421)
        & hAPP(U_17419,U_17420) = c_Option_Ooption_ONone(U_17417) )
      | hAPP(U_17419,U_17420) = hAPP(c_Option_Ooption_OSome(U_17417),U_17421) ),
    inference(miniscope,[status(thm)],[f_4261_2]) ).

fof(f_4261_4,plain,
    ( ! [U_17417,U_17418,U_17419,U_17420,U_17421] :
        ( hAPP(U_17418,U_17420) = hAPP(c_Option_Ooption_OSome(U_17417),U_17421)
        | ~ sP1109(U_17417,U_17418,U_17419,U_17420,U_17421) )
    & ! [U_17417,U_17418,U_17419,U_17420,U_17421] :
        ( hAPP(U_17419,U_17420) = c_Option_Ooption_ONone(U_17417)
        | ~ sP1109(U_17417,U_17418,U_17419,U_17420,U_17421) )
    & ! [U_17417,U_17416,U_17418,U_17419,U_17420,U_17421] :
        ( hAPP(c_Map_Omap__add(U_17416,U_17417,U_17418,U_17419),U_17420) != hAPP(c_Option_Ooption_OSome(U_17417),U_17421)
        | sP1109(U_17417,U_17418,U_17419,U_17420,U_17421)
        | hAPP(U_17419,U_17420) = hAPP(c_Option_Ooption_OSome(U_17417),U_17421) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1109])],[f_4261_3]) ).

cnf(f_4261_5,plain,
    ( hAPP(c_Map_Omap__add(U_17416,U_17417,U_17418,U_17419),U_17420) != hAPP(c_Option_Ooption_OSome(U_17417),U_17421)
    | sP1109(U_17417,U_17418,U_17419,U_17420,U_17421)
    | hAPP(U_17419,U_17420) = hAPP(c_Option_Ooption_OSome(U_17417),U_17421) ),
    inference(clausify,[status(thm)],[f_4261_4]) ).

cnf(f_4261_6,plain,
    ( hAPP(U_17419,U_17420) = c_Option_Ooption_ONone(U_17417)
    | ~ sP1109(U_17417,U_17418,U_17419,U_17420,U_17421) ),
    inference(clausify,[status(thm)],[f_4261_4]) ).

cnf(f_4261_7,plain,
    ( hAPP(U_17418,U_17420) = hAPP(c_Option_Ooption_OSome(U_17417),U_17421)
    | ~ sP1109(U_17417,U_17418,U_17419,U_17420,U_17421) ),
    inference(clausify,[status(thm)],[f_4261_4]) ).

fof(f_4262_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_4262_2,plain,
    ! [U_17427,U_17426,U_17425,U_17424,U_17423,U_17422] :
      ( ( hAPP(c_Map_Omap__add(U_17422,U_17423,U_17424,U_17425),U_17426) = hAPP(c_Option_Ooption_OSome(U_17423),U_17427)
        | ( ( hAPP(U_17424,U_17426) != hAPP(c_Option_Ooption_OSome(U_17423),U_17427)
            | hAPP(U_17425,U_17426) != c_Option_Ooption_ONone(U_17423) )
          & hAPP(U_17425,U_17426) != hAPP(c_Option_Ooption_OSome(U_17423),U_17427) ) )
      & ( ( hAPP(U_17424,U_17426) = hAPP(c_Option_Ooption_OSome(U_17423),U_17427)
          & hAPP(U_17425,U_17426) = c_Option_Ooption_ONone(U_17423) )
        | hAPP(U_17425,U_17426) = hAPP(c_Option_Ooption_OSome(U_17423),U_17427)
        | hAPP(c_Map_Omap__add(U_17422,U_17423,U_17424,U_17425),U_17426) != hAPP(c_Option_Ooption_OSome(U_17423),U_17427) ) ),
    inference(variable_rename,[status(thm)],[f_4262_1]) ).

fof(f_4262_3,plain,
    ( ! [U_17439,U_17437,U_17435,U_17433,U_17431] :
        ( ! [U_17429] : hAPP(c_Map_Omap__add(U_17429,U_17431,U_17433,U_17435),U_17437) = hAPP(c_Option_Ooption_OSome(U_17431),U_17439)
        | ( ( hAPP(U_17433,U_17437) != hAPP(c_Option_Ooption_OSome(U_17431),U_17439)
            | hAPP(U_17435,U_17437) != c_Option_Ooption_ONone(U_17431) )
          & hAPP(U_17435,U_17437) != hAPP(c_Option_Ooption_OSome(U_17431),U_17439) ) )
    & ! [U_17438,U_17436,U_17434,U_17432,U_17430] :
        ( ! [U_17428] : hAPP(c_Map_Omap__add(U_17428,U_17430,U_17432,U_17434),U_17436) != hAPP(c_Option_Ooption_OSome(U_17430),U_17438)
        | ( hAPP(U_17432,U_17436) = hAPP(c_Option_Ooption_OSome(U_17430),U_17438)
          & hAPP(U_17434,U_17436) = c_Option_Ooption_ONone(U_17430) )
        | hAPP(U_17434,U_17436) = hAPP(c_Option_Ooption_OSome(U_17430),U_17438) ) ),
    inference(miniscope,[status(thm)],[f_4262_2]) ).

fof(f_4262_4,plain,
    ( ! [U_17439,U_17435,U_17433,U_17431,U_17437] :
        ( hAPP(U_17433,U_17437) != hAPP(c_Option_Ooption_OSome(U_17431),U_17439)
        | hAPP(U_17435,U_17437) != c_Option_Ooption_ONone(U_17431)
        | ~ sP1111(U_17439,U_17435,U_17433,U_17431,U_17437) )
    & ! [U_17439,U_17435,U_17433,U_17431,U_17437] :
        ( hAPP(U_17435,U_17437) != hAPP(c_Option_Ooption_OSome(U_17431),U_17439)
        | ~ sP1111(U_17439,U_17435,U_17433,U_17431,U_17437) )
    & ! [U_17434,U_17430,U_17436,U_17432,U_17438] :
        ( hAPP(U_17432,U_17436) = hAPP(c_Option_Ooption_OSome(U_17430),U_17438)
        | ~ sP1110(U_17434,U_17430,U_17436,U_17432,U_17438) )
    & ! [U_17434,U_17430,U_17436,U_17432,U_17438] :
        ( hAPP(U_17434,U_17436) = c_Option_Ooption_ONone(U_17430)
        | ~ sP1110(U_17434,U_17430,U_17436,U_17432,U_17438) )
    & ! [U_17439,U_17435,U_17433,U_17429,U_17431,U_17437] :
        ( hAPP(c_Map_Omap__add(U_17429,U_17431,U_17433,U_17435),U_17437) = hAPP(c_Option_Ooption_OSome(U_17431),U_17439)
        | sP1111(U_17439,U_17435,U_17433,U_17431,U_17437) )
    & ! [U_17434,U_17428,U_17430,U_17436,U_17432,U_17438] :
        ( hAPP(c_Map_Omap__add(U_17428,U_17430,U_17432,U_17434),U_17436) != hAPP(c_Option_Ooption_OSome(U_17430),U_17438)
        | sP1110(U_17434,U_17430,U_17436,U_17432,U_17438)
        | hAPP(U_17434,U_17436) = hAPP(c_Option_Ooption_OSome(U_17430),U_17438) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1110,sP1111])],[f_4262_3]) ).

cnf(f_4262_5,plain,
    ( hAPP(c_Map_Omap__add(U_17428,U_17430,U_17432,U_17434),U_17436) != hAPP(c_Option_Ooption_OSome(U_17430),U_17438)
    | sP1110(U_17434,U_17430,U_17436,U_17432,U_17438)
    | hAPP(U_17434,U_17436) = hAPP(c_Option_Ooption_OSome(U_17430),U_17438) ),
    inference(clausify,[status(thm)],[f_4262_4]) ).

cnf(f_4262_6,plain,
    ( hAPP(c_Map_Omap__add(U_17429,U_17431,U_17433,U_17435),U_17437) = hAPP(c_Option_Ooption_OSome(U_17431),U_17439)
    | sP1111(U_17439,U_17435,U_17433,U_17431,U_17437) ),
    inference(clausify,[status(thm)],[f_4262_4]) ).

cnf(f_4262_7,plain,
    ( hAPP(U_17434,U_17436) = c_Option_Ooption_ONone(U_17430)
    | ~ sP1110(U_17434,U_17430,U_17436,U_17432,U_17438) ),
    inference(clausify,[status(thm)],[f_4262_4]) ).

cnf(f_4262_8,plain,
    ( hAPP(U_17432,U_17436) = hAPP(c_Option_Ooption_OSome(U_17430),U_17438)
    | ~ sP1110(U_17434,U_17430,U_17436,U_17432,U_17438) ),
    inference(clausify,[status(thm)],[f_4262_4]) ).

cnf(f_4262_9,plain,
    ( hAPP(U_17435,U_17437) != hAPP(c_Option_Ooption_OSome(U_17431),U_17439)
    | ~ sP1111(U_17439,U_17435,U_17433,U_17431,U_17437) ),
    inference(clausify,[status(thm)],[f_4262_4]) ).

cnf(f_4262_10,plain,
    ( hAPP(U_17433,U_17437) != hAPP(c_Option_Ooption_OSome(U_17431),U_17439)
    | hAPP(U_17435,U_17437) != c_Option_Ooption_ONone(U_17431)
    | ~ sP1111(U_17439,U_17435,U_17433,U_17431,U_17437) ),
    inference(clausify,[status(thm)],[f_4262_4]) ).

fof(f_4263_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_4263_2,plain,
    ! [U_17444,U_17443,U_17442,U_17441,U_17440] : hAPP(c_Map_Omap__add(U_17440,U_17441,U_17442,U_17443),U_17444) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17441),U_17441,hAPP(U_17442,U_17444),c_Option_Ooption_OSome(U_17441)),hAPP(U_17443,U_17444)),
    inference(variable_rename,[status(thm)],[f_4263_1]) ).

fof(f_4263_3,plain,
    ! [U_17442,U_17444,U_17443,U_17441,U_17440] : hAPP(c_Map_Omap__add(U_17440,U_17441,U_17442,U_17443),U_17444) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17441),U_17441,hAPP(U_17442,U_17444),c_Option_Ooption_OSome(U_17441)),hAPP(U_17443,U_17444)),
    inference(definitional_conversion,[status(esa)],[f_4263_2]) ).

cnf(f_4263_4,plain,
    hAPP(c_Map_Omap__add(U_17440,U_17441,U_17442,U_17443),U_17444) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17441),U_17441,hAPP(U_17442,U_17444),c_Option_Ooption_OSome(U_17441)),hAPP(U_17443,U_17444)),
    inference(clausify,[status(thm)],[f_4263_3]) ).

fof(f_4264_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_4264_2,plain,
    ! [U_17447,U_17446,U_17445] : c_Map_Omap__add(U_17445,U_17446,U_17447,hAPP(c_COMBK(tc_Option_Ooption(U_17446),U_17445),c_Option_Ooption_ONone(U_17446))) = U_17447,
    inference(variable_rename,[status(thm)],[f_4264_1]) ).

fof(f_4264_3,plain,
    ! [U_17447,U_17445,U_17446] : c_Map_Omap__add(U_17445,U_17446,U_17447,hAPP(c_COMBK(tc_Option_Ooption(U_17446),U_17445),c_Option_Ooption_ONone(U_17446))) = U_17447,
    inference(definitional_conversion,[status(esa)],[f_4264_2]) ).

cnf(f_4264_4,plain,
    c_Map_Omap__add(U_17445,U_17446,U_17447,hAPP(c_COMBK(tc_Option_Ooption(U_17446),U_17445),c_Option_Ooption_ONone(U_17446))) = U_17447,
    inference(clausify,[status(thm)],[f_4264_3]) ).

fof(f_4265_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_4265_2,plain,
    ! [U_17450,U_17449,U_17448] : c_Map_Omap__add(U_17448,U_17449,hAPP(c_COMBK(tc_Option_Ooption(U_17449),U_17448),c_Option_Ooption_ONone(U_17449)),U_17450) = U_17450,
    inference(variable_rename,[status(thm)],[f_4265_1]) ).

fof(f_4265_3,plain,
    ! [U_17448,U_17449,U_17450] : c_Map_Omap__add(U_17448,U_17449,hAPP(c_COMBK(tc_Option_Ooption(U_17449),U_17448),c_Option_Ooption_ONone(U_17449)),U_17450) = U_17450,
    inference(definitional_conversion,[status(esa)],[f_4265_2]) ).

cnf(f_4265_4,plain,
    c_Map_Omap__add(U_17448,U_17449,hAPP(c_COMBK(tc_Option_Ooption(U_17449),U_17448),c_Option_Ooption_ONone(U_17449)),U_17450) = U_17450,
    inference(clausify,[status(thm)],[f_4265_3]) ).

fof(f_4266_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_4266_2,plain,
    ! [U_17455,U_17454,U_17453,U_17452,U_17451] :
      ( ( hAPP(c_Map_Omap__add(U_17451,U_17452,U_17453,U_17454),U_17455) = c_Option_Ooption_ONone(U_17452)
        | hAPP(U_17453,U_17455) != c_Option_Ooption_ONone(U_17452)
        | hAPP(U_17454,U_17455) != c_Option_Ooption_ONone(U_17452) )
      & ( ( hAPP(U_17453,U_17455) = c_Option_Ooption_ONone(U_17452)
          & hAPP(U_17454,U_17455) = c_Option_Ooption_ONone(U_17452) )
        | hAPP(c_Map_Omap__add(U_17451,U_17452,U_17453,U_17454),U_17455) != c_Option_Ooption_ONone(U_17452) ) ),
    inference(variable_rename,[status(thm)],[f_4266_1]) ).

fof(f_4266_3,plain,
    ( ! [U_17465,U_17463,U_17461,U_17459] :
        ( ! [U_17457] : hAPP(c_Map_Omap__add(U_17457,U_17459,U_17461,U_17463),U_17465) = c_Option_Ooption_ONone(U_17459)
        | hAPP(U_17461,U_17465) != c_Option_Ooption_ONone(U_17459)
        | hAPP(U_17463,U_17465) != c_Option_Ooption_ONone(U_17459) )
    & ! [U_17464,U_17462,U_17460,U_17458] :
        ( ! [U_17456] : hAPP(c_Map_Omap__add(U_17456,U_17458,U_17460,U_17462),U_17464) != c_Option_Ooption_ONone(U_17458)
        | ( hAPP(U_17460,U_17464) = c_Option_Ooption_ONone(U_17458)
          & hAPP(U_17462,U_17464) = c_Option_Ooption_ONone(U_17458) ) ) ),
    inference(miniscope,[status(thm)],[f_4266_2]) ).

fof(f_4266_4,plain,
    ( ! [U_17458,U_17460,U_17462,U_17464] :
        ( hAPP(U_17460,U_17464) = c_Option_Ooption_ONone(U_17458)
        | ~ sP1112(U_17458,U_17460,U_17462,U_17464) )
    & ! [U_17458,U_17460,U_17462,U_17464] :
        ( hAPP(U_17462,U_17464) = c_Option_Ooption_ONone(U_17458)
        | ~ sP1112(U_17458,U_17460,U_17462,U_17464) )
    & ! [U_17459,U_17457,U_17461,U_17465,U_17463] :
        ( hAPP(c_Map_Omap__add(U_17457,U_17459,U_17461,U_17463),U_17465) = c_Option_Ooption_ONone(U_17459)
        | hAPP(U_17461,U_17465) != c_Option_Ooption_ONone(U_17459)
        | hAPP(U_17463,U_17465) != c_Option_Ooption_ONone(U_17459) )
    & ! [U_17456,U_17458,U_17460,U_17462,U_17464] :
        ( hAPP(c_Map_Omap__add(U_17456,U_17458,U_17460,U_17462),U_17464) != c_Option_Ooption_ONone(U_17458)
        | sP1112(U_17458,U_17460,U_17462,U_17464) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1112])],[f_4266_3]) ).

cnf(f_4266_5,plain,
    ( hAPP(c_Map_Omap__add(U_17456,U_17458,U_17460,U_17462),U_17464) != c_Option_Ooption_ONone(U_17458)
    | sP1112(U_17458,U_17460,U_17462,U_17464) ),
    inference(clausify,[status(thm)],[f_4266_4]) ).

cnf(f_4266_6,plain,
    ( hAPP(c_Map_Omap__add(U_17457,U_17459,U_17461,U_17463),U_17465) = c_Option_Ooption_ONone(U_17459)
    | hAPP(U_17461,U_17465) != c_Option_Ooption_ONone(U_17459)
    | hAPP(U_17463,U_17465) != c_Option_Ooption_ONone(U_17459) ),
    inference(clausify,[status(thm)],[f_4266_4]) ).

cnf(f_4266_7,plain,
    ( hAPP(U_17462,U_17464) = c_Option_Ooption_ONone(U_17458)
    | ~ sP1112(U_17458,U_17460,U_17462,U_17464) ),
    inference(clausify,[status(thm)],[f_4266_4]) ).

cnf(f_4266_8,plain,
    ( hAPP(U_17460,U_17464) = c_Option_Ooption_ONone(U_17458)
    | ~ sP1112(U_17458,U_17460,U_17462,U_17464) ),
    inference(clausify,[status(thm)],[f_4266_4]) ).

fof(f_4267_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_4267_2,plain,
    ! [U_17471,U_17470,U_17469,U_17468,U_17467,U_17466] :
      ( hAPP(c_Map_Omap__add(U_17470,U_17468,U_17471,U_17466),U_17467) = hAPP(c_Option_Ooption_OSome(U_17468),U_17469)
      | hAPP(U_17466,U_17467) != hAPP(c_Option_Ooption_OSome(U_17468),U_17469) ),
    inference(variable_rename,[status(thm)],[f_4267_1]) ).

fof(f_4267_3,plain,
    ! [U_17468,U_17467,U_17470,U_17471,U_17469,U_17466] :
      ( hAPP(c_Map_Omap__add(U_17470,U_17468,U_17471,U_17466),U_17467) = hAPP(c_Option_Ooption_OSome(U_17468),U_17469)
      | hAPP(U_17466,U_17467) != hAPP(c_Option_Ooption_OSome(U_17468),U_17469) ),
    inference(definitional_conversion,[status(esa)],[f_4267_2]) ).

cnf(f_4267_4,plain,
    ( hAPP(c_Map_Omap__add(U_17470,U_17468,U_17471,U_17466),U_17467) = hAPP(c_Option_Ooption_OSome(U_17468),U_17469)
    | hAPP(U_17466,U_17467) != hAPP(c_Option_Ooption_OSome(U_17468),U_17469) ),
    inference(clausify,[status(thm)],[f_4267_3]) ).

fof(f_4268_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_4268_2,plain,
    ! [U_17476,U_17475,U_17474,U_17473,U_17472] : c_Map_Omap__add(U_17472,U_17473,U_17474,c_Map_Omap__add(U_17472,U_17473,U_17475,U_17476)) = c_Map_Omap__add(U_17472,U_17473,c_Map_Omap__add(U_17472,U_17473,U_17474,U_17475),U_17476),
    inference(variable_rename,[status(thm)],[f_4268_1]) ).

fof(f_4268_3,plain,
    ! [U_17473,U_17474,U_17472,U_17475,U_17476] : c_Map_Omap__add(U_17472,U_17473,U_17474,c_Map_Omap__add(U_17472,U_17473,U_17475,U_17476)) = c_Map_Omap__add(U_17472,U_17473,c_Map_Omap__add(U_17472,U_17473,U_17474,U_17475),U_17476),
    inference(definitional_conversion,[status(esa)],[f_4268_2]) ).

cnf(f_4268_4,plain,
    c_Map_Omap__add(U_17472,U_17473,U_17474,c_Map_Omap__add(U_17472,U_17473,U_17475,U_17476)) = c_Map_Omap__add(U_17472,U_17473,c_Map_Omap__add(U_17472,U_17473,U_17474,U_17475),U_17476),
    inference(clausify,[status(thm)],[f_4268_3]) ).

fof(f_4269_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_4269_2,plain,
    ! [U_17481,U_17480,U_17479,U_17478,U_17477] :
      ( hAPP(c_Map_Omap__add(U_17477,U_17479,U_17481,U_17480),U_17478) = hAPP(U_17480,U_17478)
      | ~ hBOOL(hAPP(hAPP(c_member(U_17477),U_17478),c_Map_Odom(U_17477,U_17479,U_17480))) ),
    inference(variable_rename,[status(thm)],[f_4269_1]) ).

fof(f_4269_3,plain,
    ! [U_17477,U_17478,U_17479,U_17480,U_17481] :
      ( hAPP(c_Map_Omap__add(U_17477,U_17479,U_17481,U_17480),U_17478) = hAPP(U_17480,U_17478)
      | ~ hBOOL(hAPP(hAPP(c_member(U_17477),U_17478),c_Map_Odom(U_17477,U_17479,U_17480))) ),
    inference(definitional_conversion,[status(esa)],[f_4269_2]) ).

cnf(f_4269_4,plain,
    ( hAPP(c_Map_Omap__add(U_17477,U_17479,U_17481,U_17480),U_17478) = hAPP(U_17480,U_17478)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17477),U_17478),c_Map_Odom(U_17477,U_17479,U_17480))) ),
    inference(clausify,[status(thm)],[f_4269_3]) ).

fof(f_4270_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_4270_2,plain,
    ! [U_17486,U_17485,U_17484,U_17483,U_17482] :
      ( hAPP(c_Map_Omap__add(U_17482,U_17484,U_17486,U_17485),U_17483) = hAPP(U_17486,U_17483)
      | hBOOL(hAPP(hAPP(c_member(U_17482),U_17483),c_Map_Odom(U_17482,U_17484,U_17485))) ),
    inference(variable_rename,[status(thm)],[f_4270_1]) ).

fof(f_4270_3,plain,
    ! [U_17482,U_17483,U_17484,U_17485,U_17486] :
      ( hAPP(c_Map_Omap__add(U_17482,U_17484,U_17486,U_17485),U_17483) = hAPP(U_17486,U_17483)
      | hBOOL(hAPP(hAPP(c_member(U_17482),U_17483),c_Map_Odom(U_17482,U_17484,U_17485))) ),
    inference(definitional_conversion,[status(esa)],[f_4270_2]) ).

cnf(f_4270_4,plain,
    ( hAPP(c_Map_Omap__add(U_17482,U_17484,U_17486,U_17485),U_17483) = hAPP(U_17486,U_17483)
    | hBOOL(hAPP(hAPP(c_member(U_17482),U_17483),c_Map_Odom(U_17482,U_17484,U_17485))) ),
    inference(clausify,[status(thm)],[f_4270_3]) ).

fof(f_4271_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_4271_2,plain,
    ! [U_17491,U_17490,U_17489,U_17488,U_17487] :
      ( hAPP(c_Map_Omap__add(U_17487,U_17489,U_17490,U_17491),U_17488) = hAPP(U_17491,U_17488)
      | hBOOL(hAPP(hAPP(c_member(U_17487),U_17488),c_Map_Odom(U_17487,U_17489,U_17490))) ),
    inference(variable_rename,[status(thm)],[f_4271_1]) ).

fof(f_4271_3,plain,
    ! [U_17487,U_17488,U_17489,U_17490,U_17491] :
      ( hAPP(c_Map_Omap__add(U_17487,U_17489,U_17490,U_17491),U_17488) = hAPP(U_17491,U_17488)
      | hBOOL(hAPP(hAPP(c_member(U_17487),U_17488),c_Map_Odom(U_17487,U_17489,U_17490))) ),
    inference(definitional_conversion,[status(esa)],[f_4271_2]) ).

cnf(f_4271_4,plain,
    ( hAPP(c_Map_Omap__add(U_17487,U_17489,U_17490,U_17491),U_17488) = hAPP(U_17491,U_17488)
    | hBOOL(hAPP(hAPP(c_member(U_17487),U_17488),c_Map_Odom(U_17487,U_17489,U_17490))) ),
    inference(clausify,[status(thm)],[f_4271_3]) ).

fof(f_4272_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_4272_2,plain,
    ! [U_17495,U_17494,U_17493,U_17492] : c_Map_Odom(U_17492,U_17493,c_Map_Omap__add(U_17492,U_17493,U_17494,U_17495)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17492,tc_HOL_Obool)),c_Map_Odom(U_17492,U_17493,U_17495)),c_Map_Odom(U_17492,U_17493,U_17494)),
    inference(variable_rename,[status(thm)],[f_4272_1]) ).

fof(f_4272_3,plain,
    ! [U_17492,U_17493,U_17494,U_17495] : c_Map_Odom(U_17492,U_17493,c_Map_Omap__add(U_17492,U_17493,U_17494,U_17495)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17492,tc_HOL_Obool)),c_Map_Odom(U_17492,U_17493,U_17495)),c_Map_Odom(U_17492,U_17493,U_17494)),
    inference(definitional_conversion,[status(esa)],[f_4272_2]) ).

cnf(f_4272_4,plain,
    c_Map_Odom(U_17492,U_17493,c_Map_Omap__add(U_17492,U_17493,U_17494,U_17495)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17492,tc_HOL_Obool)),c_Map_Odom(U_17492,U_17493,U_17495)),c_Map_Odom(U_17492,U_17493,U_17494)),
    inference(clausify,[status(thm)],[f_4272_3]) ).

fof(f_4273_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_4273_2,plain,
    ! [U_17499,U_17498,U_17497,U_17496] :
      ( ( c_Fun_Oinj__on(U_17496,tc_Option_Ooption(U_17497),c_Map_Omap__add(U_17496,U_17497,U_17498,U_17499),c_Map_Odom(U_17496,U_17497,U_17499))
        | ~ c_Fun_Oinj__on(U_17496,tc_Option_Ooption(U_17497),U_17499,c_Map_Odom(U_17496,U_17497,U_17499)) )
      & ( c_Fun_Oinj__on(U_17496,tc_Option_Ooption(U_17497),U_17499,c_Map_Odom(U_17496,U_17497,U_17499))
        | ~ c_Fun_Oinj__on(U_17496,tc_Option_Ooption(U_17497),c_Map_Omap__add(U_17496,U_17497,U_17498,U_17499),c_Map_Odom(U_17496,U_17497,U_17499)) ) ),
    inference(variable_rename,[status(thm)],[f_4273_1]) ).

fof(f_4273_3,plain,
    ( ! [U_17507,U_17505,U_17503,U_17501] :
        ( c_Fun_Oinj__on(U_17501,tc_Option_Ooption(U_17503),c_Map_Omap__add(U_17501,U_17503,U_17505,U_17507),c_Map_Odom(U_17501,U_17503,U_17507))
        | ~ c_Fun_Oinj__on(U_17501,tc_Option_Ooption(U_17503),U_17507,c_Map_Odom(U_17501,U_17503,U_17507)) )
    & ! [U_17506,U_17504,U_17502,U_17500] :
        ( c_Fun_Oinj__on(U_17500,tc_Option_Ooption(U_17502),U_17506,c_Map_Odom(U_17500,U_17502,U_17506))
        | ~ c_Fun_Oinj__on(U_17500,tc_Option_Ooption(U_17502),c_Map_Omap__add(U_17500,U_17502,U_17504,U_17506),c_Map_Odom(U_17500,U_17502,U_17506)) ) ),
    inference(miniscope,[status(thm)],[f_4273_2]) ).

fof(f_4273_4,plain,
    ( ! [U_17505,U_17503,U_17501,U_17507] :
        ( c_Fun_Oinj__on(U_17501,tc_Option_Ooption(U_17503),c_Map_Omap__add(U_17501,U_17503,U_17505,U_17507),c_Map_Odom(U_17501,U_17503,U_17507))
        | ~ c_Fun_Oinj__on(U_17501,tc_Option_Ooption(U_17503),U_17507,c_Map_Odom(U_17501,U_17503,U_17507)) )
    & ! [U_17502,U_17500,U_17506,U_17504] :
        ( c_Fun_Oinj__on(U_17500,tc_Option_Ooption(U_17502),U_17506,c_Map_Odom(U_17500,U_17502,U_17506))
        | ~ c_Fun_Oinj__on(U_17500,tc_Option_Ooption(U_17502),c_Map_Omap__add(U_17500,U_17502,U_17504,U_17506),c_Map_Odom(U_17500,U_17502,U_17506)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4273_3]) ).

cnf(f_4273_5,plain,
    ( c_Fun_Oinj__on(U_17500,tc_Option_Ooption(U_17502),U_17506,c_Map_Odom(U_17500,U_17502,U_17506))
    | ~ c_Fun_Oinj__on(U_17500,tc_Option_Ooption(U_17502),c_Map_Omap__add(U_17500,U_17502,U_17504,U_17506),c_Map_Odom(U_17500,U_17502,U_17506)) ),
    inference(clausify,[status(thm)],[f_4273_4]) ).

cnf(f_4273_6,plain,
    ( c_Fun_Oinj__on(U_17501,tc_Option_Ooption(U_17503),c_Map_Omap__add(U_17501,U_17503,U_17505,U_17507),c_Map_Odom(U_17501,U_17503,U_17507))
    | ~ c_Fun_Oinj__on(U_17501,tc_Option_Ooption(U_17503),U_17507,c_Map_Odom(U_17501,U_17503,U_17507)) ),
    inference(clausify,[status(thm)],[f_4273_4]) ).

fof(f_4274_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_4274_2,plain,
    ! [U_17511,U_17510,U_17509,U_17508] :
      ( c_Map_Omap__add(U_17508,U_17509,U_17510,U_17511) = c_Map_Omap__add(U_17508,U_17509,U_17511,U_17510)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17508,tc_HOL_Obool)),c_Map_Odom(U_17508,U_17509,U_17510)),c_Map_Odom(U_17508,U_17509,U_17511)) != c_Orderings_Obot__class_Obot(tc_fun(U_17508,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4274_1]) ).

fof(f_4274_3,plain,
    ! [U_17509,U_17508,U_17510,U_17511] :
      ( c_Map_Omap__add(U_17508,U_17509,U_17510,U_17511) = c_Map_Omap__add(U_17508,U_17509,U_17511,U_17510)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17508,tc_HOL_Obool)),c_Map_Odom(U_17508,U_17509,U_17510)),c_Map_Odom(U_17508,U_17509,U_17511)) != c_Orderings_Obot__class_Obot(tc_fun(U_17508,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_4274_2]) ).

cnf(f_4274_4,plain,
    ( c_Map_Omap__add(U_17508,U_17509,U_17510,U_17511) = c_Map_Omap__add(U_17508,U_17509,U_17511,U_17510)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17508,tc_HOL_Obool)),c_Map_Odom(U_17508,U_17509,U_17510)),c_Map_Odom(U_17508,U_17509,U_17511)) != c_Orderings_Obot__class_Obot(tc_fun(U_17508,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4274_3]) ).

fof(f_4275_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_4275_2,plain,
    ! [U_17515,U_17514,U_17513,U_17512] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17512)),hAPP(c_Set_Oimage(U_17513,tc_Option_Ooption(U_17512),c_Map_Omap__add(U_17513,U_17512,U_17514,c_Map_Omap__of(U_17513,U_17512,U_17515))),c_Orderings_Otop__class_Otop(tc_fun(U_17513,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17512)),hAPP(c_Set_Oimage(U_17513,tc_Option_Ooption(U_17512),U_17514),c_Orderings_Otop__class_Otop(tc_fun(U_17513,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_4275_1]) ).

fof(f_4275_3,plain,
    ! [U_17512,U_17513,U_17514,U_17515] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17512)),hAPP(c_Set_Oimage(U_17513,tc_Option_Ooption(U_17512),c_Map_Omap__add(U_17513,U_17512,U_17514,c_Map_Omap__of(U_17513,U_17512,U_17515))),c_Orderings_Otop__class_Otop(tc_fun(U_17513,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17512)),hAPP(c_Set_Oimage(U_17513,tc_Option_Ooption(U_17512),U_17514),c_Orderings_Otop__class_Otop(tc_fun(U_17513,tc_HOL_Obool))))) ),
    inference(definitional_conversion,[status(esa)],[f_4275_2]) ).

cnf(f_4275_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17512)),hAPP(c_Set_Oimage(U_17513,tc_Option_Ooption(U_17512),c_Map_Omap__add(U_17513,U_17512,U_17514,c_Map_Omap__of(U_17513,U_17512,U_17515))),c_Orderings_Otop__class_Otop(tc_fun(U_17513,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17512)),hAPP(c_Set_Oimage(U_17513,tc_Option_Ooption(U_17512),U_17514),c_Orderings_Otop__class_Otop(tc_fun(U_17513,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_4275_3]) ).

fof(f_4276_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_4276_2,plain,
    ! [U_17521,U_17520,U_17519,U_17518] :
      ( ? [U_17517,U_17516] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17519,U_17518)),hAPP(hAPP(c_Product__Type_OPair(U_17519,U_17518),U_17517),U_17516)),U_17521))
          & U_17520 = hAPP(hAPP(c_Product__Type_OPair(U_17518,U_17519),U_17516),U_17517) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17518,U_17519)),U_17520),hAPP(c_Relation_Oconverse(U_17519,U_17518),U_17521))) ),
    inference(variable_rename,[status(thm)],[f_4276_1]) ).

fof(f_4276_3,plain,
    ! [U_17521,U_17520,U_17519,U_17518] :
      ( ? [U_17516] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17519,U_17518)),hAPP(hAPP(c_Product__Type_OPair(U_17519,U_17518),sK447(U_17521,U_17520,U_17519,U_17518)),U_17516)),U_17521))
          & U_17520 = hAPP(hAPP(c_Product__Type_OPair(U_17518,U_17519),U_17516),sK447(U_17521,U_17520,U_17519,U_17518)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17518,U_17519)),U_17520),hAPP(c_Relation_Oconverse(U_17519,U_17518),U_17521))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK447]),skolemize(U_17517,sK447(U_17521,U_17520,U_17519,U_17518))],[f_4276_2]) ).

fof(f_4276_4,plain,
    ! [U_17521,U_17520,U_17519,U_17518] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17519,U_17518)),hAPP(hAPP(c_Product__Type_OPair(U_17519,U_17518),sK447(U_17521,U_17520,U_17519,U_17518)),sK448(U_17521,U_17520,U_17519,U_17518))),U_17521))
        & U_17520 = hAPP(hAPP(c_Product__Type_OPair(U_17518,U_17519),sK448(U_17521,U_17520,U_17519,U_17518)),sK447(U_17521,U_17520,U_17519,U_17518)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17518,U_17519)),U_17520),hAPP(c_Relation_Oconverse(U_17519,U_17518),U_17521))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK448]),skolemize(U_17516,sK448(U_17521,U_17520,U_17519,U_17518))],[f_4276_3]) ).

fof(f_4276_5,plain,
    ( ! [U_17518,U_17519,U_17520,U_17521] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17519,U_17518)),hAPP(hAPP(c_Product__Type_OPair(U_17519,U_17518),sK447(U_17521,U_17520,U_17519,U_17518)),sK448(U_17521,U_17520,U_17519,U_17518))),U_17521))
        | ~ sP1113(U_17518,U_17519,U_17520,U_17521) )
    & ! [U_17518,U_17519,U_17520,U_17521] :
        ( U_17520 = hAPP(hAPP(c_Product__Type_OPair(U_17518,U_17519),sK448(U_17521,U_17520,U_17519,U_17518)),sK447(U_17521,U_17520,U_17519,U_17518))
        | ~ sP1113(U_17518,U_17519,U_17520,U_17521) )
    & ! [U_17518,U_17519,U_17520,U_17521] :
        ( sP1113(U_17518,U_17519,U_17520,U_17521)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17518,U_17519)),U_17520),hAPP(c_Relation_Oconverse(U_17519,U_17518),U_17521))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1113])],[f_4276_4]) ).

cnf(f_4276_6,plain,
    ( sP1113(U_17518,U_17519,U_17520,U_17521)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17518,U_17519)),U_17520),hAPP(c_Relation_Oconverse(U_17519,U_17518),U_17521))) ),
    inference(clausify,[status(thm)],[f_4276_5]) ).

cnf(f_4276_7,plain,
    ( U_17520 = hAPP(hAPP(c_Product__Type_OPair(U_17518,U_17519),sK448(U_17521,U_17520,U_17519,U_17518)),sK447(U_17521,U_17520,U_17519,U_17518))
    | ~ sP1113(U_17518,U_17519,U_17520,U_17521) ),
    inference(clausify,[status(thm)],[f_4276_5]) ).

cnf(f_4276_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17519,U_17518)),hAPP(hAPP(c_Product__Type_OPair(U_17519,U_17518),sK447(U_17521,U_17520,U_17519,U_17518)),sK448(U_17521,U_17520,U_17519,U_17518))),U_17521))
    | ~ sP1113(U_17518,U_17519,U_17520,U_17521) ),
    inference(clausify,[status(thm)],[f_4276_5]) ).

fof(f_4277_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_4277_2,plain,
    ! [U_17524,U_17523,U_17522] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_17522),c_Map_Odom(U_17522,U_17523,c_Map_Omap__of(U_17522,U_17523,U_17524)))),
    inference(variable_rename,[status(thm)],[f_4277_1]) ).

fof(f_4277_3,plain,
    ! [U_17524,U_17522,U_17523] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_17522),c_Map_Odom(U_17522,U_17523,c_Map_Omap__of(U_17522,U_17523,U_17524)))),
    inference(definitional_conversion,[status(esa)],[f_4277_2]) ).

cnf(f_4277_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_17522),c_Map_Odom(U_17522,U_17523,c_Map_Omap__of(U_17522,U_17523,U_17524)))),
    inference(clausify,[status(thm)],[f_4277_3]) ).

fof(f_4278_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_4278_2,plain,
    ! [U_17527,U_17526,U_17525] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17525)),hAPP(c_Set_Oimage(U_17526,tc_Option_Ooption(U_17525),c_Map_Omap__of(U_17526,U_17525,U_17527)),c_Orderings_Otop__class_Otop(tc_fun(U_17526,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_4278_1]) ).

fof(f_4278_3,plain,
    ! [U_17525,U_17526,U_17527] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17525)),hAPP(c_Set_Oimage(U_17526,tc_Option_Ooption(U_17525),c_Map_Omap__of(U_17526,U_17525,U_17527)),c_Orderings_Otop__class_Otop(tc_fun(U_17526,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_4278_2]) ).

cnf(f_4278_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17525)),hAPP(c_Set_Oimage(U_17526,tc_Option_Ooption(U_17525),c_Map_Omap__of(U_17526,U_17525,U_17527)),c_Orderings_Otop__class_Otop(tc_fun(U_17526,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_4278_3]) ).

fof(f_4279_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_4279_2,plain,
    ! [U_17531,U_17530,U_17529,U_17528] : c_Map_Omap__add(U_17528,U_17529,U_17530,c_Map_Omap__of(U_17528,U_17529,U_17531)) = c_List_Ofoldr(tc_prod(U_17528,U_17529),tc_fun(U_17528,tc_Option_Ooption(U_17529)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17528,U_17529,tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),hAPP(hAPP(c_COMBC(U_17528,tc_fun(U_17529,tc_Option_Ooption(U_17529)),tc_fun(U_17529,tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17529),tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),tc_fun(tc_fun(U_17529,tc_Option_Ooption(U_17529)),tc_fun(U_17529,tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529))))),U_17528),c_COMBB(tc_Option_Ooption(U_17529),tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529))),U_17529)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(tc_Option_Ooption(U_17529),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),tc_fun(tc_Option_Ooption(U_17529),tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),U_17528),c_COMBC(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_Option_Ooption(U_17529),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),hAPP(c_COMBC(tc_fun(U_17528,tc_Option_Ooption(U_17529)),U_17528,tc_fun(tc_Option_Ooption(U_17529),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),c_Fun_Ofun__upd(U_17528,tc_Option_Ooption(U_17529)))))),c_Option_Ooption_OSome(U_17529))),U_17531,U_17530),
    inference(variable_rename,[status(thm)],[f_4279_1]) ).

fof(f_4279_3,plain,
    ! [U_17528,U_17529,U_17530,U_17531] : c_Map_Omap__add(U_17528,U_17529,U_17530,c_Map_Omap__of(U_17528,U_17529,U_17531)) = c_List_Ofoldr(tc_prod(U_17528,U_17529),tc_fun(U_17528,tc_Option_Ooption(U_17529)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17528,U_17529,tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),hAPP(hAPP(c_COMBC(U_17528,tc_fun(U_17529,tc_Option_Ooption(U_17529)),tc_fun(U_17529,tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17529),tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),tc_fun(tc_fun(U_17529,tc_Option_Ooption(U_17529)),tc_fun(U_17529,tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529))))),U_17528),c_COMBB(tc_Option_Ooption(U_17529),tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529))),U_17529)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(tc_Option_Ooption(U_17529),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),tc_fun(tc_Option_Ooption(U_17529),tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),U_17528),c_COMBC(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_Option_Ooption(U_17529),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),hAPP(c_COMBC(tc_fun(U_17528,tc_Option_Ooption(U_17529)),U_17528,tc_fun(tc_Option_Ooption(U_17529),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),c_Fun_Ofun__upd(U_17528,tc_Option_Ooption(U_17529)))))),c_Option_Ooption_OSome(U_17529))),U_17531,U_17530),
    inference(definitional_conversion,[status(esa)],[f_4279_2]) ).

cnf(f_4279_4,plain,
    c_Map_Omap__add(U_17528,U_17529,U_17530,c_Map_Omap__of(U_17528,U_17529,U_17531)) = c_List_Ofoldr(tc_prod(U_17528,U_17529),tc_fun(U_17528,tc_Option_Ooption(U_17529)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17528,U_17529,tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),hAPP(hAPP(c_COMBC(U_17528,tc_fun(U_17529,tc_Option_Ooption(U_17529)),tc_fun(U_17529,tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17529),tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),tc_fun(tc_fun(U_17529,tc_Option_Ooption(U_17529)),tc_fun(U_17529,tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529))))),U_17528),c_COMBB(tc_Option_Ooption(U_17529),tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529))),U_17529)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(tc_Option_Ooption(U_17529),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),tc_fun(tc_Option_Ooption(U_17529),tc_fun(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),U_17528),c_COMBC(tc_fun(U_17528,tc_Option_Ooption(U_17529)),tc_Option_Ooption(U_17529),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),hAPP(c_COMBC(tc_fun(U_17528,tc_Option_Ooption(U_17529)),U_17528,tc_fun(tc_Option_Ooption(U_17529),tc_fun(U_17528,tc_Option_Ooption(U_17529)))),c_Fun_Ofun__upd(U_17528,tc_Option_Ooption(U_17529)))))),c_Option_Ooption_OSome(U_17529))),U_17531,U_17530),
    inference(clausify,[status(thm)],[f_4279_3]) ).

fof(f_4280_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_4280_2,plain,
    ! [U_17534,U_17533,U_17532] : c_Smallcheck_Oorelse(U_17532,U_17533,U_17534) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17532),U_17532,U_17534,c_Option_Ooption_OSome(U_17532)),U_17533),
    inference(variable_rename,[status(thm)],[f_4280_1]) ).

fof(f_4280_3,plain,
    ! [U_17533,U_17532,U_17534] : c_Smallcheck_Oorelse(U_17532,U_17533,U_17534) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17532),U_17532,U_17534,c_Option_Ooption_OSome(U_17532)),U_17533),
    inference(definitional_conversion,[status(esa)],[f_4280_2]) ).

cnf(f_4280_4,plain,
    c_Smallcheck_Oorelse(U_17532,U_17533,U_17534) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17532),U_17532,U_17534,c_Option_Ooption_OSome(U_17532)),U_17533),
    inference(clausify,[status(thm)],[f_4280_3]) ).

fof(f_4281_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_4281_2,plain,
    ! [U_17536,U_17535] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,U_17535,U_17536) = c_Smallcheck_Ofull__small_H(U_17535,hAPP(c_Code__Numeral_Oint__of,U_17536),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17536))),
    inference(variable_rename,[status(thm)],[f_4281_1]) ).

fof(f_4281_3,plain,
    ! [U_17535,U_17536] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,U_17535,U_17536) = c_Smallcheck_Ofull__small_H(U_17535,hAPP(c_Code__Numeral_Oint__of,U_17536),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17536))),
    inference(definitional_conversion,[status(esa)],[f_4281_2]) ).

cnf(f_4281_4,plain,
    c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,U_17535,U_17536) = c_Smallcheck_Ofull__small_H(U_17535,hAPP(c_Code__Numeral_Oint__of,U_17536),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17536))),
    inference(clausify,[status(thm)],[f_4281_3]) ).

fof(f_4282_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_4282_2,plain,
    ! [U_17539,U_17538,U_17537] :
      ( ( c_Smallcheck_Osmall_H(U_17539,U_17537,U_17538) = 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_17539,U_17537,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17538),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17539,U_17538))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17537),U_17538)) )
      & ( c_Smallcheck_Osmall_H(U_17539,U_17537,U_17538) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17537),U_17538)) ) ),
    inference(variable_rename,[status(thm)],[f_4282_1]) ).

fof(f_4282_3,plain,
    ( ! [U_17545,U_17543,U_17541] :
        ( c_Smallcheck_Osmall_H(U_17545,U_17541,U_17543) = 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_17545,U_17541,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17543),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17545,U_17543))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17541),U_17543)) )
    & ! [U_17544,U_17542,U_17540] :
        ( c_Smallcheck_Osmall_H(U_17544,U_17540,U_17542) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17540),U_17542)) ) ),
    inference(miniscope,[status(thm)],[f_4282_2]) ).

fof(f_4282_4,plain,
    ( ! [U_17543,U_17545,U_17541] :
        ( c_Smallcheck_Osmall_H(U_17545,U_17541,U_17543) = 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_17545,U_17541,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17543),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17545,U_17543))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17541),U_17543)) )
    & ! [U_17540,U_17544,U_17542] :
        ( c_Smallcheck_Osmall_H(U_17544,U_17540,U_17542) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17540),U_17542)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4282_3]) ).

cnf(f_4282_5,plain,
    ( c_Smallcheck_Osmall_H(U_17544,U_17540,U_17542) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17540),U_17542)) ),
    inference(clausify,[status(thm)],[f_4282_4]) ).

cnf(f_4282_6,plain,
    ( c_Smallcheck_Osmall_H(U_17545,U_17541,U_17543) = 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_17545,U_17541,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17543),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17545,U_17543))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17541),U_17543)) ),
    inference(clausify,[status(thm)],[f_4282_4]) ).

fof(f_4283_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_4283_2,plain,
    ! [U_17548,U_17547,U_17546] :
      ( ( ( c_Smallcheck_Osmall_H(U_17546,U_17547,U_17548) = 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_17546,U_17547,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17548),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17546,U_17548))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17547),U_17548)) )
        & ( c_Smallcheck_Osmall_H(U_17546,U_17547,U_17548) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17547),U_17548)) ) )
      | ~ 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_17546),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17547),U_17548)))) ),
    inference(variable_rename,[status(thm)],[f_4283_1]) ).

fof(f_4283_3,plain,
    ( ! [U_17546,U_17547,U_17548] :
        ( c_Smallcheck_Osmall_H(U_17546,U_17547,U_17548) = 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_17546,U_17547,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17548),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17546,U_17548))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17547),U_17548))
        | ~ sP1114(U_17546,U_17547,U_17548) )
    & ! [U_17546,U_17547,U_17548] :
        ( c_Smallcheck_Osmall_H(U_17546,U_17547,U_17548) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17547),U_17548))
        | ~ sP1114(U_17546,U_17547,U_17548) )
    & ! [U_17546,U_17547,U_17548] :
        ( sP1114(U_17546,U_17547,U_17548)
        | ~ 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_17546),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17547),U_17548)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1114])],[f_4283_2]) ).

cnf(f_4283_4,plain,
    ( sP1114(U_17546,U_17547,U_17548)
    | ~ 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_17546),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17547),U_17548)))) ),
    inference(clausify,[status(thm)],[f_4283_3]) ).

cnf(f_4283_5,plain,
    ( c_Smallcheck_Osmall_H(U_17546,U_17547,U_17548) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17547),U_17548))
    | ~ sP1114(U_17546,U_17547,U_17548) ),
    inference(clausify,[status(thm)],[f_4283_3]) ).

cnf(f_4283_6,plain,
    ( c_Smallcheck_Osmall_H(U_17546,U_17547,U_17548) = 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_17546,U_17547,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17548),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17546,U_17548))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17547),U_17548))
    | ~ sP1114(U_17546,U_17547,U_17548) ),
    inference(clausify,[status(thm)],[f_4283_3]) ).

fof(f_4284_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_4284_2,plain,
    ! [U_17550,U_17549] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),U_17549),U_17550) = c_Smallcheck_Osmall_H(U_17549,hAPP(c_Code__Numeral_Oint__of,U_17550),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17550))),
    inference(variable_rename,[status(thm)],[f_4284_1]) ).

fof(f_4284_3,plain,
    ! [U_17550,U_17549] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),U_17549),U_17550) = c_Smallcheck_Osmall_H(U_17549,hAPP(c_Code__Numeral_Oint__of,U_17550),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17550))),
    inference(definitional_conversion,[status(esa)],[f_4284_2]) ).

cnf(f_4284_4,plain,
    hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),U_17549),U_17550) = c_Smallcheck_Osmall_H(U_17549,hAPP(c_Code__Numeral_Oint__of,U_17550),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17550))),
    inference(clausify,[status(thm)],[f_4284_3]) ).

fof(f_4285_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_4285_2,plain,
    ! [U_17554,U_17553,U_17552,U_17551] :
      ( hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(U_17552,U_17551)),U_17553),U_17554) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(U_17552),hAPP(hAPP(c_COMBC(U_17552,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(U_17551,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_17552),c_Smallcheck_Osmall__class_Osmall(U_17551)),hAPP(hAPP(c_COMBB(tc_fun(U_17551,tc_prod(U_17552,U_17551)),tc_fun(U_17551,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),U_17552),hAPP(c_COMBB(tc_prod(U_17552,U_17551),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),U_17551),U_17553)),c_Product__Type_OPair(U_17552,U_17551)))),U_17554)),U_17554)
      | ~ class_Smallcheck_Osmall(U_17552)
      | ~ class_Smallcheck_Osmall(U_17551) ),
    inference(variable_rename,[status(thm)],[f_4285_1]) ).

fof(f_4285_3,plain,
    ! [U_17552,U_17551,U_17553,U_17554] :
      ( hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(U_17552,U_17551)),U_17553),U_17554) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(U_17552),hAPP(hAPP(c_COMBC(U_17552,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(U_17551,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_17552),c_Smallcheck_Osmall__class_Osmall(U_17551)),hAPP(hAPP(c_COMBB(tc_fun(U_17551,tc_prod(U_17552,U_17551)),tc_fun(U_17551,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),U_17552),hAPP(c_COMBB(tc_prod(U_17552,U_17551),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),U_17551),U_17553)),c_Product__Type_OPair(U_17552,U_17551)))),U_17554)),U_17554)
      | ~ class_Smallcheck_Osmall(U_17552)
      | ~ class_Smallcheck_Osmall(U_17551) ),
    inference(definitional_conversion,[status(esa)],[f_4285_2]) ).

cnf(f_4285_4,plain,
    ( hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(U_17552,U_17551)),U_17553),U_17554) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(U_17552),hAPP(hAPP(c_COMBC(U_17552,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(U_17551,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_17552),c_Smallcheck_Osmall__class_Osmall(U_17551)),hAPP(hAPP(c_COMBB(tc_fun(U_17551,tc_prod(U_17552,U_17551)),tc_fun(U_17551,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),U_17552),hAPP(c_COMBB(tc_prod(U_17552,U_17551),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),U_17551),U_17553)),c_Product__Type_OPair(U_17552,U_17551)))),U_17554)),U_17554)
    | ~ class_Smallcheck_Osmall(U_17552)
    | ~ class_Smallcheck_Osmall(U_17551) ),
    inference(clausify,[status(thm)],[f_4285_3]) ).

fof(f_4286_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_4286_2,plain,
    ! [U_17561,U_17560,U_17559,U_17558] :
      ( hBOOL(hAPP(hAPP(hAPP(U_17561,U_17558),U_17559),U_17560))
      | ? [U_17557,U_17556,U_17555] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(U_17561,U_17557),U_17556),U_17555))
          & ( hBOOL(hAPP(hAPP(hAPP(U_17561,U_17557),U_17556),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17555),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hAPP(U_17557,U_17555) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17556),U_17555)) )
          & 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_17557),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17556),U_17555)))) )
      | ~ 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_17558),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17559),U_17560)))) ),
    inference(variable_rename,[status(thm)],[f_4286_1]) ).

fof(f_4286_3,plain,
    ! [U_17561,U_17560,U_17559,U_17558] :
      ( hBOOL(hAPP(hAPP(hAPP(U_17561,U_17558),U_17559),U_17560))
      | ? [U_17556,U_17555] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(U_17561,sK449(U_17561,U_17560,U_17559,U_17558)),U_17556),U_17555))
          & ( hBOOL(hAPP(hAPP(hAPP(U_17561,sK449(U_17561,U_17560,U_17559,U_17558)),U_17556),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17555),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hAPP(sK449(U_17561,U_17560,U_17559,U_17558),U_17555) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17556),U_17555)) )
          & 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)),sK449(U_17561,U_17560,U_17559,U_17558)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17556),U_17555)))) )
      | ~ 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_17558),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17559),U_17560)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK449]),skolemize(U_17557,sK449(U_17561,U_17560,U_17559,U_17558))],[f_4286_2]) ).

fof(f_4286_4,plain,
    ! [U_17561,U_17560,U_17559,U_17558] :
      ( hBOOL(hAPP(hAPP(hAPP(U_17561,U_17558),U_17559),U_17560))
      | ? [U_17555] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(U_17561,sK449(U_17561,U_17560,U_17559,U_17558)),sK450(U_17561,U_17560,U_17559,U_17558)),U_17555))
          & ( hBOOL(hAPP(hAPP(hAPP(U_17561,sK449(U_17561,U_17560,U_17559,U_17558)),sK450(U_17561,U_17560,U_17559,U_17558)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17555),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hAPP(sK449(U_17561,U_17560,U_17559,U_17558),U_17555) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK450(U_17561,U_17560,U_17559,U_17558)),U_17555)) )
          & 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)),sK449(U_17561,U_17560,U_17559,U_17558)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK450(U_17561,U_17560,U_17559,U_17558)),U_17555)))) )
      | ~ 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_17558),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17559),U_17560)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK450]),skolemize(U_17556,sK450(U_17561,U_17560,U_17559,U_17558))],[f_4286_3]) ).

fof(f_4286_5,plain,
    ! [U_17561,U_17560,U_17559,U_17558] :
      ( hBOOL(hAPP(hAPP(hAPP(U_17561,U_17558),U_17559),U_17560))
      | ( ~ hBOOL(hAPP(hAPP(hAPP(U_17561,sK449(U_17561,U_17560,U_17559,U_17558)),sK450(U_17561,U_17560,U_17559,U_17558)),sK451(U_17561,U_17560,U_17559,U_17558)))
        & ( hBOOL(hAPP(hAPP(hAPP(U_17561,sK449(U_17561,U_17560,U_17559,U_17558)),sK450(U_17561,U_17560,U_17559,U_17558)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK451(U_17561,U_17560,U_17559,U_17558)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
          | hAPP(sK449(U_17561,U_17560,U_17559,U_17558),sK451(U_17561,U_17560,U_17559,U_17558)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK450(U_17561,U_17560,U_17559,U_17558)),sK451(U_17561,U_17560,U_17559,U_17558))) )
        & 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)),sK449(U_17561,U_17560,U_17559,U_17558)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK450(U_17561,U_17560,U_17559,U_17558)),sK451(U_17561,U_17560,U_17559,U_17558))))) )
      | ~ 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_17558),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17559),U_17560)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK451]),skolemize(U_17555,sK451(U_17561,U_17560,U_17559,U_17558))],[f_4286_4]) ).

fof(f_4286_6,plain,
    ( ! [U_17558,U_17559,U_17560,U_17561] :
        ( ~ hBOOL(hAPP(hAPP(hAPP(U_17561,sK449(U_17561,U_17560,U_17559,U_17558)),sK450(U_17561,U_17560,U_17559,U_17558)),sK451(U_17561,U_17560,U_17559,U_17558)))
        | ~ sP1115(U_17558,U_17559,U_17560,U_17561) )
    & ! [U_17558,U_17559,U_17560,U_17561] :
        ( hBOOL(hAPP(hAPP(hAPP(U_17561,sK449(U_17561,U_17560,U_17559,U_17558)),sK450(U_17561,U_17560,U_17559,U_17558)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK451(U_17561,U_17560,U_17559,U_17558)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hAPP(sK449(U_17561,U_17560,U_17559,U_17558),sK451(U_17561,U_17560,U_17559,U_17558)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK450(U_17561,U_17560,U_17559,U_17558)),sK451(U_17561,U_17560,U_17559,U_17558)))
        | ~ sP1115(U_17558,U_17559,U_17560,U_17561) )
    & ! [U_17558,U_17559,U_17560,U_17561] :
        ( 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)),sK449(U_17561,U_17560,U_17559,U_17558)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK450(U_17561,U_17560,U_17559,U_17558)),sK451(U_17561,U_17560,U_17559,U_17558)))))
        | ~ sP1115(U_17558,U_17559,U_17560,U_17561) )
    & ! [U_17558,U_17559,U_17560,U_17561] :
        ( hBOOL(hAPP(hAPP(hAPP(U_17561,U_17558),U_17559),U_17560))
        | sP1115(U_17558,U_17559,U_17560,U_17561)
        | ~ 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_17558),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17559),U_17560)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1115])],[f_4286_5]) ).

cnf(f_4286_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_17561,U_17558),U_17559),U_17560))
    | sP1115(U_17558,U_17559,U_17560,U_17561)
    | ~ 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_17558),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17559),U_17560)))) ),
    inference(clausify,[status(thm)],[f_4286_6]) ).

cnf(f_4286_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)),sK449(U_17561,U_17560,U_17559,U_17558)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK450(U_17561,U_17560,U_17559,U_17558)),sK451(U_17561,U_17560,U_17559,U_17558)))))
    | ~ sP1115(U_17558,U_17559,U_17560,U_17561) ),
    inference(clausify,[status(thm)],[f_4286_6]) ).

cnf(f_4286_9,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_17561,sK449(U_17561,U_17560,U_17559,U_17558)),sK450(U_17561,U_17560,U_17559,U_17558)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK451(U_17561,U_17560,U_17559,U_17558)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | hAPP(sK449(U_17561,U_17560,U_17559,U_17558),sK451(U_17561,U_17560,U_17559,U_17558)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK450(U_17561,U_17560,U_17559,U_17558)),sK451(U_17561,U_17560,U_17559,U_17558)))
    | ~ sP1115(U_17558,U_17559,U_17560,U_17561) ),
    inference(clausify,[status(thm)],[f_4286_6]) ).

cnf(f_4286_10,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(U_17561,sK449(U_17561,U_17560,U_17559,U_17558)),sK450(U_17561,U_17560,U_17559,U_17558)),sK451(U_17561,U_17560,U_17559,U_17558)))
    | ~ sP1115(U_17558,U_17559,U_17560,U_17561) ),
    inference(clausify,[status(thm)],[f_4286_6]) ).

fof(f_4287_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_4287_2,plain,
    c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies),
    inference(definitional_conversion,[status(esa)],[f_4287_1]) ).

cnf(f_4287_3,plain,
    c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies),
    inference(clausify,[status(thm)],[f_4287_2]) ).

fof(f_4288_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_4288_2,plain,
    ! [U_17568,U_17567,U_17566,U_17565,U_17564,U_17563,U_17562] :
      ( hAPP(c_Map_Omap__of(U_17563,U_17565,hAPP(hAPP(c_List_Omap(tc_prod(U_17562,U_17565),tc_prod(U_17563,U_17565)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17562,U_17565,tc_prod(U_17563,U_17565)),hAPP(hAPP(c_COMBB(U_17563,tc_fun(U_17565,tc_prod(U_17563,U_17565)),U_17562),c_Product__Type_OPair(U_17563,U_17565)),U_17564))),U_17566)),hAPP(U_17564,U_17567)) = hAPP(c_Option_Ooption_OSome(U_17565),U_17568)
      | hAPP(c_Map_Omap__of(U_17562,U_17565,U_17566),U_17567) != hAPP(c_Option_Ooption_OSome(U_17565),U_17568)
      | ~ c_Fun_Oinj__on(U_17562,U_17563,U_17564,c_Orderings_Otop__class_Otop(tc_fun(U_17562,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4288_1]) ).

fof(f_4288_3,plain,
    ! [U_17563,U_17565,U_17562,U_17564,U_17566,U_17567,U_17568] :
      ( hAPP(c_Map_Omap__of(U_17563,U_17565,hAPP(hAPP(c_List_Omap(tc_prod(U_17562,U_17565),tc_prod(U_17563,U_17565)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17562,U_17565,tc_prod(U_17563,U_17565)),hAPP(hAPP(c_COMBB(U_17563,tc_fun(U_17565,tc_prod(U_17563,U_17565)),U_17562),c_Product__Type_OPair(U_17563,U_17565)),U_17564))),U_17566)),hAPP(U_17564,U_17567)) = hAPP(c_Option_Ooption_OSome(U_17565),U_17568)
      | hAPP(c_Map_Omap__of(U_17562,U_17565,U_17566),U_17567) != hAPP(c_Option_Ooption_OSome(U_17565),U_17568)
      | ~ c_Fun_Oinj__on(U_17562,U_17563,U_17564,c_Orderings_Otop__class_Otop(tc_fun(U_17562,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_4288_2]) ).

cnf(f_4288_4,plain,
    ( hAPP(c_Map_Omap__of(U_17563,U_17565,hAPP(hAPP(c_List_Omap(tc_prod(U_17562,U_17565),tc_prod(U_17563,U_17565)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17562,U_17565,tc_prod(U_17563,U_17565)),hAPP(hAPP(c_COMBB(U_17563,tc_fun(U_17565,tc_prod(U_17563,U_17565)),U_17562),c_Product__Type_OPair(U_17563,U_17565)),U_17564))),U_17566)),hAPP(U_17564,U_17567)) = hAPP(c_Option_Ooption_OSome(U_17565),U_17568)
    | hAPP(c_Map_Omap__of(U_17562,U_17565,U_17566),U_17567) != hAPP(c_Option_Ooption_OSome(U_17565),U_17568)
    | ~ c_Fun_Oinj__on(U_17562,U_17563,U_17564,c_Orderings_Otop__class_Otop(tc_fun(U_17562,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4288_3]) ).

fof(f_4289_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_4289_2,plain,
    ! [U_17574,U_17573,U_17572,U_17571,U_17570,U_17569] : c_Map_Omap__comp(U_17569,U_17570,U_17571,U_17572,U_17573,U_17574) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17570),U_17569,c_Option_Ooption_ONone(U_17570),U_17572),hAPP(U_17573,U_17574)),
    inference(variable_rename,[status(thm)],[f_4289_1]) ).

fof(f_4289_3,plain,
    ! [U_17569,U_17571,U_17570,U_17572,U_17573,U_17574] : c_Map_Omap__comp(U_17569,U_17570,U_17571,U_17572,U_17573,U_17574) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17570),U_17569,c_Option_Ooption_ONone(U_17570),U_17572),hAPP(U_17573,U_17574)),
    inference(definitional_conversion,[status(esa)],[f_4289_2]) ).

cnf(f_4289_4,plain,
    c_Map_Omap__comp(U_17569,U_17570,U_17571,U_17572,U_17573,U_17574) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17570),U_17569,c_Option_Ooption_ONone(U_17570),U_17572),hAPP(U_17573,U_17574)),
    inference(clausify,[status(thm)],[f_4289_3]) ).

fof(f_4290_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_4290_2,plain,
    ! [U_17577,U_17576,U_17575] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_17575),tc_List_Olist(U_17576),hAPP(c_List_Omap(U_17575,U_17576),U_17577),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17575),tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_17575,U_17576,U_17577,c_Orderings_Otop__class_Otop(tc_fun(U_17575,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4290_1]) ).

fof(f_4290_3,plain,
    ! [U_17575,U_17576,U_17577] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_17575),tc_List_Olist(U_17576),hAPP(c_List_Omap(U_17575,U_17576),U_17577),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17575),tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_17575,U_17576,U_17577,c_Orderings_Otop__class_Otop(tc_fun(U_17575,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_4290_2]) ).

cnf(f_4290_4,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_17575),tc_List_Olist(U_17576),hAPP(c_List_Omap(U_17575,U_17576),U_17577),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17575),tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_17575,U_17576,U_17577,c_Orderings_Otop__class_Otop(tc_fun(U_17575,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4290_3]) ).

fof(f_4291_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_4291_2,plain,
    ! [U_17586,U_17585,U_17584,U_17583,U_17582,U_17581,U_17580] :
      ( ( c_Map_Omap__comp(U_17580,U_17581,U_17582,U_17583,U_17584,U_17585) = hAPP(c_Option_Ooption_OSome(U_17581),U_17586)
        | ! [U_17579] :
            ( hAPP(U_17583,U_17579) != hAPP(c_Option_Ooption_OSome(U_17581),U_17586)
            | hAPP(U_17584,U_17585) != hAPP(c_Option_Ooption_OSome(U_17580),U_17579) ) )
      & ( ? [U_17578] :
            ( hAPP(U_17583,U_17578) = hAPP(c_Option_Ooption_OSome(U_17581),U_17586)
            & hAPP(U_17584,U_17585) = hAPP(c_Option_Ooption_OSome(U_17580),U_17578) )
        | c_Map_Omap__comp(U_17580,U_17581,U_17582,U_17583,U_17584,U_17585) != hAPP(c_Option_Ooption_OSome(U_17581),U_17586) ) ),
    inference(variable_rename,[status(thm)],[f_4291_1]) ).

fof(f_4291_3,plain,
    ( ! [U_17600,U_17598,U_17596,U_17594,U_17592,U_17590,U_17588] :
        ( c_Map_Omap__comp(U_17588,U_17590,U_17592,U_17594,U_17596,U_17598) = hAPP(c_Option_Ooption_OSome(U_17590),U_17600)
        | ! [U_17579] :
            ( hAPP(U_17594,U_17579) != hAPP(c_Option_Ooption_OSome(U_17590),U_17600)
            | hAPP(U_17596,U_17598) != hAPP(c_Option_Ooption_OSome(U_17588),U_17579) ) )
    & ! [U_17599,U_17597,U_17595,U_17593,U_17591,U_17589,U_17587] :
        ( ? [U_17578] :
            ( hAPP(U_17593,U_17578) = hAPP(c_Option_Ooption_OSome(U_17589),U_17599)
            & hAPP(U_17595,U_17597) = hAPP(c_Option_Ooption_OSome(U_17587),U_17578) )
        | c_Map_Omap__comp(U_17587,U_17589,U_17591,U_17593,U_17595,U_17597) != hAPP(c_Option_Ooption_OSome(U_17589),U_17599) ) ),
    inference(miniscope,[status(thm)],[f_4291_2]) ).

fof(f_4291_4,plain,
    ( ! [U_17600,U_17598,U_17596,U_17594,U_17592,U_17590,U_17588] :
        ( c_Map_Omap__comp(U_17588,U_17590,U_17592,U_17594,U_17596,U_17598) = hAPP(c_Option_Ooption_OSome(U_17590),U_17600)
        | ! [U_17579] :
            ( hAPP(U_17594,U_17579) != hAPP(c_Option_Ooption_OSome(U_17590),U_17600)
            | hAPP(U_17596,U_17598) != hAPP(c_Option_Ooption_OSome(U_17588),U_17579) ) )
    & ! [U_17599,U_17597,U_17595,U_17593,U_17591,U_17589,U_17587] :
        ( ( hAPP(U_17593,sK452(U_17599,U_17597,U_17595,U_17593,U_17591,U_17589,U_17587)) = hAPP(c_Option_Ooption_OSome(U_17589),U_17599)
          & hAPP(U_17595,U_17597) = hAPP(c_Option_Ooption_OSome(U_17587),sK452(U_17599,U_17597,U_17595,U_17593,U_17591,U_17589,U_17587)) )
        | c_Map_Omap__comp(U_17587,U_17589,U_17591,U_17593,U_17595,U_17597) != hAPP(c_Option_Ooption_OSome(U_17589),U_17599) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK452]),skolemize(U_17578,sK452(U_17599,U_17597,U_17595,U_17593,U_17591,U_17589,U_17587))],[f_4291_3]) ).

fof(f_4291_5,plain,
    ( ! [U_17593,U_17589,U_17591,U_17587,U_17595,U_17599,U_17597] :
        ( hAPP(U_17593,sK452(U_17599,U_17597,U_17595,U_17593,U_17591,U_17589,U_17587)) = hAPP(c_Option_Ooption_OSome(U_17589),U_17599)
        | ~ sP1116(U_17593,U_17589,U_17591,U_17587,U_17595,U_17599,U_17597) )
    & ! [U_17593,U_17589,U_17591,U_17587,U_17595,U_17599,U_17597] :
        ( hAPP(U_17595,U_17597) = hAPP(c_Option_Ooption_OSome(U_17587),sK452(U_17599,U_17597,U_17595,U_17593,U_17591,U_17589,U_17587))
        | ~ sP1116(U_17593,U_17589,U_17591,U_17587,U_17595,U_17599,U_17597) )
    & ! [U_17579,U_17590,U_17592,U_17588,U_17594,U_17596,U_17598,U_17600] :
        ( c_Map_Omap__comp(U_17588,U_17590,U_17592,U_17594,U_17596,U_17598) = hAPP(c_Option_Ooption_OSome(U_17590),U_17600)
        | hAPP(U_17594,U_17579) != hAPP(c_Option_Ooption_OSome(U_17590),U_17600)
        | hAPP(U_17596,U_17598) != hAPP(c_Option_Ooption_OSome(U_17588),U_17579) )
    & ! [U_17593,U_17589,U_17591,U_17587,U_17595,U_17599,U_17597] :
        ( sP1116(U_17593,U_17589,U_17591,U_17587,U_17595,U_17599,U_17597)
        | c_Map_Omap__comp(U_17587,U_17589,U_17591,U_17593,U_17595,U_17597) != hAPP(c_Option_Ooption_OSome(U_17589),U_17599) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1116])],[f_4291_4]) ).

cnf(f_4291_6,plain,
    ( sP1116(U_17593,U_17589,U_17591,U_17587,U_17595,U_17599,U_17597)
    | c_Map_Omap__comp(U_17587,U_17589,U_17591,U_17593,U_17595,U_17597) != hAPP(c_Option_Ooption_OSome(U_17589),U_17599) ),
    inference(clausify,[status(thm)],[f_4291_5]) ).

cnf(f_4291_7,plain,
    ( c_Map_Omap__comp(U_17588,U_17590,U_17592,U_17594,U_17596,U_17598) = hAPP(c_Option_Ooption_OSome(U_17590),U_17600)
    | hAPP(U_17594,U_17579) != hAPP(c_Option_Ooption_OSome(U_17590),U_17600)
    | hAPP(U_17596,U_17598) != hAPP(c_Option_Ooption_OSome(U_17588),U_17579) ),
    inference(clausify,[status(thm)],[f_4291_5]) ).

cnf(f_4291_8,plain,
    ( hAPP(U_17595,U_17597) = hAPP(c_Option_Ooption_OSome(U_17587),sK452(U_17599,U_17597,U_17595,U_17593,U_17591,U_17589,U_17587))
    | ~ sP1116(U_17593,U_17589,U_17591,U_17587,U_17595,U_17599,U_17597) ),
    inference(clausify,[status(thm)],[f_4291_5]) ).

cnf(f_4291_9,plain,
    ( hAPP(U_17593,sK452(U_17599,U_17597,U_17595,U_17593,U_17591,U_17589,U_17587)) = hAPP(c_Option_Ooption_OSome(U_17589),U_17599)
    | ~ sP1116(U_17593,U_17589,U_17591,U_17587,U_17595,U_17599,U_17597) ),
    inference(clausify,[status(thm)],[f_4291_5]) ).

fof(f_4292_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_4292_2,plain,
    ! [U_17607,U_17606,U_17605,U_17604,U_17603,U_17602,U_17601] :
      ( c_Map_Omap__comp(U_17603,U_17605,U_17606,U_17607,U_17601,U_17602) = hAPP(U_17607,U_17604)
      | hAPP(U_17601,U_17602) != hAPP(c_Option_Ooption_OSome(U_17603),U_17604) ),
    inference(variable_rename,[status(thm)],[f_4292_1]) ).

fof(f_4292_3,plain,
    ! [U_17601,U_17603,U_17602,U_17607,U_17606,U_17605,U_17604] :
      ( c_Map_Omap__comp(U_17603,U_17605,U_17606,U_17607,U_17601,U_17602) = hAPP(U_17607,U_17604)
      | hAPP(U_17601,U_17602) != hAPP(c_Option_Ooption_OSome(U_17603),U_17604) ),
    inference(definitional_conversion,[status(esa)],[f_4292_2]) ).

cnf(f_4292_4,plain,
    ( c_Map_Omap__comp(U_17603,U_17605,U_17606,U_17607,U_17601,U_17602) = hAPP(U_17607,U_17604)
    | hAPP(U_17601,U_17602) != hAPP(c_Option_Ooption_OSome(U_17603),U_17604) ),
    inference(clausify,[status(thm)],[f_4292_3]) ).

fof(f_4293_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_4293_2,plain,
    ! [U_17613,U_17612,U_17611,U_17610,U_17609,U_17608] :
      ( c_Map_Omap__comp(U_17610,U_17611,U_17612,U_17613,U_17608,U_17609) = c_Option_Ooption_ONone(U_17611)
      | hAPP(U_17608,U_17609) != c_Option_Ooption_ONone(U_17610) ),
    inference(variable_rename,[status(thm)],[f_4293_1]) ).

fof(f_4293_3,plain,
    ! [U_17608,U_17609,U_17610,U_17611,U_17612,U_17613] :
      ( c_Map_Omap__comp(U_17610,U_17611,U_17612,U_17613,U_17608,U_17609) = c_Option_Ooption_ONone(U_17611)
      | hAPP(U_17608,U_17609) != c_Option_Ooption_ONone(U_17610) ),
    inference(definitional_conversion,[status(esa)],[f_4293_2]) ).

cnf(f_4293_4,plain,
    ( c_Map_Omap__comp(U_17610,U_17611,U_17612,U_17613,U_17608,U_17609) = c_Option_Ooption_ONone(U_17611)
    | hAPP(U_17608,U_17609) != c_Option_Ooption_ONone(U_17610) ),
    inference(clausify,[status(thm)],[f_4293_3]) ).

fof(f_4294_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_4294_2,plain,
    ! [U_17619,U_17618,U_17617,U_17616,U_17615,U_17614] : hAPP(hAPP(c_List_Omap(U_17614,U_17615),U_17616),hAPP(hAPP(c_List_Omap(U_17617,U_17614),U_17618),U_17619)) = hAPP(hAPP(c_List_Omap(U_17617,U_17615),hAPP(c_Fun_Ocomp(U_17614,U_17615,U_17617,U_17616),U_17618)),U_17619),
    inference(variable_rename,[status(thm)],[f_4294_1]) ).

fof(f_4294_3,plain,
    ! [U_17614,U_17615,U_17616,U_17617,U_17618,U_17619] : hAPP(hAPP(c_List_Omap(U_17614,U_17615),U_17616),hAPP(hAPP(c_List_Omap(U_17617,U_17614),U_17618),U_17619)) = hAPP(hAPP(c_List_Omap(U_17617,U_17615),hAPP(c_Fun_Ocomp(U_17614,U_17615,U_17617,U_17616),U_17618)),U_17619),
    inference(definitional_conversion,[status(esa)],[f_4294_2]) ).

cnf(f_4294_4,plain,
    hAPP(hAPP(c_List_Omap(U_17614,U_17615),U_17616),hAPP(hAPP(c_List_Omap(U_17617,U_17614),U_17618),U_17619)) = hAPP(hAPP(c_List_Omap(U_17617,U_17615),hAPP(c_Fun_Ocomp(U_17614,U_17615,U_17617,U_17616),U_17618)),U_17619),
    inference(clausify,[status(thm)],[f_4294_3]) ).

fof(f_4295_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_4295_2,plain,
    ! [U_17625,U_17624,U_17623,U_17622,U_17621,U_17620] : hAPP(hAPP(c_List_Omap(U_17620,U_17621),U_17622),hAPP(hAPP(c_List_Omap(U_17623,U_17620),U_17624),U_17625)) = hAPP(hAPP(c_List_Omap(U_17623,U_17621),hAPP(c_Fun_Ocomp(U_17620,U_17621,U_17623,U_17622),U_17624)),U_17625),
    inference(variable_rename,[status(thm)],[f_4295_1]) ).

fof(f_4295_3,plain,
    ! [U_17620,U_17621,U_17622,U_17623,U_17624,U_17625] : hAPP(hAPP(c_List_Omap(U_17620,U_17621),U_17622),hAPP(hAPP(c_List_Omap(U_17623,U_17620),U_17624),U_17625)) = hAPP(hAPP(c_List_Omap(U_17623,U_17621),hAPP(c_Fun_Ocomp(U_17620,U_17621,U_17623,U_17622),U_17624)),U_17625),
    inference(definitional_conversion,[status(esa)],[f_4295_2]) ).

cnf(f_4295_4,plain,
    hAPP(hAPP(c_List_Omap(U_17620,U_17621),U_17622),hAPP(hAPP(c_List_Omap(U_17623,U_17620),U_17624),U_17625)) = hAPP(hAPP(c_List_Omap(U_17623,U_17621),hAPP(c_Fun_Ocomp(U_17620,U_17621,U_17623,U_17622),U_17624)),U_17625),
    inference(clausify,[status(thm)],[f_4295_3]) ).

fof(f_4296_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_4296_2,plain,
    ! [U_17630,U_17629,U_17628,U_17627,U_17626] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17626),tc_List_Olist(U_17627),tc_List_Olist(U_17628),hAPP(c_List_Omap(U_17626,U_17627),U_17629)),hAPP(c_List_Omap(U_17628,U_17626),U_17630)) = hAPP(c_List_Omap(U_17628,U_17627),hAPP(c_Fun_Ocomp(U_17626,U_17627,U_17628,U_17629),U_17630)),
    inference(variable_rename,[status(thm)],[f_4296_1]) ).

fof(f_4296_3,plain,
    ! [U_17626,U_17627,U_17628,U_17629,U_17630] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17626),tc_List_Olist(U_17627),tc_List_Olist(U_17628),hAPP(c_List_Omap(U_17626,U_17627),U_17629)),hAPP(c_List_Omap(U_17628,U_17626),U_17630)) = hAPP(c_List_Omap(U_17628,U_17627),hAPP(c_Fun_Ocomp(U_17626,U_17627,U_17628,U_17629),U_17630)),
    inference(definitional_conversion,[status(esa)],[f_4296_2]) ).

cnf(f_4296_4,plain,
    hAPP(c_Fun_Ocomp(tc_List_Olist(U_17626),tc_List_Olist(U_17627),tc_List_Olist(U_17628),hAPP(c_List_Omap(U_17626,U_17627),U_17629)),hAPP(c_List_Omap(U_17628,U_17626),U_17630)) = hAPP(c_List_Omap(U_17628,U_17627),hAPP(c_Fun_Ocomp(U_17626,U_17627,U_17628,U_17629),U_17630)),
    inference(clausify,[status(thm)],[f_4296_3]) ).

fof(f_4297_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_4297_2,plain,
    ! [U_17635,U_17634,U_17633,U_17632,U_17631] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17631),tc_List_Olist(U_17632),tc_List_Olist(U_17633),hAPP(c_List_Omap(U_17631,U_17632),U_17634)),hAPP(c_List_Omap(U_17633,U_17631),U_17635)) = hAPP(c_List_Omap(U_17633,U_17632),hAPP(c_Fun_Ocomp(U_17631,U_17632,U_17633,U_17634),U_17635)),
    inference(variable_rename,[status(thm)],[f_4297_1]) ).

fof(f_4297_3,plain,
    ! [U_17631,U_17632,U_17633,U_17634,U_17635] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17631),tc_List_Olist(U_17632),tc_List_Olist(U_17633),hAPP(c_List_Omap(U_17631,U_17632),U_17634)),hAPP(c_List_Omap(U_17633,U_17631),U_17635)) = hAPP(c_List_Omap(U_17633,U_17632),hAPP(c_Fun_Ocomp(U_17631,U_17632,U_17633,U_17634),U_17635)),
    inference(definitional_conversion,[status(esa)],[f_4297_2]) ).

cnf(f_4297_4,plain,
    hAPP(c_Fun_Ocomp(tc_List_Olist(U_17631),tc_List_Olist(U_17632),tc_List_Olist(U_17633),hAPP(c_List_Omap(U_17631,U_17632),U_17634)),hAPP(c_List_Omap(U_17633,U_17631),U_17635)) = hAPP(c_List_Omap(U_17633,U_17632),hAPP(c_Fun_Ocomp(U_17631,U_17632,U_17633,U_17634),U_17635)),
    inference(clausify,[status(thm)],[f_4297_3]) ).

fof(f_4298_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_4298_2,plain,
    ! [U_17640,U_17639,U_17638,U_17637,U_17636] :
      ( U_17639 = U_17640
      | ~ c_Fun_Oinj__on(U_17636,U_17637,U_17638,c_Orderings_Otop__class_Otop(tc_fun(U_17636,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(U_17636,U_17637),U_17638),U_17639) != hAPP(hAPP(c_List_Omap(U_17636,U_17637),U_17638),U_17640) ),
    inference(variable_rename,[status(thm)],[f_4298_1]) ).

fof(f_4298_3,plain,
    ! [U_17636,U_17637,U_17638,U_17639,U_17640] :
      ( U_17639 = U_17640
      | ~ c_Fun_Oinj__on(U_17636,U_17637,U_17638,c_Orderings_Otop__class_Otop(tc_fun(U_17636,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(U_17636,U_17637),U_17638),U_17639) != hAPP(hAPP(c_List_Omap(U_17636,U_17637),U_17638),U_17640) ),
    inference(definitional_conversion,[status(esa)],[f_4298_2]) ).

cnf(f_4298_4,plain,
    ( U_17639 = U_17640
    | ~ c_Fun_Oinj__on(U_17636,U_17637,U_17638,c_Orderings_Otop__class_Otop(tc_fun(U_17636,tc_HOL_Obool)))
    | hAPP(hAPP(c_List_Omap(U_17636,U_17637),U_17638),U_17639) != hAPP(hAPP(c_List_Omap(U_17636,U_17637),U_17638),U_17640) ),
    inference(clausify,[status(thm)],[f_4298_3]) ).

fof(f_4299_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_4299_2,plain,
    ! [U_17643,U_17642,U_17641] :
      ( c_Fun_Oinj__on(U_17641,U_17642,U_17643,c_Orderings_Otop__class_Otop(tc_fun(U_17641,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(tc_List_Olist(U_17641),tc_List_Olist(U_17642),hAPP(c_List_Omap(U_17641,U_17642),U_17643),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17641),tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4299_1]) ).

fof(f_4299_3,plain,
    ! [U_17641,U_17642,U_17643] :
      ( c_Fun_Oinj__on(U_17641,U_17642,U_17643,c_Orderings_Otop__class_Otop(tc_fun(U_17641,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(tc_List_Olist(U_17641),tc_List_Olist(U_17642),hAPP(c_List_Omap(U_17641,U_17642),U_17643),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17641),tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_4299_2]) ).

cnf(f_4299_4,plain,
    ( c_Fun_Oinj__on(U_17641,U_17642,U_17643,c_Orderings_Otop__class_Otop(tc_fun(U_17641,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(tc_List_Olist(U_17641),tc_List_Olist(U_17642),hAPP(c_List_Omap(U_17641,U_17642),U_17643),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17641),tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4299_3]) ).

fof(f_4300_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_4300_2,plain,
    ! [U_17648,U_17647,U_17646,U_17645,U_17644] :
      ( ( ( hAPP(hAPP(c_List_Omap(U_17644,U_17645),U_17646),U_17647) = hAPP(hAPP(c_List_Omap(U_17644,U_17645),U_17646),U_17648)
          | U_17647 != U_17648 )
        & ( U_17647 = U_17648
          | hAPP(hAPP(c_List_Omap(U_17644,U_17645),U_17646),U_17647) != hAPP(hAPP(c_List_Omap(U_17644,U_17645),U_17646),U_17648) ) )
      | ~ c_Fun_Oinj__on(U_17644,U_17645,U_17646,c_Orderings_Otop__class_Otop(tc_fun(U_17644,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4300_1]) ).

fof(f_4300_3,plain,
    ( ! [U_17644,U_17645,U_17646,U_17647,U_17648] :
        ( hAPP(hAPP(c_List_Omap(U_17644,U_17645),U_17646),U_17647) = hAPP(hAPP(c_List_Omap(U_17644,U_17645),U_17646),U_17648)
        | U_17647 != U_17648
        | ~ sP1117(U_17644,U_17645,U_17646,U_17647,U_17648) )
    & ! [U_17644,U_17645,U_17646,U_17647,U_17648] :
        ( U_17647 = U_17648
        | hAPP(hAPP(c_List_Omap(U_17644,U_17645),U_17646),U_17647) != hAPP(hAPP(c_List_Omap(U_17644,U_17645),U_17646),U_17648)
        | ~ sP1117(U_17644,U_17645,U_17646,U_17647,U_17648) )
    & ! [U_17644,U_17645,U_17646,U_17647,U_17648] :
        ( sP1117(U_17644,U_17645,U_17646,U_17647,U_17648)
        | ~ c_Fun_Oinj__on(U_17644,U_17645,U_17646,c_Orderings_Otop__class_Otop(tc_fun(U_17644,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1117])],[f_4300_2]) ).

cnf(f_4300_4,plain,
    ( sP1117(U_17644,U_17645,U_17646,U_17647,U_17648)
    | ~ c_Fun_Oinj__on(U_17644,U_17645,U_17646,c_Orderings_Otop__class_Otop(tc_fun(U_17644,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4300_3]) ).

cnf(f_4300_5,plain,
    ( U_17647 = U_17648
    | hAPP(hAPP(c_List_Omap(U_17644,U_17645),U_17646),U_17647) != hAPP(hAPP(c_List_Omap(U_17644,U_17645),U_17646),U_17648)
    | ~ sP1117(U_17644,U_17645,U_17646,U_17647,U_17648) ),
    inference(clausify,[status(thm)],[f_4300_3]) ).

cnf(f_4300_6,plain,
    ( hAPP(hAPP(c_List_Omap(U_17644,U_17645),U_17646),U_17647) = hAPP(hAPP(c_List_Omap(U_17644,U_17645),U_17646),U_17648)
    | U_17647 != U_17648
    | ~ sP1117(U_17644,U_17645,U_17646,U_17647,U_17648) ),
    inference(clausify,[status(thm)],[f_4300_3]) ).

fof(f_4301_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_4301_2,plain,
    ! [U_17651,U_17650,U_17649] :
      ( ( c_Fun_Oinj__on(tc_List_Olist(U_17649),tc_List_Olist(U_17650),hAPP(c_List_Omap(U_17649,U_17650),U_17651),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17649),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(U_17649,U_17650,U_17651,c_Orderings_Otop__class_Otop(tc_fun(U_17649,tc_HOL_Obool))) )
      & ( c_Fun_Oinj__on(U_17649,U_17650,U_17651,c_Orderings_Otop__class_Otop(tc_fun(U_17649,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(U_17649),tc_List_Olist(U_17650),hAPP(c_List_Omap(U_17649,U_17650),U_17651),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17649),tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_4301_1]) ).

fof(f_4301_3,plain,
    ( ! [U_17657,U_17655,U_17653] :
        ( c_Fun_Oinj__on(tc_List_Olist(U_17653),tc_List_Olist(U_17655),hAPP(c_List_Omap(U_17653,U_17655),U_17657),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17653),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(U_17653,U_17655,U_17657,c_Orderings_Otop__class_Otop(tc_fun(U_17653,tc_HOL_Obool))) )
    & ! [U_17656,U_17654,U_17652] :
        ( c_Fun_Oinj__on(U_17652,U_17654,U_17656,c_Orderings_Otop__class_Otop(tc_fun(U_17652,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(U_17652),tc_List_Olist(U_17654),hAPP(c_List_Omap(U_17652,U_17654),U_17656),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17652),tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_4301_2]) ).

fof(f_4301_4,plain,
    ( ! [U_17655,U_17657,U_17653] :
        ( c_Fun_Oinj__on(tc_List_Olist(U_17653),tc_List_Olist(U_17655),hAPP(c_List_Omap(U_17653,U_17655),U_17657),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17653),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(U_17653,U_17655,U_17657,c_Orderings_Otop__class_Otop(tc_fun(U_17653,tc_HOL_Obool))) )
    & ! [U_17652,U_17654,U_17656] :
        ( c_Fun_Oinj__on(U_17652,U_17654,U_17656,c_Orderings_Otop__class_Otop(tc_fun(U_17652,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(U_17652),tc_List_Olist(U_17654),hAPP(c_List_Omap(U_17652,U_17654),U_17656),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17652),tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4301_3]) ).

cnf(f_4301_5,plain,
    ( c_Fun_Oinj__on(U_17652,U_17654,U_17656,c_Orderings_Otop__class_Otop(tc_fun(U_17652,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(tc_List_Olist(U_17652),tc_List_Olist(U_17654),hAPP(c_List_Omap(U_17652,U_17654),U_17656),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17652),tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4301_4]) ).

cnf(f_4301_6,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_17653),tc_List_Olist(U_17655),hAPP(c_List_Omap(U_17653,U_17655),U_17657),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17653),tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_17653,U_17655,U_17657,c_Orderings_Otop__class_Otop(tc_fun(U_17653,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4301_4]) ).

fof(f_4302_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_4302_2,plain,
    ! [U_17659,U_17658] : hAPP(hAPP(c_List_Omap(U_17658,U_17658),c_COMBI(U_17658)),U_17659) = U_17659,
    inference(variable_rename,[status(thm)],[f_4302_1]) ).

fof(f_4302_3,plain,
    ! [U_17658,U_17659] : hAPP(hAPP(c_List_Omap(U_17658,U_17658),c_COMBI(U_17658)),U_17659) = U_17659,
    inference(definitional_conversion,[status(esa)],[f_4302_2]) ).

cnf(f_4302_4,plain,
    hAPP(hAPP(c_List_Omap(U_17658,U_17658),c_COMBI(U_17658)),U_17659) = U_17659,
    inference(clausify,[status(thm)],[f_4302_3]) ).

fof(f_4303_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_4303_2,plain,
    ! [U_17660] : hAPP(c_List_Omap(U_17660,U_17660),c_COMBI(U_17660)) = c_Fun_Oid(tc_List_Olist(U_17660)),
    inference(variable_rename,[status(thm)],[f_4303_1]) ).

fof(f_4303_3,plain,
    ! [U_17660] : hAPP(c_List_Omap(U_17660,U_17660),c_COMBI(U_17660)) = c_Fun_Oid(tc_List_Olist(U_17660)),
    inference(definitional_conversion,[status(esa)],[f_4303_2]) ).

cnf(f_4303_4,plain,
    hAPP(c_List_Omap(U_17660,U_17660),c_COMBI(U_17660)) = c_Fun_Oid(tc_List_Olist(U_17660)),
    inference(clausify,[status(thm)],[f_4303_3]) ).

fof(f_4304_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_4304_2,plain,
    ! [U_17661] : hAPP(c_List_Omap(U_17661,U_17661),c_Fun_Oid(U_17661)) = c_Fun_Oid(tc_List_Olist(U_17661)),
    inference(variable_rename,[status(thm)],[f_4304_1]) ).

fof(f_4304_3,plain,
    ! [U_17661] : hAPP(c_List_Omap(U_17661,U_17661),c_Fun_Oid(U_17661)) = c_Fun_Oid(tc_List_Olist(U_17661)),
    inference(definitional_conversion,[status(esa)],[f_4304_2]) ).

cnf(f_4304_4,plain,
    hAPP(c_List_Omap(U_17661,U_17661),c_Fun_Oid(U_17661)) = c_Fun_Oid(tc_List_Olist(U_17661)),
    inference(clausify,[status(thm)],[f_4304_3]) ).

fof(f_4305_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_4305_2,plain,
    ! [U_17668,U_17667,U_17666,U_17665,U_17664,U_17663,U_17662] : c_List_Ofoldr(U_17662,U_17663,U_17664,hAPP(hAPP(c_List_Omap(U_17665,U_17662),U_17666),U_17667),U_17668) = c_List_Ofoldr(U_17665,U_17663,hAPP(c_Fun_Ocomp(U_17662,tc_fun(U_17663,U_17663),U_17665,U_17664),U_17666),U_17667,U_17668),
    inference(variable_rename,[status(thm)],[f_4305_1]) ).

fof(f_4305_3,plain,
    ! [U_17662,U_17663,U_17664,U_17665,U_17666,U_17667,U_17668] : c_List_Ofoldr(U_17662,U_17663,U_17664,hAPP(hAPP(c_List_Omap(U_17665,U_17662),U_17666),U_17667),U_17668) = c_List_Ofoldr(U_17665,U_17663,hAPP(c_Fun_Ocomp(U_17662,tc_fun(U_17663,U_17663),U_17665,U_17664),U_17666),U_17667,U_17668),
    inference(definitional_conversion,[status(esa)],[f_4305_2]) ).

cnf(f_4305_4,plain,
    c_List_Ofoldr(U_17662,U_17663,U_17664,hAPP(hAPP(c_List_Omap(U_17665,U_17662),U_17666),U_17667),U_17668) = c_List_Ofoldr(U_17665,U_17663,hAPP(c_Fun_Ocomp(U_17662,tc_fun(U_17663,U_17663),U_17665,U_17664),U_17666),U_17667,U_17668),
    inference(clausify,[status(thm)],[f_4305_3]) ).

fof(f_4306_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_4306_2,plain,
    ! [U_17673,U_17672,U_17671,U_17670,U_17669] : c_Map_Omap__comp(U_17669,U_17670,U_17671,U_17672,hAPP(c_COMBK(tc_Option_Ooption(U_17669),U_17671),c_Option_Ooption_ONone(U_17669)),U_17673) = c_Option_Ooption_ONone(U_17670),
    inference(variable_rename,[status(thm)],[f_4306_1]) ).

fof(f_4306_3,plain,
    ! [U_17671,U_17670,U_17669,U_17672,U_17673] : c_Map_Omap__comp(U_17669,U_17670,U_17671,U_17672,hAPP(c_COMBK(tc_Option_Ooption(U_17669),U_17671),c_Option_Ooption_ONone(U_17669)),U_17673) = c_Option_Ooption_ONone(U_17670),
    inference(definitional_conversion,[status(esa)],[f_4306_2]) ).

cnf(f_4306_4,plain,
    c_Map_Omap__comp(U_17669,U_17670,U_17671,U_17672,hAPP(c_COMBK(tc_Option_Ooption(U_17669),U_17671),c_Option_Ooption_ONone(U_17669)),U_17673) = c_Option_Ooption_ONone(U_17670),
    inference(clausify,[status(thm)],[f_4306_3]) ).

fof(f_4307_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_4307_2,plain,
    ! [U_17678,U_17677,U_17676,U_17675,U_17674] : c_Map_Omap__comp(U_17674,U_17675,U_17676,hAPP(c_COMBK(tc_Option_Ooption(U_17675),U_17674),c_Option_Ooption_ONone(U_17675)),U_17677,U_17678) = c_Option_Ooption_ONone(U_17675),
    inference(variable_rename,[status(thm)],[f_4307_1]) ).

fof(f_4307_3,plain,
    ! [U_17674,U_17675,U_17676,U_17677,U_17678] : c_Map_Omap__comp(U_17674,U_17675,U_17676,hAPP(c_COMBK(tc_Option_Ooption(U_17675),U_17674),c_Option_Ooption_ONone(U_17675)),U_17677,U_17678) = c_Option_Ooption_ONone(U_17675),
    inference(definitional_conversion,[status(esa)],[f_4307_2]) ).

cnf(f_4307_4,plain,
    c_Map_Omap__comp(U_17674,U_17675,U_17676,hAPP(c_COMBK(tc_Option_Ooption(U_17675),U_17674),c_Option_Ooption_ONone(U_17675)),U_17677,U_17678) = c_Option_Ooption_ONone(U_17675),
    inference(clausify,[status(thm)],[f_4307_3]) ).

fof(f_4308_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_4308_2,plain,
    ! [U_17686,U_17685,U_17684,U_17683,U_17682,U_17681] :
      ( ( c_Map_Omap__comp(U_17681,U_17682,U_17683,U_17684,U_17685,U_17686) = c_Option_Ooption_ONone(U_17682)
        | ( ! [U_17680] :
              ( hAPP(U_17684,U_17680) != c_Option_Ooption_ONone(U_17682)
              | hAPP(U_17685,U_17686) != hAPP(c_Option_Ooption_OSome(U_17681),U_17680) )
          & hAPP(U_17685,U_17686) != c_Option_Ooption_ONone(U_17681) ) )
      & ( ? [U_17679] :
            ( hAPP(U_17684,U_17679) = c_Option_Ooption_ONone(U_17682)
            & hAPP(U_17685,U_17686) = hAPP(c_Option_Ooption_OSome(U_17681),U_17679) )
        | hAPP(U_17685,U_17686) = c_Option_Ooption_ONone(U_17681)
        | c_Map_Omap__comp(U_17681,U_17682,U_17683,U_17684,U_17685,U_17686) != c_Option_Ooption_ONone(U_17682) ) ),
    inference(variable_rename,[status(thm)],[f_4308_1]) ).

fof(f_4308_3,plain,
    ( ! [U_17698,U_17696,U_17694,U_17692,U_17690,U_17688] :
        ( c_Map_Omap__comp(U_17688,U_17690,U_17692,U_17694,U_17696,U_17698) = c_Option_Ooption_ONone(U_17690)
        | ( ! [U_17680] :
              ( hAPP(U_17694,U_17680) != c_Option_Ooption_ONone(U_17690)
              | hAPP(U_17696,U_17698) != hAPP(c_Option_Ooption_OSome(U_17688),U_17680) )
          & hAPP(U_17696,U_17698) != c_Option_Ooption_ONone(U_17688) ) )
    & ! [U_17697,U_17695,U_17693,U_17691,U_17689,U_17687] :
        ( ? [U_17679] :
            ( hAPP(U_17693,U_17679) = c_Option_Ooption_ONone(U_17689)
            & hAPP(U_17695,U_17697) = hAPP(c_Option_Ooption_OSome(U_17687),U_17679) )
        | hAPP(U_17695,U_17697) = c_Option_Ooption_ONone(U_17687)
        | c_Map_Omap__comp(U_17687,U_17689,U_17691,U_17693,U_17695,U_17697) != c_Option_Ooption_ONone(U_17689) ) ),
    inference(miniscope,[status(thm)],[f_4308_2]) ).

fof(f_4308_4,plain,
    ( ! [U_17698,U_17696,U_17694,U_17692,U_17690,U_17688] :
        ( c_Map_Omap__comp(U_17688,U_17690,U_17692,U_17694,U_17696,U_17698) = c_Option_Ooption_ONone(U_17690)
        | ( ! [U_17680] :
              ( hAPP(U_17694,U_17680) != c_Option_Ooption_ONone(U_17690)
              | hAPP(U_17696,U_17698) != hAPP(c_Option_Ooption_OSome(U_17688),U_17680) )
          & hAPP(U_17696,U_17698) != c_Option_Ooption_ONone(U_17688) ) )
    & ! [U_17697,U_17695,U_17693,U_17691,U_17689,U_17687] :
        ( ( hAPP(U_17693,sK453(U_17697,U_17695,U_17693,U_17691,U_17689,U_17687)) = c_Option_Ooption_ONone(U_17689)
          & hAPP(U_17695,U_17697) = hAPP(c_Option_Ooption_OSome(U_17687),sK453(U_17697,U_17695,U_17693,U_17691,U_17689,U_17687)) )
        | hAPP(U_17695,U_17697) = c_Option_Ooption_ONone(U_17687)
        | c_Map_Omap__comp(U_17687,U_17689,U_17691,U_17693,U_17695,U_17697) != c_Option_Ooption_ONone(U_17689) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK453]),skolemize(U_17679,sK453(U_17697,U_17695,U_17693,U_17691,U_17689,U_17687))],[f_4308_3]) ).

fof(f_4308_5,plain,
    ( ! [U_17680,U_17690,U_17694,U_17688,U_17698,U_17696] :
        ( hAPP(U_17694,U_17680) != c_Option_Ooption_ONone(U_17690)
        | hAPP(U_17696,U_17698) != hAPP(c_Option_Ooption_OSome(U_17688),U_17680)
        | ~ sP1119(U_17680,U_17690,U_17694,U_17688,U_17698,U_17696) )
    & ! [U_17680,U_17690,U_17694,U_17688,U_17698,U_17696] :
        ( hAPP(U_17696,U_17698) != c_Option_Ooption_ONone(U_17688)
        | ~ sP1119(U_17680,U_17690,U_17694,U_17688,U_17698,U_17696) )
    & ! [U_17689,U_17695,U_17691,U_17687,U_17693,U_17697] :
        ( hAPP(U_17693,sK453(U_17697,U_17695,U_17693,U_17691,U_17689,U_17687)) = c_Option_Ooption_ONone(U_17689)
        | ~ sP1118(U_17689,U_17695,U_17691,U_17687,U_17693,U_17697) )
    & ! [U_17689,U_17695,U_17691,U_17687,U_17693,U_17697] :
        ( hAPP(U_17695,U_17697) = hAPP(c_Option_Ooption_OSome(U_17687),sK453(U_17697,U_17695,U_17693,U_17691,U_17689,U_17687))
        | ~ sP1118(U_17689,U_17695,U_17691,U_17687,U_17693,U_17697) )
    & ! [U_17680,U_17690,U_17694,U_17692,U_17688,U_17698,U_17696] :
        ( c_Map_Omap__comp(U_17688,U_17690,U_17692,U_17694,U_17696,U_17698) = c_Option_Ooption_ONone(U_17690)
        | sP1119(U_17680,U_17690,U_17694,U_17688,U_17698,U_17696) )
    & ! [U_17689,U_17695,U_17691,U_17687,U_17693,U_17697] :
        ( sP1118(U_17689,U_17695,U_17691,U_17687,U_17693,U_17697)
        | hAPP(U_17695,U_17697) = c_Option_Ooption_ONone(U_17687)
        | c_Map_Omap__comp(U_17687,U_17689,U_17691,U_17693,U_17695,U_17697) != c_Option_Ooption_ONone(U_17689) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1118,sP1119])],[f_4308_4]) ).

cnf(f_4308_6,plain,
    ( sP1118(U_17689,U_17695,U_17691,U_17687,U_17693,U_17697)
    | hAPP(U_17695,U_17697) = c_Option_Ooption_ONone(U_17687)
    | c_Map_Omap__comp(U_17687,U_17689,U_17691,U_17693,U_17695,U_17697) != c_Option_Ooption_ONone(U_17689) ),
    inference(clausify,[status(thm)],[f_4308_5]) ).

cnf(f_4308_7,plain,
    ( c_Map_Omap__comp(U_17688,U_17690,U_17692,U_17694,U_17696,U_17698) = c_Option_Ooption_ONone(U_17690)
    | sP1119(U_17680,U_17690,U_17694,U_17688,U_17698,U_17696) ),
    inference(clausify,[status(thm)],[f_4308_5]) ).

cnf(f_4308_8,plain,
    ( hAPP(U_17695,U_17697) = hAPP(c_Option_Ooption_OSome(U_17687),sK453(U_17697,U_17695,U_17693,U_17691,U_17689,U_17687))
    | ~ sP1118(U_17689,U_17695,U_17691,U_17687,U_17693,U_17697) ),
    inference(clausify,[status(thm)],[f_4308_5]) ).

cnf(f_4308_9,plain,
    ( hAPP(U_17693,sK453(U_17697,U_17695,U_17693,U_17691,U_17689,U_17687)) = c_Option_Ooption_ONone(U_17689)
    | ~ sP1118(U_17689,U_17695,U_17691,U_17687,U_17693,U_17697) ),
    inference(clausify,[status(thm)],[f_4308_5]) ).

cnf(f_4308_10,plain,
    ( hAPP(U_17696,U_17698) != c_Option_Ooption_ONone(U_17688)
    | ~ sP1119(U_17680,U_17690,U_17694,U_17688,U_17698,U_17696) ),
    inference(clausify,[status(thm)],[f_4308_5]) ).

cnf(f_4308_11,plain,
    ( hAPP(U_17694,U_17680) != c_Option_Ooption_ONone(U_17690)
    | hAPP(U_17696,U_17698) != hAPP(c_Option_Ooption_OSome(U_17688),U_17680)
    | ~ sP1119(U_17680,U_17690,U_17694,U_17688,U_17698,U_17696) ),
    inference(clausify,[status(thm)],[f_4308_5]) ).

fof(f_4309_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_4309_2,plain,
    ! [U_17703,U_17702,U_17701,U_17700,U_17699] : c_Map_Omap__of(U_17699,U_17700,hAPP(hAPP(c_List_Omap(tc_prod(U_17699,U_17701),tc_prod(U_17699,U_17700)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17699,U_17701,tc_prod(U_17699,U_17700)),hAPP(hAPP(c_COMBC(U_17699,tc_fun(U_17701,U_17700),tc_fun(U_17701,tc_prod(U_17699,U_17700))),hAPP(hAPP(c_COMBB(tc_fun(U_17700,tc_prod(U_17699,U_17700)),tc_fun(tc_fun(U_17701,U_17700),tc_fun(U_17701,tc_prod(U_17699,U_17700))),U_17699),c_COMBB(U_17700,tc_prod(U_17699,U_17700),U_17701)),c_Product__Type_OPair(U_17699,U_17700))),U_17702))),U_17703)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17701),tc_Option_Ooption(U_17700),U_17699,hAPP(c_Option_Omap(U_17701,U_17700),U_17702)),c_Map_Omap__of(U_17699,U_17701,U_17703)),
    inference(variable_rename,[status(thm)],[f_4309_1]) ).

fof(f_4309_3,plain,
    ! [U_17700,U_17699,U_17701,U_17702,U_17703] : c_Map_Omap__of(U_17699,U_17700,hAPP(hAPP(c_List_Omap(tc_prod(U_17699,U_17701),tc_prod(U_17699,U_17700)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17699,U_17701,tc_prod(U_17699,U_17700)),hAPP(hAPP(c_COMBC(U_17699,tc_fun(U_17701,U_17700),tc_fun(U_17701,tc_prod(U_17699,U_17700))),hAPP(hAPP(c_COMBB(tc_fun(U_17700,tc_prod(U_17699,U_17700)),tc_fun(tc_fun(U_17701,U_17700),tc_fun(U_17701,tc_prod(U_17699,U_17700))),U_17699),c_COMBB(U_17700,tc_prod(U_17699,U_17700),U_17701)),c_Product__Type_OPair(U_17699,U_17700))),U_17702))),U_17703)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17701),tc_Option_Ooption(U_17700),U_17699,hAPP(c_Option_Omap(U_17701,U_17700),U_17702)),c_Map_Omap__of(U_17699,U_17701,U_17703)),
    inference(definitional_conversion,[status(esa)],[f_4309_2]) ).

cnf(f_4309_4,plain,
    c_Map_Omap__of(U_17699,U_17700,hAPP(hAPP(c_List_Omap(tc_prod(U_17699,U_17701),tc_prod(U_17699,U_17700)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17699,U_17701,tc_prod(U_17699,U_17700)),hAPP(hAPP(c_COMBC(U_17699,tc_fun(U_17701,U_17700),tc_fun(U_17701,tc_prod(U_17699,U_17700))),hAPP(hAPP(c_COMBB(tc_fun(U_17700,tc_prod(U_17699,U_17700)),tc_fun(tc_fun(U_17701,U_17700),tc_fun(U_17701,tc_prod(U_17699,U_17700))),U_17699),c_COMBB(U_17700,tc_prod(U_17699,U_17700),U_17701)),c_Product__Type_OPair(U_17699,U_17700))),U_17702))),U_17703)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17701),tc_Option_Ooption(U_17700),U_17699,hAPP(c_Option_Omap(U_17701,U_17700),U_17702)),c_Map_Omap__of(U_17699,U_17701,U_17703)),
    inference(clausify,[status(thm)],[f_4309_3]) ).

fof(f_4310_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_4310_2,plain,
    ! [U_17707,U_17706,U_17705,U_17704] :
      ( c_Map_Omap__of(U_17704,U_17706,hAPP(hAPP(c_List_Omap(U_17704,tc_prod(U_17704,U_17706)),hAPP(hAPP(c_COMBS(U_17704,U_17706,tc_prod(U_17704,U_17706)),c_Product__Type_OPair(U_17704,U_17706)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17706),U_17706,U_17704),c_Option_Othe(U_17706)),U_17707))),U_17705)) = U_17707
      | hAPP(c_List_Oset(U_17704),U_17705) != c_Map_Odom(U_17704,U_17706,U_17707) ),
    inference(variable_rename,[status(thm)],[f_4310_1]) ).

fof(f_4310_3,plain,
    ! [U_17704,U_17705,U_17706,U_17707] :
      ( c_Map_Omap__of(U_17704,U_17706,hAPP(hAPP(c_List_Omap(U_17704,tc_prod(U_17704,U_17706)),hAPP(hAPP(c_COMBS(U_17704,U_17706,tc_prod(U_17704,U_17706)),c_Product__Type_OPair(U_17704,U_17706)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17706),U_17706,U_17704),c_Option_Othe(U_17706)),U_17707))),U_17705)) = U_17707
      | hAPP(c_List_Oset(U_17704),U_17705) != c_Map_Odom(U_17704,U_17706,U_17707) ),
    inference(definitional_conversion,[status(esa)],[f_4310_2]) ).

cnf(f_4310_4,plain,
    ( c_Map_Omap__of(U_17704,U_17706,hAPP(hAPP(c_List_Omap(U_17704,tc_prod(U_17704,U_17706)),hAPP(hAPP(c_COMBS(U_17704,U_17706,tc_prod(U_17704,U_17706)),c_Product__Type_OPair(U_17704,U_17706)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17706),U_17706,U_17704),c_Option_Othe(U_17706)),U_17707))),U_17705)) = U_17707
    | hAPP(c_List_Oset(U_17704),U_17705) != c_Map_Odom(U_17704,U_17706,U_17707) ),
    inference(clausify,[status(thm)],[f_4310_3]) ).

fof(f_4311_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_4311_2,plain,
    ! [U_17709,U_17708] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_17708),hAPP(c_List_Oset(U_17708),U_17709))),
    inference(variable_rename,[status(thm)],[f_4311_1]) ).

fof(f_4311_3,plain,
    ! [U_17708,U_17709] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_17708),hAPP(c_List_Oset(U_17708),U_17709))),
    inference(definitional_conversion,[status(esa)],[f_4311_2]) ).

cnf(f_4311_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_17708),hAPP(c_List_Oset(U_17708),U_17709))),
    inference(clausify,[status(thm)],[f_4311_3]) ).

fof(f_4312_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_4312_2,plain,
    ! [U_17713,U_17712,U_17711,U_17710] : hAPP(c_List_Oset(U_17710),hAPP(hAPP(c_List_Omap(U_17711,U_17710),U_17712),U_17713)) = hAPP(c_Set_Oimage(U_17711,U_17710,U_17712),hAPP(c_List_Oset(U_17711),U_17713)),
    inference(variable_rename,[status(thm)],[f_4312_1]) ).

fof(f_4312_3,plain,
    ! [U_17710,U_17711,U_17712,U_17713] : hAPP(c_List_Oset(U_17710),hAPP(hAPP(c_List_Omap(U_17711,U_17710),U_17712),U_17713)) = hAPP(c_Set_Oimage(U_17711,U_17710,U_17712),hAPP(c_List_Oset(U_17711),U_17713)),
    inference(definitional_conversion,[status(esa)],[f_4312_2]) ).

cnf(f_4312_4,plain,
    hAPP(c_List_Oset(U_17710),hAPP(hAPP(c_List_Omap(U_17711,U_17710),U_17712),U_17713)) = hAPP(c_Set_Oimage(U_17711,U_17710,U_17712),hAPP(c_List_Oset(U_17711),U_17713)),
    inference(clausify,[status(thm)],[f_4312_3]) ).

fof(f_4313_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_4313_2,plain,
    ! [U_17720,U_17719,U_17718,U_17717,U_17716] :
      ( ( hAPP(hAPP(c_List_Omap(U_17716,U_17717),U_17718),U_17719) = hAPP(hAPP(c_List_Omap(U_17716,U_17717),U_17720),U_17719)
        | ? [U_17715] :
            ( hAPP(U_17718,U_17715) != hAPP(U_17720,U_17715)
            & hBOOL(hAPP(hAPP(c_member(U_17716),U_17715),hAPP(c_List_Oset(U_17716),U_17719))) ) )
      & ( ! [U_17714] :
            ( hAPP(U_17718,U_17714) = hAPP(U_17720,U_17714)
            | ~ hBOOL(hAPP(hAPP(c_member(U_17716),U_17714),hAPP(c_List_Oset(U_17716),U_17719))) )
        | hAPP(hAPP(c_List_Omap(U_17716,U_17717),U_17718),U_17719) != hAPP(hAPP(c_List_Omap(U_17716,U_17717),U_17720),U_17719) ) ),
    inference(variable_rename,[status(thm)],[f_4313_1]) ).

fof(f_4313_3,plain,
    ( ! [U_17730,U_17728,U_17726,U_17724,U_17722] :
        ( hAPP(hAPP(c_List_Omap(U_17722,U_17724),U_17726),U_17728) = hAPP(hAPP(c_List_Omap(U_17722,U_17724),U_17730),U_17728)
        | ? [U_17715] :
            ( hAPP(U_17726,U_17715) != hAPP(U_17730,U_17715)
            & hBOOL(hAPP(hAPP(c_member(U_17722),U_17715),hAPP(c_List_Oset(U_17722),U_17728))) ) )
    & ! [U_17729,U_17727,U_17725,U_17723,U_17721] :
        ( ! [U_17714] :
            ( hAPP(U_17725,U_17714) = hAPP(U_17729,U_17714)
            | ~ hBOOL(hAPP(hAPP(c_member(U_17721),U_17714),hAPP(c_List_Oset(U_17721),U_17727))) )
        | hAPP(hAPP(c_List_Omap(U_17721,U_17723),U_17725),U_17727) != hAPP(hAPP(c_List_Omap(U_17721,U_17723),U_17729),U_17727) ) ),
    inference(miniscope,[status(thm)],[f_4313_2]) ).

fof(f_4313_4,plain,
    ( ! [U_17730,U_17728,U_17726,U_17724,U_17722] :
        ( hAPP(hAPP(c_List_Omap(U_17722,U_17724),U_17726),U_17728) = hAPP(hAPP(c_List_Omap(U_17722,U_17724),U_17730),U_17728)
        | ( hAPP(U_17726,sK454(U_17730,U_17728,U_17726,U_17724,U_17722)) != hAPP(U_17730,sK454(U_17730,U_17728,U_17726,U_17724,U_17722))
          & hBOOL(hAPP(hAPP(c_member(U_17722),sK454(U_17730,U_17728,U_17726,U_17724,U_17722)),hAPP(c_List_Oset(U_17722),U_17728))) ) )
    & ! [U_17729,U_17727,U_17725,U_17723,U_17721] :
        ( ! [U_17714] :
            ( hAPP(U_17725,U_17714) = hAPP(U_17729,U_17714)
            | ~ hBOOL(hAPP(hAPP(c_member(U_17721),U_17714),hAPP(c_List_Oset(U_17721),U_17727))) )
        | hAPP(hAPP(c_List_Omap(U_17721,U_17723),U_17725),U_17727) != hAPP(hAPP(c_List_Omap(U_17721,U_17723),U_17729),U_17727) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK454]),skolemize(U_17715,sK454(U_17730,U_17728,U_17726,U_17724,U_17722))],[f_4313_3]) ).

fof(f_4313_5,plain,
    ( ! [U_17722,U_17724,U_17728,U_17726,U_17730] :
        ( hAPP(U_17726,sK454(U_17730,U_17728,U_17726,U_17724,U_17722)) != hAPP(U_17730,sK454(U_17730,U_17728,U_17726,U_17724,U_17722))
        | ~ sP1120(U_17722,U_17724,U_17728,U_17726,U_17730) )
    & ! [U_17722,U_17724,U_17728,U_17726,U_17730] :
        ( hBOOL(hAPP(hAPP(c_member(U_17722),sK454(U_17730,U_17728,U_17726,U_17724,U_17722)),hAPP(c_List_Oset(U_17722),U_17728)))
        | ~ sP1120(U_17722,U_17724,U_17728,U_17726,U_17730) )
    & ! [U_17722,U_17724,U_17728,U_17726,U_17730] :
        ( hAPP(hAPP(c_List_Omap(U_17722,U_17724),U_17726),U_17728) = hAPP(hAPP(c_List_Omap(U_17722,U_17724),U_17730),U_17728)
        | sP1120(U_17722,U_17724,U_17728,U_17726,U_17730) )
    & ! [U_17723,U_17714,U_17727,U_17721,U_17725,U_17729] :
        ( hAPP(U_17725,U_17714) = hAPP(U_17729,U_17714)
        | ~ hBOOL(hAPP(hAPP(c_member(U_17721),U_17714),hAPP(c_List_Oset(U_17721),U_17727)))
        | hAPP(hAPP(c_List_Omap(U_17721,U_17723),U_17725),U_17727) != hAPP(hAPP(c_List_Omap(U_17721,U_17723),U_17729),U_17727) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1120])],[f_4313_4]) ).

cnf(f_4313_6,plain,
    ( hAPP(U_17725,U_17714) = hAPP(U_17729,U_17714)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17721),U_17714),hAPP(c_List_Oset(U_17721),U_17727)))
    | hAPP(hAPP(c_List_Omap(U_17721,U_17723),U_17725),U_17727) != hAPP(hAPP(c_List_Omap(U_17721,U_17723),U_17729),U_17727) ),
    inference(clausify,[status(thm)],[f_4313_5]) ).

cnf(f_4313_7,plain,
    ( hAPP(hAPP(c_List_Omap(U_17722,U_17724),U_17726),U_17728) = hAPP(hAPP(c_List_Omap(U_17722,U_17724),U_17730),U_17728)
    | sP1120(U_17722,U_17724,U_17728,U_17726,U_17730) ),
    inference(clausify,[status(thm)],[f_4313_5]) ).

cnf(f_4313_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17722),sK454(U_17730,U_17728,U_17726,U_17724,U_17722)),hAPP(c_List_Oset(U_17722),U_17728)))
    | ~ sP1120(U_17722,U_17724,U_17728,U_17726,U_17730) ),
    inference(clausify,[status(thm)],[f_4313_5]) ).

cnf(f_4313_9,plain,
    ( hAPP(U_17726,sK454(U_17730,U_17728,U_17726,U_17724,U_17722)) != hAPP(U_17730,sK454(U_17730,U_17728,U_17726,U_17724,U_17722))
    | ~ sP1120(U_17722,U_17724,U_17728,U_17726,U_17730) ),
    inference(clausify,[status(thm)],[f_4313_5]) ).

fof(f_4314_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_4314_2,plain,
    ! [U_17731] : hAPP(c_Option_Omap(U_17731,U_17731),c_COMBI(U_17731)) = c_Fun_Oid(tc_Option_Ooption(U_17731)),
    inference(variable_rename,[status(thm)],[f_4314_1]) ).

fof(f_4314_3,plain,
    ! [U_17731] : hAPP(c_Option_Omap(U_17731,U_17731),c_COMBI(U_17731)) = c_Fun_Oid(tc_Option_Ooption(U_17731)),
    inference(definitional_conversion,[status(esa)],[f_4314_2]) ).

cnf(f_4314_4,plain,
    hAPP(c_Option_Omap(U_17731,U_17731),c_COMBI(U_17731)) = c_Fun_Oid(tc_Option_Ooption(U_17731)),
    inference(clausify,[status(thm)],[f_4314_3]) ).

fof(f_4315_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_4315_2,plain,
    ! [U_17732] : hAPP(c_Option_Omap(U_17732,U_17732),c_Fun_Oid(U_17732)) = c_Fun_Oid(tc_Option_Ooption(U_17732)),
    inference(variable_rename,[status(thm)],[f_4315_1]) ).

fof(f_4315_3,plain,
    ! [U_17732] : hAPP(c_Option_Omap(U_17732,U_17732),c_Fun_Oid(U_17732)) = c_Fun_Oid(tc_Option_Ooption(U_17732)),
    inference(definitional_conversion,[status(esa)],[f_4315_2]) ).

cnf(f_4315_4,plain,
    hAPP(c_Option_Omap(U_17732,U_17732),c_Fun_Oid(U_17732)) = c_Fun_Oid(tc_Option_Ooption(U_17732)),
    inference(clausify,[status(thm)],[f_4315_3]) ).

fof(f_4316_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_4316_2,plain,
    ! [U_17737,U_17736,U_17735,U_17734,U_17733] : c_Map_Odom(U_17733,U_17734,hAPP(hAPP(c_COMBS(U_17733,tc_Option_Ooption(U_17735),tc_Option_Ooption(U_17734)),hAPP(hAPP(c_COMBB(tc_fun(U_17735,U_17734),tc_fun(tc_Option_Ooption(U_17735),tc_Option_Ooption(U_17734)),U_17733),c_Option_Omap(U_17735,U_17734)),U_17736)),U_17737)) = c_Map_Odom(U_17733,U_17735,U_17737),
    inference(variable_rename,[status(thm)],[f_4316_1]) ).

fof(f_4316_3,plain,
    ! [U_17733,U_17734,U_17735,U_17736,U_17737] : c_Map_Odom(U_17733,U_17734,hAPP(hAPP(c_COMBS(U_17733,tc_Option_Ooption(U_17735),tc_Option_Ooption(U_17734)),hAPP(hAPP(c_COMBB(tc_fun(U_17735,U_17734),tc_fun(tc_Option_Ooption(U_17735),tc_Option_Ooption(U_17734)),U_17733),c_Option_Omap(U_17735,U_17734)),U_17736)),U_17737)) = c_Map_Odom(U_17733,U_17735,U_17737),
    inference(definitional_conversion,[status(esa)],[f_4316_2]) ).

cnf(f_4316_4,plain,
    c_Map_Odom(U_17733,U_17734,hAPP(hAPP(c_COMBS(U_17733,tc_Option_Ooption(U_17735),tc_Option_Ooption(U_17734)),hAPP(hAPP(c_COMBB(tc_fun(U_17735,U_17734),tc_fun(tc_Option_Ooption(U_17735),tc_Option_Ooption(U_17734)),U_17733),c_Option_Omap(U_17735,U_17734)),U_17736)),U_17737)) = c_Map_Odom(U_17733,U_17735,U_17737),
    inference(clausify,[status(thm)],[f_4316_3]) ).

fof(f_4317_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_4317_2,plain,
    ! [U_17738] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17738)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17738),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_4317_1]) ).

fof(f_4317_3,plain,
    ! [U_17738] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17738)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17738),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_4317_2]) ).

cnf(f_4317_4,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17738)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17738),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_4317_3]) ).

fof(f_4318_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_4318_2,plain,
    ! [U_17743,U_17742,U_17741,U_17740,U_17739] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17739),tc_Option_Ooption(U_17740),tc_Option_Ooption(U_17741),hAPP(c_Option_Omap(U_17739,U_17740),U_17742)),hAPP(c_Option_Omap(U_17741,U_17739),U_17743)) = hAPP(c_Option_Omap(U_17741,U_17740),hAPP(c_Fun_Ocomp(U_17739,U_17740,U_17741,U_17742),U_17743)),
    inference(variable_rename,[status(thm)],[f_4318_1]) ).

fof(f_4318_3,plain,
    ! [U_17739,U_17740,U_17741,U_17742,U_17743] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17739),tc_Option_Ooption(U_17740),tc_Option_Ooption(U_17741),hAPP(c_Option_Omap(U_17739,U_17740),U_17742)),hAPP(c_Option_Omap(U_17741,U_17739),U_17743)) = hAPP(c_Option_Omap(U_17741,U_17740),hAPP(c_Fun_Ocomp(U_17739,U_17740,U_17741,U_17742),U_17743)),
    inference(definitional_conversion,[status(esa)],[f_4318_2]) ).

cnf(f_4318_4,plain,
    hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17739),tc_Option_Ooption(U_17740),tc_Option_Ooption(U_17741),hAPP(c_Option_Omap(U_17739,U_17740),U_17742)),hAPP(c_Option_Omap(U_17741,U_17739),U_17743)) = hAPP(c_Option_Omap(U_17741,U_17740),hAPP(c_Fun_Ocomp(U_17739,U_17740,U_17741,U_17742),U_17743)),
    inference(clausify,[status(thm)],[f_4318_3]) ).

fof(f_4319_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_4319_2,plain,
    ! [U_17749,U_17748,U_17747,U_17746,U_17745,U_17744] : hAPP(hAPP(c_Option_Omap(U_17744,U_17745),U_17746),hAPP(hAPP(c_Option_Omap(U_17747,U_17744),U_17748),U_17749)) = hAPP(hAPP(c_Option_Omap(U_17747,U_17745),hAPP(c_Fun_Ocomp(U_17744,U_17745,U_17747,U_17746),U_17748)),U_17749),
    inference(variable_rename,[status(thm)],[f_4319_1]) ).

fof(f_4319_3,plain,
    ! [U_17744,U_17745,U_17746,U_17747,U_17748,U_17749] : hAPP(hAPP(c_Option_Omap(U_17744,U_17745),U_17746),hAPP(hAPP(c_Option_Omap(U_17747,U_17744),U_17748),U_17749)) = hAPP(hAPP(c_Option_Omap(U_17747,U_17745),hAPP(c_Fun_Ocomp(U_17744,U_17745,U_17747,U_17746),U_17748)),U_17749),
    inference(definitional_conversion,[status(esa)],[f_4319_2]) ).

cnf(f_4319_4,plain,
    hAPP(hAPP(c_Option_Omap(U_17744,U_17745),U_17746),hAPP(hAPP(c_Option_Omap(U_17747,U_17744),U_17748),U_17749)) = hAPP(hAPP(c_Option_Omap(U_17747,U_17745),hAPP(c_Fun_Ocomp(U_17744,U_17745,U_17747,U_17746),U_17748)),U_17749),
    inference(clausify,[status(thm)],[f_4319_3]) ).

fof(f_4320_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_4320_2,plain,
    ! [U_17755,U_17754,U_17753,U_17752,U_17751,U_17750] : hAPP(hAPP(c_Option_Omap(U_17750,U_17751),U_17752),hAPP(hAPP(c_Option_Omap(U_17753,U_17750),U_17754),U_17755)) = hAPP(hAPP(c_Option_Omap(U_17753,U_17751),hAPP(c_Fun_Ocomp(U_17750,U_17751,U_17753,U_17752),U_17754)),U_17755),
    inference(variable_rename,[status(thm)],[f_4320_1]) ).

fof(f_4320_3,plain,
    ! [U_17750,U_17751,U_17752,U_17753,U_17754,U_17755] : hAPP(hAPP(c_Option_Omap(U_17750,U_17751),U_17752),hAPP(hAPP(c_Option_Omap(U_17753,U_17750),U_17754),U_17755)) = hAPP(hAPP(c_Option_Omap(U_17753,U_17751),hAPP(c_Fun_Ocomp(U_17750,U_17751,U_17753,U_17752),U_17754)),U_17755),
    inference(definitional_conversion,[status(esa)],[f_4320_2]) ).

cnf(f_4320_4,plain,
    hAPP(hAPP(c_Option_Omap(U_17750,U_17751),U_17752),hAPP(hAPP(c_Option_Omap(U_17753,U_17750),U_17754),U_17755)) = hAPP(hAPP(c_Option_Omap(U_17753,U_17751),hAPP(c_Fun_Ocomp(U_17750,U_17751,U_17753,U_17752),U_17754)),U_17755),
    inference(clausify,[status(thm)],[f_4320_3]) ).

fof(f_4321_1,plain,
    ! [V_h_2,V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),tc_sum(T_b,T_c),hAPP(c_Option_Omap(T_e,T_d),V_f_2)),c_Sum__Type_Osum_Osum__case(T_b,tc_Option_Ooption(T_e),T_c,V_g_2,V_h_2)) = c_Sum__Type_Osum_Osum__case(T_b,tc_Option_Ooption(T_d),T_c,hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),T_b,hAPP(c_Option_Omap(T_e,T_d),V_f_2)),V_g_2),hAPP(c_Fun_Ocomp(tc_Option_Ooption(T_e),tc_Option_Ooption(T_d),T_c,hAPP(c_Option_Omap(T_e,T_d),V_f_2)),V_h_2)),
    inference(fof_nnf,[status(thm)],[fact_option__map__o__sum__case]) ).

fof(f_4321_2,plain,
    ! [U_17762,U_17761,U_17760,U_17759,U_17758,U_17757,U_17756] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17756),tc_Option_Ooption(U_17757),tc_sum(U_17758,U_17759),hAPP(c_Option_Omap(U_17756,U_17757),U_17760)),c_Sum__Type_Osum_Osum__case(U_17758,tc_Option_Ooption(U_17756),U_17759,U_17761,U_17762)) = c_Sum__Type_Osum_Osum__case(U_17758,tc_Option_Ooption(U_17757),U_17759,hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17756),tc_Option_Ooption(U_17757),U_17758,hAPP(c_Option_Omap(U_17756,U_17757),U_17760)),U_17761),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17756),tc_Option_Ooption(U_17757),U_17759,hAPP(c_Option_Omap(U_17756,U_17757),U_17760)),U_17762)),
    inference(variable_rename,[status(thm)],[f_4321_1]) ).

fof(f_4321_3,plain,
    ! [U_17761,U_17756,U_17757,U_17758,U_17759,U_17760,U_17762] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17756),tc_Option_Ooption(U_17757),tc_sum(U_17758,U_17759),hAPP(c_Option_Omap(U_17756,U_17757),U_17760)),c_Sum__Type_Osum_Osum__case(U_17758,tc_Option_Ooption(U_17756),U_17759,U_17761,U_17762)) = c_Sum__Type_Osum_Osum__case(U_17758,tc_Option_Ooption(U_17757),U_17759,hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17756),tc_Option_Ooption(U_17757),U_17758,hAPP(c_Option_Omap(U_17756,U_17757),U_17760)),U_17761),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17756),tc_Option_Ooption(U_17757),U_17759,hAPP(c_Option_Omap(U_17756,U_17757),U_17760)),U_17762)),
    inference(definitional_conversion,[status(esa)],[f_4321_2]) ).

cnf(f_4321_4,plain,
    hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17756),tc_Option_Ooption(U_17757),tc_sum(U_17758,U_17759),hAPP(c_Option_Omap(U_17756,U_17757),U_17760)),c_Sum__Type_Osum_Osum__case(U_17758,tc_Option_Ooption(U_17756),U_17759,U_17761,U_17762)) = c_Sum__Type_Osum_Osum__case(U_17758,tc_Option_Ooption(U_17757),U_17759,hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17756),tc_Option_Ooption(U_17757),U_17758,hAPP(c_Option_Omap(U_17756,U_17757),U_17760)),U_17761),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17756),tc_Option_Ooption(U_17757),U_17759,hAPP(c_Option_Omap(U_17756,U_17757),U_17760)),U_17762)),
    inference(clausify,[status(thm)],[f_4321_3]) ).

fof(f_4322_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_4322_2,plain,
    ! [U_17767,U_17766,U_17765,U_17764,U_17763] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17763),tc_Option_Ooption(U_17764),U_17765,hAPP(c_Option_Omap(U_17763,U_17764),U_17766)),hAPP(c_COMBK(tc_Option_Ooption(U_17763),U_17765),c_Option_Ooption_ONone(U_17763))),U_17767) = c_Option_Ooption_ONone(U_17764),
    inference(variable_rename,[status(thm)],[f_4322_1]) ).

fof(f_4322_3,plain,
    ! [U_17763,U_17764,U_17765,U_17766,U_17767] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17763),tc_Option_Ooption(U_17764),U_17765,hAPP(c_Option_Omap(U_17763,U_17764),U_17766)),hAPP(c_COMBK(tc_Option_Ooption(U_17763),U_17765),c_Option_Ooption_ONone(U_17763))),U_17767) = c_Option_Ooption_ONone(U_17764),
    inference(definitional_conversion,[status(esa)],[f_4322_2]) ).

cnf(f_4322_4,plain,
    hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17763),tc_Option_Ooption(U_17764),U_17765,hAPP(c_Option_Omap(U_17763,U_17764),U_17766)),hAPP(c_COMBK(tc_Option_Ooption(U_17763),U_17765),c_Option_Ooption_ONone(U_17763))),U_17767) = c_Option_Ooption_ONone(U_17764),
    inference(clausify,[status(thm)],[f_4322_3]) ).

fof(f_4323_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_4323_2,plain,
    ! [U_17771,U_17770,U_17769,U_17768] : hAPP(hAPP(c_Option_Omap(U_17768,U_17769),U_17770),hAPP(c_Option_Ooption_OSome(U_17768),U_17771)) = hAPP(c_Option_Ooption_OSome(U_17769),hAPP(U_17770,U_17771)),
    inference(variable_rename,[status(thm)],[f_4323_1]) ).

fof(f_4323_3,plain,
    ! [U_17768,U_17769,U_17770,U_17771] : hAPP(hAPP(c_Option_Omap(U_17768,U_17769),U_17770),hAPP(c_Option_Ooption_OSome(U_17768),U_17771)) = hAPP(c_Option_Ooption_OSome(U_17769),hAPP(U_17770,U_17771)),
    inference(definitional_conversion,[status(esa)],[f_4323_2]) ).

cnf(f_4323_4,plain,
    hAPP(hAPP(c_Option_Omap(U_17768,U_17769),U_17770),hAPP(c_Option_Ooption_OSome(U_17768),U_17771)) = hAPP(c_Option_Ooption_OSome(U_17769),hAPP(U_17770,U_17771)),
    inference(clausify,[status(thm)],[f_4323_3]) ).

fof(f_4324_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_4324_2,plain,
    ! [U_17778,U_17777,U_17776,U_17775,U_17774] :
      ( ( hAPP(hAPP(c_Option_Omap(U_17774,U_17775),U_17776),U_17777) = hAPP(c_Option_Ooption_OSome(U_17775),U_17778)
        | ! [U_17773] :
            ( hAPP(U_17776,U_17773) != U_17778
            | U_17777 != hAPP(c_Option_Ooption_OSome(U_17774),U_17773) ) )
      & ( ? [U_17772] :
            ( hAPP(U_17776,U_17772) = U_17778
            & U_17777 = hAPP(c_Option_Ooption_OSome(U_17774),U_17772) )
        | hAPP(hAPP(c_Option_Omap(U_17774,U_17775),U_17776),U_17777) != hAPP(c_Option_Ooption_OSome(U_17775),U_17778) ) ),
    inference(variable_rename,[status(thm)],[f_4324_1]) ).

fof(f_4324_3,plain,
    ( ! [U_17788,U_17786,U_17784,U_17782,U_17780] :
        ( hAPP(hAPP(c_Option_Omap(U_17780,U_17782),U_17784),U_17786) = hAPP(c_Option_Ooption_OSome(U_17782),U_17788)
        | ! [U_17773] :
            ( hAPP(U_17784,U_17773) != U_17788
            | U_17786 != hAPP(c_Option_Ooption_OSome(U_17780),U_17773) ) )
    & ! [U_17787,U_17785,U_17783,U_17781,U_17779] :
        ( ? [U_17772] :
            ( hAPP(U_17783,U_17772) = U_17787
            & U_17785 = hAPP(c_Option_Ooption_OSome(U_17779),U_17772) )
        | hAPP(hAPP(c_Option_Omap(U_17779,U_17781),U_17783),U_17785) != hAPP(c_Option_Ooption_OSome(U_17781),U_17787) ) ),
    inference(miniscope,[status(thm)],[f_4324_2]) ).

fof(f_4324_4,plain,
    ( ! [U_17788,U_17786,U_17784,U_17782,U_17780] :
        ( hAPP(hAPP(c_Option_Omap(U_17780,U_17782),U_17784),U_17786) = hAPP(c_Option_Ooption_OSome(U_17782),U_17788)
        | ! [U_17773] :
            ( hAPP(U_17784,U_17773) != U_17788
            | U_17786 != hAPP(c_Option_Ooption_OSome(U_17780),U_17773) ) )
    & ! [U_17787,U_17785,U_17783,U_17781,U_17779] :
        ( ( hAPP(U_17783,sK455(U_17787,U_17785,U_17783,U_17781,U_17779)) = U_17787
          & U_17785 = hAPP(c_Option_Ooption_OSome(U_17779),sK455(U_17787,U_17785,U_17783,U_17781,U_17779)) )
        | hAPP(hAPP(c_Option_Omap(U_17779,U_17781),U_17783),U_17785) != hAPP(c_Option_Ooption_OSome(U_17781),U_17787) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK455]),skolemize(U_17772,sK455(U_17787,U_17785,U_17783,U_17781,U_17779))],[f_4324_3]) ).

fof(f_4324_5,plain,
    ( ! [U_17781,U_17783,U_17785,U_17779,U_17787] :
        ( hAPP(U_17783,sK455(U_17787,U_17785,U_17783,U_17781,U_17779)) = U_17787
        | ~ sP1121(U_17781,U_17783,U_17785,U_17779,U_17787) )
    & ! [U_17781,U_17783,U_17785,U_17779,U_17787] :
        ( U_17785 = hAPP(c_Option_Ooption_OSome(U_17779),sK455(U_17787,U_17785,U_17783,U_17781,U_17779))
        | ~ sP1121(U_17781,U_17783,U_17785,U_17779,U_17787) )
    & ! [U_17786,U_17773,U_17788,U_17780,U_17782,U_17784] :
        ( hAPP(hAPP(c_Option_Omap(U_17780,U_17782),U_17784),U_17786) = hAPP(c_Option_Ooption_OSome(U_17782),U_17788)
        | hAPP(U_17784,U_17773) != U_17788
        | U_17786 != hAPP(c_Option_Ooption_OSome(U_17780),U_17773) )
    & ! [U_17781,U_17783,U_17785,U_17779,U_17787] :
        ( sP1121(U_17781,U_17783,U_17785,U_17779,U_17787)
        | hAPP(hAPP(c_Option_Omap(U_17779,U_17781),U_17783),U_17785) != hAPP(c_Option_Ooption_OSome(U_17781),U_17787) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1121])],[f_4324_4]) ).

cnf(f_4324_6,plain,
    ( sP1121(U_17781,U_17783,U_17785,U_17779,U_17787)
    | hAPP(hAPP(c_Option_Omap(U_17779,U_17781),U_17783),U_17785) != hAPP(c_Option_Ooption_OSome(U_17781),U_17787) ),
    inference(clausify,[status(thm)],[f_4324_5]) ).

cnf(f_4324_7,plain,
    ( hAPP(hAPP(c_Option_Omap(U_17780,U_17782),U_17784),U_17786) = hAPP(c_Option_Ooption_OSome(U_17782),U_17788)
    | hAPP(U_17784,U_17773) != U_17788
    | U_17786 != hAPP(c_Option_Ooption_OSome(U_17780),U_17773) ),
    inference(clausify,[status(thm)],[f_4324_5]) ).

cnf(f_4324_8,plain,
    ( U_17785 = hAPP(c_Option_Ooption_OSome(U_17779),sK455(U_17787,U_17785,U_17783,U_17781,U_17779))
    | ~ sP1121(U_17781,U_17783,U_17785,U_17779,U_17787) ),
    inference(clausify,[status(thm)],[f_4324_5]) ).

cnf(f_4324_9,plain,
    ( hAPP(U_17783,sK455(U_17787,U_17785,U_17783,U_17781,U_17779)) = U_17787
    | ~ sP1121(U_17781,U_17783,U_17785,U_17779,U_17787) ),
    inference(clausify,[status(thm)],[f_4324_5]) ).

fof(f_4325_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_4325_2,plain,
    ! [U_17791,U_17790,U_17789] : hAPP(hAPP(c_Option_Omap(U_17789,U_17790),U_17791),c_Option_Ooption_ONone(U_17789)) = c_Option_Ooption_ONone(U_17790),
    inference(variable_rename,[status(thm)],[f_4325_1]) ).

fof(f_4325_3,plain,
    ! [U_17790,U_17791,U_17789] : hAPP(hAPP(c_Option_Omap(U_17789,U_17790),U_17791),c_Option_Ooption_ONone(U_17789)) = c_Option_Ooption_ONone(U_17790),
    inference(definitional_conversion,[status(esa)],[f_4325_2]) ).

cnf(f_4325_4,plain,
    hAPP(hAPP(c_Option_Omap(U_17789,U_17790),U_17791),c_Option_Ooption_ONone(U_17789)) = c_Option_Ooption_ONone(U_17790),
    inference(clausify,[status(thm)],[f_4325_3]) ).

fof(f_4326_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_4326_2,plain,
    ! [U_17795,U_17794,U_17793,U_17792] :
      ( ( hAPP(hAPP(c_Option_Omap(U_17792,U_17793),U_17794),U_17795) = c_Option_Ooption_ONone(U_17793)
        | U_17795 != c_Option_Ooption_ONone(U_17792) )
      & ( U_17795 = c_Option_Ooption_ONone(U_17792)
        | hAPP(hAPP(c_Option_Omap(U_17792,U_17793),U_17794),U_17795) != c_Option_Ooption_ONone(U_17793) ) ),
    inference(variable_rename,[status(thm)],[f_4326_1]) ).

fof(f_4326_3,plain,
    ( ! [U_17803,U_17801,U_17799,U_17797] :
        ( hAPP(hAPP(c_Option_Omap(U_17797,U_17799),U_17801),U_17803) = c_Option_Ooption_ONone(U_17799)
        | U_17803 != c_Option_Ooption_ONone(U_17797) )
    & ! [U_17802,U_17800,U_17798,U_17796] :
        ( U_17802 = c_Option_Ooption_ONone(U_17796)
        | hAPP(hAPP(c_Option_Omap(U_17796,U_17798),U_17800),U_17802) != c_Option_Ooption_ONone(U_17798) ) ),
    inference(miniscope,[status(thm)],[f_4326_2]) ).

fof(f_4326_4,plain,
    ( ! [U_17797,U_17803,U_17799,U_17801] :
        ( hAPP(hAPP(c_Option_Omap(U_17797,U_17799),U_17801),U_17803) = c_Option_Ooption_ONone(U_17799)
        | U_17803 != c_Option_Ooption_ONone(U_17797) )
    & ! [U_17800,U_17798,U_17802,U_17796] :
        ( U_17802 = c_Option_Ooption_ONone(U_17796)
        | hAPP(hAPP(c_Option_Omap(U_17796,U_17798),U_17800),U_17802) != c_Option_Ooption_ONone(U_17798) ) ),
    inference(definitional_conversion,[status(esa)],[f_4326_3]) ).

cnf(f_4326_5,plain,
    ( U_17802 = c_Option_Ooption_ONone(U_17796)
    | hAPP(hAPP(c_Option_Omap(U_17796,U_17798),U_17800),U_17802) != c_Option_Ooption_ONone(U_17798) ),
    inference(clausify,[status(thm)],[f_4326_4]) ).

cnf(f_4326_6,plain,
    ( hAPP(hAPP(c_Option_Omap(U_17797,U_17799),U_17801),U_17803) = c_Option_Ooption_ONone(U_17799)
    | U_17803 != c_Option_Ooption_ONone(U_17797) ),
    inference(clausify,[status(thm)],[f_4326_4]) ).

fof(f_4327_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_4327_2,plain,
    ! [U_17810,U_17809,U_17808,U_17807,U_17806,U_17805,U_17804] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17804),tc_Option_Ooption(U_17805),U_17806,hAPP(c_Option_Omap(U_17804,U_17805),U_17807)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17806,tc_Option_Ooption(U_17804)),U_17808),U_17809),hAPP(c_Option_Ooption_OSome(U_17804),U_17810))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17806,tc_Option_Ooption(U_17805)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17804),tc_Option_Ooption(U_17805),U_17806,hAPP(c_Option_Omap(U_17804,U_17805),U_17807)),U_17808)),U_17809),hAPP(c_Option_Ooption_OSome(U_17805),hAPP(U_17807,U_17810))),
    inference(variable_rename,[status(thm)],[f_4327_1]) ).

fof(f_4327_3,plain,
    ! [U_17804,U_17805,U_17806,U_17807,U_17808,U_17809,U_17810] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17804),tc_Option_Ooption(U_17805),U_17806,hAPP(c_Option_Omap(U_17804,U_17805),U_17807)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17806,tc_Option_Ooption(U_17804)),U_17808),U_17809),hAPP(c_Option_Ooption_OSome(U_17804),U_17810))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17806,tc_Option_Ooption(U_17805)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17804),tc_Option_Ooption(U_17805),U_17806,hAPP(c_Option_Omap(U_17804,U_17805),U_17807)),U_17808)),U_17809),hAPP(c_Option_Ooption_OSome(U_17805),hAPP(U_17807,U_17810))),
    inference(definitional_conversion,[status(esa)],[f_4327_2]) ).

cnf(f_4327_4,plain,
    hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17804),tc_Option_Ooption(U_17805),U_17806,hAPP(c_Option_Omap(U_17804,U_17805),U_17807)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17806,tc_Option_Ooption(U_17804)),U_17808),U_17809),hAPP(c_Option_Ooption_OSome(U_17804),U_17810))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17806,tc_Option_Ooption(U_17805)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17804),tc_Option_Ooption(U_17805),U_17806,hAPP(c_Option_Omap(U_17804,U_17805),U_17807)),U_17808)),U_17809),hAPP(c_Option_Ooption_OSome(U_17805),hAPP(U_17807,U_17810))),
    inference(clausify,[status(thm)],[f_4327_3]) ).

fof(f_4328_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_4328_2,plain,
    ! [U_17815,U_17814,U_17813,U_17812,U_17811] :
      ( ( ( hAPP(hAPP(c_List_Omap(U_17811,U_17812),U_17813),U_17814) = hAPP(hAPP(c_List_Omap(U_17811,U_17812),U_17813),U_17815)
          | U_17814 != U_17815 )
        & ( U_17814 = U_17815
          | hAPP(hAPP(c_List_Omap(U_17811,U_17812),U_17813),U_17814) != hAPP(hAPP(c_List_Omap(U_17811,U_17812),U_17813),U_17815) ) )
      | ~ c_Fun_Oinj__on(U_17811,U_17812,U_17813,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17811,tc_HOL_Obool)),hAPP(c_List_Oset(U_17811),U_17814)),hAPP(c_List_Oset(U_17811),U_17815))) ),
    inference(variable_rename,[status(thm)],[f_4328_1]) ).

fof(f_4328_3,plain,
    ( ! [U_17811,U_17812,U_17813,U_17814,U_17815] :
        ( hAPP(hAPP(c_List_Omap(U_17811,U_17812),U_17813),U_17814) = hAPP(hAPP(c_List_Omap(U_17811,U_17812),U_17813),U_17815)
        | U_17814 != U_17815
        | ~ sP1122(U_17811,U_17812,U_17813,U_17814,U_17815) )
    & ! [U_17811,U_17812,U_17813,U_17814,U_17815] :
        ( U_17814 = U_17815
        | hAPP(hAPP(c_List_Omap(U_17811,U_17812),U_17813),U_17814) != hAPP(hAPP(c_List_Omap(U_17811,U_17812),U_17813),U_17815)
        | ~ sP1122(U_17811,U_17812,U_17813,U_17814,U_17815) )
    & ! [U_17811,U_17812,U_17813,U_17814,U_17815] :
        ( sP1122(U_17811,U_17812,U_17813,U_17814,U_17815)
        | ~ c_Fun_Oinj__on(U_17811,U_17812,U_17813,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17811,tc_HOL_Obool)),hAPP(c_List_Oset(U_17811),U_17814)),hAPP(c_List_Oset(U_17811),U_17815))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1122])],[f_4328_2]) ).

cnf(f_4328_4,plain,
    ( sP1122(U_17811,U_17812,U_17813,U_17814,U_17815)
    | ~ c_Fun_Oinj__on(U_17811,U_17812,U_17813,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17811,tc_HOL_Obool)),hAPP(c_List_Oset(U_17811),U_17814)),hAPP(c_List_Oset(U_17811),U_17815))) ),
    inference(clausify,[status(thm)],[f_4328_3]) ).

cnf(f_4328_5,plain,
    ( U_17814 = U_17815
    | hAPP(hAPP(c_List_Omap(U_17811,U_17812),U_17813),U_17814) != hAPP(hAPP(c_List_Omap(U_17811,U_17812),U_17813),U_17815)
    | ~ sP1122(U_17811,U_17812,U_17813,U_17814,U_17815) ),
    inference(clausify,[status(thm)],[f_4328_3]) ).

cnf(f_4328_6,plain,
    ( hAPP(hAPP(c_List_Omap(U_17811,U_17812),U_17813),U_17814) = hAPP(hAPP(c_List_Omap(U_17811,U_17812),U_17813),U_17815)
    | U_17814 != U_17815
    | ~ sP1122(U_17811,U_17812,U_17813,U_17814,U_17815) ),
    inference(clausify,[status(thm)],[f_4328_3]) ).

fof(f_4329_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_4329_2,plain,
    ! [U_17820,U_17819,U_17818,U_17817,U_17816] :
      ( U_17819 = U_17820
      | ~ c_Fun_Oinj__on(U_17816,U_17817,U_17818,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17816,tc_HOL_Obool)),hAPP(c_List_Oset(U_17816),U_17819)),hAPP(c_List_Oset(U_17816),U_17820)))
      | hAPP(hAPP(c_List_Omap(U_17816,U_17817),U_17818),U_17819) != hAPP(hAPP(c_List_Omap(U_17816,U_17817),U_17818),U_17820) ),
    inference(variable_rename,[status(thm)],[f_4329_1]) ).

fof(f_4329_3,plain,
    ! [U_17818,U_17817,U_17819,U_17820,U_17816] :
      ( U_17819 = U_17820
      | ~ c_Fun_Oinj__on(U_17816,U_17817,U_17818,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17816,tc_HOL_Obool)),hAPP(c_List_Oset(U_17816),U_17819)),hAPP(c_List_Oset(U_17816),U_17820)))
      | hAPP(hAPP(c_List_Omap(U_17816,U_17817),U_17818),U_17819) != hAPP(hAPP(c_List_Omap(U_17816,U_17817),U_17818),U_17820) ),
    inference(definitional_conversion,[status(esa)],[f_4329_2]) ).

cnf(f_4329_4,plain,
    ( U_17819 = U_17820
    | ~ c_Fun_Oinj__on(U_17816,U_17817,U_17818,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17816,tc_HOL_Obool)),hAPP(c_List_Oset(U_17816),U_17819)),hAPP(c_List_Oset(U_17816),U_17820)))
    | hAPP(hAPP(c_List_Omap(U_17816,U_17817),U_17818),U_17819) != hAPP(hAPP(c_List_Omap(U_17816,U_17817),U_17818),U_17820) ),
    inference(clausify,[status(thm)],[f_4329_3]) ).

fof(f_4330_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_4330_2,plain,
    ! [U_17826,U_17825,U_17824,U_17823,U_17822,U_17821] :
      ( hAPP(hAPP(c_List_Omap(U_17821,U_17824),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17821,U_17824),U_17825),U_17822),U_17826)),U_17823) = hAPP(hAPP(c_List_Omap(U_17821,U_17824),U_17825),U_17823)
      | hBOOL(hAPP(hAPP(c_member(U_17821),U_17822),hAPP(c_List_Oset(U_17821),U_17823))) ),
    inference(variable_rename,[status(thm)],[f_4330_1]) ).

fof(f_4330_3,plain,
    ! [U_17821,U_17822,U_17823,U_17824,U_17825,U_17826] :
      ( hAPP(hAPP(c_List_Omap(U_17821,U_17824),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17821,U_17824),U_17825),U_17822),U_17826)),U_17823) = hAPP(hAPP(c_List_Omap(U_17821,U_17824),U_17825),U_17823)
      | hBOOL(hAPP(hAPP(c_member(U_17821),U_17822),hAPP(c_List_Oset(U_17821),U_17823))) ),
    inference(definitional_conversion,[status(esa)],[f_4330_2]) ).

cnf(f_4330_4,plain,
    ( hAPP(hAPP(c_List_Omap(U_17821,U_17824),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17821,U_17824),U_17825),U_17822),U_17826)),U_17823) = hAPP(hAPP(c_List_Omap(U_17821,U_17824),U_17825),U_17823)
    | hBOOL(hAPP(hAPP(c_member(U_17821),U_17822),hAPP(c_List_Oset(U_17821),U_17823))) ),
    inference(clausify,[status(thm)],[f_4330_3]) ).

fof(f_4331_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_4331_2,plain,
    ! [U_17830,U_17829,U_17828,U_17827] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_17827),tc_List_Olist(U_17828),hAPP(c_List_Omap(U_17827,U_17828),U_17829),U_17830)
      | ~ c_Fun_Oinj__on(U_17827,U_17828,U_17829,c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17827,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(U_17827),tc_fun(U_17827,tc_HOL_Obool),c_List_Oset(U_17827)),U_17830))) ),
    inference(variable_rename,[status(thm)],[f_4331_1]) ).

fof(f_4331_3,plain,
    ! [U_17827,U_17828,U_17829,U_17830] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_17827),tc_List_Olist(U_17828),hAPP(c_List_Omap(U_17827,U_17828),U_17829),U_17830)
      | ~ c_Fun_Oinj__on(U_17827,U_17828,U_17829,c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17827,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(U_17827),tc_fun(U_17827,tc_HOL_Obool),c_List_Oset(U_17827)),U_17830))) ),
    inference(definitional_conversion,[status(esa)],[f_4331_2]) ).

cnf(f_4331_4,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_17827),tc_List_Olist(U_17828),hAPP(c_List_Omap(U_17827,U_17828),U_17829),U_17830)
    | ~ c_Fun_Oinj__on(U_17827,U_17828,U_17829,c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17827,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(U_17827),tc_fun(U_17827,tc_HOL_Obool),c_List_Oset(U_17827)),U_17830))) ),
    inference(clausify,[status(thm)],[f_4331_3]) ).

fof(f_4332_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_4332_2,plain,
    ! [U_17834,U_17833,U_17832,U_17831] :
      ( hAPP(c_Set_Oimage(tc_prod(U_17831,U_17832),U_17831,c_Product__Type_Ofst(U_17831,U_17832)),hAPP(c_List_Oset(tc_prod(U_17831,U_17832)),U_17833)) = hAPP(c_Set_Oimage(tc_prod(U_17831,U_17832),U_17831,c_Product__Type_Ofst(U_17831,U_17832)),hAPP(c_List_Oset(tc_prod(U_17831,U_17832)),U_17834))
      | c_Map_Omap__of(U_17831,U_17832,U_17833) != c_Map_Omap__of(U_17831,U_17832,U_17834) ),
    inference(variable_rename,[status(thm)],[f_4332_1]) ).

fof(f_4332_3,plain,
    ! [U_17831,U_17832,U_17833,U_17834] :
      ( hAPP(c_Set_Oimage(tc_prod(U_17831,U_17832),U_17831,c_Product__Type_Ofst(U_17831,U_17832)),hAPP(c_List_Oset(tc_prod(U_17831,U_17832)),U_17833)) = hAPP(c_Set_Oimage(tc_prod(U_17831,U_17832),U_17831,c_Product__Type_Ofst(U_17831,U_17832)),hAPP(c_List_Oset(tc_prod(U_17831,U_17832)),U_17834))
      | c_Map_Omap__of(U_17831,U_17832,U_17833) != c_Map_Omap__of(U_17831,U_17832,U_17834) ),
    inference(definitional_conversion,[status(esa)],[f_4332_2]) ).

cnf(f_4332_4,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_17831,U_17832),U_17831,c_Product__Type_Ofst(U_17831,U_17832)),hAPP(c_List_Oset(tc_prod(U_17831,U_17832)),U_17833)) = hAPP(c_Set_Oimage(tc_prod(U_17831,U_17832),U_17831,c_Product__Type_Ofst(U_17831,U_17832)),hAPP(c_List_Oset(tc_prod(U_17831,U_17832)),U_17834))
    | c_Map_Omap__of(U_17831,U_17832,U_17833) != c_Map_Omap__of(U_17831,U_17832,U_17834) ),
    inference(clausify,[status(thm)],[f_4332_3]) ).

fof(f_4333_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_4333_2,plain,
    ! [U_17839,U_17838,U_17837,U_17836,U_17835] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17835,U_17836)),hAPP(hAPP(c_Product__Type_OPair(U_17835,U_17836),U_17838),U_17839)),hAPP(c_List_Oset(tc_prod(U_17835,U_17836)),U_17837)))
      | hAPP(c_Map_Omap__of(U_17835,U_17836,U_17837),U_17838) != hAPP(c_Option_Ooption_OSome(U_17836),U_17839) ),
    inference(variable_rename,[status(thm)],[f_4333_1]) ).

fof(f_4333_3,plain,
    ! [U_17835,U_17836,U_17837,U_17838,U_17839] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17835,U_17836)),hAPP(hAPP(c_Product__Type_OPair(U_17835,U_17836),U_17838),U_17839)),hAPP(c_List_Oset(tc_prod(U_17835,U_17836)),U_17837)))
      | hAPP(c_Map_Omap__of(U_17835,U_17836,U_17837),U_17838) != hAPP(c_Option_Ooption_OSome(U_17836),U_17839) ),
    inference(definitional_conversion,[status(esa)],[f_4333_2]) ).

cnf(f_4333_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17835,U_17836)),hAPP(hAPP(c_Product__Type_OPair(U_17835,U_17836),U_17838),U_17839)),hAPP(c_List_Oset(tc_prod(U_17835,U_17836)),U_17837)))
    | hAPP(c_Map_Omap__of(U_17835,U_17836,U_17837),U_17838) != hAPP(c_Option_Ooption_OSome(U_17836),U_17839) ),
    inference(clausify,[status(thm)],[f_4333_3]) ).

fof(f_4334_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_4334_2,plain,
    ! [U_17844,U_17843,U_17842,U_17841,U_17840] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17840,U_17841)),hAPP(hAPP(c_Product__Type_OPair(U_17840,U_17841),U_17843),U_17844)),hAPP(c_List_Oset(tc_prod(U_17840,U_17841)),U_17842)))
      | hAPP(c_Map_Omap__of(U_17840,U_17841,U_17842),U_17843) != hAPP(c_Option_Ooption_OSome(U_17841),U_17844) ),
    inference(variable_rename,[status(thm)],[f_4334_1]) ).

fof(f_4334_3,plain,
    ! [U_17840,U_17841,U_17842,U_17843,U_17844] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17840,U_17841)),hAPP(hAPP(c_Product__Type_OPair(U_17840,U_17841),U_17843),U_17844)),hAPP(c_List_Oset(tc_prod(U_17840,U_17841)),U_17842)))
      | hAPP(c_Map_Omap__of(U_17840,U_17841,U_17842),U_17843) != hAPP(c_Option_Ooption_OSome(U_17841),U_17844) ),
    inference(definitional_conversion,[status(esa)],[f_4334_2]) ).

cnf(f_4334_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17840,U_17841)),hAPP(hAPP(c_Product__Type_OPair(U_17840,U_17841),U_17843),U_17844)),hAPP(c_List_Oset(tc_prod(U_17840,U_17841)),U_17842)))
    | hAPP(c_Map_Omap__of(U_17840,U_17841,U_17842),U_17843) != hAPP(c_Option_Ooption_OSome(U_17841),U_17844) ),
    inference(clausify,[status(thm)],[f_4334_3]) ).

fof(f_4335_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_4335_2,plain,
    ! [U_17847,U_17846,U_17845] : c_Map_Odom(U_17845,U_17846,c_Map_Omap__of(U_17845,U_17846,U_17847)) = hAPP(c_Set_Oimage(tc_prod(U_17845,U_17846),U_17845,c_Product__Type_Ofst(U_17845,U_17846)),hAPP(c_List_Oset(tc_prod(U_17845,U_17846)),U_17847)),
    inference(variable_rename,[status(thm)],[f_4335_1]) ).

fof(f_4335_3,plain,
    ! [U_17845,U_17846,U_17847] : c_Map_Odom(U_17845,U_17846,c_Map_Omap__of(U_17845,U_17846,U_17847)) = hAPP(c_Set_Oimage(tc_prod(U_17845,U_17846),U_17845,c_Product__Type_Ofst(U_17845,U_17846)),hAPP(c_List_Oset(tc_prod(U_17845,U_17846)),U_17847)),
    inference(definitional_conversion,[status(esa)],[f_4335_2]) ).

cnf(f_4335_4,plain,
    c_Map_Odom(U_17845,U_17846,c_Map_Omap__of(U_17845,U_17846,U_17847)) = hAPP(c_Set_Oimage(tc_prod(U_17845,U_17846),U_17845,c_Product__Type_Ofst(U_17845,U_17846)),hAPP(c_List_Oset(tc_prod(U_17845,U_17846)),U_17847)),
    inference(clausify,[status(thm)],[f_4335_3]) ).

fof(f_4336_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_4336_2,plain,
    ! [U_17851,U_17850,U_17849,U_17848] :
      ( ( hAPP(c_Map_Omap__of(U_17848,U_17849,U_17850),U_17851) = c_Option_Ooption_ONone(U_17849)
        | hBOOL(hAPP(hAPP(c_member(U_17848),U_17851),hAPP(c_Set_Oimage(tc_prod(U_17848,U_17849),U_17848,c_Product__Type_Ofst(U_17848,U_17849)),hAPP(c_List_Oset(tc_prod(U_17848,U_17849)),U_17850)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(U_17848),U_17851),hAPP(c_Set_Oimage(tc_prod(U_17848,U_17849),U_17848,c_Product__Type_Ofst(U_17848,U_17849)),hAPP(c_List_Oset(tc_prod(U_17848,U_17849)),U_17850))))
        | hAPP(c_Map_Omap__of(U_17848,U_17849,U_17850),U_17851) != c_Option_Ooption_ONone(U_17849) ) ),
    inference(variable_rename,[status(thm)],[f_4336_1]) ).

fof(f_4336_3,plain,
    ( ! [U_17859,U_17857,U_17855,U_17853] :
        ( hAPP(c_Map_Omap__of(U_17853,U_17855,U_17857),U_17859) = c_Option_Ooption_ONone(U_17855)
        | hBOOL(hAPP(hAPP(c_member(U_17853),U_17859),hAPP(c_Set_Oimage(tc_prod(U_17853,U_17855),U_17853,c_Product__Type_Ofst(U_17853,U_17855)),hAPP(c_List_Oset(tc_prod(U_17853,U_17855)),U_17857)))) )
    & ! [U_17858,U_17856,U_17854,U_17852] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_17852),U_17858),hAPP(c_Set_Oimage(tc_prod(U_17852,U_17854),U_17852,c_Product__Type_Ofst(U_17852,U_17854)),hAPP(c_List_Oset(tc_prod(U_17852,U_17854)),U_17856))))
        | hAPP(c_Map_Omap__of(U_17852,U_17854,U_17856),U_17858) != c_Option_Ooption_ONone(U_17854) ) ),
    inference(miniscope,[status(thm)],[f_4336_2]) ).

fof(f_4336_4,plain,
    ( ! [U_17853,U_17855,U_17857,U_17859] :
        ( hAPP(c_Map_Omap__of(U_17853,U_17855,U_17857),U_17859) = c_Option_Ooption_ONone(U_17855)
        | hBOOL(hAPP(hAPP(c_member(U_17853),U_17859),hAPP(c_Set_Oimage(tc_prod(U_17853,U_17855),U_17853,c_Product__Type_Ofst(U_17853,U_17855)),hAPP(c_List_Oset(tc_prod(U_17853,U_17855)),U_17857)))) )
    & ! [U_17854,U_17858,U_17852,U_17856] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_17852),U_17858),hAPP(c_Set_Oimage(tc_prod(U_17852,U_17854),U_17852,c_Product__Type_Ofst(U_17852,U_17854)),hAPP(c_List_Oset(tc_prod(U_17852,U_17854)),U_17856))))
        | hAPP(c_Map_Omap__of(U_17852,U_17854,U_17856),U_17858) != c_Option_Ooption_ONone(U_17854) ) ),
    inference(definitional_conversion,[status(esa)],[f_4336_3]) ).

cnf(f_4336_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17852),U_17858),hAPP(c_Set_Oimage(tc_prod(U_17852,U_17854),U_17852,c_Product__Type_Ofst(U_17852,U_17854)),hAPP(c_List_Oset(tc_prod(U_17852,U_17854)),U_17856))))
    | hAPP(c_Map_Omap__of(U_17852,U_17854,U_17856),U_17858) != c_Option_Ooption_ONone(U_17854) ),
    inference(clausify,[status(thm)],[f_4336_4]) ).

cnf(f_4336_6,plain,
    ( hAPP(c_Map_Omap__of(U_17853,U_17855,U_17857),U_17859) = c_Option_Ooption_ONone(U_17855)
    | hBOOL(hAPP(hAPP(c_member(U_17853),U_17859),hAPP(c_Set_Oimage(tc_prod(U_17853,U_17855),U_17853,c_Product__Type_Ofst(U_17853,U_17855)),hAPP(c_List_Oset(tc_prod(U_17853,U_17855)),U_17857)))) ),
    inference(clausify,[status(thm)],[f_4336_4]) ).

fof(f_4337_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_4337_2,plain,
    ! [U_17862,U_17861,U_17860] : hAPP(c_Option_Omap(U_17860,U_17861),U_17862) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17861),U_17860,c_Option_Ooption_ONone(U_17861),hAPP(hAPP(c_COMBB(U_17861,tc_Option_Ooption(U_17861),U_17860),c_Option_Ooption_OSome(U_17861)),U_17862)),
    inference(variable_rename,[status(thm)],[f_4337_1]) ).

fof(f_4337_3,plain,
    ! [U_17862,U_17861,U_17860] : hAPP(c_Option_Omap(U_17860,U_17861),U_17862) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17861),U_17860,c_Option_Ooption_ONone(U_17861),hAPP(hAPP(c_COMBB(U_17861,tc_Option_Ooption(U_17861),U_17860),c_Option_Ooption_OSome(U_17861)),U_17862)),
    inference(definitional_conversion,[status(esa)],[f_4337_2]) ).

cnf(f_4337_4,plain,
    hAPP(c_Option_Omap(U_17860,U_17861),U_17862) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17861),U_17860,c_Option_Ooption_ONone(U_17861),hAPP(hAPP(c_COMBB(U_17861,tc_Option_Ooption(U_17861),U_17860),c_Option_Ooption_OSome(U_17861)),U_17862)),
    inference(clausify,[status(thm)],[f_4337_3]) ).

fof(f_4338_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_4338_2,plain,
    ( ( c_Com_OWT__bodies
      | ? [U_17864] :
          ( ~ 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_17864))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_17864),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) ) )
    & ( ! [U_17863] :
          ( 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_17863))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_17863),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_4338_1]) ).

fof(f_4338_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)),sK456))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),sK456),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) ) )
    & ( ! [U_17863] :
          ( 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_17863))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_17863),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,[sK456]),skolemize(U_17864,sK456)],[f_4338_2]) ).

fof(f_4338_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)),sK456))
      | ~ sP1123 )
    & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),sK456),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
      | ~ sP1123 )
    & ( c_Com_OWT__bodies
      | sP1123 )
    & ! [U_17863] :
        ( 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_17863))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_17863),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,[sP1123])],[f_4338_3]) ).

cnf(f_4338_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_17863))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_17863),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
    | ~ c_Com_OWT__bodies ),
    inference(clausify,[status(thm)],[f_4338_4]) ).

cnf(f_4338_6,plain,
    ( c_Com_OWT__bodies
    | sP1123 ),
    inference(clausify,[status(thm)],[f_4338_4]) ).

cnf(f_4338_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),sK456),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
    | ~ sP1123 ),
    inference(clausify,[status(thm)],[f_4338_4]) ).

cnf(f_4338_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)),sK456))
    | ~ sP1123 ),
    inference(clausify,[status(thm)],[f_4338_4]) ).

fof(f_4339_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_4339_2,plain,
    ! [U_17868,U_17867,U_17866,U_17865] : c_Map_Omap__of(U_17865,U_17866,hAPP(hAPP(c_List_Omap(U_17865,tc_prod(U_17865,U_17866)),hAPP(hAPP(c_COMBS(U_17865,U_17866,tc_prod(U_17865,U_17866)),c_Product__Type_OPair(U_17865,U_17866)),U_17867)),U_17868)) = c_Map_Orestrict__map(U_17865,U_17866,hAPP(c_Fun_Ocomp(U_17866,tc_Option_Ooption(U_17866),U_17865,c_Option_Ooption_OSome(U_17866)),U_17867),hAPP(c_List_Oset(U_17865),U_17868)),
    inference(variable_rename,[status(thm)],[f_4339_1]) ).

fof(f_4339_3,plain,
    ! [U_17865,U_17866,U_17867,U_17868] : c_Map_Omap__of(U_17865,U_17866,hAPP(hAPP(c_List_Omap(U_17865,tc_prod(U_17865,U_17866)),hAPP(hAPP(c_COMBS(U_17865,U_17866,tc_prod(U_17865,U_17866)),c_Product__Type_OPair(U_17865,U_17866)),U_17867)),U_17868)) = c_Map_Orestrict__map(U_17865,U_17866,hAPP(c_Fun_Ocomp(U_17866,tc_Option_Ooption(U_17866),U_17865,c_Option_Ooption_OSome(U_17866)),U_17867),hAPP(c_List_Oset(U_17865),U_17868)),
    inference(definitional_conversion,[status(esa)],[f_4339_2]) ).

cnf(f_4339_4,plain,
    c_Map_Omap__of(U_17865,U_17866,hAPP(hAPP(c_List_Omap(U_17865,tc_prod(U_17865,U_17866)),hAPP(hAPP(c_COMBS(U_17865,U_17866,tc_prod(U_17865,U_17866)),c_Product__Type_OPair(U_17865,U_17866)),U_17867)),U_17868)) = c_Map_Orestrict__map(U_17865,U_17866,hAPP(c_Fun_Ocomp(U_17866,tc_Option_Ooption(U_17866),U_17865,c_Option_Ooption_OSome(U_17866)),U_17867),hAPP(c_List_Oset(U_17865),U_17868)),
    inference(clausify,[status(thm)],[f_4339_3]) ).

fof(f_4340_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_4340_2,plain,
    ! [U_17871,U_17870,U_17869] :
      ( c_Map_Oran(U_17869,U_17870,c_Map_Omap__of(U_17869,U_17870,U_17871)) = hAPP(c_Set_Oimage(tc_prod(U_17869,U_17870),U_17870,c_Product__Type_Osnd(U_17869,U_17870)),hAPP(c_List_Oset(tc_prod(U_17869,U_17870)),U_17871))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17869),hAPP(hAPP(c_List_Omap(tc_prod(U_17869,U_17870),U_17869),c_Product__Type_Ofst(U_17869,U_17870)),U_17871))) ),
    inference(variable_rename,[status(thm)],[f_4340_1]) ).

fof(f_4340_3,plain,
    ! [U_17869,U_17870,U_17871] :
      ( c_Map_Oran(U_17869,U_17870,c_Map_Omap__of(U_17869,U_17870,U_17871)) = hAPP(c_Set_Oimage(tc_prod(U_17869,U_17870),U_17870,c_Product__Type_Osnd(U_17869,U_17870)),hAPP(c_List_Oset(tc_prod(U_17869,U_17870)),U_17871))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17869),hAPP(hAPP(c_List_Omap(tc_prod(U_17869,U_17870),U_17869),c_Product__Type_Ofst(U_17869,U_17870)),U_17871))) ),
    inference(definitional_conversion,[status(esa)],[f_4340_2]) ).

cnf(f_4340_4,plain,
    ( c_Map_Oran(U_17869,U_17870,c_Map_Omap__of(U_17869,U_17870,U_17871)) = hAPP(c_Set_Oimage(tc_prod(U_17869,U_17870),U_17870,c_Product__Type_Osnd(U_17869,U_17870)),hAPP(c_List_Oset(tc_prod(U_17869,U_17870)),U_17871))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17869),hAPP(hAPP(c_List_Omap(tc_prod(U_17869,U_17870),U_17869),c_Product__Type_Ofst(U_17869,U_17870)),U_17871))) ),
    inference(clausify,[status(thm)],[f_4340_3]) ).

fof(f_4341_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_4341_2,plain,
    ! [U_17874,U_17873,U_17872] :
      ( hAPP(c_List_Oset(tc_prod(U_17872,U_17873)),U_17874) = hAPP(c_Set_OCollect(tc_prod(U_17872,U_17873)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17872,U_17873,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17872,tc_fun(U_17873,tc_Option_Ooption(U_17873)),tc_fun(U_17873,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17873),tc_HOL_Obool),tc_fun(tc_fun(U_17873,tc_Option_Ooption(U_17873)),tc_fun(U_17873,tc_HOL_Obool)),U_17872),c_COMBB(tc_Option_Ooption(U_17873),tc_HOL_Obool,U_17873)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17873),tc_fun(tc_Option_Ooption(U_17873),tc_HOL_Obool),U_17872),c_fequal),c_Map_Omap__of(U_17872,U_17873,U_17874)))),c_Option_Ooption_OSome(U_17873))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17872),hAPP(hAPP(c_List_Omap(tc_prod(U_17872,U_17873),U_17872),c_Product__Type_Ofst(U_17872,U_17873)),U_17874))) ),
    inference(variable_rename,[status(thm)],[f_4341_1]) ).

fof(f_4341_3,plain,
    ! [U_17872,U_17873,U_17874] :
      ( hAPP(c_List_Oset(tc_prod(U_17872,U_17873)),U_17874) = hAPP(c_Set_OCollect(tc_prod(U_17872,U_17873)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17872,U_17873,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17872,tc_fun(U_17873,tc_Option_Ooption(U_17873)),tc_fun(U_17873,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17873),tc_HOL_Obool),tc_fun(tc_fun(U_17873,tc_Option_Ooption(U_17873)),tc_fun(U_17873,tc_HOL_Obool)),U_17872),c_COMBB(tc_Option_Ooption(U_17873),tc_HOL_Obool,U_17873)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17873),tc_fun(tc_Option_Ooption(U_17873),tc_HOL_Obool),U_17872),c_fequal),c_Map_Omap__of(U_17872,U_17873,U_17874)))),c_Option_Ooption_OSome(U_17873))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17872),hAPP(hAPP(c_List_Omap(tc_prod(U_17872,U_17873),U_17872),c_Product__Type_Ofst(U_17872,U_17873)),U_17874))) ),
    inference(definitional_conversion,[status(esa)],[f_4341_2]) ).

cnf(f_4341_4,plain,
    ( hAPP(c_List_Oset(tc_prod(U_17872,U_17873)),U_17874) = hAPP(c_Set_OCollect(tc_prod(U_17872,U_17873)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17872,U_17873,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17872,tc_fun(U_17873,tc_Option_Ooption(U_17873)),tc_fun(U_17873,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17873),tc_HOL_Obool),tc_fun(tc_fun(U_17873,tc_Option_Ooption(U_17873)),tc_fun(U_17873,tc_HOL_Obool)),U_17872),c_COMBB(tc_Option_Ooption(U_17873),tc_HOL_Obool,U_17873)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17873),tc_fun(tc_Option_Ooption(U_17873),tc_HOL_Obool),U_17872),c_fequal),c_Map_Omap__of(U_17872,U_17873,U_17874)))),c_Option_Ooption_OSome(U_17873))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17872),hAPP(hAPP(c_List_Omap(tc_prod(U_17872,U_17873),U_17872),c_Product__Type_Ofst(U_17872,U_17873)),U_17874))) ),
    inference(clausify,[status(thm)],[f_4341_3]) ).

fof(f_4342_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_4342_2,plain,
    ! [U_17878,U_17877,U_17876,U_17875] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_17875),hAPP(hAPP(c_List_Omap(U_17876,U_17875),U_17877),U_17878)))
        | ~ c_Fun_Oinj__on(U_17876,U_17875,U_17877,hAPP(c_List_Oset(U_17876),U_17878))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17876),U_17878)) )
      & ( ( c_Fun_Oinj__on(U_17876,U_17875,U_17877,hAPP(c_List_Oset(U_17876),U_17878))
          & hBOOL(hAPP(c_List_Odistinct(U_17876),U_17878)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17875),hAPP(hAPP(c_List_Omap(U_17876,U_17875),U_17877),U_17878))) ) ),
    inference(variable_rename,[status(thm)],[f_4342_1]) ).

fof(f_4342_3,plain,
    ( ! [U_17886,U_17884,U_17882,U_17880] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17880),hAPP(hAPP(c_List_Omap(U_17882,U_17880),U_17884),U_17886)))
        | ~ c_Fun_Oinj__on(U_17882,U_17880,U_17884,hAPP(c_List_Oset(U_17882),U_17886))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17882),U_17886)) )
    & ! [U_17885,U_17883,U_17881,U_17879] :
        ( ( c_Fun_Oinj__on(U_17881,U_17879,U_17883,hAPP(c_List_Oset(U_17881),U_17885))
          & hBOOL(hAPP(c_List_Odistinct(U_17881),U_17885)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17879),hAPP(hAPP(c_List_Omap(U_17881,U_17879),U_17883),U_17885))) ) ),
    inference(miniscope,[status(thm)],[f_4342_2]) ).

fof(f_4342_4,plain,
    ( ! [U_17881,U_17883,U_17879,U_17885] :
        ( c_Fun_Oinj__on(U_17881,U_17879,U_17883,hAPP(c_List_Oset(U_17881),U_17885))
        | ~ sP1124(U_17881,U_17883,U_17879,U_17885) )
    & ! [U_17881,U_17883,U_17879,U_17885] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17881),U_17885))
        | ~ sP1124(U_17881,U_17883,U_17879,U_17885) )
    & ! [U_17882,U_17880,U_17886,U_17884] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17880),hAPP(hAPP(c_List_Omap(U_17882,U_17880),U_17884),U_17886)))
        | ~ c_Fun_Oinj__on(U_17882,U_17880,U_17884,hAPP(c_List_Oset(U_17882),U_17886))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17882),U_17886)) )
    & ! [U_17881,U_17883,U_17879,U_17885] :
        ( sP1124(U_17881,U_17883,U_17879,U_17885)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17879),hAPP(hAPP(c_List_Omap(U_17881,U_17879),U_17883),U_17885))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1124])],[f_4342_3]) ).

cnf(f_4342_5,plain,
    ( sP1124(U_17881,U_17883,U_17879,U_17885)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17879),hAPP(hAPP(c_List_Omap(U_17881,U_17879),U_17883),U_17885))) ),
    inference(clausify,[status(thm)],[f_4342_4]) ).

cnf(f_4342_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17880),hAPP(hAPP(c_List_Omap(U_17882,U_17880),U_17884),U_17886)))
    | ~ c_Fun_Oinj__on(U_17882,U_17880,U_17884,hAPP(c_List_Oset(U_17882),U_17886))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17882),U_17886)) ),
    inference(clausify,[status(thm)],[f_4342_4]) ).

cnf(f_4342_7,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17881),U_17885))
    | ~ sP1124(U_17881,U_17883,U_17879,U_17885) ),
    inference(clausify,[status(thm)],[f_4342_4]) ).

cnf(f_4342_8,plain,
    ( c_Fun_Oinj__on(U_17881,U_17879,U_17883,hAPP(c_List_Oset(U_17881),U_17885))
    | ~ sP1124(U_17881,U_17883,U_17879,U_17885) ),
    inference(clausify,[status(thm)],[f_4342_4]) ).

fof(f_4343_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_4343_2,plain,
    ! [U_17890,U_17889,U_17888,U_17887] :
      ( ( ( c_Map_Omap__of(U_17887,U_17888,U_17889) = c_Map_Omap__of(U_17887,U_17888,U_17890)
          | hAPP(c_List_Oset(tc_prod(U_17887,U_17888)),U_17889) != hAPP(c_List_Oset(tc_prod(U_17887,U_17888)),U_17890) )
        & ( hAPP(c_List_Oset(tc_prod(U_17887,U_17888)),U_17889) = hAPP(c_List_Oset(tc_prod(U_17887,U_17888)),U_17890)
          | c_Map_Omap__of(U_17887,U_17888,U_17889) != c_Map_Omap__of(U_17887,U_17888,U_17890) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17887),hAPP(hAPP(c_List_Omap(tc_prod(U_17887,U_17888),U_17887),c_Product__Type_Ofst(U_17887,U_17888)),U_17890)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17887),hAPP(hAPP(c_List_Omap(tc_prod(U_17887,U_17888),U_17887),c_Product__Type_Ofst(U_17887,U_17888)),U_17889))) ),
    inference(variable_rename,[status(thm)],[f_4343_1]) ).

fof(f_4343_3,plain,
    ( ! [U_17887,U_17888,U_17889,U_17890] :
        ( c_Map_Omap__of(U_17887,U_17888,U_17889) = c_Map_Omap__of(U_17887,U_17888,U_17890)
        | hAPP(c_List_Oset(tc_prod(U_17887,U_17888)),U_17889) != hAPP(c_List_Oset(tc_prod(U_17887,U_17888)),U_17890)
        | ~ sP1125(U_17887,U_17888,U_17889,U_17890) )
    & ! [U_17887,U_17888,U_17889,U_17890] :
        ( hAPP(c_List_Oset(tc_prod(U_17887,U_17888)),U_17889) = hAPP(c_List_Oset(tc_prod(U_17887,U_17888)),U_17890)
        | c_Map_Omap__of(U_17887,U_17888,U_17889) != c_Map_Omap__of(U_17887,U_17888,U_17890)
        | ~ sP1125(U_17887,U_17888,U_17889,U_17890) )
    & ! [U_17887,U_17888,U_17889,U_17890] :
        ( sP1125(U_17887,U_17888,U_17889,U_17890)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17887),hAPP(hAPP(c_List_Omap(tc_prod(U_17887,U_17888),U_17887),c_Product__Type_Ofst(U_17887,U_17888)),U_17890)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17887),hAPP(hAPP(c_List_Omap(tc_prod(U_17887,U_17888),U_17887),c_Product__Type_Ofst(U_17887,U_17888)),U_17889))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1125])],[f_4343_2]) ).

cnf(f_4343_4,plain,
    ( sP1125(U_17887,U_17888,U_17889,U_17890)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17887),hAPP(hAPP(c_List_Omap(tc_prod(U_17887,U_17888),U_17887),c_Product__Type_Ofst(U_17887,U_17888)),U_17890)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17887),hAPP(hAPP(c_List_Omap(tc_prod(U_17887,U_17888),U_17887),c_Product__Type_Ofst(U_17887,U_17888)),U_17889))) ),
    inference(clausify,[status(thm)],[f_4343_3]) ).

cnf(f_4343_5,plain,
    ( hAPP(c_List_Oset(tc_prod(U_17887,U_17888)),U_17889) = hAPP(c_List_Oset(tc_prod(U_17887,U_17888)),U_17890)
    | c_Map_Omap__of(U_17887,U_17888,U_17889) != c_Map_Omap__of(U_17887,U_17888,U_17890)
    | ~ sP1125(U_17887,U_17888,U_17889,U_17890) ),
    inference(clausify,[status(thm)],[f_4343_3]) ).

cnf(f_4343_6,plain,
    ( c_Map_Omap__of(U_17887,U_17888,U_17889) = c_Map_Omap__of(U_17887,U_17888,U_17890)
    | hAPP(c_List_Oset(tc_prod(U_17887,U_17888)),U_17889) != hAPP(c_List_Oset(tc_prod(U_17887,U_17888)),U_17890)
    | ~ sP1125(U_17887,U_17888,U_17889,U_17890) ),
    inference(clausify,[status(thm)],[f_4343_3]) ).

fof(f_4344_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_4344_2,plain,
    ! [U_17895,U_17894,U_17893,U_17892,U_17891] :
      ( hAPP(c_Map_Omap__of(U_17891,U_17892,U_17893),U_17894) = hAPP(c_Option_Ooption_OSome(U_17892),U_17895)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17891,U_17892)),hAPP(hAPP(c_Product__Type_OPair(U_17891,U_17892),U_17894),U_17895)),hAPP(c_List_Oset(tc_prod(U_17891,U_17892)),U_17893)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17891),hAPP(hAPP(c_List_Omap(tc_prod(U_17891,U_17892),U_17891),c_Product__Type_Ofst(U_17891,U_17892)),U_17893))) ),
    inference(variable_rename,[status(thm)],[f_4344_1]) ).

fof(f_4344_3,plain,
    ! [U_17892,U_17891,U_17893,U_17894,U_17895] :
      ( hAPP(c_Map_Omap__of(U_17891,U_17892,U_17893),U_17894) = hAPP(c_Option_Ooption_OSome(U_17892),U_17895)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17891,U_17892)),hAPP(hAPP(c_Product__Type_OPair(U_17891,U_17892),U_17894),U_17895)),hAPP(c_List_Oset(tc_prod(U_17891,U_17892)),U_17893)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17891),hAPP(hAPP(c_List_Omap(tc_prod(U_17891,U_17892),U_17891),c_Product__Type_Ofst(U_17891,U_17892)),U_17893))) ),
    inference(definitional_conversion,[status(esa)],[f_4344_2]) ).

cnf(f_4344_4,plain,
    ( hAPP(c_Map_Omap__of(U_17891,U_17892,U_17893),U_17894) = hAPP(c_Option_Ooption_OSome(U_17892),U_17895)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17891,U_17892)),hAPP(hAPP(c_Product__Type_OPair(U_17891,U_17892),U_17894),U_17895)),hAPP(c_List_Oset(tc_prod(U_17891,U_17892)),U_17893)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17891),hAPP(hAPP(c_List_Omap(tc_prod(U_17891,U_17892),U_17891),c_Product__Type_Ofst(U_17891,U_17892)),U_17893))) ),
    inference(clausify,[status(thm)],[f_4344_3]) ).

fof(f_4345_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_4345_2,plain,
    ! [U_17900,U_17899,U_17898,U_17897,U_17896] :
      ( ( ( hAPP(c_Map_Omap__of(U_17896,U_17897,U_17898),U_17899) = hAPP(c_Option_Ooption_OSome(U_17897),U_17900)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17896,U_17897)),hAPP(hAPP(c_Product__Type_OPair(U_17896,U_17897),U_17899),U_17900)),hAPP(c_List_Oset(tc_prod(U_17896,U_17897)),U_17898))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17896,U_17897)),hAPP(hAPP(c_Product__Type_OPair(U_17896,U_17897),U_17899),U_17900)),hAPP(c_List_Oset(tc_prod(U_17896,U_17897)),U_17898)))
          | hAPP(c_Map_Omap__of(U_17896,U_17897,U_17898),U_17899) != hAPP(c_Option_Ooption_OSome(U_17897),U_17900) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17896),hAPP(hAPP(c_List_Omap(tc_prod(U_17896,U_17897),U_17896),c_Product__Type_Ofst(U_17896,U_17897)),U_17898))) ),
    inference(variable_rename,[status(thm)],[f_4345_1]) ).

fof(f_4345_3,plain,
    ( ! [U_17896,U_17897,U_17898,U_17899,U_17900] :
        ( hAPP(c_Map_Omap__of(U_17896,U_17897,U_17898),U_17899) = hAPP(c_Option_Ooption_OSome(U_17897),U_17900)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17896,U_17897)),hAPP(hAPP(c_Product__Type_OPair(U_17896,U_17897),U_17899),U_17900)),hAPP(c_List_Oset(tc_prod(U_17896,U_17897)),U_17898)))
        | ~ sP1126(U_17896,U_17897,U_17898,U_17899,U_17900) )
    & ! [U_17896,U_17897,U_17898,U_17899,U_17900] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17896,U_17897)),hAPP(hAPP(c_Product__Type_OPair(U_17896,U_17897),U_17899),U_17900)),hAPP(c_List_Oset(tc_prod(U_17896,U_17897)),U_17898)))
        | hAPP(c_Map_Omap__of(U_17896,U_17897,U_17898),U_17899) != hAPP(c_Option_Ooption_OSome(U_17897),U_17900)
        | ~ sP1126(U_17896,U_17897,U_17898,U_17899,U_17900) )
    & ! [U_17896,U_17897,U_17898,U_17899,U_17900] :
        ( sP1126(U_17896,U_17897,U_17898,U_17899,U_17900)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17896),hAPP(hAPP(c_List_Omap(tc_prod(U_17896,U_17897),U_17896),c_Product__Type_Ofst(U_17896,U_17897)),U_17898))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1126])],[f_4345_2]) ).

cnf(f_4345_4,plain,
    ( sP1126(U_17896,U_17897,U_17898,U_17899,U_17900)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17896),hAPP(hAPP(c_List_Omap(tc_prod(U_17896,U_17897),U_17896),c_Product__Type_Ofst(U_17896,U_17897)),U_17898))) ),
    inference(clausify,[status(thm)],[f_4345_3]) ).

cnf(f_4345_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17896,U_17897)),hAPP(hAPP(c_Product__Type_OPair(U_17896,U_17897),U_17899),U_17900)),hAPP(c_List_Oset(tc_prod(U_17896,U_17897)),U_17898)))
    | hAPP(c_Map_Omap__of(U_17896,U_17897,U_17898),U_17899) != hAPP(c_Option_Ooption_OSome(U_17897),U_17900)
    | ~ sP1126(U_17896,U_17897,U_17898,U_17899,U_17900) ),
    inference(clausify,[status(thm)],[f_4345_3]) ).

cnf(f_4345_6,plain,
    ( hAPP(c_Map_Omap__of(U_17896,U_17897,U_17898),U_17899) = hAPP(c_Option_Ooption_OSome(U_17897),U_17900)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17896,U_17897)),hAPP(hAPP(c_Product__Type_OPair(U_17896,U_17897),U_17899),U_17900)),hAPP(c_List_Oset(tc_prod(U_17896,U_17897)),U_17898)))
    | ~ sP1126(U_17896,U_17897,U_17898,U_17899,U_17900) ),
    inference(clausify,[status(thm)],[f_4345_3]) ).

fof(f_4346_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_4346_2,plain,
    ! [U_17905,U_17904,U_17903,U_17902,U_17901] :
      ( ( ( hAPP(c_Option_Ooption_OSome(U_17902),U_17904) = hAPP(c_Map_Omap__of(U_17901,U_17902,U_17903),U_17905)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17901,U_17902)),hAPP(hAPP(c_Product__Type_OPair(U_17901,U_17902),U_17905),U_17904)),hAPP(c_List_Oset(tc_prod(U_17901,U_17902)),U_17903))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17901,U_17902)),hAPP(hAPP(c_Product__Type_OPair(U_17901,U_17902),U_17905),U_17904)),hAPP(c_List_Oset(tc_prod(U_17901,U_17902)),U_17903)))
          | hAPP(c_Option_Ooption_OSome(U_17902),U_17904) != hAPP(c_Map_Omap__of(U_17901,U_17902,U_17903),U_17905) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17901),hAPP(hAPP(c_List_Omap(tc_prod(U_17901,U_17902),U_17901),c_Product__Type_Ofst(U_17901,U_17902)),U_17903))) ),
    inference(variable_rename,[status(thm)],[f_4346_1]) ).

fof(f_4346_3,plain,
    ( ! [U_17901,U_17903,U_17902,U_17904,U_17905] :
        ( hAPP(c_Option_Ooption_OSome(U_17902),U_17904) = hAPP(c_Map_Omap__of(U_17901,U_17902,U_17903),U_17905)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17901,U_17902)),hAPP(hAPP(c_Product__Type_OPair(U_17901,U_17902),U_17905),U_17904)),hAPP(c_List_Oset(tc_prod(U_17901,U_17902)),U_17903)))
        | ~ sP1127(U_17901,U_17903,U_17902,U_17904,U_17905) )
    & ! [U_17901,U_17903,U_17902,U_17904,U_17905] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17901,U_17902)),hAPP(hAPP(c_Product__Type_OPair(U_17901,U_17902),U_17905),U_17904)),hAPP(c_List_Oset(tc_prod(U_17901,U_17902)),U_17903)))
        | hAPP(c_Option_Ooption_OSome(U_17902),U_17904) != hAPP(c_Map_Omap__of(U_17901,U_17902,U_17903),U_17905)
        | ~ sP1127(U_17901,U_17903,U_17902,U_17904,U_17905) )
    & ! [U_17901,U_17903,U_17902,U_17904,U_17905] :
        ( sP1127(U_17901,U_17903,U_17902,U_17904,U_17905)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17901),hAPP(hAPP(c_List_Omap(tc_prod(U_17901,U_17902),U_17901),c_Product__Type_Ofst(U_17901,U_17902)),U_17903))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1127])],[f_4346_2]) ).

cnf(f_4346_4,plain,
    ( sP1127(U_17901,U_17903,U_17902,U_17904,U_17905)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17901),hAPP(hAPP(c_List_Omap(tc_prod(U_17901,U_17902),U_17901),c_Product__Type_Ofst(U_17901,U_17902)),U_17903))) ),
    inference(clausify,[status(thm)],[f_4346_3]) ).

cnf(f_4346_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17901,U_17902)),hAPP(hAPP(c_Product__Type_OPair(U_17901,U_17902),U_17905),U_17904)),hAPP(c_List_Oset(tc_prod(U_17901,U_17902)),U_17903)))
    | hAPP(c_Option_Ooption_OSome(U_17902),U_17904) != hAPP(c_Map_Omap__of(U_17901,U_17902,U_17903),U_17905)
    | ~ sP1127(U_17901,U_17903,U_17902,U_17904,U_17905) ),
    inference(clausify,[status(thm)],[f_4346_3]) ).

cnf(f_4346_6,plain,
    ( hAPP(c_Option_Ooption_OSome(U_17902),U_17904) = hAPP(c_Map_Omap__of(U_17901,U_17902,U_17903),U_17905)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17901,U_17902)),hAPP(hAPP(c_Product__Type_OPair(U_17901,U_17902),U_17905),U_17904)),hAPP(c_List_Oset(tc_prod(U_17901,U_17902)),U_17903)))
    | ~ sP1127(U_17901,U_17903,U_17902,U_17904,U_17905) ),
    inference(clausify,[status(thm)],[f_4346_3]) ).

fof(f_4347_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_4347_2,plain,
    ! [U_17907,U_17906] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_17906,U_17907) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17906),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17907),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_4347_1]) ).

fof(f_4347_3,plain,
    ! [U_17906,U_17907] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_17906,U_17907) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17906),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17907),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_4347_2]) ).

cnf(f_4347_4,plain,
    c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_17906,U_17907) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17906),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17907),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_4347_3]) ).

fof(f_4348_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_4348_2,plain,
    ! [U_17913,U_17912,U_17911,U_17910,U_17909] :
      ( ? [U_17908] : hAPP(c_Map_Omap__of(U_17909,U_17910,U_17913),U_17911) = hAPP(c_Option_Ooption_OSome(U_17910),U_17908)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17909,U_17910)),hAPP(hAPP(c_Product__Type_OPair(U_17909,U_17910),U_17911),U_17912)),hAPP(c_List_Oset(tc_prod(U_17909,U_17910)),U_17913))) ),
    inference(variable_rename,[status(thm)],[f_4348_1]) ).

fof(f_4348_3,plain,
    ! [U_17913,U_17912,U_17911,U_17910,U_17909] :
      ( hAPP(c_Map_Omap__of(U_17909,U_17910,U_17913),U_17911) = hAPP(c_Option_Ooption_OSome(U_17910),sK457(U_17913,U_17912,U_17911,U_17910,U_17909))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17909,U_17910)),hAPP(hAPP(c_Product__Type_OPair(U_17909,U_17910),U_17911),U_17912)),hAPP(c_List_Oset(tc_prod(U_17909,U_17910)),U_17913))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK457]),skolemize(U_17908,sK457(U_17913,U_17912,U_17911,U_17910,U_17909))],[f_4348_2]) ).

fof(f_4348_4,plain,
    ! [U_17910,U_17909,U_17911,U_17912,U_17913] :
      ( hAPP(c_Map_Omap__of(U_17909,U_17910,U_17913),U_17911) = hAPP(c_Option_Ooption_OSome(U_17910),sK457(U_17913,U_17912,U_17911,U_17910,U_17909))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17909,U_17910)),hAPP(hAPP(c_Product__Type_OPair(U_17909,U_17910),U_17911),U_17912)),hAPP(c_List_Oset(tc_prod(U_17909,U_17910)),U_17913))) ),
    inference(definitional_conversion,[status(esa)],[f_4348_3]) ).

cnf(f_4348_5,plain,
    ( hAPP(c_Map_Omap__of(U_17909,U_17910,U_17913),U_17911) = hAPP(c_Option_Ooption_OSome(U_17910),sK457(U_17913,U_17912,U_17911,U_17910,U_17909))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17909,U_17910)),hAPP(hAPP(c_Product__Type_OPair(U_17909,U_17910),U_17911),U_17912)),hAPP(c_List_Oset(tc_prod(U_17909,U_17910)),U_17913))) ),
    inference(clausify,[status(thm)],[f_4348_4]) ).

fof(f_4349_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_4349_2,plain,
    ! [U_17915,U_17914] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17914,U_17915) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17914,U_17915)),
    inference(variable_rename,[status(thm)],[f_4349_1]) ).

fof(f_4349_3,plain,
    ! [U_17915,U_17914] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17914,U_17915) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17914,U_17915)),
    inference(definitional_conversion,[status(esa)],[f_4349_2]) ).

cnf(f_4349_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17914,U_17915) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17914,U_17915)),
    inference(clausify,[status(thm)],[f_4349_3]) ).

fof(f_4350_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_4350_2,plain,
    ! [U_17917,U_17916] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17916,U_17917)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17916,U_17917),
    inference(variable_rename,[status(thm)],[f_4350_1]) ).

fof(f_4350_3,plain,
    ! [U_17916,U_17917] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17916,U_17917)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17916,U_17917),
    inference(definitional_conversion,[status(esa)],[f_4350_2]) ).

cnf(f_4350_4,plain,
    hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17916,U_17917)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17916,U_17917),
    inference(clausify,[status(thm)],[f_4350_3]) ).

fof(f_4351_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_4351_2,plain,
    ! [U_17919,U_17918] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_17918,U_17919))),
    inference(variable_rename,[status(thm)],[f_4351_1]) ).

fof(f_4351_3,plain,
    ! [U_17918,U_17919] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_17918,U_17919))),
    inference(definitional_conversion,[status(esa)],[f_4351_2]) ).

cnf(f_4351_4,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_17918,U_17919))),
    inference(clausify,[status(thm)],[f_4351_3]) ).

fof(f_4352_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_4352_2,plain,
    ! [U_17921,U_17920] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_17920),U_17921) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17920,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17921),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_4352_1]) ).

fof(f_4352_3,plain,
    ! [U_17920,U_17921] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_17920),U_17921) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17920,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17921),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_4352_2]) ).

cnf(f_4352_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_17920),U_17921) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17920,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17921),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_4352_3]) ).

fof(f_4353_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_4353_2,plain,
    ! [U_17923,U_17922] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_17922,U_17923) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17922),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_17923)),
    inference(variable_rename,[status(thm)],[f_4353_1]) ).

fof(f_4353_3,plain,
    ! [U_17922,U_17923] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_17922,U_17923) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17922),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_17923)),
    inference(definitional_conversion,[status(esa)],[f_4353_2]) ).

cnf(f_4353_4,plain,
    c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_17922,U_17923) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17922),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_17923)),
    inference(clausify,[status(thm)],[f_4353_3]) ).

fof(f_4354_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_4354_2,plain,
    ! [U_17924] :
      ( ( c_List_Onat__list(U_17924)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17924)) )
      & ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17924))
        | ~ c_List_Onat__list(U_17924) ) ),
    inference(variable_rename,[status(thm)],[f_4354_1]) ).

fof(f_4354_3,plain,
    ( ! [U_17926] :
        ( c_List_Onat__list(U_17926)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17926)) )
    & ! [U_17925] :
        ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17925))
        | ~ c_List_Onat__list(U_17925) ) ),
    inference(miniscope,[status(thm)],[f_4354_2]) ).

fof(f_4354_4,plain,
    ( ! [U_17926] :
        ( c_List_Onat__list(U_17926)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17926)) )
    & ! [U_17925] :
        ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17925))
        | ~ c_List_Onat__list(U_17925) ) ),
    inference(definitional_conversion,[status(esa)],[f_4354_3]) ).

cnf(f_4354_5,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17925))
    | ~ c_List_Onat__list(U_17925) ),
    inference(clausify,[status(thm)],[f_4354_4]) ).

cnf(f_4354_6,plain,
    ( c_List_Onat__list(U_17926)
    | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17926)) ),
    inference(clausify,[status(thm)],[f_4354_4]) ).

fof(f_4355_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_4355_2,plain,
    ! [U_17929,U_17928,U_17927] :
      ( hAPP(c_List_Oset(U_17927),c_List_Oremove1(U_17927,U_17929,U_17928)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17927,tc_HOL_Obool)),hAPP(c_List_Oset(U_17927),U_17928)),hAPP(hAPP(c_Set_Oinsert(U_17927),U_17929),c_Orderings_Obot__class_Obot(tc_fun(U_17927,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17927),U_17928)) ),
    inference(variable_rename,[status(thm)],[f_4355_1]) ).

fof(f_4355_3,plain,
    ! [U_17927,U_17928,U_17929] :
      ( hAPP(c_List_Oset(U_17927),c_List_Oremove1(U_17927,U_17929,U_17928)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17927,tc_HOL_Obool)),hAPP(c_List_Oset(U_17927),U_17928)),hAPP(hAPP(c_Set_Oinsert(U_17927),U_17929),c_Orderings_Obot__class_Obot(tc_fun(U_17927,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17927),U_17928)) ),
    inference(definitional_conversion,[status(esa)],[f_4355_2]) ).

cnf(f_4355_4,plain,
    ( hAPP(c_List_Oset(U_17927),c_List_Oremove1(U_17927,U_17929,U_17928)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17927,tc_HOL_Obool)),hAPP(c_List_Oset(U_17927),U_17928)),hAPP(hAPP(c_Set_Oinsert(U_17927),U_17929),c_Orderings_Obot__class_Obot(tc_fun(U_17927,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17927),U_17928)) ),
    inference(clausify,[status(thm)],[f_4355_3]) ).

fof(f_4356_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_4356_2,plain,
    ! [U_17933,U_17932,U_17931,U_17930] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_17932),U_17930),hAPP(c_List_Oset(U_17932),c_List_Oremove1(U_17932,U_17931,U_17933))))
          | ~ hBOOL(hAPP(hAPP(c_member(U_17932),U_17930),hAPP(c_List_Oset(U_17932),U_17933))) )
        & ( hBOOL(hAPP(hAPP(c_member(U_17932),U_17930),hAPP(c_List_Oset(U_17932),U_17933)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_17932),U_17930),hAPP(c_List_Oset(U_17932),c_List_Oremove1(U_17932,U_17931,U_17933)))) ) )
      | U_17930 = U_17931 ),
    inference(variable_rename,[status(thm)],[f_4356_1]) ).

fof(f_4356_3,plain,
    ( ! [U_17930,U_17931,U_17932,U_17933] :
        ( hBOOL(hAPP(hAPP(c_member(U_17932),U_17930),hAPP(c_List_Oset(U_17932),c_List_Oremove1(U_17932,U_17931,U_17933))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17932),U_17930),hAPP(c_List_Oset(U_17932),U_17933)))
        | ~ sP1128(U_17930,U_17931,U_17932,U_17933) )
    & ! [U_17930,U_17931,U_17932,U_17933] :
        ( hBOOL(hAPP(hAPP(c_member(U_17932),U_17930),hAPP(c_List_Oset(U_17932),U_17933)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17932),U_17930),hAPP(c_List_Oset(U_17932),c_List_Oremove1(U_17932,U_17931,U_17933))))
        | ~ sP1128(U_17930,U_17931,U_17932,U_17933) )
    & ! [U_17930,U_17931,U_17932,U_17933] :
        ( sP1128(U_17930,U_17931,U_17932,U_17933)
        | U_17930 = U_17931 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1128])],[f_4356_2]) ).

cnf(f_4356_4,plain,
    ( sP1128(U_17930,U_17931,U_17932,U_17933)
    | U_17930 = U_17931 ),
    inference(clausify,[status(thm)],[f_4356_3]) ).

cnf(f_4356_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17932),U_17930),hAPP(c_List_Oset(U_17932),U_17933)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17932),U_17930),hAPP(c_List_Oset(U_17932),c_List_Oremove1(U_17932,U_17931,U_17933))))
    | ~ sP1128(U_17930,U_17931,U_17932,U_17933) ),
    inference(clausify,[status(thm)],[f_4356_3]) ).

cnf(f_4356_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17932),U_17930),hAPP(c_List_Oset(U_17932),c_List_Oremove1(U_17932,U_17931,U_17933))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17932),U_17930),hAPP(c_List_Oset(U_17932),U_17933)))
    | ~ sP1128(U_17930,U_17931,U_17932,U_17933) ),
    inference(clausify,[status(thm)],[f_4356_3]) ).

fof(f_4357_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_4357_2,plain,
    ! [U_17937,U_17936,U_17935,U_17934] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_17934),U_17935),hAPP(c_List_Oset(U_17934),c_List_Oremove1(U_17934,U_17937,U_17936))))
      | hBOOL(hAPP(hAPP(c_member(U_17934),U_17935),hAPP(c_List_Oset(U_17934),U_17936))) ),
    inference(variable_rename,[status(thm)],[f_4357_1]) ).

fof(f_4357_3,plain,
    ! [U_17935,U_17936,U_17934,U_17937] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_17934),U_17935),hAPP(c_List_Oset(U_17934),c_List_Oremove1(U_17934,U_17937,U_17936))))
      | hBOOL(hAPP(hAPP(c_member(U_17934),U_17935),hAPP(c_List_Oset(U_17934),U_17936))) ),
    inference(definitional_conversion,[status(esa)],[f_4357_2]) ).

cnf(f_4357_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17934),U_17935),hAPP(c_List_Oset(U_17934),c_List_Oremove1(U_17934,U_17937,U_17936))))
    | hBOOL(hAPP(hAPP(c_member(U_17934),U_17935),hAPP(c_List_Oset(U_17934),U_17936))) ),
    inference(clausify,[status(thm)],[f_4357_3]) ).

fof(f_4358_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_4358_2,plain,
    ! [U_17940,U_17939,U_17938] :
      ( c_List_Oremove1(U_17938,U_17939,U_17940) = U_17940
      | hBOOL(hAPP(hAPP(c_member(U_17938),U_17939),hAPP(c_List_Oset(U_17938),U_17940))) ),
    inference(variable_rename,[status(thm)],[f_4358_1]) ).

fof(f_4358_3,plain,
    ! [U_17938,U_17939,U_17940] :
      ( c_List_Oremove1(U_17938,U_17939,U_17940) = U_17940
      | hBOOL(hAPP(hAPP(c_member(U_17938),U_17939),hAPP(c_List_Oset(U_17938),U_17940))) ),
    inference(definitional_conversion,[status(esa)],[f_4358_2]) ).

cnf(f_4358_4,plain,
    ( c_List_Oremove1(U_17938,U_17939,U_17940) = U_17940
    | hBOOL(hAPP(hAPP(c_member(U_17938),U_17939),hAPP(c_List_Oset(U_17938),U_17940))) ),
    inference(clausify,[status(thm)],[f_4358_3]) ).

fof(f_4359_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_4359_2,plain,
    ! [U_17943,U_17942,U_17941] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17941,tc_HOL_Obool)),hAPP(c_List_Oset(U_17941),c_List_Oremove1(U_17941,U_17942,U_17943))),hAPP(c_List_Oset(U_17941),U_17943))),
    inference(variable_rename,[status(thm)],[f_4359_1]) ).

fof(f_4359_3,plain,
    ! [U_17941,U_17942,U_17943] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17941,tc_HOL_Obool)),hAPP(c_List_Oset(U_17941),c_List_Oremove1(U_17941,U_17942,U_17943))),hAPP(c_List_Oset(U_17941),U_17943))),
    inference(definitional_conversion,[status(esa)],[f_4359_2]) ).

cnf(f_4359_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17941,tc_HOL_Obool)),hAPP(c_List_Oset(U_17941),c_List_Oremove1(U_17941,U_17942,U_17943))),hAPP(c_List_Oset(U_17941),U_17943))),
    inference(clausify,[status(thm)],[f_4359_3]) ).

fof(f_4360_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_4360_2,plain,
    ! [U_17947,U_17946,U_17945,U_17944] : c_List_Oremove1(U_17944,U_17945,c_List_Oremove1(U_17944,U_17946,U_17947)) = c_List_Oremove1(U_17944,U_17946,c_List_Oremove1(U_17944,U_17945,U_17947)),
    inference(variable_rename,[status(thm)],[f_4360_1]) ).

fof(f_4360_3,plain,
    ! [U_17944,U_17945,U_17946,U_17947] : c_List_Oremove1(U_17944,U_17945,c_List_Oremove1(U_17944,U_17946,U_17947)) = c_List_Oremove1(U_17944,U_17946,c_List_Oremove1(U_17944,U_17945,U_17947)),
    inference(definitional_conversion,[status(esa)],[f_4360_2]) ).

cnf(f_4360_4,plain,
    c_List_Oremove1(U_17944,U_17945,c_List_Oremove1(U_17944,U_17946,U_17947)) = c_List_Oremove1(U_17944,U_17946,c_List_Oremove1(U_17944,U_17945,U_17947)),
    inference(clausify,[status(thm)],[f_4360_3]) ).

fof(f_4361_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_4361_2,plain,
    ! [U_17950,U_17949,U_17948] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17948),c_List_Oremove1(U_17948,U_17950,U_17949)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17948),U_17949)) ),
    inference(variable_rename,[status(thm)],[f_4361_1]) ).

fof(f_4361_3,plain,
    ! [U_17948,U_17949,U_17950] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17948),c_List_Oremove1(U_17948,U_17950,U_17949)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17948),U_17949)) ),
    inference(definitional_conversion,[status(esa)],[f_4361_2]) ).

cnf(f_4361_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17948),c_List_Oremove1(U_17948,U_17950,U_17949)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17948),U_17949)) ),
    inference(clausify,[status(thm)],[f_4361_3]) ).

fof(f_4362_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_4362_2,plain,
    ! [U_17953,U_17952,U_17951] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_17951,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17951,tc_HOL_Obool)),U_17952),hAPP(hAPP(c_Set_Oinsert(U_17951),U_17953),c_Orderings_Obot__class_Obot(tc_fun(U_17951,tc_HOL_Obool))))) = c_List_Oremove1(U_17951,U_17953,c_List_Olinorder__class_Osorted__list__of__set(U_17951,U_17952))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17951),U_17952))
      | ~ class_Orderings_Olinorder(U_17951) ),
    inference(variable_rename,[status(thm)],[f_4362_1]) ).

fof(f_4362_3,plain,
    ! [U_17951,U_17952,U_17953] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_17951,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17951,tc_HOL_Obool)),U_17952),hAPP(hAPP(c_Set_Oinsert(U_17951),U_17953),c_Orderings_Obot__class_Obot(tc_fun(U_17951,tc_HOL_Obool))))) = c_List_Oremove1(U_17951,U_17953,c_List_Olinorder__class_Osorted__list__of__set(U_17951,U_17952))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17951),U_17952))
      | ~ class_Orderings_Olinorder(U_17951) ),
    inference(definitional_conversion,[status(esa)],[f_4362_2]) ).

cnf(f_4362_4,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_17951,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17951,tc_HOL_Obool)),U_17952),hAPP(hAPP(c_Set_Oinsert(U_17951),U_17953),c_Orderings_Obot__class_Obot(tc_fun(U_17951,tc_HOL_Obool))))) = c_List_Oremove1(U_17951,U_17953,c_List_Olinorder__class_Osorted__list__of__set(U_17951,U_17952))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17951),U_17952))
    | ~ class_Orderings_Olinorder(U_17951) ),
    inference(clausify,[status(thm)],[f_4362_3]) ).

fof(f_4363_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_4363_2,plain,
    ! [U_17958,U_17957,U_17956,U_17955,U_17954] :
      ( ( hAPP(c_Map_Omap__of(U_17954,U_17957,hAPP(hAPP(c_List_Ozip(U_17954,U_17957),U_17956),hAPP(hAPP(c_List_Omap(U_17954,U_17957),U_17958),U_17956))),U_17955) = c_Option_Ooption_ONone(U_17957)
        | hBOOL(hAPP(hAPP(c_member(U_17954),U_17955),hAPP(c_List_Oset(U_17954),U_17956))) )
      & ( hAPP(c_Map_Omap__of(U_17954,U_17957,hAPP(hAPP(c_List_Ozip(U_17954,U_17957),U_17956),hAPP(hAPP(c_List_Omap(U_17954,U_17957),U_17958),U_17956))),U_17955) = hAPP(c_Option_Ooption_OSome(U_17957),hAPP(U_17958,U_17955))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17954),U_17955),hAPP(c_List_Oset(U_17954),U_17956))) ) ),
    inference(variable_rename,[status(thm)],[f_4363_1]) ).

fof(f_4363_3,plain,
    ( ! [U_17968,U_17966,U_17964,U_17962,U_17960] :
        ( hAPP(c_Map_Omap__of(U_17960,U_17966,hAPP(hAPP(c_List_Ozip(U_17960,U_17966),U_17964),hAPP(hAPP(c_List_Omap(U_17960,U_17966),U_17968),U_17964))),U_17962) = c_Option_Ooption_ONone(U_17966)
        | hBOOL(hAPP(hAPP(c_member(U_17960),U_17962),hAPP(c_List_Oset(U_17960),U_17964))) )
    & ! [U_17967,U_17965,U_17963,U_17961,U_17959] :
        ( hAPP(c_Map_Omap__of(U_17959,U_17965,hAPP(hAPP(c_List_Ozip(U_17959,U_17965),U_17963),hAPP(hAPP(c_List_Omap(U_17959,U_17965),U_17967),U_17963))),U_17961) = hAPP(c_Option_Ooption_OSome(U_17965),hAPP(U_17967,U_17961))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17959),U_17961),hAPP(c_List_Oset(U_17959),U_17963))) ) ),
    inference(miniscope,[status(thm)],[f_4363_2]) ).

fof(f_4363_4,plain,
    ( ! [U_17960,U_17962,U_17964,U_17966,U_17968] :
        ( hAPP(c_Map_Omap__of(U_17960,U_17966,hAPP(hAPP(c_List_Ozip(U_17960,U_17966),U_17964),hAPP(hAPP(c_List_Omap(U_17960,U_17966),U_17968),U_17964))),U_17962) = c_Option_Ooption_ONone(U_17966)
        | hBOOL(hAPP(hAPP(c_member(U_17960),U_17962),hAPP(c_List_Oset(U_17960),U_17964))) )
    & ! [U_17961,U_17963,U_17965,U_17959,U_17967] :
        ( hAPP(c_Map_Omap__of(U_17959,U_17965,hAPP(hAPP(c_List_Ozip(U_17959,U_17965),U_17963),hAPP(hAPP(c_List_Omap(U_17959,U_17965),U_17967),U_17963))),U_17961) = hAPP(c_Option_Ooption_OSome(U_17965),hAPP(U_17967,U_17961))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17959),U_17961),hAPP(c_List_Oset(U_17959),U_17963))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4363_3]) ).

cnf(f_4363_5,plain,
    ( hAPP(c_Map_Omap__of(U_17959,U_17965,hAPP(hAPP(c_List_Ozip(U_17959,U_17965),U_17963),hAPP(hAPP(c_List_Omap(U_17959,U_17965),U_17967),U_17963))),U_17961) = hAPP(c_Option_Ooption_OSome(U_17965),hAPP(U_17967,U_17961))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17959),U_17961),hAPP(c_List_Oset(U_17959),U_17963))) ),
    inference(clausify,[status(thm)],[f_4363_4]) ).

cnf(f_4363_6,plain,
    ( hAPP(c_Map_Omap__of(U_17960,U_17966,hAPP(hAPP(c_List_Ozip(U_17960,U_17966),U_17964),hAPP(hAPP(c_List_Omap(U_17960,U_17966),U_17968),U_17964))),U_17962) = c_Option_Ooption_ONone(U_17966)
    | hBOOL(hAPP(hAPP(c_member(U_17960),U_17962),hAPP(c_List_Oset(U_17960),U_17964))) ),
    inference(clausify,[status(thm)],[f_4363_4]) ).

fof(f_4364_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_4364_2,plain,
    ! [U_17972,U_17971,U_17970,U_17969] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17971,U_17969)),hAPP(hAPP(c_List_Ozip(U_17971,U_17969),U_17972),U_17970)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17969),U_17970)) ),
    inference(variable_rename,[status(thm)],[f_4364_1]) ).

fof(f_4364_3,plain,
    ! [U_17969,U_17970,U_17971,U_17972] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17971,U_17969)),hAPP(hAPP(c_List_Ozip(U_17971,U_17969),U_17972),U_17970)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17969),U_17970)) ),
    inference(definitional_conversion,[status(esa)],[f_4364_2]) ).

cnf(f_4364_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17971,U_17969)),hAPP(hAPP(c_List_Ozip(U_17971,U_17969),U_17972),U_17970)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17969),U_17970)) ),
    inference(clausify,[status(thm)],[f_4364_3]) ).

fof(f_4365_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_4365_2,plain,
    ! [U_17976,U_17975,U_17974,U_17973] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17973,U_17975)),hAPP(hAPP(c_List_Ozip(U_17973,U_17975),U_17974),U_17976)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17973),U_17974)) ),
    inference(variable_rename,[status(thm)],[f_4365_1]) ).

fof(f_4365_3,plain,
    ! [U_17973,U_17974,U_17975,U_17976] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17973,U_17975)),hAPP(hAPP(c_List_Ozip(U_17973,U_17975),U_17974),U_17976)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17973),U_17974)) ),
    inference(definitional_conversion,[status(esa)],[f_4365_2]) ).

cnf(f_4365_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17973,U_17975)),hAPP(hAPP(c_List_Ozip(U_17973,U_17975),U_17974),U_17976)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17973),U_17974)) ),
    inference(clausify,[status(thm)],[f_4365_3]) ).

fof(f_4366_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_4366_2,plain,
    ! [U_17978,U_17977] : hAPP(hAPP(c_List_Ozip(U_17977,U_17977),U_17978),U_17978) = hAPP(hAPP(c_List_Omap(U_17977,tc_prod(U_17977,U_17977)),hAPP(hAPP(c_COMBS(U_17977,U_17977,tc_prod(U_17977,U_17977)),c_Product__Type_OPair(U_17977,U_17977)),c_COMBI(U_17977))),U_17978),
    inference(variable_rename,[status(thm)],[f_4366_1]) ).

fof(f_4366_3,plain,
    ! [U_17977,U_17978] : hAPP(hAPP(c_List_Ozip(U_17977,U_17977),U_17978),U_17978) = hAPP(hAPP(c_List_Omap(U_17977,tc_prod(U_17977,U_17977)),hAPP(hAPP(c_COMBS(U_17977,U_17977,tc_prod(U_17977,U_17977)),c_Product__Type_OPair(U_17977,U_17977)),c_COMBI(U_17977))),U_17978),
    inference(definitional_conversion,[status(esa)],[f_4366_2]) ).

cnf(f_4366_4,plain,
    hAPP(hAPP(c_List_Ozip(U_17977,U_17977),U_17978),U_17978) = hAPP(hAPP(c_List_Omap(U_17977,tc_prod(U_17977,U_17977)),hAPP(hAPP(c_COMBS(U_17977,U_17977,tc_prod(U_17977,U_17977)),c_Product__Type_OPair(U_17977,U_17977)),c_COMBI(U_17977))),U_17978),
    inference(clausify,[status(thm)],[f_4366_3]) ).

fof(f_4367_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_4367_2,plain,
    ! [U_17981,U_17980,U_17979] : hAPP(hAPP(c_List_Ozip(U_17979,U_17980),hAPP(hAPP(c_List_Omap(tc_prod(U_17979,U_17980),U_17979),c_Product__Type_Ofst(U_17979,U_17980)),U_17981)),hAPP(hAPP(c_List_Omap(tc_prod(U_17979,U_17980),U_17980),c_Product__Type_Osnd(U_17979,U_17980)),U_17981)) = U_17981,
    inference(variable_rename,[status(thm)],[f_4367_1]) ).

fof(f_4367_3,plain,
    ! [U_17979,U_17980,U_17981] : hAPP(hAPP(c_List_Ozip(U_17979,U_17980),hAPP(hAPP(c_List_Omap(tc_prod(U_17979,U_17980),U_17979),c_Product__Type_Ofst(U_17979,U_17980)),U_17981)),hAPP(hAPP(c_List_Omap(tc_prod(U_17979,U_17980),U_17980),c_Product__Type_Osnd(U_17979,U_17980)),U_17981)) = U_17981,
    inference(definitional_conversion,[status(esa)],[f_4367_2]) ).

cnf(f_4367_4,plain,
    hAPP(hAPP(c_List_Ozip(U_17979,U_17980),hAPP(hAPP(c_List_Omap(tc_prod(U_17979,U_17980),U_17979),c_Product__Type_Ofst(U_17979,U_17980)),U_17981)),hAPP(hAPP(c_List_Omap(tc_prod(U_17979,U_17980),U_17980),c_Product__Type_Osnd(U_17979,U_17980)),U_17981)) = U_17981,
    inference(clausify,[status(thm)],[f_4367_3]) ).

fof(f_4368_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_4368_2,plain,
    ! [U_17989,U_17988,U_17987,U_17986,U_17985,U_17984,U_17983,U_17982] : hAPP(hAPP(c_List_Omap(tc_prod(U_17982,U_17983),U_17984),U_17985),hAPP(hAPP(c_List_Ozip(U_17982,U_17983),U_17986),hAPP(hAPP(c_List_Omap(U_17987,U_17983),U_17988),U_17989))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17982,U_17987),U_17984),hAPP(c_Product__Type_Oprod_Oprod__case(U_17982,U_17987,U_17984),hAPP(hAPP(c_COMBB(tc_fun(U_17987,tc_prod(U_17982,U_17983)),tc_fun(U_17987,U_17984),U_17982),hAPP(c_COMBB(tc_prod(U_17982,U_17983),U_17984,U_17987),U_17985)),hAPP(hAPP(c_COMBC(U_17982,tc_fun(U_17987,U_17983),tc_fun(U_17987,tc_prod(U_17982,U_17983))),hAPP(hAPP(c_COMBB(tc_fun(U_17983,tc_prod(U_17982,U_17983)),tc_fun(tc_fun(U_17987,U_17983),tc_fun(U_17987,tc_prod(U_17982,U_17983))),U_17982),c_COMBB(U_17983,tc_prod(U_17982,U_17983),U_17987)),c_Product__Type_OPair(U_17982,U_17983))),U_17988)))),hAPP(hAPP(c_List_Ozip(U_17982,U_17987),U_17986),U_17989)),
    inference(variable_rename,[status(thm)],[f_4368_1]) ).

fof(f_4368_3,plain,
    ! [U_17982,U_17983,U_17984,U_17985,U_17986,U_17987,U_17988,U_17989] : hAPP(hAPP(c_List_Omap(tc_prod(U_17982,U_17983),U_17984),U_17985),hAPP(hAPP(c_List_Ozip(U_17982,U_17983),U_17986),hAPP(hAPP(c_List_Omap(U_17987,U_17983),U_17988),U_17989))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17982,U_17987),U_17984),hAPP(c_Product__Type_Oprod_Oprod__case(U_17982,U_17987,U_17984),hAPP(hAPP(c_COMBB(tc_fun(U_17987,tc_prod(U_17982,U_17983)),tc_fun(U_17987,U_17984),U_17982),hAPP(c_COMBB(tc_prod(U_17982,U_17983),U_17984,U_17987),U_17985)),hAPP(hAPP(c_COMBC(U_17982,tc_fun(U_17987,U_17983),tc_fun(U_17987,tc_prod(U_17982,U_17983))),hAPP(hAPP(c_COMBB(tc_fun(U_17983,tc_prod(U_17982,U_17983)),tc_fun(tc_fun(U_17987,U_17983),tc_fun(U_17987,tc_prod(U_17982,U_17983))),U_17982),c_COMBB(U_17983,tc_prod(U_17982,U_17983),U_17987)),c_Product__Type_OPair(U_17982,U_17983))),U_17988)))),hAPP(hAPP(c_List_Ozip(U_17982,U_17987),U_17986),U_17989)),
    inference(definitional_conversion,[status(esa)],[f_4368_2]) ).

cnf(f_4368_4,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_17982,U_17983),U_17984),U_17985),hAPP(hAPP(c_List_Ozip(U_17982,U_17983),U_17986),hAPP(hAPP(c_List_Omap(U_17987,U_17983),U_17988),U_17989))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17982,U_17987),U_17984),hAPP(c_Product__Type_Oprod_Oprod__case(U_17982,U_17987,U_17984),hAPP(hAPP(c_COMBB(tc_fun(U_17987,tc_prod(U_17982,U_17983)),tc_fun(U_17987,U_17984),U_17982),hAPP(c_COMBB(tc_prod(U_17982,U_17983),U_17984,U_17987),U_17985)),hAPP(hAPP(c_COMBC(U_17982,tc_fun(U_17987,U_17983),tc_fun(U_17987,tc_prod(U_17982,U_17983))),hAPP(hAPP(c_COMBB(tc_fun(U_17983,tc_prod(U_17982,U_17983)),tc_fun(tc_fun(U_17987,U_17983),tc_fun(U_17987,tc_prod(U_17982,U_17983))),U_17982),c_COMBB(U_17983,tc_prod(U_17982,U_17983),U_17987)),c_Product__Type_OPair(U_17982,U_17983))),U_17988)))),hAPP(hAPP(c_List_Ozip(U_17982,U_17987),U_17986),U_17989)),
    inference(clausify,[status(thm)],[f_4368_3]) ).

fof(f_4369_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_4369_2,plain,
    ! [U_17997,U_17996,U_17995,U_17994,U_17993,U_17992,U_17991,U_17990] : hAPP(hAPP(c_List_Omap(tc_prod(U_17990,U_17991),U_17992),U_17993),hAPP(hAPP(c_List_Ozip(U_17990,U_17991),hAPP(hAPP(c_List_Omap(U_17994,U_17990),U_17995),U_17996)),U_17997)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17994,U_17991),U_17992),hAPP(c_Product__Type_Oprod_Oprod__case(U_17994,U_17991,U_17992),hAPP(hAPP(c_COMBB(tc_fun(U_17991,tc_prod(U_17990,U_17991)),tc_fun(U_17991,U_17992),U_17994),hAPP(c_COMBB(tc_prod(U_17990,U_17991),U_17992,U_17991),U_17993)),hAPP(hAPP(c_COMBB(U_17990,tc_fun(U_17991,tc_prod(U_17990,U_17991)),U_17994),c_Product__Type_OPair(U_17990,U_17991)),U_17995)))),hAPP(hAPP(c_List_Ozip(U_17994,U_17991),U_17996),U_17997)),
    inference(variable_rename,[status(thm)],[f_4369_1]) ).

fof(f_4369_3,plain,
    ! [U_17990,U_17991,U_17992,U_17993,U_17994,U_17995,U_17996,U_17997] : hAPP(hAPP(c_List_Omap(tc_prod(U_17990,U_17991),U_17992),U_17993),hAPP(hAPP(c_List_Ozip(U_17990,U_17991),hAPP(hAPP(c_List_Omap(U_17994,U_17990),U_17995),U_17996)),U_17997)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17994,U_17991),U_17992),hAPP(c_Product__Type_Oprod_Oprod__case(U_17994,U_17991,U_17992),hAPP(hAPP(c_COMBB(tc_fun(U_17991,tc_prod(U_17990,U_17991)),tc_fun(U_17991,U_17992),U_17994),hAPP(c_COMBB(tc_prod(U_17990,U_17991),U_17992,U_17991),U_17993)),hAPP(hAPP(c_COMBB(U_17990,tc_fun(U_17991,tc_prod(U_17990,U_17991)),U_17994),c_Product__Type_OPair(U_17990,U_17991)),U_17995)))),hAPP(hAPP(c_List_Ozip(U_17994,U_17991),U_17996),U_17997)),
    inference(definitional_conversion,[status(esa)],[f_4369_2]) ).

cnf(f_4369_4,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_17990,U_17991),U_17992),U_17993),hAPP(hAPP(c_List_Ozip(U_17990,U_17991),hAPP(hAPP(c_List_Omap(U_17994,U_17990),U_17995),U_17996)),U_17997)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17994,U_17991),U_17992),hAPP(c_Product__Type_Oprod_Oprod__case(U_17994,U_17991,U_17992),hAPP(hAPP(c_COMBB(tc_fun(U_17991,tc_prod(U_17990,U_17991)),tc_fun(U_17991,U_17992),U_17994),hAPP(c_COMBB(tc_prod(U_17990,U_17991),U_17992,U_17991),U_17993)),hAPP(hAPP(c_COMBB(U_17990,tc_fun(U_17991,tc_prod(U_17990,U_17991)),U_17994),c_Product__Type_OPair(U_17990,U_17991)),U_17995)))),hAPP(hAPP(c_List_Ozip(U_17994,U_17991),U_17996),U_17997)),
    inference(clausify,[status(thm)],[f_4369_3]) ).

fof(f_4370_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_4370_2,plain,
    ! [U_18003,U_18002,U_18001,U_18000,U_17999,U_17998] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_17999),U_18001),hAPP(c_List_Oset(U_17999),U_18003)))
        & hBOOL(hAPP(hAPP(c_member(U_17998),U_18000),hAPP(c_List_Oset(U_17998),U_18002))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17998,U_17999)),hAPP(hAPP(c_Product__Type_OPair(U_17998,U_17999),U_18000),U_18001)),hAPP(c_List_Oset(tc_prod(U_17998,U_17999)),hAPP(hAPP(c_List_Ozip(U_17998,U_17999),U_18002),U_18003)))) ),
    inference(variable_rename,[status(thm)],[f_4370_1]) ).

fof(f_4370_3,plain,
    ( ! [U_17998,U_17999,U_18000,U_18001,U_18002,U_18003] :
        ( hBOOL(hAPP(hAPP(c_member(U_17999),U_18001),hAPP(c_List_Oset(U_17999),U_18003)))
        | ~ sP1129(U_17998,U_17999,U_18000,U_18001,U_18002,U_18003) )
    & ! [U_17998,U_17999,U_18000,U_18001,U_18002,U_18003] :
        ( hBOOL(hAPP(hAPP(c_member(U_17998),U_18000),hAPP(c_List_Oset(U_17998),U_18002)))
        | ~ sP1129(U_17998,U_17999,U_18000,U_18001,U_18002,U_18003) )
    & ! [U_17998,U_17999,U_18000,U_18001,U_18002,U_18003] :
        ( sP1129(U_17998,U_17999,U_18000,U_18001,U_18002,U_18003)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17998,U_17999)),hAPP(hAPP(c_Product__Type_OPair(U_17998,U_17999),U_18000),U_18001)),hAPP(c_List_Oset(tc_prod(U_17998,U_17999)),hAPP(hAPP(c_List_Ozip(U_17998,U_17999),U_18002),U_18003)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1129])],[f_4370_2]) ).

cnf(f_4370_4,plain,
    ( sP1129(U_17998,U_17999,U_18000,U_18001,U_18002,U_18003)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17998,U_17999)),hAPP(hAPP(c_Product__Type_OPair(U_17998,U_17999),U_18000),U_18001)),hAPP(c_List_Oset(tc_prod(U_17998,U_17999)),hAPP(hAPP(c_List_Ozip(U_17998,U_17999),U_18002),U_18003)))) ),
    inference(clausify,[status(thm)],[f_4370_3]) ).

cnf(f_4370_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17998),U_18000),hAPP(c_List_Oset(U_17998),U_18002)))
    | ~ sP1129(U_17998,U_17999,U_18000,U_18001,U_18002,U_18003) ),
    inference(clausify,[status(thm)],[f_4370_3]) ).

cnf(f_4370_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17999),U_18001),hAPP(c_List_Oset(U_17999),U_18003)))
    | ~ sP1129(U_17998,U_17999,U_18000,U_18001,U_18002,U_18003) ),
    inference(clausify,[status(thm)],[f_4370_3]) ).

fof(f_4371_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_4371_2,plain,
    ! [U_18009,U_18008,U_18007,U_18006,U_18005,U_18004] :
      ( hBOOL(hAPP(hAPP(c_member(U_18005),U_18007),hAPP(c_List_Oset(U_18005),U_18009)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18004,U_18005)),hAPP(hAPP(c_Product__Type_OPair(U_18004,U_18005),U_18006),U_18007)),hAPP(c_List_Oset(tc_prod(U_18004,U_18005)),hAPP(hAPP(c_List_Ozip(U_18004,U_18005),U_18008),U_18009)))) ),
    inference(variable_rename,[status(thm)],[f_4371_1]) ).

fof(f_4371_3,plain,
    ! [U_18009,U_18008,U_18007,U_18006,U_18005] :
      ( ! [U_18004] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18004,U_18005)),hAPP(hAPP(c_Product__Type_OPair(U_18004,U_18005),U_18006),U_18007)),hAPP(c_List_Oset(tc_prod(U_18004,U_18005)),hAPP(hAPP(c_List_Ozip(U_18004,U_18005),U_18008),U_18009))))
      | hBOOL(hAPP(hAPP(c_member(U_18005),U_18007),hAPP(c_List_Oset(U_18005),U_18009))) ),
    inference(miniscope,[status(thm)],[f_4371_2]) ).

fof(f_4371_4,plain,
    ! [U_18004,U_18005,U_18006,U_18007,U_18008,U_18009] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18004,U_18005)),hAPP(hAPP(c_Product__Type_OPair(U_18004,U_18005),U_18006),U_18007)),hAPP(c_List_Oset(tc_prod(U_18004,U_18005)),hAPP(hAPP(c_List_Ozip(U_18004,U_18005),U_18008),U_18009))))
      | hBOOL(hAPP(hAPP(c_member(U_18005),U_18007),hAPP(c_List_Oset(U_18005),U_18009))) ),
    inference(definitional_conversion,[status(esa)],[f_4371_3]) ).

cnf(f_4371_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18004,U_18005)),hAPP(hAPP(c_Product__Type_OPair(U_18004,U_18005),U_18006),U_18007)),hAPP(c_List_Oset(tc_prod(U_18004,U_18005)),hAPP(hAPP(c_List_Ozip(U_18004,U_18005),U_18008),U_18009))))
    | hBOOL(hAPP(hAPP(c_member(U_18005),U_18007),hAPP(c_List_Oset(U_18005),U_18009))) ),
    inference(clausify,[status(thm)],[f_4371_4]) ).

fof(f_4372_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_4372_2,plain,
    ! [U_18015,U_18014,U_18013,U_18012,U_18011,U_18010] :
      ( hBOOL(hAPP(hAPP(c_member(U_18010),U_18012),hAPP(c_List_Oset(U_18010),U_18014)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18010,U_18011)),hAPP(hAPP(c_Product__Type_OPair(U_18010,U_18011),U_18012),U_18013)),hAPP(c_List_Oset(tc_prod(U_18010,U_18011)),hAPP(hAPP(c_List_Ozip(U_18010,U_18011),U_18014),U_18015)))) ),
    inference(variable_rename,[status(thm)],[f_4372_1]) ).

fof(f_4372_3,plain,
    ! [U_18010,U_18011,U_18012,U_18013,U_18014,U_18015] :
      ( hBOOL(hAPP(hAPP(c_member(U_18010),U_18012),hAPP(c_List_Oset(U_18010),U_18014)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18010,U_18011)),hAPP(hAPP(c_Product__Type_OPair(U_18010,U_18011),U_18012),U_18013)),hAPP(c_List_Oset(tc_prod(U_18010,U_18011)),hAPP(hAPP(c_List_Ozip(U_18010,U_18011),U_18014),U_18015)))) ),
    inference(definitional_conversion,[status(esa)],[f_4372_2]) ).

cnf(f_4372_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18010),U_18012),hAPP(c_List_Oset(U_18010),U_18014)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18010,U_18011)),hAPP(hAPP(c_Product__Type_OPair(U_18010,U_18011),U_18012),U_18013)),hAPP(c_List_Oset(tc_prod(U_18010,U_18011)),hAPP(hAPP(c_List_Ozip(U_18010,U_18011),U_18014),U_18015)))) ),
    inference(clausify,[status(thm)],[f_4372_3]) ).

fof(f_4373_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_4373_2,plain,
    ! [U_18019,U_18018,U_18017,U_18016] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18016,U_18016)),hAPP(hAPP(c_Product__Type_OPair(U_18016,U_18016),U_18017),U_18018)),hAPP(c_List_Oset(tc_prod(U_18016,U_18016)),hAPP(hAPP(c_List_Ozip(U_18016,U_18016),U_18019),U_18019))))
        | U_18017 != U_18018
        | ~ hBOOL(hAPP(hAPP(c_member(U_18016),U_18017),hAPP(c_List_Oset(U_18016),U_18019))) )
      & ( ( U_18017 = U_18018
          & hBOOL(hAPP(hAPP(c_member(U_18016),U_18017),hAPP(c_List_Oset(U_18016),U_18019))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18016,U_18016)),hAPP(hAPP(c_Product__Type_OPair(U_18016,U_18016),U_18017),U_18018)),hAPP(c_List_Oset(tc_prod(U_18016,U_18016)),hAPP(hAPP(c_List_Ozip(U_18016,U_18016),U_18019),U_18019)))) ) ),
    inference(variable_rename,[status(thm)],[f_4373_1]) ).

fof(f_4373_3,plain,
    ( ! [U_18027,U_18025,U_18023,U_18021] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18021,U_18021)),hAPP(hAPP(c_Product__Type_OPair(U_18021,U_18021),U_18023),U_18025)),hAPP(c_List_Oset(tc_prod(U_18021,U_18021)),hAPP(hAPP(c_List_Ozip(U_18021,U_18021),U_18027),U_18027))))
        | U_18023 != U_18025
        | ~ hBOOL(hAPP(hAPP(c_member(U_18021),U_18023),hAPP(c_List_Oset(U_18021),U_18027))) )
    & ! [U_18026,U_18024,U_18022,U_18020] :
        ( ( U_18022 = U_18024
          & hBOOL(hAPP(hAPP(c_member(U_18020),U_18022),hAPP(c_List_Oset(U_18020),U_18026))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18020,U_18020)),hAPP(hAPP(c_Product__Type_OPair(U_18020,U_18020),U_18022),U_18024)),hAPP(c_List_Oset(tc_prod(U_18020,U_18020)),hAPP(hAPP(c_List_Ozip(U_18020,U_18020),U_18026),U_18026)))) ) ),
    inference(miniscope,[status(thm)],[f_4373_2]) ).

fof(f_4373_4,plain,
    ( ! [U_18022,U_18020,U_18026,U_18024] :
        ( U_18022 = U_18024
        | ~ sP1130(U_18022,U_18020,U_18026,U_18024) )
    & ! [U_18022,U_18020,U_18026,U_18024] :
        ( hBOOL(hAPP(hAPP(c_member(U_18020),U_18022),hAPP(c_List_Oset(U_18020),U_18026)))
        | ~ sP1130(U_18022,U_18020,U_18026,U_18024) )
    & ! [U_18025,U_18021,U_18023,U_18027] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18021,U_18021)),hAPP(hAPP(c_Product__Type_OPair(U_18021,U_18021),U_18023),U_18025)),hAPP(c_List_Oset(tc_prod(U_18021,U_18021)),hAPP(hAPP(c_List_Ozip(U_18021,U_18021),U_18027),U_18027))))
        | U_18023 != U_18025
        | ~ hBOOL(hAPP(hAPP(c_member(U_18021),U_18023),hAPP(c_List_Oset(U_18021),U_18027))) )
    & ! [U_18022,U_18020,U_18026,U_18024] :
        ( sP1130(U_18022,U_18020,U_18026,U_18024)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18020,U_18020)),hAPP(hAPP(c_Product__Type_OPair(U_18020,U_18020),U_18022),U_18024)),hAPP(c_List_Oset(tc_prod(U_18020,U_18020)),hAPP(hAPP(c_List_Ozip(U_18020,U_18020),U_18026),U_18026)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1130])],[f_4373_3]) ).

cnf(f_4373_5,plain,
    ( sP1130(U_18022,U_18020,U_18026,U_18024)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18020,U_18020)),hAPP(hAPP(c_Product__Type_OPair(U_18020,U_18020),U_18022),U_18024)),hAPP(c_List_Oset(tc_prod(U_18020,U_18020)),hAPP(hAPP(c_List_Ozip(U_18020,U_18020),U_18026),U_18026)))) ),
    inference(clausify,[status(thm)],[f_4373_4]) ).

cnf(f_4373_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18021,U_18021)),hAPP(hAPP(c_Product__Type_OPair(U_18021,U_18021),U_18023),U_18025)),hAPP(c_List_Oset(tc_prod(U_18021,U_18021)),hAPP(hAPP(c_List_Ozip(U_18021,U_18021),U_18027),U_18027))))
    | U_18023 != U_18025
    | ~ hBOOL(hAPP(hAPP(c_member(U_18021),U_18023),hAPP(c_List_Oset(U_18021),U_18027))) ),
    inference(clausify,[status(thm)],[f_4373_4]) ).

cnf(f_4373_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18020),U_18022),hAPP(c_List_Oset(U_18020),U_18026)))
    | ~ sP1130(U_18022,U_18020,U_18026,U_18024) ),
    inference(clausify,[status(thm)],[f_4373_4]) ).

cnf(f_4373_8,plain,
    ( U_18022 = U_18024
    | ~ sP1130(U_18022,U_18020,U_18026,U_18024) ),
    inference(clausify,[status(thm)],[f_4373_4]) ).

fof(f_4374_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_4374_2,plain,
    ! [U_18033,U_18032,U_18031,U_18030,U_18029,U_18028] : hAPP(hAPP(c_List_Ozip(U_18028,U_18029),U_18030),hAPP(hAPP(c_List_Omap(U_18031,U_18029),U_18032),U_18033)) = hAPP(hAPP(c_List_Omap(tc_prod(U_18028,U_18031),tc_prod(U_18028,U_18029)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18028,U_18031,tc_prod(U_18028,U_18029)),hAPP(hAPP(c_COMBC(U_18028,tc_fun(U_18031,U_18029),tc_fun(U_18031,tc_prod(U_18028,U_18029))),hAPP(hAPP(c_COMBB(tc_fun(U_18029,tc_prod(U_18028,U_18029)),tc_fun(tc_fun(U_18031,U_18029),tc_fun(U_18031,tc_prod(U_18028,U_18029))),U_18028),c_COMBB(U_18029,tc_prod(U_18028,U_18029),U_18031)),c_Product__Type_OPair(U_18028,U_18029))),U_18032))),hAPP(hAPP(c_List_Ozip(U_18028,U_18031),U_18030),U_18033)),
    inference(variable_rename,[status(thm)],[f_4374_1]) ).

fof(f_4374_3,plain,
    ! [U_18028,U_18029,U_18030,U_18031,U_18032,U_18033] : hAPP(hAPP(c_List_Ozip(U_18028,U_18029),U_18030),hAPP(hAPP(c_List_Omap(U_18031,U_18029),U_18032),U_18033)) = hAPP(hAPP(c_List_Omap(tc_prod(U_18028,U_18031),tc_prod(U_18028,U_18029)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18028,U_18031,tc_prod(U_18028,U_18029)),hAPP(hAPP(c_COMBC(U_18028,tc_fun(U_18031,U_18029),tc_fun(U_18031,tc_prod(U_18028,U_18029))),hAPP(hAPP(c_COMBB(tc_fun(U_18029,tc_prod(U_18028,U_18029)),tc_fun(tc_fun(U_18031,U_18029),tc_fun(U_18031,tc_prod(U_18028,U_18029))),U_18028),c_COMBB(U_18029,tc_prod(U_18028,U_18029),U_18031)),c_Product__Type_OPair(U_18028,U_18029))),U_18032))),hAPP(hAPP(c_List_Ozip(U_18028,U_18031),U_18030),U_18033)),
    inference(definitional_conversion,[status(esa)],[f_4374_2]) ).

cnf(f_4374_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18028,U_18029),U_18030),hAPP(hAPP(c_List_Omap(U_18031,U_18029),U_18032),U_18033)) = hAPP(hAPP(c_List_Omap(tc_prod(U_18028,U_18031),tc_prod(U_18028,U_18029)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18028,U_18031,tc_prod(U_18028,U_18029)),hAPP(hAPP(c_COMBC(U_18028,tc_fun(U_18031,U_18029),tc_fun(U_18031,tc_prod(U_18028,U_18029))),hAPP(hAPP(c_COMBB(tc_fun(U_18029,tc_prod(U_18028,U_18029)),tc_fun(tc_fun(U_18031,U_18029),tc_fun(U_18031,tc_prod(U_18028,U_18029))),U_18028),c_COMBB(U_18029,tc_prod(U_18028,U_18029),U_18031)),c_Product__Type_OPair(U_18028,U_18029))),U_18032))),hAPP(hAPP(c_List_Ozip(U_18028,U_18031),U_18030),U_18033)),
    inference(clausify,[status(thm)],[f_4374_3]) ).

fof(f_4375_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_4375_2,plain,
    ! [U_18039,U_18038,U_18037,U_18036,U_18035,U_18034] : hAPP(hAPP(c_List_Ozip(U_18034,U_18035),hAPP(hAPP(c_List_Omap(U_18036,U_18034),U_18037),U_18038)),U_18039) = hAPP(hAPP(c_List_Omap(tc_prod(U_18036,U_18035),tc_prod(U_18034,U_18035)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18036,U_18035,tc_prod(U_18034,U_18035)),hAPP(hAPP(c_COMBB(U_18034,tc_fun(U_18035,tc_prod(U_18034,U_18035)),U_18036),c_Product__Type_OPair(U_18034,U_18035)),U_18037))),hAPP(hAPP(c_List_Ozip(U_18036,U_18035),U_18038),U_18039)),
    inference(variable_rename,[status(thm)],[f_4375_1]) ).

fof(f_4375_3,plain,
    ! [U_18034,U_18035,U_18036,U_18037,U_18038,U_18039] : hAPP(hAPP(c_List_Ozip(U_18034,U_18035),hAPP(hAPP(c_List_Omap(U_18036,U_18034),U_18037),U_18038)),U_18039) = hAPP(hAPP(c_List_Omap(tc_prod(U_18036,U_18035),tc_prod(U_18034,U_18035)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18036,U_18035,tc_prod(U_18034,U_18035)),hAPP(hAPP(c_COMBB(U_18034,tc_fun(U_18035,tc_prod(U_18034,U_18035)),U_18036),c_Product__Type_OPair(U_18034,U_18035)),U_18037))),hAPP(hAPP(c_List_Ozip(U_18036,U_18035),U_18038),U_18039)),
    inference(definitional_conversion,[status(esa)],[f_4375_2]) ).

cnf(f_4375_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18034,U_18035),hAPP(hAPP(c_List_Omap(U_18036,U_18034),U_18037),U_18038)),U_18039) = hAPP(hAPP(c_List_Omap(tc_prod(U_18036,U_18035),tc_prod(U_18034,U_18035)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18036,U_18035,tc_prod(U_18034,U_18035)),hAPP(hAPP(c_COMBB(U_18034,tc_fun(U_18035,tc_prod(U_18034,U_18035)),U_18036),c_Product__Type_OPair(U_18034,U_18035)),U_18037))),hAPP(hAPP(c_List_Ozip(U_18036,U_18035),U_18038),U_18039)),
    inference(clausify,[status(thm)],[f_4375_3]) ).

fof(f_4376_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_4376_2,plain,
    ! [U_18047,U_18046,U_18045,U_18044,U_18043,U_18042,U_18041,U_18040] : hAPP(hAPP(c_List_Ozip(U_18040,U_18041),hAPP(hAPP(c_List_Omap(U_18042,U_18040),U_18043),U_18044)),hAPP(hAPP(c_List_Omap(U_18045,U_18041),U_18046),U_18047)) = hAPP(hAPP(c_List_Omap(tc_prod(U_18042,U_18045),tc_prod(U_18040,U_18041)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18042,U_18045,tc_prod(U_18040,U_18041)),hAPP(hAPP(c_COMBC(U_18042,tc_fun(U_18045,U_18041),tc_fun(U_18045,tc_prod(U_18040,U_18041))),hAPP(hAPP(c_COMBB(tc_fun(U_18041,tc_prod(U_18040,U_18041)),tc_fun(tc_fun(U_18045,U_18041),tc_fun(U_18045,tc_prod(U_18040,U_18041))),U_18042),c_COMBB(U_18041,tc_prod(U_18040,U_18041),U_18045)),hAPP(hAPP(c_COMBB(U_18040,tc_fun(U_18041,tc_prod(U_18040,U_18041)),U_18042),c_Product__Type_OPair(U_18040,U_18041)),U_18043))),U_18046))),hAPP(hAPP(c_List_Ozip(U_18042,U_18045),U_18044),U_18047)),
    inference(variable_rename,[status(thm)],[f_4376_1]) ).

fof(f_4376_3,plain,
    ! [U_18040,U_18041,U_18042,U_18043,U_18044,U_18045,U_18046,U_18047] : hAPP(hAPP(c_List_Ozip(U_18040,U_18041),hAPP(hAPP(c_List_Omap(U_18042,U_18040),U_18043),U_18044)),hAPP(hAPP(c_List_Omap(U_18045,U_18041),U_18046),U_18047)) = hAPP(hAPP(c_List_Omap(tc_prod(U_18042,U_18045),tc_prod(U_18040,U_18041)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18042,U_18045,tc_prod(U_18040,U_18041)),hAPP(hAPP(c_COMBC(U_18042,tc_fun(U_18045,U_18041),tc_fun(U_18045,tc_prod(U_18040,U_18041))),hAPP(hAPP(c_COMBB(tc_fun(U_18041,tc_prod(U_18040,U_18041)),tc_fun(tc_fun(U_18045,U_18041),tc_fun(U_18045,tc_prod(U_18040,U_18041))),U_18042),c_COMBB(U_18041,tc_prod(U_18040,U_18041),U_18045)),hAPP(hAPP(c_COMBB(U_18040,tc_fun(U_18041,tc_prod(U_18040,U_18041)),U_18042),c_Product__Type_OPair(U_18040,U_18041)),U_18043))),U_18046))),hAPP(hAPP(c_List_Ozip(U_18042,U_18045),U_18044),U_18047)),
    inference(definitional_conversion,[status(esa)],[f_4376_2]) ).

cnf(f_4376_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18040,U_18041),hAPP(hAPP(c_List_Omap(U_18042,U_18040),U_18043),U_18044)),hAPP(hAPP(c_List_Omap(U_18045,U_18041),U_18046),U_18047)) = hAPP(hAPP(c_List_Omap(tc_prod(U_18042,U_18045),tc_prod(U_18040,U_18041)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18042,U_18045,tc_prod(U_18040,U_18041)),hAPP(hAPP(c_COMBC(U_18042,tc_fun(U_18045,U_18041),tc_fun(U_18045,tc_prod(U_18040,U_18041))),hAPP(hAPP(c_COMBB(tc_fun(U_18041,tc_prod(U_18040,U_18041)),tc_fun(tc_fun(U_18045,U_18041),tc_fun(U_18045,tc_prod(U_18040,U_18041))),U_18042),c_COMBB(U_18041,tc_prod(U_18040,U_18041),U_18045)),hAPP(hAPP(c_COMBB(U_18040,tc_fun(U_18041,tc_prod(U_18040,U_18041)),U_18042),c_Product__Type_OPair(U_18040,U_18041)),U_18043))),U_18046))),hAPP(hAPP(c_List_Ozip(U_18042,U_18045),U_18044),U_18047)),
    inference(clausify,[status(thm)],[f_4376_3]) ).

fof(f_4377_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_4377_2,plain,
    ! [U_18050,U_18049,U_18048] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_18048,hAPP(hAPP(c_Set_Oinsert(U_18048),U_18050),U_18049)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18048,U_18048,c_COMBI(U_18048)),U_18050),c_List_Olinorder__class_Osorted__list__of__set(U_18048,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18048,tc_HOL_Obool)),U_18049),hAPP(hAPP(c_Set_Oinsert(U_18048),U_18050),c_Orderings_Obot__class_Obot(tc_fun(U_18048,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18048),U_18049))
      | ~ class_Orderings_Olinorder(U_18048) ),
    inference(variable_rename,[status(thm)],[f_4377_1]) ).

fof(f_4377_3,plain,
    ! [U_18048,U_18049,U_18050] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_18048,hAPP(hAPP(c_Set_Oinsert(U_18048),U_18050),U_18049)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18048,U_18048,c_COMBI(U_18048)),U_18050),c_List_Olinorder__class_Osorted__list__of__set(U_18048,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18048,tc_HOL_Obool)),U_18049),hAPP(hAPP(c_Set_Oinsert(U_18048),U_18050),c_Orderings_Obot__class_Obot(tc_fun(U_18048,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18048),U_18049))
      | ~ class_Orderings_Olinorder(U_18048) ),
    inference(definitional_conversion,[status(esa)],[f_4377_2]) ).

cnf(f_4377_4,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_18048,hAPP(hAPP(c_Set_Oinsert(U_18048),U_18050),U_18049)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18048,U_18048,c_COMBI(U_18048)),U_18050),c_List_Olinorder__class_Osorted__list__of__set(U_18048,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18048,tc_HOL_Obool)),U_18049),hAPP(hAPP(c_Set_Oinsert(U_18048),U_18050),c_Orderings_Obot__class_Obot(tc_fun(U_18048,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18048),U_18049))
    | ~ class_Orderings_Olinorder(U_18048) ),
    inference(clausify,[status(thm)],[f_4377_3]) ).

fof(f_4378_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_4378_2,plain,
    ! [U_18058,U_18057,U_18056,U_18055,U_18054,U_18053,U_18052,U_18051] :
      ( c_Map_Omap__of(U_18053,U_18051,hAPP(hAPP(c_List_Ozip(U_18053,U_18051),U_18054),U_18052)) = c_Map_Omap__of(U_18053,U_18051,hAPP(hAPP(c_List_Ozip(U_18053,U_18051),U_18054),U_18055))
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18053,tc_Option_Ooption(U_18051)),c_Map_Omap__of(U_18053,U_18051,hAPP(hAPP(c_List_Ozip(U_18053,U_18051),U_18054),U_18052))),U_18056),hAPP(c_Option_Ooption_OSome(U_18051),U_18057)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18053,tc_Option_Ooption(U_18051)),c_Map_Omap__of(U_18053,U_18051,hAPP(hAPP(c_List_Ozip(U_18053,U_18051),U_18054),U_18055))),U_18056),hAPP(c_Option_Ooption_OSome(U_18051),U_18058))
      | hBOOL(hAPP(hAPP(c_member(U_18053),U_18056),hAPP(c_List_Oset(U_18053),U_18054)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18051)),U_18055) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18053)),U_18054)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18051)),U_18052) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18053)),U_18054) ),
    inference(variable_rename,[status(thm)],[f_4378_1]) ).

fof(f_4378_3,plain,
    ! [U_18051,U_18052,U_18053,U_18054,U_18055,U_18056,U_18057,U_18058] :
      ( c_Map_Omap__of(U_18053,U_18051,hAPP(hAPP(c_List_Ozip(U_18053,U_18051),U_18054),U_18052)) = c_Map_Omap__of(U_18053,U_18051,hAPP(hAPP(c_List_Ozip(U_18053,U_18051),U_18054),U_18055))
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18053,tc_Option_Ooption(U_18051)),c_Map_Omap__of(U_18053,U_18051,hAPP(hAPP(c_List_Ozip(U_18053,U_18051),U_18054),U_18052))),U_18056),hAPP(c_Option_Ooption_OSome(U_18051),U_18057)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18053,tc_Option_Ooption(U_18051)),c_Map_Omap__of(U_18053,U_18051,hAPP(hAPP(c_List_Ozip(U_18053,U_18051),U_18054),U_18055))),U_18056),hAPP(c_Option_Ooption_OSome(U_18051),U_18058))
      | hBOOL(hAPP(hAPP(c_member(U_18053),U_18056),hAPP(c_List_Oset(U_18053),U_18054)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18051)),U_18055) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18053)),U_18054)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18051)),U_18052) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18053)),U_18054) ),
    inference(definitional_conversion,[status(esa)],[f_4378_2]) ).

cnf(f_4378_4,plain,
    ( c_Map_Omap__of(U_18053,U_18051,hAPP(hAPP(c_List_Ozip(U_18053,U_18051),U_18054),U_18052)) = c_Map_Omap__of(U_18053,U_18051,hAPP(hAPP(c_List_Ozip(U_18053,U_18051),U_18054),U_18055))
    | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18053,tc_Option_Ooption(U_18051)),c_Map_Omap__of(U_18053,U_18051,hAPP(hAPP(c_List_Ozip(U_18053,U_18051),U_18054),U_18052))),U_18056),hAPP(c_Option_Ooption_OSome(U_18051),U_18057)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18053,tc_Option_Ooption(U_18051)),c_Map_Omap__of(U_18053,U_18051,hAPP(hAPP(c_List_Ozip(U_18053,U_18051),U_18054),U_18055))),U_18056),hAPP(c_Option_Ooption_OSome(U_18051),U_18058))
    | hBOOL(hAPP(hAPP(c_member(U_18053),U_18056),hAPP(c_List_Oset(U_18053),U_18054)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18051)),U_18055) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18053)),U_18054)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18051)),U_18052) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18053)),U_18054) ),
    inference(clausify,[status(thm)],[f_4378_3]) ).

fof(f_4379_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_4379_2,plain,
    ! [U_18062,U_18061,U_18060,U_18059] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(U_18059,U_18060))),hAPP(hAPP(c_List_Ozip(U_18059,U_18060),U_18061),U_18062)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18059)),U_18061)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18060)),U_18062)),
    inference(variable_rename,[status(thm)],[f_4379_1]) ).

fof(f_4379_3,plain,
    ! [U_18060,U_18059,U_18061,U_18062] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(U_18059,U_18060))),hAPP(hAPP(c_List_Ozip(U_18059,U_18060),U_18061),U_18062)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18059)),U_18061)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18060)),U_18062)),
    inference(definitional_conversion,[status(esa)],[f_4379_2]) ).

cnf(f_4379_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(U_18059,U_18060))),hAPP(hAPP(c_List_Ozip(U_18059,U_18060),U_18061),U_18062)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18059)),U_18061)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18060)),U_18062)),
    inference(clausify,[status(thm)],[f_4379_3]) ).

fof(f_4380_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_4380_2,plain,
    ! [U_18067,U_18066,U_18065,U_18064,U_18063] :
      ( hAPP(c_List_Oset(U_18064),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18064,U_18063,U_18065),U_18066),U_18067)) = hAPP(hAPP(c_Set_Oinsert(U_18064),U_18066),hAPP(c_List_Oset(U_18064),U_18067))
      | ~ class_Orderings_Olinorder(U_18063) ),
    inference(variable_rename,[status(thm)],[f_4380_1]) ).

fof(f_4380_3,plain,
    ! [U_18063,U_18064,U_18065,U_18066,U_18067] :
      ( hAPP(c_List_Oset(U_18064),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18064,U_18063,U_18065),U_18066),U_18067)) = hAPP(hAPP(c_Set_Oinsert(U_18064),U_18066),hAPP(c_List_Oset(U_18064),U_18067))
      | ~ class_Orderings_Olinorder(U_18063) ),
    inference(definitional_conversion,[status(esa)],[f_4380_2]) ).

cnf(f_4380_4,plain,
    ( hAPP(c_List_Oset(U_18064),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18064,U_18063,U_18065),U_18066),U_18067)) = hAPP(hAPP(c_Set_Oinsert(U_18064),U_18066),hAPP(c_List_Oset(U_18064),U_18067))
    | ~ class_Orderings_Olinorder(U_18063) ),
    inference(clausify,[status(thm)],[f_4380_3]) ).

fof(f_4381_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_4381_2,plain,
    ! [U_18071,U_18070,U_18069,U_18068] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18068,U_18068,c_COMBI(U_18068)),U_18069),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18068,U_18068,c_COMBI(U_18068)),U_18070),U_18071)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18068,U_18068,c_COMBI(U_18068)),U_18070),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18068,U_18068,c_COMBI(U_18068)),U_18069),U_18071))
      | ~ class_Orderings_Olinorder(U_18068) ),
    inference(variable_rename,[status(thm)],[f_4381_1]) ).

fof(f_4381_3,plain,
    ! [U_18068,U_18069,U_18070,U_18071] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18068,U_18068,c_COMBI(U_18068)),U_18069),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18068,U_18068,c_COMBI(U_18068)),U_18070),U_18071)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18068,U_18068,c_COMBI(U_18068)),U_18070),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18068,U_18068,c_COMBI(U_18068)),U_18069),U_18071))
      | ~ class_Orderings_Olinorder(U_18068) ),
    inference(definitional_conversion,[status(esa)],[f_4381_2]) ).

cnf(f_4381_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18068,U_18068,c_COMBI(U_18068)),U_18069),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18068,U_18068,c_COMBI(U_18068)),U_18070),U_18071)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18068,U_18068,c_COMBI(U_18068)),U_18070),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18068,U_18068,c_COMBI(U_18068)),U_18069),U_18071))
    | ~ class_Orderings_Olinorder(U_18068) ),
    inference(clausify,[status(thm)],[f_4381_3]) ).

fof(f_4382_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_4382_2,plain,
    ! [U_18077,U_18076,U_18075,U_18074,U_18073,U_18072] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18076,U_18072,U_18073),U_18075),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18076,U_18072,U_18073),U_18074),U_18077)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18076,U_18072,U_18073),U_18074),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18076,U_18072,U_18073),U_18075),U_18077))
      | hAPP(U_18073,U_18074) = hAPP(U_18073,U_18075)
      | ~ class_Orderings_Olinorder(U_18072) ),
    inference(variable_rename,[status(thm)],[f_4382_1]) ).

fof(f_4382_3,plain,
    ! [U_18072,U_18073,U_18074,U_18075,U_18076,U_18077] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18076,U_18072,U_18073),U_18075),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18076,U_18072,U_18073),U_18074),U_18077)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18076,U_18072,U_18073),U_18074),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18076,U_18072,U_18073),U_18075),U_18077))
      | hAPP(U_18073,U_18074) = hAPP(U_18073,U_18075)
      | ~ class_Orderings_Olinorder(U_18072) ),
    inference(definitional_conversion,[status(esa)],[f_4382_2]) ).

cnf(f_4382_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18076,U_18072,U_18073),U_18075),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18076,U_18072,U_18073),U_18074),U_18077)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18076,U_18072,U_18073),U_18074),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18076,U_18072,U_18073),U_18075),U_18077))
    | hAPP(U_18073,U_18074) = hAPP(U_18073,U_18075)
    | ~ class_Orderings_Olinorder(U_18072) ),
    inference(clausify,[status(thm)],[f_4382_3]) ).

fof(f_4383_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_4383_2,plain,
    ! [U_18080,U_18079,U_18078] :
      ( U_18079 != U_18080
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18078)),U_18079) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18078)),U_18080) ),
    inference(variable_rename,[status(thm)],[f_4383_1]) ).

fof(f_4383_3,plain,
    ! [U_18080,U_18079] :
      ( ! [U_18078] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18078)),U_18079) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18078)),U_18080)
      | U_18079 != U_18080 ),
    inference(miniscope,[status(thm)],[f_4383_2]) ).

fof(f_4383_4,plain,
    ! [U_18080,U_18078,U_18079] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18078)),U_18079) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18078)),U_18080)
      | U_18079 != U_18080 ),
    inference(definitional_conversion,[status(esa)],[f_4383_3]) ).

cnf(f_4383_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18078)),U_18079) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18078)),U_18080)
    | U_18079 != U_18080 ),
    inference(clausify,[status(thm)],[f_4383_4]) ).

fof(f_4384_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_4384_2,plain,
    ! [U_18085,U_18084,U_18083,U_18082,U_18081] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18082)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18082,U_18081,U_18083),U_18084),U_18085)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18082)),U_18085))
      | ~ class_Orderings_Olinorder(U_18081) ),
    inference(variable_rename,[status(thm)],[f_4384_1]) ).

fof(f_4384_3,plain,
    ! [U_18081,U_18082,U_18083,U_18084,U_18085] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18082)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18082,U_18081,U_18083),U_18084),U_18085)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18082)),U_18085))
      | ~ class_Orderings_Olinorder(U_18081) ),
    inference(definitional_conversion,[status(esa)],[f_4384_2]) ).

cnf(f_4384_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18082)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18082,U_18081,U_18083),U_18084),U_18085)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18082)),U_18085))
    | ~ class_Orderings_Olinorder(U_18081) ),
    inference(clausify,[status(thm)],[f_4384_3]) ).

fof(f_4385_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_4385_2,plain,
    ! [U_18086] :
      ( c_Finite__Set_Ofun__left__comm(U_18086,tc_List_Olist(U_18086),c_List_Olinorder__class_Oinsort__key(U_18086,U_18086,c_COMBI(U_18086)))
      | ~ class_Orderings_Olinorder(U_18086) ),
    inference(variable_rename,[status(thm)],[f_4385_1]) ).

fof(f_4385_3,plain,
    ! [U_18086] :
      ( c_Finite__Set_Ofun__left__comm(U_18086,tc_List_Olist(U_18086),c_List_Olinorder__class_Oinsort__key(U_18086,U_18086,c_COMBI(U_18086)))
      | ~ class_Orderings_Olinorder(U_18086) ),
    inference(definitional_conversion,[status(esa)],[f_4385_2]) ).

cnf(f_4385_4,plain,
    ( c_Finite__Set_Ofun__left__comm(U_18086,tc_List_Olist(U_18086),c_List_Olinorder__class_Oinsort__key(U_18086,U_18086,c_COMBI(U_18086)))
    | ~ class_Orderings_Olinorder(U_18086) ),
    inference(clausify,[status(thm)],[f_4385_3]) ).

fof(f_4386_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_4386_2,plain,
    ! [U_18091,U_18090,U_18089,U_18088,U_18087] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18087)),U_18089) = U_18091
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18087)),U_18088) = U_18091 )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18087),tc_List_Olist(U_18087))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18087),tc_List_Olist(U_18087)),U_18088),U_18089)),hAPP(c_List_Olexn(U_18087,U_18090),U_18091))) ),
    inference(variable_rename,[status(thm)],[f_4386_1]) ).

fof(f_4386_3,plain,
    ( ! [U_18087,U_18088,U_18089,U_18091] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18087)),U_18089) = U_18091
        | ~ sP1131(U_18087,U_18088,U_18089,U_18091) )
    & ! [U_18087,U_18088,U_18089,U_18091] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18087)),U_18088) = U_18091
        | ~ sP1131(U_18087,U_18088,U_18089,U_18091) )
    & ! [U_18087,U_18088,U_18089,U_18090,U_18091] :
        ( sP1131(U_18087,U_18088,U_18089,U_18091)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18087),tc_List_Olist(U_18087))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18087),tc_List_Olist(U_18087)),U_18088),U_18089)),hAPP(c_List_Olexn(U_18087,U_18090),U_18091))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1131])],[f_4386_2]) ).

cnf(f_4386_4,plain,
    ( sP1131(U_18087,U_18088,U_18089,U_18091)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18087),tc_List_Olist(U_18087))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18087),tc_List_Olist(U_18087)),U_18088),U_18089)),hAPP(c_List_Olexn(U_18087,U_18090),U_18091))) ),
    inference(clausify,[status(thm)],[f_4386_3]) ).

cnf(f_4386_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18087)),U_18088) = U_18091
    | ~ sP1131(U_18087,U_18088,U_18089,U_18091) ),
    inference(clausify,[status(thm)],[f_4386_3]) ).

cnf(f_4386_6,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18087)),U_18089) = U_18091
    | ~ sP1131(U_18087,U_18088,U_18089,U_18091) ),
    inference(clausify,[status(thm)],[f_4386_3]) ).

fof(f_4387_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_4387_2,plain,
    ! [U_18098,U_18097,U_18096,U_18095,U_18094,U_18093,U_18092] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18092)),U_18095) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18096)),U_18098)
      | hAPP(hAPP(c_List_Omap(U_18092,U_18093),U_18094),U_18095) != hAPP(hAPP(c_List_Omap(U_18096,U_18093),U_18097),U_18098) ),
    inference(variable_rename,[status(thm)],[f_4387_1]) ).

fof(f_4387_3,plain,
    ! [U_18092,U_18093,U_18094,U_18095,U_18096,U_18097,U_18098] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18092)),U_18095) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18096)),U_18098)
      | hAPP(hAPP(c_List_Omap(U_18092,U_18093),U_18094),U_18095) != hAPP(hAPP(c_List_Omap(U_18096,U_18093),U_18097),U_18098) ),
    inference(definitional_conversion,[status(esa)],[f_4387_2]) ).

cnf(f_4387_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18092)),U_18095) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18096)),U_18098)
    | hAPP(hAPP(c_List_Omap(U_18092,U_18093),U_18094),U_18095) != hAPP(hAPP(c_List_Omap(U_18096,U_18093),U_18097),U_18098) ),
    inference(clausify,[status(thm)],[f_4387_3]) ).

fof(f_4388_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_4388_2,plain,
    ! [U_18102,U_18101,U_18100,U_18099] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18099)),hAPP(hAPP(c_List_Omap(U_18100,U_18099),U_18101),U_18102)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18100)),U_18102),
    inference(variable_rename,[status(thm)],[f_4388_1]) ).

fof(f_4388_3,plain,
    ! [U_18099,U_18100,U_18101,U_18102] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18099)),hAPP(hAPP(c_List_Omap(U_18100,U_18099),U_18101),U_18102)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18100)),U_18102),
    inference(definitional_conversion,[status(esa)],[f_4388_2]) ).

cnf(f_4388_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18099)),hAPP(hAPP(c_List_Omap(U_18100,U_18099),U_18101),U_18102)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18100)),U_18102),
    inference(clausify,[status(thm)],[f_4388_3]) ).

fof(f_4389_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_4389_2,plain,
    ! [U_18105,U_18104,U_18103] :
      ( c_List_Oremove1(U_18103,U_18104,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18103,U_18103,c_COMBI(U_18103)),U_18104),U_18105)) = U_18105
      | ~ class_Orderings_Olinorder(U_18103) ),
    inference(variable_rename,[status(thm)],[f_4389_1]) ).

fof(f_4389_3,plain,
    ! [U_18103,U_18104,U_18105] :
      ( c_List_Oremove1(U_18103,U_18104,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18103,U_18103,c_COMBI(U_18103)),U_18104),U_18105)) = U_18105
      | ~ class_Orderings_Olinorder(U_18103) ),
    inference(definitional_conversion,[status(esa)],[f_4389_2]) ).

cnf(f_4389_4,plain,
    ( c_List_Oremove1(U_18103,U_18104,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18103,U_18103,c_COMBI(U_18103)),U_18104),U_18105)) = U_18105
    | ~ class_Orderings_Olinorder(U_18103) ),
    inference(clausify,[status(thm)],[f_4389_3]) ).

fof(f_4390_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_4390_2,plain,
    ! [U_18107,U_18106] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_18106),hAPP(c_List_Oset(U_18106),U_18107))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18106)),U_18107))),
    inference(variable_rename,[status(thm)],[f_4390_1]) ).

fof(f_4390_3,plain,
    ! [U_18106,U_18107] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_18106),hAPP(c_List_Oset(U_18106),U_18107))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18106)),U_18107))),
    inference(definitional_conversion,[status(esa)],[f_4390_2]) ).

cnf(f_4390_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_18106),hAPP(c_List_Oset(U_18106),U_18107))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18106)),U_18107))),
    inference(clausify,[status(thm)],[f_4390_3]) ).

fof(f_4391_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_4391_2,plain,
    ! [U_18109,U_18108] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18108),U_18109))
      | hAPP(c_Finite__Set_Ocard(U_18108),hAPP(c_List_Oset(U_18108),U_18109)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18108)),U_18109) ),
    inference(variable_rename,[status(thm)],[f_4391_1]) ).

fof(f_4391_3,plain,
    ! [U_18108,U_18109] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18108),U_18109))
      | hAPP(c_Finite__Set_Ocard(U_18108),hAPP(c_List_Oset(U_18108),U_18109)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18108)),U_18109) ),
    inference(definitional_conversion,[status(esa)],[f_4391_2]) ).

cnf(f_4391_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18108),U_18109))
    | hAPP(c_Finite__Set_Ocard(U_18108),hAPP(c_List_Oset(U_18108),U_18109)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18108)),U_18109) ),
    inference(clausify,[status(thm)],[f_4391_3]) ).

fof(f_4392_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_4392_2,plain,
    ! [U_18111,U_18110] :
      ( hAPP(c_Finite__Set_Ocard(U_18110),hAPP(c_List_Oset(U_18110),U_18111)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18110)),U_18111)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18110),U_18111)) ),
    inference(variable_rename,[status(thm)],[f_4392_1]) ).

fof(f_4392_3,plain,
    ! [U_18110,U_18111] :
      ( hAPP(c_Finite__Set_Ocard(U_18110),hAPP(c_List_Oset(U_18110),U_18111)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18110)),U_18111)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18110),U_18111)) ),
    inference(definitional_conversion,[status(esa)],[f_4392_2]) ).

cnf(f_4392_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_18110),hAPP(c_List_Oset(U_18110),U_18111)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18110)),U_18111)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18110),U_18111)) ),
    inference(clausify,[status(thm)],[f_4392_3]) ).

fof(f_4393_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_4393_2,plain,
    ! [U_18116,U_18115,U_18114,U_18113,U_18112] :
      ( U_18113 = U_18116
      | c_Map_Omap__of(U_18114,U_18112,hAPP(hAPP(c_List_Ozip(U_18114,U_18112),U_18115),U_18113)) != c_Map_Omap__of(U_18114,U_18112,hAPP(hAPP(c_List_Ozip(U_18114,U_18112),U_18115),U_18116))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18114),U_18115))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18112)),U_18116) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18114)),U_18115)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18112)),U_18113) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18114)),U_18115) ),
    inference(variable_rename,[status(thm)],[f_4393_1]) ).

fof(f_4393_3,plain,
    ! [U_18112,U_18113,U_18114,U_18115,U_18116] :
      ( U_18113 = U_18116
      | c_Map_Omap__of(U_18114,U_18112,hAPP(hAPP(c_List_Ozip(U_18114,U_18112),U_18115),U_18113)) != c_Map_Omap__of(U_18114,U_18112,hAPP(hAPP(c_List_Ozip(U_18114,U_18112),U_18115),U_18116))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18114),U_18115))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18112)),U_18116) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18114)),U_18115)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18112)),U_18113) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18114)),U_18115) ),
    inference(definitional_conversion,[status(esa)],[f_4393_2]) ).

cnf(f_4393_4,plain,
    ( U_18113 = U_18116
    | c_Map_Omap__of(U_18114,U_18112,hAPP(hAPP(c_List_Ozip(U_18114,U_18112),U_18115),U_18113)) != c_Map_Omap__of(U_18114,U_18112,hAPP(hAPP(c_List_Ozip(U_18114,U_18112),U_18115),U_18116))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18114),U_18115))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18112)),U_18116) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18114)),U_18115)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18112)),U_18113) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18114)),U_18115) ),
    inference(clausify,[status(thm)],[f_4393_3]) ).

fof(f_4394_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_4394_2,plain,
    ! [U_18120,U_18119,U_18118,U_18117] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_18117,U_18119),U_18117),c_Product__Type_Ofst(U_18117,U_18119)),hAPP(hAPP(c_List_Ozip(U_18117,U_18119),U_18118),U_18120)) = U_18118
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18117)),U_18118) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18119)),U_18120) ),
    inference(variable_rename,[status(thm)],[f_4394_1]) ).

fof(f_4394_3,plain,
    ! [U_18117,U_18119,U_18118,U_18120] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_18117,U_18119),U_18117),c_Product__Type_Ofst(U_18117,U_18119)),hAPP(hAPP(c_List_Ozip(U_18117,U_18119),U_18118),U_18120)) = U_18118
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18117)),U_18118) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18119)),U_18120) ),
    inference(definitional_conversion,[status(esa)],[f_4394_2]) ).

cnf(f_4394_4,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_18117,U_18119),U_18117),c_Product__Type_Ofst(U_18117,U_18119)),hAPP(hAPP(c_List_Ozip(U_18117,U_18119),U_18118),U_18120)) = U_18118
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18117)),U_18118) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18119)),U_18120) ),
    inference(clausify,[status(thm)],[f_4394_3]) ).

fof(f_4395_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_4395_2,plain,
    ! [U_18124,U_18123,U_18122,U_18121] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_18121,U_18123),U_18123),c_Product__Type_Osnd(U_18121,U_18123)),hAPP(hAPP(c_List_Ozip(U_18121,U_18123),U_18122),U_18124)) = U_18124
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18121)),U_18122) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18123)),U_18124) ),
    inference(variable_rename,[status(thm)],[f_4395_1]) ).

fof(f_4395_3,plain,
    ! [U_18121,U_18122,U_18123,U_18124] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_18121,U_18123),U_18123),c_Product__Type_Osnd(U_18121,U_18123)),hAPP(hAPP(c_List_Ozip(U_18121,U_18123),U_18122),U_18124)) = U_18124
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18121)),U_18122) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18123)),U_18124) ),
    inference(definitional_conversion,[status(esa)],[f_4395_2]) ).

cnf(f_4395_4,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_18121,U_18123),U_18123),c_Product__Type_Osnd(U_18121,U_18123)),hAPP(hAPP(c_List_Ozip(U_18121,U_18123),U_18122),U_18124)) = U_18124
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18121)),U_18122) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18123)),U_18124) ),
    inference(clausify,[status(thm)],[f_4395_3]) ).

fof(f_4396_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_4396_2,plain,
    ! [U_18129,U_18128,U_18127,U_18126,U_18125] :
      ( ( ( hBOOL(hAPP(c_List_Odistinct(U_18126),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18126,U_18125,U_18127),U_18128),U_18129)))
          | ~ hBOOL(hAPP(c_List_Odistinct(U_18126),U_18129))
          | hBOOL(hAPP(hAPP(c_member(U_18126),U_18128),hAPP(c_List_Oset(U_18126),U_18129))) )
        & ( ( hBOOL(hAPP(c_List_Odistinct(U_18126),U_18129))
            & ~ hBOOL(hAPP(hAPP(c_member(U_18126),U_18128),hAPP(c_List_Oset(U_18126),U_18129))) )
          | ~ hBOOL(hAPP(c_List_Odistinct(U_18126),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18126,U_18125,U_18127),U_18128),U_18129))) ) )
      | ~ class_Orderings_Olinorder(U_18125) ),
    inference(variable_rename,[status(thm)],[f_4396_1]) ).

fof(f_4396_3,plain,
    ( ! [U_18126,U_18128,U_18129] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18126),U_18129))
        | ~ sP1132(U_18126,U_18128,U_18129) )
    & ! [U_18126,U_18128,U_18129] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_18126),U_18128),hAPP(c_List_Oset(U_18126),U_18129)))
        | ~ sP1132(U_18126,U_18128,U_18129) )
    & ! [U_18126,U_18125,U_18127,U_18128,U_18129] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18126),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18126,U_18125,U_18127),U_18128),U_18129)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18126),U_18129))
        | hBOOL(hAPP(hAPP(c_member(U_18126),U_18128),hAPP(c_List_Oset(U_18126),U_18129)))
        | ~ sP1133(U_18126,U_18125,U_18127,U_18128,U_18129) )
    & ! [U_18126,U_18125,U_18127,U_18128,U_18129] :
        ( sP1132(U_18126,U_18128,U_18129)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18126),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18126,U_18125,U_18127),U_18128),U_18129)))
        | ~ sP1133(U_18126,U_18125,U_18127,U_18128,U_18129) )
    & ! [U_18126,U_18125,U_18127,U_18128,U_18129] :
        ( sP1133(U_18126,U_18125,U_18127,U_18128,U_18129)
        | ~ class_Orderings_Olinorder(U_18125) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1132,sP1133])],[f_4396_2]) ).

cnf(f_4396_4,plain,
    ( sP1133(U_18126,U_18125,U_18127,U_18128,U_18129)
    | ~ class_Orderings_Olinorder(U_18125) ),
    inference(clausify,[status(thm)],[f_4396_3]) ).

cnf(f_4396_5,plain,
    ( sP1132(U_18126,U_18128,U_18129)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18126),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18126,U_18125,U_18127),U_18128),U_18129)))
    | ~ sP1133(U_18126,U_18125,U_18127,U_18128,U_18129) ),
    inference(clausify,[status(thm)],[f_4396_3]) ).

cnf(f_4396_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18126),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18126,U_18125,U_18127),U_18128),U_18129)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18126),U_18129))
    | hBOOL(hAPP(hAPP(c_member(U_18126),U_18128),hAPP(c_List_Oset(U_18126),U_18129)))
    | ~ sP1133(U_18126,U_18125,U_18127,U_18128,U_18129) ),
    inference(clausify,[status(thm)],[f_4396_3]) ).

cnf(f_4396_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_18126),U_18128),hAPP(c_List_Oset(U_18126),U_18129)))
    | ~ sP1132(U_18126,U_18128,U_18129) ),
    inference(clausify,[status(thm)],[f_4396_3]) ).

cnf(f_4396_8,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18126),U_18129))
    | ~ sP1132(U_18126,U_18128,U_18129) ),
    inference(clausify,[status(thm)],[f_4396_3]) ).

fof(f_4397_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_4397_2,plain,
    ! [U_18132,U_18131,U_18130] :
      ( 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_18130)),U_18132)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18130),U_18131),hAPP(c_List_Oset(U_18130),U_18132))) ),
    inference(variable_rename,[status(thm)],[f_4397_1]) ).

fof(f_4397_3,plain,
    ! [U_18131,U_18132,U_18130] :
      ( 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_18130)),U_18132)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18130),U_18131),hAPP(c_List_Oset(U_18130),U_18132))) ),
    inference(definitional_conversion,[status(esa)],[f_4397_2]) ).

cnf(f_4397_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_18130)),U_18132)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18130),U_18131),hAPP(c_List_Oset(U_18130),U_18132))) ),
    inference(clausify,[status(thm)],[f_4397_3]) ).

fof(f_4398_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_4398_2,plain,
    ! [U_18137,U_18136,U_18135,U_18134,U_18133] :
      ( ( ( hAPP(hAPP(c_List_Ozip(U_18133,U_18135),U_18134),U_18136) = U_18137
          | hAPP(hAPP(c_List_Omap(tc_prod(U_18133,U_18135),U_18135),c_Product__Type_Osnd(U_18133,U_18135)),U_18137) != U_18136
          | hAPP(hAPP(c_List_Omap(tc_prod(U_18133,U_18135),U_18133),c_Product__Type_Ofst(U_18133,U_18135)),U_18137) != U_18134 )
        & ( ( hAPP(hAPP(c_List_Omap(tc_prod(U_18133,U_18135),U_18135),c_Product__Type_Osnd(U_18133,U_18135)),U_18137) = U_18136
            & hAPP(hAPP(c_List_Omap(tc_prod(U_18133,U_18135),U_18133),c_Product__Type_Ofst(U_18133,U_18135)),U_18137) = U_18134 )
          | hAPP(hAPP(c_List_Ozip(U_18133,U_18135),U_18134),U_18136) != U_18137 ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18133)),U_18134) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18135)),U_18136) ),
    inference(variable_rename,[status(thm)],[f_4398_1]) ).

fof(f_4398_3,plain,
    ( ! [U_18133,U_18134,U_18135,U_18136,U_18137] :
        ( hAPP(hAPP(c_List_Omap(tc_prod(U_18133,U_18135),U_18135),c_Product__Type_Osnd(U_18133,U_18135)),U_18137) = U_18136
        | ~ sP1134(U_18133,U_18134,U_18135,U_18136,U_18137) )
    & ! [U_18133,U_18134,U_18135,U_18136,U_18137] :
        ( hAPP(hAPP(c_List_Omap(tc_prod(U_18133,U_18135),U_18133),c_Product__Type_Ofst(U_18133,U_18135)),U_18137) = U_18134
        | ~ sP1134(U_18133,U_18134,U_18135,U_18136,U_18137) )
    & ! [U_18133,U_18134,U_18135,U_18136,U_18137] :
        ( hAPP(hAPP(c_List_Ozip(U_18133,U_18135),U_18134),U_18136) = U_18137
        | hAPP(hAPP(c_List_Omap(tc_prod(U_18133,U_18135),U_18135),c_Product__Type_Osnd(U_18133,U_18135)),U_18137) != U_18136
        | hAPP(hAPP(c_List_Omap(tc_prod(U_18133,U_18135),U_18133),c_Product__Type_Ofst(U_18133,U_18135)),U_18137) != U_18134
        | ~ sP1135(U_18133,U_18134,U_18135,U_18136,U_18137) )
    & ! [U_18133,U_18134,U_18135,U_18136,U_18137] :
        ( sP1134(U_18133,U_18134,U_18135,U_18136,U_18137)
        | hAPP(hAPP(c_List_Ozip(U_18133,U_18135),U_18134),U_18136) != U_18137
        | ~ sP1135(U_18133,U_18134,U_18135,U_18136,U_18137) )
    & ! [U_18133,U_18134,U_18135,U_18136,U_18137] :
        ( sP1135(U_18133,U_18134,U_18135,U_18136,U_18137)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18133)),U_18134) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18135)),U_18136) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1134,sP1135])],[f_4398_2]) ).

cnf(f_4398_4,plain,
    ( sP1135(U_18133,U_18134,U_18135,U_18136,U_18137)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18133)),U_18134) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18135)),U_18136) ),
    inference(clausify,[status(thm)],[f_4398_3]) ).

cnf(f_4398_5,plain,
    ( sP1134(U_18133,U_18134,U_18135,U_18136,U_18137)
    | hAPP(hAPP(c_List_Ozip(U_18133,U_18135),U_18134),U_18136) != U_18137
    | ~ sP1135(U_18133,U_18134,U_18135,U_18136,U_18137) ),
    inference(clausify,[status(thm)],[f_4398_3]) ).

cnf(f_4398_6,plain,
    ( hAPP(hAPP(c_List_Ozip(U_18133,U_18135),U_18134),U_18136) = U_18137
    | hAPP(hAPP(c_List_Omap(tc_prod(U_18133,U_18135),U_18135),c_Product__Type_Osnd(U_18133,U_18135)),U_18137) != U_18136
    | hAPP(hAPP(c_List_Omap(tc_prod(U_18133,U_18135),U_18133),c_Product__Type_Ofst(U_18133,U_18135)),U_18137) != U_18134
    | ~ sP1135(U_18133,U_18134,U_18135,U_18136,U_18137) ),
    inference(clausify,[status(thm)],[f_4398_3]) ).

cnf(f_4398_7,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_18133,U_18135),U_18133),c_Product__Type_Ofst(U_18133,U_18135)),U_18137) = U_18134
    | ~ sP1134(U_18133,U_18134,U_18135,U_18136,U_18137) ),
    inference(clausify,[status(thm)],[f_4398_3]) ).

cnf(f_4398_8,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_18133,U_18135),U_18135),c_Product__Type_Osnd(U_18133,U_18135)),U_18137) = U_18136
    | ~ sP1134(U_18133,U_18134,U_18135,U_18136,U_18137) ),
    inference(clausify,[status(thm)],[f_4398_3]) ).

fof(f_4399_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_4399_2,plain,
    ! [U_18139,U_18138] : c_List_Olenlex(U_18138,U_18139) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18138),tc_List_Olist(U_18138),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18138),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),tc_List_Olist(U_18138)),c_COMBS(tc_List_Olist(U_18138),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_18138)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18138)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18138),tc_fun(tc_List_Olist(U_18138),tc_Nat_Onat),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18138),tc_Nat_Onat),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),tc_List_Olist(U_18138)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18138))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_18138)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18138))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_18138)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18138),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),tc_List_Olist(U_18138)),c_COMBS(tc_List_Olist(U_18138),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_18138)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18138)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18138),tc_fun(tc_List_Olist(U_18138),tc_Nat_Onat),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18138),tc_Nat_Onat),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),tc_List_Olist(U_18138)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18138))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_18138)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_18138))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_18138)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18138),tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),tc_List_Olist(U_18138)),c_COMBC(tc_List_Olist(U_18138),tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138))),tc_fun(tc_List_Olist(U_18138),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(U_18138)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18138)),c_member(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138))))),c_Product__Type_OPair(tc_List_Olist(U_18138),tc_List_Olist(U_18138))))),c_List_Olex(U_18138,U_18139)))))),
    inference(variable_rename,[status(thm)],[f_4399_1]) ).

fof(f_4399_3,plain,
    ! [U_18138,U_18139] : c_List_Olenlex(U_18138,U_18139) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18138),tc_List_Olist(U_18138),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18138),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),tc_List_Olist(U_18138)),c_COMBS(tc_List_Olist(U_18138),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_18138)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18138)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18138),tc_fun(tc_List_Olist(U_18138),tc_Nat_Onat),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18138),tc_Nat_Onat),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),tc_List_Olist(U_18138)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18138))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_18138)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18138))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_18138)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18138),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),tc_List_Olist(U_18138)),c_COMBS(tc_List_Olist(U_18138),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_18138)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18138)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18138),tc_fun(tc_List_Olist(U_18138),tc_Nat_Onat),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18138),tc_Nat_Onat),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),tc_List_Olist(U_18138)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18138))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_18138)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_18138))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_18138)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18138),tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),tc_List_Olist(U_18138)),c_COMBC(tc_List_Olist(U_18138),tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138))),tc_fun(tc_List_Olist(U_18138),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(U_18138)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18138)),c_member(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138))))),c_Product__Type_OPair(tc_List_Olist(U_18138),tc_List_Olist(U_18138))))),c_List_Olex(U_18138,U_18139)))))),
    inference(definitional_conversion,[status(esa)],[f_4399_2]) ).

cnf(f_4399_4,plain,
    c_List_Olenlex(U_18138,U_18139) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18138),tc_List_Olist(U_18138),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18138),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),tc_List_Olist(U_18138)),c_COMBS(tc_List_Olist(U_18138),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_18138)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18138)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18138),tc_fun(tc_List_Olist(U_18138),tc_Nat_Onat),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18138),tc_Nat_Onat),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),tc_List_Olist(U_18138)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18138))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_18138)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18138))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_18138)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18138),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),tc_List_Olist(U_18138)),c_COMBS(tc_List_Olist(U_18138),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_18138)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18138)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18138),tc_fun(tc_List_Olist(U_18138),tc_Nat_Onat),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18138),tc_Nat_Onat),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),tc_List_Olist(U_18138)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18138))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_18138)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_18138))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_18138)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18138),tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18138),tc_HOL_Obool)),tc_List_Olist(U_18138)),c_COMBC(tc_List_Olist(U_18138),tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18138),tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138))),tc_fun(tc_List_Olist(U_18138),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(U_18138)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18138)),c_member(tc_prod(tc_List_Olist(U_18138),tc_List_Olist(U_18138))))),c_Product__Type_OPair(tc_List_Olist(U_18138),tc_List_Olist(U_18138))))),c_List_Olex(U_18138,U_18139)))))),
    inference(clausify,[status(thm)],[f_4399_3]) ).

fof(f_4400_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_4400_2,plain,
    ! [U_18141,U_18140] : c_List_Olenlex(U_18140,U_18141) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_18140)),tc_List_Olist(U_18140)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_18140),c_Wellfounded_Oless__than,c_List_Olex(U_18140,U_18141))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18140),tc_List_Olist(U_18140),tc_prod(tc_Nat_Onat,tc_List_Olist(U_18140))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_18140),tc_prod(tc_Nat_Onat,tc_List_Olist(U_18140))),tc_List_Olist(U_18140)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_18140))),c_Nat_Osize__class_Osize(tc_List_Olist(U_18140)))),c_COMBI(tc_List_Olist(U_18140)))),
    inference(variable_rename,[status(thm)],[f_4400_1]) ).

fof(f_4400_3,plain,
    ! [U_18140,U_18141] : c_List_Olenlex(U_18140,U_18141) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_18140)),tc_List_Olist(U_18140)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_18140),c_Wellfounded_Oless__than,c_List_Olex(U_18140,U_18141))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18140),tc_List_Olist(U_18140),tc_prod(tc_Nat_Onat,tc_List_Olist(U_18140))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_18140),tc_prod(tc_Nat_Onat,tc_List_Olist(U_18140))),tc_List_Olist(U_18140)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_18140))),c_Nat_Osize__class_Osize(tc_List_Olist(U_18140)))),c_COMBI(tc_List_Olist(U_18140)))),
    inference(definitional_conversion,[status(esa)],[f_4400_2]) ).

cnf(f_4400_4,plain,
    c_List_Olenlex(U_18140,U_18141) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_18140)),tc_List_Olist(U_18140)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_18140),c_Wellfounded_Oless__than,c_List_Olex(U_18140,U_18141))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18140),tc_List_Olist(U_18140),tc_prod(tc_Nat_Onat,tc_List_Olist(U_18140))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_18140),tc_prod(tc_Nat_Onat,tc_List_Olist(U_18140))),tc_List_Olist(U_18140)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_18140))),c_Nat_Osize__class_Osize(tc_List_Olist(U_18140)))),c_COMBI(tc_List_Olist(U_18140)))),
    inference(clausify,[status(thm)],[f_4400_3]) ).

fof(f_4401_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_4401_2,plain,
    ! [U_18144,U_18143,U_18142] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_18142)),hAPP(c_Set_OCollect(tc_List_Olist(U_18142)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18142),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_18142)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18142),tc_fun(U_18142,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18142,tc_HOL_Obool),tc_fun(tc_fun(U_18142,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18142)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_18142,tc_HOL_Obool))),c_List_Oset(U_18142))),U_18143))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18142),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_18142)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_18142)))),U_18144)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18142),U_18143)) ),
    inference(variable_rename,[status(thm)],[f_4401_1]) ).

fof(f_4401_3,plain,
    ! [U_18142,U_18143,U_18144] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_18142)),hAPP(c_Set_OCollect(tc_List_Olist(U_18142)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18142),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_18142)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18142),tc_fun(U_18142,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18142,tc_HOL_Obool),tc_fun(tc_fun(U_18142,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18142)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_18142,tc_HOL_Obool))),c_List_Oset(U_18142))),U_18143))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18142),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_18142)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_18142)))),U_18144)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18142),U_18143)) ),
    inference(definitional_conversion,[status(esa)],[f_4401_2]) ).

cnf(f_4401_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_18142)),hAPP(c_Set_OCollect(tc_List_Olist(U_18142)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18142),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_18142)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18142),tc_fun(U_18142,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18142,tc_HOL_Obool),tc_fun(tc_fun(U_18142,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18142)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_18142,tc_HOL_Obool))),c_List_Oset(U_18142))),U_18143))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18142),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_18142)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_18142)))),U_18144)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18142),U_18143)) ),
    inference(clausify,[status(thm)],[f_4401_3]) ).

fof(f_4402_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_4402_2,plain,
    ! [U_18149,U_18148,U_18147] :
      ( ( U_18147 = U_18148
        | ? [U_18146] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18149,U_18149,tc_HOL_Obool),c_fequal),U_18146))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18149,U_18149)),U_18146),hAPP(c_List_Oset(tc_prod(U_18149,U_18149)),hAPP(hAPP(c_List_Ozip(U_18149,U_18149),U_18147),U_18148)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18149)),U_18147) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18149)),U_18148) )
      & ( ( ! [U_18145] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18149,U_18149,tc_HOL_Obool),c_fequal),U_18145))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18149,U_18149)),U_18145),hAPP(c_List_Oset(tc_prod(U_18149,U_18149)),hAPP(hAPP(c_List_Ozip(U_18149,U_18149),U_18147),U_18148)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18149)),U_18147) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18149)),U_18148) )
        | U_18147 != U_18148 ) ),
    inference(variable_rename,[status(thm)],[f_4402_1]) ).

fof(f_4402_3,plain,
    ( ! [U_18155,U_18153,U_18151] :
        ( U_18151 = U_18153
        | ? [U_18146] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18155,U_18155,tc_HOL_Obool),c_fequal),U_18146))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18155,U_18155)),U_18146),hAPP(c_List_Oset(tc_prod(U_18155,U_18155)),hAPP(hAPP(c_List_Ozip(U_18155,U_18155),U_18151),U_18153)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18155)),U_18151) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18155)),U_18153) )
    & ! [U_18154,U_18152,U_18150] :
        ( ( ! [U_18145] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18154,U_18154,tc_HOL_Obool),c_fequal),U_18145))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18154,U_18154)),U_18145),hAPP(c_List_Oset(tc_prod(U_18154,U_18154)),hAPP(hAPP(c_List_Ozip(U_18154,U_18154),U_18150),U_18152)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18154)),U_18150) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18154)),U_18152) )
        | U_18150 != U_18152 ) ),
    inference(miniscope,[status(thm)],[f_4402_2]) ).

fof(f_4402_4,plain,
    ( ! [U_18155,U_18153,U_18151] :
        ( U_18151 = U_18153
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18155,U_18155,tc_HOL_Obool),c_fequal),sK458(U_18155,U_18153,U_18151)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18155,U_18155)),sK458(U_18155,U_18153,U_18151)),hAPP(c_List_Oset(tc_prod(U_18155,U_18155)),hAPP(hAPP(c_List_Ozip(U_18155,U_18155),U_18151),U_18153)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18155)),U_18151) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18155)),U_18153) )
    & ! [U_18154,U_18152,U_18150] :
        ( ( ! [U_18145] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18154,U_18154,tc_HOL_Obool),c_fequal),U_18145))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18154,U_18154)),U_18145),hAPP(c_List_Oset(tc_prod(U_18154,U_18154)),hAPP(hAPP(c_List_Ozip(U_18154,U_18154),U_18150),U_18152)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18154)),U_18150) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18154)),U_18152) )
        | U_18150 != U_18152 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK458]),skolemize(U_18146,sK458(U_18155,U_18153,U_18151))],[f_4402_3]) ).

fof(f_4402_5,plain,
    ( ! [U_18153,U_18151,U_18155] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18155,U_18155,tc_HOL_Obool),c_fequal),sK458(U_18155,U_18153,U_18151)))
        | ~ sP1137(U_18153,U_18151,U_18155) )
    & ! [U_18153,U_18151,U_18155] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18155,U_18155)),sK458(U_18155,U_18153,U_18151)),hAPP(c_List_Oset(tc_prod(U_18155,U_18155)),hAPP(hAPP(c_List_Ozip(U_18155,U_18155),U_18151),U_18153))))
        | ~ sP1137(U_18153,U_18151,U_18155) )
    & ! [U_18145,U_18154,U_18150,U_18152] :
        ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18154,U_18154,tc_HOL_Obool),c_fequal),U_18145))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18154,U_18154)),U_18145),hAPP(c_List_Oset(tc_prod(U_18154,U_18154)),hAPP(hAPP(c_List_Ozip(U_18154,U_18154),U_18150),U_18152))))
        | ~ sP1136(U_18145,U_18154,U_18150,U_18152) )
    & ! [U_18145,U_18154,U_18150,U_18152] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18154)),U_18150) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18154)),U_18152)
        | ~ sP1136(U_18145,U_18154,U_18150,U_18152) )
    & ! [U_18153,U_18151,U_18155] :
        ( U_18151 = U_18153
        | sP1137(U_18153,U_18151,U_18155)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18155)),U_18151) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18155)),U_18153) )
    & ! [U_18145,U_18154,U_18150,U_18152] :
        ( sP1136(U_18145,U_18154,U_18150,U_18152)
        | U_18150 != U_18152 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1136,sP1137])],[f_4402_4]) ).

cnf(f_4402_6,plain,
    ( sP1136(U_18145,U_18154,U_18150,U_18152)
    | U_18150 != U_18152 ),
    inference(clausify,[status(thm)],[f_4402_5]) ).

cnf(f_4402_7,plain,
    ( U_18151 = U_18153
    | sP1137(U_18153,U_18151,U_18155)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18155)),U_18151) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18155)),U_18153) ),
    inference(clausify,[status(thm)],[f_4402_5]) ).

cnf(f_4402_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18154)),U_18150) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18154)),U_18152)
    | ~ sP1136(U_18145,U_18154,U_18150,U_18152) ),
    inference(clausify,[status(thm)],[f_4402_5]) ).

cnf(f_4402_9,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18154,U_18154,tc_HOL_Obool),c_fequal),U_18145))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18154,U_18154)),U_18145),hAPP(c_List_Oset(tc_prod(U_18154,U_18154)),hAPP(hAPP(c_List_Ozip(U_18154,U_18154),U_18150),U_18152))))
    | ~ sP1136(U_18145,U_18154,U_18150,U_18152) ),
    inference(clausify,[status(thm)],[f_4402_5]) ).

cnf(f_4402_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18155,U_18155)),sK458(U_18155,U_18153,U_18151)),hAPP(c_List_Oset(tc_prod(U_18155,U_18155)),hAPP(hAPP(c_List_Ozip(U_18155,U_18155),U_18151),U_18153))))
    | ~ sP1137(U_18153,U_18151,U_18155) ),
    inference(clausify,[status(thm)],[f_4402_5]) ).

cnf(f_4402_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18155,U_18155,tc_HOL_Obool),c_fequal),sK458(U_18155,U_18153,U_18151)))
    | ~ sP1137(U_18153,U_18151,U_18155) ),
    inference(clausify,[status(thm)],[f_4402_5]) ).

fof(f_4403_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_4403_2,plain,
    ! [U_18160,U_18159,U_18158,U_18157,U_18156] :
      ( ( ( hAPP(c_Map_Omap__of(U_18156,U_18158,hAPP(hAPP(c_List_Ozip(U_18156,U_18158),U_18157),U_18159)),U_18160) = c_Option_Ooption_ONone(U_18158)
          | hBOOL(hAPP(hAPP(c_member(U_18156),U_18160),hAPP(c_List_Oset(U_18156),U_18157))) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(U_18156),U_18160),hAPP(c_List_Oset(U_18156),U_18157)))
          | hAPP(c_Map_Omap__of(U_18156,U_18158,hAPP(hAPP(c_List_Ozip(U_18156,U_18158),U_18157),U_18159)),U_18160) != c_Option_Ooption_ONone(U_18158) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18156)),U_18157) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18158)),U_18159) ),
    inference(variable_rename,[status(thm)],[f_4403_1]) ).

fof(f_4403_3,plain,
    ( ! [U_18156,U_18157,U_18159,U_18158,U_18160] :
        ( hAPP(c_Map_Omap__of(U_18156,U_18158,hAPP(hAPP(c_List_Ozip(U_18156,U_18158),U_18157),U_18159)),U_18160) = c_Option_Ooption_ONone(U_18158)
        | hBOOL(hAPP(hAPP(c_member(U_18156),U_18160),hAPP(c_List_Oset(U_18156),U_18157)))
        | ~ sP1138(U_18156,U_18157,U_18159,U_18158,U_18160) )
    & ! [U_18156,U_18157,U_18159,U_18158,U_18160] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_18156),U_18160),hAPP(c_List_Oset(U_18156),U_18157)))
        | hAPP(c_Map_Omap__of(U_18156,U_18158,hAPP(hAPP(c_List_Ozip(U_18156,U_18158),U_18157),U_18159)),U_18160) != c_Option_Ooption_ONone(U_18158)
        | ~ sP1138(U_18156,U_18157,U_18159,U_18158,U_18160) )
    & ! [U_18156,U_18157,U_18159,U_18158,U_18160] :
        ( sP1138(U_18156,U_18157,U_18159,U_18158,U_18160)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18156)),U_18157) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18158)),U_18159) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1138])],[f_4403_2]) ).

cnf(f_4403_4,plain,
    ( sP1138(U_18156,U_18157,U_18159,U_18158,U_18160)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18156)),U_18157) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18158)),U_18159) ),
    inference(clausify,[status(thm)],[f_4403_3]) ).

cnf(f_4403_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_18156),U_18160),hAPP(c_List_Oset(U_18156),U_18157)))
    | hAPP(c_Map_Omap__of(U_18156,U_18158,hAPP(hAPP(c_List_Ozip(U_18156,U_18158),U_18157),U_18159)),U_18160) != c_Option_Ooption_ONone(U_18158)
    | ~ sP1138(U_18156,U_18157,U_18159,U_18158,U_18160) ),
    inference(clausify,[status(thm)],[f_4403_3]) ).

cnf(f_4403_6,plain,
    ( hAPP(c_Map_Omap__of(U_18156,U_18158,hAPP(hAPP(c_List_Ozip(U_18156,U_18158),U_18157),U_18159)),U_18160) = c_Option_Ooption_ONone(U_18158)
    | hBOOL(hAPP(hAPP(c_member(U_18156),U_18160),hAPP(c_List_Oset(U_18156),U_18157)))
    | ~ sP1138(U_18156,U_18157,U_18159,U_18158,U_18160) ),
    inference(clausify,[status(thm)],[f_4403_3]) ).

fof(f_4404_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_4404_2,plain,
    ! [U_18167,U_18166,U_18165,U_18164,U_18163] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_18163),U_18167),hAPP(c_List_Oset(U_18163),U_18164)))
          | ! [U_18162] : hAPP(c_Map_Omap__of(U_18163,U_18165,hAPP(hAPP(c_List_Ozip(U_18163,U_18165),U_18164),U_18166)),U_18167) != hAPP(c_Option_Ooption_OSome(U_18165),U_18162) )
        & ( ? [U_18161] : hAPP(c_Map_Omap__of(U_18163,U_18165,hAPP(hAPP(c_List_Ozip(U_18163,U_18165),U_18164),U_18166)),U_18167) = hAPP(c_Option_Ooption_OSome(U_18165),U_18161)
          | ~ hBOOL(hAPP(hAPP(c_member(U_18163),U_18167),hAPP(c_List_Oset(U_18163),U_18164))) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18163)),U_18164) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18165)),U_18166) ),
    inference(variable_rename,[status(thm)],[f_4404_1]) ).

fof(f_4404_3,plain,
    ! [U_18167,U_18166,U_18165,U_18164,U_18163] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_18163),U_18167),hAPP(c_List_Oset(U_18163),U_18164)))
          | ! [U_18162] : hAPP(c_Map_Omap__of(U_18163,U_18165,hAPP(hAPP(c_List_Ozip(U_18163,U_18165),U_18164),U_18166)),U_18167) != hAPP(c_Option_Ooption_OSome(U_18165),U_18162) )
        & ( hAPP(c_Map_Omap__of(U_18163,U_18165,hAPP(hAPP(c_List_Ozip(U_18163,U_18165),U_18164),U_18166)),U_18167) = hAPP(c_Option_Ooption_OSome(U_18165),sK459(U_18167,U_18166,U_18165,U_18164,U_18163))
          | ~ hBOOL(hAPP(hAPP(c_member(U_18163),U_18167),hAPP(c_List_Oset(U_18163),U_18164))) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18163)),U_18164) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18165)),U_18166) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK459]),skolemize(U_18161,sK459(U_18167,U_18166,U_18165,U_18164,U_18163))],[f_4404_2]) ).

fof(f_4404_4,plain,
    ( ! [U_18163,U_18164,U_18165,U_18162,U_18166,U_18167] :
        ( hBOOL(hAPP(hAPP(c_member(U_18163),U_18167),hAPP(c_List_Oset(U_18163),U_18164)))
        | hAPP(c_Map_Omap__of(U_18163,U_18165,hAPP(hAPP(c_List_Ozip(U_18163,U_18165),U_18164),U_18166)),U_18167) != hAPP(c_Option_Ooption_OSome(U_18165),U_18162)
        | ~ sP1139(U_18163,U_18164,U_18165,U_18162,U_18166,U_18167) )
    & ! [U_18163,U_18164,U_18165,U_18162,U_18166,U_18167] :
        ( hAPP(c_Map_Omap__of(U_18163,U_18165,hAPP(hAPP(c_List_Ozip(U_18163,U_18165),U_18164),U_18166)),U_18167) = hAPP(c_Option_Ooption_OSome(U_18165),sK459(U_18167,U_18166,U_18165,U_18164,U_18163))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18163),U_18167),hAPP(c_List_Oset(U_18163),U_18164)))
        | ~ sP1139(U_18163,U_18164,U_18165,U_18162,U_18166,U_18167) )
    & ! [U_18163,U_18164,U_18165,U_18162,U_18166,U_18167] :
        ( sP1139(U_18163,U_18164,U_18165,U_18162,U_18166,U_18167)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18163)),U_18164) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18165)),U_18166) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1139])],[f_4404_3]) ).

cnf(f_4404_5,plain,
    ( sP1139(U_18163,U_18164,U_18165,U_18162,U_18166,U_18167)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18163)),U_18164) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18165)),U_18166) ),
    inference(clausify,[status(thm)],[f_4404_4]) ).

cnf(f_4404_6,plain,
    ( hAPP(c_Map_Omap__of(U_18163,U_18165,hAPP(hAPP(c_List_Ozip(U_18163,U_18165),U_18164),U_18166)),U_18167) = hAPP(c_Option_Ooption_OSome(U_18165),sK459(U_18167,U_18166,U_18165,U_18164,U_18163))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18163),U_18167),hAPP(c_List_Oset(U_18163),U_18164)))
    | ~ sP1139(U_18163,U_18164,U_18165,U_18162,U_18166,U_18167) ),
    inference(clausify,[status(thm)],[f_4404_4]) ).

cnf(f_4404_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18163),U_18167),hAPP(c_List_Oset(U_18163),U_18164)))
    | hAPP(c_Map_Omap__of(U_18163,U_18165,hAPP(hAPP(c_List_Ozip(U_18163,U_18165),U_18164),U_18166)),U_18167) != hAPP(c_Option_Ooption_OSome(U_18165),U_18162)
    | ~ sP1139(U_18163,U_18164,U_18165,U_18162,U_18166,U_18167) ),
    inference(clausify,[status(thm)],[f_4404_4]) ).

fof(f_4405_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_4405_2,plain,
    ! [U_18170,U_18169,U_18168] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18168)),c_List_Oremove1(U_18168,U_18169,U_18170)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18168)),U_18170)
        | hBOOL(hAPP(hAPP(c_member(U_18168),U_18169),hAPP(c_List_Oset(U_18168),U_18170))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18168)),c_List_Oremove1(U_18168,U_18169,U_18170)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18168)),U_18170)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18168),U_18169),hAPP(c_List_Oset(U_18168),U_18170))) ) ),
    inference(variable_rename,[status(thm)],[f_4405_1]) ).

fof(f_4405_3,plain,
    ( ! [U_18176,U_18174,U_18172] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18172)),c_List_Oremove1(U_18172,U_18174,U_18176)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18172)),U_18176)
        | hBOOL(hAPP(hAPP(c_member(U_18172),U_18174),hAPP(c_List_Oset(U_18172),U_18176))) )
    & ! [U_18175,U_18173,U_18171] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18171)),c_List_Oremove1(U_18171,U_18173,U_18175)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18171)),U_18175)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18171),U_18173),hAPP(c_List_Oset(U_18171),U_18175))) ) ),
    inference(miniscope,[status(thm)],[f_4405_2]) ).

fof(f_4405_4,plain,
    ( ! [U_18172,U_18174,U_18176] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18172)),c_List_Oremove1(U_18172,U_18174,U_18176)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18172)),U_18176)
        | hBOOL(hAPP(hAPP(c_member(U_18172),U_18174),hAPP(c_List_Oset(U_18172),U_18176))) )
    & ! [U_18171,U_18175,U_18173] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18171)),c_List_Oremove1(U_18171,U_18173,U_18175)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18171)),U_18175)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18171),U_18173),hAPP(c_List_Oset(U_18171),U_18175))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4405_3]) ).

cnf(f_4405_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18171)),c_List_Oremove1(U_18171,U_18173,U_18175)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18171)),U_18175)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18171),U_18173),hAPP(c_List_Oset(U_18171),U_18175))) ),
    inference(clausify,[status(thm)],[f_4405_4]) ).

cnf(f_4405_6,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18172)),c_List_Oremove1(U_18172,U_18174,U_18176)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18172)),U_18176)
    | hBOOL(hAPP(hAPP(c_member(U_18172),U_18174),hAPP(c_List_Oset(U_18172),U_18176))) ),
    inference(clausify,[status(thm)],[f_4405_4]) ).

fof(f_4406_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_4406_2,plain,
    ! [U_18180,U_18179,U_18178,U_18177] :
      ( c_Map_Odom(U_18177,U_18179,c_Map_Omap__of(U_18177,U_18179,hAPP(hAPP(c_List_Ozip(U_18177,U_18179),U_18178),U_18180))) = hAPP(c_List_Oset(U_18177),U_18178)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18177),U_18178))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18177)),U_18178) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18179)),U_18180) ),
    inference(variable_rename,[status(thm)],[f_4406_1]) ).

fof(f_4406_3,plain,
    ! [U_18177,U_18178,U_18179,U_18180] :
      ( c_Map_Odom(U_18177,U_18179,c_Map_Omap__of(U_18177,U_18179,hAPP(hAPP(c_List_Ozip(U_18177,U_18179),U_18178),U_18180))) = hAPP(c_List_Oset(U_18177),U_18178)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18177),U_18178))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18177)),U_18178) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18179)),U_18180) ),
    inference(definitional_conversion,[status(esa)],[f_4406_2]) ).

cnf(f_4406_4,plain,
    ( c_Map_Odom(U_18177,U_18179,c_Map_Omap__of(U_18177,U_18179,hAPP(hAPP(c_List_Ozip(U_18177,U_18179),U_18178),U_18180))) = hAPP(c_List_Oset(U_18177),U_18178)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18177),U_18178))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18177)),U_18178) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18179)),U_18180) ),
    inference(clausify,[status(thm)],[f_4406_3]) ).

fof(f_4407_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_4407_2,plain,
    ! [U_18183,U_18182,U_18181] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_18181)),hAPP(c_Set_OCollect(tc_List_Olist(U_18181)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18181),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_18181)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18181),tc_fun(U_18181,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18181,tc_HOL_Obool),tc_fun(tc_fun(U_18181,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18181)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_18181,tc_HOL_Obool))),c_List_Oset(U_18181))),U_18182))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18181),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_18181)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18181)))),U_18183)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18181),U_18182)) ),
    inference(variable_rename,[status(thm)],[f_4407_1]) ).

fof(f_4407_3,plain,
    ! [U_18181,U_18182,U_18183] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_18181)),hAPP(c_Set_OCollect(tc_List_Olist(U_18181)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18181),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_18181)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18181),tc_fun(U_18181,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18181,tc_HOL_Obool),tc_fun(tc_fun(U_18181,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18181)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_18181,tc_HOL_Obool))),c_List_Oset(U_18181))),U_18182))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18181),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_18181)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18181)))),U_18183)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18181),U_18182)) ),
    inference(definitional_conversion,[status(esa)],[f_4407_2]) ).

cnf(f_4407_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_18181)),hAPP(c_Set_OCollect(tc_List_Olist(U_18181)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18181),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_18181)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18181),tc_fun(U_18181,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18181,tc_HOL_Obool),tc_fun(tc_fun(U_18181,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18181)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_18181,tc_HOL_Obool))),c_List_Oset(U_18181))),U_18182))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18181),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_18181)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18181)))),U_18183)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18181),U_18182)) ),
    inference(clausify,[status(thm)],[f_4407_3]) ).

fof(f_4408_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_4408_2,plain,
    ! [U_18185,U_18184] :
      ( ( c_Nitpick_Ocard_H(U_18184,U_18185) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_18184),U_18185)) )
      & ( c_Nitpick_Ocard_H(U_18184,U_18185) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18184)),c_Hilbert__Choice_OEps(tc_List_Olist(U_18184),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18184),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_18184)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18184),tc_fun(U_18184,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18184,tc_HOL_Obool),tc_fun(tc_fun(U_18184,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18184)),c_fequal),c_List_Oset(U_18184))),U_18185))),c_List_Odistinct(U_18184))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18184),U_18185)) ) ),
    inference(variable_rename,[status(thm)],[f_4408_1]) ).

fof(f_4408_3,plain,
    ( ! [U_18189,U_18187] :
        ( c_Nitpick_Ocard_H(U_18187,U_18189) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_18187),U_18189)) )
    & ! [U_18188,U_18186] :
        ( c_Nitpick_Ocard_H(U_18186,U_18188) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18186)),c_Hilbert__Choice_OEps(tc_List_Olist(U_18186),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18186),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_18186)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18186),tc_fun(U_18186,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18186,tc_HOL_Obool),tc_fun(tc_fun(U_18186,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18186)),c_fequal),c_List_Oset(U_18186))),U_18188))),c_List_Odistinct(U_18186))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18186),U_18188)) ) ),
    inference(miniscope,[status(thm)],[f_4408_2]) ).

fof(f_4408_4,plain,
    ( ! [U_18187,U_18189] :
        ( c_Nitpick_Ocard_H(U_18187,U_18189) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_18187),U_18189)) )
    & ! [U_18188,U_18186] :
        ( c_Nitpick_Ocard_H(U_18186,U_18188) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18186)),c_Hilbert__Choice_OEps(tc_List_Olist(U_18186),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18186),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_18186)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18186),tc_fun(U_18186,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18186,tc_HOL_Obool),tc_fun(tc_fun(U_18186,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18186)),c_fequal),c_List_Oset(U_18186))),U_18188))),c_List_Odistinct(U_18186))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18186),U_18188)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4408_3]) ).

cnf(f_4408_5,plain,
    ( c_Nitpick_Ocard_H(U_18186,U_18188) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18186)),c_Hilbert__Choice_OEps(tc_List_Olist(U_18186),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18186),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_18186)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18186),tc_fun(U_18186,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18186,tc_HOL_Obool),tc_fun(tc_fun(U_18186,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18186)),c_fequal),c_List_Oset(U_18186))),U_18188))),c_List_Odistinct(U_18186))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18186),U_18188)) ),
    inference(clausify,[status(thm)],[f_4408_4]) ).

cnf(f_4408_6,plain,
    ( c_Nitpick_Ocard_H(U_18187,U_18189) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_18187),U_18189)) ),
    inference(clausify,[status(thm)],[f_4408_4]) ).

fof(f_4409_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_4409_2,plain,
    ! [U_18195,U_18194,U_18193,U_18192] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18192),tc_List_Olist(U_18192))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18192),tc_List_Olist(U_18192)),U_18193),U_18194)),c_List_Olistrel(U_18192,U_18195)))
        | ? [U_18191] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18192,U_18192,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_18192,tc_fun(tc_prod(U_18192,U_18192),tc_HOL_Obool),tc_fun(U_18192,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18192,tc_fun(tc_fun(tc_prod(U_18192,U_18192),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18192,U_18192),tc_HOL_Obool),tc_fun(U_18192,tc_HOL_Obool)),U_18192),c_COMBC(U_18192,tc_fun(tc_prod(U_18192,U_18192),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18192,tc_prod(U_18192,U_18192)),tc_fun(U_18192,tc_fun(tc_fun(tc_prod(U_18192,U_18192),tc_HOL_Obool),tc_HOL_Obool)),U_18192),hAPP(c_COMBB(tc_prod(U_18192,U_18192),tc_fun(tc_fun(tc_prod(U_18192,U_18192),tc_HOL_Obool),tc_HOL_Obool),U_18192),c_member(tc_prod(U_18192,U_18192)))),c_Product__Type_OPair(U_18192,U_18192)))),U_18195)),U_18191))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18192,U_18192)),U_18191),hAPP(c_List_Oset(tc_prod(U_18192,U_18192)),hAPP(hAPP(c_List_Ozip(U_18192,U_18192),U_18193),U_18194)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18192)),U_18193) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18192)),U_18194) )
      & ( ( ! [U_18190] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18192,U_18192,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_18192,tc_fun(tc_prod(U_18192,U_18192),tc_HOL_Obool),tc_fun(U_18192,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18192,tc_fun(tc_fun(tc_prod(U_18192,U_18192),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18192,U_18192),tc_HOL_Obool),tc_fun(U_18192,tc_HOL_Obool)),U_18192),c_COMBC(U_18192,tc_fun(tc_prod(U_18192,U_18192),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18192,tc_prod(U_18192,U_18192)),tc_fun(U_18192,tc_fun(tc_fun(tc_prod(U_18192,U_18192),tc_HOL_Obool),tc_HOL_Obool)),U_18192),hAPP(c_COMBB(tc_prod(U_18192,U_18192),tc_fun(tc_fun(tc_prod(U_18192,U_18192),tc_HOL_Obool),tc_HOL_Obool),U_18192),c_member(tc_prod(U_18192,U_18192)))),c_Product__Type_OPair(U_18192,U_18192)))),U_18195)),U_18190))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18192,U_18192)),U_18190),hAPP(c_List_Oset(tc_prod(U_18192,U_18192)),hAPP(hAPP(c_List_Ozip(U_18192,U_18192),U_18193),U_18194)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18192)),U_18193) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18192)),U_18194) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18192),tc_List_Olist(U_18192))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18192),tc_List_Olist(U_18192)),U_18193),U_18194)),c_List_Olistrel(U_18192,U_18195))) ) ),
    inference(variable_rename,[status(thm)],[f_4409_1]) ).

fof(f_4409_3,plain,
    ( ! [U_18203,U_18201,U_18199,U_18197] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18197),tc_List_Olist(U_18197))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18197),tc_List_Olist(U_18197)),U_18199),U_18201)),c_List_Olistrel(U_18197,U_18203)))
        | ? [U_18191] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18197,U_18197,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_18197,tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_fun(U_18197,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18197,tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_fun(U_18197,tc_HOL_Obool)),U_18197),c_COMBC(U_18197,tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18197,tc_prod(U_18197,U_18197)),tc_fun(U_18197,tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool)),U_18197),hAPP(c_COMBB(tc_prod(U_18197,U_18197),tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool),U_18197),c_member(tc_prod(U_18197,U_18197)))),c_Product__Type_OPair(U_18197,U_18197)))),U_18203)),U_18191))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18197,U_18197)),U_18191),hAPP(c_List_Oset(tc_prod(U_18197,U_18197)),hAPP(hAPP(c_List_Ozip(U_18197,U_18197),U_18199),U_18201)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18197)),U_18199) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18197)),U_18201) )
    & ! [U_18202,U_18200,U_18198,U_18196] :
        ( ( ! [U_18190] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18196,U_18196,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_18196,tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_fun(U_18196,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18196,tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_fun(U_18196,tc_HOL_Obool)),U_18196),c_COMBC(U_18196,tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18196,tc_prod(U_18196,U_18196)),tc_fun(U_18196,tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool)),U_18196),hAPP(c_COMBB(tc_prod(U_18196,U_18196),tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool),U_18196),c_member(tc_prod(U_18196,U_18196)))),c_Product__Type_OPair(U_18196,U_18196)))),U_18202)),U_18190))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18196,U_18196)),U_18190),hAPP(c_List_Oset(tc_prod(U_18196,U_18196)),hAPP(hAPP(c_List_Ozip(U_18196,U_18196),U_18198),U_18200)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18196)),U_18198) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18196)),U_18200) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18196),tc_List_Olist(U_18196))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18196),tc_List_Olist(U_18196)),U_18198),U_18200)),c_List_Olistrel(U_18196,U_18202))) ) ),
    inference(miniscope,[status(thm)],[f_4409_2]) ).

fof(f_4409_4,plain,
    ( ! [U_18203,U_18201,U_18199,U_18197] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18197),tc_List_Olist(U_18197))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18197),tc_List_Olist(U_18197)),U_18199),U_18201)),c_List_Olistrel(U_18197,U_18203)))
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18197,U_18197,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_18197,tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_fun(U_18197,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18197,tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_fun(U_18197,tc_HOL_Obool)),U_18197),c_COMBC(U_18197,tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18197,tc_prod(U_18197,U_18197)),tc_fun(U_18197,tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool)),U_18197),hAPP(c_COMBB(tc_prod(U_18197,U_18197),tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool),U_18197),c_member(tc_prod(U_18197,U_18197)))),c_Product__Type_OPair(U_18197,U_18197)))),U_18203)),sK460(U_18203,U_18201,U_18199,U_18197)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18197,U_18197)),sK460(U_18203,U_18201,U_18199,U_18197)),hAPP(c_List_Oset(tc_prod(U_18197,U_18197)),hAPP(hAPP(c_List_Ozip(U_18197,U_18197),U_18199),U_18201)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18197)),U_18199) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18197)),U_18201) )
    & ! [U_18202,U_18200,U_18198,U_18196] :
        ( ( ! [U_18190] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18196,U_18196,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_18196,tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_fun(U_18196,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18196,tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_fun(U_18196,tc_HOL_Obool)),U_18196),c_COMBC(U_18196,tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18196,tc_prod(U_18196,U_18196)),tc_fun(U_18196,tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool)),U_18196),hAPP(c_COMBB(tc_prod(U_18196,U_18196),tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool),U_18196),c_member(tc_prod(U_18196,U_18196)))),c_Product__Type_OPair(U_18196,U_18196)))),U_18202)),U_18190))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18196,U_18196)),U_18190),hAPP(c_List_Oset(tc_prod(U_18196,U_18196)),hAPP(hAPP(c_List_Ozip(U_18196,U_18196),U_18198),U_18200)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18196)),U_18198) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18196)),U_18200) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18196),tc_List_Olist(U_18196))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18196),tc_List_Olist(U_18196)),U_18198),U_18200)),c_List_Olistrel(U_18196,U_18202))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK460]),skolemize(U_18191,sK460(U_18203,U_18201,U_18199,U_18197))],[f_4409_3]) ).

fof(f_4409_5,plain,
    ( ! [U_18201,U_18199,U_18197,U_18203] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18197,U_18197,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_18197,tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_fun(U_18197,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18197,tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_fun(U_18197,tc_HOL_Obool)),U_18197),c_COMBC(U_18197,tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18197,tc_prod(U_18197,U_18197)),tc_fun(U_18197,tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool)),U_18197),hAPP(c_COMBB(tc_prod(U_18197,U_18197),tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool),U_18197),c_member(tc_prod(U_18197,U_18197)))),c_Product__Type_OPair(U_18197,U_18197)))),U_18203)),sK460(U_18203,U_18201,U_18199,U_18197)))
        | ~ sP1141(U_18201,U_18199,U_18197,U_18203) )
    & ! [U_18201,U_18199,U_18197,U_18203] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18197,U_18197)),sK460(U_18203,U_18201,U_18199,U_18197)),hAPP(c_List_Oset(tc_prod(U_18197,U_18197)),hAPP(hAPP(c_List_Ozip(U_18197,U_18197),U_18199),U_18201))))
        | ~ sP1141(U_18201,U_18199,U_18197,U_18203) )
    & ! [U_18190,U_18198,U_18196,U_18200,U_18202] :
        ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18196,U_18196,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_18196,tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_fun(U_18196,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18196,tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_fun(U_18196,tc_HOL_Obool)),U_18196),c_COMBC(U_18196,tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18196,tc_prod(U_18196,U_18196)),tc_fun(U_18196,tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool)),U_18196),hAPP(c_COMBB(tc_prod(U_18196,U_18196),tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool),U_18196),c_member(tc_prod(U_18196,U_18196)))),c_Product__Type_OPair(U_18196,U_18196)))),U_18202)),U_18190))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18196,U_18196)),U_18190),hAPP(c_List_Oset(tc_prod(U_18196,U_18196)),hAPP(hAPP(c_List_Ozip(U_18196,U_18196),U_18198),U_18200))))
        | ~ sP1140(U_18190,U_18198,U_18196,U_18200,U_18202) )
    & ! [U_18190,U_18198,U_18196,U_18200,U_18202] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18196)),U_18198) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18196)),U_18200)
        | ~ sP1140(U_18190,U_18198,U_18196,U_18200,U_18202) )
    & ! [U_18201,U_18199,U_18197,U_18203] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18197),tc_List_Olist(U_18197))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18197),tc_List_Olist(U_18197)),U_18199),U_18201)),c_List_Olistrel(U_18197,U_18203)))
        | sP1141(U_18201,U_18199,U_18197,U_18203)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18197)),U_18199) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18197)),U_18201) )
    & ! [U_18190,U_18198,U_18196,U_18200,U_18202] :
        ( sP1140(U_18190,U_18198,U_18196,U_18200,U_18202)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18196),tc_List_Olist(U_18196))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18196),tc_List_Olist(U_18196)),U_18198),U_18200)),c_List_Olistrel(U_18196,U_18202))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1140,sP1141])],[f_4409_4]) ).

cnf(f_4409_6,plain,
    ( sP1140(U_18190,U_18198,U_18196,U_18200,U_18202)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18196),tc_List_Olist(U_18196))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18196),tc_List_Olist(U_18196)),U_18198),U_18200)),c_List_Olistrel(U_18196,U_18202))) ),
    inference(clausify,[status(thm)],[f_4409_5]) ).

cnf(f_4409_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18197),tc_List_Olist(U_18197))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18197),tc_List_Olist(U_18197)),U_18199),U_18201)),c_List_Olistrel(U_18197,U_18203)))
    | sP1141(U_18201,U_18199,U_18197,U_18203)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18197)),U_18199) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18197)),U_18201) ),
    inference(clausify,[status(thm)],[f_4409_5]) ).

cnf(f_4409_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18196)),U_18198) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18196)),U_18200)
    | ~ sP1140(U_18190,U_18198,U_18196,U_18200,U_18202) ),
    inference(clausify,[status(thm)],[f_4409_5]) ).

cnf(f_4409_9,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18196,U_18196,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_18196,tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_fun(U_18196,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18196,tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_fun(U_18196,tc_HOL_Obool)),U_18196),c_COMBC(U_18196,tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18196,tc_prod(U_18196,U_18196)),tc_fun(U_18196,tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool)),U_18196),hAPP(c_COMBB(tc_prod(U_18196,U_18196),tc_fun(tc_fun(tc_prod(U_18196,U_18196),tc_HOL_Obool),tc_HOL_Obool),U_18196),c_member(tc_prod(U_18196,U_18196)))),c_Product__Type_OPair(U_18196,U_18196)))),U_18202)),U_18190))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18196,U_18196)),U_18190),hAPP(c_List_Oset(tc_prod(U_18196,U_18196)),hAPP(hAPP(c_List_Ozip(U_18196,U_18196),U_18198),U_18200))))
    | ~ sP1140(U_18190,U_18198,U_18196,U_18200,U_18202) ),
    inference(clausify,[status(thm)],[f_4409_5]) ).

cnf(f_4409_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18197,U_18197)),sK460(U_18203,U_18201,U_18199,U_18197)),hAPP(c_List_Oset(tc_prod(U_18197,U_18197)),hAPP(hAPP(c_List_Ozip(U_18197,U_18197),U_18199),U_18201))))
    | ~ sP1141(U_18201,U_18199,U_18197,U_18203) ),
    inference(clausify,[status(thm)],[f_4409_5]) ).

cnf(f_4409_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_18197,U_18197,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_18197,tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_fun(U_18197,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18197,tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_fun(U_18197,tc_HOL_Obool)),U_18197),c_COMBC(U_18197,tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18197,tc_prod(U_18197,U_18197)),tc_fun(U_18197,tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool)),U_18197),hAPP(c_COMBB(tc_prod(U_18197,U_18197),tc_fun(tc_fun(tc_prod(U_18197,U_18197),tc_HOL_Obool),tc_HOL_Obool),U_18197),c_member(tc_prod(U_18197,U_18197)))),c_Product__Type_OPair(U_18197,U_18197)))),U_18203)),sK460(U_18203,U_18201,U_18199,U_18197)))
    | ~ sP1141(U_18201,U_18199,U_18197,U_18203) ),
    inference(clausify,[status(thm)],[f_4409_5]) ).

fof(f_4410_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_4410_2,plain,
    ! [U_18206,U_18205,U_18204] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18204),tc_List_Olist(U_18204))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18204),tc_List_Olist(U_18204)),U_18205),U_18205)),c_List_Olistrel(U_18204,c_Transitive__Closure_Ortrancl(U_18204,U_18206)))),
    inference(variable_rename,[status(thm)],[f_4410_1]) ).

fof(f_4410_3,plain,
    ! [U_18204,U_18205,U_18206] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18204),tc_List_Olist(U_18204))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18204),tc_List_Olist(U_18204)),U_18205),U_18205)),c_List_Olistrel(U_18204,c_Transitive__Closure_Ortrancl(U_18204,U_18206)))),
    inference(definitional_conversion,[status(esa)],[f_4410_2]) ).

cnf(f_4410_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18204),tc_List_Olist(U_18204))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18204),tc_List_Olist(U_18204)),U_18205),U_18205)),c_List_Olistrel(U_18204,c_Transitive__Closure_Ortrancl(U_18204,U_18206)))),
    inference(clausify,[status(thm)],[f_4410_3]) ).

fof(f_4411_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_4411_2,plain,
    ! [U_18210,U_18209,U_18208,U_18207] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18207)),U_18208) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18207)),U_18209)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18207),tc_List_Olist(U_18207))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18207),tc_List_Olist(U_18207)),U_18208),U_18209)),c_List_Olistrel(U_18207,U_18210))) ),
    inference(variable_rename,[status(thm)],[f_4411_1]) ).

fof(f_4411_3,plain,
    ! [U_18207,U_18208,U_18209,U_18210] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18207)),U_18208) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18207)),U_18209)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18207),tc_List_Olist(U_18207))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18207),tc_List_Olist(U_18207)),U_18208),U_18209)),c_List_Olistrel(U_18207,U_18210))) ),
    inference(definitional_conversion,[status(esa)],[f_4411_2]) ).

cnf(f_4411_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18207)),U_18208) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18207)),U_18209)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18207),tc_List_Olist(U_18207))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18207),tc_List_Olist(U_18207)),U_18208),U_18209)),c_List_Olistrel(U_18207,U_18210))) ),
    inference(clausify,[status(thm)],[f_4411_3]) ).

fof(f_4412_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_4412_2,plain,
    ! [U_18215,U_18214,U_18213,U_18212,U_18211] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18211),tc_List_Olist(U_18211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18211),tc_List_Olist(U_18211)),U_18212),U_18215)),c_List_Olistrel(U_18211,c_Transitive__Closure_Ortrancl(U_18211,U_18214))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18211),tc_List_Olist(U_18211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18211),tc_List_Olist(U_18211)),U_18213),U_18215)),c_List_Olistrel(U_18211,c_Transitive__Closure_Ortrancl(U_18211,U_18214))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18211),tc_List_Olist(U_18211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18211),tc_List_Olist(U_18211)),U_18212),U_18213)),c_List_Olistrel(U_18211,c_Transitive__Closure_Ortrancl(U_18211,U_18214)))) ),
    inference(variable_rename,[status(thm)],[f_4412_1]) ).

fof(f_4412_3,plain,
    ! [U_18211,U_18212,U_18213,U_18214,U_18215] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18211),tc_List_Olist(U_18211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18211),tc_List_Olist(U_18211)),U_18212),U_18215)),c_List_Olistrel(U_18211,c_Transitive__Closure_Ortrancl(U_18211,U_18214))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18211),tc_List_Olist(U_18211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18211),tc_List_Olist(U_18211)),U_18213),U_18215)),c_List_Olistrel(U_18211,c_Transitive__Closure_Ortrancl(U_18211,U_18214))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18211),tc_List_Olist(U_18211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18211),tc_List_Olist(U_18211)),U_18212),U_18213)),c_List_Olistrel(U_18211,c_Transitive__Closure_Ortrancl(U_18211,U_18214)))) ),
    inference(definitional_conversion,[status(esa)],[f_4412_2]) ).

cnf(f_4412_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18211),tc_List_Olist(U_18211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18211),tc_List_Olist(U_18211)),U_18212),U_18215)),c_List_Olistrel(U_18211,c_Transitive__Closure_Ortrancl(U_18211,U_18214))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18211),tc_List_Olist(U_18211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18211),tc_List_Olist(U_18211)),U_18213),U_18215)),c_List_Olistrel(U_18211,c_Transitive__Closure_Ortrancl(U_18211,U_18214))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18211),tc_List_Olist(U_18211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18211),tc_List_Olist(U_18211)),U_18212),U_18213)),c_List_Olistrel(U_18211,c_Transitive__Closure_Ortrancl(U_18211,U_18214)))) ),
    inference(clausify,[status(thm)],[f_4412_3]) ).

fof(f_4413_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_4413_2,plain,
    ! [U_18218,U_18217,U_18216] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_18216),tc_List_Olist(U_18216)),tc_HOL_Obool)),c_List_Olistrel(U_18216,U_18217)),c_List_Olistrel(U_18216,U_18218)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_18216,U_18216),tc_HOL_Obool)),U_18217),U_18218)) ),
    inference(variable_rename,[status(thm)],[f_4413_1]) ).

fof(f_4413_3,plain,
    ! [U_18216,U_18217,U_18218] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_18216),tc_List_Olist(U_18216)),tc_HOL_Obool)),c_List_Olistrel(U_18216,U_18217)),c_List_Olistrel(U_18216,U_18218)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_18216,U_18216),tc_HOL_Obool)),U_18217),U_18218)) ),
    inference(definitional_conversion,[status(esa)],[f_4413_2]) ).

cnf(f_4413_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_18216),tc_List_Olist(U_18216)),tc_HOL_Obool)),c_List_Olistrel(U_18216,U_18217)),c_List_Olistrel(U_18216,U_18218)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_18216,U_18216),tc_HOL_Obool)),U_18217),U_18218)) ),
    inference(clausify,[status(thm)],[f_4413_3]) ).

fof(f_4414_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_4414_2,plain,
    ! [U_18222,U_18221,U_18220,U_18219] :
      ( ( c_List_Olistrelp(U_18219,hAPP(hAPP(c_COMBC(U_18219,tc_fun(tc_prod(U_18219,U_18219),tc_HOL_Obool),tc_fun(U_18219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18219,tc_fun(tc_fun(tc_prod(U_18219,U_18219),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18219,U_18219),tc_HOL_Obool),tc_fun(U_18219,tc_HOL_Obool)),U_18219),c_COMBC(U_18219,tc_fun(tc_prod(U_18219,U_18219),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18219,tc_prod(U_18219,U_18219)),tc_fun(U_18219,tc_fun(tc_fun(tc_prod(U_18219,U_18219),tc_HOL_Obool),tc_HOL_Obool)),U_18219),hAPP(c_COMBB(tc_prod(U_18219,U_18219),tc_fun(tc_fun(tc_prod(U_18219,U_18219),tc_HOL_Obool),tc_HOL_Obool),U_18219),c_member(tc_prod(U_18219,U_18219)))),c_Product__Type_OPair(U_18219,U_18219)))),U_18220),U_18221,U_18222)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18219),tc_List_Olist(U_18219))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18219),tc_List_Olist(U_18219)),U_18221),U_18222)),c_List_Olistrel(U_18219,U_18220))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18219),tc_List_Olist(U_18219))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18219),tc_List_Olist(U_18219)),U_18221),U_18222)),c_List_Olistrel(U_18219,U_18220)))
        | ~ c_List_Olistrelp(U_18219,hAPP(hAPP(c_COMBC(U_18219,tc_fun(tc_prod(U_18219,U_18219),tc_HOL_Obool),tc_fun(U_18219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18219,tc_fun(tc_fun(tc_prod(U_18219,U_18219),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18219,U_18219),tc_HOL_Obool),tc_fun(U_18219,tc_HOL_Obool)),U_18219),c_COMBC(U_18219,tc_fun(tc_prod(U_18219,U_18219),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18219,tc_prod(U_18219,U_18219)),tc_fun(U_18219,tc_fun(tc_fun(tc_prod(U_18219,U_18219),tc_HOL_Obool),tc_HOL_Obool)),U_18219),hAPP(c_COMBB(tc_prod(U_18219,U_18219),tc_fun(tc_fun(tc_prod(U_18219,U_18219),tc_HOL_Obool),tc_HOL_Obool),U_18219),c_member(tc_prod(U_18219,U_18219)))),c_Product__Type_OPair(U_18219,U_18219)))),U_18220),U_18221,U_18222) ) ),
    inference(variable_rename,[status(thm)],[f_4414_1]) ).

fof(f_4414_3,plain,
    ( ! [U_18230,U_18228,U_18226,U_18224] :
        ( c_List_Olistrelp(U_18224,hAPP(hAPP(c_COMBC(U_18224,tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_fun(U_18224,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18224,tc_fun(tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_fun(U_18224,tc_HOL_Obool)),U_18224),c_COMBC(U_18224,tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18224,tc_prod(U_18224,U_18224)),tc_fun(U_18224,tc_fun(tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_HOL_Obool)),U_18224),hAPP(c_COMBB(tc_prod(U_18224,U_18224),tc_fun(tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_HOL_Obool),U_18224),c_member(tc_prod(U_18224,U_18224)))),c_Product__Type_OPair(U_18224,U_18224)))),U_18226),U_18228,U_18230)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18224),tc_List_Olist(U_18224))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18224),tc_List_Olist(U_18224)),U_18228),U_18230)),c_List_Olistrel(U_18224,U_18226))) )
    & ! [U_18229,U_18227,U_18225,U_18223] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18223),tc_List_Olist(U_18223))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18223),tc_List_Olist(U_18223)),U_18227),U_18229)),c_List_Olistrel(U_18223,U_18225)))
        | ~ c_List_Olistrelp(U_18223,hAPP(hAPP(c_COMBC(U_18223,tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_fun(U_18223,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18223,tc_fun(tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_fun(U_18223,tc_HOL_Obool)),U_18223),c_COMBC(U_18223,tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18223,tc_prod(U_18223,U_18223)),tc_fun(U_18223,tc_fun(tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_HOL_Obool)),U_18223),hAPP(c_COMBB(tc_prod(U_18223,U_18223),tc_fun(tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_HOL_Obool),U_18223),c_member(tc_prod(U_18223,U_18223)))),c_Product__Type_OPair(U_18223,U_18223)))),U_18225),U_18227,U_18229) ) ),
    inference(miniscope,[status(thm)],[f_4414_2]) ).

fof(f_4414_4,plain,
    ( ! [U_18226,U_18224,U_18228,U_18230] :
        ( c_List_Olistrelp(U_18224,hAPP(hAPP(c_COMBC(U_18224,tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_fun(U_18224,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18224,tc_fun(tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_fun(U_18224,tc_HOL_Obool)),U_18224),c_COMBC(U_18224,tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18224,tc_prod(U_18224,U_18224)),tc_fun(U_18224,tc_fun(tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_HOL_Obool)),U_18224),hAPP(c_COMBB(tc_prod(U_18224,U_18224),tc_fun(tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_HOL_Obool),U_18224),c_member(tc_prod(U_18224,U_18224)))),c_Product__Type_OPair(U_18224,U_18224)))),U_18226),U_18228,U_18230)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18224),tc_List_Olist(U_18224))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18224),tc_List_Olist(U_18224)),U_18228),U_18230)),c_List_Olistrel(U_18224,U_18226))) )
    & ! [U_18225,U_18223,U_18227,U_18229] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18223),tc_List_Olist(U_18223))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18223),tc_List_Olist(U_18223)),U_18227),U_18229)),c_List_Olistrel(U_18223,U_18225)))
        | ~ c_List_Olistrelp(U_18223,hAPP(hAPP(c_COMBC(U_18223,tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_fun(U_18223,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18223,tc_fun(tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_fun(U_18223,tc_HOL_Obool)),U_18223),c_COMBC(U_18223,tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18223,tc_prod(U_18223,U_18223)),tc_fun(U_18223,tc_fun(tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_HOL_Obool)),U_18223),hAPP(c_COMBB(tc_prod(U_18223,U_18223),tc_fun(tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_HOL_Obool),U_18223),c_member(tc_prod(U_18223,U_18223)))),c_Product__Type_OPair(U_18223,U_18223)))),U_18225),U_18227,U_18229) ) ),
    inference(definitional_conversion,[status(esa)],[f_4414_3]) ).

cnf(f_4414_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18223),tc_List_Olist(U_18223))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18223),tc_List_Olist(U_18223)),U_18227),U_18229)),c_List_Olistrel(U_18223,U_18225)))
    | ~ c_List_Olistrelp(U_18223,hAPP(hAPP(c_COMBC(U_18223,tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_fun(U_18223,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18223,tc_fun(tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_fun(U_18223,tc_HOL_Obool)),U_18223),c_COMBC(U_18223,tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18223,tc_prod(U_18223,U_18223)),tc_fun(U_18223,tc_fun(tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_HOL_Obool)),U_18223),hAPP(c_COMBB(tc_prod(U_18223,U_18223),tc_fun(tc_fun(tc_prod(U_18223,U_18223),tc_HOL_Obool),tc_HOL_Obool),U_18223),c_member(tc_prod(U_18223,U_18223)))),c_Product__Type_OPair(U_18223,U_18223)))),U_18225),U_18227,U_18229) ),
    inference(clausify,[status(thm)],[f_4414_4]) ).

cnf(f_4414_6,plain,
    ( c_List_Olistrelp(U_18224,hAPP(hAPP(c_COMBC(U_18224,tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_fun(U_18224,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18224,tc_fun(tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_fun(U_18224,tc_HOL_Obool)),U_18224),c_COMBC(U_18224,tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18224,tc_prod(U_18224,U_18224)),tc_fun(U_18224,tc_fun(tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_HOL_Obool)),U_18224),hAPP(c_COMBB(tc_prod(U_18224,U_18224),tc_fun(tc_fun(tc_prod(U_18224,U_18224),tc_HOL_Obool),tc_HOL_Obool),U_18224),c_member(tc_prod(U_18224,U_18224)))),c_Product__Type_OPair(U_18224,U_18224)))),U_18226),U_18228,U_18230)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18224),tc_List_Olist(U_18224))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18224),tc_List_Olist(U_18224)),U_18228),U_18230)),c_List_Olistrel(U_18224,U_18226))) ),
    inference(clausify,[status(thm)],[f_4414_4]) ).

fof(f_4415_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_4415_2,plain,
    ! [U_18233,U_18232,U_18231] : hAPP(c_List_Olexn(U_18231,U_18232),hAPP(c_Nat_OSuc,U_18233)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(U_18231),tc_List_Olist(U_18231)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(U_18231,tc_List_Olist(U_18231)),tc_prod(U_18231,tc_List_Olist(U_18231))),tc_prod(tc_List_Olist(U_18231),tc_List_Olist(U_18231)),c_Product__Type_Omap__pair(tc_prod(U_18231,tc_List_Olist(U_18231)),tc_List_Olist(U_18231),tc_prod(U_18231,tc_List_Olist(U_18231)),tc_List_Olist(U_18231),hAPP(c_Product__Type_Oprod_Oprod__case(U_18231,tc_List_Olist(U_18231),tc_List_Olist(U_18231)),c_List_Olist_OCons(U_18231)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18231,tc_List_Olist(U_18231),tc_List_Olist(U_18231)),c_List_Olist_OCons(U_18231)))),c_Wellfounded_Olex__prod(U_18231,tc_List_Olist(U_18231),U_18232,hAPP(c_List_Olexn(U_18231,U_18232),U_18233)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_18231),tc_List_Olist(U_18231))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18231),tc_List_Olist(U_18231),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18231),tc_fun(tc_List_Olist(U_18231),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18231),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18231),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18231),tc_HOL_Obool)),tc_List_Olist(U_18231)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_18231))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18231)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18231),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_18231)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_18231)))),hAPP(c_Nat_OSuc,U_18233))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18231),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_18231)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_18231)))),hAPP(c_Nat_OSuc,U_18233)))))),
    inference(variable_rename,[status(thm)],[f_4415_1]) ).

fof(f_4415_3,plain,
    ! [U_18231,U_18232,U_18233] : hAPP(c_List_Olexn(U_18231,U_18232),hAPP(c_Nat_OSuc,U_18233)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(U_18231),tc_List_Olist(U_18231)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(U_18231,tc_List_Olist(U_18231)),tc_prod(U_18231,tc_List_Olist(U_18231))),tc_prod(tc_List_Olist(U_18231),tc_List_Olist(U_18231)),c_Product__Type_Omap__pair(tc_prod(U_18231,tc_List_Olist(U_18231)),tc_List_Olist(U_18231),tc_prod(U_18231,tc_List_Olist(U_18231)),tc_List_Olist(U_18231),hAPP(c_Product__Type_Oprod_Oprod__case(U_18231,tc_List_Olist(U_18231),tc_List_Olist(U_18231)),c_List_Olist_OCons(U_18231)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18231,tc_List_Olist(U_18231),tc_List_Olist(U_18231)),c_List_Olist_OCons(U_18231)))),c_Wellfounded_Olex__prod(U_18231,tc_List_Olist(U_18231),U_18232,hAPP(c_List_Olexn(U_18231,U_18232),U_18233)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_18231),tc_List_Olist(U_18231))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18231),tc_List_Olist(U_18231),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18231),tc_fun(tc_List_Olist(U_18231),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18231),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18231),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18231),tc_HOL_Obool)),tc_List_Olist(U_18231)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_18231))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18231)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18231),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_18231)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_18231)))),hAPP(c_Nat_OSuc,U_18233))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18231),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_18231)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_18231)))),hAPP(c_Nat_OSuc,U_18233)))))),
    inference(definitional_conversion,[status(esa)],[f_4415_2]) ).

cnf(f_4415_4,plain,
    hAPP(c_List_Olexn(U_18231,U_18232),hAPP(c_Nat_OSuc,U_18233)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(U_18231),tc_List_Olist(U_18231)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(U_18231,tc_List_Olist(U_18231)),tc_prod(U_18231,tc_List_Olist(U_18231))),tc_prod(tc_List_Olist(U_18231),tc_List_Olist(U_18231)),c_Product__Type_Omap__pair(tc_prod(U_18231,tc_List_Olist(U_18231)),tc_List_Olist(U_18231),tc_prod(U_18231,tc_List_Olist(U_18231)),tc_List_Olist(U_18231),hAPP(c_Product__Type_Oprod_Oprod__case(U_18231,tc_List_Olist(U_18231),tc_List_Olist(U_18231)),c_List_Olist_OCons(U_18231)),hAPP(c_Product__Type_Oprod_Oprod__case(U_18231,tc_List_Olist(U_18231),tc_List_Olist(U_18231)),c_List_Olist_OCons(U_18231)))),c_Wellfounded_Olex__prod(U_18231,tc_List_Olist(U_18231),U_18232,hAPP(c_List_Olexn(U_18231,U_18232),U_18233)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_18231),tc_List_Olist(U_18231))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18231),tc_List_Olist(U_18231),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18231),tc_fun(tc_List_Olist(U_18231),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18231),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18231),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18231),tc_HOL_Obool)),tc_List_Olist(U_18231)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_18231))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18231)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18231),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_18231)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_18231)))),hAPP(c_Nat_OSuc,U_18233))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18231),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_18231)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_18231)))),hAPP(c_Nat_OSuc,U_18233)))))),
    inference(clausify,[status(thm)],[f_4415_3]) ).

fof(f_4416_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_4416_2,plain,
    ! [U_18237,U_18236,U_18235,U_18234] :
      ( U_18235 != hAPP(hAPP(c_List_Olist_OCons(U_18234),U_18237),U_18236)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18234)),U_18235)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18234)),U_18236))) ),
    inference(variable_rename,[status(thm)],[f_4416_1]) ).

fof(f_4416_3,plain,
    ! [U_18234,U_18235,U_18236,U_18237] :
      ( U_18235 != hAPP(hAPP(c_List_Olist_OCons(U_18234),U_18237),U_18236)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18234)),U_18235)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18234)),U_18236))) ),
    inference(definitional_conversion,[status(esa)],[f_4416_2]) ).

cnf(f_4416_4,plain,
    ( U_18235 != hAPP(hAPP(c_List_Olist_OCons(U_18234),U_18237),U_18236)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18234)),U_18235)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18234)),U_18236))) ),
    inference(clausify,[status(thm)],[f_4416_3]) ).

fof(f_4417_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_4417_2,plain,
    ! [U_18241,U_18240,U_18239,U_18238] :
      ( hBOOL(hAPP(hAPP(c_member(U_18238),U_18239),hAPP(c_List_Oset(U_18238),U_18241)))
      | U_18239 = U_18240
      | ~ hBOOL(hAPP(hAPP(c_member(U_18238),U_18239),hAPP(c_List_Oset(U_18238),hAPP(hAPP(c_List_Olist_OCons(U_18238),U_18240),U_18241)))) ),
    inference(variable_rename,[status(thm)],[f_4417_1]) ).

fof(f_4417_3,plain,
    ! [U_18238,U_18239,U_18240,U_18241] :
      ( hBOOL(hAPP(hAPP(c_member(U_18238),U_18239),hAPP(c_List_Oset(U_18238),U_18241)))
      | U_18239 = U_18240
      | ~ hBOOL(hAPP(hAPP(c_member(U_18238),U_18239),hAPP(c_List_Oset(U_18238),hAPP(hAPP(c_List_Olist_OCons(U_18238),U_18240),U_18241)))) ),
    inference(definitional_conversion,[status(esa)],[f_4417_2]) ).

cnf(f_4417_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18238),U_18239),hAPP(c_List_Oset(U_18238),U_18241)))
    | U_18239 = U_18240
    | ~ hBOOL(hAPP(hAPP(c_member(U_18238),U_18239),hAPP(c_List_Oset(U_18238),hAPP(hAPP(c_List_Olist_OCons(U_18238),U_18240),U_18241)))) ),
    inference(clausify,[status(thm)],[f_4417_3]) ).

fof(f_4418_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_4418_2,plain,
    ! [U_18247,U_18246,U_18245,U_18244,U_18243,U_18242] : hAPP(hAPP(c_List_Ozip(U_18242,U_18243),hAPP(hAPP(c_List_Olist_OCons(U_18242),U_18244),U_18245)),hAPP(hAPP(c_List_Olist_OCons(U_18243),U_18246),U_18247)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_18242,U_18243)),hAPP(hAPP(c_Product__Type_OPair(U_18242,U_18243),U_18244),U_18246)),hAPP(hAPP(c_List_Ozip(U_18242,U_18243),U_18245),U_18247)),
    inference(variable_rename,[status(thm)],[f_4418_1]) ).

fof(f_4418_3,plain,
    ! [U_18242,U_18243,U_18244,U_18245,U_18246,U_18247] : hAPP(hAPP(c_List_Ozip(U_18242,U_18243),hAPP(hAPP(c_List_Olist_OCons(U_18242),U_18244),U_18245)),hAPP(hAPP(c_List_Olist_OCons(U_18243),U_18246),U_18247)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_18242,U_18243)),hAPP(hAPP(c_Product__Type_OPair(U_18242,U_18243),U_18244),U_18246)),hAPP(hAPP(c_List_Ozip(U_18242,U_18243),U_18245),U_18247)),
    inference(definitional_conversion,[status(esa)],[f_4418_2]) ).

cnf(f_4418_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18242,U_18243),hAPP(hAPP(c_List_Olist_OCons(U_18242),U_18244),U_18245)),hAPP(hAPP(c_List_Olist_OCons(U_18243),U_18246),U_18247)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_18242,U_18243)),hAPP(hAPP(c_Product__Type_OPair(U_18242,U_18243),U_18244),U_18246)),hAPP(hAPP(c_List_Ozip(U_18242,U_18243),U_18245),U_18247)),
    inference(clausify,[status(thm)],[f_4418_3]) ).

fof(f_4419_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_4419_2,plain,
    ! [U_18250,U_18249,U_18248] : hAPP(c_List_Oset(U_18248),hAPP(hAPP(c_List_Olist_OCons(U_18248),U_18249),U_18250)) = hAPP(hAPP(c_Set_Oinsert(U_18248),U_18249),hAPP(c_List_Oset(U_18248),U_18250)),
    inference(variable_rename,[status(thm)],[f_4419_1]) ).

fof(f_4419_3,plain,
    ! [U_18248,U_18249,U_18250] : hAPP(c_List_Oset(U_18248),hAPP(hAPP(c_List_Olist_OCons(U_18248),U_18249),U_18250)) = hAPP(hAPP(c_Set_Oinsert(U_18248),U_18249),hAPP(c_List_Oset(U_18248),U_18250)),
    inference(definitional_conversion,[status(esa)],[f_4419_2]) ).

cnf(f_4419_4,plain,
    hAPP(c_List_Oset(U_18248),hAPP(hAPP(c_List_Olist_OCons(U_18248),U_18249),U_18250)) = hAPP(hAPP(c_Set_Oinsert(U_18248),U_18249),hAPP(c_List_Oset(U_18248),U_18250)),
    inference(clausify,[status(thm)],[f_4419_3]) ).

fof(f_4420_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_4420_2,plain,
    ! [U_18253,U_18252,U_18251] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18251,tc_HOL_Obool)),hAPP(c_List_Oset(U_18251),U_18252)),hAPP(c_List_Oset(U_18251),hAPP(hAPP(c_List_Olist_OCons(U_18251),U_18253),U_18252)))),
    inference(variable_rename,[status(thm)],[f_4420_1]) ).

fof(f_4420_3,plain,
    ! [U_18251,U_18252,U_18253] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18251,tc_HOL_Obool)),hAPP(c_List_Oset(U_18251),U_18252)),hAPP(c_List_Oset(U_18251),hAPP(hAPP(c_List_Olist_OCons(U_18251),U_18253),U_18252)))),
    inference(definitional_conversion,[status(esa)],[f_4420_2]) ).

cnf(f_4420_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18251,tc_HOL_Obool)),hAPP(c_List_Oset(U_18251),U_18252)),hAPP(c_List_Oset(U_18251),hAPP(hAPP(c_List_Olist_OCons(U_18251),U_18253),U_18252)))),
    inference(clausify,[status(thm)],[f_4420_3]) ).

fof(f_4421_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_4421_2,plain,
    ! [U_18259,U_18258,U_18257,U_18256,U_18255,U_18254] : c_List_Ofoldr(U_18254,U_18255,U_18256,hAPP(hAPP(c_List_Olist_OCons(U_18254),U_18257),U_18258),U_18259) = hAPP(hAPP(U_18256,U_18257),c_List_Ofoldr(U_18254,U_18255,U_18256,U_18258,U_18259)),
    inference(variable_rename,[status(thm)],[f_4421_1]) ).

fof(f_4421_3,plain,
    ! [U_18254,U_18255,U_18256,U_18257,U_18258,U_18259] : c_List_Ofoldr(U_18254,U_18255,U_18256,hAPP(hAPP(c_List_Olist_OCons(U_18254),U_18257),U_18258),U_18259) = hAPP(hAPP(U_18256,U_18257),c_List_Ofoldr(U_18254,U_18255,U_18256,U_18258,U_18259)),
    inference(definitional_conversion,[status(esa)],[f_4421_2]) ).

cnf(f_4421_4,plain,
    c_List_Ofoldr(U_18254,U_18255,U_18256,hAPP(hAPP(c_List_Olist_OCons(U_18254),U_18257),U_18258),U_18259) = hAPP(hAPP(U_18256,U_18257),c_List_Ofoldr(U_18254,U_18255,U_18256,U_18258,U_18259)),
    inference(clausify,[status(thm)],[f_4421_3]) ).

fof(f_4422_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_4422_2,plain,
    ! [U_18262,U_18261,U_18260] : U_18260 != hAPP(hAPP(c_List_Olist_OCons(U_18261),U_18262),U_18260),
    inference(variable_rename,[status(thm)],[f_4422_1]) ).

fof(f_4422_3,plain,
    ! [U_18260,U_18261,U_18262] : U_18260 != hAPP(hAPP(c_List_Olist_OCons(U_18261),U_18262),U_18260),
    inference(definitional_conversion,[status(esa)],[f_4422_2]) ).

cnf(f_4422_4,plain,
    U_18260 != hAPP(hAPP(c_List_Olist_OCons(U_18261),U_18262),U_18260),
    inference(clausify,[status(thm)],[f_4422_3]) ).

fof(f_4423_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_4423_2,plain,
    ! [U_18265,U_18264,U_18263] : hAPP(hAPP(c_List_Olist_OCons(U_18263),U_18264),U_18265) != U_18265,
    inference(variable_rename,[status(thm)],[f_4423_1]) ).

fof(f_4423_3,plain,
    ! [U_18263,U_18264,U_18265] : hAPP(hAPP(c_List_Olist_OCons(U_18263),U_18264),U_18265) != U_18265,
    inference(definitional_conversion,[status(esa)],[f_4423_2]) ).

cnf(f_4423_4,plain,
    hAPP(hAPP(c_List_Olist_OCons(U_18263),U_18264),U_18265) != U_18265,
    inference(clausify,[status(thm)],[f_4423_3]) ).

fof(f_4424_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_4424_2,plain,
    ! [U_18270,U_18269,U_18268,U_18267,U_18266] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_18266),U_18267),U_18268) = hAPP(hAPP(c_List_Olist_OCons(U_18266),U_18269),U_18270)
        | U_18268 != U_18270
        | U_18267 != U_18269 )
      & ( ( U_18268 = U_18270
          & U_18267 = U_18269 )
        | hAPP(hAPP(c_List_Olist_OCons(U_18266),U_18267),U_18268) != hAPP(hAPP(c_List_Olist_OCons(U_18266),U_18269),U_18270) ) ),
    inference(variable_rename,[status(thm)],[f_4424_1]) ).

fof(f_4424_3,plain,
    ( ! [U_18280,U_18278,U_18276,U_18274] :
        ( ! [U_18272] : hAPP(hAPP(c_List_Olist_OCons(U_18272),U_18274),U_18276) = hAPP(hAPP(c_List_Olist_OCons(U_18272),U_18278),U_18280)
        | U_18276 != U_18280
        | U_18274 != U_18278 )
    & ! [U_18279,U_18277,U_18275,U_18273] :
        ( ! [U_18271] : hAPP(hAPP(c_List_Olist_OCons(U_18271),U_18273),U_18275) != hAPP(hAPP(c_List_Olist_OCons(U_18271),U_18277),U_18279)
        | ( U_18275 = U_18279
          & U_18273 = U_18277 ) ) ),
    inference(miniscope,[status(thm)],[f_4424_2]) ).

fof(f_4424_4,plain,
    ( ! [U_18275,U_18277,U_18273,U_18279] :
        ( U_18275 = U_18279
        | ~ sP1142(U_18275,U_18277,U_18273,U_18279) )
    & ! [U_18275,U_18277,U_18273,U_18279] :
        ( U_18273 = U_18277
        | ~ sP1142(U_18275,U_18277,U_18273,U_18279) )
    & ! [U_18280,U_18274,U_18276,U_18272,U_18278] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18272),U_18274),U_18276) = hAPP(hAPP(c_List_Olist_OCons(U_18272),U_18278),U_18280)
        | U_18276 != U_18280
        | U_18274 != U_18278 )
    & ! [U_18275,U_18277,U_18273,U_18271,U_18279] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18271),U_18273),U_18275) != hAPP(hAPP(c_List_Olist_OCons(U_18271),U_18277),U_18279)
        | sP1142(U_18275,U_18277,U_18273,U_18279) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1142])],[f_4424_3]) ).

cnf(f_4424_5,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_18271),U_18273),U_18275) != hAPP(hAPP(c_List_Olist_OCons(U_18271),U_18277),U_18279)
    | sP1142(U_18275,U_18277,U_18273,U_18279) ),
    inference(clausify,[status(thm)],[f_4424_4]) ).

cnf(f_4424_6,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_18272),U_18274),U_18276) = hAPP(hAPP(c_List_Olist_OCons(U_18272),U_18278),U_18280)
    | U_18276 != U_18280
    | U_18274 != U_18278 ),
    inference(clausify,[status(thm)],[f_4424_4]) ).

cnf(f_4424_7,plain,
    ( U_18273 = U_18277
    | ~ sP1142(U_18275,U_18277,U_18273,U_18279) ),
    inference(clausify,[status(thm)],[f_4424_4]) ).

cnf(f_4424_8,plain,
    ( U_18275 = U_18279
    | ~ sP1142(U_18275,U_18277,U_18273,U_18279) ),
    inference(clausify,[status(thm)],[f_4424_4]) ).

fof(f_4425_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_4425_2,plain,
    ! [U_18286,U_18285,U_18284,U_18283,U_18282,U_18281] :
      ( ( c_List_Olistrelp(U_18281,U_18282,hAPP(hAPP(c_List_Olist_OCons(U_18281),U_18283),U_18284),hAPP(hAPP(c_List_Olist_OCons(U_18281),U_18285),U_18286))
        | ~ c_List_Olistrelp(U_18281,U_18282,U_18284,U_18286)
        | ~ hBOOL(hAPP(hAPP(U_18282,U_18283),U_18285)) )
      & ( ( c_List_Olistrelp(U_18281,U_18282,U_18284,U_18286)
          & hBOOL(hAPP(hAPP(U_18282,U_18283),U_18285)) )
        | ~ c_List_Olistrelp(U_18281,U_18282,hAPP(hAPP(c_List_Olist_OCons(U_18281),U_18283),U_18284),hAPP(hAPP(c_List_Olist_OCons(U_18281),U_18285),U_18286)) ) ),
    inference(variable_rename,[status(thm)],[f_4425_1]) ).

fof(f_4425_3,plain,
    ( ! [U_18298,U_18296,U_18294,U_18292,U_18290,U_18288] :
        ( c_List_Olistrelp(U_18288,U_18290,hAPP(hAPP(c_List_Olist_OCons(U_18288),U_18292),U_18294),hAPP(hAPP(c_List_Olist_OCons(U_18288),U_18296),U_18298))
        | ~ c_List_Olistrelp(U_18288,U_18290,U_18294,U_18298)
        | ~ hBOOL(hAPP(hAPP(U_18290,U_18292),U_18296)) )
    & ! [U_18297,U_18295,U_18293,U_18291,U_18289,U_18287] :
        ( ( c_List_Olistrelp(U_18287,U_18289,U_18293,U_18297)
          & hBOOL(hAPP(hAPP(U_18289,U_18291),U_18295)) )
        | ~ c_List_Olistrelp(U_18287,U_18289,hAPP(hAPP(c_List_Olist_OCons(U_18287),U_18291),U_18293),hAPP(hAPP(c_List_Olist_OCons(U_18287),U_18295),U_18297)) ) ),
    inference(miniscope,[status(thm)],[f_4425_2]) ).

fof(f_4425_4,plain,
    ( ! [U_18293,U_18287,U_18289,U_18291,U_18297,U_18295] :
        ( c_List_Olistrelp(U_18287,U_18289,U_18293,U_18297)
        | ~ sP1143(U_18293,U_18287,U_18289,U_18291,U_18297,U_18295) )
    & ! [U_18293,U_18287,U_18289,U_18291,U_18297,U_18295] :
        ( hBOOL(hAPP(hAPP(U_18289,U_18291),U_18295))
        | ~ sP1143(U_18293,U_18287,U_18289,U_18291,U_18297,U_18295) )
    & ! [U_18298,U_18288,U_18294,U_18292,U_18290,U_18296] :
        ( c_List_Olistrelp(U_18288,U_18290,hAPP(hAPP(c_List_Olist_OCons(U_18288),U_18292),U_18294),hAPP(hAPP(c_List_Olist_OCons(U_18288),U_18296),U_18298))
        | ~ c_List_Olistrelp(U_18288,U_18290,U_18294,U_18298)
        | ~ hBOOL(hAPP(hAPP(U_18290,U_18292),U_18296)) )
    & ! [U_18293,U_18287,U_18289,U_18291,U_18297,U_18295] :
        ( sP1143(U_18293,U_18287,U_18289,U_18291,U_18297,U_18295)
        | ~ c_List_Olistrelp(U_18287,U_18289,hAPP(hAPP(c_List_Olist_OCons(U_18287),U_18291),U_18293),hAPP(hAPP(c_List_Olist_OCons(U_18287),U_18295),U_18297)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1143])],[f_4425_3]) ).

cnf(f_4425_5,plain,
    ( sP1143(U_18293,U_18287,U_18289,U_18291,U_18297,U_18295)
    | ~ c_List_Olistrelp(U_18287,U_18289,hAPP(hAPP(c_List_Olist_OCons(U_18287),U_18291),U_18293),hAPP(hAPP(c_List_Olist_OCons(U_18287),U_18295),U_18297)) ),
    inference(clausify,[status(thm)],[f_4425_4]) ).

cnf(f_4425_6,plain,
    ( c_List_Olistrelp(U_18288,U_18290,hAPP(hAPP(c_List_Olist_OCons(U_18288),U_18292),U_18294),hAPP(hAPP(c_List_Olist_OCons(U_18288),U_18296),U_18298))
    | ~ c_List_Olistrelp(U_18288,U_18290,U_18294,U_18298)
    | ~ hBOOL(hAPP(hAPP(U_18290,U_18292),U_18296)) ),
    inference(clausify,[status(thm)],[f_4425_4]) ).

cnf(f_4425_7,plain,
    ( hBOOL(hAPP(hAPP(U_18289,U_18291),U_18295))
    | ~ sP1143(U_18293,U_18287,U_18289,U_18291,U_18297,U_18295) ),
    inference(clausify,[status(thm)],[f_4425_4]) ).

cnf(f_4425_8,plain,
    ( c_List_Olistrelp(U_18287,U_18289,U_18293,U_18297)
    | ~ sP1143(U_18293,U_18287,U_18289,U_18291,U_18297,U_18295) ),
    inference(clausify,[status(thm)],[f_4425_4]) ).

fof(f_4426_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_4426_2,plain,
    ! [U_18304,U_18303,U_18302,U_18301,U_18300,U_18299] :
      ( c_List_Olistrelp(U_18302,U_18299,hAPP(hAPP(c_List_Olist_OCons(U_18302),U_18300),U_18303),hAPP(hAPP(c_List_Olist_OCons(U_18302),U_18301),U_18304))
      | ~ c_List_Olistrelp(U_18302,U_18299,U_18303,U_18304)
      | ~ hBOOL(hAPP(hAPP(U_18299,U_18300),U_18301)) ),
    inference(variable_rename,[status(thm)],[f_4426_1]) ).

fof(f_4426_3,plain,
    ! [U_18299,U_18302,U_18301,U_18303,U_18304,U_18300] :
      ( c_List_Olistrelp(U_18302,U_18299,hAPP(hAPP(c_List_Olist_OCons(U_18302),U_18300),U_18303),hAPP(hAPP(c_List_Olist_OCons(U_18302),U_18301),U_18304))
      | ~ c_List_Olistrelp(U_18302,U_18299,U_18303,U_18304)
      | ~ hBOOL(hAPP(hAPP(U_18299,U_18300),U_18301)) ),
    inference(definitional_conversion,[status(esa)],[f_4426_2]) ).

cnf(f_4426_4,plain,
    ( c_List_Olistrelp(U_18302,U_18299,hAPP(hAPP(c_List_Olist_OCons(U_18302),U_18300),U_18303),hAPP(hAPP(c_List_Olist_OCons(U_18302),U_18301),U_18304))
    | ~ c_List_Olistrelp(U_18302,U_18299,U_18303,U_18304)
    | ~ hBOOL(hAPP(hAPP(U_18299,U_18300),U_18301)) ),
    inference(clausify,[status(thm)],[f_4426_3]) ).

fof(f_4427_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_4427_2,plain,
    ! [U_18309,U_18308,U_18307,U_18306,U_18305] : hAPP(hAPP(c_List_Omap(U_18305,U_18306),U_18307),hAPP(hAPP(c_List_Olist_OCons(U_18305),U_18308),U_18309)) = hAPP(hAPP(c_List_Olist_OCons(U_18306),hAPP(U_18307,U_18308)),hAPP(hAPP(c_List_Omap(U_18305,U_18306),U_18307),U_18309)),
    inference(variable_rename,[status(thm)],[f_4427_1]) ).

fof(f_4427_3,plain,
    ! [U_18305,U_18306,U_18307,U_18308,U_18309] : hAPP(hAPP(c_List_Omap(U_18305,U_18306),U_18307),hAPP(hAPP(c_List_Olist_OCons(U_18305),U_18308),U_18309)) = hAPP(hAPP(c_List_Olist_OCons(U_18306),hAPP(U_18307,U_18308)),hAPP(hAPP(c_List_Omap(U_18305,U_18306),U_18307),U_18309)),
    inference(definitional_conversion,[status(esa)],[f_4427_2]) ).

cnf(f_4427_4,plain,
    hAPP(hAPP(c_List_Omap(U_18305,U_18306),U_18307),hAPP(hAPP(c_List_Olist_OCons(U_18305),U_18308),U_18309)) = hAPP(hAPP(c_List_Olist_OCons(U_18306),hAPP(U_18307,U_18308)),hAPP(hAPP(c_List_Omap(U_18305,U_18306),U_18307),U_18309)),
    inference(clausify,[status(thm)],[f_4427_3]) ).

fof(f_4428_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_4428_2,plain,
    ! [U_18313,U_18312,U_18311,U_18310] :
      ( ( c_List_Oremove1(U_18312,U_18310,hAPP(hAPP(c_List_Olist_OCons(U_18312),U_18311),U_18313)) = hAPP(hAPP(c_List_Olist_OCons(U_18312),U_18311),c_List_Oremove1(U_18312,U_18310,U_18313))
        | U_18310 = U_18311 )
      & ( c_List_Oremove1(U_18312,U_18310,hAPP(hAPP(c_List_Olist_OCons(U_18312),U_18311),U_18313)) = U_18313
        | U_18310 != U_18311 ) ),
    inference(variable_rename,[status(thm)],[f_4428_1]) ).

fof(f_4428_3,plain,
    ( ! [U_18321,U_18319,U_18317,U_18315] :
        ( c_List_Oremove1(U_18319,U_18315,hAPP(hAPP(c_List_Olist_OCons(U_18319),U_18317),U_18321)) = hAPP(hAPP(c_List_Olist_OCons(U_18319),U_18317),c_List_Oremove1(U_18319,U_18315,U_18321))
        | U_18315 = U_18317 )
    & ! [U_18320,U_18318,U_18316,U_18314] :
        ( c_List_Oremove1(U_18318,U_18314,hAPP(hAPP(c_List_Olist_OCons(U_18318),U_18316),U_18320)) = U_18320
        | U_18314 != U_18316 ) ),
    inference(miniscope,[status(thm)],[f_4428_2]) ).

fof(f_4428_4,plain,
    ( ! [U_18321,U_18315,U_18317,U_18319] :
        ( c_List_Oremove1(U_18319,U_18315,hAPP(hAPP(c_List_Olist_OCons(U_18319),U_18317),U_18321)) = hAPP(hAPP(c_List_Olist_OCons(U_18319),U_18317),c_List_Oremove1(U_18319,U_18315,U_18321))
        | U_18315 = U_18317 )
    & ! [U_18316,U_18320,U_18314,U_18318] :
        ( c_List_Oremove1(U_18318,U_18314,hAPP(hAPP(c_List_Olist_OCons(U_18318),U_18316),U_18320)) = U_18320
        | U_18314 != U_18316 ) ),
    inference(definitional_conversion,[status(esa)],[f_4428_3]) ).

cnf(f_4428_5,plain,
    ( c_List_Oremove1(U_18318,U_18314,hAPP(hAPP(c_List_Olist_OCons(U_18318),U_18316),U_18320)) = U_18320
    | U_18314 != U_18316 ),
    inference(clausify,[status(thm)],[f_4428_4]) ).

cnf(f_4428_6,plain,
    ( c_List_Oremove1(U_18319,U_18315,hAPP(hAPP(c_List_Olist_OCons(U_18319),U_18317),U_18321)) = hAPP(hAPP(c_List_Olist_OCons(U_18319),U_18317),c_List_Oremove1(U_18319,U_18315,U_18321))
    | U_18315 = U_18317 ),
    inference(clausify,[status(thm)],[f_4428_4]) ).

fof(f_4429_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_4429_2,plain,
    ! [U_18327,U_18326,U_18325,U_18324,U_18323,U_18322] :
      ( ( ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18326,U_18322,U_18323),U_18324),hAPP(hAPP(c_List_Olist_OCons(U_18326),U_18325),U_18327)) = hAPP(hAPP(c_List_Olist_OCons(U_18326),U_18325),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18326,U_18322,U_18323),U_18324),U_18327))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18322),hAPP(U_18323,U_18324)),hAPP(U_18323,U_18325))) )
        & ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18326,U_18322,U_18323),U_18324),hAPP(hAPP(c_List_Olist_OCons(U_18326),U_18325),U_18327)) = hAPP(hAPP(c_List_Olist_OCons(U_18326),U_18324),hAPP(hAPP(c_List_Olist_OCons(U_18326),U_18325),U_18327))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18322),hAPP(U_18323,U_18324)),hAPP(U_18323,U_18325))) ) )
      | ~ class_Orderings_Olinorder(U_18322) ),
    inference(variable_rename,[status(thm)],[f_4429_1]) ).

fof(f_4429_3,plain,
    ( ! [U_18323,U_18322,U_18324,U_18325,U_18326,U_18327] :
        ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18326,U_18322,U_18323),U_18324),hAPP(hAPP(c_List_Olist_OCons(U_18326),U_18325),U_18327)) = hAPP(hAPP(c_List_Olist_OCons(U_18326),U_18325),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18326,U_18322,U_18323),U_18324),U_18327))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18322),hAPP(U_18323,U_18324)),hAPP(U_18323,U_18325)))
        | ~ sP1144(U_18323,U_18322,U_18324,U_18325,U_18326,U_18327) )
    & ! [U_18323,U_18322,U_18324,U_18325,U_18326,U_18327] :
        ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18326,U_18322,U_18323),U_18324),hAPP(hAPP(c_List_Olist_OCons(U_18326),U_18325),U_18327)) = hAPP(hAPP(c_List_Olist_OCons(U_18326),U_18324),hAPP(hAPP(c_List_Olist_OCons(U_18326),U_18325),U_18327))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18322),hAPP(U_18323,U_18324)),hAPP(U_18323,U_18325)))
        | ~ sP1144(U_18323,U_18322,U_18324,U_18325,U_18326,U_18327) )
    & ! [U_18323,U_18322,U_18324,U_18325,U_18326,U_18327] :
        ( sP1144(U_18323,U_18322,U_18324,U_18325,U_18326,U_18327)
        | ~ class_Orderings_Olinorder(U_18322) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1144])],[f_4429_2]) ).

cnf(f_4429_4,plain,
    ( sP1144(U_18323,U_18322,U_18324,U_18325,U_18326,U_18327)
    | ~ class_Orderings_Olinorder(U_18322) ),
    inference(clausify,[status(thm)],[f_4429_3]) ).

cnf(f_4429_5,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18326,U_18322,U_18323),U_18324),hAPP(hAPP(c_List_Olist_OCons(U_18326),U_18325),U_18327)) = hAPP(hAPP(c_List_Olist_OCons(U_18326),U_18324),hAPP(hAPP(c_List_Olist_OCons(U_18326),U_18325),U_18327))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18322),hAPP(U_18323,U_18324)),hAPP(U_18323,U_18325)))
    | ~ sP1144(U_18323,U_18322,U_18324,U_18325,U_18326,U_18327) ),
    inference(clausify,[status(thm)],[f_4429_3]) ).

cnf(f_4429_6,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18326,U_18322,U_18323),U_18324),hAPP(hAPP(c_List_Olist_OCons(U_18326),U_18325),U_18327)) = hAPP(hAPP(c_List_Olist_OCons(U_18326),U_18325),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18326,U_18322,U_18323),U_18324),U_18327))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18322),hAPP(U_18323,U_18324)),hAPP(U_18323,U_18325)))
    | ~ sP1144(U_18323,U_18322,U_18324,U_18325,U_18326,U_18327) ),
    inference(clausify,[status(thm)],[f_4429_3]) ).

fof(f_4430_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_4430_2,plain,
    ! [U_18330,U_18329,U_18328] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_18328),hAPP(hAPP(c_List_Olist_OCons(U_18328),U_18329),U_18330)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18328),U_18330))
        | hBOOL(hAPP(hAPP(c_member(U_18328),U_18329),hAPP(c_List_Oset(U_18328),U_18330))) )
      & ( ( hBOOL(hAPP(c_List_Odistinct(U_18328),U_18330))
          & ~ hBOOL(hAPP(hAPP(c_member(U_18328),U_18329),hAPP(c_List_Oset(U_18328),U_18330))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18328),hAPP(hAPP(c_List_Olist_OCons(U_18328),U_18329),U_18330))) ) ),
    inference(variable_rename,[status(thm)],[f_4430_1]) ).

fof(f_4430_3,plain,
    ( ! [U_18336,U_18334,U_18332] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18332),hAPP(hAPP(c_List_Olist_OCons(U_18332),U_18334),U_18336)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18332),U_18336))
        | hBOOL(hAPP(hAPP(c_member(U_18332),U_18334),hAPP(c_List_Oset(U_18332),U_18336))) )
    & ! [U_18335,U_18333,U_18331] :
        ( ( hBOOL(hAPP(c_List_Odistinct(U_18331),U_18335))
          & ~ hBOOL(hAPP(hAPP(c_member(U_18331),U_18333),hAPP(c_List_Oset(U_18331),U_18335))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18331),hAPP(hAPP(c_List_Olist_OCons(U_18331),U_18333),U_18335))) ) ),
    inference(miniscope,[status(thm)],[f_4430_2]) ).

fof(f_4430_4,plain,
    ( ! [U_18333,U_18331,U_18335] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18331),U_18335))
        | ~ sP1145(U_18333,U_18331,U_18335) )
    & ! [U_18333,U_18331,U_18335] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_18331),U_18333),hAPP(c_List_Oset(U_18331),U_18335)))
        | ~ sP1145(U_18333,U_18331,U_18335) )
    & ! [U_18336,U_18332,U_18334] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18332),hAPP(hAPP(c_List_Olist_OCons(U_18332),U_18334),U_18336)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18332),U_18336))
        | hBOOL(hAPP(hAPP(c_member(U_18332),U_18334),hAPP(c_List_Oset(U_18332),U_18336))) )
    & ! [U_18333,U_18331,U_18335] :
        ( sP1145(U_18333,U_18331,U_18335)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18331),hAPP(hAPP(c_List_Olist_OCons(U_18331),U_18333),U_18335))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1145])],[f_4430_3]) ).

cnf(f_4430_5,plain,
    ( sP1145(U_18333,U_18331,U_18335)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18331),hAPP(hAPP(c_List_Olist_OCons(U_18331),U_18333),U_18335))) ),
    inference(clausify,[status(thm)],[f_4430_4]) ).

cnf(f_4430_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18332),hAPP(hAPP(c_List_Olist_OCons(U_18332),U_18334),U_18336)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18332),U_18336))
    | hBOOL(hAPP(hAPP(c_member(U_18332),U_18334),hAPP(c_List_Oset(U_18332),U_18336))) ),
    inference(clausify,[status(thm)],[f_4430_4]) ).

cnf(f_4430_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_18331),U_18333),hAPP(c_List_Oset(U_18331),U_18335)))
    | ~ sP1145(U_18333,U_18331,U_18335) ),
    inference(clausify,[status(thm)],[f_4430_4]) ).

cnf(f_4430_8,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18331),U_18335))
    | ~ sP1145(U_18333,U_18331,U_18335) ),
    inference(clausify,[status(thm)],[f_4430_4]) ).

fof(f_4431_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_4431_2,plain,
    ! [U_18342,U_18341,U_18340,U_18339,U_18338,U_18337] :
      ( ( hAPP(c_Map_Omap__of(U_18339,U_18340,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_18339,U_18340)),hAPP(hAPP(c_Product__Type_OPair(U_18339,U_18340),U_18337),U_18341)),U_18342)),U_18338) = hAPP(c_Map_Omap__of(U_18339,U_18340,U_18342),U_18338)
        | U_18337 = U_18338 )
      & ( hAPP(c_Map_Omap__of(U_18339,U_18340,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_18339,U_18340)),hAPP(hAPP(c_Product__Type_OPair(U_18339,U_18340),U_18337),U_18341)),U_18342)),U_18338) = hAPP(c_Option_Ooption_OSome(U_18340),U_18341)
        | U_18337 != U_18338 ) ),
    inference(variable_rename,[status(thm)],[f_4431_1]) ).

fof(f_4431_3,plain,
    ( ! [U_18354,U_18352,U_18350,U_18348,U_18346,U_18344] :
        ( hAPP(c_Map_Omap__of(U_18348,U_18350,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_18348,U_18350)),hAPP(hAPP(c_Product__Type_OPair(U_18348,U_18350),U_18344),U_18352)),U_18354)),U_18346) = hAPP(c_Map_Omap__of(U_18348,U_18350,U_18354),U_18346)
        | U_18344 = U_18346 )
    & ! [U_18353,U_18351,U_18349,U_18347,U_18345,U_18343] :
        ( hAPP(c_Map_Omap__of(U_18347,U_18349,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_18347,U_18349)),hAPP(hAPP(c_Product__Type_OPair(U_18347,U_18349),U_18343),U_18351)),U_18353)),U_18345) = hAPP(c_Option_Ooption_OSome(U_18349),U_18351)
        | U_18343 != U_18345 ) ),
    inference(miniscope,[status(thm)],[f_4431_2]) ).

fof(f_4431_4,plain,
    ( ! [U_18344,U_18346,U_18348,U_18350,U_18352,U_18354] :
        ( hAPP(c_Map_Omap__of(U_18348,U_18350,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_18348,U_18350)),hAPP(hAPP(c_Product__Type_OPair(U_18348,U_18350),U_18344),U_18352)),U_18354)),U_18346) = hAPP(c_Map_Omap__of(U_18348,U_18350,U_18354),U_18346)
        | U_18344 = U_18346 )
    & ! [U_18349,U_18347,U_18343,U_18345,U_18351,U_18353] :
        ( hAPP(c_Map_Omap__of(U_18347,U_18349,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_18347,U_18349)),hAPP(hAPP(c_Product__Type_OPair(U_18347,U_18349),U_18343),U_18351)),U_18353)),U_18345) = hAPP(c_Option_Ooption_OSome(U_18349),U_18351)
        | U_18343 != U_18345 ) ),
    inference(definitional_conversion,[status(esa)],[f_4431_3]) ).

cnf(f_4431_5,plain,
    ( hAPP(c_Map_Omap__of(U_18347,U_18349,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_18347,U_18349)),hAPP(hAPP(c_Product__Type_OPair(U_18347,U_18349),U_18343),U_18351)),U_18353)),U_18345) = hAPP(c_Option_Ooption_OSome(U_18349),U_18351)
    | U_18343 != U_18345 ),
    inference(clausify,[status(thm)],[f_4431_4]) ).

cnf(f_4431_6,plain,
    ( hAPP(c_Map_Omap__of(U_18348,U_18350,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_18348,U_18350)),hAPP(hAPP(c_Product__Type_OPair(U_18348,U_18350),U_18344),U_18352)),U_18354)),U_18346) = hAPP(c_Map_Omap__of(U_18348,U_18350,U_18354),U_18346)
    | U_18344 = U_18346 ),
    inference(clausify,[status(thm)],[f_4431_4]) ).

fof(f_4432_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_4432_2,plain,
    ! [U_18357,U_18356,U_18355] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18355)),hAPP(hAPP(c_List_Olist_OCons(U_18355),U_18356),U_18357)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18355)),U_18357)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_4432_1]) ).

fof(f_4432_3,plain,
    ! [U_18355,U_18356,U_18357] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18355)),hAPP(hAPP(c_List_Olist_OCons(U_18355),U_18356),U_18357)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18355)),U_18357)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_4432_2]) ).

cnf(f_4432_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18355)),hAPP(hAPP(c_List_Olist_OCons(U_18355),U_18356),U_18357)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18355)),U_18357)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_4432_3]) ).

fof(f_4433_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_4433_2,plain,
    ! [U_18363,U_18362,U_18361,U_18360,U_18359,U_18358] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18358),tc_List_Olist(U_18358))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18358),tc_List_Olist(U_18358)),hAPP(hAPP(c_List_Olist_OCons(U_18358),U_18359),U_18362)),hAPP(hAPP(c_List_Olist_OCons(U_18358),U_18360),U_18363))),c_List_Olistrel(U_18358,U_18361)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18358),tc_List_Olist(U_18358))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18358),tc_List_Olist(U_18358)),U_18362),U_18363)),c_List_Olistrel(U_18358,U_18361)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18358,U_18358)),hAPP(hAPP(c_Product__Type_OPair(U_18358,U_18358),U_18359),U_18360)),U_18361)) ),
    inference(variable_rename,[status(thm)],[f_4433_1]) ).

fof(f_4433_3,plain,
    ! [U_18358,U_18359,U_18360,U_18361,U_18362,U_18363] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18358),tc_List_Olist(U_18358))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18358),tc_List_Olist(U_18358)),hAPP(hAPP(c_List_Olist_OCons(U_18358),U_18359),U_18362)),hAPP(hAPP(c_List_Olist_OCons(U_18358),U_18360),U_18363))),c_List_Olistrel(U_18358,U_18361)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18358),tc_List_Olist(U_18358))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18358),tc_List_Olist(U_18358)),U_18362),U_18363)),c_List_Olistrel(U_18358,U_18361)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18358,U_18358)),hAPP(hAPP(c_Product__Type_OPair(U_18358,U_18358),U_18359),U_18360)),U_18361)) ),
    inference(definitional_conversion,[status(esa)],[f_4433_2]) ).

cnf(f_4433_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18358),tc_List_Olist(U_18358))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18358),tc_List_Olist(U_18358)),hAPP(hAPP(c_List_Olist_OCons(U_18358),U_18359),U_18362)),hAPP(hAPP(c_List_Olist_OCons(U_18358),U_18360),U_18363))),c_List_Olistrel(U_18358,U_18361)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18358),tc_List_Olist(U_18358))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18358),tc_List_Olist(U_18358)),U_18362),U_18363)),c_List_Olistrel(U_18358,U_18361)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18358,U_18358)),hAPP(hAPP(c_Product__Type_OPair(U_18358,U_18358),U_18359),U_18360)),U_18361)) ),
    inference(clausify,[status(thm)],[f_4433_3]) ).

fof(f_4434_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_4434_2,plain,
    ! [U_18367,U_18366,U_18365,U_18364] : c_Map_Omap__of(U_18364,U_18365,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_18364,U_18365)),U_18366),U_18367)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18364,tc_Option_Ooption(U_18365)),c_Map_Omap__of(U_18364,U_18365,U_18367)),hAPP(c_Product__Type_Ofst(U_18364,U_18365),U_18366)),hAPP(c_Option_Ooption_OSome(U_18365),hAPP(c_Product__Type_Osnd(U_18364,U_18365),U_18366))),
    inference(variable_rename,[status(thm)],[f_4434_1]) ).

fof(f_4434_3,plain,
    ! [U_18364,U_18365,U_18366,U_18367] : c_Map_Omap__of(U_18364,U_18365,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_18364,U_18365)),U_18366),U_18367)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18364,tc_Option_Ooption(U_18365)),c_Map_Omap__of(U_18364,U_18365,U_18367)),hAPP(c_Product__Type_Ofst(U_18364,U_18365),U_18366)),hAPP(c_Option_Ooption_OSome(U_18365),hAPP(c_Product__Type_Osnd(U_18364,U_18365),U_18366))),
    inference(definitional_conversion,[status(esa)],[f_4434_2]) ).

cnf(f_4434_4,plain,
    c_Map_Omap__of(U_18364,U_18365,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_18364,U_18365)),U_18366),U_18367)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18364,tc_Option_Ooption(U_18365)),c_Map_Omap__of(U_18364,U_18365,U_18367)),hAPP(c_Product__Type_Ofst(U_18364,U_18365),U_18366)),hAPP(c_Option_Ooption_OSome(U_18365),hAPP(c_Product__Type_Osnd(U_18364,U_18365),U_18366))),
    inference(clausify,[status(thm)],[f_4434_3]) ).

fof(f_4435_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_4435_2,plain,
    ! [U_18373,U_18372,U_18371,U_18370,U_18369,U_18368] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18368),tc_List_Olist(U_18368))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18368),tc_List_Olist(U_18368)),hAPP(hAPP(c_List_Olist_OCons(U_18368),U_18369),U_18370)),hAPP(hAPP(c_List_Olist_OCons(U_18368),U_18371),U_18372))),c_List_Olex(U_18368,U_18373)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18368),tc_List_Olist(U_18368))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18368),tc_List_Olist(U_18368)),U_18370),U_18372)),c_List_Olex(U_18368,U_18373)))
            | U_18369 != U_18371 )
          & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18368)),U_18370) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18368)),U_18372)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18368,U_18368)),hAPP(hAPP(c_Product__Type_OPair(U_18368,U_18368),U_18369),U_18371)),U_18373)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18368),tc_List_Olist(U_18368))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18368),tc_List_Olist(U_18368)),U_18370),U_18372)),c_List_Olex(U_18368,U_18373)))
          & U_18369 = U_18371 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18368)),U_18370) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18368)),U_18372)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18368,U_18368)),hAPP(hAPP(c_Product__Type_OPair(U_18368,U_18368),U_18369),U_18371)),U_18373)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18368),tc_List_Olist(U_18368))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18368),tc_List_Olist(U_18368)),hAPP(hAPP(c_List_Olist_OCons(U_18368),U_18369),U_18370)),hAPP(hAPP(c_List_Olist_OCons(U_18368),U_18371),U_18372))),c_List_Olex(U_18368,U_18373))) ) ),
    inference(variable_rename,[status(thm)],[f_4435_1]) ).

fof(f_4435_3,plain,
    ( ! [U_18385,U_18383,U_18381,U_18379,U_18377,U_18375] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18375),tc_List_Olist(U_18375))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18375),tc_List_Olist(U_18375)),hAPP(hAPP(c_List_Olist_OCons(U_18375),U_18377),U_18379)),hAPP(hAPP(c_List_Olist_OCons(U_18375),U_18381),U_18383))),c_List_Olex(U_18375,U_18385)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18375),tc_List_Olist(U_18375))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18375),tc_List_Olist(U_18375)),U_18379),U_18383)),c_List_Olex(U_18375,U_18385)))
            | U_18377 != U_18381 )
          & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18375)),U_18379) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18375)),U_18383)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18375,U_18375)),hAPP(hAPP(c_Product__Type_OPair(U_18375,U_18375),U_18377),U_18381)),U_18385)) ) ) )
    & ! [U_18384,U_18382,U_18380,U_18378,U_18376,U_18374] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18374),tc_List_Olist(U_18374))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18374),tc_List_Olist(U_18374)),U_18378),U_18382)),c_List_Olex(U_18374,U_18384)))
          & U_18376 = U_18380 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18374)),U_18378) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18374)),U_18382)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18374,U_18374)),hAPP(hAPP(c_Product__Type_OPair(U_18374,U_18374),U_18376),U_18380)),U_18384)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18374),tc_List_Olist(U_18374))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18374),tc_List_Olist(U_18374)),hAPP(hAPP(c_List_Olist_OCons(U_18374),U_18376),U_18378)),hAPP(hAPP(c_List_Olist_OCons(U_18374),U_18380),U_18382))),c_List_Olex(U_18374,U_18384))) ) ),
    inference(miniscope,[status(thm)],[f_4435_2]) ).

fof(f_4435_4,plain,
    ( ! [U_18375,U_18377,U_18379,U_18383,U_18381,U_18385] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18375),tc_List_Olist(U_18375))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18375),tc_List_Olist(U_18375)),U_18379),U_18383)),c_List_Olex(U_18375,U_18385)))
        | U_18377 != U_18381
        | ~ sP1148(U_18375,U_18377,U_18379,U_18383,U_18381,U_18385) )
    & ! [U_18375,U_18377,U_18379,U_18383,U_18381,U_18385] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18375)),U_18379) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18375)),U_18383)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18375,U_18375)),hAPP(hAPP(c_Product__Type_OPair(U_18375,U_18375),U_18377),U_18381)),U_18385))
        | ~ sP1148(U_18375,U_18377,U_18379,U_18383,U_18381,U_18385) )
    & ! [U_18374,U_18376,U_18378,U_18382,U_18380,U_18384] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18374),tc_List_Olist(U_18374))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18374),tc_List_Olist(U_18374)),U_18378),U_18382)),c_List_Olex(U_18374,U_18384)))
        | ~ sP1147(U_18374,U_18376,U_18378,U_18382,U_18380,U_18384) )
    & ! [U_18374,U_18376,U_18378,U_18382,U_18380,U_18384] :
        ( U_18376 = U_18380
        | ~ sP1147(U_18374,U_18376,U_18378,U_18382,U_18380,U_18384) )
    & ! [U_18374,U_18376,U_18378,U_18382,U_18380,U_18384] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18374)),U_18378) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18374)),U_18382)
        | ~ sP1146(U_18374,U_18376,U_18378,U_18382,U_18380,U_18384) )
    & ! [U_18374,U_18376,U_18378,U_18382,U_18380,U_18384] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18374,U_18374)),hAPP(hAPP(c_Product__Type_OPair(U_18374,U_18374),U_18376),U_18380)),U_18384))
        | ~ sP1146(U_18374,U_18376,U_18378,U_18382,U_18380,U_18384) )
    & ! [U_18375,U_18377,U_18379,U_18383,U_18381,U_18385] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18375),tc_List_Olist(U_18375))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18375),tc_List_Olist(U_18375)),hAPP(hAPP(c_List_Olist_OCons(U_18375),U_18377),U_18379)),hAPP(hAPP(c_List_Olist_OCons(U_18375),U_18381),U_18383))),c_List_Olex(U_18375,U_18385)))
        | sP1148(U_18375,U_18377,U_18379,U_18383,U_18381,U_18385) )
    & ! [U_18374,U_18376,U_18378,U_18382,U_18380,U_18384] :
        ( sP1147(U_18374,U_18376,U_18378,U_18382,U_18380,U_18384)
        | sP1146(U_18374,U_18376,U_18378,U_18382,U_18380,U_18384)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18374),tc_List_Olist(U_18374))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18374),tc_List_Olist(U_18374)),hAPP(hAPP(c_List_Olist_OCons(U_18374),U_18376),U_18378)),hAPP(hAPP(c_List_Olist_OCons(U_18374),U_18380),U_18382))),c_List_Olex(U_18374,U_18384))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1146,sP1147,sP1148])],[f_4435_3]) ).

cnf(f_4435_5,plain,
    ( sP1147(U_18374,U_18376,U_18378,U_18382,U_18380,U_18384)
    | sP1146(U_18374,U_18376,U_18378,U_18382,U_18380,U_18384)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18374),tc_List_Olist(U_18374))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18374),tc_List_Olist(U_18374)),hAPP(hAPP(c_List_Olist_OCons(U_18374),U_18376),U_18378)),hAPP(hAPP(c_List_Olist_OCons(U_18374),U_18380),U_18382))),c_List_Olex(U_18374,U_18384))) ),
    inference(clausify,[status(thm)],[f_4435_4]) ).

cnf(f_4435_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18375),tc_List_Olist(U_18375))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18375),tc_List_Olist(U_18375)),hAPP(hAPP(c_List_Olist_OCons(U_18375),U_18377),U_18379)),hAPP(hAPP(c_List_Olist_OCons(U_18375),U_18381),U_18383))),c_List_Olex(U_18375,U_18385)))
    | sP1148(U_18375,U_18377,U_18379,U_18383,U_18381,U_18385) ),
    inference(clausify,[status(thm)],[f_4435_4]) ).

cnf(f_4435_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18374,U_18374)),hAPP(hAPP(c_Product__Type_OPair(U_18374,U_18374),U_18376),U_18380)),U_18384))
    | ~ sP1146(U_18374,U_18376,U_18378,U_18382,U_18380,U_18384) ),
    inference(clausify,[status(thm)],[f_4435_4]) ).

cnf(f_4435_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18374)),U_18378) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18374)),U_18382)
    | ~ sP1146(U_18374,U_18376,U_18378,U_18382,U_18380,U_18384) ),
    inference(clausify,[status(thm)],[f_4435_4]) ).

cnf(f_4435_9,plain,
    ( U_18376 = U_18380
    | ~ sP1147(U_18374,U_18376,U_18378,U_18382,U_18380,U_18384) ),
    inference(clausify,[status(thm)],[f_4435_4]) ).

cnf(f_4435_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18374),tc_List_Olist(U_18374))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18374),tc_List_Olist(U_18374)),U_18378),U_18382)),c_List_Olex(U_18374,U_18384)))
    | ~ sP1147(U_18374,U_18376,U_18378,U_18382,U_18380,U_18384) ),
    inference(clausify,[status(thm)],[f_4435_4]) ).

cnf(f_4435_11,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18375)),U_18379) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18375)),U_18383)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18375,U_18375)),hAPP(hAPP(c_Product__Type_OPair(U_18375,U_18375),U_18377),U_18381)),U_18385))
    | ~ sP1148(U_18375,U_18377,U_18379,U_18383,U_18381,U_18385) ),
    inference(clausify,[status(thm)],[f_4435_4]) ).

cnf(f_4435_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18375),tc_List_Olist(U_18375))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18375),tc_List_Olist(U_18375)),U_18379),U_18383)),c_List_Olex(U_18375,U_18385)))
    | U_18377 != U_18381
    | ~ sP1148(U_18375,U_18377,U_18379,U_18383,U_18381,U_18385) ),
    inference(clausify,[status(thm)],[f_4435_4]) ).

fof(f_4436_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_4436_2,plain,
    ! [U_18389,U_18388,U_18387,U_18386] : hAPP(c_Relation_OImage(tc_List_Olist(U_18386),tc_List_Olist(U_18386),c_List_Olistrel(U_18386,U_18387)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18386)),hAPP(hAPP(c_List_Olist_OCons(U_18386),U_18388),U_18389)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18386),tc_HOL_Obool)))) = c_List_Oset__Cons(U_18386,hAPP(c_Relation_OImage(U_18386,U_18386,U_18387),hAPP(hAPP(c_Set_Oinsert(U_18386),U_18388),c_Orderings_Obot__class_Obot(tc_fun(U_18386,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(U_18386),tc_List_Olist(U_18386),c_List_Olistrel(U_18386,U_18387)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18386)),U_18389),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18386),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_4436_1]) ).

fof(f_4436_3,plain,
    ! [U_18386,U_18388,U_18387,U_18389] : hAPP(c_Relation_OImage(tc_List_Olist(U_18386),tc_List_Olist(U_18386),c_List_Olistrel(U_18386,U_18387)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18386)),hAPP(hAPP(c_List_Olist_OCons(U_18386),U_18388),U_18389)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18386),tc_HOL_Obool)))) = c_List_Oset__Cons(U_18386,hAPP(c_Relation_OImage(U_18386,U_18386,U_18387),hAPP(hAPP(c_Set_Oinsert(U_18386),U_18388),c_Orderings_Obot__class_Obot(tc_fun(U_18386,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(U_18386),tc_List_Olist(U_18386),c_List_Olistrel(U_18386,U_18387)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18386)),U_18389),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18386),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_4436_2]) ).

cnf(f_4436_4,plain,
    hAPP(c_Relation_OImage(tc_List_Olist(U_18386),tc_List_Olist(U_18386),c_List_Olistrel(U_18386,U_18387)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18386)),hAPP(hAPP(c_List_Olist_OCons(U_18386),U_18388),U_18389)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18386),tc_HOL_Obool)))) = c_List_Oset__Cons(U_18386,hAPP(c_Relation_OImage(U_18386,U_18386,U_18387),hAPP(hAPP(c_Set_Oinsert(U_18386),U_18388),c_Orderings_Obot__class_Obot(tc_fun(U_18386,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(U_18386),tc_List_Olist(U_18386),c_List_Olistrel(U_18386,U_18387)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18386)),U_18389),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18386),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_4436_3]) ).

fof(f_4437_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_4437_2,plain,
    ! [U_18392,U_18391,U_18390] : c_List_Oset__Cons(U_18390,U_18391,U_18392) = hAPP(c_Set_OCollect(tc_List_Olist(U_18390)),hAPP(hAPP(c_COMBB(tc_fun(U_18390,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(U_18390)),c_HOL_OEx(U_18390)),hAPP(hAPP(c_COMBB(tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_fun(U_18390,tc_HOL_Obool),tc_List_Olist(U_18390)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_HOL_Obool,U_18390),c_HOL_OEx(tc_List_Olist(U_18390)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18390),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18390,tc_fun(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),tc_fun(tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),tc_List_Olist(U_18390)),c_COMBS(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_18390,tc_fun(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),tc_List_Olist(U_18390)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18390),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),U_18390),c_COMBS(tc_List_Olist(U_18390),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(U_18390)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_18390),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18390)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18390),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_List_Olist(U_18390))),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(U_18390),tc_List_Olist(U_18390)),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_fun(tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_List_Olist(U_18390))),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),tc_List_Olist(U_18390)),c_COMBB(tc_fun(tc_List_Olist(U_18390),tc_List_Olist(U_18390)),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),U_18390)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18390),tc_List_Olist(U_18390)),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_List_Olist(U_18390)),c_COMBB(tc_List_Olist(U_18390),tc_HOL_Obool,tc_List_Olist(U_18390))),c_fequal))),c_List_Olist_OCons(U_18390)))))),hAPP(hAPP(c_COMBC(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),U_18390),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_18390))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18390),c_fconj),hAPP(hAPP(c_COMBC(U_18390,tc_fun(U_18390,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18390)),U_18391)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18390),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_18390))),U_18392)))))),
    inference(variable_rename,[status(thm)],[f_4437_1]) ).

fof(f_4437_3,plain,
    ! [U_18390,U_18391,U_18392] : c_List_Oset__Cons(U_18390,U_18391,U_18392) = hAPP(c_Set_OCollect(tc_List_Olist(U_18390)),hAPP(hAPP(c_COMBB(tc_fun(U_18390,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(U_18390)),c_HOL_OEx(U_18390)),hAPP(hAPP(c_COMBB(tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_fun(U_18390,tc_HOL_Obool),tc_List_Olist(U_18390)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_HOL_Obool,U_18390),c_HOL_OEx(tc_List_Olist(U_18390)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18390),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18390,tc_fun(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),tc_fun(tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),tc_List_Olist(U_18390)),c_COMBS(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_18390,tc_fun(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),tc_List_Olist(U_18390)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18390),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),U_18390),c_COMBS(tc_List_Olist(U_18390),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(U_18390)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_18390),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18390)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18390),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_List_Olist(U_18390))),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(U_18390),tc_List_Olist(U_18390)),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_fun(tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_List_Olist(U_18390))),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),tc_List_Olist(U_18390)),c_COMBB(tc_fun(tc_List_Olist(U_18390),tc_List_Olist(U_18390)),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),U_18390)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18390),tc_List_Olist(U_18390)),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_List_Olist(U_18390)),c_COMBB(tc_List_Olist(U_18390),tc_HOL_Obool,tc_List_Olist(U_18390))),c_fequal))),c_List_Olist_OCons(U_18390)))))),hAPP(hAPP(c_COMBC(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),U_18390),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_18390))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18390),c_fconj),hAPP(hAPP(c_COMBC(U_18390,tc_fun(U_18390,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18390)),U_18391)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18390),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_18390))),U_18392)))))),
    inference(definitional_conversion,[status(esa)],[f_4437_2]) ).

cnf(f_4437_4,plain,
    c_List_Oset__Cons(U_18390,U_18391,U_18392) = hAPP(c_Set_OCollect(tc_List_Olist(U_18390)),hAPP(hAPP(c_COMBB(tc_fun(U_18390,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(U_18390)),c_HOL_OEx(U_18390)),hAPP(hAPP(c_COMBB(tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_fun(U_18390,tc_HOL_Obool),tc_List_Olist(U_18390)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_HOL_Obool,U_18390),c_HOL_OEx(tc_List_Olist(U_18390)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18390),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18390,tc_fun(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),tc_fun(tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),tc_List_Olist(U_18390)),c_COMBS(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_18390,tc_fun(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),tc_List_Olist(U_18390)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18390),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),U_18390),c_COMBS(tc_List_Olist(U_18390),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(U_18390)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_18390),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_18390)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18390),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_List_Olist(U_18390))),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(U_18390),tc_List_Olist(U_18390)),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_fun(tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_List_Olist(U_18390))),tc_fun(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool))),tc_List_Olist(U_18390)),c_COMBB(tc_fun(tc_List_Olist(U_18390),tc_List_Olist(U_18390)),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),U_18390)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18390),tc_List_Olist(U_18390)),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),tc_List_Olist(U_18390)),c_COMBB(tc_List_Olist(U_18390),tc_HOL_Obool,tc_List_Olist(U_18390))),c_fequal))),c_List_Olist_OCons(U_18390)))))),hAPP(hAPP(c_COMBC(U_18390,tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool)),U_18390),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_18390))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18390),c_fconj),hAPP(hAPP(c_COMBC(U_18390,tc_fun(U_18390,tc_HOL_Obool),tc_HOL_Obool),c_member(U_18390)),U_18391)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18390),tc_fun(tc_List_Olist(U_18390),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_18390))),U_18392)))))),
    inference(clausify,[status(thm)],[f_4437_3]) ).

fof(f_4438_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_4438_2,plain,
    ! [U_18399,U_18398,U_18397,U_18396,U_18395] :
      ( ? [U_18394,U_18393] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18395),tc_List_Olist(U_18395))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18395),tc_List_Olist(U_18395)),U_18397),U_18393)),c_List_Olistrel(U_18395,U_18399)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18395,U_18395)),hAPP(hAPP(c_Product__Type_OPair(U_18395,U_18395),U_18396),U_18394)),U_18399))
          & U_18398 = hAPP(hAPP(c_List_Olist_OCons(U_18395),U_18394),U_18393) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18395),tc_List_Olist(U_18395))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18395),tc_List_Olist(U_18395)),hAPP(hAPP(c_List_Olist_OCons(U_18395),U_18396),U_18397)),U_18398)),c_List_Olistrel(U_18395,U_18399))) ),
    inference(variable_rename,[status(thm)],[f_4438_1]) ).

fof(f_4438_3,plain,
    ! [U_18399,U_18398,U_18397,U_18396,U_18395] :
      ( ? [U_18393] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18395),tc_List_Olist(U_18395))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18395),tc_List_Olist(U_18395)),U_18397),U_18393)),c_List_Olistrel(U_18395,U_18399)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18395,U_18395)),hAPP(hAPP(c_Product__Type_OPair(U_18395,U_18395),U_18396),sK461(U_18399,U_18398,U_18397,U_18396,U_18395))),U_18399))
          & U_18398 = hAPP(hAPP(c_List_Olist_OCons(U_18395),sK461(U_18399,U_18398,U_18397,U_18396,U_18395)),U_18393) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18395),tc_List_Olist(U_18395))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18395),tc_List_Olist(U_18395)),hAPP(hAPP(c_List_Olist_OCons(U_18395),U_18396),U_18397)),U_18398)),c_List_Olistrel(U_18395,U_18399))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK461]),skolemize(U_18394,sK461(U_18399,U_18398,U_18397,U_18396,U_18395))],[f_4438_2]) ).

fof(f_4438_4,plain,
    ! [U_18399,U_18398,U_18397,U_18396,U_18395] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18395),tc_List_Olist(U_18395))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18395),tc_List_Olist(U_18395)),U_18397),sK462(U_18399,U_18398,U_18397,U_18396,U_18395))),c_List_Olistrel(U_18395,U_18399)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18395,U_18395)),hAPP(hAPP(c_Product__Type_OPair(U_18395,U_18395),U_18396),sK461(U_18399,U_18398,U_18397,U_18396,U_18395))),U_18399))
        & U_18398 = hAPP(hAPP(c_List_Olist_OCons(U_18395),sK461(U_18399,U_18398,U_18397,U_18396,U_18395)),sK462(U_18399,U_18398,U_18397,U_18396,U_18395)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18395),tc_List_Olist(U_18395))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18395),tc_List_Olist(U_18395)),hAPP(hAPP(c_List_Olist_OCons(U_18395),U_18396),U_18397)),U_18398)),c_List_Olistrel(U_18395,U_18399))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK462]),skolemize(U_18393,sK462(U_18399,U_18398,U_18397,U_18396,U_18395))],[f_4438_3]) ).

fof(f_4438_5,plain,
    ( ! [U_18396,U_18395,U_18397,U_18398,U_18399] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18395),tc_List_Olist(U_18395))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18395),tc_List_Olist(U_18395)),U_18397),sK462(U_18399,U_18398,U_18397,U_18396,U_18395))),c_List_Olistrel(U_18395,U_18399)))
        | ~ sP1149(U_18396,U_18395,U_18397,U_18398,U_18399) )
    & ! [U_18396,U_18395,U_18397,U_18398,U_18399] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18395,U_18395)),hAPP(hAPP(c_Product__Type_OPair(U_18395,U_18395),U_18396),sK461(U_18399,U_18398,U_18397,U_18396,U_18395))),U_18399))
        | ~ sP1149(U_18396,U_18395,U_18397,U_18398,U_18399) )
    & ! [U_18396,U_18395,U_18397,U_18398,U_18399] :
        ( U_18398 = hAPP(hAPP(c_List_Olist_OCons(U_18395),sK461(U_18399,U_18398,U_18397,U_18396,U_18395)),sK462(U_18399,U_18398,U_18397,U_18396,U_18395))
        | ~ sP1149(U_18396,U_18395,U_18397,U_18398,U_18399) )
    & ! [U_18396,U_18395,U_18397,U_18398,U_18399] :
        ( sP1149(U_18396,U_18395,U_18397,U_18398,U_18399)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18395),tc_List_Olist(U_18395))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18395),tc_List_Olist(U_18395)),hAPP(hAPP(c_List_Olist_OCons(U_18395),U_18396),U_18397)),U_18398)),c_List_Olistrel(U_18395,U_18399))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1149])],[f_4438_4]) ).

cnf(f_4438_6,plain,
    ( sP1149(U_18396,U_18395,U_18397,U_18398,U_18399)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18395),tc_List_Olist(U_18395))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18395),tc_List_Olist(U_18395)),hAPP(hAPP(c_List_Olist_OCons(U_18395),U_18396),U_18397)),U_18398)),c_List_Olistrel(U_18395,U_18399))) ),
    inference(clausify,[status(thm)],[f_4438_5]) ).

cnf(f_4438_7,plain,
    ( U_18398 = hAPP(hAPP(c_List_Olist_OCons(U_18395),sK461(U_18399,U_18398,U_18397,U_18396,U_18395)),sK462(U_18399,U_18398,U_18397,U_18396,U_18395))
    | ~ sP1149(U_18396,U_18395,U_18397,U_18398,U_18399) ),
    inference(clausify,[status(thm)],[f_4438_5]) ).

cnf(f_4438_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18395,U_18395)),hAPP(hAPP(c_Product__Type_OPair(U_18395,U_18395),U_18396),sK461(U_18399,U_18398,U_18397,U_18396,U_18395))),U_18399))
    | ~ sP1149(U_18396,U_18395,U_18397,U_18398,U_18399) ),
    inference(clausify,[status(thm)],[f_4438_5]) ).

cnf(f_4438_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18395),tc_List_Olist(U_18395))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18395),tc_List_Olist(U_18395)),U_18397),sK462(U_18399,U_18398,U_18397,U_18396,U_18395))),c_List_Olistrel(U_18395,U_18399)))
    | ~ sP1149(U_18396,U_18395,U_18397,U_18398,U_18399) ),
    inference(clausify,[status(thm)],[f_4438_5]) ).

fof(f_4439_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_4439_2,plain,
    ! [U_18406,U_18405,U_18404,U_18403,U_18402] :
      ( ? [U_18401,U_18400] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18402),tc_List_Olist(U_18402))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18402),tc_List_Olist(U_18402)),U_18400),U_18405)),c_List_Olistrel(U_18402,U_18406)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18402,U_18402)),hAPP(hAPP(c_Product__Type_OPair(U_18402,U_18402),U_18401),U_18404)),U_18406))
          & U_18403 = hAPP(hAPP(c_List_Olist_OCons(U_18402),U_18401),U_18400) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18402),tc_List_Olist(U_18402))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18402),tc_List_Olist(U_18402)),U_18403),hAPP(hAPP(c_List_Olist_OCons(U_18402),U_18404),U_18405))),c_List_Olistrel(U_18402,U_18406))) ),
    inference(variable_rename,[status(thm)],[f_4439_1]) ).

fof(f_4439_3,plain,
    ! [U_18406,U_18405,U_18404,U_18403,U_18402] :
      ( ? [U_18400] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18402),tc_List_Olist(U_18402))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18402),tc_List_Olist(U_18402)),U_18400),U_18405)),c_List_Olistrel(U_18402,U_18406)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18402,U_18402)),hAPP(hAPP(c_Product__Type_OPair(U_18402,U_18402),sK463(U_18406,U_18405,U_18404,U_18403,U_18402)),U_18404)),U_18406))
          & U_18403 = hAPP(hAPP(c_List_Olist_OCons(U_18402),sK463(U_18406,U_18405,U_18404,U_18403,U_18402)),U_18400) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18402),tc_List_Olist(U_18402))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18402),tc_List_Olist(U_18402)),U_18403),hAPP(hAPP(c_List_Olist_OCons(U_18402),U_18404),U_18405))),c_List_Olistrel(U_18402,U_18406))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK463]),skolemize(U_18401,sK463(U_18406,U_18405,U_18404,U_18403,U_18402))],[f_4439_2]) ).

fof(f_4439_4,plain,
    ! [U_18406,U_18405,U_18404,U_18403,U_18402] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18402),tc_List_Olist(U_18402))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18402),tc_List_Olist(U_18402)),sK464(U_18406,U_18405,U_18404,U_18403,U_18402)),U_18405)),c_List_Olistrel(U_18402,U_18406)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_18402,U_18402)),hAPP(hAPP(c_Product__Type_OPair(U_18402,U_18402),sK463(U_18406,U_18405,U_18404,U_18403,U_18402)),U_18404)),U_18406))
        & U_18403 = hAPP(hAPP(c_List_Olist_OCons(U_18402),sK463(U_18406,U_18405,U_18404,U_18403,U_18402)),sK464(U_18406,U_18405,U_18404,U_18403,U_18402)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18402),tc_List_Olist(U_18402))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18402),tc_List_Olist(U_18402)),U_18403),hAPP(hAPP(c_List_Olist_OCons(U_18402),U_18404),U_18405))),c_List_Olistrel(U_18402,U_18406))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK464]),skolemize(U_18400,sK464(U_18406,U_18405,U_18404,U_18403,U_18402))],[f_4439_3]) ).

fof(f_4439_5,plain,
    ( ! [U_18402,U_18403,U_18404,U_18405,U_18406] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18402),tc_List_Olist(U_18402))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18402),tc_List_Olist(U_18402)),sK464(U_18406,U_18405,U_18404,U_18403,U_18402)),U_18405)),c_List_Olistrel(U_18402,U_18406)))
        | ~ sP1150(U_18402,U_18403,U_18404,U_18405,U_18406) )
    & ! [U_18402,U_18403,U_18404,U_18405,U_18406] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18402,U_18402)),hAPP(hAPP(c_Product__Type_OPair(U_18402,U_18402),sK463(U_18406,U_18405,U_18404,U_18403,U_18402)),U_18404)),U_18406))
        | ~ sP1150(U_18402,U_18403,U_18404,U_18405,U_18406) )
    & ! [U_18402,U_18403,U_18404,U_18405,U_18406] :
        ( U_18403 = hAPP(hAPP(c_List_Olist_OCons(U_18402),sK463(U_18406,U_18405,U_18404,U_18403,U_18402)),sK464(U_18406,U_18405,U_18404,U_18403,U_18402))
        | ~ sP1150(U_18402,U_18403,U_18404,U_18405,U_18406) )
    & ! [U_18402,U_18403,U_18404,U_18405,U_18406] :
        ( sP1150(U_18402,U_18403,U_18404,U_18405,U_18406)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18402),tc_List_Olist(U_18402))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18402),tc_List_Olist(U_18402)),U_18403),hAPP(hAPP(c_List_Olist_OCons(U_18402),U_18404),U_18405))),c_List_Olistrel(U_18402,U_18406))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1150])],[f_4439_4]) ).

cnf(f_4439_6,plain,
    ( sP1150(U_18402,U_18403,U_18404,U_18405,U_18406)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18402),tc_List_Olist(U_18402))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18402),tc_List_Olist(U_18402)),U_18403),hAPP(hAPP(c_List_Olist_OCons(U_18402),U_18404),U_18405))),c_List_Olistrel(U_18402,U_18406))) ),
    inference(clausify,[status(thm)],[f_4439_5]) ).

cnf(f_4439_7,plain,
    ( U_18403 = hAPP(hAPP(c_List_Olist_OCons(U_18402),sK463(U_18406,U_18405,U_18404,U_18403,U_18402)),sK464(U_18406,U_18405,U_18404,U_18403,U_18402))
    | ~ sP1150(U_18402,U_18403,U_18404,U_18405,U_18406) ),
    inference(clausify,[status(thm)],[f_4439_5]) ).

cnf(f_4439_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18402,U_18402)),hAPP(hAPP(c_Product__Type_OPair(U_18402,U_18402),sK463(U_18406,U_18405,U_18404,U_18403,U_18402)),U_18404)),U_18406))
    | ~ sP1150(U_18402,U_18403,U_18404,U_18405,U_18406) ),
    inference(clausify,[status(thm)],[f_4439_5]) ).

cnf(f_4439_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18402),tc_List_Olist(U_18402))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18402),tc_List_Olist(U_18402)),sK464(U_18406,U_18405,U_18404,U_18403,U_18402)),U_18405)),c_List_Olistrel(U_18402,U_18406)))
    | ~ sP1150(U_18402,U_18403,U_18404,U_18405,U_18406) ),
    inference(clausify,[status(thm)],[f_4439_5]) ).

fof(f_4440_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_4440_2,plain,
    ! [U_18409,U_18408,U_18407] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18407)),c_List_Osublist(U_18407,U_18408,U_18409)) = 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_18407)),U_18408)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_18409)))),
    inference(variable_rename,[status(thm)],[f_4440_1]) ).

fof(f_4440_3,plain,
    ! [U_18407,U_18408,U_18409] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18407)),c_List_Osublist(U_18407,U_18408,U_18409)) = 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_18407)),U_18408)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_18409)))),
    inference(definitional_conversion,[status(esa)],[f_4440_2]) ).

cnf(f_4440_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18407)),c_List_Osublist(U_18407,U_18408,U_18409)) = 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_18407)),U_18408)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_18409)))),
    inference(clausify,[status(thm)],[f_4440_3]) ).

fof(f_4441_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_4441_2,plain,
    ! [U_18413,U_18412,U_18411,U_18410] :
      ( ( hAPP(c_Random_Opick(U_18411,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18411)),U_18412),U_18413)),U_18410) = hAPP(c_Random_Opick(U_18411,U_18413),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18410),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18411),U_18412)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18410),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18411),U_18412))) )
      & ( hAPP(c_Random_Opick(U_18411,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18411)),U_18412),U_18413)),U_18410) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18411),U_18412)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18410),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18411),U_18412))) ) ),
    inference(variable_rename,[status(thm)],[f_4441_1]) ).

fof(f_4441_3,plain,
    ( ! [U_18421,U_18419,U_18417,U_18415] :
        ( hAPP(c_Random_Opick(U_18417,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18417)),U_18419),U_18421)),U_18415) = hAPP(c_Random_Opick(U_18417,U_18421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18415),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18417),U_18419)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18415),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18417),U_18419))) )
    & ! [U_18420,U_18418,U_18416,U_18414] :
        ( hAPP(c_Random_Opick(U_18416,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18416)),U_18418),U_18420)),U_18414) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18416),U_18418)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18414),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18416),U_18418))) ) ),
    inference(miniscope,[status(thm)],[f_4441_2]) ).

fof(f_4441_4,plain,
    ( ! [U_18415,U_18417,U_18419,U_18421] :
        ( hAPP(c_Random_Opick(U_18417,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18417)),U_18419),U_18421)),U_18415) = hAPP(c_Random_Opick(U_18417,U_18421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18415),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18417),U_18419)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18415),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18417),U_18419))) )
    & ! [U_18416,U_18420,U_18414,U_18418] :
        ( hAPP(c_Random_Opick(U_18416,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18416)),U_18418),U_18420)),U_18414) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18416),U_18418)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18414),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18416),U_18418))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4441_3]) ).

cnf(f_4441_5,plain,
    ( hAPP(c_Random_Opick(U_18416,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18416)),U_18418),U_18420)),U_18414) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18416),U_18418)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18414),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18416),U_18418))) ),
    inference(clausify,[status(thm)],[f_4441_4]) ).

cnf(f_4441_6,plain,
    ( hAPP(c_Random_Opick(U_18417,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18417)),U_18419),U_18421)),U_18415) = hAPP(c_Random_Opick(U_18417,U_18421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18415),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18417),U_18419)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18415),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18417),U_18419))) ),
    inference(clausify,[status(thm)],[f_4441_4]) ).

fof(f_4442_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_4442_2,plain,
    ! [U_18424,U_18423,U_18422] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18422),c_List_Osublist(U_18422,U_18423,U_18424)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18422),U_18423)) ),
    inference(variable_rename,[status(thm)],[f_4442_1]) ).

fof(f_4442_3,plain,
    ! [U_18422,U_18424,U_18423] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18422),c_List_Osublist(U_18422,U_18423,U_18424)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18422),U_18423)) ),
    inference(definitional_conversion,[status(esa)],[f_4442_2]) ).

cnf(f_4442_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18422),c_List_Osublist(U_18422,U_18423,U_18424)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18422),U_18423)) ),
    inference(clausify,[status(thm)],[f_4442_3]) ).

fof(f_4443_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_4443_2,plain,
    ! [U_18428,U_18427,U_18426,U_18425] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_18425),U_18426),hAPP(c_List_Oset(U_18425),c_List_Osublist(U_18425,U_18427,U_18428))))
      | hBOOL(hAPP(hAPP(c_member(U_18425),U_18426),hAPP(c_List_Oset(U_18425),U_18427))) ),
    inference(variable_rename,[status(thm)],[f_4443_1]) ).

fof(f_4443_3,plain,
    ! [U_18425,U_18426,U_18427,U_18428] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_18425),U_18426),hAPP(c_List_Oset(U_18425),c_List_Osublist(U_18425,U_18427,U_18428))))
      | hBOOL(hAPP(hAPP(c_member(U_18425),U_18426),hAPP(c_List_Oset(U_18425),U_18427))) ),
    inference(definitional_conversion,[status(esa)],[f_4443_2]) ).

cnf(f_4443_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_18425),U_18426),hAPP(c_List_Oset(U_18425),c_List_Osublist(U_18425,U_18427,U_18428))))
    | hBOOL(hAPP(hAPP(c_member(U_18425),U_18426),hAPP(c_List_Oset(U_18425),U_18427))) ),
    inference(clausify,[status(thm)],[f_4443_3]) ).

fof(f_4444_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_4444_2,plain,
    ! [U_18432,U_18431,U_18430,U_18429] :
      ( hBOOL(hAPP(hAPP(c_member(U_18429),U_18430),hAPP(c_List_Oset(U_18429),U_18431)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18429),U_18430),hAPP(c_List_Oset(U_18429),c_List_Osublist(U_18429,U_18431,U_18432)))) ),
    inference(variable_rename,[status(thm)],[f_4444_1]) ).

fof(f_4444_3,plain,
    ! [U_18429,U_18430,U_18431,U_18432] :
      ( hBOOL(hAPP(hAPP(c_member(U_18429),U_18430),hAPP(c_List_Oset(U_18429),U_18431)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18429),U_18430),hAPP(c_List_Oset(U_18429),c_List_Osublist(U_18429,U_18431,U_18432)))) ),
    inference(definitional_conversion,[status(esa)],[f_4444_2]) ).

cnf(f_4444_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18429),U_18430),hAPP(c_List_Oset(U_18429),U_18431)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18429),U_18430),hAPP(c_List_Oset(U_18429),c_List_Osublist(U_18429,U_18431,U_18432)))) ),
    inference(clausify,[status(thm)],[f_4444_3]) ).

fof(f_4445_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_4445_2,plain,
    ! [U_18435,U_18434,U_18433] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18433,tc_HOL_Obool)),hAPP(c_List_Oset(U_18433),c_List_Osublist(U_18433,U_18434,U_18435))),hAPP(c_List_Oset(U_18433),U_18434))),
    inference(variable_rename,[status(thm)],[f_4445_1]) ).

fof(f_4445_3,plain,
    ! [U_18433,U_18434,U_18435] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18433,tc_HOL_Obool)),hAPP(c_List_Oset(U_18433),c_List_Osublist(U_18433,U_18434,U_18435))),hAPP(c_List_Oset(U_18433),U_18434))),
    inference(definitional_conversion,[status(esa)],[f_4445_2]) ).

cnf(f_4445_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18433,tc_HOL_Obool)),hAPP(c_List_Oset(U_18433),c_List_Osublist(U_18433,U_18434,U_18435))),hAPP(c_List_Oset(U_18433),U_18434))),
    inference(clausify,[status(thm)],[f_4445_3]) ).

fof(f_4446_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_4446_2,plain,
    ! [U_18438,U_18437,U_18436] : c_Random_Oselect__weight(U_18436,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18436)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18436),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_18437)),U_18438)) = c_Random_Oselect__weight(U_18436,U_18438),
    inference(variable_rename,[status(thm)],[f_4446_1]) ).

fof(f_4446_3,plain,
    ! [U_18436,U_18437,U_18438] : c_Random_Oselect__weight(U_18436,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18436)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18436),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_18437)),U_18438)) = c_Random_Oselect__weight(U_18436,U_18438),
    inference(definitional_conversion,[status(esa)],[f_4446_2]) ).

cnf(f_4446_4,plain,
    c_Random_Oselect__weight(U_18436,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18436)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18436),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_18437)),U_18438)) = c_Random_Oselect__weight(U_18436,U_18438),
    inference(clausify,[status(thm)],[f_4446_3]) ).

fof(f_4447_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_4447_2,plain,
    ! [U_18441,U_18440,U_18439] :
      ( hBOOL(hAPP(hAPP(c_member(U_18440),hAPP(c_Random_Opick(U_18440,U_18441),U_18439)),hAPP(c_List_Oset(U_18440),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18440),U_18440),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18440)),U_18441))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18439),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_18440),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18440)),U_18441)))) ),
    inference(variable_rename,[status(thm)],[f_4447_1]) ).

fof(f_4447_3,plain,
    ! [U_18439,U_18440,U_18441] :
      ( hBOOL(hAPP(hAPP(c_member(U_18440),hAPP(c_Random_Opick(U_18440,U_18441),U_18439)),hAPP(c_List_Oset(U_18440),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18440),U_18440),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18440)),U_18441))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18439),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_18440),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18440)),U_18441)))) ),
    inference(definitional_conversion,[status(esa)],[f_4447_2]) ).

cnf(f_4447_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18440),hAPP(c_Random_Opick(U_18440,U_18441),U_18439)),hAPP(c_List_Oset(U_18440),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18440),U_18440),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18440)),U_18441))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_18439),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_18440),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18440)),U_18441)))) ),
    inference(clausify,[status(thm)],[f_4447_3]) ).

fof(f_4448_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_4448_2,plain,
    ! [U_18444,U_18443,U_18442] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18442),hAPP(hAPP(c_List_Olist_OCons(U_18442),U_18443),U_18444)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18442),U_18443),hAPP(c_List_Omonoid__add__class_Olistsum(U_18442),U_18444))
      | ~ class_Groups_Omonoid__add(U_18442) ),
    inference(variable_rename,[status(thm)],[f_4448_1]) ).

fof(f_4448_3,plain,
    ! [U_18442,U_18443,U_18444] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18442),hAPP(hAPP(c_List_Olist_OCons(U_18442),U_18443),U_18444)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18442),U_18443),hAPP(c_List_Omonoid__add__class_Olistsum(U_18442),U_18444))
      | ~ class_Groups_Omonoid__add(U_18442) ),
    inference(definitional_conversion,[status(esa)],[f_4448_2]) ).

cnf(f_4448_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18442),hAPP(hAPP(c_List_Olist_OCons(U_18442),U_18443),U_18444)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18442),U_18443),hAPP(c_List_Omonoid__add__class_Olistsum(U_18442),U_18444))
    | ~ class_Groups_Omonoid__add(U_18442) ),
    inference(clausify,[status(thm)],[f_4448_3]) ).

fof(f_4449_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_4449_2,plain,
    ! [U_18449,U_18448,U_18447,U_18446,U_18445] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18445),hAPP(hAPP(c_List_Omap(U_18446,U_18445),hAPP(hAPP(c_COMBS(U_18446,U_18445,U_18445),hAPP(hAPP(c_COMBB(U_18445,tc_fun(U_18445,U_18445),U_18446),c_Groups_Ominus__class_Ominus(U_18445)),U_18447)),U_18448)),U_18449)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_18445),hAPP(c_List_Omonoid__add__class_Olistsum(U_18445),hAPP(hAPP(c_List_Omap(U_18446,U_18445),U_18447),U_18449))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18445),hAPP(hAPP(c_List_Omap(U_18446,U_18445),U_18448),U_18449)))
      | ~ class_Groups_Oab__group__add(U_18445) ),
    inference(variable_rename,[status(thm)],[f_4449_1]) ).

fof(f_4449_3,plain,
    ! [U_18445,U_18446,U_18447,U_18448,U_18449] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18445),hAPP(hAPP(c_List_Omap(U_18446,U_18445),hAPP(hAPP(c_COMBS(U_18446,U_18445,U_18445),hAPP(hAPP(c_COMBB(U_18445,tc_fun(U_18445,U_18445),U_18446),c_Groups_Ominus__class_Ominus(U_18445)),U_18447)),U_18448)),U_18449)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_18445),hAPP(c_List_Omonoid__add__class_Olistsum(U_18445),hAPP(hAPP(c_List_Omap(U_18446,U_18445),U_18447),U_18449))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18445),hAPP(hAPP(c_List_Omap(U_18446,U_18445),U_18448),U_18449)))
      | ~ class_Groups_Oab__group__add(U_18445) ),
    inference(definitional_conversion,[status(esa)],[f_4449_2]) ).

cnf(f_4449_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18445),hAPP(hAPP(c_List_Omap(U_18446,U_18445),hAPP(hAPP(c_COMBS(U_18446,U_18445,U_18445),hAPP(hAPP(c_COMBB(U_18445,tc_fun(U_18445,U_18445),U_18446),c_Groups_Ominus__class_Ominus(U_18445)),U_18447)),U_18448)),U_18449)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_18445),hAPP(c_List_Omonoid__add__class_Olistsum(U_18445),hAPP(hAPP(c_List_Omap(U_18446,U_18445),U_18447),U_18449))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18445),hAPP(hAPP(c_List_Omap(U_18446,U_18445),U_18448),U_18449)))
    | ~ class_Groups_Oab__group__add(U_18445) ),
    inference(clausify,[status(thm)],[f_4449_3]) ).

fof(f_4450_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_4450_2,plain,
    ! [U_18454,U_18453,U_18452,U_18451,U_18450] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18450),hAPP(hAPP(c_List_Omap(U_18451,U_18450),hAPP(hAPP(c_COMBC(U_18451,U_18450,U_18450),hAPP(hAPP(c_COMBB(U_18450,tc_fun(U_18450,U_18450),U_18451),c_Groups_Otimes__class_Otimes(U_18450)),U_18452)),U_18453)),U_18454)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18450),hAPP(c_List_Omonoid__add__class_Olistsum(U_18450),hAPP(hAPP(c_List_Omap(U_18451,U_18450),U_18452),U_18454))),U_18453)
      | ~ class_Rings_Osemiring__0(U_18450) ),
    inference(variable_rename,[status(thm)],[f_4450_1]) ).

fof(f_4450_3,plain,
    ! [U_18450,U_18451,U_18452,U_18453,U_18454] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18450),hAPP(hAPP(c_List_Omap(U_18451,U_18450),hAPP(hAPP(c_COMBC(U_18451,U_18450,U_18450),hAPP(hAPP(c_COMBB(U_18450,tc_fun(U_18450,U_18450),U_18451),c_Groups_Otimes__class_Otimes(U_18450)),U_18452)),U_18453)),U_18454)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18450),hAPP(c_List_Omonoid__add__class_Olistsum(U_18450),hAPP(hAPP(c_List_Omap(U_18451,U_18450),U_18452),U_18454))),U_18453)
      | ~ class_Rings_Osemiring__0(U_18450) ),
    inference(definitional_conversion,[status(esa)],[f_4450_2]) ).

cnf(f_4450_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18450),hAPP(hAPP(c_List_Omap(U_18451,U_18450),hAPP(hAPP(c_COMBC(U_18451,U_18450,U_18450),hAPP(hAPP(c_COMBB(U_18450,tc_fun(U_18450,U_18450),U_18451),c_Groups_Otimes__class_Otimes(U_18450)),U_18452)),U_18453)),U_18454)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18450),hAPP(c_List_Omonoid__add__class_Olistsum(U_18450),hAPP(hAPP(c_List_Omap(U_18451,U_18450),U_18452),U_18454))),U_18453)
    | ~ class_Rings_Osemiring__0(U_18450) ),
    inference(clausify,[status(thm)],[f_4450_3]) ).

fof(f_4451_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_4451_2,plain,
    ! [U_18459,U_18458,U_18457,U_18456,U_18455] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18455),hAPP(hAPP(c_List_Omap(U_18456,U_18455),hAPP(hAPP(c_COMBB(U_18455,U_18455,U_18456),hAPP(c_Groups_Otimes__class_Otimes(U_18455),U_18457)),U_18458)),U_18459)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18455),U_18457),hAPP(c_List_Omonoid__add__class_Olistsum(U_18455),hAPP(hAPP(c_List_Omap(U_18456,U_18455),U_18458),U_18459)))
      | ~ class_Rings_Osemiring__0(U_18455) ),
    inference(variable_rename,[status(thm)],[f_4451_1]) ).

fof(f_4451_3,plain,
    ! [U_18455,U_18456,U_18457,U_18458,U_18459] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18455),hAPP(hAPP(c_List_Omap(U_18456,U_18455),hAPP(hAPP(c_COMBB(U_18455,U_18455,U_18456),hAPP(c_Groups_Otimes__class_Otimes(U_18455),U_18457)),U_18458)),U_18459)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18455),U_18457),hAPP(c_List_Omonoid__add__class_Olistsum(U_18455),hAPP(hAPP(c_List_Omap(U_18456,U_18455),U_18458),U_18459)))
      | ~ class_Rings_Osemiring__0(U_18455) ),
    inference(definitional_conversion,[status(esa)],[f_4451_2]) ).

cnf(f_4451_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18455),hAPP(hAPP(c_List_Omap(U_18456,U_18455),hAPP(hAPP(c_COMBB(U_18455,U_18455,U_18456),hAPP(c_Groups_Otimes__class_Otimes(U_18455),U_18457)),U_18458)),U_18459)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18455),U_18457),hAPP(c_List_Omonoid__add__class_Olistsum(U_18455),hAPP(hAPP(c_List_Omap(U_18456,U_18455),U_18458),U_18459)))
    | ~ class_Rings_Osemiring__0(U_18455) ),
    inference(clausify,[status(thm)],[f_4451_3]) ).

fof(f_4452_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_4452_2,plain,
    ! [U_18464,U_18463,U_18462,U_18461,U_18460] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18460),hAPP(hAPP(c_List_Omap(U_18461,U_18460),hAPP(hAPP(c_COMBS(U_18461,U_18460,U_18460),hAPP(hAPP(c_COMBB(U_18460,tc_fun(U_18460,U_18460),U_18461),c_Groups_Oplus__class_Oplus(U_18460)),U_18462)),U_18463)),U_18464)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18460),hAPP(c_List_Omonoid__add__class_Olistsum(U_18460),hAPP(hAPP(c_List_Omap(U_18461,U_18460),U_18462),U_18464))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18460),hAPP(hAPP(c_List_Omap(U_18461,U_18460),U_18463),U_18464)))
      | ~ class_Groups_Ocomm__monoid__add(U_18460) ),
    inference(variable_rename,[status(thm)],[f_4452_1]) ).

fof(f_4452_3,plain,
    ! [U_18460,U_18461,U_18462,U_18463,U_18464] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18460),hAPP(hAPP(c_List_Omap(U_18461,U_18460),hAPP(hAPP(c_COMBS(U_18461,U_18460,U_18460),hAPP(hAPP(c_COMBB(U_18460,tc_fun(U_18460,U_18460),U_18461),c_Groups_Oplus__class_Oplus(U_18460)),U_18462)),U_18463)),U_18464)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18460),hAPP(c_List_Omonoid__add__class_Olistsum(U_18460),hAPP(hAPP(c_List_Omap(U_18461,U_18460),U_18462),U_18464))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18460),hAPP(hAPP(c_List_Omap(U_18461,U_18460),U_18463),U_18464)))
      | ~ class_Groups_Ocomm__monoid__add(U_18460) ),
    inference(definitional_conversion,[status(esa)],[f_4452_2]) ).

cnf(f_4452_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18460),hAPP(hAPP(c_List_Omap(U_18461,U_18460),hAPP(hAPP(c_COMBS(U_18461,U_18460,U_18460),hAPP(hAPP(c_COMBB(U_18460,tc_fun(U_18460,U_18460),U_18461),c_Groups_Oplus__class_Oplus(U_18460)),U_18462)),U_18463)),U_18464)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18460),hAPP(c_List_Omonoid__add__class_Olistsum(U_18460),hAPP(hAPP(c_List_Omap(U_18461,U_18460),U_18462),U_18464))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18460),hAPP(hAPP(c_List_Omap(U_18461,U_18460),U_18463),U_18464)))
    | ~ class_Groups_Ocomm__monoid__add(U_18460) ),
    inference(clausify,[status(thm)],[f_4452_3]) ).

fof(f_4453_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_4453_2,plain,
    ! [U_18467,U_18466,U_18465] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18465),hAPP(hAPP(c_List_Omap(U_18466,U_18465),hAPP(c_COMBK(U_18465,U_18466),c_Groups_Ozero__class_Ozero(U_18465))),U_18467)) = c_Groups_Ozero__class_Ozero(U_18465)
      | ~ class_Groups_Omonoid__add(U_18465) ),
    inference(variable_rename,[status(thm)],[f_4453_1]) ).

fof(f_4453_3,plain,
    ! [U_18465,U_18466,U_18467] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18465),hAPP(hAPP(c_List_Omap(U_18466,U_18465),hAPP(c_COMBK(U_18465,U_18466),c_Groups_Ozero__class_Ozero(U_18465))),U_18467)) = c_Groups_Ozero__class_Ozero(U_18465)
      | ~ class_Groups_Omonoid__add(U_18465) ),
    inference(definitional_conversion,[status(esa)],[f_4453_2]) ).

cnf(f_4453_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18465),hAPP(hAPP(c_List_Omap(U_18466,U_18465),hAPP(c_COMBK(U_18465,U_18466),c_Groups_Ozero__class_Ozero(U_18465))),U_18467)) = c_Groups_Ozero__class_Ozero(U_18465)
    | ~ class_Groups_Omonoid__add(U_18465) ),
    inference(clausify,[status(thm)],[f_4453_3]) ).

fof(f_4454_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_4454_2,plain,
    ! [U_18469,U_18468] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18468),hAPP(c_Groups_Oabs__class_Oabs(U_18468),hAPP(c_List_Omonoid__add__class_Olistsum(U_18468),U_18469))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18468),hAPP(hAPP(c_List_Omap(U_18468,U_18468),c_Groups_Oabs__class_Oabs(U_18468)),U_18469))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_18468) ),
    inference(variable_rename,[status(thm)],[f_4454_1]) ).

fof(f_4454_3,plain,
    ! [U_18468,U_18469] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18468),hAPP(c_Groups_Oabs__class_Oabs(U_18468),hAPP(c_List_Omonoid__add__class_Olistsum(U_18468),U_18469))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18468),hAPP(hAPP(c_List_Omap(U_18468,U_18468),c_Groups_Oabs__class_Oabs(U_18468)),U_18469))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_18468) ),
    inference(definitional_conversion,[status(esa)],[f_4454_2]) ).

cnf(f_4454_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18468),hAPP(c_Groups_Oabs__class_Oabs(U_18468),hAPP(c_List_Omonoid__add__class_Olistsum(U_18468),U_18469))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18468),hAPP(hAPP(c_List_Omap(U_18468,U_18468),c_Groups_Oabs__class_Oabs(U_18468)),U_18469))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_18468) ),
    inference(clausify,[status(thm)],[f_4454_3]) ).

fof(f_4455_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_4455_2,plain,
    ! [U_18473,U_18472,U_18471,U_18470] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_18470),hAPP(c_List_Omonoid__add__class_Olistsum(U_18470),hAPP(hAPP(c_List_Omap(U_18471,U_18470),U_18472),U_18473))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18470),hAPP(hAPP(c_List_Omap(U_18471,U_18470),hAPP(c_Fun_Ocomp(U_18470,U_18470,U_18471,c_Groups_Ouminus__class_Ouminus(U_18470)),U_18472)),U_18473))
      | ~ class_Groups_Oab__group__add(U_18470) ),
    inference(variable_rename,[status(thm)],[f_4455_1]) ).

fof(f_4455_3,plain,
    ! [U_18470,U_18471,U_18472,U_18473] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_18470),hAPP(c_List_Omonoid__add__class_Olistsum(U_18470),hAPP(hAPP(c_List_Omap(U_18471,U_18470),U_18472),U_18473))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18470),hAPP(hAPP(c_List_Omap(U_18471,U_18470),hAPP(c_Fun_Ocomp(U_18470,U_18470,U_18471,c_Groups_Ouminus__class_Ouminus(U_18470)),U_18472)),U_18473))
      | ~ class_Groups_Oab__group__add(U_18470) ),
    inference(definitional_conversion,[status(esa)],[f_4455_2]) ).

cnf(f_4455_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_18470),hAPP(c_List_Omonoid__add__class_Olistsum(U_18470),hAPP(hAPP(c_List_Omap(U_18471,U_18470),U_18472),U_18473))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18470),hAPP(hAPP(c_List_Omap(U_18471,U_18470),hAPP(c_Fun_Ocomp(U_18470,U_18470,U_18471,c_Groups_Ouminus__class_Ouminus(U_18470)),U_18472)),U_18473))
    | ~ class_Groups_Oab__group__add(U_18470) ),
    inference(clausify,[status(thm)],[f_4455_3]) ).

fof(f_4456_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_4456_2,plain,
    ! [U_18475,U_18474] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18474),U_18475) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18474,U_18474),c_COMBI(U_18474)),hAPP(c_List_Oset(U_18474),U_18475))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18474),U_18475))
      | ~ class_Groups_Ocomm__monoid__add(U_18474) ),
    inference(variable_rename,[status(thm)],[f_4456_1]) ).

fof(f_4456_3,plain,
    ! [U_18474,U_18475] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18474),U_18475) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18474,U_18474),c_COMBI(U_18474)),hAPP(c_List_Oset(U_18474),U_18475))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18474),U_18475))
      | ~ class_Groups_Ocomm__monoid__add(U_18474) ),
    inference(definitional_conversion,[status(esa)],[f_4456_2]) ).

cnf(f_4456_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18474),U_18475) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18474,U_18474),c_COMBI(U_18474)),hAPP(c_List_Oset(U_18474),U_18475))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18474),U_18475))
    | ~ class_Groups_Ocomm__monoid__add(U_18474) ),
    inference(clausify,[status(thm)],[f_4456_3]) ).

fof(f_4457_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_4457_2,plain,
    ! [U_18477,U_18476] : c_Random_Oselect__weight(U_18476,U_18477) = 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_18476,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_18476),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18476)),U_18477)))),hAPP(hAPP(c_COMBB(U_18476,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18476,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18476,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(U_18476,U_18477))),
    inference(variable_rename,[status(thm)],[f_4457_1]) ).

fof(f_4457_3,plain,
    ! [U_18476,U_18477] : c_Random_Oselect__weight(U_18476,U_18477) = 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_18476,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_18476),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18476)),U_18477)))),hAPP(hAPP(c_COMBB(U_18476,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18476,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18476,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(U_18476,U_18477))),
    inference(definitional_conversion,[status(esa)],[f_4457_2]) ).

cnf(f_4457_4,plain,
    c_Random_Oselect__weight(U_18476,U_18477) = 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_18476,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_18476),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18476)),U_18477)))),hAPP(hAPP(c_COMBB(U_18476,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18476,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18476,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(U_18476,U_18477))),
    inference(clausify,[status(thm)],[f_4457_3]) ).

fof(f_4458_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_4458_2,plain,
    ! [U_18481,U_18480,U_18479,U_18478] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18478),hAPP(hAPP(c_List_Omap(U_18479,U_18478),U_18481),U_18480)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18479,U_18478),U_18481),hAPP(c_List_Oset(U_18479),U_18480))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18479),U_18480))
      | ~ class_Groups_Ocomm__monoid__add(U_18478) ),
    inference(variable_rename,[status(thm)],[f_4458_1]) ).

fof(f_4458_3,plain,
    ! [U_18478,U_18479,U_18480,U_18481] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18478),hAPP(hAPP(c_List_Omap(U_18479,U_18478),U_18481),U_18480)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18479,U_18478),U_18481),hAPP(c_List_Oset(U_18479),U_18480))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18479),U_18480))
      | ~ class_Groups_Ocomm__monoid__add(U_18478) ),
    inference(definitional_conversion,[status(esa)],[f_4458_2]) ).

cnf(f_4458_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18478),hAPP(hAPP(c_List_Omap(U_18479,U_18478),U_18481),U_18480)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18479,U_18478),U_18481),hAPP(c_List_Oset(U_18479),U_18480))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18479),U_18480))
    | ~ class_Groups_Ocomm__monoid__add(U_18478) ),
    inference(clausify,[status(thm)],[f_4458_3]) ).

fof(f_4459_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_4459_2,plain,
    ! [U_18485,U_18484,U_18483,U_18482] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18482),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18482),U_18483),c_List_Oupto(U_18484,U_18485))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18482),U_18483),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18484,U_18485)))
      | ~ class_Groups_Ocomm__monoid__add(U_18482) ),
    inference(variable_rename,[status(thm)],[f_4459_1]) ).

fof(f_4459_3,plain,
    ! [U_18482,U_18483,U_18484,U_18485] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18482),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18482),U_18483),c_List_Oupto(U_18484,U_18485))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18482),U_18483),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18484,U_18485)))
      | ~ class_Groups_Ocomm__monoid__add(U_18482) ),
    inference(definitional_conversion,[status(esa)],[f_4459_2]) ).

cnf(f_4459_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18482),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18482),U_18483),c_List_Oupto(U_18484,U_18485))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18482),U_18483),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18484,U_18485)))
    | ~ class_Groups_Ocomm__monoid__add(U_18482) ),
    inference(clausify,[status(thm)],[f_4459_3]) ).

fof(f_4460_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_4460_2,plain,
    ! [U_18489,U_18488,U_18487,U_18486] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18486),U_18487),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18488,U_18489))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18486),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18486),U_18487),c_List_Oupto(U_18488,U_18489)))
      | ~ class_Groups_Ocomm__monoid__add(U_18486) ),
    inference(variable_rename,[status(thm)],[f_4460_1]) ).

fof(f_4460_3,plain,
    ! [U_18486,U_18487,U_18488,U_18489] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18486),U_18487),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18488,U_18489))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18486),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18486),U_18487),c_List_Oupto(U_18488,U_18489)))
      | ~ class_Groups_Ocomm__monoid__add(U_18486) ),
    inference(definitional_conversion,[status(esa)],[f_4460_2]) ).

cnf(f_4460_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18486),U_18487),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18488,U_18489))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18486),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18486),U_18487),c_List_Oupto(U_18488,U_18489)))
    | ~ class_Groups_Ocomm__monoid__add(U_18486) ),
    inference(clausify,[status(thm)],[f_4460_3]) ).

fof(f_4461_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_4461_2,plain,
    ! [U_18493,U_18492,U_18491,U_18490] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18490),hAPP(hAPP(c_List_Omap(U_18491,U_18490),hAPP(c_COMBK(U_18490,U_18491),U_18492)),U_18493)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18490),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_18490),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18491)),U_18493))),U_18492)
      | ~ class_Rings_Osemiring__1(U_18490) ),
    inference(variable_rename,[status(thm)],[f_4461_1]) ).

fof(f_4461_3,plain,
    ! [U_18490,U_18491,U_18492,U_18493] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18490),hAPP(hAPP(c_List_Omap(U_18491,U_18490),hAPP(c_COMBK(U_18490,U_18491),U_18492)),U_18493)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18490),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_18490),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18491)),U_18493))),U_18492)
      | ~ class_Rings_Osemiring__1(U_18490) ),
    inference(definitional_conversion,[status(esa)],[f_4461_2]) ).

cnf(f_4461_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18490),hAPP(hAPP(c_List_Omap(U_18491,U_18490),hAPP(c_COMBK(U_18490,U_18491),U_18492)),U_18493)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18490),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_18490),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18491)),U_18493))),U_18492)
    | ~ class_Rings_Osemiring__1(U_18490) ),
    inference(clausify,[status(thm)],[f_4461_3]) ).

fof(f_4462_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_4462_2,plain,
    ! [U_18498,U_18497,U_18496,U_18495,U_18494] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18494),hAPP(hAPP(c_List_Omap(U_18495,U_18494),U_18498),U_18497)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18494),hAPP(U_18498,U_18496)),hAPP(c_List_Omonoid__add__class_Olistsum(U_18494),hAPP(hAPP(c_List_Omap(U_18495,U_18494),U_18498),c_List_Oremove1(U_18495,U_18496,U_18497))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18495),U_18496),hAPP(c_List_Oset(U_18495),U_18497)))
      | ~ class_Groups_Ocomm__monoid__add(U_18494) ),
    inference(variable_rename,[status(thm)],[f_4462_1]) ).

fof(f_4462_3,plain,
    ! [U_18494,U_18495,U_18496,U_18497,U_18498] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18494),hAPP(hAPP(c_List_Omap(U_18495,U_18494),U_18498),U_18497)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18494),hAPP(U_18498,U_18496)),hAPP(c_List_Omonoid__add__class_Olistsum(U_18494),hAPP(hAPP(c_List_Omap(U_18495,U_18494),U_18498),c_List_Oremove1(U_18495,U_18496,U_18497))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18495),U_18496),hAPP(c_List_Oset(U_18495),U_18497)))
      | ~ class_Groups_Ocomm__monoid__add(U_18494) ),
    inference(definitional_conversion,[status(esa)],[f_4462_2]) ).

cnf(f_4462_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18494),hAPP(hAPP(c_List_Omap(U_18495,U_18494),U_18498),U_18497)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18494),hAPP(U_18498,U_18496)),hAPP(c_List_Omonoid__add__class_Olistsum(U_18494),hAPP(hAPP(c_List_Omap(U_18495,U_18494),U_18498),c_List_Oremove1(U_18495,U_18496,U_18497))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18495),U_18496),hAPP(c_List_Oset(U_18495),U_18497)))
    | ~ class_Groups_Ocomm__monoid__add(U_18494) ),
    inference(clausify,[status(thm)],[f_4462_3]) ).

fof(f_4463_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_4463_2,plain,
    ! [U_18501,U_18500,U_18499] :
      ( hBOOL(hAPP(hAPP(c_member(U_18499),hAPP(c_Product__Type_Ofst(U_18499,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(U_18499,U_18500),U_18501))),hAPP(c_List_Oset(U_18499),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18499),U_18499),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18499)),U_18500))))
      | ~ 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_18499),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18499)),U_18500)))) ),
    inference(variable_rename,[status(thm)],[f_4463_1]) ).

fof(f_4463_3,plain,
    ! [U_18499,U_18500,U_18501] :
      ( hBOOL(hAPP(hAPP(c_member(U_18499),hAPP(c_Product__Type_Ofst(U_18499,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(U_18499,U_18500),U_18501))),hAPP(c_List_Oset(U_18499),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18499),U_18499),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18499)),U_18500))))
      | ~ 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_18499),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18499)),U_18500)))) ),
    inference(definitional_conversion,[status(esa)],[f_4463_2]) ).

cnf(f_4463_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18499),hAPP(c_Product__Type_Ofst(U_18499,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(U_18499,U_18500),U_18501))),hAPP(c_List_Oset(U_18499),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18499),U_18499),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18499)),U_18500))))
    | ~ 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_18499),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18499)),U_18500)))) ),
    inference(clausify,[status(thm)],[f_4463_3]) ).

fof(f_4464_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_4464_2,plain,
    ! [U_18505,U_18504,U_18503,U_18502] :
      ( ( ( c_Nitpick_Osetsum_H(U_18503,U_18502,U_18505,U_18504) = c_Groups_Ozero__class_Ozero(U_18502)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_18503),U_18504)) )
        & ( c_Nitpick_Osetsum_H(U_18503,U_18502,U_18505,U_18504) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18502),hAPP(hAPP(c_List_Omap(U_18503,U_18502),U_18505),c_Hilbert__Choice_OEps(tc_List_Olist(U_18503),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18503),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_18503)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18503),tc_fun(U_18503,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18503,tc_HOL_Obool),tc_fun(tc_fun(U_18503,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18503)),c_fequal),c_List_Oset(U_18503))),U_18504))),c_List_Odistinct(U_18503)))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18503),U_18504)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_18502) ),
    inference(variable_rename,[status(thm)],[f_4464_1]) ).

fof(f_4464_3,plain,
    ( ! [U_18502,U_18503,U_18504,U_18505] :
        ( c_Nitpick_Osetsum_H(U_18503,U_18502,U_18505,U_18504) = c_Groups_Ozero__class_Ozero(U_18502)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_18503),U_18504))
        | ~ sP1151(U_18502,U_18503,U_18504,U_18505) )
    & ! [U_18502,U_18503,U_18504,U_18505] :
        ( c_Nitpick_Osetsum_H(U_18503,U_18502,U_18505,U_18504) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18502),hAPP(hAPP(c_List_Omap(U_18503,U_18502),U_18505),c_Hilbert__Choice_OEps(tc_List_Olist(U_18503),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18503),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_18503)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18503),tc_fun(U_18503,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18503,tc_HOL_Obool),tc_fun(tc_fun(U_18503,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18503)),c_fequal),c_List_Oset(U_18503))),U_18504))),c_List_Odistinct(U_18503)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18503),U_18504))
        | ~ sP1151(U_18502,U_18503,U_18504,U_18505) )
    & ! [U_18502,U_18503,U_18504,U_18505] :
        ( sP1151(U_18502,U_18503,U_18504,U_18505)
        | ~ class_Groups_Ocomm__monoid__add(U_18502) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1151])],[f_4464_2]) ).

cnf(f_4464_4,plain,
    ( sP1151(U_18502,U_18503,U_18504,U_18505)
    | ~ class_Groups_Ocomm__monoid__add(U_18502) ),
    inference(clausify,[status(thm)],[f_4464_3]) ).

cnf(f_4464_5,plain,
    ( c_Nitpick_Osetsum_H(U_18503,U_18502,U_18505,U_18504) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18502),hAPP(hAPP(c_List_Omap(U_18503,U_18502),U_18505),c_Hilbert__Choice_OEps(tc_List_Olist(U_18503),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18503),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_18503)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18503),tc_fun(U_18503,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18503,tc_HOL_Obool),tc_fun(tc_fun(U_18503,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18503)),c_fequal),c_List_Oset(U_18503))),U_18504))),c_List_Odistinct(U_18503)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18503),U_18504))
    | ~ sP1151(U_18502,U_18503,U_18504,U_18505) ),
    inference(clausify,[status(thm)],[f_4464_3]) ).

cnf(f_4464_6,plain,
    ( c_Nitpick_Osetsum_H(U_18503,U_18502,U_18505,U_18504) = c_Groups_Ozero__class_Ozero(U_18502)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_18503),U_18504))
    | ~ sP1151(U_18502,U_18503,U_18504,U_18505) ),
    inference(clausify,[status(thm)],[f_4464_3]) ).

fof(f_4465_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_4465_2,plain,
    ! [U_18510,U_18509,U_18508,U_18507,U_18506] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18509,U_18506,U_18507,U_18508,U_18510) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18509,U_18506,U_18507),U_18508),U_18510)
      | hBOOL(hAPP(hAPP(c_member(U_18506),hAPP(U_18507,U_18508)),hAPP(c_Set_Oimage(U_18509,U_18506,U_18507),hAPP(c_List_Oset(U_18509),U_18510))))
      | ~ class_Orderings_Olinorder(U_18506) ),
    inference(variable_rename,[status(thm)],[f_4465_1]) ).

fof(f_4465_3,plain,
    ! [U_18508,U_18507,U_18506,U_18509,U_18510] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18509,U_18506,U_18507,U_18508,U_18510) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18509,U_18506,U_18507),U_18508),U_18510)
      | hBOOL(hAPP(hAPP(c_member(U_18506),hAPP(U_18507,U_18508)),hAPP(c_Set_Oimage(U_18509,U_18506,U_18507),hAPP(c_List_Oset(U_18509),U_18510))))
      | ~ class_Orderings_Olinorder(U_18506) ),
    inference(definitional_conversion,[status(esa)],[f_4465_2]) ).

cnf(f_4465_4,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_18509,U_18506,U_18507,U_18508,U_18510) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18509,U_18506,U_18507),U_18508),U_18510)
    | hBOOL(hAPP(hAPP(c_member(U_18506),hAPP(U_18507,U_18508)),hAPP(c_Set_Oimage(U_18509,U_18506,U_18507),hAPP(c_List_Oset(U_18509),U_18510))))
    | ~ class_Orderings_Olinorder(U_18506) ),
    inference(clausify,[status(thm)],[f_4465_3]) ).

fof(f_4466_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_4466_2,plain,
    ! [U_18513] :
      ( ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18513) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_18512] :
            ( U_18512 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18512),hAPP(c_List_Oset(tc_Nat_Onat),U_18513))) ) )
      & ( ! [U_18511] :
            ( U_18511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18511),hAPP(c_List_Oset(tc_Nat_Onat),U_18513))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18513) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4466_1]) ).

fof(f_4466_3,plain,
    ( ! [U_18515] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18515) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_18512] :
            ( U_18512 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18512),hAPP(c_List_Oset(tc_Nat_Onat),U_18515))) ) )
    & ! [U_18514] :
        ( ! [U_18511] :
            ( U_18511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18511),hAPP(c_List_Oset(tc_Nat_Onat),U_18514))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18514) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4466_2]) ).

fof(f_4466_4,plain,
    ( ! [U_18515] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18515) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( sK465(U_18515) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK465(U_18515)),hAPP(c_List_Oset(tc_Nat_Onat),U_18515))) ) )
    & ! [U_18514] :
        ( ! [U_18511] :
            ( U_18511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18511),hAPP(c_List_Oset(tc_Nat_Onat),U_18514))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18514) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK465]),skolemize(U_18512,sK465(U_18515))],[f_4466_3]) ).

fof(f_4466_5,plain,
    ( ! [U_18515] :
        ( sK465(U_18515) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1152(U_18515) )
    & ! [U_18515] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK465(U_18515)),hAPP(c_List_Oset(tc_Nat_Onat),U_18515)))
        | ~ sP1152(U_18515) )
    & ! [U_18515] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18515) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP1152(U_18515) )
    & ! [U_18511,U_18514] :
        ( U_18511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18511),hAPP(c_List_Oset(tc_Nat_Onat),U_18514)))
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18514) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1152])],[f_4466_4]) ).

cnf(f_4466_6,plain,
    ( U_18511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18511),hAPP(c_List_Oset(tc_Nat_Onat),U_18514)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18514) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4466_5]) ).

cnf(f_4466_7,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18515) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP1152(U_18515) ),
    inference(clausify,[status(thm)],[f_4466_5]) ).

cnf(f_4466_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK465(U_18515)),hAPP(c_List_Oset(tc_Nat_Onat),U_18515)))
    | ~ sP1152(U_18515) ),
    inference(clausify,[status(thm)],[f_4466_5]) ).

cnf(f_4466_9,plain,
    ( sK465(U_18515) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1152(U_18515) ),
    inference(clausify,[status(thm)],[f_4466_5]) ).

fof(f_4467_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_4467_2,plain,
    ! [U_18520,U_18519,U_18518,U_18517,U_18516] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18517),c_List_Olinorder__class_Oinsort__insert__key(U_18517,U_18516,U_18519,U_18520,U_18518)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18517),U_18518))
      | ~ class_Orderings_Olinorder(U_18516) ),
    inference(variable_rename,[status(thm)],[f_4467_1]) ).

fof(f_4467_3,plain,
    ! [U_18516,U_18518,U_18519,U_18517,U_18520] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18517),c_List_Olinorder__class_Oinsort__insert__key(U_18517,U_18516,U_18519,U_18520,U_18518)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18517),U_18518))
      | ~ class_Orderings_Olinorder(U_18516) ),
    inference(definitional_conversion,[status(esa)],[f_4467_2]) ).

cnf(f_4467_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18517),c_List_Olinorder__class_Oinsort__insert__key(U_18517,U_18516,U_18519,U_18520,U_18518)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18517),U_18518))
    | ~ class_Orderings_Olinorder(U_18516) ),
    inference(clausify,[status(thm)],[f_4467_3]) ).

fof(f_4468_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_4468_2,plain,
    ! [U_18523,U_18522,U_18521] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18521,U_18521,c_COMBI(U_18521),U_18522,U_18523) = U_18523
      | ~ hBOOL(hAPP(hAPP(c_member(U_18521),U_18522),hAPP(c_List_Oset(U_18521),U_18523)))
      | ~ class_Orderings_Olinorder(U_18521) ),
    inference(variable_rename,[status(thm)],[f_4468_1]) ).

fof(f_4468_3,plain,
    ! [U_18521,U_18522,U_18523] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18521,U_18521,c_COMBI(U_18521),U_18522,U_18523) = U_18523
      | ~ hBOOL(hAPP(hAPP(c_member(U_18521),U_18522),hAPP(c_List_Oset(U_18521),U_18523)))
      | ~ class_Orderings_Olinorder(U_18521) ),
    inference(definitional_conversion,[status(esa)],[f_4468_2]) ).

cnf(f_4468_4,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_18521,U_18521,c_COMBI(U_18521),U_18522,U_18523) = U_18523
    | ~ hBOOL(hAPP(hAPP(c_member(U_18521),U_18522),hAPP(c_List_Oset(U_18521),U_18523)))
    | ~ class_Orderings_Olinorder(U_18521) ),
    inference(clausify,[status(thm)],[f_4468_3]) ).

fof(f_4469_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_4469_2,plain,
    ! [U_18526,U_18525,U_18524] :
      ( hAPP(c_List_Oset(U_18524),c_List_Olinorder__class_Oinsort__insert__key(U_18524,U_18524,c_COMBI(U_18524),U_18525,U_18526)) = hAPP(hAPP(c_Set_Oinsert(U_18524),U_18525),hAPP(c_List_Oset(U_18524),U_18526))
      | ~ class_Orderings_Olinorder(U_18524) ),
    inference(variable_rename,[status(thm)],[f_4469_1]) ).

fof(f_4469_3,plain,
    ! [U_18524,U_18525,U_18526] :
      ( hAPP(c_List_Oset(U_18524),c_List_Olinorder__class_Oinsort__insert__key(U_18524,U_18524,c_COMBI(U_18524),U_18525,U_18526)) = hAPP(hAPP(c_Set_Oinsert(U_18524),U_18525),hAPP(c_List_Oset(U_18524),U_18526))
      | ~ class_Orderings_Olinorder(U_18524) ),
    inference(definitional_conversion,[status(esa)],[f_4469_2]) ).

cnf(f_4469_4,plain,
    ( hAPP(c_List_Oset(U_18524),c_List_Olinorder__class_Oinsort__insert__key(U_18524,U_18524,c_COMBI(U_18524),U_18525,U_18526)) = hAPP(hAPP(c_Set_Oinsert(U_18524),U_18525),hAPP(c_List_Oset(U_18524),U_18526))
    | ~ class_Orderings_Olinorder(U_18524) ),
    inference(clausify,[status(thm)],[f_4469_3]) ).

fof(f_4470_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_4470_2,plain,
    ! [U_18531,U_18530,U_18529,U_18528,U_18527] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18530,U_18527,U_18528,U_18529,U_18531) = U_18531
      | ~ hBOOL(hAPP(hAPP(c_member(U_18527),hAPP(U_18528,U_18529)),hAPP(c_Set_Oimage(U_18530,U_18527,U_18528),hAPP(c_List_Oset(U_18530),U_18531))))
      | ~ class_Orderings_Olinorder(U_18527) ),
    inference(variable_rename,[status(thm)],[f_4470_1]) ).

fof(f_4470_3,plain,
    ! [U_18527,U_18528,U_18529,U_18530,U_18531] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18530,U_18527,U_18528,U_18529,U_18531) = U_18531
      | ~ hBOOL(hAPP(hAPP(c_member(U_18527),hAPP(U_18528,U_18529)),hAPP(c_Set_Oimage(U_18530,U_18527,U_18528),hAPP(c_List_Oset(U_18530),U_18531))))
      | ~ class_Orderings_Olinorder(U_18527) ),
    inference(definitional_conversion,[status(esa)],[f_4470_2]) ).

cnf(f_4470_4,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_18530,U_18527,U_18528,U_18529,U_18531) = U_18531
    | ~ hBOOL(hAPP(hAPP(c_member(U_18527),hAPP(U_18528,U_18529)),hAPP(c_Set_Oimage(U_18530,U_18527,U_18528),hAPP(c_List_Oset(U_18530),U_18531))))
    | ~ class_Orderings_Olinorder(U_18527) ),
    inference(clausify,[status(thm)],[f_4470_3]) ).

fof(f_4471_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_4471_2,plain,
    ! [U_18534,U_18533,U_18532] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18532,U_18532,c_COMBI(U_18532),U_18533,U_18534) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18532,U_18532,c_COMBI(U_18532)),U_18533),U_18534)
      | hBOOL(hAPP(hAPP(c_member(U_18532),U_18533),hAPP(c_List_Oset(U_18532),U_18534)))
      | ~ class_Orderings_Olinorder(U_18532) ),
    inference(variable_rename,[status(thm)],[f_4471_1]) ).

fof(f_4471_3,plain,
    ! [U_18532,U_18533,U_18534] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18532,U_18532,c_COMBI(U_18532),U_18533,U_18534) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18532,U_18532,c_COMBI(U_18532)),U_18533),U_18534)
      | hBOOL(hAPP(hAPP(c_member(U_18532),U_18533),hAPP(c_List_Oset(U_18532),U_18534)))
      | ~ class_Orderings_Olinorder(U_18532) ),
    inference(definitional_conversion,[status(esa)],[f_4471_2]) ).

cnf(f_4471_4,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_18532,U_18532,c_COMBI(U_18532),U_18533,U_18534) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18532,U_18532,c_COMBI(U_18532)),U_18533),U_18534)
    | hBOOL(hAPP(hAPP(c_member(U_18532),U_18533),hAPP(c_List_Oset(U_18532),U_18534)))
    | ~ class_Orderings_Olinorder(U_18532) ),
    inference(clausify,[status(thm)],[f_4471_3]) ).

fof(f_4472_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_4472_2,plain,
    ! [U_18540,U_18539,U_18538,U_18537,U_18536,U_18535] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18535),tc_List_Olist(U_18535))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18535),tc_List_Olist(U_18535)),hAPP(hAPP(c_List_Olist_OCons(U_18535),U_18536),U_18537)),hAPP(hAPP(c_List_Olist_OCons(U_18535),U_18538),U_18539))),c_List_Olexord(U_18535,U_18540)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18535),tc_List_Olist(U_18535))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18535),tc_List_Olist(U_18535)),U_18537),U_18539)),c_List_Olexord(U_18535,U_18540)))
            | U_18536 != U_18538 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18535,U_18535)),hAPP(hAPP(c_Product__Type_OPair(U_18535,U_18535),U_18536),U_18538)),U_18540)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18535),tc_List_Olist(U_18535))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18535),tc_List_Olist(U_18535)),U_18537),U_18539)),c_List_Olexord(U_18535,U_18540)))
          & U_18536 = U_18538 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18535,U_18535)),hAPP(hAPP(c_Product__Type_OPair(U_18535,U_18535),U_18536),U_18538)),U_18540))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18535),tc_List_Olist(U_18535))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18535),tc_List_Olist(U_18535)),hAPP(hAPP(c_List_Olist_OCons(U_18535),U_18536),U_18537)),hAPP(hAPP(c_List_Olist_OCons(U_18535),U_18538),U_18539))),c_List_Olexord(U_18535,U_18540))) ) ),
    inference(variable_rename,[status(thm)],[f_4472_1]) ).

fof(f_4472_3,plain,
    ( ! [U_18552,U_18550,U_18548,U_18546,U_18544,U_18542] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18542),tc_List_Olist(U_18542))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18542),tc_List_Olist(U_18542)),hAPP(hAPP(c_List_Olist_OCons(U_18542),U_18544),U_18546)),hAPP(hAPP(c_List_Olist_OCons(U_18542),U_18548),U_18550))),c_List_Olexord(U_18542,U_18552)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18542),tc_List_Olist(U_18542))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18542),tc_List_Olist(U_18542)),U_18546),U_18550)),c_List_Olexord(U_18542,U_18552)))
            | U_18544 != U_18548 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18542,U_18542)),hAPP(hAPP(c_Product__Type_OPair(U_18542,U_18542),U_18544),U_18548)),U_18552)) ) )
    & ! [U_18551,U_18549,U_18547,U_18545,U_18543,U_18541] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18541),tc_List_Olist(U_18541))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18541),tc_List_Olist(U_18541)),U_18545),U_18549)),c_List_Olexord(U_18541,U_18551)))
          & U_18543 = U_18547 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18541,U_18541)),hAPP(hAPP(c_Product__Type_OPair(U_18541,U_18541),U_18543),U_18547)),U_18551))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18541),tc_List_Olist(U_18541))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18541),tc_List_Olist(U_18541)),hAPP(hAPP(c_List_Olist_OCons(U_18541),U_18543),U_18545)),hAPP(hAPP(c_List_Olist_OCons(U_18541),U_18547),U_18549))),c_List_Olexord(U_18541,U_18551))) ) ),
    inference(miniscope,[status(thm)],[f_4472_2]) ).

fof(f_4472_4,plain,
    ( ! [U_18544,U_18542,U_18548,U_18550,U_18546,U_18552] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18542),tc_List_Olist(U_18542))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18542),tc_List_Olist(U_18542)),U_18546),U_18550)),c_List_Olexord(U_18542,U_18552)))
        | U_18544 != U_18548
        | ~ sP1154(U_18544,U_18542,U_18548,U_18550,U_18546,U_18552) )
    & ! [U_18544,U_18542,U_18548,U_18550,U_18546,U_18552] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18542,U_18542)),hAPP(hAPP(c_Product__Type_OPair(U_18542,U_18542),U_18544),U_18548)),U_18552))
        | ~ sP1154(U_18544,U_18542,U_18548,U_18550,U_18546,U_18552) )
    & ! [U_18541,U_18545,U_18549,U_18543,U_18547,U_18551] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18541),tc_List_Olist(U_18541))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18541),tc_List_Olist(U_18541)),U_18545),U_18549)),c_List_Olexord(U_18541,U_18551)))
        | ~ sP1153(U_18541,U_18545,U_18549,U_18543,U_18547,U_18551) )
    & ! [U_18541,U_18545,U_18549,U_18543,U_18547,U_18551] :
        ( U_18543 = U_18547
        | ~ sP1153(U_18541,U_18545,U_18549,U_18543,U_18547,U_18551) )
    & ! [U_18544,U_18542,U_18548,U_18550,U_18546,U_18552] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18542),tc_List_Olist(U_18542))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18542),tc_List_Olist(U_18542)),hAPP(hAPP(c_List_Olist_OCons(U_18542),U_18544),U_18546)),hAPP(hAPP(c_List_Olist_OCons(U_18542),U_18548),U_18550))),c_List_Olexord(U_18542,U_18552)))
        | sP1154(U_18544,U_18542,U_18548,U_18550,U_18546,U_18552) )
    & ! [U_18541,U_18545,U_18549,U_18543,U_18547,U_18551] :
        ( sP1153(U_18541,U_18545,U_18549,U_18543,U_18547,U_18551)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18541,U_18541)),hAPP(hAPP(c_Product__Type_OPair(U_18541,U_18541),U_18543),U_18547)),U_18551))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18541),tc_List_Olist(U_18541))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18541),tc_List_Olist(U_18541)),hAPP(hAPP(c_List_Olist_OCons(U_18541),U_18543),U_18545)),hAPP(hAPP(c_List_Olist_OCons(U_18541),U_18547),U_18549))),c_List_Olexord(U_18541,U_18551))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1153,sP1154])],[f_4472_3]) ).

cnf(f_4472_5,plain,
    ( sP1153(U_18541,U_18545,U_18549,U_18543,U_18547,U_18551)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18541,U_18541)),hAPP(hAPP(c_Product__Type_OPair(U_18541,U_18541),U_18543),U_18547)),U_18551))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18541),tc_List_Olist(U_18541))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18541),tc_List_Olist(U_18541)),hAPP(hAPP(c_List_Olist_OCons(U_18541),U_18543),U_18545)),hAPP(hAPP(c_List_Olist_OCons(U_18541),U_18547),U_18549))),c_List_Olexord(U_18541,U_18551))) ),
    inference(clausify,[status(thm)],[f_4472_4]) ).

cnf(f_4472_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18542),tc_List_Olist(U_18542))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18542),tc_List_Olist(U_18542)),hAPP(hAPP(c_List_Olist_OCons(U_18542),U_18544),U_18546)),hAPP(hAPP(c_List_Olist_OCons(U_18542),U_18548),U_18550))),c_List_Olexord(U_18542,U_18552)))
    | sP1154(U_18544,U_18542,U_18548,U_18550,U_18546,U_18552) ),
    inference(clausify,[status(thm)],[f_4472_4]) ).

cnf(f_4472_7,plain,
    ( U_18543 = U_18547
    | ~ sP1153(U_18541,U_18545,U_18549,U_18543,U_18547,U_18551) ),
    inference(clausify,[status(thm)],[f_4472_4]) ).

cnf(f_4472_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18541),tc_List_Olist(U_18541))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18541),tc_List_Olist(U_18541)),U_18545),U_18549)),c_List_Olexord(U_18541,U_18551)))
    | ~ sP1153(U_18541,U_18545,U_18549,U_18543,U_18547,U_18551) ),
    inference(clausify,[status(thm)],[f_4472_4]) ).

cnf(f_4472_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18542,U_18542)),hAPP(hAPP(c_Product__Type_OPair(U_18542,U_18542),U_18544),U_18548)),U_18552))
    | ~ sP1154(U_18544,U_18542,U_18548,U_18550,U_18546,U_18552) ),
    inference(clausify,[status(thm)],[f_4472_4]) ).

cnf(f_4472_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18542),tc_List_Olist(U_18542))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18542),tc_List_Olist(U_18542)),U_18546),U_18550)),c_List_Olexord(U_18542,U_18552)))
    | U_18544 != U_18548
    | ~ sP1154(U_18544,U_18542,U_18548,U_18550,U_18546,U_18552) ),
    inference(clausify,[status(thm)],[f_4472_4]) ).

fof(f_4473_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_4473_2,plain,
    ! [U_18556,U_18555,U_18554,U_18553] : hAPP(c_List_Oset(tc_prod(U_18553,U_18554)),hAPP(hAPP(c_List_Ozip(U_18553,U_18554),U_18555),U_18556)) = hAPP(c_Set_OCollect(tc_prod(U_18553,U_18554)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_18553,U_18554)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_18553,U_18554),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_18553,U_18554)),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_18553,U_18554)),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_18553,U_18554),tc_fun(tc_Nat_Onat,tc_prod(U_18553,U_18554)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_18553,U_18554),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(U_18553,U_18554)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_18553,U_18554)),c_COMBB(tc_prod(U_18553,U_18554),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_18554,tc_prod(U_18553,U_18554)),hAPP(hAPP(c_COMBB(U_18553,tc_fun(U_18554,tc_prod(U_18553,U_18554)),tc_Nat_Onat),c_Product__Type_OPair(U_18553,U_18554)),hAPP(c_List_Onth(U_18553),U_18555))),hAPP(c_List_Onth(U_18554),U_18556)))))),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_18553)),U_18555)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18554)),U_18556)))))),
    inference(variable_rename,[status(thm)],[f_4473_1]) ).

fof(f_4473_3,plain,
    ! [U_18553,U_18554,U_18555,U_18556] : hAPP(c_List_Oset(tc_prod(U_18553,U_18554)),hAPP(hAPP(c_List_Ozip(U_18553,U_18554),U_18555),U_18556)) = hAPP(c_Set_OCollect(tc_prod(U_18553,U_18554)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_18553,U_18554)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_18553,U_18554),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_18553,U_18554)),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_18553,U_18554)),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_18553,U_18554),tc_fun(tc_Nat_Onat,tc_prod(U_18553,U_18554)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_18553,U_18554),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(U_18553,U_18554)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_18553,U_18554)),c_COMBB(tc_prod(U_18553,U_18554),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_18554,tc_prod(U_18553,U_18554)),hAPP(hAPP(c_COMBB(U_18553,tc_fun(U_18554,tc_prod(U_18553,U_18554)),tc_Nat_Onat),c_Product__Type_OPair(U_18553,U_18554)),hAPP(c_List_Onth(U_18553),U_18555))),hAPP(c_List_Onth(U_18554),U_18556)))))),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_18553)),U_18555)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18554)),U_18556)))))),
    inference(definitional_conversion,[status(esa)],[f_4473_2]) ).

cnf(f_4473_4,plain,
    hAPP(c_List_Oset(tc_prod(U_18553,U_18554)),hAPP(hAPP(c_List_Ozip(U_18553,U_18554),U_18555),U_18556)) = hAPP(c_Set_OCollect(tc_prod(U_18553,U_18554)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_18553,U_18554)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_18553,U_18554),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_18553,U_18554)),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_18553,U_18554)),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_18553,U_18554),tc_fun(tc_Nat_Onat,tc_prod(U_18553,U_18554)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_18553,U_18554),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(U_18553,U_18554)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_18553,U_18554)),c_COMBB(tc_prod(U_18553,U_18554),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_18554,tc_prod(U_18553,U_18554)),hAPP(hAPP(c_COMBB(U_18553,tc_fun(U_18554,tc_prod(U_18553,U_18554)),tc_Nat_Onat),c_Product__Type_OPair(U_18553,U_18554)),hAPP(c_List_Onth(U_18553),U_18555))),hAPP(c_List_Onth(U_18554),U_18556)))))),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_18553)),U_18555)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18554)),U_18556)))))),
    inference(clausify,[status(thm)],[f_4473_3]) ).

fof(f_4474_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_4474_2,plain,
    ! [U_18561,U_18560,U_18559,U_18558,U_18557] :
      ( hAPP(hAPP(c_List_Onth(tc_prod(U_18558,U_18560)),hAPP(hAPP(c_List_Ozip(U_18558,U_18560),U_18559),U_18561)),U_18557) = hAPP(hAPP(c_Product__Type_OPair(U_18558,U_18560),hAPP(hAPP(c_List_Onth(U_18558),U_18559),U_18557)),hAPP(hAPP(c_List_Onth(U_18560),U_18561),U_18557))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18557),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18560)),U_18561)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18557),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18558)),U_18559))) ),
    inference(variable_rename,[status(thm)],[f_4474_1]) ).

fof(f_4474_3,plain,
    ! [U_18557,U_18558,U_18559,U_18560,U_18561] :
      ( hAPP(hAPP(c_List_Onth(tc_prod(U_18558,U_18560)),hAPP(hAPP(c_List_Ozip(U_18558,U_18560),U_18559),U_18561)),U_18557) = hAPP(hAPP(c_Product__Type_OPair(U_18558,U_18560),hAPP(hAPP(c_List_Onth(U_18558),U_18559),U_18557)),hAPP(hAPP(c_List_Onth(U_18560),U_18561),U_18557))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18557),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18560)),U_18561)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18557),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18558)),U_18559))) ),
    inference(definitional_conversion,[status(esa)],[f_4474_2]) ).

cnf(f_4474_4,plain,
    ( hAPP(hAPP(c_List_Onth(tc_prod(U_18558,U_18560)),hAPP(hAPP(c_List_Ozip(U_18558,U_18560),U_18559),U_18561)),U_18557) = hAPP(hAPP(c_Product__Type_OPair(U_18558,U_18560),hAPP(hAPP(c_List_Onth(U_18558),U_18559),U_18557)),hAPP(hAPP(c_List_Onth(U_18560),U_18561),U_18557))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18557),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18560)),U_18561)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18557),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18558)),U_18559))) ),
    inference(clausify,[status(thm)],[f_4474_3]) ).

fof(f_4475_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_4475_2,plain,
    ! [U_18566,U_18565,U_18564,U_18563,U_18562] :
      ( hAPP(hAPP(c_List_Onth(U_18565),hAPP(hAPP(c_List_Omap(U_18563,U_18565),U_18566),U_18564)),U_18562) = hAPP(U_18566,hAPP(hAPP(c_List_Onth(U_18563),U_18564),U_18562))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18562),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18563)),U_18564))) ),
    inference(variable_rename,[status(thm)],[f_4475_1]) ).

fof(f_4475_3,plain,
    ! [U_18563,U_18562,U_18564,U_18565,U_18566] :
      ( hAPP(hAPP(c_List_Onth(U_18565),hAPP(hAPP(c_List_Omap(U_18563,U_18565),U_18566),U_18564)),U_18562) = hAPP(U_18566,hAPP(hAPP(c_List_Onth(U_18563),U_18564),U_18562))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18562),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18563)),U_18564))) ),
    inference(definitional_conversion,[status(esa)],[f_4475_2]) ).

cnf(f_4475_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_18565),hAPP(hAPP(c_List_Omap(U_18563,U_18565),U_18566),U_18564)),U_18562) = hAPP(U_18566,hAPP(hAPP(c_List_Onth(U_18563),U_18564),U_18562))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18562),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18563)),U_18564))) ),
    inference(clausify,[status(thm)],[f_4475_3]) ).

fof(f_4476_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_4476_2,plain,
    ! [U_18568,U_18567] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18568),U_18567)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18568)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18567),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18568))) ),
    inference(variable_rename,[status(thm)],[f_4476_1]) ).

fof(f_4476_3,plain,
    ! [U_18567,U_18568] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18568),U_18567)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18568)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18567),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18568))) ),
    inference(definitional_conversion,[status(esa)],[f_4476_2]) ).

cnf(f_4476_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18568),U_18567)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18568)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18567),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18568))) ),
    inference(clausify,[status(thm)],[f_4476_3]) ).

fof(f_4477_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_4477_2,plain,
    ! [U_18572,U_18571,U_18570,U_18569] : hAPP(hAPP(c_List_Onth(U_18569),hAPP(hAPP(c_List_Olist_OCons(U_18569),U_18570),U_18571)),hAPP(c_Nat_OSuc,U_18572)) = hAPP(hAPP(c_List_Onth(U_18569),U_18571),U_18572),
    inference(variable_rename,[status(thm)],[f_4477_1]) ).

fof(f_4477_3,plain,
    ! [U_18569,U_18570,U_18571,U_18572] : hAPP(hAPP(c_List_Onth(U_18569),hAPP(hAPP(c_List_Olist_OCons(U_18569),U_18570),U_18571)),hAPP(c_Nat_OSuc,U_18572)) = hAPP(hAPP(c_List_Onth(U_18569),U_18571),U_18572),
    inference(definitional_conversion,[status(esa)],[f_4477_2]) ).

cnf(f_4477_4,plain,
    hAPP(hAPP(c_List_Onth(U_18569),hAPP(hAPP(c_List_Olist_OCons(U_18569),U_18570),U_18571)),hAPP(c_Nat_OSuc,U_18572)) = hAPP(hAPP(c_List_Onth(U_18569),U_18571),U_18572),
    inference(clausify,[status(thm)],[f_4477_3]) ).

fof(f_4478_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_4478_2,plain,
    ! [U_18575,U_18574,U_18573] : hAPP(hAPP(c_List_Onth(U_18573),hAPP(hAPP(c_List_Olist_OCons(U_18573),U_18574),U_18575)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_18574,
    inference(variable_rename,[status(thm)],[f_4478_1]) ).

fof(f_4478_3,plain,
    ! [U_18573,U_18574,U_18575] : hAPP(hAPP(c_List_Onth(U_18573),hAPP(hAPP(c_List_Olist_OCons(U_18573),U_18574),U_18575)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_18574,
    inference(definitional_conversion,[status(esa)],[f_4478_2]) ).

cnf(f_4478_4,plain,
    hAPP(hAPP(c_List_Onth(U_18573),hAPP(hAPP(c_List_Olist_OCons(U_18573),U_18574),U_18575)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_18574,
    inference(clausify,[status(thm)],[f_4478_3]) ).

fof(f_4479_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_4479_2,plain,
    ! [U_18579,U_18578,U_18577,U_18576] : hAPP(hAPP(c_List_Onth(U_18576),hAPP(hAPP(c_List_Olist_OCons(U_18576),U_18577),U_18578)),U_18579) = c_Nat_Onat_Onat__case(U_18576,U_18577,hAPP(c_List_Onth(U_18576),U_18578),U_18579),
    inference(variable_rename,[status(thm)],[f_4479_1]) ).

fof(f_4479_3,plain,
    ! [U_18576,U_18577,U_18578,U_18579] : hAPP(hAPP(c_List_Onth(U_18576),hAPP(hAPP(c_List_Olist_OCons(U_18576),U_18577),U_18578)),U_18579) = c_Nat_Onat_Onat__case(U_18576,U_18577,hAPP(c_List_Onth(U_18576),U_18578),U_18579),
    inference(definitional_conversion,[status(esa)],[f_4479_2]) ).

cnf(f_4479_4,plain,
    hAPP(hAPP(c_List_Onth(U_18576),hAPP(hAPP(c_List_Olist_OCons(U_18576),U_18577),U_18578)),U_18579) = c_Nat_Onat_Onat__case(U_18576,U_18577,hAPP(c_List_Onth(U_18576),U_18578),U_18579),
    inference(clausify,[status(thm)],[f_4479_3]) ).

fof(f_4480_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_4480_2,plain,
    ! [U_18586,U_18585,U_18584] :
      ( ( ! [U_18583] :
            ( hBOOL(hAPP(U_18586,U_18583))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18584),U_18583),hAPP(c_List_Oset(U_18584),U_18585))) )
        | ? [U_18582] :
            ( ~ hBOOL(hAPP(U_18586,hAPP(hAPP(c_List_Onth(U_18584),U_18585),U_18582)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18582),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18584)),U_18585))) ) )
      & ( ! [U_18581] :
            ( hBOOL(hAPP(U_18586,hAPP(hAPP(c_List_Onth(U_18584),U_18585),U_18581)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18581),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18584)),U_18585))) )
        | ? [U_18580] :
            ( ~ hBOOL(hAPP(U_18586,U_18580))
            & hBOOL(hAPP(hAPP(c_member(U_18584),U_18580),hAPP(c_List_Oset(U_18584),U_18585))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4480_1]) ).

fof(f_4480_3,plain,
    ( ! [U_18592,U_18590,U_18588] :
        ( ! [U_18583] :
            ( hBOOL(hAPP(U_18592,U_18583))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18588),U_18583),hAPP(c_List_Oset(U_18588),U_18590))) )
        | ? [U_18582] :
            ( ~ hBOOL(hAPP(U_18592,hAPP(hAPP(c_List_Onth(U_18588),U_18590),U_18582)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18582),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18588)),U_18590))) ) )
    & ! [U_18591,U_18589,U_18587] :
        ( ! [U_18581] :
            ( hBOOL(hAPP(U_18591,hAPP(hAPP(c_List_Onth(U_18587),U_18589),U_18581)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18581),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18587)),U_18589))) )
        | ? [U_18580] :
            ( ~ hBOOL(hAPP(U_18591,U_18580))
            & hBOOL(hAPP(hAPP(c_member(U_18587),U_18580),hAPP(c_List_Oset(U_18587),U_18589))) ) ) ),
    inference(miniscope,[status(thm)],[f_4480_2]) ).

fof(f_4480_4,plain,
    ( ! [U_18592,U_18590,U_18588] :
        ( ! [U_18583] :
            ( hBOOL(hAPP(U_18592,U_18583))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18588),U_18583),hAPP(c_List_Oset(U_18588),U_18590))) )
        | ? [U_18582] :
            ( ~ hBOOL(hAPP(U_18592,hAPP(hAPP(c_List_Onth(U_18588),U_18590),U_18582)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18582),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18588)),U_18590))) ) )
    & ! [U_18591,U_18589,U_18587] :
        ( ! [U_18581] :
            ( hBOOL(hAPP(U_18591,hAPP(hAPP(c_List_Onth(U_18587),U_18589),U_18581)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18581),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18587)),U_18589))) )
        | ( ~ hBOOL(hAPP(U_18591,sK466(U_18591,U_18589,U_18587)))
          & hBOOL(hAPP(hAPP(c_member(U_18587),sK466(U_18591,U_18589,U_18587)),hAPP(c_List_Oset(U_18587),U_18589))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK466]),skolemize(U_18580,sK466(U_18591,U_18589,U_18587))],[f_4480_3]) ).

fof(f_4480_5,plain,
    ( ! [U_18592,U_18590,U_18588] :
        ( ! [U_18583] :
            ( hBOOL(hAPP(U_18592,U_18583))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18588),U_18583),hAPP(c_List_Oset(U_18588),U_18590))) )
        | ( ~ hBOOL(hAPP(U_18592,hAPP(hAPP(c_List_Onth(U_18588),U_18590),sK467(U_18592,U_18590,U_18588))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK467(U_18592,U_18590,U_18588)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18588)),U_18590))) ) )
    & ! [U_18591,U_18589,U_18587] :
        ( ! [U_18581] :
            ( hBOOL(hAPP(U_18591,hAPP(hAPP(c_List_Onth(U_18587),U_18589),U_18581)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18581),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18587)),U_18589))) )
        | ( ~ hBOOL(hAPP(U_18591,sK466(U_18591,U_18589,U_18587)))
          & hBOOL(hAPP(hAPP(c_member(U_18587),sK466(U_18591,U_18589,U_18587)),hAPP(c_List_Oset(U_18587),U_18589))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK467]),skolemize(U_18582,sK467(U_18592,U_18590,U_18588))],[f_4480_4]) ).

fof(f_4480_6,plain,
    ( ! [U_18590,U_18588,U_18592] :
        ( ~ hBOOL(hAPP(U_18592,hAPP(hAPP(c_List_Onth(U_18588),U_18590),sK467(U_18592,U_18590,U_18588))))
        | ~ sP1156(U_18590,U_18588,U_18592) )
    & ! [U_18590,U_18588,U_18592] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK467(U_18592,U_18590,U_18588)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18588)),U_18590)))
        | ~ sP1156(U_18590,U_18588,U_18592) )
    & ! [U_18591,U_18587,U_18589] :
        ( ~ hBOOL(hAPP(U_18591,sK466(U_18591,U_18589,U_18587)))
        | ~ sP1155(U_18591,U_18587,U_18589) )
    & ! [U_18591,U_18587,U_18589] :
        ( hBOOL(hAPP(hAPP(c_member(U_18587),sK466(U_18591,U_18589,U_18587)),hAPP(c_List_Oset(U_18587),U_18589)))
        | ~ sP1155(U_18591,U_18587,U_18589) )
    & ! [U_18583,U_18590,U_18588,U_18592] :
        ( hBOOL(hAPP(U_18592,U_18583))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18588),U_18583),hAPP(c_List_Oset(U_18588),U_18590)))
        | sP1156(U_18590,U_18588,U_18592) )
    & ! [U_18591,U_18581,U_18587,U_18589] :
        ( hBOOL(hAPP(U_18591,hAPP(hAPP(c_List_Onth(U_18587),U_18589),U_18581)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18581),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18587)),U_18589)))
        | sP1155(U_18591,U_18587,U_18589) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1155,sP1156])],[f_4480_5]) ).

cnf(f_4480_7,plain,
    ( hBOOL(hAPP(U_18591,hAPP(hAPP(c_List_Onth(U_18587),U_18589),U_18581)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18581),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18587)),U_18589)))
    | sP1155(U_18591,U_18587,U_18589) ),
    inference(clausify,[status(thm)],[f_4480_6]) ).

cnf(f_4480_8,plain,
    ( hBOOL(hAPP(U_18592,U_18583))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18588),U_18583),hAPP(c_List_Oset(U_18588),U_18590)))
    | sP1156(U_18590,U_18588,U_18592) ),
    inference(clausify,[status(thm)],[f_4480_6]) ).

cnf(f_4480_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18587),sK466(U_18591,U_18589,U_18587)),hAPP(c_List_Oset(U_18587),U_18589)))
    | ~ sP1155(U_18591,U_18587,U_18589) ),
    inference(clausify,[status(thm)],[f_4480_6]) ).

cnf(f_4480_10,plain,
    ( ~ hBOOL(hAPP(U_18591,sK466(U_18591,U_18589,U_18587)))
    | ~ sP1155(U_18591,U_18587,U_18589) ),
    inference(clausify,[status(thm)],[f_4480_6]) ).

cnf(f_4480_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK467(U_18592,U_18590,U_18588)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18588)),U_18590)))
    | ~ sP1156(U_18590,U_18588,U_18592) ),
    inference(clausify,[status(thm)],[f_4480_6]) ).

cnf(f_4480_12,plain,
    ( ~ hBOOL(hAPP(U_18592,hAPP(hAPP(c_List_Onth(U_18588),U_18590),sK467(U_18592,U_18590,U_18588))))
    | ~ sP1156(U_18590,U_18588,U_18592) ),
    inference(clausify,[status(thm)],[f_4480_6]) ).

fof(f_4481_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_4481_2,plain,
    ! [U_18597,U_18596,U_18595] :
      ( ( U_18595 = U_18596
        | ? [U_18594] :
            ( hAPP(hAPP(c_List_Onth(U_18597),U_18595),U_18594) != hAPP(hAPP(c_List_Onth(U_18597),U_18596),U_18594)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18594),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18597)),U_18595))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18597)),U_18595) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18597)),U_18596) )
      & ( ( ! [U_18593] :
              ( hAPP(hAPP(c_List_Onth(U_18597),U_18595),U_18593) = hAPP(hAPP(c_List_Onth(U_18597),U_18596),U_18593)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18593),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18597)),U_18595))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18597)),U_18595) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18597)),U_18596) )
        | U_18595 != U_18596 ) ),
    inference(variable_rename,[status(thm)],[f_4481_1]) ).

fof(f_4481_3,plain,
    ( ! [U_18603,U_18601,U_18599] :
        ( U_18599 = U_18601
        | ? [U_18594] :
            ( hAPP(hAPP(c_List_Onth(U_18603),U_18599),U_18594) != hAPP(hAPP(c_List_Onth(U_18603),U_18601),U_18594)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18594),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18603)),U_18599))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18603)),U_18599) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18603)),U_18601) )
    & ! [U_18602,U_18600,U_18598] :
        ( ( ! [U_18593] :
              ( hAPP(hAPP(c_List_Onth(U_18602),U_18598),U_18593) = hAPP(hAPP(c_List_Onth(U_18602),U_18600),U_18593)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18593),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18602)),U_18598))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18602)),U_18598) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18602)),U_18600) )
        | U_18598 != U_18600 ) ),
    inference(miniscope,[status(thm)],[f_4481_2]) ).

fof(f_4481_4,plain,
    ( ! [U_18603,U_18601,U_18599] :
        ( U_18599 = U_18601
        | ( hAPP(hAPP(c_List_Onth(U_18603),U_18599),sK468(U_18603,U_18601,U_18599)) != hAPP(hAPP(c_List_Onth(U_18603),U_18601),sK468(U_18603,U_18601,U_18599))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK468(U_18603,U_18601,U_18599)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18603)),U_18599))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18603)),U_18599) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18603)),U_18601) )
    & ! [U_18602,U_18600,U_18598] :
        ( ( ! [U_18593] :
              ( hAPP(hAPP(c_List_Onth(U_18602),U_18598),U_18593) = hAPP(hAPP(c_List_Onth(U_18602),U_18600),U_18593)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18593),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18602)),U_18598))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18602)),U_18598) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18602)),U_18600) )
        | U_18598 != U_18600 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK468]),skolemize(U_18594,sK468(U_18603,U_18601,U_18599))],[f_4481_3]) ).

fof(f_4481_5,plain,
    ( ! [U_18599,U_18601,U_18603] :
        ( hAPP(hAPP(c_List_Onth(U_18603),U_18599),sK468(U_18603,U_18601,U_18599)) != hAPP(hAPP(c_List_Onth(U_18603),U_18601),sK468(U_18603,U_18601,U_18599))
        | ~ sP1158(U_18599,U_18601,U_18603) )
    & ! [U_18599,U_18601,U_18603] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK468(U_18603,U_18601,U_18599)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18603)),U_18599)))
        | ~ sP1158(U_18599,U_18601,U_18603) )
    & ! [U_18593,U_18598,U_18600,U_18602] :
        ( hAPP(hAPP(c_List_Onth(U_18602),U_18598),U_18593) = hAPP(hAPP(c_List_Onth(U_18602),U_18600),U_18593)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18593),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18602)),U_18598)))
        | ~ sP1157(U_18593,U_18598,U_18600,U_18602) )
    & ! [U_18593,U_18598,U_18600,U_18602] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18602)),U_18598) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18602)),U_18600)
        | ~ sP1157(U_18593,U_18598,U_18600,U_18602) )
    & ! [U_18599,U_18601,U_18603] :
        ( U_18599 = U_18601
        | sP1158(U_18599,U_18601,U_18603)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18603)),U_18599) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18603)),U_18601) )
    & ! [U_18593,U_18598,U_18600,U_18602] :
        ( sP1157(U_18593,U_18598,U_18600,U_18602)
        | U_18598 != U_18600 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1157,sP1158])],[f_4481_4]) ).

cnf(f_4481_6,plain,
    ( sP1157(U_18593,U_18598,U_18600,U_18602)
    | U_18598 != U_18600 ),
    inference(clausify,[status(thm)],[f_4481_5]) ).

cnf(f_4481_7,plain,
    ( U_18599 = U_18601
    | sP1158(U_18599,U_18601,U_18603)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18603)),U_18599) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18603)),U_18601) ),
    inference(clausify,[status(thm)],[f_4481_5]) ).

cnf(f_4481_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18602)),U_18598) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18602)),U_18600)
    | ~ sP1157(U_18593,U_18598,U_18600,U_18602) ),
    inference(clausify,[status(thm)],[f_4481_5]) ).

cnf(f_4481_9,plain,
    ( hAPP(hAPP(c_List_Onth(U_18602),U_18598),U_18593) = hAPP(hAPP(c_List_Onth(U_18602),U_18600),U_18593)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18593),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18602)),U_18598)))
    | ~ sP1157(U_18593,U_18598,U_18600,U_18602) ),
    inference(clausify,[status(thm)],[f_4481_5]) ).

cnf(f_4481_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK468(U_18603,U_18601,U_18599)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18603)),U_18599)))
    | ~ sP1158(U_18599,U_18601,U_18603) ),
    inference(clausify,[status(thm)],[f_4481_5]) ).

cnf(f_4481_11,plain,
    ( hAPP(hAPP(c_List_Onth(U_18603),U_18599),sK468(U_18603,U_18601,U_18599)) != hAPP(hAPP(c_List_Onth(U_18603),U_18601),sK468(U_18603,U_18601,U_18599))
    | ~ sP1158(U_18599,U_18601,U_18603) ),
    inference(clausify,[status(thm)],[f_4481_5]) ).

fof(f_4482_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_4482_2,plain,
    ! [U_18609,U_18608] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_18608),U_18609))
        | ? [U_18607] :
            ( ? [U_18606] :
                ( hAPP(hAPP(c_List_Onth(U_18608),U_18609),U_18607) = hAPP(hAPP(c_List_Onth(U_18608),U_18609),U_18606)
                & U_18607 != U_18606
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18606),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18608)),U_18609))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18607),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18608)),U_18609))) ) )
      & ( ! [U_18605] :
            ( ! [U_18604] :
                ( hAPP(hAPP(c_List_Onth(U_18608),U_18609),U_18605) != hAPP(hAPP(c_List_Onth(U_18608),U_18609),U_18604)
                | U_18605 = U_18604
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18604),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18608)),U_18609))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18605),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18608)),U_18609))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18608),U_18609)) ) ),
    inference(variable_rename,[status(thm)],[f_4482_1]) ).

fof(f_4482_3,plain,
    ( ! [U_18613,U_18611] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18611),U_18613))
        | ? [U_18607] :
            ( ? [U_18606] :
                ( hAPP(hAPP(c_List_Onth(U_18611),U_18613),U_18607) = hAPP(hAPP(c_List_Onth(U_18611),U_18613),U_18606)
                & U_18607 != U_18606
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18606),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18611)),U_18613))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18607),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18611)),U_18613))) ) )
    & ! [U_18612,U_18610] :
        ( ! [U_18605] :
            ( ! [U_18604] :
                ( hAPP(hAPP(c_List_Onth(U_18610),U_18612),U_18605) != hAPP(hAPP(c_List_Onth(U_18610),U_18612),U_18604)
                | U_18605 = U_18604
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18604),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18610)),U_18612))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18605),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18610)),U_18612))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18610),U_18612)) ) ),
    inference(miniscope,[status(thm)],[f_4482_2]) ).

fof(f_4482_4,plain,
    ( ! [U_18613,U_18611] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18611),U_18613))
        | ( ? [U_18606] :
              ( hAPP(hAPP(c_List_Onth(U_18611),U_18613),sK469(U_18613,U_18611)) = hAPP(hAPP(c_List_Onth(U_18611),U_18613),U_18606)
              & sK469(U_18613,U_18611) != U_18606
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18606),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18611)),U_18613))) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK469(U_18613,U_18611)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18611)),U_18613))) ) )
    & ! [U_18612,U_18610] :
        ( ! [U_18605] :
            ( ! [U_18604] :
                ( hAPP(hAPP(c_List_Onth(U_18610),U_18612),U_18605) != hAPP(hAPP(c_List_Onth(U_18610),U_18612),U_18604)
                | U_18605 = U_18604
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18604),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18610)),U_18612))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18605),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18610)),U_18612))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18610),U_18612)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK469]),skolemize(U_18607,sK469(U_18613,U_18611))],[f_4482_3]) ).

fof(f_4482_5,plain,
    ( ! [U_18613,U_18611] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18611),U_18613))
        | ( hAPP(hAPP(c_List_Onth(U_18611),U_18613),sK469(U_18613,U_18611)) = hAPP(hAPP(c_List_Onth(U_18611),U_18613),sK470(U_18613,U_18611))
          & sK469(U_18613,U_18611) != sK470(U_18613,U_18611)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK470(U_18613,U_18611)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18611)),U_18613)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK469(U_18613,U_18611)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18611)),U_18613))) ) )
    & ! [U_18612,U_18610] :
        ( ! [U_18605] :
            ( ! [U_18604] :
                ( hAPP(hAPP(c_List_Onth(U_18610),U_18612),U_18605) != hAPP(hAPP(c_List_Onth(U_18610),U_18612),U_18604)
                | U_18605 = U_18604
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18604),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18610)),U_18612))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18605),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18610)),U_18612))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18610),U_18612)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK470]),skolemize(U_18606,sK470(U_18613,U_18611))],[f_4482_4]) ).

fof(f_4482_6,plain,
    ( ! [U_18611,U_18613] :
        ( hAPP(hAPP(c_List_Onth(U_18611),U_18613),sK469(U_18613,U_18611)) = hAPP(hAPP(c_List_Onth(U_18611),U_18613),sK470(U_18613,U_18611))
        | ~ sP1159(U_18611,U_18613) )
    & ! [U_18611,U_18613] :
        ( sK469(U_18613,U_18611) != sK470(U_18613,U_18611)
        | ~ sP1159(U_18611,U_18613) )
    & ! [U_18611,U_18613] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK470(U_18613,U_18611)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18611)),U_18613)))
        | ~ sP1159(U_18611,U_18613) )
    & ! [U_18611,U_18613] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK469(U_18613,U_18611)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18611)),U_18613)))
        | ~ sP1159(U_18611,U_18613) )
    & ! [U_18611,U_18613] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18611),U_18613))
        | sP1159(U_18611,U_18613) )
    & ! [U_18605,U_18604,U_18610,U_18612] :
        ( hAPP(hAPP(c_List_Onth(U_18610),U_18612),U_18605) != hAPP(hAPP(c_List_Onth(U_18610),U_18612),U_18604)
        | U_18605 = U_18604
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18604),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18610)),U_18612)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18605),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18610)),U_18612)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18610),U_18612)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1159])],[f_4482_5]) ).

cnf(f_4482_7,plain,
    ( hAPP(hAPP(c_List_Onth(U_18610),U_18612),U_18605) != hAPP(hAPP(c_List_Onth(U_18610),U_18612),U_18604)
    | U_18605 = U_18604
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18604),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18610)),U_18612)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18605),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18610)),U_18612)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18610),U_18612)) ),
    inference(clausify,[status(thm)],[f_4482_6]) ).

cnf(f_4482_8,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18611),U_18613))
    | sP1159(U_18611,U_18613) ),
    inference(clausify,[status(thm)],[f_4482_6]) ).

cnf(f_4482_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK469(U_18613,U_18611)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18611)),U_18613)))
    | ~ sP1159(U_18611,U_18613) ),
    inference(clausify,[status(thm)],[f_4482_6]) ).

cnf(f_4482_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK470(U_18613,U_18611)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18611)),U_18613)))
    | ~ sP1159(U_18611,U_18613) ),
    inference(clausify,[status(thm)],[f_4482_6]) ).

cnf(f_4482_11,plain,
    ( sK469(U_18613,U_18611) != sK470(U_18613,U_18611)
    | ~ sP1159(U_18611,U_18613) ),
    inference(clausify,[status(thm)],[f_4482_6]) ).

cnf(f_4482_12,plain,
    ( hAPP(hAPP(c_List_Onth(U_18611),U_18613),sK469(U_18613,U_18611)) = hAPP(hAPP(c_List_Onth(U_18611),U_18613),sK470(U_18613,U_18611))
    | ~ sP1159(U_18611,U_18613) ),
    inference(clausify,[status(thm)],[f_4482_6]) ).

fof(f_4483_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_4483_2,plain,
    ! [U_18617,U_18616,U_18615,U_18614] :
      ( ( ( hAPP(hAPP(c_List_Onth(U_18614),U_18615),U_18616) = hAPP(hAPP(c_List_Onth(U_18614),U_18615),U_18617)
          | U_18616 != U_18617 )
        & ( U_18616 = U_18617
          | hAPP(hAPP(c_List_Onth(U_18614),U_18615),U_18616) != hAPP(hAPP(c_List_Onth(U_18614),U_18615),U_18617) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18617),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18614)),U_18615)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18616),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18614)),U_18615)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18614),U_18615)) ),
    inference(variable_rename,[status(thm)],[f_4483_1]) ).

fof(f_4483_3,plain,
    ( ! [U_18614,U_18616,U_18617,U_18615] :
        ( hAPP(hAPP(c_List_Onth(U_18614),U_18615),U_18616) = hAPP(hAPP(c_List_Onth(U_18614),U_18615),U_18617)
        | U_18616 != U_18617
        | ~ sP1160(U_18614,U_18616,U_18617,U_18615) )
    & ! [U_18614,U_18616,U_18617,U_18615] :
        ( U_18616 = U_18617
        | hAPP(hAPP(c_List_Onth(U_18614),U_18615),U_18616) != hAPP(hAPP(c_List_Onth(U_18614),U_18615),U_18617)
        | ~ sP1160(U_18614,U_18616,U_18617,U_18615) )
    & ! [U_18614,U_18616,U_18617,U_18615] :
        ( sP1160(U_18614,U_18616,U_18617,U_18615)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18617),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18614)),U_18615)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18616),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18614)),U_18615)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18614),U_18615)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1160])],[f_4483_2]) ).

cnf(f_4483_4,plain,
    ( sP1160(U_18614,U_18616,U_18617,U_18615)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18617),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18614)),U_18615)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18616),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18614)),U_18615)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18614),U_18615)) ),
    inference(clausify,[status(thm)],[f_4483_3]) ).

cnf(f_4483_5,plain,
    ( U_18616 = U_18617
    | hAPP(hAPP(c_List_Onth(U_18614),U_18615),U_18616) != hAPP(hAPP(c_List_Onth(U_18614),U_18615),U_18617)
    | ~ sP1160(U_18614,U_18616,U_18617,U_18615) ),
    inference(clausify,[status(thm)],[f_4483_3]) ).

cnf(f_4483_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_18614),U_18615),U_18616) = hAPP(hAPP(c_List_Onth(U_18614),U_18615),U_18617)
    | U_18616 != U_18617
    | ~ sP1160(U_18614,U_18616,U_18617,U_18615) ),
    inference(clausify,[status(thm)],[f_4483_3]) ).

fof(f_4484_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_4484_2,plain,
    ! [U_18620,U_18619,U_18618] :
      ( hBOOL(hAPP(hAPP(c_member(U_18619),hAPP(hAPP(c_List_Onth(U_18619),U_18620),U_18618)),hAPP(c_List_Oset(U_18619),U_18620)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18618),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18619)),U_18620))) ),
    inference(variable_rename,[status(thm)],[f_4484_1]) ).

fof(f_4484_3,plain,
    ! [U_18618,U_18620,U_18619] :
      ( hBOOL(hAPP(hAPP(c_member(U_18619),hAPP(hAPP(c_List_Onth(U_18619),U_18620),U_18618)),hAPP(c_List_Oset(U_18619),U_18620)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18618),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18619)),U_18620))) ),
    inference(definitional_conversion,[status(esa)],[f_4484_2]) ).

cnf(f_4484_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18619),hAPP(hAPP(c_List_Onth(U_18619),U_18620),U_18618)),hAPP(c_List_Oset(U_18619),U_18620)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18618),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18619)),U_18620))) ),
    inference(clausify,[status(thm)],[f_4484_3]) ).

fof(f_4485_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_4485_2,plain,
    ! [U_18625,U_18624,U_18623] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_18623),U_18624),hAPP(c_List_Oset(U_18623),U_18625)))
        | ! [U_18622] :
            ( hAPP(hAPP(c_List_Onth(U_18623),U_18625),U_18622) != U_18624
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18622),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18623)),U_18625))) ) )
      & ( ? [U_18621] :
            ( hAPP(hAPP(c_List_Onth(U_18623),U_18625),U_18621) = U_18624
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18621),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18623)),U_18625))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18623),U_18624),hAPP(c_List_Oset(U_18623),U_18625))) ) ),
    inference(variable_rename,[status(thm)],[f_4485_1]) ).

fof(f_4485_3,plain,
    ( ! [U_18631,U_18629,U_18627] :
        ( hBOOL(hAPP(hAPP(c_member(U_18627),U_18629),hAPP(c_List_Oset(U_18627),U_18631)))
        | ! [U_18622] :
            ( hAPP(hAPP(c_List_Onth(U_18627),U_18631),U_18622) != U_18629
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18622),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18627)),U_18631))) ) )
    & ! [U_18630,U_18628,U_18626] :
        ( ? [U_18621] :
            ( hAPP(hAPP(c_List_Onth(U_18626),U_18630),U_18621) = U_18628
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18621),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18626)),U_18630))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18626),U_18628),hAPP(c_List_Oset(U_18626),U_18630))) ) ),
    inference(miniscope,[status(thm)],[f_4485_2]) ).

fof(f_4485_4,plain,
    ( ! [U_18631,U_18629,U_18627] :
        ( hBOOL(hAPP(hAPP(c_member(U_18627),U_18629),hAPP(c_List_Oset(U_18627),U_18631)))
        | ! [U_18622] :
            ( hAPP(hAPP(c_List_Onth(U_18627),U_18631),U_18622) != U_18629
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18622),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18627)),U_18631))) ) )
    & ! [U_18630,U_18628,U_18626] :
        ( ( hAPP(hAPP(c_List_Onth(U_18626),U_18630),sK471(U_18630,U_18628,U_18626)) = U_18628
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK471(U_18630,U_18628,U_18626)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18626)),U_18630))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18626),U_18628),hAPP(c_List_Oset(U_18626),U_18630))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK471]),skolemize(U_18621,sK471(U_18630,U_18628,U_18626))],[f_4485_3]) ).

fof(f_4485_5,plain,
    ( ! [U_18628,U_18626,U_18630] :
        ( hAPP(hAPP(c_List_Onth(U_18626),U_18630),sK471(U_18630,U_18628,U_18626)) = U_18628
        | ~ sP1161(U_18628,U_18626,U_18630) )
    & ! [U_18628,U_18626,U_18630] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK471(U_18630,U_18628,U_18626)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18626)),U_18630)))
        | ~ sP1161(U_18628,U_18626,U_18630) )
    & ! [U_18622,U_18629,U_18627,U_18631] :
        ( hBOOL(hAPP(hAPP(c_member(U_18627),U_18629),hAPP(c_List_Oset(U_18627),U_18631)))
        | hAPP(hAPP(c_List_Onth(U_18627),U_18631),U_18622) != U_18629
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18622),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18627)),U_18631))) )
    & ! [U_18628,U_18626,U_18630] :
        ( sP1161(U_18628,U_18626,U_18630)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18626),U_18628),hAPP(c_List_Oset(U_18626),U_18630))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1161])],[f_4485_4]) ).

cnf(f_4485_6,plain,
    ( sP1161(U_18628,U_18626,U_18630)
    | ~ hBOOL(hAPP(hAPP(c_member(U_18626),U_18628),hAPP(c_List_Oset(U_18626),U_18630))) ),
    inference(clausify,[status(thm)],[f_4485_5]) ).

cnf(f_4485_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18627),U_18629),hAPP(c_List_Oset(U_18627),U_18631)))
    | hAPP(hAPP(c_List_Onth(U_18627),U_18631),U_18622) != U_18629
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18622),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18627)),U_18631))) ),
    inference(clausify,[status(thm)],[f_4485_5]) ).

cnf(f_4485_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK471(U_18630,U_18628,U_18626)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18626)),U_18630)))
    | ~ sP1161(U_18628,U_18626,U_18630) ),
    inference(clausify,[status(thm)],[f_4485_5]) ).

cnf(f_4485_9,plain,
    ( hAPP(hAPP(c_List_Onth(U_18626),U_18630),sK471(U_18630,U_18628,U_18626)) = U_18628
    | ~ sP1161(U_18628,U_18626,U_18630) ),
    inference(clausify,[status(thm)],[f_4485_5]) ).

fof(f_4486_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_4486_2,plain,
    ! [U_18635,U_18634,U_18633,U_18632] :
      ( ( hAPP(hAPP(c_List_Onth(U_18633),hAPP(hAPP(c_List_Olist_OCons(U_18633),U_18634),U_18635)),U_18632) = hAPP(hAPP(c_List_Onth(U_18633),U_18635),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18632),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_18632 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(U_18633),hAPP(hAPP(c_List_Olist_OCons(U_18633),U_18634),U_18635)),U_18632) = U_18634
        | U_18632 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4486_1]) ).

fof(f_4486_3,plain,
    ( ! [U_18643,U_18641,U_18639,U_18637] :
        ( hAPP(hAPP(c_List_Onth(U_18639),hAPP(hAPP(c_List_Olist_OCons(U_18639),U_18641),U_18643)),U_18637) = hAPP(hAPP(c_List_Onth(U_18639),U_18643),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18637),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_18637 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18642,U_18640,U_18638,U_18636] :
        ( hAPP(hAPP(c_List_Onth(U_18638),hAPP(hAPP(c_List_Olist_OCons(U_18638),U_18640),U_18642)),U_18636) = U_18640
        | U_18636 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4486_2]) ).

fof(f_4486_4,plain,
    ( ! [U_18637,U_18639,U_18641,U_18643] :
        ( hAPP(hAPP(c_List_Onth(U_18639),hAPP(hAPP(c_List_Olist_OCons(U_18639),U_18641),U_18643)),U_18637) = hAPP(hAPP(c_List_Onth(U_18639),U_18643),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18637),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_18637 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18642,U_18640,U_18636,U_18638] :
        ( hAPP(hAPP(c_List_Onth(U_18638),hAPP(hAPP(c_List_Olist_OCons(U_18638),U_18640),U_18642)),U_18636) = U_18640
        | U_18636 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4486_3]) ).

cnf(f_4486_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_18638),hAPP(hAPP(c_List_Olist_OCons(U_18638),U_18640),U_18642)),U_18636) = U_18640
    | U_18636 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4486_4]) ).

cnf(f_4486_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_18639),hAPP(hAPP(c_List_Olist_OCons(U_18639),U_18641),U_18643)),U_18637) = hAPP(hAPP(c_List_Onth(U_18639),U_18643),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18637),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_18637 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4486_4]) ).

fof(f_4487_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_4487_2,plain,
    ! [U_18645,U_18644] : hAPP(c_List_Oset(U_18644),U_18645) = hAPP(c_Set_OCollect(U_18644),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18644),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18644,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_18644),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_18644),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18644,tc_fun(tc_Nat_Onat,U_18644),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18644,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18644),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18644),c_COMBB(U_18644,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18644),U_18645))))),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_18644)),U_18645))))),
    inference(variable_rename,[status(thm)],[f_4487_1]) ).

fof(f_4487_3,plain,
    ! [U_18644,U_18645] : hAPP(c_List_Oset(U_18644),U_18645) = hAPP(c_Set_OCollect(U_18644),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18644),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18644,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_18644),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_18644),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18644,tc_fun(tc_Nat_Onat,U_18644),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18644,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18644),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18644),c_COMBB(U_18644,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18644),U_18645))))),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_18644)),U_18645))))),
    inference(definitional_conversion,[status(esa)],[f_4487_2]) ).

cnf(f_4487_4,plain,
    hAPP(c_List_Oset(U_18644),U_18645) = hAPP(c_Set_OCollect(U_18644),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18644),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18644,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_18644),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_18644),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18644,tc_fun(tc_Nat_Onat,U_18644),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18644,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18644),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18644),c_COMBB(U_18644,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18644),U_18645))))),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_18644)),U_18645))))),
    inference(clausify,[status(thm)],[f_4487_3]) ).

fof(f_4488_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_4488_2,plain,
    ! [U_18649,U_18648,U_18647,U_18646] :
      ( ( hAPP(hAPP(c_List_Onth(U_18647),hAPP(hAPP(c_List_Olist_OCons(U_18647),U_18648),U_18649)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18646)) = hAPP(hAPP(c_List_Onth(U_18647),U_18649),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18646)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18646) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(U_18647),hAPP(hAPP(c_List_Olist_OCons(U_18647),U_18648),U_18649)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18646)) = U_18648
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18646) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4488_1]) ).

fof(f_4488_3,plain,
    ( ! [U_18657,U_18655,U_18653,U_18651] :
        ( hAPP(hAPP(c_List_Onth(U_18653),hAPP(hAPP(c_List_Olist_OCons(U_18653),U_18655),U_18657)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18651)) = hAPP(hAPP(c_List_Onth(U_18653),U_18657),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18651)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18651) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18656,U_18654,U_18652,U_18650] :
        ( hAPP(hAPP(c_List_Onth(U_18652),hAPP(hAPP(c_List_Olist_OCons(U_18652),U_18654),U_18656)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18650)) = U_18654
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18650) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4488_2]) ).

fof(f_4488_4,plain,
    ( ! [U_18651,U_18653,U_18655,U_18657] :
        ( hAPP(hAPP(c_List_Onth(U_18653),hAPP(hAPP(c_List_Olist_OCons(U_18653),U_18655),U_18657)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18651)) = hAPP(hAPP(c_List_Onth(U_18653),U_18657),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18651)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18651) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18656,U_18652,U_18650,U_18654] :
        ( hAPP(hAPP(c_List_Onth(U_18652),hAPP(hAPP(c_List_Olist_OCons(U_18652),U_18654),U_18656)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18650)) = U_18654
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18650) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4488_3]) ).

cnf(f_4488_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_18652),hAPP(hAPP(c_List_Olist_OCons(U_18652),U_18654),U_18656)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18650)) = U_18654
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18650) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4488_4]) ).

cnf(f_4488_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_18653),hAPP(hAPP(c_List_Olist_OCons(U_18653),U_18655),U_18657)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18651)) = hAPP(hAPP(c_List_Onth(U_18653),U_18657),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18651)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18651) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4488_4]) ).

fof(f_4489_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_4489_2,plain,
    ! [U_18659,U_18658] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18658),U_18659) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18658),hAPP(c_List_Onth(U_18658),U_18659)),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_18658)),U_18659)))
      | ~ class_Groups_Ocomm__monoid__add(U_18658) ),
    inference(variable_rename,[status(thm)],[f_4489_1]) ).

fof(f_4489_3,plain,
    ! [U_18658,U_18659] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18658),U_18659) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18658),hAPP(c_List_Onth(U_18658),U_18659)),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_18658)),U_18659)))
      | ~ class_Groups_Ocomm__monoid__add(U_18658) ),
    inference(definitional_conversion,[status(esa)],[f_4489_2]) ).

cnf(f_4489_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18658),U_18659) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18658),hAPP(c_List_Onth(U_18658),U_18659)),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_18658)),U_18659)))
    | ~ class_Groups_Ocomm__monoid__add(U_18658) ),
    inference(clausify,[status(thm)],[f_4489_3]) ).

fof(f_4490_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_4490_2,plain,
    ! [U_18662,U_18661,U_18660] : hAPP(c_List_Oset(U_18660),c_List_Osublist(U_18660,U_18661,U_18662)) = hAPP(c_Set_OCollect(U_18660),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18660),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18660,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_18660),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_18660),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18660,tc_fun(tc_Nat_Onat,U_18660),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18660,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18660),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18660),c_COMBB(U_18660,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18660),U_18661))))),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_18660)),U_18661)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_18662))))),
    inference(variable_rename,[status(thm)],[f_4490_1]) ).

fof(f_4490_3,plain,
    ! [U_18660,U_18661,U_18662] : hAPP(c_List_Oset(U_18660),c_List_Osublist(U_18660,U_18661,U_18662)) = hAPP(c_Set_OCollect(U_18660),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18660),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18660,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_18660),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_18660),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18660,tc_fun(tc_Nat_Onat,U_18660),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18660,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18660),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18660),c_COMBB(U_18660,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18660),U_18661))))),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_18660)),U_18661)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_18662))))),
    inference(definitional_conversion,[status(esa)],[f_4490_2]) ).

cnf(f_4490_4,plain,
    hAPP(c_List_Oset(U_18660),c_List_Osublist(U_18660,U_18661,U_18662)) = hAPP(c_Set_OCollect(U_18660),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18660),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18660,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_18660),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_18660),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18660,tc_fun(tc_Nat_Onat,U_18660),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18660,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18660),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18660),c_COMBB(U_18660,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18660),U_18661))))),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_18660)),U_18661)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_18662))))),
    inference(clausify,[status(thm)],[f_4490_3]) ).

fof(f_4491_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_4491_2,plain,
    ! [U_18666,U_18665,U_18664,U_18663] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18663),tc_List_Olist(U_18663))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18663),tc_List_Olist(U_18663)),U_18664),U_18665)),c_List_Olex(U_18663,U_18666)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18663)),U_18664) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18663)),U_18665)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18663),tc_List_Olist(U_18663))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18663),tc_List_Olist(U_18663)),U_18664),U_18665)),c_List_Olexord(U_18663,U_18666))) )
      & ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18663)),U_18664) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18663)),U_18665)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18663),tc_List_Olist(U_18663))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18663),tc_List_Olist(U_18663)),U_18664),U_18665)),c_List_Olexord(U_18663,U_18666))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18663),tc_List_Olist(U_18663))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18663),tc_List_Olist(U_18663)),U_18664),U_18665)),c_List_Olex(U_18663,U_18666))) ) ),
    inference(variable_rename,[status(thm)],[f_4491_1]) ).

fof(f_4491_3,plain,
    ( ! [U_18674,U_18672,U_18670,U_18668] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18668),tc_List_Olist(U_18668))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18668),tc_List_Olist(U_18668)),U_18670),U_18672)),c_List_Olex(U_18668,U_18674)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18668)),U_18670) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18668)),U_18672)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18668),tc_List_Olist(U_18668))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18668),tc_List_Olist(U_18668)),U_18670),U_18672)),c_List_Olexord(U_18668,U_18674))) )
    & ! [U_18673,U_18671,U_18669,U_18667] :
        ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18667)),U_18669) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18667)),U_18671)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18667),tc_List_Olist(U_18667))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18667),tc_List_Olist(U_18667)),U_18669),U_18671)),c_List_Olexord(U_18667,U_18673))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18667),tc_List_Olist(U_18667))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18667),tc_List_Olist(U_18667)),U_18669),U_18671)),c_List_Olex(U_18667,U_18673))) ) ),
    inference(miniscope,[status(thm)],[f_4491_2]) ).

fof(f_4491_4,plain,
    ( ! [U_18673,U_18669,U_18667,U_18671] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18667)),U_18669) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18667)),U_18671)
        | ~ sP1162(U_18673,U_18669,U_18667,U_18671) )
    & ! [U_18673,U_18669,U_18667,U_18671] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18667),tc_List_Olist(U_18667))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18667),tc_List_Olist(U_18667)),U_18669),U_18671)),c_List_Olexord(U_18667,U_18673)))
        | ~ sP1162(U_18673,U_18669,U_18667,U_18671) )
    & ! [U_18668,U_18672,U_18674,U_18670] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18668),tc_List_Olist(U_18668))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18668),tc_List_Olist(U_18668)),U_18670),U_18672)),c_List_Olex(U_18668,U_18674)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18668)),U_18670) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18668)),U_18672)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18668),tc_List_Olist(U_18668))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18668),tc_List_Olist(U_18668)),U_18670),U_18672)),c_List_Olexord(U_18668,U_18674))) )
    & ! [U_18673,U_18669,U_18667,U_18671] :
        ( sP1162(U_18673,U_18669,U_18667,U_18671)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18667),tc_List_Olist(U_18667))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18667),tc_List_Olist(U_18667)),U_18669),U_18671)),c_List_Olex(U_18667,U_18673))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1162])],[f_4491_3]) ).

cnf(f_4491_5,plain,
    ( sP1162(U_18673,U_18669,U_18667,U_18671)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18667),tc_List_Olist(U_18667))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18667),tc_List_Olist(U_18667)),U_18669),U_18671)),c_List_Olex(U_18667,U_18673))) ),
    inference(clausify,[status(thm)],[f_4491_4]) ).

cnf(f_4491_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18668),tc_List_Olist(U_18668))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18668),tc_List_Olist(U_18668)),U_18670),U_18672)),c_List_Olex(U_18668,U_18674)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18668)),U_18670) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18668)),U_18672)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18668),tc_List_Olist(U_18668))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18668),tc_List_Olist(U_18668)),U_18670),U_18672)),c_List_Olexord(U_18668,U_18674))) ),
    inference(clausify,[status(thm)],[f_4491_4]) ).

cnf(f_4491_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18667),tc_List_Olist(U_18667))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18667),tc_List_Olist(U_18667)),U_18669),U_18671)),c_List_Olexord(U_18667,U_18673)))
    | ~ sP1162(U_18673,U_18669,U_18667,U_18671) ),
    inference(clausify,[status(thm)],[f_4491_4]) ).

cnf(f_4491_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18667)),U_18669) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18667)),U_18671)
    | ~ sP1162(U_18673,U_18669,U_18667,U_18671) ),
    inference(clausify,[status(thm)],[f_4491_4]) ).

fof(f_4492_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_4492_2,plain,
    ! [U_18680,U_18679,U_18678,U_18677] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18677),tc_List_Olist(U_18677))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18677),tc_List_Olist(U_18677)),U_18678),U_18679)),c_List_Olistrel(U_18677,U_18680)))
        | ? [U_18676] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18677,U_18677)),hAPP(hAPP(c_Product__Type_OPair(U_18677,U_18677),hAPP(hAPP(c_List_Onth(U_18677),U_18678),U_18676)),hAPP(hAPP(c_List_Onth(U_18677),U_18679),U_18676))),U_18680))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18677)),U_18678))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18677)),U_18678) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18677)),U_18679) )
      & ( ( ! [U_18675] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18677,U_18677)),hAPP(hAPP(c_Product__Type_OPair(U_18677,U_18677),hAPP(hAPP(c_List_Onth(U_18677),U_18678),U_18675)),hAPP(hAPP(c_List_Onth(U_18677),U_18679),U_18675))),U_18680))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18675),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18677)),U_18678))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18677)),U_18678) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18677)),U_18679) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18677),tc_List_Olist(U_18677))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18677),tc_List_Olist(U_18677)),U_18678),U_18679)),c_List_Olistrel(U_18677,U_18680))) ) ),
    inference(variable_rename,[status(thm)],[f_4492_1]) ).

fof(f_4492_3,plain,
    ( ! [U_18688,U_18686,U_18684,U_18682] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18682),tc_List_Olist(U_18682))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18682),tc_List_Olist(U_18682)),U_18684),U_18686)),c_List_Olistrel(U_18682,U_18688)))
        | ? [U_18676] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18682,U_18682)),hAPP(hAPP(c_Product__Type_OPair(U_18682,U_18682),hAPP(hAPP(c_List_Onth(U_18682),U_18684),U_18676)),hAPP(hAPP(c_List_Onth(U_18682),U_18686),U_18676))),U_18688))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18682)),U_18684))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18682)),U_18684) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18682)),U_18686) )
    & ! [U_18687,U_18685,U_18683,U_18681] :
        ( ( ! [U_18675] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18681,U_18681)),hAPP(hAPP(c_Product__Type_OPair(U_18681,U_18681),hAPP(hAPP(c_List_Onth(U_18681),U_18683),U_18675)),hAPP(hAPP(c_List_Onth(U_18681),U_18685),U_18675))),U_18687))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18675),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18681)),U_18683))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18681)),U_18683) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18681)),U_18685) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18681),tc_List_Olist(U_18681))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18681),tc_List_Olist(U_18681)),U_18683),U_18685)),c_List_Olistrel(U_18681,U_18687))) ) ),
    inference(miniscope,[status(thm)],[f_4492_2]) ).

fof(f_4492_4,plain,
    ( ! [U_18688,U_18686,U_18684,U_18682] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18682),tc_List_Olist(U_18682))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18682),tc_List_Olist(U_18682)),U_18684),U_18686)),c_List_Olistrel(U_18682,U_18688)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18682,U_18682)),hAPP(hAPP(c_Product__Type_OPair(U_18682,U_18682),hAPP(hAPP(c_List_Onth(U_18682),U_18684),sK472(U_18688,U_18686,U_18684,U_18682))),hAPP(hAPP(c_List_Onth(U_18682),U_18686),sK472(U_18688,U_18686,U_18684,U_18682)))),U_18688))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK472(U_18688,U_18686,U_18684,U_18682)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18682)),U_18684))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18682)),U_18684) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18682)),U_18686) )
    & ! [U_18687,U_18685,U_18683,U_18681] :
        ( ( ! [U_18675] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18681,U_18681)),hAPP(hAPP(c_Product__Type_OPair(U_18681,U_18681),hAPP(hAPP(c_List_Onth(U_18681),U_18683),U_18675)),hAPP(hAPP(c_List_Onth(U_18681),U_18685),U_18675))),U_18687))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18675),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18681)),U_18683))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18681)),U_18683) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18681)),U_18685) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18681),tc_List_Olist(U_18681))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18681),tc_List_Olist(U_18681)),U_18683),U_18685)),c_List_Olistrel(U_18681,U_18687))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK472]),skolemize(U_18676,sK472(U_18688,U_18686,U_18684,U_18682))],[f_4492_3]) ).

fof(f_4492_5,plain,
    ( ! [U_18682,U_18684,U_18688,U_18686] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18682,U_18682)),hAPP(hAPP(c_Product__Type_OPair(U_18682,U_18682),hAPP(hAPP(c_List_Onth(U_18682),U_18684),sK472(U_18688,U_18686,U_18684,U_18682))),hAPP(hAPP(c_List_Onth(U_18682),U_18686),sK472(U_18688,U_18686,U_18684,U_18682)))),U_18688))
        | ~ sP1164(U_18682,U_18684,U_18688,U_18686) )
    & ! [U_18682,U_18684,U_18688,U_18686] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK472(U_18688,U_18686,U_18684,U_18682)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18682)),U_18684)))
        | ~ sP1164(U_18682,U_18684,U_18688,U_18686) )
    & ! [U_18675,U_18685,U_18681,U_18683,U_18687] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18681,U_18681)),hAPP(hAPP(c_Product__Type_OPair(U_18681,U_18681),hAPP(hAPP(c_List_Onth(U_18681),U_18683),U_18675)),hAPP(hAPP(c_List_Onth(U_18681),U_18685),U_18675))),U_18687))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18675),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18681)),U_18683)))
        | ~ sP1163(U_18675,U_18685,U_18681,U_18683,U_18687) )
    & ! [U_18675,U_18685,U_18681,U_18683,U_18687] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18681)),U_18683) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18681)),U_18685)
        | ~ sP1163(U_18675,U_18685,U_18681,U_18683,U_18687) )
    & ! [U_18682,U_18684,U_18688,U_18686] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18682),tc_List_Olist(U_18682))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18682),tc_List_Olist(U_18682)),U_18684),U_18686)),c_List_Olistrel(U_18682,U_18688)))
        | sP1164(U_18682,U_18684,U_18688,U_18686)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18682)),U_18684) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18682)),U_18686) )
    & ! [U_18675,U_18685,U_18681,U_18683,U_18687] :
        ( sP1163(U_18675,U_18685,U_18681,U_18683,U_18687)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18681),tc_List_Olist(U_18681))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18681),tc_List_Olist(U_18681)),U_18683),U_18685)),c_List_Olistrel(U_18681,U_18687))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1163,sP1164])],[f_4492_4]) ).

cnf(f_4492_6,plain,
    ( sP1163(U_18675,U_18685,U_18681,U_18683,U_18687)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18681),tc_List_Olist(U_18681))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18681),tc_List_Olist(U_18681)),U_18683),U_18685)),c_List_Olistrel(U_18681,U_18687))) ),
    inference(clausify,[status(thm)],[f_4492_5]) ).

cnf(f_4492_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18682),tc_List_Olist(U_18682))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18682),tc_List_Olist(U_18682)),U_18684),U_18686)),c_List_Olistrel(U_18682,U_18688)))
    | sP1164(U_18682,U_18684,U_18688,U_18686)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18682)),U_18684) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18682)),U_18686) ),
    inference(clausify,[status(thm)],[f_4492_5]) ).

cnf(f_4492_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18681)),U_18683) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18681)),U_18685)
    | ~ sP1163(U_18675,U_18685,U_18681,U_18683,U_18687) ),
    inference(clausify,[status(thm)],[f_4492_5]) ).

cnf(f_4492_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18681,U_18681)),hAPP(hAPP(c_Product__Type_OPair(U_18681,U_18681),hAPP(hAPP(c_List_Onth(U_18681),U_18683),U_18675)),hAPP(hAPP(c_List_Onth(U_18681),U_18685),U_18675))),U_18687))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18675),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18681)),U_18683)))
    | ~ sP1163(U_18675,U_18685,U_18681,U_18683,U_18687) ),
    inference(clausify,[status(thm)],[f_4492_5]) ).

cnf(f_4492_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK472(U_18688,U_18686,U_18684,U_18682)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18682)),U_18684)))
    | ~ sP1164(U_18682,U_18684,U_18688,U_18686) ),
    inference(clausify,[status(thm)],[f_4492_5]) ).

cnf(f_4492_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18682,U_18682)),hAPP(hAPP(c_Product__Type_OPair(U_18682,U_18682),hAPP(hAPP(c_List_Onth(U_18682),U_18684),sK472(U_18688,U_18686,U_18684,U_18682))),hAPP(hAPP(c_List_Onth(U_18682),U_18686),sK472(U_18688,U_18686,U_18684,U_18682)))),U_18688))
    | ~ sP1164(U_18682,U_18684,U_18688,U_18686) ),
    inference(clausify,[status(thm)],[f_4492_5]) ).

fof(f_4493_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_4493_2,plain,
    ! [U_18691,U_18690,U_18689] :
      ( hAPP(c_Random_Opick(U_18690,hAPP(hAPP(c_List_Omap(U_18690,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18690)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18690),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18691)),hAPP(c_Code__Numeral_Oof__nat,U_18689)) = hAPP(hAPP(c_List_Onth(U_18690),U_18691),U_18689)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18689),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18690)),U_18691))) ),
    inference(variable_rename,[status(thm)],[f_4493_1]) ).

fof(f_4493_3,plain,
    ! [U_18690,U_18691,U_18689] :
      ( hAPP(c_Random_Opick(U_18690,hAPP(hAPP(c_List_Omap(U_18690,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18690)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18690),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18691)),hAPP(c_Code__Numeral_Oof__nat,U_18689)) = hAPP(hAPP(c_List_Onth(U_18690),U_18691),U_18689)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18689),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18690)),U_18691))) ),
    inference(definitional_conversion,[status(esa)],[f_4493_2]) ).

cnf(f_4493_4,plain,
    ( hAPP(c_Random_Opick(U_18690,hAPP(hAPP(c_List_Omap(U_18690,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18690)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18690),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18691)),hAPP(c_Code__Numeral_Oof__nat,U_18689)) = hAPP(hAPP(c_List_Onth(U_18690),U_18691),U_18689)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18689),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18690)),U_18691))) ),
    inference(clausify,[status(thm)],[f_4493_3]) ).

fof(f_4494_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_4494_2,plain,
    ! [U_18693,U_18692] : c_Random_Oselect(U_18692,U_18693) = 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_18692,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_18692)),U_18693)))),hAPP(hAPP(c_COMBB(U_18692,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18692,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18692,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_18692,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(U_18692),U_18693)),c_Code__Numeral_Onat__of))),
    inference(variable_rename,[status(thm)],[f_4494_1]) ).

fof(f_4494_3,plain,
    ! [U_18692,U_18693] : c_Random_Oselect(U_18692,U_18693) = 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_18692,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_18692)),U_18693)))),hAPP(hAPP(c_COMBB(U_18692,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18692,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18692,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_18692,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(U_18692),U_18693)),c_Code__Numeral_Onat__of))),
    inference(definitional_conversion,[status(esa)],[f_4494_2]) ).

cnf(f_4494_4,plain,
    c_Random_Oselect(U_18692,U_18693) = 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_18692,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_18692)),U_18693)))),hAPP(hAPP(c_COMBB(U_18692,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18692,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18692,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_18692,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(U_18692),U_18693)),c_Code__Numeral_Onat__of))),
    inference(clausify,[status(thm)],[f_4494_3]) ).

fof(f_4495_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_4495_2,plain,
    ! [U_18699,U_18698,U_18697,U_18696] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18696),tc_List_Olist(U_18696))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18696),tc_List_Olist(U_18696)),U_18697),U_18698)),c_List_Olexord(U_18696,U_18699)))
        | ( ! [U_18695] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18696,U_18696)),hAPP(hAPP(c_Product__Type_OPair(U_18696,U_18696),hAPP(hAPP(c_List_Onth(U_18696),U_18697),U_18695)),hAPP(hAPP(c_List_Onth(U_18696),U_18698),U_18695))),U_18699))
              | hAPP(hAPP(c_List_Otake(U_18696),U_18695),U_18697) != hAPP(hAPP(c_List_Otake(U_18696),U_18695),U_18698)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18695),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18696)),U_18697)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18696)),U_18698)))) )
          & ( hAPP(hAPP(c_List_Otake(U_18696),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18696)),U_18697)),U_18698) != U_18697
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18696)),U_18697)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18696)),U_18698))) ) ) )
      & ( ? [U_18694] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18696,U_18696)),hAPP(hAPP(c_Product__Type_OPair(U_18696,U_18696),hAPP(hAPP(c_List_Onth(U_18696),U_18697),U_18694)),hAPP(hAPP(c_List_Onth(U_18696),U_18698),U_18694))),U_18699))
            & hAPP(hAPP(c_List_Otake(U_18696),U_18694),U_18697) = hAPP(hAPP(c_List_Otake(U_18696),U_18694),U_18698)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18694),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18696)),U_18697)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18696)),U_18698)))) )
        | ( hAPP(hAPP(c_List_Otake(U_18696),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18696)),U_18697)),U_18698) = U_18697
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18696)),U_18697)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18696)),U_18698))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18696),tc_List_Olist(U_18696))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18696),tc_List_Olist(U_18696)),U_18697),U_18698)),c_List_Olexord(U_18696,U_18699))) ) ),
    inference(variable_rename,[status(thm)],[f_4495_1]) ).

fof(f_4495_3,plain,
    ( ! [U_18707,U_18705,U_18703,U_18701] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18701),tc_List_Olist(U_18701))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18701),tc_List_Olist(U_18701)),U_18703),U_18705)),c_List_Olexord(U_18701,U_18707)))
        | ( ! [U_18695] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18701,U_18701)),hAPP(hAPP(c_Product__Type_OPair(U_18701,U_18701),hAPP(hAPP(c_List_Onth(U_18701),U_18703),U_18695)),hAPP(hAPP(c_List_Onth(U_18701),U_18705),U_18695))),U_18707))
              | hAPP(hAPP(c_List_Otake(U_18701),U_18695),U_18703) != hAPP(hAPP(c_List_Otake(U_18701),U_18695),U_18705)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18695),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18703)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18705)))) )
          & ( hAPP(hAPP(c_List_Otake(U_18701),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18703)),U_18705) != U_18703
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18703)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18705))) ) ) )
    & ! [U_18706,U_18704,U_18702,U_18700] :
        ( ? [U_18694] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18700,U_18700)),hAPP(hAPP(c_Product__Type_OPair(U_18700,U_18700),hAPP(hAPP(c_List_Onth(U_18700),U_18702),U_18694)),hAPP(hAPP(c_List_Onth(U_18700),U_18704),U_18694))),U_18706))
            & hAPP(hAPP(c_List_Otake(U_18700),U_18694),U_18702) = hAPP(hAPP(c_List_Otake(U_18700),U_18694),U_18704)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18694),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18702)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18704)))) )
        | ( hAPP(hAPP(c_List_Otake(U_18700),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18702)),U_18704) = U_18702
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18702)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18704))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18700),tc_List_Olist(U_18700))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18700),tc_List_Olist(U_18700)),U_18702),U_18704)),c_List_Olexord(U_18700,U_18706))) ) ),
    inference(miniscope,[status(thm)],[f_4495_2]) ).

fof(f_4495_4,plain,
    ( ! [U_18707,U_18705,U_18703,U_18701] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18701),tc_List_Olist(U_18701))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18701),tc_List_Olist(U_18701)),U_18703),U_18705)),c_List_Olexord(U_18701,U_18707)))
        | ( ! [U_18695] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18701,U_18701)),hAPP(hAPP(c_Product__Type_OPair(U_18701,U_18701),hAPP(hAPP(c_List_Onth(U_18701),U_18703),U_18695)),hAPP(hAPP(c_List_Onth(U_18701),U_18705),U_18695))),U_18707))
              | hAPP(hAPP(c_List_Otake(U_18701),U_18695),U_18703) != hAPP(hAPP(c_List_Otake(U_18701),U_18695),U_18705)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18695),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18703)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18705)))) )
          & ( hAPP(hAPP(c_List_Otake(U_18701),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18703)),U_18705) != U_18703
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18703)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18705))) ) ) )
    & ! [U_18706,U_18704,U_18702,U_18700] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18700,U_18700)),hAPP(hAPP(c_Product__Type_OPair(U_18700,U_18700),hAPP(hAPP(c_List_Onth(U_18700),U_18702),sK473(U_18706,U_18704,U_18702,U_18700))),hAPP(hAPP(c_List_Onth(U_18700),U_18704),sK473(U_18706,U_18704,U_18702,U_18700)))),U_18706))
          & hAPP(hAPP(c_List_Otake(U_18700),sK473(U_18706,U_18704,U_18702,U_18700)),U_18702) = hAPP(hAPP(c_List_Otake(U_18700),sK473(U_18706,U_18704,U_18702,U_18700)),U_18704)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK473(U_18706,U_18704,U_18702,U_18700)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18702)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18704)))) )
        | ( hAPP(hAPP(c_List_Otake(U_18700),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18702)),U_18704) = U_18702
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18702)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18704))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18700),tc_List_Olist(U_18700))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18700),tc_List_Olist(U_18700)),U_18702),U_18704)),c_List_Olexord(U_18700,U_18706))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK473]),skolemize(U_18694,sK473(U_18706,U_18704,U_18702,U_18700))],[f_4495_3]) ).

fof(f_4495_5,plain,
    ( ! [U_18695,U_18701,U_18707,U_18703,U_18705] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18701,U_18701)),hAPP(hAPP(c_Product__Type_OPair(U_18701,U_18701),hAPP(hAPP(c_List_Onth(U_18701),U_18703),U_18695)),hAPP(hAPP(c_List_Onth(U_18701),U_18705),U_18695))),U_18707))
        | hAPP(hAPP(c_List_Otake(U_18701),U_18695),U_18703) != hAPP(hAPP(c_List_Otake(U_18701),U_18695),U_18705)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18695),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18703)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18705))))
        | ~ sP1167(U_18695,U_18701,U_18707,U_18703,U_18705) )
    & ! [U_18695,U_18701,U_18707,U_18703,U_18705] :
        ( hAPP(hAPP(c_List_Otake(U_18701),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18703)),U_18705) != U_18703
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18703)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18705)))
        | ~ sP1167(U_18695,U_18701,U_18707,U_18703,U_18705) )
    & ! [U_18704,U_18700,U_18702,U_18706] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18700,U_18700)),hAPP(hAPP(c_Product__Type_OPair(U_18700,U_18700),hAPP(hAPP(c_List_Onth(U_18700),U_18702),sK473(U_18706,U_18704,U_18702,U_18700))),hAPP(hAPP(c_List_Onth(U_18700),U_18704),sK473(U_18706,U_18704,U_18702,U_18700)))),U_18706))
        | ~ sP1166(U_18704,U_18700,U_18702,U_18706) )
    & ! [U_18704,U_18700,U_18702,U_18706] :
        ( hAPP(hAPP(c_List_Otake(U_18700),sK473(U_18706,U_18704,U_18702,U_18700)),U_18702) = hAPP(hAPP(c_List_Otake(U_18700),sK473(U_18706,U_18704,U_18702,U_18700)),U_18704)
        | ~ sP1166(U_18704,U_18700,U_18702,U_18706) )
    & ! [U_18704,U_18700,U_18702,U_18706] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK473(U_18706,U_18704,U_18702,U_18700)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18702)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18704))))
        | ~ sP1166(U_18704,U_18700,U_18702,U_18706) )
    & ! [U_18704,U_18700,U_18702] :
        ( hAPP(hAPP(c_List_Otake(U_18700),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18702)),U_18704) = U_18702
        | ~ sP1165(U_18704,U_18700,U_18702) )
    & ! [U_18704,U_18700,U_18702] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18702)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18704)))
        | ~ sP1165(U_18704,U_18700,U_18702) )
    & ! [U_18695,U_18701,U_18707,U_18703,U_18705] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18701),tc_List_Olist(U_18701))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18701),tc_List_Olist(U_18701)),U_18703),U_18705)),c_List_Olexord(U_18701,U_18707)))
        | sP1167(U_18695,U_18701,U_18707,U_18703,U_18705) )
    & ! [U_18704,U_18700,U_18702,U_18706] :
        ( sP1166(U_18704,U_18700,U_18702,U_18706)
        | sP1165(U_18704,U_18700,U_18702)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18700),tc_List_Olist(U_18700))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18700),tc_List_Olist(U_18700)),U_18702),U_18704)),c_List_Olexord(U_18700,U_18706))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1165,sP1166,sP1167])],[f_4495_4]) ).

cnf(f_4495_6,plain,
    ( sP1166(U_18704,U_18700,U_18702,U_18706)
    | sP1165(U_18704,U_18700,U_18702)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18700),tc_List_Olist(U_18700))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18700),tc_List_Olist(U_18700)),U_18702),U_18704)),c_List_Olexord(U_18700,U_18706))) ),
    inference(clausify,[status(thm)],[f_4495_5]) ).

cnf(f_4495_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18701),tc_List_Olist(U_18701))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18701),tc_List_Olist(U_18701)),U_18703),U_18705)),c_List_Olexord(U_18701,U_18707)))
    | sP1167(U_18695,U_18701,U_18707,U_18703,U_18705) ),
    inference(clausify,[status(thm)],[f_4495_5]) ).

cnf(f_4495_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18702)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18704)))
    | ~ sP1165(U_18704,U_18700,U_18702) ),
    inference(clausify,[status(thm)],[f_4495_5]) ).

cnf(f_4495_9,plain,
    ( hAPP(hAPP(c_List_Otake(U_18700),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18702)),U_18704) = U_18702
    | ~ sP1165(U_18704,U_18700,U_18702) ),
    inference(clausify,[status(thm)],[f_4495_5]) ).

cnf(f_4495_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK473(U_18706,U_18704,U_18702,U_18700)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18702)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18700)),U_18704))))
    | ~ sP1166(U_18704,U_18700,U_18702,U_18706) ),
    inference(clausify,[status(thm)],[f_4495_5]) ).

cnf(f_4495_11,plain,
    ( hAPP(hAPP(c_List_Otake(U_18700),sK473(U_18706,U_18704,U_18702,U_18700)),U_18702) = hAPP(hAPP(c_List_Otake(U_18700),sK473(U_18706,U_18704,U_18702,U_18700)),U_18704)
    | ~ sP1166(U_18704,U_18700,U_18702,U_18706) ),
    inference(clausify,[status(thm)],[f_4495_5]) ).

cnf(f_4495_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18700,U_18700)),hAPP(hAPP(c_Product__Type_OPair(U_18700,U_18700),hAPP(hAPP(c_List_Onth(U_18700),U_18702),sK473(U_18706,U_18704,U_18702,U_18700))),hAPP(hAPP(c_List_Onth(U_18700),U_18704),sK473(U_18706,U_18704,U_18702,U_18700)))),U_18706))
    | ~ sP1166(U_18704,U_18700,U_18702,U_18706) ),
    inference(clausify,[status(thm)],[f_4495_5]) ).

cnf(f_4495_13,plain,
    ( hAPP(hAPP(c_List_Otake(U_18701),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18703)),U_18705) != U_18703
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18703)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18705)))
    | ~ sP1167(U_18695,U_18701,U_18707,U_18703,U_18705) ),
    inference(clausify,[status(thm)],[f_4495_5]) ).

cnf(f_4495_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18701,U_18701)),hAPP(hAPP(c_Product__Type_OPair(U_18701,U_18701),hAPP(hAPP(c_List_Onth(U_18701),U_18703),U_18695)),hAPP(hAPP(c_List_Onth(U_18701),U_18705),U_18695))),U_18707))
    | hAPP(hAPP(c_List_Otake(U_18701),U_18695),U_18703) != hAPP(hAPP(c_List_Otake(U_18701),U_18695),U_18705)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18695),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18703)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18701)),U_18705))))
    | ~ sP1167(U_18695,U_18701,U_18707,U_18703,U_18705) ),
    inference(clausify,[status(thm)],[f_4495_5]) ).

fof(f_4496_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_4496_2,plain,
    ! [U_18711,U_18710,U_18709,U_18708] :
      ( hBOOL(hAPP(hAPP(c_member(U_18708),U_18709),hAPP(c_List_Oset(U_18708),U_18711)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18708),U_18709),hAPP(c_List_Oset(U_18708),hAPP(hAPP(c_List_Otake(U_18708),U_18710),U_18711)))) ),
    inference(variable_rename,[status(thm)],[f_4496_1]) ).

fof(f_4496_3,plain,
    ! [U_18708,U_18711,U_18709,U_18710] :
      ( hBOOL(hAPP(hAPP(c_member(U_18708),U_18709),hAPP(c_List_Oset(U_18708),U_18711)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18708),U_18709),hAPP(c_List_Oset(U_18708),hAPP(hAPP(c_List_Otake(U_18708),U_18710),U_18711)))) ),
    inference(definitional_conversion,[status(esa)],[f_4496_2]) ).

cnf(f_4496_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18708),U_18709),hAPP(c_List_Oset(U_18708),U_18711)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18708),U_18709),hAPP(c_List_Oset(U_18708),hAPP(hAPP(c_List_Otake(U_18708),U_18710),U_18711)))) ),
    inference(clausify,[status(thm)],[f_4496_3]) ).

fof(f_4497_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_4497_2,plain,
    ! [U_18715,U_18714,U_18713,U_18712] :
      ( hAPP(hAPP(c_List_Onth(U_18714),hAPP(hAPP(c_List_Otake(U_18714),U_18713),U_18715)),U_18712) = hAPP(hAPP(c_List_Onth(U_18714),U_18715),U_18712)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18712),U_18713)) ),
    inference(variable_rename,[status(thm)],[f_4497_1]) ).

fof(f_4497_3,plain,
    ! [U_18712,U_18714,U_18713,U_18715] :
      ( hAPP(hAPP(c_List_Onth(U_18714),hAPP(hAPP(c_List_Otake(U_18714),U_18713),U_18715)),U_18712) = hAPP(hAPP(c_List_Onth(U_18714),U_18715),U_18712)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18712),U_18713)) ),
    inference(definitional_conversion,[status(esa)],[f_4497_2]) ).

cnf(f_4497_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_18714),hAPP(hAPP(c_List_Otake(U_18714),U_18713),U_18715)),U_18712) = hAPP(hAPP(c_List_Onth(U_18714),U_18715),U_18712)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18712),U_18713)) ),
    inference(clausify,[status(thm)],[f_4497_3]) ).

fof(f_4498_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_4498_2,plain,
    ! [U_18718,U_18717,U_18716] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18716,tc_HOL_Obool)),hAPP(c_List_Oset(U_18716),hAPP(hAPP(c_List_Otake(U_18716),U_18717),U_18718))),hAPP(c_List_Oset(U_18716),U_18718))),
    inference(variable_rename,[status(thm)],[f_4498_1]) ).

fof(f_4498_3,plain,
    ! [U_18716,U_18717,U_18718] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18716,tc_HOL_Obool)),hAPP(c_List_Oset(U_18716),hAPP(hAPP(c_List_Otake(U_18716),U_18717),U_18718))),hAPP(c_List_Oset(U_18716),U_18718))),
    inference(definitional_conversion,[status(esa)],[f_4498_2]) ).

cnf(f_4498_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18716,tc_HOL_Obool)),hAPP(c_List_Oset(U_18716),hAPP(hAPP(c_List_Otake(U_18716),U_18717),U_18718))),hAPP(c_List_Oset(U_18716),U_18718))),
    inference(clausify,[status(thm)],[f_4498_3]) ).

fof(f_4499_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_4499_2,plain,
    ! [U_18722,U_18721,U_18720,U_18719] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18721,tc_HOL_Obool)),hAPP(c_List_Oset(U_18721),hAPP(hAPP(c_List_Otake(U_18721),U_18719),U_18722))),hAPP(c_List_Oset(U_18721),hAPP(hAPP(c_List_Otake(U_18721),U_18720),U_18722))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18719),U_18720)) ),
    inference(variable_rename,[status(thm)],[f_4499_1]) ).

fof(f_4499_3,plain,
    ! [U_18719,U_18720,U_18721,U_18722] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18721,tc_HOL_Obool)),hAPP(c_List_Oset(U_18721),hAPP(hAPP(c_List_Otake(U_18721),U_18719),U_18722))),hAPP(c_List_Oset(U_18721),hAPP(hAPP(c_List_Otake(U_18721),U_18720),U_18722))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18719),U_18720)) ),
    inference(definitional_conversion,[status(esa)],[f_4499_2]) ).

cnf(f_4499_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18721,tc_HOL_Obool)),hAPP(c_List_Oset(U_18721),hAPP(hAPP(c_List_Otake(U_18721),U_18719),U_18722))),hAPP(c_List_Oset(U_18721),hAPP(hAPP(c_List_Otake(U_18721),U_18720),U_18722))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18719),U_18720)) ),
    inference(clausify,[status(thm)],[f_4499_3]) ).

fof(f_4500_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_4500_2,plain,
    ! [U_18725,U_18724,U_18723] :
      ( hAPP(hAPP(c_List_Otake(U_18723),U_18725),U_18724) = U_18724
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18723)),U_18724)),U_18725)) ),
    inference(variable_rename,[status(thm)],[f_4500_1]) ).

fof(f_4500_3,plain,
    ! [U_18723,U_18724,U_18725] :
      ( hAPP(hAPP(c_List_Otake(U_18723),U_18725),U_18724) = U_18724
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18723)),U_18724)),U_18725)) ),
    inference(definitional_conversion,[status(esa)],[f_4500_2]) ).

cnf(f_4500_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_18723),U_18725),U_18724) = U_18724
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18723)),U_18724)),U_18725)) ),
    inference(clausify,[status(thm)],[f_4500_3]) ).

fof(f_4501_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_4501_2,plain,
    ! [U_18728,U_18727,U_18726] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18726),hAPP(hAPP(c_List_Otake(U_18726),U_18728),U_18727)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18726),U_18727)) ),
    inference(variable_rename,[status(thm)],[f_4501_1]) ).

fof(f_4501_3,plain,
    ! [U_18726,U_18727,U_18728] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18726),hAPP(hAPP(c_List_Otake(U_18726),U_18728),U_18727)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18726),U_18727)) ),
    inference(definitional_conversion,[status(esa)],[f_4501_2]) ).

cnf(f_4501_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18726),hAPP(hAPP(c_List_Otake(U_18726),U_18728),U_18727)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18726),U_18727)) ),
    inference(clausify,[status(thm)],[f_4501_3]) ).

fof(f_4502_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_4502_2,plain,
    ! [U_18732,U_18731,U_18730,U_18729] : hAPP(hAPP(c_List_Otake(U_18729),U_18730),hAPP(hAPP(c_List_Otake(U_18729),U_18731),U_18732)) = hAPP(hAPP(c_List_Otake(U_18729),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_18730),U_18731)),U_18732),
    inference(variable_rename,[status(thm)],[f_4502_1]) ).

fof(f_4502_3,plain,
    ! [U_18729,U_18730,U_18731,U_18732] : hAPP(hAPP(c_List_Otake(U_18729),U_18730),hAPP(hAPP(c_List_Otake(U_18729),U_18731),U_18732)) = hAPP(hAPP(c_List_Otake(U_18729),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_18730),U_18731)),U_18732),
    inference(definitional_conversion,[status(esa)],[f_4502_2]) ).

cnf(f_4502_4,plain,
    hAPP(hAPP(c_List_Otake(U_18729),U_18730),hAPP(hAPP(c_List_Otake(U_18729),U_18731),U_18732)) = hAPP(hAPP(c_List_Otake(U_18729),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_18730),U_18731)),U_18732),
    inference(clausify,[status(thm)],[f_4502_3]) ).

fof(f_4503_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_4503_2,plain,
    ! [U_18737,U_18736,U_18735,U_18734,U_18733] : hAPP(hAPP(c_List_Otake(tc_prod(U_18733,U_18734)),U_18735),hAPP(hAPP(c_List_Ozip(U_18733,U_18734),U_18736),U_18737)) = hAPP(hAPP(c_List_Ozip(U_18733,U_18734),hAPP(hAPP(c_List_Otake(U_18733),U_18735),U_18736)),hAPP(hAPP(c_List_Otake(U_18734),U_18735),U_18737)),
    inference(variable_rename,[status(thm)],[f_4503_1]) ).

fof(f_4503_3,plain,
    ! [U_18733,U_18734,U_18735,U_18736,U_18737] : hAPP(hAPP(c_List_Otake(tc_prod(U_18733,U_18734)),U_18735),hAPP(hAPP(c_List_Ozip(U_18733,U_18734),U_18736),U_18737)) = hAPP(hAPP(c_List_Ozip(U_18733,U_18734),hAPP(hAPP(c_List_Otake(U_18733),U_18735),U_18736)),hAPP(hAPP(c_List_Otake(U_18734),U_18735),U_18737)),
    inference(definitional_conversion,[status(esa)],[f_4503_2]) ).

cnf(f_4503_4,plain,
    hAPP(hAPP(c_List_Otake(tc_prod(U_18733,U_18734)),U_18735),hAPP(hAPP(c_List_Ozip(U_18733,U_18734),U_18736),U_18737)) = hAPP(hAPP(c_List_Ozip(U_18733,U_18734),hAPP(hAPP(c_List_Otake(U_18733),U_18735),U_18736)),hAPP(hAPP(c_List_Otake(U_18734),U_18735),U_18737)),
    inference(clausify,[status(thm)],[f_4503_3]) ).

fof(f_4504_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_4504_2,plain,
    ! [U_18740,U_18739,U_18738] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18738)),hAPP(hAPP(c_List_Otake(U_18738),U_18739),U_18740)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18738)),U_18740)),U_18739),
    inference(variable_rename,[status(thm)],[f_4504_1]) ).

fof(f_4504_3,plain,
    ! [U_18738,U_18739,U_18740] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18738)),hAPP(hAPP(c_List_Otake(U_18738),U_18739),U_18740)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18738)),U_18740)),U_18739),
    inference(definitional_conversion,[status(esa)],[f_4504_2]) ).

cnf(f_4504_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18738)),hAPP(hAPP(c_List_Otake(U_18738),U_18739),U_18740)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18738)),U_18740)),U_18739),
    inference(clausify,[status(thm)],[f_4504_3]) ).

fof(f_4505_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_4505_2,plain,
    ! [U_18744,U_18743,U_18742,U_18741] : hAPP(hAPP(c_List_Otake(U_18741),hAPP(c_Nat_OSuc,U_18742)),hAPP(hAPP(c_List_Olist_OCons(U_18741),U_18743),U_18744)) = hAPP(hAPP(c_List_Olist_OCons(U_18741),U_18743),hAPP(hAPP(c_List_Otake(U_18741),U_18742),U_18744)),
    inference(variable_rename,[status(thm)],[f_4505_1]) ).

fof(f_4505_3,plain,
    ! [U_18741,U_18742,U_18743,U_18744] : hAPP(hAPP(c_List_Otake(U_18741),hAPP(c_Nat_OSuc,U_18742)),hAPP(hAPP(c_List_Olist_OCons(U_18741),U_18743),U_18744)) = hAPP(hAPP(c_List_Olist_OCons(U_18741),U_18743),hAPP(hAPP(c_List_Otake(U_18741),U_18742),U_18744)),
    inference(definitional_conversion,[status(esa)],[f_4505_2]) ).

cnf(f_4505_4,plain,
    hAPP(hAPP(c_List_Otake(U_18741),hAPP(c_Nat_OSuc,U_18742)),hAPP(hAPP(c_List_Olist_OCons(U_18741),U_18743),U_18744)) = hAPP(hAPP(c_List_Olist_OCons(U_18741),U_18743),hAPP(hAPP(c_List_Otake(U_18741),U_18742),U_18744)),
    inference(clausify,[status(thm)],[f_4505_3]) ).

fof(f_4506_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_4506_2,plain,
    ! [U_18747,U_18746,U_18745] : c_List_Osublist(U_18745,U_18746,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_18747)) = hAPP(hAPP(c_List_Otake(U_18745),U_18747),U_18746),
    inference(variable_rename,[status(thm)],[f_4506_1]) ).

fof(f_4506_3,plain,
    ! [U_18745,U_18746,U_18747] : c_List_Osublist(U_18745,U_18746,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_18747)) = hAPP(hAPP(c_List_Otake(U_18745),U_18747),U_18746),
    inference(definitional_conversion,[status(esa)],[f_4506_2]) ).

cnf(f_4506_4,plain,
    c_List_Osublist(U_18745,U_18746,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_18747)) = hAPP(hAPP(c_List_Otake(U_18745),U_18747),U_18746),
    inference(clausify,[status(thm)],[f_4506_3]) ).

fof(f_4507_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_4507_2,plain,
    ! [U_18752,U_18751,U_18750,U_18749,U_18748] : hAPP(hAPP(c_List_Otake(U_18748),U_18749),hAPP(hAPP(c_List_Omap(U_18750,U_18748),U_18751),U_18752)) = hAPP(hAPP(c_List_Omap(U_18750,U_18748),U_18751),hAPP(hAPP(c_List_Otake(U_18750),U_18749),U_18752)),
    inference(variable_rename,[status(thm)],[f_4507_1]) ).

fof(f_4507_3,plain,
    ! [U_18751,U_18748,U_18749,U_18750,U_18752] : hAPP(hAPP(c_List_Otake(U_18748),U_18749),hAPP(hAPP(c_List_Omap(U_18750,U_18748),U_18751),U_18752)) = hAPP(hAPP(c_List_Omap(U_18750,U_18748),U_18751),hAPP(hAPP(c_List_Otake(U_18750),U_18749),U_18752)),
    inference(definitional_conversion,[status(esa)],[f_4507_2]) ).

cnf(f_4507_4,plain,
    hAPP(hAPP(c_List_Otake(U_18748),U_18749),hAPP(hAPP(c_List_Omap(U_18750,U_18748),U_18751),U_18752)) = hAPP(hAPP(c_List_Omap(U_18750,U_18748),U_18751),hAPP(hAPP(c_List_Otake(U_18750),U_18749),U_18752)),
    inference(clausify,[status(thm)],[f_4507_3]) ).

fof(f_4508_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_4508_2,plain,
    ! [U_18755,U_18754,U_18753] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,U_18754),U_18753),U_18755)) = 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_18754)),U_18755)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18754),U_18753))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18753),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18754))) ),
    inference(variable_rename,[status(thm)],[f_4508_1]) ).

fof(f_4508_3,plain,
    ! [U_18753,U_18754,U_18755] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,U_18754),U_18753),U_18755)) = 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_18754)),U_18755)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18754),U_18753))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18753),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18754))) ),
    inference(definitional_conversion,[status(esa)],[f_4508_2]) ).

cnf(f_4508_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,U_18754),U_18753),U_18755)) = 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_18754)),U_18755)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18754),U_18753))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18753),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18754))) ),
    inference(clausify,[status(thm)],[f_4508_3]) ).

fof(f_4509_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_4509_2,plain,
    ! [U_18757,U_18756] :
      ( c_Random_Oselect__weight(U_18757,hAPP(hAPP(c_List_Omap(U_18757,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18757)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18757),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18756)) = c_Random_Oselect(U_18757,U_18756)
      | U_18756 = c_List_Olist_ONil(U_18757) ),
    inference(variable_rename,[status(thm)],[f_4509_1]) ).

fof(f_4509_3,plain,
    ! [U_18756,U_18757] :
      ( c_Random_Oselect__weight(U_18757,hAPP(hAPP(c_List_Omap(U_18757,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18757)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18757),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18756)) = c_Random_Oselect(U_18757,U_18756)
      | U_18756 = c_List_Olist_ONil(U_18757) ),
    inference(definitional_conversion,[status(esa)],[f_4509_2]) ).

cnf(f_4509_4,plain,
    ( c_Random_Oselect__weight(U_18757,hAPP(hAPP(c_List_Omap(U_18757,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18757)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18757),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18756)) = c_Random_Oselect(U_18757,U_18756)
    | U_18756 = c_List_Olist_ONil(U_18757) ),
    inference(clausify,[status(thm)],[f_4509_3]) ).

fof(f_4510_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_4510_2,plain,
    ! [U_18760,U_18759,U_18758] :
      ( U_18759 = c_List_Olist_ONil(U_18758)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18758),tc_List_Olist(U_18758))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18758),tc_List_Olist(U_18758)),c_List_Olist_ONil(U_18758)),U_18759)),c_List_Olistrel(U_18758,U_18760))) ),
    inference(variable_rename,[status(thm)],[f_4510_1]) ).

fof(f_4510_3,plain,
    ! [U_18758,U_18759,U_18760] :
      ( U_18759 = c_List_Olist_ONil(U_18758)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18758),tc_List_Olist(U_18758))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18758),tc_List_Olist(U_18758)),c_List_Olist_ONil(U_18758)),U_18759)),c_List_Olistrel(U_18758,U_18760))) ),
    inference(definitional_conversion,[status(esa)],[f_4510_2]) ).

cnf(f_4510_4,plain,
    ( U_18759 = c_List_Olist_ONil(U_18758)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18758),tc_List_Olist(U_18758))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18758),tc_List_Olist(U_18758)),c_List_Olist_ONil(U_18758)),U_18759)),c_List_Olistrel(U_18758,U_18760))) ),
    inference(clausify,[status(thm)],[f_4510_3]) ).

fof(f_4511_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_4511_2,plain,
    ! [U_18763,U_18762,U_18761] :
      ( U_18762 = c_List_Olist_ONil(U_18761)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18761),tc_List_Olist(U_18761))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18761),tc_List_Olist(U_18761)),U_18762),c_List_Olist_ONil(U_18761))),c_List_Olistrel(U_18761,U_18763))) ),
    inference(variable_rename,[status(thm)],[f_4511_1]) ).

fof(f_4511_3,plain,
    ! [U_18761,U_18762,U_18763] :
      ( U_18762 = c_List_Olist_ONil(U_18761)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18761),tc_List_Olist(U_18761))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18761),tc_List_Olist(U_18761)),U_18762),c_List_Olist_ONil(U_18761))),c_List_Olistrel(U_18761,U_18763))) ),
    inference(definitional_conversion,[status(esa)],[f_4511_2]) ).

cnf(f_4511_4,plain,
    ( U_18762 = c_List_Olist_ONil(U_18761)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18761),tc_List_Olist(U_18761))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18761),tc_List_Olist(U_18761)),U_18762),c_List_Olist_ONil(U_18761))),c_List_Olistrel(U_18761,U_18763))) ),
    inference(clausify,[status(thm)],[f_4511_3]) ).

fof(f_4512_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_4512_2,plain,
    ! [U_18766,U_18765,U_18764] : hAPP(hAPP(c_List_Olist__update(U_18764,U_18765),U_18766),hAPP(hAPP(c_List_Onth(U_18764),U_18765),U_18766)) = U_18765,
    inference(variable_rename,[status(thm)],[f_4512_1]) ).

fof(f_4512_3,plain,
    ! [U_18764,U_18765,U_18766] : hAPP(hAPP(c_List_Olist__update(U_18764,U_18765),U_18766),hAPP(hAPP(c_List_Onth(U_18764),U_18765),U_18766)) = U_18765,
    inference(definitional_conversion,[status(esa)],[f_4512_2]) ).

cnf(f_4512_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18764,U_18765),U_18766),hAPP(hAPP(c_List_Onth(U_18764),U_18765),U_18766)) = U_18765,
    inference(clausify,[status(thm)],[f_4512_3]) ).

fof(f_4513_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_4513_2,plain,
    ! [U_18771,U_18770,U_18769,U_18768,U_18767] :
      ( hAPP(hAPP(c_List_Onth(U_18769),hAPP(hAPP(c_List_Olist__update(U_18769,U_18770),U_18767),U_18771)),U_18768) = hAPP(hAPP(c_List_Onth(U_18769),U_18770),U_18768)
      | U_18767 = U_18768 ),
    inference(variable_rename,[status(thm)],[f_4513_1]) ).

fof(f_4513_3,plain,
    ! [U_18767,U_18768,U_18769,U_18770,U_18771] :
      ( hAPP(hAPP(c_List_Onth(U_18769),hAPP(hAPP(c_List_Olist__update(U_18769,U_18770),U_18767),U_18771)),U_18768) = hAPP(hAPP(c_List_Onth(U_18769),U_18770),U_18768)
      | U_18767 = U_18768 ),
    inference(definitional_conversion,[status(esa)],[f_4513_2]) ).

cnf(f_4513_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_18769),hAPP(hAPP(c_List_Olist__update(U_18769,U_18770),U_18767),U_18771)),U_18768) = hAPP(hAPP(c_List_Onth(U_18769),U_18770),U_18768)
    | U_18767 = U_18768 ),
    inference(clausify,[status(thm)],[f_4513_3]) ).

fof(f_4514_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_4514_2,plain,
    ! [U_18775,U_18774,U_18773,U_18772] :
      ( hAPP(hAPP(c_List_Olist__update(U_18772,U_18773),U_18774),U_18775) = U_18773
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18772)),U_18773)),U_18774)) ),
    inference(variable_rename,[status(thm)],[f_4514_1]) ).

fof(f_4514_3,plain,
    ! [U_18772,U_18773,U_18774,U_18775] :
      ( hAPP(hAPP(c_List_Olist__update(U_18772,U_18773),U_18774),U_18775) = U_18773
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18772)),U_18773)),U_18774)) ),
    inference(definitional_conversion,[status(esa)],[f_4514_2]) ).

cnf(f_4514_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_18772,U_18773),U_18774),U_18775) = U_18773
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18772)),U_18773)),U_18774)) ),
    inference(clausify,[status(thm)],[f_4514_3]) ).

fof(f_4515_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_4515_2,plain,
    ! [U_18777,U_18776] : hAPP(hAPP(c_List_Otake(U_18776),U_18777),c_List_Olist_ONil(U_18776)) = c_List_Olist_ONil(U_18776),
    inference(variable_rename,[status(thm)],[f_4515_1]) ).

fof(f_4515_3,plain,
    ! [U_18776,U_18777] : hAPP(hAPP(c_List_Otake(U_18776),U_18777),c_List_Olist_ONil(U_18776)) = c_List_Olist_ONil(U_18776),
    inference(definitional_conversion,[status(esa)],[f_4515_2]) ).

cnf(f_4515_4,plain,
    hAPP(hAPP(c_List_Otake(U_18776),U_18777),c_List_Olist_ONil(U_18776)) = c_List_Olist_ONil(U_18776),
    inference(clausify,[status(thm)],[f_4515_3]) ).

fof(f_4516_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_4516_2,plain,
    ! [U_18780,U_18779,U_18778] :
      ( ( hAPP(hAPP(c_List_Otake(U_18778),U_18779),U_18780) = c_List_Olist_ONil(U_18778)
        | ( U_18780 != c_List_Olist_ONil(U_18778)
          & U_18779 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_18780 = c_List_Olist_ONil(U_18778)
        | U_18779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(U_18778),U_18779),U_18780) != c_List_Olist_ONil(U_18778) ) ),
    inference(variable_rename,[status(thm)],[f_4516_1]) ).

fof(f_4516_3,plain,
    ( ! [U_18786,U_18784,U_18782] :
        ( hAPP(hAPP(c_List_Otake(U_18782),U_18784),U_18786) = c_List_Olist_ONil(U_18782)
        | ( U_18786 != c_List_Olist_ONil(U_18782)
          & U_18784 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_18785,U_18783,U_18781] :
        ( U_18785 = c_List_Olist_ONil(U_18781)
        | U_18783 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(U_18781),U_18783),U_18785) != c_List_Olist_ONil(U_18781) ) ),
    inference(miniscope,[status(thm)],[f_4516_2]) ).

fof(f_4516_4,plain,
    ( ! [U_18786,U_18782,U_18784] :
        ( U_18786 != c_List_Olist_ONil(U_18782)
        | ~ sP1168(U_18786,U_18782,U_18784) )
    & ! [U_18786,U_18782,U_18784] :
        ( U_18784 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1168(U_18786,U_18782,U_18784) )
    & ! [U_18786,U_18782,U_18784] :
        ( hAPP(hAPP(c_List_Otake(U_18782),U_18784),U_18786) = c_List_Olist_ONil(U_18782)
        | sP1168(U_18786,U_18782,U_18784) )
    & ! [U_18783,U_18781,U_18785] :
        ( U_18785 = c_List_Olist_ONil(U_18781)
        | U_18783 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(U_18781),U_18783),U_18785) != c_List_Olist_ONil(U_18781) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1168])],[f_4516_3]) ).

cnf(f_4516_5,plain,
    ( U_18785 = c_List_Olist_ONil(U_18781)
    | U_18783 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_List_Otake(U_18781),U_18783),U_18785) != c_List_Olist_ONil(U_18781) ),
    inference(clausify,[status(thm)],[f_4516_4]) ).

cnf(f_4516_6,plain,
    ( hAPP(hAPP(c_List_Otake(U_18782),U_18784),U_18786) = c_List_Olist_ONil(U_18782)
    | sP1168(U_18786,U_18782,U_18784) ),
    inference(clausify,[status(thm)],[f_4516_4]) ).

cnf(f_4516_7,plain,
    ( U_18784 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1168(U_18786,U_18782,U_18784) ),
    inference(clausify,[status(thm)],[f_4516_4]) ).

cnf(f_4516_8,plain,
    ( U_18786 != c_List_Olist_ONil(U_18782)
    | ~ sP1168(U_18786,U_18782,U_18784) ),
    inference(clausify,[status(thm)],[f_4516_4]) ).

fof(f_4517_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_4517_2,plain,
    ! [U_18788,U_18787] : hAPP(hAPP(c_List_Otake(U_18787),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18788) = c_List_Olist_ONil(U_18787),
    inference(variable_rename,[status(thm)],[f_4517_1]) ).

fof(f_4517_3,plain,
    ! [U_18787,U_18788] : hAPP(hAPP(c_List_Otake(U_18787),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18788) = c_List_Olist_ONil(U_18787),
    inference(definitional_conversion,[status(esa)],[f_4517_2]) ).

cnf(f_4517_4,plain,
    hAPP(hAPP(c_List_Otake(U_18787),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18788) = c_List_Olist_ONil(U_18787),
    inference(clausify,[status(thm)],[f_4517_3]) ).

fof(f_4518_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_4518_2,plain,
    ! [U_18789] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18789)),c_List_Olist_ONil(U_18789)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4518_1]) ).

fof(f_4518_3,plain,
    ! [U_18789] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18789)),c_List_Olist_ONil(U_18789)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_4518_2]) ).

cnf(f_4518_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18789)),c_List_Olist_ONil(U_18789)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4518_3]) ).

fof(f_4519_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_4519_2,plain,
    ! [U_18791,U_18790] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18790)),U_18791) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_18791 != c_List_Olist_ONil(U_18790) )
      & ( U_18791 = c_List_Olist_ONil(U_18790)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18790)),U_18791) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4519_1]) ).

fof(f_4519_3,plain,
    ( ! [U_18795,U_18793] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18793)),U_18795) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_18795 != c_List_Olist_ONil(U_18793) )
    & ! [U_18794,U_18792] :
        ( U_18794 = c_List_Olist_ONil(U_18792)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18792)),U_18794) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4519_2]) ).

fof(f_4519_4,plain,
    ( ! [U_18793,U_18795] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18793)),U_18795) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_18795 != c_List_Olist_ONil(U_18793) )
    & ! [U_18794,U_18792] :
        ( U_18794 = c_List_Olist_ONil(U_18792)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18792)),U_18794) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4519_3]) ).

cnf(f_4519_5,plain,
    ( U_18794 = c_List_Olist_ONil(U_18792)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18792)),U_18794) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4519_4]) ).

cnf(f_4519_6,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18793)),U_18795) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_18795 != c_List_Olist_ONil(U_18793) ),
    inference(clausify,[status(thm)],[f_4519_4]) ).

fof(f_4520_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_4520_2,plain,
    ! [U_18799,U_18798,U_18797,U_18796] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18796)),hAPP(hAPP(c_List_Olist__update(U_18796,U_18797),U_18798),U_18799)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18796)),U_18797),
    inference(variable_rename,[status(thm)],[f_4520_1]) ).

fof(f_4520_3,plain,
    ! [U_18796,U_18797,U_18798,U_18799] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18796)),hAPP(hAPP(c_List_Olist__update(U_18796,U_18797),U_18798),U_18799)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18796)),U_18797),
    inference(definitional_conversion,[status(esa)],[f_4520_2]) ).

cnf(f_4520_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18796)),hAPP(hAPP(c_List_Olist__update(U_18796,U_18797),U_18798),U_18799)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18796)),U_18797),
    inference(clausify,[status(thm)],[f_4520_3]) ).

fof(f_4521_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_4521_2,plain,
    ! [U_18803,U_18802,U_18801,U_18800] : hAPP(hAPP(c_List_Otake(U_18800),U_18801),hAPP(hAPP(c_List_Olist_OCons(U_18800),U_18802),U_18803)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18800),c_List_Olist_ONil(U_18800),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18800),tc_List_Olist(U_18800),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18800),U_18802)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_18800),tc_List_Olist(U_18800)),c_List_Otake(U_18800)),U_18803)),U_18801),
    inference(variable_rename,[status(thm)],[f_4521_1]) ).

fof(f_4521_3,plain,
    ! [U_18800,U_18801,U_18802,U_18803] : hAPP(hAPP(c_List_Otake(U_18800),U_18801),hAPP(hAPP(c_List_Olist_OCons(U_18800),U_18802),U_18803)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18800),c_List_Olist_ONil(U_18800),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18800),tc_List_Olist(U_18800),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18800),U_18802)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_18800),tc_List_Olist(U_18800)),c_List_Otake(U_18800)),U_18803)),U_18801),
    inference(definitional_conversion,[status(esa)],[f_4521_2]) ).

cnf(f_4521_4,plain,
    hAPP(hAPP(c_List_Otake(U_18800),U_18801),hAPP(hAPP(c_List_Olist_OCons(U_18800),U_18802),U_18803)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18800),c_List_Olist_ONil(U_18800),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18800),tc_List_Olist(U_18800),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18800),U_18802)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_18800),tc_List_Olist(U_18800)),c_List_Otake(U_18800)),U_18803)),U_18801),
    inference(clausify,[status(thm)],[f_4521_3]) ).

fof(f_4522_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_4522_2,plain,
    ! [U_18807,U_18806,U_18805,U_18804] :
      ( ( c_List_Olist_ONil(U_18804) = hAPP(hAPP(c_List_Omap(U_18805,U_18804),U_18806),U_18807)
        | U_18807 != c_List_Olist_ONil(U_18805) )
      & ( U_18807 = c_List_Olist_ONil(U_18805)
        | c_List_Olist_ONil(U_18804) != hAPP(hAPP(c_List_Omap(U_18805,U_18804),U_18806),U_18807) ) ),
    inference(variable_rename,[status(thm)],[f_4522_1]) ).

fof(f_4522_3,plain,
    ( ! [U_18815,U_18813,U_18811] :
        ( ! [U_18809] : c_List_Olist_ONil(U_18809) = hAPP(hAPP(c_List_Omap(U_18811,U_18809),U_18813),U_18815)
        | U_18815 != c_List_Olist_ONil(U_18811) )
    & ! [U_18814,U_18812,U_18810] :
        ( ! [U_18808] : c_List_Olist_ONil(U_18808) != hAPP(hAPP(c_List_Omap(U_18810,U_18808),U_18812),U_18814)
        | U_18814 = c_List_Olist_ONil(U_18810) ) ),
    inference(miniscope,[status(thm)],[f_4522_2]) ).

fof(f_4522_4,plain,
    ( ! [U_18813,U_18809,U_18811,U_18815] :
        ( c_List_Olist_ONil(U_18809) = hAPP(hAPP(c_List_Omap(U_18811,U_18809),U_18813),U_18815)
        | U_18815 != c_List_Olist_ONil(U_18811) )
    & ! [U_18812,U_18810,U_18808,U_18814] :
        ( c_List_Olist_ONil(U_18808) != hAPP(hAPP(c_List_Omap(U_18810,U_18808),U_18812),U_18814)
        | U_18814 = c_List_Olist_ONil(U_18810) ) ),
    inference(definitional_conversion,[status(esa)],[f_4522_3]) ).

cnf(f_4522_5,plain,
    ( c_List_Olist_ONil(U_18808) != hAPP(hAPP(c_List_Omap(U_18810,U_18808),U_18812),U_18814)
    | U_18814 = c_List_Olist_ONil(U_18810) ),
    inference(clausify,[status(thm)],[f_4522_4]) ).

cnf(f_4522_6,plain,
    ( c_List_Olist_ONil(U_18809) = hAPP(hAPP(c_List_Omap(U_18811,U_18809),U_18813),U_18815)
    | U_18815 != c_List_Olist_ONil(U_18811) ),
    inference(clausify,[status(thm)],[f_4522_4]) ).

fof(f_4523_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_4523_2,plain,
    ! [U_18818,U_18817,U_18816] : hAPP(hAPP(c_List_Omap(U_18816,U_18817),U_18818),c_List_Olist_ONil(U_18816)) = c_List_Olist_ONil(U_18817),
    inference(variable_rename,[status(thm)],[f_4523_1]) ).

fof(f_4523_3,plain,
    ! [U_18816,U_18817,U_18818] : hAPP(hAPP(c_List_Omap(U_18816,U_18817),U_18818),c_List_Olist_ONil(U_18816)) = c_List_Olist_ONil(U_18817),
    inference(definitional_conversion,[status(esa)],[f_4523_2]) ).

cnf(f_4523_4,plain,
    hAPP(hAPP(c_List_Omap(U_18816,U_18817),U_18818),c_List_Olist_ONil(U_18816)) = c_List_Olist_ONil(U_18817),
    inference(clausify,[status(thm)],[f_4523_3]) ).

fof(f_4524_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_4524_2,plain,
    ! [U_18824,U_18823,U_18822,U_18821,U_18820,U_18819] : hAPP(hAPP(c_List_Omap(U_18819,U_18820),U_18821),hAPP(hAPP(c_List_Olist__update(U_18819,U_18822),U_18823),U_18824)) = hAPP(hAPP(c_List_Olist__update(U_18820,hAPP(hAPP(c_List_Omap(U_18819,U_18820),U_18821),U_18822)),U_18823),hAPP(U_18821,U_18824)),
    inference(variable_rename,[status(thm)],[f_4524_1]) ).

fof(f_4524_3,plain,
    ! [U_18819,U_18820,U_18821,U_18822,U_18823,U_18824] : hAPP(hAPP(c_List_Omap(U_18819,U_18820),U_18821),hAPP(hAPP(c_List_Olist__update(U_18819,U_18822),U_18823),U_18824)) = hAPP(hAPP(c_List_Olist__update(U_18820,hAPP(hAPP(c_List_Omap(U_18819,U_18820),U_18821),U_18822)),U_18823),hAPP(U_18821,U_18824)),
    inference(definitional_conversion,[status(esa)],[f_4524_2]) ).

cnf(f_4524_4,plain,
    hAPP(hAPP(c_List_Omap(U_18819,U_18820),U_18821),hAPP(hAPP(c_List_Olist__update(U_18819,U_18822),U_18823),U_18824)) = hAPP(hAPP(c_List_Olist__update(U_18820,hAPP(hAPP(c_List_Omap(U_18819,U_18820),U_18821),U_18822)),U_18823),hAPP(U_18821,U_18824)),
    inference(clausify,[status(thm)],[f_4524_3]) ).

fof(f_4525_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_4525_2,plain,
    ! [U_18828,U_18827,U_18826,U_18825] :
      ( ( hAPP(hAPP(c_List_Omap(U_18825,U_18826),U_18827),U_18828) = c_List_Olist_ONil(U_18826)
        | U_18828 != c_List_Olist_ONil(U_18825) )
      & ( U_18828 = c_List_Olist_ONil(U_18825)
        | hAPP(hAPP(c_List_Omap(U_18825,U_18826),U_18827),U_18828) != c_List_Olist_ONil(U_18826) ) ),
    inference(variable_rename,[status(thm)],[f_4525_1]) ).

fof(f_4525_3,plain,
    ( ! [U_18836,U_18834,U_18832,U_18830] :
        ( hAPP(hAPP(c_List_Omap(U_18830,U_18832),U_18834),U_18836) = c_List_Olist_ONil(U_18832)
        | U_18836 != c_List_Olist_ONil(U_18830) )
    & ! [U_18835,U_18833,U_18831,U_18829] :
        ( U_18835 = c_List_Olist_ONil(U_18829)
        | hAPP(hAPP(c_List_Omap(U_18829,U_18831),U_18833),U_18835) != c_List_Olist_ONil(U_18831) ) ),
    inference(miniscope,[status(thm)],[f_4525_2]) ).

fof(f_4525_4,plain,
    ( ! [U_18830,U_18836,U_18832,U_18834] :
        ( hAPP(hAPP(c_List_Omap(U_18830,U_18832),U_18834),U_18836) = c_List_Olist_ONil(U_18832)
        | U_18836 != c_List_Olist_ONil(U_18830) )
    & ! [U_18831,U_18835,U_18833,U_18829] :
        ( U_18835 = c_List_Olist_ONil(U_18829)
        | hAPP(hAPP(c_List_Omap(U_18829,U_18831),U_18833),U_18835) != c_List_Olist_ONil(U_18831) ) ),
    inference(definitional_conversion,[status(esa)],[f_4525_3]) ).

cnf(f_4525_5,plain,
    ( U_18835 = c_List_Olist_ONil(U_18829)
    | hAPP(hAPP(c_List_Omap(U_18829,U_18831),U_18833),U_18835) != c_List_Olist_ONil(U_18831) ),
    inference(clausify,[status(thm)],[f_4525_4]) ).

cnf(f_4525_6,plain,
    ( hAPP(hAPP(c_List_Omap(U_18830,U_18832),U_18834),U_18836) = c_List_Olist_ONil(U_18832)
    | U_18836 != c_List_Olist_ONil(U_18830) ),
    inference(clausify,[status(thm)],[f_4525_4]) ).

fof(f_4526_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_4526_2,plain,
    ! [U_18843,U_18842,U_18841,U_18840,U_18839,U_18838,U_18837] : hAPP(hAPP(c_List_Ozip(U_18837,U_18838),hAPP(hAPP(c_List_Olist__update(U_18837,U_18839),U_18840),U_18841)),hAPP(hAPP(c_List_Olist__update(U_18838,U_18842),U_18840),U_18843)) = hAPP(hAPP(c_List_Olist__update(tc_prod(U_18837,U_18838),hAPP(hAPP(c_List_Ozip(U_18837,U_18838),U_18839),U_18842)),U_18840),hAPP(hAPP(c_Product__Type_OPair(U_18837,U_18838),U_18841),U_18843)),
    inference(variable_rename,[status(thm)],[f_4526_1]) ).

fof(f_4526_3,plain,
    ! [U_18839,U_18840,U_18837,U_18838,U_18841,U_18842,U_18843] : hAPP(hAPP(c_List_Ozip(U_18837,U_18838),hAPP(hAPP(c_List_Olist__update(U_18837,U_18839),U_18840),U_18841)),hAPP(hAPP(c_List_Olist__update(U_18838,U_18842),U_18840),U_18843)) = hAPP(hAPP(c_List_Olist__update(tc_prod(U_18837,U_18838),hAPP(hAPP(c_List_Ozip(U_18837,U_18838),U_18839),U_18842)),U_18840),hAPP(hAPP(c_Product__Type_OPair(U_18837,U_18838),U_18841),U_18843)),
    inference(definitional_conversion,[status(esa)],[f_4526_2]) ).

cnf(f_4526_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18837,U_18838),hAPP(hAPP(c_List_Olist__update(U_18837,U_18839),U_18840),U_18841)),hAPP(hAPP(c_List_Olist__update(U_18838,U_18842),U_18840),U_18843)) = hAPP(hAPP(c_List_Olist__update(tc_prod(U_18837,U_18838),hAPP(hAPP(c_List_Ozip(U_18837,U_18838),U_18839),U_18842)),U_18840),hAPP(hAPP(c_Product__Type_OPair(U_18837,U_18838),U_18841),U_18843)),
    inference(clausify,[status(thm)],[f_4526_3]) ).

fof(f_4527_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_4527_2,plain,
    ! [U_18849,U_18848,U_18847,U_18846,U_18845,U_18844] : hAPP(hAPP(c_List_Olist__update(tc_prod(U_18844,U_18845),hAPP(hAPP(c_List_Ozip(U_18844,U_18845),U_18846),U_18847)),U_18848),U_18849) = hAPP(hAPP(c_List_Ozip(U_18844,U_18845),hAPP(hAPP(c_List_Olist__update(U_18844,U_18846),U_18848),hAPP(c_Product__Type_Ofst(U_18844,U_18845),U_18849))),hAPP(hAPP(c_List_Olist__update(U_18845,U_18847),U_18848),hAPP(c_Product__Type_Osnd(U_18844,U_18845),U_18849))),
    inference(variable_rename,[status(thm)],[f_4527_1]) ).

fof(f_4527_3,plain,
    ! [U_18844,U_18845,U_18846,U_18847,U_18848,U_18849] : hAPP(hAPP(c_List_Olist__update(tc_prod(U_18844,U_18845),hAPP(hAPP(c_List_Ozip(U_18844,U_18845),U_18846),U_18847)),U_18848),U_18849) = hAPP(hAPP(c_List_Ozip(U_18844,U_18845),hAPP(hAPP(c_List_Olist__update(U_18844,U_18846),U_18848),hAPP(c_Product__Type_Ofst(U_18844,U_18845),U_18849))),hAPP(hAPP(c_List_Olist__update(U_18845,U_18847),U_18848),hAPP(c_Product__Type_Osnd(U_18844,U_18845),U_18849))),
    inference(definitional_conversion,[status(esa)],[f_4527_2]) ).

cnf(f_4527_4,plain,
    hAPP(hAPP(c_List_Olist__update(tc_prod(U_18844,U_18845),hAPP(hAPP(c_List_Ozip(U_18844,U_18845),U_18846),U_18847)),U_18848),U_18849) = hAPP(hAPP(c_List_Ozip(U_18844,U_18845),hAPP(hAPP(c_List_Olist__update(U_18844,U_18846),U_18848),hAPP(c_Product__Type_Ofst(U_18844,U_18845),U_18849))),hAPP(hAPP(c_List_Olist__update(U_18845,U_18847),U_18848),hAPP(c_Product__Type_Osnd(U_18844,U_18845),U_18849))),
    inference(clausify,[status(thm)],[f_4527_3]) ).

fof(f_4528_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_4528_2,plain,
    ! [U_18851,U_18850] : c_List_Osublist(U_18850,c_List_Olist_ONil(U_18850),U_18851) = c_List_Olist_ONil(U_18850),
    inference(variable_rename,[status(thm)],[f_4528_1]) ).

fof(f_4528_3,plain,
    ! [U_18850,U_18851] : c_List_Osublist(U_18850,c_List_Olist_ONil(U_18850),U_18851) = c_List_Olist_ONil(U_18850),
    inference(definitional_conversion,[status(esa)],[f_4528_2]) ).

cnf(f_4528_4,plain,
    c_List_Osublist(U_18850,c_List_Olist_ONil(U_18850),U_18851) = c_List_Olist_ONil(U_18850),
    inference(clausify,[status(thm)],[f_4528_3]) ).

fof(f_4529_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_4529_2,plain,
    ! [U_18853,U_18852] : c_List_Osublist(U_18852,U_18853,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(U_18852),
    inference(variable_rename,[status(thm)],[f_4529_1]) ).

fof(f_4529_3,plain,
    ! [U_18852,U_18853] : c_List_Osublist(U_18852,U_18853,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(U_18852),
    inference(definitional_conversion,[status(esa)],[f_4529_2]) ).

cnf(f_4529_4,plain,
    c_List_Osublist(U_18852,U_18853,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(U_18852),
    inference(clausify,[status(thm)],[f_4529_3]) ).

fof(f_4530_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_4530_2,plain,
    ! [U_18857,U_18856,U_18855,U_18854] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18855,U_18854,U_18856),U_18857),c_List_Olist_ONil(U_18855)) = hAPP(hAPP(c_List_Olist_OCons(U_18855),U_18857),c_List_Olist_ONil(U_18855))
      | ~ class_Orderings_Olinorder(U_18854) ),
    inference(variable_rename,[status(thm)],[f_4530_1]) ).

fof(f_4530_3,plain,
    ! [U_18854,U_18855,U_18856,U_18857] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18855,U_18854,U_18856),U_18857),c_List_Olist_ONil(U_18855)) = hAPP(hAPP(c_List_Olist_OCons(U_18855),U_18857),c_List_Olist_ONil(U_18855))
      | ~ class_Orderings_Olinorder(U_18854) ),
    inference(definitional_conversion,[status(esa)],[f_4530_2]) ).

cnf(f_4530_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18855,U_18854,U_18856),U_18857),c_List_Olist_ONil(U_18855)) = hAPP(hAPP(c_List_Olist_OCons(U_18855),U_18857),c_List_Olist_ONil(U_18855))
    | ~ class_Orderings_Olinorder(U_18854) ),
    inference(clausify,[status(thm)],[f_4530_3]) ).

fof(f_4531_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_4531_2,plain,
    ! [U_18862,U_18861,U_18860,U_18859,U_18858] : hAPP(hAPP(c_List_Olist__update(U_18858,hAPP(hAPP(c_List_Olist_OCons(U_18858),U_18859),U_18860)),hAPP(c_Nat_OSuc,U_18861)),U_18862) = hAPP(hAPP(c_List_Olist_OCons(U_18858),U_18859),hAPP(hAPP(c_List_Olist__update(U_18858,U_18860),U_18861),U_18862)),
    inference(variable_rename,[status(thm)],[f_4531_1]) ).

fof(f_4531_3,plain,
    ! [U_18858,U_18859,U_18860,U_18861,U_18862] : hAPP(hAPP(c_List_Olist__update(U_18858,hAPP(hAPP(c_List_Olist_OCons(U_18858),U_18859),U_18860)),hAPP(c_Nat_OSuc,U_18861)),U_18862) = hAPP(hAPP(c_List_Olist_OCons(U_18858),U_18859),hAPP(hAPP(c_List_Olist__update(U_18858,U_18860),U_18861),U_18862)),
    inference(definitional_conversion,[status(esa)],[f_4531_2]) ).

cnf(f_4531_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18858,hAPP(hAPP(c_List_Olist_OCons(U_18858),U_18859),U_18860)),hAPP(c_Nat_OSuc,U_18861)),U_18862) = hAPP(hAPP(c_List_Olist_OCons(U_18858),U_18859),hAPP(hAPP(c_List_Olist__update(U_18858,U_18860),U_18861),U_18862)),
    inference(clausify,[status(thm)],[f_4531_3]) ).

fof(f_4532_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_4532_2,plain,
    ! [U_18865,U_18864,U_18863] : hAPP(hAPP(c_List_Olist_OCons(U_18863),U_18864),U_18865) != c_List_Olist_ONil(U_18863),
    inference(variable_rename,[status(thm)],[f_4532_1]) ).

fof(f_4532_3,plain,
    ! [U_18863,U_18865,U_18864] : hAPP(hAPP(c_List_Olist_OCons(U_18863),U_18864),U_18865) != c_List_Olist_ONil(U_18863),
    inference(definitional_conversion,[status(esa)],[f_4532_2]) ).

cnf(f_4532_4,plain,
    hAPP(hAPP(c_List_Olist_OCons(U_18863),U_18864),U_18865) != c_List_Olist_ONil(U_18863),
    inference(clausify,[status(thm)],[f_4532_3]) ).

fof(f_4533_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_4533_2,plain,
    ! [U_18868,U_18867,U_18866] : c_List_Olist_ONil(U_18866) != hAPP(hAPP(c_List_Olist_OCons(U_18866),U_18867),U_18868),
    inference(variable_rename,[status(thm)],[f_4533_1]) ).

fof(f_4533_3,plain,
    ! [U_18866,U_18867,U_18868] : c_List_Olist_ONil(U_18866) != hAPP(hAPP(c_List_Olist_OCons(U_18866),U_18867),U_18868),
    inference(definitional_conversion,[status(esa)],[f_4533_2]) ).

cnf(f_4533_4,plain,
    c_List_Olist_ONil(U_18866) != hAPP(hAPP(c_List_Olist_OCons(U_18866),U_18867),U_18868),
    inference(clausify,[status(thm)],[f_4533_3]) ).

fof(f_4534_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_4534_2,plain,
    ! [U_18872,U_18871,U_18870,U_18869] : hAPP(hAPP(c_List_Olist__update(U_18869,hAPP(hAPP(c_List_Olist_OCons(U_18869),U_18870),U_18871)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18872) = hAPP(hAPP(c_List_Olist_OCons(U_18869),U_18872),U_18871),
    inference(variable_rename,[status(thm)],[f_4534_1]) ).

fof(f_4534_3,plain,
    ! [U_18869,U_18870,U_18871,U_18872] : hAPP(hAPP(c_List_Olist__update(U_18869,hAPP(hAPP(c_List_Olist_OCons(U_18869),U_18870),U_18871)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18872) = hAPP(hAPP(c_List_Olist_OCons(U_18869),U_18872),U_18871),
    inference(definitional_conversion,[status(esa)],[f_4534_2]) ).

cnf(f_4534_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18869,hAPP(hAPP(c_List_Olist_OCons(U_18869),U_18870),U_18871)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18872) = hAPP(hAPP(c_List_Olist_OCons(U_18869),U_18872),U_18871),
    inference(clausify,[status(thm)],[f_4534_3]) ).

fof(f_4535_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_4535_2,plain,
    ! [U_18877,U_18876,U_18875,U_18874,U_18873] : hAPP(hAPP(c_List_Olist__update(U_18873,hAPP(hAPP(c_List_Olist_OCons(U_18873),U_18874),U_18875)),U_18876),U_18877) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18873),hAPP(hAPP(c_List_Olist_OCons(U_18873),U_18877),U_18875),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18873),tc_List_Olist(U_18873),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18873),U_18874)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_18873,tc_List_Olist(U_18873)),c_List_Olist__update(U_18873,U_18875)),U_18877)),U_18876),
    inference(variable_rename,[status(thm)],[f_4535_1]) ).

fof(f_4535_3,plain,
    ! [U_18873,U_18874,U_18875,U_18876,U_18877] : hAPP(hAPP(c_List_Olist__update(U_18873,hAPP(hAPP(c_List_Olist_OCons(U_18873),U_18874),U_18875)),U_18876),U_18877) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18873),hAPP(hAPP(c_List_Olist_OCons(U_18873),U_18877),U_18875),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18873),tc_List_Olist(U_18873),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18873),U_18874)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_18873,tc_List_Olist(U_18873)),c_List_Olist__update(U_18873,U_18875)),U_18877)),U_18876),
    inference(definitional_conversion,[status(esa)],[f_4535_2]) ).

cnf(f_4535_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18873,hAPP(hAPP(c_List_Olist_OCons(U_18873),U_18874),U_18875)),U_18876),U_18877) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18873),hAPP(hAPP(c_List_Olist_OCons(U_18873),U_18877),U_18875),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18873),tc_List_Olist(U_18873),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18873),U_18874)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_18873,tc_List_Olist(U_18873)),c_List_Olist__update(U_18873,U_18875)),U_18877)),U_18876),
    inference(clausify,[status(thm)],[f_4535_3]) ).

fof(f_4536_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_4536_2,plain,
    ! [U_18878] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_18878,c_Orderings_Obot__class_Obot(tc_fun(U_18878,tc_HOL_Obool))) = c_List_Olist_ONil(U_18878)
      | ~ class_Orderings_Olinorder(U_18878) ),
    inference(variable_rename,[status(thm)],[f_4536_1]) ).

fof(f_4536_3,plain,
    ! [U_18878] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_18878,c_Orderings_Obot__class_Obot(tc_fun(U_18878,tc_HOL_Obool))) = c_List_Olist_ONil(U_18878)
      | ~ class_Orderings_Olinorder(U_18878) ),
    inference(definitional_conversion,[status(esa)],[f_4536_2]) ).

cnf(f_4536_4,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_18878,c_Orderings_Obot__class_Obot(tc_fun(U_18878,tc_HOL_Obool))) = c_List_Olist_ONil(U_18878)
    | ~ class_Orderings_Olinorder(U_18878) ),
    inference(clausify,[status(thm)],[f_4536_3]) ).

fof(f_4537_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_4537_2,plain,
    ! [U_18881,U_18880,U_18879] : hAPP(hAPP(c_List_Ozip(U_18879,U_18880),U_18881),c_List_Olist_ONil(U_18880)) = c_List_Olist_ONil(tc_prod(U_18879,U_18880)),
    inference(variable_rename,[status(thm)],[f_4537_1]) ).

fof(f_4537_3,plain,
    ! [U_18879,U_18880,U_18881] : hAPP(hAPP(c_List_Ozip(U_18879,U_18880),U_18881),c_List_Olist_ONil(U_18880)) = c_List_Olist_ONil(tc_prod(U_18879,U_18880)),
    inference(definitional_conversion,[status(esa)],[f_4537_2]) ).

cnf(f_4537_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18879,U_18880),U_18881),c_List_Olist_ONil(U_18880)) = c_List_Olist_ONil(tc_prod(U_18879,U_18880)),
    inference(clausify,[status(thm)],[f_4537_3]) ).

fof(f_4538_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_4538_2,plain,
    ! [U_18884,U_18883,U_18882] : hAPP(hAPP(c_List_Ozip(U_18882,U_18883),c_List_Olist_ONil(U_18882)),U_18884) = c_List_Olist_ONil(tc_prod(U_18882,U_18883)),
    inference(variable_rename,[status(thm)],[f_4538_1]) ).

fof(f_4538_3,plain,
    ! [U_18882,U_18883,U_18884] : hAPP(hAPP(c_List_Ozip(U_18882,U_18883),c_List_Olist_ONil(U_18882)),U_18884) = c_List_Olist_ONil(tc_prod(U_18882,U_18883)),
    inference(definitional_conversion,[status(esa)],[f_4538_2]) ).

cnf(f_4538_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18882,U_18883),c_List_Olist_ONil(U_18882)),U_18884) = c_List_Olist_ONil(tc_prod(U_18882,U_18883)),
    inference(clausify,[status(thm)],[f_4538_3]) ).

fof(f_4539_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_4539_2,plain,
    ! [U_18886,U_18885] :
      ( c_List_Oupto(U_18886,U_18885) = c_List_Olist_ONil(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18885),U_18886)) ),
    inference(variable_rename,[status(thm)],[f_4539_1]) ).

fof(f_4539_3,plain,
    ! [U_18885,U_18886] :
      ( c_List_Oupto(U_18886,U_18885) = c_List_Olist_ONil(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18885),U_18886)) ),
    inference(definitional_conversion,[status(esa)],[f_4539_2]) ).

cnf(f_4539_4,plain,
    ( c_List_Oupto(U_18886,U_18885) = c_List_Olist_ONil(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18885),U_18886)) ),
    inference(clausify,[status(thm)],[f_4539_3]) ).

fof(f_4540_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_4540_2,plain,
    ! [U_18890,U_18889,U_18888,U_18887] : c_List_Ofoldr(U_18887,U_18888,U_18889,c_List_Olist_ONil(U_18887),U_18890) = U_18890,
    inference(variable_rename,[status(thm)],[f_4540_1]) ).

fof(f_4540_3,plain,
    ! [U_18888,U_18887,U_18889,U_18890] : c_List_Ofoldr(U_18887,U_18888,U_18889,c_List_Olist_ONil(U_18887),U_18890) = U_18890,
    inference(definitional_conversion,[status(esa)],[f_4540_2]) ).

cnf(f_4540_4,plain,
    c_List_Ofoldr(U_18887,U_18888,U_18889,c_List_Olist_ONil(U_18887),U_18890) = U_18890,
    inference(clausify,[status(thm)],[f_4540_3]) ).

fof(f_4541_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_4541_2,plain,
    ! [U_18893,U_18892,U_18891] : hAPP(c_Map_Omap__of(U_18891,U_18892,c_List_Olist_ONil(tc_prod(U_18891,U_18892))),U_18893) = c_Option_Ooption_ONone(U_18892),
    inference(variable_rename,[status(thm)],[f_4541_1]) ).

fof(f_4541_3,plain,
    ! [U_18891,U_18892,U_18893] : hAPP(c_Map_Omap__of(U_18891,U_18892,c_List_Olist_ONil(tc_prod(U_18891,U_18892))),U_18893) = c_Option_Ooption_ONone(U_18892),
    inference(definitional_conversion,[status(esa)],[f_4541_2]) ).

cnf(f_4541_4,plain,
    hAPP(c_Map_Omap__of(U_18891,U_18892,c_List_Olist_ONil(tc_prod(U_18891,U_18892))),U_18893) = c_Option_Ooption_ONone(U_18892),
    inference(clausify,[status(thm)],[f_4541_3]) ).

fof(f_4542_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_4542_2,plain,
    ! [U_18896,U_18895,U_18894] : hAPP(c_Map_Omap__of(U_18894,U_18895,c_List_Olist_ONil(tc_prod(U_18894,U_18895))),U_18896) = c_Option_Ooption_ONone(U_18895),
    inference(variable_rename,[status(thm)],[f_4542_1]) ).

fof(f_4542_3,plain,
    ! [U_18894,U_18895,U_18896] : hAPP(c_Map_Omap__of(U_18894,U_18895,c_List_Olist_ONil(tc_prod(U_18894,U_18895))),U_18896) = c_Option_Ooption_ONone(U_18895),
    inference(definitional_conversion,[status(esa)],[f_4542_2]) ).

cnf(f_4542_4,plain,
    hAPP(c_Map_Omap__of(U_18894,U_18895,c_List_Olist_ONil(tc_prod(U_18894,U_18895))),U_18896) = c_Option_Ooption_ONone(U_18895),
    inference(clausify,[status(thm)],[f_4542_3]) ).

fof(f_4543_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_4543_2,plain,
    ! [U_18900,U_18899,U_18898,U_18897] :
      ( ( hAPP(hAPP(c_List_Olist__update(U_18897,U_18898),U_18899),U_18900) = c_List_Olist_ONil(U_18897)
        | U_18898 != c_List_Olist_ONil(U_18897) )
      & ( U_18898 = c_List_Olist_ONil(U_18897)
        | hAPP(hAPP(c_List_Olist__update(U_18897,U_18898),U_18899),U_18900) != c_List_Olist_ONil(U_18897) ) ),
    inference(variable_rename,[status(thm)],[f_4543_1]) ).

fof(f_4543_3,plain,
    ( ! [U_18908,U_18906,U_18904,U_18902] :
        ( hAPP(hAPP(c_List_Olist__update(U_18902,U_18904),U_18906),U_18908) = c_List_Olist_ONil(U_18902)
        | U_18904 != c_List_Olist_ONil(U_18902) )
    & ! [U_18907,U_18905,U_18903,U_18901] :
        ( U_18903 = c_List_Olist_ONil(U_18901)
        | hAPP(hAPP(c_List_Olist__update(U_18901,U_18903),U_18905),U_18907) != c_List_Olist_ONil(U_18901) ) ),
    inference(miniscope,[status(thm)],[f_4543_2]) ).

fof(f_4543_4,plain,
    ( ! [U_18902,U_18908,U_18904,U_18906] :
        ( hAPP(hAPP(c_List_Olist__update(U_18902,U_18904),U_18906),U_18908) = c_List_Olist_ONil(U_18902)
        | U_18904 != c_List_Olist_ONil(U_18902) )
    & ! [U_18907,U_18903,U_18901,U_18905] :
        ( U_18903 = c_List_Olist_ONil(U_18901)
        | hAPP(hAPP(c_List_Olist__update(U_18901,U_18903),U_18905),U_18907) != c_List_Olist_ONil(U_18901) ) ),
    inference(definitional_conversion,[status(esa)],[f_4543_3]) ).

cnf(f_4543_5,plain,
    ( U_18903 = c_List_Olist_ONil(U_18901)
    | hAPP(hAPP(c_List_Olist__update(U_18901,U_18903),U_18905),U_18907) != c_List_Olist_ONil(U_18901) ),
    inference(clausify,[status(thm)],[f_4543_4]) ).

cnf(f_4543_6,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_18902,U_18904),U_18906),U_18908) = c_List_Olist_ONil(U_18902)
    | U_18904 != c_List_Olist_ONil(U_18902) ),
    inference(clausify,[status(thm)],[f_4543_4]) ).

fof(f_4544_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_4544_2,plain,
    ! [U_18911,U_18910,U_18909] : hAPP(hAPP(c_List_Olist__update(U_18909,c_List_Olist_ONil(U_18909)),U_18910),U_18911) = c_List_Olist_ONil(U_18909),
    inference(variable_rename,[status(thm)],[f_4544_1]) ).

fof(f_4544_3,plain,
    ! [U_18909,U_18910,U_18911] : hAPP(hAPP(c_List_Olist__update(U_18909,c_List_Olist_ONil(U_18909)),U_18910),U_18911) = c_List_Olist_ONil(U_18909),
    inference(definitional_conversion,[status(esa)],[f_4544_2]) ).

cnf(f_4544_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18909,c_List_Olist_ONil(U_18909)),U_18910),U_18911) = c_List_Olist_ONil(U_18909),
    inference(clausify,[status(thm)],[f_4544_3]) ).

fof(f_4545_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_4545_2,plain,
    ! [U_18914,U_18913,U_18912] : hAPP(hAPP(c_List_Olist__update(U_18912,c_List_Olist_ONil(U_18912)),U_18913),U_18914) = c_List_Olist_ONil(U_18912),
    inference(variable_rename,[status(thm)],[f_4545_1]) ).

fof(f_4545_3,plain,
    ! [U_18912,U_18913,U_18914] : hAPP(hAPP(c_List_Olist__update(U_18912,c_List_Olist_ONil(U_18912)),U_18913),U_18914) = c_List_Olist_ONil(U_18912),
    inference(definitional_conversion,[status(esa)],[f_4545_2]) ).

cnf(f_4545_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18912,c_List_Olist_ONil(U_18912)),U_18913),U_18914) = c_List_Olist_ONil(U_18912),
    inference(clausify,[status(thm)],[f_4545_3]) ).

fof(f_4546_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_4546_2,plain,
    ! [U_18919,U_18918,U_18917,U_18916,U_18915] : hAPP(hAPP(c_List_Olist__update(U_18915,hAPP(hAPP(c_List_Olist__update(U_18915,U_18916),U_18917),U_18918)),U_18917),U_18919) = hAPP(hAPP(c_List_Olist__update(U_18915,U_18916),U_18917),U_18919),
    inference(variable_rename,[status(thm)],[f_4546_1]) ).

fof(f_4546_3,plain,
    ! [U_18915,U_18916,U_18917,U_18918,U_18919] : hAPP(hAPP(c_List_Olist__update(U_18915,hAPP(hAPP(c_List_Olist__update(U_18915,U_18916),U_18917),U_18918)),U_18917),U_18919) = hAPP(hAPP(c_List_Olist__update(U_18915,U_18916),U_18917),U_18919),
    inference(definitional_conversion,[status(esa)],[f_4546_2]) ).

cnf(f_4546_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18915,hAPP(hAPP(c_List_Olist__update(U_18915,U_18916),U_18917),U_18918)),U_18917),U_18919) = hAPP(hAPP(c_List_Olist__update(U_18915,U_18916),U_18917),U_18919),
    inference(clausify,[status(thm)],[f_4546_3]) ).

fof(f_4547_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_4547_2,plain,
    ! [U_18925,U_18924,U_18923,U_18922,U_18921,U_18920] :
      ( hAPP(hAPP(c_List_Olist__update(U_18922,hAPP(hAPP(c_List_Olist__update(U_18922,U_18923),U_18920),U_18924)),U_18921),U_18925) = hAPP(hAPP(c_List_Olist__update(U_18922,hAPP(hAPP(c_List_Olist__update(U_18922,U_18923),U_18921),U_18925)),U_18920),U_18924)
      | U_18920 = U_18921 ),
    inference(variable_rename,[status(thm)],[f_4547_1]) ).

fof(f_4547_3,plain,
    ! [U_18920,U_18921,U_18922,U_18923,U_18924,U_18925] :
      ( hAPP(hAPP(c_List_Olist__update(U_18922,hAPP(hAPP(c_List_Olist__update(U_18922,U_18923),U_18920),U_18924)),U_18921),U_18925) = hAPP(hAPP(c_List_Olist__update(U_18922,hAPP(hAPP(c_List_Olist__update(U_18922,U_18923),U_18921),U_18925)),U_18920),U_18924)
      | U_18920 = U_18921 ),
    inference(definitional_conversion,[status(esa)],[f_4547_2]) ).

cnf(f_4547_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_18922,hAPP(hAPP(c_List_Olist__update(U_18922,U_18923),U_18920),U_18924)),U_18921),U_18925) = hAPP(hAPP(c_List_Olist__update(U_18922,hAPP(hAPP(c_List_Olist__update(U_18922,U_18923),U_18921),U_18925)),U_18920),U_18924)
    | U_18920 = U_18921 ),
    inference(clausify,[status(thm)],[f_4547_3]) ).

fof(f_4548_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_4548_2,plain,
    ! [U_18927,U_18926] : c_List_Oremove1(U_18926,U_18927,c_List_Olist_ONil(U_18926)) = c_List_Olist_ONil(U_18926),
    inference(variable_rename,[status(thm)],[f_4548_1]) ).

fof(f_4548_3,plain,
    ! [U_18926,U_18927] : c_List_Oremove1(U_18926,U_18927,c_List_Olist_ONil(U_18926)) = c_List_Olist_ONil(U_18926),
    inference(definitional_conversion,[status(esa)],[f_4548_2]) ).

cnf(f_4548_4,plain,
    c_List_Oremove1(U_18926,U_18927,c_List_Olist_ONil(U_18926)) = c_List_Olist_ONil(U_18926),
    inference(clausify,[status(thm)],[f_4548_3]) ).

fof(f_4549_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_4549_2,plain,
    ! [U_18928] : hBOOL(hAPP(c_List_Odistinct(U_18928),c_List_Olist_ONil(U_18928))),
    inference(variable_rename,[status(thm)],[f_4549_1]) ).

fof(f_4549_3,plain,
    ! [U_18928] : hBOOL(hAPP(c_List_Odistinct(U_18928),c_List_Olist_ONil(U_18928))),
    inference(definitional_conversion,[status(esa)],[f_4549_2]) ).

cnf(f_4549_4,plain,
    hBOOL(hAPP(c_List_Odistinct(U_18928),c_List_Olist_ONil(U_18928))),
    inference(clausify,[status(thm)],[f_4549_3]) ).

fof(f_4550_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_4550_2,plain,
    ! [U_18933,U_18932,U_18931,U_18930,U_18929] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18930,U_18929,U_18931),U_18932),U_18933) != c_List_Olist_ONil(U_18930)
      | ~ class_Orderings_Olinorder(U_18929) ),
    inference(variable_rename,[status(thm)],[f_4550_1]) ).

fof(f_4550_3,plain,
    ! [U_18929,U_18930,U_18931,U_18932,U_18933] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18930,U_18929,U_18931),U_18932),U_18933) != c_List_Olist_ONil(U_18930)
      | ~ class_Orderings_Olinorder(U_18929) ),
    inference(definitional_conversion,[status(esa)],[f_4550_2]) ).

cnf(f_4550_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18930,U_18929,U_18931),U_18932),U_18933) != c_List_Olist_ONil(U_18930)
    | ~ class_Orderings_Olinorder(U_18929) ),
    inference(clausify,[status(thm)],[f_4550_3]) ).

fof(f_4551_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_4551_2,plain,
    ! [U_18935,U_18934] : c_List_Olistrelp(U_18934,U_18935,c_List_Olist_ONil(U_18934),c_List_Olist_ONil(U_18934)),
    inference(variable_rename,[status(thm)],[f_4551_1]) ).

fof(f_4551_3,plain,
    ! [U_18935,U_18934] : c_List_Olistrelp(U_18934,U_18935,c_List_Olist_ONil(U_18934),c_List_Olist_ONil(U_18934)),
    inference(definitional_conversion,[status(esa)],[f_4551_2]) ).

cnf(f_4551_4,plain,
    c_List_Olistrelp(U_18934,U_18935,c_List_Olist_ONil(U_18934),c_List_Olist_ONil(U_18934)),
    inference(clausify,[status(thm)],[f_4551_3]) ).

fof(f_4552_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_4552_2,plain,
    ! [U_18937,U_18936] : c_List_Olistrelp(U_18936,U_18937,c_List_Olist_ONil(U_18936),c_List_Olist_ONil(U_18936)),
    inference(variable_rename,[status(thm)],[f_4552_1]) ).

fof(f_4552_3,plain,
    ! [U_18936,U_18937] : c_List_Olistrelp(U_18936,U_18937,c_List_Olist_ONil(U_18936),c_List_Olist_ONil(U_18936)),
    inference(definitional_conversion,[status(esa)],[f_4552_2]) ).

cnf(f_4552_4,plain,
    c_List_Olistrelp(U_18936,U_18937,c_List_Olist_ONil(U_18936),c_List_Olist_ONil(U_18936)),
    inference(clausify,[status(thm)],[f_4552_3]) ).

fof(f_4553_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_4553_2,plain,
    ! [U_18938] : hAPP(c_List_Oset(U_18938),c_List_Olist_ONil(U_18938)) = c_Orderings_Obot__class_Obot(tc_fun(U_18938,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4553_1]) ).

fof(f_4553_3,plain,
    ! [U_18938] : hAPP(c_List_Oset(U_18938),c_List_Olist_ONil(U_18938)) = c_Orderings_Obot__class_Obot(tc_fun(U_18938,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4553_2]) ).

cnf(f_4553_4,plain,
    hAPP(c_List_Oset(U_18938),c_List_Olist_ONil(U_18938)) = c_Orderings_Obot__class_Obot(tc_fun(U_18938,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4553_3]) ).

fof(f_4554_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_4554_2,plain,
    ! [U_18940,U_18939] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_18939,tc_HOL_Obool)) = hAPP(c_List_Oset(U_18939),U_18940)
        | U_18940 != c_List_Olist_ONil(U_18939) )
      & ( U_18940 = c_List_Olist_ONil(U_18939)
        | c_Orderings_Obot__class_Obot(tc_fun(U_18939,tc_HOL_Obool)) != hAPP(c_List_Oset(U_18939),U_18940) ) ),
    inference(variable_rename,[status(thm)],[f_4554_1]) ).

fof(f_4554_3,plain,
    ( ! [U_18944,U_18942] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_18942,tc_HOL_Obool)) = hAPP(c_List_Oset(U_18942),U_18944)
        | U_18944 != c_List_Olist_ONil(U_18942) )
    & ! [U_18943,U_18941] :
        ( U_18943 = c_List_Olist_ONil(U_18941)
        | c_Orderings_Obot__class_Obot(tc_fun(U_18941,tc_HOL_Obool)) != hAPP(c_List_Oset(U_18941),U_18943) ) ),
    inference(miniscope,[status(thm)],[f_4554_2]) ).

fof(f_4554_4,plain,
    ( ! [U_18944,U_18942] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_18942,tc_HOL_Obool)) = hAPP(c_List_Oset(U_18942),U_18944)
        | U_18944 != c_List_Olist_ONil(U_18942) )
    & ! [U_18943,U_18941] :
        ( U_18943 = c_List_Olist_ONil(U_18941)
        | c_Orderings_Obot__class_Obot(tc_fun(U_18941,tc_HOL_Obool)) != hAPP(c_List_Oset(U_18941),U_18943) ) ),
    inference(definitional_conversion,[status(esa)],[f_4554_3]) ).

cnf(f_4554_5,plain,
    ( U_18943 = c_List_Olist_ONil(U_18941)
    | c_Orderings_Obot__class_Obot(tc_fun(U_18941,tc_HOL_Obool)) != hAPP(c_List_Oset(U_18941),U_18943) ),
    inference(clausify,[status(thm)],[f_4554_4]) ).

cnf(f_4554_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_18942,tc_HOL_Obool)) = hAPP(c_List_Oset(U_18942),U_18944)
    | U_18944 != c_List_Olist_ONil(U_18942) ),
    inference(clausify,[status(thm)],[f_4554_4]) ).

fof(f_4555_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_4555_2,plain,
    ! [U_18946,U_18945] :
      ( ( hAPP(c_List_Oset(U_18945),U_18946) = c_Orderings_Obot__class_Obot(tc_fun(U_18945,tc_HOL_Obool))
        | U_18946 != c_List_Olist_ONil(U_18945) )
      & ( U_18946 = c_List_Olist_ONil(U_18945)
        | hAPP(c_List_Oset(U_18945),U_18946) != c_Orderings_Obot__class_Obot(tc_fun(U_18945,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4555_1]) ).

fof(f_4555_3,plain,
    ( ! [U_18950,U_18948] :
        ( hAPP(c_List_Oset(U_18948),U_18950) = c_Orderings_Obot__class_Obot(tc_fun(U_18948,tc_HOL_Obool))
        | U_18950 != c_List_Olist_ONil(U_18948) )
    & ! [U_18949,U_18947] :
        ( U_18949 = c_List_Olist_ONil(U_18947)
        | hAPP(c_List_Oset(U_18947),U_18949) != c_Orderings_Obot__class_Obot(tc_fun(U_18947,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4555_2]) ).

fof(f_4555_4,plain,
    ( ! [U_18948,U_18950] :
        ( hAPP(c_List_Oset(U_18948),U_18950) = c_Orderings_Obot__class_Obot(tc_fun(U_18948,tc_HOL_Obool))
        | U_18950 != c_List_Olist_ONil(U_18948) )
    & ! [U_18949,U_18947] :
        ( U_18949 = c_List_Olist_ONil(U_18947)
        | hAPP(c_List_Oset(U_18947),U_18949) != c_Orderings_Obot__class_Obot(tc_fun(U_18947,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4555_3]) ).

cnf(f_4555_5,plain,
    ( U_18949 = c_List_Olist_ONil(U_18947)
    | hAPP(c_List_Oset(U_18947),U_18949) != c_Orderings_Obot__class_Obot(tc_fun(U_18947,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4555_4]) ).

cnf(f_4555_6,plain,
    ( hAPP(c_List_Oset(U_18948),U_18950) = c_Orderings_Obot__class_Obot(tc_fun(U_18948,tc_HOL_Obool))
    | U_18950 != c_List_Olist_ONil(U_18948) ),
    inference(clausify,[status(thm)],[f_4555_4]) ).

fof(f_4556_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_4556_2,plain,
    ! [U_18951] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18951),c_List_Olist_ONil(U_18951)) = c_Groups_Ozero__class_Ozero(U_18951)
      | ~ class_Groups_Omonoid__add(U_18951) ),
    inference(variable_rename,[status(thm)],[f_4556_1]) ).

fof(f_4556_3,plain,
    ! [U_18951] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18951),c_List_Olist_ONil(U_18951)) = c_Groups_Ozero__class_Ozero(U_18951)
      | ~ class_Groups_Omonoid__add(U_18951) ),
    inference(definitional_conversion,[status(esa)],[f_4556_2]) ).

cnf(f_4556_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18951),c_List_Olist_ONil(U_18951)) = c_Groups_Ozero__class_Ozero(U_18951)
    | ~ class_Groups_Omonoid__add(U_18951) ),
    inference(clausify,[status(thm)],[f_4556_3]) ).

fof(f_4557_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_4557_2,plain,
    ! [U_18953,U_18952] :
      ( ( 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_18952)),U_18953)))
        | U_18953 = c_List_Olist_ONil(U_18952) )
      & ( U_18953 != c_List_Olist_ONil(U_18952)
        | ~ 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_18952)),U_18953))) ) ),
    inference(variable_rename,[status(thm)],[f_4557_1]) ).

fof(f_4557_3,plain,
    ( ! [U_18957,U_18955] :
        ( 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_18955)),U_18957)))
        | U_18957 = c_List_Olist_ONil(U_18955) )
    & ! [U_18956,U_18954] :
        ( U_18956 != c_List_Olist_ONil(U_18954)
        | ~ 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_18954)),U_18956))) ) ),
    inference(miniscope,[status(thm)],[f_4557_2]) ).

fof(f_4557_4,plain,
    ( ! [U_18955,U_18957] :
        ( 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_18955)),U_18957)))
        | U_18957 = c_List_Olist_ONil(U_18955) )
    & ! [U_18956,U_18954] :
        ( U_18956 != c_List_Olist_ONil(U_18954)
        | ~ 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_18954)),U_18956))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4557_3]) ).

cnf(f_4557_5,plain,
    ( U_18956 != c_List_Olist_ONil(U_18954)
    | ~ 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_18954)),U_18956))) ),
    inference(clausify,[status(thm)],[f_4557_4]) ).

cnf(f_4557_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_18955)),U_18957)))
    | U_18957 = c_List_Olist_ONil(U_18955) ),
    inference(clausify,[status(thm)],[f_4557_4]) ).

fof(f_4558_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_4558_2,plain,
    ! [U_18962,U_18961,U_18960,U_18959,U_18958] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18958,tc_HOL_Obool)),hAPP(c_List_Oset(U_18958),hAPP(hAPP(c_List_Olist__update(U_18958,U_18959),U_18962),U_18961))),U_18960))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18958),U_18961),U_18960))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18958,tc_HOL_Obool)),hAPP(c_List_Oset(U_18958),U_18959)),U_18960)) ),
    inference(variable_rename,[status(thm)],[f_4558_1]) ).

fof(f_4558_3,plain,
    ! [U_18958,U_18959,U_18960,U_18961,U_18962] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18958,tc_HOL_Obool)),hAPP(c_List_Oset(U_18958),hAPP(hAPP(c_List_Olist__update(U_18958,U_18959),U_18962),U_18961))),U_18960))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18958),U_18961),U_18960))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18958,tc_HOL_Obool)),hAPP(c_List_Oset(U_18958),U_18959)),U_18960)) ),
    inference(definitional_conversion,[status(esa)],[f_4558_2]) ).

cnf(f_4558_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18958,tc_HOL_Obool)),hAPP(c_List_Oset(U_18958),hAPP(hAPP(c_List_Olist__update(U_18958,U_18959),U_18962),U_18961))),U_18960))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18958),U_18961),U_18960))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18958,tc_HOL_Obool)),hAPP(c_List_Oset(U_18958),U_18959)),U_18960)) ),
    inference(clausify,[status(thm)],[f_4558_3]) ).

fof(f_4559_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_4559_2,plain,
    ! [U_18965,U_18964,U_18963] : hAPP(hAPP(c_List_Otake(U_18963),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_18963),U_18964),U_18965)) = hAPP(hAPP(c_List_Olist_OCons(U_18963),U_18964),c_List_Olist_ONil(U_18963)),
    inference(variable_rename,[status(thm)],[f_4559_1]) ).

fof(f_4559_3,plain,
    ! [U_18963,U_18964,U_18965] : hAPP(hAPP(c_List_Otake(U_18963),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_18963),U_18964),U_18965)) = hAPP(hAPP(c_List_Olist_OCons(U_18963),U_18964),c_List_Olist_ONil(U_18963)),
    inference(definitional_conversion,[status(esa)],[f_4559_2]) ).

cnf(f_4559_4,plain,
    hAPP(hAPP(c_List_Otake(U_18963),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_18963),U_18964),U_18965)) = hAPP(hAPP(c_List_Olist_OCons(U_18963),U_18964),c_List_Olist_ONil(U_18963)),
    inference(clausify,[status(thm)],[f_4559_3]) ).

fof(f_4560_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_4560_2,plain,
    ! [U_18969,U_18968,U_18967,U_18966] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18966,tc_HOL_Obool)),hAPP(c_List_Oset(U_18966),hAPP(hAPP(c_List_Olist__update(U_18966,U_18967),U_18968),U_18969))),hAPP(hAPP(c_Set_Oinsert(U_18966),U_18969),hAPP(c_List_Oset(U_18966),U_18967)))),
    inference(variable_rename,[status(thm)],[f_4560_1]) ).

fof(f_4560_3,plain,
    ! [U_18966,U_18967,U_18968,U_18969] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18966,tc_HOL_Obool)),hAPP(c_List_Oset(U_18966),hAPP(hAPP(c_List_Olist__update(U_18966,U_18967),U_18968),U_18969))),hAPP(hAPP(c_Set_Oinsert(U_18966),U_18969),hAPP(c_List_Oset(U_18966),U_18967)))),
    inference(definitional_conversion,[status(esa)],[f_4560_2]) ).

cnf(f_4560_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18966,tc_HOL_Obool)),hAPP(c_List_Oset(U_18966),hAPP(hAPP(c_List_Olist__update(U_18966,U_18967),U_18968),U_18969))),hAPP(hAPP(c_Set_Oinsert(U_18966),U_18969),hAPP(c_List_Oset(U_18966),U_18967)))),
    inference(clausify,[status(thm)],[f_4560_3]) ).

fof(f_4561_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_4561_2,plain,
    ! [U_18973,U_18972,U_18971,U_18970] :
      ( hAPP(hAPP(c_List_Onth(U_18971),hAPP(hAPP(c_List_Olist__update(U_18971,U_18972),U_18970),U_18973)),U_18970) = U_18973
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18970),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18971)),U_18972))) ),
    inference(variable_rename,[status(thm)],[f_4561_1]) ).

fof(f_4561_3,plain,
    ! [U_18970,U_18971,U_18972,U_18973] :
      ( hAPP(hAPP(c_List_Onth(U_18971),hAPP(hAPP(c_List_Olist__update(U_18971,U_18972),U_18970),U_18973)),U_18970) = U_18973
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18970),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18971)),U_18972))) ),
    inference(definitional_conversion,[status(esa)],[f_4561_2]) ).

cnf(f_4561_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_18971),hAPP(hAPP(c_List_Olist__update(U_18971,U_18972),U_18970),U_18973)),U_18970) = U_18973
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18970),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18971)),U_18972))) ),
    inference(clausify,[status(thm)],[f_4561_3]) ).

fof(f_4562_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_4562_2,plain,
    ! [U_18977,U_18976,U_18975,U_18974] :
      ( ( ( hAPP(hAPP(c_List_Olist__update(U_18975,U_18976),U_18974),U_18977) = U_18976
          | hAPP(hAPP(c_List_Onth(U_18975),U_18976),U_18974) != U_18977 )
        & ( hAPP(hAPP(c_List_Onth(U_18975),U_18976),U_18974) = U_18977
          | hAPP(hAPP(c_List_Olist__update(U_18975,U_18976),U_18974),U_18977) != U_18976 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18974),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18975)),U_18976))) ),
    inference(variable_rename,[status(thm)],[f_4562_1]) ).

fof(f_4562_3,plain,
    ( ! [U_18974,U_18975,U_18976,U_18977] :
        ( hAPP(hAPP(c_List_Olist__update(U_18975,U_18976),U_18974),U_18977) = U_18976
        | hAPP(hAPP(c_List_Onth(U_18975),U_18976),U_18974) != U_18977
        | ~ sP1169(U_18974,U_18975,U_18976,U_18977) )
    & ! [U_18974,U_18975,U_18976,U_18977] :
        ( hAPP(hAPP(c_List_Onth(U_18975),U_18976),U_18974) = U_18977
        | hAPP(hAPP(c_List_Olist__update(U_18975,U_18976),U_18974),U_18977) != U_18976
        | ~ sP1169(U_18974,U_18975,U_18976,U_18977) )
    & ! [U_18974,U_18975,U_18976,U_18977] :
        ( sP1169(U_18974,U_18975,U_18976,U_18977)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18974),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18975)),U_18976))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1169])],[f_4562_2]) ).

cnf(f_4562_4,plain,
    ( sP1169(U_18974,U_18975,U_18976,U_18977)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18974),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18975)),U_18976))) ),
    inference(clausify,[status(thm)],[f_4562_3]) ).

cnf(f_4562_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_18975),U_18976),U_18974) = U_18977
    | hAPP(hAPP(c_List_Olist__update(U_18975,U_18976),U_18974),U_18977) != U_18976
    | ~ sP1169(U_18974,U_18975,U_18976,U_18977) ),
    inference(clausify,[status(thm)],[f_4562_3]) ).

cnf(f_4562_6,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_18975,U_18976),U_18974),U_18977) = U_18976
    | hAPP(hAPP(c_List_Onth(U_18975),U_18976),U_18974) != U_18977
    | ~ sP1169(U_18974,U_18975,U_18976,U_18977) ),
    inference(clausify,[status(thm)],[f_4562_3]) ).

fof(f_4563_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_4563_2,plain,
    ! [U_18982,U_18981,U_18980,U_18979,U_18978] :
      ( ( ( hAPP(hAPP(c_List_Onth(U_18979),hAPP(hAPP(c_List_Olist__update(U_18979,U_18980),U_18978),U_18982)),U_18981) = hAPP(hAPP(c_List_Onth(U_18979),U_18980),U_18981)
          | U_18978 = U_18981 )
        & ( hAPP(hAPP(c_List_Onth(U_18979),hAPP(hAPP(c_List_Olist__update(U_18979,U_18980),U_18978),U_18982)),U_18981) = U_18982
          | U_18978 != U_18981 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18978),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18979)),U_18980))) ),
    inference(variable_rename,[status(thm)],[f_4563_1]) ).

fof(f_4563_3,plain,
    ( ! [U_18978,U_18979,U_18980,U_18981,U_18982] :
        ( hAPP(hAPP(c_List_Onth(U_18979),hAPP(hAPP(c_List_Olist__update(U_18979,U_18980),U_18978),U_18982)),U_18981) = hAPP(hAPP(c_List_Onth(U_18979),U_18980),U_18981)
        | U_18978 = U_18981
        | ~ sP1170(U_18978,U_18979,U_18980,U_18981,U_18982) )
    & ! [U_18978,U_18979,U_18980,U_18981,U_18982] :
        ( hAPP(hAPP(c_List_Onth(U_18979),hAPP(hAPP(c_List_Olist__update(U_18979,U_18980),U_18978),U_18982)),U_18981) = U_18982
        | U_18978 != U_18981
        | ~ sP1170(U_18978,U_18979,U_18980,U_18981,U_18982) )
    & ! [U_18978,U_18979,U_18980,U_18981,U_18982] :
        ( sP1170(U_18978,U_18979,U_18980,U_18981,U_18982)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18978),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18979)),U_18980))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1170])],[f_4563_2]) ).

cnf(f_4563_4,plain,
    ( sP1170(U_18978,U_18979,U_18980,U_18981,U_18982)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18978),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18979)),U_18980))) ),
    inference(clausify,[status(thm)],[f_4563_3]) ).

cnf(f_4563_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_18979),hAPP(hAPP(c_List_Olist__update(U_18979,U_18980),U_18978),U_18982)),U_18981) = U_18982
    | U_18978 != U_18981
    | ~ sP1170(U_18978,U_18979,U_18980,U_18981,U_18982) ),
    inference(clausify,[status(thm)],[f_4563_3]) ).

cnf(f_4563_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_18979),hAPP(hAPP(c_List_Olist__update(U_18979,U_18980),U_18978),U_18982)),U_18981) = hAPP(hAPP(c_List_Onth(U_18979),U_18980),U_18981)
    | U_18978 = U_18981
    | ~ sP1170(U_18978,U_18979,U_18980,U_18981,U_18982) ),
    inference(clausify,[status(thm)],[f_4563_3]) ).

fof(f_4564_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_4564_2,plain,
    ! [U_18984,U_18983] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18983),tc_List_Olist(U_18983))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18983),tc_List_Olist(U_18983)),c_List_Olist_ONil(U_18983)),c_List_Olist_ONil(U_18983))),c_List_Olistrel(U_18983,U_18984))),
    inference(variable_rename,[status(thm)],[f_4564_1]) ).

fof(f_4564_3,plain,
    ! [U_18984,U_18983] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18983),tc_List_Olist(U_18983))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18983),tc_List_Olist(U_18983)),c_List_Olist_ONil(U_18983)),c_List_Olist_ONil(U_18983))),c_List_Olistrel(U_18983,U_18984))),
    inference(definitional_conversion,[status(esa)],[f_4564_2]) ).

cnf(f_4564_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18983),tc_List_Olist(U_18983))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18983),tc_List_Olist(U_18983)),c_List_Olist_ONil(U_18983)),c_List_Olist_ONil(U_18983))),c_List_Olistrel(U_18983,U_18984))),
    inference(clausify,[status(thm)],[f_4564_3]) ).

fof(f_4565_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_4565_2,plain,
    ! [U_18987,U_18986,U_18985] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18985),tc_List_Olist(U_18985))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18985),tc_List_Olist(U_18985)),U_18986),c_List_Olist_ONil(U_18985))),c_List_Olexord(U_18985,U_18987))),
    inference(variable_rename,[status(thm)],[f_4565_1]) ).

fof(f_4565_3,plain,
    ! [U_18985,U_18986,U_18987] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18985),tc_List_Olist(U_18985))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18985),tc_List_Olist(U_18985)),U_18986),c_List_Olist_ONil(U_18985))),c_List_Olexord(U_18985,U_18987))),
    inference(definitional_conversion,[status(esa)],[f_4565_2]) ).

cnf(f_4565_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18985),tc_List_Olist(U_18985))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18985),tc_List_Olist(U_18985)),U_18986),c_List_Olist_ONil(U_18985))),c_List_Olexord(U_18985,U_18987))),
    inference(clausify,[status(thm)],[f_4565_3]) ).

fof(f_4566_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_4566_2,plain,
    ! [U_18990,U_18989,U_18988] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18988),tc_List_Olist(U_18988))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18988),tc_List_Olist(U_18988)),U_18989),c_List_Olist_ONil(U_18988))),c_List_Olex(U_18988,U_18990))),
    inference(variable_rename,[status(thm)],[f_4566_1]) ).

fof(f_4566_3,plain,
    ! [U_18988,U_18989,U_18990] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18988),tc_List_Olist(U_18988))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18988),tc_List_Olist(U_18988)),U_18989),c_List_Olist_ONil(U_18988))),c_List_Olex(U_18988,U_18990))),
    inference(definitional_conversion,[status(esa)],[f_4566_2]) ).

cnf(f_4566_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18988),tc_List_Olist(U_18988))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18988),tc_List_Olist(U_18988)),U_18989),c_List_Olist_ONil(U_18988))),c_List_Olex(U_18988,U_18990))),
    inference(clausify,[status(thm)],[f_4566_3]) ).

fof(f_4567_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_4567_2,plain,
    ! [U_18993,U_18992,U_18991] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18991),tc_List_Olist(U_18991))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18991),tc_List_Olist(U_18991)),c_List_Olist_ONil(U_18991)),U_18992)),c_List_Olex(U_18991,U_18993))),
    inference(variable_rename,[status(thm)],[f_4567_1]) ).

fof(f_4567_3,plain,
    ! [U_18991,U_18992,U_18993] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18991),tc_List_Olist(U_18991))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18991),tc_List_Olist(U_18991)),c_List_Olist_ONil(U_18991)),U_18992)),c_List_Olex(U_18991,U_18993))),
    inference(definitional_conversion,[status(esa)],[f_4567_2]) ).

cnf(f_4567_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18991),tc_List_Olist(U_18991))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18991),tc_List_Olist(U_18991)),c_List_Olist_ONil(U_18991)),U_18992)),c_List_Olex(U_18991,U_18993))),
    inference(clausify,[status(thm)],[f_4567_3]) ).

fof(f_4568_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_4568_2,plain,
    ! [U_18997,U_18996,U_18995,U_18994] :
      ( hBOOL(hAPP(hAPP(c_member(U_18995),U_18997),hAPP(c_List_Oset(U_18995),hAPP(hAPP(c_List_Olist__update(U_18995,U_18996),U_18994),U_18997))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18994),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18995)),U_18996))) ),
    inference(variable_rename,[status(thm)],[f_4568_1]) ).

fof(f_4568_3,plain,
    ! [U_18994,U_18995,U_18996,U_18997] :
      ( hBOOL(hAPP(hAPP(c_member(U_18995),U_18997),hAPP(c_List_Oset(U_18995),hAPP(hAPP(c_List_Olist__update(U_18995,U_18996),U_18994),U_18997))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18994),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18995)),U_18996))) ),
    inference(definitional_conversion,[status(esa)],[f_4568_2]) ).

cnf(f_4568_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18995),U_18997),hAPP(c_List_Oset(U_18995),hAPP(hAPP(c_List_Olist__update(U_18995,U_18996),U_18994),U_18997))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18994),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18995)),U_18996))) ),
    inference(clausify,[status(thm)],[f_4568_3]) ).

fof(f_4569_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_4569_2,plain,
    ! [U_18999,U_18998] :
      ( ( c_List_Oupto(U_18998,U_18999) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18998),U_18999)) )
      & ( c_List_Oupto(U_18998,U_18999) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_18998),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18998),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_18999))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18998),U_18999)) ) ),
    inference(variable_rename,[status(thm)],[f_4569_1]) ).

fof(f_4569_3,plain,
    ( ! [U_19003,U_19001] :
        ( c_List_Oupto(U_19001,U_19003) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_19001),U_19003)) )
    & ! [U_19002,U_19000] :
        ( c_List_Oupto(U_19000,U_19002) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_19000),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19000),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_19002))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_19000),U_19002)) ) ),
    inference(miniscope,[status(thm)],[f_4569_2]) ).

fof(f_4569_4,plain,
    ( ! [U_19001,U_19003] :
        ( c_List_Oupto(U_19001,U_19003) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_19001),U_19003)) )
    & ! [U_19002,U_19000] :
        ( c_List_Oupto(U_19000,U_19002) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_19000),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19000),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_19002))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_19000),U_19002)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4569_3]) ).

cnf(f_4569_5,plain,
    ( c_List_Oupto(U_19000,U_19002) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_19000),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19000),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_19002))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_19000),U_19002)) ),
    inference(clausify,[status(thm)],[f_4569_4]) ).

cnf(f_4569_6,plain,
    ( c_List_Oupto(U_19001,U_19003) = c_List_Olist_ONil(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_19001),U_19003)) ),
    inference(clausify,[status(thm)],[f_4569_4]) ).

fof(f_4570_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_4570_2,plain,
    ! [U_19006,U_19005,U_19004] :
      ( ( c_List_Osublist(U_19005,hAPP(hAPP(c_List_Olist_OCons(U_19005),U_19006),c_List_Olist_ONil(U_19005)),U_19004) = c_List_Olist_ONil(U_19005)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19004)) )
      & ( c_List_Osublist(U_19005,hAPP(hAPP(c_List_Olist_OCons(U_19005),U_19006),c_List_Olist_ONil(U_19005)),U_19004) = hAPP(hAPP(c_List_Olist_OCons(U_19005),U_19006),c_List_Olist_ONil(U_19005))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19004)) ) ),
    inference(variable_rename,[status(thm)],[f_4570_1]) ).

fof(f_4570_3,plain,
    ( ! [U_19012,U_19010,U_19008] :
        ( c_List_Osublist(U_19010,hAPP(hAPP(c_List_Olist_OCons(U_19010),U_19012),c_List_Olist_ONil(U_19010)),U_19008) = c_List_Olist_ONil(U_19010)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19008)) )
    & ! [U_19011,U_19009,U_19007] :
        ( c_List_Osublist(U_19009,hAPP(hAPP(c_List_Olist_OCons(U_19009),U_19011),c_List_Olist_ONil(U_19009)),U_19007) = hAPP(hAPP(c_List_Olist_OCons(U_19009),U_19011),c_List_Olist_ONil(U_19009))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19007)) ) ),
    inference(miniscope,[status(thm)],[f_4570_2]) ).

fof(f_4570_4,plain,
    ( ! [U_19008,U_19012,U_19010] :
        ( c_List_Osublist(U_19010,hAPP(hAPP(c_List_Olist_OCons(U_19010),U_19012),c_List_Olist_ONil(U_19010)),U_19008) = c_List_Olist_ONil(U_19010)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19008)) )
    & ! [U_19007,U_19009,U_19011] :
        ( c_List_Osublist(U_19009,hAPP(hAPP(c_List_Olist_OCons(U_19009),U_19011),c_List_Olist_ONil(U_19009)),U_19007) = hAPP(hAPP(c_List_Olist_OCons(U_19009),U_19011),c_List_Olist_ONil(U_19009))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19007)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4570_3]) ).

cnf(f_4570_5,plain,
    ( c_List_Osublist(U_19009,hAPP(hAPP(c_List_Olist_OCons(U_19009),U_19011),c_List_Olist_ONil(U_19009)),U_19007) = hAPP(hAPP(c_List_Olist_OCons(U_19009),U_19011),c_List_Olist_ONil(U_19009))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19007)) ),
    inference(clausify,[status(thm)],[f_4570_4]) ).

cnf(f_4570_6,plain,
    ( c_List_Osublist(U_19010,hAPP(hAPP(c_List_Olist_OCons(U_19010),U_19012),c_List_Olist_ONil(U_19010)),U_19008) = c_List_Olist_ONil(U_19010)
    | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19008)) ),
    inference(clausify,[status(thm)],[f_4570_4]) ).

fof(f_4571_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_4571_2,plain,
    ! [U_19016,U_19015,U_19014,U_19013] :
      ( ( hAPP(hAPP(c_List_Otake(U_19014),U_19013),hAPP(hAPP(c_List_Olist_OCons(U_19014),U_19015),U_19016)) = hAPP(hAPP(c_List_Olist_OCons(U_19014),U_19015),hAPP(hAPP(c_List_Otake(U_19014),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19013),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19016))
        | U_19013 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(U_19014),U_19013),hAPP(hAPP(c_List_Olist_OCons(U_19014),U_19015),U_19016)) = c_List_Olist_ONil(U_19014)
        | U_19013 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4571_1]) ).

fof(f_4571_3,plain,
    ( ! [U_19024,U_19022,U_19020,U_19018] :
        ( hAPP(hAPP(c_List_Otake(U_19020),U_19018),hAPP(hAPP(c_List_Olist_OCons(U_19020),U_19022),U_19024)) = hAPP(hAPP(c_List_Olist_OCons(U_19020),U_19022),hAPP(hAPP(c_List_Otake(U_19020),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19018),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19024))
        | U_19018 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19023,U_19021,U_19019,U_19017] :
        ( hAPP(hAPP(c_List_Otake(U_19019),U_19017),hAPP(hAPP(c_List_Olist_OCons(U_19019),U_19021),U_19023)) = c_List_Olist_ONil(U_19019)
        | U_19017 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4571_2]) ).

fof(f_4571_4,plain,
    ( ! [U_19018,U_19020,U_19022,U_19024] :
        ( hAPP(hAPP(c_List_Otake(U_19020),U_19018),hAPP(hAPP(c_List_Olist_OCons(U_19020),U_19022),U_19024)) = hAPP(hAPP(c_List_Olist_OCons(U_19020),U_19022),hAPP(hAPP(c_List_Otake(U_19020),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19018),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19024))
        | U_19018 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19021,U_19023,U_19019,U_19017] :
        ( hAPP(hAPP(c_List_Otake(U_19019),U_19017),hAPP(hAPP(c_List_Olist_OCons(U_19019),U_19021),U_19023)) = c_List_Olist_ONil(U_19019)
        | U_19017 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4571_3]) ).

cnf(f_4571_5,plain,
    ( hAPP(hAPP(c_List_Otake(U_19019),U_19017),hAPP(hAPP(c_List_Olist_OCons(U_19019),U_19021),U_19023)) = c_List_Olist_ONil(U_19019)
    | U_19017 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4571_4]) ).

cnf(f_4571_6,plain,
    ( hAPP(hAPP(c_List_Otake(U_19020),U_19018),hAPP(hAPP(c_List_Olist_OCons(U_19020),U_19022),U_19024)) = hAPP(hAPP(c_List_Olist_OCons(U_19020),U_19022),hAPP(hAPP(c_List_Otake(U_19020),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19018),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19024))
    | U_19018 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4571_4]) ).

fof(f_4572_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_4572_2,plain,
    ! [U_19026,U_19025] :
      ( ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19025),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19026)) = 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_19025)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19026))) )
      & ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19025),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19026)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19025)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19025)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19026)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19025)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19026))) ) ),
    inference(variable_rename,[status(thm)],[f_4572_1]) ).

fof(f_4572_3,plain,
    ( ! [U_19030,U_19028] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19028),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19030)) = 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_19028)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19030))) )
    & ! [U_19029,U_19027] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19027),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19029)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19027)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19027)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19029)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19027)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19029))) ) ),
    inference(miniscope,[status(thm)],[f_4572_2]) ).

fof(f_4572_4,plain,
    ( ! [U_19028,U_19030] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19028),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19030)) = 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_19028)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19030))) )
    & ! [U_19027,U_19029] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19027),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19029)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19027)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19027)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19029)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19027)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19029))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4572_3]) ).

cnf(f_4572_5,plain,
    ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19027),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19029)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19027)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19027)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19029)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19027)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19029))) ),
    inference(clausify,[status(thm)],[f_4572_4]) ).

cnf(f_4572_6,plain,
    ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19028),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19030)) = 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_19028)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_19030))) ),
    inference(clausify,[status(thm)],[f_4572_4]) ).

fof(f_4573_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_4573_2,plain,
    ! [U_19033,U_19032,U_19031] :
      ( hBOOL(hAPP(hAPP(c_member(U_19032),hAPP(c_Product__Type_Ofst(U_19032,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(U_19032,U_19031),U_19033))),hAPP(c_List_Oset(U_19032),U_19031)))
      | U_19031 = c_List_Olist_ONil(U_19032) ),
    inference(variable_rename,[status(thm)],[f_4573_1]) ).

fof(f_4573_3,plain,
    ! [U_19032,U_19031,U_19033] :
      ( hBOOL(hAPP(hAPP(c_member(U_19032),hAPP(c_Product__Type_Ofst(U_19032,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(U_19032,U_19031),U_19033))),hAPP(c_List_Oset(U_19032),U_19031)))
      | U_19031 = c_List_Olist_ONil(U_19032) ),
    inference(definitional_conversion,[status(esa)],[f_4573_2]) ).

cnf(f_4573_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19032),hAPP(c_Product__Type_Ofst(U_19032,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(U_19032,U_19031),U_19033))),hAPP(c_List_Oset(U_19032),U_19031)))
    | U_19031 = c_List_Olist_ONil(U_19032) ),
    inference(clausify,[status(thm)],[f_4573_3]) ).

fof(f_4574_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_4574_2,plain,
    ! [U_19035,U_19034] : hAPP(c_Relation_OImage(tc_List_Olist(U_19034),tc_List_Olist(U_19034),c_List_Olistrel(U_19034,U_19035)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19034)),c_List_Olist_ONil(U_19034)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19034),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19034)),c_List_Olist_ONil(U_19034)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19034),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4574_1]) ).

fof(f_4574_3,plain,
    ! [U_19034,U_19035] : hAPP(c_Relation_OImage(tc_List_Olist(U_19034),tc_List_Olist(U_19034),c_List_Olistrel(U_19034,U_19035)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19034)),c_List_Olist_ONil(U_19034)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19034),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19034)),c_List_Olist_ONil(U_19034)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19034),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_4574_2]) ).

cnf(f_4574_4,plain,
    hAPP(c_Relation_OImage(tc_List_Olist(U_19034),tc_List_Olist(U_19034),c_List_Olistrel(U_19034,U_19035)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19034)),c_List_Olist_ONil(U_19034)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19034),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19034)),c_List_Olist_ONil(U_19034)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19034),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4574_3]) ).

fof(f_4575_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_4575_2,plain,
    ! [U_19037,U_19036] : c_List_Oset__Cons(U_19036,U_19037,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19036)),c_List_Olist_ONil(U_19036)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19036),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(U_19036,tc_List_Olist(U_19036),hAPP(hAPP(c_COMBC(U_19036,tc_List_Olist(U_19036),tc_List_Olist(U_19036)),c_List_Olist_OCons(U_19036)),c_List_Olist_ONil(U_19036))),U_19037),
    inference(variable_rename,[status(thm)],[f_4575_1]) ).

fof(f_4575_3,plain,
    ! [U_19036,U_19037] : c_List_Oset__Cons(U_19036,U_19037,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19036)),c_List_Olist_ONil(U_19036)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19036),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(U_19036,tc_List_Olist(U_19036),hAPP(hAPP(c_COMBC(U_19036,tc_List_Olist(U_19036),tc_List_Olist(U_19036)),c_List_Olist_OCons(U_19036)),c_List_Olist_ONil(U_19036))),U_19037),
    inference(definitional_conversion,[status(esa)],[f_4575_2]) ).

cnf(f_4575_4,plain,
    c_List_Oset__Cons(U_19036,U_19037,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19036)),c_List_Olist_ONil(U_19036)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19036),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(U_19036,tc_List_Olist(U_19036),hAPP(hAPP(c_COMBC(U_19036,tc_List_Olist(U_19036),tc_List_Olist(U_19036)),c_List_Olist_OCons(U_19036)),c_List_Olist_ONil(U_19036))),U_19037),
    inference(clausify,[status(thm)],[f_4575_3]) ).

fof(f_4576_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_4576_2,plain,
    ! [U_19041,U_19040,U_19039,U_19038] :
      ( ( hAPP(hAPP(c_List_Otake(U_19039),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19038)),hAPP(hAPP(c_List_Olist_OCons(U_19039),U_19040),U_19041)) = hAPP(hAPP(c_List_Olist_OCons(U_19039),U_19040),hAPP(hAPP(c_List_Otake(U_19039),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19038)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19041))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19038) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(U_19039),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19038)),hAPP(hAPP(c_List_Olist_OCons(U_19039),U_19040),U_19041)) = c_List_Olist_ONil(U_19039)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19038) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4576_1]) ).

fof(f_4576_3,plain,
    ( ! [U_19049,U_19047,U_19045,U_19043] :
        ( hAPP(hAPP(c_List_Otake(U_19045),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19043)),hAPP(hAPP(c_List_Olist_OCons(U_19045),U_19047),U_19049)) = hAPP(hAPP(c_List_Olist_OCons(U_19045),U_19047),hAPP(hAPP(c_List_Otake(U_19045),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19043)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19049))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19043) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19048,U_19046,U_19044,U_19042] :
        ( hAPP(hAPP(c_List_Otake(U_19044),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19042)),hAPP(hAPP(c_List_Olist_OCons(U_19044),U_19046),U_19048)) = c_List_Olist_ONil(U_19044)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19042) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4576_2]) ).

fof(f_4576_4,plain,
    ( ! [U_19043,U_19045,U_19047,U_19049] :
        ( hAPP(hAPP(c_List_Otake(U_19045),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19043)),hAPP(hAPP(c_List_Olist_OCons(U_19045),U_19047),U_19049)) = hAPP(hAPP(c_List_Olist_OCons(U_19045),U_19047),hAPP(hAPP(c_List_Otake(U_19045),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19043)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19049))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19043) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19048,U_19044,U_19042,U_19046] :
        ( hAPP(hAPP(c_List_Otake(U_19044),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19042)),hAPP(hAPP(c_List_Olist_OCons(U_19044),U_19046),U_19048)) = c_List_Olist_ONil(U_19044)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19042) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4576_3]) ).

cnf(f_4576_5,plain,
    ( hAPP(hAPP(c_List_Otake(U_19044),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19042)),hAPP(hAPP(c_List_Olist_OCons(U_19044),U_19046),U_19048)) = c_List_Olist_ONil(U_19044)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19042) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4576_4]) ).

cnf(f_4576_6,plain,
    ( hAPP(hAPP(c_List_Otake(U_19045),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19043)),hAPP(hAPP(c_List_Olist_OCons(U_19045),U_19047),U_19049)) = hAPP(hAPP(c_List_Olist_OCons(U_19045),U_19047),hAPP(hAPP(c_List_Otake(U_19045),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19043)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19049))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19043) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4576_4]) ).

fof(f_4577_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_4577_2,plain,
    ! [U_19053,U_19052,U_19051,U_19050] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19050),hAPP(hAPP(c_List_Olist__update(U_19050,U_19051),U_19053),U_19052)))
      | hBOOL(hAPP(hAPP(c_member(U_19050),U_19052),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_19050,tc_HOL_Obool)),hAPP(c_List_Oset(U_19050),U_19051)),hAPP(hAPP(c_Set_Oinsert(U_19050),hAPP(hAPP(c_List_Onth(U_19050),U_19051),U_19053)),c_Orderings_Obot__class_Obot(tc_fun(U_19050,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19050),U_19051)) ),
    inference(variable_rename,[status(thm)],[f_4577_1]) ).

fof(f_4577_3,plain,
    ! [U_19050,U_19051,U_19052,U_19053] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19050),hAPP(hAPP(c_List_Olist__update(U_19050,U_19051),U_19053),U_19052)))
      | hBOOL(hAPP(hAPP(c_member(U_19050),U_19052),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_19050,tc_HOL_Obool)),hAPP(c_List_Oset(U_19050),U_19051)),hAPP(hAPP(c_Set_Oinsert(U_19050),hAPP(hAPP(c_List_Onth(U_19050),U_19051),U_19053)),c_Orderings_Obot__class_Obot(tc_fun(U_19050,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19050),U_19051)) ),
    inference(definitional_conversion,[status(esa)],[f_4577_2]) ).

cnf(f_4577_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19050),hAPP(hAPP(c_List_Olist__update(U_19050,U_19051),U_19053),U_19052)))
    | hBOOL(hAPP(hAPP(c_member(U_19050),U_19052),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_19050,tc_HOL_Obool)),hAPP(c_List_Oset(U_19050),U_19051)),hAPP(hAPP(c_Set_Oinsert(U_19050),hAPP(hAPP(c_List_Onth(U_19050),U_19051),U_19053)),c_Orderings_Obot__class_Obot(tc_fun(U_19050,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19050),U_19051)) ),
    inference(clausify,[status(thm)],[f_4577_3]) ).

fof(f_4578_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_4578_2,plain,
    ! [U_19055,U_19054] :
      ( ( ( c_List_Oupto(U_19054,U_19055) = c_List_Olist_ONil(tc_Int_Oint)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_19054),U_19055)) )
        & ( c_List_Oupto(U_19054,U_19055) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_19054),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19054),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_19055))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_19054),U_19055)) ) )
      | ~ 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_19054),U_19055))) ),
    inference(variable_rename,[status(thm)],[f_4578_1]) ).

fof(f_4578_3,plain,
    ( ! [U_19054,U_19055] :
        ( c_List_Oupto(U_19054,U_19055) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_19054),U_19055))
        | ~ sP1171(U_19054,U_19055) )
    & ! [U_19054,U_19055] :
        ( c_List_Oupto(U_19054,U_19055) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_19054),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19054),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_19055))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_19054),U_19055))
        | ~ sP1171(U_19054,U_19055) )
    & ! [U_19054,U_19055] :
        ( sP1171(U_19054,U_19055)
        | ~ 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_19054),U_19055))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1171])],[f_4578_2]) ).

cnf(f_4578_4,plain,
    ( sP1171(U_19054,U_19055)
    | ~ 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_19054),U_19055))) ),
    inference(clausify,[status(thm)],[f_4578_3]) ).

cnf(f_4578_5,plain,
    ( c_List_Oupto(U_19054,U_19055) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_19054),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19054),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_19055))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_19054),U_19055))
    | ~ sP1171(U_19054,U_19055) ),
    inference(clausify,[status(thm)],[f_4578_3]) ).

cnf(f_4578_6,plain,
    ( c_List_Oupto(U_19054,U_19055) = c_List_Olist_ONil(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_19054),U_19055))
    | ~ sP1171(U_19054,U_19055) ),
    inference(clausify,[status(thm)],[f_4578_3]) ).

fof(f_4579_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_4579_2,plain,
    ! [U_19060,U_19059,U_19058,U_19057,U_19056] :
      ( ( hAPP(c_Lazy__Sequence_Oanamorph(U_19057,U_19058,U_19059,U_19056),U_19060) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_19058),U_19057),tc_prod(U_19058,U_19057),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19058),U_19057),c_List_Olist_ONil(U_19058)),U_19060),hAPP(c_Product__Type_Oprod_Oprod__case(U_19058,U_19057,tc_prod(tc_List_Olist(U_19058),U_19057)),hAPP(hAPP(c_COMBC(U_19058,tc_fun(U_19057,tc_prod(tc_List_Olist(U_19058),U_19057)),tc_fun(U_19057,tc_prod(tc_List_Olist(U_19058),U_19057))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_19058),U_19057),tc_prod(tc_List_Olist(U_19058),U_19057)),tc_fun(tc_fun(U_19057,tc_prod(tc_List_Olist(U_19058),U_19057)),tc_fun(U_19057,tc_prod(tc_List_Olist(U_19058),U_19057))),U_19058),c_COMBB(tc_prod(tc_List_Olist(U_19058),U_19057),tc_prod(tc_List_Olist(U_19058),U_19057),U_19057)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19058),tc_fun(U_19057,tc_prod(tc_List_Olist(U_19058),U_19057))),tc_fun(tc_prod(tc_List_Olist(U_19058),U_19057),tc_prod(tc_List_Olist(U_19058),U_19057)),U_19058),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_19058),U_19057,tc_prod(tc_List_Olist(U_19058),U_19057))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19058),tc_List_Olist(U_19058)),tc_fun(tc_List_Olist(U_19058),tc_fun(U_19057,tc_prod(tc_List_Olist(U_19058),U_19057))),U_19058),hAPP(c_COMBB(tc_List_Olist(U_19058),tc_fun(U_19057,tc_prod(tc_List_Olist(U_19058),U_19057)),tc_List_Olist(U_19058)),c_Product__Type_OPair(tc_List_Olist(U_19058),U_19057))),c_List_Olist_OCons(U_19058))))),c_Lazy__Sequence_Oanamorph(U_19057,U_19058,U_19059,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19056),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(U_19059,U_19060))
        | U_19056 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Lazy__Sequence_Oanamorph(U_19057,U_19058,U_19059,U_19056),U_19060) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19058),U_19057),c_List_Olist_ONil(U_19058)),U_19060)
        | U_19056 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_4579_1]) ).

fof(f_4579_3,plain,
    ( ! [U_19070,U_19068,U_19066,U_19064,U_19062] :
        ( hAPP(c_Lazy__Sequence_Oanamorph(U_19064,U_19066,U_19068,U_19062),U_19070) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_19066),U_19064),tc_prod(U_19066,U_19064),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19066),U_19064),c_List_Olist_ONil(U_19066)),U_19070),hAPP(c_Product__Type_Oprod_Oprod__case(U_19066,U_19064,tc_prod(tc_List_Olist(U_19066),U_19064)),hAPP(hAPP(c_COMBC(U_19066,tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064)),tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_19066),U_19064),tc_prod(tc_List_Olist(U_19066),U_19064)),tc_fun(tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064)),tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064))),U_19066),c_COMBB(tc_prod(tc_List_Olist(U_19066),U_19064),tc_prod(tc_List_Olist(U_19066),U_19064),U_19064)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19066),tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064))),tc_fun(tc_prod(tc_List_Olist(U_19066),U_19064),tc_prod(tc_List_Olist(U_19066),U_19064)),U_19066),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_19066),U_19064,tc_prod(tc_List_Olist(U_19066),U_19064))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19066),tc_List_Olist(U_19066)),tc_fun(tc_List_Olist(U_19066),tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064))),U_19066),hAPP(c_COMBB(tc_List_Olist(U_19066),tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064)),tc_List_Olist(U_19066)),c_Product__Type_OPair(tc_List_Olist(U_19066),U_19064))),c_List_Olist_OCons(U_19066))))),c_Lazy__Sequence_Oanamorph(U_19064,U_19066,U_19068,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19062),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(U_19068,U_19070))
        | U_19062 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_19069,U_19067,U_19065,U_19063,U_19061] :
        ( hAPP(c_Lazy__Sequence_Oanamorph(U_19063,U_19065,U_19067,U_19061),U_19069) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19065),U_19063),c_List_Olist_ONil(U_19065)),U_19069)
        | U_19061 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_4579_2]) ).

fof(f_4579_4,plain,
    ( ! [U_19062,U_19068,U_19064,U_19066,U_19070] :
        ( hAPP(c_Lazy__Sequence_Oanamorph(U_19064,U_19066,U_19068,U_19062),U_19070) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_19066),U_19064),tc_prod(U_19066,U_19064),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19066),U_19064),c_List_Olist_ONil(U_19066)),U_19070),hAPP(c_Product__Type_Oprod_Oprod__case(U_19066,U_19064,tc_prod(tc_List_Olist(U_19066),U_19064)),hAPP(hAPP(c_COMBC(U_19066,tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064)),tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_19066),U_19064),tc_prod(tc_List_Olist(U_19066),U_19064)),tc_fun(tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064)),tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064))),U_19066),c_COMBB(tc_prod(tc_List_Olist(U_19066),U_19064),tc_prod(tc_List_Olist(U_19066),U_19064),U_19064)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19066),tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064))),tc_fun(tc_prod(tc_List_Olist(U_19066),U_19064),tc_prod(tc_List_Olist(U_19066),U_19064)),U_19066),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_19066),U_19064,tc_prod(tc_List_Olist(U_19066),U_19064))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19066),tc_List_Olist(U_19066)),tc_fun(tc_List_Olist(U_19066),tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064))),U_19066),hAPP(c_COMBB(tc_List_Olist(U_19066),tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064)),tc_List_Olist(U_19066)),c_Product__Type_OPair(tc_List_Olist(U_19066),U_19064))),c_List_Olist_OCons(U_19066))))),c_Lazy__Sequence_Oanamorph(U_19064,U_19066,U_19068,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19062),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(U_19068,U_19070))
        | U_19062 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_19061,U_19063,U_19069,U_19065,U_19067] :
        ( hAPP(c_Lazy__Sequence_Oanamorph(U_19063,U_19065,U_19067,U_19061),U_19069) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19065),U_19063),c_List_Olist_ONil(U_19065)),U_19069)
        | U_19061 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa)],[f_4579_3]) ).

cnf(f_4579_5,plain,
    ( hAPP(c_Lazy__Sequence_Oanamorph(U_19063,U_19065,U_19067,U_19061),U_19069) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19065),U_19063),c_List_Olist_ONil(U_19065)),U_19069)
    | U_19061 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4579_4]) ).

cnf(f_4579_6,plain,
    ( hAPP(c_Lazy__Sequence_Oanamorph(U_19064,U_19066,U_19068,U_19062),U_19070) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_19066),U_19064),tc_prod(U_19066,U_19064),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19066),U_19064),c_List_Olist_ONil(U_19066)),U_19070),hAPP(c_Product__Type_Oprod_Oprod__case(U_19066,U_19064,tc_prod(tc_List_Olist(U_19066),U_19064)),hAPP(hAPP(c_COMBC(U_19066,tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064)),tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_19066),U_19064),tc_prod(tc_List_Olist(U_19066),U_19064)),tc_fun(tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064)),tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064))),U_19066),c_COMBB(tc_prod(tc_List_Olist(U_19066),U_19064),tc_prod(tc_List_Olist(U_19066),U_19064),U_19064)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19066),tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064))),tc_fun(tc_prod(tc_List_Olist(U_19066),U_19064),tc_prod(tc_List_Olist(U_19066),U_19064)),U_19066),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_19066),U_19064,tc_prod(tc_List_Olist(U_19066),U_19064))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19066),tc_List_Olist(U_19066)),tc_fun(tc_List_Olist(U_19066),tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064))),U_19066),hAPP(c_COMBB(tc_List_Olist(U_19066),tc_fun(U_19064,tc_prod(tc_List_Olist(U_19066),U_19064)),tc_List_Olist(U_19066)),c_Product__Type_OPair(tc_List_Olist(U_19066),U_19064))),c_List_Olist_OCons(U_19066))))),c_Lazy__Sequence_Oanamorph(U_19064,U_19066,U_19068,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19062),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(U_19068,U_19070))
    | U_19062 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4579_4]) ).

fof(f_4580_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_4580_2,plain,
    ! [U_19071] : c_List_Olistset(U_19071,c_List_Olist_ONil(tc_fun(U_19071,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19071)),c_List_Olist_ONil(U_19071)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19071),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4580_1]) ).

fof(f_4580_3,plain,
    ! [U_19071] : c_List_Olistset(U_19071,c_List_Olist_ONil(tc_fun(U_19071,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19071)),c_List_Olist_ONil(U_19071)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19071),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_4580_2]) ).

cnf(f_4580_4,plain,
    c_List_Olistset(U_19071,c_List_Olist_ONil(tc_fun(U_19071,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19071)),c_List_Olist_ONil(U_19071)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19071),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4580_3]) ).

fof(f_4581_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_4581_2,plain,
    ! [U_19076,U_19075,U_19074,U_19073,U_19072] : hAPP(hAPP(c_List_Ozip(U_19072,U_19073),hAPP(hAPP(c_List_Olist_OCons(U_19072),U_19074),U_19075)),U_19076) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_19072,U_19073)),U_19073,c_List_Olist_ONil(tc_prod(U_19072,U_19073)),hAPP(hAPP(c_COMBC(U_19073,tc_fun(tc_List_Olist(U_19073),tc_List_Olist(tc_prod(U_19072,U_19073))),tc_fun(tc_List_Olist(U_19073),tc_List_Olist(tc_prod(U_19072,U_19073)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_19072,U_19073)),tc_List_Olist(tc_prod(U_19072,U_19073))),tc_fun(tc_fun(tc_List_Olist(U_19073),tc_List_Olist(tc_prod(U_19072,U_19073))),tc_fun(tc_List_Olist(U_19073),tc_List_Olist(tc_prod(U_19072,U_19073)))),U_19073),c_COMBB(tc_List_Olist(tc_prod(U_19072,U_19073)),tc_List_Olist(tc_prod(U_19072,U_19073)),tc_List_Olist(U_19073))),hAPP(hAPP(c_COMBB(tc_prod(U_19072,U_19073),tc_fun(tc_List_Olist(tc_prod(U_19072,U_19073)),tc_List_Olist(tc_prod(U_19072,U_19073))),U_19073),c_List_Olist_OCons(tc_prod(U_19072,U_19073))),hAPP(c_Product__Type_OPair(U_19072,U_19073),U_19074)))),hAPP(c_List_Ozip(U_19072,U_19073),U_19075))),U_19076),
    inference(variable_rename,[status(thm)],[f_4581_1]) ).

fof(f_4581_3,plain,
    ! [U_19072,U_19073,U_19074,U_19075,U_19076] : hAPP(hAPP(c_List_Ozip(U_19072,U_19073),hAPP(hAPP(c_List_Olist_OCons(U_19072),U_19074),U_19075)),U_19076) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_19072,U_19073)),U_19073,c_List_Olist_ONil(tc_prod(U_19072,U_19073)),hAPP(hAPP(c_COMBC(U_19073,tc_fun(tc_List_Olist(U_19073),tc_List_Olist(tc_prod(U_19072,U_19073))),tc_fun(tc_List_Olist(U_19073),tc_List_Olist(tc_prod(U_19072,U_19073)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_19072,U_19073)),tc_List_Olist(tc_prod(U_19072,U_19073))),tc_fun(tc_fun(tc_List_Olist(U_19073),tc_List_Olist(tc_prod(U_19072,U_19073))),tc_fun(tc_List_Olist(U_19073),tc_List_Olist(tc_prod(U_19072,U_19073)))),U_19073),c_COMBB(tc_List_Olist(tc_prod(U_19072,U_19073)),tc_List_Olist(tc_prod(U_19072,U_19073)),tc_List_Olist(U_19073))),hAPP(hAPP(c_COMBB(tc_prod(U_19072,U_19073),tc_fun(tc_List_Olist(tc_prod(U_19072,U_19073)),tc_List_Olist(tc_prod(U_19072,U_19073))),U_19073),c_List_Olist_OCons(tc_prod(U_19072,U_19073))),hAPP(c_Product__Type_OPair(U_19072,U_19073),U_19074)))),hAPP(c_List_Ozip(U_19072,U_19073),U_19075))),U_19076),
    inference(definitional_conversion,[status(esa)],[f_4581_2]) ).

cnf(f_4581_4,plain,
    hAPP(hAPP(c_List_Ozip(U_19072,U_19073),hAPP(hAPP(c_List_Olist_OCons(U_19072),U_19074),U_19075)),U_19076) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_19072,U_19073)),U_19073,c_List_Olist_ONil(tc_prod(U_19072,U_19073)),hAPP(hAPP(c_COMBC(U_19073,tc_fun(tc_List_Olist(U_19073),tc_List_Olist(tc_prod(U_19072,U_19073))),tc_fun(tc_List_Olist(U_19073),tc_List_Olist(tc_prod(U_19072,U_19073)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_19072,U_19073)),tc_List_Olist(tc_prod(U_19072,U_19073))),tc_fun(tc_fun(tc_List_Olist(U_19073),tc_List_Olist(tc_prod(U_19072,U_19073))),tc_fun(tc_List_Olist(U_19073),tc_List_Olist(tc_prod(U_19072,U_19073)))),U_19073),c_COMBB(tc_List_Olist(tc_prod(U_19072,U_19073)),tc_List_Olist(tc_prod(U_19072,U_19073)),tc_List_Olist(U_19073))),hAPP(hAPP(c_COMBB(tc_prod(U_19072,U_19073),tc_fun(tc_List_Olist(tc_prod(U_19072,U_19073)),tc_List_Olist(tc_prod(U_19072,U_19073))),U_19073),c_List_Olist_OCons(tc_prod(U_19072,U_19073))),hAPP(c_Product__Type_OPair(U_19072,U_19073),U_19074)))),hAPP(c_List_Ozip(U_19072,U_19073),U_19075))),U_19076),
    inference(clausify,[status(thm)],[f_4581_3]) ).

fof(f_4582_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_4582_2,plain,
    ! [U_19082,U_19081,U_19080,U_19079,U_19078,U_19077] : hAPP(c_List_Olist_Olist__case(U_19077,U_19078,U_19079,U_19080),hAPP(hAPP(c_List_Olist_OCons(U_19078),U_19081),U_19082)) = hAPP(hAPP(U_19080,U_19081),U_19082),
    inference(variable_rename,[status(thm)],[f_4582_1]) ).

fof(f_4582_3,plain,
    ! [U_19077,U_19078,U_19079,U_19080,U_19081,U_19082] : hAPP(c_List_Olist_Olist__case(U_19077,U_19078,U_19079,U_19080),hAPP(hAPP(c_List_Olist_OCons(U_19078),U_19081),U_19082)) = hAPP(hAPP(U_19080,U_19081),U_19082),
    inference(definitional_conversion,[status(esa)],[f_4582_2]) ).

cnf(f_4582_4,plain,
    hAPP(c_List_Olist_Olist__case(U_19077,U_19078,U_19079,U_19080),hAPP(hAPP(c_List_Olist_OCons(U_19078),U_19081),U_19082)) = hAPP(hAPP(U_19080,U_19081),U_19082),
    inference(clausify,[status(thm)],[f_4582_3]) ).

fof(f_4583_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_4583_2,plain,
    ! [U_19086,U_19085,U_19084,U_19083] : hAPP(c_List_Olist_Olist__case(U_19083,U_19084,U_19085,U_19086),c_List_Olist_ONil(U_19084)) = U_19085,
    inference(variable_rename,[status(thm)],[f_4583_1]) ).

fof(f_4583_3,plain,
    ! [U_19083,U_19084,U_19085,U_19086] : hAPP(c_List_Olist_Olist__case(U_19083,U_19084,U_19085,U_19086),c_List_Olist_ONil(U_19084)) = U_19085,
    inference(definitional_conversion,[status(esa)],[f_4583_2]) ).

cnf(f_4583_4,plain,
    hAPP(c_List_Olist_Olist__case(U_19083,U_19084,U_19085,U_19086),c_List_Olist_ONil(U_19084)) = U_19085,
    inference(clausify,[status(thm)],[f_4583_3]) ).

fof(f_4584_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_4584_2,plain,
    ! [U_19089,U_19088,U_19087] : c_List_Olistset(U_19087,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_19087,tc_HOL_Obool)),U_19088),U_19089)) = c_List_Oset__Cons(U_19087,U_19088,c_List_Olistset(U_19087,U_19089)),
    inference(variable_rename,[status(thm)],[f_4584_1]) ).

fof(f_4584_3,plain,
    ! [U_19087,U_19088,U_19089] : c_List_Olistset(U_19087,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_19087,tc_HOL_Obool)),U_19088),U_19089)) = c_List_Oset__Cons(U_19087,U_19088,c_List_Olistset(U_19087,U_19089)),
    inference(definitional_conversion,[status(esa)],[f_4584_2]) ).

cnf(f_4584_4,plain,
    c_List_Olistset(U_19087,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_19087,tc_HOL_Obool)),U_19088),U_19089)) = c_List_Oset__Cons(U_19087,U_19088,c_List_Olistset(U_19087,U_19089)),
    inference(clausify,[status(thm)],[f_4584_3]) ).

fof(f_4585_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_4585_2,plain,
    ! [U_19094,U_19093,U_19092,U_19091,U_19090] : hAPP(hAPP(c_List_Ozip(U_19090,U_19091),U_19092),hAPP(hAPP(c_List_Olist_OCons(U_19091),U_19093),U_19094)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_19090,U_19091)),U_19090,c_List_Olist_ONil(tc_prod(U_19090,U_19091)),hAPP(hAPP(c_COMBC(U_19090,tc_fun(tc_List_Olist(U_19090),tc_List_Olist(tc_prod(U_19090,U_19091))),tc_fun(tc_List_Olist(U_19090),tc_List_Olist(tc_prod(U_19090,U_19091)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_19090,U_19091)),tc_List_Olist(tc_prod(U_19090,U_19091))),tc_fun(tc_fun(tc_List_Olist(U_19090),tc_List_Olist(tc_prod(U_19090,U_19091))),tc_fun(tc_List_Olist(U_19090),tc_List_Olist(tc_prod(U_19090,U_19091)))),U_19090),c_COMBB(tc_List_Olist(tc_prod(U_19090,U_19091)),tc_List_Olist(tc_prod(U_19090,U_19091)),tc_List_Olist(U_19090))),hAPP(hAPP(c_COMBB(tc_prod(U_19090,U_19091),tc_fun(tc_List_Olist(tc_prod(U_19090,U_19091)),tc_List_Olist(tc_prod(U_19090,U_19091))),U_19090),c_List_Olist_OCons(tc_prod(U_19090,U_19091))),hAPP(hAPP(c_COMBC(U_19090,U_19091,tc_prod(U_19090,U_19091)),c_Product__Type_OPair(U_19090,U_19091)),U_19093)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19090),tc_List_Olist(U_19091),tc_List_Olist(tc_prod(U_19090,U_19091))),c_List_Ozip(U_19090,U_19091)),U_19094))),U_19092),
    inference(variable_rename,[status(thm)],[f_4585_1]) ).

fof(f_4585_3,plain,
    ! [U_19090,U_19091,U_19092,U_19093,U_19094] : hAPP(hAPP(c_List_Ozip(U_19090,U_19091),U_19092),hAPP(hAPP(c_List_Olist_OCons(U_19091),U_19093),U_19094)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_19090,U_19091)),U_19090,c_List_Olist_ONil(tc_prod(U_19090,U_19091)),hAPP(hAPP(c_COMBC(U_19090,tc_fun(tc_List_Olist(U_19090),tc_List_Olist(tc_prod(U_19090,U_19091))),tc_fun(tc_List_Olist(U_19090),tc_List_Olist(tc_prod(U_19090,U_19091)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_19090,U_19091)),tc_List_Olist(tc_prod(U_19090,U_19091))),tc_fun(tc_fun(tc_List_Olist(U_19090),tc_List_Olist(tc_prod(U_19090,U_19091))),tc_fun(tc_List_Olist(U_19090),tc_List_Olist(tc_prod(U_19090,U_19091)))),U_19090),c_COMBB(tc_List_Olist(tc_prod(U_19090,U_19091)),tc_List_Olist(tc_prod(U_19090,U_19091)),tc_List_Olist(U_19090))),hAPP(hAPP(c_COMBB(tc_prod(U_19090,U_19091),tc_fun(tc_List_Olist(tc_prod(U_19090,U_19091)),tc_List_Olist(tc_prod(U_19090,U_19091))),U_19090),c_List_Olist_OCons(tc_prod(U_19090,U_19091))),hAPP(hAPP(c_COMBC(U_19090,U_19091,tc_prod(U_19090,U_19091)),c_Product__Type_OPair(U_19090,U_19091)),U_19093)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19090),tc_List_Olist(U_19091),tc_List_Olist(tc_prod(U_19090,U_19091))),c_List_Ozip(U_19090,U_19091)),U_19094))),U_19092),
    inference(definitional_conversion,[status(esa)],[f_4585_2]) ).

cnf(f_4585_4,plain,
    hAPP(hAPP(c_List_Ozip(U_19090,U_19091),U_19092),hAPP(hAPP(c_List_Olist_OCons(U_19091),U_19093),U_19094)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_19090,U_19091)),U_19090,c_List_Olist_ONil(tc_prod(U_19090,U_19091)),hAPP(hAPP(c_COMBC(U_19090,tc_fun(tc_List_Olist(U_19090),tc_List_Olist(tc_prod(U_19090,U_19091))),tc_fun(tc_List_Olist(U_19090),tc_List_Olist(tc_prod(U_19090,U_19091)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_19090,U_19091)),tc_List_Olist(tc_prod(U_19090,U_19091))),tc_fun(tc_fun(tc_List_Olist(U_19090),tc_List_Olist(tc_prod(U_19090,U_19091))),tc_fun(tc_List_Olist(U_19090),tc_List_Olist(tc_prod(U_19090,U_19091)))),U_19090),c_COMBB(tc_List_Olist(tc_prod(U_19090,U_19091)),tc_List_Olist(tc_prod(U_19090,U_19091)),tc_List_Olist(U_19090))),hAPP(hAPP(c_COMBB(tc_prod(U_19090,U_19091),tc_fun(tc_List_Olist(tc_prod(U_19090,U_19091)),tc_List_Olist(tc_prod(U_19090,U_19091))),U_19090),c_List_Olist_OCons(tc_prod(U_19090,U_19091))),hAPP(hAPP(c_COMBC(U_19090,U_19091,tc_prod(U_19090,U_19091)),c_Product__Type_OPair(U_19090,U_19091)),U_19093)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19090),tc_List_Olist(U_19091),tc_List_Olist(tc_prod(U_19090,U_19091))),c_List_Ozip(U_19090,U_19091)),U_19094))),U_19092),
    inference(clausify,[status(thm)],[f_4585_3]) ).

fof(f_4586_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_4586_2,plain,
    ! [U_19099,U_19098,U_19097] :
      ( hBOOL(hAPP(hAPP(U_19099,U_19097),U_19098))
      | ? [U_19096,U_19095] :
          ( ~ hBOOL(hAPP(hAPP(U_19099,U_19096),U_19095))
          & ( hBOOL(hAPP(hAPP(U_19099,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19096),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_19095))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_19096),U_19095)) )
          & 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_19096),U_19095))) )
      | ~ 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_19097),U_19098))) ),
    inference(variable_rename,[status(thm)],[f_4586_1]) ).

fof(f_4586_3,plain,
    ! [U_19099,U_19098,U_19097] :
      ( hBOOL(hAPP(hAPP(U_19099,U_19097),U_19098))
      | ? [U_19095] :
          ( ~ hBOOL(hAPP(hAPP(U_19099,sK474(U_19099,U_19098,U_19097)),U_19095))
          & ( hBOOL(hAPP(hAPP(U_19099,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK474(U_19099,U_19098,U_19097)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_19095))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK474(U_19099,U_19098,U_19097)),U_19095)) )
          & 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),sK474(U_19099,U_19098,U_19097)),U_19095))) )
      | ~ 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_19097),U_19098))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK474]),skolemize(U_19096,sK474(U_19099,U_19098,U_19097))],[f_4586_2]) ).

fof(f_4586_4,plain,
    ! [U_19099,U_19098,U_19097] :
      ( hBOOL(hAPP(hAPP(U_19099,U_19097),U_19098))
      | ( ~ hBOOL(hAPP(hAPP(U_19099,sK474(U_19099,U_19098,U_19097)),sK475(U_19099,U_19098,U_19097)))
        & ( hBOOL(hAPP(hAPP(U_19099,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK474(U_19099,U_19098,U_19097)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK475(U_19099,U_19098,U_19097)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK474(U_19099,U_19098,U_19097)),sK475(U_19099,U_19098,U_19097))) )
        & 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),sK474(U_19099,U_19098,U_19097)),sK475(U_19099,U_19098,U_19097)))) )
      | ~ 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_19097),U_19098))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK475]),skolemize(U_19095,sK475(U_19099,U_19098,U_19097))],[f_4586_3]) ).

fof(f_4586_5,plain,
    ( ! [U_19097,U_19098,U_19099] :
        ( ~ hBOOL(hAPP(hAPP(U_19099,sK474(U_19099,U_19098,U_19097)),sK475(U_19099,U_19098,U_19097)))
        | ~ sP1172(U_19097,U_19098,U_19099) )
    & ! [U_19097,U_19098,U_19099] :
        ( hBOOL(hAPP(hAPP(U_19099,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK474(U_19099,U_19098,U_19097)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK475(U_19099,U_19098,U_19097)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK474(U_19099,U_19098,U_19097)),sK475(U_19099,U_19098,U_19097)))
        | ~ sP1172(U_19097,U_19098,U_19099) )
    & ! [U_19097,U_19098,U_19099] :
        ( 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),sK474(U_19099,U_19098,U_19097)),sK475(U_19099,U_19098,U_19097))))
        | ~ sP1172(U_19097,U_19098,U_19099) )
    & ! [U_19097,U_19098,U_19099] :
        ( hBOOL(hAPP(hAPP(U_19099,U_19097),U_19098))
        | sP1172(U_19097,U_19098,U_19099)
        | ~ 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_19097),U_19098))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1172])],[f_4586_4]) ).

cnf(f_4586_6,plain,
    ( hBOOL(hAPP(hAPP(U_19099,U_19097),U_19098))
    | sP1172(U_19097,U_19098,U_19099)
    | ~ 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_19097),U_19098))) ),
    inference(clausify,[status(thm)],[f_4586_5]) ).

cnf(f_4586_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),sK474(U_19099,U_19098,U_19097)),sK475(U_19099,U_19098,U_19097))))
    | ~ sP1172(U_19097,U_19098,U_19099) ),
    inference(clausify,[status(thm)],[f_4586_5]) ).

cnf(f_4586_8,plain,
    ( hBOOL(hAPP(hAPP(U_19099,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK474(U_19099,U_19098,U_19097)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK475(U_19099,U_19098,U_19097)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK474(U_19099,U_19098,U_19097)),sK475(U_19099,U_19098,U_19097)))
    | ~ sP1172(U_19097,U_19098,U_19099) ),
    inference(clausify,[status(thm)],[f_4586_5]) ).

cnf(f_4586_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_19099,sK474(U_19099,U_19098,U_19097)),sK475(U_19099,U_19098,U_19097)))
    | ~ sP1172(U_19097,U_19098,U_19099) ),
    inference(clausify,[status(thm)],[f_4586_5]) ).

fof(f_4587_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_4587_2,plain,
    ! [U_19106,U_19105,U_19104,U_19103,U_19102,U_19101,U_19100] :
      ( ( c_Map_Omap__upds(U_19100,U_19102,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19100,tc_Option_Ooption(U_19102)),U_19105),U_19101),hAPP(c_Option_Ooption_OSome(U_19102),U_19106)),U_19104,U_19103) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19100,tc_Option_Ooption(U_19102)),c_Map_Omap__upds(U_19100,U_19102,U_19105,U_19104,U_19103)),U_19101),hAPP(c_Option_Ooption_OSome(U_19102),U_19106))
        | hBOOL(hAPP(hAPP(c_member(U_19100),U_19101),hAPP(c_List_Oset(U_19100),hAPP(hAPP(c_List_Otake(U_19100),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19102)),U_19103)),U_19104)))) )
      & ( c_Map_Omap__upds(U_19100,U_19102,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19100,tc_Option_Ooption(U_19102)),U_19105),U_19101),hAPP(c_Option_Ooption_OSome(U_19102),U_19106)),U_19104,U_19103) = c_Map_Omap__upds(U_19100,U_19102,U_19105,U_19104,U_19103)
        | ~ hBOOL(hAPP(hAPP(c_member(U_19100),U_19101),hAPP(c_List_Oset(U_19100),hAPP(hAPP(c_List_Otake(U_19100),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19102)),U_19103)),U_19104)))) ) ),
    inference(variable_rename,[status(thm)],[f_4587_1]) ).

fof(f_4587_3,plain,
    ( ! [U_19120,U_19118,U_19116,U_19114,U_19112,U_19110,U_19108] :
        ( c_Map_Omap__upds(U_19108,U_19112,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19108,tc_Option_Ooption(U_19112)),U_19118),U_19110),hAPP(c_Option_Ooption_OSome(U_19112),U_19120)),U_19116,U_19114) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19108,tc_Option_Ooption(U_19112)),c_Map_Omap__upds(U_19108,U_19112,U_19118,U_19116,U_19114)),U_19110),hAPP(c_Option_Ooption_OSome(U_19112),U_19120))
        | hBOOL(hAPP(hAPP(c_member(U_19108),U_19110),hAPP(c_List_Oset(U_19108),hAPP(hAPP(c_List_Otake(U_19108),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19112)),U_19114)),U_19116)))) )
    & ! [U_19119,U_19117,U_19115,U_19113,U_19111,U_19109,U_19107] :
        ( c_Map_Omap__upds(U_19107,U_19111,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19107,tc_Option_Ooption(U_19111)),U_19117),U_19109),hAPP(c_Option_Ooption_OSome(U_19111),U_19119)),U_19115,U_19113) = c_Map_Omap__upds(U_19107,U_19111,U_19117,U_19115,U_19113)
        | ~ hBOOL(hAPP(hAPP(c_member(U_19107),U_19109),hAPP(c_List_Oset(U_19107),hAPP(hAPP(c_List_Otake(U_19107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19111)),U_19113)),U_19115)))) ) ),
    inference(miniscope,[status(thm)],[f_4587_2]) ).

fof(f_4587_4,plain,
    ( ! [U_19108,U_19110,U_19112,U_19114,U_19116,U_19118,U_19120] :
        ( c_Map_Omap__upds(U_19108,U_19112,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19108,tc_Option_Ooption(U_19112)),U_19118),U_19110),hAPP(c_Option_Ooption_OSome(U_19112),U_19120)),U_19116,U_19114) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19108,tc_Option_Ooption(U_19112)),c_Map_Omap__upds(U_19108,U_19112,U_19118,U_19116,U_19114)),U_19110),hAPP(c_Option_Ooption_OSome(U_19112),U_19120))
        | hBOOL(hAPP(hAPP(c_member(U_19108),U_19110),hAPP(c_List_Oset(U_19108),hAPP(hAPP(c_List_Otake(U_19108),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19112)),U_19114)),U_19116)))) )
    & ! [U_19111,U_19113,U_19109,U_19107,U_19115,U_19117,U_19119] :
        ( c_Map_Omap__upds(U_19107,U_19111,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19107,tc_Option_Ooption(U_19111)),U_19117),U_19109),hAPP(c_Option_Ooption_OSome(U_19111),U_19119)),U_19115,U_19113) = c_Map_Omap__upds(U_19107,U_19111,U_19117,U_19115,U_19113)
        | ~ hBOOL(hAPP(hAPP(c_member(U_19107),U_19109),hAPP(c_List_Oset(U_19107),hAPP(hAPP(c_List_Otake(U_19107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19111)),U_19113)),U_19115)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4587_3]) ).

cnf(f_4587_5,plain,
    ( c_Map_Omap__upds(U_19107,U_19111,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19107,tc_Option_Ooption(U_19111)),U_19117),U_19109),hAPP(c_Option_Ooption_OSome(U_19111),U_19119)),U_19115,U_19113) = c_Map_Omap__upds(U_19107,U_19111,U_19117,U_19115,U_19113)
    | ~ hBOOL(hAPP(hAPP(c_member(U_19107),U_19109),hAPP(c_List_Oset(U_19107),hAPP(hAPP(c_List_Otake(U_19107),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19111)),U_19113)),U_19115)))) ),
    inference(clausify,[status(thm)],[f_4587_4]) ).

cnf(f_4587_6,plain,
    ( c_Map_Omap__upds(U_19108,U_19112,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19108,tc_Option_Ooption(U_19112)),U_19118),U_19110),hAPP(c_Option_Ooption_OSome(U_19112),U_19120)),U_19116,U_19114) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19108,tc_Option_Ooption(U_19112)),c_Map_Omap__upds(U_19108,U_19112,U_19118,U_19116,U_19114)),U_19110),hAPP(c_Option_Ooption_OSome(U_19112),U_19120))
    | hBOOL(hAPP(hAPP(c_member(U_19108),U_19110),hAPP(c_List_Oset(U_19108),hAPP(hAPP(c_List_Otake(U_19108),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19112)),U_19114)),U_19116)))) ),
    inference(clausify,[status(thm)],[f_4587_4]) ).

fof(f_4588_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_4588_2,plain,
    ! [U_19124,U_19123,U_19122,U_19121] : c_Map_Omap__upds(U_19121,U_19122,U_19123,c_List_Olist_ONil(U_19121),U_19124) = U_19123,
    inference(variable_rename,[status(thm)],[f_4588_1]) ).

fof(f_4588_3,plain,
    ! [U_19122,U_19124,U_19123,U_19121] : c_Map_Omap__upds(U_19121,U_19122,U_19123,c_List_Olist_ONil(U_19121),U_19124) = U_19123,
    inference(definitional_conversion,[status(esa)],[f_4588_2]) ).

cnf(f_4588_4,plain,
    c_Map_Omap__upds(U_19121,U_19122,U_19123,c_List_Olist_ONil(U_19121),U_19124) = U_19123,
    inference(clausify,[status(thm)],[f_4588_3]) ).

fof(f_4589_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_4589_2,plain,
    ! [U_19128,U_19127,U_19126,U_19125] : c_Map_Omap__upds(U_19125,U_19126,U_19127,U_19128,c_List_Olist_ONil(U_19126)) = U_19127,
    inference(variable_rename,[status(thm)],[f_4589_1]) ).

fof(f_4589_3,plain,
    ! [U_19126,U_19127,U_19125,U_19128] : c_Map_Omap__upds(U_19125,U_19126,U_19127,U_19128,c_List_Olist_ONil(U_19126)) = U_19127,
    inference(definitional_conversion,[status(esa)],[f_4589_2]) ).

cnf(f_4589_4,plain,
    c_Map_Omap__upds(U_19125,U_19126,U_19127,U_19128,c_List_Olist_ONil(U_19126)) = U_19127,
    inference(clausify,[status(thm)],[f_4589_3]) ).

fof(f_4590_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_4590_2,plain,
    ! [U_19134,U_19133,U_19132,U_19131,U_19130,U_19129] :
      ( hAPP(c_Map_Omap__upds(U_19129,U_19132,U_19133,U_19131,U_19134),U_19130) = hAPP(U_19133,U_19130)
      | hBOOL(hAPP(hAPP(c_member(U_19129),U_19130),hAPP(c_List_Oset(U_19129),U_19131))) ),
    inference(variable_rename,[status(thm)],[f_4590_1]) ).

fof(f_4590_3,plain,
    ! [U_19129,U_19130,U_19131,U_19132,U_19133,U_19134] :
      ( hAPP(c_Map_Omap__upds(U_19129,U_19132,U_19133,U_19131,U_19134),U_19130) = hAPP(U_19133,U_19130)
      | hBOOL(hAPP(hAPP(c_member(U_19129),U_19130),hAPP(c_List_Oset(U_19129),U_19131))) ),
    inference(definitional_conversion,[status(esa)],[f_4590_2]) ).

cnf(f_4590_4,plain,
    ( hAPP(c_Map_Omap__upds(U_19129,U_19132,U_19133,U_19131,U_19134),U_19130) = hAPP(U_19133,U_19130)
    | hBOOL(hAPP(hAPP(c_member(U_19129),U_19130),hAPP(c_List_Oset(U_19129),U_19131))) ),
    inference(clausify,[status(thm)],[f_4590_3]) ).

fof(f_4591_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_4591_2,plain,
    ! [U_19140,U_19139,U_19138,U_19137,U_19136,U_19135] : c_Map_Omap__add(U_19135,U_19136,U_19137,c_Map_Omap__upds(U_19135,U_19136,U_19138,U_19139,U_19140)) = c_Map_Omap__upds(U_19135,U_19136,c_Map_Omap__add(U_19135,U_19136,U_19137,U_19138),U_19139,U_19140),
    inference(variable_rename,[status(thm)],[f_4591_1]) ).

fof(f_4591_3,plain,
    ! [U_19136,U_19135,U_19137,U_19138,U_19139,U_19140] : c_Map_Omap__add(U_19135,U_19136,U_19137,c_Map_Omap__upds(U_19135,U_19136,U_19138,U_19139,U_19140)) = c_Map_Omap__upds(U_19135,U_19136,c_Map_Omap__add(U_19135,U_19136,U_19137,U_19138),U_19139,U_19140),
    inference(definitional_conversion,[status(esa)],[f_4591_2]) ).

cnf(f_4591_4,plain,
    c_Map_Omap__add(U_19135,U_19136,U_19137,c_Map_Omap__upds(U_19135,U_19136,U_19138,U_19139,U_19140)) = c_Map_Omap__upds(U_19135,U_19136,c_Map_Omap__add(U_19135,U_19136,U_19137,U_19138),U_19139,U_19140),
    inference(clausify,[status(thm)],[f_4591_3]) ).

fof(f_4592_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_4592_2,plain,
    ! [U_19147,U_19146,U_19145,U_19144,U_19143,U_19142,U_19141] : c_Map_Omap__upds(U_19141,U_19142,U_19143,hAPP(hAPP(c_List_Olist_OCons(U_19141),U_19144),U_19145),hAPP(hAPP(c_List_Olist_OCons(U_19142),U_19146),U_19147)) = c_Map_Omap__upds(U_19141,U_19142,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19141,tc_Option_Ooption(U_19142)),U_19143),U_19144),hAPP(c_Option_Ooption_OSome(U_19142),U_19146)),U_19145,U_19147),
    inference(variable_rename,[status(thm)],[f_4592_1]) ).

fof(f_4592_3,plain,
    ! [U_19141,U_19142,U_19143,U_19144,U_19145,U_19146,U_19147] : c_Map_Omap__upds(U_19141,U_19142,U_19143,hAPP(hAPP(c_List_Olist_OCons(U_19141),U_19144),U_19145),hAPP(hAPP(c_List_Olist_OCons(U_19142),U_19146),U_19147)) = c_Map_Omap__upds(U_19141,U_19142,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19141,tc_Option_Ooption(U_19142)),U_19143),U_19144),hAPP(c_Option_Ooption_OSome(U_19142),U_19146)),U_19145,U_19147),
    inference(definitional_conversion,[status(esa)],[f_4592_2]) ).

cnf(f_4592_4,plain,
    c_Map_Omap__upds(U_19141,U_19142,U_19143,hAPP(hAPP(c_List_Olist_OCons(U_19141),U_19144),U_19145),hAPP(hAPP(c_List_Olist_OCons(U_19142),U_19146),U_19147)) = c_Map_Omap__upds(U_19141,U_19142,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19141,tc_Option_Ooption(U_19142)),U_19143),U_19144),hAPP(c_Option_Ooption_OSome(U_19142),U_19146)),U_19145,U_19147),
    inference(clausify,[status(thm)],[f_4592_3]) ).

fof(f_4593_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_4593_2,plain,
    ! [U_19154,U_19153,U_19152,U_19151,U_19150,U_19149,U_19148] :
      ( c_Map_Omap__upds(U_19148,U_19151,U_19153,U_19149,hAPP(hAPP(c_List_Olist__update(U_19151,U_19152),U_19150),U_19154)) = c_Map_Omap__upds(U_19148,U_19151,U_19153,U_19149,U_19152)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19150),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19151)),U_19152)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19148)),U_19149)),U_19150)) ),
    inference(variable_rename,[status(thm)],[f_4593_1]) ).

fof(f_4593_3,plain,
    ! [U_19148,U_19149,U_19150,U_19151,U_19152,U_19153,U_19154] :
      ( c_Map_Omap__upds(U_19148,U_19151,U_19153,U_19149,hAPP(hAPP(c_List_Olist__update(U_19151,U_19152),U_19150),U_19154)) = c_Map_Omap__upds(U_19148,U_19151,U_19153,U_19149,U_19152)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19150),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19151)),U_19152)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19148)),U_19149)),U_19150)) ),
    inference(definitional_conversion,[status(esa)],[f_4593_2]) ).

cnf(f_4593_4,plain,
    ( c_Map_Omap__upds(U_19148,U_19151,U_19153,U_19149,hAPP(hAPP(c_List_Olist__update(U_19151,U_19152),U_19150),U_19154)) = c_Map_Omap__upds(U_19148,U_19151,U_19153,U_19149,U_19152)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19150),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19151)),U_19152)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19148)),U_19149)),U_19150)) ),
    inference(clausify,[status(thm)],[f_4593_3]) ).

fof(f_4594_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_4594_2,plain,
    ! [U_19161,U_19160,U_19159,U_19158,U_19157,U_19156,U_19155] :
      ( c_Map_Omap__upds(U_19155,U_19158,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19155,tc_Option_Ooption(U_19158)),U_19159),U_19156),hAPP(c_Option_Ooption_OSome(U_19158),U_19160)),U_19157,U_19161) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19155,tc_Option_Ooption(U_19158)),c_Map_Omap__upds(U_19155,U_19158,U_19159,U_19157,U_19161)),U_19156),hAPP(c_Option_Ooption_OSome(U_19158),U_19160))
      | hBOOL(hAPP(hAPP(c_member(U_19155),U_19156),hAPP(c_List_Oset(U_19155),U_19157))) ),
    inference(variable_rename,[status(thm)],[f_4594_1]) ).

fof(f_4594_3,plain,
    ! [U_19155,U_19156,U_19157,U_19158,U_19159,U_19160,U_19161] :
      ( c_Map_Omap__upds(U_19155,U_19158,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19155,tc_Option_Ooption(U_19158)),U_19159),U_19156),hAPP(c_Option_Ooption_OSome(U_19158),U_19160)),U_19157,U_19161) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19155,tc_Option_Ooption(U_19158)),c_Map_Omap__upds(U_19155,U_19158,U_19159,U_19157,U_19161)),U_19156),hAPP(c_Option_Ooption_OSome(U_19158),U_19160))
      | hBOOL(hAPP(hAPP(c_member(U_19155),U_19156),hAPP(c_List_Oset(U_19155),U_19157))) ),
    inference(definitional_conversion,[status(esa)],[f_4594_2]) ).

cnf(f_4594_4,plain,
    ( c_Map_Omap__upds(U_19155,U_19158,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19155,tc_Option_Ooption(U_19158)),U_19159),U_19156),hAPP(c_Option_Ooption_OSome(U_19158),U_19160)),U_19157,U_19161) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19155,tc_Option_Ooption(U_19158)),c_Map_Omap__upds(U_19155,U_19158,U_19159,U_19157,U_19161)),U_19156),hAPP(c_Option_Ooption_OSome(U_19158),U_19160))
    | hBOOL(hAPP(hAPP(c_member(U_19155),U_19156),hAPP(c_List_Oset(U_19155),U_19157))) ),
    inference(clausify,[status(thm)],[f_4594_3]) ).

fof(f_4595_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_4595_2,plain,
    ! [U_19167,U_19166,U_19165,U_19164,U_19163,U_19162] :
      ( c_Map_Orestrict__map(U_19162,U_19164,c_Map_Omap__upds(U_19162,U_19164,U_19167,U_19163,U_19165),U_19166) = c_Map_Omap__upds(U_19162,U_19164,c_Map_Orestrict__map(U_19162,U_19164,U_19167,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_19162,tc_HOL_Obool)),U_19166),hAPP(c_List_Oset(U_19162),U_19163))),U_19163,U_19165)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19162,tc_HOL_Obool)),hAPP(c_List_Oset(U_19162),U_19163)),U_19166))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19162)),U_19163) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19164)),U_19165) ),
    inference(variable_rename,[status(thm)],[f_4595_1]) ).

fof(f_4595_3,plain,
    ! [U_19162,U_19163,U_19164,U_19165,U_19166,U_19167] :
      ( c_Map_Orestrict__map(U_19162,U_19164,c_Map_Omap__upds(U_19162,U_19164,U_19167,U_19163,U_19165),U_19166) = c_Map_Omap__upds(U_19162,U_19164,c_Map_Orestrict__map(U_19162,U_19164,U_19167,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_19162,tc_HOL_Obool)),U_19166),hAPP(c_List_Oset(U_19162),U_19163))),U_19163,U_19165)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19162,tc_HOL_Obool)),hAPP(c_List_Oset(U_19162),U_19163)),U_19166))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19162)),U_19163) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19164)),U_19165) ),
    inference(definitional_conversion,[status(esa)],[f_4595_2]) ).

cnf(f_4595_4,plain,
    ( c_Map_Orestrict__map(U_19162,U_19164,c_Map_Omap__upds(U_19162,U_19164,U_19167,U_19163,U_19165),U_19166) = c_Map_Omap__upds(U_19162,U_19164,c_Map_Orestrict__map(U_19162,U_19164,U_19167,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_19162,tc_HOL_Obool)),U_19166),hAPP(c_List_Oset(U_19162),U_19163))),U_19163,U_19165)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19162,tc_HOL_Obool)),hAPP(c_List_Oset(U_19162),U_19163)),U_19166))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19162)),U_19163) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19164)),U_19165) ),
    inference(clausify,[status(thm)],[f_4595_3]) ).

fof(f_4596_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_4596_2,plain,
    ! [U_19172,U_19171,U_19170,U_19169,U_19168] : c_Map_Odom(U_19168,U_19169,c_Map_Omap__upds(U_19168,U_19169,U_19170,U_19171,U_19172)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19168,tc_HOL_Obool)),hAPP(c_List_Oset(U_19168),hAPP(hAPP(c_List_Otake(U_19168),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19169)),U_19172)),U_19171))),c_Map_Odom(U_19168,U_19169,U_19170)),
    inference(variable_rename,[status(thm)],[f_4596_1]) ).

fof(f_4596_3,plain,
    ! [U_19168,U_19169,U_19170,U_19171,U_19172] : c_Map_Odom(U_19168,U_19169,c_Map_Omap__upds(U_19168,U_19169,U_19170,U_19171,U_19172)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19168,tc_HOL_Obool)),hAPP(c_List_Oset(U_19168),hAPP(hAPP(c_List_Otake(U_19168),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19169)),U_19172)),U_19171))),c_Map_Odom(U_19168,U_19169,U_19170)),
    inference(definitional_conversion,[status(esa)],[f_4596_2]) ).

cnf(f_4596_4,plain,
    c_Map_Odom(U_19168,U_19169,c_Map_Omap__upds(U_19168,U_19169,U_19170,U_19171,U_19172)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19168,tc_HOL_Obool)),hAPP(c_List_Oset(U_19168),hAPP(hAPP(c_List_Otake(U_19168),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19169)),U_19172)),U_19171))),c_Map_Odom(U_19168,U_19169,U_19170)),
    inference(clausify,[status(thm)],[f_4596_3]) ).

fof(f_4597_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_4597_2,plain,
    ! [U_19178,U_19177,U_19176,U_19175,U_19174,U_19173] :
      ( c_Map_Omap__upds(U_19173,U_19175,U_19177,hAPP(hAPP(c_List_Oappend(U_19173),U_19174),hAPP(hAPP(c_List_Olist_OCons(U_19173),U_19178),c_List_Olist_ONil(U_19173))),U_19176) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19173,tc_Option_Ooption(U_19175)),c_Map_Omap__upds(U_19173,U_19175,U_19177,U_19174,U_19176)),U_19178),hAPP(c_Option_Ooption_OSome(U_19175),hAPP(hAPP(c_List_Onth(U_19175),U_19176),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19173)),U_19174))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19173)),U_19174)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19175)),U_19176))) ),
    inference(variable_rename,[status(thm)],[f_4597_1]) ).

fof(f_4597_3,plain,
    ! [U_19173,U_19174,U_19175,U_19176,U_19177,U_19178] :
      ( c_Map_Omap__upds(U_19173,U_19175,U_19177,hAPP(hAPP(c_List_Oappend(U_19173),U_19174),hAPP(hAPP(c_List_Olist_OCons(U_19173),U_19178),c_List_Olist_ONil(U_19173))),U_19176) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19173,tc_Option_Ooption(U_19175)),c_Map_Omap__upds(U_19173,U_19175,U_19177,U_19174,U_19176)),U_19178),hAPP(c_Option_Ooption_OSome(U_19175),hAPP(hAPP(c_List_Onth(U_19175),U_19176),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19173)),U_19174))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19173)),U_19174)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19175)),U_19176))) ),
    inference(definitional_conversion,[status(esa)],[f_4597_2]) ).

cnf(f_4597_4,plain,
    ( c_Map_Omap__upds(U_19173,U_19175,U_19177,hAPP(hAPP(c_List_Oappend(U_19173),U_19174),hAPP(hAPP(c_List_Olist_OCons(U_19173),U_19178),c_List_Olist_ONil(U_19173))),U_19176) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_19173,tc_Option_Ooption(U_19175)),c_Map_Omap__upds(U_19173,U_19175,U_19177,U_19174,U_19176)),U_19178),hAPP(c_Option_Ooption_OSome(U_19175),hAPP(hAPP(c_List_Onth(U_19175),U_19176),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19173)),U_19174))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19173)),U_19174)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19175)),U_19176))) ),
    inference(clausify,[status(thm)],[f_4597_3]) ).

fof(f_4598_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_4598_2,plain,
    ! [U_19182,U_19181,U_19180,U_19179] : c_List_Osublist(U_19179,hAPP(hAPP(c_List_Olist_OCons(U_19179),U_19180),U_19181),U_19182) = hAPP(hAPP(c_List_Oappend(U_19179),hAPP(hAPP(hAPP(c_If(tc_List_Olist(U_19179)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19182)),hAPP(hAPP(c_List_Olist_OCons(U_19179),U_19180),c_List_Olist_ONil(U_19179))),c_List_Olist_ONil(U_19179))),c_List_Osublist(U_19179,U_19181,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_19182)))),
    inference(variable_rename,[status(thm)],[f_4598_1]) ).

fof(f_4598_3,plain,
    ! [U_19179,U_19180,U_19181,U_19182] : c_List_Osublist(U_19179,hAPP(hAPP(c_List_Olist_OCons(U_19179),U_19180),U_19181),U_19182) = hAPP(hAPP(c_List_Oappend(U_19179),hAPP(hAPP(hAPP(c_If(tc_List_Olist(U_19179)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19182)),hAPP(hAPP(c_List_Olist_OCons(U_19179),U_19180),c_List_Olist_ONil(U_19179))),c_List_Olist_ONil(U_19179))),c_List_Osublist(U_19179,U_19181,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_19182)))),
    inference(definitional_conversion,[status(esa)],[f_4598_2]) ).

cnf(f_4598_4,plain,
    c_List_Osublist(U_19179,hAPP(hAPP(c_List_Olist_OCons(U_19179),U_19180),U_19181),U_19182) = hAPP(hAPP(c_List_Oappend(U_19179),hAPP(hAPP(hAPP(c_If(tc_List_Olist(U_19179)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19182)),hAPP(hAPP(c_List_Olist_OCons(U_19179),U_19180),c_List_Olist_ONil(U_19179))),c_List_Olist_ONil(U_19179))),c_List_Osublist(U_19179,U_19181,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_19182)))),
    inference(clausify,[status(thm)],[f_4598_3]) ).

fof(f_4599_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_4599_2,plain,
    ! [U_19187,U_19186,U_19185,U_19184,U_19183] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19183),U_19184),hAPP(hAPP(c_List_Olist_OCons(U_19183),U_19185),c_List_Olist_ONil(U_19183))) = hAPP(hAPP(c_List_Oappend(U_19183),U_19186),hAPP(hAPP(c_List_Olist_OCons(U_19183),U_19187),c_List_Olist_ONil(U_19183)))
        | U_19185 != U_19187
        | U_19184 != U_19186 )
      & ( ( U_19185 = U_19187
          & U_19184 = U_19186 )
        | hAPP(hAPP(c_List_Oappend(U_19183),U_19184),hAPP(hAPP(c_List_Olist_OCons(U_19183),U_19185),c_List_Olist_ONil(U_19183))) != hAPP(hAPP(c_List_Oappend(U_19183),U_19186),hAPP(hAPP(c_List_Olist_OCons(U_19183),U_19187),c_List_Olist_ONil(U_19183))) ) ),
    inference(variable_rename,[status(thm)],[f_4599_1]) ).

fof(f_4599_3,plain,
    ( ! [U_19197,U_19195,U_19193,U_19191] :
        ( ! [U_19189] : hAPP(hAPP(c_List_Oappend(U_19189),U_19191),hAPP(hAPP(c_List_Olist_OCons(U_19189),U_19193),c_List_Olist_ONil(U_19189))) = hAPP(hAPP(c_List_Oappend(U_19189),U_19195),hAPP(hAPP(c_List_Olist_OCons(U_19189),U_19197),c_List_Olist_ONil(U_19189)))
        | U_19193 != U_19197
        | U_19191 != U_19195 )
    & ! [U_19196,U_19194,U_19192,U_19190] :
        ( ! [U_19188] : hAPP(hAPP(c_List_Oappend(U_19188),U_19190),hAPP(hAPP(c_List_Olist_OCons(U_19188),U_19192),c_List_Olist_ONil(U_19188))) != hAPP(hAPP(c_List_Oappend(U_19188),U_19194),hAPP(hAPP(c_List_Olist_OCons(U_19188),U_19196),c_List_Olist_ONil(U_19188)))
        | ( U_19192 = U_19196
          & U_19190 = U_19194 ) ) ),
    inference(miniscope,[status(thm)],[f_4599_2]) ).

fof(f_4599_4,plain,
    ( ! [U_19192,U_19196,U_19190,U_19194] :
        ( U_19192 = U_19196
        | ~ sP1173(U_19192,U_19196,U_19190,U_19194) )
    & ! [U_19192,U_19196,U_19190,U_19194] :
        ( U_19190 = U_19194
        | ~ sP1173(U_19192,U_19196,U_19190,U_19194) )
    & ! [U_19195,U_19191,U_19193,U_19189,U_19197] :
        ( hAPP(hAPP(c_List_Oappend(U_19189),U_19191),hAPP(hAPP(c_List_Olist_OCons(U_19189),U_19193),c_List_Olist_ONil(U_19189))) = hAPP(hAPP(c_List_Oappend(U_19189),U_19195),hAPP(hAPP(c_List_Olist_OCons(U_19189),U_19197),c_List_Olist_ONil(U_19189)))
        | U_19193 != U_19197
        | U_19191 != U_19195 )
    & ! [U_19192,U_19196,U_19190,U_19188,U_19194] :
        ( hAPP(hAPP(c_List_Oappend(U_19188),U_19190),hAPP(hAPP(c_List_Olist_OCons(U_19188),U_19192),c_List_Olist_ONil(U_19188))) != hAPP(hAPP(c_List_Oappend(U_19188),U_19194),hAPP(hAPP(c_List_Olist_OCons(U_19188),U_19196),c_List_Olist_ONil(U_19188)))
        | sP1173(U_19192,U_19196,U_19190,U_19194) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1173])],[f_4599_3]) ).

cnf(f_4599_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19188),U_19190),hAPP(hAPP(c_List_Olist_OCons(U_19188),U_19192),c_List_Olist_ONil(U_19188))) != hAPP(hAPP(c_List_Oappend(U_19188),U_19194),hAPP(hAPP(c_List_Olist_OCons(U_19188),U_19196),c_List_Olist_ONil(U_19188)))
    | sP1173(U_19192,U_19196,U_19190,U_19194) ),
    inference(clausify,[status(thm)],[f_4599_4]) ).

cnf(f_4599_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19189),U_19191),hAPP(hAPP(c_List_Olist_OCons(U_19189),U_19193),c_List_Olist_ONil(U_19189))) = hAPP(hAPP(c_List_Oappend(U_19189),U_19195),hAPP(hAPP(c_List_Olist_OCons(U_19189),U_19197),c_List_Olist_ONil(U_19189)))
    | U_19193 != U_19197
    | U_19191 != U_19195 ),
    inference(clausify,[status(thm)],[f_4599_4]) ).

cnf(f_4599_7,plain,
    ( U_19190 = U_19194
    | ~ sP1173(U_19192,U_19196,U_19190,U_19194) ),
    inference(clausify,[status(thm)],[f_4599_4]) ).

cnf(f_4599_8,plain,
    ( U_19192 = U_19196
    | ~ sP1173(U_19192,U_19196,U_19190,U_19194) ),
    inference(clausify,[status(thm)],[f_4599_4]) ).

fof(f_4600_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_4600_2,plain,
    ! [U_19204,U_19203,U_19202,U_19201,U_19200] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_19200),U_19201),U_19202) = hAPP(hAPP(c_List_Oappend(U_19200),U_19203),U_19204)
        | ( ! [U_19199] :
              ( U_19202 != hAPP(hAPP(c_List_Oappend(U_19200),U_19199),U_19204)
              | hAPP(hAPP(c_List_Olist_OCons(U_19200),U_19201),U_19199) != U_19203 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_19200),U_19201),U_19202) != U_19204
            | U_19203 != c_List_Olist_ONil(U_19200) ) ) )
      & ( ? [U_19198] :
            ( U_19202 = hAPP(hAPP(c_List_Oappend(U_19200),U_19198),U_19204)
            & hAPP(hAPP(c_List_Olist_OCons(U_19200),U_19201),U_19198) = U_19203 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_19200),U_19201),U_19202) = U_19204
          & U_19203 = c_List_Olist_ONil(U_19200) )
        | hAPP(hAPP(c_List_Olist_OCons(U_19200),U_19201),U_19202) != hAPP(hAPP(c_List_Oappend(U_19200),U_19203),U_19204) ) ),
    inference(variable_rename,[status(thm)],[f_4600_1]) ).

fof(f_4600_3,plain,
    ( ! [U_19214,U_19212,U_19210,U_19208,U_19206] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_19206),U_19208),U_19210) = hAPP(hAPP(c_List_Oappend(U_19206),U_19212),U_19214)
        | ( ! [U_19199] :
              ( U_19210 != hAPP(hAPP(c_List_Oappend(U_19206),U_19199),U_19214)
              | hAPP(hAPP(c_List_Olist_OCons(U_19206),U_19208),U_19199) != U_19212 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_19206),U_19208),U_19210) != U_19214
            | U_19212 != c_List_Olist_ONil(U_19206) ) ) )
    & ! [U_19213,U_19211,U_19209,U_19207,U_19205] :
        ( ? [U_19198] :
            ( U_19209 = hAPP(hAPP(c_List_Oappend(U_19205),U_19198),U_19213)
            & hAPP(hAPP(c_List_Olist_OCons(U_19205),U_19207),U_19198) = U_19211 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_19205),U_19207),U_19209) = U_19213
          & U_19211 = c_List_Olist_ONil(U_19205) )
        | hAPP(hAPP(c_List_Olist_OCons(U_19205),U_19207),U_19209) != hAPP(hAPP(c_List_Oappend(U_19205),U_19211),U_19213) ) ),
    inference(miniscope,[status(thm)],[f_4600_2]) ).

fof(f_4600_4,plain,
    ( ! [U_19214,U_19212,U_19210,U_19208,U_19206] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_19206),U_19208),U_19210) = hAPP(hAPP(c_List_Oappend(U_19206),U_19212),U_19214)
        | ( ! [U_19199] :
              ( U_19210 != hAPP(hAPP(c_List_Oappend(U_19206),U_19199),U_19214)
              | hAPP(hAPP(c_List_Olist_OCons(U_19206),U_19208),U_19199) != U_19212 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_19206),U_19208),U_19210) != U_19214
            | U_19212 != c_List_Olist_ONil(U_19206) ) ) )
    & ! [U_19213,U_19211,U_19209,U_19207,U_19205] :
        ( ( U_19209 = hAPP(hAPP(c_List_Oappend(U_19205),sK476(U_19213,U_19211,U_19209,U_19207,U_19205)),U_19213)
          & hAPP(hAPP(c_List_Olist_OCons(U_19205),U_19207),sK476(U_19213,U_19211,U_19209,U_19207,U_19205)) = U_19211 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_19205),U_19207),U_19209) = U_19213
          & U_19211 = c_List_Olist_ONil(U_19205) )
        | hAPP(hAPP(c_List_Olist_OCons(U_19205),U_19207),U_19209) != hAPP(hAPP(c_List_Oappend(U_19205),U_19211),U_19213) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK476]),skolemize(U_19198,sK476(U_19213,U_19211,U_19209,U_19207,U_19205))],[f_4600_3]) ).

fof(f_4600_5,plain,
    ( ! [U_19199,U_19206,U_19212,U_19208,U_19214,U_19210] :
        ( U_19210 != hAPP(hAPP(c_List_Oappend(U_19206),U_19199),U_19214)
        | hAPP(hAPP(c_List_Olist_OCons(U_19206),U_19208),U_19199) != U_19212
        | ~ sP1176(U_19199,U_19206,U_19212,U_19208,U_19214,U_19210) )
    & ! [U_19199,U_19206,U_19212,U_19208,U_19214,U_19210] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_19206),U_19208),U_19210) != U_19214
        | U_19212 != c_List_Olist_ONil(U_19206)
        | ~ sP1176(U_19199,U_19206,U_19212,U_19208,U_19214,U_19210) )
    & ! [U_19207,U_19205,U_19209,U_19211,U_19213] :
        ( U_19209 = hAPP(hAPP(c_List_Oappend(U_19205),sK476(U_19213,U_19211,U_19209,U_19207,U_19205)),U_19213)
        | ~ sP1175(U_19207,U_19205,U_19209,U_19211,U_19213) )
    & ! [U_19207,U_19205,U_19209,U_19211,U_19213] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_19205),U_19207),sK476(U_19213,U_19211,U_19209,U_19207,U_19205)) = U_19211
        | ~ sP1175(U_19207,U_19205,U_19209,U_19211,U_19213) )
    & ! [U_19207,U_19205,U_19209,U_19211,U_19213] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_19205),U_19207),U_19209) = U_19213
        | ~ sP1174(U_19207,U_19205,U_19209,U_19211,U_19213) )
    & ! [U_19207,U_19205,U_19209,U_19211,U_19213] :
        ( U_19211 = c_List_Olist_ONil(U_19205)
        | ~ sP1174(U_19207,U_19205,U_19209,U_19211,U_19213) )
    & ! [U_19199,U_19206,U_19212,U_19208,U_19214,U_19210] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_19206),U_19208),U_19210) = hAPP(hAPP(c_List_Oappend(U_19206),U_19212),U_19214)
        | sP1176(U_19199,U_19206,U_19212,U_19208,U_19214,U_19210) )
    & ! [U_19207,U_19205,U_19209,U_19211,U_19213] :
        ( sP1175(U_19207,U_19205,U_19209,U_19211,U_19213)
        | sP1174(U_19207,U_19205,U_19209,U_19211,U_19213)
        | hAPP(hAPP(c_List_Olist_OCons(U_19205),U_19207),U_19209) != hAPP(hAPP(c_List_Oappend(U_19205),U_19211),U_19213) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1174,sP1175,sP1176])],[f_4600_4]) ).

cnf(f_4600_6,plain,
    ( sP1175(U_19207,U_19205,U_19209,U_19211,U_19213)
    | sP1174(U_19207,U_19205,U_19209,U_19211,U_19213)
    | hAPP(hAPP(c_List_Olist_OCons(U_19205),U_19207),U_19209) != hAPP(hAPP(c_List_Oappend(U_19205),U_19211),U_19213) ),
    inference(clausify,[status(thm)],[f_4600_5]) ).

cnf(f_4600_7,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_19206),U_19208),U_19210) = hAPP(hAPP(c_List_Oappend(U_19206),U_19212),U_19214)
    | sP1176(U_19199,U_19206,U_19212,U_19208,U_19214,U_19210) ),
    inference(clausify,[status(thm)],[f_4600_5]) ).

cnf(f_4600_8,plain,
    ( U_19211 = c_List_Olist_ONil(U_19205)
    | ~ sP1174(U_19207,U_19205,U_19209,U_19211,U_19213) ),
    inference(clausify,[status(thm)],[f_4600_5]) ).

cnf(f_4600_9,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_19205),U_19207),U_19209) = U_19213
    | ~ sP1174(U_19207,U_19205,U_19209,U_19211,U_19213) ),
    inference(clausify,[status(thm)],[f_4600_5]) ).

cnf(f_4600_10,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_19205),U_19207),sK476(U_19213,U_19211,U_19209,U_19207,U_19205)) = U_19211
    | ~ sP1175(U_19207,U_19205,U_19209,U_19211,U_19213) ),
    inference(clausify,[status(thm)],[f_4600_5]) ).

cnf(f_4600_11,plain,
    ( U_19209 = hAPP(hAPP(c_List_Oappend(U_19205),sK476(U_19213,U_19211,U_19209,U_19207,U_19205)),U_19213)
    | ~ sP1175(U_19207,U_19205,U_19209,U_19211,U_19213) ),
    inference(clausify,[status(thm)],[f_4600_5]) ).

cnf(f_4600_12,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_19206),U_19208),U_19210) != U_19214
    | U_19212 != c_List_Olist_ONil(U_19206)
    | ~ sP1176(U_19199,U_19206,U_19212,U_19208,U_19214,U_19210) ),
    inference(clausify,[status(thm)],[f_4600_5]) ).

cnf(f_4600_13,plain,
    ( U_19210 != hAPP(hAPP(c_List_Oappend(U_19206),U_19199),U_19214)
    | hAPP(hAPP(c_List_Olist_OCons(U_19206),U_19208),U_19199) != U_19212
    | ~ sP1176(U_19199,U_19206,U_19212,U_19208,U_19214,U_19210) ),
    inference(clausify,[status(thm)],[f_4600_5]) ).

fof(f_4601_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_4601_2,plain,
    ! [U_19221,U_19220,U_19219,U_19218,U_19217] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19217),U_19218),U_19219) = hAPP(hAPP(c_List_Olist_OCons(U_19217),U_19220),U_19221)
        | ( ! [U_19216] :
              ( hAPP(hAPP(c_List_Oappend(U_19217),U_19216),U_19219) != U_19221
              | U_19218 != hAPP(hAPP(c_List_Olist_OCons(U_19217),U_19220),U_19216) )
          & ( U_19219 != hAPP(hAPP(c_List_Olist_OCons(U_19217),U_19220),U_19221)
            | U_19218 != c_List_Olist_ONil(U_19217) ) ) )
      & ( ? [U_19215] :
            ( hAPP(hAPP(c_List_Oappend(U_19217),U_19215),U_19219) = U_19221
            & U_19218 = hAPP(hAPP(c_List_Olist_OCons(U_19217),U_19220),U_19215) )
        | ( U_19219 = hAPP(hAPP(c_List_Olist_OCons(U_19217),U_19220),U_19221)
          & U_19218 = c_List_Olist_ONil(U_19217) )
        | hAPP(hAPP(c_List_Oappend(U_19217),U_19218),U_19219) != hAPP(hAPP(c_List_Olist_OCons(U_19217),U_19220),U_19221) ) ),
    inference(variable_rename,[status(thm)],[f_4601_1]) ).

fof(f_4601_3,plain,
    ( ! [U_19231,U_19229,U_19227,U_19225,U_19223] :
        ( hAPP(hAPP(c_List_Oappend(U_19223),U_19225),U_19227) = hAPP(hAPP(c_List_Olist_OCons(U_19223),U_19229),U_19231)
        | ( ! [U_19216] :
              ( hAPP(hAPP(c_List_Oappend(U_19223),U_19216),U_19227) != U_19231
              | U_19225 != hAPP(hAPP(c_List_Olist_OCons(U_19223),U_19229),U_19216) )
          & ( U_19227 != hAPP(hAPP(c_List_Olist_OCons(U_19223),U_19229),U_19231)
            | U_19225 != c_List_Olist_ONil(U_19223) ) ) )
    & ! [U_19230,U_19228,U_19226,U_19224,U_19222] :
        ( ? [U_19215] :
            ( hAPP(hAPP(c_List_Oappend(U_19222),U_19215),U_19226) = U_19230
            & U_19224 = hAPP(hAPP(c_List_Olist_OCons(U_19222),U_19228),U_19215) )
        | ( U_19226 = hAPP(hAPP(c_List_Olist_OCons(U_19222),U_19228),U_19230)
          & U_19224 = c_List_Olist_ONil(U_19222) )
        | hAPP(hAPP(c_List_Oappend(U_19222),U_19224),U_19226) != hAPP(hAPP(c_List_Olist_OCons(U_19222),U_19228),U_19230) ) ),
    inference(miniscope,[status(thm)],[f_4601_2]) ).

fof(f_4601_4,plain,
    ( ! [U_19231,U_19229,U_19227,U_19225,U_19223] :
        ( hAPP(hAPP(c_List_Oappend(U_19223),U_19225),U_19227) = hAPP(hAPP(c_List_Olist_OCons(U_19223),U_19229),U_19231)
        | ( ! [U_19216] :
              ( hAPP(hAPP(c_List_Oappend(U_19223),U_19216),U_19227) != U_19231
              | U_19225 != hAPP(hAPP(c_List_Olist_OCons(U_19223),U_19229),U_19216) )
          & ( U_19227 != hAPP(hAPP(c_List_Olist_OCons(U_19223),U_19229),U_19231)
            | U_19225 != c_List_Olist_ONil(U_19223) ) ) )
    & ! [U_19230,U_19228,U_19226,U_19224,U_19222] :
        ( ( hAPP(hAPP(c_List_Oappend(U_19222),sK477(U_19230,U_19228,U_19226,U_19224,U_19222)),U_19226) = U_19230
          & U_19224 = hAPP(hAPP(c_List_Olist_OCons(U_19222),U_19228),sK477(U_19230,U_19228,U_19226,U_19224,U_19222)) )
        | ( U_19226 = hAPP(hAPP(c_List_Olist_OCons(U_19222),U_19228),U_19230)
          & U_19224 = c_List_Olist_ONil(U_19222) )
        | hAPP(hAPP(c_List_Oappend(U_19222),U_19224),U_19226) != hAPP(hAPP(c_List_Olist_OCons(U_19222),U_19228),U_19230) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK477]),skolemize(U_19215,sK477(U_19230,U_19228,U_19226,U_19224,U_19222))],[f_4601_3]) ).

fof(f_4601_5,plain,
    ( ! [U_19216,U_19229,U_19223,U_19225,U_19231,U_19227] :
        ( hAPP(hAPP(c_List_Oappend(U_19223),U_19216),U_19227) != U_19231
        | U_19225 != hAPP(hAPP(c_List_Olist_OCons(U_19223),U_19229),U_19216)
        | ~ sP1179(U_19216,U_19229,U_19223,U_19225,U_19231,U_19227) )
    & ! [U_19216,U_19229,U_19223,U_19225,U_19231,U_19227] :
        ( U_19227 != hAPP(hAPP(c_List_Olist_OCons(U_19223),U_19229),U_19231)
        | U_19225 != c_List_Olist_ONil(U_19223)
        | ~ sP1179(U_19216,U_19229,U_19223,U_19225,U_19231,U_19227) )
    & ! [U_19226,U_19224,U_19222,U_19228,U_19230] :
        ( hAPP(hAPP(c_List_Oappend(U_19222),sK477(U_19230,U_19228,U_19226,U_19224,U_19222)),U_19226) = U_19230
        | ~ sP1178(U_19226,U_19224,U_19222,U_19228,U_19230) )
    & ! [U_19226,U_19224,U_19222,U_19228,U_19230] :
        ( U_19224 = hAPP(hAPP(c_List_Olist_OCons(U_19222),U_19228),sK477(U_19230,U_19228,U_19226,U_19224,U_19222))
        | ~ sP1178(U_19226,U_19224,U_19222,U_19228,U_19230) )
    & ! [U_19226,U_19224,U_19222,U_19228,U_19230] :
        ( U_19226 = hAPP(hAPP(c_List_Olist_OCons(U_19222),U_19228),U_19230)
        | ~ sP1177(U_19226,U_19224,U_19222,U_19228,U_19230) )
    & ! [U_19226,U_19224,U_19222,U_19228,U_19230] :
        ( U_19224 = c_List_Olist_ONil(U_19222)
        | ~ sP1177(U_19226,U_19224,U_19222,U_19228,U_19230) )
    & ! [U_19216,U_19229,U_19223,U_19225,U_19231,U_19227] :
        ( hAPP(hAPP(c_List_Oappend(U_19223),U_19225),U_19227) = hAPP(hAPP(c_List_Olist_OCons(U_19223),U_19229),U_19231)
        | sP1179(U_19216,U_19229,U_19223,U_19225,U_19231,U_19227) )
    & ! [U_19226,U_19224,U_19222,U_19228,U_19230] :
        ( sP1178(U_19226,U_19224,U_19222,U_19228,U_19230)
        | sP1177(U_19226,U_19224,U_19222,U_19228,U_19230)
        | hAPP(hAPP(c_List_Oappend(U_19222),U_19224),U_19226) != hAPP(hAPP(c_List_Olist_OCons(U_19222),U_19228),U_19230) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1177,sP1178,sP1179])],[f_4601_4]) ).

cnf(f_4601_6,plain,
    ( sP1178(U_19226,U_19224,U_19222,U_19228,U_19230)
    | sP1177(U_19226,U_19224,U_19222,U_19228,U_19230)
    | hAPP(hAPP(c_List_Oappend(U_19222),U_19224),U_19226) != hAPP(hAPP(c_List_Olist_OCons(U_19222),U_19228),U_19230) ),
    inference(clausify,[status(thm)],[f_4601_5]) ).

cnf(f_4601_7,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19223),U_19225),U_19227) = hAPP(hAPP(c_List_Olist_OCons(U_19223),U_19229),U_19231)
    | sP1179(U_19216,U_19229,U_19223,U_19225,U_19231,U_19227) ),
    inference(clausify,[status(thm)],[f_4601_5]) ).

cnf(f_4601_8,plain,
    ( U_19224 = c_List_Olist_ONil(U_19222)
    | ~ sP1177(U_19226,U_19224,U_19222,U_19228,U_19230) ),
    inference(clausify,[status(thm)],[f_4601_5]) ).

cnf(f_4601_9,plain,
    ( U_19226 = hAPP(hAPP(c_List_Olist_OCons(U_19222),U_19228),U_19230)
    | ~ sP1177(U_19226,U_19224,U_19222,U_19228,U_19230) ),
    inference(clausify,[status(thm)],[f_4601_5]) ).

cnf(f_4601_10,plain,
    ( U_19224 = hAPP(hAPP(c_List_Olist_OCons(U_19222),U_19228),sK477(U_19230,U_19228,U_19226,U_19224,U_19222))
    | ~ sP1178(U_19226,U_19224,U_19222,U_19228,U_19230) ),
    inference(clausify,[status(thm)],[f_4601_5]) ).

cnf(f_4601_11,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19222),sK477(U_19230,U_19228,U_19226,U_19224,U_19222)),U_19226) = U_19230
    | ~ sP1178(U_19226,U_19224,U_19222,U_19228,U_19230) ),
    inference(clausify,[status(thm)],[f_4601_5]) ).

cnf(f_4601_12,plain,
    ( U_19227 != hAPP(hAPP(c_List_Olist_OCons(U_19223),U_19229),U_19231)
    | U_19225 != c_List_Olist_ONil(U_19223)
    | ~ sP1179(U_19216,U_19229,U_19223,U_19225,U_19231,U_19227) ),
    inference(clausify,[status(thm)],[f_4601_5]) ).

cnf(f_4601_13,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19223),U_19216),U_19227) != U_19231
    | U_19225 != hAPP(hAPP(c_List_Olist_OCons(U_19223),U_19229),U_19216)
    | ~ sP1179(U_19216,U_19229,U_19223,U_19225,U_19231,U_19227) ),
    inference(clausify,[status(thm)],[f_4601_5]) ).

fof(f_4602_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_4602_2,plain,
    ! [U_19237,U_19236,U_19235,U_19234,U_19233,U_19232] :
      ( c_Map_Omap__upds(U_19232,U_19234,U_19236,U_19233,hAPP(hAPP(c_List_Oappend(U_19234),U_19235),U_19237)) = c_Map_Omap__upds(U_19232,U_19234,U_19236,U_19233,U_19235)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19232)),U_19233) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19234)),U_19235) ),
    inference(variable_rename,[status(thm)],[f_4602_1]) ).

fof(f_4602_3,plain,
    ! [U_19235,U_19236,U_19233,U_19232,U_19237,U_19234] :
      ( c_Map_Omap__upds(U_19232,U_19234,U_19236,U_19233,hAPP(hAPP(c_List_Oappend(U_19234),U_19235),U_19237)) = c_Map_Omap__upds(U_19232,U_19234,U_19236,U_19233,U_19235)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19232)),U_19233) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19234)),U_19235) ),
    inference(definitional_conversion,[status(esa)],[f_4602_2]) ).

cnf(f_4602_4,plain,
    ( c_Map_Omap__upds(U_19232,U_19234,U_19236,U_19233,hAPP(hAPP(c_List_Oappend(U_19234),U_19235),U_19237)) = c_Map_Omap__upds(U_19232,U_19234,U_19236,U_19233,U_19235)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19232)),U_19233) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19234)),U_19235) ),
    inference(clausify,[status(thm)],[f_4602_3]) ).

fof(f_4603_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_4603_2,plain,
    ! [U_19243,U_19242,U_19241,U_19240,U_19239,U_19238] :
      ( c_Map_Omap__upds(U_19238,U_19240,U_19242,hAPP(hAPP(c_List_Oappend(U_19238),U_19239),U_19243),U_19241) = c_Map_Omap__upds(U_19238,U_19240,U_19242,U_19239,U_19241)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19238)),U_19239) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19240)),U_19241) ),
    inference(variable_rename,[status(thm)],[f_4603_1]) ).

fof(f_4603_3,plain,
    ! [U_19238,U_19239,U_19240,U_19241,U_19242,U_19243] :
      ( c_Map_Omap__upds(U_19238,U_19240,U_19242,hAPP(hAPP(c_List_Oappend(U_19238),U_19239),U_19243),U_19241) = c_Map_Omap__upds(U_19238,U_19240,U_19242,U_19239,U_19241)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19238)),U_19239) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19240)),U_19241) ),
    inference(definitional_conversion,[status(esa)],[f_4603_2]) ).

cnf(f_4603_4,plain,
    ( c_Map_Omap__upds(U_19238,U_19240,U_19242,hAPP(hAPP(c_List_Oappend(U_19238),U_19239),U_19243),U_19241) = c_Map_Omap__upds(U_19238,U_19240,U_19242,U_19239,U_19241)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19238)),U_19239) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19240)),U_19241) ),
    inference(clausify,[status(thm)],[f_4603_3]) ).

fof(f_4604_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_4604_2,plain,
    ! [U_19247,U_19246,U_19245,U_19244] : hAPP(hAPP(c_List_Onth(U_19244),hAPP(hAPP(c_List_Oappend(U_19244),U_19245),hAPP(hAPP(c_List_Olist_OCons(U_19244),U_19246),U_19247))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19244)),U_19245)) = U_19246,
    inference(variable_rename,[status(thm)],[f_4604_1]) ).

fof(f_4604_3,plain,
    ! [U_19244,U_19245,U_19246,U_19247] : hAPP(hAPP(c_List_Onth(U_19244),hAPP(hAPP(c_List_Oappend(U_19244),U_19245),hAPP(hAPP(c_List_Olist_OCons(U_19244),U_19246),U_19247))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19244)),U_19245)) = U_19246,
    inference(definitional_conversion,[status(esa)],[f_4604_2]) ).

cnf(f_4604_4,plain,
    hAPP(hAPP(c_List_Onth(U_19244),hAPP(hAPP(c_List_Oappend(U_19244),U_19245),hAPP(hAPP(c_List_Olist_OCons(U_19244),U_19246),U_19247))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19244)),U_19245)) = U_19246,
    inference(clausify,[status(thm)],[f_4604_3]) ).

fof(f_4605_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_4605_2,plain,
    ! [U_19253,U_19252,U_19251,U_19250,U_19249,U_19248] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_19248),U_19249),U_19252) = hAPP(hAPP(c_List_Oappend(U_19248),U_19251),U_19253)
      | U_19252 != hAPP(hAPP(c_List_Oappend(U_19248),U_19250),U_19253)
      | hAPP(hAPP(c_List_Olist_OCons(U_19248),U_19249),U_19250) != U_19251 ),
    inference(variable_rename,[status(thm)],[f_4605_1]) ).

fof(f_4605_3,plain,
    ! [U_19248,U_19249,U_19250,U_19251,U_19252,U_19253] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_19248),U_19249),U_19252) = hAPP(hAPP(c_List_Oappend(U_19248),U_19251),U_19253)
      | U_19252 != hAPP(hAPP(c_List_Oappend(U_19248),U_19250),U_19253)
      | hAPP(hAPP(c_List_Olist_OCons(U_19248),U_19249),U_19250) != U_19251 ),
    inference(definitional_conversion,[status(esa)],[f_4605_2]) ).

cnf(f_4605_4,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_19248),U_19249),U_19252) = hAPP(hAPP(c_List_Oappend(U_19248),U_19251),U_19253)
    | U_19252 != hAPP(hAPP(c_List_Oappend(U_19248),U_19250),U_19253)
    | hAPP(hAPP(c_List_Olist_OCons(U_19248),U_19249),U_19250) != U_19251 ),
    inference(clausify,[status(thm)],[f_4605_3]) ).

fof(f_4606_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_4606_2,plain,
    ! [U_19257,U_19256,U_19255,U_19254] : hAPP(hAPP(c_List_Oappend(U_19254),hAPP(hAPP(c_List_Olist_OCons(U_19254),U_19255),U_19256)),U_19257) = hAPP(hAPP(c_List_Olist_OCons(U_19254),U_19255),hAPP(hAPP(c_List_Oappend(U_19254),U_19256),U_19257)),
    inference(variable_rename,[status(thm)],[f_4606_1]) ).

fof(f_4606_3,plain,
    ! [U_19254,U_19255,U_19256,U_19257] : hAPP(hAPP(c_List_Oappend(U_19254),hAPP(hAPP(c_List_Olist_OCons(U_19254),U_19255),U_19256)),U_19257) = hAPP(hAPP(c_List_Olist_OCons(U_19254),U_19255),hAPP(hAPP(c_List_Oappend(U_19254),U_19256),U_19257)),
    inference(definitional_conversion,[status(esa)],[f_4606_2]) ).

cnf(f_4606_4,plain,
    hAPP(hAPP(c_List_Oappend(U_19254),hAPP(hAPP(c_List_Olist_OCons(U_19254),U_19255),U_19256)),U_19257) = hAPP(hAPP(c_List_Olist_OCons(U_19254),U_19255),hAPP(hAPP(c_List_Oappend(U_19254),U_19256),U_19257)),
    inference(clausify,[status(thm)],[f_4606_3]) ).

fof(f_4607_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_4607_2,plain,
    ! [U_19262,U_19261,U_19260,U_19259,U_19258] : hAPP(hAPP(c_List_Olist__update(U_19258,hAPP(hAPP(c_List_Oappend(U_19258),U_19259),hAPP(hAPP(c_List_Olist_OCons(U_19258),U_19260),U_19261))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19258)),U_19259)),U_19262) = hAPP(hAPP(c_List_Oappend(U_19258),U_19259),hAPP(hAPP(c_List_Olist_OCons(U_19258),U_19262),U_19261)),
    inference(variable_rename,[status(thm)],[f_4607_1]) ).

fof(f_4607_3,plain,
    ! [U_19260,U_19261,U_19258,U_19259,U_19262] : hAPP(hAPP(c_List_Olist__update(U_19258,hAPP(hAPP(c_List_Oappend(U_19258),U_19259),hAPP(hAPP(c_List_Olist_OCons(U_19258),U_19260),U_19261))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19258)),U_19259)),U_19262) = hAPP(hAPP(c_List_Oappend(U_19258),U_19259),hAPP(hAPP(c_List_Olist_OCons(U_19258),U_19262),U_19261)),
    inference(definitional_conversion,[status(esa)],[f_4607_2]) ).

cnf(f_4607_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_19258,hAPP(hAPP(c_List_Oappend(U_19258),U_19259),hAPP(hAPP(c_List_Olist_OCons(U_19258),U_19260),U_19261))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19258)),U_19259)),U_19262) = hAPP(hAPP(c_List_Oappend(U_19258),U_19259),hAPP(hAPP(c_List_Olist_OCons(U_19258),U_19262),U_19261)),
    inference(clausify,[status(thm)],[f_4607_3]) ).

fof(f_4608_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_4608_2,plain,
    ! [U_19267,U_19266,U_19265,U_19264,U_19263] :
      ( hAPP(hAPP(c_List_Olist__update(U_19264,hAPP(hAPP(c_List_Oappend(U_19264),U_19265),U_19266)),U_19263),U_19267) = hAPP(hAPP(c_List_Oappend(U_19264),hAPP(hAPP(c_List_Olist__update(U_19264,U_19265),U_19263),U_19267)),U_19266)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19263),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19264)),U_19265))) ),
    inference(variable_rename,[status(thm)],[f_4608_1]) ).

fof(f_4608_3,plain,
    ! [U_19263,U_19264,U_19265,U_19266,U_19267] :
      ( hAPP(hAPP(c_List_Olist__update(U_19264,hAPP(hAPP(c_List_Oappend(U_19264),U_19265),U_19266)),U_19263),U_19267) = hAPP(hAPP(c_List_Oappend(U_19264),hAPP(hAPP(c_List_Olist__update(U_19264,U_19265),U_19263),U_19267)),U_19266)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19263),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19264)),U_19265))) ),
    inference(definitional_conversion,[status(esa)],[f_4608_2]) ).

cnf(f_4608_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_19264,hAPP(hAPP(c_List_Oappend(U_19264),U_19265),U_19266)),U_19263),U_19267) = hAPP(hAPP(c_List_Oappend(U_19264),hAPP(hAPP(c_List_Olist__update(U_19264,U_19265),U_19263),U_19267)),U_19266)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19263),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19264)),U_19265))) ),
    inference(clausify,[status(thm)],[f_4608_3]) ).

fof(f_4609_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_4609_2,plain,
    ! [U_19271,U_19270,U_19269,U_19268] : hAPP(hAPP(c_List_Onth(U_19268),hAPP(hAPP(c_List_Oappend(U_19268),U_19269),U_19270)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19268)),U_19269)),U_19271)) = hAPP(hAPP(c_List_Onth(U_19268),U_19270),U_19271),
    inference(variable_rename,[status(thm)],[f_4609_1]) ).

fof(f_4609_3,plain,
    ! [U_19268,U_19269,U_19270,U_19271] : hAPP(hAPP(c_List_Onth(U_19268),hAPP(hAPP(c_List_Oappend(U_19268),U_19269),U_19270)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19268)),U_19269)),U_19271)) = hAPP(hAPP(c_List_Onth(U_19268),U_19270),U_19271),
    inference(definitional_conversion,[status(esa)],[f_4609_2]) ).

cnf(f_4609_4,plain,
    hAPP(hAPP(c_List_Onth(U_19268),hAPP(hAPP(c_List_Oappend(U_19268),U_19269),U_19270)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19268)),U_19269)),U_19271)) = hAPP(hAPP(c_List_Onth(U_19268),U_19270),U_19271),
    inference(clausify,[status(thm)],[f_4609_3]) ).

fof(f_4610_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_4610_2,plain,
    ! [U_19274,U_19273,U_19272] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19272)),hAPP(hAPP(c_List_Oappend(U_19272),U_19273),U_19274)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19272)),U_19273)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19272)),U_19274)),
    inference(variable_rename,[status(thm)],[f_4610_1]) ).

fof(f_4610_3,plain,
    ! [U_19272,U_19273,U_19274] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19272)),hAPP(hAPP(c_List_Oappend(U_19272),U_19273),U_19274)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19272)),U_19273)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19272)),U_19274)),
    inference(definitional_conversion,[status(esa)],[f_4610_2]) ).

cnf(f_4610_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19272)),hAPP(hAPP(c_List_Oappend(U_19272),U_19273),U_19274)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19272)),U_19273)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19272)),U_19274)),
    inference(clausify,[status(thm)],[f_4610_3]) ).

fof(f_4611_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_4611_2,plain,
    ! [U_19280,U_19279,U_19278,U_19277,U_19276,U_19275] :
      ( hAPP(hAPP(c_List_Ozip(U_19275,U_19277),hAPP(hAPP(c_List_Oappend(U_19275),U_19276),U_19279)),hAPP(hAPP(c_List_Oappend(U_19277),U_19278),U_19280)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19275,U_19277)),hAPP(hAPP(c_List_Ozip(U_19275,U_19277),U_19276),U_19278)),hAPP(hAPP(c_List_Ozip(U_19275,U_19277),U_19279),U_19280))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19275)),U_19279) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19277)),U_19280)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19275)),U_19276) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19277)),U_19278) ),
    inference(variable_rename,[status(thm)],[f_4611_1]) ).

fof(f_4611_3,plain,
    ! [U_19275,U_19276,U_19277,U_19278,U_19279,U_19280] :
      ( hAPP(hAPP(c_List_Ozip(U_19275,U_19277),hAPP(hAPP(c_List_Oappend(U_19275),U_19276),U_19279)),hAPP(hAPP(c_List_Oappend(U_19277),U_19278),U_19280)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19275,U_19277)),hAPP(hAPP(c_List_Ozip(U_19275,U_19277),U_19276),U_19278)),hAPP(hAPP(c_List_Ozip(U_19275,U_19277),U_19279),U_19280))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19275)),U_19279) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19277)),U_19280)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19275)),U_19276) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19277)),U_19278) ),
    inference(definitional_conversion,[status(esa)],[f_4611_2]) ).

cnf(f_4611_4,plain,
    ( hAPP(hAPP(c_List_Ozip(U_19275,U_19277),hAPP(hAPP(c_List_Oappend(U_19275),U_19276),U_19279)),hAPP(hAPP(c_List_Oappend(U_19277),U_19278),U_19280)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19275,U_19277)),hAPP(hAPP(c_List_Ozip(U_19275,U_19277),U_19276),U_19278)),hAPP(hAPP(c_List_Ozip(U_19275,U_19277),U_19279),U_19280))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19275)),U_19279) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19277)),U_19280)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19275)),U_19276) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19277)),U_19278) ),
    inference(clausify,[status(thm)],[f_4611_3]) ).

fof(f_4612_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_4612_2,plain,
    ! [U_19285,U_19284,U_19283,U_19282,U_19281] : hAPP(hAPP(c_List_Omap(U_19281,U_19282),U_19283),hAPP(hAPP(c_List_Oappend(U_19281),U_19284),U_19285)) = hAPP(hAPP(c_List_Oappend(U_19282),hAPP(hAPP(c_List_Omap(U_19281,U_19282),U_19283),U_19284)),hAPP(hAPP(c_List_Omap(U_19281,U_19282),U_19283),U_19285)),
    inference(variable_rename,[status(thm)],[f_4612_1]) ).

fof(f_4612_3,plain,
    ! [U_19282,U_19281,U_19283,U_19284,U_19285] : hAPP(hAPP(c_List_Omap(U_19281,U_19282),U_19283),hAPP(hAPP(c_List_Oappend(U_19281),U_19284),U_19285)) = hAPP(hAPP(c_List_Oappend(U_19282),hAPP(hAPP(c_List_Omap(U_19281,U_19282),U_19283),U_19284)),hAPP(hAPP(c_List_Omap(U_19281,U_19282),U_19283),U_19285)),
    inference(definitional_conversion,[status(esa)],[f_4612_2]) ).

cnf(f_4612_4,plain,
    hAPP(hAPP(c_List_Omap(U_19281,U_19282),U_19283),hAPP(hAPP(c_List_Oappend(U_19281),U_19284),U_19285)) = hAPP(hAPP(c_List_Oappend(U_19282),hAPP(hAPP(c_List_Omap(U_19281,U_19282),U_19283),U_19284)),hAPP(hAPP(c_List_Omap(U_19281,U_19282),U_19283),U_19285)),
    inference(clausify,[status(thm)],[f_4612_3]) ).

fof(f_4613_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_4613_2,plain,
    ! [U_19289,U_19288,U_19287,U_19286] :
      ( ( c_List_Oremove1(U_19286,U_19287,hAPP(hAPP(c_List_Oappend(U_19286),U_19288),U_19289)) = hAPP(hAPP(c_List_Oappend(U_19286),U_19288),c_List_Oremove1(U_19286,U_19287,U_19289))
        | hBOOL(hAPP(hAPP(c_member(U_19286),U_19287),hAPP(c_List_Oset(U_19286),U_19288))) )
      & ( c_List_Oremove1(U_19286,U_19287,hAPP(hAPP(c_List_Oappend(U_19286),U_19288),U_19289)) = hAPP(hAPP(c_List_Oappend(U_19286),c_List_Oremove1(U_19286,U_19287,U_19288)),U_19289)
        | ~ hBOOL(hAPP(hAPP(c_member(U_19286),U_19287),hAPP(c_List_Oset(U_19286),U_19288))) ) ),
    inference(variable_rename,[status(thm)],[f_4613_1]) ).

fof(f_4613_3,plain,
    ( ! [U_19297,U_19295,U_19293,U_19291] :
        ( c_List_Oremove1(U_19291,U_19293,hAPP(hAPP(c_List_Oappend(U_19291),U_19295),U_19297)) = hAPP(hAPP(c_List_Oappend(U_19291),U_19295),c_List_Oremove1(U_19291,U_19293,U_19297))
        | hBOOL(hAPP(hAPP(c_member(U_19291),U_19293),hAPP(c_List_Oset(U_19291),U_19295))) )
    & ! [U_19296,U_19294,U_19292,U_19290] :
        ( c_List_Oremove1(U_19290,U_19292,hAPP(hAPP(c_List_Oappend(U_19290),U_19294),U_19296)) = hAPP(hAPP(c_List_Oappend(U_19290),c_List_Oremove1(U_19290,U_19292,U_19294)),U_19296)
        | ~ hBOOL(hAPP(hAPP(c_member(U_19290),U_19292),hAPP(c_List_Oset(U_19290),U_19294))) ) ),
    inference(miniscope,[status(thm)],[f_4613_2]) ).

fof(f_4613_4,plain,
    ( ! [U_19297,U_19291,U_19293,U_19295] :
        ( c_List_Oremove1(U_19291,U_19293,hAPP(hAPP(c_List_Oappend(U_19291),U_19295),U_19297)) = hAPP(hAPP(c_List_Oappend(U_19291),U_19295),c_List_Oremove1(U_19291,U_19293,U_19297))
        | hBOOL(hAPP(hAPP(c_member(U_19291),U_19293),hAPP(c_List_Oset(U_19291),U_19295))) )
    & ! [U_19294,U_19292,U_19296,U_19290] :
        ( c_List_Oremove1(U_19290,U_19292,hAPP(hAPP(c_List_Oappend(U_19290),U_19294),U_19296)) = hAPP(hAPP(c_List_Oappend(U_19290),c_List_Oremove1(U_19290,U_19292,U_19294)),U_19296)
        | ~ hBOOL(hAPP(hAPP(c_member(U_19290),U_19292),hAPP(c_List_Oset(U_19290),U_19294))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4613_3]) ).

cnf(f_4613_5,plain,
    ( c_List_Oremove1(U_19290,U_19292,hAPP(hAPP(c_List_Oappend(U_19290),U_19294),U_19296)) = hAPP(hAPP(c_List_Oappend(U_19290),c_List_Oremove1(U_19290,U_19292,U_19294)),U_19296)
    | ~ hBOOL(hAPP(hAPP(c_member(U_19290),U_19292),hAPP(c_List_Oset(U_19290),U_19294))) ),
    inference(clausify,[status(thm)],[f_4613_4]) ).

cnf(f_4613_6,plain,
    ( c_List_Oremove1(U_19291,U_19293,hAPP(hAPP(c_List_Oappend(U_19291),U_19295),U_19297)) = hAPP(hAPP(c_List_Oappend(U_19291),U_19295),c_List_Oremove1(U_19291,U_19293,U_19297))
    | hBOOL(hAPP(hAPP(c_member(U_19291),U_19293),hAPP(c_List_Oset(U_19291),U_19295))) ),
    inference(clausify,[status(thm)],[f_4613_4]) ).

fof(f_4614_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_4614_2,plain,
    ! [U_19303,U_19302,U_19301,U_19300,U_19299,U_19298] : c_List_Ofoldr(U_19298,U_19299,U_19300,hAPP(hAPP(c_List_Oappend(U_19298),U_19301),U_19302),U_19303) = c_List_Ofoldr(U_19298,U_19299,U_19300,U_19301,c_List_Ofoldr(U_19298,U_19299,U_19300,U_19302,U_19303)),
    inference(variable_rename,[status(thm)],[f_4614_1]) ).

fof(f_4614_3,plain,
    ! [U_19300,U_19298,U_19299,U_19301,U_19302,U_19303] : c_List_Ofoldr(U_19298,U_19299,U_19300,hAPP(hAPP(c_List_Oappend(U_19298),U_19301),U_19302),U_19303) = c_List_Ofoldr(U_19298,U_19299,U_19300,U_19301,c_List_Ofoldr(U_19298,U_19299,U_19300,U_19302,U_19303)),
    inference(definitional_conversion,[status(esa)],[f_4614_2]) ).

cnf(f_4614_4,plain,
    c_List_Ofoldr(U_19298,U_19299,U_19300,hAPP(hAPP(c_List_Oappend(U_19298),U_19301),U_19302),U_19303) = c_List_Ofoldr(U_19298,U_19299,U_19300,U_19301,c_List_Ofoldr(U_19298,U_19299,U_19300,U_19302,U_19303)),
    inference(clausify,[status(thm)],[f_4614_3]) ).

fof(f_4615_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_4615_2,plain,
    ! [U_19307,U_19306,U_19305,U_19304] : c_Map_Omap__of(U_19304,U_19305,hAPP(hAPP(c_List_Oappend(tc_prod(U_19304,U_19305)),U_19306),U_19307)) = c_Map_Omap__add(U_19304,U_19305,c_Map_Omap__of(U_19304,U_19305,U_19307),c_Map_Omap__of(U_19304,U_19305,U_19306)),
    inference(variable_rename,[status(thm)],[f_4615_1]) ).

fof(f_4615_3,plain,
    ! [U_19305,U_19304,U_19306,U_19307] : c_Map_Omap__of(U_19304,U_19305,hAPP(hAPP(c_List_Oappend(tc_prod(U_19304,U_19305)),U_19306),U_19307)) = c_Map_Omap__add(U_19304,U_19305,c_Map_Omap__of(U_19304,U_19305,U_19307),c_Map_Omap__of(U_19304,U_19305,U_19306)),
    inference(definitional_conversion,[status(esa)],[f_4615_2]) ).

cnf(f_4615_4,plain,
    c_Map_Omap__of(U_19304,U_19305,hAPP(hAPP(c_List_Oappend(tc_prod(U_19304,U_19305)),U_19306),U_19307)) = c_Map_Omap__add(U_19304,U_19305,c_Map_Omap__of(U_19304,U_19305,U_19307),c_Map_Omap__of(U_19304,U_19305,U_19306)),
    inference(clausify,[status(thm)],[f_4615_3]) ).

fof(f_4616_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_4616_2,plain,
    ! [U_19311,U_19310,U_19309,U_19308] : hAPP(hAPP(c_List_Oappend(U_19308),hAPP(hAPP(c_List_Oappend(U_19308),U_19309),U_19310)),U_19311) = hAPP(hAPP(c_List_Oappend(U_19308),U_19309),hAPP(hAPP(c_List_Oappend(U_19308),U_19310),U_19311)),
    inference(variable_rename,[status(thm)],[f_4616_1]) ).

fof(f_4616_3,plain,
    ! [U_19308,U_19309,U_19310,U_19311] : hAPP(hAPP(c_List_Oappend(U_19308),hAPP(hAPP(c_List_Oappend(U_19308),U_19309),U_19310)),U_19311) = hAPP(hAPP(c_List_Oappend(U_19308),U_19309),hAPP(hAPP(c_List_Oappend(U_19308),U_19310),U_19311)),
    inference(definitional_conversion,[status(esa)],[f_4616_2]) ).

cnf(f_4616_4,plain,
    hAPP(hAPP(c_List_Oappend(U_19308),hAPP(hAPP(c_List_Oappend(U_19308),U_19309),U_19310)),U_19311) = hAPP(hAPP(c_List_Oappend(U_19308),U_19309),hAPP(hAPP(c_List_Oappend(U_19308),U_19310),U_19311)),
    inference(clausify,[status(thm)],[f_4616_3]) ).

fof(f_4617_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_4617_2,plain,
    ! [U_19318,U_19317,U_19316,U_19315,U_19314] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19314),U_19315),U_19316) = hAPP(hAPP(c_List_Oappend(U_19314),U_19317),U_19318)
        | ! [U_19313] :
            ( ( U_19316 != hAPP(hAPP(c_List_Oappend(U_19314),U_19313),U_19318)
              | hAPP(hAPP(c_List_Oappend(U_19314),U_19315),U_19313) != U_19317 )
            & ( hAPP(hAPP(c_List_Oappend(U_19314),U_19313),U_19316) != U_19318
              | U_19315 != hAPP(hAPP(c_List_Oappend(U_19314),U_19317),U_19313) ) ) )
      & ( ? [U_19312] :
            ( ( U_19316 = hAPP(hAPP(c_List_Oappend(U_19314),U_19312),U_19318)
              & hAPP(hAPP(c_List_Oappend(U_19314),U_19315),U_19312) = U_19317 )
            | ( hAPP(hAPP(c_List_Oappend(U_19314),U_19312),U_19316) = U_19318
              & U_19315 = hAPP(hAPP(c_List_Oappend(U_19314),U_19317),U_19312) ) )
        | hAPP(hAPP(c_List_Oappend(U_19314),U_19315),U_19316) != hAPP(hAPP(c_List_Oappend(U_19314),U_19317),U_19318) ) ),
    inference(variable_rename,[status(thm)],[f_4617_1]) ).

fof(f_4617_3,plain,
    ( ! [U_19332,U_19330,U_19328,U_19326,U_19324] :
        ( hAPP(hAPP(c_List_Oappend(U_19324),U_19326),U_19328) = hAPP(hAPP(c_List_Oappend(U_19324),U_19330),U_19332)
        | ( ! [U_19322] :
              ( U_19328 != hAPP(hAPP(c_List_Oappend(U_19324),U_19322),U_19332)
              | hAPP(hAPP(c_List_Oappend(U_19324),U_19326),U_19322) != U_19330 )
          & ! [U_19321] :
              ( hAPP(hAPP(c_List_Oappend(U_19324),U_19321),U_19328) != U_19332
              | U_19326 != hAPP(hAPP(c_List_Oappend(U_19324),U_19330),U_19321) ) ) )
    & ! [U_19331,U_19329,U_19327,U_19325,U_19323] :
        ( ? [U_19320] :
            ( U_19327 = hAPP(hAPP(c_List_Oappend(U_19323),U_19320),U_19331)
            & hAPP(hAPP(c_List_Oappend(U_19323),U_19325),U_19320) = U_19329 )
        | ? [U_19319] :
            ( hAPP(hAPP(c_List_Oappend(U_19323),U_19319),U_19327) = U_19331
            & U_19325 = hAPP(hAPP(c_List_Oappend(U_19323),U_19329),U_19319) )
        | hAPP(hAPP(c_List_Oappend(U_19323),U_19325),U_19327) != hAPP(hAPP(c_List_Oappend(U_19323),U_19329),U_19331) ) ),
    inference(miniscope,[status(thm)],[f_4617_2]) ).

fof(f_4617_4,plain,
    ( ! [U_19332,U_19330,U_19328,U_19326,U_19324] :
        ( hAPP(hAPP(c_List_Oappend(U_19324),U_19326),U_19328) = hAPP(hAPP(c_List_Oappend(U_19324),U_19330),U_19332)
        | ( ! [U_19322] :
              ( U_19328 != hAPP(hAPP(c_List_Oappend(U_19324),U_19322),U_19332)
              | hAPP(hAPP(c_List_Oappend(U_19324),U_19326),U_19322) != U_19330 )
          & ! [U_19321] :
              ( hAPP(hAPP(c_List_Oappend(U_19324),U_19321),U_19328) != U_19332
              | U_19326 != hAPP(hAPP(c_List_Oappend(U_19324),U_19330),U_19321) ) ) )
    & ! [U_19331,U_19329,U_19327,U_19325,U_19323] :
        ( ? [U_19320] :
            ( U_19327 = hAPP(hAPP(c_List_Oappend(U_19323),U_19320),U_19331)
            & hAPP(hAPP(c_List_Oappend(U_19323),U_19325),U_19320) = U_19329 )
        | ( hAPP(hAPP(c_List_Oappend(U_19323),sK478(U_19331,U_19329,U_19327,U_19325,U_19323)),U_19327) = U_19331
          & U_19325 = hAPP(hAPP(c_List_Oappend(U_19323),U_19329),sK478(U_19331,U_19329,U_19327,U_19325,U_19323)) )
        | hAPP(hAPP(c_List_Oappend(U_19323),U_19325),U_19327) != hAPP(hAPP(c_List_Oappend(U_19323),U_19329),U_19331) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK478]),skolemize(U_19319,sK478(U_19331,U_19329,U_19327,U_19325,U_19323))],[f_4617_3]) ).

fof(f_4617_5,plain,
    ( ! [U_19332,U_19330,U_19328,U_19326,U_19324] :
        ( hAPP(hAPP(c_List_Oappend(U_19324),U_19326),U_19328) = hAPP(hAPP(c_List_Oappend(U_19324),U_19330),U_19332)
        | ( ! [U_19322] :
              ( U_19328 != hAPP(hAPP(c_List_Oappend(U_19324),U_19322),U_19332)
              | hAPP(hAPP(c_List_Oappend(U_19324),U_19326),U_19322) != U_19330 )
          & ! [U_19321] :
              ( hAPP(hAPP(c_List_Oappend(U_19324),U_19321),U_19328) != U_19332
              | U_19326 != hAPP(hAPP(c_List_Oappend(U_19324),U_19330),U_19321) ) ) )
    & ! [U_19331,U_19329,U_19327,U_19325,U_19323] :
        ( ( U_19327 = hAPP(hAPP(c_List_Oappend(U_19323),sK479(U_19331,U_19329,U_19327,U_19325,U_19323)),U_19331)
          & hAPP(hAPP(c_List_Oappend(U_19323),U_19325),sK479(U_19331,U_19329,U_19327,U_19325,U_19323)) = U_19329 )
        | ( hAPP(hAPP(c_List_Oappend(U_19323),sK478(U_19331,U_19329,U_19327,U_19325,U_19323)),U_19327) = U_19331
          & U_19325 = hAPP(hAPP(c_List_Oappend(U_19323),U_19329),sK478(U_19331,U_19329,U_19327,U_19325,U_19323)) )
        | hAPP(hAPP(c_List_Oappend(U_19323),U_19325),U_19327) != hAPP(hAPP(c_List_Oappend(U_19323),U_19329),U_19331) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK479]),skolemize(U_19320,sK479(U_19331,U_19329,U_19327,U_19325,U_19323))],[f_4617_4]) ).

fof(f_4617_6,plain,
    ( ! [U_19321,U_19324,U_19322,U_19326,U_19330,U_19328,U_19332] :
        ( U_19328 != hAPP(hAPP(c_List_Oappend(U_19324),U_19322),U_19332)
        | hAPP(hAPP(c_List_Oappend(U_19324),U_19326),U_19322) != U_19330
        | ~ sP1182(U_19321,U_19324,U_19322,U_19326,U_19330,U_19328,U_19332) )
    & ! [U_19321,U_19324,U_19322,U_19326,U_19330,U_19328,U_19332] :
        ( hAPP(hAPP(c_List_Oappend(U_19324),U_19321),U_19328) != U_19332
        | U_19326 != hAPP(hAPP(c_List_Oappend(U_19324),U_19330),U_19321)
        | ~ sP1182(U_19321,U_19324,U_19322,U_19326,U_19330,U_19328,U_19332) )
    & ! [U_19331,U_19327,U_19325,U_19323,U_19329] :
        ( U_19327 = hAPP(hAPP(c_List_Oappend(U_19323),sK479(U_19331,U_19329,U_19327,U_19325,U_19323)),U_19331)
        | ~ sP1181(U_19331,U_19327,U_19325,U_19323,U_19329) )
    & ! [U_19331,U_19327,U_19325,U_19323,U_19329] :
        ( hAPP(hAPP(c_List_Oappend(U_19323),U_19325),sK479(U_19331,U_19329,U_19327,U_19325,U_19323)) = U_19329
        | ~ sP1181(U_19331,U_19327,U_19325,U_19323,U_19329) )
    & ! [U_19331,U_19327,U_19325,U_19323,U_19329] :
        ( hAPP(hAPP(c_List_Oappend(U_19323),sK478(U_19331,U_19329,U_19327,U_19325,U_19323)),U_19327) = U_19331
        | ~ sP1180(U_19331,U_19327,U_19325,U_19323,U_19329) )
    & ! [U_19331,U_19327,U_19325,U_19323,U_19329] :
        ( U_19325 = hAPP(hAPP(c_List_Oappend(U_19323),U_19329),sK478(U_19331,U_19329,U_19327,U_19325,U_19323))
        | ~ sP1180(U_19331,U_19327,U_19325,U_19323,U_19329) )
    & ! [U_19321,U_19324,U_19322,U_19326,U_19330,U_19328,U_19332] :
        ( hAPP(hAPP(c_List_Oappend(U_19324),U_19326),U_19328) = hAPP(hAPP(c_List_Oappend(U_19324),U_19330),U_19332)
        | sP1182(U_19321,U_19324,U_19322,U_19326,U_19330,U_19328,U_19332) )
    & ! [U_19331,U_19327,U_19325,U_19323,U_19329] :
        ( sP1181(U_19331,U_19327,U_19325,U_19323,U_19329)
        | sP1180(U_19331,U_19327,U_19325,U_19323,U_19329)
        | hAPP(hAPP(c_List_Oappend(U_19323),U_19325),U_19327) != hAPP(hAPP(c_List_Oappend(U_19323),U_19329),U_19331) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1180,sP1181,sP1182])],[f_4617_5]) ).

cnf(f_4617_7,plain,
    ( sP1181(U_19331,U_19327,U_19325,U_19323,U_19329)
    | sP1180(U_19331,U_19327,U_19325,U_19323,U_19329)
    | hAPP(hAPP(c_List_Oappend(U_19323),U_19325),U_19327) != hAPP(hAPP(c_List_Oappend(U_19323),U_19329),U_19331) ),
    inference(clausify,[status(thm)],[f_4617_6]) ).

cnf(f_4617_8,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19324),U_19326),U_19328) = hAPP(hAPP(c_List_Oappend(U_19324),U_19330),U_19332)
    | sP1182(U_19321,U_19324,U_19322,U_19326,U_19330,U_19328,U_19332) ),
    inference(clausify,[status(thm)],[f_4617_6]) ).

cnf(f_4617_9,plain,
    ( U_19325 = hAPP(hAPP(c_List_Oappend(U_19323),U_19329),sK478(U_19331,U_19329,U_19327,U_19325,U_19323))
    | ~ sP1180(U_19331,U_19327,U_19325,U_19323,U_19329) ),
    inference(clausify,[status(thm)],[f_4617_6]) ).

cnf(f_4617_10,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19323),sK478(U_19331,U_19329,U_19327,U_19325,U_19323)),U_19327) = U_19331
    | ~ sP1180(U_19331,U_19327,U_19325,U_19323,U_19329) ),
    inference(clausify,[status(thm)],[f_4617_6]) ).

cnf(f_4617_11,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19323),U_19325),sK479(U_19331,U_19329,U_19327,U_19325,U_19323)) = U_19329
    | ~ sP1181(U_19331,U_19327,U_19325,U_19323,U_19329) ),
    inference(clausify,[status(thm)],[f_4617_6]) ).

cnf(f_4617_12,plain,
    ( U_19327 = hAPP(hAPP(c_List_Oappend(U_19323),sK479(U_19331,U_19329,U_19327,U_19325,U_19323)),U_19331)
    | ~ sP1181(U_19331,U_19327,U_19325,U_19323,U_19329) ),
    inference(clausify,[status(thm)],[f_4617_6]) ).

cnf(f_4617_13,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19324),U_19321),U_19328) != U_19332
    | U_19326 != hAPP(hAPP(c_List_Oappend(U_19324),U_19330),U_19321)
    | ~ sP1182(U_19321,U_19324,U_19322,U_19326,U_19330,U_19328,U_19332) ),
    inference(clausify,[status(thm)],[f_4617_6]) ).

cnf(f_4617_14,plain,
    ( U_19328 != hAPP(hAPP(c_List_Oappend(U_19324),U_19322),U_19332)
    | hAPP(hAPP(c_List_Oappend(U_19324),U_19326),U_19322) != U_19330
    | ~ sP1182(U_19321,U_19324,U_19322,U_19326,U_19330,U_19328,U_19332) ),
    inference(clausify,[status(thm)],[f_4617_6]) ).

fof(f_4618_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_4618_2,plain,
    ! [U_19336,U_19335,U_19334,U_19333] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19333),U_19334),U_19335) = hAPP(hAPP(c_List_Oappend(U_19333),U_19334),U_19336)
        | U_19335 != U_19336 )
      & ( U_19335 = U_19336
        | hAPP(hAPP(c_List_Oappend(U_19333),U_19334),U_19335) != hAPP(hAPP(c_List_Oappend(U_19333),U_19334),U_19336) ) ),
    inference(variable_rename,[status(thm)],[f_4618_1]) ).

fof(f_4618_3,plain,
    ( ! [U_19344,U_19342] :
        ( ! [U_19340,U_19338] : hAPP(hAPP(c_List_Oappend(U_19338),U_19340),U_19342) = hAPP(hAPP(c_List_Oappend(U_19338),U_19340),U_19344)
        | U_19342 != U_19344 )
    & ! [U_19343,U_19341] :
        ( ! [U_19339,U_19337] : hAPP(hAPP(c_List_Oappend(U_19337),U_19339),U_19341) != hAPP(hAPP(c_List_Oappend(U_19337),U_19339),U_19343)
        | U_19341 = U_19343 ) ),
    inference(miniscope,[status(thm)],[f_4618_2]) ).

fof(f_4618_4,plain,
    ( ! [U_19338,U_19344,U_19340,U_19342] :
        ( hAPP(hAPP(c_List_Oappend(U_19338),U_19340),U_19342) = hAPP(hAPP(c_List_Oappend(U_19338),U_19340),U_19344)
        | U_19342 != U_19344 )
    & ! [U_19337,U_19339,U_19343,U_19341] :
        ( hAPP(hAPP(c_List_Oappend(U_19337),U_19339),U_19341) != hAPP(hAPP(c_List_Oappend(U_19337),U_19339),U_19343)
        | U_19341 = U_19343 ) ),
    inference(definitional_conversion,[status(esa)],[f_4618_3]) ).

cnf(f_4618_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19337),U_19339),U_19341) != hAPP(hAPP(c_List_Oappend(U_19337),U_19339),U_19343)
    | U_19341 = U_19343 ),
    inference(clausify,[status(thm)],[f_4618_4]) ).

cnf(f_4618_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19338),U_19340),U_19342) = hAPP(hAPP(c_List_Oappend(U_19338),U_19340),U_19344)
    | U_19342 != U_19344 ),
    inference(clausify,[status(thm)],[f_4618_4]) ).

fof(f_4619_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_4619_2,plain,
    ! [U_19348,U_19347,U_19346,U_19345] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19345),U_19346),U_19347) = hAPP(hAPP(c_List_Oappend(U_19345),U_19348),U_19347)
        | U_19346 != U_19348 )
      & ( U_19346 = U_19348
        | hAPP(hAPP(c_List_Oappend(U_19345),U_19346),U_19347) != hAPP(hAPP(c_List_Oappend(U_19345),U_19348),U_19347) ) ),
    inference(variable_rename,[status(thm)],[f_4619_1]) ).

fof(f_4619_3,plain,
    ( ! [U_19356,U_19354,U_19352] :
        ( ! [U_19350] : hAPP(hAPP(c_List_Oappend(U_19350),U_19352),U_19354) = hAPP(hAPP(c_List_Oappend(U_19350),U_19356),U_19354)
        | U_19352 != U_19356 )
    & ! [U_19355,U_19353,U_19351] :
        ( ! [U_19349] : hAPP(hAPP(c_List_Oappend(U_19349),U_19351),U_19353) != hAPP(hAPP(c_List_Oappend(U_19349),U_19355),U_19353)
        | U_19351 = U_19355 ) ),
    inference(miniscope,[status(thm)],[f_4619_2]) ).

fof(f_4619_4,plain,
    ( ! [U_19354,U_19350,U_19352,U_19356] :
        ( hAPP(hAPP(c_List_Oappend(U_19350),U_19352),U_19354) = hAPP(hAPP(c_List_Oappend(U_19350),U_19356),U_19354)
        | U_19352 != U_19356 )
    & ! [U_19353,U_19351,U_19349,U_19355] :
        ( hAPP(hAPP(c_List_Oappend(U_19349),U_19351),U_19353) != hAPP(hAPP(c_List_Oappend(U_19349),U_19355),U_19353)
        | U_19351 = U_19355 ) ),
    inference(definitional_conversion,[status(esa)],[f_4619_3]) ).

cnf(f_4619_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19349),U_19351),U_19353) != hAPP(hAPP(c_List_Oappend(U_19349),U_19355),U_19353)
    | U_19351 = U_19355 ),
    inference(clausify,[status(thm)],[f_4619_4]) ).

cnf(f_4619_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19350),U_19352),U_19354) = hAPP(hAPP(c_List_Oappend(U_19350),U_19356),U_19354)
    | U_19352 != U_19356 ),
    inference(clausify,[status(thm)],[f_4619_4]) ).

fof(f_4620_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_4620_2,plain,
    ! [U_19362,U_19361,U_19360,U_19359,U_19358,U_19357] :
      ( hAPP(hAPP(c_List_Oappend(U_19357),U_19358),U_19361) = hAPP(hAPP(c_List_Oappend(U_19357),U_19360),U_19362)
      | U_19361 != hAPP(hAPP(c_List_Oappend(U_19357),U_19359),U_19362)
      | hAPP(hAPP(c_List_Oappend(U_19357),U_19358),U_19359) != U_19360 ),
    inference(variable_rename,[status(thm)],[f_4620_1]) ).

fof(f_4620_3,plain,
    ! [U_19357,U_19358,U_19359,U_19360,U_19361,U_19362] :
      ( hAPP(hAPP(c_List_Oappend(U_19357),U_19358),U_19361) = hAPP(hAPP(c_List_Oappend(U_19357),U_19360),U_19362)
      | U_19361 != hAPP(hAPP(c_List_Oappend(U_19357),U_19359),U_19362)
      | hAPP(hAPP(c_List_Oappend(U_19357),U_19358),U_19359) != U_19360 ),
    inference(definitional_conversion,[status(esa)],[f_4620_2]) ).

cnf(f_4620_4,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19357),U_19358),U_19361) = hAPP(hAPP(c_List_Oappend(U_19357),U_19360),U_19362)
    | U_19361 != hAPP(hAPP(c_List_Oappend(U_19357),U_19359),U_19362)
    | hAPP(hAPP(c_List_Oappend(U_19357),U_19358),U_19359) != U_19360 ),
    inference(clausify,[status(thm)],[f_4620_3]) ).

fof(f_4621_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_4621_2,plain,
    ! [U_19365,U_19364,U_19363] : hAPP(c_List_Oset(U_19363),hAPP(hAPP(c_List_Oappend(U_19363),U_19364),U_19365)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19363,tc_HOL_Obool)),hAPP(c_List_Oset(U_19363),U_19364)),hAPP(c_List_Oset(U_19363),U_19365)),
    inference(variable_rename,[status(thm)],[f_4621_1]) ).

fof(f_4621_3,plain,
    ! [U_19363,U_19364,U_19365] : hAPP(c_List_Oset(U_19363),hAPP(hAPP(c_List_Oappend(U_19363),U_19364),U_19365)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19363,tc_HOL_Obool)),hAPP(c_List_Oset(U_19363),U_19364)),hAPP(c_List_Oset(U_19363),U_19365)),
    inference(definitional_conversion,[status(esa)],[f_4621_2]) ).

cnf(f_4621_4,plain,
    hAPP(c_List_Oset(U_19363),hAPP(hAPP(c_List_Oappend(U_19363),U_19364),U_19365)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19363,tc_HOL_Obool)),hAPP(c_List_Oset(U_19363),U_19364)),hAPP(c_List_Oset(U_19363),U_19365)),
    inference(clausify,[status(thm)],[f_4621_3]) ).

fof(f_4622_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_4622_2,plain,
    ! [U_19368,U_19367,U_19366] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_19366),hAPP(hAPP(c_List_Oappend(U_19366),U_19367),U_19368)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19366),hAPP(c_List_Omonoid__add__class_Olistsum(U_19366),U_19367)),hAPP(c_List_Omonoid__add__class_Olistsum(U_19366),U_19368))
      | ~ class_Groups_Omonoid__add(U_19366) ),
    inference(variable_rename,[status(thm)],[f_4622_1]) ).

fof(f_4622_3,plain,
    ! [U_19366,U_19367,U_19368] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_19366),hAPP(hAPP(c_List_Oappend(U_19366),U_19367),U_19368)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19366),hAPP(c_List_Omonoid__add__class_Olistsum(U_19366),U_19367)),hAPP(c_List_Omonoid__add__class_Olistsum(U_19366),U_19368))
      | ~ class_Groups_Omonoid__add(U_19366) ),
    inference(definitional_conversion,[status(esa)],[f_4622_2]) ).

cnf(f_4622_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_19366),hAPP(hAPP(c_List_Oappend(U_19366),U_19367),U_19368)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19366),hAPP(c_List_Omonoid__add__class_Olistsum(U_19366),U_19367)),hAPP(c_List_Omonoid__add__class_Olistsum(U_19366),U_19368))
    | ~ class_Groups_Omonoid__add(U_19366) ),
    inference(clausify,[status(thm)],[f_4622_3]) ).

fof(f_4623_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_4623_2,plain,
    ! [U_19372,U_19371,U_19370,U_19369] : hAPP(hAPP(c_List_Otake(U_19369),U_19370),hAPP(hAPP(c_List_Oappend(U_19369),U_19371),U_19372)) = hAPP(hAPP(c_List_Oappend(U_19369),hAPP(hAPP(c_List_Otake(U_19369),U_19370),U_19371)),hAPP(hAPP(c_List_Otake(U_19369),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19370),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19369)),U_19371))),U_19372)),
    inference(variable_rename,[status(thm)],[f_4623_1]) ).

fof(f_4623_3,plain,
    ! [U_19369,U_19370,U_19371,U_19372] : hAPP(hAPP(c_List_Otake(U_19369),U_19370),hAPP(hAPP(c_List_Oappend(U_19369),U_19371),U_19372)) = hAPP(hAPP(c_List_Oappend(U_19369),hAPP(hAPP(c_List_Otake(U_19369),U_19370),U_19371)),hAPP(hAPP(c_List_Otake(U_19369),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19370),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19369)),U_19371))),U_19372)),
    inference(definitional_conversion,[status(esa)],[f_4623_2]) ).

cnf(f_4623_4,plain,
    hAPP(hAPP(c_List_Otake(U_19369),U_19370),hAPP(hAPP(c_List_Oappend(U_19369),U_19371),U_19372)) = hAPP(hAPP(c_List_Oappend(U_19369),hAPP(hAPP(c_List_Otake(U_19369),U_19370),U_19371)),hAPP(hAPP(c_List_Otake(U_19369),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19370),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19369)),U_19371))),U_19372)),
    inference(clausify,[status(thm)],[f_4623_3]) ).

fof(f_4624_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_4624_2,plain,
    ! [U_19375,U_19374,U_19373] :
      ( U_19373 = hAPP(hAPP(c_List_Oappend(U_19375),c_List_Olist_ONil(U_19375)),U_19374)
      | U_19373 != U_19374 ),
    inference(variable_rename,[status(thm)],[f_4624_1]) ).

fof(f_4624_3,plain,
    ! [U_19373,U_19375,U_19374] :
      ( U_19373 = hAPP(hAPP(c_List_Oappend(U_19375),c_List_Olist_ONil(U_19375)),U_19374)
      | U_19373 != U_19374 ),
    inference(definitional_conversion,[status(esa)],[f_4624_2]) ).

cnf(f_4624_4,plain,
    ( U_19373 = hAPP(hAPP(c_List_Oappend(U_19375),c_List_Olist_ONil(U_19375)),U_19374)
    | U_19373 != U_19374 ),
    inference(clausify,[status(thm)],[f_4624_3]) ).

fof(f_4625_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_4625_2,plain,
    ! [U_19378,U_19377,U_19376] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19376),U_19377),U_19378) = U_19378
        | U_19377 != c_List_Olist_ONil(U_19376) )
      & ( U_19377 = c_List_Olist_ONil(U_19376)
        | hAPP(hAPP(c_List_Oappend(U_19376),U_19377),U_19378) != U_19378 ) ),
    inference(variable_rename,[status(thm)],[f_4625_1]) ).

fof(f_4625_3,plain,
    ( ! [U_19384,U_19382,U_19380] :
        ( hAPP(hAPP(c_List_Oappend(U_19380),U_19382),U_19384) = U_19384
        | U_19382 != c_List_Olist_ONil(U_19380) )
    & ! [U_19383,U_19381,U_19379] :
        ( U_19381 = c_List_Olist_ONil(U_19379)
        | hAPP(hAPP(c_List_Oappend(U_19379),U_19381),U_19383) != U_19383 ) ),
    inference(miniscope,[status(thm)],[f_4625_2]) ).

fof(f_4625_4,plain,
    ( ! [U_19380,U_19382,U_19384] :
        ( hAPP(hAPP(c_List_Oappend(U_19380),U_19382),U_19384) = U_19384
        | U_19382 != c_List_Olist_ONil(U_19380) )
    & ! [U_19381,U_19383,U_19379] :
        ( U_19381 = c_List_Olist_ONil(U_19379)
        | hAPP(hAPP(c_List_Oappend(U_19379),U_19381),U_19383) != U_19383 ) ),
    inference(definitional_conversion,[status(esa)],[f_4625_3]) ).

cnf(f_4625_5,plain,
    ( U_19381 = c_List_Olist_ONil(U_19379)
    | hAPP(hAPP(c_List_Oappend(U_19379),U_19381),U_19383) != U_19383 ),
    inference(clausify,[status(thm)],[f_4625_4]) ).

cnf(f_4625_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19380),U_19382),U_19384) = U_19384
    | U_19382 != c_List_Olist_ONil(U_19380) ),
    inference(clausify,[status(thm)],[f_4625_4]) ).

fof(f_4626_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_4626_2,plain,
    ! [U_19387,U_19386,U_19385] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19385),U_19386),U_19387) = U_19386
        | U_19387 != c_List_Olist_ONil(U_19385) )
      & ( U_19387 = c_List_Olist_ONil(U_19385)
        | hAPP(hAPP(c_List_Oappend(U_19385),U_19386),U_19387) != U_19386 ) ),
    inference(variable_rename,[status(thm)],[f_4626_1]) ).

fof(f_4626_3,plain,
    ( ! [U_19393,U_19391,U_19389] :
        ( hAPP(hAPP(c_List_Oappend(U_19389),U_19391),U_19393) = U_19391
        | U_19393 != c_List_Olist_ONil(U_19389) )
    & ! [U_19392,U_19390,U_19388] :
        ( U_19392 = c_List_Olist_ONil(U_19388)
        | hAPP(hAPP(c_List_Oappend(U_19388),U_19390),U_19392) != U_19390 ) ),
    inference(miniscope,[status(thm)],[f_4626_2]) ).

fof(f_4626_4,plain,
    ( ! [U_19389,U_19391,U_19393] :
        ( hAPP(hAPP(c_List_Oappend(U_19389),U_19391),U_19393) = U_19391
        | U_19393 != c_List_Olist_ONil(U_19389) )
    & ! [U_19390,U_19392,U_19388] :
        ( U_19392 = c_List_Olist_ONil(U_19388)
        | hAPP(hAPP(c_List_Oappend(U_19388),U_19390),U_19392) != U_19390 ) ),
    inference(definitional_conversion,[status(esa)],[f_4626_3]) ).

cnf(f_4626_5,plain,
    ( U_19392 = c_List_Olist_ONil(U_19388)
    | hAPP(hAPP(c_List_Oappend(U_19388),U_19390),U_19392) != U_19390 ),
    inference(clausify,[status(thm)],[f_4626_4]) ).

cnf(f_4626_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19389),U_19391),U_19393) = U_19391
    | U_19393 != c_List_Olist_ONil(U_19389) ),
    inference(clausify,[status(thm)],[f_4626_4]) ).

fof(f_4627_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_4627_2,plain,
    ! [U_19396,U_19395,U_19394] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19394),U_19395),U_19396) = c_List_Olist_ONil(U_19394)
        | U_19396 != c_List_Olist_ONil(U_19394)
        | U_19395 != c_List_Olist_ONil(U_19394) )
      & ( ( U_19396 = c_List_Olist_ONil(U_19394)
          & U_19395 = c_List_Olist_ONil(U_19394) )
        | hAPP(hAPP(c_List_Oappend(U_19394),U_19395),U_19396) != c_List_Olist_ONil(U_19394) ) ),
    inference(variable_rename,[status(thm)],[f_4627_1]) ).

fof(f_4627_3,plain,
    ( ! [U_19402,U_19400,U_19398] :
        ( hAPP(hAPP(c_List_Oappend(U_19398),U_19400),U_19402) = c_List_Olist_ONil(U_19398)
        | U_19402 != c_List_Olist_ONil(U_19398)
        | U_19400 != c_List_Olist_ONil(U_19398) )
    & ! [U_19401,U_19399,U_19397] :
        ( ( U_19401 = c_List_Olist_ONil(U_19397)
          & U_19399 = c_List_Olist_ONil(U_19397) )
        | hAPP(hAPP(c_List_Oappend(U_19397),U_19399),U_19401) != c_List_Olist_ONil(U_19397) ) ),
    inference(miniscope,[status(thm)],[f_4627_2]) ).

fof(f_4627_4,plain,
    ( ! [U_19401,U_19397,U_19399] :
        ( U_19401 = c_List_Olist_ONil(U_19397)
        | ~ sP1183(U_19401,U_19397,U_19399) )
    & ! [U_19401,U_19397,U_19399] :
        ( U_19399 = c_List_Olist_ONil(U_19397)
        | ~ sP1183(U_19401,U_19397,U_19399) )
    & ! [U_19402,U_19400,U_19398] :
        ( hAPP(hAPP(c_List_Oappend(U_19398),U_19400),U_19402) = c_List_Olist_ONil(U_19398)
        | U_19402 != c_List_Olist_ONil(U_19398)
        | U_19400 != c_List_Olist_ONil(U_19398) )
    & ! [U_19401,U_19397,U_19399] :
        ( sP1183(U_19401,U_19397,U_19399)
        | hAPP(hAPP(c_List_Oappend(U_19397),U_19399),U_19401) != c_List_Olist_ONil(U_19397) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1183])],[f_4627_3]) ).

cnf(f_4627_5,plain,
    ( sP1183(U_19401,U_19397,U_19399)
    | hAPP(hAPP(c_List_Oappend(U_19397),U_19399),U_19401) != c_List_Olist_ONil(U_19397) ),
    inference(clausify,[status(thm)],[f_4627_4]) ).

cnf(f_4627_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19398),U_19400),U_19402) = c_List_Olist_ONil(U_19398)
    | U_19402 != c_List_Olist_ONil(U_19398)
    | U_19400 != c_List_Olist_ONil(U_19398) ),
    inference(clausify,[status(thm)],[f_4627_4]) ).

cnf(f_4627_7,plain,
    ( U_19399 = c_List_Olist_ONil(U_19397)
    | ~ sP1183(U_19401,U_19397,U_19399) ),
    inference(clausify,[status(thm)],[f_4627_4]) ).

cnf(f_4627_8,plain,
    ( U_19401 = c_List_Olist_ONil(U_19397)
    | ~ sP1183(U_19401,U_19397,U_19399) ),
    inference(clausify,[status(thm)],[f_4627_4]) ).

fof(f_4628_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_4628_2,plain,
    ! [U_19405,U_19404,U_19403] :
      ( ( U_19403 = hAPP(hAPP(c_List_Oappend(U_19404),U_19405),U_19403)
        | U_19405 != c_List_Olist_ONil(U_19404) )
      & ( U_19405 = c_List_Olist_ONil(U_19404)
        | U_19403 != hAPP(hAPP(c_List_Oappend(U_19404),U_19405),U_19403) ) ),
    inference(variable_rename,[status(thm)],[f_4628_1]) ).

fof(f_4628_3,plain,
    ( ! [U_19411,U_19409] :
        ( ! [U_19407] : U_19407 = hAPP(hAPP(c_List_Oappend(U_19409),U_19411),U_19407)
        | U_19411 != c_List_Olist_ONil(U_19409) )
    & ! [U_19410,U_19408] :
        ( ! [U_19406] : U_19406 != hAPP(hAPP(c_List_Oappend(U_19408),U_19410),U_19406)
        | U_19410 = c_List_Olist_ONil(U_19408) ) ),
    inference(miniscope,[status(thm)],[f_4628_2]) ).

fof(f_4628_4,plain,
    ( ! [U_19411,U_19407,U_19409] :
        ( U_19407 = hAPP(hAPP(c_List_Oappend(U_19409),U_19411),U_19407)
        | U_19411 != c_List_Olist_ONil(U_19409) )
    & ! [U_19408,U_19410,U_19406] :
        ( U_19406 != hAPP(hAPP(c_List_Oappend(U_19408),U_19410),U_19406)
        | U_19410 = c_List_Olist_ONil(U_19408) ) ),
    inference(definitional_conversion,[status(esa)],[f_4628_3]) ).

cnf(f_4628_5,plain,
    ( U_19406 != hAPP(hAPP(c_List_Oappend(U_19408),U_19410),U_19406)
    | U_19410 = c_List_Olist_ONil(U_19408) ),
    inference(clausify,[status(thm)],[f_4628_4]) ).

cnf(f_4628_6,plain,
    ( U_19407 = hAPP(hAPP(c_List_Oappend(U_19409),U_19411),U_19407)
    | U_19411 != c_List_Olist_ONil(U_19409) ),
    inference(clausify,[status(thm)],[f_4628_4]) ).

fof(f_4629_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_4629_2,plain,
    ! [U_19414,U_19413,U_19412] :
      ( ( U_19412 = hAPP(hAPP(c_List_Oappend(U_19413),U_19412),U_19414)
        | U_19414 != c_List_Olist_ONil(U_19413) )
      & ( U_19414 = c_List_Olist_ONil(U_19413)
        | U_19412 != hAPP(hAPP(c_List_Oappend(U_19413),U_19412),U_19414) ) ),
    inference(variable_rename,[status(thm)],[f_4629_1]) ).

fof(f_4629_3,plain,
    ( ! [U_19420,U_19418] :
        ( ! [U_19416] : U_19416 = hAPP(hAPP(c_List_Oappend(U_19418),U_19416),U_19420)
        | U_19420 != c_List_Olist_ONil(U_19418) )
    & ! [U_19419,U_19417] :
        ( ! [U_19415] : U_19415 != hAPP(hAPP(c_List_Oappend(U_19417),U_19415),U_19419)
        | U_19419 = c_List_Olist_ONil(U_19417) ) ),
    inference(miniscope,[status(thm)],[f_4629_2]) ).

fof(f_4629_4,plain,
    ( ! [U_19420,U_19416,U_19418] :
        ( U_19416 = hAPP(hAPP(c_List_Oappend(U_19418),U_19416),U_19420)
        | U_19420 != c_List_Olist_ONil(U_19418) )
    & ! [U_19419,U_19417,U_19415] :
        ( U_19415 != hAPP(hAPP(c_List_Oappend(U_19417),U_19415),U_19419)
        | U_19419 = c_List_Olist_ONil(U_19417) ) ),
    inference(definitional_conversion,[status(esa)],[f_4629_3]) ).

cnf(f_4629_5,plain,
    ( U_19415 != hAPP(hAPP(c_List_Oappend(U_19417),U_19415),U_19419)
    | U_19419 = c_List_Olist_ONil(U_19417) ),
    inference(clausify,[status(thm)],[f_4629_4]) ).

cnf(f_4629_6,plain,
    ( U_19416 = hAPP(hAPP(c_List_Oappend(U_19418),U_19416),U_19420)
    | U_19420 != c_List_Olist_ONil(U_19418) ),
    inference(clausify,[status(thm)],[f_4629_4]) ).

fof(f_4630_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_4630_2,plain,
    ! [U_19422,U_19421] : hAPP(hAPP(c_List_Oappend(U_19421),U_19422),c_List_Olist_ONil(U_19421)) = U_19422,
    inference(variable_rename,[status(thm)],[f_4630_1]) ).

fof(f_4630_3,plain,
    ! [U_19421,U_19422] : hAPP(hAPP(c_List_Oappend(U_19421),U_19422),c_List_Olist_ONil(U_19421)) = U_19422,
    inference(definitional_conversion,[status(esa)],[f_4630_2]) ).

cnf(f_4630_4,plain,
    hAPP(hAPP(c_List_Oappend(U_19421),U_19422),c_List_Olist_ONil(U_19421)) = U_19422,
    inference(clausify,[status(thm)],[f_4630_3]) ).

fof(f_4631_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_4631_2,plain,
    ! [U_19425,U_19424,U_19423] :
      ( ( c_List_Olist_ONil(U_19423) = hAPP(hAPP(c_List_Oappend(U_19423),U_19424),U_19425)
        | U_19425 != c_List_Olist_ONil(U_19423)
        | U_19424 != c_List_Olist_ONil(U_19423) )
      & ( ( U_19425 = c_List_Olist_ONil(U_19423)
          & U_19424 = c_List_Olist_ONil(U_19423) )
        | c_List_Olist_ONil(U_19423) != hAPP(hAPP(c_List_Oappend(U_19423),U_19424),U_19425) ) ),
    inference(variable_rename,[status(thm)],[f_4631_1]) ).

fof(f_4631_3,plain,
    ( ! [U_19431,U_19429,U_19427] :
        ( c_List_Olist_ONil(U_19427) = hAPP(hAPP(c_List_Oappend(U_19427),U_19429),U_19431)
        | U_19431 != c_List_Olist_ONil(U_19427)
        | U_19429 != c_List_Olist_ONil(U_19427) )
    & ! [U_19430,U_19428,U_19426] :
        ( ( U_19430 = c_List_Olist_ONil(U_19426)
          & U_19428 = c_List_Olist_ONil(U_19426) )
        | c_List_Olist_ONil(U_19426) != hAPP(hAPP(c_List_Oappend(U_19426),U_19428),U_19430) ) ),
    inference(miniscope,[status(thm)],[f_4631_2]) ).

fof(f_4631_4,plain,
    ( ! [U_19426,U_19430,U_19428] :
        ( U_19430 = c_List_Olist_ONil(U_19426)
        | ~ sP1184(U_19426,U_19430,U_19428) )
    & ! [U_19426,U_19430,U_19428] :
        ( U_19428 = c_List_Olist_ONil(U_19426)
        | ~ sP1184(U_19426,U_19430,U_19428) )
    & ! [U_19429,U_19427,U_19431] :
        ( c_List_Olist_ONil(U_19427) = hAPP(hAPP(c_List_Oappend(U_19427),U_19429),U_19431)
        | U_19431 != c_List_Olist_ONil(U_19427)
        | U_19429 != c_List_Olist_ONil(U_19427) )
    & ! [U_19426,U_19430,U_19428] :
        ( sP1184(U_19426,U_19430,U_19428)
        | c_List_Olist_ONil(U_19426) != hAPP(hAPP(c_List_Oappend(U_19426),U_19428),U_19430) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1184])],[f_4631_3]) ).

cnf(f_4631_5,plain,
    ( sP1184(U_19426,U_19430,U_19428)
    | c_List_Olist_ONil(U_19426) != hAPP(hAPP(c_List_Oappend(U_19426),U_19428),U_19430) ),
    inference(clausify,[status(thm)],[f_4631_4]) ).

cnf(f_4631_6,plain,
    ( c_List_Olist_ONil(U_19427) = hAPP(hAPP(c_List_Oappend(U_19427),U_19429),U_19431)
    | U_19431 != c_List_Olist_ONil(U_19427)
    | U_19429 != c_List_Olist_ONil(U_19427) ),
    inference(clausify,[status(thm)],[f_4631_4]) ).

cnf(f_4631_7,plain,
    ( U_19428 = c_List_Olist_ONil(U_19426)
    | ~ sP1184(U_19426,U_19430,U_19428) ),
    inference(clausify,[status(thm)],[f_4631_4]) ).

cnf(f_4631_8,plain,
    ( U_19430 = c_List_Olist_ONil(U_19426)
    | ~ sP1184(U_19426,U_19430,U_19428) ),
    inference(clausify,[status(thm)],[f_4631_4]) ).

fof(f_4632_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_4632_2,plain,
    ! [U_19433,U_19432] : hAPP(hAPP(c_List_Oappend(U_19432),c_List_Olist_ONil(U_19432)),U_19433) = U_19433,
    inference(variable_rename,[status(thm)],[f_4632_1]) ).

fof(f_4632_3,plain,
    ! [U_19432,U_19433] : hAPP(hAPP(c_List_Oappend(U_19432),c_List_Olist_ONil(U_19432)),U_19433) = U_19433,
    inference(definitional_conversion,[status(esa)],[f_4632_2]) ).

cnf(f_4632_4,plain,
    hAPP(hAPP(c_List_Oappend(U_19432),c_List_Olist_ONil(U_19432)),U_19433) = U_19433,
    inference(clausify,[status(thm)],[f_4632_3]) ).

fof(f_4633_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_4633_2,plain,
    ! [U_19438,U_19437,U_19436,U_19435,U_19434] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19434),tc_List_Olist(U_19434))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19434),tc_List_Olist(U_19434)),hAPP(hAPP(c_List_Oappend(U_19434),U_19438),U_19435)),hAPP(hAPP(c_List_Oappend(U_19434),U_19438),U_19436))),c_List_Olexord(U_19434,U_19437)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19434),tc_List_Olist(U_19434))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19434),tc_List_Olist(U_19434)),U_19435),U_19436)),c_List_Olexord(U_19434,U_19437))) ),
    inference(variable_rename,[status(thm)],[f_4633_1]) ).

fof(f_4633_3,plain,
    ! [U_19438,U_19434,U_19435,U_19436,U_19437] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19434),tc_List_Olist(U_19434))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19434),tc_List_Olist(U_19434)),hAPP(hAPP(c_List_Oappend(U_19434),U_19438),U_19435)),hAPP(hAPP(c_List_Oappend(U_19434),U_19438),U_19436))),c_List_Olexord(U_19434,U_19437)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19434),tc_List_Olist(U_19434))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19434),tc_List_Olist(U_19434)),U_19435),U_19436)),c_List_Olexord(U_19434,U_19437))) ),
    inference(definitional_conversion,[status(esa)],[f_4633_2]) ).

cnf(f_4633_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19434),tc_List_Olist(U_19434))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19434),tc_List_Olist(U_19434)),hAPP(hAPP(c_List_Oappend(U_19434),U_19438),U_19435)),hAPP(hAPP(c_List_Oappend(U_19434),U_19438),U_19436))),c_List_Olexord(U_19434,U_19437)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19434),tc_List_Olist(U_19434))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19434),tc_List_Olist(U_19434)),U_19435),U_19436)),c_List_Olexord(U_19434,U_19437))) ),
    inference(clausify,[status(thm)],[f_4633_3]) ).

fof(f_4634_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_4634_2,plain,
    ! [U_19441,U_19440,U_19439] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_19439),hAPP(hAPP(c_List_Oappend(U_19439),U_19440),U_19441)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19439,tc_HOL_Obool)),hAPP(c_List_Oset(U_19439),U_19440)),hAPP(c_List_Oset(U_19439),U_19441)) != c_Orderings_Obot__class_Obot(tc_fun(U_19439,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19439),U_19441))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19439),U_19440)) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19439,tc_HOL_Obool)),hAPP(c_List_Oset(U_19439),U_19440)),hAPP(c_List_Oset(U_19439),U_19441)) = c_Orderings_Obot__class_Obot(tc_fun(U_19439,tc_HOL_Obool))
          & hBOOL(hAPP(c_List_Odistinct(U_19439),U_19441))
          & hBOOL(hAPP(c_List_Odistinct(U_19439),U_19440)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19439),hAPP(hAPP(c_List_Oappend(U_19439),U_19440),U_19441))) ) ),
    inference(variable_rename,[status(thm)],[f_4634_1]) ).

fof(f_4634_3,plain,
    ( ! [U_19447,U_19445,U_19443] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19443),hAPP(hAPP(c_List_Oappend(U_19443),U_19445),U_19447)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19443,tc_HOL_Obool)),hAPP(c_List_Oset(U_19443),U_19445)),hAPP(c_List_Oset(U_19443),U_19447)) != c_Orderings_Obot__class_Obot(tc_fun(U_19443,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19443),U_19447))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19443),U_19445)) )
    & ! [U_19446,U_19444,U_19442] :
        ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19442,tc_HOL_Obool)),hAPP(c_List_Oset(U_19442),U_19444)),hAPP(c_List_Oset(U_19442),U_19446)) = c_Orderings_Obot__class_Obot(tc_fun(U_19442,tc_HOL_Obool))
          & hBOOL(hAPP(c_List_Odistinct(U_19442),U_19446))
          & hBOOL(hAPP(c_List_Odistinct(U_19442),U_19444)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19442),hAPP(hAPP(c_List_Oappend(U_19442),U_19444),U_19446))) ) ),
    inference(miniscope,[status(thm)],[f_4634_2]) ).

fof(f_4634_4,plain,
    ( ! [U_19444,U_19442,U_19446] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19442,tc_HOL_Obool)),hAPP(c_List_Oset(U_19442),U_19444)),hAPP(c_List_Oset(U_19442),U_19446)) = c_Orderings_Obot__class_Obot(tc_fun(U_19442,tc_HOL_Obool))
        | ~ sP1185(U_19444,U_19442,U_19446) )
    & ! [U_19444,U_19442,U_19446] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19442),U_19446))
        | ~ sP1185(U_19444,U_19442,U_19446) )
    & ! [U_19444,U_19442,U_19446] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19442),U_19444))
        | ~ sP1185(U_19444,U_19442,U_19446) )
    & ! [U_19443,U_19445,U_19447] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19443),hAPP(hAPP(c_List_Oappend(U_19443),U_19445),U_19447)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19443,tc_HOL_Obool)),hAPP(c_List_Oset(U_19443),U_19445)),hAPP(c_List_Oset(U_19443),U_19447)) != c_Orderings_Obot__class_Obot(tc_fun(U_19443,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19443),U_19447))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19443),U_19445)) )
    & ! [U_19444,U_19442,U_19446] :
        ( sP1185(U_19444,U_19442,U_19446)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19442),hAPP(hAPP(c_List_Oappend(U_19442),U_19444),U_19446))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1185])],[f_4634_3]) ).

cnf(f_4634_5,plain,
    ( sP1185(U_19444,U_19442,U_19446)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19442),hAPP(hAPP(c_List_Oappend(U_19442),U_19444),U_19446))) ),
    inference(clausify,[status(thm)],[f_4634_4]) ).

cnf(f_4634_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19443),hAPP(hAPP(c_List_Oappend(U_19443),U_19445),U_19447)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19443,tc_HOL_Obool)),hAPP(c_List_Oset(U_19443),U_19445)),hAPP(c_List_Oset(U_19443),U_19447)) != c_Orderings_Obot__class_Obot(tc_fun(U_19443,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19443),U_19447))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19443),U_19445)) ),
    inference(clausify,[status(thm)],[f_4634_4]) ).

cnf(f_4634_7,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19442),U_19444))
    | ~ sP1185(U_19444,U_19442,U_19446) ),
    inference(clausify,[status(thm)],[f_4634_4]) ).

cnf(f_4634_8,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19442),U_19446))
    | ~ sP1185(U_19444,U_19442,U_19446) ),
    inference(clausify,[status(thm)],[f_4634_4]) ).

cnf(f_4634_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19442,tc_HOL_Obool)),hAPP(c_List_Oset(U_19442),U_19444)),hAPP(c_List_Oset(U_19442),U_19446)) = c_Orderings_Obot__class_Obot(tc_fun(U_19442,tc_HOL_Obool))
    | ~ sP1185(U_19444,U_19442,U_19446) ),
    inference(clausify,[status(thm)],[f_4634_4]) ).

fof(f_4635_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_4635_2,plain,
    ! [U_19451,U_19450,U_19449,U_19448] :
      ( ( hAPP(hAPP(c_List_Onth(U_19449),hAPP(hAPP(c_List_Oappend(U_19449),U_19450),U_19451)),U_19448) = hAPP(hAPP(c_List_Onth(U_19449),U_19451),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19448),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19449)),U_19450)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19448),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19449)),U_19450))) )
      & ( hAPP(hAPP(c_List_Onth(U_19449),hAPP(hAPP(c_List_Oappend(U_19449),U_19450),U_19451)),U_19448) = hAPP(hAPP(c_List_Onth(U_19449),U_19450),U_19448)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19448),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19449)),U_19450))) ) ),
    inference(variable_rename,[status(thm)],[f_4635_1]) ).

fof(f_4635_3,plain,
    ( ! [U_19459,U_19457,U_19455,U_19453] :
        ( hAPP(hAPP(c_List_Onth(U_19455),hAPP(hAPP(c_List_Oappend(U_19455),U_19457),U_19459)),U_19453) = hAPP(hAPP(c_List_Onth(U_19455),U_19459),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19453),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19455)),U_19457)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19453),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19455)),U_19457))) )
    & ! [U_19458,U_19456,U_19454,U_19452] :
        ( hAPP(hAPP(c_List_Onth(U_19454),hAPP(hAPP(c_List_Oappend(U_19454),U_19456),U_19458)),U_19452) = hAPP(hAPP(c_List_Onth(U_19454),U_19456),U_19452)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19452),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19454)),U_19456))) ) ),
    inference(miniscope,[status(thm)],[f_4635_2]) ).

fof(f_4635_4,plain,
    ( ! [U_19453,U_19455,U_19457,U_19459] :
        ( hAPP(hAPP(c_List_Onth(U_19455),hAPP(hAPP(c_List_Oappend(U_19455),U_19457),U_19459)),U_19453) = hAPP(hAPP(c_List_Onth(U_19455),U_19459),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19453),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19455)),U_19457)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19453),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19455)),U_19457))) )
    & ! [U_19458,U_19454,U_19452,U_19456] :
        ( hAPP(hAPP(c_List_Onth(U_19454),hAPP(hAPP(c_List_Oappend(U_19454),U_19456),U_19458)),U_19452) = hAPP(hAPP(c_List_Onth(U_19454),U_19456),U_19452)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19452),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19454)),U_19456))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4635_3]) ).

cnf(f_4635_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_19454),hAPP(hAPP(c_List_Oappend(U_19454),U_19456),U_19458)),U_19452) = hAPP(hAPP(c_List_Onth(U_19454),U_19456),U_19452)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19452),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19454)),U_19456))) ),
    inference(clausify,[status(thm)],[f_4635_4]) ).

cnf(f_4635_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_19455),hAPP(hAPP(c_List_Oappend(U_19455),U_19457),U_19459)),U_19453) = hAPP(hAPP(c_List_Onth(U_19455),U_19459),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19453),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19455)),U_19457)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19453),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19455)),U_19457))) ),
    inference(clausify,[status(thm)],[f_4635_4]) ).

fof(f_4636_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_4636_2,plain,
    ! [U_19464,U_19463,U_19462,U_19461,U_19460] :
      ( ( hAPP(hAPP(c_List_Olist__update(U_19461,hAPP(hAPP(c_List_Oappend(U_19461),U_19462),U_19463)),U_19460),U_19464) = hAPP(hAPP(c_List_Oappend(U_19461),U_19462),hAPP(hAPP(c_List_Olist__update(U_19461,U_19463),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19460),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19461)),U_19462))),U_19464))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19460),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19461)),U_19462))) )
      & ( hAPP(hAPP(c_List_Olist__update(U_19461,hAPP(hAPP(c_List_Oappend(U_19461),U_19462),U_19463)),U_19460),U_19464) = hAPP(hAPP(c_List_Oappend(U_19461),hAPP(hAPP(c_List_Olist__update(U_19461,U_19462),U_19460),U_19464)),U_19463)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19460),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19461)),U_19462))) ) ),
    inference(variable_rename,[status(thm)],[f_4636_1]) ).

fof(f_4636_3,plain,
    ( ! [U_19474,U_19472,U_19470,U_19468,U_19466] :
        ( hAPP(hAPP(c_List_Olist__update(U_19468,hAPP(hAPP(c_List_Oappend(U_19468),U_19470),U_19472)),U_19466),U_19474) = hAPP(hAPP(c_List_Oappend(U_19468),U_19470),hAPP(hAPP(c_List_Olist__update(U_19468,U_19472),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19466),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19468)),U_19470))),U_19474))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19466),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19468)),U_19470))) )
    & ! [U_19473,U_19471,U_19469,U_19467,U_19465] :
        ( hAPP(hAPP(c_List_Olist__update(U_19467,hAPP(hAPP(c_List_Oappend(U_19467),U_19469),U_19471)),U_19465),U_19473) = hAPP(hAPP(c_List_Oappend(U_19467),hAPP(hAPP(c_List_Olist__update(U_19467,U_19469),U_19465),U_19473)),U_19471)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19465),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19467)),U_19469))) ) ),
    inference(miniscope,[status(thm)],[f_4636_2]) ).

fof(f_4636_4,plain,
    ( ! [U_19466,U_19468,U_19470,U_19472,U_19474] :
        ( hAPP(hAPP(c_List_Olist__update(U_19468,hAPP(hAPP(c_List_Oappend(U_19468),U_19470),U_19472)),U_19466),U_19474) = hAPP(hAPP(c_List_Oappend(U_19468),U_19470),hAPP(hAPP(c_List_Olist__update(U_19468,U_19472),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19466),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19468)),U_19470))),U_19474))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19466),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19468)),U_19470))) )
    & ! [U_19467,U_19471,U_19465,U_19469,U_19473] :
        ( hAPP(hAPP(c_List_Olist__update(U_19467,hAPP(hAPP(c_List_Oappend(U_19467),U_19469),U_19471)),U_19465),U_19473) = hAPP(hAPP(c_List_Oappend(U_19467),hAPP(hAPP(c_List_Olist__update(U_19467,U_19469),U_19465),U_19473)),U_19471)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19465),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19467)),U_19469))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4636_3]) ).

cnf(f_4636_5,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_19467,hAPP(hAPP(c_List_Oappend(U_19467),U_19469),U_19471)),U_19465),U_19473) = hAPP(hAPP(c_List_Oappend(U_19467),hAPP(hAPP(c_List_Olist__update(U_19467,U_19469),U_19465),U_19473)),U_19471)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19465),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19467)),U_19469))) ),
    inference(clausify,[status(thm)],[f_4636_4]) ).

cnf(f_4636_6,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_19468,hAPP(hAPP(c_List_Oappend(U_19468),U_19470),U_19472)),U_19466),U_19474) = hAPP(hAPP(c_List_Oappend(U_19468),U_19470),hAPP(hAPP(c_List_Olist__update(U_19468,U_19472),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19466),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19468)),U_19470))),U_19474))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19466),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19468)),U_19470))) ),
    inference(clausify,[status(thm)],[f_4636_4]) ).

fof(f_4637_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_4637_2,plain,
    ! [U_19478,U_19477,U_19476,U_19475] : c_List_Osublist(U_19475,hAPP(hAPP(c_List_Oappend(U_19475),U_19476),U_19477),U_19478) = hAPP(hAPP(c_List_Oappend(U_19475),c_List_Osublist(U_19475,U_19476,U_19478)),c_List_Osublist(U_19475,U_19477,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_19475)),U_19476)))),U_19478)))),
    inference(variable_rename,[status(thm)],[f_4637_1]) ).

fof(f_4637_3,plain,
    ! [U_19475,U_19476,U_19477,U_19478] : c_List_Osublist(U_19475,hAPP(hAPP(c_List_Oappend(U_19475),U_19476),U_19477),U_19478) = hAPP(hAPP(c_List_Oappend(U_19475),c_List_Osublist(U_19475,U_19476,U_19478)),c_List_Osublist(U_19475,U_19477,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_19475)),U_19476)))),U_19478)))),
    inference(definitional_conversion,[status(esa)],[f_4637_2]) ).

cnf(f_4637_4,plain,
    c_List_Osublist(U_19475,hAPP(hAPP(c_List_Oappend(U_19475),U_19476),U_19477),U_19478) = hAPP(hAPP(c_List_Oappend(U_19475),c_List_Osublist(U_19475,U_19476,U_19478)),c_List_Osublist(U_19475,U_19477,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_19475)),U_19476)))),U_19478)))),
    inference(clausify,[status(thm)],[f_4637_3]) ).

fof(f_4638_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_4638_2,plain,
    ! [U_19485,U_19484,U_19483,U_19482,U_19481,U_19480,U_19479] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19479),tc_List_Olist(U_19479))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19479),tc_List_Olist(U_19479)),hAPP(hAPP(c_List_Oappend(U_19479),U_19483),hAPP(hAPP(c_List_Olist_OCons(U_19479),U_19480),U_19484))),hAPP(hAPP(c_List_Oappend(U_19479),U_19483),hAPP(hAPP(c_List_Olist_OCons(U_19479),U_19481),U_19485)))),c_List_Olexord(U_19479,U_19482)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19479,U_19479)),hAPP(hAPP(c_Product__Type_OPair(U_19479,U_19479),U_19480),U_19481)),U_19482)) ),
    inference(variable_rename,[status(thm)],[f_4638_1]) ).

fof(f_4638_3,plain,
    ! [U_19479,U_19480,U_19481,U_19482,U_19483,U_19484,U_19485] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19479),tc_List_Olist(U_19479))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19479),tc_List_Olist(U_19479)),hAPP(hAPP(c_List_Oappend(U_19479),U_19483),hAPP(hAPP(c_List_Olist_OCons(U_19479),U_19480),U_19484))),hAPP(hAPP(c_List_Oappend(U_19479),U_19483),hAPP(hAPP(c_List_Olist_OCons(U_19479),U_19481),U_19485)))),c_List_Olexord(U_19479,U_19482)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19479,U_19479)),hAPP(hAPP(c_Product__Type_OPair(U_19479,U_19479),U_19480),U_19481)),U_19482)) ),
    inference(definitional_conversion,[status(esa)],[f_4638_2]) ).

cnf(f_4638_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19479),tc_List_Olist(U_19479))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19479),tc_List_Olist(U_19479)),hAPP(hAPP(c_List_Oappend(U_19479),U_19483),hAPP(hAPP(c_List_Olist_OCons(U_19479),U_19480),U_19484))),hAPP(hAPP(c_List_Oappend(U_19479),U_19483),hAPP(hAPP(c_List_Olist_OCons(U_19479),U_19481),U_19485)))),c_List_Olexord(U_19479,U_19482)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19479,U_19479)),hAPP(hAPP(c_Product__Type_OPair(U_19479,U_19479),U_19480),U_19481)),U_19482)) ),
    inference(clausify,[status(thm)],[f_4638_3]) ).

fof(f_4639_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_4639_2,plain,
    ! [U_19488,U_19487,U_19486] :
      ( hAPP(hAPP(c_List_Otake(U_19487),hAPP(c_Nat_OSuc,U_19486)),U_19488) = hAPP(hAPP(c_List_Oappend(U_19487),hAPP(hAPP(c_List_Otake(U_19487),U_19486),U_19488)),hAPP(hAPP(c_List_Olist_OCons(U_19487),hAPP(hAPP(c_List_Onth(U_19487),U_19488),U_19486)),c_List_Olist_ONil(U_19487)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19486),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19487)),U_19488))) ),
    inference(variable_rename,[status(thm)],[f_4639_1]) ).

fof(f_4639_3,plain,
    ! [U_19488,U_19486,U_19487] :
      ( hAPP(hAPP(c_List_Otake(U_19487),hAPP(c_Nat_OSuc,U_19486)),U_19488) = hAPP(hAPP(c_List_Oappend(U_19487),hAPP(hAPP(c_List_Otake(U_19487),U_19486),U_19488)),hAPP(hAPP(c_List_Olist_OCons(U_19487),hAPP(hAPP(c_List_Onth(U_19487),U_19488),U_19486)),c_List_Olist_ONil(U_19487)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19486),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19487)),U_19488))) ),
    inference(definitional_conversion,[status(esa)],[f_4639_2]) ).

cnf(f_4639_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_19487),hAPP(c_Nat_OSuc,U_19486)),U_19488) = hAPP(hAPP(c_List_Oappend(U_19487),hAPP(hAPP(c_List_Otake(U_19487),U_19486),U_19488)),hAPP(hAPP(c_List_Olist_OCons(U_19487),hAPP(hAPP(c_List_Onth(U_19487),U_19488),U_19486)),c_List_Olist_ONil(U_19487)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19486),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19487)),U_19488))) ),
    inference(clausify,[status(thm)],[f_4639_3]) ).

fof(f_4640_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_4640_2,plain,
    ! [U_19494,U_19493,U_19492,U_19491,U_19490,U_19489] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19489),tc_List_Olist(U_19489))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19489),tc_List_Olist(U_19489)),hAPP(hAPP(c_List_Oappend(U_19489),U_19490),hAPP(hAPP(c_List_Olist_OCons(U_19489),U_19491),c_List_Olist_ONil(U_19489)))),hAPP(hAPP(c_List_Oappend(U_19489),U_19492),hAPP(hAPP(c_List_Olist_OCons(U_19489),U_19493),c_List_Olist_ONil(U_19489))))),c_List_Olistrel1(U_19489,U_19494)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19489,U_19489)),hAPP(hAPP(c_Product__Type_OPair(U_19489,U_19489),U_19491),U_19493)),U_19494))
            | U_19490 != U_19492 )
          & ( U_19491 != U_19493
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19489),tc_List_Olist(U_19489))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19489),tc_List_Olist(U_19489)),U_19490),U_19492)),c_List_Olistrel1(U_19489,U_19494))) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19489,U_19489)),hAPP(hAPP(c_Product__Type_OPair(U_19489,U_19489),U_19491),U_19493)),U_19494))
          & U_19490 = U_19492 )
        | ( U_19491 = U_19493
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19489),tc_List_Olist(U_19489))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19489),tc_List_Olist(U_19489)),U_19490),U_19492)),c_List_Olistrel1(U_19489,U_19494))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19489),tc_List_Olist(U_19489))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19489),tc_List_Olist(U_19489)),hAPP(hAPP(c_List_Oappend(U_19489),U_19490),hAPP(hAPP(c_List_Olist_OCons(U_19489),U_19491),c_List_Olist_ONil(U_19489)))),hAPP(hAPP(c_List_Oappend(U_19489),U_19492),hAPP(hAPP(c_List_Olist_OCons(U_19489),U_19493),c_List_Olist_ONil(U_19489))))),c_List_Olistrel1(U_19489,U_19494))) ) ),
    inference(variable_rename,[status(thm)],[f_4640_1]) ).

fof(f_4640_3,plain,
    ( ! [U_19506,U_19504,U_19502,U_19500,U_19498,U_19496] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19496),tc_List_Olist(U_19496))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19496),tc_List_Olist(U_19496)),hAPP(hAPP(c_List_Oappend(U_19496),U_19498),hAPP(hAPP(c_List_Olist_OCons(U_19496),U_19500),c_List_Olist_ONil(U_19496)))),hAPP(hAPP(c_List_Oappend(U_19496),U_19502),hAPP(hAPP(c_List_Olist_OCons(U_19496),U_19504),c_List_Olist_ONil(U_19496))))),c_List_Olistrel1(U_19496,U_19506)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19496,U_19496)),hAPP(hAPP(c_Product__Type_OPair(U_19496,U_19496),U_19500),U_19504)),U_19506))
            | U_19498 != U_19502 )
          & ( U_19500 != U_19504
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19496),tc_List_Olist(U_19496))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19496),tc_List_Olist(U_19496)),U_19498),U_19502)),c_List_Olistrel1(U_19496,U_19506))) ) ) )
    & ! [U_19505,U_19503,U_19501,U_19499,U_19497,U_19495] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19495,U_19495)),hAPP(hAPP(c_Product__Type_OPair(U_19495,U_19495),U_19499),U_19503)),U_19505))
          & U_19497 = U_19501 )
        | ( U_19499 = U_19503
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19495),tc_List_Olist(U_19495))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19495),tc_List_Olist(U_19495)),U_19497),U_19501)),c_List_Olistrel1(U_19495,U_19505))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19495),tc_List_Olist(U_19495))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19495),tc_List_Olist(U_19495)),hAPP(hAPP(c_List_Oappend(U_19495),U_19497),hAPP(hAPP(c_List_Olist_OCons(U_19495),U_19499),c_List_Olist_ONil(U_19495)))),hAPP(hAPP(c_List_Oappend(U_19495),U_19501),hAPP(hAPP(c_List_Olist_OCons(U_19495),U_19503),c_List_Olist_ONil(U_19495))))),c_List_Olistrel1(U_19495,U_19505))) ) ),
    inference(miniscope,[status(thm)],[f_4640_2]) ).

fof(f_4640_4,plain,
    ( ! [U_19496,U_19504,U_19498,U_19500,U_19502,U_19506] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19496,U_19496)),hAPP(hAPP(c_Product__Type_OPair(U_19496,U_19496),U_19500),U_19504)),U_19506))
        | U_19498 != U_19502
        | ~ sP1188(U_19496,U_19504,U_19498,U_19500,U_19502,U_19506) )
    & ! [U_19496,U_19504,U_19498,U_19500,U_19502,U_19506] :
        ( U_19500 != U_19504
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19496),tc_List_Olist(U_19496))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19496),tc_List_Olist(U_19496)),U_19498),U_19502)),c_List_Olistrel1(U_19496,U_19506)))
        | ~ sP1188(U_19496,U_19504,U_19498,U_19500,U_19502,U_19506) )
    & ! [U_19495,U_19503,U_19505,U_19497,U_19499,U_19501] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19495,U_19495)),hAPP(hAPP(c_Product__Type_OPair(U_19495,U_19495),U_19499),U_19503)),U_19505))
        | ~ sP1187(U_19495,U_19503,U_19505,U_19497,U_19499,U_19501) )
    & ! [U_19495,U_19503,U_19505,U_19497,U_19499,U_19501] :
        ( U_19497 = U_19501
        | ~ sP1187(U_19495,U_19503,U_19505,U_19497,U_19499,U_19501) )
    & ! [U_19495,U_19503,U_19505,U_19497,U_19499,U_19501] :
        ( U_19499 = U_19503
        | ~ sP1186(U_19495,U_19503,U_19505,U_19497,U_19499,U_19501) )
    & ! [U_19495,U_19503,U_19505,U_19497,U_19499,U_19501] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19495),tc_List_Olist(U_19495))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19495),tc_List_Olist(U_19495)),U_19497),U_19501)),c_List_Olistrel1(U_19495,U_19505)))
        | ~ sP1186(U_19495,U_19503,U_19505,U_19497,U_19499,U_19501) )
    & ! [U_19496,U_19504,U_19498,U_19500,U_19502,U_19506] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19496),tc_List_Olist(U_19496))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19496),tc_List_Olist(U_19496)),hAPP(hAPP(c_List_Oappend(U_19496),U_19498),hAPP(hAPP(c_List_Olist_OCons(U_19496),U_19500),c_List_Olist_ONil(U_19496)))),hAPP(hAPP(c_List_Oappend(U_19496),U_19502),hAPP(hAPP(c_List_Olist_OCons(U_19496),U_19504),c_List_Olist_ONil(U_19496))))),c_List_Olistrel1(U_19496,U_19506)))
        | sP1188(U_19496,U_19504,U_19498,U_19500,U_19502,U_19506) )
    & ! [U_19495,U_19503,U_19505,U_19497,U_19499,U_19501] :
        ( sP1187(U_19495,U_19503,U_19505,U_19497,U_19499,U_19501)
        | sP1186(U_19495,U_19503,U_19505,U_19497,U_19499,U_19501)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19495),tc_List_Olist(U_19495))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19495),tc_List_Olist(U_19495)),hAPP(hAPP(c_List_Oappend(U_19495),U_19497),hAPP(hAPP(c_List_Olist_OCons(U_19495),U_19499),c_List_Olist_ONil(U_19495)))),hAPP(hAPP(c_List_Oappend(U_19495),U_19501),hAPP(hAPP(c_List_Olist_OCons(U_19495),U_19503),c_List_Olist_ONil(U_19495))))),c_List_Olistrel1(U_19495,U_19505))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1186,sP1187,sP1188])],[f_4640_3]) ).

cnf(f_4640_5,plain,
    ( sP1187(U_19495,U_19503,U_19505,U_19497,U_19499,U_19501)
    | sP1186(U_19495,U_19503,U_19505,U_19497,U_19499,U_19501)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19495),tc_List_Olist(U_19495))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19495),tc_List_Olist(U_19495)),hAPP(hAPP(c_List_Oappend(U_19495),U_19497),hAPP(hAPP(c_List_Olist_OCons(U_19495),U_19499),c_List_Olist_ONil(U_19495)))),hAPP(hAPP(c_List_Oappend(U_19495),U_19501),hAPP(hAPP(c_List_Olist_OCons(U_19495),U_19503),c_List_Olist_ONil(U_19495))))),c_List_Olistrel1(U_19495,U_19505))) ),
    inference(clausify,[status(thm)],[f_4640_4]) ).

cnf(f_4640_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19496),tc_List_Olist(U_19496))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19496),tc_List_Olist(U_19496)),hAPP(hAPP(c_List_Oappend(U_19496),U_19498),hAPP(hAPP(c_List_Olist_OCons(U_19496),U_19500),c_List_Olist_ONil(U_19496)))),hAPP(hAPP(c_List_Oappend(U_19496),U_19502),hAPP(hAPP(c_List_Olist_OCons(U_19496),U_19504),c_List_Olist_ONil(U_19496))))),c_List_Olistrel1(U_19496,U_19506)))
    | sP1188(U_19496,U_19504,U_19498,U_19500,U_19502,U_19506) ),
    inference(clausify,[status(thm)],[f_4640_4]) ).

cnf(f_4640_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19495),tc_List_Olist(U_19495))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19495),tc_List_Olist(U_19495)),U_19497),U_19501)),c_List_Olistrel1(U_19495,U_19505)))
    | ~ sP1186(U_19495,U_19503,U_19505,U_19497,U_19499,U_19501) ),
    inference(clausify,[status(thm)],[f_4640_4]) ).

cnf(f_4640_8,plain,
    ( U_19499 = U_19503
    | ~ sP1186(U_19495,U_19503,U_19505,U_19497,U_19499,U_19501) ),
    inference(clausify,[status(thm)],[f_4640_4]) ).

cnf(f_4640_9,plain,
    ( U_19497 = U_19501
    | ~ sP1187(U_19495,U_19503,U_19505,U_19497,U_19499,U_19501) ),
    inference(clausify,[status(thm)],[f_4640_4]) ).

cnf(f_4640_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19495,U_19495)),hAPP(hAPP(c_Product__Type_OPair(U_19495,U_19495),U_19499),U_19503)),U_19505))
    | ~ sP1187(U_19495,U_19503,U_19505,U_19497,U_19499,U_19501) ),
    inference(clausify,[status(thm)],[f_4640_4]) ).

cnf(f_4640_11,plain,
    ( U_19500 != U_19504
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19496),tc_List_Olist(U_19496))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19496),tc_List_Olist(U_19496)),U_19498),U_19502)),c_List_Olistrel1(U_19496,U_19506)))
    | ~ sP1188(U_19496,U_19504,U_19498,U_19500,U_19502,U_19506) ),
    inference(clausify,[status(thm)],[f_4640_4]) ).

cnf(f_4640_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19496,U_19496)),hAPP(hAPP(c_Product__Type_OPair(U_19496,U_19496),U_19500),U_19504)),U_19506))
    | U_19498 != U_19502
    | ~ sP1188(U_19496,U_19504,U_19498,U_19500,U_19502,U_19506) ),
    inference(clausify,[status(thm)],[f_4640_4]) ).

fof(f_4641_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_4641_2,plain,
    ! [U_19512,U_19511,U_19510,U_19509,U_19508] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19508),tc_List_Olist(U_19508))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19508),tc_List_Olist(U_19508)),U_19510),U_19511)),c_List_Olexord(U_19508,U_19512)))
      | ? [U_19507] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_19508,U_19508)),hAPP(hAPP(c_Product__Type_OPair(U_19508,U_19508),U_19507),U_19507)),U_19512))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19508),tc_List_Olist(U_19508))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19508),tc_List_Olist(U_19508)),hAPP(hAPP(c_List_Oappend(U_19508),U_19509),U_19510)),hAPP(hAPP(c_List_Oappend(U_19508),U_19509),U_19511))),c_List_Olexord(U_19508,U_19512))) ),
    inference(variable_rename,[status(thm)],[f_4641_1]) ).

fof(f_4641_3,plain,
    ! [U_19512,U_19511,U_19510,U_19509,U_19508] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19508),tc_List_Olist(U_19508))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19508),tc_List_Olist(U_19508)),U_19510),U_19511)),c_List_Olexord(U_19508,U_19512)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_19508,U_19508)),hAPP(hAPP(c_Product__Type_OPair(U_19508,U_19508),sK480(U_19512,U_19511,U_19510,U_19509,U_19508)),sK480(U_19512,U_19511,U_19510,U_19509,U_19508))),U_19512))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19508),tc_List_Olist(U_19508))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19508),tc_List_Olist(U_19508)),hAPP(hAPP(c_List_Oappend(U_19508),U_19509),U_19510)),hAPP(hAPP(c_List_Oappend(U_19508),U_19509),U_19511))),c_List_Olexord(U_19508,U_19512))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK480]),skolemize(U_19507,sK480(U_19512,U_19511,U_19510,U_19509,U_19508))],[f_4641_2]) ).

fof(f_4641_4,plain,
    ! [U_19510,U_19509,U_19508,U_19511,U_19512] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19508),tc_List_Olist(U_19508))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19508),tc_List_Olist(U_19508)),U_19510),U_19511)),c_List_Olexord(U_19508,U_19512)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_19508,U_19508)),hAPP(hAPP(c_Product__Type_OPair(U_19508,U_19508),sK480(U_19512,U_19511,U_19510,U_19509,U_19508)),sK480(U_19512,U_19511,U_19510,U_19509,U_19508))),U_19512))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19508),tc_List_Olist(U_19508))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19508),tc_List_Olist(U_19508)),hAPP(hAPP(c_List_Oappend(U_19508),U_19509),U_19510)),hAPP(hAPP(c_List_Oappend(U_19508),U_19509),U_19511))),c_List_Olexord(U_19508,U_19512))) ),
    inference(definitional_conversion,[status(esa)],[f_4641_3]) ).

cnf(f_4641_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19508),tc_List_Olist(U_19508))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19508),tc_List_Olist(U_19508)),U_19510),U_19511)),c_List_Olexord(U_19508,U_19512)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_19508,U_19508)),hAPP(hAPP(c_Product__Type_OPair(U_19508,U_19508),sK480(U_19512,U_19511,U_19510,U_19509,U_19508)),sK480(U_19512,U_19511,U_19510,U_19509,U_19508))),U_19512))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19508),tc_List_Olist(U_19508))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19508),tc_List_Olist(U_19508)),hAPP(hAPP(c_List_Oappend(U_19508),U_19509),U_19510)),hAPP(hAPP(c_List_Oappend(U_19508),U_19509),U_19511))),c_List_Olexord(U_19508,U_19512))) ),
    inference(clausify,[status(thm)],[f_4641_4]) ).

fof(f_4642_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_4642_2,plain,
    ! [U_19516,U_19515,U_19514,U_19513] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19513)),hAPP(hAPP(c_List_Olist_OCons(U_19513),U_19514),U_19516)),c_Wellfounded_Oacc(tc_List_Olist(U_19513),c_List_Olistrel1(U_19513,U_19515))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19513)),U_19516),c_Wellfounded_Oacc(tc_List_Olist(U_19513),c_List_Olistrel1(U_19513,U_19515))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19513),U_19514),c_Wellfounded_Oacc(U_19513,U_19515))) ),
    inference(variable_rename,[status(thm)],[f_4642_1]) ).

fof(f_4642_3,plain,
    ! [U_19513,U_19514,U_19515,U_19516] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19513)),hAPP(hAPP(c_List_Olist_OCons(U_19513),U_19514),U_19516)),c_Wellfounded_Oacc(tc_List_Olist(U_19513),c_List_Olistrel1(U_19513,U_19515))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19513)),U_19516),c_Wellfounded_Oacc(tc_List_Olist(U_19513),c_List_Olistrel1(U_19513,U_19515))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19513),U_19514),c_Wellfounded_Oacc(U_19513,U_19515))) ),
    inference(definitional_conversion,[status(esa)],[f_4642_2]) ).

cnf(f_4642_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19513)),hAPP(hAPP(c_List_Olist_OCons(U_19513),U_19514),U_19516)),c_Wellfounded_Oacc(tc_List_Olist(U_19513),c_List_Olistrel1(U_19513,U_19515))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19513)),U_19516),c_Wellfounded_Oacc(tc_List_Olist(U_19513),c_List_Olistrel1(U_19513,U_19515))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19513),U_19514),c_Wellfounded_Oacc(U_19513,U_19515))) ),
    inference(clausify,[status(thm)],[f_4642_3]) ).

fof(f_4643_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_4643_2,plain,
    ! [U_19519,U_19518,U_19517] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19517),tc_List_Olist(U_19517)),tc_HOL_Obool)),c_List_Olistrel1(U_19517,U_19518)),c_List_Olistrel1(U_19517,U_19519)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19517,U_19517),tc_HOL_Obool)),U_19518),U_19519)) ),
    inference(variable_rename,[status(thm)],[f_4643_1]) ).

fof(f_4643_3,plain,
    ! [U_19517,U_19518,U_19519] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19517),tc_List_Olist(U_19517)),tc_HOL_Obool)),c_List_Olistrel1(U_19517,U_19518)),c_List_Olistrel1(U_19517,U_19519)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19517,U_19517),tc_HOL_Obool)),U_19518),U_19519)) ),
    inference(definitional_conversion,[status(esa)],[f_4643_2]) ).

cnf(f_4643_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19517),tc_List_Olist(U_19517)),tc_HOL_Obool)),c_List_Olistrel1(U_19517,U_19518)),c_List_Olistrel1(U_19517,U_19519)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19517,U_19517),tc_HOL_Obool)),U_19518),U_19519)) ),
    inference(clausify,[status(thm)],[f_4643_3]) ).

fof(f_4644_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_4644_2,plain,
    ! [U_19521,U_19520] : c_List_Olistrel1(U_19520,hAPP(c_Relation_Oconverse(U_19520,U_19520),U_19521)) = hAPP(c_Relation_Oconverse(tc_List_Olist(U_19520),tc_List_Olist(U_19520)),c_List_Olistrel1(U_19520,U_19521)),
    inference(variable_rename,[status(thm)],[f_4644_1]) ).

fof(f_4644_3,plain,
    ! [U_19520,U_19521] : c_List_Olistrel1(U_19520,hAPP(c_Relation_Oconverse(U_19520,U_19520),U_19521)) = hAPP(c_Relation_Oconverse(tc_List_Olist(U_19520),tc_List_Olist(U_19520)),c_List_Olistrel1(U_19520,U_19521)),
    inference(definitional_conversion,[status(esa)],[f_4644_2]) ).

cnf(f_4644_4,plain,
    c_List_Olistrel1(U_19520,hAPP(c_Relation_Oconverse(U_19520,U_19520),U_19521)) = hAPP(c_Relation_Oconverse(tc_List_Olist(U_19520),tc_List_Olist(U_19520)),c_List_Olistrel1(U_19520,U_19521)),
    inference(clausify,[status(thm)],[f_4644_3]) ).

fof(f_4645_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_4645_2,plain,
    ! [U_19523,U_19522] : c_List_Olistrel(U_19522,c_Transitive__Closure_Ortrancl(U_19522,U_19523)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19522),c_List_Olistrel1(U_19522,U_19523)),
    inference(variable_rename,[status(thm)],[f_4645_1]) ).

fof(f_4645_3,plain,
    ! [U_19522,U_19523] : c_List_Olistrel(U_19522,c_Transitive__Closure_Ortrancl(U_19522,U_19523)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19522),c_List_Olistrel1(U_19522,U_19523)),
    inference(definitional_conversion,[status(esa)],[f_4645_2]) ).

cnf(f_4645_4,plain,
    c_List_Olistrel(U_19522,c_Transitive__Closure_Ortrancl(U_19522,U_19523)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19522),c_List_Olistrel1(U_19522,U_19523)),
    inference(clausify,[status(thm)],[f_4645_3]) ).

fof(f_4646_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_4646_2,plain,
    ! [U_19525,U_19524] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19524),tc_List_Olist(U_19524)),tc_HOL_Obool)),c_List_Olistrel1(U_19524,c_Transitive__Closure_Ortrancl(U_19524,U_19525))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19524),c_List_Olistrel1(U_19524,U_19525)))),
    inference(variable_rename,[status(thm)],[f_4646_1]) ).

fof(f_4646_3,plain,
    ! [U_19524,U_19525] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19524),tc_List_Olist(U_19524)),tc_HOL_Obool)),c_List_Olistrel1(U_19524,c_Transitive__Closure_Ortrancl(U_19524,U_19525))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19524),c_List_Olistrel1(U_19524,U_19525)))),
    inference(definitional_conversion,[status(esa)],[f_4646_2]) ).

cnf(f_4646_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19524),tc_List_Olist(U_19524)),tc_HOL_Obool)),c_List_Olistrel1(U_19524,c_Transitive__Closure_Ortrancl(U_19524,U_19525))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19524),c_List_Olistrel1(U_19524,U_19525)))),
    inference(clausify,[status(thm)],[f_4646_3]) ).

fof(f_4647_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_4647_2,plain,
    ! [U_19527,U_19526] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19526),tc_List_Olist(U_19526)),tc_HOL_Obool)),c_List_Olistrel(U_19526,U_19527)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19526),c_List_Olistrel1(U_19526,U_19527)))),
    inference(variable_rename,[status(thm)],[f_4647_1]) ).

fof(f_4647_3,plain,
    ! [U_19526,U_19527] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19526),tc_List_Olist(U_19526)),tc_HOL_Obool)),c_List_Olistrel(U_19526,U_19527)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19526),c_List_Olistrel1(U_19526,U_19527)))),
    inference(definitional_conversion,[status(esa)],[f_4647_2]) ).

cnf(f_4647_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19526),tc_List_Olist(U_19526)),tc_HOL_Obool)),c_List_Olistrel(U_19526,U_19527)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19526),c_List_Olistrel1(U_19526,U_19527)))),
    inference(clausify,[status(thm)],[f_4647_3]) ).

fof(f_4648_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_4648_2,plain,
    ! [U_19532,U_19531,U_19530,U_19529,U_19528] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19528),tc_List_Olist(U_19528))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19528),tc_List_Olist(U_19528)),hAPP(hAPP(c_List_Olist_OCons(U_19528),U_19532),U_19529)),hAPP(hAPP(c_List_Olist_OCons(U_19528),U_19532),U_19530))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19528),c_List_Olistrel1(U_19528,U_19531))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19528),tc_List_Olist(U_19528))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19528),tc_List_Olist(U_19528)),U_19529),U_19530)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19528),c_List_Olistrel1(U_19528,U_19531)))) ),
    inference(variable_rename,[status(thm)],[f_4648_1]) ).

fof(f_4648_3,plain,
    ! [U_19528,U_19529,U_19530,U_19531,U_19532] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19528),tc_List_Olist(U_19528))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19528),tc_List_Olist(U_19528)),hAPP(hAPP(c_List_Olist_OCons(U_19528),U_19532),U_19529)),hAPP(hAPP(c_List_Olist_OCons(U_19528),U_19532),U_19530))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19528),c_List_Olistrel1(U_19528,U_19531))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19528),tc_List_Olist(U_19528))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19528),tc_List_Olist(U_19528)),U_19529),U_19530)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19528),c_List_Olistrel1(U_19528,U_19531)))) ),
    inference(definitional_conversion,[status(esa)],[f_4648_2]) ).

cnf(f_4648_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19528),tc_List_Olist(U_19528))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19528),tc_List_Olist(U_19528)),hAPP(hAPP(c_List_Olist_OCons(U_19528),U_19532),U_19529)),hAPP(hAPP(c_List_Olist_OCons(U_19528),U_19532),U_19530))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19528),c_List_Olistrel1(U_19528,U_19531))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19528),tc_List_Olist(U_19528))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19528),tc_List_Olist(U_19528)),U_19529),U_19530)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19528),c_List_Olistrel1(U_19528,U_19531)))) ),
    inference(clausify,[status(thm)],[f_4648_3]) ).

fof(f_4649_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_4649_2,plain,
    ! [U_19537,U_19536,U_19535,U_19534,U_19533] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19533),tc_List_Olist(U_19533))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19533),tc_List_Olist(U_19533)),hAPP(hAPP(c_List_Olist_OCons(U_19533),U_19537),U_19534)),hAPP(hAPP(c_List_Olist_OCons(U_19533),U_19537),U_19535))),c_List_Olistrel1(U_19533,U_19536)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19533),tc_List_Olist(U_19533))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19533),tc_List_Olist(U_19533)),U_19534),U_19535)),c_List_Olistrel1(U_19533,U_19536))) ),
    inference(variable_rename,[status(thm)],[f_4649_1]) ).

fof(f_4649_3,plain,
    ! [U_19533,U_19534,U_19535,U_19536,U_19537] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19533),tc_List_Olist(U_19533))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19533),tc_List_Olist(U_19533)),hAPP(hAPP(c_List_Olist_OCons(U_19533),U_19537),U_19534)),hAPP(hAPP(c_List_Olist_OCons(U_19533),U_19537),U_19535))),c_List_Olistrel1(U_19533,U_19536)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19533),tc_List_Olist(U_19533))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19533),tc_List_Olist(U_19533)),U_19534),U_19535)),c_List_Olistrel1(U_19533,U_19536))) ),
    inference(definitional_conversion,[status(esa)],[f_4649_2]) ).

cnf(f_4649_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19533),tc_List_Olist(U_19533))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19533),tc_List_Olist(U_19533)),hAPP(hAPP(c_List_Olist_OCons(U_19533),U_19537),U_19534)),hAPP(hAPP(c_List_Olist_OCons(U_19533),U_19537),U_19535))),c_List_Olistrel1(U_19533,U_19536)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19533),tc_List_Olist(U_19533))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19533),tc_List_Olist(U_19533)),U_19534),U_19535)),c_List_Olistrel1(U_19533,U_19536))) ),
    inference(clausify,[status(thm)],[f_4649_3]) ).

fof(f_4650_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_4650_2,plain,
    ! [U_19541,U_19540,U_19539,U_19538] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19538)),U_19539) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19538)),U_19540)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19538),tc_List_Olist(U_19538))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19538),tc_List_Olist(U_19538)),U_19539),U_19540)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19538),c_List_Olistrel1(U_19538,U_19541)))) ),
    inference(variable_rename,[status(thm)],[f_4650_1]) ).

fof(f_4650_3,plain,
    ! [U_19538,U_19539,U_19540,U_19541] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19538)),U_19539) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19538)),U_19540)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19538),tc_List_Olist(U_19538))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19538),tc_List_Olist(U_19538)),U_19539),U_19540)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19538),c_List_Olistrel1(U_19538,U_19541)))) ),
    inference(definitional_conversion,[status(esa)],[f_4650_2]) ).

cnf(f_4650_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19538)),U_19539) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19538)),U_19540)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19538),tc_List_Olist(U_19538))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19538),tc_List_Olist(U_19538)),U_19539),U_19540)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19538),c_List_Olistrel1(U_19538,U_19541)))) ),
    inference(clausify,[status(thm)],[f_4650_3]) ).

fof(f_4651_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_4651_2,plain,
    ! [U_19545,U_19544,U_19543,U_19542] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19542)),U_19543) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19542)),U_19544)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19542),tc_List_Olist(U_19542))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19542),tc_List_Olist(U_19542)),U_19543),U_19544)),c_List_Olistrel1(U_19542,U_19545))) ),
    inference(variable_rename,[status(thm)],[f_4651_1]) ).

fof(f_4651_3,plain,
    ! [U_19542,U_19543,U_19544,U_19545] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19542)),U_19543) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19542)),U_19544)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19542),tc_List_Olist(U_19542))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19542),tc_List_Olist(U_19542)),U_19543),U_19544)),c_List_Olistrel1(U_19542,U_19545))) ),
    inference(definitional_conversion,[status(esa)],[f_4651_2]) ).

cnf(f_4651_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19542)),U_19543) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19542)),U_19544)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19542),tc_List_Olist(U_19542))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19542),tc_List_Olist(U_19542)),U_19543),U_19544)),c_List_Olistrel1(U_19542,U_19545))) ),
    inference(clausify,[status(thm)],[f_4651_3]) ).

fof(f_4652_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_4652_2,plain,
    ! [U_19548,U_19547,U_19546] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19546),tc_List_Olist(U_19546))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19546),tc_List_Olist(U_19546)),U_19547),c_List_Olist_ONil(U_19546))),c_List_Olistrel1(U_19546,U_19548))),
    inference(variable_rename,[status(thm)],[f_4652_1]) ).

fof(f_4652_3,plain,
    ! [U_19546,U_19547,U_19548] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19546),tc_List_Olist(U_19546))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19546),tc_List_Olist(U_19546)),U_19547),c_List_Olist_ONil(U_19546))),c_List_Olistrel1(U_19546,U_19548))),
    inference(definitional_conversion,[status(esa)],[f_4652_2]) ).

cnf(f_4652_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19546),tc_List_Olist(U_19546))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19546),tc_List_Olist(U_19546)),U_19547),c_List_Olist_ONil(U_19546))),c_List_Olistrel1(U_19546,U_19548))),
    inference(clausify,[status(thm)],[f_4652_3]) ).

fof(f_4653_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_4653_2,plain,
    ! [U_19551,U_19550,U_19549] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19549),tc_List_Olist(U_19549))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19549),tc_List_Olist(U_19549)),c_List_Olist_ONil(U_19549)),U_19550)),c_List_Olistrel1(U_19549,U_19551))),
    inference(variable_rename,[status(thm)],[f_4653_1]) ).

fof(f_4653_3,plain,
    ! [U_19549,U_19550,U_19551] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19549),tc_List_Olist(U_19549))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19549),tc_List_Olist(U_19549)),c_List_Olist_ONil(U_19549)),U_19550)),c_List_Olistrel1(U_19549,U_19551))),
    inference(definitional_conversion,[status(esa)],[f_4653_2]) ).

cnf(f_4653_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19549),tc_List_Olist(U_19549))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19549),tc_List_Olist(U_19549)),c_List_Olist_ONil(U_19549)),U_19550)),c_List_Olistrel1(U_19549,U_19551))),
    inference(clausify,[status(thm)],[f_4653_3]) ).

fof(f_4654_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_4654_2,plain,
    ! [U_19557,U_19556,U_19555,U_19554,U_19553,U_19552] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19552),tc_List_Olist(U_19552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19552),tc_List_Olist(U_19552)),hAPP(hAPP(c_List_Oappend(U_19552),U_19553),U_19556)),hAPP(hAPP(c_List_Oappend(U_19552),U_19554),U_19557))),c_List_Olistrel1(U_19552,U_19555)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19552),tc_List_Olist(U_19552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19552),tc_List_Olist(U_19552)),U_19556),U_19557)),c_List_Olistrel1(U_19552,U_19555)))
          | U_19553 != U_19554 )
        & ( U_19556 != U_19557
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19552),tc_List_Olist(U_19552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19552),tc_List_Olist(U_19552)),U_19553),U_19554)),c_List_Olistrel1(U_19552,U_19555))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4654_1]) ).

fof(f_4654_3,plain,
    ( ! [U_19552,U_19553,U_19554,U_19555,U_19556,U_19557] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19552),tc_List_Olist(U_19552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19552),tc_List_Olist(U_19552)),U_19556),U_19557)),c_List_Olistrel1(U_19552,U_19555)))
        | U_19553 != U_19554
        | ~ sP1189(U_19552,U_19553,U_19554,U_19555,U_19556,U_19557) )
    & ! [U_19552,U_19553,U_19554,U_19555,U_19556,U_19557] :
        ( U_19556 != U_19557
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19552),tc_List_Olist(U_19552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19552),tc_List_Olist(U_19552)),U_19553),U_19554)),c_List_Olistrel1(U_19552,U_19555)))
        | ~ sP1189(U_19552,U_19553,U_19554,U_19555,U_19556,U_19557) )
    & ! [U_19552,U_19553,U_19554,U_19555,U_19556,U_19557] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19552),tc_List_Olist(U_19552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19552),tc_List_Olist(U_19552)),hAPP(hAPP(c_List_Oappend(U_19552),U_19553),U_19556)),hAPP(hAPP(c_List_Oappend(U_19552),U_19554),U_19557))),c_List_Olistrel1(U_19552,U_19555)))
        | sP1189(U_19552,U_19553,U_19554,U_19555,U_19556,U_19557) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1189])],[f_4654_2]) ).

cnf(f_4654_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19552),tc_List_Olist(U_19552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19552),tc_List_Olist(U_19552)),hAPP(hAPP(c_List_Oappend(U_19552),U_19553),U_19556)),hAPP(hAPP(c_List_Oappend(U_19552),U_19554),U_19557))),c_List_Olistrel1(U_19552,U_19555)))
    | sP1189(U_19552,U_19553,U_19554,U_19555,U_19556,U_19557) ),
    inference(clausify,[status(thm)],[f_4654_3]) ).

cnf(f_4654_5,plain,
    ( U_19556 != U_19557
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19552),tc_List_Olist(U_19552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19552),tc_List_Olist(U_19552)),U_19553),U_19554)),c_List_Olistrel1(U_19552,U_19555)))
    | ~ sP1189(U_19552,U_19553,U_19554,U_19555,U_19556,U_19557) ),
    inference(clausify,[status(thm)],[f_4654_3]) ).

cnf(f_4654_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19552),tc_List_Olist(U_19552))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19552),tc_List_Olist(U_19552)),U_19556),U_19557)),c_List_Olistrel1(U_19552,U_19555)))
    | U_19553 != U_19554
    | ~ sP1189(U_19552,U_19553,U_19554,U_19555,U_19556,U_19557) ),
    inference(clausify,[status(thm)],[f_4654_3]) ).

fof(f_4655_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_4655_2,plain,
    ! [U_19561,U_19560,U_19559,U_19558] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19558),tc_List_Olist(U_19558))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19558),tc_List_Olist(U_19558)),U_19559),U_19560)),c_List_Olistrel1(U_19558,hAPP(c_Relation_Oconverse(U_19558,U_19558),U_19561))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19558),tc_List_Olist(U_19558))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19558),tc_List_Olist(U_19558)),U_19559),U_19560)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19558),tc_List_Olist(U_19558)),c_List_Olistrel1(U_19558,U_19561)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19558),tc_List_Olist(U_19558))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19558),tc_List_Olist(U_19558)),U_19559),U_19560)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19558),tc_List_Olist(U_19558)),c_List_Olistrel1(U_19558,U_19561))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19558),tc_List_Olist(U_19558))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19558),tc_List_Olist(U_19558)),U_19559),U_19560)),c_List_Olistrel1(U_19558,hAPP(c_Relation_Oconverse(U_19558,U_19558),U_19561)))) ) ),
    inference(variable_rename,[status(thm)],[f_4655_1]) ).

fof(f_4655_3,plain,
    ( ! [U_19569,U_19567,U_19565,U_19563] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19563),tc_List_Olist(U_19563))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19563),tc_List_Olist(U_19563)),U_19565),U_19567)),c_List_Olistrel1(U_19563,hAPP(c_Relation_Oconverse(U_19563,U_19563),U_19569))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19563),tc_List_Olist(U_19563))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19563),tc_List_Olist(U_19563)),U_19565),U_19567)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19563),tc_List_Olist(U_19563)),c_List_Olistrel1(U_19563,U_19569)))) )
    & ! [U_19568,U_19566,U_19564,U_19562] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19562),tc_List_Olist(U_19562))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19562),tc_List_Olist(U_19562)),U_19564),U_19566)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19562),tc_List_Olist(U_19562)),c_List_Olistrel1(U_19562,U_19568))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19562),tc_List_Olist(U_19562))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19562),tc_List_Olist(U_19562)),U_19564),U_19566)),c_List_Olistrel1(U_19562,hAPP(c_Relation_Oconverse(U_19562,U_19562),U_19568)))) ) ),
    inference(miniscope,[status(thm)],[f_4655_2]) ).

fof(f_4655_4,plain,
    ( ! [U_19563,U_19565,U_19567,U_19569] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19563),tc_List_Olist(U_19563))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19563),tc_List_Olist(U_19563)),U_19565),U_19567)),c_List_Olistrel1(U_19563,hAPP(c_Relation_Oconverse(U_19563,U_19563),U_19569))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19563),tc_List_Olist(U_19563))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19563),tc_List_Olist(U_19563)),U_19565),U_19567)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19563),tc_List_Olist(U_19563)),c_List_Olistrel1(U_19563,U_19569)))) )
    & ! [U_19568,U_19562,U_19564,U_19566] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19562),tc_List_Olist(U_19562))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19562),tc_List_Olist(U_19562)),U_19564),U_19566)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19562),tc_List_Olist(U_19562)),c_List_Olistrel1(U_19562,U_19568))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19562),tc_List_Olist(U_19562))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19562),tc_List_Olist(U_19562)),U_19564),U_19566)),c_List_Olistrel1(U_19562,hAPP(c_Relation_Oconverse(U_19562,U_19562),U_19568)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4655_3]) ).

cnf(f_4655_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19562),tc_List_Olist(U_19562))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19562),tc_List_Olist(U_19562)),U_19564),U_19566)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19562),tc_List_Olist(U_19562)),c_List_Olistrel1(U_19562,U_19568))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19562),tc_List_Olist(U_19562))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19562),tc_List_Olist(U_19562)),U_19564),U_19566)),c_List_Olistrel1(U_19562,hAPP(c_Relation_Oconverse(U_19562,U_19562),U_19568)))) ),
    inference(clausify,[status(thm)],[f_4655_4]) ).

cnf(f_4655_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19563),tc_List_Olist(U_19563))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19563),tc_List_Olist(U_19563)),U_19565),U_19567)),c_List_Olistrel1(U_19563,hAPP(c_Relation_Oconverse(U_19563,U_19563),U_19569))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19563),tc_List_Olist(U_19563))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19563),tc_List_Olist(U_19563)),U_19565),U_19567)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19563),tc_List_Olist(U_19563)),c_List_Olistrel1(U_19563,U_19569)))) ),
    inference(clausify,[status(thm)],[f_4655_4]) ).

fof(f_4656_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_4656_2,plain,
    ! [U_19573,U_19572,U_19571,U_19570] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19570),tc_List_Olist(U_19570))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19570),tc_List_Olist(U_19570)),U_19571),U_19572)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19570),c_List_Olistrel1(U_19570,U_19573))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19570),tc_List_Olist(U_19570))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19570),tc_List_Olist(U_19570)),U_19571),U_19572)),c_List_Olistrel(U_19570,U_19573))) ),
    inference(variable_rename,[status(thm)],[f_4656_1]) ).

fof(f_4656_3,plain,
    ! [U_19570,U_19571,U_19572,U_19573] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19570),tc_List_Olist(U_19570))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19570),tc_List_Olist(U_19570)),U_19571),U_19572)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19570),c_List_Olistrel1(U_19570,U_19573))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19570),tc_List_Olist(U_19570))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19570),tc_List_Olist(U_19570)),U_19571),U_19572)),c_List_Olistrel(U_19570,U_19573))) ),
    inference(definitional_conversion,[status(esa)],[f_4656_2]) ).

cnf(f_4656_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19570),tc_List_Olist(U_19570))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19570),tc_List_Olist(U_19570)),U_19571),U_19572)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19570),c_List_Olistrel1(U_19570,U_19573))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19570),tc_List_Olist(U_19570))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19570),tc_List_Olist(U_19570)),U_19571),U_19572)),c_List_Olistrel(U_19570,U_19573))) ),
    inference(clausify,[status(thm)],[f_4656_3]) ).

fof(f_4657_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_4657_2,plain,
    ! [U_19577,U_19576,U_19575,U_19574] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19574),tc_List_Olist(U_19574))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19574),tc_List_Olist(U_19574)),U_19575),U_19576)),c_List_Olistrel(U_19574,c_Transitive__Closure_Ortrancl(U_19574,U_19577))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19574),tc_List_Olist(U_19574))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19574),tc_List_Olist(U_19574)),U_19575),U_19576)),c_List_Olistrel1(U_19574,U_19577))) ),
    inference(variable_rename,[status(thm)],[f_4657_1]) ).

fof(f_4657_3,plain,
    ! [U_19574,U_19575,U_19576,U_19577] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19574),tc_List_Olist(U_19574))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19574),tc_List_Olist(U_19574)),U_19575),U_19576)),c_List_Olistrel(U_19574,c_Transitive__Closure_Ortrancl(U_19574,U_19577))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19574),tc_List_Olist(U_19574))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19574),tc_List_Olist(U_19574)),U_19575),U_19576)),c_List_Olistrel1(U_19574,U_19577))) ),
    inference(definitional_conversion,[status(esa)],[f_4657_2]) ).

cnf(f_4657_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19574),tc_List_Olist(U_19574))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19574),tc_List_Olist(U_19574)),U_19575),U_19576)),c_List_Olistrel(U_19574,c_Transitive__Closure_Ortrancl(U_19574,U_19577))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19574),tc_List_Olist(U_19574))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19574),tc_List_Olist(U_19574)),U_19575),U_19576)),c_List_Olistrel1(U_19574,U_19577))) ),
    inference(clausify,[status(thm)],[f_4657_3]) ).

fof(f_4658_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_4658_2,plain,
    ! [U_19583,U_19582,U_19581,U_19580,U_19579,U_19578] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19578),tc_List_Olist(U_19578))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19578),tc_List_Olist(U_19578)),hAPP(hAPP(c_List_Olist_OCons(U_19578),U_19579),U_19580)),hAPP(hAPP(c_List_Olist_OCons(U_19578),U_19581),U_19582))),c_List_Olistrel1(U_19578,U_19583)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19578),tc_List_Olist(U_19578))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19578),tc_List_Olist(U_19578)),U_19580),U_19582)),c_List_Olistrel1(U_19578,U_19583)))
            | U_19579 != U_19581 )
          & ( U_19580 != U_19582
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19578,U_19578)),hAPP(hAPP(c_Product__Type_OPair(U_19578,U_19578),U_19579),U_19581)),U_19583)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19578),tc_List_Olist(U_19578))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19578),tc_List_Olist(U_19578)),U_19580),U_19582)),c_List_Olistrel1(U_19578,U_19583)))
          & U_19579 = U_19581 )
        | ( U_19580 = U_19582
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19578,U_19578)),hAPP(hAPP(c_Product__Type_OPair(U_19578,U_19578),U_19579),U_19581)),U_19583)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19578),tc_List_Olist(U_19578))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19578),tc_List_Olist(U_19578)),hAPP(hAPP(c_List_Olist_OCons(U_19578),U_19579),U_19580)),hAPP(hAPP(c_List_Olist_OCons(U_19578),U_19581),U_19582))),c_List_Olistrel1(U_19578,U_19583))) ) ),
    inference(variable_rename,[status(thm)],[f_4658_1]) ).

fof(f_4658_3,plain,
    ( ! [U_19595,U_19593,U_19591,U_19589,U_19587,U_19585] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19585),tc_List_Olist(U_19585))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19585),tc_List_Olist(U_19585)),hAPP(hAPP(c_List_Olist_OCons(U_19585),U_19587),U_19589)),hAPP(hAPP(c_List_Olist_OCons(U_19585),U_19591),U_19593))),c_List_Olistrel1(U_19585,U_19595)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19585),tc_List_Olist(U_19585))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19585),tc_List_Olist(U_19585)),U_19589),U_19593)),c_List_Olistrel1(U_19585,U_19595)))
            | U_19587 != U_19591 )
          & ( U_19589 != U_19593
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19585,U_19585)),hAPP(hAPP(c_Product__Type_OPair(U_19585,U_19585),U_19587),U_19591)),U_19595)) ) ) )
    & ! [U_19594,U_19592,U_19590,U_19588,U_19586,U_19584] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19584),tc_List_Olist(U_19584))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19584),tc_List_Olist(U_19584)),U_19588),U_19592)),c_List_Olistrel1(U_19584,U_19594)))
          & U_19586 = U_19590 )
        | ( U_19588 = U_19592
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19584,U_19584)),hAPP(hAPP(c_Product__Type_OPair(U_19584,U_19584),U_19586),U_19590)),U_19594)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19584),tc_List_Olist(U_19584))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19584),tc_List_Olist(U_19584)),hAPP(hAPP(c_List_Olist_OCons(U_19584),U_19586),U_19588)),hAPP(hAPP(c_List_Olist_OCons(U_19584),U_19590),U_19592))),c_List_Olistrel1(U_19584,U_19594))) ) ),
    inference(miniscope,[status(thm)],[f_4658_2]) ).

fof(f_4658_4,plain,
    ( ! [U_19589,U_19585,U_19587,U_19591,U_19593,U_19595] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19585),tc_List_Olist(U_19585))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19585),tc_List_Olist(U_19585)),U_19589),U_19593)),c_List_Olistrel1(U_19585,U_19595)))
        | U_19587 != U_19591
        | ~ sP1192(U_19589,U_19585,U_19587,U_19591,U_19593,U_19595) )
    & ! [U_19589,U_19585,U_19587,U_19591,U_19593,U_19595] :
        ( U_19589 != U_19593
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19585,U_19585)),hAPP(hAPP(c_Product__Type_OPair(U_19585,U_19585),U_19587),U_19591)),U_19595))
        | ~ sP1192(U_19589,U_19585,U_19587,U_19591,U_19593,U_19595) )
    & ! [U_19584,U_19594,U_19586,U_19590,U_19588,U_19592] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19584),tc_List_Olist(U_19584))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19584),tc_List_Olist(U_19584)),U_19588),U_19592)),c_List_Olistrel1(U_19584,U_19594)))
        | ~ sP1191(U_19584,U_19594,U_19586,U_19590,U_19588,U_19592) )
    & ! [U_19584,U_19594,U_19586,U_19590,U_19588,U_19592] :
        ( U_19586 = U_19590
        | ~ sP1191(U_19584,U_19594,U_19586,U_19590,U_19588,U_19592) )
    & ! [U_19584,U_19594,U_19586,U_19590,U_19588,U_19592] :
        ( U_19588 = U_19592
        | ~ sP1190(U_19584,U_19594,U_19586,U_19590,U_19588,U_19592) )
    & ! [U_19584,U_19594,U_19586,U_19590,U_19588,U_19592] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19584,U_19584)),hAPP(hAPP(c_Product__Type_OPair(U_19584,U_19584),U_19586),U_19590)),U_19594))
        | ~ sP1190(U_19584,U_19594,U_19586,U_19590,U_19588,U_19592) )
    & ! [U_19589,U_19585,U_19587,U_19591,U_19593,U_19595] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19585),tc_List_Olist(U_19585))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19585),tc_List_Olist(U_19585)),hAPP(hAPP(c_List_Olist_OCons(U_19585),U_19587),U_19589)),hAPP(hAPP(c_List_Olist_OCons(U_19585),U_19591),U_19593))),c_List_Olistrel1(U_19585,U_19595)))
        | sP1192(U_19589,U_19585,U_19587,U_19591,U_19593,U_19595) )
    & ! [U_19584,U_19594,U_19586,U_19590,U_19588,U_19592] :
        ( sP1191(U_19584,U_19594,U_19586,U_19590,U_19588,U_19592)
        | sP1190(U_19584,U_19594,U_19586,U_19590,U_19588,U_19592)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19584),tc_List_Olist(U_19584))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19584),tc_List_Olist(U_19584)),hAPP(hAPP(c_List_Olist_OCons(U_19584),U_19586),U_19588)),hAPP(hAPP(c_List_Olist_OCons(U_19584),U_19590),U_19592))),c_List_Olistrel1(U_19584,U_19594))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1190,sP1191,sP1192])],[f_4658_3]) ).

cnf(f_4658_5,plain,
    ( sP1191(U_19584,U_19594,U_19586,U_19590,U_19588,U_19592)
    | sP1190(U_19584,U_19594,U_19586,U_19590,U_19588,U_19592)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19584),tc_List_Olist(U_19584))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19584),tc_List_Olist(U_19584)),hAPP(hAPP(c_List_Olist_OCons(U_19584),U_19586),U_19588)),hAPP(hAPP(c_List_Olist_OCons(U_19584),U_19590),U_19592))),c_List_Olistrel1(U_19584,U_19594))) ),
    inference(clausify,[status(thm)],[f_4658_4]) ).

cnf(f_4658_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19585),tc_List_Olist(U_19585))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19585),tc_List_Olist(U_19585)),hAPP(hAPP(c_List_Olist_OCons(U_19585),U_19587),U_19589)),hAPP(hAPP(c_List_Olist_OCons(U_19585),U_19591),U_19593))),c_List_Olistrel1(U_19585,U_19595)))
    | sP1192(U_19589,U_19585,U_19587,U_19591,U_19593,U_19595) ),
    inference(clausify,[status(thm)],[f_4658_4]) ).

cnf(f_4658_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19584,U_19584)),hAPP(hAPP(c_Product__Type_OPair(U_19584,U_19584),U_19586),U_19590)),U_19594))
    | ~ sP1190(U_19584,U_19594,U_19586,U_19590,U_19588,U_19592) ),
    inference(clausify,[status(thm)],[f_4658_4]) ).

cnf(f_4658_8,plain,
    ( U_19588 = U_19592
    | ~ sP1190(U_19584,U_19594,U_19586,U_19590,U_19588,U_19592) ),
    inference(clausify,[status(thm)],[f_4658_4]) ).

cnf(f_4658_9,plain,
    ( U_19586 = U_19590
    | ~ sP1191(U_19584,U_19594,U_19586,U_19590,U_19588,U_19592) ),
    inference(clausify,[status(thm)],[f_4658_4]) ).

cnf(f_4658_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19584),tc_List_Olist(U_19584))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19584),tc_List_Olist(U_19584)),U_19588),U_19592)),c_List_Olistrel1(U_19584,U_19594)))
    | ~ sP1191(U_19584,U_19594,U_19586,U_19590,U_19588,U_19592) ),
    inference(clausify,[status(thm)],[f_4658_4]) ).

cnf(f_4658_11,plain,
    ( U_19589 != U_19593
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19585,U_19585)),hAPP(hAPP(c_Product__Type_OPair(U_19585,U_19585),U_19587),U_19591)),U_19595))
    | ~ sP1192(U_19589,U_19585,U_19587,U_19591,U_19593,U_19595) ),
    inference(clausify,[status(thm)],[f_4658_4]) ).

cnf(f_4658_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19585),tc_List_Olist(U_19585))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19585),tc_List_Olist(U_19585)),U_19589),U_19593)),c_List_Olistrel1(U_19585,U_19595)))
    | U_19587 != U_19591
    | ~ sP1192(U_19589,U_19585,U_19587,U_19591,U_19593,U_19595) ),
    inference(clausify,[status(thm)],[f_4658_4]) ).

fof(f_4659_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_4659_2,plain,
    ! [U_19600,U_19599,U_19598,U_19597,U_19596] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19596),tc_List_Olist(U_19596))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19596),tc_List_Olist(U_19596)),hAPP(hAPP(c_List_Olist_OCons(U_19596),U_19597),U_19600)),hAPP(hAPP(c_List_Olist_OCons(U_19596),U_19598),U_19600))),c_List_Olistrel1(U_19596,U_19599)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19596,U_19596)),hAPP(hAPP(c_Product__Type_OPair(U_19596,U_19596),U_19597),U_19598)),U_19599)) ),
    inference(variable_rename,[status(thm)],[f_4659_1]) ).

fof(f_4659_3,plain,
    ! [U_19597,U_19598,U_19599,U_19596,U_19600] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19596),tc_List_Olist(U_19596))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19596),tc_List_Olist(U_19596)),hAPP(hAPP(c_List_Olist_OCons(U_19596),U_19597),U_19600)),hAPP(hAPP(c_List_Olist_OCons(U_19596),U_19598),U_19600))),c_List_Olistrel1(U_19596,U_19599)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19596,U_19596)),hAPP(hAPP(c_Product__Type_OPair(U_19596,U_19596),U_19597),U_19598)),U_19599)) ),
    inference(definitional_conversion,[status(esa)],[f_4659_2]) ).

cnf(f_4659_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19596),tc_List_Olist(U_19596))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19596),tc_List_Olist(U_19596)),hAPP(hAPP(c_List_Olist_OCons(U_19596),U_19597),U_19600)),hAPP(hAPP(c_List_Olist_OCons(U_19596),U_19598),U_19600))),c_List_Olistrel1(U_19596,U_19599)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19596,U_19596)),hAPP(hAPP(c_Product__Type_OPair(U_19596,U_19596),U_19597),U_19598)),U_19599)) ),
    inference(clausify,[status(thm)],[f_4659_3]) ).

fof(f_4660_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_4660_2,plain,
    ! [U_19603,U_19602,U_19601] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19601),tc_List_Olist(U_19601)),tc_HOL_Obool)),c_List_Olistrel1(U_19601,U_19602)),c_List_Olistrel(U_19601,U_19603)))
      | ~ c_Relation_Orefl__on(U_19601,c_Orderings_Otop__class_Otop(tc_fun(U_19601,tc_HOL_Obool)),U_19603)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19601,U_19601),tc_HOL_Obool)),U_19602),U_19603)) ),
    inference(variable_rename,[status(thm)],[f_4660_1]) ).

fof(f_4660_3,plain,
    ! [U_19601,U_19602,U_19603] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19601),tc_List_Olist(U_19601)),tc_HOL_Obool)),c_List_Olistrel1(U_19601,U_19602)),c_List_Olistrel(U_19601,U_19603)))
      | ~ c_Relation_Orefl__on(U_19601,c_Orderings_Otop__class_Otop(tc_fun(U_19601,tc_HOL_Obool)),U_19603)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19601,U_19601),tc_HOL_Obool)),U_19602),U_19603)) ),
    inference(definitional_conversion,[status(esa)],[f_4660_2]) ).

cnf(f_4660_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19601),tc_List_Olist(U_19601)),tc_HOL_Obool)),c_List_Olistrel1(U_19601,U_19602)),c_List_Olistrel(U_19601,U_19603)))
    | ~ c_Relation_Orefl__on(U_19601,c_Orderings_Otop__class_Otop(tc_fun(U_19601,tc_HOL_Obool)),U_19603)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19601,U_19601),tc_HOL_Obool)),U_19602),U_19603)) ),
    inference(clausify,[status(thm)],[f_4660_3]) ).

fof(f_4661_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_4661_2,plain,
    ! [U_19611,U_19610,U_19609,U_19608,U_19607,U_19606,U_19605,U_19604] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19604),tc_List_Olist(U_19604))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19604),tc_List_Olist(U_19604)),U_19608),U_19611)),c_List_Olistrel1(U_19604,U_19607)))
      | U_19611 != hAPP(hAPP(c_List_Oappend(U_19604),U_19609),hAPP(hAPP(c_List_Olist_OCons(U_19604),U_19606),U_19610))
      | U_19608 != hAPP(hAPP(c_List_Oappend(U_19604),U_19609),hAPP(hAPP(c_List_Olist_OCons(U_19604),U_19605),U_19610))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19604,U_19604)),hAPP(hAPP(c_Product__Type_OPair(U_19604,U_19604),U_19605),U_19606)),U_19607)) ),
    inference(variable_rename,[status(thm)],[f_4661_1]) ).

fof(f_4661_3,plain,
    ! [U_19604,U_19605,U_19606,U_19607,U_19608,U_19609,U_19610,U_19611] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19604),tc_List_Olist(U_19604))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19604),tc_List_Olist(U_19604)),U_19608),U_19611)),c_List_Olistrel1(U_19604,U_19607)))
      | U_19611 != hAPP(hAPP(c_List_Oappend(U_19604),U_19609),hAPP(hAPP(c_List_Olist_OCons(U_19604),U_19606),U_19610))
      | U_19608 != hAPP(hAPP(c_List_Oappend(U_19604),U_19609),hAPP(hAPP(c_List_Olist_OCons(U_19604),U_19605),U_19610))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19604,U_19604)),hAPP(hAPP(c_Product__Type_OPair(U_19604,U_19604),U_19605),U_19606)),U_19607)) ),
    inference(definitional_conversion,[status(esa)],[f_4661_2]) ).

cnf(f_4661_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19604),tc_List_Olist(U_19604))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19604),tc_List_Olist(U_19604)),U_19608),U_19611)),c_List_Olistrel1(U_19604,U_19607)))
    | U_19611 != hAPP(hAPP(c_List_Oappend(U_19604),U_19609),hAPP(hAPP(c_List_Olist_OCons(U_19604),U_19606),U_19610))
    | U_19608 != hAPP(hAPP(c_List_Oappend(U_19604),U_19609),hAPP(hAPP(c_List_Olist_OCons(U_19604),U_19605),U_19610))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19604,U_19604)),hAPP(hAPP(c_Product__Type_OPair(U_19604,U_19604),U_19605),U_19606)),U_19607)) ),
    inference(clausify,[status(thm)],[f_4661_3]) ).

fof(f_4662_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_4662_2,plain,
    ! [U_19617,U_19616,U_19615,U_19614,U_19613,U_19612] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19612),tc_List_Olist(U_19612))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19612),tc_List_Olist(U_19612)),hAPP(hAPP(c_List_Olist_OCons(U_19612),U_19613),U_19616)),hAPP(hAPP(c_List_Olist_OCons(U_19612),U_19614),U_19617))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19612),c_List_Olistrel1(U_19612,U_19615))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19612),tc_List_Olist(U_19612))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19612),tc_List_Olist(U_19612)),U_19616),U_19617)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19612),c_List_Olistrel1(U_19612,U_19615))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19612,U_19612)),hAPP(hAPP(c_Product__Type_OPair(U_19612,U_19612),U_19613),U_19614)),c_Transitive__Closure_Ortrancl(U_19612,U_19615))) ),
    inference(variable_rename,[status(thm)],[f_4662_1]) ).

fof(f_4662_3,plain,
    ! [U_19612,U_19613,U_19614,U_19615,U_19616,U_19617] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19612),tc_List_Olist(U_19612))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19612),tc_List_Olist(U_19612)),hAPP(hAPP(c_List_Olist_OCons(U_19612),U_19613),U_19616)),hAPP(hAPP(c_List_Olist_OCons(U_19612),U_19614),U_19617))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19612),c_List_Olistrel1(U_19612,U_19615))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19612),tc_List_Olist(U_19612))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19612),tc_List_Olist(U_19612)),U_19616),U_19617)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19612),c_List_Olistrel1(U_19612,U_19615))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19612,U_19612)),hAPP(hAPP(c_Product__Type_OPair(U_19612,U_19612),U_19613),U_19614)),c_Transitive__Closure_Ortrancl(U_19612,U_19615))) ),
    inference(definitional_conversion,[status(esa)],[f_4662_2]) ).

cnf(f_4662_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19612),tc_List_Olist(U_19612))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19612),tc_List_Olist(U_19612)),hAPP(hAPP(c_List_Olist_OCons(U_19612),U_19613),U_19616)),hAPP(hAPP(c_List_Olist_OCons(U_19612),U_19614),U_19617))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19612),c_List_Olistrel1(U_19612,U_19615))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19612),tc_List_Olist(U_19612))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19612),tc_List_Olist(U_19612)),U_19616),U_19617)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19612),c_List_Olistrel1(U_19612,U_19615))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19612,U_19612)),hAPP(hAPP(c_Product__Type_OPair(U_19612,U_19612),U_19613),U_19614)),c_Transitive__Closure_Ortrancl(U_19612,U_19615))) ),
    inference(clausify,[status(thm)],[f_4662_3]) ).

fof(f_4663_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_4663_2,plain,
    ! [U_19625,U_19624,U_19623,U_19622] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19622),tc_List_Olist(U_19622))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19622),tc_List_Olist(U_19622)),U_19623),U_19624)),c_List_Olistrel1(U_19622,U_19625)))
        | ! [U_19621,U_19620] :
            ( U_19624 != hAPP(hAPP(c_List_Olist__update(U_19622,U_19623),U_19620),U_19621)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19620),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19622)),U_19623)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19622,U_19622)),hAPP(hAPP(c_Product__Type_OPair(U_19622,U_19622),hAPP(hAPP(c_List_Onth(U_19622),U_19623),U_19620)),U_19621)),U_19625)) ) )
      & ( ? [U_19619,U_19618] :
            ( U_19624 = hAPP(hAPP(c_List_Olist__update(U_19622,U_19623),U_19618),U_19619)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19618),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19622)),U_19623)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19622,U_19622)),hAPP(hAPP(c_Product__Type_OPair(U_19622,U_19622),hAPP(hAPP(c_List_Onth(U_19622),U_19623),U_19618)),U_19619)),U_19625)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19622),tc_List_Olist(U_19622))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19622),tc_List_Olist(U_19622)),U_19623),U_19624)),c_List_Olistrel1(U_19622,U_19625))) ) ),
    inference(variable_rename,[status(thm)],[f_4663_1]) ).

fof(f_4663_3,plain,
    ( ! [U_19633,U_19631,U_19629,U_19627] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19627),tc_List_Olist(U_19627))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19627),tc_List_Olist(U_19627)),U_19629),U_19631)),c_List_Olistrel1(U_19627,U_19633)))
        | ! [U_19621,U_19620] :
            ( U_19631 != hAPP(hAPP(c_List_Olist__update(U_19627,U_19629),U_19620),U_19621)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19620),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19627)),U_19629)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19627,U_19627)),hAPP(hAPP(c_Product__Type_OPair(U_19627,U_19627),hAPP(hAPP(c_List_Onth(U_19627),U_19629),U_19620)),U_19621)),U_19633)) ) )
    & ! [U_19632,U_19630,U_19628,U_19626] :
        ( ? [U_19619,U_19618] :
            ( U_19630 = hAPP(hAPP(c_List_Olist__update(U_19626,U_19628),U_19618),U_19619)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19618),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19626)),U_19628)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19626,U_19626)),hAPP(hAPP(c_Product__Type_OPair(U_19626,U_19626),hAPP(hAPP(c_List_Onth(U_19626),U_19628),U_19618)),U_19619)),U_19632)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19626),tc_List_Olist(U_19626))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19626),tc_List_Olist(U_19626)),U_19628),U_19630)),c_List_Olistrel1(U_19626,U_19632))) ) ),
    inference(miniscope,[status(thm)],[f_4663_2]) ).

fof(f_4663_4,plain,
    ( ! [U_19633,U_19631,U_19629,U_19627] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19627),tc_List_Olist(U_19627))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19627),tc_List_Olist(U_19627)),U_19629),U_19631)),c_List_Olistrel1(U_19627,U_19633)))
        | ! [U_19621,U_19620] :
            ( U_19631 != hAPP(hAPP(c_List_Olist__update(U_19627,U_19629),U_19620),U_19621)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19620),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19627)),U_19629)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19627,U_19627)),hAPP(hAPP(c_Product__Type_OPair(U_19627,U_19627),hAPP(hAPP(c_List_Onth(U_19627),U_19629),U_19620)),U_19621)),U_19633)) ) )
    & ! [U_19632,U_19630,U_19628,U_19626] :
        ( ? [U_19618] :
            ( U_19630 = hAPP(hAPP(c_List_Olist__update(U_19626,U_19628),U_19618),sK481(U_19632,U_19630,U_19628,U_19626))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19618),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19626)),U_19628)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19626,U_19626)),hAPP(hAPP(c_Product__Type_OPair(U_19626,U_19626),hAPP(hAPP(c_List_Onth(U_19626),U_19628),U_19618)),sK481(U_19632,U_19630,U_19628,U_19626))),U_19632)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19626),tc_List_Olist(U_19626))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19626),tc_List_Olist(U_19626)),U_19628),U_19630)),c_List_Olistrel1(U_19626,U_19632))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK481]),skolemize(U_19619,sK481(U_19632,U_19630,U_19628,U_19626))],[f_4663_3]) ).

fof(f_4663_5,plain,
    ( ! [U_19633,U_19631,U_19629,U_19627] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19627),tc_List_Olist(U_19627))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19627),tc_List_Olist(U_19627)),U_19629),U_19631)),c_List_Olistrel1(U_19627,U_19633)))
        | ! [U_19621,U_19620] :
            ( U_19631 != hAPP(hAPP(c_List_Olist__update(U_19627,U_19629),U_19620),U_19621)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19620),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19627)),U_19629)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19627,U_19627)),hAPP(hAPP(c_Product__Type_OPair(U_19627,U_19627),hAPP(hAPP(c_List_Onth(U_19627),U_19629),U_19620)),U_19621)),U_19633)) ) )
    & ! [U_19632,U_19630,U_19628,U_19626] :
        ( ( U_19630 = hAPP(hAPP(c_List_Olist__update(U_19626,U_19628),sK482(U_19632,U_19630,U_19628,U_19626)),sK481(U_19632,U_19630,U_19628,U_19626))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK482(U_19632,U_19630,U_19628,U_19626)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19626)),U_19628)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19626,U_19626)),hAPP(hAPP(c_Product__Type_OPair(U_19626,U_19626),hAPP(hAPP(c_List_Onth(U_19626),U_19628),sK482(U_19632,U_19630,U_19628,U_19626))),sK481(U_19632,U_19630,U_19628,U_19626))),U_19632)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19626),tc_List_Olist(U_19626))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19626),tc_List_Olist(U_19626)),U_19628),U_19630)),c_List_Olistrel1(U_19626,U_19632))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK482]),skolemize(U_19618,sK482(U_19632,U_19630,U_19628,U_19626))],[f_4663_4]) ).

fof(f_4663_6,plain,
    ( ! [U_19628,U_19632,U_19626,U_19630] :
        ( U_19630 = hAPP(hAPP(c_List_Olist__update(U_19626,U_19628),sK482(U_19632,U_19630,U_19628,U_19626)),sK481(U_19632,U_19630,U_19628,U_19626))
        | ~ sP1193(U_19628,U_19632,U_19626,U_19630) )
    & ! [U_19628,U_19632,U_19626,U_19630] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK482(U_19632,U_19630,U_19628,U_19626)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19626)),U_19628)))
        | ~ sP1193(U_19628,U_19632,U_19626,U_19630) )
    & ! [U_19628,U_19632,U_19626,U_19630] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19626,U_19626)),hAPP(hAPP(c_Product__Type_OPair(U_19626,U_19626),hAPP(hAPP(c_List_Onth(U_19626),U_19628),sK482(U_19632,U_19630,U_19628,U_19626))),sK481(U_19632,U_19630,U_19628,U_19626))),U_19632))
        | ~ sP1193(U_19628,U_19632,U_19626,U_19630) )
    & ! [U_19620,U_19621,U_19627,U_19629,U_19631,U_19633] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19627),tc_List_Olist(U_19627))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19627),tc_List_Olist(U_19627)),U_19629),U_19631)),c_List_Olistrel1(U_19627,U_19633)))
        | U_19631 != hAPP(hAPP(c_List_Olist__update(U_19627,U_19629),U_19620),U_19621)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19620),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19627)),U_19629)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19627,U_19627)),hAPP(hAPP(c_Product__Type_OPair(U_19627,U_19627),hAPP(hAPP(c_List_Onth(U_19627),U_19629),U_19620)),U_19621)),U_19633)) )
    & ! [U_19628,U_19632,U_19626,U_19630] :
        ( sP1193(U_19628,U_19632,U_19626,U_19630)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19626),tc_List_Olist(U_19626))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19626),tc_List_Olist(U_19626)),U_19628),U_19630)),c_List_Olistrel1(U_19626,U_19632))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1193])],[f_4663_5]) ).

cnf(f_4663_7,plain,
    ( sP1193(U_19628,U_19632,U_19626,U_19630)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19626),tc_List_Olist(U_19626))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19626),tc_List_Olist(U_19626)),U_19628),U_19630)),c_List_Olistrel1(U_19626,U_19632))) ),
    inference(clausify,[status(thm)],[f_4663_6]) ).

cnf(f_4663_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19627),tc_List_Olist(U_19627))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19627),tc_List_Olist(U_19627)),U_19629),U_19631)),c_List_Olistrel1(U_19627,U_19633)))
    | U_19631 != hAPP(hAPP(c_List_Olist__update(U_19627,U_19629),U_19620),U_19621)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19620),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19627)),U_19629)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19627,U_19627)),hAPP(hAPP(c_Product__Type_OPair(U_19627,U_19627),hAPP(hAPP(c_List_Onth(U_19627),U_19629),U_19620)),U_19621)),U_19633)) ),
    inference(clausify,[status(thm)],[f_4663_6]) ).

cnf(f_4663_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19626,U_19626)),hAPP(hAPP(c_Product__Type_OPair(U_19626,U_19626),hAPP(hAPP(c_List_Onth(U_19626),U_19628),sK482(U_19632,U_19630,U_19628,U_19626))),sK481(U_19632,U_19630,U_19628,U_19626))),U_19632))
    | ~ sP1193(U_19628,U_19632,U_19626,U_19630) ),
    inference(clausify,[status(thm)],[f_4663_6]) ).

cnf(f_4663_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK482(U_19632,U_19630,U_19628,U_19626)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19626)),U_19628)))
    | ~ sP1193(U_19628,U_19632,U_19626,U_19630) ),
    inference(clausify,[status(thm)],[f_4663_6]) ).

cnf(f_4663_11,plain,
    ( U_19630 = hAPP(hAPP(c_List_Olist__update(U_19626,U_19628),sK482(U_19632,U_19630,U_19628,U_19626)),sK481(U_19632,U_19630,U_19628,U_19626))
    | ~ sP1193(U_19628,U_19632,U_19626,U_19630) ),
    inference(clausify,[status(thm)],[f_4663_6]) ).

fof(f_4664_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_4664_2,plain,
    ! [U_19641,U_19640,U_19639,U_19638] :
      ( ? [U_19637,U_19636] :
          ( ? [U_19635,U_19634] :
              ( U_19640 = hAPP(hAPP(c_List_Oappend(U_19638),U_19635),hAPP(hAPP(c_List_Olist_OCons(U_19638),U_19636),U_19634))
              & U_19639 = hAPP(hAPP(c_List_Oappend(U_19638),U_19635),hAPP(hAPP(c_List_Olist_OCons(U_19638),U_19637),U_19634)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19638,U_19638)),hAPP(hAPP(c_Product__Type_OPair(U_19638,U_19638),U_19637),U_19636)),U_19641)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19638),tc_List_Olist(U_19638))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19638),tc_List_Olist(U_19638)),U_19639),U_19640)),c_List_Olistrel1(U_19638,U_19641))) ),
    inference(variable_rename,[status(thm)],[f_4664_1]) ).

fof(f_4664_3,plain,
    ! [U_19641,U_19640,U_19639,U_19638] :
      ( ? [U_19636] :
          ( ? [U_19635,U_19634] :
              ( U_19640 = hAPP(hAPP(c_List_Oappend(U_19638),U_19635),hAPP(hAPP(c_List_Olist_OCons(U_19638),U_19636),U_19634))
              & U_19639 = hAPP(hAPP(c_List_Oappend(U_19638),U_19635),hAPP(hAPP(c_List_Olist_OCons(U_19638),sK483(U_19641,U_19640,U_19639,U_19638)),U_19634)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19638,U_19638)),hAPP(hAPP(c_Product__Type_OPair(U_19638,U_19638),sK483(U_19641,U_19640,U_19639,U_19638)),U_19636)),U_19641)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19638),tc_List_Olist(U_19638))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19638),tc_List_Olist(U_19638)),U_19639),U_19640)),c_List_Olistrel1(U_19638,U_19641))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK483]),skolemize(U_19637,sK483(U_19641,U_19640,U_19639,U_19638))],[f_4664_2]) ).

fof(f_4664_4,plain,
    ! [U_19641,U_19640,U_19639,U_19638] :
      ( ( ? [U_19635,U_19634] :
            ( U_19640 = hAPP(hAPP(c_List_Oappend(U_19638),U_19635),hAPP(hAPP(c_List_Olist_OCons(U_19638),sK484(U_19641,U_19640,U_19639,U_19638)),U_19634))
            & U_19639 = hAPP(hAPP(c_List_Oappend(U_19638),U_19635),hAPP(hAPP(c_List_Olist_OCons(U_19638),sK483(U_19641,U_19640,U_19639,U_19638)),U_19634)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19638,U_19638)),hAPP(hAPP(c_Product__Type_OPair(U_19638,U_19638),sK483(U_19641,U_19640,U_19639,U_19638)),sK484(U_19641,U_19640,U_19639,U_19638))),U_19641)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19638),tc_List_Olist(U_19638))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19638),tc_List_Olist(U_19638)),U_19639),U_19640)),c_List_Olistrel1(U_19638,U_19641))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK484]),skolemize(U_19636,sK484(U_19641,U_19640,U_19639,U_19638))],[f_4664_3]) ).

fof(f_4664_5,plain,
    ! [U_19641,U_19640,U_19639,U_19638] :
      ( ( ? [U_19634] :
            ( U_19640 = hAPP(hAPP(c_List_Oappend(U_19638),sK485(U_19641,U_19640,U_19639,U_19638)),hAPP(hAPP(c_List_Olist_OCons(U_19638),sK484(U_19641,U_19640,U_19639,U_19638)),U_19634))
            & U_19639 = hAPP(hAPP(c_List_Oappend(U_19638),sK485(U_19641,U_19640,U_19639,U_19638)),hAPP(hAPP(c_List_Olist_OCons(U_19638),sK483(U_19641,U_19640,U_19639,U_19638)),U_19634)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19638,U_19638)),hAPP(hAPP(c_Product__Type_OPair(U_19638,U_19638),sK483(U_19641,U_19640,U_19639,U_19638)),sK484(U_19641,U_19640,U_19639,U_19638))),U_19641)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19638),tc_List_Olist(U_19638))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19638),tc_List_Olist(U_19638)),U_19639),U_19640)),c_List_Olistrel1(U_19638,U_19641))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK485]),skolemize(U_19635,sK485(U_19641,U_19640,U_19639,U_19638))],[f_4664_4]) ).

fof(f_4664_6,plain,
    ! [U_19641,U_19640,U_19639,U_19638] :
      ( ( U_19640 = hAPP(hAPP(c_List_Oappend(U_19638),sK485(U_19641,U_19640,U_19639,U_19638)),hAPP(hAPP(c_List_Olist_OCons(U_19638),sK484(U_19641,U_19640,U_19639,U_19638)),sK486(U_19641,U_19640,U_19639,U_19638)))
        & U_19639 = hAPP(hAPP(c_List_Oappend(U_19638),sK485(U_19641,U_19640,U_19639,U_19638)),hAPP(hAPP(c_List_Olist_OCons(U_19638),sK483(U_19641,U_19640,U_19639,U_19638)),sK486(U_19641,U_19640,U_19639,U_19638)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19638,U_19638)),hAPP(hAPP(c_Product__Type_OPair(U_19638,U_19638),sK483(U_19641,U_19640,U_19639,U_19638)),sK484(U_19641,U_19640,U_19639,U_19638))),U_19641)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19638),tc_List_Olist(U_19638))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19638),tc_List_Olist(U_19638)),U_19639),U_19640)),c_List_Olistrel1(U_19638,U_19641))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK486]),skolemize(U_19634,sK486(U_19641,U_19640,U_19639,U_19638))],[f_4664_5]) ).

fof(f_4664_7,plain,
    ( ! [U_19638,U_19639,U_19640,U_19641] :
        ( U_19640 = hAPP(hAPP(c_List_Oappend(U_19638),sK485(U_19641,U_19640,U_19639,U_19638)),hAPP(hAPP(c_List_Olist_OCons(U_19638),sK484(U_19641,U_19640,U_19639,U_19638)),sK486(U_19641,U_19640,U_19639,U_19638)))
        | ~ sP1194(U_19638,U_19639,U_19640,U_19641) )
    & ! [U_19638,U_19639,U_19640,U_19641] :
        ( U_19639 = hAPP(hAPP(c_List_Oappend(U_19638),sK485(U_19641,U_19640,U_19639,U_19638)),hAPP(hAPP(c_List_Olist_OCons(U_19638),sK483(U_19641,U_19640,U_19639,U_19638)),sK486(U_19641,U_19640,U_19639,U_19638)))
        | ~ sP1194(U_19638,U_19639,U_19640,U_19641) )
    & ! [U_19638,U_19639,U_19640,U_19641] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19638,U_19638)),hAPP(hAPP(c_Product__Type_OPair(U_19638,U_19638),sK483(U_19641,U_19640,U_19639,U_19638)),sK484(U_19641,U_19640,U_19639,U_19638))),U_19641))
        | ~ sP1194(U_19638,U_19639,U_19640,U_19641) )
    & ! [U_19638,U_19639,U_19640,U_19641] :
        ( sP1194(U_19638,U_19639,U_19640,U_19641)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19638),tc_List_Olist(U_19638))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19638),tc_List_Olist(U_19638)),U_19639),U_19640)),c_List_Olistrel1(U_19638,U_19641))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1194])],[f_4664_6]) ).

cnf(f_4664_8,plain,
    ( sP1194(U_19638,U_19639,U_19640,U_19641)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19638),tc_List_Olist(U_19638))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19638),tc_List_Olist(U_19638)),U_19639),U_19640)),c_List_Olistrel1(U_19638,U_19641))) ),
    inference(clausify,[status(thm)],[f_4664_7]) ).

cnf(f_4664_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19638,U_19638)),hAPP(hAPP(c_Product__Type_OPair(U_19638,U_19638),sK483(U_19641,U_19640,U_19639,U_19638)),sK484(U_19641,U_19640,U_19639,U_19638))),U_19641))
    | ~ sP1194(U_19638,U_19639,U_19640,U_19641) ),
    inference(clausify,[status(thm)],[f_4664_7]) ).

cnf(f_4664_10,plain,
    ( U_19639 = hAPP(hAPP(c_List_Oappend(U_19638),sK485(U_19641,U_19640,U_19639,U_19638)),hAPP(hAPP(c_List_Olist_OCons(U_19638),sK483(U_19641,U_19640,U_19639,U_19638)),sK486(U_19641,U_19640,U_19639,U_19638)))
    | ~ sP1194(U_19638,U_19639,U_19640,U_19641) ),
    inference(clausify,[status(thm)],[f_4664_7]) ).

cnf(f_4664_11,plain,
    ( U_19640 = hAPP(hAPP(c_List_Oappend(U_19638),sK485(U_19641,U_19640,U_19639,U_19638)),hAPP(hAPP(c_List_Olist_OCons(U_19638),sK484(U_19641,U_19640,U_19639,U_19638)),sK486(U_19641,U_19640,U_19639,U_19638)))
    | ~ sP1194(U_19638,U_19639,U_19640,U_19641) ),
    inference(clausify,[status(thm)],[f_4664_7]) ).

fof(f_4665_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_4665_2,plain,
    ! [U_19643,U_19642] : hAPP(c_List_Orotate1(U_19642),U_19643) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19642),U_19642,c_List_Olist_ONil(U_19642),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19642),tc_fun(tc_List_Olist(U_19642),tc_List_Olist(U_19642)),U_19642),hAPP(c_COMBC(tc_List_Olist(U_19642),tc_List_Olist(U_19642),tc_List_Olist(U_19642)),c_List_Oappend(U_19642))),hAPP(hAPP(c_COMBC(U_19642,tc_List_Olist(U_19642),tc_List_Olist(U_19642)),c_List_Olist_OCons(U_19642)),c_List_Olist_ONil(U_19642)))),U_19643),
    inference(variable_rename,[status(thm)],[f_4665_1]) ).

fof(f_4665_3,plain,
    ! [U_19643,U_19642] : hAPP(c_List_Orotate1(U_19642),U_19643) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19642),U_19642,c_List_Olist_ONil(U_19642),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19642),tc_fun(tc_List_Olist(U_19642),tc_List_Olist(U_19642)),U_19642),hAPP(c_COMBC(tc_List_Olist(U_19642),tc_List_Olist(U_19642),tc_List_Olist(U_19642)),c_List_Oappend(U_19642))),hAPP(hAPP(c_COMBC(U_19642,tc_List_Olist(U_19642),tc_List_Olist(U_19642)),c_List_Olist_OCons(U_19642)),c_List_Olist_ONil(U_19642)))),U_19643),
    inference(definitional_conversion,[status(esa)],[f_4665_2]) ).

cnf(f_4665_4,plain,
    hAPP(c_List_Orotate1(U_19642),U_19643) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19642),U_19642,c_List_Olist_ONil(U_19642),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19642),tc_fun(tc_List_Olist(U_19642),tc_List_Olist(U_19642)),U_19642),hAPP(c_COMBC(tc_List_Olist(U_19642),tc_List_Olist(U_19642),tc_List_Olist(U_19642)),c_List_Oappend(U_19642))),hAPP(hAPP(c_COMBC(U_19642,tc_List_Olist(U_19642),tc_List_Olist(U_19642)),c_List_Olist_OCons(U_19642)),c_List_Olist_ONil(U_19642)))),U_19643),
    inference(clausify,[status(thm)],[f_4665_3]) ).

fof(f_4666_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_4666_2,plain,
    ! [U_19647,U_19646,U_19645,U_19644] :
      ( hAPP(hAPP(c_List_Olist__update(U_19645,U_19646),U_19644),U_19647) = hAPP(hAPP(c_List_Oappend(U_19645),hAPP(hAPP(c_List_Otake(U_19645),U_19644),U_19646)),hAPP(hAPP(c_List_Olist_OCons(U_19645),U_19647),hAPP(hAPP(c_List_Odrop(U_19645),hAPP(c_Nat_OSuc,U_19644)),U_19646)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19644),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19645)),U_19646))) ),
    inference(variable_rename,[status(thm)],[f_4666_1]) ).

fof(f_4666_3,plain,
    ! [U_19644,U_19645,U_19646,U_19647] :
      ( hAPP(hAPP(c_List_Olist__update(U_19645,U_19646),U_19644),U_19647) = hAPP(hAPP(c_List_Oappend(U_19645),hAPP(hAPP(c_List_Otake(U_19645),U_19644),U_19646)),hAPP(hAPP(c_List_Olist_OCons(U_19645),U_19647),hAPP(hAPP(c_List_Odrop(U_19645),hAPP(c_Nat_OSuc,U_19644)),U_19646)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19644),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19645)),U_19646))) ),
    inference(definitional_conversion,[status(esa)],[f_4666_2]) ).

cnf(f_4666_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_19645,U_19646),U_19644),U_19647) = hAPP(hAPP(c_List_Oappend(U_19645),hAPP(hAPP(c_List_Otake(U_19645),U_19644),U_19646)),hAPP(hAPP(c_List_Olist_OCons(U_19645),U_19647),hAPP(hAPP(c_List_Odrop(U_19645),hAPP(c_Nat_OSuc,U_19644)),U_19646)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19644),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19645)),U_19646))) ),
    inference(clausify,[status(thm)],[f_4666_3]) ).

fof(f_4667_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_4667_2,plain,
    ! [U_19649,U_19648] : hAPP(hAPP(c_List_Odrop(U_19648),U_19649),c_List_Olist_ONil(U_19648)) = c_List_Olist_ONil(U_19648),
    inference(variable_rename,[status(thm)],[f_4667_1]) ).

fof(f_4667_3,plain,
    ! [U_19649,U_19648] : hAPP(hAPP(c_List_Odrop(U_19648),U_19649),c_List_Olist_ONil(U_19648)) = c_List_Olist_ONil(U_19648),
    inference(definitional_conversion,[status(esa)],[f_4667_2]) ).

cnf(f_4667_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19648),U_19649),c_List_Olist_ONil(U_19648)) = c_List_Olist_ONil(U_19648),
    inference(clausify,[status(thm)],[f_4667_3]) ).

fof(f_4668_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_4668_2,plain,
    ! [U_19651,U_19650] :
      ( ( hAPP(c_List_Orotate1(U_19650),U_19651) = c_List_Olist_ONil(U_19650)
        | U_19651 != c_List_Olist_ONil(U_19650) )
      & ( U_19651 = c_List_Olist_ONil(U_19650)
        | hAPP(c_List_Orotate1(U_19650),U_19651) != c_List_Olist_ONil(U_19650) ) ),
    inference(variable_rename,[status(thm)],[f_4668_1]) ).

fof(f_4668_3,plain,
    ( ! [U_19655,U_19653] :
        ( hAPP(c_List_Orotate1(U_19653),U_19655) = c_List_Olist_ONil(U_19653)
        | U_19655 != c_List_Olist_ONil(U_19653) )
    & ! [U_19654,U_19652] :
        ( U_19654 = c_List_Olist_ONil(U_19652)
        | hAPP(c_List_Orotate1(U_19652),U_19654) != c_List_Olist_ONil(U_19652) ) ),
    inference(miniscope,[status(thm)],[f_4668_2]) ).

fof(f_4668_4,plain,
    ( ! [U_19655,U_19653] :
        ( hAPP(c_List_Orotate1(U_19653),U_19655) = c_List_Olist_ONil(U_19653)
        | U_19655 != c_List_Olist_ONil(U_19653) )
    & ! [U_19654,U_19652] :
        ( U_19654 = c_List_Olist_ONil(U_19652)
        | hAPP(c_List_Orotate1(U_19652),U_19654) != c_List_Olist_ONil(U_19652) ) ),
    inference(definitional_conversion,[status(esa)],[f_4668_3]) ).

cnf(f_4668_5,plain,
    ( U_19654 = c_List_Olist_ONil(U_19652)
    | hAPP(c_List_Orotate1(U_19652),U_19654) != c_List_Olist_ONil(U_19652) ),
    inference(clausify,[status(thm)],[f_4668_4]) ).

cnf(f_4668_6,plain,
    ( hAPP(c_List_Orotate1(U_19653),U_19655) = c_List_Olist_ONil(U_19653)
    | U_19655 != c_List_Olist_ONil(U_19653) ),
    inference(clausify,[status(thm)],[f_4668_4]) ).

fof(f_4669_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_4669_2,plain,
    ! [U_19658,U_19657,U_19656] :
      ( hAPP(hAPP(c_List_Odrop(U_19656),U_19658),U_19657) = c_List_Olist_ONil(U_19656)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19656)),U_19657)),U_19658)) ),
    inference(variable_rename,[status(thm)],[f_4669_1]) ).

fof(f_4669_3,plain,
    ! [U_19656,U_19657,U_19658] :
      ( hAPP(hAPP(c_List_Odrop(U_19656),U_19658),U_19657) = c_List_Olist_ONil(U_19656)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19656)),U_19657)),U_19658)) ),
    inference(definitional_conversion,[status(esa)],[f_4669_2]) ).

cnf(f_4669_4,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19656),U_19658),U_19657) = c_List_Olist_ONil(U_19656)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19656)),U_19657)),U_19658)) ),
    inference(clausify,[status(thm)],[f_4669_3]) ).

fof(f_4670_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_4670_2,plain,
    ! [U_19661,U_19660,U_19659] :
      ( ( hAPP(hAPP(c_List_Odrop(U_19659),U_19660),U_19661) = c_List_Olist_ONil(U_19659)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19659)),U_19661)),U_19660)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19659)),U_19661)),U_19660))
        | hAPP(hAPP(c_List_Odrop(U_19659),U_19660),U_19661) != c_List_Olist_ONil(U_19659) ) ),
    inference(variable_rename,[status(thm)],[f_4670_1]) ).

fof(f_4670_3,plain,
    ( ! [U_19667,U_19665,U_19663] :
        ( hAPP(hAPP(c_List_Odrop(U_19663),U_19665),U_19667) = c_List_Olist_ONil(U_19663)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19663)),U_19667)),U_19665)) )
    & ! [U_19666,U_19664,U_19662] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19662)),U_19666)),U_19664))
        | hAPP(hAPP(c_List_Odrop(U_19662),U_19664),U_19666) != c_List_Olist_ONil(U_19662) ) ),
    inference(miniscope,[status(thm)],[f_4670_2]) ).

fof(f_4670_4,plain,
    ( ! [U_19663,U_19665,U_19667] :
        ( hAPP(hAPP(c_List_Odrop(U_19663),U_19665),U_19667) = c_List_Olist_ONil(U_19663)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19663)),U_19667)),U_19665)) )
    & ! [U_19666,U_19664,U_19662] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19662)),U_19666)),U_19664))
        | hAPP(hAPP(c_List_Odrop(U_19662),U_19664),U_19666) != c_List_Olist_ONil(U_19662) ) ),
    inference(definitional_conversion,[status(esa)],[f_4670_3]) ).

cnf(f_4670_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19662)),U_19666)),U_19664))
    | hAPP(hAPP(c_List_Odrop(U_19662),U_19664),U_19666) != c_List_Olist_ONil(U_19662) ),
    inference(clausify,[status(thm)],[f_4670_4]) ).

cnf(f_4670_6,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19663),U_19665),U_19667) = c_List_Olist_ONil(U_19663)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19663)),U_19667)),U_19665)) ),
    inference(clausify,[status(thm)],[f_4670_4]) ).

fof(f_4671_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_4671_2,plain,
    ! [U_19671,U_19670,U_19669,U_19668] : hAPP(hAPP(c_List_Otake(U_19668),U_19669),hAPP(hAPP(c_List_Odrop(U_19668),U_19670),U_19671)) = hAPP(hAPP(c_List_Odrop(U_19668),U_19670),hAPP(hAPP(c_List_Otake(U_19668),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19669),U_19670)),U_19671)),
    inference(variable_rename,[status(thm)],[f_4671_1]) ).

fof(f_4671_3,plain,
    ! [U_19668,U_19669,U_19670,U_19671] : hAPP(hAPP(c_List_Otake(U_19668),U_19669),hAPP(hAPP(c_List_Odrop(U_19668),U_19670),U_19671)) = hAPP(hAPP(c_List_Odrop(U_19668),U_19670),hAPP(hAPP(c_List_Otake(U_19668),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19669),U_19670)),U_19671)),
    inference(definitional_conversion,[status(esa)],[f_4671_2]) ).

cnf(f_4671_4,plain,
    hAPP(hAPP(c_List_Otake(U_19668),U_19669),hAPP(hAPP(c_List_Odrop(U_19668),U_19670),U_19671)) = hAPP(hAPP(c_List_Odrop(U_19668),U_19670),hAPP(hAPP(c_List_Otake(U_19668),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19669),U_19670)),U_19671)),
    inference(clausify,[status(thm)],[f_4671_3]) ).

fof(f_4672_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_4672_2,plain,
    ! [U_19675,U_19674,U_19673,U_19672] : hAPP(hAPP(c_List_Odrop(U_19672),U_19673),hAPP(hAPP(c_List_Otake(U_19672),U_19674),U_19675)) = hAPP(hAPP(c_List_Otake(U_19672),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19674),U_19673)),hAPP(hAPP(c_List_Odrop(U_19672),U_19673),U_19675)),
    inference(variable_rename,[status(thm)],[f_4672_1]) ).

fof(f_4672_3,plain,
    ! [U_19672,U_19673,U_19674,U_19675] : hAPP(hAPP(c_List_Odrop(U_19672),U_19673),hAPP(hAPP(c_List_Otake(U_19672),U_19674),U_19675)) = hAPP(hAPP(c_List_Otake(U_19672),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19674),U_19673)),hAPP(hAPP(c_List_Odrop(U_19672),U_19673),U_19675)),
    inference(definitional_conversion,[status(esa)],[f_4672_2]) ).

cnf(f_4672_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19672),U_19673),hAPP(hAPP(c_List_Otake(U_19672),U_19674),U_19675)) = hAPP(hAPP(c_List_Otake(U_19672),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19674),U_19673)),hAPP(hAPP(c_List_Odrop(U_19672),U_19673),U_19675)),
    inference(clausify,[status(thm)],[f_4672_3]) ).

fof(f_4673_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_4673_2,plain,
    ! [U_19679,U_19678,U_19677,U_19676] :
      ( hBOOL(hAPP(hAPP(c_member(U_19676),U_19677),hAPP(c_List_Oset(U_19676),U_19679)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19676),U_19677),hAPP(c_List_Oset(U_19676),hAPP(hAPP(c_List_Odrop(U_19676),U_19678),U_19679)))) ),
    inference(variable_rename,[status(thm)],[f_4673_1]) ).

fof(f_4673_3,plain,
    ! [U_19676,U_19677,U_19678,U_19679] :
      ( hBOOL(hAPP(hAPP(c_member(U_19676),U_19677),hAPP(c_List_Oset(U_19676),U_19679)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19676),U_19677),hAPP(c_List_Oset(U_19676),hAPP(hAPP(c_List_Odrop(U_19676),U_19678),U_19679)))) ),
    inference(definitional_conversion,[status(esa)],[f_4673_2]) ).

cnf(f_4673_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19676),U_19677),hAPP(c_List_Oset(U_19676),U_19679)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19676),U_19677),hAPP(c_List_Oset(U_19676),hAPP(hAPP(c_List_Odrop(U_19676),U_19678),U_19679)))) ),
    inference(clausify,[status(thm)],[f_4673_3]) ).

fof(f_4674_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_4674_2,plain,
    ! [U_19681,U_19680] : hAPP(c_List_Oset(U_19680),hAPP(c_List_Orotate1(U_19680),U_19681)) = hAPP(c_List_Oset(U_19680),U_19681),
    inference(variable_rename,[status(thm)],[f_4674_1]) ).

fof(f_4674_3,plain,
    ! [U_19680,U_19681] : hAPP(c_List_Oset(U_19680),hAPP(c_List_Orotate1(U_19680),U_19681)) = hAPP(c_List_Oset(U_19680),U_19681),
    inference(definitional_conversion,[status(esa)],[f_4674_2]) ).

cnf(f_4674_4,plain,
    hAPP(c_List_Oset(U_19680),hAPP(c_List_Orotate1(U_19680),U_19681)) = hAPP(c_List_Oset(U_19680),U_19681),
    inference(clausify,[status(thm)],[f_4674_3]) ).

fof(f_4675_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_4675_2,plain,
    ! [U_19684,U_19683,U_19682] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19682,tc_HOL_Obool)),hAPP(c_List_Oset(U_19682),hAPP(hAPP(c_List_Odrop(U_19682),U_19683),U_19684))),hAPP(c_List_Oset(U_19682),U_19684))),
    inference(variable_rename,[status(thm)],[f_4675_1]) ).

fof(f_4675_3,plain,
    ! [U_19682,U_19683,U_19684] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19682,tc_HOL_Obool)),hAPP(c_List_Oset(U_19682),hAPP(hAPP(c_List_Odrop(U_19682),U_19683),U_19684))),hAPP(c_List_Oset(U_19682),U_19684))),
    inference(definitional_conversion,[status(esa)],[f_4675_2]) ).

cnf(f_4675_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19682,tc_HOL_Obool)),hAPP(c_List_Oset(U_19682),hAPP(hAPP(c_List_Odrop(U_19682),U_19683),U_19684))),hAPP(c_List_Oset(U_19682),U_19684))),
    inference(clausify,[status(thm)],[f_4675_3]) ).

fof(f_4676_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_4676_2,plain,
    ! [U_19686,U_19685] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_19685),hAPP(c_List_Orotate1(U_19685),U_19686)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19685),U_19686)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_19685),U_19686))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19685),hAPP(c_List_Orotate1(U_19685),U_19686))) ) ),
    inference(variable_rename,[status(thm)],[f_4676_1]) ).

fof(f_4676_3,plain,
    ( ! [U_19690,U_19688] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19688),hAPP(c_List_Orotate1(U_19688),U_19690)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19688),U_19690)) )
    & ! [U_19689,U_19687] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19687),U_19689))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19687),hAPP(c_List_Orotate1(U_19687),U_19689))) ) ),
    inference(miniscope,[status(thm)],[f_4676_2]) ).

fof(f_4676_4,plain,
    ( ! [U_19688,U_19690] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19688),hAPP(c_List_Orotate1(U_19688),U_19690)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19688),U_19690)) )
    & ! [U_19689,U_19687] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19687),U_19689))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19687),hAPP(c_List_Orotate1(U_19687),U_19689))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4676_3]) ).

cnf(f_4676_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19687),U_19689))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19687),hAPP(c_List_Orotate1(U_19687),U_19689))) ),
    inference(clausify,[status(thm)],[f_4676_4]) ).

cnf(f_4676_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19688),hAPP(c_List_Orotate1(U_19688),U_19690)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19688),U_19690)) ),
    inference(clausify,[status(thm)],[f_4676_4]) ).

fof(f_4677_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_4677_2,plain,
    ! [U_19693,U_19692,U_19691] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19691),hAPP(hAPP(c_List_Odrop(U_19691),U_19693),U_19692)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19691),U_19692)) ),
    inference(variable_rename,[status(thm)],[f_4677_1]) ).

fof(f_4677_3,plain,
    ! [U_19691,U_19692,U_19693] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19691),hAPP(hAPP(c_List_Odrop(U_19691),U_19693),U_19692)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19691),U_19692)) ),
    inference(definitional_conversion,[status(esa)],[f_4677_2]) ).

cnf(f_4677_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19691),hAPP(hAPP(c_List_Odrop(U_19691),U_19693),U_19692)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19691),U_19692)) ),
    inference(clausify,[status(thm)],[f_4677_3]) ).

fof(f_4678_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_4678_2,plain,
    ! [U_19697,U_19696,U_19695,U_19694] : hAPP(hAPP(c_List_Odrop(U_19694),U_19695),hAPP(hAPP(c_List_Odrop(U_19694),U_19696),U_19697)) = hAPP(hAPP(c_List_Odrop(U_19694),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19695),U_19696)),U_19697),
    inference(variable_rename,[status(thm)],[f_4678_1]) ).

fof(f_4678_3,plain,
    ! [U_19694,U_19695,U_19696,U_19697] : hAPP(hAPP(c_List_Odrop(U_19694),U_19695),hAPP(hAPP(c_List_Odrop(U_19694),U_19696),U_19697)) = hAPP(hAPP(c_List_Odrop(U_19694),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19695),U_19696)),U_19697),
    inference(definitional_conversion,[status(esa)],[f_4678_2]) ).

cnf(f_4678_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19694),U_19695),hAPP(hAPP(c_List_Odrop(U_19694),U_19696),U_19697)) = hAPP(hAPP(c_List_Odrop(U_19694),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19695),U_19696)),U_19697),
    inference(clausify,[status(thm)],[f_4678_3]) ).

fof(f_4679_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_4679_2,plain,
    ! [U_19699,U_19698] : hAPP(hAPP(c_List_Odrop(U_19698),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19699) = U_19699,
    inference(variable_rename,[status(thm)],[f_4679_1]) ).

fof(f_4679_3,plain,
    ! [U_19699,U_19698] : hAPP(hAPP(c_List_Odrop(U_19698),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19699) = U_19699,
    inference(definitional_conversion,[status(esa)],[f_4679_2]) ).

cnf(f_4679_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19698),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19699) = U_19699,
    inference(clausify,[status(thm)],[f_4679_3]) ).

fof(f_4680_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_4680_2,plain,
    ! [U_19704,U_19703,U_19702,U_19701,U_19700] : hAPP(hAPP(c_List_Odrop(tc_prod(U_19700,U_19701)),U_19702),hAPP(hAPP(c_List_Ozip(U_19700,U_19701),U_19703),U_19704)) = hAPP(hAPP(c_List_Ozip(U_19700,U_19701),hAPP(hAPP(c_List_Odrop(U_19700),U_19702),U_19703)),hAPP(hAPP(c_List_Odrop(U_19701),U_19702),U_19704)),
    inference(variable_rename,[status(thm)],[f_4680_1]) ).

fof(f_4680_3,plain,
    ! [U_19700,U_19701,U_19702,U_19703,U_19704] : hAPP(hAPP(c_List_Odrop(tc_prod(U_19700,U_19701)),U_19702),hAPP(hAPP(c_List_Ozip(U_19700,U_19701),U_19703),U_19704)) = hAPP(hAPP(c_List_Ozip(U_19700,U_19701),hAPP(hAPP(c_List_Odrop(U_19700),U_19702),U_19703)),hAPP(hAPP(c_List_Odrop(U_19701),U_19702),U_19704)),
    inference(definitional_conversion,[status(esa)],[f_4680_2]) ).

cnf(f_4680_4,plain,
    hAPP(hAPP(c_List_Odrop(tc_prod(U_19700,U_19701)),U_19702),hAPP(hAPP(c_List_Ozip(U_19700,U_19701),U_19703),U_19704)) = hAPP(hAPP(c_List_Ozip(U_19700,U_19701),hAPP(hAPP(c_List_Odrop(U_19700),U_19702),U_19703)),hAPP(hAPP(c_List_Odrop(U_19701),U_19702),U_19704)),
    inference(clausify,[status(thm)],[f_4680_3]) ).

fof(f_4681_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_4681_2,plain,
    ! [U_19709,U_19708,U_19707,U_19706,U_19705] : hAPP(hAPP(c_List_Odrop(U_19705),U_19706),hAPP(hAPP(c_List_Omap(U_19707,U_19705),U_19708),U_19709)) = hAPP(hAPP(c_List_Omap(U_19707,U_19705),U_19708),hAPP(hAPP(c_List_Odrop(U_19707),U_19706),U_19709)),
    inference(variable_rename,[status(thm)],[f_4681_1]) ).

fof(f_4681_3,plain,
    ! [U_19705,U_19706,U_19707,U_19708,U_19709] : hAPP(hAPP(c_List_Odrop(U_19705),U_19706),hAPP(hAPP(c_List_Omap(U_19707,U_19705),U_19708),U_19709)) = hAPP(hAPP(c_List_Omap(U_19707,U_19705),U_19708),hAPP(hAPP(c_List_Odrop(U_19707),U_19706),U_19709)),
    inference(definitional_conversion,[status(esa)],[f_4681_2]) ).

cnf(f_4681_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19705),U_19706),hAPP(hAPP(c_List_Omap(U_19707,U_19705),U_19708),U_19709)) = hAPP(hAPP(c_List_Omap(U_19707,U_19705),U_19708),hAPP(hAPP(c_List_Odrop(U_19707),U_19706),U_19709)),
    inference(clausify,[status(thm)],[f_4681_3]) ).

fof(f_4682_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_4682_2,plain,
    ! [U_19712,U_19711,U_19710] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19710)),hAPP(hAPP(c_List_Odrop(U_19710),U_19711),U_19712)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19710)),U_19712)),U_19711),
    inference(variable_rename,[status(thm)],[f_4682_1]) ).

fof(f_4682_3,plain,
    ! [U_19710,U_19711,U_19712] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19710)),hAPP(hAPP(c_List_Odrop(U_19710),U_19711),U_19712)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19710)),U_19712)),U_19711),
    inference(definitional_conversion,[status(esa)],[f_4682_2]) ).

cnf(f_4682_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19710)),hAPP(hAPP(c_List_Odrop(U_19710),U_19711),U_19712)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19710)),U_19712)),U_19711),
    inference(clausify,[status(thm)],[f_4682_3]) ).

fof(f_4683_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_4683_2,plain,
    ! [U_19714,U_19713] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19713)),hAPP(c_List_Orotate1(U_19713),U_19714)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19713)),U_19714),
    inference(variable_rename,[status(thm)],[f_4683_1]) ).

fof(f_4683_3,plain,
    ! [U_19713,U_19714] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19713)),hAPP(c_List_Orotate1(U_19713),U_19714)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19713)),U_19714),
    inference(definitional_conversion,[status(esa)],[f_4683_2]) ).

cnf(f_4683_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19713)),hAPP(c_List_Orotate1(U_19713),U_19714)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19713)),U_19714),
    inference(clausify,[status(thm)],[f_4683_3]) ).

fof(f_4684_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_4684_2,plain,
    ! [U_19718,U_19717,U_19716,U_19715] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19717,tc_HOL_Obool)),hAPP(c_List_Oset(U_19717),hAPP(hAPP(c_List_Odrop(U_19717),U_19716),U_19718))),hAPP(c_List_Oset(U_19717),hAPP(hAPP(c_List_Odrop(U_19717),U_19715),U_19718))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19715),U_19716)) ),
    inference(variable_rename,[status(thm)],[f_4684_1]) ).

fof(f_4684_3,plain,
    ! [U_19715,U_19716,U_19717,U_19718] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19717,tc_HOL_Obool)),hAPP(c_List_Oset(U_19717),hAPP(hAPP(c_List_Odrop(U_19717),U_19716),U_19718))),hAPP(c_List_Oset(U_19717),hAPP(hAPP(c_List_Odrop(U_19717),U_19715),U_19718))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19715),U_19716)) ),
    inference(definitional_conversion,[status(esa)],[f_4684_2]) ).

cnf(f_4684_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19717,tc_HOL_Obool)),hAPP(c_List_Oset(U_19717),hAPP(hAPP(c_List_Odrop(U_19717),U_19716),U_19718))),hAPP(c_List_Oset(U_19717),hAPP(hAPP(c_List_Odrop(U_19717),U_19715),U_19718))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19715),U_19716)) ),
    inference(clausify,[status(thm)],[f_4684_3]) ).

fof(f_4685_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_4685_2,plain,
    ! [U_19721,U_19720,U_19719] : hAPP(hAPP(c_List_Odrop(U_19719),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_19719),U_19720),U_19721)) = U_19721,
    inference(variable_rename,[status(thm)],[f_4685_1]) ).

fof(f_4685_3,plain,
    ! [U_19719,U_19720,U_19721] : hAPP(hAPP(c_List_Odrop(U_19719),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_19719),U_19720),U_19721)) = U_19721,
    inference(definitional_conversion,[status(esa)],[f_4685_2]) ).

cnf(f_4685_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19719),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_19719),U_19720),U_19721)) = U_19721,
    inference(clausify,[status(thm)],[f_4685_3]) ).

fof(f_4686_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_4686_2,plain,
    ! [U_19725,U_19724,U_19723,U_19722] : hAPP(hAPP(c_List_Odrop(U_19722),hAPP(c_Nat_OSuc,U_19723)),hAPP(hAPP(c_List_Olist_OCons(U_19722),U_19724),U_19725)) = hAPP(hAPP(c_List_Odrop(U_19722),U_19723),U_19725),
    inference(variable_rename,[status(thm)],[f_4686_1]) ).

fof(f_4686_3,plain,
    ! [U_19722,U_19723,U_19724,U_19725] : hAPP(hAPP(c_List_Odrop(U_19722),hAPP(c_Nat_OSuc,U_19723)),hAPP(hAPP(c_List_Olist_OCons(U_19722),U_19724),U_19725)) = hAPP(hAPP(c_List_Odrop(U_19722),U_19723),U_19725),
    inference(definitional_conversion,[status(esa)],[f_4686_2]) ).

cnf(f_4686_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19722),hAPP(c_Nat_OSuc,U_19723)),hAPP(hAPP(c_List_Olist_OCons(U_19722),U_19724),U_19725)) = hAPP(hAPP(c_List_Odrop(U_19722),U_19723),U_19725),
    inference(clausify,[status(thm)],[f_4686_3]) ).

fof(f_4687_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_4687_2,plain,
    ! [U_19730,U_19729,U_19728,U_19727,U_19726] :
      ( hAPP(hAPP(c_List_Onth(U_19726),U_19728),U_19727) = U_19729
      | hAPP(hAPP(c_List_Odrop(U_19726),U_19727),U_19728) != hAPP(hAPP(c_List_Olist_OCons(U_19726),U_19729),U_19730) ),
    inference(variable_rename,[status(thm)],[f_4687_1]) ).

fof(f_4687_3,plain,
    ! [U_19726,U_19727,U_19728,U_19729,U_19730] :
      ( hAPP(hAPP(c_List_Onth(U_19726),U_19728),U_19727) = U_19729
      | hAPP(hAPP(c_List_Odrop(U_19726),U_19727),U_19728) != hAPP(hAPP(c_List_Olist_OCons(U_19726),U_19729),U_19730) ),
    inference(definitional_conversion,[status(esa)],[f_4687_2]) ).

cnf(f_4687_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_19726),U_19728),U_19727) = U_19729
    | hAPP(hAPP(c_List_Odrop(U_19726),U_19727),U_19728) != hAPP(hAPP(c_List_Olist_OCons(U_19726),U_19729),U_19730) ),
    inference(clausify,[status(thm)],[f_4687_3]) ).

fof(f_4688_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_4688_2,plain,
    ! [U_19734,U_19733,U_19732,U_19731] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19731),U_19732),U_19733) = U_19734
        | U_19733 != hAPP(hAPP(c_List_Odrop(U_19731),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19731)),U_19732)),U_19734)
        | U_19732 != hAPP(hAPP(c_List_Otake(U_19731),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19731)),U_19732)),U_19734) )
      & ( ( U_19733 = hAPP(hAPP(c_List_Odrop(U_19731),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19731)),U_19732)),U_19734)
          & U_19732 = hAPP(hAPP(c_List_Otake(U_19731),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19731)),U_19732)),U_19734) )
        | hAPP(hAPP(c_List_Oappend(U_19731),U_19732),U_19733) != U_19734 ) ),
    inference(variable_rename,[status(thm)],[f_4688_1]) ).

fof(f_4688_3,plain,
    ( ! [U_19742,U_19740,U_19738,U_19736] :
        ( hAPP(hAPP(c_List_Oappend(U_19736),U_19738),U_19740) = U_19742
        | U_19740 != hAPP(hAPP(c_List_Odrop(U_19736),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19736)),U_19738)),U_19742)
        | U_19738 != hAPP(hAPP(c_List_Otake(U_19736),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19736)),U_19738)),U_19742) )
    & ! [U_19741,U_19739,U_19737,U_19735] :
        ( ( U_19739 = hAPP(hAPP(c_List_Odrop(U_19735),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19735)),U_19737)),U_19741)
          & U_19737 = hAPP(hAPP(c_List_Otake(U_19735),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19735)),U_19737)),U_19741) )
        | hAPP(hAPP(c_List_Oappend(U_19735),U_19737),U_19739) != U_19741 ) ),
    inference(miniscope,[status(thm)],[f_4688_2]) ).

fof(f_4688_4,plain,
    ( ! [U_19741,U_19737,U_19739,U_19735] :
        ( U_19739 = hAPP(hAPP(c_List_Odrop(U_19735),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19735)),U_19737)),U_19741)
        | ~ sP1195(U_19741,U_19737,U_19739,U_19735) )
    & ! [U_19741,U_19737,U_19739,U_19735] :
        ( U_19737 = hAPP(hAPP(c_List_Otake(U_19735),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19735)),U_19737)),U_19741)
        | ~ sP1195(U_19741,U_19737,U_19739,U_19735) )
    & ! [U_19740,U_19736,U_19742,U_19738] :
        ( hAPP(hAPP(c_List_Oappend(U_19736),U_19738),U_19740) = U_19742
        | U_19740 != hAPP(hAPP(c_List_Odrop(U_19736),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19736)),U_19738)),U_19742)
        | U_19738 != hAPP(hAPP(c_List_Otake(U_19736),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19736)),U_19738)),U_19742) )
    & ! [U_19741,U_19737,U_19739,U_19735] :
        ( sP1195(U_19741,U_19737,U_19739,U_19735)
        | hAPP(hAPP(c_List_Oappend(U_19735),U_19737),U_19739) != U_19741 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1195])],[f_4688_3]) ).

cnf(f_4688_5,plain,
    ( sP1195(U_19741,U_19737,U_19739,U_19735)
    | hAPP(hAPP(c_List_Oappend(U_19735),U_19737),U_19739) != U_19741 ),
    inference(clausify,[status(thm)],[f_4688_4]) ).

cnf(f_4688_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19736),U_19738),U_19740) = U_19742
    | U_19740 != hAPP(hAPP(c_List_Odrop(U_19736),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19736)),U_19738)),U_19742)
    | U_19738 != hAPP(hAPP(c_List_Otake(U_19736),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19736)),U_19738)),U_19742) ),
    inference(clausify,[status(thm)],[f_4688_4]) ).

cnf(f_4688_7,plain,
    ( U_19737 = hAPP(hAPP(c_List_Otake(U_19735),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19735)),U_19737)),U_19741)
    | ~ sP1195(U_19741,U_19737,U_19739,U_19735) ),
    inference(clausify,[status(thm)],[f_4688_4]) ).

cnf(f_4688_8,plain,
    ( U_19739 = hAPP(hAPP(c_List_Odrop(U_19735),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19735)),U_19737)),U_19741)
    | ~ sP1195(U_19741,U_19737,U_19739,U_19735) ),
    inference(clausify,[status(thm)],[f_4688_4]) ).

fof(f_4689_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_4689_2,plain,
    ! [U_19745,U_19744,U_19743] : hAPP(hAPP(c_List_Oappend(U_19743),hAPP(hAPP(c_List_Otake(U_19743),U_19744),U_19745)),hAPP(hAPP(c_List_Odrop(U_19743),U_19744),U_19745)) = U_19745,
    inference(variable_rename,[status(thm)],[f_4689_1]) ).

fof(f_4689_3,plain,
    ! [U_19743,U_19744,U_19745] : hAPP(hAPP(c_List_Oappend(U_19743),hAPP(hAPP(c_List_Otake(U_19743),U_19744),U_19745)),hAPP(hAPP(c_List_Odrop(U_19743),U_19744),U_19745)) = U_19745,
    inference(definitional_conversion,[status(esa)],[f_4689_2]) ).

cnf(f_4689_4,plain,
    hAPP(hAPP(c_List_Oappend(U_19743),hAPP(hAPP(c_List_Otake(U_19743),U_19744),U_19745)),hAPP(hAPP(c_List_Odrop(U_19743),U_19744),U_19745)) = U_19745,
    inference(clausify,[status(thm)],[f_4689_3]) ).

fof(f_4690_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_4690_2,plain,
    ! [U_19749,U_19748,U_19747,U_19746] : hAPP(hAPP(c_List_Odrop(U_19746),U_19747),hAPP(hAPP(c_List_Oappend(U_19746),U_19748),U_19749)) = hAPP(hAPP(c_List_Oappend(U_19746),hAPP(hAPP(c_List_Odrop(U_19746),U_19747),U_19748)),hAPP(hAPP(c_List_Odrop(U_19746),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19747),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19746)),U_19748))),U_19749)),
    inference(variable_rename,[status(thm)],[f_4690_1]) ).

fof(f_4690_3,plain,
    ! [U_19746,U_19747,U_19748,U_19749] : hAPP(hAPP(c_List_Odrop(U_19746),U_19747),hAPP(hAPP(c_List_Oappend(U_19746),U_19748),U_19749)) = hAPP(hAPP(c_List_Oappend(U_19746),hAPP(hAPP(c_List_Odrop(U_19746),U_19747),U_19748)),hAPP(hAPP(c_List_Odrop(U_19746),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19747),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19746)),U_19748))),U_19749)),
    inference(definitional_conversion,[status(esa)],[f_4690_2]) ).

cnf(f_4690_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19746),U_19747),hAPP(hAPP(c_List_Oappend(U_19746),U_19748),U_19749)) = hAPP(hAPP(c_List_Oappend(U_19746),hAPP(hAPP(c_List_Odrop(U_19746),U_19747),U_19748)),hAPP(hAPP(c_List_Odrop(U_19746),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19747),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19746)),U_19748))),U_19749)),
    inference(clausify,[status(thm)],[f_4690_3]) ).

fof(f_4691_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_4691_2,plain,
    ! [U_19753,U_19752,U_19751,U_19750] : hAPP(hAPP(c_List_Odrop(U_19750),U_19751),hAPP(hAPP(c_List_Olist_OCons(U_19750),U_19752),U_19753)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_19750),hAPP(hAPP(c_List_Olist_OCons(U_19750),U_19752),U_19753),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_19750),tc_List_Olist(U_19750)),c_List_Odrop(U_19750)),U_19753),U_19751),
    inference(variable_rename,[status(thm)],[f_4691_1]) ).

fof(f_4691_3,plain,
    ! [U_19750,U_19751,U_19752,U_19753] : hAPP(hAPP(c_List_Odrop(U_19750),U_19751),hAPP(hAPP(c_List_Olist_OCons(U_19750),U_19752),U_19753)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_19750),hAPP(hAPP(c_List_Olist_OCons(U_19750),U_19752),U_19753),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_19750),tc_List_Olist(U_19750)),c_List_Odrop(U_19750)),U_19753),U_19751),
    inference(definitional_conversion,[status(esa)],[f_4691_2]) ).

cnf(f_4691_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19750),U_19751),hAPP(hAPP(c_List_Olist_OCons(U_19750),U_19752),U_19753)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_19750),hAPP(hAPP(c_List_Olist_OCons(U_19750),U_19752),U_19753),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_19750),tc_List_Olist(U_19750)),c_List_Odrop(U_19750)),U_19753),U_19751),
    inference(clausify,[status(thm)],[f_4691_3]) ).

fof(f_4692_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_4692_2,plain,
    ! [U_19757,U_19756,U_19755,U_19754] :
      ( ( hAPP(hAPP(c_List_Odrop(U_19755),U_19754),hAPP(hAPP(c_List_Olist_OCons(U_19755),U_19756),U_19757)) = hAPP(hAPP(c_List_Odrop(U_19755),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19754),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19757)
        | U_19754 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(U_19755),U_19754),hAPP(hAPP(c_List_Olist_OCons(U_19755),U_19756),U_19757)) = hAPP(hAPP(c_List_Olist_OCons(U_19755),U_19756),U_19757)
        | U_19754 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4692_1]) ).

fof(f_4692_3,plain,
    ( ! [U_19765,U_19763,U_19761,U_19759] :
        ( hAPP(hAPP(c_List_Odrop(U_19761),U_19759),hAPP(hAPP(c_List_Olist_OCons(U_19761),U_19763),U_19765)) = hAPP(hAPP(c_List_Odrop(U_19761),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19759),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19765)
        | U_19759 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19764,U_19762,U_19760,U_19758] :
        ( hAPP(hAPP(c_List_Odrop(U_19760),U_19758),hAPP(hAPP(c_List_Olist_OCons(U_19760),U_19762),U_19764)) = hAPP(hAPP(c_List_Olist_OCons(U_19760),U_19762),U_19764)
        | U_19758 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4692_2]) ).

fof(f_4692_4,plain,
    ( ! [U_19759,U_19761,U_19763,U_19765] :
        ( hAPP(hAPP(c_List_Odrop(U_19761),U_19759),hAPP(hAPP(c_List_Olist_OCons(U_19761),U_19763),U_19765)) = hAPP(hAPP(c_List_Odrop(U_19761),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19759),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19765)
        | U_19759 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19760,U_19762,U_19764,U_19758] :
        ( hAPP(hAPP(c_List_Odrop(U_19760),U_19758),hAPP(hAPP(c_List_Olist_OCons(U_19760),U_19762),U_19764)) = hAPP(hAPP(c_List_Olist_OCons(U_19760),U_19762),U_19764)
        | U_19758 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4692_3]) ).

cnf(f_4692_5,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19760),U_19758),hAPP(hAPP(c_List_Olist_OCons(U_19760),U_19762),U_19764)) = hAPP(hAPP(c_List_Olist_OCons(U_19760),U_19762),U_19764)
    | U_19758 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4692_4]) ).

cnf(f_4692_6,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19761),U_19759),hAPP(hAPP(c_List_Olist_OCons(U_19761),U_19763),U_19765)) = hAPP(hAPP(c_List_Odrop(U_19761),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19759),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19765)
    | U_19759 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4692_4]) ).

fof(f_4693_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_4693_2,plain,
    ! [U_19769,U_19768,U_19767,U_19766] :
      ( hAPP(hAPP(c_List_Onth(U_19768),hAPP(hAPP(c_List_Odrop(U_19768),U_19766),U_19769)),U_19767) = hAPP(hAPP(c_List_Onth(U_19768),U_19769),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19766),U_19767))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19766),U_19767)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19768)),U_19769))) ),
    inference(variable_rename,[status(thm)],[f_4693_1]) ).

fof(f_4693_3,plain,
    ! [U_19767,U_19766,U_19768,U_19769] :
      ( hAPP(hAPP(c_List_Onth(U_19768),hAPP(hAPP(c_List_Odrop(U_19768),U_19766),U_19769)),U_19767) = hAPP(hAPP(c_List_Onth(U_19768),U_19769),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19766),U_19767))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19766),U_19767)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19768)),U_19769))) ),
    inference(definitional_conversion,[status(esa)],[f_4693_2]) ).

cnf(f_4693_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_19768),hAPP(hAPP(c_List_Odrop(U_19768),U_19766),U_19769)),U_19767) = hAPP(hAPP(c_List_Onth(U_19768),U_19769),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19766),U_19767))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19766),U_19767)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19768)),U_19769))) ),
    inference(clausify,[status(thm)],[f_4693_3]) ).

fof(f_4694_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_4694_2,plain,
    ! [U_19774,U_19773,U_19772,U_19771,U_19770] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19770),U_19771),U_19772) = hAPP(hAPP(c_List_Oappend(U_19770),U_19773),U_19774)
        | ( ( hAPP(hAPP(c_List_Oappend(U_19770),hAPP(hAPP(c_List_Odrop(U_19770),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19773)),U_19771)),U_19772) != U_19774
            | hAPP(hAPP(c_List_Otake(U_19770),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19773)),U_19771) != U_19773 )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19771)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19773))) )
        | ( ( U_19772 != hAPP(hAPP(c_List_Oappend(U_19770),hAPP(hAPP(c_List_Odrop(U_19770),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19771)),U_19773)),U_19774)
            | U_19771 != hAPP(hAPP(c_List_Otake(U_19770),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19771)),U_19773) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19771)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19773))) ) )
      & ( ( ( ( hAPP(hAPP(c_List_Oappend(U_19770),hAPP(hAPP(c_List_Odrop(U_19770),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19773)),U_19771)),U_19772) = U_19774
              & hAPP(hAPP(c_List_Otake(U_19770),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19773)),U_19771) = U_19773 )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19771)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19773))) )
          & ( ( U_19772 = hAPP(hAPP(c_List_Oappend(U_19770),hAPP(hAPP(c_List_Odrop(U_19770),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19771)),U_19773)),U_19774)
              & U_19771 = hAPP(hAPP(c_List_Otake(U_19770),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19771)),U_19773) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19771)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19770)),U_19773))) ) )
        | hAPP(hAPP(c_List_Oappend(U_19770),U_19771),U_19772) != hAPP(hAPP(c_List_Oappend(U_19770),U_19773),U_19774) ) ),
    inference(variable_rename,[status(thm)],[f_4694_1]) ).

fof(f_4694_3,plain,
    ( ! [U_19784,U_19782,U_19780,U_19778,U_19776] :
        ( hAPP(hAPP(c_List_Oappend(U_19776),U_19778),U_19780) = hAPP(hAPP(c_List_Oappend(U_19776),U_19782),U_19784)
        | ( ( hAPP(hAPP(c_List_Oappend(U_19776),hAPP(hAPP(c_List_Odrop(U_19776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19782)),U_19778)),U_19780) != U_19784
            | hAPP(hAPP(c_List_Otake(U_19776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19782)),U_19778) != U_19782 )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19778)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19782))) )
        | ( ( U_19780 != hAPP(hAPP(c_List_Oappend(U_19776),hAPP(hAPP(c_List_Odrop(U_19776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19778)),U_19782)),U_19784)
            | U_19778 != hAPP(hAPP(c_List_Otake(U_19776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19778)),U_19782) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19778)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19782))) ) )
    & ! [U_19783,U_19781,U_19779,U_19777,U_19775] :
        ( ( ( ( hAPP(hAPP(c_List_Oappend(U_19775),hAPP(hAPP(c_List_Odrop(U_19775),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19781)),U_19777)),U_19779) = U_19783
              & hAPP(hAPP(c_List_Otake(U_19775),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19781)),U_19777) = U_19781 )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19777)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19781))) )
          & ( ( U_19779 = hAPP(hAPP(c_List_Oappend(U_19775),hAPP(hAPP(c_List_Odrop(U_19775),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19777)),U_19781)),U_19783)
              & U_19777 = hAPP(hAPP(c_List_Otake(U_19775),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19777)),U_19781) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19777)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19781))) ) )
        | hAPP(hAPP(c_List_Oappend(U_19775),U_19777),U_19779) != hAPP(hAPP(c_List_Oappend(U_19775),U_19781),U_19783) ) ),
    inference(miniscope,[status(thm)],[f_4694_2]) ).

fof(f_4694_4,plain,
    ( ! [U_19776,U_19780,U_19778,U_19782,U_19784] :
        ( hAPP(hAPP(c_List_Oappend(U_19776),hAPP(hAPP(c_List_Odrop(U_19776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19782)),U_19778)),U_19780) != U_19784
        | hAPP(hAPP(c_List_Otake(U_19776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19782)),U_19778) != U_19782
        | ~ sP1200(U_19776,U_19780,U_19778,U_19782,U_19784) )
    & ! [U_19776,U_19780,U_19778,U_19782,U_19784] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19778)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19782)))
        | ~ sP1200(U_19776,U_19780,U_19778,U_19782,U_19784) )
    & ! [U_19776,U_19780,U_19778,U_19782,U_19784] :
        ( U_19780 != hAPP(hAPP(c_List_Oappend(U_19776),hAPP(hAPP(c_List_Odrop(U_19776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19778)),U_19782)),U_19784)
        | U_19778 != hAPP(hAPP(c_List_Otake(U_19776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19778)),U_19782)
        | ~ sP1199(U_19776,U_19780,U_19778,U_19782,U_19784) )
    & ! [U_19776,U_19780,U_19778,U_19782,U_19784] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19778)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19782)))
        | ~ sP1199(U_19776,U_19780,U_19778,U_19782,U_19784) )
    & ! [U_19777,U_19781,U_19775,U_19779,U_19783] :
        ( hAPP(hAPP(c_List_Oappend(U_19775),hAPP(hAPP(c_List_Odrop(U_19775),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19781)),U_19777)),U_19779) = U_19783
        | ~ sP1197(U_19777,U_19781,U_19775,U_19779,U_19783) )
    & ! [U_19777,U_19781,U_19775,U_19779,U_19783] :
        ( hAPP(hAPP(c_List_Otake(U_19775),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19781)),U_19777) = U_19781
        | ~ sP1197(U_19777,U_19781,U_19775,U_19779,U_19783) )
    & ! [U_19777,U_19781,U_19775,U_19779,U_19783] :
        ( U_19779 = hAPP(hAPP(c_List_Oappend(U_19775),hAPP(hAPP(c_List_Odrop(U_19775),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19777)),U_19781)),U_19783)
        | ~ sP1196(U_19777,U_19781,U_19775,U_19779,U_19783) )
    & ! [U_19777,U_19781,U_19775,U_19779,U_19783] :
        ( U_19777 = hAPP(hAPP(c_List_Otake(U_19775),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19777)),U_19781)
        | ~ sP1196(U_19777,U_19781,U_19775,U_19779,U_19783) )
    & ! [U_19777,U_19781,U_19775,U_19779,U_19783] :
        ( sP1197(U_19777,U_19781,U_19775,U_19779,U_19783)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19777)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19781)))
        | ~ sP1198(U_19777,U_19781,U_19775,U_19779,U_19783) )
    & ! [U_19777,U_19781,U_19775,U_19779,U_19783] :
        ( sP1196(U_19777,U_19781,U_19775,U_19779,U_19783)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19777)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19781)))
        | ~ sP1198(U_19777,U_19781,U_19775,U_19779,U_19783) )
    & ! [U_19776,U_19780,U_19778,U_19782,U_19784] :
        ( hAPP(hAPP(c_List_Oappend(U_19776),U_19778),U_19780) = hAPP(hAPP(c_List_Oappend(U_19776),U_19782),U_19784)
        | sP1200(U_19776,U_19780,U_19778,U_19782,U_19784)
        | sP1199(U_19776,U_19780,U_19778,U_19782,U_19784) )
    & ! [U_19777,U_19781,U_19775,U_19779,U_19783] :
        ( sP1198(U_19777,U_19781,U_19775,U_19779,U_19783)
        | hAPP(hAPP(c_List_Oappend(U_19775),U_19777),U_19779) != hAPP(hAPP(c_List_Oappend(U_19775),U_19781),U_19783) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1196,sP1197,sP1198,sP1199,sP1200])],[f_4694_3]) ).

cnf(f_4694_5,plain,
    ( sP1198(U_19777,U_19781,U_19775,U_19779,U_19783)
    | hAPP(hAPP(c_List_Oappend(U_19775),U_19777),U_19779) != hAPP(hAPP(c_List_Oappend(U_19775),U_19781),U_19783) ),
    inference(clausify,[status(thm)],[f_4694_4]) ).

cnf(f_4694_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19776),U_19778),U_19780) = hAPP(hAPP(c_List_Oappend(U_19776),U_19782),U_19784)
    | sP1200(U_19776,U_19780,U_19778,U_19782,U_19784)
    | sP1199(U_19776,U_19780,U_19778,U_19782,U_19784) ),
    inference(clausify,[status(thm)],[f_4694_4]) ).

cnf(f_4694_7,plain,
    ( sP1196(U_19777,U_19781,U_19775,U_19779,U_19783)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19777)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19781)))
    | ~ sP1198(U_19777,U_19781,U_19775,U_19779,U_19783) ),
    inference(clausify,[status(thm)],[f_4694_4]) ).

cnf(f_4694_8,plain,
    ( sP1197(U_19777,U_19781,U_19775,U_19779,U_19783)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19777)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19781)))
    | ~ sP1198(U_19777,U_19781,U_19775,U_19779,U_19783) ),
    inference(clausify,[status(thm)],[f_4694_4]) ).

cnf(f_4694_9,plain,
    ( U_19777 = hAPP(hAPP(c_List_Otake(U_19775),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19777)),U_19781)
    | ~ sP1196(U_19777,U_19781,U_19775,U_19779,U_19783) ),
    inference(clausify,[status(thm)],[f_4694_4]) ).

cnf(f_4694_10,plain,
    ( U_19779 = hAPP(hAPP(c_List_Oappend(U_19775),hAPP(hAPP(c_List_Odrop(U_19775),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19777)),U_19781)),U_19783)
    | ~ sP1196(U_19777,U_19781,U_19775,U_19779,U_19783) ),
    inference(clausify,[status(thm)],[f_4694_4]) ).

cnf(f_4694_11,plain,
    ( hAPP(hAPP(c_List_Otake(U_19775),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19781)),U_19777) = U_19781
    | ~ sP1197(U_19777,U_19781,U_19775,U_19779,U_19783) ),
    inference(clausify,[status(thm)],[f_4694_4]) ).

cnf(f_4694_12,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19775),hAPP(hAPP(c_List_Odrop(U_19775),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19775)),U_19781)),U_19777)),U_19779) = U_19783
    | ~ sP1197(U_19777,U_19781,U_19775,U_19779,U_19783) ),
    inference(clausify,[status(thm)],[f_4694_4]) ).

cnf(f_4694_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19778)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19782)))
    | ~ sP1199(U_19776,U_19780,U_19778,U_19782,U_19784) ),
    inference(clausify,[status(thm)],[f_4694_4]) ).

cnf(f_4694_14,plain,
    ( U_19780 != hAPP(hAPP(c_List_Oappend(U_19776),hAPP(hAPP(c_List_Odrop(U_19776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19778)),U_19782)),U_19784)
    | U_19778 != hAPP(hAPP(c_List_Otake(U_19776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19778)),U_19782)
    | ~ sP1199(U_19776,U_19780,U_19778,U_19782,U_19784) ),
    inference(clausify,[status(thm)],[f_4694_4]) ).

cnf(f_4694_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19778)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19782)))
    | ~ sP1200(U_19776,U_19780,U_19778,U_19782,U_19784) ),
    inference(clausify,[status(thm)],[f_4694_4]) ).

cnf(f_4694_16,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19776),hAPP(hAPP(c_List_Odrop(U_19776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19782)),U_19778)),U_19780) != U_19784
    | hAPP(hAPP(c_List_Otake(U_19776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19776)),U_19782)),U_19778) != U_19782
    | ~ sP1200(U_19776,U_19780,U_19778,U_19782,U_19784) ),
    inference(clausify,[status(thm)],[f_4694_4]) ).

fof(f_4695_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_4695_2,plain,
    ! [U_19787,U_19786,U_19785] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_19786),hAPP(hAPP(c_List_Onth(U_19786),U_19787),U_19785)),hAPP(hAPP(c_List_Odrop(U_19786),hAPP(c_Nat_OSuc,U_19785)),U_19787)) = hAPP(hAPP(c_List_Odrop(U_19786),U_19785),U_19787)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19785),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19786)),U_19787))) ),
    inference(variable_rename,[status(thm)],[f_4695_1]) ).

fof(f_4695_3,plain,
    ! [U_19785,U_19786,U_19787] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_19786),hAPP(hAPP(c_List_Onth(U_19786),U_19787),U_19785)),hAPP(hAPP(c_List_Odrop(U_19786),hAPP(c_Nat_OSuc,U_19785)),U_19787)) = hAPP(hAPP(c_List_Odrop(U_19786),U_19785),U_19787)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19785),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19786)),U_19787))) ),
    inference(definitional_conversion,[status(esa)],[f_4695_2]) ).

cnf(f_4695_4,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_19786),hAPP(hAPP(c_List_Onth(U_19786),U_19787),U_19785)),hAPP(hAPP(c_List_Odrop(U_19786),hAPP(c_Nat_OSuc,U_19785)),U_19787)) = hAPP(hAPP(c_List_Odrop(U_19786),U_19785),U_19787)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19785),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19786)),U_19787))) ),
    inference(clausify,[status(thm)],[f_4695_3]) ).

fof(f_4696_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_4696_2,plain,
    ! [U_19791,U_19790,U_19789,U_19788] :
      ( hAPP(c_List_Orotate1(U_19789),hAPP(hAPP(c_List_Olist_OCons(U_19789),U_19790),U_19791)) = hAPP(hAPP(c_List_Oappend(U_19789),U_19791),hAPP(hAPP(c_List_Olist_OCons(U_19789),U_19790),c_List_Olist_ONil(U_19789)))
      & hAPP(c_List_Orotate1(U_19788),c_List_Olist_ONil(U_19788)) = c_List_Olist_ONil(U_19788) ),
    inference(variable_rename,[status(thm)],[f_4696_1]) ).

fof(f_4696_3,plain,
    ( ! [U_19791,U_19790,U_19789] : hAPP(c_List_Orotate1(U_19789),hAPP(hAPP(c_List_Olist_OCons(U_19789),U_19790),U_19791)) = hAPP(hAPP(c_List_Oappend(U_19789),U_19791),hAPP(hAPP(c_List_Olist_OCons(U_19789),U_19790),c_List_Olist_ONil(U_19789)))
    & ! [U_19788] : hAPP(c_List_Orotate1(U_19788),c_List_Olist_ONil(U_19788)) = c_List_Olist_ONil(U_19788) ),
    inference(miniscope,[status(thm)],[f_4696_2]) ).

fof(f_4696_4,plain,
    ( ! [U_19790,U_19789,U_19791] : hAPP(c_List_Orotate1(U_19789),hAPP(hAPP(c_List_Olist_OCons(U_19789),U_19790),U_19791)) = hAPP(hAPP(c_List_Oappend(U_19789),U_19791),hAPP(hAPP(c_List_Olist_OCons(U_19789),U_19790),c_List_Olist_ONil(U_19789)))
    & ! [U_19788] : hAPP(c_List_Orotate1(U_19788),c_List_Olist_ONil(U_19788)) = c_List_Olist_ONil(U_19788) ),
    inference(definitional_conversion,[status(esa)],[f_4696_3]) ).

cnf(f_4696_5,plain,
    hAPP(c_List_Orotate1(U_19788),c_List_Olist_ONil(U_19788)) = c_List_Olist_ONil(U_19788),
    inference(clausify,[status(thm)],[f_4696_4]) ).

cnf(f_4696_6,plain,
    hAPP(c_List_Orotate1(U_19789),hAPP(hAPP(c_List_Olist_OCons(U_19789),U_19790),U_19791)) = hAPP(hAPP(c_List_Oappend(U_19789),U_19791),hAPP(hAPP(c_List_Olist_OCons(U_19789),U_19790),c_List_Olist_ONil(U_19789))),
    inference(clausify,[status(thm)],[f_4696_4]) ).

fof(f_4697_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_4697_2,plain,
    ! [U_19795,U_19794,U_19793,U_19792] :
      ( ( hAPP(hAPP(c_List_Odrop(U_19793),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19792)),hAPP(hAPP(c_List_Olist_OCons(U_19793),U_19794),U_19795)) = hAPP(hAPP(c_List_Odrop(U_19793),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19792)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19795)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19792) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(U_19793),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19792)),hAPP(hAPP(c_List_Olist_OCons(U_19793),U_19794),U_19795)) = hAPP(hAPP(c_List_Olist_OCons(U_19793),U_19794),U_19795)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19792) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4697_1]) ).

fof(f_4697_3,plain,
    ( ! [U_19803,U_19801,U_19799,U_19797] :
        ( hAPP(hAPP(c_List_Odrop(U_19799),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19797)),hAPP(hAPP(c_List_Olist_OCons(U_19799),U_19801),U_19803)) = hAPP(hAPP(c_List_Odrop(U_19799),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19797)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19803)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19797) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19802,U_19800,U_19798,U_19796] :
        ( hAPP(hAPP(c_List_Odrop(U_19798),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19796)),hAPP(hAPP(c_List_Olist_OCons(U_19798),U_19800),U_19802)) = hAPP(hAPP(c_List_Olist_OCons(U_19798),U_19800),U_19802)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19796) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4697_2]) ).

fof(f_4697_4,plain,
    ( ! [U_19797,U_19799,U_19801,U_19803] :
        ( hAPP(hAPP(c_List_Odrop(U_19799),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19797)),hAPP(hAPP(c_List_Olist_OCons(U_19799),U_19801),U_19803)) = hAPP(hAPP(c_List_Odrop(U_19799),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19797)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19803)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19797) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19798,U_19802,U_19796,U_19800] :
        ( hAPP(hAPP(c_List_Odrop(U_19798),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19796)),hAPP(hAPP(c_List_Olist_OCons(U_19798),U_19800),U_19802)) = hAPP(hAPP(c_List_Olist_OCons(U_19798),U_19800),U_19802)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19796) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4697_3]) ).

cnf(f_4697_5,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19798),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19796)),hAPP(hAPP(c_List_Olist_OCons(U_19798),U_19800),U_19802)) = hAPP(hAPP(c_List_Olist_OCons(U_19798),U_19800),U_19802)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19796) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4697_4]) ).

cnf(f_4697_6,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19799),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19797)),hAPP(hAPP(c_List_Olist_OCons(U_19799),U_19801),U_19803)) = hAPP(hAPP(c_List_Odrop(U_19799),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19797)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19803)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19797) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4697_4]) ).

fof(f_4698_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_4698_2,plain,
    ! [U_19807,U_19806,U_19805,U_19804] :
      ( hAPP(hAPP(c_List_Otake(U_19806),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19804),U_19805)),U_19807) = hAPP(hAPP(c_List_Oappend(U_19806),hAPP(hAPP(c_List_Otake(U_19806),U_19804),U_19807)),hAPP(hAPP(c_List_Otake(U_19806),U_19805),hAPP(hAPP(c_List_Odrop(U_19806),U_19804),U_19807)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19804),U_19805)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19806)),U_19807))) ),
    inference(variable_rename,[status(thm)],[f_4698_1]) ).

fof(f_4698_3,plain,
    ! [U_19804,U_19805,U_19806,U_19807] :
      ( hAPP(hAPP(c_List_Otake(U_19806),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19804),U_19805)),U_19807) = hAPP(hAPP(c_List_Oappend(U_19806),hAPP(hAPP(c_List_Otake(U_19806),U_19804),U_19807)),hAPP(hAPP(c_List_Otake(U_19806),U_19805),hAPP(hAPP(c_List_Odrop(U_19806),U_19804),U_19807)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19804),U_19805)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19806)),U_19807))) ),
    inference(definitional_conversion,[status(esa)],[f_4698_2]) ).

cnf(f_4698_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_19806),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19804),U_19805)),U_19807) = hAPP(hAPP(c_List_Oappend(U_19806),hAPP(hAPP(c_List_Otake(U_19806),U_19804),U_19807)),hAPP(hAPP(c_List_Otake(U_19806),U_19805),hAPP(hAPP(c_List_Odrop(U_19806),U_19804),U_19807)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19804),U_19805)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19806)),U_19807))) ),
    inference(clausify,[status(thm)],[f_4698_3]) ).

fof(f_4699_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_4699_2,plain,
    ! [U_19809,U_19808] :
      ( hAPP(c_List_Orotate1(U_19808),U_19809) = U_19809
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19808)),U_19809)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_4699_1]) ).

fof(f_4699_3,plain,
    ! [U_19808,U_19809] :
      ( hAPP(c_List_Orotate1(U_19808),U_19809) = U_19809
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19808)),U_19809)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(definitional_conversion,[status(esa)],[f_4699_2]) ).

cnf(f_4699_4,plain,
    ( hAPP(c_List_Orotate1(U_19808),U_19809) = U_19809
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19808)),U_19809)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_4699_3]) ).

fof(f_4700_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_4700_2,plain,
    ! [U_19814,U_19813,U_19812,U_19811,U_19810] : hAPP(hAPP(c_List_Ozip(U_19810,U_19811),U_19812),hAPP(hAPP(c_List_Oappend(U_19811),U_19813),U_19814)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19810,U_19811)),hAPP(hAPP(c_List_Ozip(U_19810,U_19811),hAPP(hAPP(c_List_Otake(U_19810),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19811)),U_19813)),U_19812)),U_19813)),hAPP(hAPP(c_List_Ozip(U_19810,U_19811),hAPP(hAPP(c_List_Odrop(U_19810),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19811)),U_19813)),U_19812)),U_19814)),
    inference(variable_rename,[status(thm)],[f_4700_1]) ).

fof(f_4700_3,plain,
    ! [U_19810,U_19811,U_19812,U_19813,U_19814] : hAPP(hAPP(c_List_Ozip(U_19810,U_19811),U_19812),hAPP(hAPP(c_List_Oappend(U_19811),U_19813),U_19814)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19810,U_19811)),hAPP(hAPP(c_List_Ozip(U_19810,U_19811),hAPP(hAPP(c_List_Otake(U_19810),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19811)),U_19813)),U_19812)),U_19813)),hAPP(hAPP(c_List_Ozip(U_19810,U_19811),hAPP(hAPP(c_List_Odrop(U_19810),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19811)),U_19813)),U_19812)),U_19814)),
    inference(definitional_conversion,[status(esa)],[f_4700_2]) ).

cnf(f_4700_4,plain,
    hAPP(hAPP(c_List_Ozip(U_19810,U_19811),U_19812),hAPP(hAPP(c_List_Oappend(U_19811),U_19813),U_19814)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19810,U_19811)),hAPP(hAPP(c_List_Ozip(U_19810,U_19811),hAPP(hAPP(c_List_Otake(U_19810),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19811)),U_19813)),U_19812)),U_19813)),hAPP(hAPP(c_List_Ozip(U_19810,U_19811),hAPP(hAPP(c_List_Odrop(U_19810),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19811)),U_19813)),U_19812)),U_19814)),
    inference(clausify,[status(thm)],[f_4700_3]) ).

fof(f_4701_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_4701_2,plain,
    ! [U_19819,U_19818,U_19817,U_19816,U_19815] : hAPP(hAPP(c_List_Ozip(U_19815,U_19816),hAPP(hAPP(c_List_Oappend(U_19815),U_19817),U_19818)),U_19819) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19815,U_19816)),hAPP(hAPP(c_List_Ozip(U_19815,U_19816),U_19817),hAPP(hAPP(c_List_Otake(U_19816),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19815)),U_19817)),U_19819))),hAPP(hAPP(c_List_Ozip(U_19815,U_19816),U_19818),hAPP(hAPP(c_List_Odrop(U_19816),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19815)),U_19817)),U_19819))),
    inference(variable_rename,[status(thm)],[f_4701_1]) ).

fof(f_4701_3,plain,
    ! [U_19815,U_19816,U_19817,U_19818,U_19819] : hAPP(hAPP(c_List_Ozip(U_19815,U_19816),hAPP(hAPP(c_List_Oappend(U_19815),U_19817),U_19818)),U_19819) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19815,U_19816)),hAPP(hAPP(c_List_Ozip(U_19815,U_19816),U_19817),hAPP(hAPP(c_List_Otake(U_19816),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19815)),U_19817)),U_19819))),hAPP(hAPP(c_List_Ozip(U_19815,U_19816),U_19818),hAPP(hAPP(c_List_Odrop(U_19816),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19815)),U_19817)),U_19819))),
    inference(definitional_conversion,[status(esa)],[f_4701_2]) ).

cnf(f_4701_4,plain,
    hAPP(hAPP(c_List_Ozip(U_19815,U_19816),hAPP(hAPP(c_List_Oappend(U_19815),U_19817),U_19818)),U_19819) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19815,U_19816)),hAPP(hAPP(c_List_Ozip(U_19815,U_19816),U_19817),hAPP(hAPP(c_List_Otake(U_19816),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19815)),U_19817)),U_19819))),hAPP(hAPP(c_List_Ozip(U_19815,U_19816),U_19818),hAPP(hAPP(c_List_Odrop(U_19816),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19815)),U_19817)),U_19819))),
    inference(clausify,[status(thm)],[f_4701_3]) ).

fof(f_4702_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_4702_2,plain,
    ! [U_19822,U_19821,U_19820] :
      ( U_19822 = hAPP(hAPP(c_List_Oappend(U_19821),hAPP(hAPP(c_List_Otake(U_19821),U_19820),U_19822)),hAPP(hAPP(c_List_Olist_OCons(U_19821),hAPP(hAPP(c_List_Onth(U_19821),U_19822),U_19820)),hAPP(hAPP(c_List_Odrop(U_19821),hAPP(c_Nat_OSuc,U_19820)),U_19822)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19820),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19821)),U_19822))) ),
    inference(variable_rename,[status(thm)],[f_4702_1]) ).

fof(f_4702_3,plain,
    ! [U_19820,U_19821,U_19822] :
      ( U_19822 = hAPP(hAPP(c_List_Oappend(U_19821),hAPP(hAPP(c_List_Otake(U_19821),U_19820),U_19822)),hAPP(hAPP(c_List_Olist_OCons(U_19821),hAPP(hAPP(c_List_Onth(U_19821),U_19822),U_19820)),hAPP(hAPP(c_List_Odrop(U_19821),hAPP(c_Nat_OSuc,U_19820)),U_19822)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19820),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19821)),U_19822))) ),
    inference(definitional_conversion,[status(esa)],[f_4702_2]) ).

cnf(f_4702_4,plain,
    ( U_19822 = hAPP(hAPP(c_List_Oappend(U_19821),hAPP(hAPP(c_List_Otake(U_19821),U_19820),U_19822)),hAPP(hAPP(c_List_Olist_OCons(U_19821),hAPP(hAPP(c_List_Onth(U_19821),U_19822),U_19820)),hAPP(hAPP(c_List_Odrop(U_19821),hAPP(c_Nat_OSuc,U_19820)),U_19822)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19820),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19821)),U_19822))) ),
    inference(clausify,[status(thm)],[f_4702_3]) ).

fof(f_4703_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_4703_2,plain,
    ! [U_19825,U_19824,U_19823] :
      ( hAPP(hAPP(c_List_Oappend(U_19824),hAPP(hAPP(c_List_Otake(U_19824),U_19823),U_19825)),hAPP(hAPP(c_List_Olist_OCons(U_19824),hAPP(c_List_Ohd(U_19824),hAPP(hAPP(c_List_Odrop(U_19824),U_19823),U_19825))),c_List_Olist_ONil(U_19824))) = hAPP(hAPP(c_List_Otake(U_19824),hAPP(c_Nat_OSuc,U_19823)),U_19825)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19823),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19824)),U_19825))) ),
    inference(variable_rename,[status(thm)],[f_4703_1]) ).

fof(f_4703_3,plain,
    ! [U_19823,U_19824,U_19825] :
      ( hAPP(hAPP(c_List_Oappend(U_19824),hAPP(hAPP(c_List_Otake(U_19824),U_19823),U_19825)),hAPP(hAPP(c_List_Olist_OCons(U_19824),hAPP(c_List_Ohd(U_19824),hAPP(hAPP(c_List_Odrop(U_19824),U_19823),U_19825))),c_List_Olist_ONil(U_19824))) = hAPP(hAPP(c_List_Otake(U_19824),hAPP(c_Nat_OSuc,U_19823)),U_19825)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19823),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19824)),U_19825))) ),
    inference(definitional_conversion,[status(esa)],[f_4703_2]) ).

cnf(f_4703_4,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19824),hAPP(hAPP(c_List_Otake(U_19824),U_19823),U_19825)),hAPP(hAPP(c_List_Olist_OCons(U_19824),hAPP(c_List_Ohd(U_19824),hAPP(hAPP(c_List_Odrop(U_19824),U_19823),U_19825))),c_List_Olist_ONil(U_19824))) = hAPP(hAPP(c_List_Otake(U_19824),hAPP(c_Nat_OSuc,U_19823)),U_19825)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19823),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19824)),U_19825))) ),
    inference(clausify,[status(thm)],[f_4703_3]) ).

fof(f_4704_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_4704_2,plain,
    ! [U_19828,U_19827,U_19826] :
      ( hAPP(c_List_Ohd(U_19827),hAPP(hAPP(c_List_Odrop(U_19827),U_19828),U_19826)) = hAPP(hAPP(c_List_Onth(U_19827),U_19826),U_19828)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19828),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19827)),U_19826)))
      | U_19826 = c_List_Olist_ONil(U_19827) ),
    inference(variable_rename,[status(thm)],[f_4704_1]) ).

fof(f_4704_3,plain,
    ! [U_19826,U_19827,U_19828] :
      ( hAPP(c_List_Ohd(U_19827),hAPP(hAPP(c_List_Odrop(U_19827),U_19828),U_19826)) = hAPP(hAPP(c_List_Onth(U_19827),U_19826),U_19828)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19828),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19827)),U_19826)))
      | U_19826 = c_List_Olist_ONil(U_19827) ),
    inference(definitional_conversion,[status(esa)],[f_4704_2]) ).

cnf(f_4704_4,plain,
    ( hAPP(c_List_Ohd(U_19827),hAPP(hAPP(c_List_Odrop(U_19827),U_19828),U_19826)) = hAPP(hAPP(c_List_Onth(U_19827),U_19826),U_19828)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19828),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19827)),U_19826)))
    | U_19826 = c_List_Olist_ONil(U_19827) ),
    inference(clausify,[status(thm)],[f_4704_3]) ).

fof(f_4705_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_4705_2,plain,
    ! [U_19831,U_19830,U_19829] :
      ( hAPP(c_List_Ohd(U_19830),hAPP(hAPP(c_List_Oappend(U_19830),U_19829),U_19831)) = hAPP(c_List_Ohd(U_19830),U_19829)
      | U_19829 = c_List_Olist_ONil(U_19830) ),
    inference(variable_rename,[status(thm)],[f_4705_1]) ).

fof(f_4705_3,plain,
    ! [U_19830,U_19829,U_19831] :
      ( hAPP(c_List_Ohd(U_19830),hAPP(hAPP(c_List_Oappend(U_19830),U_19829),U_19831)) = hAPP(c_List_Ohd(U_19830),U_19829)
      | U_19829 = c_List_Olist_ONil(U_19830) ),
    inference(definitional_conversion,[status(esa)],[f_4705_2]) ).

cnf(f_4705_4,plain,
    ( hAPP(c_List_Ohd(U_19830),hAPP(hAPP(c_List_Oappend(U_19830),U_19829),U_19831)) = hAPP(c_List_Ohd(U_19830),U_19829)
    | U_19829 = c_List_Olist_ONil(U_19830) ),
    inference(clausify,[status(thm)],[f_4705_3]) ).

fof(f_4706_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_4706_2,plain,
    ! [U_19834,U_19833,U_19832] :
      ( ( hAPP(c_List_Ohd(U_19833),hAPP(hAPP(c_List_Oappend(U_19833),U_19832),U_19834)) = hAPP(c_List_Ohd(U_19833),U_19832)
        | U_19832 = c_List_Olist_ONil(U_19833) )
      & ( hAPP(c_List_Ohd(U_19833),hAPP(hAPP(c_List_Oappend(U_19833),U_19832),U_19834)) = hAPP(c_List_Ohd(U_19833),U_19834)
        | U_19832 != c_List_Olist_ONil(U_19833) ) ),
    inference(variable_rename,[status(thm)],[f_4706_1]) ).

fof(f_4706_3,plain,
    ( ! [U_19840,U_19838,U_19836] :
        ( hAPP(c_List_Ohd(U_19838),hAPP(hAPP(c_List_Oappend(U_19838),U_19836),U_19840)) = hAPP(c_List_Ohd(U_19838),U_19836)
        | U_19836 = c_List_Olist_ONil(U_19838) )
    & ! [U_19839,U_19837,U_19835] :
        ( hAPP(c_List_Ohd(U_19837),hAPP(hAPP(c_List_Oappend(U_19837),U_19835),U_19839)) = hAPP(c_List_Ohd(U_19837),U_19839)
        | U_19835 != c_List_Olist_ONil(U_19837) ) ),
    inference(miniscope,[status(thm)],[f_4706_2]) ).

fof(f_4706_4,plain,
    ( ! [U_19836,U_19838,U_19840] :
        ( hAPP(c_List_Ohd(U_19838),hAPP(hAPP(c_List_Oappend(U_19838),U_19836),U_19840)) = hAPP(c_List_Ohd(U_19838),U_19836)
        | U_19836 = c_List_Olist_ONil(U_19838) )
    & ! [U_19839,U_19837,U_19835] :
        ( hAPP(c_List_Ohd(U_19837),hAPP(hAPP(c_List_Oappend(U_19837),U_19835),U_19839)) = hAPP(c_List_Ohd(U_19837),U_19839)
        | U_19835 != c_List_Olist_ONil(U_19837) ) ),
    inference(definitional_conversion,[status(esa)],[f_4706_3]) ).

cnf(f_4706_5,plain,
    ( hAPP(c_List_Ohd(U_19837),hAPP(hAPP(c_List_Oappend(U_19837),U_19835),U_19839)) = hAPP(c_List_Ohd(U_19837),U_19839)
    | U_19835 != c_List_Olist_ONil(U_19837) ),
    inference(clausify,[status(thm)],[f_4706_4]) ).

cnf(f_4706_6,plain,
    ( hAPP(c_List_Ohd(U_19838),hAPP(hAPP(c_List_Oappend(U_19838),U_19836),U_19840)) = hAPP(c_List_Ohd(U_19838),U_19836)
    | U_19836 = c_List_Olist_ONil(U_19838) ),
    inference(clausify,[status(thm)],[f_4706_4]) ).

fof(f_4707_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_4707_2,plain,
    ! [U_19843,U_19842,U_19841] : hAPP(c_List_Ohd(U_19841),hAPP(hAPP(c_List_Olist_OCons(U_19841),U_19842),U_19843)) = U_19842,
    inference(variable_rename,[status(thm)],[f_4707_1]) ).

fof(f_4707_3,plain,
    ! [U_19841,U_19842,U_19843] : hAPP(c_List_Ohd(U_19841),hAPP(hAPP(c_List_Olist_OCons(U_19841),U_19842),U_19843)) = U_19842,
    inference(definitional_conversion,[status(esa)],[f_4707_2]) ).

cnf(f_4707_4,plain,
    hAPP(c_List_Ohd(U_19841),hAPP(hAPP(c_List_Olist_OCons(U_19841),U_19842),U_19843)) = U_19842,
    inference(clausify,[status(thm)],[f_4707_3]) ).

fof(f_4708_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_4708_2,plain,
    ! [U_19847,U_19846,U_19845,U_19844] :
      ( hAPP(c_List_Ohd(U_19846),hAPP(hAPP(c_List_Omap(U_19845,U_19846),U_19847),U_19844)) = hAPP(U_19847,hAPP(c_List_Ohd(U_19845),U_19844))
      | U_19844 = c_List_Olist_ONil(U_19845) ),
    inference(variable_rename,[status(thm)],[f_4708_1]) ).

fof(f_4708_3,plain,
    ! [U_19844,U_19845,U_19846,U_19847] :
      ( hAPP(c_List_Ohd(U_19846),hAPP(hAPP(c_List_Omap(U_19845,U_19846),U_19847),U_19844)) = hAPP(U_19847,hAPP(c_List_Ohd(U_19845),U_19844))
      | U_19844 = c_List_Olist_ONil(U_19845) ),
    inference(definitional_conversion,[status(esa)],[f_4708_2]) ).

cnf(f_4708_4,plain,
    ( hAPP(c_List_Ohd(U_19846),hAPP(hAPP(c_List_Omap(U_19845,U_19846),U_19847),U_19844)) = hAPP(U_19847,hAPP(c_List_Ohd(U_19845),U_19844))
    | U_19844 = c_List_Olist_ONil(U_19845) ),
    inference(clausify,[status(thm)],[f_4708_3]) ).

fof(f_4709_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_4709_2,plain,
    ! [U_19849,U_19848] :
      ( hBOOL(hAPP(hAPP(c_member(U_19849),hAPP(c_List_Ohd(U_19849),U_19848)),hAPP(c_List_Oset(U_19849),U_19848)))
      | U_19848 = c_List_Olist_ONil(U_19849) ),
    inference(variable_rename,[status(thm)],[f_4709_1]) ).

fof(f_4709_3,plain,
    ! [U_19848,U_19849] :
      ( hBOOL(hAPP(hAPP(c_member(U_19849),hAPP(c_List_Ohd(U_19849),U_19848)),hAPP(c_List_Oset(U_19849),U_19848)))
      | U_19848 = c_List_Olist_ONil(U_19849) ),
    inference(definitional_conversion,[status(esa)],[f_4709_2]) ).

cnf(f_4709_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19849),hAPP(c_List_Ohd(U_19849),U_19848)),hAPP(c_List_Oset(U_19849),U_19848)))
    | U_19848 = c_List_Olist_ONil(U_19849) ),
    inference(clausify,[status(thm)],[f_4709_3]) ).

fof(f_4710_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_4710_2,plain,
    ! [U_19851,U_19850] :
      ( hAPP(c_List_Ohd(U_19851),U_19850) = hAPP(hAPP(c_List_Onth(U_19851),U_19850),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_19850 = c_List_Olist_ONil(U_19851) ),
    inference(variable_rename,[status(thm)],[f_4710_1]) ).

fof(f_4710_3,plain,
    ! [U_19850,U_19851] :
      ( hAPP(c_List_Ohd(U_19851),U_19850) = hAPP(hAPP(c_List_Onth(U_19851),U_19850),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_19850 = c_List_Olist_ONil(U_19851) ),
    inference(definitional_conversion,[status(esa)],[f_4710_2]) ).

cnf(f_4710_4,plain,
    ( hAPP(c_List_Ohd(U_19851),U_19850) = hAPP(hAPP(c_List_Onth(U_19851),U_19850),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_19850 = c_List_Olist_ONil(U_19851) ),
    inference(clausify,[status(thm)],[f_4710_3]) ).

fof(f_4711_1,plain,
    ! [T_a,V_xs] :
      ( hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),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_4711_2,plain,
    ! [U_19853,U_19852] :
      ( hAPP(c_List_Orotate1(U_19853),U_19852) = hAPP(hAPP(c_List_Oappend(U_19853),c_List_Otl(U_19853,U_19852)),hAPP(hAPP(c_List_Olist_OCons(U_19853),hAPP(c_List_Ohd(U_19853),U_19852)),c_List_Olist_ONil(U_19853)))
      | U_19852 = c_List_Olist_ONil(U_19853) ),
    inference(variable_rename,[status(thm)],[f_4711_1]) ).

fof(f_4711_3,plain,
    ! [U_19852,U_19853] :
      ( hAPP(c_List_Orotate1(U_19853),U_19852) = hAPP(hAPP(c_List_Oappend(U_19853),c_List_Otl(U_19853,U_19852)),hAPP(hAPP(c_List_Olist_OCons(U_19853),hAPP(c_List_Ohd(U_19853),U_19852)),c_List_Olist_ONil(U_19853)))
      | U_19852 = c_List_Olist_ONil(U_19853) ),
    inference(definitional_conversion,[status(esa)],[f_4711_2]) ).

cnf(f_4711_4,plain,
    ( hAPP(c_List_Orotate1(U_19853),U_19852) = hAPP(hAPP(c_List_Oappend(U_19853),c_List_Otl(U_19853,U_19852)),hAPP(hAPP(c_List_Olist_OCons(U_19853),hAPP(c_List_Ohd(U_19853),U_19852)),c_List_Olist_ONil(U_19853)))
    | U_19852 = c_List_Olist_ONil(U_19853) ),
    inference(clausify,[status(thm)],[f_4711_3]) ).

fof(f_4712_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_4712_2,plain,
    ! [U_19856,U_19855,U_19854] :
      ( hAPP(c_List_Ohd(U_19855),hAPP(c_List_Orotate(U_19855,U_19856),U_19854)) = hAPP(hAPP(c_List_Onth(U_19855),U_19854),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19856,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19855)),U_19854)))
      | U_19854 = c_List_Olist_ONil(U_19855) ),
    inference(variable_rename,[status(thm)],[f_4712_1]) ).

fof(f_4712_3,plain,
    ! [U_19854,U_19855,U_19856] :
      ( hAPP(c_List_Ohd(U_19855),hAPP(c_List_Orotate(U_19855,U_19856),U_19854)) = hAPP(hAPP(c_List_Onth(U_19855),U_19854),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19856,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19855)),U_19854)))
      | U_19854 = c_List_Olist_ONil(U_19855) ),
    inference(definitional_conversion,[status(esa)],[f_4712_2]) ).

cnf(f_4712_4,plain,
    ( hAPP(c_List_Ohd(U_19855),hAPP(c_List_Orotate(U_19855,U_19856),U_19854)) = hAPP(hAPP(c_List_Onth(U_19855),U_19854),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19856,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19855)),U_19854)))
    | U_19854 = c_List_Olist_ONil(U_19855) ),
    inference(clausify,[status(thm)],[f_4712_3]) ).

fof(f_4713_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),c_List_Otl(T_a,V_xs)),
    inference(fof_nnf,[status(thm)],[fact_drop__Suc]) ).

fof(f_4713_2,plain,
    ! [U_19859,U_19858,U_19857] : hAPP(hAPP(c_List_Odrop(U_19857),hAPP(c_Nat_OSuc,U_19858)),U_19859) = hAPP(hAPP(c_List_Odrop(U_19857),U_19858),c_List_Otl(U_19857,U_19859)),
    inference(variable_rename,[status(thm)],[f_4713_1]) ).

fof(f_4713_3,plain,
    ! [U_19857,U_19858,U_19859] : hAPP(hAPP(c_List_Odrop(U_19857),hAPP(c_Nat_OSuc,U_19858)),U_19859) = hAPP(hAPP(c_List_Odrop(U_19857),U_19858),c_List_Otl(U_19857,U_19859)),
    inference(definitional_conversion,[status(esa)],[f_4713_2]) ).

cnf(f_4713_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19857),hAPP(c_Nat_OSuc,U_19858)),U_19859) = hAPP(hAPP(c_List_Odrop(U_19857),U_19858),c_List_Otl(U_19857,U_19859)),
    inference(clausify,[status(thm)],[f_4713_3]) ).

fof(f_4714_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Otl(T_a,V_xs)) = 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_4714_2,plain,
    ! [U_19862,U_19861,U_19860] : hAPP(hAPP(c_List_Odrop(U_19860),U_19861),c_List_Otl(U_19860,U_19862)) = c_List_Otl(U_19860,hAPP(hAPP(c_List_Odrop(U_19860),U_19861),U_19862)),
    inference(variable_rename,[status(thm)],[f_4714_1]) ).

fof(f_4714_3,plain,
    ! [U_19860,U_19861,U_19862] : hAPP(hAPP(c_List_Odrop(U_19860),U_19861),c_List_Otl(U_19860,U_19862)) = c_List_Otl(U_19860,hAPP(hAPP(c_List_Odrop(U_19860),U_19861),U_19862)),
    inference(definitional_conversion,[status(esa)],[f_4714_2]) ).

cnf(f_4714_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19860),U_19861),c_List_Otl(U_19860,U_19862)) = c_List_Otl(U_19860,hAPP(hAPP(c_List_Odrop(U_19860),U_19861),U_19862)),
    inference(clausify,[status(thm)],[f_4714_3]) ).

fof(f_4715_1,plain,
    ! [V_xs,V_n,T_a] : 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),c_List_Otl(T_a,V_xs)),
    inference(fof_nnf,[status(thm)],[fact_tl__drop]) ).

fof(f_4715_2,plain,
    ! [U_19865,U_19864,U_19863] : c_List_Otl(U_19863,hAPP(hAPP(c_List_Odrop(U_19863),U_19864),U_19865)) = hAPP(hAPP(c_List_Odrop(U_19863),U_19864),c_List_Otl(U_19863,U_19865)),
    inference(variable_rename,[status(thm)],[f_4715_1]) ).

fof(f_4715_3,plain,
    ! [U_19863,U_19864,U_19865] : c_List_Otl(U_19863,hAPP(hAPP(c_List_Odrop(U_19863),U_19864),U_19865)) = hAPP(hAPP(c_List_Odrop(U_19863),U_19864),c_List_Otl(U_19863,U_19865)),
    inference(definitional_conversion,[status(esa)],[f_4715_2]) ).

cnf(f_4715_4,plain,
    c_List_Otl(U_19863,hAPP(hAPP(c_List_Odrop(U_19863),U_19864),U_19865)) = hAPP(hAPP(c_List_Odrop(U_19863),U_19864),c_List_Otl(U_19863,U_19865)),
    inference(clausify,[status(thm)],[f_4715_3]) ).

fof(f_4716_1,plain,
    ! [T_a] : 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_4716_2,plain,
    ! [U_19866] : c_List_Otl(U_19866,c_List_Olist_ONil(U_19866)) = c_List_Olist_ONil(U_19866),
    inference(variable_rename,[status(thm)],[f_4716_1]) ).

fof(f_4716_3,plain,
    ! [U_19866] : c_List_Otl(U_19866,c_List_Olist_ONil(U_19866)) = c_List_Olist_ONil(U_19866),
    inference(definitional_conversion,[status(esa)],[f_4716_2]) ).

cnf(f_4716_4,plain,
    c_List_Otl(U_19866,c_List_Olist_ONil(U_19866)) = c_List_Olist_ONil(U_19866),
    inference(clausify,[status(thm)],[f_4716_3]) ).

fof(f_4717_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_4717_2,plain,
    ! [U_19869,U_19868,U_19867] :
      ( ( hAPP(c_List_Orotate(U_19867,U_19868),U_19869) = c_List_Olist_ONil(U_19867)
        | U_19869 != c_List_Olist_ONil(U_19867) )
      & ( U_19869 = c_List_Olist_ONil(U_19867)
        | hAPP(c_List_Orotate(U_19867,U_19868),U_19869) != c_List_Olist_ONil(U_19867) ) ),
    inference(variable_rename,[status(thm)],[f_4717_1]) ).

fof(f_4717_3,plain,
    ( ! [U_19875,U_19873,U_19871] :
        ( hAPP(c_List_Orotate(U_19871,U_19873),U_19875) = c_List_Olist_ONil(U_19871)
        | U_19875 != c_List_Olist_ONil(U_19871) )
    & ! [U_19874,U_19872,U_19870] :
        ( U_19874 = c_List_Olist_ONil(U_19870)
        | hAPP(c_List_Orotate(U_19870,U_19872),U_19874) != c_List_Olist_ONil(U_19870) ) ),
    inference(miniscope,[status(thm)],[f_4717_2]) ).

fof(f_4717_4,plain,
    ( ! [U_19871,U_19873,U_19875] :
        ( hAPP(c_List_Orotate(U_19871,U_19873),U_19875) = c_List_Olist_ONil(U_19871)
        | U_19875 != c_List_Olist_ONil(U_19871) )
    & ! [U_19872,U_19874,U_19870] :
        ( U_19874 = c_List_Olist_ONil(U_19870)
        | hAPP(c_List_Orotate(U_19870,U_19872),U_19874) != c_List_Olist_ONil(U_19870) ) ),
    inference(definitional_conversion,[status(esa)],[f_4717_3]) ).

cnf(f_4717_5,plain,
    ( U_19874 = c_List_Olist_ONil(U_19870)
    | hAPP(c_List_Orotate(U_19870,U_19872),U_19874) != c_List_Olist_ONil(U_19870) ),
    inference(clausify,[status(thm)],[f_4717_4]) ).

cnf(f_4717_6,plain,
    ( hAPP(c_List_Orotate(U_19871,U_19873),U_19875) = c_List_Olist_ONil(U_19871)
    | U_19875 != c_List_Olist_ONil(U_19871) ),
    inference(clausify,[status(thm)],[f_4717_4]) ).

fof(f_4718_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Otl(T_a,V_xs)) = 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_4718_2,plain,
    ! [U_19878,U_19877,U_19876] : hAPP(hAPP(c_List_Otake(U_19876),U_19877),c_List_Otl(U_19876,U_19878)) = c_List_Otl(U_19876,hAPP(hAPP(c_List_Otake(U_19876),hAPP(c_Nat_OSuc,U_19877)),U_19878)),
    inference(variable_rename,[status(thm)],[f_4718_1]) ).

fof(f_4718_3,plain,
    ! [U_19876,U_19877,U_19878] : hAPP(hAPP(c_List_Otake(U_19876),U_19877),c_List_Otl(U_19876,U_19878)) = c_List_Otl(U_19876,hAPP(hAPP(c_List_Otake(U_19876),hAPP(c_Nat_OSuc,U_19877)),U_19878)),
    inference(definitional_conversion,[status(esa)],[f_4718_2]) ).

cnf(f_4718_4,plain,
    hAPP(hAPP(c_List_Otake(U_19876),U_19877),c_List_Otl(U_19876,U_19878)) = c_List_Otl(U_19876,hAPP(hAPP(c_List_Otake(U_19876),hAPP(c_Nat_OSuc,U_19877)),U_19878)),
    inference(clausify,[status(thm)],[f_4718_3]) ).

fof(f_4719_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_4719_2,plain,
    ! [U_19881,U_19880,U_19879] : hAPP(c_List_Oset(U_19879),hAPP(c_List_Orotate(U_19879,U_19880),U_19881)) = hAPP(c_List_Oset(U_19879),U_19881),
    inference(variable_rename,[status(thm)],[f_4719_1]) ).

fof(f_4719_3,plain,
    ! [U_19879,U_19880,U_19881] : hAPP(c_List_Oset(U_19879),hAPP(c_List_Orotate(U_19879,U_19880),U_19881)) = hAPP(c_List_Oset(U_19879),U_19881),
    inference(definitional_conversion,[status(esa)],[f_4719_2]) ).

cnf(f_4719_4,plain,
    hAPP(c_List_Oset(U_19879),hAPP(c_List_Orotate(U_19879,U_19880),U_19881)) = hAPP(c_List_Oset(U_19879),U_19881),
    inference(clausify,[status(thm)],[f_4719_3]) ).

fof(f_4720_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_4720_2,plain,
    ! [U_19884,U_19883,U_19882] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_19882),hAPP(c_List_Orotate(U_19882,U_19883),U_19884)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19882),U_19884)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_19882),U_19884))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19882),hAPP(c_List_Orotate(U_19882,U_19883),U_19884))) ) ),
    inference(variable_rename,[status(thm)],[f_4720_1]) ).

fof(f_4720_3,plain,
    ( ! [U_19890,U_19888,U_19886] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19886),hAPP(c_List_Orotate(U_19886,U_19888),U_19890)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19886),U_19890)) )
    & ! [U_19889,U_19887,U_19885] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19885),U_19889))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19885),hAPP(c_List_Orotate(U_19885,U_19887),U_19889))) ) ),
    inference(miniscope,[status(thm)],[f_4720_2]) ).

fof(f_4720_4,plain,
    ( ! [U_19886,U_19888,U_19890] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19886),hAPP(c_List_Orotate(U_19886,U_19888),U_19890)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19886),U_19890)) )
    & ! [U_19887,U_19889,U_19885] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19885),U_19889))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19885),hAPP(c_List_Orotate(U_19885,U_19887),U_19889))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4720_3]) ).

cnf(f_4720_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19885),U_19889))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19885),hAPP(c_List_Orotate(U_19885,U_19887),U_19889))) ),
    inference(clausify,[status(thm)],[f_4720_4]) ).

cnf(f_4720_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19886),hAPP(c_List_Orotate(U_19886,U_19888),U_19890)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19886),U_19890)) ),
    inference(clausify,[status(thm)],[f_4720_4]) ).

fof(f_4721_1,plain,
    ! [V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),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_4721_2,plain,
    ! [U_19892,U_19891] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19891),c_List_Otl(U_19891,U_19892)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19891),U_19892)) ),
    inference(variable_rename,[status(thm)],[f_4721_1]) ).

fof(f_4721_3,plain,
    ! [U_19891,U_19892] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19891),c_List_Otl(U_19891,U_19892)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19891),U_19892)) ),
    inference(definitional_conversion,[status(esa)],[f_4721_2]) ).

cnf(f_4721_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19891),c_List_Otl(U_19891,U_19892)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19891),U_19892)) ),
    inference(clausify,[status(thm)],[f_4721_3]) ).

fof(f_4722_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_4722_2,plain,
    ! [U_19896,U_19895,U_19894,U_19893] : hAPP(c_List_Orotate(U_19893,U_19894),hAPP(c_List_Orotate(U_19893,U_19895),U_19896)) = hAPP(c_List_Orotate(U_19893,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19894),U_19895)),U_19896),
    inference(variable_rename,[status(thm)],[f_4722_1]) ).

fof(f_4722_3,plain,
    ! [U_19893,U_19894,U_19895,U_19896] : hAPP(c_List_Orotate(U_19893,U_19894),hAPP(c_List_Orotate(U_19893,U_19895),U_19896)) = hAPP(c_List_Orotate(U_19893,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19894),U_19895)),U_19896),
    inference(definitional_conversion,[status(esa)],[f_4722_2]) ).

cnf(f_4722_4,plain,
    hAPP(c_List_Orotate(U_19893,U_19894),hAPP(c_List_Orotate(U_19893,U_19895),U_19896)) = hAPP(c_List_Orotate(U_19893,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19894),U_19895)),U_19896),
    inference(clausify,[status(thm)],[f_4722_3]) ).

fof(f_4723_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_4723_2,plain,
    ! [U_19901,U_19900,U_19899,U_19898,U_19897] : hAPP(c_List_Orotate(U_19897,U_19898),hAPP(hAPP(c_List_Omap(U_19899,U_19897),U_19900),U_19901)) = hAPP(hAPP(c_List_Omap(U_19899,U_19897),U_19900),hAPP(c_List_Orotate(U_19899,U_19898),U_19901)),
    inference(variable_rename,[status(thm)],[f_4723_1]) ).

fof(f_4723_3,plain,
    ! [U_19897,U_19898,U_19899,U_19900,U_19901] : hAPP(c_List_Orotate(U_19897,U_19898),hAPP(hAPP(c_List_Omap(U_19899,U_19897),U_19900),U_19901)) = hAPP(hAPP(c_List_Omap(U_19899,U_19897),U_19900),hAPP(c_List_Orotate(U_19899,U_19898),U_19901)),
    inference(definitional_conversion,[status(esa)],[f_4723_2]) ).

cnf(f_4723_4,plain,
    hAPP(c_List_Orotate(U_19897,U_19898),hAPP(hAPP(c_List_Omap(U_19899,U_19897),U_19900),U_19901)) = hAPP(hAPP(c_List_Omap(U_19899,U_19897),U_19900),hAPP(c_List_Orotate(U_19899,U_19898),U_19901)),
    inference(clausify,[status(thm)],[f_4723_3]) ).

fof(f_4724_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_Otl(T_c,V_xs_2)) = 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_4724_2,plain,
    ! [U_19905,U_19904,U_19903,U_19902] : hAPP(hAPP(c_List_Omap(U_19902,U_19903),U_19904),c_List_Otl(U_19902,U_19905)) = c_List_Otl(U_19903,hAPP(hAPP(c_List_Omap(U_19902,U_19903),U_19904),U_19905)),
    inference(variable_rename,[status(thm)],[f_4724_1]) ).

fof(f_4724_3,plain,
    ! [U_19902,U_19903,U_19904,U_19905] : hAPP(hAPP(c_List_Omap(U_19902,U_19903),U_19904),c_List_Otl(U_19902,U_19905)) = c_List_Otl(U_19903,hAPP(hAPP(c_List_Omap(U_19902,U_19903),U_19904),U_19905)),
    inference(definitional_conversion,[status(esa)],[f_4724_2]) ).

cnf(f_4724_4,plain,
    hAPP(hAPP(c_List_Omap(U_19902,U_19903),U_19904),c_List_Otl(U_19902,U_19905)) = c_List_Otl(U_19903,hAPP(hAPP(c_List_Omap(U_19902,U_19903),U_19904),U_19905)),
    inference(clausify,[status(thm)],[f_4724_3]) ).

fof(f_4725_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_4725_2,plain,
    ! [U_19908,U_19907,U_19906] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19906)),hAPP(c_List_Orotate(U_19906,U_19907),U_19908)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19906)),U_19908),
    inference(variable_rename,[status(thm)],[f_4725_1]) ).

fof(f_4725_3,plain,
    ! [U_19907,U_19906,U_19908] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19906)),hAPP(c_List_Orotate(U_19906,U_19907),U_19908)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19906)),U_19908),
    inference(definitional_conversion,[status(esa)],[f_4725_2]) ).

cnf(f_4725_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19906)),hAPP(c_List_Orotate(U_19906,U_19907),U_19908)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19906)),U_19908),
    inference(clausify,[status(thm)],[f_4725_3]) ).

fof(f_4726_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_4726_2,plain,
    ! [U_19911,U_19910,U_19909] : hAPP(c_List_Orotate(U_19909,U_19910),U_19911) = hAPP(c_List_Orotate(U_19909,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19910,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19909)),U_19911))),U_19911),
    inference(variable_rename,[status(thm)],[f_4726_1]) ).

fof(f_4726_3,plain,
    ! [U_19909,U_19910,U_19911] : hAPP(c_List_Orotate(U_19909,U_19910),U_19911) = hAPP(c_List_Orotate(U_19909,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19910,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19909)),U_19911))),U_19911),
    inference(definitional_conversion,[status(esa)],[f_4726_2]) ).

cnf(f_4726_4,plain,
    hAPP(c_List_Orotate(U_19909,U_19910),U_19911) = hAPP(c_List_Orotate(U_19909,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19910,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19909)),U_19911))),U_19911),
    inference(clausify,[status(thm)],[f_4726_3]) ).

fof(f_4727_1,plain,
    ! [V_xs,V_x,T_a] : 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_4727_2,plain,
    ! [U_19914,U_19913,U_19912] : c_List_Otl(U_19912,hAPP(hAPP(c_List_Olist_OCons(U_19912),U_19913),U_19914)) = U_19914,
    inference(variable_rename,[status(thm)],[f_4727_1]) ).

fof(f_4727_3,plain,
    ! [U_19912,U_19913,U_19914] : c_List_Otl(U_19912,hAPP(hAPP(c_List_Olist_OCons(U_19912),U_19913),U_19914)) = U_19914,
    inference(definitional_conversion,[status(esa)],[f_4727_2]) ).

cnf(f_4727_4,plain,
    c_List_Otl(U_19912,hAPP(hAPP(c_List_Olist_OCons(U_19912),U_19913),U_19914)) = U_19914,
    inference(clausify,[status(thm)],[f_4727_3]) ).

fof(f_4728_1,plain,
    ! [V_ys,T_a,V_xs] :
      ( c_List_Otl(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),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_4728_2,plain,
    ! [U_19917,U_19916,U_19915] :
      ( c_List_Otl(U_19916,hAPP(hAPP(c_List_Oappend(U_19916),U_19915),U_19917)) = hAPP(hAPP(c_List_Oappend(U_19916),c_List_Otl(U_19916,U_19915)),U_19917)
      | U_19915 = c_List_Olist_ONil(U_19916) ),
    inference(variable_rename,[status(thm)],[f_4728_1]) ).

fof(f_4728_3,plain,
    ! [U_19915,U_19916,U_19917] :
      ( c_List_Otl(U_19916,hAPP(hAPP(c_List_Oappend(U_19916),U_19915),U_19917)) = hAPP(hAPP(c_List_Oappend(U_19916),c_List_Otl(U_19916,U_19915)),U_19917)
      | U_19915 = c_List_Olist_ONil(U_19916) ),
    inference(definitional_conversion,[status(esa)],[f_4728_2]) ).

cnf(f_4728_4,plain,
    ( c_List_Otl(U_19916,hAPP(hAPP(c_List_Oappend(U_19916),U_19915),U_19917)) = hAPP(hAPP(c_List_Oappend(U_19916),c_List_Otl(U_19916,U_19915)),U_19917)
    | U_19915 = c_List_Olist_ONil(U_19916) ),
    inference(clausify,[status(thm)],[f_4728_3]) ).

fof(f_4729_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_4729_2,plain,
    ! [U_19920,U_19919,U_19918] : hAPP(c_List_Orotate1(U_19918),hAPP(c_List_Orotate(U_19918,U_19919),U_19920)) = hAPP(c_List_Orotate(U_19918,U_19919),hAPP(c_List_Orotate1(U_19918),U_19920)),
    inference(variable_rename,[status(thm)],[f_4729_1]) ).

fof(f_4729_3,plain,
    ! [U_19918,U_19919,U_19920] : hAPP(c_List_Orotate1(U_19918),hAPP(c_List_Orotate(U_19918,U_19919),U_19920)) = hAPP(c_List_Orotate(U_19918,U_19919),hAPP(c_List_Orotate1(U_19918),U_19920)),
    inference(definitional_conversion,[status(esa)],[f_4729_2]) ).

cnf(f_4729_4,plain,
    hAPP(c_List_Orotate1(U_19918),hAPP(c_List_Orotate(U_19918,U_19919),U_19920)) = hAPP(c_List_Orotate(U_19918,U_19919),hAPP(c_List_Orotate1(U_19918),U_19920)),
    inference(clausify,[status(thm)],[f_4729_3]) ).

fof(f_4730_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_4730_2,plain,
    ! [U_19923,U_19922,U_19921] : hAPP(c_List_Orotate(U_19921,hAPP(c_Nat_OSuc,U_19922)),U_19923) = hAPP(c_List_Orotate1(U_19921),hAPP(c_List_Orotate(U_19921,U_19922),U_19923)),
    inference(variable_rename,[status(thm)],[f_4730_1]) ).

fof(f_4730_3,plain,
    ! [U_19921,U_19922,U_19923] : hAPP(c_List_Orotate(U_19921,hAPP(c_Nat_OSuc,U_19922)),U_19923) = hAPP(c_List_Orotate1(U_19921),hAPP(c_List_Orotate(U_19921,U_19922),U_19923)),
    inference(definitional_conversion,[status(esa)],[f_4730_2]) ).

cnf(f_4730_4,plain,
    hAPP(c_List_Orotate(U_19921,hAPP(c_Nat_OSuc,U_19922)),U_19923) = hAPP(c_List_Orotate1(U_19921),hAPP(c_List_Orotate(U_19921,U_19922),U_19923)),
    inference(clausify,[status(thm)],[f_4730_3]) ).

fof(f_4731_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_4731_2,plain,
    ! [U_19925,U_19924] : c_List_Orotate(U_19924,U_19925) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(U_19924),tc_List_Olist(U_19924)),U_19925),c_List_Orotate1(U_19924)),
    inference(variable_rename,[status(thm)],[f_4731_1]) ).

fof(f_4731_3,plain,
    ! [U_19924,U_19925] : c_List_Orotate(U_19924,U_19925) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(U_19924),tc_List_Olist(U_19924)),U_19925),c_List_Orotate1(U_19924)),
    inference(definitional_conversion,[status(esa)],[f_4731_2]) ).

cnf(f_4731_4,plain,
    c_List_Orotate(U_19924,U_19925) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(U_19924),tc_List_Olist(U_19924)),U_19925),c_List_Orotate1(U_19924)),
    inference(clausify,[status(thm)],[f_4731_3]) ).

fof(f_4732_1,plain,
    ! [V_ys_2,V_xs_2,T_b] : 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,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_4732_2,plain,
    ! [U_19928,U_19927,U_19926] : c_List_Otl(U_19926,hAPP(hAPP(c_List_Oappend(U_19926),U_19927),U_19928)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19926),U_19926,c_List_Otl(U_19926,U_19928),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19926),tc_List_Olist(U_19926)),U_19926),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19926),tc_List_Olist(U_19926),tc_List_Olist(U_19926)),c_List_Oappend(U_19926)),U_19928))),U_19927),
    inference(variable_rename,[status(thm)],[f_4732_1]) ).

fof(f_4732_3,plain,
    ! [U_19926,U_19927,U_19928] : c_List_Otl(U_19926,hAPP(hAPP(c_List_Oappend(U_19926),U_19927),U_19928)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19926),U_19926,c_List_Otl(U_19926,U_19928),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19926),tc_List_Olist(U_19926)),U_19926),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19926),tc_List_Olist(U_19926),tc_List_Olist(U_19926)),c_List_Oappend(U_19926)),U_19928))),U_19927),
    inference(definitional_conversion,[status(esa)],[f_4732_2]) ).

cnf(f_4732_4,plain,
    c_List_Otl(U_19926,hAPP(hAPP(c_List_Oappend(U_19926),U_19927),U_19928)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19926),U_19926,c_List_Otl(U_19926,U_19928),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19926),tc_List_Olist(U_19926)),U_19926),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19926),tc_List_Olist(U_19926),tc_List_Olist(U_19926)),c_List_Oappend(U_19926)),U_19928))),U_19927),
    inference(clausify,[status(thm)],[f_4732_3]) ).

fof(f_4733_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_4733_2,plain,
    ! [U_19929] : c_List_Orotate(U_19929,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(U_19929)),
    inference(variable_rename,[status(thm)],[f_4733_1]) ).

fof(f_4733_3,plain,
    ! [U_19929] : c_List_Orotate(U_19929,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(U_19929)),
    inference(definitional_conversion,[status(esa)],[f_4733_2]) ).

cnf(f_4733_4,plain,
    c_List_Orotate(U_19929,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(U_19929)),
    inference(clausify,[status(thm)],[f_4733_3]) ).

fof(f_4734_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_4734_2,plain,
    ! [U_19932,U_19931,U_19930] : c_List_Orotate(U_19930,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19931),U_19932)) = hAPP(c_Fun_Ocomp(tc_List_Olist(U_19930),tc_List_Olist(U_19930),tc_List_Olist(U_19930),c_List_Orotate(U_19930,U_19931)),c_List_Orotate(U_19930,U_19932)),
    inference(variable_rename,[status(thm)],[f_4734_1]) ).

fof(f_4734_3,plain,
    ! [U_19930,U_19931,U_19932] : c_List_Orotate(U_19930,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19931),U_19932)) = hAPP(c_Fun_Ocomp(tc_List_Olist(U_19930),tc_List_Olist(U_19930),tc_List_Olist(U_19930),c_List_Orotate(U_19930,U_19931)),c_List_Orotate(U_19930,U_19932)),
    inference(definitional_conversion,[status(esa)],[f_4734_2]) ).

cnf(f_4734_4,plain,
    c_List_Orotate(U_19930,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19931),U_19932)) = hAPP(c_Fun_Ocomp(tc_List_Olist(U_19930),tc_List_Olist(U_19930),tc_List_Olist(U_19930),c_List_Orotate(U_19930,U_19931)),c_List_Orotate(U_19930,U_19932)),
    inference(clausify,[status(thm)],[f_4734_3]) ).

fof(f_4735_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_4735_2,plain,
    ! [U_19935,U_19934,U_19933] :
      ( hAPP(c_List_Orotate(U_19934,U_19933),U_19935) = U_19935
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19933,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19934)),U_19935)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4735_1]) ).

fof(f_4735_3,plain,
    ! [U_19933,U_19934,U_19935] :
      ( hAPP(c_List_Orotate(U_19934,U_19933),U_19935) = U_19935
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19933,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19934)),U_19935)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_4735_2]) ).

cnf(f_4735_4,plain,
    ( hAPP(c_List_Orotate(U_19934,U_19933),U_19935) = U_19935
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19933,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19934)),U_19935)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4735_3]) ).

fof(f_4736_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_4736_2,plain,
    ! [U_19938,U_19937,U_19936] :
      ( hAPP(c_List_Orotate(U_19936,U_19938),U_19937) = U_19937
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19936)),U_19937)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_4736_1]) ).

fof(f_4736_3,plain,
    ! [U_19936,U_19937,U_19938] :
      ( hAPP(c_List_Orotate(U_19936,U_19938),U_19937) = U_19937
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19936)),U_19937)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(definitional_conversion,[status(esa)],[f_4736_2]) ).

cnf(f_4736_4,plain,
    ( hAPP(c_List_Orotate(U_19936,U_19938),U_19937) = U_19937
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19936)),U_19937)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_4736_3]) ).

fof(f_4737_1,plain,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),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_4737_2,plain,
    ! [U_19940,U_19939] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19939)),c_List_Otl(U_19939,U_19940)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19939)),U_19940)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4737_1]) ).

fof(f_4737_3,plain,
    ! [U_19939,U_19940] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19939)),c_List_Otl(U_19939,U_19940)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19939)),U_19940)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_4737_2]) ).

cnf(f_4737_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19939)),c_List_Otl(U_19939,U_19940)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19939)),U_19940)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4737_3]) ).

fof(f_4738_1,plain,
    ! [V_xs,V_n,T_a] : 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))),c_List_Otl(T_a,V_xs)),
    inference(fof_nnf,[status(thm)],[fact_tl__take]) ).

fof(f_4738_2,plain,
    ! [U_19943,U_19942,U_19941] : c_List_Otl(U_19941,hAPP(hAPP(c_List_Otake(U_19941),U_19942),U_19943)) = hAPP(hAPP(c_List_Otake(U_19941),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19942),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_List_Otl(U_19941,U_19943)),
    inference(variable_rename,[status(thm)],[f_4738_1]) ).

fof(f_4738_3,plain,
    ! [U_19941,U_19942,U_19943] : c_List_Otl(U_19941,hAPP(hAPP(c_List_Otake(U_19941),U_19942),U_19943)) = hAPP(hAPP(c_List_Otake(U_19941),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19942),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_List_Otl(U_19941,U_19943)),
    inference(definitional_conversion,[status(esa)],[f_4738_2]) ).

cnf(f_4738_4,plain,
    c_List_Otl(U_19941,hAPP(hAPP(c_List_Otake(U_19941),U_19942),U_19943)) = hAPP(hAPP(c_List_Otake(U_19941),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19942),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_List_Otl(U_19941,U_19943)),
    inference(clausify,[status(thm)],[f_4738_3]) ).

fof(f_4739_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),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_4739_2,plain,
    ! [U_19946,U_19945,U_19944] :
      ( hAPP(hAPP(c_List_Otake(U_19945),hAPP(c_Nat_OSuc,U_19946)),U_19944) = hAPP(hAPP(c_List_Olist_OCons(U_19945),hAPP(c_List_Ohd(U_19945),U_19944)),hAPP(hAPP(c_List_Otake(U_19945),U_19946),c_List_Otl(U_19945,U_19944)))
      | U_19944 = c_List_Olist_ONil(U_19945) ),
    inference(variable_rename,[status(thm)],[f_4739_1]) ).

fof(f_4739_3,plain,
    ! [U_19944,U_19945,U_19946] :
      ( hAPP(hAPP(c_List_Otake(U_19945),hAPP(c_Nat_OSuc,U_19946)),U_19944) = hAPP(hAPP(c_List_Olist_OCons(U_19945),hAPP(c_List_Ohd(U_19945),U_19944)),hAPP(hAPP(c_List_Otake(U_19945),U_19946),c_List_Otl(U_19945,U_19944)))
      | U_19944 = c_List_Olist_ONil(U_19945) ),
    inference(definitional_conversion,[status(esa)],[f_4739_2]) ).

cnf(f_4739_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_19945),hAPP(c_Nat_OSuc,U_19946)),U_19944) = hAPP(hAPP(c_List_Olist_OCons(U_19945),hAPP(c_List_Ohd(U_19945),U_19944)),hAPP(hAPP(c_List_Otake(U_19945),U_19946),c_List_Otl(U_19945,U_19944)))
    | U_19944 = c_List_Olist_ONil(U_19945) ),
    inference(clausify,[status(thm)],[f_4739_3]) ).

fof(f_4740_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_4740_2,plain,
    ! [U_19949,U_19948,U_19947] : hAPP(c_List_Orotate(U_19947,U_19948),U_19949) = hAPP(hAPP(c_List_Oappend(U_19947),hAPP(hAPP(c_List_Odrop(U_19947),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19948,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19947)),U_19949))),U_19949)),hAPP(hAPP(c_List_Otake(U_19947),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19948,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19947)),U_19949))),U_19949)),
    inference(variable_rename,[status(thm)],[f_4740_1]) ).

fof(f_4740_3,plain,
    ! [U_19947,U_19948,U_19949] : hAPP(c_List_Orotate(U_19947,U_19948),U_19949) = hAPP(hAPP(c_List_Oappend(U_19947),hAPP(hAPP(c_List_Odrop(U_19947),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19948,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19947)),U_19949))),U_19949)),hAPP(hAPP(c_List_Otake(U_19947),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19948,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19947)),U_19949))),U_19949)),
    inference(definitional_conversion,[status(esa)],[f_4740_2]) ).

cnf(f_4740_4,plain,
    hAPP(c_List_Orotate(U_19947,U_19948),U_19949) = hAPP(hAPP(c_List_Oappend(U_19947),hAPP(hAPP(c_List_Odrop(U_19947),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19948,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19947)),U_19949))),U_19949)),hAPP(hAPP(c_List_Otake(U_19947),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19948,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19947)),U_19949))),U_19949)),
    inference(clausify,[status(thm)],[f_4740_3]) ).

fof(f_4741_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)),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_4741_2,plain,
    ! [U_19951,U_19950] :
      ( hAPP(c_Finite__Set_Ofold1(U_19950,c_Groups_Otimes__class_Otimes(U_19950)),hAPP(c_List_Oset(U_19950),U_19951)) = hAPP(c_List_Ofoldl(U_19950,U_19950,c_Groups_Otimes__class_Otimes(U_19950),hAPP(c_List_Ohd(U_19950),U_19951)),c_List_Otl(U_19950,U_19951))
      | U_19951 = c_List_Olist_ONil(U_19950)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_19950) ),
    inference(variable_rename,[status(thm)],[f_4741_1]) ).

fof(f_4741_3,plain,
    ! [U_19950,U_19951] :
      ( hAPP(c_Finite__Set_Ofold1(U_19950,c_Groups_Otimes__class_Otimes(U_19950)),hAPP(c_List_Oset(U_19950),U_19951)) = hAPP(c_List_Ofoldl(U_19950,U_19950,c_Groups_Otimes__class_Otimes(U_19950),hAPP(c_List_Ohd(U_19950),U_19951)),c_List_Otl(U_19950,U_19951))
      | U_19951 = c_List_Olist_ONil(U_19950)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_19950) ),
    inference(definitional_conversion,[status(esa)],[f_4741_2]) ).

cnf(f_4741_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_19950,c_Groups_Otimes__class_Otimes(U_19950)),hAPP(c_List_Oset(U_19950),U_19951)) = hAPP(c_List_Ofoldl(U_19950,U_19950,c_Groups_Otimes__class_Otimes(U_19950),hAPP(c_List_Ohd(U_19950),U_19951)),c_List_Otl(U_19950,U_19951))
    | U_19951 = c_List_Olist_ONil(U_19950)
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_19950) ),
    inference(clausify,[status(thm)],[f_4741_3]) ).

fof(f_4742_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_4742_2,plain,
    ! [U_19955,U_19954,U_19953,U_19952] : c_List_Olist_Olist__size(U_19952,U_19953,hAPP(hAPP(c_List_Olist_OCons(U_19952),U_19954),U_19955)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_19953,U_19954)),c_List_Olist_Olist__size(U_19952,U_19953,U_19955))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_4742_1]) ).

fof(f_4742_3,plain,
    ! [U_19952,U_19953,U_19954,U_19955] : c_List_Olist_Olist__size(U_19952,U_19953,hAPP(hAPP(c_List_Olist_OCons(U_19952),U_19954),U_19955)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_19953,U_19954)),c_List_Olist_Olist__size(U_19952,U_19953,U_19955))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_4742_2]) ).

cnf(f_4742_4,plain,
    c_List_Olist_Olist__size(U_19952,U_19953,hAPP(hAPP(c_List_Olist_OCons(U_19952),U_19954),U_19955)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_19953,U_19954)),c_List_Olist_Olist__size(U_19952,U_19953,U_19955))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_4742_3]) ).

fof(f_4743_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_4743_2,plain,
    ! [U_19961,U_19960,U_19959,U_19958,U_19957,U_19956] : hAPP(c_List_Ofoldl(U_19956,U_19957,U_19958,U_19959),hAPP(hAPP(c_List_Oappend(U_19957),U_19960),U_19961)) = hAPP(c_List_Ofoldl(U_19956,U_19957,U_19958,hAPP(c_List_Ofoldl(U_19956,U_19957,U_19958,U_19959),U_19960)),U_19961),
    inference(variable_rename,[status(thm)],[f_4743_1]) ).

fof(f_4743_3,plain,
    ! [U_19956,U_19957,U_19958,U_19959,U_19960,U_19961] : hAPP(c_List_Ofoldl(U_19956,U_19957,U_19958,U_19959),hAPP(hAPP(c_List_Oappend(U_19957),U_19960),U_19961)) = hAPP(c_List_Ofoldl(U_19956,U_19957,U_19958,hAPP(c_List_Ofoldl(U_19956,U_19957,U_19958,U_19959),U_19960)),U_19961),
    inference(definitional_conversion,[status(esa)],[f_4743_2]) ).

cnf(f_4743_4,plain,
    hAPP(c_List_Ofoldl(U_19956,U_19957,U_19958,U_19959),hAPP(hAPP(c_List_Oappend(U_19957),U_19960),U_19961)) = hAPP(c_List_Ofoldl(U_19956,U_19957,U_19958,hAPP(c_List_Ofoldl(U_19956,U_19957,U_19958,U_19959),U_19960)),U_19961),
    inference(clausify,[status(thm)],[f_4743_3]) ).

fof(f_4744_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_4744_2,plain,
    ! [U_19967,U_19966,U_19965,U_19964,U_19963,U_19962] : hAPP(c_List_Ofoldl(U_19962,U_19963,U_19964,U_19965),hAPP(hAPP(c_List_Olist_OCons(U_19963),U_19966),U_19967)) = hAPP(c_List_Ofoldl(U_19962,U_19963,U_19964,hAPP(hAPP(U_19964,U_19965),U_19966)),U_19967),
    inference(variable_rename,[status(thm)],[f_4744_1]) ).

fof(f_4744_3,plain,
    ! [U_19962,U_19963,U_19964,U_19965,U_19966,U_19967] : hAPP(c_List_Ofoldl(U_19962,U_19963,U_19964,U_19965),hAPP(hAPP(c_List_Olist_OCons(U_19963),U_19966),U_19967)) = hAPP(c_List_Ofoldl(U_19962,U_19963,U_19964,hAPP(hAPP(U_19964,U_19965),U_19966)),U_19967),
    inference(definitional_conversion,[status(esa)],[f_4744_2]) ).

cnf(f_4744_4,plain,
    hAPP(c_List_Ofoldl(U_19962,U_19963,U_19964,U_19965),hAPP(hAPP(c_List_Olist_OCons(U_19963),U_19966),U_19967)) = hAPP(c_List_Ofoldl(U_19962,U_19963,U_19964,hAPP(hAPP(U_19964,U_19965),U_19966)),U_19967),
    inference(clausify,[status(thm)],[f_4744_3]) ).

fof(f_4745_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_4745_2,plain,
    ! [U_19972,U_19971,U_19970,U_19969,U_19968] : c_List_Olist_Olist__size(U_19968,U_19969,hAPP(hAPP(c_List_Omap(U_19970,U_19968),U_19971),U_19972)) = c_List_Olist_Olist__size(U_19970,hAPP(c_Fun_Ocomp(U_19968,tc_Nat_Onat,U_19970,U_19969),U_19971),U_19972),
    inference(variable_rename,[status(thm)],[f_4745_1]) ).

fof(f_4745_3,plain,
    ! [U_19968,U_19969,U_19970,U_19971,U_19972] : c_List_Olist_Olist__size(U_19968,U_19969,hAPP(hAPP(c_List_Omap(U_19970,U_19968),U_19971),U_19972)) = c_List_Olist_Olist__size(U_19970,hAPP(c_Fun_Ocomp(U_19968,tc_Nat_Onat,U_19970,U_19969),U_19971),U_19972),
    inference(definitional_conversion,[status(esa)],[f_4745_2]) ).

cnf(f_4745_4,plain,
    c_List_Olist_Olist__size(U_19968,U_19969,hAPP(hAPP(c_List_Omap(U_19970,U_19968),U_19971),U_19972)) = c_List_Olist_Olist__size(U_19970,hAPP(c_Fun_Ocomp(U_19968,tc_Nat_Onat,U_19970,U_19969),U_19971),U_19972),
    inference(clausify,[status(thm)],[f_4745_3]) ).

fof(f_4746_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_4746_2,plain,
    ! [U_19979,U_19978,U_19977,U_19976,U_19975,U_19974,U_19973] : hAPP(c_List_Ofoldl(U_19973,U_19974,U_19975,U_19976),hAPP(hAPP(c_List_Omap(U_19977,U_19974),U_19978),U_19979)) = hAPP(c_List_Ofoldl(U_19973,U_19977,hAPP(hAPP(c_COMBC(U_19973,tc_fun(U_19977,U_19974),tc_fun(U_19977,U_19973)),hAPP(hAPP(c_COMBB(tc_fun(U_19974,U_19973),tc_fun(tc_fun(U_19977,U_19974),tc_fun(U_19977,U_19973)),U_19973),c_COMBB(U_19974,U_19973,U_19977)),U_19975)),U_19978),U_19976),U_19979),
    inference(variable_rename,[status(thm)],[f_4746_1]) ).

fof(f_4746_3,plain,
    ! [U_19973,U_19974,U_19975,U_19976,U_19977,U_19978,U_19979] : hAPP(c_List_Ofoldl(U_19973,U_19974,U_19975,U_19976),hAPP(hAPP(c_List_Omap(U_19977,U_19974),U_19978),U_19979)) = hAPP(c_List_Ofoldl(U_19973,U_19977,hAPP(hAPP(c_COMBC(U_19973,tc_fun(U_19977,U_19974),tc_fun(U_19977,U_19973)),hAPP(hAPP(c_COMBB(tc_fun(U_19974,U_19973),tc_fun(tc_fun(U_19977,U_19974),tc_fun(U_19977,U_19973)),U_19973),c_COMBB(U_19974,U_19973,U_19977)),U_19975)),U_19978),U_19976),U_19979),
    inference(definitional_conversion,[status(esa)],[f_4746_2]) ).

cnf(f_4746_4,plain,
    hAPP(c_List_Ofoldl(U_19973,U_19974,U_19975,U_19976),hAPP(hAPP(c_List_Omap(U_19977,U_19974),U_19978),U_19979)) = hAPP(c_List_Ofoldl(U_19973,U_19977,hAPP(hAPP(c_COMBC(U_19973,tc_fun(U_19977,U_19974),tc_fun(U_19977,U_19973)),hAPP(hAPP(c_COMBB(tc_fun(U_19974,U_19973),tc_fun(tc_fun(U_19977,U_19974),tc_fun(U_19977,U_19973)),U_19973),c_COMBB(U_19974,U_19973,U_19977)),U_19975)),U_19978),U_19976),U_19979),
    inference(clausify,[status(thm)],[f_4746_3]) ).

fof(f_4747_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_4747_2,plain,
    ! [U_19982,U_19981,U_19980] :
      ( c_List_Ofoldr(U_19980,U_19980,c_Groups_Oplus__class_Oplus(U_19980),U_19981,U_19982) = hAPP(c_List_Ofoldl(U_19980,U_19980,c_Groups_Oplus__class_Oplus(U_19980),U_19982),U_19981)
      | ~ class_Groups_Oab__semigroup__add(U_19980) ),
    inference(variable_rename,[status(thm)],[f_4747_1]) ).

fof(f_4747_3,plain,
    ! [U_19980,U_19981,U_19982] :
      ( c_List_Ofoldr(U_19980,U_19980,c_Groups_Oplus__class_Oplus(U_19980),U_19981,U_19982) = hAPP(c_List_Ofoldl(U_19980,U_19980,c_Groups_Oplus__class_Oplus(U_19980),U_19982),U_19981)
      | ~ class_Groups_Oab__semigroup__add(U_19980) ),
    inference(definitional_conversion,[status(esa)],[f_4747_2]) ).

cnf(f_4747_4,plain,
    ( c_List_Ofoldr(U_19980,U_19980,c_Groups_Oplus__class_Oplus(U_19980),U_19981,U_19982) = hAPP(c_List_Ofoldl(U_19980,U_19980,c_Groups_Oplus__class_Oplus(U_19980),U_19982),U_19981)
    | ~ class_Groups_Oab__semigroup__add(U_19980) ),
    inference(clausify,[status(thm)],[f_4747_3]) ).

fof(f_4748_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_4748_2,plain,
    ! [U_19985,U_19984,U_19983] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19983),U_19984),hAPP(c_List_Ofoldl(U_19983,U_19983,c_Groups_Oplus__class_Oplus(U_19983),c_Groups_Ozero__class_Ozero(U_19983)),U_19985)) = hAPP(c_List_Ofoldl(U_19983,U_19983,c_Groups_Oplus__class_Oplus(U_19983),U_19984),U_19985)
      | ~ class_Groups_Omonoid__add(U_19983) ),
    inference(variable_rename,[status(thm)],[f_4748_1]) ).

fof(f_4748_3,plain,
    ! [U_19983,U_19984,U_19985] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19983),U_19984),hAPP(c_List_Ofoldl(U_19983,U_19983,c_Groups_Oplus__class_Oplus(U_19983),c_Groups_Ozero__class_Ozero(U_19983)),U_19985)) = hAPP(c_List_Ofoldl(U_19983,U_19983,c_Groups_Oplus__class_Oplus(U_19983),U_19984),U_19985)
      | ~ class_Groups_Omonoid__add(U_19983) ),
    inference(definitional_conversion,[status(esa)],[f_4748_2]) ).

cnf(f_4748_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19983),U_19984),hAPP(c_List_Ofoldl(U_19983,U_19983,c_Groups_Oplus__class_Oplus(U_19983),c_Groups_Ozero__class_Ozero(U_19983)),U_19985)) = hAPP(c_List_Ofoldl(U_19983,U_19983,c_Groups_Oplus__class_Oplus(U_19983),U_19984),U_19985)
    | ~ class_Groups_Omonoid__add(U_19983) ),
    inference(clausify,[status(thm)],[f_4748_3]) ).

fof(f_4749_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_4749_2,plain,
    ! [U_19989,U_19988,U_19987,U_19986] :
      ( hAPP(c_List_Ofoldl(U_19986,U_19986,c_Groups_Oplus__class_Oplus(U_19986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19986),U_19987),U_19988)),U_19989) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19986),U_19987),hAPP(c_List_Ofoldl(U_19986,U_19986,c_Groups_Oplus__class_Oplus(U_19986),U_19988),U_19989))
      | ~ class_Groups_Osemigroup__add(U_19986) ),
    inference(variable_rename,[status(thm)],[f_4749_1]) ).

fof(f_4749_3,plain,
    ! [U_19986,U_19987,U_19988,U_19989] :
      ( hAPP(c_List_Ofoldl(U_19986,U_19986,c_Groups_Oplus__class_Oplus(U_19986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19986),U_19987),U_19988)),U_19989) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19986),U_19987),hAPP(c_List_Ofoldl(U_19986,U_19986,c_Groups_Oplus__class_Oplus(U_19986),U_19988),U_19989))
      | ~ class_Groups_Osemigroup__add(U_19986) ),
    inference(definitional_conversion,[status(esa)],[f_4749_2]) ).

cnf(f_4749_4,plain,
    ( hAPP(c_List_Ofoldl(U_19986,U_19986,c_Groups_Oplus__class_Oplus(U_19986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19986),U_19987),U_19988)),U_19989) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19986),U_19987),hAPP(c_List_Ofoldl(U_19986,U_19986,c_Groups_Oplus__class_Oplus(U_19986),U_19988),U_19989))
    | ~ class_Groups_Osemigroup__add(U_19986) ),
    inference(clausify,[status(thm)],[f_4749_3]) ).

fof(f_4750_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_4750_2,plain,
    ! [U_19992,U_19991,U_19990] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19990),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19991),U_19992)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19990),U_19991)) ),
    inference(variable_rename,[status(thm)],[f_4750_1]) ).

fof(f_4750_3,plain,
    ! [U_19990,U_19991,U_19992] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19990),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19991),U_19992)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19990),U_19991)) ),
    inference(definitional_conversion,[status(esa)],[f_4750_2]) ).

cnf(f_4750_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19990),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19991),U_19992)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19990),U_19991)) ),
    inference(clausify,[status(thm)],[f_4750_3]) ).

fof(f_4751_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_4751_2,plain,
    ! [U_19996,U_19995,U_19994,U_19993] : hAPP(c_List_Ofoldl(U_19993,U_19994,U_19995,U_19996),c_List_Olist_ONil(U_19994)) = U_19996,
    inference(variable_rename,[status(thm)],[f_4751_1]) ).

fof(f_4751_3,plain,
    ! [U_19993,U_19994,U_19995,U_19996] : hAPP(c_List_Ofoldl(U_19993,U_19994,U_19995,U_19996),c_List_Olist_ONil(U_19994)) = U_19996,
    inference(definitional_conversion,[status(esa)],[f_4751_2]) ).

cnf(f_4751_4,plain,
    hAPP(c_List_Ofoldl(U_19993,U_19994,U_19995,U_19996),c_List_Olist_ONil(U_19994)) = U_19996,
    inference(clausify,[status(thm)],[f_4751_3]) ).

fof(f_4752_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_4752_2,plain,
    ! [U_19997] :
      ( c_List_Omonoid__add__class_Olistsum(U_19997) = c_List_Ofoldl(U_19997,U_19997,c_Groups_Oplus__class_Oplus(U_19997),c_Groups_Ozero__class_Ozero(U_19997))
      | ~ class_Groups_Omonoid__add(U_19997) ),
    inference(variable_rename,[status(thm)],[f_4752_1]) ).

fof(f_4752_3,plain,
    ! [U_19997] :
      ( c_List_Omonoid__add__class_Olistsum(U_19997) = c_List_Ofoldl(U_19997,U_19997,c_Groups_Oplus__class_Oplus(U_19997),c_Groups_Ozero__class_Ozero(U_19997))
      | ~ class_Groups_Omonoid__add(U_19997) ),
    inference(definitional_conversion,[status(esa)],[f_4752_2]) ).

cnf(f_4752_4,plain,
    ( c_List_Omonoid__add__class_Olistsum(U_19997) = c_List_Ofoldl(U_19997,U_19997,c_Groups_Oplus__class_Oplus(U_19997),c_Groups_Ozero__class_Ozero(U_19997))
    | ~ class_Groups_Omonoid__add(U_19997) ),
    inference(clausify,[status(thm)],[f_4752_3]) ).

fof(f_4753_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_4753_2,plain,
    ! [U_19999,U_19998] :
      ( hAPP(c_List_Ofoldl(U_19998,U_19998,c_Groups_Oplus__class_Oplus(U_19998),c_Groups_Ozero__class_Ozero(U_19998)),U_19999) = c_List_Ofoldr(U_19998,U_19998,c_Groups_Oplus__class_Oplus(U_19998),U_19999,c_Groups_Ozero__class_Ozero(U_19998))
      | ~ class_Groups_Omonoid__add(U_19998) ),
    inference(variable_rename,[status(thm)],[f_4753_1]) ).

fof(f_4753_3,plain,
    ! [U_19998,U_19999] :
      ( hAPP(c_List_Ofoldl(U_19998,U_19998,c_Groups_Oplus__class_Oplus(U_19998),c_Groups_Ozero__class_Ozero(U_19998)),U_19999) = c_List_Ofoldr(U_19998,U_19998,c_Groups_Oplus__class_Oplus(U_19998),U_19999,c_Groups_Ozero__class_Ozero(U_19998))
      | ~ class_Groups_Omonoid__add(U_19998) ),
    inference(definitional_conversion,[status(esa)],[f_4753_2]) ).

cnf(f_4753_4,plain,
    ( hAPP(c_List_Ofoldl(U_19998,U_19998,c_Groups_Oplus__class_Oplus(U_19998),c_Groups_Ozero__class_Ozero(U_19998)),U_19999) = c_List_Ofoldr(U_19998,U_19998,c_Groups_Oplus__class_Oplus(U_19998),U_19999,c_Groups_Ozero__class_Ozero(U_19998))
    | ~ class_Groups_Omonoid__add(U_19998) ),
    inference(clausify,[status(thm)],[f_4753_3]) ).

fof(f_4754_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_4754_2,plain,
    ! [U_20002,U_20001,U_20000] :
      ( hAPP(c_List_Ofoldl(U_20000,U_20000,c_Groups_Oplus__class_Oplus(U_20000),U_20001),U_20002) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_20000),U_20001),c_List_Ofoldr(U_20000,U_20000,c_Groups_Oplus__class_Oplus(U_20000),U_20002,c_Groups_Ozero__class_Ozero(U_20000)))
      | ~ class_Groups_Omonoid__add(U_20000) ),
    inference(variable_rename,[status(thm)],[f_4754_1]) ).

fof(f_4754_3,plain,
    ! [U_20000,U_20001,U_20002] :
      ( hAPP(c_List_Ofoldl(U_20000,U_20000,c_Groups_Oplus__class_Oplus(U_20000),U_20001),U_20002) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_20000),U_20001),c_List_Ofoldr(U_20000,U_20000,c_Groups_Oplus__class_Oplus(U_20000),U_20002,c_Groups_Ozero__class_Ozero(U_20000)))
      | ~ class_Groups_Omonoid__add(U_20000) ),
    inference(definitional_conversion,[status(esa)],[f_4754_2]) ).

cnf(f_4754_4,plain,
    ( hAPP(c_List_Ofoldl(U_20000,U_20000,c_Groups_Oplus__class_Oplus(U_20000),U_20001),U_20002) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_20000),U_20001),c_List_Ofoldr(U_20000,U_20000,c_Groups_Oplus__class_Oplus(U_20000),U_20002,c_Groups_Ozero__class_Ozero(U_20000)))
    | ~ class_Groups_Omonoid__add(U_20000) ),
    inference(clausify,[status(thm)],[f_4754_3]) ).

fof(f_4755_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_4755_2,plain,
    ! [U_20006,U_20005] :
      ( ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20005),U_20006) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_20004] :
            ( U_20004 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20004),hAPP(c_List_Oset(tc_Nat_Onat),U_20006))) )
        | U_20005 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( ! [U_20003] :
              ( U_20003 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20003),hAPP(c_List_Oset(tc_Nat_Onat),U_20006))) )
          & U_20005 = 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_20005),U_20006) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4755_1]) ).

fof(f_4755_3,plain,
    ( ! [U_20010,U_20008] :
        ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20008),U_20010) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_20004] :
            ( U_20004 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20004),hAPP(c_List_Oset(tc_Nat_Onat),U_20010))) )
        | U_20008 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_20009,U_20007] :
        ( ( ! [U_20003] :
              ( U_20003 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20003),hAPP(c_List_Oset(tc_Nat_Onat),U_20009))) )
          & U_20007 = 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_20007),U_20009) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4755_2]) ).

fof(f_4755_4,plain,
    ( ! [U_20010,U_20008] :
        ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20008),U_20010) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( sK487(U_20010,U_20008) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK487(U_20010,U_20008)),hAPP(c_List_Oset(tc_Nat_Onat),U_20010))) )
        | U_20008 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_20009,U_20007] :
        ( ( ! [U_20003] :
              ( U_20003 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20003),hAPP(c_List_Oset(tc_Nat_Onat),U_20009))) )
          & U_20007 = 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_20007),U_20009) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK487]),skolemize(U_20004,sK487(U_20010,U_20008))],[f_4755_3]) ).

fof(f_4755_5,plain,
    ( ! [U_20010,U_20008] :
        ( sK487(U_20010,U_20008) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1202(U_20010,U_20008) )
    & ! [U_20010,U_20008] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK487(U_20010,U_20008)),hAPP(c_List_Oset(tc_Nat_Onat),U_20010)))
        | ~ sP1202(U_20010,U_20008) )
    & ! [U_20003,U_20007,U_20009] :
        ( U_20003 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20003),hAPP(c_List_Oset(tc_Nat_Onat),U_20009)))
        | ~ sP1201(U_20003,U_20007,U_20009) )
    & ! [U_20003,U_20007,U_20009] :
        ( U_20007 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1201(U_20003,U_20007,U_20009) )
    & ! [U_20010,U_20008] :
        ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20008),U_20010) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP1202(U_20010,U_20008)
        | U_20008 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_20003,U_20007,U_20009] :
        ( sP1201(U_20003,U_20007,U_20009)
        | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20007),U_20009) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1201,sP1202])],[f_4755_4]) ).

cnf(f_4755_6,plain,
    ( sP1201(U_20003,U_20007,U_20009)
    | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20007),U_20009) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4755_5]) ).

cnf(f_4755_7,plain,
    ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20008),U_20010) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP1202(U_20010,U_20008)
    | U_20008 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4755_5]) ).

cnf(f_4755_8,plain,
    ( U_20007 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1201(U_20003,U_20007,U_20009) ),
    inference(clausify,[status(thm)],[f_4755_5]) ).

cnf(f_4755_9,plain,
    ( U_20003 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20003),hAPP(c_List_Oset(tc_Nat_Onat),U_20009)))
    | ~ sP1201(U_20003,U_20007,U_20009) ),
    inference(clausify,[status(thm)],[f_4755_5]) ).

cnf(f_4755_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK487(U_20010,U_20008)),hAPP(c_List_Oset(tc_Nat_Onat),U_20010)))
    | ~ sP1202(U_20010,U_20008) ),
    inference(clausify,[status(thm)],[f_4755_5]) ).

cnf(f_4755_11,plain,
    ( sK487(U_20010,U_20008) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1202(U_20010,U_20008) ),
    inference(clausify,[status(thm)],[f_4755_5]) ).

fof(f_4756_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_4756_2,plain,
    ! [U_20012,U_20011] : c_List_Olist_Olist__size(U_20011,U_20012,c_List_Olist_ONil(U_20011)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4756_1]) ).

fof(f_4756_3,plain,
    ! [U_20011,U_20012] : c_List_Olist_Olist__size(U_20011,U_20012,c_List_Olist_ONil(U_20011)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_4756_2]) ).

cnf(f_4756_4,plain,
    c_List_Olist_Olist__size(U_20011,U_20012,c_List_Olist_ONil(U_20011)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4756_3]) ).

fof(f_4757_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_4757_2,plain,
    ! [U_20017,U_20016,U_20015,U_20014,U_20013] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_20013,U_20014,U_20015),U_20016),hAPP(c_List_Oset(U_20013),U_20017)) = hAPP(c_List_Ofoldl(U_20014,U_20013,hAPP(c_COMBC(U_20013,U_20014,U_20014),U_20015),U_20016),U_20017)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_20013,U_20014,U_20015) ),
    inference(variable_rename,[status(thm)],[f_4757_1]) ).

fof(f_4757_3,plain,
    ! [U_20013,U_20014,U_20015,U_20016,U_20017] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_20013,U_20014,U_20015),U_20016),hAPP(c_List_Oset(U_20013),U_20017)) = hAPP(c_List_Ofoldl(U_20014,U_20013,hAPP(c_COMBC(U_20013,U_20014,U_20014),U_20015),U_20016),U_20017)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_20013,U_20014,U_20015) ),
    inference(definitional_conversion,[status(esa)],[f_4757_2]) ).

cnf(f_4757_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_20013,U_20014,U_20015),U_20016),hAPP(c_List_Oset(U_20013),U_20017)) = hAPP(c_List_Ofoldl(U_20014,U_20013,hAPP(c_COMBC(U_20013,U_20014,U_20014),U_20015),U_20016),U_20017)
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_20013,U_20014,U_20015) ),
    inference(clausify,[status(thm)],[f_4757_3]) ).

fof(f_4758_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_4758_2,plain,
    ! [U_20019,U_20018] :
      ( c_Complete__Lattice_OSup__class_OSup(U_20018,hAPP(c_List_Oset(U_20018),U_20019)) = hAPP(c_List_Ofoldl(U_20018,U_20018,c_Lattices_Osemilattice__sup__class_Osup(U_20018),c_Orderings_Obot__class_Obot(U_20018)),U_20019)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20018) ),
    inference(variable_rename,[status(thm)],[f_4758_1]) ).

fof(f_4758_3,plain,
    ! [U_20019,U_20018] :
      ( c_Complete__Lattice_OSup__class_OSup(U_20018,hAPP(c_List_Oset(U_20018),U_20019)) = hAPP(c_List_Ofoldl(U_20018,U_20018,c_Lattices_Osemilattice__sup__class_Osup(U_20018),c_Orderings_Obot__class_Obot(U_20018)),U_20019)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20018) ),
    inference(definitional_conversion,[status(esa)],[f_4758_2]) ).

cnf(f_4758_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_20018,hAPP(c_List_Oset(U_20018),U_20019)) = hAPP(c_List_Ofoldl(U_20018,U_20018,c_Lattices_Osemilattice__sup__class_Osup(U_20018),c_Orderings_Obot__class_Obot(U_20018)),U_20019)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_20018) ),
    inference(clausify,[status(thm)],[f_4758_3]) ).

fof(f_4759_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_4759_2,plain,
    ! [U_20021,U_20020] :
      ( c_Complete__Lattice_OInf__class_OInf(U_20020,hAPP(c_List_Oset(U_20020),U_20021)) = hAPP(c_List_Ofoldl(U_20020,U_20020,c_Lattices_Osemilattice__inf__class_Oinf(U_20020),c_Orderings_Otop__class_Otop(U_20020)),U_20021)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20020) ),
    inference(variable_rename,[status(thm)],[f_4759_1]) ).

fof(f_4759_3,plain,
    ! [U_20020,U_20021] :
      ( c_Complete__Lattice_OInf__class_OInf(U_20020,hAPP(c_List_Oset(U_20020),U_20021)) = hAPP(c_List_Ofoldl(U_20020,U_20020,c_Lattices_Osemilattice__inf__class_Oinf(U_20020),c_Orderings_Otop__class_Otop(U_20020)),U_20021)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20020) ),
    inference(definitional_conversion,[status(esa)],[f_4759_2]) ).

cnf(f_4759_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_20020,hAPP(c_List_Oset(U_20020),U_20021)) = hAPP(c_List_Ofoldl(U_20020,U_20020,c_Lattices_Osemilattice__inf__class_Oinf(U_20020),c_Orderings_Otop__class_Otop(U_20020)),U_20021)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_20020) ),
    inference(clausify,[status(thm)],[f_4759_3]) ).

fof(f_4760_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_4760_2,plain,
    ! [U_20024,U_20023,U_20022] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_20022,hAPP(c_List_Oset(U_20022),hAPP(hAPP(c_List_Olist_OCons(U_20022),U_20023),U_20024))) = hAPP(c_List_Ofoldl(U_20022,U_20022,c_Lattices_Osemilattice__sup__class_Osup(U_20022),U_20023),U_20024)
      | ~ class_Lattices_Olattice(U_20022) ),
    inference(variable_rename,[status(thm)],[f_4760_1]) ).

fof(f_4760_3,plain,
    ! [U_20022,U_20023,U_20024] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_20022,hAPP(c_List_Oset(U_20022),hAPP(hAPP(c_List_Olist_OCons(U_20022),U_20023),U_20024))) = hAPP(c_List_Ofoldl(U_20022,U_20022,c_Lattices_Osemilattice__sup__class_Osup(U_20022),U_20023),U_20024)
      | ~ class_Lattices_Olattice(U_20022) ),
    inference(definitional_conversion,[status(esa)],[f_4760_2]) ).

cnf(f_4760_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_20022,hAPP(c_List_Oset(U_20022),hAPP(hAPP(c_List_Olist_OCons(U_20022),U_20023),U_20024))) = hAPP(c_List_Ofoldl(U_20022,U_20022,c_Lattices_Osemilattice__sup__class_Osup(U_20022),U_20023),U_20024)
    | ~ class_Lattices_Olattice(U_20022) ),
    inference(clausify,[status(thm)],[f_4760_3]) ).

fof(f_4761_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_4761_2,plain,
    ! [U_20027,U_20026,U_20025] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_20025,hAPP(c_List_Oset(U_20025),hAPP(hAPP(c_List_Olist_OCons(U_20025),U_20026),U_20027))) = hAPP(c_List_Ofoldl(U_20025,U_20025,c_Lattices_Osemilattice__inf__class_Oinf(U_20025),U_20026),U_20027)
      | ~ class_Lattices_Olattice(U_20025) ),
    inference(variable_rename,[status(thm)],[f_4761_1]) ).

fof(f_4761_3,plain,
    ! [U_20025,U_20026,U_20027] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_20025,hAPP(c_List_Oset(U_20025),hAPP(hAPP(c_List_Olist_OCons(U_20025),U_20026),U_20027))) = hAPP(c_List_Ofoldl(U_20025,U_20025,c_Lattices_Osemilattice__inf__class_Oinf(U_20025),U_20026),U_20027)
      | ~ class_Lattices_Olattice(U_20025) ),
    inference(definitional_conversion,[status(esa)],[f_4761_2]) ).

cnf(f_4761_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_20025,hAPP(c_List_Oset(U_20025),hAPP(hAPP(c_List_Olist_OCons(U_20025),U_20026),U_20027))) = hAPP(c_List_Ofoldl(U_20025,U_20025,c_Lattices_Osemilattice__inf__class_Oinf(U_20025),U_20026),U_20027)
    | ~ class_Lattices_Olattice(U_20025) ),
    inference(clausify,[status(thm)],[f_4761_3]) ).

fof(f_4762_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_4762_2,plain,
    ! [U_20030,U_20029,U_20028] :
      ( c_Big__Operators_Olinorder__class_OMin(U_20028,hAPP(c_List_Oset(U_20028),hAPP(hAPP(c_List_Olist_OCons(U_20028),U_20029),U_20030))) = hAPP(c_List_Ofoldl(U_20028,U_20028,c_Orderings_Oord__class_Omin(U_20028),U_20029),U_20030)
      | ~ class_Orderings_Olinorder(U_20028) ),
    inference(variable_rename,[status(thm)],[f_4762_1]) ).

fof(f_4762_3,plain,
    ! [U_20028,U_20029,U_20030] :
      ( c_Big__Operators_Olinorder__class_OMin(U_20028,hAPP(c_List_Oset(U_20028),hAPP(hAPP(c_List_Olist_OCons(U_20028),U_20029),U_20030))) = hAPP(c_List_Ofoldl(U_20028,U_20028,c_Orderings_Oord__class_Omin(U_20028),U_20029),U_20030)
      | ~ class_Orderings_Olinorder(U_20028) ),
    inference(definitional_conversion,[status(esa)],[f_4762_2]) ).

cnf(f_4762_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_20028,hAPP(c_List_Oset(U_20028),hAPP(hAPP(c_List_Olist_OCons(U_20028),U_20029),U_20030))) = hAPP(c_List_Ofoldl(U_20028,U_20028,c_Orderings_Oord__class_Omin(U_20028),U_20029),U_20030)
    | ~ class_Orderings_Olinorder(U_20028) ),
    inference(clausify,[status(thm)],[f_4762_3]) ).

fof(f_4763_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_4763_2,plain,
    ! [U_20033,U_20032,U_20031] :
      ( c_Big__Operators_Olinorder__class_OMax(U_20031,hAPP(c_List_Oset(U_20031),hAPP(hAPP(c_List_Olist_OCons(U_20031),U_20032),U_20033))) = hAPP(c_List_Ofoldl(U_20031,U_20031,c_Orderings_Oord__class_Omax(U_20031),U_20032),U_20033)
      | ~ class_Orderings_Olinorder(U_20031) ),
    inference(variable_rename,[status(thm)],[f_4763_1]) ).

fof(f_4763_3,plain,
    ! [U_20031,U_20032,U_20033] :
      ( c_Big__Operators_Olinorder__class_OMax(U_20031,hAPP(c_List_Oset(U_20031),hAPP(hAPP(c_List_Olist_OCons(U_20031),U_20032),U_20033))) = hAPP(c_List_Ofoldl(U_20031,U_20031,c_Orderings_Oord__class_Omax(U_20031),U_20032),U_20033)
      | ~ class_Orderings_Olinorder(U_20031) ),
    inference(definitional_conversion,[status(esa)],[f_4763_2]) ).

cnf(f_4763_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_20031,hAPP(c_List_Oset(U_20031),hAPP(hAPP(c_List_Olist_OCons(U_20031),U_20032),U_20033))) = hAPP(c_List_Ofoldl(U_20031,U_20031,c_Orderings_Oord__class_Omax(U_20031),U_20032),U_20033)
    | ~ class_Orderings_Olinorder(U_20031) ),
    inference(clausify,[status(thm)],[f_4763_3]) ).

fof(f_4764_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_4764_2,plain,
    ! [U_20036,U_20035,U_20034] :
      ( c_Big__Operators_Olattice_OInf__fin(U_20034,c_Orderings_Oord__class_Omin(U_20034),hAPP(c_List_Oset(U_20034),hAPP(hAPP(c_List_Olist_OCons(U_20034),U_20035),U_20036))) = hAPP(c_List_Ofoldl(U_20034,U_20034,c_Orderings_Oord__class_Omin(U_20034),U_20035),U_20036)
      | ~ class_Orderings_Olinorder(U_20034) ),
    inference(variable_rename,[status(thm)],[f_4764_1]) ).

fof(f_4764_3,plain,
    ! [U_20034,U_20035,U_20036] :
      ( c_Big__Operators_Olattice_OInf__fin(U_20034,c_Orderings_Oord__class_Omin(U_20034),hAPP(c_List_Oset(U_20034),hAPP(hAPP(c_List_Olist_OCons(U_20034),U_20035),U_20036))) = hAPP(c_List_Ofoldl(U_20034,U_20034,c_Orderings_Oord__class_Omin(U_20034),U_20035),U_20036)
      | ~ class_Orderings_Olinorder(U_20034) ),
    inference(definitional_conversion,[status(esa)],[f_4764_2]) ).

cnf(f_4764_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_20034,c_Orderings_Oord__class_Omin(U_20034),hAPP(c_List_Oset(U_20034),hAPP(hAPP(c_List_Olist_OCons(U_20034),U_20035),U_20036))) = hAPP(c_List_Ofoldl(U_20034,U_20034,c_Orderings_Oord__class_Omin(U_20034),U_20035),U_20036)
    | ~ class_Orderings_Olinorder(U_20034) ),
    inference(clausify,[status(thm)],[f_4764_3]) ).

fof(f_4765_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_4765_2,plain,
    ! [U_20039,U_20038,U_20037] :
      ( c_Big__Operators_Olattice_OSup__fin(U_20037,c_Orderings_Oord__class_Omax(U_20037),hAPP(c_List_Oset(U_20037),hAPP(hAPP(c_List_Olist_OCons(U_20037),U_20038),U_20039))) = hAPP(c_List_Ofoldl(U_20037,U_20037,c_Orderings_Oord__class_Omax(U_20037),U_20038),U_20039)
      | ~ class_Orderings_Olinorder(U_20037) ),
    inference(variable_rename,[status(thm)],[f_4765_1]) ).

fof(f_4765_3,plain,
    ! [U_20037,U_20038,U_20039] :
      ( c_Big__Operators_Olattice_OSup__fin(U_20037,c_Orderings_Oord__class_Omax(U_20037),hAPP(c_List_Oset(U_20037),hAPP(hAPP(c_List_Olist_OCons(U_20037),U_20038),U_20039))) = hAPP(c_List_Ofoldl(U_20037,U_20037,c_Orderings_Oord__class_Omax(U_20037),U_20038),U_20039)
      | ~ class_Orderings_Olinorder(U_20037) ),
    inference(definitional_conversion,[status(esa)],[f_4765_2]) ).

cnf(f_4765_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_20037,c_Orderings_Oord__class_Omax(U_20037),hAPP(c_List_Oset(U_20037),hAPP(hAPP(c_List_Olist_OCons(U_20037),U_20038),U_20039))) = hAPP(c_List_Ofoldl(U_20037,U_20037,c_Orderings_Oord__class_Omax(U_20037),U_20038),U_20039)
    | ~ class_Orderings_Olinorder(U_20037) ),
    inference(clausify,[status(thm)],[f_4765_3]) ).

fof(f_4766_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_4766_2,plain,
    ! [U_20043,U_20042,U_20041,U_20040] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20041,U_20040),hAPP(c_List_Oset(U_20041),U_20042)),U_20043) = hAPP(c_List_Ofoldl(U_20040,U_20041,hAPP(c_COMBC(U_20041,U_20040,U_20040),hAPP(hAPP(c_COMBB(U_20040,tc_fun(U_20040,U_20040),U_20041),c_Lattices_Osemilattice__sup__class_Osup(U_20040)),U_20043)),c_Orderings_Obot__class_Obot(U_20040)),U_20042)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20040) ),
    inference(variable_rename,[status(thm)],[f_4766_1]) ).

fof(f_4766_3,plain,
    ! [U_20040,U_20041,U_20042,U_20043] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20041,U_20040),hAPP(c_List_Oset(U_20041),U_20042)),U_20043) = hAPP(c_List_Ofoldl(U_20040,U_20041,hAPP(c_COMBC(U_20041,U_20040,U_20040),hAPP(hAPP(c_COMBB(U_20040,tc_fun(U_20040,U_20040),U_20041),c_Lattices_Osemilattice__sup__class_Osup(U_20040)),U_20043)),c_Orderings_Obot__class_Obot(U_20040)),U_20042)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20040) ),
    inference(definitional_conversion,[status(esa)],[f_4766_2]) ).

cnf(f_4766_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20041,U_20040),hAPP(c_List_Oset(U_20041),U_20042)),U_20043) = hAPP(c_List_Ofoldl(U_20040,U_20041,hAPP(c_COMBC(U_20041,U_20040,U_20040),hAPP(hAPP(c_COMBB(U_20040,tc_fun(U_20040,U_20040),U_20041),c_Lattices_Osemilattice__sup__class_Osup(U_20040)),U_20043)),c_Orderings_Obot__class_Obot(U_20040)),U_20042)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_20040) ),
    inference(clausify,[status(thm)],[f_4766_3]) ).

fof(f_4767_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_4767_2,plain,
    ! [U_20047,U_20046,U_20045,U_20044] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20045,U_20044),hAPP(c_List_Oset(U_20045),U_20046)),U_20047) = hAPP(c_List_Ofoldl(U_20044,U_20045,hAPP(c_COMBC(U_20045,U_20044,U_20044),hAPP(hAPP(c_COMBB(U_20044,tc_fun(U_20044,U_20044),U_20045),c_Lattices_Osemilattice__inf__class_Oinf(U_20044)),U_20047)),c_Orderings_Otop__class_Otop(U_20044)),U_20046)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20044) ),
    inference(variable_rename,[status(thm)],[f_4767_1]) ).

fof(f_4767_3,plain,
    ! [U_20044,U_20045,U_20046,U_20047] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20045,U_20044),hAPP(c_List_Oset(U_20045),U_20046)),U_20047) = hAPP(c_List_Ofoldl(U_20044,U_20045,hAPP(c_COMBC(U_20045,U_20044,U_20044),hAPP(hAPP(c_COMBB(U_20044,tc_fun(U_20044,U_20044),U_20045),c_Lattices_Osemilattice__inf__class_Oinf(U_20044)),U_20047)),c_Orderings_Otop__class_Otop(U_20044)),U_20046)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20044) ),
    inference(definitional_conversion,[status(esa)],[f_4767_2]) ).

cnf(f_4767_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20045,U_20044),hAPP(c_List_Oset(U_20045),U_20046)),U_20047) = hAPP(c_List_Ofoldl(U_20044,U_20045,hAPP(c_COMBC(U_20045,U_20044,U_20044),hAPP(hAPP(c_COMBB(U_20044,tc_fun(U_20044,U_20044),U_20045),c_Lattices_Osemilattice__inf__class_Oinf(U_20044)),U_20047)),c_Orderings_Otop__class_Otop(U_20044)),U_20046)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_20044) ),
    inference(clausify,[status(thm)],[f_4767_3]) ).

fof(f_4768_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_4768_2,plain,
    ! [U_20052,U_20051,U_20050,U_20049,U_20048] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20051),c_List_Olist_Olist__size(U_20048,U_20052,U_20050)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20051),hAPP(U_20052,U_20049)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20048),U_20049),hAPP(c_List_Oset(U_20048),U_20050))) ),
    inference(variable_rename,[status(thm)],[f_4768_1]) ).

fof(f_4768_3,plain,
    ! [U_20048,U_20049,U_20050,U_20051,U_20052] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20051),c_List_Olist_Olist__size(U_20048,U_20052,U_20050)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20051),hAPP(U_20052,U_20049)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20048),U_20049),hAPP(c_List_Oset(U_20048),U_20050))) ),
    inference(definitional_conversion,[status(esa)],[f_4768_2]) ).

cnf(f_4768_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20051),c_List_Olist_Olist__size(U_20048,U_20052,U_20050)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20051),hAPP(U_20052,U_20049)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20048),U_20049),hAPP(c_List_Oset(U_20048),U_20050))) ),
    inference(clausify,[status(thm)],[f_4768_3]) ).

fof(f_4769_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_4769_2,plain,
    ! [U_20057,U_20056,U_20055,U_20054,U_20053] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20056),c_List_Olist_Olist__size(U_20053,U_20057,U_20055)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20056),hAPP(U_20057,U_20054)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20053),U_20054),hAPP(c_List_Oset(U_20053),U_20055))) ),
    inference(variable_rename,[status(thm)],[f_4769_1]) ).

fof(f_4769_3,plain,
    ! [U_20053,U_20054,U_20055,U_20056,U_20057] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20056),c_List_Olist_Olist__size(U_20053,U_20057,U_20055)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20056),hAPP(U_20057,U_20054)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20053),U_20054),hAPP(c_List_Oset(U_20053),U_20055))) ),
    inference(definitional_conversion,[status(esa)],[f_4769_2]) ).

cnf(f_4769_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20056),c_List_Olist_Olist__size(U_20053,U_20057,U_20055)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20056),hAPP(U_20057,U_20054)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20053),U_20054),hAPP(c_List_Oset(U_20053),U_20055))) ),
    inference(clausify,[status(thm)],[f_4769_3]) ).

fof(f_4770_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_4770_2,plain,
    ! [U_20062,U_20061,U_20060,U_20059,U_20058] : c_Map_Omap__upds(U_20058,U_20059,U_20060,U_20061,U_20062) = hAPP(c_List_Ofoldl(tc_fun(U_20058,tc_Option_Ooption(U_20059)),tc_prod(U_20058,U_20059),hAPP(hAPP(c_COMBB(tc_fun(U_20058,tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059)))),tc_fun(tc_prod(U_20058,U_20059),tc_fun(U_20058,tc_Option_Ooption(U_20059))),tc_fun(U_20058,tc_Option_Ooption(U_20059))),c_Product__Type_Oprod_Oprod__case(U_20058,U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059)))),hAPP(hAPP(c_COMBC(tc_fun(U_20058,tc_Option_Ooption(U_20059)),tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20058,tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059))))),hAPP(hAPP(c_COMBB(tc_fun(U_20058,tc_fun(tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059))))),tc_fun(tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20058,tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059))))),tc_fun(U_20058,tc_Option_Ooption(U_20059))),c_COMBC(U_20058,tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059))))),hAPP(hAPP(c_COMBB(tc_fun(U_20058,tc_fun(tc_Option_Ooption(U_20059),tc_fun(U_20058,tc_Option_Ooption(U_20059)))),tc_fun(U_20058,tc_fun(tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059))))),tc_fun(U_20058,tc_Option_Ooption(U_20059))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_20059),tc_fun(U_20058,tc_Option_Ooption(U_20059))),tc_fun(tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059)))),U_20058),c_COMBB(tc_Option_Ooption(U_20059),tc_fun(U_20058,tc_Option_Ooption(U_20059)),U_20059))),c_Fun_Ofun__upd(U_20058,tc_Option_Ooption(U_20059))))),c_Option_Ooption_OSome(U_20059))),U_20060),hAPP(hAPP(c_List_Ozip(U_20058,U_20059),U_20061),U_20062)),
    inference(variable_rename,[status(thm)],[f_4770_1]) ).

fof(f_4770_3,plain,
    ! [U_20058,U_20059,U_20060,U_20061,U_20062] : c_Map_Omap__upds(U_20058,U_20059,U_20060,U_20061,U_20062) = hAPP(c_List_Ofoldl(tc_fun(U_20058,tc_Option_Ooption(U_20059)),tc_prod(U_20058,U_20059),hAPP(hAPP(c_COMBB(tc_fun(U_20058,tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059)))),tc_fun(tc_prod(U_20058,U_20059),tc_fun(U_20058,tc_Option_Ooption(U_20059))),tc_fun(U_20058,tc_Option_Ooption(U_20059))),c_Product__Type_Oprod_Oprod__case(U_20058,U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059)))),hAPP(hAPP(c_COMBC(tc_fun(U_20058,tc_Option_Ooption(U_20059)),tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20058,tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059))))),hAPP(hAPP(c_COMBB(tc_fun(U_20058,tc_fun(tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059))))),tc_fun(tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20058,tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059))))),tc_fun(U_20058,tc_Option_Ooption(U_20059))),c_COMBC(U_20058,tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059))))),hAPP(hAPP(c_COMBB(tc_fun(U_20058,tc_fun(tc_Option_Ooption(U_20059),tc_fun(U_20058,tc_Option_Ooption(U_20059)))),tc_fun(U_20058,tc_fun(tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059))))),tc_fun(U_20058,tc_Option_Ooption(U_20059))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_20059),tc_fun(U_20058,tc_Option_Ooption(U_20059))),tc_fun(tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059)))),U_20058),c_COMBB(tc_Option_Ooption(U_20059),tc_fun(U_20058,tc_Option_Ooption(U_20059)),U_20059))),c_Fun_Ofun__upd(U_20058,tc_Option_Ooption(U_20059))))),c_Option_Ooption_OSome(U_20059))),U_20060),hAPP(hAPP(c_List_Ozip(U_20058,U_20059),U_20061),U_20062)),
    inference(definitional_conversion,[status(esa)],[f_4770_2]) ).

cnf(f_4770_4,plain,
    c_Map_Omap__upds(U_20058,U_20059,U_20060,U_20061,U_20062) = hAPP(c_List_Ofoldl(tc_fun(U_20058,tc_Option_Ooption(U_20059)),tc_prod(U_20058,U_20059),hAPP(hAPP(c_COMBB(tc_fun(U_20058,tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059)))),tc_fun(tc_prod(U_20058,U_20059),tc_fun(U_20058,tc_Option_Ooption(U_20059))),tc_fun(U_20058,tc_Option_Ooption(U_20059))),c_Product__Type_Oprod_Oprod__case(U_20058,U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059)))),hAPP(hAPP(c_COMBC(tc_fun(U_20058,tc_Option_Ooption(U_20059)),tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20058,tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059))))),hAPP(hAPP(c_COMBB(tc_fun(U_20058,tc_fun(tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059))))),tc_fun(tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20058,tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059))))),tc_fun(U_20058,tc_Option_Ooption(U_20059))),c_COMBC(U_20058,tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059))))),hAPP(hAPP(c_COMBB(tc_fun(U_20058,tc_fun(tc_Option_Ooption(U_20059),tc_fun(U_20058,tc_Option_Ooption(U_20059)))),tc_fun(U_20058,tc_fun(tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059))))),tc_fun(U_20058,tc_Option_Ooption(U_20059))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_20059),tc_fun(U_20058,tc_Option_Ooption(U_20059))),tc_fun(tc_fun(U_20059,tc_Option_Ooption(U_20059)),tc_fun(U_20059,tc_fun(U_20058,tc_Option_Ooption(U_20059)))),U_20058),c_COMBB(tc_Option_Ooption(U_20059),tc_fun(U_20058,tc_Option_Ooption(U_20059)),U_20059))),c_Fun_Ofun__upd(U_20058,tc_Option_Ooption(U_20059))))),c_Option_Ooption_OSome(U_20059))),U_20060),hAPP(hAPP(c_List_Ozip(U_20058,U_20059),U_20061),U_20062)),
    inference(clausify,[status(thm)],[f_4770_3]) ).

fof(f_4771_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_4771_2,plain,
    ! [U_20064,U_20063] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20063),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_20064)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20063),hAPP(c_List_Oset(tc_Nat_Onat),U_20064))) ),
    inference(variable_rename,[status(thm)],[f_4771_1]) ).

fof(f_4771_3,plain,
    ! [U_20063,U_20064] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20063),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_20064)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20063),hAPP(c_List_Oset(tc_Nat_Onat),U_20064))) ),
    inference(definitional_conversion,[status(esa)],[f_4771_2]) ).

cnf(f_4771_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20063),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_20064)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20063),hAPP(c_List_Oset(tc_Nat_Onat),U_20064))) ),
    inference(clausify,[status(thm)],[f_4771_3]) ).

fof(f_4772_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_4772_2,plain,
    ! [U_20067,U_20066,U_20065] : c_List_Olist_Olist__size(U_20065,U_20066,U_20067) = 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_20065,tc_Nat_Onat),U_20066),U_20067))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20065)),U_20067)),
    inference(variable_rename,[status(thm)],[f_4772_1]) ).

fof(f_4772_3,plain,
    ! [U_20065,U_20066,U_20067] : c_List_Olist_Olist__size(U_20065,U_20066,U_20067) = 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_20065,tc_Nat_Onat),U_20066),U_20067))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20065)),U_20067)),
    inference(definitional_conversion,[status(esa)],[f_4772_2]) ).

cnf(f_4772_4,plain,
    c_List_Olist_Olist__size(U_20065,U_20066,U_20067) = 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_20065,tc_Nat_Onat),U_20066),U_20067))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20065)),U_20067)),
    inference(clausify,[status(thm)],[f_4772_3]) ).

fof(f_4773_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_4773_2,plain,
    ! [U_20070,U_20069,U_20068] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_20068),tc_List_Olist(U_20068)),tc_HOL_Obool)),c_List_Olistrel(U_20068,U_20069)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_20068),tc_List_Olist(U_20068)),c_List_Olists(U_20068,U_20070)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20068),tc_HOL_Obool),tc_List_Olist(U_20068)),c_List_Olists(U_20068,U_20070)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_20068,U_20068),tc_HOL_Obool)),U_20069),hAPP(hAPP(c_Product__Type_OSigma(U_20068,U_20068),U_20070),hAPP(c_COMBK(tc_fun(U_20068,tc_HOL_Obool),U_20068),U_20070)))) ),
    inference(variable_rename,[status(thm)],[f_4773_1]) ).

fof(f_4773_3,plain,
    ! [U_20068,U_20069,U_20070] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_20068),tc_List_Olist(U_20068)),tc_HOL_Obool)),c_List_Olistrel(U_20068,U_20069)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_20068),tc_List_Olist(U_20068)),c_List_Olists(U_20068,U_20070)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20068),tc_HOL_Obool),tc_List_Olist(U_20068)),c_List_Olists(U_20068,U_20070)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_20068,U_20068),tc_HOL_Obool)),U_20069),hAPP(hAPP(c_Product__Type_OSigma(U_20068,U_20068),U_20070),hAPP(c_COMBK(tc_fun(U_20068,tc_HOL_Obool),U_20068),U_20070)))) ),
    inference(definitional_conversion,[status(esa)],[f_4773_2]) ).

cnf(f_4773_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_20068),tc_List_Olist(U_20068)),tc_HOL_Obool)),c_List_Olistrel(U_20068,U_20069)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_20068),tc_List_Olist(U_20068)),c_List_Olists(U_20068,U_20070)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20068),tc_HOL_Obool),tc_List_Olist(U_20068)),c_List_Olists(U_20068,U_20070)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_20068,U_20068),tc_HOL_Obool)),U_20069),hAPP(hAPP(c_Product__Type_OSigma(U_20068,U_20068),U_20070),hAPP(c_COMBK(tc_fun(U_20068,tc_HOL_Obool),U_20068),U_20070)))) ),
    inference(clausify,[status(thm)],[f_4773_3]) ).

fof(f_4774_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_4774_2,plain,
    ! [U_20073,U_20072,U_20071] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20071)),U_20072),c_Wellfounded_Oacc(tc_List_Olist(U_20071),c_List_Olistrel1(U_20071,U_20073))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20071)),U_20072),c_List_Olists(U_20071,c_Wellfounded_Oacc(U_20071,U_20073)))) ),
    inference(variable_rename,[status(thm)],[f_4774_1]) ).

fof(f_4774_3,plain,
    ! [U_20071,U_20072,U_20073] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20071)),U_20072),c_Wellfounded_Oacc(tc_List_Olist(U_20071),c_List_Olistrel1(U_20071,U_20073))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20071)),U_20072),c_List_Olists(U_20071,c_Wellfounded_Oacc(U_20071,U_20073)))) ),
    inference(definitional_conversion,[status(esa)],[f_4774_2]) ).

cnf(f_4774_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20071)),U_20072),c_Wellfounded_Oacc(tc_List_Olist(U_20071),c_List_Olistrel1(U_20071,U_20073))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20071)),U_20072),c_List_Olists(U_20071,c_Wellfounded_Oacc(U_20071,U_20073)))) ),
    inference(clausify,[status(thm)],[f_4774_3]) ).

fof(f_4775_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_4775_2,plain,
    ! [U_20075,U_20074] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20074)),c_List_Olist_ONil(U_20074)),c_List_Olists(U_20074,U_20075))),
    inference(variable_rename,[status(thm)],[f_4775_1]) ).

fof(f_4775_3,plain,
    ! [U_20074,U_20075] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20074)),c_List_Olist_ONil(U_20074)),c_List_Olists(U_20074,U_20075))),
    inference(definitional_conversion,[status(esa)],[f_4775_2]) ).

cnf(f_4775_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20074)),c_List_Olist_ONil(U_20074)),c_List_Olists(U_20074,U_20075))),
    inference(clausify,[status(thm)],[f_4775_3]) ).

fof(f_4776_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_4776_2,plain,
    ! [U_20078,U_20077,U_20076] :
      ( c_Relation_Orefl__on(tc_List_Olist(U_20076),c_List_Olists(U_20076,U_20077),c_List_Olistrel(U_20076,U_20078))
      | ~ c_Relation_Orefl__on(U_20076,U_20077,U_20078) ),
    inference(variable_rename,[status(thm)],[f_4776_1]) ).

fof(f_4776_3,plain,
    ! [U_20076,U_20077,U_20078] :
      ( c_Relation_Orefl__on(tc_List_Olist(U_20076),c_List_Olists(U_20076,U_20077),c_List_Olistrel(U_20076,U_20078))
      | ~ c_Relation_Orefl__on(U_20076,U_20077,U_20078) ),
    inference(definitional_conversion,[status(esa)],[f_4776_2]) ).

cnf(f_4776_4,plain,
    ( c_Relation_Orefl__on(tc_List_Olist(U_20076),c_List_Olists(U_20076,U_20077),c_List_Olistrel(U_20076,U_20078))
    | ~ c_Relation_Orefl__on(U_20076,U_20077,U_20078) ),
    inference(clausify,[status(thm)],[f_4776_3]) ).

fof(f_4777_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_4777_2,plain,
    ! [U_20081,U_20080,U_20079] :
      ( c_Equiv__Relations_Oequiv(tc_List_Olist(U_20079),c_List_Olists(U_20079,U_20080),c_List_Olistrel(U_20079,U_20081))
      | ~ c_Equiv__Relations_Oequiv(U_20079,U_20080,U_20081) ),
    inference(variable_rename,[status(thm)],[f_4777_1]) ).

fof(f_4777_3,plain,
    ! [U_20079,U_20080,U_20081] :
      ( c_Equiv__Relations_Oequiv(tc_List_Olist(U_20079),c_List_Olists(U_20079,U_20080),c_List_Olistrel(U_20079,U_20081))
      | ~ c_Equiv__Relations_Oequiv(U_20079,U_20080,U_20081) ),
    inference(definitional_conversion,[status(esa)],[f_4777_2]) ).

cnf(f_4777_4,plain,
    ( c_Equiv__Relations_Oequiv(tc_List_Olist(U_20079),c_List_Olists(U_20079,U_20080),c_List_Olistrel(U_20079,U_20081))
    | ~ c_Equiv__Relations_Oequiv(U_20079,U_20080,U_20081) ),
    inference(clausify,[status(thm)],[f_4777_3]) ).

fof(f_4778_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_4778_2,plain,
    ! [U_20084,U_20083,U_20082] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_20082),tc_HOL_Obool)),c_List_Olists(U_20082,U_20083)),c_List_Olists(U_20082,U_20084)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20082,tc_HOL_Obool)),U_20083),U_20084)) ),
    inference(variable_rename,[status(thm)],[f_4778_1]) ).

fof(f_4778_3,plain,
    ! [U_20082,U_20083,U_20084] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_20082),tc_HOL_Obool)),c_List_Olists(U_20082,U_20083)),c_List_Olists(U_20082,U_20084)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20082,tc_HOL_Obool)),U_20083),U_20084)) ),
    inference(definitional_conversion,[status(esa)],[f_4778_2]) ).

cnf(f_4778_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_20082),tc_HOL_Obool)),c_List_Olists(U_20082,U_20083)),c_List_Olists(U_20082,U_20084)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20082,tc_HOL_Obool)),U_20083),U_20084)) ),
    inference(clausify,[status(thm)],[f_4778_3]) ).

fof(f_4779_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_4779_2,plain,
    ! [U_20085] : c_List_Olists(U_20085,c_Orderings_Otop__class_Otop(tc_fun(U_20085,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_20085),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4779_1]) ).

fof(f_4779_3,plain,
    ! [U_20085] : c_List_Olists(U_20085,c_Orderings_Otop__class_Otop(tc_fun(U_20085,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_20085),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4779_2]) ).

cnf(f_4779_4,plain,
    c_List_Olists(U_20085,c_Orderings_Otop__class_Otop(tc_fun(U_20085,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_20085),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4779_3]) ).

fof(f_4780_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_4780_2,plain,
    ! [U_20089,U_20088,U_20087,U_20086] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20086)),hAPP(hAPP(c_List_Oappend(U_20086),U_20087),U_20088)),c_List_Olists(U_20086,U_20089)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20086)),U_20088),c_List_Olists(U_20086,U_20089)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20086)),U_20087),c_List_Olists(U_20086,U_20089))) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20086)),U_20088),c_List_Olists(U_20086,U_20089)))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20086)),U_20087),c_List_Olists(U_20086,U_20089))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20086)),hAPP(hAPP(c_List_Oappend(U_20086),U_20087),U_20088)),c_List_Olists(U_20086,U_20089))) ) ),
    inference(variable_rename,[status(thm)],[f_4780_1]) ).

fof(f_4780_3,plain,
    ( ! [U_20097,U_20095,U_20093,U_20091] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20091)),hAPP(hAPP(c_List_Oappend(U_20091),U_20093),U_20095)),c_List_Olists(U_20091,U_20097)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20091)),U_20095),c_List_Olists(U_20091,U_20097)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20091)),U_20093),c_List_Olists(U_20091,U_20097))) )
    & ! [U_20096,U_20094,U_20092,U_20090] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20090)),U_20094),c_List_Olists(U_20090,U_20096)))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20090)),U_20092),c_List_Olists(U_20090,U_20096))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20090)),hAPP(hAPP(c_List_Oappend(U_20090),U_20092),U_20094)),c_List_Olists(U_20090,U_20096))) ) ),
    inference(miniscope,[status(thm)],[f_4780_2]) ).

fof(f_4780_4,plain,
    ( ! [U_20092,U_20090,U_20094,U_20096] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20090)),U_20094),c_List_Olists(U_20090,U_20096)))
        | ~ sP1203(U_20092,U_20090,U_20094,U_20096) )
    & ! [U_20092,U_20090,U_20094,U_20096] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20090)),U_20092),c_List_Olists(U_20090,U_20096)))
        | ~ sP1203(U_20092,U_20090,U_20094,U_20096) )
    & ! [U_20095,U_20091,U_20097,U_20093] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20091)),hAPP(hAPP(c_List_Oappend(U_20091),U_20093),U_20095)),c_List_Olists(U_20091,U_20097)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20091)),U_20095),c_List_Olists(U_20091,U_20097)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20091)),U_20093),c_List_Olists(U_20091,U_20097))) )
    & ! [U_20092,U_20090,U_20094,U_20096] :
        ( sP1203(U_20092,U_20090,U_20094,U_20096)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20090)),hAPP(hAPP(c_List_Oappend(U_20090),U_20092),U_20094)),c_List_Olists(U_20090,U_20096))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1203])],[f_4780_3]) ).

cnf(f_4780_5,plain,
    ( sP1203(U_20092,U_20090,U_20094,U_20096)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20090)),hAPP(hAPP(c_List_Oappend(U_20090),U_20092),U_20094)),c_List_Olists(U_20090,U_20096))) ),
    inference(clausify,[status(thm)],[f_4780_4]) ).

cnf(f_4780_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20091)),hAPP(hAPP(c_List_Oappend(U_20091),U_20093),U_20095)),c_List_Olists(U_20091,U_20097)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20091)),U_20095),c_List_Olists(U_20091,U_20097)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20091)),U_20093),c_List_Olists(U_20091,U_20097))) ),
    inference(clausify,[status(thm)],[f_4780_4]) ).

cnf(f_4780_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20090)),U_20092),c_List_Olists(U_20090,U_20096)))
    | ~ sP1203(U_20092,U_20090,U_20094,U_20096) ),
    inference(clausify,[status(thm)],[f_4780_4]) ).

cnf(f_4780_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20090)),U_20094),c_List_Olists(U_20090,U_20096)))
    | ~ sP1203(U_20092,U_20090,U_20094,U_20096) ),
    inference(clausify,[status(thm)],[f_4780_4]) ).

fof(f_4781_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_4781_2,plain,
    ! [U_20101,U_20100,U_20099,U_20098] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20098)),hAPP(hAPP(c_List_Olist_OCons(U_20098),U_20099),U_20100)),c_List_Olists(U_20098,U_20101)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20098)),U_20100),c_List_Olists(U_20098,U_20101)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20098),U_20099),U_20101)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20098)),U_20100),c_List_Olists(U_20098,U_20101)))
          & hBOOL(hAPP(hAPP(c_member(U_20098),U_20099),U_20101)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20098)),hAPP(hAPP(c_List_Olist_OCons(U_20098),U_20099),U_20100)),c_List_Olists(U_20098,U_20101))) ) ),
    inference(variable_rename,[status(thm)],[f_4781_1]) ).

fof(f_4781_3,plain,
    ( ! [U_20109,U_20107,U_20105,U_20103] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20103)),hAPP(hAPP(c_List_Olist_OCons(U_20103),U_20105),U_20107)),c_List_Olists(U_20103,U_20109)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20103)),U_20107),c_List_Olists(U_20103,U_20109)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20103),U_20105),U_20109)) )
    & ! [U_20108,U_20106,U_20104,U_20102] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20102)),U_20106),c_List_Olists(U_20102,U_20108)))
          & hBOOL(hAPP(hAPP(c_member(U_20102),U_20104),U_20108)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20102)),hAPP(hAPP(c_List_Olist_OCons(U_20102),U_20104),U_20106)),c_List_Olists(U_20102,U_20108))) ) ),
    inference(miniscope,[status(thm)],[f_4781_2]) ).

fof(f_4781_4,plain,
    ( ! [U_20104,U_20108,U_20102,U_20106] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20102)),U_20106),c_List_Olists(U_20102,U_20108)))
        | ~ sP1204(U_20104,U_20108,U_20102,U_20106) )
    & ! [U_20104,U_20108,U_20102,U_20106] :
        ( hBOOL(hAPP(hAPP(c_member(U_20102),U_20104),U_20108))
        | ~ sP1204(U_20104,U_20108,U_20102,U_20106) )
    & ! [U_20103,U_20109,U_20105,U_20107] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20103)),hAPP(hAPP(c_List_Olist_OCons(U_20103),U_20105),U_20107)),c_List_Olists(U_20103,U_20109)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20103)),U_20107),c_List_Olists(U_20103,U_20109)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20103),U_20105),U_20109)) )
    & ! [U_20104,U_20108,U_20102,U_20106] :
        ( sP1204(U_20104,U_20108,U_20102,U_20106)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20102)),hAPP(hAPP(c_List_Olist_OCons(U_20102),U_20104),U_20106)),c_List_Olists(U_20102,U_20108))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1204])],[f_4781_3]) ).

cnf(f_4781_5,plain,
    ( sP1204(U_20104,U_20108,U_20102,U_20106)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20102)),hAPP(hAPP(c_List_Olist_OCons(U_20102),U_20104),U_20106)),c_List_Olists(U_20102,U_20108))) ),
    inference(clausify,[status(thm)],[f_4781_4]) ).

cnf(f_4781_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20103)),hAPP(hAPP(c_List_Olist_OCons(U_20103),U_20105),U_20107)),c_List_Olists(U_20103,U_20109)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20103)),U_20107),c_List_Olists(U_20103,U_20109)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20103),U_20105),U_20109)) ),
    inference(clausify,[status(thm)],[f_4781_4]) ).

cnf(f_4781_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20102),U_20104),U_20108))
    | ~ sP1204(U_20104,U_20108,U_20102,U_20106) ),
    inference(clausify,[status(thm)],[f_4781_4]) ).

cnf(f_4781_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20102)),U_20106),c_List_Olists(U_20102,U_20108)))
    | ~ sP1204(U_20104,U_20108,U_20102,U_20106) ),
    inference(clausify,[status(thm)],[f_4781_4]) ).

fof(f_4782_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_4782_2,plain,
    ! [U_20114,U_20113,U_20112] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20112)),U_20113),c_List_Olists(U_20112,U_20114)))
        | ? [U_20111] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_20112),U_20111),U_20114))
            & hBOOL(hAPP(hAPP(c_member(U_20112),U_20111),hAPP(c_List_Oset(U_20112),U_20113))) ) )
      & ( ! [U_20110] :
            ( hBOOL(hAPP(hAPP(c_member(U_20112),U_20110),U_20114))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20112),U_20110),hAPP(c_List_Oset(U_20112),U_20113))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20112)),U_20113),c_List_Olists(U_20112,U_20114))) ) ),
    inference(variable_rename,[status(thm)],[f_4782_1]) ).

fof(f_4782_3,plain,
    ( ! [U_20120,U_20118,U_20116] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20116)),U_20118),c_List_Olists(U_20116,U_20120)))
        | ? [U_20111] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_20116),U_20111),U_20120))
            & hBOOL(hAPP(hAPP(c_member(U_20116),U_20111),hAPP(c_List_Oset(U_20116),U_20118))) ) )
    & ! [U_20119,U_20117,U_20115] :
        ( ! [U_20110] :
            ( hBOOL(hAPP(hAPP(c_member(U_20115),U_20110),U_20119))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20115),U_20110),hAPP(c_List_Oset(U_20115),U_20117))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20115)),U_20117),c_List_Olists(U_20115,U_20119))) ) ),
    inference(miniscope,[status(thm)],[f_4782_2]) ).

fof(f_4782_4,plain,
    ( ! [U_20120,U_20118,U_20116] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20116)),U_20118),c_List_Olists(U_20116,U_20120)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_20116),sK488(U_20120,U_20118,U_20116)),U_20120))
          & hBOOL(hAPP(hAPP(c_member(U_20116),sK488(U_20120,U_20118,U_20116)),hAPP(c_List_Oset(U_20116),U_20118))) ) )
    & ! [U_20119,U_20117,U_20115] :
        ( ! [U_20110] :
            ( hBOOL(hAPP(hAPP(c_member(U_20115),U_20110),U_20119))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20115),U_20110),hAPP(c_List_Oset(U_20115),U_20117))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20115)),U_20117),c_List_Olists(U_20115,U_20119))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK488]),skolemize(U_20111,sK488(U_20120,U_20118,U_20116))],[f_4782_3]) ).

fof(f_4782_5,plain,
    ( ! [U_20118,U_20116,U_20120] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_20116),sK488(U_20120,U_20118,U_20116)),U_20120))
        | ~ sP1205(U_20118,U_20116,U_20120) )
    & ! [U_20118,U_20116,U_20120] :
        ( hBOOL(hAPP(hAPP(c_member(U_20116),sK488(U_20120,U_20118,U_20116)),hAPP(c_List_Oset(U_20116),U_20118)))
        | ~ sP1205(U_20118,U_20116,U_20120) )
    & ! [U_20118,U_20116,U_20120] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20116)),U_20118),c_List_Olists(U_20116,U_20120)))
        | sP1205(U_20118,U_20116,U_20120) )
    & ! [U_20110,U_20117,U_20115,U_20119] :
        ( hBOOL(hAPP(hAPP(c_member(U_20115),U_20110),U_20119))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20115),U_20110),hAPP(c_List_Oset(U_20115),U_20117)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20115)),U_20117),c_List_Olists(U_20115,U_20119))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1205])],[f_4782_4]) ).

cnf(f_4782_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20115),U_20110),U_20119))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20115),U_20110),hAPP(c_List_Oset(U_20115),U_20117)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20115)),U_20117),c_List_Olists(U_20115,U_20119))) ),
    inference(clausify,[status(thm)],[f_4782_5]) ).

cnf(f_4782_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20116)),U_20118),c_List_Olists(U_20116,U_20120)))
    | sP1205(U_20118,U_20116,U_20120) ),
    inference(clausify,[status(thm)],[f_4782_5]) ).

cnf(f_4782_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20116),sK488(U_20120,U_20118,U_20116)),hAPP(c_List_Oset(U_20116),U_20118)))
    | ~ sP1205(U_20118,U_20116,U_20120) ),
    inference(clausify,[status(thm)],[f_4782_5]) ).

cnf(f_4782_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_20116),sK488(U_20120,U_20118,U_20116)),U_20120))
    | ~ sP1205(U_20118,U_20116,U_20120) ),
    inference(clausify,[status(thm)],[f_4782_5]) ).

fof(f_4783_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_4783_2,plain,
    ! [U_20122,U_20121] : c_List_Olists(U_20121,U_20122) = hAPP(c_Set_OCollect(tc_List_Olist(U_20121)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20121),tc_fun(U_20121,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_20121,tc_HOL_Obool),tc_fun(tc_fun(U_20121,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_20121)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_20121,tc_HOL_Obool))),c_List_Oset(U_20121))),U_20122)),
    inference(variable_rename,[status(thm)],[f_4783_1]) ).

fof(f_4783_3,plain,
    ! [U_20121,U_20122] : c_List_Olists(U_20121,U_20122) = hAPP(c_Set_OCollect(tc_List_Olist(U_20121)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20121),tc_fun(U_20121,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_20121,tc_HOL_Obool),tc_fun(tc_fun(U_20121,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_20121)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_20121,tc_HOL_Obool))),c_List_Oset(U_20121))),U_20122)),
    inference(definitional_conversion,[status(esa)],[f_4783_2]) ).

cnf(f_4783_4,plain,
    c_List_Olists(U_20121,U_20122) = hAPP(c_Set_OCollect(tc_List_Olist(U_20121)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20121),tc_fun(U_20121,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_20121,tc_HOL_Obool),tc_fun(tc_fun(U_20121,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_20121)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_20121,tc_HOL_Obool))),c_List_Oset(U_20121))),U_20122)),
    inference(clausify,[status(thm)],[f_4783_3]) ).

fof(f_4784_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_4784_2,plain,
    ! [U_20123] : c_List_Olists(U_20123,c_Orderings_Obot__class_Obot(tc_fun(U_20123,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_20123)),c_List_Olist_ONil(U_20123)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_20123),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4784_1]) ).

fof(f_4784_3,plain,
    ! [U_20123] : c_List_Olists(U_20123,c_Orderings_Obot__class_Obot(tc_fun(U_20123,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_20123)),c_List_Olist_ONil(U_20123)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_20123),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_4784_2]) ).

cnf(f_4784_4,plain,
    c_List_Olists(U_20123,c_Orderings_Obot__class_Obot(tc_fun(U_20123,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_20123)),c_List_Olist_ONil(U_20123)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_20123),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4784_3]) ).

fof(f_4785_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_4785_2,plain,
    ! [U_20126,U_20125,U_20124] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20124)),U_20125),c_List_Olists(U_20124,c_Wellfounded_Oacc(U_20124,U_20126))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20124)),U_20125),c_Wellfounded_Oacc(tc_List_Olist(U_20124),c_List_Olistrel1(U_20124,U_20126)))) ),
    inference(variable_rename,[status(thm)],[f_4785_1]) ).

fof(f_4785_3,plain,
    ! [U_20124,U_20125,U_20126] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20124)),U_20125),c_List_Olists(U_20124,c_Wellfounded_Oacc(U_20124,U_20126))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20124)),U_20125),c_Wellfounded_Oacc(tc_List_Olist(U_20124),c_List_Olistrel1(U_20124,U_20126)))) ),
    inference(definitional_conversion,[status(esa)],[f_4785_2]) ).

cnf(f_4785_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20124)),U_20125),c_List_Olists(U_20124,c_Wellfounded_Oacc(U_20124,U_20126))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20124)),U_20125),c_Wellfounded_Oacc(tc_List_Olist(U_20124),c_List_Olistrel1(U_20124,U_20126)))) ),
    inference(clausify,[status(thm)],[f_4785_3]) ).

fof(f_4786_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_4786_2,plain,
    ! [U_20132,U_20131,U_20130,U_20129] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20130),tc_List_Olist(U_20130))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20130),tc_List_Olist(U_20130)),U_20131),hAPP(hAPP(c_List_Oappend(U_20130),U_20131),U_20129))),c_List_Olexord(U_20130,U_20132)))
      | ! [U_20128,U_20127] : U_20129 != hAPP(hAPP(c_List_Olist_OCons(U_20130),U_20128),U_20127) ),
    inference(variable_rename,[status(thm)],[f_4786_1]) ).

fof(f_4786_3,plain,
    ! [U_20128,U_20127,U_20129,U_20130,U_20131,U_20132] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20130),tc_List_Olist(U_20130))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20130),tc_List_Olist(U_20130)),U_20131),hAPP(hAPP(c_List_Oappend(U_20130),U_20131),U_20129))),c_List_Olexord(U_20130,U_20132)))
      | U_20129 != hAPP(hAPP(c_List_Olist_OCons(U_20130),U_20128),U_20127) ),
    inference(definitional_conversion,[status(esa)],[f_4786_2]) ).

cnf(f_4786_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20130),tc_List_Olist(U_20130))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20130),tc_List_Olist(U_20130)),U_20131),hAPP(hAPP(c_List_Oappend(U_20130),U_20131),U_20129))),c_List_Olexord(U_20130,U_20132)))
    | U_20129 != hAPP(hAPP(c_List_Olist_OCons(U_20130),U_20128),U_20127) ),
    inference(clausify,[status(thm)],[f_4786_3]) ).

fof(f_4787_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_4787_2,plain,
    ! [U_20139,U_20138,U_20137] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20137),tc_List_Olist(U_20137))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20137),tc_List_Olist(U_20137)),c_List_Olist_ONil(U_20137)),U_20138)),c_List_Olexord(U_20137,U_20139)))
        | ! [U_20136,U_20135] : U_20138 != hAPP(hAPP(c_List_Olist_OCons(U_20137),U_20136),U_20135) )
      & ( ? [U_20134,U_20133] : U_20138 = hAPP(hAPP(c_List_Olist_OCons(U_20137),U_20134),U_20133)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20137),tc_List_Olist(U_20137))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20137),tc_List_Olist(U_20137)),c_List_Olist_ONil(U_20137)),U_20138)),c_List_Olexord(U_20137,U_20139))) ) ),
    inference(variable_rename,[status(thm)],[f_4787_1]) ).

fof(f_4787_3,plain,
    ( ! [U_20145,U_20143,U_20141] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20141),tc_List_Olist(U_20141))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20141),tc_List_Olist(U_20141)),c_List_Olist_ONil(U_20141)),U_20143)),c_List_Olexord(U_20141,U_20145)))
        | ! [U_20136,U_20135] : U_20143 != hAPP(hAPP(c_List_Olist_OCons(U_20141),U_20136),U_20135) )
    & ! [U_20144,U_20142,U_20140] :
        ( ? [U_20134,U_20133] : U_20142 = hAPP(hAPP(c_List_Olist_OCons(U_20140),U_20134),U_20133)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20140),tc_List_Olist(U_20140))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20140),tc_List_Olist(U_20140)),c_List_Olist_ONil(U_20140)),U_20142)),c_List_Olexord(U_20140,U_20144))) ) ),
    inference(miniscope,[status(thm)],[f_4787_2]) ).

fof(f_4787_4,plain,
    ( ! [U_20145,U_20143,U_20141] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20141),tc_List_Olist(U_20141))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20141),tc_List_Olist(U_20141)),c_List_Olist_ONil(U_20141)),U_20143)),c_List_Olexord(U_20141,U_20145)))
        | ! [U_20136,U_20135] : U_20143 != hAPP(hAPP(c_List_Olist_OCons(U_20141),U_20136),U_20135) )
    & ! [U_20144,U_20142,U_20140] :
        ( ? [U_20133] : U_20142 = hAPP(hAPP(c_List_Olist_OCons(U_20140),sK489(U_20144,U_20142,U_20140)),U_20133)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20140),tc_List_Olist(U_20140))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20140),tc_List_Olist(U_20140)),c_List_Olist_ONil(U_20140)),U_20142)),c_List_Olexord(U_20140,U_20144))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK489]),skolemize(U_20134,sK489(U_20144,U_20142,U_20140))],[f_4787_3]) ).

fof(f_4787_5,plain,
    ( ! [U_20145,U_20143,U_20141] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20141),tc_List_Olist(U_20141))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20141),tc_List_Olist(U_20141)),c_List_Olist_ONil(U_20141)),U_20143)),c_List_Olexord(U_20141,U_20145)))
        | ! [U_20136,U_20135] : U_20143 != hAPP(hAPP(c_List_Olist_OCons(U_20141),U_20136),U_20135) )
    & ! [U_20144,U_20142,U_20140] :
        ( U_20142 = hAPP(hAPP(c_List_Olist_OCons(U_20140),sK489(U_20144,U_20142,U_20140)),sK490(U_20144,U_20142,U_20140))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20140),tc_List_Olist(U_20140))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20140),tc_List_Olist(U_20140)),c_List_Olist_ONil(U_20140)),U_20142)),c_List_Olexord(U_20140,U_20144))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK490]),skolemize(U_20133,sK490(U_20144,U_20142,U_20140))],[f_4787_4]) ).

fof(f_4787_6,plain,
    ( ! [U_20135,U_20136,U_20141,U_20143,U_20145] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20141),tc_List_Olist(U_20141))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20141),tc_List_Olist(U_20141)),c_List_Olist_ONil(U_20141)),U_20143)),c_List_Olexord(U_20141,U_20145)))
        | U_20143 != hAPP(hAPP(c_List_Olist_OCons(U_20141),U_20136),U_20135) )
    & ! [U_20142,U_20140,U_20144] :
        ( U_20142 = hAPP(hAPP(c_List_Olist_OCons(U_20140),sK489(U_20144,U_20142,U_20140)),sK490(U_20144,U_20142,U_20140))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20140),tc_List_Olist(U_20140))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20140),tc_List_Olist(U_20140)),c_List_Olist_ONil(U_20140)),U_20142)),c_List_Olexord(U_20140,U_20144))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4787_5]) ).

cnf(f_4787_7,plain,
    ( U_20142 = hAPP(hAPP(c_List_Olist_OCons(U_20140),sK489(U_20144,U_20142,U_20140)),sK490(U_20144,U_20142,U_20140))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20140),tc_List_Olist(U_20140))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20140),tc_List_Olist(U_20140)),c_List_Olist_ONil(U_20140)),U_20142)),c_List_Olexord(U_20140,U_20144))) ),
    inference(clausify,[status(thm)],[f_4787_6]) ).

cnf(f_4787_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20141),tc_List_Olist(U_20141))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20141),tc_List_Olist(U_20141)),c_List_Olist_ONil(U_20141)),U_20143)),c_List_Olexord(U_20141,U_20145)))
    | U_20143 != hAPP(hAPP(c_List_Olist_OCons(U_20141),U_20136),U_20135) ),
    inference(clausify,[status(thm)],[f_4787_6]) ).

fof(f_4788_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_4788_2,plain,
    ! [U_20149,U_20148,U_20147,U_20146] :
      ( ( ( c_List_Olast(U_20147,hAPP(hAPP(c_List_Olist__update(U_20147,U_20146),U_20148),U_20149)) = c_List_Olast(U_20147,U_20146)
          | U_20148 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20147)),U_20146)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( c_List_Olast(U_20147,hAPP(hAPP(c_List_Olist__update(U_20147,U_20146),U_20148),U_20149)) = U_20149
          | U_20148 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20147)),U_20146)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) )
      | U_20146 = c_List_Olist_ONil(U_20147) ),
    inference(variable_rename,[status(thm)],[f_4788_1]) ).

fof(f_4788_3,plain,
    ( ! [U_20147,U_20146,U_20148,U_20149] :
        ( c_List_Olast(U_20147,hAPP(hAPP(c_List_Olist__update(U_20147,U_20146),U_20148),U_20149)) = c_List_Olast(U_20147,U_20146)
        | U_20148 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20147)),U_20146)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ sP1206(U_20147,U_20146,U_20148,U_20149) )
    & ! [U_20147,U_20146,U_20148,U_20149] :
        ( c_List_Olast(U_20147,hAPP(hAPP(c_List_Olist__update(U_20147,U_20146),U_20148),U_20149)) = U_20149
        | U_20148 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20147)),U_20146)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ sP1206(U_20147,U_20146,U_20148,U_20149) )
    & ! [U_20147,U_20146,U_20148,U_20149] :
        ( sP1206(U_20147,U_20146,U_20148,U_20149)
        | U_20146 = c_List_Olist_ONil(U_20147) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1206])],[f_4788_2]) ).

cnf(f_4788_4,plain,
    ( sP1206(U_20147,U_20146,U_20148,U_20149)
    | U_20146 = c_List_Olist_ONil(U_20147) ),
    inference(clausify,[status(thm)],[f_4788_3]) ).

cnf(f_4788_5,plain,
    ( c_List_Olast(U_20147,hAPP(hAPP(c_List_Olist__update(U_20147,U_20146),U_20148),U_20149)) = U_20149
    | U_20148 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20147)),U_20146)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ sP1206(U_20147,U_20146,U_20148,U_20149) ),
    inference(clausify,[status(thm)],[f_4788_3]) ).

cnf(f_4788_6,plain,
    ( c_List_Olast(U_20147,hAPP(hAPP(c_List_Olist__update(U_20147,U_20146),U_20148),U_20149)) = c_List_Olast(U_20147,U_20146)
    | U_20148 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20147)),U_20146)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ sP1206(U_20147,U_20146,U_20148,U_20149) ),
    inference(clausify,[status(thm)],[f_4788_3]) ).

fof(f_4789_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_4789_2,plain,
    ! [U_20155,U_20154,U_20153,U_20152,U_20151] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20151),hAPP(c_List_Omonoid__add__class_Olistsum(U_20151),hAPP(hAPP(c_List_Omap(U_20152,U_20151),U_20154),U_20153))),hAPP(c_List_Omonoid__add__class_Olistsum(U_20151),hAPP(hAPP(c_List_Omap(U_20152,U_20151),U_20155),U_20153))))
      | ? [U_20150] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20151),hAPP(U_20154,U_20150)),hAPP(U_20155,U_20150)))
          & hBOOL(hAPP(hAPP(c_member(U_20152),U_20150),hAPP(c_List_Oset(U_20152),U_20153))) )
      | ~ class_Groups_Oordered__ab__semigroup__add(U_20151)
      | ~ class_Groups_Omonoid__add(U_20151) ),
    inference(variable_rename,[status(thm)],[f_4789_1]) ).

fof(f_4789_3,plain,
    ! [U_20155,U_20154,U_20153,U_20152,U_20151] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20151),hAPP(c_List_Omonoid__add__class_Olistsum(U_20151),hAPP(hAPP(c_List_Omap(U_20152,U_20151),U_20154),U_20153))),hAPP(c_List_Omonoid__add__class_Olistsum(U_20151),hAPP(hAPP(c_List_Omap(U_20152,U_20151),U_20155),U_20153))))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20151),hAPP(U_20154,sK491(U_20155,U_20154,U_20153,U_20152,U_20151))),hAPP(U_20155,sK491(U_20155,U_20154,U_20153,U_20152,U_20151))))
        & hBOOL(hAPP(hAPP(c_member(U_20152),sK491(U_20155,U_20154,U_20153,U_20152,U_20151)),hAPP(c_List_Oset(U_20152),U_20153))) )
      | ~ class_Groups_Oordered__ab__semigroup__add(U_20151)
      | ~ class_Groups_Omonoid__add(U_20151) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK491]),skolemize(U_20150,sK491(U_20155,U_20154,U_20153,U_20152,U_20151))],[f_4789_2]) ).

fof(f_4789_4,plain,
    ( ! [U_20151,U_20152,U_20153,U_20154,U_20155] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20151),hAPP(U_20154,sK491(U_20155,U_20154,U_20153,U_20152,U_20151))),hAPP(U_20155,sK491(U_20155,U_20154,U_20153,U_20152,U_20151))))
        | ~ sP1207(U_20151,U_20152,U_20153,U_20154,U_20155) )
    & ! [U_20151,U_20152,U_20153,U_20154,U_20155] :
        ( hBOOL(hAPP(hAPP(c_member(U_20152),sK491(U_20155,U_20154,U_20153,U_20152,U_20151)),hAPP(c_List_Oset(U_20152),U_20153)))
        | ~ sP1207(U_20151,U_20152,U_20153,U_20154,U_20155) )
    & ! [U_20151,U_20152,U_20153,U_20154,U_20155] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20151),hAPP(c_List_Omonoid__add__class_Olistsum(U_20151),hAPP(hAPP(c_List_Omap(U_20152,U_20151),U_20154),U_20153))),hAPP(c_List_Omonoid__add__class_Olistsum(U_20151),hAPP(hAPP(c_List_Omap(U_20152,U_20151),U_20155),U_20153))))
        | sP1207(U_20151,U_20152,U_20153,U_20154,U_20155)
        | ~ class_Groups_Oordered__ab__semigroup__add(U_20151)
        | ~ class_Groups_Omonoid__add(U_20151) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1207])],[f_4789_3]) ).

cnf(f_4789_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20151),hAPP(c_List_Omonoid__add__class_Olistsum(U_20151),hAPP(hAPP(c_List_Omap(U_20152,U_20151),U_20154),U_20153))),hAPP(c_List_Omonoid__add__class_Olistsum(U_20151),hAPP(hAPP(c_List_Omap(U_20152,U_20151),U_20155),U_20153))))
    | sP1207(U_20151,U_20152,U_20153,U_20154,U_20155)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_20151)
    | ~ class_Groups_Omonoid__add(U_20151) ),
    inference(clausify,[status(thm)],[f_4789_4]) ).

cnf(f_4789_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20152),sK491(U_20155,U_20154,U_20153,U_20152,U_20151)),hAPP(c_List_Oset(U_20152),U_20153)))
    | ~ sP1207(U_20151,U_20152,U_20153,U_20154,U_20155) ),
    inference(clausify,[status(thm)],[f_4789_4]) ).

cnf(f_4789_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20151),hAPP(U_20154,sK491(U_20155,U_20154,U_20153,U_20152,U_20151))),hAPP(U_20155,sK491(U_20155,U_20154,U_20153,U_20152,U_20151))))
    | ~ sP1207(U_20151,U_20152,U_20153,U_20154,U_20155) ),
    inference(clausify,[status(thm)],[f_4789_4]) ).

fof(f_4790_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_4790_2,plain,
    ! [U_20158,U_20157,U_20156] :
      ( ( c_List_Olast(U_20157,hAPP(hAPP(c_List_Olist_OCons(U_20157),U_20158),U_20156)) = c_List_Olast(U_20157,U_20156)
        | U_20156 = c_List_Olist_ONil(U_20157) )
      & ( c_List_Olast(U_20157,hAPP(hAPP(c_List_Olist_OCons(U_20157),U_20158),U_20156)) = U_20158
        | U_20156 != c_List_Olist_ONil(U_20157) ) ),
    inference(variable_rename,[status(thm)],[f_4790_1]) ).

fof(f_4790_3,plain,
    ( ! [U_20164,U_20162,U_20160] :
        ( c_List_Olast(U_20162,hAPP(hAPP(c_List_Olist_OCons(U_20162),U_20164),U_20160)) = c_List_Olast(U_20162,U_20160)
        | U_20160 = c_List_Olist_ONil(U_20162) )
    & ! [U_20163,U_20161,U_20159] :
        ( c_List_Olast(U_20161,hAPP(hAPP(c_List_Olist_OCons(U_20161),U_20163),U_20159)) = U_20163
        | U_20159 != c_List_Olist_ONil(U_20161) ) ),
    inference(miniscope,[status(thm)],[f_4790_2]) ).

fof(f_4790_4,plain,
    ( ! [U_20160,U_20162,U_20164] :
        ( c_List_Olast(U_20162,hAPP(hAPP(c_List_Olist_OCons(U_20162),U_20164),U_20160)) = c_List_Olast(U_20162,U_20160)
        | U_20160 = c_List_Olist_ONil(U_20162) )
    & ! [U_20159,U_20161,U_20163] :
        ( c_List_Olast(U_20161,hAPP(hAPP(c_List_Olist_OCons(U_20161),U_20163),U_20159)) = U_20163
        | U_20159 != c_List_Olist_ONil(U_20161) ) ),
    inference(definitional_conversion,[status(esa)],[f_4790_3]) ).

cnf(f_4790_5,plain,
    ( c_List_Olast(U_20161,hAPP(hAPP(c_List_Olist_OCons(U_20161),U_20163),U_20159)) = U_20163
    | U_20159 != c_List_Olist_ONil(U_20161) ),
    inference(clausify,[status(thm)],[f_4790_4]) ).

cnf(f_4790_6,plain,
    ( c_List_Olast(U_20162,hAPP(hAPP(c_List_Olist_OCons(U_20162),U_20164),U_20160)) = c_List_Olast(U_20162,U_20160)
    | U_20160 = c_List_Olist_ONil(U_20162) ),
    inference(clausify,[status(thm)],[f_4790_4]) ).

fof(f_4791_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_4791_2,plain,
    ! [U_20167,U_20166,U_20165] :
      ( c_List_Olast(U_20166,hAPP(hAPP(c_List_Olist_OCons(U_20166),U_20167),U_20165)) = c_List_Olast(U_20166,U_20165)
      | U_20165 = c_List_Olist_ONil(U_20166) ),
    inference(variable_rename,[status(thm)],[f_4791_1]) ).

fof(f_4791_3,plain,
    ! [U_20165,U_20166,U_20167] :
      ( c_List_Olast(U_20166,hAPP(hAPP(c_List_Olist_OCons(U_20166),U_20167),U_20165)) = c_List_Olast(U_20166,U_20165)
      | U_20165 = c_List_Olist_ONil(U_20166) ),
    inference(definitional_conversion,[status(esa)],[f_4791_2]) ).

cnf(f_4791_4,plain,
    ( c_List_Olast(U_20166,hAPP(hAPP(c_List_Olist_OCons(U_20166),U_20167),U_20165)) = c_List_Olast(U_20166,U_20165)
    | U_20165 = c_List_Olist_ONil(U_20166) ),
    inference(clausify,[status(thm)],[f_4791_3]) ).

fof(f_4792_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_4792_2,plain,
    ! [U_20170,U_20169,U_20168] :
      ( c_List_Olast(U_20169,hAPP(hAPP(c_List_Olist_OCons(U_20169),U_20170),U_20168)) = U_20170
      | U_20168 != c_List_Olist_ONil(U_20169) ),
    inference(variable_rename,[status(thm)],[f_4792_1]) ).

fof(f_4792_3,plain,
    ! [U_20168,U_20169,U_20170] :
      ( c_List_Olast(U_20169,hAPP(hAPP(c_List_Olist_OCons(U_20169),U_20170),U_20168)) = U_20170
      | U_20168 != c_List_Olist_ONil(U_20169) ),
    inference(definitional_conversion,[status(esa)],[f_4792_2]) ).

cnf(f_4792_4,plain,
    ( c_List_Olast(U_20169,hAPP(hAPP(c_List_Olist_OCons(U_20169),U_20170),U_20168)) = U_20170
    | U_20168 != c_List_Olist_ONil(U_20169) ),
    inference(clausify,[status(thm)],[f_4792_3]) ).

fof(f_4793_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_4793_2,plain,
    ! [U_20173,U_20172,U_20171] :
      ( ( c_List_Olast(U_20172,hAPP(hAPP(c_List_Oappend(U_20172),U_20173),U_20171)) = c_List_Olast(U_20172,U_20171)
        | U_20171 = c_List_Olist_ONil(U_20172) )
      & ( c_List_Olast(U_20172,hAPP(hAPP(c_List_Oappend(U_20172),U_20173),U_20171)) = c_List_Olast(U_20172,U_20173)
        | U_20171 != c_List_Olist_ONil(U_20172) ) ),
    inference(variable_rename,[status(thm)],[f_4793_1]) ).

fof(f_4793_3,plain,
    ( ! [U_20179,U_20177,U_20175] :
        ( c_List_Olast(U_20177,hAPP(hAPP(c_List_Oappend(U_20177),U_20179),U_20175)) = c_List_Olast(U_20177,U_20175)
        | U_20175 = c_List_Olist_ONil(U_20177) )
    & ! [U_20178,U_20176,U_20174] :
        ( c_List_Olast(U_20176,hAPP(hAPP(c_List_Oappend(U_20176),U_20178),U_20174)) = c_List_Olast(U_20176,U_20178)
        | U_20174 != c_List_Olist_ONil(U_20176) ) ),
    inference(miniscope,[status(thm)],[f_4793_2]) ).

fof(f_4793_4,plain,
    ( ! [U_20177,U_20175,U_20179] :
        ( c_List_Olast(U_20177,hAPP(hAPP(c_List_Oappend(U_20177),U_20179),U_20175)) = c_List_Olast(U_20177,U_20175)
        | U_20175 = c_List_Olist_ONil(U_20177) )
    & ! [U_20176,U_20174,U_20178] :
        ( c_List_Olast(U_20176,hAPP(hAPP(c_List_Oappend(U_20176),U_20178),U_20174)) = c_List_Olast(U_20176,U_20178)
        | U_20174 != c_List_Olist_ONil(U_20176) ) ),
    inference(definitional_conversion,[status(esa)],[f_4793_3]) ).

cnf(f_4793_5,plain,
    ( c_List_Olast(U_20176,hAPP(hAPP(c_List_Oappend(U_20176),U_20178),U_20174)) = c_List_Olast(U_20176,U_20178)
    | U_20174 != c_List_Olist_ONil(U_20176) ),
    inference(clausify,[status(thm)],[f_4793_4]) ).

cnf(f_4793_6,plain,
    ( c_List_Olast(U_20177,hAPP(hAPP(c_List_Oappend(U_20177),U_20179),U_20175)) = c_List_Olast(U_20177,U_20175)
    | U_20175 = c_List_Olist_ONil(U_20177) ),
    inference(clausify,[status(thm)],[f_4793_4]) ).

fof(f_4794_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_4794_2,plain,
    ! [U_20182,U_20181,U_20180] :
      ( c_List_Olast(U_20181,hAPP(hAPP(c_List_Oappend(U_20181),U_20182),U_20180)) = c_List_Olast(U_20181,U_20180)
      | U_20180 = c_List_Olist_ONil(U_20181) ),
    inference(variable_rename,[status(thm)],[f_4794_1]) ).

fof(f_4794_3,plain,
    ! [U_20181,U_20180,U_20182] :
      ( c_List_Olast(U_20181,hAPP(hAPP(c_List_Oappend(U_20181),U_20182),U_20180)) = c_List_Olast(U_20181,U_20180)
      | U_20180 = c_List_Olist_ONil(U_20181) ),
    inference(definitional_conversion,[status(esa)],[f_4794_2]) ).

cnf(f_4794_4,plain,
    ( c_List_Olast(U_20181,hAPP(hAPP(c_List_Oappend(U_20181),U_20182),U_20180)) = c_List_Olast(U_20181,U_20180)
    | U_20180 = c_List_Olist_ONil(U_20181) ),
    inference(clausify,[status(thm)],[f_4794_3]) ).

fof(f_4795_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_4795_2,plain,
    ! [U_20185,U_20184,U_20183] :
      ( c_List_Olast(U_20184,hAPP(hAPP(c_List_Oappend(U_20184),U_20185),U_20183)) = c_List_Olast(U_20184,U_20185)
      | U_20183 != c_List_Olist_ONil(U_20184) ),
    inference(variable_rename,[status(thm)],[f_4795_1]) ).

fof(f_4795_3,plain,
    ! [U_20183,U_20184,U_20185] :
      ( c_List_Olast(U_20184,hAPP(hAPP(c_List_Oappend(U_20184),U_20185),U_20183)) = c_List_Olast(U_20184,U_20185)
      | U_20183 != c_List_Olist_ONil(U_20184) ),
    inference(definitional_conversion,[status(esa)],[f_4795_2]) ).

cnf(f_4795_4,plain,
    ( c_List_Olast(U_20184,hAPP(hAPP(c_List_Oappend(U_20184),U_20185),U_20183)) = c_List_Olast(U_20184,U_20185)
    | U_20183 != c_List_Olist_ONil(U_20184) ),
    inference(clausify,[status(thm)],[f_4795_3]) ).

fof(f_4796_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_4796_2,plain,
    ! [U_20189,U_20188,U_20187,U_20186] :
      ( c_List_Olast(U_20188,hAPP(hAPP(c_List_Omap(U_20187,U_20188),U_20189),U_20186)) = hAPP(U_20189,c_List_Olast(U_20187,U_20186))
      | U_20186 = c_List_Olist_ONil(U_20187) ),
    inference(variable_rename,[status(thm)],[f_4796_1]) ).

fof(f_4796_3,plain,
    ! [U_20186,U_20187,U_20188,U_20189] :
      ( c_List_Olast(U_20188,hAPP(hAPP(c_List_Omap(U_20187,U_20188),U_20189),U_20186)) = hAPP(U_20189,c_List_Olast(U_20187,U_20186))
      | U_20186 = c_List_Olist_ONil(U_20187) ),
    inference(definitional_conversion,[status(esa)],[f_4796_2]) ).

cnf(f_4796_4,plain,
    ( c_List_Olast(U_20188,hAPP(hAPP(c_List_Omap(U_20187,U_20188),U_20189),U_20186)) = hAPP(U_20189,c_List_Olast(U_20187,U_20186))
    | U_20186 = c_List_Olist_ONil(U_20187) ),
    inference(clausify,[status(thm)],[f_4796_3]) ).

fof(f_4797_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_4797_2,plain,
    ! [U_20191,U_20190] :
      ( hBOOL(hAPP(hAPP(c_member(U_20191),c_List_Olast(U_20191,U_20190)),hAPP(c_List_Oset(U_20191),U_20190)))
      | U_20190 = c_List_Olist_ONil(U_20191) ),
    inference(variable_rename,[status(thm)],[f_4797_1]) ).

fof(f_4797_3,plain,
    ! [U_20190,U_20191] :
      ( hBOOL(hAPP(hAPP(c_member(U_20191),c_List_Olast(U_20191,U_20190)),hAPP(c_List_Oset(U_20191),U_20190)))
      | U_20190 = c_List_Olist_ONil(U_20191) ),
    inference(definitional_conversion,[status(esa)],[f_4797_2]) ).

cnf(f_4797_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20191),c_List_Olast(U_20191,U_20190)),hAPP(c_List_Oset(U_20191),U_20190)))
    | U_20190 = c_List_Olist_ONil(U_20191) ),
    inference(clausify,[status(thm)],[f_4797_3]) ).

fof(f_4798_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_4798_2,plain,
    ! [U_20194,U_20193,U_20192] : c_List_Olast(U_20192,hAPP(hAPP(c_List_Oappend(U_20192),U_20193),hAPP(hAPP(c_List_Olist_OCons(U_20192),U_20194),c_List_Olist_ONil(U_20192)))) = U_20194,
    inference(variable_rename,[status(thm)],[f_4798_1]) ).

fof(f_4798_3,plain,
    ! [U_20192,U_20193,U_20194] : c_List_Olast(U_20192,hAPP(hAPP(c_List_Oappend(U_20192),U_20193),hAPP(hAPP(c_List_Olist_OCons(U_20192),U_20194),c_List_Olist_ONil(U_20192)))) = U_20194,
    inference(definitional_conversion,[status(esa)],[f_4798_2]) ).

cnf(f_4798_4,plain,
    c_List_Olast(U_20192,hAPP(hAPP(c_List_Oappend(U_20192),U_20193),hAPP(hAPP(c_List_Olist_OCons(U_20192),U_20194),c_List_Olist_ONil(U_20192)))) = U_20194,
    inference(clausify,[status(thm)],[f_4798_3]) ).

fof(f_4799_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_4799_2,plain,
    ! [U_20197,U_20196,U_20195] :
      ( c_List_Olast(U_20196,hAPP(hAPP(c_List_Odrop(U_20196),U_20195),U_20197)) = c_List_Olast(U_20196,U_20197)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20195),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20196)),U_20197))) ),
    inference(variable_rename,[status(thm)],[f_4799_1]) ).

fof(f_4799_3,plain,
    ! [U_20195,U_20196,U_20197] :
      ( c_List_Olast(U_20196,hAPP(hAPP(c_List_Odrop(U_20196),U_20195),U_20197)) = c_List_Olast(U_20196,U_20197)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20195),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20196)),U_20197))) ),
    inference(definitional_conversion,[status(esa)],[f_4799_2]) ).

cnf(f_4799_4,plain,
    ( c_List_Olast(U_20196,hAPP(hAPP(c_List_Odrop(U_20196),U_20195),U_20197)) = c_List_Olast(U_20196,U_20197)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20195),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20196)),U_20197))) ),
    inference(clausify,[status(thm)],[f_4799_3]) ).

fof(f_4800_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_4800_2,plain,
    ! [U_20199,U_20198] :
      ( c_List_Olast(U_20199,U_20198) = hAPP(hAPP(c_List_Onth(U_20199),U_20198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20199)),U_20198)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | U_20198 = c_List_Olist_ONil(U_20199) ),
    inference(variable_rename,[status(thm)],[f_4800_1]) ).

fof(f_4800_3,plain,
    ! [U_20198,U_20199] :
      ( c_List_Olast(U_20199,U_20198) = hAPP(hAPP(c_List_Onth(U_20199),U_20198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20199)),U_20198)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | U_20198 = c_List_Olist_ONil(U_20199) ),
    inference(definitional_conversion,[status(esa)],[f_4800_2]) ).

cnf(f_4800_4,plain,
    ( c_List_Olast(U_20199,U_20198) = hAPP(hAPP(c_List_Onth(U_20199),U_20198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20199)),U_20198)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_20198 = c_List_Olist_ONil(U_20199) ),
    inference(clausify,[status(thm)],[f_4800_3]) ).

fof(f_4801_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_4801_2,plain,
    ! [U_20203,U_20202,U_20201] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20201),tc_List_Olist(U_20201))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20201),tc_List_Olist(U_20201)),U_20203),U_20203)),c_List_Olexord(U_20201,U_20202)))
      | ? [U_20200] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_20201,U_20201)),hAPP(hAPP(c_Product__Type_OPair(U_20201,U_20201),U_20200),U_20200)),U_20202)) ),
    inference(variable_rename,[status(thm)],[f_4801_1]) ).

fof(f_4801_3,plain,
    ! [U_20203,U_20202,U_20201] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20201),tc_List_Olist(U_20201))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20201),tc_List_Olist(U_20201)),U_20203),U_20203)),c_List_Olexord(U_20201,U_20202)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_20201,U_20201)),hAPP(hAPP(c_Product__Type_OPair(U_20201,U_20201),sK492(U_20203,U_20202,U_20201)),sK492(U_20203,U_20202,U_20201))),U_20202)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK492]),skolemize(U_20200,sK492(U_20203,U_20202,U_20201))],[f_4801_2]) ).

fof(f_4801_4,plain,
    ! [U_20201,U_20202,U_20203] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20201),tc_List_Olist(U_20201))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20201),tc_List_Olist(U_20201)),U_20203),U_20203)),c_List_Olexord(U_20201,U_20202)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_20201,U_20201)),hAPP(hAPP(c_Product__Type_OPair(U_20201,U_20201),sK492(U_20203,U_20202,U_20201)),sK492(U_20203,U_20202,U_20201))),U_20202)) ),
    inference(definitional_conversion,[status(esa)],[f_4801_3]) ).

cnf(f_4801_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20201),tc_List_Olist(U_20201))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20201),tc_List_Olist(U_20201)),U_20203),U_20203)),c_List_Olexord(U_20201,U_20202)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_20201,U_20201)),hAPP(hAPP(c_Product__Type_OPair(U_20201,U_20201),sK492(U_20203,U_20202,U_20201)),sK492(U_20203,U_20202,U_20201))),U_20202)) ),
    inference(clausify,[status(thm)],[f_4801_4]) ).

fof(f_4802_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_4802_2,plain,
    ! [U_20209,U_20208,U_20207,U_20206] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20206),tc_List_Olist(U_20206))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20206),tc_List_Olist(U_20206)),U_20209),U_20208)),c_List_Olexord(U_20206,U_20207)))
      | U_20208 = U_20209
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20206),tc_List_Olist(U_20206))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20206),tc_List_Olist(U_20206)),U_20208),U_20209)),c_List_Olexord(U_20206,U_20207)))
      | ? [U_20205,U_20204] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20206,U_20206)),hAPP(hAPP(c_Product__Type_OPair(U_20206,U_20206),U_20204),U_20205)),U_20207))
          & U_20205 != U_20204
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20206,U_20206)),hAPP(hAPP(c_Product__Type_OPair(U_20206,U_20206),U_20205),U_20204)),U_20207)) ) ),
    inference(variable_rename,[status(thm)],[f_4802_1]) ).

fof(f_4802_3,plain,
    ! [U_20209,U_20208,U_20207,U_20206] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20206),tc_List_Olist(U_20206))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20206),tc_List_Olist(U_20206)),U_20209),U_20208)),c_List_Olexord(U_20206,U_20207)))
      | U_20208 = U_20209
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20206),tc_List_Olist(U_20206))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20206),tc_List_Olist(U_20206)),U_20208),U_20209)),c_List_Olexord(U_20206,U_20207)))
      | ? [U_20204] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20206,U_20206)),hAPP(hAPP(c_Product__Type_OPair(U_20206,U_20206),U_20204),sK493(U_20209,U_20208,U_20207,U_20206))),U_20207))
          & sK493(U_20209,U_20208,U_20207,U_20206) != U_20204
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20206,U_20206)),hAPP(hAPP(c_Product__Type_OPair(U_20206,U_20206),sK493(U_20209,U_20208,U_20207,U_20206)),U_20204)),U_20207)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK493]),skolemize(U_20205,sK493(U_20209,U_20208,U_20207,U_20206))],[f_4802_2]) ).

fof(f_4802_4,plain,
    ! [U_20209,U_20208,U_20207,U_20206] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20206),tc_List_Olist(U_20206))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20206),tc_List_Olist(U_20206)),U_20209),U_20208)),c_List_Olexord(U_20206,U_20207)))
      | U_20208 = U_20209
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20206),tc_List_Olist(U_20206))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20206),tc_List_Olist(U_20206)),U_20208),U_20209)),c_List_Olexord(U_20206,U_20207)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20206,U_20206)),hAPP(hAPP(c_Product__Type_OPair(U_20206,U_20206),sK494(U_20209,U_20208,U_20207,U_20206)),sK493(U_20209,U_20208,U_20207,U_20206))),U_20207))
        & sK493(U_20209,U_20208,U_20207,U_20206) != sK494(U_20209,U_20208,U_20207,U_20206)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20206,U_20206)),hAPP(hAPP(c_Product__Type_OPair(U_20206,U_20206),sK493(U_20209,U_20208,U_20207,U_20206)),sK494(U_20209,U_20208,U_20207,U_20206))),U_20207)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK494]),skolemize(U_20204,sK494(U_20209,U_20208,U_20207,U_20206))],[f_4802_3]) ).

fof(f_4802_5,plain,
    ( ! [U_20206,U_20207,U_20208,U_20209] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20206,U_20206)),hAPP(hAPP(c_Product__Type_OPair(U_20206,U_20206),sK494(U_20209,U_20208,U_20207,U_20206)),sK493(U_20209,U_20208,U_20207,U_20206))),U_20207))
        | ~ sP1208(U_20206,U_20207,U_20208,U_20209) )
    & ! [U_20206,U_20207,U_20208,U_20209] :
        ( sK493(U_20209,U_20208,U_20207,U_20206) != sK494(U_20209,U_20208,U_20207,U_20206)
        | ~ sP1208(U_20206,U_20207,U_20208,U_20209) )
    & ! [U_20206,U_20207,U_20208,U_20209] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20206,U_20206)),hAPP(hAPP(c_Product__Type_OPair(U_20206,U_20206),sK493(U_20209,U_20208,U_20207,U_20206)),sK494(U_20209,U_20208,U_20207,U_20206))),U_20207))
        | ~ sP1208(U_20206,U_20207,U_20208,U_20209) )
    & ! [U_20206,U_20207,U_20208,U_20209] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20206),tc_List_Olist(U_20206))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20206),tc_List_Olist(U_20206)),U_20209),U_20208)),c_List_Olexord(U_20206,U_20207)))
        | U_20208 = U_20209
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20206),tc_List_Olist(U_20206))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20206),tc_List_Olist(U_20206)),U_20208),U_20209)),c_List_Olexord(U_20206,U_20207)))
        | sP1208(U_20206,U_20207,U_20208,U_20209) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1208])],[f_4802_4]) ).

cnf(f_4802_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20206),tc_List_Olist(U_20206))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20206),tc_List_Olist(U_20206)),U_20209),U_20208)),c_List_Olexord(U_20206,U_20207)))
    | U_20208 = U_20209
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20206),tc_List_Olist(U_20206))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20206),tc_List_Olist(U_20206)),U_20208),U_20209)),c_List_Olexord(U_20206,U_20207)))
    | sP1208(U_20206,U_20207,U_20208,U_20209) ),
    inference(clausify,[status(thm)],[f_4802_5]) ).

cnf(f_4802_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20206,U_20206)),hAPP(hAPP(c_Product__Type_OPair(U_20206,U_20206),sK493(U_20209,U_20208,U_20207,U_20206)),sK494(U_20209,U_20208,U_20207,U_20206))),U_20207))
    | ~ sP1208(U_20206,U_20207,U_20208,U_20209) ),
    inference(clausify,[status(thm)],[f_4802_5]) ).

cnf(f_4802_8,plain,
    ( sK493(U_20209,U_20208,U_20207,U_20206) != sK494(U_20209,U_20208,U_20207,U_20206)
    | ~ sP1208(U_20206,U_20207,U_20208,U_20209) ),
    inference(clausify,[status(thm)],[f_4802_5]) ).

cnf(f_4802_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20206,U_20206)),hAPP(hAPP(c_Product__Type_OPair(U_20206,U_20206),sK494(U_20209,U_20208,U_20207,U_20206)),sK493(U_20209,U_20208,U_20207,U_20206))),U_20207))
    | ~ sP1208(U_20206,U_20207,U_20208,U_20209) ),
    inference(clausify,[status(thm)],[f_4802_5]) ).

fof(f_4803_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_4803_2,plain,
    ! [U_20216,U_20215,U_20214] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20214)),U_20215),c_List_Olists(U_20214,U_20216)))
        | ( ! [U_20213,U_20212] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20214)),U_20212),c_List_Olists(U_20214,U_20216)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_20214),U_20213),U_20216))
              | U_20215 != hAPP(hAPP(c_List_Olist_OCons(U_20214),U_20213),U_20212) )
          & U_20215 != c_List_Olist_ONil(U_20214) ) )
      & ( ? [U_20211,U_20210] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20214)),U_20210),c_List_Olists(U_20214,U_20216)))
            & hBOOL(hAPP(hAPP(c_member(U_20214),U_20211),U_20216))
            & U_20215 = hAPP(hAPP(c_List_Olist_OCons(U_20214),U_20211),U_20210) )
        | U_20215 = c_List_Olist_ONil(U_20214)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20214)),U_20215),c_List_Olists(U_20214,U_20216))) ) ),
    inference(variable_rename,[status(thm)],[f_4803_1]) ).

fof(f_4803_3,plain,
    ( ! [U_20222,U_20220,U_20218] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20218)),U_20220),c_List_Olists(U_20218,U_20222)))
        | ( ! [U_20213] :
              ( ! [U_20212] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20218)),U_20212),c_List_Olists(U_20218,U_20222)))
                  | U_20220 != hAPP(hAPP(c_List_Olist_OCons(U_20218),U_20213),U_20212) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_20218),U_20213),U_20222)) )
          & U_20220 != c_List_Olist_ONil(U_20218) ) )
    & ! [U_20221,U_20219,U_20217] :
        ( ? [U_20211] :
            ( ? [U_20210] :
                ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20217)),U_20210),c_List_Olists(U_20217,U_20221)))
                & U_20219 = hAPP(hAPP(c_List_Olist_OCons(U_20217),U_20211),U_20210) )
            & hBOOL(hAPP(hAPP(c_member(U_20217),U_20211),U_20221)) )
        | U_20219 = c_List_Olist_ONil(U_20217)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20217)),U_20219),c_List_Olists(U_20217,U_20221))) ) ),
    inference(miniscope,[status(thm)],[f_4803_2]) ).

fof(f_4803_4,plain,
    ( ! [U_20222,U_20220,U_20218] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20218)),U_20220),c_List_Olists(U_20218,U_20222)))
        | ( ! [U_20213] :
              ( ! [U_20212] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20218)),U_20212),c_List_Olists(U_20218,U_20222)))
                  | U_20220 != hAPP(hAPP(c_List_Olist_OCons(U_20218),U_20213),U_20212) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_20218),U_20213),U_20222)) )
          & U_20220 != c_List_Olist_ONil(U_20218) ) )
    & ! [U_20221,U_20219,U_20217] :
        ( ( ? [U_20210] :
              ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20217)),U_20210),c_List_Olists(U_20217,U_20221)))
              & U_20219 = hAPP(hAPP(c_List_Olist_OCons(U_20217),sK495(U_20221,U_20219,U_20217)),U_20210) )
          & hBOOL(hAPP(hAPP(c_member(U_20217),sK495(U_20221,U_20219,U_20217)),U_20221)) )
        | U_20219 = c_List_Olist_ONil(U_20217)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20217)),U_20219),c_List_Olists(U_20217,U_20221))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK495]),skolemize(U_20211,sK495(U_20221,U_20219,U_20217))],[f_4803_3]) ).

fof(f_4803_5,plain,
    ( ! [U_20222,U_20220,U_20218] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20218)),U_20220),c_List_Olists(U_20218,U_20222)))
        | ( ! [U_20213] :
              ( ! [U_20212] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20218)),U_20212),c_List_Olists(U_20218,U_20222)))
                  | U_20220 != hAPP(hAPP(c_List_Olist_OCons(U_20218),U_20213),U_20212) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_20218),U_20213),U_20222)) )
          & U_20220 != c_List_Olist_ONil(U_20218) ) )
    & ! [U_20221,U_20219,U_20217] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20217)),sK496(U_20221,U_20219,U_20217)),c_List_Olists(U_20217,U_20221)))
          & U_20219 = hAPP(hAPP(c_List_Olist_OCons(U_20217),sK495(U_20221,U_20219,U_20217)),sK496(U_20221,U_20219,U_20217))
          & hBOOL(hAPP(hAPP(c_member(U_20217),sK495(U_20221,U_20219,U_20217)),U_20221)) )
        | U_20219 = c_List_Olist_ONil(U_20217)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20217)),U_20219),c_List_Olists(U_20217,U_20221))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK496]),skolemize(U_20210,sK496(U_20221,U_20219,U_20217))],[f_4803_4]) ).

fof(f_4803_6,plain,
    ( ! [U_20222,U_20212,U_20213,U_20218,U_20220] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20218)),U_20212),c_List_Olists(U_20218,U_20222)))
        | U_20220 != hAPP(hAPP(c_List_Olist_OCons(U_20218),U_20213),U_20212)
        | ~ hBOOL(hAPP(hAPP(c_member(U_20218),U_20213),U_20222))
        | ~ sP1210(U_20222,U_20212,U_20213,U_20218,U_20220) )
    & ! [U_20222,U_20212,U_20213,U_20218,U_20220] :
        ( U_20220 != c_List_Olist_ONil(U_20218)
        | ~ sP1210(U_20222,U_20212,U_20213,U_20218,U_20220) )
    & ! [U_20221,U_20217,U_20219] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20217)),sK496(U_20221,U_20219,U_20217)),c_List_Olists(U_20217,U_20221)))
        | ~ sP1209(U_20221,U_20217,U_20219) )
    & ! [U_20221,U_20217,U_20219] :
        ( U_20219 = hAPP(hAPP(c_List_Olist_OCons(U_20217),sK495(U_20221,U_20219,U_20217)),sK496(U_20221,U_20219,U_20217))
        | ~ sP1209(U_20221,U_20217,U_20219) )
    & ! [U_20221,U_20217,U_20219] :
        ( hBOOL(hAPP(hAPP(c_member(U_20217),sK495(U_20221,U_20219,U_20217)),U_20221))
        | ~ sP1209(U_20221,U_20217,U_20219) )
    & ! [U_20222,U_20212,U_20213,U_20218,U_20220] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20218)),U_20220),c_List_Olists(U_20218,U_20222)))
        | sP1210(U_20222,U_20212,U_20213,U_20218,U_20220) )
    & ! [U_20221,U_20217,U_20219] :
        ( sP1209(U_20221,U_20217,U_20219)
        | U_20219 = c_List_Olist_ONil(U_20217)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20217)),U_20219),c_List_Olists(U_20217,U_20221))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1209,sP1210])],[f_4803_5]) ).

cnf(f_4803_7,plain,
    ( sP1209(U_20221,U_20217,U_20219)
    | U_20219 = c_List_Olist_ONil(U_20217)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20217)),U_20219),c_List_Olists(U_20217,U_20221))) ),
    inference(clausify,[status(thm)],[f_4803_6]) ).

cnf(f_4803_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20218)),U_20220),c_List_Olists(U_20218,U_20222)))
    | sP1210(U_20222,U_20212,U_20213,U_20218,U_20220) ),
    inference(clausify,[status(thm)],[f_4803_6]) ).

cnf(f_4803_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20217),sK495(U_20221,U_20219,U_20217)),U_20221))
    | ~ sP1209(U_20221,U_20217,U_20219) ),
    inference(clausify,[status(thm)],[f_4803_6]) ).

cnf(f_4803_10,plain,
    ( U_20219 = hAPP(hAPP(c_List_Olist_OCons(U_20217),sK495(U_20221,U_20219,U_20217)),sK496(U_20221,U_20219,U_20217))
    | ~ sP1209(U_20221,U_20217,U_20219) ),
    inference(clausify,[status(thm)],[f_4803_6]) ).

cnf(f_4803_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20217)),sK496(U_20221,U_20219,U_20217)),c_List_Olists(U_20217,U_20221)))
    | ~ sP1209(U_20221,U_20217,U_20219) ),
    inference(clausify,[status(thm)],[f_4803_6]) ).

cnf(f_4803_12,plain,
    ( U_20220 != c_List_Olist_ONil(U_20218)
    | ~ sP1210(U_20222,U_20212,U_20213,U_20218,U_20220) ),
    inference(clausify,[status(thm)],[f_4803_6]) ).

cnf(f_4803_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20218)),U_20212),c_List_Olists(U_20218,U_20222)))
    | U_20220 != hAPP(hAPP(c_List_Olist_OCons(U_20218),U_20213),U_20212)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20218),U_20213),U_20222))
    | ~ sP1210(U_20222,U_20212,U_20213,U_20218,U_20220) ),
    inference(clausify,[status(thm)],[f_4803_6]) ).

fof(f_4804_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_4804_2,plain,
    ! [U_20227,U_20226,U_20225,U_20224] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_20224,U_20226,U_20225)),c_List_Olist_Olist__size(U_20224,U_20227,U_20225)))
      | ? [U_20223] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_20226,U_20223)),hAPP(U_20227,U_20223)))
          & hBOOL(hAPP(hAPP(c_member(U_20224),U_20223),hAPP(c_List_Oset(U_20224),U_20225))) ) ),
    inference(variable_rename,[status(thm)],[f_4804_1]) ).

fof(f_4804_3,plain,
    ! [U_20227,U_20226,U_20225,U_20224] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_20224,U_20226,U_20225)),c_List_Olist_Olist__size(U_20224,U_20227,U_20225)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_20226,sK497(U_20227,U_20226,U_20225,U_20224))),hAPP(U_20227,sK497(U_20227,U_20226,U_20225,U_20224))))
        & hBOOL(hAPP(hAPP(c_member(U_20224),sK497(U_20227,U_20226,U_20225,U_20224)),hAPP(c_List_Oset(U_20224),U_20225))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK497]),skolemize(U_20223,sK497(U_20227,U_20226,U_20225,U_20224))],[f_4804_2]) ).

fof(f_4804_4,plain,
    ( ! [U_20226,U_20224,U_20227,U_20225] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_20226,sK497(U_20227,U_20226,U_20225,U_20224))),hAPP(U_20227,sK497(U_20227,U_20226,U_20225,U_20224))))
        | ~ sP1211(U_20226,U_20224,U_20227,U_20225) )
    & ! [U_20226,U_20224,U_20227,U_20225] :
        ( hBOOL(hAPP(hAPP(c_member(U_20224),sK497(U_20227,U_20226,U_20225,U_20224)),hAPP(c_List_Oset(U_20224),U_20225)))
        | ~ sP1211(U_20226,U_20224,U_20227,U_20225) )
    & ! [U_20226,U_20224,U_20227,U_20225] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_20224,U_20226,U_20225)),c_List_Olist_Olist__size(U_20224,U_20227,U_20225)))
        | sP1211(U_20226,U_20224,U_20227,U_20225) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1211])],[f_4804_3]) ).

cnf(f_4804_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_20224,U_20226,U_20225)),c_List_Olist_Olist__size(U_20224,U_20227,U_20225)))
    | sP1211(U_20226,U_20224,U_20227,U_20225) ),
    inference(clausify,[status(thm)],[f_4804_4]) ).

cnf(f_4804_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20224),sK497(U_20227,U_20226,U_20225,U_20224)),hAPP(c_List_Oset(U_20224),U_20225)))
    | ~ sP1211(U_20226,U_20224,U_20227,U_20225) ),
    inference(clausify,[status(thm)],[f_4804_4]) ).

cnf(f_4804_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_20226,sK497(U_20227,U_20226,U_20225,U_20224))),hAPP(U_20227,sK497(U_20227,U_20226,U_20225,U_20224))))
    | ~ sP1211(U_20226,U_20224,U_20227,U_20225) ),
    inference(clausify,[status(thm)],[f_4804_4]) ).

fof(f_4805_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_4805_2,plain,
    ! [U_20230,U_20229,U_20228] :
      ( c_List_Obutlast(U_20229,hAPP(hAPP(c_List_Otake(U_20229),U_20228),U_20230)) = hAPP(hAPP(c_List_Otake(U_20229),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20228),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_20230)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20228),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20229)),U_20230))) ),
    inference(variable_rename,[status(thm)],[f_4805_1]) ).

fof(f_4805_3,plain,
    ! [U_20229,U_20228,U_20230] :
      ( c_List_Obutlast(U_20229,hAPP(hAPP(c_List_Otake(U_20229),U_20228),U_20230)) = hAPP(hAPP(c_List_Otake(U_20229),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20228),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_20230)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20228),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20229)),U_20230))) ),
    inference(definitional_conversion,[status(esa)],[f_4805_2]) ).

cnf(f_4805_4,plain,
    ( c_List_Obutlast(U_20229,hAPP(hAPP(c_List_Otake(U_20229),U_20228),U_20230)) = hAPP(hAPP(c_List_Otake(U_20229),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20228),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_20230)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20228),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20229)),U_20230))) ),
    inference(clausify,[status(thm)],[f_4805_3]) ).

fof(f_4806_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_4806_2,plain,
    ! [U_20235,U_20234,U_20233,U_20232] :
      ( hAPP(hAPP(c_List_Otake(U_20233),U_20232),U_20234) = hAPP(hAPP(c_List_Otake(U_20233),U_20232),U_20235)
      | ? [U_20231] :
          ( hAPP(hAPP(c_List_Onth(U_20233),U_20234),U_20231) != hAPP(hAPP(c_List_Onth(U_20233),U_20235),U_20231)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20231),U_20232)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20232),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20233)),U_20235)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20232),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20233)),U_20234))) ),
    inference(variable_rename,[status(thm)],[f_4806_1]) ).

fof(f_4806_3,plain,
    ! [U_20235,U_20234,U_20233,U_20232] :
      ( hAPP(hAPP(c_List_Otake(U_20233),U_20232),U_20234) = hAPP(hAPP(c_List_Otake(U_20233),U_20232),U_20235)
      | ( hAPP(hAPP(c_List_Onth(U_20233),U_20234),sK498(U_20235,U_20234,U_20233,U_20232)) != hAPP(hAPP(c_List_Onth(U_20233),U_20235),sK498(U_20235,U_20234,U_20233,U_20232))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK498(U_20235,U_20234,U_20233,U_20232)),U_20232)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20232),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20233)),U_20235)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20232),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20233)),U_20234))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK498]),skolemize(U_20231,sK498(U_20235,U_20234,U_20233,U_20232))],[f_4806_2]) ).

fof(f_4806_4,plain,
    ( ! [U_20232,U_20233,U_20234,U_20235] :
        ( hAPP(hAPP(c_List_Onth(U_20233),U_20234),sK498(U_20235,U_20234,U_20233,U_20232)) != hAPP(hAPP(c_List_Onth(U_20233),U_20235),sK498(U_20235,U_20234,U_20233,U_20232))
        | ~ sP1212(U_20232,U_20233,U_20234,U_20235) )
    & ! [U_20232,U_20233,U_20234,U_20235] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK498(U_20235,U_20234,U_20233,U_20232)),U_20232))
        | ~ sP1212(U_20232,U_20233,U_20234,U_20235) )
    & ! [U_20232,U_20233,U_20234,U_20235] :
        ( hAPP(hAPP(c_List_Otake(U_20233),U_20232),U_20234) = hAPP(hAPP(c_List_Otake(U_20233),U_20232),U_20235)
        | sP1212(U_20232,U_20233,U_20234,U_20235)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20232),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20233)),U_20235)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20232),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20233)),U_20234))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1212])],[f_4806_3]) ).

cnf(f_4806_5,plain,
    ( hAPP(hAPP(c_List_Otake(U_20233),U_20232),U_20234) = hAPP(hAPP(c_List_Otake(U_20233),U_20232),U_20235)
    | sP1212(U_20232,U_20233,U_20234,U_20235)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20232),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20233)),U_20235)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20232),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20233)),U_20234))) ),
    inference(clausify,[status(thm)],[f_4806_4]) ).

cnf(f_4806_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK498(U_20235,U_20234,U_20233,U_20232)),U_20232))
    | ~ sP1212(U_20232,U_20233,U_20234,U_20235) ),
    inference(clausify,[status(thm)],[f_4806_4]) ).

cnf(f_4806_7,plain,
    ( hAPP(hAPP(c_List_Onth(U_20233),U_20234),sK498(U_20235,U_20234,U_20233,U_20232)) != hAPP(hAPP(c_List_Onth(U_20233),U_20235),sK498(U_20235,U_20234,U_20233,U_20232))
    | ~ sP1212(U_20232,U_20233,U_20234,U_20235) ),
    inference(clausify,[status(thm)],[f_4806_4]) ).

fof(f_4807_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_4807_2,plain,
    ! [U_20239,U_20238,U_20237,U_20236] : hAPP(hAPP(c_List_Omap(U_20236,U_20237),U_20238),c_List_Obutlast(U_20236,U_20239)) = c_List_Obutlast(U_20237,hAPP(hAPP(c_List_Omap(U_20236,U_20237),U_20238),U_20239)),
    inference(variable_rename,[status(thm)],[f_4807_1]) ).

fof(f_4807_3,plain,
    ! [U_20239,U_20236,U_20237,U_20238] : hAPP(hAPP(c_List_Omap(U_20236,U_20237),U_20238),c_List_Obutlast(U_20236,U_20239)) = c_List_Obutlast(U_20237,hAPP(hAPP(c_List_Omap(U_20236,U_20237),U_20238),U_20239)),
    inference(definitional_conversion,[status(esa)],[f_4807_2]) ).

cnf(f_4807_4,plain,
    hAPP(hAPP(c_List_Omap(U_20236,U_20237),U_20238),c_List_Obutlast(U_20236,U_20239)) = c_List_Obutlast(U_20237,hAPP(hAPP(c_List_Omap(U_20236,U_20237),U_20238),U_20239)),
    inference(clausify,[status(thm)],[f_4807_3]) ).

fof(f_4808_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_4808_2,plain,
    ! [U_20242,U_20241,U_20240] :
      ( ( c_List_Obutlast(U_20241,hAPP(hAPP(c_List_Oappend(U_20241),U_20242),U_20240)) = hAPP(hAPP(c_List_Oappend(U_20241),U_20242),c_List_Obutlast(U_20241,U_20240))
        | U_20240 = c_List_Olist_ONil(U_20241) )
      & ( c_List_Obutlast(U_20241,hAPP(hAPP(c_List_Oappend(U_20241),U_20242),U_20240)) = c_List_Obutlast(U_20241,U_20242)
        | U_20240 != c_List_Olist_ONil(U_20241) ) ),
    inference(variable_rename,[status(thm)],[f_4808_1]) ).

fof(f_4808_3,plain,
    ( ! [U_20248,U_20246,U_20244] :
        ( c_List_Obutlast(U_20246,hAPP(hAPP(c_List_Oappend(U_20246),U_20248),U_20244)) = hAPP(hAPP(c_List_Oappend(U_20246),U_20248),c_List_Obutlast(U_20246,U_20244))
        | U_20244 = c_List_Olist_ONil(U_20246) )
    & ! [U_20247,U_20245,U_20243] :
        ( c_List_Obutlast(U_20245,hAPP(hAPP(c_List_Oappend(U_20245),U_20247),U_20243)) = c_List_Obutlast(U_20245,U_20247)
        | U_20243 != c_List_Olist_ONil(U_20245) ) ),
    inference(miniscope,[status(thm)],[f_4808_2]) ).

fof(f_4808_4,plain,
    ( ! [U_20244,U_20246,U_20248] :
        ( c_List_Obutlast(U_20246,hAPP(hAPP(c_List_Oappend(U_20246),U_20248),U_20244)) = hAPP(hAPP(c_List_Oappend(U_20246),U_20248),c_List_Obutlast(U_20246,U_20244))
        | U_20244 = c_List_Olist_ONil(U_20246) )
    & ! [U_20245,U_20247,U_20243] :
        ( c_List_Obutlast(U_20245,hAPP(hAPP(c_List_Oappend(U_20245),U_20247),U_20243)) = c_List_Obutlast(U_20245,U_20247)
        | U_20243 != c_List_Olist_ONil(U_20245) ) ),
    inference(definitional_conversion,[status(esa)],[f_4808_3]) ).

cnf(f_4808_5,plain,
    ( c_List_Obutlast(U_20245,hAPP(hAPP(c_List_Oappend(U_20245),U_20247),U_20243)) = c_List_Obutlast(U_20245,U_20247)
    | U_20243 != c_List_Olist_ONil(U_20245) ),
    inference(clausify,[status(thm)],[f_4808_4]) ).

cnf(f_4808_6,plain,
    ( c_List_Obutlast(U_20246,hAPP(hAPP(c_List_Oappend(U_20246),U_20248),U_20244)) = hAPP(hAPP(c_List_Oappend(U_20246),U_20248),c_List_Obutlast(U_20246,U_20244))
    | U_20244 = c_List_Olist_ONil(U_20246) ),
    inference(clausify,[status(thm)],[f_4808_4]) ).

fof(f_4809_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_4809_2,plain,
    ! [U_20251,U_20250,U_20249] :
      ( ( c_List_Obutlast(U_20250,hAPP(hAPP(c_List_Olist_OCons(U_20250),U_20251),U_20249)) = hAPP(hAPP(c_List_Olist_OCons(U_20250),U_20251),c_List_Obutlast(U_20250,U_20249))
        | U_20249 = c_List_Olist_ONil(U_20250) )
      & ( c_List_Obutlast(U_20250,hAPP(hAPP(c_List_Olist_OCons(U_20250),U_20251),U_20249)) = c_List_Olist_ONil(U_20250)
        | U_20249 != c_List_Olist_ONil(U_20250) ) ),
    inference(variable_rename,[status(thm)],[f_4809_1]) ).

fof(f_4809_3,plain,
    ( ! [U_20257,U_20255,U_20253] :
        ( c_List_Obutlast(U_20255,hAPP(hAPP(c_List_Olist_OCons(U_20255),U_20257),U_20253)) = hAPP(hAPP(c_List_Olist_OCons(U_20255),U_20257),c_List_Obutlast(U_20255,U_20253))
        | U_20253 = c_List_Olist_ONil(U_20255) )
    & ! [U_20256,U_20254,U_20252] :
        ( c_List_Obutlast(U_20254,hAPP(hAPP(c_List_Olist_OCons(U_20254),U_20256),U_20252)) = c_List_Olist_ONil(U_20254)
        | U_20252 != c_List_Olist_ONil(U_20254) ) ),
    inference(miniscope,[status(thm)],[f_4809_2]) ).

fof(f_4809_4,plain,
    ( ! [U_20253,U_20255,U_20257] :
        ( c_List_Obutlast(U_20255,hAPP(hAPP(c_List_Olist_OCons(U_20255),U_20257),U_20253)) = hAPP(hAPP(c_List_Olist_OCons(U_20255),U_20257),c_List_Obutlast(U_20255,U_20253))
        | U_20253 = c_List_Olist_ONil(U_20255) )
    & ! [U_20254,U_20256,U_20252] :
        ( c_List_Obutlast(U_20254,hAPP(hAPP(c_List_Olist_OCons(U_20254),U_20256),U_20252)) = c_List_Olist_ONil(U_20254)
        | U_20252 != c_List_Olist_ONil(U_20254) ) ),
    inference(definitional_conversion,[status(esa)],[f_4809_3]) ).

cnf(f_4809_5,plain,
    ( c_List_Obutlast(U_20254,hAPP(hAPP(c_List_Olist_OCons(U_20254),U_20256),U_20252)) = c_List_Olist_ONil(U_20254)
    | U_20252 != c_List_Olist_ONil(U_20254) ),
    inference(clausify,[status(thm)],[f_4809_4]) ).

cnf(f_4809_6,plain,
    ( c_List_Obutlast(U_20255,hAPP(hAPP(c_List_Olist_OCons(U_20255),U_20257),U_20253)) = hAPP(hAPP(c_List_Olist_OCons(U_20255),U_20257),c_List_Obutlast(U_20255,U_20253))
    | U_20253 = c_List_Olist_ONil(U_20255) ),
    inference(clausify,[status(thm)],[f_4809_4]) ).

fof(f_4810_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_4810_2,plain,
    ! [U_20260,U_20259,U_20258] :
      ( hBOOL(hAPP(hAPP(c_member(U_20258),U_20259),hAPP(c_List_Oset(U_20258),U_20260)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20258),U_20259),hAPP(c_List_Oset(U_20258),c_List_Obutlast(U_20258,U_20260)))) ),
    inference(variable_rename,[status(thm)],[f_4810_1]) ).

fof(f_4810_3,plain,
    ! [U_20258,U_20259,U_20260] :
      ( hBOOL(hAPP(hAPP(c_member(U_20258),U_20259),hAPP(c_List_Oset(U_20258),U_20260)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20258),U_20259),hAPP(c_List_Oset(U_20258),c_List_Obutlast(U_20258,U_20260)))) ),
    inference(definitional_conversion,[status(esa)],[f_4810_2]) ).

cnf(f_4810_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20258),U_20259),hAPP(c_List_Oset(U_20258),U_20260)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20258),U_20259),hAPP(c_List_Oset(U_20258),c_List_Obutlast(U_20258,U_20260)))) ),
    inference(clausify,[status(thm)],[f_4810_3]) ).

fof(f_4811_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_4811_2,plain,
    ! [U_20262,U_20261] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20262),c_List_Obutlast(U_20262,U_20261)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20262),U_20261))
      | U_20261 = c_List_Olist_ONil(U_20262) ),
    inference(variable_rename,[status(thm)],[f_4811_1]) ).

fof(f_4811_3,plain,
    ! [U_20261,U_20262] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20262),c_List_Obutlast(U_20262,U_20261)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20262),U_20261))
      | U_20261 = c_List_Olist_ONil(U_20262) ),
    inference(definitional_conversion,[status(esa)],[f_4811_2]) ).

cnf(f_4811_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20262),c_List_Obutlast(U_20262,U_20261)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20262),U_20261))
    | U_20261 = c_List_Olist_ONil(U_20262) ),
    inference(clausify,[status(thm)],[f_4811_3]) ).

fof(f_4812_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_4812_2,plain,
    ! [U_20263] : c_List_Obutlast(U_20263,c_List_Olist_ONil(U_20263)) = c_List_Olist_ONil(U_20263),
    inference(variable_rename,[status(thm)],[f_4812_1]) ).

fof(f_4812_3,plain,
    ! [U_20263] : c_List_Obutlast(U_20263,c_List_Olist_ONil(U_20263)) = c_List_Olist_ONil(U_20263),
    inference(definitional_conversion,[status(esa)],[f_4812_2]) ).

cnf(f_4812_4,plain,
    c_List_Obutlast(U_20263,c_List_Olist_ONil(U_20263)) = c_List_Olist_ONil(U_20263),
    inference(clausify,[status(thm)],[f_4812_3]) ).

fof(f_4813_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_4813_2,plain,
    ! [U_20266,U_20265,U_20264] : c_List_Obutlast(U_20264,hAPP(hAPP(c_List_Odrop(U_20264),U_20265),U_20266)) = hAPP(hAPP(c_List_Odrop(U_20264),U_20265),c_List_Obutlast(U_20264,U_20266)),
    inference(variable_rename,[status(thm)],[f_4813_1]) ).

fof(f_4813_3,plain,
    ! [U_20264,U_20265,U_20266] : c_List_Obutlast(U_20264,hAPP(hAPP(c_List_Odrop(U_20264),U_20265),U_20266)) = hAPP(hAPP(c_List_Odrop(U_20264),U_20265),c_List_Obutlast(U_20264,U_20266)),
    inference(definitional_conversion,[status(esa)],[f_4813_2]) ).

cnf(f_4813_4,plain,
    c_List_Obutlast(U_20264,hAPP(hAPP(c_List_Odrop(U_20264),U_20265),U_20266)) = hAPP(hAPP(c_List_Odrop(U_20264),U_20265),c_List_Obutlast(U_20264,U_20266)),
    inference(clausify,[status(thm)],[f_4813_3]) ).

fof(f_4814_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_4814_2,plain,
    ! [U_20269,U_20268,U_20267] : hAPP(hAPP(c_List_Odrop(U_20267),U_20268),c_List_Obutlast(U_20267,U_20269)) = c_List_Obutlast(U_20267,hAPP(hAPP(c_List_Odrop(U_20267),U_20268),U_20269)),
    inference(variable_rename,[status(thm)],[f_4814_1]) ).

fof(f_4814_3,plain,
    ! [U_20267,U_20268,U_20269] : hAPP(hAPP(c_List_Odrop(U_20267),U_20268),c_List_Obutlast(U_20267,U_20269)) = c_List_Obutlast(U_20267,hAPP(hAPP(c_List_Odrop(U_20267),U_20268),U_20269)),
    inference(definitional_conversion,[status(esa)],[f_4814_2]) ).

cnf(f_4814_4,plain,
    hAPP(hAPP(c_List_Odrop(U_20267),U_20268),c_List_Obutlast(U_20267,U_20269)) = c_List_Obutlast(U_20267,hAPP(hAPP(c_List_Odrop(U_20267),U_20268),U_20269)),
    inference(clausify,[status(thm)],[f_4814_3]) ).

fof(f_4815_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_4815_2,plain,
    ! [U_20273,U_20272,U_20271,U_20270] :
      ( hBOOL(hAPP(hAPP(c_member(U_20270),U_20271),hAPP(c_List_Oset(U_20270),c_List_Obutlast(U_20270,hAPP(hAPP(c_List_Oappend(U_20270),U_20272),U_20273)))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_20270),U_20271),hAPP(c_List_Oset(U_20270),c_List_Obutlast(U_20270,U_20273))))
        & ~ hBOOL(hAPP(hAPP(c_member(U_20270),U_20271),hAPP(c_List_Oset(U_20270),c_List_Obutlast(U_20270,U_20272)))) ) ),
    inference(variable_rename,[status(thm)],[f_4815_1]) ).

fof(f_4815_3,plain,
    ( ! [U_20270,U_20271,U_20272,U_20273] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_20270),U_20271),hAPP(c_List_Oset(U_20270),c_List_Obutlast(U_20270,U_20273))))
        | ~ sP1213(U_20270,U_20271,U_20272,U_20273) )
    & ! [U_20270,U_20271,U_20272,U_20273] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_20270),U_20271),hAPP(c_List_Oset(U_20270),c_List_Obutlast(U_20270,U_20272))))
        | ~ sP1213(U_20270,U_20271,U_20272,U_20273) )
    & ! [U_20270,U_20271,U_20272,U_20273] :
        ( hBOOL(hAPP(hAPP(c_member(U_20270),U_20271),hAPP(c_List_Oset(U_20270),c_List_Obutlast(U_20270,hAPP(hAPP(c_List_Oappend(U_20270),U_20272),U_20273)))))
        | sP1213(U_20270,U_20271,U_20272,U_20273) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1213])],[f_4815_2]) ).

cnf(f_4815_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20270),U_20271),hAPP(c_List_Oset(U_20270),c_List_Obutlast(U_20270,hAPP(hAPP(c_List_Oappend(U_20270),U_20272),U_20273)))))
    | sP1213(U_20270,U_20271,U_20272,U_20273) ),
    inference(clausify,[status(thm)],[f_4815_3]) ).

cnf(f_4815_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_20270),U_20271),hAPP(c_List_Oset(U_20270),c_List_Obutlast(U_20270,U_20272))))
    | ~ sP1213(U_20270,U_20271,U_20272,U_20273) ),
    inference(clausify,[status(thm)],[f_4815_3]) ).

cnf(f_4815_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_20270),U_20271),hAPP(c_List_Oset(U_20270),c_List_Obutlast(U_20270,U_20273))))
    | ~ sP1213(U_20270,U_20271,U_20272,U_20273) ),
    inference(clausify,[status(thm)],[f_4815_3]) ).

fof(f_4816_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_4816_2,plain,
    ! [U_20276,U_20275,U_20274] : c_List_Obutlast(U_20274,hAPP(hAPP(c_List_Oappend(U_20274),U_20275),hAPP(hAPP(c_List_Olist_OCons(U_20274),U_20276),c_List_Olist_ONil(U_20274)))) = U_20275,
    inference(variable_rename,[status(thm)],[f_4816_1]) ).

fof(f_4816_3,plain,
    ! [U_20274,U_20275,U_20276] : c_List_Obutlast(U_20274,hAPP(hAPP(c_List_Oappend(U_20274),U_20275),hAPP(hAPP(c_List_Olist_OCons(U_20274),U_20276),c_List_Olist_ONil(U_20274)))) = U_20275,
    inference(definitional_conversion,[status(esa)],[f_4816_2]) ).

cnf(f_4816_4,plain,
    c_List_Obutlast(U_20274,hAPP(hAPP(c_List_Oappend(U_20274),U_20275),hAPP(hAPP(c_List_Olist_OCons(U_20274),U_20276),c_List_Olist_ONil(U_20274)))) = U_20275,
    inference(clausify,[status(thm)],[f_4816_3]) ).

fof(f_4817_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_4817_2,plain,
    ! [U_20279,U_20278,U_20277] :
      ( hAPP(hAPP(c_List_Otake(U_20278),U_20277),c_List_Obutlast(U_20278,U_20279)) = hAPP(hAPP(c_List_Otake(U_20278),U_20277),U_20279)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20277),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20278)),U_20279))) ),
    inference(variable_rename,[status(thm)],[f_4817_1]) ).

fof(f_4817_3,plain,
    ! [U_20277,U_20278,U_20279] :
      ( hAPP(hAPP(c_List_Otake(U_20278),U_20277),c_List_Obutlast(U_20278,U_20279)) = hAPP(hAPP(c_List_Otake(U_20278),U_20277),U_20279)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20277),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20278)),U_20279))) ),
    inference(definitional_conversion,[status(esa)],[f_4817_2]) ).

cnf(f_4817_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_20278),U_20277),c_List_Obutlast(U_20278,U_20279)) = hAPP(hAPP(c_List_Otake(U_20278),U_20277),U_20279)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20277),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20278)),U_20279))) ),
    inference(clausify,[status(thm)],[f_4817_3]) ).

fof(f_4818_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_4818_2,plain,
    ! [U_20281,U_20280] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20280)),c_List_Obutlast(U_20280,U_20281)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20280)),U_20281)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4818_1]) ).

fof(f_4818_3,plain,
    ! [U_20280,U_20281] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20280)),c_List_Obutlast(U_20280,U_20281)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20280)),U_20281)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_4818_2]) ).

cnf(f_4818_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20280)),c_List_Obutlast(U_20280,U_20281)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20280)),U_20281)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4818_3]) ).

fof(f_4819_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_4819_2,plain,
    ! [U_20283,U_20282] : c_List_Obutlast(U_20282,U_20283) = hAPP(hAPP(c_List_Otake(U_20282),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20282)),U_20283)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_20283),
    inference(variable_rename,[status(thm)],[f_4819_1]) ).

fof(f_4819_3,plain,
    ! [U_20282,U_20283] : c_List_Obutlast(U_20282,U_20283) = hAPP(hAPP(c_List_Otake(U_20282),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20282)),U_20283)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_20283),
    inference(definitional_conversion,[status(esa)],[f_4819_2]) ).

cnf(f_4819_4,plain,
    c_List_Obutlast(U_20282,U_20283) = hAPP(hAPP(c_List_Otake(U_20282),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20282)),U_20283)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_20283),
    inference(clausify,[status(thm)],[f_4819_3]) ).

fof(f_4820_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_4820_2,plain,
    ! [U_20287,U_20286,U_20285,U_20284] :
      ( ( c_List_Obutlast(U_20285,hAPP(hAPP(c_List_Olist__update(U_20285,U_20286),U_20284),U_20287)) = hAPP(hAPP(c_List_Olist__update(U_20285,c_List_Obutlast(U_20285,U_20286)),U_20284),U_20287)
        | U_20284 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20285)),U_20286)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( c_List_Obutlast(U_20285,hAPP(hAPP(c_List_Olist__update(U_20285,U_20286),U_20284),U_20287)) = c_List_Obutlast(U_20285,U_20286)
        | U_20284 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20285)),U_20286)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_4820_1]) ).

fof(f_4820_3,plain,
    ( ! [U_20295,U_20293,U_20291,U_20289] :
        ( c_List_Obutlast(U_20291,hAPP(hAPP(c_List_Olist__update(U_20291,U_20293),U_20289),U_20295)) = hAPP(hAPP(c_List_Olist__update(U_20291,c_List_Obutlast(U_20291,U_20293)),U_20289),U_20295)
        | U_20289 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20291)),U_20293)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    & ! [U_20294,U_20292,U_20290,U_20288] :
        ( c_List_Obutlast(U_20290,hAPP(hAPP(c_List_Olist__update(U_20290,U_20292),U_20288),U_20294)) = c_List_Obutlast(U_20290,U_20292)
        | U_20288 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20290)),U_20292)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_4820_2]) ).

fof(f_4820_4,plain,
    ( ! [U_20289,U_20291,U_20293,U_20295] :
        ( c_List_Obutlast(U_20291,hAPP(hAPP(c_List_Olist__update(U_20291,U_20293),U_20289),U_20295)) = hAPP(hAPP(c_List_Olist__update(U_20291,c_List_Obutlast(U_20291,U_20293)),U_20289),U_20295)
        | U_20289 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20291)),U_20293)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    & ! [U_20290,U_20294,U_20288,U_20292] :
        ( c_List_Obutlast(U_20290,hAPP(hAPP(c_List_Olist__update(U_20290,U_20292),U_20288),U_20294)) = c_List_Obutlast(U_20290,U_20292)
        | U_20288 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20290)),U_20292)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4820_3]) ).

cnf(f_4820_5,plain,
    ( c_List_Obutlast(U_20290,hAPP(hAPP(c_List_Olist__update(U_20290,U_20292),U_20288),U_20294)) = c_List_Obutlast(U_20290,U_20292)
    | U_20288 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20290)),U_20292)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_4820_4]) ).

cnf(f_4820_6,plain,
    ( c_List_Obutlast(U_20291,hAPP(hAPP(c_List_Olist__update(U_20291,U_20293),U_20289),U_20295)) = hAPP(hAPP(c_List_Olist__update(U_20291,c_List_Obutlast(U_20291,U_20293)),U_20289),U_20295)
    | U_20289 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20291)),U_20293)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_4820_4]) ).

fof(f_4821_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_4821_2,plain,
    ! [U_20297,U_20296] :
      ( hAPP(hAPP(c_List_Oappend(U_20297),c_List_Obutlast(U_20297,U_20296)),hAPP(hAPP(c_List_Olist_OCons(U_20297),c_List_Olast(U_20297,U_20296)),c_List_Olist_ONil(U_20297))) = U_20296
      | U_20296 = c_List_Olist_ONil(U_20297) ),
    inference(variable_rename,[status(thm)],[f_4821_1]) ).

fof(f_4821_3,plain,
    ! [U_20296,U_20297] :
      ( hAPP(hAPP(c_List_Oappend(U_20297),c_List_Obutlast(U_20297,U_20296)),hAPP(hAPP(c_List_Olist_OCons(U_20297),c_List_Olast(U_20297,U_20296)),c_List_Olist_ONil(U_20297))) = U_20296
      | U_20296 = c_List_Olist_ONil(U_20297) ),
    inference(definitional_conversion,[status(esa)],[f_4821_2]) ).

cnf(f_4821_4,plain,
    ( hAPP(hAPP(c_List_Oappend(U_20297),c_List_Obutlast(U_20297,U_20296)),hAPP(hAPP(c_List_Olist_OCons(U_20297),c_List_Olast(U_20297,U_20296)),c_List_Olist_ONil(U_20297))) = U_20296
    | U_20296 = c_List_Olist_ONil(U_20297) ),
    inference(clausify,[status(thm)],[f_4821_3]) ).

fof(f_4822_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_4822_2,plain,
    ! [U_20301,U_20300,U_20299,U_20298] :
      ( ( hAPP(hAPP(c_List_Oappend(U_20298),U_20299),hAPP(hAPP(c_List_Olist_OCons(U_20298),U_20300),c_List_Olist_ONil(U_20298))) = U_20301
        | c_List_Olast(U_20298,U_20301) != U_20300
        | c_List_Obutlast(U_20298,U_20301) != U_20299
        | U_20301 = c_List_Olist_ONil(U_20298) )
      & ( ( c_List_Olast(U_20298,U_20301) = U_20300
          & c_List_Obutlast(U_20298,U_20301) = U_20299
          & U_20301 != c_List_Olist_ONil(U_20298) )
        | hAPP(hAPP(c_List_Oappend(U_20298),U_20299),hAPP(hAPP(c_List_Olist_OCons(U_20298),U_20300),c_List_Olist_ONil(U_20298))) != U_20301 ) ),
    inference(variable_rename,[status(thm)],[f_4822_1]) ).

fof(f_4822_3,plain,
    ( ! [U_20309,U_20307,U_20305,U_20303] :
        ( hAPP(hAPP(c_List_Oappend(U_20303),U_20305),hAPP(hAPP(c_List_Olist_OCons(U_20303),U_20307),c_List_Olist_ONil(U_20303))) = U_20309
        | c_List_Olast(U_20303,U_20309) != U_20307
        | c_List_Obutlast(U_20303,U_20309) != U_20305
        | U_20309 = c_List_Olist_ONil(U_20303) )
    & ! [U_20308,U_20306,U_20304,U_20302] :
        ( ( c_List_Olast(U_20302,U_20308) = U_20306
          & c_List_Obutlast(U_20302,U_20308) = U_20304
          & U_20308 != c_List_Olist_ONil(U_20302) )
        | hAPP(hAPP(c_List_Oappend(U_20302),U_20304),hAPP(hAPP(c_List_Olist_OCons(U_20302),U_20306),c_List_Olist_ONil(U_20302))) != U_20308 ) ),
    inference(miniscope,[status(thm)],[f_4822_2]) ).

fof(f_4822_4,plain,
    ( ! [U_20304,U_20308,U_20302,U_20306] :
        ( c_List_Olast(U_20302,U_20308) = U_20306
        | ~ sP1214(U_20304,U_20308,U_20302,U_20306) )
    & ! [U_20304,U_20308,U_20302,U_20306] :
        ( c_List_Obutlast(U_20302,U_20308) = U_20304
        | ~ sP1214(U_20304,U_20308,U_20302,U_20306) )
    & ! [U_20304,U_20308,U_20302,U_20306] :
        ( U_20308 != c_List_Olist_ONil(U_20302)
        | ~ sP1214(U_20304,U_20308,U_20302,U_20306) )
    & ! [U_20305,U_20303,U_20307,U_20309] :
        ( hAPP(hAPP(c_List_Oappend(U_20303),U_20305),hAPP(hAPP(c_List_Olist_OCons(U_20303),U_20307),c_List_Olist_ONil(U_20303))) = U_20309
        | c_List_Olast(U_20303,U_20309) != U_20307
        | c_List_Obutlast(U_20303,U_20309) != U_20305
        | U_20309 = c_List_Olist_ONil(U_20303) )
    & ! [U_20304,U_20308,U_20302,U_20306] :
        ( sP1214(U_20304,U_20308,U_20302,U_20306)
        | hAPP(hAPP(c_List_Oappend(U_20302),U_20304),hAPP(hAPP(c_List_Olist_OCons(U_20302),U_20306),c_List_Olist_ONil(U_20302))) != U_20308 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1214])],[f_4822_3]) ).

cnf(f_4822_5,plain,
    ( sP1214(U_20304,U_20308,U_20302,U_20306)
    | hAPP(hAPP(c_List_Oappend(U_20302),U_20304),hAPP(hAPP(c_List_Olist_OCons(U_20302),U_20306),c_List_Olist_ONil(U_20302))) != U_20308 ),
    inference(clausify,[status(thm)],[f_4822_4]) ).

cnf(f_4822_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_20303),U_20305),hAPP(hAPP(c_List_Olist_OCons(U_20303),U_20307),c_List_Olist_ONil(U_20303))) = U_20309
    | c_List_Olast(U_20303,U_20309) != U_20307
    | c_List_Obutlast(U_20303,U_20309) != U_20305
    | U_20309 = c_List_Olist_ONil(U_20303) ),
    inference(clausify,[status(thm)],[f_4822_4]) ).

cnf(f_4822_7,plain,
    ( U_20308 != c_List_Olist_ONil(U_20302)
    | ~ sP1214(U_20304,U_20308,U_20302,U_20306) ),
    inference(clausify,[status(thm)],[f_4822_4]) ).

cnf(f_4822_8,plain,
    ( c_List_Obutlast(U_20302,U_20308) = U_20304
    | ~ sP1214(U_20304,U_20308,U_20302,U_20306) ),
    inference(clausify,[status(thm)],[f_4822_4]) ).

cnf(f_4822_9,plain,
    ( c_List_Olast(U_20302,U_20308) = U_20306
    | ~ sP1214(U_20304,U_20308,U_20302,U_20306) ),
    inference(clausify,[status(thm)],[f_4822_4]) ).

fof(f_4823_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_4823_2,plain,
    ! [U_20313,U_20312,U_20311,U_20310] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20310)),U_20311))),c_List_Ofoldr(tc_List_Olist(U_20312),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20312)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20312))),U_20313,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_20310)),U_20311)),c_List_Ofoldr(tc_List_Olist(U_20312),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20312)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20312),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_20312)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20312)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(U_20312),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20312)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20312),tc_List_Olist(U_20312),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20312)))),U_20313),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(variable_rename,[status(thm)],[f_4823_1]) ).

fof(f_4823_3,plain,
    ! [U_20311,U_20310,U_20312,U_20313] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20310)),U_20311))),c_List_Ofoldr(tc_List_Olist(U_20312),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20312)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20312))),U_20313,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_20310)),U_20311)),c_List_Ofoldr(tc_List_Olist(U_20312),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20312)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20312),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_20312)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20312)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(U_20312),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20312)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20312),tc_List_Olist(U_20312),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20312)))),U_20313),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_4823_2]) ).

cnf(f_4823_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_20310)),U_20311))),c_List_Ofoldr(tc_List_Olist(U_20312),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20312)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20312))),U_20313,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_20310)),U_20311)),c_List_Ofoldr(tc_List_Olist(U_20312),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20312)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20312),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_20312)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20312)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(U_20312),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20312)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20312),tc_List_Olist(U_20312),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20312)))),U_20313),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(clausify,[status(thm)],[f_4823_3]) ).

fof(f_4824_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_4824_2,plain,
    ! [U_20318,U_20317,U_20316,U_20315,U_20314] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20314,tc_HOL_Obool)),hAPP(c_List_Oset(U_20314),U_20317)),hAPP(c_List_Oset(U_20314),U_20318)) = hAPP(c_List_Oset(U_20314),U_20316)
      | c_List_Opartition(U_20314,U_20315,U_20316) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20314),tc_List_Olist(U_20314)),U_20317),U_20318) ),
    inference(variable_rename,[status(thm)],[f_4824_1]) ).

fof(f_4824_3,plain,
    ! [U_20314,U_20315,U_20316,U_20317,U_20318] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20314,tc_HOL_Obool)),hAPP(c_List_Oset(U_20314),U_20317)),hAPP(c_List_Oset(U_20314),U_20318)) = hAPP(c_List_Oset(U_20314),U_20316)
      | c_List_Opartition(U_20314,U_20315,U_20316) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20314),tc_List_Olist(U_20314)),U_20317),U_20318) ),
    inference(definitional_conversion,[status(esa)],[f_4824_2]) ).

cnf(f_4824_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20314,tc_HOL_Obool)),hAPP(c_List_Oset(U_20314),U_20317)),hAPP(c_List_Oset(U_20314),U_20318)) = hAPP(c_List_Oset(U_20314),U_20316)
    | c_List_Opartition(U_20314,U_20315,U_20316) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20314),tc_List_Olist(U_20314)),U_20317),U_20318) ),
    inference(clausify,[status(thm)],[f_4824_3]) ).

fof(f_4825_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_4825_2,plain,
    ! [U_20321,U_20320,U_20319] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20319)),hAPP(c_List_Ofilter(U_20319,U_20320),U_20321))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20319)),U_20321))),
    inference(variable_rename,[status(thm)],[f_4825_1]) ).

fof(f_4825_3,plain,
    ! [U_20319,U_20320,U_20321] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20319)),hAPP(c_List_Ofilter(U_20319,U_20320),U_20321))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20319)),U_20321))),
    inference(definitional_conversion,[status(esa)],[f_4825_2]) ).

cnf(f_4825_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20319)),hAPP(c_List_Ofilter(U_20319,U_20320),U_20321))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20319)),U_20321))),
    inference(clausify,[status(thm)],[f_4825_3]) ).

fof(f_4826_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_4826_2,plain,
    ! [U_20324,U_20323,U_20322] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20322,tc_HOL_Obool)),hAPP(c_List_Oset(U_20322),hAPP(c_List_Ofilter(U_20322,U_20323),U_20324))),hAPP(c_List_Oset(U_20322),U_20324))),
    inference(variable_rename,[status(thm)],[f_4826_1]) ).

fof(f_4826_3,plain,
    ! [U_20322,U_20323,U_20324] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20322,tc_HOL_Obool)),hAPP(c_List_Oset(U_20322),hAPP(c_List_Ofilter(U_20322,U_20323),U_20324))),hAPP(c_List_Oset(U_20322),U_20324))),
    inference(definitional_conversion,[status(esa)],[f_4826_2]) ).

cnf(f_4826_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20322,tc_HOL_Obool)),hAPP(c_List_Oset(U_20322),hAPP(c_List_Ofilter(U_20322,U_20323),U_20324))),hAPP(c_List_Oset(U_20322),U_20324))),
    inference(clausify,[status(thm)],[f_4826_3]) ).

fof(f_4827_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_4827_2,plain,
    ! [U_20326,U_20325] : hAPP(c_List_Ofilter(U_20325,U_20326),c_List_Olist_ONil(U_20325)) = c_List_Olist_ONil(U_20325),
    inference(variable_rename,[status(thm)],[f_4827_1]) ).

fof(f_4827_3,plain,
    ! [U_20325,U_20326] : hAPP(c_List_Ofilter(U_20325,U_20326),c_List_Olist_ONil(U_20325)) = c_List_Olist_ONil(U_20325),
    inference(definitional_conversion,[status(esa)],[f_4827_2]) ).

cnf(f_4827_4,plain,
    hAPP(c_List_Ofilter(U_20325,U_20326),c_List_Olist_ONil(U_20325)) = c_List_Olist_ONil(U_20325),
    inference(clausify,[status(thm)],[f_4827_3]) ).

fof(f_4828_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_4828_2,plain,
    ! [U_20331,U_20330,U_20329] :
      ( ( hAPP(c_List_Ofilter(U_20329,U_20330),U_20331) = c_List_Olist_ONil(U_20329)
        | ? [U_20328] :
            ( hBOOL(hAPP(U_20330,U_20328))
            & hBOOL(hAPP(hAPP(c_member(U_20329),U_20328),hAPP(c_List_Oset(U_20329),U_20331))) ) )
      & ( ! [U_20327] :
            ( ~ hBOOL(hAPP(U_20330,U_20327))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20329),U_20327),hAPP(c_List_Oset(U_20329),U_20331))) )
        | hAPP(c_List_Ofilter(U_20329,U_20330),U_20331) != c_List_Olist_ONil(U_20329) ) ),
    inference(variable_rename,[status(thm)],[f_4828_1]) ).

fof(f_4828_3,plain,
    ( ! [U_20337,U_20335,U_20333] :
        ( hAPP(c_List_Ofilter(U_20333,U_20335),U_20337) = c_List_Olist_ONil(U_20333)
        | ? [U_20328] :
            ( hBOOL(hAPP(U_20335,U_20328))
            & hBOOL(hAPP(hAPP(c_member(U_20333),U_20328),hAPP(c_List_Oset(U_20333),U_20337))) ) )
    & ! [U_20336,U_20334,U_20332] :
        ( ! [U_20327] :
            ( ~ hBOOL(hAPP(U_20334,U_20327))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20332),U_20327),hAPP(c_List_Oset(U_20332),U_20336))) )
        | hAPP(c_List_Ofilter(U_20332,U_20334),U_20336) != c_List_Olist_ONil(U_20332) ) ),
    inference(miniscope,[status(thm)],[f_4828_2]) ).

fof(f_4828_4,plain,
    ( ! [U_20337,U_20335,U_20333] :
        ( hAPP(c_List_Ofilter(U_20333,U_20335),U_20337) = c_List_Olist_ONil(U_20333)
        | ( hBOOL(hAPP(U_20335,sK499(U_20337,U_20335,U_20333)))
          & hBOOL(hAPP(hAPP(c_member(U_20333),sK499(U_20337,U_20335,U_20333)),hAPP(c_List_Oset(U_20333),U_20337))) ) )
    & ! [U_20336,U_20334,U_20332] :
        ( ! [U_20327] :
            ( ~ hBOOL(hAPP(U_20334,U_20327))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20332),U_20327),hAPP(c_List_Oset(U_20332),U_20336))) )
        | hAPP(c_List_Ofilter(U_20332,U_20334),U_20336) != c_List_Olist_ONil(U_20332) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK499]),skolemize(U_20328,sK499(U_20337,U_20335,U_20333))],[f_4828_3]) ).

fof(f_4828_5,plain,
    ( ! [U_20337,U_20335,U_20333] :
        ( hBOOL(hAPP(U_20335,sK499(U_20337,U_20335,U_20333)))
        | ~ sP1215(U_20337,U_20335,U_20333) )
    & ! [U_20337,U_20335,U_20333] :
        ( hBOOL(hAPP(hAPP(c_member(U_20333),sK499(U_20337,U_20335,U_20333)),hAPP(c_List_Oset(U_20333),U_20337)))
        | ~ sP1215(U_20337,U_20335,U_20333) )
    & ! [U_20337,U_20335,U_20333] :
        ( hAPP(c_List_Ofilter(U_20333,U_20335),U_20337) = c_List_Olist_ONil(U_20333)
        | sP1215(U_20337,U_20335,U_20333) )
    & ! [U_20334,U_20327,U_20332,U_20336] :
        ( ~ hBOOL(hAPP(U_20334,U_20327))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20332),U_20327),hAPP(c_List_Oset(U_20332),U_20336)))
        | hAPP(c_List_Ofilter(U_20332,U_20334),U_20336) != c_List_Olist_ONil(U_20332) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1215])],[f_4828_4]) ).

cnf(f_4828_6,plain,
    ( ~ hBOOL(hAPP(U_20334,U_20327))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20332),U_20327),hAPP(c_List_Oset(U_20332),U_20336)))
    | hAPP(c_List_Ofilter(U_20332,U_20334),U_20336) != c_List_Olist_ONil(U_20332) ),
    inference(clausify,[status(thm)],[f_4828_5]) ).

cnf(f_4828_7,plain,
    ( hAPP(c_List_Ofilter(U_20333,U_20335),U_20337) = c_List_Olist_ONil(U_20333)
    | sP1215(U_20337,U_20335,U_20333) ),
    inference(clausify,[status(thm)],[f_4828_5]) ).

cnf(f_4828_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20333),sK499(U_20337,U_20335,U_20333)),hAPP(c_List_Oset(U_20333),U_20337)))
    | ~ sP1215(U_20337,U_20335,U_20333) ),
    inference(clausify,[status(thm)],[f_4828_5]) ).

cnf(f_4828_9,plain,
    ( hBOOL(hAPP(U_20335,sK499(U_20337,U_20335,U_20333)))
    | ~ sP1215(U_20337,U_20335,U_20333) ),
    inference(clausify,[status(thm)],[f_4828_5]) ).

fof(f_4829_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_4829_2,plain,
    ! [U_20342,U_20341,U_20340] :
      ( ( hAPP(c_List_Ofilter(U_20340,U_20341),U_20342) = U_20342
        | ? [U_20339] :
            ( ~ hBOOL(hAPP(U_20341,U_20339))
            & hBOOL(hAPP(hAPP(c_member(U_20340),U_20339),hAPP(c_List_Oset(U_20340),U_20342))) ) )
      & ( ! [U_20338] :
            ( hBOOL(hAPP(U_20341,U_20338))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20340),U_20338),hAPP(c_List_Oset(U_20340),U_20342))) )
        | hAPP(c_List_Ofilter(U_20340,U_20341),U_20342) != U_20342 ) ),
    inference(variable_rename,[status(thm)],[f_4829_1]) ).

fof(f_4829_3,plain,
    ( ! [U_20348,U_20346,U_20344] :
        ( hAPP(c_List_Ofilter(U_20344,U_20346),U_20348) = U_20348
        | ? [U_20339] :
            ( ~ hBOOL(hAPP(U_20346,U_20339))
            & hBOOL(hAPP(hAPP(c_member(U_20344),U_20339),hAPP(c_List_Oset(U_20344),U_20348))) ) )
    & ! [U_20347,U_20345,U_20343] :
        ( ! [U_20338] :
            ( hBOOL(hAPP(U_20345,U_20338))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20343),U_20338),hAPP(c_List_Oset(U_20343),U_20347))) )
        | hAPP(c_List_Ofilter(U_20343,U_20345),U_20347) != U_20347 ) ),
    inference(miniscope,[status(thm)],[f_4829_2]) ).

fof(f_4829_4,plain,
    ( ! [U_20348,U_20346,U_20344] :
        ( hAPP(c_List_Ofilter(U_20344,U_20346),U_20348) = U_20348
        | ( ~ hBOOL(hAPP(U_20346,sK500(U_20348,U_20346,U_20344)))
          & hBOOL(hAPP(hAPP(c_member(U_20344),sK500(U_20348,U_20346,U_20344)),hAPP(c_List_Oset(U_20344),U_20348))) ) )
    & ! [U_20347,U_20345,U_20343] :
        ( ! [U_20338] :
            ( hBOOL(hAPP(U_20345,U_20338))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20343),U_20338),hAPP(c_List_Oset(U_20343),U_20347))) )
        | hAPP(c_List_Ofilter(U_20343,U_20345),U_20347) != U_20347 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK500]),skolemize(U_20339,sK500(U_20348,U_20346,U_20344))],[f_4829_3]) ).

fof(f_4829_5,plain,
    ( ! [U_20348,U_20346,U_20344] :
        ( ~ hBOOL(hAPP(U_20346,sK500(U_20348,U_20346,U_20344)))
        | ~ sP1216(U_20348,U_20346,U_20344) )
    & ! [U_20348,U_20346,U_20344] :
        ( hBOOL(hAPP(hAPP(c_member(U_20344),sK500(U_20348,U_20346,U_20344)),hAPP(c_List_Oset(U_20344),U_20348)))
        | ~ sP1216(U_20348,U_20346,U_20344) )
    & ! [U_20348,U_20346,U_20344] :
        ( hAPP(c_List_Ofilter(U_20344,U_20346),U_20348) = U_20348
        | sP1216(U_20348,U_20346,U_20344) )
    & ! [U_20338,U_20347,U_20343,U_20345] :
        ( hBOOL(hAPP(U_20345,U_20338))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20343),U_20338),hAPP(c_List_Oset(U_20343),U_20347)))
        | hAPP(c_List_Ofilter(U_20343,U_20345),U_20347) != U_20347 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1216])],[f_4829_4]) ).

cnf(f_4829_6,plain,
    ( hBOOL(hAPP(U_20345,U_20338))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20343),U_20338),hAPP(c_List_Oset(U_20343),U_20347)))
    | hAPP(c_List_Ofilter(U_20343,U_20345),U_20347) != U_20347 ),
    inference(clausify,[status(thm)],[f_4829_5]) ).

cnf(f_4829_7,plain,
    ( hAPP(c_List_Ofilter(U_20344,U_20346),U_20348) = U_20348
    | sP1216(U_20348,U_20346,U_20344) ),
    inference(clausify,[status(thm)],[f_4829_5]) ).

cnf(f_4829_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20344),sK500(U_20348,U_20346,U_20344)),hAPP(c_List_Oset(U_20344),U_20348)))
    | ~ sP1216(U_20348,U_20346,U_20344) ),
    inference(clausify,[status(thm)],[f_4829_5]) ).

cnf(f_4829_9,plain,
    ( ~ hBOOL(hAPP(U_20346,sK500(U_20348,U_20346,U_20344)))
    | ~ sP1216(U_20348,U_20346,U_20344) ),
    inference(clausify,[status(thm)],[f_4829_5]) ).

fof(f_4830_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_4830_2,plain,
    ! [U_20354,U_20353,U_20352,U_20351,U_20350,U_20349] :
      ( hAPP(c_List_Ofilter(U_20352,U_20350),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20352,U_20349,U_20353),U_20351),U_20354)) = hAPP(c_List_Ofilter(U_20352,U_20350),U_20354)
      | hBOOL(hAPP(U_20350,U_20351))
      | ~ class_Orderings_Olinorder(U_20349) ),
    inference(variable_rename,[status(thm)],[f_4830_1]) ).

fof(f_4830_3,plain,
    ! [U_20351,U_20349,U_20350,U_20352,U_20353,U_20354] :
      ( hAPP(c_List_Ofilter(U_20352,U_20350),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20352,U_20349,U_20353),U_20351),U_20354)) = hAPP(c_List_Ofilter(U_20352,U_20350),U_20354)
      | hBOOL(hAPP(U_20350,U_20351))
      | ~ class_Orderings_Olinorder(U_20349) ),
    inference(definitional_conversion,[status(esa)],[f_4830_2]) ).

cnf(f_4830_4,plain,
    ( hAPP(c_List_Ofilter(U_20352,U_20350),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20352,U_20349,U_20353),U_20351),U_20354)) = hAPP(c_List_Ofilter(U_20352,U_20350),U_20354)
    | hBOOL(hAPP(U_20350,U_20351))
    | ~ class_Orderings_Olinorder(U_20349) ),
    inference(clausify,[status(thm)],[f_4830_3]) ).

fof(f_4831_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_4831_2,plain,
    ! [U_20357,U_20356,U_20355] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20355),hAPP(c_List_Ofilter(U_20355,U_20357),U_20356)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20355),U_20356)) ),
    inference(variable_rename,[status(thm)],[f_4831_1]) ).

fof(f_4831_3,plain,
    ! [U_20355,U_20356,U_20357] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20355),hAPP(c_List_Ofilter(U_20355,U_20357),U_20356)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20355),U_20356)) ),
    inference(definitional_conversion,[status(esa)],[f_4831_2]) ).

cnf(f_4831_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20355),hAPP(c_List_Ofilter(U_20355,U_20357),U_20356)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20355),U_20356)) ),
    inference(clausify,[status(thm)],[f_4831_3]) ).

fof(f_4832_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_4832_2,plain,
    ! [U_20361,U_20360,U_20359,U_20358] : hAPP(c_List_Ofilter(U_20358,U_20359),c_List_Oremove1(U_20358,U_20360,U_20361)) = c_List_Oremove1(U_20358,U_20360,hAPP(c_List_Ofilter(U_20358,U_20359),U_20361)),
    inference(variable_rename,[status(thm)],[f_4832_1]) ).

fof(f_4832_3,plain,
    ! [U_20358,U_20359,U_20360,U_20361] : hAPP(c_List_Ofilter(U_20358,U_20359),c_List_Oremove1(U_20358,U_20360,U_20361)) = c_List_Oremove1(U_20358,U_20360,hAPP(c_List_Ofilter(U_20358,U_20359),U_20361)),
    inference(definitional_conversion,[status(esa)],[f_4832_2]) ).

cnf(f_4832_4,plain,
    hAPP(c_List_Ofilter(U_20358,U_20359),c_List_Oremove1(U_20358,U_20360,U_20361)) = c_List_Oremove1(U_20358,U_20360,hAPP(c_List_Ofilter(U_20358,U_20359),U_20361)),
    inference(clausify,[status(thm)],[f_4832_3]) ).

fof(f_4833_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_4833_2,plain,
    ! [U_20365,U_20364,U_20363,U_20362] :
      ( c_List_Oremove1(U_20364,U_20363,hAPP(c_List_Ofilter(U_20364,U_20362),U_20365)) = hAPP(c_List_Ofilter(U_20364,U_20362),U_20365)
      | hBOOL(hAPP(U_20362,U_20363)) ),
    inference(variable_rename,[status(thm)],[f_4833_1]) ).

fof(f_4833_3,plain,
    ! [U_20362,U_20363,U_20364,U_20365] :
      ( c_List_Oremove1(U_20364,U_20363,hAPP(c_List_Ofilter(U_20364,U_20362),U_20365)) = hAPP(c_List_Ofilter(U_20364,U_20362),U_20365)
      | hBOOL(hAPP(U_20362,U_20363)) ),
    inference(definitional_conversion,[status(esa)],[f_4833_2]) ).

cnf(f_4833_4,plain,
    ( c_List_Oremove1(U_20364,U_20363,hAPP(c_List_Ofilter(U_20364,U_20362),U_20365)) = hAPP(c_List_Ofilter(U_20364,U_20362),U_20365)
    | hBOOL(hAPP(U_20362,U_20363)) ),
    inference(clausify,[status(thm)],[f_4833_3]) ).

fof(f_4834_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_4834_2,plain,
    ! [U_20369,U_20368,U_20367,U_20366] : hAPP(c_List_Ofilter(U_20366,U_20367),hAPP(c_List_Ofilter(U_20366,U_20368),U_20369)) = hAPP(c_List_Ofilter(U_20366,hAPP(hAPP(c_COMBS(U_20366,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20366),c_fconj),U_20368)),U_20367)),U_20369),
    inference(variable_rename,[status(thm)],[f_4834_1]) ).

fof(f_4834_3,plain,
    ! [U_20366,U_20367,U_20368,U_20369] : hAPP(c_List_Ofilter(U_20366,U_20367),hAPP(c_List_Ofilter(U_20366,U_20368),U_20369)) = hAPP(c_List_Ofilter(U_20366,hAPP(hAPP(c_COMBS(U_20366,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20366),c_fconj),U_20368)),U_20367)),U_20369),
    inference(definitional_conversion,[status(esa)],[f_4834_2]) ).

cnf(f_4834_4,plain,
    hAPP(c_List_Ofilter(U_20366,U_20367),hAPP(c_List_Ofilter(U_20366,U_20368),U_20369)) = hAPP(c_List_Ofilter(U_20366,hAPP(hAPP(c_COMBS(U_20366,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20366),c_fconj),U_20368)),U_20367)),U_20369),
    inference(clausify,[status(thm)],[f_4834_3]) ).

fof(f_4835_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_4835_2,plain,
    ! [U_20372,U_20371,U_20370] : hAPP(c_Product__Type_Ofst(tc_List_Olist(U_20370),tc_List_Olist(U_20370)),c_List_Opartition(U_20370,U_20371,U_20372)) = hAPP(c_List_Ofilter(U_20370,U_20371),U_20372),
    inference(variable_rename,[status(thm)],[f_4835_1]) ).

fof(f_4835_3,plain,
    ! [U_20370,U_20371,U_20372] : hAPP(c_Product__Type_Ofst(tc_List_Olist(U_20370),tc_List_Olist(U_20370)),c_List_Opartition(U_20370,U_20371,U_20372)) = hAPP(c_List_Ofilter(U_20370,U_20371),U_20372),
    inference(definitional_conversion,[status(esa)],[f_4835_2]) ).

cnf(f_4835_4,plain,
    hAPP(c_Product__Type_Ofst(tc_List_Olist(U_20370),tc_List_Olist(U_20370)),c_List_Opartition(U_20370,U_20371,U_20372)) = hAPP(c_List_Ofilter(U_20370,U_20371),U_20372),
    inference(clausify,[status(thm)],[f_4835_3]) ).

fof(f_4836_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_4836_2,plain,
    ! [U_20375,U_20374,U_20373] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20373)),hAPP(c_List_Ofilter(U_20373,U_20374),U_20375))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20373)),hAPP(c_List_Ofilter(U_20373,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20373),c_fNot),U_20374)),U_20375))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20373)),U_20375),
    inference(variable_rename,[status(thm)],[f_4836_1]) ).

fof(f_4836_3,plain,
    ! [U_20373,U_20374,U_20375] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20373)),hAPP(c_List_Ofilter(U_20373,U_20374),U_20375))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20373)),hAPP(c_List_Ofilter(U_20373,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20373),c_fNot),U_20374)),U_20375))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20373)),U_20375),
    inference(definitional_conversion,[status(esa)],[f_4836_2]) ).

cnf(f_4836_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20373)),hAPP(c_List_Ofilter(U_20373,U_20374),U_20375))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20373)),hAPP(c_List_Ofilter(U_20373,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20373),c_fNot),U_20374)),U_20375))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20373)),U_20375),
    inference(clausify,[status(thm)],[f_4836_3]) ).

fof(f_4837_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_4837_2,plain,
    ! [U_20379,U_20378,U_20377,U_20376] :
      ( ( hAPP(c_List_Ofilter(U_20378,U_20376),hAPP(hAPP(c_List_Olist_OCons(U_20378),U_20377),U_20379)) = hAPP(c_List_Ofilter(U_20378,U_20376),U_20379)
        | hBOOL(hAPP(U_20376,U_20377)) )
      & ( hAPP(c_List_Ofilter(U_20378,U_20376),hAPP(hAPP(c_List_Olist_OCons(U_20378),U_20377),U_20379)) = hAPP(hAPP(c_List_Olist_OCons(U_20378),U_20377),hAPP(c_List_Ofilter(U_20378,U_20376),U_20379))
        | ~ hBOOL(hAPP(U_20376,U_20377)) ) ),
    inference(variable_rename,[status(thm)],[f_4837_1]) ).

fof(f_4837_3,plain,
    ( ! [U_20387,U_20385,U_20383,U_20381] :
        ( hAPP(c_List_Ofilter(U_20385,U_20381),hAPP(hAPP(c_List_Olist_OCons(U_20385),U_20383),U_20387)) = hAPP(c_List_Ofilter(U_20385,U_20381),U_20387)
        | hBOOL(hAPP(U_20381,U_20383)) )
    & ! [U_20386,U_20384,U_20382,U_20380] :
        ( hAPP(c_List_Ofilter(U_20384,U_20380),hAPP(hAPP(c_List_Olist_OCons(U_20384),U_20382),U_20386)) = hAPP(hAPP(c_List_Olist_OCons(U_20384),U_20382),hAPP(c_List_Ofilter(U_20384,U_20380),U_20386))
        | ~ hBOOL(hAPP(U_20380,U_20382)) ) ),
    inference(miniscope,[status(thm)],[f_4837_2]) ).

fof(f_4837_4,plain,
    ( ! [U_20381,U_20383,U_20385,U_20387] :
        ( hAPP(c_List_Ofilter(U_20385,U_20381),hAPP(hAPP(c_List_Olist_OCons(U_20385),U_20383),U_20387)) = hAPP(c_List_Ofilter(U_20385,U_20381),U_20387)
        | hBOOL(hAPP(U_20381,U_20383)) )
    & ! [U_20380,U_20382,U_20384,U_20386] :
        ( hAPP(c_List_Ofilter(U_20384,U_20380),hAPP(hAPP(c_List_Olist_OCons(U_20384),U_20382),U_20386)) = hAPP(hAPP(c_List_Olist_OCons(U_20384),U_20382),hAPP(c_List_Ofilter(U_20384,U_20380),U_20386))
        | ~ hBOOL(hAPP(U_20380,U_20382)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4837_3]) ).

cnf(f_4837_5,plain,
    ( hAPP(c_List_Ofilter(U_20384,U_20380),hAPP(hAPP(c_List_Olist_OCons(U_20384),U_20382),U_20386)) = hAPP(hAPP(c_List_Olist_OCons(U_20384),U_20382),hAPP(c_List_Ofilter(U_20384,U_20380),U_20386))
    | ~ hBOOL(hAPP(U_20380,U_20382)) ),
    inference(clausify,[status(thm)],[f_4837_4]) ).

cnf(f_4837_6,plain,
    ( hAPP(c_List_Ofilter(U_20385,U_20381),hAPP(hAPP(c_List_Olist_OCons(U_20385),U_20383),U_20387)) = hAPP(c_List_Ofilter(U_20385,U_20381),U_20387)
    | hBOOL(hAPP(U_20381,U_20383)) ),
    inference(clausify,[status(thm)],[f_4837_4]) ).

fof(f_4838_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_4838_2,plain,
    ! [U_20391,U_20390,U_20389,U_20388] : hAPP(c_List_Ofilter(U_20388,U_20389),hAPP(hAPP(c_List_Oappend(U_20388),U_20390),U_20391)) = hAPP(hAPP(c_List_Oappend(U_20388),hAPP(c_List_Ofilter(U_20388,U_20389),U_20390)),hAPP(c_List_Ofilter(U_20388,U_20389),U_20391)),
    inference(variable_rename,[status(thm)],[f_4838_1]) ).

fof(f_4838_3,plain,
    ! [U_20388,U_20389,U_20390,U_20391] : hAPP(c_List_Ofilter(U_20388,U_20389),hAPP(hAPP(c_List_Oappend(U_20388),U_20390),U_20391)) = hAPP(hAPP(c_List_Oappend(U_20388),hAPP(c_List_Ofilter(U_20388,U_20389),U_20390)),hAPP(c_List_Ofilter(U_20388,U_20389),U_20391)),
    inference(definitional_conversion,[status(esa)],[f_4838_2]) ).

cnf(f_4838_4,plain,
    hAPP(c_List_Ofilter(U_20388,U_20389),hAPP(hAPP(c_List_Oappend(U_20388),U_20390),U_20391)) = hAPP(hAPP(c_List_Oappend(U_20388),hAPP(c_List_Ofilter(U_20388,U_20389),U_20390)),hAPP(c_List_Ofilter(U_20388,U_20389),U_20391)),
    inference(clausify,[status(thm)],[f_4838_3]) ).

fof(f_4839_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_4839_2,plain,
    ! [U_20396,U_20395,U_20394,U_20393,U_20392] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20392)),hAPP(c_List_Ofilter(U_20392,U_20393),hAPP(hAPP(c_List_Omap(U_20394,U_20392),U_20395),U_20396))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20394)),hAPP(c_List_Ofilter(U_20394,hAPP(c_Fun_Ocomp(U_20392,tc_HOL_Obool,U_20394,U_20393),U_20395)),U_20396)),
    inference(variable_rename,[status(thm)],[f_4839_1]) ).

fof(f_4839_3,plain,
    ! [U_20392,U_20393,U_20394,U_20395,U_20396] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20392)),hAPP(c_List_Ofilter(U_20392,U_20393),hAPP(hAPP(c_List_Omap(U_20394,U_20392),U_20395),U_20396))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20394)),hAPP(c_List_Ofilter(U_20394,hAPP(c_Fun_Ocomp(U_20392,tc_HOL_Obool,U_20394,U_20393),U_20395)),U_20396)),
    inference(definitional_conversion,[status(esa)],[f_4839_2]) ).

cnf(f_4839_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20392)),hAPP(c_List_Ofilter(U_20392,U_20393),hAPP(hAPP(c_List_Omap(U_20394,U_20392),U_20395),U_20396))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20394)),hAPP(c_List_Ofilter(U_20394,hAPP(c_Fun_Ocomp(U_20392,tc_HOL_Obool,U_20394,U_20393),U_20395)),U_20396)),
    inference(clausify,[status(thm)],[f_4839_3]) ).

fof(f_4840_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_4840_2,plain,
    ! [U_20399,U_20398,U_20397] : hAPP(c_List_Oset(U_20397),hAPP(c_List_Ofilter(U_20397,U_20398),U_20399)) = hAPP(c_Set_OCollect(U_20397),hAPP(hAPP(c_COMBS(U_20397,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20397),c_fconj),hAPP(hAPP(c_COMBC(U_20397,tc_fun(U_20397,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20397)),hAPP(c_List_Oset(U_20397),U_20399)))),U_20398)),
    inference(variable_rename,[status(thm)],[f_4840_1]) ).

fof(f_4840_3,plain,
    ! [U_20397,U_20398,U_20399] : hAPP(c_List_Oset(U_20397),hAPP(c_List_Ofilter(U_20397,U_20398),U_20399)) = hAPP(c_Set_OCollect(U_20397),hAPP(hAPP(c_COMBS(U_20397,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20397),c_fconj),hAPP(hAPP(c_COMBC(U_20397,tc_fun(U_20397,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20397)),hAPP(c_List_Oset(U_20397),U_20399)))),U_20398)),
    inference(definitional_conversion,[status(esa)],[f_4840_2]) ).

cnf(f_4840_4,plain,
    hAPP(c_List_Oset(U_20397),hAPP(c_List_Ofilter(U_20397,U_20398),U_20399)) = hAPP(c_Set_OCollect(U_20397),hAPP(hAPP(c_COMBS(U_20397,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20397),c_fconj),hAPP(hAPP(c_COMBC(U_20397,tc_fun(U_20397,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20397)),hAPP(c_List_Oset(U_20397),U_20399)))),U_20398)),
    inference(clausify,[status(thm)],[f_4840_3]) ).

fof(f_4841_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_4841_2,plain,
    ! [U_20402,U_20401,U_20400] : c_List_Opartition(U_20400,U_20401,U_20402) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20400),tc_List_Olist(U_20400)),hAPP(c_List_Ofilter(U_20400,U_20401),U_20402)),hAPP(c_List_Ofilter(U_20400,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_20400,c_fNot),U_20401)),U_20402)),
    inference(variable_rename,[status(thm)],[f_4841_1]) ).

fof(f_4841_3,plain,
    ! [U_20400,U_20401,U_20402] : c_List_Opartition(U_20400,U_20401,U_20402) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20400),tc_List_Olist(U_20400)),hAPP(c_List_Ofilter(U_20400,U_20401),U_20402)),hAPP(c_List_Ofilter(U_20400,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_20400,c_fNot),U_20401)),U_20402)),
    inference(definitional_conversion,[status(esa)],[f_4841_2]) ).

cnf(f_4841_4,plain,
    c_List_Opartition(U_20400,U_20401,U_20402) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20400),tc_List_Olist(U_20400)),hAPP(c_List_Ofilter(U_20400,U_20401),U_20402)),hAPP(c_List_Ofilter(U_20400,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_20400,c_fNot),U_20401)),U_20402)),
    inference(clausify,[status(thm)],[f_4841_3]) ).

fof(f_4842_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_4842_2,plain,
    ! [U_20407,U_20406,U_20405,U_20404,U_20403] : hAPP(c_List_Ofilter(U_20403,U_20404),hAPP(hAPP(c_List_Omap(U_20405,U_20403),U_20406),U_20407)) = hAPP(hAPP(c_List_Omap(U_20405,U_20403),U_20406),hAPP(c_List_Ofilter(U_20405,hAPP(c_Fun_Ocomp(U_20403,tc_HOL_Obool,U_20405,U_20404),U_20406)),U_20407)),
    inference(variable_rename,[status(thm)],[f_4842_1]) ).

fof(f_4842_3,plain,
    ! [U_20403,U_20404,U_20405,U_20406,U_20407] : hAPP(c_List_Ofilter(U_20403,U_20404),hAPP(hAPP(c_List_Omap(U_20405,U_20403),U_20406),U_20407)) = hAPP(hAPP(c_List_Omap(U_20405,U_20403),U_20406),hAPP(c_List_Ofilter(U_20405,hAPP(c_Fun_Ocomp(U_20403,tc_HOL_Obool,U_20405,U_20404),U_20406)),U_20407)),
    inference(definitional_conversion,[status(esa)],[f_4842_2]) ).

cnf(f_4842_4,plain,
    hAPP(c_List_Ofilter(U_20403,U_20404),hAPP(hAPP(c_List_Omap(U_20405,U_20403),U_20406),U_20407)) = hAPP(hAPP(c_List_Omap(U_20405,U_20403),U_20406),hAPP(c_List_Ofilter(U_20405,hAPP(c_Fun_Ocomp(U_20403,tc_HOL_Obool,U_20405,U_20404),U_20406)),U_20407)),
    inference(clausify,[status(thm)],[f_4842_3]) ).

fof(f_4843_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_4843_2,plain,
    ! [U_20410,U_20409,U_20408] : hAPP(c_Product__Type_Osnd(tc_List_Olist(U_20408),tc_List_Olist(U_20408)),c_List_Opartition(U_20408,U_20409,U_20410)) = hAPP(c_List_Ofilter(U_20408,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_20408,c_fNot),U_20409)),U_20410),
    inference(variable_rename,[status(thm)],[f_4843_1]) ).

fof(f_4843_3,plain,
    ! [U_20408,U_20409,U_20410] : hAPP(c_Product__Type_Osnd(tc_List_Olist(U_20408),tc_List_Olist(U_20408)),c_List_Opartition(U_20408,U_20409,U_20410)) = hAPP(c_List_Ofilter(U_20408,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_20408,c_fNot),U_20409)),U_20410),
    inference(definitional_conversion,[status(esa)],[f_4843_2]) ).

cnf(f_4843_4,plain,
    hAPP(c_Product__Type_Osnd(tc_List_Olist(U_20408),tc_List_Olist(U_20408)),c_List_Opartition(U_20408,U_20409,U_20410)) = hAPP(c_List_Ofilter(U_20408,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_20408,c_fNot),U_20409)),U_20410),
    inference(clausify,[status(thm)],[f_4843_3]) ).

fof(f_4844_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_4844_2,plain,
    ! [U_20414,U_20413,U_20412,U_20411] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20411)),hAPP(c_List_Ofilter(U_20411,U_20414),U_20413))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20411)),U_20413)))
      | hBOOL(hAPP(U_20414,U_20412))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20411),U_20412),hAPP(c_List_Oset(U_20411),U_20413))) ),
    inference(variable_rename,[status(thm)],[f_4844_1]) ).

fof(f_4844_3,plain,
    ! [U_20411,U_20412,U_20413,U_20414] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20411)),hAPP(c_List_Ofilter(U_20411,U_20414),U_20413))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20411)),U_20413)))
      | hBOOL(hAPP(U_20414,U_20412))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20411),U_20412),hAPP(c_List_Oset(U_20411),U_20413))) ),
    inference(definitional_conversion,[status(esa)],[f_4844_2]) ).

cnf(f_4844_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20411)),hAPP(c_List_Ofilter(U_20411,U_20414),U_20413))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20411)),U_20413)))
    | hBOOL(hAPP(U_20414,U_20412))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20411),U_20412),hAPP(c_List_Oset(U_20411),U_20413))) ),
    inference(clausify,[status(thm)],[f_4844_3]) ).

fof(f_4845_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_4845_2,plain,
    ! [U_20417,U_20416,U_20415] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_20415,tc_HOL_Obool)),hAPP(c_List_Oset(U_20415),U_20416)),hAPP(hAPP(c_Set_Oinsert(U_20415),U_20417),c_Orderings_Obot__class_Obot(tc_fun(U_20415,tc_HOL_Obool)))) = hAPP(c_List_Oset(U_20415),hAPP(c_List_Ofilter(U_20415,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20415),c_fNot),hAPP(hAPP(c_COMBC(U_20415,U_20415,tc_HOL_Obool),c_fequal),U_20417))),U_20416)),
    inference(variable_rename,[status(thm)],[f_4845_1]) ).

fof(f_4845_3,plain,
    ! [U_20415,U_20416,U_20417] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_20415,tc_HOL_Obool)),hAPP(c_List_Oset(U_20415),U_20416)),hAPP(hAPP(c_Set_Oinsert(U_20415),U_20417),c_Orderings_Obot__class_Obot(tc_fun(U_20415,tc_HOL_Obool)))) = hAPP(c_List_Oset(U_20415),hAPP(c_List_Ofilter(U_20415,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20415),c_fNot),hAPP(hAPP(c_COMBC(U_20415,U_20415,tc_HOL_Obool),c_fequal),U_20417))),U_20416)),
    inference(definitional_conversion,[status(esa)],[f_4845_2]) ).

cnf(f_4845_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_20415,tc_HOL_Obool)),hAPP(c_List_Oset(U_20415),U_20416)),hAPP(hAPP(c_Set_Oinsert(U_20415),U_20417),c_Orderings_Obot__class_Obot(tc_fun(U_20415,tc_HOL_Obool)))) = hAPP(c_List_Oset(U_20415),hAPP(c_List_Ofilter(U_20415,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20415),c_fNot),hAPP(hAPP(c_COMBC(U_20415,U_20415,tc_HOL_Obool),c_fequal),U_20417))),U_20416)),
    inference(clausify,[status(thm)],[f_4845_3]) ).

fof(f_4846_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_4846_2,plain,
    ! [U_20424,U_20423,U_20422,U_20421,U_20420] :
      ( ( ! [U_20419] :
            ( ~ hBOOL(hAPP(U_20421,U_20419))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20420),U_20419),hAPP(c_List_Oset(U_20420),U_20424))) )
        & ! [U_20418] :
            ( hBOOL(hAPP(U_20421,U_20418))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20420),U_20418),hAPP(c_List_Oset(U_20420),U_20423))) ) )
      | c_List_Opartition(U_20420,U_20421,U_20422) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20420),tc_List_Olist(U_20420)),U_20423),U_20424) ),
    inference(variable_rename,[status(thm)],[f_4846_1]) ).

fof(f_4846_3,plain,
    ( ! [U_20421,U_20423,U_20424,U_20419,U_20420,U_20418] :
        ( ~ hBOOL(hAPP(U_20421,U_20419))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20420),U_20419),hAPP(c_List_Oset(U_20420),U_20424)))
        | ~ sP1217(U_20421,U_20423,U_20424,U_20419,U_20420,U_20418) )
    & ! [U_20421,U_20423,U_20424,U_20419,U_20420,U_20418] :
        ( hBOOL(hAPP(U_20421,U_20418))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20420),U_20418),hAPP(c_List_Oset(U_20420),U_20423)))
        | ~ sP1217(U_20421,U_20423,U_20424,U_20419,U_20420,U_20418) )
    & ! [U_20421,U_20422,U_20423,U_20424,U_20419,U_20420,U_20418] :
        ( sP1217(U_20421,U_20423,U_20424,U_20419,U_20420,U_20418)
        | c_List_Opartition(U_20420,U_20421,U_20422) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20420),tc_List_Olist(U_20420)),U_20423),U_20424) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1217])],[f_4846_2]) ).

cnf(f_4846_4,plain,
    ( sP1217(U_20421,U_20423,U_20424,U_20419,U_20420,U_20418)
    | c_List_Opartition(U_20420,U_20421,U_20422) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20420),tc_List_Olist(U_20420)),U_20423),U_20424) ),
    inference(clausify,[status(thm)],[f_4846_3]) ).

cnf(f_4846_5,plain,
    ( hBOOL(hAPP(U_20421,U_20418))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20420),U_20418),hAPP(c_List_Oset(U_20420),U_20423)))
    | ~ sP1217(U_20421,U_20423,U_20424,U_20419,U_20420,U_20418) ),
    inference(clausify,[status(thm)],[f_4846_3]) ).

cnf(f_4846_6,plain,
    ( ~ hBOOL(hAPP(U_20421,U_20419))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20420),U_20419),hAPP(c_List_Oset(U_20420),U_20424)))
    | ~ sP1217(U_20421,U_20423,U_20424,U_20419,U_20420,U_20418) ),
    inference(clausify,[status(thm)],[f_4846_3]) ).

fof(f_4847_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_4847_2,plain,
    ! [U_20426,U_20425] : c_List_Opartition(U_20425,U_20426,c_List_Olist_ONil(U_20425)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20425),tc_List_Olist(U_20425)),c_List_Olist_ONil(U_20425)),c_List_Olist_ONil(U_20425)),
    inference(variable_rename,[status(thm)],[f_4847_1]) ).

fof(f_4847_3,plain,
    ! [U_20425,U_20426] : c_List_Opartition(U_20425,U_20426,c_List_Olist_ONil(U_20425)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20425),tc_List_Olist(U_20425)),c_List_Olist_ONil(U_20425)),c_List_Olist_ONil(U_20425)),
    inference(definitional_conversion,[status(esa)],[f_4847_2]) ).

cnf(f_4847_4,plain,
    c_List_Opartition(U_20425,U_20426,c_List_Olist_ONil(U_20425)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_20425),tc_List_Olist(U_20425)),c_List_Olist_ONil(U_20425)),c_List_Olist_ONil(U_20425)),
    inference(clausify,[status(thm)],[f_4847_3]) ).

fof(f_4848_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_4848_2,plain,
    ! [U_20429,U_20428,U_20427] :
      ( hAPP(c_List_Ofilter(U_20427,hAPP(hAPP(c_COMBC(U_20427,tc_fun(U_20427,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20427)),hAPP(c_List_Oset(U_20427),c_List_Osublist(U_20427,U_20428,U_20429)))),U_20428) = c_List_Osublist(U_20427,U_20428,U_20429)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20427),U_20428)) ),
    inference(variable_rename,[status(thm)],[f_4848_1]) ).

fof(f_4848_3,plain,
    ! [U_20427,U_20428,U_20429] :
      ( hAPP(c_List_Ofilter(U_20427,hAPP(hAPP(c_COMBC(U_20427,tc_fun(U_20427,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20427)),hAPP(c_List_Oset(U_20427),c_List_Osublist(U_20427,U_20428,U_20429)))),U_20428) = c_List_Osublist(U_20427,U_20428,U_20429)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20427),U_20428)) ),
    inference(definitional_conversion,[status(esa)],[f_4848_2]) ).

cnf(f_4848_4,plain,
    ( hAPP(c_List_Ofilter(U_20427,hAPP(hAPP(c_COMBC(U_20427,tc_fun(U_20427,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20427)),hAPP(c_List_Oset(U_20427),c_List_Osublist(U_20427,U_20428,U_20429)))),U_20428) = c_List_Osublist(U_20427,U_20428,U_20429)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20427),U_20428)) ),
    inference(clausify,[status(thm)],[f_4848_3]) ).

fof(f_4849_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_4849_2,plain,
    ! [U_20433,U_20432,U_20431,U_20430] : c_List_Opartition(U_20430,U_20431,hAPP(hAPP(c_List_Olist_OCons(U_20430),U_20432),U_20433)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20430),tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_20430),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20430),tc_fun(tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),tc_fun(tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),tc_List_Olist(U_20430)),c_COMBS(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_fun(tc_List_Olist(U_20430),tc_fun(tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),tc_List_Olist(U_20430)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_fun(tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_List_Olist(U_20430)),hAPP(c_If(tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),hAPP(U_20431,U_20432)))),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20430),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_List_Olist(U_20430)),c_Product__Type_OPair(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),hAPP(c_List_Olist_OCons(U_20430),U_20432))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20430),tc_fun(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_fun(tc_fun(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),tc_List_Olist(U_20430)),c_COMBB(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_List_Olist(U_20430))),c_Product__Type_OPair(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),hAPP(c_List_Olist_OCons(U_20430),U_20432)))),c_List_Opartition(U_20430,U_20431,U_20433)),
    inference(variable_rename,[status(thm)],[f_4849_1]) ).

fof(f_4849_3,plain,
    ! [U_20430,U_20431,U_20432,U_20433] : c_List_Opartition(U_20430,U_20431,hAPP(hAPP(c_List_Olist_OCons(U_20430),U_20432),U_20433)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20430),tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_20430),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20430),tc_fun(tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),tc_fun(tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),tc_List_Olist(U_20430)),c_COMBS(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_fun(tc_List_Olist(U_20430),tc_fun(tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),tc_List_Olist(U_20430)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_fun(tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_List_Olist(U_20430)),hAPP(c_If(tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),hAPP(U_20431,U_20432)))),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20430),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_List_Olist(U_20430)),c_Product__Type_OPair(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),hAPP(c_List_Olist_OCons(U_20430),U_20432))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20430),tc_fun(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_fun(tc_fun(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),tc_List_Olist(U_20430)),c_COMBB(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_List_Olist(U_20430))),c_Product__Type_OPair(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),hAPP(c_List_Olist_OCons(U_20430),U_20432)))),c_List_Opartition(U_20430,U_20431,U_20433)),
    inference(definitional_conversion,[status(esa)],[f_4849_2]) ).

cnf(f_4849_4,plain,
    c_List_Opartition(U_20430,U_20431,hAPP(hAPP(c_List_Olist_OCons(U_20430),U_20432),U_20433)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20430),tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_20430),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20430),tc_fun(tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),tc_fun(tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),tc_List_Olist(U_20430)),c_COMBS(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_fun(tc_List_Olist(U_20430),tc_fun(tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),tc_List_Olist(U_20430)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_fun(tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_List_Olist(U_20430)),hAPP(c_If(tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),hAPP(U_20431,U_20432)))),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20430),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_List_Olist(U_20430)),c_Product__Type_OPair(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),hAPP(c_List_Olist_OCons(U_20430),U_20432))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20430),tc_fun(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430))),tc_fun(tc_fun(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_fun(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),tc_List_Olist(U_20430)),c_COMBB(tc_List_Olist(U_20430),tc_prod(tc_List_Olist(U_20430),tc_List_Olist(U_20430)),tc_List_Olist(U_20430))),c_Product__Type_OPair(tc_List_Olist(U_20430),tc_List_Olist(U_20430)))),hAPP(c_List_Olist_OCons(U_20430),U_20432)))),c_List_Opartition(U_20430,U_20431,U_20433)),
    inference(clausify,[status(thm)],[f_4849_3]) ).

fof(f_4850_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_4850_2,plain,
    ! [U_20436,U_20435,U_20434] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20434)),hAPP(c_List_Ofilter(U_20434,U_20435),U_20436)) = 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_20434)),U_20436)))),hAPP(hAPP(c_COMBB(U_20434,tc_HOL_Obool,tc_Nat_Onat),U_20435),hAPP(c_List_Onth(U_20434),U_20436))))),
    inference(variable_rename,[status(thm)],[f_4850_1]) ).

fof(f_4850_3,plain,
    ! [U_20434,U_20435,U_20436] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20434)),hAPP(c_List_Ofilter(U_20434,U_20435),U_20436)) = 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_20434)),U_20436)))),hAPP(hAPP(c_COMBB(U_20434,tc_HOL_Obool,tc_Nat_Onat),U_20435),hAPP(c_List_Onth(U_20434),U_20436))))),
    inference(definitional_conversion,[status(esa)],[f_4850_2]) ).

cnf(f_4850_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20434)),hAPP(c_List_Ofilter(U_20434,U_20435),U_20436)) = 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_20434)),U_20436)))),hAPP(hAPP(c_COMBB(U_20434,tc_HOL_Obool,tc_Nat_Onat),U_20435),hAPP(c_List_Onth(U_20434),U_20436))))),
    inference(clausify,[status(thm)],[f_4850_3]) ).

fof(f_4851_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_4851_2,plain,
    ! [U_20440,U_20439,U_20438,U_20437] : c_List_Omap__filter(U_20437,U_20438,U_20439,U_20440) = hAPP(hAPP(c_List_Omap(U_20437,U_20438),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_20438),U_20438,U_20437,c_Option_Othe(U_20438)),U_20439)),hAPP(c_List_Ofilter(U_20437,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20437),c_fNot),hAPP(hAPP(c_COMBC(U_20437,tc_Option_Ooption(U_20438),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_20438),tc_fun(tc_Option_Ooption(U_20438),tc_HOL_Obool),U_20437),c_fequal),U_20439)),c_Option_Ooption_ONone(U_20438)))),U_20440)),
    inference(variable_rename,[status(thm)],[f_4851_1]) ).

fof(f_4851_3,plain,
    ! [U_20437,U_20438,U_20439,U_20440] : c_List_Omap__filter(U_20437,U_20438,U_20439,U_20440) = hAPP(hAPP(c_List_Omap(U_20437,U_20438),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_20438),U_20438,U_20437,c_Option_Othe(U_20438)),U_20439)),hAPP(c_List_Ofilter(U_20437,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20437),c_fNot),hAPP(hAPP(c_COMBC(U_20437,tc_Option_Ooption(U_20438),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_20438),tc_fun(tc_Option_Ooption(U_20438),tc_HOL_Obool),U_20437),c_fequal),U_20439)),c_Option_Ooption_ONone(U_20438)))),U_20440)),
    inference(definitional_conversion,[status(esa)],[f_4851_2]) ).

cnf(f_4851_4,plain,
    c_List_Omap__filter(U_20437,U_20438,U_20439,U_20440) = hAPP(hAPP(c_List_Omap(U_20437,U_20438),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_20438),U_20438,U_20437,c_Option_Othe(U_20438)),U_20439)),hAPP(c_List_Ofilter(U_20437,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20437),c_fNot),hAPP(hAPP(c_COMBC(U_20437,tc_Option_Ooption(U_20438),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_20438),tc_fun(tc_Option_Ooption(U_20438),tc_HOL_Obool),U_20437),c_fequal),U_20439)),c_Option_Ooption_ONone(U_20438)))),U_20440)),
    inference(clausify,[status(thm)],[f_4851_3]) ).

fof(f_4852_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_4852_2,plain,
    ! [U_20442,U_20441] : c_List_Ofoldr(tc_List_Olist(U_20441),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20441)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20441))),c_List_Otranspose(U_20441,U_20442),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20441))),hAPP(c_List_Ofilter(tc_List_Olist(U_20441),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20441)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20441),tc_List_Olist(U_20441),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20441)))),U_20442)),
    inference(variable_rename,[status(thm)],[f_4852_1]) ).

fof(f_4852_3,plain,
    ! [U_20441,U_20442] : c_List_Ofoldr(tc_List_Olist(U_20441),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20441)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20441))),c_List_Otranspose(U_20441,U_20442),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20441))),hAPP(c_List_Ofilter(tc_List_Olist(U_20441),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20441)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20441),tc_List_Olist(U_20441),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20441)))),U_20442)),
    inference(definitional_conversion,[status(esa)],[f_4852_2]) ).

cnf(f_4852_4,plain,
    c_List_Ofoldr(tc_List_Olist(U_20441),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20441)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20441))),c_List_Otranspose(U_20441,U_20442),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20441))),hAPP(c_List_Ofilter(tc_List_Olist(U_20441),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20441)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20441),tc_List_Olist(U_20441),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20441)))),U_20442)),
    inference(clausify,[status(thm)],[f_4852_3]) ).

fof(f_4853_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_4853_2,plain,
    ! [U_20448,U_20447,U_20446,U_20445,U_20444,U_20443] :
      ( hAPP(c_Map_Omap__of(U_20443,U_20444,hAPP(c_List_Ofilter(tc_prod(U_20443,U_20444),hAPP(c_Product__Type_Oprod_Oprod__case(U_20443,U_20444,tc_HOL_Obool),U_20448)),U_20445)),U_20446) = hAPP(c_Option_Ooption_OSome(U_20444),U_20447)
      | ~ hBOOL(hAPP(hAPP(U_20448,U_20446),U_20447))
      | hAPP(c_Map_Omap__of(U_20443,U_20444,U_20445),U_20446) != hAPP(c_Option_Ooption_OSome(U_20444),U_20447) ),
    inference(variable_rename,[status(thm)],[f_4853_1]) ).

fof(f_4853_3,plain,
    ! [U_20443,U_20444,U_20445,U_20446,U_20447,U_20448] :
      ( hAPP(c_Map_Omap__of(U_20443,U_20444,hAPP(c_List_Ofilter(tc_prod(U_20443,U_20444),hAPP(c_Product__Type_Oprod_Oprod__case(U_20443,U_20444,tc_HOL_Obool),U_20448)),U_20445)),U_20446) = hAPP(c_Option_Ooption_OSome(U_20444),U_20447)
      | ~ hBOOL(hAPP(hAPP(U_20448,U_20446),U_20447))
      | hAPP(c_Map_Omap__of(U_20443,U_20444,U_20445),U_20446) != hAPP(c_Option_Ooption_OSome(U_20444),U_20447) ),
    inference(definitional_conversion,[status(esa)],[f_4853_2]) ).

cnf(f_4853_4,plain,
    ( hAPP(c_Map_Omap__of(U_20443,U_20444,hAPP(c_List_Ofilter(tc_prod(U_20443,U_20444),hAPP(c_Product__Type_Oprod_Oprod__case(U_20443,U_20444,tc_HOL_Obool),U_20448)),U_20445)),U_20446) = hAPP(c_Option_Ooption_OSome(U_20444),U_20447)
    | ~ hBOOL(hAPP(hAPP(U_20448,U_20446),U_20447))
    | hAPP(c_Map_Omap__of(U_20443,U_20444,U_20445),U_20446) != hAPP(c_Option_Ooption_OSome(U_20444),U_20447) ),
    inference(clausify,[status(thm)],[f_4853_3]) ).

fof(f_4854_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_4854_2,plain,
    ! [U_20452,U_20451,U_20450,U_20449] : c_List_Otranspose(U_20449,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20450),tc_List_Olist(U_20449)),hAPP(c_List_Omap(U_20450,U_20449),U_20451)),U_20452)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20450),tc_List_Olist(U_20449)),hAPP(c_List_Omap(U_20450,U_20449),U_20451)),c_List_Otranspose(U_20450,U_20452)),
    inference(variable_rename,[status(thm)],[f_4854_1]) ).

fof(f_4854_3,plain,
    ! [U_20449,U_20450,U_20451,U_20452] : c_List_Otranspose(U_20449,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20450),tc_List_Olist(U_20449)),hAPP(c_List_Omap(U_20450,U_20449),U_20451)),U_20452)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20450),tc_List_Olist(U_20449)),hAPP(c_List_Omap(U_20450,U_20449),U_20451)),c_List_Otranspose(U_20450,U_20452)),
    inference(definitional_conversion,[status(esa)],[f_4854_2]) ).

cnf(f_4854_4,plain,
    c_List_Otranspose(U_20449,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20450),tc_List_Olist(U_20449)),hAPP(c_List_Omap(U_20450,U_20449),U_20451)),U_20452)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20450),tc_List_Olist(U_20449)),hAPP(c_List_Omap(U_20450,U_20449),U_20451)),c_List_Otranspose(U_20450,U_20452)),
    inference(clausify,[status(thm)],[f_4854_3]) ).

fof(f_4855_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_4855_2,plain,
    ! [U_20454,U_20453] : c_List_Otranspose(U_20453,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20453)),c_List_Olist_ONil(U_20453)),U_20454)) = c_List_Otranspose(U_20453,U_20454),
    inference(variable_rename,[status(thm)],[f_4855_1]) ).

fof(f_4855_3,plain,
    ! [U_20453,U_20454] : c_List_Otranspose(U_20453,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20453)),c_List_Olist_ONil(U_20453)),U_20454)) = c_List_Otranspose(U_20453,U_20454),
    inference(definitional_conversion,[status(esa)],[f_4855_2]) ).

cnf(f_4855_4,plain,
    c_List_Otranspose(U_20453,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20453)),c_List_Olist_ONil(U_20453)),U_20454)) = c_List_Otranspose(U_20453,U_20454),
    inference(clausify,[status(thm)],[f_4855_3]) ).

fof(f_4856_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_4856_2,plain,
    ! [U_20458,U_20457] :
      ( ( c_List_Otranspose(U_20457,U_20458) = c_List_Olist_ONil(tc_List_Olist(U_20457))
        | ? [U_20456] :
            ( U_20456 != c_List_Olist_ONil(U_20457)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20457)),U_20456),hAPP(c_List_Oset(tc_List_Olist(U_20457)),U_20458))) ) )
      & ( ! [U_20455] :
            ( U_20455 = c_List_Olist_ONil(U_20457)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20457)),U_20455),hAPP(c_List_Oset(tc_List_Olist(U_20457)),U_20458))) )
        | c_List_Otranspose(U_20457,U_20458) != c_List_Olist_ONil(tc_List_Olist(U_20457)) ) ),
    inference(variable_rename,[status(thm)],[f_4856_1]) ).

fof(f_4856_3,plain,
    ( ! [U_20462,U_20460] :
        ( c_List_Otranspose(U_20460,U_20462) = c_List_Olist_ONil(tc_List_Olist(U_20460))
        | ? [U_20456] :
            ( U_20456 != c_List_Olist_ONil(U_20460)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20460)),U_20456),hAPP(c_List_Oset(tc_List_Olist(U_20460)),U_20462))) ) )
    & ! [U_20461,U_20459] :
        ( ! [U_20455] :
            ( U_20455 = c_List_Olist_ONil(U_20459)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20459)),U_20455),hAPP(c_List_Oset(tc_List_Olist(U_20459)),U_20461))) )
        | c_List_Otranspose(U_20459,U_20461) != c_List_Olist_ONil(tc_List_Olist(U_20459)) ) ),
    inference(miniscope,[status(thm)],[f_4856_2]) ).

fof(f_4856_4,plain,
    ( ! [U_20462,U_20460] :
        ( c_List_Otranspose(U_20460,U_20462) = c_List_Olist_ONil(tc_List_Olist(U_20460))
        | ( sK501(U_20462,U_20460) != c_List_Olist_ONil(U_20460)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20460)),sK501(U_20462,U_20460)),hAPP(c_List_Oset(tc_List_Olist(U_20460)),U_20462))) ) )
    & ! [U_20461,U_20459] :
        ( ! [U_20455] :
            ( U_20455 = c_List_Olist_ONil(U_20459)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20459)),U_20455),hAPP(c_List_Oset(tc_List_Olist(U_20459)),U_20461))) )
        | c_List_Otranspose(U_20459,U_20461) != c_List_Olist_ONil(tc_List_Olist(U_20459)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK501]),skolemize(U_20456,sK501(U_20462,U_20460))],[f_4856_3]) ).

fof(f_4856_5,plain,
    ( ! [U_20462,U_20460] :
        ( sK501(U_20462,U_20460) != c_List_Olist_ONil(U_20460)
        | ~ sP1218(U_20462,U_20460) )
    & ! [U_20462,U_20460] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20460)),sK501(U_20462,U_20460)),hAPP(c_List_Oset(tc_List_Olist(U_20460)),U_20462)))
        | ~ sP1218(U_20462,U_20460) )
    & ! [U_20462,U_20460] :
        ( c_List_Otranspose(U_20460,U_20462) = c_List_Olist_ONil(tc_List_Olist(U_20460))
        | sP1218(U_20462,U_20460) )
    & ! [U_20461,U_20455,U_20459] :
        ( U_20455 = c_List_Olist_ONil(U_20459)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20459)),U_20455),hAPP(c_List_Oset(tc_List_Olist(U_20459)),U_20461)))
        | c_List_Otranspose(U_20459,U_20461) != c_List_Olist_ONil(tc_List_Olist(U_20459)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1218])],[f_4856_4]) ).

cnf(f_4856_6,plain,
    ( U_20455 = c_List_Olist_ONil(U_20459)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20459)),U_20455),hAPP(c_List_Oset(tc_List_Olist(U_20459)),U_20461)))
    | c_List_Otranspose(U_20459,U_20461) != c_List_Olist_ONil(tc_List_Olist(U_20459)) ),
    inference(clausify,[status(thm)],[f_4856_5]) ).

cnf(f_4856_7,plain,
    ( c_List_Otranspose(U_20460,U_20462) = c_List_Olist_ONil(tc_List_Olist(U_20460))
    | sP1218(U_20462,U_20460) ),
    inference(clausify,[status(thm)],[f_4856_5]) ).

cnf(f_4856_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20460)),sK501(U_20462,U_20460)),hAPP(c_List_Oset(tc_List_Olist(U_20460)),U_20462)))
    | ~ sP1218(U_20462,U_20460) ),
    inference(clausify,[status(thm)],[f_4856_5]) ).

cnf(f_4856_9,plain,
    ( sK501(U_20462,U_20460) != c_List_Olist_ONil(U_20460)
    | ~ sP1218(U_20462,U_20460) ),
    inference(clausify,[status(thm)],[f_4856_5]) ).

fof(f_4857_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_4857_2,plain,
    ! [U_20465,U_20464,U_20463] : c_List_Omap__filter(U_20463,U_20464,U_20465,c_List_Olist_ONil(U_20463)) = c_List_Olist_ONil(U_20464),
    inference(variable_rename,[status(thm)],[f_4857_1]) ).

fof(f_4857_3,plain,
    ! [U_20465,U_20464,U_20463] : c_List_Omap__filter(U_20463,U_20464,U_20465,c_List_Olist_ONil(U_20463)) = c_List_Olist_ONil(U_20464),
    inference(definitional_conversion,[status(esa)],[f_4857_2]) ).

cnf(f_4857_4,plain,
    c_List_Omap__filter(U_20463,U_20464,U_20465,c_List_Olist_ONil(U_20463)) = c_List_Olist_ONil(U_20464),
    inference(clausify,[status(thm)],[f_4857_3]) ).

fof(f_4858_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_4858_2,plain,
    ! [U_20466] : c_List_Otranspose(U_20466,c_List_Olist_ONil(tc_List_Olist(U_20466))) = c_List_Olist_ONil(tc_List_Olist(U_20466)),
    inference(variable_rename,[status(thm)],[f_4858_1]) ).

fof(f_4858_3,plain,
    ! [U_20466] : c_List_Otranspose(U_20466,c_List_Olist_ONil(tc_List_Olist(U_20466))) = c_List_Olist_ONil(tc_List_Olist(U_20466)),
    inference(definitional_conversion,[status(esa)],[f_4858_2]) ).

cnf(f_4858_4,plain,
    c_List_Otranspose(U_20466,c_List_Olist_ONil(tc_List_Olist(U_20466))) = c_List_Olist_ONil(tc_List_Olist(U_20466)),
    inference(clausify,[status(thm)],[f_4858_3]) ).

fof(f_4859_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_4859_2,plain,
    ! [U_20471,U_20470,U_20469,U_20468,U_20467] : c_List_Omap__filter(U_20467,U_20468,U_20469,hAPP(hAPP(c_List_Olist_OCons(U_20467),U_20470),U_20471)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(U_20468),U_20468,c_List_Omap__filter(U_20467,U_20468,U_20469,U_20471),hAPP(hAPP(c_COMBC(U_20468,tc_List_Olist(U_20468),tc_List_Olist(U_20468)),c_List_Olist_OCons(U_20468)),c_List_Omap__filter(U_20467,U_20468,U_20469,U_20471))),hAPP(U_20469,U_20470)),
    inference(variable_rename,[status(thm)],[f_4859_1]) ).

fof(f_4859_3,plain,
    ! [U_20467,U_20468,U_20469,U_20470,U_20471] : c_List_Omap__filter(U_20467,U_20468,U_20469,hAPP(hAPP(c_List_Olist_OCons(U_20467),U_20470),U_20471)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(U_20468),U_20468,c_List_Omap__filter(U_20467,U_20468,U_20469,U_20471),hAPP(hAPP(c_COMBC(U_20468,tc_List_Olist(U_20468),tc_List_Olist(U_20468)),c_List_Olist_OCons(U_20468)),c_List_Omap__filter(U_20467,U_20468,U_20469,U_20471))),hAPP(U_20469,U_20470)),
    inference(definitional_conversion,[status(esa)],[f_4859_2]) ).

cnf(f_4859_4,plain,
    c_List_Omap__filter(U_20467,U_20468,U_20469,hAPP(hAPP(c_List_Olist_OCons(U_20467),U_20470),U_20471)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(U_20468),U_20468,c_List_Omap__filter(U_20467,U_20468,U_20469,U_20471),hAPP(hAPP(c_COMBC(U_20468,tc_List_Olist(U_20468),tc_List_Olist(U_20468)),c_List_Olist_OCons(U_20468)),c_List_Omap__filter(U_20467,U_20468,U_20469,U_20471))),hAPP(U_20469,U_20470)),
    inference(clausify,[status(thm)],[f_4859_3]) ).

fof(f_4860_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_4860_2,plain,
    ! [U_20475,U_20474,U_20473,U_20472] : hAPP(hAPP(c_List_Omap(tc_prod(U_20472,tc_Nat_Onat),U_20472),c_Product__Type_Ofst(U_20472,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20472,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20472,tc_Nat_Onat)),U_20473),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(U_20472,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(U_20472,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(U_20472,tc_Nat_Onat),U_20474),U_20475))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20472,tc_Nat_Onat),U_20472),c_Product__Type_Ofst(U_20472,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20472,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20472,tc_Nat_Onat)),U_20473),c_Product__Type_Osnd(U_20472,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(U_20472,tc_Nat_Onat),U_20474),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),U_20475)))),
    inference(variable_rename,[status(thm)],[f_4860_1]) ).

fof(f_4860_3,plain,
    ! [U_20472,U_20473,U_20474,U_20475] : hAPP(hAPP(c_List_Omap(tc_prod(U_20472,tc_Nat_Onat),U_20472),c_Product__Type_Ofst(U_20472,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20472,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20472,tc_Nat_Onat)),U_20473),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(U_20472,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(U_20472,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(U_20472,tc_Nat_Onat),U_20474),U_20475))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20472,tc_Nat_Onat),U_20472),c_Product__Type_Ofst(U_20472,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20472,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20472,tc_Nat_Onat)),U_20473),c_Product__Type_Osnd(U_20472,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(U_20472,tc_Nat_Onat),U_20474),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),U_20475)))),
    inference(definitional_conversion,[status(esa)],[f_4860_2]) ).

cnf(f_4860_4,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_20472,tc_Nat_Onat),U_20472),c_Product__Type_Ofst(U_20472,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20472,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20472,tc_Nat_Onat)),U_20473),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(U_20472,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(U_20472,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(U_20472,tc_Nat_Onat),U_20474),U_20475))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20472,tc_Nat_Onat),U_20472),c_Product__Type_Ofst(U_20472,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20472,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20472,tc_Nat_Onat)),U_20473),c_Product__Type_Osnd(U_20472,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(U_20472,tc_Nat_Onat),U_20474),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),U_20475)))),
    inference(clausify,[status(thm)],[f_4860_3]) ).

fof(f_4861_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_4861_2,plain,
    ! [U_20477,U_20476] : c_Random_Oselect__weight(U_20476,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20476),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20476,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20476,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20476)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20477)) = c_Random_Oselect__weight(U_20476,U_20477),
    inference(variable_rename,[status(thm)],[f_4861_1]) ).

fof(f_4861_3,plain,
    ! [U_20476,U_20477] : c_Random_Oselect__weight(U_20476,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20476),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20476,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20476,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20476)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20477)) = c_Random_Oselect__weight(U_20476,U_20477),
    inference(definitional_conversion,[status(esa)],[f_4861_2]) ).

cnf(f_4861_4,plain,
    c_Random_Oselect__weight(U_20476,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20476),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20476,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20476,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20476)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20477)) = c_Random_Oselect__weight(U_20476,U_20477),
    inference(clausify,[status(thm)],[f_4861_3]) ).

fof(f_4862_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_4862_2,plain,
    ! [U_20479,U_20478] : c_Random_Opick(U_20478,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20478),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20478,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20478,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20478)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20479)) = c_Random_Opick(U_20478,U_20479),
    inference(variable_rename,[status(thm)],[f_4862_1]) ).

fof(f_4862_3,plain,
    ! [U_20478,U_20479] : c_Random_Opick(U_20478,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20478),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20478,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20478,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20478)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20479)) = c_Random_Opick(U_20478,U_20479),
    inference(definitional_conversion,[status(esa)],[f_4862_2]) ).

cnf(f_4862_4,plain,
    c_Random_Opick(U_20478,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20478),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20478,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20478,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20478)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20479)) = c_Random_Opick(U_20478,U_20479),
    inference(clausify,[status(thm)],[f_4862_3]) ).

fof(f_4863_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_4863_2,plain,
    ! [U_20482,U_20481,U_20480] :
      ( hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20481)),c_List_Otranspose(U_20481,U_20482)),U_20480) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20481),U_20481),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20481),tc_Nat_Onat,U_20481),c_List_Onth(U_20481)),U_20480)),hAPP(c_List_Ofilter(tc_List_Olist(U_20481),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20481)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20480)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20481)))),U_20482))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20480),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20481))),c_List_Otranspose(U_20481,U_20482)))) ),
    inference(variable_rename,[status(thm)],[f_4863_1]) ).

fof(f_4863_3,plain,
    ! [U_20480,U_20481,U_20482] :
      ( hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20481)),c_List_Otranspose(U_20481,U_20482)),U_20480) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20481),U_20481),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20481),tc_Nat_Onat,U_20481),c_List_Onth(U_20481)),U_20480)),hAPP(c_List_Ofilter(tc_List_Olist(U_20481),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20481)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20480)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20481)))),U_20482))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20480),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20481))),c_List_Otranspose(U_20481,U_20482)))) ),
    inference(definitional_conversion,[status(esa)],[f_4863_2]) ).

cnf(f_4863_4,plain,
    ( hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20481)),c_List_Otranspose(U_20481,U_20482)),U_20480) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20481),U_20481),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20481),tc_Nat_Onat,U_20481),c_List_Onth(U_20481)),U_20480)),hAPP(c_List_Ofilter(tc_List_Olist(U_20481),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20481)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20480)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20481)))),U_20482))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20480),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20481))),c_List_Otranspose(U_20481,U_20482)))) ),
    inference(clausify,[status(thm)],[f_4863_3]) ).

fof(f_4864_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_4864_2,plain,
    ! [U_20484,U_20483] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20483))),c_List_Otranspose(U_20483,U_20484)) = c_List_Ofoldr(tc_List_Olist(U_20483),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20483)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20483))),U_20484,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4864_1]) ).

fof(f_4864_3,plain,
    ! [U_20483,U_20484] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20483))),c_List_Otranspose(U_20483,U_20484)) = c_List_Ofoldr(tc_List_Olist(U_20483),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20483)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20483))),U_20484,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_4864_2]) ).

cnf(f_4864_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20483))),c_List_Otranspose(U_20483,U_20484)) = c_List_Ofoldr(tc_List_Olist(U_20483),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20483)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20483))),U_20484,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4864_3]) ).

fof(f_4865_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_4865_2,plain,
    ! [U_20489,U_20488,U_20487,U_20486,U_20485] : hAPP(hAPP(c_List_Omap(U_20485,U_20486),U_20487),hAPP(c_List_Ofilter(U_20485,U_20488),U_20489)) = c_List_Omap__filter(U_20485,U_20486,hAPP(hAPP(c_COMBC(U_20485,tc_Option_Ooption(U_20486),tc_Option_Ooption(U_20486)),hAPP(hAPP(c_COMBS(U_20485,tc_Option_Ooption(U_20486),tc_fun(tc_Option_Ooption(U_20486),tc_Option_Ooption(U_20486))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_20486),tc_fun(tc_Option_Ooption(U_20486),tc_Option_Ooption(U_20486))),U_20485),c_If(tc_Option_Ooption(U_20486))),U_20488)),hAPP(hAPP(c_COMBB(U_20486,tc_Option_Ooption(U_20486),U_20485),c_Option_Ooption_OSome(U_20486)),U_20487))),c_Option_Ooption_ONone(U_20486)),U_20489),
    inference(variable_rename,[status(thm)],[f_4865_1]) ).

fof(f_4865_3,plain,
    ! [U_20485,U_20486,U_20487,U_20488,U_20489] : hAPP(hAPP(c_List_Omap(U_20485,U_20486),U_20487),hAPP(c_List_Ofilter(U_20485,U_20488),U_20489)) = c_List_Omap__filter(U_20485,U_20486,hAPP(hAPP(c_COMBC(U_20485,tc_Option_Ooption(U_20486),tc_Option_Ooption(U_20486)),hAPP(hAPP(c_COMBS(U_20485,tc_Option_Ooption(U_20486),tc_fun(tc_Option_Ooption(U_20486),tc_Option_Ooption(U_20486))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_20486),tc_fun(tc_Option_Ooption(U_20486),tc_Option_Ooption(U_20486))),U_20485),c_If(tc_Option_Ooption(U_20486))),U_20488)),hAPP(hAPP(c_COMBB(U_20486,tc_Option_Ooption(U_20486),U_20485),c_Option_Ooption_OSome(U_20486)),U_20487))),c_Option_Ooption_ONone(U_20486)),U_20489),
    inference(definitional_conversion,[status(esa)],[f_4865_2]) ).

cnf(f_4865_4,plain,
    hAPP(hAPP(c_List_Omap(U_20485,U_20486),U_20487),hAPP(c_List_Ofilter(U_20485,U_20488),U_20489)) = c_List_Omap__filter(U_20485,U_20486,hAPP(hAPP(c_COMBC(U_20485,tc_Option_Ooption(U_20486),tc_Option_Ooption(U_20486)),hAPP(hAPP(c_COMBS(U_20485,tc_Option_Ooption(U_20486),tc_fun(tc_Option_Ooption(U_20486),tc_Option_Ooption(U_20486))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_20486),tc_fun(tc_Option_Ooption(U_20486),tc_Option_Ooption(U_20486))),U_20485),c_If(tc_Option_Ooption(U_20486))),U_20488)),hAPP(hAPP(c_COMBB(U_20486,tc_Option_Ooption(U_20486),U_20485),c_Option_Ooption_OSome(U_20486)),U_20487))),c_Option_Ooption_ONone(U_20486)),U_20489),
    inference(clausify,[status(thm)],[f_4865_3]) ).

fof(f_4866_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_4866_2,plain,
    ! [U_20494,U_20493,U_20492,U_20491,U_20490] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20491,U_20490,U_20494),U_20492),c_List_Oremove1(U_20491,U_20492,U_20493)) = U_20493
      | hAPP(c_List_Ohd(U_20491),hAPP(c_List_Ofilter(U_20491,hAPP(hAPP(c_COMBB(U_20490,tc_HOL_Obool,U_20491),hAPP(c_fequal,hAPP(U_20494,U_20492))),U_20494)),U_20493)) != U_20492
      | ~ c_List_Olinorder__class_Osorted(U_20490,hAPP(hAPP(c_List_Omap(U_20491,U_20490),U_20494),U_20493))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20491),U_20492),hAPP(c_List_Oset(U_20491),U_20493)))
      | ~ class_Orderings_Olinorder(U_20490) ),
    inference(variable_rename,[status(thm)],[f_4866_1]) ).

fof(f_4866_3,plain,
    ! [U_20490,U_20491,U_20492,U_20493,U_20494] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20491,U_20490,U_20494),U_20492),c_List_Oremove1(U_20491,U_20492,U_20493)) = U_20493
      | hAPP(c_List_Ohd(U_20491),hAPP(c_List_Ofilter(U_20491,hAPP(hAPP(c_COMBB(U_20490,tc_HOL_Obool,U_20491),hAPP(c_fequal,hAPP(U_20494,U_20492))),U_20494)),U_20493)) != U_20492
      | ~ c_List_Olinorder__class_Osorted(U_20490,hAPP(hAPP(c_List_Omap(U_20491,U_20490),U_20494),U_20493))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20491),U_20492),hAPP(c_List_Oset(U_20491),U_20493)))
      | ~ class_Orderings_Olinorder(U_20490) ),
    inference(definitional_conversion,[status(esa)],[f_4866_2]) ).

cnf(f_4866_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20491,U_20490,U_20494),U_20492),c_List_Oremove1(U_20491,U_20492,U_20493)) = U_20493
    | hAPP(c_List_Ohd(U_20491),hAPP(c_List_Ofilter(U_20491,hAPP(hAPP(c_COMBB(U_20490,tc_HOL_Obool,U_20491),hAPP(c_fequal,hAPP(U_20494,U_20492))),U_20494)),U_20493)) != U_20492
    | ~ c_List_Olinorder__class_Osorted(U_20490,hAPP(hAPP(c_List_Omap(U_20491,U_20490),U_20494),U_20493))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20491),U_20492),hAPP(c_List_Oset(U_20491),U_20493)))
    | ~ class_Orderings_Olinorder(U_20490) ),
    inference(clausify,[status(thm)],[f_4866_3]) ).

fof(f_4867_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_4867_2,plain,
    ! [U_20497,U_20496,U_20495] : c_List_Osublist(U_20495,U_20496,U_20497) = hAPP(hAPP(c_List_Omap(tc_prod(U_20495,tc_Nat_Onat),U_20495),c_Product__Type_Ofst(U_20495,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20495,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20495,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_20495,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20495,tc_Nat_Onat))),U_20497)),hAPP(hAPP(c_List_Ozip(U_20495,tc_Nat_Onat),U_20496),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20495)),U_20496))))),
    inference(variable_rename,[status(thm)],[f_4867_1]) ).

fof(f_4867_3,plain,
    ! [U_20495,U_20496,U_20497] : c_List_Osublist(U_20495,U_20496,U_20497) = hAPP(hAPP(c_List_Omap(tc_prod(U_20495,tc_Nat_Onat),U_20495),c_Product__Type_Ofst(U_20495,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20495,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20495,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_20495,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20495,tc_Nat_Onat))),U_20497)),hAPP(hAPP(c_List_Ozip(U_20495,tc_Nat_Onat),U_20496),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20495)),U_20496))))),
    inference(definitional_conversion,[status(esa)],[f_4867_2]) ).

cnf(f_4867_4,plain,
    c_List_Osublist(U_20495,U_20496,U_20497) = hAPP(hAPP(c_List_Omap(tc_prod(U_20495,tc_Nat_Onat),U_20495),c_Product__Type_Ofst(U_20495,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20495,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20495,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_20495,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20495,tc_Nat_Onat))),U_20497)),hAPP(hAPP(c_List_Ozip(U_20495,tc_Nat_Onat),U_20496),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20495)),U_20496))))),
    inference(clausify,[status(thm)],[f_4867_3]) ).

fof(f_4868_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_4868_2,plain,
    ! [U_20498] :
      ( c_List_Olinorder__class_Osorted(U_20498,c_List_Olist_ONil(U_20498))
      | ~ class_Orderings_Olinorder(U_20498) ),
    inference(variable_rename,[status(thm)],[f_4868_1]) ).

fof(f_4868_3,plain,
    ! [U_20498] :
      ( c_List_Olinorder__class_Osorted(U_20498,c_List_Olist_ONil(U_20498))
      | ~ class_Orderings_Olinorder(U_20498) ),
    inference(definitional_conversion,[status(esa)],[f_4868_2]) ).

cnf(f_4868_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20498,c_List_Olist_ONil(U_20498))
    | ~ class_Orderings_Olinorder(U_20498) ),
    inference(clausify,[status(thm)],[f_4868_3]) ).

fof(f_4869_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_4869_2,plain,
    ! [U_20500,U_20499] :
      ( c_List_Olinorder__class_Osorted(U_20499,hAPP(hAPP(c_List_Olist_OCons(U_20499),U_20500),c_List_Olist_ONil(U_20499)))
      | ~ class_Orderings_Olinorder(U_20499) ),
    inference(variable_rename,[status(thm)],[f_4869_1]) ).

fof(f_4869_3,plain,
    ! [U_20499,U_20500] :
      ( c_List_Olinorder__class_Osorted(U_20499,hAPP(hAPP(c_List_Olist_OCons(U_20499),U_20500),c_List_Olist_ONil(U_20499)))
      | ~ class_Orderings_Olinorder(U_20499) ),
    inference(definitional_conversion,[status(esa)],[f_4869_2]) ).

cnf(f_4869_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20499,hAPP(hAPP(c_List_Olist_OCons(U_20499),U_20500),c_List_Olist_ONil(U_20499)))
    | ~ class_Orderings_Olinorder(U_20499) ),
    inference(clausify,[status(thm)],[f_4869_3]) ).

fof(f_4870_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_4870_2,plain,
    ! [U_20503,U_20502,U_20501] :
      ( c_List_Olinorder__class_Osorted(U_20501,hAPP(c_List_Ofilter(U_20501,hAPP(hAPP(c_COMBC(U_20501,U_20501,tc_HOL_Obool),c_fequal),hAPP(U_20502,U_20503))),U_20503))
      | ~ class_Orderings_Olinorder(U_20501) ),
    inference(variable_rename,[status(thm)],[f_4870_1]) ).

fof(f_4870_3,plain,
    ! [U_20501,U_20502,U_20503] :
      ( c_List_Olinorder__class_Osorted(U_20501,hAPP(c_List_Ofilter(U_20501,hAPP(hAPP(c_COMBC(U_20501,U_20501,tc_HOL_Obool),c_fequal),hAPP(U_20502,U_20503))),U_20503))
      | ~ class_Orderings_Olinorder(U_20501) ),
    inference(definitional_conversion,[status(esa)],[f_4870_2]) ).

cnf(f_4870_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20501,hAPP(c_List_Ofilter(U_20501,hAPP(hAPP(c_COMBC(U_20501,U_20501,tc_HOL_Obool),c_fequal),hAPP(U_20502,U_20503))),U_20503))
    | ~ class_Orderings_Olinorder(U_20501) ),
    inference(clausify,[status(thm)],[f_4870_3]) ).

fof(f_4871_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_4871_2,plain,
    ! [U_20508,U_20507,U_20506,U_20505,U_20504] :
      ( c_List_Olinorder__class_Osorted(U_20504,hAPP(hAPP(c_List_Omap(U_20505,U_20504),U_20506),hAPP(c_List_Ofilter(U_20505,hAPP(hAPP(c_COMBC(U_20505,U_20504,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20504,tc_fun(U_20504,tc_HOL_Obool),U_20505),c_fequal),U_20506)),hAPP(U_20507,U_20508))),U_20508)))
      | ~ class_Orderings_Olinorder(U_20504) ),
    inference(variable_rename,[status(thm)],[f_4871_1]) ).

fof(f_4871_3,plain,
    ! [U_20504,U_20505,U_20506,U_20507,U_20508] :
      ( c_List_Olinorder__class_Osorted(U_20504,hAPP(hAPP(c_List_Omap(U_20505,U_20504),U_20506),hAPP(c_List_Ofilter(U_20505,hAPP(hAPP(c_COMBC(U_20505,U_20504,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20504,tc_fun(U_20504,tc_HOL_Obool),U_20505),c_fequal),U_20506)),hAPP(U_20507,U_20508))),U_20508)))
      | ~ class_Orderings_Olinorder(U_20504) ),
    inference(definitional_conversion,[status(esa)],[f_4871_2]) ).

cnf(f_4871_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20504,hAPP(hAPP(c_List_Omap(U_20505,U_20504),U_20506),hAPP(c_List_Ofilter(U_20505,hAPP(hAPP(c_COMBC(U_20505,U_20504,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20504,tc_fun(U_20504,tc_HOL_Obool),U_20505),c_fequal),U_20506)),hAPP(U_20507,U_20508))),U_20508)))
    | ~ class_Orderings_Olinorder(U_20504) ),
    inference(clausify,[status(thm)],[f_4871_3]) ).

fof(f_4872_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_4872_2,plain,
    ! [U_20513,U_20512,U_20511,U_20510,U_20509] :
      ( c_List_Olinorder__class_Osorted(U_20509,hAPP(hAPP(c_List_Omap(U_20510,U_20509),U_20511),hAPP(c_List_Ofilter(U_20510,U_20513),U_20512)))
      | ~ c_List_Olinorder__class_Osorted(U_20509,hAPP(hAPP(c_List_Omap(U_20510,U_20509),U_20511),U_20512))
      | ~ class_Orderings_Olinorder(U_20509) ),
    inference(variable_rename,[status(thm)],[f_4872_1]) ).

fof(f_4872_3,plain,
    ! [U_20510,U_20509,U_20511,U_20512,U_20513] :
      ( c_List_Olinorder__class_Osorted(U_20509,hAPP(hAPP(c_List_Omap(U_20510,U_20509),U_20511),hAPP(c_List_Ofilter(U_20510,U_20513),U_20512)))
      | ~ c_List_Olinorder__class_Osorted(U_20509,hAPP(hAPP(c_List_Omap(U_20510,U_20509),U_20511),U_20512))
      | ~ class_Orderings_Olinorder(U_20509) ),
    inference(definitional_conversion,[status(esa)],[f_4872_2]) ).

cnf(f_4872_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20509,hAPP(hAPP(c_List_Omap(U_20510,U_20509),U_20511),hAPP(c_List_Ofilter(U_20510,U_20513),U_20512)))
    | ~ c_List_Olinorder__class_Osorted(U_20509,hAPP(hAPP(c_List_Omap(U_20510,U_20509),U_20511),U_20512))
    | ~ class_Orderings_Olinorder(U_20509) ),
    inference(clausify,[status(thm)],[f_4872_3]) ).

fof(f_4873_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_4873_2,plain,
    ! [U_20515,U_20514] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(U_20514,U_20515)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20515),U_20514),
    inference(variable_rename,[status(thm)],[f_4873_1]) ).

fof(f_4873_3,plain,
    ! [U_20515,U_20514] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(U_20514,U_20515)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20515),U_20514),
    inference(definitional_conversion,[status(esa)],[f_4873_2]) ).

cnf(f_4873_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(U_20514,U_20515)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20515),U_20514),
    inference(clausify,[status(thm)],[f_4873_3]) ).

fof(f_4874_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_4874_2,plain,
    ! [U_20517,U_20516] :
      ( c_List_Olinorder__class_Osorted(U_20516,c_List_Obutlast(U_20516,U_20517))
      | ~ c_List_Olinorder__class_Osorted(U_20516,U_20517)
      | U_20517 = c_List_Olist_ONil(U_20516)
      | ~ class_Orderings_Olinorder(U_20516) ),
    inference(variable_rename,[status(thm)],[f_4874_1]) ).

fof(f_4874_3,plain,
    ! [U_20516,U_20517] :
      ( c_List_Olinorder__class_Osorted(U_20516,c_List_Obutlast(U_20516,U_20517))
      | ~ c_List_Olinorder__class_Osorted(U_20516,U_20517)
      | U_20517 = c_List_Olist_ONil(U_20516)
      | ~ class_Orderings_Olinorder(U_20516) ),
    inference(definitional_conversion,[status(esa)],[f_4874_2]) ).

cnf(f_4874_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20516,c_List_Obutlast(U_20516,U_20517))
    | ~ c_List_Olinorder__class_Osorted(U_20516,U_20517)
    | U_20517 = c_List_Olist_ONil(U_20516)
    | ~ class_Orderings_Olinorder(U_20516) ),
    inference(clausify,[status(thm)],[f_4874_3]) ).

fof(f_4875_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_4875_2,plain,
    ! [U_20519,U_20518] :
      ( c_List_Oupt(U_20518,hAPP(c_Nat_OSuc,U_20519)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20518,U_20519)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20519),c_List_Olist_ONil(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20518),U_20519)) ),
    inference(variable_rename,[status(thm)],[f_4875_1]) ).

fof(f_4875_3,plain,
    ! [U_20518,U_20519] :
      ( c_List_Oupt(U_20518,hAPP(c_Nat_OSuc,U_20519)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20518,U_20519)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20519),c_List_Olist_ONil(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20518),U_20519)) ),
    inference(definitional_conversion,[status(esa)],[f_4875_2]) ).

cnf(f_4875_4,plain,
    ( c_List_Oupt(U_20518,hAPP(c_Nat_OSuc,U_20519)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20518,U_20519)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20519),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20518),U_20519)) ),
    inference(clausify,[status(thm)],[f_4875_3]) ).

fof(f_4876_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_4876_2,plain,
    ! [U_20521,U_20520] :
      ( ( c_List_Oupt(U_20520,hAPP(c_Nat_OSuc,U_20521)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20520),U_20521)) )
      & ( c_List_Oupt(U_20520,hAPP(c_Nat_OSuc,U_20521)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20520,U_20521)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20521),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20520),U_20521)) ) ),
    inference(variable_rename,[status(thm)],[f_4876_1]) ).

fof(f_4876_3,plain,
    ( ! [U_20525,U_20523] :
        ( c_List_Oupt(U_20523,hAPP(c_Nat_OSuc,U_20525)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20523),U_20525)) )
    & ! [U_20524,U_20522] :
        ( c_List_Oupt(U_20522,hAPP(c_Nat_OSuc,U_20524)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20522,U_20524)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20524),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20522),U_20524)) ) ),
    inference(miniscope,[status(thm)],[f_4876_2]) ).

fof(f_4876_4,plain,
    ( ! [U_20523,U_20525] :
        ( c_List_Oupt(U_20523,hAPP(c_Nat_OSuc,U_20525)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20523),U_20525)) )
    & ! [U_20524,U_20522] :
        ( c_List_Oupt(U_20522,hAPP(c_Nat_OSuc,U_20524)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20522,U_20524)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20524),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20522),U_20524)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4876_3]) ).

cnf(f_4876_5,plain,
    ( c_List_Oupt(U_20522,hAPP(c_Nat_OSuc,U_20524)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20522,U_20524)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20524),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20522),U_20524)) ),
    inference(clausify,[status(thm)],[f_4876_4]) ).

cnf(f_4876_6,plain,
    ( c_List_Oupt(U_20523,hAPP(c_Nat_OSuc,U_20525)) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20523),U_20525)) ),
    inference(clausify,[status(thm)],[f_4876_4]) ).

fof(f_4877_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_4877_2,plain,
    ! [U_20528,U_20527,U_20526] :
      ( c_List_Oupt(U_20526,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20527),U_20528)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20526,U_20527)),c_List_Oupt(U_20527,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20527),U_20528)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20526),U_20527)) ),
    inference(variable_rename,[status(thm)],[f_4877_1]) ).

fof(f_4877_3,plain,
    ! [U_20526,U_20527,U_20528] :
      ( c_List_Oupt(U_20526,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20527),U_20528)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20526,U_20527)),c_List_Oupt(U_20527,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20527),U_20528)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20526),U_20527)) ),
    inference(definitional_conversion,[status(esa)],[f_4877_2]) ).

cnf(f_4877_4,plain,
    ( c_List_Oupt(U_20526,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20527),U_20528)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20526,U_20527)),c_List_Oupt(U_20527,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20527),U_20528)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20526),U_20527)) ),
    inference(clausify,[status(thm)],[f_4877_3]) ).

fof(f_4878_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_4878_2,plain,
    ! [U_20532,U_20531,U_20530,U_20529] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20529,hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20530),hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20531),U_20532)))
          | ~ c_List_Olinorder__class_Osorted(U_20529,hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20531),U_20532))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20529),U_20530),U_20531)) )
        & ( ( c_List_Olinorder__class_Osorted(U_20529,hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20531),U_20532))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20529),U_20530),U_20531)) )
          | ~ c_List_Olinorder__class_Osorted(U_20529,hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20530),hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20531),U_20532))) ) )
      | ~ class_Orderings_Olinorder(U_20529) ),
    inference(variable_rename,[status(thm)],[f_4878_1]) ).

fof(f_4878_3,plain,
    ( ! [U_20529,U_20530,U_20531,U_20532] :
        ( c_List_Olinorder__class_Osorted(U_20529,hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20531),U_20532))
        | ~ sP1219(U_20529,U_20530,U_20531,U_20532) )
    & ! [U_20529,U_20530,U_20531,U_20532] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20529),U_20530),U_20531))
        | ~ sP1219(U_20529,U_20530,U_20531,U_20532) )
    & ! [U_20529,U_20530,U_20531,U_20532] :
        ( c_List_Olinorder__class_Osorted(U_20529,hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20530),hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20531),U_20532)))
        | ~ c_List_Olinorder__class_Osorted(U_20529,hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20531),U_20532))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20529),U_20530),U_20531))
        | ~ sP1220(U_20529,U_20530,U_20531,U_20532) )
    & ! [U_20529,U_20530,U_20531,U_20532] :
        ( sP1219(U_20529,U_20530,U_20531,U_20532)
        | ~ c_List_Olinorder__class_Osorted(U_20529,hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20530),hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20531),U_20532)))
        | ~ sP1220(U_20529,U_20530,U_20531,U_20532) )
    & ! [U_20529,U_20530,U_20531,U_20532] :
        ( sP1220(U_20529,U_20530,U_20531,U_20532)
        | ~ class_Orderings_Olinorder(U_20529) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1219,sP1220])],[f_4878_2]) ).

cnf(f_4878_4,plain,
    ( sP1220(U_20529,U_20530,U_20531,U_20532)
    | ~ class_Orderings_Olinorder(U_20529) ),
    inference(clausify,[status(thm)],[f_4878_3]) ).

cnf(f_4878_5,plain,
    ( sP1219(U_20529,U_20530,U_20531,U_20532)
    | ~ c_List_Olinorder__class_Osorted(U_20529,hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20530),hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20531),U_20532)))
    | ~ sP1220(U_20529,U_20530,U_20531,U_20532) ),
    inference(clausify,[status(thm)],[f_4878_3]) ).

cnf(f_4878_6,plain,
    ( c_List_Olinorder__class_Osorted(U_20529,hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20530),hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20531),U_20532)))
    | ~ c_List_Olinorder__class_Osorted(U_20529,hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20531),U_20532))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20529),U_20530),U_20531))
    | ~ sP1220(U_20529,U_20530,U_20531,U_20532) ),
    inference(clausify,[status(thm)],[f_4878_3]) ).

cnf(f_4878_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20529),U_20530),U_20531))
    | ~ sP1219(U_20529,U_20530,U_20531,U_20532) ),
    inference(clausify,[status(thm)],[f_4878_3]) ).

cnf(f_4878_8,plain,
    ( c_List_Olinorder__class_Osorted(U_20529,hAPP(hAPP(c_List_Olist_OCons(U_20529),U_20531),U_20532))
    | ~ sP1219(U_20529,U_20530,U_20531,U_20532) ),
    inference(clausify,[status(thm)],[f_4878_3]) ).

fof(f_4879_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_4879_2,plain,
    ! [U_20536,U_20535,U_20534,U_20533] :
      ( c_List_Olinorder__class_Osorted(U_20533,hAPP(hAPP(c_List_Olist_OCons(U_20533),U_20534),hAPP(hAPP(c_List_Olist_OCons(U_20533),U_20535),U_20536)))
      | ~ c_List_Olinorder__class_Osorted(U_20533,hAPP(hAPP(c_List_Olist_OCons(U_20533),U_20535),U_20536))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20533),U_20534),U_20535))
      | ~ class_Orderings_Olinorder(U_20533) ),
    inference(variable_rename,[status(thm)],[f_4879_1]) ).

fof(f_4879_3,plain,
    ! [U_20536,U_20535,U_20534,U_20533] :
      ( c_List_Olinorder__class_Osorted(U_20533,hAPP(hAPP(c_List_Olist_OCons(U_20533),U_20534),hAPP(hAPP(c_List_Olist_OCons(U_20533),U_20535),U_20536)))
      | ~ c_List_Olinorder__class_Osorted(U_20533,hAPP(hAPP(c_List_Olist_OCons(U_20533),U_20535),U_20536))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20533),U_20534),U_20535))
      | ~ class_Orderings_Olinorder(U_20533) ),
    inference(definitional_conversion,[status(esa)],[f_4879_2]) ).

cnf(f_4879_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20533,hAPP(hAPP(c_List_Olist_OCons(U_20533),U_20534),hAPP(hAPP(c_List_Olist_OCons(U_20533),U_20535),U_20536)))
    | ~ c_List_Olinorder__class_Osorted(U_20533,hAPP(hAPP(c_List_Olist_OCons(U_20533),U_20535),U_20536))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20533),U_20534),U_20535))
    | ~ class_Orderings_Olinorder(U_20533) ),
    inference(clausify,[status(thm)],[f_4879_3]) ).

fof(f_4880_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_4880_2,plain,
    ! [U_20539,U_20538,U_20537] :
      ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),U_20538),c_List_Oupt(U_20537,U_20539)) = c_List_Oupt(U_20537,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20537),U_20538))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20537),U_20538)),U_20539)) ),
    inference(variable_rename,[status(thm)],[f_4880_1]) ).

fof(f_4880_3,plain,
    ! [U_20538,U_20537,U_20539] :
      ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),U_20538),c_List_Oupt(U_20537,U_20539)) = c_List_Oupt(U_20537,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20537),U_20538))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20537),U_20538)),U_20539)) ),
    inference(definitional_conversion,[status(esa)],[f_4880_2]) ).

cnf(f_4880_4,plain,
    ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),U_20538),c_List_Oupt(U_20537,U_20539)) = c_List_Oupt(U_20537,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20537),U_20538))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20537),U_20538)),U_20539)) ),
    inference(clausify,[status(thm)],[f_4880_3]) ).

fof(f_4881_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_4881_2,plain,
    ! [U_20541,U_20540] :
      ( ( c_List_Oupt(U_20540,U_20541) = c_List_Olist_ONil(tc_Nat_Onat)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20541),U_20540))
          & U_20541 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20541),U_20540))
        | U_20541 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(U_20540,U_20541) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4881_1]) ).

fof(f_4881_3,plain,
    ( ! [U_20545,U_20543] :
        ( c_List_Oupt(U_20543,U_20545) = c_List_Olist_ONil(tc_Nat_Onat)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20545),U_20543))
          & U_20545 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_20544,U_20542] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20544),U_20542))
        | U_20544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(U_20542,U_20544) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4881_2]) ).

fof(f_4881_4,plain,
    ( ! [U_20545,U_20543] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20545),U_20543))
        | ~ sP1221(U_20545,U_20543) )
    & ! [U_20545,U_20543] :
        ( U_20545 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1221(U_20545,U_20543) )
    & ! [U_20545,U_20543] :
        ( c_List_Oupt(U_20543,U_20545) = c_List_Olist_ONil(tc_Nat_Onat)
        | sP1221(U_20545,U_20543) )
    & ! [U_20544,U_20542] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20544),U_20542))
        | U_20544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(U_20542,U_20544) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1221])],[f_4881_3]) ).

cnf(f_4881_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20544),U_20542))
    | U_20544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_List_Oupt(U_20542,U_20544) != c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4881_4]) ).

cnf(f_4881_6,plain,
    ( c_List_Oupt(U_20543,U_20545) = c_List_Olist_ONil(tc_Nat_Onat)
    | sP1221(U_20545,U_20543) ),
    inference(clausify,[status(thm)],[f_4881_4]) ).

cnf(f_4881_7,plain,
    ( U_20545 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1221(U_20545,U_20543) ),
    inference(clausify,[status(thm)],[f_4881_4]) ).

cnf(f_4881_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20545),U_20543))
    | ~ sP1221(U_20545,U_20543) ),
    inference(clausify,[status(thm)],[f_4881_4]) ).

fof(f_4882_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_4882_2,plain,
    ! [U_20547,U_20546] :
      ( c_List_Oupt(U_20547,U_20546) = c_List_Olist_ONil(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20546),U_20547)) ),
    inference(variable_rename,[status(thm)],[f_4882_1]) ).

fof(f_4882_3,plain,
    ! [U_20546,U_20547] :
      ( c_List_Oupt(U_20547,U_20546) = c_List_Olist_ONil(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20546),U_20547)) ),
    inference(definitional_conversion,[status(esa)],[f_4882_2]) ).

cnf(f_4882_4,plain,
    ( c_List_Oupt(U_20547,U_20546) = c_List_Olist_ONil(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20546),U_20547)) ),
    inference(clausify,[status(thm)],[f_4882_3]) ).

fof(f_4883_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_4883_2,plain,
    ! [U_20552,U_20551,U_20550] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20550,hAPP(hAPP(c_List_Olist_OCons(U_20550),U_20551),U_20552))
          | ? [U_20549] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20550),U_20551),U_20549))
              & hBOOL(hAPP(hAPP(c_member(U_20550),U_20549),hAPP(c_List_Oset(U_20550),U_20552))) )
          | ~ c_List_Olinorder__class_Osorted(U_20550,U_20552) )
        & ( ( ! [U_20548] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20550),U_20551),U_20548))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20550),U_20548),hAPP(c_List_Oset(U_20550),U_20552))) )
            & c_List_Olinorder__class_Osorted(U_20550,U_20552) )
          | ~ c_List_Olinorder__class_Osorted(U_20550,hAPP(hAPP(c_List_Olist_OCons(U_20550),U_20551),U_20552)) ) )
      | ~ class_Orderings_Olinorder(U_20550) ),
    inference(variable_rename,[status(thm)],[f_4883_1]) ).

fof(f_4883_3,plain,
    ! [U_20552,U_20551,U_20550] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20550,hAPP(hAPP(c_List_Olist_OCons(U_20550),U_20551),U_20552))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20550),U_20551),sK502(U_20552,U_20551,U_20550)))
            & hBOOL(hAPP(hAPP(c_member(U_20550),sK502(U_20552,U_20551,U_20550)),hAPP(c_List_Oset(U_20550),U_20552))) )
          | ~ c_List_Olinorder__class_Osorted(U_20550,U_20552) )
        & ( ( ! [U_20548] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20550),U_20551),U_20548))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20550),U_20548),hAPP(c_List_Oset(U_20550),U_20552))) )
            & c_List_Olinorder__class_Osorted(U_20550,U_20552) )
          | ~ c_List_Olinorder__class_Osorted(U_20550,hAPP(hAPP(c_List_Olist_OCons(U_20550),U_20551),U_20552)) ) )
      | ~ class_Orderings_Olinorder(U_20550) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK502]),skolemize(U_20549,sK502(U_20552,U_20551,U_20550))],[f_4883_2]) ).

fof(f_4883_4,plain,
    ( ! [U_20550,U_20551,U_20552] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20550),U_20551),sK502(U_20552,U_20551,U_20550)))
        | ~ sP1223(U_20550,U_20551,U_20552) )
    & ! [U_20550,U_20551,U_20552] :
        ( hBOOL(hAPP(hAPP(c_member(U_20550),sK502(U_20552,U_20551,U_20550)),hAPP(c_List_Oset(U_20550),U_20552)))
        | ~ sP1223(U_20550,U_20551,U_20552) )
    & ! [U_20550,U_20548,U_20551,U_20552] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20550),U_20551),U_20548))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20550),U_20548),hAPP(c_List_Oset(U_20550),U_20552)))
        | ~ sP1222(U_20550,U_20548,U_20551,U_20552) )
    & ! [U_20550,U_20548,U_20551,U_20552] :
        ( c_List_Olinorder__class_Osorted(U_20550,U_20552)
        | ~ sP1222(U_20550,U_20548,U_20551,U_20552) )
    & ! [U_20550,U_20548,U_20551,U_20552] :
        ( c_List_Olinorder__class_Osorted(U_20550,hAPP(hAPP(c_List_Olist_OCons(U_20550),U_20551),U_20552))
        | sP1223(U_20550,U_20551,U_20552)
        | ~ c_List_Olinorder__class_Osorted(U_20550,U_20552)
        | ~ sP1224(U_20550,U_20548,U_20551,U_20552) )
    & ! [U_20550,U_20548,U_20551,U_20552] :
        ( sP1222(U_20550,U_20548,U_20551,U_20552)
        | ~ c_List_Olinorder__class_Osorted(U_20550,hAPP(hAPP(c_List_Olist_OCons(U_20550),U_20551),U_20552))
        | ~ sP1224(U_20550,U_20548,U_20551,U_20552) )
    & ! [U_20550,U_20548,U_20551,U_20552] :
        ( sP1224(U_20550,U_20548,U_20551,U_20552)
        | ~ class_Orderings_Olinorder(U_20550) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1222,sP1223,sP1224])],[f_4883_3]) ).

cnf(f_4883_5,plain,
    ( sP1224(U_20550,U_20548,U_20551,U_20552)
    | ~ class_Orderings_Olinorder(U_20550) ),
    inference(clausify,[status(thm)],[f_4883_4]) ).

cnf(f_4883_6,plain,
    ( sP1222(U_20550,U_20548,U_20551,U_20552)
    | ~ c_List_Olinorder__class_Osorted(U_20550,hAPP(hAPP(c_List_Olist_OCons(U_20550),U_20551),U_20552))
    | ~ sP1224(U_20550,U_20548,U_20551,U_20552) ),
    inference(clausify,[status(thm)],[f_4883_4]) ).

cnf(f_4883_7,plain,
    ( c_List_Olinorder__class_Osorted(U_20550,hAPP(hAPP(c_List_Olist_OCons(U_20550),U_20551),U_20552))
    | sP1223(U_20550,U_20551,U_20552)
    | ~ c_List_Olinorder__class_Osorted(U_20550,U_20552)
    | ~ sP1224(U_20550,U_20548,U_20551,U_20552) ),
    inference(clausify,[status(thm)],[f_4883_4]) ).

cnf(f_4883_8,plain,
    ( c_List_Olinorder__class_Osorted(U_20550,U_20552)
    | ~ sP1222(U_20550,U_20548,U_20551,U_20552) ),
    inference(clausify,[status(thm)],[f_4883_4]) ).

cnf(f_4883_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20550),U_20551),U_20548))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20550),U_20548),hAPP(c_List_Oset(U_20550),U_20552)))
    | ~ sP1222(U_20550,U_20548,U_20551,U_20552) ),
    inference(clausify,[status(thm)],[f_4883_4]) ).

cnf(f_4883_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20550),sK502(U_20552,U_20551,U_20550)),hAPP(c_List_Oset(U_20550),U_20552)))
    | ~ sP1223(U_20550,U_20551,U_20552) ),
    inference(clausify,[status(thm)],[f_4883_4]) ).

cnf(f_4883_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20550),U_20551),sK502(U_20552,U_20551,U_20550)))
    | ~ sP1223(U_20550,U_20551,U_20552) ),
    inference(clausify,[status(thm)],[f_4883_4]) ).

fof(f_4884_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_4884_2,plain,
    ! [U_20559,U_20558,U_20557] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20557,hAPP(hAPP(c_List_Oappend(U_20557),U_20558),U_20559))
          | ? [U_20556] :
              ( ? [U_20555] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20557),U_20556),U_20555))
                  & hBOOL(hAPP(hAPP(c_member(U_20557),U_20555),hAPP(c_List_Oset(U_20557),U_20559))) )
              & hBOOL(hAPP(hAPP(c_member(U_20557),U_20556),hAPP(c_List_Oset(U_20557),U_20558))) )
          | ~ c_List_Olinorder__class_Osorted(U_20557,U_20559)
          | ~ c_List_Olinorder__class_Osorted(U_20557,U_20558) )
        & ( ( ! [U_20554] :
                ( ! [U_20553] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20557),U_20554),U_20553))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_20557),U_20553),hAPP(c_List_Oset(U_20557),U_20559))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_20557),U_20554),hAPP(c_List_Oset(U_20557),U_20558))) )
            & c_List_Olinorder__class_Osorted(U_20557,U_20559)
            & c_List_Olinorder__class_Osorted(U_20557,U_20558) )
          | ~ c_List_Olinorder__class_Osorted(U_20557,hAPP(hAPP(c_List_Oappend(U_20557),U_20558),U_20559)) ) )
      | ~ class_Orderings_Olinorder(U_20557) ),
    inference(variable_rename,[status(thm)],[f_4884_1]) ).

fof(f_4884_3,plain,
    ! [U_20559,U_20558,U_20557] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20557,hAPP(hAPP(c_List_Oappend(U_20557),U_20558),U_20559))
          | ( ? [U_20555] :
                ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20557),sK503(U_20559,U_20558,U_20557)),U_20555))
                & hBOOL(hAPP(hAPP(c_member(U_20557),U_20555),hAPP(c_List_Oset(U_20557),U_20559))) )
            & hBOOL(hAPP(hAPP(c_member(U_20557),sK503(U_20559,U_20558,U_20557)),hAPP(c_List_Oset(U_20557),U_20558))) )
          | ~ c_List_Olinorder__class_Osorted(U_20557,U_20559)
          | ~ c_List_Olinorder__class_Osorted(U_20557,U_20558) )
        & ( ( ! [U_20554] :
                ( ! [U_20553] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20557),U_20554),U_20553))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_20557),U_20553),hAPP(c_List_Oset(U_20557),U_20559))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_20557),U_20554),hAPP(c_List_Oset(U_20557),U_20558))) )
            & c_List_Olinorder__class_Osorted(U_20557,U_20559)
            & c_List_Olinorder__class_Osorted(U_20557,U_20558) )
          | ~ c_List_Olinorder__class_Osorted(U_20557,hAPP(hAPP(c_List_Oappend(U_20557),U_20558),U_20559)) ) )
      | ~ class_Orderings_Olinorder(U_20557) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK503]),skolemize(U_20556,sK503(U_20559,U_20558,U_20557))],[f_4884_2]) ).

fof(f_4884_4,plain,
    ! [U_20559,U_20558,U_20557] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20557,hAPP(hAPP(c_List_Oappend(U_20557),U_20558),U_20559))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20557),sK503(U_20559,U_20558,U_20557)),sK504(U_20559,U_20558,U_20557)))
            & hBOOL(hAPP(hAPP(c_member(U_20557),sK504(U_20559,U_20558,U_20557)),hAPP(c_List_Oset(U_20557),U_20559)))
            & hBOOL(hAPP(hAPP(c_member(U_20557),sK503(U_20559,U_20558,U_20557)),hAPP(c_List_Oset(U_20557),U_20558))) )
          | ~ c_List_Olinorder__class_Osorted(U_20557,U_20559)
          | ~ c_List_Olinorder__class_Osorted(U_20557,U_20558) )
        & ( ( ! [U_20554] :
                ( ! [U_20553] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20557),U_20554),U_20553))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_20557),U_20553),hAPP(c_List_Oset(U_20557),U_20559))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_20557),U_20554),hAPP(c_List_Oset(U_20557),U_20558))) )
            & c_List_Olinorder__class_Osorted(U_20557,U_20559)
            & c_List_Olinorder__class_Osorted(U_20557,U_20558) )
          | ~ c_List_Olinorder__class_Osorted(U_20557,hAPP(hAPP(c_List_Oappend(U_20557),U_20558),U_20559)) ) )
      | ~ class_Orderings_Olinorder(U_20557) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK504]),skolemize(U_20555,sK504(U_20559,U_20558,U_20557))],[f_4884_3]) ).

fof(f_4884_5,plain,
    ( ! [U_20559,U_20558,U_20557] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20557),sK503(U_20559,U_20558,U_20557)),sK504(U_20559,U_20558,U_20557)))
        | ~ sP1226(U_20559,U_20558,U_20557) )
    & ! [U_20559,U_20558,U_20557] :
        ( hBOOL(hAPP(hAPP(c_member(U_20557),sK504(U_20559,U_20558,U_20557)),hAPP(c_List_Oset(U_20557),U_20559)))
        | ~ sP1226(U_20559,U_20558,U_20557) )
    & ! [U_20559,U_20558,U_20557] :
        ( hBOOL(hAPP(hAPP(c_member(U_20557),sK503(U_20559,U_20558,U_20557)),hAPP(c_List_Oset(U_20557),U_20558)))
        | ~ sP1226(U_20559,U_20558,U_20557) )
    & ! [U_20553,U_20554,U_20559,U_20558,U_20557] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20557),U_20554),U_20553))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20557),U_20553),hAPP(c_List_Oset(U_20557),U_20559)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20557),U_20554),hAPP(c_List_Oset(U_20557),U_20558)))
        | ~ sP1225(U_20553,U_20554,U_20559,U_20558,U_20557) )
    & ! [U_20553,U_20554,U_20559,U_20558,U_20557] :
        ( c_List_Olinorder__class_Osorted(U_20557,U_20559)
        | ~ sP1225(U_20553,U_20554,U_20559,U_20558,U_20557) )
    & ! [U_20553,U_20554,U_20559,U_20558,U_20557] :
        ( c_List_Olinorder__class_Osorted(U_20557,U_20558)
        | ~ sP1225(U_20553,U_20554,U_20559,U_20558,U_20557) )
    & ! [U_20553,U_20554,U_20559,U_20558,U_20557] :
        ( c_List_Olinorder__class_Osorted(U_20557,hAPP(hAPP(c_List_Oappend(U_20557),U_20558),U_20559))
        | sP1226(U_20559,U_20558,U_20557)
        | ~ c_List_Olinorder__class_Osorted(U_20557,U_20559)
        | ~ c_List_Olinorder__class_Osorted(U_20557,U_20558)
        | ~ sP1227(U_20553,U_20554,U_20559,U_20558,U_20557) )
    & ! [U_20553,U_20554,U_20559,U_20558,U_20557] :
        ( sP1225(U_20553,U_20554,U_20559,U_20558,U_20557)
        | ~ c_List_Olinorder__class_Osorted(U_20557,hAPP(hAPP(c_List_Oappend(U_20557),U_20558),U_20559))
        | ~ sP1227(U_20553,U_20554,U_20559,U_20558,U_20557) )
    & ! [U_20553,U_20554,U_20559,U_20558,U_20557] :
        ( sP1227(U_20553,U_20554,U_20559,U_20558,U_20557)
        | ~ class_Orderings_Olinorder(U_20557) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1225,sP1226,sP1227])],[f_4884_4]) ).

cnf(f_4884_6,plain,
    ( sP1227(U_20553,U_20554,U_20559,U_20558,U_20557)
    | ~ class_Orderings_Olinorder(U_20557) ),
    inference(clausify,[status(thm)],[f_4884_5]) ).

cnf(f_4884_7,plain,
    ( sP1225(U_20553,U_20554,U_20559,U_20558,U_20557)
    | ~ c_List_Olinorder__class_Osorted(U_20557,hAPP(hAPP(c_List_Oappend(U_20557),U_20558),U_20559))
    | ~ sP1227(U_20553,U_20554,U_20559,U_20558,U_20557) ),
    inference(clausify,[status(thm)],[f_4884_5]) ).

cnf(f_4884_8,plain,
    ( c_List_Olinorder__class_Osorted(U_20557,hAPP(hAPP(c_List_Oappend(U_20557),U_20558),U_20559))
    | sP1226(U_20559,U_20558,U_20557)
    | ~ c_List_Olinorder__class_Osorted(U_20557,U_20559)
    | ~ c_List_Olinorder__class_Osorted(U_20557,U_20558)
    | ~ sP1227(U_20553,U_20554,U_20559,U_20558,U_20557) ),
    inference(clausify,[status(thm)],[f_4884_5]) ).

cnf(f_4884_9,plain,
    ( c_List_Olinorder__class_Osorted(U_20557,U_20558)
    | ~ sP1225(U_20553,U_20554,U_20559,U_20558,U_20557) ),
    inference(clausify,[status(thm)],[f_4884_5]) ).

cnf(f_4884_10,plain,
    ( c_List_Olinorder__class_Osorted(U_20557,U_20559)
    | ~ sP1225(U_20553,U_20554,U_20559,U_20558,U_20557) ),
    inference(clausify,[status(thm)],[f_4884_5]) ).

cnf(f_4884_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20557),U_20554),U_20553))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20557),U_20553),hAPP(c_List_Oset(U_20557),U_20559)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20557),U_20554),hAPP(c_List_Oset(U_20557),U_20558)))
    | ~ sP1225(U_20553,U_20554,U_20559,U_20558,U_20557) ),
    inference(clausify,[status(thm)],[f_4884_5]) ).

cnf(f_4884_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20557),sK503(U_20559,U_20558,U_20557)),hAPP(c_List_Oset(U_20557),U_20558)))
    | ~ sP1226(U_20559,U_20558,U_20557) ),
    inference(clausify,[status(thm)],[f_4884_5]) ).

cnf(f_4884_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20557),sK504(U_20559,U_20558,U_20557)),hAPP(c_List_Oset(U_20557),U_20559)))
    | ~ sP1226(U_20559,U_20558,U_20557) ),
    inference(clausify,[status(thm)],[f_4884_5]) ).

cnf(f_4884_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20557),sK503(U_20559,U_20558,U_20557)),sK504(U_20559,U_20558,U_20557)))
    | ~ sP1226(U_20559,U_20558,U_20557) ),
    inference(clausify,[status(thm)],[f_4884_5]) ).

fof(f_4885_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_4885_2,plain,
    ! [U_20563,U_20562,U_20561,U_20560] :
      ( ( c_List_Oupt(U_20560,U_20561) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20562),U_20563)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20560),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20561) != U_20563
        | U_20560 != U_20562
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20560),U_20561)) )
      & ( ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20560),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20561) = U_20563
          & U_20560 = U_20562
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20560),U_20561)) )
        | c_List_Oupt(U_20560,U_20561) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20562),U_20563) ) ),
    inference(variable_rename,[status(thm)],[f_4885_1]) ).

fof(f_4885_3,plain,
    ( ! [U_20571,U_20569,U_20567,U_20565] :
        ( c_List_Oupt(U_20565,U_20567) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20569),U_20571)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20565),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20567) != U_20571
        | U_20565 != U_20569
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20565),U_20567)) )
    & ! [U_20570,U_20568,U_20566,U_20564] :
        ( ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20564),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20566) = U_20570
          & U_20564 = U_20568
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20564),U_20566)) )
        | c_List_Oupt(U_20564,U_20566) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20568),U_20570) ) ),
    inference(miniscope,[status(thm)],[f_4885_2]) ).

fof(f_4885_4,plain,
    ( ! [U_20568,U_20566,U_20564,U_20570] :
        ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20564),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20566) = U_20570
        | ~ sP1228(U_20568,U_20566,U_20564,U_20570) )
    & ! [U_20568,U_20566,U_20564,U_20570] :
        ( U_20564 = U_20568
        | ~ sP1228(U_20568,U_20566,U_20564,U_20570) )
    & ! [U_20568,U_20566,U_20564,U_20570] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20564),U_20566))
        | ~ sP1228(U_20568,U_20566,U_20564,U_20570) )
    & ! [U_20567,U_20565,U_20569,U_20571] :
        ( c_List_Oupt(U_20565,U_20567) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20569),U_20571)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20565),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20567) != U_20571
        | U_20565 != U_20569
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20565),U_20567)) )
    & ! [U_20568,U_20566,U_20564,U_20570] :
        ( sP1228(U_20568,U_20566,U_20564,U_20570)
        | c_List_Oupt(U_20564,U_20566) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20568),U_20570) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1228])],[f_4885_3]) ).

cnf(f_4885_5,plain,
    ( sP1228(U_20568,U_20566,U_20564,U_20570)
    | c_List_Oupt(U_20564,U_20566) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20568),U_20570) ),
    inference(clausify,[status(thm)],[f_4885_4]) ).

cnf(f_4885_6,plain,
    ( c_List_Oupt(U_20565,U_20567) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20569),U_20571)
    | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20565),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20567) != U_20571
    | U_20565 != U_20569
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20565),U_20567)) ),
    inference(clausify,[status(thm)],[f_4885_4]) ).

cnf(f_4885_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20564),U_20566))
    | ~ sP1228(U_20568,U_20566,U_20564,U_20570) ),
    inference(clausify,[status(thm)],[f_4885_4]) ).

cnf(f_4885_8,plain,
    ( U_20564 = U_20568
    | ~ sP1228(U_20568,U_20566,U_20564,U_20570) ),
    inference(clausify,[status(thm)],[f_4885_4]) ).

cnf(f_4885_9,plain,
    ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20564),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20566) = U_20570
    | ~ sP1228(U_20568,U_20566,U_20564,U_20570) ),
    inference(clausify,[status(thm)],[f_4885_4]) ).

fof(f_4886_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_4886_2,plain,
    ! [U_20573,U_20572] :
      ( ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20572),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20573)) = 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_20572)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20573))) )
      & ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20572),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20573)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20572)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20572)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20573)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20572)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20573))) ) ),
    inference(variable_rename,[status(thm)],[f_4886_1]) ).

fof(f_4886_3,plain,
    ( ! [U_20577,U_20575] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20575),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20577)) = 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_20575)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20577))) )
    & ! [U_20576,U_20574] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20574),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20576)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20574)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20574)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20576)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20574)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20576))) ) ),
    inference(miniscope,[status(thm)],[f_4886_2]) ).

fof(f_4886_4,plain,
    ( ! [U_20575,U_20577] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20575),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20577)) = 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_20575)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20577))) )
    & ! [U_20576,U_20574] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20574),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20576)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20574)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20574)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20576)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20574)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20576))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4886_3]) ).

cnf(f_4886_5,plain,
    ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20574),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20576)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20574)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20574)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20576)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20574)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20576))) ),
    inference(clausify,[status(thm)],[f_4886_4]) ).

cnf(f_4886_6,plain,
    ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20575),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20577)) = 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_20575)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20577))) ),
    inference(clausify,[status(thm)],[f_4886_4]) ).

fof(f_4887_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_4887_2,plain,
    ! [U_20580,U_20579,U_20578] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),U_20578),c_List_Oupt(U_20579,U_20580)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20579),U_20578),U_20580),
    inference(variable_rename,[status(thm)],[f_4887_1]) ).

fof(f_4887_3,plain,
    ! [U_20578,U_20579,U_20580] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),U_20578),c_List_Oupt(U_20579,U_20580)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20579),U_20578),U_20580),
    inference(definitional_conversion,[status(esa)],[f_4887_2]) ).

cnf(f_4887_4,plain,
    hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),U_20578),c_List_Oupt(U_20579,U_20580)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20579),U_20578),U_20580),
    inference(clausify,[status(thm)],[f_4887_3]) ).

fof(f_4888_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_4888_2,plain,
    ! [U_20583,U_20582,U_20581] :
      ( c_List_Olinorder__class_Osorted(U_20581,hAPP(hAPP(c_List_Odrop(U_20581),U_20583),U_20582))
      | ~ c_List_Olinorder__class_Osorted(U_20581,U_20582)
      | ~ class_Orderings_Olinorder(U_20581) ),
    inference(variable_rename,[status(thm)],[f_4888_1]) ).

fof(f_4888_3,plain,
    ! [U_20581,U_20582,U_20583] :
      ( c_List_Olinorder__class_Osorted(U_20581,hAPP(hAPP(c_List_Odrop(U_20581),U_20583),U_20582))
      | ~ c_List_Olinorder__class_Osorted(U_20581,U_20582)
      | ~ class_Orderings_Olinorder(U_20581) ),
    inference(definitional_conversion,[status(esa)],[f_4888_2]) ).

cnf(f_4888_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20581,hAPP(hAPP(c_List_Odrop(U_20581),U_20583),U_20582))
    | ~ c_List_Olinorder__class_Osorted(U_20581,U_20582)
    | ~ class_Orderings_Olinorder(U_20581) ),
    inference(clausify,[status(thm)],[f_4888_3]) ).

fof(f_4889_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_4889_2,plain,
    ! [U_20585,U_20584] :
      ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(U_20584,U_20585)) = U_20584
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20584),U_20585)) ),
    inference(variable_rename,[status(thm)],[f_4889_1]) ).

fof(f_4889_3,plain,
    ! [U_20585,U_20584] :
      ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(U_20584,U_20585)) = U_20584
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20584),U_20585)) ),
    inference(definitional_conversion,[status(esa)],[f_4889_2]) ).

cnf(f_4889_4,plain,
    ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(U_20584,U_20585)) = U_20584
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20584),U_20585)) ),
    inference(clausify,[status(thm)],[f_4889_3]) ).

fof(f_4890_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_4890_2,plain,
    ! [U_20586] : c_List_Oupt(U_20586,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4890_1]) ).

fof(f_4890_3,plain,
    ! [U_20586] : c_List_Oupt(U_20586,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_4890_2]) ).

cnf(f_4890_4,plain,
    c_List_Oupt(U_20586,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4890_3]) ).

fof(f_4891_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_4891_2,plain,
    ! [U_20587] :
      ( c_List_Olinorder__class_Osorted(U_20587,c_List_Olist_ONil(U_20587))
      | ~ class_Orderings_Olinorder(U_20587) ),
    inference(variable_rename,[status(thm)],[f_4891_1]) ).

fof(f_4891_3,plain,
    ! [U_20587] :
      ( c_List_Olinorder__class_Osorted(U_20587,c_List_Olist_ONil(U_20587))
      | ~ class_Orderings_Olinorder(U_20587) ),
    inference(definitional_conversion,[status(esa)],[f_4891_2]) ).

cnf(f_4891_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20587,c_List_Olist_ONil(U_20587))
    | ~ class_Orderings_Olinorder(U_20587) ),
    inference(clausify,[status(thm)],[f_4891_3]) ).

fof(f_4892_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_4892_2,plain,
    ! [U_20590,U_20589,U_20588] :
      ( c_List_Olinorder__class_Osorted(U_20588,hAPP(hAPP(c_List_Otake(U_20588),U_20590),U_20589))
      | ~ c_List_Olinorder__class_Osorted(U_20588,U_20589)
      | ~ class_Orderings_Olinorder(U_20588) ),
    inference(variable_rename,[status(thm)],[f_4892_1]) ).

fof(f_4892_3,plain,
    ! [U_20588,U_20589,U_20590] :
      ( c_List_Olinorder__class_Osorted(U_20588,hAPP(hAPP(c_List_Otake(U_20588),U_20590),U_20589))
      | ~ c_List_Olinorder__class_Osorted(U_20588,U_20589)
      | ~ class_Orderings_Olinorder(U_20588) ),
    inference(definitional_conversion,[status(esa)],[f_4892_2]) ).

cnf(f_4892_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20588,hAPP(hAPP(c_List_Otake(U_20588),U_20590),U_20589))
    | ~ c_List_Olinorder__class_Osorted(U_20588,U_20589)
    | ~ class_Orderings_Olinorder(U_20588) ),
    inference(clausify,[status(thm)],[f_4892_3]) ).

fof(f_4893_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_4893_2,plain,
    ! [U_20592,U_20591] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20591,U_20592)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20591),U_20592),
    inference(variable_rename,[status(thm)],[f_4893_1]) ).

fof(f_4893_3,plain,
    ! [U_20591,U_20592] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20591,U_20592)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20591),U_20592),
    inference(definitional_conversion,[status(esa)],[f_4893_2]) ).

cnf(f_4893_4,plain,
    hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20591,U_20592)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20591),U_20592),
    inference(clausify,[status(thm)],[f_4893_3]) ).

fof(f_4894_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_4894_2,plain,
    ! [U_20594,U_20593] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20593),U_20594) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20593,U_20594)),
    inference(variable_rename,[status(thm)],[f_4894_1]) ).

fof(f_4894_3,plain,
    ! [U_20593,U_20594] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20593),U_20594) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20593,U_20594)),
    inference(definitional_conversion,[status(esa)],[f_4894_2]) ).

cnf(f_4894_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20593),U_20594) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20593,U_20594)),
    inference(clausify,[status(thm)],[f_4894_3]) ).

fof(f_4895_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_4895_2,plain,
    ! [U_20597,U_20596,U_20595] :
      ( U_20596 = U_20597
      | hAPP(c_List_Oset(U_20595),U_20596) != hAPP(c_List_Oset(U_20595),U_20597)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20595),U_20597))
      | ~ c_List_Olinorder__class_Osorted(U_20595,U_20597)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20595),U_20596))
      | ~ c_List_Olinorder__class_Osorted(U_20595,U_20596)
      | ~ class_Orderings_Olinorder(U_20595) ),
    inference(variable_rename,[status(thm)],[f_4895_1]) ).

fof(f_4895_3,plain,
    ! [U_20595,U_20596,U_20597] :
      ( U_20596 = U_20597
      | hAPP(c_List_Oset(U_20595),U_20596) != hAPP(c_List_Oset(U_20595),U_20597)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20595),U_20597))
      | ~ c_List_Olinorder__class_Osorted(U_20595,U_20597)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20595),U_20596))
      | ~ c_List_Olinorder__class_Osorted(U_20595,U_20596)
      | ~ class_Orderings_Olinorder(U_20595) ),
    inference(definitional_conversion,[status(esa)],[f_4895_2]) ).

cnf(f_4895_4,plain,
    ( U_20596 = U_20597
    | hAPP(c_List_Oset(U_20595),U_20596) != hAPP(c_List_Oset(U_20595),U_20597)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20595),U_20597))
    | ~ c_List_Olinorder__class_Osorted(U_20595,U_20597)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20595),U_20596))
    | ~ c_List_Olinorder__class_Osorted(U_20595,U_20596)
    | ~ class_Orderings_Olinorder(U_20595) ),
    inference(clausify,[status(thm)],[f_4895_3]) ).

fof(f_4896_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_4896_2,plain,
    ! [U_20600,U_20599,U_20598] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20598,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20598,U_20598,c_COMBI(U_20598)),U_20599),U_20600))
          | ~ c_List_Olinorder__class_Osorted(U_20598,U_20600) )
        & ( c_List_Olinorder__class_Osorted(U_20598,U_20600)
          | ~ c_List_Olinorder__class_Osorted(U_20598,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20598,U_20598,c_COMBI(U_20598)),U_20599),U_20600)) ) )
      | ~ class_Orderings_Olinorder(U_20598) ),
    inference(variable_rename,[status(thm)],[f_4896_1]) ).

fof(f_4896_3,plain,
    ( ! [U_20600,U_20598,U_20599] :
        ( c_List_Olinorder__class_Osorted(U_20598,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20598,U_20598,c_COMBI(U_20598)),U_20599),U_20600))
        | ~ c_List_Olinorder__class_Osorted(U_20598,U_20600)
        | ~ sP1229(U_20600,U_20598,U_20599) )
    & ! [U_20600,U_20598,U_20599] :
        ( c_List_Olinorder__class_Osorted(U_20598,U_20600)
        | ~ c_List_Olinorder__class_Osorted(U_20598,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20598,U_20598,c_COMBI(U_20598)),U_20599),U_20600))
        | ~ sP1229(U_20600,U_20598,U_20599) )
    & ! [U_20600,U_20598,U_20599] :
        ( sP1229(U_20600,U_20598,U_20599)
        | ~ class_Orderings_Olinorder(U_20598) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1229])],[f_4896_2]) ).

cnf(f_4896_4,plain,
    ( sP1229(U_20600,U_20598,U_20599)
    | ~ class_Orderings_Olinorder(U_20598) ),
    inference(clausify,[status(thm)],[f_4896_3]) ).

cnf(f_4896_5,plain,
    ( c_List_Olinorder__class_Osorted(U_20598,U_20600)
    | ~ c_List_Olinorder__class_Osorted(U_20598,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20598,U_20598,c_COMBI(U_20598)),U_20599),U_20600))
    | ~ sP1229(U_20600,U_20598,U_20599) ),
    inference(clausify,[status(thm)],[f_4896_3]) ).

cnf(f_4896_6,plain,
    ( c_List_Olinorder__class_Osorted(U_20598,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20598,U_20598,c_COMBI(U_20598)),U_20599),U_20600))
    | ~ c_List_Olinorder__class_Osorted(U_20598,U_20600)
    | ~ sP1229(U_20600,U_20598,U_20599) ),
    inference(clausify,[status(thm)],[f_4896_3]) ).

fof(f_4897_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_4897_2,plain,
    ! [U_20602,U_20601] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(U_20601,U_20602))),
    inference(variable_rename,[status(thm)],[f_4897_1]) ).

fof(f_4897_3,plain,
    ! [U_20602,U_20601] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(U_20601,U_20602))),
    inference(definitional_conversion,[status(esa)],[f_4897_2]) ).

cnf(f_4897_4,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(U_20601,U_20602))),
    inference(clausify,[status(thm)],[f_4897_3]) ).

fof(f_4898_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_4898_2,plain,
    ! [U_20605,U_20604,U_20603] :
      ( c_List_Olinorder__class_Osorted(U_20603,c_List_Oremove1(U_20603,U_20605,U_20604))
      | ~ c_List_Olinorder__class_Osorted(U_20603,U_20604)
      | ~ class_Orderings_Olinorder(U_20603) ),
    inference(variable_rename,[status(thm)],[f_4898_1]) ).

fof(f_4898_3,plain,
    ! [U_20604,U_20603,U_20605] :
      ( c_List_Olinorder__class_Osorted(U_20603,c_List_Oremove1(U_20603,U_20605,U_20604))
      | ~ c_List_Olinorder__class_Osorted(U_20603,U_20604)
      | ~ class_Orderings_Olinorder(U_20603) ),
    inference(definitional_conversion,[status(esa)],[f_4898_2]) ).

cnf(f_4898_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20603,c_List_Oremove1(U_20603,U_20605,U_20604))
    | ~ c_List_Olinorder__class_Osorted(U_20603,U_20604)
    | ~ class_Orderings_Olinorder(U_20603) ),
    inference(clausify,[status(thm)],[f_4898_3]) ).

fof(f_4899_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_4899_2,plain,
    ! [U_20607,U_20606] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(U_20606,U_20607)),
    inference(variable_rename,[status(thm)],[f_4899_1]) ).

fof(f_4899_3,plain,
    ! [U_20606,U_20607] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(U_20606,U_20607)),
    inference(definitional_conversion,[status(esa)],[f_4899_2]) ).

cnf(f_4899_4,plain,
    c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(U_20606,U_20607)),
    inference(clausify,[status(thm)],[f_4899_3]) ).

fof(f_4900_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_4900_2,plain,
    ! [U_20609,U_20608] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(U_20608,U_20609)),
    inference(variable_rename,[status(thm)],[f_4900_1]) ).

fof(f_4900_3,plain,
    ! [U_20609,U_20608] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(U_20608,U_20609)),
    inference(definitional_conversion,[status(esa)],[f_4900_2]) ).

cnf(f_4900_4,plain,
    c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(U_20608,U_20609)),
    inference(clausify,[status(thm)],[f_4900_3]) ).

fof(f_4901_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_4901_2,plain,
    ! [U_20611,U_20610] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20610),U_20611)) = c_List_Oupt(U_20610,U_20611),
    inference(variable_rename,[status(thm)],[f_4901_1]) ).

fof(f_4901_3,plain,
    ! [U_20610,U_20611] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20610),U_20611)) = c_List_Oupt(U_20610,U_20611),
    inference(definitional_conversion,[status(esa)],[f_4901_2]) ).

cnf(f_4901_4,plain,
    c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20610),U_20611)) = c_List_Oupt(U_20610,U_20611),
    inference(clausify,[status(thm)],[f_4901_3]) ).

fof(f_4902_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_4902_2,plain,
    ! [U_20614,U_20613,U_20612] :
      ( c_List_Olinorder__class_Osorted(U_20612,c_List_Olinorder__class_Oinsort__insert__key(U_20612,U_20612,c_COMBI(U_20612),U_20614,U_20613))
      | ~ c_List_Olinorder__class_Osorted(U_20612,U_20613)
      | ~ class_Orderings_Olinorder(U_20612) ),
    inference(variable_rename,[status(thm)],[f_4902_1]) ).

fof(f_4902_3,plain,
    ! [U_20612,U_20613,U_20614] :
      ( c_List_Olinorder__class_Osorted(U_20612,c_List_Olinorder__class_Oinsort__insert__key(U_20612,U_20612,c_COMBI(U_20612),U_20614,U_20613))
      | ~ c_List_Olinorder__class_Osorted(U_20612,U_20613)
      | ~ class_Orderings_Olinorder(U_20612) ),
    inference(definitional_conversion,[status(esa)],[f_4902_2]) ).

cnf(f_4902_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20612,c_List_Olinorder__class_Oinsort__insert__key(U_20612,U_20612,c_COMBI(U_20612),U_20614,U_20613))
    | ~ c_List_Olinorder__class_Osorted(U_20612,U_20613)
    | ~ class_Orderings_Olinorder(U_20612) ),
    inference(clausify,[status(thm)],[f_4902_3]) ).

fof(f_4903_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_4903_2,plain,
    ! [U_20616,U_20615] :
      ( c_List_Oupt(U_20615,U_20616) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20615),c_List_Oupt(hAPP(c_Nat_OSuc,U_20615),U_20616))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20615),U_20616)) ),
    inference(variable_rename,[status(thm)],[f_4903_1]) ).

fof(f_4903_3,plain,
    ! [U_20615,U_20616] :
      ( c_List_Oupt(U_20615,U_20616) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20615),c_List_Oupt(hAPP(c_Nat_OSuc,U_20615),U_20616))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20615),U_20616)) ),
    inference(definitional_conversion,[status(esa)],[f_4903_2]) ).

cnf(f_4903_4,plain,
    ( c_List_Oupt(U_20615,U_20616) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20615),c_List_Oupt(hAPP(c_Nat_OSuc,U_20615),U_20616))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20615),U_20616)) ),
    inference(clausify,[status(thm)],[f_4903_3]) ).

fof(f_4904_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_4904_2,plain,
    ! [U_20618,U_20617] :
      ( ( c_List_Oupt(U_20617,U_20618) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20617),U_20618)) )
      & ( c_List_Oupt(U_20617,U_20618) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20617),c_List_Oupt(hAPP(c_Nat_OSuc,U_20617),U_20618))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20617),U_20618)) ) ),
    inference(variable_rename,[status(thm)],[f_4904_1]) ).

fof(f_4904_3,plain,
    ( ! [U_20622,U_20620] :
        ( c_List_Oupt(U_20620,U_20622) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20620),U_20622)) )
    & ! [U_20621,U_20619] :
        ( c_List_Oupt(U_20619,U_20621) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20619),c_List_Oupt(hAPP(c_Nat_OSuc,U_20619),U_20621))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20619),U_20621)) ) ),
    inference(miniscope,[status(thm)],[f_4904_2]) ).

fof(f_4904_4,plain,
    ( ! [U_20620,U_20622] :
        ( c_List_Oupt(U_20620,U_20622) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20620),U_20622)) )
    & ! [U_20621,U_20619] :
        ( c_List_Oupt(U_20619,U_20621) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20619),c_List_Oupt(hAPP(c_Nat_OSuc,U_20619),U_20621))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20619),U_20621)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4904_3]) ).

cnf(f_4904_5,plain,
    ( c_List_Oupt(U_20619,U_20621) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20619),c_List_Oupt(hAPP(c_Nat_OSuc,U_20619),U_20621))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20619),U_20621)) ),
    inference(clausify,[status(thm)],[f_4904_4]) ).

cnf(f_4904_6,plain,
    ( c_List_Oupt(U_20620,U_20622) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20620),U_20622)) ),
    inference(clausify,[status(thm)],[f_4904_4]) ).

fof(f_4905_1,plain,
    ! [V_xs,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,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_4905_2,plain,
    ! [U_20624,U_20623] :
      ( c_List_Olinorder__class_Osorted(U_20623,c_List_Otl(U_20623,U_20624))
      | ~ c_List_Olinorder__class_Osorted(U_20623,U_20624)
      | ~ class_Orderings_Olinorder(U_20623) ),
    inference(variable_rename,[status(thm)],[f_4905_1]) ).

fof(f_4905_3,plain,
    ! [U_20623,U_20624] :
      ( c_List_Olinorder__class_Osorted(U_20623,c_List_Otl(U_20623,U_20624))
      | ~ c_List_Olinorder__class_Osorted(U_20623,U_20624)
      | ~ class_Orderings_Olinorder(U_20623) ),
    inference(definitional_conversion,[status(esa)],[f_4905_2]) ).

cnf(f_4905_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20623,c_List_Otl(U_20623,U_20624))
    | ~ c_List_Olinorder__class_Osorted(U_20623,U_20624)
    | ~ class_Orderings_Olinorder(U_20623) ),
    inference(clausify,[status(thm)],[f_4905_3]) ).

fof(f_4906_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_4906_2,plain,
    ! [U_20629,U_20628,U_20627,U_20626,U_20625] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20625,hAPP(hAPP(c_List_Omap(U_20626,U_20625),U_20627),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20626,U_20625,U_20627),U_20628),U_20629)))
          | ~ c_List_Olinorder__class_Osorted(U_20625,hAPP(hAPP(c_List_Omap(U_20626,U_20625),U_20627),U_20629)) )
        & ( c_List_Olinorder__class_Osorted(U_20625,hAPP(hAPP(c_List_Omap(U_20626,U_20625),U_20627),U_20629))
          | ~ c_List_Olinorder__class_Osorted(U_20625,hAPP(hAPP(c_List_Omap(U_20626,U_20625),U_20627),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20626,U_20625,U_20627),U_20628),U_20629))) ) )
      | ~ class_Orderings_Olinorder(U_20625) ),
    inference(variable_rename,[status(thm)],[f_4906_1]) ).

fof(f_4906_3,plain,
    ( ! [U_20625,U_20626,U_20627,U_20628,U_20629] :
        ( c_List_Olinorder__class_Osorted(U_20625,hAPP(hAPP(c_List_Omap(U_20626,U_20625),U_20627),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20626,U_20625,U_20627),U_20628),U_20629)))
        | ~ c_List_Olinorder__class_Osorted(U_20625,hAPP(hAPP(c_List_Omap(U_20626,U_20625),U_20627),U_20629))
        | ~ sP1230(U_20625,U_20626,U_20627,U_20628,U_20629) )
    & ! [U_20625,U_20626,U_20627,U_20628,U_20629] :
        ( c_List_Olinorder__class_Osorted(U_20625,hAPP(hAPP(c_List_Omap(U_20626,U_20625),U_20627),U_20629))
        | ~ c_List_Olinorder__class_Osorted(U_20625,hAPP(hAPP(c_List_Omap(U_20626,U_20625),U_20627),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20626,U_20625,U_20627),U_20628),U_20629)))
        | ~ sP1230(U_20625,U_20626,U_20627,U_20628,U_20629) )
    & ! [U_20625,U_20626,U_20627,U_20628,U_20629] :
        ( sP1230(U_20625,U_20626,U_20627,U_20628,U_20629)
        | ~ class_Orderings_Olinorder(U_20625) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1230])],[f_4906_2]) ).

cnf(f_4906_4,plain,
    ( sP1230(U_20625,U_20626,U_20627,U_20628,U_20629)
    | ~ class_Orderings_Olinorder(U_20625) ),
    inference(clausify,[status(thm)],[f_4906_3]) ).

cnf(f_4906_5,plain,
    ( c_List_Olinorder__class_Osorted(U_20625,hAPP(hAPP(c_List_Omap(U_20626,U_20625),U_20627),U_20629))
    | ~ c_List_Olinorder__class_Osorted(U_20625,hAPP(hAPP(c_List_Omap(U_20626,U_20625),U_20627),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20626,U_20625,U_20627),U_20628),U_20629)))
    | ~ sP1230(U_20625,U_20626,U_20627,U_20628,U_20629) ),
    inference(clausify,[status(thm)],[f_4906_3]) ).

cnf(f_4906_6,plain,
    ( c_List_Olinorder__class_Osorted(U_20625,hAPP(hAPP(c_List_Omap(U_20626,U_20625),U_20627),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20626,U_20625,U_20627),U_20628),U_20629)))
    | ~ c_List_Olinorder__class_Osorted(U_20625,hAPP(hAPP(c_List_Omap(U_20626,U_20625),U_20627),U_20629))
    | ~ sP1230(U_20625,U_20626,U_20627,U_20628,U_20629) ),
    inference(clausify,[status(thm)],[f_4906_3]) ).

fof(f_4907_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_4907_2,plain,
    ! [U_20634,U_20633,U_20632,U_20631,U_20630] :
      ( c_List_Olinorder__class_Osorted(U_20630,hAPP(hAPP(c_List_Omap(U_20631,U_20630),U_20632),c_List_Oremove1(U_20631,U_20634,U_20633)))
      | ~ c_List_Olinorder__class_Osorted(U_20630,hAPP(hAPP(c_List_Omap(U_20631,U_20630),U_20632),U_20633))
      | ~ class_Orderings_Olinorder(U_20630) ),
    inference(variable_rename,[status(thm)],[f_4907_1]) ).

fof(f_4907_3,plain,
    ! [U_20633,U_20630,U_20632,U_20631,U_20634] :
      ( c_List_Olinorder__class_Osorted(U_20630,hAPP(hAPP(c_List_Omap(U_20631,U_20630),U_20632),c_List_Oremove1(U_20631,U_20634,U_20633)))
      | ~ c_List_Olinorder__class_Osorted(U_20630,hAPP(hAPP(c_List_Omap(U_20631,U_20630),U_20632),U_20633))
      | ~ class_Orderings_Olinorder(U_20630) ),
    inference(definitional_conversion,[status(esa)],[f_4907_2]) ).

cnf(f_4907_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20630,hAPP(hAPP(c_List_Omap(U_20631,U_20630),U_20632),c_List_Oremove1(U_20631,U_20634,U_20633)))
    | ~ c_List_Olinorder__class_Osorted(U_20630,hAPP(hAPP(c_List_Omap(U_20631,U_20630),U_20632),U_20633))
    | ~ class_Orderings_Olinorder(U_20630) ),
    inference(clausify,[status(thm)],[f_4907_3]) ).

fof(f_4908_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_4908_2,plain,
    ! [U_20639,U_20638,U_20637,U_20636,U_20635] :
      ( c_List_Olinorder__class_Osorted(U_20635,hAPP(hAPP(c_List_Omap(U_20636,U_20635),U_20637),c_List_Olinorder__class_Oinsort__insert__key(U_20636,U_20635,U_20637,U_20639,U_20638)))
      | ~ c_List_Olinorder__class_Osorted(U_20635,hAPP(hAPP(c_List_Omap(U_20636,U_20635),U_20637),U_20638))
      | ~ class_Orderings_Olinorder(U_20635) ),
    inference(variable_rename,[status(thm)],[f_4908_1]) ).

fof(f_4908_3,plain,
    ! [U_20636,U_20635,U_20637,U_20638,U_20639] :
      ( c_List_Olinorder__class_Osorted(U_20635,hAPP(hAPP(c_List_Omap(U_20636,U_20635),U_20637),c_List_Olinorder__class_Oinsort__insert__key(U_20636,U_20635,U_20637,U_20639,U_20638)))
      | ~ c_List_Olinorder__class_Osorted(U_20635,hAPP(hAPP(c_List_Omap(U_20636,U_20635),U_20637),U_20638))
      | ~ class_Orderings_Olinorder(U_20635) ),
    inference(definitional_conversion,[status(esa)],[f_4908_2]) ).

cnf(f_4908_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20635,hAPP(hAPP(c_List_Omap(U_20636,U_20635),U_20637),c_List_Olinorder__class_Oinsort__insert__key(U_20636,U_20635,U_20637,U_20639,U_20638)))
    | ~ c_List_Olinorder__class_Osorted(U_20635,hAPP(hAPP(c_List_Omap(U_20636,U_20635),U_20637),U_20638))
    | ~ class_Orderings_Olinorder(U_20635) ),
    inference(clausify,[status(thm)],[f_4908_3]) ).

fof(f_4909_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_4909_2,plain,
    ! [U_20641,U_20640] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(U_20640,U_20641)) = c_List_Oupt(hAPP(c_Nat_OSuc,U_20640),hAPP(c_Nat_OSuc,U_20641)),
    inference(variable_rename,[status(thm)],[f_4909_1]) ).

fof(f_4909_3,plain,
    ! [U_20640,U_20641] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(U_20640,U_20641)) = c_List_Oupt(hAPP(c_Nat_OSuc,U_20640),hAPP(c_Nat_OSuc,U_20641)),
    inference(definitional_conversion,[status(esa)],[f_4909_2]) ).

cnf(f_4909_4,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(U_20640,U_20641)) = c_List_Oupt(hAPP(c_Nat_OSuc,U_20640),hAPP(c_Nat_OSuc,U_20641)),
    inference(clausify,[status(thm)],[f_4909_3]) ).

fof(f_4910_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_4910_2,plain,
    ! [U_20643,U_20642] :
      ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(U_20642,U_20643)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20643),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20642),U_20643)) ),
    inference(variable_rename,[status(thm)],[f_4910_1]) ).

fof(f_4910_3,plain,
    ! [U_20642,U_20643] :
      ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(U_20642,U_20643)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20643),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20642),U_20643)) ),
    inference(definitional_conversion,[status(esa)],[f_4910_2]) ).

cnf(f_4910_4,plain,
    ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(U_20642,U_20643)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20643),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20642),U_20643)) ),
    inference(clausify,[status(thm)],[f_4910_3]) ).

fof(f_4911_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_4911_2,plain,
    ! [U_20649,U_20648,U_20647,U_20646,U_20645,U_20644] :
      ( hAPP(c_List_Ofilter(U_20645,U_20648),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20645,U_20644,U_20646),U_20649),U_20647)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20645,U_20644,U_20646),U_20649),hAPP(c_List_Ofilter(U_20645,U_20648),U_20647))
      | ~ hBOOL(hAPP(U_20648,U_20649))
      | ~ c_List_Olinorder__class_Osorted(U_20644,hAPP(hAPP(c_List_Omap(U_20645,U_20644),U_20646),U_20647))
      | ~ class_Orderings_Olinorder(U_20644) ),
    inference(variable_rename,[status(thm)],[f_4911_1]) ).

fof(f_4911_3,plain,
    ! [U_20644,U_20645,U_20646,U_20647,U_20648,U_20649] :
      ( hAPP(c_List_Ofilter(U_20645,U_20648),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20645,U_20644,U_20646),U_20649),U_20647)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20645,U_20644,U_20646),U_20649),hAPP(c_List_Ofilter(U_20645,U_20648),U_20647))
      | ~ hBOOL(hAPP(U_20648,U_20649))
      | ~ c_List_Olinorder__class_Osorted(U_20644,hAPP(hAPP(c_List_Omap(U_20645,U_20644),U_20646),U_20647))
      | ~ class_Orderings_Olinorder(U_20644) ),
    inference(definitional_conversion,[status(esa)],[f_4911_2]) ).

cnf(f_4911_4,plain,
    ( hAPP(c_List_Ofilter(U_20645,U_20648),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20645,U_20644,U_20646),U_20649),U_20647)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20645,U_20644,U_20646),U_20649),hAPP(c_List_Ofilter(U_20645,U_20648),U_20647))
    | ~ hBOOL(hAPP(U_20648,U_20649))
    | ~ c_List_Olinorder__class_Osorted(U_20644,hAPP(hAPP(c_List_Omap(U_20645,U_20644),U_20646),U_20647))
    | ~ class_Orderings_Olinorder(U_20644) ),
    inference(clausify,[status(thm)],[f_4911_3]) ).

fof(f_4912_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_4912_2,plain,
    ! [U_20651,U_20650] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20650),hAPP(c_List_Onth(U_20650),U_20651)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20650)),U_20651))) = U_20651,
    inference(variable_rename,[status(thm)],[f_4912_1]) ).

fof(f_4912_3,plain,
    ! [U_20651,U_20650] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20650),hAPP(c_List_Onth(U_20650),U_20651)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20650)),U_20651))) = U_20651,
    inference(definitional_conversion,[status(esa)],[f_4912_2]) ).

cnf(f_4912_4,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20650),hAPP(c_List_Onth(U_20650),U_20651)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20650)),U_20651))) = U_20651,
    inference(clausify,[status(thm)],[f_4912_3]) ).

fof(f_4913_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_4913_2,plain,
    ! [U_20653,U_20652] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_20652,U_20653) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20652,hAPP(c_Nat_OSuc,U_20653))),
    inference(variable_rename,[status(thm)],[f_4913_1]) ).

fof(f_4913_3,plain,
    ! [U_20652,U_20653] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_20652,U_20653) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20652,hAPP(c_Nat_OSuc,U_20653))),
    inference(definitional_conversion,[status(esa)],[f_4913_2]) ).

cnf(f_4913_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_20652,U_20653) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20652,hAPP(c_Nat_OSuc,U_20653))),
    inference(clausify,[status(thm)],[f_4913_3]) ).

fof(f_4914_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_4914_2,plain,
    ! [U_20654] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_20654) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20654)),
    inference(variable_rename,[status(thm)],[f_4914_1]) ).

fof(f_4914_3,plain,
    ! [U_20654] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_20654) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20654)),
    inference(definitional_conversion,[status(esa)],[f_4914_2]) ).

cnf(f_4914_4,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_20654) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20654)),
    inference(clausify,[status(thm)],[f_4914_3]) ).

fof(f_4915_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_4915_2,plain,
    ! [U_20658,U_20657,U_20656,U_20655] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20655),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20655),U_20656),c_List_Oupt(U_20657,U_20658))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20655),U_20656),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20657,U_20658)))
      | ~ class_Groups_Ocomm__monoid__add(U_20655) ),
    inference(variable_rename,[status(thm)],[f_4915_1]) ).

fof(f_4915_3,plain,
    ! [U_20655,U_20656,U_20657,U_20658] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20655),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20655),U_20656),c_List_Oupt(U_20657,U_20658))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20655),U_20656),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20657,U_20658)))
      | ~ class_Groups_Ocomm__monoid__add(U_20655) ),
    inference(definitional_conversion,[status(esa)],[f_4915_2]) ).

cnf(f_4915_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20655),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20655),U_20656),c_List_Oupt(U_20657,U_20658))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20655),U_20656),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20657,U_20658)))
    | ~ class_Groups_Ocomm__monoid__add(U_20655) ),
    inference(clausify,[status(thm)],[f_4915_3]) ).

fof(f_4916_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_4916_2,plain,
    ! [U_20662,U_20661,U_20660,U_20659] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20659),U_20660),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20661,U_20662))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20659),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20659),U_20660),c_List_Oupt(U_20661,U_20662)))
      | ~ class_Groups_Ocomm__monoid__add(U_20659) ),
    inference(variable_rename,[status(thm)],[f_4916_1]) ).

fof(f_4916_3,plain,
    ! [U_20659,U_20660,U_20661,U_20662] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20659),U_20660),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20661,U_20662))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20659),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20659),U_20660),c_List_Oupt(U_20661,U_20662)))
      | ~ class_Groups_Ocomm__monoid__add(U_20659) ),
    inference(definitional_conversion,[status(esa)],[f_4916_2]) ).

cnf(f_4916_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20659),U_20660),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20661,U_20662))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20659),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20659),U_20660),c_List_Oupt(U_20661,U_20662)))
    | ~ class_Groups_Ocomm__monoid__add(U_20659) ),
    inference(clausify,[status(thm)],[f_4916_3]) ).

fof(f_4917_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_4917_2,plain,
    ! [U_20665,U_20664,U_20663] :
      ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(U_20663,U_20665)),U_20664) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20663),U_20664)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20663),U_20664)),U_20665)) ),
    inference(variable_rename,[status(thm)],[f_4917_1]) ).

fof(f_4917_3,plain,
    ! [U_20663,U_20664,U_20665] :
      ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(U_20663,U_20665)),U_20664) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20663),U_20664)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20663),U_20664)),U_20665)) ),
    inference(definitional_conversion,[status(esa)],[f_4917_2]) ).

cnf(f_4917_4,plain,
    ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(U_20663,U_20665)),U_20664) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20663),U_20664)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20663),U_20664)),U_20665)) ),
    inference(clausify,[status(thm)],[f_4917_3]) ).

fof(f_4918_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_4918_2,plain,
    ! [U_20667,U_20666] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_20666,U_20667) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20666),hAPP(c_Nat_OSuc,U_20667))),
    inference(variable_rename,[status(thm)],[f_4918_1]) ).

fof(f_4918_3,plain,
    ! [U_20666,U_20667] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_20666,U_20667) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20666),hAPP(c_Nat_OSuc,U_20667))),
    inference(definitional_conversion,[status(esa)],[f_4918_2]) ).

cnf(f_4918_4,plain,
    c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_20666,U_20667) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20666),hAPP(c_Nat_OSuc,U_20667))),
    inference(clausify,[status(thm)],[f_4918_3]) ).

fof(f_4919_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_4919_2,plain,
    ! [U_20672,U_20671,U_20670] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20670,hAPP(hAPP(c_List_Olist_OCons(U_20670),U_20671),U_20672))
          | ~ c_List_Olinorder__class_Osorted(U_20670,U_20672)
          | ? [U_20669] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20670),U_20671),U_20669))
              & hBOOL(hAPP(hAPP(c_member(U_20670),U_20669),hAPP(c_List_Oset(U_20670),U_20672))) ) )
        & ( ( c_List_Olinorder__class_Osorted(U_20670,U_20672)
            & ! [U_20668] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20670),U_20671),U_20668))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20670),U_20668),hAPP(c_List_Oset(U_20670),U_20672))) ) )
          | ~ c_List_Olinorder__class_Osorted(U_20670,hAPP(hAPP(c_List_Olist_OCons(U_20670),U_20671),U_20672)) ) )
      | ~ class_Orderings_Olinorder(U_20670) ),
    inference(variable_rename,[status(thm)],[f_4919_1]) ).

fof(f_4919_3,plain,
    ! [U_20672,U_20671,U_20670] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20670,hAPP(hAPP(c_List_Olist_OCons(U_20670),U_20671),U_20672))
          | ~ c_List_Olinorder__class_Osorted(U_20670,U_20672)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20670),U_20671),sK505(U_20672,U_20671,U_20670)))
            & hBOOL(hAPP(hAPP(c_member(U_20670),sK505(U_20672,U_20671,U_20670)),hAPP(c_List_Oset(U_20670),U_20672))) ) )
        & ( ( c_List_Olinorder__class_Osorted(U_20670,U_20672)
            & ! [U_20668] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20670),U_20671),U_20668))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20670),U_20668),hAPP(c_List_Oset(U_20670),U_20672))) ) )
          | ~ c_List_Olinorder__class_Osorted(U_20670,hAPP(hAPP(c_List_Olist_OCons(U_20670),U_20671),U_20672)) ) )
      | ~ class_Orderings_Olinorder(U_20670) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK505]),skolemize(U_20669,sK505(U_20672,U_20671,U_20670))],[f_4919_2]) ).

fof(f_4919_4,plain,
    ( ! [U_20670,U_20671,U_20672] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20670),U_20671),sK505(U_20672,U_20671,U_20670)))
        | ~ sP1232(U_20670,U_20671,U_20672) )
    & ! [U_20670,U_20671,U_20672] :
        ( hBOOL(hAPP(hAPP(c_member(U_20670),sK505(U_20672,U_20671,U_20670)),hAPP(c_List_Oset(U_20670),U_20672)))
        | ~ sP1232(U_20670,U_20671,U_20672) )
    & ! [U_20668,U_20670,U_20671,U_20672] :
        ( c_List_Olinorder__class_Osorted(U_20670,U_20672)
        | ~ sP1231(U_20668,U_20670,U_20671,U_20672) )
    & ! [U_20668,U_20670,U_20671,U_20672] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20670),U_20671),U_20668))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20670),U_20668),hAPP(c_List_Oset(U_20670),U_20672)))
        | ~ sP1231(U_20668,U_20670,U_20671,U_20672) )
    & ! [U_20668,U_20670,U_20671,U_20672] :
        ( c_List_Olinorder__class_Osorted(U_20670,hAPP(hAPP(c_List_Olist_OCons(U_20670),U_20671),U_20672))
        | ~ c_List_Olinorder__class_Osorted(U_20670,U_20672)
        | sP1232(U_20670,U_20671,U_20672)
        | ~ sP1233(U_20668,U_20670,U_20671,U_20672) )
    & ! [U_20668,U_20670,U_20671,U_20672] :
        ( sP1231(U_20668,U_20670,U_20671,U_20672)
        | ~ c_List_Olinorder__class_Osorted(U_20670,hAPP(hAPP(c_List_Olist_OCons(U_20670),U_20671),U_20672))
        | ~ sP1233(U_20668,U_20670,U_20671,U_20672) )
    & ! [U_20668,U_20670,U_20671,U_20672] :
        ( sP1233(U_20668,U_20670,U_20671,U_20672)
        | ~ class_Orderings_Olinorder(U_20670) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1231,sP1232,sP1233])],[f_4919_3]) ).

cnf(f_4919_5,plain,
    ( sP1233(U_20668,U_20670,U_20671,U_20672)
    | ~ class_Orderings_Olinorder(U_20670) ),
    inference(clausify,[status(thm)],[f_4919_4]) ).

cnf(f_4919_6,plain,
    ( sP1231(U_20668,U_20670,U_20671,U_20672)
    | ~ c_List_Olinorder__class_Osorted(U_20670,hAPP(hAPP(c_List_Olist_OCons(U_20670),U_20671),U_20672))
    | ~ sP1233(U_20668,U_20670,U_20671,U_20672) ),
    inference(clausify,[status(thm)],[f_4919_4]) ).

cnf(f_4919_7,plain,
    ( c_List_Olinorder__class_Osorted(U_20670,hAPP(hAPP(c_List_Olist_OCons(U_20670),U_20671),U_20672))
    | ~ c_List_Olinorder__class_Osorted(U_20670,U_20672)
    | sP1232(U_20670,U_20671,U_20672)
    | ~ sP1233(U_20668,U_20670,U_20671,U_20672) ),
    inference(clausify,[status(thm)],[f_4919_4]) ).

cnf(f_4919_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20670),U_20671),U_20668))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20670),U_20668),hAPP(c_List_Oset(U_20670),U_20672)))
    | ~ sP1231(U_20668,U_20670,U_20671,U_20672) ),
    inference(clausify,[status(thm)],[f_4919_4]) ).

cnf(f_4919_9,plain,
    ( c_List_Olinorder__class_Osorted(U_20670,U_20672)
    | ~ sP1231(U_20668,U_20670,U_20671,U_20672) ),
    inference(clausify,[status(thm)],[f_4919_4]) ).

cnf(f_4919_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20670),sK505(U_20672,U_20671,U_20670)),hAPP(c_List_Oset(U_20670),U_20672)))
    | ~ sP1232(U_20670,U_20671,U_20672) ),
    inference(clausify,[status(thm)],[f_4919_4]) ).

cnf(f_4919_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20670),U_20671),sK505(U_20672,U_20671,U_20670)))
    | ~ sP1232(U_20670,U_20671,U_20672) ),
    inference(clausify,[status(thm)],[f_4919_4]) ).

fof(f_4920_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_4920_2,plain,
    ! [U_20674,U_20673] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_20673,U_20674) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20673),U_20674)),
    inference(variable_rename,[status(thm)],[f_4920_1]) ).

fof(f_4920_3,plain,
    ! [U_20674,U_20673] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_20673,U_20674) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20673),U_20674)),
    inference(definitional_conversion,[status(esa)],[f_4920_2]) ).

cnf(f_4920_4,plain,
    c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_20673,U_20674) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20673),U_20674)),
    inference(clausify,[status(thm)],[f_4920_3]) ).

fof(f_4921_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_4921_2,plain,
    ! [U_20679,U_20678,U_20677,U_20676,U_20675] :
      ( hAPP(hAPP(c_List_Onth(U_20678),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20678),U_20679),c_List_Oupt(U_20677,U_20676))),U_20675) = hAPP(U_20679,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20677),U_20675))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20675),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20676),U_20677))) ),
    inference(variable_rename,[status(thm)],[f_4921_1]) ).

fof(f_4921_3,plain,
    ! [U_20677,U_20676,U_20679,U_20678,U_20675] :
      ( hAPP(hAPP(c_List_Onth(U_20678),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20678),U_20679),c_List_Oupt(U_20677,U_20676))),U_20675) = hAPP(U_20679,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20677),U_20675))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20675),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20676),U_20677))) ),
    inference(definitional_conversion,[status(esa)],[f_4921_2]) ).

cnf(f_4921_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_20678),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20678),U_20679),c_List_Oupt(U_20677,U_20676))),U_20675) = hAPP(U_20679,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20677),U_20675))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20675),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20676),U_20677))) ),
    inference(clausify,[status(thm)],[f_4921_3]) ).

fof(f_4922_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_4922_2,plain,
    ! [U_20681,U_20680] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_20680),c_List_Olinorder__class_Osorted__list__of__set(U_20680,U_20681)))
        & c_List_Olinorder__class_Osorted(U_20680,c_List_Olinorder__class_Osorted__list__of__set(U_20680,U_20681))
        & hAPP(c_List_Oset(U_20680),c_List_Olinorder__class_Osorted__list__of__set(U_20680,U_20681)) = U_20681 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20680),U_20681))
      | ~ class_Orderings_Olinorder(U_20680) ),
    inference(variable_rename,[status(thm)],[f_4922_1]) ).

fof(f_4922_3,plain,
    ( ! [U_20680,U_20681] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20680),c_List_Olinorder__class_Osorted__list__of__set(U_20680,U_20681)))
        | ~ sP1234(U_20680,U_20681) )
    & ! [U_20680,U_20681] :
        ( c_List_Olinorder__class_Osorted(U_20680,c_List_Olinorder__class_Osorted__list__of__set(U_20680,U_20681))
        | ~ sP1234(U_20680,U_20681) )
    & ! [U_20680,U_20681] :
        ( hAPP(c_List_Oset(U_20680),c_List_Olinorder__class_Osorted__list__of__set(U_20680,U_20681)) = U_20681
        | ~ sP1234(U_20680,U_20681) )
    & ! [U_20680,U_20681] :
        ( sP1234(U_20680,U_20681)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20680),U_20681))
        | ~ class_Orderings_Olinorder(U_20680) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1234])],[f_4922_2]) ).

cnf(f_4922_4,plain,
    ( sP1234(U_20680,U_20681)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20680),U_20681))
    | ~ class_Orderings_Olinorder(U_20680) ),
    inference(clausify,[status(thm)],[f_4922_3]) ).

cnf(f_4922_5,plain,
    ( hAPP(c_List_Oset(U_20680),c_List_Olinorder__class_Osorted__list__of__set(U_20680,U_20681)) = U_20681
    | ~ sP1234(U_20680,U_20681) ),
    inference(clausify,[status(thm)],[f_4922_3]) ).

cnf(f_4922_6,plain,
    ( c_List_Olinorder__class_Osorted(U_20680,c_List_Olinorder__class_Osorted__list__of__set(U_20680,U_20681))
    | ~ sP1234(U_20680,U_20681) ),
    inference(clausify,[status(thm)],[f_4922_3]) ).

cnf(f_4922_7,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20680),c_List_Olinorder__class_Osorted__list__of__set(U_20680,U_20681)))
    | ~ sP1234(U_20680,U_20681) ),
    inference(clausify,[status(thm)],[f_4922_3]) ).

fof(f_4923_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_4923_2,plain,
    ! [U_20682] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_20682) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_20682))),
    inference(variable_rename,[status(thm)],[f_4923_1]) ).

fof(f_4923_3,plain,
    ! [U_20682] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_20682) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_20682))),
    inference(definitional_conversion,[status(esa)],[f_4923_2]) ).

cnf(f_4923_4,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_20682) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_20682))),
    inference(clausify,[status(thm)],[f_4923_3]) ).

fof(f_4924_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_4924_2,plain,
    ! [U_20685,U_20684,U_20683] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20683,U_20683,c_COMBI(U_20683)),U_20684),c_List_Oremove1(U_20683,U_20684,U_20685)) = U_20685
      | ~ c_List_Olinorder__class_Osorted(U_20683,U_20685)
      | ~ hBOOL(hAPP(hAPP(c_member(U_20683),U_20684),hAPP(c_List_Oset(U_20683),U_20685)))
      | ~ class_Orderings_Olinorder(U_20683) ),
    inference(variable_rename,[status(thm)],[f_4924_1]) ).

fof(f_4924_3,plain,
    ! [U_20683,U_20684,U_20685] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20683,U_20683,c_COMBI(U_20683)),U_20684),c_List_Oremove1(U_20683,U_20684,U_20685)) = U_20685
      | ~ c_List_Olinorder__class_Osorted(U_20683,U_20685)
      | ~ hBOOL(hAPP(hAPP(c_member(U_20683),U_20684),hAPP(c_List_Oset(U_20683),U_20685)))
      | ~ class_Orderings_Olinorder(U_20683) ),
    inference(definitional_conversion,[status(esa)],[f_4924_2]) ).

cnf(f_4924_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20683,U_20683,c_COMBI(U_20683)),U_20684),c_List_Oremove1(U_20683,U_20684,U_20685)) = U_20685
    | ~ c_List_Olinorder__class_Osorted(U_20683,U_20685)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20683),U_20684),hAPP(c_List_Oset(U_20683),U_20685)))
    | ~ class_Orderings_Olinorder(U_20683) ),
    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_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_4925_2,plain,
    ! [U_20689,U_20688,U_20687,U_20686] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20686),hAPP(hAPP(c_List_Onth(U_20686),U_20687),U_20688)),hAPP(hAPP(c_List_Onth(U_20686),U_20687),U_20689)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20689),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20686)),U_20687)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20688),U_20689))
      | ~ c_List_Olinorder__class_Osorted(U_20686,U_20687)
      | ~ class_Orderings_Olinorder(U_20686) ),
    inference(variable_rename,[status(thm)],[f_4925_1]) ).

fof(f_4925_3,plain,
    ! [U_20686,U_20687,U_20688,U_20689] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20686),hAPP(hAPP(c_List_Onth(U_20686),U_20687),U_20688)),hAPP(hAPP(c_List_Onth(U_20686),U_20687),U_20689)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20689),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20686)),U_20687)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20688),U_20689))
      | ~ c_List_Olinorder__class_Osorted(U_20686,U_20687)
      | ~ class_Orderings_Olinorder(U_20686) ),
    inference(definitional_conversion,[status(esa)],[f_4925_2]) ).

cnf(f_4925_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20686),hAPP(hAPP(c_List_Onth(U_20686),U_20687),U_20688)),hAPP(hAPP(c_List_Onth(U_20686),U_20687),U_20689)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20689),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20686)),U_20687)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20688),U_20689))
    | ~ c_List_Olinorder__class_Osorted(U_20686,U_20687)
    | ~ class_Orderings_Olinorder(U_20686) ),
    inference(clausify,[status(thm)],[f_4925_3]) ).

fof(f_4926_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_4926_2,plain,
    ! [U_20695,U_20694] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20694,U_20695)
          | ? [U_20693] :
              ( ? [U_20692] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20694),hAPP(hAPP(c_List_Onth(U_20694),U_20695),U_20692)),hAPP(hAPP(c_List_Onth(U_20694),U_20695),U_20693)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20692),U_20693)) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20693),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20694)),U_20695))) ) )
        & ( ! [U_20691] :
              ( ! [U_20690] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20694),hAPP(hAPP(c_List_Onth(U_20694),U_20695),U_20690)),hAPP(hAPP(c_List_Onth(U_20694),U_20695),U_20691)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20690),U_20691)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20691),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20694)),U_20695))) )
          | ~ c_List_Olinorder__class_Osorted(U_20694,U_20695) ) )
      | ~ class_Orderings_Olinorder(U_20694) ),
    inference(variable_rename,[status(thm)],[f_4926_1]) ).

fof(f_4926_3,plain,
    ! [U_20695,U_20694] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20694,U_20695)
          | ( ? [U_20692] :
                ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20694),hAPP(hAPP(c_List_Onth(U_20694),U_20695),U_20692)),hAPP(hAPP(c_List_Onth(U_20694),U_20695),sK506(U_20695,U_20694))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20692),sK506(U_20695,U_20694))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK506(U_20695,U_20694)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20694)),U_20695))) ) )
        & ( ! [U_20691] :
              ( ! [U_20690] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20694),hAPP(hAPP(c_List_Onth(U_20694),U_20695),U_20690)),hAPP(hAPP(c_List_Onth(U_20694),U_20695),U_20691)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20690),U_20691)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20691),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20694)),U_20695))) )
          | ~ c_List_Olinorder__class_Osorted(U_20694,U_20695) ) )
      | ~ class_Orderings_Olinorder(U_20694) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK506]),skolemize(U_20693,sK506(U_20695,U_20694))],[f_4926_2]) ).

fof(f_4926_4,plain,
    ! [U_20695,U_20694] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20694,U_20695)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20694),hAPP(hAPP(c_List_Onth(U_20694),U_20695),sK507(U_20695,U_20694))),hAPP(hAPP(c_List_Onth(U_20694),U_20695),sK506(U_20695,U_20694))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK507(U_20695,U_20694)),sK506(U_20695,U_20694)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK506(U_20695,U_20694)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20694)),U_20695))) ) )
        & ( ! [U_20691] :
              ( ! [U_20690] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20694),hAPP(hAPP(c_List_Onth(U_20694),U_20695),U_20690)),hAPP(hAPP(c_List_Onth(U_20694),U_20695),U_20691)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20690),U_20691)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20691),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20694)),U_20695))) )
          | ~ c_List_Olinorder__class_Osorted(U_20694,U_20695) ) )
      | ~ class_Orderings_Olinorder(U_20694) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK507]),skolemize(U_20692,sK507(U_20695,U_20694))],[f_4926_3]) ).

fof(f_4926_5,plain,
    ( ! [U_20694,U_20695] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20694),hAPP(hAPP(c_List_Onth(U_20694),U_20695),sK507(U_20695,U_20694))),hAPP(hAPP(c_List_Onth(U_20694),U_20695),sK506(U_20695,U_20694))))
        | ~ sP1235(U_20694,U_20695) )
    & ! [U_20694,U_20695] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK507(U_20695,U_20694)),sK506(U_20695,U_20694)))
        | ~ sP1235(U_20694,U_20695) )
    & ! [U_20694,U_20695] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK506(U_20695,U_20694)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20694)),U_20695)))
        | ~ sP1235(U_20694,U_20695) )
    & ! [U_20691,U_20690,U_20694,U_20695] :
        ( c_List_Olinorder__class_Osorted(U_20694,U_20695)
        | sP1235(U_20694,U_20695)
        | ~ sP1236(U_20691,U_20690,U_20694,U_20695) )
    & ! [U_20691,U_20690,U_20694,U_20695] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20694),hAPP(hAPP(c_List_Onth(U_20694),U_20695),U_20690)),hAPP(hAPP(c_List_Onth(U_20694),U_20695),U_20691)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20690),U_20691))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20691),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20694)),U_20695)))
        | ~ c_List_Olinorder__class_Osorted(U_20694,U_20695)
        | ~ sP1236(U_20691,U_20690,U_20694,U_20695) )
    & ! [U_20691,U_20690,U_20694,U_20695] :
        ( sP1236(U_20691,U_20690,U_20694,U_20695)
        | ~ class_Orderings_Olinorder(U_20694) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1235,sP1236])],[f_4926_4]) ).

cnf(f_4926_6,plain,
    ( sP1236(U_20691,U_20690,U_20694,U_20695)
    | ~ class_Orderings_Olinorder(U_20694) ),
    inference(clausify,[status(thm)],[f_4926_5]) ).

cnf(f_4926_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20694),hAPP(hAPP(c_List_Onth(U_20694),U_20695),U_20690)),hAPP(hAPP(c_List_Onth(U_20694),U_20695),U_20691)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20690),U_20691))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20691),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20694)),U_20695)))
    | ~ c_List_Olinorder__class_Osorted(U_20694,U_20695)
    | ~ sP1236(U_20691,U_20690,U_20694,U_20695) ),
    inference(clausify,[status(thm)],[f_4926_5]) ).

cnf(f_4926_8,plain,
    ( c_List_Olinorder__class_Osorted(U_20694,U_20695)
    | sP1235(U_20694,U_20695)
    | ~ sP1236(U_20691,U_20690,U_20694,U_20695) ),
    inference(clausify,[status(thm)],[f_4926_5]) ).

cnf(f_4926_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK506(U_20695,U_20694)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20694)),U_20695)))
    | ~ sP1235(U_20694,U_20695) ),
    inference(clausify,[status(thm)],[f_4926_5]) ).

cnf(f_4926_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK507(U_20695,U_20694)),sK506(U_20695,U_20694)))
    | ~ sP1235(U_20694,U_20695) ),
    inference(clausify,[status(thm)],[f_4926_5]) ).

cnf(f_4926_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20694),hAPP(hAPP(c_List_Onth(U_20694),U_20695),sK507(U_20695,U_20694))),hAPP(hAPP(c_List_Onth(U_20694),U_20695),sK506(U_20695,U_20694))))
    | ~ sP1235(U_20694,U_20695) ),
    inference(clausify,[status(thm)],[f_4926_5]) ).

fof(f_4927_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_4927_2,plain,
    ! [U_20700,U_20699,U_20698,U_20697,U_20696] :
      ( U_20699 = U_20700
      | hAPP(c_List_Oset(U_20697),U_20699) != hAPP(c_List_Oset(U_20697),U_20700)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20696),hAPP(hAPP(c_List_Omap(U_20697,U_20696),U_20698),U_20700)))
      | ~ c_List_Olinorder__class_Osorted(U_20696,hAPP(hAPP(c_List_Omap(U_20697,U_20696),U_20698),U_20700))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20696),hAPP(hAPP(c_List_Omap(U_20697,U_20696),U_20698),U_20699)))
      | ~ c_List_Olinorder__class_Osorted(U_20696,hAPP(hAPP(c_List_Omap(U_20697,U_20696),U_20698),U_20699))
      | ~ c_Fun_Oinj__on(U_20697,U_20696,U_20698,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20697,tc_HOL_Obool)),hAPP(c_List_Oset(U_20697),U_20699)),hAPP(c_List_Oset(U_20697),U_20700)))
      | ~ class_Orderings_Olinorder(U_20696) ),
    inference(variable_rename,[status(thm)],[f_4927_1]) ).

fof(f_4927_3,plain,
    ! [U_20697,U_20696,U_20700,U_20698,U_20699] :
      ( U_20699 = U_20700
      | hAPP(c_List_Oset(U_20697),U_20699) != hAPP(c_List_Oset(U_20697),U_20700)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20696),hAPP(hAPP(c_List_Omap(U_20697,U_20696),U_20698),U_20700)))
      | ~ c_List_Olinorder__class_Osorted(U_20696,hAPP(hAPP(c_List_Omap(U_20697,U_20696),U_20698),U_20700))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20696),hAPP(hAPP(c_List_Omap(U_20697,U_20696),U_20698),U_20699)))
      | ~ c_List_Olinorder__class_Osorted(U_20696,hAPP(hAPP(c_List_Omap(U_20697,U_20696),U_20698),U_20699))
      | ~ c_Fun_Oinj__on(U_20697,U_20696,U_20698,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20697,tc_HOL_Obool)),hAPP(c_List_Oset(U_20697),U_20699)),hAPP(c_List_Oset(U_20697),U_20700)))
      | ~ class_Orderings_Olinorder(U_20696) ),
    inference(definitional_conversion,[status(esa)],[f_4927_2]) ).

cnf(f_4927_4,plain,
    ( U_20699 = U_20700
    | hAPP(c_List_Oset(U_20697),U_20699) != hAPP(c_List_Oset(U_20697),U_20700)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20696),hAPP(hAPP(c_List_Omap(U_20697,U_20696),U_20698),U_20700)))
    | ~ c_List_Olinorder__class_Osorted(U_20696,hAPP(hAPP(c_List_Omap(U_20697,U_20696),U_20698),U_20700))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20696),hAPP(hAPP(c_List_Omap(U_20697,U_20696),U_20698),U_20699)))
    | ~ c_List_Olinorder__class_Osorted(U_20696,hAPP(hAPP(c_List_Omap(U_20697,U_20696),U_20698),U_20699))
    | ~ c_Fun_Oinj__on(U_20697,U_20696,U_20698,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20697,tc_HOL_Obool)),hAPP(c_List_Oset(U_20697),U_20699)),hAPP(c_List_Oset(U_20697),U_20700)))
    | ~ class_Orderings_Olinorder(U_20696) ),
    inference(clausify,[status(thm)],[f_4927_3]) ).

fof(f_4928_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_4928_2,plain,
    ! [U_20704,U_20703,U_20702,U_20701] : hAPP(hAPP(c_List_Omap(tc_prod(U_20701,tc_Nat_Onat),U_20701),c_Product__Type_Ofst(U_20701,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20701,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20701,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_20701,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20701,tc_Nat_Onat))),U_20702)),hAPP(hAPP(c_List_Ozip(U_20701,tc_Nat_Onat),U_20703),c_List_Oupt(U_20704,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20704),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20701)),U_20703)))))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20701,tc_Nat_Onat),U_20701),c_Product__Type_Ofst(U_20701,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20701,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20701,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_20701,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_20701,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_20701,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(U_20701,tc_Nat_Onat))),U_20704))),U_20702)),hAPP(hAPP(c_List_Ozip(U_20701,tc_Nat_Onat),U_20703),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20701)),U_20703))))),
    inference(variable_rename,[status(thm)],[f_4928_1]) ).

fof(f_4928_3,plain,
    ! [U_20703,U_20701,U_20704,U_20702] : hAPP(hAPP(c_List_Omap(tc_prod(U_20701,tc_Nat_Onat),U_20701),c_Product__Type_Ofst(U_20701,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20701,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20701,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_20701,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20701,tc_Nat_Onat))),U_20702)),hAPP(hAPP(c_List_Ozip(U_20701,tc_Nat_Onat),U_20703),c_List_Oupt(U_20704,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20704),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20701)),U_20703)))))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20701,tc_Nat_Onat),U_20701),c_Product__Type_Ofst(U_20701,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20701,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20701,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_20701,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_20701,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_20701,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(U_20701,tc_Nat_Onat))),U_20704))),U_20702)),hAPP(hAPP(c_List_Ozip(U_20701,tc_Nat_Onat),U_20703),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20701)),U_20703))))),
    inference(definitional_conversion,[status(esa)],[f_4928_2]) ).

cnf(f_4928_4,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_20701,tc_Nat_Onat),U_20701),c_Product__Type_Ofst(U_20701,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20701,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20701,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_20701,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20701,tc_Nat_Onat))),U_20702)),hAPP(hAPP(c_List_Ozip(U_20701,tc_Nat_Onat),U_20703),c_List_Oupt(U_20704,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20704),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20701)),U_20703)))))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20701,tc_Nat_Onat),U_20701),c_Product__Type_Ofst(U_20701,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20701,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20701,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_20701,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_20701,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_20701,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(U_20701,tc_Nat_Onat))),U_20704))),U_20702)),hAPP(hAPP(c_List_Ozip(U_20701,tc_Nat_Onat),U_20703),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20701)),U_20703))))),
    inference(clausify,[status(thm)],[f_4928_3]) ).

fof(f_4929_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_4929_2,plain,
    ! [U_20708,U_20707,U_20706] :
      ( c_List_Otranspose(U_20707,U_20706) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_20707)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20707)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_20707),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20707)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_20707)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_20707),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20707),tc_fun(tc_Nat_Onat,U_20707),tc_Nat_Onat),c_List_Onth(U_20707)),hAPP(c_List_Onth(tc_List_Olist(U_20707)),U_20706))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20707))),U_20706)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20708))
      | ? [U_20705] :
          ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20707)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20707)),U_20706),U_20705)) != U_20708
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20705),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20707))),U_20706))) )
      | ( U_20708 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & U_20706 = c_List_Olist_ONil(tc_List_Olist(U_20707)) ) ),
    inference(variable_rename,[status(thm)],[f_4929_1]) ).

fof(f_4929_3,plain,
    ! [U_20708,U_20707,U_20706] :
      ( c_List_Otranspose(U_20707,U_20706) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_20707)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20707)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_20707),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20707)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_20707)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_20707),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20707),tc_fun(tc_Nat_Onat,U_20707),tc_Nat_Onat),c_List_Onth(U_20707)),hAPP(c_List_Onth(tc_List_Olist(U_20707)),U_20706))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20707))),U_20706)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20708))
      | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20707)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20707)),U_20706),sK508(U_20708,U_20707,U_20706))) != U_20708
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK508(U_20708,U_20707,U_20706)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20707))),U_20706))) )
      | ( U_20708 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & U_20706 = c_List_Olist_ONil(tc_List_Olist(U_20707)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK508]),skolemize(U_20705,sK508(U_20708,U_20707,U_20706))],[f_4929_2]) ).

fof(f_4929_4,plain,
    ( ! [U_20706,U_20707,U_20708] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20707)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20707)),U_20706),sK508(U_20708,U_20707,U_20706))) != U_20708
        | ~ sP1238(U_20706,U_20707,U_20708) )
    & ! [U_20706,U_20707,U_20708] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK508(U_20708,U_20707,U_20706)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20707))),U_20706)))
        | ~ sP1238(U_20706,U_20707,U_20708) )
    & ! [U_20706,U_20707,U_20708] :
        ( U_20708 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1237(U_20706,U_20707,U_20708) )
    & ! [U_20706,U_20707,U_20708] :
        ( U_20706 = c_List_Olist_ONil(tc_List_Olist(U_20707))
        | ~ sP1237(U_20706,U_20707,U_20708) )
    & ! [U_20706,U_20707,U_20708] :
        ( c_List_Otranspose(U_20707,U_20706) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_20707)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20707)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_20707),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20707)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_20707)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_20707),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20707),tc_fun(tc_Nat_Onat,U_20707),tc_Nat_Onat),c_List_Onth(U_20707)),hAPP(c_List_Onth(tc_List_Olist(U_20707)),U_20706))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20707))),U_20706)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20708))
        | sP1238(U_20706,U_20707,U_20708)
        | sP1237(U_20706,U_20707,U_20708) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1237,sP1238])],[f_4929_3]) ).

cnf(f_4929_5,plain,
    ( c_List_Otranspose(U_20707,U_20706) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_20707)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20707)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_20707),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20707)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_20707)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_20707),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20707),tc_fun(tc_Nat_Onat,U_20707),tc_Nat_Onat),c_List_Onth(U_20707)),hAPP(c_List_Onth(tc_List_Olist(U_20707)),U_20706))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20707))),U_20706)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20708))
    | sP1238(U_20706,U_20707,U_20708)
    | sP1237(U_20706,U_20707,U_20708) ),
    inference(clausify,[status(thm)],[f_4929_4]) ).

cnf(f_4929_6,plain,
    ( U_20706 = c_List_Olist_ONil(tc_List_Olist(U_20707))
    | ~ sP1237(U_20706,U_20707,U_20708) ),
    inference(clausify,[status(thm)],[f_4929_4]) ).

cnf(f_4929_7,plain,
    ( U_20708 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1237(U_20706,U_20707,U_20708) ),
    inference(clausify,[status(thm)],[f_4929_4]) ).

cnf(f_4929_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK508(U_20708,U_20707,U_20706)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20707))),U_20706)))
    | ~ sP1238(U_20706,U_20707,U_20708) ),
    inference(clausify,[status(thm)],[f_4929_4]) ).

cnf(f_4929_9,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20707)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20707)),U_20706),sK508(U_20708,U_20707,U_20706))) != U_20708
    | ~ sP1238(U_20706,U_20707,U_20708) ),
    inference(clausify,[status(thm)],[f_4929_4]) ).

fof(f_4930_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_4930_2,plain,
    ! [U_20710,U_20709] :
      ( c_List_Otranspose(U_20709,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20709)),c_List_Olist_ONil(U_20709)),U_20710)) = c_List_Otranspose(U_20709,U_20710)
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20709)),c_List_Otranspose__rel(U_20709)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20709)),c_List_Olist_ONil(U_20709)),U_20710))) ),
    inference(variable_rename,[status(thm)],[f_4930_1]) ).

fof(f_4930_3,plain,
    ! [U_20709,U_20710] :
      ( c_List_Otranspose(U_20709,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20709)),c_List_Olist_ONil(U_20709)),U_20710)) = c_List_Otranspose(U_20709,U_20710)
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20709)),c_List_Otranspose__rel(U_20709)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20709)),c_List_Olist_ONil(U_20709)),U_20710))) ),
    inference(definitional_conversion,[status(esa)],[f_4930_2]) ).

cnf(f_4930_4,plain,
    ( c_List_Otranspose(U_20709,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20709)),c_List_Olist_ONil(U_20709)),U_20710)) = c_List_Otranspose(U_20709,U_20710)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20709)),c_List_Otranspose__rel(U_20709)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20709)),c_List_Olist_ONil(U_20709)),U_20710))) ),
    inference(clausify,[status(thm)],[f_4930_3]) ).

fof(f_4931_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_4931_2,plain,
    ! [U_20711] :
      ( c_List_Otranspose(U_20711,c_List_Olist_ONil(tc_List_Olist(U_20711))) = c_List_Olist_ONil(tc_List_Olist(U_20711))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20711)),c_List_Otranspose__rel(U_20711)),c_List_Olist_ONil(tc_List_Olist(U_20711)))) ),
    inference(variable_rename,[status(thm)],[f_4931_1]) ).

fof(f_4931_3,plain,
    ! [U_20711] :
      ( c_List_Otranspose(U_20711,c_List_Olist_ONil(tc_List_Olist(U_20711))) = c_List_Olist_ONil(tc_List_Olist(U_20711))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20711)),c_List_Otranspose__rel(U_20711)),c_List_Olist_ONil(tc_List_Olist(U_20711)))) ),
    inference(definitional_conversion,[status(esa)],[f_4931_2]) ).

cnf(f_4931_4,plain,
    ( c_List_Otranspose(U_20711,c_List_Olist_ONil(tc_List_Olist(U_20711))) = c_List_Olist_ONil(tc_List_Olist(U_20711))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20711)),c_List_Otranspose__rel(U_20711)),c_List_Olist_ONil(tc_List_Olist(U_20711)))) ),
    inference(clausify,[status(thm)],[f_4931_3]) ).

fof(f_4932_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_4932_2,plain,
    ! [U_20714,U_20713,U_20712] :
      ( hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20712),U_20712),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20712),tc_Nat_Onat,U_20712),c_List_Onth(U_20712)),U_20714)),hAPP(c_List_Ofilter(tc_List_Olist(U_20712),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20712)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20714)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20712)))),c_List_Otranspose(U_20712,U_20713))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20712)),U_20713),U_20714)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20714),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20712))),U_20713)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20712),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20712))),U_20713))) ),
    inference(variable_rename,[status(thm)],[f_4932_1]) ).

fof(f_4932_3,plain,
    ! [U_20712,U_20713,U_20714] :
      ( hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20712),U_20712),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20712),tc_Nat_Onat,U_20712),c_List_Onth(U_20712)),U_20714)),hAPP(c_List_Ofilter(tc_List_Olist(U_20712),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20712)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20714)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20712)))),c_List_Otranspose(U_20712,U_20713))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20712)),U_20713),U_20714)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20714),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20712))),U_20713)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20712),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20712))),U_20713))) ),
    inference(definitional_conversion,[status(esa)],[f_4932_2]) ).

cnf(f_4932_4,plain,
    ( hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20712),U_20712),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20712),tc_Nat_Onat,U_20712),c_List_Onth(U_20712)),U_20714)),hAPP(c_List_Ofilter(tc_List_Olist(U_20712),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20712)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20714)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20712)))),c_List_Otranspose(U_20712,U_20713))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20712)),U_20713),U_20714)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20714),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20712))),U_20713)))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20712),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20712))),U_20713))) ),
    inference(clausify,[status(thm)],[f_4932_3]) ).

fof(f_4933_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_4933_2,plain,
    ! [U_20716,U_20715] : c_List_Oconcat(U_20715,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20715),tc_List_Olist(U_20715)),c_List_Olist_Olist__case(tc_List_Olist(U_20715),U_20715,c_List_Olist_ONil(U_20715),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20715),tc_fun(tc_List_Olist(U_20715),tc_List_Olist(U_20715)),U_20715),c_COMBK(tc_List_Olist(U_20715),tc_List_Olist(U_20715))),hAPP(hAPP(c_COMBC(U_20715,tc_List_Olist(U_20715),tc_List_Olist(U_20715)),c_List_Olist_OCons(U_20715)),c_List_Olist_ONil(U_20715))))),U_20716)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20715),U_20715),c_List_Ohd(U_20715)),hAPP(c_List_Ofilter(tc_List_Olist(U_20715),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20715)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20715),tc_List_Olist(U_20715),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20715)))),U_20716)),
    inference(variable_rename,[status(thm)],[f_4933_1]) ).

fof(f_4933_3,plain,
    ! [U_20715,U_20716] : c_List_Oconcat(U_20715,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20715),tc_List_Olist(U_20715)),c_List_Olist_Olist__case(tc_List_Olist(U_20715),U_20715,c_List_Olist_ONil(U_20715),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20715),tc_fun(tc_List_Olist(U_20715),tc_List_Olist(U_20715)),U_20715),c_COMBK(tc_List_Olist(U_20715),tc_List_Olist(U_20715))),hAPP(hAPP(c_COMBC(U_20715,tc_List_Olist(U_20715),tc_List_Olist(U_20715)),c_List_Olist_OCons(U_20715)),c_List_Olist_ONil(U_20715))))),U_20716)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20715),U_20715),c_List_Ohd(U_20715)),hAPP(c_List_Ofilter(tc_List_Olist(U_20715),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20715)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20715),tc_List_Olist(U_20715),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20715)))),U_20716)),
    inference(definitional_conversion,[status(esa)],[f_4933_2]) ).

cnf(f_4933_4,plain,
    c_List_Oconcat(U_20715,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20715),tc_List_Olist(U_20715)),c_List_Olist_Olist__case(tc_List_Olist(U_20715),U_20715,c_List_Olist_ONil(U_20715),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20715),tc_fun(tc_List_Olist(U_20715),tc_List_Olist(U_20715)),U_20715),c_COMBK(tc_List_Olist(U_20715),tc_List_Olist(U_20715))),hAPP(hAPP(c_COMBC(U_20715,tc_List_Olist(U_20715),tc_List_Olist(U_20715)),c_List_Olist_OCons(U_20715)),c_List_Olist_ONil(U_20715))))),U_20716)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20715),U_20715),c_List_Ohd(U_20715)),hAPP(c_List_Ofilter(tc_List_Olist(U_20715),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20715)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20715),tc_List_Olist(U_20715),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20715)))),U_20716)),
    inference(clausify,[status(thm)],[f_4933_3]) ).

fof(f_4934_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_4934_2,plain,
    ! [U_20718,U_20717] : c_Fun_Oinj__on(tc_List_Olist(U_20717),tc_List_Olist(U_20717),c_List_Orev(U_20717),U_20718),
    inference(variable_rename,[status(thm)],[f_4934_1]) ).

fof(f_4934_3,plain,
    ! [U_20717,U_20718] : c_Fun_Oinj__on(tc_List_Olist(U_20717),tc_List_Olist(U_20717),c_List_Orev(U_20717),U_20718),
    inference(definitional_conversion,[status(esa)],[f_4934_2]) ).

cnf(f_4934_4,plain,
    c_Fun_Oinj__on(tc_List_Olist(U_20717),tc_List_Olist(U_20717),c_List_Orev(U_20717),U_20718),
    inference(clausify,[status(thm)],[f_4934_3]) ).

fof(f_4935_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_4935_2,plain,
    ! [U_20721,U_20720,U_20719] : hAPP(c_List_Ofilter(U_20719,U_20720),c_List_Oconcat(U_20719,U_20721)) = c_List_Oconcat(U_20719,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20719),tc_List_Olist(U_20719)),c_List_Ofilter(U_20719,U_20720)),U_20721)),
    inference(variable_rename,[status(thm)],[f_4935_1]) ).

fof(f_4935_3,plain,
    ! [U_20719,U_20720,U_20721] : hAPP(c_List_Ofilter(U_20719,U_20720),c_List_Oconcat(U_20719,U_20721)) = c_List_Oconcat(U_20719,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20719),tc_List_Olist(U_20719)),c_List_Ofilter(U_20719,U_20720)),U_20721)),
    inference(definitional_conversion,[status(esa)],[f_4935_2]) ).

cnf(f_4935_4,plain,
    hAPP(c_List_Ofilter(U_20719,U_20720),c_List_Oconcat(U_20719,U_20721)) = c_List_Oconcat(U_20719,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20719),tc_List_Olist(U_20719)),c_List_Ofilter(U_20719,U_20720)),U_20721)),
    inference(clausify,[status(thm)],[f_4935_3]) ).

fof(f_4936_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_4936_2,plain,
    ! [U_20723,U_20722] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20722)),c_List_Oconcat(U_20722,U_20723)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20722),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20722))),U_20723)),
    inference(variable_rename,[status(thm)],[f_4936_1]) ).

fof(f_4936_3,plain,
    ! [U_20722,U_20723] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20722)),c_List_Oconcat(U_20722,U_20723)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20722),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20722))),U_20723)),
    inference(definitional_conversion,[status(esa)],[f_4936_2]) ).

cnf(f_4936_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20722)),c_List_Oconcat(U_20722,U_20723)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20722),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20722))),U_20723)),
    inference(clausify,[status(thm)],[f_4936_3]) ).

fof(f_4937_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_4937_2,plain,
    ! [U_20727,U_20726,U_20725,U_20724] :
      ( ( hAPP(c_List_Orev(U_20724),U_20725) = hAPP(hAPP(c_List_Olist_OCons(U_20724),U_20726),U_20727)
        | U_20725 != hAPP(hAPP(c_List_Oappend(U_20724),hAPP(c_List_Orev(U_20724),U_20727)),hAPP(hAPP(c_List_Olist_OCons(U_20724),U_20726),c_List_Olist_ONil(U_20724))) )
      & ( U_20725 = hAPP(hAPP(c_List_Oappend(U_20724),hAPP(c_List_Orev(U_20724),U_20727)),hAPP(hAPP(c_List_Olist_OCons(U_20724),U_20726),c_List_Olist_ONil(U_20724)))
        | hAPP(c_List_Orev(U_20724),U_20725) != hAPP(hAPP(c_List_Olist_OCons(U_20724),U_20726),U_20727) ) ),
    inference(variable_rename,[status(thm)],[f_4937_1]) ).

fof(f_4937_3,plain,
    ( ! [U_20735,U_20733,U_20731,U_20729] :
        ( hAPP(c_List_Orev(U_20729),U_20731) = hAPP(hAPP(c_List_Olist_OCons(U_20729),U_20733),U_20735)
        | U_20731 != hAPP(hAPP(c_List_Oappend(U_20729),hAPP(c_List_Orev(U_20729),U_20735)),hAPP(hAPP(c_List_Olist_OCons(U_20729),U_20733),c_List_Olist_ONil(U_20729))) )
    & ! [U_20734,U_20732,U_20730,U_20728] :
        ( U_20730 = hAPP(hAPP(c_List_Oappend(U_20728),hAPP(c_List_Orev(U_20728),U_20734)),hAPP(hAPP(c_List_Olist_OCons(U_20728),U_20732),c_List_Olist_ONil(U_20728)))
        | hAPP(c_List_Orev(U_20728),U_20730) != hAPP(hAPP(c_List_Olist_OCons(U_20728),U_20732),U_20734) ) ),
    inference(miniscope,[status(thm)],[f_4937_2]) ).

fof(f_4937_4,plain,
    ( ! [U_20731,U_20729,U_20733,U_20735] :
        ( hAPP(c_List_Orev(U_20729),U_20731) = hAPP(hAPP(c_List_Olist_OCons(U_20729),U_20733),U_20735)
        | U_20731 != hAPP(hAPP(c_List_Oappend(U_20729),hAPP(c_List_Orev(U_20729),U_20735)),hAPP(hAPP(c_List_Olist_OCons(U_20729),U_20733),c_List_Olist_ONil(U_20729))) )
    & ! [U_20730,U_20734,U_20728,U_20732] :
        ( U_20730 = hAPP(hAPP(c_List_Oappend(U_20728),hAPP(c_List_Orev(U_20728),U_20734)),hAPP(hAPP(c_List_Olist_OCons(U_20728),U_20732),c_List_Olist_ONil(U_20728)))
        | hAPP(c_List_Orev(U_20728),U_20730) != hAPP(hAPP(c_List_Olist_OCons(U_20728),U_20732),U_20734) ) ),
    inference(definitional_conversion,[status(esa)],[f_4937_3]) ).

cnf(f_4937_5,plain,
    ( U_20730 = hAPP(hAPP(c_List_Oappend(U_20728),hAPP(c_List_Orev(U_20728),U_20734)),hAPP(hAPP(c_List_Olist_OCons(U_20728),U_20732),c_List_Olist_ONil(U_20728)))
    | hAPP(c_List_Orev(U_20728),U_20730) != hAPP(hAPP(c_List_Olist_OCons(U_20728),U_20732),U_20734) ),
    inference(clausify,[status(thm)],[f_4937_4]) ).

cnf(f_4937_6,plain,
    ( hAPP(c_List_Orev(U_20729),U_20731) = hAPP(hAPP(c_List_Olist_OCons(U_20729),U_20733),U_20735)
    | U_20731 != hAPP(hAPP(c_List_Oappend(U_20729),hAPP(c_List_Orev(U_20729),U_20735)),hAPP(hAPP(c_List_Olist_OCons(U_20729),U_20733),c_List_Olist_ONil(U_20729))) ),
    inference(clausify,[status(thm)],[f_4937_4]) ).

fof(f_4938_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_4938_2,plain,
    ! [U_20738,U_20737,U_20736] : hAPP(c_List_Orev(U_20736),hAPP(hAPP(c_List_Olist_OCons(U_20736),U_20737),U_20738)) = hAPP(hAPP(c_List_Oappend(U_20736),hAPP(c_List_Orev(U_20736),U_20738)),hAPP(hAPP(c_List_Olist_OCons(U_20736),U_20737),c_List_Olist_ONil(U_20736))),
    inference(variable_rename,[status(thm)],[f_4938_1]) ).

fof(f_4938_3,plain,
    ! [U_20736,U_20737,U_20738] : hAPP(c_List_Orev(U_20736),hAPP(hAPP(c_List_Olist_OCons(U_20736),U_20737),U_20738)) = hAPP(hAPP(c_List_Oappend(U_20736),hAPP(c_List_Orev(U_20736),U_20738)),hAPP(hAPP(c_List_Olist_OCons(U_20736),U_20737),c_List_Olist_ONil(U_20736))),
    inference(definitional_conversion,[status(esa)],[f_4938_2]) ).

cnf(f_4938_4,plain,
    hAPP(c_List_Orev(U_20736),hAPP(hAPP(c_List_Olist_OCons(U_20736),U_20737),U_20738)) = hAPP(hAPP(c_List_Oappend(U_20736),hAPP(c_List_Orev(U_20736),U_20738)),hAPP(hAPP(c_List_Olist_OCons(U_20736),U_20737),c_List_Olist_ONil(U_20736))),
    inference(clausify,[status(thm)],[f_4938_3]) ).

fof(f_4939_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_4939_2,plain,
    ! [U_20739] : hAPP(c_List_Orev(U_20739),c_List_Olist_ONil(U_20739)) = c_List_Olist_ONil(U_20739),
    inference(variable_rename,[status(thm)],[f_4939_1]) ).

fof(f_4939_3,plain,
    ! [U_20739] : hAPP(c_List_Orev(U_20739),c_List_Olist_ONil(U_20739)) = c_List_Olist_ONil(U_20739),
    inference(definitional_conversion,[status(esa)],[f_4939_2]) ).

cnf(f_4939_4,plain,
    hAPP(c_List_Orev(U_20739),c_List_Olist_ONil(U_20739)) = c_List_Olist_ONil(U_20739),
    inference(clausify,[status(thm)],[f_4939_3]) ).

fof(f_4940_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_4940_2,plain,
    ! [U_20740] : c_List_Oconcat(U_20740,c_List_Olist_ONil(tc_List_Olist(U_20740))) = c_List_Olist_ONil(U_20740),
    inference(variable_rename,[status(thm)],[f_4940_1]) ).

fof(f_4940_3,plain,
    ! [U_20740] : c_List_Oconcat(U_20740,c_List_Olist_ONil(tc_List_Olist(U_20740))) = c_List_Olist_ONil(U_20740),
    inference(definitional_conversion,[status(esa)],[f_4940_2]) ).

cnf(f_4940_4,plain,
    c_List_Oconcat(U_20740,c_List_Olist_ONil(tc_List_Olist(U_20740))) = c_List_Olist_ONil(U_20740),
    inference(clausify,[status(thm)],[f_4940_3]) ).

fof(f_4941_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_4941_2,plain,
    ! [U_20742,U_20741] :
      ( ( c_List_Olist_ONil(U_20741) = hAPP(c_List_Orev(U_20741),U_20742)
        | U_20742 != c_List_Olist_ONil(U_20741) )
      & ( U_20742 = c_List_Olist_ONil(U_20741)
        | c_List_Olist_ONil(U_20741) != hAPP(c_List_Orev(U_20741),U_20742) ) ),
    inference(variable_rename,[status(thm)],[f_4941_1]) ).

fof(f_4941_3,plain,
    ( ! [U_20746,U_20744] :
        ( c_List_Olist_ONil(U_20744) = hAPP(c_List_Orev(U_20744),U_20746)
        | U_20746 != c_List_Olist_ONil(U_20744) )
    & ! [U_20745,U_20743] :
        ( U_20745 = c_List_Olist_ONil(U_20743)
        | c_List_Olist_ONil(U_20743) != hAPP(c_List_Orev(U_20743),U_20745) ) ),
    inference(miniscope,[status(thm)],[f_4941_2]) ).

fof(f_4941_4,plain,
    ( ! [U_20746,U_20744] :
        ( c_List_Olist_ONil(U_20744) = hAPP(c_List_Orev(U_20744),U_20746)
        | U_20746 != c_List_Olist_ONil(U_20744) )
    & ! [U_20745,U_20743] :
        ( U_20745 = c_List_Olist_ONil(U_20743)
        | c_List_Olist_ONil(U_20743) != hAPP(c_List_Orev(U_20743),U_20745) ) ),
    inference(definitional_conversion,[status(esa)],[f_4941_3]) ).

cnf(f_4941_5,plain,
    ( U_20745 = c_List_Olist_ONil(U_20743)
    | c_List_Olist_ONil(U_20743) != hAPP(c_List_Orev(U_20743),U_20745) ),
    inference(clausify,[status(thm)],[f_4941_4]) ).

cnf(f_4941_6,plain,
    ( c_List_Olist_ONil(U_20744) = hAPP(c_List_Orev(U_20744),U_20746)
    | U_20746 != c_List_Olist_ONil(U_20744) ),
    inference(clausify,[status(thm)],[f_4941_4]) ).

fof(f_4942_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_4942_2,plain,
    ! [U_20748,U_20747] :
      ( ( hAPP(c_List_Orev(U_20747),U_20748) = c_List_Olist_ONil(U_20747)
        | U_20748 != c_List_Olist_ONil(U_20747) )
      & ( U_20748 = c_List_Olist_ONil(U_20747)
        | hAPP(c_List_Orev(U_20747),U_20748) != c_List_Olist_ONil(U_20747) ) ),
    inference(variable_rename,[status(thm)],[f_4942_1]) ).

fof(f_4942_3,plain,
    ( ! [U_20752,U_20750] :
        ( hAPP(c_List_Orev(U_20750),U_20752) = c_List_Olist_ONil(U_20750)
        | U_20752 != c_List_Olist_ONil(U_20750) )
    & ! [U_20751,U_20749] :
        ( U_20751 = c_List_Olist_ONil(U_20749)
        | hAPP(c_List_Orev(U_20749),U_20751) != c_List_Olist_ONil(U_20749) ) ),
    inference(miniscope,[status(thm)],[f_4942_2]) ).

fof(f_4942_4,plain,
    ( ! [U_20750,U_20752] :
        ( hAPP(c_List_Orev(U_20750),U_20752) = c_List_Olist_ONil(U_20750)
        | U_20752 != c_List_Olist_ONil(U_20750) )
    & ! [U_20751,U_20749] :
        ( U_20751 = c_List_Olist_ONil(U_20749)
        | hAPP(c_List_Orev(U_20749),U_20751) != c_List_Olist_ONil(U_20749) ) ),
    inference(definitional_conversion,[status(esa)],[f_4942_3]) ).

cnf(f_4942_5,plain,
    ( U_20751 = c_List_Olist_ONil(U_20749)
    | hAPP(c_List_Orev(U_20749),U_20751) != c_List_Olist_ONil(U_20749) ),
    inference(clausify,[status(thm)],[f_4942_4]) ).

cnf(f_4942_6,plain,
    ( hAPP(c_List_Orev(U_20750),U_20752) = c_List_Olist_ONil(U_20750)
    | U_20752 != c_List_Olist_ONil(U_20750) ),
    inference(clausify,[status(thm)],[f_4942_4]) ).

fof(f_4943_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_4943_2,plain,
    ! [U_20756,U_20755] :
      ( ( c_List_Olist_ONil(U_20755) = c_List_Oconcat(U_20755,U_20756)
        | ? [U_20754] :
            ( U_20754 != c_List_Olist_ONil(U_20755)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20755)),U_20754),hAPP(c_List_Oset(tc_List_Olist(U_20755)),U_20756))) ) )
      & ( ! [U_20753] :
            ( U_20753 = c_List_Olist_ONil(U_20755)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20755)),U_20753),hAPP(c_List_Oset(tc_List_Olist(U_20755)),U_20756))) )
        | c_List_Olist_ONil(U_20755) != c_List_Oconcat(U_20755,U_20756) ) ),
    inference(variable_rename,[status(thm)],[f_4943_1]) ).

fof(f_4943_3,plain,
    ( ! [U_20760,U_20758] :
        ( c_List_Olist_ONil(U_20758) = c_List_Oconcat(U_20758,U_20760)
        | ? [U_20754] :
            ( U_20754 != c_List_Olist_ONil(U_20758)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20758)),U_20754),hAPP(c_List_Oset(tc_List_Olist(U_20758)),U_20760))) ) )
    & ! [U_20759,U_20757] :
        ( ! [U_20753] :
            ( U_20753 = c_List_Olist_ONil(U_20757)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20757)),U_20753),hAPP(c_List_Oset(tc_List_Olist(U_20757)),U_20759))) )
        | c_List_Olist_ONil(U_20757) != c_List_Oconcat(U_20757,U_20759) ) ),
    inference(miniscope,[status(thm)],[f_4943_2]) ).

fof(f_4943_4,plain,
    ( ! [U_20760,U_20758] :
        ( c_List_Olist_ONil(U_20758) = c_List_Oconcat(U_20758,U_20760)
        | ( sK509(U_20760,U_20758) != c_List_Olist_ONil(U_20758)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20758)),sK509(U_20760,U_20758)),hAPP(c_List_Oset(tc_List_Olist(U_20758)),U_20760))) ) )
    & ! [U_20759,U_20757] :
        ( ! [U_20753] :
            ( U_20753 = c_List_Olist_ONil(U_20757)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20757)),U_20753),hAPP(c_List_Oset(tc_List_Olist(U_20757)),U_20759))) )
        | c_List_Olist_ONil(U_20757) != c_List_Oconcat(U_20757,U_20759) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK509]),skolemize(U_20754,sK509(U_20760,U_20758))],[f_4943_3]) ).

fof(f_4943_5,plain,
    ( ! [U_20760,U_20758] :
        ( sK509(U_20760,U_20758) != c_List_Olist_ONil(U_20758)
        | ~ sP1239(U_20760,U_20758) )
    & ! [U_20760,U_20758] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20758)),sK509(U_20760,U_20758)),hAPP(c_List_Oset(tc_List_Olist(U_20758)),U_20760)))
        | ~ sP1239(U_20760,U_20758) )
    & ! [U_20760,U_20758] :
        ( c_List_Olist_ONil(U_20758) = c_List_Oconcat(U_20758,U_20760)
        | sP1239(U_20760,U_20758) )
    & ! [U_20753,U_20757,U_20759] :
        ( U_20753 = c_List_Olist_ONil(U_20757)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20757)),U_20753),hAPP(c_List_Oset(tc_List_Olist(U_20757)),U_20759)))
        | c_List_Olist_ONil(U_20757) != c_List_Oconcat(U_20757,U_20759) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1239])],[f_4943_4]) ).

cnf(f_4943_6,plain,
    ( U_20753 = c_List_Olist_ONil(U_20757)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20757)),U_20753),hAPP(c_List_Oset(tc_List_Olist(U_20757)),U_20759)))
    | c_List_Olist_ONil(U_20757) != c_List_Oconcat(U_20757,U_20759) ),
    inference(clausify,[status(thm)],[f_4943_5]) ).

cnf(f_4943_7,plain,
    ( c_List_Olist_ONil(U_20758) = c_List_Oconcat(U_20758,U_20760)
    | sP1239(U_20760,U_20758) ),
    inference(clausify,[status(thm)],[f_4943_5]) ).

cnf(f_4943_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20758)),sK509(U_20760,U_20758)),hAPP(c_List_Oset(tc_List_Olist(U_20758)),U_20760)))
    | ~ sP1239(U_20760,U_20758) ),
    inference(clausify,[status(thm)],[f_4943_5]) ).

cnf(f_4943_9,plain,
    ( sK509(U_20760,U_20758) != c_List_Olist_ONil(U_20758)
    | ~ sP1239(U_20760,U_20758) ),
    inference(clausify,[status(thm)],[f_4943_5]) ).

fof(f_4944_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_4944_2,plain,
    ! [U_20764,U_20763] :
      ( ( c_List_Oconcat(U_20763,U_20764) = c_List_Olist_ONil(U_20763)
        | ? [U_20762] :
            ( U_20762 != c_List_Olist_ONil(U_20763)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20763)),U_20762),hAPP(c_List_Oset(tc_List_Olist(U_20763)),U_20764))) ) )
      & ( ! [U_20761] :
            ( U_20761 = c_List_Olist_ONil(U_20763)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20763)),U_20761),hAPP(c_List_Oset(tc_List_Olist(U_20763)),U_20764))) )
        | c_List_Oconcat(U_20763,U_20764) != c_List_Olist_ONil(U_20763) ) ),
    inference(variable_rename,[status(thm)],[f_4944_1]) ).

fof(f_4944_3,plain,
    ( ! [U_20768,U_20766] :
        ( c_List_Oconcat(U_20766,U_20768) = c_List_Olist_ONil(U_20766)
        | ? [U_20762] :
            ( U_20762 != c_List_Olist_ONil(U_20766)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20766)),U_20762),hAPP(c_List_Oset(tc_List_Olist(U_20766)),U_20768))) ) )
    & ! [U_20767,U_20765] :
        ( ! [U_20761] :
            ( U_20761 = c_List_Olist_ONil(U_20765)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20765)),U_20761),hAPP(c_List_Oset(tc_List_Olist(U_20765)),U_20767))) )
        | c_List_Oconcat(U_20765,U_20767) != c_List_Olist_ONil(U_20765) ) ),
    inference(miniscope,[status(thm)],[f_4944_2]) ).

fof(f_4944_4,plain,
    ( ! [U_20768,U_20766] :
        ( c_List_Oconcat(U_20766,U_20768) = c_List_Olist_ONil(U_20766)
        | ( sK510(U_20768,U_20766) != c_List_Olist_ONil(U_20766)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20766)),sK510(U_20768,U_20766)),hAPP(c_List_Oset(tc_List_Olist(U_20766)),U_20768))) ) )
    & ! [U_20767,U_20765] :
        ( ! [U_20761] :
            ( U_20761 = c_List_Olist_ONil(U_20765)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20765)),U_20761),hAPP(c_List_Oset(tc_List_Olist(U_20765)),U_20767))) )
        | c_List_Oconcat(U_20765,U_20767) != c_List_Olist_ONil(U_20765) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK510]),skolemize(U_20762,sK510(U_20768,U_20766))],[f_4944_3]) ).

fof(f_4944_5,plain,
    ( ! [U_20766,U_20768] :
        ( sK510(U_20768,U_20766) != c_List_Olist_ONil(U_20766)
        | ~ sP1240(U_20766,U_20768) )
    & ! [U_20766,U_20768] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20766)),sK510(U_20768,U_20766)),hAPP(c_List_Oset(tc_List_Olist(U_20766)),U_20768)))
        | ~ sP1240(U_20766,U_20768) )
    & ! [U_20766,U_20768] :
        ( c_List_Oconcat(U_20766,U_20768) = c_List_Olist_ONil(U_20766)
        | sP1240(U_20766,U_20768) )
    & ! [U_20767,U_20761,U_20765] :
        ( U_20761 = c_List_Olist_ONil(U_20765)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20765)),U_20761),hAPP(c_List_Oset(tc_List_Olist(U_20765)),U_20767)))
        | c_List_Oconcat(U_20765,U_20767) != c_List_Olist_ONil(U_20765) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1240])],[f_4944_4]) ).

cnf(f_4944_6,plain,
    ( U_20761 = c_List_Olist_ONil(U_20765)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20765)),U_20761),hAPP(c_List_Oset(tc_List_Olist(U_20765)),U_20767)))
    | c_List_Oconcat(U_20765,U_20767) != c_List_Olist_ONil(U_20765) ),
    inference(clausify,[status(thm)],[f_4944_5]) ).

cnf(f_4944_7,plain,
    ( c_List_Oconcat(U_20766,U_20768) = c_List_Olist_ONil(U_20766)
    | sP1240(U_20766,U_20768) ),
    inference(clausify,[status(thm)],[f_4944_5]) ).

cnf(f_4944_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20766)),sK510(U_20768,U_20766)),hAPP(c_List_Oset(tc_List_Olist(U_20766)),U_20768)))
    | ~ sP1240(U_20766,U_20768) ),
    inference(clausify,[status(thm)],[f_4944_5]) ).

cnf(f_4944_9,plain,
    ( sK510(U_20768,U_20766) != c_List_Olist_ONil(U_20766)
    | ~ sP1240(U_20766,U_20768) ),
    inference(clausify,[status(thm)],[f_4944_5]) ).

fof(f_4945_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_4945_2,plain,
    ! [U_20771,U_20770,U_20769] :
      ( ( hAPP(c_List_Orev(U_20769),U_20770) = hAPP(hAPP(c_List_Olist_OCons(U_20769),U_20771),c_List_Olist_ONil(U_20769))
        | U_20770 != hAPP(hAPP(c_List_Olist_OCons(U_20769),U_20771),c_List_Olist_ONil(U_20769)) )
      & ( U_20770 = hAPP(hAPP(c_List_Olist_OCons(U_20769),U_20771),c_List_Olist_ONil(U_20769))
        | hAPP(c_List_Orev(U_20769),U_20770) != hAPP(hAPP(c_List_Olist_OCons(U_20769),U_20771),c_List_Olist_ONil(U_20769)) ) ),
    inference(variable_rename,[status(thm)],[f_4945_1]) ).

fof(f_4945_3,plain,
    ( ! [U_20777,U_20775,U_20773] :
        ( hAPP(c_List_Orev(U_20773),U_20775) = hAPP(hAPP(c_List_Olist_OCons(U_20773),U_20777),c_List_Olist_ONil(U_20773))
        | U_20775 != hAPP(hAPP(c_List_Olist_OCons(U_20773),U_20777),c_List_Olist_ONil(U_20773)) )
    & ! [U_20776,U_20774,U_20772] :
        ( U_20774 = hAPP(hAPP(c_List_Olist_OCons(U_20772),U_20776),c_List_Olist_ONil(U_20772))
        | hAPP(c_List_Orev(U_20772),U_20774) != hAPP(hAPP(c_List_Olist_OCons(U_20772),U_20776),c_List_Olist_ONil(U_20772)) ) ),
    inference(miniscope,[status(thm)],[f_4945_2]) ).

fof(f_4945_4,plain,
    ( ! [U_20775,U_20773,U_20777] :
        ( hAPP(c_List_Orev(U_20773),U_20775) = hAPP(hAPP(c_List_Olist_OCons(U_20773),U_20777),c_List_Olist_ONil(U_20773))
        | U_20775 != hAPP(hAPP(c_List_Olist_OCons(U_20773),U_20777),c_List_Olist_ONil(U_20773)) )
    & ! [U_20772,U_20774,U_20776] :
        ( U_20774 = hAPP(hAPP(c_List_Olist_OCons(U_20772),U_20776),c_List_Olist_ONil(U_20772))
        | hAPP(c_List_Orev(U_20772),U_20774) != hAPP(hAPP(c_List_Olist_OCons(U_20772),U_20776),c_List_Olist_ONil(U_20772)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4945_3]) ).

cnf(f_4945_5,plain,
    ( U_20774 = hAPP(hAPP(c_List_Olist_OCons(U_20772),U_20776),c_List_Olist_ONil(U_20772))
    | hAPP(c_List_Orev(U_20772),U_20774) != hAPP(hAPP(c_List_Olist_OCons(U_20772),U_20776),c_List_Olist_ONil(U_20772)) ),
    inference(clausify,[status(thm)],[f_4945_4]) ).

cnf(f_4945_6,plain,
    ( hAPP(c_List_Orev(U_20773),U_20775) = hAPP(hAPP(c_List_Olist_OCons(U_20773),U_20777),c_List_Olist_ONil(U_20773))
    | U_20775 != hAPP(hAPP(c_List_Olist_OCons(U_20773),U_20777),c_List_Olist_ONil(U_20773)) ),
    inference(clausify,[status(thm)],[f_4945_4]) ).

fof(f_4946_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_4946_2,plain,
    ! [U_20780,U_20779,U_20778] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_20778),U_20779),c_List_Olist_ONil(U_20778)) = hAPP(c_List_Orev(U_20778),U_20780)
        | U_20780 != hAPP(hAPP(c_List_Olist_OCons(U_20778),U_20779),c_List_Olist_ONil(U_20778)) )
      & ( U_20780 = hAPP(hAPP(c_List_Olist_OCons(U_20778),U_20779),c_List_Olist_ONil(U_20778))
        | hAPP(hAPP(c_List_Olist_OCons(U_20778),U_20779),c_List_Olist_ONil(U_20778)) != hAPP(c_List_Orev(U_20778),U_20780) ) ),
    inference(variable_rename,[status(thm)],[f_4946_1]) ).

fof(f_4946_3,plain,
    ( ! [U_20786,U_20784,U_20782] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_20782),U_20784),c_List_Olist_ONil(U_20782)) = hAPP(c_List_Orev(U_20782),U_20786)
        | U_20786 != hAPP(hAPP(c_List_Olist_OCons(U_20782),U_20784),c_List_Olist_ONil(U_20782)) )
    & ! [U_20785,U_20783,U_20781] :
        ( U_20785 = hAPP(hAPP(c_List_Olist_OCons(U_20781),U_20783),c_List_Olist_ONil(U_20781))
        | hAPP(hAPP(c_List_Olist_OCons(U_20781),U_20783),c_List_Olist_ONil(U_20781)) != hAPP(c_List_Orev(U_20781),U_20785) ) ),
    inference(miniscope,[status(thm)],[f_4946_2]) ).

fof(f_4946_4,plain,
    ( ! [U_20782,U_20784,U_20786] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_20782),U_20784),c_List_Olist_ONil(U_20782)) = hAPP(c_List_Orev(U_20782),U_20786)
        | U_20786 != hAPP(hAPP(c_List_Olist_OCons(U_20782),U_20784),c_List_Olist_ONil(U_20782)) )
    & ! [U_20783,U_20785,U_20781] :
        ( U_20785 = hAPP(hAPP(c_List_Olist_OCons(U_20781),U_20783),c_List_Olist_ONil(U_20781))
        | hAPP(hAPP(c_List_Olist_OCons(U_20781),U_20783),c_List_Olist_ONil(U_20781)) != hAPP(c_List_Orev(U_20781),U_20785) ) ),
    inference(definitional_conversion,[status(esa)],[f_4946_3]) ).

cnf(f_4946_5,plain,
    ( U_20785 = hAPP(hAPP(c_List_Olist_OCons(U_20781),U_20783),c_List_Olist_ONil(U_20781))
    | hAPP(hAPP(c_List_Olist_OCons(U_20781),U_20783),c_List_Olist_ONil(U_20781)) != hAPP(c_List_Orev(U_20781),U_20785) ),
    inference(clausify,[status(thm)],[f_4946_4]) ).

cnf(f_4946_6,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_20782),U_20784),c_List_Olist_ONil(U_20782)) = hAPP(c_List_Orev(U_20782),U_20786)
    | U_20786 != hAPP(hAPP(c_List_Olist_OCons(U_20782),U_20784),c_List_Olist_ONil(U_20782)) ),
    inference(clausify,[status(thm)],[f_4946_4]) ).

fof(f_4947_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_4947_2,plain,
    ! [U_20789,U_20788,U_20787] : c_List_Oconcat(U_20787,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20787)),U_20788),U_20789)) = hAPP(hAPP(c_List_Oappend(U_20787),U_20788),c_List_Oconcat(U_20787,U_20789)),
    inference(variable_rename,[status(thm)],[f_4947_1]) ).

fof(f_4947_3,plain,
    ! [U_20787,U_20788,U_20789] : c_List_Oconcat(U_20787,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20787)),U_20788),U_20789)) = hAPP(hAPP(c_List_Oappend(U_20787),U_20788),c_List_Oconcat(U_20787,U_20789)),
    inference(definitional_conversion,[status(esa)],[f_4947_2]) ).

cnf(f_4947_4,plain,
    c_List_Oconcat(U_20787,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20787)),U_20788),U_20789)) = hAPP(hAPP(c_List_Oappend(U_20787),U_20788),c_List_Oconcat(U_20787,U_20789)),
    inference(clausify,[status(thm)],[f_4947_3]) ).

fof(f_4948_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_4948_2,plain,
    ! [U_20791,U_20790] : hAPP(c_List_Orev(U_20790),c_List_Oconcat(U_20790,U_20791)) = c_List_Oconcat(U_20790,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20790),tc_List_Olist(U_20790)),c_List_Orev(U_20790)),hAPP(c_List_Orev(tc_List_Olist(U_20790)),U_20791))),
    inference(variable_rename,[status(thm)],[f_4948_1]) ).

fof(f_4948_3,plain,
    ! [U_20790,U_20791] : hAPP(c_List_Orev(U_20790),c_List_Oconcat(U_20790,U_20791)) = c_List_Oconcat(U_20790,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20790),tc_List_Olist(U_20790)),c_List_Orev(U_20790)),hAPP(c_List_Orev(tc_List_Olist(U_20790)),U_20791))),
    inference(definitional_conversion,[status(esa)],[f_4948_2]) ).

cnf(f_4948_4,plain,
    hAPP(c_List_Orev(U_20790),c_List_Oconcat(U_20790,U_20791)) = c_List_Oconcat(U_20790,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20790),tc_List_Olist(U_20790)),c_List_Orev(U_20790)),hAPP(c_List_Orev(tc_List_Olist(U_20790)),U_20791))),
    inference(clausify,[status(thm)],[f_4948_3]) ).

fof(f_4949_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_4949_2,plain,
    ! [U_20795,U_20794,U_20793,U_20792] : hAPP(c_List_Orev(U_20792),hAPP(hAPP(c_List_Omap(U_20793,U_20792),U_20794),U_20795)) = hAPP(hAPP(c_List_Omap(U_20793,U_20792),U_20794),hAPP(c_List_Orev(U_20793),U_20795)),
    inference(variable_rename,[status(thm)],[f_4949_1]) ).

fof(f_4949_3,plain,
    ! [U_20792,U_20793,U_20794,U_20795] : hAPP(c_List_Orev(U_20792),hAPP(hAPP(c_List_Omap(U_20793,U_20792),U_20794),U_20795)) = hAPP(hAPP(c_List_Omap(U_20793,U_20792),U_20794),hAPP(c_List_Orev(U_20793),U_20795)),
    inference(definitional_conversion,[status(esa)],[f_4949_2]) ).

cnf(f_4949_4,plain,
    hAPP(c_List_Orev(U_20792),hAPP(hAPP(c_List_Omap(U_20793,U_20792),U_20794),U_20795)) = hAPP(hAPP(c_List_Omap(U_20793,U_20792),U_20794),hAPP(c_List_Orev(U_20793),U_20795)),
    inference(clausify,[status(thm)],[f_4949_3]) ).

fof(f_4950_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_4950_2,plain,
    ! [U_20799,U_20798,U_20797,U_20796] : hAPP(hAPP(c_List_Omap(U_20796,U_20797),U_20798),c_List_Oconcat(U_20796,U_20799)) = c_List_Oconcat(U_20797,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20796),tc_List_Olist(U_20797)),hAPP(c_List_Omap(U_20796,U_20797),U_20798)),U_20799)),
    inference(variable_rename,[status(thm)],[f_4950_1]) ).

fof(f_4950_3,plain,
    ! [U_20796,U_20797,U_20798,U_20799] : hAPP(hAPP(c_List_Omap(U_20796,U_20797),U_20798),c_List_Oconcat(U_20796,U_20799)) = c_List_Oconcat(U_20797,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20796),tc_List_Olist(U_20797)),hAPP(c_List_Omap(U_20796,U_20797),U_20798)),U_20799)),
    inference(definitional_conversion,[status(esa)],[f_4950_2]) ).

cnf(f_4950_4,plain,
    hAPP(hAPP(c_List_Omap(U_20796,U_20797),U_20798),c_List_Oconcat(U_20796,U_20799)) = c_List_Oconcat(U_20797,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20796),tc_List_Olist(U_20797)),hAPP(c_List_Omap(U_20796,U_20797),U_20798)),U_20799)),
    inference(clausify,[status(thm)],[f_4950_3]) ).

fof(f_4951_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_4951_2,plain,
    ! [U_20801,U_20800] : hAPP(c_List_Orev(U_20800),U_20801) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20800),U_20800,hAPP(c_COMBC(U_20800,tc_List_Olist(U_20800),tc_List_Olist(U_20800)),c_List_Olist_OCons(U_20800)),c_List_Olist_ONil(U_20800)),U_20801),
    inference(variable_rename,[status(thm)],[f_4951_1]) ).

fof(f_4951_3,plain,
    ! [U_20800,U_20801] : hAPP(c_List_Orev(U_20800),U_20801) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20800),U_20800,hAPP(c_COMBC(U_20800,tc_List_Olist(U_20800),tc_List_Olist(U_20800)),c_List_Olist_OCons(U_20800)),c_List_Olist_ONil(U_20800)),U_20801),
    inference(definitional_conversion,[status(esa)],[f_4951_2]) ).

cnf(f_4951_4,plain,
    hAPP(c_List_Orev(U_20800),U_20801) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20800),U_20800,hAPP(c_COMBC(U_20800,tc_List_Olist(U_20800),tc_List_Olist(U_20800)),c_List_Olist_OCons(U_20800)),c_List_Olist_ONil(U_20800)),U_20801),
    inference(clausify,[status(thm)],[f_4951_3]) ).

fof(f_4952_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_4952_2,plain,
    ! [U_20803,U_20802] : c_List_Oconcat(U_20802,U_20803) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20802),tc_List_Olist(U_20802),c_List_Oappend(U_20802),c_List_Olist_ONil(U_20802)),U_20803),
    inference(variable_rename,[status(thm)],[f_4952_1]) ).

fof(f_4952_3,plain,
    ! [U_20803,U_20802] : c_List_Oconcat(U_20802,U_20803) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20802),tc_List_Olist(U_20802),c_List_Oappend(U_20802),c_List_Olist_ONil(U_20802)),U_20803),
    inference(definitional_conversion,[status(esa)],[f_4952_2]) ).

cnf(f_4952_4,plain,
    c_List_Oconcat(U_20802,U_20803) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20802),tc_List_Olist(U_20802),c_List_Oappend(U_20802),c_List_Olist_ONil(U_20802)),U_20803),
    inference(clausify,[status(thm)],[f_4952_3]) ).

fof(f_4953_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_4953_2,plain,
    ! [U_20806,U_20805,U_20804] : hAPP(c_List_Ofoldl(tc_List_Olist(U_20804),tc_List_Olist(U_20804),c_List_Oappend(U_20804),U_20805),U_20806) = hAPP(hAPP(c_List_Oappend(U_20804),U_20805),c_List_Oconcat(U_20804,U_20806)),
    inference(variable_rename,[status(thm)],[f_4953_1]) ).

fof(f_4953_3,plain,
    ! [U_20804,U_20805,U_20806] : hAPP(c_List_Ofoldl(tc_List_Olist(U_20804),tc_List_Olist(U_20804),c_List_Oappend(U_20804),U_20805),U_20806) = hAPP(hAPP(c_List_Oappend(U_20804),U_20805),c_List_Oconcat(U_20804,U_20806)),
    inference(definitional_conversion,[status(esa)],[f_4953_2]) ).

cnf(f_4953_4,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(U_20804),tc_List_Olist(U_20804),c_List_Oappend(U_20804),U_20805),U_20806) = hAPP(hAPP(c_List_Oappend(U_20804),U_20805),c_List_Oconcat(U_20804,U_20806)),
    inference(clausify,[status(thm)],[f_4953_3]) ).

fof(f_4954_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_4954_2,plain,
    ! [U_20809,U_20808,U_20807] : hAPP(c_List_Orev(U_20807),hAPP(hAPP(c_List_Oappend(U_20807),U_20808),U_20809)) = hAPP(hAPP(c_List_Oappend(U_20807),hAPP(c_List_Orev(U_20807),U_20809)),hAPP(c_List_Orev(U_20807),U_20808)),
    inference(variable_rename,[status(thm)],[f_4954_1]) ).

fof(f_4954_3,plain,
    ! [U_20807,U_20808,U_20809] : hAPP(c_List_Orev(U_20807),hAPP(hAPP(c_List_Oappend(U_20807),U_20808),U_20809)) = hAPP(hAPP(c_List_Oappend(U_20807),hAPP(c_List_Orev(U_20807),U_20809)),hAPP(c_List_Orev(U_20807),U_20808)),
    inference(definitional_conversion,[status(esa)],[f_4954_2]) ).

cnf(f_4954_4,plain,
    hAPP(c_List_Orev(U_20807),hAPP(hAPP(c_List_Oappend(U_20807),U_20808),U_20809)) = hAPP(hAPP(c_List_Oappend(U_20807),hAPP(c_List_Orev(U_20807),U_20809)),hAPP(c_List_Orev(U_20807),U_20808)),
    inference(clausify,[status(thm)],[f_4954_3]) ).

fof(f_4955_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_4955_2,plain,
    ! [U_20812,U_20811,U_20810] : c_List_Oconcat(U_20810,hAPP(hAPP(c_List_Oappend(tc_List_Olist(U_20810)),U_20811),U_20812)) = hAPP(hAPP(c_List_Oappend(U_20810),c_List_Oconcat(U_20810,U_20811)),c_List_Oconcat(U_20810,U_20812)),
    inference(variable_rename,[status(thm)],[f_4955_1]) ).

fof(f_4955_3,plain,
    ! [U_20810,U_20811,U_20812] : c_List_Oconcat(U_20810,hAPP(hAPP(c_List_Oappend(tc_List_Olist(U_20810)),U_20811),U_20812)) = hAPP(hAPP(c_List_Oappend(U_20810),c_List_Oconcat(U_20810,U_20811)),c_List_Oconcat(U_20810,U_20812)),
    inference(definitional_conversion,[status(esa)],[f_4955_2]) ).

cnf(f_4955_4,plain,
    c_List_Oconcat(U_20810,hAPP(hAPP(c_List_Oappend(tc_List_Olist(U_20810)),U_20811),U_20812)) = hAPP(hAPP(c_List_Oappend(U_20810),c_List_Oconcat(U_20810,U_20811)),c_List_Oconcat(U_20810,U_20812)),
    inference(clausify,[status(thm)],[f_4955_3]) ).

fof(f_4956_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_4956_2,plain,
    ! [U_20814,U_20813] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_20813),hAPP(c_List_Orev(U_20813),U_20814)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20813),U_20814)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_20813),U_20814))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20813),hAPP(c_List_Orev(U_20813),U_20814))) ) ),
    inference(variable_rename,[status(thm)],[f_4956_1]) ).

fof(f_4956_3,plain,
    ( ! [U_20818,U_20816] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20816),hAPP(c_List_Orev(U_20816),U_20818)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20816),U_20818)) )
    & ! [U_20817,U_20815] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20815),U_20817))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20815),hAPP(c_List_Orev(U_20815),U_20817))) ) ),
    inference(miniscope,[status(thm)],[f_4956_2]) ).

fof(f_4956_4,plain,
    ( ! [U_20816,U_20818] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20816),hAPP(c_List_Orev(U_20816),U_20818)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20816),U_20818)) )
    & ! [U_20817,U_20815] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20815),U_20817))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20815),hAPP(c_List_Orev(U_20815),U_20817))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4956_3]) ).

cnf(f_4956_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20815),U_20817))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20815),hAPP(c_List_Orev(U_20815),U_20817))) ),
    inference(clausify,[status(thm)],[f_4956_4]) ).

cnf(f_4956_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20816),hAPP(c_List_Orev(U_20816),U_20818)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20816),U_20818)) ),
    inference(clausify,[status(thm)],[f_4956_4]) ).

fof(f_4957_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_4957_2,plain,
    ! [U_20820,U_20819] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20819)),hAPP(c_List_Orev(U_20819),U_20820)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20819)),U_20820),
    inference(variable_rename,[status(thm)],[f_4957_1]) ).

fof(f_4957_3,plain,
    ! [U_20819,U_20820] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20819)),hAPP(c_List_Orev(U_20819),U_20820)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20819)),U_20820),
    inference(definitional_conversion,[status(esa)],[f_4957_2]) ).

cnf(f_4957_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20819)),hAPP(c_List_Orev(U_20819),U_20820)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20819)),U_20820),
    inference(clausify,[status(thm)],[f_4957_3]) ).

fof(f_4958_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_4958_2,plain,
    ! [U_20822,U_20821] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20821),hAPP(c_List_Orev(U_20821),U_20822)) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20821),U_20822)
      | ~ class_Groups_Ocomm__monoid__add(U_20821) ),
    inference(variable_rename,[status(thm)],[f_4958_1]) ).

fof(f_4958_3,plain,
    ! [U_20821,U_20822] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20821),hAPP(c_List_Orev(U_20821),U_20822)) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20821),U_20822)
      | ~ class_Groups_Ocomm__monoid__add(U_20821) ),
    inference(definitional_conversion,[status(esa)],[f_4958_2]) ).

cnf(f_4958_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20821),hAPP(c_List_Orev(U_20821),U_20822)) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20821),U_20822)
    | ~ class_Groups_Ocomm__monoid__add(U_20821) ),
    inference(clausify,[status(thm)],[f_4958_3]) ).

fof(f_4959_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_4959_2,plain,
    ! [U_20825,U_20824,U_20823] :
      ( ( hAPP(c_List_Orev(U_20823),U_20824) = hAPP(c_List_Orev(U_20823),U_20825)
        | U_20824 != U_20825 )
      & ( U_20824 = U_20825
        | hAPP(c_List_Orev(U_20823),U_20824) != hAPP(c_List_Orev(U_20823),U_20825) ) ),
    inference(variable_rename,[status(thm)],[f_4959_1]) ).

fof(f_4959_3,plain,
    ( ! [U_20831,U_20829] :
        ( ! [U_20827] : hAPP(c_List_Orev(U_20827),U_20829) = hAPP(c_List_Orev(U_20827),U_20831)
        | U_20829 != U_20831 )
    & ! [U_20830,U_20828] :
        ( ! [U_20826] : hAPP(c_List_Orev(U_20826),U_20828) != hAPP(c_List_Orev(U_20826),U_20830)
        | U_20828 = U_20830 ) ),
    inference(miniscope,[status(thm)],[f_4959_2]) ).

fof(f_4959_4,plain,
    ( ! [U_20831,U_20827,U_20829] :
        ( hAPP(c_List_Orev(U_20827),U_20829) = hAPP(c_List_Orev(U_20827),U_20831)
        | U_20829 != U_20831 )
    & ! [U_20830,U_20826,U_20828] :
        ( hAPP(c_List_Orev(U_20826),U_20828) != hAPP(c_List_Orev(U_20826),U_20830)
        | U_20828 = U_20830 ) ),
    inference(definitional_conversion,[status(esa)],[f_4959_3]) ).

cnf(f_4959_5,plain,
    ( hAPP(c_List_Orev(U_20826),U_20828) != hAPP(c_List_Orev(U_20826),U_20830)
    | U_20828 = U_20830 ),
    inference(clausify,[status(thm)],[f_4959_4]) ).

cnf(f_4959_6,plain,
    ( hAPP(c_List_Orev(U_20827),U_20829) = hAPP(c_List_Orev(U_20827),U_20831)
    | U_20829 != U_20831 ),
    inference(clausify,[status(thm)],[f_4959_4]) ).

fof(f_4960_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_4960_2,plain,
    ! [U_20834,U_20833,U_20832] :
      ( ( hAPP(c_List_Orev(U_20832),U_20833) = U_20834
        | U_20833 != hAPP(c_List_Orev(U_20832),U_20834) )
      & ( U_20833 = hAPP(c_List_Orev(U_20832),U_20834)
        | hAPP(c_List_Orev(U_20832),U_20833) != U_20834 ) ),
    inference(variable_rename,[status(thm)],[f_4960_1]) ).

fof(f_4960_3,plain,
    ( ! [U_20840,U_20838,U_20836] :
        ( hAPP(c_List_Orev(U_20836),U_20838) = U_20840
        | U_20838 != hAPP(c_List_Orev(U_20836),U_20840) )
    & ! [U_20839,U_20837,U_20835] :
        ( U_20837 = hAPP(c_List_Orev(U_20835),U_20839)
        | hAPP(c_List_Orev(U_20835),U_20837) != U_20839 ) ),
    inference(miniscope,[status(thm)],[f_4960_2]) ).

fof(f_4960_4,plain,
    ( ! [U_20836,U_20838,U_20840] :
        ( hAPP(c_List_Orev(U_20836),U_20838) = U_20840
        | U_20838 != hAPP(c_List_Orev(U_20836),U_20840) )
    & ! [U_20837,U_20839,U_20835] :
        ( U_20837 = hAPP(c_List_Orev(U_20835),U_20839)
        | hAPP(c_List_Orev(U_20835),U_20837) != U_20839 ) ),
    inference(definitional_conversion,[status(esa)],[f_4960_3]) ).

cnf(f_4960_5,plain,
    ( U_20837 = hAPP(c_List_Orev(U_20835),U_20839)
    | hAPP(c_List_Orev(U_20835),U_20837) != U_20839 ),
    inference(clausify,[status(thm)],[f_4960_4]) ).

cnf(f_4960_6,plain,
    ( hAPP(c_List_Orev(U_20836),U_20838) = U_20840
    | U_20838 != hAPP(c_List_Orev(U_20836),U_20840) ),
    inference(clausify,[status(thm)],[f_4960_4]) ).

fof(f_4961_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_4961_2,plain,
    ! [U_20842,U_20841] : hAPP(c_List_Orev(U_20841),hAPP(c_List_Orev(U_20841),U_20842)) = U_20842,
    inference(variable_rename,[status(thm)],[f_4961_1]) ).

fof(f_4961_3,plain,
    ! [U_20841,U_20842] : hAPP(c_List_Orev(U_20841),hAPP(c_List_Orev(U_20841),U_20842)) = U_20842,
    inference(definitional_conversion,[status(esa)],[f_4961_2]) ).

cnf(f_4961_4,plain,
    hAPP(c_List_Orev(U_20841),hAPP(c_List_Orev(U_20841),U_20842)) = U_20842,
    inference(clausify,[status(thm)],[f_4961_3]) ).

fof(f_4962_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_4962_2,plain,
    ! [U_20847,U_20846,U_20845,U_20844,U_20843] : c_List_Ofoldr(U_20843,U_20844,U_20845,U_20846,U_20847) = hAPP(c_List_Ofoldl(U_20844,U_20843,hAPP(c_COMBC(U_20843,U_20844,U_20844),U_20845),U_20847),hAPP(c_List_Orev(U_20843),U_20846)),
    inference(variable_rename,[status(thm)],[f_4962_1]) ).

fof(f_4962_3,plain,
    ! [U_20843,U_20844,U_20845,U_20846,U_20847] : c_List_Ofoldr(U_20843,U_20844,U_20845,U_20846,U_20847) = hAPP(c_List_Ofoldl(U_20844,U_20843,hAPP(c_COMBC(U_20843,U_20844,U_20844),U_20845),U_20847),hAPP(c_List_Orev(U_20843),U_20846)),
    inference(definitional_conversion,[status(esa)],[f_4962_2]) ).

cnf(f_4962_4,plain,
    c_List_Ofoldr(U_20843,U_20844,U_20845,U_20846,U_20847) = hAPP(c_List_Ofoldl(U_20844,U_20843,hAPP(c_COMBC(U_20843,U_20844,U_20844),U_20845),U_20847),hAPP(c_List_Orev(U_20843),U_20846)),
    inference(clausify,[status(thm)],[f_4962_3]) ).

fof(f_4963_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_4963_2,plain,
    ! [U_20852,U_20851,U_20850,U_20849,U_20848] : hAPP(c_List_Ofoldl(U_20848,U_20849,U_20850,U_20851),U_20852) = c_List_Ofoldr(U_20849,U_20848,hAPP(c_COMBC(U_20848,U_20849,U_20848),U_20850),hAPP(c_List_Orev(U_20849),U_20852),U_20851),
    inference(variable_rename,[status(thm)],[f_4963_1]) ).

fof(f_4963_3,plain,
    ! [U_20848,U_20849,U_20850,U_20851,U_20852] : hAPP(c_List_Ofoldl(U_20848,U_20849,U_20850,U_20851),U_20852) = c_List_Ofoldr(U_20849,U_20848,hAPP(c_COMBC(U_20848,U_20849,U_20848),U_20850),hAPP(c_List_Orev(U_20849),U_20852),U_20851),
    inference(definitional_conversion,[status(esa)],[f_4963_2]) ).

cnf(f_4963_4,plain,
    hAPP(c_List_Ofoldl(U_20848,U_20849,U_20850,U_20851),U_20852) = c_List_Ofoldr(U_20849,U_20848,hAPP(c_COMBC(U_20848,U_20849,U_20848),U_20850),hAPP(c_List_Orev(U_20849),U_20852),U_20851),
    inference(clausify,[status(thm)],[f_4963_3]) ).

fof(f_4964_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_4964_2,plain,
    ! [U_20854,U_20853] : hAPP(c_List_Oset(U_20853),c_List_Oconcat(U_20853,U_20854)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_20853),tc_fun(U_20853,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_20853)),U_20854)),c_List_Oset(U_20853)),
    inference(variable_rename,[status(thm)],[f_4964_1]) ).

fof(f_4964_3,plain,
    ! [U_20853,U_20854] : hAPP(c_List_Oset(U_20853),c_List_Oconcat(U_20853,U_20854)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_20853),tc_fun(U_20853,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_20853)),U_20854)),c_List_Oset(U_20853)),
    inference(definitional_conversion,[status(esa)],[f_4964_2]) ).

cnf(f_4964_4,plain,
    hAPP(c_List_Oset(U_20853),c_List_Oconcat(U_20853,U_20854)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_20853),tc_fun(U_20853,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_20853)),U_20854)),c_List_Oset(U_20853)),
    inference(clausify,[status(thm)],[f_4964_3]) ).

fof(f_4965_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_4965_2,plain,
    ! [U_20856,U_20855] : hAPP(c_List_Oset(U_20855),hAPP(c_List_Orev(U_20855),U_20856)) = hAPP(c_List_Oset(U_20855),U_20856),
    inference(variable_rename,[status(thm)],[f_4965_1]) ).

fof(f_4965_3,plain,
    ! [U_20855,U_20856] : hAPP(c_List_Oset(U_20855),hAPP(c_List_Orev(U_20855),U_20856)) = hAPP(c_List_Oset(U_20855),U_20856),
    inference(definitional_conversion,[status(esa)],[f_4965_2]) ).

cnf(f_4965_4,plain,
    hAPP(c_List_Oset(U_20855),hAPP(c_List_Orev(U_20855),U_20856)) = hAPP(c_List_Oset(U_20855),U_20856),
    inference(clausify,[status(thm)],[f_4965_3]) ).

fof(f_4966_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_4966_2,plain,
    ! [U_20860,U_20859,U_20858,U_20857] :
      ( hAPP(hAPP(c_List_Ozip(U_20857,U_20859),hAPP(c_List_Orev(U_20857),U_20858)),hAPP(c_List_Orev(U_20859),U_20860)) = hAPP(c_List_Orev(tc_prod(U_20857,U_20859)),hAPP(hAPP(c_List_Ozip(U_20857,U_20859),U_20858),U_20860))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20857)),U_20858) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20859)),U_20860) ),
    inference(variable_rename,[status(thm)],[f_4966_1]) ).

fof(f_4966_3,plain,
    ! [U_20857,U_20858,U_20859,U_20860] :
      ( hAPP(hAPP(c_List_Ozip(U_20857,U_20859),hAPP(c_List_Orev(U_20857),U_20858)),hAPP(c_List_Orev(U_20859),U_20860)) = hAPP(c_List_Orev(tc_prod(U_20857,U_20859)),hAPP(hAPP(c_List_Ozip(U_20857,U_20859),U_20858),U_20860))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20857)),U_20858) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20859)),U_20860) ),
    inference(definitional_conversion,[status(esa)],[f_4966_2]) ).

cnf(f_4966_4,plain,
    ( hAPP(hAPP(c_List_Ozip(U_20857,U_20859),hAPP(c_List_Orev(U_20857),U_20858)),hAPP(c_List_Orev(U_20859),U_20860)) = hAPP(c_List_Orev(tc_prod(U_20857,U_20859)),hAPP(hAPP(c_List_Ozip(U_20857,U_20859),U_20858),U_20860))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20857)),U_20858) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20859)),U_20860) ),
    inference(clausify,[status(thm)],[f_4966_3]) ).

fof(f_4967_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_4967_2,plain,
    ! [U_20863,U_20862,U_20861] : hAPP(c_List_Orev(U_20861),hAPP(c_List_Ofilter(U_20861,U_20862),U_20863)) = hAPP(c_List_Ofilter(U_20861,U_20862),hAPP(c_List_Orev(U_20861),U_20863)),
    inference(variable_rename,[status(thm)],[f_4967_1]) ).

fof(f_4967_3,plain,
    ! [U_20861,U_20862,U_20863] : hAPP(c_List_Orev(U_20861),hAPP(c_List_Ofilter(U_20861,U_20862),U_20863)) = hAPP(c_List_Ofilter(U_20861,U_20862),hAPP(c_List_Orev(U_20861),U_20863)),
    inference(definitional_conversion,[status(esa)],[f_4967_2]) ).

cnf(f_4967_4,plain,
    hAPP(c_List_Orev(U_20861),hAPP(c_List_Ofilter(U_20861,U_20862),U_20863)) = hAPP(c_List_Ofilter(U_20861,U_20862),hAPP(c_List_Orev(U_20861),U_20863)),
    inference(clausify,[status(thm)],[f_4967_3]) ).

fof(f_4968_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_4968_2,plain,
    ! [U_20865,U_20864] :
      ( c_List_Olast(U_20865,hAPP(c_List_Orev(U_20865),U_20864)) = hAPP(c_List_Ohd(U_20865),U_20864)
      | U_20864 = c_List_Olist_ONil(U_20865) ),
    inference(variable_rename,[status(thm)],[f_4968_1]) ).

fof(f_4968_3,plain,
    ! [U_20864,U_20865] :
      ( c_List_Olast(U_20865,hAPP(c_List_Orev(U_20865),U_20864)) = hAPP(c_List_Ohd(U_20865),U_20864)
      | U_20864 = c_List_Olist_ONil(U_20865) ),
    inference(definitional_conversion,[status(esa)],[f_4968_2]) ).

cnf(f_4968_4,plain,
    ( c_List_Olast(U_20865,hAPP(c_List_Orev(U_20865),U_20864)) = hAPP(c_List_Ohd(U_20865),U_20864)
    | U_20864 = c_List_Olist_ONil(U_20865) ),
    inference(clausify,[status(thm)],[f_4968_3]) ).

fof(f_4969_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_4969_2,plain,
    ! [U_20867,U_20866] :
      ( hAPP(c_List_Ohd(U_20867),hAPP(c_List_Orev(U_20867),U_20866)) = c_List_Olast(U_20867,U_20866)
      | U_20866 = c_List_Olist_ONil(U_20867) ),
    inference(variable_rename,[status(thm)],[f_4969_1]) ).

fof(f_4969_3,plain,
    ! [U_20866,U_20867] :
      ( hAPP(c_List_Ohd(U_20867),hAPP(c_List_Orev(U_20867),U_20866)) = c_List_Olast(U_20867,U_20866)
      | U_20866 = c_List_Olist_ONil(U_20867) ),
    inference(definitional_conversion,[status(esa)],[f_4969_2]) ).

cnf(f_4969_4,plain,
    ( hAPP(c_List_Ohd(U_20867),hAPP(c_List_Orev(U_20867),U_20866)) = c_List_Olast(U_20867,U_20866)
    | U_20866 = c_List_Olist_ONil(U_20867) ),
    inference(clausify,[status(thm)],[f_4969_3]) ).

fof(f_4970_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_4970_2,plain,
    ! [U_20869,U_20868] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20868),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20868))),c_List_Otranspose(U_20868,U_20869)))),
    inference(variable_rename,[status(thm)],[f_4970_1]) ).

fof(f_4970_3,plain,
    ! [U_20868,U_20869] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20868),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20868))),c_List_Otranspose(U_20868,U_20869)))),
    inference(definitional_conversion,[status(esa)],[f_4970_2]) ).

cnf(f_4970_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_20868),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20868))),c_List_Otranspose(U_20868,U_20869)))),
    inference(clausify,[status(thm)],[f_4970_3]) ).

fof(f_4971_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_4971_2,plain,
    ! [U_20872,U_20871,U_20870] : hAPP(c_List_Orev(U_20870),hAPP(hAPP(c_List_Otake(U_20870),U_20871),U_20872)) = hAPP(hAPP(c_List_Odrop(U_20870),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20870)),U_20872)),U_20871)),hAPP(c_List_Orev(U_20870),U_20872)),
    inference(variable_rename,[status(thm)],[f_4971_1]) ).

fof(f_4971_3,plain,
    ! [U_20870,U_20871,U_20872] : hAPP(c_List_Orev(U_20870),hAPP(hAPP(c_List_Otake(U_20870),U_20871),U_20872)) = hAPP(hAPP(c_List_Odrop(U_20870),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20870)),U_20872)),U_20871)),hAPP(c_List_Orev(U_20870),U_20872)),
    inference(definitional_conversion,[status(esa)],[f_4971_2]) ).

cnf(f_4971_4,plain,
    hAPP(c_List_Orev(U_20870),hAPP(hAPP(c_List_Otake(U_20870),U_20871),U_20872)) = hAPP(hAPP(c_List_Odrop(U_20870),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20870)),U_20872)),U_20871)),hAPP(c_List_Orev(U_20870),U_20872)),
    inference(clausify,[status(thm)],[f_4971_3]) ).

fof(f_4972_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_4972_2,plain,
    ! [U_20875,U_20874,U_20873] : hAPP(c_List_Orev(U_20873),hAPP(hAPP(c_List_Odrop(U_20873),U_20874),U_20875)) = hAPP(hAPP(c_List_Otake(U_20873),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20873)),U_20875)),U_20874)),hAPP(c_List_Orev(U_20873),U_20875)),
    inference(variable_rename,[status(thm)],[f_4972_1]) ).

fof(f_4972_3,plain,
    ! [U_20873,U_20874,U_20875] : hAPP(c_List_Orev(U_20873),hAPP(hAPP(c_List_Odrop(U_20873),U_20874),U_20875)) = hAPP(hAPP(c_List_Otake(U_20873),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20873)),U_20875)),U_20874)),hAPP(c_List_Orev(U_20873),U_20875)),
    inference(definitional_conversion,[status(esa)],[f_4972_2]) ).

cnf(f_4972_4,plain,
    hAPP(c_List_Orev(U_20873),hAPP(hAPP(c_List_Odrop(U_20873),U_20874),U_20875)) = hAPP(hAPP(c_List_Otake(U_20873),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20873)),U_20875)),U_20874)),hAPP(c_List_Orev(U_20873),U_20875)),
    inference(clausify,[status(thm)],[f_4972_3]) ).

fof(f_4973_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_4973_2,plain,
    ! [U_20878,U_20877,U_20876] : hAPP(c_List_Orotate(U_20876,U_20877),hAPP(c_List_Orev(U_20876),U_20878)) = hAPP(c_List_Orev(U_20876),hAPP(c_List_Orotate(U_20876,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20876)),U_20878)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_20877,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20876)),U_20878)))),U_20878)),
    inference(variable_rename,[status(thm)],[f_4973_1]) ).

fof(f_4973_3,plain,
    ! [U_20876,U_20877,U_20878] : hAPP(c_List_Orotate(U_20876,U_20877),hAPP(c_List_Orev(U_20876),U_20878)) = hAPP(c_List_Orev(U_20876),hAPP(c_List_Orotate(U_20876,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20876)),U_20878)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_20877,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20876)),U_20878)))),U_20878)),
    inference(definitional_conversion,[status(esa)],[f_4973_2]) ).

cnf(f_4973_4,plain,
    hAPP(c_List_Orotate(U_20876,U_20877),hAPP(c_List_Orev(U_20876),U_20878)) = hAPP(c_List_Orev(U_20876),hAPP(c_List_Orotate(U_20876,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20876)),U_20878)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_20877,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20876)),U_20878)))),U_20878)),
    inference(clausify,[status(thm)],[f_4973_3]) ).

fof(f_4974_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_4974_2,plain,
    ! [U_20882,U_20881,U_20880,U_20879] : c_List_Otranspose(U_20879,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20879)),hAPP(hAPP(c_List_Olist_OCons(U_20879),U_20880),U_20881)),U_20882)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20879)),hAPP(hAPP(c_List_Olist_OCons(U_20879),U_20880),c_List_Oconcat(U_20879,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20879),tc_List_Olist(U_20879)),c_List_Olist_Olist__case(tc_List_Olist(U_20879),U_20879,c_List_Olist_ONil(U_20879),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20879),tc_fun(tc_List_Olist(U_20879),tc_List_Olist(U_20879)),U_20879),c_COMBK(tc_List_Olist(U_20879),tc_List_Olist(U_20879))),hAPP(hAPP(c_COMBC(U_20879,tc_List_Olist(U_20879),tc_List_Olist(U_20879)),c_List_Olist_OCons(U_20879)),c_List_Olist_ONil(U_20879))))),U_20882)))),c_List_Otranspose(U_20879,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20879)),U_20881),c_List_Oconcat(tc_List_Olist(U_20879),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20879),tc_List_Olist(tc_List_Olist(U_20879))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20879)),U_20879,c_List_Olist_ONil(tc_List_Olist(U_20879)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20879),tc_List_Olist(tc_List_Olist(U_20879))),U_20879),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20879),tc_List_Olist(tc_List_Olist(U_20879)),tc_List_Olist(tc_List_Olist(U_20879))),c_List_Olist_OCons(tc_List_Olist(U_20879))),c_List_Olist_ONil(tc_List_Olist(U_20879)))))),U_20882))))),
    inference(variable_rename,[status(thm)],[f_4974_1]) ).

fof(f_4974_3,plain,
    ! [U_20879,U_20880,U_20881,U_20882] : c_List_Otranspose(U_20879,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20879)),hAPP(hAPP(c_List_Olist_OCons(U_20879),U_20880),U_20881)),U_20882)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20879)),hAPP(hAPP(c_List_Olist_OCons(U_20879),U_20880),c_List_Oconcat(U_20879,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20879),tc_List_Olist(U_20879)),c_List_Olist_Olist__case(tc_List_Olist(U_20879),U_20879,c_List_Olist_ONil(U_20879),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20879),tc_fun(tc_List_Olist(U_20879),tc_List_Olist(U_20879)),U_20879),c_COMBK(tc_List_Olist(U_20879),tc_List_Olist(U_20879))),hAPP(hAPP(c_COMBC(U_20879,tc_List_Olist(U_20879),tc_List_Olist(U_20879)),c_List_Olist_OCons(U_20879)),c_List_Olist_ONil(U_20879))))),U_20882)))),c_List_Otranspose(U_20879,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20879)),U_20881),c_List_Oconcat(tc_List_Olist(U_20879),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20879),tc_List_Olist(tc_List_Olist(U_20879))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20879)),U_20879,c_List_Olist_ONil(tc_List_Olist(U_20879)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20879),tc_List_Olist(tc_List_Olist(U_20879))),U_20879),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20879),tc_List_Olist(tc_List_Olist(U_20879)),tc_List_Olist(tc_List_Olist(U_20879))),c_List_Olist_OCons(tc_List_Olist(U_20879))),c_List_Olist_ONil(tc_List_Olist(U_20879)))))),U_20882))))),
    inference(definitional_conversion,[status(esa)],[f_4974_2]) ).

cnf(f_4974_4,plain,
    c_List_Otranspose(U_20879,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20879)),hAPP(hAPP(c_List_Olist_OCons(U_20879),U_20880),U_20881)),U_20882)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20879)),hAPP(hAPP(c_List_Olist_OCons(U_20879),U_20880),c_List_Oconcat(U_20879,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20879),tc_List_Olist(U_20879)),c_List_Olist_Olist__case(tc_List_Olist(U_20879),U_20879,c_List_Olist_ONil(U_20879),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20879),tc_fun(tc_List_Olist(U_20879),tc_List_Olist(U_20879)),U_20879),c_COMBK(tc_List_Olist(U_20879),tc_List_Olist(U_20879))),hAPP(hAPP(c_COMBC(U_20879,tc_List_Olist(U_20879),tc_List_Olist(U_20879)),c_List_Olist_OCons(U_20879)),c_List_Olist_ONil(U_20879))))),U_20882)))),c_List_Otranspose(U_20879,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20879)),U_20881),c_List_Oconcat(tc_List_Olist(U_20879),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20879),tc_List_Olist(tc_List_Olist(U_20879))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20879)),U_20879,c_List_Olist_ONil(tc_List_Olist(U_20879)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20879),tc_List_Olist(tc_List_Olist(U_20879))),U_20879),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20879),tc_List_Olist(tc_List_Olist(U_20879)),tc_List_Olist(tc_List_Olist(U_20879))),c_List_Olist_OCons(tc_List_Olist(U_20879))),c_List_Olist_ONil(tc_List_Olist(U_20879)))))),U_20882))))),
    inference(clausify,[status(thm)],[f_4974_3]) ).

fof(f_4975_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_4975_2,plain,
    ! [U_20885,U_20884,U_20883] :
      ( hAPP(hAPP(c_List_Onth(U_20884),hAPP(c_List_Orev(U_20884),U_20885)),U_20883) = hAPP(hAPP(c_List_Onth(U_20884),U_20885),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20884)),U_20885)),hAPP(c_Nat_OSuc,U_20883)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20883),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20884)),U_20885))) ),
    inference(variable_rename,[status(thm)],[f_4975_1]) ).

fof(f_4975_3,plain,
    ! [U_20883,U_20884,U_20885] :
      ( hAPP(hAPP(c_List_Onth(U_20884),hAPP(c_List_Orev(U_20884),U_20885)),U_20883) = hAPP(hAPP(c_List_Onth(U_20884),U_20885),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20884)),U_20885)),hAPP(c_Nat_OSuc,U_20883)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20883),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20884)),U_20885))) ),
    inference(definitional_conversion,[status(esa)],[f_4975_2]) ).

cnf(f_4975_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_20884),hAPP(c_List_Orev(U_20884),U_20885)),U_20883) = hAPP(hAPP(c_List_Onth(U_20884),U_20885),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20884)),U_20885)),hAPP(c_Nat_OSuc,U_20883)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20883),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20884)),U_20885))) ),
    inference(clausify,[status(thm)],[f_4975_3]) ).

fof(f_4976_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_4976_2,plain,
    ! [U_20889,U_20888,U_20887] :
      ( U_20888 = U_20889
      | ? [U_20886] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20887),tc_List_Olist(U_20887),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20887),tc_fun(tc_List_Olist(U_20887),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20887),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20887),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20887),tc_HOL_Obool)),tc_List_Olist(U_20887)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20887))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20887)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20887))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20887)))),U_20886))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20887),tc_List_Olist(U_20887))),U_20886),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20887),tc_List_Olist(U_20887))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20887),tc_List_Olist(U_20887)),U_20888),U_20889)))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20887))),U_20888) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20887))),U_20889)
      | c_List_Oconcat(U_20887,U_20888) != c_List_Oconcat(U_20887,U_20889) ),
    inference(variable_rename,[status(thm)],[f_4976_1]) ).

fof(f_4976_3,plain,
    ! [U_20889,U_20888,U_20887] :
      ( U_20888 = U_20889
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20887),tc_List_Olist(U_20887),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20887),tc_fun(tc_List_Olist(U_20887),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20887),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20887),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20887),tc_HOL_Obool)),tc_List_Olist(U_20887)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20887))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20887)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20887))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20887)))),sK511(U_20889,U_20888,U_20887)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20887),tc_List_Olist(U_20887))),sK511(U_20889,U_20888,U_20887)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20887),tc_List_Olist(U_20887))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20887),tc_List_Olist(U_20887)),U_20888),U_20889)))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20887))),U_20888) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20887))),U_20889)
      | c_List_Oconcat(U_20887,U_20888) != c_List_Oconcat(U_20887,U_20889) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK511]),skolemize(U_20886,sK511(U_20889,U_20888,U_20887))],[f_4976_2]) ).

fof(f_4976_4,plain,
    ( ! [U_20887,U_20888,U_20889] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20887),tc_List_Olist(U_20887),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20887),tc_fun(tc_List_Olist(U_20887),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20887),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20887),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20887),tc_HOL_Obool)),tc_List_Olist(U_20887)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20887))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20887)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20887))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20887)))),sK511(U_20889,U_20888,U_20887)))
        | ~ sP1241(U_20887,U_20888,U_20889) )
    & ! [U_20887,U_20888,U_20889] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20887),tc_List_Olist(U_20887))),sK511(U_20889,U_20888,U_20887)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20887),tc_List_Olist(U_20887))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20887),tc_List_Olist(U_20887)),U_20888),U_20889))))
        | ~ sP1241(U_20887,U_20888,U_20889) )
    & ! [U_20887,U_20888,U_20889] :
        ( U_20888 = U_20889
        | sP1241(U_20887,U_20888,U_20889)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20887))),U_20888) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20887))),U_20889)
        | c_List_Oconcat(U_20887,U_20888) != c_List_Oconcat(U_20887,U_20889) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1241])],[f_4976_3]) ).

cnf(f_4976_5,plain,
    ( U_20888 = U_20889
    | sP1241(U_20887,U_20888,U_20889)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20887))),U_20888) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20887))),U_20889)
    | c_List_Oconcat(U_20887,U_20888) != c_List_Oconcat(U_20887,U_20889) ),
    inference(clausify,[status(thm)],[f_4976_4]) ).

cnf(f_4976_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20887),tc_List_Olist(U_20887))),sK511(U_20889,U_20888,U_20887)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20887),tc_List_Olist(U_20887))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20887),tc_List_Olist(U_20887)),U_20888),U_20889))))
    | ~ sP1241(U_20887,U_20888,U_20889) ),
    inference(clausify,[status(thm)],[f_4976_4]) ).

cnf(f_4976_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20887),tc_List_Olist(U_20887),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20887),tc_fun(tc_List_Olist(U_20887),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20887),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20887),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20887),tc_HOL_Obool)),tc_List_Olist(U_20887)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20887))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20887)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20887))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20887)))),sK511(U_20889,U_20888,U_20887)))
    | ~ sP1241(U_20887,U_20888,U_20889) ),
    inference(clausify,[status(thm)],[f_4976_4]) ).

fof(f_4977_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_4977_2,plain,
    ! [U_20893,U_20892,U_20891] :
      ( ( ( c_List_Oconcat(U_20891,U_20892) = c_List_Oconcat(U_20891,U_20893)
          | U_20892 != U_20893 )
        & ( U_20892 = U_20893
          | c_List_Oconcat(U_20891,U_20892) != c_List_Oconcat(U_20891,U_20893) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20891))),U_20892) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20891))),U_20893)
      | ? [U_20890] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20891),tc_List_Olist(U_20891),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20891),tc_fun(tc_List_Olist(U_20891),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20891),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20891),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20891),tc_HOL_Obool)),tc_List_Olist(U_20891)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20891))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20891)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20891))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20891)))),U_20890))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20891),tc_List_Olist(U_20891))),U_20890),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20891),tc_List_Olist(U_20891))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20891),tc_List_Olist(U_20891)),U_20892),U_20893)))) ) ),
    inference(variable_rename,[status(thm)],[f_4977_1]) ).

fof(f_4977_3,plain,
    ! [U_20893,U_20892,U_20891] :
      ( ( ( c_List_Oconcat(U_20891,U_20892) = c_List_Oconcat(U_20891,U_20893)
          | U_20892 != U_20893 )
        & ( U_20892 = U_20893
          | c_List_Oconcat(U_20891,U_20892) != c_List_Oconcat(U_20891,U_20893) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20891))),U_20892) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20891))),U_20893)
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20891),tc_List_Olist(U_20891),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20891),tc_fun(tc_List_Olist(U_20891),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20891),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20891),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20891),tc_HOL_Obool)),tc_List_Olist(U_20891)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20891))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20891)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20891))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20891)))),sK512(U_20893,U_20892,U_20891)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20891),tc_List_Olist(U_20891))),sK512(U_20893,U_20892,U_20891)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20891),tc_List_Olist(U_20891))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20891),tc_List_Olist(U_20891)),U_20892),U_20893)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK512]),skolemize(U_20890,sK512(U_20893,U_20892,U_20891))],[f_4977_2]) ).

fof(f_4977_4,plain,
    ( ! [U_20891,U_20892,U_20893] :
        ( c_List_Oconcat(U_20891,U_20892) = c_List_Oconcat(U_20891,U_20893)
        | U_20892 != U_20893
        | ~ sP1243(U_20891,U_20892,U_20893) )
    & ! [U_20891,U_20892,U_20893] :
        ( U_20892 = U_20893
        | c_List_Oconcat(U_20891,U_20892) != c_List_Oconcat(U_20891,U_20893)
        | ~ sP1243(U_20891,U_20892,U_20893) )
    & ! [U_20891,U_20892,U_20893] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20891),tc_List_Olist(U_20891),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20891),tc_fun(tc_List_Olist(U_20891),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20891),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20891),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20891),tc_HOL_Obool)),tc_List_Olist(U_20891)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20891))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20891)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20891))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20891)))),sK512(U_20893,U_20892,U_20891)))
        | ~ sP1242(U_20891,U_20892,U_20893) )
    & ! [U_20891,U_20892,U_20893] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20891),tc_List_Olist(U_20891))),sK512(U_20893,U_20892,U_20891)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20891),tc_List_Olist(U_20891))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20891),tc_List_Olist(U_20891)),U_20892),U_20893))))
        | ~ sP1242(U_20891,U_20892,U_20893) )
    & ! [U_20891,U_20892,U_20893] :
        ( sP1243(U_20891,U_20892,U_20893)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20891))),U_20892) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20891))),U_20893)
        | sP1242(U_20891,U_20892,U_20893) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1242,sP1243])],[f_4977_3]) ).

cnf(f_4977_5,plain,
    ( sP1243(U_20891,U_20892,U_20893)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20891))),U_20892) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20891))),U_20893)
    | sP1242(U_20891,U_20892,U_20893) ),
    inference(clausify,[status(thm)],[f_4977_4]) ).

cnf(f_4977_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20891),tc_List_Olist(U_20891))),sK512(U_20893,U_20892,U_20891)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20891),tc_List_Olist(U_20891))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20891),tc_List_Olist(U_20891)),U_20892),U_20893))))
    | ~ sP1242(U_20891,U_20892,U_20893) ),
    inference(clausify,[status(thm)],[f_4977_4]) ).

cnf(f_4977_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20891),tc_List_Olist(U_20891),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20891),tc_fun(tc_List_Olist(U_20891),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20891),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20891),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20891),tc_HOL_Obool)),tc_List_Olist(U_20891)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20891))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20891)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20891))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20891)))),sK512(U_20893,U_20892,U_20891)))
    | ~ sP1242(U_20891,U_20892,U_20893) ),
    inference(clausify,[status(thm)],[f_4977_4]) ).

cnf(f_4977_8,plain,
    ( U_20892 = U_20893
    | c_List_Oconcat(U_20891,U_20892) != c_List_Oconcat(U_20891,U_20893)
    | ~ sP1243(U_20891,U_20892,U_20893) ),
    inference(clausify,[status(thm)],[f_4977_4]) ).

cnf(f_4977_9,plain,
    ( c_List_Oconcat(U_20891,U_20892) = c_List_Oconcat(U_20891,U_20893)
    | U_20892 != U_20893
    | ~ sP1243(U_20891,U_20892,U_20893) ),
    inference(clausify,[status(thm)],[f_4977_4]) ).

fof(f_4978_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_4978_2,plain,
    ! [U_20897,U_20896,U_20895,U_20894] :
      ( hAPP(c_List_Orev(U_20895),hAPP(hAPP(c_List_Olist__update(U_20895,U_20896),U_20894),U_20897)) = hAPP(hAPP(c_List_Olist__update(U_20895,hAPP(c_List_Orev(U_20895),U_20896)),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_20895)),U_20896)),U_20894)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_20897)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20894),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20895)),U_20896))) ),
    inference(variable_rename,[status(thm)],[f_4978_1]) ).

fof(f_4978_3,plain,
    ! [U_20897,U_20896,U_20894,U_20895] :
      ( hAPP(c_List_Orev(U_20895),hAPP(hAPP(c_List_Olist__update(U_20895,U_20896),U_20894),U_20897)) = hAPP(hAPP(c_List_Olist__update(U_20895,hAPP(c_List_Orev(U_20895),U_20896)),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_20895)),U_20896)),U_20894)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_20897)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20894),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20895)),U_20896))) ),
    inference(definitional_conversion,[status(esa)],[f_4978_2]) ).

cnf(f_4978_4,plain,
    ( hAPP(c_List_Orev(U_20895),hAPP(hAPP(c_List_Olist__update(U_20895,U_20896),U_20894),U_20897)) = hAPP(hAPP(c_List_Olist__update(U_20895,hAPP(c_List_Orev(U_20895),U_20896)),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_20895)),U_20896)),U_20894)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_20897)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20894),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20895)),U_20896))) ),
    inference(clausify,[status(thm)],[f_4978_3]) ).

fof(f_4979_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_4979_2,plain,
    ! [U_20901,U_20900,U_20899,U_20898] : c_List_Oconcat(U_20898,hAPP(hAPP(c_List_Omap(U_20899,tc_List_Olist(U_20898)),hAPP(hAPP(c_COMBC(U_20899,tc_List_Olist(U_20898),tc_List_Olist(U_20898)),hAPP(hAPP(c_COMBB(U_20898,tc_fun(tc_List_Olist(U_20898),tc_List_Olist(U_20898)),U_20899),c_List_Olist_OCons(U_20898)),U_20900)),c_List_Olist_ONil(U_20898))),U_20901)) = hAPP(hAPP(c_List_Omap(U_20899,U_20898),U_20900),U_20901),
    inference(variable_rename,[status(thm)],[f_4979_1]) ).

fof(f_4979_3,plain,
    ! [U_20898,U_20899,U_20900,U_20901] : c_List_Oconcat(U_20898,hAPP(hAPP(c_List_Omap(U_20899,tc_List_Olist(U_20898)),hAPP(hAPP(c_COMBC(U_20899,tc_List_Olist(U_20898),tc_List_Olist(U_20898)),hAPP(hAPP(c_COMBB(U_20898,tc_fun(tc_List_Olist(U_20898),tc_List_Olist(U_20898)),U_20899),c_List_Olist_OCons(U_20898)),U_20900)),c_List_Olist_ONil(U_20898))),U_20901)) = hAPP(hAPP(c_List_Omap(U_20899,U_20898),U_20900),U_20901),
    inference(definitional_conversion,[status(esa)],[f_4979_2]) ).

cnf(f_4979_4,plain,
    c_List_Oconcat(U_20898,hAPP(hAPP(c_List_Omap(U_20899,tc_List_Olist(U_20898)),hAPP(hAPP(c_COMBC(U_20899,tc_List_Olist(U_20898),tc_List_Olist(U_20898)),hAPP(hAPP(c_COMBB(U_20898,tc_fun(tc_List_Olist(U_20898),tc_List_Olist(U_20898)),U_20899),c_List_Olist_OCons(U_20898)),U_20900)),c_List_Olist_ONil(U_20898))),U_20901)) = hAPP(hAPP(c_List_Omap(U_20899,U_20898),U_20900),U_20901),
    inference(clausify,[status(thm)],[f_4979_3]) ).

fof(f_4980_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_4980_2,plain,
    ! [U_20905,U_20904,U_20903,U_20902] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20902),hAPP(hAPP(c_List_Onth(U_20902),U_20903),U_20905)),hAPP(hAPP(c_List_Onth(U_20902),U_20903),U_20904)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20905),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20902)),U_20903)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20904),U_20905))
      | ~ c_List_Olinorder__class_Osorted(U_20902,hAPP(c_List_Orev(U_20902),U_20903))
      | ~ class_Orderings_Olinorder(U_20902) ),
    inference(variable_rename,[status(thm)],[f_4980_1]) ).

fof(f_4980_3,plain,
    ! [U_20902,U_20903,U_20904,U_20905] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20902),hAPP(hAPP(c_List_Onth(U_20902),U_20903),U_20905)),hAPP(hAPP(c_List_Onth(U_20902),U_20903),U_20904)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20905),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20902)),U_20903)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20904),U_20905))
      | ~ c_List_Olinorder__class_Osorted(U_20902,hAPP(c_List_Orev(U_20902),U_20903))
      | ~ class_Orderings_Olinorder(U_20902) ),
    inference(definitional_conversion,[status(esa)],[f_4980_2]) ).

cnf(f_4980_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20902),hAPP(hAPP(c_List_Onth(U_20902),U_20903),U_20905)),hAPP(hAPP(c_List_Onth(U_20902),U_20903),U_20904)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20905),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20902)),U_20903)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20904),U_20905))
    | ~ c_List_Olinorder__class_Osorted(U_20902,hAPP(c_List_Orev(U_20902),U_20903))
    | ~ class_Orderings_Olinorder(U_20902) ),
    inference(clausify,[status(thm)],[f_4980_3]) ).

fof(f_4981_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_4981_2,plain,
    ! [U_20908,U_20907,U_20906] :
      ( ( ( c_List_Ofoldr(U_20906,U_20906,c_Orderings_Oord__class_Omax(U_20906),U_20907,U_20908) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_20906),hAPP(hAPP(c_List_Onth(U_20906),U_20907),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_20908)
          | U_20907 = c_List_Olist_ONil(U_20906) )
        & ( c_List_Ofoldr(U_20906,U_20906,c_Orderings_Oord__class_Omax(U_20906),U_20907,U_20908) = U_20908
          | U_20907 != c_List_Olist_ONil(U_20906) ) )
      | ~ c_List_Olinorder__class_Osorted(U_20906,hAPP(c_List_Orev(U_20906),U_20907))
      | ~ class_Orderings_Olinorder(U_20906) ),
    inference(variable_rename,[status(thm)],[f_4981_1]) ).

fof(f_4981_3,plain,
    ( ! [U_20908,U_20907,U_20906] :
        ( c_List_Ofoldr(U_20906,U_20906,c_Orderings_Oord__class_Omax(U_20906),U_20907,U_20908) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_20906),hAPP(hAPP(c_List_Onth(U_20906),U_20907),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_20908)
        | U_20907 = c_List_Olist_ONil(U_20906)
        | ~ sP1244(U_20908,U_20907,U_20906) )
    & ! [U_20908,U_20907,U_20906] :
        ( c_List_Ofoldr(U_20906,U_20906,c_Orderings_Oord__class_Omax(U_20906),U_20907,U_20908) = U_20908
        | U_20907 != c_List_Olist_ONil(U_20906)
        | ~ sP1244(U_20908,U_20907,U_20906) )
    & ! [U_20908,U_20907,U_20906] :
        ( sP1244(U_20908,U_20907,U_20906)
        | ~ c_List_Olinorder__class_Osorted(U_20906,hAPP(c_List_Orev(U_20906),U_20907))
        | ~ class_Orderings_Olinorder(U_20906) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1244])],[f_4981_2]) ).

cnf(f_4981_4,plain,
    ( sP1244(U_20908,U_20907,U_20906)
    | ~ c_List_Olinorder__class_Osorted(U_20906,hAPP(c_List_Orev(U_20906),U_20907))
    | ~ class_Orderings_Olinorder(U_20906) ),
    inference(clausify,[status(thm)],[f_4981_3]) ).

cnf(f_4981_5,plain,
    ( c_List_Ofoldr(U_20906,U_20906,c_Orderings_Oord__class_Omax(U_20906),U_20907,U_20908) = U_20908
    | U_20907 != c_List_Olist_ONil(U_20906)
    | ~ sP1244(U_20908,U_20907,U_20906) ),
    inference(clausify,[status(thm)],[f_4981_3]) ).

cnf(f_4981_6,plain,
    ( c_List_Ofoldr(U_20906,U_20906,c_Orderings_Oord__class_Omax(U_20906),U_20907,U_20908) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_20906),hAPP(hAPP(c_List_Onth(U_20906),U_20907),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_20908)
    | U_20907 = c_List_Olist_ONil(U_20906)
    | ~ sP1244(U_20908,U_20907,U_20906) ),
    inference(clausify,[status(thm)],[f_4981_3]) ).

fof(f_4982_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_4982_2,plain,
    ! [U_20912,U_20911,U_20910,U_20909] :
      ( c_List_Otranspose(U_20909,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20909)),hAPP(hAPP(c_List_Olist_OCons(U_20909),U_20910),U_20911)),U_20912)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20909)),hAPP(hAPP(c_List_Olist_OCons(U_20909),U_20910),c_List_Oconcat(U_20909,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20909),tc_List_Olist(U_20909)),c_List_Olist_Olist__case(tc_List_Olist(U_20909),U_20909,c_List_Olist_ONil(U_20909),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20909),tc_fun(tc_List_Olist(U_20909),tc_List_Olist(U_20909)),U_20909),c_COMBK(tc_List_Olist(U_20909),tc_List_Olist(U_20909))),hAPP(hAPP(c_COMBC(U_20909,tc_List_Olist(U_20909),tc_List_Olist(U_20909)),c_List_Olist_OCons(U_20909)),c_List_Olist_ONil(U_20909))))),U_20912)))),c_List_Otranspose(U_20909,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20909)),U_20911),c_List_Oconcat(tc_List_Olist(U_20909),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20909),tc_List_Olist(tc_List_Olist(U_20909))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20909)),U_20909,c_List_Olist_ONil(tc_List_Olist(U_20909)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20909),tc_List_Olist(tc_List_Olist(U_20909))),U_20909),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20909),tc_List_Olist(tc_List_Olist(U_20909)),tc_List_Olist(tc_List_Olist(U_20909))),c_List_Olist_OCons(tc_List_Olist(U_20909))),c_List_Olist_ONil(tc_List_Olist(U_20909)))))),U_20912)))))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20909)),c_List_Otranspose__rel(U_20909)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20909)),hAPP(hAPP(c_List_Olist_OCons(U_20909),U_20910),U_20911)),U_20912))) ),
    inference(variable_rename,[status(thm)],[f_4982_1]) ).

fof(f_4982_3,plain,
    ! [U_20909,U_20910,U_20911,U_20912] :
      ( c_List_Otranspose(U_20909,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20909)),hAPP(hAPP(c_List_Olist_OCons(U_20909),U_20910),U_20911)),U_20912)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20909)),hAPP(hAPP(c_List_Olist_OCons(U_20909),U_20910),c_List_Oconcat(U_20909,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20909),tc_List_Olist(U_20909)),c_List_Olist_Olist__case(tc_List_Olist(U_20909),U_20909,c_List_Olist_ONil(U_20909),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20909),tc_fun(tc_List_Olist(U_20909),tc_List_Olist(U_20909)),U_20909),c_COMBK(tc_List_Olist(U_20909),tc_List_Olist(U_20909))),hAPP(hAPP(c_COMBC(U_20909,tc_List_Olist(U_20909),tc_List_Olist(U_20909)),c_List_Olist_OCons(U_20909)),c_List_Olist_ONil(U_20909))))),U_20912)))),c_List_Otranspose(U_20909,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20909)),U_20911),c_List_Oconcat(tc_List_Olist(U_20909),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20909),tc_List_Olist(tc_List_Olist(U_20909))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20909)),U_20909,c_List_Olist_ONil(tc_List_Olist(U_20909)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20909),tc_List_Olist(tc_List_Olist(U_20909))),U_20909),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20909),tc_List_Olist(tc_List_Olist(U_20909)),tc_List_Olist(tc_List_Olist(U_20909))),c_List_Olist_OCons(tc_List_Olist(U_20909))),c_List_Olist_ONil(tc_List_Olist(U_20909)))))),U_20912)))))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20909)),c_List_Otranspose__rel(U_20909)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20909)),hAPP(hAPP(c_List_Olist_OCons(U_20909),U_20910),U_20911)),U_20912))) ),
    inference(definitional_conversion,[status(esa)],[f_4982_2]) ).

cnf(f_4982_4,plain,
    ( c_List_Otranspose(U_20909,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20909)),hAPP(hAPP(c_List_Olist_OCons(U_20909),U_20910),U_20911)),U_20912)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20909)),hAPP(hAPP(c_List_Olist_OCons(U_20909),U_20910),c_List_Oconcat(U_20909,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20909),tc_List_Olist(U_20909)),c_List_Olist_Olist__case(tc_List_Olist(U_20909),U_20909,c_List_Olist_ONil(U_20909),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20909),tc_fun(tc_List_Olist(U_20909),tc_List_Olist(U_20909)),U_20909),c_COMBK(tc_List_Olist(U_20909),tc_List_Olist(U_20909))),hAPP(hAPP(c_COMBC(U_20909,tc_List_Olist(U_20909),tc_List_Olist(U_20909)),c_List_Olist_OCons(U_20909)),c_List_Olist_ONil(U_20909))))),U_20912)))),c_List_Otranspose(U_20909,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20909)),U_20911),c_List_Oconcat(tc_List_Olist(U_20909),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20909),tc_List_Olist(tc_List_Olist(U_20909))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20909)),U_20909,c_List_Olist_ONil(tc_List_Olist(U_20909)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20909),tc_List_Olist(tc_List_Olist(U_20909))),U_20909),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20909),tc_List_Olist(tc_List_Olist(U_20909)),tc_List_Olist(tc_List_Olist(U_20909))),c_List_Olist_OCons(tc_List_Olist(U_20909))),c_List_Olist_ONil(tc_List_Olist(U_20909)))))),U_20912)))))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20909)),c_List_Otranspose__rel(U_20909)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20909)),hAPP(hAPP(c_List_Olist_OCons(U_20909),U_20910),U_20911)),U_20912))) ),
    inference(clausify,[status(thm)],[f_4982_3]) ).

fof(f_4983_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_4983_2,plain,
    ! [U_20914,U_20913] :
      ( ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20913))),c_List_Otranspose(U_20913,U_20914)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20913)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20913)),U_20914),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | U_20914 = c_List_Olist_ONil(tc_List_Olist(U_20913)) )
        & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20913))),c_List_Otranspose(U_20913,U_20914)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_20914 != c_List_Olist_ONil(tc_List_Olist(U_20913)) ) )
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20913),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20913))),U_20914))) ),
    inference(variable_rename,[status(thm)],[f_4983_1]) ).

fof(f_4983_3,plain,
    ( ! [U_20913,U_20914] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20913))),c_List_Otranspose(U_20913,U_20914)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20913)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20913)),U_20914),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_20914 = c_List_Olist_ONil(tc_List_Olist(U_20913))
        | ~ sP1245(U_20913,U_20914) )
    & ! [U_20913,U_20914] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20913))),c_List_Otranspose(U_20913,U_20914)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_20914 != c_List_Olist_ONil(tc_List_Olist(U_20913))
        | ~ sP1245(U_20913,U_20914) )
    & ! [U_20913,U_20914] :
        ( sP1245(U_20913,U_20914)
        | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20913),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20913))),U_20914))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1245])],[f_4983_2]) ).

cnf(f_4983_4,plain,
    ( sP1245(U_20913,U_20914)
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20913),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20913))),U_20914))) ),
    inference(clausify,[status(thm)],[f_4983_3]) ).

cnf(f_4983_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20913))),c_List_Otranspose(U_20913,U_20914)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_20914 != c_List_Olist_ONil(tc_List_Olist(U_20913))
    | ~ sP1245(U_20913,U_20914) ),
    inference(clausify,[status(thm)],[f_4983_3]) ).

cnf(f_4983_6,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20913))),c_List_Otranspose(U_20913,U_20914)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20913)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20913)),U_20914),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_20914 = c_List_Olist_ONil(tc_List_Olist(U_20913))
    | ~ sP1245(U_20913,U_20914) ),
    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_20916,U_20915] :
      ( class_Lattices_Obounded__lattice(tc_fun(U_20916,U_20915))
      | ~ class_Lattices_Obounded__lattice(U_20915) ),
    inference(variable_rename,[status(thm)],[f_4985_1]) ).

fof(f_4985_3,plain,
    ! [U_20916,U_20915] :
      ( class_Lattices_Obounded__lattice(tc_fun(U_20916,U_20915))
      | ~ class_Lattices_Obounded__lattice(U_20915) ),
    inference(definitional_conversion,[status(esa)],[f_4985_2]) ).

cnf(f_4985_4,plain,
    ( class_Lattices_Obounded__lattice(tc_fun(U_20916,U_20915))
    | ~ class_Lattices_Obounded__lattice(U_20915) ),
    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_20918,U_20917] :
      ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(U_20918,U_20917))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20917) ),
    inference(variable_rename,[status(thm)],[f_4986_1]) ).

fof(f_4986_3,plain,
    ! [U_20918,U_20917] :
      ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(U_20918,U_20917))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20917) ),
    inference(definitional_conversion,[status(esa)],[f_4986_2]) ).

cnf(f_4986_4,plain,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(U_20918,U_20917))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_20917) ),
    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_20920,U_20919] :
      ( class_Lattices_Obounded__lattice__top(tc_fun(U_20920,U_20919))
      | ~ class_Lattices_Obounded__lattice(U_20919) ),
    inference(variable_rename,[status(thm)],[f_4987_1]) ).

fof(f_4987_3,plain,
    ! [U_20920,U_20919] :
      ( class_Lattices_Obounded__lattice__top(tc_fun(U_20920,U_20919))
      | ~ class_Lattices_Obounded__lattice(U_20919) ),
    inference(definitional_conversion,[status(esa)],[f_4987_2]) ).

cnf(f_4987_4,plain,
    ( class_Lattices_Obounded__lattice__top(tc_fun(U_20920,U_20919))
    | ~ class_Lattices_Obounded__lattice(U_20919) ),
    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_20922,U_20921] :
      ( class_Lattices_Obounded__lattice__bot(tc_fun(U_20922,U_20921))
      | ~ class_Lattices_Obounded__lattice(U_20921) ),
    inference(variable_rename,[status(thm)],[f_4988_1]) ).

fof(f_4988_3,plain,
    ! [U_20921,U_20922] :
      ( class_Lattices_Obounded__lattice__bot(tc_fun(U_20922,U_20921))
      | ~ class_Lattices_Obounded__lattice(U_20921) ),
    inference(definitional_conversion,[status(esa)],[f_4988_2]) ).

cnf(f_4988_4,plain,
    ( class_Lattices_Obounded__lattice__bot(tc_fun(U_20922,U_20921))
    | ~ class_Lattices_Obounded__lattice(U_20921) ),
    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_20924,U_20923] :
      ( class_Lattices_Osemilattice__sup(tc_fun(U_20924,U_20923))
      | ~ class_Lattices_Olattice(U_20923) ),
    inference(variable_rename,[status(thm)],[f_4989_1]) ).

fof(f_4989_3,plain,
    ! [U_20923,U_20924] :
      ( class_Lattices_Osemilattice__sup(tc_fun(U_20924,U_20923))
      | ~ class_Lattices_Olattice(U_20923) ),
    inference(definitional_conversion,[status(esa)],[f_4989_2]) ).

cnf(f_4989_4,plain,
    ( class_Lattices_Osemilattice__sup(tc_fun(U_20924,U_20923))
    | ~ class_Lattices_Olattice(U_20923) ),
    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_20926,U_20925] :
      ( class_Lattices_Osemilattice__inf(tc_fun(U_20926,U_20925))
      | ~ class_Lattices_Olattice(U_20925) ),
    inference(variable_rename,[status(thm)],[f_4990_1]) ).

fof(f_4990_3,plain,
    ! [U_20925,U_20926] :
      ( class_Lattices_Osemilattice__inf(tc_fun(U_20926,U_20925))
      | ~ class_Lattices_Olattice(U_20925) ),
    inference(definitional_conversion,[status(esa)],[f_4990_2]) ).

cnf(f_4990_4,plain,
    ( class_Lattices_Osemilattice__inf(tc_fun(U_20926,U_20925))
    | ~ class_Lattices_Olattice(U_20925) ),
    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_20928,U_20927] :
      ( class_Lattices_Odistrib__lattice(tc_fun(U_20928,U_20927))
      | ~ class_Lattices_Odistrib__lattice(U_20927) ),
    inference(variable_rename,[status(thm)],[f_4991_1]) ).

fof(f_4991_3,plain,
    ! [U_20928,U_20927] :
      ( class_Lattices_Odistrib__lattice(tc_fun(U_20928,U_20927))
      | ~ class_Lattices_Odistrib__lattice(U_20927) ),
    inference(definitional_conversion,[status(esa)],[f_4991_2]) ).

cnf(f_4991_4,plain,
    ( class_Lattices_Odistrib__lattice(tc_fun(U_20928,U_20927))
    | ~ class_Lattices_Odistrib__lattice(U_20927) ),
    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_20930,U_20929] :
      ( class_Lattices_Oboolean__algebra(tc_fun(U_20930,U_20929))
      | ~ class_Lattices_Oboolean__algebra(U_20929) ),
    inference(variable_rename,[status(thm)],[f_4992_1]) ).

fof(f_4992_3,plain,
    ! [U_20930,U_20929] :
      ( class_Lattices_Oboolean__algebra(tc_fun(U_20930,U_20929))
      | ~ class_Lattices_Oboolean__algebra(U_20929) ),
    inference(definitional_conversion,[status(esa)],[f_4992_2]) ).

cnf(f_4992_4,plain,
    ( class_Lattices_Oboolean__algebra(tc_fun(U_20930,U_20929))
    | ~ class_Lattices_Oboolean__algebra(U_20929) ),
    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_20932,U_20931] :
      ( class_Orderings_Opreorder(tc_fun(U_20932,U_20931))
      | ~ class_Orderings_Opreorder(U_20931) ),
    inference(variable_rename,[status(thm)],[f_4993_1]) ).

fof(f_4993_3,plain,
    ! [U_20932,U_20931] :
      ( class_Orderings_Opreorder(tc_fun(U_20932,U_20931))
      | ~ class_Orderings_Opreorder(U_20931) ),
    inference(definitional_conversion,[status(esa)],[f_4993_2]) ).

cnf(f_4993_4,plain,
    ( class_Orderings_Opreorder(tc_fun(U_20932,U_20931))
    | ~ class_Orderings_Opreorder(U_20931) ),
    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_20934,U_20933] :
      ( class_Finite__Set_Ofinite(tc_fun(U_20933,U_20934))
      | ~ class_Finite__Set_Ofinite(U_20934)
      | ~ class_Finite__Set_Ofinite(U_20933) ),
    inference(variable_rename,[status(thm)],[f_4994_1]) ).

fof(f_4994_3,plain,
    ! [U_20934,U_20933] :
      ( class_Finite__Set_Ofinite(tc_fun(U_20933,U_20934))
      | ~ class_Finite__Set_Ofinite(U_20934)
      | ~ class_Finite__Set_Ofinite(U_20933) ),
    inference(definitional_conversion,[status(esa)],[f_4994_2]) ).

cnf(f_4994_4,plain,
    ( class_Finite__Set_Ofinite(tc_fun(U_20933,U_20934))
    | ~ class_Finite__Set_Ofinite(U_20934)
    | ~ class_Finite__Set_Ofinite(U_20933) ),
    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_20936,U_20935] :
      ( class_Lattices_Olattice(tc_fun(U_20936,U_20935))
      | ~ class_Lattices_Olattice(U_20935) ),
    inference(variable_rename,[status(thm)],[f_4995_1]) ).

fof(f_4995_3,plain,
    ! [U_20935,U_20936] :
      ( class_Lattices_Olattice(tc_fun(U_20936,U_20935))
      | ~ class_Lattices_Olattice(U_20935) ),
    inference(definitional_conversion,[status(esa)],[f_4995_2]) ).

cnf(f_4995_4,plain,
    ( class_Lattices_Olattice(tc_fun(U_20936,U_20935))
    | ~ class_Lattices_Olattice(U_20935) ),
    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_20938,U_20937] :
      ( class_Orderings_Oorder(tc_fun(U_20938,U_20937))
      | ~ class_Orderings_Oorder(U_20937) ),
    inference(variable_rename,[status(thm)],[f_4996_1]) ).

fof(f_4996_3,plain,
    ! [U_20938,U_20937] :
      ( class_Orderings_Oorder(tc_fun(U_20938,U_20937))
      | ~ class_Orderings_Oorder(U_20937) ),
    inference(definitional_conversion,[status(esa)],[f_4996_2]) ).

cnf(f_4996_4,plain,
    ( class_Orderings_Oorder(tc_fun(U_20938,U_20937))
    | ~ class_Orderings_Oorder(U_20937) ),
    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_20940,U_20939] :
      ( class_Orderings_Otop(tc_fun(U_20940,U_20939))
      | ~ class_Orderings_Otop(U_20939) ),
    inference(variable_rename,[status(thm)],[f_4997_1]) ).

fof(f_4997_3,plain,
    ! [U_20939,U_20940] :
      ( class_Orderings_Otop(tc_fun(U_20940,U_20939))
      | ~ class_Orderings_Otop(U_20939) ),
    inference(definitional_conversion,[status(esa)],[f_4997_2]) ).

cnf(f_4997_4,plain,
    ( class_Orderings_Otop(tc_fun(U_20940,U_20939))
    | ~ class_Orderings_Otop(U_20939) ),
    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_20942,U_20941] :
      ( class_Orderings_Oord(tc_fun(U_20942,U_20941))
      | ~ class_Orderings_Oord(U_20941) ),
    inference(variable_rename,[status(thm)],[f_4998_1]) ).

fof(f_4998_3,plain,
    ! [U_20941,U_20942] :
      ( class_Orderings_Oord(tc_fun(U_20942,U_20941))
      | ~ class_Orderings_Oord(U_20941) ),
    inference(definitional_conversion,[status(esa)],[f_4998_2]) ).

cnf(f_4998_4,plain,
    ( class_Orderings_Oord(tc_fun(U_20942,U_20941))
    | ~ class_Orderings_Oord(U_20941) ),
    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_20944,U_20943] :
      ( class_Orderings_Obot(tc_fun(U_20944,U_20943))
      | ~ class_Orderings_Obot(U_20943) ),
    inference(variable_rename,[status(thm)],[f_4999_1]) ).

fof(f_4999_3,plain,
    ! [U_20943,U_20944] :
      ( class_Orderings_Obot(tc_fun(U_20944,U_20943))
      | ~ class_Orderings_Obot(U_20943) ),
    inference(definitional_conversion,[status(esa)],[f_4999_2]) ).

cnf(f_4999_4,plain,
    ( class_Orderings_Obot(tc_fun(U_20944,U_20943))
    | ~ class_Orderings_Obot(U_20943) ),
    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_20946,U_20945] :
      ( class_Groups_Ouminus(tc_fun(U_20946,U_20945))
      | ~ class_Groups_Ouminus(U_20945) ),
    inference(variable_rename,[status(thm)],[f_5000_1]) ).

fof(f_5000_3,plain,
    ! [U_20945,U_20946] :
      ( class_Groups_Ouminus(tc_fun(U_20946,U_20945))
      | ~ class_Groups_Ouminus(U_20945) ),
    inference(definitional_conversion,[status(esa)],[f_5000_2]) ).

cnf(f_5000_4,plain,
    ( class_Groups_Ouminus(tc_fun(U_20946,U_20945))
    | ~ class_Groups_Ouminus(U_20945) ),
    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_20948,U_20947] :
      ( class_Groups_Ominus(tc_fun(U_20948,U_20947))
      | ~ class_Groups_Ominus(U_20947) ),
    inference(variable_rename,[status(thm)],[f_5001_1]) ).

fof(f_5001_3,plain,
    ! [U_20947,U_20948] :
      ( class_Groups_Ominus(tc_fun(U_20948,U_20947))
      | ~ class_Groups_Ominus(U_20947) ),
    inference(definitional_conversion,[status(esa)],[f_5001_2]) ).

cnf(f_5001_4,plain,
    ( class_Groups_Ominus(tc_fun(U_20948,U_20947))
    | ~ class_Groups_Ominus(U_20947) ),
    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_20950,U_20949] :
      ( class_Finite__Set_Ofinite(tc_sum(U_20949,U_20950))
      | ~ class_Finite__Set_Ofinite(U_20950)
      | ~ class_Finite__Set_Ofinite(U_20949) ),
    inference(variable_rename,[status(thm)],[f_5138_1]) ).

fof(f_5138_3,plain,
    ! [U_20950,U_20949] :
      ( class_Finite__Set_Ofinite(tc_sum(U_20949,U_20950))
      | ~ class_Finite__Set_Ofinite(U_20950)
      | ~ class_Finite__Set_Ofinite(U_20949) ),
    inference(definitional_conversion,[status(esa)],[f_5138_2]) ).

cnf(f_5138_4,plain,
    ( class_Finite__Set_Ofinite(tc_sum(U_20949,U_20950))
    | ~ class_Finite__Set_Ofinite(U_20950)
    | ~ class_Finite__Set_Ofinite(U_20949) ),
    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_20951] :
      ( class_Finite__Set_Ofinite(tc_Option_Ooption(U_20951))
      | ~ class_Finite__Set_Ofinite(U_20951) ),
    inference(variable_rename,[status(thm)],[f_5139_1]) ).

fof(f_5139_3,plain,
    ! [U_20951] :
      ( class_Finite__Set_Ofinite(tc_Option_Ooption(U_20951))
      | ~ class_Finite__Set_Ofinite(U_20951) ),
    inference(definitional_conversion,[status(esa)],[f_5139_2]) ).

cnf(f_5139_4,plain,
    ( class_Finite__Set_Ofinite(tc_Option_Ooption(U_20951))
    | ~ class_Finite__Set_Ofinite(U_20951) ),
    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_20953,U_20952] :
      ( class_Finite__Set_Ofinite(tc_prod(U_20952,U_20953))
      | ~ class_Finite__Set_Ofinite(U_20953)
      | ~ class_Finite__Set_Ofinite(U_20952) ),
    inference(variable_rename,[status(thm)],[f_5140_1]) ).

fof(f_5140_3,plain,
    ! [U_20953,U_20952] :
      ( class_Finite__Set_Ofinite(tc_prod(U_20952,U_20953))
      | ~ class_Finite__Set_Ofinite(U_20953)
      | ~ class_Finite__Set_Ofinite(U_20952) ),
    inference(definitional_conversion,[status(esa)],[f_5140_2]) ).

cnf(f_5140_4,plain,
    ( class_Finite__Set_Ofinite(tc_prod(U_20952,U_20953))
    | ~ class_Finite__Set_Ofinite(U_20953)
    | ~ class_Finite__Set_Ofinite(U_20952) ),
    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_20955,U_20954] :
      ( class_Smallcheck_Osmall(tc_prod(U_20954,U_20955))
      | ~ class_Smallcheck_Osmall(U_20955)
      | ~ class_Smallcheck_Osmall(U_20954) ),
    inference(variable_rename,[status(thm)],[f_5141_1]) ).

fof(f_5141_3,plain,
    ! [U_20955,U_20954] :
      ( class_Smallcheck_Osmall(tc_prod(U_20954,U_20955))
      | ~ class_Smallcheck_Osmall(U_20955)
      | ~ class_Smallcheck_Osmall(U_20954) ),
    inference(definitional_conversion,[status(esa)],[f_5141_2]) ).

cnf(f_5141_4,plain,
    ( class_Smallcheck_Osmall(tc_prod(U_20954,U_20955))
    | ~ class_Smallcheck_Osmall(U_20955)
    | ~ class_Smallcheck_Osmall(U_20954) ),
    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_20957,U_20956] : hAPP(c_COMBI(U_20956),U_20957) = U_20957,
    inference(variable_rename,[status(thm)],[f_5185_1]) ).

fof(f_5185_3,plain,
    ! [U_20956,U_20957] : hAPP(c_COMBI(U_20956),U_20957) = U_20957,
    inference(definitional_conversion,[status(esa)],[f_5185_2]) ).

cnf(f_5185_4,plain,
    hAPP(c_COMBI(U_20956),U_20957) = U_20957,
    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_20961,U_20960,U_20959,U_20958] : hAPP(hAPP(c_COMBK(U_20958,U_20959),U_20960),U_20961) = U_20960,
    inference(variable_rename,[status(thm)],[f_5186_1]) ).

fof(f_5186_3,plain,
    ! [U_20958,U_20959,U_20960,U_20961] : hAPP(hAPP(c_COMBK(U_20958,U_20959),U_20960),U_20961) = U_20960,
    inference(definitional_conversion,[status(esa)],[f_5186_2]) ).

cnf(f_5186_4,plain,
    hAPP(hAPP(c_COMBK(U_20958,U_20959),U_20960),U_20961) = U_20960,
    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_20967,U_20966,U_20965,U_20964,U_20963,U_20962] : hAPP(hAPP(hAPP(c_COMBB(U_20962,U_20963,U_20964),U_20965),U_20966),U_20967) = hAPP(U_20965,hAPP(U_20966,U_20967)),
    inference(variable_rename,[status(thm)],[f_5187_1]) ).

fof(f_5187_3,plain,
    ! [U_20962,U_20963,U_20964,U_20965,U_20966,U_20967] : hAPP(hAPP(hAPP(c_COMBB(U_20962,U_20963,U_20964),U_20965),U_20966),U_20967) = hAPP(U_20965,hAPP(U_20966,U_20967)),
    inference(definitional_conversion,[status(esa)],[f_5187_2]) ).

cnf(f_5187_4,plain,
    hAPP(hAPP(hAPP(c_COMBB(U_20962,U_20963,U_20964),U_20965),U_20966),U_20967) = hAPP(U_20965,hAPP(U_20966,U_20967)),
    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_20973,U_20972,U_20971,U_20970,U_20969,U_20968] : hAPP(hAPP(hAPP(c_COMBC(U_20968,U_20969,U_20970),U_20971),U_20972),U_20973) = hAPP(hAPP(U_20971,U_20973),U_20972),
    inference(variable_rename,[status(thm)],[f_5188_1]) ).

fof(f_5188_3,plain,
    ! [U_20968,U_20969,U_20970,U_20971,U_20972,U_20973] : hAPP(hAPP(hAPP(c_COMBC(U_20968,U_20969,U_20970),U_20971),U_20972),U_20973) = hAPP(hAPP(U_20971,U_20973),U_20972),
    inference(definitional_conversion,[status(esa)],[f_5188_2]) ).

cnf(f_5188_4,plain,
    hAPP(hAPP(hAPP(c_COMBC(U_20968,U_20969,U_20970),U_20971),U_20972),U_20973) = hAPP(hAPP(U_20971,U_20973),U_20972),
    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_20979,U_20978,U_20977,U_20976,U_20975,U_20974] : hAPP(hAPP(hAPP(c_COMBS(U_20974,U_20975,U_20976),U_20977),U_20978),U_20979) = hAPP(hAPP(U_20977,U_20979),hAPP(U_20978,U_20979)),
    inference(variable_rename,[status(thm)],[f_5189_1]) ).

fof(f_5189_3,plain,
    ! [U_20974,U_20975,U_20976,U_20977,U_20978,U_20979] : hAPP(hAPP(hAPP(c_COMBS(U_20974,U_20975,U_20976),U_20977),U_20978),U_20979) = hAPP(hAPP(U_20977,U_20979),hAPP(U_20978,U_20979)),
    inference(definitional_conversion,[status(esa)],[f_5189_2]) ).

cnf(f_5189_4,plain,
    hAPP(hAPP(hAPP(c_COMBS(U_20974,U_20975,U_20976),U_20977),U_20978),U_20979) = hAPP(hAPP(U_20977,U_20979),hAPP(U_20978,U_20979)),
    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_20981,U_20980] :
      ( U_20980 = U_20981
      | ~ hBOOL(hAPP(hAPP(c_fequal,U_20980),U_20981)) ),
    inference(variable_rename,[status(thm)],[f_5190_1]) ).

fof(f_5190_3,plain,
    ! [U_20980,U_20981] :
      ( U_20980 = U_20981
      | ~ hBOOL(hAPP(hAPP(c_fequal,U_20980),U_20981)) ),
    inference(definitional_conversion,[status(esa)],[f_5190_2]) ).

cnf(f_5190_4,plain,
    ( U_20980 = U_20981
    | ~ hBOOL(hAPP(hAPP(c_fequal,U_20980),U_20981)) ),
    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_20983,U_20982] :
      ( hBOOL(hAPP(hAPP(c_fequal,U_20982),U_20983))
      | U_20982 != U_20983 ),
    inference(variable_rename,[status(thm)],[f_5191_1]) ).

fof(f_5191_3,plain,
    ! [U_20982,U_20983] :
      ( hBOOL(hAPP(hAPP(c_fequal,U_20982),U_20983))
      | U_20982 != U_20983 ),
    inference(definitional_conversion,[status(esa)],[f_5191_2]) ).

cnf(f_5191_4,plain,
    ( hBOOL(hAPP(hAPP(c_fequal,U_20982),U_20983))
    | U_20982 != U_20983 ),
    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_20984] :
      ( ~ hBOOL(U_20984)
      | ~ hBOOL(hAPP(c_fNot,U_20984)) ),
    inference(variable_rename,[status(thm)],[f_5194_1]) ).

fof(f_5194_3,plain,
    ! [U_20984] :
      ( ~ hBOOL(U_20984)
      | ~ hBOOL(hAPP(c_fNot,U_20984)) ),
    inference(definitional_conversion,[status(esa)],[f_5194_2]) ).

cnf(f_5194_4,plain,
    ( ~ hBOOL(U_20984)
    | ~ hBOOL(hAPP(c_fNot,U_20984)) ),
    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_20985] :
      ( hBOOL(hAPP(c_fNot,U_20985))
      | hBOOL(U_20985) ),
    inference(variable_rename,[status(thm)],[f_5195_1]) ).

fof(f_5195_3,plain,
    ! [U_20985] :
      ( hBOOL(hAPP(c_fNot,U_20985))
      | hBOOL(U_20985) ),
    inference(definitional_conversion,[status(esa)],[f_5195_2]) ).

cnf(f_5195_4,plain,
    ( hBOOL(hAPP(c_fNot,U_20985))
    | hBOOL(U_20985) ),
    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_20987,U_20986] :
      ( hBOOL(hAPP(hAPP(c_fconj,U_20986),U_20987))
      | ~ hBOOL(U_20987)
      | ~ hBOOL(U_20986) ),
    inference(variable_rename,[status(thm)],[f_5196_1]) ).

fof(f_5196_3,plain,
    ! [U_20987] :
      ( ! [U_20986] :
          ( hBOOL(hAPP(hAPP(c_fconj,U_20986),U_20987))
          | ~ hBOOL(U_20986) )
      | ~ hBOOL(U_20987) ),
    inference(miniscope,[status(thm)],[f_5196_2]) ).

fof(f_5196_4,plain,
    ! [U_20986,U_20987] :
      ( hBOOL(hAPP(hAPP(c_fconj,U_20986),U_20987))
      | ~ hBOOL(U_20986)
      | ~ hBOOL(U_20987) ),
    inference(definitional_conversion,[status(esa)],[f_5196_3]) ).

cnf(f_5196_5,plain,
    ( hBOOL(hAPP(hAPP(c_fconj,U_20986),U_20987))
    | ~ hBOOL(U_20986)
    | ~ hBOOL(U_20987) ),
    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_20989,U_20988] :
      ( hBOOL(U_20988)
      | ~ hBOOL(hAPP(hAPP(c_fconj,U_20988),U_20989)) ),
    inference(variable_rename,[status(thm)],[f_5197_1]) ).

fof(f_5197_3,plain,
    ! [U_20989,U_20988] :
      ( hBOOL(U_20988)
      | ~ hBOOL(hAPP(hAPP(c_fconj,U_20988),U_20989)) ),
    inference(definitional_conversion,[status(esa)],[f_5197_2]) ).

cnf(f_5197_4,plain,
    ( hBOOL(U_20988)
    | ~ hBOOL(hAPP(hAPP(c_fconj,U_20988),U_20989)) ),
    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_20991,U_20990] :
      ( hBOOL(U_20991)
      | ~ hBOOL(hAPP(hAPP(c_fconj,U_20990),U_20991)) ),
    inference(variable_rename,[status(thm)],[f_5198_1]) ).

fof(f_5198_3,plain,
    ! [U_20991] :
      ( ! [U_20990] : ~ hBOOL(hAPP(hAPP(c_fconj,U_20990),U_20991))
      | hBOOL(U_20991) ),
    inference(miniscope,[status(thm)],[f_5198_2]) ).

fof(f_5198_4,plain,
    ! [U_20990,U_20991] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,U_20990),U_20991))
      | hBOOL(U_20991) ),
    inference(definitional_conversion,[status(esa)],[f_5198_3]) ).

cnf(f_5198_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_fconj,U_20990),U_20991))
    | hBOOL(U_20991) ),
    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_20993,U_20992] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20992),U_20993))
      | ~ hBOOL(U_20992) ),
    inference(variable_rename,[status(thm)],[f_5199_1]) ).

fof(f_5199_3,plain,
    ! [U_20992,U_20993] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20992),U_20993))
      | ~ hBOOL(U_20992) ),
    inference(definitional_conversion,[status(esa)],[f_5199_2]) ).

cnf(f_5199_4,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,U_20992),U_20993))
    | ~ hBOOL(U_20992) ),
    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_20995,U_20994] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20995),U_20994))
      | ~ hBOOL(U_20994) ),
    inference(variable_rename,[status(thm)],[f_5200_1]) ).

fof(f_5200_3,plain,
    ! [U_20994,U_20995] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20995),U_20994))
      | ~ hBOOL(U_20994) ),
    inference(definitional_conversion,[status(esa)],[f_5200_2]) ).

cnf(f_5200_4,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,U_20995),U_20994))
    | ~ hBOOL(U_20994) ),
    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_20997,U_20996] :
      ( hBOOL(U_20997)
      | hBOOL(U_20996)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20996),U_20997)) ),
    inference(variable_rename,[status(thm)],[f_5201_1]) ).

fof(f_5201_3,plain,
    ! [U_20997] :
      ( ! [U_20996] :
          ( hBOOL(U_20996)
          | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20996),U_20997)) )
      | hBOOL(U_20997) ),
    inference(miniscope,[status(thm)],[f_5201_2]) ).

fof(f_5201_4,plain,
    ! [U_20996,U_20997] :
      ( hBOOL(U_20996)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20996),U_20997))
      | hBOOL(U_20997) ),
    inference(definitional_conversion,[status(esa)],[f_5201_3]) ).

cnf(f_5201_5,plain,
    ( hBOOL(U_20996)
    | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20996),U_20997))
    | hBOOL(U_20997) ),
    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_20999,U_20998] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_20998),U_20999))
      | hBOOL(U_20998) ),
    inference(variable_rename,[status(thm)],[f_5202_1]) ).

fof(f_5202_3,plain,
    ! [U_20999,U_20998] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_20998),U_20999))
      | hBOOL(U_20998) ),
    inference(definitional_conversion,[status(esa)],[f_5202_2]) ).

cnf(f_5202_4,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,U_20998),U_20999))
    | hBOOL(U_20998) ),
    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_21001,U_21000] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_21001),U_21000))
      | ~ hBOOL(U_21000) ),
    inference(variable_rename,[status(thm)],[f_5203_1]) ).

fof(f_5203_3,plain,
    ! [U_21000,U_21001] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_21001),U_21000))
      | ~ hBOOL(U_21000) ),
    inference(definitional_conversion,[status(esa)],[f_5203_2]) ).

cnf(f_5203_4,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,U_21001),U_21000))
    | ~ hBOOL(U_21000) ),
    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_21003,U_21002] :
      ( hBOOL(U_21003)
      | ~ hBOOL(U_21002)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,U_21002),U_21003)) ),
    inference(variable_rename,[status(thm)],[f_5204_1]) ).

fof(f_5204_3,plain,
    ! [U_21003] :
      ( ! [U_21002] :
          ( ~ hBOOL(U_21002)
          | ~ hBOOL(hAPP(hAPP(c_fimplies,U_21002),U_21003)) )
      | hBOOL(U_21003) ),
    inference(miniscope,[status(thm)],[f_5204_2]) ).

fof(f_5204_4,plain,
    ! [U_21002,U_21003] :
      ( ~ hBOOL(U_21002)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,U_21002),U_21003))
      | hBOOL(U_21003) ),
    inference(definitional_conversion,[status(esa)],[f_5204_3]) ).

cnf(f_5204_5,plain,
    ( ~ hBOOL(U_21002)
    | ~ hBOOL(hAPP(hAPP(c_fimplies,U_21002),U_21003))
    | hBOOL(U_21003) ),
    inference(clausify,[status(thm)],[f_5204_4]) ).

fof(f_5205_1,plain,
    ! [B_x] :
      ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,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_21004] :
      ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,U_21004)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),U_21004),v_G)) ),
    inference(variable_rename,[status(thm)],[f_5205_1]) ).

fof(f_5205_3,plain,
    ! [U_21004] :
      ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,U_21004)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),U_21004),v_G)) ),
    inference(definitional_conversion,[status(esa)],[f_5205_2]) ).

cnf(f_5205_4,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,U_21004)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),U_21004),v_G)) ),
    inference(clausify,[status(thm)],[f_5205_3]) ).

fof(f_5206_1,negated_conjecture,
    ~ ! [B_Z,B_s] :
        ( v_P(B_Z,B_s)
       => ! [B_s_H] :
            ( c_Natural_Oevaln(c_Com_Ocom_OSKIP,B_s,v_n,B_s_H)
           => v_P(B_Z,B_s_H) ) ),
    inference(negate,[status(cth)],[conj_1]) ).

fof(f_5206_2,negated_conjecture,
    ? [B_Z,B_s] :
      ( ? [B_s_H] :
          ( ~ v_P(B_Z,B_s_H)
          & c_Natural_Oevaln(c_Com_Ocom_OSKIP,B_s,v_n,B_s_H) )
      & v_P(B_Z,B_s) ),
    inference(fof_nnf,[status(thm)],[f_5206_1]) ).

fof(f_5206_3,negated_conjecture,
    ? [U_21007,U_21006] :
      ( ? [U_21005] :
          ( ~ v_P(U_21007,U_21005)
          & c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_21006,v_n,U_21005) )
      & v_P(U_21007,U_21006) ),
    inference(variable_rename,[status(thm)],[f_5206_2]) ).

fof(f_5206_4,negated_conjecture,
    ? [U_21006] :
      ( ? [U_21005] :
          ( ~ v_P(sK513,U_21005)
          & c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_21006,v_n,U_21005) )
      & v_P(sK513,U_21006) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK513]),skolemize(U_21007,sK513)],[f_5206_3]) ).

fof(f_5206_5,negated_conjecture,
    ( ? [U_21005] :
        ( ~ v_P(sK513,U_21005)
        & c_Natural_Oevaln(c_Com_Ocom_OSKIP,sK514,v_n,U_21005) )
    & v_P(sK513,sK514) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK514]),skolemize(U_21006,sK514)],[f_5206_4]) ).

fof(f_5206_6,negated_conjecture,
    ( ~ v_P(sK513,sK515)
    & c_Natural_Oevaln(c_Com_Ocom_OSKIP,sK514,v_n,sK515)
    & v_P(sK513,sK514) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK515]),skolemize(U_21005,sK515)],[f_5206_5]) ).

fof(f_5206_7,negated_conjecture,
    ( ~ v_P(sK513,sK515)
    & c_Natural_Oevaln(c_Com_Ocom_OSKIP,sK514,v_n,sK515)
    & v_P(sK513,sK514) ),
    inference(definitional_conversion,[status(esa)],[f_5206_6]) ).

cnf(f_5206_8,negated_conjecture,
    v_P(sK513,sK514),
    inference(clausify,[status(thm)],[f_5206_7]) ).

cnf(f_5206_9,negated_conjecture,
    c_Natural_Oevaln(c_Com_Ocom_OSKIP,sK514,v_n,sK515),
    inference(clausify,[status(thm)],[f_5206_7]) ).

cnf(f_5206_10,negated_conjecture,
    ~ v_P(sK513,sK515),
    inference(clausify,[status(thm)],[f_5206_7]) ).

cnf(f_2123_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2123_4]) ).

cnf(f_2124_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2124_4]) ).

cnf(f_2125_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2125_4]) ).

cnf(f_2130_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2130_4]) ).

cnf(f_2132_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2132_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_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_6,axiom,
    ( c_Com_Ocom_Ocom__case(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) = c_Com_Ocom_Ocom__case(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_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_7,axiom,
    ( c_Com_Ocom_Ocom__rec(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) = c_Com_Ocom_Ocom__rec(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_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_8,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_9,axiom,
    ( c_member(Eq_x_0) = c_member(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_10,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_11,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_12,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_13,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_14,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_15,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_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_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_18,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_19,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_20,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_21,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_22,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_23,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_24,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_25,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_26,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_27,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_28,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_29,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_30,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_31,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_32,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_33,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_34,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_35,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_36,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_37,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_38,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_39,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_40,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_41,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_42,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_43,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_44,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_45,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_46,axiom,
    ( c_Sum__Type_OInl(Eq_x_0,Eq_x_1) = c_Sum__Type_OInl(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_47,axiom,
    ( c_Sum__Type_Osum_Osum__size(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Sum__Type_Osum_Osum__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_48,axiom,
    ( c_Sum__Type_OInr(Eq_x_0,Eq_x_1) = c_Sum__Type_OInr(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_49,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_50,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_51,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_52,axiom,
    ( c_Sum__Type_OProjl(Eq_x_0,Eq_x_1,Eq_x_2) = c_Sum__Type_OProjl(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_53,axiom,
    ( c_Sum__Type_OProjr(Eq_x_0,Eq_x_1,Eq_x_2) = c_Sum__Type_OProjr(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_54,axiom,
    ( c_Sum__Type_Osum_Osum__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = c_Sum__Type_Osum_Osum__rec(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_55,axiom,
    ( c_Sum__Type_OSuml(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Sum__Type_OSuml(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_56,axiom,
    ( c_Sum__Type_OSumr(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Sum__Type_OSumr(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_57,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_58,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_59,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_60,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_61,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_62,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_63,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_64,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_65,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_66,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_67,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_68,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_69,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_70,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_71,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_72,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_73,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_74,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_75,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_76,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_77,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_78,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_79,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_80,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_81,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_82,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_83,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_84,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_85,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_86,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_87,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_88,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_89,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_90,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_91,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_92,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_93,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_94,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_95,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_96,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_97,axiom,
    ( c_If(Eq_x_0) = c_If(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_98,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_99,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_100,axiom,
    ( c_COMBI(Eq_x_0) = c_COMBI(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_101,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_102,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_103,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_104,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_105,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_106,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_107,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_108,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_109,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_110,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_111,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_112,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_113,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_114,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_115,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_116,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_117,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_118,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_119,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_120,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_121,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_122,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_123,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_124,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_125,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_126,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_127,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_128,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_129,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_130,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_131,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_132,axiom,
    ( c_Sum__Type_Osum_Osum__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Sum__Type_Osum_Osum__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_133,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_134,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_135,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_136,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_137,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_138,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_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,
    ( 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_142,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_143,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_144,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_145,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_146,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_147,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_148,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_149,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_150,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_151,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_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_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_154,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_155,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_156,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_157,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_158,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_159,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_160,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_161,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_162,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_163,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_164,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_165,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_166,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_167,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_168,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_169,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_170,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_171,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_172,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_173,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_174,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_175,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_176,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_177,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_178,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_179,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_180,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_181,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_182,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_183,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_184,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_185,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_186,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_187,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_188,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_189,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_190,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_191,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_192,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_193,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_194,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_195,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_196,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_197,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_198,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_199,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_200,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_201,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_202,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_203,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_204,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_205,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_206,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_207,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_208,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_209,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_210,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_211,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_212,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_213,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_214,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_215,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_216,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_217,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_218,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_219,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_220,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_221,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_222,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_223,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_224,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_225,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_226,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_227,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_228,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_229,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_230,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_231,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_232,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_233,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_234,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_235,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_236,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_237,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_238,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_239,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_240,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_241,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_242,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_243,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_244,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_245,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_246,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_247,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_248,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_249,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_250,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_251,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_252,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_253,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_254,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_255,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_256,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_257,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_258,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_259,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_260,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_261,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_262,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_263,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_264,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_265,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_266,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_267,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_268,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_269,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_270,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_271,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_272,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_273,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_274,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_275,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_276,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_277,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_278,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_279,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_280,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_281,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_282,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_283,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_284,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_285,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_286,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_287,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_288,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_289,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_290,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_291,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_292,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_293,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_294,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_295,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_296,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_297,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_298,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_299,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_300,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_301,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_302,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_303,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_304,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_305,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_306,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_307,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_308,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_309,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_310,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_311,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_312,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_313,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_314,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_315,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_316,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_317,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_318,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_319,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_320,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_321,axiom,
    ( c_List_Otl(Eq_x_0,Eq_x_1) = c_List_Otl(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_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_323,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_324,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_325,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_326,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_327,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_328,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_329,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_330,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_331,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_332,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_333,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_334,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_335,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_336,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_337,axiom,
    ( sK2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK2(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_338,axiom,
    ( sK3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK3(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,
    ( 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_340,axiom,
    ( sK5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK5(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,
    ( 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_342,axiom,
    ( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(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_343,axiom,
    ( sK8(Eq_x_0,Eq_x_1,Eq_x_2) = sK8(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_344,axiom,
    ( sK9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK9(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_345,axiom,
    ( sK10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK10(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_346,axiom,
    ( sK11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK11(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_347,axiom,
    ( sK12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK12(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_348,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_349,axiom,
    ( sK14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK14(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_350,axiom,
    ( sK15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK15(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_351,axiom,
    ( sK16(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK16(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_352,axiom,
    ( sK17(Eq_x_0,Eq_x_1,Eq_x_2) = sK17(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_353,axiom,
    ( sK18(Eq_x_0,Eq_x_1,Eq_x_2) = sK18(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_354,axiom,
    ( sK19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK19(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,
    ( sK20(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK20(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,
    ( sK21(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK21(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_357,axiom,
    ( sK22(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK22(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_358,axiom,
    ( sK23(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK23(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_359,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_360,axiom,
    ( sK25(Eq_x_0) = sK25(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_361,axiom,
    ( sK26(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK26(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_362,axiom,
    ( sK27(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK27(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_363,axiom,
    ( sK28(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK28(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_364,axiom,
    ( sK29(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK29(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_365,axiom,
    ( sK30(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK30(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_366,axiom,
    ( sK31(Eq_x_0) = sK31(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_367,axiom,
    ( sK32(Eq_x_0,Eq_x_1) = sK32(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_368,axiom,
    ( sK33(Eq_x_0,Eq_x_1) = sK33(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,
    ( 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_370,axiom,
    ( sK35(Eq_x_0,Eq_x_1,Eq_x_2) = sK35(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_371,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_372,axiom,
    ( sK37(Eq_x_0) = sK37(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_373,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_374,axiom,
    ( sK39(Eq_x_0,Eq_x_1) = sK39(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_375,axiom,
    ( sK40(Eq_x_0,Eq_x_1) = sK40(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_376,axiom,
    ( sK41(Eq_x_0) = sK41(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_377,axiom,
    ( sK42(Eq_x_0,Eq_x_1) = sK42(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_378,axiom,
    ( sK43(Eq_x_0,Eq_x_1) = sK43(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_379,axiom,
    ( sK44(Eq_x_0,Eq_x_1) = sK44(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_380,axiom,
    ( sK45(Eq_x_0,Eq_x_1) = sK45(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,
    ( sK46(Eq_x_0) = sK46(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_382,axiom,
    ( sK47(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK47(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_383,axiom,
    ( sK48(Eq_x_0) = sK48(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_384,axiom,
    ( sK49(Eq_x_0,Eq_x_1) = sK49(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_385,axiom,
    ( sK50(Eq_x_0) = sK50(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_386,axiom,
    ( sK51(Eq_x_0) = sK51(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_387,axiom,
    ( sK52(Eq_x_0) = sK52(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_388,axiom,
    ( sK53(Eq_x_0) = sK53(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_389,axiom,
    ( sK54(Eq_x_0) = sK54(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_390,axiom,
    ( sK55(Eq_x_0) = sK55(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_391,axiom,
    ( sK56(Eq_x_0) = sK56(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_392,axiom,
    ( sK57(Eq_x_0) = sK57(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_393,axiom,
    ( sK58(Eq_x_0) = sK58(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_394,axiom,
    ( sK59(Eq_x_0,Eq_x_1) = sK59(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_395,axiom,
    ( sK60(Eq_x_0,Eq_x_1) = sK60(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_396,axiom,
    ( sK61(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK61(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_397,axiom,
    ( sK62(Eq_x_0,Eq_x_1) = sK62(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_398,axiom,
    ( sK63(Eq_x_0,Eq_x_1) = sK63(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_399,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_400,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_401,axiom,
    ( sK66(Eq_x_0,Eq_x_1,Eq_x_2) = sK66(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,
    ( 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_403,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_404,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_405,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_406,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_407,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_408,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_409,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_410,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_411,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_412,axiom,
    ( sK77(Eq_x_0,Eq_x_1) = sK77(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_413,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_414,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_415,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_416,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_417,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_418,axiom,
    ( sK83(Eq_x_0,Eq_x_1,Eq_x_2) = sK83(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,
    ( sK84(Eq_x_0,Eq_x_1,Eq_x_2) = sK84(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,
    ( 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_421,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_422,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_423,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_424,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_425,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_426,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_427,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_428,axiom,
    ( sK93(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK93(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_429,axiom,
    ( sK94(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK94(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_430,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_431,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_432,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_433,axiom,
    ( sK98(Eq_x_0,Eq_x_1,Eq_x_2) = sK98(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_434,axiom,
    ( sK99(Eq_x_0,Eq_x_1,Eq_x_2) = sK99(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_435,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_436,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_437,axiom,
    ( sK102(Eq_x_0,Eq_x_1,Eq_x_2) = sK102(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_438,axiom,
    ( sK103(Eq_x_0,Eq_x_1,Eq_x_2) = sK103(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_439,axiom,
    ( sK104(Eq_x_0,Eq_x_1,Eq_x_2) = sK104(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_440,axiom,
    ( sK105(Eq_x_0,Eq_x_1,Eq_x_2) = sK105(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_441,axiom,
    ( sK106(Eq_x_0,Eq_x_1,Eq_x_2) = sK106(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_442,axiom,
    ( sK107(Eq_x_0,Eq_x_1,Eq_x_2) = sK107(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_443,axiom,
    ( sK108(Eq_x_0,Eq_x_1,Eq_x_2) = sK108(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_444,axiom,
    ( sK109(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK109(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_445,axiom,
    ( sK110(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK110(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,
    ( sK111(Eq_x_0,Eq_x_1,Eq_x_2) = sK111(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_447,axiom,
    ( sK112(Eq_x_0,Eq_x_1,Eq_x_2) = sK112(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_448,axiom,
    ( sK113(Eq_x_0,Eq_x_1,Eq_x_2) = sK113(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_449,axiom,
    ( sK114(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK114(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_450,axiom,
    ( sK115(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK115(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_451,axiom,
    ( sK116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK116(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_452,axiom,
    ( sK117(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK117(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_453,axiom,
    ( sK118(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK118(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_454,axiom,
    ( sK119(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK119(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_455,axiom,
    ( sK120(Eq_x_0,Eq_x_1) = sK120(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_456,axiom,
    ( sK121(Eq_x_0,Eq_x_1) = sK121(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,
    ( sK122(Eq_x_0,Eq_x_1) = sK122(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_458,axiom,
    ( sK123(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK123(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_459,axiom,
    ( sK124(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK124(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_460,axiom,
    ( sK125(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK125(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_461,axiom,
    ( sK126(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK126(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_462,axiom,
    ( sK127(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK127(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_463,axiom,
    ( sK128(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK128(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_464,axiom,
    ( sK129(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK129(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_465,axiom,
    ( sK130(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK130(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_466,axiom,
    ( sK131(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK131(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_467,axiom,
    ( sK132(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK132(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_468,axiom,
    ( sK133(Eq_x_0,Eq_x_1) = sK133(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_469,axiom,
    ( sK134(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK134(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_470,axiom,
    ( sK135(Eq_x_0,Eq_x_1,Eq_x_2) = sK135(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_471,axiom,
    ( sK136(Eq_x_0) = sK136(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_472,axiom,
    ( sK137(Eq_x_0) = sK137(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_473,axiom,
    ( sK138(Eq_x_0) = sK138(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_474,axiom,
    ( sK139(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK139(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_475,axiom,
    ( sK140(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) = sK140(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_476,axiom,
    ( sK141(Eq_x_0) = sK141(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_477,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_478,axiom,
    ( sK143(Eq_x_0) = sK143(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_479,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_480,axiom,
    ( sK145(Eq_x_0,Eq_x_1,Eq_x_2) = sK145(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_481,axiom,
    ( sK146(Eq_x_0,Eq_x_1,Eq_x_2) = sK146(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_482,axiom,
    ( sK147(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK147(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_483,axiom,
    ( sK148(Eq_x_0,Eq_x_1) = sK148(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,
    ( sK149(Eq_x_0,Eq_x_1) = sK149(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_485,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_486,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_487,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_488,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_489,axiom,
    ( sK154(Eq_x_0,Eq_x_1) = sK154(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_490,axiom,
    ( sK155(Eq_x_0,Eq_x_1) = sK155(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_491,axiom,
    ( sK156(Eq_x_0,Eq_x_1) = sK156(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_492,axiom,
    ( sK157(Eq_x_0,Eq_x_1) = sK157(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_493,axiom,
    ( sK158(Eq_x_0,Eq_x_1) = sK158(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_494,axiom,
    ( sK159(Eq_x_0,Eq_x_1) = sK159(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_495,axiom,
    ( sK160(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK160(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_496,axiom,
    ( sK161(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK161(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,
    ( sK162(Eq_x_0,Eq_x_1,Eq_x_2) = sK162(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_498,axiom,
    ( sK163(Eq_x_0,Eq_x_1,Eq_x_2) = sK163(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_499,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_500,axiom,
    ( sK165(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK165(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_501,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_502,axiom,
    ( sK167(Eq_x_0,Eq_x_1,Eq_x_2) = sK167(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_503,axiom,
    ( sK168(Eq_x_0,Eq_x_1,Eq_x_2) = sK168(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_504,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_505,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_506,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_507,axiom,
    ( sK172(Eq_x_0,Eq_x_1,Eq_x_2) = sK172(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_508,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_509,axiom,
    ( sK174(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK174(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_510,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_511,axiom,
    ( sK176(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK176(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_512,axiom,
    ( sK177(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK177(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_513,axiom,
    ( sK178(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK178(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_514,axiom,
    ( sK179(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK179(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,
    ( sK180(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK180(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_516,axiom,
    ( sK181(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK181(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_517,axiom,
    ( sK182(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK182(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_518,axiom,
    ( sK183(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK183(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_519,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_520,axiom,
    ( sK185(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK185(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_521,axiom,
    ( sK186(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK186(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_522,axiom,
    ( sK187(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) = sK187(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_523,axiom,
    ( sK188(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) = sK188(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_524,axiom,
    ( sK189(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK189(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_525,axiom,
    ( sK190(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK190(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_526,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_527,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_528,axiom,
    ( sK193(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK193(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_529,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_530,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_531,axiom,
    ( sK196(Eq_x_0,Eq_x_1,Eq_x_2) = sK196(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_532,axiom,
    ( sK197(Eq_x_0,Eq_x_1,Eq_x_2) = sK197(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_533,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_534,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_535,axiom,
    ( sK200(Eq_x_0,Eq_x_1,Eq_x_2) = sK200(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_536,axiom,
    ( sK201(Eq_x_0,Eq_x_1,Eq_x_2) = sK201(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_537,axiom,
    ( sK202(Eq_x_0,Eq_x_1,Eq_x_2) = sK202(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_538,axiom,
    ( sK203(Eq_x_0,Eq_x_1,Eq_x_2) = sK203(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_539,axiom,
    ( sK204(Eq_x_0,Eq_x_1,Eq_x_2) = sK204(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_540,axiom,
    ( sK205(Eq_x_0,Eq_x_1,Eq_x_2) = sK205(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_541,axiom,
    ( sK206(Eq_x_0,Eq_x_1,Eq_x_2) = sK206(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_542,axiom,
    ( sK207(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK207(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_543,axiom,
    ( sK208(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK208(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_544,axiom,
    ( sK209(Eq_x_0,Eq_x_1,Eq_x_2) = sK209(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,
    ( sK210(Eq_x_0,Eq_x_1,Eq_x_2) = sK210(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_546,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_547,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_548,axiom,
    ( sK213(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK213(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,
    ( sK214(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK214(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,
    ( 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_551,axiom,
    ( sK216(Eq_x_0,Eq_x_1) = sK216(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_552,axiom,
    ( sK217(Eq_x_0,Eq_x_1) = sK217(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_553,axiom,
    ( sK218(Eq_x_0,Eq_x_1) = sK218(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_554,axiom,
    ( sK219(Eq_x_0,Eq_x_1) = sK219(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_555,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_556,axiom,
    ( sK221(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK221(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,
    ( sK222(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK222(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,
    ( 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_559,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_560,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_561,axiom,
    ( sK226(Eq_x_0,Eq_x_1,Eq_x_2) = sK226(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_562,axiom,
    ( sK227(Eq_x_0,Eq_x_1,Eq_x_2) = sK227(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_563,axiom,
    ( sK228(Eq_x_0,Eq_x_1,Eq_x_2) = sK228(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_564,axiom,
    ( sK229(Eq_x_0,Eq_x_1,Eq_x_2) = sK229(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_565,axiom,
    ( sK230(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK230(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,
    ( sK231(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK231(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,
    ( sK232(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK232(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,
    ( sK233(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK233(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,
    ( sK234(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK234(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_570,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_571,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_572,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_573,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_574,axiom,
    ( sK239(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK239(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_575,axiom,
    ( sK240(Eq_x_0,Eq_x_1) = sK240(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_576,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_577,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_578,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_579,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_580,axiom,
    ( sK245(Eq_x_0,Eq_x_1) = sK245(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_581,axiom,
    ( sK246(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK246(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_582,axiom,
    ( sK247(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK247(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_583,axiom,
    ( sK248(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK248(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_584,axiom,
    ( sK249(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK249(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_585,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_586,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_587,axiom,
    ( sK252(Eq_x_0,Eq_x_1) = sK252(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_588,axiom,
    ( sK253(Eq_x_0,Eq_x_1) = sK253(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_589,axiom,
    ( sK254(Eq_x_0,Eq_x_1) = sK254(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_590,axiom,
    ( sK255(Eq_x_0,Eq_x_1) = sK255(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_591,axiom,
    ( sK256(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK256(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,
    ( sK257(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK257(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,
    ( sK258(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK258(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_594,axiom,
    ( sK259(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK259(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_595,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_596,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_597,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_598,axiom,
    ( sK263(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK263(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_599,axiom,
    ( sK264(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK264(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,
    ( sK265(Eq_x_0,Eq_x_1,Eq_x_2) = sK265(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_601,axiom,
    ( sK266(Eq_x_0,Eq_x_1,Eq_x_2) = sK266(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_602,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_603,axiom,
    ( sK268(Eq_x_0,Eq_x_1,Eq_x_2) = sK268(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_604,axiom,
    ( sK269(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK269(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_605,axiom,
    ( sK270(Eq_x_0,Eq_x_1,Eq_x_2) = sK270(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_606,axiom,
    ( sK271(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK271(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_607,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_608,axiom,
    ( sK273(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK273(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_609,axiom,
    ( sK274(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK274(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_610,axiom,
    ( sK275(Eq_x_0,Eq_x_1,Eq_x_2) = sK275(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_611,axiom,
    ( sK276(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK276(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_612,axiom,
    ( sK277(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK277(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,
    ( sK278(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK278(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_614,axiom,
    ( sK279(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK279(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,
    ( sK280(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK280(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_616,axiom,
    ( sK281(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK281(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,
    ( sK282(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK282(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_618,axiom,
    ( sK283(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK283(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_619,axiom,
    ( sK284(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK284(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_620,axiom,
    ( sK285(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK285(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_621,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_622,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_623,axiom,
    ( sK288(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK288(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_624,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_625,axiom,
    ( sK290(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK290(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,
    ( sK291(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK291(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_627,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_628,axiom,
    ( sK293(Eq_x_0) = sK293(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_629,axiom,
    ( sK294(Eq_x_0) = sK294(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_630,axiom,
    ( sK295(Eq_x_0) = sK295(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_631,axiom,
    ( sK296(Eq_x_0) = sK296(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_632,axiom,
    ( sK297(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK297(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_633,axiom,
    ( sK298(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK298(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_634,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_635,axiom,
    ( sK300(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK300(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,
    ( sK301(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK301(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,
    ( sK302(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK302(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_638,axiom,
    ( sK303(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK303(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_639,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_640,axiom,
    ( sK305(Eq_x_0,Eq_x_1,Eq_x_2) = sK305(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,
    ( sK306(Eq_x_0,Eq_x_1,Eq_x_2) = sK306(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,
    ( sK307(Eq_x_0,Eq_x_1,Eq_x_2) = sK307(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_643,axiom,
    ( sK308(Eq_x_0,Eq_x_1,Eq_x_2) = sK308(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_644,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_645,axiom,
    ( sK310(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK310(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_646,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_647,axiom,
    ( sK312(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK312(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_648,axiom,
    ( sK313(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK313(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_649,axiom,
    ( sK314(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK314(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,
    ( sK315(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK315(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,
    ( sK316(Eq_x_0,Eq_x_1) = sK316(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_652,axiom,
    ( sK317(Eq_x_0,Eq_x_1) = sK317(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,
    ( sK318(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK318(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_654,axiom,
    ( sK319(Eq_x_0,Eq_x_1,Eq_x_2) = sK319(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_655,axiom,
    ( sK320(Eq_x_0,Eq_x_1,Eq_x_2) = sK320(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_656,axiom,
    ( sK321(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK321(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_657,axiom,
    ( sK322(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK322(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_658,axiom,
    ( sK323(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK323(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_659,axiom,
    ( sK324(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK324(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_660,axiom,
    ( sK325(Eq_x_0,Eq_x_1,Eq_x_2) = sK325(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_661,axiom,
    ( sK326(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK326(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_662,axiom,
    ( sK327(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK327(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_663,axiom,
    ( sK328(Eq_x_0,Eq_x_1) = sK328(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,
    ( sK329(Eq_x_0) = sK329(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_665,axiom,
    ( sK330(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK330(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_666,axiom,
    ( sK331(Eq_x_0) = sK331(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_667,axiom,
    ( sK332(Eq_x_0) = sK332(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_668,axiom,
    ( sK333(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK333(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_669,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_670,axiom,
    ( sK335(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK335(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_671,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_672,axiom,
    ( sK337(Eq_x_0,Eq_x_1) = sK337(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_673,axiom,
    ( sK338(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK338(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_674,axiom,
    ( sK339(Eq_x_0,Eq_x_1) = sK339(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_675,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_676,axiom,
    ( sK341(Eq_x_0,Eq_x_1) = sK341(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_677,axiom,
    ( sK342(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK342(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_678,axiom,
    ( sK343(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK343(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,
    ( sK344(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK344(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_680,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_681,axiom,
    ( sK346(Eq_x_0,Eq_x_1) = sK346(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_682,axiom,
    ( sK347(Eq_x_0,Eq_x_1) = sK347(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_683,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_684,axiom,
    ( sK349(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK349(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_685,axiom,
    ( sK350(Eq_x_0,Eq_x_1) = sK350(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_686,axiom,
    ( sK351(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK351(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_687,axiom,
    ( sK352(Eq_x_0) = sK352(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_688,axiom,
    ( sK353(Eq_x_0,Eq_x_1) = sK353(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_689,axiom,
    ( sK354(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK354(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_690,axiom,
    ( sK355(Eq_x_0,Eq_x_1) = sK355(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_691,axiom,
    ( sK356(Eq_x_0,Eq_x_1,Eq_x_2) = sK356(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_692,axiom,
    ( sK357(Eq_x_0,Eq_x_1,Eq_x_2) = sK357(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_693,axiom,
    ( sK358(Eq_x_0,Eq_x_1,Eq_x_2) = sK358(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_694,axiom,
    ( sK359(Eq_x_0,Eq_x_1) = sK359(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_695,axiom,
    ( sK360(Eq_x_0,Eq_x_1) = sK360(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_696,axiom,
    ( sK361(Eq_x_0,Eq_x_1,Eq_x_2) = sK361(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,
    ( sK362(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK362(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_698,axiom,
    ( sK363(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK363(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_699,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_700,axiom,
    ( sK365(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK365(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_701,axiom,
    ( sK366(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK366(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_702,axiom,
    ( sK367(Eq_x_0,Eq_x_1) = sK367(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_703,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_704,axiom,
    ( sK369(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK369(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_705,axiom,
    ( sK370(Eq_x_0,Eq_x_1,Eq_x_2) = sK370(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,
    ( sK371(Eq_x_0,Eq_x_1,Eq_x_2) = sK371(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_707,axiom,
    ( sK372(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK372(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_708,axiom,
    ( sK373(Eq_x_0,Eq_x_1) = sK373(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,
    ( sK374(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK374(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_710,axiom,
    ( sK375(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK375(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_711,axiom,
    ( sK376(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK376(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_712,axiom,
    ( sK377(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK377(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_713,axiom,
    ( sK378(Eq_x_0,Eq_x_1,Eq_x_2) = sK378(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_714,axiom,
    ( sK379(Eq_x_0,Eq_x_1,Eq_x_2) = sK379(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_715,axiom,
    ( sK380(Eq_x_0,Eq_x_1,Eq_x_2) = sK380(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_716,axiom,
    ( sK381(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK381(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_717,axiom,
    ( sK382(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK382(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_718,axiom,
    ( sK383(Eq_x_0,Eq_x_1) = sK383(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_719,axiom,
    ( sK384(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK384(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_720,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_721,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_722,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_723,axiom,
    ( sK388(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK388(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_724,axiom,
    ( sK389(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK389(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_725,axiom,
    ( sK390(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK390(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_726,axiom,
    ( sK391(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK391(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_727,axiom,
    ( sK392(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK392(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,
    ( sK393(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK393(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_729,axiom,
    ( sK394(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK394(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_730,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_731,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_732,axiom,
    ( sK397(Eq_x_0,Eq_x_1,Eq_x_2) = sK397(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,
    ( sK398(Eq_x_0,Eq_x_1,Eq_x_2) = sK398(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,
    ( sK399(Eq_x_0,Eq_x_1,Eq_x_2) = sK399(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,
    ( sK400(Eq_x_0,Eq_x_1,Eq_x_2) = sK400(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,
    ( 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_737,axiom,
    ( sK402(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK402(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_738,axiom,
    ( sK403(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK403(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_739,axiom,
    ( sK404(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK404(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_740,axiom,
    ( sK405(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK405(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_741,axiom,
    ( sK406(Eq_x_0,Eq_x_1,Eq_x_2) = sK406(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,
    ( 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_743,axiom,
    ( sK408(Eq_x_0,Eq_x_1,Eq_x_2) = sK408(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,
    ( 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_745,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_746,axiom,
    ( sK411(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK411(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_747,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_748,axiom,
    ( sK413(Eq_x_0,Eq_x_1) = sK413(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_749,axiom,
    ( sK414(Eq_x_0,Eq_x_1,Eq_x_2) = sK414(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_750,axiom,
    ( sK415(Eq_x_0,Eq_x_1,Eq_x_2) = sK415(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_751,axiom,
    ( sK416(Eq_x_0,Eq_x_1,Eq_x_2) = sK416(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_752,axiom,
    ( sK417(Eq_x_0,Eq_x_1,Eq_x_2) = sK417(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_753,axiom,
    ( sK418(Eq_x_0,Eq_x_1,Eq_x_2) = sK418(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_754,axiom,
    ( sK419(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK419(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_755,axiom,
    ( sK420(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK420(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_756,axiom,
    ( sK421(Eq_x_0,Eq_x_1) = sK421(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_757,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_758,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_759,axiom,
    ( sK424(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK424(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_760,axiom,
    ( sK425(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK425(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_761,axiom,
    ( sK426(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK426(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_762,axiom,
    ( sK427(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK427(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_763,axiom,
    ( sK428(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK428(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_764,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_765,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_766,axiom,
    ( sK431(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK431(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_767,axiom,
    ( sK432(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK432(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_768,axiom,
    ( sK433(Eq_x_0,Eq_x_1,Eq_x_2) = sK433(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,
    ( sK434(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK434(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_770,axiom,
    ( sK435(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK435(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_771,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_772,axiom,
    ( sK437(Eq_x_0,Eq_x_1,Eq_x_2) = sK437(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_773,axiom,
    ( sK438(Eq_x_0,Eq_x_1) = sK438(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_774,axiom,
    ( sK439(Eq_x_0,Eq_x_1) = sK439(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_775,axiom,
    ( sK440(Eq_x_0,Eq_x_1,Eq_x_2) = sK440(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_776,axiom,
    ( sK441(Eq_x_0,Eq_x_1) = sK441(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_777,axiom,
    ( sK442(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK442(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_778,axiom,
    ( sK443(Eq_x_0,Eq_x_1,Eq_x_2) = sK443(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_779,axiom,
    ( sK444(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK444(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_780,axiom,
    ( sK445(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK445(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_781,axiom,
    ( sK446(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK446(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_782,axiom,
    ( sK447(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK447(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_783,axiom,
    ( sK448(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK448(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_784,axiom,
    ( sK449(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK449(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,
    ( sK450(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK450(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_786,axiom,
    ( sK451(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK451(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_787,axiom,
    ( sK452(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK452(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_788,axiom,
    ( sK453(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK453(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_789,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_790,axiom,
    ( sK455(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK455(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_791,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_792,axiom,
    ( sK458(Eq_x_0,Eq_x_1,Eq_x_2) = sK458(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,
    ( 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_794,axiom,
    ( sK460(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK460(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_795,axiom,
    ( sK461(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK461(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_796,axiom,
    ( sK462(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK462(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_797,axiom,
    ( sK463(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK463(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_798,axiom,
    ( sK464(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK464(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_799,axiom,
    ( sK465(Eq_x_0) = sK465(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_800,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_801,axiom,
    ( sK467(Eq_x_0,Eq_x_1,Eq_x_2) = sK467(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_802,axiom,
    ( sK468(Eq_x_0,Eq_x_1,Eq_x_2) = sK468(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_803,axiom,
    ( sK469(Eq_x_0,Eq_x_1) = sK469(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_804,axiom,
    ( sK470(Eq_x_0,Eq_x_1) = sK470(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_805,axiom,
    ( sK471(Eq_x_0,Eq_x_1,Eq_x_2) = sK471(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_806,axiom,
    ( sK472(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK472(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,
    ( sK473(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK473(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,
    ( sK474(Eq_x_0,Eq_x_1,Eq_x_2) = sK474(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_809,axiom,
    ( sK475(Eq_x_0,Eq_x_1,Eq_x_2) = sK475(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_810,axiom,
    ( sK476(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK476(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_811,axiom,
    ( sK477(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK477(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_812,axiom,
    ( sK478(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK478(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_813,axiom,
    ( sK479(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK479(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_814,axiom,
    ( sK480(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK480(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_815,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_816,axiom,
    ( sK482(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK482(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,
    ( sK483(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK483(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,
    ( sK484(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK484(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_819,axiom,
    ( sK485(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK485(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_820,axiom,
    ( sK486(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK486(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_821,axiom,
    ( sK487(Eq_x_0,Eq_x_1) = sK487(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_822,axiom,
    ( sK488(Eq_x_0,Eq_x_1,Eq_x_2) = sK488(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_823,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_824,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_825,axiom,
    ( sK491(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK491(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_826,axiom,
    ( sK492(Eq_x_0,Eq_x_1,Eq_x_2) = sK492(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,
    ( 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_828,axiom,
    ( sK494(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK494(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_829,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_830,axiom,
    ( sK496(Eq_x_0,Eq_x_1,Eq_x_2) = sK496(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_831,axiom,
    ( sK497(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK497(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_832,axiom,
    ( sK498(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK498(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_833,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_834,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_835,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_836,axiom,
    ( sK502(Eq_x_0,Eq_x_1,Eq_x_2) = sK502(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,
    ( 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_838,axiom,
    ( sK504(Eq_x_0,Eq_x_1,Eq_x_2) = sK504(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_839,axiom,
    ( sK505(Eq_x_0,Eq_x_1,Eq_x_2) = sK505(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_840,axiom,
    ( sK506(Eq_x_0,Eq_x_1) = sK506(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_841,axiom,
    ( sK507(Eq_x_0,Eq_x_1) = sK507(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_842,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_843,axiom,
    ( sK509(Eq_x_0,Eq_x_1) = sK509(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_844,axiom,
    ( sK510(Eq_x_0,Eq_x_1) = sK510(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_845,axiom,
    ( sK511(Eq_x_0,Eq_x_1,Eq_x_2) = sK511(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_846,axiom,
    ( sK512(Eq_x_0,Eq_x_1,Eq_x_2) = sK512(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_847,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_848,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_849,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_850,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_851,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_852,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_853,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_854,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_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,
    ( 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_857,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_858,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_859,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_860,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_861,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_862,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_863,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_864,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_865,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_866,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_867,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_868,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_869,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_870,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_871,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_872,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_873,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_874,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_875,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_876,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_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_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_879,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_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_Ocomm__semiring(Eq_y_0)
    | ~ class_Rings_Ocomm__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_882,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_883,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_884,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_885,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_886,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_887,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_888,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_889,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_890,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_891,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_892,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_893,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_894,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_895,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_896,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_897,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_898,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_899,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_900,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_901,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_902,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_903,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_904,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_905,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_906,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_907,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_908,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_909,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_910,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_911,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_912,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_913,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_914,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_915,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_916,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_917,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_918,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_919,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_920,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_921,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_922,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_923,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_924,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_925,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_926,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_927,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_928,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_929,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_930,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_931,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_932,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_933,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_934,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_935,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_936,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_937,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_938,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_939,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_940,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_941,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_942,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_943,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_944,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_945,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_946,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_947,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_948,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_949,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_950,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_951,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_952,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_953,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_954,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_955,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_956,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_957,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_958,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_959,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_960,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_961,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_962,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_963,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_964,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_965,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_966,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_967,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_968,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_969,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_970,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_971,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_972,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_973,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_974,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_975,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_976,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_977,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_978,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_979,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_980,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_981,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_982,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_983,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_984,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_985,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_986,axiom,
    ( sP0(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP0(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_989,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_990,axiom,
    ( sP4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP4(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_991,axiom,
    ( sP5(Eq_y_0,Eq_y_1)
    | ~ sP5(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_992,axiom,
    ( sP6(Eq_y_0,Eq_y_1)
    | ~ sP6(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,
    ( sP7(Eq_y_0,Eq_y_1)
    | ~ sP7(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_994,axiom,
    ( sP8(Eq_y_0,Eq_y_1)
    | ~ sP8(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_995,axiom,
    ( sP9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_997,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_998,axiom,
    ( sP12(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP13(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_1000,axiom,
    ( sP14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP14(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_1001,axiom,
    ( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP15(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_1002,axiom,
    ( sP16(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP16(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_1003,axiom,
    ( sP17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP17(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_1004,axiom,
    ( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP18(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_1005,axiom,
    ( sP19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP19(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_1006,axiom,
    ( sP20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP20(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_1007,axiom,
    ( sP21(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP21(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1008,axiom,
    ( sP22(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP22(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_1009,axiom,
    ( sP23(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP23(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_1010,axiom,
    ( sP24(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP24(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1011,axiom,
    ( sP25(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP25(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1012,axiom,
    ( sP26(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP26(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_1013,axiom,
    ( sP27(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP27(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_1014,axiom,
    ( sP28(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP28(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1015,axiom,
    ( sP29(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP29(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_1016,axiom,
    ( sP30(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP30(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1017,axiom,
    ( sP31(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP31(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_1018,axiom,
    ( sP32(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP32(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_1019,axiom,
    ( sP33(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP33(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP34(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP34(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP35(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP35(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_1022,axiom,
    ( sP36(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP36(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP37(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP37(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1024,axiom,
    ( sP38(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP38(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1025,axiom,
    ( sP39(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP39(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP40(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP40(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_1027,axiom,
    ( sP41(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP41(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP42(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP42(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP43(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP43(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_1030,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_1031,axiom,
    ( sP45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP45(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP46(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP46(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_1033,axiom,
    ( sP47(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP47(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1035,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_1036,axiom,
    ( sP50(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP50(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_1037,axiom,
    ( sP51(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP51(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP52(Eq_y_0,Eq_y_1)
    | ~ sP52(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1039,axiom,
    ( sP53(Eq_y_0,Eq_y_1)
    | ~ sP53(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,
    ( sP54(Eq_y_0,Eq_y_1)
    | ~ sP54(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1041,axiom,
    ( sP55(Eq_y_0,Eq_y_1)
    | ~ sP55(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1042,axiom,
    ( sP56(Eq_y_0,Eq_y_1)
    | ~ sP56(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,
    ( sP57(Eq_y_0,Eq_y_1)
    | ~ sP57(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1044,axiom,
    ( sP58(Eq_y_0,Eq_y_1)
    | ~ sP58(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1045,axiom,
    ( sP59(Eq_y_0,Eq_y_1)
    | ~ sP59(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1046,axiom,
    ( sP60(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP60(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1048,axiom,
    ( sP62(Eq_y_0,Eq_y_1)
    | ~ sP62(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1049,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_1050,axiom,
    ( sP64(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP64(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP65(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP65(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,
    ( sP66(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP66(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_1053,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_1054,axiom,
    ( sP68(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP68(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_1055,axiom,
    ( sP69(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP69(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1056,axiom,
    ( sP70(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP70(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP71(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP71(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP72(Eq_y_0,Eq_y_1)
    | ~ sP72(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1059,axiom,
    ( sP73(Eq_y_0,Eq_y_1)
    | ~ sP73(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1060,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_1061,axiom,
    ( sP75(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP75(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP76(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP76(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1064,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_1065,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_1066,axiom,
    ( sP80(Eq_y_0,Eq_y_1)
    | ~ sP80(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1067,axiom,
    ( sP81(Eq_y_0,Eq_y_1)
    | ~ sP81(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,
    ( sP82(Eq_y_0,Eq_y_1)
    | ~ sP82(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,
    ( sP83(Eq_y_0,Eq_y_1)
    | ~ sP83(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1070,axiom,
    ( sP84(Eq_y_0,Eq_y_1)
    | ~ sP84(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,
    ( sP85(Eq_y_0,Eq_y_1)
    | ~ sP85(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,
    ( 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_1073,axiom,
    ( sP87(Eq_y_0,Eq_y_1)
    | ~ sP87(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1074,axiom,
    ( sP88(Eq_y_0,Eq_y_1)
    | ~ sP88(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,
    ( sP89(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP89(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1076,axiom,
    ( sP90(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP90(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP91(Eq_y_0,Eq_y_1)
    | ~ sP91(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1078,axiom,
    ( sP92(Eq_y_0)
    | ~ sP92(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1079,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_1080,axiom,
    ( sP94(Eq_y_0,Eq_y_1)
    | ~ sP94(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,
    ( 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_1082,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_1083,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_1084,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_1085,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_1086,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_1087,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_1088,axiom,
    ( sP102(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP102(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP103(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP103(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1091,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_1092,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_1093,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_1094,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_1095,axiom,
    ( sP109(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP109(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1097,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_1098,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_1099,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_1100,axiom,
    ( sP114(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP114(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1101,axiom,
    ( sP115(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP115(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_1102,axiom,
    ( sP116(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP117(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP117(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_1104,axiom,
    ( sP118(Eq_y_0,Eq_y_1)
    | ~ sP118(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1105,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_1106,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_1107,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_1108,axiom,
    ( sP122(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP122(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP123(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP123(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1111,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_1112,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_1113,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_1114,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_1115,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_1116,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_1117,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_1118,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_1119,axiom,
    ( sP133(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP133(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1120,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_1121,axiom,
    ( sP135(Eq_y_0,Eq_y_1)
    | ~ sP135(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1122,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_1123,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_1124,axiom,
    ( sP138(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP138(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1125,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_1126,axiom,
    ( sP140(Eq_y_0,Eq_y_1)
    | ~ sP140(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1127,axiom,
    ( sP141(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP141(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1128,axiom,
    ( sP142(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP142(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1129,axiom,
    ( sP143(Eq_y_0,Eq_y_1)
    | ~ sP143(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,
    ( sP144(Eq_y_0,Eq_y_1)
    | ~ sP144(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1131,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_1132,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_1133,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_1134,axiom,
    ( sP148(Eq_y_0,Eq_y_1)
    | ~ sP148(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1135,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_1136,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_1137,axiom,
    ( sP151(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP151(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP152(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP152(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP153(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP153(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1140,axiom,
    ( sP154(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP154(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1142,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_1143,axiom,
    ( sP157(Eq_y_0,Eq_y_1)
    | ~ sP157(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1144,axiom,
    ( sP158(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP158(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1146,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_1147,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_1148,axiom,
    ( sP162(Eq_y_0,Eq_y_1)
    | ~ sP162(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1149,axiom,
    ( sP163(Eq_y_0,Eq_y_1)
    | ~ sP163(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1150,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_1151,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_1152,axiom,
    ( sP166(Eq_y_0,Eq_y_1)
    | ~ sP166(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1153,axiom,
    ( sP167(Eq_y_0,Eq_y_1)
    | ~ sP167(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1154,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_1155,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_1156,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_1157,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_1158,axiom,
    ( sP172(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP172(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1159,axiom,
    ( sP173(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP173(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1160,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_1161,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_1162,axiom,
    ( sP176(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP176(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1164,axiom,
    ( sP178(Eq_y_0,Eq_y_1)
    | ~ sP178(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,
    ( sP179(Eq_y_0,Eq_y_1)
    | ~ sP179(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,
    ( 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_1167,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_1168,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_1169,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_1170,axiom,
    ( sP184(Eq_y_0,Eq_y_1)
    | ~ sP184(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,
    ( sP185(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP185(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP186(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP186(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1174,axiom,
    ( sP188(Eq_y_0)
    | ~ sP188(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1175,axiom,
    ( sP189(Eq_y_0)
    | ~ sP189(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1176,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_1177,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_1178,axiom,
    ( sP192(Eq_y_0)
    | ~ sP192(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1179,axiom,
    ( sP193(Eq_y_0)
    | ~ sP193(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1180,axiom,
    ( sP194(Eq_y_0,Eq_y_1)
    | ~ sP194(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1181,axiom,
    ( sP195(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP195(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP196(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP196(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1184,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_1185,axiom,
    ( sP199(Eq_y_0,Eq_y_1)
    | ~ sP199(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,
    ( sP200(Eq_y_0,Eq_y_1)
    | ~ sP200(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,
    ( sP201(Eq_y_0,Eq_y_1)
    | ~ sP201(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,
    ( sP202(Eq_y_0,Eq_y_1)
    | ~ sP202(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1189,axiom,
    ( sP203(Eq_y_0,Eq_y_1)
    | ~ sP203(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1190,axiom,
    ( sP204(Eq_y_0,Eq_y_1)
    | ~ sP204(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,
    ( sP205(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP205(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1192,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_1193,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_1194,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_1195,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_1196,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_1197,axiom,
    ( sP211(Eq_y_0,Eq_y_1)
    | ~ sP211(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,
    ( 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_1199,axiom,
    ( sP213(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP213(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP214(Eq_y_0,Eq_y_1)
    | ~ sP214(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1201,axiom,
    ( sP215(Eq_y_0,Eq_y_1)
    | ~ sP215(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1202,axiom,
    ( sP216(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP216(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1203,axiom,
    ( sP217(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP217(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1204,axiom,
    ( sP218(Eq_y_0,Eq_y_1)
    | ~ sP218(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,
    ( 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_1206,axiom,
    ( sP220(Eq_y_0,Eq_y_1)
    | ~ sP220(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,
    ( sP221(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP221(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1208,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_1209,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_1210,axiom,
    ( sP224(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP224(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_1211,axiom,
    ( sP225(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP225(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1212,axiom,
    ( sP226(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP226(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1213,axiom,
    ( sP227(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP227(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1214,axiom,
    ( sP228(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP228(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1215,axiom,
    ( sP229(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP229(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP230(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP230(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP231(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP231(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP232(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP232(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP233(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP233(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP234(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP234(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP235(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP235(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP236(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP236(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1224,axiom,
    ( sP238(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP238(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1225,axiom,
    ( sP239(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP239(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1226,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_1227,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_1228,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_1229,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_1230,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_1231,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_1232,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_1233,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_1234,axiom,
    ( sP248(Eq_y_0)
    | ~ sP248(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1235,axiom,
    ( sP249(Eq_y_0,Eq_y_1)
    | ~ sP249(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1236,axiom,
    ( sP250(Eq_y_0,Eq_y_1)
    | ~ sP250(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1237,axiom,
    ( sP251(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP251(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1238,axiom,
    ( sP252(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP252(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP253(Eq_y_0,Eq_y_1)
    | ~ sP253(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1240,axiom,
    ( sP254(Eq_y_0,Eq_y_1)
    | ~ sP254(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,
    ( sP255(Eq_y_0,Eq_y_1)
    | ~ sP255(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,
    ( sP256(Eq_y_0,Eq_y_1)
    | ~ sP256(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,
    ( sP257(Eq_y_0,Eq_y_1)
    | ~ sP257(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1244,axiom,
    ( sP258(Eq_y_0,Eq_y_1)
    | ~ sP258(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1245,axiom,
    ( sP259(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP259(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_1246,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_1247,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_1248,axiom,
    ( sP262(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP262(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1249,axiom,
    ( sP263(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP263(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1250,axiom,
    ( sP264(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP264(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_1251,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_1252,axiom,
    ( sP266(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP266(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_1253,axiom,
    ( sP267(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP267(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_1254,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_1255,axiom,
    ( sP269(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP269(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1256,axiom,
    ( sP270(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP270(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1258,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_1259,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_1260,axiom,
    ( sP274(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP274(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP275(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP275(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1263,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_1264,axiom,
    ( sP278(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP278(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1265,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_1266,axiom,
    ( sP280(Eq_y_0,Eq_y_1)
    | ~ sP280(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1267,axiom,
    ( sP281(Eq_y_0,Eq_y_1)
    | ~ sP281(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1268,axiom,
    ( sP282(Eq_y_0,Eq_y_1)
    | ~ sP282(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1269,axiom,
    ( sP283(Eq_y_0,Eq_y_1)
    | ~ sP283(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1270,axiom,
    ( sP284(Eq_y_0,Eq_y_1)
    | ~ sP284(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1271,axiom,
    ( sP285(Eq_y_0,Eq_y_1)
    | ~ sP285(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1272,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_1273,axiom,
    ( sP287(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP287(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_1274,axiom,
    ( sP288(Eq_y_0,Eq_y_1)
    | ~ sP288(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1275,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_1276,axiom,
    ( sP290(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP290(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_1277,axiom,
    ( sP291(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP291(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1279,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_1280,axiom,
    ( sP294(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP294(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP295(Eq_y_0,Eq_y_1)
    | ~ sP295(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1282,axiom,
    ( sP296(Eq_y_0,Eq_y_1)
    | ~ sP296(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1283,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_1284,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_1285,axiom,
    ( sP299(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP299(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP300(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP300(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_1287,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_1288,axiom,
    ( sP302(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP302(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP303(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP303(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_1290,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_1291,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_1292,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_1293,axiom,
    ( sP307(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP307(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP308(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP308(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP309(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP309(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP310(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP310(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP311(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP311(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_1298,axiom,
    ( sP312(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP312(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_1299,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_1300,axiom,
    ( sP314(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP314(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1302,axiom,
    ( sP316(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP316(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_1303,axiom,
    ( sP317(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP317(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_1304,axiom,
    ( sP318(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP318(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_1305,axiom,
    ( sP319(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP319(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_1306,axiom,
    ( sP320(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP320(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP321(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP321(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1308,axiom,
    ( sP322(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP322(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1309,axiom,
    ( sP323(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP323(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1310,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_1311,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_1312,axiom,
    ( sP326(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP326(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_1313,axiom,
    ( sP327(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP327(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_1314,axiom,
    ( sP328(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP328(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_1315,axiom,
    ( sP329(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP329(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_1316,axiom,
    ( sP330(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP330(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_1317,axiom,
    ( sP331(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP331(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_1318,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_1319,axiom,
    ( sP333(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP333(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP334(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP334(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1321,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_1322,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_1323,axiom,
    ( sP337(Eq_y_0,Eq_y_1)
    | ~ sP337(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1324,axiom,
    ( sP338(Eq_y_0,Eq_y_1)
    | ~ sP338(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,
    ( sP339(Eq_y_0,Eq_y_1)
    | ~ sP339(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,
    ( sP340(Eq_y_0,Eq_y_1)
    | ~ sP340(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,
    ( sP341(Eq_y_0,Eq_y_1)
    | ~ sP341(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1328,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_1329,axiom,
    ( sP343(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP343(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP344(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP344(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1331,axiom,
    ( sP345(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP345(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP346(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP346(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1333,axiom,
    ( sP347(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP347(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1334,axiom,
    ( sP348(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP348(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1335,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_1336,axiom,
    ( sP350(Eq_y_0,Eq_y_1)
    | ~ sP350(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,
    ( sP351(Eq_y_0,Eq_y_1)
    | ~ sP351(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,
    ( 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_1339,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_1340,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_1341,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_1342,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_1343,axiom,
    ( sP357(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP357(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1344,axiom,
    ( sP358(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP358(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP359(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP359(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1347,axiom,
    ( sP361(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP361(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1349,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_1350,axiom,
    ( sP364(Eq_y_0,Eq_y_1)
    | ~ sP364(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,
    ( 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_1352,axiom,
    ( sP366(Eq_y_0,Eq_y_1)
    | ~ sP366(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,
    ( sP367(Eq_y_0,Eq_y_1)
    | ~ sP367(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,
    ( sP368(Eq_y_0,Eq_y_1)
    | ~ sP368(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,
    ( 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_1356,axiom,
    ( sP370(Eq_y_0,Eq_y_1)
    | ~ sP370(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,
    ( sP371(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP371(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1358,axiom,
    ( sP372(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP372(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1359,axiom,
    ( sP373(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP373(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1360,axiom,
    ( sP374(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP374(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1361,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_1362,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_1363,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_1364,axiom,
    ( sP378(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP378(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1365,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_1366,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_1367,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_1368,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_1369,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_1370,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_1371,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_1372,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_1373,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_1374,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_1375,axiom,
    ( sP389(Eq_y_0,Eq_y_1)
    | ~ sP389(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1376,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_1377,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_1378,axiom,
    ( sP392(Eq_y_0,Eq_y_1)
    | ~ sP392(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1379,axiom,
    ( sP393(Eq_y_0,Eq_y_1)
    | ~ sP393(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,
    ( 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_1381,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_1382,axiom,
    ( sP396(Eq_y_0,Eq_y_1)
    | ~ sP396(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1383,axiom,
    ( sP397(Eq_y_0)
    | ~ sP397(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1384,axiom,
    ( sP398(Eq_y_0,Eq_y_1)
    | ~ sP398(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1385,axiom,
    ( sP399(Eq_y_0,Eq_y_1)
    | ~ sP399(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1386,axiom,
    ( sP400(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP400(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP401(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP401(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP402(Eq_y_0,Eq_y_1)
    | ~ sP402(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1389,axiom,
    ( sP403(Eq_y_0,Eq_y_1)
    | ~ sP403(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1390,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_1391,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_1392,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_1393,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_1394,axiom,
    ( sP408(Eq_y_0)
    | ~ sP408(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1395,axiom,
    ( sP409(Eq_y_0,Eq_y_1)
    | ~ sP409(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1396,axiom,
    ( sP410(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP410(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP411(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP411(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1399,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_1400,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_1401,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_1402,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_1403,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_1404,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_1405,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_1406,axiom,
    ( sP420(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP420(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP421(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP421(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP422(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP422(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP423(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP423(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1410,axiom,
    ( sP424(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP424(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1412,axiom,
    ( sP426(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP426(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP427(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP427(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1415,axiom,
    ( sP429(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP429(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP430(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP430(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP431(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP431(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP432(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP432(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1420,axiom,
    ( sP434(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP434(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1422,axiom,
    ( sP436(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP436(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_1423,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_1424,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_1425,axiom,
    ( sP439(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP439(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP440(Eq_y_0,Eq_y_1)
    | ~ sP440(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1427,axiom,
    ( sP441(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP441(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1429,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_1430,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_1431,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_1432,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_1433,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_1434,axiom,
    ( sP448(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP448(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP449(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP449(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1437,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_1438,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_1439,axiom,
    ( sP453(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP453(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1441,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_1442,axiom,
    ( sP456(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP456(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP457(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP457(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1445,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_1446,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_1447,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_1448,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_1449,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_1450,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_1451,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_1452,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_1453,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_1454,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_1455,axiom,
    ( sP469(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP469(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1457,axiom,
    ( sP471(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP471(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1459,axiom,
    ( sP473(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP473(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1461,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_1462,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_1463,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_1464,axiom,
    ( sP478(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP478(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP479(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP479(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1467,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_1468,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_1469,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_1470,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_1471,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_1472,axiom,
    ( sP486(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP486(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1474,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_1475,axiom,
    ( sP489(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP489(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1477,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_1478,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_1479,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_1480,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_1481,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_1482,axiom,
    ( sP496(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP496(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP497(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP497(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1485,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_1486,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_1487,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_1488,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_1489,axiom,
    ( sP503(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP503(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP504(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP504(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1492,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_1493,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_1494,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_1495,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_1496,axiom,
    ( sP510(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP510(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP511(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP511(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1499,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_1500,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_1501,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_1502,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_1503,axiom,
    ( sP517(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP517(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP518(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP518(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1506,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_1507,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_1508,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_1509,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_1510,axiom,
    ( sP524(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP524(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP525(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP525(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1513,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_1514,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_1515,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_1516,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_1517,axiom,
    ( sP531(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP531(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP532(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP532(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1520,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_1521,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_1522,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_1523,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_1524,axiom,
    ( sP538(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP538(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1525,axiom,
    ( sP539(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP539(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1526,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_1527,axiom,
    ( sP541(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP541(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1528,axiom,
    ( sP542(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP542(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1529,axiom,
    ( sP543(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP543(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1530,axiom,
    ( sP544(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP544(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1531,axiom,
    ( sP545(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP545(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1532,axiom,
    ( sP546(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP546(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP547(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP547(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP548(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP548(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1535,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_1536,axiom,
    ( sP550(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP550(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP551(Eq_y_0)
    | ~ sP551(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1538,axiom,
    ( sP552(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP552(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1539,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_1540,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_1541,axiom,
    ( sP555(Eq_y_0,Eq_y_1)
    | ~ sP555(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1542,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_1543,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_1544,axiom,
    ( sP558(Eq_y_0,Eq_y_1)
    | ~ sP558(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1545,axiom,
    ( sP559(Eq_y_0)
    | ~ sP559(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1546,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_1547,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_1548,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_1549,axiom,
    ( sP563(Eq_y_0,Eq_y_1)
    | ~ sP563(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,
    ( sP564(Eq_y_0,Eq_y_1)
    | ~ sP564(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,
    ( sP565(Eq_y_0,Eq_y_1)
    | ~ sP565(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,
    ( sP566(Eq_y_0,Eq_y_1)
    | ~ sP566(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1553,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_1554,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_1555,axiom,
    ( sP569(Eq_y_0,Eq_y_1)
    | ~ sP569(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,
    ( sP570(Eq_y_0,Eq_y_1)
    | ~ sP570(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,
    ( 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_1558,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_1559,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_1560,axiom,
    ( sP574(Eq_y_0,Eq_y_1)
    | ~ sP574(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,
    ( 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_1562,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_1563,axiom,
    ( sP577(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP577(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP578(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP578(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP579(Eq_y_0,Eq_y_1)
    | ~ sP579(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1566,axiom,
    ( sP580(Eq_y_0,Eq_y_1)
    | ~ sP580(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1567,axiom,
    ( sP581(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP581(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP582(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP582(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1570,axiom,
    ( sP584(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP584(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP585(Eq_y_0,Eq_y_1)
    | ~ sP585(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1572,axiom,
    ( sP586(Eq_y_0,Eq_y_1)
    | ~ sP586(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1573,axiom,
    ( sP587(Eq_y_0,Eq_y_1)
    | ~ sP587(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1574,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_1575,axiom,
    ( sP589(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP589(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1577,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_1578,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_1579,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_1580,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_1581,axiom,
    ( sP595(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP595(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP596(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP596(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1584,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_1585,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_1586,axiom,
    ( sP600(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP600(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1587,axiom,
    ( sP601(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP601(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1588,axiom,
    ( sP602(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP602(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1589,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_1590,axiom,
    ( sP604(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP604(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1591,axiom,
    ( sP605(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP605(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_1592,axiom,
    ( sP606(Eq_y_0,Eq_y_1)
    | ~ sP606(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,
    ( sP607(Eq_y_0,Eq_y_1)
    | ~ sP607(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1594,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_1595,axiom,
    ( sP609(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP609(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1597,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_1598,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_1599,axiom,
    ( sP613(Eq_y_0,Eq_y_1)
    | ~ sP613(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,
    ( sP614(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP614(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1601,axiom,
    ( sP615(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP615(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1602,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_1603,axiom,
    ( sP617(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP617(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1604,axiom,
    ( sP618(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP618(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1605,axiom,
    ( sP619(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP619(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1606,axiom,
    ( sP620(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP620(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1607,axiom,
    ( sP621(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP621(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1608,axiom,
    ( sP622(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP622(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1609,axiom,
    ( sP623(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP623(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1610,axiom,
    ( sP624(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP624(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1611,axiom,
    ( sP625(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP625(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP626(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP626(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_1613,axiom,
    ( sP627(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP627(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1615,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_1616,axiom,
    ( sP630(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP630(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP631(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP631(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP632(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP632(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP633(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP633(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1621,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_1622,axiom,
    ( sP636(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP636(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP637(Eq_y_0,Eq_y_1)
    | ~ sP637(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1624,axiom,
    ( sP638(Eq_y_0,Eq_y_1)
    | ~ sP638(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1625,axiom,
    ( sP639(Eq_y_0,Eq_y_1)
    | ~ sP639(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1626,axiom,
    ( sP640(Eq_y_0,Eq_y_1)
    | ~ sP640(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1627,axiom,
    ( sP641(Eq_y_0,Eq_y_1)
    | ~ sP641(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1628,axiom,
    ( sP642(Eq_y_0,Eq_y_1)
    | ~ sP642(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1629,axiom,
    ( sP643(Eq_y_0,Eq_y_1)
    | ~ sP643(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1630,axiom,
    ( sP644(Eq_y_0,Eq_y_1)
    | ~ sP644(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1631,axiom,
    ( sP645(Eq_y_0,Eq_y_1)
    | ~ sP645(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,
    ( sP646(Eq_y_0,Eq_y_1)
    | ~ sP646(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,
    ( sP647(Eq_y_0,Eq_y_1)
    | ~ sP647(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,
    ( sP648(Eq_y_0,Eq_y_1)
    | ~ sP648(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,
    ( sP649(Eq_y_0,Eq_y_1)
    | ~ sP649(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,
    ( sP650(Eq_y_0,Eq_y_1)
    | ~ sP650(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1637,axiom,
    ( sP651(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP651(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP652(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP652(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP653(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP653(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP654(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP654(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP655(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP655(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP656(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP656(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP657(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP657(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1644,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_1645,axiom,
    ( sP659(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP659(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP660(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP660(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP661(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP661(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP662(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP662(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_1649,axiom,
    ( sP663(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP663(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_1650,axiom,
    ( sP664(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP664(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_1651,axiom,
    ( sP665(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP665(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP666(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP666(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_1653,axiom,
    ( sP667(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP667(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP668(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP668(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1655,axiom,
    ( sP669(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP669(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1656,axiom,
    ( sP670(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP670(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP671(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP671(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_1658,axiom,
    ( sP672(Eq_y_0,Eq_y_1)
    | ~ sP672(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1659,axiom,
    ( sP673(Eq_y_0,Eq_y_1)
    | ~ sP673(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1660,axiom,
    ( sP674(Eq_y_0,Eq_y_1)
    | ~ sP674(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1661,axiom,
    ( sP675(Eq_y_0,Eq_y_1)
    | ~ sP675(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1662,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_1663,axiom,
    ( sP677(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP677(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_1664,axiom,
    ( sP678(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP678(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_1665,axiom,
    ( sP679(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP679(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_1666,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_1667,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_1668,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_1669,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_1670,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_1671,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_1672,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_1673,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_1674,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_1675,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_1676,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_1677,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_1678,axiom,
    ( sP692(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP692(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP693(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP693(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP694(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP694(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP695(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP695(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP696(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP696(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP697(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP697(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP698(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP698(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP699(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP699(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP700(Eq_y_0,Eq_y_1)
    | ~ sP700(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1687,axiom,
    ( sP701(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP701(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_1688,axiom,
    ( sP702(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP702(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_1689,axiom,
    ( sP703(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)
    | ~ sP703(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_1690,axiom,
    ( sP704(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP704(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_1691,axiom,
    ( sP705(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP705(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_1692,axiom,
    ( sP706(Eq_y_0,Eq_y_1)
    | ~ sP706(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1693,axiom,
    ( sP707(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP707(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1695,axiom,
    ( sP709(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP709(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP710(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP710(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP711(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP711(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1699,axiom,
    ( sP713(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP713(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1701,axiom,
    ( sP715(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP715(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1702,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_1703,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_1704,axiom,
    ( sP718(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP718(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_1705,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_1706,axiom,
    ( sP720(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP720(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP721(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP721(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_1708,axiom,
    ( sP722(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP722(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP723(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP723(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1710,axiom,
    ( sP724(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP724(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP725(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP725(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP726(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP726(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_1713,axiom,
    ( sP727(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP727(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP728(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP728(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,
    ( sP729(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP729(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP730(Eq_y_0,Eq_y_1)
    | ~ sP730(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,
    ( sP731(Eq_y_0,Eq_y_1)
    | ~ sP731(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,
    ( sP732(Eq_y_0)
    | ~ sP732(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1719,axiom,
    ( sP733(Eq_y_0,Eq_y_1)
    | ~ sP733(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1720,axiom,
    ( sP734(Eq_y_0,Eq_y_1)
    | ~ sP734(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1721,axiom,
    ( sP735(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP735(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_1722,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_1723,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_1724,axiom,
    ( sP738(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP738(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP739(Eq_y_0)
    | ~ sP739(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1726,axiom,
    ( sP740(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP740(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1728,axiom,
    ( sP742(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP742(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP743(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)
    | ~ sP743(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_1730,axiom,
    ( sP744(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP744(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_1731,axiom,
    ( sP745(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP745(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_1732,axiom,
    ( sP746(Eq_y_0,Eq_y_1)
    | ~ sP746(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1733,axiom,
    ( sP747(Eq_y_0,Eq_y_1)
    | ~ sP747(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1734,axiom,
    ( sP748(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP748(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP749(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP749(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP750(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP750(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1737,axiom,
    ( sP751(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP751(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1738,axiom,
    ( sP752(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP752(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1739,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_1740,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_1741,axiom,
    ( sP755(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP755(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP756(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP756(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1744,axiom,
    ( sP758(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP758(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_1745,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_1746,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_1747,axiom,
    ( sP761(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP761(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1748,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_1749,axiom,
    ( sP763(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP763(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_1750,axiom,
    ( sP764(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP764(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_1751,axiom,
    ( sP765(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP765(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP766(Eq_y_0,Eq_y_1)
    | ~ sP766(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1753,axiom,
    ( sP767(Eq_y_0,Eq_y_1)
    | ~ sP767(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1754,axiom,
    ( sP768(Eq_y_0,Eq_y_1)
    | ~ sP768(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1755,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_1756,axiom,
    ( sP770(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP770(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP771(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP771(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP772(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP772(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP773(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP773(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP774(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP774(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP775(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP775(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP776(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP776(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP777(Eq_y_0,Eq_y_1)
    | ~ sP777(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,
    ( sP778(Eq_y_0,Eq_y_1)
    | ~ sP778(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1765,axiom,
    ( sP779(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP779(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1766,axiom,
    ( sP780(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP780(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP781(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP781(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP782(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP782(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1770,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_1771,axiom,
    ( sP785(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP785(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1773,axiom,
    ( sP787(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP787(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1775,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_1776,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_1777,axiom,
    ( sP791(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP791(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP792(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP792(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP793(Eq_y_0,Eq_y_1)
    | ~ sP793(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1780,axiom,
    ( sP794(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP794(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP795(Eq_y_0,Eq_y_1)
    | ~ sP795(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1782,axiom,
    ( sP796(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP796(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP797(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP797(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1785,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_1786,axiom,
    ( sP800(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP800(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP801(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP801(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_1788,axiom,
    ( sP802(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP802(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1790,axiom,
    ( sP804(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP804(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP805(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP805(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP806(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP806(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP807(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP807(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1795,axiom,
    ( sP809(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP809(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP810(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP810(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,
    ( 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_1798,axiom,
    ( sP812(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP812(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,
    ( sP813(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP813(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_1800,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_1801,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_1802,axiom,
    ( sP816(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP816(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP817(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP817(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1805,axiom,
    ( sP819(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP819(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_1806,axiom,
    ( sP820(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP820(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP821(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP821(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP822(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP822(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_1809,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_1810,axiom,
    ( sP824(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP824(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP825(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP825(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,
    ( sP826(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP826(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_1813,axiom,
    ( sP827(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP827(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_1814,axiom,
    ( sP828(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP828(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_1815,axiom,
    ( sP829(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP829(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_1816,axiom,
    ( sP830(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP830(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP831(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP831(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP832(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP832(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,
    ( sP833(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP833(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_1820,axiom,
    ( sP834(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)
    | ~ sP834(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_1821,axiom,
    ( sP835(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP835(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_1822,axiom,
    ( sP836(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP836(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_1823,axiom,
    ( sP837(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP837(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,
    ( sP838(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP838(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP839(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP839(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP840(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP840(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP841(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP841(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP842(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP842(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_1829,axiom,
    ( sP843(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP843(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,
    ( sP844(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP844(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1832,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_1833,axiom,
    ( sP847(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP847(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP848(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP848(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP849(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP849(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1837,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_1838,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_1839,axiom,
    ( sP853(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP853(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1840,axiom,
    ( sP854(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP854(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP855(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP855(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP856(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP856(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_1843,axiom,
    ( sP857(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP857(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_1844,axiom,
    ( sP858(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP858(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_1845,axiom,
    ( sP859(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP859(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_1846,axiom,
    ( sP860(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP860(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_1847,axiom,
    ( sP861(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP861(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP862(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP862(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_1849,axiom,
    ( sP863(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP863(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_1850,axiom,
    ( sP864(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP864(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_1851,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_1852,axiom,
    ( sP866(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP866(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1853,axiom,
    ( sP867(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP867(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_1854,axiom,
    ( sP868(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP868(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP869(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP869(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_1856,axiom,
    ( sP870(Eq_y_0,Eq_y_1)
    | ~ sP870(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1857,axiom,
    ( sP871(Eq_y_0,Eq_y_1)
    | ~ sP871(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1858,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_1859,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_1860,axiom,
    ( sP874(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP874(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1861,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_1862,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_1863,axiom,
    ( sP877(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP877(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1864,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_1865,axiom,
    ( sP879(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP879(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1867,axiom,
    ( sP881(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP881(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP882(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP882(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP883(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP883(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1871,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_1872,axiom,
    ( sP886(Eq_y_0,Eq_y_1)
    | ~ sP886(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1873,axiom,
    ( sP887(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP887(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP888(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP888(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP889(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP889(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP890(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP890(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1878,axiom,
    ( sP892(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP892(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP893(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP893(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_1880,axiom,
    ( sP894(Eq_y_0,Eq_y_1)
    | ~ sP894(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1881,axiom,
    ( sP895(Eq_y_0,Eq_y_1)
    | ~ sP895(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1882,axiom,
    ( sP896(Eq_y_0,Eq_y_1)
    | ~ sP896(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1883,axiom,
    ( sP897(Eq_y_0,Eq_y_1)
    | ~ sP897(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1884,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_1885,axiom,
    ( sP899(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP899(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1887,axiom,
    ( sP901(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP901(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,
    ( 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_1889,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_1890,axiom,
    ( sP904(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP904(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP905(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP905(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP906(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP906(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP907(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP907(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP908(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP908(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP909(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP909(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP910(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP910(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP911(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP911(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP912(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP912(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_1899,axiom,
    ( sP913(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP913(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_1900,axiom,
    ( sP914(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP914(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,
    ( sP915(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP915(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,
    ( sP916(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP916(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1904,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_1905,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_1906,axiom,
    ( sP920(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP920(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1908,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_1909,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_1910,axiom,
    ( sP924(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP924(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP925(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP925(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP926(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP926(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1914,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_1915,axiom,
    ( sP929(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP929(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP930(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP930(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP931(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP931(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_1918,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_1919,axiom,
    ( sP933(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP933(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,
    ( sP934(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP934(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_1921,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_1922,axiom,
    ( sP936(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP936(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_1923,axiom,
    ( sP937(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP937(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,
    ( sP938(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP938(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,
    ( sP939(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP939(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP940(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP940(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,
    ( sP941(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP941(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP942(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP942(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1929,axiom,
    ( sP943(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP943(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1930,axiom,
    ( sP944(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP944(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP945(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP945(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP946(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP946(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP947(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP947(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_1934,axiom,
    ( sP948(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP948(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_1935,axiom,
    ( sP949(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP949(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP950(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP950(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_1937,axiom,
    ( sP951(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP951(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_1938,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_1939,axiom,
    ( sP953(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP953(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,
    ( sP954(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP954(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1942,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_1943,axiom,
    ( sP957(Eq_y_0,Eq_y_1)
    | ~ sP957(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1944,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_1945,axiom,
    ( sP959(Eq_y_0,Eq_y_1)
    | ~ sP959(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1946,axiom,
    ( sP960(Eq_y_0,Eq_y_1)
    | ~ sP960(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1947,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_1948,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_1949,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_1950,axiom,
    ( sP964(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP964(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_1951,axiom,
    ( sP965(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP965(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_1952,axiom,
    ( sP966(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP966(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_1953,axiom,
    ( sP967(Eq_y_0)
    | ~ sP967(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1954,axiom,
    ( sP968(Eq_y_0)
    | ~ sP968(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1955,axiom,
    ( sP969(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP969(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_1956,axiom,
    ( sP970(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP970(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,
    ( sP971(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP971(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1959,axiom,
    ( sP973(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP973(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_1960,axiom,
    ( sP974(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP974(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_1961,axiom,
    ( sP975(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP975(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,
    ( sP976(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP976(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_1963,axiom,
    ( sP977(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP977(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_1964,axiom,
    ( sP978(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP978(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_1965,axiom,
    ( sP979(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP979(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_1966,axiom,
    ( sP980(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP980(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP981(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP981(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_1968,axiom,
    ( sP982(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP982(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_1969,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_1970,axiom,
    ( sP984(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP984(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP985(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP985(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1972,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_1973,axiom,
    ( sP987(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP987(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1975,axiom,
    ( sP989(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP989(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1977,axiom,
    ( sP991(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP991(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1978,axiom,
    ( sP992(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP992(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP993(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP993(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP994(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP994(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1982,axiom,
    ( sP996(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP996(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1983,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_1984,axiom,
    ( sP998(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP998(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_1985,axiom,
    ( sP999(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP999(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_1986,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_1987,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_1988,axiom,
    ( sP1002(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1002(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_1989,axiom,
    ( sP1003(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP1003(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_1990,axiom,
    ( sP1004(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1004(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1005(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1005(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_1992,axiom,
    ( sP1006(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1006(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1994,axiom,
    ( sP1008(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1008(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1995,axiom,
    ( sP1009(Eq_y_0,Eq_y_1)
    | ~ sP1009(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1996,axiom,
    ( sP1010(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1010(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,
    ( sP1011(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1011(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1012(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1012(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_1999,axiom,
    ( sP1013(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1013(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,
    ( 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_2001,axiom,
    ( sP1015(Eq_y_0,Eq_y_1)
    | ~ sP1015(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2002,axiom,
    ( sP1016(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1016(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1017(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1017(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2004,axiom,
    ( sP1018(Eq_y_0,Eq_y_1)
    | ~ sP1018(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2005,axiom,
    ( sP1019(Eq_y_0,Eq_y_1)
    | ~ sP1019(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2006,axiom,
    ( sP1020(Eq_y_0,Eq_y_1)
    | ~ sP1020(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2007,axiom,
    ( sP1021(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1021(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1022(Eq_y_0,Eq_y_1)
    | ~ sP1022(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,
    ( sP1023(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1023(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1024(Eq_y_0,Eq_y_1)
    | ~ sP1024(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2011,axiom,
    ( sP1025(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1025(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1026(Eq_y_0,Eq_y_1)
    | ~ sP1026(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2013,axiom,
    ( sP1027(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1027(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,
    ( sP1028(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1028(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_2015,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_2016,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_2017,axiom,
    ( sP1031(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1031(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_2018,axiom,
    ( sP1032(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1032(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1033(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1033(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1034(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1034(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1035(Eq_y_0,Eq_y_1)
    | ~ sP1035(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2022,axiom,
    ( sP1036(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1036(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_2023,axiom,
    ( sP1037(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1037(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_2024,axiom,
    ( sP1038(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1038(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_2025,axiom,
    ( sP1039(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1039(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_2026,axiom,
    ( sP1040(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1040(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_2027,axiom,
    ( sP1041(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1041(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1042(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1042(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1043(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP1043(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_2030,axiom,
    ( sP1044(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP1044(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_2031,axiom,
    ( sP1045(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1045(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_2032,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_2033,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_2034,axiom,
    ( sP1048(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1048(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1049(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1049(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1050(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1050(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2038,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_2039,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_2040,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_2041,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_2042,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_2043,axiom,
    ( sP1057(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1057(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1058(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1058(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1059(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1059(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_2046,axiom,
    ( sP1060(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1060(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_2047,axiom,
    ( sP1061(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1061(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_2048,axiom,
    ( sP1062(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1062(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_2049,axiom,
    ( sP1063(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP1063(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_2050,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_2051,axiom,
    ( sP1065(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1065(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_2053,axiom,
    ( sP1067(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1067(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1068(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1068(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_2055,axiom,
    ( sP1069(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1069(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2056,axiom,
    ( sP1070(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1070(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_2057,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_2058,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_2059,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_2060,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_2061,axiom,
    ( sP1075(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1075(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_2063,axiom,
    ( sP1077(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1077(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2065,axiom,
    ( sP1079(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1079(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1080(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1080(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1081(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1081(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1082(Eq_y_0,Eq_y_1)
    | ~ sP1082(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2069,axiom,
    ( sP1083(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1083(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1084(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1084(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1085(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1085(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1086(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1086(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_2073,axiom,
    ( sP1087(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1087(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_2074,axiom,
    ( sP1088(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1088(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_2075,axiom,
    ( sP1089(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1089(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_2076,axiom,
    ( sP1090(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1090(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_2077,axiom,
    ( sP1091(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1091(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_2078,axiom,
    ( sP1092(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1092(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_2079,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_2080,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_2081,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_2082,axiom,
    ( sP1096(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1096(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2084,axiom,
    ( sP1098(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1098(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1099(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1099(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1100(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1100(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1101(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1101(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_2089,axiom,
    ( sP1103(Eq_y_0,Eq_y_1)
    | ~ sP1103(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2090,axiom,
    ( sP1104(Eq_y_0,Eq_y_1)
    | ~ sP1104(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2091,axiom,
    ( sP1105(Eq_y_0,Eq_y_1)
    | ~ sP1105(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2092,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_2093,axiom,
    ( sP1107(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1107(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1108(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1108(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_2095,axiom,
    ( sP1109(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1109(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,
    ( sP1110(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1110(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_2097,axiom,
    ( sP1111(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1111(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_2098,axiom,
    ( sP1112(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1112(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1113(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1113(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1114(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1114(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1115(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1115(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1116(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1116(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_2103,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_2104,axiom,
    ( sP1118(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1118(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_2105,axiom,
    ( sP1119(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1119(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_2106,axiom,
    ( sP1120(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1120(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,
    ( 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_2108,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_2109,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_2110,axiom,
    ( sP1125(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1125(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1126(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1126(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_2112,axiom,
    ( sP1127(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1127(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,
    ( sP1128(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1128(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1129(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1129(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_2115,axiom,
    ( sP1130(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1130(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2117,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_2118,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_2119,axiom,
    ( sP1134(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1134(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_2120,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_2121,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_2122,axiom,
    ( sP1137(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1137(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1138(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1138(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_2124,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_2125,axiom,
    ( sP1140(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1140(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_2126,axiom,
    ( sP1141(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1141(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1142(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1142(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2129,axiom,
    ( sP1144(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1144(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_2130,axiom,
    ( sP1145(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1145(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1146(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1146(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_2132,axiom,
    ( sP1147(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1147(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_2133,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_2134,axiom,
    ( sP1149(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1149(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_2135,axiom,
    ( sP1150(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1150(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,
    ( sP1151(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1151(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1152(Eq_y_0)
    | ~ sP1152(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2138,axiom,
    ( sP1153(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1153(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_2139,axiom,
    ( sP1154(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1154(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_2140,axiom,
    ( sP1155(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1155(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_2142,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_2143,axiom,
    ( sP1158(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1158(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2144,axiom,
    ( sP1159(Eq_y_0,Eq_y_1)
    | ~ sP1159(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2145,axiom,
    ( sP1160(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1160(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1161(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1161(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1162(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1162(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1163(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1163(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_2149,axiom,
    ( sP1164(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1164(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1165(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1165(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1166(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1166(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1167(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1167(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,
    ( sP1168(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1168(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1169(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1169(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2156,axiom,
    ( sP1171(Eq_y_0,Eq_y_1)
    | ~ sP1171(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2157,axiom,
    ( sP1172(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1172(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1173(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1173(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1174(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1174(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_2160,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_2161,axiom,
    ( sP1176(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1176(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,
    ( sP1177(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1177(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_2163,axiom,
    ( sP1178(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1178(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_2164,axiom,
    ( sP1179(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1179(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,
    ( sP1180(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1180(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_2166,axiom,
    ( sP1181(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1181(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_2167,axiom,
    ( sP1182(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1182(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_2168,axiom,
    ( sP1183(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1183(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1184(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1184(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1185(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1185(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_2172,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_2173,axiom,
    ( sP1188(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1188(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_2174,axiom,
    ( sP1189(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1189(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_2175,axiom,
    ( sP1190(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1190(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_2176,axiom,
    ( sP1191(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1191(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_2177,axiom,
    ( sP1192(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1192(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_2178,axiom,
    ( sP1193(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1193(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1194(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1194(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1195(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1195(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1196(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1196(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_2182,axiom,
    ( sP1197(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1197(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,
    ( sP1198(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1198(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_2184,axiom,
    ( sP1199(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1199(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_2185,axiom,
    ( sP1200(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1200(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_2186,axiom,
    ( sP1201(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1201(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1202(Eq_y_0,Eq_y_1)
    | ~ sP1202(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2188,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_2189,axiom,
    ( sP1204(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1204(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1205(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1205(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2191,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_2192,axiom,
    ( sP1207(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1207(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,
    ( 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_2194,axiom,
    ( sP1209(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1209(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1210(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1210(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_2196,axiom,
    ( sP1211(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1211(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1212(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1212(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1213(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1213(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2200,axiom,
    ( sP1215(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1215(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2201,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_2202,axiom,
    ( sP1217(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1217(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_2203,axiom,
    ( sP1218(Eq_y_0,Eq_y_1)
    | ~ sP1218(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2204,axiom,
    ( sP1219(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1219(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2206,axiom,
    ( sP1221(Eq_y_0,Eq_y_1)
    | ~ sP1221(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,
    ( 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_2208,axiom,
    ( sP1223(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1223(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1224(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1224(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2211,axiom,
    ( sP1226(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1226(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2212,axiom,
    ( sP1227(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1227(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_2213,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_2214,axiom,
    ( sP1229(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1229(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1230(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1230(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_2216,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_2217,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_2218,axiom,
    ( sP1233(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1233(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2220,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_2221,axiom,
    ( sP1236(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1236(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2222,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_2223,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_2224,axiom,
    ( sP1239(Eq_y_0,Eq_y_1)
    | ~ sP1239(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2225,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_2226,axiom,
    ( sP1241(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1241(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2227,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(equality_2228,axiom,
    ( sP1243(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1243(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2229,axiom,
    ( sP1244(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1244(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2230,axiom,
    ( sP1245(Eq_y_0,Eq_y_1)
    | ~ sP1245(Eq_x_0,Eq_x_1)
    | 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  : SWW342+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04  This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04  % Command  : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38  % Computer : n020.cluster.edu
% 0.10/0.38  % Model    : x86_64 x86_64
% 0.10/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38  % Memory   : 8046.5625MB
% 0.10/0.38  % OS       : Linux 6.8.0-71-generic
% 0.10/0.38  % CPULimit : 300
% 0.10/0.38  % WCLimit  : 300
% 0.10/0.38  % DateTime : Sun Sep 20 05:23:02 UTC 2026
% 0.10/0.39  % CPUTime  : 
% 218.63/218.90  % SZS status Theorem for theBenchmark
% 218.63/218.90  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------